- FindStat

Identifier

Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000007: Permutations ⟶ ℤ

Values

[1] => [] => [] => [] => 0

[2] => [] => [] => [] => 0

[1,1] => [1] => [[1]] => [1] => 1

[3] => [] => [] => [] => 0

[2,1] => [1] => [[1]] => [1] => 1

[1,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[4] => [] => [] => [] => 0

[3,1] => [1] => [[1]] => [1] => 1

[2,2] => [2] => [[1,2]] => [1,2] => 1

[2,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[5] => [] => [] => [] => 0

[4,1] => [1] => [[1]] => [1] => 1

[3,2] => [2] => [[1,2]] => [1,2] => 1

[3,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[2,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[2,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[6] => [] => [] => [] => 0

[5,1] => [1] => [[1]] => [1] => 1

[4,2] => [2] => [[1,2]] => [1,2] => 1

[4,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[3,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[3,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[3,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[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] => 3

[2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[7] => [] => [] => [] => 0

[6,1] => [1] => [[1]] => [1] => 1

[5,2] => [2] => [[1,2]] => [1,2] => 1

[5,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[4,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[4,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[4,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[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] => 3

[3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[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] => 6

[8] => [] => [] => [] => 0

[7,1] => [1] => [[1]] => [1] => 1

[6,2] => [2] => [[1,2]] => [1,2] => 1

[6,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[5,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[5,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[5,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[4,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[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] => 3

[4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[3,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 2

[3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 3

[3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[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] => 4

[2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 5

[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] => 6

[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] => 7

[9] => [] => [] => [] => 0

[8,1] => [1] => [[1]] => [1] => 1

[7,2] => [2] => [[1,2]] => [1,2] => 1

[7,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[6,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[6,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[6,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[5,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[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] => 3

[5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[4,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 2

[4,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 2

[4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 3

[4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 2

[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] => 4

[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] => 4

[3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 5

[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] => 6

[2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 4

[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] => 5

[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] => 6

[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] => 7

[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 8

[10] => [] => [] => [] => 0

[9,1] => [1] => [[1]] => [1] => 1

[8,2] => [2] => [[1,2]] => [1,2] => 1

[8,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[7,3] => [3] => [[1,2,3]] => [1,2,3] => 1

>>> Load all 878 entries. <<<

[7,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[7,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[6,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[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] => 3

[6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[5,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[5,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 2

[5,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 2

[5,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 3

[5,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[5,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[5,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 2

[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] => 2

[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] => 4

[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] => 4

[4,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 5

[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] => 6

[3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 3

[3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 3

[3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 4

[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] => 5

[3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 4

[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] => 5

[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] => 6

[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] => 7

[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] => 5

[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] => 6

[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] => 7

[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 8

[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] => 9

[11] => [] => [] => [] => 0

[10,1] => [1] => [[1]] => [1] => 1

[9,2] => [2] => [[1,2]] => [1,2] => 1

[9,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[8,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[8,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[8,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[7,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[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] => 3

[7,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[6,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[6,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 2

[6,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 2

[6,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 3

[6,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[6,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[5,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 2

[5,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 2

[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] => 2

[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] => 4

[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] => 4

[5,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 5

[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] => 6

[4,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 2

[4,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 3

[4,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 4

[4,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 3

[4,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 3

[4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 4

[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] => 5

[4,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 4

[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] => 5

[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] => 6

[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] => 7

[3,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 3

[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] => 5

[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] => 6

[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] => 5

[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] => 6

[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] => 7

[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 8

[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] => 5

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 10

[12] => [] => [] => [] => 0

[11,1] => [1] => [[1]] => [1] => 1

[10,2] => [2] => [[1,2]] => [1,2] => 1

[10,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[9,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[9,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[9,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[8,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[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] => 3

[8,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[7,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[7,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 2

[7,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 2

[7,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 3

[7,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[7,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[7,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[6,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 1

