Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
[1,0] => [1] => [1] => {{1}}
[1,0,1,0] => [2,1] => [2,1] => {{1,2}}
[1,1,0,0] => [1,2] => [1,2] => {{1},{2}}
[1,0,1,0,1,0] => [2,3,1] => [3,2,1] => {{1,3},{2}}
[1,0,1,1,0,0] => [2,1,3] => [2,1,3] => {{1,2},{3}}
[1,1,0,0,1,0] => [1,3,2] => [1,3,2] => {{1},{2,3}}
[1,1,0,1,0,0] => [3,1,2] => [3,1,2] => {{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] => [2,3,4,1] => [4,2,3,1] => {{1,4},{2},{3}}
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [3,2,1,4] => {{1,3},{2},{4}}
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,1,4,3] => {{1,2},{3,4}}
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [4,2,1,3] => {{1,3,4},{2}}
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => {{1,2},{3},{4}}
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [1,4,3,2] => {{1},{2,4},{3}}
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [1,3,2,4] => {{1},{2,3},{4}}
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [3,4,1,2] => {{1,3},{2,4}}
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [4,1,3,2] => {{1,2,4},{3}}
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [3,1,2,4] => {{1,2,3},{4}}
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [1,2,4,3] => {{1},{2},{3,4}}
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => {{1},{2,3,4}}
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [4,1,2,3] => {{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] => [2,3,4,5,1] => [5,2,3,4,1] => {{1,5},{2},{3},{4}}
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => {{1,4},{2},{3},{5}}
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [3,2,1,5,4] => {{1,3},{2},{4,5}}
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [5,2,3,1,4] => {{1,4,5},{2},{3}}
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => {{1,3},{2},{4},{5}}
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [2,1,5,4,3] => {{1,2},{3,5},{4}}
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [2,1,4,3,5] => {{1,2},{3,4},{5}}
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [4,2,5,1,3] => {{1,4},{2},{3,5}}
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [5,2,1,4,3] => {{1,3,5},{2},{4}}
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [4,2,1,3,5] => {{1,3,4},{2},{5}}
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [2,1,3,5,4] => {{1,2},{3},{4,5}}
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [2,1,5,3,4] => {{1,2},{3,4,5}}
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [5,2,1,3,4] => {{1,3,4,5},{2}}
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => {{1,2},{3},{4},{5}}
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [1,5,3,4,2] => {{1},{2,5},{3},{4}}
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [1,4,3,2,5] => {{1},{2,4},{3},{5}}
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [1,5,3,2,4] => {{1},{2,4,5},{3}}
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => {{1},{2,3},{4},{5}}
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [3,5,1,4,2] => {{1,3},{2,5},{4}}
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [3,4,1,2,5] => {{1,3},{2,4},{5}}
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [4,5,3,1,2] => {{1,4},{2,5},{3}}
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [5,1,3,4,2] => {{1,2,5},{3},{4}}
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [4,1,3,2,5] => {{1,2,4},{3},{5}}
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [3,1,2,5,4] => {{1,2,3},{4,5}}
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [3,5,1,2,4] => {{1,3},{2,4,5}}
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [5,1,3,2,4] => {{1,2,4,5},{3}}
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [3,1,2,4,5] => {{1,2,3},{4},{5}}
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [1,2,5,4,3] => {{1},{2},{3,5},{4}}
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => {{1},{2},{3,4},{5}}
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,4,5,2,3] => {{1},{2,4},{3,5}}
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [1,5,2,4,3] => {{1},{2,3,5},{4}}
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [1,4,2,3,5] => {{1},{2,3,4},{5}}
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [4,1,5,2,3] => {{1,2,4},{3,5}}
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [4,5,2,1,3] => {{1,4},{2,3,5}}
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [5,1,2,4,3] => {{1,2,3,5},{4}}
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [4,1,2,3,5] => {{1,2,3,4},{5}}
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [1,2,3,5,4] => {{1},{2},{3},{4,5}}
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => {{1},{2},{3,4,5}}
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [1,5,2,3,4] => {{1},{2,3,4,5}}
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [5,1,2,3,4] => {{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] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => {{1,6},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => {{1,5},{2},{3},{4},{6}}
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => {{1,4},{2},{3},{5,6}}
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => {{1,5,6},{2},{3},{4}}
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => {{1,4},{2},{3},{5},{6}}
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => {{1,3},{2},{4,6},{5}}
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => {{1,3},{2},{4,5},{6}}
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [5,2,3,6,1,4] => {{1,5},{2},{3},{4,6}}
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [6,2,3,1,5,4] => {{1,4,6},{2},{3},{5}}
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [5,2,3,1,4,6] => {{1,4,5},{2},{3},{6}}
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => {{1,3},{2},{4},{5,6}}
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [3,2,1,6,4,5] => {{1,3},{2},{4,5,6}}
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [6,2,3,1,4,5] => {{1,4,5,6},{2},{3}}
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => {{1,2},{3,6},{4},{5}}
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => {{1,2},{3,5},{4},{6}}
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [2,1,6,4,3,5] => {{1,2},{3,5,6},{4}}
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}}
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [4,2,6,1,5,3] => {{1,4},{2},{3,6},{5}}
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => {{1,4},{2},{3,5},{6}}
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [5,2,6,4,1,3] => {{1,5},{2},{3,6},{4}}
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [6,2,1,4,5,3] => {{1,3,6},{2},{4},{5}}
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [5,2,1,4,3,6] => {{1,3,5},{2},{4},{6}}
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [4,2,1,3,6,5] => {{1,3,4},{2},{5,6}}
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [4,2,6,1,3,5] => {{1,4},{2},{3,5,6}}
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [6,2,1,4,3,5] => {{1,3,5,6},{2},{4}}
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => {{1,3,4},{2},{5},{6}}
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => {{1,2},{3},{4,6},{5}}
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}}
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [2,1,5,6,3,4] => {{1,2},{3,5},{4,6}}
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [2,1,6,3,5,4] => {{1,2},{3,4,6},{5}}
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}}
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [5,2,1,6,3,4] => {{1,3,5},{2},{4,6}}
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [5,2,6,3,1,4] => {{1,5},{2},{3,4,6}}
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => {{1,3,4,6},{2},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => {{1,3,4,5},{2},{6}}
>>> Load all 1922 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}}
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [2,1,3,6,4,5] => {{1,2},{3},{4,5,6}}
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => {{1,3,4,5,6},{2}}
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => {{1},{2,6},{3},{4},{5}}
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => {{1},{2,5},{3},{4},{6}}
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => {{1},{2,4},{3},{5,6}}
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [1,6,3,4,2,5] => {{1},{2,5,6},{3},{4}}
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}}
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}}
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}}
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [1,5,3,6,2,4] => {{1},{2,5},{3},{4,6}}
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [1,6,3,2,5,4] => {{1},{2,4,6},{3},{5}}
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,5,3,2,4,6] => {{1},{2,4,5},{3},{6}}
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}}
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [1,6,3,2,4,5] => {{1},{2,4,5,6},{3}}
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [3,6,1,4,5,2] => {{1,3},{2,6},{4},{5}}
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [3,5,1,4,2,6] => {{1,3},{2,5},{4},{6}}
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [3,4,1,2,6,5] => {{1,3},{2,4},{5,6}}
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [3,6,1,4,2,5] => {{1,3},{2,5,6},{4}}
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}}
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [4,6,3,1,5,2] => {{1,4},{2,6},{3},{5}}
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [4,5,3,1,2,6] => {{1,4},{2,5},{3},{6}}
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [5,6,3,4,1,2] => {{1,5},{2,6},{3},{4}}
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [6,1,3,4,5,2] => {{1,2,6},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [5,1,3,4,2,6] => {{1,2,5},{3},{4},{6}}
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [4,1,3,2,6,5] => {{1,2,4},{3},{5,6}}
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [4,6,3,1,2,5] => {{1,4},{2,5,6},{3}}
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => {{1,2,5,6},{3},{4}}
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => {{1,2,4},{3},{5},{6}}
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [3,1,2,6,5,4] => {{1,2,3},{4,6},{5}}
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [3,1,2,5,4,6] => {{1,2,3},{4,5},{6}}
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [3,5,1,6,2,4] => {{1,3},{2,5},{4,6}}
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [3,6,1,2,5,4] => {{1,3},{2,4,6},{5}}
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [3,5,1,2,4,6] => {{1,3},{2,4,5},{6}}
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [5,1,3,6,2,4] => {{1,2,5},{3},{4,6}}
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [5,6,3,2,1,4] => {{1,5},{2,4,6},{3}}
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => {{1,2,4,6},{3},{5}}
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => {{1,2,4,5},{3},{6}}
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [3,1,2,4,6,5] => {{1,2,3},{4},{5,6}}
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [3,6,1,2,4,5] => {{1,3},{2,4,5,6}}
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => {{1,2,4,5,6},{3}}
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => {{1,2,3},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => {{1},{2},{3,6},{4},{5}}
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}}
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}}
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [1,2,6,4,3,5] => {{1},{2},{3,5,6},{4}}
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}}
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [1,4,6,2,5,3] => {{1},{2,4},{3,6},{5}}
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => {{1},{2,4},{3,5},{6}}
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [1,5,6,4,2,3] => {{1},{2,5},{3,6},{4}}
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [1,6,2,4,5,3] => {{1},{2,3,6},{4},{5}}
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,5,2,4,3,6] => {{1},{2,3,5},{4},{6}}
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [1,4,6,2,3,5] => {{1},{2,4},{3,5,6}}
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [1,6,2,4,3,5] => {{1},{2,3,5,6},{4}}
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => {{1},{2,3,4},{5},{6}}
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [4,1,6,2,5,3] => {{1,2,4},{3,6},{5}}
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [4,1,5,2,3,6] => {{1,2,4},{3,5},{6}}
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => {{1,4},{2,5},{3,6}}
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [4,6,2,1,5,3] => {{1,4},{2,3,6},{5}}
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [4,5,2,1,3,6] => {{1,4},{2,3,5},{6}}
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [5,1,6,4,2,3] => {{1,2,5},{3,6},{4}}
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [5,6,2,4,1,3] => {{1,5},{2,3,6},{4}}
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => {{1,2,3,6},{4},{5}}
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => {{1,2,3,5},{4},{6}}
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}}
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [4,1,6,2,3,5] => {{1,2,4},{3,5,6}}
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [4,6,2,1,3,5] => {{1,4},{2,3,5,6}}
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => {{1,2,3,5,6},{4}}
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => {{1,2,3,4},{5},{6}}
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}}
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}}
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}}
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [1,2,6,3,5,4] => {{1},{2},{3,4,6},{5}}
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}}
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [1,5,2,6,3,4] => {{1},{2,3,5},{4,6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [1,5,6,3,2,4] => {{1},{2,5},{3,4,6}}
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [1,6,2,3,5,4] => {{1},{2,3,4,6},{5}}
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => {{1},{2,3,4,5},{6}}
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [5,1,2,6,3,4] => {{1,2,3,5},{4,6}}
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [5,1,6,3,2,4] => {{1,2,5},{3,4,6}}
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [5,6,2,3,1,4] => {{1,5},{2,3,4,6}}
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => {{1,2,3,4,6},{5}}
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => {{1,2,3,4,5},{6}}
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}}
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}}
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => {{1},{2},{3,4,5,6}}
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => {{1},{2,3,4,5,6}}
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => {{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] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => {{1,7},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => {{1,6},{2},{3},{4},{5},{7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => {{1,5},{2},{3},{4},{6,7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [7,2,3,4,5,1,6] => {{1,6,7},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => {{1,5},{2},{3},{4},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => {{1,4},{2},{3},{5,7},{6}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => {{1,4},{2},{3},{5,6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [6,2,3,4,7,1,5] => {{1,6},{2},{3},{4},{5,7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [7,2,3,4,1,6,5] => {{1,5,7},{2},{3},{4},{6}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [6,2,3,4,1,5,7] => {{1,5,6},{2},{3},{4},{7}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => {{1,4},{2},{3},{5},{6,7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [4,2,3,1,7,5,6] => {{1,4},{2},{3},{5,6,7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [7,2,3,4,1,5,6] => {{1,5,6,7},{2},{3},{4}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => {{1,4},{2},{3},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => {{1,3},{2},{4,7},{5},{6}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => {{1,3},{2},{4,6},{5},{7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => {{1,3},{2},{4,5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [3,2,1,7,5,4,6] => {{1,3},{2},{4,6,7},{5}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => {{1,3},{2},{4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [5,2,3,7,1,6,4] => {{1,5},{2},{3},{4,7},{6}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [5,2,3,6,1,4,7] => {{1,5},{2},{3},{4,6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [6,2,3,7,5,1,4] => {{1,6},{2},{3},{4,7},{5}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [7,2,3,1,5,6,4] => {{1,4,7},{2},{3},{5},{6}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [6,2,3,1,5,4,7] => {{1,4,6},{2},{3},{5},{7}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [5,2,3,1,4,7,6] => {{1,4,5},{2},{3},{6,7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [5,2,3,7,1,4,6] => {{1,5},{2},{3},{4,6,7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [7,2,3,1,5,4,6] => {{1,4,6,7},{2},{3},{5}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [5,2,3,1,4,6,7] => {{1,4,5},{2},{3},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => {{1,3},{2},{4},{5,7},{6}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => {{1,3},{2},{4},{5,6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [3,2,1,6,7,4,5] => {{1,3},{2},{4,6},{5,7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [3,2,1,7,4,6,5] => {{1,3},{2},{4,5,7},{6}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [3,2,1,6,4,5,7] => {{1,3},{2},{4,5,6},{7}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [6,2,3,1,7,4,5] => {{1,4,6},{2},{3},{5,7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [6,2,3,7,4,1,5] => {{1,6},{2},{3},{4,5,7}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [7,2,3,1,4,6,5] => {{1,4,5,7},{2},{3},{6}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [6,2,3,1,4,5,7] => {{1,4,5,6},{2},{3},{7}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => {{1,3},{2},{4},{5},{6,7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [3,2,1,4,7,5,6] => {{1,3},{2},{4},{5,6,7}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [3,2,1,7,4,5,6] => {{1,3},{2},{4,5,6,7}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [7,2,3,1,4,5,6] => {{1,4,5,6,7},{2},{3}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => {{1,2},{3,7},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => {{1,2},{3,6},{4},{5},{7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => {{1,2},{3,5},{4},{6,7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [2,1,7,4,5,3,6] => {{1,2},{3,6,7},{4},{5}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => {{1,2},{3,5},{4},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => {{1,2},{3,4},{5,7},{6}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,1,6,4,7,3,5] => {{1,2},{3,6},{4},{5,7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [2,1,7,4,3,6,5] => {{1,2},{3,5,7},{4},{6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [2,1,6,4,3,5,7] => {{1,2},{3,5,6},{4},{7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [2,1,7,4,3,5,6] => {{1,2},{3,5,6,7},{4}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => {{1,2},{3,4},{5},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [4,2,7,1,5,6,3] => {{1,4},{2},{3,7},{5},{6}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [4,2,6,1,5,3,7] => {{1,4},{2},{3,6},{5},{7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [4,2,5,1,3,7,6] => {{1,4},{2},{3,5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [4,2,7,1,5,3,6] => {{1,4},{2},{3,6,7},{5}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [4,2,5,1,3,6,7] => {{1,4},{2},{3,5},{6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [5,2,7,4,1,6,3] => {{1,5},{2},{3,7},{4},{6}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [5,2,6,4,1,3,7] => {{1,5},{2},{3,6},{4},{7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [6,2,7,4,5,1,3] => {{1,6},{2},{3,7},{4},{5}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [7,2,1,4,5,6,3] => {{1,3,7},{2},{4},{5},{6}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [6,2,1,4,5,3,7] => {{1,3,6},{2},{4},{5},{7}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [5,2,1,4,3,7,6] => {{1,3,5},{2},{4},{6,7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [5,2,7,4,1,3,6] => {{1,5},{2},{3,6,7},{4}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [7,2,1,4,5,3,6] => {{1,3,6,7},{2},{4},{5}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [5,2,1,4,3,6,7] => {{1,3,5},{2},{4},{6},{7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [4,2,1,3,7,6,5] => {{1,3,4},{2},{5,7},{6}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [4,2,1,3,6,5,7] => {{1,3,4},{2},{5,6},{7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [4,2,6,1,7,3,5] => {{1,4},{2},{3,6},{5,7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [4,2,7,1,3,6,5] => {{1,4},{2},{3,5,7},{6}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [4,2,6,1,3,5,7] => {{1,4},{2},{3,5,6},{7}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [6,2,1,4,7,3,5] => {{1,3,6},{2},{4},{5,7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [6,2,7,4,3,1,5] => {{1,6},{2},{3,5,7},{4}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [7,2,1,4,3,6,5] => {{1,3,5,7},{2},{4},{6}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [6,2,1,4,3,5,7] => {{1,3,5,6},{2},{4},{7}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [4,2,1,3,5,7,6] => {{1,3,4},{2},{5},{6,7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [4,2,1,3,7,5,6] => {{1,3,4},{2},{5,6,7}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [4,2,7,1,3,5,6] => {{1,4},{2},{3,5,6,7}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [7,2,1,4,3,5,6] => {{1,3,5,6,7},{2},{4}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [4,2,1,3,5,6,7] => {{1,3,4},{2},{5},{6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => {{1,2},{3},{4