Identifier
Mp00028:
Dyck paths
—reverse⟶
Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00187: Skew partitions —conjugate⟶ Skew partitions
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00187: Skew partitions —conjugate⟶ Skew partitions
Images
[1,0] => [1,0] => [[1],[]] => [[1],[]]
[1,0,1,0] => [1,0,1,0] => [[1,1],[]] => [[2],[]]
[1,1,0,0] => [1,1,0,0] => [[2],[]] => [[1,1],[]]
[1,0,1,0,1,0] => [1,0,1,0,1,0] => [[1,1,1],[]] => [[3],[]]
[1,0,1,1,0,0] => [1,1,0,0,1,0] => [[2,2],[1]] => [[2,2],[1]]
[1,1,0,0,1,0] => [1,0,1,1,0,0] => [[2,1],[]] => [[2,1],[]]
[1,1,0,1,0,0] => [1,1,0,1,0,0] => [[3],[]] => [[1,1,1],[]]
[1,1,1,0,0,0] => [1,1,1,0,0,0] => [[2,2],[]] => [[2,2],[]]
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [[1,1,1,1],[]] => [[4],[]]
[1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => [[3,3],[2]]
[1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [[2,2,1],[1]] => [[3,2],[1]]
[1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => [[3,3],[2]] => [[2,2,2],[1,1]]
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => [[2,2,2],[1]] => [[3,3],[1]]
[1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => [[2,1,1],[]] => [[3,1],[]]
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => [[3,2],[1]] => [[2,2,1],[1]]
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => [[3,1],[]] => [[2,1,1],[]]
[1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0] => [[4],[]] => [[1,1,1,1],[]]
[1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => [[3,2],[]] => [[2,2,1],[]]
[1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => [[2,2,1],[]] => [[3,2],[]]
[1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[3,3],[1]] => [[2,2,2],[1]]
[1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => [[2,2,2],[]] => [[3,3],[]]
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => [[3,3],[]] => [[2,2,2],[]]
[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],[]] => [[5],[]]
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => [[4,4],[3]]
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => [[4,3],[2]]
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => [[3,3,3],[2,2]]
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => [[4,4],[2]]
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]] => [[4,2],[1]]
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => [[3,3,2],[2,1]]
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]] => [[3,2,2],[1,1]]
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]] => [[2,2,2,2],[1,1,1]]
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]] => [[3,3,2],[1,1]]
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]] => [[4,3],[1]]
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => [[3,3,3],[2,1]]
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]] => [[4,4],[1]]
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => [[3,3,3],[1,1]]
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1],[]] => [[4,1],[]]
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => [[3,3,1],[2]]
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]] => [[3,2,1],[1]]
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]] => [[2,2,2,1],[1,1]]
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]] => [[3,3,1],[1]]
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => [[3,1,1],[]] => [[3,1,1],[]]
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]] => [[2,2,1,1],[1]]
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => [[4,1],[]] => [[2,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => [[5],[]] => [[1,1,1,1,1],[]]
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => [[4,2],[]] => [[2,2,1,1],[]]
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => [[3,2,1],[]] => [[3,2,1],[]]
[1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => [[2,2,2,1],[1]]
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]] => [[3,3,1],[]]
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => [[2,2,2,1],[]]
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1],[]] => [[4,2],[]]
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => [[3,3,2],[2]]
[1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]] => [[3,2,2],[1]]
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => [[2,2,2,2],[1,1]]
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => [[3,3,2],[1]]
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1],[]] => [[4,3],[]]
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => [[3,3,3],[2]]
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2],[]] => [[4,4],[]]
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [[3,3,3],[1]] => [[3,3,3],[1]]
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]] => [[3,2,2],[]]
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => [[2,2,2,2],[1]]
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [[3,3,2],[]] => [[3,3,2],[]]
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [[4,4],[]] => [[2,2,2,2],[]]
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [[3,3,3],[]] => [[3,3,3],[]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1],[]] => [[6],[]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]] => [[5,5],[4]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => [[5,4],[3]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => [[4,4,4],[3,3]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => [[5,5],[3]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => [[5,3],[2]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => [[4,4,3],[3,2]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => [[4,3,3],[2,2]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => [[3,3,3,3],[2,2,2]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => [[4,4,3],[2,2]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => [[5,4],[2]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => [[4,4,4],[3,2]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2],[1,1]] => [[5,5],[2]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2]] => [[4,4,4],[2,2]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]] => [[5,2],[1]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => [[4,4,2],[3,1]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => [[4,3,2],[2,1]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => [[3,3,3,2],[2,2,1]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => [[4,4,2],[2,1]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]] => [[4,2,2],[1,1]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => [[3,3,2,2],[2,1,1]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]] => [[3,2,2,2],[1,1,1]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]] => [[2,2,2,2,2],[1,1,1,1]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]] => [[3,3,2,2],[1,1,1]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]] => [[4,3,2],[1,1]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => [[3,3,3,2],[2,1,1]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2],[2]] => [[4,4,2],[1,1]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[4,4,3],[3]] => [[3,3,3,2],[1,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]] => [[5,3],[1]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => [[4,4,3],[3,1]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => [[4,3,3],[2,1]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => [[3,3,3,3],[2,2,1]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1]] => [[4,4,3],[2,1]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1],[1]] => [[5,4],[1]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1,1]] => [[4,4,4],[3,1]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2],[1]] => [[5,5],[1]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1]] => [[4,4,4],[2,1]]
>>> Load all 1141 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1],[2]] => [[4,3,3],[1,1]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4],[3,1]] => [[3,3,3,3],[2,1,1]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2],[2]] => [[4,4,3],[1,1]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[4,4,4],[3]] => [[3,3,3,3],[1,1,1]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3],[2]] => [[4,4,4],[1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1],[]] => [[5,1],[]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => [[4,4,1],[3]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => [[4,3,1],[2]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => [[3,3,3,1],[2,2]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => [[4,4,1],[2]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]] => [[4,2,1],[1]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => [[3,3,2,1],[2,1]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]] => [[3,2,2,1],[1,1]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]] => [[2,2,2,2,1],[1,1,1]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]] => [[3,3,2,1],[1,1]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]] => [[4,3,1],[1]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => [[3,3,3,1],[2,1]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2],[1]] => [[4,4,1],[1]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[4,3,3],[2]] => [[3,3,3,1],[1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1],[]] => [[4,1,1],[]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => [[3,3,1,1],[2]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]] => [[3,2,1,1],[1]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]] => [[2,2,2,1,1],[1,1]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]] => [[3,3,1,1],[1]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1],[]] => [[3,1,1,1],[]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]] => [[2,2,1,1,1],[1]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1],[]] => [[2,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]] => [[1,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]] => [[2,2,1,1,1],[]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1],[]] => [[3,2,1,1],[]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => [[2,2,2,1,1],[1]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2],[]] => [[3,3,1,1],[]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3],[]] => [[2,2,2,1,1],[]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1],[]] => [[4,2,1],[]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => [[3,3,2,1],[2]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]] => [[3,2,2,1],[1]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => [[2,2,2,2,1],[1,1]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [[4,3,2],[1]] => [[3,3,2,1],[1]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1],[]] => [[4,3,1],[]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3],[1,1]] => [[3,3,3,1],[2]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2],[]] => [[4,4,1],[]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[4,3,3],[1]] => [[3,3,3,1],[1]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1],[]] => [[3,2,2,1],[]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[5,4],[1]] => [[2,2,2,2,1],[1]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2],[]] => [[3,3,2,1],[]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4],[]] => [[2,2,2,2,1],[]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[4,3,3],[]] => [[3,3,3,1],[]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1],[]] => [[5,2],[]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => [[4,4,2],[3]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => [[4,3,2],[2]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => [[3,3,3,2],[2,2]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1]] => [[4,4,2],[2]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]] => [[4,2,2],[1]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => [[3,3,2,2],[2,1]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]] => [[3,2,2,2],[1,1]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => [[2,2,2,2,2],[1,1,1]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [[4,4,2],[2]] => [[3,3,2,2],[1,1]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1],[1]] => [[4,3,2],[