Identifier
-
Mp00084:
Standard tableaux
—conjugate⟶
Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000439: Dyck paths ⟶ ℤ (values match St000025The number of initial rises of a Dyck path.)
Values
[[1]] => [[1]] => [1] => [1,0] => 2
[[1,2]] => [[1],[2]] => [2,1] => [1,1,0,0] => 3
[[1],[2]] => [[1,2]] => [1,2] => [1,0,1,0] => 2
[[1,2,3]] => [[1],[2],[3]] => [3,2,1] => [1,1,1,0,0,0] => 4
[[1,3],[2]] => [[1,2],[3]] => [3,1,2] => [1,1,1,0,0,0] => 4
[[1,2],[3]] => [[1,3],[2]] => [2,1,3] => [1,1,0,0,1,0] => 3
[[1],[2],[3]] => [[1,2,3]] => [1,2,3] => [1,0,1,0,1,0] => 2
[[1,2,3,4]] => [[1],[2],[3],[4]] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => 5
[[1,3,4],[2]] => [[1,2],[3],[4]] => [4,3,1,2] => [1,1,1,1,0,0,0,0] => 5
[[1,2,4],[3]] => [[1,3],[2],[4]] => [4,2,1,3] => [1,1,1,1,0,0,0,0] => 5
[[1,2,3],[4]] => [[1,4],[2],[3]] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 4
[[1,3],[2,4]] => [[1,2],[3,4]] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 4
[[1,2],[3,4]] => [[1,3],[2,4]] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => 3
[[1,4],[2],[3]] => [[1,2,3],[4]] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 5
[[1,3],[2],[4]] => [[1,2,4],[3]] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 4
[[1,2],[3],[4]] => [[1,3,4],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 3
[[1],[2],[3],[4]] => [[1,2,3,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 2
[[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 6
[[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => 6
[[1,2,4,5],[3]] => [[1,3],[2],[4],[5]] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => 6
[[1,2,3,5],[4]] => [[1,4],[2],[3],[5]] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => 6
[[1,2,3,4],[5]] => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 5
[[1,3,5],[2,4]] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => 6
[[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => 6
[[1,3,4],[2,5]] => [[1,2],[3,5],[4]] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 5
[[1,2,4],[3,5]] => [[1,3],[2,5],[4]] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 5
[[1,2,3],[4,5]] => [[1,4],[2,5],[3]] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 4
[[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => 6
[[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => 6
[[1,2,5],[3],[4]] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => 6
[[1,3,4],[2],[5]] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 5
[[1,2,4],[3],[5]] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 5
[[1,2,3],[4],[5]] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 4
[[1,4],[2,5],[3]] => [[1,2,3],[4,5]] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 5
[[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2],[3,5],[4]] => [[1,3,4],[2,5]] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 3
[[1,3],[2,4],[5]] => [[1,2,5],[3,4]] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 4
[[1,2],[3,4],[5]] => [[1,3,5],[2,4]] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 3
[[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 6
[[1,4],[2],[3],[5]] => [[1,2,3,5],[4]] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 5
[[1,3],[2],[4],[5]] => [[1,2,4,5],[3]] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 4
[[1,2],[3],[4],[5]] => [[1,3,4,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 2
[[1,2,3,4,5,6]] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,3,4,5,6],[2]] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,4,5,6],[3]] => [[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,3,5,6],[4]] => [[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,3,4,6],[5]] => [[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,3,4,5],[6]] => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,3,5,6],[2,4]] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,5,6],[3,4]] => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,3,4,6],[2,5]] => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,4,6],[3,5]] => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,3,6],[4,5]] => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,3,4,5],[2,6]] => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[[1,2,4,5],[3,6]] => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[[1,2,3,5],[4,6]] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[[1,2,3,4],[5,6]] => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 5
[[1,4,5,6],[2],[3]] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,3,5,6],[2],[4]] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,5,6],[3],[4]] => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,3,4,6],[2],[5]] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,4,6],[3],[5]] => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,3,6],[4],[5]] => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,3,4,5],[2],[6]] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,2,4,5],[3],[6]] => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,2,3,5],[4],[6]] => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,2,3,4],[5],[6]] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[1,3,5],[2,4,6]] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[[1,2,5],[3,4,6]] => [[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[[1,3,4],[2,5,6]] => [[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 5
[[1,2,4],[3,5,6]] => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 5
[[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 4
[[1,4,6],[2,5],[3]] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,6],[3,5],[4]] => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,3,6],[2,4],[5]] => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,6],[3,4],[5]] => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,4,5],[2,6],[3]] => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[[1,3,5],[2,6],[4]] => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[[1,2,5],[3,6],[4]] => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[[1,3,4],[2,6],[5]] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 5
[[1,2,4],[3,6],[5]] => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 5
[[1,2,3],[4,6],[5]] => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 4
[[1,3,5],[2,4],[6]] => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,2,5],[3,4],[6]] => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,3,4],[2,5],[6]] => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[[1,2,4],[3,5],[6]] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[[1,2,3],[4,5],[6]] => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 4
[[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,4,6],[2],[3],[5]] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,3,6],[2],[4],[5]] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,2,6],[3],[4],[5]] => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,4,5],[2],[3],[6]] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,3,5],[2],[4],[6]] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,2,5],[3],[4],[6]] => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,3,4],[2],[5],[6]] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[1,2,4],[3],[5],[6]] => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[1,2,3],[4],[5],[6]] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[[1,4],[2,5],[3,6]] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 5
[[1,3],[2,5],[4,6]] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 4
>>> Load all 964 entries. <<<[[1,2],[3,5],[4,6]] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[1,3],[2,4],[5,6]] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[1,5],[2,6],[3],[4]] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 5
[[1,3],[2,6],[4],[5]] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 4
[[1,2],[3,6],[4],[5]] => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 3
[[1,4],[2,5],[3],[6]] => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[[1,3],[2,5],[4],[6]] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 4
[[1,2],[3,5],[4],[6]] => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[[1,3],[2,4],[5],[6]] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[[1,2],[3,4],[5],[6]] => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[[1,5],[2],[3],[4],[6]] => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[1,4],[2],[3],[5],[6]] => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[1,3],[2],[4],[5],[6]] => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[[1,2],[3],[4],[5],[6]] => [[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 3
[[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 2
[[1,2,3,4,5,6,7]] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,5,6,7],[2]] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,4,5,6,7],[3]] => [[1,3],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,5,6,7],[4]] => [[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,4,6,7],[5]] => [[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,4,5,7],[6]] => [[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,4,5,6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,3,5,6,7],[2,4]] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,5,6,7],[3,4]] => [[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,6,7],[2,5]] => [[1,2],[3,5],[4],[6],[7]] => [7,6,4,3,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,4,6,7],[3,5]] => [[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,6,7],[4,5]] => [[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,5,7],[2,6]] => [[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,4,5,7],[3,6]] => [[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,5,7],[4,6]] => [[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,4,7],[5,6]] => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,5,6],[2,7]] => [[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[[1,2,4,5,6],[3,7]] => [[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[[1,2,3,5,6],[4,7]] => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[[1,2,3,4,6],[5,7]] => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[[1,2,3,4,5],[6,7]] => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 6
[[1,4,5,6,7],[2],[3]] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,5,6,7],[2],[4]] => [[1,2,4],[3],[5],[6],[7]] => [7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,5,6,7],[3],[4]] => [[1,3,4],[2],[5],[6],[7]] => [7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,6,7],[2],[5]] => [[1,2,5],[3],[4],[6],[7]] => [7,6,4,3,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,4,6,7],[3],[5]] => [[1,3,5],[2],[4],[6],[7]] => [7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,6,7],[4],[5]] => [[1,4,5],[2],[3],[6],[7]] => [7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,5,7],[2],[6]] => [[1,2,6],[3],[4],[5],[7]] => [7,5,4,3,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,4,5,7],[3],[6]] => [[1,3,6],[2],[4],[5],[7]] => [7,5,4,2,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,5,7],[4],[6]] => [[1,4,6],[2],[3],[5],[7]] => [7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,4,7],[5],[6]] => [[1,5,6],[2],[3],[4],[7]] => [7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,5,6],[2],[7]] => [[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,4,5,6],[3],[7]] => [[1,3,7],[2],[4],[5],[6]] => [6,5,4,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,3,5,6],[4],[7]] => [[1,4,7],[2],[3],[5],[6]] => [6,5,3,2,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,3,4,6],[5],[7]] => [[1,5,7],[2],[3],[4],[6]] => [6,4,3,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,3,4,5],[6],[7]] => [[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[1,3,5,7],[2,4,6]] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,5,7],[3,4,6]] => [[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,7],[2,5,6]] => [[1,2],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,4,7],[3,5,6]] => [[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,7],[4,5,6]] => [[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,5,6],[2,4,7]] => [[1,2],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[[1,2,5,6],[3,4,7]] => [[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[[1,3,4,6],[2,5,7]] => [[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[[1,2,4,6],[3,5,7]] => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[[1,2,3,6],[4,5,7]] => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[[1,3,4,5],[2,6,7]] => [[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6
