Identifier
-
Mp00083:
Standard tableaux
—shape⟶
Integer partitions
St000185: Integer partitions ⟶ ℤ
Values
[[1]] => [1] => 0
[[1,2]] => [2] => 0
[[1],[2]] => [1,1] => 1
[[1,2,3]] => [3] => 0
[[1,3],[2]] => [2,1] => 1
[[1,2],[3]] => [2,1] => 1
[[1],[2],[3]] => [1,1,1] => 3
[[1,2,3,4]] => [4] => 0
[[1,3,4],[2]] => [3,1] => 1
[[1,2,4],[3]] => [3,1] => 1
[[1,2,3],[4]] => [3,1] => 1
[[1,3],[2,4]] => [2,2] => 2
[[1,2],[3,4]] => [2,2] => 2
[[1,4],[2],[3]] => [2,1,1] => 3
[[1,3],[2],[4]] => [2,1,1] => 3
[[1,2],[3],[4]] => [2,1,1] => 3
[[1],[2],[3],[4]] => [1,1,1,1] => 6
[[1,2,3,4,5]] => [5] => 0
[[1,3,4,5],[2]] => [4,1] => 1
[[1,2,4,5],[3]] => [4,1] => 1
[[1,2,3,5],[4]] => [4,1] => 1
[[1,2,3,4],[5]] => [4,1] => 1
[[1,3,5],[2,4]] => [3,2] => 2
[[1,2,5],[3,4]] => [3,2] => 2
[[1,3,4],[2,5]] => [3,2] => 2
[[1,2,4],[3,5]] => [3,2] => 2
[[1,2,3],[4,5]] => [3,2] => 2
[[1,4,5],[2],[3]] => [3,1,1] => 3
[[1,3,5],[2],[4]] => [3,1,1] => 3
[[1,2,5],[3],[4]] => [3,1,1] => 3
[[1,3,4],[2],[5]] => [3,1,1] => 3
[[1,2,4],[3],[5]] => [3,1,1] => 3
[[1,2,3],[4],[5]] => [3,1,1] => 3
[[1,4],[2,5],[3]] => [2,2,1] => 4
[[1,3],[2,5],[4]] => [2,2,1] => 4
[[1,2],[3,5],[4]] => [2,2,1] => 4
[[1,3],[2,4],[5]] => [2,2,1] => 4
[[1,2],[3,4],[5]] => [2,2,1] => 4
[[1,5],[2],[3],[4]] => [2,1,1,1] => 6
[[1,4],[2],[3],[5]] => [2,1,1,1] => 6
[[1,3],[2],[4],[5]] => [2,1,1,1] => 6
[[1,2],[3],[4],[5]] => [2,1,1,1] => 6
[[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]] => [5,1] => 1
[[1,2,4,5,6],[3]] => [5,1] => 1
[[1,2,3,5,6],[4]] => [5,1] => 1
[[1,2,3,4,6],[5]] => [5,1] => 1
[[1,2,3,4,5],[6]] => [5,1] => 1
[[1,3,5,6],[2,4]] => [4,2] => 2
[[1,2,5,6],[3,4]] => [4,2] => 2
[[1,3,4,6],[2,5]] => [4,2] => 2
[[1,2,4,6],[3,5]] => [4,2] => 2
[[1,2,3,6],[4,5]] => [4,2] => 2
[[1,3,4,5],[2,6]] => [4,2] => 2
[[1,2,4,5],[3,6]] => [4,2] => 2
[[1,2,3,5],[4,6]] => [4,2] => 2
[[1,2,3,4],[5,6]] => [4,2] => 2
[[1,4,5,6],[2],[3]] => [4,1,1] => 3
[[1,3,5,6],[2],[4]] => [4,1,1] => 3
[[1,2,5,6],[3],[4]] => [4,1,1] => 3
[[1,3,4,6],[2],[5]] => [4,1,1] => 3
[[1,2,4,6],[3],[5]] => [4,1,1] => 3
[[1,2,3,6],[4],[5]] => [4,1,1] => 3
[[1,3,4,5],[2],[6]] => [4,1,1] => 3
[[1,2,4,5],[3],[6]] => [4,1,1] => 3
[[1,2,3,5],[4],[6]] => [4,1,1] => 3
[[1,2,3,4],[5],[6]] => [4,1,1] => 3
[[1,3,5],[2,4,6]] => [3,3] => 3
[[1,2,5],[3,4,6]] => [3,3] => 3
[[1,3,4],[2,5,6]] => [3,3] => 3
[[1,2,4],[3,5,6]] => [3,3] => 3
[[1,2,3],[4,5,6]] => [3,3] => 3
[[1,4,6],[2,5],[3]] => [3,2,1] => 4
[[1,3,6],[2,5],[4]] => [3,2,1] => 4
[[1,2,6],[3,5],[4]] => [3,2,1] => 4
[[1,3,6],[2,4],[5]] => [3,2,1] => 4
[[1,2,6],[3,4],[5]] => [3,2,1] => 4
[[1,4,5],[2,6],[3]] => [3,2,1] => 4
[[1,3,5],[2,6],[4]] => [3,2,1] => 4
[[1,2,5],[3,6],[4]] => [3,2,1] => 4
[[1,3,4],[2,6],[5]] => [3,2,1] => 4
[[1,2,4],[3,6],[5]] => [3,2,1] => 4
[[1,2,3],[4,6],[5]] => [3,2,1] => 4
[[1,3,5],[2,4],[6]] => [3,2,1] => 4
[[1,2,5],[3,4],[6]] => [3,2,1] => 4
[[1,3,4],[2,5],[6]] => [3,2,1] => 4
[[1,2,4],[3,5],[6]] => [3,2,1] => 4
[[1,2,3],[4,5],[6]] => [3,2,1] => 4
[[1,5,6],[2],[3],[4]] => [3,1,1,1] => 6
[[1,4,6],[2],[3],[5]] => [3,1,1,1] => 6
[[1,3,6],[2],[4],[5]] => [3,1,1,1] => 6
[[1,2,6],[3],[4],[5]] => [3,1,1,1] => 6
[[1,4,5],[2],[3],[6]] => [3,1,1,1] => 6
[[1,3,5],[2],[4],[6]] => [3,1,1,1] => 6
[[1,2,5],[3],[4],[6]] => [3,1,1,1] => 6
[[1,3,4],[2],[5],[6]] => [3,1,1,1] => 6
[[1,2,4],[3],[5],[6]] => [3,1,1,1] => 6
[[1,2,3],[4],[5],[6]] => [3,1,1,1] => 6
[[1,4],[2,5],[3,6]] => [2,2,2] => 6
[[1,3],[2,5],[4,6]] => [2,2,2] => 6
>>> Load all 1621 entries. <<<[[1,2],[3,5],[4,6]] => [2,2,2] => 6
[[1,3],[2,4],[5,6]] => [2,2,2] => 6
[[1,2],[3,4],[5,6]] => [2,2,2] => 6
[[1,5],[2,6],[3],[4]] => [2,2,1,1] => 7
[[1,4],[2,6],[3],[5]] => [2,2,1,1] => 7
[[1,3],[2,6],[4],[5]] => [2,2,1,1] => 7
[[1,2],[3,6],[4],[5]] => [2,2,1,1] => 7
[[1,4],[2,5],[3],[6]] => [2,2,1,1] => 7
[[1,3],[2,5],[4],[6]] => [2,2,1,1] => 7
[[1,2],[3,5],[4],[6]] => [2,2,1,1] => 7
[[1,3],[2,4],[5],[6]] => [2,2,1,1] => 7
[[1,2],[3,4],[5],[6]] => [2,2,1,1] => 7
[[1,6],[2],[3],[4],[5]] => [2,1,1,1,1] => 10
[[1,5],[2],[3],[4],[6]] => [2,1,1,1,1] => 10
[[1,4],[2],[3],[5],[6]] => [2,1,1,1,1] => 10
[[1,3],[2],[4],[5],[6]] => [2,1,1,1,1] => 10
[[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 10
[[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]] => [6,1] => 1
[[1,2,4,5,6,7],[3]] => [6,1] => 1
[[1,2,3,5,6,7],[4]] => [6,1] => 1
[[1,2,3,4,6,7],[5]] => [6,1] => 1
[[1,2,3,4,5,7],[6]] => [6,1] => 1
[[1,2,3,4,5,6],[7]] => [6,1] => 1
[[1,3,5,6,7],[2,4]] => [5,2] => 2
[[1,2,5,6,7],[3,4]] => [5,2] => 2
[[1,3,4,6,7],[2,5]] => [5,2] => 2
[[1,2,4,6,7],[3,5]] => [5,2] => 2
[[1,2,3,6,7],[4,5]] => [5,2] => 2
[[1,3,4,5,7],[2,6]] => [5,2] => 2
[[1,2,4,5,7],[3,6]] => [5,2] => 2
[[1,2,3,5,7],[4,6]] => [5,2] => 2
[[1,2,3,4,7],[5,6]] => [5,2] => 2
[[1,3,4,5,6],[2,7]] => [5,2] => 2
[[1,2,4,5,6],[3,7]] => [5,2] => 2
[[1,2,3,5,6],[4,7]] => [5,2] => 2
[[1,2,3,4,6],[5,7]] => [5,2] => 2
[[1,2,3,4,5],[6,7]] => [5,2] => 2
[[1,4,5,6,7],[2],[3]] => [5,1,1] => 3
[[1,3,5,6,7],[2],[4]] => [5,1,1] => 3
[[1,2,5,6,7],[3],[4]] => [5,1,1] => 3
[[1,3,4,6,7],[2],[5]] => [5,1,1] => 3
[[1,2,4,6,7],[3],[5]] => [5,1,1] => 3
[[1,2,3,6,7],[4],[5]] => [5,1,1] => 3
[[1,3,4,5,7],[2],[6]] => [5,1,1] => 3
[[1,2,4,5,7],[3],[6]] => [5,1,1] => 3
[[1,2,3,5,7],[4],[6]] => [5,1,1] => 3
[[1,2,3,4,7],[5],[6]] => [5,1,1] => 3
[[1,3,4,5,6],[2],[7]] => [5,1,1] => 3
[[1,2,4,5,6],[3],[7]] => [5,1,1] => 3
[[1,2,3,5,6],[4],[7]] => [5,1,1] => 3
[[1,2,3,4,6],[5],[7]] => [5,1,1] => 3
[[1,2,3,4,5],[6],[7]] => [5,1,1] => 3
[[1,3,5,7],[2,4,6]] => [4,3] => 3
[[1,2,5,7],[3,4,6]] => [4,3] => 3
[[1,3,4,7],[2,5,6]] => [4,3] => 3
[[1,2,4,7],[3,5,6]] => [4,3] => 3
[[1,2,3,7],[4,5,6]] => [4,3] => 3
[[1,3,5,6],[2,4,7]] => [4,3] => 3
[[1,2,5,6],[3,4,7]] => [4,3] => 3
[[1,3,4,6],[2,5,7]] => [4,3] => 3
[[1,2,4,6],[3,5,7]] => [4,3] => 3
[[1,2,3,6],[4,5,7]] => [4,3] => 3
[[1,3,4,5],[2,6,7]] => [4,3] => 3
[[1,2,4,5],[3,6,7]] => [4,3] => 3
[[1,2,3,5],[4,6,7]] => [4,3] => 3
[[1,2,3,4],[5,6,7]] => [4,3] => 3
[[1,4,6,7],[2,5],[3]] => [4,2,1] => 4
[[1,3,6,7],[2,5],[4]] => [4,2,1] => 4
[[1,2,6,7],[3,5],[4]] => [4,2,1] => 4
[[1,3,6,7],[2,4],[5]] => [4,2,1] => 4
[[1,2,6,7],[3,4],[5]] => [4,2,1] => 4
[[1,4,5,7],[2,6],[3]] => [4,2,1] => 4
[[1,3,5,7],[2,6],[4]] => [4,2,1] => 4
[[1,2,5,7],[3,6],[4]] => [4,2,1] => 4
[[1,3,4,7],[2,6],[5]] => [4,2,1] => 4
[[1,2,4,7],[3,6],[5]] => [4,2,1] => 4
[[1,2,3,7],[4,6],[5]] => [4,2,1] => 4
[[1,3,5,7],[2,4],[6]] => [4,2,1] => 4
[[1,2,5,7],[3,4],[6]] => [4,2,1] => 4
[[1,3,4,7],[2,5],[6]] => [4,2,1] => 4
[[1,2,4,7],[3,5],[6]] => [4,2,1] => 4
[[1,2,3,7],[4,5],[6]] => [4,2,1] => 4
[[1,4,5,6],[2,7],[3]] => [4,2,1] => 4
[[1,3,5,6],[2,7],[4]] => [4,2,1] => 4
[[1,2,5,6],[3,7],[4]] => [4,2,1] => 4
[[1,3,4,6],[2,7],[5]] => [4,2,1] => 4
[[1,2,4,6],[3,7],[5]] => [4,2,1] => 4
[[1,2,3,6],[4,7],[5]] => [4,2,1] => 4
[[1,3,4,5],[2,7],[6]] => [4,2,1] => 4
[[1,2,4,5],[3,7],[6]] => [4,2,1] => 4
[[1,2,3,5],[4,7],[6]] => [4,2,1] => 4
[[1,2,3,4],[5,7],[6]] => [4,2,1] => 4
[[1,3,5,6],[2,4],[7]] => [4,2,1] => 4
[[1,2,5,6],[3,4],[7]] => [4,2,1] => 4
[[1,3,4,6],[2,5],[7]] => [4,2,1] => 4
[[1,2,4,6],[3,5],[7]] => [4,2,1] => 4
[[1,2,3,6],[4,5],[7]] => [4,2,1] => 4
[[1,3,4,5],[2,6],[7]] => [4,2,1] => 4
[[1,2,4,5],[3,6],[7]] => [4,2,1] => 4
[[1,2,3,5],[4,6],[7]] => [4,2,1] => 4
[[1,2,3,4],[5,6],[7]] => [4,2,1] => 4
[[1,5,6,7],[2],[3],[4]] => [4,1,1,1] => 6
[[1,4,6,7],[2],[3],[5]] => [4,1,1,1] => 6
[[1,3,6,7],[2],[4],[5]] => [4,1,1,1] => 6
[[1,2,6,7],[3],[4],[5]] => [4,1,1,1] => 6
[[1,4,5,7],[2],[3],[6]] => [4,1,1,1] => 6
[[1,3,5,7],[2],[4],[6]] => [4,1,1,1] => 6
[[1,2,5,7],[3],[4],[6]] => [4,1,1,1] => 6
[[1,3,4,7],[2],[5],[6]] => [4,1,1,1] => 6
[[1,2,4,7],[3],[5],[6]] => [4,1,1,1] => 6
[[1,2,3,7],[4],[5],[6]] => [4,1,1,1] => 6
[[1,4,5,6],[2],[3],[7]] => [4,1,1,1] => 6
[[1,3,5,6],[2],[4],[7]] => [4,1,1,1] => 6
[[1,2,5,6],[3],[4],[7]] => [4,1,1,1] => 6
[[1,3,4,6],[2],[5],[7]] => [4,1,1,1] => 6
[[1,2,4,6],[3],[5],[7]] => [4,1,1,1] => 6
[[1,2,3,6],[4],[5],[7]] => [4,1,1,1] => 6
[[1,3,4,5],[2],[6],[7]] => [4,1,1,1] => 6
[[1,2,4,5],[3],[6],[7]] => [4,1,1,1] => 6
[[1,2,3,5],[4],[6],[7]] => [4,1,1,1] => 6
[[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 6
[[1,4,6],[2,5,7],[3]] => [3,3,1] => 5
[[1,3,6],[2,5,7],[4]] => [3,3,1] => 5
[[1,2,6],[3,5,7],[4]] => [3,3,1] => 5
[[1,3,6],[2,4,7],[5]] => [3,3,1] => 5
[[1,2,6],[3,4,7],[5]] => [3,3,1] => 5
[[1,4,5],[2,6,7],[3]] => [3,3,1] => 5
[[1,3,5],[2,6,7],[4]] => [3,3,1] => 5
[[1,2,5],[3,6,7],[4]] => [3,3,1] => 5
[[1,3,4],[2,6,7],[5]] => [3,3,1] => 5
[[1,2,4],[3,6,7],[5]] => [3,3,1] => 5
[[1,2,3],[4,6,7],[5]] => [3,3,1] => 5
[[1,3,5],[2,4,7],[6]] => [3,3,1] => 5
[[1,2,5],[3,4,7],[6]] => [3,3,1] => 5
[[1,3,4],[2,5,7],[6]] => [3,3,1] => 5
[[1,2,4],[3,5,7],[6]] => [3,3,1] => 5
[[1,2,3],[4,5,7],[6]] => [3,3,1] => 5
[[1,3,5],[2,4,6],[7]] => [3,3,1] => 5
[[1,2,5],[3,4,6],[7]] => [3,3,1] => 5
[[1,3,4],[2,5,6],[7]] => [3,3,1] => 5
[[1,2,4],[3,5,6],[7]] => [3,3,1] => 5
[[1,2,3],[4,5,6],[7]] => [3,3,1] => 5
[[1,4,7],[2,5],[3,6]] => [3,2,2] => 6
[[1,3,7],[2,5],[4,6]] => [3,2,2] => 6
[[1,2,7],[3,5],[4,6]] => [3,2,2] => 6
[[1,3,7],[2,4],[5,6]] => [3,2,2] => 6
[[1,2,7],[3,4],[5,6]] => [3,2,2] => 6
[[1,4,6],[2,5],[3,7]] => [3,2,2] => 6
[[1,3,6],[2,5],[4,7]] => [3,2,2] => 6
[[1,2,6],[3,5],[4,7]] => [3,2,2] => 6
[[1,3,6],[2,4],[5,7]] => [3,2,2] => 6
[[1,2,6],[3,4],[5,7]] => [3,2,2] => 6
