Processing math: 100%

Identifier
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00112: Set partitions —complement⟶ Set partitions
Images
[1,0] => [1] => {{1}} => {{1}}
[1,0,1,0] => [2,1] => {{1,2}} => {{1,2}}
[1,1,0,0] => [1,2] => {{1},{2}} => {{1},{2}}
[1,0,1,0,1,0] => [2,1,3] => {{1,2},{3}} => {{1},{2,3}}
[1,0,1,1,0,0] => [2,3,1] => {{1,2,3}} => {{1,2,3}}
[1,1,0,0,1,0] => [3,1,2] => {{1,2,3}} => {{1,2,3}}
[1,1,0,1,0,0] => [1,3,2] => {{1},{2,3}} => {{1,2},{3}}
[1,1,1,0,0,0] => [1,2,3] => {{1},{2},{3}} => {{1},{2},{3}}
[1,0,1,0,1,0,1,0] => [2,1,4,3] => {{1,2},{3,4}} => {{1,2},{3,4}}
[1,0,1,0,1,1,0,0] => [2,4,1,3] => {{1,2,3,4}} => {{1,2,3,4}}
[1,0,1,1,0,0,1,0] => [2,1,3,4] => {{1,2},{3},{4}} => {{1},{2},{3,4}}
[1,0,1,1,0,1,0,0] => [2,3,1,4] => {{1,2,3},{4}} => {{1},{2,3,4}}
[1,0,1,1,1,0,0,0] => [2,3,4,1] => {{1,2,3,4}} => {{1,2,3,4}}
[1,1,0,0,1,0,1,0] => [3,1,4,2] => {{1,2,3,4}} => {{1,2,3,4}}
[1,1,0,0,1,1,0,0] => [3,4,1,2] => {{1,3},{2,4}} => {{1,3},{2,4}}
[1,1,0,1,0,0,1,0] => [3,1,2,4] => {{1,2,3},{4}} => {{1},{2,3,4}}
[1,1,0,1,0,1,0,0] => [1,3,2,4] => {{1},{2,3},{4}} => {{1},{2,3},{4}}
[1,1,0,1,1,0,0,0] => [1,3,4,2] => {{1},{2,3,4}} => {{1,2,3},{4}}
[1,1,1,0,0,0,1,0] => [4,1,2,3] => {{1,2,3,4}} => {{1,2,3,4}}
[1,1,1,0,0,1,0,0] => [1,4,2,3] => {{1},{2,3,4}} => {{1,2,3},{4}}
[1,1,1,0,1,0,0,0] => [1,2,4,3] => {{1},{2},{3,4}} => {{1,2},{3},{4}}
[1,1,1,1,0,0,0,0] => [1,2,3,4] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}}
[1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => {{1,2},{3,4},{5}} => {{1},{2,3},{4,5}}
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}}
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => {{1,2},{3,4,5}} => {{1,2,3},{4,5}}
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => {{1,2,4},{3,5}} => {{1,3},{2,4,5}}
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => {{1,2},{3,4,5}} => {{1,2,3},{4,5}}
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => {{1,2},{3},{4,5}} => {{1,2},{3},{4,5}}
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => {{1,2,3},{4,5}} => {{1,2},{3,4,5}}
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => {{1},{2},{3},{4,5}}
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => {{1},{2},{3,4,5}}
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}}
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}}
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => {{1,3},{2,4},{5}} => {{1},{2,4},{3,5}}
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => {{1,3},{2,4,5}} => {{1,2,4},{3,5}}
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => {{1,3},{2,4,5}} => {{1,2,4},{3,5}}
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => {{1,2,3},{4,5}} => {{1,2},{3,4,5}}
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}} => {{1,2},{3,4},{5}}
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => {{1},{2,3,4,5}} => {{1,2,3,4},{5}}
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => {{1,2,3},{4},{5}} => {{1},{2},{3,4,5}}
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => {{1},{2,3},{4},{5}} => {{1},{2},{3,4},{5}}
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => {{1},{2,3,4},{5}} => {{1},{2,3,4},{5}}
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => {{1},{2,3,4,5}} => {{1,2,3,4},{5}}
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => {{1,2,4},{3,5}} => {{1,3},{2,4,5}}
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => {{1},{2,3,4,5}} => {{1,2,3,4},{5}}
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => {{1},{2,4},{3,5}} => {{1,3},{2,4},{5}}
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}}
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => {{1},{2,3,4},{5}} => {{1},{2,3,4},{5}}
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => {{1},{2},{3,4},{5}} => {{1},{2,3},{4},{5}}
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => {{1},{2},{3,4,5}} => {{1,2,3},{4},{5}}
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => {{1},{2,3,4,5}} => {{1,2,3,4},{5}}
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => {{1},{2},{3,4,5}} => {{1,2,3},{4},{5}}
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => {{1},{2},{3},{4,5}} => {{1,2},{3},{4},{5}}
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}}
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => {{1,2,3,4},{5,6}} => {{1,2},{3,4,5,6}}
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => {{1,2},{3,4,5,6}} => {{1,2,3,4},{5,6}}
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => {{1,2,4},{3,5,6}} => {{1,2,4},{3,5,6}}
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => {{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}}
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => {{1},{2,3,4},{5,6}}
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => {{1,2,4},{3,5},{6}} => {{1},{2,4},{3,5,6}}
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => {{1,2,3,4},{5,6}}
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => {{1,2,4},{3,5,6}} => {{1,2,4},{3,5,6}}
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => {{1,2},{3,4,5,6}} => {{1,2,3,4},{5,6}}
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => {{1,2},{3,5},{4,6}} => {{1,3},{2,4},{5,6}}
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => {{1,2,3,5},{4,6}} => {{1,3},{2,4,5,6}}
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}} => {{1},{2,3,4},{5,6}}
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => {{1},{2,3},{4},{5,6}}
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => {{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => {{1,2,3},{4},{5,6}}
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}}
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => {{1,2,3,5},{4,6}} => {{1,3},{2,4,5,6}}
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}} => {{1,2,3,4},{5,6}}
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => {{1,2},{3},{4,5,6}} => {{1,2,3},{4},{5,6}}
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}}
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}}
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => {{1,2},{3},{4,5,6}}
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => {{1,2},{3,4,5,6}}
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
>>> Load all 2181 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5,6}}
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => {{1},{2},{3},{4,5,6}}
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}}
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => {{1,2,3,4},{5,6}} => {{1,2},{3,4,5,6}}
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => {{1,3},{2,4},{5,6}} => {{1,2},{3,5},{4,6}}
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => {{1,3},{2,4,5,6}} => {{1,2,3,5},{4,6}}
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}}
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}} => {{1},{2},{3,5},{4,6}}
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => {{1,3},{2,4,5},{6}} => {{1},{2,3,5},{4,6}}
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => {{1,3},{2,4,5,6}} => {{1,2,3,5},{4,6}}
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => {{1,3,5},{2,4,6}}
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => {{1,3},{2,4,5,6}} => {{1,2,3,5},{4,6}}
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => {{1,2,3,5},{4,6}} => {{1,3},{2,4,5,6}}
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => {{1,3},{2,5},{4,6}} => {{1,3},{2,5},{4,6}}
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => {{1,3,4,6},{2,5}} => {{1,3,4,6},{2,5}}
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => {{1,3},{2,4,5},{6}} => {{1},{2,3,5},{4,6}}
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => {{1,2,3},{4,5},{6}} => {{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => {{1},{2,3},{4,5},{6}}
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}}
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}}
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => {{1,2,3},{4,5},{6}}
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => {{1},{2,3,5},{4,6}} => {{1,3},{2,4,5},{6}}
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => {{1,3},{2,4,5,6}} => {{1,2,3,5},{4,6}}
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}}
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}} => {{1,2,3},{4,5},{6}}
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => {{1,2,3},{4},{5,6}} => {{1,2},{3},{4,5,6}}
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => {{1,2},{3},{4,5},{6}}
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => {{1,2},{3,4,5},{6}}
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => {{1,2,3},{4},{5},{6}} => {{1},{2},{3},{4,5,6}}
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => {{1},{2},{3},{4,5},{6}}
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => {{1},{2},{3,4,5},{6}}
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}}
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => {{1,2,4},{3,5,6}} => {{1,2,4},{3,5,6}}
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => {{1,3,4,6},{2,5}} => {{1,3,4,6},{2,5}}
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => {{1,4},{2,5},{3,6}}
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => {{1,2,4},{3,5},{6}} => {{1},{2,4},{3,5,6}}
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}}
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => {{1},{2,4},{3,5},{6}} => {{1},{2,4},{3,5},{6}}
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => {{1},{2,4},{3,5,6}} => {{1,2,4},{3,5},{6}}
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => {{1,2,4},{3,5,6}} => {{1,2,4},{3,5,6}}
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => {{1},{2,4},{3,5,6}} => {{1,2,4},{3,5},{6}}
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}} => {{1,2},{3,4,5,6}}
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}} => {{1,2},{3,4,5},{6}}
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => {{1,2},{3,4},{5},{6}}
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => {{1},{2},{3,4,5,6}} => {{1,2,3,4},{5},{6}}
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}}
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => {{1},{2,3,4},{5},{6}} => {{1},{2},{3,4,5},{6}}
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => {{1},{2},{3,4},{5},{6}}
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => {{1},{2,3,4},{5},{6}}
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => {{1,2,3,4},{5},{6}}
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => {{1,3,5},{2,4,6}} => {{1,3,5},{2,4,6}}
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => {{1,2,3,5},{4,6}} => {{1,3},{2,4,5,6}}
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => {{1},{2,3,5},{4,6}} => {{1,3},{2,4,5},{6}}
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => {{1},{2},{3,4,5,6}} => {{1,2,3,4},{5},{6}}
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}} => {{1,3},{2,4},{5},{6}}
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}}
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}} => {{1},{2,3,4},{5},{6}}
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => {{1},{2,3},{4},{5},{6}}
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => {{1,2,3},{4},{5},{6}}
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => {{1},{2},{3,4,5,6}} => {{1,2,3,4},{5},{6}}
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}} => {{1,2,3},{4},{5},{6}}
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => {{1,2},{3},{4},{5},{6}}
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7] => {{1,2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => {{1,2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7] => {{1,2,4},{3,5,6},{7}} => {{1},{2,3,5},{4,6,7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => {{1,2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5] => {{1,2,4},{3,5,6,7}} => {{1,2,3,5},{4,6,7}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5] => {{1,2},{3,4,6},{5,7}} => {{1,3},{2,4,5},{6,7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5] => {{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,7,3,5] => {{1,2,4},{3,6},{5,7}} => {{1,3},{2,5},{4,6,7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5] => {{1,2,4,5,7},{3,6}} => {{1,3,4,6,7},{2,5}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6,7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,7,3,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6] => {{1,2,4},{3,5,6,7}} => {{1,2,3,5},{4,6,7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6] => {{1,2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6,7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => {{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6] => {{1,2,4},{3,5},{6,7}} => {{1,2},{3,5},{4,6,7}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,3,6] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6] => {{1,2,4},{3,5,6,7}} => {{1,2,3,5},{4,6,7}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => {{1,2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => {{1,2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7] => {{1,2,4},{3,5},{6},{7}} => {{1},{2},{3,5},{4,6,7}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,7] => {{1,2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7] => {{1,2,4},{3,5,6},{7}} => {{1},{2,3,5},{4,6,7}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3] => {{1,2,4},{3,5,6,7}} => {{1,2,3,5},{4,6,7}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3] => {{1,2,4,6},{3,5,7}} => {{1,3,5},{2,4,6,7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => {{1,2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => {{1,2},{3,5},{4,6},{7}} => {{1},{2,4},{3,5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7] => {{1,2,3,5},{4,6},{7}} => {{1},{2,4},{3,5,6,7}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => {{1,2},{3,5},{4,6,7}} => {{1,2,4},{3,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4] => {{1,2,3,5},{4,6,7}} => {{1,2,4},{3,5,6,7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4] => {{1,2,4,5,7},{3,6}} => {{1,3,4,6,7},{2,5}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,5,6,7,1,3,4] => {{1,2,5},{3,6},{4,7}} => {{1,4},{2,5},{3,6,7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => {{1,2},{3,5},{4,6,7}} => {{1,2,4},{3,5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,5,1,7,3,4,6] => {{1,2,3,5},{4,6,7}} => {{1,2,4},{3,5,6,7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6] => {{1,2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => {{1,2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6,7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,1,7,4,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => {{1,2,3,5},{4,6,7}} => {{1,2,4},{3,5,6,7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => {{1,2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => {{1,2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7] => {{1,2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => {{1,2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6,7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7] => {{1,2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7] => {{1,2,3,5},{4,6},{7}} => {{1},{2,4},{3,5,6,7}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => {{1,2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6,7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4] => {{1,2,3,5},{4,6,7}} => {{1,2,4},{3,5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => {{1,2},{3,4,6},{5,7}} => {{1,3},{2,4,5},{6,7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5] => {{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => {{1,2,4,6},{3,5,7}} => {{1,3,5},{2,4,6,7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => {{1,2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6,7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => {{1,2},{3},{4,6},{5,7}} => {{1,3},{2,4},{5},{6,7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5] => {{1,2,3},{4,6},{5,7}} => {{1,3},{2,4},{5,6,7}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,7,4,5] => {{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => {{1,2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6,7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7] => {{1,2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => {{1,2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6,7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,7] => {{1,2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6,7}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7] => {{1,2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => {{1,2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6,7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5] => {{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => {{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => {{1,2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => {{1,2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6,7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6] => {{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => {{1,2