1]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3],[2,1]] => [[3,3,3,2],[2,1]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2],[1]] => [[4,4,2],[1]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[4,4,3],[2]] => [[3,3,3,2],[1,1]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1],[]] => [[5,3],[]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1,1]] => [[4,4,3],[3]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1],[1,1]] => [[4,3,3],[2]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4],[2,2]] => [[3,3,3,3],[2,2]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1]] => [[4,4,3],[2]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1],[]] => [[5,4],[]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1,1]] => [[4,4,4],[3]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2],[]] => [[5,5],[]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1]] => [[4,4,4],[2]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[3,3,3,1],[1]] => [[4,3,3],[1]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4],[2,1]] => [[3,3,3,3],[2,1]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2],[1]] => [[4,4,3],[1]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4],[2]] => [[3,3,3,3],[1,1]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3],[1]] => [[4,4,4],[1]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1],[]] => [[4,2,2],[]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2],[1,1]] => [[3,3,2,2],[2]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[4,4,1],[1]] => [[3,2,2,2],[1]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [[5,5],[2]] => [[2,2,2,2,2],[1,1]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [[4,4,2],[1]] => [[3,3,2,2],[1]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1],[]] => [[4,3,2],[]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3],[1,1]] => [[3,3,3,2],[2]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2],[]] => [[4,4,2],[]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3],[1]] => [[3,3,3,2],[1]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1],[]] => [[3,2,2,2],[]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [[5,5],[1]] => [[2,2,2,2,2],[1]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [[4,4,2],[]] => [[3,3,2,2],[]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5],[]] => [[2,2,2,2,2],[]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3],[]] => [[3,3,3,2],[]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[3,3,3,1],[]] => [[4,3,3],[]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4],[1,1]] => [[3,3,3,3],[2]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2],[]] => [[4,4,3],[]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4],[1]] => [[3,3,3,3],[1]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3],[]] => [[4,4,4],[]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[4,4,4],[]] => [[3,3,3,3],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1],[]] => [[7],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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]] => [[6,6],[5]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]] => [[6,5],[4]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]] => [[5,5,5],[4,4]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1]] => [[6,6],[4]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => [[6,4],[3]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => [[5,5,4],[4,3]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]] => [[5,4,4],[3,3]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => [[4,4,4,4],[3,3,3]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2]] => [[5,5,4],[3,3]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1]] => [[6,5],[3]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,1]] => [[5,5,5],[4,3]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1]] => [[6,6],[3]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2]] => [[5,5,5],[3,3]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => [[6,3],[2]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => [[5,5,3],[4,2]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => [[5,4,3],[3,2]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => [[4,4,4,3],[3,3,2]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1]] => [[5,5,3],[3,2]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => [[5,3,3],[2,2]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => [[4,4,3,3],[3,2,2]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => [[4,3,3,3],[2,2,2]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => [[3,3,3,3,3],[2,2,2,2]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3]] => [[4,4,3,3],[2,2,2]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2]] => [[5,4,3],[2,2]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,1]] => [[4,4,4,3],[3,2,2]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2]] => [[5,5,3],[2,2]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3]] => [[4,4,4,3],[2,2,2]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1]] => [[6,4],[2]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,2],[2,2,1,1]] => [[5,5,4],[4,2]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,1],[2,2,1]] => [[5,4,4],[3,2]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3,2]] => [[4,4,4,4],[3,3,2]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,2],[2,2,1]] => [[5,5,4],[3,2]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1]] => [[6,5],[2]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2,1,1]] => [[5,5,5],[4,2]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1]] => [[6,6],[2]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2,1]] => [[5,5,5],[3,2]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3,1],[2,2]] => [[5,4,4],[2,2]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3,1]] => [[4,4,4,4],[3,2,2]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3,2],[2,2]] => [[5,5,4],[2,2]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3]] => [[4,4,4,4],[2,2,2]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2]] => [[5,5,5],[2,2]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]] => [[6,2],[1]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => [[5,5,2],[4,1]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => [[5,4,2],[3,1]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => [[4,4,4,2],[3,3,1]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1]] => [[5,5,2],[3,1]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => [[5,3,2],[2,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => [[4,4,3,2],[3,2,1]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => [[4,3,3,2],[2,2,1]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => [[3,3,3,3,2],[2,2,2,1]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2]] => [[4,4,3,2],[2,2,1]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1]] => [[5,4,2],[2,1]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,1]] => [[4,4,4,2],[3,2,1]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1]] => [[5,5,2],[2,1]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2]] => [[4,4,4,2],[2,2,1]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]] => [[5,2,2],[1,1]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => [[4,4,2,2],[3,1,1]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => [[4,3,2,2],[2,1,1]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => [[3,3,3,2,2],[2,2,1,1]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1]] => [[4,4,2,2],[2,1,1]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]] => [[4,2,2,2],[1,1,1]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => [[3,3,2,2,2],[2,1,1,1]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]] => [[3,2,2,2,2],[1,1,1,1]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]] => [[2,2,2,2,2,2],[1,1,1,1,1]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4]] => [[3,3,2,2,2],[1,1,1,1]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2,1],[3]] => [[4,3,2,2],[1,1,1]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[5,5,3],[4,1]] => [[3,3,3,2,2],[2,1,1,1]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[4,4,2,2],[3]] => [[4,4,2,2],[1,1,1]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[5,5,3],[4]] => [[3,3,3,2,2],[1,1,1,1]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1,1],[2]] => [[5,3,2],[1,1]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[4,4,3,2],[3,1,1]] => [[4,4,3,2],[3,1,1]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3,1],[3,1]] => [[4,3,3,2],[2,1,1]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[5,5,4],[4,2]] => [[3,3,3,3,2],[2,2,1,1]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[4,4,3,2],[3,1]] => [[4,4,3,2],[2,1,1]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2,1],[2]] => [[5,4,2],[1,1]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[4,4,3,3],[3,1,1]] => [[4,4,4,2],[3,1,1]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2,2],[2]] => [[5,5,2],[1,1]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[4,4,3,3],[3,1]] => [[4,4,4,2],[2,1,1]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[4,4,3,1],[3]] => [[4,3,3,2],[1,1,1]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[5,5,4],[4,1]] => [[3,3,3,3,2],[2,1,1,1]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[4,4,3,2],[3]] => [[4,4,3,2],[1,1,1]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[5,5,4],[4]] => [[3,3,3,3,2],[1,1,1,1]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[4,4,3,3],[3]] => [[4,4,4,2],[1,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1,1],[1]] => [[6,3],[1]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,2],[2,1,1,1]] => [[5,5,3],[4,1]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,1],[2,1,1]] => [[5,4,3],[3,1]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[4,4,4,3],[3,2,2]] => [[4,4,4,3],[3,3,1]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,2],[2,1,1]] => [[5,5,3],[3,1]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1,1],[2,1]] => [[5,3,3],[2,1]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[4,4,4,2],[3,2,1]] => [[4,4,3,3],[3,2,1]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4,1],[3,2]] => [[4,3,3,3],[2,2,1]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[5,5,5],[4,3]] => [[3,3,3,3,3],[2,2,2,1]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[4,4,4,2],[3,2]] => [[4,4,3,3],[2,2,1]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2,1],[2,1]] => [[5,4,3],[2,1]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[4,4,4,3],[3,2,1]] => [[4,4,4,3],[3,2,1]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2,2],[2,1]] => [[5,5,3],[2,1]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[4,4,4,3],[3,2]] => [[4,4,4,3],[2,2,1]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1,1],[1]] => [[6,4],[1]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[3,3,3,3,2],[2,1,1,1]] => [[5,5,4],[4,1]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3,1],[2,1,1]] => [[5,4,4],[3,1]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2,2]] => [[4,4,4,4],[3,3,1]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3,2],[2,1,1]] => [[5,5,4],[3,1]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2,1],[1]] => [[6,5],[1]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1,1,1]] => [[5,5,5],[4,1]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2,2],[1]] => [[6,6],[1]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1,1]] => [[5,5,5],[3,1]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3,1],[2,1]] => [[5,4,4],[2,1]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2,1]] => [[4,4,4,4],[3,2,1]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3,2],[2,1]] => [[5,5,4],[2,1]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2]] => [[4,4,4,4],[2,2,1]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1]] => [[5,5,5],[2,1]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1,1],[2]] => [[5,3,3],[1,1]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[4,4,4,2],[3,1,1]] => [[4,4,3,3],[3,1,1]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