Identifier
-
Mp00207:
Standard tableaux
—horizontal strip sizes⟶
Integer compositions
St000008: Integer compositions ⟶ ℤ
Values
[[1]] => [1] => 0
[[1,2]] => [2] => 0
[[1],[2]] => [1,1] => 1
[[1,2,3]] => [3] => 0
[[1,3],[2]] => [1,2] => 1
[[1,2],[3]] => [2,1] => 2
[[1],[2],[3]] => [1,1,1] => 3
[[1,2,3,4]] => [4] => 0
[[1,3,4],[2]] => [1,3] => 1
[[1,2,4],[3]] => [2,2] => 2
[[1,2,3],[4]] => [3,1] => 3
[[1,3],[2,4]] => [1,2,1] => 4
[[1,2],[3,4]] => [2,2] => 2
[[1,4],[2],[3]] => [1,1,2] => 3
[[1,3],[2],[4]] => [1,2,1] => 4
[[1,2],[3],[4]] => [2,1,1] => 5
[[1],[2],[3],[4]] => [1,1,1,1] => 6
[[1,2,3,4,5]] => [5] => 0
[[1,3,4,5],[2]] => [1,4] => 1
[[1,2,4,5],[3]] => [2,3] => 2
[[1,2,3,5],[4]] => [3,2] => 3
[[1,2,3,4],[5]] => [4,1] => 4
[[1,3,5],[2,4]] => [1,2,2] => 4
[[1,2,5],[3,4]] => [2,3] => 2
[[1,3,4],[2,5]] => [1,3,1] => 5
[[1,2,4],[3,5]] => [2,2,1] => 6
[[1,2,3],[4,5]] => [3,2] => 3
[[1,4,5],[2],[3]] => [1,1,3] => 3
[[1,3,5],[2],[4]] => [1,2,2] => 4
[[1,2,5],[3],[4]] => [2,1,2] => 5
[[1,3,4],[2],[5]] => [1,3,1] => 5
[[1,2,4],[3],[5]] => [2,2,1] => 6
[[1,2,3],[4],[5]] => [3,1,1] => 7
[[1,4],[2,5],[3]] => [1,1,2,1] => 7
[[1,3],[2,5],[4]] => [1,2,2] => 4
[[1,2],[3,5],[4]] => [2,1,2] => 5
[[1,3],[2,4],[5]] => [1,2,1,1] => 8
[[1,2],[3,4],[5]] => [2,2,1] => 6
[[1,5],[2],[3],[4]] => [1,1,1,2] => 6
[[1,4],[2],[3],[5]] => [1,1,2,1] => 7
[[1,3],[2],[4],[5]] => [1,2,1,1] => 8
[[1,2],[3],[4],[5]] => [2,1,1,1] => 9
[[1],[2],[3],[4],[5]] => [1,1,1,1,1] => 10
[[1,2,3,4,5,6]] => [6] => 0
[[1,3,4,5,6],[2]] => [1,5] => 1
[[1,2,4,5,6],[3]] => [2,4] => 2
[[1,2,3,5,6],[4]] => [3,3] => 3
[[1,2,3,4,6],[5]] => [4,2] => 4
[[1,2,3,4,5],[6]] => [5,1] => 5
[[1,3,5,6],[2,4]] => [1,2,3] => 4
[[1,2,5,6],[3,4]] => [2,4] => 2
[[1,3,4,6],[2,5]] => [1,3,2] => 5
[[1,2,4,6],[3,5]] => [2,2,2] => 6
[[1,2,3,6],[4,5]] => [3,3] => 3
[[1,3,4,5],[2,6]] => [1,4,1] => 6
[[1,2,4,5],[3,6]] => [2,3,1] => 7
[[1,2,3,5],[4,6]] => [3,2,1] => 8
[[1,2,3,4],[5,6]] => [4,2] => 4
[[1,4,5,6],[2],[3]] => [1,1,4] => 3
[[1,3,5,6],[2],[4]] => [1,2,3] => 4
[[1,2,5,6],[3],[4]] => [2,1,3] => 5
[[1,3,4,6],[2],[5]] => [1,3,2] => 5
[[1,2,4,6],[3],[5]] => [2,2,2] => 6
[[1,2,3,6],[4],[5]] => [3,1,2] => 7
[[1,3,4,5],[2],[6]] => [1,4,1] => 6
[[1,2,4,5],[3],[6]] => [2,3,1] => 7
[[1,2,3,5],[4],[6]] => [3,2,1] => 8
[[1,2,3,4],[5],[6]] => [4,1,1] => 9
[[1,3,5],[2,4,6]] => [1,2,2,1] => 9
[[1,2,5],[3,4,6]] => [2,3,1] => 7
[[1,3,4],[2,5,6]] => [1,3,2] => 5
[[1,2,4],[3,5,6]] => [2,2,2] => 6
[[1,2,3],[4,5,6]] => [3,3] => 3
[[1,4,6],[2,5],[3]] => [1,1,2,2] => 7
[[1,3,6],[2,5],[4]] => [1,2,3] => 4
[[1,2,6],[3,5],[4]] => [2,1,3] => 5
[[1,3,6],[2,4],[5]] => [1,2,1,2] => 8
[[1,2,6],[3,4],[5]] => [2,2,2] => 6
[[1,4,5],[2,6],[3]] => [1,1,3,1] => 8
[[1,3,5],[2,6],[4]] => [1,2,2,1] => 9
[[1,2,5],[3,6],[4]] => [2,1,2,1] => 10
[[1,3,4],[2,6],[5]] => [1,3,2] => 5
[[1,2,4],[3,6],[5]] => [2,2,2] => 6
[[1,2,3],[4,6],[5]] => [3,1,2] => 7
[[1,3,5],[2,4],[6]] => [1,2,2,1] => 9
[[1,2,5],[3,4],[6]] => [2,3,1] => 7
[[1,3,4],[2,5],[6]] => [1,3,1,1] => 10
[[1,2,4],[3,5],[6]] => [2,2,1,1] => 11
[[1,2,3],[4,5],[6]] => [3,2,1] => 8
[[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[[1,4,6],[2],[3],[5]] => [1,1,2,2] => 7
[[1,3,6],[2],[4],[5]] => [1,2,1,2] => 8
[[1,2,6],[3],[4],[5]] => [2,1,1,2] => 9
[[1,4,5],[2],[3],[6]] => [1,1,3,1] => 8
[[1,3,5],[2],[4],[6]] => [1,2,2,1] => 9
[[1,2,5],[3],[4],[6]] => [2,1,2,1] => 10
[[1,3,4],[2],[5],[6]] => [1,3,1,1] => 10
[[1,2,4],[3],[5],[6]] => [2,2,1,1] => 11
[[1,2,3],[4],[5],[6]] => [3,1,1,1] => 12
[[1,4],[2,5],[3,6]] => [1,1,2,2] => 7
[[1,3],[2,5],[4,6]] => [1,2,2,1] => 9
>>> Load all 1355 entries. <<<[[1,2],[3,5],[4,6]] => [2,1,2,1] => 10
[[1,3],[2,4],[5,6]] => [1,2,1,2] => 8
[[1,2],[3,4],[5,6]] => [2,2,2] => 6
[[1,5],[2,6],[3],[4]] => [1,1,1,2,1] => 11
[[1,4],[2,6],[3],[5]] => [1,1,2,2] => 7
[[1,3],[2,6],[4],[5]] => [1,2,1,2] => 8
[[1,2],[3,6],[4],[5]] => [2,1,1,2] => 9
[[1,4],[2,5],[3],[6]] => [1,1,2,1,1] => 12
[[1,3],[2,5],[4],[6]] => [1,2,2,1] => 9
[[1,2],[3,5],[4],[6]] => [2,1,2,1] => 10
[[1,3],[2,4],[5],[6]] => [1,2,1,1,1] => 13
[[1,2],[3,4],[5],[6]] => [2,2,1,1] => 11
[[1,6],[2],[3],[4],[5]] => [1,1,1,1,2] => 10
[[1,5],[2],[3],[4],[6]] => [1,1,1,2,1] => 11
[[1,4],[2],[3],[5],[6]] => [1,1,2,1,1] => 12
[[1,3],[2],[4],[5],[6]] => [1,2,1,1,1] => 13
[[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 14
[[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => 15
[[1,2,3,4,5,6,7]] => [7] => 0
[[1,3,4,5,6,7],[2]] => [1,6] => 1
[[1,2,4,5,6,7],[3]] => [2,5] => 2
[[1,2,3,5,6,7],[4]] => [3,4] => 3
[[1,2,3,4,6,7],[5]] => [4,3] => 4
[[1,2,3,4,5,7],[6]] => [5,2] => 5
[[1,2,3,4,5,6],[7]] => [6,1] => 6
[[1,3,5,6,7],[2,4]] => [1,2,4] => 4
[[1,2,5,6,7],[3,4]] => [2,5] => 2
[[1,3,4,6,7],[2,5]] => [1,3,3] => 5
[[1,2,4,6,7],[3,5]] => [2,2,3] => 6
[[1,2,3,6,7],[4,5]] => [3,4] => 3
[[1,3,4,5,7],[2,6]] => [1,4,2] => 6
[[1,2,4,5,7],[3,6]] => [2,3,2] => 7
[[1,2,3,5,7],[4,6]] => [3,2,2] => 8
[[1,2,3,4,7],[5,6]] => [4,3] => 4
[[1,3,4,5,6],[2,7]] => [1,5,1] => 7
[[1,2,4,5,6],[3,7]] => [2,4,1] => 8
[[1,2,3,5,6],[4,7]] => [3,3,1] => 9
[[1,2,3,4,6],[5,7]] => [4,2,1] => 10
[[1,2,3,4,5],[6,7]] => [5,2] => 5
[[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[[1,3,5,6,7],[2],[4]] => [1,2,4] => 4
[[1,2,5,6,7],[3],[4]] => [2,1,4] => 5
[[1,3,4,6,7],[2],[5]] => [1,3,3] => 5
[[1,2,4,6,7],[3],[5]] => [2,2,3] => 6
[[1,2,3,6,7],[4],[5]] => [3,1,3] => 7
[[1,3,4,5,7],[2],[6]] => [1,4,2] => 6
[[1,2,4,5,7],[3],[6]] => [2,3,2] => 7
[[1,2,3,5,7],[4],[6]] => [3,2,2] => 8
[[1,2,3,4,7],[5],[6]] => [4,1,2] => 9
[[1,3,4,5,6],[2],[7]] => [1,5,1] => 7
[[1,2,4,5,6],[3],[7]] => [2,4,1] => 8
[[1,2,3,5,6],[4],[7]] => [3,3,1] => 9
[[1,2,3,4,6],[5],[7]] => [4,2,1] => 10
[[1,2,3,4,5],[6],[7]] => [5,1,1] => 11
[[1,3,5,7],[2,4,6]] => [1,2,2,2] => 9
[[1,2,5,7],[3,4,6]] => [2,3,2] => 7
[[1,3,4,7],[2,5,6]] => [1,3,3] => 5
[[1,2,4,7],[3,5,6]] => [2,2,3] => 6
[[1,2,3,7],[4,5,6]] => [3,4] => 3
[[1,3,5,6],[2,4,7]] => [1,2,3,1] => 10
[[1,2,5,6],[3,4,7]] => [2,4,1] => 8
[[1,3,4,6],[2,5,7]] => [1,3,2,1] => 11
[[1,2,4,6],[3,5,7]] => [2,2,2,1] => 12
[[1,2,3,6],[4,5,7]] => [3,3,1] => 9
[[1,3,4,5],[2,6,7]] => [1,4,2] => 6
[[1,2,4,5],[3,6,7]] => [2,3,2] => 7
[[1,2,3,5],[4,6,7]] => [3,2,2] => 8
[[1,2,3,4],[5,6,7]] => [4,3] => 4
[[1,4,6,7],[2,5],[3]] => [1,1,2,3] => 7
[[1,3,6,7],[2,5],[4]] => [1,2,4] => 4
[[1,2,6,7],[3,5],[4]] => [2,1,4] => 5
[[1,3,6,7],[2,4],[5]] => [1,2,1,3] => 8
[[1,2,6,7],[3,4],[5]] => [2,2,3] => 6
[[1,4,5,7],[2,6],[3]] => [1,1,3,2] => 8
[[1,3,5,7],[2,6],[4]] => [1,2,2,2] => 9
[[1,2,5,7],[3,6],[4]] => [2,1,2,2] => 10
[[1,3,4,7],[2,6],[5]] => [1,3,3] => 5
[[1,2,4,7],[3,6],[5]] => [2,2,3] => 6
[[1,2,3,7],[4,6],[5]] => [3,1,3] => 7
[[1,3,5,7],[2,4],[6]] => [1,2,2,2] => 9
[[1,2,5,7],[3,4],[6]] => [2,3,2] => 7
[[1,3,4,7],[2,5],[6]] => [1,3,1,2] => 10
[[1,2,4,7],[3,5],[6]] => [2,2,1,2] => 11
[[1,2,3,7],[4,5],[6]] => [3,2,2] => 8
[[1,4,5,6],[2,7],[3]] => [1,1,4,1] => 9
[[1,3,5,6],[2,7],[4]] => [1,2,3,1] => 10
[[1,2,5,6],[3,7],[4]] => [2,1,3,1] => 11
[[1,3,4,6],[2,7],[5]] => [1,3,2,1] => 11
[[1,2,4,6],[3,7],[5]] => [2,2,2,1] => 12
[[1,2,3,6],[4,7],[5]] => [3,1,2,1] => 13
[[1,3,4,5],[2,7],[6]] => [1,4,2] => 6
[[1,2,4,5],[3,7],[6]] => [2,3,2] => 7
[[1,2,3,5],[4,7],[6]] => [3,2,2] => 8
[[1,2,3,4],[5,7],[6]] => [4,1,2] => 9
[[1,3,5,6],[2,4],[7]] => [1,2,3,1] => 10
[[1,2,5,6],[3,4],[7]] => [2,4,1] => 8
[[1,3,4,6],[2,5],[7]] => [1,3,2,1] => 11
[[1,2,4,6],[3,5],[7]] => [2,2,2,1] => 12
[[1,2,3,6],[4,5],[7]] => [3,3,1] => 9
[[1,3,4,5],[2,6],[7]] => [1,4,1,1] => 12
[[1,2,4,5],[3,6],[7]] => [2,3,1,1] => 13
[[1,2,3,5],[4,6],[7]] => [3,2,1,1] => 14
[[1,2,3,4],[5,6],[7]] => [4,2,1] => 10
[[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[[1,3,6,7],[2],[4],[5]] => [1,2,1,3] => 8
[[1,2,6,7],[3],[4],[5]] => [2,1,1,3] => 9
[[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[[1,3,5,7],[2],[4],[6]] => [1,2,2,2] => 9
[[1,2,5,7],[3],[4],[6]] => [2,1,2,2] => 10
[[1,3,4,7],[2],[5],[6]] => [1,3,1,2] => 10
[[1,2,4,7],[3],[5],[6]] => [2,2,1,2] => 11
