Identifier
Values
[1,1] => [1] => [[1]] => [[1]] => 1
[2,1] => [1] => [[1]] => [[1]] => 1
[1,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[3,1] => [1] => [[1]] => [[1]] => 1
[2,2] => [2] => [[1,2]] => [[1],[2]] => 1
[2,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[1,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[4,1] => [1] => [[1]] => [[1]] => 1
[3,2] => [2] => [[1,2]] => [[1],[2]] => 1
[3,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[2,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[2,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[5,1] => [1] => [[1]] => [[1]] => 1
[4,2] => [2] => [[1,2]] => [[1],[2]] => 1
[4,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[3,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[3,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[3,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[2,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[2,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[6,1] => [1] => [[1]] => [[1]] => 1
[5,2] => [2] => [[1,2]] => [[1],[2]] => 1
[5,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[4,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[4,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[4,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[3,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[3,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[3,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[2,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[2,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[7,1] => [1] => [[1]] => [[1]] => 1
[6,2] => [2] => [[1,2]] => [[1],[2]] => 1
[6,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[5,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[5,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[5,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[4,4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 1
[4,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[4,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[4,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[3,3,2] => [3,2] => [[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => 2
[3,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 3
[3,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[3,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 3
[2,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => 4
[2,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => 5
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 7
[8,1] => [1] => [[1]] => [[1]] => 1
[7,2] => [2] => [[1,2]] => [[1],[2]] => 1
[7,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[6,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[6,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[6,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[5,4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 1
[5,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[5,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[5,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[4,4,1] => [4,1] => [[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => 2
[4,3,2] => [3,2] => [[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => 2
[4,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 3
[4,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[4,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 2
[3,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => 3
[3,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => 4
[3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 3
[3,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => 4
[3,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => 5
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[2,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => 4
[2,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => 5
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => 6
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 7
[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]] => [[1,2,3,4,5,6,7,8]] => 8
[9,1] => [1] => [[1]] => [[1]] => 1
[8,2] => [2] => [[1,2]] => [[1],[2]] => 1
[8,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[7,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[7,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[7,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[6,4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 1
[6,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[6,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[6,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[5,5] => [5] => [[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => 1
[5,4,1] => [4,1] => [[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => 2
[5,3,2] => [3,2] => [[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => 2
>>> Load all 556 entries. <<<
[5,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 3
[5,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[5,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[5,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[4,4,2] => [4,2] => [[1,2,5,6],[3,4]] => [[1,3],[2,4],[5],[6]] => 2
[4,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => [[1,2,3],[4],[5],[6]] => 3
[4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 2
[4,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => 3
[4,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => 4
[4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 3
[4,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => 4
[4,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => 5
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[3,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7]] => 3
[3,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7]] => 3
[3,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7]] => 4
[3,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7]] => 5
[3,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => 4
[3,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => 5
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => 6
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 7
[2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => 4
[2,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8]] => 5
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8]] => 6
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[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]] => [[1,2,3,4,5,6,7,8]] => 8
[10,1] => [1] => [[1]] => [[1]] => 1
[9,2] => [2] => [[1,2]] => [[1],[2]] => 1
[9,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[8,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[8,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[8,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[7,4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 1
[7,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[7,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[7,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[7,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[6,5] => [5] => [[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => 1
[6,4,1] => [4,1] => [[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => 2
[6,3,2] => [3,2] => [[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => 2
[6,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 3
[6,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[6,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[5,5,1] => [5,1] => [[1,3,4,5,6],[2]] => [[1,2],[3],[4],[5],[6]] => 2
[5,4,2] => [4,2] => [[1,2,5,6],[3,4]] => [[1,3],[2,4],[5],[6]] => 2
[5,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => [[1,2,3],[4],[5],[6]] => 3
[5,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 2
[5,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => 3
[5,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => 4
[5,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 3
[5,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => 4
[5,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => 5
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[4,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => [[1,4],[2,5],[3,6],[7]] => 2
[4,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => [[1,2,4],[3,5],[6],[7]] => 3
[4,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7]] => 4
[4,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7]] => 3
[4,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7]] => 3
[4,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7]] => 4
[4,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7]] => 5
[4,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => 4
[4,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => 5