[6,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 2

[6,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 2

[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] => 2

[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] => 4

[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] => 4

[6,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 5

[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] => 6

[5,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 2

[5,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 3

[5,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 2

[5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 3

[5,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 4

[5,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 3

[5,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 3

[5,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 4

[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] => 5

[5,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 4

[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] => 5

[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] => 6

[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] => 7

[4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 2

[4,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 3

[4,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 3

[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] => 5

[4,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 3

[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] => 5

[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] => 6

[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] => 5

[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] => 6

[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] => 7

[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 8

[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] => 3

[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] => 4

[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] => 5

[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] => 4

[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] => 5

[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] => 6

[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] => 7

[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] => 5

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 10

[13] => [] => [] => [] => 0

[12,1] => [1] => [[1]] => [1] => 1

[11,2] => [2] => [[1,2]] => [1,2] => 1

[11,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[10,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[10,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[10,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[9,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[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] => 3

[9,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[8,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[8,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 2

[8,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 2

[8,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 3

[8,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[8,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[8,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[7,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 1

[7,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 2

[7,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 2

[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] => 2

[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] => 4

[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] => 4

[7,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 5

[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] => 6

[6,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 2

[6,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 2

[6,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 3

[6,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 2

[6,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 3

[6,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 4

[6,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 3

[6,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 3

[6,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 4

[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] => 5

[6,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 4

[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] => 5

[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] => 6

[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] => 7

[5,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 2

[5,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 3

[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] => 2

[5,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 3

[5,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 3

[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] => 5

[5,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 3

[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] => 5

[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] => 6

[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] => 5

[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] => 6

[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] => 7

[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 8

[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] => 3

[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] => 3

[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] => 4

[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] => 4

[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] => 5

[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] => 6

[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] => 3

[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] => 4

[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] => 5

[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] => 4

[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] => 5

[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] => 6

[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] => 7

[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] => 5

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 4

[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] => 4

[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] => 6

[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] => 6

[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] => 7

[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] => 8

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 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] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,3,2,1] => 12

[14] => [] => [] => [] => 0

[13,1] => [1] => [[1]] => [1] => 1

[12,2] => [2] => [[1,2]] => [1,2] => 1

[12,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[11,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[11,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[11,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[10,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[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] => 3

[10,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[9,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[9,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 2

[9,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 2

[9,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 3

[9,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[9,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[9,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[8,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 1

[8,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 2

[8,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 2

[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] => 2

[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] => 4

[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] => 4

[8,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 5

[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] => 6

[7,7] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 1

[7,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 2

[7,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 2

[7,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 3

[7,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 2

[7,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 3

[7,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 4

[7,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 3

[7,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 3

[7,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 4

[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] => 5

[7,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 4

[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] => 5

[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] => 6

[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] => 7

[6,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 2

[6,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 3

[6,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 2

[6,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 3

[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] => 2

[6,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 3

[6,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 3

[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] => 5

[6,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 3

[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] => 5

[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] => 6

[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] => 5

[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] => 6

[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] => 7

[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 8

[5,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 2

[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] => 3

[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] => 3

[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] => 4

[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] => 5

[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] => 3

[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] => 3

[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] => 4

[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] => 4

[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] => 5

[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] => 6

[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] => 3

[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] => 4

[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] => 5

[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] => 4

[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] => 5

[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] => 6

[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] => 7

[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] => 5

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 3

[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] => 4

[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] => 3

[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] => 4

[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] => 4

[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] => 6

[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] => 7

[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] => 4

[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] => 4

[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] => 6

[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] => 6

[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] => 7

[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] => 8

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 10

[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] => 12

[15] => [] => [] => [] => 0

[14,1] => [1] => [[1]] => [1] => 1

[13,2] => [2] => [[1,2]] => [1,2] => 1

[13,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[12,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[12,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[12,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[11,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[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] => 3

[11,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[10,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[10,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 2

[10,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 2

[10,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 3

[10,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[10,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[10,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[9,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 1

