Identifier
Mp00099:
Dyck paths
—bounce path⟶
Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
[1,0] => [1,0] => [1] => {{1}}
[1,0,1,0] => [1,0,1,0] => [1,2] => {{1},{2}}
[1,1,0,0] => [1,1,0,0] => [2,1] => {{1,2}}
[1,0,1,0,1,0] => [1,0,1,0,1,0] => [1,2,3] => {{1},{2},{3}}
[1,0,1,1,0,0] => [1,0,1,1,0,0] => [1,3,2] => {{1},{2,3}}
[1,1,0,0,1,0] => [1,1,0,0,1,0] => [2,1,3] => {{1,2},{3}}
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [1,3,2] => {{1},{2,3}}
[1,1,1,0,0,0] => [1,1,1,0,0,0] => [3,1,2] => {{1,2,3}}
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => {{1},{2},{3},{4}}
[1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => {{1},{2},{3,4}}
[1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => {{1},{2,3},{4}}
[1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => {{1},{2},{3,4}}
[1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => {{1},{2,3,4}}
[1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => {{1,2},{3},{4}}
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => {{1,2},{3,4}}
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => {{1},{2,3},{4}}
[1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => {{1,2},{3,4}}
[1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => {{1},{2,3,4}}
[1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => [3,1,2,4] => {{1,2,3},{4}}
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => {{1,2},{3,4}}
[1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => {{1},{2,3,4}}
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => {{1,2,3,4}}
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => {{1},{2},{3},{4,5}}
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => {{1},{2},{3,4},{5}}
[1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => {{1},{2},{3},{4,5}}
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => {{1},{2},{3,4,5}}
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => {{1},{2,3},{4},{5}}
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => {{1},{2},{3,4},{5}}
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => {{1},{2},{3,4,5}}
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => {{1},{2,3,4},{5}}
[1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
[1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => {{1},{2},{3,4,5}}
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => {{1},{2,3,4,5}}
[1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => {{1,2},{3},{4},{5}}
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => {{1,2},{3},{4,5}}
[1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => {{1,2},{3,4},{5}}
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => {{1,2},{3},{4,5}}
[1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => {{1,2},{3,4,5}}
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => {{1},{2,3},{4},{5}}
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
[1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => {{1,2},{3,4},{5}}
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
[1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => {{1,2},{3,4,5}}
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => {{1},{2,3,4},{5}}
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => {{1,2},{3,4,5}}
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => {{1},{2,3,4,5}}
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => {{1,2,3},{4},{5}}
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => {{1,2,3},{4,5}}
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => {{1,2},{3,4},{5}}
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => {{1,2,3},{4,5}}
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => {{1,2},{3,4,5}}
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => {{1},{2,3,4},{5}}
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => {{1,2,3},{4,5}}
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => {{1,2},{3,4,5}}
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => {{1},{2,3,4,5}}
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => {{1,2,3,4},{5}}
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => {{1,2,3},{4,5}}
[1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => {{1,2},{3,4,5}}
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => {{1},{2,3,4,5}}
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => {{1,2,3,4,5}}
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}}
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}}
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}}
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}}
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}}
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}}
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => {{1},{2},{3,4,5,6}}
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}}
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}}
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}}
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}}
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}}
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}}
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}}
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}}
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => {{1},{2},{3,4,5,6}}
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => {{1},{2,3,4},{5},{6}}
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}}
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}}
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => {{1},{2},{3,4,5,6}}
>>> Load all 2628 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => {{1},{2,3,4,5},{6}}
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => {{1},{2},{3,4,5,6}}
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => {{1},{2,3,4,5,6}}
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}}
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => {{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}}
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => {{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}}
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => {{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}}
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}}
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}}
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}}
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}}
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => {{1},{2,3,4},{5},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}}
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}}
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => {{1},{2,3,4,5},{6}}
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => {{1},{2,3,4,5,6}}
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => {{1,2,3},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => {{1,2,3},{4},{5,6}}
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => {{1,2,3},{4,5},{6}}
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => {{1,2,3},{4},{5,6}}
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}}
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => {{1,2,3},{4,5},{6}}
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}}
