Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
St001695: Standard tableaux ⟶ ℤ
Values
[1,1,1] => [1,1] => [1] => [[1]] => 0
[2,1,1] => [1,1] => [1] => [[1]] => 0
[1,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[3,1,1] => [1,1] => [1] => [[1]] => 0
[2,2,1] => [2,1] => [1] => [[1]] => 0
[2,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[4,1,1] => [1,1] => [1] => [[1]] => 0
[3,2,1] => [2,1] => [1] => [[1]] => 0
[3,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[2,2,2] => [2,2] => [2] => [[1,2]] => 0
[2,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[2,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[5,1,1] => [1,1] => [1] => [[1]] => 0
[4,2,1] => [2,1] => [1] => [[1]] => 0
[4,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[3,3,1] => [3,1] => [1] => [[1]] => 0
[3,2,2] => [2,2] => [2] => [[1,2]] => 0
[3,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[3,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[2,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[2,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[6,1,1] => [1,1] => [1] => [[1]] => 0
[5,2,1] => [2,1] => [1] => [[1]] => 0
[5,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[4,3,1] => [3,1] => [1] => [[1]] => 0
[4,2,2] => [2,2] => [2] => [[1,2]] => 0
[4,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[4,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[3,3,2] => [3,2] => [2] => [[1,2]] => 0
[3,3,1,1] => [3,1,1] => [1,1] => [[1],[2]] => 0
[3,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[3,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[2,2,2,2] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[2,2,2,1,1] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[7,1,1] => [1,1] => [1] => [[1]] => 0
[6,2,1] => [2,1] => [1] => [[1]] => 0
[6,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[5,3,1] => [3,1] => [1] => [[1]] => 0
[5,2,2] => [2,2] => [2] => [[1,2]] => 0
[5,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[5,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[4,4,1] => [4,1] => [1] => [[1]] => 0
[4,3,2] => [3,2] => [2] => [[1,2]] => 0
[4,3,1,1] => [3,1,1] => [1,1] => [[1],[2]] => 0
[4,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[4,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[3,3,3] => [3,3] => [3] => [[1,2,3]] => 0
[3,3,2,1] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[3,3,1,1,1] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[3,2,2,2] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[3,2,2,1,1] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[2,2,2,2,1] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[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],[2],[3],[4],[5],[6],[7]] => 0
[8,1,1] => [1,1] => [1] => [[1]] => 0
[7,2,1] => [2,1] => [1] => [[1]] => 0
[7,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[6,3,1] => [3,1] => [1] => [[1]] => 0
[6,2,2] => [2,2] => [2] => [[1,2]] => 0
[6,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[6,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[5,4,1] => [4,1] => [1] => [[1]] => 0
[5,3,2] => [3,2] => [2] => [[1,2]] => 0
[5,3,1,1] => [3,1,1] => [1,1] => [[1],[2]] => 0
[5,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[5,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[4,4,2] => [4,2] => [2] => [[1,2]] => 0
[4,4,1,1] => [4,1,1] => [1,1] => [[1],[2]] => 0
[4,3,3] => [3,3] => [3] => [[1,2,3]] => 0
[4,3,2,1] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[4,3,1,1,1] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[4,2,2,2] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[4,2,2,1,1] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[3,3,3,1] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[3,3,2,2] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[3,3,2,1,1] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[3,2,2,2,1] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[2,2,2,2,2] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
>>> Load all 987 entries. <<<[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[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] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[9,1,1] => [1,1] => [1] => [[1]] => 0
[8,2,1] => [2,1] => [1] => [[1]] => 0
[8,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[7,3,1] => [3,1] => [1] => [[1]] => 0
[7,2,2] => [2,2] => [2] => [[1,2]] => 0
[7,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[7,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[6,4,1] => [4,1] => [1] => [[1]] => 0
[6,3,2] => [3,2] => [2] => [[1,2]] => 0
[6,3,1,1] => [3,1,1] => [1,1] => [[1],[2]] => 0
[6,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[6,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[5,5,1] => [5,1] => [1] => [[1]] => 0
[5,4,2] => [4,2] => [2] => [[1,2]] => 0
[5,4,1,1] => [4,1,1] => [1,1] => [[1],[2]] => 0
[5,3,3] => [3,3] => [3] => [[1,2,3]] => 0
[5,3,2,1] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[5,3,1,1,1] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[5,2,2,2] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[5,2,2,1,1] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[4,4,3] => [4,3] => [3] => [[1,2,3]] => 0
