Identifier
Mp00327:
Dyck paths
—inverse Kreweras complement⟶
Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Images
[1,0] => [1,0] => {{1}}
[1,0,1,0] => [1,1,0,0] => {{1,2}}
[1,1,0,0] => [1,0,1,0] => {{1},{2}}
[1,0,1,0,1,0] => [1,1,1,0,0,0] => {{1,2,3}}
[1,0,1,1,0,0] => [1,1,0,1,0,0] => {{1,3},{2}}
[1,1,0,0,1,0] => [1,0,1,1,0,0] => {{1},{2,3}}
[1,1,0,1,0,0] => [1,1,0,0,1,0] => {{1,2},{3}}
[1,1,1,0,0,0] => [1,0,1,0,1,0] => {{1},{2},{3}}
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => {{1,2,3,4}}
[1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => {{1,2,4},{3}}
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => {{1,3,4},{2}}
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => {{1,4},{2,3}}
[1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => {{1,4},{2},{3}}
[1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}}
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}}
[1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}}
[1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}}
[1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}}
[1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}}
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}}
[1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}}
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}}
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}}
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => {{1,2,3,5},{4}}
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => {{1,2,4,5},{3}}
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => {{1,2,5},{3,4}}
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => {{1,2,5},{3},{4}}
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => {{1,3,4,5},{2}}
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4}}
[1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => {{1,4,5},{2,3}}
[1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3,4}}
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => {{1,5},{2,3},{4}}
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => {{1,4,5},{2},{3}}
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3}}
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => {{1,5},{2},{3,4}}
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4}}
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}}
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}}
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}}
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}}
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}}
[1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}}
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}}
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}}
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}}
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}}
[1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}}
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}}
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}}
[1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}}
[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}}
[1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}}
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}}
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}}
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}}
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}}
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}}
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}}
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}}
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}}
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}}
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}}
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}}
[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}}
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3,4,6},{5}}
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2,3,5,6},{4}}
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3,6},{4,5}}
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3,6},{4},{5}}
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,4,5,6},{3}}
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2,4,6},{3},{5}}
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,5,6},{3,4}}
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,6},{3,4,5}}
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2,6},{3,4},{5}}
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2,5,6},{3},{4}}
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,6},{3,5},{4}}
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2,6},{3},{4,5}}
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,6},{3},{4},{5}}
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => {{1,3,4,5,6},{2}}
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => {{1,3,4,6},{2},{5}}
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4}}
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => {{1,3,6},{2},{4,5}}
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => {{1,3,6},{2},{4},{5}}
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2,3}}
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => {{1,4,6},{2,3},{5}}
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => {{1,5,6},{2,3,4}}
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => {{1,6},{2,3,4,5}}
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => {{1,6},{2,3,4},{5}}
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => {{1,5,6},{2,3},{4}}
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => {{1,6},{2,3,5},{4}}
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5}}
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => {{1,6},{2,3},{4},{5}}
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2},{3}}
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5}}
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => {{1,5,6},{2,4},{3}}
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => {{1,6},{2,4,5},{3}}
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => {{1,6},{2,4},{3},{5}}
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4}}
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4}}
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => {{1,6},{2},{3,4,5}}
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => {{1,6},{2},{3,4},{5}}
>>> Load all 2055 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => {{1,5,6},{2},{3},{4}}
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => {{1,6},{2,5},{3},{4}}
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => {{1,6},{2},{3,5},{4}}
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => {{1,6},{2},{3},{4,5}}
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5}}
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}}
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}}
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}}
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}}
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}}
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}}
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}}
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}}
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}}
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}}
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}}
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}}
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}}
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}}
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}}
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}}
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}}
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}}
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}}
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}}
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}}
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}}
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}}
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}}
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}}
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}}
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}}
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}}
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}}
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}}
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}}
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}}
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}}
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}}
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}}
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}}
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}}
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}}
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}}
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}}
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}}
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}}
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}}
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}}
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}}
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}}
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}}
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}}
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}}
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}}
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}}
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}}
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}}
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}}
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}}
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}}
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}}
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}}
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}}
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}}
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}}
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}}
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}}
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}}
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}}
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}}
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}}
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}}
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}}
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}}
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}}
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}}
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}}
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}}
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}}
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}}
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}}
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}}
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}}
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}}
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}}
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}}
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}}
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}}
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}}
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}}
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}}
