Identifier
-
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001330: Graphs ⟶ ℤ
Values
[[1,2]] => [1,2] => ([],2) => ([],1) => 1
[[2,2]] => [1,2] => ([],2) => ([],1) => 1
[[1],[2]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[1,3]] => [1,2] => ([],2) => ([],1) => 1
[[2,3]] => [1,2] => ([],2) => ([],1) => 1
[[3,3]] => [1,2] => ([],2) => ([],1) => 1
[[1],[3]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[2],[3]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[1,1,2]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,2,2]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,2,2]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,1],[2]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,2],[2]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,4]] => [1,2] => ([],2) => ([],1) => 1
[[2,4]] => [1,2] => ([],2) => ([],1) => 1
[[3,4]] => [1,2] => ([],2) => ([],1) => 1
[[4,4]] => [1,2] => ([],2) => ([],1) => 1
[[1],[4]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[2],[4]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[3],[4]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[1,1,3]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,2,3]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,3,3]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,2,3]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,3,3]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,3,3]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,1],[3]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,2],[3]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,3],[2]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,3],[3]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,2],[3]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,3],[3]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1],[2],[3]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,2]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,2,2]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,2,2]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,2,2]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,1],[2]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,2],[2]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,2,2],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,1],[2,2]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,5]] => [1,2] => ([],2) => ([],1) => 1
[[2,5]] => [1,2] => ([],2) => ([],1) => 1
[[3,5]] => [1,2] => ([],2) => ([],1) => 1
[[4,5]] => [1,2] => ([],2) => ([],1) => 1
[[5,5]] => [1,2] => ([],2) => ([],1) => 1
[[1],[5]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[2],[5]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[3],[5]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[4],[5]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[1,1,4]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,2,4]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,3,4]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,4,4]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,2,4]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,3,4]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,4,4]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,3,4]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,4,4]] => [1,2,3] => ([],3) => ([],1) => 1
[[4,4,4]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,1],[4]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,2],[4]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,4],[2]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,3],[4]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,4],[3]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,4],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,2],[4]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,3],[4]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,4],[3]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,4],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[3,3],[4]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[3,4],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1],[2],[4]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1],[3],[4]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[2],[3],[4]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,3]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,2,3]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,3,3]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,2,3]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,3,3]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,3,3,3]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,2,3]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,3,3]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,3,3,3]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,3,3,3]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,1],[3]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,2],[3]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,3],[2]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,1,3],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,2,2],[3]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,2,3],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,2,3],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,3,3],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,3,3],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,2,2],[3]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,2,3],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,3,3],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,1],[2,3]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[3,3]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,2],[2,3]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2],[3,3]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
>>> Load all 2095 entries. <<<[[2,2],[3,3]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[2],[3]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2],[3]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,1,1,2]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,2,2]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,2,2,2]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,2,2,2]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,2,2,2]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,1],[2]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,1,2],[2]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,2,2],[2]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,2,2],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,1,1],[2,2]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,2],[2,2]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,6]] => [1,2] => ([],2) => ([],1) => 1
[[2,6]] => [1,2] => ([],2) => ([],1) => 1
[[3,6]] => [1,2] => ([],2) => ([],1) => 1
[[4,6]] => [1,2] => ([],2) => ([],1) => 1
[[5,6]] => [1,2] => ([],2) => ([],1) => 1
[[6,6]] => [1,2] => ([],2) => ([],1) => 1
[[1],[6]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[2],[6]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[3],[6]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[4],[6]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[5],[6]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[1,1,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,2,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,3,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,4,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,5,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,2,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,3,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,4,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,5,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,3,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,4,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,5,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[4,4,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[4,5,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[5,5,5]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,1],[5]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,2],[5]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,5],[2]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,3],[5]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,5],[3]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,4],[5]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,5],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,5],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,2],[5]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,3],[5]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,5],[3]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,4],[5]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,5],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,5],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[3,3],[5]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[3,4],[5]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[3,5],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[3,5],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[4,4],[5]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[4,5],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1],[2],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1],[3],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1],[4],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[2],[3],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[2],[4],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[3],[4],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,2,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,3,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,4,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,2,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,3,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,4,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,3,3,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,3,4,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,4,4,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,2,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,3,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,4,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,3,3,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,3,4,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,4,4,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,3,3,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,3,4,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,4,4,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[4,4,4,4]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,1],[4]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,2],[4]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,4],[2]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,1,3],[4]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,4],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,1,4],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,2,2],[4]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,2,4],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,2,3],[4]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,2,4],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,3,4],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,2,4],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,4,4],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,3,3],[4]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,3,4],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,3,4],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,4,4],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,4,4],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,2,2],[4]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,2,3],[4]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,2,4],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,2,4],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,3,3],[4]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,3,4],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,3,4],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,4,4],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,4,4],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[3,3,3],[4]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[3,3,4],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[3,4,4],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,1],[2,4]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[3,4]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[4,4]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,2],[2,4]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2],[3,4]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,3],[2,4]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2],[4,4]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,3],[3,4]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3],[4,4]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,2],[3,4]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,2],[4,4]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,3],[3,4]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3],[4,4]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[3,3],[4,4]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[2],[4]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[3],[4]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3],[4]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2],[3]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4],[2],[4]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4],[3],[4]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,2],[3],[4]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,4],[3],[4]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1],[2],[3],[4]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,1,1,1,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,2,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,3,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,2,2,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,2,3,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,3,3,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,2,2,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,2,3,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,3,3,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,3,3,3,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,2,2,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,2,3,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,3,3,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,3,3,3,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,3,3,3,3]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,1],[3]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,1,2],[3]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,1,3],[2]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,1,3],