Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00112: Set partitions —complement⟶ Set partitions
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00112: Set partitions —complement⟶ Set partitions
Images
[1,0] => [1] => {{1}} => {{1}}
[1,0,1,0] => [2,1] => {{1,2}} => {{1,2}}
[1,1,0,0] => [1,2] => {{1},{2}} => {{1},{2}}
[1,0,1,0,1,0] => [3,2,1] => {{1,3},{2}} => {{1,3},{2}}
[1,0,1,1,0,0] => [2,3,1] => {{1,2,3}} => {{1,2,3}}
[1,1,0,0,1,0] => [3,1,2] => {{1,2,3}} => {{1,2,3}}
[1,1,0,1,0,0] => [2,1,3] => {{1,2},{3}} => {{1},{2,3}}
[1,1,1,0,0,0] => [1,2,3] => {{1},{2},{3}} => {{1},{2},{3}}
[1,0,1,0,1,0,1,0] => [4,3,2,1] => {{1,4},{2,3}} => {{1,4},{2,3}}
[1,0,1,0,1,1,0,0] => [3,4,2,1] => {{1,2,3,4}} => {{1,2,3,4}}
[1,0,1,1,0,0,1,0] => [4,2,3,1] => {{1,4},{2},{3}} => {{1,4},{2},{3}}
[1,0,1,1,0,1,0,0] => [3,2,4,1] => {{1,3,4},{2}} => {{1,2,4},{3}}
[1,0,1,1,1,0,0,0] => [2,3,4,1] => {{1,2,3,4}} => {{1,2,3,4}}
[1,1,0,0,1,0,1,0] => [4,3,1,2] => {{1,2,3,4}} => {{1,2,3,4}}
[1,1,0,0,1,1,0,0] => [3,4,1,2] => {{1,3},{2,4}} => {{1,3},{2,4}}
[1,1,0,1,0,0,1,0] => [4,2,1,3] => {{1,3,4},{2}} => {{1,2,4},{3}}
[1,1,0,1,0,1,0,0] => [3,2,1,4] => {{1,3},{2},{4}} => {{1},{2,4},{3}}
[1,1,0,1,1,0,0,0] => [2,3,1,4] => {{1,2,3},{4}} => {{1},{2,3,4}}
[1,1,1,0,0,0,1,0] => [4,1,2,3] => {{1,2,3,4}} => {{1,2,3,4}}
[1,1,1,0,0,1,0,0] => [3,1,2,4] => {{1,2,3},{4}} => {{1},{2,3,4}}
[1,1,1,0,1,0,0,0] => [2,1,3,4] => {{1,2},{3},{4}} => {{1},{2},{3,4}}
[1,1,1,1,0,0,0,0] => [1,2,3,4] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}}
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => {{1,5},{2,4},{3}} => {{1,5},{2,4},{3}}
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => {{1,2,4,5},{3}} => {{1,2,4,5},{3}}
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => {{1,5},{2,3,4}} => {{1,5},{2,3,4}}
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => {{1,3,5},{2,4}} => {{1,3,5},{2,4}}
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => {{1,5},{2,3,4}} => {{1,5},{2,3,4}}
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => {{1,5},{2,3},{4}} => {{1,5},{2},{3,4}}
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => {{1,4,5},{2,3}} => {{1,2,5},{3,4}}
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => {{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}}
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => {{1,4,5},{2},{3}} => {{1,2,5},{3},{4}}
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => {{1,3,4,5},{2}} => {{1,2,3,5},{4}}
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => {{1,2,4,5},{3}} => {{1,2,4,5},{3}}
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => {{1,4},{2,5},{3}} => {{1,4},{2,5},{3}}
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => {{1,4},{2,3,5}} => {{1,3,4},{2,5}}
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => {{1,4},{2,3,5}} => {{1,3,4},{2,5}}
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => {{1,4,5},{2,3}} => {{1,2,5},{3,4}}
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => {{1,4},{2,3},{5}} => {{1},{2,5},{3,4}}
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}}
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => {{1,4,5},{2},{3}} => {{1,2,5},{3},{4}}
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => {{1,4},{2},{3},{5}} => {{1},{2,5},{3},{4}}
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => {{1,3,4},{2},{5}} => {{1},{2,3,5},{4}}
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}}
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => {{1,3,5},{2,4}} => {{1,3,5},{2,4}}
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}}
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => {{1,3},{2,4},{5}} => {{1},{2,4},{3,5}}
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => {{1,3,4,5},{2}} => {{1,2,3,5},{4}}
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => {{1,3,4},{2},{5}} => {{1},{2,3,5},{4}}
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => {{1,3},{2},{4},{5}} => {{1},{2},{3,5},{4}}
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => {{1},{2},{3,4,5}}
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => {{1,2,3,4,5}} => {{1,2,3,4,5}}
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}}
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => {{1,2,3},{4},{5}} => {{1},{2},{3,4,5}}
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => {{1},{2},{3},{4,5}}
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => {{1,6},{2,5},{3,4}} => {{1,6},{2,5},{3,4}}
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => {{1,2,5,6},{3,4}} => {{1,2,5,6},{3,4}}
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => {{1,6},{2,3,4,5}} => {{1,6},{2,3,4,5}}
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => {{1,3,4,6},{2,5}} => {{1,3,4,6},{2,5}}
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => {{1,6},{2,5},{3},{4}} => {{1,6},{2,5},{3},{4}}
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => {{1,2,5,6},{3},{4}} => {{1,2,5,6},{3},{4}}
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => {{1,6},{2,4,5},{3}} => {{1,6},{2,3,5},{4}}
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => {{1,2,4,5,6},{3}} => {{1,2,3,5,6},{4}}
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => {{1,4,6},{2,5},{3}} => {{1,3,6},{2,5},{4}}
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => {{1,6},{2,3,4,5}} => {{1,6},{2,3,4,5}}
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => {{1,4,6},{2,3,5}} => {{1,3,6},{2,4,5}}
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => {{1,6},{2,3,4,5}} => {{1,6},{2,3,4,5}}
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => {{1,6},{2,4},{3,5}} => {{1,6},{2,4},{3,5}}
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => {{1,3,5,6},{2,4}} => {{1,2,4,6},{3,5}}
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => {{1,6},{2,4,5},{3}} => {{1,6},{2,3,5},{4}}
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => {{1,2,4,5,6},{3}} => {{1,2,3,5,6},{4}}
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => {{1,6},{2,4},{3},{5}} => {{1,6},{2},{3,5},{4}}
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => {{1,5,6},{2,4},{3}} => {{1,2,6},{3,5},{4}}
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => {{1,2,4,5,6},{3}} => {{1,2,3,5,6},{4}}
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => {{1,6},{2,3,4},{5}} => {{1,6},{2},{3,4,5}}
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => {{1,5,6},{2,3,4}} => {{1,2,6},{3,4,5}}
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => {{1,3,5,6},{2,4}} => {{1,2,4,6},{3,5}}
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => {{1,6},{2,3,4,5}} => {{1,6},{2,3,4,5}}
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => {{1,6},{2,3,4},{5}} => {{1,6},{2},{3,4,5}}
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => {{1,5,6},{2,3,4}} => {{1,2,6},{3,4,5}}
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => {{1,6},{2,3},{4},{5}} => {{1,6},{2},{3},{4,5}}
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => {{1,5,6},{2,3},{4}} => {{1,2,6},{3},{4,5}}
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => {{1,4,5,6},{2,3}} => {{1,2,3,6},{4,5}}
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
>>> Load all 1947 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => {{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}}
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => {{1,5,6},{2},{3},{4}} => {{1,2,6},{3},{4},{5}}
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => {{1,4,5,6},{2},{3}} => {{1,2,3,6},{4},{5}}
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => {{1,3,4,5,6},{2}} => {{1,2,3,4,6},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => {{1,2,5,6},{3,4}} => {{1,2,5,6},{3,4}}
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => {{1,5},{2,6},{3,4}} => {{1,5},{2,6},{3,4}}
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => {{1,5},{2,3,4,6}} => {{1,3,4,5},{2,6}}
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => {{1,2,5,6},{3},{4}} => {{1,2,5,6},{3},{4}}
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => {{1,5},{2,6},{3},{4}} => {{1,5},{2,6},{3},{4}}
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => {{1,2,4,5,6},{3}} => {{1,2,3,5,6},{4}}
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => {{1,5},{2,4,6},{3}} => {{1,3,5},{2,6},{4}}
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => {{1,2,4,5,6},{3}} => {{1,2,3,5,6},{4}}
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => {{1,5},{2,3,4,6}} => {{1,3,4,5},{2,6}}
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => {{1,3,5},{2,4,6}}
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => {{1,5},{2,3,4,6}} => {{1,3,4,5},{2,6}}
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => {{1,3,5,6},{2,4}} => {{1,2,4,6},{3,5}}
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => {{1,5},{2,4},{3,6}} => {{1,4},{2,6},{3,5}}
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => {{1,2,4,5},{3,6}} => {{1,4},{2,3,5,6}}
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => {{1,2,4,5,6},{3}} => {{1,2,3,5,6},{4}}
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => {{1,5},{2,4,6},{3}} => {{1,3,5},{2,6},{4}}
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => {{1,5,6},{2,4},{3}} => {{1,2,6},{3,5},{4}}
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}} => {{1},{2,6},{3,5},{4}}
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => {{1,2,4,5},{3},{6}} => {{1},{2,3,5,6},{4}}
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => {{1,5,6},{2,3,4}} => {{1,2,6},{3,4,5}}
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => {{1,5},{2,3,4},{6}} => {{1},{2,6},{3,4,5}}
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => {{1,3,5},{2,4},{6}} => {{1},{2,4,6},{3,5}}
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => {{1,5},{2,3,4,6}} => {{1,3,4,5},{2,6}}
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => {{1,5,6},{2,3,4}} => {{1,2,6},{3,4,5}}
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => {{1,5},{2,3,4},{6}} => {{1},{2,6},{3,4,5}}
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => {{1,5,6},{2,3},{4}} => {{1,2,6},{3},{4,5}}
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => {{1,5},{2,3},{4},{6}} => {{1},{2,6},{3},{4,5}}
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => {{1,4,5},{2,3},{6}} => {{1},{2,3,6},{4,5}}
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => {{1,5,6},{2},{3},{4}} => {{1,2,6},{3},{4},{5}}
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => {{1,5},{2},{3},{4},{6}} => {{1},{2,6},{3},{4},{5}}
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => {{1,4,5},{2},{3},{6}} => {{1},{2,3,6},{4},{5}}
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => {{1,3,4,5},{2},{6}} => {{1},{2,3,4,6},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => {{1,3,4,6},{2,5}} => {{1,3,4,6},{2,5}}
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => {{1,2,4,5},{3,6}} => {{1,4},{2,3,5,6}}
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => {{1,4},{2,5},{3,6}}
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => {{1,4,6},{2,5},{3}} => {{1,3,6},{2,5},{4}}
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => {{1,2,4,5,6},{3}} => {{1,2,3,5,6},{4}}
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => {{1,2,4,5,6},{3}} => {{1,2,3,5,6},{4}}
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => {{1,2,4,5},{3},{6}} => {{1},{2,3,5,6},{4}}
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => {{1,4},{2,5},{3},{6}} => {{1},{2,5},{3,6},{4}}
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => {{1,4},{2,3,5},{6}} => {{1},{2,4,5},{3,6}}
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => {{1,4,6},{2,3,5}} => {{1,3,6},{2,4,5}}
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => {{1,4},{2,3,5},{6}} => {{1},{2,4,5},{3,6}}
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => {{1,4,5,6},{2,3}} => {{1,2,3,6},{4,5}}
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => {{1,4,5},{2,3},{6}} => {{1},{2,3,6},{4,5}}
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}} => {{1},{2},{3,6},{4,5}}
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}}
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => {{1,4,5,6},{2},{3}} => {{1,2,3,6},{4},{5}}
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => {{1,4,5},{2},{3},{6}} => {{1},{2,3,6},{4},{5}}
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => {{1,4},{2},{3},{5},{6}} => {{1},{2},{3,6},{4},{5}}
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => {{1,3,4},{2},{5},{6}} => {{1},{2},{3,4,6},{5}}
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}}
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => {{1,3,5},{2,4,6}} => {{1,3,5},{2,4,6}}
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => {{1,3,5,6},{2,4}} => {{1,2,4,6},{3,5}}
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => {{1,3,5},{2,4},{6}} => {{1},{2,4,6},{3,5}}
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}}
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}} => {{1},{2},{3,5},{4,6}}
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => {{1,3,4,5,6},{2}} => {{1,2,3,4,6},{5}}
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => {{1,3,4,5},{2},{6}} => {{1},{2,3,4,6},{5}}
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => {{1,3,4},{2},{5},{6}} => {{1},{2},{3,4,6},{5}}
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}} => {{1},{2},{3},{4,6},{5}}
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => {{1},{2},{3},{4,5,6}}
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}}
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => {{1,2,3},{4},{5},{6}} => {{1},{2},{3},{4,5,6}}
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5,6}}
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => {{1,7},{2,6},{3,5},{4}} => {{1,7},{2,6},{3,5},{4}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => {{1,2,6,7},{3,5},{4}} => {{1,2,6,7},{3,5},{4}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => {{1,7},{2,3,5,6},{4}} => {{1,7},{2,3,5,6},{4}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => {{1,3,5,7},{2,6},{4}} => {{1,3,5,7},{2,6},{4}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => {{1,7},{2,6},{3,4,5}} => {{1,7},{2,6},{3,4,5}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => {{1,2,6,7},{3,4,5}} => {{1,2,6,7},{3,4,5}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => {{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] => [5,6,4,7,3,2,1] => {{1,3,4,5,7},{2,6}} => {{1,3,4,5,7},{2,6}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => {{1,7},{2,4,6},{3,5}} => {{1,7},{2,4,6},{3,5}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => {{1,2,4,6,7},{3,5}} => {{1,2,4,6,7},{3,5}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => {{1,4,7},{2,3,5,6}} => {{1,4,7},{2,3,5,6}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => {{1,7},{2,6},{3,4,5}} => {{1,7},{2,6},{3,4,5}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => {{1,2,6,7},{3,4,5}} => {{1,2,6,7},{3,4,5}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => {{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] => [5,6,7,3,4,2,1] => {{1,3,4,5,7},{2,6}} => {{1,3,4,5,7},{2,6}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => {{1,7},{2,6},{3,4},{5}} => {{1,7},{2,6},{3},{4,5}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => {{1,2,6,7},{3,4},{5}} => {{1,2,6,7},{3},{4,5}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => {{1,7},{2,5,6},{3,4}} => {{1,7},{2,3,6},{4,5}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => {{1,2,5,6,7},{3,4}} => {{1,2,3,6,7},{4,5}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => {{1,5,7},{2,6},{3,4}} => {{1,3,7},{2,6},{4,5}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => {{1,5,7},{2,3,4,6}} => {{1,3,7},{2,4,5,6}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => {{1,7},{2,6},{3},{4},{5}} => {{1,7},{2,6},{3},{4},{5}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => {{1,2,6,7},{3},{4},{5}} => {{1,2,6,7},{3},{4},{5}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => {{1,7},{2,5,6},{3},{4}} => {{1,7},{2,3,6},{4},{5}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => {{1,2,5,6,7},{3},{4}} => {{1,2,3,6,7},{4},{5}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => {{1,5,7},{2,6},{3},{4}} => {{1,3,7},{2,6},{4},{5}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => {{1,7},{2,4,5,6},{3}} => {{1,7},{2,3,4,6},{5}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => {{1,5,7},{2,4,6},{3}} => {{1,3,7},{2,4,6},{5}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => {{1,5,7},{2,3,4,6}} => {{1,3,7},{2,4,5,6}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => {{1,3,5,7},{2,4,6}} => {{1,3,5,7},{2,4,6}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => {{1,7},{2,3,5,6},{4}} => {{1,7},{2,3,5,6},{4}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => {{1,7},{2,5},{3,6},{4}} => {{1,7},{2,5},{3,6},{4}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => {{1,3,6,7},{2,5},{4}} => {{1,2,5,7},{3,6},{4}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => {{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] => [7,5,4,6,2,3,1] => {{1,7},{2,5},{3,4,6}} => {{1,7},{2,4,5},{3,6}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => {{1,2,4,5,7},{3,6}} => {{1,3,4,6,7},{2,5}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => {{1,4,7},{2,5},{3,6}} => {{1,4,7},{2,5},{3,6}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => {{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] => [7,5,6,3,2,4,