Identifier
-
Mp00083:
Standard tableaux
—shape⟶
Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
St001697: Standard tableaux ⟶ ℤ
Values
[[1]] => [1] => [[1]] => 0
[[1,2]] => [2] => [[1,2]] => 0
[[1],[2]] => [1,1] => [[1],[2]] => 1
[[1,2,3]] => [3] => [[1,2,3]] => 0
[[1,3],[2]] => [2,1] => [[1,2],[3]] => 1
[[1,2],[3]] => [2,1] => [[1,2],[3]] => 1
[[1],[2],[3]] => [1,1,1] => [[1],[2],[3]] => 3
[[1,2,3,4]] => [4] => [[1,2,3,4]] => 0
[[1,3,4],[2]] => [3,1] => [[1,2,3],[4]] => 1
[[1,2,4],[3]] => [3,1] => [[1,2,3],[4]] => 1
[[1,2,3],[4]] => [3,1] => [[1,2,3],[4]] => 1
[[1,3],[2,4]] => [2,2] => [[1,2],[3,4]] => 2
[[1,2],[3,4]] => [2,2] => [[1,2],[3,4]] => 2
[[1,4],[2],[3]] => [2,1,1] => [[1,2],[3],[4]] => 3
[[1,3],[2],[4]] => [2,1,1] => [[1,2],[3],[4]] => 3
[[1,2],[3],[4]] => [2,1,1] => [[1,2],[3],[4]] => 3
[[1],[2],[3],[4]] => [1,1,1,1] => [[1],[2],[3],[4]] => 6
[[1,2,3,4,5]] => [5] => [[1,2,3,4,5]] => 0
[[1,3,4,5],[2]] => [4,1] => [[1,2,3,4],[5]] => 1
[[1,2,4,5],[3]] => [4,1] => [[1,2,3,4],[5]] => 1
[[1,2,3,5],[4]] => [4,1] => [[1,2,3,4],[5]] => 1
[[1,2,3,4],[5]] => [4,1] => [[1,2,3,4],[5]] => 1
[[1,3,5],[2,4]] => [3,2] => [[1,2,3],[4,5]] => 2
[[1,2,5],[3,4]] => [3,2] => [[1,2,3],[4,5]] => 2
[[1,3,4],[2,5]] => [3,2] => [[1,2,3],[4,5]] => 2
[[1,2,4],[3,5]] => [3,2] => [[1,2,3],[4,5]] => 2
[[1,2,3],[4,5]] => [3,2] => [[1,2,3],[4,5]] => 2
[[1,4,5],[2],[3]] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[[1,3,5],[2],[4]] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[[1,2,5],[3],[4]] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[[1,3,4],[2],[5]] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[[1,2,4],[3],[5]] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[[1,2,3],[4],[5]] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[[1,4],[2,5],[3]] => [2,2,1] => [[1,2],[3,4],[5]] => 4
[[1,3],[2,5],[4]] => [2,2,1] => [[1,2],[3,4],[5]] => 4
[[1,2],[3,5],[4]] => [2,2,1] => [[1,2],[3,4],[5]] => 4
[[1,3],[2,4],[5]] => [2,2,1] => [[1,2],[3,4],[5]] => 4
[[1,2],[3,4],[5]] => [2,2,1] => [[1,2],[3,4],[5]] => 4
[[1,5],[2],[3],[4]] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 6
[[1,4],[2],[3],[5]] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 6
[[1,3],[2],[4],[5]] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 6
[[1,2],[3],[4],[5]] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 6
[[1],[2],[3],[4],[5]] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 10
[[1,2,3,4,5,6]] => [6] => [[1,2,3,4,5,6]] => 0
[[1,3,4,5,6],[2]] => [5,1] => [[1,2,3,4,5],[6]] => 1
[[1,2,4,5,6],[3]] => [5,1] => [[1,2,3,4,5],[6]] => 1
[[1,2,3,5,6],[4]] => [5,1] => [[1,2,3,4,5],[6]] => 1
[[1,2,3,4,6],[5]] => [5,1] => [[1,2,3,4,5],[6]] => 1
[[1,2,3,4,5],[6]] => [5,1] => [[1,2,3,4,5],[6]] => 1
[[1,3,5,6],[2,4]] => [4,2] => [[1,2,3,4],[5,6]] => 2
[[1,2,5,6],[3,4]] => [4,2] => [[1,2,3,4],[5,6]] => 2
[[1,3,4,6],[2,5]] => [4,2] => [[1,2,3,4],[5,6]] => 2
[[1,2,4,6],[3,5]] => [4,2] => [[1,2,3,4],[5,6]] => 2
[[1,2,3,6],[4,5]] => [4,2] => [[1,2,3,4],[5,6]] => 2
[[1,3,4,5],[2,6]] => [4,2] => [[1,2,3,4],[5,6]] => 2
[[1,2,4,5],[3,6]] => [4,2] => [[1,2,3,4],[5,6]] => 2
[[1,2,3,5],[4,6]] => [4,2] => [[1,2,3,4],[5,6]] => 2
[[1,2,3,4],[5,6]] => [4,2] => [[1,2,3,4],[5,6]] => 2
[[1,4,5,6],[2],[3]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[[1,3,5,6],[2],[4]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[[1,2,5,6],[3],[4]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[[1,3,4,6],[2],[5]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[[1,2,4,6],[3],[5]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[[1,2,3,6],[4],[5]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[[1,3,4,5],[2],[6]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[[1,2,4,5],[3],[6]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[[1,2,3,5],[4],[6]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[[1,2,3,4],[5],[6]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[[1,3,5],[2,4,6]] => [3,3] => [[1,2,3],[4,5,6]] => 3
[[1,2,5],[3,4,6]] => [3,3] => [[1,2,3],[4,5,6]] => 3
[[1,3,4],[2,5,6]] => [3,3] => [[1,2,3],[4,5,6]] => 3
[[1,2,4],[3,5,6]] => [3,3] => [[1,2,3],[4,5,6]] => 3
[[1,2,3],[4,5,6]] => [3,3] => [[1,2,3],[4,5,6]] => 3
[[1,4,6],[2,5],[3]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,3,6],[2,5],[4]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,2,6],[3,5],[4]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,3,6],[2,4],[5]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,2,6],[3,4],[5]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,4,5],[2,6],[3]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,3,5],[2,6],[4]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,2,5],[3,6],[4]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,3,4],[2,6],[5]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,2,4],[3,6],[5]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,2,3],[4,6],[5]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,3,5],[2,4],[6]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,2,5],[3,4],[6]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,3,4],[2,5],[6]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,2,4],[3,5],[6]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,2,3],[4,5],[6]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 4
[[1,5,6],[2],[3],[4]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 6
[[1,4,6],[2],[3],[5]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 6
[[1,3,6],[2],[4],[5]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 6
[[1,2,6],[3],[4],[5]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 6
[[1,4,5],[2],[3],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 6
[[1,3,5],[2],[4],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 6
[[1,2,5],[3],[4],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 6
[[1,3,4],[2],[5],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 6
[[1,2,4],[3],[5],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 6
[[1,2,3],[4],[5],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 6
[[1,4],[2,5],[3,6]] => [2,2,2] => [[1,2],[3,4],[5,6]] => 6
[[1,3],[2,5],[4,6]] => [2,2,2] => [[1,2],[3,4],[5,6]] => 6
>>> Load all 1115 entries. <<<[[1,2],[3,5],[4,6]] => [2,2,2] => [[1,2],[3,4],[5,6]] => 6
[[1,3],[2,4],[5,6]] => [2,2,2] => [[1,2],[3,4],[5,6]] => 6
[[1,2],[3,4],[5,6]] => [2,2,2] => [[1,2],[3,4],[5,6]] => 6
[[1,5],[2,6],[3],[4]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 7
[[1,4],[2,6],[3],[5]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 7
[[1,3],[2,6],[4],[5]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 7
[[1,2],[3,6],[4],[5]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 7
[[1,4],[2,5],[3],[6]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 7
[[1,3],[2,5],[4],[6]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 7
[[1,2],[3,5],[4],[6]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 7
[[1,3],[2,4],[5],[6]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 7
[[1,2],[3,4],[5],[6]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 7
[[1,6],[2],[3],[4],[5]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 10
[[1,5],[2],[3],[4],[6]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 10
[[1,4],[2],[3],[5],[6]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 10
[[1,3],[2],[4],[5],[6]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 10
[[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 10
[[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 15
[[1,2,3,4,5,6,7]] => [7] => [[1,2,3,4,5,6,7]] => 0
[[1,3,4,5,6,7],[2]] => [6,1] => [[1,2,3,4,5,6],[7]] => 1
[[1,2,4,5,6,7],[3]] => [6,1] => [[1,2,3,4,5,6],[7]] => 1
[[1,2,3,5,6,7],[4]] => [6,1] => [[1,2,3,4,5,6],[7]] => 1
[[1,2,3,4,6,7],[5]] => [6,1] => [[1,2,3,4,5,6],[7]] => 1
[[1,2,3,4,5,7],[6]] => [6,1] => [[1,2,3,4,5,6],[7]] => 1
[[1,2,3,4,5,6],[7]] => [6,1] => [[1,2,3,4,5,6],[7]] => 1
[[1,3,5,6,7],[2,4]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,2,5,6,7],[3,4]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,3,4,6,7],[2,5]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,2,4,6,7],[3,5]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,2,3,6,7],[4,5]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,3,4,5,7],[2,6]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,2,4,5,7],[3,6]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,2,3,5,7],[4,6]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,2,3,4,7],[5,6]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,3,4,5,6],[2,7]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,2,4,5,6],[3,7]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,2,3,5,6],[4,7]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,2,3,4,6],[5,7]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,2,3,4,5],[6,7]] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[[1,4,5,6,7],[2],[3]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,3,5,6,7],[2],[4]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,2,5,6,7],[3],[4]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,3,4,6,7],[2],[5]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,2,4,6,7],[3],[5]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,2,3,6,7],[4],[5]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,3,4,5,7],[2],[6]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,2,4,5,7],[3],[6]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