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,2,2],[3]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,2,3],[2]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,2,3],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,3,3],[2]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,3,3],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,2,2],[3]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,2,2,3],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,2,3],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,3,3],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,3,3],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,3,3,3],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,3,3,3],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,2,2,2],[3]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,2,2,3],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,3,3],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,3,3,3],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,1,1],[2,3]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,1],[3,3]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,2],[2,3]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,3],[2,2]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,2],[3,3]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,3],[2,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,3],[3,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,2,2],[2,3]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2],[3,3]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,2,3],[2,3]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,3],[3,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,2,2],[3,3]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,2,3],[3,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,1],[2],[3]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,3],[2],[3]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,3],[2],[3]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1],[2,2],[3]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,1,1,2]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,1,2,2]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,2,2,2]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,2,2,2,2]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,2,2,2,2]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,2,2,2,2]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,1,1],[2]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,1,1,2],[2]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,2,2],[2]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2,2],[2]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,2,2],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,1],[2,2]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,1,2],[2,2]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2],[2,2]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,1],[2,2,2]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,7]] => [1,2] => ([],2) => ([],1) => 1
[[2,7]] => [1,2] => ([],2) => ([],1) => 1
[[3,7]] => [1,2] => ([],2) => ([],1) => 1
[[4,7]] => [1,2] => ([],2) => ([],1) => 1
[[5,7]] => [1,2] => ([],2) => ([],1) => 1
[[6,7]] => [1,2] => ([],2) => ([],1) => 1
[[7,7]] => [1,2] => ([],2) => ([],1) => 1
[[1],[7]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[2],[7]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[3],[7]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[4],[7]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[5],[7]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[6],[7]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[1,1,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,2,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,3,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,4,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,5,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,6,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,2,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,3,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,4,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,5,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,6,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,3,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,4,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,5,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,6,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[4,4,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[4,5,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[4,6,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[5,5,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[5,6,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[6,6,6]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,1],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,2],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,6],[2]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,3],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,6],[3]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,4],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,6],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,5],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,6],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,6],[6]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,2],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,3],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,6],[3]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,4],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,6],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,5],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,6],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,6],[6]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[3,3],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[3,4],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[3,6],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[3,5],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[3,6],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[3,6],[6]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[4,4],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[4,5],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[4,6],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[4,6],[6]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[5,5],[6]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[5,6],[6]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1],[2],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1],[3],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1],[4],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1],[5],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[2],[3],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[2],[4],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[2],[5],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[3],[4],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[3],[5],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[4],[5],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,2,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,3,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,4,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,2,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,3,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,4,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,3,3,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,3,4,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,3,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,4,4,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,4,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,5,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,2,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,3,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,4,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,3,3,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,3,4,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,3,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,4,4,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,4,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,5,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,3,3,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,3,4,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,3,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,4,4,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,4,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,5,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[4,4,4,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[4,4,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[4,5,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[5,5,5,5]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,1],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,2],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,5],[2]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,1,3],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,5],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,1,4],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,5],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,1,5],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,2,2],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,2,5],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,2,3],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,2,5],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,3,5],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,2,4],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,2,5],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,4,5],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,2,5],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,5,5],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,3,3],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,3,5],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,3,4],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,3,5],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,4,5],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,3,5],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,5,5],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,4,4],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,4,5],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,4,5],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,5,5],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,5,5],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,2,2],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,2,3],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,2,5],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,2,4],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,2,5],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,2,5],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,3,3],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,3,5],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,3,4],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,3,5],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,4,5],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,3,5],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,5,5],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,4,4],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,4,5],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,4,5],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,5,5],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,5,5],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[3,3,3],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[3,3,4],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[3,3,5],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[3,3,5],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[3,4,4],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[3,4,5],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[3,4,5],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[3,5,5],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[3,5,5],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[4,4,4],[5]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[4,4,5],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[4,5,5],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,1],[2,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[3,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[4,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[5,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,2],[2,5]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2],[3,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,3],[2,5]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2],[4,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,4],[2,5]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2],[5,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,3],[3,5]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3],[4,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,4],[3,5]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3],[5,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,4],[4,5]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,4],[5,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,2],[3,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,2],[4,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,2],[5,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,3],[3,5]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3],[4,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,4],[3,5]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3],[5,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,4],[4,5]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,4],[5,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[3,3],[4,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[3,3],[5,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[3,4],[4,5]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[3,4],[5,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[4,4],[5,5]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[2],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[3],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5],[2],[3]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5],[2],[4]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,5],[2],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5],[3],[4]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,5],[3],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,5],[4],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,2],[3],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,3],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,5],[3],[4]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,5],[3],