Identifier
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Images
[[1,2]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[2,2]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[1],[2]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[1,3]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[2,3]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[3,3]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[1],[3]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[2],[3]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[1,1,2]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,2,2]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,2,2]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,1],[2]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,2],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,4]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[2,4]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[3,4]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[4,4]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[1],[4]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[2],[4]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[3],[4]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[1,1,3]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,2,3]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,3,3]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,2,3]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,3,3]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,3,3]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,1],[3]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,2],[3]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,3],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,3],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,2],[3]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,3],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1],[2],[3]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1,1,1,2]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,2,2]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,2,2]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,2,2]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,1],[2]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,2],[2]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,2,2],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,1],[2,2]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,5]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[2,5]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[3,5]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[4,5]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[5,5]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[1],[5]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[2],[5]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[3],[5]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[4],[5]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[1,1,4]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,2,4]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,3,4]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,4,4]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,2,4]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,3,4]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,4,4]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,3,4]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,4,4]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4,4,4]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,1],[4]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,2],[4]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,4],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,3],[4]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,4],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,4],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,2],[4]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,3],[4]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,4],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,4],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[3,3],[4]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[3,4],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1],[2],[4]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1],[3],[4]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[2],[3],[4]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1,1,1,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,2,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,2,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,3,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,2,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,3,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,3,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,1],[3]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,2],[3]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,3],[2]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,1,3],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,2,2],[3]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,2,3],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,2,3],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,3,3],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,3,3],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,2,2],[3]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,2,3],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,3,3],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,1],[2,3]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[3,3]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,2],[2,3]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,2],[3,3]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
>>> Load all 2468 entries. <<<
[[2,2],[3,3]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[2],[3]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,2],[2],[3]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,3],[2],[3]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,1,1,1,2]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,2]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,2]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1],[2]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,2],[2]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,2,2],[2]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,2,2,2],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,1,1],[2,2]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,2],[2,2]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,6]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[2,6]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[3,6]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[4,6]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[5,6]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[6,6]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[1],[6]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[2],[6]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[3],[6]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[4],[6]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[5],[6]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[1,1,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,2,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,3,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,4,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,5,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,2,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,3,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,4,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,5,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,3,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,4,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,5,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4,4,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4,5,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[5,5,5]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,1],[5]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,2],[5]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,5],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,3],[5]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,5],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,4],[5]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,5],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,5],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,2],[5]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,3],[5]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,5],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,4],[5]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,5],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,5],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[3,3],[5]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[3,4],[5]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[3,5],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[3,5],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[4,4],[5]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[4,5],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1],[2],[5]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1],[3],[5]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1],[4],[5]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[2],[3],[5]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[2],[4],[5]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[3],[4],[5]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1,1,1,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,2,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,2,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,3,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,3,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,4,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,2,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,3,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,3,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,4,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,3,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,3,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,4,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[4,4,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,1],[4]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,2],[4]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,4],[2]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,1,3],[4]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,4],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,1,4],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,2,2],[4]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,2,4],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,2,3],[4]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,2,4],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,3,4],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,2,4],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,4,4],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,3,3],[4]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,3,4],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,3,4],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,4,4],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,4,4],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,2,2],[4]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,2,3],[4]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,2,4],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,2,4],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,3,3],[4]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,3,4],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,3,4],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,4,4],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,4,4],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[3,3,3],[4]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[3,3,4],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[3,4,4],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,1],[2,4]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[3,4]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[4,4]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,2],[2,4]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,2],[3,4]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,3],[2,4]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,2],[4,4]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,3],[3,4]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,3],[4,4]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,2],[3,4]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,2],[4,4]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,3],[3,4]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[2,3],[4,4]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[3,3],[4,4]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[2],[4]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,1],[3],[4]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,2],[2],[4]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,2],[3],[4]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,3],[2],[4]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,4],[2],[3]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,4],[2],[4]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,3],[3],[4]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,4],[3],[4]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[2,2],[3],[4]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[2,3],[3],[4]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[2,4],[3],[4]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1],[2],[3],[4]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[1,1,1,1,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,2,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,2,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,3,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,3,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1],[3]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,2],[3]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,3],[2]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,1,3],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,2,2],[3]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2,3],[2]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,2,3],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,3,3],[2]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,3,3],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,2,2,2],[3]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,2,3],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,2,3],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,3,3],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,3,3],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,3,3,3],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,3,3,3],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,2,2,2],[3]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,2,3],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,3,3],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,3,3,3],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,1,1],[2,3]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,1],[3,3]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,2],[2,3]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,1,3],[2,2]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,2],[3,3]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,3],[2,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,3],[3,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,2,2],[2,3]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,2,2],[3,3]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,2,3],[2,3]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,2,3],[3,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,2,2],[3,3]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,2,3],[3,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,1],[2],[3]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2],[2],[3]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,3],[2],[3]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,2],[2],[3]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,3],[2],[3]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3,3],[2],[3]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1],[2,2],[3]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[2,3],[3]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,2],[2,3],[3]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,1,1,1,1,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,2,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,2,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,2,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1],[2]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,1,2],[2]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,2,2],[2]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,2,2,2],[2]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,2,2,2,2],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,1,1,1],[2,2]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,2],[2,2]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,2,2],[2,2]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,1],[2,2,2]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,7]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[2,7]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[3,7]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[4,7]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[5,7]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[6,7]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