Identifier
Mp00099:
Dyck paths
—bounce path⟶
Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Mp00220: Set partitions —Yip⟶ Set partitions
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Mp00220: Set partitions —Yip⟶ Set partitions
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
Images
[1,0] => [1,0] => {{1}} => {{1}} => {{1}}
[1,0,1,0] => [1,0,1,0] => {{1},{2}} => {{1},{2}} => {{1},{2}}
[1,1,0,0] => [1,1,0,0] => {{1,2}} => {{1,2}} => {{1,2}}
[1,0,1,0,1,0] => [1,0,1,0,1,0] => {{1},{2},{3}} => {{1},{2},{3}} => {{1},{2},{3}}
[1,0,1,1,0,0] => [1,0,1,1,0,0] => {{1},{2,3}} => {{1,3},{2}} => {{1},{2,3}}
[1,1,0,0,1,0] => [1,1,0,0,1,0] => {{1,2},{3}} => {{1,2},{3}} => {{1,2},{3}}
[1,1,0,1,0,0] => [1,0,1,1,0,0] => {{1},{2,3}} => {{1,3},{2}} => {{1},{2,3}}
[1,1,1,0,0,0] => [1,1,1,0,0,0] => {{1,2,3}} => {{1,2,3}} => {{1,2,3}}
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}} => {{1},{2},{3},{4}}
[1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => {{1,4},{2},{3}} => {{1},{2},{3,4}}
[1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => {{1,3},{2},{4}} => {{1},{2,3},{4}}
[1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => {{1,4},{2},{3}} => {{1},{2},{3,4}}
[1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => {{1,3,4},{2}} => {{1},{2,3,4}}
[1,1,0,0,1,0,1,0] => [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] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => {{1,2,4},{3}} => {{1,2},{3,4}}
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => {{1,3},{2},{4}} => {{1},{2,3},{4}}
[1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => {{1,2,4},{3}} => {{1,2},{3,4}}
[1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => {{1,3,4},{2}} => {{1},{2,3,4}}
[1,1,1,0,0,0,1,0] => [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] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => {{1,2,4},{3}} => {{1,2},{3,4}}
[1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => {{1,3,4},{2}} => {{1},{2,3,4}}
[1,1,1,1,0,0,0,0] => [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] => [1,0,1,0,1,0,1,0,1,0] => {{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] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => {{1,5},{2},{3},{4}} => {{1},{2},{3},{4,5}}
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => {{1,4},{2},{3},{5}} => {{1},{2},{3,4},{5}}
[1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => {{1,5},{2},{3},{4}} => {{1},{2},{3},{4,5}}
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => {{1,4,5},{2},{3}} => {{1},{2},{3,4,5}}
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => {{1,3},{2},{4},{5}} => {{1},{2,3},{4},{5}}
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1,3,5},{2},{4}} => {{1},{2,3},{4,5}}
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => {{1,4},{2},{3},{5}} => {{1},{2},{3,4},{5}}
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1,3,5},{2},{4}} => {{1},{2,3},{4,5}}
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => {{1,4,5},{2},{3}} => {{1},{2},{3,4,5}}
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => {{1,3,4},{2},{5}} => {{1},{2,3,4},{5}}
[1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1,3,5},{2},{4}} => {{1},{2,3},{4,5}}
[1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => {{1,4,5},{2},{3}} => {{1},{2},{3,4,5}}
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => {{1,3,4,5},{2}} => {{1},{2,3,4,5}}
[1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => {{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] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => {{1,2,5},{3},{4}} => {{1,2},{3},{4,5}}
[1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => {{1,2,4},{3},{5}} => {{1,2},{3,4},{5}}
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => {{1,2,5},{3},{4}} => {{1,2},{3},{4,5}}
[1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2,4,5},{3}} => {{1,2},{3,4,5}}
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => {{1,3},{2},{4},{5}} => {{1},{2,3},{4},{5}}
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1,3,5},{2},{4}} => {{1},{2,3},{4,5}}
[1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => {{1,2,4},{3},{5}} => {{1,2},{3,4},{5}}
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1,3,5},{2},{4}} => {{1},{2,3},{4,5}}
[1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2,4,5},{3}} => {{1,2},{3,4,5}}
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => {{1,3,4},{2},{5}} => {{1},{2,3,4},{5}}
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1,3,5},{2},{4}} => {{1},{2,3},{4,5}}
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2,4,5},{3}} => {{1,2},{3,4,5}}
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => {{1,3,4,5},{2}} => {{1},{2,3,4,5}}
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => {{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] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => {{1,2,3,5},{4}} => {{1,2,3},{4,5}}
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => {{1,2,4},{3},{5}} => {{1,2},{3,4},{5}}
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => {{1,2,3,5},{4}} => {{1,2,3},{4,5}}
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2,4,5},{3}} => {{1,2},{3,4,5}}
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => {{1,3,4},{2},{5}} => {{1},{2,3,4},{5}}
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => {{1,2,3,5},{4}} => {{1,2,3},{4,5}}
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2,4,5},{3}} => {{1,2},{3,4,5}}
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => {{1,3,4,5},{2}} => {{1},{2,3,4,5}}
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => {{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] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => {{1,2,3,5},{4}} => {{1,2,3},{4,5}}
[1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2,4,5},{3}} => {{1,2},{3,4,5}}
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => {{1,3,4,5},{2}} => {{1},{2,3,4,5}}
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => {{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] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => {{1,6},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5,6}}
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => {{1,5},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6}}
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => {{1,6},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5,6}}
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => {{1,5,6},{2},{3},{4}} => {{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => {{1,4},{2},{3},{5},{6}} => {{1},{2},{3,4},{5},{6}}
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => {{1,4,6},{2},{3},{5}} => {{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => {{1,5},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6}}
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => {{1,4,6},{2},{3},{5}} => {{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => {{1,5,6},{2},{3},{4}} => {{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => {{1,4,5},{2},{3},{6}} => {{1},{2},{3,4,5},{6}}
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => {{1,4,6},{2},{3},{5}} => {{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => {{1,5,6},{2},{3},{4}} => {{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => {{1,4,5,6},{2},{3}} => {{1},{2},{3,4,5,6}}
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => {{1,3},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => {{1,3,6},{2},{4},{5}} => {{1},{2,3},{4},{5,6}}
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1,3,5},{2},{4},{6}} => {{1},{2,3},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => {{1,3,6},{2},{4},{5}} => {{1},{2,3},{4},{5,6}}
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => {{1,4},{2},{3},{5},{6}} => {{1},{2},{3,4},{5},{6}}
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => {{1,4,6},{2},{3},{5}} => {{1},{2},{3,4},{5,6}}
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1,3,5},{2},{4},{6}} => {{1},{2,3},{4,5},{6}}
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => {{1,4,6},{2},{3},{5}} => {{1},{2},{3,4},{5,6}}
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => {{1,4,5},{2},{3},{6}} => {{1},{2},{3,4,5},{6}}
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => {{1,4,6},{2},{3},{5}} => {{1},{2},{3,4},{5,6}}
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => {{1,4,5,6},{2},{3}} => {{1},{2},{3,4,5,6}}
