Identifier
-
Mp00040:
Integer compositions
—to partition⟶
Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
St000733: Standard tableaux ⟶ ℤ
Values
[1] => [1] => [[1]] => [[1]] => 1
[1,1] => [1,1] => [[1],[2]] => [[1,2]] => 1
[2] => [2] => [[1,2]] => [[1],[2]] => 2
[1,1,1] => [1,1,1] => [[1],[2],[3]] => [[1,2,3]] => 1
[1,2] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[2,1] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[3] => [3] => [[1,2,3]] => [[1],[2],[3]] => 3
[1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1,2,3,4]] => 1
[1,1,2] => [2,1,1] => [[1,2],[3],[4]] => [[1,3,4],[2]] => 1
[1,2,1] => [2,1,1] => [[1,2],[3],[4]] => [[1,3,4],[2]] => 1
[1,3] => [3,1] => [[1,2,3],[4]] => [[1,4],[2],[3]] => 1
[2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [[1,3,4],[2]] => 1
[2,2] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[3,1] => [3,1] => [[1,2,3],[4]] => [[1,4],[2],[3]] => 1
[4] => [4] => [[1,2,3,4]] => [[1],[2],[3],[4]] => 4
[1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => 1
[1,1,1,2] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,3,4,5],[2]] => 1
[1,1,2,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,3,4,5],[2]] => 1
[1,1,3] => [3,1,1] => [[1,2,3],[4],[5]] => [[1,4,5],[2],[3]] => 1
[1,2,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,3,4,5],[2]] => 1
[1,2,2] => [2,2,1] => [[1,2],[3,4],[5]] => [[1,3,5],[2,4]] => 1
[1,3,1] => [3,1,1] => [[1,2,3],[4],[5]] => [[1,4,5],[2],[3]] => 1
[1,4] => [4,1] => [[1,2,3,4],[5]] => [[1,5],[2],[3],[4]] => 1
[2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,3,4,5],[2]] => 1
[2,1,2] => [2,2,1] => [[1,2],[3,4],[5]] => [[1,3,5],[2,4]] => 1
[2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [[1,3,5],[2,4]] => 1
[2,3] => [3,2] => [[1,2,3],[4,5]] => [[1,4],[2,5],[3]] => 2
[3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [[1,4,5],[2],[3]] => 1
[3,2] => [3,2] => [[1,2,3],[4,5]] => [[1,4],[2,5],[3]] => 2
[4,1] => [4,1] => [[1,2,3,4],[5]] => [[1,5],[2],[3],[4]] => 1
[5] => [5] => [[1,2,3,4,5]] => [[1],[2],[3],[4],[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]] => 1
[1,1,1,1,2] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,3,4,5,6],[2]] => 1
[1,1,1,2,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,3,4,5,6],[2]] => 1
[1,1,1,3] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,4,5,6],[2],[3]] => 1
[1,1,2,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,3,4,5,6],[2]] => 1
[1,1,2,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3,5,6],[2,4]] => 1
[1,1,3,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,4,5,6],[2],[3]] => 1
[1,1,4] => [4,1,1] => [[1,2,3,4],[5],[6]] => [[1,5,6],[2],[3],[4]] => 1
[1,2,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,3,4,5,6],[2]] => 1
[1,2,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3,5,6],[2,4]] => 1
[1,2,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3,5,6],[2,4]] => 1
[1,2,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,4,6],[2,5],[3]] => 1
[1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,4,5,6],[2],[3]] => 1
[1,3,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,4,6],[2,5],[3]] => 1
[1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [[1,5,6],[2],[3],[4]] => 1
[1,5] => [5,1] => [[1,2,3,4,5],[6]] => [[1,6],[2],[3],[4],[5]] => 1
[2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,3,4,5,6],[2]] => 1
[2,1,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3,5,6],[2,4]] => 1
[2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3,5,6],[2,4]] => 1
[2,1,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,4,6],[2,5],[3]] => 1
[2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3,5,6],[2,4]] => 1
[2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => 2
[2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,4,6],[2,5],[3]] => 1
[2,4] => [4,2] => [[1,2,3,4],[5,6]] => [[1,5],[2,6],[3],[4]] => 2
[3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,4,5,6],[2],[3]] => 1
[3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,4,6],[2,5],[3]] => 1
[3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,4,6],[2,5],[3]] => 1
[3,3] => [3,3] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => 3
[4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [[1,5,6],[2],[3],[4]] => 1
[4,2] => [4,2] => [[1,2,3,4],[5,6]] => [[1,5],[2,6],[3],[4]] => 2
[5,1] => [5,1] => [[1,2,3,4,5],[6]] => [[1,6],[2],[3],[4],[5]] => 1
[6] => [6] => [[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],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,2] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2]] => 1
[1,1,1,1,2,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2]] => 1
[1,1,1,1,3] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,4,5,6,7],[2],[3]] => 1
[1,1,1,2,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2]] => 1
[1,1,1,2,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 1
[1,1,1,3,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,4,5,6,7],[2],[3]] => 1
[1,1,1,4] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4]] => 1
[1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2]] => 1
[1,1,2,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 1
[1,1,2,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 1
[1,1,2,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,4,5,6,7],[2],[3]] => 1
[1,1,3,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4]] => 1
[1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [[1,6,7],[2],[3],[4],[5]] => 1
[1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2]] => 1
[1,2,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 1
[1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 1
[1,2,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 1
[1,2,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3,5,7],[2,4,6]] => 1
[1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[1,2,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,5,7],[2,6],[3],[4]] => 1
[1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,4,5,6,7],[2],[3]] => 1
[1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[1,4,7],[2,5],[3,6]] => 1
[1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4]] => 1
[1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,5,7],[2,6],[3],[4]] => 1
[1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [[1,6,7],[2],[3],[4],[5]] => 1
[1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 1
[2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2]] => 1
[2,1,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 1
[2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 1
[2,1,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 1
[2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3,5,7],[2,4,6]] => 1
>>> Load all 1026 entries. <<<[2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,5,7],[2,6],[3],[4]] => 1
[2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => 1
[2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3,5,7],[2,4,6]] => 1
[2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3,5,7],[2,4,6]] => 1
[2,2,3] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[1,4,6],[2,5,7],[3]] => 2
[2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[1,4,6],[2,5,7],[3]] => 2
[2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,5,7],[2,6],[3],[4]] => 1
[2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => [[1,6],[2,7],[3],[4],[5]] => 2
[3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,4,5,6,7],[2],[3]] => 1
[3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[1,4,7],[2,5],[3,6]] => 1
[3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => 1
[3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[1,4,6],[2,5,7],[3]] => 2
[3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[1,4,7],[2,5],[3,6]] => 1
[3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => [[1,5],[2,6],[3,7],[4]] => 3
[4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4]] => 1
[4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,5,7],[2,6],[3],[4]] => 1
[4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,5,7],[2,6],[3],[4]] => 1
[4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [[1,5],[2,6],[3,7],[4]] => 3
[5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [[1,6,7],[2],[3],[4],[5]] => 1
[5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [[1,6],[2,7],[3],[4],[5]] => 2
[6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 1
[7] => [7] => [[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],[2],[3],[4],[5],[6],[7],[8]] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => 1
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => 1
[1,1,1,1,1,3] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => 1
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => 1