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,5],[4],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[3,3],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[3,5],[4],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1],[2],[3],[5]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1],[2],[4],[5]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1],[3],[4],[5]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[2],[3],[4],[5]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,1,1,1,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,2,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,3,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,2,2,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,2,3,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,2,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,3,3,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,3,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,4,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,2,2,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,2,3,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,2,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,3,3,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,3,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,4,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,3,3,3,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,3,3,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,3,4,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,4,4,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,2,2,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,2,3,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,2,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,3,3,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,3,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,4,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,3,3,3,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,3,3,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,3,4,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,4,4,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,3,3,3,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,3,3,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,3,4,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,4,4,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[4,4,4,4,4]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,1],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,1,2],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,1,4],[2]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,1,3],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,1,4],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,1,4],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,2,2],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,2,4],[2]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,2,3],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,2,4],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,3,4],[2]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,2,4],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,4,4],[2]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,3,3],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,3,4],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,3,4],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,4,4],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,4,4],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,2,2],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,2,2,4],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,2,3],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,2,2,4],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,3,4],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,2,4],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,4,4],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,3,3],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,2,3,4],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,3,3,4],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,3,4],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,4,4],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,3,4,4],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,4,4],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,4,4,4],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,3,3,3],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,3,3,4],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,3,3,4],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,3,4,4],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,3,4,4],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,4,4,4],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,4,4,4],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,2,2,2],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,2,2,3],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,2,2,4],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,2,4],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,3,3],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,2,3,4],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,3,4],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,4,4],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,4,4],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,3,3,3],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,3,3,4],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,3,3,4],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,3,4,4],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,3,4,4],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,4,4,4],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,4,4,4],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[3,3,3,3],[4]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[3,3,3,4],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[3,3,4,4],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[3,4,4,4],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,1,1],[2,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,1],[3,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,1],[4,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,2],[2,4]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,4],[2,2]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,2],[3,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,3],[2,4]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,4],[2,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,2],[4,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,4],[2,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,3],[3,4]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,4],[3,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,4],[3,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,4],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,2,2],[2,4]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2],[3,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,2,3],[2,4]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,4],[2,3]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2],[4,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,2,4],[2,4]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,3],[3,4]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,4],[3,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,3,3],[2,4]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,2,4],[3,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,3,4],[2,4]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,4],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,3,3],[3,4]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,3,4],[3,4]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,3,4],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,2,2],[3,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,2,2],[4,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,2,3],[3,4]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,2,4],[3,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,2,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,2,4],[3,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,2,4],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,3,3],[3,4]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,3,4],[3,4]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[2,3,4],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[3,3,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[3,3,4],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,1],[2],[4]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1],[3],[4]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,2],[3],[4]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,4],[2],[3]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,4],[2],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,4],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,2],[3],[4]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2],[3]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,4],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4,4],[2],[3]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4,4],[2],[4]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4,4],[3],[4]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,2,2],[3],[4]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2,4],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,4,4],[3],[4]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1],[2,2],[4]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[2,3],[4]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[3,3],[4]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3,3],[4]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2],[3,3],[4]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[2],[3],[4]] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,4],[2],[3],[4]] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,1,1,1,1,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,1,2,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,1,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,2,2,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,2,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,2,2,2,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,2,2,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,2,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,2,2,2,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,2,2,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,2,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,3,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,2,2,2,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,2,2,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,2,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,3,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[3,3,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,1,1],[3]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,1,1,2],[3]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,1,1,3],[2]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,1,3],[3]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,2,2],[3]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,1,2,3],[2]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,2,3],[3]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,3,3],[2]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,3,3],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2,2],[3]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,2,2,3],[2]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2,3],[3]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,3,3],[2]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,3,3],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,3,3,3],[2]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,3,3,3],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,2,2],[3]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,2,2,2,3],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,2,3],[3]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,3,3],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,3,3],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,3,3,3],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,3,3,3],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,3,3,3,3],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,3,3,3,3],[3]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[2,2,2,2,2],[3]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[2,2,2,2,3],[3]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,2,3,3],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,3,3,3],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,3,3,3,3],[3]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,1],[2,3]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,1,1],[3,3]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,1,2],[2,3]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,1,3],[2,2]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,1,2],[3,3]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,1,3],[2,3]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,1,3],[3,3]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2],[2,3]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2,3],[2,2]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2],[3,3]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,2,3],[2,3]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,1,3,3],[2,2]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,2,3],[3,3]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,3,3],[2,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,3,3],[3,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,2,2,2],[2,3]] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2,2],[3,3]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,2,2,3],[2,3]] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2,3],[3,3]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,2,3,3],[2,3]] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,3,3],[3,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,2,2,2],[3,3]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[2,2,2,3],[3,3]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,2,3,3],[3,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,1,1],[2],[3]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,3],[2],[3]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,3,3],[2],[3]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,3,3],[2],[3]] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,1],[2,2,3]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,1],[2,3,3]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,1],[3,3,3]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,2],[2,2,3]] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2],[2,3,3]] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2],[3,3,3]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,2,2],[2,3,3]] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2],[3,3,3]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[2,2,2],[3,3,3]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,1],[2,2],[3]] => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,3],[2,2],[3]] => [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1],[2,2],[3,3]] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,1,1,1],[2]] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 2