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => {{1,3,4},{2},{5},{6}} => {{1},{2,3,4},{5},{6}}
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1,3,5},{2},{4},{6}} => {{1},{2,3},{4,5},{6}}
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => {{1,4,5},{2},{3},{6}} => {{1},{2},{3,4,5},{6}}
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => {{1,4,5,6},{2},{3}} => {{1},{2},{3,4,5,6}}
>>> Load all 2203 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => {{1,3,4,5},{2},{6}} => {{1},{2,3,4,5},{6}}
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => {{1,4,5,6},{2},{3}} => {{1},{2},{3,4,5,6}}
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => {{1,3,4,5,6},{2}} => {{1},{2,3,4,5,6}}
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => {{1,2,6},{3},{4},{5}} => {{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => {{1,2,5},{3},{4},{6}} => {{1,2},{3},{4,5},{6}}
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => {{1,2,6},{3},{4},{5}} => {{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => {{1,2,5,6},{3},{4}} => {{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => {{1,2,4},{3},{5},{6}} => {{1,2},{3,4},{5},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2,4,6},{3},{5}} => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => {{1,2,5},{3},{4},{6}} => {{1,2},{3},{4,5},{6}}
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2,4,6},{3},{5}} => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => {{1,2,5,6},{3},{4}} => {{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1,2,4,5},{3},{6}} => {{1,2},{3,4,5},{6}}
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2,4,6},{3},{5}} => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => {{1,2,5,6},{3},{4}} => {{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,5,6},{3}} => {{1,2},{3,4,5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => {{1,3},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => {{1,3,6},{2},{4},{5}} => {{1},{2,3},{4},{5,6}}
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1,3,5},{2},{4},{6}} => {{1},{2,3},{4,5},{6}}
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => {{1,3,6},{2},{4},{5}} => {{1},{2,3},{4},{5,6}}
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => {{1,2,4},{3},{5},{6}} => {{1,2},{3,4},{5},{6}}
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2,4,6},{3},{5}} => {{1,2},{3,4},{5,6}}
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1,3,5},{2},{4},{6}} => {{1},{2,3},{4,5},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2,4,6},{3},{5}} => {{1,2},{3,4},{5,6}}
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1,2,4,5},{3},{6}} => {{1,2},{3,4,5},{6}}
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2,4,6},{3},{5}} => {{1,2},{3,4},{5,6}}
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,5,6},{3}} => {{1,2},{3,4,5,6}}
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => {{1,3,4},{2},{5},{6}} => {{1},{2,3,4},{5},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1,3,5},{2},{4},{6}} => {{1},{2,3},{4,5},{6}}
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1,2,4,5},{3},{6}} => {{1,2},{3,4,5},{6}}
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,5,6},{3}} => {{1,2},{3,4,5,6}}
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => {{1,3,4,5},{2},{6}} => {{1},{2,3,4,5},{6}}
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,3,5,6},{2},{4}} => {{1},{2,3},{4,5,6}}
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,5,6},{3}} => {{1,2},{3,4,5,6}}
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => {{1,3,4,5,6},{2}} => {{1},{2,3,4,5,6}}
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{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] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => {{1,2,3,6},{4},{5}} => {{1,2,3},{4},{5,6}}
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => {{1,2,3,5},{4},{6}} => {{1,2,3},{4,5},{6}}
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => {{1,2,3,6},{4},{5}} => {{1,2,3},{4},{5,6}}
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}} => {{1,2,3},{4,5,6}}
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => {{1,2,4},{3},{5},{6}} => {{1,2},{3,4},{5},{6}}
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2,4,6},{3},{5}} => {{1,2},{3,4},{5,6}}
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => {{1,2,3,5},{4},{6}} => {{1,2,3},{4,5},{6}}
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2,4,6},{3},{5}} => {{1,2},{3,4},{5,6}}
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}} => {{1,2,3},{4,5,6}}
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1,2,4,5},{3},{6}} => {{1,2},{3,4,5},{6}}
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2,4,6},{3},{5}} => {{1,2},{3,4},{5,6}}
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}} => {{1,2,3},{4,5,6}}
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,5,6},{3}} => {{1,2},{3,4,5,6}}
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => {{1,3,4},{2},{5},{6}} => {{1},{2,3,4},{5},{6}}
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => {{1,2,3,5},{4},{6}} => {{1,2,3},{4,5},{6}}
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}} => {{1,2,3},{4,5,6}}
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1,2,4,5},{3},{6}} => {{1,2},{3,4,5},{6}}
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}} => {{1,2,3},{4,5,6}}
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,5,6},{3}} => {{1,2},{3,4,5,6}}
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => {{1,3,4,5},{2},{6}} => {{1},{2,3,4,5},{6}}
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,3,4,6},{2},{5}} => {{1},{2,3,4},{5,6}}
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}} => {{1,2,3},{4,5,6}}
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,5,6},{3}} => {{1,2},{3,4,5,6}}
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => {{1,3,4,5,6},{2}} => {{1},{2,3,4,5,6}}
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{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] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => {{1,2,3,4,6},{5}} => {{1,2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => {{1,2,3,5},{4},{6}} => {{1,2,3},{4,5},{6}}
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => {{1,2,3,4,6},{5}} => {{1,2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}} => {{1,2,3},{4,5,6}}
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1,2,4,5},{3},{6}} => {{1,2},{3,4,5},{6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => {{1,2,3,4,6},{5}} => {{1,2,3,4},{5,6}}
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}} => {{1,2,3},{4,5,6}}
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,5,6},{3}} => {{1,2},{3,4,5,6}}
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => {{1,3,4,5},{2},{6}} => {{1},{2,3,4,5},{6}}
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => {{1,2,3,4,6},{5}} => {{1,2,3,4},{5,6}}
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}} => {{1,2,3},{4,5,6}}
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,5,6},{3}} => {{1,2},{3,4,5,6}}
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => {{1,3,4,5,6},{2}} => {{1},{2,3,4,5,6}}
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{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] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => {{1,2,3,4,6},{5}} => {{1,2,3,4},{5,6}}
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}} => {{1,2,3},{4,5,6}}
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,4,5,6},{3}} => {{1,2},{3,4,5,6}}
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => {{1,3,4,5,6},{2}} => {{1},{2,3,4,5,6}}