,2,3,5,7],[4],[6]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,2,3,4,7],[5],[6]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,3,4,5,6],[2],[7]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,2,4,5,6],[3],[7]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,2,3,5,6],[4],[7]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,2,3,4,6],[5],[7]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,2,3,4,5],[6],[7]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[[1,3,5,7],[2,4,6]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,2,5,7],[3,4,6]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,3,4,7],[2,5,6]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,2,4,7],[3,5,6]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,2,3,7],[4,5,6]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,3,5,6],[2,4,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,2,5,6],[3,4,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,3,4,6],[2,5,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,2,4,6],[3,5,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,2,3,6],[4,5,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,3,4,5],[2,6,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,2,4,5],[3,6,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,2,3,5],[4,6,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,2,3,4],[5,6,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 3
[[1,4,6,7],[2,5],[3]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,6,7],[2,5],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,6,7],[3,5],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,6,7],[2,4],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,6,7],[3,4],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,4,5,7],[2,6],[3]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,5,7],[2,6],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,5,7],[3,6],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,4,7],[2,6],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,4,7],[3,6],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,3,7],[4,6],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,5,7],[2,4],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,5,7],[3,4],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,4,7],[2,5],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,4,7],[3,5],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,3,7],[4,5],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,4,5,6],[2,7],[3]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,5,6],[2,7],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,5,6],[3,7],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,4,6],[2,7],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,4,6],[3,7],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,3,6],[4,7],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,4,5],[2,7],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,4,5],[3,7],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,3,5],[4,7],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,3,4],[5,7],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,5,6],[2,4],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,5,6],[3,4],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,4,6],[2,5],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,4,6],[3,5],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,3,6],[4,5],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,3,4,5],[2,6],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,4,5],[3,6],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,3,5],[4,6],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,2,3,4],[5,6],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[[1,5,6,7],[2],[3],[4]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,4,6,7],[2],[3],[5]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,3,6,7],[2],[4],[5]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,2,6,7],[3],[4],[5]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,4,5,7],[2],[3],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,3,5,7],[2],[4],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,2,5,7],[3],[4],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,3,4,7],[2],[5],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,2,4,7],[3],[5],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,2,3,7],[4],[5],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,4,5,6],[2],[3],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,3,5,6],[2],[4],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,2,5,6],[3],[4],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,3,4,6],[2],[5],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,2,4,6],[3],[5],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,2,3,6],[4],[5],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,3,4,5],[2],[6],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,2,4,5],[3],[6],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,2,3,5],[4],[6],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 6
[[1,4,6],[2,5,7],[3]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,3,6],[2,5,7],[4]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,6],[3,5,7],[4]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,3,6],[2,4,7],[5]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,6],[3,4,7],[5]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,4,5],[2,6,7],[3]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,3,5],[2,6,7],[4]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,5],[3,6,7],[4]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,3,4],[2,6,7],[5]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,4],[3,6,7],[5]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,3],[4,6,7],[5]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,3,5],[2,4,7],[6]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,5],[3,4,7],[6]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,3,4],[2,5,7],[6]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,4],[3,5,7],[6]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,3],[4,5,7],[6]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,3,5],[2,4,6],[7]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,5],[3,4,6],[7]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,3,4],[2,5,6],[7]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,4],[3,5,6],[7]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,2,3],[4,5,6],[7]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 5
[[1,4,7],[2,5],[3,6]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,3,7],[2,5],[4,6]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,2,7],[3,5],[4,6]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,3,7],[2,4],[5,6]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,2,7],[3,4],[5,6]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,4,6],[2,5],[3,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,3,6],[2,5],[4,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,2,6],[3,5],[4,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,3,6],[2,4],[5,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,2,6],[3,4],[5,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,4,5],[2,6],[3,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,3,5],[2,6],[4,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,2,5],[3,6],[4,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,3,4],[2,6],[5,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,2,4],[3,6],[5,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,2,3],[4,6],[5,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,3,5],[2,4],[6,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,2,5],[3,4],[6,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,3,4],[2,5],[6,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,2,4],[3,5],[6,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,2,3],[4,5],[6,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 6
[[1,5,7],[2,6],[3],[4]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,4,7],[2,6],[3],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,7],[2,6],[4],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,7],[3,6],[4],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,4,7],[2,5],[3],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,7],[2,5],[4],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,7],[3,5],[4],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,7],[2,4],[5],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,7],[3,4],[5],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,5,6],[2,7],[3],[4]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,4,6],[2,7],[3],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,6],[2,7],[4],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,6],[3,7],[4],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,4,5],[2,7],[3],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,5],[2,7],[4],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,5],[3,7],[4],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,4],[2,7],[5],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,4],[3,7],[5],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,3],[4,7],[5],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,4,6],[2,5],[3],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,6],[2,5],[4],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,6],[3,5],[4],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,6],[2,4],[5],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,6],[3,4],[5],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,4,5],[2,6],[3],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,5],[2,6],[4],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,5],[3,6],[4],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,4],[2,6],[5],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,4],[3,6],[5],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,3],[4,6],[5],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,5],[2,4],[6],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,5],[3,4],[6],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,3,4],[2,5],[6],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,4],[3,5],[6],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 7