4,1],[3,1]] => [[4,3,3,3],[2,1,1]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[5,5,5],[4,2]] => [[3,3,3,3,3],[2,2,1,1]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[4,4,4,2],[3,1]] => [[4,4,3,3],[2,1,1]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2,1],[2]] => [[5,4,3],[1,1]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1,1]] => [[4,4,4,3],[3,1,1]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2,2],[2]] => [[5,5,3],[1,1]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => [[4,4,4,3],[2,1,1]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[4,4,4,1],[3]] => [[4,3,3,3],[1,1,1]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[5,5,5],[4,1]] => [[3,3,3,3,3],[2,1,1,1]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[4,4,4,2],[3]] => [[4,4,3,3],[1,1,1]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[5,5,5],[4]] => [[3,3,3,3,3],[1,1,1,1]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[4,4,4,3],[3]] => [[4,4,4,3],[1,1,1]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3,1],[2]] => [[5,4,4],[1,1]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1,1]] => [[4,4,4,4],[3,1,1]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3,2],[2]] => [[5,5,4],[1,1]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1]] => [[4,4,4,4],[2,1,1]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[3,3,3,3,3],[2]] => [[5,5,5],[1,1]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[4,4,4,4],[3]] => [[4,4,4,4],[1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1],[]] => [[6,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]] => [[5,5,1],[4]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => [[5,4,1],[3]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => [[4,4,4,1],[3,3]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1]] => [[5,5,1],[3]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => [[5,3,1],[2]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => [[4,4,3,1],[3,2]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => [[4,3,3,1],[2,2]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => [[3,3,3,3,1],[2,2,2]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2]] => [[4,4,3,1],[2,2]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1]] => [[5,4,1],[2]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,1]] => [[4,4,4,1],[3,2]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1]] => [[5,5,1],[2]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2]] => [[4,4,4,1],[2,2]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => [[5,2,1],[1]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => [[4,4,2,1],[3,1]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => [[4,3,2,1],[2,1]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => [[3,3,3,2,1],[2,2,1]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1]] => [[4,4,2,1],[2,1]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => [[4,2,2,1],[1,1]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => [[3,3,2,2,1],[2,1,1]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => [[3,2,2,2,1],[1,1,1]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]] => [[2,2,2,2,2,1],[1,1,1,1]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3]] => [[3,3,2,2,1],[1,1,1]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2,1],[2]] => [[4,3,2,1],[1,1]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[5,4,3],[3,1]] => [[3,3,3,2,1],[2,1,1]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[4,3,2,2],[2]] => [[4,4,2,1],[1,1]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[5,4,3],[3]] => [[3,3,3,2,1],[1,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1,1],[1]] => [[5,3,1],[1]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[4,3,3,2],[2,1,1]] => [[4,4,3,1],[3,1]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3,1],[2,1]] => [[4,3,3,1],[2,1]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[5,4,4],[3,2]] => [[3,3,3,3,1],[2,2,1]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[4,3,3,2],[2,1]] => [[4,4,3,1],[2,1]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2,1],[1]] => [[5,4,1],[1]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[4,3,3,3],[2,1,1]] => [[4,4,4,1],[3,1]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2,2],[1]] => [[5,5,1],[1]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[4,3,3,3],[2,1]] => [[4,4,4,1],[2,1]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[4,3,3,1],[2]] => [[4,3,3,1],[1,1]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[5,4,4],[3,1]] => [[3,3,3,3,1],[2,1,1]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[4,3,3,2],[2]] => [[4,4,3,1],[1,1]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[5,4,4],[3]] => [[3,3,3,3,1],[1,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[4,3,3,3],[2]] => [[4,4,4,1],[1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1],[]] => [[5,1,1],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => [[4,4,1,1],[3]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => [[4,3,1,1],[2]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => [[3,3,3,1,1],[2,2]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1]] => [[4,4,1,1],[2]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => [[4,2,1,1],[1]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => [[3,3,2,1,1],[2,1]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => [[3,2,2,1,1],[1,1]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => [[2,2,2,2,1,1],[1,1,1]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2]] => [[3,3,2,1,1],[1,1]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2,1],[1]] => [[4,3,1,1],[1]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[5,3,3],[2,1]] => [[3,3,3,1,1],[2,1]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[4,2,2,2],[1]] => [[4,4,1,1],[1]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[5,3,3],[2]] => [[3,3,3,1,1],[1,1]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1],[]] => [[4,1,1,1],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => [[3,3,1,1,1],[2]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => [[3,2,1,1,1],[1]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => [[2,2,2,1,1,1],[1,1]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1]] => [[3,3,1,1,1],[1]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1],[]] => [[3,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]] => [[2,2,1,1,1,1],[1]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1],[]] => [[2,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]] => [[1,1,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2],[]] => [[2,2,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1],[]] => [[3,2,1,1,1],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[6,3],[1]] => [[2,2,2,1,1,1],[1]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2],[]] => [[3,3,1,1,1],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3],[]] => [[2,2,2,1,1,1],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1],[]] => [[4,2,1,1],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1,1]] => [[3,3,2,1,1],[2]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3,1],[1]] => [[3,2,2,1,1],[1]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[6,4],[2]] => [[2,2,2,2,1,1],[1,1]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1]] => [[3,3,2,1,1],[1]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1],[]] => [[4,3,1,1],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1,1]] => [[3,3,3,1,1],[2]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,2],[]] => [[4,4,1,1],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1]] => [[3,3,3,1,1],[1]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1],[]] => [[3,2,2,1,1],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[6,4],[1]] => [[2,2,2,2,1,1],[1]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[5,3,2],[]] => [[3,3,2,1,1],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[6,4],[]] => [[2,2,2,2,1,1],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[5,3,3],[]] => [[3,3,3,1,1],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1],[]] => [[5,2,1],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[4,3,2,2],[1,1,1]] => [[4,4,2,1],[3]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2,1],[1,1]] => [[4,3,2,1],[2]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[5,4,3],[2,2]] => [[3,3,3,2,1],[2,2]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[4,3,2,2],[1,1]] => [[4,4,2,1],[2]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1,1],[1]] => [[4,2,2,1],[1]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2,1]] => [[3,3,2,2,1],[2,1]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4,1],[2]] => [[3,2,2,2,1],[1,1]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[6,5],[3]] => [[2,2,2,2,2,1],[1,1,1]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2]] => [[3,3,2,2,1],[1,1]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,1],[1]] => [[4,3,2,1],[1]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2,1]] => [[3,3,3,2,1],[2,1]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,2],[1]] => [[4,4,2,1],[1]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => [[3,3,3,2,1],[1,1]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1],[]] => [[5,3,1],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1,1]] => [[4,4,3,1],[3]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,1],[1,1]] => [[4,3,3,1],[2]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[5,4,4],[2,2]] => [[3,3,3,3,1],[2,2]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1]] => [[4,4,3,1],[2]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,1],[]] => [[5,4,1],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1,1]] => [[4,4,4,1],[3]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,2],[]] => [[5,5,1],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1]] => [[4,4,4,1],[2]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,1],[1]] => [[4,3,3,1],[1]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => [[3,3,3,3,1],[2,1]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]] => [[4,4,3,1],[1]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2]] => [[3,3,3,3,1],[1,1]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[4,3,3,3],[1]] => [[4,4,4,1],[1]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1],[]] => [[4,2,2,1],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1,1]] => [[3,3,2,2,1],[2]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[5,4,1],[1]] => [[3,2,2,2,1],[1]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[6,5],[2]] => [[2,2,2,2,2,1],[1,1]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => [[3,3,2,2,1],[1]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,1],[]] => [[4,3,2,1],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => [[3,3,3,2,1],[2]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,2],[]] => [[4,4,2,1],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => [[3,3,3,2,1],[1]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4,1],[]] => [[3,2,2,2,1],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[6,5],[1]] => [[2,2,2,2,2,1],[1]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[5,4,2],[]] => [[3,3,2,2,1],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[6,5],[]] => [[2,2,2,2,2,1],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[5,4,3],[]] => [[3,3,3,2,1],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[4,3,3,1],[]] => [[4,3,3,1],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1,1]] => [[3,3,3,3,1],[2]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[4,3,3,2],[]] => [[4,4,3,1],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1]] => [[3,3,3,3,1],[1]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[4,3,3,3],[]] => [[4,4,4,1],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[5,4,4],[]] => [[3,3,3,3,1],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1],[]] => [[6,2],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,2],[1,1,1,1]] => [[5,5,2],[4]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,1],[1,1,1]] => [[5,4,2],[3]