Identifier
Images
[] => {}
[1,0] => {{1}}
[1,0,1,0] => {{1},{2}}
[1,1,0,0] => {{1,2}}
[1,0,1,0,1,0] => {{1},{2},{3}}
[1,0,1,1,0,0] => {{1},{2,3}}
[1,1,0,0,1,0] => {{1,2},{3}}
[1,1,0,1,0,0] => {{1,3},{2}}
[1,1,1,0,0,0] => {{1,2,3}}
[1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}}
[1,0,1,0,1,1,0,0] => {{1},{2},{3,4}}
[1,0,1,1,0,0,1,0] => {{1},{2,3},{4}}
[1,0,1,1,0,1,0,0] => {{1},{2,4},{3}}
[1,0,1,1,1,0,0,0] => {{1},{2,3,4}}
[1,1,0,0,1,0,1,0] => {{1,2},{3},{4}}
[1,1,0,0,1,1,0,0] => {{1,2},{3,4}}
[1,1,0,1,0,0,1,0] => {{1,3},{2},{4}}
[1,1,0,1,0,1,0,0] => {{1,4},{2},{3}}
[1,1,0,1,1,0,0,0] => {{1,3,4},{2}}
[1,1,1,0,0,0,1,0] => {{1,2,3},{4}}
[1,1,1,0,0,1,0,0] => {{1,4},{2,3}}
[1,1,1,0,1,0,0,0] => {{1,2,4},{3}}
[1,1,1,1,0,0,0,0] => {{1,2,3,4}}
[1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}}
[1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}}
[1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}}
[1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}}
[1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}}
[1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}}
[1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}}
[1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}}
[1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}}
[1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}}
[1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}}
[1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}}
[1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}}
[1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}}
[1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}}
[1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}}
[1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}}
[1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}}
[1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}}
[1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}}
[1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}}
[1,1,0,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4}}
[1,1,0,1,0,1,1,0,0,0] => {{1,4,5},{2},{3}}
[1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}}
[1,1,0,1,1,0,0,1,0,0] => {{1,5},{2},{3,4}}
[1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4}}
[1,1,0,1,1,1,0,0,0,0] => {{1,3,4,5},{2}}
[1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}}
[1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}}
[1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}}
[1,1,1,0,0,1,0,1,0,0] => {{1,5},{2,3},{4}}
[1,1,1,0,0,1,1,0,0,0] => {{1,4,5},{2,3}}
[1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}}
[1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,0] => {{1,2,5},{3},{4}}
[1,1,1,0,1,1,0,0,0,0] => {{1,2,4,5},{3}}
[1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}}
[1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3,4}}
[1,1,1,1,0,0,1,0,0,0] => {{1,2,5},{3,4}}
[1,1,1,1,0,1,0,0,0,0] => {{1,2,3,5},{4}}
[1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}}
[1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}}
[1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}}
[1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}}
[1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}}
[1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}}
[1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}}
[1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}}
[1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}}
[1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}}
[1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}}
[1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}}
[1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}}
[1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}}
[1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}}
[1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}}
[1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}}
[1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}}
[1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}}
[1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}}
[1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}}
[1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}}
[1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}}
[1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}}
[1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}}
[1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}}
[1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}}
[1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}}
[1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}}
[1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}}
[1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}}
[1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}}
>>> Load all 6550 entries. <<<
[1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}}
[1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}}
[1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}}
[1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}}
[1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}}
[1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}}
[1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}}
[1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}}
[1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}}
[1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}}
[1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}}
[1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}}
[1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}}
[1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}}
[1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}}
[1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}}
[1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}}
[1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}}
[1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}}
[1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,0,0,0] => {{1,5,6},{2},{3},{4}}
[1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}}
[1,1,0,1,0,1,1,0,0,1,0,0] => {{1,6},{2},{3},{4,5}}
[1,1,0,1,0,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5}}
[1,1,0,1,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2},{3}}
[1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}}
[1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}}
[1,1,0,1,1,0,0,1,0,1,0,0] => {{1,6},{2},{3,4},{5}}
[1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4}}
[1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}}
[1,1,0,1,1,0,1,0,0,1,0,0] => {{1,6},{2},{3,5},{4}}
[1,1,0,1,1,0,1,0,1,0,0,0] => {{1,3,6},{2},{4},{5}}
[1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4}}
[1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}}
[1,1,0,1,1,1,0,0,0,1,0,0] => {{1,6},{2},{3,4,5}}
[1,1,0,1,1,1,0,0,1,0,0,0] => {{1,3,6},{2},{4,5}}
[1,1,0,1,1,1,0,1,0,0,0,0] => {{1,3,4,6},{2},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0] => {{1,3,4,5,6},{2}}
[1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}}
[1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}}
[1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}}
[1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}}
[1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}}
[1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}}
[1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}}
[1,1,1,0,0,1,0,1,0,1,0,0] => {{1,6},{2,3},{4},{5}}
[1,1,1,0,0,1,0,1,1,0,0,0] => {{1,5,6},{2,3},{4}}
[1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}}
[1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5}}
[1,1,1,0,0,1,1,0,1,0,0,0] => {{1,4,6},{2,3},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2,3}}
