Identifier
-
Mp00106:
Standard tableaux
—catabolism⟶
Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
St000763: Integer compositions ⟶ ℤ
Values
[[1]] => [[1]] => [1] => [1] => 1
[[1,2]] => [[1,2]] => [1,2] => [2] => 1
[[1],[2]] => [[1,2]] => [1,2] => [2] => 1
[[1,2,3]] => [[1,2,3]] => [1,2,3] => [3] => 1
[[1,3],[2]] => [[1,2],[3]] => [3,1,2] => [1,2] => 3
[[1,2],[3]] => [[1,2,3]] => [1,2,3] => [3] => 1
[[1],[2],[3]] => [[1,2],[3]] => [3,1,2] => [1,2] => 3
[[1,2,3,4]] => [[1,2,3,4]] => [1,2,3,4] => [4] => 1
[[1,3,4],[2]] => [[1,2,4],[3]] => [3,1,2,4] => [1,3] => 3
[[1,2,4],[3]] => [[1,2,3],[4]] => [4,1,2,3] => [1,3] => 3
[[1,2,3],[4]] => [[1,2,3,4]] => [1,2,3,4] => [4] => 1
[[1,3],[2,4]] => [[1,2,4],[3]] => [3,1,2,4] => [1,3] => 3
[[1,2],[3,4]] => [[1,2,3,4]] => [1,2,3,4] => [4] => 1
[[1,4],[2],[3]] => [[1,2],[3],[4]] => [4,3,1,2] => [1,1,2] => 4
[[1,3],[2],[4]] => [[1,2,4],[3]] => [3,1,2,4] => [1,3] => 3
[[1,2],[3],[4]] => [[1,2,3],[4]] => [4,1,2,3] => [1,3] => 3
[[1],[2],[3],[4]] => [[1,2],[3],[4]] => [4,3,1,2] => [1,1,2] => 4
[[1,2,3,4,5]] => [[1,2,3,4,5]] => [1,2,3,4,5] => [5] => 1
[[1,3,4,5],[2]] => [[1,2,4,5],[3]] => [3,1,2,4,5] => [1,4] => 3
[[1,2,4,5],[3]] => [[1,2,3,5],[4]] => [4,1,2,3,5] => [1,4] => 3
[[1,2,3,5],[4]] => [[1,2,3,4],[5]] => [5,1,2,3,4] => [1,4] => 3
[[1,2,3,4],[5]] => [[1,2,3,4,5]] => [1,2,3,4,5] => [5] => 1
[[1,3,5],[2,4]] => [[1,2,4],[3,5]] => [3,5,1,2,4] => [2,3] => 3
[[1,2,5],[3,4]] => [[1,2,3,4],[5]] => [5,1,2,3,4] => [1,4] => 3
[[1,3,4],[2,5]] => [[1,2,4,5],[3]] => [3,1,2,4,5] => [1,4] => 3
[[1,2,4],[3,5]] => [[1,2,3,5],[4]] => [4,1,2,3,5] => [1,4] => 3
[[1,2,3],[4,5]] => [[1,2,3,4,5]] => [1,2,3,4,5] => [5] => 1
[[1,4,5],[2],[3]] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => [1,1,3] => 4
[[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => [1,1,3] => 4
[[1,2,5],[3],[4]] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => [1,1,3] => 4
[[1,3,4],[2],[5]] => [[1,2,4,5],[3]] => [3,1,2,4,5] => [1,4] => 3
[[1,2,4],[3],[5]] => [[1,2,3,5],[4]] => [4,1,2,3,5] => [1,4] => 3
[[1,2,3],[4],[5]] => [[1,2,3,4],[5]] => [5,1,2,3,4] => [1,4] => 3
[[1,4],[2,5],[3]] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => [1,1,3] => 4
[[1,3],[2,5],[4]] => [[1,2,4,5],[3]] => [3,1,2,4,5] => [1,4] => 3
[[1,2],[3,5],[4]] => [[1,2,3,5],[4]] => [4,1,2,3,5] => [1,4] => 3
[[1,3],[2,4],[5]] => [[1,2,4],[3,5]] => [3,5,1,2,4] => [2,3] => 3
[[1,2],[3,4],[5]] => [[1,2,3,4],[5]] => [5,1,2,3,4] => [1,4] => 3
[[1,5],[2],[3],[4]] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => [1,1,1,2] => 5
[[1,4],[2],[3],[5]] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => [1,1,3] => 4
[[1,3],[2],[4],[5]] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => [1,1,3] => 4
[[1,2],[3],[4],[5]] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => [1,1,3] => 4
[[1],[2],[3],[4],[5]] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => [1,1,1,2] => 5
[[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [6] => 1
[[1,3,4,5,6],[2]] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [1,5] => 3
[[1,2,4,5,6],[3]] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [1,5] => 3
[[1,2,3,5,6],[4]] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [1,5] => 3
[[1,2,3,4,6],[5]] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [1,5] => 3
[[1,2,3,4,5],[6]] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [6] => 1
[[1,3,5,6],[2,4]] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [2,4] => 3
[[1,2,5,6],[3,4]] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [2,4] => 3
[[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [2,4] => 3
[[1,2,4,6],[3,5]] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [2,4] => 3
[[1,2,3,6],[4,5]] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [1,5] => 3
[[1,3,4,5],[2,6]] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [1,5] => 3
[[1,2,4,5],[3,6]] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [1,5] => 3
[[1,2,3,5],[4,6]] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [1,5] => 3
[[1,2,3,4],[5,6]] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [6] => 1
[[1,4,5,6],[2],[3]] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [1,1,4] => 4
[[1,3,5,6],[2],[4]] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [1,1,4] => 4
[[1,2,5,6],[3],[4]] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [1,1,4] => 4
[[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [1,1,4] => 4
[[1,2,4,6],[3],[5]] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [1,1,4] => 4
[[1,2,3,6],[4],[5]] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [1,1,4] => 4
[[1,3,4,5],[2],[6]] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [1,5] => 3
[[1,2,4,5],[3],[6]] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [1,5] => 3
[[1,2,3,5],[4],[6]] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [1,5] => 3
[[1,2,3,4],[5],[6]] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [1,5] => 3
[[1,3,5],[2,4,6]] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [2,4] => 3
[[1,2,5],[3,4,6]] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [1,5] => 3
[[1,3,4],[2,5,6]] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [1,5] => 3
[[1,2,4],[3,5,6]] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [1,5] => 3
[[1,2,3],[4,5,6]] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [6] => 1
[[1,4,6],[2,5],[3]] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [1,2,3] => 6
[[1,3,6],[2,5],[4]] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [1,1,4] => 4
[[1,2,6],[3,5],[4]] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [1,1,4] => 4
[[1,3,6],[2,4],[5]] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [1,2,3] => 6
[[1,2,6],[3,4],[5]] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [1,1,4] => 4
[[1,4,5],[2,6],[3]] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [1,1,4] => 4
[[1,3,5],[2,6],[4]] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [1,1,4] => 4
[[1,2,5],[3,6],[4]] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [1,1,4] => 4
[[1,3,4],[2,6],[5]] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [1,5] => 3
[[1,2,4],[3,6],[5]] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [1,5] => 3
[[1,2,3],[4,6],[5]] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [1,5] => 3
[[1,3,5],[2,4],[6]] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [2,4] => 3
[[1,2,5],[3,4],[6]] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [2,4] => 3
[[1,3,4],[2,5],[6]] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [2,4] => 3
[[1,2,4],[3,5],[6]] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [2,4] => 3
[[1,2,3],[4,5],[6]] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [1,5] => 3
[[1,5,6],[2],[3],[4]] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [1,1,1,3] => 5
[[1,4,6],[2],[3],[5]] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [1,1,1,3] => 5
[[1,3,6],[2],[4],[5]] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [1,1,1,3] => 5
[[1,2,6],[3],[4],[5]] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [1,1,1,3] => 5
[[1,4,5],[2],[3],[6]] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [1,1,4] => 4
[[1,3,5],[2],[4],[6]] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [1,1,4] => 4
[[1,2,5],[3],[4],[6]] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [1,1,4] => 4
[[1,3,4],[2],[5],[6]] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [1,1,4] => 4
[[1,2,4],[3],[5],[6]] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [1,1,4] => 4
[[1,2,3],[4],[5],[6]] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [1,1,4] => 4
[[1,4],[2,5],[3,6]] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [1,2,3] => 6
[[1,3],[2,5],[4,6]] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [2,4] => 3
>>> Load all 1248 entries. <<<[[1,2],[3,5],[4,6]] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [2,4] => 3
[[1,3],[2,4],[5,6]] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [2,4] => 3
[[1,2],[3,4],[5,6]] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [2,4] => 3
[[1,5],[2,6],[3],[4]] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [1,1,1,3] => 5
[[1,4],[2,6],[3],[5]] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [1,1,4] => 4
[[1,3],[2,6],[4],[5]] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [1,1,4] => 4
[[1,2],[3,6],[4],[5]] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [1,1,4] => 4
[[1,4],[2,5],[3],[6]] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [1,2,3] => 6
[[1,3],[2,5],[4],[6]] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [1,1,4] => 4
[[1,2],[3,5],[4],[6]] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [1,1,4] => 4
[[1,3],[2,4],[5],[6]] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [1,2,3] => 6
[[1,2],[3,4],[5],[6]] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [1,1,4] => 4
[[1,6],[2],[3],[4],[5]] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [1,1,1,1,2] => 6
[[1,5],[2],[3],[4],[6]] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [1,1,1,3] => 5
[[1,4],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [1,1,1,3] => 5
[[1,3],[2],[4],[5],[6]] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [1,1,1,3] => 5
[[1,2],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [1,1,1,3] => 5
[[1],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [1,1,1,1,2] => 6
[[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => [7] => 1
[[1,3,4,5,6,7],[2]] => [[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [1,6] => 3
[[1,2,4,5,6,7],[3]] => [[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [1,6] => 3
[[1,2,3,5,6,7],[4]] => [[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [1,6] => 3
[[1,2,3,4,6,7],[5]] => [[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [1,6] => 3
[[1,2,3,4,5,7],[6]] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [1,6] => 3
[[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => [7] => 1
[[1,3,5,6,7],[2,4]] => [[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => [2,5] => 3
[[1,2,5,6,7],[3,4]] => [[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => [2,5] => 3
[[1,3,4,6,7],[2,5]] => [[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => [2,5] => 3
[[1,2,4,6,7],[3,5]] => [[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => [2,5] => 3
[[1,2,3,6,7],[4,5]] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [2,5] => 3
[[1,3,4,5,7],[2,6]] => [[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => [2,5] => 3
[[1,2,4,5,7],[3,6]] => [[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => [2,5] => 3
[[1,2,3,5,7],[4,6]] => [[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => [2,5] => 3
[[1,2,3,4,7],[5,6]] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [1,6] => 3
[[1,3,4,5,6],[2,7]] => [[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [1,6] => 3
[[1,2,4,5,6],[3,7]] => [[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [1,6] => 3
[[1,2,3,5,6],[4,7]] => [[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [1,6] => 3
[[1,2,3,4,6],[5,7]] => [[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [1,6] => 3
[[1,2,3,4,5],[6,7]] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => [7] => 1
[[1,4,5,6,7],[2],[3]] => [[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => [1,1,5] => 4
[[1,3,5,6,7],[2],[4]] => [[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => [1,1,5] => 4
[[1,2,5,6,7],[3],[4]] => [[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => [1,1,5] => 4
[[1,3,4,6,7],[2],[5]] => [[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => [1,1,5] => 4
[[1,2,4,6,7],[3],[5]] => [[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => [1,1,5] => 4
[[1,2,3,6,7],[4],[5]] => [[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => [1,1,5] => 4
[[1,3,4,5,7],[2],[6]] => [[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => [1,1,5] => 4
[[1,2,4,5,7],[3],[6]] => [[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => [1,1,5] => 4
[[1,2,3,5,7],[4],[6]] => [[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => [1,1,5] => 4
[[1,2,3,4,7],[5],[6]] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [1,1,5] => 4
[[1,3,4,5,6],[2],[7]] => [[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [1,6] => 3
[[1,2,4,5,6],[3],[7]] => [[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [1,6] => 3
[[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [1,6] => 3
[[1,2,3,4,6],[5],[7]] => [[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [1,6] => 3
[[1,2,3,4,5],[6],[7]] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [1,6] => 3
[[1,3,5,7],[2,4,6]] => [[1,2,4,6],[3,5,7]] => [3,5,7,1,2,4,6] => [3,4] => 3
[[1,2,5,7],[3,4,6]] => [[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => [2,5] => 3
[[1,3,4,7],[2,5,6]] => [[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => [2,5] => 3
[[1,2,4,7],[3,5,6]] => [[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => [2,5] => 3
[[1,2,3,7],[4,5,6]] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [1,6] => 3
[[1,3,5,6],[2,4,7]] => [[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => [2,5] => 3
[[1,2,5,6],[3,4,7]] => [[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => [2,5] => 3
[[1,3,4,6],[2,5,7]] => [[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => [2,5] => 3
[[1,2,4,6],[3,5,7]] => [[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => [2,5] => 3
[[1,2,3,6],[4,5,7]] => [[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [1,6] => 3
[[1,3,4,5],[2,6,7]] => [[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [1,6] => 3
[[1,2,4,5],[3,6,7]] => [[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [1,6] => 3
[[1,2,3,5],[4,6,7]] => [[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [1,6] => 3
[[1,2,3,4],[5,6,7]] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => [7] => 1
[[1,4,6,7],[2,5],[3]] => [[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [1,2,4] => 6
[[1,3,6,7],[2,5],[4]] => [[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => [1,2,4] => 6
[[1,2,6,7],[3,5],[4]] => [[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => [1,2,4] => 6
[[1,3,6,7],[2,4],[5]] => [[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => [1,2,4] => 6
[[1,2,6,7],[3,4],[5]] => [[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => [1,2,4] => 6
[[1,4,5,7],[2,6],[3]] => [[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => [1,2,4] => 6
[[1,3,5,7],[2,6],[4]] => [[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => [1,2,4] => 6
[[1,2,5,7],[3,6],[4]] => [[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => [1,2,4] => 6
[[1,3,4,7],[2,6],[5]] => [[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => [1,1,5] => 4
