Identifier
-
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001128: Integer partitions ⟶ ℤ
Values
[[1,1,2]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,2,2]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,2,2]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,1,3]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,2,3]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,3,3]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,2,3]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,3,3]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,3,3]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,1,1,2]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,2,2]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,2,2]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,2,2]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,2],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,1],[2,2]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1,4]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,2,4]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,3,4]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,4,4]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,2,4]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,3,4]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,4,4]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,3,4]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,4,4]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[4,4,4]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,1,1,3]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,2,3]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,3,3]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,2,3]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,3,3]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,3,3,3]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,2,3]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,3,3]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,3,3,3]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,3,3,3]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,3],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,3,3],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,3,3],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,3,3],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,1],[2,3]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1],[3,3]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,2],[3,3]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,2],[3,3]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,3],[2],[3]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,1,1,1,2]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,2],[2]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,2,2,2],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,1,2],[2,2]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,2,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,3,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,4,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,5,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,2,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,3,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,4,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,5,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,3,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,4,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,5,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[4,4,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[4,5,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[5,5,5]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,1,1,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,2,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,3,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,4,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,2,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,3,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,4,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,3,3,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,3,4,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,4,4,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,2,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,3,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,4,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,3,3,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,3,4,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,4,4,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,3,3,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,3,4,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,4,4,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[4,4,4,4]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,4],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,3,4],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,4,4],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,3,4],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,4,4],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,4,4],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,3,4],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,4,4],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,4,4],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[3,4,4],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,1],[2,4]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1],[3,4]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1],[4,4]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,2],[3,4]] => [3,4,1,2] => [2,2] => [2] => 1
>>> Load all 1437 entries. <<<[[1,2],[4,4]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,3],[4,4]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,2],[3,4]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,2],[4,4]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,3],[4,4]] => [3,4,1,2] => [2,2] => [2] => 1
[[3,3],[4,4]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,4],[2],[3]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,4],[2],[4]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,4],[3],[4]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[2,4],[3],[4]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1],[2],[3],[4]] => [4,3,2,1] => [2,2] => [2] => 1
[[1,1,1,1,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,3,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,3,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,3],[2]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,3,3],[2]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,3,3],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,2,2,3],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,3,3],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,3,3],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,3,3,3],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,3,3],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,2,3,3],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,3,3,3],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,1,2],[2,3]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,1,3],[2,2]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,3],[2,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,3],[3,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,2,3],[3,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,2,3],[3,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,1],[2],[3]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,2,3],[2],[3]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,3,3],[2],[3]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,1],[2,3],[3]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,2],[2,3],[3]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,1,1,1,1,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,1,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,2,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,2,2],[2]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,2,2,2],[2]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,2,2,2,2],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,1],[2,2]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,2,2],[2,2]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,1],[2,2,2]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,2,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,3,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,4,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,5,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,6,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,2,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,3,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,4,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,5,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,6,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,3,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,4,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,5,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,6,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[4,4,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[4,5,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[4,6,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[5,5,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[5,6,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[6,6,6]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,1,1,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,2,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,3,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,4,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,2,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,3,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,4,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,3,3,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,3,4,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,3,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,4,4,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,4,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,5,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,2,