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => {{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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => {{1,7},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => {{1,6},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => {{1,7},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => {{1,6,7},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => {{1,5},{2},{3},{4},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => {{1,5,7},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => {{1,6},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => {{1,5,7},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => {{1,6,7},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => {{1,5,6},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => {{1,5,7},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => {{1,6,7},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => {{1,5,6,7},{2},{3},{4}} => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => {{1,4},{2},{3},{5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => {{1,4,7},{2},{3},{5},{6}} => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => {{1,4,6},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => {{1,4,7},{2},{3},{5},{6}} => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => {{1,5},{2},{3},{4},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => {{1,5,7},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => {{1,4,6},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => {{1,5,7},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => {{1,5,6},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => {{1,5,7},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => {{1,5,6,7},{2},{3},{4}} => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => {{1,4,5},{2},{3},{6},{7}} => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => {{1,4,6},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => {{1,5,6},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => {{1,5,6,7},{2},{3},{4}} => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => {{1,4,5,6},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => {{1,5,6,7},{2},{3},{4}} => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => {{1,4,5,6,7},{2},{3}} => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => {{1,3},{2},{4},{5},{6},{7}} => {{1},{2,3},{4},{5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => {{1,3,7},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => {{1,3,6},{2},{4},{5},{7}} => {{1},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => {{1,3,7},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => {{1,3,6,7},{2},{4},{5}} => {{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => {{1,3,5},{2},{4},{6},{7}} => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => {{1,3,6},{2},{4},{5},{7}} => {{1},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => {{1,3,6,7},{2},{4},{5}} => {{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => {{1,3,6,7},{2},{4},{5}} => {{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => {{1,4},{2},{3},{5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => {{1,4,7},{2},{3},{5},{6}} => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => {{1,4,6},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => {{1,4,7},{2},{3},{5},{6}} => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => {{1,3,5},{2},{4},{6},{7}} => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => {{1,4,6},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => {{1,4,5},{2},{3},{6},{7}} => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => {{1,4,6},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => {{1,4,5,6},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1,4,6,7},{2},{3},{5}} => {{1},{2},{3,4},{5,6,7}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => {{1,4,5,6,7},{2},{3}} => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => {{1,3,4},{2},{5},{6},{7}} => {{1},{2,3,4},{5},{6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => {{1,3,4,7},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => {{1,3,4,7},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => {{1,3,5},{2},{4},{6},{7}} => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => {{1,4,5},{2},{3},{6},{7}} => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => {{1,4,5,6},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1,4,5,7},{2},{3},{6}} => {{1},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => {{1,4,5,6,7},{2},{3}} => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => {{1,3,4,5},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => {{1,4,5,6},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => {{1,4,5,6,7},{2},{3}} => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => {{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => {{1,4,5,6,7},{2},{3}} => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => {{1,3,4,5,6,7},{2}} => {{1},{2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => {{1,2,7},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => {{1,2,6},{3},{4},{5},{7}} => {{1,2},{3},{4},{5,6},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => {{1,2,7},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => {{1,2,6,7},{3},{4},{5}} => {{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => {{1,2,5},{3},{4},{6},{7}} => {{1,2},{3},{4,5},{6},{7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => {{1,2,5,7},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => {{1,2,6},{3},{4},{5},{7}} => {{1,2},{3},{4},{5,6},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => {{1,2,5,7},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => {{1,2,6,7},{3},{4},{5}} => {{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => {{1,2,5,6},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => {{1,2,5,7},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => {{1,2,6,7},{3},{4},{5}} => {{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => {{1,2,5,6,7},{3},{4}} => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => {{1,2,4},{3},{5},{6},{7}} => {{1,2},{3,4},{5},{6},{7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => {{1,2,4,7},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => {{1,2,4,7},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => {{1,2,5},{3},{4},{6},{7}} => {{1,2},{3},{4,5},{6},{7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => {{1,2,5,7},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => {{1,2,5,7},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => {{1,2,5,6},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => {{1,2,5,7},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => {{1,2,5,6,7},{3},{4}} => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => {{1,2,4,5},{3},{6},{7}} => {{1,2},{3,4,5},{6},{7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => {{1,2,5,6},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => {{1,2,5,6,7},{3},{4}} => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => {{1,2,5,6,7},{3},{4}} => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => {{1,3},{2},{4},{5},{6},{7}} => {{1},{2,3},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => {{1,3,7},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6,7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => {{1,3,6},{2},{4},{5},{7}} => {{1},{2,3},{4},{5,6},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => {{1,3,7},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6,7}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => {{1,3,6,7},{2},{4},{5}} => {{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => {{1,3,5},{2},{4},{6},{7}} => {{1},{2,3},{4,5},{6},{7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => {{1,3,6},{2},{4},{5},{7}} => {{1},{2,3},{4},{5,6},{7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => {{1,3,6,7},{2},{4},{5}} => {{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => {{1,3,6,7},{2},{4},{5}} => {{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => {{1,2,4},{3},{5},{6},{7}} => {{1,2},{3,4},{5},{6},{7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => {{1,2,4,7},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => {{1,2,4,7},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => {{1,3,5},{2},{4},{6},{7}} => {{1},{2,3},{4,5},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => {{1,2,4,5},{3},{6},{7}} => {{1,2},{3,4,5},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => {{1,3,4},{2},{5},{6},{7}} => {{1},{2,3,4},{5},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => {{1,3,4,7},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => {{1,3,4,7},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => {{1,3,5},{2},{4},{6},{7}} => {{1},{2,3},{4,5},{6},{7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1,3,5,7},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => {{1,2,4,5},{3},{6},{7}} => {{1,2},{3,4,5},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => {{1,3,4,5},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => {{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