,7},{5},{6}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => {{1,2},{3},{4,6},{5},{7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [2,1,3,7,5,4,6] => {{1,2},{3},{4,6,7},{5}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => {{1,2},{3},{4,5},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,1,5,7,3,6,4] => {{1,2},{3,5},{4,7},{6}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [2,1,5,6,3,4,7] => {{1,2},{3,5},{4,6},{7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,1,6,7,5,3,4] => {{1,2},{3,6},{4,7},{5}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [2,1,7,3,5,6,4] => {{1,2},{3,4,7},{5},{6}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [2,1,6,3,5,4,7] => {{1,2},{3,4,6},{5},{7}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [2,1,5,7,3,4,6] => {{1,2},{3,5},{4,6,7}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [2,1,7,3,5,4,6] => {{1,2},{3,4,6,7},{5}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [2,1,5,3,4,6,7] => {{1,2},{3,4,5},{6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [5,2,1,7,3,6,4] => {{1,3,5},{2},{4,7},{6}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [5,2,1,6,3,4,7] => {{1,3,5},{2},{4,6},{7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [5,2,6,7,1,3,4] => {{1,5},{2},{3,6},{4,7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [5,2,7,3,1,6,4] => {{1,5},{2},{3,4,7},{6}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [5,2,6,3,1,4,7] => {{1,5},{2},{3,4,6},{7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [6,2,1,7,5,3,4] => {{1,3,6},{2},{4,7},{5}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [6,2,7,3,5,1,4] => {{1,6},{2},{3,4,7},{5}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [7,2,1,3,5,6,4] => {{1,3,4,7},{2},{5},{6}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [6,2,1,3,5,4,7] => {{1,3,4,6},{2},{5},{7}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [5,2,1,3,4,7,6] => {{1,3,4,5},{2},{6,7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [5,2,1,7,3,4,6] => {{1,3,5},{2},{4,6,7}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [5,2,7,3,1,4,6] => {{1,5},{2},{3,4,6,7}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [7,2,1,3,5,4,6] => {{1,3,4,6,7},{2},{5}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [5,2,1,3,4,6,7] => {{1,3,4,5},{2},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => {{1,2},{3},{4},{5,7},{6}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => {{1,2},{3},{4},{5,6},{7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [2,1,3,6,7,4,5] => {{1,2},{3},{4,6},{5,7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [2,1,3,7,4,6,5] => {{1,2},{3},{4,5,7},{6}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [2,1,3,6,4,5,7] => {{1,2},{3},{4,5,6},{7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [2,1,6,3,7,4,5] => {{1,2},{3,4,6},{5,7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [2,1,6,7,4,3,5] => {{1,2},{3,6},{4,5,7}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [2,1,7,3,4,6,5] => {{1,2},{3,4,5,7},{6}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [6,2,1,3,7,4,5] => {{1,3,4,6},{2},{5,7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [6,2,1,7,4,3,5] => {{1,3,6},{2},{4,5,7}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [6,2,7,3,4,1,5] => {{1,6},{2},{3,4,5,7}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [7,2,1,3,4,6,5] => {{1,3,4,5,7},{2},{6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [6,2,1,3,4,5,7] => {{1,3,4,5,6},{2},{7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => {{1,2},{3},{4},{5},{6,7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [2,1,3,4,7,5,6] => {{1,2},{3},{4},{5,6,7}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [2,1,3,7,4,5,6] => {{1,2},{3},{4,5,6,7}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [7,2,1,3,4,5,6] => {{1,3,4,5,6,7},{2}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => {{1},{2,7},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => {{1},{2,6},{3},{4},{5},{7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => {{1},{2,5},{3},{4},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [1,7,3,4,5,2,6] => {{1},{2,6,7},{3},{4},{5}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => {{1},{2,5},{3},{4},{6},{7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => {{1},{2,4},{3},{5,7},{6}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => {{1},{2,4},{3},{5,6},{7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [1,6,3,4,7,2,5] => {{1},{2,6},{3},{4},{5,7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [1,7,3,4,2,6,5] => {{1},{2,5,7},{3},{4},{6}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [1,6,3,4,2,5,7] => {{1},{2,5,6},{3},{4},{7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => {{1},{2,4},{3},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [1,4,3,2,7,5,6] => {{1},{2,4},{3},{5,6,7}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [1,7,3,4,2,5,6] => {{1},{2,5,6,7},{3},{4}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => {{1},{2,4},{3},{5},{6},{7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => {{1},{2,3},{4,7},{5},{6}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => {{1},{2,3},{4,6},{5},{7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,7,5,4,6] => {{1},{2,3},{4,6,7},{5}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [1,5,3,7,2,6,4] => {{1},{2,5},{3},{4,7},{6}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [1,5,3,6,2,4,7] => {{1},{2,5},{3},{4,6},{7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [1,6,3,7,5,2,4] => {{1},{2,6},{3},{4,7},{5}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [1,7,3,2,5,6,4] => {{1},{2,4,7},{3},{5},{6}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [1,6,3,2,5,4,7] => {{1},{2,4,6},{3},{5},{7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [1,5,3,2,4,7,6] => {{1},{2,4,5},{3},{6,7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [1,5,3,7,2,4,6] => {{1},{2,5},{3},{4,6,7}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [1,7,3,2,5,4,6] => {{1},{2,4,6,7},{3},{5}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [1,5,3,2,4,6,7] => {{1},{2,4,5},{3},{6},{7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => {{1},{2,3},{4},{5,7},{6}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [1,3,2,6,7,4,5] => {{1},{2,3},{4,6},{5,7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,7,4,6,5] => {{1},{2,3},{4,5,7},{6}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [1,6,3,2,7,4,5] => {{1},{2,4,6},{3},{5,7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [1,6,3,7,4,2,5] => {{1},{2,6},{3},{4,5,7}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [1,7,3,2,4,6,5] => {{1},{2,4,5,7},{3},{6}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [1,6,3,2,4,5,7] => {{1},{2,4,5,6},{3},{7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [1,7,3,2,4,5,6] => {{1},{2,4,5,6,7},{3}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [3,7,1,4,5,6,2] => {{1,3},{2,7},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [3,6,1,4,5,2,7] => {{1,3},{2,6},{4},{5},{7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [3,5,1,4,2,7,6] => {{1,3},{2,5},{4},{6,7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [3,7,1,4,5,2,6] => {{1,3},{2,6,7},{4},{5}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [3,5,1,4,2,6,7] => {{1,3},{2,5},{4},{6},{7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [3,4,1,2,7,6,5] => {{1,3},{2,4},{5,7},{6}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [3,4,1,2,6,5,7] => {{1,3},{2,4},{5,6},{7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [3,6,1,4,7,2,5] => {{1,3},{2,6},{4},{5,7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [3,7,1,4,2,6,5] => {{1,3},{2,5,7},{4},{6}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [3,6,1,4,2,5,7] => {{1,3},{2,5,6},{4},{7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [3,4,1,2,5,7,6] => {{1,3},{2,4},{5},{6,7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [3,4,1,2,7,5,6] => {{1,3},{2,4},{5,6,7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [3,7,1,4,2,5,6] => {{1,3},{2,5,6,7},{4}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => {{1,3},{2,4},{5},{6},{7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [4,7,3,1,5,6,2] => {{1,4},{2,7},{3},{5},{6}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [4,6,3,1,5,2,7] => {{1,4},{2,6},{3},{5},{7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [4,5,3,1,2,7,6] => {{1,4},{2,5},{3},{6,7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [4,7,3,1,5,2,6] => {{1,4},{2,6,7},{3},{5}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [4,5,3,1,2,6,7] => {{1,4},{2,5},{3},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [5,7,3,4,1,6,2] => {{1,5},{2,7},{3},{4},{6}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [5,6,3,4,1,2,7] => {{1,5},{2,6},{3},{4},{7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [6,7,3,4,5,1,2] => {{1,6},{2,7},{3},{4},{5}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [7,1,3,4,5,6,2] => {{1,2,7},{3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [6,1,3,4,5,2,7] => {{1,2,6},{3},{4},{5},{7}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [5,1,3,4,2,7,6] => {{1,2,5},{3},{4},{6,7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [5,7,3,4,1,2,6] => {{1,5},{2,6,7},{3},{4}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [7,1,3,4,5,2,6] => {{1,2,6,7},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [5,1,3,4,2,6,7] => {{1,2,5},{3},{4},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [4,1,3,2,7,6,5] => {{1,2,4},{3},{5,7},{6}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [4,1,3,2,6,5,7] => {{1,2,4},{3},{5,6},{7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [4,6,3,1,7,2,5] => {{1,4},{2,6},{3},{5,7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [4,7,3,1,2,6,5] => {{1,4},{2,5,7},{3},{6}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [4,6,3,1,2,5,7] => {{1,4},{2,5,6},{3},{7}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [6,1,3,4,7,2,5] => {{1,2,6},{3},{4},{5,7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [6,7,3,4,2,1,5] => {{1,6},{2,5,7},{3},{4}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [7,1,3,4,2,6,5] => {{1,2,5,7},{3},{4},{6}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [6,1,3,4,2,5,7] => {{1,2,5,6},{3},{4},{7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [4,1,3,2,5,7,6] => {{1,2,4},{3},{5},{6,7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [4,1,3,2,7,5,6] => {{1,2,4},{3},{5,6,7}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [4,7,3,1,2,5,6] => {{1,4},{2,5,6,7},{3}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [7,1,3,4,2,5,6] => {{1,2,5,6,7},{3},{4}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => {{1,2,4},{3},{5},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [3,1,2,7,5,6,4] => {{1,2,3},{4,7},{5},{6}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [3,1,2,6,5,4,7] => {{1,2,3},{4,6},{5},{7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [3,1,2,7,5,4,6] => {{1,2,3},{4,6,7},{5}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [3,1,2,5,4,6,7] => {{1,2,3},{4,5},{6},{7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [3,5,1,7,2,6,4] => {{1,3},{2,5},{4,7},{6}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [3,5,1,6,2,4,7] => {{1,3},{2,5},{4,6},{7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [3,6,1,7,5,2,4] => {{1,3},{2,6},{4,7},{5}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [3,7,1,2,5,6,4] => {{1,3},{2,4,7},{5},{6}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [3,6,1,2,5,4,7] => {{1,3},{2,4,6},{5},{7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [3,5,1,2,4,7,6] => {{1,3},{2,4,5},{6,7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [3,5,1,7,2,4,6] => {{1,3},{2,5},{4,6,7}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [3,7,1,2,5,4,6] => {{1,3},{2,4,6,7},{5}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [3,5,1,2,4,6,7] => {{1,3},{2,4,5},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [5,1,3,7,2,6,4] => {{1,2,5},{3},{4,7},{6}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [5,1,3,6,2,4,7] => {{1,2,5},{3},{4,6},{7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [5,6,3,7,1,2,4] => {{1,5},{2,6},{3},{4,7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [5,7,3,2,1,6,4] => {{1,5},{2,4,7},{3},{6}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [5,6,3,2,1,4,7] => {{1,5},{2,4,6},{3},{7}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [6,1,3,7,5,2,4] => {{1,2,6},{3},{4,7},{5}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [6,7,3,2,5,1,4] => {{1,6},{2,4,7},{3},{5}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [7,1,3,2,5,6,4] => {{1,2,4,7},{3},{5},{6}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [6,1,3,2,5,4,7] => {{1,2,4,6},{3},{5},{7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [5,1,3,2,4,7,6] => {{1,2,4,5},{3},{6,7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [5,1,3,7,2,4,6] => {{1,2,5},{3},{4,6,7}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [5,7,3,2,1,4,6] => {{1,5},{2,4,6,7},{3}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [7,1,3,2,5,4,6] => {{1,2,4,6,7},{3},{5}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [5,1,3,2,4,6,7] => {{1,2,4,5},{3},{6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [3,1,2,4,7,6,5] => {{1,2,3},{4},{5,7},{6}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [3,1,2,4,6,5,7] => {{1,2,3},{4},{5,6},{7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [3,1,2,6,7,4,5] => {{1,2,3},{4,6},{5,7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [3,1,2,7,4,6,5] => {{1,2,3},{4,5,7},{6}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [3,6,1,2,7,4,5] => {{1,3},{2,4,6},{5,7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [3,6,1,7,4,2,5] => {{1,3},{2,6},{4,5,7}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [3,7,1,2,4,6,5] => {{1,3},{2,4,5,7},{6}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [3,6,1,2,4,5,7] => {{1,3},{2,4,5,6},{7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [6,1,3,2,7,4,5] => {{1,2,4,6},{3},{5,7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [6,1,3,7,4,2,5] => {{1,2,6},{3},{4,5,7}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [6,7,3,2,4,1,5] => {{1,6},{2,4,5,7},{3}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [7,1,3,2,4,6,5] => {{1,2,4,5,7},{3},{6}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [6,1,3,2,4,5,7] => {{1,2,4,5,6},{3},{7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [3,1,2,4,5,7,6] => {{1,2,3},{4},{5},{6,7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [3,1,2,4,7,5,6] => {{1,2,3},{4},{5,6,7}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [3,7,1,2,4,5,6] => {{1,3},{2,4,5,6,7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [7,1,3,2,4,5,6] => {{1,2,4,5,6,7},{3}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => {{1},{2},{3,7},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => {{1},{2},{3,6},{4},{5},{7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => {{1},{2},{3,5},{4},{6,7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [1,2,7,4,5,3,6] => {{1},{2},{3,6,7},{4},{5}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => {{1},{2},{3,5},{4},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => {{1},{2},{3,4},{5,7},{6}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [1,2,6,4,7,3,5] => {{1},{2},{3,6},{4},{5,7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [1,2,7,4,3,6,5] => {{1},{2},{3,5,7},{4},{6}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [1,2,6,4,3,5,7] => {{1},{2},{3,5,6},{4},{7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [1,2,7,4,3,5,6] => {{1},{2},{3,5,6,7},{4}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [1,4,7,2,5,6,3] => {{1},{2,4},{3,7},{5},{6}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [1,4,6,2,5,3,7] => {{1},{2,4},{3,6},{5},{7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [1,4,5,2,3,7,6] => {{1},{2,4},{3,5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [1,4,7,2,5,3,6] => {{1},{2,4},{3,6,7},{5}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [1,4,5,2,3,6,7] => {{1},{2,4},{3,5},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [1,5,7,4,2,6,3] => {{1},{2,5},{3,7},{4},{6}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [1,5,6,4,2,3,7] => {{1},{2,5},{3,6},{4},{7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [1,6,7,4,5,2,3] => {{1},{2,6},{3,7},{4},{5}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [1,7,2,4,5,6,3] => {{1},{2,3,7},{4},{5},{6}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [1,6,2,4,5,3,7] => {{1},{2,3,6},{4},{5},{7}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [1,5,2,4,3,7,6] => {{1},{2,3,5},{4},{6,7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [1,5,7,4,2,3,6] => {{1},{2,5},{3,6,7},{4}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [1,7,2,4,5,3,6] => {{1},{2,3,6,7},{4},{5}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [1,5,2,4,3,6,7] => {{1},{2,3,5},{4},{6},{7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [1,4,2,3,7,6,5] => {{1},{2,3,4},{5,7},{6}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [1,4,6,2,7,3,5] => {{1},{2,4},{3,6},{5,7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [1,4,7,2,3,6,5] => {{1},{2,4},{3,5,7},{6}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [1,4,6,2,3,5,7] => {{1},{2,4},{3,5,6},{7}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [1,6,2,4,7,3,5] => {{1},{2,3,6},{4},{5,7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [1,6,7,4,3,2,5] => {{1},{2,6},{3,5,7},{4}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [1,7,2,4,3,6,5] => {{1},{2,3,5,7},{4},{6}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [1,6,2,4,3,5,7] => {{1},{2,3,5,6},{4},{7}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [1,4,7,2,3,5,6] => {{1},{2,4},{3,5,6,7}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [1,7,2,4,3,5,6] => {{1},{2,3,5,6,7},{4}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [1,4,2,3,5,6,7] => {{1},{2,3,4},{5},{6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [4,1,7,2,5,6,3] => {{1,2,4},{3,7},{5},{6}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [4,1,6,2,5,3,7] => {{1,2,4},{3,6},{5},{7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [4,1,5,2,3,7,6] => {{1,2,4},{3,5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [4,1,7,2,5,3,6] => {{1,2,4},{3,6,7},{5}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [4,1,5,2,3,6,7] => {{1,2,4},{3,5},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [4,5,7,1,2,6,3] => {{1,4},{2,5},{3,7},{6}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => {{1,4},{2,5},{3,6},{7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [4,6,7,1,5,2,3] => {{1,4},{2,6},{3,7},{5}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [4,7,2,1,5,6,3] => {{1,4},{2,3,7},{5},{6}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [4,6,2,1,5,3,7] => {{1,4},{2,3,6},{5},{7}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [4,5,2,1,3,7,6] => {{1,4},{2,3,5},{6,7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [4,5,7,1,2,3,6] => {{1,4},{2,5},{3,6,7}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [4,7,2,1,5,3,6] => {{1,4},{2,3,6,7},{5}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [4,5,2,1,3,6,7] => {{1,4},{2,3,5},{6},{7}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [5,1,7,4,2,6,3] => {{1,2,5},{3,7},{4},{6}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [5,1,6,4,2,3,7] => {{1,2,5},{3,6},{4},{7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [5,6,7,4,1,2,3] => {{1,5},{2,6},{3,7},{4}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [5,7,2,4,1,6,3] => {{1,5},{2,3,7},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [5,6,2,4,1,3,7] => {{1,5},{2,3,6},{4},{7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [6,1,7,4,5,2,3] => {{1,2,6},{3,7},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [6,7,2,4,5,1,3] => {{1,6},{2,3,7},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [7,1,2,4,5,6,3] => {{1,2,3,7},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => {{1,2,3,6},{4},{5},{7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [5,1,2,4,3,7,6] => {{1,2,3,5},{4},{6,7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [5,1,7,4,2,3,6] => {{1,2,5},{3,6,7},{4}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [5,7,2,4,1,3,6] => {{1,5},{2,3,6,7},{4}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [7,1,2,4,5,3,6] => {{1,2,3,6,7},{4},{5}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => {{1,2,3,5},{4},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [4,1,2,3,7,6,5] => {{1,2,3,4},{5,7},{6}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [4,1,2,3,6,5,7] => {{1,2,3,4},{5,6},{7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [4,1,6,2,7,3,5] => {{1,2,4},{3,6},{5,7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [4,1,7,2,3,6,5] => {{1,2,4},{3,5,7},{6}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [4,1,6,2,3,5,7] => {{1,2,4},{3,5,6},{7}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [4,6,2,1,7,3,5] => {{1,4},{2,3,6},{5,7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [4,6,7,1,3,2,5] => {{1,4},{2,6},{3,5,7}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [4,7,2,1,3,6,5] => {{1,4},{2,3,5,7},{6}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [4,6,2,1,3,5,7] => {{1,4},{2,3,5,6},{7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [6,1,2,4,7,3,5] => {{1,2,3,6},{4},{5,7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [6,1,7,4,3,2,5] => {{1,2,6},{3,5,7},{4}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [6,7,2,4,3,1,5] => {{1,6},{2,3,5,7},{4}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [7,1,2,4,3,6,5] => {{1,2,3,5,7},{4},{6}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [6,1,2,4,3,5,7] => {{1,2,3,5,6},{4},{7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [4,1,2,3,5,7,6] => {{1,2,3,4},{5},{6,7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [4,1,7,2,3,5,6] => {{1,2,4},{3,5,6,7}