Identifier
Mp00138:
Dyck paths
—to noncrossing partition⟶
Set partitions
Mp00215: Set partitions —Wachs-White⟶ Set partitions
Mp00115: Set partitions —Kasraoui-Zeng⟶ Set partitions
Mp00215: Set partitions —Wachs-White⟶ Set partitions
Mp00115: Set partitions —Kasraoui-Zeng⟶ Set partitions
Images
[1,0] => {{1}} => {{1}} => {{1}}
[1,0,1,0] => {{1},{2}} => {{1},{2}} => {{1},{2}}
[1,1,0,0] => {{1,2}} => {{1,2}} => {{1,2}}
[1,0,1,0,1,0] => {{1},{2},{3}} => {{1},{2},{3}} => {{1},{2},{3}}
[1,0,1,1,0,0] => {{1},{2,3}} => {{1,2},{3}} => {{1,2},{3}}
[1,1,0,0,1,0] => {{1,2},{3}} => {{1},{2,3}} => {{1},{2,3}}
[1,1,0,1,0,0] => {{1,3},{2}} => {{1,3},{2}} => {{1,3},{2}}
[1,1,1,0,0,0] => {{1,2,3}} => {{1,2,3}} => {{1,2,3}}
[1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}} => {{1},{2},{3},{4}}
[1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => {{1,2},{3},{4}} => {{1,2},{3},{4}}
[1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => {{1},{2,3},{4}} => {{1},{2,3},{4}}
[1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => {{1,3},{2},{4}} => {{1,3},{2},{4}}
[1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => {{1,2,3},{4}} => {{1,2,3},{4}}
[1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => {{1},{2},{3,4}} => {{1},{2},{3,4}}
[1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => {{1,2},{3,4}} => {{1,2},{3,4}}
[1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => {{1},{2,4},{3}} => {{1},{2,4},{3}}
[1,1,0,1,0,1,0,0] => {{1,4},{2},{3}} => {{1,4},{2},{3}} => {{1,4},{2},{3}}
[1,1,0,1,1,0,0,0] => {{1,3,4},{2}} => {{1,2,4},{3}} => {{1,2,4},{3}}
[1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => {{1},{2,3,4}} => {{1},{2,3,4}}
[1,1,1,0,0,1,0,0] => {{1,4},{2,3}} => {{1,4},{2,3}} => {{1,3},{2,4}}
[1,1,1,0,1,0,0,0] => {{1,2,4},{3}} => {{1,3},{2,4}} => {{1,4},{2,3}}
[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] => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => {{1,2},{3},{4},{5}} => {{1,2},{3},{4},{5}}
[1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => {{1},{2,3},{4},{5}} => {{1},{2,3},{4},{5}}
[1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => {{1,3},{2},{4},{5}} => {{1,3},{2},{4},{5}}
[1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => {{1,2,3},{4},{5}} => {{1,2,3},{4},{5}}
[1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => {{1},{2},{3,4},{5}} => {{1},{2},{3,4},{5}}
[1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1,2},{3,4},{5}} => {{1,2},{3,4},{5}}
[1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => {{1},{2,4},{3},{5}} => {{1},{2,4},{3},{5}}
[1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => {{1,4},{2},{3},{5}} => {{1,4},{2},{3},{5}}
[1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => {{1,2,4},{3},{5}} => {{1,2,4},{3},{5}}
[1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => {{1},{2,3,4},{5}} => {{1},{2,3,4},{5}}
[1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => {{1,4},{2,3},{5}} => {{1,3},{2,4},{5}}
[1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => {{1,3},{2,4},{5}} => {{1,4},{2,3},{5}}
[1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => {{1,2,3,4},{5}} => {{1,2,3,4},{5}}
[1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => {{1},{2},{3},{4,5}} => {{1},{2},{3},{4,5}}
[1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => {{1,2},{3},{4,5}} => {{1,2},{3},{4,5}}
[1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => {{1},{2,3},{4,5}} => {{1},{2,3},{4,5}}
[1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => {{1,3},{2},{4,5}} => {{1,3},{2},{4,5}}
[1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2,3},{4,5}} => {{1,2,3},{4,5}}
[1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => {{1},{2},{3,5},{4}} => {{1},{2},{3,5},{4}}
[1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => {{1,2},{3,5},{4}} => {{1,2},{3,5},{4}}
[1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => {{1},{2,5},{3},{4}} => {{1},{2,5},{3},{4}}
[1,1,0,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}}
[1,1,0,1,0,1,1,0,0,0] => {{1,4,5},{2},{3}} => {{1,2,5},{3},{4}} => {{1,2,5},{3},{4}}
[1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => {{1},{2,3,5},{4}} => {{1},{2,3,5},{4}}
[1,1,0,1,1,0,0,1,0,0] => {{1,5},{2},{3,4}} => {{1,5},{2,3},{4}} => {{1,3},{2,5},{4}}
[1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4}} => {{1,3},{2,5},{4}} => {{1,5},{2,3},{4}}
[1,1,0,1,1,1,0,0,0,0] => {{1,3,4,5},{2}} => {{1,2,3,5},{4}} => {{1,2,3,5},{4}}
[1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => {{1},{2},{3,4,5}} => {{1},{2},{3,4,5}}
[1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => {{1,2},{3,4,5}} => {{1,2},{3,4,5}}
[1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => {{1},{2,5},{3,4}} => {{1},{2,4},{3,5}}
[1,1,1,0,0,1,0,1,0,0] => {{1,5},{2,3},{4}} => {{1,5},{2},{3,4}} => {{1,4},{2},{3,5}}
[1,1,1,0,0,1,1,0,0,0] => {{1,4,5},{2,3}} => {{1,2,5},{3,4}} => {{1,2,4},{3,5}}
[1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => {{1},{2,4},{3,5}} => {{1},{2,5},{3,4}}
[1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3}} => {{1,5},{2,4},{3}} => {{1,4},{2,5},{3}}
[1,1,1,0,1,0,1,0,0,0] => {{1,2,5},{3},{4}} => {{1,4},{2},{3,5}} => {{1,5},{2},{3,4}}
[1,1,1,0,1,1,0,0,0,0] => {{1,2,4,5},{3}} => {{1,2,4},{3,5}} => {{1,2,5},{3,4}}
[1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}} => {{1},{2,3,4,5}}
[1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3,4}} => {{1,5},{2,3,4}} => {{1,3,5},{2,4}}
[1,1,1,1,0,0,1,0,0,0] => {{1,2,5},{3,4}} => {{1,4},{2,3,5}} => {{1,3,4},{2,5}}
[1,1,1,1,0,1,0,0,0,0] => {{1,2,3,5},{4}} => {{1,3},{2,4,5}} => {{1,4,5},{2,3}}
[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] => {{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => {{1,2},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => {{1},{2,3},{4},{5},{6}} => {{1},{2,3},{4},{5},{6}}
[1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => {{1,3},{2},{4},{5},{6}} => {{1,3},{2},{4},{5},{6}}
[1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => {{1,2,3},{4},{5},{6}} => {{1,2,3},{4},{5},{6}}
[1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => {{1},{2},{3,4},{5},{6}} => {{1},{2},{3,4},{5},{6}}
[1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => {{1,2},{3,4},{5},{6}} => {{1,2},{3,4},{5},{6}}
[1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => {{1},{2,4},{3},{5},{6}} => {{1},{2,4},{3},{5},{6}}
[1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => {{1,4},{2},{3},{5},{6}} => {{1,4},{2},{3},{5},{6}}
[1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}} => {{1,2,4},{3},{5},{6}} => {{1,2,4},{3},{5},{6}}
[1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => {{1},{2,3,4},{5},{6}} => {{1},{2,3,4},{5},{6}}
[1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}} => {{1,4},{2,3},{5},{6}} => {{1,3},{2,4},{5},{6}}
[1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => {{1,3},{2,4},{5},{6}} => {{1,4},{2,3},{5},{6}}
[1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => {{1,2,3,4},{5},{6}} => {{1,2,3,4},{5},{6}}
[1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => {{1},{2},{3},{4,5},{6}} => {{1},{2},{3},{4,5},{6}}
[1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => {{1,2},{3},{4,5},{6}} => {{1,2},{3},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1},{2,3},{4,5},{6}} => {{1},{2,3},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}} => {{1,3},{2},{4,5},{6}} => {{1,3},{2},{4,5},{6}}
[1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,2,3},{4,5},{6}} => {{1,2,3},{4,5},{6}}
[1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => {{1},{2},{3,5},{4},{6}} => {{1},{2},{3,5},{4},{6}}
[1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}} => {{1,2},{3,5},{4},{6}} => {{1,2},{3,5},{4},{6}}
[1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}} => {{1},{2,5},{3},{4},{6}} => {{1},{2,5},{3},{4},{6}}
[1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => {{1,5},{2},{3},{4},{6}} => {{1,5},{2},{3},{4},{6}}
[1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => {{1,2,5},{3},{4},{6}} => {{1,2,5},{3},{4},{6}}
[1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}} => {{1},{2,3,5},{4},{6}} => {{1},{2,3,5},{4},{6}}
[1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => {{1,5},{2,3},{4},{6}} => {{1,3},{2,5},{4},{6}}
[1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => {{1,3},{2,5},{4},{6}} => {{1,5},{2,3},{4},{6}}
[1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => {{1,2,3,5},{4},{6}} => {{1,2,3,5},{4},{6}}
[1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => {{1},{2},{3,4,5},{6}} => {{1},{2},{3,4,5},{6}}
[1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,2},{3,4,5},{6}} => {{1,2},{3,4,5},{6}}
[1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}} => {{1},{2,5},{3,4},{6}} => {{1},{2,4},{3,5},{6}}
[1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => {{1,5},{2},{3,4},{6}} => {{1,4},{2},{3,5},{6}}
[1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => {{1,2,5},{3,4},{6}} => {{1,2,4},{3,5},{6}}
[1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => {{1},{2,4},{3,5},{6}} => {{1},{2,5},{3,4},{6}}
[1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => {{1,5},{2,4},{3},{6}} => {{1,4},{2,5},{3},{6}}
[1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => {{1,4},{2},{3,5},{6}} => {{1,5},{2},{3,4},{6}}
[1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => {{1,2,4},{3,5},{6}} => {{1,2,5},{3,4},{6}}
>>> Load all 1953 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}}
[1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => {{1,5},{2,3,4},{6}} => {{1,3,5},{2,4},{6}}
[1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => {{1,4},{2,3,5},{6}} => {{1,3,4},{2,5},{6}}
[1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => {{1,3},{2,4,5},{6}} => {{1,4,5},{2,3},{6}}
[1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}} => {{1,2,3,4,5},{6}}
[1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5,6}} => {{1},{2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => {{1},{2,3},{4},{5,6}} => {{1},{2,3},{4},{5,6}}
[1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}} => {{1,3},{2},{4},{5,6}} => {{1,3},{2},{4},{5,6}}
[1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => {{1,2,3},{4},{5,6}} => {{1,2,3},{4},{5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => {{1},{2},{3,4},{5,6}} => {{1},{2},{3,4},{5,6}}
[1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}} => {{1},{2,4},{3},{5,6}} => {{1},{2,4},{3},{5,6}}
[1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}} => {{1,4},{2},{3},{5,6}} => {{1,4},{2},{3},{5,6}}
[1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => {{1,2,4},{3},{5,6}} => {{1,2,4},{3},{5,6}}
[1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1},{2,3,4},{5,6}} => {{1},{2,3,4},{5,6}}
[1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => {{1,4},{2,3},{5,6}} => {{1,3},{2,4},{5,6}}
[1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => {{1,3},{2,4},{5,6}} => {{1,4},{2,3},{5,6}}
[1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,3,4},{5,6}} => {{1,2,3,4},{5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => {{1},{2},{3},{4,6},{5}} => {{1},{2},{3},{4,6},{5}}
[1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}} => {{1,2},{3},{4,6},{5}} => {{1,2},{3},{4,6},{5}}
[1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}} => {{1},{2,3},{4,6},{5}} => {{1},{2,3},{4,6},{5}}
[1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => {{1,3},{2},{4,6},{5}} => {{1,3},{2},{4,6},{5}}
[1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => {{1,2,3},{4,6},{5}} => {{1,2,3},{4,6},{5}}
[1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => {{1},{2},{3,6},{4},{5}} => {{1},{2},{3,6},{4},{5}}
[1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => {{1,2},{3,6},{4},{5}} => {{1,2},{3,6},{4},{5}}
[1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => {{1},{2,6},{3},{4},{5}} => {{1},{2,6},{3},{4},{5}}
[1,1,0,1,0,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,0,0,0] => {{1,5,6},{2},{3},{4}} => {{1,2,6},{3},{4},{5}} => {{1,2,6},{3},{4},{5}}
[1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => {{1},{2,3,6},{4},{5}} => {{1},{2,3,6},{4},{5}}
[1,1,0,1,0,1,1,0,0,1,0,0] => {{1,6},{2},{3},{4,5}} => {{1,6},{2,3},{4},{5}} => {{1,3},{2,6},{4},{5}}
[1,1,0,1,0,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5}} => {{1,3},{2,6},{4},{5}} => {{1,6},{2,3},{4},{5}}
[1,1,0,1,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2},{3}} => {{1,2,3,6},{4},{5}} => {{1,2,3,6},{4},{5}}
[1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}} => {{1},{2},{3,4,6},{5}} => {{1},{2},{3,4,6},{5}}
[1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => {{1,2},{3,4,6},{5}} => {{1,2},{3,4,6},{5}}
[1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => {{1},{2,6},{3,4},{5}} => {{1},{2,4},{3,6},{5}}
[1,1,0,1,1,0,0,1,0,1,0,0] => {{1,6},{2},{3,4},{5}} => {{1,6},{2},{3,4},{5}} => {{1,4},{2},{3,6},{5}}
[1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4}} => {{1,2,6},{3,4},{5}} => {{1,2,4},{3,6},{5}}
[1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => {{1},{2,4},{3,6},{5}} => {{1},{2,6},{3,4},{5}}
[1,1,0,1,1,0,1,0,0,1,0,0] => {{1,6},{2},{3,5},{4}} => {{1,6},{2,4},{3},{5}} => {{1,4},{2,6},{3},{5}}
[1,1,0,1,1,0,1,0,1,0,0,0] => {{1,3,6},{2},{4},{5}} => {{1,4},{2},{3,6},{5}} => {{1,6},{2},{3,4},{5}}
[1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4}} => {{1,2,4},{3,6},{5}} => {{1,2,6},{3,4},{5}}
[1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => {{1},{2,3,4,6},{5}} => {{1},{2,3,4,6},{5}}
[1,1,0,1,1,1,0,0,0,1,0,0] => {{1,6},{2},{3,4,5}} => {{1,6},{2,3,4},{5}} => {{1,3,6},{2,4},{5}}
[1,1,0,1,1,1,0,0,1,0,0,0] => {{1,3,6},{2},{4,5}} => {{1,4},{2,3,6},{5}} => {{1,3,4},{2,6},{5}}
[1,1,0,1,1,1,0,1,0,0,0,0] => {{1,3,4,6},{2},{5}} => {{1,3},{2,4,6},{5}} => {{1,4,6},{2,3},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0] => {{1,3,4,5,6},{2}} => {{1,2,3,4,6},{5}} => {{1,2,3,4,6},{5}}
[1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => {{1},{2},{3},{4,5,6}} => {{1},{2},{3},{4,5,6}}
[1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => {{1,2},{3},{4,5,6}} => {{1,2},{3},{4,5,6}}
[1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => {{1},{2,3},{4,5,6}} => {{1},{2,3},{4,5,6}}
[1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => {{1,3},{2},{4,5,6}} => {{1,3},{2},{4,5,6}}
[1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}}
[1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => {{1},{2},{3,6},{4,5}} => {{1},{2},{3,5},{4,6}}
[1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => {{1,2},{3,6},{4,5}} => {{1,2},{3,5},{4,6}}
[1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => {{1},{2,6},{3},{4,5}} => {{1},{2,5},{3},{4,6}}
[1,1,1,0,0,1,0,1,0,1,0,0] => {{1,6},{2,3},{4},{5}} => {{1,6},{2},{3},{4,5}} => {{1,5},{2},{3},{4,6}}
[1,1,1,0,0,1,0,1,1,0,0,0] => {{1,5,6},{2,3},{4}} => {{1,2,6},{3},{4,5}} => {{1,2,5},{3},{4,6}}
[1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => {{1},{2,3,6},{4,5}} => {{1},{2,3,5},{4,6}}
[1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5}} => {{1,6},{2,3},{4,5}} => {{1,3},{2,5},{4,6}}
[1,1,1,0,0,1,1,0,1,0,0,0] => {{1,4,6},{2,3},{5}} => {{1,3},{2,6},{4,5}} => {{1,5},{2,3},{4,6}}
[1,1,1,0,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2,3}} => {{1,2,3,6},{4,5}} => {{1,2,3,5},{4,6}}
[1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => {{1},{2},{3,5},{4,6}} => {{1},{2},{3,6},{4,5}}
[1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => {{1,2},{3,5},{4,6}} => {{1,2},{3,6},{4,5}}
[1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => {{1},{2,6},{3,5},{4}} => {{1},{2,5},{3,6},{4}}
[1,1,1,0,1,0,0,1,0,1,0,0] => {{1,6},{2,4},{3},{5}} => {{1,6},{2},{3,5},{4}} => {{1,5},{2},{3,6},{4}}
[1,1,1,0,1,0,0,1,1,0,0,0] => {{1,5,6},{2,4},{3}} => {{1,2,6},{3,5},{4}} => {{1,2,5},{3,6},{4}}
[1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => {{1},{2,5},{3},{4,6}} => {{1},{2,6},{3},{4,5}}
[1,1,1,0,1,0,1,0,0,1,0,0] => {{1,6},{2,5},{3},{4}} => {{1,6},{2,5},{3},{4}} => {{1,5},{2,6},{3},{4}}
[1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,6},{3},{4},{5}} => {{1,5},{2},{3},{4,6}} => {{1,6},{2},{3},{4,5}}
[1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2,5,6},{3},{4}} => {{1,2,5},{3},{4,6}} => {{1,2,6},{3},{4,5}}
[1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => {{1},{2,3,5},{4,6}} => {{1},{2,3,6},{4,5}}
[1,1,1,0,1,1,0,0,0,1,0,0] => {{1,6},{2,4,5},{3}} => {{1,6},{2,3,5},{4}} => {{1,3,6},{2,5},{4}}
[1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2,6},{3},{4,5}} => {{1,5},{2,3},{4,6}} => {{1,3},{2,6},{4,5}}
[1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2,4,6},{3},{5}} => {{1,3},{2,5},{4,6}} => {{1,6},{2,3},{4,5}}
[1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,4,5,6},{3}} => {{1,2,3,5},{4,6}} => {{1,2,3,6},{4,5}}
[1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}} => {{1},{2},{3,4,5,6}}
[1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => {{1,2},{3,4,5,6}} => {{1,2},{3,4,5,6}}
[1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => {{1},{2,6},{3,4,5}} => {{1},{2,4,6},{3,5}}
[1,1,1,1,0,0,0,1,0,1,0,0] => {{1,6},{2,3,4},{5}} => {{1,6},{2},{3,4,5}} => {{1,4,6},{2},{3,5}}
[1,1,1,1,0,0,0,1,1,0,0,0] => {{1,5,6},{2,3,4}} => {{1,2,6},{3,4,5}} => {{1,2,4,6},{3,5}}
[1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => {{1},{2,5},{3,4,6}} => {{1},{2,4,5},{3,6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4}} => {{1,6},{2,5},{3,4}} => {{1,4},{2,5},{3,6}}
[1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2,6},{3,4},{5}} => {{1,5},{2},{3,4,6}} => {{1,4,5},{2},{3,6}}
[1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,5,6},{3,4}} => {{1,2,5},{3,4,6}} => {{1,2,4,5},{3,6}}
[1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => {{1},{2,4},{3,5,6}} => {{1},{2,5,6},{3,4}}
[1,1,1,1,0,1,0,0,0,1,0,0] => {{1,6},{2,3,5},{4}} => {{1,6},{2,4},{3,5}} => {{1,5},{2,4},{3,6}}
[1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,6},{3,5},{4}} => {{1,5},{2,4},{3,6}} => {{1,6},{2,4},{3,5}}
[1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3,6},{4},{5}} => {{1,4},{2},{3,5,6}} => {{1,5,6},{2},{3,4}}
[1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2,3,5,6},{4}} => {{1,2,4},{3,5,6}} => {{1,2,5,6},{3,4}}
[1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}} => {{1},{2,3,4,5,6}}
[1,1,1,1,1,0,0,0,0,1,0,0] => {{1,6},{2,3,4,5}} => {{1,6},{2,3,4,5}} => {{1,3,5},{2,4,6}}
[1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,6},{3,4,5}} => {{1,5},{2,3,4,6}} => {{1,3,6},{2,4,5}}
[1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3,6},{4,5}} => {{1,4},{2,3,5,6}} => {{1,3,4},{2,5,6}}
[1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3,4,6},{5}} => {{1,3},{2,4,5,6}} => {{1,4,5,6},{2,3}}
[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] => {{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6},{7}} => {{1,2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6},{7}} => {{1},{2,3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => {{1,3},{2},{4},{5},{6},{7}} => {{1,3},{2},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6},{7}} => {{1,2,3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6},{7}} => {{1,2},{3,4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}} => {{1},{2,4},{3},{5},{6},{7}} => {{1},{2,4},{3},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}} => {{1,4},{2},{3},{5},{6},{7}} => {{1,4},{2},{3},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}} => {{1,2,4},{3},{5},{6},{7}} => {{1,2,4},{3},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6},{7}} => {{1},{2,3,4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}} => {{1,4},{2,3},{5},{6},{7}} => {{1,3},{2,4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}} => {{1,3},{2,4},{5},{6},{7}} => {{1,4},{2,3},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6},{7}} => {{1,2,3,4},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6},{7}} => {{1,2},{3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6},{7}} => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}} => {{1,3},{2},{4,5},{6},{7}} => {{1,3},{2},{4,5},{6},{7}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6},{7}} => {{1,2,3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6},{7}} => {{1,2},{3,5},{4},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}} => {{1},{2,5},{3},{4},{6},{7}} => {{1},{2,5},{3},{4},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}} => {{1,5},{2},{3},{4},{6},{7}} => {{1,5},{2},{3},{4},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}} => {{1,2,5},{3},{4},{6},{7}} => {{1,2,5},{3},{4},{6},{7}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}} => {{1},{2,3,5},{4},{6},{7}} => {{1},{2,3,5},{4},{6},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}} => {{1,5},{2,3},{4},{6},{7}} => {{1,3},{2,5},{4},{6},{7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}} => {{1,3},{2,5},{4},{6},{7}} => {{1,5},{2,3},{4},{6},{7}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}} => {{1,2,3,5},{4},{6},{7}} => {{1,2,3,5},{4},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6},{7}} => {{1,2},{3,4,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}} => {{1},{2,5},{3,4},{6},{7}} => {{1},{2,4},{3,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}} => {{1,5},{2},{3,4},{6},{7}} => {{1,4},{2},{3,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}} => {{1,2,5},{3,4},{6},{7}} => {{1,2,4},{3,5},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}} => {{1},{2,4},{3,5},{6},{7}} => {{1},{2,5},{3,4},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}} => {{1,5},{2,4},{3},{6},{7}} => {{1,4},{2,5},{3},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => {{1,4},{2},{3,5},{6},{7}} => {{1,5},{2},{3,4},{6},{7}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}} => {{1,2,4},{3,5},{6},{7}} => {{1,2,5},{3,4},{6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6},{7}} => {{1},{2,3,4,5},{6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}} => {{1,5},{2,3,4},{6},{7}} => {{1,3,5},{2,4},{6},{7}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}} => {{1,4},{2,3,5},{6},{7}} => {{1,3,4},{2,5},{6},{7}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}} => {{1,3},{2,4,5},{6},{7}} => {{1,4,5},{2,3},{6},{7}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}} => {{1,2,3,4,5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6},{7}} => {{1},{2},{3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6},{7}} => {{1,2},{3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}} => {{1,3},{2},{4},{5,6},{7}} => {{1,3},{2},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6},{7}} => {{1,2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6},{7}} => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}} => {{1},{2,4},{3},{5,6},{7}} => {{1},{2,4},{3},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}} => {{1,4},{2},{3},{5,6},{7}} => {{1,4},{2},{3},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}} => {{1,2,4},{3},{5,6},{7}} => {{1,2,4},{3},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}} => {{1,4},{2,3},{5,6},{7}} => {{1,3},{2,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}} => {{1,3},{2,4},{5,6},{7}} => {{1,4},{2,3},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,2,3,4},{5,6},{7}} => {{1,2,3,4},{5,6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}} => {{1},{2},{3},{4,6},{5},{7}} => {{1},{2},{3},{4,6},{5},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}} => {{1,2},{3},{4,6},{5},{7}} => {{1,2},{3},{4,6},{5},{7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}} => {{1},{2,3},{4,6},{5},{7}} => {{1},{2,3},{4,6},{5},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}} => {{1,3},{2},{4,6},{5},{7}} => {{1,3},{2},{4,6},{5},{7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}} => {{1,2,3},{4,6},{5},{7}} => {{1,2,3},{4,6},{5},{7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}} => {{1},{2},{3,6},{4},{5},{7}} => {{1},{2},{3,6},{4},{5},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}} => {{1,2},{3,6},{4},{5},{7}} => {{1,2},{3,6},{4},{5},{7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}} => {{1},{2,6},{3},{4},{5},{7}} => {{1},{2,6},{3},{4},{5},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => {{1,6},{2},{3},{4},{5},{7}} => {{1,6},{2},{3},{4},{5},{7}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}} => {{1,2,6},{3},{4},{5},{7}} => {{1,2,6},{3},{4},{5},{7}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}} => {{1},{2,3,6},{4},{5},{7}} => {{1},{2,3,6},{4},{5},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}} => {{1,6},{2,3},{4},{5},{7}} => {{1,3},{2,6},{4},{5},{7}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}} => {{1,3},{2,6},{4},{5},{7}} => {{1,6},{2,3},{4},{5},{7}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}} => {{1,2,3,6},{4},{5},{7}} => {{1,2,3,6},{4},{5},{7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}} => {{1},{2},{3,4,6},{5},{7}} => {{1},{2},{3,4,6},{5},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}} => {{1,2},{3,4,6},{5},{7}} => {{1,2},{3,4,6},{5},{7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}} => {{1},{2,6},{3,4},{5},{7}} => {{1},{2,4},{3,6},{5},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}} => {{1,6},{2},{3,4},{5},{7}} => {{1,4},{2},{3,6},{5},{7}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}} => {{1,2,6},{3,4},{5},{7}} => {{1,2,4},{3,6},{5},{7}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}} => {{1},{2,4},{3,6},{5},{7}} => {{1},{2,6},{3,4},{5},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}} => {{1,6},{2,4},{3},{5},{7}} => {{1,4},{2,6},{3},{5},{7}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}} => {{1,4},{2},{3,6},{5},{7}} => {{1,6},{2},{3,4},{5},{7}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}} => {{1,2,4},{3,6},{5},{7}} => {{1,2,6},{3,4},{5},{7}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}} => {{1},{2,3,4,6},{5},{7}} => {{1},{2,3,4,6},{5},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}} => {{1,6},{2,3,4},{5},{7}} => {{1,3,6},{2,4},{5},{7}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}} => {{1,4},{2,3,6},{5},{7}} => {{1,3,4},{2,6},{5},{7}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}} => {{1,3},{2,4,6},{5},{7}} => {{1,4,6},{2,3},{5},{7}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}} => {{1,2,3,4,6},{5},{7}} => {{1,2,3,4,6},{5},{7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6},{7}} => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6},{7}} => {{1,2},{3},{4,5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}} => {{1,3},{2},{4,5,6},{7}} => {{1,3},{2},{4,5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,2,3},{4,5,6},{7}} => {{1,2,3},{4,5,6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}} => {{1},{2},{3,6},{4,5},{7}} => {{1},{2},{3,5},{4,6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}} => {{1,2},{3,6},{4,5},{7}} => {{1,2},{3,5},{4,6},{7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}} => {{1},{2,6},{3},{4,5},{7}} => {{1},{2,5},{3},{4,6},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}} => {{1,6},{2},{3},{4,5},{7}} => {{1,5},{