Identifier
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00115: Set partitions —Kasraoui-Zeng⟶ Set partitions
Mp00217: Set partitions —Wachs-White-rho ⟶ Set partitions
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00115: Set partitions —Kasraoui-Zeng⟶ Set partitions
Mp00217: Set partitions —Wachs-White-rho ⟶ Set partitions
Images
[1,0] => [1] => {{1}} => {{1}} => {{1}}
[1,0,1,0] => [1,2] => {{1},{2}} => {{1},{2}} => {{1},{2}}
[1,1,0,0] => [2,1] => {{1,2}} => {{1,2}} => {{1,2}}
[1,0,1,0,1,0] => [1,2,3] => {{1},{2},{3}} => {{1},{2},{3}} => {{1},{2},{3}}
[1,0,1,1,0,0] => [1,3,2] => {{1},{2,3}} => {{1},{2,3}} => {{1},{2,3}}
[1,1,0,0,1,0] => [2,1,3] => {{1,2},{3}} => {{1,2},{3}} => {{1,2},{3}}
[1,1,0,1,0,0] => [2,3,1] => {{1,2,3}} => {{1,2,3}} => {{1,2,3}}
[1,1,1,0,0,0] => [3,2,1] => {{1,3},{2}} => {{1,3},{2}} => {{1,3},{2}}
[1,0,1,0,1,0,1,0] => [1,2,3,4] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}} => {{1},{2},{3},{4}}
[1,0,1,0,1,1,0,0] => [1,2,4,3] => {{1},{2},{3,4}} => {{1},{2},{3,4}} => {{1},{2},{3,4}}
[1,0,1,1,0,0,1,0] => [1,3,2,4] => {{1},{2,3},{4}} => {{1},{2,3},{4}} => {{1},{2,3},{4}}
[1,0,1,1,0,1,0,0] => [1,3,4,2] => {{1},{2,3,4}} => {{1},{2,3,4}} => {{1},{2,3,4}}
[1,0,1,1,1,0,0,0] => [1,4,3,2] => {{1},{2,4},{3}} => {{1},{2,4},{3}} => {{1},{2,4},{3}}
[1,1,0,0,1,0,1,0] => [2,1,3,4] => {{1,2},{3},{4}} => {{1,2},{3},{4}} => {{1,2},{3},{4}}
[1,1,0,0,1,1,0,0] => [2,1,4,3] => {{1,2},{3,4}} => {{1,2},{3,4}} => {{1,2},{3,4}}
[1,1,0,1,0,0,1,0] => [2,3,1,4] => {{1,2,3},{4}} => {{1,2,3},{4}} => {{1,2,3},{4}}
[1,1,0,1,0,1,0,0] => [2,3,4,1] => {{1,2,3,4}} => {{1,2,3,4}} => {{1,2,3,4}}
[1,1,0,1,1,0,0,0] => [2,4,3,1] => {{1,2,4},{3}} => {{1,2,4},{3}} => {{1,2,4},{3}}
[1,1,1,0,0,0,1,0] => [3,2,1,4] => {{1,3},{2},{4}} => {{1,3},{2},{4}} => {{1,3},{2},{4}}
[1,1,1,0,0,1,0,0] => [3,2,4,1] => {{1,3,4},{2}} => {{1,3,4},{2}} => {{1,3,4},{2}}
[1,1,1,0,1,0,0,0] => [4,2,3,1] => {{1,4},{2},{3}} => {{1,4},{2},{3}} => {{1,4},{2},{3}}
[1,1,1,1,0,0,0,0] => [4,3,2,1] => {{1,4},{2,3}} => {{1,3},{2,4}} => {{1,4},{2,3}}
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => {{1},{2},{3},{4,5}} => {{1},{2},{3},{4,5}} => {{1},{2},{3},{4,5}}
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => {{1},{2},{3,4},{5}} => {{1},{2},{3,4},{5}} => {{1},{2},{3,4},{5}}
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => {{1},{2},{3,4,5}} => {{1},{2},{3,4,5}} => {{1},{2},{3,4,5}}
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => {{1},{2},{3,5},{4}} => {{1},{2},{3,5},{4}} => {{1},{2},{3,5},{4}}
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => {{1},{2,3},{4},{5}} => {{1},{2,3},{4},{5}} => {{1},{2,3},{4},{5}}
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}} => {{1},{2,3},{4,5}} => {{1},{2,3},{4,5}}
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => {{1},{2,3,4},{5}} => {{1},{2,3,4},{5}} => {{1},{2,3,4},{5}}
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => {{1},{2,3,4,5}} => {{1},{2,3,4,5}} => {{1},{2,3,4,5}}
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => {{1},{2,3,5},{4}} => {{1},{2,3,5},{4}} => {{1},{2,3,5},{4}}
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => {{1},{2,4},{3},{5}} => {{1},{2,4},{3},{5}} => {{1},{2,4},{3},{5}}
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => {{1},{2,4,5},{3}} => {{1},{2,4,5},{3}} => {{1},{2,4,5},{3}}
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => {{1},{2,5},{3},{4}} => {{1},{2,5},{3},{4}} => {{1},{2,5},{3},{4}}
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => {{1},{2,5},{3,4}} => {{1},{2,4},{3,5}} => {{1},{2,5},{3,4}}
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => {{1,2},{3},{4},{5}} => {{1,2},{3},{4},{5}}
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => {{1,2},{3},{4,5}} => {{1,2},{3},{4,5}} => {{1,2},{3},{4,5}}
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => {{1,2},{3,4},{5}} => {{1,2},{3,4},{5}} => {{1,2},{3,4},{5}}
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => {{1,2},{3,4,5}} => {{1,2},{3,4,5}} => {{1,2},{3,4,5}}
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => {{1,2},{3,5},{4}} => {{1,2},{3,5},{4}} => {{1,2},{3,5},{4}}
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => {{1,2,3},{4},{5}} => {{1,2,3},{4},{5}}
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => {{1,2,3},{4,5}} => {{1,2,3},{4,5}} => {{1,2,3},{4,5}}
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => {{1,2,3,4},{5}} => {{1,2,3,4},{5}} => {{1,2,3,4},{5}}
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => {{1,2,3,5},{4}} => {{1,2,3,5},{4}} => {{1,2,3,5},{4}}
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => {{1,2,4},{3},{5}} => {{1,2,4},{3},{5}} => {{1,2,4},{3},{5}}
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => {{1,2,4,5},{3}} => {{1,2,4,5},{3}} => {{1,2,4,5},{3}}
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => {{1,2,5},{3},{4}} => {{1,2,5},{3},{4}} => {{1,2,5},{3},{4}}
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => {{1,2,5},{3,4}} => {{1,2,4},{3,5}} => {{1,2,5},{3,4}}
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => {{1,3},{2},{4},{5}} => {{1,3},{2},{4},{5}} => {{1,3},{2},{4},{5}}
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => {{1,3},{2},{4,5}} => {{1,3},{2},{4,5}} => {{1,3},{2},{4,5}}
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => {{1,3,4},{2},{5}} => {{1,3,4},{2},{5}} => {{1,3,4},{2},{5}}
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => {{1,3,4,5},{2}} => {{1,3,4,5},{2}} => {{1,3,4,5},{2}}
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => {{1,3,5},{2},{4}} => {{1,3,5},{2},{4}} => {{1,3,5},{2},{4}}
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => {{1,4},{2},{3},{5}} => {{1,4},{2},{3},{5}} => {{1,4},{2},{3},{5}}
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => {{1,4,5},{2},{3}} => {{1,4,5},{2},{3}} => {{1,4,5},{2},{3}}
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => {{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}}
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => {{1,5},{2},{3,4}} => {{1,4},{2},{3,5}} => {{1,5},{2},{3,4}}
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => {{1,4},{2,3},{5}} => {{1,3},{2,4},{5}} => {{1,4},{2,3},{5}}
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => {{1,4,5},{2,3}} => {{1,3},{2,4,5}} => {{1,4,5},{2,3}}
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => {{1,5},{2,3},{4}} => {{1,3},{2,5},{4}} => {{1,5},{2,3},{4}}
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => {{1,5},{2,3,4}} => {{1,3,5},{2,4}} => {{1,5},{2,3,4}}
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => {{1,5},{2,4},{3}} => {{1,4},{2,5},{3}} => {{1,5},{2,4},{3}}
[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},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}}
[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},{2},{3},{4},{5,6}} => {{1},{2},{3},{4},{5,6}}
[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},{2},{3},{4,5},{6}} => {{1},{2},{3},{4,5},{6}}
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => {{1},{2},{3},{4,5,6}} => {{1},{2},{3},{4,5,6}}
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}} => {{1},{2},{3},{4,6},{5}} => {{1},{2},{3},{4,6},{5}}
[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},{2},{3,4},{5},{6}} => {{1},{2},{3,4},{5},{6}}
[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},{2},{3,4},{5,6}} => {{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => {{1},{2},{3,4,5},{6}} => {{1},{2},{3,4,5},{6}}
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => {{1},{2},{3,4,5,6}} => {{1},{2},{3,4,5,6}}
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => {{1},{2},{3,4,6},{5}} => {{1},{2},{3,4,6},{5}} => {{1},{2},{3,4,6},{5}}
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}} => {{1},{2},{3,5},{4},{6}} => {{1},{2},{3,5},{4},{6}}
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => {{1},{2},{3,5,6},{4}} => {{1},{2},{3,5,6},{4}} => {{1},{2},{3,5,6},{4}}
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => {{1},{2},{3,6},{4},{5}} => {{1},{2},{3,6},{4},{5}} => {{1},{2},{3,6},{4},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => {{1},{2},{3,6},{4,5}} => {{1},{2},{3,5},{4,6}} => {{1},{2},{3,6},{4,5}}
[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},{2,3},{4},{5},{6}} => {{1},{2,3},{4},{5},{6}}
[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},{2,3},{4},{5,6}} => {{1},{2,3},{4},{5,6}}
[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},{2,3},{4,5},{6}} => {{1},{2,3},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => {{1},{2,3},{4,5,6}} => {{1},{2,3},{4,5,6}}
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}} => {{1},{2,3},{4,6},{5}} => {{1},{2,3},{4,6},{5}}
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => {{1},{2,3,4},{5},{6}} => {{1},{2,3,4},{5},{6}}
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => {{1},{2,3,4},{5,6}} => {{1},{2,3,4},{5,6}}
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}}
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => {{1},{2,3,4,5,6}} => {{1},{2,3,4,5,6}}
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => {{1},{2,3,4,6},{5}} => {{1},{2,3,4,6},{5}} => {{1},{2,3,4,6},{5}}
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => {{1},{2,3,5},{4},{6}} => {{1},{2,3,5},{4},{6}} => {{1},{2,3,5},{4},{6}}
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => {{1},{2,3,5,6},{4}} => {{1},{2,3,5,6},{4}} => {{1},{2,3,5,6},{4}}
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => {{1},{2,3,6},{4},{5}} => {{1},{2,3,6},{4},{5}} => {{1},{2,3,6},{4},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => {{1},{2,3,6},{4,5}} => {{1},{2,3,5},{4,6}} => {{1},{2,3,6},{4,5}}
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}} => {{1},{2,4},{3},{5},{6}} => {{1},{2,4},{3},{5},{6}}
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => {{1},{2,4},{3},{5,6}} => {{1},{2,4},{3},{5,6}} => {{1},{2,4},{3},{5,6}}
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => {{1},{2,4,5},{3},{6}} => {{1},{2,4,5},{3},{6}} => {{1},{2,4,5},{3},{6}}
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => {{1},{2,4,5,6},{3}} => {{1},{2,4,5,6},{3}} => {{1},{2,4,5,6},{3}}
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => {{1},{2,4,6},{3},{5}} => {{1},{2,4,6},{3},{5}} => {{1},{2,4,6},{3},{5}}
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => {{1},{2,5},{3},{4},{6}} => {{1},{2,5},{3},{4},{6}} => {{1},{2,5},{3},{4},{6}}
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => {{1},{2,5,6},{3},{4}} => {{1},{2,5,6},{3},{4}} => {{1},{2,5,6},{3},{4}}
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => {{1},{2,6},{3},{4},{5}} => {{1},{2,6},{3},{4},{5}} => {{1},{2,6},{3},{4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => {{1},{2,6},{3},{4,5}} => {{1},{2,5},{3},{4,6}} => {{1},{2,6},{3},{4,5}}
>>> Load all 1538 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => {{1},{2,5},{3,4},{6}} => {{1},{2,4},{3,5},{6}} => {{1},{2,5},{3,4},{6}}
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => {{1},{2,5,6},{3,4}} => {{1},{2,4},{3,5,6}} => {{1},{2,5,6},{3,4}}
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => {{1},{2,6},{3,4},{5}} => {{1},{2,4},{3,6},{5}} => {{1},{2,6},{3,4},{5}}
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => {{1},{2,6},{3,4,5}} => {{1},{2,4,6},{3,5}} => {{1},{2,6},{3,4,5}}
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => {{1},{2,6},{3,5},{4}} => {{1},{2,5},{3,6},{4}} => {{1},{2,6},{3,5},{4}}
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => {{1,2},{3},{4,5},{6}} => {{1,2},{3},{4,5},{6}}
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => {{1,2},{3},{4,5,6}} => {{1,2},{3},{4,5,6}}
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => {{1,2},{3},{4,6},{5}} => {{1,2},{3},{4,6},{5}} => {{1,2},{3},{4,6},{5}}
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => {{1,2},{3,4},{5},{6}} => {{1,2},{3,4},{5},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => {{1,2},{3,4,5},{6}} => {{1,2},{3,4,5},{6}}
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => {{1,2},{3,4,5,6}} => {{1,2},{3,4,5,6}}
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => {{1,2},{3,4,6},{5}} => {{1,2},{3,4,6},{5}} => {{1,2},{3,4,6},{5}}
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => {{1,2},{3,5},{4},{6}} => {{1,2},{3,5},{4},{6}} => {{1,2},{3,5},{4},{6}}
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => {{1,2},{3,5,6},{4}} => {{1,2},{3,5,6},{4}} => {{1,2},{3,5,6},{4}}
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => {{1,2},{3,6},{4},{5}} => {{1,2},{3,6},{4},{5}} => {{1,2},{3,6},{4},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => {{1,2},{3,6},{4,5}} => {{1,2},{3,5},{4,6}} => {{1,2},{3,6},{4,5}}
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => {{1,2,3},{4},{5},{6}} => {{1,2,3},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => {{1,2,3},{4},{5,6}} => {{1,2,3},{4},{5,6}}
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => {{1,2,3},{4,5},{6}} => {{1,2,3},{4,5},{6}}
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}}
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => {{1,2,3},{4,6},{5}} => {{1,2,3},{4,6},{5}} => {{1,2,3},{4,6},{5}}
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => {{1,2,3,4},{5},{6}} => {{1,2,3,4},{5},{6}}
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => {{1,2,3,4},{5,6}} => {{1,2,3,4},{5,6}}
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => {{1,2,3,4,5},{6}} => {{1,2,3,4,5},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => {{1,2,3,4,6},{5}} => {{1,2,3,4,6},{5}} => {{1,2,3,4,6},{5}}
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => {{1,2,3,5},{4},{6}} => {{1,2,3,5},{4},{6}} => {{1,2,3,5},{4},{6}}
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => {{1,2,3,5,6},{4}} => {{1,2,3,5,6},{4}} => {{1,2,3,5,6},{4}}
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => {{1,2,3,6},{4},{5}} => {{1,2,3,6},{4},{5}} => {{1,2,3,6},{4},{5}}
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => {{1,2,3,6},{4,5}} => {{1,2,3,5},{4,6}} => {{1,2,3,6},{4,5}}
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => {{1,2,4},{3},{5},{6}} => {{1,2,4},{3},{5},{6}} => {{1,2,4},{3},{5},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => {{1,2,4},{3},{5,6}} => {{1,2,4},{3},{5,6}} => {{1,2,4},{3},{5,6}}
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => {{1,2,4,5},{3},{6}} => {{1,2,4,5},{3},{6}} => {{1,2,4,5},{3},{6}}
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => {{1,2,4,5,6},{3}} => {{1,2,4,5,6},{3}} => {{1,2,4,5,6},{3}}
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => {{1,2,4,6},{3},{5}} => {{1,2,4,6},{3},{5}} => {{1,2,4,6},{3},{5}}
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => {{1,2,5},{3},{4},{6}} => {{1,2,5},{3},{4},{6}} => {{1,2,5},{3},{4},{6}}
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => {{1,2,5,6},{3},{4}} => {{1,2,5,6},{3},{4}} => {{1,2,5,6},{3},{4}}
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => {{1,2,6},{3},{4},{5}} => {{1,2,6},{3},{4},{5}} => {{1,2,6},{3},{4},{5}}
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => {{1,2,6},{3},{4,5}} => {{1,2,5},{3},{4,6}} => {{1,2,6},{3},{4,5}}
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => {{1,2,5},{3,4},{6}} => {{1,2,4},{3,5},{6}} => {{1,2,5},{3,4},{6}}
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => {{1,2,5,6},{3,4}} => {{1,2,4},{3,5,6}} => {{1,2,5,6},{3,4}}
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => {{1,2,6},{3,4},{5}} => {{1,2,4},{3,6},{5}} => {{1,2,6},{3,4},{5}}
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => {{1,2,6},{3,4,5}} => {{1,2,4,6},{3,5}} => {{1,2,6},{3,4,5}}
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => {{1,2,6},{3,5},{4}} => {{1,2,5},{3,6},{4}} => {{1,2,6},{3,5},{4}}
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}} => {{1,3},{2},{4},{5},{6}} => {{1,3},{2},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => {{1,3},{2},{4},{5,6}} => {{1,3},{2},{4},{5,6}} => {{1,3},{2},{4},{5,6}}
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => {{1,3},{2},{4,5},{6}} => {{1,3},{2},{4,5},{6}} => {{1,3},{2},{4,5},{6}}
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => {{1,3},{2},{4,5,6}} => {{1,3},{2},{4,5,6}} => {{1,3},{2},{4,5,6}}
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => {{1,3},{2},{4,6},{5}} => {{1,3},{2},{4,6},{5}} => {{1,3},{2},{4,6},{5}}
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => {{1,3,4},{2},{5},{6}} => {{1,3,4},{2},{5},{6}} => {{1,3,4},{2},{5},{6}}
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => {{1,3,4},{2},{5,6}} => {{1,3,4},{2},{5,6}} => {{1,3,4},{2},{5,6}}
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => {{1,3,4,5},{2},{6}} => {{1,3,4,5},{2},{6}} => {{1,3,4,5},{2},{6}}
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => {{1,3,4,5,6},{2}} => {{1,3,4,5,6},{2}} => {{1,3,4,5,6},{2}}
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => {{1,3,4,6},{2},{5}} => {{1,3,4,6},{2},{5}} => {{1,3,4,6},{2},{5}}
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => {{1,3,5},{2},{4},{6}} => {{1,3,5},{2},{4},{6}} => {{1,3,5},{2},{4},{6}}
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => {{1,3,5,6},{2},{4}} => {{1,3,5,6},{2},{4}} => {{1,3,5,6},{2},{4}}
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => {{1,3,6},{2},{4},{5}} => {{1,3,6},{2},{4},{5}} => {{1,3,6},{2},{4},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => {{1,3,6},{2},{4,5}} => {{1,3,5},{2},{4,6}} => {{1,3,6},{2},{4,5}}
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => {{1,4},{2},{3},{5},{6}} => {{1,4},{2},{3},{5},{6}} => {{1,4},{2},{3},{5},{6}}
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => {{1,4},{2},{3},{5,6}} => {{1,4},{2},{3},{5,6}} => {{1,4},{2},{3},{5,6}}
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => {{1,4,5},{2},{3},{6}} => {{1,4,5},{2},{3},{6}} => {{1,4,5},{2},{3},{6}}
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => {{1,4,5,6},{2},{3}} => {{1,4,5,6},{2},{3}} => {{1,4,5,6},{2},{3}}
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => {{1,4,6},{2},{3},{5}} => {{1,4,6},{2},{3},{5}} => {{1,4,6},{2},{3},{5}}
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => {{1,5},{2},{3},{4},{6}} => {{1,5},{2},{3},{4},{6}} => {{1,5},{2},{3},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => {{1,5,6},{2},{3},{4}} => {{1,5,6},{2},{3},{4}} => {{1,5,6},{2},{3},{4}}
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => {{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}}
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => {{1,6},{2},{3},{4,5}} => {{1,5},{2},{3},{4,6}} => {{1,6},{2},{3},{4,5}}
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => {{1,5},{2},{3,4},{6}} => {{1,4},{2},{3,5},{6}} => {{1,5},{2},{3,4},{6}}
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => {{1,5,6},{2},{3,4}} => {{1,4},{2},{3,5,6}} => {{1,5,6},{2},{3,4}}
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => {{1,6},{2},{3,4},{5}} => {{1,4},{2},{3,6},{5}} => {{1,6},{2},{3,4},{5}}
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => {{1,6},{2},{3,4,5}} => {{1,4,6},{2},{3,5}} => {{1,6},{2},{3,4,5}}
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => {{1,6},{2},{3,5},{4}} => {{1,5},{2},{3,6},{4}} => {{1,6},{2},{3,5},{4}}
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}} => {{1,3},{2,4},{5},{6}} => {{1,4},{2,3},{5},{6}}
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => {{1,4},{2,3},{5,6}} => {{1,3},{2,4},{5,6}} => {{1,4},{2,3},{5,6}}
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => {{1,4,5},{2,3},{6}} => {{1,3},{2,4,5},{6}} => {{1,4,5},{2,3},{6}}
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => {{1,4,5,6},{2,3}} => {{1,3},{2,4,5,6}} => {{1,4,5,6},{2,3}}
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => {{1,4,6},{2,3},{5}} => {{1,3},{2,4,6},{5}} => {{1,4,6},{2,3},{5}}
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => {{1,5},{2,3},{4},{6}} => {{1,3},{2,5},{4},{6}} => {{1,5},{2,3},{4},{6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => {{1,5,6},{2,3},{4}} => {{1,3},{2,5,6},{4}} => {{1,5,6},{2,3},{4}}
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => {{1,6},{2,3},{4},{5}} => {{1,3},{2,6},{4},{5}} => {{1,6},{2,3},{4},{5}}
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => {{1,6},{2,3},{4,5}} => {{1,3},{2,5},{4,6}} => {{1,6},{2,3},{4,5}}
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => {{1,5},{2,3,4},{6}} => {{1,3,5},{2,4},{6}} => {{1,5},{2,3,4},{6}}
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => {{1,5,6},{2,3,4}} => {{1,3,5,6},{2,4}} => {{1,5,6},{2,3,4}}
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => {{1,6},{2,3,4},{5}} => {{1,3,6},{2,4},{5}} => {{1,6},{2,3,4},{5}}
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => {{1,6},{2,3,4,5}} => {{1,3,5},{2,4,6}} => {{1,6},{2,3,4,5}}
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => {{1,6},{2,3,5},{4}} => {{1,3,6},{2,5},{4}} => {{1,6},{2,3,5},{4}}
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}} => {{1,4},{2,5},{3},{6}} => {{1,5},{2,4},{3},{6}}
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => {{1,5,6},{2,4},{3}} => {{1,4},{2,5,6},{3}} => {{1,5,6},{2,4},{3}}
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => {{1,6},{2,4},{3},{5}} => {{1,4},{2,6},{3},{5}} => {{1,6},{2,4},{3},{5}}
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => {{1,6},{2,4,5},{3}} => {{1,4,6},{2,5},{3}} => {{1,6},{2,4,5},{3}}
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => {{1,6},{2,5},{3},{4}} => {{1,5},{2,6},{3},{4}} => {{1,6},{2,5},{3},{4}}
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => {{1,6},{2,5},{3,4}} => {{1,4},{2,5},{3,6}} => {{1,6},{2,5},{3,4}}
[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},{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] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => {{1},{2},{3},{4},{5},{6,7}} => {{1},{2},{3},{4},{5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}} => {{1},{2},{3},{4},{5,6},{7}} => {{1},{2},{3},{4},{5,6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}} => {{1},{2},{3},{4},{5,6,7}} => {{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => {{1},{2},{3},{4},{5,7},{6}} => {{1},{2},{3},{4},{5,7},{6}} => {{1},{2},{3},{4},{5,7},{6}}
[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},{2},{3},{4,5},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}} => {{1},{2},{3},{4,5},{6,7}} => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}} => {{1},{2},{3},{4,5,6},{7}} => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}} => {{1},{2},{3},{4,5,6,7}} => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => {{1},{2},{3},{4,5,7},{6}} => {{1},{2},{3},{4,5,7},{6}} => {{1},{2},{3},{4,5,7},{6}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}} => {{1},{2},{3},{4,6},{5},{7}} => {{1},{2},{3},{4,6},{5},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => {{1},{2},{3},{4,6,7},{5}} => {{1},{2},{3},{4,6,7},{5}} => {{1},{2},{3},{4,6,7},{5}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => {{1},{2},{3},{4,7},{5},{6}} => {{1},{2},{3},{4,7},{5},{6}} => {{1},{2},{3},{4,7},{5},{6}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => {{1},{2},{3},{4,7},{5,6}} => {{1},{2},{3},{4,6},{5,7}} => {{1},{2},{3},{4,7},{5,6}}