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [4,7,2,1,3,5,6] => {{1,4},{2,3,5,6,7}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [7,1,2,4,3,5,6] => {{1,2,3,5,6,7},{4}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => {{1,2,3,4},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => {{1},{2},{3},{4,7},{5},{6}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [1,2,3,7,5,4,6] => {{1},{2},{3},{4,6,7},{5}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [1,2,5,7,3,6,4] => {{1},{2},{3,5},{4,7},{6}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [1,2,5,6,3,4,7] => {{1},{2},{3,5},{4,6},{7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [1,2,6,7,5,3,4] => {{1},{2},{3,6},{4,7},{5}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [1,2,7,3,5,6,4] => {{1},{2},{3,4,7},{5},{6}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [1,2,6,3,5,4,7] => {{1},{2},{3,4,6},{5},{7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [1,2,5,7,3,4,6] => {{1},{2},{3,5},{4,6,7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [1,2,7,3,5,4,6] => {{1},{2},{3,4,6,7},{5}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [1,2,5,3,4,6,7] => {{1},{2},{3,4,5},{6},{7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [1,5,2,7,3,6,4] => {{1},{2,3,5},{4,7},{6}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [1,5,2,6,3,4,7] => {{1},{2,3,5},{4,6},{7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [1,5,6,7,2,3,4] => {{1},{2,5},{3,6},{4,7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [1,5,7,3,2,6,4] => {{1},{2,5},{3,4,7},{6}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [1,5,6,3,2,4,7] => {{1},{2,5},{3,4,6},{7}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [1,6,2,7,5,3,4] => {{1},{2,3,6},{4,7},{5}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [1,6,7,3,5,2,4] => {{1},{2,6},{3,4,7},{5}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [1,7,2,3,5,6,4] => {{1},{2,3,4,7},{5},{6}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [1,6,2,3,5,4,7] => {{1},{2,3,4,6},{5},{7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,5,2,7,3,4,6] => {{1},{2,3,5},{4,6,7}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [1,5,7,3,2,4,6] => {{1},{2,5},{3,4,6,7}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [1,7,2,3,5,4,6] => {{1},{2,3,4,6,7},{5}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [1,5,2,3,4,6,7] => {{1},{2,3,4,5},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [5,1,2,7,3,6,4] => {{1,2,3,5},{4,7},{6}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [5,1,2,6,3,4,7] => {{1,2,3,5},{4,6},{7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [5,1,6,7,2,3,4] => {{1,2,5},{3,6},{4,7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [5,1,7,3,2,6,4] => {{1,2,5},{3,4,7},{6}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [5,1,6,3,2,4,7] => {{1,2,5},{3,4,6},{7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [5,6,2,7,1,3,4] => {{1,5},{2,3,6},{4,7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [5,6,7,3,1,2,4] => {{1,5},{2,6},{3,4,7}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [5,7,2,3,1,6,4] => {{1,5},{2,3,4,7},{6}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [5,6,2,3,1,4,7] => {{1,5},{2,3,4,6},{7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [6,1,2,7,5,3,4] => {{1,2,3,6},{4,7},{5}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [6,1,7,3,5,2,4] => {{1,2,6},{3,4,7},{5}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [6,7,2,3,5,1,4] => {{1,6},{2,3,4,7},{5}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => {{1,2,3,4,7},{5},{6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => {{1,2,3,4,6},{5},{7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [5,1,2,3,4,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [5,1,2,7,3,4,6] => {{1,2,3,5},{4,6,7}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [5,1,7,3,2,4,6] => {{1,2,5},{3,4,6,7}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [5,7,2,3,1,4,6] => {{1,5},{2,3,4,6,7}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [7,1,2,3,5,4,6] => {{1,2,3,4,6,7},{5}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => {{1},{2},{3},{4},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [1,2,3,6,7,4,5] => {{1},{2},{3},{4,6},{5,7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [1,2,3,7,4,6,5] => {{1},{2},{3},{4,5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,6,4,5,7] => {{1},{2},{3},{4,5,6},{7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [1,2,6,3,7,4,5] => {{1},{2},{3,4,6},{5,7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [1,2,6,7,4,3,5] => {{1},{2},{3,6},{4,5,7}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [1,2,7,3,4,6,5] => {{1},{2},{3,4,5,7},{6}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => {{1},{2},{3,4,5,6},{7}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [1,6,2,3,7,4,5] => {{1},{2,3,4,6},{5,7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,6,2,7,4,3,5] => {{1},{2,3,6},{4,5,7}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [1,6,7,3,4,2,5] => {{1},{2,6},{3,4,5,7}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [1,7,2,3,4,6,5] => {{1},{2,3,4,5,7},{6}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [1,6,2,3,4,5,7] => {{1},{2,3,4,5,6},{7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [6,1,2,3,7,4,5] => {{1,2,3,4,6},{5,7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [6,1,2,7,4,3,5] => {{1,2,3,6},{4,5,7}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [6,1,7,3,4,2,5] => {{1,2,6},{3,4,5,7}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [6,7,2,3,4,1,5] => {{1,6},{2,3,4,5,7}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => {{1,2,3,4,5,7},{6}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => {{1,2,3,4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,6,7}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,5,6,7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => {{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] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => {{1,8},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => {{1,7},{2},{3},{4},{5},{6},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => {{1,6},{2},{3},{4},{5},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [8,2,3,4,5,6,1,7] => {{1,7,8},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => {{1,6},{2},{3},{4},{5},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => {{1,5},{2},{3},{4},{6,8},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => [7,2,3,4,5,8,1,6] => {{1,7},{2},{3},{4},{5},{6,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [8,2,3,4,5,1,7,6] => {{1,6,8},{2},{3},{4},{5},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6,8] => [7,2,3,4,5,1,6,8] => {{1,6,7},{2},{3},{4},{5},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => {{1,5},{2},{3},{4},{6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => [5,2,3,4,1,8,6,7] => {{1,5},{2},{3},{4},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [8,2,3,4,5,1,6,7] => {{1,6,7,8},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => {{1,5},{2},{3},{4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => {{1,4},{2},{3},{5,8},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8] => [4,2,3,1,7,6,5,8] => {{1,4},{2},{3},{5,7},{6},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => {{1,4},{2},{3},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => [4,2,3,1,6,5,7,8] => {{1,4},{2},{3},{5,6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,6,1,7,8,5] => [6,2,3,4,8,1,7,5] => {{1,6},{2},{3},{4},{5,8},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,4,6,7,1,8,5] => [7,2,3,4,8,6,1,5] => {{1,7},{2},{3},{4},{5,8},{6}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => [8,2,3,4,1,6,7,5] => {{1,5,8},{2},{3},{4},{6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => [7,2,3,4,1,6,5,8] => {{1,5,7},{2},{3},{4},{6},{8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,8,5,7] => [6,2,3,4,8,1,5,7] => {{1,6},{2},{3},{4},{5,7,8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,1,5,7,8,6] => [4,2,3,1,5,8,7,6] => {{1,4},{2},{3},{5},{6,8},{7}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => {{1,4},{2},{3},{5},{6,7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [4,2,3,1,7,8,5,6] => {{1,4},{2},{3},{5,7},{6,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [4,2,3,1,8,5,7,6] => {{1,4},{2},{3},{5,6,8},{7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,4,7,1,8,5,6] => [7,2,3,4,8,5,1,6] => {{1,7},{2},{3},{4},{5,6,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,7,8,1,5,6] => [8,2,3,4,1,5,7,6] => {{1,5,6,8},{2},{3},{4},{7}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [7,2,3,4,1,5,6,8] => {{1,5,6,7},{2},{3},{4},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => [4,2,3,1,5,8,6,7] => {{1,4},{2},{3},{5},{6,7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [4,2,3,1,8,5,6,7] => {{1,4},{2},{3},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [8,2,3,4,1,5,6,7] => {{1,5,6,7,8},{2},{3},{4}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => {{1,4},{2},{3},{5},{6},{7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => {{1,3},{2},{4,8},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => {{1,3},{2},{4,7},{5},{6},{8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,5,6,4,8,7] => [3,2,1,6,5,4,8,7] => {{1,3},{2},{4,6},{5},{7,8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,5,6,8,4,7] => [3,2,1,8,5,6,4,7] => {{1,3},{2},{4,7,8},{5},{6}}
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,4,7,8] => [3,2,1,6,5,4,7,8] => {{1,3},{2},{4,6},{5},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => {{1,3},{2},{4,5},{6,7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,7,8,4,6] => [3,2,1,8,5,4,7,6] => {{1,3},{2},{4,6,8},{5},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6,8] => [3,2,1,7,5,4,6,8] => {{1,3},{2},{4,6,7},{5},{8}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,5,8,4,6,7] => [3,2,1,8,5,4,6,7] => {{1,3},{2},{4,6,7,8},{5}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,5,4,6,7,8] => [3,2,1,5,4,6,7,8] => {{1,3},{2},{4,5},{6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,4] => [5,2,3,8,1,6,7,4] => {{1,5},{2},{3},{4,8},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,5,1,6,7,4,8] => [5,2,3,7,1,6,4,8] => {{1,5},{2},{3},{4,7},{6},{8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,5,1,6,4,8,7] => [5,2,3,6,1,4,8,7] => {{1,5},{2},{3},{4,6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,5,1,6,4,7,8] => [5,2,3,6,1,4,7,8] => {{1,5},{2},{3},{4,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => [6,2,3,8,5,1,7,4] => {{1,6},{2},{3},{4,8},{5},{7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,5,6,1,7,4,8] => [6,2,3,7,5,1,4,8] => {{1,6},{2},{3},{4,7},{5},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,5,6,7,1,8,4] => [7,2,3,8,5,6,1,4] => {{1,7},{2},{3},{4,8},{5},{6}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => [8,2,3,1,5,6,7,4] => {{1,4,8},{2},{3},{5},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,6,7,1,4,8] => [7,2,3,1,5,6,4,8] => {{1,4,7},{2},{3},{5},{6},{8}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,6,1,4,8,7] => [6,2,3,1,5,4,8,7] => {{1,4,6},{2},{3},{5},{7,8}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,8,1,4,7] => [8,2,3,1,5,6,4,7] => {{1,4,7,8},{2},{3},{5},{6}}
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [6,2,3,1,5,4,7,8] => {{1,4,6},{2},{3},{5},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,7,4,8,6] => [5,2,3,7,1,8,4,6] => {{1,5},{2},{3},{4,7},{6,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,7,8,4,6] => [5,2,3,8,1,4,7,6] => {{1,5},{2},{3},{4,6,8},{7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,7,1,8,4,6] => [7,2,3,8,5,4,1,6] => {{1,7},{2},{3},{4,6,8},{5}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,7,8,1,4,6] => [8,2,3,1,5,4,7,6] => {{1,4,6,8},{2},{3},{5},{7}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,5,1,4,8,6,7] => [5,2,3,1,4,8,6,7] => {{1,4,5},{2},{3},{6,7,8}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [5,2,3,8,1,4,6,7] => {{1,5},{2},{3},{4,6,7,8}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,1,4,6,7,8] => [5,2,3,1,4,6,7,8] => {{1,4,5},{2},{3},{6},{7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => {{1,3},{2},{4},{5,8},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => {{1,3},{2},{4},{5,7},{6},{8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,6,4,7,8,5] => [3,2,1,6,8,4,7,5] => {{1,3},{2},{4,6},{5,8},{7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [3,2,1,6,7,4,5,8] => {{1,3},{2},{4,6},{5,7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,6,7,4,8,5] => [3,2,1,7,8,6,4,5] => {{1,3},{2},{4,7},{5,8},{6}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,4,5] => [3,2,1,8,4,6,7,5] => {{1,3},{2},{4,5,8},{6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,6,7,4,5,8] => [3,2,1,7,4,6,5,8] => {{1,3},{2},{4,5,7},{6},{8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [3,2,1,6,8,4,5,7] => {{1,3},{2},{4,6},{5,7,8}}
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,4,5,7] => [3,2,1,8,4,6,5,7] => {{1,3},{2},{4,5,7,8},{6}}
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => [3,2,1,6,4,5,7,8] => {{1,3},{2},{4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,1,4,7,8,5] => [6,2,3,1,8,4,7,5] => {{1,4,6},{2},{3},{5,8},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,6,1,7,4,8,5] => [6,2,3,7,8,1,4,5] => {{1,6},{2},{3},{4,7},{5,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => [6,2,3,8,4,1,7,5] => {{1,6},{2},{3},{4,5,8},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,7,4,5,8] => [6,2,3,7,4,1,5,8] => {{1,6},{2},{3},{4,5,7},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,6,7,1,4,8,5] => [7,2,3,1,8,6,4,5] => {{1,4,7},{2},{3},{5,8},{6}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,6,7,1,8,4,5] => [7,2,3,8,4,6,1,5] => {{1,7},{2},{3},{4,5,8},{6}}
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,6,7,1,4,5,8] => [7,2,3,1,4,6,5,8] => {{1,4,5,7},{2},{3},{6},{8}}
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => [6,2,3,8,4,1,5,7] => {{1,6},{2},{3},{4,5,7,8}}
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,6,8,1,4,5,7] => [8,2,3,1,4,6,5,7] => {{1,4,5,7,8},{2},{3},{6}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,6,1,4,5,7,8] => [6,2,3,1,4,5,7,8] => {{1,4,5,6},{2},{3},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => {{1,3},{2},{4},{5},{6,8},{7}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => {{1,3},{2},{4},{5},{6,7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [3,2,1,4,8,5,7,6] => {{1,3},{2},{4},{5,6,8},{7}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,7,4,5,8,6] => [3,2,1,7,4,8,5,6] => {{1,3},{2},{4,5,7},{6,8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,2,1,7,8,5,4,6] => {{1,3},{2},{4,7},{5,6,8}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,7,8,4,5,6] => [3,2,1,8,4,5,7,6] => {{1,3},{2},{4,5,6,8},{7}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,1,7,4,5,6,8] => [3,2,1,7,4,5,6,8] => {{1,3},{2},{4,5,6,7},{8}}
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [8,2,3,1,4,5,7,6] => {{1,4,5,6,8},{2},{3},{7}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6,8] => [7,2,3,1,4,5,6,8] => {{1,4,5,6,7},{2},{3},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => {{1,3},{2},{4},{5},{6},{7,8}}
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [3,2,1,4,8,5,6,7] => {{1,3},{2},{4},{5,6,7,8}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => [3,2,1,8,4,5,6,7] => {{1,3},{2},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [8,2,3,1,4,5,6,7] => {{1,4,5,6,7,8},{2},{3}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => {{1,2},{3,8},{4},{5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => {{1,2},{3,6},{4},{5},{7,8}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3,7,8,6] => [2,1,5,4,3,8,7,6] => {{1,2},{3,5},{4},{6,8},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => [2,1,7,4,5,8,3,6] => {{1,2},{3,7},{4},{5},{6,8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4,5,7,8,3,6] => [2,1,8,4,5,3,7,6] => {{1,2},{3,6,8},{4},{5},{7}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => {{1,2},{3,5},{4},{6},{7,8}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => {{1,2},{3,5},{4},{6},{7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => {{1,2},{3,4},{5,8},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [2,1,4,3,8,6,5,7] => {{1,2},{3,4},{5,7,8},{6}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,6,3,7,8,5] => [2,1,6,4,8,3,7,5] => {{1,2},{3,6},{4},{5,8},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,7,3,8,5] => [2,1,7,4,8,6,3,5] => {{1,2},{3,7},{4},{5,8},{6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,8,7] => [2,1,6,4,3,5,8,7] => {{1,2},{3,5,6},{4},{7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [2,1,8,4,3,6,5,7] => {{1,2},{3,5,7,8},{4},{6}}
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,6,3,5,7,8] => [2,1,6,4,3,5,7,8] => {{1,2},{3,5,6},{4},{7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => {{1,2},{3,4},{5},{6,8},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,7,8,5,6] => {{1,2},{3,4},{5,7},{6,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,5,7,6] => {{1,2},{3,4},{5,6,8},{7}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,7,3,5,8,6] => [2,1,7,4,3,8,5,6] => {{1,2},{3,5,7},{4},{6,8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,4,7,3,8,5,6] => [2,1,7,4,8,5,3,6] => {{1,2},{3,7},{4},{5,6,8}}
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,4,7,8,3,5,6] => [2,1,8,4,3,5,7,6] => {{1,2},{3,5,6,8},{4},{7}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => {{1,2},{3,4},{5},{6},{7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => {{1,2},{3,4},{5},{6},{7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,3] => [4,2,8,1,5,6,7,3] => {{1,4},{2},{3,8},{5},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,5,6,7,3,8] => [4,2,7,1,5,6,3,8] => {{1,4},{2},{3,7},{5},{6},{8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,6,3,8,7] => [4,2,6,1,5,3,8,7] => {{1,4},{2},{3,6},{5},{7,8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,5,6,8,3,7] => [4,2,8,1,5,6,3,7] => {{1,4},{2},{3,7,8},{5},{6}}
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => [4,2,6,1,5,3,7,8] => {{1,4},{2},{3,6},{5},{7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,5,3,7,8,6] => [4,2,5,1,3,8,7,6] => {{1,4},{2},{3,5},{6,8},{7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [4,2,5,1,3,7,6,8] => {{1,4},{2},{3,5},{6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,4,1,5,7,3,8,6] => [4,2,7,1,5,8,3,6] => {{1,4},{2},{3,7},{5},{6,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,5,7,8,3,6] => [4,2,8,1,5,3,7,6] => {{1,4},{2},{3,6,8},{5},{7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => [4,2,5,1,3,6,8,7] => {{1,4},{2},{3,5},{6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [4,2,5,1,3,8,6,7] => {{1,4},{2},{3,5},{6,7,8}}
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,4,1,5,8,3,6,7] => [4,2,8,1,5,3,6,7] => {{1,4},{2},{3,6,7,8},{5}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,3,6,7,8] => [4,2,5,1,3,6,7,8] => {{1,4},{2},{3,5},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,4,5,1,6,7,8,3] => [5,2,8,4,1,6,7,3] => {{1,5},{2},{3,8},{4},{6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,4,5,1,6,7,3,8] => [5,2,7,4,1,6,3,8] => {{1,5},{2},{3,7},{4},{6},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,4,5,1,6,3,8,7] => [5,2,6,4,1,3,8,7] => {{1,5},{2},{3,6},{4},{7,8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,4,5,1,6,8,3,7] => [5,2,8,4,1,6,3,7] => {{1,5},{2},{3,7,8},{4},{6}}
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,4,5,1,6,3,7,8] => [5,2,6,4,1,3,7,8] => {{1,5},{2},{3,6},{4},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => [6,2,8,4,5,1,7,3] => {{1,6},{2},{3,8},{4},{5},{7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,6,1,7,3,8] => [6,2,7,4,5,1,3,8] => {{1,6},{2},{3,7},{4},{5},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => [7,2,8,4,5,6,1,3] => {{1,7},{2},{3,8},{4},{5},{6}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,1,3] => [8,2,1,4,5,6,7,3] => {{1,3,8},{2},{4},{5},{6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,1,3,8] => [7,2,1,4,5,6,3,8] => {{1,3,7},{2},{4},{5},{6},{8}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,6,1,8,3,7] => [6,2,8,4,5,1,3,7] => {{1,6},{2},{3,7,8},{4},{5}}
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [6,2,1,4,5,3,7,8] => {{1,3,6},{2},{4},{5},{7},{8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,4,5,1,7,3,8,6] => [5,2,7,4,1,8,3,6] => {{1,5},{2},{3,7},{4},{6,8}}
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6,8] => [5,2,7,4,1,3,6,8] => {{1,5},{2},{3,6,7},{4},{8}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,7,1,3,8,6] => [7,2,1,4,5,8,3,6] => {{1,3,7},{2},{4},{5},{6,8}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,7,1,8,3,6] => [7,2,8,4,5,3,1,6] => {{1,7},{2},{3,6,8},{4},{5}}
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [5,2,8,4,1,3,6,7] => {{1,5},{2},{3,6,7,8},{4}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [5,2,1,4,3,6,7,8] => {{1,3,5},{2},{4},{6},{7},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => [4,2,1,3,6,5,8,7] => {{1,3,4},{2},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,8,5,7] => [4,2,1,3,8,6,5,7] => {{1,3,4},{2},{5,7,8},{6}}
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,6,5,7,8] => [4,2,1,3,6,5,7,8] => {{1,3,4},{2},{5,6},{7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [4,2,6,1,8,3,7,5] => {{1,4},{2},{3,6},{5,8},{7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [4,2,6,1,7,3,5,8] => {{1,4},{2},{3,6},{5,7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => [4,2,7,1,8,6,3,5] => {{1,4},{2},{3,7},{5,8},{6}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [4,2,6,1,8,3,5,7] => {{1,4},{2},{3,6},{5,7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => [4,2,8,1,3,6,5,7] => {{1,4},{2},{3,5,7,8},{6}}