2},{3},{4,6},{7}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}} => {{1,2,6},{3},{4,5},{7}} => {{1,2,5},{3},{4,6},{7}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}} => {{1},{2,3,6},{4,5},{7}} => {{1},{2,3,5},{4,6},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}} => {{1,6},{2,3},{4,5},{7}} => {{1,3},{2,5},{4,6},{7}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}} => {{1,3},{2,6},{4,5},{7}} => {{1,5},{2,3},{4,6},{7}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}} => {{1,2,3,6},{4,5},{7}} => {{1,2,3,5},{4,6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}} => {{1},{2},{3,5},{4,6},{7}} => {{1},{2},{3,6},{4,5},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}} => {{1,2},{3,5},{4,6},{7}} => {{1,2},{3,6},{4,5},{7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}} => {{1},{2,6},{3,5},{4},{7}} => {{1},{2,5},{3,6},{4},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}} => {{1,6},{2},{3,5},{4},{7}} => {{1,5},{2},{3,6},{4},{7}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}} => {{1,2,6},{3,5},{4},{7}} => {{1,2,5},{3,6},{4},{7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => {{1},{2,5},{3},{4,6},{7}} => {{1},{2,6},{3},{4,5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}} => {{1,6},{2,5},{3},{4},{7}} => {{1,5},{2,6},{3},{4},{7}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => {{1,5},{2},{3},{4,6},{7}} => {{1,6},{2},{3},{4,5},{7}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}} => {{1,2,5},{3},{4,6},{7}} => {{1,2,6},{3},{4,5},{7}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}} => {{1},{2,3,5},{4,6},{7}} => {{1},{2,3,6},{4,5},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}} => {{1,6},{2,3,5},{4},{7}} => {{1,3,6},{2,5},{4},{7}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}} => {{1,5},{2,3},{4,6},{7}} => {{1,3},{2,6},{4,5},{7}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}} => {{1,3},{2,5},{4,6},{7}} => {{1,6},{2,3},{4,5},{7}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}} => {{1,2,3,5},{4,6},{7}} => {{1,2,3,6},{4,5},{7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6},{7}} => {{1},{2},{3,4,5,6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,2},{3,4,5,6},{7}} => {{1,2},{3,4,5,6},{7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}} => {{1},{2,6},{3,4,5},{7}} => {{1},{2,4,6},{3,5},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}} => {{1,6},{2},{3,4,5},{7}} => {{1,4,6},{2},{3,5},{7}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}} => {{1,2,6},{3,4,5},{7}} => {{1,2,4,6},{3,5},{7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}} => {{1},{2,5},{3,4,6},{7}} => {{1},{2,4,5},{3,6},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}} => {{1,6},{2,5},{3,4},{7}} => {{1,4},{2,5},{3,6},{7}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}} => {{1,5},{2},{3,4,6},{7}} => {{1,4,5},{2},{3,6},{7}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}} => {{1,2,5},{3,4,6},{7}} => {{1,2,4,5},{3,6},{7}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}} => {{1},{2,4},{3,5,6},{7}} => {{1},{2,5,6},{3,4},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}} => {{1,6},{2,4},{3,5},{7}} => {{1,5},{2,4},{3,6},{7}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}} => {{1,5},{2,4},{3,6},{7}} => {{1,6},{2,4},{3,5},{7}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}} => {{1,4},{2},{3,5,6},{7}} => {{1,5,6},{2},{3,4},{7}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}} => {{1,2,4},{3,5,6},{7}} => {{1,2,5,6},{3,4},{7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => {{1,6},{2,3,4,5},{7}} => {{1,3,5},{2,4,6},{7}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => {{1,5},{2,3,4,6},{7}} => {{1,3,6},{2,4,5},{7}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => {{1,4},{2,3,5,6},{7}} => {{1,3,4},{2,5,6},{7}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => {{1,3},{2,4,5,6},{7}} => {{1,4,5,6},{2,3},{7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}} => {{1,2,3,4,5,6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6,7}} => {{1},{2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6,7}} => {{1},{2,3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}} => {{1,3},{2},{4},{5},{6,7}} => {{1,3},{2},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6,7}} => {{1,2,3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6,7}} => {{1},{2},{3,4},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6,7}} => {{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}} => {{1},{2,4},{3},{5},{6,7}} => {{1},{2,4},{3},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}} => {{1,4},{2},{3},{5},{6,7}} => {{1,4},{2},{3},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}} => {{1,2,4},{3},{5},{6,7}} => {{1,2,4},{3},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6,7}} => {{1},{2,3,4},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}} => {{1,4},{2,3},{5},{6,7}} => {{1,3},{2,4},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}} => {{1,3},{2,4},{5},{6,7}} => {{1,4},{2,3},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6,7}} => {{1,2,3,4},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6,7}} => {{1},{2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6,7}} => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6,7}} => {{1},{2,3},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}} => {{1,3},{2},{4,5},{6,7}} => {{1,3},{2},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6,7}} => {{1,2,3},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6,7}} => {{1},{2},{3,5},{4},{6,7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6,7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}} => {{1},{2,5},{3},{4},{6,7}} => {{1},{2,5},{3},{4},{6,7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}} => {{1,5},{2},{3},{4},{6,7}} => {{1,5},{2},{3},{4},{6,7}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}} => {{1,2,5},{3},{4},{6,7}} => {{1,2,5},{3},{4},{6,7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}} => {{1},{2,3,5},{4},{6,7}} => {{1},{2,3,5},{4},{6,7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}} => {{1,5},{2,3},{4},{6,7}} => {{1,3},{2,5},{4},{6,7}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}} => {{1,3},{2,5},{4},{6,7}} => {{1,5},{2,3},{4},{6,7}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}} => {{1,2,3,5},{4},{6,7}} => {{1,2,3,5},{4},{6,7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6,7}} => {{1},{2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}} => {{1},{2,5},{3,4},{6,7}} => {{1},{2,4},{3,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}} => {{1,5},{2},{3,4},{6,7}} => {{1,4},{2},{3,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}} => {{1,2,5},{3,4},{6,7}} => {{1,2,4},{3,5},{6,7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}} => {{1},{2,4},{3,5},{6,7}} => {{1},{2,5},{3,4},{6,7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}} => {{1,5},{2,4},{3},{6,7}} => {{1,4},{2,5},{3},{6,7}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}} => {{1,4},{2},{3,5},{6,7}} => {{1,5},{2},{3,4},{6,7}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}} => {{1,2,4},{3,5},{6,7}} => {{1,2,5},{3,4},{6,7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6,7}} => {{1},{2,3,4,5},{6,7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}} => {{1,5},{2,3,4},{6,7}} => {{1,3,5},{2,4},{6,7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}} => {{1,4},{2,3,5},{6,7}} => {{1,3,4},{2,5},{6,7}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}} => {{1,3},{2,4,5},{6,7}} => {{1,4,5},{2,3},{6,7}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5},{6,7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,7},{6}} => {{1},{2},{3},{4},{5,7},{6}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}} => {{1,2},{3},{4},{5,7},{6}} => {{1,2},{3},{4},{5,7},{6}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}} => {{1},{2,3},{4},{5,7},{6}} => {{1},{2,3},{4},{5,7},{6}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}} => {{1,3},{2},{4},{5,7},{6}} => {{1,3},{2},{4},{5,7},{6}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}} => {{1,2,3},{4},{5,7},{6}} => {{1,2,3},{4},{5,7},{6}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}} => {{1},{2},{3,4},{5,7},{6}} => {{1},{2},{3,4},{5,7},{6}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}} => {{1,2},{3,4},{5,7},{6}} => {{1,2},{3,4},{5,7},{6}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}} => {{1},{2,4},{3},{5,7},{6}} => {{1},{2,4},{3},{5,7},{6}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}} => {{1,4},{2},{3},{5,7},{6}} => {{1,4},{2},{3},{5,7},{6}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}} => {{1,2,4},{3},{5,7},{6}} => {{1,2,4},{3},{5,7},{6}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}} => {{1},{2,3,4},{5,7},{6}} => {{1},{2,3,4},{5,7},{6}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}} => {{1,4},{2,3},{5,7},{6}} => {{1,3},{2,4},{5,7},{6}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}} => {{1,3},{2,4},{5,7},{6}} => {{1,4},{2,3},{5,7},{6}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}} => {{1,2,3,4},{5,7},{6}} => {{1,2,3,4},{5,7},{6}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5},{6}} => {{1},{2},{3},{4,7},{5},{6}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}} => {{1,2},{3},{4,7},{5},{6}} => {{1,2},{3},{4,7},{5},{6}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}} => {{1},{2,3},{4,7},{5},{6}} => {{1},{2,3},{4,7},{5},{6}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}} => {{1,3},{2},{4,7},{5},{6}} => {{1,3},{2},{4,7},{5},{6}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}} => {{1,2,3},{4,7},{5},{6}} => {{1,2,3},{4,7},{5},{6}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5},{6}} => {{1},{2},{3,7},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}} => {{1,2},{3,7},{4},{5},{6}} => {{1,2},{3,7},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5},{6}} => {{1},{2,7},{3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4},{5}} => {{1,2,7},{3},{4},{5},{6}} => {{1,2,7},{3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}} => {{1},{2,3,7},{4},{5},{6}} => {{1},{2,3,7},{4},{5},{6}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2},{3},{4},{5,6}} => {{1,7},{2,3},{4},{5},{6}} => {{1,3},{2,7},{4},{5},{6}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3},{4},{6}} => {{1,3},{2,7},{4},{5},{6}} => {{1,7},{2,3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3},{4}} => {{1,2,3,7},{4},{5},{6}} => {{1,2,3,7},{4},{5},{6}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}} => {{1},{2},{3,4,7},{5},{6}} => {{1},{2},{3,4,7},{5},{6}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}} => {{1,2},{3,4,7},{5},{6}} => {{1,2},{3,4,7},{5},{6}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}} => {{1},{2,7},{3,4},{5},{6}} => {{1},{2,4},{3,7},{5},{6}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2},{3},{4,5},{6}} => {{1,7},{2},{3,4},{5},{6}} => {{1,4},{2},{3,7},{5},{6}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4,5}} => {{1,2,7},{3,4},{5},{6}} => {{1,2,4},{3,7},{5},{6}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}} => {{1},{2,4},{3,7},{5},{6}} => {{1},{2,7},{3,4},{5},{6}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2},{3},{4,6},{5}} => {{1,7},{2,4},{3},{5},{6}} => {{1,4},{2,7},{3},{5},{6}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2},{3},{5},{6}} => {{1,4},{2},{3,7},{5},{6}} => {{1,7},{2},{3,4},{5},{6}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2},{3},{5}} => {{1,2,4},{3,7},{5},{6}} => {{1,2,7},{3,4},{5},{6}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}} => {{1},{2,3,4,7},{5},{6}} => {{1},{2,3,4,7},{5},{6}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2},{3},{4,5,6}} => {{1,7},{2,3,4},{5},{6}} => {{1,3,7},{2,4},{5},{6}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2},{3},{5,6}} => {{1,4},{2,3,7},{5},{6}} => {{1,3,4},{2,7},{5},{6}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2},{3},{6}} => {{1,3},{2,4,7},{5},{6}} => {{1,4,7},{2,3},{5},{6}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2},{3}} => {{1,2,3,4,7},{5},{6}} => {{1,2,3,4,7},{5},{6}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}} => {{1},{2},{3},{4,5,7},{6}} => {{1},{2},{3},{4,5,7},{6}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}} => {{1,2},{3},{4,5,7},{6}} => {{1,2},{3},{4,5,7},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}} => {{1},{2,3},{4,5,7},{6}} => {{1},{2,3},{4,5,7},{6}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}} => {{1,3},{2},{4,5,7},{6}} => {{1,3},{2},{4,5,7},{6}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}} => {{1,2,3},{4,5,7},{6}} => {{1,2,3},{4,5,7},{6}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}} => {{1},{2},{3,7},{4,5},{6}} => {{1},{2},{3,5},{4,7},{6}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}} => {{1,2},{3,7},{4,5},{6}} => {{1,2},{3,5},{4,7},{6}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}} => {{1},{2,7},{3},{4,5},{6}} => {{1},{2,5},{3},{4,7},{6}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2},{3,4},{5},{6}} => {{1,7},{2},{3},{4,5},{6}} => {{1,5},{2},{3},{4,7},{6}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3,4},{5}} => {{1,2,7},{3},{4,5},{6}} => {{1,2,5},{3},{4,7},{6}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}} => {{1},{2,3,7},{4,5},{6}} => {{1},{2,3,5},{4,7},{6}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2},{3,4},{5,6}} => {{1,7},{2,3},{4,5},{6}} => {{1,3},{2,5},{4,7},{6}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3,4},{6}} => {{1,3},{2,7},{4,5},{6}} => {{1,5},{2,3},{4,7},{6}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3,4}} => {{1,2,3,7},{4,5},{6}} => {{1,2,3,5},{4,7},{6}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}} => {{1},{2},{3,5},{4,7},{6}} => {{1},{2},{3,7},{4,5},{6}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}} => {{1,2},{3,5},{4,7},{6}} => {{1,2},{3,7},{4,5},{6}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}} => {{1},{2,7},{3,5},{4},{6}} => {{1},{2,5},{3,7},{4},{6}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2},{3,5},{4},{6}} => {{1,7},{2},{3,5},{4},{6}} => {{1,5},{2},{3,7},{4},{6}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,5},{4}} => {{1,2,7},{3,5},{4},{6}} => {{1,2,5},{3,7},{4},{6}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}} => {{1},{2,5},{3},{4,7},{6}} => {{1},{2,7},{3},{4,5},{6}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4},{5}} => {{1,7},{2,5},{3},{4},{6}} => {{1,5},{2,7},{3},{4},{6}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,3,7},{2},{4},{5},{6}} => {{1,5},{2},{3},{4,7},{6}} => {{1,7},{2},{3},{4,5},{6}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4},{5}} => {{1,2,5},{3},{4,7},{6}} => {{1,2,7},{3},{4,5},{6}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3,5},{4,7},{6}} => {{1},{2,3,7},{4,5},{6}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2},{3,5,6},{4}} => {{1,7},{2,3,5},{4},{6}} => {{1,3,7},{2,5},{4},{6}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,3,7},{2},{4},{5,6}} => {{1,5},{2,3},{4,7},{6}} => {{1,3},{2,7},{4,5},{6}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5,7},{2},{4},{6}} => {{1,3},{2,5},{4,7},{6}} => {{1,7},{2,3},{4,5},{6}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,3,5,6,7},{2},{4}} => {{1,2,3,5},{4,7},{6}} => {{1,2,3,7},{4,5},{6}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}} => {{1},{2},{3,4,5,7},{6}} => {{1},{2},{3,4,5,7},{6}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}} => {{1,2},{3,4,5,7},{6}} => {{1,2},{3,4,5,7},{6}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}} => {{1},{2,7},{3,4,5},{6}} => {{1},{2,4,7},{3,5},{6}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2},{3,4,5},{6}} => {{1,7},{2},{3,4,5},{6}} => {{1,4,7},{2},{3,5},{6}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,4,5}} => {{1,2,7},{3,4,5},{6}} => {{1,2,4,7},{3,5},{6}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}} => {{1},{2,5},{3,4,7},{6}} => {{1},{2,4,5},{3,7},{6}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4,5}} => {{1,7},{2,5},{3,4},{6}} => {{1,4},{2,5},{3,7},{6}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,3,7},{2},{4,5},{6}} => {{1,5},{2},{3,4,7},{6}} => {{1,4,5},{2},{3,7},{6}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4,5}} => {{1,2,5},{3,4,7},{6}} => {{1,2,4,5},{3,7},{6}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}} => {{1},{2,4},{3,5,7},{6}} => {{1},{2,5,7},{3,4},{6}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2},{3,4,6},{5}} => {{1,7},{2,4},{3,5},{6}} => {{1,5},{2,4},{3,7},{6}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5}} => {{1,5},{2,4},{3,7},{6}} => {{1,7},{2,4},{3,5},{6}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,3,4,7},{2},{5},{6}} => {{1,4},{2},{3,5,7},{6}} => {{1,5,7},{2},{3,4},{6}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,3,4,6,7},{2},{5}} => {{1,2,4},{3,5,7},{6}} => {{1,2,5,7},{3,4},{6}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,7},{6}} => {{1},{2,3,4,5,7},{6}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2},{3,4,5,6}} => {{1,7},{2,3,4,5},{6}} => {{1,3,5},{2,4,7},{6}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,3,7},{2},{4,5,6}} => {{1,5},{2,3,4,7},{6}} => {{1,3,7},{2,4,5},{6}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,3,4,7},{2},{5,6}} => {{1,4},{2,3,5,7},{6}} => {{1,3,4},{2,5,7},{6}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,3,4,5,7},{2},{6}} => {{1,3},{2,4,5,7},{6}} => {{1,4,5,7},{2,3},{6}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,3,4,5,6,7},{2}} => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5,7},{6}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6,7}} => {{1},{2},{3},{4},{5,6,7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6,7}} => {{1,2},{3},{4},{5,6,7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6,7}} => {{1},{2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}} => {{1,3},{2},{4},{5,6,7}} => {{1,3},{2},{4},{5,6,7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6,7}} => {{1},{2},{3,4},{5,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{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] => {{1,2,3},{4,6},{5},{7}} => {{1},{2,4},{3},{5,6,7}} => {{1},{2,4},{3},{5,6,7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}} => {{1,4},{2},{3},{5,6,7}} => {{1,4},{2},{3},{5,6,7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}} => {{1,2,4},{3},{5,6,7}} => {{1,2,4},{3},{5,6,7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6,7}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}} => {{1,4},{2,3},{5,6,7}} => {{1,3},{2,4},{5,6,7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}} => {{1,3},{2,4},{5,6,7}} => {{1,4},{2,3},{5,6,7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}} => {{1,2,3,4},{5,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5,6}} => {{1},{2},{3},{4,6},{5,7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}} => {{1,2},{3},{4,7},{5,6}} => {{1,2},{3},{4,6},{5,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}} => {{1},{2,3},{4,7},{5,6}} => {{1},{2,3},{4,6},{5,7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}} => {{1,3},{2},{4,7},{5,6}} => {{1,3},{2},{4,6},{5,7}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}} => {{1,2,3},{4,7},{5,6}} => {{1,2,3},{4,6},{5,7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5,6}} => {{1},{2},{3,6},{4},{5,7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}} => {{1,2},{3,7},{4},{5,6}} => {{1,2},{3,6},{4},{5,7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5,6}} => {{1},{2,6},{3},{4},{5,7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2,3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5,6}} => {{1,6},{2},{3},{4},{5,7}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3},{4},{5}} => {{1,2,7},{3},{4},{5,6}} => {{1,2,6},{3},{4},{5,7}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}} => {{1},{2,3,7},{4},{5,6}} => {{1},{2,3,6},{4},{5,7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2,3},{4},{5,6}} => {{1,7},{2,3},{4},{5,6}} => {{1,3},{2,6},{4},{5,7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3},{4},{6}} => {{1,3},{2,7},{4},{5,6}} => {{1,6},{2,3},{4},{5,7}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3},{4}} => {{1,2,3,7},{4},{5,6}} => {{1,2,3,6},{4},{5,7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}} => {{1},{2},{3,4,7},{5,6}} => {{1},{2},{3,4,6},{5,7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}} => {{1,2},{3,4,7},{5,6}} => {{1,2},{3,4,6},{5,7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}} => {{1},{2,7},{3,4},{5,6}} => {{1},{2,4},{3,6},{5,7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2,3},{4,5},{6}} => {{1,7},{2},{3,4},{5,6}} => {{1,4},{2},{3,6},{5,7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2,3},{4,5}} => {{1,2,7},{3,4},{5,6}} => {{1,2,4},{3,6},{5,7}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}} => {{1},{2,4},{3,7},{5,6}} => {{1},{2,6},{3,4},{5,7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2,3},{4,6},{5}} => {{1,7},{2,4},{3},{5,6}} => {{1,4},{2,6},{3},{5,7}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2,3},{5},{6}} => {{1,4},{2},{3,7},{5,6}} => {{1,6},{2},{3,4},{5,7}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2,3},{5}} => {{1,2,4},{3,7},{5,6}} => {{1,2,6},{3,4},{5,7}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}} => {{1},{2,3,4,7},{5,6}} => {{1},{2,3,4,6},{5,7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2,3},{4,5,6}} => {{1,7},{2,3,4},{5,6}} => {{1,3,6},{2,4},{5,7}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2,3},{5,6}} => {{1,4},{2,3,7},{5,6}} => {{1,3,4},{2,6},{5,7}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2,3},{6}} => {{1,3},{2,4,7},{5,6}} => {{1,4,6},{2,3},{5,7}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2,3}} => {{1,2,3,4,7},{5,6}} => {{1,2,3,4,6},{5,7}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}} => {{1},{2},{3},{4,6},{5,7}} => {{1},{2},{3},{4,7},{5,6}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}} => {{1,2},{3},{4,6},{5,7}} => {{1,2},{3},{4,7},{5,6}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}} => {{1},{2,3},{4,6},{5,7}} => {{1},{2,3},{4,7},{5,6}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}} => {{1,3},{2},{4,6},{5,7}} => {{1,3},{2},{4,7},{5,6}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}} => {{1,2,3},{4,6},{5,7}} => {{1,2,3},{4,7},{5,6}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}} => {{1},{2},{3,7},{4,6},{5}} => {{1},{2},{3,6},{4,7},{5}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}} => {{1,2},{3,7},{4,6},{5}} => {{1,2},{3,6},{4,7},{5}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}} => {{1},{2,7},{3},{4,6},{5}} => {{1},{2,6},{3},{4,7},{5}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2,4},{3},{5},{6}} => {{1,7},{2},{3},{4,6},{5}} => {{1,6},{2},{3},{4,7},{5}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,4},{3},{5}} => {{1,2,7},{3},{4,6},{5}} => {{1,2,6},{3},{4,7},{5}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}} => {{1},{2,3,7},{4,6},{5}} => {{1},{2,3,6},{4,7},{5}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2,4},{3},{5,6}} => {{1,7},{2,3},{4,6},{5}} => {{1,3},{2,6},{4,7},{5}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6}} => {{1,3},{2,7},{4,6},{5}} => {{1,6},{2,3},{4,7},{5}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,4},{3}} => {{1,2,3,7},{4,6},{5}} => {{1,2,3,6},{4,7},{5}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}} => {{1},{2},{3,6},{4},{5,7}} => {{1},{2},{3,7},{4},{5,6}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}} => {{1,2},{3,6},{4},{5,7}} => {{1,2},{3,7},{4},{5,6}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}} => {{1},{2,7},{3,6},{4},{5}} => {{1},{2,6},{3,7},{4},{5}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3},{4},{6}} => {{1,7},{2},{3,6},{4},{5}} => {{1,6},{2},{3,7},{4},{5}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3},{4}} => {{1,2,7},{3,6},{4},{5}} => {{1,2,6},{3,7},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}} => {{1},{2,6},{3},{4},{5,7}} => {{1},{2,7},{3},{4},{5,6}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4},{5}} => {{1,7},{2,6},{3},{4},{5}} => {{1,6},{2,7},{3},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3},{4},{5},{6}} => {{1,6},{2},{3},{4},{5,7}} => {{1,7},{2},{3},{4},{5,6}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4},{5}} => {{1,2,6},{3},{4},{5,7}} => {{1,2,7},{3},{4},{5,6}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}} => {{1},{2,3,6},{4},{5,7}} => {{1},{2,3,7},{4},{5,6}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3},{4}} => {{1,7},{2,3,6},{4},{5}} => {{1,3,7},{2,6},{4},{5}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3},{4},{5,6}} => {{1,6},{2,3},{4},{5,7}} => {{1,3},{2,7},{4},{5,6}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3},{4},{6}} => {{1,3},{2,6},{4},{5,7}} => {{1,7},{2,3},{4},{5,6}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3},{4}} => {{1,2,3,6},{4},{5,7}} => {{1,2,3,7},{4},{5,6}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}} => {{1},{2},{3,4,6},{5,7}} => {{1},{2},{3,4,7},{5,6}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}} => {{1,2},{3,4,6},{5,7}} => {{1,2},{3,4,7},{5,6}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}} => {{1},{2,7},{3,4,6},{5}} => {{1},{2,4,7},{3,6},{5}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2,4,5},{3},{6}} => {{1,7},{2},{3,4,6},{5}} => {{1,4,7},{2},{3,6},{5}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,4,5},{3}} => {{1,2,7},{3,4,6},{5}} => {{1,2,4,7},{3,6},{5}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}} => {{1},{2,6},{3,4},{5,7}} => {{1},{2,4},{3,7},{5,6}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4,5}} => {{1,7},{2,6},{3,4},{5}} => {{1,4},{2,6},{3,7},{5}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3},{4,5},{6}} => {{1,6},{2},{3,4},{5,7}} => {{1,4},{2},{3,7},{5,6}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4,5}} => {{1,2,6},{3,4},{5,7}} => {{1,2,4},{3,7},{5,6}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}} => {{1},{2,4},{3,6},{5,7}} => {{1},{2,7},{3,4},{5,6}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5}} => {{1,7},{2,4},{3,6},{5}} => {{1,6},{2,4},{3,7},{5}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3},{4,6},{5}} => {{1,6},{2,4},{3},{5,7}} => {{1,4},{2,7},{3},{5,6}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,4,7},{3},{5},{6}} => {{1,4},{2},{3,6},{5,7}} => {{1,7},{2},{3,4},{5,6}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,4,6,7},{3},{5}} => {{1,2,4},{3,6},{5,7}} => {{1,2,7},{3,4},{5,6}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6},{5,7}} => {{1},{2,3,4,7},{5,6}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2,4,5,6},{3}} => {{1,7},{2,3,4,6},{5}} => {{1,3,6},{2,4,7},{5}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3},{4,5,6}} => {{1,6},{2,3,4},{5,7}} => {{1,3,7},{2,4},{5,6}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,4,7},{3},{5,6}} => {{1,4},{2,3,6},{5,7}} => {{1,3,4},{2,7},{5,6}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,4,5,7},{3},{6}} => {{1,3},{2,4,