[[1,2,4,5],[3,6,7]] => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6
[[1,2,3,5],[4,6,7]] => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6
[[1,2,3,4],[5,6,7]] => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 5
[[1,4,6,7],[2,5],[3]] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,6,7],[2,5],[4]] => [[1,2,4],[3,5],[6],[7]] => [7,6,3,5,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,6,7],[3,5],[4]] => [[1,3,4],[2,5],[6],[7]] => [7,6,2,5,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,6,7],[2,4],[5]] => [[1,2,5],[3,4],[6],[7]] => [7,6,3,4,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,6,7],[3,4],[5]] => [[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,4,5,7],[2,6],[3]] => [[1,2,3],[4,6],[5],[7]] => [7,5,4,6,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,5,7],[2,6],[4]] => [[1,2,4],[3,6],[5],[7]] => [7,5,3,6,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,5,7],[3,6],[4]] => [[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,7],[2,6],[5]] => [[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,4,7],[3,6],[5]] => [[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,7],[4,6],[5]] => [[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,5,7],[2,4],[6]] => [[1,2,6],[3,4],[5],[7]] => [7,5,3,4,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,5,7],[3,4],[6]] => [[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,7],[2,5],[6]] => [[1,2,6],[3,5],[4],[7]] => [7,4,3,5,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,4,7],[3,5],[6]] => [[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,7],[4,5],[6]] => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,4,5,6],[2,7],[3]] => [[1,2,3],[4,7],[5],[6]] => [6,5,4,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,3,5,6],[2,7],[4]] => [[1,2,4],[3,7],[5],[6]] => [6,5,3,7,1,2,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,2,5,6],[3,7],[4]] => [[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,3,4,6],[2,7],[5]] => [[1,2,5],[3,7],[4],[6]] => [6,4,3,7,1,2,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,2,4,6],[3,7],[5]] => [[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,2,3,6],[4,7],[5]] => [[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,3,4,5],[2,7],[6]] => [[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[[1,2,4,5],[3,7],[6]] => [[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[[1,2,3,5],[4,7],[6]] => [[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[[1,2,3,4],[5,7],[6]] => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 5
[[1,3,5,6],[2,4],[7]] => [[1,2,7],[3,4],[5],[6]] => [6,5,3,4,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,5,6],[3,4],[7]] => [[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,3,4,6],[2,5],[7]] => [[1,2,7],[3,5],[4],[6]] => [6,4,3,5,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,4,6],[3,5],[7]] => [[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,3,6],[4,5],[7]] => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,3,4,5],[2,6],[7]] => [[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[[1,2,4,5],[3,6],[7]] => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[[1,2,3,5],[4,6],[7]] => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[[1,2,3,4],[5,6],[7]] => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[1,5,6,7],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,4,6,7],[2],[3],[5]] => [[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,6,7],[2],[4],[5]] => [[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,6,7],[3],[4],[5]] => [[1,3,4,5],[2],[6],[7]] => [7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,4,5,7],[2],[3],[6]] => [[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,5,7],[3],[4],[6]] => [[1,3,4,6],[2],[5],[7]] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,4,7],[2],[5],[6]] => [[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,4,7],[3],[5],[6]] => [[1,3,5,6],[2],[4],[7]] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,3,7],[4],[5],[6]] => [[1,4,5,6],[2],[3],[7]] => [7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,4,5,6],[2],[3],[7]] => [[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,3,5,6],[2],[4],[7]] => [[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,5,6],[3],[4],[7]] => [[1,3,4,7],[2],[5],[6]] => [6,5,2,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,3,4,6],[2],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,4,6],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6]] => [6,4,2,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,3,6],[4],[5],[7]] => [[1,4,5,7],[2],[3],[6]] => [6,3,2,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,3,4,5],[2],[6],[7]] => [[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[1,2,4,5],[3],[6],[7]] => [[1,3,6,7],[2],[4],[5]] => [5,4,2,1,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[1,2,3,5],[4],[6],[7]] => [[1,4,6,7],[2],[3],[5]] => [5,3,2,1,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[1,2,3,4],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[[1,4,6],[2,5,7],[3]] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[[1,3,6],[2,5,7],[4]] => [[1,2,4],[3,5],[6,7]] => [6,7,3,5,1,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[[1,2,6],[3,5,7],[4]] => [[1,3,4],[2,5],[6,7]] => [6,7,2,5,1,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[[1,3,6],[2,4,7],[5]] => [[1,2,5],[3,4],[6,7]] => [6,7,3,4,1,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[[1,2,6],[3,4,7],[5]] => [[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[[1,4,5],[2,6,7],[3]] => [[1,2,3],[4,6],[5,7]] => [5,7,4,6,1,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[[1,3,5],[2,6,7],[4]] => [[1,2,4],[3,6],[5,7]] => [5,7,3,6,1,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[[1,2,5],[3,6,7],[4]] => [[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 5
[[1,2,4],[3,6,7],[5]] => [[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 5
[[1,2,3],[4,6,7],[5]] => [[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 4
[[1,3,5],[2,4,7],[6]] => [[1,2,6],[3,4],[5,7]] => [5,7,3,4,1,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[[1,2,5],[3,4,7],[6]] => [[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[[1,3,4],[2,5,7],[6]] => [[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 5
[[1,2,4],[3,5,7],[6]] => [[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 5
[[1,2,3],[4,5,7],[6]] => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 4
[[1,3,5],[2,4,6],[7]] => [[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[[1,2,5],[3,4,6],[7]] => [[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[[1,3,4],[2,5,6],[7]] => [[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 5
[[1,2,4],[3,5,6],[7]] => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 5
[[1,2,3],[4,5,6],[7]] => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 4
[[1,4,7],[2,5],[3,6]] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,7],[2,5],[4,6]] => [[1,2,4],[3,5,6],[7]] => [7,3,5,6,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,7],[3,5],[4,6]] => [[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,7],[2,4],[5,6]] => [[1,2,5],[3,4,6],[7]] => [7,3,4,6,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,7],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,4,6],[2,5],[3,7]] => [[1,2,3],[4,5,7],[6]] => [6,4,5,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,3,6],[2,5],[4,7]] => [[1,2,4],[3,5,7],[6]] => [6,3,5,7,1,2,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,2,6],[3,5],[4,7]] => [[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,3,6],[2,4],[5,7]] => [[1,2,5],[3,4,7],[6]] => [6,3,4,7,1,2,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,2,6],[3,4],[5,7]] => [[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[[1,4,5],[2,6],[3,7]] => [[1,2,3],[4,6,7],[5]] => [5,4,6,7,1,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[[1,3,5],[2,6],[4,7]] => [[1,2,4],[3,6,7],[5]] => [5,3,6,7,1,2,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[[1,2,5],[3,6],[4,7]] => [[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[[1,3,4],[2,6],[5,7]] => [[1,2,5],[3,6,7],[4]] => [4,3,6,7,1,2,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 5
[[1,2,4],[3,6],[5,7]] => [[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 5
[[1,2,3],[4,6],[5,7]] => [[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 4
[[1,3,5],[2,4],[6,7]] => [[1,2,6],[3,4,7],[5]] => [5,3,4,7,1,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[[1,2,5],[3,4],[6,7]] => [[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[[1,3,4],[2,5],[6,7]] => [[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 5
[[1,2,4],[3,5],[6,7]] => [[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 5
[[1,2,3],[4,5],[6,7]] => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 4
[[1,5,7],[2,6],[3],[4]] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,4,7],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,7],[2,6],[4],[5]] => [[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,7],[3,6],[4],[5]] => [[1,3,4,5],[2,6],[7]] => [7,2,6,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,4,7],[2,5],[3],[6]] => [[1,2,3,6],[4,5],[7]] => [7,4,5,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,7],[2,5],[4],[6]] => [[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,7],[3,5],[4],[6]] => [[1,3,4,6],[2,5],[7]] => [7,2,5,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,7],[2,4],[5],[6]] => [[1,2,5,6],[3,4],[7]] => [7,3,4,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,7],[3,4],[5],[6]] => [[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,5,6],[2,7],[3],[4]] => [[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[[1,4,6],[2,7],[3],[5]] => [[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[[1,3,6],[2,7],[4],[5]] => [[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[[1,2,6],[3,7],[4],[5]] => [[1,3,4,5],[2,7],[6]] => [6,2,7,1,3,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[[1,4,5],[2,7],[3],[6]] => [[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6
[[1,3,5],[2,7],[4],[6]] => [[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6
[[1,2,5],[3,7],[4],[6]] => [[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 6
[[1,3,4],[2,7],[5],[6]] => [[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 5
[[1,2,4],[3,7],[5],[6]] => [[1,3,5,6],[2,7],[4]] => [4,2,7,1,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 5
[[1,2,3],[4,7],[5],[6]] => [[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 4
[[1,4,6],[2,5],[3],[7]] => [[1,2,3,7],[4,5],[6]] => [6,4,5,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,3,6],[2,5],[4],[7]] => [[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,6],[3,5],[4],[7]] => [[1,3,4,7],[2,5],[6]] => [6,2,5,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,3,6],[2,4],[5],[7]] => [[1,2,5,7],[3,4],[6]] => [6,3,4,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,6],[3,4],[5],[7]] => [[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,4,5],[2,6],[3],[7]] => [[1,2,3,7],[4,6],[5]] => [5,4,6,1,2,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[[1,3,5],[2,6],[4],[7]] => [[1,2,4,7],[3,6],[5]] => [5,3,6,1,2,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[[1,2,5],[3,6],[4],[7]] => [[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[[1,3,4],[2,6],[5],[7]] => [[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 5
[[1,2,4],[3,6],[5],[7]] => [[1,3,5,7],[2,6],[4]] => [4,2,6,1,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 5
[[1,2,3],[4,6],[5],[7]] => [[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 4