[1,1,1,1,2,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => 1
[1,1,1,1,4] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]] => 1
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => 1
[1,1,1,2,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[1,1,1,2,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => 1
[1,1,1,3,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,1,1,4,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]] => 1
[1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,6,7,8],[2],[3],[4],[5]] => 1
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => 1
[1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[1,1,2,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[1,1,2,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 1
[1,1,2,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,1,2,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => 1
[1,1,3,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,1,3,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,1,3,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,4,7,8],[2,5],[3,6]] => 1
[1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]] => 1
[1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,6,7,8],[2],[3],[4],[5]] => 1
[1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,7,8],[2],[3],[4],[5],[6]] => 1
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => 1
[1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[1,2,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[1,2,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 1
[1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 1
[1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 1
[1,2,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,2,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,6,8],[2,7],[3],[4],[5]] => 1
[1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => 1
[1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,4,7,8],[2,5],[3,6]] => 1
[1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,4,7,8],[2,5],[3,6]] => 1
[1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,5,8],[2,6],[3,7],[4]] => 1
[1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]] => 1
[1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,5,8],[2,6],[3,7],[4]] => 1
[1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,6,7,8],[2],[3],[4],[5]] => 1
[1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,6,8],[2,7],[3],[4],[5]] => 1
[1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,7,8],[2],[3],[4],[5],[6]] => 1
[1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => 1
[2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[2,1,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 1
[2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 1
[2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 1
[2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,6,8],[2,7],[3],[4],[5]] => 1
[2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => 1
[2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 1
[2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 1
[2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => 1
[2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => 2
[2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,5,7],[2,6,8],[3],[4]] => 2
[2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,4,7],[2,5,8],[3,6]] => 2
[2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,5,7],[2,6,8],[3],[4]] => 2
[2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,6,8],[2,7],[3],[4],[5]] => 1
[2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[1,7],[2,8],[3],[4],[5],[6]] => 2
[3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => 1
[3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,4,7,8],[2,5],[3,6]] => 1
[3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,4,7,8],[2,5],[3,6]] => 1
[3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,5,8],[2,6],[3,7],[4]] => 1
[3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1
[3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1
[3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,4,7],[2,5,8],[3,6]] => 2
[3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,4,7,8],[2,5],[3,6]] => 1
[3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,4,7],[2,5,8],[3,6]] => 2
[3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,5,8],[2,6],[3,7],[4]] => 1
[3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[1,6],[2,7],[3,8],[4],[5]] => 3
[4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]] => 1
[4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,5,8],[2,6],[3,7],[4]] => 1
[4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1
[4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,5,7],[2,6,8],[3],[4]] => 2
[4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,5,8],[2,6],[3,7],[4]] => 1
[4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => 4
[5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,6,7,8],[2],[3],[4],[5]] => 1
[5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,6,8],[2,7],[3],[4],[5]] => 1
[5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,6,8],[2,7],[3],[4],[5]] => 1
[5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[1,6],[2,7],[3,8],[4],[5]] => 3
[6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,7,8],[2],[3],[4],[5],[6]] => 1
[6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[1,7],[2,8],[3],[4],[5],[6]] => 2
[7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[8] => [8] => [[1,2,3,4,5,6,7,8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 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]] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => 1
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => 1
[1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => 1
[1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => 1
[1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => 1
[1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,5,6,7,8,9],[2],[3],[4]] => 1
[1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => 1
[1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,1,1,1,2,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => 1
[1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,5,6,7,8,9],[2],[3],[4]] => 1
[1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,6,7,8,9],[2],[3],[4],[5]] => 1
[1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => 1
[1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,1,1,2,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,1,1,2,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[1,1,1,2,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,1,2,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => 1
[1,1,1,3,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,1,3,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,1,3,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 1
[1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,5,6,7,8,9],[2],[3],[4]] => 1
[1,1,1,4,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,6,7,8,9],[2],[3],[4],[5]] => 1
[1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 1
[1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => 1
[1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,1,2,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,1,2,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[1,1,2,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,2,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,1,2,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[1,1,2,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[1,1,2,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,1,2,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,2,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,1,2,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,1,2,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => 1
[1,1,3,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,3,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,3,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 1
[1,1,3,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,1,3,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,1,3,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 1
[1,1,3,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,5,6,7,8,9],[2],[3],[4]] => 1
[1,1,4,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,1,4,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,1,4,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,6,7,8,9],[2],[3],[4],[5]] => 1
[1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 1
[1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 1
[1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => 1