[1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}}
[1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}}
[1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}}
[1,1,1,0,1,0,0,1,0,1,0,0] => {{1,6},{2,4},{3},{5}}
[1,1,1,0,1,0,0,1,1,0,0,0] => {{1,5,6},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,0,0] => {{1,6},{2,5},{3},{4}}
[1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,6},{3},{4},{5}}
[1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2,5,6},{3},{4}}
[1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}}
[1,1,1,0,1,1,0,0,0,1,0,0] => {{1,6},{2,4,5},{3}}
[1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2,6},{3},{4,5}}
[1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2,4,6},{3},{5}}
[1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,4,5,6},{3}}
[1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}}
[1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}}
[1,1,1,1,0,0,0,1,0,1,0,0] => {{1,6},{2,3,4},{5}}
[1,1,1,1,0,0,0,1,1,0,0,0] => {{1,5,6},{2,3,4}}
[1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4}}
[1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2,6},{3,4},{5}}
[1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,5,6},{3,4}}
[1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}}
[1,1,1,1,0,1,0,0,0,1,0,0] => {{1,6},{2,3,5},{4}}
[1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,6},{3,5},{4}}
[1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3,6},{4},{5}}
[1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2,3,5,6},{4}}
[1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}}
[1,1,1,1,1,0,0,0,0,1,0,0] => {{1,6},{2,3,4,5}}
[1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,6},{3,4,5}}
[1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3,6},{4,5}}
[1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3,4,6},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2},{3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2},{3},{4},{5,6}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3},{4},{6}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3},{4}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2},{3},{4,5},{6}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4,5}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2},{3},{4,6},{5}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2},{3},{5},{6}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2},{3},{5}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2},{3},{4,5,6}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2},{3},{5,6}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2},{3},{6}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2},{3}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2},{3,4},{5},{6}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3,4},{5}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2},{3,4},{5,6}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3,4},{6}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3,4}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2},{3,5},{4},{6}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,5},{4}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4},{5}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,3,7},{2},{4},{5},{6}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4},{5}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2},{3,5,6},{4}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,3,7},{2},{4},{5,6}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5,7},{2},{4},{6}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,3,5,6,7},{2},{4}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2},{3,4,5},{6}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,4,5}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4,5}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,3,7},{2},{4,5},{6}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4,5}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2},{3,4,6},{5}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,3,4,7},{2},{5},{6}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,3,4,6,7},{2},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2},{3,4,5,6}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,3,7},{2},{4,5,6}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,3,4,7},{2},{5,6}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,3,4,5,7},{2},{6}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,3,4,5,6,7},{2}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4,6},{5},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2,3},{4},{5},{6}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3},{4},{5}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2,3},{4},{5,6}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3},{4},{6}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3},{4}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2,3},{4,5},{6}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2,3},{4,5}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2,3},{4,6},{5}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2,3},{5},{6}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2,3},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2,3},{4,5,6}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2,3},{5,6}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2,3},{6}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2,3}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2,4},{3},{5},{6}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,4},{3},{5}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2,4},{3},{5,6}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3},{4}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4},{5}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3},{4}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3},{4},{5,6}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3},{4},{6}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3},{4}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2,4,5},{3},{6}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,4,5},{3}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4,5}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3},{4,5},{6}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4,5}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3},{4,6},{5}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,4,7},{3},{5},{6}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,4,6,7},{3},{5}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2,4,5,6},{3}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3},{4,5,6}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,4,7},{3},{5,6}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,4,5,7},{3},{6}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,4,5,6,7},{3}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,7},{2,3,4},{5},{6}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3,4},{5}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,7},{2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3,4},{6}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3,4}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3,4},{6}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3,4}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4},{5}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3,4},{5},{6}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4},{5}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3,4}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3,4},{5,6}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3,4},{6}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3,4}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,7},{2,3,5},{4},{6}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