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => 6
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 7
[3,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8]] => 3
[3,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => [[1,2,3,6],[4,7],[5,8]] => 4
[3,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8]] => 4
[3,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8]] => 5
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7],[8]] => 6
[3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => 4
[3,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8]] => 5
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8]] => 6
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[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]] => [[1,2,3,4,5,6,7,8]] => 8
[11,1] => [1] => [[1]] => [[1]] => 1
[10,2] => [2] => [[1,2]] => [[1],[2]] => 1
[10,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[9,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[9,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[9,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[8,4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 1
[8,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[8,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[8,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[8,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[7,5] => [5] => [[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => 1
[7,4,1] => [4,1] => [[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => 2
[7,3,2] => [3,2] => [[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => 2
[7,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 3
[7,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[7,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[7,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[6,6] => [6] => [[1,2,3,4,5,6]] => [[1],[2],[3],[4],[5],[6]] => 1
[6,5,1] => [5,1] => [[1,3,4,5,6],[2]] => [[1,2],[3],[4],[5],[6]] => 2
[6,4,2] => [4,2] => [[1,2,5,6],[3,4]] => [[1,3],[2,4],[5],[6]] => 2
[6,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => [[1,2,3],[4],[5],[6]] => 3
[6,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 2
[6,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => 3
[6,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => 4
[6,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 3
[6,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => 4
[6,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => 5
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[5,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => [[1,3],[2,4],[5],[6],[7]] => 2
[5,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => [[1,2,3],[4],[5],[6],[7]] => 3
[5,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => [[1,4],[2,5],[3,6],[7]] => 2
[5,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => [[1,2,4],[3,5],[6],[7]] => 3
[5,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7]] => 4
[5,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7]] => 3
[5,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7]] => 3
[5,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7]] => 4
[5,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7]] => 5
[5,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => 4
[5,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => 5
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => 6
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 7
[4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => 2
[4,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7],[8]] => 3
[4,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7],[8]] => 3
[4,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[4,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[4,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8]] => 3
[4,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => [[1,2,3,6],[4,7],[5,8]] => 4
[4,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8]] => 4
[4,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8]] => 5
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7],[8]] => 6
[4,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => 4
[4,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8]] => 5
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8]] => 6
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[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]] => [[1,2,3,4,5,6,7,8]] => 8
[12,1] => [1] => [[1]] => [[1]] => 1
[11,2] => [2] => [[1,2]] => [[1],[2]] => 1
[11,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[10,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[10,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[10,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[9,4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 1
[9,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[9,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[9,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[9,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[8,5] => [5] => [[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => 1
[8,4,1] => [4,1] => [[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => 2
[8,3,2] => [3,2] => [[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => 2
[8,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 3
[8,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[8,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[8,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[7,6] => [6] => [[1,2,3,4,5,6]] => [[1],[2],[3],[4],[5],[6]] => 1
[7,5,1] => [5,1] => [[1,3,4,5,6],[2]] => [[1,2],[3],[4],[5],[6]] => 2
[7,4,2] => [4,2] => [[1,2,5,6],[3,4]] => [[1,3],[2,4],[5],[6]] => 2
[7,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => [[1,2,3],[4],[5],[6]] => 3
[7,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 2
[7,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => 3
[7,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => 4
[7,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 3
[7,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => 4
[7,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => 5
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[6,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => [[1,2],[3],[4],[5],[6],[7]] => 2
[6,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => [[1,3],[2,4],[5],[6],[7]] => 2
[6,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => [[1,2,3],[4],[5],[6],[7]] => 3
[6,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => [[1,4],[2,5],[3,6],[7]] => 2
[6,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => [[1,2,4],[3,5],[6],[7]] => 3
[6,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7]] => 4
[6,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7]] => 3
[6,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7]] => 3
[6,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7]] => 4
[6,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7]] => 5
[6,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => 4
[6,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => 5
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => 6
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 7
[5,5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[5,5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => [[1,2,4],[3,5],[6],[7],[8]] => 3
[5,5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[5,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => 2
[5,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7],[8]] => 3
[5,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7],[8]] => 3
[5,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[5,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[5,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8]] => 3
[5,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => [[1,2,3,6],[4,7],[5,8]] => 4
[5,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8]] => 4
[5,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8]] => 5
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7],[8]] => 6
[5,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => 4
[5,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8]] => 5
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8]] => 6
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[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]] => [[1,2,3,4,5,6,7,8]] => 8
[13,1] => [1] => [[1]] => [[1]] => 1
[12,2] => [2] => [[1,2]] => [[1],[2]] => 1
[12,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[11,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[11,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[11,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[10,4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 1
