Identifier
-
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
St000054: Permutations ⟶ ℤ
Values
[[1]] => [1] => [1] => [1] => 1
[[1,2]] => [1,2] => [1,2] => [1,2] => 1
[[1],[2]] => [2,1] => [2,1] => [2,1] => 2
[[1,2,3]] => [1,2,3] => [1,2,3] => [1,3,2] => 1
[[1,3],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[[1,2],[3]] => [3,1,2] => [1,3,2] => [1,3,2] => 1
[[1],[2],[3]] => [3,2,1] => [3,2,1] => [3,2,1] => 3
[[1,2,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 1
[[1,3,4],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,4,3] => 2
[[1,2,4],[3]] => [3,1,2,4] => [1,3,2,4] => [1,4,3,2] => 1
[[1,2,3],[4]] => [4,1,2,3] => [1,2,4,3] => [1,4,3,2] => 1
[[1,3],[2,4]] => [2,4,1,3] => [2,1,4,3] => [2,1,4,3] => 2
[[1,2],[3,4]] => [3,4,1,2] => [1,3,4,2] => [1,4,3,2] => 1
[[1,4],[2],[3]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 3
[[1,3],[2],[4]] => [4,2,1,3] => [2,4,1,3] => [2,4,1,3] => 2
[[1,2],[3],[4]] => [4,3,1,2] => [1,4,3,2] => [1,4,3,2] => 1
[[1],[2],[3],[4]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 4
[[1,2,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => 1
[[1,3,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,5,4,3] => 2
[[1,2,4,5],[3]] => [3,1,2,4,5] => [1,3,2,4,5] => [1,5,4,3,2] => 1
[[1,2,3,5],[4]] => [4,1,2,3,5] => [1,2,4,3,5] => [1,5,4,3,2] => 1
[[1,2,3,4],[5]] => [5,1,2,3,4] => [1,2,3,5,4] => [1,5,4,3,2] => 1
[[1,3,5],[2,4]] => [2,4,1,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => 2
[[1,2,5],[3,4]] => [3,4,1,2,5] => [1,3,4,2,5] => [1,5,4,3,2] => 1
[[1,3,4],[2,5]] => [2,5,1,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => 2
[[1,2,4],[3,5]] => [3,5,1,2,4] => [1,3,2,5,4] => [1,5,4,3,2] => 1
[[1,2,3],[4,5]] => [4,5,1,2,3] => [1,2,4,5,3] => [1,5,4,3,2] => 1
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,5,4] => 3
[[1,3,5],[2],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => [2,5,1,4,3] => 2
[[1,2,5],[3],[4]] => [4,3,1,2,5] => [1,4,3,2,5] => [1,5,4,3,2] => 1
[[1,3,4],[2],[5]] => [5,2,1,3,4] => [2,1,5,3,4] => [2,1,5,4,3] => 2
[[1,2,4],[3],[5]] => [5,3,1,2,4] => [1,3,5,2,4] => [1,5,4,3,2] => 1
[[1,2,3],[4],[5]] => [5,4,1,2,3] => [1,2,5,4,3] => [1,5,4,3,2] => 1
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [3,2,1,5,4] => [3,2,1,5,4] => 3
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [2,4,1,5,3] => [2,5,1,4,3] => 2
[[1,2],[3,5],[4]] => [4,3,5,1,2] => [1,4,3,5,2] => [1,5,4,3,2] => 1
[[1,3],[2,4],[5]] => [5,2,4,1,3] => [2,1,5,4,3] => [2,1,5,4,3] => 2
[[1,2],[3,4],[5]] => [5,3,4,1,2] => [1,3,5,4,2] => [1,5,4,3,2] => 1
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 4
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [3,5,2,1,4] => [3,5,2,1,4] => 3
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => 2
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 5
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 1
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,6,5,4,3] => 2
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => [1,6,5,4,3,2] => 1
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [1,2,4,3,5,6] => [1,6,5,4,3,2] => 1
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [1,2,3,5,4,6] => [1,6,5,4,3,2] => 1
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [1,2,3,4,6,5] => [1,6,5,4,3,2] => 1
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 2
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [1,3,4,2,5,6] => [1,6,5,4,3,2] => 1
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 2
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [1,3,2,5,4,6] => [1,6,5,4,3,2] => 1
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => [1,2,4,5,3,6] => [1,6,5,4,3,2] => 1
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 2
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [1,3,2,4,6,5] => [1,6,5,4,3,2] => 1
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [1,2,4,3,6,5] => [1,6,5,4,3,2] => 1
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [1,2,3,5,6,4] => [1,6,5,4,3,2] => 1
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,6,5,4] => 3
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 2
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [1,4,3,2,5,6] => [1,6,5,4,3,2] => 1
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 2
[[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [1,3,5,2,4,6] => [1,6,5,4,3,2] => 1
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [1,2,5,4,3,6] => [1,6,5,4,3,2] => 1
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 2
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [1,3,2,6,4,5] => [1,6,5,4,3,2] => 1
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [1,2,4,6,3,5] => [1,6,5,4,3,2] => 1
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [1,2,3,6,5,4] => [1,6,5,4,3,2] => 1
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 2
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [1,3,4,2,6,5] => [1,6,5,4,3,2] => 1
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 2
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [1,3,2,5,6,4] => [1,6,5,4,3,2] => 1
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [1,2,4,5,6,3] => [1,6,5,4,3,2] => 1
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [3,2,1,5,4,6] => [3,2,1,6,5,4] => 3
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [2,6,1,5,4,3] => 2
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [1,4,3,5,2,6] => [1,6,5,4,3,2] => 1
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [2,1,5,4,3,6] => [2,1,6,5,4,3] => 2
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => [1,3,5,4,2,6] => [1,6,5,4,3,2] => 1
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [3,2,1,4,6,5] => [3,2,1,6,5,4] => 3
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [2,4,1,3,6,5] => [2,6,1,5,4,3] => 2
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [1,4,3,2,6,5] => [1,6,5,4,3,2] => 1
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [2,1,5,3,6,4] => [2,1,6,5,4,3] => 2
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [1,3,5,2,6,4] => [1,6,5,4,3,2] => 1
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [1,2,5,4,6,3] => [1,6,5,4,3,2] => 1
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [2,1,4,6,3,5] => [2,1,6,5,4,3] => 2
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [1,3,4,6,2,5] => [1,6,5,4,3,2] => 1
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [2,1,3,6,5,4] => [2,1,6,5,4,3] => 2
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [1,3,2,6,5,4] => [1,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [1,2,4,6,5,3] => [1,6,5,4,3,2] => 1
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,6,5] => 4
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [3,5,2,1,4,6] => [3,6,2,1,5,4] => 3
[[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => [2,5,4,1,3,6] => [2,6,5,1,4,3] => 2
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [1,5,4,3,2,6] => [1,6,5,4,3,2] => 1
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [3,2,6,1,4,5] => [3,2,6,1,5,4] => 3
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 2
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [1,4,6,3,2,5] => [1,6,5,4,3,2] => 1
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [2,1,6,5,3,4] => [2,1,6,5,4,3] => 2
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [1,3,6,5,2,4] => [1,6,5,4,3,2] => 1
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [1,2,6,5,4,3] => [1,6,5,4,3,2] => 1
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 3
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [2,4,1,6,5,3] => [2,6,1,5,4,3] => 2
>>> Load all 967 entries. <<<[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [1,4,3,6,5,2] => [1,6,5,4,3,2] => 1
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [2,1,5,6,4,3] => [2,1,6,5,4,3] => 2
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [1,3,5,6,4,2] => [1,6,5,4,3,2] => 1
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [3,5,2,1,6,4] => [3,6,2,1,5,4] => 3
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [2,5,4,1,6,3] => [2,6,5,1,4,3] => 2
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [1,5,4,3,6,2] => [1,6,5,4,3,2] => 1
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [3,2,6,1,5,4] => [3,2,6,1,5,4] => 3
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [2,4,6,1,5,3] => [2,6,5,1,4,3] => 2
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [1,4,6,3,5,2] => [1,6,5,4,3,2] => 1
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [1,3,6,5,4,2] => [1,6,5,4,3,2] => 1
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 5
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [4,6,3,2,1,5] => [4,6,3,2,1,5] => 4
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [3,6,5,2,1,4] => [3,6,5,2,1,4] => 3
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [2,6,5,4,1,3] => [2,6,5,4,1,3] => 2
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 1
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 6
[[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,5,6,7],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,7,6,5,4,3] => 2
[[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [1,2,4,3,5,6,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [1,2,3,5,4,6,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [1,2,3,4,6,5,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => [1,7,6,5,4,3,2] => 1
[[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => [2,1,4,3,5,6,7] => [2,1,7,6,5,4,3] => 2
[[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => [1,3,4,2,5,6,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,6,7],[2,5]] => [2,5,1,3,4,6,7] => [2,1,3,5,4,6,7] => [2,1,7,6,5,4,3] => 2
[[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => [1,3,2,5,4,6,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,6,7],[4,5]] => [4,5,1,2,3,6,7] => [1,2,4,5,3,6,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,5,7],[2,6]] => [2,6,1,3,4,5,7] => [2,1,3,4,6,5,7] => [2,1,7,6,5,4,3] => 2
[[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => [1,3,2,4,6,5,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => [1,2,4,3,6,5,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => [1,2,3,5,6,4,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,5,6],[2,7]] => [2,7,1,3,4,5,6] => [2,1,3,4,5,7,6] => [2,1,7,6,5,4,3] => 2
[[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => [1,3,2,4,5,7,6] => [1,7,6,5,4,3,2] => 1
[[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => [1,2,4,3,5,7,6] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => [1,2,3,5,4,7,6] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [1,2,3,4,6,7,5] => [1,7,6,5,4,3,2] => 1
[[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => [1,4,3,2,5,6,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,6,7],[2],[5]] => [5,2,1,3,4,6,7] => [2,1,5,3,4,6,7] => [2,1,7,6,5,4,3] => 2
[[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => [1,3,5,2,4,6,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => [1,2,5,4,3,6,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,5,7],[2],[6]] => [6,2,1,3,4,5,7] => [2,1,3,6,4,5,7] => [2,1,7,6,5,4,3] => 2
[[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => [1,3,2,6,4,5,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => [1,2,4,6,3,5,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => [1,2,3,6,5,4,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,5,6],[2],[7]] => [7,2,1,3,4,5,6] => [2,1,3,4,7,5,6] => [2,1,7,6,5,4,3] => 2
[[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => [1,3,2,4,7,5,6] => [1,7,6,5,4,3,2] => 1
[[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => [1,2,4,3,7,5,6] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => [1,2,3,5,7,4,6] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [1,2,3,4,7,6,5] => [1,7,6,5,4,3,2] => 1
[[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [2,1,4,3,6,5,7] => [2,1,7,6,5,4,3] => 2