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6,7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6] => {{1,2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6,7}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => {{1,2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6,7}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6,7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6,7}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7] => {{1,2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7] => {{1,3},{2,4},{5,6},{7}} => {{1},{2,3},{4,6},{5,7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7] => {{1,3},{2,4,5,6},{7}} => {{1},{2,3,4,6},{5,7}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5] => {{1,3},{2,4},{5,6,7}} => {{1,2,3},{4,6},{5,7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5] => {{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5] => {{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5] => {{1,3},{2,4,6},{5,7}} => {{1,3},{2,4,6},{5,7}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5] => {{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6] => {{1,3},{2,4},{5,6,7}} => {{1,2,3},{4,6},{5,7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,7,2,5,6] => {{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => {{1,2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6] => {{1,3},{2,4},{5},{6,7}} => {{1,2},{3},{4,6},{5,7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6] => {{1,3},{2,4,5},{6,7}} => {{1,2},{3,4,6},{5,7}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6] => {{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => {{1,3,5},{2,4,6,7}} => {{1,2,4,6},{3,5,7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => {{1,3},{2,4},{5},{6},{7}} => {{1},{2},{3},{4,6},{5,7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7] => {{1,3},{2,4,5},{6},{7}} => {{1},{2},{3,4,6},{5,7}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7] => {{1,3},{2,4,5,6},{7}} => {{1},{2,3,4,6},{5,7}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7] => {{1,3,5},{2,4,6},{7}} => {{1},{2,4,6},{3,5,7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2] => {{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2] => {{1,3,5},{2,4,6,7}} => {{1,2,4,6},{3,5,7}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7] => {{1,3},{2,4,5,6},{7}} => {{1},{2,3,4,6},{5,7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => {{1,2,3,5},{4,6},{7}} => {{1},{2,4},{3,5,6,7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7] => {{1,3},{2,5},{4,6},{7}} => {{1},{2,4},{3,6},{5,7}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => {{1,3,4,6},{2,5},{7}} => {{1},{2,4,5,7},{3,6}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4] => {{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => {{1,2,3,5},{4,6,7}} => {{1,2,4},{3,5,6,7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4] => {{1,3},{2,5},{4,6,7}} => {{1,2,4},{3,6},{5,7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4] => {{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4] => {{1,2,3,5,6},{4,7}} => {{1,4},{2,3,5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6] => {{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => {{1,2,3,5},{4,6,7}} => {{1,2,4},{3,5,6,7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6] => {{1,3},{2,5},{4,6,7}} => {{1,2,4},{3,6},{5,7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => {{1,3},{2,4,5},{6,7}} => {{1,2},{3,4,6},{5,7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => {{1},{2,3,4,5},{6,7}} => {{1,2},{3,4,5,6},{7}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => {{1},{2,3},{4,5,6,7}} => {{1,2,3,4},{5,6},{7}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => {{1},{2,3,5},{4,6,7}} => {{1,2,4},{3,5,6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7] => {{1,3},{2,4,5},{6},{7}} => {{1},{2},{3,4,6},{5,7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7] => {{1,2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => {{1},{2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6},{7}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7] => {{1,2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => {{1},{2,3,5},{4,6},{7}} => {{1},{2,4},{3,5,6},{7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}} => {{1,2,3,4},{5,6},{7}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => {{1},{2,3,5},{4,6,7}} => {{1,2,4},{3,5,6},{7}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => {{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5] => {{1,3},{2,4,6},{5,7}} => {{1,3},{2,4,6},{5,7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,6,1,7,2,4,5] => {{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5] => {{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => {{1},{2,3},{4,5,6,7}} => {{1,2,3,4},{5,6},{7}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,7,4,5] => {{1,2,3},{4,6},{5,7}} => {{1,3},{2,4},{5,6,7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => {{1},{2,3},{4,6},{5,7}} => {{1,3},{2,4},{5,6},{7}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => {{1},{2,3,4,6},{5,7}} => {{1,3},{2,4,5,6},{7}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => {{1,3},{2,4,5,6},{7}} => {{1},{2,3,4,6},{5,7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,7] => {{1,2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6,7}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6},{7}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5] => {{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6},{7}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}} => {{1,2,3},{4,5,6},{7}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => {{1},{2,3,4,6},{5,7}} => {{1,3},{2,4,5,6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6] => {{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}} => {{1,2,3,4},{5,6},{7}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6] => {{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6},{7}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => {{1},{2,3,4},{5,6,7}} => {{1,2,3},{4,5,6},{7}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => {{1,2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6,7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6},{7}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6},{7}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}} => {{1,2},{3,4,5,6},{7}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6,7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6},{7}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6},{7}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6},{7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => {{1,2,4},{3,5,6},{7}} => {{1},{2,3,5},{4,6,7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => {{1,3,4,6},{2,5},{7}} => {{1},{2,4,5,7},{3,6}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => {{1,4},{2,5},{3,6},{7}} => {{1},{2,5},{3,6},{4,7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => {{1,2,4},{3,5,6,7}} => {{1,2,3,5},{4,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3] => {{1,4},{2,5},{3,6,7}} => {{1,2,5},{3,6},{4,7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3] => {{1,2,4,6},{3,5,7}} => {{1,3,5},{2,4,6,7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3] => {{1,4},{2,3,5,6,7}} => {{1,2,3,5,6},{4,7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => {{1,2,4},{3,5,6,7}} => {{1,2,3,5},{4,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,5,7,1,2,3,6] => {{1,4},{2,5},{3,6,7}} => {{1,2,5},{3,6},{4,7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => {{1,2,4},{3,5},{6,7}} => {{1,2},{3,5},{4,6,7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => {{1},{2,3,4,5},{6,7}} => {{1,2},{3,4,5,6},{7}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => {{1},{2,4},{3,5},{6,7}} => {{1,2},{3,5},{4,6},{7}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => {{1},{2,4},{3,5,6,7}} => {{1,2,3,5},{4,6},{7}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => {{1,2,4},{3,5},{6},{7}} => {{1},{2},{3,5},{4,6,7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => {{1},{2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6},{7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => {{1},{2,4},{3,5},{6},{7}} => {{1},{2},{3,5},{4,6},{7}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => {{1},{2,4},{3,5,6},{7}} => {{1},{2,3,5},{4,6},{7}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => {{1},{2,4},{3,5,6,7}} => {{1,2,3,5},{4,6},{7}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => {{1},{2,4,6},{3,5,7}} => {{1,3,5},{2,4,6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => {{1,2,4},{3,6},{5,7}} => {{1,3},{2,5},{4,6,7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5] => {{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => {{1,2,4,5,7},{3,6}} => {{1,3,4,6,7},{2,5}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5] => {{1,4},{2,3,5,6,7}} => {{1,2,3,5,6},{4,7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => {{1,2,4},{3,5,6,7}} => {{1,2,3,5},{4,6,7}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => {{1},{2,4},{3,5,6,7}} => {{1,2,3,5},{4,6},{7}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5] => {{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => {{1},{2,3,4,6},{5,7}} => {{1,3},{2,4,5,6},{7}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => {{1},{2,4},{3,6},{5,7}} => {{1,3},{2,5},{4,6},{7}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => {{1},{2,4,5,7},{3,6}} => {{1,3,4,6},{2,5},{7}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => {{1,2,4},{3,5,6},{7}} => {{1},{2,3,5},{4,6,7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => {{1},{2,4},{3,5,6},{7}} => {{1},{2,3,5},{4,6},{7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7] => {{1,2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6},{7}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => {{1},{2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6},{7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => {{1},{2,3,4},{5,6,7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6},{7}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => {{1},{2},{3,4,6},{5,7}} => {{1,3},{2,4,5},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => {{1,2,4},{3,5,6,7}} => {{1,2,3,5},{4,6,7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => {{1},{2,4},{3,5,6,7}} => {{1,2,3,5},{4,6},{7}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6},{7}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => {{1,2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6,7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6},{7}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6},{7}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6},{7}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6},{7}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6},{7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => {{1,2,4,5,7},{3,6}} => {{1,3,4,6,7},{2,5}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => {{1,2,5},{3,6},{4,7}} => {{1,4},{2,5},{3,6,7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4] => {{1,2,3,5,6},{4,7}} => {{1,4},{2,3,5,6,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => {{1,3,5},{2,4,6,7}} => {{1,2,4,6},{3,5,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => {{1,2,3,5},{4,6,7}} => {{1,2,4},{3,5,6,7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => {{1},{2,3,5},{4,6,7}} => {{1,2,4},{3,5,6},{7}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => {{1},{2,4,5,7},{3,6}} => {{1,3,4,6},{2,5},{7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => {{1},{2,5},{3,6},{4,7}} => {{1,4},{2,5},{3,6},{7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => {{1,3,5},{2,4,6},{7}} => {{1},{2,4,6},{3,5,7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => {{1,2,3,5},{4,6},{7}} => {{1},{2,4},{3,5,6,7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => {{1},{2,3,5},{4,6},{7}} => {{1},{2,4},{3,5,6},{7}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => {{1},{2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6},{7}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => {{1},{2},{3,5},{4,6},{7}} => {{1},{2,4},{3,5},{6},{7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => {{1},{2},{3,5},{4,6,7}} => {{1,2,4},{3,5},{6},{7}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6] => {{1,3,5},{2,4,6,7}} => {{1,2,4,6},{3,5,7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6] => {{1,2,3,5},{4,6,7}} => {{1,2,4},{3,5,6,7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => {{1},{2,3,5},{4,6,7}} => {{1,2,4},{3,5,6},{7}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => {{1},{2},{3,5},{4,6,7}} => {{1,2,4},{3,5},{6},{7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}} => {{1,2},{3,4,5,6},{7}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6},{7}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6},{7}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => {{1},{2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6},{7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => {{1},{2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6},{7}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => {{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6},{7}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => {{1,2,4,6},{3,5,7}} => {{1,3,5},{2,4,6,7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => {{1},{2,4,6},{3,5,7}} => {{1,3,5},{2,4,6},{7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => {{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => {{1},{2,3,4,6},{5,7}} => {{1,3},{2,4,5,6},{7}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => {{1},{2},{3,4,6},{5,7}} => {{1,3},{2,4,5},{6},{7}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => {{1},{2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6},{7}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => {{1},{2},{3},{4,6},{5,7}} => {{1,3},{2,4},{5},{6},{7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => {{1},{2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6},{7}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => {{1},{2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6},{7}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6},{7}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6},{7}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6},{7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6},{7}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6,7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,8,7] => {{1,2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7] => {{1,2,4},{3,5,6},{7,8}} => {{1,2},{3,4,6},{5,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,8,5,7] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,8,5,7] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,8,3,5,7] => {{1,2},{3,4,6},{5,7,8}} => {{1,2,4},{3,5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => {{1,2,4},{3,6},{5,7,8}} => {{1,2,4},{3,6},{5,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7,8] => {{1,2,4},{3,5,6},{7},{8}} => {{1},{2},{3,4,6},{5,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5,8] => {{1,2},{3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5,8] => {{1,2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5,8] => {{1,2,4},{3,5,6,7},{8}} => {{1},{2,3,4,6},{5,7,8}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => {{1,2,4,5,7},{3,6},{8}} => {{1},{2,4,5,7,8},{3,6}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,6,3,7,8,5] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,3,8,5] => {{1,2},{3,4,6},{5,7,8}} => {{1,2,4},{3,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,6,1,7,3,8,5] => {{1,2,4},{3,6},{5,7,8}} => {{1,2,4},{3,6},{5,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,8,5] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,6,7,8,3,5] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,6,7,8,3,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,6,7,8,1,3,5] => {{1,2,3,4,6,7},{5,8}} => {{1,4},{2,3,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,8,6] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,3,7,5,8,6] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,7,3,5,8,6] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,7,3,5,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,4,7,1,3,5,8,6] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,7,8,5,6] => {{1,2},{3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,7,8,5,6] => {{1,2,3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,7,3,8,5,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,7,8,3,5,6] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,8,3,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,8] => {{1,2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6,8] => {{1,2,4},{3,5},{6,7},{8}} => {{1},{2,3},{4,6},{5,7,8}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6,8] => {{1,2,4},{3,5,6,7},{8}} => {{1},{2,3,4,6},{5,7,8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,7,8,6] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,7,8,6] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,5,7,3,8,6] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,1,5,7,3,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,1,7,3,8,6] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,5,7,8,3,6] => {{1,2},{3,4,5,7},{6,8}} => {{1,3},{2,4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,7,8,3,6] => {{1,2,4},{3,5,7},{6,8}} => {{1,3},{2,4,6},{5,7,8}}