[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},{2},{3,4},{5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}} => {{1},{2},{3,4},{5},{6,7}} => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}} => {{1},{2},{3,4},{5,6},{7}} => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}} => {{1},{2},{3,4},{5,6,7}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => {{1},{2},{3,4},{5,7},{6}} => {{1},{2},{3,4},{5,7},{6}} => {{1},{2},{3,4},{5,7},{6}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}} => {{1},{2},{3,4,5},{6,7}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}} => {{1},{2},{3,4,5,6},{7}} => {{1},{2},{3,4,5,6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}} => {{1},{2},{3,4,5,6,7}} => {{1},{2},{3,4,5,6,7}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => {{1},{2},{3,4,5,7},{6}} => {{1},{2},{3,4,5,7},{6}} => {{1},{2},{3,4,5,7},{6}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => {{1},{2},{3,4,6},{5},{7}} => {{1},{2},{3,4,6},{5},{7}} => {{1},{2},{3,4,6},{5},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => {{1},{2},{3,4,6,7},{5}} => {{1},{2},{3,4,6,7},{5}} => {{1},{2},{3,4,6,7},{5}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => {{1},{2},{3,4,7},{5},{6}} => {{1},{2},{3,4,7},{5},{6}} => {{1},{2},{3,4,7},{5},{6}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => {{1},{2},{3,4,7},{5,6}} => {{1},{2},{3,4,6},{5,7}} => {{1},{2},{3,4,7},{5,6}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => {{1},{2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => {{1},{2},{3,5},{4},{6,7}} => {{1},{2},{3,5},{4},{6,7}} => {{1},{2},{3,5},{4},{6,7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => {{1},{2},{3,5,6},{4},{7}} => {{1},{2},{3,5,6},{4},{7}} => {{1},{2},{3,5,6},{4},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => {{1},{2},{3,5,6,7},{4}} => {{1},{2},{3,5,6,7},{4}} => {{1},{2},{3,5,6,7},{4}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => {{1},{2},{3,5,7},{4},{6}} => {{1},{2},{3,5,7},{4},{6}} => {{1},{2},{3,5,7},{4},{6}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => {{1},{2},{3,6},{4},{5},{7}} => {{1},{2},{3,6},{4},{5},{7}} => {{1},{2},{3,6},{4},{5},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => {{1},{2},{3,6,7},{4},{5}} => {{1},{2},{3,6,7},{4},{5}} => {{1},{2},{3,6,7},{4},{5}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => {{1},{2},{3,7},{4},{5},{6}} => {{1},{2},{3,7},{4},{5},{6}} => {{1},{2},{3,7},{4},{5},{6}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => {{1},{2},{3,7},{4},{5,6}} => {{1},{2},{3,6},{4},{5,7}} => {{1},{2},{3,7},{4},{5,6}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => {{1},{2},{3,6},{4,5},{7}} => {{1},{2},{3,5},{4,6},{7}} => {{1},{2},{3,6},{4,5},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => {{1},{2},{3,6,7},{4,5}} => {{1},{2},{3,5},{4,6,7}} => {{1},{2},{3,6,7},{4,5}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => {{1},{2},{3,7},{4,5},{6}} => {{1},{2},{3,5},{4,7},{6}} => {{1},{2},{3,7},{4,5},{6}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => {{1},{2},{3,7},{4,5,6}} => {{1},{2},{3,5,7},{4,6}} => {{1},{2},{3,7},{4,5,6}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => {{1},{2},{3,7},{4,6},{5}} => {{1},{2},{3,6},{4,7},{5}} => {{1},{2},{3,7},{4,6},{5}}
[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},{2,3},{4},{5},{6},{7}} => {{1},{2,3},{4},{5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}} => {{1},{2,3},{4},{5},{6,7}} => {{1},{2,3},{4},{5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}} => {{1},{2,3},{4},{5,6,7}} => {{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => {{1},{2,3},{4},{5,7},{6}} => {{1},{2,3},{4},{5,7},{6}} => {{1},{2,3},{4},{5,7},{6}}
[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},{2,3},{4,5},{6},{7}} => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}} => {{1},{2,3},{4,5},{6,7}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}} => {{1},{2,3},{4,5,6},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}} => {{1},{2,3},{4,5,6,7}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => {{1},{2,3},{4,5,7},{6}} => {{1},{2,3},{4,5,7},{6}} => {{1},{2,3},{4,5,7},{6}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => {{1},{2,3},{4,6},{5},{7}} => {{1},{2,3},{4,6},{5},{7}} => {{1},{2,3},{4,6},{5},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => {{1},{2,3},{4,6,7},{5}} => {{1},{2,3},{4,6,7},{5}} => {{1},{2,3},{4,6,7},{5}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => {{1},{2,3},{4,7},{5},{6}} => {{1},{2,3},{4,7},{5},{6}} => {{1},{2,3},{4,7},{5},{6}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => {{1},{2,3},{4,7},{5,6}} => {{1},{2,3},{4,6},{5,7}} => {{1},{2,3},{4,7},{5,6}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => {{1},{2,3,4},{5},{6},{7}} => {{1},{2,3,4},{5},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}} => {{1},{2,3,4},{5},{6,7}} => {{1},{2,3,4},{5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}} => {{1},{2,3,4},{5,6},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}} => {{1},{2,3,4},{5,6,7}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => {{1},{2,3,4},{5,7},{6}} => {{1},{2,3,4},{5,7},{6}} => {{1},{2,3,4},{5,7},{6}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}} => {{1},{2,3,4,5},{6},{7}} => {{1},{2,3,4,5},{6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}} => {{1},{2,3,4,5},{6,7}} => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}} => {{1},{2,3,4,5,6,7}} => {{1},{2,3,4,5,6,7}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => {{1},{2,3,4,5,7},{6}} => {{1},{2,3,4,5,7},{6}} => {{1},{2,3,4,5,7},{6}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => {{1},{2,3,4,6},{5},{7}} => {{1},{2,3,4,6},{5},{7}} => {{1},{2,3,4,6},{5},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => {{1},{2,3,4,6,7},{5}} => {{1},{2,3,4,6,7},{5}} => {{1},{2,3,4,6,7},{5}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => {{1},{2,3,4,7},{5},{6}} => {{1},{2,3,4,7},{5},{6}} => {{1},{2,3,4,7},{5},{6}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => {{1},{2,3,4,7},{5,6}} => {{1},{2,3,4,6},{5,7}} => {{1},{2,3,4,7},{5,6}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => {{1},{2,3,5},{4},{6},{7}} => {{1},{2,3,5},{4},{6},{7}} => {{1},{2,3,5},{4},{6},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => {{1},{2,3,5},{4},{6,7}} => {{1},{2,3,5},{4},{6,7}} => {{1},{2,3,5},{4},{6,7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => {{1},{2,3,5,6},{4},{7}} => {{1},{2,3,5,6},{4},{7}} => {{1},{2,3,5,6},{4},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => {{1},{2,3,5,6,7},{4}} => {{1},{2,3,5,6,7},{4}} => {{1},{2,3,5,6,7},{4}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => {{1},{2,3,5,7},{4},{6}} => {{1},{2,3,5,7},{4},{6}} => {{1},{2,3,5,7},{4},{6}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => {{1},{2,3,6},{4},{5},{7}} => {{1},{2,3,6},{4},{5},{7}} => {{1},{2,3,6},{4},{5},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => {{1},{2,3,6,7},{4},{5}} => {{1},{2,3,6,7},{4},{5}} => {{1},{2,3,6,7},{4},{5}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => {{1},{2,3,7},{4},{5},{6}} => {{1},{2,3,7},{4},{5},{6}} => {{1},{2,3,7},{4},{5},{6}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => {{1},{2,3,7},{4},{5,6}} => {{1},{2,3,6},{4},{5,7}} => {{1},{2,3,7},{4},{5,6}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => {{1},{2,3,6},{4,5},{7}} => {{1},{2,3,5},{4,6},{7}} => {{1},{2,3,6},{4,5},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => {{1},{2,3,6,7},{4,5}} => {{1},{2,3,5},{4,6,7}} => {{1},{2,3,6,7},{4,5}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => {{1},{2,3,7},{4,5},{6}} => {{1},{2,3,5},{4,7},{6}} => {{1},{2,3,7},{4,5},{6}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => {{1},{2,3,7},{4,5,6}} => {{1},{2,3,5,7},{4,6}} => {{1},{2,3,7},{4,5,6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => {{1},{2,3,7},{4,6},{5}} => {{1},{2,3,6},{4,7},{5}} => {{1},{2,3,7},{4,6},{5}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => {{1},{2,4},{3},{5},{6},{7}} => {{1},{2,4},{3},{5},{6},{7}} => {{1},{2,4},{3},{5},{6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => {{1},{2,4},{3},{5},{6,7}} => {{1},{2,4},{3},{5},{6,7}} => {{1},{2,4},{3},{5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => {{1},{2,4},{3},{5,6},{7}} => {{1},{2,4},{3},{5,6},{7}} => {{1},{2,4},{3},{5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => {{1},{2,4},{3},{5,6,7}} => {{1},{2,4},{3},{5,6,7}} => {{1},{2,4},{3},{5,6,7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => {{1},{2,4},{3},{5,7},{6}} => {{1},{2,4},{3},{5,7},{6}} => {{1},{2,4},{3},{5,7},{6}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => {{1},{2,4,5},{3},{6},{7}} => {{1},{2,4,5},{3},{6},{7}} => {{1},{2,4,5},{3},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => {{1},{2,4,5},{3},{6,7}} => {{1},{2,4,5},{3},{6,7}} => {{1},{2,4,5},{3},{6,7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => {{1},{2,4,5,6},{3},{7}} => {{1},{2,4,5,6},{3},{7}} => {{1},{2,4,5,6},{3},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => {{1},{2,4,5,6,7},{3}} => {{1},{2,4,5,6,7},{3}} => {{1},{2,4,5,6,7},{3}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => {{1},{2,4,5,7},{3},{6}} => {{1},{2,4,5,7},{3},{6}} => {{1},{2,4,5,7},{3},{6}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => {{1},{2,4,6},{3},{5},{7}} => {{1},{2,4,6},{3},{5},{7}} => {{1},{2,4,6},{3},{5},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => {{1},{2,4,6,7},{3},{5}} => {{1},{2,4,6,7},{3},{5}} => {{1},{2,4,6,7},{3},{5}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => {{1},{2,4,7},{3},{5},{6}} => {{1},{2,4,7},{3},{5},{6}} => {{1},{2,4,7},{3},{5},{6}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => {{1},{2,4,7},{3},{5,6}} => {{1},{2,4,6},{3},{5,7}} => {{1},{2,4,7},{3},{5,6}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => {{1},{2,5},{3},{4},{6},{7}} => {{1},{2,5},{3},{4},{6},{7}} => {{1},{2,5},{3},{4},{6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => {{1},{2,5},{3},{4},{6,7}} => {{1},{2,5},{3},{4},{6,7}} => {{1},{2,5},{3},{4},{6,7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => {{1},{2,5,6},{3},{4},{7}} => {{1},{2,5,6},{3},{4},{7}} => {{1},{2,5,6},{3},{4},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => {{1},{2,5,6,7},{3},{4}} => {{1},{2,5,6,7},{3},{4}} => {{1},{2,5,6,7},{3},{4}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => {{1},{2,5,7},{3},{4},{6}} => {{1},{2,5,7},{3},{4},{6}} => {{1},{2,5,7},{3},{4},{6}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => {{1},{2,6},{3},{4},{5},{7}} => {{1},{2,6},{3},{4},{5},{7}} => {{1},{2,6},{3},{4},{5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => {{1},{2,6,7},{3},{4},{5}} => {{1},{2,6,7},{3},{4},{5}} => {{1},{2,6,7},{3},{4},{5}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => {{1},{2,7},{3},{4},{5},{6}} => {{1},{2,7},{3},{4},{5},{6}} => {{1},{2,7},{3},{4},{5},{6}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => {{1},{2,7},{3},{4},{5,6}} => {{1},{2,6},{3},{4},{5,7}} => {{1},{2,7},{3},{4},{5,6}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => {{1},{2,6},{3},{4,5},{7}} => {{1},{2,5},{3},{4,6},{7}} => {{1},{2,6},{3},{4,5},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => {{1},{2,6,7},{3},{4,5}} => {{1},{2,5},{3},{4,6,7}} => {{1},{2,6,7},{3},{4,5}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => {{1},{2,7},{3},{4,5},{6}} => {{1},{2,5},{3},{4,7},{6}} => {{1},{2,7},{3},{4,5},{6}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => {{1},{2,7},{3},{4,5,6}} => {{1},{2,5,7},{3},{4,6}} => {{1},{2,7},{3},{4,5,6}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => {{1},{2,7},{3},{4,6},{5}} => {{1},{2,6},{3},{4,7},{5}} => {{1},{2,7},{3},{4,6},{5}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => {{1},{2,5},{3,4},{6},{7}} => {{1},{2,4},{3,5},{6},{7}} => {{1},{2,5},{3,4},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => {{1},{2,5},{3,4},{6,7}} => {{1},{2,4},{3,5},{6,7}} => {{1},{2,5},{3,4},{6,7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => {{1},{2,5,6},{3,4},{7}} => {{1},{2,4},{3,5,6},{7}} => {{1},{2,5,6},{3,4},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => {{1},{2,5,6,7},{3,4}} => {{1},{2,4},{3,5,6,7}} => {{1},{2,5,6,7},{3,4}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => {{1},{2,5,7},{3,4},{6}} => {{1},{2,4},{3,5,7},{6}} => {{1},{2,5,7},{3,4},{6}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => {{1},{2,6},{3,4},{5},{7}} => {{1},{2,4},{3,6},{5},{7}} => {{1},{2,6},{3,4},{5},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => {{1},{2,6,7},{3,4},{5}} => {{1},{2,4},{3,6,7},{5}} => {{1},{2,6,7},{3,4},{5}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => {{1},{2,7},{3,4},{5},{6}} => {{1},{2,4},{3,7},{5},{6}} => {{1},{2,7},{3,4},{5},{6}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => {{1},{2,7},{3,4},{5,6}} => {{1},{2,4},{3,6},{5,7}} => {{1},{2,7},{3,4},{5,6}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => {{1},{2,6},{3,4,5},{7}} => {{1},{2,4,6},{3,5},{7}} => {{1},{2,6},{3,4,5},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => {{1},{2,6,7},{3,4,5}} => {{1},{2,4,6,7},{3,5}} => {{1},{2,6,7},{3,4,5}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => {{1},{2,7},{3,4,5},{6}} => {{1},{2,4,7},{3,5},{6}} => {{1},{2,7},{3,4,5},{6}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => {{1},{2,7},{3,4,5,6}} => {{1},{2,4,6},{3,5,7}} => {{1},{2,7},{3,4,5,6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => {{1},{2,7},{3,4,6},{5}} => {{1},{2,4,7},{3,6},{5}} => {{1},{2,7},{3,4,6},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => {{1},{2,6},{3,5},{4},{7}} => {{1},{2,5},{3,6},{4},{7}} => {{1},{2,6},{3,5},{4},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => {{1},{2,6,7},{3,5},{4}} => {{1},{2,5},{3,6,7},{4}} => {{1},{2,6,7},{3,5},{4}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => {{1},{2,7},{3,5},{4},{6}} => {{1},{2,5},{3,7},{4},{6}} => {{1},{2,7},{3,5},{4},{6}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => {{1},{2,7},{3,5,6},{4}} => {{1},{2,5,7},{3,6},{4}} => {{1},{2,7},{3,5,6},{4}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => {{1},{2,7},{3,6},{4},{5}} => {{1},{2,6},{3,7},{4},{5}} => {{1},{2,7},{3,6},{4},{5}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => {{1},{2,7},{3,6},{4,5}} => {{1},{2,5},{3,6},{4,7}} => {{1},{2,7},{3,6},{4,5}}
[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}} => {{1,2},{3},{4},{5},{6},{7}} => {{1,2},{3},{4},{5},{6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => {{1,2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => {{1,2},{3},{4},{5,6},{7}} => {{1,2},{3},{4},{5,6},{7}} => {{1,2},{3},{4},{5,6},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => {{1,2},{3},{4},{5,6,7}} => {{1,2},{3},{4},{5,6,7}} => {{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => {{1,2},{3},{4},{5,7},{6}} => {{1,2},{3},{4},{5,7},{6}} => {{1,2},{3},{4},{5,7},{6}}
[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}} => {{1,2},{3},{4,5},{6},{7}} => {{1,2},{3},{4,5},{6},{7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}} => {{1,2},{3},{4,5},{6,7}} => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => {{1,2},{3},{4,5,6},{7}} => {{1,2},{3},{4,5,6},{7}} => {{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => {{1,2},{3},{4,5,6,7}} => {{1,2},{3},{4,5,6,7}} => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => {{1,2},{3},{4,5,7},{6}} => {{1,2},{3},{4,5,7},{6}} => {{1,2},{3},{4,5,7},{6}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => {{1,2},{3},{4,6},{5},{7}} => {{1,2},{3},{4,6},{5},{7}} => {{1,2},{3},{4,6},{5},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => {{1,2},{3},{4,6,7},{5}} => {{1,2},{3},{4,6,7},{5}} => {{1,2},{3},{4,6,7},{5}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => {{1,2},{3},{4,7},{5},{6}} => {{1,2},{3},{4,7},{5},{6}} => {{1,2},{3},{4,7},{5},{6}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => {{1,2},{3},{4,7},{5,6}} => {{1,2},{3},{4,6},{5,7}} => {{1,2},{3},{4,7},{5,6}}
[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}} => {{1,2},{3,4},{5},{6},{7}} => {{1,2},{3,4},{5},{6},{7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}} => {{1,2},{3,4},{5},{6,7}} => {{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}} => {{1,2},{3,4},{5,6},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => {{1,2},{3,4},{5,6,7}} => {{1,2},{3,4},{5,6,7}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => {{1,2},{3,4},{5,7},{6}} => {{1,2},{3,4},{5,7},{6}} => {{1,2},{3,4},{5,7},{6}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => {{1,2},{3,4,5},{6},{7}} => {{1,2},{3,4,5},{6},{7}} => {{1,2},{3,4,5},{6},{7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => {{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => {{1,2},{3,4,5,6},{7}} => {{1,2},{3,4,5,6},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => {{1,2},{3,4,5,6,7}} => {{1,2},{3,4,5,6,7}} => {{1,2},{3,4,5,6,7}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => {{1,2},{3,4,5,7},{6}} => {{1,2},{3,4,5,7},{6}} => {{1,2},{3,4,5,7},{6}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => {{1,2},{3,4,6},{5},{7}} => {{1,2},{3,4,6},{5},{7}} => {{1,2},{3,4,6},{5},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => {{1,2},{3,4,6,7},{5}} => {{1,2},{3,4,6,7},{5}} => {{1,2},{3,4,6,7},{5}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => {{1,2},{3,4,7},{5},{6}} => {{1,2},{3,4,7},{5},{6}} => {{1,2},{3,4,7},{5},{6}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => {{1,2},{3,4,7},{5,6}} => {{1,2},{3,4,6},{5,7}} => {{1,2},{3,4,7},{5,6}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => {{1,2},{3,5},{4},{6},{7}} => {{1,2},{3,5},{4},{6},{7}} => {{1,2},{3,5},{4},{6},{7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => {{1,2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6,7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => {{1,2},{3,5,6},{4},{7}} => {{1,2},{3,5,6},{4},{7}} => {{1,2},{3,5,6},{4},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => {{1,2},{3,5,6,7},{4}} => {{1,2},{3,5,6,7},{4}} => {{1,2},{3,5,6,7},{4}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => {{1,2},{3,5,7},{4},{6}} => {{1,2},{3,5,7},{4},{6}} => {{1,2},{3,5,7},{4},{6}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => {{1,2},{3,6},{4},{5},{7}} => {{1,2},{3,6},{4},{5},{7}} => {{1,2},{3,6},{4},{5},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => {{1,2},{3,6,7},{4},{5}} => {{1,2},{3,6,7},{4},{5}} => {{1,2},{3,6,7},{4},{5}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => {{1,2},{3,7},{4},{5},{6}} => {{1,2},{3,7},{4},{5},{6}} => {{1,2},{3,7},{4},{5},{6}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => {{1,2},{3,7},{4},{5,6}} => {{1,2},{3,6},{4},{5,7}} => {{1,2},{3,7},{4},{5,6}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => {{1,2},{3,6},{4,5},{7}} => {{1,2},{3,5},{4,6},{7}} => {{1,2},{3,6},{4,5},{7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => {{1,2},{3,6,7},{4,5}} => {{1,2},{3,5},{4,6,7}} => {{1,2},{3,6,7},{4,5}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => {{1,2},{3,7},{4,5},{6}} => {{1,2},{3,5},{4,7},{6}} => {{1,2},{3,7},{4,5},{6}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => {{1,2},{3,7},{4,5,6}} => {{1,2},{3,5,7},{4,6}} => {{1,2},{3,7},{4,5,6}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => {{1,2},{3,7},{4,6},{5}} => {{1,2},{3,6},{4,7},{5}} => {{1,2},{3,7},{4,6},{5}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => {{1,2,3},{4},{5},{6},{7}} => {{1,2,3},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => {{1,2,3},{4},{5},{6,7}} => {{1,2,3},{4},{5},{6,7}} => {{1,2,3},{4},{5},{6,7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => {{1,2,3},{4},{5,6},{7}} => {{1,2,3},{4},{5,6},{7}} => {{1,2,3},{4},{5,6},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => {{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => {{1,2,3},{4},{5,7},{6}} => {{1,2,3},{4},{5,7},{6}} => {{1,2,3},{4},{5,7},{6}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => {{1,2,3},{4,5},{6},{7}} => {{1,2,3},{4,5},{6},{7}} => {{1,2,3},{4,5},{6},{7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => {{1,2,3},{4,5},{6,7}} => {{1,2,3},{4,5},{6,7}} => {{1,2,3},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => {{1,2,3},{4,5,6},{7}} => {{1,2,3},{4,5,6},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => {{1,2,3},{4,5,6,7}} => {{1,2,3},{4,5,6,7}} => {{1,2,3},{4,5,6,7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => {{1,2,3},{4,5,7},{6}} => {{1,2,3},{4,5,7},{6}} => {{1,2,3},{4,5,7},{6}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => {{1,2,3},{4,6},{5},{7}} => {{1,2,3},{4,6},{5},{7}} => {{1,2,3},{4,6},{5},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => {{1,2,3},{4,6,7},{5}} => {{1,2,3},{4,6,7},{5}} => {{1,2,3},{4,6,7},{5}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => {{1,2,3},{4,7},{5},{6}} => {{1,2,3},{4,7},{5},{6}} => {{1,2,3},{4,7},{5},{6}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => {{1,2,3},{4,7},{5,6}} => {{1,2,3},{4,6},{5,7}} => {{1,2,3},{4,7},{5,6}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => {{1,2,3,4},{5},{6},{7}} => {{1,2,3,4},{5},{6},{7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => {{1,2,3,4},{5},{6,7}} => {{1,2,3,4},{5},{6,7}} => {{1,2,3,4},{5},{6,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => {{1,2,3,4},{5,6},{7}} => {{1,2,3,4},{5,6},{7}} => {{1,2,3,4},{5,6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4},{5,6,7}} => {{1,2,3,4},{5,6,7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => {{1,2,3,4},{5,7},{6}} => {{1,2,3,4},{5,7},{6}} => {{1,2,3,4},{5,7},{6}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => {{1,2,3,4,5},{6},{7}} => {{1,2,3,4,5},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}} => {{1,2,3,4,5,6},{7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5,7},{6}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => {{1,2,3,4,6},{5},{7}} => {{1,2,3,4,6},{5},{7}} => {{1,2,3,4,6},{5},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => {{1,2,3,4,6,7},{5}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4,6,7},{5}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => {{1,2,3,4,7},{5},{6}} => {{1,2,3,4,7},{5},{6}} => {{1,2,3,4,7},{5},{6}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => {{1,2,3,4,7},{5,6}} => {{1,2,3,4,6},{5,7}} => {{1,2,3,4,7},{5,6}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => {{1,2,3,5},{4},{6},{7}} => {{1,2,3,5},{4},{6},{7}} => {{1,2,3,5},{4},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => {{1,2,3,5},{4},{6,7}} => {{1,2,3,5},{4},{6,7}} => {{1,2,3,5},{4},{6,7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => {{1,2,3,5,6},{4},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3,5,6},{4},{7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => {{1,2,3,5,7},{4},{6}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3,5,7},{4},{6}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => {{1,2,3,6},{4},{5},{7}} => {{1,2,3,6},{4},{5},{7}} => {{1,2,3,6},{4},{5},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => {{1,2,3,6,7},{4},{5}} => {{1,2,3,6,7},{4},{5}} => {{1,2,3,6,7},{4},{5}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => {{1,2,3,7},{4},{5},{6}} => {{1,2,3,7},{4},{5},{6}} => {{1,2,3,7},{4},{5},{6}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => {{1,2,3,7},{4},{5,6}} => {{1,2,3,6},{4},{5,7}} => {{1,2,3,7},{4},{5,6}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => {{1,2,3,6},{4,5},{7}} => {{1,2,3,5},{4,6},{7}} => {{1,2,3,6},{4,5},{7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => {{1,2,3,6,7},{4,5}} => {{1,2,3,5},{4,6,7}} => {{1,2,3,6,7},{4,5}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => {{1,2,3,7},{4,5},{6}} => {{1,2,3,5},{4,7},{6}} => {{1,2,3,7},{4,5},{6}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => {{1,2,3,7},{4,5,6}} => {{1,2,3,5,7},{4,6}} => {{1,2,3,7},{4,5,6}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => {{1,2,3,7},{4,6},{5}} => {{1,2,3,6},{4,7},{5}} => {{1,2,3,7},{4,6},{5}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => {{1,2,4},{3},{5},{6},{7}} => {{1,2,4},{3},{5},{6},{7}} => {{1,2,4},{3},{5},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => {{1,2,4},{3},{5},{6,7}} => {{1,2,4},{3},{5},{6,7}} => {{1,2,4},{3},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => {{1,2,4},{3},{5,6},{7}} => {{1,2,4},{3},{5,6},{7}} => {{1,2,4},{3},{5,6},{7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => {{1,2,4},{3},{5,6,7}} => {{1,2,4},{3},{5,6,7}} => {{1,2,4},{3},{5,6,7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => {{1,2,4},{3},{5,7},{6}} => {{1,2,4},{3},{5,7},{6}} => {{1,2,4},{3},{5,7},{6}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => {{1,2,4,5},{3},{6},{7}} => {{1,2,4,5},{3},{6},{7}} => {{1,2,4,5},{3},{6},{7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => {{1,2,4,5},{3},{6,7}} => {{1,2,4,5},{3},{6,7}} => {{1,2,4,5},{3},{6,7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => {{1,2,4,5,6},{3},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2,4,5,6},{3},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => {{1,2,4,5,6,7},{3}} => {{1,2,4,5,6,7},{3}} => {{1,2,4,5,6,7},{3}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => {{1,2,4,5,7},{3},{6}} => {{1,2,4,5,7},{3},{6}} => {{1,2,4,5,7},{3},{6}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => {{1,2,4,6},{3},{