Identifier
-
Mp00225:
Semistandard tableaux
—weight⟶
Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001569: Permutations ⟶ ℤ
Values
[[1,2]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2,2]] => [2] => [1,0,1,0] => [3,1,2] => 1
[[1],[2]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[1,3]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2,3]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3,3]] => [2] => [1,0,1,0] => [3,1,2] => 1
[[1],[3]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2],[3]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[1,1,2]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2,2]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2,2]] => [3] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[[1,1],[2]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2],[2]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,4]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2,4]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3,4]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[4,4]] => [2] => [1,0,1,0] => [3,1,2] => 1
[[1],[4]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2],[4]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3],[4]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[1,1,3]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2,3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3,3]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2,3]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,3,3]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,3,3]] => [3] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[[1,1],[3]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2],[3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3],[2]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3],[3]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2],[3]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,3],[3]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1],[2],[3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,1,1,2]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1,2,2]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2,2,2]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,2,2]] => [4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,1,1],[2]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1,2],[2]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2,2],[2]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,5]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2,5]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3,5]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[4,5]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[5,5]] => [2] => [1,0,1,0] => [3,1,2] => 1
[[1],[5]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2],[5]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3],[5]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[4],[5]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[1,1,4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2,4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3,4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,4,4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2,4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,3,4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,4,4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,3,4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,4,4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,4,4]] => [3] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[[1,1],[4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,4],[2]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,4],[3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,4],[4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2],[4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,3],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,4],[3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,4],[4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,3],[4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,4],[4]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1],[2],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1],[3],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2],[3],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,1,1,3]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1,2,3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,3,3]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2,2,3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,3,3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,3,3]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,2,3]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,3,3]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3,3,3]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,3,3]] => [4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,1,1],[3]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1,2],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,3],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,3],[3]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2,2],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,3],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,3],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,3],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,3],[3]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,2],[3]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,3],[3]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3,3],[3]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1],[2,3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[3,3]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2],[2,3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[3,3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
>>> Load all 1200 entries. <<<[[2,2],[3,3]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,1],[2],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[2],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[2],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,1,2,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2,2,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,1,2],[2]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2,2],[2]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,1],[2,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2],[2,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,6]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2,6]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3,6]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[4,6]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[5,6]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[6,6]] => [2] => [1,0,1,0] => [3,1,2] => 1
[[1],[6]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2],[6]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3],[6]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[4],[6]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[5],[6]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[1,1,5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2,5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3,5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,4,5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,5,5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2,5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,3,5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,4,5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,5,5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,3,5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,4,5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,5,5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,4,5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,5,5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,5,5]] => [3] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[[1,1],[5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,5],[2]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,5],[3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,4],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,5],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,5],[5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2],[5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,3],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,5],[3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,4],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,5],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,5],[5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,3],[5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,4],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,5],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,5],[5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,4],[5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,5],[5]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1],[2],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1],[3],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1],[4],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2],[3],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2],[4],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3],[4],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,1,1,4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1,2,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,3,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,4,4]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2,2,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,3,4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,4,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,3,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,4,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,4,4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,2,4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,3,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,4,4]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3,3,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3,4,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,4,4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,3,4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,4,4]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[3,4,4,4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[4,4,4,4]] => [4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,1,1],[4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1,2],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,4],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,4],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,4],[4]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2,2],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,4],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,3],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,4],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,4],[2]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,4],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,4],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,4],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,4],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,4],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,4],[4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,2],[4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,4],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,4],[4]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3,3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3,4],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3,4],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,4],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,4],[4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,3],[4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,4],[4]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[3,4,4],[4]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1],[2,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[3,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[4,4]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2],[2,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[3,4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3],[2,4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2],[4,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[3,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[4,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[3,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[4,4]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3],[3,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3],[4,4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3],[4,4]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,1],[2],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[2],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[3],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3],[2],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[2],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[2],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4],[3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3],[3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4],[