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,5,7,1,8,3,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,7,8,1,3,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,4,8,3,5,6,7] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,8,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,4,8,1,3,5,6,7] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,7] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,4,5,8,3,6,7] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,5,8,3,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,8,7] => {{1,2},{3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,8,7] => {{1,2,3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,8,7] => {{1,2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,8,7] => {{1,2,4},{3,5,6},{7,8}} => {{1,2},{3,4,6},{5,7,8}}
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,4,5,6,8,3,7] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,4,1,5,6,8,3,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,4,5,1,6,8,3,7] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,4,5,6,1,8,3,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,4,5,6,8,1,3,7] => {{1,2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7,8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => {{1,2},{3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7,8] => {{1,2,4},{3,5},{6},{7},{8}} => {{1},{2},{3},{4,6},{5,7,8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7,8] => {{1,2,4},{3,5,6},{7},{8}} => {{1},{2},{3,4,6},{5,7,8}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3,8] => {{1,2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3,8] => {{1,2,4,6},{3,5,7},{8}} => {{1},{2,4,6},{3,5,7,8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,3] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,5,6,7,8,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,4,5,1,6,7,8,3] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,4,5,6,1,7,8,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,4,5,6,7,1,8,3] => {{1,2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7,8}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7] => {{1,2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7,8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7] => {{1,2},{3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6},{7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,8,7] => {{1,2,3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,8,4,7] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,8,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,5,6,8,3,4,7] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,5,1,6,8,3,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => {{1,2,5},{3,6},{4,7,8}} => {{1,2,5},{3,6},{4,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7,8] => {{1,2,3,5},{4,6},{7},{8}} => {{1},{2},{3,5},{4,6,7,8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4,8] => {{1,2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4,8] => {{1,2},{3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6},{7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4,8] => {{1,2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4,8] => {{1,2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4,8] => {{1,2,4,5,7},{3,6},{8}} => {{1},{2,4,5,7,8},{3,6}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,5,1,3,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,8,4] => {{1,2},{3,5},{4,6,7,8}} => {{1,2,3,5},{4,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5,6,1,3,7,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,8,4] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5,6,7,1,3,8,4] => {{1,2,5},{3,6},{4,7,8}} => {{1,2,5},{3,6},{4,7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,5,6,7,8,3,4] => {{1,2},{3,5,7},{4,6,8}} => {{1,3,5},{2,4,6},{7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5,1,6,7,8,3,4] => {{1,2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5,6,1,7,8,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5,6,7,1,8,3,4] => {{1,2,5},{3,4,6,7,8}} => {{1,2,3,5,6},{4,7,8}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5,6,7,8,1,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,8,6] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,7,3,4,8,6] => {{1,2},{3,5},{4,6,7,8}} => {{1,2,3,5},{4,6},{7,8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,7,3,4,8,6] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,5,7,1,3,4,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,7,8,4,6] => {{1,2},{3,4,5,7},{6,8}} => {{1,3},{2,4,5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,8,4,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,7,3,8,4,6] => {{1,2},{3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,7,8,3,4,6] => {{1,2},{3,5,6,8},{4,7}} => {{1,3,4,6},{2,5},{7,8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,7,8,3,4,6] => {{1,2,3,5,6,8},{4,7}} => {{1,3,4,6,7,8},{2,5}}
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,5,7,1,8,3,4,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => {{1,2,5},{3,4,6,7,8}} => {{1,2,3,5,6},{4,7,8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6,8] => {{1,2},{3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6,8] => {{1,2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6,8] => {{1,2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7,8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,7,8,6] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,3},{4,5},{6},{7,8}}
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,8,6] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,7,8,4,6] => {{1,2,3},{4,5,7},{6,8}} => {{1,3},{2,4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,7,1,8,4,6] => {{1,2,3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6,7,8}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,7,8,1,4,6] => {{1,2,3,5,6,8},{4,7}} => {{1,3,4,6,7,8},{2,5}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,8,4,6,7] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,5,1,3,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,8,3,4,6,7] => {{1,2},{3,5},{4,6,7,8}} => {{1,2,3,5},{4,6},{7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,5,1,8,3,4,6,7] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,5,8,1,3,4,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,3,5,1,4,8,6,7] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,5,8,4,6,7] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,8,1,4,6,7] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,8,7] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6},{7,8}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,8,7] => {{1,2,3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6,7,8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,5,6,8,4,7] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7,8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,5,6,8,4,7] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,1,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,6,1,8,4,7] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,6,8,1,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7,8] => {{1,2},{3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7,8] => {{1,2,3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7,8] => {{1,2,3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => {{1,2,3,5},{4,6},{7},{8}} => {{1},{2},{3,5},{4,6,7,8}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4,8] => {{1,2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,5,6,7,8,4] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7,8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,5,6,7,8,4] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,5,1,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,5,6,1,7,8,4] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,5,6,7,1,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,6,7,8,1,4] => {{1,2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7,8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5] => {{1,2},{3,4,6},{5,7,8}} => {{1,2,4},{3,5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,7,4,8,5] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,6,7,3,4,8,5] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,6,1,7,3,4,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => {{1,2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,6,3,7,8,4,5] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,6,1,3,7,8,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,6,1,7,3,8,4,5] => {{1,2,3,5,6,8},{4,7}} => {{1,3,4,6,7,8},{2,5}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,6,7,1,3,8,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,6,7,8,3,4,5] => {{1,2},{3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,6,1,7,8,3,4,5] => {{1,2,3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,6,7,1,8,3,4,5] => {{1,2,3,4,6,7},{5,8}} => {{1,4},{2,3,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5,8] => {{1,2},{3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6},{7,8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5,8] => {{1,2,4,6},{3,5,7},{8}} => {{1},{2,4,6},{3,5,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,8] => {{1,2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,4,8,5] => {{1,2},{3},{4,6},{5,7,8}} => {{1,2,4},{3,5},{6},{7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,3,6,7,8,4,5] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,3,1,6,7,8,4,5] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,8,4,5] => {{1,2,3,5,6,8},{4,7}} => {{1,3,4,6,7,8},{2,5}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,3,6,7,8,1,4,5] => {{1,2,3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6,7,8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,8,4,5,7] => {{1,2},{3,4,6},{5,7,8}} => {{1,2,4},{3,5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,8,4,5,7] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,1,6,8,3,4,5,7] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,6,1,8,3,4,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,6,8,1,3,4,5,7] => {{1,2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7,8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,8,5,7] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,8,5,7] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,8,4,5,7] => {{1,2,3},{4,6},{5,7,8}} => {{1,2,4},{3,5},{6,7,8}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6},{7,8}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}} => {{1,2},{3,4},{5},{6,7,8}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,8,5,7] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,8,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,8,1,5,7] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7,8] => {{1,2,3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7,8] => {{1,2},{3},{4},{5,6},{7},{8}} => {{1},{2},{3,4},{5},{6},{7,8}}
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5,8] => {{1,2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5,8] => {{1,2,3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6,7,8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,6,7,8,5] => {{1,2},{3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6},{7,8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,6,7,8,5] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,3,4,6,1,7,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,7,8,1,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,7,3,8,4,5,6] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,7,1,3,8,4,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,7,8,3,4,5,6] => {{1,2},{3,5,7},{4,6,8}} => {{1,3,5},{2,4,6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => {{1,2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,7,8,1,3,4,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,1,7,3,4,8,5,6] => {{1,2},{3,4,5,7},{6,8}} => {{1,3},{2,4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,7,4,8,5,6] => {{1,2},{3},{4,5,7},{6,8}} => {{1,3},{2,4,5},{6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,7,4,8,5,6] => {{1,2,3},{4,5,7},{6,8}} => {{1,3},{2,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,1,4,8,5,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,7,8,4,5,6] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,1,7,8,4,5,6] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => {{1,2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,7,3,4,5,8,6] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,7,4,5,8,6] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,7,1,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,3,4,7,5,8,6] => {{1,2},{3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6},{7,8}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,4,1,7,5,8,6] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,3,4,7,8,5,6] => {{1,2},{3},{4},{5,7},{6,8}} => {{1,3},{2,4},{5},{6},{7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,1,4,7,8,5,6] => {{1,2,3},{4},{5,7},{6,8}} => {{1,3},{2,4},{5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => {{1,2,3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,4,7,1,8,5,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,4,7,8,1,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => {{1,2},{3},{4},{5,6,7},{8}} => {{1},{2,3,4},{5},{6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6,8] => {{1,2},{3},{4},{5},{6,7},{8}} => {{1},{2,3},{4},{5},{6},{7,8}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6,8] => {{1,2,3,4},{5},{6,7},{8}} => {{1},{2,3},{4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,8] => {{1,2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,8,6] => {{1,2},{3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6},{7,8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,7,8,6] => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,7,8,6] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,6] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,4,5,7,1,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,5,7,8,1,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,8,4,5,6,7] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,1,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,8,1,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,4,8,5,6,7] => {{1,2},{3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,1,4,8,5,6,7] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,3,4,5,8,6,7] => {{1,2},{3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6},{7,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,3,4,1,5,8,6,7] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,8,6,7] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,3,4,5,8,1,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6},{7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,8,7] => {{1,2,3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,8,7] => {{1,2,3,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,8,7] => {{1,2,3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8] => {{1,2,3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => {{1,3},{2,4},{5,6},{7,8}} => {{1,2},{3,4},{5,7},{6,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,8,7] => {{1,3},{2,4,5,6},{7,8}} => {{1,2},{3,4,5,7},{6,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,8,5,7] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,8,5,7] => {{1,3},{2,4},{5,6,7,8}} => {{1,2,3,4},{5,7},{6,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,8,5,7] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,8,2,5,7] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,8,2,5,7] => {{1,3},{2,4,6},{5,7,8}} => {{1,2,4},{3,5,7},{6,8}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7,8] => {{1,3},{2,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,7},{6,8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5,8] => {{1,2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5,8] => {{1,3},{2,4},{5,6,7},{8}} => {{1},{2,3,4},{5,7},{6,8}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5,8] => {{1,3},{2,4,5,6,7},{8}} => {{1},{2,3,4,5,7},{6,8}}
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5,8] => {{1,3},{2,4,6},{5,7},{8}} => {{1},{2,4},{3,5,7},{6,8}}
