Identifier
-
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001621: Lattices ⟶ ℤ
Values
[[1,2]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[2,2]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[1],[2]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,3]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[2,3]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[3,3]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[1],[3]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[2],[3]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,1,2]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,1],[2]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,4]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[2,4]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[3,4]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[4,4]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[1],[4]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[2],[4]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[3],[4]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,1,3]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,1],[3]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2],[3]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,3],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,2],[3]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,3],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,1,1,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,2],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,2],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,5]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[2,5]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[3,5]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[4,5]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[5,5]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[1],[5]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[2],[5]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[3],[5]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[4],[5]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,1,4]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,1],[4]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2],[4]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,4],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,3],[4]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,4],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,4],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,2],[4]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,3],[4]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,4],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,4],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[3,3],[4]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[3,4],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,1,1,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,3],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,1,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,3],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,3,3],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,2,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,3,3],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,1,1,1,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,1,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,2],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,6]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[2,6]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[3,6]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[4,6]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[5,6]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[6,6]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[1],[6]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[2],[6]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
>>> Load all 799 entries. <<<[[3],[6]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[4],[6]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[5],[6]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,1,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,2,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,2,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[5,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,1],[5]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2],[5]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,5],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,3],[5]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,5],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,4],[5]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,5],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,5],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,2],[5]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,3],[5]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,5],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,4],[5]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,5],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,5],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[3,3],[5]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[3,4],[5]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[3,5],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[3,5],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[4,4],[5]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[4,5],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,1,1,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[4,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,4],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,1,4],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,1,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,4],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,4],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,4],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,4,4],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,3,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,3,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,4,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,4,4],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,2,4],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,2,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,3,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,3,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,4,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,4,4],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[3,3,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[3,4,4],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,1,1,1,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,1,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,1,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,3],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,2,3,3],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,3,3],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,3,3],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,3,3,3],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,1,1,1,1,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,1,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,7]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[2,7]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[3,7]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[4,7]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[5,7]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[6,7]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[7,7]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[1],[7]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[2],[7]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[3],[7]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[4],[7]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[5],[7]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[6],[7]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,1,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,2,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,3,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,4,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,5,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,2,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,3,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,4,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,5,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,3,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,4,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,5,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4,4,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4,5,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[5,5,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[5,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[6,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,1],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,6],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,3],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,6],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,4],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,6],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,5],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,6],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,6],[6]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,2],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,3],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,6],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,4],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,6],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,5],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,6],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,6],[6]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[3,3],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[3,4],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[3,6],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[3,5],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[3,6],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[3,6],[6]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[4,4],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[4,5],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[4,6],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[4,6],[6]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[5,5],[6]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[5,6],[6]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,1,1,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,2,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,2,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,2,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,3,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,3,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,3,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,3,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,3,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,3,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[4,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[4,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[4,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[5,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,5],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,1,5],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,1,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,1,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,5],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,5],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,5],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,4,5],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,5,5],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,3,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,3,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,4,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,3,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,5,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,4,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,4,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,5,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,5,5],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,2,5],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,2,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,2,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,3,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,3,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,4,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,3,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,5,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,4,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,4,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,5,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,5,5],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[3,3,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[3,3,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[3,4,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[3,4,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[3,5,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[3,5,5],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[4,4,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[4,5,5],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,1,1,1,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,1,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,1,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,1,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,2,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,2,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,2,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,2,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,2,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,2,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,3,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,3,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,3,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,3,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,3,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,3,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[4,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,2,3,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,2,4,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,3,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,4,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,4,4,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,3,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,4,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,4,4,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,4,4,4],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,3,3,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,3,4,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,4,4,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,4,4,4],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[3,4,4,4],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,1,1,1,1,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,1,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,1,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,2,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,2,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,2,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,2,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,2,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,2,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,3,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,2,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,2,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,2,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,3,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[3,3,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,8]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[2,8]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[3,8]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[4,8]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[5,8]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[6,8]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[7,8]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[8,8]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[1],[8]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[2],[8]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[3],[8]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[4],[8]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[5],[8]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[6],[8]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[7],[8]] => [2,1] => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,1,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,2,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,3,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,4,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,5,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,6,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,7,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,2,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,3,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,4,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,5,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,6,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[2,7,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,3,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,4,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,5,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,6,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[3,7,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4,4,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4,5,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4,6,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4,7,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[5,5,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[5,6,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[5,7,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[6,6,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[6,7,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[7,7,7]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[1,1],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,7],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,3],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,7],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,4],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,7],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,5],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,7],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,6],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,7],[6]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,7],[7]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,2],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,3],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,7],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,4],