[[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => [1,3,4,2,6,5,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => [2,1,3,5,6,4,7] => [2,1,7,6,5,4,3] => 2
[[1,2,4,7],[3,5,6]] => [3,5,6,1,2,4,7] => [1,3,2,5,6,4,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,7],[4,5,6]] => [4,5,6,1,2,3,7] => [1,2,4,5,6,3,7] => [1,7,6,5,4,3,2] => 1
[[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => [2,1,4,3,5,7,6] => [2,1,7,6,5,4,3] => 2
[[1,2,5,6],[3,4,7]] => [3,4,7,1,2,5,6] => [1,3,4,2,5,7,6] => [1,7,6,5,4,3,2] => 1
[[1,3,4,6],[2,5,7]] => [2,5,7,1,3,4,6] => [2,1,3,5,4,7,6] => [2,1,7,6,5,4,3] => 2
[[1,2,4,6],[3,5,7]] => [3,5,7,1,2,4,6] => [1,3,2,5,4,7,6] => [1,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,5,7]] => [4,5,7,1,2,3,6] => [1,2,4,5,3,7,6] => [1,7,6,5,4,3,2] => 1
[[1,3,4,5],[2,6,7]] => [2,6,7,1,3,4,5] => [2,1,3,4,6,7,5] => [2,1,7,6,5,4,3] => 2
[[1,2,4,5],[3,6,7]] => [3,6,7,1,2,4,5] => [1,3,2,4,6,7,5] => [1,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,6,7]] => [4,6,7,1,2,3,5] => [1,2,4,3,6,7,5] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => [1,2,3,5,6,7,4] => [1,7,6,5,4,3,2] => 1
[[1,2,6,7],[3,5],[4]] => [4,3,5,1,2,6,7] => [1,4,3,5,2,6,7] => [1,7,6,5,4,3,2] => 1
[[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => [2,1,5,4,3,6,7] => [2,1,7,6,5,4,3] => 2
[[1,2,6,7],[3,4],[5]] => [5,3,4,1,2,6,7] => [1,3,5,4,2,6,7] => [1,7,6,5,4,3,2] => 1
[[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [1,4,3,2,6,5,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => [2,1,5,3,6,4,7] => [2,1,7,6,5,4,3] => 2
[[1,2,4,7],[3,6],[5]] => [5,3,6,1,2,4,7] => [1,3,5,2,6,4,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,7],[4,6],[5]] => [5,4,6,1,2,3,7] => [1,2,5,4,6,3,7] => [1,7,6,5,4,3,2] => 1
[[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => [2,1,4,6,3,5,7] => [2,1,7,6,5,4,3] => 2
[[1,2,5,7],[3,4],[6]] => [6,3,4,1,2,5,7] => [1,3,4,6,2,5,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,7],[2,5],[6]] => [6,2,5,1,3,4,7] => [2,1,3,6,5,4,7] => [2,1,7,6,5,4,3] => 2
[[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => [1,3,2,6,5,4,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,7],[4,5],[6]] => [6,4,5,1,2,3,7] => [1,2,4,6,5,3,7] => [1,7,6,5,4,3,2] => 1
[[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => [1,4,3,2,5,7,6] => [1,7,6,5,4,3,2] => 1
[[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => [2,1,5,3,4,7,6] => [2,1,7,6,5,4,3] => 2
[[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => [1,3,5,2,4,7,6] => [1,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => [1,2,5,4,3,7,6] => [1,7,6,5,4,3,2] => 1
[[1,3,4,5],[2,7],[6]] => [6,2,7,1,3,4,5] => [2,1,3,6,4,7,5] => [2,1,7,6,5,4,3] => 2
[[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => [1,3,2,6,4,7,5] => [1,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => [1,2,4,6,3,7,5] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => [1,2,3,6,5,7,4] => [1,7,6,5,4,3,2] => 1
[[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => [2,1,4,3,7,5,6] => [2,1,7,6,5,4,3] => 2
[[1,2,5,6],[3,4],[7]] => [7,3,4,1,2,5,6] => [1,3,4,2,7,5,6] => [1,7,6,5,4,3,2] => 1
[[1,3,4,6],[2,5],[7]] => [7,2,5,1,3,4,6] => [2,1,3,5,7,4,6] => [2,1,7,6,5,4,3] => 2
[[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => [1,3,2,5,7,4,6] => [1,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,5],[7]] => [7,4,5,1,2,3,6] => [1,2,4,5,7,3,6] => [1,7,6,5,4,3,2] => 1
[[1,3,4,5],[2,6],[7]] => [7,2,6,1,3,4,5] => [2,1,3,4,7,6,5] => [2,1,7,6,5,4,3] => 2
[[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => [1,3,2,4,7,6,5] => [1,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => [1,2,4,3,7,6,5] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [1,2,3,5,7,6,4] => [1,7,6,5,4,3,2] => 1
[[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => [1,5,4,3,2,6,7] => [1,7,6,5,4,3,2] => 1
[[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => [1,4,6,3,2,5,7] => [1,7,6,5,4,3,2] => 1
[[1,3,4,7],[2],[5],[6]] => [6,5,2,1,3,4,7] => [2,1,6,5,3,4,7] => [2,1,7,6,5,4,3] => 2
[[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => [1,3,6,5,2,4,7] => [1,7,6,5,4,3,2] => 1
[[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => [1,2,6,5,4,3,7] => [1,7,6,5,4,3,2] => 1
[[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => [1,4,3,7,2,5,6] => [1,7,6,5,4,3,2] => 1
[[1,3,4,6],[2],[5],[7]] => [7,5,2,1,3,4,6] => [2,1,5,7,3,4,6] => [2,1,7,6,5,4,3] => 2
[[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => [1,3,5,7,2,4,6] => [1,7,6,5,4,3,2] => 1
[[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => [1,2,5,7,4,3,6] => [1,7,6,5,4,3,2] => 1
[[1,3,4,5],[2],[6],[7]] => [7,6,2,1,3,4,5] => [2,1,3,7,6,4,5] => [2,1,7,6,5,4,3] => 2
[[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => [1,3,2,7,6,4,5] => [1,7,6,5,4,3,2] => 1
[[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => [1,2,4,7,6,3,5] => [1,7,6,5,4,3,2] => 1
[[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => [1,7,6,5,4,3,2] => 1
[[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => [1,4,3,5,2,7,6] => [1,7,6,5,4,3,2] => 1
[[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => [2,1,5,4,3,7,6] => [2,1,7,6,5,4,3] => 2
[[1,2,6],[3,4,7],[5]] => [5,3,4,7,1,2,6] => [1,3,5,4,2,7,6] => [1,7,6,5,4,3,2] => 1
[[1,2,5],[3,6,7],[4]] => [4,3,6,7,1,2,5] => [1,4,3,2,6,7,5] => [1,7,6,5,4,3,2] => 1
[[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [2,1,5,3,6,7,4] => [2,1,7,6,5,4,3] => 2
[[1,2,4],[3,6,7],[5]] => [5,3,6,7,1,2,4] => [1,3,5,2,6,7,4] => [1,7,6,5,4,3,2] => 1
[[1,2,3],[4,6,7],[5]] => [5,4,6,7,1,2,3] => [1,2,5,4,6,7,3] => [1,7,6,5,4,3,2] => 1
[[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => [2,1,4,6,3,7,5] => [2,1,7,6,5,4,3] => 2
[[1,2,5],[3,4,7],[6]] => [6,3,4,7,1,2,5] => [1,3,4,6,2,7,5] => [1,7,6,5,4,3,2] => 1
[[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => [2,1,3,6,5,7,4] => [2,1,7,6,5,4,3] => 2
[[1,2,4],[3,5,7],[6]] => [6,3,5,7,1,2,4] => [1,3,2,6,5,7,4] => [1,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,7],[6]] => [6,4,5,7,1,2,3] => [1,2,4,6,5,7,3] => [1,7,6,5,4,3,2] => 1
[[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => [2,1,4,3,7,6,5] => [2,1,7,6,5,4,3] => 2
[[1,2,5],[3,4,6],[7]] => [7,3,4,6,1,2,5] => [1,3,4,2,7,6,5] => [1,7,6,5,4,3,2] => 1
[[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => [2,1,3,5,7,6,4] => [2,1,7,6,5,4,3] => 2
[[1,2,4],[3,5,6],[7]] => [7,3,5,6,1,2,4] => [1,3,2,5,7,6,4] => [1,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => [1,2,4,5,7,6,3] => [1,7,6,5,4,3,2] => 1
[[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => [1,4,3,6,5,2,7] => [1,7,6,5,4,3,2] => 1
[[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [2,1,5,6,4,3,7] => [2,1,7,6,5,4,3] => 2
[[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => [1,3,5,6,4,2,7] => [1,7,6,5,4,3,2] => 1
[[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => [1,4,3,5,7,2,6] => [1,7,6,5,4,3,2] => 1
[[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => [2,1,5,4,7,3,6] => [2,1,7,6,5,4,3] => 2
[[1,2,6],[3,4],[5,7]] => [5,7,3,4,1,2,6] => [1,3,5,4,7,2,6] => [1,7,6,5,4,3,2] => 1
[[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => [1,4,3,2,7,6,5] => [1,7,6,5,4,3,2] => 1
[[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => [2,1,5,3,7,6,4] => [2,1,7,6,5,4,3] => 2
[[1,2,4],[3,6],[5,7]] => [5,7,3,6,1,2,4] => [1,3,5,2,7,6,4] => [1,7,6,5,4,3,2] => 1
[[1,2,3],[4,6],[5,7]] => [5,7,4,6,1,2,3] => [1,2,5,4,7,6,3] => [1,7,6,5,4,3,2] => 1
[[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => [2,1,4,6,7,3,5] => [2,1,7,6,5,4,3] => 2
[[1,2,5],[3,4],[6,7]] => [6,7,3,4,1,2,5] => [1,3,4,6,7,2,5] => [1,7,6,5,4,3,2] => 1
[[1,3,4],[2,5],[6,7]] => [6,7,2,5,1,3,4] => [2,1,3,6,7,5,4] => [2,1,7,6,5,4,3] => 2
[[1,2,4],[3,5],[6,7]] => [6,7,3,5,1,2,4] => [1,3,2,6,7,5,4] => [1,7,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => [1,2,4,6,7,5,3] => [1,7,6,5,4,3,2] => 1
[[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => [1,5,4,3,6,2,7] => [1,7,6,5,4,3,2] => 1
[[1,2,7],[3,5],[4],[6]] => [6,4,3,5,1,2,7] => [1,4,6,3,5,2,7] => [1,7,6,5,4,3,2] => 1
[[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => [2,1,6,5,4,3,7] => [2,1,7,6,5,4,3] => 2
[[1,2,7],[3,4],[5],[6]] => [6,5,3,4,1,2,7] => [1,3,6,5,4,2,7] => [1,7,6,5,4,3,2] => 1
[[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [1,5,4,3,2,7,6] => [1,7,6,5,4,3,2] => 1
[[1,2,5],[3,7],[4],[6]] => [6,4,3,7,1,2,5] => [1,4,6,3,2,7,5] => [1,7,6,5,4,3,2] => 1
[[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [2,1,6,5,3,7,4] => [2,1,7,6,5,4,3] => 2
[[1,2,4],[3,7],[5],[6]] => [6,5,3,7,1,2,4] => [1,3,6,5,2,7,4] => [1,7,6,5,4,3,2] => 1
[[1,2,3],[4,7],[5],[6]] => [6,5,4,7,1,2,3] => [1,2,6,5,4,7,3] => [1,7,6,5,4,3,2] => 1
[[1,2,6],[3,5],[4],[7]] => [7,4,3,5,1,2,6] => [1,4,3,7,5,2,6] => [1,7,6,5,4,3,2] => 1
[[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => [2,1,5,7,4,3,6] => [2,1,7,6,5,4,3] => 2
[[1,2,6],[3,4],[5],[7]] => [7,5,3,4,1,2,6] => [1,3,5,7,4,2,6] => [1,7,6,5,4,3,2] => 1
[[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => [1,4,3,7,2,6,5] => [1,7,6,5,4,3,2] => 1
[[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => [2,1,5,7,3,6,4] => [2,1,7,6,5,4,3] => 2
[[1,2,4],[3,6],[5],[7]] => [7,5,3,6,1,2,4] => [1,3,5,7,2,6,4] => [1,7,6,5,4,3,2] => 1
[[1,2,3],[4,6],[5],[7]] => [7,5,4,6,1,2,3] => [1,2,5,7,4,6,3] => [1,7,6,5,4,3,2] => 1
[[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => [2,1,4,7,6,3,5] => [2,1,7,6,5,4,3] => 2
[[1,2,5],[3,4],[6],[7]] => [7,6,3,4,1,2,5] => [1,3,4,7,6,2,5] => [1,7,6,5,4,3,2] => 1
[[1,3,4],[2,5],[6],[7]] => [7,6,2,5,1,3,4] => [2,1,3,7,6,5,4] => [2,1,7,6,5,4,3] => 2
[[1,2,4],[3,5],[6],[7]] => [7,6,3,5,1,2,4] => [1,3,2,7,6,5,4] => [1,7,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => [1,2,4,7,6,5,3] => [1,7,6,5,4,3,2] => 1
[[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,7,6] => 5
[[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => [1,6,5,4,3,2,7] => [1,7,6,5,4,3,2] => 1
[[1,2,6],[3],[4],[5],[7]] => [7,5,4,3,1,2,6] => [1,5,7,4,3,2,6] => [1,7,6,5,4,3,2] => 1
[[1,2,5],[3],[4],[6],[7]] => [7,6,4,3,1,2,5] => [1,4,7,6,3,2,5] => [1,7,6,5,4,3,2] => 1
[[1,3,4],[2],[5],[6],[7]] => [7,6,5,2,1,3,4] => [2,1,7,6,5,3,4] => [2,1,7,6,5,4,3] => 2
[[1,2,4],[3],[5],[6],[7]] => [7,6,5,3,1,2,4] => [1,3,7,6,5,2,4] => [1,7,6,5,4,3,2] => 1
[[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [1,2,7,6,5,4,3] => [1,7,6,5,4,3,2] => 1
[[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [1,5,4,3,7,6,2] => [1,7,6,5,4,3,2] => 1
[[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => [1,4,6,3,7,5,2] => [1,7,6,5,4,3,2] => 1
[[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => [2,1,6,5,7,4,3] => [2,1,7,6,5,4,3] => 2
[[1,2],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2] => [1,3,6,5,7,4,2] => [1,7,6,5,4,3,2] => 1
[[1,2],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2] => [1,4,3,7,6,5,2] => [1,7,6,5,4,3,2] => 1
[[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => [2,1,5,7,6,4,3] => [2,1,7,6,5,4,3] => 2
[[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => [1,3,5,7,6,4,2] => [1,7,6,5,4,3,2] => 1
[[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 5
[[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => [1,6,5,4,3,7,2] => [1,7,6,5,4,3,2] => 1
[[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => [1,5,7,4,3,6,2] => [1,7,6,5,4,3,2] => 1
[[1,2],[3,5],[4],[6],[7]] => [7,6,4,3,5,1,2] => [1,4,7,6,3,5,2] => [1,7,6,5,4,3,2] => 1
[[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 2
[[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => [1,3,7,6,5,4,2] => [1,7,6,5,4,3,2] => 1
[[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 6
[[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 7