1] => {{1,7},{2,5},{3,4,6}} => {{1,7},{2,4,5},{3,6}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => {{1,7},{2,5,6},{3,4}} => {{1,7},{2,3,6},{4,5}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => {{1,2,5,6,7},{3,4}} => {{1,2,3,6,7},{4,5}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => {{1,7},{2,5},{3,4},{6}} => {{1,7},{2},{3,6},{4,5}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => {{1,6,7},{2,5},{3,4}} => {{1,2,7},{3,6},{4,5}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => {{1,2,5,6,7},{3,4}} => {{1,2,3,6,7},{4,5}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => {{1,7},{2,3,4,5},{6}} => {{1,7},{2},{3,4,5,6}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => {{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => {{1,7},{2,5,6},{3},{4}} => {{1,7},{2,3,6},{4},{5}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => {{1,2,5,6,7},{3},{4}} => {{1,2,3,6,7},{4},{5}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => {{1,7},{2,5},{3},{4},{6}} => {{1,7},{2},{3,6},{4},{5}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => {{1,6,7},{2,5},{3},{4}} => {{1,2,7},{3,6},{4},{5}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => {{1,2,5,6,7},{3},{4}} => {{1,2,3,6,7},{4},{5}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => {{1,7},{2,4,5},{3},{6}} => {{1,7},{2},{3,4,6},{5}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => {{1,6,7},{2,4,5},{3}} => {{1,2,7},{3,4,6},{5}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => {{1,4,6,7},{2,5},{3}} => {{1,2,4,7},{3,6},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => {{1,7},{2,3,4,5},{6}} => {{1,7},{2},{3,4,5,6}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => {{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => {{1,4,6,7},{2,3,5}} => {{1,2,4,7},{3,5,6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => {{1,7},{2,4,6},{3,5}} => {{1,7},{2,4,6},{3,5}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => {{1,2,4,6,7},{3,5}} => {{1,2,4,6,7},{3,5}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => {{1,3,5,7},{2,4,6}} => {{1,3,5,7},{2,4,6}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => {{1,7},{2,3,4,5},{6}} => {{1,7},{2},{3,4,5,6}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => {{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => {{1,7},{2,4},{3,5},{6}} => {{1,7},{2},{3,5},{4,6}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => {{1,6,7},{2,4},{3,5}} => {{1,2,7},{3,5},{4,6}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => {{1,3,5,6,7},{2,4}} => {{1,2,3,5,7},{4,6}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => {{1,7},{2,4,5,6},{3}} => {{1,7},{2,3,4,6},{5}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => {{1,7},{2,4,5},{3},{6}} => {{1,7},{2},{3,4,6},{5}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => {{1,6,7},{2,4,5},{3}} => {{1,2,7},{3,4,6},{5}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => {{1,7},{2,4},{3},{5},{6}} => {{1,7},{2},{3},{4,6},{5}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => {{1,6,7},{2,4},{3},{5}} => {{1,2,7},{3},{4,6},{5}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => {{1,5,6,7},{2,4},{3}} => {{1,2,3,7},{4,6},{5}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => {{1,7},{2,3,4},{5},{6}} => {{1,7},{2},{3},{4,5,6}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => {{1,6,7},{2,3,4},{5}} => {{1,2,7},{3},{4,5,6}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => {{1,5,6,7},{2,3,4}} => {{1,2,3,7},{4,5,6}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => {{1,3,5,6,7},{2,4}} => {{1,2,3,5,7},{4,6}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => {{1,7},{2,3,4,5},{6}} => {{1,7},{2},{3,4,5,6}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => {{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => {{1,7},{2,3,4},{5},{6}} => {{1,7},{2},{3},{4,5,6}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => {{1,6,7},{2,3,4},{5}} => {{1,2,7},{3},{4,5,6}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => {{1,5,6,7},{2,3,4}} => {{1,2,3,7},{4,5,6}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => {{1,7},{2,3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5,6}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => {{1,6,7},{2,3},{4},{5}} => {{1,2,7},{3},{4},{5,6}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => {{1,5,6,7},{2,3},{4}} => {{1,2,3,7},{4},{5,6}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => {{1,4,5,6,7},{2,3}} => {{1,2,3,4,7},{5,6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => {{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => {{1,6,7},{2},{3},{4},{5}} => {{1,2,7},{3},{4},{5},{6}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => {{1,5,6,7},{2},{3},{4}} => {{1,2,3,7},{4},{5},{6}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => {{1,4,5,6,7},{2},{3}} => {{1,2,3,4,7},{5},{6}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => {{1,3,4,5,6,7},{2}} => {{1,2,3,4,5,7},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => {{1,2,6,7},{3,5},{4}} => {{1,2,6,7},{3,5},{4}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => {{1,6},{2,7},{3,5},{4}} => {{1,6},{2,7},{3,5},{4}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => {{1,6},{2,3,5,7},{4}} => {{1,3,5,6},{2,7},{4}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => {{1,2,6,7},{3,4,5}} => {{1,2,6,7},{3,4,5}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => {{1,6},{2,7},{3,4,5}} => {{1,6},{2,7},{3,4,5}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => {{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] => [6,5,4,7,3,1,2] => {{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => {{1,2,4,6,7},{3,5}} => {{1,2,4,6,7},{3,5}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => {{1,6},{2,4,7},{3,5}} => {{1,4,6},{2,7},{3,5}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => {{1,3,5,6},{2,4,7}} => {{1,4,6},{2,3,5,7}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => {{1,2,6,7},{3,4,5}} => {{1,2,6,7},{3,4,5}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => {{1,6},{2,7},{3,4,5}} => {{1,6},{2,7},{3,4,5}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => {{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] => [6,5,7,3,4,1,2] => {{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => {{1,2,6,7},{3,4},{5}} => {{1,2,6,7},{3},{4,5}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => {{1,6},{2,7},{3,4},{5}} => {{1,6},{2,7},{3},{4,5}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => {{1,2,5,6,7},{3,4}} => {{1,2,3,6,7},{4,5}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => {{1,6},{2,5,7},{3,4}} => {{1,3,6},{2,7},{4,5}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => {{1,2,5,6,7},{3,4}} => {{1,2,3,6,7},{4,5}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => {{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => {{1,3,4,6},{2,5,7}} => {{1,3,6},{2,4,5,7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => {{1,2,6,7},{3},{4},{5}} => {{1,2,6,7},{3},{4},{5}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => {{1,6},{2,7},{3},{4},{5}} => {{1,6},{2,7},{3},{4},{5}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => {{1,2,5,6,7},{3},{4}} => {{1,2,3,6,7},{4},{5}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => {{1,6},{2,5,7},{3},{4}} => {{1,3,6},{2,7},{4},{5}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => {{1,2,5,6,7},{3},{4}} => {{1,2,3,6,7},{4},{5}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => {{1,6},{2,4,5,7},{3}} => {{1,3,4,6},{2,7},{5}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => {{1,4,6},{2,5,7},{3}} => {{1,3,6},{2,4,7},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => {{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => {{1,4,6},{2,3,5,7}} => {{1,3,5,6},{2,4,7}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => {{1,6},{2,3,5,7},{4}} => {{1,3,5,6},{2,7},{4}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => {{1,3,6,7},{2,5},{4}} => {{1,2,5,7},{3,6},{4}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => {{1,6},{2,5},{3,7},{4}} => {{1,5},{2,7},{3,6},{4}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => {{1,2,5,6},{3,7},{4}} => {{1,5},{2,3,6,7},{4}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => {{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] => [6,7,4,5,2,1,3] => {{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => {{1,6},{2,5},{3,4,7}} => {{1,4,5},{2,7},{3,6}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => {{1,2,5,6},{3,4,7}} => {{1,4,5},{2,3,6,7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => {{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => {{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] => [6,7,5,3,2,1,4] => {{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => {{1,6},{2,5},{3,4,7}} => {{1,4,5},{2,7},{3,6}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => {{1,2,5,6},{3,4,7}} => {{1,4,5},{2,3,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => {{1,2,5,6,7},{3,4}} => {{1,2,3,6,7},{4,5}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => {{1,6},{2,5,7},{3,4}} => {{1,3,6},{2,7},{4,5}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => {{1,6,7},{2,5},{3,4}} => {{1,2,7},{3,6},{4,5}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => {{1,6},{2,5},{3,4},{7}} => {{1},{2,7},{3,6},{4,5}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => {{1,2,5,6},{3,4},{7}} => {{1},{2,3,6,7},{4,5}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => {{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => {{1,6},{2,3,4,5},{7}} => {{1},{2,7},{3,4,5,6}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => {{1,3,4,6},{2,5},{7}} => {{1},{2,4,5,7},{3,6}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => {{1,2,5,6,7},{3},{4}} => {{1,2,3,6,7},{4},{5}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => {{1,6},{2,5,7},{3},{4}} => {{1,3,6},{2,7},{4},{5}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => {{1,6,7},{2,5},{3},{4}} => {{1,2,7},{3,6},{4},{5}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => {{1,6},{2,5},{3},{4},{7}} => {{1},{2,7},{3,6},{4},{5}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => {{1,2,5,6},{3},{4},{7}} => {{1},{2,3,6,7},{4},{5}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => {{1,6,7},{2,4,5},{3}} => {{1,2,7},{3,4,6},{5}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => {{1,6},{2,4,5},{3},{7}} => {{1},{2,7},{3,4,6},{5}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => {{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6,7},{5}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => {{1,4,6},{2,5},{3},{7}} => {{1},{2,4,7},{3,6},{5}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => {{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => {{1,6},{2,3,4,5},{7}} => {{1},{2,7},{3,4,5,6}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => {{1,4,6},{2,3,5},{7}} => {{1},{2,4,7},{3,5,6}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => {{1,2,4,6,7},{3,5}} => {{1,2,4,6,7},{3,5}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => {{1,6},{2,4,7},{3,5}} => {{1,4,6},{2,7},{3,5}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => {{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => {{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => {{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => {{1,6},{2,3,4,5},{7}} => {{1},{2,7},{3,4,5,6}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => {{1,6,7},{2,4},{3,5}} => {{1,2,7},{3,5},{4,6}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => {{1,6},{2,4},{3,5},{7}} => {{1},{2,7},{3,5},{4,6}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => {{1,3,5,6},{2,4},{7}} => {{1},{2,3,5,7},{4,6}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => {{1,6},{2,4,5,7},{3}} => {{1,3,4,6},{2,7},{5}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => {{1,6,7},{2,4,5},{3}} => {{1,2,7},{3,4,6},{5}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => {{1,6},{2,4,5},{3},{7}} => {{1},{2,7},{3,4,6},{5}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => {{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6,7},{5}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => {{1,6,7},{2,4},{3},{5}} => {{1,2,7},{3},{4,6},{5}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => {{1,6},{2,4},{3},{5},{7}} => {{1},{2,7},{3},{4,6},{5}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => {{1,5,6},{2,4},{3},{7}} => {{1},{2,3,7},{4,6},{5}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => {{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6,7},{5}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => {{1,6,7},{2,3,4},{5}} => {{1,2,7},{3},{4,5,6}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => {{1,6},{2,3,4},{5},{7}} => {{1},{2,7},{3},{4,5,6}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => {{1,5,6},{2,3,4},{7}} => {{1},{2,3,7},{4,5,6}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => {{1,3,5,6},{2,4},{7}} => {{1},{2,3,5,7},{4,6}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => {{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => {{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => {{1,6},{2,3,4,5},{7}} => {{1},{2,7},{3,4,5,6}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => {{1,6,7},{2,3,4},{5}} => {{1,2,7},{3},{4,5,6}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => {{1,6},{2,3,4},{5},{7}} => {{1},{2,7},{3},{4,5,6}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => {{1,5,6},{2,3,4},{7}} => {{1},{2,3,7},{4,5,6}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => {{1,6,7},{2,3},{4},{5}} => {{1,2,7},{3},{4},{5,6}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => {{1,6},{2,3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5,6}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => {{1,5,6},{2,3},{4},{7}} => {{1},{2,3,7},{4},{5,6}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => {{1,4,5,6},{2,3},{7}} => {{1},{2,3,4,7},{5,6}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => {{1,6,7},{2},{3},{4},{5}} => {{1,2,7},{3},{4},{5},{6}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => {{1,6},{2},{3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5},{6}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => {{1,5,6},{2},{3},{4},{7}} => {{1},{2,3,7},{4},{5},{6}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => {{1,4,5,6},{2},{3},{7}} => {{1},{2,3,4,7},{5},{6}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => {{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,7},{6}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => {{1,3,5,7},{2,6},{4}} => {{1,3,5,7},{2,6},{4}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => {{1,2,5,6},{3,7},{4}} => {{1,5},{2,3,6,7},{4}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => {{1,5},{2,6},{3,7},{4}} => {{1,5},{2,6},{3,7},{4}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => {{1,3,4,5,7},{2,6}} => {{1,3,4,5,7},{2,6}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => {{1,2,5,6},{3,4,7}} => {{1,4,5},{2,3,6,7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => {{1,5},{2,6},{3,4,7}} => {{1,4,5},{2,6},{3,7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => {{1,3,5,7},{2,4,6}} => {{1,3,5,7},{2,4,6}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => {{1,5},{2,3,4,6,7}} => {{1,2,4,5,6},{3,7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => {{1,3,4,5,7},{2,6}} => {{1,3,4,5,7},{2,6}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => {{1,2,5,6},{3,4,7}} => {{1,4,5},{2,3,6,7}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => {{1,5},{2,6},{3,4,7}} => {{1,4,5},{2,6},{3,7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => {{1,5,7},{2,6},{3,4}} => {{1,3,7},{2,6},{4,5}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => {{1,2,5,6,7},{3,4}} => {{1,2,3,6,7},{4,5}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => {{1,2,5,6,7},{3,4}} => {{1,2,3,6,7},{4,5}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => {{1,2,5,6},{3,4},{7}} => {{1},{2,3,6,7},{4,5}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => {{1,5},{2,6},{3,4},{7}} => {{1},{2,6},{3,7},{4,5}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => {{1,5},{2,3,4,6},{7}} => {{1},{2,4,5,6},{3,7}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => {{1,5,7},{2,6},{3},{4}} => {{1,3,7},{2,6},{4},{5}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => {{1,2,5,6,7},{3},{4}} => {{1,2,3,6,7},{4},{5}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => {{1,2,5,6,7},{3},{4}} => {{1,2,3,6,7},{4},{5}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => {{1,2,5,6},{3},{4},{7}} => {{1},{2,3,6,7},{4},{5}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => {{1,5},{2,6},{3},{4},{7}} => {{1},{2,6},{3,7},{4},{5}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => {{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6,7},{5}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => {{1,5},{2,4,6},{3},{7}} => {{1},{2,4,6},{3,7},{5}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => {{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6,7},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => {{1,5},{2,3,4,6},{7}} => {{1},{2,4,5,6},{3,7}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => {{1,3,5},{2,4,6},{7}} => {{1},{2,4,6},{3,5,7}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => {{1,3,5,6},{2,4,7}} => {{1,4,6},{2,3,5,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => {{1,2,4,5,7},{3,6}} => {{1,3,4,6,7},{2,5}