[[1,6,7],[2],[3],[4],[5]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,5,7],[2],[3],[4],[6]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,4,7],[2],[3],[5],[6]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,3,7],[2],[4],[5],[6]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,2,7],[3],[4],[5],[6]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,5,6],[2],[3],[4],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,4,6],[2],[3],[5],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,3,6],[2],[4],[5],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,2,6],[3],[4],[5],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,4,5],[2],[3],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,3,5],[2],[4],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,2,5],[3],[4],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,3,4],[2],[5],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,2,4],[3],[5],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[[1,5],[2,6],[3,7],[4]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,4],[2,6],[3,7],[5]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,3],[2,6],[4,7],[5]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,2],[3,6],[4,7],[5]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,4],[2,5],[3,7],[6]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,3],[2,5],[4,7],[6]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,2],[3,5],[4,7],[6]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,3],[2,4],[5,7],[6]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,2],[3,4],[5,7],[6]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,4],[2,5],[3,6],[7]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,3],[2,5],[4,6],[7]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,2],[3,5],[4,6],[7]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,3],[2,4],[5,6],[7]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 9
[[1,6],[2,7],[3],[4],[5]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,5],[2,7],[3],[4],[6]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,4],[2,7],[3],[5],[6]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,3],[2,7],[4],[5],[6]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,2],[3,7],[4],[5],[6]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,5],[2,6],[3],[4],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,4],[2,6],[3],[5],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,3],[2,6],[4],[5],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,2],[3,6],[4],[5],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,4],[2,5],[3],[6],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,3],[2,5],[4],[6],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,2],[3,5],[4],[6],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,3],[2,4],[5],[6],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 11
[[1,7],[2],[3],[4],[5],[6]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[[1,6],[2],[3],[4],[5],[7]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[[1,5],[2],[3],[4],[6],[7]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[[1,4],[2],[3],[5],[6],[7]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[[1,3],[2],[4],[5],[6],[7]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 21
[[1,2,3,4,5,6,7,8]] => [8] => [[1,2,3,4,5,6,7,8]] => 0
[[1,3,4,5,6,7,8],[2]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 1
[[1,2,4,5,6,7,8],[3]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 1
[[1,2,3,5,6,7,8],[4]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 1
[[1,2,3,4,6,7,8],[5]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 1
[[1,2,3,4,5,7,8],[6]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 1
[[1,2,3,4,5,6,8],[7]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 1
[[1,2,3,4,5,6,7],[8]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 1
[[1,3,5,6,7,8],[2,4]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,5,6,7,8],[3,4]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,3,4,6,7,8],[2,5]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,4,6,7,8],[3,5]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,3,6,7,8],[4,5]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,3,4,5,7,8],[2,6]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,4,5,7,8],[3,6]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,3,5,7,8],[4,6]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,3,4,7,8],[5,6]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,3,4,5,6,8],[2,7]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,4,5,6,8],[3,7]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,3,5,6,8],[4,7]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,3,4,6,8],[5,7]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,3,4,5,8],[6,7]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,3,4,5,6,7],[2,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,4,5,6,7],[3,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,3,5,6,7],[4,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,3,4,6,7],[5,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,3,4,5,7],[6,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,2,3,4,5,6],[7,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[[1,4,5,6,7,8],[2],[3]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,3,5,6,7,8],[2],[4]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,5,6,7,8],[3],[4]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,3,4,6,7,8],[2],[5]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,4,6,7,8],[3],[5]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,3,6,7,8],[4],[5]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,3,4,5,7,8],[2],[6]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,4,5,7,8],[3],[6]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,3,5,7,8],[4],[6]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,3,4,7,8],[5],[6]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,3,4,5,6,8],[2],[7]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,4,5,6,8],[3],[7]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,3,5,6,8],[4],[7]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,3,4,6,8],[5],[7]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,3,4,5,8],[6],[7]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,3,4,5,6,7],[2],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,4,5,6,7],[3],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,3,5,6,7],[4],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,3,4,6,7],[5],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,3,4,5,7],[6],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,2,3,4,5,6],[7],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[[1,3,5,7,8],[2,4,6]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,5,7,8],[3,4,6]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,3,4,7,8],[2,5,6]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,4,7,8],[3,5,6]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,3,7,8],[4,5,6]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,3,5,6,8],[2,4,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,5,6,8],[3,4,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,3,4,6,8],[2,5,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,4,6,8],[3,5,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,3,6,8],[4,5,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,3,4,5,8],[2,6,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,4,5,8],[3,6,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,3,5,8],[4,6,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,3,4,8],[5,6,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,3,5,6,7],[2,4,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,5,6,7],[3,4,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,3,4,6,7],[2,5,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,4,6,7],[3,5,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,3,6,7],[4,5,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,3,4,5,7],[2,6,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,4,5,7],[3,6,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,3,5,7],[4,6,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,3,4,7],[5,6,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,3,4,5,6],[2,7,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,4,5,6],[3,7,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,3,5,6],[4,7,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,3,4,6],[5,7,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,2,3,4,5],[6,7,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 3