1,3,5,6,7},{2},{4}} => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => {{1,3,4,5,6,7},{2}} => {{1},{2,3,4,5,6,7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => {{1,2,3,7},{4},{5},{6}} => {{1,2,3},{4},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => {{1,2,3,6},{4},{5},{7}} => {{1,2,3},{4},{5,6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => {{1,2,3,7},{4},{5},{6}} => {{1,2,3},{4},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => {{1,2,3,6,7},{4},{5}} => {{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => {{1,2,3,5},{4},{6},{7}} => {{1,2,3},{4,5},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => {{1,2,3,6},{4},{5},{7}} => {{1,2,3},{4},{5,6},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => {{1,2,3,6,7},{4},{5}} => {{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => {{1,2,3,6,7},{4},{5}} => {{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => {{1,2,4},{3},{5},{6},{7}} => {{1,2},{3,4},{5},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => {{1,2,4,7},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => {{1,2,4,7},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => {{1,2,3,5},{4},{6},{7}} => {{1,2,3},{4,5},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => {{1,2,4,5},{3},{6},{7}} => {{1,2},{3,4,5},{6},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,4,6,7},{3},{5}} => {{1,2},{3,4},{5,6,7}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => {{1,3,4},{2},{5},{6},{7}} => {{1},{2,3,4},{5},{6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => {{1,3,4,7},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => {{1,3,4,7},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => {{1,2,3,5},{4},{6},{7}} => {{1,2,3},{4,5},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => {{1,2,4,5},{3},{6},{7}} => {{1,2},{3,4,5},{6},{7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => {{1,3,4,5},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => {{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1,3,4,6,7},{2},{5}} => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => {{1,3,4,5,6,7},{2}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{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] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => {{1,2,3,4,7},{5},{6}} => {{1,2,3,4},{5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => {{1,2,3,4,6},{5},{7}} => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => {{1,2,3,4,7},{5},{6}} => {{1,2,3,4},{5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => {{1,2,3,5},{4},{6},{7}} => {{1,2,3},{4,5},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => {{1,2,3,4,6},{5},{7}} => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2,3,5,7},{4},{6}} => {{1,2,3},{4,5},{6,7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => {{1,2,4,5},{3},{6},{7}} => {{1,2},{3,4,5},{6},{7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => {{1,2,3,4,6},{5},{7}} => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2,4,5,7},{3},{6}} => {{1,2},{3,4,5},{6,7}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => {{1,3,4,5},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => {{1,2,3,4,6},{5},{7}} => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => {{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1,3,4,5,7},{2},{6}} => {{1},{2,3,4,5},{6,7}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => {{1,3,4,5,6,7},{2}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{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] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => {{1,2,3,4,6},{5},{7}} => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1,2,3,5,6},{4},{7}} => {{1,2,3},{4,5,6},{7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1,2,4,5,6},{3},{7}} => {{1,2},{3,4,5,6},{7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => {{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,6},{7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => {{1,3,4,5,6,7},{2}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{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] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4,6,7},{5}} => {{1,2,3,4},{5,6,7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,5,6,7},{4}} => {{1,2,3},{4,5,6,7}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,4,5,6,7},{3}} => {{1,2},{3,4,5,6,7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => {{1,3,4,5,6,7},{2}} => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,8}} => {{1,8},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8}} => {{1,7},{2},{3},{4},{5},{6},{8}} => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,8}} => {{1,8},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8}} => {{1,7,8},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,6},{7},{8}} => {{1,6},{2},{3},{4},{5},{7},{8}} => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}} => {{1,6,8},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8}} => {{1,7},{2},{3},{4},{5},{6},{8}} => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}} => {{1,6,8},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8}} => {{1,7,8},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8}} => {{1,6,7},{2},{3},{4},{5},{8}} => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}} => {{1,6,8},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8}} => {{1,7,8},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}} => {{1,6,7,8},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8}} => {{1,5},{2},{3},{4},{6},{7},{8}} => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}} => {{1,5,8},{2},{3},{4},{6},{7}} => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8}} => {{1,5,7},{2},{3},{4},{6},{8}} => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}} => {{1,5,8},{2},{3},{4},{6},{7}} => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,6},{7},{8}} => {{1,6},{2},{3},{4},{5},{7},{8}} => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}} => {{1,6,8},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8}} => {{1,5,7},{2},{3},{4},{6},{8}} => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}} => {{1,6,8},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8}} => {{1,6,7},{2},{3},{4},{5},{8}} => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}} => {{1,6,8},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}} => {{1,6,7,8},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4,5,6},{7},{8}} => {{1,5,6},{2},{3},{4},{7},{8}} => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8}} => {{1,5,7},{2},{3},{4},{6},{8}} => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8}} => {{1,6,7},{2},{3},{4},{5},{8}} => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}} => {{1,6,7,8},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4,5,6,7},{8}} => {{1,5,6,7},{2},{3},{4},{8}} => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}} => {{1,6,7,8},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}} => {{1,5,6,7,8},{2},{3},{4}} => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}} => {{1,4,6},{2},{3},{5},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8}} => {{1,5},{2},{3},{4},{6},{7},{8}} => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}} => {{1,5,8},{2},{3},{4},{6},{7}} => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8}} => {{1,5,7},{2},{3},{4},{6},{8}} => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}} => {{1,5,8},{2},{3},{4},{6},{7}} => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}} => {{1,4,6},{2},{3},{5},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8}} => {{1,5,7},{2},{3},{4},{6},{8}} => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4,5,6},{7},{8}} => {{1,5,6},{2},{3},{4},{7},{8}} => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8}} => {{1,5,7},{2},{3},{4},{6},{8}} => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4,5,6,7},{8}} => {{1,5,6,7},{2},{3},{4},{8}} => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}} => {{1,5,7,8},{2},{3},{4},{6}} => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}} => {{1,5,6,7,8},{2},{3},{4}} => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8}} => {{1,4,5},{2},{3},{6},{7},{8}} => {{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}} => {{1,4,6},{2},{3},{5},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4,5,6},{7},{8}} => {{1,5,6},{2},{3},{4},{7},