Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
St000734: Standard tableaux ⟶ ℤ
Values
[1,1] => [1] => [[1]] => 1
[2,1] => [1] => [[1]] => 1
[1,1,1] => [1,1] => [[1],[2]] => 1
[3,1] => [1] => [[1]] => 1
[2,2] => [2] => [[1,2]] => 2
[2,1,1] => [1,1] => [[1],[2]] => 1
[1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[4,1] => [1] => [[1]] => 1
[3,2] => [2] => [[1,2]] => 2
[3,1,1] => [1,1] => [[1],[2]] => 1
[2,2,1] => [2,1] => [[1,2],[3]] => 2
[2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[5,1] => [1] => [[1]] => 1
[4,2] => [2] => [[1,2]] => 2
[4,1,1] => [1,1] => [[1],[2]] => 1
[3,3] => [3] => [[1,2,3]] => 3
[3,2,1] => [2,1] => [[1,2],[3]] => 2
[3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[2,2,2] => [2,2] => [[1,2],[3,4]] => 2
[2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[6,1] => [1] => [[1]] => 1
[5,2] => [2] => [[1,2]] => 2
[5,1,1] => [1,1] => [[1],[2]] => 1
[4,3] => [3] => [[1,2,3]] => 3
[4,2,1] => [2,1] => [[1,2],[3]] => 2
[4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[3,3,1] => [3,1] => [[1,2,3],[4]] => 3
[3,2,2] => [2,2] => [[1,2],[3,4]] => 2
[3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[7,1] => [1] => [[1]] => 1
[6,2] => [2] => [[1,2]] => 2
[6,1,1] => [1,1] => [[1],[2]] => 1
[5,3] => [3] => [[1,2,3]] => 3
[5,2,1] => [2,1] => [[1,2],[3]] => 2
[5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[4,4] => [4] => [[1,2,3,4]] => 4
[4,3,1] => [3,1] => [[1,2,3],[4]] => 3
[4,2,2] => [2,2] => [[1,2],[3,4]] => 2
[4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[3,3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[8,1] => [1] => [[1]] => 1
[7,2] => [2] => [[1,2]] => 2
[7,1,1] => [1,1] => [[1],[2]] => 1
[6,3] => [3] => [[1,2,3]] => 3
[6,2,1] => [2,1] => [[1,2],[3]] => 2
[6,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[5,4] => [4] => [[1,2,3,4]] => 4
[5,3,1] => [3,1] => [[1,2,3],[4]] => 3
[5,2,2] => [2,2] => [[1,2],[3,4]] => 2
[5,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[4,4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[4,3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[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] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[9,1] => [1] => [[1]] => 1
[8,2] => [2] => [[1,2]] => 2
[8,1,1] => [1,1] => [[1],[2]] => 1
[7,3] => [3] => [[1,2,3]] => 3
[7,2,1] => [2,1] => [[1,2],[3]] => 2
[7,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[6,4] => [4] => [[1,2,3,4]] => 4
[6,3,1] => [3,1] => [[1,2,3],[4]] => 3
[6,2,2] => [2,2] => [[1,2],[3,4]] => 2
[6,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[5,5] => [5] => [[1,2,3,4,5]] => 5
[5,4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[5,3,2] => [3,2] => [[1,2,3],[4,5]] => 3
>>> Load all 1041 entries. <<<[5,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[5,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[5,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[5,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[4,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[4,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[4,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[4,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[3,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[3,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[2,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[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]] => 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],[9]] => 1
[10,1] => [1] => [[1]] => 1
[9,2] => [2] => [[1,2]] => 2
[9,1,1] => [1,1] => [[1],[2]] => 1
[8,3] => [3] => [[1,2,3]] => 3
[8,2,1] => [2,1] => [[1,2],[3]] => 2
[8,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[7,4] => [4] => [[1,2,3,4]] => 4
[7,3,1] => [3,1] => [[1,2,3],[4]] => 3
[7,2,2] => [2,2] => [[1,2],[3,4]] => 2
[7,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[7,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[6,5] => [5] => [[1,2,3,4,5]] => 5
[6,4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[6,3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[6,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[6,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[6,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[5,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[5,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[5,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[5,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[5,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[5,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[5,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[5,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[5,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[4,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[4,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[4,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[4,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[4,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[4,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[4,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[4,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[3,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[3,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[3,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[3,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[3,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[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]] => 1
[2,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 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],[9],[10]] => 1
[11,1] => [1] => [[1]] => 1
[10,2] => [2] => [[1,2]] => 2
[10,1,1] => [1,1] => [[1],[2]] => 1
[9,3] => [3] => [[1,2,3]] => 3
[9,2,1] => [2,1] => [[1,2],[3]] => 2
[9,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[8,4] => [4] => [[1,2,3,4]] => 4
[8,3,1] => [3,1] => [[1,2,3],[4]] => 3
[8,2,2] => [2,2] => [[1,2],[3,4]] => 2
[8,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[8,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[7,5] => [5] => [[1,2,3,4,5]] => 5
[7,4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[7,3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[7,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[7,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[7,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[7,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[6,6] => [6] => [[1,2,3,4,5,6]] => 6
[6,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[6,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[6,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[6,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[6,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[6,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[6,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[6,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[6,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[5,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[5,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[5,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[5,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[5,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[5,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[5,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[5,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[5,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[5,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[4,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[4,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[4,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[4,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[4,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[4,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[4,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[4,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[4,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[4,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[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]] => 1
[3,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[3,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[3,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[3,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[3,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[3,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[2,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[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],[7],[8],[9],[10]] => 1
[12,1] => [1] => [[1]] => 1
[11,2] => [2] => [[1,2]] => 2
[11,1,1] => [1,1] => [[1],[2]] => 1
[10,3] => [3] => [[1,2,3]] => 3
[10,2,1] => [2,1] => [[1,2],[3]] => 2
[10,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[9,4] => [4] => [[1,2,3,4]] => 4
[9,3,1] => [3,1] => [[1,2,3],[4]] => 3
[9,2,2] => [2,2] => [[1,2],[3,4]] => 2
[9,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[9,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[8,5] => [5] => [[1,2,3,4,5]] => 5
[8,4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[8,3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[8,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[8,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[8,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[8,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[7,6] => [6] => [[1,2,3,4,5,6]] => 6
