- FindStat

Identifier

Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
St001696: Standard tableaux ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => 0

[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => 0

[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [5,3,3] => [[1,2,3,4,5],[6,7,8],[9,10,11]] => 0

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

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

[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [5,4,3,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]] => 0

[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 0

[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 0

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

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

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

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

[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 0

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => 0

[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 0

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

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

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

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

[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 0

[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 0

[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 0

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

[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 0

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

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

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

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

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

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

[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 0

>>> Load all 693 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 0

[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 0

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

[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 0

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [5,3,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]] => 0

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

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => 0

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => 0

[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [5,3,3] => [[1,2,3,4,5],[6,7,8],[9,10,11]] => 0

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

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

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [5,4,3,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]] => 0

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 0

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 0

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

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

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

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

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 0

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => 0

[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 0

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

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

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

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

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 0

[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => 0

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 0

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 0

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

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 0

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

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

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

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

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

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

[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 0

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

[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [5,2,2,1,1] => [[1,2,3,4,5],[6,7],[8,9],[10],[11]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 0

[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 0

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 0

[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 0

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 0

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

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

[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 0

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

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

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

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

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

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

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

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

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

[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 0

[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 0

[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => [5,3,3,1,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]] => 0

[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => [5,3,1,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10],[11]] => 0

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

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

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

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

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

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

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

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 0

[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 0

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

[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 0

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [5,3,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]] => 0

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

[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => 0

[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => 0

[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [5,3,3] => [[1,2,3,4,5],[6,7,8],[9,10,11]] => 0

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

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

[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [5,4,3,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]] => 0

[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 0

[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 0

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

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

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

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

[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 0

[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => 0

[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 0

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

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

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

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

[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 0

[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => 0

[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 0

[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 0

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

[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 0

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

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

[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 0

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

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

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

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

[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => [4,4,3,1,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]] => 0

[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 0

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

[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [5,2,2,1,1] => [[1,2,3,4,5],[6,7],[8,9],[10],[11]] => 0

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

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

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

[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 0

[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 0

[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 0

[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => [5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => 0

[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 0

[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 0

[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 0

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

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

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 0

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

[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => 0

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

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

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

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

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

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

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

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

[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 0

[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 0

[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 0

[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 0

[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => 0

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

[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => [4,4,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => [4,2,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9,10],[11]] => 0

[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => [4,3,2,2] => [[1,2,3,4],[5,6,7],[8,9],[10,11]] => 0

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => [5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => 0

[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 0

[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 0

[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,4] => [4,4,2,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]] => 0

[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => [4,4,3,2] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]] => 0

[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1] => [5,4,2,2] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]] => 0

[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3] => [5,4,2,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]] => 0

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 0

[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1] => [5,3,1,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10],[11]] => 0

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

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

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

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

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

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

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

[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 0

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

[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => [3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 0

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

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

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

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

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

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

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

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

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

[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => 0

[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => 0

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

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

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

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

[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 0

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 0

[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3,1] => [5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => 0

[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 0

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

[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 0

[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 0

[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 0

[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 0

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

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

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 0

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

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

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

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

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

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

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

[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => [7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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]] => 0

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

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

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

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

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

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

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => [5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => 0

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

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

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

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

[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0] => [8,2,1] => [5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => 0

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 0

[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 0

[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 0

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

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

[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 0

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

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

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

[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

Description

The natural major index of a standard Young tableau.
A natural descent of a standard tableau

$T$ is an entry

$i$ such that

$i+1$ appears in a higher row than

$i$ in English notation.
The natural major index of a tableau with natural descent set

$D$ is then

$\sum_{d\in D} d$ .

Map

2-conjugate

Description

Return a partition with the same number of odd parts and number of even parts interchanged with the number of cells with zero leg and odd arm length.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by

$s$ and interchanges the number of parts divisible by

$s$ and the number of cells with zero leg length and arm length congruent to

$s-1$ modulo

$s$ .
In particular, for

$s=1$ the involution is conjugation, hence the name.

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.