5},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1,2,4,6},{3},{5},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => {{1,2,4,6,7},{3},{5}} => {{1,2,4,6,7},{3},{5}} => {{1,2,4,6,7},{3},{5}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => {{1,2,4,7},{3},{5},{6}} => {{1,2,4,7},{3},{5},{6}} => {{1,2,4,7},{3},{5},{6}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => {{1,2,4,7},{3},{5,6}} => {{1,2,4,6},{3},{5,7}} => {{1,2,4,7},{3},{5,6}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => {{1,2,5},{3},{4},{6},{7}} => {{1,2,5},{3},{4},{6},{7}} => {{1,2,5},{3},{4},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => {{1,2,5},{3},{4},{6,7}} => {{1,2,5},{3},{4},{6,7}} => {{1,2,5},{3},{4},{6,7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => {{1,2,5,6},{3},{4},{7}} => {{1,2,5,6},{3},{4},{7}} => {{1,2,5,6},{3},{4},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => {{1,2,5,6,7},{3},{4}} => {{1,2,5,6,7},{3},{4}} => {{1,2,5,6,7},{3},{4}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => {{1,2,5,7},{3},{4},{6}} => {{1,2,5,7},{3},{4},{6}} => {{1,2,5,7},{3},{4},{6}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => {{1,2,6},{3},{4},{5},{7}} => {{1,2,6},{3},{4},{5},{7}} => {{1,2,6},{3},{4},{5},{7}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => {{1,2,6,7},{3},{4},{5}} => {{1,2,6,7},{3},{4},{5}} => {{1,2,6,7},{3},{4},{5}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => {{1,2,7},{3},{4},{5},{6}} => {{1,2,7},{3},{4},{5},{6}} => {{1,2,7},{3},{4},{5},{6}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => {{1,2,7},{3},{4},{5,6}} => {{1,2,6},{3},{4},{5,7}} => {{1,2,7},{3},{4},{5,6}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => {{1,2,6},{3},{4,5},{7}} => {{1,2,5},{3},{4,6},{7}} => {{1,2,6},{3},{4,5},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => {{1,2,6,7},{3},{4,5}} => {{1,2,5},{3},{4,6,7}} => {{1,2,6,7},{3},{4,5}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => {{1,2,7},{3},{4,5},{6}} => {{1,2,5},{3},{4,7},{6}} => {{1,2,7},{3},{4,5},{6}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => {{1,2,7},{3},{4,5,6}} => {{1,2,5,7},{3},{4,6}} => {{1,2,7},{3},{4,5,6}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => {{1,2,7},{3},{4,6},{5}} => {{1,2,6},{3},{4,7},{5}} => {{1,2,7},{3},{4,6},{5}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => {{1,2,5},{3,4},{6},{7}} => {{1,2,4},{3,5},{6},{7}} => {{1,2,5},{3,4},{6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => {{1,2,5},{3,4},{6,7}} => {{1,2,4},{3,5},{6,7}} => {{1,2,5},{3,4},{6,7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => {{1,2,5,6},{3,4},{7}} => {{1,2,4},{3,5,6},{7}} => {{1,2,5,6},{3,4},{7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => {{1,2,5,6,7},{3,4}} => {{1,2,4},{3,5,6,7}} => {{1,2,5,6,7},{3,4}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => {{1,2,5,7},{3,4},{6}} => {{1,2,4},{3,5,7},{6}} => {{1,2,5,7},{3,4},{6}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => {{1,2,6},{3,4},{5},{7}} => {{1,2,4},{3,6},{5},{7}} => {{1,2,6},{3,4},{5},{7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => {{1,2,6,7},{3,4},{5}} => {{1,2,4},{3,6,7},{5}} => {{1,2,6,7},{3,4},{5}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => {{1,2,7},{3,4},{5},{6}} => {{1,2,4},{3,7},{5},{6}} => {{1,2,7},{3,4},{5},{6}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => {{1,2,7},{3,4},{5,6}} => {{1,2,4},{3,6},{5,7}} => {{1,2,7},{3,4},{5,6}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => {{1,2,6},{3,4,5},{7}} => {{1,2,4,6},{3,5},{7}} => {{1,2,6},{3,4,5},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => {{1,2,6,7},{3,4,5}} => {{1,2,4,6,7},{3,5}} => {{1,2,6,7},{3,4,5}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => {{1,2,7},{3,4,5},{6}} => {{1,2,4,7},{3,5},{6}} => {{1,2,7},{3,4,5},{6}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => {{1,2,7},{3,4,5,6}} => {{1,2,4,6},{3,5,7}} => {{1,2,7},{3,4,5,6}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => {{1,2,7},{3,4,6},{5}} => {{1,2,4,7},{3,6},{5}} => {{1,2,7},{3,4,6},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => {{1,2,6},{3,5},{4},{7}} => {{1,2,5},{3,6},{4},{7}} => {{1,2,6},{3,5},{4},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => {{1,2,6,7},{3,5},{4}} => {{1,2,5},{3,6,7},{4}} => {{1,2,6,7},{3,5},{4}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => {{1,2,7},{3,5},{4},{6}} => {{1,2,5},{3,7},{4},{6}} => {{1,2,7},{3,5},{4},{6}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => {{1,2,7},{3,5,6},{4}} => {{1,2,5,7},{3,6},{4}} => {{1,2,7},{3,5,6},{4}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => {{1,2,7},{3,6},{4},{5}} => {{1,2,6},{3,7},{4},{5}} => {{1,2,7},{3,6},{4},{5}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => {{1,2,7},{3,6},{4,5}} => {{1,2,5},{3,6},{4,7}} => {{1,2,7},{3,6},{4,5}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => {{1,3},{2},{4},{5},{6},{7}} => {{1,3},{2},{4},{5},{6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => {{1,3},{2},{4},{5},{6,7}} => {{1,3},{2},{4},{5},{6,7}} => {{1,3},{2},{4},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => {{1,3},{2},{4},{5,6},{7}} => {{1,3},{2},{4},{5,6},{7}} => {{1,3},{2},{4},{5,6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => {{1,3},{2},{4},{5,6,7}} => {{1,3},{2},{4},{5,6,7}} => {{1,3},{2},{4},{5,6,7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => {{1,3},{2},{4},{5,7},{6}} => {{1,3},{2},{4},{5,7},{6}} => {{1,3},{2},{4},{5,7},{6}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => {{1,3},{2},{4,5},{6},{7}} => {{1,3},{2},{4,5},{6},{7}} => {{1,3},{2},{4,5},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => {{1,3},{2},{4,5},{6,7}} => {{1,3},{2},{4,5},{6,7}} => {{1,3},{2},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => {{1,3},{2},{4,5,6},{7}} => {{1,3},{2},{4,5,6},{7}} => {{1,3},{2},{4,5,6},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => {{1,3},{2},{4,5,6,7}} => {{1,3},{2},{4,5,6,7}} => {{1,3},{2},{4,5,6,7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => {{1,3},{2},{4,5,7},{6}} => {{1,3},{2},{4,5,7},{6}} => {{1,3},{2},{4,5,7},{6}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => {{1,3},{2},{4,6},{5},{7}} => {{1,3},{2},{4,6},{5},{7}} => {{1,3},{2},{4,6},{5},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => {{1,3},{2},{4,6,7},{5}} => {{1,3},{2},{4,6,7},{5}} => {{1,3},{2},{4,6,7},{5}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => {{1,3},{2},{4,7},{5},{6}} => {{1,3},{2},{4,7},{5},{6}} => {{1,3},{2},{4,7},{5},{6}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => {{1,3},{2},{4,7},{5,6}} => {{1,3},{2},{4,6},{5,7}} => {{1,3},{2},{4,7},{5,6}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => {{1,3,4},{2},{5},{6},{7}} => {{1,3,4},{2},{5},{6},{7}} => {{1,3,4},{2},{5},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => {{1,3,4},{2},{5},{6,7}} => {{1,3,4},{2},{5},{6,7}} => {{1,3,4},{2},{5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => {{1,3,4},{2},{5,6},{7}} => {{1,3,4},{2},{5,6},{7}} => {{1,3,4},{2},{5,6},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => {{1,3,4},{2},{5,6,7}} => {{1,3,4},{2},{5,6,7}} => {{1,3,4},{2},{5,6,7}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => {{1,3,4},{2},{5,7},{6}} => {{1,3,4},{2},{5,7},{6}} => {{1,3,4},{2},{5,7},{6}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => {{1,3,4,5},{2},{6},{7}} => {{1,3,4,5},{2},{6},{7}} => {{1,3,4,5},{2},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => {{1,3,4,5},{2},{6,7}} => {{1,3,4,5},{2},{6,7}} => {{1,3,4,5},{2},{6,7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => {{1,3,4,5,6},{2},{7}} => {{1,3,4,5,6},{2},{7}} => {{1,3,4,5,6},{2},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => {{1,3,4,5,6,7},{2}} => {{1,3,4,5,6,7},{2}} => {{1,3,4,5,6,7},{2}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => {{1,3,4,5,7},{2},{6}} => {{1,3,4,5,7},{2},{6}} => {{1,3,4,5,7},{2},{6}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => {{1,3,4,6},{2},{5},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1,3,4,6},{2},{5},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => {{1,3,4,6,7},{2},{5}} => {{1,3,4,6,7},{2},{5}} => {{1,3,4,6,7},{2},{5}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => {{1,3,4,7},{2},{5},{6}} => {{1,3,4,7},{2},{5},{6}} => {{1,3,4,7},{2},{5},{6}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => {{1,3,4,7},{2},{5,6}} => {{1,3,4,6},{2},{5,7}} => {{1,3,4,7},{2},{5,6}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => {{1,3,5},{2},{4},{6},{7}} => {{1,3,5},{2},{4},{6},{7}} => {{1,3,5},{2},{4},{6},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => {{1,3,5},{2},{4},{6,7}} => {{1,3,5},{2},{4},{6,7}} => {{1,3,5},{2},{4},{6,7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => {{1,3,5,6},{2},{4},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1,3,5,6},{2},{4},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => {{1,3,5,6,7},{2},{4}} => {{1,3,5,6,7},{2},{4}} => {{1,3,5,6,7},{2},{4}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => {{1,3,5,7},{2},{4},{6}} => {{1,3,5,7},{2},{4},{6}} => {{1,3,5,7},{2},{4},{6}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => {{1,3,6},{2},{4},{5},{7}} => {{1,3,6},{2},{4},{5},{7}} => {{1,3,6},{2},{4},{5},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => {{1,3,6,7},{2},{4},{5}} => {{1,3,6,7},{2},{4},{5}} => {{1,3,6,7},{2},{4},{5}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => {{1,3,7},{2},{4},{5},{6}} => {{1,3,7},{2},{4},{5},{6}} => {{1,3,7},{2},{4},{5},{6}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => {{1,3,7},{2},{4},{5,6}} => {{1,3,6},{2},{4},{5,7}} => {{1,3,7},{2},{4},{5,6}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => {{1,3,6},{2},{4,5},{7}} => {{1,3,5},{2},{4,6},{7}} => {{1,3,6},{2},{4,5},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => {{1,3,6,7},{2},{4,5}} => {{1,3,5},{2},{4,6,7}} => {{1,3,6,7},{2},{4,5}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => {{1,3,7},{2},{4,5},{6}} => {{1,3,5},{2},{4,7},{6}} => {{1,3,7},{2},{4,5},{6}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => {{1,3,7},{2},{4,5,6}} => {{1,3,5,7},{2},{4,6}} => {{1,3,7},{2},{4,5,6}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => {{1,3,7},{2},{4,6},{5}} => {{1,3,6},{2},{4,7},{5}} => {{1,3,7},{2},{4,6},{5}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => {{1,4},{2},{3},{5},{6},{7}} => {{1,4},{2},{3},{5},{6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => {{1,4},{2},{3},{5},{6,7}} => {{1,4},{2},{3},{5},{6,7}} => {{1,4},{2},{3},{5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => {{1,4},{2},{3},{5,6},{7}} => {{1,4},{2},{3},{5,6},{7}} => {{1,4},{2},{3},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => {{1,4},{2},{3},{5,6,7}} => {{1,4},{2},{3},{5,6,7}} => {{1,4},{2},{3},{5,6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => {{1,4},{2},{3},{5,7},{6}} => {{1,4},{2},{3},{5,7},{6}} => {{1,4},{2},{3},{5,7},{6}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => {{1,4,5},{2},{3},{6},{7}} => {{1,4,5},{2},{3},{6},{7}} => {{1,4,5},{2},{3},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => {{1,4,5},{2},{3},{6,7}} => {{1,4,5},{2},{3},{6,7}} => {{1,4,5},{2},{3},{6,7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => {{1,4,5,6},{2},{3},{7}} => {{1,4,5,6},{2},{3},{7}} => {{1,4,5,6},{2},{3},{7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => {{1,4,5,6,7},{2},{3}} => {{1,4,5,6,7},{2},{3}} => {{1,4,5,6,7},{2},{3}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => {{1,4,5,7},{2},{3},{6}} => {{1,4,5,7},{2},{3},{6}} => {{1,4,5,7},{2},{3},{6}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => {{1,4,6},{2},{3},{5},{7}} => {{1,4,6},{2},{3},{5},{7}} => {{1,4,6},{2},{3},{5},{7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => {{1,4,6,7},{2},{3},{5}} => {{1,4,6,7},{2},{3},{5}} => {{1,4,6,7},{2},{3},{5}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => {{1,4,7},{2},{3},{5},{6}} => {{1,4,7},{2},{3},{5},{6}} => {{1,4,7},{2},{3},{5},{6}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => {{1,4,7},{2},{3},{5,6}} => {{1,4,6},{2},{3},{5,7}} => {{1,4,7},{2},{3},{5,6}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => {{1,5},{2},{3},{4},{6},{7}} => {{1,5},{2},{3},{4},{6},{7}} => {{1,5},{2},{3},{4},{6},{7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => {{1,5},{2},{3},{4},{6,7}} => {{1,5},{2},{3},{4},{6,7}} => {{1,5},{2},{3},{4},{6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => {{1,5,6},{2},{3},{4},{7}} => {{1,5,6},{2},{3},{4},{7}} => {{1,5,6},{2},{3},{4},{7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => {{1,5,6,7},{2},{3},{4}} => {{1,5,6,7},{2},{3},{4}} => {{1,5,6,7},{2},{3},{4}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => {{1,5,7},{2},{3},{4},{6}} => {{1,5,7},{2},{3},{4},{6}} => {{1,5,7},{2},{3},{4},{6}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => {{1,6},{2},{3},{4},{5},{7}} => {{1,6},{2},{3},{4},{5},{7}} => {{1,6},{2},{3},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => {{1,6,7},{2},{3},{4},{5}} => {{1,6,7},{2},{3},{4},{5}} => {{1,6,7},{2},{3},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => {{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => {{1,7},{2},{3},{4},{5,6}} => {{1,6},{2},{3},{4},{5,7}} => {{1,7},{2},{3},{4},{5,6}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => {{1,6},{2},{3},{4,5},{7}} => {{1,5},{2},{3},{4,6},{7}} => {{1,6},{2},{3},{4,5},{7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => {{1,6,7},{2},{3},{4,5}} => {{1,5},{2},{3},{4,6,7}} => {{1,6,7},{2},{3},{4,5}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => {{1,7},{2},{3},{4,5},{6}} => {{1,5},{2},{3},{4,7},{6}} => {{1,7},{2},{3},{4,5},{6}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => {{1,7},{2},{3},{4,5,6}} => {{1,5,7},{2},{3},{4,6}} => {{1,7},{2},{3},{4,5,6}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => {{1,7},{2},{3},{4,6},{5}} => {{1,6},{2},{3},{4,7},{5}} => {{1,7},{2},{3},{4,6},{5}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => {{1,5},{2},{3,4},{6},{7}} => {{1,4},{2},{3,5},{6},{7}} => {{1,5},{2},{3,4},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => {{1,5},{2},{3,4},{6,7}} => {{1,4},{2},{3,5},{6,7}} => {{1,5},{2},{3,4},{6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => {{1,5,6},{2},{3,4},{7}} => {{1,4},{2},{3,5,6},{7}} => {{1,5,6},{2},{3,4},{7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => {{1,5,6,7},{2},{3,4}} => {{1,4},{2},{3,5,6,7}} => {{1,5,6,7},{2},{3,4}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => {{1,5,7},{2},{3,4},{6}} => {{1,4},{2},{3,5,7},{6}} => {{1,5,7},{2},{3,4},{6}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => {{1,6},{2},{3,4},{5},{7}} => {{1,4},{2},{3,6},{5},{7}} => {{1,6},{2},{3,4},{5},{7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => {{1,6,7},{2},{3,4},{5}} => {{1,4},{2},{3,6,7},{5}} => {{1,6,7},{2},{3,4},{5}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => {{1,7},{2},{3,4},{5},{6}} => {{1,4},{2},{3,7},{5},{6}} => {{1,7},{2},{3,4},{5},{6}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => {{1,7},{2},{3,4},{5,6}} => {{1,4},{2},{3,6},{5,7}} => {{1,7},{2},{3,4},{5,6}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => {{1,6},{2},{3,4,5},{7}} => {{1,4,6},{2},{3,5},{7}} => {{1,6},{2},{3,4,5},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => {{1,6,7},{2},{3,4,5}} => {{1,4,6,7},{2},{3,5}} => {{1,6,7},{2},{3,4,5}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => {{1,7},{2},{3,4,5},{6}} => {{1,4,7},{2},{3,5},{6}} => {{1,7},{2},{3,4,5},{6}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => {{1,7},{2},{3,4,5,6}} => {{1,4,6},{2},{3,5,7}} => {{1,7},{2},{3,4,5,6}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => {{1,7},{2},{3,4,6},{5}} => {{1,4,7},{2},{3,6},{5}} => {{1,7},{2},{3,4,6},{5}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => {{1,6},{2},{3,5},{4},{7}} => {{1,5},{2},{3,6},{4},{7}} => {{1,6},{2},{3,5},{4},{7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => {{1,6,7},{2},{3,5},{4}} => {{1,5},{2},{3,6,7},{4}} => {{1,6,7},{2},{3,5},{4}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => {{1,7},{2},{3,5},{4},{6}} => {{1,5},{2},{3,7},{4},{6}} => {{1,7},{2},{3,5},{4},{6}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => {{1,7},{2},{3,5,6},{4}} => {{1,5,7},{2},{3,6},{4}} => {{1,7},{2},{3,5,6},{4}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => {{1,7},{2},{3,6},{4},{5}} => {{1,6},{2},{3,7},{4},{5}} => {{1,7},{2},{3,6},{4},{5}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => {{1,7},{2},{3,6},{4,5}} => {{1,5},{2},{3,6},{4,7}} => {{1,7},{2},{3,6},{4,5}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => {{1,4},{2,3},{5},{6},{7}} => {{1,3},{2,4},{5},{6},{7}} => {{1,4},{2,3},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => {{1,4},{2,3},{5},{6,7}} => {{1,3},{2,4},{5},{6,7}} => {{1,4},{2,3},{5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => {{1,4},{2,3},{5,6},{7}} => {{1,3},{2,4},{5,6},{7}} => {{1,4},{2,3},{5,6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => {{1,4},{2,3},{5,6,7}} => {{1,3},{2,4},{5,6,7}} => {{1,4},{2,3},{5,6,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => {{1,4},{2,3},{5,7},{6}} => {{1,3},{2,4},{5,7},{6}} => {{1,4},{2,3},{5,7},{6}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => {{1,4,5},{2,3},{6},{7}} => {{1,3},{2,4,5},{6},{7}} => {{1,4,5},{2,3},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => {{1,4,5},{2,3},{6,7}} => {{1,3},{2,4,5},{6,7}} => {{1,4,5},{2,3},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => {{1,4,5,6},{2,3},{7}} => {{1,3},{2,4,5,6},{7}} => {{1,4,5,6},{2,3},{7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => {{1,4,5,6,7},{2,3}} => {{1,3},{2,4,5,6,7}} => {{1,4,5,6,7},{2,3}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => {{1,4,5,7},{2,3},{6}} => {{1,3},{2,4,5,7},{6}} => {{1,4,5,7},{2,3},{6}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => {{1,4,6},{2,3},{5},{7}} => {{1,3},{2,4,6},{5},{7}} => {{1,4,6},{2,3},{5},{7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => {{1,4,6,7},{2,3},{5}} => {{1,3},{2,4,6,7},{5}} => {{1,4,6,7},{2,3},{5}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => {{1,4,7},{2,3},{5},{6}} => {{1,3},{2,4,7},{5},{6}} => {{1,4,7},{2,3},{5},{6}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => {{1,4,7},{2,3},{5,6}} => {{1,3},{2,4,6},{5,7}} => {{1,4,7},{2,3},{5,6}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => {{1,5},{2,3},{4},{6},{7}} => {{1,3},{2,5},{4},{6},{7}} => {{1,5},{2,3},{4},{6},{7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => {{1,5},{2,3},{4},{6,7}} => {{1,3},{2,5},{4},{6,7}} => {{1,5},{2,3},{4},{6,7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => {{1,5,6},{2,3},{4},{7}} => {{1,3},{2,5,6},{4},{7}} => {{1,5,6},{2,3},{4},{7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => {{1,5,6,7},{2,3},{4}} => {{1,3},{2,5,6,7},{4}} => {{1,5,6,7},{2,3},{4}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => {{1,5,7},{2,3},{4},{6}} => {{1,3},{2,5,7},{4},{6}} => {{1,5,7},{2,3},{4},{6}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => {{1,6},{2,3},{4},{5},{7}} => {{1,3},{2,6},{4},{5},{7}} => {{1,6},{2,3},{4},{5},{7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => {{1,6,7},{2,3},{4},{5}} => {{1,3},{2,6,7},{4},{5}} => {{1,6,7},{2,3},{4},{5}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => {{1,7},{2,3},{4},{5},{6}} => {{1,3},{2,7},{4},{5},{6}} => {{1,7},{2,3},{4},{5},{6}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => {{1,7},{2,3},{4},{5,6}} => {{1,3},{2,6},{4},{5,7}} => {{1,7},{2,3},{4},{5,6}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => {{1,6},{2,3},{4,5},{7}} => {{1,3},{2,5},{4,6},{7}} => {{1,6},{2,3},{4,5},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => {{1,6,7},{2,3},{4,5}} => {{1,3},{2,5},{4,6,7}} => {{1,6,7},{2,3},{4,5}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => {{1,7},{2,3},{4,5},{6}} => {{1,3},{2,5},{4,7},{6}} => {{1,7},{2,3},{4,5},{6}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => {{1,7},{2,3},{4,5,6}} => {{1,3},{2,5,7},{4,6}} => {{1,7},{2,3},{4,5,6}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => {{1,7},{2,3},{4,6},{5}} => {{1,3},{2,6},{4,7},{5}} => {{1,7},{2,3},{4,6},{5}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => {{1,5},{2,3,4},{6},{7}} => {{1,3,5},{2,4},{6},{7}} => {{1,5},{2,3,4},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => {{1,5},{2,3,4},{6,7}} => {{1,3,5},{2,4},{6,7}} => {{1,5},{2,3,4},{6,7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => {{1,5,6},{2,3,4},{7}} => {{1,3,5,6},{2,4},{7}} => {{1,5,6},{2,3,4},{7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => {{1,5,6,7},{2,3,4}} => {{1,3,5,6,7},{2,4}} => {{1,5,6,7},{2,3,4}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => {{1,5,7},{2,3,4},{6}} => {{1,3,5,7},{2,4},{6}} => {{1,5,7},{2,3,4},{6}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => {{1,6},{2,3,4},{5},{7}} => {{1,3,6},{2,4},{5},{7}} => {{1,6},{2,3,4},{5},{7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => {{1,6,7},{2,3,4},{5}} => {{1,3,6,7},{2,4},{5}} => {{1,6,7},{2,3,4},{5}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => {{1,7},{2,3,4},{5},{6}} => {{1,3,7},{2,4},{5},{6}} => {{1,7},{2,3,4},{5},{6}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => {{1,7},{2,3,4},{5,6}} => {{1,3,6},{2,4},{5,7}} => {{1,7},{2,3,4},{5,6}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => {{1,6},{2,3,4,5},{7}} => {{1,3,5},{2,4,6},{7}} => {{1,6},{2,3,4,5},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => {{1,6,7},{2,3,4,5}} => {{1,3,5},{2,4,6,7}} => {{1,6,7},{2,3,4,5}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => {{1,7},{2,3,4,5},{6}} => {{1,3,5},{2,4,7},{6}} => {{1,7},{2,3,4,5},{6}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => {{1,7},{2,3,4,5,6}} => {{1,3,5,7},{2,4,6}} => {{1,7},{2,3,4,5,6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => {{1,7},{2,3,4,6},{5}} => {{1,3,6},{2,4,7},{5}} => {{1,7},{2,3,4,6},{5}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => {{1,6},{2,3,5},{4},{7}} => {{1,3,6},{2,5},{4},{7}} => {{1,6},{2,3,5},{4},{7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => {{1,6,7},{2,3,5},{4}} => {{1,3,6,7},{2,5},{4}} => {{1,6,7},{2,3,5},{4}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => {{1,7},{2,3,5},{4},{6}} => {{1,3,7},{2,5},{4},{6}} => {{1,7},{2,3,5},{4},{6}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => {{1,7},{2,3,5,6},{4}} => {{1,3,6},{2,5,7},{4}} => {{1,7},{2,3,5,6},{4}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => {{1,7},{2,3,6},{4},{5}} => {{1,3,7},{2,6},{4},{5}} => {{1,7},{2,3,6},{4},{5}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => {{1,7},{2,3,6},{4,5}} => {{1,3,6},{2,5},{4,7}} => {{1,7},{2,3,6},{4,5}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => {{1,5},{2,4},{3},{6},{7}} => {{1,4},{2,5},{3},{6},{7}} => {{1,5},{2,4},{3},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => {{1,5},{2,4},{3},{6,7}} => {{1,4},{2,5},{3},{6,7}} => {{1,5},{2,4},{3},{6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => {{1,5,6},{2,4},{3},{7}} => {{1,4},{2,5,6},{3},{7}} => {{1,5,6},{2,4},{3},{7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => {{1,5,6,7},{2,4},{3}} => {{1,4},{2,5,6,7},{3}} => {{1,5,6,7},{2,4},{3}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => {{1,5,7},{2,4},{3},{6}} => {{1,4},{2,5,7},{3},{6}} => {{1,5,7},{2,4},{3},{6}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => {{1,6},{2,4},{3},{5},{7}} => {{1,4},{2,6},{3},{5},{7}} => {{1,6},{2,4},{3},{5},{7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => {{1,6,7},{2,4},{3},{5}} => {{1,4},{2,6,7},{3},{5}} => {{1,6,7},{2,4},{3},{5}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => {{1,7},{2,4},{3},{5},{6}} => {{1,4},{2,7},{3},{5},{6}} => {{1,7},{2,4},{3},{5},{6}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => {{1,7},{2,4},{3},{5,6}} => {{1,4},{2,6},{3},{5,7}} => {{1,7},{2,4},{3},{5,6}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => {{1,6},{2,4,5},{3},{7}} => {{1,4,6},{2,5},{3},{7}} => {{1,6},{2,4,5},{3},{7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => {{1,6,7},{2,4,5},{3}} => {{1,4,6,7},{2,5},{3}} => {{1,6,7},{2,4,5},{3}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => {{1,7},{2,4,5},{3},{6}} => {{1,4,7},{2,5},{3},{6}} => {{1,7},{2,4,5},{3},{6}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => {{1,7},{2,4,5,6},{3}} => {{1,4,6},{2,5,7},{3}} => {{1,7},{2,4,5,6},{3}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => {{1,7},{2,4,6},{3},{5}} => {{1,4,7},{2,6},{3},{5}} => {{1,7},{2,4,6},{3},{5}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => {{1,6},{2,5},{3},{4},{7}} => {{1,5},{2,6},{3},{4},{7}} => {{1,6},{2,5},{3},{4},{7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => {{1,6,7},{2,5},{3},{4}} => {{1,5},{2,6,7},{3},{4}} => {{1,6,7},{2,5},{3},{4}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => {{1,7},{2,5},{3},{4},{6}} => {{1,5},{2,7},{3},{4},{6}} => {{1,7},{2,5},{3},{4},{6}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => {{1,7},{2,5,6},{3},{4}} => {{1,5,7},{2,6},{3},{4}} => {{1,7},{2,5,6},{3},{4}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => {{1,7},{2,6},{3},{4},{5}} => {{1,6},{2,7},{3},{4},{5}} => {{1,7},{2,6},{3},{4},{5}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => {{1,7},{2,6},{3},{4,5}} => {{1,5},{2,6},{3},{4,7}} => {{1,7},{2,6},{3},{4,5}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => {{1,6},{2,5},{3,4},{7}} => {{1,4},{2,5},{3,6},{7}} => {{1,6},{2,5},{3,4},{7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => {{1,6,7},{2,5},{3,4}} => {{1,4},{2,5},{3,6,7}} => {{1,6,7},{2,5},{3,4}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => {{1,7},{2,5},{3,4},{6}} => {{1,4},{2,5},{3,7},{6}} => {{1,7},{2,5},{3,4},{6}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => {{1,7},{2,5,6},{3,4}} => {{1,4},{2,5,7},{3,6}} => {{1,7},{2,5,6},{3,4}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => {{1,7},{2,6},{3,4},{5}} => {{1,4},{2,6},{3,7},{5}} => {{1,7},{2,6},{3,4},{5}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => {{1,7},{2,6},{3,4,5}} => {{1,4,7},{2,5},{3,6}} => {{1,7},{2,6},{3,4,5}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => {{1,7},{2,6},{3,5},{4}} => {{1,5},{2,6},{3,7},{4}} => {{1,7},{2,6},{3,5},{4}}