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,7},{6}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,6,7},{5}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5,6}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5},{6}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,5,6,7},{4}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,5,7},{4},{6}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4,5}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,7},{4,5,6}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4,5},{6}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4},{5}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4,6},{5}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4},{5,6}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4},{5},{6}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,4,5,6,7},{3}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,4,5,7},{3},{6}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,4,6,7},{3},{5}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,4,7},{3},{5,6}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,4,7},{3},{5},{6}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3,4}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3,4},{6}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4,5}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,7},{3,4,5,6}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,7},{3,4,5},{6}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4},{5}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,7},{3,4,6},{5}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3,4},{5},{6}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3},{4}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3},{4},{6}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,5},{4}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3,5,6},{4}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3,5},{4},{6}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4,5}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4,5}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3},{4,5,6}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3},{4,5},{6}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4},{5}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4},{5}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3},{4,6},{5}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3},{4},{5,6}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,3,4,5,6,7},{2}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,3,4,5,7},{2},{6}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,3,4,6,7},{2},{5}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,3,4,7},{2},{5,6}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,3,4,7},{2},{5},{6}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,3,5,6,7},{2},{4}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5,7},{2},{4},{6}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4,5}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,3,7},{2},{4,5,6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,3,7},{2},{4,5},{6}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4},{5}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,3,7},{2},{4},{5,6}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,3,7},{2},{4},{5},{6}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2,3}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2,3},{6}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2,3},{5}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2,3},{5,6}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2,3},{5},{6}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3,4}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3,4},{6}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,4,5}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,7},{2,3,4,5,6}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,7},{2,3,4,5},{6}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3,4},{5}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,7},{2,3,4,6},{5}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,7},{2,3,4},{5,6}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,7},{2,3,4},{5},{6}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3},{4}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3},{4},{6}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,5},{4}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,7},{2,3,5,6},{4}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,7},{2,3,5},{4},{6}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2,3},{4,5}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4,5}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2,3},{4,5,6}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2,3},{4,5},{6}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3},{4},{5}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4},{5}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2,3},{4,6},{5}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2,3},{4},{5,6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2,3},{4},{5},{6}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2},{3}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2},{3},{6}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2},{3},{5}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2},{3},{5,6}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2},{3},{5},{6}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,4},{3}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,4,5},{3}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2,4,5,6},{3}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2,4,5},{3},{6}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,4},{3},{5}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2,4},{3},{5,6}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2,4},{3},{5},{6}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3,4}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3,4},{6}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3,4}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3,4}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3,4},{6}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,4,5}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4,5}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2},{3,4,5,6}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2},{3,4,5},{6}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3,4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4},{5}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2},{3,4,6},{5}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2},{3,4},{5,6}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2},{3,4},{5},{6}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3},{4}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3},{4},{6}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3},{4}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3},{4}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3},{4},{6}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,5},{4}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2},{3,5,6},{4}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2},{3,5},{4},{6}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4,5}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4,5}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4,5}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2},{3},{4,5,6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2},{3},{4,5},{6}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4},{5}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2},{3},{4,6},{5}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2},{3},{4},{5,6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4,6},{5},{7}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}}
[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}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8},{6}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6,7}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8},{5}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,6,8},{5},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,7,8},{5,6}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6,7}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6},{7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,7,8},{5},{6}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,7},{6}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8},{4}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,5,6,8},{4},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,5,7,8},{4},{6}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,5,8},{4},{6,7}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,5,8},{4},{6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4,5}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,6,8},{4,5},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,5,6}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6,7}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6},{7}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,5},{6}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,7},{6}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,5},{6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4},{5}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,6,8},{4},{5},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,6},{5}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,6,7},{5}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,6},{5},{7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4},{5,6}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,7},{5,6}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,6},{7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4},{5},{6}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,7},{5},{6}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,7},{6}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5},{6,7}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8},{3}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,4,5,6,8},{3},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,4,5,7,8},{3},{6}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,4,5,8},{3},{6,7}}
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,4,5,8},{3},{6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,4,6,7,8},{3},{5}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,4,6,8},{3},{5},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,4,7,8},{3},{5,6}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,6,7}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,6},{7}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,4,7,8},{3},{5},{6}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,7},{6}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,4,8},{3},{5},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,5,6,7,8},{3,4}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,5,6,8},{3,4},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,5,7,8},{3,4},{6}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,5,8},{3,4},{6,7}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,5,8},{3,4},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,4,5}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,4,5},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,5,6}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,6,7}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4,5,6},{7}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,5},{6}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,7},{6}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,4,5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3,4,5},{6},{7}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,4},{5}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,4},{5},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,6},{5}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,6,7},{5}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4,6},{5},{7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4,7},{5,6}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4},{5,6},{7}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4},{5},{6}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4,7},{5},{6}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,4},{5,7},{6}}
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,4},{5},{6,7}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3,4},{5},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,5,6,7,8},{3},{4}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,5,6,8},{3},{4},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,5,7,8},{3},{4},{6}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,5,8},{3},{4},{6,7}}
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,5,8},{3},{4},{6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,5},{4}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,5},{4},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,5,6},{4}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,5,6,7},{4}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,5,6},{4},{7}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,5},{4},{6}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,5,7},{4},{6}}
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,5},{4},{6,7}}
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3,5},{4},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3},{4,5}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3},{4,5},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,6},{4,5}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3,6,7},{4,5}}
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,6},{4,5},{7}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,5,6}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,5,6}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,5,6,7}}
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3},{4,5,6},{7}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,5},{6}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,5},{6}}
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,5,7},{6}}
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,5},{6,7}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3},{4,5},{6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3},{4},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3},{4},{5},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,6},{4},{5}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3,6,7},{4},{5}}
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,6},{4},{5},{7}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,6},{5}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,6},{5}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,6,7},{5}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3},{4,6},{5},{7}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4},{5,6}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4},{5,6}}