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,7,8,5] => {{1,3},{2,4},{5,6,7,8}} => {{1,2,3,4},{5,7},{6,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,6,2,7,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,6,2,7,8,5] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [3,4,6,1,2,7,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,6,7,2,8,5] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,6,7,2,8,5] => {{1,3},{2,4,6},{5,7,8}} => {{1,2,4},{3,5,7},{6,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [3,4,6,1,7,2,8,5] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,6,7,8,2,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,6,7,8,2,5] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [3,4,6,1,7,8,2,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,4,6,7,1,8,2,5] => {{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,6,7,8,1,2,5] => {{1,3,6},{2,4,7},{5,8}} => {{1,4},{2,5,7},{3,6,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,8,6] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,7,5,8,6] => {{1,3},{2,4},{5,6,7,8}} => {{1,2,3,4},{5,7},{6,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,7,2,5,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,7,1,2,5,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,7,8,5,6] => {{1,2,3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6] => {{1,3},{2,4},{5,7},{6,8}} => {{1,3},{2,4},{5,7},{6,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => {{1,3,5,7},{2,4,6,8}} => {{1,3,5,7},{2,4,6,8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6,8] => {{1,3},{2,4},{5,6,7},{8}} => {{1},{2,3,4},{5,7},{6,8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => {{1,3},{2,4},{5},{6,7},{8}} => {{1},{2,3},{4},{5,7},{6,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6,8] => {{1,2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6,8] => {{1,3},{2,4,5},{6,7},{8}} => {{1},{2,3},{4,5,7},{6,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6,8] => {{1,3},{2,4,5,6,7},{8}} => {{1},{2,3,4,5,7},{6,8}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => {{1,3,5},{2,4,6,7},{8}} => {{1},{2,3,5,7},{4,6,8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,7,8,6] => {{1,3},{2,4},{5},{6,7,8}} => {{1,2,3},{4},{5,7},{6,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,7,8,6] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,7,8,6] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,4,5,7,2,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [3,4,1,5,7,2,8,6] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,8,6] => {{1,3,5},{2,4,6,7,8}} => {{1,2,3,5,7},{4,6,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,8,2,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,5,7,8,2,6] => {{1,3},{2,4,5,7},{6,8}} => {{1,3},{2,4,5,7},{6,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [3,4,5,1,7,8,2,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,7,1,8,2,6] => {{1,3,5},{2,4,7},{6,8}} => {{1,3},{2,5,7},{4,6,8}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,7,8,1,2,6] => {{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,2,8,5,6,7] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,8,5,6,7] => {{1,3},{2,4},{5,6,7,8}} => {{1,2,3,4},{5,7},{6,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,8,2,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,8,2,5,6,7] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,4,8,1,2,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,8,6,7] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,2,5,8,6,7] => {{1,3},{2,4},{5},{6,7,8}} => {{1,2,3},{4},{5,7},{6,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,4,5,1,2,8,6,7] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,4,5,8,2,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,5,8,2,6,7] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => {{1,3,5},{2,4,6,7,8}} => {{1,2,3,5,7},{4,6,8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,8,7] => {{1,3},{2,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,7},{6,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,8,7] => {{1,2,3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,8,7] => {{1,3},{2,4,5,6},{7,8}} => {{1,2},{3,4,5,7},{6,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,8,7] => {{1,3,5},{2,4,6},{7,8}} => {{1,2},{3,5,7},{4,6,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [3,4,1,5,6,8,2,7] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,4,5,6,1,8,2,7] => {{1,3,5},{2,4,6,7,8}} => {{1,2,3,5,7},{4,6,8}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,6,8,1,2,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8] => {{1,3},{2,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,7},{6,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7,8] => {{1,3},{2,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,7},{6,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7,8] => {{1,3},{2,4,5,6},{7},{8}} => {{1},{2},{3,4,5,7},{6,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => {{1,3,5},{2,4,6},{7},{8}} => {{1},{2},{3,5,7},{4,6,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2,8] => {{1,3},{2,4,5,6,7},{8}} => {{1},{2,3,4,5,7},{6,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2,8] => {{1,3,5},{2,4,6,7},{8}} => {{1},{2,3,5,7},{4,6,8}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,5,6,7,8,2] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,4,5,1,6,7,8,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,4,5,6,1,7,8,2] => {{1,3,5},{2,4,6,7,8}} => {{1,2,3,5,7},{4,6,8}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => {{1,3,5,7},{2,4,6,8}} => {{1,3,5,7},{2,4,6,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => {{1,3},{2,4,5,6},{7,8}} => {{1,2},{3,4,5,7},{6,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,8,7] => {{1,2,3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7] => {{1,3},{2,5},{4,6},{7,8}} => {{1,2},{3,5},{4,7},{6,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,8,7] => {{1,3,4,6},{2,5},{7,8}} => {{1,2},{3,5,6,8},{4,7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,8,4,7] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,8,4,7] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,8,4,7] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,5,6,8,2,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,5,1,6,8,2,4,7] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => {{1,2,3,5,6},{4,7,8}} => {{1,2,5},{3,4,6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7,8] => {{1,2,3,5},{4,6},{7},{8}} => {{1},{2},{3,5},{4,6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7,8] => {{1,3},{2,5},{4,6},{7},{8}} => {{1},{2},{3,5},{4,7},{6,8}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7,8] => {{1,3,4,6},{2,5},{7},{8}} => {{1},{2},{3,5,6,8},{4,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => {{1,3},{2,4,5,6,7},{8}} => {{1},{2,3,4,5,7},{6,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4,8] => {{1,3},{2,5},{4,6,7},{8}} => {{1},{2,3,5},{4,7},{6,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4,8] => {{1,3,4,6,7},{2,5},{8}} => {{1},{2,3,5,6,8},{4,7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4,8] => {{1,3},{2,4,5,6,7},{8}} => {{1},{2,3,4,5,7},{6,8}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => {{1,2,3,5,6},{4,7},{8}} => {{1},{2,5},{3,4,6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,5,1,2,6,7,8,4] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,5,6,2,7,8,4] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => {{1,3},{2,5},{4,6,7,8}} => {{1,2,3,5},{4,7},{6,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5,6,1,2,7,8,4] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,5,6,7,2,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5,6,1,7,2,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,8,4] => {{1,2,3,5,6},{4,7,8}} => {{1,2,5},{3,4,6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,5,6,7,8,2,4] => {{1,2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => {{1,3,4,6,8},{2,5,7}} => {{1,3,5,6,8},{2,4,7}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5,6,7,1,8,2,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5,6,7,8,1,2,4] => {{1,3,6},{2,4,5,7,8}} => {{1,2,4,5,7},{3,6,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,7,4,8,6] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,7,2,4,8,6] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,7,2,4,8,6] => {{1,3},{2,5},{4,6,7,8}} => {{1,2,3,5},{4,7},{6,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,7,1,2,4,8,6] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,7,8,4,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,7,8,4,6] => {{1,3},{2,4,5,7},{6,8}} => {{1,3},{2,4,5,7},{6,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,7,2,8,4,6] => {{1,2,3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,7,2,8,4,6] => {{1,3},{2,5},{4,7},{6,8}} => {{1,3},{2,5},{4,7},{6,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,7,8,2,4,6] => {{1,2,3,5,6,8},{4,7}} => {{1,3,4,6,7,8},{2,5}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,7,8,2,4,6] => {{1,3},{2,5,6,8},{4,7}} => {{1,3,4,7},{2,5},{6,8}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6,8] => {{1,3},{2,4,5,6,7},{8}} => {{1},{2,3,4,5,7},{6,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6,8] => {{1,2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6,8] => {{1,3},{2,5},{4,6,7},{8}} => {{1},{2,3,5},{4,7},{6,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6,8] => {{1,3,4,6,7},{2,5},{8}} => {{1},{2,3,5,6,8},{4,7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,8] => {{1,2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => {{1,3},{2,4,5},{6,7},{8}} => {{1},{2,3},{4,5,7},{6,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => {{1,2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6,8] => {{1},{2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => {{1},{2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => {{1},{2,3},{4,5},{6,7,8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,7,4,8,6] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,7,4,8,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,8,6] => {{1},{2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7},{8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,7,8,4,6] => {{1},{2,3},{4,5,7},{6,8}} => {{1,3},{2,4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => {{1},{2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7},{8}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,6] => {{1},{2,3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6,7},{8}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,7,8,2,4,6] => {{1},{2,3,5,6,8},{4,7}} => {{1,3,4,6,7},{2,5},{8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,8,4,6,7] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,8,2,4,6,7] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,5,1,8,2,4,6,7] => {{1,3},{2,5},{4,6,7,8}} => {{1,2,3,5},{4,7},{6,8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,4,8,6,7] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,5,8,4,6,7] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,5,8,4,6,7] => {{1},{2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => {{1},{2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7},{8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,8,7] => {{1,3},{2,4,5},{6},{7,8}} => {{1,2},{3},{4,5,7},{6,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,8,7] => {{1,2,3},{4,5},{6},{7,8}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6,7},{8}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,8,7] => {{1},{2,3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6,7},{8}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,8,7] => {{1},{2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,8,7] => {{1},{2,3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6,7},{8}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,5,6,8,4,7] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,2,6,8,4,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,6,2,8,4,7] => {{1},{2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7},{8}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,6,8,2,4,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7,8] => {{1,3},{2,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,7},{6,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7},{8}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7,8] => {{1},{2,3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6,7},{8}}
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => {{1},{2,3,5},{4,6},{7},{8}} => {{1},{2},{3,5},{4,6,7},{8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4,8] => {{1,2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4,8] => {{1},{2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7},{8}}
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,8] => {{1},{2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7},{8}}
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,5,6,7,8,4] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,5,6,7,8,4] => {{1},{2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,5,6,2,7,8,4] => {{1},{2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7},{8}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,6,7,8,2,4] => {{1},{2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7},{8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,6,1,2,7,4,8,5] => {{1,3},{2,4,6},{5,7,8}} => {{1,2,4},{3,5,7},{6,8}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,6,1,7,2,4,8,5] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,6,7,1,2,4,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,6,1,2,7,8,4,5] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,6,7,2,8,4,5] => {{1,2,3,5,6,8},{4,7}} => {{1,3,4,6,7,8},{2,5}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,6,1,7,2,8,4,5] => {{1,3},{2,5,6,8},{4,7}} => {{1,3,4,7},{2,5},{6,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,6,7,1,2,8,4,5] => {{1,3,4,7},{2,5,6,8}} => {{1,3,4,7},{2,5,6,8}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,6,1,7,8,2,4,5] => {{1,3},{2,6},{4,7},{5,8}} => {{1,4},{2,5},{3,7},{6,8}}
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5,8] => {{1,2,3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => {{1,3},{2,4,5,6,7},{8}} => {{1},{2,3,4,5,7},{6,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5,8] => {{1,2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5,8] => {{1},{2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5,8] => {{1},{2,3},{4,6},{5,7},{8}} => {{1},{2,4},{3,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5,8] => {{1},{2,3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,7,8,5] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,8,5] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,7,8,5] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,6,7,4,8,5] => {{1,2,3},{4,6},{5,7,8}} => {{1,2,4},{3,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,4,8,5] => {{1},{2,3},{4,6},{5,7,8}} => {{1,2,4},{3,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,6,2,7,4,8,5] => {{1},{2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,8,5] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,2,6,7,8,4,5] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,2,6,7,8,4,5] => {{1},{2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,6,7,8,2,4,5] => {{1},{2,3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6,7},{8}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,8,4,5,7] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,8,4,5,7] => {{1,3},{2,4,6},{5,7,8}} => {{1,2,4},{3,5,7},{6,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,6,8,2,4,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,6,1,8,2,4,5,7] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,6,8,1,2,4,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,8,5,7] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,8,5,7] => {{1},{2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,8,4,5,7] => {{1,2,3},{4,6},{5,7,8}} => {{1,2,4},{3,5},{6,7,8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,8,4,5,7] => {{1},{2,3},{4,6},{5,7,8}} => {{1,2,4},{3,5},{6,7},{8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,8,7] => {{1,3},{2,4,5,6},{7,8}} => {{1,2},{3,4,5,7},{6,8}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}} => {{1,2},{3,4},{5},{6,7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6,7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,8,7] => {{1},{2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,8,5,7] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,8,5,7] => {{1},{2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7},{8}}
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,8,2,5,7] => {{1},{2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7},{8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7,8] => {{1,3},{2,4,5,6},{7},{8}} => {{1},{2},{3,4,5,7},{6,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6,7},{8}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7,8] => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5,8] => {{1},{2,3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6,7},{8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,6,7,8,5] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,6,7,8,5] => {{1},{2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7},{8}}
