0 : 0:{}:{}

 1 : 0:{1}:{(1,1)}
     1:{2}:{(0,1),(2,1),(3,1)}
     2:{1}:{(1,1)}
     3:{3}:{(1,1)}

 2 : 0:{2}:{(1,1),(2,1)}
     1:{1}:{(0,1),(3,1)}
     2:{3}:{(0,1)}
     3:{2}:{(1,1),(4,1)}
     4:{3}:{(3,1)}

 3 : 0:{3}:{(1,1)}
     1:{2}:{(0,1),(2,1)}
     2:{1}:{(1,1),(3,1)}
     3:{2}:{(2,1),(4,1)}
     4:{3}:{(3,1)}

 4 : 0:{1,3}:{(1,1)}
     1:{2}:{(0,1),(2,1)}
     2:{1}:{(1,1)}

 5 : 0:{1,3}:{(1,1)}
     1:{2}:{(0,1),(2,1)}
     2:{1}:{(1,1)}

 6 : 0:{2,3}:{(1,1)}
     1:{1,3}:{(0,1),(2,1)}
     2:{2}:{(1,1)}

 7 : 0:{1,2}:{(1,1)}
     1:{1,3}:{(0,1),(2,1)}
     2:{2,3}:{(1,1),(3,1)}
     3:{1,3}:{(2,1),(4,1)}
     4:{1,2}:{(3,1)}

 8 : 0:{1,3}:{(1,1)}
     1:{2}:{(0,1),(2,1)}
     2:{1}:{(1,1)}

 9 : 0:{2,3}:{(1,1)}
     1:{1,3}:{(0,1),(2,1)}
     2:{2}:{(1,1)}

10 : 0:{1,2}:{(1,1)}
     1:{1,3}:{(0,1),(3,1)}
     2:{1,2}:{(4,1)}
     3:{2,3}:{(1,1),(4,1)}
     4:{1,3}:{(2,1),(3,1)}

11 : 0:{2,3}:{(1,1)}
     1:{1,3}:{(0,1),(2,1)}
     2:{2}:{(1,1)}

12 : 0:{1,2}:{(2,1)}
     1:{2,3}:{(2,1)}
     2:{1,3}:{(0,1),(1,1),(3,1)}
     3:{2,3}:{(2,1)}

13 : 0:{1,2,3}:{}