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,7},{5,6}}
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4},{5,6,7}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3},{4},{5,6},{7}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4},{5},{6}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4},{5},{6}}
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,7},{5},{6}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3},{4},{5,7},{6}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3},{4},{5},{6,7}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3},{4},{5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8},{2}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,8},{2},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,3,4,5,7,8},{2},{6}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,3,4,5,8},{2},{6,7}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,3,4,5,8},{2},{6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,3,4,6,7,8},{2},{5}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,3,4,6,8},{2},{5},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,3,4,7,8},{2},{5,6}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,6,7}}
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,3,4,7,8},{2},{5},{6}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,7},{6}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,3,4,8},{2},{5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,8},{2},{5},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,3,5,6,7,8},{2},{4}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,3,5,6,8},{2},{4},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,3,5,7,8},{2},{4},{6}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,3,5,8},{2},{4},{6,7}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,3,5,8},{2},{4},{6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,3,6,7,8},{2},{4,5}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,3,6,8},{2},{4,5},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,5,6}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,5,6,7}}
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,3,8},{2},{4,5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,5,7},{6}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,3,8},{2},{4,5},{6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,3,6,7,8},{2},{4},{5}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,3,6,8},{2},{4},{5},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,6},{5}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,6,7},{5}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,3,8},{2},{4,6},{5},{7}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4},{5,6}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,7},{5,6}}
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,3,8},{2},{4},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4},{5},{6}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,7},{5},{6}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,3,8},{2},{4},{5,7},{6}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,3,8},{2},{4},{5},{6,7}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,8},{2},{4},{5},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2,3}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,4,5,6,8},{2,3},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,4,5,7,8},{2,3},{6}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,4,5,8},{2,3},{6,7}}
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,4,5,8},{2,3},{6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,4,6,7,8},{2,3},{5}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,4,6,8},{2,3},{5},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,4,7,8},{2,3},{5,6}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,4,8},{2,3},{5,6,7}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,4,8},{2,3},{5,6},{7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,4,7,8},{2,3},{5},{6}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,4,8},{2,3},{5,7},{6}}
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,4,8},{2,3},{5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,4,8},{2,3},{5},{6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,3,4}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,3,4},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,3,4},{6}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,3,4},{6,7}}
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2,3,4},{6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,4,5}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,4,5},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,4,5,6}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,6,7}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,4,5,6},{7}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3,4,5},{6}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,7},{6}}
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3,4,5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2,3,4,5},{6},{7}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,4},{5}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,4},{5},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,4,6},{5}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,6,7},{5}}
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,4,6},{5},{7}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3,4},{5,6}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,4,7},{5,6}}
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,3,4},{5,6,7}}
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2,3,4},{5,6},{7}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3,4},{5},{6}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,4,7},{5},{6}}
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,3,4},{5,7},{6}}
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,3,4},{5},{6,7}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,3,4},{5},{6},{7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,3},{4}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,3},{4},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,3},{4},{6}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,3},{4},{6,7}}
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2,3},{4},{6},{7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,5},{4}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,5},{4},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,5,6},{4}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,5,6,7},{4}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,5,6},{4},{7}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3,5},{4},{6}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,5,7},{4},{6}}
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3,5},{4},{6,7}}
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2,3,5},{4},{6},{7}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3},{4,5}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3},{4,5},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,6},{4,5}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3,6,7},{4,5}}
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3,6},{4,5},{7}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,5,6}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,5,6}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3},{4,5,6},{7}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,5},{6}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,5},{6}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3},{4,5,7},{6}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3},{4,5},{6,7}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,3},{4,5},{6},{7}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3},{4},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3},{4},{5},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,6},{4},{5}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3,6,7},{4},{5}}
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3,6},{4},{5},{7}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,6},{5}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,6},{5}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,3},{4,6,7},{5}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2,3},{4,6},{5},{7}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4},{5,6}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4},{5,6}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,3},{4,7},{5,6}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,3},{4},{5,6,7}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3},{4},{5},{6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4},{5},{6}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,3},{4,7},{5},{6}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,3},{4},{5,7},{6}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,3},{4},{5},{6,7}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,3},{4},{5},{6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2},{3}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,4,5,6,8},{2},{3},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,4,5,7,8},{2},{3},{6}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,4,5,8},{2},{3},{6,7}}
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,4,5,8},{2},{3},{6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,4,6,7,8},{2},{3},{5}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,4,6,8},{2},{3},{5},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,4,7,8},{2},{3},{5,6}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,4,8},{2},{3},{5,6,7}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,4,8},{2},{3},{5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,4,7,8},{2},{3},{5},{6}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,4,8},{2},{3},{5,7},{6}}
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,4,8},{2},{3},{5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,4,8},{2},{3},{5},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,4},{3}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,4},{3},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,4},{3},{6}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,4},{3},{6,7}}
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2,4},{3},{6},{7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,4,5},{3}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,4,5},{3},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,4,5,6},{3}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,4,5,6,7},{3}}
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,4,5,6},{3},{7}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,4,5},{3},{6}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,4,5,7},{3},{6}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,4,5},{3},{6,7}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2,4,5},{3},{6},{7}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,4},{3},{5}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,4},{3},{5},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,4,6},{3},{5}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,4,6,7},{3},{5}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,4,6},{3},{5},{7}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,4},{3},{5,6}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,4,7},{3},{5,6}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,4},{3},{5,6,7}}
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2,4},{3},{5,6},{7}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2,4},{3},{5},{6}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,4,7},{3},{5},{6}}
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,4},{3},{5,7},{6}}
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,4},{3},{5},{6,7}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,4},{3},{5},{6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2},{3,4}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2},{3,4},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2},{3,4},{6}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2},{3,4},{6,7}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2},{3,4},{6},{7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,5},{3,4}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,5},{3,4},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,5,6},{3,4}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,5,6,7},{3,4}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2,5,6},{3,4},{7}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,5},{3,4},{6}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,5,7},{3,4},{6}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,5},{3,4},{6,7}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,5},{3,4},{6},{7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,4,5}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,4,5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,4,5}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,4,5}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,4,5},{7}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,5,6}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,5,6}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,5,6,7}}
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2},{3,4,5,6},{7}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,5},{6}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,5},{6}}