[[1,3,5],[2,4],[6],[7]] => [[1,2,6,7],[3,4],[5]] => [5,3,4,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[1,2,5],[3,4],[6],[7]] => [[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[1,3,4],[2,5],[6],[7]] => [[1,2,6,7],[3,5],[4]] => [4,3,5,1,2,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[[1,2,4],[3,5],[6],[7]] => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[[1,6,7],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,5,7],[2],[3],[4],[6]] => [[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,4,7],[2],[3],[5],[6]] => [[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,3,7],[2],[4],[5],[6]] => [[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,2,7],[3],[4],[5],[6]] => [[1,3,4,5,6],[2],[7]] => [7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,5,6],[2],[3],[4],[7]] => [[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,4,6],[2],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,3,6],[2],[4],[5],[7]] => [[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,2,6],[3],[4],[5],[7]] => [[1,3,4,5,7],[2],[6]] => [6,2,1,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,4,5],[2],[3],[6],[7]] => [[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[1,3,5],[2],[4],[6],[7]] => [[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[1,2,5],[3],[4],[6],[7]] => [[1,3,4,6,7],[2],[5]] => [5,2,1,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[1,3,4],[2],[5],[6],[7]] => [[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[[1,2,4],[3],[5],[6],[7]] => [[1,3,5,6,7],[2],[4]] => [4,2,1,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[[1,2,3],[4],[5],[6],[7]] => [[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[1,5],[2,6],[3,7],[4]] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[[1,4],[2,6],[3,7],[5]] => [[1,2,3,5],[4,6,7]] => [4,6,7,1,2,3,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[[1,3],[2,6],[4,7],[5]] => [[1,2,4,5],[3,6,7]] => [3,6,7,1,2,4,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 4
[[1,2],[3,6],[4,7],[5]] => [[1,3,4,5],[2,6,7]] => [2,6,7,1,3,4,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 3
[[1,4],[2,5],[3,7],[6]] => [[1,2,3,6],[4,5,7]] => [4,5,7,1,2,3,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 5
[[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => [3,5,7,1,2,4,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[[1,2],[3,5],[4,7],[6]] => [[1,3,4,6],[2,5,7]] => [2,5,7,1,3,4,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[[1,3],[2,4],[5,7],[6]] => [[1,2,5,6],[3,4,7]] => [3,4,7,1,2,5,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 4
[[1,2],[3,4],[5,7],[6]] => [[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[[1,4],[2,5],[3,6],[7]] => [[1,2,3,7],[4,5,6]] => [4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[[1,3],[2,5],[4,6],[7]] => [[1,2,4,7],[3,5,6]] => [3,5,6,1,2,4,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[[1,2],[3,5],[4,6],[7]] => [[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[[1,3],[2,4],[5,6],[7]] => [[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 4
[[1,2],[3,4],[5,6],[7]] => [[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 3
[[1,6],[2,7],[3],[4],[5]] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[[1,4],[2,7],[3],[5],[6]] => [[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 5
[[1,3],[2,7],[4],[5],[6]] => [[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 4
[[1,2],[3,7],[4],[5],[6]] => [[1,3,4,5,6],[2,7]] => [2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[[1,5],[2,6],[3],[4],[7]] => [[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[[1,4],[2,6],[3],[5],[7]] => [[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 5
[[1,3],[2,6],[4],[5],[7]] => [[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 4
[[1,2],[3,6],[4],[5],[7]] => [[1,3,4,5,7],[2,6]] => [2,6,1,3,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3
[[1,4],[2,5],[3],[6],[7]] => [[1,2,3,6,7],[4,5]] => [4,5,1,2,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5
[[1,3],[2,5],[4],[6],[7]] => [[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 4
[[1,2],[3,5],[4],[6],[7]] => [[1,3,4,6,7],[2,5]] => [2,5,1,3,4,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[[1,3],[2,4],[5],[6],[7]] => [[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[[1,6],[2],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[1,5],[2],[3],[4],[6],[7]] => [[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[1,4],[2],[3],[5],[6],[7]] => [[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[[1,3],[2],[4],[5],[6],[7]] => [[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[1,2],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2]] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[[1,2,3,4,5,6,7,8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,5,6,7,8],[2]] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,5,6,7,8],[3]] => [[1,3],[2],[4],[5],[6],[7],[8]] => [8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,5,6,7,8],[4]] => [[1,4],[2],[3],[5],[6],[7],[8]] => [8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,6,7,8],[5]] => [[1,5],[2],[3],[4],[6],[7],[8]] => [8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,5,7,8],[6]] => [[1,6],[2],[3],[4],[5],[7],[8]] => [8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,5,6,8],[7]] => [[1,7],[2],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,5,6,7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,5,6,7,8],[2,4]] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,6,7,8],[3,4]] => [[1,3],[2,4],[5],[6],[7],[8]] => [8,7,6,5,2,4,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,6,7,8],[3,5]] => [[1,3],[2,5],[4],[6],[7],[8]] => [8,7,6,4,2,5,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,6,7,8],[4,5]] => [[1,4],[2,5],[3],[6],[7],[8]] => [8,7,6,3,2,5,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,5,7,8],[3,6]] => [[1,3],[2,6],[4],[5],[7],[8]] => [8,7,5,4,2,6,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,5,7,8],[4,6]] => [[1,4],[2,6],[3],[5],[7],[8]] => [8,7,5,3,2,6,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,7,8],[5,6]] => [[1,5],[2,6],[3],[4],[7],[8]] => [8,7,4,3,2,6,1,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,5,6,8],[2,7]] => [[1,2],[3,7],[4],[5],[6],[8]] => [8,6,5,4,3,7,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,5,6,8],[4,7]] => [[1,4],[2,7],[3],[5],[6],[8]] => [8,6,5,3,2,7,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,5,8],[6,7]] => [[1,6],[2,7],[3],[4],[5],[8]] => [8,5,4,3,2,7,1,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,5,6,7],[2,8]] => [[1,2],[3,8],[4],[5],[6],[7]] => [7,6,5,4,3,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 8
[[1,2,4,5,6,7],[3,8]] => [[1,3],[2,8],[4],[5],[6],[7]] => [7,6,5,4,2,8,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 8
[[1,2,3,4,6,7],[5,8]] => [[1,5],[2,8],[3],[4],[6],[7]] => [7,6,4,3,2,8,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 8
[[1,2,3,4,5,7],[6,8]] => [[1,6],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 8
[[1,4,5,6,7,8],[2],[3]] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,6,7,8],[2],[4]] => [[1,2,4],[3],[5],[6],[7],[8]] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,6,7,8],[3],[4]] => [[1,3,4],[2],[5],[6],[7],[8]] => [8,7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,6,7,8],[2],[5]] => [[1,2,5],[3],[4],[6],[7],[8]] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,6,7,8],[3],[5]] => [[1,3,5],[2],[4],[6],[7],[8]] => [8,7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,6,7,8],[4],[5]] => [[1,4,5],[2],[3],[6],[7],[8]] => [8,7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,5,7,8],[2],[6]] => [[1,2,6],[3],[4],[5],[7],[8]] => [8,7,5,4,3,1,2,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,5,7,8],[4],[6]] => [[1,4,6],[2],[3],[5],[7],[8]] => [8,7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,7,8],[5],[6]] => [[1,5,6],[2],[3],[4],[7],[8]] => [8,7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,5,6,8],[2],[7]] => [[1,2,7],[3],[4],[5],[6],[8]] => [8,6,5,4,3,1,2,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,5,6,8],[3],[7]] => [[1,3,7],[2],[4],[5],[6],[8]] => [8,6,5,4,2,1,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,5,6,8],[4],[7]] => [[1,4,7],[2],[3],[5],[6],[8]] => [8,6,5,3,2,1,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,6,8],[5],[7]] => [[1,5,7],[2],[3],[4],[6],[8]] => [8,6,4,3,2,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,5,8],[6],[7]] => [[1,6,7],[2],[3],[4],[5],[8]] => [8,5,4,3,2,1,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,5,6,7],[2],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,4,5,6,7],[3],[8]] => [[1,3,8],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,5,6,7],[4],[8]] => [[1,4,8],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,4,6,7],[5],[8]] => [[1,5,8],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,4,5,7],[6],[8]] => [[1,6,8],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,5,7,8],[2,4,6]] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,7,8],[3,4,6]] => [[1,3],[2,4],[5,6],[7],[8]] => [8,7,5,6,2,4,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,7,8],[2,5,6]] => [[1,2],[3,5],[4,6],[7],[8]] => [8,7,4,6,3,5,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,7,8],[3,5,6]] => [[1,3],[2,5],[4,6],[7],[8]] => [8,7,4,6,2,5,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,7,8],[4,5,6]] => [[1,4],[2,5],[3,6],[7],[8]] => [8,7,3,6,2,5,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,6,8],[2,4,7]] => [[1,2],[3,4],[5,7],[6],[8]] => [8,6,5,7,3,4,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,6,8],[3,4,7]] => [[1,3],[2,4],[5,7],[6],[8]] => [8,6,5,7,2,4,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,6,8],[2,5,7]] => [[1,2],[3,5],[4,7],[6],[8]] => [8,6,4,7,3,5,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,6,8],[3,5,7]] => [[1,3],[2,5],[4,7],[6],[8]] => [8,6,4,7,2,5,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,6,8],[4,5,7]] => [[1,4],[2,5],[3,7],[6],[8]] => [8,6,3,7,2,5,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,5,8],[2,6,7]] => [[1,2],[3,6],[4,7],[5],[8]] => [8,5,4,7,3,6,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,5,8],[3,6,7]] => [[1,3],[2,6],[4,7],[5],[8]] => [8,5,4,7,2,6,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,5,8],[4,6,7]] => [[1,4],[2,6],[3,7],[5],[8]] => [8,5,3,7,2,6,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,8],[5,6,7]] => [[1,5],[2,6],[3,7],[4],[8]] => [8,4,3,7,2,6,1,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,6,7],[2,4,8]] => [[1,2],[3,4],[5,8],[6],[7]] => [7,6,5,8,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,2,5,6,7],[3,4,8]] => [[1,3],[2,4],[5,8],[6],[7]] => [7,6,5,8,2,4,1,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,2,4,6,7],[3,5,8]] => [[1,3],[2,5],[4,8],[6],[7]] => [7,6,4,8,2,5,1,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,2,3,6,7],[4,5,8]] => [[1,4],[2,5],[3,8],[6],[7]] => [7,6,3,8,2,5,1,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,2,4,5,7],[3,6,8]] => [[1,3],[2,6],[4,8],[5],[7]] => [7,5,4,8,2,6,1,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,2,3,5,7],[4,6,8]] => [[1,4],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,2,3,4,7],[5,6,8]] => [[1,5],[2,6],[3,8],[4],[7]] => [7,4,3,8,2,6,1,5] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,3,4,5,6],[2,7,8]] => [[1,2],[3,7],[4,8],[5],[6]] => [6,5,4,8,3,7,1,2] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,2,4,5,6],[3,7,8]] => [[1,3],[2,7],[4,8],[5],[6]] => [6,5,4,8,2,7,1,3] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,2,3,5,6],[4,7,8]] => [[1,4],[2,7],[3,8],[5],[6]] => [6,5,3,8,2,7,1,4] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,2,3,4,6],[5,7,8]] => [[1,5],[2,7],[3,8],[4],[6]] => [6,4,3,8,2,7,1,5] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,2,3,4,5],[6,7,8]] => [[1,6],[2,7],[3,8],[4],[5]] => [5,4,3,8,2,7,1,6] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 6