3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1],[2],[3],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,1,1,3,3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2,2,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2,3,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,3,3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,2,2,3,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,2,3,3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,2,3,3,3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,1,3],[3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2,2],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2,3],[2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2,3],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,3],[2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,3],[3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,2,2,3],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2,3,3],[2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,2,3],[3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,2,3,3],[3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,1],[3,3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2],[2,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3],[2,2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2],[3,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3],[2,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3],[3,3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,2,2],[3,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2,3],[2,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,2],[3,3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,2,3],[3,3]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2],[2],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3],[2],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2,3],[2],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[2,2],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[2,3],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2],[2,3],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,1,2,2,2]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,1,2,2],[2]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,1,2],[2,2]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,1],[2,2,2]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2,7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3,7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[4,7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[5,7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[6,7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[7,7]] => [2] => [1,0,1,0] => [3,1,2] => 1
[[1],[7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2],[7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3],[7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[4],[7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[5],[7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[6],[7]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[1,1,6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2,6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3,6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,4,6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,5,6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,6,6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2,6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,3,6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,4,6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,5,6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,6,6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,3,6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,4,6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,5,6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,6,6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,4,6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,5,6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4,6,6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,5,6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,6,6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[6,6,6]] => [3] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[[1,1],[6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,6],[2]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,6],[3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,4],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,6],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,5],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,6],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,6],[6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2],[6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,3],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,6],[3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,4],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,6],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,5],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,6],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,6],[6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,3],[6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,4],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,6],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,5],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,6],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,6],[6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,4],[6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,5],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4,6],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4,6],[6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,5],[6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,6],[6]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1],[2],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1],[3],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1],[4],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1],[5],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2],[3],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2],[4],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2],[5],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3],[4],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3],[5],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4],[5],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,1,1,5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1,2,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,3,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,5,5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2,2,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,3,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,4,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,3,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,4,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5,5,5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,2,5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,3,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,5,5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3,3,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3,4,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3,5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5,5,5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,3,5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3,5,5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[3,4,4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4,5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5,5,5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[4,4,4,5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[4,4,5,5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[4,5,5,5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[5,5,5,5]] => [4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,1,1],[5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1,2],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,5],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,3],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,5],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,5],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,5],[5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2,2],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,5],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,3],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,5],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,5],[2]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,5],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4,5],[2]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,5],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5,5],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,3],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,5],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,5],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4,5],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,5],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5,5],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,5],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,5],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5,5],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5,5],[5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,2],[5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,3],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,5],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,5],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,5],[5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3,3],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3,5],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3,4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3,5],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,4,5],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3,5],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5,5],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,5],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,5],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5,5],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5,5],[5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,3],[5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3,5],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3,5],[5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[3,4,4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4,5],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4,5],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5,5],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5,5],[5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[4,4,4],[5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[4,4,5],[5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[4,5,5],[5]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1],[2,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[3,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[5,5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2],[2,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[3,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3],[2,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2],[4,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[2,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2],[5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[3,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[4,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[3,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3],[5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4],[4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4],[5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[3,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[5,5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3],[3,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3],[4,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,4],[3,5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3],[5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4],[4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4],[5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3],[4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3],[5,5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[3,4],[4,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4],[5,5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,4],[5,5]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,1],[2],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[3],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[2],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[3],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3],[2],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[2],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2],[4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[2],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[2],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[2],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[3],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[3],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[3],