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => {{1},{2,3,4},{5},{6}}
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => {{1,2,3},{4,5},{6}}
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}}
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => {{1},{2,3,4,5},{6}}
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}}
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => {{1},{2,3,4,5,6}}
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => {{1,2,3,4},{5},{6}}
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => {{1,2,3},{4,5},{6}}
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}}
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => {{1},{2,3,4,5},{6}}
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}}
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => {{1},{2,3,4,5,6}}
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => {{1,2,3,4,5},{6}}
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}}
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}}
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => {{1},{2,3,4,5,6}}
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => {{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => {{1},{2},{3,4,5,6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => {{1},{2},{3,4,5,6},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => {{1},{2,3,4},{5},{6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => {{1},{2},{3,4,5,6},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => {{1},{2,3,4,5},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => {{1},{2},{3,4,5,6},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => {{1,2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => {{1,2},{3},{4},{5,6},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => {{1,2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => {{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => {{1,2},{3},{4,5},{6},{7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => {{1,2},{3},{4},{5,6},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => {{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => {{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => {{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => {{1,2},{3,4},{5},{6},{7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => {{1,2},{3},{4,5},{6},{7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => {{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => {{1,2},{3,4,5},{6},{7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => {{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => {{1,2},{3,4},{5},{6},{7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => {{1,2},{3,4,5},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => {{1},{2,3,4},{5},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => {{1,2},{3,4,5},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => {{1},{2,3,4,5},{6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => {{1},{2,3,4,5,6},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => {{1,2,3},{4},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => {{1,2,3},{4},{5,6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => {{1,2,3},{4},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => {{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => {{1,2,3},{4,5},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => {{1,2,3},{4},{5,6},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => {{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => {{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => {{1,2},{3,4},{5},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => {{1,2,3},{4,5},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => {{1,2},{3,4,5},{6},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => {{1},{2,3,4},{5},{6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => {{1,2,3},{4,5},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => {{1,2},{3,4,5},{6},{7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => {{1},{2,3,4,5},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => {{1},{2,3,4,5,6},{7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => {{1,2,3,4},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => {{1,2,3,4},{5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => {{1,2,3,4},{5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => {{1,2,3},{4,5},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => {{1,2},{3,4,5},{6},{7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => {{1},{2,3,4,5},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => {{1},{2,3,4,5,6},{7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => {{1},{2,3,4,5,6},{7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => {{1,2,3,4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => {{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => {{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,8] => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => {{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,8] => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,8] => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => {{1},{2},{3,4},{5},{6},{7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => {{1},{2},{3,4},{5},{6},{7,8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => {{1},{2},{3,4},{5},{6,7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => {{1},{2},{3,4},{5},{6},{7,8}}
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => {{1},{2},{3,4},{5},{6,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => {{1},{2},{3,4},{5},{6,7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => {{1},{2},{3,4},{5},{6,7,8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => {{1},{2},{3,4},{5},{6,7,8}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,3,4,6,7,8] => {{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => {{1},{2},{3,4,5},{6},{7,8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => {{1},{2},{3,4,5},{6},{7,8}}
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => {{1},{2},{3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => {{1},{2,3},{4},{5},{6},{7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => {{1},{2,3},{4},{5},{6},{7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => {{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => {{1},{2,3},{4},{5,6},{7},{8}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => {{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => {{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => {{1},{2,3},{4},{5,6,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => {{1},{2,3},{4},{5,6},{7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => {{1},{2,3},{4},{5,6,7,8}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => {{1},{2,3},{4},{5,6,7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => {{1},{2,3},{4},{5,6,7,8}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => {{1},{2},{3,4},{5},{6},{7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => {{1},{2},{3,4},{5},{6},{7,8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => {{1},{2},{3,4},{5},{6,7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => {{1},{2},{3,4},{5},{6},{7,8}}