[[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,6,7,8],[2]] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => [1,2,3,4,6,5,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,7,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,6,7,8],[2,4]] => [2,4,1,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,6,7,8],[3,4]] => [3,4,1,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,6,7,8],[2,5]] => [2,5,1,3,4,6,7,8] => [2,1,3,5,4,6,7,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,6,7,8],[3,5]] => [3,5,1,2,4,6,7,8] => [1,3,2,5,4,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6,7,8],[4,5]] => [4,5,1,2,3,6,7,8] => [1,2,4,5,3,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,7,8],[2,6]] => [2,6,1,3,4,5,7,8] => [2,1,3,4,6,5,7,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5,7,8],[3,6]] => [3,6,1,2,4,5,7,8] => [1,3,2,4,6,5,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => [1,2,4,3,6,5,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,6,8],[2,7]] => [2,7,1,3,4,5,6,8] => [2,1,3,4,5,7,6,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [1,3,2,4,5,7,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => [1,2,4,3,5,7,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [1,2,3,5,4,7,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => [1,2,3,4,6,7,5,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,6,7],[2,8]] => [2,8,1,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => [1,3,2,4,5,6,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => [1,2,4,3,5,6,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => [1,2,3,5,4,6,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => [1,2,3,4,6,5,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,6,7,8],[2],[3]] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [3,2,1,8,7,6,5,4] => 3
[[1,2,5,6,7,8],[3],[4]] => [4,3,1,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,6,7,8],[2],[5]] => [5,2,1,3,4,6,7,8] => [2,1,5,3,4,6,7,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,6,7,8],[3],[5]] => [5,3,1,2,4,6,7,8] => [1,3,5,2,4,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6,7,8],[4],[5]] => [5,4,1,2,3,6,7,8] => [1,2,5,4,3,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,7,8],[2],[6]] => [6,2,1,3,4,5,7,8] => [2,1,3,6,4,5,7,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,5,7,8],[4],[6]] => [6,4,1,2,3,5,7,8] => [1,2,4,6,3,5,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,6,8],[2],[7]] => [7,2,1,3,4,5,6,8] => [2,1,3,4,7,5,6,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => [1,2,4,3,7,5,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6,8],[5],[7]] => [7,5,1,2,3,4,6,8] => [1,2,3,5,7,4,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => [1,2,3,4,7,6,5,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,6,7],[2],[8]] => [8,2,1,3,4,5,6,7] => [2,1,3,4,5,8,6,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [1,3,2,4,5,8,6,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => [1,2,4,3,5,8,6,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => [1,2,3,5,4,8,6,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => [1,2,3,4,6,8,5,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,8,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,7,8],[2,4,6]] => [2,4,6,1,3,5,7,8] => [2,1,4,3,6,5,7,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,7,8],[4,5,6]] => [4,5,6,1,2,3,7,8] => [1,2,4,5,6,3,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,6,8],[3,5,7]] => [3,5,7,1,2,4,6,8] => [1,3,2,5,4,7,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6,8],[4,5,7]] => [4,5,7,1,2,3,6,8] => [1,2,4,5,3,7,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,8],[2,6,7]] => [2,6,7,1,3,4,5,8] => [2,1,3,4,6,7,5,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5,8],[3,6,7]] => [3,6,7,1,2,4,5,8] => [1,3,2,4,6,7,5,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,8],[4,6,7]] => [4,6,7,1,2,3,5,8] => [1,2,4,3,6,7,5,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,8],[5,6,7]] => [5,6,7,1,2,3,4,8] => [1,2,3,5,6,7,4,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,6,7],[2,4,8]] => [2,4,8,1,3,5,6,7] => [2,1,4,3,5,6,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,6,7],[3,4,8]] => [3,4,8,1,2,5,6,7] => [1,3,4,2,5,6,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,6,7],[2,5,8]] => [2,5,8,1,3,4,6,7] => [2,1,3,5,4,6,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4,5,7],[2,6,8]] => [2,6,8,1,3,4,5,7] => [2,1,3,4,6,5,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,5,7],[4,6,8]] => [4,6,8,1,2,3,5,7] => [1,2,4,3,6,5,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,7],[5,6,8]] => [5,6,8,1,2,3,4,7] => [1,2,3,5,6,4,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,6],[2,7,8]] => [2,7,8,1,3,4,5,6] => [2,1,3,4,5,7,8,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5,6],[3,7,8]] => [3,7,8,1,2,4,5,6] => [1,3,2,4,5,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,6],[4,7,8]] => [4,7,8,1,2,3,5,6] => [1,2,4,3,5,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6],[5,7,8]] => [5,7,8,1,2,3,4,6] => [1,2,3,5,4,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => [1,2,3,4,6,7,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,4,6,7,8],[2,5],[3]] => [3,2,5,1,4,6,7,8] => [3,2,1,5,4,6,7,8] => [3,2,1,8,7,6,5,4] => 3
[[1,2,6,7,8],[3,5],[4]] => [4,3,5,1,2,6,7,8] => [1,4,3,5,2,6,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,6,7,8],[2,4],[5]] => [5,2,4,1,3,6,7,8] => [2,1,5,4,3,6,7,8] => [2,1,8,7,6,5,4,3] => 2
[[1,3,5,7,8],[2,4],[6]] => [6,2,4,1,3,5,7,8] => [2,1,4,6,3,5,7,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,7,8],[3,4],[6]] => [6,3,4,1,2,5,7,8] => [1,3,4,6,2,5,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,7,8],[4,5],[6]] => [6,4,5,1,2,3,7,8] => [1,2,4,6,5,3,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,6,8],[2,7],[3]] => [3,2,7,1,4,5,6,8] => [3,2,1,4,5,7,6,8] => [3,2,1,8,7,6,5,4] => 3
[[1,2,4,6,8],[3,7],[5]] => [5,3,7,1,2,4,6,8] => [1,3,5,2,4,7,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,5,8],[3,7],[6]] => [6,3,7,1,2,4,5,8] => [1,3,2,6,4,7,5,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [1,2,4,6,3,7,5,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [1,2,3,6,5,7,4,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => [1,3,2,5,7,4,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6,8],[4,5],[7]] => [7,4,5,1,2,3,6,8] => [1,2,4,5,7,3,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [1,2,3,5,7,6,4,8] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,6,7],[2,8],[3]] => [3,2,8,1,4,5,6,7] => [3,2,1,4,5,6,8,7] => [3,2,1,8,7,6,5,4] => 3
[[1,3,4,6,7],[2,8],[5]] => [5,2,8,1,3,4,6,7] => [2,1,5,3,4,6,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4,5,7],[2,8],[6]] => [6,2,8,1,3,4,5,7] => [2,1,3,6,4,5,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [1,2,4,6,3,5,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [1,2,3,6,5,4,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,6],[2,8],[7]] => [7,2,8,1,3,4,5,6] => [2,1,3,4,7,5,8,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,5,6],[4,8],[7]] => [7,4,8,1,2,3,5,6] => [1,2,4,3,7,5,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6],[5,8],[7]] => [7,5,8,1,2,3,4,6] => [1,2,3,5,7,4,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,8],[7]] => [7,6,8,1,2,3,4,5] => [1,2,3,4,7,6,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,6,7],[2,4],[8]] => [8,2,4,1,3,5,6,7] => [2,1,4,3,5,8,6,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,6,7],[3,4],[8]] => [8,3,4,1,2,5,6,7] => [1,3,4,2,5,8,6,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => [1,3,2,5,4,8,6,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6,7],[4,5],[8]] => [8,4,5,1,2,3,6,7] => [1,2,4,5,3,8,6,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,5,7],[3,6],[8]] => [8,3,6,1,2,4,5,7] => [1,3,2,4,6,8,5,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,7],[4,6],[8]] => [8,4,6,1,2,3,5,7] => [1,2,4,3,6,8,5,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => [1,2,3,5,6,8,4,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,6],[2,7],[8]] => [8,2,7,1,3,4,5,6] => [2,1,3,4,5,8,7,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => [1,3,2,4,5,8,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => [1,2,4,3,5,8,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => [1,2,3,5,4,8,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [1,2,3,4,6,8,7,5] => [1,8,7,6,5,4,3,2] => 1
[[1,5,6,7,8],[2],[3],[4]] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,3,2,1,8,7,6,5] => 4
[[1,2,3,7,8],[4],[5],[6]] => [6,5,4,1,2,3,7,8] => [1,2,6,5,4,3,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,6,8],[2],[3],[7]] => [7,3,2,1,4,5,6,8] => [3,2,1,7,4,5,6,8] => [3,2,1,8,7,6,5,4] => 3
[[1,3,4,6,8],[2],[5],[7]] => [7,5,2,1,3,4,6,8] => [2,1,5,7,3,4,6,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [1,3,5,7,2,4,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => [1,2,3,7,6,5,4,8] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,6,7],[2],[3],[8]] => [8,3,2,1,4,5,6,7] => [3,2,1,4,8,5,6,7] => [3,2,1,8,7,6,5,4] => 3
[[1,2,5,6,7],[3],[4],[8]] => [8,4,3,1,2,5,6,7] => [1,4,3,2,8,5,6,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,6,7],[2],[5],[8]] => [8,5,2,1,3,4,6,7] => [2,1,5,3,8,4,6,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,6,7],[4],[5],[8]] => [8,5,4,1,2,3,6,7] => [1,2,5,4,8,3,6,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5,7],[4],[6],[8]] => [8,6,4,1,2,3,5,7] => [1,2,4,6,8,3,5,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,7],[5],[6],[8]] => [8,6,5,1,2,3,4,7] => [1,2,3,6,8,5,4,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5,6],[2],[7],[8]] => [8,7,2,1,3,4,5,6] => [2,1,3,4,8,7,5,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,5,6],[4],[7],[8]] => [8,7,4,1,2,3,5,6] => [1,2,4,3,8,7,5,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6],[5],[7],[8]] => [8,7,5,1,2,3,4,6] => [1,2,3,5,8,7,4,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [1,2,3,4,8,7,6,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,7],[2,4,6,8]] => [2,4,6,8,1,3,5,7] => [2,1,4,3,6,5,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,7],[3,4,6,8]] => [3,4,6,8,1,2,5,7] => [1,3,4,2,6,5,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,7],[2,5,6,8]] => [2,5,6,8,1,3,4,7] => [2,1,3,5,6,4,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,7],[3,5,6,8]] => [3,5,6,8,1,2,4,7] => [1,3,2,5,6,4,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,7],[4,5,6,8]] => [4,5,6,8,1,2,3,7] => [1,2,4,5,6,3,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,6],[2,4,7,8]] => [2,4,7,8,1,3,5,6] => [2,1,4,3,5,7,8,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,6],[3,4,7,8]] => [3,4,7,8,1,2,5,6] => [1,3,4,2,5,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,6],[2,5,7,8]] => [2,5,7,8,1,3,4,6] => [2,1,3,5,4,7,8,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,6],[3,5,7,8]] => [3,5,7,8,1,2,4,6] => [1,3,2,5,4,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => [1,2,4,5,3,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5],[2,6,7,8]] => [2,6,7,8,1,3,4,5] => [2,1,3,4,6,7,8,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5],[3,6,7,8]] => [3,6,7,8,1,2,4,5] => [1,3,2,4,6,7,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,6,7,8]] => [4,6,7,8,1,2,3,5] => [1,2,4,3,6,7,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [1,2,3,5,6,7,8,4] => [1,8,7,6,5,4,3,2] => 1
[[1,4,6,8],[2,5,7],[3]] => [3,2,5,7,1,4,6,8] => [3,2,1,5,4,7,6,8] => [3,2,1,8,7,6,5,4] => 3