[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},{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] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}} => {{1},{2},{3},{4},{5},{6},{7,8}} => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => {{1},{2},{3},{4},{5},{6,7},{8}} => {{1},{2},{3},{4},{5},{6,7},{8}} => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => {{1},{2},{3},{4},{5},{6,7,8}} => {{1},{2},{3},{4},{5},{6,7,8}} => {{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => {{1},{2},{3},{4},{5},{6,8},{7}} => {{1},{2},{3},{4},{5},{6,8},{7}} => {{1},{2},{3},{4},{5},{6,8},{7}}
[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},{2},{3},{4},{5,6},{7},{8}} => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => {{1},{2},{3},{4},{5,6},{7,8}} => {{1},{2},{3},{4},{5,6},{7,8}} => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => {{1},{2},{3},{4},{5,6,7},{8}} => {{1},{2},{3},{4},{5,6,7},{8}} => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => {{1},{2},{3},{4},{5,6,7,8}} => {{1},{2},{3},{4},{5,6,7,8}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => {{1},{2},{3},{4},{5,6,8},{7}} => {{1},{2},{3},{4},{5,6,8},{7}} => {{1},{2},{3},{4},{5,6,8},{7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => {{1},{2},{3},{4},{5,7},{6},{8}} => {{1},{2},{3},{4},{5,7},{6},{8}} => {{1},{2},{3},{4},{5,7},{6},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => {{1},{2},{3},{4},{5,7,8},{6}} => {{1},{2},{3},{4},{5,7,8},{6}} => {{1},{2},{3},{4},{5,7,8},{6}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => {{1},{2},{3},{4},{5,8},{6},{7}} => {{1},{2},{3},{4},{5,8},{6},{7}} => {{1},{2},{3},{4},{5,8},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => {{1},{2},{3},{4},{5,8},{6,7}} => {{1},{2},{3},{4},{5,7},{6,8}} => {{1},{2},{3},{4},{5,8},{6,7}}
[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},{2},{3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => {{1},{2},{3},{4,5},{6},{7,8}} => {{1},{2},{3},{4,5},{6},{7,8}} => {{1},{2},{3},{4,5},{6},{7,8}}
[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},{2},{3},{4,5},{6,7},{8}} => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => {{1},{2},{3},{4,5},{6,7,8}} => {{1},{2},{3},{4,5},{6,7,8}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => {{1},{2},{3},{4,5,6},{7},{8}} => {{1},{2},{3},{4,5,6},{7},{8}} => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => {{1},{2},{3},{4,5,6,7},{8}} => {{1},{2},{3},{4,5,6,7},{8}} => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => {{1},{2},{3},{4,5,6,7,8}} => {{1},{2},{3},{4,5,6,7,8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => {{1},{2},{3},{4,5,6,8},{7}} => {{1},{2},{3},{4,5,6,8},{7}} => {{1},{2},{3},{4,5,6,8},{7}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => {{1},{2},{3},{4,5,7},{6},{8}} => {{1},{2},{3},{4,5,7},{6},{8}} => {{1},{2},{3},{4,5,7},{6},{8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => {{1},{2},{3},{4,5,7,8},{6}} => {{1},{2},{3},{4,5,7,8},{6}} => {{1},{2},{3},{4,5,7,8},{6}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => {{1},{2},{3},{4,5,8},{6},{7}} => {{1},{2},{3},{4,5,8},{6},{7}} => {{1},{2},{3},{4,5,8},{6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => {{1},{2},{3},{4,6,7,8},{5}} => {{1},{2},{3},{4,6,7,8},{5}} => {{1},{2},{3},{4,6,7,8},{5}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => {{1},{2},{3},{4,6,8},{5},{7}} => {{1},{2},{3},{4,6,8},{5},{7}} => {{1},{2},{3},{4,6,8},{5},{7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => {{1},{2},{3},{4,7},{5},{6},{8}} => {{1},{2},{3},{4,7},{5},{6},{8}} => {{1},{2},{3},{4,7},{5},{6},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => {{1},{2},{3},{4,7,8},{5},{6}} => {{1},{2},{3},{4,7,8},{5},{6}} => {{1},{2},{3},{4,7,8},{5},{6}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => {{1},{2},{3},{4,8},{5},{6},{7}} => {{1},{2},{3},{4,8},{5},{6},{7}} => {{1},{2},{3},{4,8},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => {{1},{2},{3},{4,7,8},{5,6}} => {{1},{2},{3},{4,6},{5,7,8}} => {{1},{2},{3},{4,7,8},{5,6}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => {{1},{2},{3},{4,8},{5,6},{7}} => {{1},{2},{3},{4,6},{5,8},{7}} => {{1},{2},{3},{4,8},{5,6},{7}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => {{1},{2},{3},{4,8},{5,7},{6}} => {{1},{2},{3},{4,7},{5,8},{6}} => {{1},{2},{3},{4,8},{5,7},{6}}
[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},{2},{3,4},{5},{6},{7,8}} => {{1},{2},{3,4},{5},{6},{7,8}}
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => {{1},{2},{3,4},{5},{6,8},{7}} => {{1},{2},{3,4},{5},{6,8},{7}} => {{1},{2},{3,4},{5},{6,8},{7}}
[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},{2},{3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}} => {{1},{2},{3,4},{5,6},{7,8}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => {{1},{2},{3,4},{5,6,7,8}} => {{1},{2},{3,4},{5,6,7,8}} => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => {{1},{2},{3,4},{5,6,8},{7}} => {{1},{2},{3,4},{5,6,8},{7}} => {{1},{2},{3,4},{5,6,8},{7}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => {{1},{2},{3,4},{5,8},{6},{7}} => {{1},{2},{3,4},{5,8},{6},{7}} => {{1},{2},{3,4},{5,8},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => {{1},{2},{3,4,5},{6,7,8}} => {{1},{2},{3,4,5},{6,7,8}} => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => {{1},{2},{3,4,5,6},{7,8}} => {{1},{2},{3,4,5,6},{7,8}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => {{1},{2},{3,4,5,6,7,8}} => {{1},{2},{3,4,5,6,7,8}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => {{1},{2},{3,4,5,6,8},{7}} => {{1},{2},{3,4,5,6,8},{7}} => {{1},{2},{3,4,5,6,8},{7}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => {{1},{2},{3,4,5,8},{6},{7}} => {{1},{2},{3,4,5,8},{6},{7}} => {{1},{2},{3,4,5,8},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => {{1},{2},{3,4,5,8},{6,7}} => {{1},{2},{3,4,5,7},{6,8}} => {{1},{2},{3,4,5,8},{6,7}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => {{1},{2},{3,4,6,8},{5},{7}} => {{1},{2},{3,4,6,8},{5},{7}} => {{1},{2},{3,4,6,8},{5},{7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => {{1},{2},{3,4,7,8},{5},{6}} => {{1},{2},{3,4,7,8},{5},{6}} => {{1},{2},{3,4,7,8},{5},{6}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => {{1},{2},{3,4,8},{5},{6},{7}} => {{1},{2},{3,4,8},{5},{6},{7}} => {{1},{2},{3,4,8},{5},{6},{7}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => {{1},{2},{3,4,7,8},{5,6}} => {{1},{2},{3,4,6},{5,7,8}} => {{1},{2},{3,4,7,8},{5,6}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => {{1},{2},{3,5},{4},{6,7,8}} => {{1},{2},{3,5},{4},{6,7,8}} => {{1},{2},{3,5},{4},{6,7,8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => {{1},{2},{3,5,6,7,8},{4}} => {{1},{2},{3,5,6,7,8},{4}} => {{1},{2},{3,5,6,7,8},{4}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => {{1},{2},{3,5,7,8},{4},{6}} => {{1},{2},{3,5,7,8},{4},{6}} => {{1},{2},{3,5,7,8},{4},{6}}
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => {{1},{2},{3,5,8},{4},{6},{7}} => {{1},{2},{3,5,8},{4},{6},{7}} => {{1},{2},{3,5,8},{4},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => {{1},{2},{3,6,7,8},{4},{5}} => {{1},{2},{3,6,7,8},{4},{5}} => {{1},{2},{3,6,7,8},{4},{5}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => {{1},{2},{3,7,8},{4},{5},{6}} => {{1},{2},{3,7,8},{4},{5},{6}} => {{1},{2},{3,7,8},{4},{5},{6}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => {{1},{2},{3,8},{4},{5},{6},{7}} => {{1},{2},{3,8},{4},{5},{6},{7}} => {{1},{2},{3,8},{4},{5},{6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => {{1},{2},{3,6,7,8},{4,5}} => {{1},{2},{3,5},{4,6,7,8}} => {{1},{2},{3,6,7,8},{4,5}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => {{1},{2},{3,8},{4,5},{6},{7}} => {{1},{2},{3,5},{4,8},{6},{7}} => {{1},{2},{3,8},{4,5},{6},{7}}
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => {{1},{2},{3,8},{4,5,6,7}} => {{1},{2},{3,5,7},{4,6,8}} => {{1},{2},{3,8},{4,5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => {{1},{2},{3,8},{4,6},{5},{7}} => {{1},{2},{3,6},{4,8},{5},{7}} => {{1},{2},{3,8},{4,6},{5},{7}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => {{1},{2},{3,8},{4,7},{5},{6}} => {{1},{2},{3,7},{4,8},{5},{6}} => {{1},{2},{3,8},{4,7},{5},{6}}
[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},{2,3},{4},{5},{6},{7},{8}} => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => {{1},{2,3},{4},{5},{6},{7,8}} => {{1},{2,3},{4},{5},{6},{7,8}} => {{1},{2,3},{4},{5},{6},{7,8}}
[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},{2,3},{4},{5},{6,7},{8}} => {{1},{2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => {{1},{2,3},{4},{5},{6,7,8}} => {{1},{2,3},{4},{5},{6,7,8}} => {{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => {{1},{2,3},{4},{5},{6,8},{7}} => {{1},{2,3},{4},{5},{6,8},{7}} => {{1},{2,3},{4},{5},{6,8},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => {{1},{2,3},{4},{5,6,7,8}} => {{1},{2,3},{4},{5,6,7,8}} => {{1},{2,3},{4},{5,6,7,8}}
[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},{2,3},{4,5},{6},{7},{8}} => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => {{1},{2,3},{4,5},{6,7,8}} => {{1},{2,3},{4,5},{6,7,8}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => {{1},{2,3},{4,5},{6,8},{7}} => {{1},{2,3},{4,5},{6,8},{7}} => {{1},{2,3},{4,5},{6,8},{7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => {{1},{2,3},{4,5,6},{7},{8}} => {{1},{2,3},{4,5,6},{7},{8}} => {{1},{2,3},{4,5,6},{7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => {{1},{2,3},{4,5,6},{7,8}} => {{1},{2,3},{4,5,6},{7,8}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => {{1},{2,3},{4,5,6,7},{8}} => {{1},{2,3},{4,5,6,7},{8}} => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => {{1},{2,3},{4,5,6,7,8}} => {{1},{2,3},{4,5,6,7,8}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => {{1},{2,3},{4,5,7},{6},{8}} => {{1},{2,3},{4,5,7},{6},{8}} => {{1},{2,3},{4,5,7},{6},{8}}
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => {{1},{2,3},{4,5,8},{6,7}} => {{1},{2,3},{4,5,7},{6,8}} => {{1},{2,3},{4,5,8},{6,7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => {{1},{2,3},{4,6,7},{5},{8}} => {{1},{2,3},{4,6,7},{5},{8}} => {{1},{2,3},{4,6,7},{5},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => {{1},{2,3},{4,6,7,8},{5}} => {{1},{2,3},{4,6,7,8},{5}} => {{1},{2,3},{4,6,7,8},{5}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => {{1},{2,3},{4,6,8},{5},{7}} => {{1},{2,3},{4,6,8},{5},{7}} => {{1},{2,3},{4,6,8},{5},{7}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => {{1},{2,3},{4,7},{5,6},{8}} => {{1},{2,3},{4,6},{5,7},{8}} => {{1},{2,3},{4,7},{5,6},{8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => {{1},{2,3},{4,7,8},{5,6}} => {{1},{2,3},{4,6},{5,7,8}} => {{1},{2,3},{4,7,8},{5,6}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => {{1},{2,3},{4,8},{5,6,7}} => {{1},{2,3},{4,6,8},{5,7}} => {{1},{2,3},{4,8},{5,6,7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => {{1},{2,3,4},{5},{6},{7},{8}} => {{1},{2,3,4},{5},{6},{7},{8}} => {{1},{2,3,4},{5},{6},{7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}} => {{1},{2,3,4},{5},{6,7},{8}} => {{1},{2,3,4},{5},{6,7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => {{1},{2,3,4},{5},{6,7,8}} => {{1},{2,3,4},{5},{6,7,8}} => {{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}} => {{1},{2,3,4},{5,6},{7,8}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => {{1},{2,3,4},{5,6,7,8}} => {{1},{2,3,4},{5,6,7,8}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => {{1},{2,3,4},{5,6,8},{7}} => {{1},{2,3,4},{5,6,8},{7}} => {{1},{2,3,4},{5,6,8},{7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => {{1},{2,3,4},{5,7,8},{6}} => {{1},{2,3,4},{5,7,8},{6}} => {{1},{2,3,4},{5,7,8},{6}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => {{1},{2,3,4},{5,8},{6,7}} => {{1},{2,3,4},{5,7},{6,8}} => {{1},{2,3,4},{5,8},{6,7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}} => {{1},{2,3,4,5},{6},{7},{8}} => {{1},{2,3,4,5},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => {{1},{2,3,4,5},{6,7},{8}} => {{1},{2,3,4,5},{6,7},{8}} => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => {{1},{2,3,4,5},{6,7,8}} => {{1},{2,3,4,5},{6,7,8}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => {{1},{2,3,4,5,6},{7,8}} => {{1},{2,3,4,5,6},{7,8}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => {{1},{2,3,4,5,6,7,8}} => {{1},{2,3,4,5,6,7,8}} => {{1},{2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => {{1},{2,3,4,5,6,8},{7}} => {{1},{2,3,4,5,6,8},{7}} => {{1},{2,3,4,5,6,8},{7}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => {{1},{2,3,4,5,7},{6},{8}} => {{1},{2,3,4,5,7},{6},{8}} => {{1},{2,3,4,5,7},{6},{8}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => {{1},{2,3,4,5,7,8},{6}} => {{1},{2,3,4,5,7,8},{6}} => {{1},{2,3,4,5,7,8},{6}}
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => {{1},{2,3,4,5,8},{6},{7}} => {{1},{2,3,4,5,8},{6},{7}} => {{1},{2,3,4,5,8},{6},{7}}
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => {{1},{2,3,4,5,8},{6,7}} => {{1},{2,3,4,5,7},{6,8}} => {{1},{2,3,4,5,8},{6,7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => {{1},{2,3,4,6,7,8},{5}} => {{1},{2,3,4,6,7,8},{5}} => {{1},{2,3,4,6,7,8},{5}}
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => {{1},{2,3,4,8},{5},{6},{7}} => {{1},{2,3,4,8},{5},{6},{7}} => {{1},{2,3,4,8},{5},{6},{7}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => {{1},{2,3,4,8},{5,7},{6}} => {{1},{2,3,4,7},{5,8},{6}} => {{1},{2,3,4,8},{5,7},{6}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => {{1},{2,3,5},{4},{6,7},{8}} => {{1},{2,3,5},{4},{6,7},{8}} => {{1},{2,3,5},{4},{6,7},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => {{1},{2,3,5},{4},{6,7,8}} => {{1},{2,3,5},{4},{6,7,8}} => {{1},{2,3,5},{4},{6,7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => {{1},{2,3,5,7},{4},{6},{8}} => {{1},{2,3,5,7},{4},{6},{8}} => {{1},{2,3,5,7},{4},{6},{8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => {{1},{2,3,5,7,8},{4},{6}} => {{1},{2,3,5,7,8},{4},{6}} => {{1},{2,3,5,7,8},{4},{6}}
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => {{1},{2,3,5,8},{4},{6,7}} => {{1},{2,3,5,7},{4},{6,8}} => {{1},{2,3,5,8},{4},{6,7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => {{1},{2,3,6,7},{4},{5},{8}} => {{1},{2,3,6,7},{4},{5},{8}} => {{1},{2,3,6,7},{4},{5},{8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => {{1},{2,3,6,7,8},{4},{5}} => {{1},{2,3,6,7,8},{4},{5}} => {{1},{2,3,6,7,8},{4},{5}}
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => {{1},{2,3,6,8},{4},{5},{7}} => {{1},{2,3,6,8},{4},{5},{7}} => {{1},{2,3,6,8},{4},{5},{7}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => {{1},{2,3,7},{4},{5},{6},{8}} => {{1},{2,3,7},{4},{5},{6},{8}} => {{1},{2,3,7},{4},{5},{6},{8}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => {{1},{2,3,7,8},{4},{5},{6}} => {{1},{2,3,7,8},{4},{5},{6}} => {{1},{2,3,7,8},{4},{5},{6}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => {{1},{2,3,8},{4},{5},{6},{7}} => {{1},{2,3,8},{4},{5},{6},{7}} => {{1},{2,3,8},{4},{5},{6},{7}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => {{1},{2,3,8},{4},{5,6,7}} => {{1},{2,3,6,8},{4},{5,7}} => {{1},{2,3,8},{4},{5,6,7}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => {{1},{2,3,6},{4,5},{7,8}} => {{1},{2,3,5},{4,6},{7,8}} => {{1},{2,3,6},{4,5},{7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => {{1},{2,3,6,7},{4,5},{8}} => {{1},{2,3,5},{4,6,7},{8}} => {{1},{2,3,6,7},{4,5},{8}}
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => {{1},{2,3,6,8},{4,5},{7}} => {{1},{2,3,5},{4,6,8},{7}} => {{1},{2,3,6,8},{4,5},{7}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => {{1},{2,3,8},{4,5},{6,7}} => {{1},{2,3,5},{4,7},{6,8}} => {{1},{2,3,8},{4,5},{6,7}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => {{1},{2,3,8},{4,5,7},{6}} => {{1},{2,3,5,8},{4,7},{6}} => {{1},{2,3,8},{4,5,7},{6}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => {{1},{2,3,8},{4,6,7},{5}} => {{1},{2,3,6,8},{4,7},{5}} => {{1},{2,3,8},{4,6,7},{5}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => {{1},{2,3,8},{4,7},{5,6}} => {{1},{2,3,6},{4,7},{5,8}} => {{1},{2,3,8},{4,7},{5,6}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => {{1},{2,4},{3},{5},{6},{7},{8}} => {{1},{2,4},{3},{5},{6},{7},{8}} => {{1},{2,4},{3},{5},{6},{7},{8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => {{1},{2,4},{3},{5},{6},{7,8}} => {{1},{2,4},{3},{5},{6},{7,8}} => {{1},{2,4},{3},{5},{6},{7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => {{1},{2,4},{3},{5},{6,7,8}} => {{1},{2,4},{3},{5},{6,7,8}} => {{1},{2,4},{3},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => {{1},{2,4},{3},{5},{6,8},{7}} => {{1},{2,4},{3},{5},{6,8},{7}} => {{1},{2,4},{3},{5},{6,8},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => {{1},{2,4},{3},{5,6,7,8}} => {{1},{2,4},{3},{5,6,7,8}} => {{1},{2,4},{3},{5,6,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => {{1},{2,4},{3},{5,6,8},{7}} => {{1},{2,4},{3},{5,6,8},{7}} => {{1},{2,4},{3},{5,6,8},{7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => {{1},{2,4},{3},{5,7},{6},{8}} => {{1},{2,4},{3},{5,7},{6},{8}} => {{1},{2,4},{3},{5,7},{6},{8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => {{1},{2,4},{3},{5,7,8},{6}} => {{1},{2,4},{3},{5,7,8},{6}} => {{1},{2,4},{3},{5,7,8},{6}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => {{1},{2,4,5},{3},{6,7},{8}} => {{1},{2,4,5},{3},{6,7},{8}} => {{1},{2,4,5},{3},{6,7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => {{1},{2,4,5,6},{3},{7},{8}} => {{1},{2,4,5,6},{3},{7},{8}} => {{1},{2,4,5,6},{3},{7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => {{1},{2,4,5,6,7,8},{3}} => {{1},{2,4,5,6,7,8},{3}} => {{1},{2,4,5,6,7,8},{3}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => {{1},{2,4,5,7},{3},{6},{8}} => {{1},{2,4,5,7},{3},{6},{8}} => {{1},{2,4,5,7},{3},{6},{8}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => {{1},{2,4,5,8},{3},{6},{7}} => {{1},{2,4,5,8},{3},{6},{7}} => {{1},{2,4,5,8},{3},{6},{7}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => {{1},{2,4,5,8},{3},{6,7}} => {{1},{2,4,5,7},{3},{6,8}} => {{1},{2,4,5,8},{3},{6,7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => {{1},{2,4,6,7},{3},{5},{8}} => {{1},{2,4,6,7},{3},{5},{8}} => {{1},{2,4,6,7},{3},{5},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => {{1},{2,4,6,7,8},{3},{5}} => {{1},{2,4,6,7,8},{3},{5}} => {{1},{2,4,6,7,8},{3},{5}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => {{1},{2,4,6,8},{3},{5},{7}} => {{1},{2,4,6,8},{3},{5},{7}} => {{1},{2,4,6,8},{3},{5},{7}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => {{1},{2,4,8},{3},{5},{6},{7}} => {{1},{2,4,8},{3},{5},{6},{7}} => {{1},{2,4,8},{3},{5},{6},{7}}
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => {{1},{2,4,8},{3},{5},{6,7}} => {{1},{2,4,7},{3},{5},{6,8}} => {{1},{2,4,8},{3},{5},{6,7}}
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => {{1},{2,4,8},{3},{5,6,7}} => {{1},{2,4,6,8},{3},{5,7}} => {{1},{2,4,8},{3},{5,6,7}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => {{1},{2,4,8},{3},{5,7},{6}} => {{1},{2,4,7},{3},{5,8},{6}} => {{1},{2,4,8},{3},{5,7},{6}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => {{1},{2,5},{3},{4},{6,8},{7}} => {{1},{2,5},{3},{4},{6,8},{7}} => {{1},{2,5},{3},{4},{6,8},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => {{1},{2,5,6,7,8},{3},{4}} => {{1},{2,5,6,7,8},{3},{4}} => {{1},{2,5,6,7,8},{3},{4}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => {{1},{2,5,8},{3},{4},{6},{7}} => {{1},{2,5,8},{3},{4},{6},{7}} => {{1},{2,5,8},{3},{4},{6},{7}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => {{1},{2,7},{3},{4},{5},{6},{8}} => {{1},{2,7},{3},{4},{5},{6},{8}} => {{1},{2,7},{3},{4},{5},{6},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => {{1},{2,7,8},{3},{4},{5},{6}} => {{1},{2,7,8},{3},{4},{5},{6}} => {{1},{2,7,8},{3},{4},{5},{6}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => {{1},{2,8},{3},{4},{5},{6},{7}} => {{1},{2,8},{3},{4},{5},{6},{7}} => {{1},{2,8},{3},{4},{5},{6},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => {{1},{2,6,8},{3},{4,5},{7}} => {{1},{2,5},{3},{4,6,8},{7}} => {{1},{2,6,8},{3},{4,5},{7}}
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => {{1},{2,8},{3},{4,5},{6,7}} => {{1},{2,5},{3},{4,7},{6,8}} => {{1},{2,8},{3},{4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => {{1},{2,5},{3,4},{6,7},{8}} => {{1},{2,4},{3,5},{6,7},{8}} => {{1},{2,5},{3,4},{6,7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => {{1},{2,5},{3,4},{6,7,8}} => {{1},{2,4},{3,5},{6,7,8}} => {{1},{2,5},{3,4},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => {{1},{2,5,6,7,8},{3,4}} => {{1},{2,4},{3,5,6,7,8}} => {{1},{2,5,6,7,8},{3,4}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => {{1},{2,5,6,8},{3,4},{7}} => {{1},{2,4},{3,5,6,8},{7}} => {{1},{2,5,6,8},{3,4},{7}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => {{1},{2,5,8},{3,4},{6,7}} => {{1},{2,4},{3,5,7},{6,8}} => {{1},{2,5,8},{3,4},{6,7}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => {{1},{2,8},{3,4},{5},{6},{7}} => {{1},{2,4},{3,8},{5},{6},{7}} => {{1},{2,8},{3,4},{5},{6},{7}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => {{1},{2,8},{3,4},{5},{6,7}} => {{1},{2,4},{3,7},{5},{6,8}} => {{1},{2,8},{3,4},{5},{6,7}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => {{1},{2,7,8},{3,4},{5,6}} => {{1},{2,4},{3,6},{5,7,8}} => {{1},{2,7,8},{3,4},{5,6}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => {{1},{2,8},{3,4},{5,6},{7}} => {{1},{2,4},{3,6},{5,8},{7}} => {{1},{2,8},{3,4},{5,6},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => {{1},{2,6,8},{3,4,5},{7}} => {{1},{2,4,6,8},{3,5},{7}} => {{1},{2,6,8},{3,4,5},{7}}