,5},{4}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3,5},{4},{6}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,5},{4}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4},{5}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4},{5}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4},{5},{6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4},{5}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,7},{2,3,5,6},{4}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3,5,6},{4}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4},{5,6}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,5,7},{4},{6}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,5,6,7},{4}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,7},{2,3,4,5},{6}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,4,5}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4,5}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,7},{3,4,5},{6}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4,5}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4,5}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4,5}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4,5},{6}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4,5}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,7},{2,3,4,6},{5}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,7},{3,4,6},{5}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4,6},{5}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5},{6}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,6,7},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,7},{2,3,4,5,6}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,7},{3,4,5,6}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,7},{4,5,6}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5,6}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,7},{6}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{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},{2},{3},{4},{5},{6},{7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,8},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5,7},{6},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5,7,8},{6}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6,7}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5,6,8},{7}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3},{4,5},{6,8},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5},{6,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4,6},{5},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3},{4,6},{5},{7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4,7},{5},{6},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4,7,8},{5},{6}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3},{4,6,7},{5},{8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3},{4,8},{5},{6,7}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3},{4,6,8},{5},{7}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3},{4,6,7,8},{5}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,5,6},{7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3},{4,7},{5,6},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5,6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3},{4,7,8},{5,6}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3},{4,5,7},{6},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,7},{6}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4,5,8},{6},{7}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3},{4,5,7,8},{6}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,6,7}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3},{4,5,8},{6,7}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3},{4,5,6,8},{7}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6},{7,8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5},{6,7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5},{6,8},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5},{6,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,4},{5,7},{6},{8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,4},{5,8},{6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,4},{5,7,8},{6}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,4},{5,8},{6,7}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4},{5,6,8},{7}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4},{5,6,7,8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,5},{4},{6},{7,8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,5},{4},{6,7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4},{6,8},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,5},{4},{6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,6},{4},{5},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,6},{4},{5},{7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,7},{4},{5},{6},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4},{5},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5},{6}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,6,7},{4},{5},{8}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,8},{4},{5},{6,7}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,6,8},{4},{5},{7}}
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,6,7,8},{4},{5}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,5,6},{4},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,5,6},{4},{7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,7},{4},{5,6},{8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4},{5,6},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5,6}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,5,7},{4},{6},{8}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4},{5,7},{6}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,5,8},{4},{6},{7}}
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,5,7,8},{4},{6}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,5,6,7},{4},{8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4},{5,6,7}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,5,8},{4},{6,7}}
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,5,6,8},{4},{7}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,5,6,7,8},{4}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2},{3,4,5},{6},{7,8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2},{3,4,5},{6,8},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2},{3,4,5},{6,7,8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2},{3,6},{4,5},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2},{3,6},{4,5},{7,8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2},{3,7},{4,5},{6},{8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5},{6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,5},{6}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2},{3,6,7},{4,5},{8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2},{3,8},{4,5},{6,7}}
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2},{3,6,8},{4,5},{7}}
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2},{3,6,7,8},{4,5}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,6},{5},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,6},{5},{7,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2},{3,7},{4,6},{5},{8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,6},{5},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,6},{5}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,7},{5},{6},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5},{6}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,8},{5},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,7,8},{5},{6}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,6,7},{5},{8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4,6,7},{5}}
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5},{6,7}}