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,3,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,4,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,3,3,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,3,4,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,3,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,4,4,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,4,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,5,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,3,3,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,3,4,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,3,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,4,4,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,4,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,5,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[4,4,4,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[4,4,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[4,5,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[5,5,5,5]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,5],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,3,5],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,4,5],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,5,5],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,3,5],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,4,5],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,5,5],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,4,5],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,5,5],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,5,5],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,3,5],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,4,5],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,5,5],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,4,5],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,5,5],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,5,5],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[3,4,5],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[3,5,5],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[3,5,5],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[4,5,5],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,1],[2,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1],[3,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1],[4,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1],[5,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,2],[3,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,2],[4,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,2],[5,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,3],[4,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,3],[5,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,4],[5,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,2],[3,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,2],[4,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,2],[5,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,3],[4,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,3],[5,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,4],[5,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[3,3],[4,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[3,3],[5,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[3,4],[5,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[4,4],[5,5]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,5],[2],[3]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,5],[2],[4]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,5],[2],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,5],[3],[4]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,5],[3],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,5],[4],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[2,5],[3],[4]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[2,5],[3],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[2,5],[4],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[3,5],[4],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1],[2],[3],[5]] => [4,3,2,1] => [2,2] => [2] => 1
[[1],[2],[4],[5]] => [4,3,2,1] => [2,2] => [2] => 1
[[1],[3],[4],[5]] => [4,3,2,1] => [2,2] => [2] => 1
[[2],[3],[4],[5]] => [4,3,2,1] => [2,2] => [2] => 1
[[1,1,1,1,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,2,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,2,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,2,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,3,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,4,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,2,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,3,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,3,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,3,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,4,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,3,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,3,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,3,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,4,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[4,4,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,4],[2]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,3,4],[2]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,4,4],[2]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,3,4],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,4,4],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,4,4],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,2,2,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,3,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,4,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,3,4],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,3,3,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,4,4],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,3,4,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,4,4],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,4,4,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,3,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,4,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,4,4],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,4,4,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,4,4,4],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,2,3,4],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,2,4,4],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,2,4,4],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,3,3,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,3,4,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,3,4,4],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,4,4,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,4,4,4],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[3,3,4,4],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[3,4,4,4],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,1,2],[2,4]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,1,4],[2,2]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,3],[2,4]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,1,4],[2,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,4],[2,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,3],[3,4]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,1,4],[3,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,4],[3,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,4],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,2,3],[3,4]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,2,4],[3,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,2,4],[3,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,2,4],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,3,4],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,2,3],[3,4]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[2,2,4],[3,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,2,4],[3,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,2,4],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,3,4],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[3,3,4],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,1],[2],[4]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,1,1],[3],[4]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,1,2],[3],[4]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,2,2],[3],[4]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,2,4],[2],[3]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,2,4],[2],[4]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,3,4],[2],[3]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,4],[2],[4]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,4,4],[2],[3]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,4,4],[2],[4]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,4],[3],[4]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,4,4],[3],[4]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,2,2],[3],[4]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[2,3,4],[3],[4]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[2,4,4],[3],[4]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,1],[2,4],[3]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,1],[2,4],[4]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,1],[3,4],[4]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,2],[2,4],[3]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,2],[2,4],[4]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,2],[3,4],[4]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,3],[2,4],[4]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,3],[3,4],[4]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[2,2],[3,4],[4]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[2,3],[3,4],[4]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,3],[2],[3],[4]] => [5,3,2,1,4] => [3,2] => [2] => 1
[[1,4],[2],[3],[4]] => [4,3,2,1,5] => [2,2,1] => [2,1] => 2