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,6,3,5,7,8] => [4,2,6,1,3,5,7,8] => {{1,4},{2},{3,5,6},{7},{8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [6,2,7,4,8,1,3,5] => {{1,6},{2},{3,7},{4},{5,8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,6,1,7,8,3,5] => [6,2,8,4,3,1,7,5] => {{1,6},{2},{3,5,8},{4},{7}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,6,7,1,8,3,5] => [7,2,8,4,3,6,1,5] => {{1,7},{2},{3,5,8},{4},{6}}
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [7,2,1,4,3,6,5,8] => {{1,3,5,7},{2},{4},{6},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [6,2,1,4,3,5,8,7] => {{1,3,5,6},{2},{4},{7,8}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [6,2,8,4,3,1,5,7] => {{1,6},{2},{3,5,7,8},{4}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [8,2,1,4,3,6,5,7] => {{1,3,5,7,8},{2},{4},{6}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,6,1,3,5,7,8] => [6,2,1,4,3,5,7,8] => {{1,3,5,6},{2},{4},{7},{8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,3,5,7,8,6] => [4,2,1,3,5,8,7,6] => {{1,3,4},{2},{5},{6,8},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => [4,2,1,3,7,8,5,6] => {{1,3,4},{2},{5,7},{6,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,3,7,8,5,6] => [4,2,1,3,8,5,7,6] => {{1,3,4},{2},{5,6,8},{7}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,5,8,6] => [4,2,7,1,3,8,5,6] => {{1,4},{2},{3,5,7},{6,8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,7,3,8,5,6] => [4,2,7,1,8,5,3,6] => {{1,4},{2},{3,7},{5,6,8}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,7,8,3,5,6] => [4,2,8,1,3,5,7,6] => {{1,4},{2},{3,5,6,8},{7}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => [7,2,8,4,3,5,1,6] => {{1,7},{2},{3,5,6,8},{4}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [8,2,1,4,3,5,7,6] => {{1,3,5,6,8},{2},{4},{7}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6,8] => [7,2,1,4,3,5,6,8] => {{1,3,5,6,7},{2},{4},{8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,3,5,8,6,7] => [4,2,1,3,5,8,6,7] => {{1,3,4},{2},{5},{6,7,8}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => [4,2,1,3,8,5,6,7] => {{1,3,4},{2},{5,6,7,8}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,8,3,5,6,7] => [4,2,8,1,3,5,6,7] => {{1,4},{2},{3,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8] => [4,2,1,3,5,6,7,8] => {{1,3,4},{2},{5},{6},{7},{8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => {{1,2},{3},{4,8},{5},{6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,6,4,8,7] => [2,1,3,6,5,4,8,7] => {{1,2},{3},{4,6},{5},{7,8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => {{1,2},{3},{4,5},{6,8},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,1,3,5,7,4,8,6] => [2,1,3,7,5,8,4,6] => {{1,2},{3},{4,7},{5},{6,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,1,3,5,7,8,4,6] => [2,1,3,8,5,4,7,6] => {{1,2},{3},{4,6,8},{5},{7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => {{1,2},{3},{4,5},{6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,1,3,5,8,4,6,7] => [2,1,3,8,5,4,6,7] => {{1,2},{3},{4,6,7,8},{5}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => {{1,2},{3},{4,5},{6},{7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [2,1,5,8,3,6,7,4] => {{1,2},{3,5},{4,8},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [2,1,5,6,3,4,8,7] => {{1,2},{3,5},{4,6},{7,8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,1,5,3,6,8,4,7] => [2,1,5,8,3,6,4,7] => {{1,2},{3,5},{4,7,8},{6}}
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,1,5,3,6,4,7,8] => [2,1,5,6,3,4,7,8] => {{1,2},{3,5},{4,6},{7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,5,6,3,7,8,4] => [2,1,6,8,5,3,7,4] => {{1,2},{3,6},{4,8},{5},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,5,6,7,3,8,4] => [2,1,7,8,5,6,3,4] => {{1,2},{3,7},{4,8},{5},{6}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => [2,1,8,3,5,6,7,4] => {{1,2},{3,4,8},{5},{6},{7}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,1,6,3,5,4,8,7] => {{1,2},{3,4,6},{5},{7,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [2,1,5,7,3,8,4,6] => {{1,2},{3,5},{4,7},{6,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6,8] => [2,1,5,7,3,4,6,8] => {{1,2},{3,5},{4,6,7},{8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,5,7,3,4,8,6] => [2,1,7,3,5,8,4,6] => {{1,2},{3,4,7},{5},{6,8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [2,1,7,8,5,4,3,6] => {{1,2},{3,7},{4,6,8},{5}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => [2,1,8,3,5,4,7,6] => {{1,2},{3,4,6,8},{5},{7}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,5,3,4,6,8,7] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,1,5,3,8,4,6,7] => [2,1,5,8,3,4,6,7] => {{1,2},{3,5},{4,6,7,8}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,5,3,4,6,7,8] => [2,1,5,3,4,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,4] => [5,2,1,8,3,6,7,4] => {{1,3,5},{2},{4,8},{6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,1,3,6,4,8,7] => [5,2,1,6,3,4,8,7] => {{1,3,5},{2},{4,6},{7,8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,1,3,6,8,4,7] => [5,2,1,8,3,6,4,7] => {{1,3,5},{2},{4,7,8},{6}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,1,3,6,4,7,8] => [5,2,1,6,3,4,7,8] => {{1,3,5},{2},{4,6},{7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,5,1,6,3,7,8,4] => [5,2,6,8,1,3,7,4] => {{1,5},{2},{3,6},{4,8},{7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,1,6,3,7,4,8] => [5,2,6,7,1,3,4,8] => {{1,5},{2},{3,6},{4,7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => [5,2,7,8,1,6,3,4] => {{1,5},{2},{3,7},{4,8},{6}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,1,6,7,8,3,4] => [5,2,8,3,1,6,7,4] => {{1,5},{2},{3,4,8},{6},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,1,6,7,3,4,8] => [5,2,7,3,1,6,4,8] => {{1,5},{2},{3,4,7},{6},{8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,1,6,3,8,4,7] => [5,2,6,8,1,3,4,7] => {{1,5},{2},{3,6},{4,7,8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,5,6,1,3,7,8,4] => [6,2,1,8,5,3,7,4] => {{1,3,6},{2},{4,8},{5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,5,6,1,7,3,8,4] => [6,2,7,8,5,1,3,4] => {{1,6},{2},{3,7},{4,8},{5}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,5,6,1,7,8,3,4] => [6,2,8,3,5,1,7,4] => {{1,6},{2},{3,4,8},{5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,5,6,1,7,3,4,8] => [6,2,7,3,5,1,4,8] => {{1,6},{2},{3,4,7},{5},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,5,6,7,1,8,3,4] => [7,2,8,3,5,6,1,4] => {{1,7},{2},{3,4,8},{5},{6}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => [8,2,1,3,5,6,7,4] => {{1,3,4,8},{2},{5},{6},{7}}
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,5,6,1,8,3,4,7] => [6,2,8,3,5,1,4,7] => {{1,6},{2},{3,4,7,8},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,7,8,6] => [5,2,1,3,4,8,7,6] => {{1,3,4,5},{2},{6,8},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,7,4,8,6] => [5,2,1,7,3,8,4,6] => {{1,3,5},{2},{4,7},{6,8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,7,8,4,6] => [5,2,1,8,3,4,7,6] => {{1,3,5},{2},{4,6,8},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6,8] => [5,2,1,7,3,4,6,8] => {{1,3,5},{2},{4,6,7},{8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => [5,2,7,3,1,8,4,6] => {{1,5},{2},{3,4,7},{6,8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,5,1,7,3,8,4,6] => [5,2,7,8,1,4,3,6] => {{1,5},{2},{3,7},{4,6,8}}
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,5,1,7,8,3,4,6] => [5,2,8,3,1,4,7,6] => {{1,5},{2},{3,4,6,8},{7}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,5,7,1,3,4,8,6] => [7,2,1,3,5,8,4,6] => {{1,3,4,7},{2},{5},{6,8}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,5,1,3,8,4,6,7] => [5,2,1,8,3,4,6,7] => {{1,3,5},{2},{4,6,7,8}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,5,1,8,3,4,6,7] => [5,2,8,3,1,4,6,7] => {{1,5},{2},{3,4,6,7,8}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,4,6,7,8] => [5,2,1,3,4,6,7,8] => {{1,3,4,5},{2},{6},{7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => {{1,2},{3},{4},{5,8},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => {{1,2},{3},{4},{5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,1,3,4,6,8,5,7] => [2,1,3,4,8,6,5,7] => {{1,2},{3},{4},{5,7,8},{6}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => {{1,2},{3},{4},{5,6},{7},{8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,6,7,4,8,5] => [2,1,3,7,8,6,4,5] => {{1,2},{3},{4,7},{5,8},{6}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,6,7,8,4,5] => [2,1,3,8,4,6,7,5] => {{1,2},{3},{4,5,8},{6},{7}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,6,4,5,8,7] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,1,3,6,4,5,7,8] => [2,1,3,6,4,5,7,8] => {{1,2},{3},{4,5,6},{7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [2,1,6,3,8,4,7,5] => {{1,2},{3,4,6},{5,8},{7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,1,6,3,4,7,5,8] => [2,1,6,3,7,4,5,8] => {{1,2},{3,4,6},{5,7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [2,1,6,7,8,3,4,5] => {{1,2},{3,6},{4,7},{5,8}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,6,7,3,4,8,5] => [2,1,7,3,8,6,4,5] => {{1,2},{3,4,7},{5,8},{6}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [2,1,8,3,4,6,7,5] => {{1,2},{3,4,5,8},{6},{7}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => [2,1,6,3,8,4,5,7] => {{1,2},{3,4,6},{5,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,1,6,3,8,4,5,7] => [2,1,6,8,4,3,5,7] => {{1,2},{3,6},{4,5,7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,1,3,7,8,4,5] => [6,2,1,8,4,3,7,5] => {{1,3,6},{2},{4,5,8},{7}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,6,1,7,3,4,8,5] => [6,2,7,3,8,1,4,5] => {{1,6},{2},{3,4,7},{5,8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,6,1,7,3,8,4,5] => [6,2,7,8,4,1,3,5] => {{1,6},{2},{3,7},{4,5,8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => [7,2,1,3,8,6,4,5] => {{1,3,4,7},{2},{5,8},{6}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,6,7,1,8,3,4,5] => [7,2,8,3,4,6,1,5] => {{1,7},{2},{3,4,5,8},{6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,8,5,7] => [6,2,1,3,8,4,5,7] => {{1,3,4,6},{2},{5,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,6,1,8,3,4,5,7] => [6,2,8,3,4,1,5,7] => {{1,6},{2},{3,4,5,7,8}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [8,2,1,3,4,6,5,7] => {{1,3,4,5,7,8},{2},{6}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => {{1,2},{3},{4},{5},{6,8},{7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => {{1,2},{3},{4},{5},{6,7},{8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,4,7,5,8,6] => [2,1,3,4,7,8,5,6] => {{1,2},{3},{4},{5,7},{6,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,1,3,4,7,8,5,6] => [2,1,3,4,8,5,7,6] => {{1,2},{3},{4},{5,6,8},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => [2,1,3,4,7,5,6,8] => {{1,2},{3},{4},{5,6,7},{8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,7,4,5,8,6] => [2,1,3,7,4,8,5,6] => {{1,2},{3},{4,5,7},{6,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,3,7,8,4,5,6] => [2,1,3,8,4,5,7,6] => {{1,2},{3},{4,5,6,8},{7}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,7,3,4,5,8,6] => [2,1,7,3,4,8,5,6] => {{1,2},{3,4,5,7},{6,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,1,7,3,4,8,5,6] => [2,1,7,3,8,5,4,6] => {{1,2},{3,4,7},{5,6,8}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,7,1,3,4,5,8,6] => [7,2,1,3,4,8,5,6] => {{1,3,4,5,7},{2},{6,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,1,3,4,8,5,6] => [7,2,1,3,8,5,4,6] => {{1,3,4,7},{2},{5,6,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,7,1,3,8,4,5,6] => [7,2,1,8,4,5,3,6] => {{1,3,7},{2},{4,5,6,8}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => [7,2,8,3,4,5,1,6] => {{1,7},{2},{3,4,5,6,8}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [8,2,1,3,4,5,7,6] => {{1,3,4,5,6,8},{2},{7}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => [7,2,1,3,4,5,6,8] => {{1,3,4,5,6,7},{2},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [2,1,3,4,5,8,6,7] => {{1,2},{3},{4},{5},{6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [2,1,3,4,8,5,6,7] => {{1,2},{3},{4},{5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [2,1,3,8,4,5,6,7] => {{1,2},{3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [8,2,1,3,4,5,6,7] => {{1,3,4,5,6,7,8},{2}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => {{1},{2,8},{3},{4},{5},{6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => {{1},{2,7},{3},{4},{5},{6},{8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,8,2,7] => [1,8,3,4,5,6,2,7] => {{1},{2,7,8},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => {{1},{2,6},{3},{4},{5},{7},{8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => {{1},{2,5},{3},{4},{6,8},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,5,7,2,8,6] => [1,7,3,4,5,8,2,6] => {{1},{2,7},{3},{4},{5},{6,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => [1,8,3,4,5,2,7,6] => {{1},{2,6,8},{3},{4},{5},{7}}
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,5,8,2,6,7] => [1,8,3,4,5,2,6,7] => {{1},{2,6,7,8},{3},{4},{5}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => {{1},{2,5},{3},{4},{6},{7},{8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,5] => [1,4,3,2,8,6,7,5] => {{1},{2,4},{3},{5,8},{6},{7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => {{1},{2,4},{3},{5,7},{6},{8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,6,2,7,8,5] => [1,6,3,4,8,2,7,5] => {{1},{2,6},{3},{4},{5,8},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => [1,7,3,4,8,6,2,5] => {{1},{2,7},{3},{4},{5,8},{6}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,6,7,8,2,5] => [1,8,3,4,2,6,7,5] => {{1},{2,5,8},{3},{4},{6},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,7,2,5,8] => [1,7,3,4,2,6,5,8] => {{1},{2,5,7},{3},{4},{6},{8}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,8,7] => [1,6,3,4,2,5,8,7] => {{1},{2,5,6},{3},{4},{7,8}}
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => [1,6,3,4,2,5,7,8] => {{1},{2,5,6},{3},{4},{7},{8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => {{1},{2,4},{3},{5},{6,8},{7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => {{1},{2,4},{3},{5},{6,7},{8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,2,7,5,8,6] => [1,4,3,2,7,8,5,6] => {{1},{2,4},{3},{5,7},{6,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,4,7,2,5,8,6] => [1,7,3,4,2,8,5,6] => {{1},{2,5,7},{3},{4},{6,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,4,7,2,8,5,6] => [1,7,3,4,8,5,2,6] => {{1},{2,7},{3},{4},{5,6,8}}
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [1,7,3,4,2,5,6,8] => {{1},{2,5,6,7},{3},{4},{8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => {{1},{2,4},{3},{5},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,3,4,2,5,8,6,7] => [1,4,3,2,5,8,6,7] => {{1},{2,4},{3},{5},{6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,4,3,2,8,5,6,7] => {{1},{2,4},{3},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,8,3,4,2,5,6,7] => {{1},{2,5,6,7,8},{3},{4}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => {{1},{2,4},{3},{5},{6},{7},{8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => {{1},{2,3},{4,6},{5},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,5,6,8,4,7] => [1,3,2,8,5,6,4,7] => {{1},{2,3},{4,7,8},{5},{6}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => {{1},{2,3},{4,6},{5},{7},{8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => {{1},{2,3},{4,5},{6,8},{7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,7,4,8,6] => [1,3,2,7,5,8,4,6] => {{1},{2,3},{4,7},{5},{6,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,7,8,4,6] => [1,3,2,8,5,4,7,6] => {{1},{2,3},{4,6,8},{5},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6,8] => [1,3,2,7,5,4,6,8] => {{1},{2,3},{4,6,7},{5},{8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [1,3,2,8,5,4,6,7] => {{1},{2,3},{4,6,7,8},{5}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,5,2,6,7,8,4] => [1,5,3,8,2,6,7,4] => {{1},{2,5},{3},{4,8},{6},{7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,5,2,6,7,4,8] => [1,5,3,7,2,6,4,8] => {{1},{2,5},{3},{4,7},{6},{8}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,5,2,6,8,4,7] => [1,5,3,8,2,6,4,7] => {{1},{2,5},{3},{4,7,8},{6}}
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,5,2,6,4,7,8] => [1,5,3,6,2,4,7,8] => {{1},{2,5},{3},{4,6},{7},{8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,5,6,2,7,8,4] => [1,6,3,8,5,2,7,4] => {{1},{2,6},{3},{4,8},{5},{7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => [1,6,3,7,5,2,4,8] => {{1},{2,6},{3},{4,7},{5},{8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,5,6,7,2,8,4] => [1,7,3,8,5,6,2,4] => {{1},{2,7},{3},{4,8},{5},{6}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => [1,8,3,2,5,6,7,4] => {{1},{2,4,8},{3},{5},{6},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,6,7,2,4,8] => [1,7,3,2,5,6,4,8] => {{1},{2,4,7},{3},{5},{6},{8}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,5,6,2,8,4,7] => [1,6,3,8,5,2,4,7] => {{1},{2,6},{3},{4,7,8},{5}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,6,8,2,4,7] => [1,8,3,2,5,6,4,7] => {{1},{2,4,7,8},{3},{5},{6}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [1,6,3,2,5,4,7,8] => {{1},{2,4,6},{3},{5},{7},{8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,7,8,6] => [1,5,3,2,4,8,7,6] => {{1},{2,4,5},{3},{6,8},{7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6,8] => [1,5,3,2,4,7,6,8] => {{1},{2,4,5},{3},{6,7},{8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,7,4,8,6] => [1,5,3,7,2,8,4,6] => {{1},{2,5},{3},{4,7},{6,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,7,8,4,6] => [1,5,3,8,2,4,7,6] => {{1},{2,5},{3},{4,6,8},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6,8] => [1,5,3,7,2,4,6,8] => {{1},{2,5},{3},{4,6,7},{8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,7,2,8,4,6] => [1,7,3,8,5,4,2,6] => {{1},{2,7},{3},{4,6,8},{5}}
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => [1,8,3,2,5,4,7,6] => {{1},{2,4,6,8},{3},{5},{7}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [1,7,3,2,5,4,6,8] => {{1},{2,4,6,7},{3},{5},{8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,5,2,4,6,8,7] => [1,5,3,2,4,6,8,7] => {{1},{2,4,5},{3},{6},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,5,2,4,8,6,7] => [1,5,3,2,4,8,6,7] => {{1},{2,4,5},{3},{6,7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [1,5,3,8,2,4,6,7] => {{1},{2,5},{3},{4,6,7,8}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,8,3,2,5,4,6,7] => {{1},{2,4,6,7,8},{3},{5}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,2,4,6,7,8] => [1,5,3,2,4,6,7,8] => {{1},{2,4,5},{3},{6},{7},{8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,6,7,5] => {{1},{2,3},{4},{5,8},{6},{7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => {{1},{2,3},{4},{5,7},{6},{8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,4,6,8,5,7] => [1,3,2,4,8,6,5,7] => {{1},{2,3},{4},{5,7,8},{6}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => {{1},{2,3},{4},{5,6},{7},{8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,2,6,4,7,8,5] => [1,3,2,6,8,4,7,5] => {{1},{2,3},{4,6},{5,8},{7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [1,3,2,6,7,4,5,8] => {{1},{2,3},{4,6},{5,7},{8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,7,8,4,5] => [1,3,2,8,4,6,7,5] => {{1},{2,3},{4,5,8},{6},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,2,6,7,4,5,8] => [1,3,2,7,4,6,5,8] => {{1},{2,3},{4,5,7},{6},{8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [1,3,2,6,8,4,5,7] => {{1},{2,3},{4,6},{5,7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,6,8,4,5,7] => [1,3,2,8,4,6,5,7] => {{1},{2,3},{4,5,7,8},{6}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,6,2,4,7,8,5] => [1,6,3,2,8,4,7,5] => {{1},{2,4,6},{3},{5,8},{7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,2,4,7,5,8] => [1,6,3,2,7,4,5,8] => {{1},{2,4,6},{3},{5,7},{8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,2,7,4,8,5] => [1,6,3,7,8,2,4,5] => {{1},{2,6},{3},{4,7},{5,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => [1,6,3,8,4,2,7,5] => {{1},{2,6},{3},{4,5,8},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,7,4,5,8] => [1,6,3,7,4,2,5,8] => {{1},{2,6},{3},{4,5,7},{8}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,6,7,2,4,8,5] => [1,7,3,2,8,6,4,5] => {{1},{2,4,7},{3},{5,8},{6}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,6,7,2,8,4,5] => [1,7,3,8,4,6,2,5] => {{1},{2,7},{3},{4,5,8},{6}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,5,8] => [1,7,3,2,4,6,5,8] => {{1},{2,4,5,7},{3},{6},{8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,6,2,4,8,5,7] => [1,6,3,2,8,4,5,7] => {{1},{2,4,6},{3},{5,7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,6,2,8,4,5,7] => [1,6,3,8,4,2,5,7] => {{1},{2,6},{3},{4,5,7,8}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,6,2,4,5,7,8] => [1,6,3,2,4,5,7,8] => {{1},{2,4,5,6},{3},{7},{8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => {{1},{2,3},{4},{5},{6,8},{7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,3,2,4,7,5,8,6] => [1,3,2,4,7,8,5,6] => {{1},{2,3},{4},{5,7},{6,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,3,2,4,8,5,7,6] => {{1},{2,3},{4},{5,6,8},{7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,3,2,7,4,5,8,6] => [1,3,2,7,4,8,5,6] => {{1},{2,3},{4,5,7},{6,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,3,2,7,8,5,4,6] => {{1},{2,3},{4,7},{5,6,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,3,2,7,8,4,5,6] => [1,3,2,8,4,5,7,6] => {{1},{2,3},{4,5,6,8},{7}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,2,4,5,8,6] => [1,7,3,2,4,8,5,6] => {{1},{2,4,5,7},{3},{6,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,7,2,4,8,5,6] => [1,7,3,2,8,5,4,6] => {{1},{2,4,7},{3},{5,6,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,7,3,8,4,5,2,6] => {{1},{2,7},{3},{4,5,6,8}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [1,8,3,2,4,5,7,6] => {{1},{2,4,5,6,8},{3},{7}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6,8] => [1,7,3,2,4,5,6,8] => {{1},{2,4,5,6,7},{3},{8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => {{1},{2,3},{4},{5},{6},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,6,7] => {{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [1,3,2,4,8,5,6,7] => {{1},{2,3},{4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [1,8,3,2,4,5,6,7] => {{1},{2,4,5,6,7,8},{3}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [3,8,1,4,5,6,7,2] => {{1,3},{2,8},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => [3,7,1,4,5,6,2,8] => {{1,3},{2,7},{4},{5},{6},{8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,5,6,2,8,7] => [3,6,1,4,5,2,8,7] => {{1,3},{2,6},{4},{5},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,8,2,7] => [3,8,1,4,5,6,2,7] => {{1,3},{2,7,8},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,4,5,6,2,7,8] => [3,6,1,4,5,2,7,8] => {{1,3},{2,6},{4},{5},{7},{8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,5,2,7,8,6] => [3,5,1,4,2,8,7,6] => {{1,3},{2,5},{4},{6,8},{7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6,8] => [3,5,1,4,2,7,6,8] => {{1,3},{2,5},{4},{6,7},{8}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6,8] => [3,7,1,4,5,2,6,8] => {{1,3},{2,6,7},{4},{5},{8}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => [3,5,1,4,2,6,7,8] => {{1,3},{2,5},{4},{6},{7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [3,4,1,2,8,6,7,5] => {{1,3},{2,4},{5,8},{6},{7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,4,2,6,7,5,8] => [3,4,1,2,7,6,5,8] => {{1,3},{2,4},{5,7},{6},{8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [3,4,1,2,6,5,8,7] => {{1,3},{2,4},{5,6},{7,8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [3,4,1,2,8,6,5,7] => {{1,3},{2,4},{5,7,8},{6}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,1,4,2,6,5,7,8] => [3,4,1,2,6,5,7,8] => {{1,3},{2,4},{5,6},{7},{8}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,1,4,6,2,7,5,8] => [3,6,1,4,7,2,5,8] => {{1,3},{2,6},{4},{5,7},{8}}