6},{5,7}} => {{1,4,7},{2,3},{5,6}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,4,5,6,7},{3}} => {{1,2,3,4,6},{5,7}} => {{1,2,3,4,7},{5,6}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}} => {{1},{2},{3},{4,5,6,7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6,7}} => {{1,2},{3},{4,5,6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6,7}} => {{1},{2,3},{4,5,6,7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}} => {{1,3},{2},{4,5,6,7}} => {{1,3},{2},{4,5,6,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}} => {{1},{2},{3,7},{4,5,6}} => {{1},{2},{3,5,7},{4,6}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}} => {{1,2},{3,7},{4,5,6}} => {{1,2},{3,5,7},{4,6}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}} => {{1},{2,7},{3},{4,5,6}} => {{1},{2,5,7},{3},{4,6}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,7},{2,3,4},{5},{6}} => {{1,7},{2},{3},{4,5,6}} => {{1,5,7},{2},{3},{4,6}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3,4},{5}} => {{1,2,7},{3},{4,5,6}} => {{1,2,5,7},{3},{4,6}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}} => {{1},{2,3,7},{4,5,6}} => {{1},{2,3,5,7},{4,6}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,7},{2,3,4},{5,6}} => {{1,7},{2,3},{4,5,6}} => {{1,3},{2,5,7},{4,6}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3,4},{6}} => {{1,3},{2,7},{4,5,6}} => {{1,5,7},{2,3},{4,6}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3,4}} => {{1,2,3,7},{4,5,6}} => {{1,2,3,5,7},{4,6}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}} => {{1},{2},{3,6},{4,5,7}} => {{1},{2},{3,5,6},{4,7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}} => {{1,2},{3,6},{4,5,7}} => {{1,2},{3,5,6},{4,7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}} => {{1},{2,7},{3,6},{4,5}} => {{1},{2,5},{3,6},{4,7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3,4},{6}} => {{1,7},{2},{3,6},{4,5}} => {{1,5},{2},{3,6},{4,7}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3,4}} => {{1,2,7},{3,6},{4,5}} => {{1,2,5},{3,6},{4,7}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}} => {{1},{2,6},{3},{4,5,7}} => {{1},{2,5,6},{3},{4,7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4},{5}} => {{1,7},{2,6},{3},{4,5}} => {{1,5},{2,6},{3},{4,7}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3,4},{5},{6}} => {{1,6},{2},{3},{4,5,7}} => {{1,5,6},{2},{3},{4,7}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4},{5}} => {{1,2,6},{3},{4,5,7}} => {{1,2,5,6},{3},{4,7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => {{1},{2,3,6},{4,5,7}} => {{1},{2,3,5,6},{4,7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3,4}} => {{1,7},{2,3,6},{4,5}} => {{1,3,6},{2,5},{4,7}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3,4},{5,6}} => {{1,6},{2,3},{4,5,7}} => {{1,3},{2,5,6},{4,7}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3,4},{6}} => {{1,3},{2,6},{4,5,7}} => {{1,5,6},{2,3},{4,7}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3,4}} => {{1,2,3,6},{4,5,7}} => {{1,2,3,5,6},{4,7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}} => {{1},{2},{3,5},{4,6,7}} => {{1},{2},{3,6,7},{4,5}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}} => {{1,2},{3,5},{4,6,7}} => {{1,2},{3,6,7},{4,5}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}} => {{1},{2,7},{3,5},{4,6}} => {{1},{2,6},{3,5},{4,7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,7},{2,3,5},{4},{6}} => {{1,7},{2},{3,5},{4,6}} => {{1,6},{2},{3,5},{4,7}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,5},{4}} => {{1,2,7},{3,5},{4,6}} => {{1,2,6},{3,5},{4,7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => {{1},{2,6},{3,5},{4,7}} => {{1},{2,7},{3,5},{4,6}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4}} => {{1,7},{2,6},{3,5},{4}} => {{1,5},{2,6},{3,7},{4}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3,5},{4},{6}} => {{1,6},{2},{3,5},{4,7}} => {{1,7},{2},{3,5},{4,6}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,5},{4}} => {{1,2,6},{3,5},{4,7}} => {{1,2,7},{3,5},{4,6}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => {{1},{2,5},{3},{4,6,7}} => {{1},{2,6,7},{3},{4,5}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4},{5}} => {{1,7},{2,5},{3},{4,6}} => {{1,6},{2,5},{3},{4,7}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4},{5}} => {{1,6},{2,5},{3},{4,7}} => {{1,7},{2,5},{3},{4,6}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4},{5},{6}} => {{1,5},{2},{3},{4,6,7}} => {{1,6,7},{2},{3},{4,5}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4},{5}} => {{1,2,5},{3},{4,6,7}} => {{1,2,6,7},{3},{4,5}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => {{1},{2,3,5},{4,6,7}} => {{1},{2,3,6,7},{4,5}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,7},{2,3,5,6},{4}} => {{1,7},{2,3,5},{4,6}} => {{1,3,5},{2,6},{4,7}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3,5,6},{4}} => {{1,6},{2,3,5},{4,7}} => {{1,3,5},{2,7},{4,6}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4},{5,6}} => {{1,5},{2,3},{4,6,7}} => {{1,3},{2,6,7},{4,5}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,5,7},{4},{6}} => {{1,3},{2,5},{4,6,7}} => {{1,6,7},{2,3},{4,5}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5},{4,6,7}} => {{1,2,3,6,7},{4,5}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}} => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}} => {{1,2},{3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => {{1},{2,7},{3,4,5,6}} => {{1},{2,4,6},{3,5,7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,7},{2,3,4,5},{6}} => {{1,7},{2},{3,4,5,6}} => {{1,4,6},{2},{3,5,7}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}} => {{1,2,4,6},{3,5,7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => {{1},{2,6},{3,4,5,7}} => {{1},{2,4,7},{3,5,6}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4,5}} => {{1,7},{2,6},{3,4,5}} => {{1,4,7},{2,5},{3,6}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,7},{3,4,5},{6}} => {{1,6},{2},{3,4,5,7}} => {{1,4,7},{2},{3,5,6}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4,5}} => {{1,2,6},{3,4,5,7}} => {{1,2,4,7},{3,5,6}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => {{1},{2,5},{3,4,6,7}} => {{1},{2,4,5},{3,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4,5}} => {{1,7},{2,5},{3,4,6}} => {{1,4,7},{2,6},{3,5}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4,5}} => {{1,6},{2,5},{3,4,7}} => {{1,4,6},{2,7},{3,5}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4,5},{6}} => {{1,5},{2},{3,4,6,7}} => {{1,4,5},{2},{3,6,7}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4,5}} => {{1,2,5},{3,4,6,7}} => {{1,2,4,5},{3,6,7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => {{1},{2,4},{3,5,6,7}} => {{1},{2,5,6,7},{3,4}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,7},{2,3,4,6},{5}} => {{1,7},{2,4},{3,5,6}} => {{1,5,7},{2,4},{3,6}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,7},{3,4,6},{5}} => {{1,6},{2,4},{3,5,7}} => {{1,5,6},{2,4},{3,7}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4,6},{5}} => {{1,5},{2,4},{3,6,7}} => {{1,6,7},{2,4},{3,5}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5},{6}} => {{1,4},{2},{3,5,6,7}} => {{1,5,6,7},{2},{3,4}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,6,7},{5}} => {{1,2,4},{3,5,6,7}} => {{1,2,5,6,7},{3,4}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}} => {{1,3,5,7},{2,4,6}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,7},{3,4,5,6}} => {{1,6},{2,3,4,5,7}} => {{1,3,5,6},{2,4,7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,7},{4,5,6}} => {{1,5},{2,3,4,6,7}} => {{1,3,6,7},{2,4,5}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5,6}} => {{1,4},{2,3,5,6,7}} => {{1,3,4},{2,5,6,7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,7},{6}} => {{1,3},{2,4,5,6,7}} => {{1,4,5,6,7},{2,3}}
[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] => {{1},{2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6},{7},{8}} => {{1,2},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8}} => {{1},{2,3},{4},{5},{6},{7},{8}} => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6},{7},{8}} => {{1,3},{2},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6},{7},{8}} => {{1,2,3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}} => {{1,2},{3,4},{5},{6},{7},{8}} => {{1,2},{3,4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5,7},{6},{8}} => {{1},{2,4},{3},{5},{6},{7},{8}} => {{1},{2,4},{3},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6},{7}} => {{1,4},{2},{3},{5},{6},{7},{8}} => {{1,4},{2},{3},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5,7,8},{6}} => {{1,2,4},{3},{5},{6},{7},{8}} => {{1,2,4},{3},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8}} => {{1},{2,3,4},{5},{6},{7},{8}} => {{1},{2,3,4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6,7}} => {{1,4},{2,3},{5},{6},{7},{8}} => {{1,3},{2,4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5,6,8},{7}} => {{1,3},{2,4},{5},{6},{7},{8}} => {{1,4},{2,3},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6},{7},{8}} => {{1,2,3,4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}} => {{1,2},{3},{4,5},{6},{7},{8}} => {{1,2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6},{7},{8}} => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,2,3},{4,5},{6},{7},{8}} => {{1,2,3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5},{6},{7}} => {{1,5},{2},{3},{4},{6},{7},{8}} => {{1,5},{2},{3},{4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4,7,8},{5},{6}} => {{1,2,5},{3},{4},{6},{7},{8}} => {{1,2,5},{3},{4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3},{4,6,7,8},{5}} => {{1,2,3,5},{4},{6},{7},{8}} => {{1,2,3,5},{4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6},{7},{8}} => {{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5,6},{7}} => {{1,5},{2},{3,4},{6},{7},{8}} => {{1,4},{2},{3,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3},{4,7,8},{5,6}} => {{1,2,5},{3,4},{6},{7},{8}} => {{1,2,4},{3,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6},{7},{8}} => {{1,4},{2,5},{3},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4,5,8},{6},{7}} => {{1,4},{2},{3,5},{6},{7},{8}} => {{1,5},{2},{3,4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3},{4,5,7,8},{6}} => {{1,2,4},{3,5},{6},{7},{8}} => {{1,2,5},{3,4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6},{7},{8}} => {{1},{2,3,4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,6,7}} => {{1,5},{2,3,4},{6},{7},{8}} => {{1,3,5},{2,4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}} => {{1,2,3,4,5},{6},{7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,6},{7},{8}} => {{1,2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7},{8}} => {{1,2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,4},{5,8},{6},{7}} => {{1,4},{2},{3},{5,6},{7},{8}} => {{1,4},{2},{3},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6},{7},{8}} => {{1,3},{2,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7},{8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,5},{4},{6,7,8}} => {{1,2,3},{4,6},{5},{7},{8}} => {{1,2,3},{4,6},{5},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4},{5},{6},{7}} => {{1,6},{2},{3},{4},{5},{7},{8}} => {{1,6},{2},{3},{4},{5},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5},{6}} => {{1,2,6},{3},{4},{5},{7},{8}} => {{1,2,6},{3},{4},{5},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5,6}} => {{1,2,6},{3,4},{5},{7},{8}} => {{1,2,4},{3,6},{5},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,5,8},{4},{6},{7}} => {{1,4},{2},{3,6},{5},{7},{8}} => {{1,6},{2},{3,4},{5},{7},{8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4},{5,6,7}} => {{1,6},{2,3,4},{5},{7},{8}} => {{1,3,6},{2,4},{5},{7},{8}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,5,8},{4},{6,7}} => {{1,4},{2,3,6},{5},{7},{8}} => {{1,3,4},{2,6},{5},{7},{8}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,5,6,7,8},{4}} => {{1,2,3,4,6},{5},{7},{8}} => {{1,2,3,4,6},{5},{7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6},{7},{8}} => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2},{3,4,5},{6,7,8}} => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5},{6},{7}} => {{1,6},{2},{3},{4,5},{7},{8}} => {{1,5},{2},{3},{4,6},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2},{3,8},{4,5},{6,7}} => {{1,6},{2,3},{4,5},{7},{8}} => {{1,3},{2,5},{4,6},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2},{3,6,7,8},{4,5}} => {{1,2,3,6},{4,5},{7},{8}} => {{1,2,3,5},{4,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,6},{5},{7}} => {{1,6},{2},{3,5},{4},{7},{8}} => {{1,5},{2},{3,6},{4},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,6},{5}} => {{1,2,6},{3,5},{4},{7},{8}} => {{1,2,5},{3,6},{4},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5},{6}} => {{1,6},{2,5},{3},{4},{7},{8}} => {{1,5},{2,6},{3},{4},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,8},{5},{6},{7}} => {{1,5},{2},{3},{4,6},{7},{8}} => {{1,6},{2},{3},{4,5},{7},{8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4,6,7},{5}} => {{1,6},{2,3,5},{4},{7},{8}} => {{1,3,6},{2,5},{4},{7},{8}}
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5},{6,7}} => {{1,5},{2,3},{4,6},{7},{8}} => {{1,3},{2,6},{4,5},{7},{8}}
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,6,8},{5},{7}} => {{1,3},{2,5},{4,6},{7},{8}} => {{1,6},{2,3},{4,5},{7},{8}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,6,7,8},{5}} => {{1,2,3,5},{4,6},{7},{8}} => {{1,2,3,6},{4,5},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2},{3,7},{4,5,6},{8}} => {{1},{2,6},{3,4,5},{7},{8}} => {{1},{2,4,6},{3,5},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5,6},{7}} => {{1,6},{2},{3,4,5},{7},{8}} => {{1,4,6},{2},{3,5},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,5,6}} => {{1,2,6},{3,4,5},{7},{8}} => {{1,2,4,6},{3,5},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5,6}} => {{1,6},{2,5},{3,4},{7},{8}} => {{1,4},{2,5},{3,6},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2},{3,4,7,8},{5,6}} => {{1,2,5},{3,4,6},{7},{8}} => {{1,2,4,5},{3,6},{7},{8}}
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5,7},{6}} => {{1,5},{2,4},{3,6},{7},{8}} => {{1,6},{2,4},{3,5},{7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2},{3,8},{4,5,6,7}} => {{1,6},{2,3,4,5},{7},{8}} => {{1,3,5},{2,4,6},{7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5,6,7}} => {{1,5},{2,3,4,6},{7},{8}} => {{1,3,6},{2,4,5},{7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6,7}} => {{1,4},{2,3,5,6},{7},{8}} => {{1,3,4},{2,5,6},{7},{8}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}} => {{1,2,3,4,5,6},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,7},{8}} => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6,7},{8}} => {{1,2},{3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6,7},{8}} => {{1},{2,3},{4},{5},{6,7},{8}} => {{1},{2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4},{5,8},{6,7}} => {{1,4},{2,3},{5},{6,7},{8}} => {{1,3},{2,4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7},{8}} => {{1,2,3,4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6,7},{8}} => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5},{6,8},{7}} => {{1,3},{2},{4,5},{6,7},{8}} => {{1,3},{2},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,3},{4,6,7},{5},{8}} => {{1},{2,3,5},{4},{6,7},{8}} => {{1},{2,3,5},{4},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,3},{4,8},{5},{6,7}} => {{1,5},{2,3},{4},{6,7},{8}} => {{1,3},{2,5},{4},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,3},{4,6,8},{5},{7}} => {{1,3},{2,5},{4},{6,7},{8}} => {{1,5},{2,3},{4},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,3},{4,6,7,8},{5}} => {{1,2,3,5},{4},{6,7},{8}} => {{1,2,3,5},{4},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,3},{4,7},{5,6},{8}} => {{1},{2,5},{3,4},{6,7},{8}} => {{1},{2,4},{3,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,3},{4,8},{5,6},{7}} => {{1,5},{2},{3,4},{6,7},{8}} => {{1,4},{2},{3,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,3},{4,7,8},{5,6}} => {{1,2,5},{3,4},{6,7},{8}} => {{1,2,4},{3,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3},{4,5,7},{6},{8}} => {{1},{2,4},{3,5},{6,7},{8}} => {{1},{2,5},{3,4},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6,7},{8}} => {{1,4},{2,5},{3},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3},{4,5,7,8},{6}} => {{1,2,4},{3,5},{6,7},{8}} => {{1,2,5},{3,4},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7},{8}} => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6,7}} => {{1,4},{2,3,5},{6,7},{8}} => {{1,3,4},{2,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3},{4,5,6,8},{7}} => {{1,3},{2,4,5},{6,7},{8}} => {{1,4,5},{2,3},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7},{8}} => {{1,2,3,4,5},{6,7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,7},{6},{8}} => {{1},{2},{3},{4},{5,7},{6},{8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5},{6,8},{7}} => {{1,3},{2},{4},{5,7},{6},{8}} => {{1,3},{2},{4},{5,7},{6},{8}}
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5},{6,7,8}} => {{1,2,3},{4},{5,7},{6},{8}} => {{1,2,3},{4},{5,7},{6},{8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6},{7,8}} => {{1,2},{3,4},{5,7},{6},{8}} => {{1,2},{3,4},{5,7},{6},{8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5,7},{6},{8}} => {{1},{2,4},{3},{5,7},{6},{8}} => {{1},{2,4},{3},{5,7},{6},{8}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,4},{3},{5,7,8},{6}} => {{1,2,4},{3},{5,7},{6},{8}} => {{1,2,4},{3},{5,7},{6},{8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,4},{3},{5,8},{6,7}} => {{1,4},{2,3},{5,7},{6},{8}} => {{1,3},{2,4},{5,7},{6},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3},{4},{6,8},{7}} => {{1,3},{2},{4,7},{5},{6},{8}} => {{1,3},{2},{4,7},{5},{6},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,7},{3},{4},{5},{6},{8}} => {{1},{2,7},{3},{4},{5},{6},{8}} => {{1},{2,7},{3},{4},{5},{6},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3},{4},{5},{6},{7}} => {{1,7},{2},{3},{4},{5},{6},{8}} => {{1,7},{2},{3},{4},{5},{6},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4},{5},{6}} => {{1,2,7},{3},{4},{5},{6},{8}} => {{1,2,7},{3},{4},{5},{6},{8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4},{5,6,7}} => {{1,7},{2,3,4},{5},{6},{8}} => {{1,3,7},{2,4},{5},{6},{8}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3},{4}} => {{1,2,3,4,7},{5},{6},{8}} => {{1,2,3,4,7},{5},{6},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,4,5},{3},{6,7},{8}} => {{1},{2,3},{4,5,7},{6},{8}} => {{1},{2,3},{4,5,7},{6},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,4,5},{3},{6,8},{7}} => {{1,3},{2},{4,5,7},{6},{8}} => {{1,3},{2},{4,5,7},{6},{8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3},{4,5},{7,8}} => {{1,2},{3,7},{4,5},{6},{8}} => {{1,2},{3,5},{4,7},{6},{8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3},{4,5},{6,7}} => {{1,7},{2,3},{4,5},{6},{8}} => {{1,3},{2,5},{4,7},{6},{8}}
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3},{4,5}} => {{1,2,3,7},{4,5},{6},{8}} => {{1,2,3,5},{4,7},{6},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,4,6,7},{3},{5},{8}} => {{1},{2,3,5},{4,7},{6},{8}} => {{1},{2,3,7},{4,5},{6},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4,6,7},{5}} => {{1,7},{2,3,5},{4},{6},{8}} => {{1,3,7},{2,5},{4},{6},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5},{6,7}} => {{1,5},{2,3},{4,7},{6},{8}} => {{1,3},{2,7},{4,5},{6},{8}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,4,6,8},{3},{5},{7}} => {{1,3},{2,5},{4,7},{6},{8}} => {{1,7},{2,3},{4,5},{6},{8}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,4,6,7,8},{3},{5}} => {{1,2,3,5},{4,7},{6},{8}} => {{1,2,3,7},{4,5},{6},{8}}
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,5,6}} => {{1,2,7},{3,4,5},{6},{8}} => {{1,2,4,7},{3,5},{6},{8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4,7},{5,6}} => {{1,7},{2,5},{3,4},{6},{8}} => {{1,4},{2,5},{3,7},{6},{8}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,4,7,8},{3},{5,6}} => {{1,2,5},{3,4,7},{6},{8}} => {{1,2,4,5},{3,7},{6},{8}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,4,5,7},{3},{6},{8}} => {{1},{2,4},{3,5,7},{6},{8}} => {{1},{2,5,7},{3,4},{6},{8}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,7},{6}} => {{1,5},{2,4},{3,7},{6},{8}} => {{1,7},{2,4},{3,5},{6},{8}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,4,5,7,8},{3},{6}} => {{1,2,4},{3,5,7},{6},{8}} => {{1,2,5,7},{3,4},{6},{8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,4,5,6,7},{3},{8}} => {{1},{2,3,4,5,7},{6},{8}} => {{1},{2,3,4,5,7},{6},{8}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6,7}} => {{1,5},{2,3,4,7},{6},{8}} => {{1,3,7},{2,4,5},{6},{8}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,4,5,8},{3},{6,7}} => {{1,4},{2,3,5,7},{6},{8}} => {{1,3,4},{2,5,7},{6},{8}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,4,5,6,8},{3},{7}} => {{1,3},{2,4,5,7},{6},{8}} => {{1,4,5,7},{2,3},{6},{8}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7},{6},{8}} => {{1,2,3,4,5,7},{6},{8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7},{8}} => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6,7},{8}} => {{1,2},{3,4},{5,6,7},{8}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3,4},{5,7,8},{6}} => {{1,2,4},{3},{5,6,7},{8}} => {{1,2,4},{3},{5,6,7},{8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6,7},{8}} => {{1,3},{2,4},{5,6,7},{8}}
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3,4},{5,6,8},{7}} => {{1,3},{2,4},{5,6,7},{8}} => {{1,4},{2,3},{5,6,7},{8}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3,4},{6,7},{8}} => {{1},{2,3},{4,7},{5,6},{8}} => {{1},{2,3},{4,6},{5,7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3,4},{6,8},{7}} => {{1,3},{2},{4,7},{5,6},{8}} => {{1,3},{2},{4,6},{5,7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5},{6},{7}} => {{1,7},{2},{3},{4},{5,6},{8}} => {{1,6},{2},{3},{4},{5,7},{8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,4},{5},{8}} => {{1},{2,3,7},{4},{5,6},{8}} => {{1},{2,3,6},{4},{5,7},{8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,4},{5},{6,7}} => {{1,7},{2,3},{4},{5,6},{8}} => {{1,3},{2,6},{4},{5,7},{8}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,4},{5}} => {{1,2,3,7},{4},{5,6},{8}} => {{1,2,3,6},{4},{5,7},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,4},{5,6},{8}} => {{1},{2,7},{3,4},{5,6},{8}} => {{1},{2,4},{3,6},{5,7},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5,6},{7}} => {{1,7},{2},{3,4},{5,6},{8}} => {{1,4},{2},{3,6},{5,7},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4},{5,6}} => {{1,2,7},{3,4},{5,6},{8}} => {{1,2,4},{3,6},{5,7},{8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,4},{5,7},{6}} => {{1,7},{2,4},{3},{5,6},{8}} => {{1,4},{2,6},{3},{5,7},{8}}
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1},{2,5,7,8},{3,4},{6}} => {{1,2,4},{3,7},{5,6},{8}} => {{1,2,6},{3,4},{5,7},{8}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,4},{5,6,7}} => {{1,7},{2,3,4},{5,6},{8}} => {{1,3,6},{2,4},{5,7},{8}}
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1},{2,5,8},{3,4},{6,7}} => {{1,4},{2,3,7},{5,6},{8}} => {{1,3,4},{2,6},{5,7},{8}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3,4}} => {{1,2,3,4,7},{5,6},{8}} => {{1,2,3,4,6},{5,7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,5},{4},{6,7},{8}} => {{1},{2,3},{4,6},{5,7},{8}} => {{1},{2,3},{4,7},{5,6},{8}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,5},{4},{6,7,8}} => {{1,2,3},{4,6},{5,7},{8}} => {{1,2,3},{4,7},{5,6},{8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,5},{4},{7,8}} => {{1,2},{3,7},{4,6},{5},{8}} => {{1,2},{3,6},{4,7},{5},{8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,5},{4},{6},{7}} => {{1,7},{2},{3},{4,6},{5},{8}} => {{1,6},{2},{3},{4,7},{5},{8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,5},{4},{8}} => {{1},{2,3,7},{4,6},{5},{8}} => {{1},{2,3,6},{4,7},{5},{8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,5},{4},{6,7}} => {{1,7},{2,3},{4,6},{5},{8}} => {{1,3},{2,6},{4,7},{5},{8}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,5},{4},{7}} => {{1,3},{2,7},{4,6},{5},{8}} => {{1,6},{2,3},{4,7},{5},{8}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,5},{4}} => {{1,2,3,7},{4,6},{5},{8}} => {{1,2,3,6},{4,7},{5},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5},{6}} => {{1,7},{2,6},{3},{4},{5},{8}} => {{1,6},{2,7},{3},{4},{5},{8}}
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4},{5},{6}} => {{1,2,6},{3},{4},{5,7},{8}} => {{1,2,7},{3},{4},{5,6},{8}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,6,7,8},{4},{5}} => {{1,2,3,6},{4},{5,7},{8}} => {{1,2,3,7},{4},{5,6},{8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,5,6},{4},{8}} => {{1},{2,7},{3,4,6},{5},{8}} => {{1},{2,4,7},{3,6},{5},{8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,5,6},{4},{7}} => {{1,7},{2},{3,4,6},{5},{8}} => {{1,4,7},{2},{3,6},{5},{8}}
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,5,6},{4}} => {{1,2,7},{3,4,6},{5},{8}} => {{1,2,4,7},{3,6},{5},{8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5,6}} => {{1,7},{2,6},{3,4},{5},{8}} => {{1,4},{2,6},{3,7},{5},{8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,5,7},{4},{6}} => {{1,7},{2,4},{3,6},{5},{8}} => {{1,6},{2,4},{3,7},{5},{8}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6},{7}} => {{1,4},{2},{3,6},{5,7},{8}} => {{1,7},{2},{3,4},{5,6},{8}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,5,7,8},{4},{6}} => {{1,2,4},{3,6},{5,7},{8}} => {{1,2,7},{3,4},{5,6},{8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,5,6,7},{4},{8}} => {{1},{2,3,4,6},{5,7},{8}} => {{1},{2,3,4,7},{5,6},{8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,5,6,7},{4}} => {{1,7},{2,3,4,6},{5},{8}} => {{1,3,6},{2,4,7},{5},{8}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5,6,7}} => {{1,6},{2,3,4},{5,7},{8}} => {{1,3,7},{2,4},{5,6},{8}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6,7}} => {{1,4},{2,3,6},{5,7},{8}} => {{1,3,4},{2,7},{5,6},{8}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,5,6,8},{4},{7}} => {{1,3},{2,4,6},{5,7},{8}} => {{1,4,7},{2,3},{5,6},{8}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8},{4}} => {{1,2,3,4,6},{5,7},{8}} => {{1,2,3,4,7},{5,6},{8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7},{8}} => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6,7},{8}} => {{1,2},{3},{4,5,6,7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7},{8}} => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1},{2,6},{3,4,5},{7},{8}} => {{1},{2},{3,7},{4,5,6},{8}} => {{1},{2},{3,5,7},{4,6},{8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4,5},{6},{7}} => {{1,7},{2},{3},{4,5,6},{8}} => {{1,5,7},{2},{3},{4,6},{8}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,4,5},{6,7}} => {{1,7},{2,3},{4,5,6},{8}} => {{1,3},{2,5,7},{4,6},{8}}