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => {{1,5},{2,3,4,6,7}} => {{1,2,4,5,6},{3,7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => {{1,5,7},{2,3,4,6}} => {{1,3,7},{2,4,5,6}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => {{1,5},{2,3,4,6},{7}} => {{1},{2,4,5,6},{3,7}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => {{1,3,5,6,7},{2,4}} => {{1,2,3,5,7},{4,6}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => {{1,3,5,6},{2,4},{7}} => {{1},{2,3,5,7},{4,6}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => {{1,5},{2,4},{3,6},{7}} => {{1},{2,5},{3,7},{4,6}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => {{1,2,4,5},{3,6},{7}} => {{1},{2,5},{3,4,6,7}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => {{1,5,7},{2,4,6},{3}} => {{1,3,7},{2,4,6},{5}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => {{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6,7},{5}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => {{1,5},{2,4,6},{3},{7}} => {{1},{2,4,6},{3,7},{5}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => {{1,5,6,7},{2,4},{3}} => {{1,2,3,7},{4,6},{5}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => {{1,5,6},{2,4},{3},{7}} => {{1},{2,3,7},{4,6},{5}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => {{1,5},{2,4},{3},{6},{7}} => {{1},{2},{3,7},{4,6},{5}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => {{1,2,4,5},{3},{6},{7}} => {{1},{2},{3,4,6,7},{5}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => {{1,5,6,7},{2,3,4}} => {{1,2,3,7},{4,5,6}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => {{1,5,6},{2,3,4},{7}} => {{1},{2,3,7},{4,5,6}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => {{1,5},{2,3,4},{6},{7}} => {{1},{2},{3,7},{4,5,6}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => {{1,3,5},{2,4},{6},{7}} => {{1},{2},{3,5,7},{4,6}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => {{1,5,7},{2,3,4,6}} => {{1,3,7},{2,4,5,6}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => {{1,5},{2,3,4,6},{7}} => {{1},{2,4,5,6},{3,7}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => {{1,5,6,7},{2,3,4}} => {{1,2,3,7},{4,5,6}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => {{1,5,6},{2,3,4},{7}} => {{1},{2,3,7},{4,5,6}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => {{1,5},{2,3,4},{6},{7}} => {{1},{2},{3,7},{4,5,6}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => {{1,5,6,7},{2,3},{4}} => {{1,2,3,7},{4},{5,6}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => {{1,5,6},{2,3},{4},{7}} => {{1},{2,3,7},{4},{5,6}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => {{1,5},{2,3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5,6}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => {{1,4,5},{2,3},{6},{7}} => {{1},{2},{3,4,7},{5,6}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => {{1,5,6,7},{2},{3},{4}} => {{1,2,3,7},{4},{5},{6}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => {{1,5,6},{2},{3},{4},{7}} => {{1},{2,3,7},{4},{5},{6}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => {{1,5},{2},{3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5},{6}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => {{1,4,5},{2},{3},{6},{7}} => {{1},{2},{3,4,7},{5},{6}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => {{1,3,4,5},{2},{6},{7}} => {{1},{2},{3,4,5,7},{6}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => {{1,4,7},{2,3,5,6}} => {{1,4,7},{2,3,5,6}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => {{1,4,7},{2,5},{3,6}} => {{1,4,7},{2,5},{3,6}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => {{1,3,4,6},{2,5,7}} => {{1,3,6},{2,4,5,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => {{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => {{1,3,4,6},{2,5},{7}} => {{1},{2,4,5,7},{3,6}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => {{1,2,4,5},{3,6},{7}} => {{1},{2,5},{3,4,6,7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => {{1,4},{2,5},{3,6},{7}} => {{1},{2,5},{3,6},{4,7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => {{1,4,6},{2,5,7},{3}} => {{1,3,6},{2,4,7},{5}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => {{1,4,6,7},{2,5},{3}} => {{1,2,4,7},{3,6},{5}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => {{1,4,6},{2,5},{3},{7}} => {{1},{2,4,7},{3,6},{5}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => {{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6,7},{5}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => {{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6,7},{5}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => {{1,2,4,5},{3},{6},{7}} => {{1},{2},{3,4,6,7},{5}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => {{1,4},{2,5},{3},{6},{7}} => {{1},{2},{3,6},{4,7},{5}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => {{1,4},{2,3,5},{6},{7}} => {{1},{2},{3,5,6},{4,7}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => {{1,4,6},{2,3,5,7}} => {{1,3,5,6},{2,4,7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => {{1,4,6,7},{2,3,5}} => {{1,2,4,7},{3,5,6}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => {{1,4,6},{2,3,5},{7}} => {{1},{2,4,7},{3,5,6}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => {{1,4},{2,3,5},{6},{7}} => {{1},{2},{3,5,6},{4,7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => {{1,4,5,6,7},{2,3}} => {{1,2,3,4,7},{5,6}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => {{1,4,5,6},{2,3},{7}} => {{1},{2,3,4,7},{5,6}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => {{1,4,5},{2,3},{6},{7}} => {{1},{2},{3,4,7},{5,6}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => {{1,4},{2,3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5,6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => {{1,4,5,6,7},{2},{3}} => {{1,2,3,4,7},{5},{6}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => {{1,4,5,6},{2},{3},{7}} => {{1},{2,3,4,7},{5},{6}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => {{1,4,5},{2},{3},{6},{7}} => {{1},{2},{3,4,7},{5},{6}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5},{6}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => {{1,3,4},{2},{5},{6},{7}} => {{1},{2},{3},{4,5,7},{6}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => {{1,3,5,7},{2,4,6}} => {{1,3,5,7},{2,4,6}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => {{1,3,5},{2,4,6},{7}} => {{1},{2,4,6},{3,5,7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => {{1,3,5,6,7},{2,4}} => {{1,2,3,5,7},{4,6}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => {{1,3,5,6},{2,4},{7}} => {{1},{2,3,5,7},{4,6}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => {{1,3,5},{2,4},{6},{7}} => {{1},{2},{3,5,7},{4,6}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => {{1,3},{2,4},{5},{6},{7}} => {{1},{2},{3},{4,6},{5,7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => {{1,3,4,5,6,7},{2}} => {{1,2,3,4,5,7},{6}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => {{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,7},{6}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => {{1,3,4,5},{2},{6},{7}} => {{1},{2},{3,4,5,7},{6}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => {{1,3,4},{2},{5},{6},{7}} => {{1},{2},{3},{4,5,7},{6}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,7},{6}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6,7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6,7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6,7}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => {{1,8},{2,7},{3,6},{4,5}} => {{1,8},{2,7},{3,6},{4,5}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => {{1,2,7,8},{3,6},{4,5}} => {{1,2,7,8},{3,6},{4,5}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => {{1,8},{2,3,6,7},{4,5}} => {{1,8},{2,3,6,7},{4,5}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => {{1,2,3,6,7,8},{4,5}} => {{1,2,3,6,7,8},{4,5}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => {{1,3,6,8},{2,7},{4,5}} => {{1,3,6,8},{2,7},{4,5}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => {{1,8},{2,7},{3,4,5,6}} => {{1,8},{2,7},{3,4,5,6}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => {{1,2,7,8},{3,4,5,6}} => {{1,2,7,8},{3,4,5,6}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => {{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] => [6,7,5,8,4,3,2,1] => {{1,3,4,5,6,8},{2,7}} => {{1,3,4,5,6,8},{2,7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => {{1,8},{2,4,5,7},{3,6}} => {{1,8},{2,4,5,7},{3,6}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => {{1,4,5,8},{2,3,6,7}} => {{1,4,5,8},{2,3,6,7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => {{1,8},{2,7},{3,6},{4},{5}} => {{1,8},{2,7},{3,6},{4},{5}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => {{1,2,7,8},{3,6},{4},{5}} => {{1,2,7,8},{3,6},{4},{5}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => {{1,8},{2,3,6,7},{4},{5}} => {{1,8},{2,3,6,7},{4},{5}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3,6,7,8},{4},{5}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => {{1,8},{2,7},{3,5,6},{4}} => {{1,8},{2,7},{3,4,6},{5}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => {{1,8},{2,3,5,6,7},{4}} => {{1,8},{2,3,4,6,7},{5}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => {{1,3,5,6,8},{2,7},{4}} => {{1,3,4,6,8},{2,7},{5}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => {{1,8},{2,5,7},{3,6},{4}} => {{1,8},{2,4,7},{3,6},{5}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => {{1,2,5,7,8},{3,6},{4}} => {{1,2,4,7,8},{3,6},{5}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => {{1,5,8},{2,3,6,7},{4}} => {{1,4,8},{2,3,6,7},{5}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => {{1,8},{2,7},{3,4,5,6}} => {{1,8},{2,7},{3,4,5,6}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => {{1,3,4,5,6,8},{2,7}} => {{1,3,4,5,6,8},{2,7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => {{1,2,5,7,8},{3,4,6}} => {{1,2,4,7,8},{3,5,6}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => {{1,5,8},{2,3,4,6,7}} => {{1,4,8},{2,3,5,6,7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => {{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => {{1,5,8},{2,4,7},{3,6}} => {{1,4,8},{2,5,7},{3,6}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => {{1,8},{2,7},{3,4,5,6}} => {{1,8},{2,7},{3,4,5,6}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => {{1,2,7,8},{3,4,5,6}} => {{1,2,7,8},{3,4,5,6}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => {{1,8},{2,7},{3,5},{4,6}} => {{1,8},{2,7},{3,5},{4,6}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => {{1,2,7,8},{3,5},{4,6}} => {{1,2,7,8},{3,5},{4,6}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => {{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => {{1,4,6,8},{2,7},{3,5}} => {{1,3,5,8},{2,7},{4,6}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => {{1,4,6,8},{2,3,5,7}} => {{1,3,5,8},{2,4,6,7}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => {{1,8},{2,7},{3,5,6},{4}} => {{1,8},{2,7},{3,4,6},{5}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => {{1,2,7,8},{3,5,6},{4}} => {{1,2,7,8},{3,4,6},{5}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => {{1,8},{2,3,5,6,7},{4}} => {{1,8},{2,3,4,6,7},{5}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => {{1,3,5,6,8},{2,7},{4}} => {{1,3,4,6,8},{2,7},{5}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => {{1,8},{2,7},{3,5},{4},{6}} => {{1,8},{2,7},{3},{4,6},{5}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => {{1,2,7,8},{3,5},{4},{6}} => {{1,2,7,8},{3},{4,6},{5}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => {{1,8},{2,6,7},{3,5},{4}} => {{1,8},{2,3,7},{4,6},{5}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => {{1,2,6,7,8},{3,5},{4}} => {{1,2,3,7,8},{4,6},{5}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => {{1,6,8},{2,7},{3,5},{4}} => {{1,3,8},{2,7},{4,6},{5}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => {{1,6,8},{2,3,5,7},{4}} => {{1,3,8},{2,4,6,7},{5}}
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => {{1,8},{2,7},{3,4,5},{6}} => {{1,8},{2,7},{3},{4,5,6}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => {{1,6,8},{2,7},{3,4,5}} => {{1,3,8},{2,7},{4,5,6}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => {{1,6,8},{2,3,4,5,7}} => {{1,3,8},{2,4,5,6,7}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => {{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => {{1,6,8},{2,4,7},{3,5}} => {{1,3,8},{2,5,7},{4,6}}
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => {{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => {{1,8},{2,7},{3,4,5,6}} => {{1,8},{2,7},{3,4,5,6}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => {{1,2,7,8},{3,4,5,6}} => {{1,2,7,8},{3,4,5,6}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => {{1,3,4,5,6,8},{2,7}} => {{1,3,4,5,6,8},{2,7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => {{1,8},{2,7},{3,4,5},{6}} => {{1,8},{2,7},{3},{4,5,6}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => {{1,2,7,8},{3,4,5},{6}} => {{1,2,7,8},{3},{4,5,6}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => {{1,2,6,7,8},{3,4,5}} => {{1,2,3,7,8},{4,5,6}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => {{1,8},{2,7},{3,4},{5},{6}} => {{1,8},{2,7},{3},{4},{5,6}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => {{1,8},{2,6,7},{3,4},{5}} => {{1,8},{2,3,7},{4},{5,6}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => {{1,2,6,7,8},{3,4},{5}} => {{1,2,3,7,8},{4},{5,6}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => {{1,8},{2,5,6,7},{3,4}} => {{1,8},{2,3,4,7},{5,6}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => {{1,6,8},{2,5,7},{3,4}} => {{1,3,8},{2,4,7},{5,6}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => {{1,8},{2,7},{3},{4},{5},{6}} => {{1,8},{2,7},{3},{4},{5},{6}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => {{1,2,7,8},{3},{4},{5},{6}} => {{1,2,7,8},{3},{4},{5},{6}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => {{1,2,6,7,8},{3},{4},{5}} => {{1,2,3,7,8},{4},{5},{6}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => {{1,8},{2,5,6,7},{3},{4}} => {{1,8},{2,3,4,7},{5},{6}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => {{1,8},{2,4,5,6,7},{3}} => {{1,8},{2,3,4,5,7},{6}}
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => {{1,6,8},{2,3,4,5,7}} => {{1,3,8},{2,4,5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => {{1,4,6,8},{2,3,5,7}} => {{1,3,5,8},{2,4,6,7}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => {{1,8},{2,3,6,7},{4,5}} => {{1,8},{2,3,6,7},{4,5}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => {{1,2,3,6,7,8},{4,5}} => {{1,2,3,6,7,8},{4,5}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => {{1,8},{2,6},{3,7},{4,5}} => {{1,8},{2,6},{3,7},{4,5}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => {{1,3,7,8},{2,6},{4,5}} => {{1,2,6,8},{3,7},{4,5}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => {{1,8},{2,6},{3,4,5,7}} => {{1,8},{2,4,5,6},{3,7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => {{1,4,5,8},{2,6},{3,7}} => {{1,4,5,8},{2,6},{3,7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => {{1,8},{2,3,6,7},{4},{5}} => {{1,8},{2,3,6,7},{4},{5}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => {{1,8},{2,6},{3,7},{4},{5}} => {{1,8},{2,6},{3,7},{4},{5}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => {{1,3,7,8},{2,6},{4},{5}} => {{1,2,6,8},{3,7},{4},{5}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3,6,7,8},{4},{5}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => {{1,8},{2,3,5,6,7},{4}} => {{1,8},{2,3,4,6,7},{5}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => {{1,8},{2,6},{3,5,7},{4}} => {{1,8},{2,4,6},{3,7},{5}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => {{1,3,5,7,8},{2,6},{4}} => {{1,2,4,6,8},{3,7},{5}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => {{1,8},{2,3,5,6,7},{4}} => {{1,8},{2,3,4,6,7},{5}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => {{1,2,5,6,8},{3,7},{4}} => {{1,3,4,7,8},{2,6},{5}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => {{1,8},{2,6},{3,4,5,7}} => {{1,8},{2,4,5,6},{3,7}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => {{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] => [8,6,7,5,3,2,4,1] => {{1,8},{2,6},{3,4,5,7}} => {{1,8},{2,4,5,6},{3,7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => {{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] => [8,6,5,7,3,2,4,1] => {{1,8},{2,6},{3,5},{4,7}} => {{1,8},{2,5},{3,7},{4,6}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => {{1,4,7,8},{2,6},{3,5}} => {{1,2,5,8},{3,7},{4,6}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => {{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => {{1,8},{2,3,5,6},{4,7}} => {{1,8},{2,5},{3,4,6,7}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => {{1,8},{2,3,5,6,7},{4}} => {{1,8},{2,3,4,6,7},{5}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,5,1] => {{1,8},{2,6},{3,5,7},{4}} => {{1,8},{2,4,6},{3,7},{5}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => {{1,3,5,7,8},{2,6},{4}} => {{1,2,4,6,8},{3,7},{5}}
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => {{1,8},{2,6,7},{3,5},{4}} => {{1,8},{2,3,7},{4,6},{5}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => {{1,2,6,7,8},{3,5},{4}} => {{1,2,3,7,8},{4,6},{5}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => {{1,8},{2,6},{3,5},{4},{7}} => {{1,8},{2},{3,7},{4,6},{5}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => {{1,7,8},{2,6},{3,5},{4}} => {{1,2,8},{3,7},{4,6},{5}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => {{1,2,6,7,8},{3,5},{4}} => {{1,2,3,7,8},{4,6},{5}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => {{1,8},{2,3,5,6},{4},{7}} => {{1,8},{2},{3,4,6,7},{5}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => {{1,7,8},{2,3,5,6},{4}} => {{1,2,8},{3,4,6,7},{5}}