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,6,8},{5},{7}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,6,7,8},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2},{3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2},{3,7},{4,5,6},{8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5,6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,5,6}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2},{3,4,7},{5,6},{8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5,6}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2},{3,4,8},{5,6},{7}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2},{3,4,7,8},{5,6}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,7},{6},{8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4,5,7},{6}}
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5,7},{6}}
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6},{7}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,7,8},{6}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2},{3,8},{4,5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5,6,7}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6,7}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,8},{7}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5},{6,8},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6,7,8}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5,6},{7},{8}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4},{5,6},{7,8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4},{5,7},{6},{8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4},{5,8},{6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4},{5,7,8},{6}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4},{5,6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4},{5,8},{6,7}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4},{5,6,8},{7}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4},{5,6,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4,5},{6},{7,8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5},{6,8},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,3},{4,6},{5},{7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,3},{4,6},{5},{7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,3},{4,7},{5},{6},{8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,3},{4,8},{5},{6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,3},{4,7,8},{5},{6}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,3},{4,6,7},{5},{8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,3},{4,8},{5},{6,7}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,3},{4,6,8},{5},{7}}
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,3},{4,6,7,8},{5}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3},{4,5,6},{7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,3},{4,7},{5,6},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,3},{4,8},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,3},{4,7,8},{5,6}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3},{4,5,7},{6},{8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3},{4,8},{5,7},{6}}
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6},{7}}
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3},{4,5,7,8},{6}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,3},{4,8},{5,6,7}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6,7}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3},{4,5,6,8},{7}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6},{7,8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5},{6,7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5},{6,8},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5},{6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5,6},{7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6},{7,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5,7},{6},{8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,4},{3},{5,8},{6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,4},{3},{5,7,8},{6}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,4},{3},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,4},{3},{5,8},{6,7}}
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,4},{3},{5,6,8},{7}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,4},{3},{5,6,7,8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,5},{3},{4},{6},{7,8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3},{4},{6,7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3},{4},{6,8},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,5},{3},{4},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,6},{3},{4},{5},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,6},{3},{4},{5},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,7},{3},{4},{5},{6},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3},{4},{5},{6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4},{5},{6}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3},{4},{5},{8}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,8},{3},{4},{5},{6,7}}
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3},{4},{5},{7}}
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3},{4},{5}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,5,6},{3},{4},{7},{8}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,5,6},{3},{4},{7,8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,7},{3},{4},{5,6},{8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,8},{3},{4},{5,6},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4},{5,6}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,5,7},{3},{4},{6},{8}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4},{5,7},{6}}
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,5,8},{3},{4},{6},{7}}
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,5,7,8},{3},{4},{6}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,5,6,7},{3},{4},{8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4},{5,6,7}}
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,5,8},{3},{4},{6,7}}
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,5,6,8},{3},{4},{7}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3},{4}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7},{8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,4,5},{3},{6},{7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,4,5},{3},{6,7},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,4,5},{3},{6,8},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,4,5},{3},{6,7,8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,6},{3},{4,5},{7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3},{4,5},{7,8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3},{4,5},{6},{8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3},{4,5},{6},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,5},{6}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3},{4,5},{8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3},{4,5},{6,7}}
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3},{4,5},{7}}
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3},{4,5}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,4,6},{3},{5},{7},{8}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,4,6},{3},{5},{7,8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3},{4,6},{5},{8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3},{4,6},{5},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,6},{5}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,4,7},{3},{5},{6},{8}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4,7},{5},{6}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,4,8},{3},{5},{6},{7}}