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4,5},{7}} => {{1,3},{2,7},{4,5,6},{8}} => {{1,5,7},{2,3},{4,6},{8}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,4,5}} => {{1,2,3,7},{4,5,6},{8}} => {{1,2,3,5,7},{4,6},{8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1},{2,3,6},{4,5},{7,8}} => {{1,2},{3,6},{4,5,7},{8}} => {{1,2},{3,5,6},{4,7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,6},{4,5},{8}} => {{1},{2,7},{3,6},{4,5},{8}} => {{1},{2,5},{3,6},{4,7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,6},{4,5},{7}} => {{1,7},{2},{3,6},{4,5},{8}} => {{1,5},{2},{3,6},{4,7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,6},{4,5}} => {{1,2,7},{3,6},{4,5},{8}} => {{1,2,5},{3,6},{4,7},{8}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5},{6}} => {{1,7},{2,6},{3},{4,5},{8}} => {{1,5},{2,6},{3},{4,7},{8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4,5},{8}} => {{1},{2,3,6},{4,5,7},{8}} => {{1},{2,3,5,6},{4,7},{8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,6,7},{4,5}} => {{1,7},{2,3,6},{4,5},{8}} => {{1,3,6},{2,5},{4,7},{8}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6,7}} => {{1,6},{2,3},{4,5,7},{8}} => {{1,3},{2,5,6},{4,7},{8}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4,5},{7}} => {{1,3},{2,6},{4,5,7},{8}} => {{1,5,6},{2,3},{4,7},{8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,6},{5},{7,8}} => {{1,2},{3,5},{4,6,7},{8}} => {{1,2},{3,6,7},{4,5},{8}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,6},{5}} => {{1,2,7},{3,5},{4,6},{8}} => {{1,2,6},{3,5},{4,7},{8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,6},{5}} => {{1,7},{2,6},{3,5},{4},{8}} => {{1,5},{2,6},{3,7},{4},{8}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,6},{5}} => {{1,2,6},{3,5},{4,7},{8}} => {{1,2,7},{3,5},{4,6},{8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5},{6}} => {{1,7},{2,5},{3},{4,6},{8}} => {{1,6},{2,5},{3},{4,7},{8}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,7,8},{5},{6}} => {{1,2,5},{3},{4,6,7},{8}} => {{1,2,6,7},{3},{4,5},{8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,6,7},{5}} => {{1,7},{2,3,5},{4,6},{8}} => {{1,3,5},{2,6},{4,7},{8}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,6,7},{5}} => {{1,6},{2,3,5},{4,7},{8}} => {{1,3,5},{2,7},{4,6},{8}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,6,8},{5},{7}} => {{1,3},{2,5},{4,6,7},{8}} => {{1,6,7},{2,3},{4,5},{8}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8},{5}} => {{1,2,3,5},{4,6,7},{8}} => {{1,2,3,6,7},{4,5},{8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4,5,6},{8}} => {{1},{2,6},{3,4,5,7},{8}} => {{1},{2,4,7},{3,5,6},{8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5,6}} => {{1,7},{2,6},{3,4,5},{8}} => {{1,4,7},{2,5},{3,6},{8}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5,6},{7}} => {{1,6},{2},{3,4,5,7},{8}} => {{1,4,7},{2},{3,5,6},{8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5,6}} => {{1,7},{2,5},{3,4,6},{8}} => {{1,4,7},{2,6},{3,5},{8}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,7},{5,6}} => {{1,6},{2,5},{3,4,7},{8}} => {{1,4,6},{2,7},{3,5},{8}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6},{7}} => {{1,5},{2},{3,4,6,7},{8}} => {{1,4,5},{2},{3,6,7},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,7},{6},{8}} => {{1},{2,4},{3,5,6,7},{8}} => {{1},{2,5,6,7},{3,4},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,7},{6}} => {{1,7},{2,4},{3,5,6},{8}} => {{1,5,7},{2,4},{3,6},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,5,7},{6}} => {{1,6},{2,4},{3,5,7},{8}} => {{1,5,6},{2,4},{3,7},{8}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,7},{6}} => {{1,5},{2,4},{3,6,7},{8}} => {{1,6,7},{2,4},{3,5},{8}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}} => {{1,4},{2},{3,5,6,7},{8}} => {{1,5,6,7},{2},{3,4},{8}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8},{6}} => {{1,2,4},{3,5,6,7},{8}} => {{1,2,5,6,7},{3,4},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,6,7}} => {{1,7},{2,3,4,5,6},{8}} => {{1,3,5,7},{2,4,6},{8}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}} => {{1,5},{2,3,4,6,7},{8}} => {{1,3,6,7},{2,4,5},{8}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}} => {{1,4},{2,3,5,6,7},{8}} => {{1,3,4},{2,5,6,7},{8}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}} => {{1,3},{2,4,5,6,7},{8}} => {{1,4,5,6,7},{2,3},{8}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}} => {{1,2,3,4,5,6,7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7,8}} => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6,7},{8}} => {{1},{2,3},{4},{5},{6},{7,8}} => {{1},{2,3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6},{7,8}} => {{1,3},{2},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6},{7,8}} => {{1,2,3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4},{5,6},{7},{8}} => {{1},{2},{3,4},{5},{6},{7,8}} => {{1},{2},{3,4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4},{5,8},{6,7}} => {{1,4},{2,3},{5},{6},{7,8}} => {{1,3},{2,4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6},{7,8}} => {{1,2,3,4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6},{7,8}} => {{1},{2},{3},{4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3},{4,8},{5},{6},{7}} => {{1,5},{2},{3},{4},{6},{7,8}} => {{1,5},{2},{3},{4},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3},{4,6,7,8},{5}} => {{1,2,3,5},{4},{6},{7,8}} => {{1,2,3,5},{4},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6},{7,8}} => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3},{4,8},{5,6},{7}} => {{1,5},{2},{3,4},{6},{7,8}} => {{1,4},{2},{3,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6},{7,8}} => {{1,4},{2,5},{3},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6},{7,8}} => {{1},{2,3,4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6,7}} => {{1,4},{2,3,5},{6},{7,8}} => {{1,3,4},{2,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3},{4,5,6,8},{7}} => {{1,3},{2,4,5},{6},{7,8}} => {{1,4,5},{2,3},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7,8}} => {{1,2,3,4,5},{6},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6},{7,8}} => {{1},{2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6},{7,8}} => {{1,2,3},{4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6},{7,8}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,4},{5,7},{6},{8}} => {{1},{2,4},{3},{5,6},{7,8}} => {{1},{2,4},{3},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,4},{5,8},{6},{7}} => {{1,4},{2},{3},{5,6},{7,8}} => {{1,4},{2},{3},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,4},{5,7,8},{6}} => {{1,2,4},{3},{5,6},{7,8}} => {{1,2,4},{3},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6},{7,8}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6},{7,8}} => {{1,3},{2,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4},{5,6,8},{7}} => {{1,3},{2,4},{5,6},{7,8}} => {{1,4},{2,3},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4},{6,8},{7}} => {{1,3},{2},{4,6},{5},{7,8}} => {{1,3},{2},{4,6},{5},{7,8}}
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1,2},{3,5},{4},{6,7,8}} => {{1,2,3},{4,6},{5},{7,8}} => {{1,2,3},{4,6},{5},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4},{5},{7,8}} => {{1,2},{3,6},{4},{5},{7,8}} => {{1,2},{3,6},{4},{5},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,8},{4},{5},{6},{7}} => {{1,6},{2},{3},{4},{5},{7,8}} => {{1,6},{2},{3},{4},{5},{7,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4},{5},{6,7}} => {{1,6},{2,3},{4},{5},{7,8}} => {{1,3},{2,6},{4},{5},{7,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1,2},{3,6,8},{4},{5},{7}} => {{1,3},{2,6},{4},{5},{7,8}} => {{1,6},{2,3},{4},{5},{7,8}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4},{5}} => {{1,2,3,6},{4},{5},{7,8}} => {{1,2,3,6},{4},{5},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,5,6},{4},{7,8}} => {{1,2},{3,4,6},{5},{7,8}} => {{1,2},{3,4,6},{5},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4},{5,6}} => {{1,2,6},{3,4},{5},{7,8}} => {{1,2,4},{3,6},{5},{7,8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,5,7,8},{4},{6}} => {{1,2,4},{3,6},{5},{7,8}} => {{1,2,6},{3,4},{5},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1,2},{3,5,6,7},{4},{8}} => {{1},{2,3,4,6},{5},{7,8}} => {{1},{2,3,4,6},{5},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4},{5,6,7}} => {{1,6},{2,3,4},{5},{7,8}} => {{1,3,6},{2,4},{5},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1,2},{3,5,8},{4},{6,7}} => {{1,4},{2,3,6},{5},{7,8}} => {{1,3,4},{2,6},{5},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1,2},{3,5,6,8},{4},{7}} => {{1,3},{2,4,6},{5},{7,8}} => {{1,4,6},{2,3},{5},{7,8}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1,2},{3,5,6,7,8},{4}} => {{1,2,3,4,6},{5},{7,8}} => {{1,2,3,4,6},{5},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2},{3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6},{7,8}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2},{3,4,5},{6,8},{7}} => {{1,3},{2},{4,5,6},{7,8}} => {{1,3},{2},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8}} => {{1,2},{3,6},{4,5},{7,8}} => {{1,2},{3,5},{4,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1,2},{3,7},{4,5},{6},{8}} => {{1},{2,6},{3},{4,5},{7,8}} => {{1},{2,5},{3},{4,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,5},{6}} => {{1,2,6},{3},{4,5},{7,8}} => {{1,2,5},{3},{4,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1,2},{3,6,7},{4,5},{8}} => {{1},{2,3,6},{4,5},{7,8}} => {{1},{2,3,5},{4,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,5},{6,7}} => {{1,6},{2,3},{4,5},{7,8}} => {{1,3},{2,5},{4,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1,2},{3,6,8},{4,5},{7}} => {{1,3},{2,6},{4,5},{7,8}} => {{1,5},{2,3},{4,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4,5}} => {{1,2,3,6},{4,5},{7,8}} => {{1,2,3,5},{4,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2},{3,4,6},{5},{7,8}} => {{1,2},{3,5},{4,6},{7,8}} => {{1,2},{3,6},{4,5},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1,2},{3,7},{4,6},{5},{8}} => {{1},{2,6},{3,5},{4},{7,8}} => {{1},{2,5},{3,6},{4},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,6},{5}} => {{1,2,6},{3,5},{4},{7,8}} => {{1,2,5},{3,6},{4},{7,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5},{6}} => {{1,6},{2,5},{3},{4},{7,8}} => {{1,5},{2,6},{3},{4},{7,8}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2},{3,4,7,8},{5},{6}} => {{1,2,5},{3},{4,6},{7,8}} => {{1,2,6},{3},{4,5},{7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,6,7},{5}} => {{1,6},{2,3,5},{4},{7,8}} => {{1,3,6},{2,5},{4},{7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6,7}} => {{1,5},{2,3},{4,6},{7,8}} => {{1,3},{2,6},{4,5},{7,8}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2},{3,4,6,8},{5},{7}} => {{1,3},{2,5},{4,6},{7,8}} => {{1,6},{2,3},{4,5},{7,8}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2},{3,4,6,7,8},{5}} => {{1,2,3,5},{4,6},{7,8}} => {{1,2,3,6},{4,5},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1,2},{3,8},{4,5,6},{7}} => {{1,6},{2},{3,4,5},{7,8}} => {{1,4,6},{2},{3,5},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2},{3,4,7},{5,6},{8}} => {{1},{2,5},{3,4,6},{7,8}} => {{1},{2,4,5},{3,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5,6}} => {{1,6},{2,5},{3,4},{7,8}} => {{1,4},{2,5},{3,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5,6},{7}} => {{1,5},{2},{3,4,6},{7,8}} => {{1,4,5},{2},{3,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2},{3,4,7,8},{5,6}} => {{1,2,5},{3,4,6},{7,8}} => {{1,2,4,5},{3,6},{7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2},{3,4,5,7},{6},{8}} => {{1},{2,4},{3,5,6},{7,8}} => {{1},{2,5,6},{3,4},{7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,7},{6}} => {{1,6},{2,4},{3,5},{7,8}} => {{1,5},{2,4},{3,6},{7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,7},{6}} => {{1,5},{2,4},{3,6},{7,8}} => {{1,6},{2,4},{3,5},{7,8}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6},{7}} => {{1,4},{2},{3,5,6},{7,8}} => {{1,5,6},{2},{3,4},{7,8}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2},{3,4,5,7,8},{6}} => {{1,2,4},{3,5,6},{7,8}} => {{1,2,5,6},{3,4},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1},{2,3,4,5,6},{7,8}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,6,7}} => {{1,6},{2,3,4,5},{7,8}} => {{1,3,5},{2,4,6},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,6,7}} => {{1,5},{2,3,4,6},{7,8}} => {{1,3,6},{2,4,5},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6,7}} => {{1,4},{2,3,5,6},{7,8}} => {{1,3,4},{2,5,6},{7,8}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2},{3,4,5,6,8},{7}} => {{1,3},{2,4,5,6},{7,8}} => {{1,4,5,6},{2,3},{7,8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,8},{7}} => {{1},{2},{3},{4},{5},{6,8},{7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6,8},{7}} => {{1,2},{3},{4},{5},{6,8},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6,8},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,8},{7}} => {{1,2,3},{4},{5},{6,8},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4},{5,7},{6},{8}} => {{1},{2,4},{3},{5},{6,8},{7}} => {{1},{2,4},{3},{5},{6,8},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4},{5,7,8},{6}} => {{1,2,4},{3},{5},{6,8},{7}} => {{1,2,4},{3},{5},{6,8},{7}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4},{5,8},{6,7}} => {{1,4},{2,3},{5},{6,8},{7}} => {{1,3},{2,4},{5},{6,8},{7}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,8},{7}} => {{1,2,3,4},{5},{6,8},{7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,8},{7}} => {{1},{2,3},{4,5},{6,8},{7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5},{6,8},{7}} => {{1,3},{2},{4,5},{6,8},{7}} => {{1,3},{2},{4,5},{6,8},{7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,6},{5},{7,8}} => {{1,2},{3,5},{4},{6,8},{7}} => {{1,2},{3,5},{4},{6,8},{7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,3},{2},{4,7},{5},{6},{8}} => {{1},{2,5},{3},{4},{6,8},{7}} => {{1},{2,5},{3},{4},{6,8},{7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,3},{2},{4,6,7},{5},{8}} => {{1},{2,3,5},{4},{6,8},{7}} => {{1},{2,3,5},{4},{6,8},{7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,3},{2},{4,8},{5},{6,7}} => {{1,5},{2,3},{4},{6,8},{7}} => {{1,3},{2,5},{4},{6,8},{7}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,6,8},{5},{7}} => {{1,3},{2,5},{4},{6,8},{7}} => {{1,5},{2,3},{4},{6,8},{7}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,3},{2},{4,6,7,8},{5}} => {{1,2,3,5},{4},{6,8},{7}} => {{1,2,3,5},{4},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,3},{2},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6,8},{7}} => {{1,2},{3,4,5},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,3},{2},{4,7},{5,6},{8}} => {{1},{2,5},{3,4},{6,8},{7}} => {{1},{2,4},{3,5},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,3},{2},{4,8},{5,6},{7}} => {{1,5},{2},{3,4},{6,8},{7}} => {{1,4},{2},{3,5},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,3},{2},{4,7,8},{5,6}} => {{1,2,5},{3,4},{6,8},{7}} => {{1,2,4},{3,5},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3},{2},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6,8},{7}} => {{1,4},{2,5},{3},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,3},{2},{4,5,7,8},{6}} => {{1,2,4},{3,5},{6,8},{7}} => {{1,2,5},{3,4},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,3},{2},{4,8},{5,6,7}} => {{1,5},{2,3,4},{6,8},{7}} => {{1,3,5},{2,4},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,3},{2},{4,5,8},{6,7}} => {{1,4},{2,3,5},{6,8},{7}} => {{1,3,4},{2,5},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,5,6,8},{7}} => {{1,3},{2,4,5},{6,8},{7}} => {{1,4,5},{2,3},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,3},{2},{4,5,6,7,8}} => {{1,2,3,4,5},{6,8},{7}} => {{1,2,3,4,5},{6,8},{7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,8},{6},{7}} => {{1},{2},{3},{4},{5,8},{6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5,6},{7},{8}} => {{1},{2},{3,4},{5,8},{6},{7}} => {{1},{2},{3,4},{5,8},{6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6},{7,8}} => {{1,2},{3,4},{5,8},{6},{7}} => {{1,2},{3,4},{5,8},{6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,4},{2},{3},{5,8},{6},{7}} => {{1,4},{2},{3},{5,8},{6},{7}} => {{1,4},{2},{3},{5,8},{6},{7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2},{3},{5,8},{6,7}} => {{1,4},{2,3},{5,8},{6},{7}} => {{1,3},{2,4},{5,8},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8}} => {{1},{2},{3},{4,8},{5},{6},{7}} => {{1},{2},{3},{4,8},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2},{3},{4},{6},{7,8}} => {{1,2},{3},{4,8},{5},{6},{7}} => {{1,2},{3},{4,8},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8}} => {{1},{2},{3,8},{4},{5},{6},{7}} => {{1},{2},{3,8},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2},{3},{4},{5},{7,8}} => {{1,2},{3,8},{4},{5},{6},{7}} => {{1,2},{3,8},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8}} => {{1},{2,8},{3},{4},{5},{6},{7}} => {{1},{2,8},{3},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2},{3},{4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4},{5},{6}} => {{1,2,8},{3},{4},{5},{6},{7}} => {{1,2,8},{3},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3},{4},{5},{8}} => {{1},{2,3,8},{4},{5},{6},{7}} => {{1},{2,3,8},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2},{3},{4},{5},{6,7}} => {{1,8},{2,3},{4},{5},{6},{7}} => {{1,3},{2,8},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3},{4},{5},{7}} => {{1,3},{2,8},{4},{5},{6},{7}} => {{1,8},{2,3},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3},{4},{5}} => {{1,2,3,8},{4},{5},{6},{7}} => {{1,2,3,8},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2},{3},{4},{7},{8}} => {{1},{2},{3,4,8},{5},{6},{7}} => {{1},{2},{3,4,8},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5,6},{8}} => {{1},{2,8},{3,4},{5},{6},{7}} => {{1},{2,4},{3,8},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2},{3},{4},{5,6},{7}} => {{1,8},{2},{3,4},{5},{6},{7}} => {{1,4},{2},{3,8},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2},{3},{4},{6},{8}} => {{1},{2,4},{3,8},{5},{6},{7}} => {{1},{2,8},{3,4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2},{3},{4},{5,7},{6}} => {{1,8},{2,4},{3},{5},{6},{7}} => {{1,4},{2,8},{3},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2},{3},{4},{6}} => {{1,2,4},{3,8},{5},{6},{7}} => {{1,2,8},{3,4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2},{3},{4},{8}} => {{1},{2,3,4,8},{5},{6},{7}} => {{1},{2,3,4,8},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2},{3},{4},{5,6,7}} => {{1,8},{2,3,4},{5},{6},{7}} => {{1,3,8},{2,4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2},{3},{4},{6,7}} => {{1,4},{2,3,8},{5},{6},{7}} => {{1,3,4},{2,8},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2},{3},{4},{7}} => {{1,3},{2,4,8},{5},{6},{7}} => {{1,4,8},{2,3},{5},{6},{7}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2},{3},{4}} => {{1,2,3,4,8},{5},{6},{7}} => {{1,2,3,4,8},{5},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7},{8}} => {{1},{2},{3},{4,5,8},{6},{7}} => {{1},{2},{3},{4,5,8},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,4,5},{2},{3},{6,7,8}} => {{1,2,3},{4,5,8},{6},{7}} => {{1,2,3},{4,5,8},{6},{7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3},{4,5},{7},{8}} => {{1},{2},{3,8},{4,5},{6},{7}} => {{1},{2},{3,5},{4,8},{6},{7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3},{4,5},{6},{7}} => {{1,8},{2},{3},{4,5},{6},{7}} => {{1,5},{2},{3},{4,8},{6},{7}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3},{4,5},{8}} => {{1},{2,3,8},{4,5},{6},{7}} => {{1},{2,3,5},{4,8},{6},{7}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3},{4,5}} => {{1,2,3,8},{4,5},{6},{7}} => {{1,2,3,5},{4,8},{6},{7}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,4,6},{2},{3},{5},{7},{8}} => {{1},{2},{3,5},{4,8},{6},{7}} => {{1},{2},{3,8},{4,5},{6},{7}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,4,6},{2},{3},{5},{7,8}} => {{1,2},{3,5},{4,8},{6},{7}} => {{1,2},{3,8},{4,5},{6},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4,6},{5},{8}} => {{1},{2,8},{3,5},{4},{6},{7}} => {{1},{2,5},{3,8},{4},{6},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2},{3},{4,6},{5},{7}} => {{1,8},{2},{3,5},{4},{6},{7}} => {{1,5},{2},{3,8},{4},{6},{7}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2},{3},{4,7},{5},{6}} => {{1,8},{2,5},{3},{4},{6},{7}} => {{1,5},{2,8},{3},{4},{6},{7}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,4,8},{2},{3},{5},{6},{7}} => {{1,5},{2},{3},{4,8},{6},{7}} => {{1,8},{2},{3},{4,5},{6},{7}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,4,6,7,8},{2},{3},{5}} => {{1,2,3,5},{4,8},{6},{7}} => {{1,2,3,8},{4,5},{6},{7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,4,5,6},{2},{3},{7},{8}} => {{1},{2},{3,4,5,8},{6},{7}} => {{1},{2},{3,4,5,8},{6},{7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,4,5,6},{2},{3},{7,8}} => {{1,2},{3,4,5,8},{6},{7}} => {{1,2},{3,4,5,8},{6},{7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4,5,6},{8}} => {{1},{2,8},{3,4,5},{6},{7}} => {{1},{2,4,8},{3,5},{6},{7}}
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,4,7,8},{2},{3},{5,6}} => {{1,2,5},{3,4,8},{6},{7}} => {{1,2,4,5},{3,8},{6},{7}}
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,4,5,7,8},{2},{3},{6}} => {{1,2,4},{3,5,8},{6},{7}} => {{1,2,5,8},{3,4},{6},{7}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,4,5,6,7},{2},{3},{8}} => {{1},{2,3,4,5,8},{6},{7}} => {{1},{2,3,4,5,8},{6},{7}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,4,8},{2},{3},{5,6,7}} => {{1,5},{2,3,4,8},{6},{7}} => {{1,3,8},{2,4,5},{6},{7}}
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,4,5,8},{2},{3},{6,7}} => {{1,4},{2,3,5,8},{6},{7}} => {{1,3,4},{2,5,8},{6},{7}}
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,4,5,6,8},{2},{3},{7}} => {{1,3},{2,4,5,8},{6},{7}} => {{1,4,5,8},{2,3},{6},{7}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2},{3}} => {{1,2,3,4,5,8},{6},{7}} => {{1,2,3,4,5,8},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,8},{7}} => {{1},{2},{3},{4},{5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,3,4},{2},{5},{6,8},{7}} => {{1,3},{2},{4},{5,6,8},{7}} => {{1,3},{2},{4},{5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,3,4},{2},{5},{6,7,8}} => {{1,2,3},{4},{5,6,8},{7}} => {{1,2,3},{4},{5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,3,4},{2},{5,6},{7,8}} => {{1,2},{3,4},{5,6,8},{7}} => {{1,2},{3,4},{5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,3,4},{2},{5,7,8},{6}} => {{1,2,4},{3},{5,6,8},{7}} => {{1,2,4},{3},{5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,3,4},{2},{5,6,7},{8}} => {{1},{2,3,4},{5,6,8},{7}} => {{1},{2,3,4},{5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,3,4},{2},{5,8},{6,7}} => {{1,4},{2,3},{5,6,8},{7}} => {{1,3},{2,4},{5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,3,4},{2},{5,6,8},{7}} => {{1,3},{2,4},{5,6,8},{7}} => {{1,4},{2,3},{5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,3,4},{2},{5,6,7,8}} => {{1,2,3,4},{5,6,8},{7}} => {{1,2,3,4},{5,6,8},{7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7},{8}} => {{1},{2},{3},{4,8},{5,6},{7}} => {{1},{2},{3},{4,6},{5,8},{7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2},{3,4},{6},{7,8}} => {{1,2},{3},{4,8},{5,6},{7}} => {{1,2},{3},{4,6},{5,8},{7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2},{3,4},{6,7},{8}} => {{1},{2,3},{4,8},{5,6},{7}} => {{1},{2,3},{4,6},{5,8},{7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2},{3,4},{6,8},{7}} => {{1,3},{2},{4,8},{5,6},{7}} => {{1,3},{2},{4,6},{5,8},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5,6},{7}} => {{1,6},{2},{3},{4},{5,8},{7}}
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,4},{5}} => {{1,2,3,8},{4},{5,6},{7}} => {{1,2,3,6},{4},{5,8},{7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2},{3,4},{7,8}} => {{1,2},{3,4,8},{5,6},{7}} => {{1,2},{3,4,6},{5,8},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2},{3,4},{5,6},{8}} => {{1},{2,8},{3,4},{5,6},{7}} => {{1},{2,4},{3,6},{5,8},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2},{3,4},{5,6},{7}} => {{1,8},{2},{3,4},{5,6},{7}} => {{1,4},{2},{3,6},{5,8},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4},{5,6}} => {{1,2,8},{3,4},{5,6},{7}} => {{1,2,4},{3,6},{5,8},{7}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2},{3,4},{6}} => {{1,2,4},{3,8},{5,6},{7}} => {{1,2,6},{3,4},{5,8},{7}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2},{3,4},{8}} => {{1},{2,3,4,8},{5,6},{7}} => {{1},{2,3,4,6},{5,8},{7}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,4},{5,6,7}} => {{1,8},{2,3,4},{5,6},{7}} => {{1,3,6},{2,4},{5,8},{7}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2},{3,4},{6,7}} => {{1,4},{2,3,8},{5,6},{7}} => {{1,3,4},{2,6},{5,8},{7}}
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2},{3,4},{7}} => {{1,3},{2,4,8},{5,6},{7}} => {{1,4,6},{2,3},{5,8},{7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7},{8}} => {{1},{2},{3},{4,6},{5,8},{7}} => {{1},{2},{3},{4,8},{5,6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,5},{2},{4},{6,8},{7}} => {{1,3},{2},{4,6},{5,8},{7}} => {{1,3},{2},{4,8},{5,6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,3,5},{2},{4},{6,7,8}} => {{1,2,3},{4,6},{5,8},{7}} => {{1,2,3},{4,8},{5,6},{7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,5},{4},{7},{8}} => {{1},{2},{3,8},{4,6},{5},{7}} => {{1},{2},{3,6},{4,8},{5},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,5},{4},{6},{7}} => {{1,8},{2},{3},{4,6},{5},{7}} => {{1,6},{2},{3},{4,8},{5},{7}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,5},{4}} => {{1,2,3,8},{4,6},{5},{7}} => {{1,2,3,6},{4,8},{5},{7}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,3,7},{2},{4},{5},{6},{8}} => {{1},{2,6},{3},{4},{5,8},{7}} => {{1},{2,8},{3},{4},{5,6},{7}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,8},{2},{4},{5},{6},{7}} => {{1,6},{2},{3},{4},{5,8},{7}} => {{1,8},{2},{3},{4},{5,6},{7}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,3,6,7},{2},{4},{5},{8}} => {{1},{2,3,6},{4},{5,8},{7}} => {{1},{2,3,8},{4},{5,6},{7}}
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,3,6,7,8},{2},{4},{5}} => {{1,2,3,6},{4},{5,8},{7}} => {{1,2,3,8},{4},{5,6},{7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,3,5,6},{2},{4},{7,8}} => {{1,2},{3,4,6},{5,8},{7}} => {{1,2},{3,4,8},{5,6},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3,5,6},{4},{8}} => {{1},{2,8},{3,4,6},{5},{7}} => {{1},{2,4,8},{3,6},{5},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,5,6},{4}} => {{1,2,8},{3,4,6},{5},{7}} => {{1,2,4,8},{3,6},{5},{7}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4},{5,6}} => {{1,8},{2,6},{3,4},{5},{7}} => {{1,4},{2,6},{3,8},{5},{7}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4},{5,6}} => {{1,2,6},{3,4},{5,8},{7}} => {{1,2,4},{3,8},{5,6},{7}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,4},{3,6},{5,8},{7}} => {{1},{2,8},{3,4},{5,6},{7}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,3,5,7,8},{2},{4},{6}} => {{1,2,4},{3,6},{5,8},{7}} => {{1,2,8},{3,4},{5,6},{7}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,3,5,6,7},{2},{4},{8}} => {{1},{2,3,4,6},{5,8},{7}} => {{1},{2,3,4,8},{5,6},{7}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,5,6,7},{4}} => {{1,8},{2,3,4,6},{5},{7}} => {{1,3,6},{2,4,8},{5},{7}}