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => {{1,3,5,7,8},{2,6},{4}} => {{1,2,4,6,8},{3,7},{5}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => {{1,8},{2,6},{3,4,5},{7}} => {{1,8},{2},{3,7},{4,5,6}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => {{1,7,8},{2,6},{3,4,5}} => {{1,2,8},{3,7},{4,5,6}}
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => {{1,2,6,7,8},{3,4,5}} => {{1,2,3,7,8},{4,5,6}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => {{1,8},{2,3,4,5,6},{7}} => {{1,8},{2},{3,4,5,6,7}}
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => {{1,7,8},{2,4,6},{3,5}} => {{1,2,8},{3,5,7},{4,6}}
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => {{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => {{1,4,7,8},{2,3,5,6}} => {{1,2,5,8},{3,4,6,7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => {{1,8},{2,6},{3,4,5,7}} => {{1,8},{2,4,5,6},{3,7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => {{1,8},{2,6,7},{3,4,5}} => {{1,8},{2,3,7},{4,5,6}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => {{1,2,6,7,8},{3,4,5}} => {{1,2,3,7,8},{4,5,6}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => {{1,8},{2,6},{3,4,5},{7}} => {{1,8},{2},{3,7},{4,5,6}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => {{1,7,8},{2,6},{3,4,5}} => {{1,2,8},{3,7},{4,5,6}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => {{1,8},{2,3,4,5,6},{7}} => {{1,8},{2},{3,4,5,6,7}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => {{1,8},{2,6,7},{3,4},{5}} => {{1,8},{2,3,7},{4},{5,6}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => {{1,2,6,7,8},{3,4},{5}} => {{1,2,3,7,8},{4},{5,6}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => {{1,8},{2,6},{3,4},{5},{7}} => {{1,8},{2},{3,7},{4},{5,6}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => {{1,7,8},{2,6},{3,4},{5}} => {{1,2,8},{3,7},{4},{5,6}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => {{1,8},{2,5,6},{3,4},{7}} => {{1,8},{2},{3,4,7},{5,6}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => {{1,7,8},{2,5,6},{3,4}} => {{1,2,8},{3,4,7},{5,6}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => {{1,8},{2,3,4,5,6},{7}} => {{1,8},{2},{3,4,5,6,7}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => {{1,5,7,8},{2,3,4,6}} => {{1,2,4,8},{3,5,6,7}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => {{1,8},{2,6},{3},{4},{5},{7}} => {{1,8},{2},{3,7},{4},{5},{6}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => {{1,7,8},{2,6},{3},{4},{5}} => {{1,2,8},{3,7},{4},{5},{6}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => {{1,5,7,8},{2,6},{3},{4}} => {{1,2,4,8},{3,7},{5},{6}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => {{1,8},{2,4,5,6},{3},{7}} => {{1,8},{2},{3,4,5,7},{6}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => {{1,5,7,8},{2,4,6},{3}} => {{1,2,4,8},{3,5,7},{6}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => {{1,8},{2,3,4,5,6},{7}} => {{1,8},{2},{3,4,5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => {{1,3,5,7,8},{2,4,6}} => {{1,2,4,6,8},{3,5,7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => {{1,8},{2,4,5,7},{3,6}} => {{1,8},{2,4,5,7},{3,6}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => {{1,3,6,8},{2,4,5,7}} => {{1,3,6,8},{2,4,5,7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => {{1,8},{2,3,5,6},{4,7}} => {{1,8},{2,5},{3,4,6,7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => {{1,4,7,8},{2,3,5,6}} => {{1,2,5,8},{3,4,6,7}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => {{1,8},{2,5},{3,6},{4,7}} => {{1,8},{2,5},{3,6},{4,7}}
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => {{1,3,6,8},{2,5,7},{4}} => {{1,3,6,8},{2,4,7},{5}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => {{1,8},{2,3,5,6,7},{4}} => {{1,8},{2,3,4,6,7},{5}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => {{1,8},{2,3,5,6},{4},{7}} => {{1,8},{2},{3,4,6,7},{5}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => {{1,7,8},{2,3,5,6},{4}} => {{1,2,8},{3,4,6,7},{5}}
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => {{1,8},{2,5},{3,6},{4},{7}} => {{1,8},{2},{3,6},{4,7},{5}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => {{1,7,8},{2,5},{3,6},{4}} => {{1,2,8},{3,6},{4,7},{5}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => {{1,3,6,7,8},{2,5},{4}} => {{1,2,3,6,8},{4,7},{5}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => {{1,7,8},{2,5},{3,4,6}} => {{1,2,8},{3,5,6},{4,7}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => {{1,4,7,8},{2,5},{3,6}} => {{1,2,5,8},{3,6},{4,7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => {{1,8},{2,5,7},{3,4,6}} => {{1,8},{2,4,7},{3,5,6}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => {{1,2,5,7,8},{3,4,6}} => {{1,2,4,7,8},{3,5,6}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => {{1,3,4,6,8},{2,5,7}} => {{1,3,5,6,8},{2,4,7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => {{1,8},{2,3,4,5,6},{7}} => {{1,8},{2},{3,4,5,6,7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => {{1,8},{2,5,6,7},{3,4}} => {{1,8},{2,3,4,7},{5,6}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => {{1,8},{2,5,6},{3,4},{7}} => {{1,8},{2},{3,4,7},{5,6}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => {{1,8},{2,5},{3,4},{6},{7}} => {{1,8},{2},{3},{4,7},{5,6}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => {{1,7,8},{2,5},{3,4},{6}} => {{1,2,8},{3},{4,7},{5,6}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => {{1,6,7,8},{2,5},{3,4}} => {{1,2,3,8},{4,7},{5,6}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => {{1,8},{2,3,4,5},{6},{7}} => {{1,8},{2},{3},{4,5,6,7}}
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => {{1,8},{2,5},{3},{4},{6},{7}} => {{1,8},{2},{3},{4,7},{5},{6}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => {{1,7,8},{2,4,5},{3},{6}} => {{1,2,8},{3},{4,5,7},{6}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => {{1,8},{2,3,4,5},{6},{7}} => {{1,8},{2},{3},{4,5,6,7}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => {{1,6,7,8},{2,3,4,5}} => {{1,2,3,8},{4,5,6,7}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => {{1,4,6,7,8},{2,3,5}} => {{1,2,3,5,8},{4,6,7}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => {{1,3,5,7,8},{2,4,6}} => {{1,2,4,6,8},{3,5,7}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => {{1,7,8},{2,4,6},{3,5}} => {{1,2,8},{3,5,7},{4,6}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => {{1,3,5,7,8},{2,4,6}} => {{1,2,4,6,8},{3,5,7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => {{1,8},{2,3,4,5,6},{7}} => {{1,8},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => {{1,8},{2,3,4,5},{6},{7}} => {{1,8},{2},{3},{4,5,6,7}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => {{1,6,7,8},{2,3,4,5}} => {{1,2,3,8},{4,5,6,7}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => {{1,8},{2,4},{3,5},{6},{7}} => {{1,8},{2},{3},{4,6},{5,7}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => {{1,7,8},{2,4},{3,5},{6}} => {{1,2,8},{3},{4,6},{5,7}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => {{1,6,7,8},{2,4},{3,5}} => {{1,2,3,8},{4,6},{5,7}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => {{1,3,5,6,7,8},{2,4}} => {{1,2,3,4,6,8},{5,7}}
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => {{1,7,8},{2,4,5,6},{3}} => {{1,2,8},{3,4,5,7},{6}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => {{1,7,8},{2,4,5},{3},{6}} => {{1,2,8},{3},{4,5,7},{6}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => {{1,8},{2,4},{3},{5},{6},{7}} => {{1,8},{2},{3},{4},{5,7},{6}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => {{1,7,8},{2,4},{3},{5},{6}} => {{1,2,8},{3},{4},{5,7},{6}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => {{1,5,6,7,8},{2,4},{3}} => {{1,2,3,4,8},{5,7},{6}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => {{1,8},{2,3,4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5,6,7}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => {{1,5,6,7,8},{2,3,4}} => {{1,2,3,4,8},{5,6,7}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => {{1,3,5,6,7,8},{2,4}} => {{1,2,3,4,6,8},{5,7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => {{1,8},{2,3,4,5,6},{7}} => {{1,8},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => {{1,6,7,8},{2,3,4,5}} => {{1,2,3,8},{4,5,6,7}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => {{1,8},{2,3,4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5,6,7}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => {{1,5,6,7,8},{2,3,4}} => {{1,2,3,4,8},{5,6,7}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => {{1,8},{2,3},{4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5},{6,7}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => {{1,7,8},{2,3},{4},{5},{6}} => {{1,2,8},{3},{4},{5},{6,7}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => {{1,5,6,7,8},{2,3},{4}} => {{1,2,3,4,8},{5},{6,7}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => {{1,4,5,6,7,8},{2,3}} => {{1,2,3,4,5,8},{6,7}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => {{1,8},{2},{3},{4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5},{6},{7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => {{1,7,8},{2},{3},{4},{5},{6}} => {{1,2,8},{3},{4},{5},{6},{7}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => {{1,6,7,8},{2},{3},{4},{5}} => {{1,2,3,8},{4},{5},{6},{7}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => {{1,5,6,7,8},{2},{3},{4}} => {{1,2,3,4,8},{5},{6},{7}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => {{1,4,5,6,7,8},{2},{3}} => {{1,2,3,4,5,8},{6},{7}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => {{1,3,4,5,6,7,8},{2}} => {{1,2,3,4,5,6,8},{7}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => {{1,2,7,8},{3,6},{4,5}} => {{1,2,7,8},{3,6},{4,5}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => {{1,7},{2,8},{3,6},{4,5}} => {{1,7},{2,8},{3,6},{4,5}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => {{1,2,3,6,7,8},{4,5}} => {{1,2,3,6,7,8},{4,5}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => {{1,2,3,6,7,8},{4,5}} => {{1,2,3,6,7,8},{4,5}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => {{1,2,7,8},{3,4,5,6}} => {{1,2,7,8},{3,4,5,6}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => {{1,7},{2,8},{3,4,5,6}} => {{1,7},{2,8},{3,4,5,6}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => {{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] => [7,6,5,8,4,3,1,2] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => {{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] => [6,5,7,8,4,3,1,2] => {{1,3,6,7},{2,4,5,8}} => {{1,4,5,7},{2,3,6,8}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => {{1,2,7,8},{3,6},{4},{5}} => {{1,2,7,8},{3,6},{4},{5}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => {{1,7},{2,8},{3,6},{4},{5}} => {{1,7},{2,8},{3,6},{4},{5}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3,6,7,8},{4},{5}}
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3,6,7,8},{4},{5}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => {{1,2,7,8},{3,5,6},{4}} => {{1,2,7,8},{3,4,6},{5}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => {{1,2,5,7,8},{3,6},{4}} => {{1,2,4,7,8},{3,6},{5}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => {{1,7},{2,5,8},{3,6},{4}} => {{1,4,7},{2,8},{3,6},{5}}
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => {{1,3,6,7},{2,5,8},{4}} => {{1,4,7},{2,3,6,8},{5}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => {{1,7},{2,8},{3,4,5,6}} => {{1,7},{2,8},{3,4,5,6}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => {{1,2,5,7,8},{3,4,6}} => {{1,2,4,7,8},{3,5,6}}
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => {{1,3,4,6,7},{2,5,8}} => {{1,4,7},{2,3,5,6,8}}
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => {{1,4,7},{2,5,8},{3,6}} => {{1,4,7},{2,5,8},{3,6}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => {{1,2,7,8},{3,4,5,6}} => {{1,2,7,8},{3,4,5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => {{1,7},{2,8},{3,4,5,6}} => {{1,7},{2,8},{3,4,5,6}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => {{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] => [8,7,5,6,3,4,1,2] => {{1,2,7,8},{3,5},{4,6}} => {{1,2,7,8},{3,5},{4,6}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => {{1,7},{2,8},{3,5},{4,6}} => {{1,7},{2,8},{3,5},{4,6}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => {{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => {{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => {{1,3,5,7},{2,4,6,8}} => {{1,3,5,7},{2,4,6,8}}
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,1,2] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => {{1,7},{2,8},{3,5},{4},{6}} => {{1,7},{2,8},{3},{4,6},{5}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => {{1,2,6,7,8},{3,5},{4}} => {{1,2,3,7,8},{4,6},{5}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => {{1,7},{2,6,8},{3,5},{4}} => {{1,3,7},{2,8},{4,6},{5}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => {{1,3,5,7},{2,6,8},{4}} => {{1,3,7},{2,4,6,8},{5}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => {{1,2,7,8},{3,4,5},{6}} => {{1,2,7,8},{3},{4,5,6}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => {{1,7},{2,8},{3,4,5},{6}} => {{1,7},{2,8},{3},{4,5,6}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => {{1,2,6,7,8},{3,4,5}} => {{1,2,3,7,8},{4,5,6}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => {{1,3,4,5,7},{2,6,8}} => {{1,3,7},{2,4,5,6,8}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => {{1,4,7},{2,3,5,6,8}} => {{1,3,4,6,7},{2,5,8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => {{1,2,7,8},{3,4,5,6}} => {{1,2,7,8},{3,4,5,6}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => {{1,7},{2,8},{3,4,5,6}} => {{1,7},{2,8},{3,4,5,6}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => {{1,7},{2,8},{3,4,5},{6}} => {{1,7},{2,8},{3},{4,5,6}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => {{1,7},{2,6,8},{3,4,5}} => {{1,3,7},{2,8},{4,5,6}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => {{1,2,7,8},{3,4},{5},{6}} => {{1,2,7,8},{3},{4},{5,6}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => {{1,7},{2,8},{3,4},{5},{6}} => {{1,7},{2,8},{3},{4},{5,6}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => {{1,7},{2,5,6,8},{3,4}} => {{1,3,4,7},{2,8},{5,6}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => {{1,5,7},{2,6,8},{3,4}} => {{1,3,7},{2,4,8},{5,6}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => {{1,5,7},{2,3,4,6,8}} => {{1,3,5,6,7},{2,4,8}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => {{1,2,7,8},{3},{4},{5},{6}} => {{1,2,7,8},{3},{4},{5},{6}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => {{1,7},{2,8},{3},{4},{5},{6}} => {{1,7},{2,8},{3},{4},{5},{6}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => {{1,7},{2,6,8},{3},{4},{5}} => {{1,3,7},{2,8},{4},{5},{6}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => {{1,7},{2,5,6,8},{3},{4}} => {{1,3,4,7},{2,8},{5},{6}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => {{1,5,7},{2,6,8},{3},{4}} => {{1,3,7},{2,4,8},{5},{6}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => {{1,5,7},{2,4,6,8},{3}} => {{1,3,5,7},{2,4,8},{6}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => {{1,5,7},{2,3,4,6,8}} => {{1,3,5,6,7},{2,4,8}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => {{1,3,5,7},{2,4,6,8}} => {{1,3,5,7},{2,4,6,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => {{1,2,3,6,7,8},{4,5}} => {{1,2,3,6,7,8},{4,5}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => {{1,3,7,8},{2,6},{4,5}} => {{1,2,6,8},{3,7},{4,5}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => {{1,7},{2,6},{3,8},{4,5}} => {{1,6},{2,8},{3,7},{4,5}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => {{1,2,6,7},{3,8},{4,5}} => {{1,6},{2,3,7,8},{4,5}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => {{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] => [7,8,5,6,4,2,1,3] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => {{1,7},{2,6},{3,4,5,8}} => {{1,4,5,6},{2,8},{3,7}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => {{1,2,6,7},{3,4,5,8}} => {{1,4,5,6},{2,3,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3,6,7,8},{4},{5}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => {{1,7},{2,6},{3,8},{4},{5}} => {{1,6},{2,8},{3,7},{4},{5}}
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => {{1,2,6,7},{3,5,8},{4}} => {{1,4,6},{2,3,7,8},{5}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => {{1,3,5,7,8},{2,6},{4}} => {{1,2,4,6,8},{3,7},{5}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => {{1,7},{2,6},{3,4,5,8}} => {{1,4,5,6},{2,8},{3,7}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => {{1,3,5,7,8},{2,4,6}} => {{1,2,4,6,8},{3,5,7}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => {{1,4,7},{2,3,5,6,8}} => {{1,3,4,6,7},{2,5,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => {{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] => [7,8,6,5,3,2,1,4] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => {{1,7},{2,6},{3,4,5,8}} => {{1,4,5,6},{2,8},{3,7}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => {{1,2,6,7},{3,4,5,8}} => {{1,4,5,6},{2,3,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => {{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => {{1,4,7,8},{2,6},{3,5}} => {{1,2,5,8},{3,7},{4,6}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => {{1,7},{2,6},{3,5},{4,8}} => {{1,5},{2,8},{3,7},{4,6}}