[[1,4,5],[2,6],[3,7]] => [3,2,2] => 6
[[1,3,5],[2,6],[4,7]] => [3,2,2] => 6
[[1,2,5],[3,6],[4,7]] => [3,2,2] => 6
[[1,3,4],[2,6],[5,7]] => [3,2,2] => 6
[[1,2,4],[3,6],[5,7]] => [3,2,2] => 6
[[1,2,3],[4,6],[5,7]] => [3,2,2] => 6
[[1,3,5],[2,4],[6,7]] => [3,2,2] => 6
[[1,2,5],[3,4],[6,7]] => [3,2,2] => 6
[[1,3,4],[2,5],[6,7]] => [3,2,2] => 6
[[1,2,4],[3,5],[6,7]] => [3,2,2] => 6
[[1,2,3],[4,5],[6,7]] => [3,2,2] => 6
[[1,5,7],[2,6],[3],[4]] => [3,2,1,1] => 7
[[1,4,7],[2,6],[3],[5]] => [3,2,1,1] => 7
[[1,3,7],[2,6],[4],[5]] => [3,2,1,1] => 7
[[1,2,7],[3,6],[4],[5]] => [3,2,1,1] => 7
[[1,4,7],[2,5],[3],[6]] => [3,2,1,1] => 7
[[1,3,7],[2,5],[4],[6]] => [3,2,1,1] => 7
[[1,2,7],[3,5],[4],[6]] => [3,2,1,1] => 7
[[1,3,7],[2,4],[5],[6]] => [3,2,1,1] => 7
[[1,2,7],[3,4],[5],[6]] => [3,2,1,1] => 7
[[1,5,6],[2,7],[3],[4]] => [3,2,1,1] => 7
[[1,4,6],[2,7],[3],[5]] => [3,2,1,1] => 7
[[1,3,6],[2,7],[4],[5]] => [3,2,1,1] => 7
[[1,2,6],[3,7],[4],[5]] => [3,2,1,1] => 7
[[1,4,5],[2,7],[3],[6]] => [3,2,1,1] => 7
[[1,3,5],[2,7],[4],[6]] => [3,2,1,1] => 7
[[1,2,5],[3,7],[4],[6]] => [3,2,1,1] => 7
[[1,3,4],[2,7],[5],[6]] => [3,2,1,1] => 7
[[1,2,4],[3,7],[5],[6]] => [3,2,1,1] => 7
[[1,2,3],[4,7],[5],[6]] => [3,2,1,1] => 7
[[1,4,6],[2,5],[3],[7]] => [3,2,1,1] => 7
[[1,3,6],[2,5],[4],[7]] => [3,2,1,1] => 7
[[1,2,6],[3,5],[4],[7]] => [3,2,1,1] => 7
[[1,3,6],[2,4],[5],[7]] => [3,2,1,1] => 7
[[1,2,6],[3,4],[5],[7]] => [3,2,1,1] => 7
[[1,4,5],[2,6],[3],[7]] => [3,2,1,1] => 7
[[1,3,5],[2,6],[4],[7]] => [3,2,1,1] => 7
[[1,2,5],[3,6],[4],[7]] => [3,2,1,1] => 7
[[1,3,4],[2,6],[5],[7]] => [3,2,1,1] => 7
[[1,2,4],[3,6],[5],[7]] => [3,2,1,1] => 7
[[1,2,3],[4,6],[5],[7]] => [3,2,1,1] => 7
[[1,3,5],[2,4],[6],[7]] => [3,2,1,1] => 7
[[1,2,5],[3,4],[6],[7]] => [3,2,1,1] => 7
[[1,3,4],[2,5],[6],[7]] => [3,2,1,1] => 7
[[1,2,4],[3,5],[6],[7]] => [3,2,1,1] => 7
[[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 7
[[1,6,7],[2],[3],[4],[5]] => [3,1,1,1,1] => 10
[[1,5,7],[2],[3],[4],[6]] => [3,1,1,1,1] => 10
[[1,4,7],[2],[3],[5],[6]] => [3,1,1,1,1] => 10
[[1,3,7],[2],[4],[5],[6]] => [3,1,1,1,1] => 10
[[1,2,7],[3],[4],[5],[6]] => [3,1,1,1,1] => 10
[[1,5,6],[2],[3],[4],[7]] => [3,1,1,1,1] => 10
[[1,4,6],[2],[3],[5],[7]] => [3,1,1,1,1] => 10
[[1,3,6],[2],[4],[5],[7]] => [3,1,1,1,1] => 10
[[1,2,6],[3],[4],[5],[7]] => [3,1,1,1,1] => 10
[[1,4,5],[2],[3],[6],[7]] => [3,1,1,1,1] => 10
[[1,3,5],[2],[4],[6],[7]] => [3,1,1,1,1] => 10
[[1,2,5],[3],[4],[6],[7]] => [3,1,1,1,1] => 10
[[1,3,4],[2],[5],[6],[7]] => [3,1,1,1,1] => 10
[[1,2,4],[3],[5],[6],[7]] => [3,1,1,1,1] => 10
[[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 10
[[1,5],[2,6],[3,7],[4]] => [2,2,2,1] => 9
[[1,4],[2,6],[3,7],[5]] => [2,2,2,1] => 9
[[1,3],[2,6],[4,7],[5]] => [2,2,2,1] => 9
[[1,2],[3,6],[4,7],[5]] => [2,2,2,1] => 9
[[1,4],[2,5],[3,7],[6]] => [2,2,2,1] => 9
[[1,3],[2,5],[4,7],[6]] => [2,2,2,1] => 9
[[1,2],[3,5],[4,7],[6]] => [2,2,2,1] => 9
[[1,3],[2,4],[5,7],[6]] => [2,2,2,1] => 9
[[1,2],[3,4],[5,7],[6]] => [2,2,2,1] => 9
[[1,4],[2,5],[3,6],[7]] => [2,2,2,1] => 9
[[1,3],[2,5],[4,6],[7]] => [2,2,2,1] => 9
[[1,2],[3,5],[4,6],[7]] => [2,2,2,1] => 9
[[1,3],[2,4],[5,6],[7]] => [2,2,2,1] => 9
[[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 9
[[1,6],[2,7],[3],[4],[5]] => [2,2,1,1,1] => 11
[[1,5],[2,7],[3],[4],[6]] => [2,2,1,1,1] => 11
[[1,4],[2,7],[3],[5],[6]] => [2,2,1,1,1] => 11
[[1,3],[2,7],[4],[5],[6]] => [2,2,1,1,1] => 11
[[1,2],[3,7],[4],[5],[6]] => [2,2,1,1,1] => 11
[[1,5],[2,6],[3],[4],[7]] => [2,2,1,1,1] => 11
[[1,4],[2,6],[3],[5],[7]] => [2,2,1,1,1] => 11
[[1,3],[2,6],[4],[5],[7]] => [2,2,1,1,1] => 11
[[1,2],[3,6],[4],[5],[7]] => [2,2,1,1,1] => 11
[[1,4],[2,5],[3],[6],[7]] => [2,2,1,1,1] => 11
[[1,3],[2,5],[4],[6],[7]] => [2,2,1,1,1] => 11
[[1,2],[3,5],[4],[6],[7]] => [2,2,1,1,1] => 11
[[1,3],[2,4],[5],[6],[7]] => [2,2,1,1,1] => 11
[[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 11
[[1,7],[2],[3],[4],[5],[6]] => [2,1,1,1,1,1] => 15
[[1,6],[2],[3],[4],[5],[7]] => [2,1,1,1,1,1] => 15
[[1,5],[2],[3],[4],[6],[7]] => [2,1,1,1,1,1] => 15
[[1,4],[2],[3],[5],[6],[7]] => [2,1,1,1,1,1] => 15
[[1,3],[2],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 15
[[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 15
[[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]] => [7,1] => 1
[[1,2,4,5,6,7,8],[3]] => [7,1] => 1
[[1,2,3,5,6,7,8],[4]] => [7,1] => 1
[[1,2,3,4,6,7,8],[5]] => [7,1] => 1
[[1,2,3,4,5,7,8],[6]] => [7,1] => 1
[[1,2,3,4,5,6,8],[7]] => [7,1] => 1
[[1,2,3,4,5,6,7],[8]] => [7,1] => 1
[[1,3,5,6,7,8],[2,4]] => [6,2] => 2
[[1,2,5,6,7,8],[3,4]] => [6,2] => 2
[[1,3,4,6,7,8],[2,5]] => [6,2] => 2
[[1,2,4,6,7,8],[3,5]] => [6,2] => 2
[[1,2,3,6,7,8],[4,5]] => [6,2] => 2
[[1,3,4,5,7,8],[2,6]] => [6,2] => 2
[[1,2,4,5,7,8],[3,6]] => [6,2] => 2
[[1,2,3,5,7,8],[4,6]] => [6,2] => 2
[[1,2,3,4,7,8],[5,6]] => [6,2] => 2
[[1,3,4,5,6,8],[2,7]] => [6,2] => 2
[[1,2,4,5,6,8],[3,7]] => [6,2] => 2
[[1,2,3,5,6,8],[4,7]] => [6,2] => 2
[[1,2,3,4,6,8],[5,7]] => [6,2] => 2
[[1,2,3,4,5,8],[6,7]] => [6,2] => 2
[[1,3,4,5,6,7],[2,8]] => [6,2] => 2
[[1,2,4,5,6,7],[3,8]] => [6,2] => 2
[[1,2,3,5,6,7],[4,8]] => [6,2] => 2
[[1,2,3,4,6,7],[5,8]] => [6,2] => 2
[[1,2,3,4,5,7],[6,8]] => [6,2] => 2
[[1,2,3,4,5,6],[7,8]] => [6,2] => 2
[[1,4,5,6,7,8],[2],[3]] => [6,1,1] => 3
[[1,3,5,6,7,8],[2],[4]] => [6,1,1] => 3
[[1,2,5,6,7,8],[3],[4]] => [6,1,1] => 3
[[1,3,4,6,7,8],[2],[5]] => [6,1,1] => 3
[[1,2,4,6,7,8],[3],[5]] => [6,1,1] => 3
[[1,2,3,6,7,8],[4],[5]] => [6,1,1] => 3
[[1,3,4,5,7,8],[2],[6]] => [6,1,1] => 3
[[1,2,4,5,7,8],[3],[6]] => [6,1,1] => 3
[[1,2,3,5,7,8],[4],[6]] => [6,1,1] => 3
[[1,2,3,4,7,8],[5],[6]] => [6,1,1] => 3
[[1,3,4,5,6,8],[2],[7]] => [6,1,1] => 3
[[1,2,4,5,6,8],[3],[7]] => [6,1,1] => 3
[[1,2,3,5,6,8],[4],[7]] => [6,1,1] => 3
[[1,2,3,4,6,8],[5],[7]] => [6,1,1] => 3
[[1,2,3,4,5,8],[6],[7]] => [6,1,1] => 3
[[1,3,4,5,6,7],[2],[8]] => [6,1,1] => 3
[[1,2,4,5,6,7],[3],[8]] => [6,1,1] => 3
[[1,2,3,5,6,7],[4],[8]] => [6,1,1] => 3
[[1,2,3,4,6,7],[5],[8]] => [6,1,1] => 3
[[1,2,3,4,5,7],[6],[8]] => [6,1,1] => 3
[[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 3
[[1,3,5,7,8],[2,4,6]] => [5,3] => 3
[[1,2,5,7,8],[3,4,6]] => [5,3] => 3
[[1,3,4,7,8],[2,5,6]] => [5,3] => 3
[[1,2,4,7,8],[3,5,6]] => [5,3] => 3
[[1,2,3,7,8],[4,5,6]] => [5,3] => 3
[[1,3,5,6,8],[2,4,7]] => [5,3] => 3
[[1,2,5,6,8],[3,4,7]] => [5,3] => 3
[[1,3,4,6,8],[2,5,7]] => [5,3] => 3
[[1,2,4,6,8],[3,5,7]] => [5,3] => 3
[[1,2,3,6,8],[4,5,7]] => [5,3] => 3
[[1,3,4,5,8],[2,6,7]] => [5,3] => 3
[[1,2,4,5,8],[3,6,7]] => [5,3] => 3
[[1,2,3,5,8],[4,6,7]] => [5,3] => 3
[[1,2,3,4,8],[5,6,7]] => [5,3] => 3
[[1,3,5,6,7],[2,4,8]] => [5,3] => 3
[[1,2,5,6,7],[3,4,8]] => [5,3] => 3
[[1,3,4,6,7],[2,5,8]] => [5,3] => 3
[[1,2,4,6,7],[3,5,8]] => [5,3] => 3
[[1,2,3,6,7],[4,5,8]] => [5,3] => 3
[[1,3,4,5,7],[2,6,8]] => [5,3] => 3
[[1,2,4,5,7],[3,6,8]] => [5,3] => 3
[[1,2,3,5,7],[4,6,8]] => [5,3] => 3
[[1,2,3,4,7],[5,6,8]] => [5,3] => 3
[[1,3,4,5,6],[2,7,8]] => [5,3] => 3
[[1,2,4,5,6],[3,7,8]] => [5,3] => 3
[[1,2,3,5,6],[4,7,8]] => [5,3] => 3
[[1,2,3,4,6],[5,7,8]] => [5,3] => 3
[[1,2,3,4,5],[6,7,8]] => [5,3] => 3
[[1,4,6,7,8],[2,5],[3]] => [5,2,1] => 4
[[1,3,6,7,8],[2,5],[4]] => [5,2,1] => 4
[[1,2,6,7,8],[3,5],[4]] => [5,2,1] => 4
[[1,3,6,7,8],[2,4],[5]] => [5,2,1] => 4
[[1,2,6,7,8],[3,4],[5]] => [5,2,1] => 4
[[1,4,5,7,8],[2,6],[3]] => [5,2,1] => 4
[[1,3,5,7,8],[2,6],[4]] => [5,2,1] => 4
[[1,2,5,7,8],[3,6],[4]] => [5,2,1] => 4
[[1,3,4,7,8],[2,6],[5]] => [5,2,1] => 4
[[1,2,4,7,8],[3,6],[5]] => [5,2,1] => 4
[[1,2,3,7,8],[4,6],[5]] => [5,2,1] => 4
[[1,3,5,7,8],[2,4],[6]] => [5,2,1] => 4
[[1,2,5,7,8],[3,4],[6]] => [5,2,1] => 4
[[1,3,4,7,8],[2,5],[6]] => [5,2,1] => 4
[[1,2,4,7,8],[3,5],[6]] => [5,2,1] => 4
[[1,2,3,7,8],[4,5],[6]] => [5,2,1] => 4
[[1,4,5,6,8],[2,7],[3]] => [5,2,1] => 4
[[1,3,5,6,8],[2,7],[4]] => [5,2,1] => 4
[[1,2,5,6,8],[3,7],[4]] => [5,2,1] => 4
[[1,3,4,6,8],[2,7],[5]] => [5,2,1] => 4
[[1,2,4,6,8],[3,7],[5]] => [5,2,1] => 4
[[1,2,3,6,8],[4,7],[5]] => [5,2,1] => 4
[[1,3,4,5,8],[2,7],[6]] => [5,2,1] => 4
[[1,2,4,5,8],[3,7],[6]] => [5,2,1] => 4
[[1,2,3,5,8],[4,7],[6]] => [5,2,1] => 4
[[1,2,3,4,8],[5,7],[6]] => [5,2,1] => 4
[[1,3,5,6,8],[2,4],[7]] => [5,2,1] => 4
[[1,2,5,6,8],[3,4],[7]] => [5,2,1] => 4
[[1,3,4,6,8],[2,5],[7]] => [5,2,1] => 4
[[1,2,4,6,8],[3,5],[7]] => [5,2,1] => 4
[[1,2,3,6,8],[4,5],[7]] => [5,2,1] => 4
[[1,3,4,5,8],[2,6],[7]] => [5,2,1] => 4
[[1,2,4,5,8],[3,6],[7]] => [5,2,1] => 4
[[1,2,3,5,8],[4,6],[7]] => [5,2,1] => 4
[[1,2,3,4,8],[5,6],[7]] => [5,2,1] => 4
[[1,4,5,6,7],[2,8],[3]] => [5,2,1] => 4
[[1,3,5,6,7],[2,8],[4]] => [5,2,1] => 4
[[1,2,5,6,7],[3,8],[4]] => [5,2,1] => 4
[[1,3,4,6,7],[2,8],[5]] => [5,2,1] => 4
[[1,2,4,6,7],[3,8],[5]] => [5,2,1] => 4
[[1,2,3,6,7],[4,8],[5]] => [5,2,1] => 4
[[1,3,4,5,7],[2,8],[6]] => [5,2,1] => 4
[[1,2,4,5,7],[3,8],[6]] => [5,2,1] => 4
[[1,2,3,5,7],[4,8],[6]] => [5,2,1] => 4
[[1,2,3,4,7],[5,8],[6]] => [5,2,1] => 4
[[1,3,4,5,6],[2,8],[7]] => [5,2,1] => 4
[[1,2,4,5,6],[3,8],[7]] => [5,2,1] => 4
[[1,2,3,5,6],[4,8],[7]] => [5,2,1] => 4
[[1,2,3,4,6],[5,8],[7]] => [5,2,1] => 4
[[1,2,3,4,5],[6,8],[7]] => [5,2,1] => 4
[[1,3,5,6,7],[2,4],[8]] => [5,2,1] => 4
[[1,2,5,6,7],[3,4],[8]] => [5,2,1] => 4
[[1,3,4,6,7],[2,5],[8]] => [5,2,1] => 4
[[1,2,4,6,7],[3,5],[8]] => [5,2,1] => 4
[[1,2,3,6,7],[4,5],[8]] => [5,2,1] => 4
[[1,3,4,5,7],[2,6],[8]] => [5,2,1] => 4
