Identifier
-
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001199: Dyck paths ⟶ ℤ
Values
[[1],[2]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[1],[3]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[2],[3]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[1,1],[2]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1],[4]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[2],[4]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[3],[4]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[1,1],[3]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,2],[3]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,2],[3]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1],[2],[3]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1,1,1],[2]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1],[2,2]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1],[5]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[2],[5]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[3],[5]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[4],[5]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[1,1],[4]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,2],[4]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,3],[4]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,2],[4]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,3],[4]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[3,3],[4]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1],[2],[4]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1],[3],[4]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[2],[3],[4]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1,1,1],[3]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,2],[3]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2,2],[3]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2,2],[3]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1],[2,3]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[3,3]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,2],[2,3]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,2],[3,3]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,2],[3,3]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[2],[3]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,2],[2],[3]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,1,1],[2]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1],[2,2]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1],[6]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[2],[6]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[3],[6]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[4],[6]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[5],[6]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[1,1],[5]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,2],[5]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,3],[5]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,4],[5]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,2],[5]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,3],[5]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,4],[5]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[3,3],[5]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[3,4],[5]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[4,4],[5]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1],[2],[5]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1],[3],[5]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1],[4],[5]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[2],[3],[5]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[2],[4],[5]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[3],[4],[5]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1,1,1],[4]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,2],[4]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,3],[4]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2,2],[4]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2,3],[4]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3,3],[4]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2,2],[4]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2,3],[4]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,3,3],[4]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[3,3,3],[4]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1],[2,4]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[3,4]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[4,4]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,2],[2,4]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,2],[3,4]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,3],[2,4]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,2],[4,4]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,3],[3,4]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,3],[4,4]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,2],[3,4]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,2],[4,4]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,3],[3,4]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[2,3],[4,4]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[3,3],[4,4]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[2],[4]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,1],[3],[4]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,2],[2],[4]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2],[3],[4]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,3],[2],[4]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3],[3],[4]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2],[3],[4]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[2,3],[3],[4]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1],[2],[3],[4]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1,1,1,1],[3]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1,2],[3]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,2,2],[3]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2,2],[3]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,2,2],[3]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1],[2,3]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,1],[3,3]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,2],[2,3]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
>>> Load all 1011 entries. <<<[[1,1,2],[3,3]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,2],[2,3]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,2,2],[3,3]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,2,2],[3,3]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,1],[2],[3]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,1,2],[2],[3]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2],[2],[3]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1],[2,2],[3]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,1],[2,3],[3]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,2],[2,3],[3]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,1,1,1,1],[2]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,1],[2,2]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,1],[2,2,2]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1],[7]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[2],[7]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[3],[7]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[4],[7]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[5],[7]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[6],[7]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[1,1],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,2],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,3],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,4],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,5],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,2],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,3],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,4],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,5],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[3,3],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[3,4],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[3,5],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[4,4],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[4,5],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[5,5],[6]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1],[2],[6]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1],[3],[6]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1],[4],[6]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1],[5],[6]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[2],[3],[6]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[2],[4],[6]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[2],[5],[6]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[3],[4],[6]