[[1,2,6,8],[3,5,7],[4]] => [4,3,5,7,1,2,6,8] => [1,4,3,5,2,7,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,6,8],[2,4,7],[5]] => [5,2,4,7,1,3,6,8] => [2,1,5,4,3,7,6,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,6,8],[3,4,7],[5]] => [5,3,4,7,1,2,6,8] => [1,3,5,4,2,7,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,5,8],[3,6,7],[4]] => [4,3,6,7,1,2,5,8] => [1,4,3,2,6,7,5,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,8],[2,6,7],[5]] => [5,2,6,7,1,3,4,8] => [2,1,5,3,6,7,4,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,8],[3,6,7],[5]] => [5,3,6,7,1,2,4,8] => [1,3,5,2,6,7,4,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,8],[4,6,7],[5]] => [5,4,6,7,1,2,3,8] => [1,2,5,4,6,7,3,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,8],[2,4,7],[6]] => [6,2,4,7,1,3,5,8] => [2,1,4,6,3,7,5,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,8],[3,4,7],[6]] => [6,3,4,7,1,2,5,8] => [1,3,4,6,2,7,5,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,8],[3,5,7],[6]] => [6,3,5,7,1,2,4,8] => [1,3,2,6,5,7,4,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,8],[4,5,7],[6]] => [6,4,5,7,1,2,3,8] => [1,2,4,6,5,7,3,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,8],[3,5,6],[7]] => [7,3,5,6,1,2,4,8] => [1,3,2,5,7,6,4,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,6,7],[2,4,8],[5]] => [5,2,4,8,1,3,6,7] => [2,1,5,4,3,6,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,7],[3,6,8],[5]] => [5,3,6,8,1,2,4,7] => [1,3,5,2,6,4,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,7],[2,4,8],[6]] => [6,2,4,8,1,3,5,7] => [2,1,4,6,3,5,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,7],[3,4,8],[6]] => [6,3,4,8,1,2,5,7] => [1,3,4,6,2,5,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,7],[2,5,8],[6]] => [6,2,5,8,1,3,4,7] => [2,1,3,6,5,4,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,7],[3,5,8],[6]] => [6,3,5,8,1,2,4,7] => [1,3,2,6,5,4,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,6],[2,7,8],[3]] => [3,2,7,8,1,4,5,6] => [3,2,1,4,5,7,8,6] => [3,2,1,8,7,6,5,4] => 3
[[1,2,5,6],[3,7,8],[4]] => [4,3,7,8,1,2,5,6] => [1,4,3,2,5,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,6],[3,7,8],[5]] => [5,3,7,8,1,2,4,6] => [1,3,5,2,4,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,7,8],[5]] => [5,4,7,8,1,2,3,6] => [1,2,5,4,3,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,5],[3,7,8],[6]] => [6,3,7,8,1,2,4,5] => [1,3,2,6,4,7,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,7,8],[6]] => [6,4,7,8,1,2,3,5] => [1,2,4,6,3,7,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,7,8],[6]] => [6,5,7,8,1,2,3,4] => [1,2,3,6,5,7,8,4] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,6],[2,4,8],[7]] => [7,2,4,8,1,3,5,6] => [2,1,4,3,7,5,8,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,6],[3,4,8],[7]] => [7,3,4,8,1,2,5,6] => [1,3,4,2,7,5,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,6],[3,5,8],[7]] => [7,3,5,8,1,2,4,6] => [1,3,2,5,7,4,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,5,8],[7]] => [7,4,5,8,1,2,3,6] => [1,2,4,5,7,3,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5],[2,6,8],[7]] => [7,2,6,8,1,3,4,5] => [2,1,3,4,7,6,8,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5],[3,6,8],[7]] => [7,3,6,8,1,2,4,5] => [1,3,2,4,7,6,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,6,8],[7]] => [7,4,6,8,1,2,3,5] => [1,2,4,3,7,6,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,8],[7]] => [7,5,6,8,1,2,3,4] => [1,2,3,5,7,6,8,4] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,7],[2,4,6],[8]] => [8,2,4,6,1,3,5,7] => [2,1,4,3,6,8,5,7] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4,7],[2,5,6],[8]] => [8,2,5,6,1,3,4,7] => [2,1,3,5,6,8,4,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,7],[4,5,6],[8]] => [8,4,5,6,1,2,3,7] => [1,2,4,5,6,8,3,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,6],[2,4,7],[8]] => [8,2,4,7,1,3,5,6] => [2,1,4,3,5,8,7,6] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4,6],[2,5,7],[8]] => [8,2,5,7,1,3,4,6] => [2,1,3,5,4,8,7,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,6],[3,5,7],[8]] => [8,3,5,7,1,2,4,6] => [1,3,2,5,4,8,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,5,7],[8]] => [8,4,5,7,1,2,3,6] => [1,2,4,5,3,8,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,5],[3,6,7],[8]] => [8,3,6,7,1,2,4,5] => [1,3,2,4,6,8,7,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,6,7],[8]] => [8,4,6,7,1,2,3,5] => [1,2,4,3,6,8,7,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => [1,2,3,5,6,8,7,4] => [1,8,7,6,5,4,3,2] => 1
[[1,4,7,8],[2,5],[3,6]] => [3,6,2,5,1,4,7,8] => [3,2,1,6,5,4,7,8] => [3,2,1,8,7,6,5,4] => 3
[[1,2,7,8],[3,5],[4,6]] => [4,6,3,5,1,2,7,8] => [1,4,3,6,5,2,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,7,8],[2,4],[5,6]] => [5,6,2,4,1,3,7,8] => [2,1,5,6,4,3,7,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,7,8],[3,4],[5,6]] => [5,6,3,4,1,2,7,8] => [1,3,5,6,4,2,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,4,6,8],[2,5],[3,7]] => [3,7,2,5,1,4,6,8] => [3,2,1,5,7,4,6,8] => [3,2,1,8,7,6,5,4] => 3
[[1,2,6,8],[3,4],[5,7]] => [5,7,3,4,1,2,6,8] => [1,3,5,4,7,2,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,8],[2,6],[3,7]] => [3,7,2,6,1,4,5,8] => [3,2,1,4,7,6,5,8] => [3,2,1,8,7,6,5,4] => 3
[[1,2,5,8],[3,6],[4,7]] => [4,7,3,6,1,2,5,8] => [1,4,3,2,7,6,5,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,8],[3,6],[5,7]] => [5,7,3,6,1,2,4,8] => [1,3,5,2,7,6,4,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,8],[2,4],[6,7]] => [6,7,2,4,1,3,5,8] => [2,1,4,6,7,3,5,8] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4,8],[2,5],[6,7]] => [6,7,2,5,1,3,4,8] => [2,1,3,6,7,5,4,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,8],[4,5],[6,7]] => [6,7,4,5,1,2,3,8] => [1,2,4,6,7,5,3,8] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,7],[2,6],[3,8]] => [3,8,2,6,1,4,5,7] => [3,2,1,4,6,8,5,7] => [3,2,1,8,7,6,5,4] => 3
[[1,3,4,7],[2,6],[5,8]] => [5,8,2,6,1,3,4,7] => [2,1,5,3,6,8,4,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,7],[3,6],[5,8]] => [5,8,3,6,1,2,4,7] => [1,3,5,2,6,8,4,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,7],[2,4],[6,8]] => [6,8,2,4,1,3,5,7] => [2,1,4,6,3,8,5,7] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4,7],[2,5],[6,8]] => [6,8,2,5,1,3,4,7] => [2,1,3,6,5,8,4,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,7],[3,5],[6,8]] => [6,8,3,5,1,2,4,7] => [1,3,2,6,5,8,4,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,7],[4,5],[6,8]] => [6,8,4,5,1,2,3,7] => [1,2,4,6,5,8,3,7] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,6],[2,7],[3,8]] => [3,8,2,7,1,4,5,6] => [3,2,1,4,5,8,7,6] => [3,2,1,8,7,6,5,4] => 3
[[1,2,5,6],[3,7],[4,8]] => [4,8,3,7,1,2,5,6] => [1,4,3,2,5,8,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,6],[3,7],[5,8]] => [5,8,3,7,1,2,4,6] => [1,3,5,2,4,8,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,7],[5,8]] => [5,8,4,7,1,2,3,6] => [1,2,5,4,3,8,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5],[2,7],[6,8]] => [6,8,2,7,1,3,4,5] => [2,1,3,6,4,8,7,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5],[3,7],[6,8]] => [6,8,3,7,1,2,4,5] => [1,3,2,6,4,8,7,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,7],[6,8]] => [6,8,4,7,1,2,3,5] => [1,2,4,6,3,8,7,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,7],[6,8]] => [6,8,5,7,1,2,3,4] => [1,2,3,6,5,8,7,4] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,6],[2,4],[7,8]] => [7,8,2,4,1,3,5,6] => [2,1,4,3,7,8,5,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,6],[3,4],[7,8]] => [7,8,3,4,1,2,5,6] => [1,3,4,2,7,8,5,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4,6],[3,5],[7,8]] => [7,8,3,5,1,2,4,6] => [1,3,2,5,7,8,4,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,5],[7,8]] => [7,8,4,5,1,2,3,6] => [1,2,4,5,7,8,3,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5],[2,6],[7,8]] => [7,8,2,6,1,3,4,5] => [2,1,3,4,7,8,6,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,5],[4,6],[7,8]] => [7,8,4,6,1,2,3,5] => [1,2,4,3,7,8,6,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [1,2,3,5,7,8,6,4] => [1,8,7,6,5,4,3,2] => 1
[[1,5,7,8],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8] => [4,3,2,1,6,5,7,8] => [4,3,2,1,8,7,6,5] => 4
[[1,2,7,8],[3,6],[4],[5]] => [5,4,3,6,1,2,7,8] => [1,5,4,3,6,2,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,5,6,8],[2,7],[3],[4]] => [4,3,2,7,1,5,6,8] => [4,3,2,1,5,7,6,8] => [4,3,2,1,8,7,6,5] => 4
[[1,2,4,8],[3,7],[5],[6]] => [6,5,3,7,1,2,4,8] => [1,3,6,5,2,7,4,8] => [1,8,7,6,5,4,3,2] => 1
[[1,4,6,8],[2,5],[3],[7]] => [7,3,2,5,1,4,6,8] => [3,2,1,7,5,4,6,8] => [3,2,1,8,7,6,5,4] => 3
[[1,2,6,8],[3,4],[5],[7]] => [7,5,3,4,1,2,6,8] => [1,3,5,7,4,2,6,8] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,8],[2,6],[3],[7]] => [7,3,2,6,1,4,5,8] => [3,2,1,7,4,6,5,8] => [3,2,1,8,7,6,5,4] => 3
[[1,2,4,8],[3,6],[5],[7]] => [7,5,3,6,1,2,4,8] => [1,3,5,7,2,6,4,8] => [1,8,7,6,5,4,3,2] => 1
[[1,5,6,7],[2,8],[3],[4]] => [4,3,2,8,1,5,6,7] => [4,3,2,1,5,6,8,7] => [4,3,2,1,8,7,6,5] => 4
[[1,2,5,7],[3,8],[4],[6]] => [6,4,3,8,1,2,5,7] => [1,4,6,3,2,5,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,7],[2,8],[5],[6]] => [6,5,2,8,1,3,4,7] => [2,1,6,5,3,4,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,4,5,6],[2,8],[3],[7]] => [7,3,2,8,1,4,5,6] => [3,2,1,7,4,5,8,6] => [3,2,1,8,7,6,5,4] => 3
[[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => [1,4,3,7,2,5,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,6],[2,8],[5],[7]] => [7,5,2,8,1,3,4,6] => [2,1,5,7,3,4,8,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [1,3,5,7,2,4,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,8],[5],[7]] => [7,5,4,8,1,2,3,6] => [1,2,5,7,4,3,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,8],[6],[7]] => [7,6,4,8,1,2,3,5] => [1,2,4,7,6,3,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,8],[6],[7]] => [7,6,5,8,1,2,3,4] => [1,2,3,7,6,5,8,4] => [1,8,7,6,5,4,3,2] => 1
[[1,4,6,7],[2,5],[3],[8]] => [8,3,2,5,1,4,6,7] => [3,2,1,5,8,4,6,7] => [3,2,1,8,7,6,5,4] => 3
[[1,2,6,7],[3,5],[4],[8]] => [8,4,3,5,1,2,6,7] => [1,4,3,5,8,2,6,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,6,7],[2,4],[5],[8]] => [8,5,2,4,1,3,6,7] => [2,1,5,4,8,3,6,7] => [2,1,8,7,6,5,4,3] => 2
[[1,4,5,7],[2,6],[3],[8]] => [8,3,2,6,1,4,5,7] => [3,2,1,4,8,6,5,7] => [3,2,1,8,7,6,5,4] => 3
[[1,3,5,7],[2,4],[6],[8]] => [8,6,2,4,1,3,5,7] => [2,1,4,6,8,3,5,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5,7],[3,4],[6],[8]] => [8,6,3,4,1,2,5,7] => [1,3,4,6,8,2,5,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,7],[4,5],[6],[8]] => [8,6,4,5,1,2,3,7] => [1,2,4,6,8,5,3,7] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,6],[2,7],[3],[8]] => [8,3,2,7,1,4,5,6] => [3,2,1,4,8,5,7,6] => [3,2,1,8,7,6,5,4] => 3
[[1,3,4,6],[2,7],[5],[8]] => [8,5,2,7,1,3,4,6] => [2,1,5,3,8,4,7,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,6],[4,7],[5],[8]] => [8,5,4,7,1,2,3,6] => [1,2,5,4,8,3,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,7],[6],[8]] => [8,6,4,7,1,2,3,5] => [1,2,4,6,8,3,7,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,7],[6],[8]] => [8,6,5,7,1,2,3,4] => [1,2,3,6,8,5,7,4] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5,6],[2,4],[7],[8]] => [8,7,2,4,1,3,5,6] => [2,1,4,3,8,7,5,6] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4,6],[2,5],[7],[8]] => [8,7,2,5,1,3,4,6] => [2,1,3,5,8,7,4,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,6],[3,5],[7],[8]] => [8,7,3,5,1,2,4,6] => [1,3,2,5,8,7,4,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,5],[7],[8]] => [8,7,4,5,1,2,3,6] => [1,2,4,5,8,7,3,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5],[2,6],[7],[8]] => [8,7,2,6,1,3,4,5] => [2,1,3,4,8,7,6,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5],[3,6],[7],[8]] => [8,7,3,6,1,2,4,5] => [1,3,2,4,8,7,6,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,6],[7],[8]] => [8,7,4,6,1,2,3,5] => [1,2,4,3,8,7,6,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [1,2,3,5,8,7,6,4] => [1,8,7,6,5,4,3,2] => 1
[[1,6,7,8],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,8,7,6] => 5