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[4,4,3,3],[2,2,2]] => [[4,4,4,2],[3,3]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,2],[1,1,1]] => [[5,5,2],[3]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1,1],[1,1]] => [[5,3,2],[2]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[4,4,3,2],[2,2,1]] => [[4,4,3,2],[3,2]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3,1],[2,2]] => [[4,3,3,2],[2,2]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[5,5,4],[3,3]] => [[3,3,3,3,2],[2,2,2]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[4,4,3,2],[2,2]] => [[4,4,3,2],[2,2]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2,1],[1,1]] => [[5,4,2],[2]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[4,4,3,3],[2,2,1]] => [[4,4,4,2],[3,2]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2,2],[1,1]] => [[5,5,2],[2]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[4,4,3,3],[2,2]] => [[4,4,4,2],[2,2]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1,1],[1]] => [[5,2,2],[1]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[4,4,2,2],[2,1,1]] => [[4,4,2,2],[3,1]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2,1],[2,1]] => [[4,3,2,2],[2,1]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[5,5,3],[3,2]] => [[3,3,3,2,2],[2,2,1]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[4,4,2,2],[2,1]] => [[4,4,2,2],[2,1]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1,1],[2]] => [[4,2,2,2],[1,1]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3,1]] => [[3,3,2,2,2],[2,1,1]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5,1],[3]] => [[3,2,2,2,2],[1,1,1]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[6,6],[4]] => [[2,2,2,2,2,2],[1,1,1,1]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3]] => [[3,3,2,2,2],[1,1,1]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,1],[2]] => [[4,3,2,2],[1,1]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3,1]] => [[3,3,3,2,2],[2,1,1]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,2],[2]] => [[4,4,2,2],[1,1]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => [[3,3,3,2,2],[1,1,1]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1,1],[1]] => [[5,3,2],[1]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1,1]] => [[4,4,3,2],[3,1]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,1],[2,1]] => [[4,3,3,2],[2,1]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4],[3,2]] => [[3,3,3,3,2],[2,2,1]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => [[4,4,3,2],[2,1]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2,1],[1]] => [[5,4,2],[1]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1,1]] => [[4,4,4,2],[3,1]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2,2],[1]] => [[5,5,2],[1]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => [[4,4,4,2],[2,1]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,1],[2]] => [[4,3,3,2],[1,1]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => [[3,3,3,3,2],[2,1,1]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => [[4,4,3,2],[1,1]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3]] => [[3,3,3,3,2],[1,1,1]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[4,4,3,3],[2]] => [[4,4,4,2],[1,1]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1],[]] => [[6,3],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1,1,1]] => [[5,5,3],[4]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,1],[1,1,1]] => [[5,4,3],[3]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,2]] => [[4,4,4,3],[3,3]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1,1]] => [[5,5,3],[3]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1,1],[1,1]] => [[5,3,3],[2]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,1],[2,2]] => [[4,3,3,3],[2,2]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[5,5,5],[3,3]] => [[3,3,3,3,3],[2,2,2]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2]] => [[4,4,3,3],[2,2]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,1],[1,1]] => [[5,4,3],[2]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,1]] => [[4,4,4,3],[3,2]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1]] => [[5,5,3],[2]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2]] => [[4,4,4,3],[2,2]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1,1],[]] => [[6,4],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1,1,1]] => [[5,5,4],[4]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,1],[1,1,1]] => [[5,4,4],[3]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,2]] => [[4,4,4,4],[3,3]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1,1]] => [[5,5,4],[3]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,1],[]] => [[6,5],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1,1,1]] => [[5,5,5],[4]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2],[]] => [[6,6],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1,1]] => [[5,5,5],[3]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3,1],[1,1]] => [[5,4,4],[2]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,1]] => [[4,4,4,4],[3,2]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1]] => [[5,5,4],[2]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2]] => [[4,4,4,4],[2,2]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1]] => [[5,5,5],[2]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[3,3,3,1,1],[1]] => [[5,3,3],[1]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1,1]] => [[4,4,3,3],[3,1]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,1],[2,1]] => [[4,3,3,3],[2,1]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[5,5,5],[3,2]] => [[3,3,3,3,3],[2,2,1]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => [[4,4,3,3],[2,1]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2,1],[1]] => [[5,4,3],[1]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]] => [[4,4,4,3],[3,1]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2,2],[1]] => [[5,5,3],[1]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => [[4,4,4,3],[2,1]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,1],[2]] => [[4,3,3,3],[1,1]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3,1]] => [[3,3,3,3,3],[2,1,1]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]] => [[4,4,3,3],[1,1]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3]] => [[3,3,3,3,3],[1,1,1]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[4,4,4,3],[2]] => [[4,4,4,3],[1,1]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,1],[1]] => [[5,4,4],[1]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1,1]] => [[4,4,4,4],[3,1]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,2],[1]] => [[5,5,4],[1]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1]] => [[4,4,4,4],[2,1]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[3,3,3,3,3],[1]] => [[5,5,5],[1]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[4,4,4,4],[2]] => [[4,4,4,4],[1,1]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1],[]] => [[5,2,2],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[4,4,2,2],[1,1,1]] => [[4,4,2,2],[3]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2,1],[1,1]] => [[4,3,2,2],[2]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[5,5,3],[2,2]] => [[3,3,3,2,2],[2,2]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[4,4,2,2],[1,1]] => [[4,4,2,2],[2]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[4,4,1,1],[1]] => [[4,2,2,2],[1]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2,1]] => [[3,3,2,2,2],[2,1]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[5,5,1],[2]] => [[3,2,2,2,2],[1,1]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[6,6],[3]] => [[2,2,2,2,2,2],[1,1,1]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => [[3,3,2,2,2],[1,1]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[4,4,2,1],[1]] => [[4,3,2,2],[1]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => [[3,3,3,2,2],[2,1]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[4,4,2,2],[1]] => [[4,4,2,2],[1]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => [[3,3,3,2,2],[1,1]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1,1],[]] => [[5,3,2],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1,1]] => [[4,4,3,2],[3]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,1],[1,1]] => [[4,3,3,2],[2]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[5,5,4],[2,2]] => [[3,3,3,3,2],[2,2]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => [[4,4,3,2],[2]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2,1],[]] => [[5,4,2],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1,1]] => [[4,4,4,2],[3]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2,2],[]] => [[5,5,2],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => [[4,4,4,2],[2]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => [[4,3,3,2],[1]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => [[3,3,3,3,2],[2,1]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => [[4,4,3,2],[1]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2]] => [[3,3,3,3,2],[1,1]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[4,4,3,3],[1]] => [[4,4,4,2],[1]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1,1],[]] => [[4,2,2,2],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[5,5,2],[1,1]] => [[3,3,2,2,2],[2]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[5,5,1],[1]] => [[3,2,2,2,2],[1]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[6,6],[2]] => [[2,2,2,2,2,2],[1,1]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[5,5,2],[1]] => [[3,3,2,2,2],[1]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[4,4,2,1],[]] => [[4,3,2,2],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1,1]] => [[3,3,3,2,2],[2]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[4,4,2,2],[]] => [[4,4,2,2],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1]] => [[3,3,3,2,2],[1]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5,1],[]] => [[3,2,2,2,2],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[6,6],[1]] => [[2,2,2,2,2,2],[1]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[5,5,2],[]] => [[3,3,2,2,2],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[6,6],[]] => [[2,2,2,2,2,2],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[5,5,3],[]] => [[3,3,3,2,2],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,1],[]] => [[4,3,3,2],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[5,5,4],[1,1]] => [[3,3,3,3,2],[2]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,2],[]] => [[4,4,3,2],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[5,5,4],[1]] => [[3,3,3,3,2],[1]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[4,4,3,3],[]] => [[4,4,4,2],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[5,5,4],[]] => [[3,3,3,3,2],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[3,3,3,1,1],[]] => [[5,3,3],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1,1]] => [[4,4,3,3],[3]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,1],[1,1]] => [[4,3,3,3],[2]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[5,5,5],[2,2]] => [[3,3,3,3,3],[2,2]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1]] => [[4,4,3,3],[2]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2,1],[]] => [[5,4,3],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1,1]] => [[4,4,4,3],[3]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2,2],[]] => [[5,5,3],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1]] => [[4,4,4,3],[2]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,1],[1]] => [[4,3,3,3],[1]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[5,5,5],[2,1]] => [[3,3,3,3,3],[2,1]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,2],[1]] => [[4,4,3,3],[1]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[5,5,5],[2]] => [[3,3,3,3,3],[1,1]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[4,4,4,3],[1]] => [[4,4,4,3],[1]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3,1],[]] => [[5,4,4],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[4,4,4,4],[1,1,1]] => [[4,4,4,4],[3]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