[[1,2,3,7],[4],[5],[6]] => [3,1,1,2] => 12
[[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[[1,3,5,6],[2],[4],[7]] => [1,2,3,1] => 10
[[1,2,5,6],[3],[4],[7]] => [2,1,3,1] => 11
[[1,3,4,6],[2],[5],[7]] => [1,3,2,1] => 11
[[1,2,4,6],[3],[5],[7]] => [2,2,2,1] => 12
[[1,2,3,6],[4],[5],[7]] => [3,1,2,1] => 13
[[1,3,4,5],[2],[6],[7]] => [1,4,1,1] => 12
[[1,2,4,5],[3],[6],[7]] => [2,3,1,1] => 13
[[1,2,3,5],[4],[6],[7]] => [3,2,1,1] => 14
[[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 15
[[1,4,6],[2,5,7],[3]] => [1,1,2,2,1] => 13
[[1,3,6],[2,5,7],[4]] => [1,2,3,1] => 10
[[1,2,6],[3,5,7],[4]] => [2,1,3,1] => 11
[[1,3,6],[2,4,7],[5]] => [1,2,1,2,1] => 14
[[1,2,6],[3,4,7],[5]] => [2,2,2,1] => 12
[[1,4,5],[2,6,7],[3]] => [1,1,3,2] => 8
[[1,3,5],[2,6,7],[4]] => [1,2,2,2] => 9
[[1,2,5],[3,6,7],[4]] => [2,1,2,2] => 10
[[1,3,4],[2,6,7],[5]] => [1,3,3] => 5
[[1,2,4],[3,6,7],[5]] => [2,2,3] => 6
[[1,2,3],[4,6,7],[5]] => [3,1,3] => 7
[[1,3,5],[2,4,7],[6]] => [1,2,2,2] => 9
[[1,2,5],[3,4,7],[6]] => [2,3,2] => 7
[[1,3,4],[2,5,7],[6]] => [1,3,1,2] => 10
[[1,2,4],[3,5,7],[6]] => [2,2,1,2] => 11
[[1,2,3],[4,5,7],[6]] => [3,2,2] => 8
[[1,3,5],[2,4,6],[7]] => [1,2,2,1,1] => 15
[[1,2,5],[3,4,6],[7]] => [2,3,1,1] => 13
[[1,3,4],[2,5,6],[7]] => [1,3,2,1] => 11
[[1,2,4],[3,5,6],[7]] => [2,2,2,1] => 12
[[1,2,3],[4,5,6],[7]] => [3,3,1] => 9
[[1,4,7],[2,5],[3,6]] => [1,1,2,3] => 7
[[1,3,7],[2,5],[4,6]] => [1,2,2,2] => 9
[[1,2,7],[3,5],[4,6]] => [2,1,2,2] => 10
[[1,3,7],[2,4],[5,6]] => [1,2,1,3] => 8
[[1,2,7],[3,4],[5,6]] => [2,2,3] => 6
[[1,4,6],[2,5],[3,7]] => [1,1,2,2,1] => 13
[[1,3,6],[2,5],[4,7]] => [1,2,3,1] => 10
[[1,2,6],[3,5],[4,7]] => [2,1,3,1] => 11
[[1,3,6],[2,4],[5,7]] => [1,2,1,2,1] => 14
[[1,2,6],[3,4],[5,7]] => [2,2,2,1] => 12
[[1,4,5],[2,6],[3,7]] => [1,1,3,2] => 8
[[1,3,5],[2,6],[4,7]] => [1,2,2,2] => 9
[[1,2,5],[3,6],[4,7]] => [2,1,2,2] => 10
[[1,3,4],[2,6],[5,7]] => [1,3,2,1] => 11
[[1,2,4],[3,6],[5,7]] => [2,2,2,1] => 12
[[1,2,3],[4,6],[5,7]] => [3,1,2,1] => 13
[[1,3,5],[2,4],[6,7]] => [1,2,2,2] => 9
[[1,2,5],[3,4],[6,7]] => [2,3,2] => 7
[[1,3,4],[2,5],[6,7]] => [1,3,1,2] => 10
[[1,2,4],[3,5],[6,7]] => [2,2,1,2] => 11
[[1,2,3],[4,5],[6,7]] => [3,2,2] => 8
[[1,5,7],[2,6],[3],[4]] => [1,1,1,2,2] => 11
[[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 7
[[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 9
[[1,4,7],[2,5],[3],[6]] => [1,1,2,1,2] => 12
[[1,3,7],[2,5],[4],[6]] => [1,2,2,2] => 9
[[1,2,7],[3,5],[4],[6]] => [2,1,2,2] => 10
[[1,3,7],[2,4],[5],[6]] => [1,2,1,1,2] => 13
[[1,2,7],[3,4],[5],[6]] => [2,2,1,2] => 11
[[1,5,6],[2,7],[3],[4]] => [1,1,1,3,1] => 12
[[1,4,6],[2,7],[3],[5]] => [1,1,2,2,1] => 13
[[1,3,6],[2,7],[4],[5]] => [1,2,1,2,1] => 14
[[1,2,6],[3,7],[4],[5]] => [2,1,1,2,1] => 15
[[1,4,5],[2,7],[3],[6]] => [1,1,3,2] => 8
[[1,3,5],[2,7],[4],[6]] => [1,2,2,2] => 9
[[1,2,5],[3,7],[4],[6]] => [2,1,2,2] => 10
[[1,3,4],[2,7],[5],[6]] => [1,3,1,2] => 10
[[1,2,4],[3,7],[5],[6]] => [2,2,1,2] => 11
[[1,2,3],[4,7],[5],[6]] => [3,1,1,2] => 12
[[1,4,6],[2,5],[3],[7]] => [1,1,2,2,1] => 13
[[1,3,6],[2,5],[4],[7]] => [1,2,3,1] => 10
[[1,2,6],[3,5],[4],[7]] => [2,1,3,1] => 11
[[1,3,6],[2,4],[5],[7]] => [1,2,1,2,1] => 14
[[1,2,6],[3,4],[5],[7]] => [2,2,2,1] => 12
[[1,4,5],[2,6],[3],[7]] => [1,1,3,1,1] => 14
[[1,3,5],[2,6],[4],[7]] => [1,2,2,1,1] => 15
[[1,2,5],[3,6],[4],[7]] => [2,1,2,1,1] => 16
[[1,3,4],[2,6],[5],[7]] => [1,3,2,1] => 11
[[1,2,4],[3,6],[5],[7]] => [2,2,2,1] => 12
[[1,2,3],[4,6],[5],[7]] => [3,1,2,1] => 13
[[1,3,5],[2,4],[6],[7]] => [1,2,2,1,1] => 15
[[1,2,5],[3,4],[6],[7]] => [2,3,1,1] => 13
[[1,3,4],[2,5],[6],[7]] => [1,3,1,1,1] => 16
[[1,2,4],[3,5],[6],[7]] => [2,2,1,1,1] => 17
[[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 14
[[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[[1,4,7],[2],[3],[5],[6]] => [1,1,2,1,2] => 12
[[1,3,7],[2],[4],[5],[6]] => [1,2,1,1,2] => 13
[[1,2,7],[3],[4],[5],[6]] => [2,1,1,1,2] => 14
[[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[[1,4,6],[2],[3],[5],[7]] => [1,1,2,2,1] => 13
[[1,3,6],[2],[4],[5],[7]] => [1,2,1,2,1] => 14
[[1,2,6],[3],[4],[5],[7]] => [2,1,1,2,1] => 15
[[1,4,5],[2],[3],[6],[7]] => [1,1,3,1,1] => 14
[[1,3,5],[2],[4],[6],[7]] => [1,2,2,1,1] => 15
[[1,2,5],[3],[4],[6],[7]] => [2,1,2,1,1] => 16
[[1,3,4],[2],[5],[6],[7]] => [1,3,1,1,1] => 16
[[1,2,4],[3],[5],[6],[7]] => [2,2,1,1,1] => 17
[[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 18
[[1,5],[2,6],[3,7],[4]] => [1,1,1,2,2] => 11
[[1,4],[2,6],[3,7],[5]] => [1,1,2,2,1] => 13
[[1,3],[2,6],[4,7],[5]] => [1,2,1,2,1] => 14
[[1,2],[3,6],[4,7],[5]] => [2,1,1,2,1] => 15
[[1,4],[2,5],[3,7],[6]] => [1,1,2,1,2] => 12
[[1,3],[2,5],[4,7],[6]] => [1,2,2,2] => 9
[[1,2],[3,5],[4,7],[6]] => [2,1,2,2] => 10
[[1,3],[2,4],[5,7],[6]] => [1,2,1,1,2] => 13
[[1,2],[3,4],[5,7],[6]] => [2,2,1,2] => 11
[[1,4],[2,5],[3,6],[7]] => [1,1,2,2,1] => 13
[[1,3],[2,5],[4,6],[7]] => [1,2,2,1,1] => 15
[[1,2],[3,5],[4,6],[7]] => [2,1,2,1,1] => 16
[[1,3],[2,4],[5,6],[7]] => [1,2,1,2,1] => 14
[[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 12
[[1,6],[2,7],[3],[4],[5]] => [1,1,1,1,2,1] => 16
[[1,5],[2,7],[3],[4],[6]] => [1,1,1,2,2] => 11
[[1,4],[2,7],[3],[5],[6]] => [1,1,2,1,2] => 12
[[1,3],[2,7],[4],[5],[6]] => [1,2,1,1,2] => 13
[[1,2],[3,7],[4],[5],[6]] => [2,1,1,1,2] => 14
[[1,5],[2,6],[3],[4],[7]] => [1,1,1,2,1,1] => 17
[[1,4],[2,6],[3],[5],[7]] => [1,1,2,2,1] => 13
[[1,3],[2,6],[4],[5],[7]] => [1,2,1,2,1] => 14
[[1,2],[3,6],[4],[5],[7]] => [2,1,1,2,1] => 15
[[1,4],[2,5],[3],[6],[7]] => [1,1,2,1,1,1] => 18
[[1,3],[2,5],[4],[6],[7]] => [1,2,2,1,1] => 15
[[1,2],[3,5],[4],[6],[7]] => [2,1,2,1,1] => 16
[[1,3],[2,4],[5],[6],[7]] => [1,2,1,1,1,1] => 19
[[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 17
[[1,7],[2],[3],[4],[5],[6]] => [1,1,1,1,1,2] => 15
[[1,6],[2],[3],[4],[5],[7]] => [1,1,1,1,2,1] => 16
[[1,5],[2],[3],[4],[6],[7]] => [1,1,1,2,1,1] => 17
[[1,4],[2],[3],[5],[6],[7]] => [1,1,2,1,1,1] => 18
[[1,3],[2],[4],[5],[6],[7]] => [1,2,1,1,1,1] => 19
[[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 20
[[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => 21
[[1,2,3,4,5,6,7,8]] => [8] => 0
[[1,3,4,5,6,7,8],[2]] => [1,7] => 1
[[1,2,4,5,6,7,8],[3]] => [2,6] => 2
[[1,2,3,5,6,7,8],[4]] => [3,5] => 3
[[1,2,3,4,6,7,8],[5]] => [4,4] => 4
[[1,2,3,4,5,7,8],[6]] => [5,3] => 5
[[1,2,3,4,5,6,8],[7]] => [6,2] => 6
[[1,2,3,4,5,6,7],[8]] => [7,1] => 7
[[1,3,5,6,7,8],[2,4]] => [1,2,5] => 4
[[1,2,5,6,7,8],[3,4]] => [2,6] => 2
[[1,3,4,6,7,8],[2,5]] => [1,3,4] => 5
[[1,2,4,6,7,8],[3,5]] => [2,2,4] => 6
[[1,2,3,6,7,8],[4,5]] => [3,5] => 3
[[1,3,4,5,7,8],[2,6]] => [1,4,3] => 6
[[1,2,4,5,7,8],[3,6]] => [2,3,3] => 7
[[1,2,3,5,7,8],[4,6]] => [3,2,3] => 8
[[1,2,3,4,7,8],[5,6]] => [4,4] => 4
[[1,3,4,5,6,8],[2,7]] => [1,5,2] => 7
[[1,2,4,5,6,8],[3,7]] => [2,4,2] => 8
[[1,2,3,5,6,8],[4,7]] => [3,3,2] => 9
[[1,2,3,4,6,8],[5,7]] => [4,2,2] => 10
[[1,2,3,4,5,8],[6,7]] => [5,3] => 5
[[1,3,4,5,6,7],[2,8]] => [1,6,1] => 8
[[1,2,4,5,6,7],[3,8]] => [2,5,1] => 9
[[1,2,3,5,6,7],[4,8]] => [3,4,1] => 10
[[1,2,3,4,6,7],[5,8]] => [4,3,1] => 11
[[1,2,3,4,5,7],[6,8]] => [5,2,1] => 12
[[1,2,3,4,5,6],[7,8]] => [6,2] => 6
[[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[[1,3,5,6,7,8],[2],[4]] => [1,2,5] => 4
[[1,2,5,6,7,8],[3],[4]] => [2,1,5] => 5
[[1,3,4,6,7,8],[2],[5]] => [1,3,4] => 5
[[1,2,4,6,7,8],[3],[5]] => [2,2,4] => 6
[[1,2,3,6,7,8],[4],[5]] => [3,1,4] => 7
[[1,3,4,5,7,8],[2],[6]] => [1,4,3] => 6
[[1,2,4,5,7,8],[3],[6]] => [2,3,3] => 7
[[1,2,3,5,7,8],[4],[6]] => [3,2,3] => 8
[[1,2,3,4,7,8],[5],[6]] => [4,1,3] => 9
[[1,3,4,5,6,8],[2],[7]] => [1,5,2] => 7
[[1,2,4,5,6,8],[3],[7]] => [2,4,2] => 8
[[1,2,3,5,6,8],[4],[7]] => [3,3,2] => 9
[[1,2,3,4,6,8],[5],[7]] => [4,2,2] => 10
[[1,2,3,4,5,8],[6],[7]] => [5,1,2] => 11
[[1,3,4,5,6,7],[2],[8]] => [1,6,1] => 8
[[1,2,4,5,6,7],[3],[8]] => [2,5,1] => 9
[[1,2,3,5,6,7],[4],[8]] => [3,4,1] => 10
[[1,2,3,4,6,7],[5],[8]] => [4,3,1] => 11
[[1,2,3,4,5,7],[6],[8]] => [5,2,1] => 12