[[1,2,4,5,7],[3,6],[8]] => [5,2,1] => 4
[[1,2,3,5,7],[4,6],[8]] => [5,2,1] => 4
[[1,2,3,4,7],[5,6],[8]] => [5,2,1] => 4
[[1,3,4,5,6],[2,7],[8]] => [5,2,1] => 4
[[1,2,4,5,6],[3,7],[8]] => [5,2,1] => 4
[[1,2,3,5,6],[4,7],[8]] => [5,2,1] => 4
[[1,2,3,4,6],[5,7],[8]] => [5,2,1] => 4
[[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 4
[[1,5,6,7,8],[2],[3],[4]] => [5,1,1,1] => 6
[[1,4,6,7,8],[2],[3],[5]] => [5,1,1,1] => 6
[[1,3,6,7,8],[2],[4],[5]] => [5,1,1,1] => 6
[[1,2,6,7,8],[3],[4],[5]] => [5,1,1,1] => 6
[[1,4,5,7,8],[2],[3],[6]] => [5,1,1,1] => 6
[[1,3,5,7,8],[2],[4],[6]] => [5,1,1,1] => 6
[[1,2,5,7,8],[3],[4],[6]] => [5,1,1,1] => 6
[[1,3,4,7,8],[2],[5],[6]] => [5,1,1,1] => 6
[[1,2,4,7,8],[3],[5],[6]] => [5,1,1,1] => 6
[[1,2,3,7,8],[4],[5],[6]] => [5,1,1,1] => 6
[[1,4,5,6,8],[2],[3],[7]] => [5,1,1,1] => 6
[[1,3,5,6,8],[2],[4],[7]] => [5,1,1,1] => 6
[[1,2,5,6,8],[3],[4],[7]] => [5,1,1,1] => 6
[[1,3,4,6,8],[2],[5],[7]] => [5,1,1,1] => 6
[[1,2,4,6,8],[3],[5],[7]] => [5,1,1,1] => 6
[[1,2,3,6,8],[4],[5],[7]] => [5,1,1,1] => 6
[[1,3,4,5,8],[2],[6],[7]] => [5,1,1,1] => 6
[[1,2,4,5,8],[3],[6],[7]] => [5,1,1,1] => 6
[[1,2,3,5,8],[4],[6],[7]] => [5,1,1,1] => 6
[[1,2,3,4,8],[5],[6],[7]] => [5,1,1,1] => 6
[[1,4,5,6,7],[2],[3],[8]] => [5,1,1,1] => 6
[[1,3,5,6,7],[2],[4],[8]] => [5,1,1,1] => 6
[[1,2,5,6,7],[3],[4],[8]] => [5,1,1,1] => 6
[[1,3,4,6,7],[2],[5],[8]] => [5,1,1,1] => 6
[[1,2,4,6,7],[3],[5],[8]] => [5,1,1,1] => 6
[[1,2,3,6,7],[4],[5],[8]] => [5,1,1,1] => 6
[[1,3,4,5,7],[2],[6],[8]] => [5,1,1,1] => 6
[[1,2,4,5,7],[3],[6],[8]] => [5,1,1,1] => 6
[[1,2,3,5,7],[4],[6],[8]] => [5,1,1,1] => 6
[[1,2,3,4,7],[5],[6],[8]] => [5,1,1,1] => 6
[[1,3,4,5,6],[2],[7],[8]] => [5,1,1,1] => 6
[[1,2,4,5,6],[3],[7],[8]] => [5,1,1,1] => 6
[[1,2,3,5,6],[4],[7],[8]] => [5,1,1,1] => 6
[[1,2,3,4,6],[5],[7],[8]] => [5,1,1,1] => 6
[[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 6
[[1,3,5,7],[2,4,6,8]] => [4,4] => 4
[[1,2,5,7],[3,4,6,8]] => [4,4] => 4
[[1,3,4,7],[2,5,6,8]] => [4,4] => 4
[[1,2,4,7],[3,5,6,8]] => [4,4] => 4
[[1,2,3,7],[4,5,6,8]] => [4,4] => 4
[[1,3,5,6],[2,4,7,8]] => [4,4] => 4
[[1,2,5,6],[3,4,7,8]] => [4,4] => 4
[[1,3,4,6],[2,5,7,8]] => [4,4] => 4
[[1,2,4,6],[3,5,7,8]] => [4,4] => 4
[[1,2,3,6],[4,5,7,8]] => [4,4] => 4
[[1,3,4,5],[2,6,7,8]] => [4,4] => 4
[[1,2,4,5],[3,6,7,8]] => [4,4] => 4
[[1,2,3,5],[4,6,7,8]] => [4,4] => 4
[[1,2,3,4],[5,6,7,8]] => [4,4] => 4
[[1,4,6,8],[2,5,7],[3]] => [4,3,1] => 5
[[1,3,6,8],[2,5,7],[4]] => [4,3,1] => 5
[[1,2,6,8],[3,5,7],[4]] => [4,3,1] => 5
[[1,3,6,8],[2,4,7],[5]] => [4,3,1] => 5
[[1,2,6,8],[3,4,7],[5]] => [4,3,1] => 5
[[1,4,5,8],[2,6,7],[3]] => [4,3,1] => 5
[[1,3,5,8],[2,6,7],[4]] => [4,3,1] => 5
[[1,2,5,8],[3,6,7],[4]] => [4,3,1] => 5
[[1,3,4,8],[2,6,7],[5]] => [4,3,1] => 5
[[1,2,4,8],[3,6,7],[5]] => [4,3,1] => 5
[[1,2,3,8],[4,6,7],[5]] => [4,3,1] => 5
[[1,3,5,8],[2,4,7],[6]] => [4,3,1] => 5
[[1,2,5,8],[3,4,7],[6]] => [4,3,1] => 5
[[1,3,4,8],[2,5,7],[6]] => [4,3,1] => 5
[[1,2,4,8],[3,5,7],[6]] => [4,3,1] => 5
[[1,2,3,8],[4,5,7],[6]] => [4,3,1] => 5
[[1,3,5,8],[2,4,6],[7]] => [4,3,1] => 5
[[1,2,5,8],[3,4,6],[7]] => [4,3,1] => 5
[[1,3,4,8],[2,5,6],[7]] => [4,3,1] => 5
[[1,2,4,8],[3,5,6],[7]] => [4,3,1] => 5
[[1,2,3,8],[4,5,6],[7]] => [4,3,1] => 5
[[1,4,6,7],[2,5,8],[3]] => [4,3,1] => 5
[[1,3,6,7],[2,5,8],[4]] => [4,3,1] => 5
[[1,2,6,7],[3,5,8],[4]] => [4,3,1] => 5
[[1,3,6,7],[2,4,8],[5]] => [4,3,1] => 5
[[1,2,6,7],[3,4,8],[5]] => [4,3,1] => 5
[[1,4,5,7],[2,6,8],[3]] => [4,3,1] => 5
[[1,3,5,7],[2,6,8],[4]] => [4,3,1] => 5
[[1,2,5,7],[3,6,8],[4]] => [4,3,1] => 5
[[1,3,4,7],[2,6,8],[5]] => [4,3,1] => 5
[[1,2,4,7],[3,6,8],[5]] => [4,3,1] => 5
[[1,2,3,7],[4,6,8],[5]] => [4,3,1] => 5
[[1,3,5,7],[2,4,8],[6]] => [4,3,1] => 5
[[1,2,5,7],[3,4,8],[6]] => [4,3,1] => 5
[[1,3,4,7],[2,5,8],[6]] => [4,3,1] => 5
[[1,2,4,7],[3,5,8],[6]] => [4,3,1] => 5
[[1,2,3,7],[4,5,8],[6]] => [4,3,1] => 5
[[1,4,5,6],[2,7,8],[3]] => [4,3,1] => 5
[[1,3,5,6],[2,7,8],[4]] => [4,3,1] => 5
[[1,2,5,6],[3,7,8],[4]] => [4,3,1] => 5
[[1,3,4,6],[2,7,8],[5]] => [4,3,1] => 5
[[1,2,4,6],[3,7,8],[5]] => [4,3,1] => 5
[[1,2,3,6],[4,7,8],[5]] => [4,3,1] => 5
[[1,3,4,5],[2,7,8],[6]] => [4,3,1] => 5
[[1,2,4,5],[3,7,8],[6]] => [4,3,1] => 5
[[1,2,3,5],[4,7,8],[6]] => [4,3,1] => 5
[[1,2,3,4],[5,7,8],[6]] => [4,3,1] => 5
[[1,3,5,6],[2,4,8],[7]] => [4,3,1] => 5
[[1,2,5,6],[3,4,8],[7]] => [4,3,1] => 5
[[1,3,4,6],[2,5,8],[7]] => [4,3,1] => 5
[[1,2,4,6],[3,5,8],[7]] => [4,3,1] => 5
[[1,2,3,6],[4,5,8],[7]] => [4,3,1] => 5
[[1,3,4,5],[2,6,8],[7]] => [4,3,1] => 5
[[1,2,4,5],[3,6,8],[7]] => [4,3,1] => 5
[[1,2,3,5],[4,6,8],[7]] => [4,3,1] => 5
[[1,2,3,4],[5,6,8],[7]] => [4,3,1] => 5
[[1,3,5,7],[2,4,6],[8]] => [4,3,1] => 5
[[1,2,5,7],[3,4,6],[8]] => [4,3,1] => 5
[[1,3,4,7],[2,5,6],[8]] => [4,3,1] => 5
[[1,2,4,7],[3,5,6],[8]] => [4,3,1] => 5
[[1,2,3,7],[4,5,6],[8]] => [4,3,1] => 5
[[1,3,5,6],[2,4,7],[8]] => [4,3,1] => 5
[[1,2,5,6],[3,4,7],[8]] => [4,3,1] => 5
[[1,3,4,6],[2,5,7],[8]] => [4,3,1] => 5
[[1,2,4,6],[3,5,7],[8]] => [4,3,1] => 5
[[1,2,3,6],[4,5,7],[8]] => [4,3,1] => 5
[[1,3,4,5],[2,6,7],[8]] => [4,3,1] => 5
[[1,2,4,5],[3,6,7],[8]] => [4,3,1] => 5
[[1,2,3,5],[4,6,7],[8]] => [4,3,1] => 5
[[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 5
[[1,4,7,8],[2,5],[3,6]] => [4,2,2] => 6
[[1,3,7,8],[2,5],[4,6]] => [4,2,2] => 6
[[1,2,7,8],[3,5],[4,6]] => [4,2,2] => 6
[[1,3,7,8],[2,4],[5,6]] => [4,2,2] => 6
[[1,2,7,8],[3,4],[5,6]] => [4,2,2] => 6
[[1,4,6,8],[2,5],[3,7]] => [4,2,2] => 6
[[1,3,6,8],[2,5],[4,7]] => [4,2,2] => 6
[[1,2,6,8],[3,5],[4,7]] => [4,2,2] => 6
[[1,3,6,8],[2,4],[5,7]] => [4,2,2] => 6
[[1,2,6,8],[3,4],[5,7]] => [4,2,2] => 6
[[1,4,5,8],[2,6],[3,7]] => [4,2,2] => 6
[[1,3,5,8],[2,6],[4,7]] => [4,2,2] => 6
[[1,2,5,8],[3,6],[4,7]] => [4,2,2] => 6
[[1,3,4,8],[2,6],[5,7]] => [4,2,2] => 6
[[1,2,4,8],[3,6],[5,7]] => [4,2,2] => 6
[[1,2,3,8],[4,6],[5,7]] => [4,2,2] => 6
[[1,3,5,8],[2,4],[6,7]] => [4,2,2] => 6
[[1,2,5,8],[3,4],[6,7]] => [4,2,2] => 6
[[1,3,4,8],[2,5],[6,7]] => [4,2,2] => 6
[[1,2,4,8],[3,5],[6,7]] => [4,2,2] => 6
[[1,2,3,8],[4,5],[6,7]] => [4,2,2] => 6
[[1,4,6,7],[2,5],[3,8]] => [4,2,2] => 6
[[1,3,6,7],[2,5],[4,8]] => [4,2,2] => 6
[[1,2,6,7],[3,5],[4,8]] => [4,2,2] => 6
[[1,3,6,7],[2,4],[5,8]] => [4,2,2] => 6
[[1,2,6,7],[3,4],[5,8]] => [4,2,2] => 6
[[1,4,5,7],[2,6],[3,8]] => [4,2,2] => 6
[[1,3,5,7],[2,6],[4,8]] => [4,2,2] => 6
[[1,2,5,7],[3,6],[4,8]] => [4,2,2] => 6
[[1,3,4,7],[2,6],[5,8]] => [4,2,2] => 6
[[1,2,4,7],[3,6],[5,8]] => [4,2,2] => 6
[[1,2,3,7],[4,6],[5,8]] => [4,2,2] => 6
[[1,3,5,7],[2,4],[6,8]] => [4,2,2] => 6
[[1,2,5,7],[3,4],[6,8]] => [4,2,2] => 6
[[1,3,4,7],[2,5],[6,8]] => [4,2,2] => 6
[[1,2,4,7],[3,5],[6,8]] => [4,2,2] => 6
[[1,2,3,7],[4,5],[6,8]] => [4,2,2] => 6
[[1,4,5,6],[2,7],[3,8]] => [4,2,2] => 6
[[1,3,5,6],[2,7],[4,8]] => [4,2,2] => 6
[[1,2,5,6],[3,7],[4,8]] => [4,2,2] => 6
[[1,3,4,6],[2,7],[5,8]] => [4,2,2] => 6
[[1,2,4,6],[3,7],[5,8]] => [4,2,2] => 6
[[1,2,3,6],[4,7],[5,8]] => [4,2,2] => 6
[[1,3,4,5],[2,7],[6,8]] => [4,2,2] => 6
[[1,2,4,5],[3,7],[6,8]] => [4,2,2] => 6
[[1,2,3,5],[4,7],[6,8]] => [4,2,2] => 6
[[1,2,3,4],[5,7],[6,8]] => [4,2,2] => 6
[[1,3,5,6],[2,4],[7,8]] => [4,2,2] => 6
[[1,2,5,6],[3,4],[7,8]] => [4,2,2] => 6
[[1,3,4,6],[2,5],[7,8]] => [4,2,2] => 6
[[1,2,4,6],[3,5],[7,8]] => [4,2,2] => 6
[[1,2,3,6],[4,5],[7,8]] => [4,2,2] => 6
[[1,3,4,5],[2,6],[7,8]] => [4,2,2] => 6
[[1,2,4,5],[3,6],[7,8]] => [4,2,2] => 6
[[1,2,3,5],[4,6],[7,8]] => [4,2,2] => 6
[[1,2,3,4],[5,6],[7,8]] => [4,2,2] => 6
[[1,5,7,8],[2,6],[3],[4]] => [4,2,1,1] => 7
[[1,4,7,8],[2,6],[3],[5]] => [4,2,1,1] => 7
[[1,3,7,8],[2,6],[4],[5]] => [4,2,1,1] => 7
[[1,2,7,8],[3,6],[4],[5]] => [4,2,1,1] => 7
[[1,4,7,8],[2,5],[3],[6]] => [4,2,1,1] => 7
[[1,3,7,8],[2,5],[4],[6]] => [4,2,1,1] => 7
[[1,2,7,8],[3,5],[4],[6]] => [4,2,1,1] => 7
[[1,3,7,8],[2,4],[5],[6]] => [4,2,1,1] => 7
[[1,2,7,8],[3,4],[5],[6]] => [4,2,1,1] => 7
[[1,5,6,8],[2,7],[3],[4]] => [4,2,1,1] => 7
[[1,4,6,8],[2,7],[3],[5]] => [4,2,1,1] => 7
[[1,3,6,8],[2,7],[4],[5]] => [4,2,1,1] => 7
[[1,2,6,8],[3,7],[4],[5]] => [4,2,1,1] => 7
[[1,4,5,8],[2,7],[3],[6]] => [4,2,1,1] => 7
[[1,3,5,8],[2,7],[4],[6]] => [4,2,1,1] => 7
[[1,2,5,8],[3,7],[4],[6]] => [4,2,1,1] => 7
[[1,3,4,8],[2,7],[5],[6]] => [4,2,1,1] => 7
[[1,2,4,8],[3,7],[5],[6]] => [4,2,1,1] => 7
[[1,2,3,8],[4,7],[5],[6]] => [4,2,1,1] => 7
[[1,4,6,8],[2,5],[3],[7]] => [4,2,1,1] => 7
[[1,3,6,8],[2,5],[4],[7]] => [4,2,1,1] => 7
[[1,2,6,8],[3,5],[4],[7]] => [4,2,1,1] => 7
[[1,3,6,8],[2,4],[5],[7]] => [4,2,1,1] => 7
[[1,2,6,8],[3,4],[5],[7]] => [4,2,1,1] => 7
[[1,4,5,8],[2,6],[3],[7]] => [4,2,1,1] => 7
[[1,3,5,8],[2,6],[4],[7]] => [4,2,1,1] => 7
[[1,2,5,8],[3,6],[4],[7]] => [4,2,1,1] => 7
[[1,3,4,8],[2,6],[5],[7]] => [4,2,1,1] => 7
[[1,2,4,8],[3,6],[5],[7]] => [4,2,1,1] => 7
[[1,2,3,8],[4,6],[5],[7]] => [4,2,1,1] => 7
[[1,3,5,8],[2,4],[6],[7]] => [4,2,1,1] => 7
[[1,2,5,8],[3,4],[6],[7]] => [4,2,1,1] => 7
[[1,3,4,8],[2,5],[6],[7]] => [4,2,1,1] => 7
[[1,2,4,8],[3,5],[6],[7]] => [4,2,1,1] => 7
[[1,2,3,8],[4,5],[6],[7]] => [4,2,1,1] => 7
[[1,5,6,7],[2,8],[3],[4]] => [4,2,1,1] => 7
[[1,4,6,7],[2,8],[3],[5]] => [4,2,1,1] => 7
[[1,3,6,7],[2,8],[4],[5]] => [4,2,1,1] => 7
[[1,2,6,7],[3,8],[4],[5]] => [4,2,1,1] => 7
[[1,4,5,7],[2,8],[3],[6]] => [4,2,1,1] => 7
[[1,3,5,7],[2,8],[4],[6]] => [4,2,1,1] => 7
[[1,2,5,7],[3,8],[4],[6]] => [4,2,1,1] => 7