[[1,4,6,7,8],[2,5],[3]] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,6,7,8],[2,5],[4]] => [[1,2,4],[3,5],[6],[7],[8]] => [8,7,6,3,5,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,6,7,8],[3,5],[4]] => [[1,3,4],[2,5],[6],[7],[8]] => [8,7,6,2,5,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,6,7,8],[2,4],[5]] => [[1,2,5],[3,4],[6],[7],[8]] => [8,7,6,3,4,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,6,7,8],[3,4],[5]] => [[1,3,5],[2,4],[6],[7],[8]] => [8,7,6,2,4,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,5,7,8],[2,6],[3]] => [[1,2,3],[4,6],[5],[7],[8]] => [8,7,5,4,6,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,7,8],[2,6],[4]] => [[1,2,4],[3,6],[5],[7],[8]] => [8,7,5,3,6,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,7,8],[3,6],[4]] => [[1,3,4],[2,6],[5],[7],[8]] => [8,7,5,2,6,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,7,8],[2,6],[5]] => [[1,2,5],[3,6],[4],[7],[8]] => [8,7,4,3,6,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,7,8],[3,6],[5]] => [[1,3,5],[2,6],[4],[7],[8]] => [8,7,4,2,6,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,7,8],[4,6],[5]] => [[1,4,5],[2,6],[3],[7],[8]] => [8,7,3,2,6,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,7,8],[2,4],[6]] => [[1,2,6],[3,4],[5],[7],[8]] => [8,7,5,3,4,1,2,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,7,8],[4,5],[6]] => [[1,4,6],[2,5],[3],[7],[8]] => [8,7,3,2,5,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,5,6,8],[2,7],[3]] => [[1,2,3],[4,7],[5],[6],[8]] => [8,6,5,4,7,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,6,8],[2,7],[4]] => [[1,2,4],[3,7],[5],[6],[8]] => [8,6,5,3,7,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,6,8],[2,7],[5]] => [[1,2,5],[3,7],[4],[6],[8]] => [8,6,4,3,7,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,6,8],[4,7],[5]] => [[1,4,5],[2,7],[3],[6],[8]] => [8,6,3,2,7,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,5,8],[4,7],[6]] => [[1,4,6],[2,7],[3],[5],[8]] => [8,5,3,2,7,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,6,8],[2,4],[7]] => [[1,2,7],[3,4],[5],[6],[8]] => [8,6,5,3,4,1,2,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,6,8],[3,4],[7]] => [[1,3,7],[2,4],[5],[6],[8]] => [8,6,5,2,4,1,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,6,8],[4,5],[7]] => [[1,4,7],[2,5],[3],[6],[8]] => [8,6,3,2,5,1,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,5,8],[2,6],[7]] => [[1,2,7],[3,6],[4],[5],[8]] => [8,5,4,3,6,1,2,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,5,8],[3,6],[7]] => [[1,3,7],[2,6],[4],[5],[8]] => [8,5,4,2,6,1,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,5,8],[4,6],[7]] => [[1,4,7],[2,6],[3],[5],[8]] => [8,5,3,2,6,1,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,5,6,7],[2,8],[3]] => [[1,2,3],[4,8],[5],[6],[7]] => [7,6,5,4,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,3,5,6,7],[2,8],[4]] => [[1,2,4],[3,8],[5],[6],[7]] => [7,6,5,3,8,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,2,5,6,7],[3,8],[4]] => [[1,3,4],[2,8],[5],[6],[7]] => [7,6,5,2,8,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,3,4,6,7],[2,8],[5]] => [[1,2,5],[3,8],[4],[6],[7]] => [7,6,4,3,8,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,2,3,6,7],[4,8],[5]] => [[1,4,5],[2,8],[3],[6],[7]] => [7,6,3,2,8,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,2,4,5,7],[3,8],[6]] => [[1,3,6],[2,8],[4],[5],[7]] => [7,5,4,2,8,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,2,3,5,7],[4,8],[6]] => [[1,4,6],[2,8],[3],[5],[7]] => [7,5,3,2,8,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,3,5,6,7],[2,4],[8]] => [[1,2,8],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,6,7],[4,5],[8]] => [[1,4,8],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,4,5,7],[3,6],[8]] => [[1,3,8],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,5,7],[4,6],[8]] => [[1,4,8],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,5,6,7,8],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,6,7,8],[2],[3],[5]] => [[1,2,3,5],[4],[6],[7],[8]] => [8,7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,6,7,8],[2],[4],[5]] => [[1,2,4,5],[3],[6],[7],[8]] => [8,7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,6,7,8],[3],[4],[5]] => [[1,3,4,5],[2],[6],[7],[8]] => [8,7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,5,7,8],[2],[3],[6]] => [[1,2,3,6],[4],[5],[7],[8]] => [8,7,5,4,1,2,3,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,7,8],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7],[8]] => [8,7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,7,8],[3],[4],[6]] => [[1,3,4,6],[2],[5],[7],[8]] => [8,7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,7,8],[3],[5],[6]] => [[1,3,5,6],[2],[4],[7],[8]] => [8,7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,7,8],[4],[5],[6]] => [[1,4,5,6],[2],[3],[7],[8]] => [8,7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,5,6,8],[2],[3],[7]] => [[1,2,3,7],[4],[5],[6],[8]] => [8,6,5,4,1,2,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,6,8],[3],[4],[7]] => [[1,3,4,7],[2],[5],[6],[8]] => [8,6,5,2,1,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,6,8],[2],[5],[7]] => [[1,2,5,7],[3],[4],[6],[8]] => [8,6,4,3,1,2,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,6,8],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6],[8]] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,6,8],[4],[5],[7]] => [[1,4,5,7],[2],[3],[6],[8]] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,5,8],[3],[6],[7]] => [[1,3,6,7],[2],[4],[5],[8]] => [8,5,4,2,1,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,5,8],[4],[6],[7]] => [[1,4,6,7],[2],[3],[5],[8]] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,4,8],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4],[8]] => [8,4,3,2,1,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,5,6,7],[2],[3],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,5,6,7],[3],[4],[8]] => [[1,3,4,8],[2],[5],[6],[7]] => [7,6,5,2,1,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,4,6,7],[2],[5],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => [7,6,4,3,1,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,4,6,7],[3],[5],[8]] => [[1,3,5,8],[2],[4],[6],[7]] => [7,6,4,2,1,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,6,7],[4],[5],[8]] => [[1,4,5,8],[2],[3],[6],[7]] => [7,6,3,2,1,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,4,5,7],[2],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => [7,5,4,3,1,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,5,7],[4],[6],[8]] => [[1,4,6,8],[2],[3],[5],[7]] => [7,5,3,2,1,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,4,7],[5],[6],[8]] => [[1,5,6,8],[2],[3],[4],[7]] => [7,4,3,2,1,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,5,7],[2,4,6,8]] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,2,5,7],[3,4,6,8]] => [[1,3],[2,4],[5,6],[7,8]] => [7,8,5,6,2,4,1,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,3,4,7],[2,5,6,8]] => [[1,2],[3,5],[4,6],[7,8]] => [7,8,4,6,3,5,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,2,4,7],[3,5,6,8]] => [[1,3],[2,5],[4,6],[7,8]] => [7,8,4,6,2,5,1,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,2,3,7],[4,5,6,8]] => [[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,3,5,6],[2,4,7,8]] => [[1,2],[3,4],[5,7],[6,8]] => [6,8,5,7,3,4,1,2] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,2,5,6],[3,4,7,8]] => [[1,3],[2,4],[5,7],[6,8]] => [6,8,5,7,2,4,1,3] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,3,4,6],[2,5,7,8]] => [[1,2],[3,5],[4,7],[6,8]] => [6,8,4,7,3,5,1,2] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,2,4,6],[3,5,7,8]] => [[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,2,3,6],[4,5,7,8]] => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,3,4,5],[2,6,7,8]] => [[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,2,4,5],[3,6,7,8]] => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,2,3,5],[4,6,7,8]] => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[[1,4,6,8],[2,5,7],[3]] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,6,8],[2,5,7],[4]] => [[1,2,4],[3,5],[6,7],[8]] => [8,6,7,3,5,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,6,8],[3,5,7],[4]] => [[1,3,4],[2,5],[6,7],[8]] => [8,6,7,2,5,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,6,8],[2,4,7],[5]] => [[1,2,5],[3,4],[6,7],[8]] => [8,6,7,3,4,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,6,8],[3,4,7],[5]] => [[1,3,5],[2,4],[6,7],[8]] => [8,6,7,2,4,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,8],[3,6,7],[4]] => [[1,3,4],[2,6],[5,7],[8]] => [8,5,7,2,6,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,8],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7],[8]] => [8,4,7,3,6,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,8],[3,6,7],[5]] => [[1,3,5],[2,6],[4,7],[8]] => [8,4,7,2,6,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,8],[4,6,7],[5]] => [[1,4,5],[2,6],[3,7],[8]] => [8,3,7,2,6,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,8],[3,4,7],[6]] => [[1,3,6],[2,4],[5,7],[8]] => [8,5,7,2,4,1,3,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,8],[2,5,7],[6]] => [[1,2,6],[3,5],[4,7],[8]] => [8,4,7,3,5,1,2,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,8],[4,5,7],[6]] => [[1,4,6],[2,5],[3,7],[8]] => [8,3,7,2,5,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,8],[2,4,6],[7]] => [[1,2,7],[3,4],[5,6],[8]] => [8,5,6,3,4,1,2,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,8],[3,4,6],[7]] => [[1,3,7],[2,4],[5,6],[8]] => [8,5,6,2,4,1,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,8],[3,5,6],[7]] => [[1,3,7],[2,5],[4,6],[8]] => [8,4,6,2,5,1,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,8],[4,5,6],[7]] => [[1,4,7],[2,5],[3,6],[8]] => [8,3,6,2,5,1,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,6,7],[2,5,8],[4]] => [[1,2,4],[3,5],[6,8],[7]] => [7,6,8,3,5,1,2,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,2,6,7],[3,5,8],[4]] => [[1,3,4],[2,5],[6,8],[7]] => [7,6,8,2,5,1,3,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,4,5,7],[2,6,8],[3]] => [[1,2,3],[4,6],[5,8],[7]] => [7,5,8,4,6,1,2,3] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,3,5,7],[2,6,8],[4]] => [[1,2,4],[3,6],[5,8],[7]] => [7,5,8,3,6,1,2,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,2,5,7],[3,6,8],[4]] => [[1,3,4],[2,6],[5,8],[7]] => [7,5,8,2,6,1,3,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,2,4,7],[3,6,8],[5]] => [[1,3,5],[2,6],[4,8],[7]] => [7,4,8,2,6,1,3,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,2,3,7],[4,6,8],[5]] => [[1,4,5],[2,6],[3,8],[7]] => [7,3,8,2,6,1,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,3,5,7],[2,4,8],[6]] => [[1,2,6],[3,4],[5,8],[7]] => [7,5,8,3,4,1,2,6] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,2,5,7],[3,4,8],[6]] => [[1,3,6],[2,4],[5,8],[7]] => [7,5,8,2,4,1,3,6] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,3,4,7],[2,5,8],[6]] => [[1,2,6],[3,5],[4,8],[7]] => [7,4,8,3,5,1,2,6] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,2,3,7],[4,5,8],[6]] => [[1,4,6],[2,5],[3,8],[7]] => [7,3,8,2,5,1,4,6] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,2,5,6],[3,7,8],[4]] => [[1,3,4],[2,7],[5,8],[6]] => [6,5,8,2,7,1,3,4] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,3,4,6],[2,7,8],[5]] => [[1,2,5],[3,7],[4,8],[6]] => [6,4,8,3,7,1,2,5] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,2,4,6],[3,7,8],[5]] => [[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,2,3,6],[4,7,8],[5]] => [[1,4,5],[2,7],[3,8],[6]] => [6,3,8,2,7,1,4,5] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,3,4,5],[2,7,8],[6]] => [[1,2,6],[3,7],[4,8],[5]] => [5,4,8,3,7,1,2,6] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 6
[[1,2,4,5],[3,7,8],[6]] => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 6
[[1,2,3,5],[4,7,8],[6]] => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 6
[[1,3,5,6],[2,4,8],[7]] => [[1,2,7],[3,4],[5,8],[6]] => [6,5,8,3,4,1,2,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,2,5,6],[3,4,8],[7]] => [[1,3,7],[2,4],[5,8],[6]] => [6,5,8,2,4,1,3,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,3,4,6],[2,5,8],[7]] => [[1,2,7],[3,5],[4,8],[6]] => [6,4,8,3,5,1,2,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,2,4,6],[3,5,8],[7]] => [[1,3,7],[2,5],[4,8],[6]] => [6,4,8,2,5,1,3,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,2,3,6],[4,5,8],[7]] => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,3,4,5],[2,6,8],[7]] => [[1,2,7],[3,6],[4,8],[5]] => [5,4,8,3,6,1,2,7] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 6