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[3],[5],[6]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[4],[5],[6]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1,1,1],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,2],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,3],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,4],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2,2],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2,3],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2,4],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3,3],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3,4],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,4,4],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2,2],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2,3],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2,4],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,3,3],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,3,4],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,4,4],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[3,3,3],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[3,3,4],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[3,4,4],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[4,4,4],[5]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1],[2,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[3,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[4,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[5,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,2],[2,5]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,2],[3,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,3],[2,5]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,2],[4,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,4],[2,5]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,2],[5,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,3],[3,5]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,3],[4,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,4],[3,5]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,3],[5,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,4],[4,5]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,4],[5,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,2],[3,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,2],[4,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,2],[5,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,3],[3,5]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[2,3],[4,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,4],[3,5]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[2,3],[5,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,4],[4,5]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[2,4],[5,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[3,3],[4,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[3,3],[5,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[3,4],[4,5]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[3,4],[5,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[4,4],[5,5]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[2],[5]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,1],[3],[5]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,1],[4],[5]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,2],[2],[5]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2],[3],[5]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,3],[2],[5]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2],[4],[5]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,4],[2],[5]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3],[3],[5]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3],[4],[5]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,4],[3],[5]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,4],[4],[5]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2],[3],[5]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[2,2],[4],[5]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[2,3],[3],[5]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[2,3],[4],[5]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[2,4],[3],[5]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[2,4],[4],[5]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[3,3],[4],[5]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[3,4],[4],[5]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1],[2],[3],[5]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1],[2],[4],[5]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1],[3],[4],[5]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[2],[3],[4],[5]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1,1,1,1],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1,2],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1,3],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,2,2],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,2,3],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,3,3],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2,2],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2,3],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3,3],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3,3],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,2,2],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,2,3],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,3,3],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,3,3],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,3,3,3],[4]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1],[2,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,1],[3,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,1],[4,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,2],[2,4]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,1,2],[3,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,3],[2,4]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,1,2],[4,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,3],[3,4]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,1,3],[4,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,2],[2,4]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,2,2],[3,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,3],[2,4]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,2,2],[4,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,3],[3,4]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,3,3],[2,4]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,2,3],[4,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,3,3],[3,4]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,3,3],[4,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,2,2],[3,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,2,2],[4,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,2,3],[3,4]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[2,2,3],[4,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,3,3],[3,4]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[2,3,3],[4,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[3,3,3],[4,4]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,1],[2],[4]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,1,1],[3],[4]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,1,2],[2],[4]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,2],[3],[4]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,1,3],[2],[4]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,3],[3],[4]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2],[2],[4]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2],[3],[4]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,2,3],[2],[4]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3],[3],[4]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3],[2],[4]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3],[3],[4]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,2],[3],[4]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[2,2,3],[3],[4]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,3],[3],[4]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1],[2,2],[4]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,1],[2,3],[4]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,1],[2,4],[3]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,1],[2,4],[4]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,1],[3,3],[4]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,1],[3,4],[4]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,2],[2,3],[4]] => [5,2,4,1,3] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 2
[[1,2],[2,4],[3]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,2],[2,4],[4]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,2],[3,3],[4]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,3],[2,4],[3]] => [3,2,5,1,4] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 1