[4,4,2,1] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[4,4,1,1,1] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[4,3,3,1] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[4,3,2,2] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[4,3,2,1,1] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[4,2,2,2,1] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[3,3,3,2] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[3,3,3,1,1] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[3,3,2,2,1] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[3,2,2,2,2] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[10,1,1] => [1,1] => [1] => [[1]] => 0
[9,2,1] => [2,1] => [1] => [[1]] => 0
[9,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[8,3,1] => [3,1] => [1] => [[1]] => 0
[8,2,2] => [2,2] => [2] => [[1,2]] => 0
[8,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[8,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[7,4,1] => [4,1] => [1] => [[1]] => 0
[7,3,2] => [3,2] => [2] => [[1,2]] => 0
[7,3,1,1] => [3,1,1] => [1,1] => [[1],[2]] => 0
[7,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[7,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[6,5,1] => [5,1] => [1] => [[1]] => 0
[6,4,2] => [4,2] => [2] => [[1,2]] => 0
[6,4,1,1] => [4,1,1] => [1,1] => [[1],[2]] => 0
[6,3,3] => [3,3] => [3] => [[1,2,3]] => 0
[6,3,2,1] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[6,3,1,1,1] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[6,2,2,2] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[6,2,2,1,1] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[5,5,2] => [5,2] => [2] => [[1,2]] => 0
[5,5,1,1] => [5,1,1] => [1,1] => [[1],[2]] => 0
[5,4,3] => [4,3] => [3] => [[1,2,3]] => 0
[5,4,2,1] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[5,4,1,1,1] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[5,3,3,1] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[5,3,2,2] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[5,3,2,1,1] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[5,2,2,2,1] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[4,4,4] => [4,4] => [4] => [[1,2,3,4]] => 0
[4,4,3,1] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[4,4,2,2] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[4,4,2,1,1] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[4,3,3,2] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[4,3,3,1,1] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[4,3,2,2,1] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[4,2,2,2,2] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[3,3,3,3] => [3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[3,3,3,2,1] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[3,3,2,2,2] => [3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[11,1,1] => [1,1] => [1] => [[1]] => 0
[10,2,1] => [2,1] => [1] => [[1]] => 0
[10,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[9,3,1] => [3,1] => [1] => [[1]] => 0
[9,2,2] => [2,2] => [2] => [[1,2]] => 0
[9,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[9,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[8,4,1] => [4,1] => [1] => [[1]] => 0
[8,3,2] => [3,2] => [2] => [[1,2]] => 0
[8,3,1,1] => [3,1,1] => [1,1] => [[1],[2]] => 0
[8,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[8,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[7,5,1] => [5,1] => [1] => [[1]] => 0
[7,4,2] => [4,2] => [2] => [[1,2]] => 0
[7,4,1,1] => [4,1,1] => [1,1] => [[1],[2]] => 0
[7,3,3] => [3,3] => [3] => [[1,2,3]] => 0
[7,3,2,1] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[7,3,1,1,1] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[7,2,2,2] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[7,2,2,1,1] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[6,6,1] => [6,1] => [1] => [[1]] => 0
[6,5,2] => [5,2] => [2] => [[1,2]] => 0
[6,5,1,1] => [5,1,1] => [1,1] => [[1],[2]] => 0
[6,4,3] => [4,3] => [3] => [[1,2,3]] => 0
[6,4,2,1] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[6,4,1,1,1] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[6,3,3,1] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[6,3,2,2] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[6,3,2,1,1] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[6,2,2,2,1] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[5,5,3] => [5,3] => [3] => [[1,2,3]] => 0
[5,5,2,1] => [5,2,1] => [2,1] => [[1,2],[3]] => 0
[5,5,1,1,1] => [5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[5,4,4] => [4,4] => [4] => [[1,2,3,4]] => 0
[5,4,3,1] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[5,4,2,2] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[5,4,2,1,1] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[5,3,3,2] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[5,3,3,1,1] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[5,3,2,2,1] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[5,2,2,2,2] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[4,4,4,1] => [4,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[4,4,3,2] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[4,4,3,1,1] => [4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[4,4,2,2,1] => [4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[4,3,3,3] => [3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[4,3,3,2,1] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[4,3,2,2,2] => [3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[3,3,3,3,1] => [3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[3,3,3,2,2] => [3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[12,1,1] => [1,1] => [1] => [[1]] => 0