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4},{5,6,7}} => {{1,6},{2,3,4},{5,8},{7}} => {{1,3,8},{2,4},{5,6},{7}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,3,5,8},{2},{4},{6,7}} => {{1,4},{2,3,6},{5,8},{7}} => {{1,3,4},{2,8},{5,6},{7}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,3,5,6,8},{2},{4},{7}} => {{1,3},{2,4,6},{5,8},{7}} => {{1,4,8},{2,3},{5,6},{7}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,3,5,6,7,8},{2},{4}} => {{1,2,3,4,6},{5,8},{7}} => {{1,2,3,4,8},{5,6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7},{8}} => {{1},{2},{3},{4,5,6,8},{7}} => {{1},{2},{3},{4,5,6,8},{7}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,3,4,5},{2},{6},{7,8}} => {{1,2},{3},{4,5,6,8},{7}} => {{1,2},{3},{4,5,6,8},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,3,4,5},{2},{6,7},{8}} => {{1},{2,3},{4,5,6,8},{7}} => {{1},{2,3},{4,5,6,8},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,4,5},{2},{6,8},{7}} => {{1,3},{2},{4,5,6,8},{7}} => {{1,3},{2},{4,5,6,8},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,3,4,5},{2},{6,7,8}} => {{1,2,3},{4,5,6,8},{7}} => {{1,2,3},{4,5,6,8},{7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,4,5},{7},{8}} => {{1},{2},{3,8},{4,5,6},{7}} => {{1},{2},{3,5,8},{4,6},{7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,4,5},{7,8}} => {{1,2},{3,8},{4,5,6},{7}} => {{1,2},{3,5,8},{4,6},{7}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,5},{6}} => {{1,2,8},{3},{4,5,6},{7}} => {{1,2,5,8},{3},{4,6},{7}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3,4,5},{8}} => {{1},{2,3,8},{4,5,6},{7}} => {{1},{2,3,5,8},{4,6},{7}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2},{3,4,5},{6,7}} => {{1,8},{2,3},{4,5,6},{7}} => {{1,3},{2,5,8},{4,6},{7}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,4,5},{7}} => {{1,3},{2,8},{4,5,6},{7}} => {{1,5,8},{2,3},{4,6},{7}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,3,6},{2},{4,5},{7,8}} => {{1,2},{3,6},{4,5,8},{7}} => {{1,2},{3,5,6},{4,8},{7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3,6},{4,5},{8}} => {{1},{2,8},{3,6},{4,5},{7}} => {{1},{2,5},{3,6},{4,8},{7}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,6},{4,5}} => {{1,2,8},{3,6},{4,5},{7}} => {{1,2,5},{3,6},{4,8},{7}}
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,5},{6}} => {{1,2,6},{3},{4,5,8},{7}} => {{1,2,5,6},{3},{4,8},{7}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,3,6,7},{2},{4,5},{8}} => {{1},{2,3,6},{4,5,8},{7}} => {{1},{2,3,5,6},{4,8},{7}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,6,7},{4,5}} => {{1,8},{2,3,6},{4,5},{7}} => {{1,3,6},{2,5},{4,8},{7}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,5},{6,7}} => {{1,6},{2,3},{4,5,8},{7}} => {{1,3},{2,5,6},{4,8},{7}}
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,3,6,8},{2},{4,5},{7}} => {{1,3},{2,6},{4,5,8},{7}} => {{1,5,6},{2,3},{4,8},{7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,3,4,6},{2},{5},{7,8}} => {{1,2},{3,5},{4,6,8},{7}} => {{1,2},{3,6,8},{4,5},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,6},{5}} => {{1,2,8},{3,5},{4,6},{7}} => {{1,2,6},{3,5},{4,8},{7}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,6},{5},{8}} => {{1},{2,6},{3,5},{4,8},{7}} => {{1},{2,8},{3,5},{4,6},{7}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,6},{5}} => {{1,2,6},{3,5},{4,8},{7}} => {{1,2,8},{3,5},{4,6},{7}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,3,4,7},{2},{5},{6},{8}} => {{1},{2,5},{3},{4,6,8},{7}} => {{1},{2,6,8},{3},{4,5},{7}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,3,4,7,8},{2},{5},{6}} => {{1,2,5},{3},{4,6,8},{7}} => {{1,2,6,8},{3},{4,5},{7}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,3,4,6,7},{2},{5},{8}} => {{1},{2,3,5},{4,6,8},{7}} => {{1},{2,3,6,8},{4,5},{7}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,6,7},{5}} => {{1,8},{2,3,5},{4,6},{7}} => {{1,3,5},{2,6},{4,8},{7}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,6,7},{5}} => {{1,6},{2,3,5},{4,8},{7}} => {{1,3,5},{2,8},{4,6},{7}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,3,4,6,8},{2},{5},{7}} => {{1,3},{2,5},{4,6,8},{7}} => {{1,6,8},{2,3},{4,5},{7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,3,4,5,6},{2},{7},{8}} => {{1},{2},{3,4,5,6,8},{7}} => {{1},{2},{3,4,5,6,8},{7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,3,4,5,6},{2},{7,8}} => {{1,2},{3,4,5,6,8},{7}} => {{1,2},{3,4,5,6,8},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2},{3,4,5,6},{7}} => {{1,8},{2},{3,4,5,6},{7}} => {{1,4,6},{2},{3,5,8},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,5,6}} => {{1,2,8},{3,4,5,6},{7}} => {{1,2,4,6},{3,5,8},{7}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,5,6},{8}} => {{1},{2,6},{3,4,5,8},{7}} => {{1},{2,4,8},{3,5,6},{7}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4,5,6}} => {{1,8},{2,6},{3,4,5},{7}} => {{1,4,8},{2,5},{3,6},{7}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,3,8},{2},{4,5,6},{7}} => {{1,6},{2},{3,4,5,8},{7}} => {{1,4,8},{2},{3,5,6},{7}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,3,4,7},{2},{5,6},{8}} => {{1},{2,5},{3,4,6,8},{7}} => {{1},{2,4,5},{3,6,8},{7}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2},{3,4,7},{5,6}} => {{1,8},{2,5},{3,4,6},{7}} => {{1,4,8},{2,6},{3,5},{7}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,7},{5,6}} => {{1,6},{2,5},{3,4,8},{7}} => {{1,4,6},{2,8},{3,5},{7}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,6},{7}} => {{1,5},{2},{3,4,6,8},{7}} => {{1,4,5},{2},{3,6,8},{7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,4,5,7},{2},{6},{8}} => {{1},{2,4},{3,5,6,8},{7}} => {{1},{2,5,6,8},{3,4},{7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,5,7},{6}} => {{1,8},{2,4},{3,5,6},{7}} => {{1,5,8},{2,4},{3,6},{7}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,5,7},{6}} => {{1,6},{2,4},{3,5,8},{7}} => {{1,5,6},{2,4},{3,8},{7}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,7},{6}} => {{1,5},{2,4},{3,6,8},{7}} => {{1,6,8},{2,4},{3,5},{7}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,3,4,5,8},{2},{6},{7}} => {{1,4},{2},{3,5,6,8},{7}} => {{1,5,6,8},{2},{3,4},{7}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,3,4,5,7,8},{2},{6}} => {{1,2,4},{3,5,6,8},{7}} => {{1,2,5,6,8},{3,4},{7}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,8},{7}} => {{1},{2,3,4,5,6,8},{7}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,5,6,7}} => {{1,8},{2,3,4,5,6},{7}} => {{1,3,5,8},{2,4,6},{7}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,3,4,5,8},{2},{6,7}} => {{1,4},{2,3,5,6,8},{7}} => {{1,3,4},{2,5,6,8},{7}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,8},{2},{7}} => {{1,3},{2,4,5,6,8},{7}} => {{1,4,5,6,8},{2,3},{7}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8},{2}} => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6,8},{7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,7,8}} => {{1},{2},{3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6,7,8}} => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6,7,8}} => {{1,3},{2},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7,8}} => {{1,2},{3,4},{5},{6,7,8}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4},{5,7},{6},{8}} => {{1},{2,4},{3},{5},{6,7,8}} => {{1},{2,4},{3},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4},{5,8},{6,7}} => {{1,4},{2,3},{5},{6,7,8}} => {{1,3},{2,4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4},{5,6,8},{7}} => {{1,3},{2,4},{5},{6,7,8}} => {{1,4},{2,3},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3,4},{5},{6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6,7,8}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7,8}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2,3},{4,6},{5},{7},{8}} => {{1},{2},{3,5},{4},{6,7,8}} => {{1},{2},{3,5},{4},{6,7,8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2,3},{4,6},{5},{7,8}} => {{1,2},{3,5},{4},{6,7,8}} => {{1,2},{3,5},{4},{6,7,8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2,3},{4,6,7},{5},{8}} => {{1},{2,3,5},{4},{6,7,8}} => {{1},{2,3,5},{4},{6,7,8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2,3},{4,8},{5},{6,7}} => {{1,5},{2,3},{4},{6,7,8}} => {{1,3},{2,5},{4},{6,7,8}}
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2,3},{4,6,8},{5},{7}} => {{1,3},{2,5},{4},{6,7,8}} => {{1,5},{2,3},{4},{6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6,7,8}} => {{1},{2},{3,4,5},{6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6,7,8}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2,3},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6,7,8}} => {{1,4},{2,5},{3},{6,7,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2,3},{4,5,8},{6},{7}} => {{1,4},{2},{3,5},{6,7,8}} => {{1,5},{2},{3,4},{6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7,8}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2,3},{4,8},{5,6,7}} => {{1,5},{2,3,4},{6,7,8}} => {{1,3,5},{2,4},{6,7,8}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,8},{6,7}} => {{1},{2},{3},{4},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6},{7,8}} => {{1,2},{3},{4},{5,8},{6,7}} => {{1,2},{3},{4},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,4},{2,3},{5},{6,7},{8}} => {{1},{2,3},{4},{5,8},{6,7}} => {{1},{2,3},{4},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,4},{2,3},{5},{6,8},{7}} => {{1,3},{2},{4},{5,8},{6,7}} => {{1,3},{2},{4},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,4},{2,3},{5},{6,7,8}} => {{1,2,3},{4},{5,8},{6,7}} => {{1,2,3},{4},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,4},{2,3},{5,6},{7},{8}} => {{1},{2},{3,4},{5,8},{6,7}} => {{1},{2},{3,4},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,8}} => {{1,2},{3,4},{5,8},{6,7}} => {{1,2},{3,4},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,4},{2,3},{5,7},{6},{8}} => {{1},{2,4},{3},{5,8},{6,7}} => {{1},{2,4},{3},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,4},{2,3},{5,8},{6},{7}} => {{1,4},{2},{3},{5,8},{6,7}} => {{1,4},{2},{3},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,4},{2,3},{5,7,8},{6}} => {{1,2,4},{3},{5,8},{6,7}} => {{1,2,4},{3},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,4},{2,3},{5,6,7},{8}} => {{1},{2,3,4},{5,8},{6,7}} => {{1},{2,3,4},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,8},{6,7}} => {{1,4},{2,3},{5,8},{6,7}} => {{1,3},{2,4},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,4},{2,3},{5,6,8},{7}} => {{1,3},{2,4},{5,8},{6,7}} => {{1,4},{2,3},{5,7},{6,8}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,4},{2,3},{5,6,7,8}} => {{1,2,3,4},{5,8},{6,7}} => {{1,2,3,4},{5,7},{6,8}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,3},{4},{6,7},{8}} => {{1},{2,3},{4,8},{5},{6,7}} => {{1},{2,3},{4,7},{5},{6,8}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,3},{4},{6,8},{7}} => {{1,3},{2},{4,8},{5},{6,7}} => {{1,3},{2},{4,7},{5},{6,8}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,3},{4},{6,7,8}} => {{1,2,3},{4,8},{5},{6,7}} => {{1,2,3},{4,7},{5},{6,8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4},{5},{7,8}} => {{1,2},{3,8},{4},{5},{6,7}} => {{1,2},{3,7},{4},{5},{6,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,3},{4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5},{6,7}} => {{1,7},{2},{3},{4},{5},{6,8}}
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3},{4},{5}} => {{1,2,3,8},{4},{5},{6,7}} => {{1,2,3,7},{4},{5},{6,8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,3},{4},{7,8}} => {{1,2},{3,4,8},{5},{6,7}} => {{1,2},{3,4,7},{5},{6,8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,3},{4},{5,6},{8}} => {{1},{2,8},{3,4},{5},{6,7}} => {{1},{2,4},{3,7},{5},{6,8}}
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4},{5,6}} => {{1,2,8},{3,4},{5},{6,7}} => {{1,2,4},{3,7},{5},{6,8}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,3},{4},{6}} => {{1,2,4},{3,8},{5},{6,7}} => {{1,2,7},{3,4},{5},{6,8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,3},{4},{5,6,7}} => {{1,8},{2,3,4},{5},{6,7}} => {{1,3,7},{2,4},{5},{6,8}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,3},{4},{6,7}} => {{1,4},{2,3,8},{5},{6,7}} => {{1,3,4},{2,7},{5},{6,8}}
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,3},{4},{7}} => {{1,3},{2,4,8},{5},{6,7}} => {{1,4,7},{2,3},{5},{6,8}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,3},{4}} => {{1,2,3,4,8},{5},{6,7}} => {{1,2,3,4,7},{5},{6,8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,4,5},{2,3},{6},{7,8}} => {{1,2},{3},{4,5,8},{6,7}} => {{1,2},{3},{4,5,7},{6,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,4,5},{2,3},{6,7},{8}} => {{1},{2,3},{4,5,8},{6,7}} => {{1},{2,3},{4,5,7},{6,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,4,5},{2,3},{6,8},{7}} => {{1,3},{2},{4,5,8},{6,7}} => {{1,3},{2},{4,5,7},{6,8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,3},{4,5},{7},{8}} => {{1},{2},{3,8},{4,5},{6,7}} => {{1},{2},{3,5},{4,7},{6,8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,8}} => {{1,2},{3,8},{4,5},{6,7}} => {{1,2},{3,5},{4,7},{6,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3},{4,5},{6},{8}} => {{1},{2,8},{3},{4,5},{6,7}} => {{1},{2,5},{3},{4,7},{6,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,5},{6}} => {{1,2,8},{3},{4,5},{6,7}} => {{1,2,5},{3},{4,7},{6,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3},{4,5},{8}} => {{1},{2,3,8},{4,5},{6,7}} => {{1},{2,3,5},{4,7},{6,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3},{4,5},{6,7}} => {{1,8},{2,3},{4,5},{6,7}} => {{1,3},{2,5},{4,7},{6,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3},{4,5},{7}} => {{1,3},{2,8},{4,5},{6,7}} => {{1,5},{2,3},{4,7},{6,8}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3},{4,5}} => {{1,2,3,8},{4,5},{6,7}} => {{1,2,3,5},{4,7},{6,8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,4,6},{2,3},{5},{7},{8}} => {{1},{2},{3,5},{4,8},{6,7}} => {{1},{2},{3,7},{4,5},{6,8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,4,6},{2,3},{5},{7,8}} => {{1,2},{3,5},{4,8},{6,7}} => {{1,2},{3,7},{4,5},{6,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,3},{4,6},{5},{8}} => {{1},{2,8},{3,5},{4},{6,7}} => {{1},{2,5},{3,7},{4},{6,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,6},{5}} => {{1,2,8},{3,5},{4},{6,7}} => {{1,2,5},{3,7},{4},{6,8}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,4,8},{2,3},{5},{6},{7}} => {{1,5},{2},{3},{4,8},{6,7}} => {{1,7},{2},{3},{4,5},{6,8}}
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,4,7,8},{2,3},{5},{6}} => {{1,2,5},{3},{4,8},{6,7}} => {{1,2,7},{3},{4,5},{6,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,4,6,7},{2,3},{5},{8}} => {{1},{2,3,5},{4,8},{6,7}} => {{1},{2,3,7},{4,5},{6,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,3},{4,6,7},{5}} => {{1,8},{2,3,5},{4},{6,7}} => {{1,3,7},{2,5},{4},{6,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,4,8},{2,3},{5},{6,7}} => {{1,5},{2,3},{4,8},{6,7}} => {{1,3},{2,7},{4,5},{6,8}}
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,4,6,8},{2,3},{5},{7}} => {{1,3},{2,5},{4,8},{6,7}} => {{1,7},{2,3},{4,5},{6,8}}
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,4,6,7,8},{2,3},{5}} => {{1,2,3,5},{4,8},{6,7}} => {{1,2,3,7},{4,5},{6,8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,4,5,6},{2,3},{7,8}} => {{1,2},{3,4,5,8},{6,7}} => {{1,2},{3,4,5,7},{6,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2,3},{4,5,6},{8}} => {{1},{2,8},{3,4,5},{6,7}} => {{1},{2,4,7},{3,5},{6,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3},{4,5,6},{7}} => {{1,8},{2},{3,4,5},{6,7}} => {{1,4,7},{2},{3,5},{6,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,4,7},{2,3},{5,6},{8}} => {{1},{2,5},{3,4,8},{6,7}} => {{1},{2,4,5},{3,7},{6,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,3},{4,7},{5,6}} => {{1,8},{2,5},{3,4},{6,7}} => {{1,4},{2,5},{3,7},{6,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,4,8},{2,3},{5,6},{7}} => {{1,5},{2},{3,4,8},{6,7}} => {{1,4,5},{2},{3,7},{6,8}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,4,7,8},{2,3},{5,6}} => {{1,2,5},{3,4,8},{6,7}} => {{1,2,4,5},{3,7},{6,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,4,5,7},{2,3},{6},{8}} => {{1},{2,4},{3,5,8},{6,7}} => {{1},{2,5,7},{3,4},{6,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3},{4,5,7},{6}} => {{1,8},{2,4},{3,5},{6,7}} => {{1,5},{2,4},{3,7},{6,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,4,8},{2,3},{5,7},{6}} => {{1,5},{2,4},{3,8},{6,7}} => {{1,7},{2,4},{3,5},{6,8}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,4,5,8},{2,3},{6},{7}} => {{1,4},{2},{3,5,8},{6,7}} => {{1,5,7},{2},{3,4},{6,8}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,4,5,7,8},{2,3},{6}} => {{1,2,4},{3,5,8},{6,7}} => {{1,2,5,7},{3,4},{6,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,4,5,6,7},{2,3},{8}} => {{1},{2,3,4,5,8},{6,7}} => {{1},{2,3,4,5,7},{6,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3},{4,5,6,7}} => {{1,8},{2,3,4,5},{6,7}} => {{1,3,5},{2,4,7},{6,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,4,8},{2,3},{5,6,7}} => {{1,5},{2,3,4,8},{6,7}} => {{1,3,7},{2,4,5},{6,8}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,4,5,8},{2,3},{6,7}} => {{1,4},{2,3,5,8},{6,7}} => {{1,3,4},{2,5,7},{6,8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2,3}} => {{1,2,3,4,5,8},{6,7}} => {{1,2,3,4,5,7},{6,8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,7},{6,8}} => {{1},{2},{3},{4},{5,8},{6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,4},{3},{5,6},{7,8}} => {{1,2},{3,4},{5,7},{6,8}} => {{1,2},{3,4},{5,8},{6,7}}
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,4},{3},{5,7,8},{6}} => {{1,2,4},{3},{5,7},{6,8}} => {{1,2,4},{3},{5,8},{6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,4},{3},{5,6,7},{8}} => {{1},{2,3,4},{5,7},{6,8}} => {{1},{2,3,4},{5,8},{6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,4},{3},{5,8},{6,7}} => {{1,4},{2,3},{5,7},{6,8}} => {{1,3},{2,4},{5,8},{6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,4},{3},{5,6,8},{7}} => {{1,3},{2,4},{5,7},{6,8}} => {{1,4},{2,3},{5,8},{6,7}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,4},{3},{5,6,7,8}} => {{1,2,3,4},{5,7},{6,8}} => {{1,2,3,4},{5,8},{6,7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7},{8}} => {{1},{2},{3},{4,8},{5,7},{6}} => {{1},{2},{3},{4,7},{5,8},{6}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2,4},{3},{6},{7,8}} => {{1,2},{3},{4,8},{5,7},{6}} => {{1,2},{3},{4,7},{5,8},{6}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,4},{3},{6,7},{8}} => {{1},{2,3},{4,8},{5,7},{6}} => {{1},{2,3},{4,7},{5,8},{6}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,4},{3},{6,8},{7}} => {{1,3},{2},{4,8},{5,7},{6}} => {{1,3},{2},{4,7},{5,8},{6}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,4},{3},{6,7,8}} => {{1,2,3},{4,8},{5,7},{6}} => {{1,2,3},{4,7},{5,8},{6}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,4},{3},{5},{6},{7}} => {{1,8},{2},{3},{4},{5,7},{6}} => {{1,7},{2},{3},{4},{5,8},{6}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,4},{3},{5}} => {{1,2,3,8},{4},{5,7},{6}} => {{1,2,3,7},{4},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,4},{3},{7,8}} => {{1,2},{3,4,8},{5,7},{6}} => {{1,2},{3,4,7},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,4},{3},{5,6},{8}} => {{1},{2,8},{3,4},{5,7},{6}} => {{1},{2,4},{3,7},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,4},{3},{5,6}} => {{1,2,8},{3,4},{5,7},{6}} => {{1,2,4},{3,7},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,4},{3},{6},{8}} => {{1},{2,4},{3,8},{5,7},{6}} => {{1},{2,7},{3,4},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,4},{3},{5,7},{6}} => {{1,8},{2,4},{3},{5,7},{6}} => {{1,4},{2,7},{3},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,4},{3},{6}} => {{1,2,4},{3,8},{5,7},{6}} => {{1,2,7},{3,4},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,4},{3},{8}} => {{1},{2,3,4,8},{5,7},{6}} => {{1},{2,3,4,7},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,4},{3},{5,6,7}} => {{1,8},{2,3,4},{5,7},{6}} => {{1,3,7},{2,4},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,4},{3},{6,7}} => {{1,4},{2,3,8},{5,7},{6}} => {{1,3,4},{2,7},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,4},{3},{7}} => {{1,3},{2,4,8},{5,7},{6}} => {{1,4,7},{2,3},{5,8},{6}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,4},{3}} => {{1,2,3,4,8},{5,7},{6}} => {{1,2,3,4,7},{5,8},{6}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,5},{3},{4},{6,7,8}} => {{1,2,3},{4,7},{5},{6,8}} => {{1,2,3},{4,8},{5},{6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,5},{3},{4},{7},{8}} => {{1},{2},{3,8},{4,7},{5},{6}} => {{1},{2},{3,7},{4,8},{5},{6}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3},{4},{7,8}} => {{1,2},{3,8},{4,7},{5},{6}} => {{1,2},{3,7},{4,8},{5},{6}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,5},{3},{4},{6},{7}} => {{1,8},{2},{3},{4,7},{5},{6}} => {{1,7},{2},{3},{4,8},{5},{6}}
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,5},{3},{4},{6}} => {{1,2,8},{3},{4,7},{5},{6}} => {{1,2,7},{3},{4,8},{5},{6}}
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,5},{3},{4}} => {{1,2,3,8},{4,7},{5},{6}} => {{1,2,3,7},{4,8},{5},{6}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3},{4},{5},{7,8}} => {{1,2},{3,7},{4},{5},{6,8}} => {{1,2},{3,8},{4},{5},{6,7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3},{4},{5},{8}} => {{1},{2,8},{3,7},{4},{5},{6}} => {{1},{2,7},{3,8},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3},{4},{5}} => {{1,2,8},{3,7},{4},{5},{6}} => {{1,2,7},{3,8},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4},{5},{6}} => {{1,8},{2,7},{3},{4},{5},{6}} => {{1,7},{2,8},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3},{4},{5},{6},{7}} => {{1,7},{2},{3},{4},{5},{6,8}} => {{1,8},{2},{3},{4},{5},{6,7}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3},{4},{5}} => {{1,2,3,7},{4},{5},{6,8}} => {{1,2,3,8},{4},{5},{6,7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,5,6},{3},{4},{7,8}} => {{1,2},{3,4,7},{5},{6,8}} => {{1,2},{3,4,8},{5},{6,7}}
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,5,6},{3},{4}} => {{1,2,8},{3,4,7},{5},{6}} => {{1,2,4,8},{3,7},{5},{6}}
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4},{5,6}} => {{1,2,7},{3,4},{5},{6,8}} => {{1,2,4},{3,8},{5},{6,7}}
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,5,8},{3},{4},{6},{7}} => {{1,4},{2},{3,7},{5},{6,8}} => {{1,8},{2},{3,4},{5},{6,7}}
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,5,7,8},{3},{4},{6}} => {{1,2,4},{3,7},{5},{6,8}} => {{1,2,8},{3,4},{5},{6,7}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,5,6,7},{3},{4},{8}} => {{1},{2,3,4,7},{5},{6,8}} => {{1},{2,3,4,8},{5},{6,7}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,5,6,7},{3},{4}} => {{1,8},{2,3,4,7},{5},{6}} => {{1,3,7},{2,4,8},{5},{6}}
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4},{5,6,7}} => {{1,7},{2,3,4},{5},{6,8}} => {{1,3,8},{2,4},{5},{6,7}}
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,5,8},{3},{4},{6,7}} => {{1,4},{2,3,7},{5},{6,8}} => {{1,3,4},{2,8},{5},{6,7}}
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,5,6,8},{3},{4},{7}} => {{1,3},{2,4,7},{5},{6,8}} => {{1,4,8},{2,3},{5},{6,7}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7},{5},{6,8}} => {{1,2,3,4,8},{5},{6,7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,4,5},{3},{6},{7,8}} => {{1,2},{3},{4,5,7},{6,8}} => {{1,2},{3},{4,5,8},{6,7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,4,5},{3},{6,8},{7}} => {{1,3},{2},{4,5,7},{6,8}} => {{1,3},{2},{4,5,8},{6,7}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,4,5},{3},{6,7,8}} => {{1,2,3},{4,5,7},{6,8}} => {{1,2,3},{4,5,8},{6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,4,5},{3},{7,8}} => {{1,2},{3,8},{4,5,7},{6}} => {{1,2},{3,5,8},{4,7},{6}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,4,5},{3},{6},{8}} => {{1},{2,8},{3},{4,5,7},{6}} => {{1},{2,5,8},{3},{4,7},{6}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,4,5},{3},{6}} => {{1,2,8},{3},{4,5,7},{6}} => {{1,2,5,8},{3},{4,7},{6}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,4,5},{3},{8}} => {{1},{2,3,8},{4,5,7},{6}} => {{1},{2,3,5,8},{4,7},{6}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,4,5},{3},{6,7}} => {{1,8},{2,3},{4,5,7},{6}} => {{1,3},{2,5,8},{4,7},{6}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,4,5},{3},{7}} => {{1,3},{2,8},{4,5,7},{6}} => {{1,5,8},{2,3},{4,7},{6}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3},{4,5},{7,8}} => {{1,2},{3,7},{4,5},{6,8}} => {{1,2},{3,5},{4,8},{6,7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3},{4,5},{8}} => {{1},{2,8},{3,7},{4,5},{6}} => {{1},{2,5},{3,7},{4,8},{6}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3},{4,5}} => {{1,2,8},{3,7},{4,5},{6}} => {{1,2,5},{3,7},{4,8},{6}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,5},{6}} => {{1,8},{2,7},{3},{4,5},{6}} => {{1,5},{2,7},{3},{4,8},{6}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,5},{6}} => {{1,2,7},{3},{4,5},{6,8}} => {{1,2,5},{3},{4,8},{6,7}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3},{4,5}} => {{1,8},{2,3,7},{4,5},{6}} => {{1,3,7},{2,5},{4,8},{6}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,5},{6,7}} => {{1,7},{2,3},{4,5},{6,8}} => {{1,3},{2,5},{4,8},{6,7}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3},{4,5},{7}} => {{1,3},{2,7},{4,5},{6,8}} => {{1,5},{2,3},{4,8},{6,7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,4,6},{3},{5},{7,8}} => {{1,2},{3,5},{4,7},{6,8}} => {{1,2},{3,8},{4,5},{6,7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2,4,6},{3},{5},{8}} => {{1},{2,8},{3,5},{4,7},{6}} => {{1},{2,7},{3,5},{4,8},{6}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,4,6},{3},{5}} => {{1,2,8},{3,5},{4,7},{6}} => {{1,2,7},{3,5},{4,8},{6}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,6},{5}} => {{1,8},{2,7},{3,5},{4},{6}} => {{1,5},{2,7},{3,8},{4},{6}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,6},{5}} => {{1,2,7},{3,5},{4},{6,8}} => {{1,2,5},{3,8},{4},{6,7}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,4,7},{3},{5},{6}} => {{1,8},{2,5},{3},{4,7},{6}} => {{1,7},{2,5},{3},{4,8},{6}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,4,8},{3},{5},{6},{7}} => {{1,5},{2},{3},{4,7},{6,8}} => {{1,8},{2},{3},{4,5},{6,7}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,4,7,8},{3},{5},{6}} => {{1,2,5},{3},{4,7},{6,8}} => {{1,2,8},{3},{4,5},{6,7}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,4,6,7},{3},{5}} => {{1,8},{2,3,5},{4,7},{6}} => {{1,3,5},{2,7},{4,8},{6}}