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,6,7,8,5] => {{1},{2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,4,6,7,2,8,5] => {{1},{2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,7,2,8,4,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,7,1,2,8,4,5,6] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,7,8,2,4,5,6] => {{1,2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,7,8,1,2,4,5,6] => {{1,3,4,6,8},{2,5,7}} => {{1,3,5,6,8},{2,4,7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [3,7,1,2,4,8,5,6] => {{1,3},{2,4,5,7},{6,8}} => {{1,3},{2,4,5,7},{6,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,7,4,8,5,6] => {{1,2,3},{4,5,7},{6,8}} => {{1,3},{2,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,3,2,7,4,8,5,6] => {{1},{2,3},{4,5,7},{6,8}} => {{1,3},{2,4,5},{6,7},{8}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,3,7,2,4,8,5,6] => {{1},{2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7},{8}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,7,8,4,5,6] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => {{1},{2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7},{8}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,7,2,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,7,1,2,4,5,8,6] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,3,7,2,4,5,8,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [3,1,2,4,7,5,8,6] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => {{1},{2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7},{8}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,3,4,2,7,5,8,6] => {{1},{2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,8,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,2,4,7,8,5,6] => {{1,2,3},{4},{5,7},{6,8}} => {{1,3},{2,4},{5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,3,2,4,7,8,5,6] => {{1},{2,3},{4},{5,7},{6,8}} => {{1,3},{2,4},{5},{6,7},{8}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,3,4,2,7,8,5,6] => {{1},{2,3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6,7},{8}}
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,3,4,7,8,2,5,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6,8] => {{1,3},{2,4,5,6,7},{8}} => {{1},{2,3,4,5,7},{6,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7},{8}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}} => {{1},{2,3},{4},{5},{6,7},{8}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}} => {{1},{2,3},{4},{5,6,7},{8}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6,8] => {{1},{2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,8,6] => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7,8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,7,8,6] => {{1},{2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7},{8}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,7,8,6] => {{1},{2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7},{8}}
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,7,8,6] => {{1},{2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,3,4,5,7,8,2,6] => {{1},{2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,8,1,2,4,5,6,7] => {{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,3,8,2,4,5,6,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,4,8,5,6,7] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,3,2,4,8,5,6,7] => {{1},{2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7},{8}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,2,4,5,8,6,7] => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => {{1},{2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7},{8}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,3,4,2,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7},{8}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,3,4,5,2,8,6,7] => {{1},{2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,3,4,5,8,2,6,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => {{1,2,3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,8,7] => {{1},{2,3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,6,7},{8}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,8,7] => {{1},{2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,3,4,5,6,8,2,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8] => {{1,2,3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8] => {{1},{2,3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8] => {{1},{2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7,8] => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7] => {{1,2,4},{3,5,6},{7,8}} => {{1,2},{3,4,6},{5,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,8,7] => {{1,3,4,6},{2,5},{7,8}} => {{1,2},{3,5,6,8},{4,7}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,8,7] => {{1,4},{2,5},{3,6},{7,8}} => {{1,2},{3,6},{4,7},{5,8}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,8,3,7] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,8,3,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,8,3,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,8,3,7] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => {{1,4},{2,5},{3,6,7,8}} => {{1,2,3,6},{4,7},{5,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,5,6,8,2,3,7] => {{1,2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [4,5,1,6,8,2,3,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => {{1,4},{2,3,5,6,7,8}} => {{1,2,3,4,6,7},{5,8}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8] => {{1,2,4},{3,5,6},{7},{8}} => {{1},{2},{3,4,6},{5,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7,8] => {{1,3,4,6},{2,5},{7},{8}} => {{1},{2},{3,5,6,8},{4,7}}
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8] => {{1,4},{2,5},{3,6},{7},{8}} => {{1},{2},{3,6},{4,7},{5,8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3,8] => {{1,3,4,6,7},{2,5},{8}} => {{1},{2,3,5,6,8},{4,7}}
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3,8] => {{1,4},{2,5},{3,6,7},{8}} => {{1},{2,3,6},{4,7},{5,8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3,8] => {{1,2,4,6},{3,5,7},{8}} => {{1},{2,4,6},{3,5,7,8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3,8] => {{1,4},{2,3,5,6,7},{8}} => {{1},{2,3,4,6,7},{5,8}}
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,6,7,8,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [4,5,1,6,2,7,8,3] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [4,5,6,1,2,7,8,3] => {{1,4},{2,5},{3,6,7,8}} => {{1,2,3,6},{4,7},{5,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [4,1,5,6,7,2,8,3] => {{1,2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5,1,6,7,2,8,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5,6,1,7,2,8,3] => {{1,4},{2,3,5,6,7,8}} => {{1,2,3,4,6,7},{5,8}}
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,8,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,1,5,6,7,8,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5,1,6,7,8,2,3] => {{1,3,4,6,8},{2,5,7}} => {{1,3,5,6,8},{2,4,7}}
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => {{1,4},{2,5,7},{3,6,8}} => {{1,3,6},{2,4,7},{5,8}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,3] => {{1,2,4,5,7},{3,6,8}} => {{1,3,6},{2,4,5,7,8}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,7,3,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,5,1,7,2,3,8,6] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,7,8,3,6] => {{1,2,4},{3,5,7},{6,8}} => {{1,3},{2,4,6},{5,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,7,8,3,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,1,5,7,2,8,3,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,5,1,7,2,8,3,6] => {{1,3,4,7},{2,5},{6,8}} => {{1,3},{2,5,6,8},{4,7}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,5,7,1,2,8,3,6] => {{1,4},{2,5},{3,7},{6,8}} => {{1,3},{2,6},{4,7},{5,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,5,1,7,8,2,3,6] => {{1,3,4,7},{2,5,6,8}} => {{1,3,4,7},{2,5,6,8}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => {{1,2,4,5,6,8},{3,7}} => {{1,3,4,5,7,8},{2,6}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6,8] => {{1,2,4},{3,5,6,7},{8}} => {{1},{2,3,4,6},{5,7,8}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6,8] => {{1,2,4},{3,5},{6,7},{8}} => {{1},{2,3},{4,6},{5,7,8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6,8] => {{1,2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => {{1,2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,8] => {{1},{2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6,8] => {{1},{2,4},{3,5},{6,7},{8}} => {{1},{2,3},{4,6},{5,7},{8}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6,8] => {{1},{2,4},{3,5,6,7},{8}} => {{1},{2,3,4,6},{5,7},{8}}
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,7,8,6] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,7,8,6] => {{1},{2,4},{3,5},{6,7,8}} => {{1,2,3},{4,6},{5,7},{8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,7,3,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,7,3,8,6] => {{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,8,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,7,8,3,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,7,8,3,6] => {{1},{2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7},{8}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,7,8,3,6] => {{1},{2,4},{3,5,7},{6,8}} => {{1,3},{2,4,6},{5,7},{8}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,7,8,2,3,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,8,3,6,7] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,8,3,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,8,2,3,6,7] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [4,5,8,1,2,3,6,7] => {{1,4},{2,5},{3,6,7,8}} => {{1,2,3,6},{4,7},{5,8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,8,6,7] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,8,6,7] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,8,6,7] => {{1},{2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => {{1},{2,4},{3,5},{6,7,8}} => {{1,2,3},{4,6},{5,7},{8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,8,3,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,8,3,6,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => {{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,8,7] => {{1},{2,3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,8,7] => {{1},{2,4},{3,5,6},{7,8}} => {{1,2},{3,4,6},{5,7},{8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,5,6,8,3,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,5,2,6,8,3,7] => {{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,5,6,8,2,3,7] => {{1},{2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7},{8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => {{1,2,4},{3,5},{6},{7},{8}} => {{1},{2},{3},{4,6},{5,7,8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7,8] => {{1},{2,4},{3,5},{6},{7},{8}} => {{1},{2},{3},{4,6},{5,7},{8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3,8] => {{1},{2,4},{3,5,6,7},{8}} => {{1},{2,3,4,6},{5,7},{8}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3,8] => {{1},{2,4,6},{3,5,7},{8}} => {{1},{2,4,6},{3,5,7},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,8,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,3] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,5,2,6,7,8,3] => {{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,5,6,2,7,8,3] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,5,6,7,2,8,3] => {{1},{2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7},{8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,3] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5] => {{1,2,4},{3,6},{5,7,8}} => {{1,2,4},{3,6},{5,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,6,7,2,3,8,5] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,6,7,1,2,3,8,5] => {{1,4},{2,3,5,6,7,8}} => {{1,2,3,4,6,7},{5,8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,6,1,2,7,8,3,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,6,1,7,2,8,3,5] => {{1,3,4,7},{2,5,6,8}} => {{1,3,4,7},{2,5,6,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,6,7,1,2,8,3,5] => {{1,4},{2,5,6,8},{3,7}} => {{1,3,4,7},{2,6},{5,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,6,7,8,2,3,5] => {{1,2,3,4,6,7},{5,8}} => {{1,4},{2,3,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,6,1,7,8,2,3,5] => {{1,3,4,7},{2,6},{5,8}} => {{1,4},{2,5,6,8},{3,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => {{1,4},{2,6},{3,7},{5,8}} => {{1,4},{2,6},{3,7},{5,8}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => {{1,4,5,8},{2,6},{3,7}} => {{1,4,5,8},{2,6},{3,7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5,8] => {{1,2,4},{3,6},{5,7},{8}} => {{1},{2,4},{3,6},{5,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5,8] => {{1,2,3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5,8] => {{1,2,4,5,7},{3,6},{8}} => {{1},{2,4,5,7,8},{3,6}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5,8] => {{1,4},{2,3,5,6,7},{8}} => {{1},{2,3,4,6,7},{5,8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5,8] => {{1,2,4},{3,5,6,7},{8}} => {{1},{2,3,4,6},{5,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => {{1,2,3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5,8] => {{1},{2,3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6,7},{8}}
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5,8] => {{1},{2,4},{3,6},{5,7},{8}} => {{1},{2,4},{3,6},{5,7},{8}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => {{1},{2,4,5,7},{3,6},{8}} => {{1},{2,4,5,7},{3,6},{8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,6,2,3,7,8,5] => {{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,6,7,3,8,5] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,2,7,3,8,5] => {{1},{2,4},{3,6},{5,7,8}} => {{1,2,4},{3,6},{5,7},{8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,6,7,8,3,5] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => {{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,6,7,2,8,3,5] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,6,7,8,2,3,5] => {{1},{2,3,4,6,7},{5,8}} => {{1,4},{2,3,5,6,7},{8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,8,3,5,7] => {{1,2,4},{3,6},{5,7,8}} => {{1,2,4},{3,6},{5,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,8,3,5,7] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,8,2,3,5,7] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,8,2,3,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,8,1,2,3,5,7] => {{1,4},{2,3,5,6,7,8}} => {{1,2,3,4,6,7},{5,8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,8,5,7] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,8,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => {{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,8,3,5,7] => {{1},{2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7},{8}}
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => {{1},{2,4},{3,6},{5,7,8}} => {{1,2,4},{3,6},{5,7},{8}}
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => {{1},{2,4,5,7,8},{3,6}} => {{1,2,4,5,7},{3,6},{8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,8,7] => {{1,2,4},{3,5,6},{7,8}} => {{1,2},{3,4,6},{5,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,8,7] => {{1},{2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,8,7] => {{1},{2,4},{3,5,6},{7,8}} => {{1,2},{3,4,6},{5,7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6,7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,8,7] => {{1},{2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7},{8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,8,5,7] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,8,5,7] => {{1},{2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,8,5,7] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,8,3,5,7] => {{1},{2},{3,4,6},{5,7,8}} => {{1,2,4},{3,5,6},{7},{8}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => {{1,2,4},{3,5,6},{7},{8}} => {{1},{2},{3,4,6},{5,7,8}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7,8] => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6,7},{8}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}}