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => {{1},{2},{3,4},{5},{6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => {{1},{2},{3,4},{5},{6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => {{1},{2},{3,4},{5},{6,7,8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => {{1},{2},{3,4},{5},{6,7,8}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,3,4,6,7,8] => {{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => {{1},{2},{3,4,5},{6},{7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => {{1},{2},{3,4,5},{6},{7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => {{1},{2},{3,4,5,6},{7},{8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => {{1},{2,3,4},{5},{6},{7},{8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,3,4,6,7,8] => {{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => {{1},{2},{3,4,5},{6},{7,8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => {{1},{2},{3,4,5},{6},{7,8}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => {{1},{2},{3,4,5,6},{7},{8}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => {{1},{2},{3,4,5,6},{7},{8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => {{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => {{1,2},{3},{4},{5,6},{7},{8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => {{1,2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => {{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => {{1,2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => {{1,2},{3},{4},{5,6,7},{8}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => {{1,2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => {{1,2},{3},{4,5},{6},{7},{8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => {{1,2},{3},{4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => {{1,2},{3},{4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => {{1,2},{3},{4},{5,6},{7},{8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => {{1,2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => {{1,2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => {{1,2},{3},{4},{5,6,7},{8}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => {{1,2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,4,5,7,8] => {{1,2},{3},{4,5,6},{7},{8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => {{1,2},{3},{4},{5,6,7},{8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => {{1,2},{3,4},{5},{6},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => {{1,2},{3,4},{5},{6},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => {{1,2},{3},{4,5},{6},{7},{8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => {{1,2},{3},{4,5},{6},{7,8}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => {{1,2},{3},{4,5},{6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,4,5,7,8] => {{1,2},{3},{4,5,6},{7},{8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,4,5,7,8] => {{1,2},{3},{4,5,6},{7},{8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => {{1},{2,3},{4},{5},{6},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => {{1},{2,3},{4},{5},{6},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => {{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => {{1},{2,3},{4},{5,6},{7},{8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => {{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => {{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => {{1},{2,3},{4},{5,6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => {{1},{2,3},{4},{5,6},{7},{8}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => {{1},{2,3},{4},{5,6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => {{1},{2,3},{4},{5,6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => {{1},{2,3},{4},{5,6,7,8}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => {{1,2},{3,4},{5},{6},{7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => {{1,2},{3,4},{5},{6},{7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => {{1},{2,3,4},{5},{6},{7},{8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}}
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8] => {{1,2,3},{4},{5},{6},{7},{8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,8,7] => {{1,2,3},{4},{5},{6},{7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,2,4,5,7,6,8] => {{1,2,3},{4},{5},{6,7},{8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,8,7] => {{1,2,3},{4},{5},{6},{7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => {{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,2,4,5,7,6,8] => {{1,2,3},{4},{5},{6,7},{8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => {{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => {{1,2,3},{4},{5,6,7},{8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => {{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => {{1,2,3},{4},{5,6,7},{8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => {{1,2,3},{4},{5,6,7},{8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => {{1,2},{3,4},{5},{6},{7,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => {{1,2},{3,4},{5},{6},{7,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => {{1},{2,3,4},{5},{6},{7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => {{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => {{1},{2,3,4},{5,6},{7},{8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,3,5,6,8,7] => {{1,2,3,4},{5},{6},{7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,3,5,7,6,8] => {{1,2,3,4},{5},{6,7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,3,5,6,8,7] => {{1,2,3,4},{5},{6},{7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,3,5,8,6,7] => {{1,2,3,4},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,3,5,7,6,8] => {{1,2,3,4},{5},{6,7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,3,5,8,6,7] => {{1,2,3,4},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,3,5,8,6,7] => {{1,2,3,4},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => {{1},{2,3,4,5},{6},{7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,4,6,8,7] => {{1,2,3,4,5},{6},{7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,4,6,8,7] => {{1,2,3,4,5},{6},{7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,7,9] => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9,11] => {{1,2,3,4,5,6,7,8,9,10},{11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,8,10] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,7,9] => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,8,10] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,7,9] => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,8,10] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,7,9] => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,8,10] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,7,9] => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,8,10] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,7,9] => {{1},{2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => {{1,2,3,4,5,6,7},{8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{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] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,8,10] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9] => {{1,2,3,4,5,6,7},{8},{9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,7,9] => {{1},{2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,8,10] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,1,2,3,4,5,6,7,10,9] => {{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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,2,3,4,5,6,8,9] => {{1},{2,3,4,5,6,7},{8},{9}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => {{1},{2},{3},{4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,7,9,10] => {{1,2,3,4,5,6,7,8},{9},{10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,2,3,4,5,6,7,8,10] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,2,3,4,5,6,8,9] => {{1},{2,3,4,5,6,7},{8},{9}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => {{1},{2},{3},{4,5,6,7,8,9}}
