Identifier
-
Mp00083:
Standard tableaux
—shape⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000993: Integer partitions ⟶ ℤ
Values
[[1],[2],[3],[4]] => [1,1,1,1] => [1,1,1] => [1,1] => 2
[[1,5],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 2
[[1],[2],[3],[4],[5]] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,5,6],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,6],[2],[3],[5]] => [3,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,6],[2],[4],[5]] => [3,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,6],[3],[4],[5]] => [3,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,5],[2],[3],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,5],[2],[4],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,5],[3],[4],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,4],[2],[5],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4],[3],[5],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3],[4],[5],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4],[2,5],[3,6]] => [2,2,2] => [2,2] => [2] => 1
[[1,3],[2,5],[4,6]] => [2,2,2] => [2,2] => [2] => 1
[[1,2],[3,5],[4,6]] => [2,2,2] => [2,2] => [2] => 1
[[1,3],[2,4],[5,6]] => [2,2,2] => [2,2] => [2] => 1
[[1,2],[3,4],[5,6]] => [2,2,2] => [2,2] => [2] => 1
[[1,5],[2,6],[3],[4]] => [2,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4],[2,6],[3],[5]] => [2,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3],[2,6],[4],[5]] => [2,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2],[3,6],[4],[5]] => [2,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4],[2,5],[3],[6]] => [2,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3],[2,5],[4],[6]] => [2,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2],[3,5],[4],[6]] => [2,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3],[2,4],[5],[6]] => [2,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2],[3,4],[5],[6]] => [2,2,1,1] => [2,1,1] => [1,1] => 2
[[1,6],[2],[3],[4],[5]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,5],[2],[3],[4],[6]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4],[2],[3],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3],[2],[4],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,5,6,7],[2],[3],[4]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,6,7],[2],[3],[5]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,6,7],[2],[4],[5]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,6,7],[3],[4],[5]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,5,7],[2],[3],[6]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,5,7],[2],[4],[6]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,5,7],[3],[4],[6]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,4,7],[2],[5],[6]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4,7],[3],[5],[6]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,7],[4],[5],[6]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,5,6],[2],[3],[7]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,5,6],[2],[4],[7]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,5,6],[3],[4],[7]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,4,6],[2],[5],[7]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4,6],[3],[5],[7]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,6],[4],[5],[7]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,4,5],[2],[6],[7]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4,5],[3],[6],[7]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,5],[4],[6],[7]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,7],[2,5],[3,6]] => [3,2,2] => [2,2] => [2] => 1
[[1,3,7],[2,5],[4,6]] => [3,2,2] => [2,2] => [2] => 1
[[1,2,7],[3,5],[4,6]] => [3,2,2] => [2,2] => [2] => 1
[[1,3,7],[2,4],[5,6]] => [3,2,2] => [2,2] => [2] => 1
[[1,2,7],[3,4],[5,6]] => [3,2,2] => [2,2] => [2] => 1
[[1,4,6],[2,5],[3,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,3,6],[2,5],[4,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,2,6],[3,5],[4,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,3,6],[2,4],[5,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,2,6],[3,4],[5,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,4,5],[2,6],[3,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,3,5],[2,6],[4,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,2,5],[3,6],[4,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,3,4],[2,6],[5,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,2,4],[3,6],[5,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,2,3],[4,6],[5,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,3,5],[2,4],[6,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,2,5],[3,4],[6,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,3,4],[2,5],[6,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,2,4],[3,5],[6,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,2,3],[4,5],[6,7]] => [3,2,2] => [2,2] => [2] => 1
[[1,5,7],[2,6],[3],[4]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,7],[2,6],[3],[5]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,7],[2,6],[4],[5]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,7],[3,6],[4],[5]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,7],[2,5],[3],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,7],[2,5],[4],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,7],[3,5],[4],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,7],[2,4],[5],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,7],[3,4],[5],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,5,6],[2,7],[3],[4]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,6],[2,7],[3],[5]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,6],[2,7],[4],[5]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,6],[3,7],[4],[5]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,5],[2,7],[3],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5],[2,7],[4],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5],[3,7],[4],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4],[2,7],[5],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4],[3,7],[5],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3],[4,7],[5],[6]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,6],[2,5],[3],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,6],[2,5],[4],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,6],[3,5],[4],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,6],[2,4],[5],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,6],[3,4],[5],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
>>> Load all 1052 entries. <<<[[1,4,5],[2,6],[3],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5],[2,6],[4],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5],[3,6],[4],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4],[2,6],[5],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4],[3,6],[5],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3],[4,6],[5],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5],[2,4],[6],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5],[3,4],[6],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4],[2,5],[6],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4],[3,5],[6],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => [2,1,1] => [1,1] => 2
[[1,6,7],[2],[3],[4],[5]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,5,7],[2],[3],[4],[6]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4,7],[2],[3],[5],[6]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,7],[2],[4],[5],[6]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,7],[3],[4],[5],[6]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,5,6],[2],[3],[4],[7]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4,6],[2],[3],[5],[7]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,6],[2],[4],[5],[7]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,6],[3],[4],[5],[7]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4,5],[2],[3],[6],[7]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,5],[2],[4],[6],[7]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,5],[3],[4],[6],[7]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,4],[2],[5],[6],[7]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,4],[3],[5],[6],[7]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,5],[2,6],[3,7],[4]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4],[2,6],[3,7],[5]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3],[2,6],[4,7],[5]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2],[3,6],[4,7],[5]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4],[2,5],[3,7],[6]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3],[2,5],[4,7],[6]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2],[3,5],[4,7],[6]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3],[2,4],[5,7],[6]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2],[3,4],[5,7],[6]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