[[1,1,1,1,1,2],[2]] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,2,2],[2]] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2,2,2],[2]] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,2,2,2,2],[2]] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,2,2,2,2,2],[2]] => [2,1,3,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,1],[2,2]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 2
[[1,1,1,1,2],[2,2]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2,2],[2,2]] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,2,2,2],[2,2]] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1],[2,2,2]] => [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 2
[[1,1,1,2],[2,2,2]] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 2
[[1,8]] => [1,2] => ([],2) => ([],1) => 1
[[2,8]] => [1,2] => ([],2) => ([],1) => 1
[[3,8]] => [1,2] => ([],2) => ([],1) => 1
[[4,8]] => [1,2] => ([],2) => ([],1) => 1
[[5,8]] => [1,2] => ([],2) => ([],1) => 1
[[6,8]] => [1,2] => ([],2) => ([],1) => 1
[[7,8]] => [1,2] => ([],2) => ([],1) => 1
[[8,8]] => [1,2] => ([],2) => ([],1) => 1
[[1],[8]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[2],[8]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[3],[8]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[4],[8]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[5],[8]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[6],[8]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[7],[8]] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 2
[[1,1,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,2,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,3,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,4,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,5,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,6,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,7,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,2,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,3,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,4,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,5,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,6,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[2,7,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,3,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,4,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,5,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,6,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[3,7,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[4,4,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[4,5,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[4,6,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[4,7,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[5,5,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[5,6,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[5,7,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[6,6,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[6,7,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[7,7,7]] => [1,2,3] => ([],3) => ([],1) => 1
[[1,1],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,2],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,7],[2]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,3],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,7],[3]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,4],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,7],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,5],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,7],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,6],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[1,7],[6]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1,7],[7]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,2],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,3],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,7],[3]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,4],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,7],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,5],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,7],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,6],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[2,7],[6]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[2,7],[7]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[3,3],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[3,4],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[3,7],[4]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[3,5],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[3,7],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[3,6],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[3,7],[6]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[3,7],[7]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[4,4],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[4,5],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[4,7],[5]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[4,6],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[4,7],[6]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[4,7],[7]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[5,5],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[5,6],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[5,7],[6]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[5,7],[7]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[6,6],[7]] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
[[6,7],[7]] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2
[[1],[2],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1],[3],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1],[4],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1],[5],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1],[6],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[2],[3],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[2],[4],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[2],[5],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[2],[6],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[3],[4],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[3],[5],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[3],[6],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[4],[5],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[4],[6],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[5],[6],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,2,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,3,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,4,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,2,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,3,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,4,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,2,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,3,3,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,3,4,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,3,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,3,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,4,4,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,4,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,4,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,5,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,5,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,6,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,2,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,3,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,4,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,2,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,3,3,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,3,4,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,3,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,3,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,4,4,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,4,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,4,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,5,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,5,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[2,6,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,3,3,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,3,4,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,3,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,3,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,4,4,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,4,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,4,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,5,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,5,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[3,6,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[4,4,4,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[4,4,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[4,4,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[4,5,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[4,5,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[4,6,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[5,5,5,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[5,5,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[5,6,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[6,6,6,6]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[1,1,1],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,2],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,6],[2]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,1,3],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,6],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,1,4],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,6],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,1,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,1,6],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,1,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,2,2],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,2,6],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,2,3],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,2,6],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,3,6],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,2,4],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,2,6],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,4,6],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,2,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,2,6],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,5,6],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,2,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,6,6],[2]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,3,3],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,3,6],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,3,4],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,3,6],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,4,6],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,3,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,3,6],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,5,6],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,3,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,6,6],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,4,4],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,4,6],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,4,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,4,6],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,5,6],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,4,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,6,6],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,5,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[1,5,6],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,5,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[1,6,6],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,6,6],[6]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,2,2],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,2,3],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,2,6],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,2,4],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,2,6],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,2,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,2,6],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,2,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,3,3],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,3,6],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,3,4],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,3,6],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,4,6],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,3,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,3,6],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,5,6],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,3,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,6,6],[3]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,4,4],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,4,6],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,4,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,4,6],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,5,6],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,4,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,6,6],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,5,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[2,5,6],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,5,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[2,6,6],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[2,6,6],[6]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[3,3,3],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[3,3,4],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[3,3,6],[4]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[3,3,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[3,3,6],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[3,3,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[3,4,4],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[3,4,6],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[3,4,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[3,4,6],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[3,5,6],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[3,4,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[3,6,6],[4]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[3,5,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[3,5,6],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[3,5,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[3,6,6],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[3,6,6],[6]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[4,4,4],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[4,4,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[4,4,6],[5]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[4,4,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[4,5,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[4,5,6],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[4,5,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[4,6,6],[5]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[4,6,6],[6]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[5,5,5],[6]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2