{8}} => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4,5,6,7},{8}} => {{1,5,6,7},{2},{3},{4},{8}} => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}} => {{1,5,6,8},{2},{3},{4},{7}} => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}} => {{1,5,6,7,8},{2},{3},{4}} => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4,5,6,7},{8}} => {{1,5,6,7},{2},{3},{4},{8}} => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}} => {{1,5,6,7,8},{2},{3},{4}} => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}} => {{1,4,5,6,7},{2},{3},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}} => {{1,5,6,7,8},{2},{3},{4}} => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => {{1,4,5,6,7,8},{2},{3}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8}} => {{1,3},{2},{4},{5},{6},{7},{8}} => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}} => {{1,3,8},{2},{4},{5},{6},{7}} => {{1},{2,3},{4},{5},{6},{7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6,7},{8}} => {{1,3,7},{2},{4},{5},{6},{8}} => {{1},{2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}} => {{1,3,8},{2},{4},{5},{6},{7}} => {{1},{2,3},{4},{5},{6},{7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6,7,8}} => {{1,3,7,8},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6,7},{8}} => {{1,3,7},{2},{4},{5},{6},{8}} => {{1},{2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6,7,8}} => {{1,3,7,8},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6,7,8}} => {{1,3,7,8},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8}} => {{1,3,5},{2},{4},{6},{7},{8}} => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}} => {{1,4,6},{2},{3},{5},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8}} => {{1,3,5},{2},{4},{6},{7},{8}} => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}} => {{1,4,6},{2},{3},{5},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8}} => {{1,4,5},{2},{3},{6},{7},{8}} => {{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}} => {{1,4,6},{2},{3},{5},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}} => {{1,4,6,8},{2},{3},{5},{7}} => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}} => {{1,4,5,6,7},{2},{3},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => {{1,4,5,6,7,8},{2},{3}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8}} => {{1,3,4},{2},{5},{6},{7},{8}} => {{1},{2,3,4},{5},{6},{7},{8}}
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => {{1,3,4,7,8},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => {{1,3,4,7,8},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => {{1,3,4,7,8},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8}} => {{1,3,5},{2},{4},{6},{7},{8}} => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8}} => {{1,4,5},{2},{3},{6},{7},{8}} => {{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}} => {{1,4,5,6,7},{2},{3},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => {{1,4,5,6,7,8},{2},{3}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7},{8}} => {{1,3,4,5},{2},{6},{7},{8}} => {{1},{2,3,4,5},{6},{7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}} => {{1,3,4,5,8},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}} => {{1,3,4,5,8},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}} => {{1,4,5,6,7},{2},{3},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => {{1,4,5,6,8},{2},{3},{7}} => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => {{1,4,5,6,7,8},{2},{3}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}} => {{1,3,4,5,6},{2},{7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}} => {{1,4,5,6,7},{2},{3},{8}} => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => {{1,4,5,6,7,8},{2},{3}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => {{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => {{1,4,5,6,7,8},{2},{3}} => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => {{1,3,4,5,6,7,8},{2}} => {{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7,8}} => {{1,2,8},{3},{4},{5},{6},{7}} => {{1,2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6,7},{8}} => {{1,2,7},{3},{4},{5},{6},{8}} => {{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7,8}} => {{1,2,8},{3},{4},{5},{6},{7}} => {{1,2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5},{6,7,8}} => {{1,2,7,8},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4},{5,6},{7},{8}} => {{1,2,6},{3},{4},{5},{7},{8}} => {{1,2},{3},{4},{5,6},{7},{8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6,7},{8}} => {{1,2,7},{3},{4},{5},{6},{8}} => {{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5},{6,7,8}} => {{1,2,7,8},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5},{6,7,8}} => {{1,2,7,8},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}} => {{1,2,6,7,8},{3},{4},{5}} => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8}} => {{1,2,5},{3},{4},{6},{7},{8}} => {{1,2},{3},{4,5},{6},{7},{8}}
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4},{5,6},{7},{8}} => {{1,2,6},{3},{4},{5},{7},{8}} => {{1,2},{3},{4},{5,6},{7},{8}}
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}} => {{1,2,6,7,8},{3},{4},{5}} => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}} => {{1,2,6,7,8},{3},{4},{5}} => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7},{8}} => {{1,2,5,6,7},{3},{4},{8}} => {{1,2},{3},{4,5,6,7},{8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}} => {{1,2,6,7,8},{3},{4},{5}} => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,5,6,7,8},{3},{4}} => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8}} => {{1,2,4},{3},{5},{6},{7},{8}} => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,4,7,8},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,4,7,8},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,4,7,8},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8}} => {{1,2,5},{3},{4},{6},{7},{8}} => {{1,2},{3},{4,5},{6},{7},{8}}
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7},{8}} => {{1,2,5,6,7},{3},{4},{8}} => {{1,2},{3},{4,5,6,7},{8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,5,7,8},{3},{4},{6}} => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,5,6,7,8},{3},{4}} => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7},{8}} => {{1,2,5,6,7},{3},{4},{8}} => {{1,2},{3},{4,5,6,7},{8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2,5,6,8},{3},{4},{7}} => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,5,6,7,8},{3},{4}} => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7},{8}} => {{1,2,5,6,7},{3},{4},{8}} => {{1,2},{3},{4,5,6,7},{8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,5,6,7,8},{3},{4}} => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}} => {{1,2,5,6,7,8},{3},{4}} => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8}} => {{1,3},{2},{4},{5},{6},{7},{8}} => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}} => {{1,3,8},{2},{4},{5},{6},{7}} => {{1},{2,3},{4},{5},{6},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6,7},{8}} => {{1,3,7},{2},{4},{5},{6},{8}} => {{1},{2,3},{4},{5},{6,7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}} => {{1,3,8},{2},{4},{5},{6},{7}} => {{1},{2,3},{4},{5},{6},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6,7,8}} => {{1,3,7,8},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6,7},{8}} => {{1,3,7},{2},{4},{5},{6},{8}} => {{1},{2,3},{4},{5},{6,7},{8}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6,7,8}} => {{1,3,7,8},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6,7,8}} => {{1,3,7,8},{2},{4},{5},{6}} => {{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8}} => {{1,3,5},{2},{4},{6},{7},{8}} => {{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8}} => {{1,2,4},{3},{5},{6},{7},{8}} => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,4,7,8},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,4,7,8},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,4,7,8},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8}} => {{1,3,5},{2},{4},{6},{7},{8}} => {{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8}} => {{1,3,4},{2},{5},{6},{7},{8}} => {{1},{2,3,4},{5},{6},{7},{8}}
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => {{1,3,4,7,8},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => {{1,3,4,7,8},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => {{1,3,4,7,8},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7,8}}