[[1,1,1,1,1,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,1,2,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,1,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,2,2,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,2,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,2,2,2,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,2,2,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,2,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,2,2,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,2,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,2,2,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,2,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[3,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,2,3],[2]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,1,3,3],[2]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,1,3,3],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,2,2,3],[2]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,2,3,3],[2]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,2,3,3],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,3,3,3],[2]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,3,3,3],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,2,2,2,3],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,3,3],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,3,3],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,3,3,3],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,3,3,3],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,3,3,3,3],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,3,3],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,3,3],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[2,2,3,3,3],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[2,3,3,3,3],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,1],[2,3]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,1,1],[3,3]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,1,2],[3,3]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,2,2],[2,3]] => [3,6,1,2,4,5] => [4,2] => [2] => 1
[[1,1,2,3],[2,2]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,2,2],[3,3]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,2,3],[2,3]] => [3,5,1,2,4,6] => [3,2,1] => [2,1] => 2
[[1,1,3,3],[2,2]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,3,3],[2,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,3,3],[3,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,2,2,2],[3,3]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,2,3,3],[2,3]] => [2,4,1,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,3,3],[3,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[2,2,2,2],[3,3]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[2,2,3,3],[3,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,1,2],[2],[3]] => [6,4,1,2,3,5] => [4,2] => [2] => 1
[[1,1,1,3],[2],[3]] => [5,4,1,2,3,6] => [3,2,1] => [2,1] => 2
[[1,1,3,3],[2],[3]] => [4,3,1,2,5,6] => [4,1,1] => [1,1] => 1
[[1,2,2,3],[2],[3]] => [5,2,1,3,4,6] => [4,1,1] => [1,1] => 1
[[1,2,3,3],[2],[3]] => [4,2,1,3,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,3,3,3],[2],[3]] => [3,2,1,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1],[2,2,3]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,1],[2,3,3]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,1],[3,3,3]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,2],[2,3,3]] => [3,5,6,1,2,4] => [4,2] => [2] => 1
[[1,1,2],[3,3,3]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,2,2],[3,3,3]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[2,2,2],[3,3,3]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,1],[2,3],[3]] => [5,4,6,1,2,3] => [4,2] => [2] => 1
[[1,1,3],[2,3],[3]] => [4,3,5,1,2,6] => [3,2,1] => [2,1] => 2
[[1,2,3],[2,3],[3]] => [4,2,5,1,3,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1],[2,2],[3,3]] => [5,6,3,4,1,2] => [2,2,1,1] => [2,1,1] => 2
[[1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,1,2,2],[2]] => [5,1,2,3,4,6,7] => [5,1,1] => [1,1] => 1
[[1,1,1,2,2,2],[2]] => [4,1,2,3,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[[1,1,2,2,2,2],[2]] => [3,1,2,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,2,2,2],[2]] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,1,2],[2,2]] => [5,6,1,2,3,4,7] => [3,3,1] => [3,1] => 3
[[1,1,1,2,2],[2,2]] => [4,5,1,2,3,6,7] => [5,1,1] => [1,1] => 1
[[1,1,2,2,2],[2,2]] => [3,4,1,2,5,6,7] => [2,2,1,1,1] => [2,1,1,1] => 2
[[1,1,1,2],[2,2,2]] => [4,5,6,1,2,3,7] => [2,2,2,1] => [2,2,1] => 2
[[1,1,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,2,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,3,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,4,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,5,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,6,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,7,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,2,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,3,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,4,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,5,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,6,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[2,7,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,3,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,4,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,5,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,6,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[3,7,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[4,4,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[4,5,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[4,6,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[4,7,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[5,5,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[5,6,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[5,7,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[6,6,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[6,7,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[7,7,7]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,1,1,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,2,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,3,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,4,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,2,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,3,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,4,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,3,3,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,3,4,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,3,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,3,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,4,4,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,4,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,4,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,5,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,5,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,6,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,2,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,3,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,4,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,2,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,3,3,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,3,4,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,3,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,3,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,4,4,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,4,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,4,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,5,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,5,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[2,6,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,3,3,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,3,4,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,3,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,3,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,4,4,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,4,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,4,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,5,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,5,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[3,6,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[4,4,4,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[4,4,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[4,4,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[4,5,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[4,5,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[4,6,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[5,5,5,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[5,5,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[5,6,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[6,6,6,6]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,2,6],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,3,6],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,4,6],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,5,6],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,6,6],[2]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,3,6],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,4,6],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,5,6],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,6,6],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,4,6],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,5,6],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,6,6],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,5,6],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,6,6],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,6,6],[6]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,3,6],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,4,6],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,5,6],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,6,6],[3]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,4,6],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,5,6],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,6,6],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,5,6],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,6,6],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[2,6,6],[6]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[3,4,6],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[3,5,6],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[3,6,6],[4]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[3,5,6],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[3,6,6],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[3,6,6],[6]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[4,5,6],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[4,6,6],[5]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[4,6,6],[6]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[5,6,6],[6]] => [2,1,3,4] => [2,1,1] => [1,1] => 1