[[5,5,6],[6]] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2
[[5,6,6],[6]] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2
[[1,1],[2,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[3,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[4,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[5,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,2],[2,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2],[3,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,3],[2,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2],[4,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,4],[2,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2],[5,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,5],[2,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,3],[3,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3],[4,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,4],[3,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3],[5,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,5],[3,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,4],[4,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,4],[5,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,5],[4,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,4],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,5],[5,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,5],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,2],[3,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,2],[4,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,2],[5,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,2],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,3],[3,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3],[4,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,4],[3,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3],[5,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,5],[3,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,4],[4,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,4],[5,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,5],[4,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,4],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[2,5],[5,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,5],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[3,3],[4,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[3,3],[5,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[3,3],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[3,4],[4,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[3,4],[5,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[3,5],[4,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[3,4],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[3,5],[5,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[3,5],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[4,4],[5,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[4,4],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[4,5],[5,6]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[[4,5],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[5,5],[6,6]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2
[[1,1],[2],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[3],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,6],[2],[3]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,6],[2],[4]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,6],[2],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,6],[2],[6]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,6],[3],[4]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,6],[3],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,6],[3],[6]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,6],[4],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,6],[4],[6]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,6],[5],[6]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,2],[3],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,3],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,6],[3],[4]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,3],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,6],[3],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,6],[3],[6]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,4],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,6],[4],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,6],[4],[6]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,6],[5],[6]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[3,3],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[3,3],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[3,4],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[3,6],[4],[5]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[3,6],[4],[6]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[3,6],[5],[6]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[4,4],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
[[4,6],[5],[6]] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 3
[[1],[2],[3],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1],[2],[4],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1],[2],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1],[3],[4],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1],[3],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1],[4],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[2],[3],[4],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[2],[3],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[2],[4],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[3],[4],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,1,1,1,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,2,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,3,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,2,2,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,2,3,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,2,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,2,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,3,3,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,3,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,3,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,4,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,4,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,2,2,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,2,3,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,2,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,2,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,3,3,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,3,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,3,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,4,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,4,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,2,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,3,3,3,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,3,3,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,3,3,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,3,4,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,3,4,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,3,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,4,4,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,4,4,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,4,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,5,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,2,2,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,2,3,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,2,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,2,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,3,3,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,3,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,3,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,4,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,4,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,2,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,3,3,3,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,3,3,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,3,3,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,3,4,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,3,4,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,3,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,4,4,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,4,4,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,4,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[2,5,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,3,3,3,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,3,3,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,3,3,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,3,4,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,3,4,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,3,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,4,4,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,4,4,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,4,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[3,5,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[4,4,4,4,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[4,4,4,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[4,4,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[4,5,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[5,5,5,5,5]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[1,1,1,1],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,1,2],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,1,5],[2]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,1,3],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,1,5],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,1,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,1,5],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,1,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,2,2],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,2,5],[2]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,2,3],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,2,5],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,3,5],[2]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,2,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,2,5],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,4,5],[2]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,2,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,5,5],[2]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,3,3],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,3,5],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,3,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,3,5],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,4,5],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,3,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,5,5],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,4,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,1,4,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,4,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,5,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,1,5,5],[5]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,2,2],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,2,2,5],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,2,3],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,2,2,5],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,3,5],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,2,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,2,2,5],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,4,5],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,2,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,5,5],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,3,3],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,2,3,5],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,3,3,5],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,3,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,2,3,5],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,4,5],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,3,4,5],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,3,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,5,5],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,3,5,5],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,4,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,2,4,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,4,4,5],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,4,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,2,5,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,4,5,5],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,2,5,5],[5]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,5,5,5],[2]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,3,3,3],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,3,3,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,3,3,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,3,3,5],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,3,4,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,3,3,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,3,5,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,3,4,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,3,4,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,4,4,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,3,4,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,3,5,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,4,5,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,3,5,5],[5]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,5,5,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,4,4,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[1,4,4,5],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,4,4,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,4,5,5],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,4,5,5],[5]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