[7,7]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[1],[7]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[2],[7]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[3],[7]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[4],[7]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[5],[7]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[6],[7]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[1,1,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,2,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,3,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,4,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,5,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,2,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,3,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,4,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,5,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,3,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,4,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,5,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4,4,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4,5,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[5,5,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[5,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[6,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,1],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,2],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,6],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,3],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,6],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,4],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,6],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,5],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,6],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,6],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,2],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,3],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,6],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,4],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,6],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,5],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,6],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,6],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[3,3],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[3,4],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[3,6],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[3,5],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[3,6],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[3,6],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[4,4],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[4,5],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[4,6],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[4,6],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[5,5],[6]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[5,6],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1],[2],[6]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1],[3],[6]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1],[4],[6]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1],[5],[6]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[2],[3],[6]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[2],[4],[6]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[2],[5],[6]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[3],[4],[6]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[3],[5],[6]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[4],[5],[6]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1,1,1,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,2,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,2,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,3,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,3,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,3,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,4,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,4,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,5,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,2,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,3,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,3,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,3,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,4,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,4,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,5,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,3,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,3,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,3,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,4,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,4,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,5,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[4,4,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[4,4,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[4,5,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[5,5,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,1],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,2],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,5],[2]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,1,3],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,5],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,1,4],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,5],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,1,5],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,2,2],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,2,5],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,2,3],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,2,5],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,3,5],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,2,4],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,2,5],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,4,5],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,2,5],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,5,5],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,3,3],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,3,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,3,4],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,3,5],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,4,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,3,5],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,5,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,4,4],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,4,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,4,5],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,5,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,5,5],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,2,2],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,2,3],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,2,5],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,2,4],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,2,5],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,2,5],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,3,3],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,3,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,3,4],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,3,5],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,4,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,3,5],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,5,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,4,4],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,4,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,4,5],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,5,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,5,5],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[3,3,3],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[3,3,4],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[3,3,5],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[3,3,5],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[3,4,4],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[3,4,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[3,4,5],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[3,5,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[3,5,5],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[4,4,4],[5]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[4,4,5],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[4,5,5],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,1],[2,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[3,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[4,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[5,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,2],[2,5]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,2],[3,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,3],[2,5]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,2],[4,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,4],[2,5]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,2],[5,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,3],[3,5]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,3],[4,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,4],[3,5]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,3],[5,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,4],[4,5]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,4],[5,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,2],[3,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,2],[4,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,2],[5,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,3],[3,5]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[2,3],[4,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,4],[3,5]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[2,3],[5,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,4],[4,5]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[2,4],[5,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[3,3],[4,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[3,3],[5,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[3,4],[4,5]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[3,4],[5,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[4,4],[5,5]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[2],[5]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,1],[3],[5]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,1],[4],[5]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,2],[2],[5]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,2],[3],[5]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,3],[2],[5]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,5],[2],[3]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,2],[4],[5]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,4],[2],[5]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,5],[2],[4]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,5],[2],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,3],[3],[5]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,3],[4],[5]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,4],[3],[5]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,5],[3],[4]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,5],[3],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,4],[4],[5]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,5],[4],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[2,2],[3],[5]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[2,2],[4],[5]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[2,3],[3],[5]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[2,3],[4],[5]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[2,4],[3],[5]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[2,5],[3],[4]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[2,5],[3],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[2,4],[4],[5]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[2,5],[4],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[3,3],[4],[5]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[3,4],[4],[5]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[3,5],[4],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1],[2],[3],[5]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[1],[2],[4],[5]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[1],[3],[4],[5]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[2],[3],[4],[5]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[1,1,1,1,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,2,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,2,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,2,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,3,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,3,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,4,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,2,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,2,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,3,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,3,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,3,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,4,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,3,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,3,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,3,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,4,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[4,4,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,2],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,4],[2]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,1,3],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,4],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,1,4],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,2,2],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2,4],[2]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,2,3],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2,4],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,3,4],[2]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,2,4],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,4,4],[2]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,3,3],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,3,4],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,3,4],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,4,4],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,4,4],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,2,2,2],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,2,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,2,3],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,2,4],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,3,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,2,4],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,4,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,3,3],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,3,4],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,3,3,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,3,4],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,4,4],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,3,4,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,4,4],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,4,4,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,3,3,3],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,3,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,3,3,4],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3,4,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,3,4,4],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,4,4,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,4,4,4],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,2,2,2],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,2,3],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,2,4],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,2,4],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,3,3],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,3,4],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,2,3,4],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,4,4],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,2,4,4],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,3,3,3],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,3,3,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,3,3,4],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,3,4,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,3,4,4],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,4,4,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,4,4,4],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[3,3,3,3],[4]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[3,3,3,4],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[3,3,4,4],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[3,4,4,4],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,1,1],[2,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,1],[3,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,1],[4,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,2],[2,4]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,1,4],[2,2]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,2],[3,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,3],[2,4]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,1,4],[2,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,2],[4,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,4],[2,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,3],[3,4]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,1,4],[3,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