[[1,1],[2,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1],[3,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1],[4,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1],[5,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,1],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,2],[3,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,2],[4,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,2],[5,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,2],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,3],[4,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,3],[5,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,3],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,4],[5,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,4],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,5],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,2],[3,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,2],[4,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,2],[5,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,2],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,3],[4,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,3],[5,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,3],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,4],[5,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,4],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[2,5],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[3,3],[4,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[3,3],[5,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[3,3],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[3,4],[5,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[3,4],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[3,5],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[4,4],[5,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[4,4],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[4,5],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[5,5],[6,6]] => [3,4,1,2] => [2,2] => [2] => 1
[[1,6],[2],[3]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,6],[2],[4]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,6],[2],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,6],[2],[6]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,6],[3],[4]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,6],[3],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,6],[3],[6]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,6],[4],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,6],[4],[6]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1,6],[5],[6]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[2,6],[3],[4]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[2,6],[3],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[2,6],[3],[6]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[2,6],[4],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[2,6],[4],[6]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[2,6],[5],[6]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[3,6],[4],[5]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[3,6],[4],[6]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[3,6],[5],[6]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[4,6],[5],[6]] => [3,2,1,4] => [2,1,1] => [1,1] => 1
[[1],[2],[3],[6]] => [4,3,2,1] => [2,2] => [2] => 1
[[1],[2],[4],[6]] => [4,3,2,1] => [2,2] => [2] => 1
[[1],[2],[5],[6]] => [4,3,2,1] => [2,2] => [2] => 1
[[1],[3],[4],[6]] => [4,3,2,1] => [2,2] => [2] => 1
[[1],[3],[5],[6]] => [4,3,2,1] => [2,2] => [2] => 1
[[1],[4],[5],[6]] => [4,3,2,1] => [2,2] => [2] => 1
[[2],[3],[4],[6]] => [4,3,2,1] => [2,2] => [2] => 1
[[2],[3],[5],[6]] => [4,3,2,1] => [2,2] => [2] => 1
[[2],[4],[5],[6]] => [4,3,2,1] => [2,2] => [2] => 1
[[3],[4],[5],[6]] => [4,3,2,1] => [2,2] => [2] => 1
[[1,1,1,1,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,2,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,3,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,2,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,3,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,3,3,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,3,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,3,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,4,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,4,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,2,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,3,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,3,3,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,3,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,3,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,4,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,4,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,2,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,3,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,3,4,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,3,4,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,3,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,4,4,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,4,4,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,4,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,5,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,2,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,3,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,3,3,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,3,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,3,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,4,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,4,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,3,3,3,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,3,3,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,3,3,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,3,4,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,3,4,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,3,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,4,4,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,4,4,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,4,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,5,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,3,3,3,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,3,3,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,3,3,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,3,4,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,3,4,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,3,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,4,4,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,4,4,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,4,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,5,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[4,4,4,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[4,4,4,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[4,4,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[4,5,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[5,5,5,5,5]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,5],[2]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,3,5],[2]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,4,5],[2]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,5,5],[2]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,3,5],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,4,5],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,5,5],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,4,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,5,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,1,5,5],[5]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,2,2,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,3,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,4,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,5,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,3,5],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,3,3,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,4,5],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,3,4,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,5,5],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,3,5,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,4,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,4,4,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,5,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,4,5,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,5,5],[5]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,5,5,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,3,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,4,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,5,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,4,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,4,4,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,5,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,4,5,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,5,5],[5]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,5,5,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,4,4,5],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,4,5,5],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,4,5,5],[5]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[1,5,5,5],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,5,5,5],[5]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,2,3,5],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,2,4,5],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,2,5,5],[3]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,2,4,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,2,5,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,2,5,5],[5]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,3,3,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,3,4,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,3,5,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,3,4,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,4,4,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,3,5,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,4,5,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,3,5,5],[5]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,5,5,5],[3]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,4,4,5],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,4,5,5],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,4,5,5],[5]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[2,5,5,5],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,5,5,5],[5]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[3,3,4,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[3,3,5,5],[4]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[3,3,5,5],[5]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[3,4,4,5],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[3,4,5,5],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[3,4,5,5],[5]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[3,5,5,5],[4]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[3,5,5,5],[5]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[4,4,5,5],[5]] => [3,1,2,4,5] => [3,1,1] => [1,1] => 1