[[1,4,6,7,8],[2,5],[3]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,6,7,8],[2,5],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,6,7,8],[3,5],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,6,7,8],[2,4],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,6,7,8],[3,4],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,4,5,7,8],[2,6],[3]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,5,7,8],[2,6],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,5,7,8],[3,6],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,7,8],[2,6],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,7,8],[3,6],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,7,8],[4,6],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,5,7,8],[2,4],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,5,7,8],[3,4],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,7,8],[2,5],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,7,8],[3,5],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,7,8],[4,5],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,4,5,6,8],[2,7],[3]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,5,6,8],[2,7],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,5,6,8],[3,7],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,6,8],[2,7],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,6,8],[3,7],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,6,8],[4,7],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,5,8],[2,7],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,5,8],[3,7],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,5,8],[4,7],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,4,8],[5,7],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,5,6,8],[2,4],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,5,6,8],[3,4],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,6,8],[2,5],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,6,8],[3,5],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,6,8],[4,5],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,5,8],[2,6],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,5,8],[3,6],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,5,8],[4,6],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,4,8],[5,6],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,4,5,6,7],[2,8],[3]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,5,6,7],[2,8],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,5,6,7],[3,8],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,6,7],[2,8],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,6,7],[3,8],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,6,7],[4,8],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,5,7],[2,8],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,5,7],[3,8],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,5,7],[4,8],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,4,7],[5,8],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,5,6],[2,8],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,5,6],[3,8],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,5,6],[4,8],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,4,6],[5,8],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,4,5],[6,8],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,5,6,7],[2,4],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,5,6,7],[3,4],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,6,7],[2,5],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,6,7],[3,5],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,6,7],[4,5],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,5,7],[2,6],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,5,7],[3,6],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,5,7],[4,6],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,4,7],[5,6],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,3,4,5,6],[2,7],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,4,5,6],[3,7],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,5,6],[4,7],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,4,6],[5,7],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,2,3,4,5],[6,7],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 4
[[1,5,6,7,8],[2],[3],[4]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,4,6,7,8],[2],[3],[5]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,6,7,8],[2],[4],[5]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,6,7,8],[3],[4],[5]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,4,5,7,8],[2],[3],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,5,7,8],[2],[4],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,5,7,8],[3],[4],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,4,7,8],[2],[5],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,4,7,8],[3],[5],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,3,7,8],[4],[5],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,4,5,6,8],[2],[3],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,5,6,8],[2],[4],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,5,6,8],[3],[4],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,4,6,8],[2],[5],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,4,6,8],[3],[5],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,3,6,8],[4],[5],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,4,5,8],[2],[6],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,4,5,8],[3],[6],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,3,5,8],[4],[6],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,3,4,8],[5],[6],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,4,5,6,7],[2],[3],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,5,6,7],[2],[4],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,5,6,7],[3],[4],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,4,6,7],[2],[5],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,4,6,7],[3],[5],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,3,6,7],[4],[5],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,4,5,7],[2],[6],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,4,5,7],[3],[6],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,3,5,7],[4],[6],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,3,4,7],[5],[6],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,4,5,6],[2],[7],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,4,5,6],[3],[7],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,3,5,6],[4],[7],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,3,4,6],[5],[7],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[[1,3,5,7],[2,4,6,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,2,5,7],[3,4,6,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,3,4,7],[2,5,6,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,2,4,7],[3,5,6,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,2,3,7],[4,5,6,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,3,5,6],[2,4,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,2,5,6],[3,4,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,3,4,6],[2,5,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,2,4,6],[3,5,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,2,3,6],[4,5,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,3,4,5],[2,6,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,2,4,5],[3,6,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,2,3,5],[4,6,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,2,3,4],[5,6,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[[1,4,6,8],[2,5,7],[3]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,6,8],[2,5,7],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,6,8],[3,5,7],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,6,8],[2,4,7],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,6,8],[3,4,7],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,4,5,8],[2,6,7],[3]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,5,8],[2,6,7],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,5,8],[3,6,7],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,8],[2,6,7],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,8],[3,6,7],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,8],[4,6,7],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,5,8],[2,4,7],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,5,8],[3,4,7],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,8],[2,5,7],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,8],[3,5,7],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,8],[4,5,7],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,5,8],[2,4,6],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,5,8],[3,4,6],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,8],[2,5,6],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,8],[3,5,6],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,8],[4,5,6],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,4,6,7],[2,5,8],[3]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,6,7],[2,5,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,6,7],[3,5,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,6,7],[2,4,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,6,7],[3,4,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,4,5,7],[2,6,8],[3]