[[1,2,4,5],[3,6,8],[7]] => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 6
[[1,2,3,5],[4,6,8],[7]] => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 6
[[1,3,5,7],[2,4,6],[8]] => [[1,2,8],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,7],[4,5,6],[8]] => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,5,6],[2,4,7],[8]] => [[1,2,8],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[[1,3,4,6],[2,5,7],[8]] => [[1,2,8],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[[1,2,4,6],[3,5,7],[8]] => [[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[[1,2,3,6],[4,5,7],[8]] => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[[1,2,4,5],[3,6,7],[8]] => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 6
[[1,2,3,5],[4,6,7],[8]] => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 6
[[1,4,7,8],[2,5],[3,6]] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,7,8],[2,5],[4,6]] => [[1,2,4],[3,5,6],[7],[8]] => [8,7,3,5,6,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,7,8],[3,5],[4,6]] => [[1,3,4],[2,5,6],[7],[8]] => [8,7,2,5,6,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,7,8],[2,4],[5,6]] => [[1,2,5],[3,4,6],[7],[8]] => [8,7,3,4,6,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,7,8],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7],[8]] => [8,7,2,4,6,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,6,8],[2,5],[3,7]] => [[1,2,3],[4,5,7],[6],[8]] => [8,6,4,5,7,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,6,8],[2,5],[4,7]] => [[1,2,4],[3,5,7],[6],[8]] => [8,6,3,5,7,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,6,8],[3,5],[4,7]] => [[1,3,4],[2,5,7],[6],[8]] => [8,6,2,5,7,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,6,8],[3,4],[5,7]] => [[1,3,5],[2,4,7],[6],[8]] => [8,6,2,4,7,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,5,8],[2,6],[3,7]] => [[1,2,3],[4,6,7],[5],[8]] => [8,5,4,6,7,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,8],[2,6],[4,7]] => [[1,2,4],[3,6,7],[5],[8]] => [8,5,3,6,7,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,8],[3,6],[4,7]] => [[1,3,4],[2,6,7],[5],[8]] => [8,5,2,6,7,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,8],[3,6],[5,7]] => [[1,3,5],[2,6,7],[4],[8]] => [8,4,2,6,7,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,8],[4,6],[5,7]] => [[1,4,5],[2,6,7],[3],[8]] => [8,3,2,6,7,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,8],[3,4],[6,7]] => [[1,3,6],[2,4,7],[5],[8]] => [8,5,2,4,7,1,3,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,8],[3,5],[6,7]] => [[1,3,6],[2,5,7],[4],[8]] => [8,4,2,5,7,1,3,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,8],[4,5],[6,7]] => [[1,4,6],[2,5,7],[3],[8]] => [8,3,2,5,7,1,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,6,7],[2,5],[3,8]] => [[1,2,3],[4,5,8],[6],[7]] => [7,6,4,5,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,3,6,7],[2,5],[4,8]] => [[1,2,4],[3,5,8],[6],[7]] => [7,6,3,5,8,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,2,6,7],[3,4],[5,8]] => [[1,3,5],[2,4,8],[6],[7]] => [7,6,2,4,8,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,4,5,7],[2,6],[3,8]] => [[1,2,3],[4,6,8],[5],[7]] => [7,5,4,6,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,3,5,7],[2,6],[4,8]] => [[1,2,4],[3,6,8],[5],[7]] => [7,5,3,6,8,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,2,5,7],[3,6],[4,8]] => [[1,3,4],[2,6,8],[5],[7]] => [7,5,2,6,8,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,2,3,7],[4,6],[5,8]] => [[1,4,5],[2,6,8],[3],[7]] => [7,3,2,6,8,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,3,4,7],[2,5],[6,8]] => [[1,2,6],[3,5,8],[4],[7]] => [7,4,3,5,8,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,2,4,7],[3,5],[6,8]] => [[1,3,6],[2,5,8],[4],[7]] => [7,4,2,5,8,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 8
[[1,4,5,6],[2,7],[3,8]] => [[1,2,3],[4,7,8],[5],[6]] => [6,5,4,7,8,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 7
[[1,2,5,6],[3,7],[4,8]] => [[1,3,4],[2,7,8],[5],[6]] => [6,5,2,7,8,1,3,4] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 7
[[1,3,4,6],[2,7],[5,8]] => [[1,2,5],[3,7,8],[4],[6]] => [6,4,3,7,8,1,2,5] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 7
[[1,2,4,6],[3,7],[5,8]] => [[1,3,5],[2,7,8],[4],[6]] => [6,4,2,7,8,1,3,5] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 7
[[1,2,3,6],[4,7],[5,8]] => [[1,4,5],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 7
[[1,5,7,8],[2,6],[3],[4]] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,7,8],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7],[8]] => [8,7,4,6,1,2,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,7,8],[2,6],[4],[5]] => [[1,2,4,5],[3,6],[7],[8]] => [8,7,3,6,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,7,8],[3,6],[4],[5]] => [[1,3,4,5],[2,6],[7],[8]] => [8,7,2,6,1,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,7,8],[2,5],[3],[6]] => [[1,2,3,6],[4,5],[7],[8]] => [8,7,4,5,1,2,3,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,7,8],[2,5],[4],[6]] => [[1,2,4,6],[3,5],[7],[8]] => [8,7,3,5,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,7,8],[3,5],[4],[6]] => [[1,3,4,6],[2,5],[7],[8]] => [8,7,2,5,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,7,8],[2,4],[5],[6]] => [[1,2,5,6],[3,4],[7],[8]] => [8,7,3,4,1,2,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,7,8],[3,4],[5],[6]] => [[1,3,5,6],[2,4],[7],[8]] => [8,7,2,4,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,5,6,8],[2,7],[3],[4]] => [[1,2,3,4],[5,7],[6],[8]] => [8,6,5,7,1,2,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,6,8],[2,7],[4],[5]] => [[1,2,4,5],[3,7],[6],[8]] => [8,6,3,7,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,5,8],[2,7],[3],[6]] => [[1,2,3,6],[4,7],[5],[8]] => [8,5,4,7,1,2,3,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,8],[2,7],[4],[6]] => [[1,2,4,6],[3,7],[5],[8]] => [8,5,3,7,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,8],[3,7],[4],[6]] => [[1,3,4,6],[2,7],[5],[8]] => [8,5,2,7,1,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,4,8],[2,7],[5],[6]] => [[1,2,5,6],[3,7],[4],[8]] => [8,4,3,7,1,2,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,8],[3,7],[5],[6]] => [[1,3,5,6],[2,7],[4],[8]] => [8,4,2,7,1,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,8],[4,7],[5],[6]] => [[1,4,5,6],[2,7],[3],[8]] => [8,3,2,7,1,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,6,8],[2,5],[3],[7]] => [[1,2,3,7],[4,5],[6],[8]] => [8,6,4,5,1,2,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,6,8],[3,5],[4],[7]] => [[1,3,4,7],[2,5],[6],[8]] => [8,6,2,5,1,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,6,8],[2,4],[5],[7]] => [[1,2,5,7],[3,4],[6],[8]] => [8,6,3,4,1,2,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,6,8],[3,4],[5],[7]] => [[1,3,5,7],[2,4],[6],[8]] => [8,6,2,4,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,8],[2,6],[4],[7]] => [[1,2,4,7],[3,6],[5],[8]] => [8,5,3,6,1,2,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,8],[3,6],[5],[7]] => [[1,3,5,7],[2,6],[4],[8]] => [8,4,2,6,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,8],[4,6],[5],[7]] => [[1,4,5,7],[2,6],[3],[8]] => [8,3,2,6,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,8],[2,4],[6],[7]] => [[1,2,6,7],[3,4],[5],[8]] => [8,5,3,4,1,2,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,8],[3,5],[6],[7]] => [[1,3,6,7],[2,5],[4],[8]] => [8,4,2,5,1,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,8],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3],[8]] => [8,3,2,5,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,5,6,7],[2,8],[3],[4]] => [[1,2,3,4],[5,8],[6],[7]] => [7,6,5,8,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,4,6,7],[2,8],[3],[5]] => [[1,2,3,5],[4,8],[6],[7]] => [7,6,4,8,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,2,6,7],[3,8],[4],[5]] => [[1,3,4,5],[2,8],[6],[7]] => [7,6,2,8,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,4,5,7],[2,8],[3],[6]] => [[1,2,3,6],[4,8],[5],[7]] => [7,5,4,8,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,3,5,7],[2,8],[4],[6]] => [[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,3,4,7],[2,8],[5],[6]] => [[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,2,4,7],[3,8],[5],[6]] => [[1,3,5,6],[2,8],[4],[7]] => [7,4,2,8,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,2,3,7],[4,8],[5],[6]] => [[1,4,5,6],[2,8],[3],[7]] => [7,3,2,8,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,4,5,6],[2,8],[3],[7]] => [[1,2,3,7],[4,8],[5],[6]] => [6,5,4,8,1,2,3,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,3,5,6],[2,8],[4],[7]] => [[1,2,4,7],[3,8],[5],[6]] => [6,5,3,8,1,2,4,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,2,5,6],[3,8],[4],[7]] => [[1,3,4,7],[2,8],[5],[6]] => [6,5,2,8,1,3,4,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,3,4,6],[2,8],[5],[7]] => [[1,2,5,7],[3,8],[4],[6]] => [6,4,3,8,1,2,5,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,2,4,6],[3,8],[5],[7]] => [[1,3,5,7],[2,8],[4],[6]] => [6,4,2,8,1,3,5,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,2,3,6],[4,8],[5],[7]] => [[1,4,5,7],[2,8],[3],[6]] => [6,3,2,8,1,4,5,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,3,4,5],[2,8],[6],[7]] => [[1,2,6,7],[3,8],[4],[5]] => [5,4,3,8,1,2,6,7] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 6
[[1,2,3,5],[4,8],[6],[7]] => [[1,4,6,7],[2,8],[3],[5]] => [5,3,2,8,1,4,6,7] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 6
[[1,4,6,7],[2,5],[3],[8]] => [[1,2,3,8],[4,5],[6],[7]] => [7,6,4,5,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,6,7],[2,5],[4],[8]] => [[1,2,4,8],[3,5],[6],[7]] => [7,6,3,5,1,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,4,5,7],[2,6],[3],[8]] => [[1,2,3,8],[4,6],[5],[7]] => [7,5,4,6,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,8],[3,6],[5],[7]] => [7,5,3,6,1,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,5,7],[3,6],[4],[8]] => [[1,3,4,8],[2,6],[5],[7]] => [7,5,2,6,1,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,4,7],[2,6],[5],[8]] => [[1,2,5,8],[3,6],[4],[7]] => [7,4,3,6,1,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,4,7],[3,6],[5],[8]] => [[1,3,5,8],[2,6],[4],[7]] => [7,4,2,6,1,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,7],[4,6],[5],[8]] => [[1,4,5,8],[2,6],[3],[7]] => [7,3,2,6,1,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,5,7],[2,4],[6],[8]] => [[1,2,6,8],[3,4],[5],[7]] => [7,5,3,4,1,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,5],[4],[7]] => [7,4,2,5,1,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,7],[4,5],[6],[8]] => [[1,4,6,8],[2,5],[3],[7]] => [7,3,2,5,1,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,5,6],[2,7],[4],[8]] => [[1,2,4,8],[3,7],[5],[6]] => [6,5,3,7,1,2,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 7
[[1,2,5,6],[3,7],[4],[8]] => [[1,3,4,8],[2,7],[5],[6]] => [6,5,2,7,1,3,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 7
[[1,3,4,6],[2,7],[5],[8]] => [[1,2,5,8],[3,7],[4],[6]] => [6,4,3,7,1,2,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 7
[[1,2,4,6],[3,7],[5],[8]] => [[1,3,5,8],[2,7],[4],[6]] => [6,4,2,7,1,3,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 7
[[1,2,3,6],[4,7],[5],[8]] => [[1,4,5,8],[2,7],[3],[6]] => [6,3,2,7,1,4,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 7
[[1,3,4,5],[2,7],[6],[8]] => [[1,2,6,8],[3,7],[4],[5]] => [5,4,3,7,1,2,6,8] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 6
[[1,2,3,5],[4,7],[6],[8]] => [[1,4,6,8],[2,7],[3],[5]] => [5,3,2,7,1,4,6,8] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 6