[[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 13
[[1,3,5,7,8],[2,4,6]] => [1,2,2,3] => 9
[[1,2,5,7,8],[3,4,6]] => [2,3,3] => 7
[[1,3,4,7,8],[2,5,6]] => [1,3,4] => 5
[[1,2,4,7,8],[3,5,6]] => [2,2,4] => 6
[[1,2,3,7,8],[4,5,6]] => [3,5] => 3
[[1,3,5,6,8],[2,4,7]] => [1,2,3,2] => 10
[[1,2,5,6,8],[3,4,7]] => [2,4,2] => 8
[[1,3,4,6,8],[2,5,7]] => [1,3,2,2] => 11
[[1,2,4,6,8],[3,5,7]] => [2,2,2,2] => 12
[[1,2,3,6,8],[4,5,7]] => [3,3,2] => 9
[[1,3,4,5,8],[2,6,7]] => [1,4,3] => 6
[[1,2,4,5,8],[3,6,7]] => [2,3,3] => 7
[[1,2,3,5,8],[4,6,7]] => [3,2,3] => 8
[[1,2,3,4,8],[5,6,7]] => [4,4] => 4
[[1,3,5,6,7],[2,4,8]] => [1,2,4,1] => 11
[[1,2,5,6,7],[3,4,8]] => [2,5,1] => 9
[[1,3,4,6,7],[2,5,8]] => [1,3,3,1] => 12
[[1,2,4,6,7],[3,5,8]] => [2,2,3,1] => 13
[[1,2,3,6,7],[4,5,8]] => [3,4,1] => 10
[[1,3,4,5,7],[2,6,8]] => [1,4,2,1] => 13
[[1,2,4,5,7],[3,6,8]] => [2,3,2,1] => 14
[[1,2,3,5,7],[4,6,8]] => [3,2,2,1] => 15
[[1,2,3,4,7],[5,6,8]] => [4,3,1] => 11
[[1,3,4,5,6],[2,7,8]] => [1,5,2] => 7
[[1,2,4,5,6],[3,7,8]] => [2,4,2] => 8
[[1,2,3,5,6],[4,7,8]] => [3,3,2] => 9
[[1,2,3,4,6],[5,7,8]] => [4,2,2] => 10
[[1,2,3,4,5],[6,7,8]] => [5,3] => 5
[[1,4,6,7,8],[2,5],[3]] => [1,1,2,4] => 7
[[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 5
[[1,3,6,7,8],[2,4],[5]] => [1,2,1,4] => 8
[[1,2,6,7,8],[3,4],[5]] => [2,2,4] => 6
[[1,4,5,7,8],[2,6],[3]] => [1,1,3,3] => 8
[[1,3,5,7,8],[2,6],[4]] => [1,2,2,3] => 9
[[1,2,5,7,8],[3,6],[4]] => [2,1,2,3] => 10
[[1,3,4,7,8],[2,6],[5]] => [1,3,4] => 5
[[1,2,4,7,8],[3,6],[5]] => [2,2,4] => 6
[[1,2,3,7,8],[4,6],[5]] => [3,1,4] => 7
[[1,3,5,7,8],[2,4],[6]] => [1,2,2,3] => 9
[[1,2,5,7,8],[3,4],[6]] => [2,3,3] => 7
[[1,3,4,7,8],[2,5],[6]] => [1,3,1,3] => 10
[[1,2,4,7,8],[3,5],[6]] => [2,2,1,3] => 11
[[1,2,3,7,8],[4,5],[6]] => [3,2,3] => 8
[[1,4,5,6,8],[2,7],[3]] => [1,1,4,2] => 9
[[1,3,5,6,8],[2,7],[4]] => [1,2,3,2] => 10
[[1,2,5,6,8],[3,7],[4]] => [2,1,3,2] => 11
[[1,3,4,6,8],[2,7],[5]] => [1,3,2,2] => 11
[[1,2,4,6,8],[3,7],[5]] => [2,2,2,2] => 12
[[1,2,3,6,8],[4,7],[5]] => [3,1,2,2] => 13
[[1,3,4,5,8],[2,7],[6]] => [1,4,3] => 6
[[1,2,4,5,8],[3,7],[6]] => [2,3,3] => 7
[[1,2,3,5,8],[4,7],[6]] => [3,2,3] => 8
[[1,2,3,4,8],[5,7],[6]] => [4,1,3] => 9
[[1,3,5,6,8],[2,4],[7]] => [1,2,3,2] => 10
[[1,2,5,6,8],[3,4],[7]] => [2,4,2] => 8
[[1,3,4,6,8],[2,5],[7]] => [1,3,2,2] => 11
[[1,2,4,6,8],[3,5],[7]] => [2,2,2,2] => 12
[[1,2,3,6,8],[4,5],[7]] => [3,3,2] => 9
[[1,3,4,5,8],[2,6],[7]] => [1,4,1,2] => 12
[[1,2,4,5,8],[3,6],[7]] => [2,3,1,2] => 13
[[1,2,3,5,8],[4,6],[7]] => [3,2,1,2] => 14
[[1,2,3,4,8],[5,6],[7]] => [4,2,2] => 10
[[1,4,5,6,7],[2,8],[3]] => [1,1,5,1] => 10
[[1,3,5,6,7],[2,8],[4]] => [1,2,4,1] => 11
[[1,2,5,6,7],[3,8],[4]] => [2,1,4,1] => 12
[[1,3,4,6,7],[2,8],[5]] => [1,3,3,1] => 12
[[1,2,4,6,7],[3,8],[5]] => [2,2,3,1] => 13
[[1,2,3,6,7],[4,8],[5]] => [3,1,3,1] => 14
[[1,3,4,5,7],[2,8],[6]] => [1,4,2,1] => 13
[[1,2,4,5,7],[3,8],[6]] => [2,3,2,1] => 14
[[1,2,3,5,7],[4,8],[6]] => [3,2,2,1] => 15
[[1,2,3,4,7],[5,8],[6]] => [4,1,2,1] => 16
[[1,3,4,5,6],[2,8],[7]] => [1,5,2] => 7
[[1,2,4,5,6],[3,8],[7]] => [2,4,2] => 8
[[1,2,3,5,6],[4,8],[7]] => [3,3,2] => 9
[[1,2,3,4,6],[5,8],[7]] => [4,2,2] => 10
[[1,2,3,4,5],[6,8],[7]] => [5,1,2] => 11
[[1,3,5,6,7],[2,4],[8]] => [1,2,4,1] => 11
[[1,2,5,6,7],[3,4],[8]] => [2,5,1] => 9
[[1,3,4,6,7],[2,5],[8]] => [1,3,3,1] => 12
[[1,2,4,6,7],[3,5],[8]] => [2,2,3,1] => 13
[[1,2,3,6,7],[4,5],[8]] => [3,4,1] => 10
[[1,3,4,5,7],[2,6],[8]] => [1,4,2,1] => 13
[[1,2,4,5,7],[3,6],[8]] => [2,3,2,1] => 14
[[1,2,3,5,7],[4,6],[8]] => [3,2,2,1] => 15
[[1,2,3,4,7],[5,6],[8]] => [4,3,1] => 11
[[1,3,4,5,6],[2,7],[8]] => [1,5,1,1] => 14
[[1,2,4,5,6],[3,7],[8]] => [2,4,1,1] => 15
[[1,2,3,5,6],[4,7],[8]] => [3,3,1,1] => 16
[[1,2,3,4,6],[5,7],[8]] => [4,2,1,1] => 17
[[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 12
[[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4] => 7
[[1,3,6,7,8],[2],[4],[5]] => [1,2,1,4] => 8
[[1,2,6,7,8],[3],[4],[5]] => [2,1,1,4] => 9
[[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[[1,3,5,7,8],[2],[4],[6]] => [1,2,2,3] => 9
[[1,2,5,7,8],[3],[4],[6]] => [2,1,2,3] => 10
[[1,3,4,7,8],[2],[5],[6]] => [1,3,1,3] => 10
[[1,2,4,7,8],[3],[5],[6]] => [2,2,1,3] => 11
[[1,2,3,7,8],[4],[5],[6]] => [3,1,1,3] => 12
[[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 9
[[1,3,5,6,8],[2],[4],[7]] => [1,2,3,2] => 10
[[1,2,5,6,8],[3],[4],[7]] => [2,1,3,2] => 11
[[1,3,4,6,8],[2],[5],[7]] => [1,3,2,2] => 11
[[1,2,4,6,8],[3],[5],[7]] => [2,2,2,2] => 12
[[1,2,3,6,8],[4],[5],[7]] => [3,1,2,2] => 13
[[1,3,4,5,8],[2],[6],[7]] => [1,4,1,2] => 12
[[1,2,4,5,8],[3],[6],[7]] => [2,3,1,2] => 13
[[1,2,3,5,8],[4],[6],[7]] => [3,2,1,2] => 14
[[1,2,3,4,8],[5],[6],[7]] => [4,1,1,2] => 15
[[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[[1,3,5,6,7],[2],[4],[8]] => [1,2,4,1] => 11
[[1,2,5,6,7],[3],[4],[8]] => [2,1,4,1] => 12
[[1,3,4,6,7],[2],[5],[8]] => [1,3,3,1] => 12
[[1,2,4,6,7],[3],[5],[8]] => [2,2,3,1] => 13
[[1,2,3,6,7],[4],[5],[8]] => [3,1,3,1] => 14
[[1,3,4,5,7],[2],[6],[8]] => [1,4,2,1] => 13
[[1,2,4,5,7],[3],[6],[8]] => [2,3,2,1] => 14
[[1,2,3,5,7],[4],[6],[8]] => [3,2,2,1] => 15
[[1,2,3,4,7],[5],[6],[8]] => [4,1,2,1] => 16
[[1,3,4,5,6],[2],[7],[8]] => [1,5,1,1] => 14
[[1,2,4,5,6],[3],[7],[8]] => [2,4,1,1] => 15
[[1,2,3,5,6],[4],[7],[8]] => [3,3,1,1] => 16
[[1,2,3,4,6],[5],[7],[8]] => [4,2,1,1] => 17
[[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 18
[[1,3,5,7],[2,4,6,8]] => [1,2,2,2,1] => 16
[[1,2,5,7],[3,4,6,8]] => [2,3,2,1] => 14
[[1,3,4,7],[2,5,6,8]] => [1,3,3,1] => 12
[[1,2,4,7],[3,5,6,8]] => [2,2,3,1] => 13
[[1,2,3,7],[4,5,6,8]] => [3,4,1] => 10
[[1,3,5,6],[2,4,7,8]] => [1,2,3,2] => 10
[[1,2,5,6],[3,4,7,8]] => [2,4,2] => 8
[[1,3,4,6],[2,5,7,8]] => [1,3,2,2] => 11
[[1,2,4,6],[3,5,7,8]] => [2,2,2,2] => 12
[[1,2,3,6],[4,5,7,8]] => [3,3,2] => 9
[[1,3,4,5],[2,6,7,8]] => [1,4,3] => 6
[[1,2,4,5],[3,6,7,8]] => [2,3,3] => 7
[[1,2,3,5],[4,6,7,8]] => [3,2,3] => 8
[[1,2,3,4],[5,6,7,8]] => [4,4] => 4
[[1,4,6,8],[2,5,7],[3]] => [1,1,2,2,2] => 13
[[1,3,6,8],[2,5,7],[4]] => [1,2,3,2] => 10
[[1,2,6,8],[3,5,7],[4]] => [2,1,3,2] => 11
[[1,3,6,8],[2,4,7],[5]] => [1,2,1,2,2] => 14
[[1,2,6,8],[3,4,7],[5]] => [2,2,2,2] => 12
[[1,4,5,8],[2,6,7],[3]] => [1,1,3,3] => 8
[[1,3,5,8],[2,6,7],[4]] => [1,2,2,3] => 9
[[1,2,5,8],[3,6,7],[4]] => [2,1,2,3] => 10
[[1,3,4,8],[2,6,7],[5]] => [1,3,4] => 5
[[1,2,4,8],[3,6,7],[5]] => [2,2,4] => 6
[[1,2,3,8],[4,6,7],[5]] => [3,1,4] => 7
[[1,3,5,8],[2,4,7],[6]] => [1,2,2,3] => 9
[[1,2,5,8],[3,4,7],[6]] => [2,3,3] => 7
[[1,3,4,8],[2,5,7],[6]] => [1,3,1,3] => 10
[[1,2,4,8],[3,5,7],[6]] => [2,2,1,3] => 11
[[1,2,3,8],[4,5,7],[6]] => [3,2,3] => 8
[[1,3,5,8],[2,4,6],[7]] => [1,2,2,1,2] => 15
[[1,2,5,8],[3,4,6],[7]] => [2,3,1,2] => 13
[[1,3,4,8],[2,5,6],[7]] => [1,3,2,2] => 11
[[1,2,4,8],[3,5,6],[7]] => [2,2,2,2] => 12
[[1,2,3,8],[4,5,6],[7]] => [3,3,2] => 9
[[1,4,6,7],[2,5,8],[3]] => [1,1,2,3,1] => 14
[[1,3,6,7],[2,5,8],[4]] => [1,2,4,1] => 11
[[1,2,6,7],[3,5,8],[4]] => [2,1,4,1] => 12
[[1,3,6,7],[2,4,8],[5]] => [1,2,1,3,1] => 15
[[1,2,6,7],[3,4,8],[5]] => [2,2,3,1] => 13
[[1,4,5,7],[2,6,8],[3]] => [1,1,3,2,1] => 15
[[1,3,5,7],[2,6,8],[4]] => [1,2,2,2,1] => 16
[[1,2,5,7],[3,6,8],[4]] => [2,1,2,2,1] => 17
[[1,3,4,7],[2,6,8],[5]] => [1,3,3,1] => 12
[[1,2,4,7],[3,6,8],[5]] => [2,2,3,1] => 13
[[1,2,3,7],[4,6,8],[5]] => [3,1,3,1] => 14
[[1,3,5,7],[2,4,8],[6]] => [1,2,2,2,1] => 16
[[1,2,5,7],[3,4,8],[6]] => [2,3,2,1] => 14
[[1,3,4,7],[2,5,8],[6]] => [1,3,1,2,1] => 17
[[1,2,4,7],[3,5,8],[6]] => [2,2,1,2,1] => 18
[[1,2,3,7],[4,5,8],[6]] => [3,2,2,1] => 15
[[1,4,5,6],[2,7,8],[3]] => [1,1,4,2] => 9
[[1,3,5,6],[2,7,8],[4]] => [1,2,3,2] => 10
[[1,2,5,6],[3,7,8],[4]] => [2,1,3,2] => 11
[[1,3,4,6],[2,7,8],[5]] => [1,3,2,2] => 11
[[1,2,4,6],[3,7,8],[5]] => [2,2,2,2] => 12
[[1,2,3,6],[4,7,8],[5]] => [3,1,2,2] => 13
[[1,3,4,5],[2,7,8],[6]] => [1,4,3] => 6
[[1,2,4,5],[3,7,8],[6]] => [2,3,3] => 7
[[1,2,3,5],[4,7,8],[6]] => [3,2,3] => 8