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,1,4,6,7,2,5,8] => [3,7,1,4,2,6,5,8] => {{1,3},{2,5,7},{4},{6},{8}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,8,7] => [3,6,1,4,2,5,8,7] => {{1,3},{2,5,6},{4},{7,8}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => [3,8,1,4,2,6,5,7] => {{1,3},{2,5,7,8},{4},{6}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => [3,4,1,2,5,8,7,6] => {{1,3},{2,4},{5},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,2,5,7,6,8] => [3,4,1,2,5,7,6,8] => {{1,3},{2,4},{5},{6,7},{8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [3,4,1,2,7,8,5,6] => {{1,3},{2,4},{5,7},{6,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,4,2,7,8,5,6] => [3,4,1,2,8,5,7,6] => {{1,3},{2,4},{5,6,8},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,4,2,7,5,6,8] => [3,4,1,2,7,5,6,8] => {{1,3},{2,4},{5,6,7},{8}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,7,2,5,8,6] => [3,7,1,4,2,8,5,6] => {{1,3},{2,5,7},{4},{6,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,2,5,6,8,7] => [3,4,1,2,5,6,8,7] => {{1,3},{2,4},{5},{6},{7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,2,5,8,6,7] => [3,4,1,2,5,8,6,7] => {{1,3},{2,4},{5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [3,4,1,2,8,5,6,7] => {{1,3},{2,4},{5,6,7,8}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => {{1,3},{2,4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [4,8,3,1,5,6,7,2] => {{1,4},{2,8},{3},{5},{6},{7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,5,6,7,2,8] => [4,7,3,1,5,6,2,8] => {{1,4},{2,7},{3},{5},{6},{8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,4,1,5,6,2,8,7] => [4,6,3,1,5,2,8,7] => {{1,4},{2,6},{3},{5},{7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,4,1,5,6,2,7,8] => [4,6,3,1,5,2,7,8] => {{1,4},{2,6},{3},{5},{7},{8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,4,1,5,2,7,8,6] => [4,5,3,1,2,8,7,6] => {{1,4},{2,5},{3},{6,8},{7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,7,8,2,6] => [4,8,3,1,5,2,7,6] => {{1,4},{2,6,8},{3},{5},{7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,4,1,5,2,6,8,7] => [4,5,3,1,2,6,8,7] => {{1,4},{2,5},{3},{6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,2,8,6,7] => [4,5,3,1,2,8,6,7] => {{1,4},{2,5},{3},{6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [5,8,3,4,1,6,7,2] => {{1,5},{2,8},{3},{4},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,5,1,6,7,2,8] => [5,7,3,4,1,6,2,8] => {{1,5},{2,7},{3},{4},{6},{8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,1,6,2,8,7] => [5,6,3,4,1,2,8,7] => {{1,5},{2,6},{3},{4},{7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,5,1,6,8,2,7] => [5,8,3,4,1,6,2,7] => {{1,5},{2,7,8},{3},{4},{6}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,1,6,2,7,8] => [5,6,3,4,1,2,7,8] => {{1,5},{2,6},{3},{4},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => [6,8,3,4,5,1,7,2] => {{1,6},{2,8},{3},{4},{5},{7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => [6,7,3,4,5,1,2,8] => {{1,6},{2,7},{3},{4},{5},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [7,8,3,4,5,6,1,2] => {{1,7},{2,8},{3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => [8,1,3,4,5,6,7,2] => {{1,2,8},{3},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => [7,1,3,4,5,6,2,8] => {{1,2,7},{3},{4},{5},{6},{8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [6,1,3,4,5,2,7,8] => {{1,2,6},{3},{4},{5},{7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6,8] => [5,1,3,4,2,7,6,8] => {{1,2,5},{3},{4},{6,7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,5,1,7,2,8,6] => [5,7,3,4,1,8,2,6] => {{1,5},{2,7},{3},{4},{6,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => [7,1,3,4,5,8,2,6] => {{1,2,7},{3},{4},{5},{6,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,5,7,1,8,2,6] => [7,8,3,4,5,2,1,6] => {{1,7},{2,6,8},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,5,1,2,6,8,7] => [5,1,3,4,2,6,8,7] => {{1,2,5},{3},{4},{6},{7,8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,5,1,2,8,6,7] => [5,1,3,4,2,8,6,7] => {{1,2,5},{3},{4},{6,7,8}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,5,1,8,2,6,7] => [5,8,3,4,1,2,6,7] => {{1,5},{2,6,7,8},{3},{4}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [8,1,3,4,5,2,6,7] => {{1,2,6,7,8},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [5,1,3,4,2,6,7,8] => {{1,2,5},{3},{4},{6},{7},{8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,5] => [4,1,3,2,8,6,7,5] => {{1,2,4},{3},{5,8},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => {{1,2,4},{3},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,8,5,7] => [4,1,3,2,8,6,5,7] => {{1,2,4},{3},{5,7,8},{6}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,4,1,6,2,7,8,5] => [4,6,3,1,8,2,7,5] => {{1,4},{2,6},{3},{5,8},{7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,6,2,7,5,8] => [4,6,3,1,7,2,5,8] => {{1,4},{2,6},{3},{5,7},{8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => [4,7,3,1,8,6,2,5] => {{1,4},{2,7},{3},{5,8},{6}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,6,7,8,2,5] => [4,8,3,1,2,6,7,5] => {{1,4},{2,5,8},{3},{6},{7}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,8,2,5,7] => [4,8,3,1,2,6,5,7] => {{1,4},{2,5,7,8},{3},{6}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,4,1,6,2,5,7,8] => [4,6,3,1,2,5,7,8] => {{1,4},{2,5,6},{3},{7},{8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,4,6,1,2,7,5,8] => [6,1,3,4,7,2,5,8] => {{1,2,6},{3},{4},{5,7},{8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [6,7,3,4,8,1,2,5] => {{1,6},{2,7},{3},{4},{5,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => [6,8,3,4,2,1,7,5] => {{1,6},{2,5,8},{3},{4},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,4,6,1,7,2,5,8] => [6,7,3,4,2,1,5,8] => {{1,6},{2,5,7},{3},{4},{8}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,4,6,7,1,8,2,5] => [7,8,3,4,2,6,1,5] => {{1,7},{2,5,8},{3},{4},{6}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,1,2,5] => [8,1,3,4,2,6,7,5] => {{1,2,5,8},{3},{4},{6},{7}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,8,7] => [6,1,3,4,2,5,8,7] => {{1,2,5,6},{3},{4},{7,8}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [8,1,3,4,2,6,5,7] => {{1,2,5,7,8},{3},{4},{6}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,6,1,2,5,7,8] => [6,1,3,4,2,5,7,8] => {{1,2,5,6},{3},{4},{7},{8}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [4,1,3,2,5,7,6,8] => {{1,2,4},{3},{5},{6,7},{8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => [4,1,3,2,7,8,5,6] => {{1,2,4},{3},{5,7},{6,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [4,1,3,2,8,5,7,6] => {{1,2,4},{3},{5,6,8},{7}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,4,1,7,2,5,8,6] => [4,7,3,1,2,8,5,6] => {{1,4},{2,5,7},{3},{6,8}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,7,2,8,5,6] => [4,7,3,1,8,5,2,6] => {{1,4},{2,7},{3},{5,6,8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,4,7,1,2,5,8,6] => [7,1,3,4,2,8,5,6] => {{1,2,5,7},{3},{4},{6,8}}
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [7,8,3,4,2,5,1,6] => {{1,7},{2,5,6,8},{3},{4}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [4,1,3,2,8,5,6,7] => {{1,2,4},{3},{5,6,7,8}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [4,1,3,2,5,6,7,8] => {{1,2,4},{3},{5},{6},{7},{8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,4] => [3,1,2,8,5,6,7,4] => {{1,2,3},{4,8},{5},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,5,6,8,4,7] => [3,1,2,8,5,6,4,7] => {{1,2,3},{4,7,8},{5},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,7,4,8,6] => [3,1,2,7,5,8,4,6] => {{1,2,3},{4,7},{5},{6,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,7,8,4,6] => [3,1,2,8,5,4,7,6] => {{1,2,3},{4,6,8},{5},{7}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6,8] => [3,1,2,7,5,4,6,8] => {{1,2,3},{4,6,7},{5},{8}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,5,4,6,8,7] => [3,1,2,5,4,6,8,7] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [3,5,1,6,2,4,8,7] => {{1,3},{2,5},{4,6},{7,8}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,5,2,6,8,4,7] => [3,5,1,8,2,6,4,7] => {{1,3},{2,5},{4,7,8},{6}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,4,7,8] => [3,5,1,6,2,4,7,8] => {{1,3},{2,5},{4,6},{7},{8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,5,6,2,7,8,4] => [3,6,1,8,5,2,7,4] => {{1,3},{2,6},{4,8},{5},{7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,5,6,2,7,4,8] => [3,6,1,7,5,2,4,8] => {{1,3},{2,6},{4,7},{5},{8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,5,6,7,2,8,4] => [3,7,1,8,5,6,2,4] => {{1,3},{2,7},{4,8},{5},{6}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,2,4] => [3,8,1,2,5,6,7,4] => {{1,3},{2,4,8},{5},{6},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,5,6,7,2,4,8] => [3,7,1,2,5,6,4,8] => {{1,3},{2,4,7},{5},{6},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => [3,6,1,8,5,2,4,7] => {{1,3},{2,6},{4,7,8},{5}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,5,6,8,2,4,7] => [3,8,1,2,5,6,4,7] => {{1,3},{2,4,7,8},{5},{6}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [3,5,1,2,4,8,7,6] => {{1,3},{2,4,5},{6,8},{7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6,8] => [3,5,1,2,4,7,6,8] => {{1,3},{2,4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [3,5,1,7,2,8,4,6] => {{1,3},{2,5},{4,7},{6,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,7,8,4,6] => [3,5,1,8,2,4,7,6] => {{1,3},{2,5},{4,6,8},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => [3,5,1,7,2,4,6,8] => {{1,3},{2,5},{4,6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,7,8,2,4,6] => [3,8,1,2,5,4,7,6] => {{1,3},{2,4,6,8},{5},{7}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6,8] => [3,7,1,2,5,4,6,8] => {{1,3},{2,4,6,7},{5},{8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,5,2,4,6,8,7] => [3,5,1,2,4,6,8,7] => {{1,3},{2,4,5},{6},{7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,5,2,4,8,6,7] => [3,5,1,2,4,8,6,7] => {{1,3},{2,4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [3,5,1,8,2,4,6,7] => {{1,3},{2,5},{4,6,7,8}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,5,2,4,6,7,8] => [3,5,1,2,4,6,7,8] => {{1,3},{2,4,5},{6},{7},{8}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [5,1,3,7,2,6,4,8] => {{1,2,5},{3},{4,7},{6},{8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7] => [5,1,3,6,2,4,8,7] => {{1,2,5},{3},{4,6},{7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,1,2,6,8,4,7] => [5,1,3,8,2,6,4,7] => {{1,2,5},{3},{4,7,8},{6}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,5,1,2,6,4,7,8] => [5,1,3,6,2,4,7,8] => {{1,2,5},{3},{4,6},{7},{8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,5,1,6,2,7,8,4] => [5,6,3,8,1,2,7,4] => {{1,5},{2,6},{3},{4,8},{7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [5,6,3,7,1,2,4,8] => {{1,5},{2,6},{3},{4,7},{8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,5,1,6,7,2,8,4] => [5,7,3,8,1,6,2,4] => {{1,5},{2,7},{3},{4,8},{6}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,5,1,6,7,8,2,4] => [5,8,3,2,1,6,7,4] => {{1,5},{2,4,8},{3},{6},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,5,1,6,7,2,4,8] => [5,7,3,2,1,6,4,8] => {{1,5},{2,4,7},{3},{6},{8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [5,6,3,2,1,4,8,7] => {{1,5},{2,4,6},{3},{7,8}}
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,5,1,6,8,2,4,7] => [5,8,3,2,1,6,4,7] => {{1,5},{2,4,7,8},{3},{6}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => [5,6,3,2,1,4,7,8] => {{1,5},{2,4,6},{3},{7},{8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => [6,1,3,8,5,2,7,4] => {{1,2,6},{3},{4,8},{5},{7}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,5,6,1,2,7,4,8] => [6,1,3,7,5,2,4,8] => {{1,2,6},{3},{4,7},{5},{8}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [6,7,3,8,5,1,2,4] => {{1,6},{2,7},{3},{4,8},{5}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,5,6,1,7,8,2,4] => [6,8,3,2,5,1,7,4] => {{1,6},{2,4,8},{3},{5},{7}}
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,5,6,1,7,2,4,8] => [6,7,3,2,5,1,4,8] => {{1,6},{2,4,7},{3},{5},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,5,6,7,1,8,2,4] => [7,8,3,2,5,6,1,4] => {{1,7},{2,4,8},{3},{5},{6}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,1,2,4] => [8,1,3,2,5,6,7,4] => {{1,2,4,8},{3},{5},{6},{7}}
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [7,1,3,2,5,6,4,8] => {{1,2,4,7},{3},{5},{6},{8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [6,1,3,2,5,4,8,7] => {{1,2,4,6},{3},{5},{7,8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,5,6,1,2,8,4,7] => [6,1,3,8,5,2,4,7] => {{1,2,6},{3},{4,7,8},{5}}
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [6,8,3,2,5,1,4,7] => {{1,6},{2,4,7,8},{3},{5}}
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [8,1,3,2,5,6,4,7] => {{1,2,4,7,8},{3},{5},{6}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [5,1,3,2,4,7,6,8] => {{1,2,4,5},{3},{6,7},{8}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,7,8,4,6] => [5,1,3,8,2,4,7,6] => {{1,2,5},{3},{4,6,8},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6,8] => [5,1,3,7,2,4,6,8] => {{1,2,5},{3},{4,6,7},{8}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [5,7,3,8,1,4,2,6] => {{1,5},{2,7},{3},{4,6,8}}
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,7,8,2,4,6] => [5,8,3,2,1,4,7,6] => {{1,5},{2,4,6,8},{3},{7}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6,8] => [5,7,3,2,1,4,6,8] => {{1,5},{2,4,6,7},{3},{8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => [7,1,3,2,5,8,4,6] => {{1,2,4,7},{3},{5},{6,8}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [8,1,3,2,5,4,7,6] => {{1,2,4,6,8},{3},{5},{7}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => [7,1,3,2,5,4,6,8] => {{1,2,4,6,7},{3},{5},{8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,5,1,2,4,6,8,7] => [5,1,3,2,4,6,8,7] => {{1,2,4,5},{3},{6},{7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,5,1,2,4,8,6,7] => [5,1,3,2,4,8,6,7] => {{1,2,4,5},{3},{6,7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,5,1,2,8,4,6,7] => [5,1,3,8,2,4,6,7] => {{1,2,5},{3},{4,6,7,8}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,5,8,1,2,4,6,7] => [8,1,3,2,5,4,6,7] => {{1,2,4,6,7,8},{3},{5}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,5,1,2,4,6,7,8] => [5,1,3,2,4,6,7,8] => {{1,2,4,5},{3},{6},{7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => [3,1,2,4,8,6,7,5] => {{1,2,3},{4},{5,8},{6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [3,1,2,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,2,4,6,8,5,7] => [3,1,2,4,8,6,5,7] => {{1,2,3},{4},{5,7,8},{6}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,2,6,4,7,8,5] => [3,1,2,6,8,4,7,5] => {{1,2,3},{4,6},{5,8},{7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [3,1,2,7,8,6,4,5] => {{1,2,3},{4,7},{5,8},{6}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,6,7,8,4,5] => [3,1,2,8,4,6,7,5] => {{1,2,3},{4,5,8},{6},{7}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,6,4,5,8,7] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [3,1,2,6,4,8,5,7] => [3,1,2,6,8,4,5,7] => {{1,2,3},{4,6},{5,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [3,6,1,7,8,2,4,5] => {{1,3},{2,6},{4,7},{5,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [3,1,6,2,7,4,5,8] => [3,6,1,7,4,2,5,8] => {{1,3},{2,6},{4,5,7},{8}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,6,7,2,8,4,5] => [3,7,1,8,4,6,2,5] => {{1,3},{2,7},{4,5,8},{6}}
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => [3,7,1,2,4,6,5,8] => {{1,3},{2,4,5,7},{6},{8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [3,6,1,2,4,5,8,7] => {{1,3},{2,4,5,6},{7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [3,1,6,2,4,8,5,7] => [3,6,1,2,8,4,5,7] => {{1,3},{2,4,6},{5,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [3,1,6,2,8,4,5,7] => [3,6,1,8,4,2,5,7] => {{1,3},{2,6},{4,5,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => [3,8,1,2,4,6,5,7] => {{1,3},{2,4,5,7,8},{6}}
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,6,2,4,5,7,8] => [3,6,1,2,4,5,7,8] => {{1,3},{2,4,5,6},{7},{8}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => [6,1,3,2,8,4,7,5] => {{1,2,4,6},{3},{5,8},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [3,6,1,2,7,8,4,5] => [6,1,3,8,4,2,7,5] => {{1,2,6},{3},{4,5,8},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [3,6,1,2,7,4,5,8] => [6,1,3,7,4,2,5,8] => {{1,2,6},{3},{4,5,7},{8}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [6,7,3,2,8,1,4,5] => {{1,6},{2,4,7},{3},{5,8}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [6,7,3,8,4,1,2,5] => {{1,6},{2,7},{3},{4,5,8}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [6,8,3,2,4,1,7,5] => {{1,6},{2,4,5,8},{3},{7}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,6,1,7,2,4,5,8] => [6,7,3,2,4,1,5,8] => {{1,6},{2,4,5,7},{3},{8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,6,7,1,2,4,8,5] => [7,1,3,2,8,6,4,5] => {{1,2,4,7},{3},{5,8},{6}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => [7,1,3,8,4,6,2,5] => {{1,2,7},{3},{4,5,8},{6}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [3,6,7,1,8,2,4,5] => [7,8,3,2,4,6,1,5] => {{1,7},{2,4,5,8},{3},{6}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [8,1,3,2,4,6,7,5] => {{1,2,4,5,8},{3},{6},{7}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,6,8,1,2,4,5,7] => [8,1,3,2,4,6,5,7] => {{1,2,4,5,7,8},{3},{6}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [3,1,2,4,5,7,6,8] => {{1,2,3},{4},{5},{6,7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => [3,1,2,4,7,8,5,6] => {{1,2,3},{4},{5,7},{6,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,2,4,7,8,5,6] => [3,1,2,4,8,5,7,6] => {{1,2,3},{4},{5,6,8},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [3,1,2,4,7,5,6,8] => {{1,2,3},{4},{5,6,7},{8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,7,4,5,8,6] => [3,1,2,7,4,8,5,6] => {{1,2,3},{4,5,7},{6,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,2,7,8,4,5,6] => [3,1,2,8,4,5,7,6] => {{1,2,3},{4,5,6,8},{7}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,2,7,4,5,6,8] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,7,2,4,5,8,6] => [3,7,1,2,4,8,5,6] => {{1,3},{2,4,5,7},{6,8}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => [3,8,1,2,4,5,7,6] => {{1,3},{2,4,5,6,8},{7}}
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6,8] => [3,7,1,2,4,5,6,8] => {{1,3},{2,4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => [7,1,3,2,4,8,5,6] => {{1,2,4,5,7},{3},{6,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [3,7,1,2,4,8,5,6] => [7,1,3,2,8,5,4,6] => {{1,2,4,7},{3},{5,6,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [3,7,1,2,8,4,5,6] => [7,1,3,8,4,5,2,6] => {{1,2,7},{3},{4,5,6,8}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [8,1,3,2,4,5,7,6] => {{1,2,4,5,6,8},{3},{7}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => [7,1,3,2,4,5,6,8] => {{1,2,4,5,6,7},{3},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [3,1,2,4,5,6,8,7] => {{1,2,3},{4},{5},{6},{7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [3,1,2,4,5,8,6,7] => {{1,2,3},{4},{5},{6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [3,1,2,4,8,5,6,7] => {{1,2,3},{4},{5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [3,8,1,2,4,5,6,7] => {{1,3},{2,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [8,1,3,2,4,5,6,7] => {{1,2,4,5,6,7,8},{3}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => {{1,2,3},{4},{5},{6},{7},{8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => {{1},{2},{3,8},{4},{5},{6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,6,8,3,7] => [1,2,8,4,5,6,3,7] => {{1},{2},{3,7,8},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,3,7,8] => [1,2,6,4,5,3,7,8] => {{1},{2},{3,6},{4},{5},{7},{8}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => {{1},{2},{3,5},{4},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => [1,2,7,4,5,8,3,6] => {{1},{2},{3,7},{4},{5},{6,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,7,8,3,6] => [1,2,8,4,5,3,7,6] => {{1},{2},{3,6,8},{4},{5},{7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,4,5,3,6,8,7] => [1,2,5,4,3,6,8,7] => {{1},{2},{3,5},{4},{6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,4,5,3,8,6,7] => [1,2,5,4,3,8,6,7] => {{1},{2},{3,5},{4},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => {{1},{2},{3,5},{4},{6},{7},{8}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,6,7,5] => {{1},{2},{3,4},{5,8},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,6,3,7,8,5] => [1,2,6,4,8,3,7,5] => {{1},{2},{3,6},{4},{5,8},{7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,6,3,7,5,8] => [1,2,6,4,7,3,5,8] => {{1},{2},{3,6},{4},{5,7},{8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,6,7,3,8,5] => [1,2,7,4,8,6,3,5] => {{1},{2},{3,7},{4},{5,8},{6}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,6,7,8,3,5] => [1,2,8,4,3,6,7,5] => {{1},{2},{3,5,8},{4},{6},{7}}
