Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
St001695: Standard tableaux ⟶ ℤ
Values
[1,0,1,0,1,0] => [2,1] => [1] => [[1]] => 0
[1,0,1,1,0,0] => [1,1] => [1] => [[1]] => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[1,0,1,0,1,1,0,0] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[1,0,1,1,0,0,1,0] => [3,1,1] => [1,1] => [[1],[2]] => 0
[1,0,1,1,0,1,0,0] => [2,1,1] => [1,1] => [[1],[2]] => 0
[1,0,1,1,1,0,0,0] => [1,1,1] => [1,1] => [[1],[2]] => 0
[1,1,0,0,1,0,1,0] => [3,2] => [2] => [[1,2]] => 0
[1,1,0,0,1,1,0,0] => [2,2] => [2] => [[1,2]] => 0
[1,1,0,1,0,0,1,0] => [3,1] => [1] => [[1]] => 0
[1,1,0,1,0,1,0,0] => [2,1] => [1] => [[1]] => 0
[1,1,0,1,1,0,0,0] => [1,1] => [1] => [[1]] => 0
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [1,1] => [[1],[2]] => 0
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [1,1] => [[1],[2]] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [1,1] => [[1],[2]] => 0
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [3] => [[1,2,3]] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [3] => [[1,2,3]] => 0
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [2] => [[1,2]] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [2] => [[1,2]] => 0
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [2] => [[1,2]] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [1] => [[1]] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [1] => [[1]] => 0
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1] => [[1]] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [1] => [[1]] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
>>> Load all 999 entries. <<<[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [2] => [[1,2]] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [2] => [[1,2]] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [2] => [[1,2]] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [2] => [[1,2]] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [1] => [[1]] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [1] => [[1]] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [1] => [[1]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1] => [[1]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [1] => [[1]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 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],[2],[3],[4],[5]] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 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],[2],[3],[4]] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => [4,3,1] => [[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] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [5] => [[1,2,3,4,5]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [5] => [[1,2,3,4,5]] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [1] => [[1]] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [1] => [[1]] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [1] => [[1]] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [1] => [[1]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1] => [[1]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [1] => [[1]] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 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],[2],[3],[4],[5],[6]] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 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],[2],[3],[4],[5]] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 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],[2],[3],[4]] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => [4,3,1] => [[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] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [5,1,1] => [[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] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 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],[2],[3]] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [7,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [7,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => [5,1] => [[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] => [5,1] => [[1,2,3,4,5],[6]] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => [6] => [[1,2,3,4,5,6]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [6] => [[1,2,3,4,5,6]] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [5] => [[1,2,3,4,5]] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [5] => [[1,2,3,4,5]] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [5] => [[1,2,3,4,5]] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [1] => [[1]] => 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],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [1] => [[1]] => 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] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 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],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [1,1] => [[1],[2]] => 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] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 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] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 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] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => [5] => [[1,2,3,4,5]] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,5] => [5] => [[1,2,3,4,5]] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => [6] => [[1,2,3,4,5,6]] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => [7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,6] => [6] => [[1,2,3,4,5,6]] => 0
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => [7] => [[1,2,3,4,5,6,7]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [9,7] => [7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,8] => [8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8] => [8] => [[1,2,3,4,5,6,7,8]] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 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] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 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] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 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] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 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] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 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] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 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],[2],[3],[4],[5],[6]] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 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] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 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] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 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] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 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] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 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] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 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] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 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] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 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] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 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] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 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],[2],[3],[4],[5]] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 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],[2],[3],[4]] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1] => [5,1,1] => [[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] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 0
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 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],[2],[3]] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [4,2] => [[1,2,3,4],[5,6]] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [1,1] => [[1],[2]] => 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],[2]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => [6] => [[1,2,3,4,5,6]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [6] => [[1,2,3,4,5,6]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [5] => [[1,2,3,4,5]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [5] => [[1,2,3,4,5]] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [3] => [[1,2,3]] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [1] => [[1]] => 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]] => 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]] => 0
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [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],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [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],[2]] => 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],[2],[3]] => 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],[2],[3],[4]] => 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],[2],[3],[4],[5]] => 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],[2],[3],[4],[5],[6]] => 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] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => [2,1] => [[1,2],[3]] => 0
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 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] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [3] => [[1,2,3]] => 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] => [[1,2,3],[4,5,6]] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [1,1] => [[1],[2]] => 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] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 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],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [1,1] => [[1],[2]] => 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] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 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] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [6] => [[1,2,3,4,5,6]] => 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] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 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] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 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] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 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] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1] => [[1]] => 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] => [1] => [[1]] => 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] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [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] => [2,1] => [[1,2],[3]] => 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] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 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] => [2,1] => [[1,2],[3]] => 0
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => [7] => [[1,2,3,4,5,6,7]] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => [1,1,1] => [[1],[2],[3]] => 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] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 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] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 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] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [2] => [[1,2]] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [7,6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => [5,1] => [[1,2,3,4,5],[6]] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [4,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [3,1] => [[1,2,3],[4]] => 0
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [2,2] => [[1,2],[3,4]] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [1] => [[1]] => 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] => [1,1,1] => [[1],[2],[3]] => 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] => [1,1,1,1] => [[1],[2],[3],[4]] => 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] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7] => [7] => [[1,2,3,4,5,6,7]] => 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] => [1,1] => [[1],[2]] => 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] => [2,2,1] => [[1,2],[3,4],[5]] => 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],[2]] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [1,1] => [[1],[2]] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [8,3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 0
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 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] => [2,1,1] => [[1,2],[3],[4]] => 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] => [2] => [[1,2]] => 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] => [[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]] => 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] => [1] => [[1]] => 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] => [1] => [[1]] => 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] => [1] => [[1]] => 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] => [1] => [[1]] => 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] => [1] => [[1]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [5] => [[1,2,3,4,5]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [4] => [[1,2,3,4]] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [3,1] => [[1,2,3],[4]] => 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] => [2,2,1] => [[1,2],[3,4],[5]] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [3,2] => [[1,2,3],[4,5]] => 0
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searching the database for the individual values of this statistic
Description
The natural comajor 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 comajor index of a tableau of size $n$ with natural descent set $D$ is then $\sum_{d\in D} n-d$.
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 comajor index of a tableau of size $n$ with natural descent set $D$ is then $\sum_{d\in D} n-d$.
Map
first row removal
Description
Removes the first entry of an integer partition
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 $(n-1,\ldots,2,1)$.
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.
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