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,5,7},{6}}
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2},{3,4,5},{6,7}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,4,5},{6},{7}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,4},{5},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,4},{5},{7}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,6},{5}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,6},{5}}
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,6,7},{5}}
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2},{3,4,6},{5},{7}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4},{5,6}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5,6}}
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2},{3,4,7},{5,6}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,4},{5,6,7}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2},{3,4},{5,6},{7}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,4},{5},{6}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5},{6}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2},{3,4,7},{5},{6}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2},{3,4},{5,7},{6}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2},{3,4},{5},{6,7}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,4},{5},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2},{3},{4}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2},{3},{4},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2},{3},{4},{6}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2},{3},{4},{6,7}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2},{3},{4},{6},{7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,5},{3},{4}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,5},{3},{4},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,5,6},{3},{4}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,5,6,7},{3},{4}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2,5,6},{3},{4},{7}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,5},{3},{4},{6}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,5,7},{3},{4},{6}}
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,5},{3},{4},{6,7}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,5},{3},{4},{6},{7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,5},{4}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,5},{4},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,5},{4}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,5},{4}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,5},{4},{7}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,5,6},{4}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,5,6},{4}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,5,6,7},{4}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2},{3,5,6},{4},{7}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,5},{4},{6}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,5},{4},{6}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2},{3,5,7},{4},{6}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2},{3,5},{4},{6,7}}
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,5},{4},{6},{7}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3},{4,5}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3},{4,5},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3},{4,5}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3},{4,5}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3},{4,5},{7}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,6},{4,5}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4,5}}
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,6,7},{4,5}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2},{3,6},{4,5},{7}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4,5,6}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,5,6}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4,5,6}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2},{3},{4,5,6,7}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2},{3},{4,5,6},{7}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4,5},{6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,5},{6}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4,5},{6}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2},{3},{4,5,7},{6}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2},{3},{4,5},{6,7}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3},{4,5},{6},{7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3},{4},{5},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3},{4},{5},{7}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,6},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,6,7},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2},{3,6},{4},{5},{7}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4,6},{5}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,6},{5}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4,6},{5}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2},{3},{4,6,7},{5}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2},{3},{4,6},{5},{7}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4},{5,6}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4},{5,6}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4},{5,6}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2},{3},{4,7},{5,6}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2},{3},{4},{5,6,7}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2},{3},{4},{5,6},{7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4},{5},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4},{5},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4},{5},{6}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2},{3},{4,7},{5},{6}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2},{3},{4},{5,7},{6}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2},{3},{4},{5},{6,7}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2},{3},{4},{5},{6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8},{6}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8},{5}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,6,8},{5},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1},{2,3,4,7,8},{5,6}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6},{7}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,7,8},{5},{6}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,7},{6}}
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5},{6},{7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8},{4}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,5,6,8},{4},{7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,5,7,8},{4},{6}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6,7}}
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6},{7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1},{2,3,6,7,8},{4,5}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4,5},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,5,6}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,5,6,7}}
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5,6},{7}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,5},{6}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,5,7},{6}}
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6},{7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,6,7,8},{4},{5}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4},{5},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,6},{5}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,6,7},{5}}
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,6},{5},{7}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4},{5,6}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,7},{5,6}}
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4},{5,6},{7}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4},{5},{6}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,7},{5},{6}}
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5,7},{6}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,8},{4},{5},{6},{7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8},{3}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,4,5,6,8},{3},{7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,4,5,7,8},{3},{6}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,4,5,8},{3},{6,7}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,4,5,8},{3},{6},{7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,4,6,7,8},{3},{5}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,4,6,8},{3},{5},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,4,7,8},{3},{5,6}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6,7}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6},{7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,4,7,8},{3},{5},{6}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,7},{6}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,4,8},{3},{5},{6},{7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3,4}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1},{2,5,6,8},{3,4},{7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1},{2,5,7,8},{3,4},{6}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1},{2,5,8},{3,4},{6,7}}
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1},{2,5,8},{3,4},{6},{7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,4,5}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4,5},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,5,6}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,6,7}}
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,4,5,6},{7}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,5},{6}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,7},{6}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4,5},{6},{7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,4},{5}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4},{5},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,6},{5}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,6,7},{5}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,4,6},{5},{7}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5,6}}
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5,6},{7}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3,4},{5},{6}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5},{6}}
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,4},{5,7},{6}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,4},{5},{6,7}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5},{6},{7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3},{4}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,5,6,8},{3},{4},{7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,5,7,8},{3},{4},{6}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,5,8},{3},{4},{6,7}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,5,8},{3},{4},{6},{7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,5},{4}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,5},{4},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,5,6},{4}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,5,6,7},{4}}
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,5,6},{4},{7}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3,5},{4},{6}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,5,7},{4},{6}}
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,5},{4},{6,7}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,5},{4},{6},{7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3},{4,5}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3},{4,5},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,6},{4,5}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,6,7},{4,5}}
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,6},{4,5},{7}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,5,6}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5,6}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3},{4,5,6,7}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3},{4,5,6},{7}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,5},{6}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5},{6}}
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4,5,7},{6}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3},{4,5},{6,7}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3},{4,5},{6},{7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3},{4},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3},{4},{5},{7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,6},{4},{5}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,6,7},{4},{5}}
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,6},{4},{5},{7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,6},{5}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,6},{5}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4,6,7},{5}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3},{4,6},{5},{7}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4},{5,6}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5,6}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4,7},{5,6}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4},{5,6,7}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,8},{3},{4},{5,6},{7}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4},{5},{6}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5},{6}}