[[1,2,3,4],[5,7,8],[6]] => [4,1,3] => 9
[[1,3,5,6],[2,4,8],[7]] => [1,2,3,2] => 10
[[1,2,5,6],[3,4,8],[7]] => [2,4,2] => 8
[[1,3,4,6],[2,5,8],[7]] => [1,3,2,2] => 11
[[1,2,4,6],[3,5,8],[7]] => [2,2,2,2] => 12
[[1,2,3,6],[4,5,8],[7]] => [3,3,2] => 9
[[1,3,4,5],[2,6,8],[7]] => [1,4,1,2] => 12
[[1,2,4,5],[3,6,8],[7]] => [2,3,1,2] => 13
[[1,2,3,5],[4,6,8],[7]] => [3,2,1,2] => 14
[[1,2,3,4],[5,6,8],[7]] => [4,2,2] => 10
[[1,3,5,7],[2,4,6],[8]] => [1,2,2,2,1] => 16
[[1,2,5,7],[3,4,6],[8]] => [2,3,2,1] => 14
[[1,3,4,7],[2,5,6],[8]] => [1,3,3,1] => 12
[[1,2,4,7],[3,5,6],[8]] => [2,2,3,1] => 13
[[1,2,3,7],[4,5,6],[8]] => [3,4,1] => 10
[[1,3,5,6],[2,4,7],[8]] => [1,2,3,1,1] => 17
[[1,2,5,6],[3,4,7],[8]] => [2,4,1,1] => 15
[[1,3,4,6],[2,5,7],[8]] => [1,3,2,1,1] => 18
[[1,2,4,6],[3,5,7],[8]] => [2,2,2,1,1] => 19
[[1,2,3,6],[4,5,7],[8]] => [3,3,1,1] => 16
[[1,3,4,5],[2,6,7],[8]] => [1,4,2,1] => 13
[[1,2,4,5],[3,6,7],[8]] => [2,3,2,1] => 14
[[1,2,3,5],[4,6,7],[8]] => [3,2,2,1] => 15
[[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 11
[[1,4,7,8],[2,5],[3,6]] => [1,1,2,4] => 7
[[1,3,7,8],[2,5],[4,6]] => [1,2,2,3] => 9
[[1,2,7,8],[3,5],[4,6]] => [2,1,2,3] => 10
[[1,3,7,8],[2,4],[5,6]] => [1,2,1,4] => 8
[[1,2,7,8],[3,4],[5,6]] => [2,2,4] => 6
[[1,4,6,8],[2,5],[3,7]] => [1,1,2,2,2] => 13
[[1,3,6,8],[2,5],[4,7]] => [1,2,3,2] => 10
[[1,2,6,8],[3,5],[4,7]] => [2,1,3,2] => 11
[[1,3,6,8],[2,4],[5,7]] => [1,2,1,2,2] => 14
[[1,2,6,8],[3,4],[5,7]] => [2,2,2,2] => 12
[[1,4,5,8],[2,6],[3,7]] => [1,1,3,3] => 8
[[1,3,5,8],[2,6],[4,7]] => [1,2,2,3] => 9
[[1,2,5,8],[3,6],[4,7]] => [2,1,2,3] => 10
[[1,3,4,8],[2,6],[5,7]] => [1,3,2,2] => 11
[[1,2,4,8],[3,6],[5,7]] => [2,2,2,2] => 12
[[1,2,3,8],[4,6],[5,7]] => [3,1,2,2] => 13
[[1,3,5,8],[2,4],[6,7]] => [1,2,2,3] => 9
[[1,2,5,8],[3,4],[6,7]] => [2,3,3] => 7
[[1,3,4,8],[2,5],[6,7]] => [1,3,1,3] => 10
[[1,2,4,8],[3,5],[6,7]] => [2,2,1,3] => 11
[[1,2,3,8],[4,5],[6,7]] => [3,2,3] => 8
[[1,4,6,7],[2,5],[3,8]] => [1,1,2,3,1] => 14
[[1,3,6,7],[2,5],[4,8]] => [1,2,4,1] => 11
[[1,2,6,7],[3,5],[4,8]] => [2,1,4,1] => 12
[[1,3,6,7],[2,4],[5,8]] => [1,2,1,3,1] => 15
[[1,2,6,7],[3,4],[5,8]] => [2,2,3,1] => 13
[[1,4,5,7],[2,6],[3,8]] => [1,1,3,2,1] => 15
[[1,3,5,7],[2,6],[4,8]] => [1,2,2,2,1] => 16
[[1,2,5,7],[3,6],[4,8]] => [2,1,2,2,1] => 17
[[1,3,4,7],[2,6],[5,8]] => [1,3,3,1] => 12
[[1,2,4,7],[3,6],[5,8]] => [2,2,3,1] => 13
[[1,2,3,7],[4,6],[5,8]] => [3,1,3,1] => 14
[[1,3,5,7],[2,4],[6,8]] => [1,2,2,2,1] => 16
[[1,2,5,7],[3,4],[6,8]] => [2,3,2,1] => 14
[[1,3,4,7],[2,5],[6,8]] => [1,3,1,2,1] => 17
[[1,2,4,7],[3,5],[6,8]] => [2,2,1,2,1] => 18
[[1,2,3,7],[4,5],[6,8]] => [3,2,2,1] => 15
[[1,4,5,6],[2,7],[3,8]] => [1,1,4,2] => 9
[[1,3,5,6],[2,7],[4,8]] => [1,2,3,2] => 10
[[1,2,5,6],[3,7],[4,8]] => [2,1,3,2] => 11
[[1,3,4,6],[2,7],[5,8]] => [1,3,2,2] => 11
[[1,2,4,6],[3,7],[5,8]] => [2,2,2,2] => 12
[[1,2,3,6],[4,7],[5,8]] => [3,1,2,2] => 13
[[1,3,4,5],[2,7],[6,8]] => [1,4,2,1] => 13
[[1,2,4,5],[3,7],[6,8]] => [2,3,2,1] => 14
[[1,2,3,5],[4,7],[6,8]] => [3,2,2,1] => 15
[[1,2,3,4],[5,7],[6,8]] => [4,1,2,1] => 16
[[1,3,5,6],[2,4],[7,8]] => [1,2,3,2] => 10
[[1,2,5,6],[3,4],[7,8]] => [2,4,2] => 8
[[1,3,4,6],[2,5],[7,8]] => [1,3,2,2] => 11
[[1,2,4,6],[3,5],[7,8]] => [2,2,2,2] => 12
[[1,2,3,6],[4,5],[7,8]] => [3,3,2] => 9
[[1,3,4,5],[2,6],[7,8]] => [1,4,1,2] => 12
[[1,2,4,5],[3,6],[7,8]] => [2,3,1,2] => 13
[[1,2,3,5],[4,6],[7,8]] => [3,2,1,2] => 14
[[1,2,3,4],[5,6],[7,8]] => [4,2,2] => 10
[[1,5,7,8],[2,6],[3],[4]] => [1,1,1,2,3] => 11
[[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 7
[[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[[1,4,7,8],[2,5],[3],[6]] => [1,1,2,1,3] => 12
[[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3] => 9
[[1,2,7,8],[3,5],[4],[6]] => [2,1,2,3] => 10
[[1,3,7,8],[2,4],[5],[6]] => [1,2,1,1,3] => 13
[[1,2,7,8],[3,4],[5],[6]] => [2,2,1,3] => 11
[[1,5,6,8],[2,7],[3],[4]] => [1,1,1,3,2] => 12
[[1,4,6,8],[2,7],[3],[5]] => [1,1,2,2,2] => 13
[[1,3,6,8],[2,7],[4],[5]] => [1,2,1,2,2] => 14
[[1,2,6,8],[3,7],[4],[5]] => [2,1,1,2,2] => 15
[[1,4,5,8],[2,7],[3],[6]] => [1,1,3,3] => 8
[[1,3,5,8],[2,7],[4],[6]] => [1,2,2,3] => 9
[[1,2,5,8],[3,7],[4],[6]] => [2,1,2,3] => 10
[[1,3,4,8],[2,7],[5],[6]] => [1,3,1,3] => 10
[[1,2,4,8],[3,7],[5],[6]] => [2,2,1,3] => 11
[[1,2,3,8],[4,7],[5],[6]] => [3,1,1,3] => 12
[[1,4,6,8],[2,5],[3],[7]] => [1,1,2,2,2] => 13
[[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => 10
[[1,2,6,8],[3,5],[4],[7]] => [2,1,3,2] => 11
[[1,3,6,8],[2,4],[5],[7]] => [1,2,1,2,2] => 14
[[1,2,6,8],[3,4],[5],[7]] => [2,2,2,2] => 12
[[1,4,5,8],[2,6],[3],[7]] => [1,1,3,1,2] => 14
[[1,3,5,8],[2,6],[4],[7]] => [1,2,2,1,2] => 15
[[1,2,5,8],[3,6],[4],[7]] => [2,1,2,1,2] => 16
[[1,3,4,8],[2,6],[5],[7]] => [1,3,2,2] => 11
[[1,2,4,8],[3,6],[5],[7]] => [2,2,2,2] => 12
[[1,2,3,8],[4,6],[5],[7]] => [3,1,2,2] => 13
[[1,3,5,8],[2,4],[6],[7]] => [1,2,2,1,2] => 15
[[1,2,5,8],[3,4],[6],[7]] => [2,3,1,2] => 13
[[1,3,4,8],[2,5],[6],[7]] => [1,3,1,1,2] => 16
[[1,2,4,8],[3,5],[6],[7]] => [2,2,1,1,2] => 17
[[1,2,3,8],[4,5],[6],[7]] => [3,2,1,2] => 14
[[1,5,6,7],[2,8],[3],[4]] => [1,1,1,4,1] => 13
[[1,4,6,7],[2,8],[3],[5]] => [1,1,2,3,1] => 14
[[1,3,6,7],[2,8],[4],[5]] => [1,2,1,3,1] => 15
[[1,2,6,7],[3,8],[4],[5]] => [2,1,1,3,1] => 16
[[1,4,5,7],[2,8],[3],[6]] => [1,1,3,2,1] => 15
[[1,3,5,7],[2,8],[4],[6]] => [1,2,2,2,1] => 16
[[1,2,5,7],[3,8],[4],[6]] => [2,1,2,2,1] => 17
[[1,3,4,7],[2,8],[5],[6]] => [1,3,1,2,1] => 17
[[1,2,4,7],[3,8],[5],[6]] => [2,2,1,2,1] => 18
[[1,2,3,7],[4,8],[5],[6]] => [3,1,1,2,1] => 19
[[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2] => 9
[[1,3,5,6],[2,8],[4],[7]] => [1,2,3,2] => 10
[[1,2,5,6],[3,8],[4],[7]] => [2,1,3,2] => 11
[[1,3,4,6],[2,8],[5],[7]] => [1,3,2,2] => 11
[[1,2,4,6],[3,8],[5],[7]] => [2,2,2,2] => 12
[[1,2,3,6],[4,8],[5],[7]] => [3,1,2,2] => 13
[[1,3,4,5],[2,8],[6],[7]] => [1,4,1,2] => 12
[[1,2,4,5],[3,8],[6],[7]] => [2,3,1,2] => 13
[[1,2,3,5],[4,8],[6],[7]] => [3,2,1,2] => 14
[[1,2,3,4],[5,8],[6],[7]] => [4,1,1,2] => 15
[[1,4,6,7],[2,5],[3],[8]] => [1,1,2,3,1] => 14
[[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1] => 11
[[1,2,6,7],[3,5],[4],[8]] => [2,1,4,1] => 12
[[1,3,6,7],[2,4],[5],[8]] => [1,2,1,3,1] => 15
[[1,2,6,7],[3,4],[5],[8]] => [2,2,3,1] => 13
[[1,4,5,7],[2,6],[3],[8]] => [1,1,3,2,1] => 15
[[1,3,5,7],[2,6],[4],[8]] => [1,2,2,2,1] => 16
[[1,2,5,7],[3,6],[4],[8]] => [2,1,2,2,1] => 17
[[1,3,4,7],[2,6],[5],[8]] => [1,3,3,1] => 12
[[1,2,4,7],[3,6],[5],[8]] => [2,2,3,1] => 13
[[1,2,3,7],[4,6],[5],[8]] => [3,1,3,1] => 14
[[1,3,5,7],[2,4],[6],[8]] => [1,2,2,2,1] => 16
[[1,2,5,7],[3,4],[6],[8]] => [2,3,2,1] => 14
[[1,3,4,7],[2,5],[6],[8]] => [1,3,1,2,1] => 17
[[1,2,4,7],[3,5],[6],[8]] => [2,2,1,2,1] => 18
[[1,2,3,7],[4,5],[6],[8]] => [3,2,2,1] => 15
[[1,4,5,6],[2,7],[3],[8]] => [1,1,4,1,1] => 16
[[1,3,5,6],[2,7],[4],[8]] => [1,2,3,1,1] => 17
[[1,2,5,6],[3,7],[4],[8]] => [2,1,3,1,1] => 18
[[1,3,4,6],[2,7],[5],[8]] => [1,3,2,1,1] => 18
[[1,2,4,6],[3,7],[5],[8]] => [2,2,2,1,1] => 19
[[1,2,3,6],[4,7],[5],[8]] => [3,1,2,1,1] => 20
[[1,3,4,5],[2,7],[6],[8]] => [1,4,2,1] => 13
[[1,2,4,5],[3,7],[6],[8]] => [2,3,2,1] => 14
[[1,2,3,5],[4,7],[6],[8]] => [3,2,2,1] => 15
[[1,2,3,4],[5,7],[6],[8]] => [4,1,2,1] => 16
[[1,3,5,6],[2,4],[7],[8]] => [1,2,3,1,1] => 17
[[1,2,5,6],[3,4],[7],[8]] => [2,4,1,1] => 15
[[1,3,4,6],[2,5],[7],[8]] => [1,3,2,1,1] => 18
[[1,2,4,6],[3,5],[7],[8]] => [2,2,2,1,1] => 19
[[1,2,3,6],[4,5],[7],[8]] => [3,3,1,1] => 16
[[1,3,4,5],[2,6],[7],[8]] => [1,4,1,1,1] => 19
[[1,2,4,5],[3,6],[7],[8]] => [2,3,1,1,1] => 20
[[1,2,3,5],[4,6],[7],[8]] => [3,2,1,1,1] => 21
[[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 17
[[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3] => 12
[[1,3,7,8],[2],[4],[5],[6]] => [1,2,1,1,3] => 13
[[1,2,7,8],[3],[4],[5],[6]] => [2,1,1,1,3] => 14
[[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[[1,4,6,8],[2],[3],[5],[7]] => [1,1,2,2,2] => 13
[[1,3,6,8],[2],[4],[5],[7]] => [1,2,1,2,2] => 14