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,4,7,8},{3},{5},{6}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,4,6,7},{3},{5},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4,6,7},{5}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5},{6,7}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,4,6,8},{3},{5},{7}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,4,6,7,8},{3},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,4,5,6},{3},{7},{8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,4,5,6},{3},{7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3},{4,5,6},{8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3},{4,5,6},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,5,6}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,4,7},{3},{5,6},{8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4,7},{5,6}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6},{7}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,4,7,8},{3},{5,6}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,4,5,7},{3},{6},{8}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4,5,7},{6}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,7},{6}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,4,5,8},{3},{6},{7}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,4,5,7,8},{3},{6}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,4,5,6,7},{3},{8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3},{4,5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,4,5,8},{3},{6,7}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,4,5,6,8},{3},{7}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8},{3}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6},{7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3,4},{5},{6,7},{8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3,4},{5},{6,8},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3,4},{5,6},{7},{8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3,4},{5,7},{6},{8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3,4},{5,8},{6},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3,4},{5,7,8},{6}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3,4},{5,8},{6,7}}
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3,4},{5,6,8},{7}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4},{5,6,7,8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1},{2,5},{3,4},{6},{7,8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3,4},{6,7},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3,4},{6,8},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1},{2,5},{3,4},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1},{2,6},{3,4},{5},{7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,4},{5},{7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,4},{5},{6},{8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5},{6},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3,4},{5},{6}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,4},{5},{8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,4},{5},{6,7}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4},{5},{7}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,4},{5}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1},{2,5,6},{3,4},{7},{8}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1},{2,5,6},{3,4},{7,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,4},{5,6},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5,6},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4},{5,6}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1},{2,5,7},{3,4},{6},{8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,4},{5,7},{6}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1},{2,5,8},{3,4},{6},{7}}
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1},{2,5,7,8},{3,4},{6}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1},{2,5,6,7},{3,4},{8}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,4},{5,6,7}}
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1},{2,5,8},{3,4},{6,7}}
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1},{2,5,6,8},{3,4},{7}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3,4}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,5},{4},{6},{7,8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,5},{4},{6,7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,5},{4},{6,8},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,5},{4},{6,7,8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1},{2,6},{3,5},{4},{7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,5},{4},{7,8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,5},{4},{6},{8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,5},{4},{6},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3,5},{4},{6}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,5},{4},{8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,5},{4},{6,7}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,5},{4},{7}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,5},{4}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,6},{4},{5},{7},{8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,6},{4},{5},{7,8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,6},{4},{5},{8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,6},{4},{5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,6},{4},{5}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,7},{4},{5},{6},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5},{6}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,8},{4},{5},{6},{7}}
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4},{5},{6}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4},{5},{8}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,6,7},{4},{5}}
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5},{6,7}}
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4},{5},{7}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,6,7,8},{4},{5}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,5,6},{4},{7},{8}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,5,6},{4},{7,8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,5,6},{4},{8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,5,6},{4},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,5,6},{4}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4},{5,6},{8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5,6}}
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4},{5,6},{7}}
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4},{5,6}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,5,7},{4},{6},{8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,5,7},{4},{6}}
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5,7},{6}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6},{7}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,5,7,8},{4},{6}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,5,6,7},{4},{8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,5,6,7},{4}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5,6,7}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6,7}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,5,6,8},{4},{7}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8},{4}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4,5},{6},{7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4,5},{6,8},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1},{2,6},{3,4,5},{7},{8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,4,5},{7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,4,5},{6},{8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4,5},{6},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,5},{6}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,4,5},{8}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,4,5},{6,7}}