[[1,3,4,7],[2,8],[5],[6]] => [4,2,1,1] => 7
[[1,2,4,7],[3,8],[5],[6]] => [4,2,1,1] => 7
[[1,2,3,7],[4,8],[5],[6]] => [4,2,1,1] => 7
[[1,4,5,6],[2,8],[3],[7]] => [4,2,1,1] => 7
[[1,3,5,6],[2,8],[4],[7]] => [4,2,1,1] => 7
[[1,2,5,6],[3,8],[4],[7]] => [4,2,1,1] => 7
[[1,3,4,6],[2,8],[5],[7]] => [4,2,1,1] => 7
[[1,2,4,6],[3,8],[5],[7]] => [4,2,1,1] => 7
[[1,2,3,6],[4,8],[5],[7]] => [4,2,1,1] => 7
[[1,3,4,5],[2,8],[6],[7]] => [4,2,1,1] => 7
[[1,2,4,5],[3,8],[6],[7]] => [4,2,1,1] => 7
[[1,2,3,5],[4,8],[6],[7]] => [4,2,1,1] => 7
[[1,2,3,4],[5,8],[6],[7]] => [4,2,1,1] => 7
[[1,4,6,7],[2,5],[3],[8]] => [4,2,1,1] => 7
[[1,3,6,7],[2,5],[4],[8]] => [4,2,1,1] => 7
[[1,2,6,7],[3,5],[4],[8]] => [4,2,1,1] => 7
[[1,3,6,7],[2,4],[5],[8]] => [4,2,1,1] => 7
[[1,2,6,7],[3,4],[5],[8]] => [4,2,1,1] => 7
[[1,4,5,7],[2,6],[3],[8]] => [4,2,1,1] => 7
[[1,3,5,7],[2,6],[4],[8]] => [4,2,1,1] => 7
[[1,2,5,7],[3,6],[4],[8]] => [4,2,1,1] => 7
[[1,3,4,7],[2,6],[5],[8]] => [4,2,1,1] => 7
[[1,2,4,7],[3,6],[5],[8]] => [4,2,1,1] => 7
[[1,2,3,7],[4,6],[5],[8]] => [4,2,1,1] => 7
[[1,3,5,7],[2,4],[6],[8]] => [4,2,1,1] => 7
[[1,2,5,7],[3,4],[6],[8]] => [4,2,1,1] => 7
[[1,3,4,7],[2,5],[6],[8]] => [4,2,1,1] => 7
[[1,2,4,7],[3,5],[6],[8]] => [4,2,1,1] => 7
[[1,2,3,7],[4,5],[6],[8]] => [4,2,1,1] => 7
[[1,4,5,6],[2,7],[3],[8]] => [4,2,1,1] => 7
[[1,3,5,6],[2,7],[4],[8]] => [4,2,1,1] => 7
[[1,2,5,6],[3,7],[4],[8]] => [4,2,1,1] => 7
[[1,3,4,6],[2,7],[5],[8]] => [4,2,1,1] => 7
[[1,2,4,6],[3,7],[5],[8]] => [4,2,1,1] => 7
[[1,2,3,6],[4,7],[5],[8]] => [4,2,1,1] => 7
[[1,3,4,5],[2,7],[6],[8]] => [4,2,1,1] => 7
[[1,2,4,5],[3,7],[6],[8]] => [4,2,1,1] => 7
[[1,2,3,5],[4,7],[6],[8]] => [4,2,1,1] => 7
[[1,2,3,4],[5,7],[6],[8]] => [4,2,1,1] => 7
[[1,3,5,6],[2,4],[7],[8]] => [4,2,1,1] => 7
[[1,2,5,6],[3,4],[7],[8]] => [4,2,1,1] => 7
[[1,3,4,6],[2,5],[7],[8]] => [4,2,1,1] => 7
[[1,2,4,6],[3,5],[7],[8]] => [4,2,1,1] => 7
[[1,2,3,6],[4,5],[7],[8]] => [4,2,1,1] => 7
[[1,3,4,5],[2,6],[7],[8]] => [4,2,1,1] => 7
[[1,2,4,5],[3,6],[7],[8]] => [4,2,1,1] => 7
[[1,2,3,5],[4,6],[7],[8]] => [4,2,1,1] => 7
[[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 7
[[1,6,7,8],[2],[3],[4],[5]] => [4,1,1,1,1] => 10
[[1,5,7,8],[2],[3],[4],[6]] => [4,1,1,1,1] => 10
[[1,4,7,8],[2],[3],[5],[6]] => [4,1,1,1,1] => 10
[[1,3,7,8],[2],[4],[5],[6]] => [4,1,1,1,1] => 10
[[1,2,7,8],[3],[4],[5],[6]] => [4,1,1,1,1] => 10
[[1,5,6,8],[2],[3],[4],[7]] => [4,1,1,1,1] => 10
[[1,4,6,8],[2],[3],[5],[7]] => [4,1,1,1,1] => 10
[[1,3,6,8],[2],[4],[5],[7]] => [4,1,1,1,1] => 10
[[1,2,6,8],[3],[4],[5],[7]] => [4,1,1,1,1] => 10
[[1,4,5,8],[2],[3],[6],[7]] => [4,1,1,1,1] => 10
[[1,3,5,8],[2],[4],[6],[7]] => [4,1,1,1,1] => 10
[[1,2,5,8],[3],[4],[6],[7]] => [4,1,1,1,1] => 10
[[1,3,4,8],[2],[5],[6],[7]] => [4,1,1,1,1] => 10
[[1,2,4,8],[3],[5],[6],[7]] => [4,1,1,1,1] => 10
[[1,2,3,8],[4],[5],[6],[7]] => [4,1,1,1,1] => 10
[[1,5,6,7],[2],[3],[4],[8]] => [4,1,1,1,1] => 10
[[1,4,6,7],[2],[3],[5],[8]] => [4,1,1,1,1] => 10
[[1,3,6,7],[2],[4],[5],[8]] => [4,1,1,1,1] => 10
[[1,2,6,7],[3],[4],[5],[8]] => [4,1,1,1,1] => 10
[[1,4,5,7],[2],[3],[6],[8]] => [4,1,1,1,1] => 10
[[1,3,5,7],[2],[4],[6],[8]] => [4,1,1,1,1] => 10
[[1,2,5,7],[3],[4],[6],[8]] => [4,1,1,1,1] => 10
[[1,3,4,7],[2],[5],[6],[8]] => [4,1,1,1,1] => 10
[[1,2,4,7],[3],[5],[6],[8]] => [4,1,1,1,1] => 10
[[1,2,3,7],[4],[5],[6],[8]] => [4,1,1,1,1] => 10
[[1,4,5,6],[2],[3],[7],[8]] => [4,1,1,1,1] => 10
[[1,3,5,6],[2],[4],[7],[8]] => [4,1,1,1,1] => 10
[[1,2,5,6],[3],[4],[7],[8]] => [4,1,1,1,1] => 10
[[1,3,4,6],[2],[5],[7],[8]] => [4,1,1,1,1] => 10
[[1,2,4,6],[3],[5],[7],[8]] => [4,1,1,1,1] => 10
[[1,2,3,6],[4],[5],[7],[8]] => [4,1,1,1,1] => 10
[[1,3,4,5],[2],[6],[7],[8]] => [4,1,1,1,1] => 10
[[1,2,4,5],[3],[6],[7],[8]] => [4,1,1,1,1] => 10
[[1,2,3,5],[4],[6],[7],[8]] => [4,1,1,1,1] => 10
[[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => 10
[[1,4,7],[2,5,8],[3,6]] => [3,3,2] => 7
[[1,3,7],[2,5,8],[4,6]] => [3,3,2] => 7
[[1,2,7],[3,5,8],[4,6]] => [3,3,2] => 7
[[1,3,7],[2,4,8],[5,6]] => [3,3,2] => 7
[[1,2,7],[3,4,8],[5,6]] => [3,3,2] => 7
[[1,4,6],[2,5,8],[3,7]] => [3,3,2] => 7
[[1,3,6],[2,5,8],[4,7]] => [3,3,2] => 7
[[1,2,6],[3,5,8],[4,7]] => [3,3,2] => 7
[[1,3,6],[2,4,8],[5,7]] => [3,3,2] => 7
[[1,2,6],[3,4,8],[5,7]] => [3,3,2] => 7
[[1,4,5],[2,6,8],[3,7]] => [3,3,2] => 7
[[1,3,5],[2,6,8],[4,7]] => [3,3,2] => 7
[[1,2,5],[3,6,8],[4,7]] => [3,3,2] => 7
[[1,3,4],[2,6,8],[5,7]] => [3,3,2] => 7
[[1,2,4],[3,6,8],[5,7]] => [3,3,2] => 7
[[1,2,3],[4,6,8],[5,7]] => [3,3,2] => 7
[[1,3,5],[2,4,8],[6,7]] => [3,3,2] => 7
[[1,2,5],[3,4,8],[6,7]] => [3,3,2] => 7
[[1,3,4],[2,5,8],[6,7]] => [3,3,2] => 7
[[1,2,4],[3,5,8],[6,7]] => [3,3,2] => 7
[[1,2,3],[4,5,8],[6,7]] => [3,3,2] => 7
[[1,4,6],[2,5,7],[3,8]] => [3,3,2] => 7
[[1,3,6],[2,5,7],[4,8]] => [3,3,2] => 7
[[1,2,6],[3,5,7],[4,8]] => [3,3,2] => 7
[[1,3,6],[2,4,7],[5,8]] => [3,3,2] => 7
[[1,2,6],[3,4,7],[5,8]] => [3,3,2] => 7
[[1,4,5],[2,6,7],[3,8]] => [3,3,2] => 7
[[1,3,5],[2,6,7],[4,8]] => [3,3,2] => 7
[[1,2,5],[3,6,7],[4,8]] => [3,3,2] => 7
[[1,3,4],[2,6,7],[5,8]] => [3,3,2] => 7
[[1,2,4],[3,6,7],[5,8]] => [3,3,2] => 7
[[1,2,3],[4,6,7],[5,8]] => [3,3,2] => 7
[[1,3,5],[2,4,7],[6,8]] => [3,3,2] => 7
[[1,2,5],[3,4,7],[6,8]] => [3,3,2] => 7
[[1,3,4],[2,5,7],[6,8]] => [3,3,2] => 7
[[1,2,4],[3,5,7],[6,8]] => [3,3,2] => 7
[[1,2,3],[4,5,7],[6,8]] => [3,3,2] => 7
[[1,3,5],[2,4,6],[7,8]] => [3,3,2] => 7
[[1,2,5],[3,4,6],[7,8]] => [3,3,2] => 7
[[1,3,4],[2,5,6],[7,8]] => [3,3,2] => 7
[[1,2,4],[3,5,6],[7,8]] => [3,3,2] => 7
[[1,2,3],[4,5,6],[7,8]] => [3,3,2] => 7
[[1,5,7],[2,6,8],[3],[4]] => [3,3,1,1] => 8
[[1,4,7],[2,6,8],[3],[5]] => [3,3,1,1] => 8
[[1,3,7],[2,6,8],[4],[5]] => [3,3,1,1] => 8
[[1,2,7],[3,6,8],[4],[5]] => [3,3,1,1] => 8
[[1,4,7],[2,5,8],[3],[6]] => [3,3,1,1] => 8
[[1,3,7],[2,5,8],[4],[6]] => [3,3,1,1] => 8
[[1,2,7],[3,5,8],[4],[6]] => [3,3,1,1] => 8
[[1,3,7],[2,4,8],[5],[6]] => [3,3,1,1] => 8
[[1,2,7],[3,4,8],[5],[6]] => [3,3,1,1] => 8
[[1,5,6],[2,7,8],[3],[4]] => [3,3,1,1] => 8
[[1,4,6],[2,7,8],[3],[5]] => [3,3,1,1] => 8
[[1,3,6],[2,7,8],[4],[5]] => [3,3,1,1] => 8
[[1,2,6],[3,7,8],[4],[5]] => [3,3,1,1] => 8
[[1,4,5],[2,7,8],[3],[6]] => [3,3,1,1] => 8
[[1,3,5],[2,7,8],[4],[6]] => [3,3,1,1] => 8
[[1,2,5],[3,7,8],[4],[6]] => [3,3,1,1] => 8
[[1,3,4],[2,7,8],[5],[6]] => [3,3,1,1] => 8
[[1,2,4],[3,7,8],[5],[6]] => [3,3,1,1] => 8
[[1,2,3],[4,7,8],[5],[6]] => [3,3,1,1] => 8
[[1,4,6],[2,5,8],[3],[7]] => [3,3,1,1] => 8
[[1,3,6],[2,5,8],[4],[7]] => [3,3,1,1] => 8
[[1,2,6],[3,5,8],[4],[7]] => [3,3,1,1] => 8
[[1,3,6],[2,4,8],[5],[7]] => [3,3,1,1] => 8
[[1,2,6],[3,4,8],[5],[7]] => [3,3,1,1] => 8
[[1,4,5],[2,6,8],[3],[7]] => [3,3,1,1] => 8
[[1,3,5],[2,6,8],[4],[7]] => [3,3,1,1] => 8
[[1,2,5],[3,6,8],[4],[7]] => [3,3,1,1] => 8
[[1,3,4],[2,6,8],[5],[7]] => [3,3,1,1] => 8
[[1,2,4],[3,6,8],[5],[7]] => [3,3,1,1] => 8
[[1,2,3],[4,6,8],[5],[7]] => [3,3,1,1] => 8
[[1,3,5],[2,4,8],[6],[7]] => [3,3,1,1] => 8
[[1,2,5],[3,4,8],[6],[7]] => [3,3,1,1] => 8
[[1,3,4],[2,5,8],[6],[7]] => [3,3,1,1] => 8
[[1,2,4],[3,5,8],[6],[7]] => [3,3,1,1] => 8
[[1,2,3],[4,5,8],[6],[7]] => [3,3,1,1] => 8
[[1,4,6],[2,5,7],[3],[8]] => [3,3,1,1] => 8
[[1,3,6],[2,5,7],[4],[8]] => [3,3,1,1] => 8
[[1,2,6],[3,5,7],[4],[8]] => [3,3,1,1] => 8
[[1,3,6],[2,4,7],[5],[8]] => [3,3,1,1] => 8
[[1,2,6],[3,4,7],[5],[8]] => [3,3,1,1] => 8
[[1,4,5],[2,6,7],[3],[8]] => [3,3,1,1] => 8
[[1,3,5],[2,6,7],[4],[8]] => [3,3,1,1] => 8
[[1,2,5],[3,6,7],[4],[8]] => [3,3,1,1] => 8
[[1,3,4],[2,6,7],[5],[8]] => [3,3,1,1] => 8
[[1,2,4],[3,6,7],[5],[8]] => [3,3,1,1] => 8
[[1,2,3],[4,6,7],[5],[8]] => [3,3,1,1] => 8
[[1,3,5],[2,4,7],[6],[8]] => [3,3,1,1] => 8
[[1,2,5],[3,4,7],[6],[8]] => [3,3,1,1] => 8
[[1,3,4],[2,5,7],[6],[8]] => [3,3,1,1] => 8
[[1,2,4],[3,5,7],[6],[8]] => [3,3,1,1] => 8
[[1,2,3],[4,5,7],[6],[8]] => [3,3,1,1] => 8
[[1,3,5],[2,4,6],[7],[8]] => [3,3,1,1] => 8
[[1,2,5],[3,4,6],[7],[8]] => [3,3,1,1] => 8
[[1,3,4],[2,5,6],[7],[8]] => [3,3,1,1] => 8
[[1,2,4],[3,5,6],[7],[8]] => [3,3,1,1] => 8
[[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 8
[[1,5,8],[2,6],[3,7],[4]] => [3,2,2,1] => 9
[[1,4,8],[2,6],[3,7],[5]] => [3,2,2,1] => 9
[[1,3,8],[2,6],[4,7],[5]] => [3,2,2,1] => 9
[[1,2,8],[3,6],[4,7],[5]] => [3,2,2,1] => 9
[[1,4,8],[2,5],[3,7],[6]] => [3,2,2,1] => 9
[[1,3,8],[2,5],[4,7],[6]] => [3,2,2,1] => 9
[[1,2,8],[3,5],[4,7],[6]] => [3,2,2,1] => 9
[[1,3,8],[2,4],[5,7],[6]] => [3,2,2,1] => 9
[[1,2,8],[3,4],[5,7],[6]] => [3,2,2,1] => 9
[[1,4,8],[2,5],[3,6],[7]] => [3,2,2,1] => 9
[[1,3,8],[2,5],[4,6],[7]] => [3,2,2,1] => 9
[[1,2,8],[3,5],[4,6],[7]] => [3,2,2,1] => 9
[[1,3,8],[2,4],[5,6],[7]] => [3,2,2,1] => 9
[[1,2,8],[3,4],[5,6],[7]] => [3,2,2,1] => 9
[[1,5,7],[2,6],[3,8],[4]] => [3,2,2,1] => 9
[[1,4,7],[2,6],[3,8],[5]] => [3,2,2,1] => 9
[[1,3,7],[2,6],[4,8],[5]] => [3,2,2,1] => 9
[[1,2,7],[3,6],[4,8],[5]] => [3,2,2,1] => 9
[[1,4,7],[2,5],[3,8],[6]] => [3,2,2,1] => 9
[[1,3,7],[2,5],[4,8],[6]] => [3,2,2,1] => 9
[[1,2,7],[3,5],[4,8],[6]] => [3,2,2,1] => 9
[[1,3,7],[2,4],[5,8],[6]] => [3,2,2,1] => 9
[[1,2,7],[3,4],[5,8],[6]] => [3,2,2,1] => 9
[[1,5,6],[2,7],[3,8],[4]] => [3,2,2,1] => 9
[[1,4,6],[2,7],[3,8],[5]] => [3,2,2,1] => 9
[[1,3,6],[2,7],[4,8],[5]] => [3,2,2,1] => 9
[[1,2,6],[3,7],[4,8],[5]] => [3,2,2,1] => 9
[[1,4,5],[2,7],[3,8],[6]] => [3,2,2,1] => 9
[[1,3,5],[2,7],[4,8],[6]] => [3,2,2,1] => 9
[[1,2,5],[3,7],[4,8],[6]] => [3,2,2,1] => 9