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => {{1,2,6,7},{3,5},{4,8}} => {{1,5},{2,3,7,8},{4,6}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => {{1,4,7,8},{2,3,5,6}} => {{1,2,5,8},{3,4,6,7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => {{1,7},{2,3,5,6},{4,8}} => {{1,5},{2,8},{3,4,6,7}}
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => {{1,2,3,5,6,7},{4,8}} => {{1,5},{2,3,4,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => {{1,3,5,7},{2,6},{4,8}} => {{1,5},{2,4,6,8},{3,7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => {{1,3,5,7,8},{2,6},{4}} => {{1,2,4,6,8},{3,7},{5}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => {{1,7},{2,6},{3,5,8},{4}} => {{1,4,6},{2,8},{3,7},{5}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => {{1,2,6,7},{3,5,8},{4}} => {{1,4,6},{2,3,7,8},{5}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => {{1,2,6,7,8},{3,5},{4}} => {{1,2,3,7,8},{4,6},{5}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => {{1,7},{2,6,8},{3,5},{4}} => {{1,3,7},{2,8},{4,6},{5}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => {{1,7,8},{2,6},{3,5},{4}} => {{1,2,8},{3,7},{4,6},{5}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => {{1,7},{2,6},{3,5},{4},{8}} => {{1},{2,8},{3,7},{4,6},{5}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => {{1,2,6,7},{3,5},{4},{8}} => {{1},{2,3,7,8},{4,6},{5}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => {{1,7,8},{2,3,5,6},{4}} => {{1,2,8},{3,4,6,7},{5}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => {{1,7},{2,3,5,6},{4},{8}} => {{1},{2,8},{3,4,6,7},{5}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => {{1,2,3,5,6,7},{4},{8}} => {{1},{2,3,4,6,7,8},{5}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => {{1,3,5,7},{2,6},{4},{8}} => {{1},{2,4,6,8},{3,7},{5}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => {{1,2,6,7,8},{3,4,5}} => {{1,2,3,7,8},{4,5,6}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => {{1,7},{2,6,8},{3,4,5}} => {{1,3,7},{2,8},{4,5,6}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => {{1,7,8},{2,6},{3,4,5}} => {{1,2,8},{3,7},{4,5,6}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => {{1,7},{2,6},{3,4,5},{8}} => {{1},{2,8},{3,7},{4,5,6}}
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => {{1,2,6,7},{3,4,5},{8}} => {{1},{2,3,7,8},{4,5,6}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => {{1,7},{2,3,4,5,6},{8}} => {{1},{2,8},{3,4,5,6,7}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => {{1,3,4,5,7},{2,6},{8}} => {{1},{2,4,5,6,8},{3,7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => {{1,7,8},{2,4,6},{3,5}} => {{1,2,8},{3,5,7},{4,6}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => {{1,4,7},{2,3,5,6},{8}} => {{1},{2,5,8},{3,4,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => {{1,2,6,7},{3,4,5,8}} => {{1,4,5,6},{2,3,7,8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => {{1,2,6,7,8},{3,4,5}} => {{1,2,3,7,8},{4,5,6}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => {{1,7,8},{2,6},{3,4,5}} => {{1,2,8},{3,7},{4,5,6}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => {{1,7},{2,6},{3,4,5},{8}} => {{1},{2,8},{3,7},{4,5,6}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => {{1,2,6,7},{3,4,5},{8}} => {{1},{2,3,7,8},{4,5,6}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => {{1,7},{2,3,4,5,6},{8}} => {{1},{2,8},{3,4,5,6,7}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => {{1,3,4,5,7},{2,6},{8}} => {{1},{2,4,5,6,8},{3,7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => {{1,7},{2,6},{3,4},{5},{8}} => {{1},{2,8},{3,7},{4},{5,6}}
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => {{1,2,6,7},{3,4},{5},{8}} => {{1},{2,3,7,8},{4},{5,6}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => {{1,7},{2,5,6},{3,4},{8}} => {{1},{2,8},{3,4,7},{5,6}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => {{1,2,5,6,7},{3,4},{8}} => {{1},{2,3,4,7,8},{5,6}}
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => {{1,5,7},{2,6},{3,4},{8}} => {{1},{2,4,8},{3,7},{5,6}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => {{1,5,7},{2,3,4,6},{8}} => {{1},{2,4,8},{3,5,6,7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => {{1,2,6,7,8},{3},{4},{5}} => {{1,2,3,7,8},{4},{5},{6}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => {{1,7},{2,6,8},{3},{4},{5}} => {{1,3,7},{2,8},{4},{5},{6}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => {{1,7},{2,6},{3},{4},{5},{8}} => {{1},{2,8},{3,7},{4},{5},{6}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => {{1,7,8},{2,4,5,6},{3}} => {{1,2,8},{3,4,5,7},{6}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => {{1,5,7},{2,4,6},{3},{8}} => {{1},{2,4,8},{3,5,7},{6}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => {{1,7},{2,3,4,5,6},{8}} => {{1},{2,8},{3,4,5,6,7}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => {{1,3,5,7},{2,4,6},{8}} => {{1},{2,4,6,8},{3,5,7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => {{1,7},{2,4,5,8},{3,6}} => {{1,4,5,7},{2,8},{3,6}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => {{1,4,7,8},{2,3,5,6}} => {{1,2,5,8},{3,4,6,7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => {{1,7},{2,3,5,6},{4,8}} => {{1,5},{2,8},{3,4,6,7}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => {{1,2,3,5,6,7},{4,8}} => {{1,5},{2,3,4,6,7,8}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => {{1,4,7,8},{2,5},{3,6}} => {{1,2,5,8},{3,6},{4,7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => {{1,7},{2,5},{3,6},{4,8}} => {{1,5},{2,8},{3,6},{4,7}}
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => {{1,3,6,7},{2,5},{4,8}} => {{1,5},{2,3,6,8},{4,7}}
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => {{1,2,3,5,6,7},{4,8}} => {{1,5},{2,3,4,6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => {{1,2,5,7,8},{3,6},{4}} => {{1,2,4,7,8},{3,6},{5}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => {{1,7,8},{2,3,5,6},{4}} => {{1,2,8},{3,4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => {{1,7},{2,3,5,6},{4},{8}} => {{1},{2,8},{3,4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => {{1,2,3,5,6,7},{4},{8}} => {{1},{2,3,4,6,7,8},{5}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => {{1,7,8},{2,5},{3,6},{4}} => {{1,2,8},{3,6},{4,7},{5}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => {{1,7},{2,5},{3,6},{4},{8}} => {{1},{2,8},{3,6},{4,7},{5}}
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => {{1,2,3,5,6,7},{4},{8}} => {{1},{2,3,4,6,7,8},{5}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => {{1,7},{2,3,4,5,6},{8}} => {{1},{2,8},{3,4,5,6,7}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => {{1,7},{2,5},{3,4,6},{8}} => {{1},{2,8},{3,5,6},{4,7}}
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => {{1,3,4,6,7},{2,5},{8}} => {{1},{2,3,5,6,8},{4,7}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => {{1,2,4,5,7},{3,6},{8}} => {{1},{2,4,5,7,8},{3,6}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => {{1,4,7},{2,5},{3,6},{8}} => {{1},{2,5,8},{3,6},{4,7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => {{1,2,5,7,8},{3,4,6}} => {{1,2,4,7,8},{3,5,6}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => {{1,7},{2,3,4,5,6},{8}} => {{1},{2,8},{3,4,5,6,7}}
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => {{1,3,4,6,7},{2,5},{8}} => {{1},{2,3,5,6,8},{4,7}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => {{1,7},{2,5,6,8},{3,4}} => {{1,3,4,7},{2,8},{5,6}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => {{1,7},{2,5,6},{3,4},{8}} => {{1},{2,8},{3,4,7},{5,6}}
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => {{1,2,5,6,7},{3,4},{8}} => {{1},{2,3,4,7,8},{5,6}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => {{1,7,8},{2,5},{3,4},{6}} => {{1,2,8},{3},{4,7},{5,6}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => {{1,7},{2,5},{3,4},{6},{8}} => {{1},{2,8},{3},{4,7},{5,6}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => {{1,6,7},{2,5},{3,4},{8}} => {{1},{2,3,8},{4,7},{5,6}}
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => {{1,2,5,6,7},{3,4},{8}} => {{1},{2,3,4,7,8},{5,6}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => {{1,7},{2,3,4,5},{6},{8}} => {{1},{2,8},{3},{4,5,6,7}}
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => {{1,7},{2,5,6,8},{3},{4}} => {{1,3,4,7},{2,8},{5},{6}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => {{1,2,5,6,7},{3},{4},{8}} => {{1},{2,3,4,7,8},{5},{6}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => {{1,7},{2,5},{3},{4},{6},{8}} => {{1},{2,8},{3},{4,7},{5},{6}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => {{1,2,5,6,7},{3},{4},{8}} => {{1},{2,3,4,7,8},{5},{6}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => {{1,7,8},{2,4,5},{3},{6}} => {{1,2,8},{3},{4,5,7},{6}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => {{1,7},{2,4,5},{3},{6},{8}} => {{1},{2,8},{3},{4,5,7},{6}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => {{1,2,4,5,6,7},{3},{8}} => {{1},{2,3,4,5,7,8},{6}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => {{1,4,6,7},{2,5},{3},{8}} => {{1},{2,3,5,8},{4,7},{6}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => {{1,4,6,7},{2,3,5},{8}} => {{1},{2,3,5,8},{4,6,7}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => {{1,3,5,7,8},{2,4,6}} => {{1,2,4,6,8},{3,5,7}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => {{1,2,4,6,7},{3,5,8}} => {{1,4,6},{2,3,5,7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => {{1,7,8},{2,4,6},{3,5}} => {{1,2,8},{3,5,7},{4,6}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => {{1,7},{2,4,6},{3,5},{8}} => {{1},{2,8},{3,5,7},{4,6}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => {{1,2,4,6,7},{3,5},{8}} => {{1},{2,3,5,7,8},{4,6}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => {{1,7},{2,3,4,5,6},{8}} => {{1},{2,8},{3,4,5,6,7}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => {{1,3,5,7},{2,4,6},{8}} => {{1},{2,4,6,8},{3,5,7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => {{1,7},{2,3,4,5,6},{8}} => {{1},{2,8},{3,4,5,6,7}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => {{1,7,8},{2,4},{3,5},{6}} => {{1,2,8},{3},{4,6},{5,7}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => {{1,7},{2,4},{3,5},{6},{8}} => {{1},{2,8},{3},{4,6},{5,7}}
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => {{1,3,5,6,7},{2,4},{8}} => {{1},{2,3,4,6,8},{5,7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => {{1,7,8},{2,4,5,6},{3}} => {{1,2,8},{3,4,5,7},{6}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => {{1,7},{2,4,5,6},{3},{8}} => {{1},{2,8},{3,4,5,7},{6}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => {{1,2,4,5,6,7},{3},{8}} => {{1},{2,3,4,5,7,8},{6}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => {{1,7,8},{2,4,5},{3},{6}} => {{1,2,8},{3},{4,5,7},{6}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => {{1,7},{2,4,5},{3},{6},{8}} => {{1},{2,8},{3},{4,5,7},{6}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => {{1,6,7},{2,4,5},{3},{8}} => {{1},{2,3,8},{4,5,7},{6}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => {{1,5,6,7},{2,4},{3},{8}} => {{1},{2,3,4,8},{5,7},{6}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => {{1,7,8},{2,3,4},{5},{6}} => {{1,2,8},{3},{4},{5,6,7}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => {{1,3,5,6,7},{2,4},{8}} => {{1},{2,3,4,6,8},{5,7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => {{1,7},{2,3,4,5,6,8}} => {{1,3,4,5,6,7},{2,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => {{1,7},{2,3,4,5,6},{8}} => {{1},{2,8},{3,4,5,6,7}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => {{1,7},{2,3,4},{5},{6},{8}} => {{1},{2,8},{3},{4},{5,6,7}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => {{1,6,7},{2,3,4},{5},{8}} => {{1},{2,3,8},{4},{5,6,7}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => {{1,5,6,7},{2,3,4},{8}} => {{1},{2,3,4,8},{5,6,7}}
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => {{1,7,8},{2,3},{4},{5},{6}} => {{1,2,8},{3},{4},{5},{6,7}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => {{1,6,7},{2,3},{4},{5},{8}} => {{1},{2,3,8},{4},{5},{6,7}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => {{1,4,5,6,7},{2,3},{8}} => {{1},{2,3,4,5,8},{6,7}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => {{1,7,8},{2},{3},{4},{5},{6}} => {{1,2,8},{3},{4},{5},{6},{7}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => {{1,7},{2},{3},{4},{5},{6},{8}} => {{1},{2,8},{3},{4},{5},{6},{7}}
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => {{1,6,7},{2},{3},{4},{5},{8}} => {{1},{2,3,8},{4},{5},{6},{7}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => {{1,5,6,7},{2},{3},{4},{8}} => {{1},{2,3,4,8},{5},{6},{7}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => {{1,4,5,6,7},{2},{3},{8}} => {{1},{2,3,4,5,8},{6},{7}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => {{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,8},{7}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => {{1,3,6,8},{2,7},{4,5}} => {{1,3,6,8},{2,7},{4,5}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => {{1,2,3,6,7,8},{4,5}} => {{1,2,3,6,7,8},{4,5}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => {{1,2,6,7},{3,8},{4,5}} => {{1,6},{2,3,7,8},{4,5}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => {{1,6},{2,7},{3,8},{4,5}} => {{1,6},{2,7},{3,8},{4,5}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => {{1,2,6,7},{3,4,5,8}} => {{1,4,5,6},{2,3,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => {{1,6},{2,7},{3,4,5,8}} => {{1,4,5,6},{2,7},{3,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => {{1,3,6,8},{2,4,5,7}} => {{1,3,6,8},{2,4,5,7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => {{1,6},{2,3,4,5,7,8}} => {{1,2,4,5,6,7},{3,8}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => {{1,3,6,8},{2,7},{4},{5}} => {{1,3,6,8},{2,7},{4},{5}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3,6,7,8},{4},{5}}
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => {{1,6},{2,7},{3,8},{4},{5}} => {{1,6},{2,7},{3,8},{4},{5}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => {{1,3,5,6,8},{2,7},{4}} => {{1,3,4,6,8},{2,7},{5}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => {{1,2,6,7},{3,5,8},{4}} => {{1,4,6},{2,3,7,8},{5}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => {{1,3,6,8},{2,5,7},{4}} => {{1,3,6,8},{2,4,7},{5}}
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => {{1,6},{2,3,5,7,8},{4}} => {{1,2,4,6,7},{3,8},{5}}
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => {{1,3,4,5,6,8},{2,7}} => {{1,3,4,5,6,8},{2,7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => {{1,6},{2,7},{3,4,5,8}} => {{1,4,5,6},{2,7},{3,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => {{1,3,4,6,8},{2,5,7}} => {{1,3,5,6,8},{2,4,7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => {{1,6},{2,3,4,5,7,8}} => {{1,2,4,5,6,7},{3,8}}
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => {{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => {{1,3,4,5,6,8},{2,7}} => {{1,3,4,5,6,8},{2,7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => {{1,2,6,7},{3,4,5,8}} => {{1,4,5,6},{2,3,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => {{1,4,6,8},{2,7},{3,5}} => {{1,3,5,8},{2,7},{4,6}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => {{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => {{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => {{1,2,6,7},{3,5},{4,8}} => {{1,5},{2,3,7,8},{4,6}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => {{1,6},{2,7},{3,5},{4,8}} => {{1,5},{2,7},{3,8},{4,6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => {{1,2,3,5,6,7},{4,8}} => {{1,5},{2,3,4,6,7,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => {{1,6},{2,3,5,7},{4,8}} => {{1,5},{2,4,6,7},{3,8}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => {{1,2,3,5,6,7},{4,8}} => {{1,5},{2,3,4,6,7,8}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => {{1,3,5,6,8},{2,7},{4}} => {{1,3,4,6,8},{2,7},{5}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => {{1,6},{2,7},{3,5,8},{4}} => {{1,4,6},{2,7},{3,8},{5}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => {{1,6,8},{2,7},{3,5},{4}} => {{1,3,8},{2,7},{4,6},{5}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => {{1,2,6,7,8},{3,5},{4}} => {{1,2,3,7,8},{4,6},{5}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => {{1,2,6,7,8},{3,5},{4}} => {{1,2,3,7,8},{4,6},{5}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => {{1,2,6,7},{3,5},{4},{8}} => {{1},{2,3,7,8},{4,6},{5}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => {{1,6},{2,7},{3,5},{4},{8}} => {{1},{2,7},{3,8},{4,6},{5}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => {{1,2,3,5,6,7},{4},{8}} => {{1},{2,3,4,6,7,8},{5}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => {{1,2,6,7,8},{3,4,5}} => {{1,2,3,7,8},{4,5,6}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => {{1,2,6,7},{3,4,5},{8}} => {{1},{2,3,7,8},{4,5,6}}