4],[2,5],[3,6],[7]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3],[2,5],[4,6],[7]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2],[3,5],[4,6],[7]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3],[2,4],[5,6],[7]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,6],[2,7],[3],[4],[5]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,5],[2,7],[3],[4],[6]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4],[2,7],[3],[5],[6]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3],[2,7],[4],[5],[6]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2],[3,7],[4],[5],[6]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,5],[2,6],[3],[4],[7]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4],[2,6],[3],[5],[7]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3],[2,6],[4],[5],[7]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2],[3,6],[4],[5],[7]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4],[2,5],[3],[6],[7]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3],[2,5],[4],[6],[7]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2],[3,5],[4],[6],[7]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3],[2,4],[5],[6],[7]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,7],[2],[3],[4],[5],[6]] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,6],[2],[3],[4],[5],[7]] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,5],[2],[3],[4],[6],[7]] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,4],[2],[3],[5],[6],[7]] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,3],[2],[4],[5],[6],[7]] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,5,6,7,8],[2],[3],[4]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,6,7,8],[2],[3],[5]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,6,7,8],[2],[4],[5]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,6,7,8],[3],[4],[5]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,5,7,8],[2],[3],[6]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,5,7,8],[2],[4],[6]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,5,7,8],[3],[4],[6]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,4,7,8],[2],[5],[6]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4,7,8],[3],[5],[6]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,7,8],[4],[5],[6]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,5,6,8],[2],[3],[7]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,5,6,8],[2],[4],[7]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,5,6,8],[3],[4],[7]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,4,6,8],[2],[5],[7]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4,6,8],[3],[5],[7]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,6,8],[4],[5],[7]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,4,5,8],[2],[6],[7]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4,5,8],[3],[6],[7]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,5,8],[4],[6],[7]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,4,8],[5],[6],[7]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,5,6,7],[2],[3],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,5,6,7],[2],[4],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,5,6,7],[3],[4],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,4,6,7],[2],[5],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4,6,7],[3],[5],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,6,7],[4],[5],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,4,5,7],[2],[6],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4,5,7],[3],[6],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,5,7],[4],[6],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,4,7],[5],[6],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,3,4,5,6],[2],[7],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4,5,6],[3],[7],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,5,6],[4],[7],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,4,6],[5],[7],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => [1,1,1] => [1,1] => 2
[[1,4,7,8],[2,5],[3,6]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,7,8],[2,5],[4,6]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,7,8],[3,5],[4,6]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,7,8],[2,4],[5,6]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,7,8],[3,4],[5,6]] => [4,2,2] => [2,2] => [2] => 1
[[1,4,6,8],[2,5],[3,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,6,8],[2,5],[4,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,6,8],[3,5],[4,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,6,8],[2,4],[5,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,6,8],[3,4],[5,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,4,5,8],[2,6],[3,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,5,8],[2,6],[4,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,5,8],[3,6],[4,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,4,8],[2,6],[5,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,4,8],[3,6],[5,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,3,8],[4,6],[5,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,5,8],[2,4],[6,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,5,8],[3,4],[6,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,4,8],[2,5],[6,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,4,8],[3,5],[6,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,3,8],[4,5],[6,7]] => [4,2,2] => [2,2] => [2] => 1
[[1,4,6,7],[2,5],[3,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,6,7],[2,5],[4,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,6,7],[3,5],[4,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,6,7],[2,4],[5,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,6,7],[3,4],[5,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,4,5,7],[2,6],[3,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,5,7],[2,6],[4,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,5,7],[3,6],[4,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,4,7],[2,6],[5,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,4,7],[3,6],[5,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,3,7],[4,6],[5,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,5,7],[2,4],[6,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,5,7],[3,4],[6,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,4,7],[2,5],[6,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,4,7],[3,5],[6,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,3,7],[4,5],[6,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,4,5,6],[2,7],[3,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,5,6],[2,7],[4,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,5,6],[3,7],[4,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,4,6],[2,7],[5,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,4,6],[3,7],[5,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,3,6],[4,7],[5,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,4,5],[2,7],[6,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,4,5],[3,7],[6,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,3,5],[4,7],[6,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,3,4],[5,7],[6,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,5,6],[2,4],[7,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,5,6],[3,4],[7,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,4,6],[2,5],[7,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,4,6],[3,5],[7,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,3,6],[4,5],[7,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,3,4,5],[2,6],[7,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,4,5],[3,6],[7,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,3,5],[4,6],[7,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,2,3,4],[5,6],[7,8]] => [4,2,2] => [2,2] => [2] => 1
