Identifier
Values
[1,0,1,0] => [1] => [[1]] => [[1]] => 1
[1,0,1,0,1,0] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[1,0,1,1,0,0] => [1,1] => [[1],[2]] => [[1],[2]] => 2
[1,1,0,0,1,0] => [2] => [[1,2]] => [[1,2]] => 1
[1,1,0,1,0,0] => [1] => [[1]] => [[1]] => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,2,6],[3,4],[5]] => 1
[1,0,1,0,1,1,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [[1,3],[2,5],[4]] => 2
[1,0,1,1,0,0,1,0] => [3,1,1] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 1
[1,0,1,1,0,1,0,0] => [2,1,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 1
[1,0,1,1,1,0,0,0] => [1,1,1] => [[1],[2],[3]] => [[1],[2],[3]] => 3
[1,1,0,0,1,0,1,0] => [3,2] => [[1,2,3],[4,5]] => [[1,2,5],[3,4]] => 1
[1,1,0,0,1,1,0,0] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[1,1,0,1,0,0,1,0] => [3,1] => [[1,2,3],[4]] => [[1,2,4],[3]] => 1
[1,1,0,1,0,1,0,0] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[1,1,0,1,1,0,0,0] => [1,1] => [[1],[2]] => [[1],[2]] => 2
[1,1,1,0,0,0,1,0] => [3] => [[1,2,3]] => [[1,2,3]] => 1
[1,1,1,0,0,1,0,0] => [2] => [[1,2]] => [[1,2]] => 1
[1,1,1,0,1,0,0,0] => [1] => [[1]] => [[1]] => 1
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,2,8],[3,4],[5,6],[7]] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3],[2,5],[4,7],[6]] => 3
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,2,5],[3,4,8],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,2,3,8],[4,5],[6],[7]] => 1
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,2,7],[3,4],[5],[6]] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3],[2,6],[4],[5]] => 2
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 1
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 1
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1],[2],[3],[4]] => 4
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,2,5],[3,4,8],[6,7]] => 2
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,3,8],[4,5],[6,7]] => 1
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[1,2,7],[3,4],[5,6]] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3],[2,5],[4,6]] => 3
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,2,3,8],[4,5,6],[7]] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[1,2,5],[3,4,7],[6]] => 2
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,2,3,7],[4,5],[6]] => 1
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,2,6],[3,4],[5]] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [[1,3],[2,5],[4]] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 1
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [[1],[2],[3]] => 3
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [[1,2,3,7],[4,5,6]] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [[1,2,5],[3,4,6]] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [[1,2,3,4],[5,6]] => [[1,2,3,6],[4,5]] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [[1,2,3],[4,5]] => [[1,2,5],[3,4]] => 1
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [[1,2,3],[4]] => [[1,2,4],[3]] => 1
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [[1],[2]] => [[1],[2]] => 2
[1,1,1,1,0,0,0,0,1,0] => [4] => [[1,2,3,4]] => [[1,2,3,4]] => 1
[1,1,1,1,0,0,0,1,0,0] => [3] => [[1,2,3]] => [[1,2,3]] => 1
[1,1,1,1,0,0,1,0,0,0] => [2] => [[1,2]] => [[1,2]] => 1
[1,1,1,1,0,1,0,0,0,0] => [1] => [[1]] => [[1]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3],[2,5],[4,8],[6],[7]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,2,8],[3,4],[5],[6],[7]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3],[2,7],[4],[5],[6]] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1],[2],[3],[4],[5]] => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [[1,2,9],[3,4],[5,6],[7,8]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3],[2,5],[4,7],[6,8]] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,2,8],[3,4],[5,6],[7]] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,2,5],[3,4,8],[6],[7]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,2,3,8],[4,5],[6],[7]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,2,7],[3,4],[5],[6]] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3],[2,6],[4],[5]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1],[2],[3],[4]] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,2,5],[3,4,8],[6,7]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [[1,2,3,4,9],[5,6],[7,8]] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,3,8],[4,5],[6,7]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[1,2,7],[3,4],[5,6]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3],[2,5],[4,6]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,2,3,8],[4,5,6],[7]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[1,2,5],[3,4,7],[6]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,2,3,4,8],[5,6],[7]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,2,3,7],[4,5],[6]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,2,6],[3,4],[5]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [[1,3],[2,5],[4]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [[1],[2],[3]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [[1,2,3,4,9],[5,6,7,8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,2,3,7],[4,5,6,8]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [[1,2,3,7],[4,5,6]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [[1,2,5],[3,4,6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [[1,2,3,4,5],[6,7]] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [[1,2,3,6],[4,5]] => 1
>>> Load all 415 entries. <<<
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [[1,2,5],[3,4]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [[1,2,3],[4]] => [[1,2,4],[3]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [[1],[2]] => [[1],[2]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [[1,2,3,4]] => [[1,2,3,4]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [[1,2,3]] => [[1,2,3]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [[1,2]] => [[1,2]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [[1]] => [[1]] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3],[2,8],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1],[2],[3],[4],[5],[6]] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [[1,3],[2,5],[4,7],[6,9],[8,10]] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3],[2,5],[4,8],[6],[7]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,2,8],[3,4],[5],[6],[7]] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3],[2,7],[4],[5],[6]] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1],[2],[3],[4],[5]] => 