[11,2,1] => [2,1] => [1] => [[1]] => 0
[11,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[10,3,1] => [3,1] => [1] => [[1]] => 0
[10,2,2] => [2,2] => [2] => [[1,2]] => 0
[10,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[10,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[9,4,1] => [4,1] => [1] => [[1]] => 0
[9,3,2] => [3,2] => [2] => [[1,2]] => 0
[9,3,1,1] => [3,1,1] => [1,1] => [[1],[2]] => 0
[9,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[9,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[8,5,1] => [5,1] => [1] => [[1]] => 0
[8,4,2] => [4,2] => [2] => [[1,2]] => 0
[8,4,1,1] => [4,1,1] => [1,1] => [[1],[2]] => 0
[8,3,3] => [3,3] => [3] => [[1,2,3]] => 0
[8,3,2,1] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[8,3,1,1,1] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[8,2,2,2] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[8,2,2,1,1] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[7,6,1] => [6,1] => [1] => [[1]] => 0
[7,5,2] => [5,2] => [2] => [[1,2]] => 0
[7,5,1,1] => [5,1,1] => [1,1] => [[1],[2]] => 0
[7,4,3] => [4,3] => [3] => [[1,2,3]] => 0
[7,4,2,1] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[7,4,1,1,1] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[7,3,3,1] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[7,3,2,2] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[7,3,2,1,1] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[7,2,2,2,1] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[7,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[6,6,2] => [6,2] => [2] => [[1,2]] => 0
[6,6,1,1] => [6,1,1] => [1,1] => [[1],[2]] => 0
[6,5,3] => [5,3] => [3] => [[1,2,3]] => 0
[6,5,2,1] => [5,2,1] => [2,1] => [[1,2],[3]] => 0
[6,5,1,1,1] => [5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[6,4,4] => [4,4] => [4] => [[1,2,3,4]] => 0
[6,4,3,1] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[6,4,2,2] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[6,4,2,1,1] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[6,3,3,2] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[6,3,3,1,1] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[6,3,2,2,1] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[6,2,2,2,2] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[5,5,4] => [5,4] => [4] => [[1,2,3,4]] => 0
[5,5,3,1] => [5,3,1] => [3,1] => [[1,2,3],[4]] => 0
[5,5,2,2] => [5,2,2] => [2,2] => [[1,2],[3,4]] => 0
[5,5,2,1,1] => [5,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[5,4,4,1] => [4,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[5,4,3,2] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[5,4,3,1,1] => [4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[5,4,2,2,1] => [4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[5,3,3,3] => [3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[5,3,3,2,1] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[5,3,2,2,2] => [3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[4,4,4,2] => [4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[4,4,4,1,1] => [4,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[4,4,3,3] => [4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[4,4,3,2,1] => [4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[4,4,2,2,2] => [4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[4,3,3,3,1] => [3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[4,3,3,2,2] => [3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[4,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[3,3,3,3,2] => [3,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[13,1,1] => [1,1] => [1] => [[1]] => 0
[12,2,1] => [2,1] => [1] => [[1]] => 0
[12,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[11,3,1] => [3,1] => [1] => [[1]] => 0
[11,2,2] => [2,2] => [2] => [[1,2]] => 0
[11,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[11,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[10,4,1] => [4,1] => [1] => [[1]] => 0
[10,3,2] => [3,2] => [2] => [[1,2]] => 0
[10,3,1,1] => [3,1,1] => [1,1] => [[1],[2]] => 0
[10,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[10,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[9,5,1] => [5,1] => [1] => [[1]] => 0
[9,4,2] => [4,2] => [2] => [[1,2]] => 0
[9,4,1,1] => [4,1,1] => [1,1] => [[1],[2]] => 0
[9,3,3] => [3,3] => [3] => [[1,2,3]] => 0
[9,3,2,1] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[9,3,1,1,1] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[9,2,2,2] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[9,2,2,1,1] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[8,6,1] => [6,1] => [1] => [[1]] => 0
[8,5,2] => [5,2] => [2] => [[1,2]] => 0
[8,5,1,1] => [5,1,1] => [1,1] => [[1],[2]] => 0
[8,4,3] => [4,3] => [3] => [[1,2,3]] => 0
[8,4,2,1] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[8,4,1,1,1] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[8,3,3,1] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[8,3,2,2] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[8,3,2,1,1] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[8,2,2,2,1] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[8,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[7,7,1] => [7,1] => [1] => [[1]] => 0