[[1,2],[3,4],[4]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,3],[2,4],[4]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,3],[3,4],[4]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[2,2],[3,3],[4]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[2,2],[3,4],[4]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[2,3],[3,4],[4]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,1],[2],[3],[4]] => [5,4,3,1,2] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1,2],[2],[3],[4]] => [5,4,2,1,3] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,3],[2],[3],[4]] => [5,3,2,1,4] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1,1,1],[3]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,1,2],[3]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,2,2],[3]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2,2,2],[3]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,2,2],[3]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,2,2,2,2],[3]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,1],[2,3]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,1,1],[3,3]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,1,2],[2,3]] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,1,1,2],[3,3]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,2,2],[2,3]] => [3,6,1,2,4,5] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,1,2,2],[3,3]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,2,2,2],[2,3]] => [2,6,1,3,4,5] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,2,2,2],[3,3]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[2,2,2,2],[3,3]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,1,1],[2],[3]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,1,1,2],[2],[3]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2,2],[2],[3]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,2],[2],[3]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1],[2,2,3]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[2,3,3]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[3,3,3]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,2],[2,2,3]] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,1,2],[2,3,3]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,1,2],[3,3,3]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,2],[2,3,3]] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2,2],[3,3,3]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[2,2,2],[3,3,3]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[2,2],[3]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,1,1],[2,3],[3]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,2],[2,2],[3]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2],[2,3],[3]] => [5,3,6,1,2,4] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2,2],[2,3],[3]] => [5,2,6,1,3,4] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,1],[2,2],[3,3]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,1,1,1,1,1],[2]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,1,1,1],[2,2]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,1,1,1],[2,2,2]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1],[8]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[2],[8]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[3],[8]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[4],[8]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[5],[8]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[6],[8]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[7],[8]] => [2,1] => [1,2] => [1,0,1,0] => 1
[[1,1],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,2],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,3],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,4],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,5],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1,6],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,2],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,3],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,4],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,5],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[2,6],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[3,3],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[3,4],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[3,5],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[3,6],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[4,4],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[4,5],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[4,6],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[5,5],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[5,6],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[6,6],[7]] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0] => 1
[[1],[2],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1],[3],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1],[4],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1],[5],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1],[6],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[2],[3],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[2],[4],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[2],[5],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[2],[6],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[3],[4],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[3],[5],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[3],[6],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[4],[5],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[4],[6],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[5],[6],[7]] => [3,2,1] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1,1,1],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,2],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,3],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,4],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2,2],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2,3],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2,4],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3,3],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3,4],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,4,4],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,4,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,5,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2,2],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2,3],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2,4],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,3,3],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,3,4],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,3,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,4,4],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,4,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[2,5,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[3,3,3],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[3,3,4],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[3,3,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[3,4,4],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[3,4,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[3,5,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[4,4,4],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[4,4,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[4,5,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[5,5,5],[6]] => [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[[1,1],[2,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[3,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[4,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[5,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,2],[2,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,2],[3,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,3],[2,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,2],[4,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,4],[2,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,2],[5,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,5],[2,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,2],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,3],[3,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,3],[4,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,4],[3,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,3],[5,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,5],[3,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,3],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,4],[4,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,4],[5,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,5],[4,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,4],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