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => {{1},{2,8},{3,4,5},{6},{7}} => {{1},{2,4,8},{3,5},{6},{7}} => {{1},{2,8},{3,4,5},{6},{7}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => {{1},{2,8},{3,4,5,6,7}} => {{1},{2,4,6,8},{3,5,7}} => {{1},{2,8},{3,4,5,6,7}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => {{1},{2,8},{3,4,6},{5},{7}} => {{1},{2,4,8},{3,6},{5},{7}} => {{1},{2,8},{3,4,6},{5},{7}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => {{1},{2,8},{3,4,6,7},{5}} => {{1},{2,4,7},{3,6,8},{5}} => {{1},{2,8},{3,4,6,7},{5}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => {{1},{2,8},{3,4,7},{5,6}} => {{1},{2,4,7},{3,6},{5,8}} => {{1},{2,8},{3,4,7},{5,6}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => {{1},{2,6},{3,5},{4},{7,8}} => {{1},{2,5},{3,6},{4},{7,8}} => {{1},{2,6},{3,5},{4},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => {{1},{2,6,8},{3,5},{4},{7}} => {{1},{2,5},{3,6,8},{4},{7}} => {{1},{2,6,8},{3,5},{4},{7}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => {{1},{2,8},{3,5},{4},{6},{7}} => {{1},{2,5},{3,8},{4},{6},{7}} => {{1},{2,8},{3,5},{4},{6},{7}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => {{1},{2,8},{3,5,6},{4},{7}} => {{1},{2,5,8},{3,6},{4},{7}} => {{1},{2,8},{3,5,6},{4},{7}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => {{1},{2,8},{3,5,6,7},{4}} => {{1},{2,5,7},{3,6,8},{4}} => {{1},{2,8},{3,5,6,7},{4}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => {{1},{2,8},{3,5,7},{4},{6}} => {{1},{2,5,8},{3,7},{4},{6}} => {{1},{2,8},{3,5,7},{4},{6}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => {{1},{2,8},{3,7},{4},{5},{6}} => {{1},{2,7},{3,8},{4},{5},{6}} => {{1},{2,8},{3,7},{4},{5},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => {{1},{2,7},{3,6},{4,5},{8}} => {{1},{2,5},{3,6},{4,7},{8}} => {{1},{2,7},{3,6},{4,5},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => {{1},{2,7,8},{3,6},{4,5}} => {{1},{2,5},{3,6},{4,7,8}} => {{1},{2,7,8},{3,6},{4,5}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => {{1},{2,8},{3,6,7},{4,5}} => {{1},{2,5},{3,6,8},{4,7}} => {{1},{2,8},{3,6,7},{4,5}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => {{1},{2,8},{3,7},{4,5,6}} => {{1},{2,5,8},{3,6},{4,7}} => {{1},{2,8},{3,7},{4,5,6}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => {{1},{2,8},{3,7},{4,6},{5}} => {{1},{2,6},{3,7},{4,8},{5}} => {{1},{2,8},{3,7},{4,6},{5}}
[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}} => {{1,2},{3},{4},{5},{6},{7},{8}} => {{1,2},{3},{4},{5},{6},{7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6},{7,8}}
[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}} => {{1,2},{3},{4},{5},{6,7},{8}} => {{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => {{1,2},{3},{4},{5},{6,7,8}} => {{1,2},{3},{4},{5},{6,7,8}} => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => {{1,2},{3},{4},{5},{6,8},{7}} => {{1,2},{3},{4},{5},{6,8},{7}} => {{1,2},{3},{4},{5},{6,8},{7}}
[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}} => {{1,2},{3},{4},{5,6},{7},{8}} => {{1,2},{3},{4},{5,6},{7},{8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => {{1,2},{3},{4},{5,6,7,8}} => {{1,2},{3},{4},{5,6,7,8}} => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => {{1,2},{3},{4},{5,8},{6},{7}} => {{1,2},{3},{4},{5,8},{6},{7}} => {{1,2},{3},{4},{5,8},{6},{7}}
[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}} => {{1,2},{3},{4,5},{6},{7},{8}} => {{1,2},{3},{4,5},{6},{7},{8}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2},{3},{4,5},{6,7,8}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2},{3},{4,5,6},{7,8}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => {{1,2},{3},{4,5,6,7,8}} => {{1,2},{3},{4,5,6,7,8}} => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => {{1,2},{3},{4,5,8},{6},{7}} => {{1,2},{3},{4,5,8},{6},{7}} => {{1,2},{3},{4,5,8},{6},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => {{1,2},{3},{4,6,8},{5},{7}} => {{1,2},{3},{4,6,8},{5},{7}} => {{1,2},{3},{4,6,8},{5},{7}}
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => {{1,2},{3},{4,8},{5},{6},{7}} => {{1,2},{3},{4,8},{5},{6},{7}} => {{1,2},{3},{4,8},{5},{6},{7}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => {{1,2},{3},{4,8},{5,6,7}} => {{1,2},{3},{4,6,8},{5,7}} => {{1,2},{3},{4,8},{5,6,7}}
[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}} => {{1,2},{3,4},{5},{6},{7},{8}} => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2},{3,4},{5},{6,7,8}} => {{1,2},{3,4},{5},{6,7,8}}
[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}} => {{1,2},{3,4},{5,6},{7},{8}} => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => {{1,2},{3,4},{5,6,7},{8}} => {{1,2},{3,4},{5,6,7},{8}} => {{1,2},{3,4},{5,6,7},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => {{1,2},{3,4},{5,6,7,8}} => {{1,2},{3,4},{5,6,7,8}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => {{1,2},{3,4},{5,6,8},{7}} => {{1,2},{3,4},{5,6,8},{7}} => {{1,2},{3,4},{5,6,8},{7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => {{1,2},{3,4},{5,7,8},{6}} => {{1,2},{3,4},{5,7,8},{6}} => {{1,2},{3,4},{5,7,8},{6}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => {{1,2},{3,4},{5,8},{6},{7}} => {{1,2},{3,4},{5,8},{6},{7}} => {{1,2},{3,4},{5,8},{6},{7}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => {{1,2},{3,4},{5,8},{6,7}} => {{1,2},{3,4},{5,7},{6,8}} => {{1,2},{3,4},{5,8},{6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}} => {{1,2},{3,4,5},{6},{7},{8}} => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => {{1,2},{3,4,5},{6},{7,8}} => {{1,2},{3,4,5},{6},{7,8}} => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => {{1,2},{3,4,5},{6,8},{7}} => {{1,2},{3,4,5},{6,8},{7}} => {{1,2},{3,4,5},{6,8},{7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => {{1,2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => {{1,2},{3,4,5,6,7},{8}} => {{1,2},{3,4,5,6,7},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => {{1,2},{3,4,5,6,7,8}} => {{1,2},{3,4,5,6,7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => {{1,2},{3,4,5,6,8},{7}} => {{1,2},{3,4,5,6,8},{7}} => {{1,2},{3,4,5,6,8},{7}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => {{1,2},{3,4,5,8},{6},{7}} => {{1,2},{3,4,5,8},{6},{7}} => {{1,2},{3,4,5,8},{6},{7}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => {{1,2},{3,4,5,8},{6,7}} => {{1,2},{3,4,5,7},{6,8}} => {{1,2},{3,4,5,8},{6,7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => {{1,2},{3,4,6},{5},{7,8}} => {{1,2},{3,4,6},{5},{7,8}} => {{1,2},{3,4,6},{5},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => {{1,2},{3,4,6,8},{5},{7}} => {{1,2},{3,4,6,8},{5},{7}} => {{1,2},{3,4,6,8},{5},{7}}
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => {{1,2},{3,4,8},{5},{6},{7}} => {{1,2},{3,4,8},{5},{6},{7}} => {{1,2},{3,4,8},{5},{6},{7}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => {{1,2},{3,4,8},{5},{6,7}} => {{1,2},{3,4,7},{5},{6,8}} => {{1,2},{3,4,8},{5},{6,7}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => {{1,2},{3,4,7,8},{5,6}} => {{1,2},{3,4,6},{5,7,8}} => {{1,2},{3,4,7,8},{5,6}}
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => {{1,2},{3,4,8},{5,6},{7}} => {{1,2},{3,4,6},{5,8},{7}} => {{1,2},{3,4,8},{5,6},{7}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => {{1,2},{3,4,8},{5,6,7}} => {{1,2},{3,4,6,8},{5,7}} => {{1,2},{3,4,8},{5,6,7}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => {{1,2},{3,4,8},{5,7},{6}} => {{1,2},{3,4,7},{5,8},{6}} => {{1,2},{3,4,8},{5,7},{6}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => {{1,2},{3,5},{4},{6},{7},{8}} => {{1,2},{3,5},{4},{6},{7},{8}} => {{1,2},{3,5},{4},{6},{7},{8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => {{1,2},{3,5},{4},{6},{7,8}} => {{1,2},{3,5},{4},{6},{7,8}} => {{1,2},{3,5},{4},{6},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => {{1,2},{3,5},{4},{6,8},{7}} => {{1,2},{3,5},{4},{6,8},{7}} => {{1,2},{3,5},{4},{6,8},{7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => {{1,2},{3,5,6},{4},{7,8}} => {{1,2},{3,5,6},{4},{7,8}} => {{1,2},{3,5,6},{4},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => {{1,2},{3,5,6,7},{4},{8}} => {{1,2},{3,5,6,7},{4},{8}} => {{1,2},{3,5,6,7},{4},{8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => {{1,2},{3,5,6,7,8},{4}} => {{1,2},{3,5,6,7,8},{4}} => {{1,2},{3,5,6,7,8},{4}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => {{1,2},{3,5,7,8},{4},{6}} => {{1,2},{3,5,7,8},{4},{6}} => {{1,2},{3,5,7,8},{4},{6}}
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => {{1,2},{3,5,8},{4},{6},{7}} => {{1,2},{3,5,8},{4},{6},{7}} => {{1,2},{3,5,8},{4},{6},{7}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => {{1,2},{3,5,8},{4},{6,7}} => {{1,2},{3,5,7},{4},{6,8}} => {{1,2},{3,5,8},{4},{6,7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => {{1,2},{3,6},{4},{5},{7,8}} => {{1,2},{3,6},{4},{5},{7,8}} => {{1,2},{3,6},{4},{5},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => {{1,2},{3,6,7,8},{4},{5}} => {{1,2},{3,6,7,8},{4},{5}} => {{1,2},{3,6,7,8},{4},{5}}
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => {{1,2},{3,6,8},{4},{5},{7}} => {{1,2},{3,6,8},{4},{5},{7}} => {{1,2},{3,6,8},{4},{5},{7}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => {{1,2},{3,8},{4},{5},{6},{7}} => {{1,2},{3,8},{4},{5},{6},{7}} => {{1,2},{3,8},{4},{5},{6},{7}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => {{1,2},{3,8},{4},{5},{6,7}} => {{1,2},{3,7},{4},{5},{6,8}} => {{1,2},{3,8},{4},{5},{6,7}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => {{1,2},{3,7,8},{4},{5,6}} => {{1,2},{3,6},{4},{5,7,8}} => {{1,2},{3,7,8},{4},{5,6}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => {{1,2},{3,8},{4},{5,6,7}} => {{1,2},{3,6,8},{4},{5,7}} => {{1,2},{3,8},{4},{5,6,7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => {{1,2},{3,6},{4,5},{7,8}} => {{1,2},{3,5},{4,6},{7,8}} => {{1,2},{3,6},{4,5},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => {{1,2},{3,8},{4,5},{6},{7}} => {{1,2},{3,5},{4,8},{6},{7}} => {{1,2},{3,8},{4,5},{6},{7}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => {{1,2},{3,8},{4,5},{6,7}} => {{1,2},{3,5},{4,7},{6,8}} => {{1,2},{3,8},{4,5},{6,7}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => {{1,2},{3,8},{4,5,6},{7}} => {{1,2},{3,5,8},{4,6},{7}} => {{1,2},{3,8},{4,5,6},{7}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => {{1,2},{3,8},{4,5,6,7}} => {{1,2},{3,5,7},{4,6,8}} => {{1,2},{3,8},{4,5,6,7}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => {{1,2},{3,8},{4,5,7},{6}} => {{1,2},{3,5,8},{4,7},{6}} => {{1,2},{3,8},{4,5,7},{6}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => {{1,2},{3,7},{4,6},{5},{8}} => {{1,2},{3,6},{4,7},{5},{8}} => {{1,2},{3,7},{4,6},{5},{8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => {{1,2},{3,7,8},{4,6},{5}} => {{1,2},{3,6},{4,7,8},{5}} => {{1,2},{3,7,8},{4,6},{5}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => {{1,2},{3,8},{4,6,7},{5}} => {{1,2},{3,6,8},{4,7},{5}} => {{1,2},{3,8},{4,6,7},{5}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => {{1,2},{3,8},{4,7},{5,6}} => {{1,2},{3,6},{4,7},{5,8}} => {{1,2},{3,8},{4,7},{5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => {{1,2,3},{4},{5},{6},{7},{8}} => {{1,2,3},{4},{5},{6},{7},{8}} => {{1,2,3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => {{1,2,3},{4},{5},{6},{7,8}} => {{1,2,3},{4},{5},{6},{7,8}} => {{1,2,3},{4},{5},{6},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}} => {{1,2,3},{4},{5,6},{7,8}} => {{1,2,3},{4},{5,6},{7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3},{4},{5,6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => {{1,2,3},{4},{5,7,8},{6}} => {{1,2,3},{4},{5,7,8},{6}} => {{1,2,3},{4},{5,7,8},{6}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => {{1,2,3},{4},{5,8},{6,7}} => {{1,2,3},{4},{5,7},{6,8}} => {{1,2,3},{4},{5,8},{6,7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => {{1,2,3},{4,5},{6},{7},{8}} => {{1,2,3},{4,5},{6},{7},{8}} => {{1,2,3},{4,5},{6},{7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3},{4,5,6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => {{1,2,3},{4,5,7,8},{6}} => {{1,2,3},{4,5,7,8},{6}} => {{1,2,3},{4,5,7,8},{6}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => {{1,2,3},{4,6},{5},{7},{8}} => {{1,2,3},{4,6},{5},{7},{8}} => {{1,2,3},{4,6},{5},{7},{8}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => {{1,2,3},{4,6},{5},{7,8}} => {{1,2,3},{4,6},{5},{7,8}} => {{1,2,3},{4,6},{5},{7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => {{1,2,3},{4,6,7},{5},{8}} => {{1,2,3},{4,6,7},{5},{8}} => {{1,2,3},{4,6,7},{5},{8}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => {{1,2,3},{4,6,8},{5},{7}} => {{1,2,3},{4,6,8},{5},{7}} => {{1,2,3},{4,6,8},{5},{7}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => {{1,2,3},{4,8},{5,7},{6}} => {{1,2,3},{4,7},{5,8},{6}} => {{1,2,3},{4,8},{5,7},{6}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}} => {{1,2,3,4},{5},{6},{7},{8}} => {{1,2,3,4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => {{1,2,3,4},{5},{6},{7,8}} => {{1,2,3,4},{5},{6},{7,8}} => {{1,2,3,4},{5},{6},{7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => {{1,2,3,4},{5},{6,7},{8}} => {{1,2,3,4},{5},{6,7},{8}} => {{1,2,3,4},{5},{6,7},{8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => {{1,2,3,4},{5},{6,8},{7}} => {{1,2,3,4},{5},{6,8},{7}} => {{1,2,3,4},{5},{6,8},{7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}} => {{1,2,3,4},{5,6},{7},{8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => {{1,2,3,4},{5,6,8},{7}} => {{1,2,3,4},{5,6,8},{7}} => {{1,2,3,4},{5,6,8},{7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => {{1,2,3,4},{5,7,8},{6}} => {{1,2,3,4},{5,7,8},{6}} => {{1,2,3,4},{5,7,8},{6}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => {{1,2,3,4},{5,8},{6,7}} => {{1,2,3,4},{5,7},{6,8}} => {{1,2,3,4},{5,8},{6,7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1,2,3,4,5},{6},{7},{8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => {{1,2,3,4,5},{6},{7,8}} => {{1,2,3,4,5},{6},{7,8}} => {{1,2,3,4,5},{6},{7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => {{1,2,3,4,5},{6,7},{8}} => {{1,2,3,4,5},{6,7},{8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}} => {{1,2,3,4,5},{6,8},{7}} => {{1,2,3,4,5},{6,8},{7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1,2,3,4,5,6},{7},{8}} => {{1,2,3,4,5,6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1,2,3,4,5,6,7},{8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6,8},{7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => {{1,2,3,4,5,7},{6},{8}} => {{1,2,3,4,5,7},{6},{8}} => {{1,2,3,4,5,7},{6},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5,7,8},{6}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => {{1,2,3,4,5,8},{6},{7}} => {{1,2,3,4,5,8},{6},{7}} => {{1,2,3,4,5,8},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => {{1,2,3,4,5,8},{6,7}} => {{1,2,3,4,5,7},{6,8}} => {{1,2,3,4,5,8},{6,7}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => {{1,2,3,4,6},{5},{7},{8}} => {{1,2,3,4,6},{5},{7},{8}} => {{1,2,3,4,6},{5},{7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4,6,7},{5},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4,6,7,8},{5}}
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4,6,8},{5},{7}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => {{1,2,3,4,7},{5},{6},{8}} => {{1,2,3,4,7},{5},{6},{8}} => {{1,2,3,4,7},{5},{6},{8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => {{1,2,3,4,7,8},{5},{6}} => {{1,2,3,4,7,8},{5},{6}} => {{1,2,3,4,7,8},{5},{6}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => {{1,2,3,4,8},{5},{6},{7}} => {{1,2,3,4,8},{5},{6},{7}} => {{1,2,3,4,8},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => {{1,2,3,4,8},{5},{6,7}} => {{1,2,3,4,7},{5},{6,8}} => {{1,2,3,4,8},{5},{6,7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => {{1,2,3,4,7},{5,6},{8}} => {{1,2,3,4,6},{5,7},{8}} => {{1,2,3,4,7},{5,6},{8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => {{1,2,3,4,7,8},{5,6}} => {{1,2,3,4,6},{5,7,8}} => {{1,2,3,4,7,8},{5,6}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => {{1,2,3,4,8},{5,6},{7}} => {{1,2,3,4,6},{5,8},{7}} => {{1,2,3,4,8},{5,6},{7}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => {{1,2,3,4,8},{5,6,7}} => {{1,2,3,4,6,8},{5,7}} => {{1,2,3,4,8},{5,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => {{1,2,3,5},{4},{6},{7},{8}} => {{1,2,3,5},{4},{6},{7},{8}} => {{1,2,3,5},{4},{6},{7},{8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => {{1,2,3,5},{4},{6},{7,8}} => {{1,2,3,5},{4},{6},{7,8}} => {{1,2,3,5},{4},{6},{7,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => {{1,2,3,5},{4},{6,7},{8}} => {{1,2,3,5},{4},{6,7},{8}} => {{1,2,3,5},{4},{6,7},{8}}
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => {{1,2,3,5},{4},{6,8},{7}} => {{1,2,3,5},{4},{6,8},{7}} => {{1,2,3,5},{4},{6,8},{7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3,5,6,7},{4},{8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,5,6,7,8},{4}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => {{1,2,3,5,7,8},{4},{6}} => {{1,2,3,5,7,8},{4},{6}} => {{1,2,3,5,7,8},{4},{6}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => {{1,2,3,5,8},{4},{6},{7}} => {{1,2,3,5,8},{4},{6},{7}} => {{1,2,3,5,8},{4},{6},{7}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => {{1,2,3,6},{4},{5},{7,8}} => {{1,2,3,6},{4},{5},{7,8}} => {{1,2,3,6},{4},{5},{7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3,6,7,8},{4},{5}}
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => {{1,2,3,6,8},{4},{5},{7}} => {{1,2,3,6,8},{4},{5},{7}} => {{1,2,3,6,8},{4},{5},{7}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => {{1,2,3,7,8},{4},{5},{6}} => {{1,2,3,7,8},{4},{5},{6}} => {{1,2,3,7,8},{4},{5},{6}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => {{1,2,3,8},{4},{5},{6},{7}} => {{1,2,3,8},{4},{5},{6},{7}} => {{1,2,3,8},{4},{5},{6},{7}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => {{1,2,3,7,8},{4},{5,6}} => {{1,2,3,6},{4},{5,7,8}} => {{1,2,3,7,8},{4},{5,6}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => {{1,2,3,8},{4},{5,6,7}} => {{1,2,3,6,8},{4},{5,7}} => {{1,2,3,8},{4},{5,6,7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => {{1,2,3,6},{4,5},{7},{8}} => {{1,2,3,5},{4,6},{7},{8}} => {{1,2,3,6},{4,5},{7},{8}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => {{1,2,3,6},{4,5},{7,8}} => {{1,2,3,5},{4,6},{7,8}} => {{1,2,3,6},{4,5},{7,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => {{1,2,3,6,7,8},{4,5}} => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,6,7,8},{4,5}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => {{1,2,3,7},{4,5},{6},{8}} => {{1,2,3,5},{4,7},{6},{8}} => {{1,2,3,7},{4,5},{6},{8}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => {{1,2,3,8},{4,5},{6},{7}} => {{1,2,3,5},{4,8},{6},{7}} => {{1,2,3,8},{4,5},{6},{7}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => {{1,2,3,7},{4,5,6},{8}} => {{1,2,3,5,7},{4,6},{8}} => {{1,2,3,7},{4,5,6},{8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => {{1,2,3,7,8},{4,5,6}} => {{1,2,3,5,7,8},{4,6}} => {{1,2,3,7,8},{4,5,6}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => {{1,2,3,8},{4,5,6,7}} => {{1,2,3,5,7},{4,6,8}} => {{1,2,3,8},{4,5,6,7}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => {{1,2,3,7},{4,6},{5},{8}} => {{1,2,3,6},{4,7},{5},{8}} => {{1,2,3,7},{4,6},{5},{8}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => {{1,2,3,8},{4,6},{5},{7}} => {{1,2,3,6},{4,8},{5},{7}} => {{1,2,3,8},{4,6},{5},{7}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => {{1,2,3,8},{4,7},{5,6}} => {{1,2,3,6},{4,7},{5,8}} => {{1,2,3,8},{4,7},{5,6}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => {{1,2,4},{3},{5},{6},{7},{8}} => {{1,2,4},{3},{5},{6},{7},{8}} => {{1,2,4},{3},{5},{6},{7},{8}}
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => {{1,2,4},{3},{5},{6,8},{7}} => {{1,2,4},{3},{5},{6,8},{7}} => {{1,2,4},{3},{5},{6,8},{7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => {{1,2,4},{3},{5,6},{7,8}} => {{1,2,4},{3},{5,6},{7,8}} => {{1,2,4},{3},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => {{1,2,4},{3},{5,6,7,8}} => {{1,2,4},{3},{5,6,7,8}} => {{1,2,4},{3},{5,6,7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => {{1,2,4},{3},{5,6,8},{7}} => {{1,2,4},{3},{5,6,8},{7}} => {{1,2,4},{3},{5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => {{1,2,4},{3},{5,7,8},{6}} => {{1,2,4},{3},{5,7,8},{6}} => {{1,2,4},{3},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => {{1,2,4},{3},{5,8},{6,7}} => {{1,2,4},{3},{5,7},{6,8}} => {{1,2,4},{3},{5,8},{6,7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => {{1,2,4,5},{3},{6},{7,8}} => {{1,2,4,5},{3},{6},{7,8}} => {{1,2,4,5},{3},{6},{7,8}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => {{1,2,4,5},{3},{6,7,8}} => {{1,2,4,5},{3},{6,7,8}} => {{1,2,4,5},{3},{6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => {{1,2,4,5},{3},{6,8},{7}} => {{1,2,4,5},{3},{6,8},{7}} => {{1,2,4,5},{3},{6,8},{7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => {{1,2,4,5,6},{3},{7,8}} => {{1,2,4,5,6},{3},{7,8}} => {{1,2,4,5,6},{3},{7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => {{1,2,4,5,6,7,8},{3}} => {{1,2,4,5,6,7,8},{3}} => {{1,2,4,5,6,7,8},{3}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => {{1,2,4,5,6,8},{3},{7}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2,4,5,6,8},{3},{7}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => {{1,2,4,5,7,8},{3},{6}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2,4,5,7,8},{3},{6}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => {{1,2,4,5,8},{3},{6},{7}} => {{1,2,4,5,8},{3},{6},{7}} => {{1,2,4,5,8},{3},{6},{7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => {{1,2,4,6},{3},{5},{7},{8}} => {{1,2,4,6},{3},{5},{7},{8}} => {{1,2,4,6},{3},{5},{7},{8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => {{1,2,4,6},{3},{5},{7,8}} => {{1,2,4,6},{3},{5},{7,8}} => {{1,2,4,6},{3},{5},{7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => {{1,2,4,6,7,8},{3},{5}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2,4,6,7,8},{3},{5}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => {{1,2,4,6,8},{3},{5},{7}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2,4,6,8},{3},{5},{7}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => {{1,2,4,7,8},{3},{5},{6}} => {{1,2,4,7,8},{3},{5},{6}} => {{1,2,4,7,8},{3},{5},{6}}
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => {{1,2,4,8},{3},{5},{6},{7}} => {{1,2,4,8},{3},{5},{6},{7}} => {{1,2,4,8},{3},{5},{6},{7}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => {{1,2,4,7,8},{3},{5,6}} => {{1,2,4,6},{3},{5,7,8}} => {{1,2,4,7,8},{3},{5,6}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => {{1,2,4,8},{3},{5,6},{7}} => {{1,2,4,6},{3},{5,8},{7}} => {{1,2,4,8},{3},{5,6},{7}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => {{1,2,4,8},{3},{5,7},{6}} => {{1,2,4,7},{3},{5,8},{6}} => {{1,2,4,8},{3},{5,7},{6}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => {{1,2,5},{3},{4},{6},{7},{8}} => {{1,2,5},{3},{4},{6},{7},{8}} => {{1,2,5},{3},{4},{6},{7},{8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => {{1,2,5,6,7},{3},{4},{8}} => {{1,2,5,6,7},{3},{4},{8}} => {{1,2,5,6,7},{3},{4},{8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,5,6,7,8},{3},{4}} => {{1,2,5,6,7,8},{3},{4}}
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => {{1,2,5,6,8},{3},{4},{7}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2,5,6,8},{3},{4},{7}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => {{1,2,5,7,8},{3},{4},{6}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2,5,7,8},{3},{4},{6}}
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => {{1,2,5,8},{3},{4},{6},{7}} => {{1,2,5,8},{3},{4},{6},{7}} => {{1,2,5,8},{3},{4},{6},{7}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => {{1,2,5,8},{3},{4},{6,7}} => {{1,2,5,7},{3},{4},{6,8}} => {{1,2,5,8},{3},{4},{6,7}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => {{1,2,6},{3},{4},{5},{7},{8}} => {{1,2,6},{3},{4},{5},{7},{8}} => {{1,2,6},{3},{4},{5},{7},{8}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => {{1,2,6,7,8},{3},{4},{5}} => {{1,2,6,7,8},{3},{4},{5}} => {{1,2,6,7,8},{3},{4},{5}}