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4,7},{5},{6}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4},{5,7},{6}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,8},{3},{4},{5},{6,7}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2},{3,4,5,6,8},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2},{3,4,5,7,8},{6}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6,7}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6},{7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2},{3,4,6,7,8},{5}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2},{3,4,6,8},{5},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2},{3,4,7,8},{5,6}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,6,7}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5,6},{7}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2},{3,4,7,8},{5},{6}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,7},{6}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6,7}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6},{7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1,2},{3,5,6,7,8},{4}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1,2},{3,5,6,8},{4},{7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,5,7,8},{4},{6}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1,2},{3,5,8},{4},{6,7}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1,2},{3,5,8},{4},{6},{7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4,5}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1,2},{3,6,8},{4,5},{7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,5,6}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,6,7}}
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1,2},{3,8},{4,5,6},{7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,5},{6}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,7},{6}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1,2},{3,8},{4,5},{6},{7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4},{5}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1,2},{3,6,8},{4},{5},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,6},{5}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,6,7},{5}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1,2},{3,8},{4,6},{5},{7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4},{5,6}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5,6}}
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1,2},{3,8},{4},{5,6},{7}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1,2},{3,7,8},{4},{5},{6}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5},{6}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1,2},{3,8},{4},{5,7},{6}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4},{5},{6,7}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,8},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2,3},{4,5,6,8},{7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2,3},{4,5,7,8},{6}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2,3},{4,5,8},{6,7}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2,3},{4,5,8},{6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2,3},{4,6,7,8},{5}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2,3},{4,6,8},{5},{7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2,3},{4,7,8},{5,6}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2,3},{4,8},{5,6,7}}
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2,3},{4,8},{5,6},{7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2,3},{4,7,8},{5},{6}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2,3},{4,8},{5,7},{6}}
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2,3},{4,8},{5},{6,7}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2,3},{4,8},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3,4},{5,6,8},{7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3,4},{5,7,8},{6}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3,4},{5,8},{6,7}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3,4},{5,8},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4,5},{6,8},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4,5},{6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3,4},{5},{6,7,8}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3,4},{5},{6,8},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,6},{5},{7,8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,6},{5},{7},{8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}}
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6},{7,8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3,4},{5,7},{6},{8}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4},{5},{6,7},{8}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,6,7,8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4},{5,6,8},{7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4},{5,7,8},{6}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4},{5,8},{6,7}}
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4},{5,8},{6},{7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,5},{4},{6,7,8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,5},{4},{6,8},{7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,5,6},{4},{7,8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,5,6},{4},{7},{8}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,5},{4},{6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,5,7},{4},{6},{8}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,5},{4},{6,7},{8}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7},{8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5},{6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2,3},{4,5},{6,8},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,6},{4,5},{7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,6,7},{4,5},{8}}
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,6},{4,5},{7},{8}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}}
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5},{6},{8}}
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2,3},{4,5,7},{6},{8}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7},{8}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5},{6,8},{7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,6},{4},{5},{7,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,6,7},{4},{5},{8}}
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,6},{4},{5},{7},{8}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2,3},{4,6},{5},{7,8}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,6},{5},{8}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2,3},{4,6,7},{5},{8}}
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2,3},{4,6},{5},{7},{8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7,8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4},{5,6},{8}}
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2,3},{4,7},{5,6},{8}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4},{5,6,7},{8}}
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4},{5,6},{7},{8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7,8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4},{5},{6},{8}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2,3},{4,7},{5},{6},{8}}
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4},{5,7},{6},{8}}
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5},{6,7},{8}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3},{4,5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3},{4,5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6,7}}
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6},{7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3},{4,6,7,8},{5}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3},{4,6,8},{5},{7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3},{4,7,8},{5,6}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3},{4,8},{5,6,7}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3},{4,8},{5,6},{7}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3},{4,7,8},{5},{6}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3},{4,8},{5,7},{6}}
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3},{4,8},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3},{4,8},{5},{6},{7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,4},{3},{5,6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,4},{3},{5,6,8},{7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,4},{3},{5,7,8},{6}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,4},{3},{5,8},{6,7}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,4},{3},{5,8},{6},{7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,4,5},{3},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,4,5},{3},{6,8},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,4,5,6},{3},{7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,4,5,6,7},{3},{8}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,4,5,6},{3},{7},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,4,5},{3},{6},{7,8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,4,5,7},{3},{6},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,4,5},{3},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7},{8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,4},{3},{5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,4},{3},{5},{6,8},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,4,6},{3},{5},{7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,4,6,7},{3},{5},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,4,6},{3},{5},{7},{8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,4},{3},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,4,7},{3},{5,6},{8}}
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,4},{3},{5,6,7},{8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,4},{3},{5,6},{7},{8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6},{7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,4,7},{3},{5},{6},{8}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,4},{3},{5,7},{6},{8}}
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,4},{3},{5},{6,7},{8}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7},{8}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4},{5,6,8},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,4},{5,7,8},{6}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,8},{6,7}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,4},{5,8},{6},{7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,5},{3,4},{6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,5},{3,4},{6,8},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,5,6},{3,4},{7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,5,6,7},{3,4},{8}}
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,5,6},{3,4},{7},{8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,5},{3,4},{6},{7,8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,5,7},{3,4},{6},{8}}
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,5},{3,4},{6,7},{8}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7},{8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2},{3,4,5},{6,8},{7}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,4,5},{7,8}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3,4,5},{8}}
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3,4,5},{7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4,5,6},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2},{3,4,5,6},{7},{8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3,4,5},{6},{8}}
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2},{3,4,5,7},{6},{8}}
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2},{3,4,5},{6,7},{8}}
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3,4},{5},{6,8},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,4},{5},{7,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3,4},{5},{8}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3,4},{5},{7},{8}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2},{3,4,6},{5},{7,8}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4,6},{5},{8}}
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2},{3,4,6,7},{5},{8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2},{3,4,6},{5},{7},{8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4},{5,6},{8}}
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2},{3,4,7},{5,6},{8}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4},{5,6,7},{8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6},{7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3,4},{5},{6},{8}}