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => {{1},{2},{3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6},{7},{8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5,8] => {{1,2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,6,7,8,5] => {{1},{2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,6,7,8,5] => {{1},{2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,6,7,8,3,5] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,7,2,8,3,5,6] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,7,1,2,8,3,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,7,8,2,3,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,7,1,8,2,3,5,6] => {{1,3,4,6,8},{2,5,7}} => {{1,3,5,6,8},{2,4,7}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,7,8,1,2,3,5,6] => {{1,4},{2,5,7},{3,6,8}} => {{1,3,6},{2,4,7},{5,8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,7,2,3,8,5,6] => {{1,2,4},{3,5,7},{6,8}} => {{1,3},{2,4,6},{5,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,7,1,2,3,8,5,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,2,7,3,8,5,6] => {{1},{2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7},{8}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,7,2,3,8,5,6] => {{1},{2,4},{3,5,7},{6,8}} => {{1,3},{2,4,6},{5,7},{8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,7,8,3,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,7,8,3,5,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => {{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,7,2,3,5,8,6] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,7,1,2,3,5,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,2,7,3,5,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,2,7,3,5,8,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,7,2,3,5,8,6] => {{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,2,3,7,5,8,6] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,2,3,7,5,8,6] => {{1},{2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,4,3,7,5,8,6] => {{1},{2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,8,6] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,3,7,8,5,6] => {{1,2,3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,3,7,8,5,6] => {{1},{2,3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6,7},{8}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => {{1},{2},{3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6},{7},{8}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,4,7,3,8,5,6] => {{1},{2},{3,4,5,7},{6,8}} => {{1,3},{2,4,5,6},{7},{8}}
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,4,7,8,3,5,6] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6,8] => {{1,2,4},{3,5,6,7},{8}} => {{1},{2,3,4,6},{5,7,8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6,8] => {{1},{2,4},{3,5,6,7},{8}} => {{1},{2,3,4,6},{5,7},{8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6,8] => {{1,2,3,4},{5},{6,7},{8}} => {{1},{2,3},{4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}} => {{1},{2,3},{4},{5,6,7},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6,8] => {{1},{2},{3,4},{5},{6,7},{8}} => {{1},{2,3},{4},{5,6},{7},{8}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6},{7},{8}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6,8] => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,8,6] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,7,8,6] => {{1},{2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7},{8}}
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,7,8,6] => {{1},{2},{3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6},{7},{8}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,7,8,6] => {{1},{2},{3,4,5},{6,7,8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,4,5,7,3,8,6] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,4,5,7,8,3,6] => {{1},{2},{3,4,5,7},{6,8}} => {{1,3},{2,4,5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,8,2,3,5,6,7] => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,8,1,2,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,8,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,4,2,8,3,5,6,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,4,8,2,3,5,6,7] => {{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,2,3,5,8,6,7] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,3,5,8,6,7] => {{1},{2},{3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,4,5,3,8,6,7] => {{1},{2},{3,4,5},{6,7,8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,4,5,8,3,6,7] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => {{1,2,3,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,6,7},{8}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,8,7] => {{1},{2},{3,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,6},{7},{8}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,8,7] => {{1},{2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7},{8}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,4,5,6,8,3,7] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8] => {{1},{2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7},{8}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8] => {{1},{2},{3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7,8] => {{1},{2},{3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6},{7},{8}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3,8] => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,3] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,6,1,2,7,3,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,6,7,2,3,8,4] => {{1,2,5},{3,6},{4,7,8}} => {{1,2,5},{3,6},{4,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,6,1,7,2,3,8,4] => {{1,2,3,5,6},{4,7,8}} => {{1,2,5},{3,4,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,1,2,3,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,6,1,2,7,8,3,4] => {{1,3,5,7},{2,4,6,8}} => {{1,3,5,7},{2,4,6,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [5,1,6,7,2,8,3,4] => {{1,2,5},{3,4,6,7,8}} => {{1,2,3,5,6},{4,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,6,7,1,2,8,3,4] => {{1,2,4,5,6,8},{3,7}} => {{1,3,4,5,7,8},{2,6}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,1,6,7,8,2,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [5,6,1,7,8,2,3,4] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => {{1,4,5,8},{2,6},{3,7}} => {{1,4,5,8},{2,6},{3,7}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => {{1,5},{2,6},{3,7},{4,8}} => {{1,5},{2,6},{3,7},{4,8}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4,8] => {{1,2,4,5,7},{3,6},{8}} => {{1},{2,4,5,7,8},{3,6}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4,8] => {{1,2,3,5,6},{4,7},{8}} => {{1},{2,5},{3,4,6,7,8}}
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => {{1,2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7,8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4,8] => {{1},{2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => {{1},{2,5},{3,6},{4,7},{8}} => {{1},{2,5},{3,6},{4,7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [5,6,1,2,3,7,8,4] => {{1,3,5},{2,4,6,7,8}} => {{1,2,3,5,7},{4,6,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,8,4] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => {{1},{2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,5,6,2,3,7,8,4] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,8,4] => {{1},{2,5},{3,6},{4,7,8}} => {{1,2,5},{3,6},{4,7},{8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [5,1,2,6,7,8,3,4] => {{1,2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7,8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,5,2,6,7,8,3,4] => {{1},{2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7},{8}}
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,5,6,7,2,8,3,4] => {{1},{2,5},{3,4,6,7,8}} => {{1,2,3,5,6},{4,7},{8}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,5,6,7,8,2,3,4] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,6,2,8,3,4,7] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,6,1,2,8,3,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,6,1,8,2,3,4,7] => {{1,2,3,5,6},{4,7,8}} => {{1,2,5},{3,4,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,6,8,1,2,3,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,8,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,8,4,7] => {{1,3,5},{2,4,6,7,8}} => {{1,2,3,5,7},{4,6,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,8,4,7] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,8,4,7] => {{1},{2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7},{8}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,1,2,6,8,3,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,8,3,4,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => {{1},{2,4,5,7,8},{3,6}} => {{1,2,4,5,7},{3,6},{8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => {{1},{2,5},{3,6},{4,7,8}} => {{1,2,5},{3,6},{4,7},{8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,8,7] => {{1,3,5},{2,4,6},{7,8}} => {{1,2},{3,5,7},{4,6,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,8,7] => {{1,2,3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6,7,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,8,7] => {{1},{2,3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6,7},{8}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,8,7] => {{1},{2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,8,7] => {{1},{2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,8,7] => {{1},{2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7},{8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,8,4,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,8,4,7] => {{1},{2},{3,5},{4,6,7,8}} => {{1,2,3,5},{4,6},{7},{8}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,2,5,6,8,3,4,7] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7,8] => {{1,2,3,5},{4,6},{7},{8}} => {{1},{2},{3,5},{4,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7,8] => {{1},{2,3,5},{4,6},{7},{8}} => {{1},{2},{3,5},{4,6,7},{8}}
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7,8] => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7,8] => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7,8] => {{1},{2},{3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6},{7},{8}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => {{1},{2},{3,5},{4,6},{7},{8}} => {{1},{2},{3,5},{4,6},{7},{8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4,8] => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,6,7,8,4] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,2,5,3,6,7,8,4] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,2,5,6,3,7,8,4] => {{1},{2},{3,5},{4,6,7,8}} => {{1,2,3,5},{4,6},{7},{8}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,2,5,6,7,3,8,4] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,5,6,7,8,3,4] => {{1},{2},{3,5,7},{4,6,8}} => {{1,3,5},{2,4,6},{7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,7,2,8,3,4,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,7,1,2,8,3,4,6] => {{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,7,8,2,3,4,6] => {{1,2,5},{3,4,6,7,8}} => {{1,2,3,5,6},{4,7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,7,1,8,2,3,4,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,7,8,1,2,3,4,6] => {{1,2,4,5,7},{3,6,8}} => {{1,3,6},{2,4,5,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,7,2,3,8,4,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,7,1,2,3,8,4,6] => {{1,3,5},{2,4,7},{6,8}} => {{1,3},{2,5,7},{4,6,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,7,3,8,4,6] => {{1,2,3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,7,3,8,4,6] => {{1},{2,3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6,7},{8}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,5,7,2,3,8,4,6] => {{1},{2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7},{8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,7,8,3,4,6] => {{1,2,3,5,6,8},{4,7}} => {{1,3,4,6,7,8},{2,5}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,7,8,3,4,6] => {{1},{2,3,5,6,8},{4,7}} => {{1,3,4,6,7},{2,5},{8}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => {{1},{2,5},{3,4,6,7,8}} => {{1,2,3,5,6},{4,7},{8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,7,2,3,4,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => {{1,3,5},{2,4,6,7,8}} => {{1,2,3,5,7},{4,6,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,7,3,4,8,6] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,7,3,4,8,6] => {{1},{2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7},{8}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,5,7,2,3,4,8,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,7,4,8,6] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,8,6] => {{1},{2},{3,5},{4,6,7,8}} => {{1,2,3,5},{4,6},{7},{8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,7,8,4,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,8,4,6] => {{1},{2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7},{8}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => {{1},{2},{3,4,5,7},{6,8}} => {{1,3},{2,4,5,6},{7},{8}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,7,8,3,4,6] => {{1},{2},{3,5,6,8},{4,7}} => {{1,3,4,6},{2,5},{7},{8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6,8] => {{1,3,5},{2,4,6,7},{8}} => {{1},{2,3,5,7},{4,6,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6,8] => {{1,2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6,8] => {{1},{2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7},{8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6,8] => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6},{7},{8}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6},{7},{8}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,8] => {{1},{2},{3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,8,6] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,7,8,6] => {{1},{2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,7,8,6] => {{1},{2},{3,4,5},{6,7,8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,7,8,6] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,2,3},{4,5},{6},{7},{8}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,7,4,8,6] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,7,8,4,6] => {{1},{2},{3},{4,5,7},{6,8}} => {{1,3},{2,4,5},{6},{7},{8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,8,2,3,4,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,8,1,2,3,4,6,7] => {{1,3,5},{2,4,6,7,8}} => {{1,2,3,5,7},{4,6,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,8,3,4,6,7] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,5,2,8,3,4,6,7] => {{1},{2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7},{8}}
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,5,8,2,3,4,6,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,3,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,5,2,3,8,4,6,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => {{1},{2},{3,5},{4,6,7,8}} => {{1,2,3,5},{4,6},{7},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,2,3},{4,5},{6},{7},{8}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,5,8,4,6,7] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => {{1,2,3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6,7},{8}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,8,7] => {{1},{2},{3},{4,5},{6},{7,8}} => {{1,2},{3},{4,5},{6},{7},{8}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,8,7] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,5,6,8,4,7] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7},{8}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7,8] => {{1},{2},{3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6},{7},{8}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => {{1},{2},{3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7,8] => {{1},{2},{3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4,8] => {{1},{2},{3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,5] => {{1,2,3,4,6,7},{5,8}} => {{1,4},{2,3,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,7,1,2,8,3,4,5] => {{1,3,6},{2,4,7},{5,8}} => {{1,4},{2,5,7},{3,6,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [6,1,7,8,2,3,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,7,1,8,2,3,4,5] => {{1,3,6},{2,4,5,7,8}} => {{1,2,4,5,7},{3,6,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,7,2,3,8,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,7,1,2,3,8,4,5] => {{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [6,1,2,7,3,8,4,5] => {{1,2,3,5,6,8},{4,7}} => {{1,3,4,6,7,8},{2,5}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,5] => {{1},{2,3,5,6,8},{4,7}} => {{1,3,4,6,7},{2,5},{8}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,6,7,2,3,8,4,5] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [6,1,2,7,8,3,4,5] => {{1,2,3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,6,2,7,8,3,4,5] => {{1},{2,3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6,7},{8}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => {{1},{2,3,4,6,7},{5,8}} => {{1,4},{2,3,5,6,7},{8}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,7,2,3,4,8,5] => {{1,2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,7,1,2,3,4,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [6,1,2,7,3,4,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,6,2,7,3,4,8,5] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,6,7,2,3,4,8,5] => {{1},{2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [6,1,2,3,7,4,8,5] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => {{1},{2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,3,7,4,8,5] => {{1},{2},{3,4,6},{5,7,8}} => {{1,2,4},{3,5,6},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,8,5] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [6,1,2,3,7,8,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,6,2,3,7,8,4,5] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,7,3,8,4,5] => {{1},{2},{3,5,6,8},{4,7}} => {{1,3,4,6},{2,5},{7},{8}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,7,8,3,4,5] => {{1},{2},{3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6},{7},{8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5,8] => {{1,2,4,6},{3,5,7},{8}} => {{1},{2,4,6},{3,5,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