[[1,2,7,8],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8] => [1,6,5,4,3,2,7,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,5,8],[3],[4],[6],[7]] => [7,6,4,3,1,2,5,8] => [1,4,7,6,3,2,5,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,8],[2],[5],[6],[7]] => [7,6,5,2,1,3,4,8] => [2,1,7,6,5,3,4,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => [1,2,7,6,5,4,3,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,6,7],[3],[4],[5],[8]] => [8,5,4,3,1,2,6,7] => [1,5,4,8,3,2,6,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,5,7],[3],[4],[6],[8]] => [8,6,4,3,1,2,5,7] => [1,4,6,8,3,2,5,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,7],[2],[5],[6],[8]] => [8,6,5,2,1,3,4,7] => [2,1,6,8,5,3,4,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,7],[3],[5],[6],[8]] => [8,6,5,3,1,2,4,7] => [1,3,6,8,5,2,4,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,7],[4],[5],[6],[8]] => [8,6,5,4,1,2,3,7] => [1,2,6,8,5,4,3,7] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5,6],[2],[3],[7],[8]] => [8,7,3,2,1,4,5,6] => [3,2,1,8,7,4,5,6] => [3,2,1,8,7,6,5,4] => 3
[[1,3,4,6],[2],[5],[7],[8]] => [8,7,5,2,1,3,4,6] => [2,1,5,8,7,3,4,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,6],[3],[5],[7],[8]] => [8,7,5,3,1,2,4,6] => [1,3,5,8,7,2,4,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,6],[4],[5],[7],[8]] => [8,7,5,4,1,2,3,6] => [1,2,5,8,7,4,3,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4,5],[2],[6],[7],[8]] => [8,7,6,2,1,3,4,5] => [2,1,3,8,7,6,4,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4,5],[3],[6],[7],[8]] => [8,7,6,3,1,2,4,5] => [1,3,2,8,7,6,4,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,5],[4],[6],[7],[8]] => [8,7,6,4,1,2,3,5] => [1,2,4,8,7,6,3,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [1,2,3,8,7,6,5,4] => [1,8,7,6,5,4,3,2] => 1
[[1,4,7],[2,5,8],[3,6]] => [3,6,2,5,8,1,4,7] => [3,2,1,6,5,4,8,7] => [3,2,1,8,7,6,5,4] => 3
[[1,3,7],[2,4,8],[5,6]] => [5,6,2,4,8,1,3,7] => [2,1,5,6,4,3,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,3,6],[2,4,8],[5,7]] => [5,7,2,4,8,1,3,6] => [2,1,5,4,7,3,8,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,6],[3,4,8],[5,7]] => [5,7,3,4,8,1,2,6] => [1,3,5,4,7,2,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5],[2,6,8],[3,7]] => [3,7,2,6,8,1,4,5] => [3,2,1,4,7,6,8,5] => [3,2,1,8,7,6,5,4] => 3
[[1,2,5],[3,6,8],[4,7]] => [4,7,3,6,8,1,2,5] => [1,4,3,2,7,6,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4],[3,6,8],[5,7]] => [5,7,3,6,8,1,2,4] => [1,3,5,2,7,6,8,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,6,8],[5,7]] => [5,7,4,6,8,1,2,3] => [1,2,5,4,7,6,8,3] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5],[2,4,8],[6,7]] => [6,7,2,4,8,1,3,5] => [2,1,4,6,7,3,8,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5] => [1,3,4,6,7,2,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,6],[2,4,7],[5,8]] => [5,8,2,4,7,1,3,6] => [2,1,5,4,3,8,7,6] => [2,1,8,7,6,5,4,3] => 2
[[1,4,5],[2,6,7],[3,8]] => [3,8,2,6,7,1,4,5] => [3,2,1,4,6,8,7,5] => [3,2,1,8,7,6,5,4] => 3
[[1,2,5],[3,6,7],[4,8]] => [4,8,3,6,7,1,2,5] => [1,4,3,2,6,8,7,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4],[2,6,7],[5,8]] => [5,8,2,6,7,1,3,4] => [2,1,5,3,6,8,7,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3],[4,6,7],[5,8]] => [5,8,4,6,7,1,2,3] => [1,2,5,4,6,8,7,3] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5],[2,4,7],[6,8]] => [6,8,2,4,7,1,3,5] => [2,1,4,6,3,8,7,5] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4],[2,5,7],[6,8]] => [6,8,2,5,7,1,3,4] => [2,1,3,6,5,8,7,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4],[3,5,7],[6,8]] => [6,8,3,5,7,1,2,4] => [1,3,2,6,5,8,7,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,7],[6,8]] => [6,8,4,5,7,1,2,3] => [1,2,4,6,5,8,7,3] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5],[2,4,6],[7,8]] => [7,8,2,4,6,1,3,5] => [2,1,4,3,7,8,6,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5],[3,4,6],[7,8]] => [7,8,3,4,6,1,2,5] => [1,3,4,2,7,8,6,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4],[3,5,6],[7,8]] => [7,8,3,5,6,1,2,4] => [1,3,2,5,7,8,6,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => [1,2,4,5,7,8,6,3] => [1,8,7,6,5,4,3,2] => 1
[[1,5,7],[2,6,8],[3],[4]] => [4,3,2,6,8,1,5,7] => [4,3,2,1,6,5,8,7] => [4,3,2,1,8,7,6,5] => 4
[[1,3,7],[2,4,8],[5],[6]] => [6,5,2,4,8,1,3,7] => [2,1,6,5,4,3,8,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,7],[3,4,8],[5],[6]] => [6,5,3,4,8,1,2,7] => [1,3,6,5,4,2,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,5,6],[2,7,8],[3],[4]] => [4,3,2,7,8,1,5,6] => [4,3,2,1,5,7,8,6] => [4,3,2,1,8,7,6,5] => 4
[[1,2,6],[3,7,8],[4],[5]] => [5,4,3,7,8,1,2,6] => [1,5,4,3,2,7,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,5],[3,7,8],[4],[6]] => [6,4,3,7,8,1,2,5] => [1,4,6,3,2,7,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4],[2,7,8],[5],[6]] => [6,5,2,7,8,1,3,4] => [2,1,6,5,3,7,8,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4],[3,7,8],[5],[6]] => [6,5,3,7,8,1,2,4] => [1,3,6,5,2,7,8,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,7,8],[5],[6]] => [6,5,4,7,8,1,2,3] => [1,2,6,5,4,7,8,3] => [1,8,7,6,5,4,3,2] => 1
[[1,4,6],[2,5,8],[3],[7]] => [7,3,2,5,8,1,4,6] => [3,2,1,7,5,4,8,6] => [3,2,1,8,7,6,5,4] => 3
[[1,3,6],[2,4,8],[5],[7]] => [7,5,2,4,8,1,3,6] => [2,1,5,7,4,3,8,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,6],[3,4,8],[5],[7]] => [7,5,3,4,8,1,2,6] => [1,3,5,7,4,2,8,6] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5],[2,6,8],[3],[7]] => [7,3,2,6,8,1,4,5] => [3,2,1,7,4,6,8,5] => [3,2,1,8,7,6,5,4] => 3
[[1,3,4],[2,6,8],[5],[7]] => [7,5,2,6,8,1,3,4] => [2,1,5,7,3,6,8,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4],[3,6,8],[5],[7]] => [7,5,3,6,8,1,2,4] => [1,3,5,7,2,6,8,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,6,8],[5],[7]] => [7,5,4,6,8,1,2,3] => [1,2,5,7,4,6,8,3] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5],[2,4,8],[6],[7]] => [7,6,2,4,8,1,3,5] => [2,1,4,7,6,3,8,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5],[3,4,8],[6],[7]] => [7,6,3,4,8,1,2,5] => [1,3,4,7,6,2,8,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4],[3,5,8],[6],[7]] => [7,6,3,5,8,1,2,4] => [1,3,2,7,6,5,8,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,6],[3,5,7],[4],[8]] => [8,4,3,5,7,1,2,6] => [1,4,3,5,8,2,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,6],[2,4,7],[5],[8]] => [8,5,2,4,7,1,3,6] => [2,1,5,4,8,3,7,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,6],[3,4,7],[5],[8]] => [8,5,3,4,7,1,2,6] => [1,3,5,4,8,2,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,4,5],[2,6,7],[3],[8]] => [8,3,2,6,7,1,4,5] => [3,2,1,4,8,6,7,5] => [3,2,1,8,7,6,5,4] => 3
[[1,2,5],[3,6,7],[4],[8]] => [8,4,3,6,7,1,2,5] => [1,4,3,2,8,6,7,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4],[2,6,7],[5],[8]] => [8,5,2,6,7,1,3,4] => [2,1,5,3,8,6,7,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3],[4,6,7],[5],[8]] => [8,5,4,6,7,1,2,3] => [1,2,5,4,8,6,7,3] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5],[2,4,7],[6],[8]] => [8,6,2,4,7,1,3,5] => [2,1,4,6,8,3,7,5] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4],[2,5,7],[6],[8]] => [8,6,2,5,7,1,3,4] => [2,1,3,6,8,5,7,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3],[4,5,7],[6],[8]] => [8,6,4,5,7,1,2,3] => [1,2,4,6,8,5,7,3] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5],[2,4,6],[7],[8]] => [8,7,2,4,6,1,3,5] => [2,1,4,3,8,7,6,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5],[3,4,6],[7],[8]] => [8,7,3,4,6,1,2,5] => [1,3,4,2,8,7,6,5] => [1,8,7,6,5,4,3,2] => 1
[[1,2,4],[3,5,6],[7],[8]] => [8,7,3,5,6,1,2,4] => [1,3,2,5,8,7,6,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => [1,2,4,5,8,7,6,3] => [1,8,7,6,5,4,3,2] => 1
[[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [4,3,2,1,7,6,5,8] => [4,3,2,1,8,7,6,5] => 4
[[1,2,8],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2,8] => [1,4,6,3,7,5,2,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,8],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2,8] => [1,3,6,5,7,4,2,8] => [1,8,7,6,5,4,3,2] => 1
[[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [3,2,1,7,6,5,4,8] => [3,2,1,8,7,6,5,4] => 3
[[1,2,8],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2,8] => [1,3,5,7,6,4,2,8] => [1,8,7,6,5,4,3,2] => 1
[[1,5,7],[2,6],[3,8],[4]] => [4,3,8,2,6,1,5,7] => [4,3,2,1,6,8,5,7] => [4,3,2,1,8,7,6,5] => 4
[[1,2,7],[3,6],[4,8],[5]] => [5,4,8,3,6,1,2,7] => [1,5,4,3,6,8,2,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,7],[2,4],[5,8],[6]] => [6,5,8,2,4,1,3,7] => [2,1,6,5,4,8,3,7] => [2,1,8,7,6,5,4,3] => 2
[[1,5,6],[2,7],[3,8],[4]] => [4,3,8,2,7,1,5,6] => [4,3,2,1,5,8,7,6] => [4,3,2,1,8,7,6,5] => 4
[[1,2,6],[3,7],[4,8],[5]] => [5,4,8,3,7,1,2,6] => [1,5,4,3,2,8,7,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,5],[3,7],[4,8],[6]] => [6,4,8,3,7,1,2,5] => [1,4,6,3,2,8,7,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4],[2,7],[5,8],[6]] => [6,5,8,2,7,1,3,4] => [2,1,6,5,3,8,7,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3],[4,7],[5,8],[6]] => [6,5,8,4,7,1,2,3] => [1,2,6,5,4,8,7,3] => [1,8,7,6,5,4,3,2] => 1
[[1,4,6],[2,5],[3,8],[7]] => [7,3,8,2,5,1,4,6] => [3,2,1,7,5,8,4,6] => [3,2,1,8,7,6,5,4] => 3
[[1,2,6],[3,5],[4,8],[7]] => [7,4,8,3,5,1,2,6] => [1,4,3,7,5,8,2,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,6],[2,4],[5,8],[7]] => [7,5,8,2,4,1,3,6] => [2,1,5,7,4,8,3,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,6],[3,4],[5,8],[7]] => [7,5,8,3,4,1,2,6] => [1,3,5,7,4,8,2,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,5],[3,6],[4,8],[7]] => [7,4,8,3,6,1,2,5] => [1,4,3,7,2,8,6,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4],[2,6],[5,8],[7]] => [7,5,8,2,6,1,3,4] => [2,1,5,7,3,8,6,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4],[3,6],[5,8],[7]] => [7,5,8,3,6,1,2,4] => [1,3,5,7,2,8,6,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,6],[5,8],[7]] => [7,5,8,4,6,1,2,3] => [1,2,5,7,4,8,6,3] => [1,8,7,6,5,4,3,2] => 1
[[1,2,5],[3,4],[6,8],[7]] => [7,6,8,3,4,1,2,5] => [1,3,4,7,6,8,2,5] => [1,8,7,6,5,4,3,2] => 1
[[1,4,7],[2,5],[3,6],[8]] => [8,3,6,2,5,1,4,7] => [3,2,1,6,8,5,4,7] => [3,2,1,8,7,6,5,4] => 3
[[1,2,7],[3,5],[4,6],[8]] => [8,4,6,3,5,1,2,7] => [1,4,3,6,8,5,2,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,7],[2,4],[5,6],[8]] => [8,5,6,2,4,1,3,7] => [2,1,5,6,8,4,3,7] => [2,1,8,7,6,5,4,3] => 2
[[1,2,7],[3,4],[5,6],[8]] => [8,5,6,3,4,1,2,7] => [1,3,5,6,8,4,2,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,6],[2,4],[5,7],[8]] => [8,5,7,2,4,1,3,6] => [2,1,5,4,8,7,3,6] => [2,1,8,7,6,5,4,3] => 2
[[1,2,6],[3,4],[5,7],[8]] => [8,5,7,3,4,1,2,6] => [1,3,5,4,8,7,2,6] => [1,8,7,6,5,4,3,2] => 1
[[1,2,5],[3,6],[4,7],[8]] => [8,4,7,3,6,1,2,5] => [1,4,3,2,8,7,6,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4],[2,6],[5,7],[8]] => [8,5,7,2,6,1,3,4] => [2,1,5,3,8,7,6,4] => [2,1,8,7,6,5,4,3] => 2
[[1,3,5],[2,4],[6,7],[8]] => [8,6,7,2,4,1,3,5] => [2,1,4,6,8,7,3,5] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4],[2,5],[6,7],[8]] => [8,6,7,2,5,1,3,4] => [2,1,3,6,8,7,5,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4],[3,5],[6,7],[8]] => [8,6,7,3,5,1,2,4] => [1,3,2,6,8,7,5,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => [1,2,4,6,8,7,5,3] => [1,8,7,6,5,4,3,2] => 1
[[1,6,8],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6,8] => [5,4,3,2,1,7,6,8] => [5,4,3,2,1,8,7,6] => 5
[[1,2,8],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2,8] => [1,5,7,4,3,6,2,8] => [1,8,7,6,5,4,3,2] => 1
[[1,3,8],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3,8] => [2,1,7,6,5,4,3,8] => [2,1,8,7,6,5,4,3] => 2
[[1,2,8],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2,8] => [1,3,7,6,5,4,2,8] => [1,8,7,6,5,4,3,2] => 1
[[1,6,7],[2,8],[3],[4],[5]] => [5,4,3,2,8,1,6,7] => [5,4,3,2,1,6,8,7] => [5,4,3,2,1,8,7,6] => 5
[[1,2,7],[3,8],[4],[5],[6]] => [6,5,4,3,8,1,2,7] => [1,6,5,4,3,2,8,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4],[2,8],[5],[6],[7]] => [7,6,5,2,8,1,3,4] => [2,1,7,6,5,3,8,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,3],[4,8],[5],[6],[7]] => [7,6,5,4,8,1,2,3] => [1,2,7,6,5,4,8,3] => [1,8,7,6,5,4,3,2] => 1
