Processing math: 100%

Identifier
Values
[1,0] => [[1],[]] => [] => 0
[1,0,1,0] => [[1,1],[]] => [] => 0
[1,1,0,0] => [[2],[]] => [] => 0
[1,0,1,0,1,0] => [[1,1,1],[]] => [] => 0
[1,0,1,1,0,0] => [[2,1],[]] => [] => 0
[1,1,0,0,1,0] => [[2,2],[1]] => [1] => 0
[1,1,0,1,0,0] => [[3],[]] => [] => 0
[1,1,1,0,0,0] => [[2,2],[]] => [] => 0
[1,0,1,0,1,0,1,0] => [[1,1,1,1],[]] => [] => 0
[1,0,1,0,1,1,0,0] => [[2,1,1],[]] => [] => 0
[1,0,1,1,0,0,1,0] => [[2,2,1],[1]] => [1] => 0
[1,0,1,1,0,1,0,0] => [[3,1],[]] => [] => 0
[1,0,1,1,1,0,0,0] => [[2,2,1],[]] => [] => 0
[1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => [1,1] => 0
[1,1,0,0,1,1,0,0] => [[3,2],[1]] => [1] => 0
[1,1,0,1,0,0,1,0] => [[3,3],[2]] => [2] => 1
[1,1,0,1,0,1,0,0] => [[4],[]] => [] => 0
[1,1,0,1,1,0,0,0] => [[3,3],[1]] => [1] => 0
[1,1,1,0,0,0,1,0] => [[2,2,2],[1]] => [1] => 0
[1,1,1,0,0,1,0,0] => [[3,2],[]] => [] => 0
[1,1,1,0,1,0,0,0] => [[2,2,2],[]] => [] => 0
[1,1,1,1,0,0,0,0] => [[3,3],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1],[]] => [] => 0
[1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]] => [1] => 0
[1,0,1,0,1,1,0,1,0,0] => [[3,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1],[]] => [] => 0
[1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]] => [1] => 0
[1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]] => [2] => 1
[1,0,1,1,0,1,0,1,0,0] => [[4,1],[]] => [] => 0
[1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]] => [1] => 0
[1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]] => [1] => 0
[1,0,1,1,1,0,0,1,0,0] => [[3,2,1],[]] => [] => 0
[1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1],[]] => [] => 0
[1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]] => [] => 0
[1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => [1,1] => 0
[1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => [2,1] => 0
[1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]] => [1] => 0
[1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => [1,1] => 0
[1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]] => [2] => 1
[1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]] => [3] => 1
[1,1,0,1,0,1,0,1,0,0] => [[5],[]] => [] => 0
[1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => [2] => 1
[1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => [2,1] => 0
[1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => [1] => 0
[1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => [1,1] => 0
[1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => [1] => 0
[1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => [1,1] => 0
[1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]] => [1] => 0
[1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]] => [2] => 1
[1,1,1,0,0,1,0,1,0,0] => [[4,2],[]] => [] => 0
[1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => [1] => 0
[1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]] => [1] => 0
[1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]] => [] => 0
[1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2],[]] => [] => 0
[1,1,1,0,1,1,0,0,0,0] => [[3,3,2],[]] => [] => 0
[1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => [2] => 1
[1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => [] => 0
[1,1,1,1,0,0,1,0,0,0] => [[3,3,3],[1]] => [1] => 0
[1,1,1,1,0,1,0,0,0,0] => [[4,4],[]] => [] => 0
[1,1,1,1,1,0,0,0,0,0] => [[3,3,3],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]] => [1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1],[]] => [] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]] => [1] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1],[]] => [] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]] => [1] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]] => [1] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1],[]] => [] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => [2,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]] => [1] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]] => [2] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]] => [3] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1],[]] => [] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]] => [2] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => [2,1] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]] => [1] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [[4,4,1],[1]] => [1] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]] => [1] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]] => [2] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1],[]] => [] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1],[1]] => [1] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1],[1]] => [1] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1],[]] => [] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1],[]] => [] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1],[]] => [] => 0
>>> Load all 676 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1],[2]] => [2] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1],[]] => [] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [[3,3,3,1],[1]] => [1] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1],[]] => [] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [[3,3,3,1],[]] => [] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => [1,1] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => [2,1] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]] => [1] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => [2,1] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => [2,1,1] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => [1,1] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2],[1,1]] => [1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]] => [2] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => [2,2] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]] => [3] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]] => [4] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]] => [] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => [3] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => [3,2] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => [2] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4],[2,2]] => [2,2] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [[5,5],[2]] => [2] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => [2,2,1] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => [2,1] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => [3,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => [1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3],[2,1]] => [2,1] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1,1]] => [2,1,1] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3],[1,1]] => [1,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3],[1,1]] => [1,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [[5,4],[1]] => [1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4],[2,1]] => [2,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [[5,5],[1]] => [1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4],[1,1]] => [1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => [1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => [2,1] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]] => [1] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1]] => [1,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => [2,2] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]] => [2] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]] => [3] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]] => [] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [[4,4,2],[2]] => [2] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1]] => [2,1] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [[4,3,2],[1]] => [1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1]] => [1,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [[4,4,2],[1]] => [1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2],[1,1]] => [1,1] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2],[1]] => [1] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2],[2]] => [2] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2],[]] => [] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2],[1]] => [1] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2],[1]] => [1] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2],[]] => [] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2],[]] => [] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2],[]] => [] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2],[2]] => [2] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2],[]] => [] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2],[1]] => [1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [[4,4,2],[]] => [] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2],[]] => [] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2]] => [2,2] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [[4,3,3],[2]] => [2] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [[4,4,3],[3]] => [3] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3],[]] => [] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [[4,4,3],[2]] => [2] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1]] => [2,1] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [[4,3,3],[1]] => [1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1]] => [1,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3],[1]] => [1] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [[4,4,4],[3]] => [3] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4],[]] => [] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4],[2]] => [2] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5],[]] => [] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4],[1]] => [1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3],[2]] => [2] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [[4,3,3],[]] => [] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3],[1]] => [1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3],[]] => [] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3],[]] => [] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [[4,4,4],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]] => [1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => [1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]] => [2] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1],[]] => [] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => [2,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => [1] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]] => [3] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1,1],[]] => [] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => [2,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => [1] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => [3,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => [2] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => [3,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => [3] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]] => [4] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1],[]] => [] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,1],[1,1]] => [1,1] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1],[]] => [] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1],[]] => [] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,1],[]] => [] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,1],[]] => [] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[4,4,2,1],[]] => [] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2,1],[]] => [] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1],[]] => [] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => [1] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4,1],[]] => [] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,1],[2]] => [2] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5,1],[]] => [] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,1],[1]] => [1] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[4,3,3,1],[]] => [] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,1],[1]] => [1] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,1],[]] => [] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3,1],[]] => [] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[4,4,4,1],[]] => [] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => [1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => [2,1] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => [4,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]] => [1] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => [3,2] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => [4,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => [2] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => [3,3] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => [4,3] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => [3] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]] => [4] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]] => [5] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]] => [] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[6,6],[4]] => [4] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[5,5,5],[4,3]] => [4,3] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[6,5],[3]] => [3] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[5,5,5],[3,3]] => [3,3] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[6,6],[3]] => [3] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3,2]] => [3,3,2] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[6,4],[2]] => [2] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4],[3,2]] => [3,2] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2,2]] => [3,2,2] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[5,4,4],[2,2]] => [2,2] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,2]] => [2,2,2] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[5,5,4],[2,2]] => [2,2] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[5,5,5],[4,2]] => [4,2] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[6,5],[2]] => [2] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[5,5,5],[3,2]] => [3,2] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[6,6],[2]] => [2] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[5,5,5],[2,2]] => [2,2] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[6,3],[1]] => [1] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3,1]] => [3,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2,1]] => [2,1] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,1]] => [2,2,1] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => [2,1] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1,1]] => [1,1] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1,1]] => [2,1,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => [1,1] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]] => [2,1,1] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1,1]] => [1,1] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3,1]] => [3,3,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[6,4],[1]] => [1] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2,1]] => [3,2,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => [2,1] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,1]] => [2,2,1] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => [2,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[5,5,5],[4,1]] => [4,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[6,5],[1]] => [1] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[6,6],[1]] => [1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[5,5,5],[2,1]] => [2,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1,1]] => [3,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1,1]] => [1,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1,1]] => [2,1,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[5,5,4],[1,1]] => [1,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[4,4,4,4],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[5,5,5],[1,1]] => [1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2],[]] => [] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3]] => [3] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2]] => [2] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2]] => [2,2] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => [2] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1]] => [1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => [2,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1]] => [1,1] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1,1]] => [1,1,1] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => [1,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => [1] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => [2,1] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[5,5,2],[1]] => [1] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1]] => [1,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2],[]] => [] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,2],[2]] => [2] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,2],[1]] => [1] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1]] => [1,1] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[4,4,2,2],[1]] => [1] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1]] => [1,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,2],[]] => [] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2,2],[1]] => [1] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,2],[]] => [] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2],[]] => [] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2,2],[]] => [] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,2],[]] => [] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2,2],[1]] => [1] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[4,4,2,2],[]] => [] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2,2],[]] => [] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[5,3,2],[]] => [] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => [2] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]] => [1] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1]] => [1,1] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => [1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[4,4,4,2],[3]] => [3] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[5,4,2],[]] => [] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]] => [2] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[5,5,2],[]] => [] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,2],[1]] => [1] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3,2],[2]] => [2] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[4,3,3,2],[]] => [] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,2],[1]] => [1] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,2],[]] => [] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3,2],[]] => [] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[4,4,4,2],[]] => [] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3],[]] => [] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => [3] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => [2] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2]] => [2,2] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => [2] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2,1]] => [2,2,1] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1]] => [1] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => [2,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1,1]] => [2,1,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1]] => [1,1] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1,1]] => [1,1,1] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => [1,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => [3,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => [1] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => [2,1] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1]] => [1] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1]] => [1,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[6,4],[]] => [] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3]] => [3] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2]] => [3,2] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2]] => [2] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2]] => [2,2] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2]] => [2] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[5,5,5],[4]] => [4] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[6,5],[]] => [] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3]] => [3] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[6,6],[]] => [] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[5,5,5],[2]] => [2] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1]] => [3,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1]] => [1] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1]] => [2,1] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[5,5,4],[1]] => [1] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[4,4,4,4],[1,1]] => [1,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[5,5,5],[1]] => [1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2]] => [2,2] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[4,3,3,3],[2]] => [2] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[4,4,3,3],[3]] => [3] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[5,3,3],[]] => [] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[4,4,3,3],[2]] => [2] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1]] => [2,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[4,3,3,3],[1]] => [1] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1]] => [1,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[4,4,3,3],[1]] => [1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[4,4,4,3],[3]] => [3] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[5,4,3],[]] => [] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[4,4,4,3],[2]] => [2] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[5,5,3],[]] => [] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[4,4,4,3],[1]] => [1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[3,3,3,3,3],[2]] => [2] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[4,3,3,3],[]] => [] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[3,3,3,3,3],[1]] => [1] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[4,4,3,3],[]] => [] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[3,3,3,3,3],[]] => [] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[4,4,4,3],[]] => [] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[4,4,4,4],[3]] => [3] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[5,4,4],[]] => [] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[4,4,4,4],[2]] => [2] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[5,5,4],[]] => [] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[4,4,4,4],[1]] => [1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[5,5,5],[]] => [] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[4,4,4,4],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1,1],[1]] => [1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1,1],[1]] => [1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1,1],[2,1]] => [2,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1,1],[2]] => [2] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1,1],[]] => [] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1,1],[2,1]] => [2,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1,1],[3,1]] => [3,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1,1],[3,2]] => [3,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1,1],[]] => [] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2,1],[2,1]] => [2,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3,1],[3,2]] => [3,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3,1],[4,2]] => [4,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4,1],[3,3]] => [3,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4,1],[4,3]] => [4,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4,1],[3]] => [3] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1],[]] => [] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,1],[]] => [] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2,1],[]] => [] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3,1],[]] => [] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[5,5,5,1],[1]] => [1] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[3,3,3,3,3,1],[]] => [] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[4,4,4,3,1],[]] => [] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[5,5,4,1],[]] => [] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[4,4,4,4,1],[1]] => [1] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[5,5,5,1],[]] => [] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[4,4,4,4,1],[]] => [] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[6,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[6,5,2],[4,1]] => [4,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[6,4,3],[3,2]] => [3,2] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[6,5,3],[4,2]] => [4,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[6,6,3],[5,2]] => [5,2] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[6,4,4],[3,3]] => [3,3] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[6,5,4],[4,3]] => [4,3] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[6,6,4],[5,3]] => [5,3] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[7,4],[3]] => [3] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[6,6,6],[5,5]] => [5,5] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[7,7],[6]] => [6] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8],[]] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[7,7],[5]] => [5] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[6,6,6],[5,4]] => [5,4] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[6,6,6],[4,4]] => [4,4] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[7,7],[4]] => [4] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[5,5,5,5],[4,4,3]] => [4,4,3] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[5,5,5,5],[4,3,3]] => [4,3,3] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[5,5,5,5],[3,3,3]] => [3,3,3] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[6,6,6],[5,3]] => [5,3] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[4,4,4,4,4],[3,3,3,2]] => [3,3,3,2] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3,2,2]] => [3,3,2,2] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2,2,2]] => [3,2,2,2] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[5,5,5,5],[4,4,2]] => [4,4,2] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[5,5,5,5],[4,3,2]] => [4,3,2] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[5,5,5,5],[3,3,2]] => [3,3,2] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[6,6,6],[4,2]] => [4,2] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[5,5,5,5],[4,2,2]] => [4,2,2] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[5,5,5,5],[3,2,2]] => [3,2,2] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2,1,1]] => [2,2,2,1,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[4,4,4,4,4],[3,3,3,1]] => [3,3,3,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[5,5,5,5],[4,4,1]] => [4,4,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[5,5,5,5],[4,3,1]] => [4,3,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[5,5,5,5],[3,3,1]] => [3,3,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[5,5,5,5],[4,2,1]] => [4,2,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[5,5,5,5],[3,2,1]] => [3,2,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,2],[]] => [] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,2],[]] => [] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[7,3],[]] => [] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[4,4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3,2]] => [3,3,2] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2,2]] => [3,2,2] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3,1]] => [3,3,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2,1]] => [3,2,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[5,5,5,5],[4,1]] => [4,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[3,3,3,3,3,3],[2]] => [2] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[4,4,4,4,3],[3]] => [3] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[5,5,5,4],[4]] => [4] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[4,4,4,4,4],[3,1]] => [3,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[5,5,5,5],[4]] => [4] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[4,4,4,4,4],[3]] => [3] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[5,5,5,5,5],[4]] => [4] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[5,5,5,5,1],[]] => [] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[5,5,5,5,5,5],[4]] => [4] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[4,4,4,4,4,4],[3]] => [3] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[4,4,4,4,4,1],[]] => [] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[5,5,5,5,5,1],[]] => [] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[6,6,6,6,6,6],[5]] => [5] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[6,6,6,6,6],[5]] => [5] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[5,5,5,5,4],[4]] => [4] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[5,5,5,5,5],[4,1]] => [4,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[5,5,5,4,1],[]] => [] => 0
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[5,5,5,5,1],[1]] => [1] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[6,6,6,6,1],[]] => [] => 0
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[6,6,6,6,6,1],[]] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[9],[]] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[8,8],[6]] => [6] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,2],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1,1],[]] => [] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1,1],[]] => [] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1,1,1],[]] => [] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,1,1],[]] => [] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1,1,1],[]] => [] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,2,1],[]] => [] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,1,1],[]] => [] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[9,1],[]] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[10],[]] => [] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4,4],[3,3,3,3,3]] => [3,3,3,3,3] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[5,5,5,5,5],[4,4,4,4]] => [4,4,4,4] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[6,6,6,6],[5,5,5]] => [5,5,5] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[7,7,7],[6,6]] => [6,6] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[8,8],[7]] => [7] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]] => [2,2,2,2,2,2,2] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,3],[2,2,2,2,2,1]] => [2,2,2,2,2,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4,4,4],[3,3,3,3,3,3]] => [3,3,3,3,3,3] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4,4],[3,3,3,3,2]] => [3,3,3,3,2] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[5,5,5,5,5,5],[4,4,4,4,4]] => [4,4,4,4,4] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[5,5,5,5,5],[4,4,4,3]] => [4,4,4,3] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[6,6,6,6,6],[5,5,5,5]] => [5,5,5,5] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[6,6,6,6],[5,5,4]] => [5,5,4] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[7,7,7,7],[6,6,6]] => [6,6,6] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[7,7,7],[6,5]] => [6,5] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[8,8,8],[7,7]] => [7,7] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[9,9],[8]] => [8] => 4
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Description
The number of cells of the partition whose leg is zero and arm is odd.
This statistic is equidistributed with St000143The largest repeated part of a partition., see [1].
Map
skew partition
Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let D be a Dyck path of semilength n. The parallelogram polyomino γ(D) is defined as follows: let ˜D=d0d1d2n+1 be the Dyck path obtained by prepending an up step and appending a down step to D. Then, the upper path of γ(D) corresponds to the sequence of steps of ˜D with even indices, and the lower path of γ(D) corresponds to the sequence of steps of ˜D with odd indices.
This map returns the skew partition definded by the diagram of γ(D).
Map
inner shape
Description
The inner shape of a skew partition.