[[4,5,5,5],[5]] => [2,1,3,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,1,2],[2,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,1,5],[2,2]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,3],[2,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,1,5],[2,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,4],[2,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,1,5],[2,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,5],[2,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,3],[3,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,1,5],[3,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,4],[3,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,1,5],[3,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,5],[3,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,4],[4,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,1,5],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,5],[4,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,5],[5,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,2,3],[3,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,2,5],[3,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,2,4],[3,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,2,5],[3,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,2,5],[3,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,2,4],[4,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,2,5],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,2,5],[4,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,2,5],[5,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,3,4],[4,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[1,3,5],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,3,5],[4,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,3,5],[5,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,4,5],[5,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,2,3],[3,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[2,2,5],[3,3]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,2,4],[3,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[2,2,5],[3,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,2,5],[3,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,2,4],[4,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[2,2,5],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,2,5],[4,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,2,5],[5,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,3,4],[4,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[2,3,5],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,3,5],[4,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,3,5],[5,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[2,4,5],[5,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[3,3,4],[4,5]] => [3,5,1,2,4] => [3,2] => [2] => 1
[[3,3,5],[4,4]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[3,3,5],[4,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[3,3,5],[5,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[3,4,5],[5,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[4,4,5],[5,5]] => [3,4,1,2,5] => [2,2,1] => [2,1] => 2
[[1,1,1],[2],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,1,1],[3],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,1,1],[4],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,1,2],[3],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,1,2],[4],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,1,3],[4],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,2,2],[3],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,2,5],[2],[3]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,2,2],[4],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,2,5],[2],[4]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,2,5],[2],[5]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,3,5],[2],[3]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,2,3],[4],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,3,5],[2],[4]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,5],[2],[5]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,5,5],[2],[3]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,4,5],[2],[4]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,4,5],[2],[5]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,5,5],[2],[4]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,5,5],[2],[5]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,3,3],[4],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[1,3,5],[3],[4]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,3,5],[3],[5]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,4,5],[3],[4]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,4,5],[3],[5]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,5,5],[3],[4]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,5,5],[3],[5]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,4,5],[4],[5]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[1,5,5],[4],[5]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,2,2],[3],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[2,2,2],[4],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[2,2,3],[4],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[2,3,3],[4],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[2,3,5],[3],[4]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[2,3,5],[3],[5]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[2,4,5],[3],[4]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,4,5],[3],[5]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[2,5,5],[3],[4]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,5,5],[3],[5]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[2,4,5],[4],[5]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[2,5,5],[4],[5]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[3,3,3],[4],[5]] => [5,4,1,2,3] => [3,2] => [2] => 1
[[3,4,5],[4],[5]] => [4,2,1,3,5] => [3,1,1] => [1,1] => 1
[[3,5,5],[4],[5]] => [3,2,1,4,5] => [2,1,1,1] => [1,1,1] => 1
[[1,1],[2,5],[3]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,1],[2,5],[4]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,1],[2,5],[5]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,1],[3,5],[4]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,1],[3,5],[5]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,1],[4,5],[5]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,2],[2,5],[3]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,2],[2,5],[4]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,2],[2,5],[5]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,2],[3,5],[4]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,2],[3,5],[5]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,3],[2,5],[5]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,2],[4,5],[5]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,4],[2,5],[5]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,3],[3,5],[4]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,3],[3,5],[5]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,3],[4,5],[5]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[1,4],[3,5],[5]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,4],[4,5],[5]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[2,2],[3,5],[4]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[2,2],[3,5],[5]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[2,2],[4,5],[5]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[2,3],[3,5],[4]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[2,3],[3,5],[5]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[2,3],[4,5],[5]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[2,4],[3,5],[5]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[2,4],[4,5],[5]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[3,3],[4,5],[5]] => [4,3,5,1,2] => [3,2] => [2] => 1
[[3,4],[4,5],[5]] => [4,2,5,1,3] => [2,2,1] => [2,1] => 2
[[1,3],[2],[3],[5]] => [5,3,2,1,4] => [3,2] => [2] => 1
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [3,2] => [2] => 1
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => [2,2,1] => [2,1] => 2
[[1,5],[2],[3],[5]] => [4,3,2,1,5] => [2,2,1] => [2,1] => 2
[[1,4],[2],[4],[5]] => [5,3,2,1,4] => [3,2] => [2] => 1
[[1,5],[2],[4],[5]] => [4,3,2,1,5] => [2,2,1] => [2,1] => 2
[[1,4],[3],[4],[5]] => [5,3,2,1,4] => [3,2] => [2] => 1
[[1,5],[3],[4],[5]] => [4,3,2,1,5] => [2,2,1] => [2,1] => 2
[[2,4],[3],[4],[5]] => [5,3,2,1,4] => [3,2] => [2] => 1
[[2,5],[3],[4],[5]] => [4,3,2,1,5] => [2,2,1] => [2,1] => 2
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [2,2,1] => [2,1] => 2
