- FindStat

Identifier

Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000883: Permutations ⟶ ℤ

Values

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

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

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

[1,0,1,0,1,0] => [2,1] => [[1,2],[3]] => [3,1,2] => 1

[1,0,1,1,0,0] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,0,0,1,0] => [2] => [[1,2]] => [1,2] => 1

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

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

[1,0,1,0,1,0,1,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1

[1,0,1,0,1,1,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2

[1,0,1,1,0,0,1,0] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 1

[1,0,1,1,0,1,0,0] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1

[1,0,1,1,1,0,0,0] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[1,1,0,0,1,0,1,0] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 1

[1,1,0,0,1,1,0,0] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2

[1,1,0,1,0,0,1,0] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 1

[1,1,0,1,0,1,0,0] => [2,1] => [[1,2],[3]] => [3,1,2] => 1

[1,1,0,1,1,0,0,0] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,1,0,0,0,1,0] => [3] => [[1,2,3]] => [1,2,3] => 1

[1,1,1,0,0,1,0,0] => [2] => [[1,2]] => [1,2] => 1

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

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

[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 1

[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 2

[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 1

[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 1

[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3

[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 1

[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 2

[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 1

[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 1

[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2

[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 1

[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1

[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1

[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 1

[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 2

[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 1

[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 1

[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3

[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 1

[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 2

[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 1

[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1

[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2

[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 1

[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 1

[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1

[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[1,1,1,0,0,0,1,0,1,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 1

[1,1,1,0,0,0,1,1,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 2

[1,1,1,0,0,1,0,0,1,0] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 1

[1,1,1,0,0,1,0,1,0,0] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 1

[1,1,1,0,0,1,1,0,0,0] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2

[1,1,1,0,1,0,0,0,1,0] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 1

[1,1,1,0,1,0,0,1,0,0] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 1

[1,1,1,0,1,0,1,0,0,0] => [2,1] => [[1,2],[3]] => [3,1,2] => 1

[1,1,1,0,1,1,0,0,0,0] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,1,1,0,0,0,0,1,0] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[1,1,1,1,0,0,0,1,0,0] => [3] => [[1,2,3]] => [1,2,3] => 1

[1,1,1,1,0,0,1,0,0,0] => [2] => [[1,2]] => [1,2] => 1

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

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

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

[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4

[1,0,1,1,0,1,0,1,1,0,0,0] => [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] => 2

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

[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 1

[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3

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

[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 2

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

[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => 1

[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 1

[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2

[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => 1

[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => 1

[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 1

[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1

[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => 2

[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => 1

[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => 1

[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4

[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => 3

[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 1

[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 2

[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => 1

[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 1

[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 1

[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3

[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => 2

[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => 1

[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 1

[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 2

[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => 1

[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 1

[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 1

[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2

[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => 1

>>> Load all 584 entries. <<<

[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 1

[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1

[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1

[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => 1

[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 3

[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => 2

[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => 1

[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 1

[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 2

[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => 1

[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 1

[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 1

[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3

[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => 1

[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => 2

[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => 1

[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 1

[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 2

[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 1

[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 1

[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1

[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2

[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 1

[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 1

[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 1

[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1

[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 1

[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 2

[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 1

[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 1

[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 2

[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 1

[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 1

[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 1

[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2

[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 1

[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 1

[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 1

[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [[1,2],[3]] => [3,1,2] => 1

[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [[1,2,3]] => [1,2,3] => 1

[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [[1,2]] => [1,2] => 1

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

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

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

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

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

[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [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] => 2

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

[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => 1

[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2

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

[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => 1

[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 1

[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1

[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 6

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

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

[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [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] => 2

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

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 1

[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3

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

[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 2

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

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => 1

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 1

[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2

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

[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => 1

[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => 1

[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 1

[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1

[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => 2

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => 1

[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => 1

[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => 3

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 1

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 2

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => 1

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 1

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 1

[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => 2

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => 1

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 1

[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 2

[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [10,9,7,8,1,2,3,4,5,6] => 1

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => 1

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 1

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 1

[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2

[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => 1

[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => 1

[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 1

[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1

[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1

[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => 1

[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 3

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => 2

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => 1

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 1

[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 2

[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [9,10,7,8,1,2,3,4,5,6] => 1

[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => 1

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 1

[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 1

[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => 1

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => 2

[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [10,7,8,9,1,2,3,4,5,6] => 1

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => 1

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 1

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 2

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => 1

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 1

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 1

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2

[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 1

[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 1

[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 1

[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 1

[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1

[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => 2

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => 1

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 1

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 2

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 1

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 1

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 1

[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 2

[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 1

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 1

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 1

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 1

[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2

[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 1

[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 1

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 1

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 1

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [3,1,2] => 1

[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 1

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [[1,2,3]] => [1,2,3] => 1

[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [[1,2]] => [1,2] => 1

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

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

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

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

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

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

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

[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 7

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

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

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

[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [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] => 2