,5],[5,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[1,5],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,2],[3,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,2],[4,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,2],[5,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,2],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,3],[3,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[2,3],[4,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,4],[3,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[2,3],[5,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,5],[3,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[2,3],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,4],[4,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[2,4],[5,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,5],[4,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[2,4],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[2,5],[5,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[2,5],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[3,3],[4,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[3,3],[5,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[3,3],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[3,4],[4,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[3,4],[5,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[3,5],[4,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[3,4],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[3,5],[5,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[3,5],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[4,4],[5,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[4,4],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[4,5],[5,6]] => [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 1
[[4,5],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[5,5],[6,6]] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[[1,1],[2],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,1],[3],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,1],[4],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,1],[5],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,2],[2],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2],[3],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,3],[2],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2],[4],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,4],[2],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,2],[5],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,5],[2],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3],[3],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3],[4],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,4],[3],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,3],[5],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,5],[3],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,4],[4],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,4],[5],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[1,5],[4],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1,5],[5],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[2,2],[3],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[2,2],[4],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[2,2],[5],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[2,3],[3],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[2,3],[4],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[2,4],[3],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[2,3],[5],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[2,5],[3],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[2,4],[4],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[2,4],[5],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[2,5],[4],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[2,5],[5],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[3,3],[4],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[3,3],[5],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[3,4],[4],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[3,4],[5],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[3,5],[4],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[3,5],[5],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[4,4],[5],[6]] => [4,3,1,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[[4,5],[5],[6]] => [4,2,1,3] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[[1],[2],[3],[6]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1],[2],[4],[6]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1],[2],[5],[6]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1],[3],[4],[6]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1],[3],[5],[6]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1],[4],[5],[6]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[2],[3],[4],[6]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[2],[3],[5],[6]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[2],[4],[5],[6]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[3],[4],[5],[6]] => [4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1,1,1,1],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1,2],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1,3],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,2,2],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,2,3],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,2,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,3,3],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,3,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,4,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2,2],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2,3],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3,3],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,4,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3,3],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,4,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,4,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,2,2],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,2,3],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,2,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,3,3],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,3,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,4,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,3,3],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,3,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,4,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,4,4,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,3,3,3],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,3,3,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,3,4,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,4,4,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,4,4,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1],[2,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,1],[3,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,1],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,1],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,2],[2,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,1,2],[3,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,3],[2,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,1,2],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,4],[2,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,1,2],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,3],[3,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,1,3],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,4],[3,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,1,3],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,4],[4,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,1,4],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,2],[2,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,2,2],[3,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,3],[2,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,2,2],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,4],[2,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,2,2],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,3],[3,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,3,3],[2,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,2,3],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,4],[3,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,3,4],[2,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,2,3],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,4],[4,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,4,4],[2,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,2,4],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,3,3],[3,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,3,3],