[9,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 2

[9,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 2

[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] => 2

[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] => 4

[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] => 4

[9,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 5

[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] => 6

[8,7] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 1

[8,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 2

[8,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 2

[8,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 3

[8,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 2

[8,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 3

[8,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 4

[8,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 3

[8,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 3

[8,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 4

[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] => 5

[8,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 4

[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] => 5

[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] => 6

[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] => 7

[7,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 2

[7,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 2

[7,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 3

[7,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 2

[7,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 3

[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] => 2

[7,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 3

[7,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 3

[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] => 5

[7,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 3

[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] => 5

[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] => 6

[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] => 5

[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] => 6

[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] => 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]] => [8,7,6,5,4,3,2,1] => 8

[6,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 2

[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] => 3

[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] => 4

[6,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 2

[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] => 3

[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] => 3

[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] => 4

[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] => 5

[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] => 3

[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] => 3

[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] => 4

[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] => 4

[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] => 5

[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] => 6

[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] => 3

[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] => 4

[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] => 5

[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] => 4

[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] => 5

[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] => 6

[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] => 7

[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] => 5

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 2

[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] => 3

[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] => 3

[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] => 4

[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] => 4

[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] => 6

[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] => 3

[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] => 4

[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] => 3

[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] => 4

[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] => 4

[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] => 6

[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] => 7

[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] => 4

[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] => 4

[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] => 6

[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] => 6

[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] => 7

[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] => 8

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 10

[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] => 12

[16] => [] => [] => [] => 0

[15,1] => [1] => [[1]] => [1] => 1

[14,2] => [2] => [[1,2]] => [1,2] => 1

[14,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[13,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[13,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[13,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[12,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[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] => 3

[12,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[11,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[11,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 2

[11,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 2

[11,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 3

[11,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[11,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[11,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[10,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 1

[10,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 2

[10,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 2

[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] => 2

[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] => 4

[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] => 4

[10,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 5

[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] => 6

[9,7] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 1

[9,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 2

[9,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 2

[9,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 3

[9,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 2

[9,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 3

[9,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 4

[9,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 3

[9,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 3

[9,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 4

[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] => 5

[9,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 4

[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] => 5

[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] => 6

[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] => 7

[8,8] => [8] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => 1

[8,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 2

[8,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 2

[8,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 3

[8,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 2

[8,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 3

[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] => 2

[8,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 3

[8,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 3

[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] => 5

[8,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 3

[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] => 5

[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] => 6

[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] => 5

[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] => 6

[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] => 7

[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 8

[7,7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => 2

[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] => 3

[7,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 2

[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] => 3

[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] => 4

[7,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 2

[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] => 3

[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] => 3

[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] => 4

[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] => 5

[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] => 3

[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] => 3

[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] => 4

[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] => 4

[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] => 5

[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] => 6

[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] => 3

[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] => 4

[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] => 5

[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] => 4

[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] => 5

[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] => 6

[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] => 7

[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] => 5

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 2

[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] => 3

[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] => 3

[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] => 4

[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] => 2

[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] => 3

[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] => 3

[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] => 4

[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] => 4

[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] => 6

[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] => 3

[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] => 4

[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] => 3

[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] => 4

[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] => 4

[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] => 6

[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] => 7

[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] => 4

[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] => 4

[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] => 6

[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] => 6

[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] => 7

[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] => 8

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 10

[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] => 12

[17] => [] => [] => [] => 0

[16,1] => [1] => [[1]] => [1] => 1

[15,2] => [2] => [[1,2]] => [1,2] => 1

[15,1,1] => [1,1] => [[1],[2]] => [2,1] => 2

[14,3] => [3] => [[1,2,3]] => [1,2,3] => 1

[14,2,1] => [2,1] => [[1,2],[3]] => [3,1,2] => 2

[14,1,1,1] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[13,4] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[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] => 3

