Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000245: Permutations ⟶ ℤ
Values
[1] => [] => [] => [] => 0
[2] => [] => [] => [] => 0
[1,1] => [1] => [[1]] => [1] => 0
[3] => [] => [] => [] => 0
[2,1] => [1] => [[1]] => [1] => 0
[1,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[4] => [] => [] => [] => 0
[3,1] => [1] => [[1]] => [1] => 0
[2,2] => [2] => [[1,2]] => [1,2] => 1
[2,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[1,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[5] => [] => [] => [] => 0
[4,1] => [1] => [[1]] => [1] => 0
[3,2] => [2] => [[1,2]] => [1,2] => 1
[3,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[2,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[2,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[6] => [] => [] => [] => 0
[5,1] => [1] => [[1]] => [1] => 0
[4,2] => [2] => [[1,2]] => [1,2] => 1
[4,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[3,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[3,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[3,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[2,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[7] => [] => [] => [] => 0
[6,1] => [1] => [[1]] => [1] => 0
[5,2] => [2] => [[1,2]] => [1,2] => 1
[5,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[4,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[4,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[4,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[3,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[3,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[8] => [] => [] => [] => 0
[7,1] => [1] => [[1]] => [1] => 0
[6,2] => [2] => [[1,2]] => [1,2] => 1
[6,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[5,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[5,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[5,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[4,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 3
[4,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[4,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[3,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 3
[3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3
[2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 0
[9] => [] => [] => [] => 0
[8,1] => [1] => [[1]] => [1] => 0
[7,2] => [2] => [[1,2]] => [1,2] => 1
[7,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[6,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[6,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[6,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[5,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 3
[5,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[5,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[5,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[4,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 3
[4,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 3
[4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 4
[3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 3
[3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 2
[3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3
[3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3
[2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 0
[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]] => [8,7,6,5,4,3,2,1] => 0
[10] => [] => [] => [] => 0
[9,1] => [1] => [[1]] => [1] => 0
[8,2] => [2] => [[1,2]] => [1,2] => 1
[8,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[7,3] => [3] => [[1,2,3]] => [1,2,3] => 2
>>> Load all 878 entries. <<<[7,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[7,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[6,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 3
[6,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[6,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[6,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[5,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 4
[5,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 3
[5,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 3
[5,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[5,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[5,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[5,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 4
[4,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 3
[4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 4
[4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 3
[4,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 2
[4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3
[4,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[4,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 4
[3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 4
[3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 3
[3,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 2
[3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3
[3,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 0
[2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4
[2,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 0
[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]] => [9,8,7,6,5,4,3,2,1] => 0
[11] => [] => [] => [] => 0
[10,1] => [1] => [[1]] => [1] => 0
[9,2] => [2] => [[1,2]] => [1,2] => 1
[9,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[8,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[8,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[8,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[7,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 3
[7,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[7,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[7,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[7,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[6,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 4
[6,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 3
[6,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 3
[6,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[6,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[6,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[5,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 4
[5,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 4
[5,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 3
[5,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 4
[5,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 3
[5,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 2
[5,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3
[5,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[5,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[4,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 5
[4,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 4
[4,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 3
[4,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 4
[4,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 4
[4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 3
[4,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 2
[4,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3
[4,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 0
[3,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 5
[3,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 4
[3,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 4
[3,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 3
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 2
[3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4
[3,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 0
[2,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => 3
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => 2
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => 1
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => 0
[12] => [] => [] => [] => 0
[11,1] => [1] => [[1]] => [1] => 0
[10,2] => [2] => [[1,2]] => [1,2] => 1
[10,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[9,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[9,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[9,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[8,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 3
[8,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[8,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[8,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[8,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[7,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 4
[7,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 3
[7,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 3
[7,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[7,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[7,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[7,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[6,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 5
[6,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 4
[6,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 4
[6,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 3
[6,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 4
[6,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 3
[6,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 2
[6,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3
[6,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[6,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[5,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 5
[5,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 4
[5,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 5
[5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 4
[5,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 3
[5,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 4
[5,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 4
[5,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 3
[5,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 2
[5,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3
[5,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 0
[4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 6
[4,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 5
[4,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 5
[4,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 4
[4,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => 3
[4,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 5
[4,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 4
[4,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 4
[4,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 3
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 2
[4,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4
[4,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 0
[3,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 6
[3,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 5
[3,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 4
[3,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => 5
[3,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 4
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => 3
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => 2
[3,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => 3
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => 2
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => 1
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => 0
[2,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => 5
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => 4
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,3,4,1,2] => 3
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => 2
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => 1
[2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => 0
[13] => [] => [] => [] => 0
[12,1] => [1] => [[1]] => [1] => 0