[[1,1,1,1,1,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,1,2,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,1,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,1,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,2,2,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,2,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,2,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,3,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,3,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,2,2,2,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,2,2,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,2,2,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,2,3,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,2,3,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,2,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,3,3,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,3,3,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,3,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,4,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,2,2,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,2,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,2,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,3,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,3,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,3,3,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,3,3,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,3,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,4,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,2,2,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,2,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,2,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,3,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,3,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,3,3,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,3,3,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,3,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,4,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[3,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[3,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[3,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[3,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[3,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[4,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,2,4],[2]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,1,3,4],[2]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,1,4,4],[2]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,1,3,4],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,1,4,4],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,1,4,4],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,2,2,4],[2]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,2,3,4],[2]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,2,4,4],[2]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,2,3,4],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,3,3,4],[2]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,2,4,4],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,3,4,4],[2]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,2,4,4],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,4,4,4],[2]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,3,3,4],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,3,4,4],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,1,4,4,4],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,1,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,2,2,2,4],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,3,4],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,4,4],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,3,4],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,3,3,4],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,4,4],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,3,4,4],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,4,4],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,4,4,4],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,3,3,4],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,3,3,3,4],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,3,4,4],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,3,3,4,4],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,4,4,4],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,3,4,4,4],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,4,4,4,4],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,3,4],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,4,4],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,3,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,3,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,4,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,4,4,4,4],[4]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,3,4],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[2,2,2,4,4],[3]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[2,2,2,4,4],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[2,2,3,3,4],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[2,2,3,4,4],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[2,2,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[2,2,4,4,4],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[2,2,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[2,3,3,3,4],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,3,3,4,4],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,3,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[2,3,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,3,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[2,4,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,4,4,4,4],[4]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[3,3,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[3,3,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[3,4,4,4,4],[4]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,1],[2,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,1,1],[3,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,1,1],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,1,2],[3,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,1,2],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,1,3],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,2,2],[2,4]] => [3,6,1,2,4,5] => [4,2] => [2] => 1
[[1,1,2,4],[2,2]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,2,2],[3,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,2,3],[2,4]] => [3,6,1,2,4,5] => [4,2] => [2] => 1
[[1,1,2,4],[2,3]] => [3,5,1,2,4,6] => [3,2,1] => [2,1] => 2
[[1,1,3,4],[2,2]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,2,2],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,2,4],[2,4]] => [3,5,1,2,4,6] => [3,2,1] => [2,1] => 2
[[1,1,4,4],[2,2]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,3,3],[2,4]] => [3,6,1,2,4,5] => [4,2] => [2] => 1
[[1,1,3,4],[2,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,2,3],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,3,4],[2,4]] => [3,5,1,2,4,6] => [3,2,1] => [2,1] => 2
[[1,1,4,4],[2,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,4,4],[2,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,3,3],[3,4]] => [3,6,1,2,4,5] => [4,2] => [2] => 1
[[1,1,3,4],[3,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,3,3],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,1,3,4],[3,4]] => [3,5,1,2,4,6] => [3,2,1] => [2,1] => 2
[[1,1,4,4],[3,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,4,4],[3,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,4,4],[4,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,2,2,2],[3,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,2,2,2],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,2,3,4],[2,3]] => [2,4,1,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,2,3],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,2,4,4],[2,3]] => [2,4,1,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,4,4],[2,4]] => [2,4,1,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,3,3],[3,4]] => [3,6,1,2,4,5] => [4,2] => [2] => 1
[[1,2,3,4],[3,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,2,3,3],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,2,3,4],[3,4]] => [3,5,1,2,4,6] => [3,2,1] => [2,1] => 2
[[1,2,4,4],[3,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,2,4,4],[3,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,3,4,4],[2,4]] => [2,4,1,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,4,4],[4,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,3,3,3],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,3,4,4],[3,4]] => [2,4,1,3,5,6] => [4,1,1] => [1,1] => 1
[[1,3,4,4],[4,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[2,2,2,2],[3,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[2,2,2,2],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[2,2,2,3],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[2,2,3,3],[3,4]] => [3,6,1,2,4,5] => [4,2] => [2] => 1
[[2,2,3,4],[3,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[2,2,3,3],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[2,2,3,4],[3,4]] => [3,5,1,2,4,6] => [3,2,1] => [2,1] => 2
[[2,2,4,4],[3,3]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[2,2,4,4],[3,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[2,2,4,4],[4,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[2,3,3,3],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[2,3,4,4],[3,4]] => [2,4,1,3,5,6] => [4,1,1] => [1,1] => 1
[[2,3,4,4],[4,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[3,3,3,3],[4,4]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[3,3,4,4],[4,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,1,2],[2],[4]] => [6,4,1,2,3,5] => [4,2] => [2] => 1
[[1,1,1,3],[2],[4]] => [6,4,1,2,3,5] => [4,2] => [2] => 1
[[1,1,1,4],[2],[3]] => [5,4,1,2,3,6] => [3,2,1] => [2,1] => 2
[[1,1,1,4],[2],[4]] => [5,4,1,2,3,6] => [3,2,1] => [2,1] => 2
[[1,1,1,3],[3],[4]] => [6,4,1,2,3,5] => [4,2] => [2] => 1
[[1,1,1,4],[3],[4]] => [5,4,1,2,3,6] => [3,2,1] => [2,1] => 2
[[1,1,2,3],[3],[4]] => [6,4,1,2,3,5] => [4,2] => [2] => 1
[[1,1,3,4],[2],[3]] => [4,3,1,2,5,6] => [4,1,1] => [1,1] => 1
[[1,1,2,4],[3],[4]] => [5,4,1,2,3,6] => [3,2,1] => [2,1] => 2
[[1,1,4,4],[2],[3]] => [4,3,1,2,5,6] => [4,1,1] => [1,1] => 1
[[1,1,4,4],[2],[4]] => [4,3,1,2,5,6] => [4,1,1] => [1,1] => 1
[[1,1,4,4],[3],[4]] => [4,3,1,2,5,6] => [4,1,1] => [1,1] => 1