[[1,3,4],[2,7],[5,8],[6]] => [3,2,2,1] => 9
[[1,2,4],[3,7],[5,8],[6]] => [3,2,2,1] => 9
[[1,2,3],[4,7],[5,8],[6]] => [3,2,2,1] => 9
[[1,4,6],[2,5],[3,8],[7]] => [3,2,2,1] => 9
[[1,3,6],[2,5],[4,8],[7]] => [3,2,2,1] => 9
[[1,2,6],[3,5],[4,8],[7]] => [3,2,2,1] => 9
[[1,3,6],[2,4],[5,8],[7]] => [3,2,2,1] => 9
[[1,2,6],[3,4],[5,8],[7]] => [3,2,2,1] => 9
[[1,4,5],[2,6],[3,8],[7]] => [3,2,2,1] => 9
[[1,3,5],[2,6],[4,8],[7]] => [3,2,2,1] => 9
[[1,2,5],[3,6],[4,8],[7]] => [3,2,2,1] => 9
[[1,3,4],[2,6],[5,8],[7]] => [3,2,2,1] => 9
[[1,2,4],[3,6],[5,8],[7]] => [3,2,2,1] => 9
[[1,2,3],[4,6],[5,8],[7]] => [3,2,2,1] => 9
[[1,3,5],[2,4],[6,8],[7]] => [3,2,2,1] => 9
[[1,2,5],[3,4],[6,8],[7]] => [3,2,2,1] => 9
[[1,3,4],[2,5],[6,8],[7]] => [3,2,2,1] => 9
[[1,2,4],[3,5],[6,8],[7]] => [3,2,2,1] => 9
[[1,2,3],[4,5],[6,8],[7]] => [3,2,2,1] => 9
[[1,4,7],[2,5],[3,6],[8]] => [3,2,2,1] => 9
[[1,3,7],[2,5],[4,6],[8]] => [3,2,2,1] => 9
[[1,2,7],[3,5],[4,6],[8]] => [3,2,2,1] => 9
[[1,3,7],[2,4],[5,6],[8]] => [3,2,2,1] => 9
[[1,2,7],[3,4],[5,6],[8]] => [3,2,2,1] => 9
[[1,4,6],[2,5],[3,7],[8]] => [3,2,2,1] => 9
[[1,3,6],[2,5],[4,7],[8]] => [3,2,2,1] => 9
[[1,2,6],[3,5],[4,7],[8]] => [3,2,2,1] => 9
[[1,3,6],[2,4],[5,7],[8]] => [3,2,2,1] => 9
[[1,2,6],[3,4],[5,7],[8]] => [3,2,2,1] => 9
[[1,4,5],[2,6],[3,7],[8]] => [3,2,2,1] => 9
[[1,3,5],[2,6],[4,7],[8]] => [3,2,2,1] => 9
[[1,2,5],[3,6],[4,7],[8]] => [3,2,2,1] => 9
[[1,3,4],[2,6],[5,7],[8]] => [3,2,2,1] => 9
[[1,2,4],[3,6],[5,7],[8]] => [3,2,2,1] => 9
[[1,2,3],[4,6],[5,7],[8]] => [3,2,2,1] => 9
[[1,3,5],[2,4],[6,7],[8]] => [3,2,2,1] => 9
[[1,2,5],[3,4],[6,7],[8]] => [3,2,2,1] => 9
[[1,3,4],[2,5],[6,7],[8]] => [3,2,2,1] => 9
[[1,2,4],[3,5],[6,7],[8]] => [3,2,2,1] => 9
[[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 9
[[1,6,8],[2,7],[3],[4],[5]] => [3,2,1,1,1] => 11
[[1,5,8],[2,7],[3],[4],[6]] => [3,2,1,1,1] => 11
[[1,4,8],[2,7],[3],[5],[6]] => [3,2,1,1,1] => 11
[[1,3,8],[2,7],[4],[5],[6]] => [3,2,1,1,1] => 11
[[1,2,8],[3,7],[4],[5],[6]] => [3,2,1,1,1] => 11
[[1,5,8],[2,6],[3],[4],[7]] => [3,2,1,1,1] => 11
[[1,4,8],[2,6],[3],[5],[7]] => [3,2,1,1,1] => 11
[[1,3,8],[2,6],[4],[5],[7]] => [3,2,1,1,1] => 11
[[1,2,8],[3,6],[4],[5],[7]] => [3,2,1,1,1] => 11
[[1,4,8],[2,5],[3],[6],[7]] => [3,2,1,1,1] => 11
[[1,3,8],[2,5],[4],[6],[7]] => [3,2,1,1,1] => 11
[[1,2,8],[3,5],[4],[6],[7]] => [3,2,1,1,1] => 11
[[1,3,8],[2,4],[5],[6],[7]] => [3,2,1,1,1] => 11
[[1,2,8],[3,4],[5],[6],[7]] => [3,2,1,1,1] => 11
[[1,6,7],[2,8],[3],[4],[5]] => [3,2,1,1,1] => 11
[[1,5,7],[2,8],[3],[4],[6]] => [3,2,1,1,1] => 11
[[1,4,7],[2,8],[3],[5],[6]] => [3,2,1,1,1] => 11
[[1,3,7],[2,8],[4],[5],[6]] => [3,2,1,1,1] => 11
[[1,2,7],[3,8],[4],[5],[6]] => [3,2,1,1,1] => 11
[[1,5,6],[2,8],[3],[4],[7]] => [3,2,1,1,1] => 11
[[1,4,6],[2,8],[3],[5],[7]] => [3,2,1,1,1] => 11
[[1,3,6],[2,8],[4],[5],[7]] => [3,2,1,1,1] => 11
[[1,2,6],[3,8],[4],[5],[7]] => [3,2,1,1,1] => 11
[[1,4,5],[2,8],[3],[6],[7]] => [3,2,1,1,1] => 11
[[1,3,5],[2,8],[4],[6],[7]] => [3,2,1,1,1] => 11
[[1,2,5],[3,8],[4],[6],[7]] => [3,2,1,1,1] => 11
[[1,3,4],[2,8],[5],[6],[7]] => [3,2,1,1,1] => 11
[[1,2,4],[3,8],[5],[6],[7]] => [3,2,1,1,1] => 11
[[1,2,3],[4,8],[5],[6],[7]] => [3,2,1,1,1] => 11
[[1,5,7],[2,6],[3],[4],[8]] => [3,2,1,1,1] => 11
[[1,4,7],[2,6],[3],[5],[8]] => [3,2,1,1,1] => 11
[[1,3,7],[2,6],[4],[5],[8]] => [3,2,1,1,1] => 11
[[1,2,7],[3,6],[4],[5],[8]] => [3,2,1,1,1] => 11
[[1,4,7],[2,5],[3],[6],[8]] => [3,2,1,1,1] => 11
[[1,3,7],[2,5],[4],[6],[8]] => [3,2,1,1,1] => 11
[[1,2,7],[3,5],[4],[6],[8]] => [3,2,1,1,1] => 11
[[1,3,7],[2,4],[5],[6],[8]] => [3,2,1,1,1] => 11
[[1,2,7],[3,4],[5],[6],[8]] => [3,2,1,1,1] => 11
[[1,5,6],[2,7],[3],[4],[8]] => [3,2,1,1,1] => 11
[[1,4,6],[2,7],[3],[5],[8]] => [3,2,1,1,1] => 11
[[1,3,6],[2,7],[4],[5],[8]] => [3,2,1,1,1] => 11
[[1,2,6],[3,7],[4],[5],[8]] => [3,2,1,1,1] => 11
[[1,4,5],[2,7],[3],[6],[8]] => [3,2,1,1,1] => 11
[[1,3,5],[2,7],[4],[6],[8]] => [3,2,1,1,1] => 11
[[1,2,5],[3,7],[4],[6],[8]] => [3,2,1,1,1] => 11
[[1,3,4],[2,7],[5],[6],[8]] => [3,2,1,1,1] => 11
[[1,2,4],[3,7],[5],[6],[8]] => [3,2,1,1,1] => 11
[[1,2,3],[4,7],[5],[6],[8]] => [3,2,1,1,1] => 11
[[1,4,6],[2,5],[3],[7],[8]] => [3,2,1,1,1] => 11
[[1,3,6],[2,5],[4],[7],[8]] => [3,2,1,1,1] => 11
[[1,2,6],[3,5],[4],[7],[8]] => [3,2,1,1,1] => 11
[[1,3,6],[2,4],[5],[7],[8]] => [3,2,1,1,1] => 11
[[1,2,6],[3,4],[5],[7],[8]] => [3,2,1,1,1] => 11
[[1,4,5],[2,6],[3],[7],[8]] => [3,2,1,1,1] => 11
[[1,3,5],[2,6],[4],[7],[8]] => [3,2,1,1,1] => 11
[[1,2,5],[3,6],[4],[7],[8]] => [3,2,1,1,1] => 11
[[1,3,4],[2,6],[5],[7],[8]] => [3,2,1,1,1] => 11
[[1,2,4],[3,6],[5],[7],[8]] => [3,2,1,1,1] => 11
[[1,2,3],[4,6],[5],[7],[8]] => [3,2,1,1,1] => 11
[[1,3,5],[2,4],[6],[7],[8]] => [3,2,1,1,1] => 11
[[1,2,5],[3,4],[6],[7],[8]] => [3,2,1,1,1] => 11
[[1,3,4],[2,5],[6],[7],[8]] => [3,2,1,1,1] => 11
[[1,2,4],[3,5],[6],[7],[8]] => [3,2,1,1,1] => 11
[[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 11
[[1,7,8],[2],[3],[4],[5],[6]] => [3,1,1,1,1,1] => 15
[[1,6,8],[2],[3],[4],[5],[7]] => [3,1,1,1,1,1] => 15
[[1,5,8],[2],[3],[4],[6],[7]] => [3,1,1,1,1,1] => 15
[[1,4,8],[2],[3],[5],[6],[7]] => [3,1,1,1,1,1] => 15
[[1,3,8],[2],[4],[5],[6],[7]] => [3,1,1,1,1,1] => 15
[[1,2,8],[3],[4],[5],[6],[7]] => [3,1,1,1,1,1] => 15
[[1,6,7],[2],[3],[4],[5],[8]] => [3,1,1,1,1,1] => 15
[[1,5,7],[2],[3],[4],[6],[8]] => [3,1,1,1,1,1] => 15
[[1,4,7],[2],[3],[5],[6],[8]] => [3,1,1,1,1,1] => 15
[[1,3,7],[2],[4],[5],[6],[8]] => [3,1,1,1,1,1] => 15
[[1,2,7],[3],[4],[5],[6],[8]] => [3,1,1,1,1,1] => 15
[[1,5,6],[2],[3],[4],[7],[8]] => [3,1,1,1,1,1] => 15
[[1,4,6],[2],[3],[5],[7],[8]] => [3,1,1,1,1,1] => 15
[[1,3,6],[2],[4],[5],[7],[8]] => [3,1,1,1,1,1] => 15
[[1,2,6],[3],[4],[5],[7],[8]] => [3,1,1,1,1,1] => 15
[[1,4,5],[2],[3],[6],[7],[8]] => [3,1,1,1,1,1] => 15
[[1,3,5],[2],[4],[6],[7],[8]] => [3,1,1,1,1,1] => 15
[[1,2,5],[3],[4],[6],[7],[8]] => [3,1,1,1,1,1] => 15
[[1,3,4],[2],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 15
[[1,2,4],[3],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 15
[[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 15
[[1,5],[2,6],[3,7],[4,8]] => [2,2,2,2] => 12
[[1,4],[2,6],[3,7],[5,8]] => [2,2,2,2] => 12
[[1,3],[2,6],[4,7],[5,8]] => [2,2,2,2] => 12
[[1,2],[3,6],[4,7],[5,8]] => [2,2,2,2] => 12
[[1,4],[2,5],[3,7],[6,8]] => [2,2,2,2] => 12
[[1,3],[2,5],[4,7],[6,8]] => [2,2,2,2] => 12
[[1,2],[3,5],[4,7],[6,8]] => [2,2,2,2] => 12
[[1,3],[2,4],[5,7],[6,8]] => [2,2,2,2] => 12
[[1,2],[3,4],[5,7],[6,8]] => [2,2,2,2] => 12
[[1,4],[2,5],[3,6],[7,8]] => [2,2,2,2] => 12
[[1,3],[2,5],[4,6],[7,8]] => [2,2,2,2] => 12
[[1,2],[3,5],[4,6],[7,8]] => [2,2,2,2] => 12
[[1,3],[2,4],[5,6],[7,8]] => [2,2,2,2] => 12
[[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => 12
[[1,6],[2,7],[3,8],[4],[5]] => [2,2,2,1,1] => 13
[[1,5],[2,7],[3,8],[4],[6]] => [2,2,2,1,1] => 13
[[1,4],[2,7],[3,8],[5],[6]] => [2,2,2,1,1] => 13
[[1,3],[2,7],[4,8],[5],[6]] => [2,2,2,1,1] => 13
[[1,2],[3,7],[4,8],[5],[6]] => [2,2,2,1,1] => 13
[[1,5],[2,6],[3,8],[4],[7]] => [2,2,2,1,1] => 13
[[1,4],[2,6],[3,8],[5],[7]] => [2,2,2,1,1] => 13
[[1,3],[2,6],[4,8],[5],[7]] => [2,2,2,1,1] => 13
[[1,2],[3,6],[4,8],[5],[7]] => [2,2,2,1,1] => 13
[[1,4],[2,5],[3,8],[6],[7]] => [2,2,2,1,1] => 13
[[1,3],[2,5],[4,8],[6],[7]] => [2,2,2,1,1] => 13
[[1,2],[3,5],[4,8],[6],[7]] => [2,2,2,1,1] => 13
[[1,3],[2,4],[5,8],[6],[7]] => [2,2,2,1,1] => 13
[[1,2],[3,4],[5,8],[6],[7]] => [2,2,2,1,1] => 13
[[1,5],[2,6],[3,7],[4],[8]] => [2,2,2,1,1] => 13
[[1,4],[2,6],[3,7],[5],[8]] => [2,2,2,1,1] => 13
[[1,3],[2,6],[4,7],[5],[8]] => [2,2,2,1,1] => 13
[[1,2],[3,6],[4,7],[5],[8]] => [2,2,2,1,1] => 13
[[1,4],[2,5],[3,7],[6],[8]] => [2,2,2,1,1] => 13
[[1,3],[2,5],[4,7],[6],[8]] => [2,2,2,1,1] => 13
[[1,2],[3,5],[4,7],[6],[8]] => [2,2,2,1,1] => 13
[[1,3],[2,4],[5,7],[6],[8]] => [2,2,2,1,1] => 13
[[1,2],[3,4],[5,7],[6],[8]] => [2,2,2,1,1] => 13
[[1,4],[2,5],[3,6],[7],[8]] => [2,2,2,1,1] => 13
[[1,3],[2,5],[4,6],[7],[8]] => [2,2,2,1,1] => 13
[[1,2],[3,5],[4,6],[7],[8]] => [2,2,2,1,1] => 13
[[1,3],[2,4],[5,6],[7],[8]] => [2,2,2,1,1] => 13
[[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 13
[[1,7],[2,8],[3],[4],[5],[6]] => [2,2,1,1,1,1] => 16
[[1,6],[2,8],[3],[4],[5],[7]] => [2,2,1,1,1,1] => 16
[[1,5],[2,8],[3],[4],[6],[7]] => [2,2,1,1,1,1] => 16
[[1,4],[2,8],[3],[5],[6],[7]] => [2,2,1,1,1,1] => 16
[[1,3],[2,8],[4],[5],[6],[7]] => [2,2,1,1,1,1] => 16
[[1,2],[3,8],[4],[5],[6],[7]] => [2,2,1,1,1,1] => 16
[[1,6],[2,7],[3],[4],[5],[8]] => [2,2,1,1,1,1] => 16
[[1,5],[2,7],[3],[4],[6],[8]] => [2,2,1,1,1,1] => 16
[[1,4],[2,7],[3],[5],[6],[8]] => [2,2,1,1,1,1] => 16
[[1,3],[2,7],[4],[5],[6],[8]] => [2,2,1,1,1,1] => 16
[[1,2],[3,7],[4],[5],[6],[8]] => [2,2,1,1,1,1] => 16
[[1,5],[2,6],[3],[4],[7],[8]] => [2,2,1,1,1,1] => 16
[[1,4],[2,6],[3],[5],[7],[8]] => [2,2,1,1,1,1] => 16
[[1,3],[2,6],[4],[5],[7],[8]] => [2,2,1,1,1,1] => 16
[[1,2],[3,6],[4],[5],[7],[8]] => [2,2,1,1,1,1] => 16
[[1,4],[2,5],[3],[6],[7],[8]] => [2,2,1,1,1,1] => 16
[[1,3],[2,5],[4],[6],[7],[8]] => [2,2,1,1,1,1] => 16
[[1,2],[3,5],[4],[6],[7],[8]] => [2,2,1,1,1,1] => 16
[[1,3],[2,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 16
[[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 16
[[1,8],[2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1,1] => 21
[[1,7],[2],[3],[4],[5],[6],[8]] => [2,1,1,1,1,1,1] => 21