5,8] => {{1},{2,4,6},{3,5,7},{8}} => {{1},{2,4,6},{3,5,7},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => {{1,2,3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5,8] => {{1},{2,3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6,7},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5,8] => {{1},{2},{3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6},{7},{8}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5,8] => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,8] => {{1},{2},{3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,8,5] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,7,8,5] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,7,8,5] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,2,3,6,7,4,8,5] => {{1},{2},{3},{4,6},{5,7,8}} => {{1,2,4},{3,5},{6},{7},{8}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,6,7,8,4,5] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,8,2,3,4,5,7] => {{1,2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,8,1,2,3,4,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,8,3,4,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,6,2,8,3,4,5,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,6,8,2,3,4,5,7] => {{1},{2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7},{8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,8,4,5,7] => {{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,8,4,5,7] => {{1},{2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7},{8}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => {{1},{2},{3,4,6},{5,7,8}} => {{1,2,4},{3,5,6},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,8,5,7] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,8,5,7] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,8,4,5,7] => {{1},{2},{3},{4,6},{5,7,8}} => {{1,2,4},{3,5},{6},{7},{8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7},{8}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7] => {{1},{2},{3},{4},{5,6},{7,8}} => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7] => {{1},{2},{3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6},{7},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7,8] => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7,8] => {{1},{2},{3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6},{7},{8}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => {{1},{2},{3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8] => {{1},{2},{3},{4},{5,6},{7},{8}} => {{1},{2},{3,4},{5},{6},{7},{8}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5,8] => {{1},{2},{3},{4},{5,6,7},{8}} => {{1},{2,3,4},{5},{6},{7},{8}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,5] => {{1},{2},{3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => {{1,3,5,7},{2,4,6,8}} => {{1,3,5,7},{2,4,6,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,8,3,4,5,6] => {{1,2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,7,2,8,3,4,5,6] => {{1},{2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,8,2,3,4,5,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1,2,3,8,4,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,7,2,3,8,4,5,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => {{1},{2},{3,5,7},{4,6,8}} => {{1,3,5},{2,4,6},{7},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1,2,3,4,8,5,6] => {{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => {{1},{2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => {{1},{2},{3,4,5,7},{6,8}} => {{1,3},{2,4,5,6},{7},{8}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,6] => {{1},{2},{3},{4,5,7},{6,8}} => {{1,3},{2,4,5},{6},{7},{8}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,7,8,4,5,6] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,2,7,3,4,5,8,6] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,2,3,7,4,5,8,6] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6] => {{1},{2},{3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6},{7},{8}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6] => {{1},{2},{3},{4},{5,7},{6,8}} => {{1,3},{2,4},{5},{6},{7},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6,8] => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => {{1},{2},{3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,8] => {{1},{2},{3},{4},{5,6,7},{8}} => {{1},{2,3,4},{5},{6},{7},{8}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8] => {{1},{2},{3},{4},{5},{6,7},{8}} => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6] => {{1},{2},{3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,7] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,7] => {{1},{2},{3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,7] => {{1},{2},{3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,1,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}} => {{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9,11] => {{1,2,3,4,5,6,7,8,9,10},{11}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9,10] => {{1,2,3,4,5,6,7,8},{9},{10}} => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,1,2,3,4,5,9,6,7] => {{1,2,3,4,5,6,8},{7,9}} => {{1,3},{2,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,9,8] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => {{1,2,3,4,5,6,7,8},{9},{10}} => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,8,9,1,7] => {{1,2,3,4,5,6,8},{7,9}} => {{1,3},{2,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,10,1,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => {{1,2,3,4,5,6,7,8,9,10},{11}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,11,9] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,10,7,8] => {{1,2,3,4,5,6,7,9},{8,10}} => {{1,3},{2,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9,10] => {{1,2,3,4,5,6,7},{8},{9},{10}} => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,1,2,3,4,9,5,6,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,9,6] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => {{1,2,3,4,5,6,7},{8},{9},{10}} => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,9,1,7,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,9,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,10,9] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,7,8,9,1,6] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,10,1,8] => {{1,2,3,4,5,6,7,9},{8,10}} => {{1,3},{2,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8,9,10] => {{1,2,3,4,5,6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1,2,3,9,4,5,6,7] => {{1,2,3,4,6,8},{5,7,9}} => {{1,3,5},{2,4,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => {{1,2,3,4,5,6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,9,7,8] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3},{4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,9,7] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3},{4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,7,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,1,10,8] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,11,10] => {{1,2,3,4,5,6,7,8,9},{10,11}} => {{1,2},{3,4,5,6,7,8,9,10,11}}
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,6,7,8,9,1,5] => {{1,2,3,4,6,8},{5,7,9}} => {{1,3,5},{2,4,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,8,9,10,1,7] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,1,2,3,4,10,5,6,7,8] => {{1,2,3,4,5,7,9},{6,8,10}} => {{1,3,5},{2,4,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,9,10] => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1,2,9,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9] => {{1,2,3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9] => {{1,2,3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [2,3,4,5,9,1,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7,9] => {{1,2,3,4,5,6},{7,8},{9}} => {{1},{2,3},{4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,9,10,8] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,6,7,8,9,1,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,7,8,9,10,1,6] => {{1,2,3,4,5,7,9},{6,8,10}} => {{1,3,5},{2,4,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,9,10,6] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,9,2,3,4,5,6,7] => {{1,2,4,6,8},{3,5,7,9}} => {{1,3,5,7},{2,4,6,8,9}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4},{5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,9,1,2,3,4,5,6,8] => {{1,3,5,7},{2,4,6,8,9}} => {{1,2,4,6,8},{3,5,7,9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4},{5,6,7,8,9}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,9,6] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4},{5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,10,1,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,9,8,10] => {{1,2,3,4,5,6,7},{8,9},{10}} => {{1},{2,3},{4,5,6,7,8,9,10}}
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,9,2] => {{1,3,5,7},{2,4,6,8,9}} => {{1,2,4,6,8},{3,5,7,9}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,1,3] => {{1,2,4,6,8},{3,5,7,9}} => {{1,3,5,7},{2,4,6,8,9}}
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,6,7,8,9,10,1,5] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9,10] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,9,2,3,4,5,6,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => {{1,2},{3},{4},{5},{6},{7},{8,9}} => {{1,2},{3},{4},{5},{6},{7},{8,9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9,10] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6,9] => {{1,3,5,7},{2,4,6,8},{9}} => {{1},{2,4,6,8},{3,5,7,9}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [6,9,1,2,3,4,5,7,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,9,10,7] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,9,2] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => {{1,3,5,7},{2,4,6,8},{9}} => {{1},{2,4,6,8},{3,5,7,9}}
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,9,3] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,5,6,7,8,9,10,1,4] => {{1,2,3,5,7,9},{4,6,8,10}} => {{1,3,5,7},{2,4,6,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,1,10,2,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,10,1,2,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,9,6] => {{1,3,5,7},{2,4,6,8,9}} => {{1,2,4,6,8},{3,5,7,9}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,9,5] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,5},{6,7,8,9}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,8,6,9,7] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4},{5,6,7,8,9}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,8,9] => {{1,2,3,4,5},{6,7},{8},{9}} => {{1},{2},{3,4},{5,6,7,8,9}}
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,9,1,2,8] => {{1,3,5,7},{2,4,6,8,9}} => {{1,2,4,6,8},{3,5,7,9}}
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,3,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,10,2] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,10,1,3] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[] => [] => {} => {}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,9,8] => {{1},{2,3,4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6,7,8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,6,7,8,9,2,4,5] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6,9,8] => {{1},{2,3,4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6,7,8},{9}}
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,8,9,2,7] => {{1},{2,3,4,5,6,8},{7,9}} => {{1,3},{2,4,5,6,7,8},{9}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,3,9,2,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,9,8] => {{1},{2,3},{4},{5},{6},{7},{8,9}} => {{1,2},{3},{4},{5},{6},{7,8},{9}}
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,9,8] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,9,2,8] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9] => {{1},{2,3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8,9] => {{1},{2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2,9] => {{1},{2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,9,8] => {{1},{2,3,4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6,7,8},{9}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,9,3] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,9,3] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,5,6,7,8,9,2,3] => {{1},{2,4,6,8},{3,5,7,9}} => {{1,3,5,7},{2,4,6,8},{9}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,9,8] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{8},{9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8,9] => {{1},{2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9] => {{1},{2},{3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7},{8},{9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7,8,9] => {{1},{2},{3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7},{8},{9}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,3] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{8},{9}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,5,2,6,7,8,9,3,4] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,5,6,7,8,9,2,3,4] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,5,6,7,3,8,9,4] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6},{7},{8},{9}}
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => {{1},{2},{3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7},{8},{9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => {{1},{2},{3},{4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6},{7},{8},{9}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,4] => {{1},{2},{3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7},{8},{9}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,9] => {{1},{2},{3},{4},{5,6},{7,8},{9}} => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,9,5,7,8] => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,9,5,8] => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => {{1},{2},{3},{4},{5,6},{7},{8},{9}} => {{1},{2},{3},{4,5},{6},{7},{8},{9}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,5] => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,7,8,9,2,3,4,5,6] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,9,6] => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,7,9,2,3,4,5,6,8] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,9,8] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,9,6,8] => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1,2,3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9] => {{1},{2},{3},{4},{5},{6,7},{8},{9}} => {{1},{2},{3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6,9] => {{1},{2},{3},{4},{5},{6,7,8},{9}} => {{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,6] => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1,2,3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,8,2,9,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,8,9,2,3,4,5,6,7] => {{1},{2,4,6,8},{3,5,7,9}} => {{1,3,5,7},{2,4,6,8},{9}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [1,8,2,3,4,5,9,6,7] => {{1},{2,3,4,5,6,8},{7,9}} => {{1,3},{2,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,8,9,5,6,7] => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,9,7] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{8},{9}}