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,7],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,5],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,7],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,6],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[2,7],[6]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[2,7],[7]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[3,3],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[3,4],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[3,7],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[3,5],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[3,7],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[3,6],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[3,7],[6]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[3,7],[7]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[4,4],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[4,5],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[4,7],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[4,6],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[4,7],[6]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[4,7],[7]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[5,5],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[5,6],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[5,7],[6]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[5,7],[7]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[6,6],[7]] => [3,1,2] => ([(1,2)],3) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[6,7],[7]] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,1,1,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,2,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,3,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,4,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,2,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,3,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,4,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,3,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,4,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,4,4,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,4,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,4,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,5,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,5,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,6,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,2,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,3,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,4,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,2,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,3,3,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,3,4,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,3,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,3,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,4,4,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,4,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,4,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,5,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,5,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[2,6,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,3,3,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,3,4,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,3,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,3,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,4,4,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,4,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,4,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,5,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,5,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[3,6,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[4,4,4,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[4,4,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[4,4,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[4,5,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[4,5,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[4,6,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[5,5,5,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[5,5,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[5,6,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[6,6,6,6]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,1,6],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,1,6],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,1,6],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,1,6],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,1,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,6],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,6],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,6],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,6],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,4,6],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,6],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,5,6],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,6,6],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,3,6],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,3,6],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,4,6],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,3,6],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,5,6],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,3,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,6,6],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,4,6],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,4,6],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,5,6],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,4,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,6,6],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,5,6],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,5,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,6,6],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,6,6],[6]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,2,6],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,2,6],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,2,6],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,2,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,3,6],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,3,6],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,4,6],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,3,6],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,5,6],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,3,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,6,6],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,4,6],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,4,6],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,5,6],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,4,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,6,6],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,5,6],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,5,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[2,6,6],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[2,6,6],[6]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[3,3,6],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[3,3,6],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[3,3,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[3,4,6],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[3,4,6],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[3,5,6],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[3,4,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[3,6,6],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[3,5,6],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[3,5,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[3,6,6],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[3,6,6],[6]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[4,4,6],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[4,4,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[4,5,6],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[4,5,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[4,6,6],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[4,6,6],[6]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[5,5,6],[6]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[5,6,6],[6]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,1,1,1,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,1,2,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,1,3,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,1,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,1,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,2,2,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,2,3,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,2,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,2,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,3,3,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,3,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,3,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,4,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,4,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,1,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,2,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,3,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,3,3,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,3,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,3,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,4,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,4,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,3,3,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,3,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,3,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,4,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,4,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,4,4,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,4,4,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,4,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,5,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,2,2,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,2,3,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,2,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,2,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,3,3,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,3,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,3,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,4,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,4,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,2,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,3,3,3,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,3,3,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,3,3,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,3,4,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,3,4,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,3,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,4,4,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,4,4,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,4,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[2,5,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,3,3,3,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,3,3,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,3,3,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,3,4,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,3,4,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,3,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,4,4,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,4,4,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,4,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[3,5,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[4,4,4,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[4,4,4,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[4,4,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[4,5,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[5,5,5,5,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,2,5],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,2,3,5],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,2,4,5],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,2,5,5],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,3,5],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,4,5],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,5,5],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,4,4,5],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,4,5,5],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,5,5,5],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,3,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,4,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,3,5,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,4,4,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,4,5,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,5,5,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,4,4,5],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,4,5,5],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,5,5,5],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,5,5,5],[5]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,3,3,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,3,4,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,3,5,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,4,4,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,4,5,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,5,5,5],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,4,4,5],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,4,5,5],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,5,5,5],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[2,5,5,5],[5]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[3,4,4,5],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[3,4,5,5],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[3,5,5,5],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[3,5,5,5],[5]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[4,5,5,5],[5]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,1,1,1,1,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,1,2,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,1,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,1,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,2,2,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,2,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,2,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,3,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,3,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,1,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,2,2,2,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,2,2,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,2,2,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,2,3,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,2,3,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,2,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,3,3,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,3,3,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,3,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,1,4,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,2,2,2,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,2,2,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,2,2,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,2,3,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,2,3,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,2,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,3,3,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,3,3,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,3,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,4,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,3,3,3,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,3,3,3,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,3,3,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,3,4,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,4,4,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,2,2,2,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,2,2,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,2,2,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,2,3,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,2,3,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,2,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,3,3,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,3,3,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,3,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,2,4,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,3,3,3,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,3,3,3,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,3,3,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,3,4,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[2,4,4,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[3,3,3,3,3,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[3,3,3,3,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[3,3,3,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[3,3,4,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[3,4,4,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[4,4,4,4,4,4]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1]] => [1] => ([],1) => ([(0,1)],2) => 1
[[2]] => [1] => ([],1) => ([(0,1)],2) => 1
[[1,1]] => [1,2] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
[[3]] => [1] => ([],1) => ([(0,1)],2) => 1
[[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
[[4]] => [1] => ([],1) => ([(0,1)],2) => 1
[[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[5]] => [1] => ([],1) => ([(0,1)],2) => 1
[[1,1,1,1,1]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[6]] => [1] => ([],1) => ([(0,1)],2) => 1
[[1,1,1,1,1,1]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
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Generating function
F(2,2)=2 q+q2
F(2,3)=3 q+2 q2
F(3,2)=3 q+2 q2
F(2,4)=4 q+3 q2
F(2,5)=5 q+4 q2
F(2,6)=6 q+5 q2
F(2,7)=7 q+6 q2
F(2,8)=8 q+7 q2
Description
The number of atoms of a lattice.
An element of a lattice is an atom if it covers the least element.
An element of a lattice is an atom if it covers the least element.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).
Map
order ideals
Description
The lattice of order ideals of a poset.
An order ideal I in a poset P is a downward closed set, i.e., a∈I and b≤a implies b∈I. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.
An order ideal I in a poset P is a downward closed set, i.e., a∈I and b≤a implies b∈I. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation π of length n, this poset has vertices
{(i,π(i)) : 1≤i≤n}
and the cover relation is given by (w,x)≤(y,z) if w≤y and x≤z.
For example, the permutation [3,1,5,4,2] is mapped to the poset with cover relations
{(2,1)≺(5,2), (2,1)≺(4,4), (2,1)≺(3,5), (1,3)≺(4,4), (1,3)≺(3,5)}.
For a permutation π of length n, this poset has vertices
{(i,π(i)) : 1≤i≤n}
and the cover relation is given by (w,x)≤(y,z) if w≤y and x≤z.
For example, the permutation [3,1,5,4,2] is mapped to the poset with cover relations
{(2,1)≺(5,2), (2,1)≺(4,4), (2,1)≺(3,5), (1,3)≺(4,4), (1,3)≺(3,5)}.
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