[[1,5,7,8],[2,6],[3],[4]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,7,8],[2,6],[3],[5]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,7,8],[2,6],[4],[5]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,7,8],[3,6],[4],[5]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,7,8],[2,5],[3],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,7,8],[2,5],[4],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,7,8],[3,5],[4],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,7,8],[2,4],[5],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,7,8],[3,4],[5],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,5,6,8],[2,7],[3],[4]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,6,8],[2,7],[3],[5]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,6,8],[2,7],[4],[5]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,6,8],[3,7],[4],[5]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,5,8],[2,7],[3],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5,8],[2,7],[4],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,8],[3,7],[4],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,8],[2,7],[5],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,8],[3,7],[5],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,8],[4,7],[5],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,6,8],[2,5],[3],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,6,8],[2,5],[4],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,6,8],[3,5],[4],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,6,8],[2,4],[5],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,6,8],[3,4],[5],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,5,8],[2,6],[3],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5,8],[2,6],[4],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,8],[3,6],[4],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,8],[2,6],[5],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,8],[3,6],[5],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,8],[4,6],[5],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5,8],[2,4],[6],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,8],[3,4],[6],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,8],[2,5],[6],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,8],[3,5],[6],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,8],[4,5],[6],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,5,6,7],[2,8],[3],[4]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,6,7],[2,8],[3],[5]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,6,7],[2,8],[4],[5]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,6,7],[3,8],[4],[5]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,5,7],[2,8],[3],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5,7],[2,8],[4],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,7],[3,8],[4],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,7],[2,8],[5],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,7],[3,8],[5],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,7],[4,8],[5],[6]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,5,6],[2,8],[3],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5,6],[2,8],[4],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,6],[3,8],[4],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,6],[2,8],[5],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,6],[3,8],[5],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,6],[4,8],[5],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,5],[2,8],[6],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,5],[3,8],[6],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,5],[4,8],[6],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,4],[5,8],[6],[7]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,6,7],[2,5],[3],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,6,7],[2,5],[4],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,6,7],[3,5],[4],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,6,7],[2,4],[5],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,6,7],[3,4],[5],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,5,7],[2,6],[3],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5,7],[2,6],[4],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,7],[3,6],[4],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,7],[2,6],[5],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,7],[3,6],[5],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,7],[4,6],[5],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5,7],[2,4],[6],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,7],[3,4],[6],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,7],[2,5],[6],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,7],[3,5],[6],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,7],[4,5],[6],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,4,5,6],[2,7],[3],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5,6],[2,7],[4],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,6],[3,7],[4],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,6],[2,7],[5],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,6],[3,7],[5],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,6],[4,7],[5],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,5],[2,7],[6],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,5],[3,7],[6],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,5],[4,7],[6],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,4],[5,7],[6],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,5,6],[2,4],[7],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,6],[3,4],[7],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,6],[2,5],[7],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,6],[3,5],[7],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,6],[4,5],[7],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,3,4,5],[2,6],[7],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,5],[3,6],[7],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,5],[4,6],[7],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => [2,1,1] => [1,1] => 2
[[1,6,7,8],[2],[3],[4],[5]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,5,7,8],[2],[3],[4],[6]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4,7,8],[2],[3],[5],[6]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,7,8],[2],[4],[5],[6]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,7,8],[3],[4],[5],[6]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,5,6,8],[2],[3],[4],[7]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4,6,8],[2],[3],[5],[7]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,6,8],[2],[4],[5],[7]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,6,8],[3],[4],[5],[7]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4,5,8],[2],[3],[6],[7]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,5,8],[2],[4],[6],[7]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,5,8],[3],[4],[6],[7]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,4,8],[2],[5],[6],[7]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,4,8],[3],[5],[6],[7]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,3,8],[4],[5],[6],[7]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,5,6,7],[2],[3],[4],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4,6,7],[2],[3],[5],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,6,7],[2],[4],[5],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,6,7],[3],[4],[5],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4,5,7],[2],[3],[6],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,5,7],[2],[4],[6],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,5,7],[3],[4],[6],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,4,7],[2],[5],[6],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,4,7],[3],[5],[6],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,3,7],[4],[5],[6],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4,5,6],[2],[3],[7],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,5,6],[2],[4],[7],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,5,6],[3],[4],[7],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,4,6],[2],[5],[7],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,4,6],[3],[5],[7],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,3,6],[4],[5],[7],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,3,4,5],[2],[6],[7],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,4,5],[3],[6],[7],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,3,5],[4],[6],[7],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,4,7],[2,5,8],[3,6]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,7],[2,5,8],[4,6]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,7],[3,5,8],[4,6]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,7],[2,4,8],[5,6]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,7],[3,4,8],[5,6]] => [3,3,2] => [3,2] => [2] => 1
[[1,4,6],[2,5,8],[3,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,6],[2,5,8],[4,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,6],[3,5,8],[4,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,6],[2,4,8],[5,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,6],[3,4,8],[5,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,4,5],[2,6,8],[3,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,5],[2,6,8],[4,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,5],[3,6,8],[4,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,4],[2,6,8],[5,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,4],[3,6,8],[5,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,3],[4,6,8],[5,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,5],[2,4,8],[6,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,5],[3,4,8],[6,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,4],[2,5,8],[6,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,4],[3,5,8],[6,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,3],[4,5,8],[6,7]] => [3,3,2] => [3,2] => [2] => 1