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => {{1,2,6,8},{3},{4},{5},{7}} => {{1,2,6,8},{3},{4},{5},{7}} => {{1,2,6,8},{3},{4},{5},{7}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => {{1,2,7},{3},{4},{5},{6},{8}} => {{1,2,7},{3},{4},{5},{6},{8}} => {{1,2,7},{3},{4},{5},{6},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => {{1,2,8},{3},{4},{5},{6},{7}} => {{1,2,8},{3},{4},{5},{6},{7}} => {{1,2,8},{3},{4},{5},{6},{7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => {{1,2,6},{3},{4,5},{7,8}} => {{1,2,5},{3},{4,6},{7,8}} => {{1,2,6},{3},{4,5},{7,8}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => {{1,2,7,8},{3},{4,5},{6}} => {{1,2,5},{3},{4,7,8},{6}} => {{1,2,7,8},{3},{4,5},{6}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => {{1,2,8},{3},{4,5},{6,7}} => {{1,2,5},{3},{4,7},{6,8}} => {{1,2,8},{3},{4,5},{6,7}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => {{1,2,7,8},{3},{4,5,6}} => {{1,2,5,7,8},{3},{4,6}} => {{1,2,7,8},{3},{4,5,6}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => {{1,2,8},{3},{4,5,6,7}} => {{1,2,5,7},{3},{4,6,8}} => {{1,2,8},{3},{4,5,6,7}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => {{1,2,8},{3},{4,5,7},{6}} => {{1,2,5,8},{3},{4,7},{6}} => {{1,2,8},{3},{4,5,7},{6}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => {{1,2,8},{3},{4,7},{5,6}} => {{1,2,6},{3},{4,7},{5,8}} => {{1,2,8},{3},{4,7},{5,6}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => {{1,2,5},{3,4},{6},{7},{8}} => {{1,2,4},{3,5},{6},{7},{8}} => {{1,2,5},{3,4},{6},{7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => {{1,2,5},{3,4},{6},{7,8}} => {{1,2,4},{3,5},{6},{7,8}} => {{1,2,5},{3,4},{6},{7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => {{1,2,5},{3,4},{6,7},{8}} => {{1,2,4},{3,5},{6,7},{8}} => {{1,2,5},{3,4},{6,7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => {{1,2,5},{3,4},{6,8},{7}} => {{1,2,4},{3,5},{6,8},{7}} => {{1,2,5},{3,4},{6,8},{7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => {{1,2,5,6},{3,4},{7,8}} => {{1,2,4},{3,5,6},{7,8}} => {{1,2,5,6},{3,4},{7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => {{1,2,5,6,7,8},{3,4}} => {{1,2,4},{3,5,6,7,8}} => {{1,2,5,6,7,8},{3,4}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => {{1,2,5,6,8},{3,4},{7}} => {{1,2,4},{3,5,6,8},{7}} => {{1,2,5,6,8},{3,4},{7}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => {{1,2,5,7,8},{3,4},{6}} => {{1,2,4},{3,5,7,8},{6}} => {{1,2,5,7,8},{3,4},{6}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => {{1,2,5,8},{3,4},{6},{7}} => {{1,2,4},{3,5,8},{6},{7}} => {{1,2,5,8},{3,4},{6},{7}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => {{1,2,5,8},{3,4},{6,7}} => {{1,2,4},{3,5,7},{6,8}} => {{1,2,5,8},{3,4},{6,7}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => {{1,2,6},{3,4},{5},{7,8}} => {{1,2,4},{3,6},{5},{7,8}} => {{1,2,6},{3,4},{5},{7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,6,4,3,5,7,8,1] => {{1,2,6,7,8},{3,4},{5}} => {{1,2,4},{3,6,7,8},{5}} => {{1,2,6,7,8},{3,4},{5}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => {{1,2,6,8},{3,4},{5},{7}} => {{1,2,4},{3,6,8},{5},{7}} => {{1,2,6,8},{3,4},{5},{7}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => {{1,2,7,8},{3,4},{5},{6}} => {{1,2,4},{3,7,8},{5},{6}} => {{1,2,7,8},{3,4},{5},{6}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => {{1,2,8},{3,4},{5},{6},{7}} => {{1,2,4},{3,8},{5},{6},{7}} => {{1,2,8},{3,4},{5},{6},{7}}
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => {{1,2,8},{3,4},{5},{6,7}} => {{1,2,4},{3,7},{5},{6,8}} => {{1,2,8},{3,4},{5},{6,7}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => {{1,2,7,8},{3,4},{5,6}} => {{1,2,4},{3,6},{5,7,8}} => {{1,2,7,8},{3,4},{5,6}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => {{1,2,8},{3,4},{5,6},{7}} => {{1,2,4},{3,6},{5,8},{7}} => {{1,2,8},{3,4},{5,6},{7}}
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => {{1,2,8},{3,4},{5,7},{6}} => {{1,2,4},{3,7},{5,8},{6}} => {{1,2,8},{3,4},{5,7},{6}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => {{1,2,6},{3,4,5},{7},{8}} => {{1,2,4,6},{3,5},{7},{8}} => {{1,2,6},{3,4,5},{7},{8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => {{1,2,6,7,8},{3,4,5}} => {{1,2,4,6,7,8},{3,5}} => {{1,2,6,7,8},{3,4,5}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => {{1,2,8},{3,4,5},{6},{7}} => {{1,2,4,8},{3,5},{6},{7}} => {{1,2,8},{3,4,5},{6},{7}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => {{1,2,7},{3,4,5,6},{8}} => {{1,2,4,6},{3,5,7},{8}} => {{1,2,7},{3,4,5,6},{8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => {{1,2,7,8},{3,4,5,6}} => {{1,2,4,6},{3,5,7,8}} => {{1,2,7,8},{3,4,5,6}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => {{1,2,8},{3,4,5,6},{7}} => {{1,2,4,6},{3,5,8},{7}} => {{1,2,8},{3,4,5,6},{7}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => {{1,2,8},{3,4,5,6,7}} => {{1,2,4,6,8},{3,5,7}} => {{1,2,8},{3,4,5,6,7}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => {{1,2,7},{3,4,6},{5},{8}} => {{1,2,4,7},{3,6},{5},{8}} => {{1,2,7},{3,4,6},{5},{8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => {{1,2,7,8},{3,4,6},{5}} => {{1,2,4,7,8},{3,6},{5}} => {{1,2,7,8},{3,4,6},{5}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => {{1,2,8},{3,4,6},{5},{7}} => {{1,2,4,8},{3,6},{5},{7}} => {{1,2,8},{3,4,6},{5},{7}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => {{1,2,8},{3,4,7},{5,6}} => {{1,2,4,7},{3,6},{5,8}} => {{1,2,8},{3,4,7},{5,6}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => {{1,2,6},{3,5},{4},{7,8}} => {{1,2,5},{3,6},{4},{7,8}} => {{1,2,6},{3,5},{4},{7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => {{1,2,6,8},{3,5},{4},{7}} => {{1,2,5},{3,6,8},{4},{7}} => {{1,2,6,8},{3,5},{4},{7}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => {{1,2,7,8},{3,5},{4},{6}} => {{1,2,5},{3,7,8},{4},{6}} => {{1,2,7,8},{3,5},{4},{6}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => {{1,2,8},{3,5},{4},{6,7}} => {{1,2,5},{3,7},{4},{6,8}} => {{1,2,8},{3,5},{4},{6,7}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => {{1,2,7,8},{3,5,6},{4}} => {{1,2,5,7,8},{3,6},{4}} => {{1,2,7,8},{3,5,6},{4}}
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => {{1,2,8},{3,5,7},{4},{6}} => {{1,2,5,8},{3,7},{4},{6}} => {{1,2,8},{3,5,7},{4},{6}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => {{1,2,7,8},{3,6},{4},{5}} => {{1,2,6},{3,7,8},{4},{5}} => {{1,2,7,8},{3,6},{4},{5}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => {{1,2,8},{3,7},{4},{5,6}} => {{1,2,6},{3,7},{4},{5,8}} => {{1,2,8},{3,7},{4},{5,6}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => {{1,2,7},{3,6},{4,5},{8}} => {{1,2,5},{3,6},{4,7},{8}} => {{1,2,7},{3,6},{4,5},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => {{1,2,7,8},{3,6},{4,5}} => {{1,2,5},{3,6},{4,7,8}} => {{1,2,7,8},{3,6},{4,5}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => {{1,2,8},{3,7},{4,5},{6}} => {{1,2,5},{3,7},{4,8},{6}} => {{1,2,8},{3,7},{4,5},{6}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => {{1,2,8},{3,7},{4,5,6}} => {{1,2,5,8},{3,6},{4,7}} => {{1,2,8},{3,7},{4,5,6}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => {{1,2,8},{3,7},{4,6},{5}} => {{1,2,6},{3,7},{4,8},{5}} => {{1,2,8},{3,7},{4,6},{5}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}} => {{1,3},{2},{4},{5},{6},{7},{8}} => {{1,3},{2},{4},{5},{6},{7},{8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => {{1,3},{2},{4},{5},{6},{7,8}} => {{1,3},{2},{4},{5},{6},{7,8}} => {{1,3},{2},{4},{5},{6},{7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => {{1,3},{2},{4},{5},{6,7,8}} => {{1,3},{2},{4},{5},{6,7,8}} => {{1,3},{2},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => {{1,3},{2},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => {{1,3},{2},{4},{5,6,7,8}} => {{1,3},{2},{4},{5,6,7,8}} => {{1,3},{2},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => {{1,3},{2},{4},{5,6,8},{7}} => {{1,3},{2},{4},{5,6,8},{7}} => {{1,3},{2},{4},{5,6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => {{1,3},{2},{4},{5,7},{6},{8}} => {{1,3},{2},{4},{5,7},{6},{8}} => {{1,3},{2},{4},{5,7},{6},{8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => {{1,3},{2},{4},{5,7,8},{6}} => {{1,3},{2},{4},{5,7,8},{6}} => {{1,3},{2},{4},{5,7,8},{6}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => {{1,3},{2},{4,5},{6},{7},{8}} => {{1,3},{2},{4,5},{6},{7},{8}} => {{1,3},{2},{4,5},{6},{7},{8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => {{1,3},{2},{4,5},{6,7},{8}} => {{1,3},{2},{4,5},{6,7},{8}} => {{1,3},{2},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => {{1,3},{2},{4,5,6},{7},{8}} => {{1,3},{2},{4,5,6},{7},{8}} => {{1,3},{2},{4,5,6},{7},{8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => {{1,3},{2},{4,5,6,7,8}} => {{1,3},{2},{4,5,6,7,8}} => {{1,3},{2},{4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => {{1,3},{2},{4,5,6,8},{7}} => {{1,3},{2},{4,5,6,8},{7}} => {{1,3},{2},{4,5,6,8},{7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => {{1,3},{2},{4,5,7},{6},{8}} => {{1,3},{2},{4,5,7},{6},{8}} => {{1,3},{2},{4,5,7},{6},{8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => {{1,3},{2},{4,5,7,8},{6}} => {{1,3},{2},{4,5,7,8},{6}} => {{1,3},{2},{4,5,7,8},{6}}
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => {{1,3},{2},{4,5,8},{6,7}} => {{1,3},{2},{4,5,7},{6,8}} => {{1,3},{2},{4,5,8},{6,7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => {{1,3},{2},{4,6},{5},{7},{8}} => {{1,3},{2},{4,6},{5},{7},{8}} => {{1,3},{2},{4,6},{5},{7},{8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => {{1,3},{2},{4,6},{5},{7,8}} => {{1,3},{2},{4,6},{5},{7,8}} => {{1,3},{2},{4,6},{5},{7,8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => {{1,3},{2},{4,6,7},{5},{8}} => {{1,3},{2},{4,6,7},{5},{8}} => {{1,3},{2},{4,6,7},{5},{8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => {{1,3},{2},{4,6,7,8},{5}} => {{1,3},{2},{4,6,7,8},{5}} => {{1,3},{2},{4,6,7,8},{5}}
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => {{1,3},{2},{4,6,8},{5},{7}} => {{1,3},{2},{4,6,8},{5},{7}} => {{1,3},{2},{4,6,8},{5},{7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => {{1,3},{2},{4,7},{5},{6},{8}} => {{1,3},{2},{4,7},{5},{6},{8}} => {{1,3},{2},{4,7},{5},{6},{8}}
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => {{1,3},{2},{4,8},{5},{6,7}} => {{1,3},{2},{4,7},{5},{6,8}} => {{1,3},{2},{4,8},{5},{6,7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => {{1,3},{2},{4,7,8},{5,6}} => {{1,3},{2},{4,6},{5,7,8}} => {{1,3},{2},{4,7,8},{5,6}}
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => {{1,3},{2},{4,8},{5,6},{7}} => {{1,3},{2},{4,6},{5,8},{7}} => {{1,3},{2},{4,8},{5,6},{7}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => {{1,3},{2},{4,8},{5,6,7}} => {{1,3},{2},{4,6,8},{5,7}} => {{1,3},{2},{4,8},{5,6,7}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => {{1,3},{2},{4,8},{5,7},{6}} => {{1,3},{2},{4,7},{5,8},{6}} => {{1,3},{2},{4,8},{5,7},{6}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => {{1,3,4},{2},{5},{6},{7},{8}} => {{1,3,4},{2},{5},{6},{7},{8}} => {{1,3,4},{2},{5},{6},{7},{8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => {{1,3,4},{2},{5},{6},{7,8}} => {{1,3,4},{2},{5},{6},{7,8}} => {{1,3,4},{2},{5},{6},{7,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => {{1,3,4},{2},{5},{6,7,8}} => {{1,3,4},{2},{5},{6,7,8}} => {{1,3,4},{2},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => {{1,3,4},{2},{5},{6,8},{7}} => {{1,3,4},{2},{5},{6,8},{7}} => {{1,3,4},{2},{5},{6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => {{1,3,4},{2},{5,6},{7,8}} => {{1,3,4},{2},{5,6},{7,8}} => {{1,3,4},{2},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => {{1,3,4},{2},{5,6,7},{8}} => {{1,3,4},{2},{5,6,7},{8}} => {{1,3,4},{2},{5,6,7},{8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => {{1,3,4},{2},{5,6,7,8}} => {{1,3,4},{2},{5,6,7,8}} => {{1,3,4},{2},{5,6,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => {{1,3,4},{2},{5,6,8},{7}} => {{1,3,4},{2},{5,6,8},{7}} => {{1,3,4},{2},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => {{1,3,4},{2},{5,7,8},{6}} => {{1,3,4},{2},{5,7,8},{6}} => {{1,3,4},{2},{5,7,8},{6}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => {{1,3,4},{2},{5,8},{6,7}} => {{1,3,4},{2},{5,7},{6,8}} => {{1,3,4},{2},{5,8},{6,7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => {{1,3,4,5},{2},{6},{7},{8}} => {{1,3,4,5},{2},{6},{7},{8}} => {{1,3,4,5},{2},{6},{7},{8}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => {{1,3,4,5},{2},{6,8},{7}} => {{1,3,4,5},{2},{6,8},{7}} => {{1,3,4,5},{2},{6,8},{7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => {{1,3,4,5,6},{2},{7},{8}} => {{1,3,4,5,6},{2},{7},{8}} => {{1,3,4,5,6},{2},{7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => {{1,3,4,5,6,7},{2},{8}} => {{1,3,4,5,6,7},{2},{8}} => {{1,3,4,5,6,7},{2},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => {{1,3,4,5,6,7,8},{2}} => {{1,3,4,5,6,7,8},{2}} => {{1,3,4,5,6,7,8},{2}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => {{1,3,4,5,6,8},{2},{7}} => {{1,3,4,5,6,8},{2},{7}} => {{1,3,4,5,6,8},{2},{7}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => {{1,3,4,5,7,8},{2},{6}} => {{1,3,4,5,7,8},{2},{6}} => {{1,3,4,5,7,8},{2},{6}}
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => {{1,3,4,5,8},{2},{6},{7}} => {{1,3,4,5,8},{2},{6},{7}} => {{1,3,4,5,8},{2},{6},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => {{1,3,4,6,8},{2},{5},{7}} => {{1,3,4,6,8},{2},{5},{7}} => {{1,3,4,6,8},{2},{5},{7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => {{1,3,4,7,8},{2},{5},{6}} => {{1,3,4,7,8},{2},{5},{6}} => {{1,3,4,7,8},{2},{5},{6}}
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => {{1,3,4,8},{2},{5},{6},{7}} => {{1,3,4,8},{2},{5},{6},{7}} => {{1,3,4,8},{2},{5},{6},{7}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => {{1,3,4,7,8},{2},{5,6}} => {{1,3,4,6},{2},{5,7,8}} => {{1,3,4,7,8},{2},{5,6}}
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => {{1,3,4,8},{2},{5,6,7}} => {{1,3,4,6,8},{2},{5,7}} => {{1,3,4,8},{2},{5,6,7}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => {{1,3,4,8},{2},{5,7},{6}} => {{1,3,4,7},{2},{5,8},{6}} => {{1,3,4,8},{2},{5,7},{6}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => {{1,3,5},{2},{4},{6},{7},{8}} => {{1,3,5},{2},{4},{6},{7},{8}} => {{1,3,5},{2},{4},{6},{7},{8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => {{1,3,5},{2},{4},{6},{7,8}} => {{1,3,5},{2},{4},{6},{7,8}} => {{1,3,5},{2},{4},{6},{7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => {{1,3,5},{2},{4},{6,7},{8}} => {{1,3,5},{2},{4},{6,7},{8}} => {{1,3,5},{2},{4},{6,7},{8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => {{1,3,5},{2},{4},{6,7,8}} => {{1,3,5},{2},{4},{6,7,8}} => {{1,3,5},{2},{4},{6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => {{1,3,5},{2},{4},{6,8},{7}} => {{1,3,5},{2},{4},{6,8},{7}} => {{1,3,5},{2},{4},{6,8},{7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => {{1,3,5,6},{2},{4},{7,8}} => {{1,3,5,6},{2},{4},{7,8}} => {{1,3,5,6},{2},{4},{7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => {{1,3,5,6,7,8},{2},{4}} => {{1,3,5,6,7,8},{2},{4}} => {{1,3,5,6,7,8},{2},{4}}
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => {{1,3,5,6,8},{2},{4},{7}} => {{1,3,5,6,8},{2},{4},{7}} => {{1,3,5,6,8},{2},{4},{7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => {{1,3,5,7},{2},{4},{6},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1,3,5,7},{2},{4},{6},{8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => {{1,3,5,7,8},{2},{4},{6}} => {{1,3,5,7,8},{2},{4},{6}} => {{1,3,5,7,8},{2},{4},{6}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => {{1,3,5,8},{2},{4},{6},{7}} => {{1,3,5,8},{2},{4},{6},{7}} => {{1,3,5,8},{2},{4},{6},{7}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => {{1,3,7},{2},{4},{5},{6},{8}} => {{1,3,7},{2},{4},{5},{6},{8}} => {{1,3,7},{2},{4},{5},{6},{8}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => {{1,3,8},{2},{4},{5},{6},{7}} => {{1,3,8},{2},{4},{5},{6},{7}} => {{1,3,8},{2},{4},{5},{6},{7}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => {{1,3,7,8},{2},{4},{5,6}} => {{1,3,6},{2},{4},{5,7,8}} => {{1,3,7,8},{2},{4},{5,6}}
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => {{1,3,6,8},{2},{4,5},{7}} => {{1,3,5},{2},{4,6,8},{7}} => {{1,3,6,8},{2},{4,5},{7}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => {{1,3,8},{2},{4,5},{6,7}} => {{1,3,5},{2},{4,7},{6,8}} => {{1,3,8},{2},{4,5},{6,7}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => {{1,3,7},{2},{4,5,6},{8}} => {{1,3,5,7},{2},{4,6},{8}} => {{1,3,7},{2},{4,5,6},{8}}
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => {{1,3,8},{2},{4,5,6},{7}} => {{1,3,5,8},{2},{4,6},{7}} => {{1,3,8},{2},{4,5,6},{7}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => {{1,3,8},{2},{4,5,7},{6}} => {{1,3,5,8},{2},{4,7},{6}} => {{1,3,8},{2},{4,5,7},{6}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => {{1,3,7},{2},{4,6},{5},{8}} => {{1,3,6},{2},{4,7},{5},{8}} => {{1,3,7},{2},{4,6},{5},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => {{1,3,7,8},{2},{4,6},{5}} => {{1,3,6},{2},{4,7,8},{5}} => {{1,3,7,8},{2},{4,6},{5}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => {{1,3,8},{2},{4,7},{5,6}} => {{1,3,6},{2},{4,7},{5,8}} => {{1,3,8},{2},{4,7},{5,6}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => {{1,4},{2},{3},{5},{6},{7},{8}} => {{1,4},{2},{3},{5},{6},{7},{8}} => {{1,4},{2},{3},{5},{6},{7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => {{1,4},{2},{3},{5},{6,7,8}} => {{1,4},{2},{3},{5},{6,7,8}} => {{1,4},{2},{3},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => {{1,4},{2},{3},{5},{6,8},{7}} => {{1,4},{2},{3},{5},{6,8},{7}} => {{1,4},{2},{3},{5},{6,8},{7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => {{1,4},{2},{3},{5,6},{7},{8}} => {{1,4},{2},{3},{5,6},{7},{8}} => {{1,4},{2},{3},{5,6},{7},{8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => {{1,4},{2},{3},{5,6},{7,8}} => {{1,4},{2},{3},{5,6},{7,8}} => {{1,4},{2},{3},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => {{1,4},{2},{3},{5,6,7,8}} => {{1,4},{2},{3},{5,6,7,8}} => {{1,4},{2},{3},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => {{1,4},{2},{3},{5,6,8},{7}} => {{1,4},{2},{3},{5,6,8},{7}} => {{1,4},{2},{3},{5,6,8},{7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => {{1,4},{2},{3},{5,7},{6},{8}} => {{1,4},{2},{3},{5,7},{6},{8}} => {{1,4},{2},{3},{5,7},{6},{8}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => {{1,4},{2},{3},{5,8},{6},{7}} => {{1,4},{2},{3},{5,8},{6},{7}} => {{1,4},{2},{3},{5,8},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => {{1,4,5},{2},{3},{6},{7},{8}} => {{1,4,5},{2},{3},{6},{7},{8}} => {{1,4,5},{2},{3},{6},{7},{8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => {{1,4,5},{2},{3},{6,7,8}} => {{1,4,5},{2},{3},{6,7,8}} => {{1,4,5},{2},{3},{6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => {{1,4,5},{2},{3},{6,8},{7}} => {{1,4,5},{2},{3},{6,8},{7}} => {{1,4,5},{2},{3},{6,8},{7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => {{1,4,5,6},{2},{3},{7},{8}} => {{1,4,5,6},{2},{3},{7},{8}} => {{1,4,5,6},{2},{3},{7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => {{1,4,5,6},{2},{3},{7,8}} => {{1,4,5,6},{2},{3},{7,8}} => {{1,4,5,6},{2},{3},{7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => {{1,4,5,6,7},{2},{3},{8}} => {{1,4,5,6,7},{2},{3},{8}} => {{1,4,5,6,7},{2},{3},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => {{1,4,5,6,7,8},{2},{3}} => {{1,4,5,6,7,8},{2},{3}} => {{1,4,5,6,7,8},{2},{3}}
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => {{1,4,5,6,8},{2},{3},{7}} => {{1,4,5,6,8},{2},{3},{7}} => {{1,4,5,6,8},{2},{3},{7}}
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => {{1,4,6,8},{2},{3},{5},{7}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1,4,6,8},{2},{3},{5},{7}}
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => {{1,4,8},{2},{3},{5},{6},{7}} => {{1,4,8},{2},{3},{5},{6},{7}} => {{1,4,8},{2},{3},{5},{6},{7}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => {{1,4,7,8},{2},{3},{5,6}} => {{1,4,6},{2},{3},{5,7,8}} => {{1,4,7,8},{2},{3},{5,6}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => {{1,5},{2},{3},{4},{6},{7},{8}} => {{1,5},{2},{3},{4},{6},{7},{8}} => {{1,5},{2},{3},{4},{6},{7},{8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => {{1,5},{2},{3},{4},{6},{7,8}} => {{1,5},{2},{3},{4},{6},{7,8}} => {{1,5},{2},{3},{4},{6},{7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => {{1,5},{2},{3},{4},{6,7,8}} => {{1,5},{2},{3},{4},{6,7,8}} => {{1,5},{2},{3},{4},{6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => {{1,5},{2},{3},{4},{6,8},{7}} => {{1,5},{2},{3},{4},{6,8},{7}} => {{1,5},{2},{3},{4},{6,8},{7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => {{1,5,6},{2},{3},{4},{7},{8}} => {{1,5,6},{2},{3},{4},{7},{8}} => {{1,5,6},{2},{3},{4},{7},{8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => {{1,5,6,7},{2},{3},{4},{8}} => {{1,5,6,7},{2},{3},{4},{8}} => {{1,5,6,7},{2},{3},{4},{8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => {{1,5,6,7,8},{2},{3},{4}} => {{1,5,6,7,8},{2},{3},{4}} => {{1,5,6,7,8},{2},{3},{4}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => {{1,5,7},{2},{3},{4},{6},{8}} => {{1,5,7},{2},{3},{4},{6},{8}} => {{1,5,7},{2},{3},{4},{6},{8}}
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => {{1,5,8},{2},{3},{4},{6},{7}} => {{1,5,8},{2},{3},{4},{6},{7}} => {{1,5,8},{2},{3},{4},{6},{7}}