[7,6,2] => [6,2] => [2] => [[1,2]] => 0
[7,6,1,1] => [6,1,1] => [1,1] => [[1],[2]] => 0
[7,5,3] => [5,3] => [3] => [[1,2,3]] => 0
[7,5,2,1] => [5,2,1] => [2,1] => [[1,2],[3]] => 0
[7,5,1,1,1] => [5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[7,4,4] => [4,4] => [4] => [[1,2,3,4]] => 0
[7,4,3,1] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[7,4,2,2] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[7,4,2,1,1] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[7,3,3,2] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[7,3,3,1,1] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[7,3,2,2,1] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[7,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[7,2,2,2,2] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[6,6,3] => [6,3] => [3] => [[1,2,3]] => 0
[6,6,2,1] => [6,2,1] => [2,1] => [[1,2],[3]] => 0
[6,6,1,1,1] => [6,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[6,5,4] => [5,4] => [4] => [[1,2,3,4]] => 0
[6,5,3,1] => [5,3,1] => [3,1] => [[1,2,3],[4]] => 0
[6,5,2,2] => [5,2,2] => [2,2] => [[1,2],[3,4]] => 0
[6,5,2,1,1] => [5,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[6,4,4,1] => [4,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[6,4,3,2] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[6,4,3,1,1] => [4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[6,4,2,2,1] => [4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[6,3,3,3] => [3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[6,3,3,2,1] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[6,3,2,2,2] => [3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[5,5,5] => [5,5] => [5] => [[1,2,3,4,5]] => 0
[5,5,4,1] => [5,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[5,5,3,2] => [5,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[5,5,3,1,1] => [5,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[5,5,2,2,1] => [5,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[5,4,4,2] => [4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[5,4,4,1,1] => [4,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[5,4,3,3] => [4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[5,4,3,2,1] => [4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[5,4,2,2,2] => [4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[5,3,3,3,1] => [3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[5,3,3,2,2] => [3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[5,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[4,4,4,3] => [4,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[4,4,4,2,1] => [4,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[4,4,3,3,1] => [4,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[4,4,3,2,2] => [4,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[4,3,3,3,2] => [3,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[4,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[14,1,1] => [1,1] => [1] => [[1]] => 0
[13,2,1] => [2,1] => [1] => [[1]] => 0
[13,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[12,3,1] => [3,1] => [1] => [[1]] => 0
[12,2,2] => [2,2] => [2] => [[1,2]] => 0
[12,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[12,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[11,4,1] => [4,1] => [1] => [[1]] => 0
[11,3,2] => [3,2] => [2] => [[1,2]] => 0
[11,3,1,1] => [3,1,1] => [1,1] => [[1],[2]] => 0
[11,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[11,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[10,5,1] => [5,1] => [1] => [[1]] => 0
[10,4,2] => [4,2] => [2] => [[1,2]] => 0
[10,4,1,1] => [4,1,1] => [1,1] => [[1],[2]] => 0
[10,3,3] => [3,3] => [3] => [[1,2,3]] => 0
[10,3,2,1] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[10,3,1,1,1] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[10,2,2,2] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[10,2,2,1,1] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[9,6,1] => [6,1] => [1] => [[1]] => 0
[9,5,2] => [5,2] => [2] => [[1,2]] => 0
[9,5,1,1] => [5,1,1] => [1,1] => [[1],[2]] => 0
[9,4,3] => [4,3] => [3] => [[1,2,3]] => 0
[9,4,2,1] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[9,4,1,1,1] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[9,3,3,1] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[9,3,2,2] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[9,3,2,1,1] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[9,2,2,2,1] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[9,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[8,7,1] => [7,1] => [1] => [[1]] => 0
[8,6,2] => [6,2] => [2] => [[1,2]] => 0
[8,6,1,1] => [6,1,1] => [1,1] => [[1],[2]] => 0
[8,5,3] => [5,3] => [3] => [[1,2,3]] => 0
[8,5,2,1] => [5,2,1] => [2,1] => [[1,2],[3]] => 0
[8,5,1,1,1] => [5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[8,4,4] => [4,4] => [4] => [[1,2,3,4]] => 0
[8,4,3,1] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[8,4,2,2] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[8,4,2,1,1] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[8,3,3,2] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[8,3,3,1,1] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[8,3,2,2,1] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[8,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[8,2,2,2,2] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[8,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[7,7,2] => [7,2] => [2] => [[1,2]] => 0