[13,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[12,5] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[12,4,1] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 2

[12,3,2] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 2

[12,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 3

[12,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 3

[12,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 4

[12,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[11,6] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 1

[11,5,1] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 2

[11,4,2] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 2

[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] => 2

[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] => 4

[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] => 4

[11,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 5

[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] => 6

[10,7] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 1

[10,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 2

[10,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 2

[10,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 3

[10,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 2

[10,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 3

[10,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 4

[10,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 3

[10,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 3

[10,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 4

[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] => 5

[10,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 4

[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] => 5

[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] => 6

[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] => 7

[9,8] => [8] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => 1

[9,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 2

[9,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 2

[9,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 3

[9,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 2

[9,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 3

[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] => 2

[9,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 3

[9,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 3

[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] => 5

[9,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 3

[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] => 5

[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] => 6

[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] => 5

[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] => 6

[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] => 7

[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 8

[8,8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => 2

[8,7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => 2

[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] => 3

[8,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 2

[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] => 3

[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] => 4

[8,5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 2

[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] => 3

[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] => 3

[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] => 4

[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] => 5

[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] => 3

[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] => 3

[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] => 4

[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] => 4

[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] => 5

[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] => 6

[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] => 3

[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] => 4

[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] => 5

[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] => 4

[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] => 5

[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] => 6

[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] => 7

[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] => 5

[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] => 6

[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] => 7

[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] => 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]] => [9,8,7,6,5,4,3,2,1] => 9

[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] => 2

[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] => 3

[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] => 4

[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] => 2

[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] => 3

[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] => 3

[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] => 4

[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] => 2

[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] => 3

[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] => 3

[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] => 4

[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] => 4

[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] => 6

[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] => 3

[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] => 4

[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] => 3

[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] => 4

[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] => 4

[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] => 6

[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] => 7

[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] => 4

[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] => 4

[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] => 6

[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] => 6

[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] => 7

[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] => 8

[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] => 6

[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] => 7

[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] => 8

[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] => 9

[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] => 10

[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] => 12

[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] => 2

[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] => 2

[10,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 2

[10,10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => 1

[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] => 2

[9,6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 2

[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] => 2

[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] => 2

[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] => 2

[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] => 2

[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] => 2

[9,9] => [9] => [[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => 1

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$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 1 + q + q^{2}$

$F_{4} = 1 + 2\ q + q^{2} + q^{3}$

$F_{5} = 1 + 2\ q + 2\ q^{2} + q^{3} + q^{4}$

$F_{6} = 1 + 3\ q + 3\ q^{2} + 2\ q^{3} + q^{4} + q^{5}$

$F_{7} = 1 + 3\ q + 4\ q^{2} + 3\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$

$F_{8} = 1 + 4\ q + 5\ q^{2} + 5\ q^{3} + 3\ q^{4} + 2\ q^{5} + q^{6} + q^{7}$

$F_{9} = 1 + 4\ q + 7\ q^{2} + 6\ q^{3} + 5\ q^{4} + 3\ q^{5} + 2\ q^{6} + q^{7} + q^{8}$

$F_{10} = 1 + 5\ q + 8\ q^{2} + 9\ q^{3} + 7\ q^{4} + 5\ q^{5} + 3\ q^{6} + 2\ q^{7} + q^{8} + q^{9}$

$F_{11} = 1 + 5\ q + 10\ q^{2} + 11\ q^{3} + 10\ q^{4} + 7\ q^{5} + 5\ q^{6} + 3\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$

Description

The number of saliances of the permutation.
A saliance is a right-to-left maximum. This can be described as an occurrence of the mesh pattern

$([1], {(1,1)})$ , i.e., the upper right quadrant is shaded, see [1].

Map

first row removal

Description

Removes the first entry of an integer partition

Map

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.

Map

initial tableau

Description

Sends an integer partition to the standard tableau obtained by filling the numbers

$1$ through

$n$ row by row.