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

[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => 1

[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2

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

[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => 1

[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 1

[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 6

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

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

[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4

[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [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] => 2

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

[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 1

[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3

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

[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 2

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

[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => 1

[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 1

[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2

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

[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => 1

[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => 1

[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 1

[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => 2

[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => 1

[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => 1

[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 4

[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => 3

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 1

[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 2

[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => 1

[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 1

[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 1

[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3

[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => 2

[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => 1

[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 1

[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 2

[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [10,9,7,8,1,2,3,4,5,6] => 1

[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => 1

[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 1

[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 1

[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2

[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => 1

[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => 1

[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => 1

[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 1

[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1

[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 3

[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => 2

[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => 1

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 2

[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [9,10,7,8,1,2,3,4,5,6] => 1

[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => 1

[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 1

[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 1

[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3

[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => 1

[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => 2

[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [10,7,8,9,1,2,3,4,5,6] => 1

[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => 1

[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 2

[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [10,8,9,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => 1

[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 1

[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 1

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2

[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 1

[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 1

[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 1

[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 1

[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

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

[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => 2

[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => 1

[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 1

[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 2

[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [8,9,10,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 1

[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 1

[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 1

[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 2

[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 1

[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 1

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 1

[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 1

[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2

[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 1

[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 1

[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 1

[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 1

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [3,1,2] => 1

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 1

[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [[1,2,3]] => [1,2,3] => 1

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [[1,2]] => [1,2] => 1

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

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

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => 1

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

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => [[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => 1

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => 1

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

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

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => 1

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => 1

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [9,10,1,2,3,4,5,6,7,8] => 1

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => 1

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

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

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

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

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

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

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

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

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

[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1

[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 7

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

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

[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => 1

[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 2

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

[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => 1

[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 1

[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1

[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 6

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

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

[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 4

[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 1

[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 3

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

[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 2

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

[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 1

[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 2

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

[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => 1

[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1

[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => 2

[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => 3

[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 2

[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 1

[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 1

[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3

[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 2

[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 1

[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 1

[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => 1

[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => 1

[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 1

[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 1

[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1

[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 3

[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => 2

[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => 1

[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 2

[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 1

[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 1

[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3

[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => 1

[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => 2

[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [10,7,8,9,1,2,3,4,5,6] => 1

[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => 1

[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 2

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [10,8,9,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => 1

[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 1

[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 1

[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1

[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 1

[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 1

[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 1

[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1

[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

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

[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => 2

[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 2

[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [8,9,10,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 1

[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 2

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 1

[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 1

[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 1

[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 1

[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 1

[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 1

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [3,1,2] => 1

[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 1

[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [[1,2,3]] => [1,2,3] => 1

[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [[1,2]] => [1,2] => 1

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

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

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

[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [[1,2]] => [1,2] => 1

[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 2

[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 1

[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [[1,2]] => [1,2] => 1

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

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => 1

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => [[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => 1

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => 1

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

[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 4

[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 5

[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 6

[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 7

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

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 1

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 1

[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [[1,2,3,4]] => [1,2,3,4] => 1

[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => [1,2,3] => 1

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => 1

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

[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2

[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 2

[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 3

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

[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1

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

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

[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => 1

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

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

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

[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 1

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

[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 1

[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 1

[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => 1

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

[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [3,1,2] => 1

[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [3,1,2] => 1

[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 1

[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => [1,2,3] => 1

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [10,8,9,1,2,3,4,5,6,7] => 1

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

[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [4,1,2,3] => 1

[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 1

[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => 1

[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 1

[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 3

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 1

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 1

[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 1

[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1

[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 1

[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1

[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 1

[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 1

[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [3,2,1] => 3

[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 1

[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 2

[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 1

[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [3,4,1,2] => 2

[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 2

[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => [1,2,3] => 1

[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [2,1] => 2

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => 1

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 1

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 1

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 1

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 1

[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => 2

[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 2

[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => 1

[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 3

[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 2

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$F_{1} = q$

$F_{2} = 2\ q$

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

$F_{4} = 10\ q + 3\ q^{2} + q^{3}$

$F_{5} = 29\ q + 9\ q^{2} + 3\ q^{3} + q^{4}$

Description

The number of longest increasing subsequences of a permutation.

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

to partition

Description

The cut-out partition of a Dyck path.
The partition

$\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition

$(n-1,\ldots,2,1)$ when cutting out

$D$ considered as a path from

$(0,0)$ to

$(n,n)$ .
In other words,

$\lambda_{i}$ is the number of down-steps before the

$(n+1-i)$ -th up-step of

$D$ .
This map is a bijection between Dyck paths of size

$n$ and partitions inside the staircase partition

$(n-1,\ldots,2,1)$ .

Map

initial tableau

Description

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

$1$ through

$n$ row by row.