[[1,4,6],[2,5,7],[3,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,6],[2,5,7],[4,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,6],[3,5,7],[4,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,6],[2,4,7],[5,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,6],[3,4,7],[5,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,4,5],[2,6,7],[3,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,5],[2,6,7],[4,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,5],[3,6,7],[4,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,4],[2,6,7],[5,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,4],[3,6,7],[5,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,3],[4,6,7],[5,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,5],[2,4,7],[6,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,5],[3,4,7],[6,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,4],[2,5,7],[6,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,4],[3,5,7],[6,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,3],[4,5,7],[6,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,5],[2,4,6],[7,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,5],[3,4,6],[7,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,3,4],[2,5,6],[7,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,4],[3,5,6],[7,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,2,3],[4,5,6],[7,8]] => [3,3,2] => [3,2] => [2] => 1
[[1,5,7],[2,6,8],[3],[4]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,4,7],[2,6,8],[3],[5]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,7],[2,6,8],[4],[5]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,7],[3,6,8],[4],[5]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,4,7],[2,5,8],[3],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,7],[2,5,8],[4],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,7],[3,5,8],[4],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,7],[2,4,8],[5],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,7],[3,4,8],[5],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,5,6],[2,7,8],[3],[4]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,4,6],[2,7,8],[3],[5]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,6],[2,7,8],[4],[5]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,6],[3,7,8],[4],[5]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,4,5],[2,7,8],[3],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,5],[2,7,8],[4],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,5],[3,7,8],[4],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,4],[2,7,8],[5],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,4],[3,7,8],[5],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,3],[4,7,8],[5],[6]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,4,6],[2,5,8],[3],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,6],[2,5,8],[4],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,6],[3,5,8],[4],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,6],[2,4,8],[5],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,6],[3,4,8],[5],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,4,5],[2,6,8],[3],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,5],[2,6,8],[4],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,5],[3,6,8],[4],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,4],[2,6,8],[5],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,4],[3,6,8],[5],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,3],[4,6,8],[5],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,5],[2,4,8],[6],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,5],[3,4,8],[6],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,4],[2,5,8],[6],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,4],[3,5,8],[6],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,3],[4,5,8],[6],[7]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,4,6],[2,5,7],[3],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,6],[2,5,7],[4],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,6],[3,5,7],[4],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,6],[2,4,7],[5],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,6],[3,4,7],[5],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,4,5],[2,6,7],[3],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,5],[2,6,7],[4],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,5],[3,6,7],[4],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,4],[2,6,7],[5],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,4],[3,6,7],[5],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,3],[4,6,7],[5],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,5],[2,4,7],[6],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,5],[3,4,7],[6],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,4],[2,5,7],[6],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,4],[3,5,7],[6],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,3],[4,5,7],[6],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,5],[2,4,6],[7],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,5],[3,4,6],[7],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,4],[2,5,6],[7],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,4],[3,5,6],[7],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => [3,1,1] => [1,1] => 2
[[1,5,8],[2,6],[3,7],[4]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,8],[2,6],[3,7],[5]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,8],[2,6],[4,7],[5]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,8],[3,6],[4,7],[5]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,8],[2,5],[3,7],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,8],[2,5],[4,7],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,8],[3,5],[4,7],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,8],[2,4],[5,7],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,8],[3,4],[5,7],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,8],[2,5],[3,6],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,8],[2,5],[4,6],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,8],[3,5],[4,6],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,8],[2,4],[5,6],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,8],[3,4],[5,6],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,5,7],[2,6],[3,8],[4]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,7],[2,6],[3,8],[5]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,7],[2,6],[4,8],[5]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,7],[3,6],[4,8],[5]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,7],[2,5],[3,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,7],[2,5],[4,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,7],[3,5],[4,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,7],[2,4],[5,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,7],[3,4],[5,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,5,6],[2,7],[3,8],[4]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,6],[2,7],[3,8],[5]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,6],[2,7],[4,8],[5]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,6],[3,7],[4,8],[5]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,5],[2,7],[3,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,5],[2,7],[4,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,5],[3,7],[4,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,4],[2,7],[5,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,4],[3,7],[5,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,3],[4,7],[5,8],[6]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,6],[2,5],[3,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,6],[2,5],[4,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,6],[3,5],[4,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,6],[2,4],[5,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,6],[3,4],[5,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,5],[2,6],[3,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,5],[2,6],[4,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,5],[3,6],[4,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,4],[2,6],[5,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,4],[3,6],[5,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,3],[4,6],[5,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,5],[2,4],[6,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,5],[3,4],[6,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,4],[2,5],[6,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,4],[3,5],[6,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,3],[4,5],[6,8],[7]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,7],[2,5],[3,6],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,7],[2,5],[4,6],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,7