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,9,7] => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,9,7] => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1,2,3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,8,9,6,7] => {{1},{2},{3},{4},{5},{6,8},{7,9}} => {{1,3},{2,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7,9] => {{1},{2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9}} => {{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,7] => {{1},{2},{3},{4},{5},{6},{7,8,9}} => {{1,2,3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,9,3,4,5,6,7,8] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{8},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => {{1},{2},{3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1,2,3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,8] => {{1},{2},{3},{4},{5},{6},{7,8,9}} => {{1,2,3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => {{1,2},{3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}} => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}} => {{1},{2,3},{4,5},{6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,9] => {{1,2,3,4,5,6},{7,8},{9}} => {{1},{2,3},{4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,9,8] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2},{3,4,5,6,7,8,9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,9,8] => {{1,2,3,4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6,7,8,9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7,9] => {{1,2,4},{3,5,6},{7,8},{9}} => {{1},{2,3},{4,5,7},{6,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => {{1,2,3,4,5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7,9] => {{1,2,3,4,6},{5,7,8},{9}} => {{1},{2,3,5},{4,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,8,9,5,7] => {{1,2,3,4,5,6,8},{7,9}} => {{1,3},{2,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,9,7] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4},{5,6,7,8,9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,9,8,10] => {{1,2,3,4,5,6,7},{8,9},{10}} => {{1},{2,3},{4,5,6,7,8,9,10}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,9,8] => {{1,2,3},{4,5,6,7},{8,9}} => {{1,2},{3,4,5,6},{7,8,9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => {{1,2,3,4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7,8,9,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => {{1,2,3},{4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7},{8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7,9] => {{1,2,4,5,7,8},{3,6},{9}} => {{1},{2,3,5,6,8,9},{4,7}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,4,6,1,8,3,9,5,10,7] => {{1,2,4},{3,6},{5,8},{7,9,10}} => {{1,2,4},{3,6},{5,8},{7,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,10,7,9] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}} => {{1},{2,3},{4,5},{6,7,8,9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [2,3,1,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7,8,9}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,9,8] => {{1,2,3,4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [1,7,2,8,3,9,4,10,5,6] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,9,8,10] => {{1,2,3,4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7,9] => {{1,2,3,4},{5,6,7,8},{9}} => {{1},{2,3,4,5},{6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => {{1,2},{3,4},{5,6},{7},{8},{9}} => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7,8,9] => {{1,2,4},{3,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,7},{6,8,9}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => {{1,2},{3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,9,3] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{8,9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,8,7,9] => {{1,2,3,4,5,6},{7,8},{9}} => {{1},{2,3},{4,5,6,7,8,9}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,6,7,8,9,3,4] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{8,9}}
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,5,6,7,8,9,1,3,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,6,7,8,9,1,3,4,5] => {{1,2,6},{3,7},{4,8},{5,9}} => {{1,5},{2,6},{3,7},{4,8,9}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,7,8,9,1,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,8,9,1,3,4,5,6,7] => {{1,2,4,6,8},{3,5,7,9}} => {{1,3,5,7},{2,4,6,8,9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{8,9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,9,1,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}} => {{1},{2,3},{4,5},{6,7,8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7,9] => {{1,2,3,4,5,6},{7,8},{9}} => {{1},{2,3},{4,5,6,7,8,9}}
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,7,8,9,1,2,5,6] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,4,8,9,2,5,6,7] => {{1,2,3,4,6,8},{5,7,9}} => {{1,3,5},{2,4,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8,9] => {{1,3},{2,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,8},{7,9}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,2] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7,9] => {{1,2,4},{3,5,6},{7,8},{9}} => {{1},{2,3},{4,5,7},{6,8,9}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8,9] => {{1,2,4},{3,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,7},{6,8,9}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8,9] => {{1,4},{2,5},{3,6},{7},{8},{9}} => {{1},{2},{3},{4,7},{5,8},{6,9}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,6,7,8,9,3] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,1,5,6,7,8,9,2,3] => {{1,2,4,6,8},{3,5,7,9}} => {{1,3,5,7},{2,4,6,8,9}}
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => {{1,4,7},{2,5,8},{3,6,9}} => {{1,4,7},{2,5,8},{3,6,9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,9] => {{1,2,4,5,7,8},{3,6},{9}} => {{1},{2,3,5,6,8,9},{4,7}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => {{1,5},{2,6},{3,7},{4,8},{9}} => {{1},{2,6},{3,7},{4,8},{5,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,1,6,7,8,9,2,3,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,5] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,1,7,8,9,2,3,4,5] => {{1,2,6},{3,7},{4,8},{5,9}} => {{1,5},{2,6},{3,7},{4,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [7,1,8,9,2,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => {{1,4,7},{2,5,8},{3,6,9}} => {{1,4,7},{2,5,8},{3,6,9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => {{1,2},{3,4},{5,6},{7,8},{9},{10}} => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,9,10,3] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8},{9,10}}
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,5,6,7,8,9,10,1,3,4] => {{1,2,5,8},{3,6,9},{4,7,10}} => {{1,4,7},{2,5,8},{3,6,9,10}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,8,9,10,5] => {{1,2,4,6},{3,5,7,8,9,10}} => {{1,2,3,4,6,8},{5,7,9,10}}
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6,7,8,9,10,1,3,4,5] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,8,9,10,1,3,4,5,6,7] => {{1,2,5,8},{3,6,9},{4,7,10}} => {{1,4,7},{2,5,8},{3,6,9,10}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8},{9,10}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,10,1,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7,10,9] => {{1,3},{2,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,9},{8,10}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,6,8,10,1,2,5,7,9] => {{1,3,6},{2,4,5,7,8,9,10}} => {{1,2,3,4,6,7,9},{5,8,10}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,8,6,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}} => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8,9,10] => {{1,3},{2,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,9},{8,10}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => {{1,4},{2,5},{3,6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,8},{6,9},{7,10}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => {{1,5},{2,6},{3,7},{4,8},{9},{10}} => {{1},{2},{3,7},{4,8},{5,9},{6,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,6,7,8,9,10,2,3,4] => {{1,2,5,8},{3,6,9},{4,7,10}} => {{1,4,7},{2,5,8},{3,6,9,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [6,1,7,8,9,10,2,3,4,5] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => {{1,6},{2,7},{3,8},{4,9},{5,10}} => {{1,6},{2,7},{3,8},{4,9},{5,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [7,1,8,2,9,3,10,4,5,6] => {{1,2,3,4,6,7,8,10},{5,9}} => {{1,3,4,5,7,8,9,10},{2,6}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [7,1,8,9,2,3,10,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [7,8,9,1,2,3,10,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [7,1,8,9,10,2,3,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [8,1,9,2,10,3,4,5,6,7] => {{1,2,4,5,7,8,10},{3,6,9}} => {{1,3,4,6,7,9,10},{2,5,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [8,1,9,10,2,3,4,5,6,7] => {{1,2,5,8},{3,6,9},{4,7,10}} => {{1,4,7},{2,5,8},{3,6,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7,9] => {{1,2,3,4,5,6},{7,8},{9}} => {{1},{2,3},{4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,9,6,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,9,8] => {{1,2,3,4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6},{7,8,9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7,10,9] => {{1,2,3,4,5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6,7,8,9,10}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5,9] => {{1,2,3,4,6},{5,7,8},{9}} => {{1},{2,3,5},{4,6,7,8,9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6,10,9] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,9,6,10,8] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,9,6,8,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => {{1,2,3},{4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7},{8,9,10}}
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,10,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}} => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}} => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,10,7,9] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,10,8] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}} => {{1},{2,3},{4,5},{6,7,8,9}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,8,7,9] => {{1,2,4},{3,5,6},{7,8},{9}} => {{1},{2,3},{4,5,7},{6,8,9}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,8,3,9,5,7] => {{1,2,4},{3,6},{5,8},{7,9}} => {{1,3},{2,5},{4,7},{6,8,9}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,2] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10},{11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8,10] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,8,2,3,9,4,5,6] => {{1,2,4,7},{3,5,8},{6,9}} => {{1,4},{2,5,7},{3,6,8,9}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6,9] => {{1,2,4},{3,5,6,7,8},{9}} => {{1},{2,3,4,5,7},{6,8,9}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,10,7] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,10,6] => {{1},{2},{3},{4},{5},{6,7,8,9,10}} => {{1,2,3,4,5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,10,5] => {{1},{2},{3},{4},{5,6,7,8,9,10}} => {{1,2,3,4,5,6},{7},{8},{9},{10}}
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,10,4] => {{1},{2},{3},{4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7},{8},{9},{10}}
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,10,3] => {{1},{2},{3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7,9] => {{1,2,3,4,5,6},{7,8},{9}} => {{1},{2,3},{4,5,6,7,8,9}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,8,7,9] => {{1,2,3,4,5,6},{7,8},{9}} => {{1},{2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,5,6,7,8,9,1,2,4] => {{1,3,4,6,7,9},{2,5,8}} => {{1,3,4,6,7,9},{2,5,8}}
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,6,7,8,9,1,2,3,5] => {{1,2,3,4,6,7,8},{5,9}} => {{1,5},{2,3,4,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,8,9,1,2,3,4,5,7] => {{1,3,4,6,7,9},{2,5,8}} => {{1,3,4,6,7,9},{2,5,8}}
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7,10,9] => {{1,2,3,4,5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6,7,8,9,10}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,7,5,8,6,9] => {{1,2,3,4},{5,6,7,8},{9}} => {{1},{2,3,4,5},{6,7,8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6,9,8] => {{1,2,3,4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6,7,8,9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6,9,8] => {{1,2,3,4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,9,1,2,4,6,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,8,2,9,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,9,1,2,3,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,8,9,1,2,3,4,6,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,8,1,9,2,3,4,5,6] => {{1,3,4,6,7,9},{2,5,8}} => {{1,3,4,6,7,9},{2,5,8}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => {{1},{2},{3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8},{9},{10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [6,7,8,1,9,2,3,4,5] => {{1,2,3,4,6,7,8},{5,9}} => {{1,5},{2,3,4,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => {{1},{2},{3},{4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => {{1},{2},{3},{4},{5,6,7,8,9,10}} => {{1,2,3,4,5,6},{7},{8},{9},{10}}
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,5,6,7,8,1,9,2,3] => {{1,3,4,6,7,9},{2,5,8}} => {{1,3,4,6,7,9},{2,5,8}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => {{1},{2},{3},{4},{5},{6,7,8,9,10}} => {{1,2,3,4,5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,7,3,8,5,6,9] => {{1,2,3,4,5,7},{6,8},{9}} => {{1},{2,4},{3,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,9,6,10,8] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,7,8,9,10,2,3,4,5,6] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7,10,9] => {{1,2,3,4,5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2,10] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10},{11}}
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,10,2,9] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [5,6,1,7,2,8,3,9,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,10,9] => {{1},{2},{3},{4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7},{8},{9},{10}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,9,3] => {{1,2,4,5,7},{3,6,8,9}} => {{1,2,4,7},{3,5,6,8,9}}
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,5,6,7,8,1,9,2,10,3] => {{1,3,4,6,7,9,10},{2,5,8}} => {{1,2,4,5,7,8,10},{3,6,9}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,6,7,1,8,2,9,3,10,4] => {{1,3,4,5,7,8,9,10},{2,6}} => {{1,2,3,4,6,7,8,10},{5,9}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [2,6,1,7,3,8,4,9,5] => {{1,2,3,5,6,8,9},{4,7}} => {{1,2,4,5,7,8,9},{3,6}}
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,1,10,3] => {{1,2,4,6,8},{3,5,7,9,10}} => {{1,2,4,6,8},{3,5,7,9,10}}
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,6,7,8,9,1,4,5] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8,10] => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}} => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,10,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}} => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,6,7,8,9,10,2,3,4,5] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,4,5,6,7,8,9,10,2,3] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => {{1},{2},{3},{4,5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,9,6,7,10,8] => {{1},{2},{3},{4},{5},{6,7,8,9,10}} => {{1,2,3,4,5},{6},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,8,3,10,5,7,9] => {{1,2,4},{3,6},{5,8},{7,9,10}} => {{1,2,4},{3,6},{5,8},{7,9,10}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,6,2,8,3,9,5,10,7] => {{1,2,4},{3,6},{5,8},{7,9,10}} => {{1,2,4},{3,6},{5,8},{7,9,10}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,8,1,2,9,3,4,6,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,9,6] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,9,1,2,3,4,5,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,9,6,10,8] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,3,9,1,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,5,6,7,8,9,4] => {{1,2},{3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7},{8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,10,2,3,4,5,6,7,9] => {{1,2,4,6,8},{3,5,7,9,10}} => {{1,2,4,6,8},{3,5,7,9,10}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,5,6,7,8,9,4] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [2,3,4,10,1,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,5,6,7,8,9,3] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,7,9,1,2,3,4,6,8] => {{1,2,4,5,7},{3,6,8,9}} => {{1,2,4,7},{3,5,6,8,9}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7,8,9}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => {{1,2},{3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9,10] => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => {{1,3,5,7,9,11},{2,4,6,8,10,12}} => {{1,3,5,7,9,11},{2,4,6,8,10,12}}
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => {{1},{2},{3},{4},{5},{6},{7,8},{9},{10}} => {{1},{2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}} => {{1},{2},{3},{4,5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => {{1},{2},{3},{4},{5,6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,6},{7},{8},{9},{10}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,5,6,7,8,9,2,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,10,11,2] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,5,1,6,7,9,4,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,7,2,9,3,4,6,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [4,1,2,8,3,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,2,10,9] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,9,10,6] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7,8,9] => {{1,2,3,4},{5,6},{7},{8},{9}} => {{1},{2},{3},{4,5},{6,7,8,9}}
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,9,10,5] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7,8,9] => {{1,2,3},{4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,1,5,6,7,8,9,10,4] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,11,1,3,4,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0] => [1,2,9,3,4,5,6,7,10,8] => {{1},{2},{3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8},{9},{10}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,9,5] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,8,9,5] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => {{1},{2},{3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8},{9},{10}}
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
to cycle type
Description
Let π=c1…cr a permutation of size n decomposed in its cyclic parts. The associated set partition of [n] then is S=S1∪⋯∪Sr such that Si is the set of integers in the cycle ci.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
Map
complement
Description
The complement of a set partition obtained by replacing i with n+1−i.