[1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[1,2,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,2,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,2,1,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[1,2,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[1,2,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,2,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,2,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,2,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,2,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[1,2,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[1,2,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[1,2,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,2,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3,5,7,9],[2,4,6,8]] => 1
[1,2,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,2,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,2,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,2,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,2,3,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[1,2,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,2,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[1,2,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 1
[1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => 1
[1,3,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,3,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,3,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 1
[1,3,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,3,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,3,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 1
[1,3,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[1,3,2,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,3,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[1,3,2,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[1,3,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 1
[1,3,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[1,3,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[1,3,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[1,6,9],[2,7],[3,8],[4],[5]] => 1
[1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,5,6,7,8,9],[2],[3],[4]] => 1
[1,4,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,4,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,4,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[1,4,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[1,4,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[1,4,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [[1,5,9],[2,6],[3,7],[4,8]] => 1
[1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,6,7,8,9],[2],[3],[4],[5]] => 1
[1,5,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[1,5,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[1,6,9],[2,7],[3,8],[4],[5]] => 1
[1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 1
[1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 1
[1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 1
[1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 1
[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]] => [[1,3,4,5,6,7,8,9],[2]] => 1
[2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[2,1,1,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[2,1,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[2,1,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[2,1,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[2,1,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[2,1,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[2,1,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[2,1,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3,5,7,9],[2,4,6,8]] => 1
[2,1,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,1,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[2,1,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,1,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,1,3,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[2,1,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[2,1,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 1
[2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => 1
[2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[2,2,1,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[2,2,1,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3,5,7,9],[2,4,6,8]] => 1
[2,2,1,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,2,1,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3,5,7,8,9],[2,4,6]] => 1
[2,2,2,1,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3,5,7,9],[2,4,6,8]] => 1
[2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3,5,7,9],[2,4,6,8]] => 1
[2,2,2,3] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [[1,4,6,8],[2,5,7,9],[3]] => 2
[2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,2,3,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [[1,4,6,8],[2,5,7,9],[3]] => 2
[2,2,4,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [[1,6,8],[2,7,9],[3],[4],[5]] => 2
[2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[2,3,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,3,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,3,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[2,3,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[2,3,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [[1,4,6,8],[2,5,7,9],[3]] => 2
[2,3,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[2,3,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [[1,5,8],[2,6,9],[3,7],[4]] => 2
[2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[2,4,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[2,4,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [[1,5,8],[2,6,9],[3,7],[4]] => 2
[2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [[1,6,8],[2,7,9],[3],[4],[5]] => 2
[2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 1
[2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 2
[3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => 1
[3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 1
[3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[3,1,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 1
[3,1,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[3,1,2,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[3,1,2,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 1
[3,1,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[1,6,9],[2,7],[3,8],[4],[5]] => 1
[3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 1
[3,2,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[3,2,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[3,2,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 1
[3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [[1,4,6,8],[2,5,7,9],[3]] => 2
[3,2,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[3,2,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [[1,5,8],[2,6,9],[3,7],[4]] => 2
[3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [[1,4,7,8,9],[2,5],[3,6]] => 1
[3,3,1,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [[1,4,7,9],[2,5,8],[3,6]] => 1
[3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [[1,4,7],[2,5,8],[3,6,9]] => 3
[3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [[1,5,8],[2,6,9],[3,7],[4]] => 2
[3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[1,6,9],[2,7],[3,8],[4],[5]] => 1
[3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 3
[4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,5,6,7,8,9],[2],[3],[4]] => 1
[4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [[1,5,9],[2,6],[3,7],[4,8]] => 1
[4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 1
[4,2,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 1
[4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [[1,5,8],[2,6,9],[3,7],[4]] => 2
[4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 1
[4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [[1,5,8],[2,6,9],[3,7],[4]] => 2
[4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [[1,5,9],[2,6],[3,7],[4,8]] => 1
[4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [[1,6],[2,7],[3,8],[4,9],[5]] => 4
[5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,6,7,8,9],[2],[3],[4],[5]] => 1
[5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[1,6,9],[2,7],[3,8],[4],[5]] => 1
[5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 1
[5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [[1,6,8],[2,7,9],[3],[4],[5]] => 2
[5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[1,6,9],[2,7],[3,8],[4],[5]] => 1
[5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [[1,6],[2,7],[3,8],[4,9],[5]] => 4
[6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 1