],[3,5],[4,6],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,7],[2,4],[5,6],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,7],[3,4],[5,6],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,6],[2,5],[3,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,6],[2,5],[4,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,6],[3,5],[4,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,6],[2,4],[5,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,6],[3,4],[5,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,4,5],[2,6],[3,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,5],[2,6],[4,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,5],[3,6],[4,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,4],[2,6],[5,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,4],[3,6],[5,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,3],[4,6],[5,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,5],[2,4],[6,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,5],[3,4],[6,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,3,4],[2,5],[6,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,4],[3,5],[6,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,6,8],[2,7],[3],[4],[5]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,5,8],[2,7],[3],[4],[6]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,8],[2,7],[3],[5],[6]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,8],[2,7],[4],[5],[6]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,8],[3,7],[4],[5],[6]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,5,8],[2,6],[3],[4],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,8],[2,6],[3],[5],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,8],[2,6],[4],[5],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,8],[3,6],[4],[5],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,8],[2,5],[3],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,8],[2,5],[4],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,8],[3,5],[4],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,8],[2,4],[5],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,8],[3,4],[5],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,6,7],[2,8],[3],[4],[5]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,5,7],[2,8],[3],[4],[6]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,7],[2,8],[3],[5],[6]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,7],[2,8],[4],[5],[6]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,7],[3,8],[4],[5],[6]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,5,6],[2,8],[3],[4],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,6],[2,8],[3],[5],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,6],[2,8],[4],[5],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,6],[3,8],[4],[5],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,5],[2,8],[3],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,5],[2,8],[4],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,5],[3,8],[4],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,4],[2,8],[5],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,4],[3,8],[5],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,3],[4,8],[5],[6],[7]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,5,7],[2,6],[3],[4],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,7],[2,6],[3],[5],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,7],[2,6],[4],[5],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,7],[3,6],[4],[5],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,7],[2,5],[3],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,7],[2,5],[4],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,7],[3,5],[4],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,7],[2,4],[5],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,7],[3,4],[5],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,5,6],[2,7],[3],[4],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,6],[2,7],[3],[5],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,6],[2,7],[4],[5],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,6],[3,7],[4],[5],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,5],[2,7],[3],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,5],[2,7],[4],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,5],[3,7],[4],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,4],[2,7],[5],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,4],[3,7],[5],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,3],[4,7],[5],[6],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,6],[2,5],[3],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,6],[2,5],[4],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,6],[3,5],[4],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,6],[2,4],[5],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,6],[3,4],[5],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,4,5],[2,6],[3],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,5],[2,6],[4],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,5],[3,6],[4],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,4],[2,6],[5],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,4],[3,6],[5],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,3],[4,6],[5],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,5],[2,4],[6],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,5],[3,4],[6],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,3,4],[2,5],[6],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,4],[3,5],[6],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,7,8],[2],[3],[4],[5],[6]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,6,8],[2],[3],[4],[5],[7]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,5,8],[2],[3],[4],[6],[7]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,4,8],[2],[3],[5],[6],[7]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,3,8],[2],[4],[5],[6],[7]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,8],[3],[4],[5],[6],[7]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,6,7],[2],[3],[4],[5],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,5,7],[2],[3],[4],[6],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,4,7],[2],[3],[5],[6],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,3,7],[2],[4],[5],[6],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,7],[3],[4],[5],[6],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,5,6],[2],[3],[4],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,4,6],[2],[3],[5],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,3,6],[2],[4],[5],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,6],[3],[4],[5],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,4,5],[2],[3],[6],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,3,5],[2],[4],[6],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,5],[3],[4],[6],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,3,4],[2],[5],[6],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,4],[3],[5],[6],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,5],[2,6],[3,7],[4,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,4],[2,6],[3,7],[5,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,3],[2,6],[4,7],[5,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2],[3,6],[4,7],[5,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,4],[2,5],[3,7],[6,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,3],[2,5],[4,7],[6,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2],[3,5],[4,7],[6,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,3],[2,4],[5,7],[6,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2],[3,4],[5,7],[6,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,4],[2,5],[3,6],[7,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,3],[2,5],[4,6],[7,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2],[3,5],[4,6],[7,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,3],[2,4],[5,6],[7,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,6],[2,7],[3,8],[4],[5]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,5],[2,7],[3,8],[4],[6]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,4],[2,7],[3,8],[5],[6]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,3],[2,7],[4,8],[5],[6]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2],[3,7],[4,8],[5],[6]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,5],[2,6],[3,8],[4],[7]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,4],[2,6],[3,8],[5],[7]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,3],[2,6],[4,8],[5],[7]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2],[3,6],[4,8],[5],[7]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,4],[2,5],[3,8],[6],[7]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,3],[2,5],[4,8],[6],[7]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2],[3,5],[4,8],[6],[7]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