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,6,7},{5}} => {{1,7},{2,3,5},{4},{6,8}} => {{1,3,8},{2,5},{4},{6,7}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5},{6,7}} => {{1,5},{2,3},{4,7},{6,8}} => {{1,3},{2,8},{4,5},{6,7}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,4,6,8},{3},{5},{7}} => {{1,3},{2,5},{4,7},{6,8}} => {{1,8},{2,3},{4,5},{6,7}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,4,6,7,8},{3},{5}} => {{1,2,3,5},{4,7},{6,8}} => {{1,2,3,8},{4,5},{6,7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,4,5,6},{3},{7,8}} => {{1,2},{3,4,5,7},{6,8}} => {{1,2},{3,4,5,8},{6,7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,4,5,6},{3},{8}} => {{1},{2,8},{3,4,5,7},{6}} => {{1},{2,4,7},{3,5,8},{6}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,4,5,6},{3},{7}} => {{1,8},{2},{3,4,5,7},{6}} => {{1,4,7},{2},{3,5,8},{6}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,4,5,6},{3}} => {{1,2,8},{3,4,5,7},{6}} => {{1,2,4,7},{3,5,8},{6}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,5,6}} => {{1,8},{2,7},{3,4,5},{6}} => {{1,4,8},{2,5},{3,7},{6}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3},{4,5,6},{7}} => {{1,7},{2},{3,4,5},{6,8}} => {{1,4,8},{2},{3,5},{6,7}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,4,7},{3},{5,6},{8}} => {{1},{2,5},{3,4,7},{6,8}} => {{1},{2,4,5},{3,8},{6,7}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,4,7},{3},{5,6}} => {{1,8},{2,5},{3,4,7},{6}} => {{1,4,8},{2,7},{3,5},{6}}
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,7},{5,6}} => {{1,7},{2,5},{3,4},{6,8}} => {{1,4},{2,5},{3,8},{6,7}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,6},{7}} => {{1,5},{2},{3,4,7},{6,8}} => {{1,4,5},{2},{3,8},{6,7}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,4,5,7},{3},{6},{8}} => {{1},{2,4},{3,5,7},{6,8}} => {{1},{2,5,8},{3,4},{6,7}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,4,5,7},{3},{6}} => {{1,8},{2,4},{3,5,7},{6}} => {{1,5,8},{2,4},{3,7},{6}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,5,7},{6}} => {{1,7},{2,4},{3,5},{6,8}} => {{1,5},{2,4},{3,8},{6,7}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,7},{6}} => {{1,5},{2,4},{3,7},{6,8}} => {{1,8},{2,4},{3,5},{6,7}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,4,5,8},{3},{6},{7}} => {{1,4},{2},{3,5,7},{6,8}} => {{1,5,8},{2},{3,4},{6,7}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,4,5,7,8},{3},{6}} => {{1,2,4},{3,5,7},{6,8}} => {{1,2,5,8},{3,4},{6,7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,4,5,6,7},{3},{8}} => {{1},{2,3,4,5,7},{6,8}} => {{1},{2,3,4,5,8},{6,7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,4,5,6,7},{3}} => {{1,8},{2,3,4,5,7},{6}} => {{1,3,5,8},{2,4,7},{6}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,5,6,7}} => {{1,7},{2,3,4,5},{6,8}} => {{1,3,5},{2,4,8},{6,7}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,6,7}} => {{1,5},{2,3,4,7},{6,8}} => {{1,3,8},{2,4,5},{6,7}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,4,5,8},{3},{6,7}} => {{1,4},{2,3,5,7},{6,8}} => {{1,3,4},{2,5,8},{6,7}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,4,5,6,8},{3},{7}} => {{1,3},{2,4,5,7},{6,8}} => {{1,4,5,8},{2,3},{6,7}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7},{6,8}} => {{1,2,3,4,5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,6,7,8}} => {{1,2},{3},{4},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4},{5},{6,7},{8}} => {{1},{2,3},{4},{5,6,7,8}} => {{1},{2,3},{4},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3,4},{5},{6,8},{7}} => {{1,3},{2},{4},{5,6,7,8}} => {{1,3},{2},{4},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6,7,8}} => {{1},{2},{3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6,7,8}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3,4},{5,7,8},{6}} => {{1,2,4},{3},{5,6,7,8}} => {{1,2,4},{3},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7,8}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6,7,8}} => {{1,3},{2,4},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3,4},{5,6,8},{7}} => {{1,3},{2,4},{5,6,7,8}} => {{1,4},{2,3},{5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7},{8}} => {{1},{2},{3},{4,8},{5,6,7}} => {{1},{2},{3},{4,6,8},{5,7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,3,4},{6,8},{7}} => {{1,3},{2},{4,8},{5,6,7}} => {{1,3},{2},{4,6,8},{5,7}}
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,3,4},{6,7,8}} => {{1,2,3},{4,8},{5,6,7}} => {{1,2,3},{4,6,8},{5,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2,3,4},{5},{7},{8}} => {{1},{2},{3,8},{4},{5,6,7}} => {{1},{2},{3,6,8},{4},{5,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,3,4},{5},{7,8}} => {{1,2},{3,8},{4},{5,6,7}} => {{1,2},{3,6,8},{4},{5,7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,3,4},{5},{6},{8}} => {{1},{2,8},{3},{4},{5,6,7}} => {{1},{2,6,8},{3},{4},{5,7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,3,4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5,6,7}} => {{1,6,8},{2},{3},{4},{5,7}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,3,4},{5},{6,7}} => {{1,8},{2,3},{4},{5,6,7}} => {{1,3},{2,6,8},{4},{5,7}}
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,4},{5},{7}} => {{1,3},{2,8},{4},{5,6,7}} => {{1,6,8},{2,3},{4},{5,7}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,4},{5}} => {{1,2,3,8},{4},{5,6,7}} => {{1,2,3,6,8},{4},{5,7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2,3,4},{7},{8}} => {{1},{2},{3,4,8},{5,6,7}} => {{1},{2},{3,4,6,8},{5,7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,3,4},{5,6},{8}} => {{1},{2,8},{3,4},{5,6,7}} => {{1},{2,4},{3,6,8},{5,7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2,3,4},{5,6},{7}} => {{1,8},{2},{3,4},{5,6,7}} => {{1,4},{2},{3,6,8},{5,7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,3,4},{6},{8}} => {{1},{2,4},{3,8},{5,6,7}} => {{1},{2,6,8},{3,4},{5,7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,3,4},{5,7},{6}} => {{1,8},{2,4},{3},{5,6,7}} => {{1,4},{2,6,8},{3},{5,7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,3,4},{8}} => {{1},{2,3,4,8},{5,6,7}} => {{1},{2,3,4,6,8},{5,7}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,3,4}} => {{1,2,3,4,8},{5,6,7}} => {{1,2,3,4,6,8},{5,7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,5},{3,4},{6},{7,8}} => {{1,2},{3},{4,7},{5,6,8}} => {{1,2},{3},{4,6,7},{5,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,5},{3,4},{6,7},{8}} => {{1},{2,3},{4,7},{5,6,8}} => {{1},{2,3},{4,6,7},{5,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,5},{3,4},{6,8},{7}} => {{1,3},{2},{4,7},{5,6,8}} => {{1,3},{2},{4,6,7},{5,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,5},{3,4},{6,7,8}} => {{1,2,3},{4,7},{5,6,8}} => {{1,2,3},{4,6,7},{5,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,5},{3,4},{7},{8}} => {{1},{2},{3,8},{4,7},{5,6}} => {{1},{2},{3,6},{4,7},{5,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8}} => {{1,2},{3,8},{4,7},{5,6}} => {{1,2},{3,6},{4,7},{5,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,5},{3,4},{6},{8}} => {{1},{2,8},{3},{4,7},{5,6}} => {{1},{2,6},{3},{4,7},{5,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,5},{3,4},{6}} => {{1,2,8},{3},{4,7},{5,6}} => {{1,2,6},{3},{4,7},{5,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,5},{3,4},{8}} => {{1},{2,3,8},{4,7},{5,6}} => {{1},{2,3,6},{4,7},{5,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,5},{3,4},{6,7}} => {{1,8},{2,3},{4,7},{5,6}} => {{1,3},{2,6},{4,7},{5,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,5},{3,4},{7}} => {{1,3},{2,8},{4,7},{5,6}} => {{1,6},{2,3},{4,7},{5,8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,5},{3,4}} => {{1,2,3,8},{4,7},{5,6}} => {{1,2,3,6},{4,7},{5,8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3,4},{5},{7},{8}} => {{1},{2},{3,7},{4},{5,6,8}} => {{1},{2},{3,6,7},{4},{5,8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,4},{5},{7,8}} => {{1,2},{3,7},{4},{5,6,8}} => {{1,2},{3,6,7},{4},{5,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,4},{5},{8}} => {{1},{2,8},{3,7},{4},{5,6}} => {{1},{2,6},{3,7},{4},{5,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,4},{5},{7}} => {{1,8},{2},{3,7},{4},{5,6}} => {{1,6},{2},{3,7},{4},{5,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,4},{5}} => {{1,2,8},{3,7},{4},{5,6}} => {{1,2,6},{3,7},{4},{5,8}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4},{5},{6}} => {{1,2,7},{3},{4},{5,6,8}} => {{1,2,6,7},{3},{4},{5,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,4},{5}} => {{1,8},{2,3,7},{4},{5,6}} => {{1,3,7},{2,6},{4},{5,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,4},{5},{6,7}} => {{1,7},{2,3},{4},{5,6,8}} => {{1,3},{2,6,7},{4},{5,8}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,4},{5},{7}} => {{1,3},{2,7},{4},{5,6,8}} => {{1,6,7},{2,3},{4},{5,8}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,4},{5}} => {{1,2,3,7},{4},{5,6,8}} => {{1,2,3,6,7},{4},{5,8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,5,6},{3,4},{7},{8}} => {{1},{2},{3,4,7},{5,6,8}} => {{1},{2},{3,4,6,7},{5,8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,5,6},{3,4},{7,8}} => {{1,2},{3,4,7},{5,6,8}} => {{1,2},{3,4,6,7},{5,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2,5,6},{3,4},{8}} => {{1},{2,8},{3,4,7},{5,6}} => {{1},{2,4,7},{3,6},{5,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2,5,6},{3,4},{7}} => {{1,8},{2},{3,4,7},{5,6}} => {{1,4,7},{2},{3,6},{5,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,5,6},{3,4}} => {{1,2,8},{3,4,7},{5,6}} => {{1,2,4,7},{3,6},{5,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4},{5,6},{8}} => {{1},{2,7},{3,4},{5,6,8}} => {{1},{2,4},{3,6,7},{5,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5,6}} => {{1,8},{2,7},{3,4},{5,6}} => {{1,4},{2,6},{3,7},{5,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4},{5,6},{7}} => {{1,7},{2},{3,4},{5,6,8}} => {{1,4},{2},{3,6,7},{5,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,5,7},{3,4},{6},{8}} => {{1},{2,4},{3,7},{5,6,8}} => {{1},{2,6,7},{3,4},{5,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,5,7},{3,4},{6}} => {{1,8},{2,4},{3,7},{5,6}} => {{1,6},{2,4},{3,7},{5,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,4},{5,7},{6}} => {{1,7},{2,4},{3},{5,6,8}} => {{1,4},{2,6,7},{3},{5,8}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,5,8},{3,4},{6},{7}} => {{1,4},{2},{3,7},{5,6,8}} => {{1,6,7},{2},{3,4},{5,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,5,6,7},{3,4}} => {{1,8},{2,3,4,7},{5,6}} => {{1,3,6},{2,4,7},{5,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4},{5,6,7}} => {{1,7},{2,3,4},{5,6,8}} => {{1,3,6,7},{2,4},{5,8}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7},{5,6,8}} => {{1,2,3,4,6,7},{5,8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7},{8}} => {{1},{2},{3},{4,6},{5,7,8}} => {{1},{2},{3},{4,7,8},{5,6}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,5},{4},{6},{7,8}} => {{1,2},{3},{4,6},{5,7,8}} => {{1,2},{3},{4,7,8},{5,6}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,5},{4},{6,7},{8}} => {{1},{2,3},{4,6},{5,7,8}} => {{1},{2,3},{4,7,8},{5,6}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,5},{4},{6,8},{7}} => {{1,3},{2},{4,6},{5,7,8}} => {{1,3},{2},{4,7,8},{5,6}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,5},{4},{6,7,8}} => {{1,2,3},{4,6},{5,7,8}} => {{1,2,3},{4,7,8},{5,6}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3,5},{4},{7,8}} => {{1,2},{3,8},{4,6},{5,7}} => {{1,2},{3,7},{4,6},{5,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3,5},{4},{6}} => {{1,2,8},{3},{4,6},{5,7}} => {{1,2,7},{3},{4,6},{5,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3,5},{4},{8}} => {{1},{2,3,8},{4,6},{5,7}} => {{1},{2,3,7},{4,6},{5,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3,5},{4},{6,7}} => {{1,8},{2,3},{4,6},{5,7}} => {{1,3},{2,7},{4,6},{5,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,5},{4},{7}} => {{1,3},{2,8},{4,6},{5,7}} => {{1,7},{2,3},{4,6},{5,8}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,5},{4}} => {{1,2,3,8},{4,6},{5,7}} => {{1,2,3,7},{4,6},{5,8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,5},{4},{7,8}} => {{1,2},{3,7},{4,6},{5,8}} => {{1,2},{3,8},{4,6},{5,7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,5},{4},{8}} => {{1},{2,8},{3,7},{4,6},{5}} => {{1},{2,6},{3,7},{4,8},{5}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,5},{4}} => {{1,2,8},{3,7},{4,6},{5}} => {{1,2,6},{3,7},{4,8},{5}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,5},{4},{6}} => {{1,8},{2,7},{3},{4,6},{5}} => {{1,6},{2,7},{3},{4,8},{5}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,5},{4},{6}} => {{1,2,7},{3},{4,6},{5,8}} => {{1,2,8},{3},{4,6},{5,7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3,5},{4},{8}} => {{1},{2,3,7},{4,6},{5,8}} => {{1},{2,3,8},{4,6},{5,7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,5},{4}} => {{1,8},{2,3,7},{4,6},{5}} => {{1,3,7},{2,6},{4,8},{5}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,5},{4},{6,7}} => {{1,7},{2,3},{4,6},{5,8}} => {{1,3},{2,8},{4,6},{5,7}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,5},{4},{7}} => {{1,3},{2,7},{4,6},{5,8}} => {{1,8},{2,3},{4,6},{5,7}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,5},{4}} => {{1,2,3,7},{4,6},{5,8}} => {{1,2,3,8},{4,6},{5,7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,6},{4},{5},{7,8}} => {{1,2},{3,6},{4},{5,7,8}} => {{1,2},{3,7,8},{4},{5,6}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,6},{4},{5}} => {{1,2,8},{3,6},{4},{5,7}} => {{1,2,7},{3,6},{4},{5,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4},{5}} => {{1,8},{2,7},{3,6},{4},{5}} => {{1,6},{2,7},{3,8},{4},{5}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,6},{4},{5}} => {{1,2,7},{3,6},{4},{5,8}} => {{1,2,8},{3,6},{4},{5,7}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4},{5},{6}} => {{1,2,6},{3},{4},{5,7,8}} => {{1,2,7,8},{3},{4},{5,6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,6,7},{4},{5},{8}} => {{1},{2,3,6},{4},{5,7,8}} => {{1},{2,3,7,8},{4},{5,6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3,6,7},{4},{5}} => {{1,8},{2,3,6},{4},{5,7}} => {{1,3,6},{2,7},{4},{5,8}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3,6,7},{4},{5}} => {{1,7},{2,3,6},{4},{5,8}} => {{1,3,6},{2,8},{4},{5,7}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5},{6,7}} => {{1,6},{2,3},{4},{5,7,8}} => {{1,3},{2,7,8},{4},{5,6}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,6,8},{4},{5},{7}} => {{1,3},{2,6},{4},{5,7,8}} => {{1,7,8},{2,3},{4},{5,6}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3,6},{4},{5,7,8}} => {{1,2,3,7,8},{4},{5,6}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,5,6},{4},{7},{8}} => {{1},{2},{3,4,6},{5,7,8}} => {{1},{2},{3,4,7,8},{5,6}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,5,6},{4},{7,8}} => {{1,2},{3,4,6},{5,7,8}} => {{1,2},{3,4,7,8},{5,6}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,5,6},{4},{8}} => {{1},{2,8},{3,4,6},{5,7}} => {{1},{2,4,6},{3,7},{5,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,5,6},{4},{7}} => {{1,8},{2},{3,4,6},{5,7}} => {{1,4,6},{2},{3,7},{5,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,5,6},{4}} => {{1,2,8},{3,4,6},{5,7}} => {{1,2,4,6},{3,7},{5,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,5,6},{4},{8}} => {{1},{2,7},{3,4,6},{5,8}} => {{1},{2,4,6},{3,8},{5,7}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,5,6},{4}} => {{1,8},{2,7},{3,4,6},{5}} => {{1,4,8},{2,6},{3,7},{5}}
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,5,6},{4},{7}} => {{1,7},{2},{3,4,6},{5,8}} => {{1,4,6},{2},{3,8},{5,7}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4},{5,6},{8}} => {{1},{2,6},{3,4},{5,7,8}} => {{1},{2,4},{3,7,8},{5,6}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4},{5,6}} => {{1,8},{2,6},{3,4},{5,7}} => {{1,4},{2,7},{3,6},{5,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4},{5,6}} => {{1,7},{2,6},{3,4},{5,8}} => {{1,4},{2,8},{3,6},{5,7}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,6},{7}} => {{1,6},{2},{3,4},{5,7,8}} => {{1,4},{2},{3,7,8},{5,6}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,5,7},{4},{6},{8}} => {{1},{2,4},{3,6},{5,7,8}} => {{1},{2,7,8},{3,4},{5,6}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,5,7},{4},{6}} => {{1,8},{2,4},{3,6},{5,7}} => {{1,7},{2,4},{3,6},{5,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,5,7},{4},{6}} => {{1,7},{2,4},{3,6},{5,8}} => {{1,8},{2,4},{3,6},{5,7}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,7},{6}} => {{1,6},{2,4},{3},{5,7,8}} => {{1,4},{2,7,8},{3},{5,6}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,5,8},{4},{6},{7}} => {{1,4},{2},{3,6},{5,7,8}} => {{1,7,8},{2},{3,4},{5,6}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,5,7,8},{4},{6}} => {{1,2,4},{3,6},{5,7,8}} => {{1,2,7,8},{3,4},{5,6}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => {{1},{2,3,4,6},{5,7,8}} => {{1},{2,3,4,7,8},{5,6}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,5,6,7},{4}} => {{1,8},{2,3,4,6},{5,7}} => {{1,3,7},{2,4,6},{5,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,5,6,7},{4}} => {{1,7},{2,3,4,6},{5,8}} => {{1,3,8},{2,4,6},{5,7}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,5,8},{4},{6,7}} => {{1,4},{2,3,6},{5,7,8}} => {{1,3,4},{2,7,8},{5,6}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6},{5,7,8}} => {{1,2,3,4,7,8},{5,6}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}} => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6,7,8}} => {{1,2},{3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7,8}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4,5},{6,8},{7}} => {{1,3},{2},{4,5,6,7,8}} => {{1,3},{2},{4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2,3,4,5},{7},{8}} => {{1},{2},{3,8},{4,5,6,7}} => {{1},{2},{3,5,7},{4,6,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3,4,5},{7,8}} => {{1,2},{3,8},{4,5,6,7}} => {{1,2},{3,5,7},{4,6,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3,4,5},{6,7}} => {{1,8},{2,3},{4,5,6,7}} => {{1,3},{2,5,7},{4,6,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,4,5},{7}} => {{1,3},{2,8},{4,5,6,7}} => {{1,5,7},{2,3},{4,6,8}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,4,5}} => {{1,2,3,8},{4,5,6,7}} => {{1,2,3,5,7},{4,6,8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3,4,5},{7},{8}} => {{1},{2},{3,7},{4,5,6,8}} => {{1},{2},{3,5,8},{4,6,7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,4,5},{7,8}} => {{1,2},{3,7},{4,5,6,8}} => {{1,2},{3,5,8},{4,6,7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,4,5},{8}} => {{1},{2,8},{3,7},{4,5,6}} => {{1},{2,5,8},{3,6},{4,7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,4,5},{7}} => {{1,8},{2},{3,7},{4,5,6}} => {{1,5,8},{2},{3,6},{4,7}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,4,5}} => {{1,2,8},{3,7},{4,5,6}} => {{1,2,5,8},{3,6},{4,7}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3,4,5},{6},{8}} => {{1},{2,7},{3},{4,5,6,8}} => {{1},{2,5,8},{3},{4,6,7}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,5},{6}} => {{1,8},{2,7},{3},{4,5,6}} => {{1,5,8},{2,6},{3},{4,7}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,5},{6}} => {{1,2,7},{3},{4,5,6,8}} => {{1,2,5,8},{3},{4,6,7}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3,4,5},{8}} => {{1},{2,3,7},{4,5,6,8}} => {{1},{2,3,5,8},{4,6,7}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,4,5},{6,7}} => {{1,7},{2,3},{4,5,6,8}} => {{1,3},{2,5,8},{4,6,7}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,4,5},{7}} => {{1,3},{2,7},{4,5,6,8}} => {{1,5,8},{2,3},{4,6,7}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,4,5}} => {{1,2,3,7},{4,5,6,8}} => {{1,2,3,5,8},{4,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,6},{4,5},{7},{8}} => {{1},{2},{3,6},{4,5,7,8}} => {{1},{2},{3,5,6},{4,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,6},{4,5},{7,8}} => {{1,2},{3,6},{4,5,7,8}} => {{1,2},{3,5,6},{4,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2,3,6},{4,5},{8}} => {{1},{2,8},{3,6},{4,5,7}} => {{1},{2,5,8},{3,7},{4,6}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3,6},{4,5},{7}} => {{1,8},{2},{3,6},{4,5,7}} => {{1,5,8},{2},{3,7},{4,6}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,6},{4,5}} => {{1,2,8},{3,6},{4,5,7}} => {{1,2,5,8},{3,7},{4,6}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,6},{4,5},{8}} => {{1},{2,7},{3,6},{4,5,8}} => {{1},{2,5,7},{3,8},{4,6}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4,5}} => {{1,8},{2,7},{3,6},{4,5}} => {{1,5},{2,6},{3,7},{4,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,6},{4,5},{7}} => {{1,7},{2},{3,6},{4,5,8}} => {{1,5,7},{2},{3,8},{4,6}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,6},{4,5}} => {{1,2,7},{3,6},{4,5,8}} => {{1,2,5,7},{3,8},{4,6}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5},{6},{8}} => {{1},{2,6},{3},{4,5,7,8}} => {{1},{2,5,6},{3},{4,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,5},{6}} => {{1,8},{2,6},{3},{4,5,7}} => {{1,5,8},{2,7},{3},{4,6}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,5},{6}} => {{1,7},{2,6},{3},{4,5,8}} => {{1,5,7},{2,8},{3},{4,6}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,5},{6},{7}} => {{1,6},{2},{3},{4,5,7,8}} => {{1,5,6},{2},{3},{4,7,8}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,5},{6}} => {{1,2,6},{3},{4,5,7,8}} => {{1,2,5,6},{3},{4,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,6,7},{4,5},{8}} => {{1},{2,3,6},{4,5,7,8}} => {{1},{2,3,5,6},{4,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3,6,7},{4,5}} => {{1,8},{2,3,6},{4,5,7}} => {{1,3,7},{2,5,8},{4,6}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5},{6,7}} => {{1,6},{2,3},{4,5,7,8}} => {{1,3},{2,5,6},{4,7,8}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,6,8},{4,5},{7}} => {{1,3},{2,6},{4,5,7,8}} => {{1,5,6},{2,3},{4,7,8}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4,5}} => {{1,2,3,6},{4,5,7,8}} => {{1,2,3,5,6},{4,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,6},{5},{7},{8}} => {{1},{2},{3,5},{4,6,7,8}} => {{1},{2},{3,6,7,8},{4,5}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,6},{5},{7,8}} => {{1,2},{3,5},{4,6,7,8}} => {{1,2},{3,6,7,8},{4,5}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,4,6},{5},{8}} => {{1},{2,8},{3,5},{4,6,7}} => {{1},{2,6,8},{3,5},{4,7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,4,6},{5},{7}} => {{1,8},{2},{3,5},{4,6,7}} => {{1,6,8},{2},{3,5},{4,7}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4,6},{5},{8}} => {{1},{2,7},{3,5},{4,6,8}} => {{1},{2,6,7},{3,5},{4,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,6},{5}} => {{1,8},{2,7},{3,5},{4,6}} => {{1,6},{2,5},{3,7},{4,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4,6},{5},{7}} => {{1,7},{2},{3,5},{4,6,8}} => {{1,6,7},{2},{3,5},{4,8}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,6},{5}} => {{1,2,7},{3,5},{4,6,8}} => {{1,2,6,7},{3,5},{4,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,6},{5},{8}} => {{1},{2,6},{3,5},{4,7,8}} => {{1},{2,7,8},{3,5},{4,6}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,6},{5}} => {{1,8},{2,6},{3,5},{4,7}} => {{1,7},{2,5},{3,6},{4,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,6},{5}} => {{1,7},{2,6},{3,5},{4,8}} => {{1,8},{2,5},{3,6},{4,7}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,6},{5},{7}} => {{1,6},{2},{3,5},{4,7,8}} => {{1,7,8},{2},{3,5},{4,6}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,6},{5}} => {{1,2,6},{3,5},{4,7,8}} => {{1,2,7,8},{3,5},{4,6}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => {{1},{2,5},{3},{4,6,7,8}} => {{1},{2,6,7,8},{3},{4,5}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,4,7},{5},{6}} => {{1,8},{2,5},{3},{4,6,7}} => {{1,6,8},{2,5},{3},{4,7}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4,7},{5},{6}} => {{1,7},{2,5},{3},{4,6,8}} => {{1,6,7},{2,5},{3},{4,8}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,7},{5},{6}} => {{1,6},{2,5},{3},{4,7,8}} => {{1,7,8},{2,5},{3},{4,6}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5},{6},{7}} => {{1,5},{2},{3},{4,6,7,8}} => {{1,6,7,8},{2},{3},{4,5}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => {{1},{2,3,5},{4,6,7,8}} => {{1},{2,3,6,7,8},{4,5}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,6,7},{5}} => {{1,7},{2,3,5},{4,6,8}} => {{1,3,5},{2,6,7},{4,8}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,6,7},{5}} => {{1,6},{2,3,5},{4,7,8}} => {{1,3,5},{2,7,8},{4,6}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5},{6,7}} => {{1,5},{2,3},{4,6,7,8}} => {{1,3},{2,6,7,8},{4,5}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,6,8},{5},{7}} => {{1,3},{2,5},{4,6,7,8}} => {{1,6,7,8},{2,3},{4,5}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,6,7,8},{4,5}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}} => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,4,5,6},{8}} => {{1},{2,8},{3,4,5,6,7}} => {{1},{2,4,6,8},{3,5,7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,4,5,6},{7}} => {{1,8},{2},{3,4,5,6,7}} => {{1,4,6,8},{2},{3,5,7}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,4,5,6}} => {{1,2,8},{3,4,5,6,7}} => {{1,2,4,6,8},{3,5,7}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4,5,6},{8}} => {{1},{2,7},{3,4,5,6,8}} => {{1},{2,4,6,7},{3,5,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,5,6}} => {{1,8},{2,7},{3,4,5,6}} => {{1,4,7},{2,5,8},{3,6}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,5,6}} => {{1,2,7},{3,4,5,6,8}} => {{1,2,4,6,7},{3,5,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => {{1},{2,6},{3,4,5,7,8}} => {{1},{2,4,7,8},{3,5,6}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,5,6}} => {{1,7},{2,6},{3,4,5,8}} => {{1,4,6},{2,5,7},{3,8}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6},{7}} => {{1,6},{2},{3,4,5,7,8}} => {{1,4,7,8},{2},{3,5,6}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,5,6}} => {{1,2,6},{3,4,5,7,8}} => {{1,2,4,7,8},{3,5,6}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => {{1},{2,5},{3,4,6,7,8}} => {{1},{2,4,5},{3,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,4,7},{5,6}} => {{1,8},{2,5},{3,4,6,7}} => {{1,4,7},{2,6,8},{3,5}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4,7},{5,6}} => {{1,7},{2,5},{3,4,6,8}} => {{1,4,8},{2,6,7},{3,5}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,7},{5,6}} => {{1,6},{2,5},{3,4,7,8}} => {{1,4,6},{2,7,8},{3,5}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6},{7}} => {{1,5},{2},{3,4,6,7,8}} => {{1,4,5},{2},{3,6,7,8}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,7,8},{5,6}} => {{1,2,5},{3,4,6,7,8}} => {{1,2,4,5},{3,6,7,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => {{1},{2,4},{3,5,6,7,8}} => {{1},{2,5,6,7,8},{3,4}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,7},{6}} => {{1,8},{2,4},{3,5,6,7}} => {{1,5,7},{2,4},{3,6,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,7},{6}} => {{1,7},{2,4},{3,5,6,8}} => {{1,5,8},{2,4},{3,6,7}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,7},{6}} => {{1,6},{2,4},{3,5,7,8}} => {{1,5,6},{2,4},{3,7,8}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6},{7}} => {{1,4},{2},{3,5,6,7,8}} => {{1,5,6,7,8},{2},{3,4}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8},{6}} => {{1,2,4},{3,5,6,7,8}} => {{1,2,5,6,7,8},{3,4}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}} => {{1,3,5,7},{2,4,6,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,6,7}} => {{1,7},{2,3,4,5,6,8}} => {{1,3,5,8},{2,4,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6,7}} => {{1,6},{2,3,4,5,7,8}} => {{1,3,5,6},{2,4,7,8}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6,7}} => {{1,5},{2,3,4,6,7,8}} => {{1,3,6,7,8},{2,4,5}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6,7}} => {{1,4},{2,3,5,6,7,8}} => {{1,3,4},{2,5,6,7,8}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8},{7}} => {{1,3},{2,4,5,6,7,8}} => {{1,4,5,6,7,8},{2,3}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}} => {{1},{2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{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}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => {{1},{2,4},{3,5,6,7,8,9}} => {{1},{2,5,6,7,8,9},{3,4}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,9},{8}} => {{1,3},{2,4,5,6,7,8},{9}} => {{1,4,5,6,7,8},{2,3},{9}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}} => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => {{1},{2,4},{3,5,6,7,8,9,10}} => {{1},{2,5,6,7,8,9,10},{3,4}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => {{1},{2,5},{3,4,6,7,8,9}} => {{1},{2,4,5},{3,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => {{1},{2,3,5},{4,6,7,8,9}} => {{1},{2,3,6,7,8,9},{4,5}}