3,2],[]] => [[5,5,4],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[4,4,4,4],[1,1]] => [[4,4,4,4],[2]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[3,3,3,3,3],[]] => [[5,5,5],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[4,4,4,4],[1]] => [[4,4,4,4],[1]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[4,4,4,1],[]] => [[4,3,3,3],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[5,5,5],[1,1]] => [[3,3,3,3,3],[2]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[4,4,4,2],[]] => [[4,4,3,3],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[5,5,5],[1]] => [[3,3,3,3,3],[1]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[4,4,4,3],[]] => [[4,4,4,3],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[5,5,5],[]] => [[3,3,3,3,3],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[4,4,4,4],[]] => [[4,4,4,4],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1],[]] => [[8],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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]] => [[7,7],[6]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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]] => [[6,6,6],[5,5]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [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]] => [[7,7],[5]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [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]] => [[5,5,5,5],[4,4,4]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,2],[2,2,2,2]] => [[6,6,5],[4,4]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [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]] => [[7,6],[4]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [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]] => [[6,6,6],[5,4]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [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]] => [[7,7],[4]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [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]] => [[6,6,6],[4,4]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[5,5,5,5],[4,4,4]] => [[4,4,4,4,4],[3,3,3,3]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,2],[3,3,3]] => [[5,5,4,4],[3,3,3]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,3],[3,3,3]] => [[5,5,5,4],[3,3,3]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,1,1],[1,1,1]] => [[7,5],[3]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3,2],[2,2,2,1,1]] => [[6,6,5],[5,3]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [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]] => [[5,5,5,5],[4,4,3]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [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]] => [[7,6],[3]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2],[1,1,1]] => [[7,7],[3]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2,1]] => [[6,6,6],[4,3]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2]] => [[6,6,6],[3,3]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [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]] => [[7,3],[2]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [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]] => [[6,6,3],[5,2]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[6,6,6],[5,5]] => [[3,3,3,3,3,3],[2,2,2,2,2]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5,2],[4,4]] => [[4,4,3,3,3],[2,2,2,2]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[5,5,5,3],[4,4]] => [[4,4,4,3,3],[2,2,2,2]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2,2,2],[2,2]] => [[6,6,3],[2,2]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[4,4,4,3,3],[3,3]] => [[5,5,5,3],[2,2,2]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [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]] => [[7,6],[2]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,1,1,1]] => [[6,6,6],[5,2]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,2,2],[1,1]] => [[7,7],[2]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,1]] => [[6,6,6],[3,2]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[3,3,3,3,3,1],[2,2]] => [[6,5,5],[2,2]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3]] => [[5,5,5,5],[2,2,2]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [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]] => [[6,6,2],[5,1]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1,1],[2]] => [[6,2,2],[1,1]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[7,7],[6]] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6,2],[5]] => [[3,3,2,2,2,2],[1,1,1,1,1]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[5,5,2,2],[4]] => [[4,4,2,2,2],[1,1,1,1]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[6,6,3],[5]] => [[3,3,3,2,2,2],[1,1,1,1,1]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[4,4,2,2,1],[3]] => [[5,4,2,2],[1,1,1]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[4,4,2,2,2],[3]] => [[5,5,2,2],[1,1,1]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[5,5,3,3],[4]] => [[4,4,4,2,2],[1,1,1,1]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[5,5,4,4],[4]] => [[4,4,4,4,2],[1,1,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1,1,1],[1]] => [[7,3],[1]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2,2,1],[1]] => [[7,6],[1]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3,3],[2,1,1,1,1]] => [[6,6,6],[5,1]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2,2,2],[1]] => [[7,7],[1]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2]] => [[5,5,5,5],[2,2,1]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[4,4,4,2,2],[3,1,1]] => [[5,5,3,3],[3,1,1]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[5,5,5,4],[4]] => [[4,4,4,4,3],[1,1,1,1]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3,1,1],[2]] => [[6,4,4],[1,1]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[4,4,4,4,2],[3,1,1,1]] => [[5,5,4,4],[4,1,1]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[5,5,5,5],[4,2,2]] => [[4,4,4,4,4],[3,3,1,1]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[3,3,3,3,3,1],[2]] => [[6,5,5],[1,1]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[3,3,3,3,3,3],[2]] => [[6,6,6],[1,1]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[4,4,4,4,4],[3,1]] => [[5,5,5,5],[2,1,1]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[4,4,4,4,1],[3]] => [[5,4,4,4],[1,1,1]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[5,5,5,5],[4,1,1]] => [[4,4,4,4,4],[3,1,1,1]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[5,5,5,5],[4,1]] => [[4,4,4,4,4],[2,1,1,1]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[4,4,4,4,3],[3]] => [[5,5,5,4],[1,1,1]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[5,5,5,5],[4]] => [[4,4,4,4,4],[1,1,1,1]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[4,4,4,4,4],[3]] => [[5,5,5,5],[1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1],[]] => [[7,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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]] => [[6,6,1],[5]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [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]] => [[6,5,1],[4]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,3],[2,2,2,2]] => [[5,5,5,1],[4,4]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,2],[1,1,1,1]] => [[6,6,1],[4]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [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]] => [[6,4,1],[3]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,1],[2,2,2]] => [[5,4,4,1],[3,3]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1,1],[1,1]] => [[6,3,1],[2]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[6,5,5],[4,4]] => [[3,3,3,3,3,1],[2,2,2,2]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2,2,2],[1,1]] => [[6,6,1],[2]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1,1],[1]] => [[6,2,1],[1]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[7,6],[5]] => [[2,2,2,2,2,2,1],[1,1,1,1,1]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [[4,3,2,2,2],[2]] => [[5,5,2,1],[1,1]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2,2,2],[1]] => [[6,6,1],[1]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [[4,3,3,2,2],[2]] => [[5,5,3,1],[1,1]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[5,4,4,1],[3]] => [[4,3,3,3,1],[1,1,1]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[5,4,4,3],[3]] => [[4,4,4,3,1],[1,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[4,3,3,3,1],[2]] => [[5,4,4,1],[1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[5,4,4,4],[3,1,1]] => [[4,4,4,4,1],[3,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [[4,3,3,3,2],[2]] => [[5,5,4,1],[1,1]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[4,3,3,3,3],[2]] => [[5,5,5,1],[1,1]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[5,4,4,4],[3]] => [[4,4,4,4,1],[1,1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1],[]] => [[6,1,1],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2,2],[1,1,1,1]] => [[5,5,1,1],[4]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2,1],[1,1,1]] => [[5,4,1,1],[3]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[5,3,3,3],[2,2,2]] => [[4,4,4,1,1],[3,3]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2,2],[1,1,1]] => [[5,5,1,1],[3]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1,1],[1,1]] => [[5,3,1,1],[2]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3,1],[2,2]] => [[4,3,3,1,1],[2,2]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,2,1],[1,1]] => [[5,4,1,1],[2]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[5,3,3,3],[2,2]] => [[4,4,4,1,1],[2,2]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [[5,3,3,3],[2]] => [[4,4,4,1,1],[1,1]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1],[]] => [[5,1,1,1],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2,2],[1,1,1]] => [[4,4,1,1,1],[3]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1,1],[1]] => [[4,2,1,1,1],[1]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1],[]] => [[4,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[6,2,2],[1,1]] => [[3,3,1,1,1,1],[2]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1],[]] => [[3,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[7,2],[1]] => [[2,2,1,1,1,1,1],[1]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1],[]] => [[2,1,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8],[]] => [[1,1,1,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,2],[]] => [[2,2,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,1],[]] => [[3,2,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[7,3],[1]] => [[2,2,2,1,1,1,1],[1]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,2],[]] => [[3,3,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[7,3],[]] => [[2,2,2,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1,1],[]] => [[4,2,1,1,1],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[6,3,2],[1,1]] => [[3,3,2,1,1,1],[2]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[7,4],[2]] => [[2,2,2,2,1,1,1],[1,1]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [[6,3,2],[1]] => [[3,3,2,1,1,1],[1]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2,1],[]] => [[4,3,1,1,1],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[6,3,3],[1,1]] => [[3,3,3,1,1,1],[2]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2,2],[]] => [[4,4,1,1,1],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3,1],[]] => [[3,2,2,1,1,1],[]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[7,4],[]] => [[2,2,2,2,1,1,1],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1,1],[]] => [[5,2,1,1],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[7,5],[3]] => [[2,2,2,2,2,1,1],[1,1,1]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1,1],[]] => [[5,3,1,1],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1,1],[]] => [[4,2,2,1,1],[]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[7,5],[]] => [[2,2,2,2,2,1,1],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[6,4,4],[1,1]] => [[3,3,3,3,1,1],[2]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [[6,4,