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4,5},{7}}
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,4,5}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1},{2,3,6},{4,5},{7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1},{2,3,6},{4,5},{7,8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,6},{4,5},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,6},{4,5},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,6},{4,5}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1},{2,3,7},{4,5},{6},{8}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5},{6}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6},{7}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,5},{6}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4,5},{8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,6,7},{4,5}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6,7}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4,5},{7}}
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1},{2,3,6,7,8},{4,5}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,6},{5},{7},{8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,6},{5},{7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,4,6},{5},{8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,4,6},{5},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,6},{5}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4,6},{5},{8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,6},{5}}
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,6},{5},{7}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,6},{5}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,7},{5},{6},{8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5},{6}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,7},{5},{6}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5},{6},{7}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,7,8},{5},{6}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,6,7},{5},{8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,6,7},{5}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,6,7},{5}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5},{6,7}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,6,8},{5},{7}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,4,5,6},{8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,5,6}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4,5,6},{8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5,6}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,5,6}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1},{2,3,4,7},{5,6},{8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5,6}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,7},{5,6}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6},{7}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1},{2,3,4,7,8},{5,6}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,7},{6},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,7},{6}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,5,7},{6}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,7},{6}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,6,7}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,5,6,7}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6,7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5},{6,8},{7}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4},{5,6},{7},{8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4},{5,7},{6},{8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4},{5,8},{6},{7}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4},{5,7,8},{6}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4},{5,6,7},{8}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4},{5,8},{6,7}}
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4},{5,6,8},{7}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6,7},{8}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3},{4,5},{6,8},{7}}
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3},{4,6},{5},{7},{8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3},{4,6},{5},{7,8}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3},{4,7},{5},{6},{8}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3},{4,8},{5},{6},{7}}
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3},{4,7,8},{5},{6}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3},{4,6,7},{5},{8}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3},{4,8},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3},{4,6,8},{5},{7}}
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3},{4,6,7,8},{5}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3},{4,5,6},{7},{8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3},{4,7},{5,6},{8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3},{4,8},{5,6},{7}}
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3},{4,7,8},{5,6}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3},{4,5,7},{6},{8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3},{4,8},{5,7},{6}}
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6},{7}}
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3},{4,5,7,8},{6}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7},{8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3},{4,8},{5,6,7}}
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6,7}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3},{4,5,6,8},{7}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3,4},{5},{6,7},{8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3,4},{5},{6,8},{7}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5,6},{7},{8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,4},{5,7},{6},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,4},{5,8},{6},{7}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,4},{5,7,8},{6}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4},{5,6,7},{8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,8},{6,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4},{5,6,8},{7}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7},{8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1,2},{3,5},{4},{6},{7,8}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1,2},{3,5},{4},{6,7},{8}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4},{6,8},{7}}
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1,2},{3,5},{4},{6,7,8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1,2},{3,6},{4},{5},{7},{8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4},{5},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1,2},{3,7},{4},{5},{6},{8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,8},{4},{5},{6},{7}}
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1,2},{3,7,8},{4},{5},{6}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1,2},{3,6,7},{4},{5},{8}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4},{5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1,2},{3,6,8},{4},{5},{7}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4},{5}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1,2},{3,5,6},{4},{7},{8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,5,6},{4},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1,2},{3,7},{4},{5,6},{8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1,2},{3,8},{4},{5,6},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4},{5,6}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1,2},{3,5,7},{4},{6},{8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1,2},{3,8},{4},{5,7},{6}}
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1,2},{3,5,8},{4},{6},{7}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,5,7,8},{4},{6}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1,2},{3,5,6,7},{4},{8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4},{5,6,7}}