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9},{7,8}} => {{1,4},{2,3,5,6,7,8},{9}} => {{1,3,4},{2,5,6,7,8},{9}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8,9},{7}} => {{1,2,4},{3,5,6,7,8},{9}} => {{1,2,5,6,7,8},{3,4},{9}}
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,10},{9}} => {{1,3},{2,4,5,6,7,8,9},{10}} => {{1,4,5,6,7,8,9},{2,3},{10}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10},{11}} => {{1,2,3,4,5,6,7,8,9,10},{11}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,4,5,6,7,8},{3},{9}} => {{1},{2,3,4,5,6,8},{7,9}} => {{1},{2,3,4,5,6,9},{7,8}}
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8,9},{4}} => {{1,2,3,4,5,7},{6,8},{9}} => {{1,2,3,4,5,8},{6,7},{9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,9},{8}} => {{1},{2,3,4,5,6,7,9},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{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}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{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}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8,9},{3}} => {{1,2,3,4,5,6,8},{7},{9}} => {{1,2,3,4,5,6,8},{7},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{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}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,10},{9}} => {{1},{2,3,4,5,6,7,8,10},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{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}}
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8,9,10},{3}} => {{1,2,3,4,5,6,7,9},{8},{10}} => {{1,2,3,4,5,6,7,9},{8},{10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,7,8},{9},{10}} => {{1},{2},{3,4,5,6,7,8,9,10}} => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{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}}
[] => {} => {} => {}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,8,9},{2},{3},{4},{5},{6},{7}} => {{1,2,9},{3},{4},{5},{6},{7},{8}} => {{1,2,9},{3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6},{7,8}} => {{1,9},{2,3},{4},{5},{6},{7},{8}} => {{1,3},{2,9},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2},{3},{4},{5},{6},{8}} => {{1,3},{2,9},{4},{5},{6},{7},{8}} => {{1,9},{2,3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2},{3},{4},{5},{6}} => {{1,2,3,9},{4},{5},{6},{7},{8}} => {{1,2,3,9},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6,7},{8}} => {{1,9},{2},{3,4},{5},{6},{7},{8}} => {{1,4},{2},{3,9},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6,8},{7}} => {{1,9},{2,4},{3},{5},{6},{7},{8}} => {{1,4},{2,9},{3},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2},{3},{4},{5}} => {{1,2,3,4,9},{5},{6},{7},{8}} => {{1,2,3,4,9},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,5,6,7,8,9},{2},{3},{4}} => {{1,2,3,4,5,9},{6},{7},{8}} => {{1,2,3,4,5,9},{6},{7},{8}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,4,9},{2},{3},{5},{6},{7},{8}} => {{1,6},{2},{3},{4},{5,9},{7},{8}} => {{1,9},{2},{3},{4},{5,6},{7},{8}}
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9},{2},{3}} => {{1,2,3,4,5,6,9},{7},{8}} => {{1,2,3,4,5,6,9},{7},{8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2},{3,4},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6,7},{8}} => {{1,7},{2},{3},{4},{5},{6,9},{8}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9},{2}} => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7,9},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,3},{4},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6},{7,8}} => {{1,8},{2},{3},{4},{5},{6},{7,9}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,8,9},{2,3},{4,5},{6,7}} => {{1,2,9},{3,4},{5,6},{7,8}} => {{1,2,4},{3,6},{5,8},{7,9}}
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9},{2,3}} => {{1,2,3,4,5,6,9},{7,8}} => {{1,2,3,4,5,6,8},{7,9}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,4},{3},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6,8},{7}} => {{1,8},{2},{3},{4},{5},{6,9},{7}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,9},{2,8},{3},{4},{5},{6},{7}} => {{1,9},{2,8},{3},{4},{5},{6},{7}} => {{1,8},{2,9},{3},{4},{5},{6},{7}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8,9},{3}} => {{1,2,3,4,5,6,8},{7,9}} => {{1,2,3,4,5,6,9},{7,8}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,5,6,7,8,9},{2,3,4}} => {{1,2,3,4,5,9},{6,7,8}} => {{1,2,3,4,5,7,9},{6,8}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2,3,4,5}} => {{1,2,3,4,9},{5,6,7,8}} => {{1,2,3,4,6,8},{5,7,9}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,7},{4,6},{5}} => {{1,9},{2,8},{3,7},{4,6},{5}} => {{1,6},{2,7},{3,8},{4,9},{5}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3,4,5,6}} => {{1,2,3,9},{4,5,6,7,8}} => {{1,2,3,5,7,9},{4,6,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2,3,4,5,6,7}} => {{1,2,9},{3,4,5,6,7,8}} => {{1,2,4,6,8},{3,5,7,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,5,6,7,8}} => {{1,9},{2,3,4,5,6,7,8}} => {{1,3,5,7,9},{2,4,6,8}}
[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] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => {{1,2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,9},{8}} => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => {{1,3},{2},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,9},{7},{8}} => {{1,4},{2},{3},{5},{6},{7},{8},{9}} => {{1,4},{2},{3},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,9},{6},{7},{8}} => {{1,5},{2},{3},{4},{6},{7},{8},{9}} => {{1,5},{2},{3},{4},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,9},{5},{6},{7},{8}} => {{1,6},{2},{3},{4},{5},{7},{8},{9}} => {{1,6},{2},{3},{4},{5},{7},{8},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,9},{4},{5},{6},{7},{8}} => {{1,7},{2},{3},{4},{5},{6},{8},{9}} => {{1,7},{2},{3},{4},{5},{6},{8},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,9},{3},{4},{5},{6},{7},{8}} => {{1,8},{2},{3},{4},{5},{6},{7},{9}} => {{1,8},{2},{3},{4},{5},{6},{7},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9}} => {{1,2,3},{4},{5},{6},{7},{8},{9}} => {{1,2,3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5},{6,9},{7,8}} => {{1,4},{2,3},{5},{6},{7},{8},{9}} => {{1,3},{2,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} => {{1,4},{2},{3},{5},{6},{7},{8},{9},{10}} => {{1,4},{2},{3},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,9},{6,7},{8}} => {{1,5},{2},{3,4},{6},{7},{8},{9}} => {{1,4},{2},{3,5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} => {{1,5},{2},{3},{4},{6},{7},{8},{9},{10}} => {{1,5},{2},{3},{4},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,9},{5,6},{7},{8}} => {{1,6},{2},{3},{4,5},{7},{8},{9}} => {{1,5},{2},{3},{4,6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => {{1,6},{2},{3},{4},{5},{7},{8},{9},{10}} => {{1,6},{2},{3},{4},{5},{7},{8},{9},{10}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,9},{4,5},{6},{7},{8}} => {{1,7},{2},{3},{4},{5,6},{8},{9}} => {{1,6},{2},{3},{4},{5,7},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} => {{1,7},{2},{3},{4},{5},{6},{8},{9},{10}} => {{1,7},{2},{3},{4},{5},{6},{8},{9},{10}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,9},{3,4},{5},{6},{7},{8}} => {{1,8},{2},{3},{4},{5},{6,7},{9}} => {{1,7},{2},{3},{4},{5},{6,8},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}} => {{1,8},{2},{3},{4},{5},{6},{7},{9},{10}} => {{1,8},{2},{3},{4},{5},{6},{7},{9},{10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}} => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,9},{8}} => {{1,3},{2,4},{5},{6},{7},{8},{9}} => {{1,4},{2,3},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{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}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4},{5,6,9},{7},{8}} => {{1,4},{2},{3,5},{6},{7},{8},{9}} => {{1,5},{2},{3,4},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{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}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{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}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{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}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{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}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,10},{2,9},{3},{4},{5},{6},{7},{8}} => {{1,10},{2,9},{3},{4},{5},{6},{7},{8}} => {{1,9},{2,10},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7,8},{9}} => {{1},{2,3},{4},{5},{6},{7},{8},{9}} => {{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1,2},{3,4},{5},{6},{7},{8},{9}} => {{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7,8},{9}} => {{1},{2,3,4},{5},{6},{7},{8},{9}} => {{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{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}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{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}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{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}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{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}}
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{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}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,8},{9}} => {{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{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}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{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}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{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}}
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{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}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8},{9}} => {{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{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}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{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}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => {{1},{2},{3},{4},{5},{6},{7},{8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{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}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6},{7,8},{9}} => {{1},{2,3},{4},{5},{6},{7},{8,9}} => {{1},{2,3},{4},{5},{6},{7},{8,9}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5,6},{7},{8},{9}} => {{1},{2},{3},{4,5},{6,7},{8,9}} => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7,8},{9}} => {{1},{2,3},{4,5},{6,7},{8,9}} => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{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}}
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{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}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7},{8,9}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,8,9}} => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6},{7,8,9}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{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}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6},{7,8,9}} => {{1},{2},{3},{4,5,6},{7,8,9}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{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}}
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{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}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8},{9}} => {{1},{2},{3},{4,5},{6,7,8,9}} => {{1},{2},{3},{4,5},{6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7,8},{9}} => {{1},{2,3},{4,5},{6,7,8,9}} => {{1},{2,3},{4,5},{6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3,4},{5,6,7},{8},{9}} => {{1},{2},{3,4,5},{6,7,8,9}} => {{1},{2},{3,4,5},{6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{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}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5,6,7,8},{9}} => {{1},{2,3,4,5},{6,7,8,9}} => {{1},{2,3,4,5},{6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{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}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4,5},{6,7},{8},{9}} => {{1},{2},{3,4},{5,6,7,8,9}} => {{1},{2},{3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5},{6,7,8},{9}} => {{1},{2,3,4},{5,6,7,8,9}} => {{1},{2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6,7,8,9}} => {{1},{2},{3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6},{7,8},{9}} => {{1},{2,3},{4,5,6,7,8,9}} => {{1},{2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{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}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{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}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{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}}
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{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}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{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}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{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}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{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}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{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}}
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{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}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{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}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}} => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5,6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,6},{7,8},{9,10}} => {{1},{2},{3},{4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5,6},{7,8},{9},{10}} => {{1},{2},{3,4},{5,6},{7,8},{9,10}} => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{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}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{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}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7},{8,9,10}} => {{1},{2},{3},{4},{5},{6,7},{8,9,10}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7},{8,9,10}} => {{1},{2,3},{4,5},{6,7},{8,9,10}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{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}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{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}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{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}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{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}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5,6,7,8},{9},{10}} => {{1},{2},{3,4,5,6},{7,8,9,10}} => {{1},{2},{3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{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}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{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}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7,8,9,10}} => {{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7,8,9,10}} => {{1},{2,3},{4,5},{6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4,5},{6,7,8,9},{10}} => {{1},{2,3,4,5},{6,7,8,9,10}} => {{1},{2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{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}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,6,7,8,9,10}} => {{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5,6},{7,8,9},{10}} => {{1},{2,3,4},{5,6,7,8,9,10}} => {{1},{2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{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}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5,6,7},{8},{9},{10}} => {{1},{2},{3},{4,5,6,7,8,9,10}} => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6,7},{8,9},{10}} => {{1},{2,3},{4,5,6,7,8,9,10}} => {{1},{2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{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}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{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] => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,9},{8}} => {{1},{2},{3},{4},{5},{6},{7,9},{8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,9},{7},{8}} => {{1},{2},{3},{4},{5},{6,9},{7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,9},{6},{7},{8}} => {{1},{2},{3},{4},{5,9},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8},{9}} => {{1},{2},{3},{4,9},{5},{6},{7},{8}} => {{1},{2},{3},{4,9},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8},{9}} => {{1},{2},{3,9},{4},{5},{6},{7},{8}} => {{1},{2},{3,9},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,8},{2},{3},{4},{5},{6},{7},{9}} => {{1},{2,9},{3},{4},{5},{6},{7},{8}} => {{1},{2,9},{3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,9},{8}} => {{1},{2},{3},{4},{5},{6,7,9},{8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,9},{7},{8}} => {{1},{2},{3},{4},{5,6,9},{7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,5,6},{2},{3},{4},{7},{8},{9}} => {{1},{2},{3},{4,5,9},{6},{7},{8}} => {{1},{2},{3},{4,5,9},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,6,7},{2},{3},{4},{5},{8},{9}} => {{1},{2},{3,4,9},{5},{6},{7},{8}} => {{1},{2},{3,4,9},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8},{9},{10}} => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,7,8},{2},{3},{4},{5},{6},{9}} => {{1},{2,3,9},{4},{5},{6},{7},{8}} => {{1},{2,3,9},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,8},{2},{3},{4},{5},{6},{7},{9},{10}} => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5},{6},{7,9},{8}} => {{1,3},{2},{4},{5},{6},{7},{8,9}} => {{1,3},{2},{4},{5},{6},{7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => {{1,2,10},{3},{4},{5},{6},{7},{8},{9}} => {{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5},{6},{7,9},{8}} => {{1,3},{2},{4},{5},{6},{7,9},{8}} => {{1,3},{2},{4},{5},{6},{7,9},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6},{7},{8,9}} => {{1,2},{3},{4},{5},{6},{7,9},{8}} => {{1,2},{3},{4},{5},{6},{7,9},{8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,8},{7,9}} => {{1},{2},{3},{4},{5},{6,9},{7,8}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9,10},{2}} => {{1,2,3,4,5,6,7,8,10},{9}} => {{1,2,3,4,5,6,7,8,10},{9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => {{1,10},{2,3,4,5,6,7,8,9}} => {{1,10},{2,3,4,5,6,7,8,9}} => {{1,3,5,7,9},{2,4,6,8,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => {{1,11},{2,3,4,5,6,7,8,9,10}} => {{1,11},{2,3,4,5,6,7,8,9,10}} => {{1,3,5,7,9,11},{2,4,6,8,10}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,9},{7,8}} => {{1},{2},{3},{4},{5},{6,8},{7,9}}
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,6},{5,7,8,9,10}} => {{1,2,3,4,7,8,9,10},{5,6}}
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2,3,4,5,6,7,9},{8,10}} => {{1,2,3,4,5,6,7,10},{8,9}}
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,3},{2},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7,9},{8}} => {{1,2,3,4,5,6},{7,9},{8}}
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,4},{3},{5,6,7,8,9}} => {{1,2,3,4,5},{6,8},{7,9}} => {{1,2,3,4,5},{6,9},{7,8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,8},{6},{7},{9}} => {{1},{2},{3},{4},{5,8},{6},{7},{9}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4},{5,6},{7},{8},{9}} => {{1,10},{2},{3},{4},{5,6},{7},{8},{9}} => {{1,6},{2},{3},{4},{5,10},{7},{8},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,8,9},{3},{4},{5},{6},{7}} => {{1,2,8},{3},{4},{5},{6},{7},{9}} => {{1,2,8},{3},{4},{5},{6},{7},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,7},{2},{3},{4},{5},{6},{8,9}} => {{1,2},{3,9},{4},{5},{6},{7},{8}} => {{1,2},{3,9},{4},{5},{6},{7},{8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,9},{4},{5},{6},{7},{8}} => {{1,7},{2},{3},{4},{5},{6},{8,9}} => {{1,7},{2},{3},{4},{5},{6},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2},{3},{4},{5},{6},{7}} => {{1,2,3,10},{4},{5},{6},{7},{8},{9}} => {{1,2,3,10},{4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,5,6,7,8,9},{4}} => {{1,2,3,4,5,7},{6},{8,9}} => {{1,2,3,4,5,7},{6},{8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4,5,6},{7,9},{8}} => {{1,3},{2},{4,5,6,7,8,9}} => {{1,3},{2},{4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5,8},{6},{7},{9}} => {{1},{2,5},{3},{4},{6},{7},{8},{9}} => {{1},{2,5},{3},{4},{6},{7},{8},{9}}
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9,10},{2},{3}} => {{1,2,3,4,5,6,7,10},{8},{9}} => {{1,2,3,4,5,6,7,10},{8},{9}}
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,5,6,7,8,9,10},{2},{3},{4}} => {{1,2,3,4,5,6,10},{7},{8},{9}} => {{1,2,3,4,5,6,10},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,6,7,8,9,10},{2},{3},{4},{5}} => {{1,2,3,4,5,10},{6},{7},{8},{9}} => {{1,2,3,4,5,10},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,7,8,9,10},{2},{3},{4},{5},{6}} => {{1,2,3,4,10},{5},{6},{7},{8},{9}} => {{1,2,3,4,10},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,4},{2},{3},{5},{6,9},{7},{8}} => {{1,4},{2},{3},{5},{6,9},{7},{8}} => {{1,4},{2},{3},{5},{6,9},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,2,11},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1,2,11},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,7,8,9,10},{3,4,5,6}} => {{1,2,3,4,9},{5,6,7,8,10}} => {{1,2,3,4,6,8,9},{5,7,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,7,8,9,10},{2,3,4,5,6}} => {{1,2,3,4,10},{5,6,7,8,9}} => {{1,2,3,4,6,8,10},{5,7,9}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,10},{3,9},{4,8},{5,7},{6}} => {{1,9},{2,8},{3,7},{4,6},{5},{10}} => {{1,6},{2,7},{3,8},{4,9},{5},{10}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,10},{5,9},{6,8},{7}} => {{1,7},{2,6},{3,5},{4},{8,10},{9}} => {{1,5},{2,6},{3,7},{4},{8,10},{9}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6,10},{7,9},{8}} => {{1,5},{2,4},{3},{6,10},{7,9},{8}} => {{1,4},{2,5},{3},{6,9},{7,10},{8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,7},{2,6},{3,5},{4},{8,10},{9}} => {{1,3},{2},{4,10},{5,9},{6,8},{7}} => {{1,3},{2},{4,8},{5,9},{6,10},{7}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3,7},{4,6},{5},{10}} => {{1},{2,10},{3,9},{4,8},{5,7},{6}} => {{1},{2,7},{3,8},{4,9},{5,10},{6}}
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}} => {{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}} => {{1,7},{2,8},{3,9},{4,10},{5,11},{6},{12}}
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,12},{5,11},{6,10},{7,9},{8}} => {{1,9},{2,8},{3,7},{4,6},{5},{10,12},{11}} => {{1,6},{2,7},{3,8},{4,9},{5},{10,12},{11}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6,12},{7,11},{8,10},{9}} => {{1,7},{2,6},{3,5},{4},{8,12},{9,11},{10}} => {{1,5},{2,6},{3,7},{4},{8,11},{9,12},{10}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4},{8,12},{9,11},{10}} => {{1,5},{2,4},{3},{6,12},{7,11},{8,10},{9}} => {{1,4},{2,5},{3},{6,10},{7,11},{8,12},{9}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,8},{3,7},{4,6},{5},{10,12},{11}} => {{1,3},{2},{4,12},{5,11},{6,10},{7,9},{8}} => {{1,3},{2},{4,9},{5,10},{6,11},{7,12},{8}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}} => {{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}} => {{1},{2,8},{3,9},{4,10},{5,11},{6,12},{7}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9},{10,11}} => {{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1,2,3,4,5,6,7,8,9,11},{10}} => {{1,2,3,4,5,6,7,8,9,11},{10}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => {{1,12},{2,3,4,5,6,7,8,9,10,11}} => {{1,12},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,5,7,9,11},{2,4,6,8,10,12}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,8,9},{7}} => {{1,2,4},{3},{5},{6},{7},{8},{9}} => {{1,2,4},{3},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8,9},{10,11}} => {{1,2},{3,4,5,6,7,8,9,10,11}} => {{1,2},{3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2,3,4,5,6,7}} => {{1,2,3,10},{4,5,6,7,8,9}} => {{1,2,3,5,7,9},{4,6,8,10}}
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,5,6,7,8,9},{3,4}} => {{1,2,3,4,5,8},{6,7},{9}} => {{1,2,3,4,5,7},{6,8},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,8},{3},{4},{5},{6},{7},{9}} => {{1},{2,8},{3},{4},{5},{6},{7},{9}} => {{1},{2,8},{3},{4},{5},{6},{7},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => {{1,9,10},{2,3,4,5,6,7,8}} => {{1,2,10},{3,4,5,6,7,8,9}} => {{1,2,4,6,8,10},{3,5,7,9}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,6,7,8,9,10},{2,3,4,5}} => {{1,2,3,4,5,10},{6,7,8,9}} => {{1,2,3,4,5,7,9},{6,8,10}}
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,5,6,7,8,9,10},{2,3,4}} => {{1,2,3,4,5,6,10},{7,8,9}} => {{1,2,3,4,5,6,8,10},{7,9}}
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9,10},{2,3}} => {{1,2,3,4,5,6,7,10},{8,9}} => {{1,2,3,4,5,6,7,9},{8,10}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,8},{2},{3},{4},{5},{6,7},{9}} => {{1},{2,9},{3,4},{5},{6},{7},{8}} => {{1},{2,4},{3,9},{5},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,9},{3},{4},{5},{6},{7},{8},{10}} => {{1},{2,9},{3},{4},{5},{6},{7},{8},{10}} => {{1},{2,9},{3},{4},{5},{6},{7},{8},{10}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,9},{6,7},{8}} => {{1},{2},{3},{4},{5,7},{6,9},{8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,10},{8,9}} => {{1,2},{3,4},{5,6},{7,9},{8,10}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,8},{9,10}} => {{1,2},{3,4},{5,10},{6,7},{8,9}} => {{1,2},{3,4},{5,7},{6,9},{8,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,3},{4,5},{6,7},{9,10}} => {{1,2},{3,10},{4,5},{6,7},{8,9}} => {{1,2},{3,5},{4,7},{6,9},{8,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,3},{4,5},{6,7},{8,9}} => {{1,10},{2,3},{4,5},{6,7},{8,9}} => {{1,3},{2,5},{4,7},{6,9},{8,10}}