[7,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[7,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[7,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[7,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[7,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[7,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[7,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[7,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[7,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[6,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[6,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[6,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[6,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[6,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[6,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[6,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[6,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[6,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[6,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[6,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[6,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[5,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[5,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[5,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[5,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[5,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[5,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[5,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[5,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[5,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[5,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[5,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[5,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[5,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[5,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[4,4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[4,4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[4,4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[4,4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[4,4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[4,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[4,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[4,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[4,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[4,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[4,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[3,3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[3,3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
[3,3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[3,3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[3,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[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],[7],[8],[9],[10]] => 1
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[13,1] => [1] => [[1]] => 1
[12,2] => [2] => [[1,2]] => 2
[12,1,1] => [1,1] => [[1],[2]] => 1
[11,3] => [3] => [[1,2,3]] => 3
[11,2,1] => [2,1] => [[1,2],[3]] => 2
[11,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[10,4] => [4] => [[1,2,3,4]] => 4
[10,3,1] => [3,1] => [[1,2,3],[4]] => 3
[10,2,2] => [2,2] => [[1,2],[3,4]] => 2
[10,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[10,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[9,5] => [5] => [[1,2,3,4,5]] => 5
[9,4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[9,3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[9,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[9,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[9,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[9,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[8,6] => [6] => [[1,2,3,4,5,6]] => 6
[8,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[8,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[8,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[8,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[8,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[8,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[8,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[8,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[8,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[7,7] => [7] => [[1,2,3,4,5,6,7]] => 7
[7,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[7,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[7,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[7,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[7,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[7,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[7,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[7,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[7,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[7,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[7,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[7,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[6,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[6,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[6,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[6,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[6,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[6,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[6,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[6,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[6,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[6,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[6,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[6,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[6,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[6,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[6,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[6,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[5,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[5,5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[5,5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[5,5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[5,5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[5,4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[5,4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[5,4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[5,4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[5,4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[5,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[5,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[5,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[5,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[5,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[5,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[4,4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
[4,4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[4,4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[4,4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[4,4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[4,4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[4,4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[4,3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[4,3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
[4,3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[4,3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[4,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[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],[7],[8],[9],[10]] => 1
[3,3,3,3,2] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 3
[3,3,3,3,1,1] => [3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 3
[3,3,3,2,2,1] => [3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 3
[3,3,2,2,2,2] => [3,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11]] => 3
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[14,1] => [1] => [[1]] => 1
[13,2] => [2] => [[1,2]] => 2
[13,1,1] => [1,1] => [[1],[2]] => 1
[12,3] => [3] => [[1,2,3]] => 3
[12,2,1] => [2,1] => [[1,2],[3]] => 2
[12,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[11,4] => [4] => [[1,2,3,4]] => 4
[11,3,1] => [3,1] => [[1,2,3],[4]] => 3
[11,2,2] => [2,2] => [[1,2],[3,4]] => 2
[11,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[11,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[10,5] => [5] => [[1,2,3,4,5]] => 5
[10,4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[10,3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[10,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[10,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[10,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[10,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[9,6] => [6] => [[1,2,3,4,5,6]] => 6
[9,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[9,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[9,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[9,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[9,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[9,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[9,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[9,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[9,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[8,7] => [7] => [[1,2,3,4,5,6,7]] => 7