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => {{1},{2},{3,4,5,6,7,8,9,10}}
[] => [] => [] => {}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{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] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{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] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{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] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{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] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{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] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{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] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{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] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => {{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] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8] => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,4,7,5,6,9,8] => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => {{1},{2},{3},{4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => {{1},{2},{3},{4},{5,6},{7,8},{9,10}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8] => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,4,7,5,6,9,8] => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,4,7,5,6,9,8] => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,4,7,5,6,9,8] => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10,11}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,4,7,5,6,9,8] => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,9,12,10,11] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11,12}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => {{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => {{1},{2},{3},{4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => {{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => {{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => {{1},{2},{3},{4},{5},{6,7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => {{1},{2},{3},{4},{5,6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => {{1},{2},{3},{4},{5,6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,4,7,5,6,9,8] => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => {{1},{2},{3},{4,5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => {{1},{2},{3,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => {{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => {{1},{2,3},{4},{5},{6},{7},{8,9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,7,8] => {{1},{2,3},{4},{5},{6},{7,8,9}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8,9] => {{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,2,3,4,5,6,8,9] => {{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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => {{1,2},{3},{4},{5},{6},{7},{8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => {{1,2},{3},{4},{5},{6},{7,8},{9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,7,8] => {{1,2},{3},{4},{5},{6},{7,8,9}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5,8,6,7,9] => {{1,2},{3},{4},{5},{6,7,8},{9}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5,9,6,7,8] => {{1,2},{3},{4},{5},{6,7,8,9}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => {{1,2},{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] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9] => {{1,2,3},{4},{5},{6},{7},{8},{9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,7,9,8] => {{1,2,3},{4},{5},{6},{7},{8,9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,6,9,7,8] => {{1,2,3},{4},{5},{6},{7,8,9}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7,9] => {{1,2,3},{4},{5,6},{7,8},{9}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{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] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => {{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] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,3,5,9,6,7,8] => {{1,2,3,4},{5},{6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => {{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] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,2,3,4,7,6,8,9] => {{1,2,3,4,5},{6,7},{8},{9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,4,9,6,7,8] => {{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] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,5,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => {{1,2,3,4,5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => {{1},{2},{3},{4},{5},{6},{7,8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => {{1},{2},{3},{4},{5,6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => {{1},{2},{3},{4,5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => {{1},{2},{3},{4,5},{6,7},{8,9},{10}}
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => {{1},{2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,7,10,8,9] => {{1,2},{3},{4},{5},{6},{7},{8,9,10}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,3,4,5,6,7,10,9] => {{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] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9,10] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => {{1,2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,6,5,10,7,8,9] => {{1,2,3,4},{5,6},{7,8,9,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{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] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{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] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8,9,10] => {{1,2,3,4,5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5,7,8,9,10] => {{1,2,3,4,5,6},{7},{8},{9},{10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9,10] => {{1,2,3,4,5,6,7},{8},{9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => {{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] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => {{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => {{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => {{1,2},{3,4},{5,6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8,9] => {{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9,10] => {{1,2},{3,4},{5,6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => {{1,2},{3,4},{5,6},{7,8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => {{1,2},{3},{4},{5},{6},{7},{8,9}}