4],[]] => [[3,3,3,3,1,1],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1,1],[]] => [[6,2,1],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[7,6],[4]] => [[2,2,2,2,2,2,1],[1,1,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1,1],[]] => [[6,3,1],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,1,1],[]] => [[6,4,1],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,2,1],[]] => [[6,5,1],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,2,2],[]] => [[6,6,1],[]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [[4,3,3,3,3],[1,1,1]] => [[5,5,5,1],[3]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1,1],[]] => [[5,2,2,1],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[6,5,1],[]] => [[3,2,2,2,2,1],[]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[7,6],[]] => [[2,2,2,2,2,2,1],[]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [[6,5,4],[]] => [[3,3,3,3,2,1],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[5,4,4,2],[1,1,1]] => [[4,4,3,3,1],[3]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [[4,3,3,3,3],[]] => [[5,5,5,1],[]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [[5,4,4,4],[1]] => [[4,4,4,4,1],[1]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[6,5,5],[1,1]] => [[3,3,3,3,3,1],[2]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [[6,5,5],[1]] => [[3,3,3,3,3,1],[1]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [[5,4,4,3],[]] => [[4,4,4,3,1],[]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [[6,5,5],[]] => [[3,3,3,3,3,1],[]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[5,4,4,4],[]] => [[4,4,4,4,1],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1,1],[]] => [[7,2],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,2,2],[1,1,1,1,1]] => [[6,6,2],[5]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[5,5,4,4],[3,3,3]] => [[4,4,4,4,2],[3,3,3]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[6,6,5],[4,4]] => [[3,3,3,3,3,2],[2,2,2,2]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2,2,1],[1,1]] => [[6,5,2],[2]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [[4,4,3,3,3],[2,2,1]] => [[5,5,5,2],[3,2]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[5,5,4,4],[3,3]] => [[4,4,4,4,2],[2,2,2]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[4,4,3,3,3],[2,2]] => [[5,5,5,2],[2,2]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1,1,1],[1]] => [[6,2,2],[1]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5,1,1],[3]] => [[4,2,2,2,2],[1,1,1]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[6,6,1],[4]] => [[3,2,2,2,2,2],[1,1,1,1]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[7,7],[5]] => [[2,2,2,2,2,2,2],[1,1,1,1,1]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2,2,2],[1]] => [[6,6,2],[1]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[5,5,4,4],[3,1,1]] => [[4,4,4,4,2],[3,1,1]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1,1],[]] => [[7,3],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,2,2],[1,1,1,1]] => [[6,6,3],[4]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[4,4,4,3,3],[2,2,2]] => [[5,5,5,3],[3,3]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[6,6,6],[4,4]] => [[3,3,3,3,3,3],[2,2,2,2]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [[4,4,4,3,3],[2,2]] => [[5,5,5,3],[2,2]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2,2],[1,1,1,1,1]] => [[6,6,4],[5]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2,2],[1,1,1,1]] => [[6,6,4],[4]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[5,5,5,5],[3,3,3]] => [[4,4,4,4,4],[3,3,3]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,2],[1,1,1,1,1]] => [[6,6,5],[5]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,2],[1,1,1,1]] => [[6,6,5],[4]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2,1],[]] => [[7,6],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,3],[1,1,1,1,1]] => [[6,6,6],[5]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2,2],[]] => [[7,7],[]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,3],[1,1,1,1]] => [[6,6,6],[4]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [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]] => [[6,5,5],[3]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[4,4,4,4,1],[2,2]] => [[5,4,4,4],[2,2]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[3,3,3,3,3,1],[1,1]] => [[6,5,5],[2]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [[3,3,3,3,3,2],[1,1]] => [[6,6,5],[2]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [[5,5,5,3],[3]] => [[4,4,4,3,3],[1,1,1]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [[4,4,4,4,4],[2,1]] => [[5,5,5,5],[2,1]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [[4,4,4,4,2],[2]] => [[5,5,4,4],[1,1]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[4,4,4,4,4],[2]] => [[5,5,5,5],[1,1]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1,1],[]] => [[6,2,2],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[5,5,3,3],[2,2,2]] => [[4,4,4,2,2],[3,3]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[5,5,3,1],[2,2]] => [[4,3,3,2,2],[2,2]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[6,6,4],[3,3]] => [[3,3,3,3,2,2],[2,2,2]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[5,5,3,2],[2,2]] => [[4,4,3,2,2],[2,2]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[4,4,2,2,2],[1,1]] => [[5,5,2,2],[2]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[5,5,3,3],[2,2]] => [[4,4,4,2,2],[2,2]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[6,6,2],[3,1]] => [[3,3,2,2,2,2],[2,1,1]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[7,7],[4]] => [[2,2,2,2,2,2,2],[1,1,1,1]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[4,4,3,2,2],[1,1,1]] => [[5,5,3,2],[3]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[6,6,5],[3,3]] => [[3,3,3,3,3,2],[2,2,2]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[4,4,3,3,3],[1,1,1,1]] => [[5,5,5,2],[4]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2,2,2],[]] => [[6,6,2],[]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[6,6,5],[3]] => [[3,3,3,3,3,2],[1,1,1]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [[4,4,3,3,2],[1]] => [[5,5,4,2],[1]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [[4,4,3,3,3],[1]] => [[5,5,5,2],[1]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[5,5,2,2],[1,1,1]] => [[4,4,2,2,2],[3]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[6,6,3],[2,2]] => [[3,3,3,2,2,2],[2,2]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[5,5,2,2],[1,1]] => [[4,4,2,2,2],[2]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[7,7],[3]] => [[2,2,2,2,2,2,2],[1,1,1]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [[6,6,3],[2]] => [[3,3,3,2,2,2],[1,1]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[6,6,4],[2,2]] => [[3,3,3,3,2,2],[2,2]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5,1,1],[]] => [[4,2,2,2,2],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[6,6,2],[1,1]] => [[3,3,2,2,2,2],[2]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[7,7],[2]] => [[2,2,2,2,2,2,2],[1,1]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[6,6,3],[1,1]] => [[3,3,3,2,2,2],[2]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [[6,6,3],[1]] => [[3,3,3,2,2,2],[1]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[6,6,1],[]] => [[3,2,2,2,2,2],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[7,7],[1]] => [[2,2,2,2,2,2,2],[1]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[6,6,2],[]] => [[3,3,2,2,2,2],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[7,7],[]] => [[2,2,2,2,2,2,2],[]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[6,6,3],[]] => [[3,3,3,2,2,2],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[5,5,3,1],[]] => [[4,3,3,2,2],[]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [[6,6,4],[1]] => [[3,3,3,3,2,2],[1]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [[5,5,3,3],[]] => [[4,4,4,2,2],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,1,1],[]] => [[5,3,3,2],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[4,4,3,3,1],[]] => [[5,4,4,2],[]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[5,5,4,4],[1]] => [[4,4,4,4,2],[1]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[5,5,4,1],[]] => [[4,3,3,3,2],[]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [[6,6,5],[1]] => [[3,3,3,3,3,2],[1]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[5,5,4,4],[]] => [[4,4,4,4,2],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[3,3,3,1,1,1],[]] => [[6,3,3],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[4,4,4,2,2],[1,1,1,1]] => [[5,5,3,3],[4]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[5,5,5,3],[2,2,2]] => [[4,4,4,3,3],[3,3]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[4,4,4,2,2],[1,1,1]] => [[5,5,3,3],[3]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[5,5,5,2],[2,2,1]] => [[4,4,3,3,3],[3,2]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [[5,5,5,2],[2]] => [[4,4,3,3,3],[1,1]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[6,6,6],[3]] => [[3,3,3,3,3,3],[1,1,1]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [[5,5,5,4],[2,1]] => [[4,4,4,4,3],[2,1]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [[4,4,4,3,3],[1]] => [[5,5,5,3],[1]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3,1,1],[]] => [[6,4,4],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[4,4,4,4,2],[1,1,1,1]] => [[5,5,4,4],[4]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [[4,4,4,4,2],[1,1,1]] => [[5,5,4,4],[3]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [[4,4,4,4,3],[1,1,1]] => [[5,5,5,4],[3]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [[4,4,4,4,3],[1,1]] => [[5,5,5,4],[2]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[3,3,3,3,3,1],[]] => [[6,5,5],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[4,4,4,4,4],[1,1,1,1]] => [[5,5,5,5],[4]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[3,3,3,3,3,3],[]] => [[6,6,6],[]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[4,4,4,4,4],[1,1]] => [[5,5,5,5],[2]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[4,4,4,4,1],[1]] => [[5,4,4,4],[1]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[5,5,5,5],[2,1,1]] => [[4,4,4,4,4],[3,1]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [[4,4,4,4,2],[1]] => [[5,5,4,4],[1]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[4,4,4,4,3],[1]] => [[5,5,5,4],[1]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [[4,4,4,4,4],[1]] => [[5,5,5,5],[1]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[4,4,4,1,1],[]] => [[5,3,3,3],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[5,5,5,2],[1,1,1]] => [[4,4,3,3,3],[3]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[5,5,5,1],[1]] => [[4,3,3,3,3],[1]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[4,4,4,3,1],[]] => [[5,4,4,3],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [[4,4,4,3,2],[]] => [[5,5,4,3],[]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[5,5,5,4],[1,1]] => [[4,4,4,4,3],[2]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [[4,4,4,3,3],[]] => [[5,5,5,3],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[5,5,5,1],[]] => [[4,3,3,3,3],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[6,6,6],[1,1]] => [[3,3,3,3,3,3],[2]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [[5,5,5,2],[]] => [[4,4,3,3,3],[]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[6,6,6],[]] => [[3,3,3,3,3,3],[]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[5,5,5,4],[]] => [[4,4,4,4,3],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[4,4,4,4,1],[]] => [[5,4,4,4],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[5,5,5,5],[1,1,1]] => [[4,4,4,4,4],[3]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [[4,4,4,4,2],[]] => [[5,5,4,4],[]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [[5,5,5,5],[1,1]] => [[4,4,4,4,4],[2]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [[4,4,4,4,3],[]] => [[5,5,5,4],[]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[5,5,5,5],[1]] => [[4,4,4,4,4],[1]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