,3],[4,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,4],[3,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,4],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,2,2],[2,4]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,2,2],[3,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,2,3],[2,4]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,2,4],[2,3]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,2,2],[4,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,2,4],[2,4]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,2,3],[3,4]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,2,4],[3,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,3,3],[2,4]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,2,3],[4,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,2,4],[3,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,3,4],[2,4]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,2,4],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,3,3],[3,4]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,3,3],[4,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,3,4],[3,4]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,3,4],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,2,2],[3,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,2,2],[4,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,2,3],[3,4]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[2,2,4],[3,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,2,3],[4,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,2,4],[3,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,2,4],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,3,3],[3,4]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[2,3,3],[4,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,3,4],[3,4]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[2,3,4],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[3,3,3],[4,4]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[3,3,4],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,1],[2],[4]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1],[3],[4]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2],[2],[4]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2],[3],[4]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,3],[2],[4]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,4],[2],[3]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,4],[2],[4]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,3],[3],[4]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,4],[3],[4]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,2],[2],[4]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,2],[3],[4]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,3],[2],[4]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,4],[2],[3]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,4],[2],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,3],[3],[4]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,3],[2],[4]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,4],[2],[3]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,2,4],[3],[4]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3,4],[2],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,4,4],[2],[3]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,4,4],[2],[4]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,3,3],[3],[4]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,4],[3],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,4,4],[3],[4]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,2,2],[3],[4]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,3],[3],[4]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,4],[3],[4]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,3,3],[3],[4]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[2,3,4],[3],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,4,4],[3],[4]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1],[2,2],[4]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[2,3],[4]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[2,4],[3]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,1],[2,4],[4]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,1],[3,3],[4]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[3,4],[4]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,2],[2,3],[4]] => [5,2,4,1,3] => [4,5,1,2,3] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,2],[2,4],[3]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,2],[2,4],[4]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,2],[3,3],[4]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,3],[2,4],[3]] => [3,2,5,1,4] => [5,3,2,1,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
[[1,2],[3,4],[4]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,3],[2,4],[4]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,3],[3,4],[4]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[2,2],[3,3],[4]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,2],[3,4],[4]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[2,3],[3,4],[4]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,1],[2],[3],[4]] => [5,4,3,1,2] => [3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,2],[2],[3],[4]] => [5,4,2,1,3] => [2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,3],[2],[3],[4]] => [5,3,2,1,4] => [2,3,5,1,4] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,4],[2],[3],[4]] => [4,3,2,1,5] => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,1,1,1,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,2,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,2,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,2,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[3,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1],[3]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,1,2],[3]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,1,3],[2]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,1,3],[3]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,2,2],[3]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,2,3],[2]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,1,2,3],[3]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,3,3],[2]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,1,3,3],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,2,2,2],[3]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2,2,3],[2]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,2,2,3],[3]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,2,3,3],[2]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,2,3,3],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,3,3,3],[2]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,3,3,3],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,2,2,2,2],[3]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,2,2,3],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,3],[3]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,2,3,3],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,3],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,3,3,3],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,3],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,3,3,3,3],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,3],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2],[3]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,2,2,2,3],[3]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[2,2,2,3,3],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[2,2,3,3,3],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[2,3,3,3,3],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,1,1,1],[2,3]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,1],[3,3]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,2],[2,3]] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,1,1,3],[2,2]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,1,2],[3,3]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,3],[2,3]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,1,3],[3,3]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,2,2],[2,3]] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0]
[[1,1,2,3],[2,2]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,2,2],[3,3]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,2,3],[2,3]] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0]
[[1,1,3,3],[2,2]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,2,3],[3,3]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,3,3],[2,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,3,3],[3,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,2,2,2],[2,3]] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
[[1,2,2,2],[3,3]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,2,2,3],[2,3]] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
[[1,2,2,3],[3,3]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,2,3,3],[2,3]] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0]
[[1,2,3,3],[3,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[2,2,2,2],[3,3]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[2,2,2,3],[3,3]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[2,2,3,3],[3,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,1,1],[2],[3]] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,2],[2],[3]] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,3],[2],[3]] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,2,2],[2],[3]] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2,3],[2],[3]] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,3,3],[2],[3]] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,2,2],[2],[3]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,2,3],[2],[3]] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,3,3],[2],[3]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,3,3,3],[2],[3]] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,1],[2,2,3]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,1],[2,3,3]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,1],[3,3,3]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,2],[2,2,3]] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
[[1,1,2],[2,3,3]] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0]
[[1,1,2],[3,3,3]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,2,2],[2,3,3]] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0]
[[1,2,2],[3,3,3]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[2,2,2],[3,3,3]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,1],[2,2],[3]] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1],[2,3],[3]] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,1,2],[2,2],[3]] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2],[2,3],[3]] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,1,3],[2,2],[3]] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,3],[2,3],[3]] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,2,2],[2,3],[3]] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,2,3],[2,3],[3]] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => [4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,1],[2,2],[3,3]] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1,1],[2]] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1,1,1,2],[2]] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,1,1,2,2],[2]] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,1,1,2,2,2],[2]] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,1,2,2,2,2],[2]] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,2],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1],[2,2]] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,1,1,1,2],[2,2]] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,1,1,2,2],[2,2]] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[1,1,2,2,2],[2,2]] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[1,1,1,1],[2,2,2]] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[1,1,1,2],[2,2,2]] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[1,8]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[2,8]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[3,8]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[4,8]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[5,8]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[6,8]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[7,8]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[8,8]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[1],[8]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[2],[8]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[3],[8]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[4],[8]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[5],[8]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[6],[8]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[7],[8]] => [2,1] => [2,1] => [2,1] => [1,1,0,0]
[[1,1,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,2,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,3,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,4,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,5,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,2,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,3,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,4,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,5,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[2,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,3,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,4,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,5,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[3,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4,4,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4,5,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[5,5,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[5,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[5,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[6,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[6,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[7,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[1,1],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,2],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,7],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,3],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,7],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,4],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,7],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,5],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,7],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,6],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[1,7],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,2],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,3],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,7],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,4],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,7],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,5],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,7],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,6],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[2,7],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[2,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[3,3],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[3,4],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[3,7],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[3,5],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[3,7],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[3,6],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[3,7],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[3,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[4,4],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[4,5],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[4,7],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[4,6],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[4,7],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[4,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[5,5],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[5,6],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[5,7],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[5,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[6,6],[7]] => [3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0]
[[6,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
[[1],[2],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1],[3],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1],[4],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1],[5],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1],[6],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[2],[3],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[2],[4],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[2],[5],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[2],[6],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[3],[4],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[3],[5],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[3],[6],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[4],[5],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[4],[6],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[5],[6],[7]] => [3,2,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