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,5,7],[2,6,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,5,7],[3,6,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,7],[2,6,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,7],[3,6,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,7],[4,6,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,5,7],[2,4,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,5,7],[3,4,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,7],[2,5,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,7],[3,5,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,7],[4,5,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,4,5,6],[2,7,8],[3]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,5,6],[2,7,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,5,6],[3,7,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,6],[2,7,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,6],[3,7,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,6],[4,7,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,5],[2,7,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,5],[3,7,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,5],[4,7,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,4],[5,7,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,5,6],[2,4,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,5,6],[3,4,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,6],[2,5,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,6],[3,5,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,6],[4,5,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,5],[2,6,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,5],[3,6,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,5],[4,6,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,4],[5,6,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,5,7],[2,4,6],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,5,7],[3,4,6],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,7],[2,5,6],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,7],[3,5,6],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,7],[4,5,6],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,5,6],[2,4,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,5,6],[3,4,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,6],[2,5,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,6],[3,5,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,6],[4,5,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,3,4,5],[2,6,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,4,5],[3,6,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,5],[4,6,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,2,3,4],[5,6,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 5
[[1,4,7,8],[2,5],[3,6]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,7,8],[2,5],[4,6]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,7,8],[3,5],[4,6]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,7,8],[2,4],[5,6]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,7,8],[3,4],[5,6]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,4,6,8],[2,5],[3,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,6,8],[2,5],[4,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,6,8],[3,5],[4,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,6,8],[2,4],[5,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,6,8],[3,4],[5,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,4,5,8],[2,6],[3,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,5,8],[2,6],[4,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,5,8],[3,6],[4,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,4,8],[2,6],[5,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,4,8],[3,6],[5,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,3,8],[4,6],[5,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,5,8],[2,4],[6,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,5,8],[3,4],[6,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,4,8],[2,5],[6,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,4,8],[3,5],[6,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,3,8],[4,5],[6,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,4,6,7],[2,5],[3,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,6,7],[2,5],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,6,7],[3,5],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,6,7],[2,4],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,6,7],[3,4],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,4,5,7],[2,6],[3,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,5,7],[2,6],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,5,7],[3,6],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,4,7],[2,6],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,4,7],[3,6],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,3,7],[4,6],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,5,7],[2,4],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,5,7],[3,4],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,4,7],[2,5],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,4,7],[3,5],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,3,7],[4,5],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,4,5,6],[2,7],[3,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,5,6],[2,7],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,5,6],[3,7],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,4,6],[2,7],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,4,6],[3,7],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,3,6],[4,7],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,4,5],[2,7],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,4,5],[3,7],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,3,5],[4,7],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,3,4],[5,7],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,5,6],[2,4],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,5,6],[3,4],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,4,6],[2,5],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,4,6],[3,5],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,3,6],[4,5],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,3,4,5],[2,6],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,4,5],[3,6],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,3,5],[4,6],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,2,3,4],[5,6],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 6
[[1,5,7,8],[2,6],[3],[4]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,7,8],[2,6],[3],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,7,8],[2,6],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,7,8],[3,6],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,7,8],[2,5],[3],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,7,8],[2,5],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,7,8],[3,5],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,7,8],[2,4],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,7,8],[3,4],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,5,6,8],[2,7],[3],[4]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,6,8],[2,7],[3],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,6,8],[2,7],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,6,8],[3,7],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,5,8],[2,7],[3],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,5,8],[2,7],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,5,8],[3,7],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,8],[2,7],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,8],[3,7],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,8],[4,7],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,6,8],[2,5],[3],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,6,8],[2,5],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,6,8],[3,5],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,6,8],[2,4],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,6,8],[3,4],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,5,8],[2,6],[3],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,5,8],[2,6],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,5,8],[3,6],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,8],[2,6],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,8],[3,6],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,8],[4,6],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,5,8],[2,4],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,5,8],[3,4],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,8],[2,5],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,8],[3,5],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,8],[4,5],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,5,6,7],[2,8],[3],[4]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,6,7],[2,8],[3],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,6,7],[2,8],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,6,7],[3,8],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,5,7],[2,8],[3],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,5,7],[2,8],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,5,7],[3,8],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,7],[2,8],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,7],[3,8],