[[1,2,4,7],[3,6],[5]] => [[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => [1,1,5] => 4
[[1,2,3,7],[4,6],[5]] => [[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => [1,1,5] => 4
[[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => [1,2,4] => 6
[[1,2,5,7],[3,4],[6]] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [1,2,4] => 6
[[1,3,4,7],[2,5],[6]] => [[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => [1,2,4] => 6
[[1,2,4,7],[3,5],[6]] => [[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => [1,2,4] => 6
[[1,2,3,7],[4,5],[6]] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [1,1,5] => 4
[[1,4,5,6],[2,7],[3]] => [[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => [1,1,5] => 4
[[1,3,5,6],[2,7],[4]] => [[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => [1,1,5] => 4
[[1,2,5,6],[3,7],[4]] => [[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => [1,1,5] => 4
[[1,3,4,6],[2,7],[5]] => [[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => [1,1,5] => 4
[[1,2,4,6],[3,7],[5]] => [[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => [1,1,5] => 4
[[1,2,3,6],[4,7],[5]] => [[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => [1,1,5] => 4
[[1,3,4,5],[2,7],[6]] => [[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [1,6] => 3
[[1,2,4,5],[3,7],[6]] => [[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [1,6] => 3
[[1,2,3,5],[4,7],[6]] => [[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [1,6] => 3
[[1,2,3,4],[5,7],[6]] => [[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [1,6] => 3
[[1,3,5,6],[2,4],[7]] => [[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => [2,5] => 3
[[1,2,5,6],[3,4],[7]] => [[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => [2,5] => 3
[[1,3,4,6],[2,5],[7]] => [[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => [2,5] => 3
[[1,2,4,6],[3,5],[7]] => [[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => [2,5] => 3
[[1,2,3,6],[4,5],[7]] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [2,5] => 3
[[1,3,4,5],[2,6],[7]] => [[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => [2,5] => 3
[[1,2,4,5],[3,6],[7]] => [[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => [2,5] => 3
[[1,2,3,5],[4,6],[7]] => [[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => [2,5] => 3
[[1,2,3,4],[5,6],[7]] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [1,6] => 3
[[1,5,6,7],[2],[3],[4]] => [[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => [1,1,1,4] => 5
[[1,4,6,7],[2],[3],[5]] => [[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => [1,1,1,4] => 5
[[1,3,6,7],[2],[4],[5]] => [[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => [1,1,1,4] => 5
[[1,2,6,7],[3],[4],[5]] => [[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => [1,1,1,4] => 5
[[1,4,5,7],[2],[3],[6]] => [[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => [1,1,1,4] => 5
[[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => [1,1,1,4] => 5
[[1,2,5,7],[3],[4],[6]] => [[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => [1,1,1,4] => 5
[[1,3,4,7],[2],[5],[6]] => [[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => [1,1,1,4] => 5
[[1,2,4,7],[3],[5],[6]] => [[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => [1,1,1,4] => 5
[[1,2,3,7],[4],[5],[6]] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [1,1,1,4] => 5
[[1,4,5,6],[2],[3],[7]] => [[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => [1,1,5] => 4
[[1,3,5,6],[2],[4],[7]] => [[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => [1,1,5] => 4
[[1,2,5,6],[3],[4],[7]] => [[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => [1,1,5] => 4
[[1,3,4,6],[2],[5],[7]] => [[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => [1,1,5] => 4
[[1,2,4,6],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => [1,1,5] => 4
[[1,2,3,6],[4],[5],[7]] => [[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => [1,1,5] => 4
[[1,3,4,5],[2],[6],[7]] => [[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => [1,1,5] => 4
[[1,2,4,5],[3],[6],[7]] => [[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => [1,1,5] => 4
[[1,2,3,5],[4],[6],[7]] => [[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => [1,1,5] => 4
[[1,2,3,4],[5],[6],[7]] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [1,1,5] => 4
[[1,4,6],[2,5,7],[3]] => [[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [1,2,4] => 6
[[1,3,6],[2,5,7],[4]] => [[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => [1,1,5] => 4
[[1,2,6],[3,5,7],[4]] => [[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => [1,1,5] => 4
[[1,3,6],[2,4,7],[5]] => [[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => [1,2,4] => 6
[[1,2,6],[3,4,7],[5]] => [[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => [1,1,5] => 4
[[1,4,5],[2,6,7],[3]] => [[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => [1,1,5] => 4
[[1,3,5],[2,6,7],[4]] => [[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => [1,1,5] => 4
[[1,2,5],[3,6,7],[4]] => [[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => [1,1,5] => 4
[[1,3,4],[2,6,7],[5]] => [[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [1,6] => 3
[[1,2,4],[3,6,7],[5]] => [[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [1,6] => 3
[[1,2,3],[4,6,7],[5]] => [[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [1,6] => 3
[[1,3,5],[2,4,7],[6]] => [[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => [2,5] => 3
[[1,2,5],[3,4,7],[6]] => [[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => [2,5] => 3
[[1,3,4],[2,5,7],[6]] => [[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => [2,5] => 3
[[1,2,4],[3,5,7],[6]] => [[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => [2,5] => 3
[[1,2,3],[4,5,7],[6]] => [[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [1,6] => 3
[[1,3,5],[2,4,6],[7]] => [[1,2,4,6],[3,5,7]] => [3,5,7,1,2,4,6] => [3,4] => 3
[[1,2,5],[3,4,6],[7]] => [[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => [2,5] => 3
[[1,3,4],[2,5,6],[7]] => [[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => [2,5] => 3
[[1,2,4],[3,5,6],[7]] => [[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => [2,5] => 3
[[1,2,3],[4,5,6],[7]] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [1,6] => 3
[[1,4,7],[2,5],[3,6]] => [[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => [2,2,3] => 4
[[1,3,7],[2,5],[4,6]] => [[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => [1,2,4] => 6
[[1,2,7],[3,5],[4,6]] => [[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => [1,2,4] => 6
[[1,3,7],[2,4],[5,6]] => [[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => [1,2,4] => 6
[[1,2,7],[3,4],[5,6]] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [1,2,4] => 6
[[1,4,6],[2,5],[3,7]] => [[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [1,2,4] => 6
[[1,3,6],[2,5],[4,7]] => [[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => [1,2,4] => 6
[[1,2,6],[3,5],[4,7]] => [[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => [1,2,4] => 6
[[1,3,6],[2,4],[5,7]] => [[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => [1,2,4] => 6
[[1,2,6],[3,4],[5,7]] => [[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => [1,2,4] => 6
[[1,4,5],[2,6],[3,7]] => [[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => [1,2,4] => 6
[[1,3,5],[2,6],[4,7]] => [[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => [1,2,4] => 6
[[1,2,5],[3,6],[4,7]] => [[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => [1,2,4] => 6
[[1,3,4],[2,6],[5,7]] => [[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => [2,5] => 3
[[1,2,4],[3,6],[5,7]] => [[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => [2,5] => 3
[[1,2,3],[4,6],[5,7]] => [[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => [2,5] => 3
[[1,3,5],[2,4],[6,7]] => [[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => [2,5] => 3
[[1,2,5],[3,4],[6,7]] => [[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => [2,5] => 3
[[1,3,4],[2,5],[6,7]] => [[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => [2,5] => 3
[[1,2,4],[3,5],[6,7]] => [[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => [2,5] => 3
[[1,2,3],[4,5],[6,7]] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [2,5] => 3
[[1,5,7],[2,6],[3],[4]] => [[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [1,1,2,3] => 8
[[1,4,7],[2,6],[3],[5]] => [[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => [1,1,1,4] => 5
[[1,3,7],[2,6],[4],[5]] => [[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => [1,1,1,4] => 5
[[1,2,7],[3,6],[4],[5]] => [[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => [1,1,1,4] => 5
[[1,4,7],[2,5],[3],[6]] => [[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => [1,1,2,3] => 8
[[1,3,7],[2,5],[4],[6]] => [[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => [1,1,1,4] => 5
[[1,2,7],[3,5],[4],[6]] => [[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => [1,1,1,4] => 5
[[1,3,7],[2,4],[5],[6]] => [[1,2,4],[3,5],[6],[7]] => [7,6,3,5,1,2,4] => [1,1,2,3] => 8
[[1,2,7],[3,4],[5],[6]] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [1,1,1,4] => 5
[[1,5,6],[2,7],[3],[4]] => [[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => [1,1,1,4] => 5
[[1,4,6],[2,7],[3],[5]] => [[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => [1,1,1,4] => 5
[[1,3,6],[2,7],[4],[5]] => [[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => [1,1,1,4] => 5
[[1,2,6],[3,7],[4],[5]] => [[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => [1,1,1,4] => 5
[[1,4,5],[2,7],[3],[6]] => [[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => [1,1,5] => 4
[[1,3,5],[2,7],[4],[6]] => [[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => [1,1,5] => 4
[[1,2,5],[3,7],[4],[6]] => [[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => [1,1,5] => 4
[[1,3,4],[2,7],[5],[6]] => [[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => [1,1,5] => 4
[[1,2,4],[3,7],[5],[6]] => [[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => [1,1,5] => 4
[[1,2,3],[4,7],[5],[6]] => [[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => [1,1,5] => 4
[[1,4,6],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [1,2,4] => 6
[[1,3,6],[2,5],[4],[7]] => [[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => [1,2,4] => 6
[[1,2,6],[3,5],[4],[7]] => [[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => [1,2,4] => 6
[[1,3,6],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => [1,2,4] => 6
[[1,2,6],[3,4],[5],[7]] => [[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => [1,2,4] => 6
[[1,4,5],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => [1,2,4] => 6
[[1,3,5],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => [1,2,4] => 6
[[1,2,5],[3,6],[4],[7]] => [[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => [1,2,4] => 6
[[1,3,4],[2,6],[5],[7]] => [[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => [1,1,5] => 4
[[1,2,4],[3,6],[5],[7]] => [[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => [1,1,5] => 4
[[1,2,3],[4,6],[5],[7]] => [[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => [1,1,5] => 4
[[1,3,5],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => [1,2,4] => 6
[[1,2,5],[3,4],[6],[7]] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [1,2,4] => 6
[[1,3,4],[2,5],[6],[7]] => [[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => [1,2,4] => 6
[[1,2,4],[3,5],[6],[7]] => [[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => [1,2,4] => 6
[[1,2,3],[4,5],[6],[7]] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [1,1,5] => 4
[[1,6,7],[2],[3],[4],[5]] => [[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => [1,1,1,1,3] => 6
[[1,5,7],[2],[3],[4],[6]] => [[1,2,6],[3],[4],[5],[7]] => [7,5,4,3,1,2,6] => [1,1,1,1,3] => 6
[[1,4,7],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6],[7]] => [7,6,4,3,1,2,5] => [1,1,1,1,3] => 6
[[1,3,7],[2],[4],[5],[6]] => [[1,2,4],[3],[5],[6],[7]] => [7,6,5,3,1,2,4] => [1,1,1,1,3] => 6
[[1,2,7],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [1,1,1,1,3] => 6
[[1,5,6],[2],[3],[4],[7]] => [[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => [1,1,1,4] => 5
[[1,4,6],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => [1,1,1,4] => 5
[[1,3,6],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => [1,1,1,4] => 5
[[1,2,6],[3],[4],[5],[7]] => [[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => [1,1,1,4] => 5
[[1,4,5],[2],[3],[6],[7]] => [[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => [1,1,1,4] => 5
[[1,3,5],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => [1,1,1,4] => 5
[[1,2,5],[3],[4],[6],[7]] => [[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => [1,1,1,4] => 5
[[1,3,4],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => [1,1,1,4] => 5
[[1,2,4],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => [1,1,1,4] => 5
[[1,2,3],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [1,1,1,4] => 5
[[1,5],[2,6],[3,7],[4]] => [[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [1,1,2,3] => 8
[[1,4],[2,6],[3,7],[5]] => [[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => [1,2,4] => 6
[[1,3],[2,6],[4,7],[5]] => [[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => [1,2,4] => 6
[[1,2],[3,6],[4,7],[5]] => [[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => [1,2,4] => 6
[[1,4],[2,5],[3,7],[6]] => [[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [1,2,4] => 6
[[1,3],[2,5],[4,7],[6]] => [[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => [1,2,4] => 6
[[1,2],[3,5],[4,7],[6]] => [[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => [1,2,4] => 6
[[1,3],[2,4],[5,7],[6]] => [[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => [1,2,4] => 6
[[1,2],[3,4],[5,7],[6]] => [[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => [1,2,4] => 6
[[1,4],[2,5],[3,6],[7]] => [[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => [2,2,3] => 4
[[1,3],[2,5],[4,6],[7]] => [[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => [1,2,4] => 6
[[1,2],[3,5],[4,6],[7]] => [[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => [1,2,4] => 6
[[1,3],[2,4],[5,6],[7]] => [[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => [1,2,4] => 6
[[1,2],[3,4],[5,6],[7]] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [1,2,4] => 6
[[1,6],[2,7],[3],[4],[5]] => [[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => [1,1,1,1,3] => 6
[[1,5],[2,7],[3],[4],[6]] => [[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => [1,1,1,4] => 5
[[1,4],[2,7],[3],[5],[6]] => [[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => [1,1,1,4] => 5