[[1,1,1,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,2,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,2,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,2,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,3,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,3,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,3,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,3,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,4,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,4,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,4,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,5,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,5,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,2,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,2,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,3,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,3,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,3,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,3,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,4,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,4,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,4,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,5,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,5,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[2,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,3,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,3,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,3,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,3,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,4,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,4,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,4,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,5,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,5,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[3,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[4,4,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[4,4,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[4,4,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[4,5,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[4,5,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[4,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[5,5,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[5,5,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[5,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[6,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[1,1,1],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,2],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,6],[2]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,1,3],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,6],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,1,4],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,6],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,1,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,1,6],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,1,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,2,2],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,2,6],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,2,3],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,2,6],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,3,6],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,2,4],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,2,6],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,4,6],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,2,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,2,6],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,5,6],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,2,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,6,6],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,3,3],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,3,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,3,4],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,3,6],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,4,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,3,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,3,6],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,5,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,3,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,6,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,4,4],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,4,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,4,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,4,6],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,5,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,4,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,6,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,5,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[1,5,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,5,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[1,6,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,6,6],[6]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,2,2],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,2,3],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,2,6],[3]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,2,4],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,2,6],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,2,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,2,6],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,2,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,3,3],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,3,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,3,4],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,3,6],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,4,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,3,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,3,6],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,5,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,3,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,6,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,4,4],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,4,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,4,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,4,6],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,5,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,4,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,6,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,5,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[2,5,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,5,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[2,6,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[2,6,6],[6]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[3,3,3],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[3,3,4],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[3,3,6],[4]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[3,3,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[3,3,6],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[3,3,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[3,4,4],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[3,4,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[3,4,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[3,4,6],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[3,5,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[3,4,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[3,6,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[3,5,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[3,5,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[3,5,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[3,6,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[3,6,6],[6]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[4,4,4],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[4,4,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[4,4,6],[5]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[4,4,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[4,5,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[4,5,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[4,5,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[4,6,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[4,6,6],[6]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[5,5,5],[6]] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
[[5,5,6],[6]] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
[[5,6,6],[6]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
[[1,1],[2,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[3,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[4,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[5,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,2],[2,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,2],[3,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,3],[2,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,2],[4,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,4],[2,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,2],[5,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,5],[2,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,2],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,3],[3,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,3],[4,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,4],[3,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,3],[5,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,5],[3,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,3],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,4],[4,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,4],[5,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,5],[4,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,4],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,5],[5,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[1,5],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,2],[3,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,2],[4,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,2],[5,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,2],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,3],[3,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[2,3],[4,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,4],[3,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[2,3],[5,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,5],[3,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[2,3],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,4],[4,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[2,4],[5,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,5],[4,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[2,4],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[2,5],[5,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[2,5],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[3,3],[4,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[3,3],[5,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[3,3],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[3,4],[4,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[3,4],[5,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[3,5],[4,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[3,4],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[3,5],[5,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[3,5],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[4,4],[5,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[4,4],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[4,5],[5,6]] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
[[4,5],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[5,5],[6,6]] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
[[1,1],[2],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,1],[3],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,1],[4],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,1],[5],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,2],[2],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,2],[3],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,3],[2],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,6],[2],[3]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,2],[4],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,4],[2],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,6],[2],[4]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,2],[5],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,5],[2],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,6],[2],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,6],[2],[6]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,3],[3],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,3],[4],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,4],[3],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,6],[3],[4]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,3],[5],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,5],[3],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,6],[3],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,6],[3],[6]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,4],[4],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,4],[5],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[1,5],[4],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,6],[4],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,6],[4],[6]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1,5],[5],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[1,6],[5],[6]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[2,2],[3],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[2,2],[4],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[2,2],[5],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[2,3],[3],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[2,3],[4],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[2,4],[3],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[2,6],[3],[4]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[2,3],[5],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[2,5],[3],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[2,6],[3],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[2,6],[3],[6]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[2,4],[4],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[2,4],[5],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[2,5],[4],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[2,6],[4],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[2,6],[4],[6]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[2,5],[5],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[2,6],[5],[6]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[3,3],[4],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[3,3],[5],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[3,4],[4],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[3,4],[5],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[3,5],[4],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[3,6],[4],[5]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[3,6],[4],[6]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[3,5],[5],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[3,6],[5],[6]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[4,4],[5],[6]] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
[[4,5],[5],[6]] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
[[4,6],[5],[6]] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
[[1],[2],[3],[6]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[1],[2],[4],[6]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[1],[2],[5],[6]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[1],[3],[4],[6]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[1],[3],[5],[6]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[1],[4],[5],[6]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[2],[3],[4],[6]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[2],[3],[5],[6]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[2],[4],[5],[6]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[3],[4],[5],[6]] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