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1,2},{3,5,8},{4},{6,7}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1,2},{3,5,6,8},{4},{7}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1,2},{3,5,6,7,8},{4}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7},{8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2},{3,4,5},{6,7},{8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2},{3,4,5},{6,8},{7}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1,2},{3,6},{4,5},{7},{8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1,2},{3,7},{4,5},{6},{8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1,2},{3,8},{4,5},{6},{7}}
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,5},{6}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1,2},{3,6,7},{4,5},{8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1,2},{3,6,8},{4,5},{7}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4,5}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2},{3,4,6},{5},{7},{8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2},{3,4,6},{5},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1,2},{3,7},{4,6},{5},{8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1,2},{3,8},{4,6},{5},{7}}
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,6},{5}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2},{3,4,7},{5},{6},{8}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5},{6}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6},{7}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2},{3,4,7,8},{5},{6}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2},{3,4,6,7},{5},{8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,6,7},{5}}
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6,7}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2},{3,4,6,8},{5},{7}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2},{3,4,6,7,8},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2},{3,4,5,6},{7},{8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1,2},{3,7},{4,5,6},{8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1,2},{3,8},{4,5,6},{7}}
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,5,6}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2},{3,4,7},{5,6},{8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5,6}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5,6},{7}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2},{3,4,7,8},{5,6}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2},{3,4,5,7},{6},{8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,7},{6}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,7},{6}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6},{7}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2},{3,4,5,7,8},{6}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,6,7}}
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,6,7}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6,7}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2},{3,4,5,6,8},{7}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5},{6,7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5},{6,8},{7}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5,6},{7},{8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4},{5,6},{7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4},{5,7},{6},{8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4},{5,8},{6},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4},{5,7,8},{6}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4},{5,6,7},{8}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4},{5,8},{6,7}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4},{5,6,8},{7}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4},{5,6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4,5},{6},{7,8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6,7},{8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5},{6,8},{7}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4,6},{5},{7},{8}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,6},{5},{7,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,3},{2},{4,7},{5},{6},{8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,3},{2},{4,8},{5},{6},{7}}
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,3},{2},{4,7,8},{5},{6}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,3},{2},{4,6,7},{5},{8}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,3},{2},{4,8},{5},{6,7}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,6,8},{5},{7}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,3},{2},{4,6,7,8},{5}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,3},{2},{4,5,6},{7},{8}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,3},{2},{4,5,6},{7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,3},{2},{4,7},{5,6},{8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,3},{2},{4,8},{5,6},{7}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,3},{2},{4,7,8},{5,6}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,3},{2},{4,5,7},{6},{8}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3},{2},{4,8},{5,7},{6}}
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,3},{2},{4,5,8},{6},{7}}
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,3},{2},{4,5,7,8},{6}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,3},{2},{4,5,6,7},{8}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,3},{2},{4,8},{5,6,7}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,3},{2},{4,5,8},{6,7}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,5,6,8},{7}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,3},{2},{4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6},{7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5},{6,7},{8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5},{6,8},{7}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5},{6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5,6},{7},{8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6},{7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5,7},{6},{8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,4},{2},{3},{5,8},{6},{7}}
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,4},{2},{3},{5,7,8},{6}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,4},{2},{3},{5,6,7},{8}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2},{3},{5,8},{6,7}}
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,4},{2},{3},{5,6,8},{7}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,4},{2},{3},{5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2},{3},{4},{6},{7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2},{3},{4},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2},{3},{4},{6,8},{7}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2},{3},{4},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2},{3},{4},{5},{7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2},{3},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3},{4},{5},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2},{3},{4},{5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3},{4},{5},{7}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2},{3},{4},{7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2},{3},{4},{7,8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5,6},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2},{3},{4},{5,6},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4},{5,6}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2},{3},{4},{6},{8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2},{3},{4},{5,7},{6}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2},{3},{4},{6},{7}}