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => {{1,3,5,6},{2,4,7},{8}} => {{1},{2,5,7},{3,4,6,8}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => {{1,3,4,5,6,8},{2,7}} => {{1,3,4,5,6,8},{2,7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => {{1,6},{2,7},{3,4,5,8}} => {{1,4,5,6},{2,7},{3,8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => {{1,6,8},{2,7},{3,4,5}} => {{1,3,8},{2,7},{4,5,6}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => {{1,2,6,7,8},{3,4,5}} => {{1,2,3,7,8},{4,5,6}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => {{1,2,6,7},{3,4,5},{8}} => {{1},{2,3,7,8},{4,5,6}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => {{1,6},{2,3,4,5,7},{8}} => {{1},{2,4,5,6,7},{3,8}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => {{1,6},{2,5,7},{3,4},{8}} => {{1},{2,4,7},{3,8},{5,6}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => {{1,6},{2,3,4,5,7},{8}} => {{1},{2,4,5,6,7},{3,8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => {{1,6,8},{2,7},{3},{4},{5}} => {{1,3,8},{2,7},{4},{5},{6}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => {{1,2,6,7,8},{3},{4},{5}} => {{1,2,3,7,8},{4},{5},{6}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => {{1,2,6,7,8},{3},{4},{5}} => {{1,2,3,7,8},{4},{5},{6}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => {{1,2,5,6,7},{3},{4},{8}} => {{1},{2,3,4,7,8},{5},{6}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => {{1,6},{2,3,4,5,7},{8}} => {{1},{2,4,5,6,7},{3,8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => {{1,3,6,7},{2,4,5,8}} => {{1,4,5,7},{2,3,6,8}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => {{1,6},{2,3,4,5,7,8}} => {{1,2,4,5,6,7},{3,8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => {{1,4,6,8},{2,3,5,7}} => {{1,3,5,8},{2,4,6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => {{1,2,3,5,6,7},{4,8}} => {{1,5},{2,3,4,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => {{1,6},{2,3,5,7},{4,8}} => {{1,5},{2,4,6,7},{3,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => {{1,3,6,7},{2,5},{4,8}} => {{1,5},{2,3,6,8},{4,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => {{1,6},{2,5},{3,7},{4,8}} => {{1,5},{2,6},{3,8},{4,7}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => {{1,2,5,6},{3,7},{4,8}} => {{1,5},{2,6},{3,4,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => {{1,3,6,7},{2,5,8},{4}} => {{1,4,7},{2,3,6,8},{5}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => {{1,2,5,6,8},{3,7},{4}} => {{1,3,4,7,8},{2,6},{5}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => {{1,6},{2,3,5,7,8},{4}} => {{1,2,4,6,7},{3,8},{5}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => {{1,2,3,5,6,7},{4},{8}} => {{1},{2,3,4,6,7,8},{5}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => {{1,3,6,7,8},{2,5},{4}} => {{1,2,3,6,8},{4,7},{5}}
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => {{1,6},{2,5},{3,7},{4},{8}} => {{1},{2,6},{3,8},{4,7},{5}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => {{1,3,4,6,7},{2,5},{8}} => {{1},{2,3,5,6,8},{4,7}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => {{1,3,4,6,7},{2,5},{8}} => {{1},{2,3,5,6,8},{4,7}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => {{1,3,4,6,7},{2,5,8}} => {{1,4,7},{2,3,5,6,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => {{1,2,5,6,8},{3,4,7}} => {{1,3,4,7,8},{2,5,6}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => {{1,6},{2,3,4,5,7,8}} => {{1,2,4,5,6,7},{3,8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => {{1,6,8},{2,3,4,5,7}} => {{1,3,8},{2,4,5,6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => {{1,6,8},{2,5,7},{3,4}} => {{1,3,8},{2,4,7},{5,6}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => {{1,2,5,6,7},{3,4},{8}} => {{1},{2,3,4,7,8},{5,6}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => {{1,6},{2,5,7},{3,4},{8}} => {{1},{2,4,7},{3,8},{5,6}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => {{1,6,7,8},{2,5},{3,4}} => {{1,2,3,8},{4,7},{5,6}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => {{1,6,7},{2,5},{3,4},{8}} => {{1},{2,3,8},{4,7},{5,6}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => {{1,6},{2,5},{3,4},{7},{8}} => {{1},{2},{3,8},{4,7},{5,6}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => {{1,2,5,6},{3,4},{7},{8}} => {{1},{2},{3,4,7,8},{5,6}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => {{1,6,7,8},{2,3,4,5}} => {{1,2,3,8},{4,5,6,7}}
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => {{1,3,4,6},{2,5},{7},{8}} => {{1},{2},{3,5,6,8},{4,7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => {{1,6,8},{2,5,7},{3},{4}} => {{1,3,8},{2,4,7},{5},{6}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => {{1,2,5,6,7},{3},{4},{8}} => {{1},{2,3,4,7,8},{5},{6}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => {{1,6},{2,5},{3},{4},{7},{8}} => {{1},{2},{3,8},{4,7},{5},{6}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => {{1,6,7},{2,4,5},{3},{8}} => {{1},{2,3,8},{4,5,7},{6}}
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => {{1,2,4,5,6},{3},{7},{8}} => {{1},{2},{3,4,5,7,8},{6}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => {{1,6,7,8},{2,3,4,5}} => {{1,2,3,8},{4,5,6,7}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => {{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => {{1,2,4,6,7},{3,5,8}} => {{1,4,6},{2,3,5,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => {{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => {{1,2,4,6,7},{3,5},{8}} => {{1},{2,3,5,7,8},{4,6}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => {{1,6},{2,4,7},{3,5},{8}} => {{1},{2,5,7},{3,8},{4,6}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => {{1,6},{2,3,4,5,7},{8}} => {{1},{2,4,5,6,7},{3,8}}
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => {{1,6,7,8},{2,4},{3,5}} => {{1,2,3,8},{4,6},{5,7}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => {{1,3,5,6},{2,4},{7},{8}} => {{1},{2},{3,4,6,8},{5,7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => {{1,6,8},{2,4,5,7},{3}} => {{1,3,8},{2,4,5,7},{6}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => {{1,2,4,5,6,7},{3},{8}} => {{1},{2,3,4,5,7,8},{6}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => {{1,6},{2,4,5,7},{3},{8}} => {{1},{2,4,5,7},{3,8},{6}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => {{1,6,7},{2,4,5},{3},{8}} => {{1},{2,3,8},{4,5,7},{6}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => {{1,2,4,5,6},{3},{7},{8}} => {{1},{2},{3,4,5,7,8},{6}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => {{1,5,6},{2,4},{3},{7},{8}} => {{1},{2},{3,4,8},{5,7},{6}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => {{1,2,4,5,6},{3},{7},{8}} => {{1},{2},{3,4,5,7,8},{6}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => {{1,3,5,6},{2,4},{7},{8}} => {{1},{2},{3,4,6,8},{5,7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => {{1,6,8},{2,3,4,5,7}} => {{1,3,8},{2,4,5,6,7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => {{1,6},{2,3,4,5,7},{8}} => {{1},{2,4,5,6,7},{3,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => {{1,6,7,8},{2,3,4,5}} => {{1,2,3,8},{4,5,6,7}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => {{1,6},{2,3,4,5},{7},{8}} => {{1},{2},{3,8},{4,5,6,7}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => {{1,6,7,8},{2,3,4},{5}} => {{1,2,3,8},{4},{5,6,7}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => {{1,6,7},{2,3,4},{5},{8}} => {{1},{2,3,8},{4},{5,6,7}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => {{1,4,5,6},{2,3},{7},{8}} => {{1},{2},{3,4,5,8},{6,7}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => {{1,6,7,8},{2},{3},{4},{5}} => {{1,2,3,8},{4},{5},{6},{7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => {{1,6,7},{2},{3},{4},{5},{8}} => {{1},{2,3,8},{4},{5},{6},{7}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => {{1,6},{2},{3},{4},{5},{7},{8}} => {{1},{2},{3,8},{4},{5},{6},{7}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => {{1,5,6},{2},{3},{4},{7},{8}} => {{1},{2},{3,4,8},{5},{6},{7}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => {{1,4,5,6},{2},{3},{7},{8}} => {{1},{2},{3,4,5,8},{6},{7}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => {{1,3,4,5,6},{2},{7},{8}} => {{1},{2},{3,4,5,6,8},{7}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => {{1,4,5,8},{2,3,6,7}} => {{1,4,5,8},{2,3,6,7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => {{1,4,5,8},{2,6},{3,7}} => {{1,4,5,8},{2,6},{3,7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => {{1,3,5,7},{2,4,6,8}} => {{1,3,5,7},{2,4,6,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => {{1,3,5,7},{2,6},{4,8}} => {{1,5},{2,4,6,8},{3,7}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => {{1,2,3,5,6,7},{4,8}} => {{1,5},{2,3,4,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => {{1,2,3,5,6,7},{4,8}} => {{1,5},{2,3,4,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => {{1,2,5,6},{3,7},{4,8}} => {{1,5},{2,6},{3,4,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => {{1,5},{2,6},{3,7},{4,8}} => {{1,5},{2,6},{3,7},{4,8}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => {{1,5,8},{2,3,6,7},{4}} => {{1,4,8},{2,3,6,7},{5}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => {{1,3,5,7,8},{2,6},{4}} => {{1,2,4,6,8},{3,7},{5}}
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => {{1,3,5,7},{2,6,8},{4}} => {{1,3,7},{2,4,6,8},{5}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => {{1,3,5,7,8},{2,6},{4}} => {{1,2,4,6,8},{3,7},{5}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => {{1,3,5,7},{2,6},{4},{8}} => {{1},{2,4,6,8},{3,7},{5}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => {{1,5},{2,6},{3,7},{4},{8}} => {{1},{2,6},{3,7},{4,8},{5}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => {{1,3,4,5,7},{2,6,8}} => {{1,3,7},{2,4,5,6,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => {{1,5},{2,6},{3,4,7},{8}} => {{1},{2,5,6},{3,7},{4,8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => {{1,3,5,7,8},{2,4,6}} => {{1,2,4,6,8},{3,5,7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => {{1,3,5,7},{2,4,6},{8}} => {{1},{2,4,6,8},{3,5,7}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => {{1,5},{2,3,4,6,7},{8}} => {{1},{2,3,5,6,7},{4,8}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => {{1,5,8},{2,3,4,6,7}} => {{1,4,8},{2,3,5,6,7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => {{1,5,8},{2,6},{3,4,7}} => {{1,4,8},{2,5,6},{3,7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => {{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => {{1,3,4,5,7},{2,6,8}} => {{1,3,7},{2,4,5,6,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => {{1,5},{2,6},{3,4,7},{8}} => {{1},{2,5,6},{3,7},{4,8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => {{1,5,7},{2,6,8},{3,4}} => {{1,3,7},{2,4,8},{5,6}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => {{1,5,7,8},{2,6},{3,4}} => {{1,2,4,8},{3,7},{5,6}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => {{1,5,7},{2,6},{3,4},{8}} => {{1},{2,4,8},{3,7},{5,6}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => {{1,2,5,6,7},{3,4},{8}} => {{1},{2,3,4,7,8},{5,6}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => {{1,2,5,6},{3,4},{7},{8}} => {{1},{2},{3,4,7,8},{5,6}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => {{1,5},{2,6},{3,4},{7},{8}} => {{1},{2},{3,7},{4,8},{5,6}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => {{1,5},{2,3,4,6},{7},{8}} => {{1},{2},{3,5,6,7},{4,8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => {{1,5,7},{2,6,8},{3},{4}} => {{1,3,7},{2,4,8},{5},{6}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => {{1,5,7,8},{2,6},{3},{4}} => {{1,2,4,8},{3,7},{5},{6}}
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => {{1,2,5,6,7},{3},{4},{8}} => {{1},{2,3,4,7,8},{5},{6}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => {{1,5},{2,6},{3},{4},{7},{8}} => {{1},{2},{3,7},{4,8},{5},{6}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => {{1,2,4,5,6},{3},{7},{8}} => {{1},{2},{3,4,5,7,8},{6}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => {{1,5},{2,4,6},{3},{7},{8}} => {{1},{2},{3,5,7},{4,8},{6}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => {{1,3,5},{2,4,6},{7},{8}} => {{1},{2},{3,5,7},{4,6,8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => {{1,5,8},{2,4,7},{3,6}} => {{1,4,8},{2,5,7},{3,6}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => {{1,5,8},{2,3,4,6,7}} => {{1,4,8},{2,3,5,6,7}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => {{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => {{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => {{1,3,5,6},{2,4,7},{8}} => {{1},{2,5,7},{3,4,6,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => {{1,2,4,5,7},{3,6},{8}} => {{1},{2,4,5,7,8},{3,6}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => {{1,5},{2,3,4,6,7},{8}} => {{1},{2,3,5,6,7},{4,8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => {{1,5,7},{2,3,4,6,8}} => {{1,3,5,6,7},{2,4,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => {{1,5,7,8},{2,3,4,6}} => {{1,2,4,8},{3,5,6,7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => {{1,5,7},{2,3,4,6},{8}} => {{1},{2,4,8},{3,5,6,7}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => {{1,5},{2,3,4,6},{7},{8}} => {{1},{2},{3,5,6,7},{4,8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => {{1,3,5,6,7},{2,4},{8}} => {{1},{2,3,4,6,8},{5,7}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => {{1,3,5,6},{2,4},{7},{8}} => {{1},{2},{3,4,6,8},{5,7}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => {{1,2,4,5},{3,6},{7},{8}} => {{1},{2},{3,6},{4,5,7,8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => {{1,5,7},{2,4,6,8},{3}} => {{1,3,5,7},{2,4,8},{6}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => {{1,5,7,8},{2,4,6},{3}} => {{1,2,4,8},{3,5,7},{6}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => {{1,5,7},{2,4,6},{3},{8}} => {{1},{2,4,8},{3,5,7},{6}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => {{1,2,4,5,6,7},{3},{8}} => {{1},{2,3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => {{1,2,4,5,6,7},{3},{8}} => {{1},{2,3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => {{1,2,4,5,6},{3},{7},{8}} => {{1},{2},{3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => {{1,5},{2,4,6},{3},{7},{8}} => {{1},{2},{3,5,7},{4,8},{6}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => {{1,5,6,7,8},{2,4},{3}} => {{1,2,3,4,8},{5,7},{6}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => {{1,5,6,7},{2,4},{3},{8}} => {{1},{2,3,4,8},{5,7},{6}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => {{1,5,6},{2,4},{3},{7},{8}} => {{1},{2},{3,4,8},{5,7},{6}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => {{1,5},{2,4},{3},{6},{7},{8}} => {{1},{2},{3},{4,8},{5,7},{6}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => {{1,2,4,5},{3},{6},{7},{8}} => {{1},{2},{3},{4,5,7,8},{6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => {{1,5,6,7,8},{2,3,4}} => {{1,2,3,4,8},{5,6,7}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => {{1,5,6},{2,3,4},{7},{8}} => {{1},{2},{3,4,8},{5,6,7}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => {{1,5},{2,3,4},{6},{7},{8}} => {{1},{2},{3},{4,8},{5,6,7}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => {{1,3,5},{2,4},{6},{7},{8}} => {{1},{2},{3},{4,6,8},{5,7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => {{1,5,7},{2,3,4,6,8}} => {{1,3,5,6,7},{2,4,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => {{1,5,7},{2,3,4,6},{8}} => {{1},{2,4,8},{3,5,6,7}}