,3],[2,4],[5,8],[6],[7]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2],[3,4],[5,8],[6],[7]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,5],[2,6],[3,7],[4],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,4],[2,6],[3,7],[5],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,3],[2,6],[4,7],[5],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2],[3,6],[4,7],[5],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,4],[2,5],[3,7],[6],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,3],[2,5],[4,7],[6],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2],[3,5],[4,7],[6],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,3],[2,4],[5,7],[6],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2],[3,4],[5,7],[6],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,4],[2,5],[3,6],[7],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,3],[2,5],[4,6],[7],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2],[3,5],[4,6],[7],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,3],[2,4],[5,6],[7],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,7],[2,8],[3],[4],[5],[6]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,6],[2,8],[3],[4],[5],[7]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,5],[2,8],[3],[4],[6],[7]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,4],[2,8],[3],[5],[6],[7]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,3],[2,8],[4],[5],[6],[7]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2],[3,8],[4],[5],[6],[7]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,6],[2,7],[3],[4],[5],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,5],[2,7],[3],[4],[6],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,4],[2,7],[3],[5],[6],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,3],[2,7],[4],[5],[6],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2],[3,7],[4],[5],[6],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,5],[2,6],[3],[4],[7],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,4],[2,6],[3],[5],[7],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,3],[2,6],[4],[5],[7],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2],[3,6],[4],[5],[7],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,4],[2,5],[3],[6],[7],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,3],[2,5],[4],[6],[7],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2],[3,5],[4],[6],[7],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,3],[2,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,8],[2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,7],[2],[3],[4],[5],[6],[8]] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,6],[2],[3],[4],[5],[7],[8]] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,5],[2],[3],[4],[6],[7],[8]] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,4],[2],[3],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,3],[2],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[[1,2,3,4,5,6],[7],[8],[9]] => [6,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,4,5],[6,7],[8,9]] => [5,2,2] => [2,2] => [2] => 1
[[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,4,5],[6],[7],[8],[9]] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => [3,2] => [2] => 1
[[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,3,4],[5],[6],[7],[8],[9]] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,3],[4,5,6],[7,8,9]] => [3,3,3] => [3,3] => [3] => 1
[[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[[1,2,3],[4,5],[6,7],[8,9]] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,2],[3,4],[5,6],[7,8],[9]] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 2
[[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[[1,2,3,4,5,6,7],[8],[9],[10]] => [7,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,3,4,5,6],[7,8],[9,10]] => [6,2,2] => [2,2] => [2] => 1
[[1,2,3,4,5,6],[7,8],[9],[10]] => [6,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,3,4,5],[6,7,8],[9,10]] => [5,3,2] => [3,2] => [2] => 1
[[1,2,3,4,5],[6,7,8],[9],[10]] => [5,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,3,4,5],[6,7],[8,9],[10]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,3,4,5],[6,7],[8],[9],[10]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,3,4],[5,6,7,8],[9,10]] => [4,4,2] => [4,2] => [2] => 1
[[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => [4,1,1] => [1,1] => 2
[[1,2,3,4],[5,6,7],[8,9,10]] => [4,3,3] => [3,3] => [3] => 1
[[1,2,3,4],[5,6,7],[8,9],[10]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[1,2,3,4],[5,6,7],[8],[9],[10]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[[1,2,3,4],[5,6],[7,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,4],[5,6],[7,8],[9],[10]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2,3,4],[5,6],[7],[8],[9],[10]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,2,3],[4,5,6],[7,8,9],[10]] => [3,3,3,1] => [3,3,1] => [3,1] => 1
[[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[[1,2,3],[4,5,6],[7,8],[9],[10]] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 4
[[1,2,3],[4,5],[6,7],[8,9],[10]] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 2
[[1,2,3],[4,5],[6,7],[8],[9],[10]] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[[1,2],[3,4],[5,6],[7,8],[9,10]] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 2
[[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 8
[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,5,6,7,8,9],[2],[3],[4]] => [6,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,7,8,9],[3,4],[5,6]] => [5,2,2] => [2,2] => [2] => 1
[[1,4,7,8,9],[2,6],[3],[5]] => [5,2,1,1] => [2,1,1] => [1,1] => 2
[[1,6,7,8,9],[2],[3],[4],[5]] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,5,9],[3,4,8],[6,7]] => [4,3,2] => [3,2] => [2] => 1
[[1,4,5,9],[2,7,8],[3],[6]] => [4,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,8,9],[2,5],[4,7],[6]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[1,5,8,9],[2,7],[3],[4],[6]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,7,8,9],[2],[3],[4],[5],[6]] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,3,6],[2,5,9],[4,8],[7]] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[[1,5,6],[2,8,9],[3],[4],[7]] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[[1,2,9],[3,4],[5,6],[7,8]] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[[1,4,9],[2,6],[3,8],[5],[7]] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,6,9],[2,8],[3],[4],[5],[7]] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,3],[2,5],[4,7],[6,9],[8]] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 2
[[1,5],[2,7],[3,9],[4],[6],[8]] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[[1,5,6,7,8,9,10],[2],[3],[4]] => [7,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,7,8,9,10],[3,4],[5,6]] => [6,2,2] => [2,2] => [2] => 1
[[1,4,7,8,9,10],[2,6],[3],[5]] => [6,2,1,1] => [2,1,1] => [1,1] => 2
[[1,6,7,8,9,10],[2],[3],[4],[5]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,5,9,10],[3,4,8],[6,7]] => [5,3,2] => [3,2] => [2] => 1
[[1,4,5,9,10],[2,7,8],[3],[6]] => [5,3,1,1] => [3,1,1] => [1,1] => 2
[[1,3,8,9,10],[2,5],[4,7],[6]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[1,5,8,9,10],[2,7],[3],[4],[6]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,7,8,9,10],[2],[3],[4],[5],[6]] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,5,6],[3,4,9,10],[7,8]] => [4,4,2] => [4,2] => [2] => 1
[[1,4,5,6],[2,8,9,10],[3],[7]] => [4,4,1,1] => [4,1,1] => [1,1] => 2
[[1,2,3,10],[4,5,6],[7,8,9]] => [4,3,3] => [3,3] => [3] => 1
[[1,3,6,10],[2,5,9],[4,8],[7]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[1,5,6,10],[2,8,9],[3],[4],[7]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[[1,2,9,10],[3,4],[5,6],[7,8]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,4,9,10],[2,6],[3,8],[5],[7]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,6,9,10],[2,8],[3],[4],[5],[7]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,3,4],[2,6,7],[5,9,10],[8]] => [3,3,3,1] => [3,3,1] => [3,1] => 1
[[1,2,7],[3,4,10],[5,6],[8,9]] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[[1,4,7],[2,6,10],[3,9],[5],[8]] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[[1,6,7],[2,9,10],[3],[4],[5],[8]] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 4
[[1,3,10],[2,5],[4,7],[6,9],[8]] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 2
[[1,5,10],[2,7],[3,9],[4],[6],[8]] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[1,7,10],[2,9],[3],[4],[5],[6],[8]] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[[1,4],[2,6],[3,8],[5,10],[7],[9]] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 2