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2},{3,4,7},{5},{6},{8}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,4},{5,7},{6},{8}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3,4},{5},{6,7},{8}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4},{5,6,8},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4},{5,7,8},{6}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4},{5,8},{6,7}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4},{5,8},{6},{7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,5},{3},{4},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,5},{3},{4},{6,8},{7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,5,6},{3},{4},{7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,5,6,7},{3},{4},{8}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,5,6},{3},{4},{7},{8}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,5},{3},{4},{6},{7,8}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,5,7},{3},{4},{6},{8}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,5},{3},{4},{6,7},{8}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7},{8}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1,2},{3,5},{4},{6,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4},{6,8},{7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,5},{4},{7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3,5},{4},{8}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3,5},{4},{7},{8}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,5,6},{4},{7,8}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,5,6},{4},{8}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1,2},{3,5,6,7},{4},{8}}
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1,2},{3,5,6},{4},{7},{8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1,2},{3,5},{4},{6},{7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3,5},{4},{6},{8}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1,2},{3,5,7},{4},{6},{8}}
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1,2},{3,5},{4},{6,7},{8}}
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7},{8}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3},{4,5},{6,8},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3},{4,5},{7,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3},{4,5},{8}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3},{4,5},{7},{8}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,6},{4,5},{8}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1,2},{3,6,7},{4,5},{8}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1,2},{3,6},{4,5},{7},{8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3},{4,5,6},{8}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1,2},{3,7},{4,5,6},{8}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7},{8}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3},{4,5,6},{7},{8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5},{6},{7,8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3},{4,5},{6},{8}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1,2},{3,7},{4,5},{6},{8}}
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3},{4,5,7},{6},{8}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6,7},{8}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5},{6,8},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3},{4},{5},{7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3},{4},{5},{8}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3},{4},{5},{7},{8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4},{5},{7,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,6},{4},{5},{8}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1,2},{3,6,7},{4},{5},{8}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1,2},{3,6},{4},{5},{7},{8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3},{4,6},{5},{7,8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3},{4,6},{5},{8}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1,2},{3,7},{4,6},{5},{8}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3},{4,6,7},{5},{8}}
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3},{4,6},{5},{7},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4},{5,6},{7,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3},{4},{5,6},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1,2},{3,7},{4},{5,6},{8}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3},{4,7},{5,6},{8}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4},{5,6,7},{8}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4},{5,6},{7},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3},{4},{5},{6},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1,2},{3,7},{4},{5},{6},{8}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3},{4,7},{5},{6},{8}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4},{5,7},{6},{8}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,8},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,7,8},{6}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6,7}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,6,7,8},{5}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,6,8},{5},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2},{3,4,7,8},{5,6}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5,6,7}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2},{3,4,8},{5,6},{7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,7,8},{5},{6}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5,7},{6}}
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,8},{5},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,5,6,7,8},{4}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,5,6,8},{4},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,5,7,8},{4},{6}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,5,8},{4},{6,7}}
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,5,8},{4},{6},{7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2},{3,6,7,8},{4,5}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2},{3,6,8},{4,5},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,5,6}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2},{3,8},{4,5,6,7}}
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5,6},{7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,5},{6}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4,5,7},{6}}
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2},{3,8},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5},{6},{7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,6,7,8},{4},{5}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,6,8},{4},{5},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,6},{5}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4,6,7},{5}}
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,6},{5},{7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5,6}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5,6}}
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4},{5,6},{7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5},{6}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5},{6}}
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4},{5,7},{6}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,8},{4},{5},{6,7}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4},{5},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,3},{2},{4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,3},{2},{4,5,7,8},{6}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,3},{2},{4,5,8},{6,7}}
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,3},{2},{4,5,8},{6},{7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,3},{2},{4,6,7,8},{5}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,6,8},{5},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,3},{2},{4,7,8},{5,6}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,3},{2},{4,8},{5,6,7}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,3},{2},{4,8},{5,6},{7}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,3},{2},{4,7,8},{5},{6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3},{2},{4,8},{5,7},{6}}
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,3},{2},{4,8},{5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,3},{2},{4,8},{5},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,3,4},{2},{5,6,7,8}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,3,4},{2},{5,6,8},{7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,3,4},{2},{5,7,8},{6}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,3,4},{2},{5,8},{6,7}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,3,4},{2},{5,8},{6},{7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,3,4,5},{2},{6,7,8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,4,5},{2},{6,8},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,3,4,5,6},{2},{7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7},{2},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,3,4,5,6},{2},{7},{8}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,3,4,5},{2},{6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,4,5,7},{2},{6},{8}}
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,3,4,5},{2},{6,7},{8}}
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,3,4},{2},{5},{6,7,8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,3,4},{2},{5},{6,8},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,3,4,6},{2},{5},{7,8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,3,4,6,7},{2},{5},{8}}
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,3,4,6},{2},{5},{7},{8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,3,4},{2},{5,6},{7,8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,3,4,7},{2},{5,6},{8}}
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,3,4},{2},{5,6,7},{8}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,3,4},{2},{5,6},{7},{8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6},{7,8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,3,4,7},{2},{5},{6},{8}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,3,4},{2},{5,7},{6},{8}}
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,3,4},{2},{5},{6,7},{8}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7},{8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4},{5,6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4},{5,6,8},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4},{5,7,8},{6}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4},{5,8},{6,7}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4},{5,8},{6},{7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,3,5},{2},{4},{6,7,8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,5},{2},{4},{6,8},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,3,5,6},{2},{4},{7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,3,5,6,7},{2},{4},{8}}
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,3,5,6},{2},{4},{7},{8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,3,5},{2},{4},{6},{7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,5,7},{2},{4},{6},{8}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,3,5},{2},{4},{6,7},{8}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7},{8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5},{6,7,8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5},{6,8},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,3,6},{2},{4,5},{7,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,3,6,7},{2},{4,5},{8}}
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,3,6},{2},{4,5},{7},{8}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,3},{2},{4,5,6},{7,8}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,5,6},{8}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,3},{2},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,3},{2},{4,5,6},{7},{8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4,5},{6},{7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,5},{6},{8}}
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,3},{2},{4,5,7},{6},{8}}
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6,7},{8}}
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7},{8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5},{6,7,8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5},{6,8},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,3,6},{2},{4},{5},{7,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,3,6,7},{2},{4},{5},{8}}
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,3,6},{2},{4},{5},{7},{8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,6},{5},{7,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,6},{5},{8}}
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,3},{2},{4,6,7},{5},{8}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4,6},{5},{7},{8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4},{5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4},{5,6},{8}}
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,3},{2},{4,7},{5,6},{8}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4},{5,6,7},{8}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5,6},{7},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6},{7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,3,7},{2},{4},{5},{6},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,3},{2},{4,7},{5},{6},{8}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4},{5,7},{6},{8}}
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5},{6,7},{8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3},{4,5,6,8},{7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3},{4,5,7,8},{6}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6,7}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6},{7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,3},{4,6,7,8},{5}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,3},{4,6,8},{5},{7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,3},{4,7,8},{5,6}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,3},{4,8},{5,6,7}}