[7,7,1,1] => [7,1,1] => [1,1] => [[1],[2]] => 0
[7,6,3] => [6,3] => [3] => [[1,2,3]] => 0
[7,6,2,1] => [6,2,1] => [2,1] => [[1,2],[3]] => 0
[7,6,1,1,1] => [6,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[7,5,4] => [5,4] => [4] => [[1,2,3,4]] => 0
[7,5,3,1] => [5,3,1] => [3,1] => [[1,2,3],[4]] => 0
[7,5,2,2] => [5,2,2] => [2,2] => [[1,2],[3,4]] => 0
[7,5,2,1,1] => [5,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[7,4,4,1] => [4,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[7,4,3,2] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[7,4,3,1,1] => [4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[7,4,2,2,1] => [4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[7,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[7,3,3,3] => [3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[7,3,3,2,1] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[7,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[7,3,2,2,2] => [3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[7,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[7,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[6,6,4] => [6,4] => [4] => [[1,2,3,4]] => 0
[6,6,3,1] => [6,3,1] => [3,1] => [[1,2,3],[4]] => 0
[6,6,2,2] => [6,2,2] => [2,2] => [[1,2],[3,4]] => 0
[6,6,2,1,1] => [6,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[6,5,5] => [5,5] => [5] => [[1,2,3,4,5]] => 0
[6,5,4,1] => [5,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[6,5,3,2] => [5,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[6,5,3,1,1] => [5,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[6,5,2,2,1] => [5,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[6,4,4,2] => [4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[6,4,4,1,1] => [4,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[6,4,3,3] => [4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[6,4,3,2,1] => [4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[6,4,2,2,2] => [4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[6,3,3,3,1] => [3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[6,3,3,2,2] => [3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[6,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[5,5,5,1] => [5,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 0
[5,5,4,2] => [5,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[5,5,4,1,1] => [5,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[5,5,3,3] => [5,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[5,5,3,2,1] => [5,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[5,5,2,2,2] => [5,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[5,4,4,3] => [4,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[5,4,4,2,1] => [4,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[5,4,3,3,1] => [4,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[5,4,3,2,2] => [4,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[5,3,3,3,2] => [3,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[5,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[5,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[5,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[4,4,4,4] => [4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[4,4,4,3,1] => [4,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[4,4,4,2,2] => [4,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[4,4,3,3,2] => [4,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[4,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[4,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[15,1,1] => [1,1] => [1] => [[1]] => 0
[14,2,1] => [2,1] => [1] => [[1]] => 0
[14,1,1,1] => [1,1,1] => [1,1] => [[1],[2]] => 0
[13,3,1] => [3,1] => [1] => [[1]] => 0
[13,2,2] => [2,2] => [2] => [[1,2]] => 0
[13,2,1,1] => [2,1,1] => [1,1] => [[1],[2]] => 0
[13,1,1,1,1] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[12,4,1] => [4,1] => [1] => [[1]] => 0
[12,3,2] => [3,2] => [2] => [[1,2]] => 0
[12,3,1,1] => [3,1,1] => [1,1] => [[1],[2]] => 0
[12,2,2,1] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[12,2,1,1,1] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[11,5,1] => [5,1] => [1] => [[1]] => 0
[11,4,2] => [4,2] => [2] => [[1,2]] => 0
[11,4,1,1] => [4,1,1] => [1,1] => [[1],[2]] => 0
[11,3,3] => [3,3] => [3] => [[1,2,3]] => 0
[11,3,2,1] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[11,3,1,1,1] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[11,2,2,2] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[11,2,2,1,1] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[10,6,1] => [6,1] => [1] => [[1]] => 0
[10,5,2] => [5,2] => [2] => [[1,2]] => 0
[10,5,1,1] => [5,1,1] => [1,1] => [[1],[2]] => 0
[10,4,3] => [4,3] => [3] => [[1,2,3]] => 0
[10,4,2,1] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[10,4,1,1,1] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[10,3,3,1] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[10,3,2,2] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[10,3,2,1,1] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[10,2,2,2,1] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[10,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[9,7,1] => [7,1] => [1] => [[1]] => 0