[1,5,5,5],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,5,5,5],[5]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,2,2,2],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,2,2,3],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,2,2,5],[3]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,2,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,2,2,5],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,2,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,3,3],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,2,3,5],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,3,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,2,3,5],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,4,5],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,3,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,5,5],[3]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,4,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,2,4,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,4,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,5,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,2,5,5],[5]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,3,3,3],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,3,3,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,3,3,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,3,3,5],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,3,4,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,3,3,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,3,5,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,3,4,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,3,4,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,4,4,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,3,4,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,3,5,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,4,5,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,3,5,5],[5]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,5,5,5],[3]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,4,4,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[2,4,4,5],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,4,4,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,4,5,5],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,4,5,5],[5]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[2,5,5,5],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[2,5,5,5],[5]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[3,3,3,3],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[3,3,3,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[3,3,3,5],[4]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[3,3,3,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[3,3,4,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[3,3,4,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[3,3,4,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[3,3,5,5],[4]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[3,3,5,5],[5]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[3,4,4,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[3,4,4,5],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[3,4,4,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[3,4,5,5],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[3,4,5,5],[5]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[3,5,5,5],[4]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[3,5,5,5],[5]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[4,4,4,4],[5]] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2
[[4,4,4,5],[5]] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[4,4,5,5],[5]] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2
[[4,5,5,5],[5]] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2
[[1,1,1],[2,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,1],[3,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,1],[4,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,1],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,2],[2,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,5],[2,2]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,2],[3,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,3],[2,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,5],[2,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,2],[4,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,4],[2,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,5],[2,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,2],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,5],[2,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,3],[3,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,5],[3,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,3],[4,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,4],[3,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,5],[3,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,3],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,5],[3,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,4],[4,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,5],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,4],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,1,5],[4,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,5],[5,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,2,2],[2,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2],[3,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,2,3],[2,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,5],[2,3]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2],[4,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,2,4],[2,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,5],[2,4]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,2,5],[2,5]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,3],[3,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,5],[3,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,3,3],[2,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,3],[4,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,2,4],[3,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,5],[3,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,3,4],[2,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3,5],[2,4]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,3],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,2,5],[3,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,3,5],[2,5]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,4],[4,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,5],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,4,4],[2,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,4],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,2,5],[4,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,4,5],[2,5]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,5],[5,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,3,3],[3,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3,3],[4,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,3,4],[3,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3,5],[3,4]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,3,3],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,3,5],[3,5]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,3,4],[4,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3,5],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,4,4],[3,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3,4],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,3,5],[4,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,4,5],[3,5]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,3,5],[5,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,4,4],[4,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,4,4],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[1,4,5],[4,5]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,4,5],[5,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,2,2],[3,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,2,2],[4,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,2,2],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,2,3],[3,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,2,5],[3,3]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,2,3],[4,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,2,4],[3,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,2,5],[3,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,2,3],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,2,5],[3,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,2,4],[4,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,2,5],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,2,4],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,2,5],[4,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,2,5],[5,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,3,3],[3,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3,3],[4,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,3,4],[3,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3,5],[3,4]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[2,3,3],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,3,5],[3,5]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[2,3,4],[4,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3,5],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,4,4],[3,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3,4],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,3,5],[4,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,4,5],[3,5]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[2,3,5],[5,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[2,4,4],[4,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,4,4],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[2,4,5],[4,5]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[2,4,5],[5,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[3,3,3],[4,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[3,3,3],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[3,3,4],[4,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[3,3,5],[4,4]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[3,3,4],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[3,3,5],[4,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[3,3,5],[5,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[3,4,4],[4,5]] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[[3,4,4],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[3,4,5],[4,5]] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[[3,4,5],[5,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[4,4,4],[5,5]] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2
[[4,4,5],[5,5]] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2
[[1,1,1],[2],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1],[3],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,2],[3],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,5],[2],[3]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,2],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,5],[2],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,5],[2],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,5],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,5],[3],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,2],[3],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,2],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2],[3]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4,5],[2],[3]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,5],[3],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,5,5],[2],[3]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4,5],[2],[4]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,5,5],[2],[4]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,5,5],[2],[5]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5],[3],[4]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,5,5],[3],[4]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,5,5],[3],[5]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,5,5],[4],[5]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,2,2],[3],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2,2],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2,5],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,2,5],[3],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,2,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,3,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,4,5],[3],[4]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,3,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,5,5],[3],[4]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,5,5],[3],[5]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,5,5],[4],[5]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[3,3,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[3,3,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[3,5,5],[4],[5]] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1],[2,2],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[2,3],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[2,4],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[3,3],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[3,4],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[4,4],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3,3],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3,4],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[4,4],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[4,4],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2],[3,3],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2],[3,4],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2],[4,4],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,3],[4,4],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[3,3],[4,4],[5]] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[2],[3],[5]] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,1],[2],[4],[5]] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,1],[3],[4],[5]] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,5],[2],[3],[5]] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,5],[2],[4],[5]] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,5],[3],[4],[5]] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[2,2],[3],[4],[5]] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[2,5],[3],[4],[5]] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[[1,1,1,1,1,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,1,2,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,1,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,1,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,2,2,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,2,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,2,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,2,2,2,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,2,2,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,2,2,