[[1,2,6,8],[3],[4],[5],[7]] => [2,1,1,2,2] => 15
[[1,4,5,8],[2],[3],[6],[7]] => [1,1,3,1,2] => 14
[[1,3,5,8],[2],[4],[6],[7]] => [1,2,2,1,2] => 15
[[1,2,5,8],[3],[4],[6],[7]] => [2,1,2,1,2] => 16
[[1,3,4,8],[2],[5],[6],[7]] => [1,3,1,1,2] => 16
[[1,2,4,8],[3],[5],[6],[7]] => [2,2,1,1,2] => 17
[[1,2,3,8],[4],[5],[6],[7]] => [3,1,1,1,2] => 18
[[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[[1,4,6,7],[2],[3],[5],[8]] => [1,1,2,3,1] => 14
[[1,3,6,7],[2],[4],[5],[8]] => [1,2,1,3,1] => 15
[[1,2,6,7],[3],[4],[5],[8]] => [2,1,1,3,1] => 16
[[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1] => 15
[[1,3,5,7],[2],[4],[6],[8]] => [1,2,2,2,1] => 16
[[1,2,5,7],[3],[4],[6],[8]] => [2,1,2,2,1] => 17
[[1,3,4,7],[2],[5],[6],[8]] => [1,3,1,2,1] => 17
[[1,2,4,7],[3],[5],[6],[8]] => [2,2,1,2,1] => 18
[[1,2,3,7],[4],[5],[6],[8]] => [3,1,1,2,1] => 19
[[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1] => 16
[[1,3,5,6],[2],[4],[7],[8]] => [1,2,3,1,1] => 17
[[1,2,5,6],[3],[4],[7],[8]] => [2,1,3,1,1] => 18
[[1,3,4,6],[2],[5],[7],[8]] => [1,3,2,1,1] => 18
[[1,2,4,6],[3],[5],[7],[8]] => [2,2,2,1,1] => 19
[[1,2,3,6],[4],[5],[7],[8]] => [3,1,2,1,1] => 20
[[1,3,4,5],[2],[6],[7],[8]] => [1,4,1,1,1] => 19
[[1,2,4,5],[3],[6],[7],[8]] => [2,3,1,1,1] => 20
[[1,2,3,5],[4],[6],[7],[8]] => [3,2,1,1,1] => 21
[[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => 22
[[1,4,7],[2,5,8],[3,6]] => [1,1,2,3,1] => 14
[[1,3,7],[2,5,8],[4,6]] => [1,2,2,2,1] => 16
[[1,2,7],[3,5,8],[4,6]] => [2,1,2,2,1] => 17
[[1,3,7],[2,4,8],[5,6]] => [1,2,1,3,1] => 15
[[1,2,7],[3,4,8],[5,6]] => [2,2,3,1] => 13
[[1,4,6],[2,5,8],[3,7]] => [1,1,2,2,2] => 13
[[1,3,6],[2,5,8],[4,7]] => [1,2,3,2] => 10
[[1,2,6],[3,5,8],[4,7]] => [2,1,3,2] => 11
[[1,3,6],[2,4,8],[5,7]] => [1,2,1,2,2] => 14
[[1,2,6],[3,4,8],[5,7]] => [2,2,2,2] => 12
[[1,4,5],[2,6,8],[3,7]] => [1,1,3,3] => 8
[[1,3,5],[2,6,8],[4,7]] => [1,2,2,3] => 9
[[1,2,5],[3,6,8],[4,7]] => [2,1,2,3] => 10
[[1,3,4],[2,6,8],[5,7]] => [1,3,2,2] => 11
[[1,2,4],[3,6,8],[5,7]] => [2,2,2,2] => 12
[[1,2,3],[4,6,8],[5,7]] => [3,1,2,2] => 13
[[1,3,5],[2,4,8],[6,7]] => [1,2,2,3] => 9
[[1,2,5],[3,4,8],[6,7]] => [2,3,3] => 7
[[1,3,4],[2,5,8],[6,7]] => [1,3,1,3] => 10
[[1,2,4],[3,5,8],[6,7]] => [2,2,1,3] => 11
[[1,2,3],[4,5,8],[6,7]] => [3,2,3] => 8
[[1,4,6],[2,5,7],[3,8]] => [1,1,2,2,2] => 13
[[1,3,6],[2,5,7],[4,8]] => [1,2,3,2] => 10
[[1,2,6],[3,5,7],[4,8]] => [2,1,3,2] => 11
[[1,3,6],[2,4,7],[5,8]] => [1,2,1,2,2] => 14
[[1,2,6],[3,4,7],[5,8]] => [2,2,2,2] => 12
[[1,4,5],[2,6,7],[3,8]] => [1,1,3,2,1] => 15
[[1,3,5],[2,6,7],[4,8]] => [1,2,2,2,1] => 16
[[1,2,5],[3,6,7],[4,8]] => [2,1,2,2,1] => 17
[[1,3,4],[2,6,7],[5,8]] => [1,3,3,1] => 12
[[1,2,4],[3,6,7],[5,8]] => [2,2,3,1] => 13
[[1,2,3],[4,6,7],[5,8]] => [3,1,3,1] => 14
[[1,3,5],[2,4,7],[6,8]] => [1,2,2,2,1] => 16
[[1,2,5],[3,4,7],[6,8]] => [2,3,2,1] => 14
[[1,3,4],[2,5,7],[6,8]] => [1,3,1,2,1] => 17
[[1,2,4],[3,5,7],[6,8]] => [2,2,1,2,1] => 18
[[1,2,3],[4,5,7],[6,8]] => [3,2,2,1] => 15
[[1,3,5],[2,4,6],[7,8]] => [1,2,2,1,2] => 15
[[1,2,5],[3,4,6],[7,8]] => [2,3,1,2] => 13
[[1,3,4],[2,5,6],[7,8]] => [1,3,2,2] => 11
[[1,2,4],[3,5,6],[7,8]] => [2,2,2,2] => 12
[[1,2,3],[4,5,6],[7,8]] => [3,3,2] => 9
[[1,5,7],[2,6,8],[3],[4]] => [1,1,1,2,2,1] => 18
[[1,4,7],[2,6,8],[3],[5]] => [1,1,2,3,1] => 14
[[1,3,7],[2,6,8],[4],[5]] => [1,2,1,3,1] => 15
[[1,2,7],[3,6,8],[4],[5]] => [2,1,1,3,1] => 16
[[1,4,7],[2,5,8],[3],[6]] => [1,1,2,1,2,1] => 19
[[1,3,7],[2,5,8],[4],[6]] => [1,2,2,2,1] => 16
[[1,2,7],[3,5,8],[4],[6]] => [2,1,2,2,1] => 17
[[1,3,7],[2,4,8],[5],[6]] => [1,2,1,1,2,1] => 20
[[1,2,7],[3,4,8],[5],[6]] => [2,2,1,2,1] => 18
[[1,5,6],[2,7,8],[3],[4]] => [1,1,1,3,2] => 12
[[1,4,6],[2,7,8],[3],[5]] => [1,1,2,2,2] => 13
[[1,3,6],[2,7,8],[4],[5]] => [1,2,1,2,2] => 14
[[1,2,6],[3,7,8],[4],[5]] => [2,1,1,2,2] => 15
[[1,4,5],[2,7,8],[3],[6]] => [1,1,3,3] => 8
[[1,3,5],[2,7,8],[4],[6]] => [1,2,2,3] => 9
[[1,2,5],[3,7,8],[4],[6]] => [2,1,2,3] => 10
[[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => 10
[[1,2,4],[3,7,8],[5],[6]] => [2,2,1,3] => 11
[[1,2,3],[4,7,8],[5],[6]] => [3,1,1,3] => 12
[[1,4,6],[2,5,8],[3],[7]] => [1,1,2,2,2] => 13
[[1,3,6],[2,5,8],[4],[7]] => [1,2,3,2] => 10
[[1,2,6],[3,5,8],[4],[7]] => [2,1,3,2] => 11
[[1,3,6],[2,4,8],[5],[7]] => [1,2,1,2,2] => 14
[[1,2,6],[3,4,8],[5],[7]] => [2,2,2,2] => 12
[[1,4,5],[2,6,8],[3],[7]] => [1,1,3,1,2] => 14
[[1,3,5],[2,6,8],[4],[7]] => [1,2,2,1,2] => 15
[[1,2,5],[3,6,8],[4],[7]] => [2,1,2,1,2] => 16
[[1,3,4],[2,6,8],[5],[7]] => [1,3,2,2] => 11
[[1,2,4],[3,6,8],[5],[7]] => [2,2,2,2] => 12
[[1,2,3],[4,6,8],[5],[7]] => [3,1,2,2] => 13
[[1,3,5],[2,4,8],[6],[7]] => [1,2,2,1,2] => 15
[[1,2,5],[3,4,8],[6],[7]] => [2,3,1,2] => 13
[[1,3,4],[2,5,8],[6],[7]] => [1,3,1,1,2] => 16
[[1,2,4],[3,5,8],[6],[7]] => [2,2,1,1,2] => 17
[[1,2,3],[4,5,8],[6],[7]] => [3,2,1,2] => 14
[[1,4,6],[2,5,7],[3],[8]] => [1,1,2,2,1,1] => 20
[[1,3,6],[2,5,7],[4],[8]] => [1,2,3,1,1] => 17
[[1,2,6],[3,5,7],[4],[8]] => [2,1,3,1,1] => 18
[[1,3,6],[2,4,7],[5],[8]] => [1,2,1,2,1,1] => 21
[[1,2,6],[3,4,7],[5],[8]] => [2,2,2,1,1] => 19
[[1,4,5],[2,6,7],[3],[8]] => [1,1,3,2,1] => 15
[[1,3,5],[2,6,7],[4],[8]] => [1,2,2,2,1] => 16
[[1,2,5],[3,6,7],[4],[8]] => [2,1,2,2,1] => 17
[[1,3,4],[2,6,7],[5],[8]] => [1,3,3,1] => 12
[[1,2,4],[3,6,7],[5],[8]] => [2,2,3,1] => 13
[[1,2,3],[4,6,7],[5],[8]] => [3,1,3,1] => 14
[[1,3,5],[2,4,7],[6],[8]] => [1,2,2,2,1] => 16
[[1,2,5],[3,4,7],[6],[8]] => [2,3,2,1] => 14
[[1,3,4],[2,5,7],[6],[8]] => [1,3,1,2,1] => 17
[[1,2,4],[3,5,7],[6],[8]] => [2,2,1,2,1] => 18
[[1,2,3],[4,5,7],[6],[8]] => [3,2,2,1] => 15
[[1,3,5],[2,4,6],[7],[8]] => [1,2,2,1,1,1] => 22
[[1,2,5],[3,4,6],[7],[8]] => [2,3,1,1,1] => 20
[[1,3,4],[2,5,6],[7],[8]] => [1,3,2,1,1] => 18
[[1,2,4],[3,5,6],[7],[8]] => [2,2,2,1,1] => 19
[[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 16
[[1,5,8],[2,6],[3,7],[4]] => [1,1,1,2,3] => 11
[[1,4,8],[2,6],[3,7],[5]] => [1,1,2,2,2] => 13
[[1,3,8],[2,6],[4,7],[5]] => [1,2,1,2,2] => 14
[[1,2,8],[3,6],[4,7],[5]] => [2,1,1,2,2] => 15
[[1,4,8],[2,5],[3,7],[6]] => [1,1,2,1,3] => 12
[[1,3,8],[2,5],[4,7],[6]] => [1,2,2,3] => 9
[[1,2,8],[3,5],[4,7],[6]] => [2,1,2,3] => 10
[[1,3,8],[2,4],[5,7],[6]] => [1,2,1,1,3] => 13
[[1,2,8],[3,4],[5,7],[6]] => [2,2,1,3] => 11
[[1,4,8],[2,5],[3,6],[7]] => [1,1,2,2,2] => 13
[[1,3,8],[2,5],[4,6],[7]] => [1,2,2,1,2] => 15
[[1,2,8],[3,5],[4,6],[7]] => [2,1,2,1,2] => 16
[[1,3,8],[2,4],[5,6],[7]] => [1,2,1,2,2] => 14
[[1,2,8],[3,4],[5,6],[7]] => [2,2,2,2] => 12
[[1,5,7],[2,6],[3,8],[4]] => [1,1,1,2,2,1] => 18
[[1,4,7],[2,6],[3,8],[5]] => [1,1,2,3,1] => 14
[[1,3,7],[2,6],[4,8],[5]] => [1,2,1,3,1] => 15
[[1,2,7],[3,6],[4,8],[5]] => [2,1,1,3,1] => 16
[[1,4,7],[2,5],[3,8],[6]] => [1,1,2,1,2,1] => 19
[[1,3,7],[2,5],[4,8],[6]] => [1,2,2,2,1] => 16
[[1,2,7],[3,5],[4,8],[6]] => [2,1,2,2,1] => 17
[[1,3,7],[2,4],[5,8],[6]] => [1,2,1,1,2,1] => 20
[[1,2,7],[3,4],[5,8],[6]] => [2,2,1,2,1] => 18
[[1,5,6],[2,7],[3,8],[4]] => [1,1,1,3,2] => 12
[[1,4,6],[2,7],[3,8],[5]] => [1,1,2,2,2] => 13
[[1,3,6],[2,7],[4,8],[5]] => [1,2,1,2,2] => 14
[[1,2,6],[3,7],[4,8],[5]] => [2,1,1,2,2] => 15
[[1,4,5],[2,7],[3,8],[6]] => [1,1,3,2,1] => 15
[[1,3,5],[2,7],[4,8],[6]] => [1,2,2,2,1] => 16
[[1,2,5],[3,7],[4,8],[6]] => [2,1,2,2,1] => 17
[[1,3,4],[2,7],[5,8],[6]] => [1,3,1,2,1] => 17
[[1,2,4],[3,7],[5,8],[6]] => [2,2,1,2,1] => 18
[[1,2,3],[4,7],[5,8],[6]] => [3,1,1,2,1] => 19
[[1,4,6],[2,5],[3,8],[7]] => [1,1,2,2,2] => 13
[[1,3,6],[2,5],[4,8],[7]] => [1,2,3,2] => 10
[[1,2,6],[3,5],[4,8],[7]] => [2,1,3,2] => 11
[[1,3,6],[2,4],[5,8],[7]] => [1,2,1,2,2] => 14
[[1,2,6],[3,4],[5,8],[7]] => [2,2,2,2] => 12
[[1,4,5],[2,6],[3,8],[7]] => [1,1,3,1,2] => 14
[[1,3,5],[2,6],[4,8],[7]] => [1,2,2,1,2] => 15
[[1,2,5],[3,6],[4,8],[7]] => [2,1,2,1,2] => 16
[[1,3,4],[2,6],[5,8],[7]] => [1,3,2,2] => 11
[[1,2,4],[3,6],[5,8],[7]] => [2,2,2,2] => 12
[[1,2,3],[4,6],[5,8],[7]] => [3,1,2,2] => 13
[[1,3,5],[2,4],[6,8],[7]] => [1,2,2,1,2] => 15
[[1,2,5],[3,4],[6,8],[7]] => [2,3,1,2] => 13