[[1,2,2,4],[2],[3]] => [5,2,1,3,4,6] => [4,1,1] => [1,1] => 1
[[1,2,2,4],[2],[4]] => [5,2,1,3,4,6] => [4,1,1] => [1,1] => 1
[[1,2,2,3],[3],[4]] => [6,4,1,2,3,5] => [4,2] => [2] => 1
[[1,2,3,4],[2],[3]] => [4,2,1,3,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,2,2,4],[3],[4]] => [5,4,1,2,3,6] => [3,2,1] => [2,1] => 2
[[1,2,3,4],[2],[4]] => [5,2,1,3,4,6] => [4,1,1] => [1,1] => 1
[[1,2,4,4],[2],[3]] => [4,2,1,3,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,2,4,4],[2],[4]] => [4,2,1,3,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,3,3,4],[2],[3]] => [3,2,1,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,4],[2],[4]] => [5,2,1,3,4,6] => [4,1,1] => [1,1] => 1
[[1,3,4,4],[2],[3]] => [3,2,1,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,2,4,4],[3],[4]] => [4,3,1,2,5,6] => [4,1,1] => [1,1] => 1
[[1,3,4,4],[2],[4]] => [4,2,1,3,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,4,4,4],[2],[3]] => [3,2,1,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,4,4,4],[2],[4]] => [3,2,1,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,4],[3],[4]] => [5,2,1,3,4,6] => [4,1,1] => [1,1] => 1
[[1,3,4,4],[3],[4]] => [4,2,1,3,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,4,4,4],[3],[4]] => [3,2,1,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,2,2,3],[3],[4]] => [6,4,1,2,3,5] => [4,2] => [2] => 1
[[2,2,2,4],[3],[4]] => [5,4,1,2,3,6] => [3,2,1] => [2,1] => 2
[[2,2,4,4],[3],[4]] => [4,3,1,2,5,6] => [4,1,1] => [1,1] => 1
[[2,3,3,4],[3],[4]] => [5,2,1,3,4,6] => [4,1,1] => [1,1] => 1
[[2,3,4,4],[3],[4]] => [4,2,1,3,5,6] => [3,1,1,1] => [1,1,1] => 1
[[2,4,4,4],[3],[4]] => [3,2,1,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1],[2,2,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,1],[2,3,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,1],[2,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,1],[3,3,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,1],[3,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,1],[4,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,2],[2,3,4]] => [3,5,6,1,2,4] => [4,2] => [2] => 1
[[1,1,2],[2,4,4]] => [3,5,6,1,2,4] => [4,2] => [2] => 1
[[1,1,2],[3,3,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,2],[3,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,3],[2,4,4]] => [3,5,6,1,2,4] => [4,2] => [2] => 1
[[1,1,2],[4,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,3],[3,4,4]] => [3,5,6,1,2,4] => [4,2] => [2] => 1
[[1,1,3],[4,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,2,2],[3,3,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,2,3],[2,3,4]] => [2,4,6,1,3,5] => [3,3] => [3] => 1
[[1,2,2],[3,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,2,2],[4,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,2,3],[3,4,4]] => [3,5,6,1,2,4] => [4,2] => [2] => 1
[[1,2,3],[4,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,3,3],[4,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[2,2,2],[3,3,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[2,2,2],[3,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[2,2,2],[4,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[2,2,3],[3,4,4]] => [3,5,6,1,2,4] => [4,2] => [2] => 1
[[2,2,3],[4,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[2,3,3],[4,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[3,3,3],[4,4,4]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,1,1],[2,4],[3]] => [5,4,6,1,2,3] => [4,2] => [2] => 1
[[1,1,1],[2,4],[4]] => [5,4,6,1,2,3] => [4,2] => [2] => 1
[[1,1,1],[3,4],[4]] => [5,4,6,1,2,3] => [4,2] => [2] => 1
[[1,1,2],[2,3],[4]] => [6,3,5,1,2,4] => [3,3] => [3] => 1
[[1,1,3],[2,4],[3]] => [4,3,6,1,2,5] => [4,2] => [2] => 1
[[1,1,4],[2,3],[3]] => [4,3,5,1,2,6] => [3,2,1] => [2,1] => 2
[[1,1,2],[3,4],[4]] => [5,4,6,1,2,3] => [4,2] => [2] => 1
[[1,1,4],[2,4],[3]] => [4,3,5,1,2,6] => [3,2,1] => [2,1] => 2
[[1,1,4],[2,4],[4]] => [4,3,5,1,2,6] => [3,2,1] => [2,1] => 2
[[1,1,4],[3,4],[4]] => [4,3,5,1,2,6] => [3,2,1] => [2,1] => 2
[[1,2,2],[2,3],[4]] => [6,2,5,1,3,4] => [3,2,1] => [2,1] => 2
[[1,2,3],[2,4],[3]] => [4,2,6,1,3,5] => [3,2,1] => [2,1] => 2
[[1,2,4],[2,3],[3]] => [4,2,5,1,3,6] => [2,2,1,1] => [2,1,1] => 2
[[1,2,2],[3,4],[4]] => [5,4,6,1,2,3] => [4,2] => [2] => 1
[[1,2,4],[2,3],[4]] => [5,2,4,1,3,6] => [4,1,1] => [1,1] => 1
[[1,2,4],[2,4],[3]] => [4,2,5,1,3,6] => [2,2,1,1] => [2,1,1] => 2
[[1,2,4],[2,4],[4]] => [4,2,5,1,3,6] => [2,2,1,1] => [2,1,1] => 2
[[1,3,4],[2,4],[3]] => [3,2,5,1,4,6] => [4,1,1] => [1,1] => 1
[[1,2,4],[3,4],[4]] => [4,3,5,1,2,6] => [3,2,1] => [2,1] => 2
[[1,3,4],[2,4],[4]] => [4,2,5,1,3,6] => [2,2,1,1] => [2,1,1] => 2
[[1,3,4],[3,4],[4]] => [4,2,5,1,3,6] => [2,2,1,1] => [2,1,1] => 2
[[2,2,2],[3,4],[4]] => [5,4,6,1,2,3] => [4,2] => [2] => 1
[[2,2,4],[3,4],[4]] => [4,3,5,1,2,6] => [3,2,1] => [2,1] => 2
[[2,3,4],[3,4],[4]] => [4,2,5,1,3,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1,1],[2],[3],[4]] => [6,5,4,1,2,3] => [4,2] => [2] => 1
[[1,1,2],[2],[3],[4]] => [6,5,3,1,2,4] => [3,2,1] => [2,1] => 2
[[1,1,4],[2],[3],[4]] => [5,4,3,1,2,6] => [4,1,1] => [1,1] => 1
[[1,2,2],[2],[3],[4]] => [6,5,2,1,3,4] => [3,3] => [3] => 1
[[1,3,3],[2],[3],[4]] => [6,3,2,1,4,5] => [4,2] => [2] => 1
[[1,3,4],[2],[3],[4]] => [5,3,2,1,4,6] => [3,2,1] => [2,1] => 2
[[1,4,4],[2],[3],[4]] => [4,3,2,1,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,1],[2,2],[3,4]] => [5,6,3,4,1,2] => [2,2,1,1] => [2,1,1] => 2
[[1,1],[2,2],[4,4]] => [5,6,3,4,1,2] => [2,2,1,1] => [2,1,1] => 2
[[1,1],[2,3],[3,4]] => [4,6,3,5,1,2] => [3,2,1] => [2,1] => 2
[[1,1],[2,3],[4,4]] => [5,6,3,4,1,2] => [2,2,1,1] => [2,1,1] => 2
[[1,1],[3,3],[4,4]] => [5,6,3,4,1,2] => [2,2,1,1] => [2,1,1] => 2
[[1,2],[2,3],[3,4]] => [4,6,2,5,1,3] => [3,3] => [3] => 1
[[1,2],[2,3],[4,4]] => [5,6,2,4,1,3] => [3,2,1] => [2,1] => 2
[[1,2],[3,3],[4,4]] => [5,6,3,4,1,2] => [2,2,1,1] => [2,1,1] => 2
[[2,2],[3,3],[4,4]] => [5,6,3,4,1,2] => [2,2,1,1] => [2,1,1] => 2
[[1,1],[2,2],[3],[4]] => [6,5,3,4,1,2] => [4,1,1] => [1,1] => 1
[[1,1],[2,4],[3],[4]] => [5,4,3,6,1,2] => [3,2,1] => [2,1] => 2
[[1,2],[2,4],[3],[4]] => [5,4,2,6,1,3] => [4,2] => [2] => 1
[[1,3],[2,4],[3],[4]] => [5,3,2,6,1,4] => [2,2,2] => [2,2] => 1
[[1,1,1,1,1,1,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,1,1,2,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,1,1,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,1,2,2,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,1,2,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,1,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[3,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,1,2,3],[2]] => [5,1,2,3,4,6,7] => [5,1,1] => [1,1] => 1
[[1,1,1,1,3,3],[2]] => [5,1,2,3,4,6,7] => [5,1,1] => [1,1] => 1
[[1,1,1,1,3,3],[3]] => [5,1,2,3,4,6,7] => [5,1,1] => [1,1] => 1
[[1,1,1,2,2,3],[2]] => [4,1,2,3,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[[1,1,1,2,3,3],[2]] => [4,1,2,3,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[[1,1,1,2,3,3],[3]] => [5,1,2,3,4,6,7] => [5,1,1] => [1,1] => 1
[[1,1,1,3,3,3],[2]] => [4,1,2,3,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[[1,1,1,3,3,3],[3]] => [4,1,2,3,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[[1,1,2,2,2,3],[2]] => [3,1,2,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,2,3,3],[2]] => [3,1,2,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => [5,1,1] => [1,1] => 1
[[1,1,2,3,3,3],[2]] => [3,1,2,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[[1,1,3,3,3,3],[2]] => [3,1,2,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[[1,1,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[[1,2,2,2,2,3],[2]] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,2,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => [5,1,1] => [1,1] => 1
[[1,2,2,3,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[[1,2,3,3,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,3,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,3,3,3,3,3],[3]] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => [5,1,1] => [1,1] => 1
[[2,2,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[[2,2,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[[2,3,3,3,3,3],[3]] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,1,2],[2,3]] => [5,7,1,2,3,4,6] => [4,3] => [3] => 1
[[1,1,1,1,3],[2,2]] => [5,6,1,2,3,4,7] => [3,3,1] => [3,1] => 3
[[1,1,1,1,3],[2,3]] => [5,6,1,2,3,4,7] => [3,3,1] => [3,1] => 3
[[1,1,1,1,3],[3,3]] => [5,6,1,2,3,4,7] => [3,3,1] => [3,1] => 3
[[1,1,1,2,3],[2,2]] => [4,5,1,2,3,6,7] => [5,1,1] => [1,1] => 1
[[1,1,1,3,3],[2,2]] => [4,5,1,2,3,6,7] => [5,1,1] => [1,1] => 1
[[1,1,1,2,3],[3,3]] => [5,6,1,2,3,4,7] => [3,3,1] => [3,1] => 3
[[1,1,1,3,3],[2,3]] => [4,5,1,2,3,6,7] => [5,1,1] => [1,1] => 1
[[1,1,1,3,3],[3,3]] => [4,5,1,2,3,6,7] => [5,1,1] => [1,1] => 1
[[1,1,2,2,2],[2,3]] => [3,7,1,2,4,5,6] => [5,2] => [2] => 1
[[1,1,2,2,3],[2,2]] => [3,4,1,2,5,6,7] => [2,2,1,1,1] => [2,1,1,1] => 2
[[1,1,2,2,3],[2,3]] => [3,6,1,2,4,5,7] => [4,2,1] => [2,1] => 2
[[1,1,2,3,3],[2,2]] => [3,4,1,2,5,6,7] => [2,2,1,1,1] => [2,1,1,1] => 2
[[1,1,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => [3,3,1] => [3,1] => 3
[[1,1,2,3,3],[2,3]] => [3,5,1,2,4,6,7] => [3,2,1,1] => [2,1,1] => 2
[[1,1,3,3,3],[2,2]] => [3,4,1,2,5,6,7] => [2,2,1,1,1] => [2,1,1,1] => 2
[[1,1,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => [5,1,1] => [1,1] => 1
[[1,1,3,3,3],[2,3]] => [3,4,1,2,5,6,7] => [2,2,1,1,1] => [2,1,1,1] => 2
[[1,1,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => [2,2,1,1,1] => [2,1,1,1] => 2
[[1,2,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => [3,3,1] => [3,1] => 3
[[1,2,2,3,3],[2,3]] => [2,5,1,3,4,6,7] => [5,1,1] => [1,1] => 1
[[1,2,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => [5,1,1] => [1,1] => 1
[[1,2,3,3,3],[2,3]] => [2,4,1,3,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[[1,2,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => [2,2,1,1,1] => [2,1,1,1] => 2
[[2,2,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => [3,3,1] => [3,1] => 3
[[2,2,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => [5,1,1] => [1,1] => 1
[[2,2,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => [2,2,1,1,1] => [2,1,1,1] => 2
[[1,1,1,1,1],[2],[3]] => [7,6,1,2,3,4,5] => [4,3] => [3] => 1
[[1,1,1,2,2],[2],[3]] => [7,4,1,2,3,5,6] => [5,2] => [2] => 1