[[1,3],[2,7],[4],[5],[6]] => [[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => [1,1,1,4] => 5
[[1,2],[3,7],[4],[5],[6]] => [[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => [1,1,1,4] => 5
[[1,5],[2,6],[3],[4],[7]] => [[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [1,1,2,3] => 8
[[1,4],[2,6],[3],[5],[7]] => [[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => [1,1,1,4] => 5
[[1,3],[2,6],[4],[5],[7]] => [[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => [1,1,1,4] => 5
[[1,2],[3,6],[4],[5],[7]] => [[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => [1,1,1,4] => 5
[[1,4],[2,5],[3],[6],[7]] => [[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => [1,1,2,3] => 8
[[1,3],[2,5],[4],[6],[7]] => [[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => [1,1,1,4] => 5
[[1,2],[3,5],[4],[6],[7]] => [[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => [1,1,1,4] => 5
[[1,3],[2,4],[5],[6],[7]] => [[1,2,4],[3,5],[6],[7]] => [7,6,3,5,1,2,4] => [1,1,2,3] => 8
[[1,2],[3,4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [1,1,1,4] => 5
[[1,7],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2] => 7
[[1,6],[2],[3],[4],[5],[7]] => [[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => [1,1,1,1,3] => 6
[[1,5],[2],[3],[4],[6],[7]] => [[1,2,6],[3],[4],[5],[7]] => [7,5,4,3,1,2,6] => [1,1,1,1,3] => 6
[[1,4],[2],[3],[5],[6],[7]] => [[1,2,5],[3],[4],[6],[7]] => [7,6,4,3,1,2,5] => [1,1,1,1,3] => 6
[[1,3],[2],[4],[5],[6],[7]] => [[1,2,4],[3],[5],[6],[7]] => [7,6,5,3,1,2,4] => [1,1,1,1,3] => 6
[[1,2],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [1,1,1,1,3] => 6
[[1],[2],[3],[4],[5],[6],[7]] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2] => 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] => [8] => 1
[[1,3,4,5,6,7,8],[2]] => [[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [1,7] => 3
[[1,2,4,5,6,7,8],[3]] => [[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => [1,7] => 3
[[1,2,3,5,6,7,8],[4]] => [[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => [1,7] => 3
[[1,2,3,4,6,7,8],[5]] => [[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => [1,7] => 3
[[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [1,7] => 3
[[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [1,7] => 3
[[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => [8] => 1
[[1,3,5,6,7,8],[2,4]] => [[1,2,4,6,7,8],[3,5]] => [3,5,1,2,4,6,7,8] => [2,6] => 3
[[1,2,5,6,7,8],[3,4]] => [[1,2,3,4,7,8],[5,6]] => [5,6,1,2,3,4,7,8] => [2,6] => 3
[[1,3,4,6,7,8],[2,5]] => [[1,2,4,5,7,8],[3,6]] => [3,6,1,2,4,5,7,8] => [2,6] => 3
[[1,2,4,6,7,8],[3,5]] => [[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => [2,6] => 3
[[1,2,3,6,7,8],[4,5]] => [[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => [2,6] => 3
[[1,3,4,5,7,8],[2,6]] => [[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [2,6] => 3
[[1,2,4,5,7,8],[3,6]] => [[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => [2,6] => 3
[[1,2,3,5,7,8],[4,6]] => [[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [2,6] => 3
[[1,2,3,4,7,8],[5,6]] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [2,6] => 3
[[1,3,4,5,6,8],[2,7]] => [[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => [2,6] => 3
[[1,2,4,5,6,8],[3,7]] => [[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => [2,6] => 3
[[1,2,3,5,6,8],[4,7]] => [[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => [2,6] => 3
[[1,2,3,4,6,8],[5,7]] => [[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => [2,6] => 3
[[1,2,3,4,5,8],[6,7]] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [1,7] => 3
[[1,3,4,5,6,7],[2,8]] => [[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [1,7] => 3
[[1,2,4,5,6,7],[3,8]] => [[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => [1,7] => 3
[[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => [1,7] => 3
[[1,2,3,4,6,7],[5,8]] => [[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => [1,7] => 3
[[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [1,7] => 3
[[1,2,3,4,5,6],[7,8]] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => [8] => 1
[[1,4,5,6,7,8],[2],[3]] => [[1,2,5,6,7,8],[3],[4]] => [4,3,1,2,5,6,7,8] => [1,1,6] => 4
[[1,3,5,6,7,8],[2],[4]] => [[1,2,4,6,7,8],[3],[5]] => [5,3,1,2,4,6,7,8] => [1,1,6] => 4
[[1,2,5,6,7,8],[3],[4]] => [[1,2,3,6,7,8],[4],[5]] => [5,4,1,2,3,6,7,8] => [1,1,6] => 4
[[1,3,4,6,7,8],[2],[5]] => [[1,2,4,5,7,8],[3],[6]] => [6,3,1,2,4,5,7,8] => [1,1,6] => 4
[[1,2,4,6,7,8],[3],[5]] => [[1,2,3,5,7,8],[4],[6]] => [6,4,1,2,3,5,7,8] => [1,1,6] => 4
[[1,2,3,6,7,8],[4],[5]] => [[1,2,3,4,7,8],[5],[6]] => [6,5,1,2,3,4,7,8] => [1,1,6] => 4
[[1,3,4,5,7,8],[2],[6]] => [[1,2,4,5,6,8],[3],[7]] => [7,3,1,2,4,5,6,8] => [1,1,6] => 4
[[1,2,4,5,7,8],[3],[6]] => [[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => [1,1,6] => 4
[[1,2,3,5,7,8],[4],[6]] => [[1,2,3,4,6,8],[5],[7]] => [7,5,1,2,3,4,6,8] => [1,1,6] => 4
[[1,2,3,4,7,8],[5],[6]] => [[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => [1,1,6] => 4
[[1,3,4,5,6,8],[2],[7]] => [[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [1,1,6] => 4
[[1,2,4,5,6,8],[3],[7]] => [[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => [1,1,6] => 4
[[1,2,3,5,6,8],[4],[7]] => [[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => [1,1,6] => 4
[[1,2,3,4,6,8],[5],[7]] => [[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => [1,1,6] => 4
[[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [1,1,6] => 4
[[1,3,4,5,6,7],[2],[8]] => [[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [1,7] => 3
[[1,2,4,5,6,7],[3],[8]] => [[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => [1,7] => 3
[[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => [1,7] => 3
[[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => [1,7] => 3
[[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [1,7] => 3
[[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [1,7] => 3
[[1,3,5,7,8],[2,4,6]] => [[1,2,4,6,8],[3,5,7]] => [3,5,7,1,2,4,6,8] => [3,5] => 3
[[1,2,5,7,8],[3,4,6]] => [[1,2,3,4,6],[5,7,8]] => [5,7,8,1,2,3,4,6] => [3,5] => 3
[[1,3,4,7,8],[2,5,6]] => [[1,2,4,5,6],[3,7,8]] => [3,7,8,1,2,4,5,6] => [3,5] => 3
[[1,2,4,7,8],[3,5,6]] => [[1,2,3,5,6],[4,7,8]] => [4,7,8,1,2,3,5,6] => [3,5] => 3
[[1,2,3,7,8],[4,5,6]] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [2,6] => 3
[[1,3,5,6,8],[2,4,7]] => [[1,2,4,6,7],[3,5,8]] => [3,5,8,1,2,4,6,7] => [3,5] => 3
[[1,2,5,6,8],[3,4,7]] => [[1,2,3,4,7],[5,6,8]] => [5,6,8,1,2,3,4,7] => [3,5] => 3
[[1,3,4,6,8],[2,5,7]] => [[1,2,4,5,7],[3,6,8]] => [3,6,8,1,2,4,5,7] => [3,5] => 3
[[1,2,4,6,8],[3,5,7]] => [[1,2,3,5,7],[4,6,8]] => [4,6,8,1,2,3,5,7] => [3,5] => 3
[[1,2,3,6,8],[4,5,7]] => [[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => [2,6] => 3
[[1,3,4,5,8],[2,6,7]] => [[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => [2,6] => 3
[[1,2,4,5,8],[3,6,7]] => [[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => [2,6] => 3
[[1,2,3,5,8],[4,6,7]] => [[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => [2,6] => 3
[[1,2,3,4,8],[5,6,7]] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [1,7] => 3
[[1,3,5,6,7],[2,4,8]] => [[1,2,4,6,7,8],[3,5]] => [3,5,1,2,4,6,7,8] => [2,6] => 3
[[1,2,5,6,7],[3,4,8]] => [[1,2,3,4,7,8],[5,6]] => [5,6,1,2,3,4,7,8] => [2,6] => 3
[[1,3,4,6,7],[2,5,8]] => [[1,2,4,5,7,8],[3,6]] => [3,6,1,2,4,5,7,8] => [2,6] => 3
[[1,2,4,6,7],[3,5,8]] => [[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => [2,6] => 3
[[1,2,3,6,7],[4,5,8]] => [[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => [2,6] => 3
[[1,3,4,5,7],[2,6,8]] => [[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [2,6] => 3
[[1,2,4,5,7],[3,6,8]] => [[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => [2,6] => 3
[[1,2,3,5,7],[4,6,8]] => [[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [2,6] => 3
[[1,2,3,4,7],[5,6,8]] => [[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [1,7] => 3
[[1,3,4,5,6],[2,7,8]] => [[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [1,7] => 3
[[1,2,4,5,6],[3,7,8]] => [[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => [1,7] => 3
[[1,2,3,5,6],[4,7,8]] => [[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => [1,7] => 3
[[1,2,3,4,6],[5,7,8]] => [[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => [1,7] => 3
[[1,2,3,4,5],[6,7,8]] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => [8] => 1
[[1,3,6,7,8],[2,5],[4]] => [[1,2,4,5,8],[3,7],[6]] => [6,3,7,1,2,4,5,8] => [1,2,5] => 6
[[1,2,6,7,8],[3,5],[4]] => [[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [1,2,5] => 6
[[1,3,6,7,8],[2,4],[5]] => [[1,2,4,7,8],[3,5],[6]] => [6,3,5,1,2,4,7,8] => [1,2,5] => 6
[[1,2,6,7,8],[3,4],[5]] => [[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [1,2,5] => 6
[[1,3,5,7,8],[2,6],[4]] => [[1,2,4,6,8],[3,7],[5]] => [5,3,7,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5,7,8],[3,6],[4]] => [[1,2,3,6,8],[4,7],[5]] => [5,4,7,1,2,3,6,8] => [1,2,5] => 6
[[1,3,4,7,8],[2,6],[5]] => [[1,2,4,5,6],[3,8],[7]] => [7,3,8,1,2,4,5,6] => [1,2,5] => 6
[[1,2,4,7,8],[3,6],[5]] => [[1,2,3,5,6],[4,8],[7]] => [7,4,8,1,2,3,5,6] => [1,2,5] => 6
[[1,2,3,7,8],[4,6],[5]] => [[1,2,3,4,6],[5,8],[7]] => [7,5,8,1,2,3,4,6] => [1,2,5] => 6
[[1,3,5,7,8],[2,4],[6]] => [[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5,7,8],[3,4],[6]] => [[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [1,2,5] => 6
[[1,3,4,7,8],[2,5],[6]] => [[1,2,4,5,8],[3,6],[7]] => [7,3,6,1,2,4,5,8] => [1,2,5] => 6
[[1,2,4,7,8],[3,5],[6]] => [[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => [1,2,5] => 6
[[1,2,3,7,8],[4,5],[6]] => [[1,2,3,4,5],[6,8],[7]] => [7,6,8,1,2,3,4,5] => [1,2,5] => 6
[[1,4,5,6,8],[2,7],[3]] => [[1,2,5,6,7],[3,8],[4]] => [4,3,8,1,2,5,6,7] => [1,2,5] => 6
[[1,3,5,6,8],[2,7],[4]] => [[1,2,4,6,7],[3,8],[5]] => [5,3,8,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5,6,8],[3,7],[4]] => [[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => [1,2,5] => 6
[[1,3,4,6,8],[2,7],[5]] => [[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => [1,2,5] => 6
[[1,2,4,6,8],[3,7],[5]] => [[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [1,2,5] => 6
[[1,2,3,6,8],[4,7],[5]] => [[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [1,2,5] => 6
[[1,3,4,5,8],[2,7],[6]] => [[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [1,1,6] => 4
[[1,2,4,5,8],[3,7],[6]] => [[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => [1,1,6] => 4
[[1,2,3,5,8],[4,7],[6]] => [[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => [1,1,6] => 4
[[1,2,3,4,8],[5,7],[6]] => [[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => [1,1,6] => 4
[[1,3,5,6,8],[2,4],[7]] => [[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5,6,8],[3,4],[7]] => [[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => [1,2,5] => 6
[[1,3,4,6,8],[2,5],[7]] => [[1,2,4,5,7],[3,6],[8]] => [8,3,6,1,2,4,5,7] => [1,2,5] => 6
[[1,2,4,6,8],[3,5],[7]] => [[1,2,3,5,7],[4,6],[8]] => [8,4,6,1,2,3,5,7] => [1,2,5] => 6
[[1,2,3,6,8],[4,5],[7]] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [1,2,5] => 6
[[1,3,4,5,8],[2,6],[7]] => [[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => [1,2,5] => 6
[[1,2,4,5,8],[3,6],[7]] => [[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => [1,2,5] => 6
[[1,2,3,5,8],[4,6],[7]] => [[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => [1,2,5] => 6
[[1,2,3,4,8],[5,6],[7]] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [1,1,6] => 4
[[1,4,5,6,7],[2,8],[3]] => [[1,2,5,6,7,8],[3],[4]] => [4,3,1,2,5,6,7,8] => [1,1,6] => 4
[[1,3,5,6,7],[2,8],[4]] => [[1,2,4,6,7,8],[3],[5]] => [5,3,1,2,4,6,7,8] => [1,1,6] => 4
[[1,2,5,6,7],[3,8],[4]] => [[1,2,3,6,7,8],[4],[5]] => [5,4,1,2,3,6,7,8] => [1,1,6] => 4
[[1,3,4,6,7],[2,8],[5]] => [[1,2,4,5,7,8],[3],[6]] => [6,3,1,2,4,5,7,8] => [1,1,6] => 4
[[1,2,4,6,7],[3,8],[5]] => [[1,2,3,5,7,8],[4],[6]] => [6,4,1,2,3,5,7,8] => [1,1,6] => 4
[[1,2,3,6,7],[4,8],[5]] => [[1,2,3,4,7,8],[5],[6]] => [6,5,1,2,3,4,7,8] => [1,1,6] => 4
[[1,3,4,5,7],[2,8],[6]] => [[1,2,4,5,6,8],[3],[7]] => [7,3,1,2,4,5,6,8] => [1,1,6] => 4
[[1,2,4,5,7],[3,8],[6]] => [[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => [1,1,6] => 4
[[1,2,3,5,7],[4,8],[6]] => [[1,2,3,4,6,8],[5],[7]] => [7,5,1,2,3,4,6,8] => [1,1,6] => 4
[[1,2,3,4,7],[5,8],[6]] => [[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => [1,1,6] => 4
[[1,3,4,5,6],[2,8],[7]] => [[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [1,7] => 3
[[1,2,4,5,6],[3,8],[7]] => [[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => [1,7] => 3
[[1,2,3,5,6],[4,8],[7]] => [[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => [1,7] => 3
[[1,2,3,4,6],[5,8],[7]] => [[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => [1,7] => 3
[[1,2,3,4,5],[6,8],[7]] => [[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [1,7] => 3
[[1,3,5,6,7],[2,4],[8]] => [[1,2,4,6,7,8],[3,5]] => [3,5,1,2,4,6,7,8] => [2,6] => 3
[[1,2,5,6,7],[3,4],[8]] => [[1,2,3,4,7,8],[5,6]] => [5,6,1,2,3,4,7,8] => [2,6] => 3
[[1,3,4,6,7],[2,5],[8]] => [[1,2,4,5,7,8],[3,6]] => [3,6,1,2,4,5,7,8] => [2,6] => 3
[[1,2,4,6,7],[3,5],[8]] => [[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => [2,6] => 3
[[1,2,3,6,7],[4,5],[8]] => [[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => [2,6] => 3
[[1,3,4,5,7],[2,6],[8]] => [[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [2,6] => 3
[[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => [2,6] => 3
[[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [2,6] => 3
[[1,2,3,4,7],[5,6],[8]] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [2,6] => 3
[[1,3,4,5,6],[2,7],[8]] => [[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => [2,6] => 3
[[1,2,4,5,6],[3,7],[8]] => [[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => [2,6] => 3
[[1,2,3,5,6],[4,7],[8]] => [[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => [2,6] => 3
[[1,2,3,4,6],[5,7],[8]] => [[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => [2,6] => 3
[[1,2,3,4,5],[6,7],[8]] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [1,7] => 3
[[1,5,6,7,8],[2],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => [5,4,3,1,2,6,7,8] => [1,1,1,5] => 5
[[1,4,6,7,8],[2],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => [6,4,3,1,2,5,7,8] => [1,1,1,5] => 5
[[1,2,6,7,8],[3],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => [6,5,4,1,2,3,7,8] => [1,1,1,5] => 5
[[1,4,5,7,8],[2],[3],[6]] => [[1,2,5,6,8],[3],[4],[7]] => [7,4,3,1,2,5,6,8] => [1,1,1,5] => 5
[[1,3,5,7,8],[2],[4],[6]] => [[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [1,1,1,5] => 5
[[1,2,5,7,8],[3],[4],[6]] => [[1,2,3,6,8],[4],[5],[7]] => [7,5,4,1,2,3,6,8] => [1,1,1,5] => 5