[11,2] => [2] => [[1,2]] => [1,2] => 1
[11,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[10,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[10,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[10,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[9,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 3
[9,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[9,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[9,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[9,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[8,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 4
[8,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 3
[8,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 3
[8,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[8,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[8,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[8,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[7,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 5
[7,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 4
[7,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 4
[7,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 3
[7,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 4
[7,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 3
[7,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 2
[7,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3
[7,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[7,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[6,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 5
[6,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 5
[6,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 4
[6,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 5
[6,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 4
[6,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 3
[6,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 4
[6,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 4
[6,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 3
[6,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 2
[6,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3
[6,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 0
[5,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 6
[5,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 5
[5,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => 4
[5,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 6
[5,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 5
[5,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 5
[5,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 4
[5,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => 3
[5,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 5
[5,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 4
[5,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 4
[5,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 3
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 2
[5,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4
[5,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 0
[4,4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => 6
[4,4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 6
[4,4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 5
[4,4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 5
[4,4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => 4
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => 3
[4,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 6
[4,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 5
[4,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 4
[4,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => 5
[4,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 4
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => 3
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => 2
[4,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => 3
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => 2
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => 1
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => 0
[3,3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => 6
[3,3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => 6
[3,3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [10,9,7,8,4,5,6,1,2,3] => 5
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [10,9,8,7,4,5,6,1,2,3] => 4
[3,3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,4,5,1,2,3] => 5
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,4,5,1,2,3] => 4
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,5,1,2,3] => 3
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => 2
[3,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => 5
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => 4
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,3,4,1,2] => 3
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => 2
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => 1
[3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,3,2,1] => 0
[14] => [] => [] => [] => 0
[13,1] => [1] => [[1]] => [1] => 0
[12,2] => [2] => [[1,2]] => [1,2] => 1
[12,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[11,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[11,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[11,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[10,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 3
[10,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[10,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[10,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[10,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[9,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 4
[9,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 3
[9,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 3
[9,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[9,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[9,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[9,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[8,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 5
[8,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 4
[8,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 4
[8,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 3
[8,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 4
[8,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 3
[8,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 2
[8,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3
[8,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[8,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[7,7] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 6
[7,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 5
[7,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 5
[7,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 4
[7,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 5
[7,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 4
[7,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 3
[7,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 4
[7,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 4
[7,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 3
[7,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 2
[7,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3
[7,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 0
[6,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 6
[6,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 5
[6,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 6
[6,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 5
[6,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => 4
[6,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 6
[6,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 5
[6,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 5
[6,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 4
[6,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => 3
[6,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 5
[6,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 4
[6,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 4
[6,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 3
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 2
[6,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4
[6,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 0
[5,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 7
[5,5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => 6
[5,5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => 6
[5,5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => 5
[5,5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => 4
[5,4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => 6
[5,4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 6
[5,4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 5
[5,4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 5
[5,4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => 4
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => 3
[5,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 6
[5,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 5
[5,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 4
[5,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => 5
[5,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 4
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => 3
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => 2
[5,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => 3
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => 2
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => 1
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => 0
[4,4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => 7
[4,4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => 6
[4,4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => 7
[4,4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 6
[4,4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [10,9,8,5,6,7,1,2,3,4] => 5
[4,4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => 6
[4,4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,1,2,3,4] => 5
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,1,2,3,4] => 4
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => 3
[4,3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => 6
[4,3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => 6
[4,3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [10,9,7,8,4,5,6,1,2,3] => 5
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [10,9,8,7,4,5,6,1,2,3] => 4
[4,3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,4,5,1,2,3] => 5
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,4,5,1,2,3] => 4
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,5,1,2,3] => 3
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => 2
[4,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => 5
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => 4
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,3,4,1,2] => 3
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => 2
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => 1
[4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,3,2,1] => 0
[15] => [] => [] => [] => 0
[14,1] => [1] => [[1]] => [1] => 0
[13,2] => [2] => [[1,2]] => [1,2] => 1
[13,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[12,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[12,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[12,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[11,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 3
[11,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[11,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[11,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[11,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[10,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 4