[8,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[8,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[8,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[8,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[8,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[8,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[8,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[8,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[8,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[8,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[8,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[8,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[7,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[7,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[7,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[7,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[7,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[7,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[7,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[7,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[7,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[7,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[7,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[7,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[7,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[7,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[7,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[7,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[7,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[6,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[6,6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[6,6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[6,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[6,5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[6,5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[6,5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[6,5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[6,4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[6,4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[6,4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[6,4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[6,4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[6,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[6,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[6,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[6,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[6,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[6,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[5,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[5,5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[5,5,3,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[5,5,3,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[5,5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
[5,5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[5,4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
[5,4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[5,4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[5,4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[5,4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[5,4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[5,4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[5,3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[5,3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
[5,3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[5,3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[5,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[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],[7],[8],[9],[10]] => 1
[4,4,4,3] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => 4
[4,4,4,2,1] => [4,4,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11]] => 4
[4,4,4,1,1,1] => [4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => 4
[4,4,3,3,1] => [4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 4
[4,4,3,2,2] => [4,3,2,2] => [[1,2,3,4],[5,6,7],[8,9],[10,11]] => 4
[4,4,3,2,1,1] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 4
[4,4,2,2,2,1] => [4,2,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9,10],[11]] => 4
[4,3,3,3,2] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 3
[4,3,3,3,1,1] => [3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 3
[4,3,3,2,2,1] => [3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 3
[4,3,2,2,2,2] => [3,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11]] => 3
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[3,3,3,3,3] => [3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]] => 3
[3,3,3,3,2,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[3,3,3,2,2,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13]] => 2
[15,1] => [1] => [[1]] => 1
[14,2] => [2] => [[1,2]] => 2
[14,1,1] => [1,1] => [[1],[2]] => 1
[13,3] => [3] => [[1,2,3]] => 3
[13,2,1] => [2,1] => [[1,2],[3]] => 2
[13,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[12,4] => [4] => [[1,2,3,4]] => 4
[12,3,1] => [3,1] => [[1,2,3],[4]] => 3
[12,2,2] => [2,2] => [[1,2],[3,4]] => 2
[12,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[12,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[11,5] => [5] => [[1,2,3,4,5]] => 5
[11,4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[11,3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[11,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[11,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[11,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[11,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[10,6] => [6] => [[1,2,3,4,5,6]] => 6
[10,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[10,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[10,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[10,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[10,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[10,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[10,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[10,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[10,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[9,7] => [7] => [[1,2,3,4,5,6,7]] => 7
[9,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[9,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[9,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[9,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[9,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[9,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[9,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[9,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[9,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[9,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[9,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[9,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[8,8] => [8] => [[1,2,3,4,5,6,7,8]] => 8
[8,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[8,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[8,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[8,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[8,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[8,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[8,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[8,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[8,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[8,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[8,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[8,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[8,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[8,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[8,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[8,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[8,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[7,7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[7,7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[7,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[7,6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[7,6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[7,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[7,5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[7,5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[7,5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[7,5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[7,4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[7,4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[7,4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[7,4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[7,4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[7,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[7,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[7,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[7,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[7,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[7,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[6,6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[6,6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[6,6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
[6,6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[6,6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[6,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[6,5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[6,5,3,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[6,5,3,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[6,5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