[6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 1
[6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 1
[6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 3
[7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 1
[7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 2
[8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 1
[9] => [9] => [[1,2,3,4,5,6,7,8,9]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 9
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => 1
[1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => 1
[1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 1
[1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => 1
[1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 1
[1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 1
[1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,1,2,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => 1
[1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,1,3,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,1,3,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[1,1,1,1,4,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 1
[1,1,1,1,4,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,1,1,5,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 1
[1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 1
[1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,2,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,1,1,2,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,2,3,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,1,2,4,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,1,2,5] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => 1
[1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,3,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,1,3,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,1,3,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[1,1,1,3,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,1,1,4,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 1
[1,1,1,4,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,1,4,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,1,4,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,1,1,5,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 1
[1,1,1,5,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,1,1,6,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 1
[1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 1
[1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,2,1,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,2,1,2,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,1,2,1,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,2,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,2,1,3,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,2,1,4,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,2,1,5] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,1,2,2,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,1,2,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[1,1,2,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,2,2,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,2,3,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,2,3,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,2,3,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,1,2,4,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,2,4,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,1,2,5,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,1,2,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => 1
[1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,3,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,3,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,3,1,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,3,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[1,1,3,1,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,1,3,2,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,3,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,1,3,2,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,1,3,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[1,1,3,3,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,1,3,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,1,3,5] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 1
[1,1,4,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,4,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,4,1,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,1,4,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,1,4,2,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,1,4,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,1,4,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 1
[1,1,5,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 1
[1,1,5,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,1,5,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,1,5,3] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[1,1,6,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 1
[1,1,6,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 1
[1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 1
[1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,2,1,1,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,2,1,1,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,2,1,1,3,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,1,1,4,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,2,1,1,5] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,2,1,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,2,1,2,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,2,1,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[1,2,1,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,1,2,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,2,1,3,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,1,3,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,1,3,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,2,1,4,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,2,1,4,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,2,1,5,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,2,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,2,2,1,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,2,2,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[1,2,2,1,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,2,1,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[1,2,2,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[1,2,2,2,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[1,2,2,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,2,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[1,2,2,4,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,2,2,5] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,2,3,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,3,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,2,3,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,2,3,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[1,2,3,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,2,3,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[1,2,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,2,4,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,2,4,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,2,4,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[1,2,5,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,2,5,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[1,2,6,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[1,2,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 1
[1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => 1
[1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,3,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,3,1,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,3,1,1,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,3,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[1,3,1,1,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,3,1,2,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,3,1,2,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,3,1,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,3,1,2,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,3,1,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[1,3,1,3,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,3,1,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,3,1,5] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[1,3,2,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,3,2,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,3,2,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,3,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[1,3,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[1,3,2,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,3,2,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[1,3,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[1,3,3,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,3,3,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[1,3,3,3] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [[1,4,7,10],[2,5,8],[3,6,9]] => 1