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,7],[4,8],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,5,6],[2,8],[3],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,5,6],[2,8],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,5,6],[3,8],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,6],[2,8],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,6],[3,8],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,6],[4,8],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,5],[2,8],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,5],[3,8],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,5],[4,8],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,4],[5,8],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,6,7],[2,5],[3],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,6,7],[2,5],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,6,7],[3,5],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,6,7],[2,4],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,6,7],[3,4],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,5,7],[2,6],[3],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,5,7],[2,6],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,5,7],[3,6],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,7],[2,6],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,7],[3,6],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,7],[4,6],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,5,7],[2,4],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,5,7],[3,4],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,7],[2,5],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,7],[3,5],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,7],[4,5],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,4,5,6],[2,7],[3],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,5,6],[2,7],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,5,6],[3,7],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,6],[2,7],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,6],[3,7],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,6],[4,7],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,5],[2,7],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,5],[3,7],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,5],[4,7],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,4],[5,7],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,5,6],[2,4],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,5,6],[3,4],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,6],[2,5],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,6],[3,5],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,6],[4,5],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,3,4,5],[2,6],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,4,5],[3,6],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,5],[4,6],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 7
[[1,6,7,8],[2],[3],[4],[5]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,5,7,8],[2],[3],[4],[6]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,4,7,8],[2],[3],[5],[6]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,3,7,8],[2],[4],[5],[6]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,7,8],[3],[4],[5],[6]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,5,6,8],[2],[3],[4],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,4,6,8],[2],[3],[5],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,3,6,8],[2],[4],[5],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,6,8],[3],[4],[5],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,4,5,8],[2],[3],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,3,5,8],[2],[4],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,5,8],[3],[4],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,3,4,8],[2],[5],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,4,8],[3],[5],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,3,8],[4],[5],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,5,6,7],[2],[3],[4],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,4,6,7],[2],[3],[5],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,3,6,7],[2],[4],[5],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,6,7],[3],[4],[5],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,4,5,7],[2],[3],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,3,5,7],[2],[4],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,5,7],[3],[4],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,3,4,7],[2],[5],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,4,7],[3],[5],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,3,7],[4],[5],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,4,5,6],[2],[3],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,3,5,6],[2],[4],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,5,6],[3],[4],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,3,4,6],[2],[5],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,4,6],[3],[5],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,3,6],[4],[5],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,3,4,5],[2],[6],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,4,5],[3],[6],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,3,5],[4],[6],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[[1,4,7],[2,5,8],[3,6]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,7],[2,5,8],[4,6]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,7],[3,5,8],[4,6]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,7],[2,4,8],[5,6]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,7],[3,4,8],[5,6]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,4,6],[2,5,8],[3,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,6],[2,5,8],[4,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,6],[3,5,8],[4,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,6],[2,4,8],[5,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,6],[3,4,8],[5,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,4,5],[2,6,8],[3,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,5],[2,6,8],[4,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,5],[3,6,8],[4,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,4],[2,6,8],[5,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,4],[3,6,8],[5,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,3],[4,6,8],[5,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,5],[2,4,8],[6,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,5],[3,4,8],[6,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,4],[2,5,8],[6,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,4],[3,5,8],[6,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,3],[4,5,8],[6,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,4,6],[2,5,7],[3,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,6],[2,5,7],[4,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,6],[3,5,7],[4,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,6],[2,4,7],[5,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,6],[3,4,7],[5,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,4,5],[2,6,7],[3,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,5],[2,6,7],[4,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,5],[3,6,7],[4,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,4],[2,6,7],[5,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,4],[3,6,7],[5,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,3],[4,6,7],[5,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,5],[2,4,7],[6,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,5],[3,4,7],[6,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,4],[2,5,7],[6,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,4],[3,5,7],[6,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,3],[4,5,7],[6,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,5],[2,4,6],[7,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,5],[3,4,6],[7,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,3,4],[2,5,6],[7,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,4],[3,5,6],[7,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,2,3],[4,5,6],[7,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 7