[[1,1,1,1,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,2,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,2,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,2,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,2,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,2,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,2,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,3,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,3,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,3,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,3,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,3,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,4,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,4,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,4,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,5,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,2,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,2,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,2,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,2,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,3,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,3,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,3,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,3,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,3,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,3,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,4,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,4,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,4,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[2,5,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,3,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,3,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,3,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,3,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,3,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,3,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,4,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,4,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,4,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[3,5,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[4,4,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[4,4,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[4,4,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[4,5,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[5,5,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,2],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,5],[2]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,1,3],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,5],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,1,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,1,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,2,2],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2,5],[2]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,2,3],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2,5],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,3,5],[2]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,2,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,4,5],[2]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,2,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,5,5],[2]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,3,3],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,3,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,3,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,3,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,4,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,3,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,5,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,4,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,4,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,4,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,5,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1,5,5],[5]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,2,2,2],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,2,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,2,3],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,2,5],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,3,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,2,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,2,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,2,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,5,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,3,3],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,3,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,3,3,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,3,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,3,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,4,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,3,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,3,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,5,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,3,5,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,4,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,4,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,4,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,4,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,5,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,4,5,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,2,5,5],[5]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,5,5,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,3,3,3],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,3,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,3,3,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,3,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3,4,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,3,3,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,3,4,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,4,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,4,4,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,3,4,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3,5,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,4,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,3,5,5],[5]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,5,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,4,4,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[1,4,4,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,4,4,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,4,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,4,5,5],[5]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,5,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,5,5,5],[5]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,2,2,2],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,2,3],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,2,5],[3]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,2,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,2,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,2,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,3,3],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,3,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,2,3,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,3,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,4,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,2,3,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,5,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,2,4,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,4,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,2,4,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,5,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,2,5,5],[5]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,3,3,3],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,3,3,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,3,3,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,3,3,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,3,4,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,3,3,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,3,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,3,4,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,3,4,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,4,4,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,3,4,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,3,5,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,4,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,3,5,5],[5]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,5,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,4,4,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[2,4,4,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,4,4,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,4,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,4,5,5],[5]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,5,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[2,5,5,5],[5]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[3,3,3,3],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[3,3,3,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[3,3,3,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[3,3,3,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[3,3,4,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[3,3,4,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[3,3,4,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[3,3,5,5],[4]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[3,3,5,5],[5]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[3,4,4,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[3,4,4,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[3,4,4,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[3,4,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[3,4,5,5],[5]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[3,5,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[3,5,5,5],[5]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[4,4,4,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
[[4,4,4,5],[5]] => [4,1,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
[[4,4,5,5],[5]] => [3,1,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[4,5,5,5],[5]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
[[1,1,1],[2,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,1],[3,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,1],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,1],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,2],[2,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,1,5],[2,2]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,2],[3,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,3],[2,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,1,5],[2,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,2],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,4],[2,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,1,5],[2,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,2],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,5],[2,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,3],[3,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,1,5],[3,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,3],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,4],[3,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,1,5],[3,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,3],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,5],[3,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,4],[4,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,1,5],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,4],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,1,5],[4,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,5],[5,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,2,2],[2,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,2,2],[3,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,2,3],[2,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,2,5],[2,3]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,2,2],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,2,4],[2,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,2,5],[2,4]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,2,2],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,2,5],[2,5]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,2,3],[3,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,2,5],[3,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,3,3],[2,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,2,3],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,2,4],[3,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,2,5],[3,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,3,4],[2,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,3,5],[2,4]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,2,3],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,2,5],[3,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,3,5],[2,5]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,2,4],[4,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,2,5],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,4,4],[2,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,2,4],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,2,5],[4,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,4,5],[2,5]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,2,5],[5,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,3,3],[3,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,3,3],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,3,4],[3,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,3,5],[3,4]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,3,3],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,3,5],[3,5]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,3,4],[4,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[1,3,5],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,4,4],[3,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,3,4],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,3,5],[4,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,4,5],[3,5]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,3,5],[5,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,4,4],[4,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[1,4,4],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[1,4,5],[4,5]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[1,4,5],[5,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,2,2],[3,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,2,2],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,2,2],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,2,3],[3,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[2,2,5],[3,3]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,2,3],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,2,4],[3,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[2,2,5],[3,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,2,3],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,2,5],[3,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,2,4],[4,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[2,2,5],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,2,4],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,2,5],[4,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,2,5],[5,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,3,3],[3,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[2,3,3],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,3,4],[3,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[2,3,5],[3,4]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[2,3,3],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,3,5],[3,5]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[2,3,4],[4,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[2,3,5],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,4,4],[3,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[2,3,4],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,3,5],[4,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,4,5],[3,5]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[2,3,5],[5,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[2,4,4],[4,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[2,4,4],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[2,4,5],[4,5]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[2,4,5],[5,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[3,3,3],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[3,3,3],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[3,3,4],[4,5]] => [3,5,1,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
[[3,3,5],[4,4]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[3,3,4],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[3,3,5],[4,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[3,3,5],[5,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[3,4,4],[4,5]] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
[[3,4,4],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[3,4,5],[4,5]] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
[[3,4,5],[5,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[4,4,4],[5,5]] => [4,5,1,2,3] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
[[4,4,5],[5,5]] => [3,4,1,2,5] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