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[3],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4],[4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5],[4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[3],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3],[3],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3],[4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,4],[3],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,5],[3],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,5],[3],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4],[4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5],[4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3],[4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4],[4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5],[4],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1],[2],[3],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1],[2],[4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1],[3],[4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2],[3],[4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,1,1,4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2,2,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2,4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,3,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4,4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,2,2,4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,3,4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,2,4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,2,3,3,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,3,4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4,4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,3,3,4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,3,4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[3,3,4,4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,1,4],[4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2,2],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2,4],[2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4,4],[2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,3],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,4],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4,4],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4,4],[4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,2,2,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2,4,4],[2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,3,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,4,4],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,2,4],[4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,2,3,3],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,3,4],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,3,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4,4],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4,4],[4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,3,3,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,3,4,4],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,3,4],[4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[3,3,4,4],[4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,1],[4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2],[2,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4],[2,2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2],[4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4],[2,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3],[3,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4],[3,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3],[4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4],[3,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4],[4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,2,2],[4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2,4],[2,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,3],[4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,4],[3,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,2],[4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,2,3],[3,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4],[3,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,3],[4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4],[3,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4],[4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,3,3],[4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,3,4],[3,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,3],[4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[3,3,4],[4,4]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2],[2],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4],[2],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3],[3],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4],[3],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2,4],[2],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,4],[3],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,3],[3],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4],[3],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,3,4],[3],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[2,2],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[2,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[3,3],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[3,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2],[2,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3],[3,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2],[3,3],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2],[3,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,3],[3,4],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,1,3,3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2,2,3,3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,2,3,3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,1,3,3],[3]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2,2,3],[3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,2,3,3],[2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,2,3,3],[3]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,1,3],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2,2],[3,3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,2,3],[2,3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,3,3],[2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,2,3],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2,3],[2],[3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,1],[3,3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2],[2,3,3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,2],[3,3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2],[2,3],[3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,3],[2,2],[3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1],[2,2],[3,3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2,8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3,8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[4,8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[5,8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[6,8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[7,8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[8,8]] => [2] => [1,0,1,0] => [3,1,2] => 1
[[1],[8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[2],[8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[3],[8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[4],[8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[5],[8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[6],[8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[7],[8]] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[[1,1,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,4,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,5,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,6,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,7,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,3,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,4,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,5,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,6,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,7,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,3,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,4,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,5,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,6,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,7,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,4,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,5,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4,6,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4,7,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,5,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,6,7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[5,7,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[6,6,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[6,7,7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[7,7,7]] => [3] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[[1,1],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1,2],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,7],[2]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,3],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,7],[3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,4],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,7],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,5],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,7],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,6],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,7],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,7],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,2],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,3],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,7],[3]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,4],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,7],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,5],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,7],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,6],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,7],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2,7],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,3],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,4],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,7],[4]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,5],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,7],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,6],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,7],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3,7],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,4],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,5],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4,7],[5]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4,6],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4,7],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4,7],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,5],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,6],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[5,7],[6]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[5,7],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[6,6],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[6,7],[7]] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[1],[2],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1],[3],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1],[4],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1],[5],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1],[6],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2],[3],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2],[4],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2],[5],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[2],[6],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3],[4],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3],[5],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[3],[6],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4],[5],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[4],[6],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[5],[6],[7]] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 2