[[1,3,4,7,8],[2],[5],[6]] => [[1,2,4,5,8],[3],[6],[7]] => [7,6,3,1,2,4,5,8] => [1,1,1,5] => 5
[[1,2,4,7,8],[3],[5],[6]] => [[1,2,3,5,8],[4],[6],[7]] => [7,6,4,1,2,3,5,8] => [1,1,1,5] => 5
[[1,2,3,7,8],[4],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => [1,1,1,5] => 5
[[1,4,5,6,8],[2],[3],[7]] => [[1,2,5,6,7],[3],[4],[8]] => [8,4,3,1,2,5,6,7] => [1,1,1,5] => 5
[[1,3,5,6,8],[2],[4],[7]] => [[1,2,4,6,7],[3],[5],[8]] => [8,5,3,1,2,4,6,7] => [1,1,1,5] => 5
[[1,2,5,6,8],[3],[4],[7]] => [[1,2,3,6,7],[4],[5],[8]] => [8,5,4,1,2,3,6,7] => [1,1,1,5] => 5
[[1,2,4,6,8],[3],[5],[7]] => [[1,2,3,5,7],[4],[6],[8]] => [8,6,4,1,2,3,5,7] => [1,1,1,5] => 5
[[1,2,3,6,8],[4],[5],[7]] => [[1,2,3,4,7],[5],[6],[8]] => [8,6,5,1,2,3,4,7] => [1,1,1,5] => 5
[[1,2,4,5,8],[3],[6],[7]] => [[1,2,3,5,6],[4],[7],[8]] => [8,7,4,1,2,3,5,6] => [1,1,1,5] => 5
[[1,2,3,5,8],[4],[6],[7]] => [[1,2,3,4,6],[5],[7],[8]] => [8,7,5,1,2,3,4,6] => [1,1,1,5] => 5
[[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [1,1,1,5] => 5
[[1,4,5,6,7],[2],[3],[8]] => [[1,2,5,6,7,8],[3],[4]] => [4,3,1,2,5,6,7,8] => [1,1,6] => 4
[[1,3,5,6,7],[2],[4],[8]] => [[1,2,4,6,7,8],[3],[5]] => [5,3,1,2,4,6,7,8] => [1,1,6] => 4
[[1,2,5,6,7],[3],[4],[8]] => [[1,2,3,6,7,8],[4],[5]] => [5,4,1,2,3,6,7,8] => [1,1,6] => 4
[[1,3,4,6,7],[2],[5],[8]] => [[1,2,4,5,7,8],[3],[6]] => [6,3,1,2,4,5,7,8] => [1,1,6] => 4
[[1,2,4,6,7],[3],[5],[8]] => [[1,2,3,5,7,8],[4],[6]] => [6,4,1,2,3,5,7,8] => [1,1,6] => 4
[[1,2,3,6,7],[4],[5],[8]] => [[1,2,3,4,7,8],[5],[6]] => [6,5,1,2,3,4,7,8] => [1,1,6] => 4
[[1,3,4,5,7],[2],[6],[8]] => [[1,2,4,5,6,8],[3],[7]] => [7,3,1,2,4,5,6,8] => [1,1,6] => 4
[[1,2,4,5,7],[3],[6],[8]] => [[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => [1,1,6] => 4
[[1,2,3,5,7],[4],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => [7,5,1,2,3,4,6,8] => [1,1,6] => 4
[[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => [1,1,6] => 4
[[1,3,4,5,6],[2],[7],[8]] => [[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [1,1,6] => 4
[[1,2,4,5,6],[3],[7],[8]] => [[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => [1,1,6] => 4
[[1,2,3,5,6],[4],[7],[8]] => [[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => [1,1,6] => 4
[[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => [1,1,6] => 4
[[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [1,1,6] => 4
[[1,3,5,7],[2,4,6,8]] => [[1,2,4,6,8],[3,5,7]] => [3,5,7,1,2,4,6,8] => [3,5] => 3
[[1,2,5,7],[3,4,6,8]] => [[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [2,6] => 3
[[1,3,4,7],[2,5,6,8]] => [[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [2,6] => 3
[[1,2,4,7],[3,5,6,8]] => [[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => [2,6] => 3
[[1,2,3,7],[4,5,6,8]] => [[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [1,7] => 3
[[1,3,5,6],[2,4,7,8]] => [[1,2,4,6,7,8],[3,5]] => [3,5,1,2,4,6,7,8] => [2,6] => 3
[[1,2,5,6],[3,4,7,8]] => [[1,2,3,4,7,8],[5,6]] => [5,6,1,2,3,4,7,8] => [2,6] => 3
[[1,3,4,6],[2,5,7,8]] => [[1,2,4,5,7,8],[3,6]] => [3,6,1,2,4,5,7,8] => [2,6] => 3
[[1,2,4,6],[3,5,7,8]] => [[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => [2,6] => 3
[[1,2,3,6],[4,5,7,8]] => [[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => [1,7] => 3
[[1,3,4,5],[2,6,7,8]] => [[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [1,7] => 3
[[1,2,4,5],[3,6,7,8]] => [[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => [1,7] => 3
[[1,2,3,5],[4,6,7,8]] => [[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => [1,7] => 3
[[1,2,3,4],[5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => [8] => 1
[[1,4,6,8],[2,5,7],[3]] => [[1,2,5,7],[3,6,8],[4]] => [4,3,6,8,1,2,5,7] => [1,3,4] => 6
[[1,3,6,8],[2,5,7],[4]] => [[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => [1,2,5] => 6
[[1,2,6,8],[3,5,7],[4]] => [[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [1,2,5] => 6
[[1,3,6,8],[2,4,7],[5]] => [[1,2,4,7],[3,5,8],[6]] => [6,3,5,8,1,2,4,7] => [1,3,4] => 6
[[1,2,6,8],[3,4,7],[5]] => [[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [1,2,5] => 6
[[1,4,5,8],[2,6,7],[3]] => [[1,2,5,6,7],[3,8],[4]] => [4,3,8,1,2,5,6,7] => [1,2,5] => 6
[[1,3,5,8],[2,6,7],[4]] => [[1,2,4,6,7],[3,8],[5]] => [5,3,8,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5,8],[3,6,7],[4]] => [[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => [1,2,5] => 6
[[1,3,4,8],[2,6,7],[5]] => [[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [1,1,6] => 4
[[1,2,4,8],[3,6,7],[5]] => [[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => [1,1,6] => 4
[[1,2,3,8],[4,6,7],[5]] => [[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => [1,1,6] => 4
[[1,3,5,8],[2,4,7],[6]] => [[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5,8],[3,4,7],[6]] => [[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => [1,2,5] => 6
[[1,3,4,8],[2,5,7],[6]] => [[1,2,4,5,7],[3,6],[8]] => [8,3,6,1,2,4,5,7] => [1,2,5] => 6
[[1,2,4,8],[3,5,7],[6]] => [[1,2,3,5,7],[4,6],[8]] => [8,4,6,1,2,3,5,7] => [1,2,5] => 6
[[1,2,3,8],[4,5,7],[6]] => [[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => [1,1,6] => 4
[[1,3,5,8],[2,4,6],[7]] => [[1,2,4,6],[3,5,7],[8]] => [8,3,5,7,1,2,4,6] => [1,3,4] => 6
[[1,2,5,8],[3,4,6],[7]] => [[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => [1,2,5] => 6
[[1,3,4,8],[2,5,6],[7]] => [[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => [1,2,5] => 6
[[1,2,4,8],[3,5,6],[7]] => [[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => [1,2,5] => 6
[[1,2,3,8],[4,5,6],[7]] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [1,1,6] => 4
[[1,3,6,7],[2,5,8],[4]] => [[1,2,4,5,8],[3,7],[6]] => [6,3,7,1,2,4,5,8] => [1,2,5] => 6
[[1,2,6,7],[3,5,8],[4]] => [[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [1,2,5] => 6
[[1,3,6,7],[2,4,8],[5]] => [[1,2,4,7,8],[3,5],[6]] => [6,3,5,1,2,4,7,8] => [1,2,5] => 6
[[1,2,6,7],[3,4,8],[5]] => [[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [1,2,5] => 6
[[1,3,5,7],[2,6,8],[4]] => [[1,2,4,6,8],[3,7],[5]] => [5,3,7,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5,7],[3,6,8],[4]] => [[1,2,3,6,8],[4,7],[5]] => [5,4,7,1,2,3,6,8] => [1,2,5] => 6
[[1,3,4,7],[2,6,8],[5]] => [[1,2,4,5,6,8],[3],[7]] => [7,3,1,2,4,5,6,8] => [1,1,6] => 4
[[1,2,4,7],[3,6,8],[5]] => [[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => [1,1,6] => 4
[[1,2,3,7],[4,6,8],[5]] => [[1,2,3,4,6,8],[5],[7]] => [7,5,1,2,3,4,6,8] => [1,1,6] => 4
[[1,3,5,7],[2,4,8],[6]] => [[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5,7],[3,4,8],[6]] => [[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [1,2,5] => 6
[[1,3,4,7],[2,5,8],[6]] => [[1,2,4,5,8],[3,6],[7]] => [7,3,6,1,2,4,5,8] => [1,2,5] => 6
[[1,2,4,7],[3,5,8],[6]] => [[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => [1,2,5] => 6
[[1,2,3,7],[4,5,8],[6]] => [[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => [1,1,6] => 4
[[1,4,5,6],[2,7,8],[3]] => [[1,2,5,6,7,8],[3],[4]] => [4,3,1,2,5,6,7,8] => [1,1,6] => 4
[[1,3,5,6],[2,7,8],[4]] => [[1,2,4,6,7,8],[3],[5]] => [5,3,1,2,4,6,7,8] => [1,1,6] => 4
[[1,2,5,6],[3,7,8],[4]] => [[1,2,3,6,7,8],[4],[5]] => [5,4,1,2,3,6,7,8] => [1,1,6] => 4
[[1,3,4,6],[2,7,8],[5]] => [[1,2,4,5,7,8],[3],[6]] => [6,3,1,2,4,5,7,8] => [1,1,6] => 4
[[1,2,4,6],[3,7,8],[5]] => [[1,2,3,5,7,8],[4],[6]] => [6,4,1,2,3,5,7,8] => [1,1,6] => 4
[[1,2,3,6],[4,7,8],[5]] => [[1,2,3,4,7,8],[5],[6]] => [6,5,1,2,3,4,7,8] => [1,1,6] => 4
[[1,3,4,5],[2,7,8],[6]] => [[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [1,7] => 3
[[1,2,4,5],[3,7,8],[6]] => [[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => [1,7] => 3
[[1,2,3,5],[4,7,8],[6]] => [[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => [1,7] => 3
[[1,2,3,4],[5,7,8],[6]] => [[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => [1,7] => 3
[[1,3,5,6],[2,4,8],[7]] => [[1,2,4,6,7,8],[3,5]] => [3,5,1,2,4,6,7,8] => [2,6] => 3
[[1,2,5,6],[3,4,8],[7]] => [[1,2,3,4,7,8],[5,6]] => [5,6,1,2,3,4,7,8] => [2,6] => 3
[[1,3,4,6],[2,5,8],[7]] => [[1,2,4,5,7,8],[3,6]] => [3,6,1,2,4,5,7,8] => [2,6] => 3
[[1,2,4,6],[3,5,8],[7]] => [[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => [2,6] => 3
[[1,2,3,6],[4,5,8],[7]] => [[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => [2,6] => 3
[[1,3,4,5],[2,6,8],[7]] => [[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [2,6] => 3
[[1,2,4,5],[3,6,8],[7]] => [[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => [2,6] => 3
[[1,2,3,5],[4,6,8],[7]] => [[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [2,6] => 3
[[1,2,3,4],[5,6,8],[7]] => [[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [1,7] => 3
[[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6,8],[3,5,7]] => [3,5,7,1,2,4,6,8] => [3,5] => 3
[[1,2,5,7],[3,4,6],[8]] => [[1,2,3,4,6],[5,7,8]] => [5,7,8,1,2,3,4,6] => [3,5] => 3
[[1,3,4,7],[2,5,6],[8]] => [[1,2,4,5,6],[3,7,8]] => [3,7,8,1,2,4,5,6] => [3,5] => 3
[[1,2,4,7],[3,5,6],[8]] => [[1,2,3,5,6],[4,7,8]] => [4,7,8,1,2,3,5,6] => [3,5] => 3
[[1,2,3,7],[4,5,6],[8]] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [2,6] => 3
[[1,3,5,6],[2,4,7],[8]] => [[1,2,4,6,7],[3,5,8]] => [3,5,8,1,2,4,6,7] => [3,5] => 3
[[1,2,5,6],[3,4,7],[8]] => [[1,2,3,4,7],[5,6,8]] => [5,6,8,1,2,3,4,7] => [3,5] => 3
[[1,3,4,6],[2,5,7],[8]] => [[1,2,4,5,7],[3,6,8]] => [3,6,8,1,2,4,5,7] => [3,5] => 3
[[1,2,4,6],[3,5,7],[8]] => [[1,2,3,5,7],[4,6,8]] => [4,6,8,1,2,3,5,7] => [3,5] => 3
[[1,2,3,6],[4,5,7],[8]] => [[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => [2,6] => 3
[[1,3,4,5],[2,6,7],[8]] => [[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => [2,6] => 3
[[1,2,4,5],[3,6,7],[8]] => [[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => [2,6] => 3
[[1,2,3,5],[4,6,7],[8]] => [[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => [2,6] => 3
[[1,2,3,4],[5,6,7],[8]] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [1,7] => 3
[[1,4,7,8],[2,5],[3,6]] => [[1,2,5,8],[3,6],[4,7]] => [4,7,3,6,1,2,5,8] => [2,2,4] => 4
[[1,2,7,8],[3,5],[4,6]] => [[1,2,3,5],[4,6],[7,8]] => [7,8,4,6,1,2,3,5] => [2,2,4] => 4
[[1,3,7,8],[2,4],[5,6]] => [[1,2,4,6],[3,5],[7,8]] => [7,8,3,5,1,2,4,6] => [2,2,4] => 4
[[1,2,7,8],[3,4],[5,6]] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [2,2,4] => 4
[[1,3,6,8],[2,5],[4,7]] => [[1,2,4,5],[3,7],[6,8]] => [6,8,3,7,1,2,4,5] => [2,2,4] => 4
[[1,2,6,8],[3,5],[4,7]] => [[1,2,3,5],[4,7],[6,8]] => [6,8,4,7,1,2,3,5] => [2,2,4] => 4
[[1,3,6,8],[2,4],[5,7]] => [[1,2,4,7],[3,5],[6,8]] => [6,8,3,5,1,2,4,7] => [2,2,4] => 4
[[1,2,6,8],[3,4],[5,7]] => [[1,2,3,4],[5,7],[6,8]] => [6,8,5,7,1,2,3,4] => [2,2,4] => 4
[[1,4,5,8],[2,6],[3,7]] => [[1,2,5,6],[3,7],[4,8]] => [4,8,3,7,1,2,5,6] => [2,2,4] => 4
[[1,3,5,8],[2,6],[4,7]] => [[1,2,4,6],[3,7],[5,8]] => [5,8,3,7,1,2,4,6] => [2,2,4] => 4
[[1,2,5,8],[3,6],[4,7]] => [[1,2,3,6],[4,7],[5,8]] => [5,8,4,7,1,2,3,6] => [2,2,4] => 4
[[1,3,4,8],[2,6],[5,7]] => [[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => [1,2,5] => 6
[[1,2,4,8],[3,6],[5,7]] => [[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => [1,2,5] => 6
[[1,2,3,8],[4,6],[5,7]] => [[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => [1,2,5] => 6
[[1,3,5,8],[2,4],[6,7]] => [[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5,8],[3,4],[6,7]] => [[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => [1,2,5] => 6
[[1,3,4,8],[2,5],[6,7]] => [[1,2,4,5,7],[3,6],[8]] => [8,3,6,1,2,4,5,7] => [1,2,5] => 6
[[1,2,4,8],[3,5],[6,7]] => [[1,2,3,5,7],[4,6],[8]] => [8,4,6,1,2,3,5,7] => [1,2,5] => 6
[[1,2,3,8],[4,5],[6,7]] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [1,2,5] => 6
[[1,3,6,7],[2,5],[4,8]] => [[1,2,4,5,8],[3,7],[6]] => [6,3,7,1,2,4,5,8] => [1,2,5] => 6
[[1,2,6,7],[3,5],[4,8]] => [[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [1,2,5] => 6
[[1,3,6,7],[2,4],[5,8]] => [[1,2,4,7,8],[3,5],[6]] => [6,3,5,1,2,4,7,8] => [1,2,5] => 6
[[1,2,6,7],[3,4],[5,8]] => [[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [1,2,5] => 6
[[1,3,5,7],[2,6],[4,8]] => [[1,2,4,6,8],[3,7],[5]] => [5,3,7,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5,7],[3,6],[4,8]] => [[1,2,3,6,8],[4,7],[5]] => [5,4,7,1,2,3,6,8] => [1,2,5] => 6
[[1,3,4,7],[2,6],[5,8]] => [[1,2,4,5,6],[3,8],[7]] => [7,3,8,1,2,4,5,6] => [1,2,5] => 6
[[1,2,4,7],[3,6],[5,8]] => [[1,2,3,5,6],[4,8],[7]] => [7,4,8,1,2,3,5,6] => [1,2,5] => 6
[[1,2,3,7],[4,6],[5,8]] => [[1,2,3,4,6],[5,8],[7]] => [7,5,8,1,2,3,4,6] => [1,2,5] => 6
[[1,3,5,7],[2,4],[6,8]] => [[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5,7],[3,4],[6,8]] => [[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [1,2,5] => 6
[[1,3,4,7],[2,5],[6,8]] => [[1,2,4,5,8],[3,6],[7]] => [7,3,6,1,2,4,5,8] => [1,2,5] => 6
[[1,2,4,7],[3,5],[6,8]] => [[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => [1,2,5] => 6
[[1,2,3,7],[4,5],[6,8]] => [[1,2,3,4,5],[6,8],[7]] => [7,6,8,1,2,3,4,5] => [1,2,5] => 6
[[1,4,5,6],[2,7],[3,8]] => [[1,2,5,6,7],[3,8],[4]] => [4,3,8,1,2,5,6,7] => [1,2,5] => 6
[[1,3,5,6],[2,7],[4,8]] => [[1,2,4,6,7],[3,8],[5]] => [5,3,8,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5,6],[3,7],[4,8]] => [[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => [1,2,5] => 6
[[1,3,4,6],[2,7],[5,8]] => [[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => [1,2,5] => 6
[[1,2,4,6],[3,7],[5,8]] => [[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [1,2,5] => 6
[[1,2,3,6],[4,7],[5,8]] => [[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [1,2,5] => 6
[[1,3,4,5],[2,7],[6,8]] => [[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => [2,6] => 3
[[1,2,4,5],[3,7],[6,8]] => [[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => [2,6] => 3
[[1,2,3,5],[4,7],[6,8]] => [[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => [2,6] => 3
[[1,2,3,4],[5,7],[6,8]] => [[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => [2,6] => 3
[[1,3,5,6],[2,4],[7,8]] => [[1,2,4,6,7,8],[3,5]] => [3,5,1,2,4,6,7,8] => [2,6] => 3
[[1,2,5,6],[3,4],[7,8]] => [[1,2,3,4,7,8],[5,6]] => [5,6,1,2,3,4,7,8] => [2,6] => 3
[[1,3,4,6],[2,5],[7,8]] => [[1,2,4,5,7,8],[3,6]] => [3,6,1,2,4,5,7,8] => [2,6] => 3
[[1,2,4,6],[3,5],[7,8]] => [[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => [2,6] => 3
[[1,2,3,6],[4,5],[7,8]] => [[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => [2,6] => 3
[[1,3,4,5],[2,6],[7,8]] => [[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [2,6] => 3
[[1,2,4,5],[3,6],[7,8]] => [[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => [2,6] => 3
[[1,2,3,5],[4,6],[7,8]] => [[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [2,6] => 3
[[1,2,3,4],[5,6],[7,8]] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [2,6] => 3