[[1,6,7,8],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,5,7,8],[2],[3],[4],[6]] => [[1,2,3,4,6],[5],[7],[8]] => [8,7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,7,8],[2],[3],[5],[6]] => [[1,2,3,5,6],[4],[7],[8]] => [8,7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,7,8],[3],[4],[5],[6]] => [[1,3,4,5,6],[2],[7],[8]] => [8,7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,5,6,8],[2],[3],[4],[7]] => [[1,2,3,4,7],[5],[6],[8]] => [8,6,5,1,2,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,6,8],[2],[3],[5],[7]] => [[1,2,3,5,7],[4],[6],[8]] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,5,8],[2],[3],[6],[7]] => [[1,2,3,6,7],[4],[5],[8]] => [8,5,4,1,2,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,5,8],[2],[4],[6],[7]] => [[1,2,4,6,7],[3],[5],[8]] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,5,8],[3],[4],[6],[7]] => [[1,3,4,6,7],[2],[5],[8]] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,4,8],[3],[5],[6],[7]] => [[1,3,5,6,7],[2],[4],[8]] => [8,4,2,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,3,8],[4],[5],[6],[7]] => [[1,4,5,6,7],[2],[3],[8]] => [8,3,2,1,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,5,6,7],[2],[3],[4],[8]] => [[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,4,7],[2],[5],[6],[8]] => [[1,2,5,6,8],[3],[4],[7]] => [7,4,3,1,2,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3,7],[4],[5],[6],[8]] => [[1,4,5,6,8],[2],[3],[7]] => [7,3,2,1,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,4,7],[2,5,8],[3,6]] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,3,7],[2,5,8],[4,6]] => [[1,2,4],[3,5,6],[7,8]] => [7,8,3,5,6,1,2,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,2,7],[3,5,8],[4,6]] => [[1,3,4],[2,5,6],[7,8]] => [7,8,2,5,6,1,3,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,3,7],[2,4,8],[5,6]] => [[1,2,5],[3,4,6],[7,8]] => [7,8,3,4,6,1,2,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,2,7],[3,4,8],[5,6]] => [[1,3,5],[2,4,6],[7,8]] => [7,8,2,4,6,1,3,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,4,6],[2,5,8],[3,7]] => [[1,2,3],[4,5,7],[6,8]] => [6,8,4,5,7,1,2,3] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,3,6],[2,5,8],[4,7]] => [[1,2,4],[3,5,7],[6,8]] => [6,8,3,5,7,1,2,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,2,6],[3,5,8],[4,7]] => [[1,3,4],[2,5,7],[6,8]] => [6,8,2,5,7,1,3,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,4,5],[2,6,8],[3,7]] => [[1,2,3],[4,6,7],[5,8]] => [5,8,4,6,7,1,2,3] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,3,5],[2,6,8],[4,7]] => [[1,2,4],[3,6,7],[5,8]] => [5,8,3,6,7,1,2,4] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,2,5],[3,6,8],[4,7]] => [[1,3,4],[2,6,7],[5,8]] => [5,8,2,6,7,1,3,4] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,3,4],[2,6,8],[5,7]] => [[1,2,5],[3,6,7],[4,8]] => [4,8,3,6,7,1,2,5] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[[1,2,3],[4,6,8],[5,7]] => [[1,4,5],[2,6,7],[3,8]] => [3,8,2,6,7,1,4,5] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[[1,2,5],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8]] => [5,8,2,4,7,1,3,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,3,4],[2,5,8],[6,7]] => [[1,2,6],[3,5,7],[4,8]] => [4,8,3,5,7,1,2,6] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[[1,2,4],[3,5,8],[6,7]] => [[1,3,6],[2,5,7],[4,8]] => [4,8,2,5,7,1,3,6] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[[1,2,3],[4,5,8],[6,7]] => [[1,4,6],[2,5,7],[3,8]] => [3,8,2,5,7,1,4,6] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[[1,4,6],[2,5,7],[3,8]] => [[1,2,3],[4,5,8],[6,7]] => [6,7,4,5,8,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 7
[[1,3,6],[2,5,7],[4,8]] => [[1,2,4],[3,5,8],[6,7]] => [6,7,3,5,8,1,2,4] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 7
[[1,3,6],[2,4,7],[5,8]] => [[1,2,5],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 7
[[1,4,5],[2,6,7],[3,8]] => [[1,2,3],[4,6,8],[5,7]] => [5,7,4,6,8,1,2,3] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 6
[[1,2,5],[3,6,7],[4,8]] => [[1,3,4],[2,6,8],[5,7]] => [5,7,2,6,8,1,3,4] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 6
[[1,3,4],[2,6,7],[5,8]] => [[1,2,5],[3,6,8],[4,7]] => [4,7,3,6,8,1,2,5] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 5
[[1,2,3],[4,6,7],[5,8]] => [[1,4,5],[2,6,8],[3,7]] => [3,7,2,6,8,1,4,5] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 4
[[1,3,5],[2,4,7],[6,8]] => [[1,2,6],[3,4,8],[5,7]] => [5,7,3,4,8,1,2,6] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 6
[[1,2,5],[3,4,7],[6,8]] => [[1,3,6],[2,4,8],[5,7]] => [5,7,2,4,8,1,3,6] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 6
[[1,3,4],[2,5,7],[6,8]] => [[1,2,6],[3,5,8],[4,7]] => [4,7,3,5,8,1,2,6] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 5
[[1,2,4],[3,5,7],[6,8]] => [[1,3,6],[2,5,8],[4,7]] => [4,7,2,5,8,1,3,6] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 5
[[1,5,7],[2,6,8],[3],[4]] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,4,7],[2,6,8],[3],[5]] => [[1,2,3,5],[4,6],[7,8]] => [7,8,4,6,1,2,3,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,4,7],[2,5,8],[3],[6]] => [[1,2,3,6],[4,5],[7,8]] => [7,8,4,5,1,2,3,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,3,7],[2,5,8],[4],[6]] => [[1,2,4,6],[3,5],[7,8]] => [7,8,3,5,1,2,4,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,2,7],[3,5,8],[4],[6]] => [[1,3,4,6],[2,5],[7,8]] => [7,8,2,5,1,3,4,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,3,7],[2,4,8],[5],[6]] => [[1,2,5,6],[3,4],[7,8]] => [7,8,3,4,1,2,5,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,2,7],[3,4,8],[5],[6]] => [[1,3,5,6],[2,4],[7,8]] => [7,8,2,4,1,3,5,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,5,6],[2,7,8],[3],[4]] => [[1,2,3,4],[5,7],[6,8]] => [6,8,5,7,1,2,3,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,3,6],[2,7,8],[4],[5]] => [[1,2,4,5],[3,7],[6,8]] => [6,8,3,7,1,2,4,5] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,2,6],[3,7,8],[4],[5]] => [[1,3,4,5],[2,7],[6,8]] => [6,8,2,7,1,3,4,5] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,4,5],[2,7,8],[3],[6]] => [[1,2,3,6],[4,7],[5,8]] => [5,8,4,7,1,2,3,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,3,5],[2,7,8],[4],[6]] => [[1,2,4,6],[3,7],[5,8]] => [5,8,3,7,1,2,4,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,2,5],[3,7,8],[4],[6]] => [[1,3,4,6],[2,7],[5,8]] => [5,8,2,7,1,3,4,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,3,4],[2,7,8],[5],[6]] => [[1,2,5,6],[3,7],[4,8]] => [4,8,3,7,1,2,5,6] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[[1,2,4],[3,7,8],[5],[6]] => [[1,3,5,6],[2,7],[4,8]] => [4,8,2,7,1,3,5,6] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[[1,2,3],[4,7,8],[5],[6]] => [[1,4,5,6],[2,7],[3,8]] => [3,8,2,7,1,4,5,6] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[[1,4,6],[2,5,8],[3],[7]] => [[1,2,3,7],[4,5],[6,8]] => [6,8,4,5,1,2,3,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,3,6],[2,5,8],[4],[7]] => [[1,2,4,7],[3,5],[6,8]] => [6,8,3,5,1,2,4,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,3,6],[2,4,8],[5],[7]] => [[1,2,5,7],[3,4],[6,8]] => [6,8,3,4,1,2,5,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,2,6],[3,4,8],[5],[7]] => [[1,3,5,7],[2,4],[6,8]] => [6,8,2,4,1,3,5,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,4,5],[2,6,8],[3],[7]] => [[1,2,3,7],[4,6],[5,8]] => [5,8,4,6,1,2,3,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,3,5],[2,6,8],[4],[7]] => [[1,2,4,7],[3,6],[5,8]] => [5,8,3,6,1,2,4,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,2,4],[3,6,8],[5],[7]] => [[1,3,5,7],[2,6],[4,8]] => [4,8,2,6,1,3,5,7] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[[1,2,3],[4,6,8],[5],[7]] => [[1,4,5,7],[2,6],[3,8]] => [3,8,2,6,1,4,5,7] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[[1,3,5],[2,4,8],[6],[7]] => [[1,2,6,7],[3,4],[5,8]] => [5,8,3,4,1,2,6,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,2,5],[3,4,8],[6],[7]] => [[1,3,6,7],[2,4],[5,8]] => [5,8,2,4,1,3,6,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,2,4],[3,5,8],[6],[7]] => [[1,3,6,7],[2,5],[4,8]] => [4,8,2,5,1,3,6,7] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[[1,2,6],[3,5,7],[4],[8]] => [[1,3,4,8],[2,5],[6,7]] => [6,7,2,5,1,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 7
[[1,3,6],[2,4,7],[5],[8]] => [[1,2,5,8],[3,4],[6,7]] => [6,7,3,4,1,2,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 7
[[1,3,5],[2,6,7],[4],[8]] => [[1,2,4,8],[3,6],[5,7]] => [5,7,3,6,1,2,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 6
[[1,2,5],[3,6,7],[4],[8]] => [[1,3,4,8],[2,6],[5,7]] => [5,7,2,6,1,3,4,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 6
[[1,3,4],[2,6,7],[5],[8]] => [[1,2,5,8],[3,6],[4,7]] => [4,7,3,6,1,2,5,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 5
[[1,2,3],[4,6,7],[5],[8]] => [[1,4,5,8],[2,6],[3,7]] => [3,7,2,6,1,4,5,8] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[[1,3,5],[2,4,7],[6],[8]] => [[1,2,6,8],[3,4],[5,7]] => [5,7,3,4,1,2,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 6
[[1,2,5],[3,4,7],[6],[8]] => [[1,3,6,8],[2,4],[5,7]] => [5,7,2,4,1,3,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 6
[[1,3,4],[2,5,7],[6],[8]] => [[1,2,6,8],[3,5],[4,7]] => [4,7,3,5,1,2,6,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 5
[[1,2,3],[4,5,7],[6],[8]] => [[1,4,6,8],[2,5],[3,7]] => [3,7,2,5,1,4,6,8] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[[1,5,8],[2,6],[3,7],[4]] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,8],[2,6],[3,7],[5]] => [[1,2,3,5],[4,6,7],[8]] => [8,4,6,7,1,2,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,8],[3,6],[4,7],[5]] => [[1,3,4,5],[2,6,7],[8]] => [8,2,6,7,1,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8]] => [8,3,5,7,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,8],[2,5],[3,6],[7]] => [[1,2,3,7],[4,5,6],[8]] => [8,4,5,6,1,2,3,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,8],[2,5],[4,6],[7]] => [[1,2,4,7],[3,5,6],[8]] => [8,3,5,6,1,2,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,8],[3,5],[4,6],[7]] => [[1,3,4,7],[2,5,6],[8]] => [8,2,5,6,1,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,8],[2,4],[5,6],[7]] => [[1,2,5,7],[3,4,6],[8]] => [8,3,4,6,1,2,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,8],[3,4],[5,6],[7]] => [[1,3,5,7],[2,4,6],[8]] => [8,2,4,6,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,5,7],[2,6],[3,8],[4]] => [[1,2,3,4],[5,6,8],[7]] => [7,5,6,8,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,4,7],[2,6],[3,8],[5]] => [[1,2,3,5],[4,6,8],[7]] => [7,4,6,8,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,4,7],[2,5],[3,8],[6]] => [[1,2,3,6],[4,5,8],[7]] => [7,4,5,8,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,3,7],[2,5],[4,8],[6]] => [[1,2,4,6],[3,5,8],[7]] => [7,3,5,8,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,3,7],[2,4],[5,8],[6]] => [[1,2,5,6],[3,4,8],[7]] => [7,3,4,8,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,2,7],[3,4],[5,8],[6]] => [[1,3,5,6],[2,4,8],[7]] => [7,2,4,8,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 8
[[1,5,6],[2,7],[3,8],[4]] => [[1,2,3,4],[5,7,8],[6]] => [6,5,7,8,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 7
[[1,4,6],[2,7],[3,8],[5]] => [[1,2,3,5],[4,7,8],[6]] => [6,4,7,8,1,2,3,5] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 7
[[1,3,6],[2,7],[4,8],[5]] => [[1,2,4,5],[3,7,8],[6]] => [6,3,7,8,1,2,4,5] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 7
[[1,2,6],[3,7],[4,8],[5]] => [[1,3,4,5],[2,7,8],[6]] => [6,2,7,8,1,3,4,5] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 7
[[1,4,6],[2,5],[3,8],[7]] => [[1,2,3,7],[4,5,8],[6]] => [6,4,5,8,1,2,3,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,3,6],[2,5],[4,8],[7]] => [[1,2,4,7],[3,5,8],[6]] => [6,3,5,8,1,2,4,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,2,6],[3,5],[4,8],[7]] => [[1,3,4,7],[2,5,8],[6]] => [6,2,5,8,1,3,4,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,3,6],[2,4],[5,8],[7]] => [[1,2,5,7],[3,4,8],[6]] => [6,3,4,8,1,2,5,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,2,6],[3,4],[5,8],[7]] => [[1,3,5,7],[2,4,8],[6]] => [6,2,4,8,1,3,5,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 7
[[1,2,5],[3,4],[6,8],[7]] => [[1,3,6,7],[2,4,8],[5]] => [5,2,4,8,1,3,6,7] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 6
[[1,4,7],[2,5],[3,6],[8]] => [[1,2,3,8],[4,5,6],[7]] => [7,4,5,6,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,7],[2,5],[4,6],[8]] => [[1,2,4,8],[3,5,6],[7]] => [7,3,5,6,1,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,7],[2,4],[5,6],[8]] => [[1,2,5,8],[3,4,6],[7]] => [7,3,4,6,1,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,7],[3,4],[5,6],[8]] => [[1,3,5,8],[2,4,6],[7]] => [7,2,4,6,1,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,6],[2,5],[4,7],[8]] => [[1,2,4,8],[3,5,7],[6]] => [6,3,5,7,1,2,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 7