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,2,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,2,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,2,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,2,2,2,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,2,2,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,2,2,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,2,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,2,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,2,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,3,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,3,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,3,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,3,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,4,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,2,2,2,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,2,2,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,2,2,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,2,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,2,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,2,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,2,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,3,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,3,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,3,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,3,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[2,4,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[3,3,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[3,3,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[3,3,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[3,3,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[3,4,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[4,4,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,1,1,1,1],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,1,1,2],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,1,1,4],[2]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,1,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,1,1,4],[3]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,1,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,2,2],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,1,2,4],[2]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,2,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,1,2,4],[3]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,3,4],[2]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,2,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,4,4],[2]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,3,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,1,3,4],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,3,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,4,4],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,4,4],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2,2],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,2,2,4],[2]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,2,2,4],[3]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,3,4],[2]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,4,4],[2]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,3,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,2,3,4],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,3,3,4],[2]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,3,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,4,4],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,3,4,4],[2]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,2,4,4],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,4,4,4],[2]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,3,3,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,1,3,3,4],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,3,3,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,3,4,4],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,3,4,4],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,4,4,4],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,1,4,4,4],[4]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,2,2],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,2,2,2,4],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,2,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,2,2,2,4],[3]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,3,4],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,2,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,4,4],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,3,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,2,2,3,4],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,3,3,4],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,3,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,4,4],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,3,4,4],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,2,4,4],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,4,4,4],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,3,3,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,2,3,3,4],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,3,3,3,4],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,3,3,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,3,4,4],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,3,3,4,4],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,3,4,4],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,4,4,4],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,3,4,4,4],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,2,4,4,4],[4]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,4,4,4,4],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,3,3,3,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,3,3,3,4],[3]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,3,3,3,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,3,3,4,4],[3]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,3,3,4,4],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,3,4,4,4],[3]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,3,4,4,4],[4]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,4,4,4,4],[3]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,4,4,4,4],[4]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[2,2,2,2,2],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[2,2,2,2,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[2,2,2,2,4],[3]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,2,2,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,2,3,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[2,2,2,3,4],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,2,3,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,2,4,4],[3]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,2,4,4],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,3,3,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[2,2,3,3,4],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,3,3,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,3,4,4],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,3,4,4],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,4,4,4],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,2,4,4,4],[4]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,3,3,3,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[2,3,3,3,4],[3]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[2,3,3,3,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,3,3,4,4],[3]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[2,3,3,4,4],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,3,4,4,4],[3]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[2,3,4,4,4],[4]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[2,4,4,4,4],[3]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[2,4,4,4,4],[4]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[3,3,3,3,3],[4]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[3,3,3,3,4],[4]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[3,3,3,4,4],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[3,3,4,4,4],[4]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[3,4,4,4,4],[4]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,1,1,1],[2,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,1,1],[3,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,1,1],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,1,2],[2,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,1,4],[2,2]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,1,2],[3,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,1,3],[2,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,1,4],[2,3]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,1,2],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,1,4],[2,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,1,3],[3,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,1,4],[3,3]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,1,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,1,4],[3,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,1,4],[4,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2],[2,4]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2,4],[2,2]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2],[3,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,2,3],[2,4]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2,4],[2,3]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,1,3,4],[2,2]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,2,2],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,2,4],[2,4]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,1,4,4],[2,2]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,2,3],[3,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2,4],[3,3]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,3,3],[2,4]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,3,4],[2,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,2,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,2,4],[3,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,3,4],[2,4]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,1,4,4],[2,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,2,4],[4,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,4,4],[2,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,3,3],[3,4]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,3,4],[3,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,1,3,4],[3,4]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,1,4,4],[3,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,3,4],[4,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,4,4],[3,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,4,4],[4,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,2,2,2],[2,4]] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2,2],[3,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,2,2,3],[2,4]] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2,4],[2,3]] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2,2],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,2,2,4],[2,4]] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2,3],[3,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2,4],[3,3]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,2,3,3],[2,4]] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,3,4],[2,3]] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,2,2,4],[3,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,2,3,4],[2,4]] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,4,4],[2,3]] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2,4],[4,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,2,4,4],[2,4]] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,3,3],[3,4]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,3,4],[3,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,3,3,3],[2,4]] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,2,3,4],[3,4]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,4,4],[3,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,3,3,4],[2,4]] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,3,4],[4,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,2,4,4],[3,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,3,4,4],[2,4]] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,4,4],[4,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,3,3,3],[3,4]] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,3,3,4],[3,4]] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,3,3,4],[4,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,3,4,4],[3,4]] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,3,4,4],[4,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,2,2,2],[3,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[2,2,2,2],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[2,2,2,3],[3,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,2,2,4],[3,3]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,2,2,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[2,2,2,4],[3,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,2,2,4],[4,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,2,3,3],[3,4]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,2,3,4],[3,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,2,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[2,2,3,4],[3,4]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[2,2,4,4],[3,3]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,2,3,4],[4,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,2,4,4],[3,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,2,4,4],[4,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,3,3,3],[3,4]] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[2,3,3,4],[3,4]] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[2,3,3,4],[4,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[2,3,4,4],[3,4]] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[2,3,4,4],[4,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[3,3,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[3,3,3,4],[4,4]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[3,3,4,4],[4,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,1,1,1],[2],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,1],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,4],[2],[3]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,1,4],[2],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,1,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,2,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,3,4],[2],[3]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,4,4],[2],[3]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,4,4],[2],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,4,4],[3],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,2,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,3,4],[2],[3]] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,4],[2],[3]] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,4],[3],