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,7,8,9,10},{4,5,6}} => {{1,2,3,4,8},{5,6,7,9,10}} => {{1,2,3,4,6,9,10},{5,7,8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,4,5,6,7,8},{2,3},{9}} => {{1},{2,3,4,5,6,9},{7,8}} => {{1},{2,3,4,5,6,8},{7,9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,6},{7,10},{8,9}} => {{1,4},{2,3},{5,6},{7,8},{9,10}} => {{1,3},{2,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,10},{6,7},{8,9}} => {{1,6},{2,3},{4,5},{7,8},{9,10}} => {{1,3},{2,5},{4,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,10},{4,5},{6,7},{8,9}} => {{1,8},{2,3},{4,5},{6,7},{9,10}} => {{1,3},{2,5},{4,7},{6,8},{9,10}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8},{9,10}} => {{1,2},{3,4},{5,10},{6,9},{7,8}} => {{1,2},{3,4},{5,8},{6,9},{7,10}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8},{9,10}} => {{1,2},{3,4},{5,8},{6,7},{9,10}} => {{1,2},{3,4},{5,7},{6,8},{9,10}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,8},{4,7},{5,6},{9,10}} => {{1,2},{3,8},{4,7},{5,6},{9,10}} => {{1,2},{3,6},{4,7},{5,8},{9,10}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,3},{4,7},{5,6},{9,10}} => {{1,2},{3,10},{4,7},{5,6},{8,9}} => {{1,2},{3,6},{4,7},{5,9},{8,10}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,7},{3,4},{5,6},{9,10}} => {{1,2},{3,10},{4,9},{5,6},{7,8}} => {{1,2},{3,6},{4,8},{5,9},{7,10}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,7},{3,6},{4,5},{9,10}} => {{1,2},{3,10},{4,9},{5,8},{6,7}} => {{1,2},{3,7},{4,8},{5,9},{6,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,8},{6,7},{9,10}} => {{1,2},{3,6},{4,5},{7,8},{9,10}} => {{1,2},{3,5},{4,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,8},{6,7},{9,10}} => {{1,2},{3,6},{4,5},{7,10},{8,9}} => {{1,2},{3,5},{4,6},{7,9},{8,10}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,5},{3,4},{6,7},{9,10}} => {{1,2},{3,10},{4,5},{6,9},{7,8}} => {{1,2},{3,5},{4,8},{6,9},{7,10}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,8},{4,5},{6,7},{9,10}} => {{1,2},{3,8},{4,5},{6,7},{9,10}} => {{1,2},{3,5},{4,7},{6,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,4},{5,10},{6,9},{7,8}} => {{1,6},{2,5},{3,4},{7,8},{9,10}} => {{1,4},{2,5},{3,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,10},{6,9},{7,8}} => {{1,6},{2,5},{3,4},{7,10},{8,9}} => {{1,4},{2,5},{3,6},{7,9},{8,10}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,10},{2,5},{3,4},{6,9},{7,8}} => {{1,10},{2,5},{3,4},{6,9},{7,8}} => {{1,4},{2,5},{3,8},{6,9},{7,10}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,10},{4,5},{6,9},{7,8}} => {{1,8},{2,5},{3,4},{6,7},{9,10}} => {{1,4},{2,5},{3,7},{6,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,10},{2,3},{4,5},{6,9},{7,8}} => {{1,10},{2,5},{3,4},{6,7},{8,9}} => {{1,4},{2,5},{3,7},{6,9},{8,10}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,4},{5,6},{7,8}} => {{1,10},{2,9},{3,4},{5,6},{7,8}} => {{1,4},{2,6},{3,8},{5,9},{7,10}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,6},{4,5},{7,8}} => {{1,10},{2,9},{3,4},{5,8},{6,7}} => {{1,4},{2,7},{3,8},{5,9},{6,10}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,4},{5,8},{6,7}} => {{1,10},{2,9},{3,6},{4,5},{7,8}} => {{1,5},{2,6},{3,8},{4,9},{7,10}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,8},{4,5},{6,7}} => {{1,10},{2,9},{3,8},{4,5},{6,7}} => {{1,5},{2,7},{3,8},{4,9},{6,10}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,10},{4,9},{5,6},{7,8}} => {{1,8},{2,7},{3,4},{5,6},{9,10}} => {{1,4},{2,6},{3,7},{5,8},{9,10}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,10},{2,3},{4,9},{5,6},{7,8}} => {{1,10},{2,7},{3,4},{5,6},{8,9}} => {{1,4},{2,6},{3,7},{5,9},{8,10}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,8},{4,7},{5,6}} => {{1,10},{2,9},{3,8},{4,7},{5,6}} => {{1,6},{2,7},{3,8},{4,9},{5,10}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,10},{4,9},{5,8},{6,7}} => {{1,8},{2,7},{3,6},{4,5},{9,10}} => {{1,5},{2,6},{3,7},{4,8},{9,10}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,3},{4,9},{5,8},{6,7}} => {{1,10},{2,7},{3,6},{4,5},{8,9}} => {{1,5},{2,6},{3,7},{4,9},{8,10}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,6},{7,10},{8,9}} => {{1,4},{2,3},{5,6},{7,10},{8,9}} => {{1,3},{2,4},{5,6},{7,9},{8,10}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,6},{2,5},{3,4},{7,10},{8,9}} => {{1,4},{2,3},{5,10},{6,9},{7,8}} => {{1,3},{2,4},{5,8},{6,9},{7,10}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5},{7,10},{8,9}} => {{1,4},{2,3},{5,8},{6,7},{9,10}} => {{1,3},{2,4},{5,7},{6,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5},{7,10},{8,9}} => {{1,4},{2,3},{5,10},{6,7},{8,9}} => {{1,3},{2,4},{5,7},{6,9},{8,10}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,10},{4,7},{5,6},{8,9}} => {{1,8},{2,3},{4,7},{5,6},{9,10}} => {{1,3},{2,6},{4,7},{5,8},{9,10}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,3},{4,7},{5,6},{8,9}} => {{1,10},{2,3},{4,7},{5,6},{8,9}} => {{1,3},{2,6},{4,7},{5,9},{8,10}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,7},{3,4},{5,6},{8,9}} => {{1,10},{2,3},{4,9},{5,6},{7,8}} => {{1,3},{2,6},{4,8},{5,9},{7,10}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,7},{3,6},{4,5},{8,9}} => {{1,10},{2,3},{4,9},{5,8},{6,7}} => {{1,3},{2,7},{4,8},{5,9},{6,10}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,10},{6,7},{8,9}} => {{1,6},{2,3},{4,5},{7,10},{8,9}} => {{1,3},{2,5},{4,6},{7,9},{8,10}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,5},{3,4},{6,7},{8,9}} => {{1,10},{2,3},{4,5},{6,9},{7,8}} => {{1,3},{2,5},{4,8},{6,9},{7,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}} => {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}} => {{1,2},{3,4},{5,6},{7,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}} => {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}} => {{1,2},{3,4},{5,6},{7,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}} => {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}} => {{1,2},{3,4},{5,6},{7,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}} => {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}} => {{1,2},{3,4},{5,6},{7,9},{8,11},{10,12}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}} => {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}} => {{1,2},{3,4},{5,8},{6,9},{7,10},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}} => {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}} => {{1,2},{3,4},{5,8},{6,9},{7,11},{10,12}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}} => {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}} => {{1,2},{3,4},{5,8},{6,10},{7,11},{9,12}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}} => {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}} => {{1,2},{3,4},{5,9},{6,10},{7,11},{8,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}} => {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}} => {{1,2},{3,4},{5,7},{6,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}} => {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}} => {{1,2},{3,4},{5,7},{6,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}} => {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}} => {{1,2},{3,4},{5,7},{6,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}} => {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}} => {{1,2},{3,4},{5,7},{6,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}} => {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}} => {{1,2},{3,4},{5,7},{6,9},{8,11},{10,12}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}} => {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}} => {{1,2},{3,6},{4,7},{5,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}} => {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}} => {{1,2},{3,6},{4,7},{5,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}} => {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}} => {{1,2},{3,6},{4,7},{5,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}} => {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}} => {{1,2},{3,6},{4,7},{5,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}} => {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}} => {{1,2},{3,6},{4,7},{5,9},{8,11},{10,12}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}} => {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}} => {{1,2},{3,6},{4,8},{5,10},{7,11},{9,12}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}} => {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}} => {{1,2},{3,6},{4,9},{5,10},{7,11},{8,12}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}} => {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}} => {{1,2},{3,7},{4,8},{5,10},{6,11},{9,12}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}} => {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}} => {{1,2},{3,7},{4,9},{5,10},{6,11},{8,12}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}} => {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}} => {{1,2},{3,6},{4,8},{5,9},{7,10},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}} => {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}} => {{1,2},{3,6},{4,8},{5,9},{7,11},{10,12}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}} => {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}} => {{1,2},{3,8},{4,9},{5,10},{6,11},{7,12}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}} => {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}} => {{1,2},{3,7},{4,8},{5,9},{6,10},{11,12}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}} => {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}} => {{1,2},{3,7},{4,8},{5,9},{6,11},{10,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}} => {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}} => {{1,2},{3,5},{4,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}} => {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}} => {{1,2},{3,5},{4,6},{7,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}} => {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}} => {{1,2},{3,5},{4,6},{7,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}} => {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}} => {{1,2},{3,5},{4,6},{7,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}} => {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}} => {{1,2},{3,5},{4,6},{7,9},{8,11},{10,12}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}} => {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}} => {{1,2},{3,5},{4,8},{6,9},{7,10},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}} => {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}} => {{1,2},{3,5},{4,8},{6,9},{7,11},{10,12}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}} => {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}} => {{1,2},{3,5},{4,8},{6,10},{7,11},{9,12}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}} => {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}} => {{1,2},{3,5},{4,9},{6,10},{7,11},{8,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}} => {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}} => {{1,2},{3,5},{4,7},{6,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}} => {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}} => {{1,2},{3,5},{4,7},{6,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}} => {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}} => {{1,2},{3,5},{4,7},{6,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}} => {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}} => {{1,2},{3,5},{4,7},{6,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}} => {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}} => {{1,2},{3,5},{4,7},{6,9},{8,11},{10,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}} => {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}} => {{1,4},{2,5},{3,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}} => {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}} => {{1,4},{2,5},{3,6},{7,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}} => {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}} => {{1,4},{2,5},{3,6},{7,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}} => {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}} => {{1,4},{2,5},{3,6},{7,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}} => {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}} => {{1,4},{2,5},{3,6},{7,9},{8,11},{10,12}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}} => {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}} => {{1,4},{2,5},{3,8},{6,9},{7,10},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}} => {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}} => {{1,4},{2,5},{3,8},{6,9},{7,11},{10,12}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}} => {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}} => {{1,4},{2,5},{3,8},{6,10},{7,11},{9,12}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}} => {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}} => {{1,4},{2,5},{3,9},{6,10},{7,11},{8,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}} => {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}} => {{1,4},{2,5},{3,7},{6,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}} => {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}} => {{1,4},{2,5},{3,7},{6,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}} => {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}} => {{1,4},{2,5},{3,7},{6,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}} => {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}} => {{1,4},{2,5},{3,7},{6,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}} => {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}} => {{1,4},{2,5},{3,7},{6,9},{8,11},{10,12}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}} => {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}} => {{1,4},{2,6},{3,8},{5,9},{7,10},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}} => {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}} => {{1,4},{2,6},{3,8},{5,9},{7,11},{10,12}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}} => {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}} => {{1,4},{2,8},{3,9},{5,10},{6,11},{7,12}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}} => {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}} => {{1,4},{2,7},{3,8},{5,9},{6,10},{11,12}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}} => {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}} => {{1,4},{2,7},{3,8},{5,9},{6,11},{10,12}}
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}} => {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}} => {{1,5},{2,6},{3,8},{4,9},{7,10},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}} => {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}} => {{1,5},{2,6},{3,8},{4,9},{7,11},{10,12}}
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}} => {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}} => {{1,5},{2,8},{3,9},{4,10},{6,11},{7,12}}
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}} => {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}} => {{1,5},{2,7},{3,8},{4,9},{6,10},{11,12}}
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}} => {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}} => {{1,5},{2,7},{3,8},{4,9},{6,11},{10,12}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}} => {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}} => {{1,4},{2,6},{3,8},{5,10},{7,11},{9,12}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}} => {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}} => {{1,4},{2,7},{3,8},{5,10},{6,11},{9,12}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}} => {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}} => {{1,4},{2,6},{3,9},{5,10},{7,11},{8,12}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}} => {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}} => {{1,4},{2,7},{3,9},{5,10},{6,11},{8,12}}
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}} => {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}} => {{1,6},{2,8},{3,9},{4,10},{5,11},{7,12}}
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}} => {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}} => {{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}} => {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}} => {{1,5},{2,6},{3,8},{4,10},{7,11},{9,12}}
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}} => {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}} => {{1,5},{2,7},{3,8},{4,10},{6,11},{9,12}}
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}} => {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}} => {{1,5},{2,6},{3,9},{4,10},{7,11},{8,12}}
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}} => {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}} => {{1,5},{2,7},{3,9},{4,10},{6,11},{8,12}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}} => {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}} => {{1,4},{2,6},{3,7},{5,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}} => {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}} => {{1,4},{2,6},{3,7},{5,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}} => {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}} => {{1,4},{2,6},{3,7},{5,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}} => {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}} => {{1,4},{2,6},{3,7},{5,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}} => {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}} => {{1,4},{2,6},{3,7},{5,9},{8,11},{10,12}}
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}} => {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}} => {{1,6},{2,7},{3,8},{4,9},{5,10},{11,12}}
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}} => {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}} => {{1,6},{2,7},{3,8},{4,9},{5,11},{10,12}}
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}} => {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}} => {{1,6},{2,7},{3,8},{4,10},{5,11},{9,12}}
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}} => {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}} => {{1,6},{2,7},{3,9},{4,10},{5,11},{8,12}}
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}} => {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}} => {{1,5},{2,6},{3,7},{4,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}} => {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}} => {{1,5},{2,6},{3,7},{4,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}} => {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}} => {{1,5},{2,6},{3,7},{4,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}} => {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}} => {{1,5},{2,6},{3,7},{4,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}} => {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}} => {{1,5},{2,6},{3,7},{4,9},{8,11},{10,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}} => {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}} => {{1,3},{2,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}} => {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}} => {{1,3},{2,4},{5,6},{7,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}} => {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}} => {{1,3},{2,4},{5,6},{7,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}} => {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}} => {{1,3},{2,4},{5,6},{7,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}} => {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}} => {{1,3},{2,4},{5,6},{7,9},{8,11},{10,12}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}} => {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}} => {{1,3},{2,4},{5,8},{6,9},{7,10},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}} => {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}} => {{1,3},{2,4},{5,8},{6,9},{7,11},{10,12}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}} => {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}} => {{1,3},{2,4},{5,8},{6,10},{7,11},{9,12}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}} => {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}} => {{1,3},{2,4},{5,9},{6,10},{7,11},{8,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}} => {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}} => {{1,3},{2,4},{5,7},{6,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}} => {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}} => {{1,3},{2,4},{5,7},{6,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}} => {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}} => {{1,3},{2,4},{5,7},{6,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}} => {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}} => {{1,3},{2,4},{5,7},{6,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}} => {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}} => {{1,3},{2,4},{5,7},{6,9},{8,11},{10,12}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}} => {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}} => {{1,3},{2,6},{4,7},{5,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}} => {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}} => {{1,3},{2,6},{4,7},{5,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}} => {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}} => {{1,3},{2,6},{4,7},{5,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}} => {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}} => {{1,3},{2,6},{4,7},{5,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}} => {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}} => {{1,3},{2,6},{4,7},{5,9},{8,11},{10,12}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}} => {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}} => {{1,3},{2,6},{4,8},{5,10},{7,11},{9,12}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}} => {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}} => {{1,3},{2,6},{4,9},{5,10},{7,11},{8,12}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}} => {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}} => {{1,3},{2,7},{4,8},{5,10},{6,11},{9,12}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}} => {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}} => {{1,3},{2,7},{4,9},{5,10},{6,11},{8,12}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}} => {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}} => {{1,3},{2,6},{4,8},{5,9},{7,10},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}} => {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}} => {{1,3},{2,6},{4,8},{5,9},{7,11},{10,12}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}} => {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}} => {{1,3},{2,8},{4,9},{5,10},{6,11},{7,12}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}} => {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}} => {{1,3},{2,7},{4,8},{5,9},{6,10},{11,12}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}} => {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}} => {{1,3},{2,7},{4,8},{5,9},{6,11},{10,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}} => {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}} => {{1,3},{2,5},{4,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}} => {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}} => {{1,3},{2,5},{4,6},{7,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}} => {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}} => {{1,3},{2,5},{4,6},{7,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}} => {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}} => {{1,3},{2,5},{4,6},{7,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}} => {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}} => {{1,3},{2,5},{4,6},{7,9},{8,11},{10,12}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}} => {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}} => {{1,3},{2,5},{4,8},{6,9},{7,10},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}} => {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}} => {{1,3},{2,5},{4,8},{6,9},{7,11},{10,12}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}} => {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}} => {{1,3},{2,5},{4,8},{6,10},{7,11},{9,12}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}} => {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}} => {{1,3},{2,5},{4,9},{6,10},{7,11},{8,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}} => {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}} => {{1,3},{2,5},{4,7},{6,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}} => {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}} => {{1,3},{2,5},{4,7},{6,8},{9,11},{10,12}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}} => {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}} => {{1,3},{2,5},{4,7},{6,10},{8,11},{9,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}} => {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}} => {{1,3},{2,5},{4,7},{6,9},{8,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}} => {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}} => {{1,3},{2,5},{4,7},{6,9},{8,11},{10,12}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8,9,10},{11,12}} => {{1,2},{3,4,5,6,7,8,9,10,11,12}} => {{1,2},{3,4,5,6,7,8,9,10,11,12}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,3,4,5,6},{2},{7,8,9}} => {{1,2,3},{4,5,6,7,9},{8}} => {{1,2,3},{4,5,6,7,9},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,7},{2},{3},{4},{5,6},{8},{9}} => {{1},{2},{3,9},{4,5},{6},{7},{8}} => {{1},{2},{3,5},{4,9},{6},{7},{8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2},{3},{4,5},{7},{8},{9}} => {{1},{2},{3},{4,9},{5,6},{7},{8}} => {{1},{2},{3},{4,6},{5,9},{7},{8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2,3,4},{5,6,7}} => {{1,2,3,10},{4,5,6},{7,8,9}} => {{1,2,3,5,8,10},{4,6},{7,9}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,8},{2,7},{3,6},{4,5},{9}} => {{1},{2,9},{3,8},{4,7},{5,6}} => {{1},{2,6},{3,7},{4,8},{5,9}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,9},{3,8},{4,7},{5,6}} => {{1,8},{2,7},{3,6},{4,5},{9}} => {{1,5},{2,6},{3,7},{4,8},{9}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,9},{3,8},{4,7},{5},{6}} => {{1,8},{2,7},{3,6},{4},{5},{9}} => {{1,6},{2,7},{3,8},{4},{5},{9}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,8},{2,7},{3,5,6},{4},{9}} => {{1},{2,9},{3,8},{4,5,7},{6}} => {{1},{2,5,9},{3,7},{4,8},{6}}
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
Wachs-White
Description
A transformation of set partitions due to Wachs and White.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection $\gamma$.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with $(i,j)$ to the cell in the $i$-th column from the right and the $j$-th row from the top.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection $\gamma$.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with $(i,j)$ to the cell in the $i$-th column from the right and the $j$-th row from the top.
Map
Kasraoui-Zeng
Description
The Kasraoui-Zeng involution.
This is defined in [1] and yields the set partition with the number of nestings and crossings exchanged.
This is defined in [1] and yields the set partition with the number of nestings and crossings exchanged.
searching the database
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