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => {{1,5,6,7,8},{2,3,4}} => {{1,2,3,4,8},{5,6,7}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => {{1,5},{2,3,4},{6},{7},{8}} => {{1},{2},{3},{4,8},{5,6,7}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => {{1,5},{2,3},{4},{6},{7},{8}} => {{1},{2},{3},{4,8},{5},{6,7}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => {{1,4,5},{2,3},{6},{7},{8}} => {{1},{2},{3},{4,5,8},{6,7}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => {{1,5,6,7,8},{2},{3},{4}} => {{1,2,3,4,8},{5},{6},{7}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => {{1,5,6,7},{2},{3},{4},{8}} => {{1},{2,3,4,8},{5},{6},{7}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => {{1,5},{2},{3},{4},{6},{7},{8}} => {{1},{2},{3},{4,8},{5},{6},{7}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => {{1,4,5},{2},{3},{6},{7},{8}} => {{1},{2},{3},{4,5,8},{6},{7}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => {{1,3,4,5},{2},{6},{7},{8}} => {{1},{2},{3},{4,5,6,8},{7}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => {{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => {{1,4,7},{2,5,8},{3,6}} => {{1,4,7},{2,5,8},{3,6}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => {{1,4,7},{2,3,5,6,8}} => {{1,3,4,6,7},{2,5,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => {{1,4,7},{2,3,5,6,8}} => {{1,3,4,6,7},{2,5,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => {{1,4,7,8},{2,3,5,6}} => {{1,2,5,8},{3,4,6,7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => {{1,4,7},{2,3,5,6},{8}} => {{1},{2,5,8},{3,4,6,7}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => {{1,4,7,8},{2,5},{3,6}} => {{1,2,5,8},{3,6},{4,7}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => {{1,4,7},{2,5},{3,6},{8}} => {{1},{2,5,8},{3,6},{4,7}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => {{1,3,4,6,7},{2,5},{8}} => {{1},{2,3,5,6,8},{4,7}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => {{1,3,4,6,8},{2,5,7}} => {{1,3,5,6,8},{2,4,7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => {{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => {{1,3,4,6},{2,5},{7},{8}} => {{1},{2},{3,5,6,8},{4,7}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => {{1,4},{2,5},{3,6},{7},{8}} => {{1},{2},{3,6},{4,7},{5,8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => {{1,4,6},{2,5,7},{3},{8}} => {{1},{2,4,7},{3,5,8},{6}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => {{1,4,6,7,8},{2,5},{3}} => {{1,2,3,5,8},{4,7},{6}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => {{1,4,6,7},{2,5},{3},{8}} => {{1},{2,3,5,8},{4,7},{6}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => {{1,2,4,5,6,7},{3},{8}} => {{1},{2,3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => {{1,2,4,5,6},{3},{7},{8}} => {{1},{2},{3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => {{1,2,4,5},{3},{6},{7},{8}} => {{1},{2},{3},{4,5,7,8},{6}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => {{1,4,6,8},{2,3,5,7}} => {{1,3,5,8},{2,4,6,7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => {{1,4,6,7,8},{2,3,5}} => {{1,2,3,5,8},{4,6,7}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => {{1,4,5,6,7,8},{2,3}} => {{1,2,3,4,5,8},{6,7}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => {{1,4,5,6,7},{2,3},{8}} => {{1},{2,3,4,5,8},{6,7}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => {{1,4,5},{2,3},{6},{7},{8}} => {{1},{2},{3},{4,5,8},{6,7}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => {{1,4},{2,3},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,8},{6,7}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => {{1,4,5,6,7,8},{2},{3}} => {{1,2,3,4,5,8},{6},{7}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => {{1,4,5,6,7},{2},{3},{8}} => {{1},{2,3,4,5,8},{6},{7}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => {{1,4,5,6},{2},{3},{7},{8}} => {{1},{2},{3,4,5,8},{6},{7}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => {{1,4,5},{2},{3},{6},{7},{8}} => {{1},{2},{3},{4,5,8},{6},{7}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => {{1,4},{2},{3},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,8},{6},{7}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => {{1,3,4},{2},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,8},{7}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => {{1,3,5,7},{2,4,6,8}} => {{1,3,5,7},{2,4,6,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => {{1,3,5,7,8},{2,4,6}} => {{1,2,4,6,8},{3,5,7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => {{1,3,5,7},{2,4,6},{8}} => {{1},{2,4,6,8},{3,5,7}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => {{1,3,5,6,7,8},{2,4}} => {{1,2,3,4,6,8},{5,7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => {{1,3,5,6,7},{2,4},{8}} => {{1},{2,3,4,6,8},{5,7}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => {{1,3,5,6},{2,4},{7},{8}} => {{1},{2},{3,4,6,8},{5,7}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => {{1,3,5},{2,4},{6},{7},{8}} => {{1},{2},{3},{4,6,8},{5,7}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => {{1,3},{2,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,7},{6,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => {{1,3,4,5,6,7,8},{2}} => {{1,2,3,4,5,6,8},{7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => {{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,8},{7}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => {{1,3,4,5},{2},{6},{7},{8}} => {{1},{2},{3},{4,5,6,8},{7}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => {{1,3,4},{2},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,8},{7}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,8},{7}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => {{1,2,3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => {{1,2,3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,7,8}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => {{1,3,4,5,6,7,8,9},{2}} => {{1,2,3,4,5,6,7,9},{8}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => {{1,3,4,5,6,7,8,9},{2}} => {{1,2,3,4,5,6,7,9},{8}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => {{1,3,4,5,6,7,8,9,10},{2}} => {{1,2,3,4,5,6,7,8,10},{9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => {{1,4,5,6,7,8,9},{2},{3}} => {{1,2,3,4,5,6,9},{7},{8}}
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => {{1,4,5,6,7,8,9},{2},{3}} => {{1,2,3,4,5,6,9},{7},{8}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => {{1,3,4,5,6,7,8,9,10},{2}} => {{1,2,3,4,5,6,7,8,10},{9}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}} => {{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,1,3,4,5,6,7,8,9,10] => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1,2,3,4,5,6,7,8,9,11},{10}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,1,4,5,6,7,8,9] => {{1,4,5,6,7,8,9,10},{2},{3}} => {{1,2,3,4,5,6,7,10},{8},{9}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [9,4,1,2,3,5,6,7,8] => {{1,3,5,6,7,8,9},{2,4}} => {{1,2,3,4,5,7,9},{6,8}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,1,5,6,7,8] => {{1,5,6,7,8,9},{2},{3},{4}} => {{1,2,3,4,5,9},{6},{7},{8}}
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => {{1,4,5,6,7,8,9},{2,3}} => {{1,2,3,4,5,6,9},{7,8}}
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,10,1] => {{1,4,5,6,7,8,9,10},{2},{3}} => {{1,2,3,4,5,6,7,10},{8},{9}}
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1,2,3,4,5,6,7,8,9,11},{10}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [12,2,1,3,4,5,6,7,8,9,10,11] => {{1,3,4,5,6,7,8,9,10,11,12},{2}} => {{1,2,3,4,5,6,7,8,9,10,12},{11}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [11,3,1,2,4,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [10,4,1,2,3,5,6,7,8,9] => {{1,3,5,6,7,8,9,10},{2,4}} => {{1,2,3,4,5,6,8,10},{7,9}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,1,5,6,7,8,9] => {{1,5,6,7,8,9,10},{2},{3},{4}} => {{1,2,3,4,5,6,10},{7},{8},{9}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,4,1,2,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,1,6,7,8] => {{1,6,7,8,9},{2},{3},{4},{5}} => {{1,2,3,4,9},{5},{6},{7},{8}}
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,10,1] => {{1,4,5,6,7,8,9,10},{2,3}} => {{1,2,3,4,5,6,7,10},{8,9}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,1,6,7,8,9] => {{1,6,7,8,9,10},{2},{3},{4},{5}} => {{1,2,3,4,5,10},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [9,6,1,2,3,4,5,7,8] => {{1,3,5,7,8,9},{2,4,6}} => {{1,2,3,5,7,9},{4,6,8}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,1,7,8] => {{1,7,8,9},{2},{3},{4},{5},{6}} => {{1,2,3,9},{4},{5},{6},{7},{8}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [6,2,3,4,5,7,8,9,10,1] => {{1,6,7,8,9,10},{2},{3},{4},{5}} => {{1,2,3,4,5,10},{6},{7},{8},{9}}
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,3,6,7,8,9,1] => {{1,5,6,7,8,9},{2,3,4}} => {{1,2,3,4,5,9},{6,7,8}}
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,2,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [10,6,1,2,3,4,5,7,8,9] => {{1,3,5,7,8,9,10},{2,4,6}} => {{1,2,3,4,6,8,10},{5,7,9}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,1,7,8,9] => {{1,7,8,9,10},{2},{3},{4},{5},{6}} => {{1,2,3,4,10},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,1,8] => {{1,8,9},{2},{3},{4},{5},{6},{7}} => {{1,2,9},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => {{1,8,9},{2},{3},{4},{5},{6},{7}} => {{1,2,9},{3},{4},{5},{6},{7},{8}}
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,7,8,9,1] => {{1,5,6,7,8,9},{2,4},{3}} => {{1,2,3,4,5,9},{6,8},{7}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [10,7,1,2,3,4,5,6,8,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,1,8,9] => {{1,8,9,10},{2},{3},{4},{5},{6},{7}} => {{1,2,3,10},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => {{1,3,5,7,9},{2,4,6,8}} => {{1,3,5,7,9},{2,4,6,8}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [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}}
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,6,7,8,9,10,1] => {{1,5,6,7,8,9,10},{2,4},{3}} => {{1,2,3,4,5,6,10},{7,9},{8}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => {{1,3,5,7,9},{2,4,6,8}} => {{1,3,5,7,9},{2,4,6,8}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,1,9] => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => {{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,4,5,6,7,8,1] => {{1,9},{2,3},{4},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => {{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [5,3,4,6,7,8,9,1,2] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [4,5,3,6,7,8,9,1,2] => {{1,4,6,8},{2,5,7,9},{3}} => {{1,3,5,8},{2,4,6,9},{7}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,10,1] => {{1,3,5,7,9,10},{2,4,6,8}} => {{1,2,4,6,8,10},{3,5,7,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [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}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [9,3,4,2,5,6,7,8,1] => {{1,9},{2,3,4},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [6,5,4,2,3,7,8,9,1] => {{1,6,7,8,9},{2,3,4,5}} => {{1,2,3,4,9},{5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,6,7,2,3,4,8,9,1] => {{1,3,5,7,8,9},{2,4,6}} => {{1,2,3,5,7,9},{4,6,8}}
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,3,5,6,7,8,9,10,1,2] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => {{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] => [8,7,6,5,4,3,2,1,9] => {{1,8},{2,7},{3,6},{4,5},{9}} => {{1},{2,9},{3,8},{4,7},{5,6}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => {{1,2,7,8},{3,6},{4,5},{9}} => {{1},{2,3,8,9},{4,7},{5,6}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8,6,5,7,4,3,2,1,9] => {{1,8},{2,3,4,5,6,7},{9}} => {{1},{2,9},{3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7,6,5,8,4,3,2,1,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [6,5,7,8,4,3,2,1,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => {{1,8},{2,7},{3,6},{4},{5},{9}} => {{1},{2,9},{3,8},{4,7},{5},{6}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => {{1,8},{2,7},{3,5,6},{4},{9}} => {{1},{2,9},{3,8},{4,5,7},{6}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,1,9] => {{1,6,7,8},{2,5},{3,4},{9}} => {{1},{2,3,4,9},{5,8},{6,7}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,1,9] => {{1,8},{2},{3},{4},{5},{6},{7},{9}} => {{1},{2,9},{3},{4},{5},{6},{7},{8}}
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1,9] => {{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,9},{8}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => {{1,2,7,8},{3,6},{4,5},{9}} => {{1},{2,3,8,9},{4,7},{5,6}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => {{1,7},{2,8},{3,5},{4,6},{9}} => {{1},{2,8},{3,9},{4,6},{5,7}}
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => {{1,3,5,7},{2,4,6,8},{9}} => {{1},{2,4,6,8},{3,5,7,9}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,4,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => {{1,7},{2,6},{3,5},{4},{8},{9}} => {{1},{2},{3,9},{4,8},{5,7},{6}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8,7,6,3,4,2,1,5,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,3,1,4,9] => {{1,2,4,5,7,8},{3,6},{9}} => {{1},{2,3,5,6,8,9},{4,7}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,2,3,4,5,6,1,8,9] => {{1,7},{2},{3},{4},{5},{6},{8},{9}} => {{1},{2},{3,9},{4},{5},{6},{7},{8}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,6,5,3,2,1,4,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => {{1,6},{2,5},{3,4},{7},{8},{9}} => {{1},{2},{3},{4,9},{5,8},{6,7}}
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,2,6,1,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,1,7,8,9] => {{1,6},{2},{3},{4},{5},{7},{8},{9}} => {{1},{2},{3},{4,9},{5},{6},{7},{8}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => {{1,5},{2,6},{3,7},{4,8},{9}} => {{1},{2,6},{3,7},{4,8},{5,9}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [8,7,5,3,1,2,4,6,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => {{1,5},{2,6},{3},{4},{7},{8},{9}} => {{1},{2},{3},{4,8},{5,9},{6},{7}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => {{1,5},{2,4},{3},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,9},{6,8},{7}}
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,3,4,1,6,7,8,9] => {{1,5},{2},{3},{4},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,9},{6},{7},{8}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => {{1,4},{2,5},{3,6},{7},{8},{9}} => {{1},{2},{3},{4,7},{5,8},{6,9}}
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => {{1,4},{2,3},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,9},{7,8}}
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => {{1,4},{2},{3},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,9},{7},{8}}
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9] => {{1,3,4},{2},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,9},{8}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => {{1,3,5,7},{2,4,6,8},{9}} => {{1},{2,4,6,8},{3,5,7,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,3,1,2,4,5,6,7,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1,2,4,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => {{1,3},{2,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,8},{7,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => {{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,9},{8}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,9},{8}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [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}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => {{1,2,3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => {{1,9},{2,8},{3,7},{4,6},{5}} => {{1,9},{2,8},{3,7},{4,6},{5}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => {{1,2,8,9},{3,7},{4,6},{5}} => {{1,2,8,9},{3,7},{4,6},{5}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => {{1,2,3,7,8,9},{4,6},{5}} => {{1,2,3,7,8,9},{4,6},{5}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4,6,7,8,9},{5}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => {{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] => [8,7,6,5,4,9,3,2,1] => {{1,2,3,6,7,8,9},{4,5}} => {{1,2,3,4,7,8,9},{5,6}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => {{1,2,7,8,9},{3,6},{4,5}} => {{1,2,3,8,9},{4,7},{5,6}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => {{1,8,9},{2,7},{3,6},{4,5}} => {{1,2,9},{3,8},{4,7},{5,6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => {{1,10},{2,9},{3,8},{4,7},{5,6}} => {{1,10},{2,9},{3,8},{4,7},{5,6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => {{1,2,9,10},{3,8},{4,7},{5,6}} => {{1,2,9,10},{3,8},{4,7},{5,6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => {{1,3,7,9},{2,8},{4,6},{5}} => {{1,3,7,9},{2,8},{4,6},{5}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => {{1,2,3,8,9,10},{4,7},{5,6}} => {{1,2,3,8,9,10},{4,7},{5,6}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => {{1,2,4,6,8,9},{3,7},{5}} => {{1,2,4,6,8,9},{3,7},{5}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => {{1,2,3,4,7,8,9,10},{5,6}} => {{1,2,3,4,7,8,9,10},{5,6}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => {{1,2,3,5,7,8,9},{4,6}} => {{1,2,3,5,7,8,9},{4,6}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => {{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] => [8,7,6,4,5,9,3,2,1] => {{1,2,3,6,7,8,9},{4},{5}} => {{1,2,3,4,7,8,9},{5},{6}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4,5,7,8,9,10},{6}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => {{1,2,7,8,9},{3,4,5,6}} => {{1,2,3,8,9},{4,5,6,7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => {{1,2,3,7,8,9,10},{4,6},{5}} => {{1,2,3,4,8,9,10},{5,7},{6}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => {{1,8,9},{2,3,6,7},{4,5}} => {{1,2,9},{3,4,7,8},{5,6}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => {{1,2,8,9,10},{3,7},{4,6},{5}} => {{1,2,3,9,10},{4,8},{5,7},{6}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => {{1,9,10},{2,8},{3,7},{4,6},{5}} => {{1,2,10},{3,9},{4,8},{5,7},{6}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => {{1,9},{2,8},{3,7},{4,6},{5},{10}} => {{1},{2,10},{3,9},{4,8},{5,7},{6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => {{1,3,8,10},{2,9},{4,7},{5,6}} => {{1,3,8,10},{2,9},{4,7},{5,6}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [7,6,8,9,5,4,3,2,1] => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4,6,7,8,9},{5}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => {{1,4,6,9},{2,3,7,8},{5}} => {{1,4,6,9},{2,3,7,8},{5}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => {{1,10},{2,9},{3,8},{4,7},{5,6},{11}} => {{1},{2,11},{3,10},{4,9},{5,8},{6,7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,7,9,10,6,5,4,3,2,1] => {{1,2,3,4,7,8,9,10},{5,6}} => {{1,2,3,4,7,8,9,10},{5,6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => {{1,4,7,10},{2,3,8,9},{5,6}} => {{1,4,7,10},{2,3,8,9},{5,6}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => {{1,5,9},{2,4,6,8},{3,7}} => {{1,5,9},{2,4,6,8},{3,7}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => {{1,5,6,10},{2,4,7,9},{3,8}} => {{1,5,6,10},{2,4,7,9},{3,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,1,5,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,9,1] => {{1,7,8,9},{2,6},{3,5},{4}} => {{1,2,3,9},{4,8},{5,7},{6}}