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,3},{4,8},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,3},{4,7,8},{5},{6}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3},{4,8},{5,7},{6}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,3},{4,8},{5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,3},{4,8},{5},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,4},{2,3},{5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,4},{2,3},{5,6,8},{7}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,4},{2,3},{5,7,8},{6}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,8},{6,7}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,4},{2,3},{5,8},{6},{7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,4,5},{2,3},{6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,4,5},{2,3},{6,8},{7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,4,5,6},{2,3},{7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,4,5,6,7},{2,3},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,4,5,6},{2,3},{7},{8}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,4,5},{2,3},{6},{7,8}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,4,5,7},{2,3},{6},{8}}
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,4,5},{2,3},{6,7},{8}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7},{8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,4},{2,3},{5},{6,7,8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,4},{2,3},{5},{6,8},{7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,4,6},{2,3},{5},{7,8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,4,6,7},{2,3},{5},{8}}
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,4,6},{2,3},{5},{7},{8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,4,7},{2,3},{5,6},{8}}
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,4},{2,3},{5,6,7},{8}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,4},{2,3},{5,6},{7},{8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6},{7,8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,4,7},{2,3},{5},{6},{8}}
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,4},{2,3},{5,7},{6},{8}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,4},{2,3},{5},{6,7},{8}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7},{8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3,4},{5,6,8},{7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3,4},{5,7,8},{6}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3,4},{5,8},{6,7}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3,4},{5,8},{6},{7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,3,4},{6,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,3,4},{6,8},{7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,3,4},{7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,3,4},{8}}
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2,3,4},{7},{8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2,3,4},{6},{7,8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,3,4},{6},{8}}
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,3,4},{6,7},{8}}
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4,5},{6,8},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3,4,5},{7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3,4,5},{8}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2,3,4,5},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,4,5,6},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3,4,5},{6},{8}}
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,7},{6},{8}}
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4,5},{6,7},{8}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7},{8}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3,4},{5},{6,8},{7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,3,4},{5},{7,8}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3,4},{5},{8}}
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2,3,4},{5},{7},{8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,6},{5},{7,8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,4,6},{5},{8}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,6,7},{5},{8}}
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,6},{5},{7},{8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,3,4},{5,6},{8}}
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1},{2,3,4,7},{5,6},{8}}
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5,6,7},{8}}
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3,4},{5,6},{7},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6},{7,8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,3,4},{5},{6},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,7},{5},{6},{8}}
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3,4},{5,7},{6},{8}}
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3,4},{5},{6,7},{8}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4},{5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4},{5,6,8},{7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4},{5,7,8},{6}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4},{5,8},{6,7}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4},{5,8},{6},{7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,3},{4},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,3},{4},{6,8},{7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,3},{4},{7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,3},{4},{8}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2,3},{4},{7},{8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2,3},{4},{6},{7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,3},{4},{6},{8}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,3},{4},{6,7},{8}}
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7},{8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,5},{4},{6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,5},{4},{6,8},{7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3,5},{4},{7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3,5},{4},{8}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2,3,5},{4},{7},{8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,5,6},{4},{7,8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,5,6},{4},{8}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,5,6,7},{4},{8}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,5,6},{4},{7},{8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,5},{4},{6},{7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3,5},{4},{6},{8}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,5,7},{4},{6},{8}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,5},{4},{6,7},{8}}
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7},{8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5},{6,8},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3},{4,5},{8}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,3},{4,5},{7},{8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1},{2,3,6},{4,5},{7,8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2,3,6},{4,5},{8}}
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4,5},{8}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1},{2,3,6},{4,5},{7},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2,3},{4,5,6},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4,5,6},{8}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3},{4,5,6,7},{8}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3},{4,5,6},{7},{8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4,5},{6},{7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3},{4,5},{6},{8}}
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1},{2,3,7},{4,5},{6},{8}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3},{4,5,7},{6},{8}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5},{6,8},{7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4},{5},{7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3},{4},{5},{8}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2,3},{4},{5},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,6},{4},{5},{7,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2,3,6},{4},{5},{8}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4},{5},{8}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,6},{4},{5},{7},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,3},{4,6},{5},{7,8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,3},{4,6},{5},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4,6},{5},{8}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,3},{4,6,7},{5},{8}}
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,3},{4,6},{5},{7},{8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4},{5,6},{7,8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,3},{4},{5,6},{8}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4},{5,6},{8}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,3},{4,7},{5,6},{8}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4},{5,6,7},{8}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5,6},{7},{8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,3},{4},{5},{6},{8}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,7},{4},{5},{6},{8}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,3},{4,7},{5},{6},{8}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4},{5,7},{6},{8}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6,7},{8}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3},{4,5,6,8},{7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3},{4,5,7,8},{6}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3},{4,5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4,5,8},{6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3},{4,6,7,8},{5}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3},{4,6,8},{5},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3},{4,7,8},{5,6}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,6,7}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5,6},{7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4,7,8},{5},{6}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,7},{6}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3},{4,8},{5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,4},{2},{3},{5,6,7,8}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,4},{2},{3},{5,6,8},{7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,4},{2},{3},{5,7,8},{6}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2},{3},{5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,4},{2},{3},{5,8},{6},{7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,4,5},{2},{3},{6,7,8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,4,5},{2},{3},{6,8},{7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,4,5,6},{2},{3},{7,8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,4,5,6,7},{2},{3},{8}}
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,4,5,6},{2},{3},{7},{8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,4,5},{2},{3},{6},{7,8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,4,5,7},{2},{3},{6},{8}}
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,4,5},{2},{3},{6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5},{6,7,8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5},{6,8},{7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,4,6},{2},{3},{5},{7,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,4,6,7},{2},{3},{5},{8}}
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,4,6},{2},{3},{5},{7},{8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,4,7},{2},{3},{5,6},{8}}
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,4},{2},{3},{5,6,7},{8}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5,6},{7},{8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6},{7,8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,4,7},{2},{3},{5},{6},{8}}
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5,7},{6},{8}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5},{6,7},{8}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,4},{3},{5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,4},{3},{5,6,8},{7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,4},{3},{5,7,8},{6}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,4},{3},{5,8},{6,7}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,4},{3},{5,8},{6},{7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,4},{3},{6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,4},{3},{6,8},{7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,4},{3},{7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,4},{3},{8}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2,4},{3},{7},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2,4},{3},{6},{7,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,4},{3},{6},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,4},{3},{6,7},{8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,4,5},{3},{6,7,8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,4,5},{3},{6,8},{7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,4,5},{3},{7,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,4,5},{3},{8}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2,4,5},{3},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,4,5,6},{3},{7,8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,4,5,6},{3},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,4,5,6,7},{3},{8}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,4,5,6},{3},{7},{8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,4,5},{3},{6},{7,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,4,5},{3},{6},{8}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,4,5,7},{3},{6},{8}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,4,5},{3},{6,7},{8}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7},{8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5},{6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5},{6,8},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,4},{3},{5},{7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2,4},{3},{5},{8}}