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8}} => {{1,3,5},{2},{4},{6},{7},{8}} => {{1},{2,3},{4,5},{6},{7},{8}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => {{1,3,5,7,8},{2},{4},{6}} => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7},{8}} => {{1,3,4,5},{2},{6},{7},{8}} => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}} => {{1,3,4,5,8},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}} => {{1,3,4,5,8},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,3,5,6,8},{2},{4},{7}} => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}} => {{1,3,4,5,6},{2},{7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => {{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => {{1,3,5,6,7,8},{2},{4}} => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => {{1,3,4,5,6,7,8},{2}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7,8}} => {{1,2,3,8},{4},{5},{6},{7}} => {{1,2,3},{4},{5},{6},{7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7,8}} => {{1,2,3,8},{4},{5},{6},{7}} => {{1,2,3},{4},{5},{6},{7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3,7,8},{4},{5},{6}} => {{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7,8}} => {{1,2,3,6,8},{4},{5},{7}} => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7,8}} => {{1,2,3,6,8},{4},{5},{7}} => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3,7,8},{4},{5},{6}} => {{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7,8}} => {{1,2,3,6,8},{4},{5},{7}} => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5},{6,7,8}} => {{1,2,3,7,8},{4},{5},{6}} => {{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7,8}} => {{1,2,3,6,8},{4},{5},{7}} => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7,8}} => {{1,2,3,6,8},{4},{5},{7}} => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7,8}} => {{1,2,3,6,8},{4},{5},{7}} => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3,5,6},{4},{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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,6,7,8},{4},{5}} => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8}} => {{1,2,4},{3},{5},{6},{7},{8}} => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,4,7,8},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,4,7,8},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => {{1,2,4,7,8},{3},{5},{6}} => {{1,2},{3,4},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2,4,6,8},{3},{5},{7}} => {{1,2},{3,4},{5,6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{1,2,4,6,7,8},{3},{5}} => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8}} => {{1,3,4},{2},{5},{6},{7},{8}} => {{1},{2,3,4},{5},{6},{7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => {{1,3,4,7,8},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => {{1,3,4,7,8},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => {{1,3,4,7,8},{2},{5},{6}} => {{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7},{8}} => {{1,3,4,5},{2},{6},{7},{8}} => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}} => {{1,3,4,5,8},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}} => {{1,3,4,5,8},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => {{1,3,4,6,8},{2},{5},{7}} => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}} => {{1,3,4,5,6},{2},{7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => {{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}} => {{1,3,4,6,7,8},{2},{5}} => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => {{1,3,4,5,6,7,8},{2}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6},{7,8}} => {{1,2,3,4,8},{5},{6},{7}} => {{1,2,3,4},{5},{6},{7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4},{5},{6,7},{8}} => {{1,2,3,4,7},{5},{6},{8}} => {{1,2,3,4},{5},{6,7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6},{7,8}} => {{1,2,3,4,8},{5},{6},{7}} => {{1,2,3,4},{5},{6},{7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3,4,7,8},{5},{6}} => {{1,2,3,4},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8}} => {{1,2,3,4,6},{5},{7},{8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4},{5},{6,7},{8}} => {{1,2,3,4,7},{5},{6},{8}} => {{1,2,3,4},{5},{6,7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3,4,7,8},{5},{6}} => {{1,2,3,4},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3,4,7,8},{5},{6}} => {{1,2,3,4},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8}} => {{1,2,3,4,6},{5},{7},{8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}} => {{1,2,3,5,7},{4},{6},{8}} => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8}} => {{1,2,3,4,6},{5},{7},{8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,4,5,7,8},{3},{6}} => {{1,2},{3,4,5},{6,7,8}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7},{8}} => {{1,3,4,5},{2},{6},{7},{8}} => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}} => {{1,3,4,5,8},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}} => {{1,3,4,5,8},{2},{6},{7}} => {{1},{2,3,4,5},{6},{7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8}} => {{1,2,3,4,6},{5},{7},{8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}} => {{1,3,4,5,6},{2},{7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => {{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}} => {{1,3,4,5,7,8},{2},{6}} => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => {{1,3,4,5,6,7,8},{2}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{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] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4,5},{6},{7,8}} => {{1,2,3,4,5,8},{6},{7}} => {{1,2,3,4,5},{6},{7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => {{1,2,3,4,5,7},{6},{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] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4,5},{6},{7,8}} => {{1,2,3,4,5,8},{6},{7}} => {{1,2,3,4,5},{6},{7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8}} => {{1,2,3,4,6},{5},{7},{8}} => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => {{1,2,3,4,5,7},{6},{8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2,3,4,6,8},{5},{7}} => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1,2,3,5,6},{4},{7},{8}} => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => {{1,2,3,4,5,7},{6},{8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2,3,5,6,8},{4},{7}} => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => {{1,2,3,4,5,7},{6},{8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{1,2,4,5,6,8},{3},{7}} => {{1,2},{3,4,5,6},{7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}} => {{1,3,4,5,6},{2},{7},{8}} => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => {{1,2,3,4,5,7},{6},{8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => {{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => {{1,3,4,5,6,8},{2},{7}} => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => {{1,3,4,5,6,7,8},{2}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{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] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => {{1,2,3,4,5,7},{6},{8}} => {{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => {{1,2,4,5,6,7},{3},{8}} => {{1,2},{3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => {{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => {{1,3,4,5,6,7,8},{2}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{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] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,5,6,7,8},{4}} => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => {{1,2,4,5,6,7,8},{3}} => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => {{1,3,4,5,6,7,8},{2}} => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{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] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{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] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => {{1,3,4,5,6,7,8,9},{2}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{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] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8},{9}} => {{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,4,5,6,7,8,9},{2},{3}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,3,4,5,6,7,8,9,10},{2}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{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] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8},{9}