[[1,3,4],[2,5],[6,8],[7]] => [1,3,1,1,2] => 16
[[1,2,4],[3,5],[6,8],[7]] => [2,2,1,1,2] => 17
[[1,2,3],[4,5],[6,8],[7]] => [3,2,1,2] => 14
[[1,4,7],[2,5],[3,6],[8]] => [1,1,2,3,1] => 14
[[1,3,7],[2,5],[4,6],[8]] => [1,2,2,2,1] => 16
[[1,2,7],[3,5],[4,6],[8]] => [2,1,2,2,1] => 17
[[1,3,7],[2,4],[5,6],[8]] => [1,2,1,3,1] => 15
[[1,2,7],[3,4],[5,6],[8]] => [2,2,3,1] => 13
[[1,4,6],[2,5],[3,7],[8]] => [1,1,2,2,1,1] => 20
[[1,3,6],[2,5],[4,7],[8]] => [1,2,3,1,1] => 17
[[1,2,6],[3,5],[4,7],[8]] => [2,1,3,1,1] => 18
[[1,3,6],[2,4],[5,7],[8]] => [1,2,1,2,1,1] => 21
[[1,2,6],[3,4],[5,7],[8]] => [2,2,2,1,1] => 19
[[1,4,5],[2,6],[3,7],[8]] => [1,1,3,2,1] => 15
[[1,3,5],[2,6],[4,7],[8]] => [1,2,2,2,1] => 16
[[1,2,5],[3,6],[4,7],[8]] => [2,1,2,2,1] => 17
[[1,3,4],[2,6],[5,7],[8]] => [1,3,2,1,1] => 18
[[1,2,4],[3,6],[5,7],[8]] => [2,2,2,1,1] => 19
[[1,2,3],[4,6],[5,7],[8]] => [3,1,2,1,1] => 20
[[1,3,5],[2,4],[6,7],[8]] => [1,2,2,2,1] => 16
[[1,2,5],[3,4],[6,7],[8]] => [2,3,2,1] => 14
[[1,3,4],[2,5],[6,7],[8]] => [1,3,1,2,1] => 17
[[1,2,4],[3,5],[6,7],[8]] => [2,2,1,2,1] => 18
[[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 15
[[1,6,8],[2,7],[3],[4],[5]] => [1,1,1,1,2,2] => 16
[[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[[1,5,8],[2,6],[3],[4],[7]] => [1,1,1,2,1,2] => 17
[[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2] => 13
[[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2] => 14
[[1,2,8],[3,6],[4],[5],[7]] => [2,1,1,2,2] => 15
[[1,4,8],[2,5],[3],[6],[7]] => [1,1,2,1,1,2] => 18
[[1,3,8],[2,5],[4],[6],[7]] => [1,2,2,1,2] => 15
[[1,2,8],[3,5],[4],[6],[7]] => [2,1,2,1,2] => 16
[[1,3,8],[2,4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[[1,2,8],[3,4],[5],[6],[7]] => [2,2,1,1,2] => 17
[[1,6,7],[2,8],[3],[4],[5]] => [1,1,1,1,3,1] => 17
[[1,5,7],[2,8],[3],[4],[6]] => [1,1,1,2,2,1] => 18
[[1,4,7],[2,8],[3],[5],[6]] => [1,1,2,1,2,1] => 19
[[1,3,7],[2,8],[4],[5],[6]] => [1,2,1,1,2,1] => 20
[[1,2,7],[3,8],[4],[5],[6]] => [2,1,1,1,2,1] => 21
[[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => 12
[[1,4,6],[2,8],[3],[5],[7]] => [1,1,2,2,2] => 13
[[1,3,6],[2,8],[4],[5],[7]] => [1,2,1,2,2] => 14
[[1,2,6],[3,8],[4],[5],[7]] => [2,1,1,2,2] => 15
[[1,4,5],[2,8],[3],[6],[7]] => [1,1,3,1,2] => 14
[[1,3,5],[2,8],[4],[6],[7]] => [1,2,2,1,2] => 15
[[1,2,5],[3,8],[4],[6],[7]] => [2,1,2,1,2] => 16
[[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2] => 16
[[1,2,4],[3,8],[5],[6],[7]] => [2,2,1,1,2] => 17
[[1,2,3],[4,8],[5],[6],[7]] => [3,1,1,1,2] => 18
[[1,5,7],[2,6],[3],[4],[8]] => [1,1,1,2,2,1] => 18
[[1,4,7],[2,6],[3],[5],[8]] => [1,1,2,3,1] => 14
[[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1] => 15
[[1,2,7],[3,6],[4],[5],[8]] => [2,1,1,3,1] => 16
[[1,4,7],[2,5],[3],[6],[8]] => [1,1,2,1,2,1] => 19
[[1,3,7],[2,5],[4],[6],[8]] => [1,2,2,2,1] => 16
[[1,2,7],[3,5],[4],[6],[8]] => [2,1,2,2,1] => 17
[[1,3,7],[2,4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[[1,2,7],[3,4],[5],[6],[8]] => [2,2,1,2,1] => 18
[[1,5,6],[2,7],[3],[4],[8]] => [1,1,1,3,1,1] => 19
[[1,4,6],[2,7],[3],[5],[8]] => [1,1,2,2,1,1] => 20
[[1,3,6],[2,7],[4],[5],[8]] => [1,2,1,2,1,1] => 21
[[1,2,6],[3,7],[4],[5],[8]] => [2,1,1,2,1,1] => 22
[[1,4,5],[2,7],[3],[6],[8]] => [1,1,3,2,1] => 15
[[1,3,5],[2,7],[4],[6],[8]] => [1,2,2,2,1] => 16
[[1,2,5],[3,7],[4],[6],[8]] => [2,1,2,2,1] => 17
[[1,3,4],[2,7],[5],[6],[8]] => [1,3,1,2,1] => 17
[[1,2,4],[3,7],[5],[6],[8]] => [2,2,1,2,1] => 18
[[1,2,3],[4,7],[5],[6],[8]] => [3,1,1,2,1] => 19
[[1,4,6],[2,5],[3],[7],[8]] => [1,1,2,2,1,1] => 20
[[1,3,6],[2,5],[4],[7],[8]] => [1,2,3,1,1] => 17
[[1,2,6],[3,5],[4],[7],[8]] => [2,1,3,1,1] => 18
[[1,3,6],[2,4],[5],[7],[8]] => [1,2,1,2,1,1] => 21
[[1,2,6],[3,4],[5],[7],[8]] => [2,2,2,1,1] => 19
[[1,4,5],[2,6],[3],[7],[8]] => [1,1,3,1,1,1] => 21
[[1,3,5],[2,6],[4],[7],[8]] => [1,2,2,1,1,1] => 22
[[1,2,5],[3,6],[4],[7],[8]] => [2,1,2,1,1,1] => 23
[[1,3,4],[2,6],[5],[7],[8]] => [1,3,2,1,1] => 18
[[1,2,4],[3,6],[5],[7],[8]] => [2,2,2,1,1] => 19
[[1,2,3],[4,6],[5],[7],[8]] => [3,1,2,1,1] => 20
[[1,3,5],[2,4],[6],[7],[8]] => [1,2,2,1,1,1] => 22
[[1,2,5],[3,4],[6],[7],[8]] => [2,3,1,1,1] => 20
[[1,3,4],[2,5],[6],[7],[8]] => [1,3,1,1,1,1] => 23
[[1,2,4],[3,5],[6],[7],[8]] => [2,2,1,1,1,1] => 24
[[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 21
[[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[[1,4,8],[2],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[[1,3,8],[2],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[[1,2,8],[3],[4],[5],[6],[7]] => [2,1,1,1,1,2] => 20
[[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[[1,4,7],[2],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[[1,3,7],[2],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[[1,2,7],[3],[4],[5],[6],[8]] => [2,1,1,1,2,1] => 21
[[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 19
[[1,4,6],[2],[3],[5],[7],[8]] => [1,1,2,2,1,1] => 20
[[1,3,6],[2],[4],[5],[7],[8]] => [1,2,1,2,1,1] => 21
[[1,2,6],[3],[4],[5],[7],[8]] => [2,1,1,2,1,1] => 22
[[1,4,5],[2],[3],[6],[7],[8]] => [1,1,3,1,1,1] => 21
[[1,3,5],[2],[4],[6],[7],[8]] => [1,2,2,1,1,1] => 22
[[1,2,5],[3],[4],[6],[7],[8]] => [2,1,2,1,1,1] => 23
[[1,3,4],[2],[5],[6],[7],[8]] => [1,3,1,1,1,1] => 23
[[1,2,4],[3],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 24
[[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 25
[[1,5],[2,6],[3,7],[4,8]] => [1,1,1,2,2,1] => 18
[[1,4],[2,6],[3,7],[5,8]] => [1,1,2,2,2] => 13
[[1,3],[2,6],[4,7],[5,8]] => [1,2,1,2,2] => 14
[[1,2],[3,6],[4,7],[5,8]] => [2,1,1,2,2] => 15
[[1,4],[2,5],[3,7],[6,8]] => [1,1,2,1,2,1] => 19
[[1,3],[2,5],[4,7],[6,8]] => [1,2,2,2,1] => 16
[[1,2],[3,5],[4,7],[6,8]] => [2,1,2,2,1] => 17
[[1,3],[2,4],[5,7],[6,8]] => [1,2,1,1,2,1] => 20
[[1,2],[3,4],[5,7],[6,8]] => [2,2,1,2,1] => 18
[[1,4],[2,5],[3,6],[7,8]] => [1,1,2,2,2] => 13
[[1,3],[2,5],[4,6],[7,8]] => [1,2,2,1,2] => 15
[[1,2],[3,5],[4,6],[7,8]] => [2,1,2,1,2] => 16
[[1,3],[2,4],[5,6],[7,8]] => [1,2,1,2,2] => 14
[[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => 12
[[1,6],[2,7],[3,8],[4],[5]] => [1,1,1,1,2,2] => 16
[[1,5],[2,7],[3,8],[4],[6]] => [1,1,1,2,2,1] => 18
[[1,4],[2,7],[3,8],[5],[6]] => [1,1,2,1,2,1] => 19
[[1,3],[2,7],[4,8],[5],[6]] => [1,2,1,1,2,1] => 20
[[1,2],[3,7],[4,8],[5],[6]] => [2,1,1,1,2,1] => 21
[[1,5],[2,6],[3,8],[4],[7]] => [1,1,1,2,1,2] => 17
[[1,4],[2,6],[3,8],[5],[7]] => [1,1,2,2,2] => 13
[[1,3],[2,6],[4,8],[5],[7]] => [1,2,1,2,2] => 14
[[1,2],[3,6],[4,8],[5],[7]] => [2,1,1,2,2] => 15
[[1,4],[2,5],[3,8],[6],[7]] => [1,1,2,1,1,2] => 18
[[1,3],[2,5],[4,8],[6],[7]] => [1,2,2,1,2] => 15
[[1,2],[3,5],[4,8],[6],[7]] => [2,1,2,1,2] => 16
[[1,3],[2,4],[5,8],[6],[7]] => [1,2,1,1,1,2] => 19
[[1,2],[3,4],[5,8],[6],[7]] => [2,2,1,1,2] => 17
[[1,5],[2,6],[3,7],[4],[8]] => [1,1,1,2,2,1] => 18
[[1,4],[2,6],[3,7],[5],[8]] => [1,1,2,2,1,1] => 20
[[1,3],[2,6],[4,7],[5],[8]] => [1,2,1,2,1,1] => 21
[[1,2],[3,6],[4,7],[5],[8]] => [2,1,1,2,1,1] => 22
[[1,4],[2,5],[3,7],[6],[8]] => [1,1,2,1,2,1] => 19
[[1,3],[2,5],[4,7],[6],[8]] => [1,2,2,2,1] => 16
[[1,2],[3,5],[4,7],[6],[8]] => [2,1,2,2,1] => 17
[[1,3],[2,4],[5,7],[6],[8]] => [1,2,1,1,2,1] => 20
[[1,2],[3,4],[5,7],[6],[8]] => [2,2,1,2,1] => 18
[[1,4],[2,5],[3,6],[7],[8]] => [1,1,2,2,1,1] => 20
[[1,3],[2,5],[4,6],[7],[8]] => [1,2,2,1,1,1] => 22
[[1,2],[3,5],[4,6],[7],[8]] => [2,1,2,1,1,1] => 23
[[1,3],[2,4],[5,6],[7],[8]] => [1,2,1,2,1,1] => 21
[[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 19
[[1,7],[2,8],[3],[4],[5],[6]] => [1,1,1,1,1,2,1] => 22
[[1,6],[2,8],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[[1,5],[2,8],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[[1,2],[3,8],[4],[5],[6],[7]] => [2,1,1,1,1,2] => 20
[[1,6],[2,7],[3],[4],[5],[8]] => [1,1,1,1,2,1,1] => 23
[[1,5],[2,7],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[[1,2],[3,7],[4],[5],[6],[8]] => [2,1,1,1,2,1] => 21
[[1,5],[2,6],[3],[4],[7],[8]] => [1,1,1,2,1,1,1] => 24
[[1,4],[2,6],[3],[5],[7],[8]] => [1,1,2,2,1,1] => 20