[[1,2,7],[3,5],[4],[6],[8]] => [8,6,4,3,5,1,2,7] => [1,4,6,8,3,5,2,7] => [1,8,7,6,5,4,3,2] => 1
[[1,3,7],[2,4],[5],[6],[8]] => [8,6,5,2,4,1,3,7] => [2,1,6,8,5,4,3,7] => [2,1,8,7,6,5,4,3] => 2
[[1,3,4],[2,7],[5],[6],[8]] => [8,6,5,2,7,1,3,4] => [2,1,6,8,5,3,7,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4],[3,7],[5],[6],[8]] => [8,6,5,3,7,1,2,4] => [1,3,6,8,5,2,7,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,7],[5],[6],[8]] => [8,6,5,4,7,1,2,3] => [1,2,6,8,5,4,7,3] => [1,8,7,6,5,4,3,2] => 1
[[1,3,6],[2,4],[5],[7],[8]] => [8,7,5,2,4,1,3,6] => [2,1,5,8,7,4,3,6] => [2,1,8,7,6,5,4,3] => 2
[[1,4,5],[2,6],[3],[7],[8]] => [8,7,3,2,6,1,4,5] => [3,2,1,8,7,4,6,5] => [3,2,1,8,7,6,5,4] => 3
[[1,2,5],[3,6],[4],[7],[8]] => [8,7,4,3,6,1,2,5] => [1,4,3,8,7,2,6,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4],[2,6],[5],[7],[8]] => [8,7,5,2,6,1,3,4] => [2,1,5,8,7,3,6,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4],[3,6],[5],[7],[8]] => [8,7,5,3,6,1,2,4] => [1,3,5,8,7,2,6,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,6],[5],[7],[8]] => [8,7,5,4,6,1,2,3] => [1,2,5,8,7,4,6,3] => [1,8,7,6,5,4,3,2] => 1
[[1,3,5],[2,4],[6],[7],[8]] => [8,7,6,2,4,1,3,5] => [2,1,4,8,7,6,3,5] => [2,1,8,7,6,5,4,3] => 2
[[1,2,5],[3,4],[6],[7],[8]] => [8,7,6,3,4,1,2,5] => [1,3,4,8,7,6,2,5] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4],[2,5],[6],[7],[8]] => [8,7,6,2,5,1,3,4] => [2,1,3,8,7,6,5,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4],[3,5],[6],[7],[8]] => [8,7,6,3,5,1,2,4] => [1,3,2,8,7,6,5,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => [1,2,4,8,7,6,5,3] => [1,8,7,6,5,4,3,2] => 1
[[1,7,8],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,8,7] => 6
[[1,2,8],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8] => [1,7,6,5,4,3,2,8] => [1,8,7,6,5,4,3,2] => 1
[[1,2,7],[3],[4],[5],[6],[8]] => [8,6,5,4,3,1,2,7] => [1,6,8,5,4,3,2,7] => [1,8,7,6,5,4,3,2] => 1
[[1,2,6],[3],[4],[5],[7],[8]] => [8,7,5,4,3,1,2,6] => [1,5,8,7,4,3,2,6] => [1,8,7,6,5,4,3,2] => 1
[[1,3,4],[2],[5],[6],[7],[8]] => [8,7,6,5,2,1,3,4] => [2,1,8,7,6,5,3,4] => [2,1,8,7,6,5,4,3] => 2
[[1,2,4],[3],[5],[6],[7],[8]] => [8,7,6,5,3,1,2,4] => [1,3,8,7,6,5,2,4] => [1,8,7,6,5,4,3,2] => 1
[[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => [1,2,8,7,6,5,4,3] => [1,8,7,6,5,4,3,2] => 1
[[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 4
[[1,2],[3,5],[4,7],[6,8]] => [6,8,4,7,3,5,1,2] => [1,4,6,3,8,7,5,2] => [1,8,7,6,5,4,3,2] => 1
[[1,3],[2,4],[5,7],[6,8]] => [6,8,5,7,2,4,1,3] => [2,1,6,5,8,7,4,3] => [2,1,8,7,6,5,4,3] => 2
[[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => [3,2,1,7,8,6,5,4] => [3,2,1,8,7,6,5,4] => 3
[[1,2],[3,5],[4,6],[7,8]] => [7,8,4,6,3,5,1,2] => [1,4,3,7,8,6,5,2] => [1,8,7,6,5,4,3,2] => 1
[[1,3],[2,4],[5,6],[7,8]] => [7,8,5,6,2,4,1,3] => [2,1,5,7,8,6,4,3] => [2,1,8,7,6,5,4,3] => 2
[[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => [1,3,5,7,8,6,4,2] => [1,8,7,6,5,4,3,2] => 1
[[1,6],[2,7],[3,8],[4],[5]] => [5,4,3,8,2,7,1,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 5
[[1,2],[3,7],[4,8],[5],[6]] => [6,5,4,8,3,7,1,2] => [1,6,5,4,3,8,7,2] => [1,8,7,6,5,4,3,2] => 1
[[1,2],[3,6],[4,8],[5],[7]] => [7,5,4,8,3,6,1,2] => [1,5,7,4,3,8,6,2] => [1,8,7,6,5,4,3,2] => 1
[[1,3],[2,4],[5,8],[6],[7]] => [7,6,5,8,2,4,1,3] => [2,1,7,6,5,8,4,3] => [2,1,8,7,6,5,4,3] => 2
[[1,2],[3,6],[4,7],[5],[8]] => [8,5,4,7,3,6,1,2] => [1,5,4,8,3,7,6,2] => [1,8,7,6,5,4,3,2] => 1
[[1,2],[3,5],[4,7],[6],[8]] => [8,6,4,7,3,5,1,2] => [1,4,6,8,3,7,5,2] => [1,8,7,6,5,4,3,2] => 1
[[1,3],[2,4],[5,7],[6],[8]] => [8,6,5,7,2,4,1,3] => [2,1,6,8,5,7,4,3] => [2,1,8,7,6,5,4,3] => 2
[[1,4],[2,5],[3,6],[7],[8]] => [8,7,3,6,2,5,1,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 3
[[1,2],[3,5],[4,6],[7],[8]] => [8,7,4,6,3,5,1,2] => [1,4,3,8,7,6,5,2] => [1,8,7,6,5,4,3,2] => 1
[[1,3],[2,4],[5,6],[7],[8]] => [8,7,5,6,2,4,1,3] => [2,1,5,8,7,6,4,3] => [2,1,8,7,6,5,4,3] => 2
[[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => [1,3,5,8,7,6,4,2] => [1,8,7,6,5,4,3,2] => 1
[[1,7],[2,8],[3],[4],[5],[6]] => [6,5,4,3,2,8,1,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 6
[[1,2],[3,8],[4],[5],[6],[7]] => [7,6,5,4,3,8,1,2] => [1,7,6,5,4,3,8,2] => [1,8,7,6,5,4,3,2] => 1
[[1,2],[3,7],[4],[5],[6],[8]] => [8,6,5,4,3,7,1,2] => [1,6,8,5,4,3,7,2] => [1,8,7,6,5,4,3,2] => 1
[[1,2],[3,6],[4],[5],[7],[8]] => [8,7,5,4,3,6,1,2] => [1,5,8,7,4,3,6,2] => [1,8,7,6,5,4,3,2] => 1
[[1,2],[3,5],[4],[6],[7],[8]] => [8,7,6,4,3,5,1,2] => [1,4,8,7,6,3,5,2] => [1,8,7,6,5,4,3,2] => 1
[[1,3],[2,4],[5],[6],[7],[8]] => [8,7,6,5,2,4,1,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 2
[[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => [1,3,8,7,6,5,4,2] => [1,8,7,6,5,4,3,2] => 1
[[1,8],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 7
[[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 1
[[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 8
[[1,3,5,7,9],[2,4,6,8,10]] => [2,4,6,8,10,1,3,5,7,9] => [2,1,4,3,6,5,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,5,7,8],[2,4,6,9,10]] => [2,4,6,9,10,1,3,5,7,8] => [2,1,4,3,6,5,7,9,10,8] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,9],[2,4,7,8,10]] => [2,4,7,8,10,1,3,5,6,9] => [2,1,4,3,5,7,8,6,10,9] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,8],[2,4,7,9,10]] => [2,4,7,9,10,1,3,5,6,8] => [2,1,4,3,5,7,6,9,10,8] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,7],[2,4,8,9,10]] => [2,4,8,9,10,1,3,5,6,7] => [2,1,4,3,5,6,8,9,10,7] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,7,9],[2,5,6,8,10]] => [2,5,6,8,10,1,3,4,7,9] => [2,1,3,5,6,4,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,7,8],[2,5,6,9,10]] => [2,5,6,9,10,1,3,4,7,8] => [2,1,3,5,6,4,7,9,10,8] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,9],[2,5,7,8,10]] => [2,5,7,8,10,1,3,4,6,9] => [2,1,3,5,4,7,8,6,10,9] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,8],[2,5,7,9,10]] => [2,5,7,9,10,1,3,4,6,8] => [2,1,3,5,4,7,6,9,10,8] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,7],[2,5,8,9,10]] => [2,5,8,9,10,1,3,4,6,7] => [2,1,3,5,4,6,8,9,10,7] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,9],[2,6,7,8,10]] => [2,6,7,8,10,1,3,4,5,9] => [2,1,3,4,6,7,8,5,10,9] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,8],[2,6,7,9,10]] => [2,6,7,9,10,1,3,4,5,8] => [2,1,3,4,6,7,5,9,10,8] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,7],[2,6,8,9,10]] => [2,6,8,9,10,1,3,4,5,7] => [2,1,3,4,6,5,8,9,10,7] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,6],[2,7,8,9,10]] => [2,7,8,9,10,1,3,4,5,6] => [2,1,3,4,5,7,8,9,10,6] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,5,7,9],[3,4,6,8,10]] => [3,4,6,8,10,1,2,5,7,9] => [1,3,4,2,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,5,7,8],[3,4,6,9,10]] => [3,4,6,9,10,1,2,5,7,8] => [1,3,4,2,6,5,7,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,5,6,9],[3,4,7,8,10]] => [3,4,7,8,10,1,2,5,6,9] => [1,3,4,2,5,7,8,6,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,5,6,8],[3,4,7,9,10]] => [3,4,7,9,10,1,2,5,6,8] => [1,3,4,2,5,7,6,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,5,6,7],[3,4,8,9,10]] => [3,4,8,9,10,1,2,5,6,7] => [1,3,4,2,5,6,8,9,10,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,7,9],[3,5,6,8,10]] => [3,5,6,8,10,1,2,4,7,9] => [1,3,2,5,6,4,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,7,8],[3,5,6,9,10]] => [3,5,6,9,10,1,2,4,7,8] => [1,3,2,5,6,4,7,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,6,9],[3,5,7,8,10]] => [3,5,7,8,10,1,2,4,6,9] => [1,3,2,5,4,7,8,6,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,6,8],[3,5,7,9,10]] => [3,5,7,9,10,1,2,4,6,8] => [1,3,2,5,4,7,6,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,6,7],[3,5,8,9,10]] => [3,5,8,9,10,1,2,4,6,7] => [1,3,2,5,4,6,8,9,10,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,5,9],[3,6,7,8,10]] => [3,6,7,8,10,1,2,4,5,9] => [1,3,2,4,6,7,8,5,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,5,8],[3,6,7,9,10]] => [3,6,7,9,10,1,2,4,5,8] => [1,3,2,4,6,7,5,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,5,7],[3,6,8,9,10]] => [3,6,8,9,10,1,2,4,5,7] => [1,3,2,4,6,5,8,9,10,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,5,6],[3,7,8,9,10]] => [3,7,8,9,10,1,2,4,5,6] => [1,3,2,4,5,7,8,9,10,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,7,9],[4,5,6,8,10]] => [4,5,6,8,10,1,2,3,7,9] => [1,2,4,5,6,3,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,7,8],[4,5,6,9,10]] => [4,5,6,9,10,1,2,3,7,8] => [1,2,4,5,6,3,7,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,6,9],[4,5,7,8,10]] => [4,5,7,8,10,1,2,3,6,9] => [1,2,4,5,3,7,8,6,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,6,8],[4,5,7,9,10]] => [4,5,7,9,10,1,2,3,6,8] => [1,2,4,5,3,7,6,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,6,7],[4,5,8,9,10]] => [4,5,8,9,10,1,2,3,6,7] => [1,2,4,5,3,6,8,9,10,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,5,9],[4,6,7,8,10]] => [4,6,7,8,10,1,2,3,5,9] => [1,2,4,3,6,7,8,5,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,5,8],[4,6,7,9,10]] => [4,6,7,9,10,1,2,3,5,8] => [1,2,4,3,6,7,5,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,5,7],[4,6,8,9,10]] => [4,6,8,9,10,1,2,3,5,7] => [1,2,4,3,6,5,8,9,10,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,5,6],[4,7,8,9,10]] => [4,7,8,9,10,1,2,3,5,6] => [1,2,4,3,5,7,8,9,10,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,9],[5,6,7,8,10]] => [5,6,7,8,10,1,2,3,4,9] => [1,2,3,5,6,7,8,4,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,8],[5,6,7,9,10]] => [5,6,7,9,10,1,2,3,4,8] => [1,2,3,5,6,7,4,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,7],[5,6,8,9,10]] => [5,6,8,9,10,1,2,3,4,7] => [1,2,3,5,6,4,8,9,10,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6],[5,7,8,9,10]] => [5,7,8,9,10,1,2,3,4,6] => [1,2,3,5,4,7,8,9,10,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => [1,2,3,4,6,7,8,9,10,5] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [2,4,6,8,10,12,1,3,5,7,9,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [2,4,6,8,11,12,1,3,5,7,9,10] => [2,1,4,3,6,5,8,7,9,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => [2,4,6,9,10,12,1,3,5,7,8,11] => [2,1,4,3,6,5,7,9,10,8,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [2,4,6,9,11,12,1,3,5,7,8,10] => [2,1,4,3,6,5,7,9,8,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [2,4,6,10,11,12,1,3,5,7,8,9] => [2,1,4,3,6,5,7,8,10,11,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => [2,4,7,8,10,12,1,3,5,6,9,11] => [2,1,4,3,5,7,8,6,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => [2,4,7,8,11,12,1,3,5,6,9,10] => [2,1,4,3,5,7,8,6,9,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => [2,4,7,9,10,12,1,3,5,6,8,11] => [2,1,4,3,5,7,6,9,10,8,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [2,4,7,9,11,12,1,3,5,6,8,10] => [2,1,4,3,5,7,6,9,8,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => [2,4,7,10,11,12,1,3,5,6,8,9] => [2,1,4,3,5,7,6,8,10,11,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [2,4,8,9,10,12,1,3,5,6,7,11] => [2,1,4,3,5,6,8,9,10,7,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => [2,4,8,9,11,12,1,3,5,6,7,10] => [2,1,4,3,5,6,8,9,7,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [2,4,8,10,11,12,1,3,5,6,7,9] => [2,1,4,3,5,6,8,7,10,11,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => [2,4,9,10,11,12,1,3,5,6,7,8] => [2,1,4,3,5,6,7,9,10,11,12,8] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => [2,5,6,8,10,12,1,3,4,7,9,11] => [2,1,3,5,6,4,8,7,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => [2,5,6,8,11,12,1,3,4,7,9,10] => [2,1,3,5,6,4,8,7,9,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => [2,5,6,9,10,12,1,3,4,7,8,11] => [2,1,3,5,6,4,7,9,10,8,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => [2,5,6,9,11,12,1,3,4,7,8,10] => [2,1,3,5,6,4,7,9,8,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => [2,5,6,10,11,12,1,3,4,7,8,9] => [2,1,3,5,6,4,7,8,10,11,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => [2,5,7,8,10,12,1,3,4,6,9,11] => [2,1,3,5,4,7,8,6,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => [2,5,7,8,11,12,1,3,4,6,9,10] => [2,1,3,5,4,7,8,6,9,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => [2,5,7,9,10,12,1,3,4,6,8,11] => [2,1,3,5,4,7,6,9,10,8,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [2,5,7,9,11,12,1,3,4,6,8,10] => [2,1,3,5,4,7,6,9,8,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => [2,5,7,10,11,12,1,3,4,6,8,9] => [2,1,3,5,4,7,6,8,10,11,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => [2,5,8,9,10,12,1,3,4,6,7,11] => [2,1,3,5,4,6,8,9,10,7,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => [2,5,8,9,11,12,1,3,4,6,7,10] => [2,1,3,5,4,6,8,9,7,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => [2,5,8,10,11,12,1,3,4,6,7,9] => [2,1,3,5,4,6,8,7,10,11,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => [2,5,9,10,11,12,1,3,4,6,7,8] => [2,1,3,5,4,6,7,9,10,11,12,8] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [2,6,7,8,10,12,1,3,4,5,9,11] => [2,1,3,4,6,7,8,5,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => [2,6,7,8,11,12,1,3,4,5,9,10] => [2,1,3,4,6,7,8,5,9,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => [2,6,7,9,10,12,1,3,4,5,8,11] => [2,1,3,4,6,7,5,9,10,8,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => [2,6,7,9,11,12,1,3,4,5,8,10] => [2,1,3,4,6,7,5,9,8,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [2,6,7,10,11,12,1,3,4,5,8,9] => [2,1,3,4,6,7,5,8,10,11,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [2,6,8,9,10,12,1,3,4,5,7,11] => [2,1,3,4,6,5,8,9,10,7,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => [2,6,8,9,11,12,1,3,4,5,7,10] => [2,1,3,4,6,5,8,9,7,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => [2,6,8,10,11,12,1,3,4,5,7,9] => [2,1,3,4,6,5,8,7,10,11,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => [2,6,9,10,11,12,1,3,4,5,7,8] => [2,1,3,4,6,5,7,9,10,11,12,8] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,6,11],[2,7,8,9,10,12]] => [2,7,8,9,10,12,1,3,4,5,6,11] => [2,1,3,4,5,7,8,9,10,6,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => [2,7,8,9,11,12,1,3,4,5,6,10] => [2,1,3,4,5,7,8,9,6,11,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => [2,7,8,10,11,12,1,3,4,5,6,9] => [2,1,3,4,5,7,8,6,10,11,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => [2,7,9,10,11,12,1,3,4,5,6,8] => [2,1,3,4,5,7,6,9,10,11,12,8] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => [2,8,9,10,11,12,1,3,4,5,6,7] => [2,1,3,4,5,6,8,9,10,11,12,7] => [2,1,12,11,10,9,8,7,6,5,4,3] => 2
[[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,9,8] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,9,7] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,9,8,7] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,7,8,9,6] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => [1,2,3,4,5,7,9,8,6] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,9,8,7,6] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => [1,2,3,4,6,7,8,9,5] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => [1,2,3,4,6,7,9,8,5] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => [1,2,3,4,6,8,9,7,5] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => [1,2,3,4,6,9,8,7,5] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [1,2,3,4,9,8,7,6,5] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => [1,2,3,5,6,7,9,8,4] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => [1,2,3,5,6,8,9,7,4] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => [1,2,3,5,6,9,8,7,4] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => [1,2,3,5,7,9,8,6,4] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => [1,2,3,5,9,8,7,6,4] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [1,2,3,9,8,7,6,5,4] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => [1,2,4,5,7,8,9,6,3] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => [1,2,4,5,7,9,8,6,3] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => [1,2,4,5,9,8,7,6,3] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => [1,2,4,6,8,9,7,5,3] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => [1,2,4,6,9,8,7,5,3] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => [1,2,4,9,8,7,6,5,3] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => [1,2,9,8,7,6,5,4,3] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => [1,3,5,7,9,8,6,4,2] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => [1,3,5,9,8,7,6,4,2] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => [1,3,9,8,7,6,5,4,2] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 1
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 9
[[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7,8],[9,10]] => [9,10,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,10,9,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7],[8,9,10]] => [8,9,10,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,9,10,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7],[8,9],[10]] => [10,8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,10,9,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,10,9,8,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => [1,2,3,4,5,7,8,9,10,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7,8,9],[10]] => [10,7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,7,8,10,9,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7,8],[9,10]] => [9,10,7,8,1,2,3,4,5,6] => [1,2,3,4,5,7,9,10,8,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7,8],[9],[10]] => [10,9,7,8,1,2,3,4,5,6] => [1,2,3,4,5,7,10,9,8,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [10,9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,10,9,8,7,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => [1,2,3,4,6,7,8,10,9,5] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => [1,2,3,4,6,7,9,10,8,5] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => [1,2,3,4,6,7,10,9,8,5] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => [1,2,3,4,6,8,10,9,7,5] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,1,2,3,4,5] => [1,2,3,4,6,10,9,8,7,5] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,1,2,3,4,5] => [1,2,3,4,10,9,8,7,6,5] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => [1,2,3,5,6,7,9,10,8,4] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => [1,2,3,5,6,7,10,9,8,4] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => [1,2,3,5,6,8,9,10,7,4] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => [1,2,3,5,6,8,10,9,7,4] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6,7],[8],[9],[10]] => [10,9,8,5,6,7,1,2,3,4] => [1,2,3,5,6,10,9,8,7,4] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => [1,2,3,5,7,9,10,8,6,4] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,1,2,3,4] => [1,2,3,5,7,10,9,8,6,4] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,1,2,3,4] => [1,2,3,5,10,9,8,7,6,4] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => [1,2,3,10,9,8,7,6,5,4] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => [1,2,4,5,7,8,10,9,6,3] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => [1,2,4,5,7,9,10,8,6,3] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,6],[7,8],[9],[10]] => [10,9,7,8,4,5,6,1,2,3] => [1,2,4,5,7,10,9,8,6,3] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5,6],[7],[8],[9],[10]] => [10,9,8,7,4,5,6,1,2,3] => [1,2,4,5,10,9,8,7,6,3] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,4,5,1,2,3] => [1,2,4,6,8,10,9,7,5,3] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,4,5,1,2,3] => [1,2,4,6,10,9,8,7,5,3] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,5,1,2,3] => [1,2,4,10,9,8,7,6,5,3] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => [1,2,10,9,8,7,6,5,4,3] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => [1,3,5,7,9,10,8,6,4,2] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => [1,3,5,7,10,9,8,6,4,2] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,3,4,1,2] => [1,3,5,10,9,8,7,6,4,2] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => [1,3,10,9,8,7,6,5,4,2] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 10
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,3,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => 12
[[1,2,5,6,7,8,9],[3,4]] => [3,4,1,2,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,7,8,9],[4,5,6]] => [4,5,6,1,2,3,7,8,9] => [1,2,4,5,6,3,7,8,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,9],[5,6,7,8]] => [5,6,7,8,1,2,3,4,9] => [1,2,3,5,6,7,8,4,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,7,8,9],[3,4],[5,6]] => [5,6,3,4,1,2,7,8,9] => [1,3,5,6,4,2,7,8,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,5,9],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5,9] => [1,3,4,6,7,2,8,5,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,9],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2,9] => [1,3,5,7,8,6,4,2,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 8
[[1,3,4,5,6,7,8,9,10],[2]] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,5,6,7,8,9,10],[3,4]] => [3,4,1,2,5,6,7,8,9,10] => [1,3,4,2,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,7,8,9,10],[4,5,6]] => [4,5,6,1,2,3,7,8,9,10] => [1,2,4,5,6,3,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,5,6,7,8,9,10],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,10,9,8,7,6,5] => 4
[[1,2,3,4,9,10],[5,6,7,8]] => [5,6,7,8,1,2,3,4,9,10] => [1,2,3,5,6,7,8,4,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,3,4,8,9,10],[2,6,7],[5]] => [5,2,6,7,1,3,4,8,9,10] => [2,1,5,3,6,7,4,8,9,10] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,7,8,9,10],[3,4],[5,6]] => [5,6,3,4,1,2,7,8,9,10] => [1,3,5,6,4,2,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,3,4,5,10],[2,7,8,9],[6]] => [6,2,7,8,9,1,3,4,5,10] => [2,1,3,6,4,7,8,9,5,10] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,5,9,10],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5,9,10] => [1,3,4,6,7,2,8,5,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,7,8,9,10],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,10,9,8,7] => 6
[[1,2,5,6],[3,4,9,10],[7,8]] => [7,8,3,4,9,10,1,2,5,6] => [1,3,4,2,7,8,5,9,10,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,10],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3,10] => [1,2,4,5,7,8,9,6,3,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,9,10],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2,9,10] => [1,3,5,7,8,6,4,2,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,3,4],[2,6,7],[5,9,10],[8]] => [8,5,9,10,2,6,7,1,3,4] => [2,1,5,3,8,6,9,10,7,4] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,7],[3,4,10],[5,6],[8,9]] => [8,9,5,6,3,4,10,1,2,7] => [1,3,5,6,8,9,4,2,10,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,10,9] => 8
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => 9
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,10,1,9] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => 8
[[1,7],[2,8],[3,9],[4,10],[5],[6]] => [6,5,4,10,3,9,2,8,1,7] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,3,2,1,10,9,8,7] => 6
[[1,7,10],[2,8],[3,9],[4],[5],[6]] => [6,5,4,3,9,2,8,1,7,10] => [6,5,4,3,2,1,9,8,7,10] => [6,5,4,3,2,1,10,9,8,7] => 6
[[1,7,9],[2,8,10],[3],[4],[5],[6]] => [6,5,4,3,2,8,10,1,7,9] => [6,5,4,3,2,1,8,7,10,9] => [6,5,4,3,2,1,10,9,8,7] => 6
[[1,7,9,10],[2,8],[3],[4],[5],[6]] => [6,5,4,3,2,8,1,7,9,10] => [6,5,4,3,2,1,8,7,9,10] => [6,5,4,3,2,1,10,9,8,7] => 6
[[1,5,9],[2,6,10],[3,7],[4,8]] => [4,8,3,7,2,6,10,1,5,9] => [4,3,2,1,8,7,6,5,10,9] => [4,3,2,1,10,9,8,7,6,5] => 4
[[1,5,9,10],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5,9,10] => [4,3,2,1,8,7,6,5,9,10] => [4,3,2,1,10,9,8,7,6,5] => 4
[[1,5,8],[2,6,9],[3,7,10],[4]] => [4,3,7,10,2,6,9,1,5,8] => [4,3,2,1,7,6,5,10,9,8] => [4,3,2,1,10,9,8,7,6,5] => 4