} => {{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,4,5,6,7,8,9},{2},{3}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8},{9}} => {{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,4,5,6,7,8,9},{2},{3}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8},{9}} => {{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,4,5,6,7,8,9},{2},{3}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [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}} => {{1,2,3,4,5,7,8},{6},{9}} => {{1,2,3,4,5},{6,7,8},{9}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8},{9}} => {{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,4,5,6,7,8,9},{2},{3}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [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}} => {{1,2,3,4,5,6,8},{7},{9}} => {{1,2,3,4,5,6},{7,8},{9}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8},{9}} => {{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7},{8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,4,5,6,7,8,9},{2},{3}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => {{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}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6},{7,8},{9}} => {{1,2,3,4,5,6,8},{7},{9}} => {{1,2,3,4,5,6},{7,8},{9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [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}} => {{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,4,5,6,7,8,9},{2},{3}} => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [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}} => {{1,2,3,4,5,6,7,9},{8},{10}} => {{1,2,3,4,5,6,7},{8,9},{10}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [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}} => {{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2,3,4,5,6,7,8,10},{9}} => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [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}} => {{1,2,3,4,5,7,8},{6},{9}} => {{1,2,3,4,5},{6,7,8},{9}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [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}} => {{1,2,3,4,5,7,8},{6},{9}} => {{1,2,3,4,5},{6,7,8},{9}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => {{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}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [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}} => {{1,2,3,4,5,6,7,9},{8},{10}} => {{1,2,3,4,5,6,7},{8,9},{10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9},{10}} => {{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [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}} => {{1,2,3,4,5,7,8},{6},{9}} => {{1,2,3,4,5},{6,7,8},{9}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => {{1,3,4,5,6,7,8,9},{2}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => {{1,3,4,5,6,7,8,9},{2}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => {{1,3,4,5,6,7,8,9},{2}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => {{1,3,4,5,6,7,8,9},{2}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => {{1,3,4,5,6,7,8,9},{2}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [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}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [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}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => {{1,3,4,5,6,7,8,9},{2}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2,3,4,5,6,7,9},{8}} => {{1,2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => {{1,2,4,5,6,7,8,9},{3}} => {{1,2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => {{1,3,4,5,6,7,8,9},{2}} => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1,7,9},{2},{3},{4},{5},{6},{8}} => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1,7,9},{2},{3},{4},{5},{6},{8}} => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9}} => {{1,8,9},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1,7,9},{2},{3},{4},{5},{6},{8}} => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6,7},{8,9}} => {{1,6,7,9},{2},{3},{4},{5},{8}} => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}} => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9}} => {{1,8,9},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6,7},{8,9}} => {{1,6,7,9},{2},{3},{4},{5},{8}} => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1,7,8,9},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6,7},{8,9}} => {{1,6,7,9},{2},{3},{4},{5},{8}} => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6,7},{8,9}} => {{1,6,7,9},{2},{3},{4},{5},{8}} => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}} => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => {{1},{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] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6},{7,8,9}} => {{1,6,8,9},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1,8,9,10},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6,7},{8,9}} => {{1,6,7,9},{2},{3},{4},{5},{8}} => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1,7,8,9},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1,7,8,9},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1,8,9,10},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1,8,9,10},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7,8},{9}} => {{1,8},{2},{3},{4},{5},{6},{7},{9}} => {{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1,7,9},{2},{3},{4},{5},{6},{8}} => {{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] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7,8},{9}} => {{1,7,8},{2},{3},{4},{5},{6},{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] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6},{7,8,9}} => {{1,6,8,9},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6,7},{8,9}} => {{1,6,7,9},{2},{3},{4},{5},{8}} => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8},{9}} => {{1,5},{2},{3},{4},{6},{7},{8},{9}} => {{1},{2},{3},{4,5},{6},{7},{8},{9}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7},{8},{9}} => {{1,4},{2},{3},{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] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8},{9}} => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => {{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7},{8,9}} => {{1,3,9},{2},{4},{5},{6},{7},{8}} => {{1},{2,3},{4},{5},{6},{7},{8,9}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8},{9}} => {{1,3,4},{2},{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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8,9}} => {{1,2,9},{3},{4},{5},{6},{7},{8}} => {{1,2},{3},{4},{5},{6},{7},{8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6},{7,8},{9}} => {{1,2,8},{3},{4},{5},{6},{7},{9}} => {{1,2},{3},{4},{5},{6},{7,8},{9}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8},{9}} => {{1,2,5},{3},{4},{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] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8},{9}} => {{1,2,4},{3},{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] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,5,6,7,8,9},{4}} => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,6,7,8,9},{5}} => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5},{6,7,8},{9}} => {{1,2,3,4,5,7,8},{6},{9}} => {{1,2,3,4,5},{6,7,8},{9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4,5,7,8,9},{6}} => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => {{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] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6},{7,8},{9}} => {{1,2,3,4,5,6,8},{7},{9}} => {{1,2,3,4,5,6},{7,8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3,4,5,6,8,9},{7}} => {{1,2,3,4,5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}} => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}} => {{1,7},{2},{3},{4},{5},{6},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => {{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] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6,7},{8,9},{10}} => {{1,2,3,4,5,6,7,9},{8},{10}} => {{1,2,3,4,5,6,7},{8,9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{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] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8},{9}} => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => {{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8},{9}} => {{1,2,4},{3},{5},{6},{7},{8},{9}} => {{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8},{9}} => {{1,3,4},{2},{5},{6},{7},{8},{9}} => {{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8,9}} => {{1,2,9},{3},{4},{5},{6},{7},{8}} => {{1,2},{3},{4},{5},{6},{7},{8,9}}