[[1,5,7,8],[2,6],[3],[4]] => [[1,2,6,8],[3,7],[4],[5]] => [5,4,3,7,1,2,6,8] => [1,1,2,4] => 8
[[1,4,7,8],[2,6],[3],[5]] => [[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => [1,1,2,4] => 8
[[1,3,7,8],[2,6],[4],[5]] => [[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [1,1,2,4] => 8
[[1,2,7,8],[3,6],[4],[5]] => [[1,2,3,6],[4,8],[5],[7]] => [7,5,4,8,1,2,3,6] => [1,1,2,4] => 8
[[1,4,7,8],[2,5],[3],[6]] => [[1,2,5,8],[3,6],[4],[7]] => [7,4,3,6,1,2,5,8] => [1,1,2,4] => 8
[[1,2,7,8],[3,5],[4],[6]] => [[1,2,3,5],[4,8],[6],[7]] => [7,6,4,8,1,2,3,5] => [1,1,2,4] => 8
[[1,3,7,8],[2,4],[5],[6]] => [[1,2,4,8],[3,5],[6],[7]] => [7,6,3,5,1,2,4,8] => [1,1,2,4] => 8
[[1,2,7,8],[3,4],[5],[6]] => [[1,2,3,4],[5,8],[6],[7]] => [7,6,5,8,1,2,3,4] => [1,1,2,4] => 8
[[1,5,6,8],[2,7],[3],[4]] => [[1,2,6,7],[3,8],[4],[5]] => [5,4,3,8,1,2,6,7] => [1,1,2,4] => 8
[[1,4,6,8],[2,7],[3],[5]] => [[1,2,5,7],[3,8],[4],[6]] => [6,4,3,8,1,2,5,7] => [1,1,2,4] => 8
[[1,3,6,8],[2,7],[4],[5]] => [[1,2,4,7],[3,8],[5],[6]] => [6,5,3,8,1,2,4,7] => [1,1,2,4] => 8
[[1,2,6,8],[3,7],[4],[5]] => [[1,2,3,7],[4,8],[5],[6]] => [6,5,4,8,1,2,3,7] => [1,1,2,4] => 8
[[1,4,5,8],[2,7],[3],[6]] => [[1,2,5,6,7],[3],[4],[8]] => [8,4,3,1,2,5,6,7] => [1,1,1,5] => 5
[[1,3,5,8],[2,7],[4],[6]] => [[1,2,4,6,7],[3],[5],[8]] => [8,5,3,1,2,4,6,7] => [1,1,1,5] => 5
[[1,2,5,8],[3,7],[4],[6]] => [[1,2,3,6,7],[4],[5],[8]] => [8,5,4,1,2,3,6,7] => [1,1,1,5] => 5
[[1,2,4,8],[3,7],[5],[6]] => [[1,2,3,5,7],[4],[6],[8]] => [8,6,4,1,2,3,5,7] => [1,1,1,5] => 5
[[1,2,3,8],[4,7],[5],[6]] => [[1,2,3,4,7],[5],[6],[8]] => [8,6,5,1,2,3,4,7] => [1,1,1,5] => 5
[[1,3,6,8],[2,5],[4],[7]] => [[1,2,4,5],[3,7],[6],[8]] => [8,6,3,7,1,2,4,5] => [1,1,2,4] => 8
[[1,2,6,8],[3,5],[4],[7]] => [[1,2,3,5],[4,7],[6],[8]] => [8,6,4,7,1,2,3,5] => [1,1,2,4] => 8
[[1,3,6,8],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6],[8]] => [8,6,3,5,1,2,4,7] => [1,1,2,4] => 8
[[1,2,6,8],[3,4],[5],[7]] => [[1,2,3,4],[5,7],[6],[8]] => [8,6,5,7,1,2,3,4] => [1,1,2,4] => 8
[[1,4,5,8],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4],[8]] => [8,4,3,7,1,2,5,6] => [1,1,2,4] => 8
[[1,3,5,8],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5],[8]] => [8,5,3,7,1,2,4,6] => [1,1,2,4] => 8
[[1,2,5,8],[3,6],[4],[7]] => [[1,2,3,6],[4,7],[5],[8]] => [8,5,4,7,1,2,3,6] => [1,1,2,4] => 8
[[1,2,4,8],[3,6],[5],[7]] => [[1,2,3,5,6],[4],[7],[8]] => [8,7,4,1,2,3,5,6] => [1,1,1,5] => 5
[[1,2,3,8],[4,6],[5],[7]] => [[1,2,3,4,6],[5],[7],[8]] => [8,7,5,1,2,3,4,6] => [1,1,1,5] => 5
[[1,3,5,8],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7],[8]] => [8,7,3,5,1,2,4,6] => [1,1,2,4] => 8
[[1,2,5,8],[3,4],[6],[7]] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [1,1,2,4] => 8
[[1,3,4,8],[2,5],[6],[7]] => [[1,2,4,5],[3,6],[7],[8]] => [8,7,3,6,1,2,4,5] => [1,1,2,4] => 8
[[1,2,4,8],[3,5],[6],[7]] => [[1,2,3,5],[4,6],[7],[8]] => [8,7,4,6,1,2,3,5] => [1,1,2,4] => 8
[[1,2,3,8],[4,5],[6],[7]] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [1,1,1,5] => 5
[[1,5,6,7],[2,8],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => [5,4,3,1,2,6,7,8] => [1,1,1,5] => 5
[[1,4,6,7],[2,8],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => [6,4,3,1,2,5,7,8] => [1,1,1,5] => 5
[[1,2,6,7],[3,8],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => [6,5,4,1,2,3,7,8] => [1,1,1,5] => 5
[[1,4,5,7],[2,8],[3],[6]] => [[1,2,5,6,8],[3],[4],[7]] => [7,4,3,1,2,5,6,8] => [1,1,1,5] => 5
[[1,3,5,7],[2,8],[4],[6]] => [[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [1,1,1,5] => 5
[[1,2,5,7],[3,8],[4],[6]] => [[1,2,3,6,8],[4],[5],[7]] => [7,5,4,1,2,3,6,8] => [1,1,1,5] => 5
[[1,3,4,7],[2,8],[5],[6]] => [[1,2,4,5,8],[3],[6],[7]] => [7,6,3,1,2,4,5,8] => [1,1,1,5] => 5
[[1,2,4,7],[3,8],[5],[6]] => [[1,2,3,5,8],[4],[6],[7]] => [7,6,4,1,2,3,5,8] => [1,1,1,5] => 5
[[1,2,3,7],[4,8],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => [1,1,1,5] => 5
[[1,4,5,6],[2,8],[3],[7]] => [[1,2,5,6,7,8],[3],[4]] => [4,3,1,2,5,6,7,8] => [1,1,6] => 4
[[1,3,5,6],[2,8],[4],[7]] => [[1,2,4,6,7,8],[3],[5]] => [5,3,1,2,4,6,7,8] => [1,1,6] => 4
[[1,2,5,6],[3,8],[4],[7]] => [[1,2,3,6,7,8],[4],[5]] => [5,4,1,2,3,6,7,8] => [1,1,6] => 4
[[1,3,4,6],[2,8],[5],[7]] => [[1,2,4,5,7,8],[3],[6]] => [6,3,1,2,4,5,7,8] => [1,1,6] => 4
[[1,2,4,6],[3,8],[5],[7]] => [[1,2,3,5,7,8],[4],[6]] => [6,4,1,2,3,5,7,8] => [1,1,6] => 4
[[1,2,3,6],[4,8],[5],[7]] => [[1,2,3,4,7,8],[5],[6]] => [6,5,1,2,3,4,7,8] => [1,1,6] => 4
[[1,3,4,5],[2,8],[6],[7]] => [[1,2,4,5,6,8],[3],[7]] => [7,3,1,2,4,5,6,8] => [1,1,6] => 4
[[1,2,4,5],[3,8],[6],[7]] => [[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => [1,1,6] => 4
[[1,2,3,5],[4,8],[6],[7]] => [[1,2,3,4,6,8],[5],[7]] => [7,5,1,2,3,4,6,8] => [1,1,6] => 4
[[1,2,3,4],[5,8],[6],[7]] => [[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => [1,1,6] => 4
[[1,3,6,7],[2,5],[4],[8]] => [[1,2,4,5,8],[3,7],[6]] => [6,3,7,1,2,4,5,8] => [1,2,5] => 6
[[1,2,6,7],[3,5],[4],[8]] => [[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [1,2,5] => 6
[[1,3,6,7],[2,4],[5],[8]] => [[1,2,4,7,8],[3,5],[6]] => [6,3,5,1,2,4,7,8] => [1,2,5] => 6
[[1,2,6,7],[3,4],[5],[8]] => [[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [1,2,5] => 6
[[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,6,8],[3,7],[5]] => [5,3,7,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5,7],[3,6],[4],[8]] => [[1,2,3,6,8],[4,7],[5]] => [5,4,7,1,2,3,6,8] => [1,2,5] => 6
[[1,3,4,7],[2,6],[5],[8]] => [[1,2,4,5,6],[3,8],[7]] => [7,3,8,1,2,4,5,6] => [1,2,5] => 6
[[1,2,4,7],[3,6],[5],[8]] => [[1,2,3,5,6],[4,8],[7]] => [7,4,8,1,2,3,5,6] => [1,2,5] => 6
[[1,2,3,7],[4,6],[5],[8]] => [[1,2,3,4,6],[5,8],[7]] => [7,5,8,1,2,3,4,6] => [1,2,5] => 6
[[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5,7],[3,4],[6],[8]] => [[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [1,2,5] => 6
[[1,3,4,7],[2,5],[6],[8]] => [[1,2,4,5,8],[3,6],[7]] => [7,3,6,1,2,4,5,8] => [1,2,5] => 6
[[1,2,4,7],[3,5],[6],[8]] => [[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => [1,2,5] => 6
[[1,2,3,7],[4,5],[6],[8]] => [[1,2,3,4,5],[6,8],[7]] => [7,6,8,1,2,3,4,5] => [1,2,5] => 6
[[1,4,5,6],[2,7],[3],[8]] => [[1,2,5,6,7],[3,8],[4]] => [4,3,8,1,2,5,6,7] => [1,2,5] => 6
[[1,3,5,6],[2,7],[4],[8]] => [[1,2,4,6,7],[3,8],[5]] => [5,3,8,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5,6],[3,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => [1,2,5] => 6
[[1,3,4,6],[2,7],[5],[8]] => [[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => [1,2,5] => 6
[[1,2,4,6],[3,7],[5],[8]] => [[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [1,2,5] => 6
[[1,2,3,6],[4,7],[5],[8]] => [[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [1,2,5] => 6
[[1,3,4,5],[2,7],[6],[8]] => [[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [1,1,6] => 4
[[1,2,4,5],[3,7],[6],[8]] => [[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => [1,1,6] => 4
[[1,2,3,5],[4,7],[6],[8]] => [[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => [1,1,6] => 4
[[1,2,3,4],[5,7],[6],[8]] => [[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => [1,1,6] => 4
[[1,3,5,6],[2,4],[7],[8]] => [[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5,6],[3,4],[7],[8]] => [[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => [1,2,5] => 6
[[1,3,4,6],[2,5],[7],[8]] => [[1,2,4,5,7],[3,6],[8]] => [8,3,6,1,2,4,5,7] => [1,2,5] => 6
[[1,2,4,6],[3,5],[7],[8]] => [[1,2,3,5,7],[4,6],[8]] => [8,4,6,1,2,3,5,7] => [1,2,5] => 6
[[1,2,3,6],[4,5],[7],[8]] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [1,2,5] => 6
[[1,3,4,5],[2,6],[7],[8]] => [[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => [1,2,5] => 6
[[1,2,4,5],[3,6],[7],[8]] => [[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => [1,2,5] => 6
[[1,2,3,5],[4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => [1,2,5] => 6
[[1,2,3,4],[5,6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [1,1,6] => 4
[[1,6,7,8],[2],[3],[4],[5]] => [[1,2,7,8],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8] => [1,1,1,1,4] => 6
[[1,4,7,8],[2],[3],[5],[6]] => [[1,2,5,8],[3],[4],[6],[7]] => [7,6,4,3,1,2,5,8] => [1,1,1,1,4] => 6
[[1,3,7,8],[2],[4],[5],[6]] => [[1,2,4,8],[3],[5],[6],[7]] => [7,6,5,3,1,2,4,8] => [1,1,1,1,4] => 6
[[1,2,7,8],[3],[4],[5],[6]] => [[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4] => 6
[[1,5,6,8],[2],[3],[4],[7]] => [[1,2,6,7],[3],[4],[5],[8]] => [8,5,4,3,1,2,6,7] => [1,1,1,1,4] => 6
[[1,4,6,8],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6],[8]] => [8,6,4,3,1,2,5,7] => [1,1,1,1,4] => 6
[[1,3,6,8],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6],[8]] => [8,6,5,3,1,2,4,7] => [1,1,1,1,4] => 6
[[1,2,6,8],[3],[4],[5],[7]] => [[1,2,3,7],[4],[5],[6],[8]] => [8,6,5,4,1,2,3,7] => [1,1,1,1,4] => 6
[[1,4,5,8],[2],[3],[6],[7]] => [[1,2,5,6],[3],[4],[7],[8]] => [8,7,4,3,1,2,5,6] => [1,1,1,1,4] => 6
[[1,3,5,8],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7],[8]] => [8,7,5,3,1,2,4,6] => [1,1,1,1,4] => 6
[[1,2,5,8],[3],[4],[6],[7]] => [[1,2,3,6],[4],[5],[7],[8]] => [8,7,5,4,1,2,3,6] => [1,1,1,1,4] => 6
[[1,3,4,8],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7],[8]] => [8,7,6,3,1,2,4,5] => [1,1,1,1,4] => 6
[[1,2,4,8],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7],[8]] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4] => 6
[[1,2,3,8],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4] => 6
[[1,5,6,7],[2],[3],[4],[8]] => [[1,2,6,7,8],[3],[4],[5]] => [5,4,3,1,2,6,7,8] => [1,1,1,5] => 5
[[1,4,6,7],[2],[3],[5],[8]] => [[1,2,5,7,8],[3],[4],[6]] => [6,4,3,1,2,5,7,8] => [1,1,1,5] => 5
[[1,2,6,7],[3],[4],[5],[8]] => [[1,2,3,7,8],[4],[5],[6]] => [6,5,4,1,2,3,7,8] => [1,1,1,5] => 5
[[1,4,5,7],[2],[3],[6],[8]] => [[1,2,5,6,8],[3],[4],[7]] => [7,4,3,1,2,5,6,8] => [1,1,1,5] => 5
[[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [1,1,1,5] => 5
[[1,2,5,7],[3],[4],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => [7,5,4,1,2,3,6,8] => [1,1,1,5] => 5
[[1,3,4,7],[2],[5],[6],[8]] => [[1,2,4,5,8],[3],[6],[7]] => [7,6,3,1,2,4,5,8] => [1,1,1,5] => 5
[[1,2,4,7],[3],[5],[6],[8]] => [[1,2,3,5,8],[4],[6],[7]] => [7,6,4,1,2,3,5,8] => [1,1,1,5] => 5
[[1,2,3,7],[4],[5],[6],[8]] => [[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => [1,1,1,5] => 5
[[1,4,5,6],[2],[3],[7],[8]] => [[1,2,5,6,7],[3],[4],[8]] => [8,4,3,1,2,5,6,7] => [1,1,1,5] => 5
[[1,3,5,6],[2],[4],[7],[8]] => [[1,2,4,6,7],[3],[5],[8]] => [8,5,3,1,2,4,6,7] => [1,1,1,5] => 5
[[1,2,5,6],[3],[4],[7],[8]] => [[1,2,3,6,7],[4],[5],[8]] => [8,5,4,1,2,3,6,7] => [1,1,1,5] => 5
[[1,2,4,6],[3],[5],[7],[8]] => [[1,2,3,5,7],[4],[6],[8]] => [8,6,4,1,2,3,5,7] => [1,1,1,5] => 5
[[1,2,3,6],[4],[5],[7],[8]] => [[1,2,3,4,7],[5],[6],[8]] => [8,6,5,1,2,3,4,7] => [1,1,1,5] => 5
[[1,2,4,5],[3],[6],[7],[8]] => [[1,2,3,5,6],[4],[7],[8]] => [8,7,4,1,2,3,5,6] => [1,1,1,5] => 5
[[1,2,3,5],[4],[6],[7],[8]] => [[1,2,3,4,6],[5],[7],[8]] => [8,7,5,1,2,3,4,6] => [1,1,1,5] => 5
[[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [1,1,1,5] => 5
[[1,4,7],[2,5,8],[3,6]] => [[1,2,5,8],[3,6],[4,7]] => [4,7,3,6,1,2,5,8] => [2,2,4] => 4
[[1,3,7],[2,5,8],[4,6]] => [[1,2,4,5,8],[3,6],[7]] => [7,3,6,1,2,4,5,8] => [1,2,5] => 6
[[1,2,7],[3,5,8],[4,6]] => [[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => [1,2,5] => 6
[[1,3,7],[2,4,8],[5,6]] => [[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => [1,2,5] => 6
[[1,2,7],[3,4,8],[5,6]] => [[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [1,2,5] => 6
[[1,3,6],[2,5,8],[4,7]] => [[1,2,4,5,8],[3,7],[6]] => [6,3,7,1,2,4,5,8] => [1,2,5] => 6
[[1,2,6],[3,5,8],[4,7]] => [[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [1,2,5] => 6
[[1,3,6],[2,4,8],[5,7]] => [[1,2,4,7,8],[3,5],[6]] => [6,3,5,1,2,4,7,8] => [1,2,5] => 6
[[1,2,6],[3,4,8],[5,7]] => [[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [1,2,5] => 6
[[1,3,5],[2,6,8],[4,7]] => [[1,2,4,6,8],[3,7],[5]] => [5,3,7,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5],[3,6,8],[4,7]] => [[1,2,3,6,8],[4,7],[5]] => [5,4,7,1,2,3,6,8] => [1,2,5] => 6
[[1,3,4],[2,6,8],[5,7]] => [[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [2,6] => 3
[[1,2,4],[3,6,8],[5,7]] => [[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => [2,6] => 3
[[1,2,3],[4,6,8],[5,7]] => [[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [2,6] => 3
[[1,3,5],[2,4,8],[6,7]] => [[1,2,4,6,7,8],[3,5]] => [3,5,1,2,4,6,7,8] => [2,6] => 3
[[1,2,5],[3,4,8],[6,7]] => [[1,2,3,4,7,8],[5,6]] => [5,6,1,2,3,4,7,8] => [2,6] => 3
[[1,3,4],[2,5,8],[6,7]] => [[1,2,4,5,7,8],[3,6]] => [3,6,1,2,4,5,7,8] => [2,6] => 3
[[1,2,4],[3,5,8],[6,7]] => [[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => [2,6] => 3
[[1,2,3],[4,5,8],[6,7]] => [[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => [2,6] => 3
[[1,4,6],[2,5,7],[3,8]] => [[1,2,5,7],[3,6,8],[4]] => [4,3,6,8,1,2,5,7] => [1,3,4] => 6
[[1,3,6],[2,5,7],[4,8]] => [[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => [1,2,5] => 6
[[1,2,6],[3,5,7],[4,8]] => [[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [1,2,5] => 6
[[1,3,6],[2,4,7],[5,8]] => [[1,2,4,7],[3,5,8],[6]] => [6,3,5,8,1,2,4,7] => [1,3,4] => 6
[[1,2,6],[3,4,7],[5,8]] => [[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [1,2,5] => 6
[[1,4,5],[2,6,7],[3,8]] => [[1,2,5,6,7],[3,8],[4]] => [4,3,8,1,2,5,6,7] => [1,2,5] => 6
[[1,3,5],[2,6,7],[4,8]] => [[1,2,4,6,7],[3,8],[5]] => [5,3,8,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5],[3,6,7],[4,8]] => [[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => [1,2,5] => 6
[[1,3,4],[2,6,7],[5,8]] => [[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => [2,6] => 3
[[1,2,4],[3,6,7],[5,8]] => [[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => [2,6] => 3
[[1,2,3],[4,6,7],[5,8]] => [[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => [2,6] => 3
[[1,3,5],[2,4,7],[6,8]] => [[1,2,4,6,7],[3,5,8]] => [3,5,8,1,2,4,6,7] => [3,5] => 3
[[1,2,5],[3,4,7],[6,8]] => [[1,2,3,4,7],[5,6,8]] => [5,6,8,1,2,3,4,7] => [3,5] => 3
[[1,3,4],[2,5,7],[6,8]] => [[1,2,4,5,7],[3,6,8]] => [3,6,8,1,2,4,5,7] => [3,5] => 3
[[1,2,4],[3,5,7],[6,8]] => [[1,2,3,5,7],[4,6,8]] => [4,6,8,1,2,3,5,7] => [3,5] => 3
[[1,2,3],[4,5,7],[6,8]] => [[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => [2,6] => 3
[[1,3,5],[2,4,6],[7,8]] => [[1,2,4,6,8],[3,5,7]] => [3,5,7,1,2,4,6,8] => [3,5] => 3
[[1,2,5],[3,4,6],[7,8]] => [[1,2,3,4,6],[5,7,8]] => [5,7,8,1,2,3,4,6] => [3,5] => 3
[[1,3,4],[2,5,6],[7,8]] => [[1,2,4,5,6],[3,7,8]] => [3,7,8,1,2,4,5,6] => [3,5] => 3
[[1,2,4],[3,5,6],[7,8]] => [[1,2,3,5,6],[4,7,8]] => [4,7,8,1,2,3,5,6] => [3,5] => 3
[[1,2,3],[4,5,6],[7,8]] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [2,6] => 3