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => [1,2,8,4,3,6,5,7] => {{1},{2},{3,5,7,8},{4},{6}}
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [1,2,6,4,3,5,7,8] => {{1},{2},{3,5,6},{4},{7},{8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => {{1},{2},{3,4},{5},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => {{1},{2},{3,4},{5},{6,7},{8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => [1,2,4,3,7,8,5,6] => {{1},{2},{3,4},{5,7},{6,8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,4,3,7,8,5,6] => [1,2,4,3,8,5,7,6] => {{1},{2},{3,4},{5,6,8},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,4,7,3,8,5,6] => [1,2,7,4,8,5,3,6] => {{1},{2},{3,7},{4},{5,6,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,4,7,8,3,5,6] => [1,2,8,4,3,5,7,6] => {{1},{2},{3,5,6,8},{4},{7}}
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [1,2,7,4,3,5,6,8] => {{1},{2},{3,5,6,7},{4},{8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => {{1},{2},{3,4},{5},{6},{7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,8,6,7] => {{1},{2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,2,8,4,3,5,6,7] => {{1},{2},{3,5,6,7,8},{4}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => {{1},{2},{3,4},{5},{6},{7},{8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [1,4,8,2,5,6,7,3] => {{1},{2,4},{3,8},{5},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => [1,4,7,2,5,6,3,8] => {{1},{2,4},{3,7},{5},{6},{8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,4,2,5,6,8,3,7] => [1,4,8,2,5,6,3,7] => {{1},{2,4},{3,7,8},{5},{6}}
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,2,5,6,3,7,8] => [1,4,6,2,5,3,7,8] => {{1},{2,4},{3,6},{5},{7},{8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [1,4,5,2,3,7,6,8] => {{1},{2,4},{3,5},{6,7},{8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [1,4,7,2,5,8,3,6] => {{1},{2,4},{3,7},{5},{6,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6,8] => [1,4,7,2,5,3,6,8] => {{1},{2,4},{3,6,7},{5},{8}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,4,5,2,3,8,6,7] => {{1},{2,4},{3,5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [1,4,5,2,3,6,7,8] => {{1},{2,4},{3,5},{6},{7},{8}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [1,5,8,4,2,6,7,3] => {{1},{2,5},{3,8},{4},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,5,2,6,7,3,8] => [1,5,7,4,2,6,3,8] => {{1},{2,5},{3,7},{4},{6},{8}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,5,2,6,8,3,7] => [1,5,8,4,2,6,3,7] => {{1},{2,5},{3,7,8},{4},{6}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,5,6,4,2,3,7,8] => {{1},{2,5},{3,6},{4},{7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,4,5,6,2,7,8,3] => [1,6,8,4,5,2,7,3] => {{1},{2,6},{3,8},{4},{5},{7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,4,5,6,2,7,3,8] => [1,6,7,4,5,2,3,8] => {{1},{2,6},{3,7},{4},{5},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,2,8,3] => [1,7,8,4,5,6,2,3] => {{1},{2,7},{3,8},{4},{5},{6}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,2,3] => [1,8,2,4,5,6,7,3] => {{1},{2,3,8},{4},{5},{6},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => [1,7,2,4,5,6,3,8] => {{1},{2,3,7},{4},{5},{6},{8}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,4,5,6,2,8,3,7] => [1,6,8,4,5,2,3,7] => {{1},{2,6},{3,7,8},{4},{5}}
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [1,6,2,4,5,3,7,8] => {{1},{2,3,6},{4},{5},{7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,4,5,2,3,7,8,6] => [1,5,2,4,3,8,7,6] => {{1},{2,3,5},{4},{6,8},{7}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6,8] => [1,5,2,4,3,7,6,8] => {{1},{2,3,5},{4},{6,7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [1,5,7,4,2,8,3,6] => {{1},{2,5},{3,7},{4},{6,8}}
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6,8] => [1,5,7,4,2,3,6,8] => {{1},{2,5},{3,6,7},{4},{8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [1,7,2,4,5,8,3,6] => {{1},{2,3,7},{4},{5},{6,8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,4,5,7,2,8,3,6] => [1,7,8,4,5,3,2,6] => {{1},{2,7},{3,6,8},{4},{5}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [1,7,2,4,5,3,6,8] => {{1},{2,3,6,7},{4},{5},{8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,5,2,3,8,6,7] => [1,5,2,4,3,8,6,7] => {{1},{2,3,5},{4},{6,7,8}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [1,5,8,4,2,3,6,7] => {{1},{2,5},{3,6,7,8},{4}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,2,3,6,7,8] => [1,5,2,4,3,6,7,8] => {{1},{2,3,5},{4},{6},{7},{8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,8,5,7] => [1,4,2,3,8,6,5,7] => {{1},{2,3,4},{5,7,8},{6}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,6,5,7,8] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,6,3,7,8,5] => [1,4,6,2,8,3,7,5] => {{1},{2,4},{3,6},{5,8},{7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [1,4,6,2,7,3,5,8] => {{1},{2,4},{3,6},{5,7},{8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,6,7,3,8,5] => [1,4,7,2,8,6,3,5] => {{1},{2,4},{3,7},{5,8},{6}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,4,8,2,3,6,7,5] => {{1},{2,4},{3,5,8},{6},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,6,7,3,5,8] => [1,4,7,2,3,6,5,8] => {{1},{2,4},{3,5,7},{6},{8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,8,7] => [1,4,6,2,3,5,8,7] => {{1},{2,4},{3,5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,4,6,2,8,3,5,7] => {{1},{2,4},{3,6},{5,7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,8,3,5,7] => [1,4,8,2,3,6,5,7] => {{1},{2,4},{3,5,7,8},{6}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => [1,4,6,2,3,5,7,8] => {{1},{2,4},{3,5,6},{7},{8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,4,6,2,3,7,8,5] => [1,6,2,4,8,3,7,5] => {{1},{2,3,6},{4},{5,8},{7}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,4,6,2,3,7,5,8] => [1,6,2,4,7,3,5,8] => {{1},{2,3,6},{4},{5,7},{8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [1,6,7,4,8,2,3,5] => {{1},{2,6},{3,7},{4},{5,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => [1,6,8,4,3,2,7,5] => {{1},{2,6},{3,5,8},{4},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,7,3,5,8] => [1,6,7,4,3,2,5,8] => {{1},{2,6},{3,5,7},{4},{8}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,4,6,7,2,3,8,5] => [1,7,2,4,8,6,3,5] => {{1},{2,3,7},{4},{5,8},{6}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => [1,7,8,4,3,6,2,5] => {{1},{2,7},{3,5,8},{4},{6}}
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [1,7,2,4,3,6,5,8] => {{1},{2,3,5,7},{4},{6},{8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,8,7] => [1,6,2,4,3,5,8,7] => {{1},{2,3,5,6},{4},{7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,8,5,7] => [1,6,2,4,8,3,5,7] => {{1},{2,3,6},{4},{5,7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [1,6,8,4,3,2,5,7] => {{1},{2,6},{3,5,7,8},{4}}
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,8,2,4,3,6,5,7] => {{1},{2,3,5,7,8},{4},{6}}
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,6,2,3,5,7,8] => [1,6,2,4,3,5,7,8] => {{1},{2,3,5,6},{4},{7},{8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,4,2,3,5,7,8,6] => [1,4,2,3,5,8,7,6] => {{1},{2,3,4},{5},{6,8},{7}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [1,4,2,3,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,4,2,3,7,5,8,6] => [1,4,2,3,7,8,5,6] => {{1},{2,3,4},{5,7},{6,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,3,7,8,5,6] => [1,4,2,3,8,5,7,6] => {{1},{2,3,4},{5,6,8},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,4,2,7,3,5,8,6] => [1,4,7,2,3,8,5,6] => {{1},{2,4},{3,5,7},{6,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [1,4,7,2,8,5,3,6] => {{1},{2,4},{3,7},{5,6,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [1,4,8,2,3,5,7,6] => {{1},{2,4},{3,5,6,8},{7}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [1,4,7,2,3,5,6,8] => {{1},{2,4},{3,5,6,7},{8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,4,7,2,3,5,8,6] => [1,7,2,4,3,8,5,6] => {{1},{2,3,5,7},{4},{6,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => [1,7,8,4,3,5,2,6] => {{1},{2,7},{3,5,6,8},{4}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6,8] => [1,7,2,4,3,5,6,8] => {{1},{2,3,5,6,7},{4},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => [1,4,2,3,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [1,4,8,2,3,5,6,7] => {{1},{2,4},{3,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [1,8,2,4,3,5,6,7] => {{1},{2,3,5,6,7,8},{4}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => {{1},{2,3,4},{5},{6},{7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [4,1,8,2,5,6,7,3] => {{1,2,4},{3,8},{5},{6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [4,1,6,2,5,3,8,7] => {{1,2,4},{3,6},{5},{7,8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => [4,1,5,2,3,8,7,6] => {{1,2,4},{3,5},{6,8},{7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => [4,1,5,2,3,7,6,8] => {{1,2,4},{3,5},{6,7},{8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,5,7,3,8,6] => [4,1,7,2,5,8,3,6] => {{1,2,4},{3,7},{5},{6,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,5,7,8,3,6] => [4,1,8,2,5,3,7,6] => {{1,2,4},{3,6,8},{5},{7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,5,3,8,6,7] => [4,1,5,2,3,8,6,7] => {{1,2,4},{3,5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => [4,1,5,2,3,6,7,8] => {{1,2,4},{3,5},{6},{7},{8}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [4,5,8,1,2,6,7,3] => {{1,4},{2,5},{3,8},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,5,2,6,7,3,8] => [4,5,7,1,2,6,3,8] => {{1,4},{2,5},{3,7},{6},{8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [4,5,6,1,2,3,8,7] => {{1,4},{2,5},{3,6},{7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [4,5,8,1,2,6,3,7] => {{1,4},{2,5},{3,7,8},{6}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,1,5,2,6,3,7,8] => [4,5,6,1,2,3,7,8] => {{1,4},{2,5},{3,6},{7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,1,5,6,2,7,3,8] => [4,6,7,1,5,2,3,8] => {{1,4},{2,6},{3,7},{5},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,5,6,7,2,8,3] => [4,7,8,1,5,6,2,3] => {{1,4},{2,7},{3,8},{5},{6}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,2,3] => [4,8,2,1,5,6,7,3] => {{1,4},{2,3,8},{5},{6},{7}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,5,6,2,3,8,7] => [4,6,2,1,5,3,8,7] => {{1,4},{2,3,6},{5},{7,8}}
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => [4,8,2,1,5,6,3,7] => {{1,4},{2,3,7,8},{5},{6}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,1,5,6,2,3,7,8] => [4,6,2,1,5,3,7,8] => {{1,4},{2,3,6},{5},{7},{8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [4,5,2,1,3,8,7,6] => {{1,4},{2,3,5},{6,8},{7}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6,8] => [4,5,2,1,3,7,6,8] => {{1,4},{2,3,5},{6,7},{8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [4,5,7,1,2,8,3,6] => {{1,4},{2,5},{3,7},{6,8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [4,5,8,1,2,3,7,6] => {{1,4},{2,5},{3,6,8},{7}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,5,7,2,8,3,6] => [4,7,8,1,5,3,2,6] => {{1,4},{2,7},{3,6,8},{5}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6,8] => [4,7,2,1,5,3,6,8] => {{1,4},{2,3,6,7},{5},{8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,1,5,2,3,8,6,7] => [4,5,2,1,3,8,6,7] => {{1,4},{2,3,5},{6,7,8}}
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,5,2,8,3,6,7] => [4,5,8,1,2,3,6,7] => {{1,4},{2,5},{3,6,7,8}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,5,2,3,6,7,8] => [4,5,2,1,3,6,7,8] => {{1,4},{2,3,5},{6},{7},{8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [5,1,7,4,2,6,3,8] => {{1,2,5},{3,7},{4},{6},{8}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [5,1,6,4,2,3,8,7] => {{1,2,5},{3,6},{4},{7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,5,1,2,6,8,3,7] => [5,1,8,4,2,6,3,7] => {{1,2,5},{3,7,8},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,5,1,6,2,7,8,3] => [5,6,8,4,1,2,7,3] => {{1,5},{2,6},{3,8},{4},{7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [5,6,7,4,1,2,3,8] => {{1,5},{2,6},{3,7},{4},{8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => [5,7,8,4,1,6,2,3] => {{1,5},{2,7},{3,8},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,5,1,6,7,8,2,3] => [5,8,2,4,1,6,7,3] => {{1,5},{2,3,8},{4},{6},{7}}
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [4,5,1,6,7,2,3,8] => [5,7,2,4,1,6,3,8] => {{1,5},{2,3,7},{4},{6},{8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [4,5,1,6,2,8,3,7] => [5,6,8,4,1,2,3,7] => {{1,5},{2,6},{3,7,8},{4}}
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [4,5,1,6,8,2,3,7] => [5,8,2,4,1,6,3,7] => {{1,5},{2,3,7,8},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,1,6,2,3,7,8] => [5,6,2,4,1,3,7,8] => {{1,5},{2,3,6},{4},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,1,2,7,8,3] => [6,1,8,4,5,2,7,3] => {{1,2,6},{3,8},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,1,2,7,3,8] => [6,1,7,4,5,2,3,8] => {{1,2,6},{3,7},{4},{5},{8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => [6,7,8,4,5,1,2,3] => {{1,6},{2,7},{3,8},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,6,1,7,8,2,3] => [6,8,2,4,5,1,7,3] => {{1,6},{2,3,8},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => [7,8,2,4,5,6,1,3] => {{1,7},{2,3,8},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => [8,1,2,4,5,6,7,3] => {{1,2,3,8},{4},{5},{6},{7}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [7,1,2,4,5,6,3,8] => {{1,2,3,7},{4},{5},{6},{8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [6,1,2,4,5,3,8,7] => {{1,2,3,6},{4},{5},{7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,6,1,2,8,3,7] => [6,1,8,4,5,2,3,7] => {{1,2,6},{3,7,8},{4},{5}}
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [8,1,2,4,5,6,3,7] => {{1,2,3,7,8},{4},{5},{6}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [4,5,1,2,7,8,3,6] => [5,1,8,4,2,3,7,6] => {{1,2,5},{3,6,8},{4},{7}}
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => [5,1,7,4,2,3,6,8] => {{1,2,5},{3,6,7},{4},{8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [4,5,1,7,2,8,3,6] => [5,7,8,4,1,3,2,6] => {{1,5},{2,7},{3,6,8},{4}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [4,5,1,7,8,2,3,6] => [5,8,2,4,1,3,7,6] => {{1,5},{2,3,6,8},{4},{7}}
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6,8] => [5,7,2,4,1,3,6,8] => {{1,5},{2,3,6,7},{4},{8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [7,1,8,4,5,3,2,6] => {{1,2,7},{3,6,8},{4},{5}}
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [8,1,2,4,5,3,7,6] => {{1,2,3,6,8},{4},{5},{7}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,5,1,2,3,6,8,7] => [5,1,2,4,3,6,8,7] => {{1,2,3,5},{4},{6},{7,8}}
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => [5,1,8,4,2,3,6,7] => {{1,2,5},{3,6,7,8},{4}}
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,5,1,8,2,3,6,7] => [5,8,2,4,1,3,6,7] => {{1,5},{2,3,6,7,8},{4}}
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [8,1,2,4,5,3,6,7] => {{1,2,3,6,7,8},{4},{5}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [5,1,2,4,3,6,7,8] => {{1,2,3,5},{4},{6},{7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [4,1,2,3,8,6,7,5] => {{1,2,3,4},{5,8},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [4,1,2,3,7,6,5,8] => {{1,2,3,4},{5,7},{6},{8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,8,5,7] => [4,1,2,3,8,6,5,7] => {{1,2,3,4},{5,7,8},{6}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [4,1,2,3,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,6,3,7,8,5] => [4,1,6,2,8,3,7,5] => {{1,2,4},{3,6},{5,8},{7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5,8] => [4,1,6,2,7,3,5,8] => {{1,2,4},{3,6},{5,7},{8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,8,7] => [4,1,6,2,3,5,8,7] => {{1,2,4},{3,5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [4,1,6,2,8,3,5,7] => {{1,2,4},{3,6},{5,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,8,3,5,7] => [4,1,8,2,3,6,5,7] => {{1,2,4},{3,5,7,8},{6}}
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,6,3,5,7,8] => [4,1,6,2,3,5,7,8] => {{1,2,4},{3,5,6},{7},{8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [4,6,2,1,8,3,7,5] => {{1,4},{2,3,6},{5,8},{7}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,6,2,3,7,5,8] => [4,6,2,1,7,3,5,8] => {{1,4},{2,3,6},{5,7},{8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [4,6,7,1,8,2,3,5] => {{1,4},{2,6},{3,7},{5,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,6,2,7,3,5,8] => [4,6,7,1,3,2,5,8] => {{1,4},{2,6},{3,5,7},{8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,6,7,2,8,3,5] => [4,7,8,1,3,6,2,5] => {{1,4},{2,7},{3,5,8},{6}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,6,7,8,2,3,5] => [4,8,2,1,3,6,7,5] => {{1,4},{2,3,5,8},{6},{7}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,6,7,2,3,5,8] => [4,7,2,1,3,6,5,8] => {{1,4},{2,3,5,7},{6},{8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => [4,6,2,1,3,5,8,7] => {{1,4},{2,3,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,8,2,3,5,7] => [4,8,2,1,3,6,5,7] => {{1,4},{2,3,5,7,8},{6}}
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,6,2,3,5,7,8] => [4,6,2,1,3,5,7,8] => {{1,4},{2,3,5,6},{7},{8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [4,6,1,2,3,7,8,5] => [6,1,2,4,8,3,7,5] => {{1,2,3,6},{4},{5,8},{7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [6,1,2,4,7,3,5,8] => {{1,2,3,6},{4},{5,7},{8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,6,1,2,7,3,8,5] => [6,1,7,4,8,2,3,5] => {{1,2,6},{3,7},{4},{5,8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [4,6,1,7,2,8,3,5] => [6,7,8,4,3,1,2,5] => {{1,6},{2,7},{3,5,8},{4}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => [6,7,2,4,3,1,5,8] => {{1,6},{2,3,5,7},{4},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [4,6,7,1,2,8,3,5] => [7,1,8,4,3,6,2,5] => {{1,2,7},{3,5,8},{4},{6}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [7,8,2,4,3,6,1,5] => {{1,7},{2,3,5,8},{4},{6}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,8,7] => [6,1,2,4,3,5,8,7] => {{1,2,3,5,6},{4},{7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,8,5,7] => [6,1,2,4,8,3,5,7] => {{1,2,3,6},{4},{5,7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,8,3,5,7] => [6,1,8,4,3,2,5,7] => {{1,2,6},{3,5,7,8},{4}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => [6,8,2,4,3,1,5,7] => {{1,6},{2,3,5,7,8},{4}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [8,1,2,4,3,6,5,7] => {{1,2,3,5,7,8},{4},{6}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [4,6,1,2,3,5,7,8] => [6,1,2,4,3,5,7,8] => {{1,2,3,5,6},{4},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [4,1,2,3,5,8,7,6] => {{1,2,3,4},{5},{6,8},{7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [4,1,2,3,5,7,6,8] => {{1,2,3,4},{5},{6,7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [4,1,2,3,7,8,5,6] => {{1,2,3,4},{5,7},{6,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [4,1,2,3,8,5,7,6] => {{1,2,3,4},{5,6,8},{7}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,7,3,5,8,6] => [4,1,7,2,3,8,5,6] => {{1,2,4},{3,5,7},{6,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [4,1,2,7,3,8,5,6] => [4,1,7,2,8,5,3,6] => {{1,2,4},{3,7},{5,6,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => [4,1,8,2,3,5,7,6] => {{1,2,4},{3,5,6,8},{7}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,1,2,7,3,5,6,8] => [4,1,7,2,3,5,6,8] => {{1,2,4},{3,5,6,7},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,7,2,3,8,5,6] => [4,7,2,1,8,5,3,6] => {{1,4},{2,3,7},{5,6,8}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => [4,8,2,1,3,5,7,6] => {{1,4},{2,3,5,6,8},{7}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [4,7,1,2,8,3,5,6] => [7,1,8,4,3,5,2,6] => {{1,2,7},{3,5,6,8},{4}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => [7,8,2,4,3,5,1,6] => {{1,7},{2,3,5,6,8},{4}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,7,8,1,2,3,5,6] => [8,1,2,4,3,5,7,6] => {{1,2,3,5,6,8},{4},{7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [4,1,2,3,5,6,8,7] => {{1,2,3,4},{5},{6},{7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [4,1,2,3,5,8,6,7] => {{1,2,3,4},{5},{6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,8,3,5,6,7] => [4,1,8,2,3,5,6,7] => {{1,2,4},{3,5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [4,8,2,1,3,5,6,7] => {{1,4},{2,3,5,6,7,8}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [8,1,2,4,3,5,6,7] => {{1,2,3,5,6,7,8},{4}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => {{1},{2},{3},{4,8},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => {{1},{2},{3},{4,7},{5},{6},{8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => {{1},{2},{3},{4,6},{5},{7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,8,4,7] => [1,2,3,8,5,6,4,7] => {{1},{2},{3},{4,7,8},{5},{6}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => {{1},{2},{3},{4,6},{5},{7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => {{1},{2},{3},{4,5},{6,8},{7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => [1,2,3,7,5,8,4,6] => {{1},{2},{3},{4,7},{5},{6,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => [1,2,3,8,5,4,7,6] => {{1},{2},{3},{4,6,8},{5},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => [1,2,3,7,5,4,6,8] => {{1},{2},{3},{4,6,7},{5},{8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => {{1},{2},{3},{4,5},{6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,5,8,4,6,7] => [1,2,3,8,5,4,6,7] => {{1},{2},{3},{4,6,7,8},{5}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [1,2,5,8,3,6,7,4] => {{1},{2},{3,5},{4,8},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,2,5,3,6,7,4,8] => [1,2,5,7,3,6,4,8] => {{1},{2},{3,5},{4,7},{6},{8}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,5,3,6,4,8,7] => [1,2,5,6,3,4,8,7] => {{1},{2},{3,5},{4,6},{7,8}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,2,5,3,6,8,4,7] => [1,2,5,8,3,6,4,7] => {{1},{2},{3,5},{4,7,8},{6}}