[[1,6],[2,8],[3,10],[4],[5],[7],[9]] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[[1,2,4],[3,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2,5],[3,6],[4,7],[8],[9]] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2,3,5],[4,6],[7],[8],[9]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,6],[3,7],[4,8],[5,9]] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,6],[4,7],[5,8],[9]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,4,6],[3,5,7],[8],[9]] => [4,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,3,4,6],[5,7],[8],[9]] => [5,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,7],[3,5,8],[6,9]] => [4,3,2] => [3,2] => [2] => 1
[[1,2,3,4,7],[5,8],[6,9]] => [5,2,2] => [2,2] => [2] => 1
[[1,2,4],[3,5],[6],[7],[8],[9],[10]] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,2,5],[3,6],[4,7],[8],[9],[10]] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[1,2,3,5],[4,6],[7],[8],[9],[10]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2,6],[3,7],[4,8],[5,9],[10]] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 2
[[1,2,3,6],[4,7],[5,8],[9],[10]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2,4,6],[3,5,7],[8],[9],[10]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[[1,2,3,4,6],[5,7],[8],[9],[10]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,3,7],[4,8],[5,9],[6,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,7],[3,5,8],[6,9],[10]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[1,2,3,4,7],[5,8],[6,9],[10]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,3,5,7],[4,6,8],[9],[10]] => [5,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,3,4,5,7],[6,8],[9],[10]] => [6,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,8],[3,6,9],[4,7,10]] => [4,3,3] => [3,3] => [3] => 1
[[1,2,3,5,8],[4,6,9],[7,10]] => [5,3,2] => [3,2] => [2] => 1
[[1,2,3,4,5,8],[6,9],[7,10]] => [6,2,2] => [2,2] => [2] => 1
[[1,2,3,4,9],[5,6],[7,8]] => [5,2,2] => [2,2] => [2] => 1
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[[1,2,6,7,8,9],[3],[4],[5]] => [6,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,7,8,9],[3],[4],[5],[6]] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,8,9],[3],[4],[5],[6],[7]] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,6,7,8,9,10],[3],[4],[5]] => [7,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,7,8,9,10],[3],[4],[5],[6]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,8,9,10],[3],[4],[5],[6],[7]] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,9,10],[3],[4],[5],[6],[7],[8]] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,2,5,6,9],[3,8],[4],[7]] => [5,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,6,7,8],[3],[4],[9]] => [6,1,1,1] => [1,1,1] => [1,1] => 2
[[1,2,4,5],[3,7],[6,9],[8]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,6,7],[3,9],[4],[5],[8]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,5,6],[3,8],[4],[7],[9]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,7,8],[3],[4],[5],[6],[9]] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 4
[[1,2,3,4,9,10],[5,6],[7,8]] => [6,2,2] => [2,2] => [2] => 1
[[1,2,5,6,9,10],[3,8],[4],[7]] => [6,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,3,4,7,8],[5,6],[9,10]] => [6,2,2] => [2,2] => [2] => 1
[[1,2,5,6,7,8],[3,10],[4],[9]] => [6,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,4,5,10],[3,7],[6,9],[8]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,6,7,10],[3,9],[4],[5],[8]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,4,5,8,9],[3,7],[6],[10]] => [6,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,6,7,8,9],[3],[4],[5],[10]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[[1,2,5,6],[3,8],[4,10],[7],[9]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2,7,8],[3,10],[4],[5],[6],[9]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2,4,5],[3,7],[6,9],[8],[10]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2,6,7],[3,9],[4],[5],[8],[10]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2,8,9],[3],[4],[5],[6],[7],[10]] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,2,4,5],[3,8],[6,9],[7,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,8],[3,9],[4],[5],[6],[7]] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2,7],[3,8],[4,9],[5],[6]] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2,7,9],[3,8],[4],[5],[6]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,6,9],[3,7],[4,8],[5]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,6,8],[3,7,9],[4],[5]] => [4,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,6,8,9],[3,7],[4],[5]] => [5,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,8],[3,6,9],[4,7]] => [4,3,2] => [3,2] => [2] => 1
[[1,2,5,8,9],[3,6],[4,7]] => [5,2,2] => [2,2] => [2] => 1
[[1,2,9],[3,10],[4],[5],[6],[7],[8]] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 5
[[1,2,8],[3,9],[4,10],[5],[6],[7]] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[1,2,8,10],[3,9],[4],[5],[6],[7]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 4
[[1,2,7],[3,8],[4,9],[5,10],[6]] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 2
[[1,2,7,10],[3,8],[4,9],[5],[6]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,2,7,9],[3,8,10],[4],[5],[6]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[[1,2,7,9,10],[3,8],[4],[5],[6]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[[1,2,6,10],[3,7],[4,8],[5,9]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,6,9],[3,7,10],[4,8],[5]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[1,2,6,9,10],[3,7],[4,8],[5]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,6,8,10],[3,7,9],[4],[5]] => [5,3,1,1] => [3,1,1] => [1,1] => 2
[[1,2,6,8,9,10],[3,7],[4],[5]] => [6,2,1,1] => [2,1,1] => [1,1] => 2
[[1,2,5,8,10],[3,6,9],[4,7]] => [5,3,2] => [3,2] => [2] => 1
[[1,2,5,8,9,10],[3,6],[4,7]] => [6,2,2] => [2,2] => [2] => 1
[[1,2,3,4],[5,6],[7,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,4],[5,7],[6,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,4],[5,7],[6,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,4],[5,8],[6,9],[7,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,5],[4,6],[7,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,5],[4,6],[7,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,5],[4,7],[6,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,5],[4,7],[6,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,5],[4,8],[6,9],[7,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,6],[4,7],[5,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,6],[4,7],[5,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,6],[4,8],[5,9],[7,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,6],[3,5],[7,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,6],[3,5],[7,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,7],[3,5],[6,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,7],[3,5],[6,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,8],[3,5],[6,9],[7,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,5],[3,6],[7,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,5],[3,6],[7,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,5],[3,7],[6,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,5],[3,7],[6,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,6],[3,7],[5,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,6],[3,7],[5,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,6],[3,8],[5,9],[7,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,4,7],[3,8],[5,9],[6,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,5,8],[3,6],[4,7],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,5,9],[3,6],[4,7],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,5,7],[3,6],[4,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,5,7],[3,6],[4,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,5,8],[3,6],[4,9],[7,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,5,6],[3,7],[4,8],[9,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,5,6],[3,7],[4,9],[8,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,5,6],[3,8],[4,9],[7,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,5,7],[3,8],[4,9],[6,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,6,9],[3,7],[4,8],[5,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,6,8],[3,7],[4,9],[5,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,6,7],[3,8],[4,9],[5,10]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,2,3,4],[5,6],[7,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,6],[7,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,6],[7,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,6],[7,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,7],[6,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,7],[6,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,7],[6,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,7],[6,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,7],[6,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,8],[6,9],[7,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,8],[6,9],[7,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,8],[6,10],[7,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,4],[5,9],[6,10],