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,3,4],[3,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,3,3],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,3,4],[4,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,4,4],[3,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,3,4],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,4,4],[4,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,4,4],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,2,2],[3,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,2,2],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,2,2],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,2,3],[3,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[2,2,3],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,2,4],[3,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[2,2,3],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,2,4],[4,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[2,2,4],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,3,3],[3,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[2,3,3],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,3,4],[3,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[2,3,3],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,3,4],[4,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[2,4,4],[3,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[2,3,4],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[2,4,4],[4,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[2,4,4],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[3,3,3],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[3,3,3],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[3,3,4],[4,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 1
[[3,3,4],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[3,4,4],[4,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 1
[[3,4,4],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[4,4,4],[5,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,1,1],[2],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,1,1],[3],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,1,1],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,1,2],[2],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,2],[3],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,1,3],[2],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,2],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,1,4],[2],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,3],[3],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,3],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,1,4],[3],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,4],[4],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2],[2],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2],[3],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,2,3],[2],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,2],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,2,4],[2],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3],[3],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3],[2],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,2,4],[3],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,4],[2],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,4],[4],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,4],[2],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3],[3],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,3,4],[3],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,4],[4],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,4],[3],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,4],[4],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,2],[3],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[2,2,2],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[2,2,3],[3],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,3],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[2,2,4],[3],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,4],[4],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,3],[3],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,3],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[2,3,4],[3],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,4],[4],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,4,4],[3],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,4,4],[4],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,3,3],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[3,3,4],[4],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,4,4],[4],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1],[2,2],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,1],[2,3],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,1],[2,5],[3]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,1],[2,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,1],[2,5],[4]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,1],[2,5],[5]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,1],[3,3],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,1],[3,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,1],[3,5],[4]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,1],[3,5],[5]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,1],[4,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,1],[4,5],[5]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,2],[2,3],[5]] => [5,2,4,1,3] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 2
[[1,2],[2,5],[3]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,2],[2,4],[5]] => [5,2,4,1,3] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 2
[[1,2],[2,5],[4]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,2],[2,5],[5]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,2],[3,3],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,3],[2,5],[3]] => [3,2,5,1,4] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 1
[[1,2],[3,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,2],[3,5],[4]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,3],[2,4],[5]] => [5,2,4,1,3] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 2
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 1
[[1,2],[3,5],[5]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,3],[2,5],[5]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,2],[4,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,4],[2,5],[4]] => [3,2,5,1,4] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 1
[[1,2],[4,5],[5]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,4],[2,5],[5]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,3],[3,4],[5]] => [5,2,4,1,3] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 2
[[1,3],[3,5],[4]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,3],[3,5],[5]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,3],[4,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,4],[3,5],[4]] => [3,2,5,1,4] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 1
[[1,3],[4,5],[5]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,4],[3,5],[5]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,4],[4,5],[5]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[2,2],[3,3],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[2,2],[3,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[2,2],[3,5],[4]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[2,2],[3,5],[5]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[2,2],[4,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[2,2],[4,5],[5]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[2,3],[3,4],[5]] => [5,2,4,1,3] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 2
[[2,3],[3,5],[4]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[2,3],[3,5],[5]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[2,3],[4,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[2,4],[3,5],[4]] => [3,2,5,1,4] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 1
[[2,3],[4,5],[5]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[2,4],[3,5],[5]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[2,4],[4,5],[5]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[3,3],[4,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[[3,3],[4,5],[5]] => [4,3,5,1,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 1