[[1,5,7],[2,6,8],[3],[4]] => [[1,2,6,8],[3,7],[4],[5]] => [5,4,3,7,1,2,6,8] => [1,1,2,4] => 8
[[1,4,7],[2,6,8],[3],[5]] => [[1,2,5,6,8],[3],[4],[7]] => [7,4,3,1,2,5,6,8] => [1,1,1,5] => 5
[[1,3,7],[2,6,8],[4],[5]] => [[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [1,1,1,5] => 5
[[1,2,7],[3,6,8],[4],[5]] => [[1,2,3,6,8],[4],[5],[7]] => [7,5,4,1,2,3,6,8] => [1,1,1,5] => 5
[[1,4,7],[2,5,8],[3],[6]] => [[1,2,5,8],[3,6],[4],[7]] => [7,4,3,6,1,2,5,8] => [1,1,2,4] => 8
[[1,3,7],[2,5,8],[4],[6]] => [[1,2,4,5,8],[3],[6],[7]] => [7,6,3,1,2,4,5,8] => [1,1,1,5] => 5
[[1,2,7],[3,5,8],[4],[6]] => [[1,2,3,5,8],[4],[6],[7]] => [7,6,4,1,2,3,5,8] => [1,1,1,5] => 5
[[1,3,7],[2,4,8],[5],[6]] => [[1,2,4,8],[3,5],[6],[7]] => [7,6,3,5,1,2,4,8] => [1,1,2,4] => 8
[[1,2,7],[3,4,8],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => [1,1,1,5] => 5
[[1,5,6],[2,7,8],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => [5,4,3,1,2,6,7,8] => [1,1,1,5] => 5
[[1,4,6],[2,7,8],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => [6,4,3,1,2,5,7,8] => [1,1,1,5] => 5
[[1,2,6],[3,7,8],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => [6,5,4,1,2,3,7,8] => [1,1,1,5] => 5
[[1,4,5],[2,7,8],[3],[6]] => [[1,2,5,6,7,8],[3],[4]] => [4,3,1,2,5,6,7,8] => [1,1,6] => 4
[[1,3,5],[2,7,8],[4],[6]] => [[1,2,4,6,7,8],[3],[5]] => [5,3,1,2,4,6,7,8] => [1,1,6] => 4
[[1,2,5],[3,7,8],[4],[6]] => [[1,2,3,6,7,8],[4],[5]] => [5,4,1,2,3,6,7,8] => [1,1,6] => 4
[[1,3,4],[2,7,8],[5],[6]] => [[1,2,4,5,7,8],[3],[6]] => [6,3,1,2,4,5,7,8] => [1,1,6] => 4
[[1,2,4],[3,7,8],[5],[6]] => [[1,2,3,5,7,8],[4],[6]] => [6,4,1,2,3,5,7,8] => [1,1,6] => 4
[[1,2,3],[4,7,8],[5],[6]] => [[1,2,3,4,7,8],[5],[6]] => [6,5,1,2,3,4,7,8] => [1,1,6] => 4
[[1,3,6],[2,5,8],[4],[7]] => [[1,2,4,5,8],[3,7],[6]] => [6,3,7,1,2,4,5,8] => [1,2,5] => 6
[[1,2,6],[3,5,8],[4],[7]] => [[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [1,2,5] => 6
[[1,3,6],[2,4,8],[5],[7]] => [[1,2,4,7,8],[3,5],[6]] => [6,3,5,1,2,4,7,8] => [1,2,5] => 6
[[1,2,6],[3,4,8],[5],[7]] => [[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [1,2,5] => 6
[[1,3,5],[2,6,8],[4],[7]] => [[1,2,4,6,8],[3,7],[5]] => [5,3,7,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5],[3,6,8],[4],[7]] => [[1,2,3,6,8],[4,7],[5]] => [5,4,7,1,2,3,6,8] => [1,2,5] => 6
[[1,3,4],[2,6,8],[5],[7]] => [[1,2,4,5,6,8],[3],[7]] => [7,3,1,2,4,5,6,8] => [1,1,6] => 4
[[1,2,4],[3,6,8],[5],[7]] => [[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => [1,1,6] => 4
[[1,2,3],[4,6,8],[5],[7]] => [[1,2,3,4,6,8],[5],[7]] => [7,5,1,2,3,4,6,8] => [1,1,6] => 4
[[1,3,5],[2,4,8],[6],[7]] => [[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5],[3,4,8],[6],[7]] => [[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [1,2,5] => 6
[[1,3,4],[2,5,8],[6],[7]] => [[1,2,4,5,8],[3,6],[7]] => [7,3,6,1,2,4,5,8] => [1,2,5] => 6
[[1,2,4],[3,5,8],[6],[7]] => [[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => [1,2,5] => 6
[[1,2,3],[4,5,8],[6],[7]] => [[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => [1,1,6] => 4
[[1,4,6],[2,5,7],[3],[8]] => [[1,2,5,7],[3,6,8],[4]] => [4,3,6,8,1,2,5,7] => [1,3,4] => 6
[[1,3,6],[2,5,7],[4],[8]] => [[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => [1,2,5] => 6
[[1,2,6],[3,5,7],[4],[8]] => [[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [1,2,5] => 6
[[1,3,6],[2,4,7],[5],[8]] => [[1,2,4,7],[3,5,8],[6]] => [6,3,5,8,1,2,4,7] => [1,3,4] => 6
[[1,2,6],[3,4,7],[5],[8]] => [[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [1,2,5] => 6
[[1,4,5],[2,6,7],[3],[8]] => [[1,2,5,6,7],[3,8],[4]] => [4,3,8,1,2,5,6,7] => [1,2,5] => 6
[[1,3,5],[2,6,7],[4],[8]] => [[1,2,4,6,7],[3,8],[5]] => [5,3,8,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5],[3,6,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => [1,2,5] => 6
[[1,3,4],[2,6,7],[5],[8]] => [[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [1,1,6] => 4
[[1,2,4],[3,6,7],[5],[8]] => [[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => [1,1,6] => 4
[[1,2,3],[4,6,7],[5],[8]] => [[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => [1,1,6] => 4
[[1,3,5],[2,4,7],[6],[8]] => [[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5],[3,4,7],[6],[8]] => [[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => [1,2,5] => 6
[[1,3,4],[2,5,7],[6],[8]] => [[1,2,4,5,7],[3,6],[8]] => [8,3,6,1,2,4,5,7] => [1,2,5] => 6
[[1,2,4],[3,5,7],[6],[8]] => [[1,2,3,5,7],[4,6],[8]] => [8,4,6,1,2,3,5,7] => [1,2,5] => 6
[[1,2,3],[4,5,7],[6],[8]] => [[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => [1,1,6] => 4
[[1,3,5],[2,4,6],[7],[8]] => [[1,2,4,6],[3,5,7],[8]] => [8,3,5,7,1,2,4,6] => [1,3,4] => 6
[[1,2,5],[3,4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => [1,2,5] => 6
[[1,3,4],[2,5,6],[7],[8]] => [[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => [1,2,5] => 6
[[1,2,4],[3,5,6],[7],[8]] => [[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => [1,2,5] => 6
[[1,2,3],[4,5,6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [1,1,6] => 4
[[1,5,8],[2,6],[3,7],[4]] => [[1,2,6],[3,7],[4,8],[5]] => [5,4,8,3,7,1,2,6] => [1,2,2,3] => 7
[[1,4,8],[2,6],[3,7],[5]] => [[1,2,5,6],[3,7],[4],[8]] => [8,4,3,7,1,2,5,6] => [1,1,2,4] => 8
[[1,3,8],[2,6],[4,7],[5]] => [[1,2,4,6],[3,7],[5],[8]] => [8,5,3,7,1,2,4,6] => [1,1,2,4] => 8
[[1,2,8],[3,6],[4,7],[5]] => [[1,2,3,6],[4,7],[5],[8]] => [8,5,4,7,1,2,3,6] => [1,1,2,4] => 8
[[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,5],[3,7],[6],[8]] => [8,6,3,7,1,2,4,5] => [1,1,2,4] => 8
[[1,2,8],[3,5],[4,7],[6]] => [[1,2,3,5],[4,7],[6],[8]] => [8,6,4,7,1,2,3,5] => [1,1,2,4] => 8
[[1,3,8],[2,4],[5,7],[6]] => [[1,2,4,7],[3,5],[6],[8]] => [8,6,3,5,1,2,4,7] => [1,1,2,4] => 8
[[1,2,8],[3,4],[5,7],[6]] => [[1,2,3,4],[5,7],[6],[8]] => [8,6,5,7,1,2,3,4] => [1,1,2,4] => 8
[[1,4,8],[2,5],[3,6],[7]] => [[1,2,5],[3,6],[4,7],[8]] => [8,4,7,3,6,1,2,5] => [1,2,2,3] => 7
[[1,3,8],[2,5],[4,6],[7]] => [[1,2,4,5],[3,6],[7],[8]] => [8,7,3,6,1,2,4,5] => [1,1,2,4] => 8
[[1,2,8],[3,5],[4,6],[7]] => [[1,2,3,5],[4,6],[7],[8]] => [8,7,4,6,1,2,3,5] => [1,1,2,4] => 8
[[1,3,8],[2,4],[5,6],[7]] => [[1,2,4,6],[3,5],[7],[8]] => [8,7,3,5,1,2,4,6] => [1,1,2,4] => 8
[[1,2,8],[3,4],[5,6],[7]] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [1,1,2,4] => 8
[[1,5,7],[2,6],[3,8],[4]] => [[1,2,6,8],[3,7],[4],[5]] => [5,4,3,7,1,2,6,8] => [1,1,2,4] => 8
[[1,4,7],[2,6],[3,8],[5]] => [[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => [1,1,2,4] => 8
[[1,3,7],[2,6],[4,8],[5]] => [[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [1,1,2,4] => 8
[[1,2,7],[3,6],[4,8],[5]] => [[1,2,3,6],[4,8],[5],[7]] => [7,5,4,8,1,2,3,6] => [1,1,2,4] => 8
[[1,4,7],[2,5],[3,8],[6]] => [[1,2,5,8],[3,6],[4],[7]] => [7,4,3,6,1,2,5,8] => [1,1,2,4] => 8
[[1,2,7],[3,5],[4,8],[6]] => [[1,2,3,5],[4,8],[6],[7]] => [7,6,4,8,1,2,3,5] => [1,1,2,4] => 8
[[1,3,7],[2,4],[5,8],[6]] => [[1,2,4,8],[3,5],[6],[7]] => [7,6,3,5,1,2,4,8] => [1,1,2,4] => 8
[[1,2,7],[3,4],[5,8],[6]] => [[1,2,3,4],[5,8],[6],[7]] => [7,6,5,8,1,2,3,4] => [1,1,2,4] => 8
[[1,5,6],[2,7],[3,8],[4]] => [[1,2,6,7],[3,8],[4],[5]] => [5,4,3,8,1,2,6,7] => [1,1,2,4] => 8
[[1,4,6],[2,7],[3,8],[5]] => [[1,2,5,7],[3,8],[4],[6]] => [6,4,3,8,1,2,5,7] => [1,1,2,4] => 8
[[1,3,6],[2,7],[4,8],[5]] => [[1,2,4,7],[3,8],[5],[6]] => [6,5,3,8,1,2,4,7] => [1,1,2,4] => 8
[[1,2,6],[3,7],[4,8],[5]] => [[1,2,3,7],[4,8],[5],[6]] => [6,5,4,8,1,2,3,7] => [1,1,2,4] => 8
[[1,4,5],[2,7],[3,8],[6]] => [[1,2,5,6,7],[3,8],[4]] => [4,3,8,1,2,5,6,7] => [1,2,5] => 6
[[1,3,5],[2,7],[4,8],[6]] => [[1,2,4,6,7],[3,8],[5]] => [5,3,8,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5],[3,7],[4,8],[6]] => [[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => [1,2,5] => 6
[[1,3,4],[2,7],[5,8],[6]] => [[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => [1,2,5] => 6
[[1,2,4],[3,7],[5,8],[6]] => [[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [1,2,5] => 6
[[1,2,3],[4,7],[5,8],[6]] => [[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [1,2,5] => 6
[[1,3,6],[2,5],[4,8],[7]] => [[1,2,4,5,8],[3,7],[6]] => [6,3,7,1,2,4,5,8] => [1,2,5] => 6
[[1,2,6],[3,5],[4,8],[7]] => [[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [1,2,5] => 6
[[1,3,6],[2,4],[5,8],[7]] => [[1,2,4,7,8],[3,5],[6]] => [6,3,5,1,2,4,7,8] => [1,2,5] => 6
[[1,2,6],[3,4],[5,8],[7]] => [[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [1,2,5] => 6
[[1,3,5],[2,6],[4,8],[7]] => [[1,2,4,6,8],[3,7],[5]] => [5,3,7,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5],[3,6],[4,8],[7]] => [[1,2,3,6,8],[4,7],[5]] => [5,4,7,1,2,3,6,8] => [1,2,5] => 6
[[1,3,4],[2,6],[5,8],[7]] => [[1,2,4,5,6],[3,8],[7]] => [7,3,8,1,2,4,5,6] => [1,2,5] => 6
[[1,2,4],[3,6],[5,8],[7]] => [[1,2,3,5,6],[4,8],[7]] => [7,4,8,1,2,3,5,6] => [1,2,5] => 6
[[1,2,3],[4,6],[5,8],[7]] => [[1,2,3,4,6],[5,8],[7]] => [7,5,8,1,2,3,4,6] => [1,2,5] => 6
[[1,3,5],[2,4],[6,8],[7]] => [[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => [1,2,5] => 6
[[1,2,5],[3,4],[6,8],[7]] => [[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [1,2,5] => 6
[[1,3,4],[2,5],[6,8],[7]] => [[1,2,4,5,8],[3,6],[7]] => [7,3,6,1,2,4,5,8] => [1,2,5] => 6
[[1,2,4],[3,5],[6,8],[7]] => [[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => [1,2,5] => 6
[[1,2,3],[4,5],[6,8],[7]] => [[1,2,3,4,5],[6,8],[7]] => [7,6,8,1,2,3,4,5] => [1,2,5] => 6
[[1,4,7],[2,5],[3,6],[8]] => [[1,2,5,8],[3,6],[4,7]] => [4,7,3,6,1,2,5,8] => [2,2,4] => 4
[[1,2,7],[3,5],[4,6],[8]] => [[1,2,3,5],[4,6],[7,8]] => [7,8,4,6,1,2,3,5] => [2,2,4] => 4
[[1,3,7],[2,4],[5,6],[8]] => [[1,2,4,6],[3,5],[7,8]] => [7,8,3,5,1,2,4,6] => [2,2,4] => 4
[[1,2,7],[3,4],[5,6],[8]] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [2,2,4] => 4
[[1,3,6],[2,5],[4,7],[8]] => [[1,2,4,5],[3,7],[6,8]] => [6,8,3,7,1,2,4,5] => [2,2,4] => 4
[[1,2,6],[3,5],[4,7],[8]] => [[1,2,3,5],[4,7],[6,8]] => [6,8,4,7,1,2,3,5] => [2,2,4] => 4
[[1,3,6],[2,4],[5,7],[8]] => [[1,2,4,7],[3,5],[6,8]] => [6,8,3,5,1,2,4,7] => [2,2,4] => 4
[[1,2,6],[3,4],[5,7],[8]] => [[1,2,3,4],[5,7],[6,8]] => [6,8,5,7,1,2,3,4] => [2,2,4] => 4
[[1,4,5],[2,6],[3,7],[8]] => [[1,2,5,6],[3,7],[4,8]] => [4,8,3,7,1,2,5,6] => [2,2,4] => 4
[[1,3,5],[2,6],[4,7],[8]] => [[1,2,4,6],[3,7],[5,8]] => [5,8,3,7,1,2,4,6] => [2,2,4] => 4
[[1,2,5],[3,6],[4,7],[8]] => [[1,2,3,6],[4,7],[5,8]] => [5,8,4,7,1,2,3,6] => [2,2,4] => 4
[[1,3,4],[2,6],[5,7],[8]] => [[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => [1,2,5] => 6
[[1,2,4],[3,6],[5,7],[8]] => [[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => [1,2,5] => 6
[[1,2,3],[4,6],[5,7],[8]] => [[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => [1,2,5] => 6
[[1,3,5],[2,4],[6,7],[8]] => [[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => [1,2,5] => 6
[[1,2,5],[3,4],[6,7],[8]] => [[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => [1,2,5] => 6
[[1,3,4],[2,5],[6,7],[8]] => [[1,2,4,5,7],[3,6],[8]] => [8,3,6,1,2,4,5,7] => [1,2,5] => 6
[[1,2,4],[3,5],[6,7],[8]] => [[1,2,3,5,7],[4,6],[8]] => [8,4,6,1,2,3,5,7] => [1,2,5] => 6
[[1,2,3],[4,5],[6,7],[8]] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [1,2,5] => 6
[[1,6,8],[2,7],[3],[4],[5]] => [[1,2,7],[3,8],[4],[5],[6]] => [6,5,4,3,8,1,2,7] => [1,1,1,2,3] => 10
[[1,5,8],[2,7],[3],[4],[6]] => [[1,2,6,7],[3],[4],[5],[8]] => [8,5,4,3,1,2,6,7] => [1,1,1,1,4] => 6
[[1,4,8],[2,7],[3],[5],[6]] => [[1,2,5,7],[3],[4],[6],[8]] => [8,6,4,3,1,2,5,7] => [1,1,1,1,4] => 6
[[1,3,8],[2,7],[4],[5],[6]] => [[1,2,4,7],[3],[5],[6],[8]] => [8,6,5,3,1,2,4,7] => [1,1,1,1,4] => 6
[[1,2,8],[3,7],[4],[5],[6]] => [[1,2,3,7],[4],[5],[6],[8]] => [8,6,5,4,1,2,3,7] => [1,1,1,1,4] => 6
[[1,4,8],[2,6],[3],[5],[7]] => [[1,2,5,6],[3],[4],[7],[8]] => [8,7,4,3,1,2,5,6] => [1,1,1,1,4] => 6
[[1,3,8],[2,6],[4],[5],[7]] => [[1,2,4,6],[3],[5],[7],[8]] => [8,7,5,3,1,2,4,6] => [1,1,1,1,4] => 6
[[1,2,8],[3,6],[4],[5],[7]] => [[1,2,3,6],[4],[5],[7],[8]] => [8,7,5,4,1,2,3,6] => [1,1,1,1,4] => 6
[[1,4,8],[2,5],[3],[6],[7]] => [[1,2,5],[3,6],[4],[7],[8]] => [8,7,4,3,6,1,2,5] => [1,1,1,2,3] => 10
[[1,3,8],[2,5],[4],[6],[7]] => [[1,2,4,5],[3],[6],[7],[8]] => [8,7,6,3,1,2,4,5] => [1,1,1,1,4] => 6
[[1,2,8],[3,5],[4],[6],[7]] => [[1,2,3,5],[4],[6],[7],[8]] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4] => 6
[[1,3,8],[2,4],[5],[6],[7]] => [[1,2,4],[3,5],[6],[7],[8]] => [8,7,6,3,5,1,2,4] => [1,1,1,2,3] => 10
[[1,2,8],[3,4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4] => 6
[[1,6,7],[2,8],[3],[4],[5]] => [[1,2,7,8],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8] => [1,1,1,1,4] => 6
[[1,4,7],[2,8],[3],[5],[6]] => [[1,2,5,8],[3],[4],[6],[7]] => [7,6,4,3,1,2,5,8] => [1,1,1,1,4] => 6
[[1,3,7],[2,8],[4],[5],[6]] => [[1,2,4,8],[3],[5],[6],[7]] => [7,6,5,3,1,2,4,8] => [1,1,1,1,4] => 6
[[1,2,7],[3,8],[4],[5],[6]] => [[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4] => 6
[[1,5,6],[2,8],[3],[4],[7]] => [[1,2,6,7,8],[3],[4],[5]] => [5,4,3,1,2,6,7,8] => [1,1,1,5] => 5
[[1,4,6],[2,8],[3],[5],[7]] => [[1,2,5,7,8],[3],[4],[6]] => [6,4,3,1,2,5,7,8] => [1,1,1,5] => 5
[[1,2,6],[3,8],[4],[5],[7]] => [[1,2,3,7,8],[4],[5],[6]] => [6,5,4,1,2,3,7,8] => [1,1,1,5] => 5
[[1,4,5],[2,8],[3],[6],[7]] => [[1,2,5,6,8],[3],[4],[7]] => [7,4,3,1,2,5,6,8] => [1,1,1,5] => 5
[[1,3,5],[2,8],[4],[6],[7]] => [[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [1,1,1,5] => 5
[[1,2,5],[3,8],[4],[6],[7]] => [[1,2,3,6,8],[4],[5],[7]] => [7,5,4,1,2,3,6,8] => [1,1,1,5] => 5
[[1,3,4],[2,8],[5],[6],[7]] => [[1,2,4,5,8],[3],[6],[7]] => [7,6,3,1,2,4,5,8] => [1,1,1,5] => 5
[[1,2,4],[3,8],[5],[6],[7]] => [[1,2,3,5,8],[4],[6],[7]] => [7,6,4,1,2,3,5,8] => [1,1,1,5] => 5
[[1,2,3],[4,8],[5],[6],[7]] => [[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => [1,1,1,5] => 5
[[1,5,7],[2,6],[3],[4],[8]] => [[1,2,6,8],[3,7],[4],[5]] => [5,4,3,7,1,2,6,8] => [1,1,2,4] => 8
[[1,4,7],[2,6],[3],[5],[8]] => [[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => [1,1,2,4] => 8
[[1,3,7],[2,6],[4],[5],[8]] => [[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [1,1,2,4] => 8
[[1,2,7],[3,6],[4],[5],[8]] => [[1,2,3,6],[4,8],[5],[7]] => [7,5,4,8,1,2,3,6] => [1,1,2,4] => 8
[[1,4,7],[2,5],[3],[6],[8]] => [[1,2,5,8],[3,6],[4],[7]] => [7,4,3,6,1,2,5,8] => [1,1,2,4] => 8
[[1,2,7],[3,5],[4],[6],[8]] => [[1,2,3,5],[4,8],[6],[7]] => [7,6,4,8,1,2,3,5] => [1,1,2,4] => 8
[[1,3,7],[2,4],[5],[6],[8]] => [[1,2,4,8],[3,5],[6],[7]] => [7,6,3,5,1,2,4,8] => [1,1,2,4] => 8
[[1,2,7],[3,4],[5],[6],[8]] => [[1,2,3,4],[5,8],[6],[7]] => [7,6,5,8,1,2,3,4] => [1,1,2,4] => 8
[[1,5,6],[2,7],[3],[4],[8]] => [[1,2,6,7],[3,8],[4],[5]] => [5,4,3,8,1,2,6,7] => [1,1,2,4] => 8
[[1,4,6],[2,7],[3],[5],[8]] => [[1,2,5,7],[3,8],[4],[6]] => [6,4,3,8,1,2,5,7] => [1,1,2,4] => 8