[[1,5,7],[2,6,8],[3],[4]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,4,7],[2,6,8],[3],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,7],[2,6,8],[4],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,7],[3,6,8],[4],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,4,7],[2,5,8],[3],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,7],[2,5,8],[4],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,7],[3,5,8],[4],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,7],[2,4,8],[5],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,7],[3,4,8],[5],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,5,6],[2,7,8],[3],[4]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,4,6],[2,7,8],[3],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,6],[2,7,8],[4],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,6],[3,7,8],[4],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,4,5],[2,7,8],[3],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,5],[2,7,8],[4],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,5],[3,7,8],[4],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,4],[2,7,8],[5],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,4],[3,7,8],[5],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,3],[4,7,8],[5],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,4,6],[2,5,8],[3],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,6],[2,5,8],[4],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,6],[3,5,8],[4],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,6],[2,4,8],[5],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,6],[3,4,8],[5],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,4,5],[2,6,8],[3],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,5],[2,6,8],[4],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,5],[3,6,8],[4],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,4],[2,6,8],[5],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,4],[3,6,8],[5],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,3],[4,6,8],[5],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,5],[2,4,8],[6],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,5],[3,4,8],[6],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,4],[2,5,8],[6],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,4],[3,5,8],[6],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,3],[4,5,8],[6],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,4,6],[2,5,7],[3],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,6],[2,5,7],[4],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,6],[3,5,7],[4],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,6],[2,4,7],[5],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,6],[3,4,7],[5],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,4,5],[2,6,7],[3],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,5],[2,6,7],[4],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,5],[3,6,7],[4],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,4],[2,6,7],[5],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,4],[3,6,7],[5],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,3],[4,6,7],[5],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,5],[2,4,7],[6],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,5],[3,4,7],[6],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,4],[2,5,7],[6],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,4],[3,5,7],[6],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,3],[4,5,7],[6],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,5],[2,4,6],[7],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,5],[3,4,6],[7],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,3,4],[2,5,6],[7],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,4],[3,5,6],[7],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 8
[[1,5,8],[2,6],[3,7],[4]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,8],[2,6],[3,7],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,8],[2,6],[4,7],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,8],[3,6],[4,7],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,8],[2,5],[3,7],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,8],[2,5],[4,7],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,8],[3,5],[4,7],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,8],[2,4],[5,7],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,8],[3,4],[5,7],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,8],[2,5],[3,6],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,8],[2,5],[4,6],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,8],[3,5],[4,6],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,8],[2,4],[5,6],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,8],[3,4],[5,6],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,5,7],[2,6],[3,8],[4]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,7],[2,6],[3,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,7],[2,6],[4,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,7],[3,6],[4,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,7],[2,5],[3,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,7],[2,5],[4,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,7],[3,5],[4,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,7],[2,4],[5,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,7],[3,4],[5,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,5,6],[2,7],[3,8],[4]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,6],[2,7],[3,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,6],[2,7],[4,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,6],[3,7],[4,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,5],[2,7],[3,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,5],[2,7],[4,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,5],[3,7],[4,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,4],[2,7],[5,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,4],[3,7],[5,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,3],[4,7],[5,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,6],[2,5],[3,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,6],[2,5],[4,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,6],[3,5],[4,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,6],[2,4],[5,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,6],[3,4],[5,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,5],[2,6],[3,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,5],[2,6],[4,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,5],[3,6],[4,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,4],[2,6],[5,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,4],[3,6],[5,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,3],[4,6],[5,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,5],[2,4],[6,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,5],[3,4],[6,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,4],[2,5],[6,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,4],[3,5],[6,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,3],[4,5],[6,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,7],[2,5],[3,6],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,7],[2,5],[4,6],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,7],[3,5],[4,6],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,7],[2,4],[5,6],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,7],[3,4],[5,6],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,6],[2,5],[3,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,6],[2,5],[4,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,6],[3,5],[4,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,6],[2,4],[5,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,6],[3,4],[5,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,4,5],[2,6],[3,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,5],[2,6],[4,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,5],[3,6],[4,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,4],[2,6],[5,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,4],[3,6],[5,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,3],[4,6],[5,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,5],[2,4],[6,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,5],[3,4],[6,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,3,4],[2,5],[6,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,4],[3,5],[6,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 9
[[1,6,8],[2,7],[3],[4],[5]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,5,8],[2,7],[3],[4],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,8],[2,7],[3],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,8],[2,7],[4],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,8],[3,7],[4],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,5,8],[2,6],[3],[4],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,8],[2,6],[3],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,8],[2,6],[4],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,8],[3,6],[4],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,8],[2,5],[3],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,8],[2,5],[4],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,8],[3,5],[4],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,8],[2,4],[5],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,8],[3,4],[5],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,6,7],[2,8],[3],[4],[5]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,5,7],[2,8],[3],[4],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,7],[2,8],[3],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,7],[2,8],[4],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,7],[3,8],[4],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,5,6],[2,8],[3],[4],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,6],[2,8],[3],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,6],[2,8],[4],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,6],[3,8],[4],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,5],[2,8],[3],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,5],[2,8],[4],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,5],[3,8],[4],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,4],[2,8],[5],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,4],[3,8],[5],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,3],[4,8],[5],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,5,7],[2,6],[3],[4],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,7],[2,6],[3],