[[1,1,1,6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1,2,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,3,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,6,6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2,2,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,3,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,4,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,3,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,4,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4,6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5,5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5,6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,6,6,6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,2,6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,3,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,6,6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3,3,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3,4,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3,5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3,6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,4,6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5,5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5,6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,6,6,6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,3,6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3,5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3,6,6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[3,4,4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4,5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[3,4,6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5,5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5,6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,6,6,6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[4,4,4,6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[4,4,5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,4,6,6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[4,5,5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,5,6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,6,6,6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[5,5,5,6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[5,5,6,6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[5,6,6,6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[6,6,6,6]] => [4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,1,1],[6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1,2],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,6],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,3],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,6],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,6],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1,6],[6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2,2],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,6],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2,3],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,6],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,6],[2]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,6],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4,6],[2]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,6],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5,6],[2]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2,6],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,6,6],[2]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,3],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,6],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3,4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,6],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4,6],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,6],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5,6],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3,6],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,6,6],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,6],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4,5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4,6],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5,6],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4,6],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,6,6],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5,5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5,6],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,6,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,6,6],[6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,2],[6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[2,2,3],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,6],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,6],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2,6],[6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3,3],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3,6],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3,4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3,6],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,4,6],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3,5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3,6],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,5,6],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3,6],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,6,6],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,6],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4,5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,4,6],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,5,6],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,4,6],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,6,6],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5,5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5,6],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,6,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,6,6],[6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,3],[6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[3,3,4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3,6],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3,5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3,6],[6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[3,4,4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4,6],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4,5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[3,4,6],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[3,5,6],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[3,4,6],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,6,6],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5,5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5,6],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,6,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,6,6],[6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[4,4,4],[6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[4,4,5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,4,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,4,6],[6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[4,5,5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,5,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,5,6],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,6,6],[5]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,6,6],[6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[5,5,5],[6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[5,5,6],[6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[5,6,6],[6]] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[[1,1],[2,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[3,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[6,6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,2],[2,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[3,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3],[2,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2],[4,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[2,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2],[5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[2,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2],[6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[3,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[4,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[3,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3],[5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[3,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3],[6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4],[4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4],[5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[4,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5],[5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5],[6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[3,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[6,6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[2,3],[3,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3],[4,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,4],[3,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3],[5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,5],[3,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3],[6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4],[4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4],[5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,5],[4,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,4],[6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5],[5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5],[6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3],[4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3],[5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3],[6,6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[3,4],[4,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4],[5,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[3,5],[4,6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[3,4],[6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5],[5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5],[6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,4],[5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,4],[6,6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[4,5],[5,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,5],[6,6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[5,5],[6,6]] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[[1,1],[2],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[3],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,1],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[2],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,2],[3],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3],[2],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,6],[2],[3]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2],[4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[2],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,6],[2],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,2],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[2],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,6],[2],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,6],[2],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[3],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,3],[4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,4],[3],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,6],[3],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,3],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[3],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,6],[3],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,6],[3],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4],[4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,4],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,5],[4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,6],[4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,6],[4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,5],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1,6],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[3],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,2],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3],[3],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,3],[4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,4],[3],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,6],[3],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,3],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,5],[3],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,6],[3],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,6],[3],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4],[4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,4],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,5],[4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,6],[4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2,6],[4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,5],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[2,6],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3],[4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,3],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4],[4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,4],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[3,5],[4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[3,6],[4],[5]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[3,6],[4],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,5],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[3,6],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,4],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,5],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[4,6],[5],[6]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 2