[10,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 3
[10,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 3
[10,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[10,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[10,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[10,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[9,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 5
[9,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 4
[9,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 4
[9,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 3
[9,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 4
[9,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 3
[9,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 2
[9,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3
[9,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[9,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[8,7] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 6
[8,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 5
[8,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 5
[8,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 4
[8,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 5
[8,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 4
[8,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 3
[8,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 4
[8,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 4
[8,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 3
[8,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 2
[8,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3
[8,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 0
[7,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 6
[7,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 6
[7,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 5
[7,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 6
[7,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 5
[7,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => 4
[7,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 6
[7,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 5
[7,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 5
[7,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 4
[7,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => 3
[7,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 5
[7,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 4
[7,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 4
[7,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 3
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 2
[7,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4
[7,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1
[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]] => [8,7,6,5,4,3,2,1] => 0
[6,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 7
[6,6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => 6
[6,6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => 5
[6,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 7
[6,5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => 6
[6,5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => 6
[6,5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => 5
[6,5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => 4
[6,4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => 6
[6,4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 6
[6,4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 5
[6,4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 5
[6,4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => 4
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => 3
[6,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 6
[6,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 5
[6,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 4
[6,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => 5
[6,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 4
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => 3
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => 2
[6,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => 3
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => 2
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => 1
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => 0
[5,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => 8
[5,5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => 7
[5,5,3,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => 7
[5,5,3,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => 6
[5,5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => 6
[5,5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,1,2,3,4,5] => 5
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,1,2,3,4,5] => 4
[5,4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => 7
[5,4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => 6
[5,4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => 7
[5,4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 6
[5,4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [10,9,8,5,6,7,1,2,3,4] => 5
[5,4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => 6
[5,4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,1,2,3,4] => 5
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,1,2,3,4] => 4
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => 3
[5,3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => 6
[5,3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => 6
[5,3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [10,9,7,8,4,5,6,1,2,3] => 5
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [10,9,8,7,4,5,6,1,2,3] => 4
[5,3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,4,5,1,2,3] => 5
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,4,5,1,2,3] => 4
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,5,1,2,3] => 3
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => 2
[5,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => 5
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => 4
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,3,4,1,2] => 3
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => 2
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => 1
[5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,3,2,1] => 0
[16] => [] => [] => [] => 0
[15,1] => [1] => [[1]] => [1] => 0
[14,2] => [2] => [[1,2]] => [1,2] => 1
[14,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[13,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[13,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[13,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[12,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 3
[12,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[12,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[12,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[12,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[11,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 4
[11,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 3
[11,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 3
[11,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[11,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[11,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[11,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[10,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 5
[10,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 4
[10,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 4
[10,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 3
[10,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 4
[10,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 3
[10,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 2
[10,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3
[10,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[10,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[9,7] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 6
[9,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 5
[9,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 5
[9,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 4
[9,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 5
[9,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 4
[9,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 3
[9,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 4
[9,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 4
[9,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 3
[9,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 2
[9,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3
[9,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 0
[8,8] => [8] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => 7
[8,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 6
[8,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 6
[8,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 5
[8,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 6
[8,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 5
[8,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => 4
[8,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 6
[8,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 5
[8,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 5
[8,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 4
[8,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => 3
[8,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 5
[8,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 4
[8,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 4
[8,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 3
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 2
[8,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4
[8,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 0
[7,7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => 7
[7,7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => 6
[7,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 7
[7,6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => 6
[7,6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => 5
[7,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 7
[7,5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => 6
[7,5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => 6
[7,5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => 5
[7,5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => 4
[7,4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => 6
[7,4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 6
[7,4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 5
[7,4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 5
[7,4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => 4
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => 3
[7,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 6
[7,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 5
[7,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 4
[7,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => 5
[7,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 4
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => 3
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => 2
[7,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => 3
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => 2
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => 1
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => 0
[6,6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => 8
[6,6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [10,7,8,9,1,2,3,4,5,6] => 7
[6,6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [9,10,7,8,1,2,3,4,5,6] => 7
[6,6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [10,9,7,8,1,2,3,4,5,6] => 6