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [1,2,5,6,3,4,7,8] => {{1},{2},{3,5},{4,6},{7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [1,2,6,8,5,3,7,4] => {{1},{2},{3,6},{4,8},{5},{7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => [1,2,6,7,5,3,4,8] => {{1},{2},{3,6},{4,7},{5},{8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [1,2,7,8,5,6,3,4] => {{1},{2},{3,7},{4,8},{5},{6}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => [1,2,8,3,5,6,7,4] => {{1},{2},{3,4,8},{5},{6},{7}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,5,6,3,8,4,7] => [1,2,6,8,5,3,4,7] => {{1},{2},{3,6},{4,7,8},{5}}
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,2,5,6,8,3,4,7] => [1,2,8,3,5,6,4,7] => {{1},{2},{3,4,7,8},{5},{6}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,2,6,3,5,4,7,8] => {{1},{2},{3,4,6},{5},{7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => [1,2,5,3,4,8,7,6] => {{1},{2},{3,4,5},{6,8},{7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,2,5,3,7,4,8,6] => [1,2,5,7,3,8,4,6] => {{1},{2},{3,5},{4,7},{6,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,2,5,3,7,8,4,6] => [1,2,5,8,3,4,7,6] => {{1},{2},{3,5},{4,6,8},{7}}
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6,8] => [1,2,5,7,3,4,6,8] => {{1},{2},{3,5},{4,6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,2,5,7,3,4,8,6] => [1,2,7,3,5,8,4,6] => {{1},{2},{3,4,7},{5},{6,8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => [1,2,7,8,5,4,3,6] => {{1},{2},{3,7},{4,6,8},{5}}
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,2,5,7,8,3,4,6] => [1,2,8,3,5,4,7,6] => {{1},{2},{3,4,6,8},{5},{7}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [1,2,7,3,5,4,6,8] => {{1},{2},{3,4,6,7},{5},{8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,2,5,3,4,6,8,7] => [1,2,5,3,4,6,8,7] => {{1},{2},{3,4,5},{6},{7,8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [1,2,5,8,3,4,6,7] => {{1},{2},{3,5},{4,6,7,8}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [1,2,8,3,5,4,6,7] => {{1},{2},{3,4,6,7,8},{5}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => [1,2,5,3,4,6,7,8] => {{1},{2},{3,4,5},{6},{7},{8}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,5,2,3,6,7,4,8] => [1,5,2,7,3,6,4,8] => {{1},{2,3,5},{4,7},{6},{8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => [1,5,2,6,3,4,8,7] => {{1},{2,3,5},{4,6},{7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,5,2,3,6,8,4,7] => [1,5,2,8,3,6,4,7] => {{1},{2,3,5},{4,7,8},{6}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => [1,5,2,6,3,4,7,8] => {{1},{2,3,5},{4,6},{7},{8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => [1,5,6,8,2,3,7,4] => {{1},{2,5},{3,6},{4,8},{7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [1,5,6,7,2,3,4,8] => {{1},{2,5},{3,6},{4,7},{8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,5,2,6,7,3,8,4] => [1,5,7,8,2,6,3,4] => {{1},{2,5},{3,7},{4,8},{6}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,7,8,3,4] => [1,5,8,3,2,6,7,4] => {{1},{2,5},{3,4,8},{6},{7}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,2,6,7,3,4,8] => [1,5,7,3,2,6,4,8] => {{1},{2,5},{3,4,7},{6},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,5,6,8,2,3,4,7] => {{1},{2,5},{3,6},{4,7,8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [1,5,6,3,2,4,7,8] => {{1},{2,5},{3,4,6},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => [1,6,2,8,5,3,7,4] => {{1},{2,3,6},{4,8},{5},{7}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,5,6,2,3,7,4,8] => [1,6,2,7,5,3,4,8] => {{1},{2,3,6},{4,7},{5},{8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,5,6,2,7,3,8,4] => [1,6,7,8,5,2,3,4] => {{1},{2,6},{3,7},{4,8},{5}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,6,2,7,8,3,4] => [1,6,8,3,5,2,7,4] => {{1},{2,6},{3,4,8},{5},{7}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,5,6,7,2,3,8,4] => [1,7,2,8,5,6,3,4] => {{1},{2,3,7},{4,8},{5},{6}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,6,7,2,8,3,4] => [1,7,8,3,5,6,2,4] => {{1},{2,7},{3,4,8},{5},{6}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => [1,8,2,3,5,6,7,4] => {{1},{2,3,4,8},{5},{6},{7}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => [1,6,2,8,5,3,4,7] => {{1},{2,3,6},{4,7,8},{5}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => [1,6,8,3,5,2,4,7] => {{1},{2,6},{3,4,7,8},{5}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [1,8,2,3,5,6,4,7] => {{1},{2,3,4,7,8},{5},{6}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [1,5,2,3,4,8,7,6] => {{1},{2,3,4,5},{6,8},{7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,7,4,8,6] => [1,5,2,7,3,8,4,6] => {{1},{2,3,5},{4,7},{6,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,7,8,4,6] => [1,5,2,8,3,4,7,6] => {{1},{2,3,5},{4,6,8},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => [1,5,2,7,3,4,6,8] => {{1},{2,3,5},{4,6,7},{8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,5,2,7,3,4,8,6] => [1,5,7,3,2,8,4,6] => {{1},{2,5},{3,4,7},{6,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,5,7,8,2,4,3,6] => {{1},{2,5},{3,7},{4,6,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,5,2,7,8,3,4,6] => [1,5,8,3,2,4,7,6] => {{1},{2,5},{3,4,6,8},{7}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [1,5,7,3,2,4,6,8] => {{1},{2,5},{3,4,6,7},{8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,5,7,2,3,4,8,6] => [1,7,2,3,5,8,4,6] => {{1},{2,3,4,7},{5},{6,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,2,3,8,4,6] => [1,7,2,8,5,4,3,6] => {{1},{2,3,7},{4,6,8},{5}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,7,8,3,5,4,2,6] => {{1},{2,7},{3,4,6,8},{5}}
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6,8] => [1,7,2,3,5,4,6,8] => {{1},{2,3,4,6,7},{5},{8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,5,2,3,4,6,8,7] => [1,5,2,3,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,5,2,3,8,4,6,7] => [1,5,2,8,3,4,6,7] => {{1},{2,3,5},{4,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [1,5,8,3,2,4,6,7] => {{1},{2,5},{3,4,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [1,8,2,3,5,4,6,7] => {{1},{2,3,4,6,7,8},{5}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [5,1,2,8,3,6,7,4] => {{1,2,3,5},{4,8},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,6,7,4,8] => [5,1,2,7,3,6,4,8] => {{1,2,3,5},{4,7},{6},{8}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,2,3,6,4,8,7] => [5,1,2,6,3,4,8,7] => {{1,2,3,5},{4,6},{7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => [5,1,2,6,3,4,7,8] => {{1,2,3,5},{4,6},{7},{8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,2,6,7,8,3,4] => [5,1,8,3,2,6,7,4] => {{1,2,5},{3,4,8},{6},{7}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,3,4,8,7] => [5,1,6,3,2,4,8,7] => {{1,2,5},{3,4,6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,1,2,6,8,3,4,7] => [5,1,8,3,2,6,4,7] => {{1,2,5},{3,4,7,8},{6}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => [5,1,6,3,2,4,7,8] => {{1,2,5},{3,4,6},{7},{8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [5,6,2,8,1,3,7,4] => {{1,5},{2,3,6},{4,8},{7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,1,6,2,3,7,4,8] => [5,6,2,7,1,3,4,8] => {{1,5},{2,3,6},{4,7},{8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [5,6,7,8,1,2,3,4] => {{1,5},{2,6},{3,7},{4,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,6,2,7,8,3,4] => [5,6,8,3,1,2,7,4] => {{1,5},{2,6},{3,4,8},{7}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,1,6,2,7,3,4,8] => [5,6,7,3,1,2,4,8] => {{1,5},{2,6},{3,4,7},{8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,6,7,2,3,8,4] => [5,7,2,8,1,6,3,4] => {{1,5},{2,3,7},{4,8},{6}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [5,1,6,7,2,8,3,4] => [5,7,8,3,1,6,2,4] => {{1,5},{2,7},{3,4,8},{6}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,2,3,4] => [5,8,2,3,1,6,7,4] => {{1,5},{2,3,4,8},{6},{7}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,1,6,7,2,3,4,8] => [5,7,2,3,1,6,4,8] => {{1,5},{2,3,4,7},{6},{8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => [5,6,2,8,1,3,4,7] => {{1,5},{2,3,6},{4,7,8}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,1,6,8,2,3,4,7] => [5,8,2,3,1,6,4,7] => {{1,5},{2,3,4,7,8},{6}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [6,1,2,8,5,3,7,4] => {{1,2,3,6},{4,8},{5},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => [6,1,7,8,5,2,3,4] => {{1,2,6},{3,7},{4,8},{5}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => [6,1,8,3,5,2,7,4] => {{1,2,6},{3,4,8},{5},{7}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => [6,7,2,8,5,1,3,4] => {{1,6},{2,3,7},{4,8},{5}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [5,6,1,7,2,8,3,4] => [6,7,8,3,5,1,2,4] => {{1,6},{2,7},{3,4,8},{5}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,6,1,7,8,2,3,4] => [6,8,2,3,5,1,7,4] => {{1,6},{2,3,4,8},{5},{7}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => [7,1,2,8,5,6,3,4] => {{1,2,3,7},{4,8},{5},{6}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => [7,1,8,3,5,6,2,4] => {{1,2,7},{3,4,8},{5},{6}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [7,8,2,3,5,6,1,4] => {{1,7},{2,3,4,8},{5},{6}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => {{1,2,3,4,8},{5},{6},{7}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [7,1,2,3,5,6,4,8] => {{1,2,3,4,7},{5},{6},{8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => [6,1,2,8,5,3,4,7] => {{1,2,3,6},{4,7,8},{5}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,6,1,8,2,3,4,7] => [6,8,2,3,5,1,4,7] => {{1,6},{2,3,4,7,8},{5}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [8,1,2,3,5,6,4,7] => {{1,2,3,4,7,8},{5},{6}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,1,2,3,4,7,8] => [6,1,2,3,5,4,7,8] => {{1,2,3,4,6},{5},{7},{8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [5,1,2,3,4,8,7,6] => {{1,2,3,4,5},{6,8},{7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,7,4,8,6] => [5,1,2,7,3,8,4,6] => {{1,2,3,5},{4,7},{6,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6,8] => [5,1,2,7,3,4,6,8] => {{1,2,3,5},{4,6,7},{8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [5,1,7,3,2,8,4,6] => {{1,2,5},{3,4,7},{6,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,7,3,8,4,6] => [5,1,7,8,2,4,3,6] => {{1,2,5},{3,7},{4,6,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,7,8,3,4,6] => [5,1,8,3,2,4,7,6] => {{1,2,5},{3,4,6,8},{7}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6,8] => [5,1,7,3,2,4,6,8] => {{1,2,5},{3,4,6,7},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [5,1,7,2,3,8,4,6] => [5,7,2,8,1,4,3,6] => {{1,5},{2,3,7},{4,6,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [5,7,8,3,1,4,2,6] => {{1,5},{2,7},{3,4,6,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,7,1,2,3,4,8,6] => [7,1,2,3,5,8,4,6] => {{1,2,3,4,7},{5},{6,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => [7,1,8,3,5,4,2,6] => {{1,2,7},{3,4,6,8},{5}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,7,1,8,2,3,4,6] => [7,8,2,3,5,4,1,6] => {{1,7},{2,3,4,6,8},{5}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [8,1,2,3,5,4,7,6] => {{1,2,3,4,6,8},{5},{7}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [5,1,2,3,4,6,8,7] => {{1,2,3,4,5},{6},{7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [5,1,2,8,3,4,6,7] => {{1,2,3,5},{4,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [5,1,8,3,2,4,6,7] => {{1,2,5},{3,4,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [5,8,2,3,1,4,6,7] => {{1,5},{2,3,4,6,7,8}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [8,1,2,3,5,4,6,7] => {{1,2,3,4,6,7,8},{5}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => {{1},{2},{3},{4},{5,8},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => {{1},{2},{3},{4},{5,7},{6},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,6,8,5,7] => [1,2,3,4,8,6,5,7] => {{1},{2},{3},{4},{5,7,8},{6}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [1,2,3,6,8,4,7,5] => {{1},{2},{3},{4,6},{5,8},{7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [1,2,3,6,7,4,5,8] => {{1},{2},{3},{4,6},{5,7},{8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [1,2,3,7,8,6,4,5] => {{1},{2},{3},{4,7},{5,8},{6}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,2,3,6,7,8,4,5] => [1,2,3,8,4,6,7,5] => {{1},{2},{3},{4,5,8},{6},{7}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,6,7,4,5,8] => [1,2,3,7,4,6,5,8] => {{1},{2},{3},{4,5,7},{6},{8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => [1,2,3,6,8,4,5,7] => {{1},{2},{3},{4,6},{5,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,6,8,4,5,7] => [1,2,3,8,4,6,5,7] => {{1},{2},{3},{4,5,7,8},{6}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => {{1},{2},{3},{4,5,6},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [1,2,6,3,8,4,7,5] => {{1},{2},{3,4,6},{5,8},{7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,2,6,3,4,7,5,8] => [1,2,6,3,7,4,5,8] => {{1},{2},{3,4,6},{5,7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => [1,2,6,7,8,3,4,5] => {{1},{2},{3,6},{4,7},{5,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,2,6,3,7,8,4,5] => [1,2,6,8,4,3,7,5] => {{1},{2},{3,6},{4,5,8},{7}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,2,6,3,7,4,5,8] => [1,2,6,7,4,3,5,8] => {{1},{2},{3,6},{4,5,7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => [1,2,7,3,8,6,4,5] => {{1},{2},{3,4,7},{5,8},{6}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,2,6,7,3,8,4,5] => [1,2,7,8,4,6,3,5] => {{1},{2},{3,7},{4,5,8},{6}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => [1,2,8,3,4,6,7,5] => {{1},{2},{3,4,5,8},{6},{7}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [1,2,7,3,4,6,5,8] => {{1},{2},{3,4,5,7},{6},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,2,6,3,4,8,5,7] => [1,2,6,3,8,4,5,7] => {{1},{2},{3,4,6},{5,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [1,2,6,8,4,3,5,7] => {{1},{2},{3,6},{4,5,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [1,2,8,3,4,6,5,7] => {{1},{2},{3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => [1,2,6,3,4,5,7,8] => {{1},{2},{3,4,5,6},{7},{8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [1,6,2,3,7,4,5,8] => {{1},{2,3,4,6},{5,7},{8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => [1,6,2,7,8,3,4,5] => {{1},{2,3,6},{4,7},{5,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,3,7,8,4,5] => [1,6,2,8,4,3,7,5] => {{1},{2,3,6},{4,5,8},{7}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [1,6,7,8,4,2,3,5] => {{1},{2,6},{3,7},{4,5,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,6,2,7,8,3,4,5] => [1,6,8,3,4,2,7,5] => {{1},{2,6},{3,4,5,8},{7}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [1,6,7,3,4,2,5,8] => {{1},{2,6},{3,4,5,7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,6,7,2,3,4,8,5] => [1,7,2,3,8,6,4,5] => {{1},{2,3,4,7},{5,8},{6}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,7,2,3,8,4,5] => [1,7,2,8,4,6,3,5] => {{1},{2,3,7},{4,5,8},{6}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,8,2,3,4,6,7,5] => {{1},{2,3,4,5,8},{6},{7}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => [1,7,2,3,4,6,5,8] => {{1},{2,3,4,5,7},{6},{8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,6,2,3,8,4,5,7] => {{1},{2,3,4,6},{5,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,6,2,3,8,4,5,7] => [1,6,2,8,4,3,5,7] => {{1},{2,3,6},{4,5,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => [1,6,8,3,4,2,5,7] => {{1},{2,6},{3,4,5,7,8}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [1,8,2,3,4,6,5,7] => {{1},{2,3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [6,1,2,3,8,4,7,5] => {{1,2,3,4,6},{5,8},{7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [6,1,2,3,7,4,5,8] => {{1,2,3,4,6},{5,7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => [6,1,2,7,8,3,4,5] => {{1,2,3,6},{4,7},{5,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,1,2,3,7,8,4,5] => [6,1,2,8,4,3,7,5] => {{1,2,3,6},{4,5,8},{7}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,7,3,4,8,5] => [6,1,7,3,8,2,4,5] => {{1,2,6},{3,4,7},{5,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,1,2,7,3,8,4,5] => [6,1,7,8,4,2,3,5] => {{1,2,6},{3,7},{4,5,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,1,2,7,8,3,4,5] => [6,1,8,3,4,2,7,5] => {{1,2,6},{3,4,5,8},{7}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => [6,1,7,3,4,2,5,8] => {{1,2,6},{3,4,5,7},{8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,7,2,3,4,8,5] => [6,7,2,3,8,1,4,5] => {{1,6},{2,3,4,7},{5,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,1,7,2,3,8,4,5] => [6,7,2,8,4,1,3,5] => {{1,6},{2,3,7},{4,5,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,1,7,2,8,3,4,5] => [6,7,8,3,4,1,2,5] => {{1,6},{2,7},{3,4,5,8}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => [6,8,2,3,4,1,7,5] => {{1,6},{2,3,4,5,8},{7}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => [6,7,2,3,4,1,5,8] => {{1,6},{2,3,4,5,7},{8}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,7,1,2,8,3,4,5] => [7,1,8,3,4,6,2,5] => {{1,2,7},{3,4,5,8},{6}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => [7,8,2,3,4,6,1,5] => {{1,7},{2,3,4,5,8},{6}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [8,1,2,3,4,6,7,5] => {{1,2,3,4,5,8},{6},{7}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => [7,1,2,3,4,6,5,8] => {{1,2,3,4,5,7},{6},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,8,5,7] => [6,1,2,3,8,4,5,7] => {{1,2,3,4,6},{5,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,8,4,5,7] => [6,1,2,8,4,3,5,7] => {{1,2,3,6},{4,5,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => [6,1,8,3,4,2,5,7] => {{1,2,6},{3,4,5,7,8}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [6,8,2,3,4,1,5,7] => {{1,6},{2,3,4,5,7,8}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [8,1,2,3,4,6,5,7] => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => {{1},{2},{3},{4},{5},{6,8},{7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [1,2,3,4,7,8,5,6] => {{1},{2},{3},{4},{5,7},{6,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [1,2,3,4,8,5,7,6] => {{1},{2},{3},{4},{5,6,8},{7}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [1,2,3,4,7,5,6,8] => {{1},{2},{3},{4},{5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [1,2,3,7,4,8,5,6] => {{1},{2},{3},{4,5,7},{6,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [1,2,3,7,8,5,4,6] => {{1},{2},{3},{4,7},{5,6,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,3,7,8,4,5,6] => [1,2,3,8,4,5,7,6] => {{1},{2},{3},{4,5,6,8},{7}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6,8] => {{1},{2},{3},{4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [1,2,7,3,4,8,5,6] => {{1},{2},{3,4,5,7},{6,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,2,7,3,4,8,5,6] => [1,2,7,3,8,5,4,6] => {{1},{2},{3,4,7},{5,6,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [1,2,7,8,4,5,3,6] => {{1},{2},{3,7},{4,5,6,8}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,2,8,3,4,5,7,6] => {{1},{2},{3,4,5,6,8},{7}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => [1,2,7,3,4,5,6,8] => {{1},{2},{3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [1,7,2,3,4,8,5,6] => {{1},{2,3,4,5,7},{6,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,7,2,3,8,5,4,6] => {{1},{2,3,4,7},{5,6,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [1,7,2,8,4,5,3,6] => {{1},{2,3,7},{4,5,6,8}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [1,7,8,3,4,5,2,6] => {{1},{2,7},{3,4,5,6,8}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [1,8,2,3,4,5,7,6] => {{1},{2,3,4,5,6,8},{7}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [7,1,2,3,4,8,5,6] => {{1,2,3,4,5,7},{6,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [7,1,2,3,8,5,4,6] => {{1,2,3,4,7},{5,6,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => [7,1,2,8,4,5,3,6] => {{1,2,3,7},{4,5,6,8}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => [7,1,8,3,4,5,2,6] => {{1,2,7},{3,4,5,6,8}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [7,8,2,3,4,5,1,6] => {{1,7},{2,3,4,5,6,8}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [8,1,2,3,4,5,7,6] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6,8] => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => {{1},{2},{3},{4},{5},{6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,3,4,8,5,6,7] => {{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] => [1,2,3,8,4,5,6,7] => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,8,3,4,5,6,7] => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => {{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] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => {{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] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => {{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] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => {{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] => [8,1,2,3,4,5,6,9,7] => [8,1,2,3,4,5,9,6,7] => {{1,2,3,4,5,6,8},{7,9}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [9,2,1,3,4,5,6,7,8] => {{1,3,4,5,6,7,8,9},{2}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => {{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] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => {{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] => [9,1,2,3,4,5,6,7,10,8] => [9,1,2,3,4,5,6,10,7,8] => {{1,2,3,4,5,6,7,9},{8,10}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => [1,8,2,3,4,5,9,6,7] => {{1},{2,3,4,5,6,8},{7,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [7,1,2,3,4,5,6,9,8] => {{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] => [2,1,9,3,4,5,6,7,8] => [2,1,9,3,4,5,6,7,8] => {{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] => [2,8,1,3,4,5,6,7,9] => [8,2,1,3,4,5,6,7,9] => {{1,3,4,5,6,7,8},{2},{9}}