[[1,1,1],[2],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1],[3],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2],[2],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,2],[3],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,3],[2],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,5],[2],[3]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,2],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,4],[2],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,5],[2],[4]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,5],[2],[5]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,3],[3],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,3],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,4],[3],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,5],[3],[4]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,5],[3],[5]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,1,4],[4],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,5],[4],[5]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,2],[2],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,2],[3],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,3],[2],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,5],[2],[3]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,2],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,4],[2],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,5],[2],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,5],[2],[5]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,2,3],[3],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,3],[2],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,5],[2],[3]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,2,3],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,4],[3],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,2,5],[3],[4]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3,4],[2],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,5],[2],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,2,5],[3],[5]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3,5],[2],[5]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,5,5],[2],[3]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,2,4],[4],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,4,4],[2],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,4,5],[2],[4]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,2,5],[4],[5]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,4,5],[2],[5]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,5,5],[2],[4]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,5,5],[2],[5]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,3,3],[3],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,3],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,4],[3],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,3,5],[3],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3,5],[3],[5]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3,4],[4],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,4,4],[3],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,4,5],[3],[4]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,3,5],[4],[5]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,4,5],[3],[5]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,5,5],[3],[4]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,5,5],[3],[5]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,4,4],[4],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,4,5],[4],[5]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,5,5],[4],[5]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,2,2],[3],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,2],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,3],[3],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,3],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,4],[3],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,5],[3],[4]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,5],[3],[5]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2,4],[4],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,2,5],[4],[5]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,3,3],[3],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[2,3,3],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[2,3,4],[3],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[2,3,5],[3],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,3,5],[3],[5]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,3,4],[4],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,4,4],[3],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[2,4,5],[3],[4]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,3,5],[4],[5]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,4,5],[3],[5]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,5,5],[3],[4]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,5,5],[3],[5]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[2,4,4],[4],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[2,4,5],[4],[5]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,5,5],[4],[5]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[3,3,3],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
[[3,3,4],[4],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
[[3,3,5],[4],[5]] => [4,3,1,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[3,4,4],[4],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
[[3,4,5],[4],[5]] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
[[3,5,5],[4],[5]] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
[[1,1],[2,2],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[2,3],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[2,5],[3]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,1],[2,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[2,5],[4]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,1],[2,5],[5]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,1],[3,3],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[3,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[3,5],[4]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,1],[3,5],[5]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,1],[4,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[4,5],[5]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,2],[2,3],[5]] => [5,2,4,1,3] => [4,5,1,2,3] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,2],[2,5],[3]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,2],[2,4],[5]] => [5,2,4,1,3] => [4,5,1,2,3] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,2],[2,5],[4]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,2],[2,5],[5]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,2],[3,3],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,3],[2,5],[3]] => [3,2,5,1,4] => [5,3,2,1,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
[[1,2],[3,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,2],[3,5],[4]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,3],[2,4],[5]] => [5,2,4,1,3] => [4,5,1,2,3] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [5,3,2,1,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
[[1,2],[3,5],[5]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,3],[2,5],[5]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,2],[4,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,4],[2,5],[4]] => [3,2,5,1,4] => [5,3,2,1,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
[[1,2],[4,5],[5]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,4],[2,5],[5]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,3],[3,4],[5]] => [5,2,4,1,3] => [4,5,1,2,3] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
[[1,3],[3,5],[4]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,3],[3,5],[5]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,3],[4,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,4],[3,5],[4]] => [3,2,5,1,4] => [5,3,2,1,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
[[1,3],[4,5],[5]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,4],[3,5],[5]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,4],[4,5],[5]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[2,2],[3,3],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,2],[3,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,2],[3,5],[4]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[2,2],[3,5],[5]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[2,2],[4,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,2],[4,5],[5]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[2,3],[3,4],[5]] => [5,2,4,1,3] => [4,5,1,2,3] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
[[2,3],[3,5],[4]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[2,3],[3,5],[5]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[2,3],[4,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,4],[3,5],[4]] => [3,2,5,1,4] => [5,3,2,1,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
[[2,3],[4,5],[5]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[2,4],[3,5],[5]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[2,4],[4,5],[5]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[3,3],[4,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
[[3,3],[4,5],[5]] => [4,3,5,1,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
[[3,4],[4,5],[5]] => [4,2,5,1,3] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
[[1,1],[2],[3],[5]] => [5,4,3,1,2] => [3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[2],[4],[5]] => [5,4,3,1,2] => [3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1],[3],[4],[5]] => [5,4,3,1,2] => [3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,2],[2],[3],[5]] => [5,4,2,1,3] => [2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,2],[2],[4],[5]] => [5,4,2,1,3] => [2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,3],[2],[3],[5]] => [5,3,2,1,4] => [2,3,5,1,4] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => [3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => [2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [2,3,5,1,4] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,5],[2],[3],[5]] => [4,3,2,1,5] => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,4],[2],[4],[5]] => [5,3,2,1,4] => [2,3,5,1,4] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,5],[2],[4],[5]] => [4,3,2,1,5] => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1,3],[3],[4],[5]] => [5,4,2,1,3] => [2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,4],[3],[4],[5]] => [5,3,2,1,4] => [2,3,5,1,4] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
[[1,5],[3],[4],[5]] => [4,3,2,1,5] => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[2,2],[3],[4],[5]] => [5,4,3,1,2] => [3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
[[2,3],[3],[4],[5]] => [5,4,2,1,3] => [2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
[[2,4],[3],[4],[5]] => [5,3,2,1,4] => [2,3,5,1,4] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
[[2,5],[3],[4],[5]] => [4,3,2,1,5] => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
[[1,1,1,1,1,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,2,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,2,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,2,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[2,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[3,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[3,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[3,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[3,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[3,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[4,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,1,2],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,1,4],[2]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,1,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,1,4],[3]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,1,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,2,2],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,2,4],[2]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,1,2,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,2,4],[3]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,3,4],[2]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,1,2,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,4,4],[2]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,1,3,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,3,4],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,1,3,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,4,4],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,1,4,4],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,2,2,2],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2,2,4],[2]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,2,2,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2,2,4],[3]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,2,3,4],[2]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,2,2,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,2,4,4],[2]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,2,3,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2,3,4],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,3,3,4],[2]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,2,3,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,2,4,4],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,3,4,4],[2]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,2,4,4],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,4,4,4],[2]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,3,3,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,3,3,4],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,3,3,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,3,4,4],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,4,4,4],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,2,2,2,2],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,2,2,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,2,2,4],[3]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,2,3,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,2,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,2,3,4],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,3,3,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,2,4,4],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,3,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,2,4,4],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,4,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,3,4],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,3,3,3,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,3,4,4],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,3,3,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,4,4,4],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,3,4,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,4,4,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,3,3,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3,3,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,3,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,3,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,3,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,4,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,4,4,4,4],[4]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,2,2,2,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,2,2,2,4],[3]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[2,2,2,2,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[2,2,2,3,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,2,2,3,4],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[2,2,2,3,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[2,2,2,4,4],[3]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[2,2,2,4,4],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[2,2,3,3,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,2,3,3,4],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[2,2,3,3,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[2,2,3,4,4],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[2,2,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[2,2,4,4,4],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[2,2,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[2,3,3,3,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,3,3,3,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[2,3,3,3,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[2,3,3,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[2,3,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[2,3,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[2,3,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[2,4,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[2,4,4,4,4],[4]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[3,3,3,3,3],[4]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[3,3,3,3,4],[4]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[3,3,3,4,4],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[3,3,4,4,4],[4]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[3,4,4,4,4],[4]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,1,1,1],[2,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,1],[3,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,1],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,2],[2,4]] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,1,1,4],[2,2]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,1,2],[3,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,3],[2,4]] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,1,1,4],[2,3]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,1,2],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,4],[2,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,1,3],[3,4]] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,1,1,4],[3,3]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,1,3],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,1,4],[3,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,1,4],[4,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,2,2],[2,4]] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0]
[[1,1,2,4],[2,2]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,2,2],[3,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,2,3],[2,4]] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0]
[[1,1,2,4],[2,3]] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0]
[[1,1,3,4],[2,2]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,2,2],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,2,4],[2,4]] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0]
[[1,1,4,4],[2,2]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,2,3],[3,4]] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,1,2,4],[3,3]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,3,3],[2,4]] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0]
[[1,1,3,4],[2,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,2,3],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,2,4],[3,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,3,4],[2,4]] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0]
[[1,1,4,4],[2,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,2,4],[4,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,4,4],[2,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,3,3],[3,4]] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0]
[[1,1,3,4],[3,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,3,3],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1,3,4],[3,4]] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0]
[[1,1,4,4],[3,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,3,4],[4,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,1,4,4],[3,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,4,4],[4,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,2,2,2],[2,4]] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
[[1,2,2,2],[3,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,2,2,3],[2,4]] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
[[1,2,2,4],[2,3]] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
[[1,2,2,2],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,2,2,4],[2,4]] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
[[1,2,2,3],[3,4]] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,2,2,4],[3,3]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,2,3,3],[2,4]] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
[[1,2,3,4],[2,3]] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0]