[6,5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[6,4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
[6,4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[6,4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[6,4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[6,4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[6,4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[6,4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[6,3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[6,3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
[6,3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[6,3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[6,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[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],[7],[8],[9],[10]] => 1
[5,5,4,2] => [5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => 5
[5,5,4,1,1] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 5
[5,5,3,3] => [5,3,3] => [[1,2,3,4,5],[6,7,8],[9,10,11]] => 5
[5,5,3,2,1] => [5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 5
[5,5,3,1,1,1] => [5,3,1,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10],[11]] => 5
[5,5,2,2,2] => [5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => 5
[5,5,2,2,1,1] => [5,2,2,1,1] => [[1,2,3,4,5],[6,7],[8,9],[10],[11]] => 5
[5,4,4,3] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => 4
[5,4,4,2,1] => [4,4,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11]] => 4
[5,4,4,1,1,1] => [4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => 4
[5,4,3,3,1] => [4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 4
[5,4,3,2,2] => [4,3,2,2] => [[1,2,3,4],[5,6,7],[8,9],[10,11]] => 4
[5,4,3,2,1,1] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 4
[5,4,2,2,2,1] => [4,2,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9,10],[11]] => 4
[5,3,3,3,2] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 3
[5,3,3,3,1,1] => [3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 3
[5,3,3,2,2,1] => [3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 3
[5,3,2,2,2,2] => [3,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11]] => 3
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[4,4,4,4] => [4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12]] => 4
[4,4,4,3,1] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
[4,4,4,2,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[4,4,4,2,1,1] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 4
[4,4,3,3,2] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
[4,4,3,3,1,1] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
[4,4,3,2,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[4,3,3,3,3] => [3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]] => 3
[4,3,3,3,2,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[4,3,3,2,2,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[3,3,3,3,3,1] => [3,3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13]] => 3
[3,3,3,3,2,2] => [3,3,3,2,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12,13]] => 3
[3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11],[12,13]] => 3
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13]] => 2
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14]] => 2
[16,1] => [1] => [[1]] => 1
[15,2] => [2] => [[1,2]] => 2
[15,1,1] => [1,1] => [[1],[2]] => 1
[14,3] => [3] => [[1,2,3]] => 3
[14,2,1] => [2,1] => [[1,2],[3]] => 2
[14,1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[13,4] => [4] => [[1,2,3,4]] => 4
[13,3,1] => [3,1] => [[1,2,3],[4]] => 3
[13,2,2] => [2,2] => [[1,2],[3,4]] => 2
[13,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[13,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[12,5] => [5] => [[1,2,3,4,5]] => 5
[12,4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[12,3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[12,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[12,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[12,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[12,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[11,6] => [6] => [[1,2,3,4,5,6]] => 6
[11,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[11,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[11,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[11,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[11,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[11,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[11,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[11,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[11,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[10,7] => [7] => [[1,2,3,4,5,6,7]] => 7
[10,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[10,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[10,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[10,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[10,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[10,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[10,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[10,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[10,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[10,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[10,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[10,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[9,8] => [8] => [[1,2,3,4,5,6,7,8]] => 8
[9,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[9,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[9,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[9,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[9,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[9,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[9,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[9,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[9,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[9,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[9,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[9,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[9,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[9,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[9,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[9,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[9,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[8,8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[8,7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[8,7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[8,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[8,6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[8,6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[8,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[8,5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[8,5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[8,5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[8,5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[8,4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[8,4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[8,4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[8,4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[8,4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[8,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[8,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[8,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[8,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[8,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[8,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[7,7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[7,7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[7,7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[7,6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[7,6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[7,6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
[7,6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[7,6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[7,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[7,5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[7,5,3,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[7,5,3,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[7,5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
[7,5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[7,4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
[7,4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[7,4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[7,4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[7,4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[7,4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[7,4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[7,3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[7,3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
[7,3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[7,3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[7,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[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],[7],[8],[9],[10]] => 1
[6,5,4,2] => [5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => 5
[6,5,4,1,1] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 5
[6,5,3,3] => [5,3,3] => [[1,2,3,4,5],[6,7,8],[9,10,11]] => 5
[6,5,3,2,1] => [5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 5
[6,5,3,1,1,1] => [5,3,1,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10],[11]] => 5