[[1,6],[2],[3],[4],[5],[7],[8]] => [2,1,1,1,1,1,1] => 21
[[1,5],[2],[3],[4],[6],[7],[8]] => [2,1,1,1,1,1,1] => 21
[[1,4],[2],[3],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 21
[[1,3],[2],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 21
[[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 21
[[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1] => 28
[[1,3,5,7,9],[2,4,6,8,10]] => [5,5] => 5
[[1,3,5,7,8],[2,4,6,9,10]] => [5,5] => 5
[[1,3,5,6,9],[2,4,7,8,10]] => [5,5] => 5
[[1,3,5,6,8],[2,4,7,9,10]] => [5,5] => 5
[[1,3,5,6,7],[2,4,8,9,10]] => [5,5] => 5
[[1,3,4,7,9],[2,5,6,8,10]] => [5,5] => 5
[[1,3,4,7,8],[2,5,6,9,10]] => [5,5] => 5
[[1,3,4,6,9],[2,5,7,8,10]] => [5,5] => 5
[[1,3,4,6,8],[2,5,7,9,10]] => [5,5] => 5
[[1,3,4,6,7],[2,5,8,9,10]] => [5,5] => 5
[[1,3,4,5,9],[2,6,7,8,10]] => [5,5] => 5
[[1,3,4,5,8],[2,6,7,9,10]] => [5,5] => 5
[[1,3,4,5,7],[2,6,8,9,10]] => [5,5] => 5
[[1,3,4,5,6],[2,7,8,9,10]] => [5,5] => 5
[[1,2,5,7,9],[3,4,6,8,10]] => [5,5] => 5
[[1,2,5,7,8],[3,4,6,9,10]] => [5,5] => 5
[[1,2,5,6,9],[3,4,7,8,10]] => [5,5] => 5
[[1,2,5,6,8],[3,4,7,9,10]] => [5,5] => 5
[[1,2,5,6,7],[3,4,8,9,10]] => [5,5] => 5
[[1,2,4,7,9],[3,5,6,8,10]] => [5,5] => 5
[[1,2,4,7,8],[3,5,6,9,10]] => [5,5] => 5
[[1,2,4,6,9],[3,5,7,8,10]] => [5,5] => 5
[[1,2,4,6,8],[3,5,7,9,10]] => [5,5] => 5
[[1,2,4,6,7],[3,5,8,9,10]] => [5,5] => 5
[[1,2,4,5,9],[3,6,7,8,10]] => [5,5] => 5
[[1,2,4,5,8],[3,6,7,9,10]] => [5,5] => 5
[[1,2,4,5,7],[3,6,8,9,10]] => [5,5] => 5
[[1,2,4,5,6],[3,7,8,9,10]] => [5,5] => 5
[[1,2,3,7,9],[4,5,6,8,10]] => [5,5] => 5
[[1,2,3,7,8],[4,5,6,9,10]] => [5,5] => 5
[[1,2,3,6,9],[4,5,7,8,10]] => [5,5] => 5
[[1,2,3,6,8],[4,5,7,9,10]] => [5,5] => 5
[[1,2,3,6,7],[4,5,8,9,10]] => [5,5] => 5
[[1,2,3,5,9],[4,6,7,8,10]] => [5,5] => 5
[[1,2,3,5,8],[4,6,7,9,10]] => [5,5] => 5
[[1,2,3,5,7],[4,6,8,9,10]] => [5,5] => 5
[[1,2,3,5,6],[4,7,8,9,10]] => [5,5] => 5
[[1,2,3,4,9],[5,6,7,8,10]] => [5,5] => 5
[[1,2,3,4,8],[5,6,7,9,10]] => [5,5] => 5
[[1,2,3,4,7],[5,6,8,9,10]] => [5,5] => 5
[[1,2,3,4,6],[5,7,8,9,10]] => [5,5] => 5
[[1,2,3,4,5],[6,7,8,9,10]] => [5,5] => 5
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [6,6] => 6
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [6,6] => 6
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => [6,6] => 6
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [6,6] => 6
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [6,6] => 6
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => [6,6] => 6
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => [6,6] => 6
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => [6,6] => 6
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [6,6] => 6
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => [6,6] => 6
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [6,6] => 6
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => [6,6] => 6
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [6,6] => 6
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => [6,6] => 6
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => [6,6] => 6
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => [6,6] => 6
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => [6,6] => 6
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => [6,6] => 6
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => [6,6] => 6
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => [6,6] => 6
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => [6,6] => 6
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => [6,6] => 6
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [6,6] => 6
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => [6,6] => 6
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => [6,6] => 6
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => [6,6] => 6
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => [6,6] => 6
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => [6,6] => 6
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [6,6] => 6
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => [6,6] => 6
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => [6,6] => 6
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => [6,6] => 6
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [6,6] => 6
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [6,6] => 6
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => [6,6] => 6
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => [6,6] => 6
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => [6,6] => 6
[[1,3,4,5,6,11],[2,7,8,9,10,12]] => [6,6] => 6
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => [6,6] => 6
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => [6,6] => 6
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => [6,6] => 6
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => [6,6] => 6
[[1,2,5,7,9,11],[3,4,6,8,10,12]] => [6,6] => 6
[[1,2,5,7,9,10],[3,4,6,8,11,12]] => [6,6] => 6
[[1,2,5,7,8,11],[3,4,6,9,10,12]] => [6,6] => 6
[[1,2,5,7,8,10],[3,4,6,9,11,12]] => [6,6] => 6
[[1,2,5,7,8,9],[3,4,6,10,11,12]] => [6,6] => 6
[[1,2,5,6,9,11],[3,4,7,8,10,12]] => [6,6] => 6
[[1,2,5,6,9,10],[3,4,7,8,11,12]] => [6,6] => 6
[[1,2,5,6,8,11],[3,4,7,9,10,12]] => [6,6] => 6
[[1,2,5,6,8,10],[3,4,7,9,11,12]] => [6,6] => 6
[[1,2,5,6,8,9],[3,4,7,10,11,12]] => [6,6] => 6
[[1,2,5,6,7,11],[3,4,8,9,10,12]] => [6,6] => 6
[[1,2,5,6,7,10],[3,4,8,9,11,12]] => [6,6] => 6
[[1,2,5,6,7,9],[3,4,8,10,11,12]] => [6,6] => 6
[[1,2,5,6,7,8],[3,4,9,10,11,12]] => [6,6] => 6
[[1,2,4,7,9,11],[3,5,6,8,10,12]] => [6,6] => 6
[[1,2,4,7,9,10],[3,5,6,8,11,12]] => [6,6] => 6
[[1,2,4,7,8,11],[3,5,6,9,10,12]] => [6,6] => 6
[[1,2,4,7,8,10],[3,5,6,9,11,12]] => [6,6] => 6
[[1,2,4,7,8,9],[3,5,6,10,11,12]] => [6,6] => 6
[[1,2,4,6,9,11],[3,5,7,8,10,12]] => [6,6] => 6
[[1,2,4,6,9,10],[3,5,7,8,11,12]] => [6,6] => 6
[[1,2,4,6,8,11],[3,5,7,9,10,12]] => [6,6] => 6
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [6,6] => 6
[[1,2,4,6,8,9],[3,5,7,10,11,12]] => [6,6] => 6
[[1,2,4,6,7,11],[3,5,8,9,10,12]] => [6,6] => 6
[[1,2,4,6,7,10],[3,5,8,9,11,12]] => [6,6] => 6
[[1,2,4,6,7,9],[3,5,8,10,11,12]] => [6,6] => 6
[[1,2,4,6,7,8],[3,5,9,10,11,12]] => [6,6] => 6
[[1,2,4,5,9,11],[3,6,7,8,10,12]] => [6,6] => 6
[[1,2,4,5,9,10],[3,6,7,8,11,12]] => [6,6] => 6
[[1,2,4,5,8,11],[3,6,7,9,10,12]] => [6,6] => 6
[[1,2,4,5,8,10],[3,6,7,9,11,12]] => [6,6] => 6
[[1,2,4,5,8,9],[3,6,7,10,11,12]] => [6,6] => 6
[[1,2,4,5,7,11],[3,6,8,9,10,12]] => [6,6] => 6
[[1,2,4,5,7,10],[3,6,8,9,11,12]] => [6,6] => 6
[[1,2,4,5,7,9],[3,6,8,10,11,12]] => [6,6] => 6
[[1,2,4,5,7,8],[3,6,9,10,11,12]] => [6,6] => 6
[[1,2,4,5,6,11],[3,7,8,9,10,12]] => [6,6] => 6
[[1,2,4,5,6,10],[3,7,8,9,11,12]] => [6,6] => 6
[[1,2,4,5,6,9],[3,7,8,10,11,12]] => [6,6] => 6
[[1,2,4,5,6,8],[3,7,9,10,11,12]] => [6,6] => 6
[[1,2,4,5,6,7],[3,8,9,10,11,12]] => [6,6] => 6
[[1,2,3,7,9,11],[4,5,6,8,10,12]] => [6,6] => 6
[[1,2,3,7,9,10],[4,5,6,8,11,12]] => [6,6] => 6
[[1,2,3,7,8,11],[4,5,6,9,10,12]] => [6,6] => 6
[[1,2,3,7,8,10],[4,5,6,9,11,12]] => [6,6] => 6
[[1,2,3,7,8,9],[4,5,6,10,11,12]] => [6,6] => 6
[[1,2,3,6,9,11],[4,5,7,8,10,12]] => [6,6] => 6
[[1,2,3,6,9,10],[4,5,7,8,11,12]] => [6,6] => 6
[[1,2,3,6,8,11],[4,5,7,9,10,12]] => [6,6] => 6
[[1,2,3,6,8,10],[4,5,7,9,11,12]] => [6,6] => 6
[[1,2,3,6,8,9],[4,5,7,10,11,12]] => [6,6] => 6
[[1,2,3,6,7,11],[4,5,8,9,10,12]] => [6,6] => 6
[[1,2,3,6,7,10],[4,5,8,9,11,12]] => [6,6] => 6
[[1,2,3,6,7,9],[4,5,8,10,11,12]] => [6,6] => 6
[[1,2,3,6,7,8],[4,5,9,10,11,12]] => [6,6] => 6
[[1,2,3,5,9,11],[4,6,7,8,10,12]] => [6,6] => 6
[[1,2,3,5,9,10],[4,6,7,8,11,12]] => [6,6] => 6
[[1,2,3,5,8,11],[4,6,7,9,10,12]] => [6,6] => 6
[[1,2,3,5,8,10],[4,6,7,9,11,12]] => [6,6] => 6
[[1,2,3,5,8,9],[4,6,7,10,11,12]] => [6,6] => 6
[[1,2,3,5,7,11],[4,6,8,9,10,12]] => [6,6] => 6
[[1,2,3,5,7,10],[4,6,8,9,11,12]] => [6,6] => 6
[[1,2,3,5,7,9],[4,6,8,10,11,12]] => [6,6] => 6
[[1,2,3,5,7,8],[4,6,9,10,11,12]] => [6,6] => 6
[[1,2,3,5,6,11],[4,7,8,9,10,12]] => [6,6] => 6
[[1,2,3,5,6,10],[4,7,8,9,11,12]] => [6,6] => 6
[[1,2,3,5,6,9],[4,7,8,10,11,12]] => [6,6] => 6
[[1,2,3,5,6,8],[4,7,9,10,11,12]] => [6,6] => 6
[[1,2,3,5,6,7],[4,8,9,10,11,12]] => [6,6] => 6
[[1,2,3,4,9,11],[5,6,7,8,10,12]] => [6,6] => 6
[[1,2,3,4,9,10],[5,6,7,8,11,12]] => [6,6] => 6
[[1,2,3,4,8,11],[5,6,7,9,10,12]] => [6,6] => 6
[[1,2,3,4,8,10],[5,6,7,9,11,12]] => [6,6] => 6
[[1,2,3,4,8,9],[5,6,7,10,11,12]] => [6,6] => 6
[[1,2,3,4,7,11],[5,6,8,9,10,12]] => [6,6] => 6
[[1,2,3,4,7,10],[5,6,8,9,11,12]] => [6,6] => 6
[[1,2,3,4,7,9],[5,6,8,10,11,12]] => [6,6] => 6
[[1,2,3,4,7,8],[5,6,9,10,11,12]] => [6,6] => 6
[[1,2,3,4,6,11],[5,7,8,9,10,12]] => [6,6] => 6
[[1,2,3,4,6,10],[5,7,8,9,11,12]] => [6,6] => 6
[[1,2,3,4,6,9],[5,7,8,10,11,12]] => [6,6] => 6
[[1,2,3,4,6,8],[5,7,9,10,11,12]] => [6,6] => 6
[[1,2,3,4,6,7],[5,8,9,10,11,12]] => [6,6] => 6
[[1,2,3,4,5,11],[6,7,8,9,10,12]] => [6,6] => 6
[[1,2,3,4,5,10],[6,7,8,9,11,12]] => [6,6] => 6
[[1,2,3,4,5,9],[6,7,8,10,11,12]] => [6,6] => 6
[[1,2,3,4,5,8],[6,7,9,10,11,12]] => [6,6] => 6
[[1,2,3,4,5,7],[6,8,9,10,11,12]] => [6,6] => 6
[[1,2,3,4,5,6],[7,8,9,10,11,12]] => [6,6] => 6
[[1,2,3,4,5,6,7,8,9]] => [9] => 0
[[1,2,3,4,5,6,7,8],[9]] => [8,1] => 1
[[1,2,3,4,5,6,7],[8,9]] => [7,2] => 2
[[1,2,3,4,5,6,7],[8],[9]] => [7,1,1] => 3
[[1,2,3,4,5,6],[7,8,9]] => [6,3] => 3