[7,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,6],[7,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,6],[7,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,6],[7,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,6],[7,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,6],[7,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,7],[6,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,7],[6,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,7],[6,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,7],[6,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,7],[6,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,8],[6,9],[7,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,8],[6,9],[7,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,8],[6,10],[7,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,5],[4,9],[6,10],[7,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,6],[4,7],[5,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,6],[4,7],[5,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,6],[4,7],[5,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,6],[4,7],[5,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,6],[4,7],[5,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,6],[4,8],[5,9],[7,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,6],[4,8],[5,9],[7,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,6],[4,8],[5,10],[7,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,6],[4,9],[5,10],[7,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,7],[4,8],[5,9],[6,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,7],[4,8],[5,9],[6,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,7],[4,8],[5,10],[6,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,7],[4,9],[5,10],[6,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,3,8],[4,9],[5,10],[6,11],[7,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,5],[7,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,5],[7,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,5],[7,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,5],[7,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,5],[7,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,7],[3,5],[6,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,7],[3,5],[6,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,7],[3,5],[6,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,7],[3,5],[6,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,7],[3,5],[6,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,8],[3,5],[6,9],[7,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,8],[3,5],[6,9],[7,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,8],[3,5],[6,10],[7,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,9],[3,5],[6,10],[7,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,6],[7,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,6],[7,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,6],[7,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,6],[7,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,6],[7,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,7],[6,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,7],[6,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,7],[6,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,7],[6,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,7],[6,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,8],[6,9],[7,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,8],[6,9],[7,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,8],[6,10],[7,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,5],[3,9],[6,10],[7,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,7],[5,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,7],[5,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,7],[5,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,7],[5,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,7],[5,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,8],[5,9],[7,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,8],[5,9],[7,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,8],[5,10],[7,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,6],[3,9],[5,10],[7,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,7],[3,8],[5,9],[6,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,7],[3,8],[5,9],[6,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,7],[3,8],[5,10],[6,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,7],[3,9],[5,10],[6,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,4,8],[3,9],[5,10],[6,11],[7,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,8],[3,6],[4,7],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,8],[3,6],[4,7],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,9],[3,6],[4,7],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,9],[3,6],[4,7],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,10],[3,6],[4,7],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,7],[3,6],[4,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,7],[3,6],[4,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,7],[3,6],[4,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,7],[3,6],[4,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,7],[3,6],[4,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,8],[3,6],[4,9],[7,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,8],[3,6],[4,9],[7,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,8],[3,6],[4,10],[7,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,9],[3,6],[4,10],[7,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,6],[3,7],[4,8],[9,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,6],[3,7],[4,8],[9,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,6],[3,7],[4,9],[8,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,6],[3,7],[4,9],[8,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,6],[3,7],[4,10],[8,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,6],[3,8],[4,9],[7,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,6],[3,8],[4,9],[7,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,6],[3,8],[4,10],[7,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,6],[3,9],[4,10],[7,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,7],[3,8],[4,9],[6,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,7],[3,8],[4,9],[6,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,7],[3,8],[4,10],[6,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,7],[3,9],[4,10],[6,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,5,8],[3,9],[4,10],[6,11],[7,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,10],[3,7],[4,8],[5,9],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,11],[3,7],[4,8],[5,9],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,9],[3,7],[4,8],[5,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,9],[3,7],[4,8],[5,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,10],[3,7],[4,8],[5,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,8],[3,7],[4,9],[5,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,8],[3,7],[4,9],[5,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,8],[3,7],[4,10],[5,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,9],[3,7],[4,10],[5,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,7],[3,8],[4,9],[5,10],[11,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,7],[3,8],[4,9],[5,11],[10,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,7],[3,8],[4,10],[5,11],[9,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,7],[3,9],[4,10],[5,11],[8,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,6,8],[3,9],[4,10],[5,11],[7,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,7,12],[3,8],[4,9],[5,10],[6,11]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,7,11],[3,8],[4,9],[5,10],[6,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,7,10],[3,8],[4,9],[5,11],[6,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,7,9],[3,8],[4,10],[5,11],[6,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,7,8],[3,9],[4,10],[5,11],[6,12]] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[[1,2,8],[3,9],[4,10],[5,11],[6,12],[7]] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 3
[[1,2,3,7],[4,8],[5,9],[6]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,4,8],[3,5,9],[6,10],[7]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[1,2,3,4,8],[5,9],[6,10],[7]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[1,2,3,6,9],[4,7,10],[5,8]] => [5,3,2] => [3,2] => [2] => 1
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Description
The multiplicity of the largest part of an integer partition.
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shape
Description
Sends a tableau to its shape.
Map
first row removal
Description
Removes the first entry of an integer partition
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