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,7],[2,6],[4],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,7],[3,6],[4],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,7],[2,5],[3],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,7],[2,5],[4],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,7],[3,5],[4],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,7],[2,4],[5],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,7],[3,4],[5],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,5,6],[2,7],[3],[4],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,6],[2,7],[3],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,6],[2,7],[4],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,6],[3,7],[4],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,5],[2,7],[3],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,5],[2,7],[4],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,5],[3,7],[4],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,4],[2,7],[5],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,4],[3,7],[5],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,3],[4,7],[5],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,6],[2,5],[3],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,6],[2,5],[4],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,6],[3,5],[4],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,6],[2,4],[5],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,6],[3,4],[5],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,4,5],[2,6],[3],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,5],[2,6],[4],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,5],[3,6],[4],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,4],[2,6],[5],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,4],[3,6],[5],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,3],[4,6],[5],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,5],[2,4],[6],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,5],[3,4],[6],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,3,4],[2,5],[6],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,4],[3,5],[6],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 11
[[1,7,8],[2],[3],[4],[5],[6]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,6,8],[2],[3],[4],[5],[7]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,5,8],[2],[3],[4],[6],[7]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,4,8],[2],[3],[5],[6],[7]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,3,8],[2],[4],[5],[6],[7]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,2,8],[3],[4],[5],[6],[7]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,6,7],[2],[3],[4],[5],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,5,7],[2],[3],[4],[6],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,4,7],[2],[3],[5],[6],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,3,7],[2],[4],[5],[6],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,2,7],[3],[4],[5],[6],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,5,6],[2],[3],[4],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,4,6],[2],[3],[5],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,3,6],[2],[4],[5],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,2,6],[3],[4],[5],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,4,5],[2],[3],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,3,5],[2],[4],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,2,5],[3],[4],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,3,4],[2],[5],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,2,4],[3],[5],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[[1,5],[2,6],[3,7],[4,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,4],[2,6],[3,7],[5,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,3],[2,6],[4,7],[5,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,2],[3,6],[4,7],[5,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,4],[2,5],[3,7],[6,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,3],[2,5],[4,7],[6,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,2],[3,5],[4,7],[6,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,3],[2,4],[5,7],[6,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,2],[3,4],[5,7],[6,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,4],[2,5],[3,6],[7,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,3],[2,5],[4,6],[7,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,2],[3,5],[4,6],[7,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,3],[2,4],[5,6],[7,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 12
[[1,6],[2,7],[3,8],[4],[5]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,5],[2,7],[3,8],[4],[6]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,4],[2,7],[3,8],[5],[6]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,3],[2,7],[4,8],[5],[6]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,2],[3,7],[4,8],[5],[6]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,5],[2,6],[3,8],[4],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,4],[2,6],[3,8],[5],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,3],[2,6],[4,8],[5],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,2],[3,6],[4,8],[5],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,4],[2,5],[3,8],[6],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,3],[2,5],[4,8],[6],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,2],[3,5],[4,8],[6],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,3],[2,4],[5,8],[6],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,2],[3,4],[5,8],[6],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,5],[2,6],[3,7],[4],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,4],[2,6],[3,7],[5],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,3],[2,6],[4,7],[5],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,2],[3,6],[4,7],[5],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,4],[2,5],[3,7],[6],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,3],[2,5],[4,7],[6],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,2],[3,5],[4,7],[6],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,3],[2,4],[5,7],[6],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,2],[3,4],[5,7],[6],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,4],[2,5],[3,6],[7],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,3],[2,5],[4,6],[7],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,2],[3,5],[4,6],[7],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,3],[2,4],[5,6],[7],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 13
[[1,7],[2,8],[3],[4],[5],[6]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,6],[2,8],[3],[4],[5],[7]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,5],[2,8],[3],[4],[6],[7]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,4],[2,8],[3],[5],[6],[7]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,3],[2,8],[4],[5],[6],[7]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,2],[3,8],[4],[5],[6],[7]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,6],[2,7],[3],[4],[5],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,5],[2,7],[3],[4],[6],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,4],[2,7],[3],[5],[6],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,3],[2,7],[4],[5],[6],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,2],[3,7],[4],[5],[6],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,5],[2,6],[3],[4],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,4],[2,6],[3],[5],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,3],[2,6],[4],[5],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,2],[3,6],[4],[5],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,4],[2,5],[3],[6],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,3],[2,5],[4],[6],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,2],[3,5],[4],[6],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,3],[2,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 16
[[1,8],[2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[[1,7],[2],[3],[4],[5],[6],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[[1,6],[2],[3],[4],[5],[7],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[[1,5],[2],[3],[4],[6],[7],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[[1,4],[2],[3],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[[1,3],[2],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 28
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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 shifted natural comajor index of a standard Young tableau.
A natural descent of a standard tableau $T$ is an entry $i$ such that $i+1$ appears in a higher row than $i$ in English notation.
The natural comajor index of a tableau of shape $\lambda$, size $n$ with natural descent set $D$ is then $b(\lambda)+\sum_{d\in D} n-d$, where $b(\lambda) = \sum_i (i-1)\lambda_i$.
A natural descent of a standard tableau $T$ is an entry $i$ such that $i+1$ appears in a higher row than $i$ in English notation.
The natural comajor index of a tableau of shape $\lambda$, size $n$ with natural descent set $D$ is then $b(\lambda)+\sum_{d\in D} n-d$, where $b(\lambda) = \sum_i (i-1)\lambda_i$.
Map
shape
Description
Sends a tableau to its shape.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
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