[[1,1,1,2,3],[2],[3]] => [6,4,1,2,3,5,7] => [4,2,1] => [2,1] => 2
[[1,1,1,3,3],[2],[3]] => [5,4,1,2,3,6,7] => [3,2,1,1] => [2,1,1] => 2
[[1,1,2,3,3],[2],[3]] => [5,3,1,2,4,6,7] => [5,1,1] => [1,1] => 1
[[1,1,3,3,3],[2],[3]] => [4,3,1,2,5,6,7] => [4,1,1,1] => [1,1,1] => 1
[[1,2,2,2,3],[2],[3]] => [6,2,1,3,4,5,7] => [5,1,1] => [1,1] => 1
[[1,2,2,3,3],[2],[3]] => [5,2,1,3,4,6,7] => [4,1,1,1] => [1,1,1] => 1
[[1,2,3,3,3],[2],[3]] => [4,2,1,3,5,6,7] => [3,1,1,1,1] => [1,1,1,1] => 1
[[1,3,3,3,3],[2],[3]] => [3,2,1,4,5,6,7] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,2],[2,2,3]] => [4,5,7,1,2,3,6] => [3,2,2] => [2,2] => 1
[[1,1,1,3],[2,2,2]] => [4,5,6,1,2,3,7] => [2,2,2,1] => [2,2,1] => 2
[[1,1,1,2],[2,3,3]] => [4,6,7,1,2,3,5] => [5,2] => [2] => 1
[[1,1,1,3],[2,2,3]] => [4,5,6,1,2,3,7] => [2,2,2,1] => [2,2,1] => 2
[[1,1,1,3],[2,3,3]] => [4,5,6,1,2,3,7] => [2,2,2,1] => [2,2,1] => 2
[[1,1,1,3],[3,3,3]] => [4,5,6,1,2,3,7] => [2,2,2,1] => [2,2,1] => 2
[[1,1,2,3],[2,3,3]] => [3,5,6,1,2,4,7] => [4,2,1] => [2,1] => 2
[[1,1,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => [2,2,2,1] => [2,2,1] => 2
[[1,2,2,2],[2,3,3]] => [2,6,7,1,3,4,5] => [4,3] => [3] => 1
[[1,2,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => [2,2,2,1] => [2,2,1] => 2
[[2,2,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => [2,2,2,1] => [2,2,1] => 2
[[1,1,1,1],[2,2],[3]] => [7,5,6,1,2,3,4] => [3,2,2] => [2,2] => 1
[[1,1,1,1],[2,3],[3]] => [6,5,7,1,2,3,4] => [5,2] => [2] => 1
[[1,1,1,3],[2,3],[3]] => [5,4,6,1,2,3,7] => [4,2,1] => [2,1] => 2
[[1,1,2,2],[2,3],[3]] => [6,3,7,1,2,4,5] => [4,3] => [3] => 1
[[1,1,3,3],[2,2],[3]] => [5,3,4,1,2,6,7] => [5,1,1] => [1,1] => 1
[[1,1,3,3],[2,3],[3]] => [4,3,5,1,2,6,7] => [3,2,1,1] => [2,1,1] => 2
[[1,2,2,2],[2,3],[3]] => [6,2,7,1,3,4,5] => [3,3,1] => [3,1] => 3
[[1,2,2,3],[2,3],[3]] => [5,2,6,1,3,4,7] => [5,1,1] => [1,1] => 1
[[1,2,3,3],[2,3],[3]] => [4,2,5,1,3,6,7] => [2,2,1,1,1] => [2,1,1,1] => 2
[[1,1,1],[2,2,2],[3]] => [7,4,5,6,1,2,3] => [4,3] => [3] => 1
[[1,1,1],[2,3,3],[3]] => [5,4,6,7,1,2,3] => [5,2] => [2] => 1
[[1,1,2],[2,3,3],[3]] => [5,3,6,7,1,2,4] => [3,2,2] => [2,2] => 1
[[1,2,2],[2,3,3],[3]] => [5,2,6,7,1,3,4] => [2,2,2,1] => [2,2,1] => 2
[[1,1,2],[2,2],[3,3]] => [6,7,3,4,1,2,5] => [5,1,1] => [1,1] => 1
[[1,1,3],[2,2],[3,3]] => [5,6,3,4,1,2,7] => [2,2,1,1,1] => [2,1,1,1] => 2
[[1,1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[1,1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[1,1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[1,1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[1,1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[1,1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[1,2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[2,2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[1,1,1,1,1,2,2],[2]] => [6,1,2,3,4,5,7,8] => [6,1,1] => [1,1] => 1
[[1,1,1,1,2,2,2],[2]] => [5,1,2,3,4,6,7,8] => [5,1,1,1] => [1,1,1] => 1
[[1,1,1,2,2,2,2],[2]] => [4,1,2,3,5,6,7,8] => [4,1,1,1,1] => [1,1,1,1] => 1
[[1,1,2,2,2,2,2],[2]] => [3,1,2,4,5,6,7,8] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,2,2,2,2,2],[2]] => [2,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1,1,1,1],[2,2]] => [7,8,1,2,3,4,5,6] => [4,4] => [4] => 1
[[1,1,1,2,2,2],[2,2]] => [4,5,1,2,3,6,7,8] => [5,1,1,1] => [1,1,1] => 1
[[1,1,2,2,2,2],[2,2]] => [3,4,1,2,5,6,7,8] => [2,2,1,1,1,1] => [2,1,1,1,1] => 2
[[1,1,1,2,2],[2,2,2]] => [4,5,6,1,2,3,7,8] => [2,2,2,1,1] => [2,2,1,1] => 2
[[1,1,1,1],[2,2,2,2]] => [5,6,7,8,1,2,3,4] => [2,2,2,2] => [2,2,2] => 1
[[1,1,1,1],[2,2,2],[3,3],[4]] => [10,8,9,5,6,7,1,2,3,4] => [6,2,2] => [2,2] => 1
[[1,1,1,2],[2,2,2],[3,3],[4]] => [10,8,9,4,5,6,1,2,3,7] => [3,2,2,1,1,1] => [2,2,1,1,1] => 2
[[1,1,1,2],[2,2,3],[3,3],[4]] => [10,7,8,4,5,9,1,2,3,6] => [8,1,1] => [1,1] => 1
[[1,1,1,3],[2,2,3],[3,3],[4]] => [10,6,7,4,5,8,1,2,3,9] => [5,3,1,1] => [3,1,1] => 3
[[1,1,2,3],[2,2,3],[3,3],[4]] => [10,6,7,3,4,8,1,2,5,9] => [7,3] => [3] => 1
[[1,1,1,1],[2,2,2],[3,4],[4]] => [9,8,10,5,6,7,1,2,3,4] => [8,2] => [2] => 1
[[1,1,1,2],[2,2,2],[3,4],[4]] => [9,8,10,4,5,6,1,2,3,7] => [5,2,1,1,1] => [2,1,1,1] => 2
[[1,1,1,2],[2,2,3],[3,4],[4]] => [9,7,10,4,5,8,1,2,3,6] => [8,1,1] => [1,1] => 1
[[1,1,1,3],[2,2,3],[3,4],[4]] => [9,6,10,4,5,7,1,2,3,8] => [8,1,1] => [1,1] => 1
[[1,1,1,1],[2,2,4],[3,4],[4]] => [8,7,9,5,6,10,1,2,3,4] => [4,4,2] => [4,2] => 2
[[1,1,1,2],[2,2,4],[3,4],[4]] => [8,7,9,4,5,10,1,2,3,6] => [4,2,2,1,1] => [2,2,1,1] => 2
[[1,1,1,3],[2,2,4],[3,4],[4]] => [8,6,9,4,5,10,1,2,3,7] => [6,2,1,1] => [2,1,1] => 2
[[1,1,1,4],[2,2,4],[3,4],[4]] => [7,6,8,4,5,9,1,2,3,10] => [5,2,1,1,1] => [2,1,1,1] => 2
[[1,1,2,2],[2,2,4],[3,4],[4]] => [8,7,9,3,4,10,1,2,5,6] => [4,4,2] => [4,2] => 2
[[1,1,2,3],[2,2,4],[3,4],[4]] => [8,6,9,3,4,10,1,2,5,7] => [6,4] => [4] => 1
[[1,1,2,4],[2,2,4],[3,4],[4]] => [7,6,8,3,4,9,1,2,5,10] => [7,2,1] => [2,1] => 2
[[1,1,1,1],[2,3,3],[3,4],[4]] => [9,6,10,5,7,8,1,2,3,4] => [7,3] => [3] => 1
[[1,1,1,2],[2,3,3],[3,4],[4]] => [9,6,10,4,7,8,1,2,3,5] => [6,3,1] => [3,1] => 3
[[1,1,2,2],[2,3,3],[3,4],[4]] => [9,6,10,3,7,8,1,2,4,5] => [7,3] => [3] => 1
[[1,1,1,1],[2,3,4],[3,4],[4]] => [8,6,9,5,7,10,1,2,3,4] => [8,2] => [2] => 1
[[1,1,1,2],[2,3,4],[3,4],[4]] => [8,6,9,4,7,10,1,2,3,5] => [7,2,1] => [2,1] => 2
[[1,1,1,3],[2,3,4],[3,4],[4]] => [8,5,9,4,6,10,1,2,3,7] => [7,2,1] => [2,1] => 2
[[1,1,1,4],[2,3,4],[3,4],[4]] => [7,5,8,4,6,9,1,2,3,10] => [6,2,1,1] => [2,1,1] => 2
[[1,1,2,2],[2,3,4],[3,4],[4]] => [8,6,9,3,7,10,1,2,4,5] => [7,3] => [3] => 1
[[1,1,2,3],[2,3,4],[3,4],[4]] => [8,5,9,3,6,10,1,2,4,7] => [7,3] => [3] => 1
[[1,1,2,4],[2,3,4],[3,4],[4]] => [7,5,8,3,6,9,1,2,4,10] => [7,2,1] => [2,1] => 2
[[1,1,3,4],[2,3,4],[3,4],[4]] => [7,4,8,3,5,9,1,2,6,10] => [4,2,2,1,1] => [2,2,1,1] => 2
[[1,2,2,3],[2,3,3],[3,4],[4]] => [9,5,10,2,6,7,1,3,4,8] => [7,3] => [3] => 1
[[1,2,2,4],[2,3,4],[3,4],[4]] => [7,5,8,2,6,9,1,3,4,10] => [5,2,2,1] => [2,2,1] => 2
[[1,2,3,3],[2,3,4],[3,4],[4]] => [8,4,9,2,5,10,1,3,6,7] => [7,2,1] => [2,1] => 2
[[1,2,3,4],[2,3,4],[3,4],[4]] => [7,4,8,2,5,9,1,3,6,10] => [2,2,2,2,1,1] => [2,2,2,1,1] => 2
[[1,1,1]] => [1,2,3] => [1,1,1] => [1,1] => 1
[[1,1,1,1]] => [1,2,3,4] => [1,1,1,1] => [1,1,1] => 1
[[1,1,1,1,1]] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,1,1,1]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [4,1,1] => [1,1] => 1
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [4,2] => [2] => 1
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [3,3] => [3] => 1
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [3,2,1] => [2,1] => 2
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [4,2] => [2] => 1
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [4,2] => [2] => 1
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [3,2,1] => [2,1] => 2
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [3,3] => [3] => 1
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [3,2,1] => [2,1] => 2
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [4,1,1] => [1,1] => 1
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [4,2] => [2] => 1
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [4,2] => [2] => 1
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [4,1,1] => [1,1] => 1
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [4,2] => [2] => 1
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [3,2,1] => [2,1] => 2
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [4,1,1] => [1,1] => 1
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [3,3] => [3] => 1
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [4,1,1] => [1,1] => 1
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [4,1,1] => [1,1] => 1
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [3,3] => [3] => 1
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [3,1,1,1] => [1,1,1] => 1
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [3,2,1] => [2,1] => 2
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [4,2] => [2] => 1
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [4,1,1] => [1,1] => 1
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [4,1,1] => [1,1] => 1
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [4,2] => [2] => 1
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [4,2] => [2] => 1
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [3,2,1] => [2,1] => 2
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [2,2,2] => [2,2] => 1
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [3,2,1] => [2,1] => 2
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [2,2,1,1] => [2,1,1] => 2
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [3,3] => [3] => 1
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [3,2,1] => [2,1] => 2
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [2,2,1,1] => [2,1,1] => 2
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [4,2] => [2] => 1
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [3,2,1] => [2,1] => 2
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [3,2,1] => [2,1] => 2
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [3,2,1] => [2,1] => 2
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [4,2] => [2] => 1
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [2,2,1,1] => [2,1,1] => 2
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [2,2,2] => [2,2] => 1
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [2,2,1,1] => [2,1,1] => 2
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [2,2,2] => [2,2] => 1
[[1,1,1,1,2,2,2],[3,3],[4]] => [10,8,9,1,2,3,4,5,6,7] => [4,3,3] => [3,3] => 1
[[1,1,1,2,2,2,2],[3,3],[4]] => [10,8,9,1,2,3,4,5,6,7] => [4,3,3] => [3,3] => 1
search for individual values
searching the database for the individual values of this statistic
Description
The exponens consonantiae of a partition.
This is the quotient of the least common multiple and the greatest common divior of the parts of the partiton. See [1, Caput sextum, §19-§22].
This is the quotient of the least common multiple and the greatest common divior of the parts of the partiton. See [1, Caput sextum, §19-§22].
Map
cycle type
Description
The cycle type of a permutation as a partition.
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
first row removal
Description
Removes the first entry of an integer partition
searching the database
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