[[1,2,6],[3,5],[4,7],[8]] => [[1,3,4,8],[2,5,7],[6]] => [6,2,5,7,1,3,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 7
[[1,3,5],[2,4],[6,7],[8]] => [[1,2,6,8],[3,4,7],[5]] => [5,3,4,7,1,2,6,8] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 6
[[1,2,5],[3,4],[6,7],[8]] => [[1,3,6,8],[2,4,7],[5]] => [5,2,4,7,1,3,6,8] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 6
[[1,6,8],[2,7],[3],[4],[5]] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,5,8],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,8],[2,7],[3],[5],[6]] => [[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,8],[2,7],[4],[5],[6]] => [[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,5,8],[2,6],[3],[4],[7]] => [[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,8],[2,5],[3],[6],[7]] => [[1,2,3,6,7],[4,5],[8]] => [8,4,5,1,2,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,8],[2,5],[4],[6],[7]] => [[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,8],[2,4],[5],[6],[7]] => [[1,2,5,6,7],[3,4],[8]] => [8,3,4,1,2,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,8],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4],[8]] => [8,2,4,1,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,6,7],[2,8],[3],[4],[5]] => [[1,2,3,4,5],[6,8],[7]] => [7,6,8,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,5,7],[2,8],[3],[4],[6]] => [[1,2,3,4,6],[5,8],[7]] => [7,5,8,1,2,3,4,6] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,3,7],[2,8],[4],[5],[6]] => [[1,2,4,5,6],[3,8],[7]] => [7,3,8,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,2,7],[3,8],[4],[5],[6]] => [[1,3,4,5,6],[2,8],[7]] => [7,2,8,1,3,4,5,6] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 8
[[1,5,6],[2,8],[3],[4],[7]] => [[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,4,6],[2,8],[3],[5],[7]] => [[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,3,6],[2,8],[4],[5],[7]] => [[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,2,6],[3,8],[4],[5],[7]] => [[1,3,4,5,7],[2,8],[6]] => [6,2,8,1,3,4,5,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 7
[[1,4,5],[2,8],[3],[6],[7]] => [[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 6
[[1,2,5],[3,8],[4],[6],[7]] => [[1,3,4,6,7],[2,8],[5]] => [5,2,8,1,3,4,6,7] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 6
[[1,5,7],[2,6],[3],[4],[8]] => [[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,4,7],[2,6],[3],[5],[8]] => [[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,7],[2,6],[4],[5],[8]] => [[1,2,4,5,8],[3,6],[7]] => [7,3,6,1,2,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,4,7],[2,5],[3],[6],[8]] => [[1,2,3,6,8],[4,5],[7]] => [7,4,5,1,2,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,7],[2,5],[4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,7],[2,4],[5],[6],[8]] => [[1,2,5,6,8],[3,4],[7]] => [7,3,4,1,2,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,5,6],[2,7],[3],[4],[8]] => [[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[[1,4,6],[2,7],[3],[5],[8]] => [[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[[1,3,6],[2,7],[4],[5],[8]] => [[1,2,4,5,8],[3,7],[6]] => [6,3,7,1,2,4,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[[1,2,6],[3,7],[4],[5],[8]] => [[1,3,4,5,8],[2,7],[6]] => [6,2,7,1,3,4,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[[1,4,5],[2,7],[3],[6],[8]] => [[1,2,3,6,8],[4,7],[5]] => [5,4,7,1,2,3,6,8] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 6
[[1,3,5],[2,7],[4],[6],[8]] => [[1,2,4,6,8],[3,7],[5]] => [5,3,7,1,2,4,6,8] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 6
[[1,2,5],[3,7],[4],[6],[8]] => [[1,3,4,6,8],[2,7],[5]] => [5,2,7,1,3,4,6,8] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 6
[[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,6,8],[2],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,5,8],[2],[3],[4],[6],[7]] => [[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,4,8],[2],[3],[5],[6],[7]] => [[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,3,8],[2],[4],[5],[6],[7]] => [[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,2,8],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2],[8]] => [8,2,1,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,6,7],[2],[3],[4],[5],[8]] => [[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,5,7],[2],[3],[4],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => [7,5,1,2,3,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,4,7],[2],[3],[5],[6],[8]] => [[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3,7],[2],[4],[5],[6],[8]] => [[1,2,4,5,6,8],[3],[7]] => [7,3,1,2,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,7],[3],[4],[5],[6],[8]] => [[1,3,4,5,6,8],[2],[7]] => [7,2,1,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,2,3],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => [3,2,1,4,5,6,7,8] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[[1,5],[2,6],[3,7],[4,8]] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 6
[[1,4],[2,5],[3,7],[6,8]] => [[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 5
[[1,6],[2,7],[3,8],[4],[5]] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 7
[[1,5],[2,7],[3,8],[4],[6]] => [[1,2,3,4,6],[5,7,8]] => [5,7,8,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 6
[[1,4],[2,7],[3,8],[5],[6]] => [[1,2,3,5,6],[4,7,8]] => [4,7,8,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 5
[[1,3],[2,7],[4,8],[5],[6]] => [[1,2,4,5,6],[3,7,8]] => [3,7,8,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 4
[[1,2],[3,7],[4,8],[5],[6]] => [[1,3,4,5,6],[2,7,8]] => [2,7,8,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[[1,5],[2,6],[3,8],[4],[7]] => [[1,2,3,4,7],[5,6,8]] => [5,6,8,1,2,3,4,7] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 6
[[1,4],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8]] => [4,6,8,1,2,3,5,7] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 5
[[1,4],[2,5],[3,8],[6],[7]] => [[1,2,3,6,7],[4,5,8]] => [4,5,8,1,2,3,6,7] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 5
[[1,5],[2,6],[3,7],[4],[8]] => [[1,2,3,4,8],[5,6,7]] => [5,6,7,1,2,3,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 6
[[1,7],[2,8],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 7
[[1,5],[2,8],[3],[4],[6],[7]] => [[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 6
[[1,4],[2,8],[3],[5],[6],[7]] => [[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 5
[[1,3],[2,8],[4],[5],[6],[7]] => [[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[[1,2],[3,8],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2,8]] => [2,8,1,3,4,5,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
[[1,6],[2,7],[3],[4],[5],[8]] => [[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 7
[[1,5],[2,7],[3],[4],[6],[8]] => [[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 6
[[1,3],[2,7],[4],[5],[6],[8]] => [[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => [2,4,1,3,5,6,7,8] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[[1,7],[2],[3],[4],[5],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
[[1,3],[2],[4],[5],[6],[7],[8]] => [[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => [2,1,3,4,5,6,7,8] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[[1,3,5,7,9],[2,4,6,8,10]] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,5,6,9],[2,4,7,8,10]] => [[1,2],[3,4],[5,7],[6,8],[9,10]] => [9,10,6,8,5,7,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,4,7,9],[2,5,6,8,10]] => [[1,2],[3,5],[4,6],[7,8],[9,10]] => [9,10,7,8,4,6,3,5,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,4,6,9],[2,5,7,8,10]] => [[1,2],[3,5],[4,7],[6,8],[9,10]] => [9,10,6,8,4,7,3,5,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,4,5,9],[2,6,7,8,10]] => [[1,2],[3,6],[4,7],[5,8],[9,10]] => [9,10,5,8,4,7,3,6,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,5,7,9],[3,4,6,8,10]] => [[1,3],[2,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,2,4,1,3] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,5,6,9],[3,4,7,8,10]] => [[1,3],[2,4],[5,7],[6,8],[9,10]] => [9,10,6,8,5,7,2,4,1,3] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,4,7,9],[3,5,6,8,10]] => [[1,3],[2,5],[4,6],[7,8],[9,10]] => [9,10,7,8,4,6,2,5,1,3] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,4,6,9],[3,5,7,8,10]] => [[1,3],[2,5],[4,7],[6,8],[9,10]] => [9,10,6,8,4,7,2,5,1,3] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,4,5,9],[3,6,7,8,10]] => [[1,3],[2,6],[4,7],[5,8],[9,10]] => [9,10,5,8,4,7,2,6,1,3] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,7,9],[4,5,6,8,10]] => [[1,4],[2,5],[3,6],[7,8],[9,10]] => [9,10,7,8,3,6,2,5,1,4] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,6,9],[4,5,7,8,10]] => [[1,4],[2,5],[3,7],[6,8],[9,10]] => [9,10,6,8,3,7,2,5,1,4] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,5,9],[4,6,7,8,10]] => [[1,4],[2,6],[3,7],[5,8],[9,10]] => [9,10,5,8,3,7,2,6,1,4] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,4,9],[5,6,7,8,10]] => [[1,5],[2,6],[3,7],[4,8],[9,10]] => [9,10,4,8,3,7,2,6,1,5] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,4,5,6,7,8,9]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,4,5,6,7,8],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => [3,2,1,4,5,6,7,8,9] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
[[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => [2,4,1,3,5,6,7,8,9] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => [2,1,3,4,5,6,7,8,9] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[[1,2,3,4,5,6,7,8,9,10]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,3,4,5,6,7,8,9],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => [3,2,1,4,5,6,7,8,9,10] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => [2,1,3,4,5,6,7,8,9,10] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[[1,3,4,5,6,7,8,9],[2]] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,5,6,7,8,9],[3,4]] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,2,4,1,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,4,5,6,7,8,9],[2],[3]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,7,8,9],[4,5,6]] => [[1,4],[2,5],[3,6],[7],[8],[9]] => [9,8,7,3,6,2,5,1,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,6,7,8,9],[2,5],[4]] => [[1,2,4],[3,5],[6],[7],[8],[9]] => [9,8,7,6,3,5,1,2,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,5,6,7,8,9],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,4,9],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8],[9]] => [9,4,8,3,7,2,6,1,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,4,8,9],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7],[8],[9]] => [9,8,4,7,3,6,1,2,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,7,8,9],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7],[8],[9]] => [9,8,7,2,4,6,1,3,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,4,7,8,9],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7],[8],[9]] => [9,8,7,4,6,1,2,3,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,6,7,8,9],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,5,9],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8],[9]] => [9,5,8,2,4,7,1,3,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,4,5,9],[2,7,8],[3],[6]] => [[1,2,3,6],[4,7],[5,8],[9]] => [9,5,8,4,7,1,2,3,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,8,9],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8],[9]] => [9,8,3,5,7,1,2,4,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,5,8,9],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8],[9]] => [9,8,5,7,1,2,3,4,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,7,8,9],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,9],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8],[9]] => [9,2,4,6,8,1,3,5,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,4,9],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8],[9]] => [9,4,6,8,1,2,3,5,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,6,9],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8],[9]] => [9,6,8,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [[1,2,3,4,5,6,8],[7,9]] => [7,9,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 8