[10,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[10,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[10,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[10,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[9,5] => [5] => [[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => 1
[9,4,1] => [4,1] => [[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => 2
[9,3,2] => [3,2] => [[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => 2
[9,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 3
[9,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[9,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[9,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[8,6] => [6] => [[1,2,3,4,5,6]] => [[1],[2],[3],[4],[5],[6]] => 1
[8,5,1] => [5,1] => [[1,3,4,5,6],[2]] => [[1,2],[3],[4],[5],[6]] => 2
[8,4,2] => [4,2] => [[1,2,5,6],[3,4]] => [[1,3],[2,4],[5],[6]] => 2
[8,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => [[1,2,3],[4],[5],[6]] => 3
[8,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 2
[8,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => 3
[8,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => 4
[8,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 3
[8,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => 4
[8,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => 5
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[7,7] => [7] => [[1,2,3,4,5,6,7]] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[7,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => [[1,2],[3],[4],[5],[6],[7]] => 2
[7,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => [[1,3],[2,4],[5],[6],[7]] => 2
[7,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => [[1,2,3],[4],[5],[6],[7]] => 3
[7,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => [[1,4],[2,5],[3,6],[7]] => 2
[7,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => [[1,2,4],[3,5],[6],[7]] => 3
[7,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7]] => 4
[7,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7]] => 3
[7,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7]] => 3
[7,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7]] => 4
[7,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7]] => 5
[7,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => 4
[7,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => 5
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => 6
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 7
[6,6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[6,6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[6,5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[6,5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => [[1,2,4],[3,5],[6],[7],[8]] => 3
[6,5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[6,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => 2
[6,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7],[8]] => 3
[6,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7],[8]] => 3
[6,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[6,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[6,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8]] => 3
[6,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => [[1,2,3,6],[4,7],[5,8]] => 4
[6,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8]] => 4
[6,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8]] => 5
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7],[8]] => 6
[6,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => 4
[6,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8]] => 5
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8]] => 6
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[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]] => [[1,2,3,4,5,6,7,8]] => 8
[14,1] => [1] => [[1]] => [[1]] => 1
[13,2] => [2] => [[1,2]] => [[1],[2]] => 1
[13,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[12,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[12,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[12,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[11,4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 1
[11,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[11,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[11,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[11,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[10,5] => [5] => [[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => 1
[10,4,1] => [4,1] => [[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => 2
[10,3,2] => [3,2] => [[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => 2
[10,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 3
[10,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[10,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[10,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[9,6] => [6] => [[1,2,3,4,5,6]] => [[1],[2],[3],[4],[5],[6]] => 1
[9,5,1] => [5,1] => [[1,3,4,5,6],[2]] => [[1,2],[3],[4],[5],[6]] => 2
[9,4,2] => [4,2] => [[1,2,5,6],[3,4]] => [[1,3],[2,4],[5],[6]] => 2
[9,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => [[1,2,3],[4],[5],[6]] => 3
[9,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 2
[9,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => 3
[9,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => 4
[9,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 3
[9,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => 4
[9,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => 5
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[8,7] => [7] => [[1,2,3,4,5,6,7]] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[8,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => [[1,2],[3],[4],[5],[6],[7]] => 2
[8,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => [[1,3],[2,4],[5],[6],[7]] => 2
[8,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => [[1,2,3],[4],[5],[6],[7]] => 3
[8,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => [[1,4],[2,5],[3,6],[7]] => 2
[8,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => [[1,2,4],[3,5],[6],[7]] => 3
[8,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7]] => 4
[8,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7]] => 3
[8,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7]] => 3
[8,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7]] => 4
[8,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7]] => 5
[8,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => 4
[8,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => 5
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => 6
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 7
[7,7,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[7,6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[7,6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[7,5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[7,5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => [[1,2,4],[3,5],[6],[7],[8]] => 3
[7,5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[7,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => 2
[7,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7],[8]] => 3
[7,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7],[8]] => 3
[7,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[7,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[7,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8]] => 3
[7,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => [[1,2,3,6],[4,7],[5,8]] => 4
[7,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8]] => 4
[7,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8]] => 5
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7],[8]] => 6
[7,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => 4
[7,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8]] => 5
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8]] => 6
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[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]] => [[1,2,3,4,5,6,7,8]] => 8
[15,1] => [1] => [[1]] => [[1]] => 1
[14,2] => [2] => [[1,2]] => [[1],[2]] => 1
[14,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[13,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[13,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[13,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[12,4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 1
[12,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[12,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[12,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[12,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[11,5] => [5] => [[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => 1