[[1,5,8,10],[2,6,9],[3,7],[4]] => [4,3,7,2,6,9,1,5,8,10] => [4,3,2,1,7,6,5,9,8,10] => [4,3,2,1,10,9,8,7,6,5] => 4
[[1,5,8,9,10],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8,9,10] => [4,3,2,1,7,6,5,8,9,10] => [4,3,2,1,10,9,8,7,6,5] => 4
[[1,5,7,9],[2,6,8,10],[3],[4]] => [4,3,2,6,8,10,1,5,7,9] => [4,3,2,1,6,5,8,7,10,9] => [4,3,2,1,10,9,8,7,6,5] => 4
[[1,5,7,9,10],[2,6,8],[3],[4]] => [4,3,2,6,8,1,5,7,9,10] => [4,3,2,1,6,5,8,7,9,10] => [4,3,2,1,10,9,8,7,6,5] => 4
[[1,5,7,8,9,10],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8,9,10] => [4,3,2,1,6,5,7,8,9,10] => [4,3,2,1,10,9,8,7,6,5] => 4
[[1,3,5,7,9,10],[2,4,6,8]] => [2,4,6,8,1,3,5,7,9,10] => [2,1,4,3,6,5,8,7,9,10] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,5,7,8,9,10],[2,4,6]] => [2,4,6,1,3,5,7,8,9,10] => [2,1,4,3,6,5,7,8,9,10] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,5,6,7,8,9,10],[2,4]] => [2,4,1,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,4],[3,5],[6],[7],[8],[9]] => [9,8,7,6,3,5,1,2,4] => [1,3,2,9,8,7,6,5,4] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,5],[3,6],[4,7],[8],[9]] => [9,8,4,7,3,6,1,2,5] => [1,4,3,2,9,8,7,6,5] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,5],[4,6],[7],[8],[9]] => [9,8,7,4,6,1,2,3,5] => [1,2,4,3,9,8,7,6,5] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,6],[3,7],[4,8],[5,9]] => [5,9,4,8,3,7,1,2,6] => [1,5,4,3,2,9,8,7,6] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,6],[4,7],[5,8],[9]] => [9,5,8,4,7,1,2,3,6] => [1,2,5,4,3,9,8,7,6] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,4,6],[3,5,7],[8],[9]] => [9,8,3,5,7,1,2,4,6] => [1,3,2,5,4,9,8,7,6] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6],[5,7],[8],[9]] => [9,8,5,7,1,2,3,4,6] => [1,2,3,5,4,9,8,7,6] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,4,7],[3,5,8],[6,9]] => [6,9,3,5,8,1,2,4,7] => [1,3,2,6,5,4,9,8,7] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,7],[5,8],[6,9]] => [6,9,5,8,1,2,3,4,7] => [1,2,3,6,5,4,9,8,7] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,5,7],[4,6,8],[9]] => [9,4,6,8,1,2,3,5,7] => [1,2,4,3,6,5,9,8,7] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,7],[6,8],[9]] => [9,6,8,1,2,3,4,5,7] => [1,2,3,4,6,5,9,8,7] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,4,6,8],[3,5,7,9]] => [3,5,7,9,1,2,4,6,8] => [1,3,2,5,4,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6,8],[5,7,9]] => [5,7,9,1,2,3,4,6,8] => [1,2,3,5,4,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,8],[7,9]] => [7,9,1,2,3,4,5,6,8] => [1,2,3,4,5,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => 1
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,2,4,1,3] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,4],[3,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,3,5,1,2,4] => [1,3,2,10,9,8,7,6,5,4] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,5],[2,6],[3,7],[4,8],[9],[10]] => [10,9,4,8,3,7,2,6,1,5] => [4,3,2,1,10,9,8,7,6,5] => [4,3,2,1,10,9,8,7,6,5] => 4
[[1,2,5],[3,6],[4,7],[8],[9],[10]] => [10,9,8,4,7,3,6,1,2,5] => [1,4,3,2,10,9,8,7,6,5] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,3,5],[2,4,6],[7],[8],[9],[10]] => [10,9,8,7,2,4,6,1,3,5] => [2,1,4,3,10,9,8,7,6,5] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,3,5],[4,6],[7],[8],[9],[10]] => [10,9,8,7,4,6,1,2,3,5] => [1,2,4,3,10,9,8,7,6,5] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,6],[3,7],[4,8],[5,9],[10]] => [10,5,9,4,8,3,7,1,2,6] => [1,5,4,3,2,10,9,8,7,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,3,6],[2,4,7],[5,8],[9],[10]] => [10,9,5,8,2,4,7,1,3,6] => [2,1,5,4,3,10,9,8,7,6] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,3,6],[4,7],[5,8],[9],[10]] => [10,9,5,8,4,7,1,2,3,6] => [1,2,5,4,3,10,9,8,7,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,6],[3,5,7],[8],[9],[10]] => [10,9,8,3,5,7,1,2,4,6] => [1,3,2,5,4,10,9,8,7,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6],[5,7],[8],[9],[10]] => [10,9,8,5,7,1,2,3,4,6] => [1,2,3,5,4,10,9,8,7,6] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,3,7],[2,4,8],[5,9],[6,10]] => [6,10,5,9,2,4,8,1,3,7] => [2,1,6,5,4,3,10,9,8,7] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,3,7],[4,8],[5,9],[6,10]] => [6,10,5,9,4,8,1,2,3,7] => [1,2,6,5,4,3,10,9,8,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,7],[3,5,8],[6,9],[10]] => [10,6,9,3,5,8,1,2,4,7] => [1,3,2,6,5,4,10,9,8,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,7],[5,8],[6,9],[10]] => [10,6,9,5,8,1,2,3,4,7] => [1,2,3,6,5,4,10,9,8,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,3,5,7],[2,4,6,8],[9],[10]] => [10,9,2,4,6,8,1,3,5,7] => [2,1,4,3,6,5,10,9,8,7] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,3,5,7],[4,6,8],[9],[10]] => [10,9,4,6,8,1,2,3,5,7] => [1,2,4,3,6,5,10,9,8,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,7],[6,8],[9],[10]] => [10,9,6,8,1,2,3,4,5,7] => [1,2,3,4,6,5,10,9,8,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,5,8],[3,6,9],[4,7,10]] => [4,7,10,3,6,9,1,2,5,8] => [1,4,3,2,7,6,5,10,9,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,3,5,8],[2,4,6,9],[7,10]] => [7,10,2,4,6,9,1,3,5,8] => [2,1,4,3,7,6,5,10,9,8] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,3,5,8],[4,6,9],[7,10]] => [7,10,4,6,9,1,2,3,5,8] => [1,2,4,3,7,6,5,10,9,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,8],[6,9],[7,10]] => [7,10,6,9,1,2,3,4,5,8] => [1,2,3,4,7,6,5,10,9,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,6,8],[3,5,7,9],[10]] => [10,3,5,7,9,1,2,4,6,8] => [1,3,2,5,4,7,6,10,9,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6,8],[5,7,9],[10]] => [10,5,7,9,1,2,3,4,6,8] => [1,2,3,5,4,7,6,10,9,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,8],[7,9],[10]] => [10,7,9,1,2,3,4,5,6,8] => [1,2,3,4,5,7,6,10,9,8] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,5,7,9],[4,6,8,10]] => [4,6,8,10,1,2,3,5,7,9] => [1,2,4,3,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,7,9],[6,8,10]] => [6,8,10,1,2,3,4,5,7,9] => [1,2,3,4,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7,9],[8,10]] => [8,10,1,2,3,4,5,6,7,9] => [1,2,3,4,5,6,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2],[3,7],[4,8],[5,9],[6,10]] => [6,10,5,9,4,8,3,7,1,2] => [1,6,5,4,3,10,9,8,7,2] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => [6,12,5,11,4,10,3,9,2,8,1,7] => [6,5,4,3,2,1,12,11,10,9,8,7] => [6,5,4,3,2,1,12,11,10,9,8,7] => 6
[[1,2,3,4,5,6,7,9],[8]] => [8,1,2,3,4,5,6,7,9] => [1,2,3,4,5,6,8,7,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,9],[7,8]] => [7,8,1,2,3,4,5,6,9] => [1,2,3,4,5,7,8,6,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => [1,8,7,6,5,4,3,2,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7,8,10],[9]] => [9,1,2,3,4,5,6,7,8,10] => [1,2,3,4,5,6,7,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7,10],[8,9]] => [8,9,1,2,3,4,5,6,7,10] => [1,2,3,4,5,6,8,9,7,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,10],[7,8,9]] => [7,8,9,1,2,3,4,5,6,10] => [1,2,3,4,5,7,8,9,6,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2,10] => [1,9,8,7,6,5,4,3,2,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,4,5,6,7,8,9,10],[3]] => [3,1,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,3,4,5,6,7,8,9],[2,10]] => [2,10,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,10,9] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,6,7,8,9],[2],[10]] => [10,2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,10,8,9] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5,6,7,8],[2,9,10]] => [2,9,10,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,9,10,8] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4,5],[2,7,8],[6,10],[9]] => [9,6,10,2,7,8,1,3,4,5] => [2,1,3,6,4,9,7,10,8,5] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,3,4],[2],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,2,1,3,4] => [2,1,10,9,8,7,6,5,3,4] => [2,1,10,9,8,7,6,5,4,3] => 2
[[1,2,4,6,8,10],[3,5,7,9]] => [3,5,7,9,1,2,4,6,8,10] => [1,3,2,5,4,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6,8,10],[5,7,9]] => [5,7,9,1,2,3,4,6,8,10] => [1,2,3,5,4,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,5,6,7,8,9,10],[4]] => [4,1,2,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,9,10],[7,8]] => [7,8,1,2,3,4,5,6,9,10] => [1,2,3,4,5,7,8,6,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,6,7,8,9,10],[5]] => [5,1,2,3,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,7,9,10],[8]] => [8,1,2,3,4,5,6,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,8,9,10],[7]] => [7,1,2,3,4,5,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,7,8,9,10],[6]] => [6,1,2,3,4,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,5,9],[3,4,8],[6,7],[10]] => [10,6,7,3,4,8,1,2,5,9] => [1,3,4,6,7,2,10,8,5,9] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,6,7,8,9],[4,5]] => [4,5,1,2,3,6,7,8,9] => [1,2,4,5,3,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,5,6,7,8,9],[3],[4]] => [4,3,1,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,4,7],[3,6,10],[5,9],[8]] => [8,5,9,3,6,10,1,2,4,7] => [1,3,5,2,8,6,9,4,10,7] => [1,10,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6,8],[7],[9]] => [9,7,1,2,3,4,5,6,8] => [1,2,3,4,5,7,9,6,8] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,7,9],[6,8]] => [6,8,1,2,3,4,5,7,9] => [1,2,3,4,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,4,5,6,7,8],[3,9]] => [3,9,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,9,8] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,3,4,5,6],[7,9],[8]] => [8,7,9,1,2,3,4,5,6] => [1,2,3,4,5,8,7,9,6] => [1,9,8,7,6,5,4,3,2] => 1
[[1,2,4,5,6,7],[3,8,9]] => [3,8,9,1,2,4,5,6,7] => [1,3,2,4,5,6,8,9,7] => [1,9,8,7,6,5,4,3,2] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,1,1 5,3,1,1 13,8,3,1,1 38,24,9,3,1,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + q^{2} + q^{3}$
$F_{4} = 5\ q + 3\ q^{2} + q^{3} + q^{4}$
$F_{5} = 13\ q + 8\ q^{2} + 3\ q^{3} + q^{4} + q^{5}$
$F_{6} = 38\ q + 24\ q^{2} + 9\ q^{3} + 3\ q^{4} + q^{5} + q^{6}$
Description
The first entry of the permutation.
This can be described as 1 plus the number of occurrences of the vincular pattern ([2,1], {(0,0),(0,1),(0,2)}), i.e., the first column is shaded, see [1].
This statistic is related to the number of deficiencies St000703The number of deficiencies of a permutation. as follows: consider the arc diagram of a permutation $\pi$ of $n$, together with its rotations, obtained by conjugating with the long cycle $(1,\dots,n)$. Drawing the labels $1$ to $n$ in this order on a circle, and the arcs $(i, \pi(i))$ as straight lines, the rotation of $\pi$ is obtained by replacing each number $i$ by $(i\bmod n) +1$. Then, $\pi(1)-1$ is the number of rotations of $\pi$ where the arc $(1, \pi(1))$ is a deficiency. In particular, if $O(\pi)$ is the orbit of rotations of $\pi$, then the number of deficiencies of $\pi$ equals
$$ \frac{1}{|O(\pi)|}\sum_{\sigma\in O(\pi)} (\sigma(1)-1). $$
This can be described as 1 plus the number of occurrences of the vincular pattern ([2,1], {(0,0),(0,1),(0,2)}), i.e., the first column is shaded, see [1].
This statistic is related to the number of deficiencies St000703The number of deficiencies of a permutation. as follows: consider the arc diagram of a permutation $\pi$ of $n$, together with its rotations, obtained by conjugating with the long cycle $(1,\dots,n)$. Drawing the labels $1$ to $n$ in this order on a circle, and the arcs $(i, \pi(i))$ as straight lines, the rotation of $\pi$ is obtained by replacing each number $i$ by $(i\bmod n) +1$. Then, $\pi(1)-1$ is the number of rotations of $\pi$ where the arc $(1, \pi(1))$ is a deficiency. In particular, if $O(\pi)$ is the orbit of rotations of $\pi$, then the number of deficiencies of $\pi$ equals
$$ \frac{1}{|O(\pi)|}\sum_{\sigma\in O(\pi)} (\sigma(1)-1). $$
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
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