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4,4,4],[2],[3]] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4,4,4],[2],[4]] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,4,4,4],[3],[4]] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,2,2,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,2,4,4],[3],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,4,4,4],[3],[4]] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,1],[2,2,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,1],[2,3,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,1],[2,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,1],[3,3,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,1],[3,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,1],[4,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,2],[2,2,4]] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2],[2,3,4]] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,3],[2,2,4]] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2],[2,4,4]] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2],[3,3,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,3],[2,3,4]] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2],[3,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,3],[2,4,4]] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2],[4,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,3],[3,3,4]] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,3],[3,4,4]] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,3],[4,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,2,2],[2,3,4]] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2],[2,4,4]] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2],[3,3,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,2,2],[3,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,2,3],[2,4,4]] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2],[4,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,2,3],[3,3,4]] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,3],[3,4,4]] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3,3],[2,4,4]] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,3],[4,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,3,3],[3,4,4]] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3,3],[4,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[2,2,2],[3,3,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[2,2,2],[3,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[2,2,2],[4,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[2,2,3],[3,3,4]] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,2,3],[3,4,4]] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,2,3],[4,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[2,3,3],[3,4,4]] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[2,3,3],[4,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[3,3,3],[4,4,4]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,1,1],[2,2],[4]] => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1],[2,3],[4]] => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1],[3,3],[4]] => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,4],[2,2],[3]] => [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,4],[2,2],[4]] => [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,2],[3,3],[4]] => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,4],[2,3],[4]] => [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,4],[3,3],[4]] => [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,2],[3,3],[4]] => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,3],[4]] => [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[2,2,2],[3,3],[4]] => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2,4],[3,3],[4]] => [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,1],[2],[3],[4]] => [6,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,1,4],[2],[3],[4]] => [5,4,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,4,4],[2],[3],[4]] => [4,3,2,1,5,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,1],[2,2],[3,4]] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[2,2],[4,4]] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[2,3],[4,4]] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[3,3],[4,4]] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3,3],[4,4]] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[2,2],[3,3],[4,4]] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1],[2,2],[3],[4]] => [6,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,1,1,1,1,1,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,1,1,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,1,1,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,1,2,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,1,2,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,1,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,2,2,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,2,2,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,2,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,2,2,2,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,2,2,2,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,2,2,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,2,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[2,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[2,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[2,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[2,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[2,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[2,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[3,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 1
[[1,1,1,1,1,1],[3]] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 2
[[1,1,1,1,1,2],[3]] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 2
[[1,1,1,1,1,3],[2]] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,1,3],[3]] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,2,2],[3]] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 2
[[1,1,1,1,2,3],[2]] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,2,3],[3]] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,3,3],[2]] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,3,3],[3]] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2,2,2],[3]] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 2
[[1,1,1,2,2,3],[2]] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2,2,3],[3]] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2,3,3],[2]] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2,3,3],[3]] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,3,3,3],[2]] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,3,3,3],[3]] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 2
[[1,1,2,2,2,3],[2]] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,2,2,2,3],[3]] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,2,2,3,3],[2]] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,2,3,3,3],[2]] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,3,3,3,3],[2]] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,1,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,2,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 2
[[1,2,2,2,2,3],[2]] => [2,1,3,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2
[[1,2,2,2,2,3],[3]] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,2,2,2,3,3],[2]] => [2,1,3,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2
[[1,2,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,2,2,3,3,3],[2]] => [2,1,3,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2
[[1,2,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,2,3,3,3,3],[2]] => [2,1,3,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2
[[1,2,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[1,3,3,3,3,3],[2]] => [2,1,3,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2
[[1,3,3,3,3,3],[3]] => [2,1,3,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2
[[2,2,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 2
[[2,2,2,2,2,3],[3]] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[2,2,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[2,2,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[2,2,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2
[[2,3,3,3,3,3],[3]] => [2,1,3,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,1],[2,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 2
[[1,1,1,1,1],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 2
[[1,1,1,1,2],[2,3]] => [5,7,1,2,3,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,1,1,3],[2,2]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 2
[[1,1,1,1,3],[2,3]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,3],[3,3]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2,2],[2,3]] => [4,7,1,2,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,1,2,3],[2,2]] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 2
[[1,1,1,2,3],[2,3]] => [4,6,1,2,3,5,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,1,1,3,3],[2,2]] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2,3],[3,3]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,1,3,3],[2,3]] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,1,3,3],[3,3]] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,2,2,2],[2,3]] => [3,7,1,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2,2,3],[2,2]] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 2
[[1,1,2,2,3],[2,3]] => [3,6,1,2,4,5,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,1,2,3,3],[2,2]] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,2,3,3],[2,3]] => [3,5,1,2,4,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,1,3,3,3],[2,2]] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,3,3,3],[2,3]] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,2,2,2,2],[2,3]] => [2,7,1,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 2
[[1,2,2,2,3],[2,3]] => [2,6,1,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,2,2,3,3],[2,3]] => [2,5,1,3,4,6,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,2,3,3,3],[2,3]] => [2,4,1,3,5,6,7] => ([(3,6),(4,5),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[2,2,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 2
[[2,2,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[2,2,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[2,2,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1,1],[2],[3]] => [7,6,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,1,3],[2],[3]] => [6,5,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,1,3,3],[2],[3]] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,3,3,3],[2],[3]] => [4,3,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,3,3,3],[2],[3]] => [3,2,1,4,5,6,7] => ([(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,1,1],[2,2,3]] => [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 2
[[1,1,1,1],[2,3,3]] => [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 2
[[1,1,1,1],[3,3,3]] => [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 2
[[1,1,1,2],[2,2,3]] => [4,5,7,1,2,3,6] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,1,3],[2,2,2]] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2],[2,3,3]] => [4,6,7,1,2,3,5] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,1,3],[2,2,3]] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 2
[[1,1,1,2],[3,3,3]] => [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 2
[[1,1,1,3],[2,3,3]] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 2
[[1,1,1,3],[3,3,3]] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 2
[[1,1,2,2],[2,2,3]] => [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2,2],[2,3,3]] => [3,6,7,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,1,2,3],[2,2,3]] => [3,4,6,1,2,5,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,1,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 2
[[1,1,2,3],[2,3,3]] => [3,5,6,1,2,4,7] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,1,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 2
[[1,2,2,2],[2,3,3]] => [2,6,7,1,3,4,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 2
[[1,2,2,3],[2,3,3]] => [2,5,6,1,3,4,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 2
[[2,2,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 2
[[2,2,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 2
[[1,1,1,1],[2,2],[3]] => [7,5,6,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1,3],[2,2],[3]] => [6,4,5,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,3,3],[2,2],[3]] => [5,3,4,1,2,6,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,1],[2,2,2],[3]] => [7,4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,1],[2,2],[3,3]] => [6,7,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,1,3],[2,2],[3,3]] => [5,6,3,4,1,2,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,1,1,1],[2,2,2,2]] => [5,6,7,8,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,1)],2) => 2
[[1]] => [1] => ([],1) => ([],1) => 1
[[2]] => [1] => ([],1) => ([],1) => 1
[[1,1]] => [1,2] => ([],2) => ([],1) => 1
[[3]] => [1] => ([],1) => ([],1) => 1
[[1,1,1]] => [1,2,3] => ([],3) => ([],1) => 1
[[4]] => [1] => ([],1) => ([],1) => 1
[[1,1,1,1]] => [1,2,3,4] => ([],4) => ([],1) => 1
[[5]] => [1] => ([],1) => ([],1) => 1
[[1,1,1,1,1]] => [1,2,3,4,5] => ([],5) => ([],1) => 1
[[6]] => [1] => ([],1) => ([],1) => 1
[[1,1,1,1,1,1]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => ([],6) => ([],1) => 1
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Generating function
$F_{(2, 2)} = 2\ q + q^{2}$
$F_{(2, 3)} = 3\ q + 2\ q^{2}$
$F_{(3, 2)} = 3\ q + 2\ q^{2}$
$F_{(2, 4)} = 4\ q + 3\ q^{2}$
$F_{(3, 3)} = 6\ q + 6\ q^{2} + q^{3}$
$F_{(4, 2)} = 4\ q + 4\ q^{2}$
$F_{(2, 5)} = 5\ q + 4\ q^{2}$
$F_{(3, 4)} = 10\ q + 12\ q^{2} + 3\ q^{3}$
$F_{(5, 2)} = 5\ q + 6\ q^{2}$
$F_{(2, 6)} = 6\ q + 5\ q^{2}$
$F_{(3, 5)} = 15\ q + 20\ q^{2} + 6\ q^{3}$
$F_{(6, 2)} = 6\ q + 9\ q^{2}$
$F_{(2, 7)} = 7\ q + 6\ q^{2}$
$F_{(3, 6)} = 21\ q + 30\ q^{2} + 10\ q^{3}$
$F_{(7, 2)} = 7\ q + 12\ q^{2}$
$F_{(2, 8)} = 8\ q + 7\ q^{2}$
$F_{(3, 7)} = 28\ q + 42\ q^{2} + 15\ q^{3}$
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Map
de-duplicate
Description
The de-duplicate of a graph.
Let $G = (V, E)$ be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods $\{N_v | v \in V\}$ of $G$, and has an edge $(N_a, N_b)$ between two vertices if and only if $(a, b)$ is an edge of $G$. This is well-defined, because if $N_a = N_c$ and $N_b = N_d$, then $(a, b)\in E$ if and only if $(c, d)\in E$.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
Let $G = (V, E)$ be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods $\{N_v | v \in V\}$ of $G$, and has an edge $(N_a, N_b)$ between two vertices if and only if $(a, b)$ is an edge of $G$. This is well-defined, because if $N_a = N_c$ and $N_b = N_d$, then $(a, b)\in E$ if and only if $(c, d)\in E$.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
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
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
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