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2,4},{3},{5},{7},{8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,4,6},{3},{5},{7,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2,4,6},{3},{5},{8}}
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,4,6,7},{3},{5},{8}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,4,6},{3},{5},{7},{8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6},{7,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,4},{3},{5,6},{8}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,4,7},{3},{5,6},{8}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,4},{3},{5,6,7},{8}}
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5,6},{7},{8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6},{7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,4},{3},{5},{6},{8}}
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,4,7},{3},{5},{6},{8}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5,7},{6},{8}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5},{6,7},{8}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4},{5,6,7,8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4},{5,6,8},{7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,4},{5,7,8},{6}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,4},{5,8},{6,7}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,4},{5,8},{6},{7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2},{3,4},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2},{3,4},{6,8},{7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2},{3,4},{7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2},{3,4},{8}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2},{3,4},{7},{8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2},{3,4},{6},{7,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2},{3,4},{6},{8}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2},{3,4},{6,7},{8}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7},{8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1},{2,5},{3,4},{6,7,8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3,4},{6,8},{7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,5},{3,4},{8}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,5},{3,4},{7},{8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1},{2,5,6},{3,4},{7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2,5,6},{3,4},{8}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1},{2,5,6,7},{3,4},{8}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1},{2,5,6},{3,4},{7},{8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1},{2,5},{3,4},{6},{7,8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,5},{3,4},{6},{8}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1},{2,5,7},{3,4},{6},{8}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3,4},{6,7},{8}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7},{8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2},{3,4,5},{6,7,8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2},{3,4,5},{6,8},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,4,5},{7,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3,4,5},{8}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,4,5},{7},{8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,4,5},{7,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,4,5},{8}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,4,5},{8}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1},{2,6},{3,4,5},{7},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2},{3,4,5,6},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,4,5,6},{8}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2},{3,4,5,6},{7},{8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2},{3,4,5},{6},{7,8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2},{3,4,5},{6},{8}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,4,5},{6},{8}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,7},{6},{8}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2},{3,4,5},{6,7},{8}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5},{6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5},{6,8},{7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,4},{5},{7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3,4},{5},{8}}
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,4},{5},{7},{8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,4},{5},{7,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,4},{5},{8}}
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,4},{5},{8}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1},{2,6},{3,4},{5},{7},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,6},{5},{7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3,4,6},{5},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,4,6},{5},{8}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,6,7},{5},{8}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,6},{5},{7},{8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2},{3,4},{5,6},{8}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,4},{5,6},{8}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2},{3,4,7},{5,6},{8}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4},{5,6,7},{8}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6},{7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2},{3,4},{5},{6},{8}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,4},{5},{6},{8}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,7},{5},{6},{8}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,4},{5,7},{6},{8}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5},{6,7},{8}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5,6,8},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5,7,8},{6}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6,7}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6},{7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2},{3},{4},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2},{3},{4},{6,8},{7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2},{3},{4},{7,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2},{3},{4},{8}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2},{3},{4},{7},{8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2},{3},{4},{6},{7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2},{3},{4},{6},{8}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2},{3},{4},{6,7},{8}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,5},{3},{4},{6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3},{4},{6,8},{7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3},{4},{7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,5},{3},{4},{8}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,5},{3},{4},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,5,6},{3},{4},{7,8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2,5,6},{3},{4},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,5,6,7},{3},{4},{8}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,5,6},{3},{4},{7},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,5},{3},{4},{6},{7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,5},{3},{4},{6},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,5,7},{3},{4},{6},{8}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3},{4},{6,7},{8}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7},{8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,5},{4},{6,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4},{6,8},{7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,5},{4},{7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3,5},{4},{8}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,5},{4},{7},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,5},{4},{7,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,5},{4},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,5},{4},{8}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1},{2,6},{3,5},{4},{7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,5,6},{4},{7,8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3,5,6},{4},{8}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,5,6},{4},{8}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,5,6,7},{4},{8}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,5,6},{4},{7},{8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,5},{4},{6},{7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2},{3,5},{4},{6},{8}}
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,5},{4},{6},{8}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,5,7},{4},{6},{8}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,5},{4},{6,7},{8}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3},{4,5},{6,8},{7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3},{4,5},{7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3},{4,5},{8}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3},{4,5},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3},{4,5},{7,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3},{4,5},{8}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3},{4,5},{8}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,6},{3},{4,5},{7},{8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2},{3,6},{4,5},{7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3,6},{4,5},{8}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,6},{4,5},{8}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2},{3,6,7},{4,5},{8}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2},{3,6},{4,5},{7},{8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4,5,6},{8}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3},{4,5,6},{8}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2},{3,7},{4,5,6},{8}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4,5,6},{7},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2},{3},{4,5},{6},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3},{4,5},{6},{8}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2},{3,7},{4,5},{6},{8}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3},{4,5,7},{6},{8}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,8},{7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2},{3},{4},{5},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3},{4},{5},{8}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,6},{3},{4},{5},{7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3},{4},{5},{8}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3},{4},{5},{8}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,6},{3},{4},{5},{7},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,6},{4},{5},{7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3,6},{4},{5},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,6},{4},{5},{8}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,6,7},{4},{5},{8}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,6},{4},{5},{7},{8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3},{4,6},{5},{7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4,6},{5},{8}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3},{4,6},{5},{8}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2},{3,7},{4,6},{5},{8}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3},{4,6,7},{5},{8}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4,6},{5},{7},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5,6},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,7},{3},{4},{5,6},{8}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,7},{4},{5,6},{8}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3},{4,7},{5,6},{8}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,7},{3},{4},{5},{6},{8}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,7},{4},{5},{6},{8}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4,7},{5},{6},{8}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5,7},{6},{8}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8}}
Map
inverse Kreweras complement
Description
Return the inverse of the Kreweras complement of a Dyck path, regarded as a noncrossing set partition.
To identify Dyck paths and noncrossing set partitions, this maps uses the following classical bijection. The number of down steps after the $i$-th up step of the Dyck path is the size of the block of the set partition whose maximal element is $i$. If $i$ is not a maximal element of a block, the $(i+1)$-st step is also an up step.
To identify Dyck paths and noncrossing set partitions, this maps uses the following classical bijection. The number of down steps after the $i$-th up step of the Dyck path is the size of the block of the set partition whose maximal element is $i$. If $i$ is not a maximal element of a block, the $(i+1)$-st step is also an up step.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
searching the database
Sorry, this map was not found in the database.