[[1,3,6],[2,7],[4],[5],[8]] => [[1,2,4,7],[3,8],[5],[6]] => [6,5,3,8,1,2,4,7] => [1,1,2,4] => 8
[[1,2,6],[3,7],[4],[5],[8]] => [[1,2,3,7],[4,8],[5],[6]] => [6,5,4,8,1,2,3,7] => [1,1,2,4] => 8
[[1,4,5],[2,7],[3],[6],[8]] => [[1,2,5,6,7],[3],[4],[8]] => [8,4,3,1,2,5,6,7] => [1,1,1,5] => 5
[[1,3,5],[2,7],[4],[6],[8]] => [[1,2,4,6,7],[3],[5],[8]] => [8,5,3,1,2,4,6,7] => [1,1,1,5] => 5
[[1,2,5],[3,7],[4],[6],[8]] => [[1,2,3,6,7],[4],[5],[8]] => [8,5,4,1,2,3,6,7] => [1,1,1,5] => 5
[[1,2,4],[3,7],[5],[6],[8]] => [[1,2,3,5,7],[4],[6],[8]] => [8,6,4,1,2,3,5,7] => [1,1,1,5] => 5
[[1,2,3],[4,7],[5],[6],[8]] => [[1,2,3,4,7],[5],[6],[8]] => [8,6,5,1,2,3,4,7] => [1,1,1,5] => 5
[[1,3,6],[2,5],[4],[7],[8]] => [[1,2,4,5],[3,7],[6],[8]] => [8,6,3,7,1,2,4,5] => [1,1,2,4] => 8
[[1,2,6],[3,5],[4],[7],[8]] => [[1,2,3,5],[4,7],[6],[8]] => [8,6,4,7,1,2,3,5] => [1,1,2,4] => 8
[[1,3,6],[2,4],[5],[7],[8]] => [[1,2,4,7],[3,5],[6],[8]] => [8,6,3,5,1,2,4,7] => [1,1,2,4] => 8
[[1,2,6],[3,4],[5],[7],[8]] => [[1,2,3,4],[5,7],[6],[8]] => [8,6,5,7,1,2,3,4] => [1,1,2,4] => 8
[[1,4,5],[2,6],[3],[7],[8]] => [[1,2,5,6],[3,7],[4],[8]] => [8,4,3,7,1,2,5,6] => [1,1,2,4] => 8
[[1,3,5],[2,6],[4],[7],[8]] => [[1,2,4,6],[3,7],[5],[8]] => [8,5,3,7,1,2,4,6] => [1,1,2,4] => 8
[[1,2,5],[3,6],[4],[7],[8]] => [[1,2,3,6],[4,7],[5],[8]] => [8,5,4,7,1,2,3,6] => [1,1,2,4] => 8
[[1,2,4],[3,6],[5],[7],[8]] => [[1,2,3,5,6],[4],[7],[8]] => [8,7,4,1,2,3,5,6] => [1,1,1,5] => 5
[[1,2,3],[4,6],[5],[7],[8]] => [[1,2,3,4,6],[5],[7],[8]] => [8,7,5,1,2,3,4,6] => [1,1,1,5] => 5
[[1,3,5],[2,4],[6],[7],[8]] => [[1,2,4,6],[3,5],[7],[8]] => [8,7,3,5,1,2,4,6] => [1,1,2,4] => 8
[[1,2,5],[3,4],[6],[7],[8]] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [1,1,2,4] => 8
[[1,3,4],[2,5],[6],[7],[8]] => [[1,2,4,5],[3,6],[7],[8]] => [8,7,3,6,1,2,4,5] => [1,1,2,4] => 8
[[1,2,4],[3,5],[6],[7],[8]] => [[1,2,3,5],[4,6],[7],[8]] => [8,7,4,6,1,2,3,5] => [1,1,2,4] => 8
[[1,2,3],[4,5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [1,1,1,5] => 5
[[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,8],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,3] => 7
[[1,6,8],[2],[3],[4],[5],[7]] => [[1,2,7],[3],[4],[5],[6],[8]] => [8,6,5,4,3,1,2,7] => [1,1,1,1,1,3] => 7
[[1,5,8],[2],[3],[4],[6],[7]] => [[1,2,6],[3],[4],[5],[7],[8]] => [8,7,5,4,3,1,2,6] => [1,1,1,1,1,3] => 7
[[1,4,8],[2],[3],[5],[6],[7]] => [[1,2,5],[3],[4],[6],[7],[8]] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,3] => 7
[[1,3,8],[2],[4],[5],[6],[7]] => [[1,2,4],[3],[5],[6],[7],[8]] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,3] => 7
[[1,2,8],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,3] => 7
[[1,6,7],[2],[3],[4],[5],[8]] => [[1,2,7,8],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8] => [1,1,1,1,4] => 6
[[1,4,7],[2],[3],[5],[6],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => [7,6,4,3,1,2,5,8] => [1,1,1,1,4] => 6
[[1,3,7],[2],[4],[5],[6],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => [7,6,5,3,1,2,4,8] => [1,1,1,1,4] => 6
[[1,2,7],[3],[4],[5],[6],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4] => 6
[[1,5,6],[2],[3],[4],[7],[8]] => [[1,2,6,7],[3],[4],[5],[8]] => [8,5,4,3,1,2,6,7] => [1,1,1,1,4] => 6
[[1,4,6],[2],[3],[5],[7],[8]] => [[1,2,5,7],[3],[4],[6],[8]] => [8,6,4,3,1,2,5,7] => [1,1,1,1,4] => 6
[[1,3,6],[2],[4],[5],[7],[8]] => [[1,2,4,7],[3],[5],[6],[8]] => [8,6,5,3,1,2,4,7] => [1,1,1,1,4] => 6
[[1,2,6],[3],[4],[5],[7],[8]] => [[1,2,3,7],[4],[5],[6],[8]] => [8,6,5,4,1,2,3,7] => [1,1,1,1,4] => 6
[[1,4,5],[2],[3],[6],[7],[8]] => [[1,2,5,6],[3],[4],[7],[8]] => [8,7,4,3,1,2,5,6] => [1,1,1,1,4] => 6
[[1,3,5],[2],[4],[6],[7],[8]] => [[1,2,4,6],[3],[5],[7],[8]] => [8,7,5,3,1,2,4,6] => [1,1,1,1,4] => 6
[[1,2,5],[3],[4],[6],[7],[8]] => [[1,2,3,6],[4],[5],[7],[8]] => [8,7,5,4,1,2,3,6] => [1,1,1,1,4] => 6
[[1,3,4],[2],[5],[6],[7],[8]] => [[1,2,4,5],[3],[6],[7],[8]] => [8,7,6,3,1,2,4,5] => [1,1,1,1,4] => 6
[[1,2,4],[3],[5],[6],[7],[8]] => [[1,2,3,5],[4],[6],[7],[8]] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4] => 6
[[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4] => 6
[[1,5],[2,6],[3,7],[4,8]] => [[1,2,6],[3,7],[4,8],[5]] => [5,4,8,3,7,1,2,6] => [1,2,2,3] => 7
[[1,4],[2,6],[3,7],[5,8]] => [[1,2,5,6],[3,7],[4,8]] => [4,8,3,7,1,2,5,6] => [2,2,4] => 4
[[1,3],[2,6],[4,7],[5,8]] => [[1,2,4,6],[3,7],[5,8]] => [5,8,3,7,1,2,4,6] => [2,2,4] => 4
[[1,2],[3,6],[4,7],[5,8]] => [[1,2,3,6],[4,7],[5,8]] => [5,8,4,7,1,2,3,6] => [2,2,4] => 4
[[1,3],[2,5],[4,7],[6,8]] => [[1,2,4,5],[3,7],[6,8]] => [6,8,3,7,1,2,4,5] => [2,2,4] => 4
[[1,2],[3,5],[4,7],[6,8]] => [[1,2,3,5],[4,7],[6,8]] => [6,8,4,7,1,2,3,5] => [2,2,4] => 4
[[1,3],[2,4],[5,7],[6,8]] => [[1,2,4,7],[3,5],[6,8]] => [6,8,3,5,1,2,4,7] => [2,2,4] => 4
[[1,2],[3,4],[5,7],[6,8]] => [[1,2,3,4],[5,7],[6,8]] => [6,8,5,7,1,2,3,4] => [2,2,4] => 4
[[1,4],[2,5],[3,6],[7,8]] => [[1,2,5,8],[3,6],[4,7]] => [4,7,3,6,1,2,5,8] => [2,2,4] => 4
[[1,2],[3,5],[4,6],[7,8]] => [[1,2,3,5],[4,6],[7,8]] => [7,8,4,6,1,2,3,5] => [2,2,4] => 4
[[1,3],[2,4],[5,6],[7,8]] => [[1,2,4,6],[3,5],[7,8]] => [7,8,3,5,1,2,4,6] => [2,2,4] => 4
[[1,2],[3,4],[5,6],[7,8]] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [2,2,4] => 4
[[1,6],[2,7],[3,8],[4],[5]] => [[1,2,7],[3,8],[4],[5],[6]] => [6,5,4,3,8,1,2,7] => [1,1,1,2,3] => 10
[[1,5],[2,7],[3,8],[4],[6]] => [[1,2,6,7],[3,8],[4],[5]] => [5,4,3,8,1,2,6,7] => [1,1,2,4] => 8
[[1,4],[2,7],[3,8],[5],[6]] => [[1,2,5,7],[3,8],[4],[6]] => [6,4,3,8,1,2,5,7] => [1,1,2,4] => 8
[[1,3],[2,7],[4,8],[5],[6]] => [[1,2,4,7],[3,8],[5],[6]] => [6,5,3,8,1,2,4,7] => [1,1,2,4] => 8
[[1,2],[3,7],[4,8],[5],[6]] => [[1,2,3,7],[4,8],[5],[6]] => [6,5,4,8,1,2,3,7] => [1,1,2,4] => 8
[[1,5],[2,6],[3,8],[4],[7]] => [[1,2,6,8],[3,7],[4],[5]] => [5,4,3,7,1,2,6,8] => [1,1,2,4] => 8
[[1,4],[2,6],[3,8],[5],[7]] => [[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => [1,1,2,4] => 8
[[1,3],[2,6],[4,8],[5],[7]] => [[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [1,1,2,4] => 8
[[1,2],[3,6],[4,8],[5],[7]] => [[1,2,3,6],[4,8],[5],[7]] => [7,5,4,8,1,2,3,6] => [1,1,2,4] => 8
[[1,4],[2,5],[3,8],[6],[7]] => [[1,2,5,8],[3,6],[4],[7]] => [7,4,3,6,1,2,5,8] => [1,1,2,4] => 8
[[1,2],[3,5],[4,8],[6],[7]] => [[1,2,3,5],[4,8],[6],[7]] => [7,6,4,8,1,2,3,5] => [1,1,2,4] => 8
[[1,3],[2,4],[5,8],[6],[7]] => [[1,2,4,8],[3,5],[6],[7]] => [7,6,3,5,1,2,4,8] => [1,1,2,4] => 8
[[1,2],[3,4],[5,8],[6],[7]] => [[1,2,3,4],[5,8],[6],[7]] => [7,6,5,8,1,2,3,4] => [1,1,2,4] => 8
[[1,5],[2,6],[3,7],[4],[8]] => [[1,2,6],[3,7],[4,8],[5]] => [5,4,8,3,7,1,2,6] => [1,2,2,3] => 7
[[1,4],[2,6],[3,7],[5],[8]] => [[1,2,5,6],[3,7],[4],[8]] => [8,4,3,7,1,2,5,6] => [1,1,2,4] => 8
[[1,3],[2,6],[4,7],[5],[8]] => [[1,2,4,6],[3,7],[5],[8]] => [8,5,3,7,1,2,4,6] => [1,1,2,4] => 8
[[1,2],[3,6],[4,7],[5],[8]] => [[1,2,3,6],[4,7],[5],[8]] => [8,5,4,7,1,2,3,6] => [1,1,2,4] => 8
[[1,3],[2,5],[4,7],[6],[8]] => [[1,2,4,5],[3,7],[6],[8]] => [8,6,3,7,1,2,4,5] => [1,1,2,4] => 8
[[1,2],[3,5],[4,7],[6],[8]] => [[1,2,3,5],[4,7],[6],[8]] => [8,6,4,7,1,2,3,5] => [1,1,2,4] => 8
[[1,3],[2,4],[5,7],[6],[8]] => [[1,2,4,7],[3,5],[6],[8]] => [8,6,3,5,1,2,4,7] => [1,1,2,4] => 8
[[1,2],[3,4],[5,7],[6],[8]] => [[1,2,3,4],[5,7],[6],[8]] => [8,6,5,7,1,2,3,4] => [1,1,2,4] => 8
[[1,4],[2,5],[3,6],[7],[8]] => [[1,2,5],[3,6],[4,7],[8]] => [8,4,7,3,6,1,2,5] => [1,2,2,3] => 7
[[1,3],[2,5],[4,6],[7],[8]] => [[1,2,4,5],[3,6],[7],[8]] => [8,7,3,6,1,2,4,5] => [1,1,2,4] => 8
[[1,2],[3,5],[4,6],[7],[8]] => [[1,2,3,5],[4,6],[7],[8]] => [8,7,4,6,1,2,3,5] => [1,1,2,4] => 8
[[1,3],[2,4],[5,6],[7],[8]] => [[1,2,4,6],[3,5],[7],[8]] => [8,7,3,5,1,2,4,6] => [1,1,2,4] => 8
[[1,2],[3,4],[5,6],[7],[8]] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [1,1,2,4] => 8
[[1,7],[2,8],[3],[4],[5],[6]] => [[1,2,8],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,3] => 7
[[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8] => [1,1,1,1,4] => 6
[[1,4],[2,8],[3],[5],[6],[7]] => [[1,2,5,8],[3],[4],[6],[7]] => [7,6,4,3,1,2,5,8] => [1,1,1,1,4] => 6
[[1,3],[2,8],[4],[5],[6],[7]] => [[1,2,4,8],[3],[5],[6],[7]] => [7,6,5,3,1,2,4,8] => [1,1,1,1,4] => 6
[[1,2],[3,8],[4],[5],[6],[7]] => [[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4] => 6
[[1,6],[2,7],[3],[4],[5],[8]] => [[1,2,7],[3,8],[4],[5],[6]] => [6,5,4,3,8,1,2,7] => [1,1,1,2,3] => 10
[[1,5],[2,7],[3],[4],[6],[8]] => [[1,2,6,7],[3],[4],[5],[8]] => [8,5,4,3,1,2,6,7] => [1,1,1,1,4] => 6
[[1,4],[2,7],[3],[5],[6],[8]] => [[1,2,5,7],[3],[4],[6],[8]] => [8,6,4,3,1,2,5,7] => [1,1,1,1,4] => 6
[[1,3],[2,7],[4],[5],[6],[8]] => [[1,2,4,7],[3],[5],[6],[8]] => [8,6,5,3,1,2,4,7] => [1,1,1,1,4] => 6
[[1,2],[3,7],[4],[5],[6],[8]] => [[1,2,3,7],[4],[5],[6],[8]] => [8,6,5,4,1,2,3,7] => [1,1,1,1,4] => 6
[[1,4],[2,6],[3],[5],[7],[8]] => [[1,2,5,6],[3],[4],[7],[8]] => [8,7,4,3,1,2,5,6] => [1,1,1,1,4] => 6
[[1,3],[2,6],[4],[5],[7],[8]] => [[1,2,4,6],[3],[5],[7],[8]] => [8,7,5,3,1,2,4,6] => [1,1,1,1,4] => 6
[[1,2],[3,6],[4],[5],[7],[8]] => [[1,2,3,6],[4],[5],[7],[8]] => [8,7,5,4,1,2,3,6] => [1,1,1,1,4] => 6
[[1,4],[2,5],[3],[6],[7],[8]] => [[1,2,5],[3,6],[4],[7],[8]] => [8,7,4,3,6,1,2,5] => [1,1,1,2,3] => 10
[[1,3],[2,5],[4],[6],[7],[8]] => [[1,2,4,5],[3],[6],[7],[8]] => [8,7,6,3,1,2,4,5] => [1,1,1,1,4] => 6
[[1,2],[3,5],[4],[6],[7],[8]] => [[1,2,3,5],[4],[6],[7],[8]] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4] => 6
[[1,3],[2,4],[5],[6],[7],[8]] => [[1,2,4],[3,5],[6],[7],[8]] => [8,7,6,3,5,1,2,4] => [1,1,1,2,3] => 10
[[1,2],[3,4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4] => 6
[[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2] => 8
[[1,7],[2],[3],[4],[5],[6],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,3] => 7
[[1,6],[2],[3],[4],[5],[7],[8]] => [[1,2,7],[3],[4],[5],[6],[8]] => [8,6,5,4,3,1,2,7] => [1,1,1,1,1,3] => 7
[[1,5],[2],[3],[4],[6],[7],[8]] => [[1,2,6],[3],[4],[5],[7],[8]] => [8,7,5,4,3,1,2,6] => [1,1,1,1,1,3] => 7
[[1,4],[2],[3],[5],[6],[7],[8]] => [[1,2,5],[3],[4],[6],[7],[8]] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,3] => 7
[[1,3],[2],[4],[5],[6],[7],[8]] => [[1,2,4],[3],[5],[6],[7],[8]] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,3] => 7
[[1,2],[3],[4],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,3] => 7
[[1],[2],[3],[4],[5],[6],[7],[8]] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2] => 8
[[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] => [9] => 1
[[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] => [9] => 1
[[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] => [9] => 1
[[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,8] => 3
[[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] => [9] => 1
[[1,2,3,4,5,6],[7,8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,8] => 3
[[1,2,3,4,5,6],[7],[8],[9]] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [1,1,7] => 4
[[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] => [9] => 1
[[1,2,3,4,5],[6,7,8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,8] => 3
[[1,2,3,4,5],[6,7],[8,9]] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [2,7] => 3
[[1,2,3,4,5],[6,7],[8],[9]] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [1,1,7] => 4
[[1,2,3,4,5],[6],[7],[8],[9]] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6] => 5
[[1,2,3,4],[5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,8] => 3
[[1,2,3,4],[5,6,7],[8,9]] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [2,7] => 3
[[1,2,3,4],[5,6,7],[8],[9]] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [1,1,7] => 4
[[1,2,3,4],[5,6],[7,8],[9]] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => [1,2,6] => 6
[[1,2,3,4],[5,6],[7],[8],[9]] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6] => 5
[[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,5] => 6
[[1,2,3],[4,5,6],[7,8,9]] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => [3,6] => 3
[[1,2,3],[4,5,6],[7,8],[9]] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => [1,2,6] => 6
[[1,2,3],[4,5,6],[7],[8],[9]] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6] => 5
[[1,2,3],[4,5],[6,7],[8,9]] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => [2,2,5] => 4
[[1,2,3],[4,5],[6,7],[8],[9]] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => [1,1,2,5] => 8
[[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,5] => 6
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,4] => 7
[[1,2],[3,4],[5,6],[7,8],[9]] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => [1,2,2,4] => 7
[[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => [1,1,1,2,4] => 10
[[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,4] => 7
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,3] => 8
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2] => 9
[[1,3,4,5,6,7,8,9],[2]] => [[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [1,8] => 3
[[1,2,5,6,7,8,9],[3,4]] => [[1,2,3,4,7,8,9],[5,6]] => [5,6,1,2,3,4,7,8,9] => [2,7] => 3
[[1,4,5,6,7,8,9],[2],[3]] => [[1,2,5,6,7,8,9],[3],[4]] => [4,3,1,2,5,6,7,8,9] => [1,1,7] => 4
[[1,2,3,7,8,9],[4,5,6]] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => [3,6] => 3
[[1,3,6,7,8,9],[2,5],[4]] => [[1,2,4,5,8,9],[3,7],[6]] => [6,3,7,1,2,4,5,8,9] => [1,2,6] => 6
[[1,5,6,7,8,9],[2],[3],[4]] => [[1,2,6,7,8,9],[3],[4],[5]] => [5,4,3,1,2,6,7,8,9] => [1,1,1,6] => 5
[[1,2,3,4,9],[5,6,7,8]] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,8] => 3
[[1,3,4,8,9],[2,6,7],[5]] => [[1,2,4,5,6,7],[3,9],[8]] => [8,3,9,1,2,4,5,6,7] => [1,2,6] => 6
[[1,2,7,8,9],[3,4],[5,6]] => [[1,2,3,4,9],[5,6],[7,8]] => [7,8,5,6,1,2,3,4,9] => [2,2,5] => 4
[[1,4,7,8,9],[2,6],[3],[5]] => [[1,2,5,6,9],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6,9] => [1,1,2,5] => 8
[[1,6,7,8,9],[2],[3],[4],[5]] => [[1,2,7,8,9],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8,9] => [1,1,1,1,5] => 6
[[1,3,4,5],[2,7,8,9],[6]] => [[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [1,8] => 3
[[1,2,5,9],[3,4,8],[6,7]] => [[1,2,3,4,7,8],[5,6],[9]] => [9,5,6,1,2,3,4,7,8] => [1,2,6] => 6
[[1,4,5,9],[2,7,8],[3],[6]] => [[1,2,5,6,7,8],[3],[4],[9]] => [9,4,3,1,2,5,6,7,8] => [1,1,1,6] => 5
[[1,3,8,9],[2,5],[4,7],[6]] => [[1,2,4,5],[3,7],[6,9],[8]] => [8,6,9,3,7,1,2,4,5] => [1,2,2,4] => 7
[[1,5,8,9],[2,7],[3],[4],[6]] => [[1,2,6,7],[3,9],[4],[5],[8]] => [8,5,4,3,9,1,2,6,7] => [1,1,1,2,4] => 10
[[1,7,8,9],[2],[3],[4],[5],[6]] => [[1,2,8,9],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8,9] => [1,1,1,1,1,4] => 7
[[1,3,6],[2,5,9],[4,8],[7]] => [[1,2,4,5,8,9],[3,7],[6]] => [6,3,7,1,2,4,5,8,9] => [1,2,6] => 6
[[1,5,6],[2,8,9],[3],[4],[7]] => [[1,2,6,7,8,9],[3],[4],[5]] => [5,4,3,1,2,6,7,8,9] => [1,1,1,6] => 5