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{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] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => {{1},{2,3},{4},{5},{6},{7},{8,9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => {{1},{2,3},{4},{5},{6},{7},{8,9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => {{1},{2,3},{4},{5},{6},{7},{8,9}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8,9] => {{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,1,2,3,4,5,6,7,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,1,2,3,4,5,6,7,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,2,3,4,7,6,8,9] => {{1,2,3,4,5},{6,7},{8},{9}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => {{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => {{1},{2},{3},{4,5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => {{1},{2},{3},{4},{5},{6},{7,8},{9},{10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,7,8,9] => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,7,8,9] => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,7,8,9] => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => {{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] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,3,5,9,6,7,8] => {{1,2,3,4},{5},{6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{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] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{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] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => {{1},{2},{3},{4},{5,6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => {{1},{2},{3},{4},{5},{6,7},{8},{9}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => {{1},{2},{3},{4,5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => {{1,2},{3,4},{5,6},{7},{8},{9}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{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] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,9,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,1,2,3,4,5,6,7,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => {{1},{2},{3},{4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8] => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}}
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => {{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => {{1},{2},{3,4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10,11}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10},{11}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => {{1},{2},{3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => {{1,2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10},{11}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,2,3,4,7,6,8,9] => {{1,2,3,4,5},{6,7},{8},{9}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,2,3,4,7,6,8,9] => {{1,2,3,4,5},{6,7},{8},{9}}
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,7,8] => {{1},{2,3},{4},{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] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10,11}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => {{1},{2},{3},{4},{5,6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => {{1},{2},{3},{4},{5,6},{7},{8},{9},{10}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => {{1},{2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => {{1,2},{3,4},{5,6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => {{1},{2},{3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5,9,6,7,8] => {{1,2},{3},{4},{5},{6,7,8,9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,3,4,5,6,7,10,9] => {{1,2},{3,4,5,6,7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5,9,6,7,8] => {{1,2},{3},{4},{5},{6,7,8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => {{1,2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => {{1},{2},{3},{4},{5,6},{7,8},{9}}
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,3,4,5,6,7,9] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,6,5,10,7,8,9] => {{1,2,3,4},{5,6},{7,8,9,10}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,1,2,3,4,5,6,7,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,7,9,8] => {{1,2,3},{4},{5},{6},{7},{8,9}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,6,5,10,7,8,9] => {{1,2,3,4},{5,6},{7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,7,8] => {{1,2},{3},{4},{5},{6},{7,8,9}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,4,7,5,6,9,8] => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => {{1},{2},{3},{4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => {{1},{2},{3},{4,5},{6,7},{8,9},{10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9,10,11] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11},{12}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,9,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,1,2,3,4,5,6,7,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,3,4,5,6,7,10,9] => {{1,2},{3,4,5,6,7,8},{9,10}}
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,3,4,5,6,7,10,9] => {{1,2},{3,4,5,6,7,8},{9,10}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10,11}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => {{1,2},{3,4},{5,6},{7},{8},{9}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,6,5,10,7,8,9] => {{1,2,3,4},{5,6},{7,8,9,10}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,3,4,5,6,7,10,9] => {{1,2},{3,4,5,6,7,8},{9,10}}
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,3,4,5,6,7,10,9] => {{1,2},{3,4,5,6,7,8},{9,10}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,7,8,9] => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => {{1,2},{3,4},{5,6},{7,8},{9},{10}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => {{1,2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,7,8,9] => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,7,8,9] => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9,10] => {{1,2},{3,4},{5,6},{7},{8},{9},{10}}
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,9] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,7,8] => {{1},{2,3},{4},{5},{6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}}
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,6,9,7,8] => {{1,2,3},{4},{5},{6},{7,8,9}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,3,4,5,6,7,10,9] => {{1,2},{3,4,5,6,7,8},{9,10}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,2,3,4,7,6,8,9] => {{1,2,3,4,5},{6,7},{8},{9}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,2,3,4,7,6,8,9] => {{1,2,3,4,5},{6,7},{8},{9}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,1,2,3,4,5,6,10,8,9] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,3,5,9,6,7,8] => {{1,2,3,4},{5},{6,7,8,9}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}
Map
bounce path
Description
Sends a Dyck path $D$ of length $2n$ to its bounce path.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
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].
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