[9,6,2] => [6,2] => [2] => [[1,2]] => 0
[9,6,1,1] => [6,1,1] => [1,1] => [[1],[2]] => 0
[9,5,3] => [5,3] => [3] => [[1,2,3]] => 0
[9,5,2,1] => [5,2,1] => [2,1] => [[1,2],[3]] => 0
[9,5,1,1,1] => [5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[9,4,4] => [4,4] => [4] => [[1,2,3,4]] => 0
[9,4,3,1] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[9,4,2,2] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[9,4,2,1,1] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[9,3,3,2] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[9,3,3,1,1] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[9,3,2,2,1] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[9,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[9,2,2,2,2] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[9,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[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],[2],[3],[4],[5],[6],[7]] => 0
[8,8,1] => [8,1] => [1] => [[1]] => 0
[8,7,2] => [7,2] => [2] => [[1,2]] => 0
[8,7,1,1] => [7,1,1] => [1,1] => [[1],[2]] => 0
[8,6,3] => [6,3] => [3] => [[1,2,3]] => 0
[8,6,2,1] => [6,2,1] => [2,1] => [[1,2],[3]] => 0
[8,6,1,1,1] => [6,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[8,5,4] => [5,4] => [4] => [[1,2,3,4]] => 0
[8,5,3,1] => [5,3,1] => [3,1] => [[1,2,3],[4]] => 0
[8,5,2,2] => [5,2,2] => [2,2] => [[1,2],[3,4]] => 0
[8,5,2,1,1] => [5,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[8,4,4,1] => [4,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[8,4,3,2] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[8,4,3,1,1] => [4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[8,4,2,2,1] => [4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[8,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[8,3,3,3] => [3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[8,3,3,2,1] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[8,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[8,3,2,2,2] => [3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[8,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[8,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[7,7,3] => [7,3] => [3] => [[1,2,3]] => 0
[7,7,2,1] => [7,2,1] => [2,1] => [[1,2],[3]] => 0
[7,7,1,1,1] => [7,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[7,6,4] => [6,4] => [4] => [[1,2,3,4]] => 0
[7,6,3,1] => [6,3,1] => [3,1] => [[1,2,3],[4]] => 0
[7,6,2,2] => [6,2,2] => [2,2] => [[1,2],[3,4]] => 0
[7,6,2,1,1] => [6,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[7,5,5] => [5,5] => [5] => [[1,2,3,4,5]] => 0
[7,5,4,1] => [5,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[7,5,3,2] => [5,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[7,5,3,1,1] => [5,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[7,5,2,2,1] => [5,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[7,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[7,4,4,2] => [4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[7,4,4,1,1] => [4,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[7,4,3,3] => [4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[7,4,3,2,1] => [4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[7,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[7,4,2,2,2] => [4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[7,3,3,3,1] => [3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[7,3,3,2,2] => [3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[7,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[6,6,5] => [6,5] => [5] => [[1,2,3,4,5]] => 0
[6,6,4,1] => [6,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[6,6,3,2] => [6,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[6,6,3,1,1] => [6,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[6,6,2,2,1] => [6,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[6,6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[6,5,5,1] => [5,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 0
[6,5,4,2] => [5,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[6,5,4,1,1] => [5,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[6,5,3,3] => [5,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[6,5,3,2,1] => [5,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[6,5,2,2,2] => [5,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[6,4,4,3] => [4,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[6,4,4,2,1] => [4,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[6,4,3,3,1] => [4,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[6,4,3,2,2] => [4,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[6,3,3,3,2] => [3,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[6,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[6,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[5,5,5,2] => [5,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 0
[5,5,5,1,1] => [5,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 0