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [10,2,1,3,4,5,6,7,8,9] => {{1,3,4,5,6,7,8,9,10},{2}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,11,9] => [10,1,2,3,4,5,6,7,11,8,9] => {{1,2,3,4,5,6,7,8,10},{9,11}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [8,1,2,3,4,5,6,7,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8,10] => [9,2,1,3,4,5,6,7,8,10] => {{1,3,4,5,6,7,8,9},{2},{10}}
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,11,1,3,4,5,6,7,8,9,10] => [11,2,1,3,4,5,6,7,8,9,10] => {{1,3,4,5,6,7,8,9,10,11},{2}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [1,2,3,8,4,5,6,9,7] => [1,2,3,8,4,5,9,6,7] => {{1},{2},{3},{4,5,6,8},{7,9}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,9,8] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7,9] => [2,1,8,3,4,5,6,7,9] => {{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] => [2,9,10,1,3,4,5,6,7,8] => [10,2,1,3,4,5,6,7,9,8] => {{1,3,4,5,6,7,8,10},{2},{9}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,12,1,3,4,5,6,7,8,9,10,11] => [12,2,1,3,4,5,6,7,8,9,10,11] => {{1,3,4,5,6,7,8,9,10,11,12},{2}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [1,2,3,9,4,5,6,7,10,8] => [1,2,3,9,4,5,6,10,7,8] => {{1},{2},{3},{4,5,6,7,9},{8,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,8,5,6,9,7] => [1,2,3,4,8,5,9,6,7] => {{1},{2},{3},{4},{5,6,8},{7,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,1,3,4,5,9,6,7,8] => [2,1,3,4,5,9,6,7,8] => {{1,2},{3},{4},{5},{6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7] => [1,2,3,4,5,8,9,6,7] => {{1},{2},{3},{4},{5},{6,8},{7,9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,9,8] => [3,1,2,4,5,6,7,9,8] => {{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] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => {{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] => [2,1,3,4,5,6,9,7,8] => [2,1,3,4,5,6,9,7,8] => {{1,2},{3},{4},{5},{6},{7,8,9}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => {{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,5,9,6,7,10,8] => [1,2,3,4,5,9,6,10,7,8] => {{1},{2},{3},{4},{5},{6,7,9},{8,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => {{1},{2},{3},{4},{5},{6},{7,9},{8}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => {{1,2},{3},{4},{5},{6},{7},{8,9}}
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,9,2,4,5,6,7,8] => [1,9,3,2,4,5,6,7,8] => {{1},{2,4,5,6,7,8,9},{3}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => {{1,3},{2},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,6,9,7,10,8] => [1,2,3,4,5,6,9,10,7,8] => {{1},{2},{3},{4},{5},{6},{7,9},{8,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,8,9,6] => [7,1,2,3,4,9,5,8,6] => {{1,2,3,4,5,7},{6,9},{8}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,7,10,8,9] => [2,1,3,4,5,6,7,10,8,9] => {{1,2},{3},{4},{5},{6},{7},{8,9,10}}
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,9,1,4,5,6,7,8] => [9,2,3,1,4,5,6,7,8] => {{1,4,5,6,7,8,9},{2},{3}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,8,9,7] => [6,1,2,3,4,5,9,8,7] => {{1,2,3,4,5,6},{7,9},{8}}
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => {{1,3},{2},{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] => [3,4,5,6,7,8,9,1,2] => [9,1,3,4,5,6,7,8,2] => {{1,2,9},{3},{4},{5},{6},{7},{8}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,1,2,4,5,6,9,7,8] => [3,1,2,4,5,6,9,7,8] => {{1,2,3},{4},{5},{6},{7,8,9}}
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,9,2,4,5,6,7,8] => [3,9,1,2,4,5,6,7,8] => {{1,3},{2,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,9,1,2,4,5,6,7,8] => [9,1,3,2,4,5,6,7,8] => {{1,2,4,5,6,7,8,9},{3}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => {{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] => [1,4,2,3,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => {{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] => [4,1,2,3,5,9,6,7,8] => [4,1,2,3,5,9,6,7,8] => {{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] => [4,1,2,3,9,5,6,7,8] => [4,1,2,3,9,5,6,7,8] => {{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] => [4,1,2,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,1,6,2,7,3,9,4,8] => [5,6,7,9,1,2,3,4,8] => {{1,5},{2,6},{3,7},{4,8,9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5,1,2,3,4,9,6,7,8] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [5,9,1,2,3,4,6,7,8] => [9,1,2,3,5,4,6,7,8] => {{1,2,3,4,6,7,8,9},{5}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,9,7,8] => [6,1,2,3,4,5,9,7,8] => {{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] => [6,1,2,3,4,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8,9] => [1,7,2,3,4,5,6,8,9] => {{1},{2,3,4,5,6,7},{8},{9}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [7,1,8,2,9,3,4,5,6] => [7,8,9,3,4,5,1,2,6] => {{1,7},{2,8},{3,4,5,6,9}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [9,1,2,3,4,5,7,8,6] => {{1,2,3,4,5,6,9},{7},{8}}
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [7,9,1,2,3,4,5,6,8] => [9,1,2,3,4,5,7,6,8] => {{1,2,3,4,5,6,8,9},{7}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9] => [7,1,2,3,4,5,6,8,9] => {{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] => [1,2,3,4,5,8,9,6,7] => [1,2,3,4,5,9,6,8,7] => {{1},{2},{3},{4},{5},{6,7,9},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [1,2,3,4,8,9,5,6,7] => [1,2,3,4,9,5,6,8,7] => {{1},{2},{3},{4},{5,6,7,9},{8}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,9,2,3,4,5,6,8,7] => {{1},{2,3,4,5,6,7,9},{8}}
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7,9] => [1,8,2,3,4,5,6,7,9] => {{1},{2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [8,1,2,3,9,4,5,6,7] => [8,1,2,9,4,5,6,3,7] => {{1,2,3,8},{4,5,6,7,9}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [8,1,9,2,3,4,5,6,7] => [8,9,2,3,4,5,6,1,7] => {{1,8},{2,3,4,5,6,7,9}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [9,1,2,3,4,5,6,8,7] => {{1,2,3,4,5,6,7,9},{8}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7,9] => {{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] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,9,7,8] => {{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] => [1,2,3,4,5,9,6,7,8] => [1,2,3,4,5,9,6,7,8] => {{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] => [1,2,3,4,9,5,6,7,8] => [1,2,3,4,9,5,6,7,8] => {{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] => [1,2,3,9,4,5,6,7,8] => [1,2,3,9,4,5,6,7,8] => {{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] => [1,2,9,3,4,5,6,7,8] => [1,2,9,3,4,5,6,7,8] => {{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] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => {{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] => [9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => {{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] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => {{1,9},{2},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => {{1,8},{2},{3},{4},{5},{6},{7},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => [9,2,3,4,5,6,7,1,8] => {{1,8,9},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => {{1,7},{2},{3},{4},{5},{6},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => [10,2,3,4,5,6,7,8,1,9] => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,1,2] => [10,1,3,4,5,6,7,8,9,2] => {{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => [11,2,3,4,5,6,7,8,9,1,10] => {{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,9,1,7,8] => [9,2,3,4,5,6,1,7,8] => {{1,7,8,9},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => {{1,6},{2},{3},{4},{5},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [11,1,3,4,5,6,7,8,9,10,2] => {{1,2,11},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => [10,2,3,4,5,6,7,1,8,9] => {{1,8,9,10},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,1,6,7,8] => [9,2,3,4,5,1,6,7,8] => {{1,6,7,8,9},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => {{1,5},{2},{3},{4},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,10,1,7,8,9] => [10,2,3,4,5,6,1,7,8,9] => {{1,7,8,9,10},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,9,1,5,6,7,8] => [9,2,3,4,1,5,6,7,8] => {{1,5,6,7,8,9},{2},{3},{4}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => {{1,4},{2},{3},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,10,1,6,7,8,9] => [10,2,3,4,5,1,6,7,8,9] => {{1,6,7,8,9,10},{2},{3},{4},{5}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,5,6,1,2,3,9,10,7,8] => [6,1,2,4,5,3,10,7,9,8] => {{1,2,3,6},{4},{5},{7,8,10},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => {{1,7},{2},{3},{4},{5},{6},{8,9}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8] => [3,2,1,5,4,7,6,9,8] => {{1,3},{2},{4,5},{6,7},{8,9}}
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,5,4,6,7,8,9] => [3,2,1,5,4,6,7,8,9] => {{1,3},{2},{4,5},{6},{7},{8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => {{1,2},{3,9},{4},{5},{6},{7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,7,8,9] => [2,1,4,3,6,5,7,8,9] => {{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] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => {{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] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => {{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] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2] => {{1},{2,9},{3},{4},{5},{6},{7},{8}}
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => {{1},{2,4},{3},{5},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => {{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] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,8,7] => {{1},{2,3},{4},{5},{6},{7,9},{8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => {{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] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => {{1},{2},{3,9},{4},{5},{6},{7},{8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => {{1},{2},{3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => {{1},{2},{3},{4,9},{5},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => {{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] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => {{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] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => {{1},{2},{3},{4},{5,9},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => {{1},{2},{3},{4},{5,6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => {{1},{2},{3},{4},{5},{6,9},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => {{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] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => {{1},{2},{3},{4},{5},{6,7},{8},{9}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => {{1,3},{2},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,8,7,9,10] => [2,1,4,3,6,5,8,7,9,10] => {{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] => [2,1,4,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => {{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] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2] => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => {{1},{2,3},{4,5},{6,7},{8,10},{9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => {{1},{2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => {{1},{2},{3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => {{1},{2},{3},{4,5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,6,5,8,7,10,9] => {{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] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => {{1},{2},{3},{4},{5,6},{7},{8},{9},{10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => {{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] => [3,1,4,5,6,7,8,9,2] => [3,9,1,4,5,6,7,8,2] => {{1,3},{2,9},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,2] => [6,9,3,4,5,1,7,8,2] => {{1,6},{2,9},{3},{4},{5},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,1,8,9,2] => [7,9,3,4,5,6,1,8,2] => {{1,7},{2,9},{3},{4},{5},{6},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,1,9,2] => [8,9,3,4,5,6,7,1,2] => {{1,8},{2,9},{3},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [3,10,1,4,5,6,7,8,9,2] => {{1,3},{2,10},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,8,1,9,10,2] => [8,10,3,4,5,6,7,1,9,2] => {{1,8},{2,10},{3},{4},{5},{6},{7},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,1,10,2] => [9,10,3,4,5,6,7,8,1,2] => {{1,9},{2,10},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8,10] => {{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] => [1,10,2,3,4,5,6,7,8,9] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => {{1,2,3,4,5,6,7,8,9,10},{11}}
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [1,10,2,3,4,5,6,7,9,8] => {{1},{2,3,4,5,6,7,8,10},{9}}
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,8,2,9] => [3,8,1,4,5,6,7,2,9] => {{1,3},{2,8},{4},{5},{6},{7},{9}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => {{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] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,10,8,9] => {{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] => [1,2,3,4,5,6,7,8,11,9,10] => [1,2,3,4,5,6,7,8,11,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,4,7,5,8,9,6] => [1,2,3,4,7,9,5,8,6] => {{1},{2},{3},{4},{5,7},{6,9},{8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,3,6,4,7,8,9,5] => [1,2,3,6,9,4,7,8,5] => {{1},{2},{3},{4,6},{5,9},{7},{8}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,9,4] => [1,2,5,9,3,6,7,8,4] => {{1},{2},{3,5},{4,9},{6},{7},{8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,9,3] => [1,4,9,2,5,6,7,8,3] => {{1},{2,4},{3,9},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,9] => {{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] => [8,1,2,3,4,5,6,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => {{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] => [7,1,2,3,4,5,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => {{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] => [6,1,2,3,4,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => {{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] => [5,1,2,3,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => {{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] => [4,1,2,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [11,1,2,3,4,5,6,7,8,9,10] => {{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] => [3,1,4,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => {{1,3},{2,4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,1,6,2,7,8,9] => [5,6,3,4,1,2,7,8,9] => {{1,5},{2,6},{3},{4},{7},{8},{9}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,1,4,8,9,2,5,6,7] => [3,9,1,4,2,5,6,8,7] => {{1,3},{2,5,6,7,9},{4},{8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,6,8,7,9] => [4,1,2,3,5,6,8,7,9] => {{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] => [5,1,2,3,4,7,6,8,9] => [5,1,2,3,4,7,6,8,9] => {{1,2,3,4,5},{6,7},{8},{9}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [1,2,3,9,5,4,6,7,8] => {{1},{2},{3},{4,6,7,8,9},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,7,9,6,8] => [1,2,3,4,5,9,7,6,8] => {{1},{2},{3},{4},{5},{6,8,9},{7}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [1,2,3,4,5,6,10,7,8,9] => {{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] => [1,2,3,4,6,9,5,7,8] => [1,2,3,4,9,6,5,7,8] => {{1},{2},{3},{4},{5,7,8,9},{6}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [1,2,3,4,5,10,6,7,8,9] => {{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] => [1,2,3,4,10,5,6,7,8,9] => {{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] => [1,2,4,9,3,5,6,7,8] => [1,2,9,4,3,5,6,7,8] => {{1},{2},{3,5,6,7,8,9},{4}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [1,2,3,10,4,5,6,7,8,9] => {{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] => [1,2,10,3,4,5,6,7,8,9] => [1,2,10,3,4,5,6,7,8,9] => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,4,7,5,8,6,9] => [1,2,3,4,7,8,5,6,9] => {{1},{2},{3},{4},{5,7},{6,8},{9}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,9,8] => [3,5,1,2,4,7,6,9,8] => {{1,3},{2,4,5},{6,7},{8,9}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,9] => [3,5,1,6,2,4,8,7,9] => {{1,3},{2,5},{4,6},{7,8},{9}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,9] => [3,4,1,2,6,5,8,7,9] => {{1,3},{2,4},{5,6},{7,8},{9}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8,10] => [3,1,2,5,4,7,6,9,8,10] => {{1,2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [3,4,1,2,6,5,8,7,10,9] => {{1,3},{2,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8,10] => [1,9,2,3,4,5,6,7,8,10] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [6,7,8,9,10,1,2,3,4,5] => {{1,6},{2,7},{3,8},{4,9},{5,10}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => [7,8,9,10,11,12,1,2,3,4,5,6] => {{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,8,9,12,10,11] => [1,2,3,4,5,6,7,8,9,12,10,11] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11,12}}
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,10,2,4,5,6,7,8,9] => [3,10,1,2,4,5,6,7,8,9] => {{1,3},{2,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => [3,1,2,4,5,6,7,8,9,10,11,12] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11},{12}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,11,2] => [3,11,1,4,5,6,7,8,9,10,2] => {{1,3},{2,11},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => {{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] => [6,7,8,9,10,1,2,3,4,5] => [10,1,2,3,4,6,7,8,9,5] => {{1,2,3,4,5,10},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => [9,10,2,3,4,5,6,7,1,8] => {{1,9},{2,3,4,5,6,7,8,10}}
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,10,1,4,5,6,7,8,9] => [10,2,3,1,4,5,6,7,8,9] => {{1,4,5,6,7,8,9,10},{2},{3}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,10,1,5,6,7,8,9] => [10,2,3,4,1,5,6,7,8,9] => {{1,5,6,7,8,9,10},{2},{3},{4}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,7,8,9,5] => [6,1,2,3,9,4,7,8,5] => {{1,2,3,4,6},{5,9},{7},{8}}
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [5,10,1,2,3,4,6,7,8,9] => [10,1,2,3,5,4,6,7,8,9] => {{1,2,3,4,6,7,8,9,10},{5}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [10,1,2,3,4,5,6,7,9,8] => {{1,2,3,4,5,6,7,8,10},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,8,1,9,7] => [8,2,3,4,5,6,9,1,7] => {{1,8},{2},{3},{4},{5},{6},{7,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,7,9,1,10,8] => [9,2,3,4,5,6,7,10,1,8] => {{1,9},{2},{3},{4},{5},{6},{7},{8,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,10,1,11,2] => [10,11,3,4,5,6,7,8,9,1,2] => {{1,10},{2,11},{3},{4},{5},{6},{7},{8},{9}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,9] => [4,1,2,3,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,1,9,3] => [8,2,9,4,5,6,7,1,3] => {{1,8},{2},{3,9},{4},{5},{6},{7}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => [3,1,2,10,4,5,6,7,8,9] => {{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] => [5,1,2,3,4,10,6,7,8,9] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,10,1,11,9] => [10,2,3,4,5,6,7,8,11,1,9] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9,11}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,9,1,10,3] => [9,2,10,4,5,6,7,8,1,3] => {{1,9},{2},{3,10},{4},{5},{6},{7},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,1,3,4,5,8,6,7,9] => [2,1,3,4,5,8,6,7,9] => {{1,2},{3},{4},{5},{6,7,8},{9}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,9,8] => [1,4,5,2,3,7,6,9,8] => {{1},{2,4},{3,5},{6,7},{8,9}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,9] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,10,9] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [2,1,7,8,9,10,3,4,5,6] => [2,1,10,3,4,5,7,8,9,6] => {{1,2},{3,4,5,6,10},{7},{8},{9}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [3,4,1,2,8,9,10,5,6,7] => [4,1,3,2,10,5,6,8,9,7] => {{1,2,4},{3},{5,6,7,10},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,6,7,8,1,2,3,4,10,9] => [8,1,2,3,5,6,7,4,10,9] => {{1,2,3,4,8},{5},{6},{7},{9,10}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,7,1,8,2,9,3] => [7,8,9,4,5,6,1,2,3] => {{1,7},{2,8},{3,9},{4},{5},{6}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,9,10,7] => [8,1,2,3,4,5,10,6,9,7] => {{1,2,3,4,5,6,8},{7,10},{9}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,9,8] => [1,2,3,4,7,5,6,9,8] => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7,9] => [8,2,1,4,3,6,5,7,9] => {{1,3,5,7,8},{2},{4},{6},{9}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,6,2,7,3,8,4,9,5,10] => [1,6,7,8,9,2,3,4,5,10] => {{1},{2,6},{3,7},{4,8},{5,9},{10}}
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [12,1,2,3,4,5,6,7,8,9,10,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [4,2,5,1,3,7,6,9,8,10] => {{1,4},{2},{3,5},{6,7},{8,9},{10}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,6,3,5,4,10,7,9,8,12,11] => {{1,2},{3,4,6},{5},{7,8,10},{9},{11,12}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,9,8] => [1,5,3,2,4,7,6,9,8] => {{1},{2,4,5},{3},{6,7},{8,9}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8] => [4,2,5,1,3,7,6,9,8] => {{1,4},{2},{3,5},{6,7},{8,9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,8,5,9,7] => [4,1,6,2,8,3,9,5,7] => {{1,2,4},{3,6},{5,8},{7,9}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,2,7,3,8,4,9,5] => [1,6,7,8,9,2,3,4,5] => {{1},{2,6},{3,7},{4,8},{5,9}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,9] => [5,6,7,8,1,2,3,4,9] => {{1,5},{2,6},{3,7},{4,8},{9}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,9,8] => [3,1,2,7,5,4,6,9,8] => {{1,2,3},{4,6,7},{5},{8,9}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [8,1,9,2,10,3,4,5,6,7] => [8,9,10,3,4,5,6,1,2,7] => {{1,8},{2,9},{3,4,5,6,7,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,10,11,1,12,2] => [11,12,3,4,5,6,7,8,9,10,1,2] => {{1,11},{2,12},{3},{4},{5},{6},{7},{8},{9},{10}}
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
searching the database
Sorry, this map was not found in the database.