[[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 4
[[1,2,3,4,5,6],[7],[8],[9]] => [6,1,1,1] => 6
[[1,2,3,4,5],[6,7,8,9]] => [5,4] => 4
[[1,2,3,4,5],[6,7,8],[9]] => [5,3,1] => 5
[[1,2,3,4,5],[6,7],[8,9]] => [5,2,2] => 6
[[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 7
[[1,2,3,4,5],[6],[7],[8],[9]] => [5,1,1,1,1] => 10
[[1,2,3,4],[5,6,7,8],[9]] => [4,4,1] => 6
[[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => 7
[[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 8
[[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 9
[[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 11
[[1,2,3,4],[5],[6],[7],[8],[9]] => [4,1,1,1,1,1] => 15
[[1,2,3],[4,5,6],[7,8,9]] => [3,3,3] => 9
[[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 10
[[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 12
[[1,2,3],[4,5],[6,7],[8,9]] => [3,2,2,2] => 12
[[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 13
[[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 16
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => 21
[[1,2],[3,4],[5,6],[7,8],[9]] => [2,2,2,2,1] => 16
[[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 18
[[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 22
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => 28
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [1,1,1,1,1,1,1,1,1] => 36
[[1,2,3,4,5,6,7,8,9,10]] => [10] => 0
[[1,2,3,4,5,6,7,8,9],[10]] => [9,1] => 1
[[1,2,3,4,5,6,7,8],[9,10]] => [8,2] => 2
[[1,2,3,4,5,6,7,8],[9],[10]] => [8,1,1] => 3
[[1,2,3,4,5,6,7],[8,9,10]] => [7,3] => 3
[[1,2,3,4,5,6,7],[8,9],[10]] => [7,2,1] => 4
[[1,2,3,4,5,6,7],[8],[9],[10]] => [7,1,1,1] => 6
[[1,2,3,4,5,6],[7,8,9,10]] => [6,4] => 4
[[1,2,3,4,5,6],[7,8,9],[10]] => [6,3,1] => 5
[[1,2,3,4,5,6],[7,8],[9,10]] => [6,2,2] => 6
[[1,2,3,4,5,6],[7,8],[9],[10]] => [6,2,1,1] => 7
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [6,1,1,1,1] => 10
[[1,2,3,4,5],[6,7,8,9],[10]] => [5,4,1] => 6
[[1,2,3,4,5],[6,7,8],[9,10]] => [5,3,2] => 7
[[1,2,3,4,5],[6,7,8],[9],[10]] => [5,3,1,1] => 8
[[1,2,3,4,5],[6,7],[8,9],[10]] => [5,2,2,1] => 9
[[1,2,3,4,5],[6,7],[8],[9],[10]] => [5,2,1,1,1] => 11
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => [5,1,1,1,1,1] => 15
[[1,2,3,4],[5,6,7,8],[9,10]] => [4,4,2] => 8
[[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => 9
[[1,2,3,4],[5,6,7],[8,9,10]] => [4,3,3] => 9
[[1,2,3,4],[5,6,7],[8,9],[10]] => [4,3,2,1] => 10
[[1,2,3,4],[5,6,7],[8],[9],[10]] => [4,3,1,1,1] => 12
[[1,2,3,4],[5,6],[7,8],[9,10]] => [4,2,2,2] => 12
[[1,2,3,4],[5,6],[7,8],[9],[10]] => [4,2,2,1,1] => 13
[[1,2,3,4],[5,6],[7],[8],[9],[10]] => [4,2,1,1,1,1] => 16
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [4,1,1,1,1,1,1] => 21
[[1,2,3],[4,5,6],[7,8,9],[10]] => [3,3,3,1] => 12
[[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => 13
[[1,2,3],[4,5,6],[7,8],[9],[10]] => [3,3,2,1,1] => 14
[[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 17
[[1,2,3],[4,5],[6,7],[8,9],[10]] => [3,2,2,2,1] => 16
[[1,2,3],[4,5],[6,7],[8],[9],[10]] => [3,2,2,1,1,1] => 18
[[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [3,2,1,1,1,1,1] => 22
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [3,1,1,1,1,1,1,1] => 28
[[1,2],[3,4],[5,6],[7,8],[9,10]] => [2,2,2,2,2] => 20
[[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 21
[[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [2,2,2,1,1,1,1] => 24
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 29
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [2,1,1,1,1,1,1,1,1] => 36
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [1,1,1,1,1,1,1,1,1,1] => 45
[[1,3,4,5,6,7,8,9],[2]] => [8,1] => 1
[[1,2,5,6,7,8,9],[3,4]] => [7,2] => 2
[[1,4,5,6,7,8,9],[2],[3]] => [7,1,1] => 3
[[1,2,3,7,8,9],[4,5,6]] => [6,3] => 3
[[1,3,6,7,8,9],[2,5],[4]] => [6,2,1] => 4
[[1,5,6,7,8,9],[2],[3],[4]] => [6,1,1,1] => 6
[[1,2,3,4,9],[5,6,7,8]] => [5,4] => 4
[[1,3,4,8,9],[2,6,7],[5]] => [5,3,1] => 5
[[1,2,7,8,9],[3,4],[5,6]] => [5,2,2] => 6
[[1,4,7,8,9],[2,6],[3],[5]] => [5,2,1,1] => 7
[[1,6,7,8,9],[2],[3],[4],[5]] => [5,1,1,1,1] => 10
[[1,3,4,5],[2,7,8,9],[6]] => [4,4,1] => 6
[[1,2,5,9],[3,4,8],[6,7]] => [4,3,2] => 7
[[1,4,5,9],[2,7,8],[3],[6]] => [4,3,1,1] => 8
[[1,3,8,9],[2,5],[4,7],[6]] => [4,2,2,1] => 9
[[1,5,8,9],[2,7],[3],[4],[6]] => [4,2,1,1,1] => 11
[[1,7,8,9],[2],[3],[4],[5],[6]] => [4,1,1,1,1,1] => 15
[[1,3,6],[2,5,9],[4,8],[7]] => [3,3,2,1] => 10
[[1,5,6],[2,8,9],[3],[4],[7]] => [3,3,1,1,1] => 12
[[1,2,9],[3,4],[5,6],[7,8]] => [3,2,2,2] => 12
[[1,4,9],[2,6],[3,8],[5],[7]] => [3,2,2,1,1] => 13
[[1,6,9],[2,8],[3],[4],[5],[7]] => [3,2,1,1,1,1] => 16
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [3,1,1,1,1,1,1] => 21
[[1,3],[2,5],[4,7],[6,9],[8]] => [2,2,2,2,1] => 16
[[1,5],[2,7],[3,9],[4],[6],[8]] => [2,2,2,1,1,1] => 18
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [2,2,1,1,1,1,1] => 22
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1,1] => 28
[[1,3,4,5,6,7,8,9,10],[2]] => [9,1] => 1
[[1,2,5,6,7,8,9,10],[3,4]] => [8,2] => 2
[[1,4,5,6,7,8,9,10],[2],[3]] => [8,1,1] => 3
[[1,2,3,7,8,9,10],[4,5,6]] => [7,3] => 3
[[1,3,6,7,8,9,10],[2,5],[4]] => [7,2,1] => 4
[[1,5,6,7,8,9,10],[2],[3],[4]] => [7,1,1,1] => 6
[[1,2,3,4,9,10],[5,6,7,8]] => [6,4] => 4
[[1,3,4,8,9,10],[2,6,7],[5]] => [6,3,1] => 5
[[1,2,7,8,9,10],[3,4],[5,6]] => [6,2,2] => 6
[[1,4,7,8,9,10],[2,6],[3],[5]] => [6,2,1,1] => 7
[[1,6,7,8,9,10],[2],[3],[4],[5]] => [6,1,1,1,1] => 10
[[1,3,4,5,10],[2,7,8,9],[6]] => [5,4,1] => 6
[[1,2,5,9,10],[3,4,8],[6,7]] => [5,3,2] => 7
[[1,4,5,9,10],[2,7,8],[3],[6]] => [5,3,1,1] => 8
[[1,3,8,9,10],[2,5],[4,7],[6]] => [5,2,2,1] => 9
[[1,5,8,9,10],[2,7],[3],[4],[6]] => [5,2,1,1,1] => 11
[[1,7,8,9,10],[2],[3],[4],[5],[6]] => [5,1,1,1,1,1] => 15
[[1,2,5,6],[3,4,9,10],[7,8]] => [4,4,2] => 8
[[1,4,5,6],[2,8,9,10],[3],[7]] => [4,4,1,1] => 9
[[1,2,3,10],[4,5,6],[7,8,9]] => [4,3,3] => 9
[[1,3,6,10],[2,5,9],[4,8],[7]] => [4,3,2,1] => 10
[[1,5,6,10],[2,8,9],[3],[4],[7]] => [4,3,1,1,1] => 12
[[1,2,9,10],[3,4],[5,6],[7,8]] => [4,2,2,2] => 12
[[1,4,9,10],[2,6],[3,8],[5],[7]] => [4,2,2,1,1] => 13
[[1,6,9,10],[2,8],[3],[4],[5],[7]] => [4,2,1,1,1,1] => 16
[[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [4,1,1,1,1,1,1] => 21
[[1,3,4],[2,6,7],[5,9,10],[8]] => [3,3,3,1] => 12
[[1,2,7],[3,4,10],[5,6],[8,9]] => [3,3,2,2] => 13
[[1,4,7],[2,6,10],[3,9],[5],[8]] => [3,3,2,1,1] => 14
[[1,6,7],[2,9,10],[3],[4],[5],[8]] => [3,3,1,1,1,1] => 17
[[1,3,10],[2,5],[4,7],[6,9],[8]] => [3,2,2,2,1] => 16
[[1,5,10],[2,7],[3,9],[4],[6],[8]] => [3,2,2,1,1,1] => 18
[[1,7,10],[2,9],[3],[4],[5],[6],[8]] => [3,2,1,1,1,1,1] => 22
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1,1,1] => 28
[[1,4],[2,6],[3,8],[5,10],[7],[9]] => [2,2,2,2,1,1] => 21
[[1,6],[2,8],[3,10],[4],[5],[7],[9]] => [2,2,2,1,1,1,1] => 24
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [2,2,1,1,1,1,1,1] => 29
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1,1] => 36
[[1,2,4],[3,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 16
[[1,2,5],[3,6],[4,7],[8],[9]] => [3,2,2,1,1] => 13
[[1,2,3,5],[4,6],[7],[8],[9]] => [4,2,1,1,1] => 11
[[1,2,6],[3,7],[4,8],[5,9]] => [3,2,2,2] => 12
[[1,2,3,6],[4,7],[5,8],[9]] => [4,2,2,1] => 9
[[1,2,4,6],[3,5,7],[8],[9]] => [4,3,1,1] => 8
[[1,2,3,4,6],[5,7],[8],[9]] => [5,2,1,1] => 7
[[1,2,4,7],[3,5,8],[6,9]] => [4,3,2] => 7
[[1,2,3,4,7],[5,8],[6,9]] => [5,2,2] => 6
[[1,2,3,5,7],[4,6,8],[9]] => [5,3,1] => 5
[[1,2,3,4,5,7],[6,8],[9]] => [6,2,1] => 4
[[1,2,4,6,8],[3,5,7,9]] => [5,4] => 4
[[1,2,3,4,6,8],[5,7,9]] => [6,3] => 3
[[1,2,3,4,5,6,8],[7,9]] => [7,2] => 2
[[1,2,4],[3,5],[6],[7],[8],[9],[10]] => [3,2,1,1,1,1,1] => 22
[[1,2,5],[3,6],[4,7],[8],[9],[10]] => [3,2,2,1,1,1] => 18
[[1,2,3,5],[4,6],[7],[8],[9],[10]] => [4,2,1,1,1,1] => 16
[[1,2,6],[3,7],[4,8],[5,9],[10]] => [3,2,2,2,1] => 16
[[1,2,3,6],[4,7],[5,8],[9],[10]] => [4,2,2,1,1] => 13
[[1,2,4,6],[3,5,7],[8],[9],[10]] => [4,3,1,1,1] => 12
[[1,2,3,4,6],[5,7],[8],[9],[10]] => [5,2,1,1,1] => 11
[[1,2,3,7],[4,8],[5,9],[6,10]] => [4,2,2,2] => 12
[[1,2,4,7],[3,5,8],[6,9],[10]] => [4,3,2,1] => 10
[[1,2,3,4,7],[5,8],[6,9],[10]] => [5,2,2,1] => 9
[[1,2,3,5,7],[4,6,8],[9],[10]] => [5,3,1,1] => 8
[[1,2,3,4,5,7],[6,8],[9],[10]] => [6,2,1,1] => 7
[[1,2,5,8],[3,6,9],[4,7,10]] => [4,3,3] => 9
[[1,2,3,5,8],[4,6,9],[7,10]] => [5,3,2] => 7
[[1,2,3,4,5,8],[6,9],[7,10]] => [6,2,2] => 6
[[1,2,4,6,8],[3,5,7,9],[10]] => [5,4,1] => 6
[[1,2,3,4,6,8],[5,7,9],[10]] => [6,3,1] => 5
[[1,2,3,4,5,6,8],[7,9],[10]] => [7,2,1] => 4
[[1,2,3,5,7,9],[4,6,8,10]] => [6,4] => 4
[[1,2,3,4,5,7,9],[6,8,10]] => [7,3] => 3
[[1,2,3,4,5,6,7,9],[8,10]] => [8,2] => 2
[[1,2,3,4,5,6,7,9],[8]] => [8,1] => 1
[[1,2,3,4,9],[5,6],[7,8]] => [5,2,2] => 6
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1,1] => 21
[[1,2,3,4,5,6,7,8,10],[9]] => [9,1] => 1
[[1,2,3,4,5,6,10],[7,8,9]] => [7,3] => 3
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1,1] => 28
[[1,2,4,5,6,7,8,9],[3]] => [8,1] => 1
[[1,2,5,7,9],[3,6,8],[4]] => [5,3,1] => 5
[[1,2,4,5,6,7,8,9,10],[3]] => [9,1] => 1
[[1,2,5,7,9,10],[3,6,8],[4]] => [6,3,1] => 5
[[1,2,4,6,8,10],[3,5,7,9]] => [6,4] => 4
[[1,2,4,6,8,9,10],[3,5,7]] => [7,3] => 3
[[1,2,4,6,7,8,10],[3,5,9]] => [7,3] => 3
[[1,2,4,6,7,9,10],[3,5,8]] => [7,3] => 3
[[1,2,4,6,7,8,9,10],[3,5]] => [8,2] => 2
[[1,2,4,5,6,8,10],[3,7,9]] => [7,3] => 3
[[1,2,4,5,6,9,10],[3,7,8]] => [7,3] => 3