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [[1,2,9],[3,4],[5,6],[7,8]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3],[2,5],[4,7],[6,8]] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,2,8],[3,4],[5,6],[7]] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,2,5],[3,4,8],[6],[7]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,2,3,8],[4,5],[6],[7]] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,2,7],[3,4],[5],[6]] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3],[2,6],[4],[5]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1],[2],[3],[4]] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,2,5],[3,4,8],[6,7]] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [[1,2,3,4,9],[5,6],[7,8]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,3,8],[4,5],[6,7]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[1,2,7],[3,4],[5,6]] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3],[2,5],[4,6]] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,2,3,8],[4,5,6],[7]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[1,2,5],[3,4,7],[6]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,2,3,4,8],[5,6],[7]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,2,3,7],[4,5],[6]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,2,6],[3,4],[5]] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [[1,3],[2,5],[4]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [[1],[2],[3]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,2,3,4,9],[5,6,7,8,10]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [[1,2,3,4,9],[5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,2,3,7],[4,5,6,8]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [[1,2,3,7],[4,5,6]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [[1,2,5],[3,4,6]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[1,2,3,4,5,8],[6,7]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [[1,2,3,4,5],[6,7]] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [[1,2,3,6],[4,5]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [[1,2,5],[3,4]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [[1,2,4],[3]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [[1],[2]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [[1,2,3,4]] => [[1,2,3,4]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [[1,2,3]] => [[1,2,3]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [[1,2]] => [[1,2]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [[1]] => [[1]] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1],[2],[3],[4],[5],[6],[7]] => 7
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] => 6
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3],[2,8],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1],[2],[3],[4],[5],[6]] => 6
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [[1,3],[2,5],[4,7],[6,9],[8,10]] => 5
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3],[2,5],[4,8],[6],[7]] => 3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,2,8],[3,4],[5],[6],[7]] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3],[2,7],[4],[5],[6]] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1],[2],[3],[4],[5]] => 5
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [[1,2,9],[3,4],[5,6],[7,8]] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[1,3],[2,5],[4,7],[6,8]] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,2,8],[3,4],[5,6],[7]] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,2,5],[3,4,8],[6],[7]] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,2,3,8],[4,5],[6],[7]] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,2,7],[3,4],[5],[6]] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3],[2,6],[4],[5]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1],[2],[3],[4]] => 4
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,2,5],[3,4,8],[6,7]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [[1,2,3,4,9],[5,6],[7,8]] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,3,8],[4,5],[6,7]] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[1,2,7],[3,4],[5,6]] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3],[2,5],[4,6]] => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,2,3,8],[4,5,6],[7]] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[1,2,5],[3,4,7],[6]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,2,3,4,8],[5,6],[7]] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,2,3,7],[4,5],[6]] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,2,6],[3,4],[5]] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [[1,3],[2,5],[4]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,9],[7],[8]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [[1],[2],[3]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,2,3,4,9],[5,6,7,8,10]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [[1,2,3,4,9],[5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,2,3,7],[4,5,6,8]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [[1,2,3,4,5,6,10],[7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [[1,2,3,7],[4,5,6]] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [[1,2,5],[3,4,6]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [[1,2,3,4,5,6,9],[7,8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[1,2,3,4,5,8],[6,7]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [[1,2,3,4,5],[6,7]] => [[1,2,3,4,7],[5,6]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [[1,2,3,6],[4,5]] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [[1,2,5],[3,4]] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [[1,2,4],[3]] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [[1],[2]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [[1,2,3,4]] => [[1,2,3,4]] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [[1,2,3]] => [[1,2,3]] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [[1,2]] => [[1,2]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [[1]] => [[1]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => [[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => [[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,9],[8]] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 9
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => [[1,2,3,4,5,6,13],[7,8,9,10,11,12,14]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,8] => [[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16]] => [[1,2,3,4,5,6,7,15],[8,9,10,11,12,13,14,16]] => 2
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1],[2],[3],[4],[5],[6],[7]] => 7
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] => 6
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[1,3],[2,8],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1],[2],[3],[4],[5],[6]] => 6
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [[1,3],[2,5],[4,7],[6,9],[8,10]] => 5