[4,4,4,4,4],[]] => [[5,5,5,5],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[5,5,5,5],[]] => [[4,4,4,4,4],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[5,5,5,5,1],[]] => [[5,4,4,4,4],[]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[5,5,5,5,5],[4]] => [[5,5,5,5,5],[1,1,1,1]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [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],[]] => [[6,5,5,5,5],[]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[4,4,4,4,4,1],[]] => [[6,5,5,5],[]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [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]] => [[6,6,6,6],[1,1,1]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[5,5,5,5,5,5],[4]] => [[6,6,6,6,6],[1,1,1,1]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [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],[]] => [[6,5,5,5,5,5],[]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [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],[]] => [[5,4,4,4,4,4],[]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[5,5,5,5,1],[1]] => [[5,4,4,4,4],[1]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[5,5,5,4,1],[]] => [[5,4,4,4,3],[]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [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]] => [[5,5,5,5,5],[2,1,1,1]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[5,5,5,5,4],[4]] => [[5,5,5,5,4],[1,1,1,1]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[6,6,6,6,6],[5]] => [[5,5,5,5,5,5],[1,1,1,1,1]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[6,6,6,6,6,6],[5]] => [[6,6,6,6,6,6],[1,1,1,1,1]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[5,5,5,5,5,1],[1]] => [[6,5,5,5,5],[1]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[6,6,6,1],[]] => [[4,3,3,3,3,3],[]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[4,4,4,4,4,4,1],[]] => [[7,6,6,6],[]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[4,4,4,4,4,1],[1,1]] => [[6,5,5,5],[2]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[3,3,3,3,3,3,1],[]] => [[7,6,6],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[5,5,5,5,2],[1,1,1,1]] => [[5,5,4,4,4],[4]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[5,5,5,5,5],[4,1,1,1]] => [[5,5,5,5,5],[4,1,1,1]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[5,4,4,4,4],[3]] => [[5,5,5,5,1],[1,1,1]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [[5,5,4,4,4],[4]] => [[5,5,5,5,2],[1,1,1,1]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[7,7,7,1],[]] => [[4,3,3,3,3,3,3],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[4,4,4,4,1,1],[]] => [[6,4,4,4],[]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[4,4,4,4,4,1],[3]] => [[6,5,5,5],[1,1,1]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[6,6,6,2],[1,1,1]] => [[4,4,3,3,3,3],[3]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [[6,5,5,5],[4]] => [[4,4,4,4,4,1],[1,1,1,1]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[4,4,4,4,4,4],[3,3]] => [[6,6,6,6],[2,2,2]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[6,6,6,6,2],[1,1,1,1]] => [[5,5,4,4,4,4],[4]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[6,5,5,5,5],[4]] => [[5,5,5,5,5,1],[1,1,1,1]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[5,5,5,5,5,1],[4]] => [[6,5,5,5,5],[1,1,1,1]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[6,6,3,1],[]] => [[4,3,3,2,2,2],[]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[5,5,5,5,5,5],[4,4]] => [[6,6,6,6,6],[2,2,2,2]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[9],[]] => [[1,1,1,1,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,2],[]] => [[2,2,1,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,3],[1]] => [[2,2,2,1,1,1,1,1],[1]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,2,2],[]] => [[3,3,1,1,1,1,1],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[8,6],[4]] => [[2,2,2,2,2,2,1,1],[1,1,1,1]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[8,7],[5]] => [[2,2,2,2,2,2,2,1],[1,1,1,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[7,6,6],[4,4]] => [[3,3,3,3,3,3,1],[2,2,2,2]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,2,2,2],[]] => [[7,7,1],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[8,7],[4]] => [[2,2,2,2,2,2,2,1],[1,1,1,1]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [[6,5,5,4],[]] => [[4,4,4,4,3,1],[]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[6,5,5,5],[1,1,1]] => [[4,4,4,4,4,1],[3]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [[6,5,5,5],[1]] => [[4,4,4,4,4,1],[1]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [[5,4,4,4,4],[]] => [[5,5,5,5,1],[]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [[6,5,5,5],[]] => [[4,4,4,4,4,1],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[8,8],[6]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[7,7,7],[5,5]] => [[3,3,3,3,3,3,3],[2,2,2,2,2]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[6,6,6,6],[4,4,4]] => [[4,4,4,4,4,4],[3,3,3,3]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,3,3],[1,1,1,1,1,1]] => [[7,7,7],[6]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2,2,2],[]] => [[8,8],[]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[5,5,5,5,5],[3,3,3]] => [[5,5,5,5,5],[3,3,3]]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [[6,6,6,3],[4]] => [[4,4,4,3,3,3],[1,1,1,1]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[4,4,4,4,4,2],[2]] => [[6,6,5,5],[1,1]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [[5,5,5,5,5],[3]] => [[5,5,5,5,5],[1,1,1]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[8,8],[5]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[7,7,6],[4,4]] => [[3,3,3,3,3,3,2],[2,2,2,2]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[7,7,6],[4]] => [[3,3,3,3,3,3,2],[1,1,1,1]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[8,8],[4]] => [[2,2,2,2,2,2,2,2],[1,1,1,1]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[8,8],[3]] => [[2,2,2,2,2,2,2,2],[1,1,1]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[8,8],[2]] => [[2,2,2,2,2,2,2,2],[1,1]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[7,7,3],[1]] => [[3,3,3,2,2,2,2],[1]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[8,8],[1]] => [[2,2,2,2,2,2,2,2],[1]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[8,8],[]] => [[2,2,2,2,2,2,2,2],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [[7,7,3],[]] => [[3,3,3,2,2,2,2],[]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[6,6,5,5],[1,1]] => [[4,4,4,4,4,2],[2]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [[6,6,5,5],[]] => [[4,4,4,4,4,2],[]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[6,6,6,2],[3]] => [[4,4,3,3,3,3],[1,1,1]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[7,7,7],[4]] => [[3,3,3,3,3,3,3],[1,1,1,1]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [[4,4,4,4,4,4],[1,1,1]] => [[6,6,6,6],[3]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [[5,5,5,5,4],[2]] => [[5,5,5,5,4],[1,1]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [[4,4,4,4,4,3],[1]] => [[6,6,6,5],[1]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [[5,5,5,5,5],[2]] => [[5,5,5,5,5],[1,1]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[4,4,4,3,3,3],[]] => [[6,6,6,3],[]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [[6,6,6,5],[2]] => [[4,4,4,4,4,3],[1,1]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [[6,6,6,4],[1]] => [[4,4,4,4,3,3],[1]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [[6,6,6,4],[]] => [[4,4,4,4,3,3],[]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[6,6,6,5],[1,1,1]] => [[4,4,4,4,4,3],[3]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [[6,6,6,5],[1]] => [[4,4,4,4,4,3],[1]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [[6,6,6,5],[]] => [[4,4,4,4,4,3],[]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [[5,5,5,5,3],[1]] => [[5,5,5,4,4],[1]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [[6,6,6,6],[2]] => [[4,4,4,4,4,4],[1,1]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[5,5,5,5,5],[1,1,1,1]] => [[5,5,5,5,5],[4]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[4,4,4,4,4,4],[]] => [[6,6,6,6],[]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[5,5,5,5,5],[1]] => [[5,5,5,5,5],[1]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[6,6,6,6],[1,1,1]] => [[4,4,4,4,4,4],[3]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[5,5,5,5,2],[]] => [[5,5,4,4,4],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[6,6,6,6],[1,1]] => [[4,4,4,4,4,4],[2]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [[5,5,5,5,3],[]] => [[5,5,5,4,4],[]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [[6,6,6,6],[1]] => [[4,4,4,4,4,4],[1]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [[5,5,5,5,4],[]] => [[5,5,5,5,4],[]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[6,6,6,6],[]] => [[4,4,4,4,4,4],[]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[5,5,5,5,5],[]] => [[5,5,5,5,5],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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],[]] => [[9],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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]] => [[8,8],[7]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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]] => [[7,7,7],[6,6]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [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]] => [[5,5,5,5,5],[4,4,4,4]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[7,7,7],[6,6]] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[8,8],[7]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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],[]] => [[10],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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]] => [[9,9],[8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [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]] => [[8,8],[6]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [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]] => [[7,7,7],[6,5]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[9,9],[8]] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[10],[]] => [[1,1,1,1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1,1]] => [[10,10],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [[9,9],[7]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1]] => [[8,8],[5]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,3],[2,2,2,2,2]] => [[7,7,7],[5,5]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[9,9],[7]] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[11],[]] => [[1,1,1,1,1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2,2],[1,1,1,1]] => [[8,8],[4]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [[8,8,8],[6,6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[9,9],[6]] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2,2],[1,1,1]] => [[8,8],[3]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,3],[2,2,2,2]] => [[7,7,7],[4,4]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[9,9],[5]] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,2,2,2],[1,1]] => [[8,8],[2]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2]] => [[8,8,8],[5,5]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3,3,3],[2,1,1,1,1,1]] => [[7,7,7],[6,1]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[9,9],[4]] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2,2,2,2],[1]] => [[8,8],[1]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[4,4,4,4,4,4],[3,3,3]] => [[6,6,6,6],[3,3,3]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[9,9],[3]] => [[2,2,2,2,2,2,2,2,2],[1,1,1]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4,4,4],[3,3,3,3]] => [[7,7,7,7],[4,4,4]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[9,9],[2]] => [[2,2,2,2,2,2,2,2,2],[1,1]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,3,3,3],[1,1,1,1,1,1,1]] => [[8,8,8],[7]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[9,9],[1]] => [[2,2,2,2,2,2,2,2,2],[1]