[[1,2,2,3],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,2,2,4],[3,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,2,3,4],[2,4]] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
[[1,2,4,4],[2,3]] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0]
[[1,2,2,4],[4,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,2,4,4],[2,4]] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0]
[[1,2,3,3],[3,4]] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0]
[[1,2,3,4],[3,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,3,3,3],[2,4]] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
[[1,2,3,3],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,2,3,4],[3,4]] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0]
[[1,2,4,4],[3,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,3,3,4],[2,4]] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
[[1,2,3,4],[4,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,2,4,4],[3,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,3,4,4],[2,4]] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0]
[[1,2,4,4],[4,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,3,3,3],[3,4]] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
[[1,3,3,3],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,3,3,4],[3,4]] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
[[1,3,3,4],[4,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,3,4,4],[3,4]] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0]
[[1,3,4,4],[4,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[2,2,2,2],[3,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[2,2,2,2],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[2,2,2,3],[3,4]] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[2,2,2,4],[3,3]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[2,2,2,3],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[2,2,2,4],[3,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[2,2,2,4],[4,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[2,2,3,3],[3,4]] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0]
[[2,2,3,4],[3,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[2,2,3,3],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[2,2,3,4],[3,4]] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0]
[[2,2,4,4],[3,3]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[2,2,3,4],[4,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[2,2,4,4],[3,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[2,2,4,4],[4,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[2,3,3,3],[3,4]] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
[[2,3,3,3],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[2,3,3,4],[3,4]] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
[[2,3,3,4],[4,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[2,3,4,4],[3,4]] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0]
[[2,3,4,4],[4,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[3,3,3,3],[4,4]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[3,3,3,4],[4,4]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[3,3,4,4],[4,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,1,1,1],[2],[4]] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,1],[3],[4]] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,2],[2],[4]] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,2],[3],[4]] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,3],[2],[4]] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,4],[2],[3]] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,4],[2],[4]] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,1,3],[3],[4]] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,4],[3],[4]] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,2,2],[2],[4]] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2,2],[3],[4]] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2,3],[2],[4]] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2,4],[2],[3]] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,2,4],[2],[4]] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,2,3],[3],[4]] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,3,3],[2],[4]] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,3,4],[2],[3]] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,2,4],[3],[4]] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,3,4],[2],[4]] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,4,4],[2],[3]] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,4,4],[2],[4]] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1,3,3],[3],[4]] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,3,4],[3],[4]] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,4,4],[3],[4]] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,2,2],[2],[4]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,2,2],[3],[4]] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,2,3],[2],[4]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,2,4],[2],[3]] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,2,4],[2],[4]] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,2,3],[3],[4]] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,3],[2],[4]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,4],[2],[3]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,2,4],[3],[4]] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,3,4],[2],[4]] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,4,4],[2],[3]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,4,4],[2],[4]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,3,3],[3],[4]] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,3,3],[2],[4]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,3,4],[2],[3]] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,2,3,4],[3],[4]] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3,3,4],[2],[4]] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3,4,4],[2],[3]] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,2,4,4],[3],[4]] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,3,4,4],[2],[4]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,4,4,4],[2],[3]] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,4,4,4],[2],[4]] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,3,3,3],[3],[4]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,3,4],[3],[4]] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3,4,4],[3],[4]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,4,4,4],[3],[4]] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[2,2,2,2],[3],[4]] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,2,2,3],[3],[4]] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,2,2,4],[3],[4]] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[2,2,3,3],[3],[4]] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,2,3,4],[3],[4]] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[2,2,4,4],[3],[4]] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[2,3,3,3],[3],[4]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,3,3,4],[3],[4]] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[2,3,4,4],[3],[4]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[2,4,4,4],[3],[4]] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,1,1],[2,2,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,1],[2,3,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,1],[2,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,1],[3,3,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,1],[3,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,1],[4,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,2],[2,2,4]] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
[[1,1,2],[2,3,4]] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0]
[[1,1,3],[2,2,4]] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
[[1,1,2],[2,4,4]] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0]
[[1,1,2],[3,3,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,3],[2,3,4]] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
[[1,1,2],[3,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,3],[2,4,4]] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0]
[[1,1,2],[4,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,3],[3,3,4]] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
[[1,1,3],[3,4,4]] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0]
[[1,1,3],[4,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,2,2],[2,3,4]] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0]
[[1,2,2],[2,4,4]] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0]
[[1,2,2],[3,3,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,2,3],[2,3,4]] => [2,4,6,1,3,5] => [6,2,1,4,3,5] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0]
[[1,2,2],[3,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,2,3],[2,4,4]] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0]
[[1,2,2],[4,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,2,3],[3,3,4]] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
[[1,2,3],[3,4,4]] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0]
[[1,3,3],[2,4,4]] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0]
[[1,2,3],[4,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,3,3],[3,4,4]] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0]
[[1,3,3],[4,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[2,2,2],[3,3,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[2,2,2],[3,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[2,2,2],[4,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[2,2,3],[3,3,4]] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
[[2,2,3],[3,4,4]] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0]
[[2,2,3],[4,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[2,3,3],[3,4,4]] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0]
[[2,3,3],[4,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[3,3,3],[4,4,4]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,1,1],[2,2],[4]] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1],[2,3],[4]] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1],[2,4],[3]] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,1,1],[2,4],[4]] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,1,1],[3,3],[4]] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1],[3,4],[4]] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,1,2],[2,2],[4]] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2],[2,3],[4]] => [6,3,5,1,2,4] => [5,1,6,2,3,4] => [6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2],[2,4],[3]] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,1,3],[2,2],[4]] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,4],[2,2],[3]] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,2],[2,4],[4]] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,1,4],[2,2],[4]] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,2],[3,3],[4]] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,3],[2,3],[4]] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,3],[2,4],[3]] => [4,3,6,1,2,5] => [6,1,4,3,2,5] => [4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0]
[[1,1,4],[2,3],[3]] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,1,2],[3,4],[4]] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,1,3],[2,4],[4]] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,1,4],[2,3],[4]] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,4],[2,4],[3]] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,1,4],[2,4],[4]] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,1,3],[3,3],[4]] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,3],[3,4],[4]] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,1,4],[3,3],[4]] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,1,4],[3,4],[4]] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,2,2],[2,3],[4]] => [6,2,5,1,3,4] => [5,6,1,3,2,4] => [6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,2],[2,4],[3]] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,2,2],[2,4],[4]] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,2,2],[3,3],[4]] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3],[2,3],[4]] => [6,2,4,1,3,5] => [4,6,1,2,3,5] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3],[2,4],[3]] => [4,2,6,1,3,5] => [6,4,1,2,3,5] => [4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0]
[[1,2,4],[2,3],[3]] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => [4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,2,2],[3,4],[4]] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,2,3],[2,4],[4]] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,2,4],[2,3],[4]] => [5,2,4,1,3,6] => [4,5,1,2,3,6] => [5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,4],[2,4],[3]] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => [4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,2,4],[2,4],[4]] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => [4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,2,3],[3,3],[4]] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,3],[2,4],[3]] => [3,2,6,1,4,5] => [6,3,2,1,4,5] => [3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0]
[[1,2,3],[3,4],[4]] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,2,4],[3,3],[4]] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3,3],[2,4],[4]] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,3,4],[2,4],[3]] => [3,2,5,1,4,6] => [5,3,2,1,4,6] => [3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
[[1,2,4],[3,4],[4]] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,3,4],[2,4],[4]] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => [4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,3,3],[3,4],[4]] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,3,4],[3,4],[4]] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => [4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[2,2,2],[3,3],[4]] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,2,2],[3,4],[4]] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[2,2,3],[3,3],[4]] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[2,2,3],[3,4],[4]] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[2,2,4],[3,3],[4]] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[2,2,4],[3,4],[4]] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[2,3,3],[3,4],[4]] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[2,3,4],[3,4],[4]] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => [4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,1,1],[2],[3],[4]] => [6,5,4,1,2,3] => [4,1,2,5,6,3] => [6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,2],[2],[3],[4]] => [6,5,3,1,2,4] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,3],[2],[3],[4]] => [6,4,3,1,2,5] => [3,1,4,6,2,5] => [6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,4],[2],[3],[4]] => [5,4,3,1,2,6] => [3,1,4,5,2,6] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,2],[2],[3],[4]] => [6,5,2,1,3,4] => [2,5,1,3,6,4] => [6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3],[2],[3],[4]] => [6,4,2,1,3,5] => [2,4,1,6,3,5] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,4],[2],[3],[4]] => [5,4,2,1,3,6] => [2,4,1,5,3,6] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3,3],[2],[3],[4]] => [6,3,2,1,4,5] => [2,3,6,1,4,5] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,4],[2],[3],[4]] => [5,3,2,1,4,6] => [2,3,5,1,4,6] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,4,4],[2],[3],[4]] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,1],[2,2],[3,4]] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1],[2,2],[4,4]] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1],[2,3],[3,4]] => [4,6,3,5,1,2] => [5,1,6,4,3,2] => [4,6,2,1,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,1],[2,3],[4,4]] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1],[3,3],[4,4]] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,2],[2,3],[3,4]] => [4,6,2,5,1,3] => [5,6,1,4,2,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,2],[2,3],[4,4]] => [5,6,2,4,1,3] => [4,6,1,2,5,3] => [5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,2],[3,3],[4,4]] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[2,2],[3,3],[4,4]] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,1],[2,2],[3],[4]] => [6,5,3,4,1,2] => [4,1,5,3,6,2] => [6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1],[2,3],[3],[4]] => [6,4,3,5,1,2] => [5,1,4,6,3,2] => [6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1],[2,4],[3],[4]] => [5,4,3,6,1,2] => [6,1,4,5,3,2] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0]
[[1,2],[2,3],[3],[4]] => [6,4,2,5,1,3] => [5,4,1,6,2,3] => [6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2],[2,4],[3],[4]] => [5,4,2,6,1,3] => [6,4,1,5,2,3] => [5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0]
[[1,3],[2,4],[3],[4]] => [5,3,2,6,1,4] => [6,3,5,1,2,4] => [5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0]