[1,3,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,3,4,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[1,3,5,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[1,3,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 1
[1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 1
[1,4,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,4,1,1,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,4,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,4,1,2,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,4,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,4,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 1
[1,4,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[1,4,2,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,4,2,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[1,4,2,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[1,4,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[1,4,3,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[1,4,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 1
[1,4,5] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 1
[1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 1
[1,5,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,5,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,5,1,3] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[1,5,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[1,5,2,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[1,5,3,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[1,5,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 1
[1,6,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 1
[1,6,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[1,6,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[1,6,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 1
[1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 1
[1,7,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 1
[1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 1
[1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[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]] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[2,1,1,1,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[2,1,1,1,2,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,1,1,1,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[2,1,1,1,3,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,1,1,4,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[2,1,1,1,5] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,1,1,2,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,1,1,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[2,1,1,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,1,2,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[2,1,1,3,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,1,3,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,1,3,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[2,1,1,4,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[2,1,1,4,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,1,1,5,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[2,1,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,1,2,1,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,1,2,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[2,1,2,1,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,2,1,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,1,2,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[2,1,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[2,1,2,2,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,1,2,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,2,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,1,2,4,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,1,2,5] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[2,1,3,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,3,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[2,1,3,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,1,3,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,1,3,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[2,1,3,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[2,1,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[2,1,4,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,1,4,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,1,4,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[2,1,5,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[2,1,5,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[2,1,6,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[2,1,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 1
[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]] => [[1,3,5,6,7,8,9,10],[2,4]] => 1
[2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,2,1,1,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,2,1,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[2,2,1,1,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,2,1,1,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,2,1,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[2,2,1,2,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,2,1,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,2,1,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,2,1,4,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,2,1,5] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 1
[2,2,2,1,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[2,2,2,1,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[2,2,2,1,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 1
[2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [[1,3,5,7,9],[2,4,6,8,10]] => 2
[2,2,2,3,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,2,2,4] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 2
[2,2,3,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,2,3,1,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,2,3,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,2,3,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [[1,4,7,9],[2,5,8,10],[3,6]] => 2
[2,2,4,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,2,4,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 2
[2,2,5,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[2,2,6] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [[1,7,9],[2,8,10],[3],[4],[5],[6]] => 2
[2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[2,3,1,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,3,1,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,3,1,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[2,3,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,3,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,3,1,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[2,3,1,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[2,3,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[2,3,2,1,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,3,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[2,3,2,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [[1,4,7,9],[2,5,8,10],[3,6]] => 2
[2,3,3,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[2,3,3,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [[1,4,7,9],[2,5,8,10],[3,6]] => 2
[2,3,4,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[2,3,5] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [[1,6,9],[2,7,10],[3,8],[4],[5]] => 2
[2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[2,4,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,4,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,4,1,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[2,4,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[2,4,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 2
[2,4,3,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[2,4,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [[1,5,9],[2,6,10],[3,7],[4,8]] => 2
[2,5,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[2,5,1,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[2,5,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[2,5,3] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [[1,6,9],[2,7,10],[3,8],[4],[5]] => 2