[11,4,1] => [4,1] => [[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => 2
[11,3,2] => [3,2] => [[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => 2
[11,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 3
[11,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[11,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[11,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[10,6] => [6] => [[1,2,3,4,5,6]] => [[1],[2],[3],[4],[5],[6]] => 1
[10,5,1] => [5,1] => [[1,3,4,5,6],[2]] => [[1,2],[3],[4],[5],[6]] => 2
[10,4,2] => [4,2] => [[1,2,5,6],[3,4]] => [[1,3],[2,4],[5],[6]] => 2
[10,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => [[1,2,3],[4],[5],[6]] => 3
[10,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 2
[10,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => 3
[10,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => 4
[10,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 3
[10,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => 4
[10,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => 5
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[9,7] => [7] => [[1,2,3,4,5,6,7]] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[9,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => [[1,2],[3],[4],[5],[6],[7]] => 2
[9,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => [[1,3],[2,4],[5],[6],[7]] => 2
[9,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => [[1,2,3],[4],[5],[6],[7]] => 3
[9,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => [[1,4],[2,5],[3,6],[7]] => 2
[9,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => [[1,2,4],[3,5],[6],[7]] => 3
[9,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7]] => 4
[9,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7]] => 3
[9,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7]] => 3
[9,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7]] => 4
[9,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7]] => 5
[9,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => 4
[9,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => 5
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => 6
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 7
[8,8] => [8] => [[1,2,3,4,5,6,7,8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[8,7,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[8,6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[8,6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[8,5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[8,5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => [[1,2,4],[3,5],[6],[7],[8]] => 3
[8,5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[8,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => 2
[8,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7],[8]] => 3
[8,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7],[8]] => 3
[8,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[8,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[8,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8]] => 3
[8,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => [[1,2,3,6],[4,7],[5,8]] => 4
[8,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8]] => 4
[8,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8]] => 5
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7],[8]] => 6
[8,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => 4
[8,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8]] => 5
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8]] => 6
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[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]] => [[1,2,3,4,5,6,7,8]] => 8
[16,1] => [1] => [[1]] => [[1]] => 1
[15,2] => [2] => [[1,2]] => [[1],[2]] => 1
[15,1,1] => [1,1] => [[1],[2]] => [[1,2]] => 2
[14,3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 1
[14,2,1] => [2,1] => [[1,3],[2]] => [[1,2],[3]] => 2
[14,1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 3
[13,4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 1
[13,3,1] => [3,1] => [[1,3,4],[2]] => [[1,2],[3],[4]] => 2
[13,2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[13,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => [[1,2,3],[4]] => 3
[13,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 4
[12,5] => [5] => [[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => 1
[12,4,1] => [4,1] => [[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => 2
[12,3,2] => [3,2] => [[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => 2
[12,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 3
[12,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => 3
[12,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => 4
[12,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 5
[11,6] => [6] => [[1,2,3,4,5,6]] => [[1],[2],[3],[4],[5],[6]] => 1
[11,5,1] => [5,1] => [[1,3,4,5,6],[2]] => [[1,2],[3],[4],[5],[6]] => 2
[11,4,2] => [4,2] => [[1,2,5,6],[3,4]] => [[1,3],[2,4],[5],[6]] => 2
[11,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => [[1,2,3],[4],[5],[6]] => 3
[11,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 2
[11,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => 3
[11,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => 4
[11,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 3
[11,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => 4
[11,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => 5
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => 6
[10,7] => [7] => [[1,2,3,4,5,6,7]] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[10,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => [[1,2],[3],[4],[5],[6],[7]] => 2
[10,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => [[1,3],[2,4],[5],[6],[7]] => 2
[10,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => [[1,2,3],[4],[5],[6],[7]] => 3
[10,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => [[1,4],[2,5],[3,6],[7]] => 2
[10,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => [[1,2,4],[3,5],[6],[7]] => 3
[10,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7]] => 4
[10,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7]] => 3
[10,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7]] => 3
[10,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7]] => 4
[10,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7]] => 5
[10,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => 4
[10,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => 5
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => 6
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 7
[9,8] => [8] => [[1,2,3,4,5,6,7,8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[9,7,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[9,6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[9,6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[9,5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[9,5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => [[1,2,4],[3,5],[6],[7],[8]] => 3
[9,5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[9,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => 2
[9,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7],[8]] => 3
[9,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7],[8]] => 3
[9,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[9,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[9,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8]] => 3
[9,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => [[1,2,3,6],[4,7],[5,8]] => 4
[9,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8]] => 4
[9,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8]] => 5
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7],[8]] => 6
[9,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => 4
[9,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => [[1,2,3,5,7],[4,6,8]] => 5
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8]] => 6
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[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]] => [[1,2,3,4,5,6,7,8]] => 8
[10,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The number of factors of a standard tableaux under concatenation.
The concatenation of two standard Young tableaux $T_1$ and $T_2$ is obtained by adding the largest entry of $T_1$ to each entry of $T_2$, and then appending the rows of the result to $T_1$, see [1, dfn 2.10].
This statistic returns the maximal number of standard tableaux such that their concatenation is the given tableau.
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a partition.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
conjugate
Description
Sends a standard tableau to its conjugate tableau.