[[1,2,4,5,7,8,10],[3,6,9]] => [7,3] => 3
[[1,2,4,5,7,9,10],[3,6,8]] => [7,3] => 3
[[1,2,4,5,7,8,9,10],[3,6]] => [8,2] => 2
[[1,2,4,5,6,7,8,10],[3,9]] => [8,2] => 2
[[1,2,4,5,6,7,9,10],[3,8]] => [8,2] => 2
[[1,2,4,5,6,8,9,10],[3,7]] => [8,2] => 2
[[1,2,3,4,6,8,10],[5,7,9]] => [7,3] => 3
[[1,2,3,4,6,9,10],[5,7,8]] => [7,3] => 3
[[1,2,3,4,7,8,10],[5,6,9]] => [7,3] => 3
[[1,2,3,4,7,9,10],[5,6,8]] => [7,3] => 3
[[1,2,3,4,7,8,9,10],[5,6]] => [8,2] => 2
[[1,2,3,5,6,8,10],[4,7,9]] => [7,3] => 3
[[1,2,3,5,6,9,10],[4,7,8]] => [7,3] => 3
[[1,2,3,5,7,8,10],[4,6,9]] => [7,3] => 3
[[1,2,3,5,7,9,10],[4,6,8]] => [7,3] => 3
[[1,2,3,5,7,8,9,10],[4,6]] => [8,2] => 2
[[1,2,3,5,6,7,8,10],[4,9]] => [8,2] => 2
[[1,2,3,5,6,7,9,10],[4,8]] => [8,2] => 2
[[1,2,3,5,6,8,9,10],[4,7]] => [8,2] => 2
[[1,2,3,5,6,7,8,9,10],[4]] => [9,1] => 1
[[1,2,3,4,5,6,8,10],[7,9]] => [8,2] => 2
[[1,2,3,4,5,6,9,10],[7,8]] => [8,2] => 2
[[1,2,3,4,5,7,8,10],[6,9]] => [8,2] => 2
[[1,2,3,4,5,7,9,10],[6,8]] => [8,2] => 2
[[1,2,3,4,5,8,9,10],[6,7]] => [8,2] => 2
[[1,2,3,4,6,7,8,10],[5,9]] => [8,2] => 2
[[1,2,3,4,6,7,9,10],[5,8]] => [8,2] => 2
[[1,2,3,4,6,8,9,10],[5,7]] => [8,2] => 2
[[1,2,3,4,6,7,8,9,10],[5]] => [9,1] => 1
[[1,2,3,4,5,6,7,9,10],[8]] => [9,1] => 1
[[1,2,3,4,5,6,8,9,10],[7]] => [9,1] => 1
[[1,2,3,4,5,7,8,9,10],[6]] => [9,1] => 1
[[1,2,4,6,8,10,12],[3,5,7,9,11]] => [7,5] => 5
[[1,2,5,6,7,8,9],[3],[4]] => [7,1,1] => 3
[[1,2,6,7,8,9],[3],[4],[5]] => [6,1,1,1] => 6
[[1,2,7,8,9],[3],[4],[5],[6]] => [5,1,1,1,1] => 10
[[1,2,8,9],[3],[4],[5],[6],[7]] => [4,1,1,1,1,1] => 15
[[1,2,5,6,7,8,9,10],[3],[4]] => [8,1,1] => 3
[[1,2,6,7,8,9,10],[3],[4],[5]] => [7,1,1,1] => 6
[[1,2,7,8,9,10],[3],[4],[5],[6]] => [6,1,1,1,1] => 10
[[1,2,8,9,10],[3],[4],[5],[6],[7]] => [5,1,1,1,1,1] => 15
[[1,2,9,10],[3],[4],[5],[6],[7],[8]] => [4,1,1,1,1,1,1] => 21
[[1,2,3,4,7,8,9],[5,6]] => [7,2] => 2
[[1,2,4,5,8,9],[3,7],[6]] => [6,2,1] => 4
[[1,2,4,5,6,7],[3,9],[8]] => [6,2,1] => 4
[[1,2,5,6,9],[3,8],[4],[7]] => [5,2,1,1] => 7
[[1,2,3,4,7,8],[5,6],[9]] => [6,2,1] => 4
[[1,2,5,6,7,8],[3],[4],[9]] => [6,1,1,1] => 6
[[1,2,4,5],[3,7],[6,9],[8]] => [4,2,2,1] => 9
[[1,2,6,7],[3,9],[4],[5],[8]] => [4,2,1,1,1] => 11
[[1,2,5,6],[3,8],[4],[7],[9]] => [4,2,1,1,1] => 11
[[1,2,7,8],[3],[4],[5],[6],[9]] => [4,1,1,1,1,1] => 15
[[1,2,4,5,8,9,10],[3,7],[6]] => [7,2,1] => 4
[[1,2,4,5,6,7],[3,9,10],[8]] => [6,3,1] => 5
[[1,2,3,4,9,10],[5,6],[7,8]] => [6,2,2] => 6
[[1,2,5,6,9,10],[3,8],[4],[7]] => [6,2,1,1] => 7
[[1,2,4,5,6,7,8,9],[3],[10]] => [8,1,1] => 3
[[1,2,3,4,7,8],[5,6],[9,10]] => [6,2,2] => 6
[[1,2,5,6,7,8],[3,10],[4],[9]] => [6,2,1,1] => 7
[[1,2,4,5,10],[3,7],[6,9],[8]] => [5,2,2,1] => 9
[[1,2,6,7,10],[3,9],[4],[5],[8]] => [5,2,1,1,1] => 11
[[1,2,4,5,8,9],[3,7],[6],[10]] => [6,2,1,1] => 7
[[1,2,6,7,8,9],[3],[4],[5],[10]] => [6,1,1,1,1] => 10
[[1,2,5,6],[3,8],[4,10],[7],[9]] => [4,2,2,1,1] => 13
[[1,2,7,8],[3,10],[4],[5],[6],[9]] => [4,2,1,1,1,1] => 16
[[1,2,4,5],[3,7],[6,9],[8],[10]] => [4,2,2,1,1] => 13
[[1,2,6,7],[3,9],[4],[5],[8],[10]] => [4,2,1,1,1,1] => 16
[[1,2,8,9],[3],[4],[5],[6],[7],[10]] => [4,1,1,1,1,1,1] => 21
[[1,2,3,5,7,9],[4,6,8]] => [6,3] => 3
[[1,2,3,4,5,7,9],[6,8]] => [7,2] => 2
[[1,2,4,5],[3,8],[6,9],[7,10]] => [4,2,2,2] => 12
[[1,2,8],[3,9],[4],[5],[6],[7]] => [3,2,1,1,1,1] => 16
[[1,2,7],[3,8],[4,9],[5],[6]] => [3,2,2,1,1] => 13
[[1,2,7,9],[3,8],[4],[5],[6]] => [4,2,1,1,1] => 11
[[1,2,6,9],[3,7],[4,8],[5]] => [4,2,2,1] => 9
[[1,2,6,8],[3,7,9],[4],[5]] => [4,3,1,1] => 8
[[1,2,6,8,9],[3,7],[4],[5]] => [5,2,1,1] => 7
[[1,2,5,8],[3,6,9],[4,7]] => [4,3,2] => 7
[[1,2,5,8,9],[3,6],[4,7]] => [5,2,2] => 6
[[1,2,5,7,8,9],[3,6],[4]] => [6,2,1] => 4
[[1,2,4,6,8,9],[3,5,7]] => [6,3] => 3
[[1,2,4,6,7,8,9],[3,5]] => [7,2] => 2
[[1,2,9],[3,10],[4],[5],[6],[7],[8]] => [3,2,1,1,1,1,1] => 22
[[1,2,8],[3,9],[4,10],[5],[6],[7]] => [3,2,2,1,1,1] => 18
[[1,2,8,10],[3,9],[4],[5],[6],[7]] => [4,2,1,1,1,1] => 16
[[1,2,7],[3,8],[4,9],[5,10],[6]] => [3,2,2,2,1] => 16
[[1,2,7,10],[3,8],[4,9],[5],[6]] => [4,2,2,1,1] => 13
[[1,2,7,9],[3,8,10],[4],[5],[6]] => [4,3,1,1,1] => 12
[[1,2,7,9,10],[3,8],[4],[5],[6]] => [5,2,1,1,1] => 11
[[1,2,6,10],[3,7],[4,8],[5,9]] => [4,2,2,2] => 12
[[1,2,6,9],[3,7,10],[4,8],[5]] => [4,3,2,1] => 10
[[1,2,6,9,10],[3,7],[4,8],[5]] => [5,2,2,1] => 9
[[1,2,6,8,10],[3,7,9],[4],[5]] => [5,3,1,1] => 8
[[1,2,6,8,9,10],[3,7],[4],[5]] => [6,2,1,1] => 7
[[1,2,5,8,10],[3,6,9],[4,7]] => [5,3,2] => 7
[[1,2,5,8,9,10],[3,6],[4,7]] => [6,2,2] => 6
[[1,2,5,7,9],[3,6,8,10],[4]] => [5,4,1] => 6
[[1,2,5,7,8,9,10],[3,6],[4]] => [7,2,1] => 4
[[1,2,3,4],[5,6],[7,9],[8,10]] => [4,2,2,2] => 12
[[1,2,3,4],[5,7],[6,8],[9,10]] => [4,2,2,2] => 12
[[1,2,3,4],[5,7],[6,9],[8,10]] => [4,2,2,2] => 12
[[1,2,3,4],[5,8],[6,9],[7,10]] => [4,2,2,2] => 12
[[1,2,3,5],[4,6],[7,8],[9,10]] => [4,2,2,2] => 12
[[1,2,3,5],[4,6],[7,9],[8,10]] => [4,2,2,2] => 12
[[1,2,3,5],[4,7],[6,8],[9,10]] => [4,2,2,2] => 12
[[1,2,3,5],[4,7],[6,9],[8,10]] => [4,2,2,2] => 12
[[1,2,3,5],[4,8],[6,9],[7,10]] => [4,2,2,2] => 12
[[1,2,3,6],[4,7],[5,8],[9,10]] => [4,2,2,2] => 12
[[1,2,3,6],[4,7],[5,9],[8,10]] => [4,2,2,2] => 12
[[1,2,3,6],[4,8],[5,9],[7,10]] => [4,2,2,2] => 12
[[1,2,4,6],[3,5],[7,8],[9,10]] => [4,2,2,2] => 12
[[1,2,4,6],[3,5],[7,9],[8,10]] => [4,2,2,2] => 12
[[1,2,4,7],[3,5],[6,8],[9,10]] => [4,2,2,2] => 12
[[1,2,4,7],[3,5],[6,9],[8,10]] => [4,2,2,2] => 12
[[1,2,4,8],[3,5],[6,9],[7,10]] => [4,2,2,2] => 12
[[1,2,4,5],[3,6],[7,8],[9,10]] => [4,2,2,2] => 12
[[1,2,4,5],[3,6],[7,9],[8,10]] => [4,2,2,2] => 12
[[1,2,4,5],[3,7],[6,8],[9,10]] => [4,2,2,2] => 12
[[1,2,4,5],[3,7],[6,9],[8,10]] => [4,2,2,2] => 12
[[1,2,4,6],[3,7],[5,8],[9,10]] => [4,2,2,2] => 12
[[1,2,4,6],[3,7],[5,9],[8,10]] => [4,2,2,2] => 12
[[1,2,4,6],[3,8],[5,9],[7,10]] => [4,2,2,2] => 12
[[1,2,4,7],[3,8],[5,9],[6,10]] => [4,2,2,2] => 12
[[1,2,5,8],[3,6],[4,7],[9,10]] => [4,2,2,2] => 12
[[1,2,5,9],[3,6],[4,7],[8,10]] => [4,2,2,2] => 12
[[1,2,5,7],[3,6],[4,8],[9,10]] => [4,2,2,2] => 12
[[1,2,5,7],[3,6],[4,9],[8,10]] => [4,2,2,2] => 12
[[1,2,5,8],[3,6],[4,9],[7,10]] => [4,2,2,2] => 12
[[1,2,5,6],[3,7],[4,8],[9,10]] => [4,2,2,2] => 12
[[1,2,5,6],[3,7],[4,9],[8,10]] => [4,2,2,2] => 12
[[1,2,5,6],[3,8],[4,9],[7,10]] => [4,2,2,2] => 12
[[1,2,5,7],[3,8],[4,9],[6,10]] => [4,2,2,2] => 12
[[1,2,6,9],[3,7],[4,8],[5,10]] => [4,2,2,2] => 12
[[1,2,6,8],[3,7],[4,9],[5,10]] => [4,2,2,2] => 12
[[1,2,6,7],[3,8],[4,9],[5,10]] => [4,2,2,2] => 12
[[1,2,3,7],[4,8],[5,9],[6]] => [4,2,2,1] => 9
[[1,2,3,5,8],[4,6,9],[7]] => [5,3,1] => 5
[[1,2,3,4,5,8],[6,9],[7]] => [6,2,1] => 4
[[1,2,4,8],[3,5,9],[6,10],[7]] => [4,3,2,1] => 10
[[1,2,3,4,8],[5,9],[6,10],[7]] => [5,2,2,1] => 9
[[1,2,3,6,9],[4,7,10],[5,8]] => [5,3,2] => 7
[[1,2,4,6,9],[3,5,7,10],[8]] => [5,4,1] => 6
[[1,2,3,4,6,9],[5,7,10],[8]] => [6,3,1] => 5
[[1,2,3,4,5,6,9],[7,10],[8]] => [7,2,1] => 4
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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 1,2,0,1 1,3,2,3,0,0,1 1,4,5,6,5,0,4,0,0,0,1 1,5,9,15,16,0,15,9,0,0,5,0,0,0,0,1 1,6,14,29,35,21,41,35,0,14,15,14,0,0,0,6,0,0,0,0,0,1 1,7,20,49,78,70,91,132,56,70,35,64,14,28,0,21,20,0,0,0,0,7,0,0,0,0,0,0,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + q^{3}$
$F_{4} = 1 + 3\ q + 2\ q^{2} + 3\ q^{3} + q^{6}$
$F_{5} = 1 + 4\ q + 5\ q^{2} + 6\ q^{3} + 5\ q^{4} + 4\ q^{6} + q^{10}$
$F_{6} = 1 + 5\ q + 9\ q^{2} + 15\ q^{3} + 16\ q^{4} + 15\ q^{6} + 9\ q^{7} + 5\ q^{10} + q^{15}$
$F_{7} = 1 + 6\ q + 14\ q^{2} + 29\ q^{3} + 35\ q^{4} + 21\ q^{5} + 41\ q^{6} + 35\ q^{7} + 14\ q^{9} + 15\ q^{10} + 14\ q^{11} + 6\ q^{15} + q^{21}$
$F_{8} = 1 + 7\ q + 20\ q^{2} + 49\ q^{3} + 78\ q^{4} + 70\ q^{5} + 91\ q^{6} + 132\ q^{7} + 56\ q^{8} + 70\ q^{9} + 35\ q^{10} + 64\ q^{11} + 14\ q^{12} + 28\ q^{13} + 21\ q^{15} + 20\ q^{16} + 7\ q^{21} + q^{28}$
Description
The weighted size of a partition.
Let $\lambda = (\lambda_0\geq\lambda_1 \geq \dots\geq\lambda_m)$ be an integer partition. Then the weighted size of $\lambda$ is
$$\sum_{i=0}^m i \cdot \lambda_i.$$
This is also the sum of the leg lengths of the cells in $\lambda$, or
$$ \sum_i \binom{\lambda^{\prime}_i}{2} $$
where $\lambda^{\prime}$ is the conjugate partition of $\lambda$.
This is the minimal number of inversions a permutation with the given shape can have, see [1, cor.2.2].
This is also the smallest possible sum of the entries of a semistandard tableau (allowing 0 as a part) of shape $\lambda=(\lambda_0,\lambda_1,\ldots,\lambda_m)$, obtained uniquely by placing $i-1$ in all the cells of the $i$th row of $\lambda$, see [2, eq.7.103].
Let $\lambda = (\lambda_0\geq\lambda_1 \geq \dots\geq\lambda_m)$ be an integer partition. Then the weighted size of $\lambda$ is
$$\sum_{i=0}^m i \cdot \lambda_i.$$
This is also the sum of the leg lengths of the cells in $\lambda$, or
$$ \sum_i \binom{\lambda^{\prime}_i}{2} $$
where $\lambda^{\prime}$ is the conjugate partition of $\lambda$.
This is the minimal number of inversions a permutation with the given shape can have, see [1, cor.2.2].
This is also the smallest possible sum of the entries of a semistandard tableau (allowing 0 as a part) of shape $\lambda=(\lambda_0,\lambda_1,\ldots,\lambda_m)$, obtained uniquely by placing $i-1$ in all the cells of the $i$th row of $\lambda$, see [2, eq.7.103].
Map
shape
Description
Sends a tableau to its shape.
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