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => {{1,5,8},{2},{3},{4},{6,7}} => {{1,5,7},{2},{3},{4},{6,8}} => {{1,5,8},{2},{3},{4},{6,7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => {{1,6},{2},{3},{4},{5},{7},{8}} => {{1,6},{2},{3},{4},{5},{7},{8}} => {{1,6},{2},{3},{4},{5},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => {{1,6},{2},{3},{4},{5},{7,8}} => {{1,6},{2},{3},{4},{5},{7,8}} => {{1,6},{2},{3},{4},{5},{7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => {{1,6,7},{2},{3},{4},{5},{8}} => {{1,6,7},{2},{3},{4},{5},{8}} => {{1,6,7},{2},{3},{4},{5},{8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => {{1,6,7,8},{2},{3},{4},{5}} => {{1,6,7,8},{2},{3},{4},{5}} => {{1,6,7,8},{2},{3},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => {{1,6,8},{2},{3},{4},{5},{7}} => {{1,6,8},{2},{3},{4},{5},{7}} => {{1,6,8},{2},{3},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => {{1,7},{2},{3},{4},{5},{6},{8}} => {{1,7},{2},{3},{4},{5},{6},{8}} => {{1,7},{2},{3},{4},{5},{6},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => {{1,7,8},{2},{3},{4},{5},{6}} => {{1,7,8},{2},{3},{4},{5},{6}} => {{1,7,8},{2},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => {{1,8},{2},{3},{4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5},{6},{7}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => {{1,8},{2},{3},{4},{5},{6,7}} => {{1,7},{2},{3},{4},{5},{6,8}} => {{1,8},{2},{3},{4},{5},{6,7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => {{1,6},{2},{3},{4,5},{7},{8}} => {{1,5},{2},{3},{4,6},{7},{8}} => {{1,6},{2},{3},{4,5},{7},{8}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => {{1,8},{2},{3},{4,5},{6},{7}} => {{1,5},{2},{3},{4,8},{6},{7}} => {{1,8},{2},{3},{4,5},{6},{7}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => {{1,7},{2},{3},{4,5,6},{8}} => {{1,5,7},{2},{3},{4,6},{8}} => {{1,7},{2},{3},{4,5,6},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => {{1,7},{2},{3},{4,6},{5},{8}} => {{1,6},{2},{3},{4,7},{5},{8}} => {{1,7},{2},{3},{4,6},{5},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => {{1,8},{2},{3},{4,6},{5},{7}} => {{1,6},{2},{3},{4,8},{5},{7}} => {{1,8},{2},{3},{4,6},{5},{7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => {{1,5},{2},{3,4},{6},{7},{8}} => {{1,4},{2},{3,5},{6},{7},{8}} => {{1,5},{2},{3,4},{6},{7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => {{1,5},{2},{3,4},{6,8},{7}} => {{1,4},{2},{3,5},{6,8},{7}} => {{1,5},{2},{3,4},{6,8},{7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => {{1,5,6},{2},{3,4},{7,8}} => {{1,4},{2},{3,5,6},{7,8}} => {{1,5,6},{2},{3,4},{7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => {{1,5,6,7},{2},{3,4},{8}} => {{1,4},{2},{3,5,6,7},{8}} => {{1,5,6,7},{2},{3,4},{8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => {{1,5,7,8},{2},{3,4},{6}} => {{1,4},{2},{3,5,7,8},{6}} => {{1,5,7,8},{2},{3,4},{6}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => {{1,7},{2},{3,4},{5,6},{8}} => {{1,4},{2},{3,6},{5,7},{8}} => {{1,7},{2},{3,4},{5,6},{8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => {{1,7,8},{2},{3,4},{5,6}} => {{1,4},{2},{3,6},{5,7,8}} => {{1,7,8},{2},{3,4},{5,6}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => {{1,8},{2},{3,4},{5,6,7}} => {{1,4},{2},{3,6,8},{5,7}} => {{1,8},{2},{3,4},{5,6,7}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => {{1,7,8},{2},{3,4,5},{6}} => {{1,4,7,8},{2},{3,5},{6}} => {{1,7,8},{2},{3,4,5},{6}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => {{1,8},{2},{3,4,5},{6,7}} => {{1,4,7},{2},{3,5},{6,8}} => {{1,8},{2},{3,4,5},{6,7}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => {{1,8},{2},{3,4,5,6,7}} => {{1,4,6,8},{2},{3,5,7}} => {{1,8},{2},{3,4,5,6,7}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => {{1,8},{2},{3,4,5,7},{6}} => {{1,4,7},{2},{3,5,8},{6}} => {{1,8},{2},{3,4,5,7},{6}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => {{1,7},{2},{3,4,6},{5},{8}} => {{1,4,7},{2},{3,6},{5},{8}} => {{1,7},{2},{3,4,6},{5},{8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => {{1,7,8},{2},{3,4,6},{5}} => {{1,4,7,8},{2},{3,6},{5}} => {{1,7,8},{2},{3,4,6},{5}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => {{1,8},{2},{3,4,7},{5,6}} => {{1,4,7},{2},{3,6},{5,8}} => {{1,8},{2},{3,4,7},{5,6}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => {{1,6},{2},{3,5},{4},{7},{8}} => {{1,5},{2},{3,6},{4},{7},{8}} => {{1,6},{2},{3,5},{4},{7},{8}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => {{1,8},{2},{3,7},{4},{5},{6}} => {{1,7},{2},{3,8},{4},{5},{6}} => {{1,8},{2},{3,7},{4},{5},{6}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => {{1,8},{2},{3,7},{4},{5,6}} => {{1,6},{2},{3,7},{4},{5,8}} => {{1,8},{2},{3,7},{4},{5,6}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => {{1,7},{2},{3,6},{4,5},{8}} => {{1,5},{2},{3,6},{4,7},{8}} => {{1,7},{2},{3,6},{4,5},{8}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => {{1,8},{2},{3,6,7},{4,5}} => {{1,5},{2},{3,6,8},{4,7}} => {{1,8},{2},{3,6,7},{4,5}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => {{1,8},{2},{3,7},{4,5,6}} => {{1,5,8},{2},{3,6},{4,7}} => {{1,8},{2},{3,7},{4,5,6}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => {{1,4},{2,3},{5},{6},{7},{8}} => {{1,3},{2,4},{5},{6},{7},{8}} => {{1,4},{2,3},{5},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => {{1,4},{2,3},{5},{6},{7,8}} => {{1,3},{2,4},{5},{6},{7,8}} => {{1,4},{2,3},{5},{6},{7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => {{1,4},{2,3},{5},{6,7,8}} => {{1,3},{2,4},{5},{6,7,8}} => {{1,4},{2,3},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => {{1,4},{2,3},{5,6},{7,8}} => {{1,3},{2,4},{5,6},{7,8}} => {{1,4},{2,3},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => {{1,4},{2,3},{5,6,7},{8}} => {{1,3},{2,4},{5,6,7},{8}} => {{1,4},{2,3},{5,6,7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => {{1,4},{2,3},{5,6,7,8}} => {{1,3},{2,4},{5,6,7,8}} => {{1,4},{2,3},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => {{1,4},{2,3},{5,6,8},{7}} => {{1,3},{2,4},{5,6,8},{7}} => {{1,4},{2,3},{5,6,8},{7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => {{1,4},{2,3},{5,7,8},{6}} => {{1,3},{2,4},{5,7,8},{6}} => {{1,4},{2,3},{5,7,8},{6}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => {{1,4},{2,3},{5,8},{6,7}} => {{1,3},{2,4},{5,7},{6,8}} => {{1,4},{2,3},{5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => {{1,4,5},{2,3},{6,8},{7}} => {{1,3},{2,4,5},{6,8},{7}} => {{1,4,5},{2,3},{6,8},{7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => {{1,4,5,6},{2,3},{7,8}} => {{1,3},{2,4,5,6},{7,8}} => {{1,4,5,6},{2,3},{7,8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => {{1,4,5,6,7},{2,3},{8}} => {{1,3},{2,4,5,6,7},{8}} => {{1,4,5,6,7},{2,3},{8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => {{1,4,5,6,7,8},{2,3}} => {{1,3},{2,4,5,6,7,8}} => {{1,4,5,6,7,8},{2,3}}
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => {{1,4,5,6,8},{2,3},{7}} => {{1,3},{2,4,5,6,8},{7}} => {{1,4,5,6,8},{2,3},{7}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => {{1,4,5,7},{2,3},{6},{8}} => {{1,3},{2,4,5,7},{6},{8}} => {{1,4,5,7},{2,3},{6},{8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => {{1,4,5,7,8},{2,3},{6}} => {{1,3},{2,4,5,7,8},{6}} => {{1,4,5,7,8},{2,3},{6}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => {{1,4,5,8},{2,3},{6,7}} => {{1,3},{2,4,5,7},{6,8}} => {{1,4,5,8},{2,3},{6,7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => {{1,4,6},{2,3},{5},{7,8}} => {{1,3},{2,4,6},{5},{7,8}} => {{1,4,6},{2,3},{5},{7,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => {{1,4,6,7},{2,3},{5},{8}} => {{1,3},{2,4,6,7},{5},{8}} => {{1,4,6,7},{2,3},{5},{8}}
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => {{1,4,6,8},{2,3},{5},{7}} => {{1,3},{2,4,6,8},{5},{7}} => {{1,4,6,8},{2,3},{5},{7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => {{1,4,7,8},{2,3},{5},{6}} => {{1,3},{2,4,7,8},{5},{6}} => {{1,4,7,8},{2,3},{5},{6}}
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => {{1,4,8},{2,3},{5},{6},{7}} => {{1,3},{2,4,8},{5},{6},{7}} => {{1,4,8},{2,3},{5},{6},{7}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => {{1,4,8},{2,3},{5},{6,7}} => {{1,3},{2,4,7},{5},{6,8}} => {{1,4,8},{2,3},{5},{6,7}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => {{1,4,8},{2,3},{5,6,7}} => {{1,3},{2,4,6,8},{5,7}} => {{1,4,8},{2,3},{5,6,7}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => {{1,4,8},{2,3},{5,7},{6}} => {{1,3},{2,4,7},{5,8},{6}} => {{1,4,8},{2,3},{5,7},{6}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => {{1,5},{2,3},{4},{6,7},{8}} => {{1,3},{2,5},{4},{6,7},{8}} => {{1,5},{2,3},{4},{6,7},{8}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => {{1,5},{2,3},{4},{6,8},{7}} => {{1,3},{2,5},{4},{6,8},{7}} => {{1,5},{2,3},{4},{6,8},{7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => {{1,5,6},{2,3},{4},{7,8}} => {{1,3},{2,5,6},{4},{7,8}} => {{1,5,6},{2,3},{4},{7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => {{1,5,6,7,8},{2,3},{4}} => {{1,3},{2,5,6,7,8},{4}} => {{1,5,6,7,8},{2,3},{4}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => {{1,8},{2,3},{4},{5},{6},{7}} => {{1,3},{2,8},{4},{5},{6},{7}} => {{1,8},{2,3},{4},{5},{6},{7}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => {{1,8},{2,3},{4},{5,6,7}} => {{1,3},{2,6,8},{4},{5,7}} => {{1,8},{2,3},{4},{5,6,7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => {{1,6},{2,3},{4,5},{7},{8}} => {{1,3},{2,5},{4,6},{7},{8}} => {{1,6},{2,3},{4,5},{7},{8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => {{1,6},{2,3},{4,5},{7,8}} => {{1,3},{2,5},{4,6},{7,8}} => {{1,6},{2,3},{4,5},{7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => {{1,6,7},{2,3},{4,5},{8}} => {{1,3},{2,5},{4,6,7},{8}} => {{1,6,7},{2,3},{4,5},{8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => {{1,6,7,8},{2,3},{4,5}} => {{1,3},{2,5},{4,6,7,8}} => {{1,6,7,8},{2,3},{4,5}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => {{1,7},{2,3},{4,5},{6},{8}} => {{1,3},{2,5},{4,7},{6},{8}} => {{1,7},{2,3},{4,5},{6},{8}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => {{1,8},{2,3},{4,5},{6,7}} => {{1,3},{2,5},{4,7},{6,8}} => {{1,8},{2,3},{4,5},{6,7}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => {{1,8},{2,3},{4,5,6},{7}} => {{1,3},{2,5,8},{4,6},{7}} => {{1,8},{2,3},{4,5,6},{7}}
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => {{1,8},{2,3},{4,5,7},{6}} => {{1,3},{2,5,8},{4,7},{6}} => {{1,8},{2,3},{4,5,7},{6}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => {{1,8},{2,3},{4,6,7},{5}} => {{1,3},{2,6,8},{4,7},{5}} => {{1,8},{2,3},{4,6,7},{5}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => {{1,8},{2,3},{4,7},{5,6}} => {{1,3},{2,6},{4,7},{5,8}} => {{1,8},{2,3},{4,7},{5,6}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => {{1,5},{2,3,4},{6},{7},{8}} => {{1,3,5},{2,4},{6},{7},{8}} => {{1,5},{2,3,4},{6},{7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => {{1,5},{2,3,4},{6,8},{7}} => {{1,3,5},{2,4},{6,8},{7}} => {{1,5},{2,3,4},{6,8},{7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => {{1,5,6,7,8},{2,3,4}} => {{1,3,5,6,7,8},{2,4}} => {{1,5,6,7,8},{2,3,4}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => {{1,5,7},{2,3,4},{6},{8}} => {{1,3,5,7},{2,4},{6},{8}} => {{1,5,7},{2,3,4},{6},{8}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => {{1,5,8},{2,3,4},{6},{7}} => {{1,3,5,8},{2,4},{6},{7}} => {{1,5,8},{2,3,4},{6},{7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => {{1,6},{2,3,4},{5},{7,8}} => {{1,3,6},{2,4},{5},{7,8}} => {{1,6},{2,3,4},{5},{7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => {{1,8},{2,3,4},{5},{6},{7}} => {{1,3,8},{2,4},{5},{6},{7}} => {{1,8},{2,3,4},{5},{6},{7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,2,6,5,1,8] => {{1,7},{2,3,4},{5,6},{8}} => {{1,3,6},{2,4},{5,7},{8}} => {{1,7},{2,3,4},{5,6},{8}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => {{1,8},{2,3,4},{5,6},{7}} => {{1,3,6},{2,4},{5,8},{7}} => {{1,8},{2,3,4},{5,6},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => {{1,6,7,8},{2,3,4,5}} => {{1,3,5},{2,4,6,7,8}} => {{1,6,7,8},{2,3,4,5}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => {{1,6,8},{2,3,4,5},{7}} => {{1,3,5},{2,4,6,8},{7}} => {{1,6,8},{2,3,4,5},{7}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => {{1,8},{2,3,4,5},{6},{7}} => {{1,3,5},{2,4,8},{6},{7}} => {{1,8},{2,3,4,5},{6},{7}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => {{1,8},{2,3,4,5},{6,7}} => {{1,3,5},{2,4,7},{6,8}} => {{1,8},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => {{1,7},{2,3,4,5,6},{8}} => {{1,3,5,7},{2,4,6},{8}} => {{1,7},{2,3,4,5,6},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => {{1,7,8},{2,3,4,5,6}} => {{1,3,5,7,8},{2,4,6}} => {{1,7,8},{2,3,4,5,6}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => {{1,8},{2,3,4,5,6,7}} => {{1,3,5,7},{2,4,6,8}} => {{1,8},{2,3,4,5,6,7}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => {{1,8},{2,3,4,5,7},{6}} => {{1,3,5,8},{2,4,7},{6}} => {{1,8},{2,3,4,5,7},{6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => {{1,7},{2,3,4,6},{5},{8}} => {{1,3,6},{2,4,7},{5},{8}} => {{1,7},{2,3,4,6},{5},{8}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => {{1,8},{2,3,4,7},{5,6}} => {{1,3,6},{2,4,7},{5,8}} => {{1,8},{2,3,4,7},{5,6}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => {{1,6},{2,3,5},{4},{7,8}} => {{1,3,6},{2,5},{4},{7,8}} => {{1,6},{2,3,5},{4},{7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => {{1,6,7},{2,3,5},{4},{8}} => {{1,3,6,7},{2,5},{4},{8}} => {{1,6,7},{2,3,5},{4},{8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => {{1,6,7,8},{2,3,5},{4}} => {{1,3,6,7,8},{2,5},{4}} => {{1,6,7,8},{2,3,5},{4}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => {{1,7},{2,3,5},{4},{6},{8}} => {{1,3,7},{2,5},{4},{6},{8}} => {{1,7},{2,3,5},{4},{6},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => {{1,7},{2,3,5,6},{4},{8}} => {{1,3,6},{2,5,7},{4},{8}} => {{1,7},{2,3,5,6},{4},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => {{1,7,8},{2,3,5,6},{4}} => {{1,3,6},{2,5,7,8},{4}} => {{1,7,8},{2,3,5,6},{4}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => {{1,8},{2,3,5,6,7},{4}} => {{1,3,6,8},{2,5,7},{4}} => {{1,8},{2,3,5,6,7},{4}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => {{1,8},{2,3,5,7},{4},{6}} => {{1,3,7},{2,5,8},{4},{6}} => {{1,8},{2,3,5,7},{4},{6}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => {{1,7,8},{2,3,6},{4},{5}} => {{1,3,7,8},{2,6},{4},{5}} => {{1,7,8},{2,3,6},{4},{5}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => {{1,8},{2,3,7},{4},{5,6}} => {{1,3,7},{2,6},{4},{5,8}} => {{1,8},{2,3,7},{4},{5,6}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => {{1,7},{2,3,6},{4,5},{8}} => {{1,3,6},{2,5},{4,7},{8}} => {{1,7},{2,3,6},{4,5},{8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => {{1,7,8},{2,3,6},{4,5}} => {{1,3,6},{2,5},{4,7,8}} => {{1,7,8},{2,3,6},{4,5}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => {{1,8},{2,3,6},{4,5},{7}} => {{1,3,6},{2,5},{4,8},{7}} => {{1,8},{2,3,6},{4,5},{7}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => {{1,8},{2,3,7},{4,5,6}} => {{1,3,6},{2,5,8},{4,7}} => {{1,8},{2,3,7},{4,5,6}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => {{1,8},{2,3,7},{4,6},{5}} => {{1,3,7},{2,6},{4,8},{5}} => {{1,8},{2,3,7},{4,6},{5}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => {{1,5},{2,4},{3},{6},{7},{8}} => {{1,4},{2,5},{3},{6},{7},{8}} => {{1,5},{2,4},{3},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => {{1,5},{2,4},{3},{6,7,8}} => {{1,4},{2,5},{3},{6,7,8}} => {{1,5},{2,4},{3},{6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => {{1,5},{2,4},{3},{6,8},{7}} => {{1,4},{2,5},{3},{6,8},{7}} => {{1,5},{2,4},{3},{6,8},{7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => {{1,5,6},{2,4},{3},{7,8}} => {{1,4},{2,5,6},{3},{7,8}} => {{1,5,6},{2,4},{3},{7,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => {{1,5,6,7},{2,4},{3},{8}} => {{1,4},{2,5,6,7},{3},{8}} => {{1,5,6,7},{2,4},{3},{8}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => {{1,5,6,8},{2,4},{3},{7}} => {{1,4},{2,5,6,8},{3},{7}} => {{1,5,6,8},{2,4},{3},{7}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => {{1,5,7},{2,4},{3},{6},{8}} => {{1,4},{2,5,7},{3},{6},{8}} => {{1,5,7},{2,4},{3},{6},{8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => {{1,5,7,8},{2,4},{3},{6}} => {{1,4},{2,5,7,8},{3},{6}} => {{1,5,7,8},{2,4},{3},{6}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => {{1,5,8},{2,4},{3},{6,7}} => {{1,4},{2,5,7},{3},{6,8}} => {{1,5,8},{2,4},{3},{6,7}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => {{1,8},{2,4},{3},{5},{6},{7}} => {{1,4},{2,8},{3},{5},{6},{7}} => {{1,8},{2,4},{3},{5},{6},{7}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => {{1,7},{2,4},{3},{5,6},{8}} => {{1,4},{2,6},{3},{5,7},{8}} => {{1,7},{2,4},{3},{5,6},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => {{1,7,8},{2,4},{3},{5,6}} => {{1,4},{2,6},{3},{5,7,8}} => {{1,7,8},{2,4},{3},{5,6}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => {{1,8},{2,4},{3},{5,6,7}} => {{1,4},{2,6,8},{3},{5,7}} => {{1,8},{2,4},{3},{5,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => {{1,6},{2,4,5},{3},{7,8}} => {{1,4,6},{2,5},{3},{7,8}} => {{1,6},{2,4,5},{3},{7,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => {{1,7},{2,4,5},{3},{6},{8}} => {{1,4,7},{2,5},{3},{6},{8}} => {{1,7},{2,4,5},{3},{6},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => {{1,7,8},{2,4,5},{3},{6}} => {{1,4,7,8},{2,5},{3},{6}} => {{1,7,8},{2,4,5},{3},{6}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => {{1,8},{2,4,5,6},{3},{7}} => {{1,4,6},{2,5,8},{3},{7}} => {{1,8},{2,4,5,6},{3},{7}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => {{1,8},{2,4,5,6,7},{3}} => {{1,4,6,8},{2,5,7},{3}} => {{1,8},{2,4,5,6,7},{3}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => {{1,8},{2,4,5,7},{3},{6}} => {{1,4,7},{2,5,8},{3},{6}} => {{1,8},{2,4,5,7},{3},{6}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => {{1,7},{2,4,6},{3},{5},{8}} => {{1,4,7},{2,6},{3},{5},{8}} => {{1,7},{2,4,6},{3},{5},{8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => {{1,7,8},{2,4,6},{3},{5}} => {{1,4,7,8},{2,6},{3},{5}} => {{1,7,8},{2,4,6},{3},{5}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => {{1,8},{2,4,7},{3},{5},{6}} => {{1,4,8},{2,7},{3},{5},{6}} => {{1,8},{2,4,7},{3},{5},{6}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => {{1,6},{2,5},{3},{4},{7},{8}} => {{1,5},{2,6},{3},{4},{7},{8}} => {{1,6},{2,5},{3},{4},{7},{8}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => {{1,8},{2,5,6,7},{3},{4}} => {{1,5,7},{2,6,8},{3},{4}} => {{1,8},{2,5,6,7},{3},{4}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => {{1,8},{2,5,7},{3},{4},{6}} => {{1,5,8},{2,7},{3},{4},{6}} => {{1,8},{2,5,7},{3},{4},{6}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => {{1,8},{2,7},{3},{4},{5},{6}} => {{1,7},{2,8},{3},{4},{5},{6}} => {{1,8},{2,7},{3},{4},{5},{6}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => {{1,7},{2,6},{3},{4,5},{8}} => {{1,5},{2,6},{3},{4,7},{8}} => {{1,7},{2,6},{3},{4,5},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => {{1,7,8},{2,6},{3},{4,5}} => {{1,5},{2,6},{3},{4,7,8}} => {{1,7,8},{2,6},{3},{4,5}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => {{1,8},{2,7},{3},{4,5,6}} => {{1,5,8},{2,6},{3},{4,7}} => {{1,8},{2,7},{3},{4,5,6}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => {{1,8},{2,7},{3},{4,6},{5}} => {{1,6},{2,7},{3},{4,8},{5}} => {{1,8},{2,7},{3},{4,6},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => {{1,6},{2,5},{3,4},{7},{8}} => {{1,4},{2,5},{3,6},{7},{8}} => {{1,6},{2,5},{3,4},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => {{1,6},{2,5},{3,4},{7,8}} => {{1,4},{2,5},{3,6},{7,8}} => {{1,6},{2,5},{3,4},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => {{1,6,7},{2,5},{3,4},{8}} => {{1,4},{2,5},{3,6,7},{8}} => {{1,6,7},{2,5},{3,4},{8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => {{1,6,7,8},{2,5},{3,4}} => {{1,4},{2,5},{3,6,7,8}} => {{1,6,7,8},{2,5},{3,4}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => {{1,6,8},{2,5},{3,4},{7}} => {{1,4},{2,5},{3,6,8},{7}} => {{1,6,8},{2,5},{3,4},{7}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => {{1,7,8},{2,5},{3,4},{6}} => {{1,4},{2,5},{3,7,8},{6}} => {{1,7,8},{2,5},{3,4},{6}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => {{1,8},{2,5},{3,4},{6,7}} => {{1,4},{2,5},{3,7},{6,8}} => {{1,8},{2,5},{3,4},{6,7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => {{1,7},{2,5,6},{3,4},{8}} => {{1,4},{2,5,7},{3,6},{8}} => {{1,7},{2,5,6},{3,4},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => {{1,8},{2,5,6},{3,4},{7}} => {{1,4},{2,5,8},{3,6},{7}} => {{1,8},{2,5,6},{3,4},{7}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => {{1,8},{2,5,7},{3,4},{6}} => {{1,4},{2,5,8},{3,7},{6}} => {{1,8},{2,5,7},{3,4},{6}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => {{1,7,8},{2,6},{3,4},{5}} => {{1,4},{2,6},{3,7,8},{5}} => {{1,7,8},{2,6},{3,4},{5}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => {{1,8},{2,6},{3,4},{5},{7}} => {{1,4},{2,6},{3,8},{5},{7}} => {{1,8},{2,6},{3,4},{5},{7}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => {{1,8},{2,6,7},{3,4},{5}} => {{1,4},{2,6,8},{3,7},{5}} => {{1,8},{2,6,7},{3,4},{5}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => {{1,8},{2,7},{3,4},{5,6}} => {{1,4},{2,6},{3,7},{5,8}} => {{1,8},{2,7},{3,4},{5,6}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => {{1,7},{2,6},{3,4,5},{8}} => {{1,4,7},{2,5},{3,6},{8}} => {{1,7},{2,6},{3,4,5},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => {{1,7,8},{2,6},{3,4,5}} => {{1,4,7,8},{2,5},{3,6}} => {{1,7,8},{2,6},{3,4,5}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => {{1,8},{2,6},{3,4,5},{7}} => {{1,4,8},{2,5},{3,6},{7}} => {{1,8},{2,6},{3,4,5},{7}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => {{1,8},{2,7},{3,4,5},{6}} => {{1,4,8},{2,5},{3,7},{6}} => {{1,8},{2,7},{3,4,5},{6}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => {{1,8},{2,7},{3,4,5,6}} => {{1,4,7},{2,5,8},{3,6}} => {{1,8},{2,7},{3,4,5,6}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => {{1,8},{2,7},{3,4,6},{5}} => {{1,4,8},{2,6},{3,7},{5}} => {{1,8},{2,7},{3,4,6},{5}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => {{1,7},{2,6},{3,5},{4},{8}} => {{1,5},{2,6},{3,7},{4},{8}} => {{1,7},{2,6},{3,5},{4},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => {{1,7,8},{2,6},{3,5},{4}} => {{1,5},{2,6},{3,7,8},{4}} => {{1,7,8},{2,6},{3,5},{4}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => {{1,8},{2,6,7},{3,5},{4}} => {{1,5},{2,6,8},{3,7},{4}} => {{1,8},{2,6,7},{3,5},{4}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => {{1,8},{2,7},{3,5},{4},{6}} => {{1,5},{2,7},{3,8},{4},{6}} => {{1,8},{2,7},{3,5},{4},{6}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => {{1,8},{2,7},{3,5,6},{4}} => {{1,5,8},{2,6},{3,7},{4}} => {{1,8},{2,7},{3,5,6},{4}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => {{1,8},{2,7},{3,6},{4},{5}} => {{1,6},{2,7},{3,8},{4},{5}} => {{1,8},{2,7},{3,6},{4},{5}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => {{1,8},{2,7},{3,6},{4,5}} => {{1,5},{2,6},{3,7},{4,8}} => {{1,8},{2,7},{3,6},{4,5}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => {{1,8},{2,7},{3,6},{4,5},{9}} => {{1,5},{2,6},{3,7},{4,8},{9}} => {{1,8},{2,7},{3,6},{4,5},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => {{1,8},{2,7},{3,6},{4,5},{9},{10}} => {{1,5},{2,6},{3,7},{4,8},{9},{10}} => {{1,8},{2,7},{3,6},{4,5},{9},{10}}
[] => [] => {} => {} => {}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7,9},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6,8,9},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => {{1,2,3,4,5,6,9},{7},{8}} => {{1,2,3,4,5,6,9},{7},{8}} => {{1,2,3,4,5,6,9},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => {{1,2,3,4,5,6,9},{7,8}} => {{1,2,3,4,5,6,8},{7,9}} => {{1,2,3,4,5,6,9},{7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,1] => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5,7,8,9},{6}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,8,6,7,9,1] => {{1,2,3,4,5,8,9},{6},{7}} => {{1,2,3,4,5,8,9},{6},{7}} => {{1,2,3,4,5,8,9},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,9,6,7,8,1] => {{1,2,3,4,5,9},{6},{7},{8}} => {{1,2,3,4,5,9},{6},{7},{8}} => {{1,2,3,4,5,9},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,7,8,6,1] => {{1,2,3,4,5,9},{6,7,8}} => {{1,2,3,4,5,7,9},{6,8}} => {{1,2,3,4,5,9},{6,7,8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,1] => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4,6,7,8,9},{5}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,9,5,6,7,8,1] => {{1,2,3,4,9},{5},{6},{7},{8}} => {{1,2,3,4,9},{5},{6},{7},{8}} => {{1,2,3,4,9},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,9,6,7,8,5,1] => {{1,2,3,4,9},{5,6,7,8}} => {{1,2,3,4,6,8},{5,7,9}} => {{1,2,3,4,9},{5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,6,4,5,7,8,9,1] => {{1,2,3,6,7,8,9},{4},{5}} => {{1,2,3,6,7,8,9},{4},{5}} => {{1,2,3,6,7,8,9},{4},{5}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,9,4,5,6,7,8,1] => {{1,2,3,9},{4},{5},{6},{7},{8}} => {{1,2,3,9},{4},{5},{6},{7},{8}} => {{1,2,3,9},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,9,5,6,7,8,4,1] => {{1,2,3,9},{4,5,6,7,8}} => {{1,2,3,5,7,9},{4,6,8}} => {{1,2,3,9},{4,5,6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => {{1,2,4,5,6,7,8,9},{3}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2,4,5,6,7,8,9},{3}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,9,3,4,5,6,7,8,1] => {{1,2,9},{3},{4},{5},{6},{7},{8}} => {{1,2,9},{3},{4},{5},{6},{7},{8}} => {{1,2,9},{3},{4},{5},{6},{7},{8}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,9,4,5,6,7,8,3,1] => {{1,2,9},{3,4,5,6,7,8}} => {{1,2,4,6,8},{3,5,7,9}} => {{1,2,9},{3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => {{1,3,4,5,6,7,8,9},{2}} => {{1,3,4,5,6,7,8,9},{2}} => {{1,3,4,5,6,7,8,9},{2}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,9,4,5,6,7,8,1] => {{1,3,9},{2},{4},{5},{6},{7},{8}} => {{1,3,9},{2},{4},{5},{6},{7},{8}} => {{1,3,9},{2},{4},{5},{6},{7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => {{1,4,5,6,7,8,9},{2},{3}} => {{1,4,5,6,7,8,9},{2},{3}} => {{1,4,5,6,7,8,9},{2},{3}}
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,2,3,4,9,6,7,8,1] => {{1,5,9},{2},{3},{4},{6},{7},{8}} => {{1,5,9},{2},{3},{4},{6},{7},{8}} => {{1,5,9},{2},{3},{4},{6},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [7,2,3,4,5,6,9,8,1] => {{1,7,9},{2},{3},{4},{5},{6},{8}} => {{1,7,9},{2},{3},{4},{5},{6},{8}} => {{1,7,9},{2},{3},{4},{5},{6},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => {{1,8,9},{2},{3},{4},{5},{6},{7}} => {{1,8,9},{2},{3},{4},{5},{6},{7}} => {{1,8,9},{2},{3},{4},{5},{6},{7}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,3,2,4,5,6,7,8,1] => {{1,9},{2,3},{4},{5},{6},{7},{8}} => {{1,3},{2,9},{4},{5},{6},{7},{8}} => {{1,9},{2,3},{4},{5},{6},{7},{8}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => {{1,9},{2,3,4,5,6,7,8}} => {{1,3,5,7,9},{2,4,6,8}} => {{1,9},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => {{1,9},{2,8},{3,7},{4,6},{5}} => {{1,6},{2,7},{3,8},{4,9},{5}} => {{1,9},{2,8},{3,7},{4,6},{5}}