[[3,4],[4,5],[5]] => [4,2,5,1,3] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,1],[2],[3],[5]] => [5,4,3,1,2] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1,1],[2],[4],[5]] => [5,4,3,1,2] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1,1],[3],[4],[5]] => [5,4,3,1,2] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1,2],[2],[3],[5]] => [5,4,2,1,3] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,2],[2],[4],[5]] => [5,4,2,1,3] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,3],[2],[3],[5]] => [5,3,2,1,4] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4],[2],[4],[5]] => [5,3,2,1,4] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3],[3],[4],[5]] => [5,4,2,1,3] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,4],[3],[4],[5]] => [5,3,2,1,4] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2],[3],[4],[5]] => [5,4,3,1,2] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[[2,3],[3],[4],[5]] => [5,4,2,1,3] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[[2,4],[3],[4],[5]] => [5,3,2,1,4] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[[1,1,1,1,1],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,1,2],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,1,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,2,2],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,2,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,3,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2,2,2],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2,2,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2,3,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,3,3,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,2,2],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,2,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,3,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,3,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3,3,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,2,2,2,2],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,2,2,2,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,2,2,3,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,2,3,3,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,3,3,3,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[3,3,3,3,3],[4]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,1],[2,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,1,1],[3,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,1,1],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,1,2],[2,4]] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,1,1,2],[3,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,1,3],[2,4]] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,1,1,2],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,1,3],[3,4]] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,1,1,3],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,2,2],[2,4]] => [3,6,1,2,4,5] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,1,2,2],[3,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,2,3],[2,4]] => [3,6,1,2,4,5] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,1,2,2],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,2,3],[3,4]] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,1,3,3],[2,4]] => [3,6,1,2,4,5] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,1,2,3],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,3,3],[3,4]] => [3,6,1,2,4,5] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,1,3,3],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,2,2,2],[2,4]] => [2,6,1,3,4,5] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,2,2,2],[3,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,2,2,3],[2,4]] => [2,6,1,3,4,5] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,2,2,2],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,2,2,3],[3,4]] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,2,3,3],[2,4]] => [2,6,1,3,4,5] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,2,2,3],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,2,3,3],[3,4]] => [3,6,1,2,4,5] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,3,3,3],[2,4]] => [2,6,1,3,4,5] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,2,3,3],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,3,3,3],[3,4]] => [2,6,1,3,4,5] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,3,3,3],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[2,2,2,2],[3,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[2,2,2,2],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[2,2,2,3],[3,4]] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[2,2,2,3],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[2,2,3,3],[3,4]] => [3,6,1,2,4,5] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[2,2,3,3],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[2,3,3,3],[3,4]] => [2,6,1,3,4,5] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[2,3,3,3],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[3,3,3,3],[4,4]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,1,1,1],[2],[4]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,1,1,1],[3],[4]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,1,1,2],[2],[4]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,2],[3],[4]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,1,1,3],[2],[4]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,3],[3],[4]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2,2],[2],[4]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2,2],[3],[4]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,1,2,3],[2],[4]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2,3],[3],[4]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,3,3],[2],[4]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,3,3],[3],[4]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,2],[2],[4]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,2],[3],[4]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,2,2,3],[2],[4]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,3],[3],[4]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,3],[2],[4]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,3],[3],[4]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3,3],[2],[4]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3,3],[3],[4]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,2,2,2],[3],[4]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[2,2,2,3],[3],[4]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,2,3,3],[3],[4]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,3,3,3],[3],[4]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1],[2,2,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[2,3,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[2,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[3,3,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[3,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[4,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,2],[2,2,4]] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,1,2],[2,3,4]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,1,3],[2,2,4]] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,1,2],[2,4,4]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,1,2],[3,3,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,3],[2,3,4]] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,1,2],[3,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,3],[2,4,4]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,1,2],[4,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,3],[3,3,4]] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,1,3],[3,4,4]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,1,3],[4,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,2],[2,3,4]] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2,2],[2,4,4]] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2,2],[3,3,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3],[2,3,4]] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,2,2],[3,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3],[2,4,4]] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2,2],[4,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3],[3,3,4]] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,2,3],[3,4,4]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,3,3],[2,4,4]] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2,3],[4,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3,3],[3,4,4]] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,3,3],[4,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[2,2,2],[3,3,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[2,2,2],[3,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[2,2,2],[4,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[2,2,3],[3,3,4]] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[2,2,3],[3,4,4]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[2,2,3],[4,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[2,3,3],[3,4,4]] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[2,3,3],[4,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[3,3,3],[4,4,4]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[2,2],[4]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,1,1],[2,3],[4]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,1,1],[2,4],[3]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[2,4],[4]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