[6,5,2,2,2] => [5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => 5
[6,5,2,2,1,1] => [5,2,2,1,1] => [[1,2,3,4,5],[6,7],[8,9],[10],[11]] => 5
[6,4,4,3] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => 4
[6,4,4,2,1] => [4,4,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11]] => 4
[6,4,4,1,1,1] => [4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => 4
[6,4,3,3,1] => [4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 4
[6,4,3,2,2] => [4,3,2,2] => [[1,2,3,4],[5,6,7],[8,9],[10,11]] => 4
[6,4,3,2,1,1] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 4
[6,4,2,2,2,1] => [4,2,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9,10],[11]] => 4
[6,3,3,3,2] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 3
[6,3,3,3,1,1] => [3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 3
[6,3,3,2,2,1] => [3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 3
[6,3,2,2,2,2] => [3,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11]] => 3
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[5,5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 5
[5,5,4,2,1] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
[5,5,4,1,1,1] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 5
[5,5,3,3,1] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
[5,5,3,2,2] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
[5,5,3,2,1,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
[5,5,2,2,2,1] => [5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => 5
[5,4,4,4] => [4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12]] => 4
[5,4,4,3,1] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
[5,4,4,2,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[5,4,4,2,1,1] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 4
[5,4,3,3,2] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
[5,4,3,3,1,1] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
[5,4,3,2,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[5,3,3,3,3] => [3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]] => 3
[5,3,3,3,2,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[5,3,3,2,2,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[4,4,4,3,2] => [4,4,3,2] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]] => 4
[4,4,4,3,1,1] => [4,4,3,1,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]] => 4
[4,4,4,2,2,1] => [4,4,2,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]] => 4
[4,4,3,3,3] => [4,3,3,3] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12,13]] => 4
[4,4,3,3,2,1] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 4
[4,3,3,3,3,1] => [3,3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13]] => 3
[4,3,3,3,2,2] => [3,3,3,2,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12,13]] => 3
[4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11],[12,13]] => 3
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13]] => 2
[3,3,3,3,3,2] => [3,3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14]] => 3
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12],[13,14]] => 3
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14]] => 2
[6,5,4,3,2,1] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 5
[5,5,4,3,2,1] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 5
[6,4,4,3,2,1] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 4
[5,4,4,3,2,1] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 4
[4,4,4,3,2,1] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 4
[6,5,3,3,2,1] => [5,3,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]] => 5
[5,5,3,3,2,1] => [5,3,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]] => 5
[6,4,3,3,2,1] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 4
[5,4,3,3,2,1] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 4
[6,3,3,3,2,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[6,5,4,2,2,1] => [5,4,2,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]] => 5
[5,5,4,2,2,1] => [5,4,2,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]] => 5
[6,4,4,2,2,1] => [4,4,2,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]] => 4
[5,4,4,2,2,1] => [4,4,2,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]] => 4
[6,5,3,2,2,1] => [5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => 5
[5,5,3,2,2,1] => [5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => 5
[6,4,3,2,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[6,5,2,2,2,1] => [5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => 5
[6,5,4,3,1,1] => [5,4,3,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]] => 5
[5,5,4,3,1,1] => [5,4,3,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]] => 5
[6,4,4,3,1,1] => [4,4,3,1,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]] => 4
[5,4,4,3,1,1] => [4,4,3,1,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]] => 4
[6,5,3,3,1,1] => [5,3,3,1,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]] => 5
[5,5,3,3,1,1] => [5,3,3,1,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]] => 5
[6,4,3,3,1,1] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
[6,5,4,2,1,1] => [5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => 5
[5,5,4,2,1,1] => [5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => 5
[6,4,4,2,1,1] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 4
[6,5,3,2,1,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
[6,5,4,1,1,1] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 5
[6,5,4,3,2] => [5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => 5
[5,5,4,3,2] => [5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => 5
[6,4,4,3,2] => [4,4,3,2] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]] => 4
[5,4,4,3,2] => [4,4,3,2] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]] => 4
[6,5,3,3,2] => [5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => 5
[5,5,3,3,2] => [5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => 5
[6,4,3,3,2] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
[6,5,4,2,2] => [5,4,2,2] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]] => 5
[5,5,4,2,2] => [5,4,2,2] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]] => 5
[6,4,4,2,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[6,5,3,2,2] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
[6,5,4,3,1] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 5
[5,5,4,3,1] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 5
[6,4,4,3,1] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
[6,5,3,3,1] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
[6,5,4,2,1] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
[6,5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 5
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[4,3,3,3,3,2] => [3,3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14]] => 3
[7,5,4,3,2,1] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 5
[7,4,4,3,2,1] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 4
[7,4,3,3,2,1] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 4
[7,3,3,3,2,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[7,4,3,2,1,1] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 4
[5,4,3,3,3] => [4,3,3,3] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12,13]] => 4
[7,3,3,3,3] => [3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]] => 3
[7,5,4,3,2] => [5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => 5
[7,5,4,3,1] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 5
[7,5,4,2,1] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
[7,5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 5
[2,2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16]] => 2
[3,3,3,3,3,3] => [3,3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15]] => 3
[2,2,2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18]] => 2
[3,3,3,3,3,3,3] => [3,3,3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[16,17,18]] => 3
[3,3,3,3,3,2,2] => [3,3,3,3,2,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14],[15,16]] => 3
[4,3,3,3,3,3] => [3,3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15]] => 3
[4,4,4,4,4] => [4,4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]] => 4
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[6,6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 6
[7,6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 6
[10,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[10,10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[11,7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[9,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[8,6,4,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 6
[8,6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[10,6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[15,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[7,7,7] => [7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => 7
[9,6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[10,7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[8,5,4,2] => [5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => 5
[9,9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 9
[8,5,4,3,2,1] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 5
[5,4,4,4,4] => [4,4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]] => 4
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searching the database for the individual values of this statistic
Description
The last entry in the first row of a standard tableau.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
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