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,3,4,5,6,7,8,9,10},{2}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7},{8,9}} => {{1,3,9},{2},{4},{5},{6},{7},{8}} => {{1},{2,3},{4},{5},{6},{7},{8,9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7},{8,9}} => {{1,3,9},{2},{4},{5},{6},{7},{8}} => {{1},{2,3},{4},{5},{6},{7},{8,9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7},{8,9}} => {{1,3,9},{2},{4},{5},{6},{7},{8}} => {{1},{2,3},{4},{5},{6},{7},{8,9}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8},{9}} => {{1,3,4},{2},{5},{6},{7},{8},{9}} => {{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,3,4,5,6,7,8,9,10},{2}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2,3,4,5,6,7,8,10},{9}} => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8,9},{10,11}} => {{1,2,3,4,5,6,7,8,9,11},{10}} => {{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [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}} => {{1,2,3,4,5,6,7,8,10},{9}} => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8},{9}} => {{1,2,4},{3},{5},{6},{7},{8},{9}} => {{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,3,4,5,6,7,8,9,10},{2}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,3,4,5,6,7,8,9,10},{2}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,3,4,5,6,7,8,9,10},{2}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,3,4,5,6,7,8,9,10},{2}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,3,4,5,6,7,8,9,10},{2}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => {{1,3,4,5,6,7,8,9,10},{2}} => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8},{9}} => {{1,5},{2},{3},{4},{6},{7},{8},{9}} => {{1},{2},{3},{4,5},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8},{9}} => {{1,2,5},{3},{4},{6},{7},{8},{9}} => {{1,2},{3},{4,5},{6},{7},{8},{9}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => {{1,3,4,5,6,7,9},{2},{8}} => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1,7,9},{2},{3},{4},{5},{6},{8}} => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [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}} => {{1,2,3,4,5,6,7,8,9,11},{10}} => {{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2,3,4,5,6,7,8,10},{9}} => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8,9}} => {{1,7,8,9},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9}} => {{1,8,9},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [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}} => {{1,2,3,4,5,6,7,8,9,11},{10}} => {{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [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}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [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}} => {{1,7,8},{2},{3},{4},{5},{6},{9}} => {{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7},{8},{9}} => {{1,4},{2},{3},{5},{6},{7},{8},{9}} => {{1},{2},{3,4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [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}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7,8},{9}} => {{1,8},{2},{3},{4},{5},{6},{7},{9}} => {{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [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}} => {{1,6,8,9},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}} => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6},{7,8},{9}} => {{1,2,8},{3},{4},{5},{6},{7},{9}} => {{1,2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [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}} => {{1,6,8,9},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [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}} => {{1,6,8,9},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [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}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1,7,9},{2},{3},{4},{5},{6},{8}} => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [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}} => {{1,6,8,9},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7,8},{9}} => {{1,7,8},{2},{3},{4},{5},{6},{9}} => {{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}} => {{1,7},{2},{3},{4},{5},{6},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [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}} => {{1,6,8,9},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}} => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [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}} => {{1,2,3,4,5,7,8},{6},{9}} => {{1,2,3,4,5},{6,7,8},{9}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => {{1,2,4,5,6,7,8},{3},{9}} => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2,3,4,5,6,7,8,10},{9}} => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6},{7,8,9}} => {{1,6,8,9},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [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}} => {{1,6,8,9},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6,7},{8,9}} => {{1,6,7,9},{2},{3},{4},{5},{8}} => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [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}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [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}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0] => [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}} => {{1,2,3,4,5,6,7,8,9,11},{10}} => {{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2,3,4,5,6,7,8,10},{9}} => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [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}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,6,7,8,9,10},{5}} => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{1,2,3,4,5,6,7,9,10},{8}} => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5,7,8,9,10},{6}} => {{1,2,3,4,5},{6,7,8,9,10}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [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}} => {{1,6,8,9},{2},{3},{4},{5},{7}} => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{1,2,3,4,5,6,8,9,10},{7}} => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,4,5,6,7,8,9,10},{3}} => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,5,6,7,8,9,10},{4}} => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [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}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2,4,6,8,10},{3},{5},{7},{9}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => {{1},{2,3,4,5,6,7,8,9,10,11}}
Map
bounce path
Description
Sends a Dyck path D of length 2n to its bounce path.
This path is formed by starting at the endpoint (n,n) of D and travelling west until encountering the first vertical step of D, then south until hitting the diagonal, then west again to hit D, etc. until the point (0,0) is reached.
This map is the first part of the zeta map Mp00030zeta map.
This path is formed by starting at the endpoint (n,n) of D and travelling west until encountering the first vertical step of D, then south until hitting the diagonal, then west again to hit D, etc. until the point (0,0) is reached.
This map is the first part of the zeta map Mp00030zeta map.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
Yip
Description
A transformation of set partitions due to Yip.
Return the set partition of {1,...,n} corresponding to the set of arcs, interpreted as a rook placement, applying Yip's bijection ψ.
Return the set partition of {1,...,n} corresponding to the set of arcs, interpreted as a rook placement, applying Yip's bijection ψ.
Map
dual major index to intertwining number
Description
A bijection sending the dual major index of a set partition to its intertwining number.
More precisely, St000493The los statistic of a set partition.(P)=St000490The intertwining number of a set partition.(ϕ(P)) for all set partitions P.
This is the inverse of Mp00171intertwining number to dual major index.
More precisely, St000493The los statistic of a set partition.(P)=St000490The intertwining number of a set partition.(ϕ(P)) for all set partitions P.
This is the inverse of Mp00171intertwining number to dual major index.
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