[[1,2,9],[3,4],[5,6],[7,8]] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => [1,2,2,4] => 7
[[1,4,9],[2,6],[3,8],[5],[7]] => [[1,2,5,6],[3,8],[4],[7],[9]] => [9,7,4,3,8,1,2,5,6] => [1,1,1,2,4] => 10
[[1,6,9],[2,8],[3],[4],[5],[7]] => [[1,2,7,8],[3],[4],[5],[6],[9]] => [9,6,5,4,3,1,2,7,8] => [1,1,1,1,1,4] => 7
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,3] => 8
[[1,3],[2,5],[4,7],[6,9],[8]] => [[1,2,4,5],[3,7],[6,9],[8]] => [8,6,9,3,7,1,2,4,5] => [1,2,2,4] => 7
[[1,5],[2,7],[3,9],[4],[6],[8]] => [[1,2,6,7],[3,9],[4],[5],[8]] => [8,5,4,3,9,1,2,6,7] => [1,1,1,2,4] => 10
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [[1,2,8,9],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8,9] => [1,1,1,1,1,4] => 7
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2] => 9
[[1,8],[2,9],[3],[4],[5],[6],[7]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,3] => 8
[[1,5,9],[2,6],[3,7],[4,8]] => [[1,2,6],[3,7],[4,8],[5,9]] => [5,9,4,8,3,7,1,2,6] => [2,2,2,3] => 5
[[1,3,5,7,9],[2,4,6,8]] => [[1,2,4,6,8],[3,5,7,9]] => [3,5,7,9,1,2,4,6,8] => [4,5] => 3
[[1,3],[2,4],[5],[6],[7],[8],[9]] => [[1,2,4],[3,5],[6],[7],[8],[9]] => [9,8,7,6,3,5,1,2,4] => [1,1,1,1,2,3] => 12
[[1,4],[2,5],[3,6],[7],[8],[9]] => [[1,2,5],[3,6],[4,7],[8],[9]] => [9,8,4,7,3,6,1,2,5] => [1,1,2,2,3] => 9
[[1,2,4],[3,5],[6],[7],[8],[9]] => [[1,2,3,5],[4,6],[7],[8],[9]] => [9,8,7,4,6,1,2,3,5] => [1,1,1,2,4] => 10
[[1,5],[2,6],[3,7],[4,8],[9]] => [[1,2,6],[3,7],[4,8],[5,9]] => [5,9,4,8,3,7,1,2,6] => [2,2,2,3] => 5
[[1,2,5],[3,6],[4,7],[8],[9]] => [[1,2,3,6],[4,7],[5,8],[9]] => [9,5,8,4,7,1,2,3,6] => [1,2,2,4] => 7
[[1,3,5],[2,4,6],[7],[8],[9]] => [[1,2,4,6],[3,5,7],[8],[9]] => [9,8,3,5,7,1,2,4,6] => [1,1,3,4] => 8
[[1,2,3,5],[4,6],[7],[8],[9]] => [[1,2,3,4,6],[5,7],[8],[9]] => [9,8,5,7,1,2,3,4,6] => [1,1,2,5] => 8
[[1,3,6],[2,4,7],[5,8],[9]] => [[1,2,4,7],[3,5,8],[6,9]] => [6,9,3,5,8,1,2,4,7] => [2,3,4] => 6
[[1,2,3,6],[4,7],[5,8],[9]] => [[1,2,3,4,7],[5,8],[6,9]] => [6,9,5,8,1,2,3,4,7] => [2,2,5] => 4
[[1,2,4,6],[3,5,7],[8],[9]] => [[1,2,3,5,7],[4,6,8],[9]] => [9,4,6,8,1,2,3,5,7] => [1,3,5] => 6
[[1,2,3,4,6],[5,7],[8],[9]] => [[1,2,3,4,5,7],[6,8],[9]] => [9,6,8,1,2,3,4,5,7] => [1,2,6] => 6
[[1,2,3,4,7],[5,8],[6,9]] => [[1,2,3,4,5,8],[6,9],[7]] => [7,6,9,1,2,3,4,5,8] => [1,2,6] => 6
[[1,3,5,7],[2,4,6,8],[9]] => [[1,2,4,6,8],[3,5,7,9]] => [3,5,7,9,1,2,4,6,8] => [4,5] => 3
[[1,2,3,5,7],[4,6,8],[9]] => [[1,2,3,4,6,8],[5,7,9]] => [5,7,9,1,2,3,4,6,8] => [3,6] => 3
[[1,2,3,4,5,7],[6,8],[9]] => [[1,2,3,4,5,6,8],[7,9]] => [7,9,1,2,3,4,5,6,8] => [2,7] => 3
[[1,2,3,4,6,8],[5,7,9]] => [[1,2,3,4,5,7,9],[6,8]] => [6,8,1,2,3,4,5,7,9] => [2,7] => 3
[[1,2,3,4,5,6,8],[7,9]] => [[1,2,3,4,5,6,7,9],[8]] => [8,1,2,3,4,5,6,7,9] => [1,8] => 3
[[1,2,3,4,5,6,7,9],[8]] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,8] => 3
[[1,2,3,4,5,6,9],[7,8]] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,8] => 3
[[1,2,3,4,5,6,9],[7],[8]] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [1,1,7] => 4
[[1,2,3,4,5,9],[6,7,8]] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,8] => 3
[[1,2,3,4,5,9],[6,7],[8]] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [1,1,7] => 4
[[1,2,3,4,5,9],[6],[7],[8]] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6] => 5
[[1,2,3,4,9],[5,6,7],[8]] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [1,1,7] => 4
[[1,2,3,4,9],[5,6],[7,8]] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => [1,2,6] => 6
[[1,2,3,4,9],[5,6],[7],[8]] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6] => 5
[[1,2,3,4,9],[5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,5] => 6
[[1,2,3,7],[4,5,6,9],[8]] => [[1,2,3,4,5,6,9],[7,8]] => [7,8,1,2,3,4,5,6,9] => [2,7] => 3
[[1,2,3,9],[4,5,6],[7,8]] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => [1,2,6] => 6
[[1,2,3,9],[4,5,6],[7],[8]] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6] => 5
[[1,2,3,9],[4,5],[6,7],[8]] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => [1,1,2,5] => 8
[[1,2,3,9],[4,5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,5] => 6
[[1,2,3,9],[4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,4] => 7
[[1,2,9],[3,4],[5,6],[7],[8]] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => [1,1,1,2,4] => 10
[[1,2,9],[3,4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,4] => 7
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,3] => 8
[[1,2,4],[3,5,7],[6,8],[9]] => [[1,2,3,5,7],[4,6,8],[9]] => [9,4,6,8,1,2,3,5,7] => [1,3,5] => 6
[[1,4],[2,6],[3,8],[5],[7],[9]] => [[1,2,5,6],[3,8],[4],[7],[9]] => [9,7,4,3,8,1,2,5,6] => [1,1,1,2,4] => 10
[[1,6],[2,8],[3],[4],[5],[7],[9]] => [[1,2,7,8],[3],[4],[5],[6],[9]] => [9,6,5,4,3,1,2,7,8] => [1,1,1,1,1,4] => 7
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,3] => 8
[[1,3,4,5,6,7,8],[2,9]] => [[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [1,8] => 3
[[1,3,4,5,6,7,8],[2],[9]] => [[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [1,8] => 3
[[1,3,4,5,6,7],[2,8,9]] => [[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [1,8] => 3
[[1,3,4,5,6,7],[2,9],[8]] => [[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [1,8] => 3
[[1,3,4,5,6],[2,7,8,9]] => [[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [1,8] => 3
[[1,3,4,5,6],[2,8,9],[7]] => [[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [1,8] => 3
[[1,3,4,5,6],[2,8],[7,9]] => [[1,2,4,5,6,7,8],[3,9]] => [3,9,1,2,4,5,6,7,8] => [2,7] => 3
[[1,3,4,5],[2,7,8],[6,9]] => [[1,2,4,5,6,7,8],[3,9]] => [3,9,1,2,4,5,6,7,8] => [2,7] => 3
[[1,3,4,5],[2,7],[6,9],[8]] => [[1,2,4,5,6,7],[3,9],[8]] => [8,3,9,1,2,4,5,6,7] => [1,2,6] => 6
[[1,3,4],[2,6,7],[5,8,9]] => [[1,2,4,5,6,7],[3,8,9]] => [3,8,9,1,2,4,5,6,7] => [3,6] => 3
[[1,3,4],[2,6,7],[5,9],[8]] => [[1,2,4,5,6,7],[3,9],[8]] => [8,3,9,1,2,4,5,6,7] => [1,2,6] => 6
[[1,2,5,6,7,8],[3,4,9]] => [[1,2,3,4,7,8,9],[5,6]] => [5,6,1,2,3,4,7,8,9] => [2,7] => 3
[[1,2,5,6,7,8],[3,4],[9]] => [[1,2,3,4,7,8,9],[5,6]] => [5,6,1,2,3,4,7,8,9] => [2,7] => 3
[[1,4,5,6,7,8],[2],[3],[9]] => [[1,2,5,6,7,8,9],[3],[4]] => [4,3,1,2,5,6,7,8,9] => [1,1,7] => 4
[[1,2,3,7,8],[4,5,6,9]] => [[1,2,3,4,5,6,9],[7,8]] => [7,8,1,2,3,4,5,6,9] => [2,7] => 3
[[1,2,3,7,8],[4,5,6],[9]] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => [3,6] => 3
[[1,3,6,7,8],[2,5],[4,9]] => [[1,2,4,5,8,9],[3,7],[6]] => [6,3,7,1,2,4,5,8,9] => [1,2,6] => 6
[[1,3,6,7,8],[2,5],[4],[9]] => [[1,2,4,5,8,9],[3,7],[6]] => [6,3,7,1,2,4,5,8,9] => [1,2,6] => 6
[[1,5,6,7,8],[2],[3],[4],[9]] => [[1,2,6,7,8,9],[3],[4],[5]] => [5,4,3,1,2,6,7,8,9] => [1,1,1,6] => 5
[[1,3,4,8],[2,6,7],[5,9]] => [[1,2,4,5,6,7],[3,9],[8]] => [8,3,9,1,2,4,5,6,7] => [1,2,6] => 6
[[1,3,4,8],[2,6,7],[5],[9]] => [[1,2,4,5,6,7],[3,9],[8]] => [8,3,9,1,2,4,5,6,7] => [1,2,6] => 6
[[1,2,7,8],[3,4],[5,6],[9]] => [[1,2,3,4,9],[5,6],[7,8]] => [7,8,5,6,1,2,3,4,9] => [2,2,5] => 4
[[1,4,7,8],[2,6],[3],[5],[9]] => [[1,2,5,6,9],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6,9] => [1,1,2,5] => 8
[[1,6,7,8],[2],[3],[4],[5],[9]] => [[1,2,7,8,9],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8,9] => [1,1,1,1,5] => 6
[[1,2,5],[3,4,8],[6,7],[9]] => [[1,2,3,4,7,8],[5,6],[9]] => [9,5,6,1,2,3,4,7,8] => [1,2,6] => 6
[[1,4,5],[2,7,8],[3],[6],[9]] => [[1,2,5,6,7,8],[3],[4],[9]] => [9,4,3,1,2,5,6,7,8] => [1,1,1,6] => 5
[[1,3,8],[2,5],[4,7],[6,9]] => [[1,2,4,5],[3,7],[6,9],[8]] => [8,6,9,3,7,1,2,4,5] => [1,2,2,4] => 7
[[1,3,8],[2,5],[4,7],[6],[9]] => [[1,2,4,5],[3,7],[6,9],[8]] => [8,6,9,3,7,1,2,4,5] => [1,2,2,4] => 7
[[1,5,8],[2,7],[3],[4],[6],[9]] => [[1,2,6,7],[3,9],[4],[5],[8]] => [8,5,4,3,9,1,2,6,7] => [1,1,1,2,4] => 10
[[1,7,8],[2],[3],[4],[5],[6],[9]] => [[1,2,8,9],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8,9] => [1,1,1,1,1,4] => 7
[[1,2,3,4,8,9],[5,6,7]] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [2,7] => 3
[[1,2,3,8,9],[4,5],[6,7]] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => [2,2,5] => 4
[[1,2,5,6],[3,4,8,9],[7]] => [[1,2,3,4,7,8,9],[5,6]] => [5,6,1,2,3,4,7,8,9] => [2,7] => 3
[[1,2,8,9],[3],[4],[5],[6],[7]] => [[1,2,3,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,4] => 7
[[1,2,3,4,7,8,9],[5,6]] => [[1,2,3,4,5,6,9],[7,8]] => [7,8,1,2,3,4,5,6,9] => [2,7] => 3
[[1,2,3,4,7,8],[5,6],[9]] => [[1,2,3,4,5,6,9],[7,8]] => [7,8,1,2,3,4,5,6,9] => [2,7] => 3
[[1,2,3,4,5,7],[6],[8],[9]] => [[1,2,3,4,5,6,8],[7],[9]] => [9,7,1,2,3,4,5,6,8] => [1,1,7] => 4
[[1,2,3,4],[5,6,7,9],[8]] => [[1,2,3,4,5,6,7,9],[8]] => [8,1,2,3,4,5,6,7,9] => [1,8] => 3
[[1,2,3,4,5,6,8],[7],[9]] => [[1,2,3,4,5,6,7,9],[8]] => [8,1,2,3,4,5,6,7,9] => [1,8] => 3
[[1,2,3,5,7,9],[4,6,8]] => [[1,2,3,4,6,8],[5,7,9]] => [5,7,9,1,2,3,4,6,8] => [3,6] => 3
[[1,2,3,4,5,7,9],[6,8]] => [[1,2,3,4,5,6,8],[7,9]] => [7,9,1,2,3,4,5,6,8] => [2,7] => 3
[[1,2,8],[3,9],[4],[5],[6],[7]] => [[1,2,3,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,4] => 7
[[1,5,8],[2,7],[3,9],[4],[6]] => [[1,2,6,7],[3,9],[4],[5],[8]] => [8,5,4,3,9,1,2,6,7] => [1,1,1,2,4] => 10
[[1,4,7],[2,6,9],[3,8],[5]] => [[1,2,5,6,9],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6,9] => [1,1,2,5] => 8
[[1,3,6,7,8],[2,4],[5,9]] => [[1,2,4,7,8,9],[3,5],[6]] => [6,3,5,1,2,4,7,8,9] => [1,2,6] => 6
[[1,2],[3,9],[4],[5],[6],[7],[8]] => [[1,2,3,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,4] => 7
[[1,2,3,4,5],[6,9],[7],[8]] => [[1,2,3,4,5,6,9],[7],[8]] => [8,7,1,2,3,4,5,6,9] => [1,1,7] => 4
[[1,2,3,4,5,6],[7,9],[8]] => [[1,2,3,4,5,6,7,9],[8]] => [8,1,2,3,4,5,6,7,9] => [1,8] => 3
[[1,3,9],[2,4],[5],[6],[7],[8]] => [[1,2,4],[3,5],[6],[7],[8],[9]] => [9,8,7,6,3,5,1,2,4] => [1,1,1,1,2,3] => 12
[[1,4,9],[2,5],[3,6],[7],[8]] => [[1,2,5],[3,6],[4,7],[8],[9]] => [9,8,4,7,3,6,1,2,5] => [1,1,2,2,3] => 9
[[1,2,4,9],[3,5],[6],[7],[8]] => [[1,2,3,5],[4,6],[7],[8],[9]] => [9,8,7,4,6,1,2,3,5] => [1,1,1,2,4] => 10
[[1,2,5,9],[3,6],[4,7],[8]] => [[1,2,3,6],[4,7],[5,8],[9]] => [9,5,8,4,7,1,2,3,6] => [1,2,2,4] => 7
[[1,3,5,9],[2,4,6],[7],[8]] => [[1,2,4,6],[3,5,7],[8],[9]] => [9,8,3,5,7,1,2,4,6] => [1,1,3,4] => 8
[[1,2,3,5,9],[4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8],[9]] => [9,8,5,7,1,2,3,4,6] => [1,1,2,5] => 8
[[1,3,6,9],[2,4,7],[5,8]] => [[1,2,4,7],[3,5,8],[6,9]] => [6,9,3,5,8,1,2,4,7] => [2,3,4] => 6
[[1,2,3,6,9],[4,7],[5,8]] => [[1,2,3,4,7],[5,8],[6,9]] => [6,9,5,8,1,2,3,4,7] => [2,2,5] => 4
[[1,2,4,6,9],[3,5,7],[8]] => [[1,2,3,5,7],[4,6,8],[9]] => [9,4,6,8,1,2,3,5,7] => [1,3,5] => 6
[[1,2,3,4,6,9],[5,7],[8]] => [[1,2,3,4,5,7],[6,8],[9]] => [9,6,8,1,2,3,4,5,7] => [1,2,6] => 6
[[1,3,4,5,6,7,9],[2,8]] => [[1,2,4,5,6,7,8],[3,9]] => [3,9,1,2,4,5,6,7,8] => [2,7] => 3
[[1,2,3,4,5,8],[6,9],[7]] => [[1,2,3,4,5,6,9],[7],[8]] => [8,7,1,2,3,4,5,6,9] => [1,1,7] => 4
[[1,2,3,4,5,8,9],[6,7]] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [2,7] => 3
[[1,2,3,4,7,9],[5,6],[8]] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => [1,2,6] => 6
[[1,2,3,4,6],[5,7,9],[8]] => [[1,2,3,4,5,7,9],[6,8]] => [6,8,1,2,3,4,5,7,9] => [2,7] => 3
[[1,2,3,4,6],[5,8],[7,9]] => [[1,2,3,4,5,7,8],[6,9]] => [6,9,1,2,3,4,5,7,8] => [2,7] => 3
[[1,2,3,5],[4,6,8],[7,9]] => [[1,2,3,4,6,8],[5,7,9]] => [5,7,9,1,2,3,4,6,8] => [3,6] => 3
[[1,3,4,5,8,9],[2,7],[6]] => [[1,2,4,5,6,7],[3,9],[8]] => [8,3,9,1,2,4,5,6,7] => [1,2,6] => 6
[[1,2,3,4,7,9],[5,8],[6]] => [[1,2,3,4,5,8],[6,9],[7]] => [7,6,9,1,2,3,4,5,8] => [1,2,6] => 6
[[1,2,3,6],[4,5,7,9],[8]] => [[1,2,3,4,5,7,9],[6,8]] => [6,8,1,2,3,4,5,7,9] => [2,7] => 3
[[1,4,5,6],[2,8,9],[3],[7]] => [[1,2,5,6,7,8,9],[3],[4]] => [4,3,1,2,5,6,7,8,9] => [1,1,7] => 4
[[1,2,5,6,7,9],[3,4],[8]] => [[1,2,3,4,7,8],[5,6],[9]] => [9,5,6,1,2,3,4,7,8] => [1,2,6] => 6
[[1,2,3,6,9],[4,5],[7],[8]] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => [1,1,2,5] => 8
[[1,2,7,9],[3,4],[5,6],[8]] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => [1,2,2,4] => 7
[[1,2,5,9],[3,4],[6],[7],[8]] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => [1,1,1,2,4] => 10
[[1,4,7],[2,6],[3,9],[5],[8]] => [[1,2,5,6,9],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6,9] => [1,1,2,5] => 8
[[1,6,7],[2,9],[3],[4],[5],[8]] => [[1,2,7,8,9],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8,9] => [1,1,1,1,5] => 6
[[1,4,5,6,7,8],[2,9],[3]] => [[1,2,5,6,7,8,9],[3],[4]] => [4,3,1,2,5,6,7,8,9] => [1,1,7] => 4
[[1,5,6,7,8],[2,9],[3],[4]] => [[1,2,6,7,8,9],[3],[4],[5]] => [5,4,3,1,2,6,7,8,9] => [1,1,1,6] => 5
[[1,2,3,6],[4,5,7,8],[9]] => [[1,2,3,4,5,7,8],[6,9]] => [6,9,1,2,3,4,5,7,8] => [2,7] => 3
[[1,6,7,8],[2,9],[3],[4],[5]] => [[1,2,7,8,9],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8,9] => [1,1,1,1,5] => 6
[[1,7,8],[2,9],[3],[4],[5],[6]] => [[1,2,8,9],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8,9] => [1,1,1,1,1,4] => 7
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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:
2,0,2 3,0,5,2 3,0,14,7,2 4,0,32,24,9,7 4,0,70,48,40,61,2,7
F1=q
F2=2 q
F3=2 q+2 q3
F4=3 q+5 q3+2 q4
F5=3 q+14 q3+7 q4+2 q5
F6=4 q+32 q3+24 q4+9 q5+7 q6
F7=4 q+70 q3+48 q4+40 q5+61 q6+2 q7+7 q8
Description
The sum of the positions of the strong records of an integer composition.
A strong record is an element ai such that ai>aj for all j<i. This statistic is the sum of the positions of the strong records.
A strong record is an element ai such that ai>aj for all j<i. This statistic is the sum of the positions of the strong records.
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.
Map
catabolism
Description
Remove the first row of the standard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry k into tableau T is as follows:
If k is larger than all entries in the first column, place k at the bottom of the first column and the procedure is finished. Otherwise, place k in the first column, replacing the smallest entry, y, greater than k. Now insert y into the second column using the same procedure: if y is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place y in the second column, replacing, or 'bumping', the smallest entry, z, larger than y. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
The algorithm for column-inserting an entry k into tableau T is as follows:
If k is larger than all entries in the first column, place k at the bottom of the first column and the procedure is finished. Otherwise, place k in the first column, replacing the smallest entry, y, greater than k. Now insert y into the second column using the same procedure: if y is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place y in the second column, replacing, or 'bumping', the smallest entry, z, larger than y. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.
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