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,4,5,6,7,8,9,10],[2]] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,5,6,7,8,9,10],[3,4]] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,2,4,1,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,4,5,6,7,8,9,10],[2],[3]] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,3,7,8,9,10],[4,5,6]] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => [10,9,8,7,3,6,2,5,1,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,3,6,7,8,9,10],[2,5],[4]] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,3,5,1,2,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,5,6,7,8,9,10],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,3,4,9,10],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => [10,9,4,8,3,7,2,6,1,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,3,4,8,9,10],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7],[8],[9],[10]] => [10,9,8,4,7,3,6,1,2,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,7,8,9,10],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7],[8],[9],[10]] => [10,9,8,7,2,4,6,1,3,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,4,7,8,9,10],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7],[8],[9],[10]] => [10,9,8,7,4,6,1,2,3,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,6,7,8,9,10],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,3,4,5,10],[2,7,8,9],[6]] => [[1,2,6],[3,7],[4,8],[5,9],[10]] => [10,5,9,4,8,3,7,1,2,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,5,9,10],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8],[9],[10]] => [10,9,5,8,2,4,7,1,3,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,4,5,9,10],[2,7,8],[3],[6]] => [[1,2,3,6],[4,7],[5,8],[9],[10]] => [10,9,5,8,4,7,1,2,3,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,3,8,9,10],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8],[9],[10]] => [10,9,8,3,5,7,1,2,4,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,5,8,9,10],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8],[9],[10]] => [10,9,8,5,7,1,2,3,4,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,7,8,9,10],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [10,9,8,7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,3,10],[4,5,6],[7,8,9]] => [[1,4,7],[2,5,8],[3,6,9],[10]] => [10,3,6,9,2,5,8,1,4,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,3,6,10],[2,5,9],[4,8],[7]] => [[1,2,4,7],[3,5,8],[6,9],[10]] => [10,6,9,3,5,8,1,2,4,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,5,6,10],[2,8,9],[3],[4],[7]] => [[1,2,3,4,7],[5,8],[6,9],[10]] => [10,6,9,5,8,1,2,3,4,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,9,10],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8],[9],[10]] => [10,9,2,4,6,8,1,3,5,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,4,9,10],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8],[9],[10]] => [10,9,4,6,8,1,2,3,5,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,6,9,10],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8],[9],[10]] => [10,9,6,8,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,3,10],[2,5],[4,7],[6,9],[8]] => [[1,2,4,6,8],[3,5,7,9],[10]] => [10,3,5,7,9,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,5,10],[2,7],[3,9],[4],[6],[8]] => [[1,2,3,4,6,8],[5,7,9],[10]] => [10,5,7,9,1,2,3,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,7,10],[2,9],[3],[4],[5],[6],[8]] => [[1,2,3,4,5,6,8],[7,9],[10]] => [10,7,9,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,6,8,9],[2,7],[3],[4],[5]] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,5,9],[2,6],[3,7],[4,8]] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,5,8,9],[2,6],[3,7],[4]] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,5,7,8,9],[2,6],[3],[4]] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,4,7,8,9],[2,5],[3,6]] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,4,6,8],[2,5,7,9],[3]] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 9
[[1,4,6,7,8,9],[2,5],[3]] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,5,7,9],[2,4,6,8]] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,5,7,8,9],[2,4,6]] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,5,6,7,8,9],[2,4]] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => [[1,2,3,4,5,6,7,8],[9,10]] => [9,10,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,7,9],[2,8,10],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7,8],[9,10]] => [9,10,7,8,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,7,9,10],[2,8],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [10,9,7,8,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,6,9,10],[2,7],[3,8],[4],[5]] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,6,8,9,10],[2,7],[3],[4],[5]] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,1,2,3,4,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,5,9],[2,6,10],[3,7],[4,8]] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,5,9,10],[2,6],[3,7],[4,8]] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,5,8,9,10],[2,6],[3,7],[4]] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [10,9,8,5,6,7,1,2,3,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,5,7,9],[2,6,8,10],[3],[4]] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 10
[[1,5,7,9,10],[2,6,8],[3],[4]] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,1,2,3,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,5,7,8,9,10],[2,6],[3],[4]] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,4,7,10],[2,5,8],[3,6,9]] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,4,7,8,9,10],[2,5],[3,6]] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [10,9,8,7,4,5,6,1,2,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,4,6,8,10],[2,5,7,9],[3]] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,4,5,1,2,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,4,6,8,9,10],[2,5,7],[3]] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,4,5,1,2,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,4,6,7,8,9,10],[2,5],[3]] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,3,5,7,9,10],[2,4,6,8]] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,3,5,7,8,9,10],[2,4,6]] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,3,5,6,7,8,9,10],[2,4]] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,4,6,8],[3,5,7,9]] => [[1,3],[2,5],[4,7],[6,9],[8]] => [8,6,9,4,7,2,5,1,3] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 9
[[1,2,3,4,5,6,8],[7,9]] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,9,1,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 9
[[1,2,3,4,5,6,7,9],[8]] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,4,5,6,9],[7,8]] => [[1,7],[2,8],[3],[4],[5],[6],[9]] => [9,6,5,4,3,2,8,1,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,4,5,6,9],[7],[8]] => [[1,7,8],[2],[3],[4],[5],[6],[9]] => [9,6,5,4,3,2,1,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,3,4,5,9],[6],[7],[8]] => [[1,6,7,8],[2],[3],[4],[5],[9]] => [9,5,4,3,2,1,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2],[9]] => [9,2,1,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3],[2,9],[4],[5],[6],[7],[8]] => [[1,2,4,5,6,7,8],[3,9]] => [3,9,1,2,4,5,6,7,8] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 4
[[1,2,3,4,5,6,7,8,10],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [10,8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,3,4,5,6,7,10],[8],[9]] => [[1,8,9],[2],[3],[4],[5],[6],[7],[10]] => [10,7,6,5,4,3,2,1,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2],[10]] => [10,2,1,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,4,5,6,7,8,9],[3]] => [[1,3],[2],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,4,6,7,8,9],[2,5]] => [[1,2],[3,5],[4],[6],[7],[8],[9]] => [9,8,7,6,4,3,5,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,5,6,7,8,9],[2],[4]] => [[1,2,4],[3],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,4,6,7,8,9],[2],[3],[5]] => [[1,2,3,5],[4],[6],[7],[8],[9]] => [9,8,7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,5,7,8],[2,4,6,9]] => [[1,2],[3,4],[5,6],[7,9],[8]] => [8,7,9,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 9
[[1,5,7,8,9],[2],[3],[4],[6]] => [[1,2,3,4,6],[5],[7],[8],[9]] => [9,8,7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,6,8,9],[2],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6],[8],[9]] => [9,8,6,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,7,9],[2],[3],[4],[5],[6],[8]] => [[1,2,3,4,5,6,8],[7],[9]] => [9,7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [[1,2,3,4,5,6,7,9],[8]] => [8,1,2,3,4,5,6,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9
[[1,2,4,5,6,7,8,9,10],[3]] => [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [[1,2,3,4,5,6,7,8,10],[9]] => [9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10
[[1,3,4,5,6,7,8],[2,9]] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,9,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 9
[[1,3,4,5,6,7,8],[2],[9]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9
[[1,3,4,5,6,7,8,9],[2],[10]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,4,5,6,7,8,9,10],[3]] => [3,1,2,4,5,6,7,8,9,10] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
[[1,2,3,5,6,7,8,9,10],[4]] => [[1,4],[2],[3],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,3,4,6,7,8,9,10],[5]] => [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,3,4,5,6,7,9,10],[8]] => [[1,8],[2],[3],[4],[5],[6],[7],[9],[10]] => [10,9,7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,3,4,5,6,8,9,10],[7]] => [[1,7],[2],[3],[4],[5],[6],[8],[9],[10]] => [10,9,8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,3,4,5,7,8,9,10],[6]] => [[1,6],[2],[3],[4],[5],[7],[8],[9],[10]] => [10,9,8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,4,5,6,7,8],[2],[3],[9]] => [[1,2,3,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9
[[1,2,5,6,7,8,9],[3],[4]] => [[1,3,4],[2],[5],[6],[7],[8],[9]] => [9,8,7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,2,4,5,6,7,8,9],[3],[10]] => [[1,3,10],[2],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,2,1,3,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10
[[1,2,3,4,5,6,8],[7],[9]] => [[1,7,9],[2],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9
[[1,2,3,4,5,6,7,9],[8],[10]] => [[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,1,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10
[[1,2,6,9],[3,7,10],[4,8],[5]] => [[1,3,4,5],[2,7,8],[6,10],[9]] => [9,6,10,2,7,8,1,3,4,5] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 10
[[1,6],[2,8],[3,9],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8,9]] => [6,8,9,1,2,3,4,5,7] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 7
[[1,2],[3,9],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2,9]] => [2,9,1,3,4,5,6,7,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
[[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2,10]] => [2,10,1,3,4,5,6,7,8,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 3
[[1,3,9],[2,4],[5,8],[6],[7]] => [[1,2,5,6,7],[3,4,8],[9]] => [9,3,4,8,1,2,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[[1,3,5,7,10],[2,4,6,8],[9]] => [[1,2,9],[3,4],[5,6],[7,8],[10]] => [10,7,8,5,6,3,4,1,2,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
[[1,2,9],[3],[4],[5],[6],[7],[8],[10]] => [[1,3,4,5,6,7,8,10],[2],[9]] => [9,2,1,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10
[[1,7,8],[2,9],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7,9],[8]] => [8,7,9,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 9
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,2 1,2,3,4 1,3,5,7,10 1,6,10,14,19,26 1,10,19,29,41,56,76
F1=q2
F2=q2+q3
F3=q2+q3+2 q4
F4=q2+2 q3+3 q4+4 q5
F5=q2+3 q3+5 q4+7 q5+10 q6
F6=q2+6 q3+10 q4+14 q5+19 q6+26 q7
F7=q2+10 q3+19 q4+29 q5+41 q6+56 q7+76 q8
Description
The position of the first down step of a Dyck path.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
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
conjugate
Description
Sends a standard tableau to its conjugate tableau.
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