[[1,1,1,1,1,1,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,2,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,2,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[2,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[3,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1,1],[3]] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1,1,1,2],[3]] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1,1,1,3],[2]] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,1,1,1,3],[3]] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,1,1,2,2],[3]] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1,1,2,3],[2]] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,1,1,1,2,3],[3]] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,1,1,3,3],[2]] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,1,1,1,3,3],[3]] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,1,1,2,2,2],[3]] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1,2,2,3],[2]] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,1,1,2,2,3],[3]] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,1,2,3,3],[2]] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,1,1,2,3,3],[3]] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,1,1,3,3,3],[2]] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,1,1,3,3,3],[3]] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,1,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,2,2,2,3],[2]] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,2,3],[3]] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,2,2,3,3],[2]] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,1,2,3,3,3],[2]] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,1,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,1,3,3,3,3],[2]] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,1,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,2,2,2,3],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,3],[3]] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,2,2,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,2,2,3,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,2,3,3,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,3,3,3,3],[3]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[2,2,2,2,2,3],[3]] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[2,2,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[2,2,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[2,2,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[2,3,3,3,3,3],[3]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1],[2,3]] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,1,1,1,1],[3,3]] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,1,1,1,2],[2,3]] => [5,7,1,2,3,4,6] => [7,1,2,3,5,4,6] => [5,7,6,4,3,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[1,1,1,1,3],[2,2]] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,1,1,1,2],[3,3]] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,1,1,1,3],[2,3]] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,1,1,1,3],[3,3]] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,1,1,2,2],[2,3]] => [4,7,1,2,3,5,6] => [7,1,2,4,3,5,6] => [4,7,6,5,3,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[1,1,1,2,3],[2,2]] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[1,1,1,2,2],[3,3]] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,1,1,2,3],[2,3]] => [4,6,1,2,3,5,7] => [6,1,2,4,3,5,7] => [4,6,5,3,2,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[1,1,1,3,3],[2,2]] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[1,1,1,2,3],[3,3]] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,1,1,3,3],[2,3]] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[1,1,1,3,3],[3,3]] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[1,1,2,2,2],[2,3]] => [3,7,1,2,4,5,6] => [7,1,3,2,4,5,6] => [3,7,6,5,4,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[1,1,2,2,3],[2,2]] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[1,1,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,1,2,2,3],[2,3]] => [3,6,1,2,4,5,7] => [6,1,3,2,4,5,7] => [3,6,5,4,2,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[1,1,2,3,3],[2,2]] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[1,1,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,1,2,3,3],[2,3]] => [3,5,1,2,4,6,7] => [5,1,3,2,4,6,7] => [3,5,4,2,1,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[1,1,3,3,3],[2,2]] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[1,1,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[1,1,3,3,3],[2,3]] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[1,1,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[1,2,2,2,2],[2,3]] => [2,7,1,3,4,5,6] => [7,2,1,3,4,5,6] => [2,7,6,5,4,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,2,2,2,3],[2,3]] => [2,6,1,3,4,5,7] => [6,2,1,3,4,5,7] => [2,6,5,4,3,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,2,2,3,3],[2,3]] => [2,5,1,3,4,6,7] => [5,2,1,3,4,6,7] => [2,5,4,3,1,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[1,2,3,3,3],[2,3]] => [2,4,1,3,5,6,7] => [4,2,1,3,5,6,7] => [2,4,3,1,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[1,2,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[2,2,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[2,2,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[2,2,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[2,2,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[1,1,1,1,1],[2],[3]] => [7,6,1,2,3,4,5] => [6,1,2,3,4,7,5] => [7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1,1,2],[2],[3]] => [7,5,1,2,3,4,6] => [5,1,2,3,7,4,6] => [7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1,1,3],[2],[3]] => [6,5,1,2,3,4,7] => [5,1,2,3,6,4,7] => [6,4,3,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,1,2,2],[2],[3]] => [7,4,1,2,3,5,6] => [4,1,2,7,3,5,6] => [7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1,2,3],[2],[3]] => [6,4,1,2,3,5,7] => [4,1,2,6,3,5,7] => [6,5,3,2,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,1,3,3],[2],[3]] => [5,4,1,2,3,6,7] => [4,1,2,5,3,6,7] => [5,3,2,1,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,1,2,2,2],[2],[3]] => [7,3,1,2,4,5,6] => [3,1,7,2,4,5,6] => [7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,2,2,3],[2],[3]] => [6,3,1,2,4,5,7] => [3,1,6,2,4,5,7] => [6,5,4,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,2,3,3],[2],[3]] => [5,3,1,2,4,6,7] => [3,1,5,2,4,6,7] => [5,4,2,1,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,1,3,3,3],[2],[3]] => [4,3,1,2,5,6,7] => [3,1,4,2,5,6,7] => [4,2,1,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,2,2,2,2],[2],[3]] => [7,2,1,3,4,5,6] => [2,7,1,3,4,5,6] => [7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,2,2,3],[2],[3]] => [6,2,1,3,4,5,7] => [2,6,1,3,4,5,7] => [6,5,4,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,2,3,3],[2],[3]] => [5,2,1,3,4,6,7] => [2,5,1,3,4,6,7] => [5,4,3,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,2,3,3,3],[2],[3]] => [4,2,1,3,5,6,7] => [2,4,1,3,5,6,7] => [4,3,1,2,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,3,3,3,3],[2],[3]] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,1,1,1],[2,2,3]] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[1,1,1,1],[2,3,3]] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[1,1,1,1],[3,3,3]] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[1,1,1,2],[2,2,3]] => [4,5,7,1,2,3,6] => [7,1,2,4,5,3,6] => [4,5,7,6,3,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[1,1,1,3],[2,2,2]] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[1,1,1,2],[2,3,3]] => [4,6,7,1,2,3,5] => [7,1,2,4,3,6,5] => [4,6,7,5,3,2,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[1,1,1,3],[2,2,3]] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[1,1,1,2],[3,3,3]] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[1,1,1,3],[2,3,3]] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[1,1,1,3],[3,3,3]] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[1,1,2,2],[2,2,3]] => [3,4,7,1,2,5,6] => [7,1,3,4,2,5,6] => [3,4,7,6,5,2,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[1,1,2,2],[2,3,3]] => [3,6,7,1,2,4,5] => [7,1,3,2,4,6,5] => [3,6,7,5,4,2,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[1,1,2,3],[2,2,3]] => [3,4,6,1,2,5,7] => [6,1,3,4,2,5,7] => [3,4,6,5,2,1,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[1,1,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[1,1,2,3],[2,3,3]] => [3,5,6,1,2,4,7] => [6,1,3,2,5,4,7] => [3,5,6,4,2,1,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[1,1,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[1,2,2,2],[2,3,3]] => [2,6,7,1,3,4,5] => [7,2,1,3,4,6,5] => [2,6,7,5,4,3,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[1,2,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[1,2,2,3],[2,3,3]] => [2,5,6,1,3,4,7] => [6,2,1,3,5,4,7] => [2,5,6,4,3,1,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[1,2,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[2,2,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[2,2,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[1,1,1,1],[2,2],[3]] => [7,5,6,1,2,3,4] => [6,1,2,3,7,5,4] => [7,4,3,2,1,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1,1],[2,3],[3]] => [6,5,7,1,2,3,4] => [7,1,2,3,6,5,4] => [6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,1,1,2],[2,2],[3]] => [7,4,5,1,2,3,6] => [5,1,2,7,4,3,6] => [7,6,3,2,1,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1,2],[2,3],[3]] => [6,4,7,1,2,3,5] => [7,1,2,6,3,4,5] => [6,4,7,5,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,1,1,3],[2,2],[3]] => [6,4,5,1,2,3,7] => [5,1,2,6,4,3,7] => [6,3,2,1,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,1,3],[2,3],[3]] => [5,4,6,1,2,3,7] => [6,1,2,5,4,3,7] => [5,4,6,3,2,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[1,1,2,2],[2,2],[3]] => [7,3,4,1,2,5,6] => [4,1,7,3,2,5,6] => [7,6,5,2,1,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,2,2],[2,3],[3]] => [6,3,7,1,2,4,5] => [7,1,6,2,4,3,5] => [6,3,7,5,4,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,1,2,3],[2,2],[3]] => [6,3,4,1,2,5,7] => [4,1,6,3,2,5,7] => [6,5,2,1,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,1,2,3],[2,3],[3]] => [5,3,6,1,2,4,7] => [6,1,5,2,3,4,7] => [5,3,6,4,2,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[1,1,3,3],[2,2],[3]] => [5,3,4,1,2,6,7] => [4,1,5,3,2,6,7] => [5,2,1,4,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,1,3,3],[2,3],[3]] => [4,3,5,1,2,6,7] => [5,1,4,3,2,6,7] => [4,3,5,2,1,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[1,2,2,2],[2,3],[3]] => [6,2,7,1,3,4,5] => [7,6,1,3,4,2,5] => [6,2,7,5,4,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,2,2,3],[2,3],[3]] => [5,2,6,1,3,4,7] => [6,5,1,3,2,4,7] => [5,2,6,4,3,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[1,2,3,3],[2,3],[3]] => [4,2,5,1,3,6,7] => [5,4,1,2,3,6,7] => [4,2,5,3,1,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[1,1,1],[2,2,2],[3]] => [7,4,5,6,1,2,3] => [6,1,2,7,4,5,3] => [7,3,2,1,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,1,1],[2,2,3],[3]] => [6,4,5,7,1,2,3] => [7,1,2,6,4,5,3] => [6,5,4,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,1,1],[2,3,3],[3]] => [5,4,6,7,1,2,3] => [7,1,2,5,4,6,3] => [5,4,6,7,3,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[1,1,2],[2,2,3],[3]] => [6,3,4,7,1,2,5] => [7,1,6,3,2,4,5] => [6,4,3,7,5,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,1,2],[2,3,3],[3]] => [5,3,6,7,1,2,4] => [7,1,5,2,3,6,4] => [5,3,6,7,4,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[1,2,2],[2,3,3],[3]] => [5,2,6,7,1,3,4] => [7,5,1,3,2,6,4] => [5,2,6,7,4,3,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[1,1,1],[2,2],[3,3]] => [6,7,4,5,1,2,3] => [5,1,2,7,4,6,3] => [6,7,3,2,1,5,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,1,2],[2,2],[3,3]] => [6,7,3,4,1,2,5] => [4,1,7,3,2,6,5] => [6,7,5,2,1,4,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,1,3],[2,2],[3,3]] => [5,6,3,4,1,2,7] => [4,1,6,3,5,2,7] => [5,6,2,1,4,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[2,2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1,1,1],[2]] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,1,1,1,1,1,2],[2]] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6,8] => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,1,1,1,1,2,2],[2]] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7,8] => [6,5,4,3,2,1,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[1,1,1,1,2,2,2],[2]] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7,8] => [5,4,3,2,1,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[1,1,1,2,2,2,2],[2]] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => [4,3,2,1,5,6,7,8] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[1,1,2,2,2,2,2],[2]] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,2,2,2,2,2],[2]] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1,1],[2,2]] => [7,8,1,2,3,4,5,6] => [8,1,2,3,4,5,7,6] => [7,8,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[1,1,1,1,1,2],[2,2]] => [6,7,1,2,3,4,5,8] => [7,1,2,3,4,6,5,8] => [6,7,5,4,3,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[1,1,1,1,2,2],[2,2]] => [5,6,1,2,3,4,7,8] => [6,1,2,3,5,4,7,8] => [5,6,4,3,2,1,7,8] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[1,1,1,2,2,2],[2,2]] => [4,5,1,2,3,6,7,8] => [5,1,2,4,3,6,7,8] => [4,5,3,2,1,6,7,8] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[1,1,2,2,2,2],[2,2]] => [3,4,1,2,5,6,7,8] => [4,1,3,2,5,6,7,8] => [3,4,2,1,5,6,7,8] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,1,1,1,1],[2,2,2]] => [6,7,8,1,2,3,4,5] => [8,1,2,3,4,6,7,5] => [6,7,8,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[1,1,1,1,2],[2,2,2]] => [5,6,7,1,2,3,4,8] => [7,1,2,3,5,6,4,8] => [5,6,7,4,3,2,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[1,1,1,2,2],[2,2,2]] => [4,5,6,1,2,3,7,8] => [6,1,2,4,5,3,7,8] => [4,5,6,3,2,1,7,8] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[1,1,1,1],[2,2,2,2]] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => [5,6,7,8,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[1]] => [1] => [1] => [1] => [1,0]
[[1,1,2,3],[2,2,3],[3,3],[4]] => [10,6,7,3,4,8,1,2,5,9] => [8,1,7,3,2,10,6,4,5,9] => [10,9,5,2,1,8,4,3,7,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[[1,1,2,3],[2,3,4],[3,4],[4]] => [8,5,9,3,6,10,1,2,4,7] => [10,1,9,2,8,3,4,5,6,7] => [8,5,9,6,3,10,7,4,2,1] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[[2]] => [1] => [1] => [1] => [1,0]
[[1,1]] => [1,2] => [1,2] => [1,2] => [1,0,1,0]
[[3]] => [1] => [1] => [1] => [1,0]
[[1,1,1]] => [1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
[[4]] => [1] => [1] => [1] => [1,0]
[[1,1,1,1]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
[[5]] => [1] => [1] => [1] => [1,0]
[[1,1,1,1,1]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
[[6]] => [1] => [1] => [1] => [1,0]
[[1,1,1,1,1,1]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [4,1,2,5,6,3] => [6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0]
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0]
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [5,1,6,2,3,4] => [6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [6,1,4,3,2,5] => [4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0]
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [3,1,4,6,2,5] => [6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [3,1,4,5,2,6] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [3,1,4,5,6,2] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [5,6,1,3,2,4] => [6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0]
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [6,2,1,4,3,5] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0]
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [4,6,1,2,3,5] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0]
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [4,5,1,2,3,6] => [5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [4,5,1,2,6,3] => [6,3,1,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [2,5,1,3,6,4] => [6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [6,4,1,2,3,5] => [4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0]
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [2,4,1,6,3,5] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
[[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => [2,4,1,5,3,6] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0]
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [4,1,5,3,6,2] => [6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0]
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [6,3,2,1,4,5] => [3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0]
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [5,3,2,1,4,6] => [3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [5,6,3,1,2,4] => [3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [5,3,6,1,2,4] => [6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [2,3,6,1,4,5] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [2,3,5,1,4,6] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [2,3,5,1,6,4] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [5,1,4,6,3,2] => [6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => [4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0]
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [5,6,1,4,2,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [5,4,1,6,2,3] => [6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [5,1,6,4,3,2] => [4,6,2,1,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0]
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [6,3,4,2,1,5] => [4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0]
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [2,3,4,6,1,5] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [6,1,4,5,3,2] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0]
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [4,6,1,2,5,3] => [5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [6,4,1,5,2,3] => [5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0]
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0]
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [6,3,5,1,2,4] => [5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0]
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
[[1,1,1,1,2,2,2],[3,3],[4]] => [10,8,9,1,2,3,4,5,6,7] => [9,1,2,3,4,5,6,10,8,7] => [10,7,6,5,4,3,2,1,9,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[[1,1,1,2,2,2,2],[3,3],[4]] => [10,8,9,1,2,3,4,5,6,7] => [9,1,2,3,4,5,6,10,8,7] => [10,7,6,5,4,3,2,1,9,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[[1,1,1,1,2,2,3],[3,4],[4]] => [9,7,10,1,2,3,4,5,6,8] => [10,1,2,3,4,5,9,6,7,8] => [9,7,10,8,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[[1,1,1,2,2,2,3],[3,4],[4]] => [9,7,10,1,2,3,4,5,6,8] => [10,1,2,3,4,5,9,6,7,8] => [9,7,10,8,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[[1,1,2,2,2,2,3],[3,4],[4]] => [9,7,10,1,2,3,4,5,6,8] => [10,1,2,3,4,5,9,6,7,8] => [9,7,10,8,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
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
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
searching the database
Sorry, this map was not found in the database.