1],[3,3],[4]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,1,1],[3,4],[4]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,2],[2,2],[4]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2],[2,3],[4]] => [6,3,5,1,2,4] => [4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[1,1,2],[2,4],[3]] => [5,3,6,1,2,4] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,1,3],[2,2],[4]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,2],[2,4],[4]] => [5,3,6,1,2,4] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,1,2],[3,3],[4]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,1,3],[2,3],[4]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,3],[2,4],[3]] => [4,3,6,1,2,5] => [5,2,1,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,1,2],[3,4],[4]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,1,3],[2,4],[4]] => [5,3,6,1,2,4] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,1,3],[3,3],[4]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,3],[3,4],[4]] => [5,3,6,1,2,4] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2,2],[2,3],[4]] => [6,2,5,1,3,4] => [4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[1,2,2],[2,4],[3]] => [5,2,6,1,3,4] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2,2],[2,4],[4]] => [5,2,6,1,3,4] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2,2],[3,3],[4]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3],[2,3],[4]] => [6,2,4,1,3,5] => [5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3],[2,4],[3]] => [4,2,6,1,3,5] => [5,3,1,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,2,2],[3,4],[4]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3],[2,4],[4]] => [5,2,6,1,3,4] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2,3],[3,3],[4]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3],[2,4],[3]] => [3,2,6,1,4,5] => [5,4,1,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,2,3],[3,4],[4]] => [5,3,6,1,2,4] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,3,3],[2,4],[4]] => [5,2,6,1,3,4] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,3,3],[3,4],[4]] => [5,2,6,1,3,4] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[2,2,2],[3,3],[4]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[2,2,2],[3,4],[4]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[2,2,3],[3,3],[4]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,2,3],[3,4],[4]] => [5,3,6,1,2,4] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[2,3,3],[3,4],[4]] => [5,2,6,1,3,4] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,1,1],[2],[3],[4]] => [6,5,4,1,2,3] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[1,1,2],[2],[3],[4]] => [6,5,3,1,2,4] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,1,3],[2],[3],[4]] => [6,4,3,1,2,5] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2],[2],[3],[4]] => [6,5,2,1,3,4] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,2,3],[2],[3],[4]] => [6,4,2,1,3,5] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3],[2],[3],[4]] => [6,3,2,1,4,5] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1],[2,2],[3,4]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,1],[2,2],[4,4]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,1],[2,3],[3,4]] => [4,6,3,5,1,2] => [2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[1,1],[2,3],[4,4]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,1],[3,3],[4,4]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2],[2,3],[3,4]] => [4,6,2,5,1,3] => [3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[[1,2],[2,3],[4,4]] => [5,6,2,4,1,3] => [3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[1,2],[3,3],[4,4]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[2,2],[3,3],[4,4]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,1],[2,2],[3],[4]] => [6,5,3,4,1,2] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[1,1],[2,3],[3],[4]] => [6,4,3,5,1,2] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,1],[2,4],[3],[4]] => [5,4,3,6,1,2] => [2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2],[2,3],[3],[4]] => [6,4,2,5,1,3] => [3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[1,2],[2,4],[3],[4]] => [5,4,2,6,1,3] => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[[1,3],[2,4],[3],[4]] => [5,3,2,6,1,4] => [4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[[1,1,1,1,1,1],[3]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,1,1,1,2],[3]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,1,1,2,2],[3]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,1,2,2,2],[3]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[2,2,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,1,1,1],[2,3]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,1,1,1,1],[3,3]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,1,1,1,2],[2,3]] => [5,7,1,2,3,4,6] => [6,4,3,2,1,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[[1,1,1,1,2],[3,3]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,1,1,2,2],[2,3]] => [4,7,1,2,3,5,6] => [6,5,3,2,1,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[[1,1,1,2,2],[3,3]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,1,2,2,2],[2,3]] => [3,7,1,2,4,5,6] => [6,5,4,2,1,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[[1,1,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,2,2,2],[2,3]] => [2,7,1,3,4,5,6] => [6,5,4,3,1,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[[1,2,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[2,2,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,1,1,1,1],[2],[3]] => [7,6,1,2,3,4,5] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[[1,1,1,1,2],[2],[3]] => [7,5,1,2,3,4,6] => [6,4,3,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,1,2,2],[2],[3]] => [7,4,1,2,3,5,6] => [6,5,3,2,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,2,2,2],[2],[3]] => [7,3,1,2,4,5,6] => [6,5,4,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2,2,2,2],[2],[3]] => [7,2,1,3,4,5,6] => [6,5,4,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,1,1],[2,2,3]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1,1],[2,3,3]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1,1],[3,3,3]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1,2],[2,2,3]] => [4,5,7,1,2,3,6] => [6,3,2,1,7,5,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[[1,1,1,2],[2,3,3]] => [4,6,7,1,2,3,5] => [5,3,2,1,7,6,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[[1,1,1,2],[3,3,3]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,1,2,2],[2,2,3]] => [3,4,7,1,2,5,6] => [6,5,2,1,7,4,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[[1,1,2,2],[2,3,3]] => [3,6,7,1,2,4,5] => [5,4,2,1,7,6,3] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[[1,1,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,2,2],[2,3,3]] => [2,6,7,1,3,4,5] => [5,4,3,1,7,6,2] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[[1,2,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[2,2,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1,1],[2,2],[3]] => [7,5,6,1,2,3,4] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,1,1,1],[2,3],[3]] => [6,5,7,1,2,3,4] => [4,3,2,1,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,1,1,2],[2,2],[3]] => [7,4,5,1,2,3,6] => [6,3,2,1,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,1,2],[2,3],[3]] => [6,4,7,1,2,3,5] => [5,3,2,1,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[[1,1,2,2],[2,2],[3]] => [7,3,4,1,2,5,6] => [6,5,2,1,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,1,2,2],[2,3],[3]] => [6,3,7,1,2,4,5] => [5,4,2,1,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[[1,2,2,2],[2,3],[3]] => [6,2,7,1,3,4,5] => [5,4,3,1,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[[1,1,1],[2,2,2],[3]] => [7,4,5,6,1,2,3] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,1,1],[2,2,3],[3]] => [6,4,5,7,1,2,3] => [3,2,1,7,5,4,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,1,1],[2,3,3],[3]] => [5,4,6,7,1,2,3] => [3,2,1,7,6,4,5] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,1,2],[2,2,3],[3]] => [6,3,4,7,1,2,5] => [5,2,1,7,4,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[[1,1,2],[2,3,3],[3]] => [5,3,6,7,1,2,4] => [4,2,1,7,6,3,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[[1,2,2],[2,3,3],[3]] => [5,2,6,7,1,3,4] => [4,3,1,7,6,2,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[[1,1,1],[2,2],[3,3]] => [6,7,4,5,1,2,3] => [3,2,1,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,1,2],[2,2],[3,3]] => [6,7,3,4,1,2,5] => [5,2,1,4,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [5,2,1,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [5,3,1,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [5,4,1,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
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Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
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