[2,6,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[2,6,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [[1,7,9],[2,8,10],[3],[4],[5],[6]] => 2
[2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 1
[2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 2
[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]] => [[1,4,5,6,7,8,9,10],[2],[3]] => 1
[3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[3,1,1,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[3,1,1,1,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[3,1,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[3,1,1,1,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[3,1,1,2,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[3,1,1,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[3,1,1,2,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,1,1,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[3,1,1,3,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,1,1,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[3,1,1,5] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[3,1,2,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[3,1,2,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[3,1,2,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,1,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[3,1,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[3,1,2,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,1,2,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[3,1,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[3,1,3,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,1,3,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,1,3,3] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [[1,4,7,10],[2,5,8],[3,6,9]] => 1
[3,1,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[3,1,4,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[3,1,5,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[3,1,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 1
[3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 1
[3,2,1,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[3,2,1,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[3,2,1,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,2,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[3,2,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[3,2,1,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,2,1,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 1
[3,2,2,1,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 1
[3,2,2,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [[1,4,7,9],[2,5,8,10],[3,6]] => 2
[3,2,3,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,2,3,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [[1,4,7,9],[2,5,8,10],[3,6]] => 2
[3,2,4,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[3,2,5] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [[1,6,9],[2,7,10],[3,8],[4],[5]] => 2
[3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 1
[3,3,1,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,3,1,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,3,1,3] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [[1,4,7,10],[2,5,8],[3,6,9]] => 1
[3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 1
[3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [[1,4,7,9],[2,5,8,10],[3,6]] => 2
[3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [[1,4,7,10],[2,5,8],[3,6,9]] => 1
[3,3,4] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [[1,5,8],[2,6,9],[3,7,10],[4]] => 3
[3,4,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[3,4,1,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[3,4,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[3,4,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [[1,5,8],[2,6,9],[3,7,10],[4]] => 3
[3,5,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[3,5,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [[1,6,9],[2,7,10],[3,8],[4],[5]] => 2
[3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 1
[3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 3
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 1
[4,1,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[4,1,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[4,1,1,1,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[4,1,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[4,1,1,2,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[4,1,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 1
[4,1,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[4,1,2,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[4,1,2,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[4,1,2,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[4,1,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[4,1,3,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[4,1,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 1
[4,1,5] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 1
[4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 1
[4,2,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[4,2,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[4,2,1,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 1
[4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 2
[4,2,3,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[4,2,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [[1,5,9],[2,6,10],[3,7],[4,8]] => 2
[4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 1
[4,3,1,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 1
[4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [[1,5,8],[2,6,9],[3,7,10],[4]] => 3
[4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 1
[4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [[1,5,9],[2,6,10],[3,7],[4,8]] => 2
[4,5,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 1
[4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 4
[5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 1
[5,1,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[5,1,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[5,1,1,3] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[5,1,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[5,1,2,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[5,1,3,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[5,1,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 1
[5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 1
[5,2,1,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 1
[5,2,3] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [[1,6,9],[2,7,10],[3,8],[4],[5]] => 2
[5,3,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 1
[5,3,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [[1,6,9],[2,7,10],[3,8],[4],[5]] => 2
[5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 1
[5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 5
[6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 1
[6,1,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[6,1,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[6,1,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 1
[6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 1
[6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [[1,7,9],[2,8,10],[3],[4],[5],[6]] => 2
[6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 1
[6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 4
[7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 1
[7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 1
[7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 1
[7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 3
[8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 1
[8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 2
[9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 10
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 2
[6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 6
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,0,1 6,1,0,1 13,2,0,0,1 27,3,1,0,0,1 56,5,2,0,0,0,1 115,9,2,1,0,0,0,1 235,15,3,2,0,0,0,0,1 478,25,5,2,1,0,0,0,0,1
F1=q
F2=q+q2
F3=3 q+q3
F4=6 q+q2+q4
F5=13 q+2 q2+q5
F6=27 q+3 q2+q3+q6
F7=56 q+5 q2+2 q3+q7
F8=115 q+9 q2+2 q3+q4+q8
F9=235 q+15 q2+3 q3+2 q4+q9
F10=478 q+25 q2+5 q3+2 q4+q5+q10
Description
The row containing the largest entry of a standard tableau.
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to partition
Description
Sends a composition to the partition obtained by sorting the entries.
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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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conjugate
Description
Sends a standard tableau to its conjugate tableau.
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