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => {{1,3,4,6,7,9},{2,5,8}} => {{1,3,4,6,7,9},{2,5,8}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => {{1,2,5,6,9,10},{3,4,7,8}} => {{1,2,5,6,9,10},{3,4,7,8}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,10,1] => {{1,8,9,10},{2,7},{3,6},{4,5}} => {{1,2,3,10},{4,9},{5,8},{6,7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,9,6,7,5,4,3,2,1] => {{1,2,8,9},{3,4,6,7},{5}} => {{1,2,8,9},{3,4,6,7},{5}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,2,1] => {{1,9},{2,3,4,5,6,7,8}} => {{1,9},{2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,3,1] => {{1,2,3,7,8,9},{4,6},{5}} => {{1,2,3,7,8,9},{4,6},{5}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,3,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,5,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,3,4,5,6,7,1] => {{1,9},{2,3,4,5,6,7,8}} => {{1,9},{2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => {{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] => [9,8,7,6,5,4,3,1,2] => {{1,2,8,9},{3,7},{4,6},{5}} => {{1,2,8,9},{3,7},{4,6},{5}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,1,2] => {{1,2,3,7,8,9},{4,6},{5}} => {{1,2,3,7,8,9},{4,6},{5}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,3,1,2] => {{1,2,3,7,8,9},{4},{5},{6}} => {{1,2,3,7,8,9},{4},{5},{6}}
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,1,2] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => {{1,2,8,9},{3,4,6,7},{5}} => {{1,2,8,9},{3,4,6,7},{5}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => {{1,2,8,9},{3,4,5,6,7}} => {{1,2,8,9},{3,4,5,6,7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [9,8,3,4,5,6,7,1,2] => {{1,2,8,9},{3},{4},{5},{6},{7}} => {{1,2,8,9},{3},{4},{5},{6},{7}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [8,9,3,4,5,6,7,1,2] => {{1,8},{2,9},{3},{4},{5},{6},{7}} => {{1,8},{2,9},{3},{4},{5},{6},{7}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => {{1,3,7,9},{2,8},{4,6},{5}} => {{1,3,7,9},{2,8},{4,6},{5}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => {{1,3,7,9},{2,8},{4,5,6}} => {{1,3,7,9},{2,8},{4,5,6}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => {{1,3,7,9},{2,8},{4},{5},{6}} => {{1,3,7,9},{2,8},{4},{5},{6}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => {{1,7},{2,8},{3,9},{4},{5},{6}} => {{1,7},{2,8},{3,9},{4},{5},{6}}
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => {{1,4,7},{2,5,8},{3,6,9}} => {{1,4,7},{2,5,8},{3,6,9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => {{1,4,6,9},{2,3,7,8},{5}} => {{1,4,6,9},{2,3,7,8},{5}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => {{1,4,5,6,9},{2,3,7,8}} => {{1,4,5,6,9},{2,3,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => {{1,4,5,6,9},{2,7},{3,8}} => {{1,4,5,6,9},{2,7},{3,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => {{1,4,6,9},{2,3,5,7,8}} => {{1,4,6,9},{2,3,5,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => {{1,5,9},{2,4,6,8},{3,7}} => {{1,5,9},{2,4,6,8},{3,7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [7,8,9,6,1,2,3,4,5] => {{1,3,5,7,9},{2,4,6,8}} => {{1,3,5,7,9},{2,4,6,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => {{1,5,9},{2,3,4,6,7,8}} => {{1,5,9},{2,3,4,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => {{1,5,9},{2,6},{3,7},{4,8}} => {{1,5,9},{2,6},{3,7},{4,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => {{1,3,4,6,7,9},{2,5,8}} => {{1,3,4,6,7,9},{2,5,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => {{1,4,7},{2,5,8},{3,6,9}} => {{1,4,7},{2,5,8},{3,6,9}}
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => {{1,4,7,10},{2,3,5,6,8,9}} => {{1,4,7,10},{2,3,5,6,8,9}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,2,1] => {{1,10},{2,3,4,5,6,7,8,9}} => {{1,10},{2,3,4,5,6,7,8,9}}
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => {{1,4,7,10},{2,5,8},{3,6,9}} => {{1,4,7,10},{2,5,8},{3,6,9}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,2,3,4,1] => {{1,3,8,10},{2,4,5,6,7,9}} => {{1,3,8,10},{2,4,5,6,7,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,3,4,5,6,7,8,1] => {{1,10},{2,3,4,5,6,7,8,9}} => {{1,10},{2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => {{1,2,9,10},{3,8},{4,7},{5,6}} => {{1,2,9,10},{3,8},{4,7},{5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => {{1,2,9,10},{3,4,7,8},{5,6}} => {{1,2,9,10},{3,4,7,8},{5,6}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => {{1,2,9,10},{3,4,7,8},{5},{6}} => {{1,2,9,10},{3,4,7,8},{5},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => {{1,2,9,10},{3,7},{4,8},{5},{6}} => {{1,2,9,10},{3,7},{4,8},{5},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => {{1,9},{2,10},{3,7},{4,8},{5},{6}} => {{1,9},{2,10},{3,7},{4,8},{5},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,5,6,3,4,1,2] => {{1,3,7,9},{2,4,8,10},{5},{6}} => {{1,3,7,9},{2,4,8,10},{5},{6}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,3,4,5,6,1,2] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [10,9,3,4,5,6,7,8,1,2] => {{1,2,9,10},{3},{4},{5},{6},{7},{8}} => {{1,2,9,10},{3},{4},{5},{6},{7},{8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [9,10,3,4,5,6,7,8,1,2] => {{1,9},{2,10},{3},{4},{5},{6},{7},{8}} => {{1,9},{2,10},{3},{4},{5},{6},{7},{8}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,1,2] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => {{1,3,8,10},{2,9},{4,7},{5,6}} => {{1,3,8,10},{2,9},{4,7},{5,6}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => {{1,3,8,10},{2,9},{4,5,6,7}} => {{1,3,8,10},{2,9},{4,5,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => {{1,2,3,8,9,10},{4,6},{5,7}} => {{1,2,3,8,9,10},{4,6},{5,7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => {{1,4,7,10},{2,3,8,9},{5,6}} => {{1,4,7,10},{2,3,8,9},{5,6}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => {{1,3,7,9},{2,4,8,10},{5},{6}} => {{1,3,7,9},{2,4,8,10},{5},{6}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,5,6,1,2,3,4] => {{1,7},{2,8},{3,9},{4,10},{5},{6}} => {{1,7},{2,8},{3,9},{4,10},{5},{6}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => {{1,5,6,10},{2,4,7,9},{3,8}} => {{1,5,6,10},{2,4,7,9},{3,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => {{1,6},{2,7},{3,8},{4,9},{5,10}} => {{1,6},{2,7},{3,8},{4,9},{5,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => {{1,2,5,6,9,10},{3,4,7,8}} => {{1,2,5,6,9,10},{3,4,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => {{1,4,7,10},{2,3,5,6,8,9}} => {{1,4,7,10},{2,3,5,6,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => {{1,4,7,10},{2,5,8},{3,6,9}} => {{1,4,7,10},{2,5,8},{3,6,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,1,3] => {{1,2,3,7,8,9},{4,6},{5}} => {{1,2,3,7,8,9},{4,6},{5}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,1,4] => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4,6,7,8,9},{5}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,1,5] => {{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] => [9,8,7,5,4,3,2,1,6] => {{1,2,3,6,7,8,9},{4,5}} => {{1,2,3,4,7,8,9},{5,6}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,2,1,7] => {{1,2,7,8,9},{3,6},{4,5}} => {{1,2,3,8,9},{4,7},{5,6}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1,8] => {{1,8,9},{2,7},{3,6},{4,5}} => {{1,2,9},{3,8},{4,7},{5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,1,3] => {{1,2,3,8,9,10},{4,7},{5,6}} => {{1,2,3,8,9,10},{4,7},{5,6}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,1,4] => {{1,2,4,6,8,9},{3,7},{5}} => {{1,2,4,6,8,9},{3,7},{5}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,1,4] => {{1,2,3,4,7,8,9,10},{5,6}} => {{1,2,3,4,7,8,9,10},{5,6}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,4,2,1,5] => {{1,2,3,5,7,8,9},{4,6}} => {{1,2,3,5,7,8,9},{4,6}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,1,5] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,3,2,1,6] => {{1,2,3,6,7,8,9},{4},{5}} => {{1,2,3,4,7,8,9},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,4,3,2,1,6] => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4,5,7,8,9,10},{6}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [9,8,5,6,4,3,2,1,7] => {{1,2,7,8,9},{3,4,5,6}} => {{1,2,3,8,9},{4,5,6,7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,4,3,2,1,7] => {{1,2,3,7,8,9,10},{4,6},{5}} => {{1,2,3,4,8,9,10},{5,7},{6}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,6,7,5,4,3,2,1,8] => {{1,8,9},{2,3,6,7},{4,5}} => {{1,2,9},{3,4,7,8},{5,6}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,2,1,8] => {{1,2,8,9,10},{3,7},{4,6},{5}} => {{1,2,3,9,10},{4,8},{5,7},{6}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,1,9] => {{1,9,10},{2,8},{3,7},{4,6},{5}} => {{1,2,10},{3,9},{4,8},{5,7},{6}}
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => {{1,7,8,9},{2,6},{3,5},{4}} => {{1,2,3,9},{4,8},{5,7},{6}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,3,2,1,5,6] => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3,4,5,7,8,9},{6}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,2,1,4,5] => {{1,3,5,7,9},{2,4,6,8}} => {{1,3,5,7,9},{2,4,6,8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,1,3,4] => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4,6,7,8,9},{5}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => {{1,2,3,4,5,6,7,8,9,10},{11}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,2,1,3,4,5,6,7,8,10] => {{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,10},{9}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [9,8,6,1,2,3,4,5,7] => {{1,4,7,9},{2,5,8},{3,6}} => {{1,3,6,9},{2,5,8},{4,7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,1,2,3,5] => {{1,4,5,6,9},{2,3,7,8}} => {{1,4,5,6,9},{2,3,7,8}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => {{1,2,3,4,5,6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => {{1,2,3,4,5,6,7},{8},{9},{10}} => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => {{1,2,3,4,5,6,7,8},{9},{10}} => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [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}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,1,3,4,5] => {{1,6},{2,3,4,5,7,8,9}} => {{1,2,3,5,6,7,8},{4,9}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,5,1] => {{1,9},{2,3,4,5,6,7,8}} => {{1,9},{2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [10,8,7,6,9,5,4,3,2,1] => {{1,10},{2,3,4,5,6,7,8,9}} => {{1,10},{2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,5,1,2] => {{1,2,8,9},{3,4,5,6,7}} => {{1,2,8,9},{3,4,5,6,7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,5,3,2,1,10] => {{1,9},{2,8},{3,7},{4,5,6},{10}} => {{1},{2,10},{3,9},{4,8},{5,6,7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,1,2,8] => {{1,2,7,8,9},{3,6},{4,5}} => {{1,2,3,8,9},{4,7},{5,6}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,9,1] => {{1,2,7,8,9},{3,6},{4,5}} => {{1,2,3,8,9},{4,7},{5,6}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,3,2,1,4] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,6,5,8,9,4,3,2,1,10] => {{1,3,5,7,9},{2,4,6,8},{10}} => {{1},{2,4,6,8,10},{3,5,7,9}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,8,9,2,1,3] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,1,10] => {{1,7,8,9},{2,6},{3,5},{4},{10}} => {{1},{2,3,4,10},{5,9},{6,8},{7}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => {{1,7},{2,6},{3,5},{4},{8},{9},{10}} => {{1},{2},{3},{4,10},{5,9},{6,8},{7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,1,6,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [5,6,7,4,8,9,1,2,3] => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3,4,5,7,8,9},{6}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,1,4,5,6] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,1,2,3,4] => {{1,6},{2,3,4,5,7,8,9}} => {{1,2,3,5,6,7,8},{4,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => {{1,2,3,4,5,6,7,8},{9},{10}} => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => {{1,2,3,4,5,6,7},{8},{9},{10}} => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => {{1,2,3,4,5,6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => {{1,9},{2,8},{3,7},{4,5,6},{10}} => {{1},{2,10},{3,9},{4,8},{5,6,7}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [9,10,6,7,4,5,2,3,1,8] => {{1,9},{2,3,4,5,6,7,8,10}} => {{1,3,4,5,6,7,8,9},{2,10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => {{1,8},{2,7},{3,6},{4,5},{9},{10}} => {{1},{2},{3,10},{4,9},{5,8},{6,7}}
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => {{1,3},{2,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,9},{8,10}}
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => {{1,4},{2,5},{3,6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,8},{6,9},{7,10}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => {{1,5},{2,6},{3,7},{4,8},{9},{10}} => {{1},{2},{3,7},{4,8},{5,9},{6,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => {{1,2,4,5,6,7,9,10,11,12},{3,8}} => {{1,2,3,4,6,7,8,9,11,12},{5,10}}
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,6,5,4,3,2,1,8,9] => {{1,8,9,10},{2,7},{3,6},{4,5}} => {{1,2,3,10},{4,9},{5,8},{6,7}}
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => {{1,2,3,4,5,6,7,8,9,10},{11}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => {{1,6},{2,5},{3,4},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,10},{6,9},{7,8}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [5,4,6,7,8,9,10,3,2,1] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,4,1] => {{1,9},{2,3,4,6,7,8},{5}} => {{1,9},{2,3,4,6,7,8},{5}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => {{1,5},{2,4},{3},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,10},{7,9},{8}}
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => {{1,4},{2,3},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,10},{8,9}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,1,10] => {{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,2,11},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => {{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,2,11},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,4,3,2,1,5,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [7,6,8,5,9,4,3,2,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,1,2,3,4,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,2,1,3,4] => {{1,2,3,4,7,8,9,10},{5},{6}} => {{1,2,3,4,7,8,9,10},{5},{6}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,3,4,1,2,5] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [11,10,1,2,3,4,5,6,7,8,9] => {{1,3,5,7,9,11},{2,4,6,8,10}} => {{1,3,5,7,9,11},{2,4,6,8,10}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [9,8,4,1,2,3,5,6,7] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,2,1,3,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,9,1] => {{1,2,3,6,7,8,9},{4,5}} => {{1,2,3,4,7,8,9},{5,6}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [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}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [10,7,8,5,6,3,4,1,2,9] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,1,2,9] => {{1,2,8,9,10},{3,7},{4,6},{5}} => {{1,2,3,9,10},{4,8},{5,7},{6}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,2,1,8] => {{1,8,9},{2,3,4,5,6,7}} => {{1,2,9},{3,4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9,10] => {{1,3,5,7},{2,4,6,8},{9},{10}} => {{1},{2},{3,5,7,9},{4,6,8,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,10,1] => {{1,2,8,9,10},{3,7},{4,6},{5}} => {{1,2,3,9,10},{4,8},{5,7},{6}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,1,4,5] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,1,10] => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,3,1,2,4,6,8,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [11,12,9,10,7,8,5,6,3,4,1,2] => {{1,11},{2,12},{3,9},{4,10},{5,7},{6,8}} => {{1,11},{2,12},{3,9},{4,10},{5,7},{6,8}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => {{1,7},{2,8},{3,5},{4,6},{9},{10}} => {{1},{2},{3,9},{4,10},{5,7},{6,8}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => {{1,3,5,7,9,11},{2,4,6,8,10,12}} => {{1,3,5,7,9,11},{2,4,6,8,10,12}}
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => {{1,3,5,7,9,11},{2,4,6,8,10}} => {{1,3,5,7,9,11},{2,4,6,8,10}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [9,4,5,6,7,8,2,1,3] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,2,1,3,4] => {{1,4,7,9},{2,3,5,6,8}} => {{1,3,6,9},{2,4,5,7,8}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [11,3,4,5,6,7,8,9,10,1,2] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [10,4,5,6,7,8,9,2,1,3] => {{1,3,5,7,9,10},{2,4,6,8}} => {{1,2,4,6,8,10},{3,5,7,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [11,8,9,10,1,2,3,4,5,6,7] => {{1,3,5,7,9,11},{2,4,6,8,10}} => {{1,3,5,7,9,11},{2,4,6,8,10}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,2,4,5,6,7,8,9,1] => {{1,10},{2,3},{4},{5},{6},{7},{8},{9}} => {{1,10},{2},{3},{4},{5},{6},{7},{8,9}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,4,5,1,6] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9,10] => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => {{1,7},{2,8},{3,9},{4},{5},{6},{10}} => {{1},{2,8},{3,9},{4,10},{5},{6},{7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,2,1,3,9] => {{1,2,3,7,8,9,10},{4,6},{5}} => {{1,2,3,4,8,9,10},{5,7},{6}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,7,8,9,10,1,2] => {{1,2,5,6,7,8,9,10},{3,4}} => {{1,2,3,4,5,6,9,10},{7,8}}
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
to cycle type
Description
Let π=c1…cr a permutation of size n decomposed in its cyclic parts. The associated set partition of [n] then is S=S1∪⋯∪Sr such that Si is the set of integers in the cycle ci.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
Map
complement
Description
The complement of a set partition obtained by replacing i with n+1−i.
searching the database
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