[[1],[2],[3],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1],[2],[4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1],[2],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1],[3],[4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1],[3],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1],[4],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2],[3],[4],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2],[3],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[2],[4],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[3],[4],[5],[6]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[[1,1,1,5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2,2,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,3,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4,4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5,5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,2,2,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,3,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,4,4,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,2,5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,2,3,3,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,3,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4,4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5,5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,3,3,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,4,4,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,3,5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[3,3,4,4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,4,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,5,5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[3,4,4,5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[4,4,4,5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[4,4,5,5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,1,5],[5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2,2],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2,5],[2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5,5],[2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,3],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,5],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5,5],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4,4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5,5],[5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,2,2,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2,5,5],[2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,3,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,5,5],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,4,4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,4,5,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,2,5],[5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,2,3,3],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,3,5],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,3,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5,5],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4,4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5,5],[5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,3,3,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,3,5,5],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,4,4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,4,5,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,3,5],[5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[3,3,4,4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,4,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,5,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,5,5],[5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[3,4,4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,4,5,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[4,4,4,5],[5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[4,4,5,5],[5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,1],[5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2],[2,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5],[2,2]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,2],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5],[2,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3],[3,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5],[3,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5],[3,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4],[4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5],[4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5],[4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5],[5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,2,2],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2,5],[2,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,3],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,5],[3,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,4,4],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,4,5],[4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,2],[5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,2,3],[3,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5],[3,3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,3],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5],[3,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4],[4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5],[4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5],[4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5],[5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[2,3,3],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,3,5],[3,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,4,4],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,4,5],[4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,3],[5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[3,3,4],[4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,5],[4,4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,4],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,5],[4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,5],[5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[3,4,4],[5,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,4,5],[4,5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[4,4,4],[5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[4,4,5],[5,5]] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[[1,1,2],[2],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5],[2],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,3],[3],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5],[3],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,4],[4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,5],[4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2,5],[2],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3,5],[3],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,4,5],[4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,3],[3],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5],[3],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,4],[4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2,5],[4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,3,5],[3],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,4,5],[4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,4],[4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3,5],[4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,4,5],[4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[2,2],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[2,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[3,3],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[3,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[4,4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1],[4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,2],[2,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,3],[3,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,4],[4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2],[3,3],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2],[3,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2],[4,4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,2],[4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,3],[3,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[2,4],[4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3],[4,4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,3],[4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[3,4],[4,5],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[[1,1,1,4,4,4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2,2,4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,3,3,4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,2,4,4,4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[2,2,3,3,4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[3,3,3,4,4,4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,1,4,4],[4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2,2,4],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,2,4,4],[2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,3,3,4],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,3,4,4],[3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,2,4,4],[4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[2,2,3,3,4],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,3,4,4],[3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[3,3,3,4,4],[4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,1,4],[4,4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2,2],[4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,2,4],[2,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,4,4],[2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,3,3],[4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,3,4],[3,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,4,4],[3,3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,2,4],[4,4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[2,2,3,3],[4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,3,4],[3,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,4,4],[3,3]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[3,3,3,4],[4,4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2,4],[2],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,3,4],[3],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,3,4],[3],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,1],[4,4,4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2],[2,4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,3],[3,4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,2],[4,4,4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[2,2,3],[3,4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[3,3,3],[4,4,4]] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
[[1,1,2],[2,4],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,4],[2,2],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,3],[3,4],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1,4],[3,3],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,3],[3,4],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2,4],[3,3],[4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1],[2,2],[4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1,1],[3,3],[4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[2,2],[3,3],[4,4]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[[1]] => [1] => [1,0] => [2,1] => 1
[[2]] => [1] => [1,0] => [2,1] => 1
[[1,1]] => [2] => [1,0,1,0] => [3,1,2] => 1
[[3]] => [1] => [1,0] => [2,1] => 1
[[1,1,1]] => [3] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[[4]] => [1] => [1,0] => [2,1] => 1
[[1,1,1,1]] => [4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[5]] => [1] => [1,0] => [2,1] => 1
[[6]] => [1] => [1,0] => [2,1] => 1
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Generating function
$F_{(2, 2)} = 3\ q$
$F_{(2, 3)} = 5\ q$
$F_{(3, 2)} = q + 4\ q^{2}$
$F_{(2, 4)} = 7\ q$
$F_{(3, 3)} = q + 12\ q^{2}$
$F_{(4, 2)} = 4\ q + 4\ q^{2}$
$F_{(2, 5)} = 9\ q$
$F_{(3, 4)} = q + 24\ q^{2}$
$F_{(4, 3)} = 7\ q + 23\ q^{2}$
$F_{(2, 6)} = 11\ q$
$F_{(3, 5)} = q + 40\ q^{2}$
$F_{(4, 4)} = 10\ q + 67\ q^{2}$
$F_{(2, 7)} = 13\ q$
$F_{(3, 6)} = q + 60\ q^{2}$
$F_{(4, 5)} = 13\ q + 146\ q^{2}$
$F_{(2, 8)} = 15\ q$
$F_{(3, 7)} = q + 84\ q^{2}$
$F_{(4, 6)} = 16\ q + 270\ q^{2}$
Description
The maximal modular displacement of a permutation.
This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.
This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.
Map
weight
Description
The weight of a semistandard tableau as an integer partition.
The weight (or content) of a semistandard tableaux $T$ with maximal entry $m$ is the weak composition $(\alpha_1, \dots, \alpha_m)$ such that $\alpha_i$ is the number of letters $i$ occurring in $T$.
This map returns the integer partition obtained by sorting the weight into decreasing order and omitting zeros.
Since semistandard tableaux are bigraded by the size of the partition and the maximal occurring entry, this map is not graded.
The weight (or content) of a semistandard tableaux $T$ with maximal entry $m$ is the weak composition $(\alpha_1, \dots, \alpha_m)$ such that $\alpha_i$ is the number of letters $i$ occurring in $T$.
This map returns the integer partition obtained by sorting the weight into decreasing order and omitting zeros.
Since semistandard tableaux are bigraded by the size of the partition and the maximal occurring entry, this map is not graded.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
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