[[1,3],[2,6],[4],[5],[7],[8]] => [1,2,1,2,1,1] => 21
[[1,2],[3,6],[4],[5],[7],[8]] => [2,1,1,2,1,1] => 22
[[1,4],[2,5],[3],[6],[7],[8]] => [1,1,2,1,1,1,1] => 25
[[1,3],[2,5],[4],[6],[7],[8]] => [1,2,2,1,1,1] => 22
[[1,2],[3,5],[4],[6],[7],[8]] => [2,1,2,1,1,1] => 23
[[1,3],[2,4],[5],[6],[7],[8]] => [1,2,1,1,1,1,1] => 26
[[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 24
[[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2] => 21
[[1,7],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,1] => 22
[[1,6],[2],[3],[4],[5],[7],[8]] => [1,1,1,1,2,1,1] => 23
[[1,5],[2],[3],[4],[6],[7],[8]] => [1,1,1,2,1,1,1] => 24
[[1,4],[2],[3],[5],[6],[7],[8]] => [1,1,2,1,1,1,1] => 25
[[1,3],[2],[4],[5],[6],[7],[8]] => [1,2,1,1,1,1,1] => 26
[[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 27
[[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1] => 28
[[1,3,4,5,9],[2,6,7,8,10]] => [1,4,4,1] => 15
[[1,2,4,6,7],[3,5,8,9,10]] => [2,2,3,3] => 13
[[1,2,3,6,8],[4,5,7,9,10]] => [3,3,2,2] => 17
[[1,2,3,5,7],[4,6,8,9,10]] => [3,2,2,3] => 15
[[1,2,3,4,5],[6,7,8,9,10]] => [5,5] => 5
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [2,2,2,2,2,2] => 30
[[1,2,4,6,7,8],[3,5,9,10,11,12]] => [2,2,4,4] => 14
[[1,2,3,6,8,9],[4,5,7,10,11,12]] => [3,3,3,3] => 18
[[1,2,3,5,7,8],[4,6,9,10,11,12]] => [3,2,3,4] => 16
[[1,2,3,5,6,9],[4,7,8,10,11,12]] => [3,3,3,3] => 18
[[1,2,3,4,8,10],[5,6,7,9,11,12]] => [4,4,2,2] => 22
[[1,2,3,4,7,9],[5,6,8,10,11,12]] => [4,3,2,3] => 20
[[1,2,3,4,6,8],[5,7,9,10,11,12]] => [4,2,2,4] => 18
[[1,2,3,4,5,6],[7,8,9,10,11,12]] => [6,6] => 6
[[1,2,3,4,5,6,7,8],[9]] => [8,1] => 8
[[1,2,3,4,5,6,7],[8],[9]] => [7,1,1] => 15
[[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 14
[[1,2,3,4,5,6,7,8,9],[10]] => [9,1] => 9
[[1,2,3,4,5,6,7,8],[9],[10]] => [8,1,1] => 17
[[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => 21
[[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => 17
[[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 33
[[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 29
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 41
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [1,1,1,1,1,1,1,1,1,1] => 45
[[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => [4,4,2,2] => 22
[[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 38
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [2,2,2,2,2,2] => 30
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [1,1,1,1,1,1,1,1,1,1,1,1] => 66
[[1,3,4,5,6,7,8,9],[2]] => [1,8] => 1
[[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => 1
[[1,4,5,6],[2,8,9,10],[3],[7]] => [1,1,4,4] => 9
[[1,2,7],[3,4,10],[5,6],[8,9]] => [2,2,3,3] => 13
[[1,6,7],[2,9,10],[3],[4],[5],[8]] => [1,1,1,1,3,3] => 17
[[1,4],[2,6],[3,8],[5,10],[7],[9]] => [1,1,2,2,2,2] => 21
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [1,1,1,1,1,1,2,2] => 29
[[1,4,5,6,7],[2,9,10,11,12],[3],[8]] => [1,1,5,5] => 10
[[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => [2,2,4,4] => 14
[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => [1,1,2,2,3,3] => 22
[[1,5,8],[2,6,9],[3,7],[4]] => [1,1,1,2,3,1] => 19
[[1,8],[2,9],[3,10],[4],[5],[6],[7]] => [1,1,1,1,1,1,2,2] => 29
[[1,8,10],[2,9],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2,2] => 29
[[1,4,6,8,10],[2,5,7,9],[3]] => [1,1,2,2,2,2] => 21
[[1,3,6],[2,4,7],[5,8],[9]] => [1,2,1,2,2,1] => 22
[[1,2,3,4,5,6,8],[7,9]] => [6,2,1] => 14
[[1,4],[2,5],[3,6],[7],[8],[9],[10]] => [1,1,2,2,1,1,1,1] => 37
[[1,2,4],[3,5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 41
[[1,2,4,6,8],[3,5,7,9],[10]] => [2,2,2,2,1,1] => 29
[[1,2],[3,4],[5,8],[6,9],[7,10]] => [2,2,1,1,2,2] => 25
[[1,2],[3,5],[4,7],[6,8],[9,10]] => [2,1,2,2,1,2] => 25
[[1,2],[3,6],[4,7],[5,8],[9,10]] => [2,1,1,2,2,2] => 23
[[1,2],[3,6],[4,8],[5,9],[7,10]] => [2,1,1,2,2,2] => 23
[[1,4],[2,5],[3,6],[7,8],[9,10]] => [1,1,2,2,2,2] => 21
[[1,4],[2,6],[3,7],[5,8],[9,10]] => [1,1,2,2,2,2] => 21
[[1,4],[2,6],[3,8],[5,9],[7,10]] => [1,1,2,2,2,2] => 21
[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]] => [2,1,2,1,1,2,1,2] => 42
[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]] => [2,1,1,2,1,1,2,2] => 40
[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]] => [2,1,1,1,2,2,1,2] => 40
[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]] => [2,1,1,1,1,2,2,2] => 38
[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]] => [1,1,2,2,1,1,2,2] => 38
[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]] => [1,1,2,1,2,2,1,2] => 38
[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]] => [1,1,2,1,1,2,2,2] => 36
[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]] => [1,1,2,1,1,2,2,2] => 36
[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]] => [1,1,2,2,1,1,2,2] => 38
[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]] => [1,1,2,1,2,2,1,2] => 38
[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]] => [1,1,2,1,1,2,2,2] => 36
[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]] => [1,1,1,1,2,2,2,2] => 34
[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]] => [1,1,1,1,2,2,2,2] => 34
[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]] => [1,1,1,1,2,2,2,2] => 34
[[1,2,3,4,5,10],[6,7,8,9]] => [5,5] => 5
[[1,2,3,4,10],[5,6,7],[8],[9]] => [4,3,1,2] => 19
[[1,2,3,10],[4,5,6],[7,8],[9]] => [3,3,2,2] => 17
[[1,2,3,10],[4,5],[6,7],[8,9]] => [3,2,2,3] => 15
[[1,2,3,10],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,2] => 29
[[1,2,10],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,2] => 27
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,2] => 35
[[1,3,6,8],[2,7,9],[4],[5]] => [1,2,1,2,2,1] => 22
[[1,5,8],[2,6],[3,7],[4,9]] => [1,1,1,2,3,1] => 19
[[1,2,8],[3,4],[5,6],[7,9],[10]] => [2,2,2,2,1,1] => 29
[[1,6,8],[2,9],[3],[4],[5],[7],[10]] => [1,1,1,1,2,2,1,1] => 33
[[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => [1,1,1,1,1,1,2,2] => 29
[[1,3,4,5,6,7,8],[2,9]] => [1,7,1] => 9
[[1,3,4,5,6,7,8],[2],[9]] => [1,7,1] => 9
[[1,3,4,5,6,7],[2,8,9]] => [1,6,2] => 8
[[1,3,4,5,6,7],[2,9],[8]] => [1,6,2] => 8
[[1,3,4,5,6,7],[2],[8],[9]] => [1,6,1,1] => 16
[[1,3,4,5,6],[2,8],[7,9]] => [1,5,2,1] => 15
[[1,3,4,5,6],[2,8],[7],[9]] => [1,5,2,1] => 15
[[1,3,4,5],[2,7,8],[6,9]] => [1,4,3,1] => 14
[[1,3,4,5],[2,7,8],[6],[9]] => [1,4,3,1] => 14
[[1,3,4,5],[2,7],[6,9],[8]] => [1,4,2,2] => 13
[[1,3,4,5],[2],[6],[7],[8],[9]] => [1,4,1,1,1,1] => 27
[[1,3,4],[2,6],[5],[7],[8],[9]] => [1,3,2,1,1,1] => 26
[[1,3,4,5,6,7,8,9],[2,10]] => [1,8,1] => 10
[[1,3,4,5,6,7,8,9],[2],[10]] => [1,8,1] => 10
[[1,3,4,5,6,7,8],[2],[9],[10]] => [1,7,1,1] => 18
[[1,3,4,5,6,7],[2,9],[8,10]] => [1,6,2,1] => 17
[[1,3,4,5,6,7],[2,9],[8],[10]] => [1,6,2,1] => 17
[[1,3,4,5,6],[2,8,9],[7,10]] => [1,5,3,1] => 16
[[1,3,4,5,6],[2,8,9],[7],[10]] => [1,5,3,1] => 16
[[1,3,4,5,6],[2],[7],[8],[9],[10]] => [1,5,1,1,1,1] => 31
[[1,3,4,5],[2,7,8,9],[6,10]] => [1,4,4,1] => 15
[[1,3,4,5],[2,7,8,9],[6],[10]] => [1,4,4,1] => 15
[[1,2,4,6,7,9,10],[3,5,8]] => [2,2,3,3] => 13
[[1,2,3,5,6,8,10],[4,7,9]] => [3,3,2,2] => 17
[[1,2,3,5,7,9,10],[4,6,8]] => [3,2,2,3] => 15
[[1,2,3,4,5,8,9,10],[6,7]] => [5,5] => 5
[[1,2,3,4,5,7,8,9,10],[6]] => [5,5] => 5
[[1,2,4,6,8,10,12],[3,5,7,9,11]] => [2,2,2,2,2,2] => 30
[[1,2,4,6,7,8,11,12],[3,5,9,10]] => [2,2,4,4] => 14
[[1,2,4,6,7,8,10,11,12],[3,5,9]] => [2,2,4,4] => 14
[[1,2,3,4,6,8,11,12],[5,7,9,10]] => [4,2,2,4] => 18
[[1,2,3,4,7,8,10,12],[5,6,9,11]] => [4,4,2,2] => 22
[[1,2,3,4,7,9,11,12],[5,6,8,10]] => [4,3,2,3] => 20
[[1,2,3,5,6,9,11,12],[4,7,8,10]] => [3,3,3,3] => 18
[[1,2,3,5,7,8,11,12],[4,6,9,10]] => [3,2,3,4] => 16
[[1,2,3,5,7,8,10,11,12],[4,6,9]] => [3,2,3,4] => 16
[[1,2,3,5,6,8,9,11,12],[4,7,10]] => [3,3,3,3] => 18
[[1,2,3,4,5,6,10,11,12],[7,8,9]] => [6,6] => 6
[[1,2,3,4,6,7,8,10,12],[5,9,11]] => [4,4,2,2] => 22
[[1,2,3,4,6,7,9,11,12],[5,8,10]] => [4,3,2,3] => 20
[[1,2,3,4,6,8,10,11,12],[5,7,9]] => [4,2,2,4] => 18
[[1,2,3,4,5,6,9,10,11,12],[7,8]] => [6,6] => 6
[[1,2,3,4,5,6,8,9,10,11,12],[7]] => [6,6] => 6