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[1,3],[2,5],[4,8],[6],[7]] => 3
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[1,2,8],[3,4],[5],[6],[7]] => 1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[1,3],[2,7],[4],[5],[6]] => 2
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1],[2],[3],[4],[5]] => 5
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,2,8],[3,4],[5,6],[7]] => 1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[1,2,5],[3,4,8],[6],[7]] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,2,3,8],[4,5],[6],[7]] => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,2,7],[3,4],[5],[6]] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3],[2,6],[4],[5]] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1],[2],[3],[4]] => 4
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,2,5],[3,4,8],[6,7]] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,3,8],[4,5],[6,7]] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[1,2,7],[3,4],[5,6]] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3],[2,5],[4,6]] => 3
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,2,3,8],[4,5,6],[7]] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[1,2,5],[3,4,7],[6]] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[1,2,3,4,8],[5,6],[7]] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[1,2,3,7],[4,5],[6]] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,2,6],[3,4],[5]] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [[1,3],[2,5],[4]] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,9],[7],[8]] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [[1],[2],[3]] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,2,3,4,9],[5,6,7,8,10]] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,2,3,7],[4,5,6,8]] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [[1,2,3,4,5,6,10],[7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [[1,2,3,7],[4,5,6]] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [[1,2,5],[3,4,6]] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [[1,2,3,4,5,6,9],[7,8]] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [[1,2,3,6],[4,5]] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [[1,2,5],[3,4]] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [[1,2,4],[3]] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [[1],[2]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [[1,2,3,4]] => [[1,2,3,4]] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [[1,2,3]] => [[1,2,3]] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [[1,2]] => [[1,2]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [[1]] => [[1]] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [[1],[2]] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [[1,2]] => [[1,2]] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [[1],[2]] => 2
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [[1,3],[2,5],[4]] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [[1,2,5],[3,4]] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [[1,2]] => [[1,2]] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => [[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => [[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,9],[8]] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [[1]] => [[1]] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [[1],[2],[3]] => 3
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [[1],[2],[3],[4]] => 4
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [[1],[2],[3],[4],[5]] => 5
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [[1],[2],[3],[4],[5],[6]] => 6
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1],[2],[3],[4],[5],[6],[7]] => 7
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [[1]] => [[1]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [[1,2,3,4]] => [[1,2,3,4]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => [[1,2,3]] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [[1,2,5],[3,4,6]] => 2
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 1
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 1
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 9
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 1
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,9] => [[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17,18]] => [[1,2,3,4,5,6,7,8,17],[9,10,11,12,13,14,15,16,18]] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [[1,2,4],[3]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => 2
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [[1,3],[2]] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [[1,2,6],[3,4],[5]] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => [[1,2,3]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => [[1,2,3,4,5,6,13],[7,8,9,10,11,12,14]] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [[1,2,4],[3]] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [[1,2,3,6],[4,5]] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,2,3,8],[4,5,6],[7]] => 1
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [[1,3],[2,5],[4,6]] => 3
[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] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] => 6
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 1
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 1
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[1,2,8],[3,4],[5,6],[7]] => 1
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [[1],[2],[3]] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,10] => [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]] => [[1,2,3,4,5,6,7,8,9,19],[10,11,12,13,14,15,16,17,18,20]] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 1
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [[1,3],[2,6],[4],[5]] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[1,2,7],[3,4],[5],[6]] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [[1,2,5],[3,4,6]] => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => [[1,2,3]] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [[1],[2]] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,9],[8]] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,2,3,4,9],[5,6,7,8,10]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[1,2,3,7],[4,5,6,8]] => 2
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[1,2,5],[3,4,8],[6,7]] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The row containing the largest entry of a standard tableau.
Map
inverse promotion
Description
The inverse promotion of a standard Young tableau.
This map replaces the entry $1$ of the tableau with $n+1$, uses the jeu de taquin to move it to the outer rim, and finally decreases all entries by one.
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.