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [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]] => [[8,6],[5]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [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]] => [[8,7],[5]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [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]] => [[8,5],[4]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,2,1],[2,2,2,2,1]] => [[7,6,5],[5,4]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2,2,2],[2,1,1,1,1,1]] => [[7,7,2],[6,1]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[5,5,5,5,2],[4,1,1,1]] => [[5,5,4,4,4],[4,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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],[]] => [[8,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,2,2],[1,1,1,1,1,1]] => [[7,7,1],[6]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [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]] => [[7,6,1],[5]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => [[7,2,1],[1]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[5,4,4,4,1],[3]] => [[5,4,4,4,1],[1,1,1]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1,1,1],[]] => [[8,2],[]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [[5,5,4,4,4],[3,3]] => [[5,5,5,5,2],[2,2,2]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[5,5,3,3,3],[2,2]] => [[5,5,5,2,2],[2,2]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[5,5,5,3,3],[2,2,2]] => [[5,5,5,3,3],[3,3]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[5,5,5,2,2],[1,1,1]] => [[5,5,3,3,3],[3]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1,1,1,1],[1,1,1]] => [[9,4],[3]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[4,4,4,4,4,4,4],[3,3,3]] => [[7,7,7,7],[3,3,3]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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],[]] => [[9,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [[8,8,1],[7]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[5,5,4,4,4,4],[3,3]] => [[6,6,6,6,2],[2,2,2]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[6,6,4,4,4],[3,3]] => [[5,5,5,5,2,2],[2,2,2]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[5,5,5,3,3,3],[2,2,2]] => [[6,6,6,3,3],[3,3]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[6,6,6,3,3],[2,2,2]] => [[5,5,5,3,3,3],[3,3]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[5,5,5,5,2,2],[1,1,1,1]] => [[6,6,4,4,4],[4]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[6,6,6,6,6],[]] => [[5,5,5,5,5,5],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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],[]] => [[7,1,1],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1,1],[]] => [[6,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1,1],[]] => [[5,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1,1],[]] => [[4,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1,1],[]] => [[3,1,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,1],[]] => [[2,1,1,1,1,1,1,1],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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],[]] => [[8,1,1],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [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],[]] => [[7,2,1],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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],[]] => [[7,1,1,1],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1,1,1],[]] => [[6,2,1,1],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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],[]] => [[6,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1,1,1],[]] => [[5,2,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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],[]] => [[5,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,1,1],[]] => [[4,2,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1,1,1],[]] => [[4,1,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,2,1],[]] => [[3,2,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,1,1],[]] => [[3,1,1,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[9,1],[]] => [[2,1,1,1,1,1,1,1,1],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[4,4,4,4,4,4,4],[1,1,1,1]] => [[7,7,7,7],[4]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[4,4,4,3,3,3,3],[]] => [[7,7,7,3],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[4,4,4,4,4,4,4,4],[1,1,1,1,1]] => [[8,8,8,8],[5]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[8,8,3],[]] => [[3,3,3,2,2,2,2,2],[]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[8,8,8],[5]] => [[3,3,3,3,3,3,3,3],[1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1,1,1,1],[]] => [[10,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,3,3],[2,2,2,2,2]] => [[6,6,6,1],[5,5]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[9,2],[]] => [[2,2,1,1,1,1,1,1,1],[]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [[6,6,6,6,5],[]] => [[5,5,5,5,5,4],[]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [[6,6,6,6,6],[1]] => [[5,5,5,5,5,5],[1]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [[6,6,6,6,6,6],[1]] => [[6,6,6,6,6,6],[1]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [[5,5,5,5,5,5],[1,1]] => [[6,6,6,6,6],[2]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [[5,5,5,5,4,4],[]] => [[6,6,6,6,4],[]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [[6,6,6,6,6,5],[]] => [[6,6,6,6,6,5],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[5,3,3,3,3],[2,2,2,2]] => [[5,5,5,1,1],[4,4]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2,2,2],[1,1,1,1,1]] => [[6,6,1,1],[5]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2,2,1],[]] => [[8,7],[]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [[6,5,5,5,5],[]] => [[5,5,5,5,5,1],[]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[6,6,6,6,6],[1,1,1,1]] => [[5,5,5,5,5,5],[4]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[5,5,5,5,5,5],[]] => [[6,6,6,6,6],[]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [[5,5,5,5,5,5],[1]] => [[6,6,6,6,6],[1]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [[6,6,6,5,5],[]] => [[5,5,5,5,5,3],[]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [[5,5,5,5,5,5],[2]] => [[6,6,6,6,6],[1,1]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [[6,6,5,5,5],[]] => [[5,5,5,5,5,2],[]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [[5,5,5,5,5,5],[3]] => [[6,6,6,6,6],[1,1,1]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,3,2],[1,1,1,1,1,1]] => [[7,7,6],[6]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2,2,2,2],[1]] => [[7,7,1],[1]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,2,2,1],[]] => [[7,6,1],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,2,2,2,2],[]] => [[8,8,1],[]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [[7,7,7,7,7],[]] => [[5,5,5,5,5,5,5],[]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [[6,4,4,4],[3]] => [[4,4,4,4,1,1],[1,1,1]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [[4,4,4,3,3,3],[2,2,2]] => [[6,6,6,3],[3,3]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[6,6,3,3],[2,2]] => [[4,4,4,2,2,2],[2,2]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[4,4,4,4,2,2],[1,1,1,1]] => [[6,6,4,4],[4]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[7,7,1],[5]] => [[3,2,2,2,2,2,2],[1,1,1,1,1]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[7,7,2],[6]] => [[3,3,2,2,2,2,2],[1,1,1,1,1,1]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,2],[1]] => [[2,2,1,1,1,1,1,1],[1]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[8,7],[6]] => [[2,2,2,2,2,2,2,1],[1,1,1,1,1,1]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[9,9],[]] => [[2,2,2,2,2,2,2,2,2],[]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[6,6,4,4],[3,3]] => [[4,4,4,4,2,2],[2,2,2]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[6,6,6,3],[2,2,2]] => [[4,4,4,3,3,3],[3,3]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[5,5,5,5,5,2],[]] => [[6,6,5,5,5],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[4,4,4,2,2,2],[1,1,1]] => [[6,6,3,3],[3]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[6,6,6,6,6],[1,1,1]] => [[5,5,5,5,5,5],[3]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[5,5,5,5,5,3],[]] => [[6,6,6,5,5],[]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [[4,4,3,3,3,3],[2,2]] => [[6,6,6,2],[2,2]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[6,6,6,6,6],[1,1]] => [[5,5,5,5,5,5],[2]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [[5,5,5,5,5,4],[]] => [[6,6,6,6,5],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[6,6,6,2],[2,2,1]] => [[4,4,3,3,3,3],[3,2]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[5,4,4,4,2],[3]] => [[5,5,4,4,1],[1,1,1]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[4,4,4,3,2,2],[1,1,1,1]] => [[6,6,4,3],[4]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[5,5,4,4,4],[3,3,1]] => [[5,5,5,5,2],[3,2,2]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4,1],[3,3,3,3]] => [[6,5,5,5],[4,4,4]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,1,1],[2,2,2,2]] => [[7,5,5],[4,4]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1,1,1,1],[2,2]] => [[8,3,3],[2,2]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1,1,1,1],[3]] => [[7,2,2,2],[1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[6,5,5,5],[4,4,4]] => [[4,4,4,4,4,1],[3,3,3,3]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4,2],[3,3,3,3,1]] => [[6,6,5,5],[5,4,4]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[9,5],[3]] => [[2,2,2,2,2,1,1,1,1],[1,1,1]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2,2,2,1],[]] => [[9,8],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[7,7,1],[]] => [[3,2,2,2,2,2,2],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[3,3,3,3,3,3,3,1],[]] => [[8,7,7],[]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,3,1],[1,1,1,1]] => [[7,6,6],[4]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[8,8,1],[]] => [[3,2,2,2,2,2,2,2],[]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [[7,6,6,6],[]] => [[4,4,4,4,4,4,1],[]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [[7,6,6,6,6],[]] => [[5,5,5,5,5,5,1],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1,1,1,1],[]] => [[9,1,1],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2,2,2,2],[1,1,1,1,1,1]] => [[7,7,1,1],[6]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2,2,1],[1,1,1,1]] => [[6,5,1,1],[4]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [[5,5,5,4,4],[4,4]] => [[5,5,5,5,3],[2,2,2,2]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,3,3],[3,3,3]] => [[6,6,6,4],[3,3,3]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4,3],[3,3,3,3]] => [[6,6,6,5],[4,4,4]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,2],[2,2,2,2,2]] => [[7,7,6],[5,5]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[7,7,6],[5,5]] => [[3,3,3,3,3,3,2],[2,2,2,2,2]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[7,7,5],[4,4]] => [[3,3,3,3,3,2,2],[2,2,2,2]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[7,7,4],[3,3]] => [[3,3,3,3,2,2,2],[2,2,2]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[7,7,3],[2,2]] => [[3,3,3,2,2,2,2],[2,2]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[7,7,2],[1,1]] => [[3,3,2,2,2,2,2],[2]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,2,1,1],[]] => [[6,4,1,1],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2,1,1],[1,1]] => [[5,3,1,1,1],[2]]
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
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 $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.
Map
conjugate
Description
The conjugate of the skew partition.
The conjugate of a skew partition $\lambda$ is the skew partition $\lambda^*$ whose Ferrers diagram is obtained from the Ferrers diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate of a skew partition $\lambda$ is the skew partition $\lambda^*$ whose Ferrers diagram is obtained from the Ferrers diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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