[6,6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [10,9,8,7,1,2,3,4,5,6] => 5
[6,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => 8
[6,5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => 7
[6,5,3,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => 7
[6,5,3,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => 6
[6,5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => 6
[6,5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,1,2,3,4,5] => 5
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,1,2,3,4,5] => 4
[6,4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => 7
[6,4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => 6
[6,4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => 7
[6,4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 6
[6,4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [10,9,8,5,6,7,1,2,3,4] => 5
[6,4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => 6
[6,4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,1,2,3,4] => 5
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,1,2,3,4] => 4
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => 3
[6,3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => 6
[6,3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => 6
[6,3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [10,9,7,8,4,5,6,1,2,3] => 5
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [10,9,8,7,4,5,6,1,2,3] => 4
[6,3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,4,5,1,2,3] => 5
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,4,5,1,2,3] => 4
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,5,1,2,3] => 3
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => 2
[6,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => 5
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => 4
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,3,4,1,2] => 3
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => 2
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => 1
[6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,3,2,1] => 0
[17] => [] => [] => [] => 0
[16,1] => [1] => [[1]] => [1] => 0
[15,2] => [2] => [[1,2]] => [1,2] => 1
[15,1,1] => [1,1] => [[1],[2]] => [2,1] => 0
[14,3] => [3] => [[1,2,3]] => [1,2,3] => 2
[14,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 1
[14,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 0
[13,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 3
[13,3,1] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 2
[13,2,2] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2
[13,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1
[13,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 0
[12,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 4
[12,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 3
[12,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 3
[12,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[12,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[12,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1
[12,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 0
[11,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 5
[11,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 4
[11,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 4
[11,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 3
[11,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 4
[11,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 3
[11,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 2
[11,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3
[11,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2
[11,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 0
[10,7] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 6
[10,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 5
[10,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 5
[10,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 4
[10,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 5
[10,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 4
[10,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 3
[10,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 4
[10,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 4
[10,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 3
[10,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 2
[10,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3
[10,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 0
[9,8] => [8] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => 7
[9,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 6
[9,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 6
[9,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 5
[9,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 6
[9,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 5
[9,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => 4
[9,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 6
[9,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 5
[9,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 5
[9,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 4
[9,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => 3
[9,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 5
[9,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 4
[9,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 4
[9,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 3
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 2
[9,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4
[9,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 0
[8,8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => 7
[8,7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => 7
[8,7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => 6
[8,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 7
[8,6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => 6
[8,6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => 5
[8,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 7
[8,5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => 6
[8,5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => 6
[8,5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => 5
[8,5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => 4
[8,4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => 6
[8,4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 6
[8,4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 5
[8,4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 5
[8,4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => 4
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => 3
[8,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 6
[8,3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 5
[8,3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 4
[8,3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => 5
[8,3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 4
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => 3
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => 2
[8,2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => 3
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => 2
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => 1
[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]] => [9,8,7,6,5,4,3,2,1] => 0
[7,7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [8,9,10,1,2,3,4,5,6,7] => 8
[7,7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [10,8,9,1,2,3,4,5,6,7] => 7
[7,7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => 6
[7,6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => 8
[7,6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [10,7,8,9,1,2,3,4,5,6] => 7
[7,6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [9,10,7,8,1,2,3,4,5,6] => 7
[7,6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [10,9,7,8,1,2,3,4,5,6] => 6
[7,6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [10,9,8,7,1,2,3,4,5,6] => 5
[7,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => 8
[7,5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => 7
[7,5,3,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => 7
[7,5,3,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => 6
[7,5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => 6
[7,5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,1,2,3,4,5] => 5
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,1,2,3,4,5] => 4
[7,4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => 7
[7,4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => 6
[7,4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => 7
[7,4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 6
[7,4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [10,9,8,5,6,7,1,2,3,4] => 5
[7,4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => 6
[7,4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,1,2,3,4] => 5
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,1,2,3,4] => 4
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => 3
[7,3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => 6
[7,3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => 6
[7,3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [10,9,7,8,4,5,6,1,2,3] => 5
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [10,9,8,7,4,5,6,1,2,3] => 4
[7,3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,4,5,1,2,3] => 5
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,4,5,1,2,3] => 4
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,5,1,2,3] => 3
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => 2
[7,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => 5
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => 4
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,3,4,1,2] => 3
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => 2
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => 1
[7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => 0
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,3,2,1] => 0
[6,6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [7,8,9,10,11,12,1,2,3,4,5,6] => 10
[7,6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [7,8,9,10,11,12,1,2,3,4,5,6] => 10
[10,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 6
[10,10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => 9
[11,7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [8,9,10,1,2,3,4,5,6,7] => 8
[9,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 7
[8,6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => 8
[10,6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => 8
[15,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => 8
[9,6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => 8
[10,7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [8,9,10,1,2,3,4,5,6,7] => 8
[9,9] => [9] => [[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => 8
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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:
4,1 5,2 6,3,2 7,4,4 8,5,6,3 9,6,8,6,1 10,7,10,9,6 11,8,12,12,11,2
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 3$
$F_{4} = 4 + q$
$F_{5} = 5 + 2\ q$
$F_{6} = 6 + 3\ q + 2\ q^{2}$
$F_{7} = 7 + 4\ q + 4\ q^{2}$
$F_{8} = 8 + 5\ q + 6\ q^{2} + 3\ q^{3}$
$F_{9} = 9 + 6\ q + 8\ q^{2} + 6\ q^{3} + q^{4}$
$F_{10} = 10 + 7\ q + 10\ q^{2} + 9\ q^{3} + 6\ q^{4}$
$F_{11} = 11 + 8\ q + 12\ q^{2} + 12\ q^{3} + 11\ q^{4} + 2\ q^{5}$
Description
The number of ascents of a permutation.
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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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first row removal
Description
Removes the first entry of an integer partition
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reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
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