[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},{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] => [1,2,3,4,5,6,7,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => {{1},{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] => [1,2,3,4,5,6,8,9,7] => {{1},{2},{3},{4},{5},{6},{7,8,9}} => {{1},{2},{3},{4},{5},{6},{7,8,9}} => {{1},{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] => [1,2,3,4,5,7,8,9,6] => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1},{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] => [1,2,3,4,6,7,8,9,5] => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1},{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] => [1,2,3,5,6,7,8,9,4] => {{1},{2},{3},{4,5,6,7,8,9}} => {{1},{2},{3},{4,5,6,7,8,9}} => {{1},{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] => [1,2,4,5,6,7,8,9,3] => {{1},{2},{3,4,5,6,7,8,9}} => {{1},{2},{3,4,5,6,7,8,9}} => {{1},{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] => [1,3,4,5,6,7,8,9,2] => {{1},{2,3,4,5,6,7,8,9}} => {{1},{2,3,4,5,6,7,8,9}} => {{1},{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] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{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] => [1,2,3,4,5,6,7,8,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1},{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] => [1,2,3,4,5,6,9,8,7] => {{1},{2},{3},{4},{5},{6},{7,9},{8}} => {{1},{2},{3},{4},{5},{6},{7,9},{8}} => {{1},{2},{3},{4},{5},{6},{7,9},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}} => {{1},{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] => [1,2,3,4,5,8,7,9,6] => {{1},{2},{3},{4},{5},{6,8,9},{7}} => {{1},{2},{3},{4},{5},{6,8,9},{7}} => {{1},{2},{3},{4},{5},{6,8,9},{7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1},{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] => [1,2,3,4,7,6,8,9,5] => {{1},{2},{3},{4},{5,7,8,9},{6}} => {{1},{2},{3},{4},{5,7,8,9},{6}} => {{1},{2},{3},{4},{5,7,8,9},{6}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => {{1},{2},{3},{4},{5},{6,7,8,9,10}} => {{1},{2},{3},{4},{5},{6,7,8,9,10}} => {{1},{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] => [1,2,3,6,5,7,8,9,4] => {{1},{2},{3},{4,6,7,8,9},{5}} => {{1},{2},{3},{4,6,7,8,9},{5}} => {{1},{2},{3},{4,6,7,8,9},{5}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => {{1},{2},{3},{4},{5,6,7,8,9,10}} => {{1},{2},{3},{4},{5,6,7,8,9,10}} => {{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => {{1},{2},{3,5,6,7,8,9},{4}} => {{1},{2},{3,5,6,7,8,9},{4}} => {{1},{2},{3,5,6,7,8,9},{4}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => {{1},{2},{3},{4,5,6,7,8,9,10}} => {{1},{2},{3},{4,5,6,7,8,9,10}} => {{1},{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] => [1,4,3,5,6,7,8,9,2] => {{1},{2,4,5,6,7,8,9},{3}} => {{1},{2,4,5,6,7,8,9},{3}} => {{1},{2,4,5,6,7,8,9},{3}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => {{1},{2},{3,4,5,6,7,8,9,10}} => {{1},{2},{3,4,5,6,7,8,9,10}} => {{1},{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] => [1,3,4,5,6,7,8,9,10,2] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1},{2,3,4,5,6,7,8,9,10}} => {{1},{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] => [2,3,4,5,6,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => {{1},{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] => [1,2,3,4,5,6,7,10,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,9,7,8,6] => {{1},{2},{3},{4},{5},{6,9},{7},{8}} => {{1},{2},{3},{4},{5},{6,9},{7},{8}} => {{1},{2},{3},{4},{5},{6,9},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => {{1},{2},{3},{4},{5},{6,9},{7,8}} => {{1},{2},{3},{4},{5},{6,8},{7,9}} => {{1},{2},{3},{4},{5},{6,9},{7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => {{1,3,4,5,6,7,8,9,10},{2}} => {{1,3,4,5,6,7,8,9,10},{2}} => {{1,3,4,5,6,7,8,9,10},{2}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1},{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] => [2,3,4,5,6,7,8,9,10,11,1] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,6,10,8,9,7] => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,9,6,7,8,5] => {{1},{2},{3},{4},{5,9},{6},{7},{8}} => {{1},{2},{3},{4},{5,9},{6},{7},{8}} => {{1},{2},{3},{4},{5,9},{6},{7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,10,1] => {{1,4,5,6,7,8,9,10},{2},{3}} => {{1,4,5,6,7,8,9,10},{2},{3}} => {{1,4,5,6,7,8,9,10},{2},{3}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1,3,4,5,6,7,8,9,10,11},{2}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,5,10,7,8,9,6] => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,9,5,6,7,8,4] => {{1},{2},{3},{4,9},{5},{6},{7},{8}} => {{1},{2},{3},{4,9},{5},{6},{7},{8}} => {{1},{2},{3},{4,9},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,4,10,6,7,8,9,5] => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,9,4,5,6,7,8,3] => {{1},{2},{3,9},{4},{5},{6},{7},{8}} => {{1},{2},{3,9},{4},{5},{6},{7},{8}} => {{1},{2},{3,9},{4},{5},{6},{7},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8,3,4,5,6,7,9,2] => {{1},{2,8,9},{3},{4},{5},{6},{7}} => {{1},{2,8,9},{3},{4},{5},{6},{7}} => {{1},{2,8,9},{3},{4},{5},{6},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,2,3,4,5,7,8,9,10,1] => {{1,6,7,8,9,10},{2},{3},{4},{5}} => {{1,6,7,8,9,10},{2},{3},{4},{5}} => {{1,6,7,8,9,10},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,3,10,5,6,7,8,9,4] => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9,3,4,5,6,7,8,2] => {{1},{2,9},{3},{4},{5},{6},{7},{8}} => {{1},{2,9},{3},{4},{5},{6},{7},{8}} => {{1},{2,9},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,10,4,5,6,7,8,9,3] => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,10,3,4,5,6,7,8,9,2] => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => {{1,9,10},{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] => [1,2,3,4,5,6,8,7,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9}} => {{1},{2},{3},{4},{5},{6},{7,8},{9}} => {{1},{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] => [1,2,3,4,5,7,6,9,8] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1},{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] => [1,2,3,5,4,6,7,8,9] => {{1},{2},{3},{4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4,5},{6},{7},{8},{9}} => {{1},{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] => [1,2,3,5,4,7,6,9,8] => {{1},{2},{3},{4,5},{6,7},{8,9}} => {{1},{2},{3},{4,5},{6,7},{8,9}} => {{1},{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] => [1,2,4,3,5,6,7,8,9] => {{1},{2},{3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3,4},{5},{6},{7},{8},{9}} => {{1},{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] => [1,3,2,4,5,6,7,8,9] => {{1},{2,3},{4},{5},{6},{7},{8},{9}} => {{1},{2,3},{4},{5},{6},{7},{8},{9}} => {{1},{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] => [1,3,2,4,5,6,7,9,8] => {{1},{2,3},{4},{5},{6},{7},{8,9}} => {{1},{2,3},{4},{5},{6},{7},{8,9}} => {{1},{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] => [1,3,2,4,5,6,9,8,7] => {{1},{2,3},{4},{5},{6},{7,9},{8}} => {{1},{2,3},{4},{5},{6},{7,9},{8}} => {{1},{2,3},{4},{5},{6},{7,9},{8}}
[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},{2,3},{4,5},{6},{7},{8},{9}} => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}} => {{1},{2,3},{4,5},{6,7},{8,9}} => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => {{1,2},{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] => [2,1,3,4,5,6,7,9,8] => {{1,2},{3},{4},{5},{6},{7},{8,9}} => {{1,2},{3},{4},{5},{6},{7},{8,9}} => {{1,2},{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] => [2,1,3,4,5,6,8,7,9] => {{1,2},{3},{4},{5},{6},{7,8},{9}} => {{1,2},{3},{4},{5},{6},{7,8},{9}} => {{1,2},{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] => [2,1,4,3,5,6,7,8,9] => {{1,2},{3,4},{5},{6},{7},{8},{9}} => {{1,2},{3,4},{5},{6},{7},{8},{9}} => {{1,2},{3,4},{5},{6},{7},{8},{9}}
[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}} => {{1,2},{3,4},{5,6},{7},{8},{9}} => {{1,2},{3,4},{5,6},{7},{8},{9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}} => {{1,2},{3,4},{5,6},{7,8},{9}} => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => {{1,3},{2},{4},{5},{6},{7},{8},{9}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => {{1,3},{2},{4,5},{6},{7},{8},{9}} => {{1,3},{2},{4,5},{6},{7},{8},{9}} => {{1,3},{2},{4,5},{6},{7},{8},{9}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => {{1,3},{2},{4,5},{6,7},{8,9}} => {{1,3},{2},{4,5},{6,7},{8,9}} => {{1,3},{2},{4,5},{6,7},{8,9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => {{1,4},{2,3},{5},{6},{7},{8},{9}} => {{1,3},{2,4},{5},{6},{7},{8},{9}} => {{1,4},{2,3},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => {{1,6},{2,5},{3,4},{7},{8},{9}} => {{1,4},{2,5},{3,6},{7},{8},{9}} => {{1,6},{2,5},{3,4},{7},{8},{9}}
[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},{2},{3},{4},{5},{6},{7},{8,9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}} => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}} => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => {{1},{2},{3},{4},{5,6},{7,8},{9,10}} => {{1},{2},{3},{4},{5,6},{7,8},{9,10}} => {{1},{2},{3},{4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}} => {{1},{2},{3,4},{5,6},{7,8},{9,10}} => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1,2},{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] => [2,1,3,4,5,6,7,8,10,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,2},{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] => [2,1,4,3,5,6,7,8,9,10] => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}} => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}} => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}}
[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}} => {{1,2},{3,4},{5,6},{7},{8},{9},{10}} => {{1,2},{3,4},{5,6},{7},{8},{9},{10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => {{1,2},{3,4},{5,6},{7,8},{9},{10}} => {{1,2},{3,4},{5,6},{7,8},{9},{10}} => {{1,2},{3,4},{5,6},{7,8},{9},{10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => {{1,3},{2},{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] => [3,2,1,5,4,7,6,9,8,10] => {{1,3},{2},{4,5},{6,7},{8,9},{10}} => {{1,3},{2},{4,5},{6,7},{8,9},{10}} => {{1,3},{2},{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] => [4,3,2,1,5,6,7,8,9,10] => {{1,4},{2,3},{5},{6},{7},{8},{9},{10}} => {{1,3},{2,4},{5},{6},{7},{8},{9},{10}} => {{1,4},{2,3},{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] => [6,5,4,3,2,1,7,8,9,10] => {{1,6},{2,5},{3,4},{7},{8},{9},{10}} => {{1,4},{2,5},{3,6},{7},{8},{9},{10}} => {{1,6},{2,5},{3,4},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => {{1,10},{2,9},{3,8},{4,7},{5,6}} => {{1,6},{2,7},{3,8},{4,9},{5,10}} => {{1,10},{2,9},{3,8},{4,7},{5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => {{1,2,3},{4},{5},{6},{7},{8},{9}} => {{1,2,3},{4},{5},{6},{7},{8},{9}} => {{1,2,3},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1,2,3,4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}} => {{1,2,3,4,5,6},{7},{8},{9}} => {{1,2,3,4,5,6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => {{1,2,3,4,5,6,7},{8},{9}} => {{1,2,3,4,5,6,7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1,2,3,4,5,6,7,8},{9}} => {{1,2,3,4,5,6,7,8},{9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => {{1,2,3},{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] => [2,4,3,1,5,6,7,8,9] => {{1,2,4},{3},{5},{6},{7},{8},{9}} => {{1,2,4},{3},{5},{6},{7},{8},{9}} => {{1,2,4},{3},{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] => [2,3,4,1,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => {{1,2,3,4,5},{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] => [2,3,4,5,6,1,7,8,9,10] => {{1,2,3,4,5,6},{7},{8},{9},{10}} => {{1,2,3,4,5,6},{7},{8},{9},{10}} => {{1,2,3,4,5,6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => {{1,2,3,4,5,6,7},{8},{9},{10}} => {{1,2,3,4,5,6,7},{8},{9},{10}} => {{1,2,3,4,5,6,7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => {{1,2,3,4,5,6,8},{7},{9}} => {{1,2,3,4,5,6,8},{7},{9}} => {{1,2,3,4,5,6,8},{7},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => {{1,2,3,4,5,6,7,8},{9},{10}} => {{1,2,3,4,5,6,7,8},{9},{10}} => {{1,2,3,4,5,6,7,8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1,2,3,4,5,6,7,8,9},{10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => {{1,2,3,4,5,6,7,8,10},{9}} => {{1,2,3,4,5,6,7,8,10},{9}} => {{1,2,3,4,5,6,7,8,10},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,2,3,4,5,6,7,1,9] => {{1,8},{2},{3},{4},{5},{6},{7},{9}} => {{1,8},{2},{3},{4},{5},{6},{7},{9}} => {{1,8},{2},{3},{4},{5},{6},{7},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,2,3,4,5,6,1,8,9] => {{1,7},{2},{3},{4},{5},{6},{8},{9}} => {{1,7},{2},{3},{4},{5},{6},{8},{9}} => {{1,7},{2},{3},{4},{5},{6},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,2,3,4,5,1,7,8,9] => {{1,6},{2},{3},{4},{5},{7},{8},{9}} => {{1,6},{2},{3},{4},{5},{7},{8},{9}} => {{1,6},{2},{3},{4},{5},{7},{8},{9}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8,9] => {{1,5},{2},{3},{4},{6},{7},{8},{9}} => {{1,5},{2},{3},{4},{6},{7},{8},{9}} => {{1,5},{2},{3},{4},{6},{7},{8},{9}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8,9] => {{1,4},{2},{3},{5},{6},{7},{8},{9}} => {{1,4},{2},{3},{5},{6},{7},{8},{9}} => {{1,4},{2},{3},{5},{6},{7},{8},{9}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => {{1,3,4},{2},{5},{6},{7},{8},{9}} => {{1,3,4},{2},{5},{6},{7},{8},{9}} => {{1,3,4},{2},{5},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2,3,4,5,6,1,9,8] => {{1,7},{2},{3},{4},{5},{6},{8,9}} => {{1,7},{2},{3},{4},{5},{6},{8,9}} => {{1,7},{2},{3},{4},{5},{6},{8,9}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,9,4,5,6,7,8,3] => {{1,2},{3,9},{4},{5},{6},{7},{8}} => {{1,2},{3,9},{4},{5},{6},{7},{8}} => {{1,2},{3,9},{4},{5},{6},{7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,8,3,4,5,6,7,1,9] => {{1,2,8},{3},{4},{5},{6},{7},{9}} => {{1,2,8},{3},{4},{5},{6},{7},{9}} => {{1,2,8},{3},{4},{5},{6},{7},{9}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,10,3,4,5,6,7,8,9,1] => {{1,2,10},{3},{4},{5},{6},{7},{8},{9}} => {{1,2,10},{3},{4},{5},{6},{7},{8},{9}} => {{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,6,4,5,7,8,9,10,1] => {{1,2,3,6,7,8,9,10},{4},{5}} => {{1,2,3,6,7,8,9,10},{4},{5}} => {{1,2,3,6,7,8,9,10},{4},{5}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4,6,7,8,9,10},{5}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,9,4,3,5,6,7,8,2] => {{1},{2,9},{3,4},{5},{6},{7},{8}} => {{1},{2,4},{3,9},{5},{6},{7},{8}} => {{1},{2,9},{3,4},{5},{6},{7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => {{1,3,4,5,6,7,8},{2},{9}} => {{1,3,4,5,6,7,8},{2},{9}} => {{1,3,4,5,6,7,8},{2},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => {{1},{2,3,4,5,6,7,9},{8}} => {{1},{2,3,4,5,6,7,9},{8}} => {{1},{2,3,4,5,6,7,9},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2,3,4,5,6,7},{8,9}} => {{1,2,3,4,5,6,7},{8,9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2},{3,4,5,6,7,8,9}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => {{1,2,3,4,5,6},{7,9},{8}} => {{1,2,3,4,5,6},{7,9},{8}} => {{1,2,3,4,5,6},{7,9},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => {{1,2,3,4,5,6,7,10},{8,9}} => {{1,2,3,4,5,6,7,9},{8,10}} => {{1,2,3,4,5,6,7,10},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,10,8,9,7,1] => {{1,2,3,4,5,6,10},{7,8,9}} => {{1,2,3,4,5,6,8,10},{7,9}} => {{1,2,3,4,5,6,10},{7,8,9}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,10,7,8,9,6,1] => {{1,2,3,4,5,10},{6,7,8,9}} => {{1,2,3,4,5,7,9},{6,8,10}} => {{1,2,3,4,5,10},{6,7,8,9}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,10,6,7,8,9,5,1] => {{1,2,3,4,10},{5,6,7,8,9}} => {{1,2,3,4,6,8,10},{5,7,9}} => {{1,2,3,4,10},{5,6,7,8,9}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,10,5,6,7,8,9,4,1] => {{1,2,3,10},{4,5,6,7,8,9}} => {{1,2,3,5,7,9},{4,6,8,10}} => {{1,2,3,10},{4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,3,4,5,6,7,8,9,2,1] => {{1,10},{2,3,4,5,6,7,8,9}} => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,10},{2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,10,6,7,8,9,1] => {{1,2,3,4,5,10},{6},{7},{8},{9}} => {{1,2,3,4,5,10},{6},{7},{8},{9}} => {{1,2,3,4,5,10},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,10,1] => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5,7,8,9,10},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => {{1,2,3,4,5,6},{7,8},{9}} => {{1,2,3,4,5,6},{7,8},{9}} => {{1,2,3,4,5,6},{7,8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => {{1,2,3,4,5},{6,7},{8},{9}} => {{1,2,3,4,5},{6,7},{8},{9}} => {{1,2,3,4,5},{6,7},{8},{9}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}} => {{1,2,3},{4,5},{6,7},{8,9}} => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2,4,6,8,10},{3},{5},{7},{9}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => {{1,2,3},{4,5},{6,7},{8,9},{10}} => {{1,2,3},{4,5},{6,7},{8,9},{10}} => {{1,2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,8,9,1] => {{1,2,3,4,5,6,7,10},{8},{9}} => {{1,2,3,4,5,6,7,10},{8},{9}} => {{1,2,3,4,5,6,7,10},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,10,7,8,9,1] => {{1,2,3,4,5,6,10},{7},{8},{9}} => {{1,2,3,4,5,6,10},{7},{8},{9}} => {{1,2,3,4,5,6,10},{7},{8},{9}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,10,5,6,7,8,9,1] => {{1,2,3,4,10},{5},{6},{7},{8},{9}} => {{1,2,3,4,10},{5},{6},{7},{8},{9}} => {{1,2,3,4,10},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,10,4,5,6,7,8,9,1] => {{1,2,3,10},{4},{5},{6},{7},{8},{9}} => {{1,2,3,10},{4},{5},{6},{7},{8},{9}} => {{1,2,3,10},{4},{5},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => {{1,2,3,4,5,6,7,8,9,11},{10}} => {{1,2,3,4,5,6,7,8,9,11},{10}} => {{1,2,3,4,5,6,7,8,9,11},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [11,2,3,4,5,6,7,8,9,10,1] => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1,10] => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => {{1},{2},{3},{4},{5},{6,7,9},{8}} => {{1},{2},{3},{4},{5},{6,7,9},{8}} => {{1},{2},{3},{4},{5},{6,7,9},{8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => {{1,3},{2},{4,5,6,7,8,9}} => {{1,3},{2},{4,5,6,7,8,9}} => {{1,3},{2},{4,5,6,7,8,9}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => {{1},{2,3,4},{5},{6},{7},{8},{9}} => {{1},{2,3,4},{5},{6},{7},{8},{9}} => {{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2},{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] => [2,3,1,5,6,7,8,9,4] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => {{1},{2},{3},{4},{5},{6,7,8},{9}} => {{1},{2},{3},{4},{5},{6,7,8},{9}} => {{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => {{1},{2,3,4,5,6,7},{8,9}} => {{1},{2,3,4,5,6,7},{8,9}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => {{1,2,3,4,5,6,7,8,9,10},{11}} => {{1,2,3,4,5,6,7,8,9,10},{11}} => {{1,2,3,4,5,6,7,8,9,10},{11}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => {{1},{2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,5,7,6,8,1,9] => {{1,2,3,4,5,7,8},{6},{9}} => {{1,2,3,4,5,7,8},{6},{9}} => {{1,2,3,4,5,7,8},{6},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [11,3,4,5,6,7,8,9,10,2,1] => {{1,11},{2,3,4,5,6,7,8,9,10}} => {{1,3,5,7,9,11},{2,4,6,8,10}} => {{1,11},{2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,9,4,5,6,7,8,2] => {{1},{2,3,9},{4},{5},{6},{7},{8}} => {{1},{2,3,9},{4},{5},{6},{7},{8}} => {{1},{2,3,9},{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] => [2,3,4,5,6,7,8,1,10,9] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => {{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,10,11},{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] => [1,3,4,5,6,7,8,9,2,10] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,8,7,9] => {{1,3,4},{2},{5,6},{7,8},{9}} => {{1,3,4},{2},{5,6},{7,8},{9}} => {{1,3,4},{2},{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] => [3,2,4,1,6,5,8,7,10,9] => {{1,3,4},{2},{5,6},{7,8},{9,10}} => {{1,3,4},{2},{5,6},{7,8},{9,10}} => {{1,3,4},{2},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,9,8,1,10] => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,9,5,4,6,7,8,3] => {{1},{2},{3,9},{4,5},{6},{7},{8}} => {{1},{2},{3,5},{4,9},{6},{7},{8}} => {{1},{2},{3,9},{4,5},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,6,8,7,9,2] => {{1},{2,3,4,5,6,8,9},{7}} => {{1},{2,3,4,5,6,8,9},{7}} => {{1},{2,3,4,5,6,8,9},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => {{1},{2,3,4,5,6,7,8,10},{9}} => {{1},{2,3,4,5,6,7,8,10},{9}} => {{1},{2,3,4,5,6,7,8,10},{9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => {{1},{2,3},{4,5},{6,7},{8,9,10}} => {{1},{2,3},{4,5},{6,7},{8,9,10}} => {{1},{2,3},{4,5},{6,7},{8,9,10}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,4,9,7,6,8,5] => {{1},{2},{3},{4},{5,9},{6,7},{8}} => {{1},{2},{3},{4},{5,7},{6,9},{8}} => {{1},{2},{3},{4},{5,9},{6,7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,9,6,5,7,8,4] => {{1},{2},{3},{4,9},{5,6},{7},{8}} => {{1},{2},{3},{4,6},{5,9},{7},{8}} => {{1},{2},{3},{4,9},{5,6},{7},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => {{1,2},{3,4},{5,6,7,8,9}} => {{1,2},{3,4},{5,6,7,8,9}} => {{1,2},{3,4},{5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => {{1,2,3,4,5,6,7,9},{8},{10}} => {{1,2,3,4,5,6,7,9},{8},{10}} => {{1,2,3,4,5,6,7,9},{8},{10}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,10,9,2] => {{1},{2,4,6,8,10},{3},{5},{7},{9}} => {{1},{2,4,6,8,10},{3},{5},{7},{9}} => {{1},{2,4,6,8,10},{3},{5},{7},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8,2,3,4,5,6,7,10,9,1] => {{1,8,10},{2},{3},{4},{5},{6},{7},{9}} => {{1,8,10},{2},{3},{4},{5},{6},{7},{9}} => {{1,8,10},{2},{3},{4},{5},{6},{7},{9}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,10,4,5,6,7,8,9,1] => {{1,3,10},{2},{4},{5},{6},{7},{8},{9}} => {{1,3,10},{2},{4},{5},{6},{7},{8},{9}} => {{1,3,10},{2},{4},{5},{6},{7},{8},{9}}
[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}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8,10] => {{1,2,3,4,5,6,7},{8,9},{10}} => {{1,2,3,4,5,6,7},{8,9},{10}} => {{1,2,3,4,5,6,7},{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] => [2,3,4,5,6,7,8,9,1,11,10] => {{1,2,3,4,5,6,7,8,9},{10,11}} => {{1,2,3,4,5,6,7,8,9},{10,11}} => {{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,7,8,10,9,1] => {{1,3,4,5,6,7,8,10},{2},{9}} => {{1,3,4,5,6,7,8,10},{2},{9}} => {{1,3,4,5,6,7,8,10},{2},{9}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,12,11,1] => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,5,8,9,10,7] => {{1,2,3,4},{5,6},{7,8,9,10}} => {{1,2,3,4},{5,6},{7,8,9,10}} => {{1,2,3,4},{5,6},{7,8,9,10}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,10,5] => {{1,2},{3,4},{5,6,7,8,9,10}} => {{1,2},{3,4},{5,6,7,8,9,10}} => {{1,2},{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] => [2,1,4,3,6,5,8,9,10,7] => {{1,2},{3,4},{5,6},{7,8,9,10}} => {{1,2},{3,4},{5,6},{7,8,9,10}} => {{1,2},{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] => [2,3,4,1,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}} => {{1,2,3,4},{5,6},{7,8},{9}} => {{1,2,3,4},{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] => [2,3,4,5,1,7,6,9,8,10] => {{1,2,3,4,5},{6,7},{8,9},{10}} => {{1,2,3,4,5},{6,7},{8,9},{10}} => {{1,2,3,4,5},{6,7},{8,9},{10}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => {{1},{2,3,4,5},{6,7},{8,9}} => {{1},{2,3,4,5},{6,7},{8,9}} => {{1},{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] => [2,3,4,5,1,7,6,9,8] => {{1,2,3,4,5},{6,7},{8,9}} => {{1,2,3,4,5},{6,7},{8,9}} => {{1,2,3,4,5},{6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => {{1,2,3,4,5,6},{7,8},{9,10}} => {{1,2,3,4,5,6},{7,8},{9,10}} => {{1,2,3,4,5,6},{7,8},{9,10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}} => {{1,2,3,4},{5,6},{7,8},{9,10}} => {{1,2,3,4},{5,6},{7,8},{9,10}}
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
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].
Map
Kasraoui-Zeng
Description
The Kasraoui-Zeng involution.
This is defined in [1] and yields the set partition with the number of nestings and crossings exchanged.
This is defined in [1] and yields the set partition with the number of nestings and crossings exchanged.
Map
Wachs-White-rho
Description
A transformation of set partitions due to Wachs and White.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection $\rho$.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with $(i,j)$ to the cell in the $i$-th column from the right and the $j$-th row from the top.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection $\rho$.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with $(i,j)$ to the cell in the $i$-th column from the right and the $j$-th row from the top.
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