[[1,4,5,6,7,8],[2],[3],[9]] => [1,1,6,1] => 11
[[1,3,6,7,8],[2,5],[4,9]] => [1,2,5,1] => 12
[[1,3,6,7,8],[2,5],[4],[9]] => [1,2,5,1] => 12
[[1,3,4,8],[2,6,7],[5,9]] => [1,3,4,1] => 13
[[1,3,4,8],[2,6,7],[5],[9]] => [1,3,4,1] => 13
[[1,2,7,8],[3,4],[5,6],[9]] => [2,2,4,1] => 14
[[1,6,7,8],[2],[3],[4],[5],[9]] => [1,1,1,1,4,1] => 18
[[1,5,8],[2,7],[3],[4],[6],[9]] => [1,1,1,2,3,1] => 19
[[1,4,5,6,7,8,9],[2],[3],[10]] => [1,1,7,1] => 12
[[1,3,6,7,8,9],[2,5],[4,10]] => [1,2,6,1] => 13
[[1,3,6,7,8,9],[2,5],[4],[10]] => [1,2,6,1] => 13
[[1,3,4,8,9],[2,6,7],[5,10]] => [1,3,5,1] => 14
[[1,3,4,8,9],[2,6,7],[5],[10]] => [1,3,5,1] => 14
[[1,6,7,8,9],[2],[3],[4],[5],[10]] => [1,1,1,1,5,1] => 19
[[1,2,5,6,10],[3,8,9],[4],[7]] => [2,1,3,4] => 11
[[1,2,4,7],[3,6,10],[5,9],[8]] => [2,2,3,3] => 13
[[1,2,7,10],[3,9],[4],[5],[6],[8]] => [2,1,1,1,2,3] => 21
[[1,2,6],[3,8],[4,10],[5],[7],[9]] => [2,1,1,2,2,2] => 23
[[1,2,5,6,7,8],[3],[4],[9]] => [2,1,5,1] => 13
[[1,2,5,6,9,10],[3,8],[4],[7]] => [2,1,3,4] => 11
[[1,6,10,12],[2,7,11],[3,8],[4,9],[5]] => [1,1,1,1,2,2,2,2] => 34
[[1,6,10],[2,7,11],[3,8,12],[4,9],[5]] => [1,1,1,1,2,2,2,2] => 34
[[1,6,8,10,12],[2,7,9,11],[3],[4],[5]] => [1,1,1,1,2,2,2,2] => 34
[[1,4],[2,6],[3],[5],[7],[8],[9],[10]] => [1,1,2,2,1,1,1,1] => 37
[[1,4],[2,8],[3],[5],[6],[7],[9],[10]] => [1,1,2,1,1,2,1,1] => 35
[[1,6],[2,8],[3],[4],[5],[7],[9],[10]] => [1,1,1,1,2,2,1,1] => 33
[[1,4],[2,6],[3,8],[5,10],[7],[9],[11],[12]] => [1,1,2,2,2,2,1,1] => 42
[[1,4],[2,6],[3],[5],[7],[8],[9],[10],[11],[12]] => [1,1,2,2,1,1,1,1,1,1] => 58
[[1,4],[2,8],[3,9],[5],[6],[7],[10],[11],[12]] => [1,1,2,1,1,2,1,1,1,1] => 56
[[1,4],[2,10],[3],[5],[6],[7],[8],[9],[11],[12]] => [1,1,2,1,1,1,1,2,1,1] => 54
[[1,4],[2,8],[3],[5],[6],[7],[9],[10],[11],[12]] => [1,1,2,1,1,2,1,1,1,1] => 56
[[1,6],[2,8],[3,9],[4],[5],[7],[10],[11],[12]] => [1,1,1,1,2,2,1,1,1,1] => 54
[[1,6],[2,7],[3,10],[4],[5],[8],[9],[11],[12]] => [1,1,1,1,2,1,1,2,1,1] => 52
[[1,8],[2,10],[3],[4],[5],[6],[7],[9],[11],[12]] => [1,1,1,1,1,1,2,2,1,1] => 50
[[1,6],[2,10],[3],[4],[5],[7],[8],[9],[11],[12]] => [1,1,1,1,2,1,1,2,1,1] => 52
[[1,6],[2,8],[3],[4],[5],[7],[9],[10],[11],[12]] => [1,1,1,1,2,2,1,1,1,1] => 54
[[1,2,3,4,5,6,8],[7],[9]] => [6,2,1] => 14
[[1,2,4],[3],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 41
[[1,2,3],[4,5,6],[7,8,10],[9]] => [3,3,2,2] => 17
[[1,2,3,5,6],[4,8],[7,10],[9]] => [3,3,2,2] => 17
[[1,2,3,7],[4,5,8,10],[6,9]] => [3,2,2,3] => 15
[[1,2,4,7,10],[3,6,9],[5,8]] => [2,2,3,3] => 13
[[1,2,3,5,7,10],[4,6,9],[8]] => [3,2,2,3] => 15
[[1,2,7,10],[3,8],[4,9],[5],[6]] => [2,1,1,1,2,3] => 21
[[1,2,7,9,10],[3,8],[4],[5],[6]] => [2,1,1,1,2,3] => 21
[[1,2,6,10],[3,7],[4,8],[5,9]] => [2,1,1,2,2,2] => 23
[[1,2,6,8,10],[3,7,9],[4],[5]] => [2,1,1,2,2,2] => 23
[[1,2,4,8],[3,5],[6,9],[7,10]] => [2,2,1,1,2,2] => 25
[[1,2,5,7],[3,6],[4,8],[9,10]] => [2,1,2,2,1,2] => 25
[[1,2,6,8],[3,7],[4,9],[5,10]] => [2,1,1,2,2,2] => 23
[[1,2,3,4],[5,6],[7,9],[8,10],[11,12]] => [4,2,1,2,1,2] => 36
[[1,2,3,5],[4,6],[7,8],[9,10],[11,12]] => [3,2,1,2,2,2] => 32
[[1,2,3,5],[4,7],[6,9],[8,10],[11,12]] => [3,2,2,2,1,2] => 34
[[1,2,3,5],[4,8],[6,9],[7,10],[11,12]] => [3,2,1,2,2,2] => 32
[[1,2,3,5],[4,8],[6,10],[7,11],[9,12]] => [3,2,1,2,2,2] => 32
[[1,2,4,6],[3,5],[7,8],[9,10],[11,12]] => [2,2,2,2,2,2] => 30
[[1,2,4,6],[3,7],[5,8],[9,10],[11,12]] => [2,2,2,2,2,2] => 30
[[1,2,4,6],[3,8],[5,9],[7,10],[11,12]] => [2,2,2,2,2,2] => 30
[[1,2,4,6],[3,8],[5,10],[7,11],[9,12]] => [2,2,2,2,2,2] => 30
[[1,2,5,8],[3,6],[4,7],[9,10],[11,12]] => [2,1,2,3,2,2] => 28
[[1,2,8],[3,9],[4,10],[5,11],[6,12],[7]] => [2,1,1,1,1,2,2,2] => 38
[[1,3,4,7],[2,8],[5],[6],[9]] => [1,3,1,2,1,1] => 25
[[1,3,4,5,6,9],[2],[7],[8]] => [1,5,1,2] => 14
[[1,3,4,5,6,7,10],[2],[8],[9]] => [1,6,1,2] => 16
[[1,5,8],[2,7],[3,9],[4],[6]] => [1,1,1,2,3,1] => 19
[[1,4,8],[2,6,10],[3,7],[5,9]] => [1,1,2,2,2,2] => 21
[[1,4,8,10],[2,6],[3,7],[5,9]] => [1,1,2,2,2,2] => 21
[[1,4,6,8],[2,7,9,10],[3],[5]] => [1,1,2,2,2,2] => 21
[[1,4,6,8,10],[2,7,9],[3],[5]] => [1,1,2,2,2,2] => 21
[[1,5,8],[2,6],[3,7],[4],[9]] => [1,1,1,2,3,1] => 19
[[1,5,7,8],[2,6],[3],[4],[9]] => [1,1,1,2,3,1] => 19
[[1,3,6,8],[2,4,7],[5,9]] => [1,2,1,2,2,1] => 22
[[1,3,5,6,7,8],[2,4],[9]] => [1,2,5,1] => 12
[[1,2,4,6,7,8],[3,5,9]] => [2,2,4,1] => 14
[[1,6],[2,7],[3,8],[4,9],[5],[10]] => [1,1,1,1,2,2,1,1] => 33
[[1,6,8],[2,7,9],[3],[4],[5],[10]] => [1,1,1,1,2,2,1,1] => 33
[[1,4,8],[2,5,9],[3,6],[7,10]] => [1,1,2,2,2,2] => 21
[[1,3,5,6,7,8,9],[2,4],[10]] => [1,2,6,1] => 13
[[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,2] => 35
[[1,2,7],[3,8,10],[4,9],[5],[6]] => [2,1,1,1,2,3] => 21
[[1,2,6],[3,7,10],[4,8],[5,9]] => [2,1,1,2,2,2] => 23
[[1,2,6,8],[3,7,9,10],[4],[5]] => [2,1,1,2,2,2] => 23
[[1,2,4,8],[3,5,9],[6,10],[7,11],[12]] => [2,2,1,1,2,2,1,1] => 46
[[1,4,8],[2,5,9],[3,6,10],[7,11],[12]] => [1,1,2,2,2,2,1,1] => 42
[[1,2,3,4,6],[5,9,10],[7],[8]] => [4,2,1,3] => 17
[[1,2,4,7],[3,5,6,10],[8,9]] => [2,2,3,3] => 13
[[1,2,3,5,7],[4,6,9,10],[8]] => [3,2,2,3] => 15
[[1,2,5],[3,6,10],[4,7],[8],[9]] => [2,1,2,2,1,2] => 25
[[1,2,5,10],[3,6],[4,7],[8],[9]] => [2,1,2,2,1,2] => 25
[[1,2,3,5,10],[4,6],[7],[8],[9]] => [3,2,1,1,1,2] => 29
[[1,2,4,6],[3,5,7,10],[8],[9]] => [2,2,2,1,1,2] => 27
[[1,2,4,6,10],[3,5,7],[8],[9]] => [2,2,2,1,1,2] => 27
[[1,2,4,6,8],[3,5,7,9],[10],[11],[12]] => [2,2,2,2,1,1,1,1] => 50
[[1,3,6],[2,7],[4,8],[5],[9]] => [1,2,1,2,2,1] => 22
[[1,3,4,6],[2,7],[5],[8],[9]] => [1,3,2,1,1,1] => 26
[[1,3,4,5,6,8],[2,9],[7]] => [1,5,2,1] => 15
[[1,3,4,5,7,9],[2,6,8]] => [1,4,2,2] => 13
[[1,3,4,5,6,7,9],[2,8]] => [1,6,2] => 8
[[1,4,6],[2,5,7],[3],[8],[9],[10]] => [1,1,2,2,1,1,1,1] => 37
[[1,3,4,5,6,7,9],[2,10],[8]] => [1,6,2,1] => 17
[[1,2,4,8],[3,5,9],[6,10],[7]] => [2,2,1,1,2,2] => 25
[[1,2,3,4,7,10],[5,6],[8],[9]] => [4,3,1,2] => 19
[[1,2,3,5],[4,6,8],[7],[9],[10]] => [3,2,1,2,1,1] => 31
[[1,2,4],[3,6],[5,8],[7],[9],[10]] => [2,2,2,2,1,1] => 29
[[1,3,5,8],[2,4,6],[7],[9]] => [1,2,2,1,2,1] => 23
[[1,3,6],[2,7],[4,8],[5,9]] => [1,2,1,2,2,1] => 22
[[1,4,6],[2,5],[3,8],[7,10],[9]] => [1,1,2,2,2,2] => 21
[[1,4,6],[2,5],[3],[7],[8],[9],[10]] => [1,1,2,2,1,1,1,1] => 37
[[1,4,6,8,9],[2,7,10,11,12],[3],[5]] => [1,1,2,2,3,3] => 22
[[1,4,5,8,10],[2,7,9,11,12],[3],[6]] => [1,1,3,3,2,2] => 26
[[1,4,5,7,9],[2,8,10,11,12],[3],[6]] => [1,1,3,2,2,3] => 24
[[1,6,7,8,9],[2,10],[3],[4],[5]] => [1,1,1,1,5,1] => 19
[[1,4,5,6,7,8],[2,9],[3]] => [1,1,6,1] => 11
[[1,6,7,8],[2,9],[3],[4],[5]] => [1,1,1,1,4,1] => 18
[[1,4,5,6,7,8,9],[2,10],[3]] => [1,1,7,1] => 12
[[1,4,8],[2,6],[3,9],[5,10],[7]] => [1,1,2,2,2,2] => 21
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,1,1 1,1,2,2,2,1,1 1,1,2,3,4,4,4,3,2,1,1 1,1,2,4,5,7,9,10,9,9,7,5,3,2,1,1 1,1,2,4,6,9,13,17,20,23,24,24,21,20,15,12,8,5,3,2,1,1 1,1,2,4,7,10,16,23,32,40,50,56,62,68,67,63,59,50,43,32,27,18,13,8,5,3,2,1,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + q + q^{2} + q^{3}$
$F_{4} = 1 + q + 2\ q^{2} + 2\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{5} = 1 + q + 2\ q^{2} + 3\ q^{3} + 4\ q^{4} + 4\ q^{5} + 4\ q^{6} + 3\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$
$F_{6} = 1 + q + 2\ q^{2} + 4\ q^{3} + 5\ q^{4} + 7\ q^{5} + 9\ q^{6} + 10\ q^{7} + 9\ q^{8} + 9\ q^{9} + 7\ q^{10} + 5\ q^{11} + 3\ q^{12} + 2\ q^{13} + q^{14} + q^{15}$
$F_{7} = 1 + q + 2\ q^{2} + 4\ q^{3} + 6\ q^{4} + 9\ q^{5} + 13\ q^{6} + 17\ q^{7} + 20\ q^{8} + 23\ q^{9} + 24\ q^{10} + 24\ q^{11} + 21\ q^{12} + 20\ q^{13} + 15\ q^{14} + 12\ q^{15} + 8\ q^{16} + 5\ q^{17} + 3\ q^{18} + 2\ q^{19} + q^{20} + q^{21}$
$F_{8} = 1 + q + 2\ q^{2} + 4\ q^{3} + 7\ q^{4} + 10\ q^{5} + 16\ q^{6} + 23\ q^{7} + 32\ q^{8} + 40\ q^{9} + 50\ q^{10} + 56\ q^{11} + 62\ q^{12} + 68\ q^{13} + 67\ q^{14} + 63\ q^{15} + 59\ q^{16} + 50\ q^{17} + 43\ q^{18} + 32\ q^{19} + 27\ q^{20} + 18\ q^{21} + 13\ q^{22} + 8\ q^{23} + 5\ q^{24} + 3\ q^{25} + 2\ q^{26} + q^{27} + q^{28}$
Description
The major index of the composition.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!