[5,5,4,3] => [5,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[5,5,4,2,1] => [5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[5,5,3,3,1] => [5,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[5,5,3,2,2] => [5,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[5,4,4,4] => [4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[5,4,4,3,1] => [4,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[5,4,4,2,2] => [4,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[5,4,3,3,2] => [4,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[5,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[5,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[6,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[5,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[6,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[6,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[5,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[6,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[6,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[5,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[6,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[6,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[6,5,3,3,2] => [5,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[5,5,3,3,2] => [5,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[6,4,3,3,2] => [4,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[6,5,4,2,2] => [5,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[5,5,4,2,2] => [5,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[6,4,4,2,2] => [4,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[6,5,3,2,2] => [5,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[6,5,4,3,1] => [5,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[5,5,4,3,1] => [5,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[6,4,4,3,1] => [4,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[6,5,3,3,1] => [5,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[6,5,4,2,1] => [5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[6,5,4,3] => [5,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[6,6,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[7,6,3,2,2,1] => [6,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[7,6,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[7,6,3,2,1,1] => [6,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[7,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[7,6,5,1,1,1] => [6,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0
[7,5,4,3,1] => [5,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[7,6,5,2,1] => [6,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0
[6,6,5,2,1] => [6,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0
[7,6,4,2,1] => [6,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[6,6,4,2,1] => [6,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[7,5,4,2,1] => [5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[7,6,3,2,1] => [6,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[6,6,3,2,1] => [6,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[7,6,5,3] => [6,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[7,6,4,3] => [6,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[7,5,4,3] => [5,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[7,6,5,2] => [6,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 0
[7,6,5] => [6,5] => [5] => [[1,2,3,4,5]] => 0
[6,6,6] => [6,6] => [6] => [[1,2,3,4,5,6]] => 0
[7,6,6] => [6,6] => [6] => [[1,2,3,4,5,6]] => 0
[10,4,4] => [4,4] => [4] => [[1,2,3,4]] => 0
[11,7,3] => [7,3] => [3] => [[1,2,3]] => 0
[9,6,3] => [6,3] => [3] => [[1,2,3]] => 0
[8,6,4,2] => [6,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[8,6,4] => [6,4] => [4] => [[1,2,3,4]] => 0
[10,6,4] => [6,4] => [4] => [[1,2,3,4]] => 0
[8,7,6] => [7,6] => [6] => [[1,2,3,4,5,6]] => 0
[9,8,7] => [8,7] => [7] => [[1,2,3,4,5,6,7]] => 0
[15,5,5] => [5,5] => [5] => [[1,2,3,4,5]] => 0
[7,7,7] => [7,7] => [7] => [[1,2,3,4,5,6,7]] => 0
[11,7,5,1] => [7,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 0
[9,6,4] => [6,4] => [4] => [[1,2,3,4]] => 0
[10,7,3] => [7,3] => [3] => [[1,2,3]] => 0
[8,5,4,2] => [5,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[9,6,5,3] => [6,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[10,7,5,3] => [7,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[9,6,4,3] => [6,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[9,7,4] => [7,4] => [4] => [[1,2,3,4]] => 0
[8,5,5,1] => [5,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 0
[9,5,5,1] => [5,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 0
[9,7,5,3] => [7,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[8,8,8] => [8,8] => [8] => [[1,2,3,4,5,6,7,8]] => 0
[7,7,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[8,7,5] => [7,5] => [5] => [[1,2,3,4,5]] => 0
[6,6,6,1] => [6,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 0
[6,6,6,1,1] => [6,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0
search for individual values
searching the database for the individual values of this statistic
Description
The 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 size $n$ with natural descent set $D$ is then $\sum_{d\in D} n-d$.
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 size $n$ with natural descent set $D$ is then $\sum_{d\in D} n-d$.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
Map
first row removal
Description
Removes the first entry of an integer partition
searching the database
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