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2},{3},{4},{6}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2},{3},{4},{8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2},{3},{4},{5,6,7}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2},{3},{4},{6,7}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2},{3},{4},{7}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2},{3},{4}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7},{8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,4,5},{2},{3},{6},{7,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,4,5},{2},{3},{6,7},{8}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,4,5},{2},{3},{6,8},{7}}
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,4,5},{2},{3},{6,7,8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3},{4,5},{7},{8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3},{4,5},{7,8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2},{3},{4,5},{6},{8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3},{4,5},{6},{7}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4,5},{6}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3},{4,5},{8}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2},{3},{4,5},{6,7}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3},{4,5},{7}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3},{4,5}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,4,6},{2},{3},{5},{7},{8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,4,6},{2},{3},{5},{7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4,6},{5},{8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2},{3},{4,6},{5},{7}}
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4,6},{5}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,4,7},{2},{3},{5},{6},{8}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2},{3},{4,7},{5},{6}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,4,8},{2},{3},{5},{6},{7}}
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,4,7,8},{2},{3},{5},{6}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,4,6,7},{2},{3},{5},{8}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2},{3},{4,6,7},{5}}
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,4,8},{2},{3},{5},{6,7}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,4,6,8},{2},{3},{5},{7}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,4,6,7,8},{2},{3},{5}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,4,5,6},{2},{3},{7},{8}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,4,5,6},{2},{3},{7,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4,5,6},{8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2},{3},{4,5,6},{7}}
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4,5,6}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,4,7},{2},{3},{5,6},{8}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2},{3},{4,7},{5,6}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,4,8},{2},{3},{5,6},{7}}
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,4,7,8},{2},{3},{5,6}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,4,5,7},{2},{3},{6},{8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2},{3},{4,5,7},{6}}
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,4,8},{2},{3},{5,7},{6}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,4,5,8},{2},{3},{6},{7}}
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,4,5,7,8},{2},{3},{6}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,4,5,6,7},{2},{3},{8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2},{3},{4,5,6,7}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,4,8},{2},{3},{5,6,7}}
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,4,5,8},{2},{3},{6,7}}
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,4,5,6,8},{2},{3},{7}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2},{3}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7},{8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6},{7,8}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,3,4},{2},{5},{6,7},{8}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,3,4},{2},{5},{6,8},{7}}
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,3,4},{2},{5},{6,7,8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,3,4},{2},{5,6},{7},{8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,3,4},{2},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,3,4},{2},{5,7},{6},{8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,3,4},{2},{5,8},{6},{7}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,3,4},{2},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,3,4},{2},{5,6,7},{8}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,3,4},{2},{5,8},{6,7}}
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,3,4},{2},{5,6,8},{7}}
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,3,4},{2},{5,6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7},{8}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2},{3,4},{6},{7,8}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2},{3,4},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2},{3,4},{6,8},{7}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2},{3,4},{6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,4},{5},{7},{8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,4},{5},{7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2},{3,4},{5},{6},{8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,4},{5},{6},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,4},{5},{6}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3,4},{5},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2},{3,4},{5},{6,7}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,4},{5},{7}}
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,4},{5}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2},{3,4},{7},{8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2},{3,4},{7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2},{3,4},{5,6},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2},{3,4},{5,6},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4},{5,6}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2},{3,4},{6},{8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2},{3,4},{5,7},{6}}
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2},{3,4},{6},{7}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2},{3,4},{6}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2},{3,4},{8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,4},{5,6,7}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2},{3,4},{6,7}}
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2},{3,4},{7}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2},{3,4}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7},{8}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,3,5},{2},{4},{6},{7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,3,5},{2},{4},{6,7},{8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,5},{2},{4},{6,8},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,3,5},{2},{4},{6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,5},{4},{7},{8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,5},{4},{7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2},{3,5},{4},{6},{8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,5},{4},{6},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,5},{4},{6}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3,5},{4},{8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2},{3,5},{4},{6,7}}
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,5},{4},{7}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,5},{4}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,3,6},{2},{4},{5},{7},{8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,3,6},{2},{4},{5},{7,8}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3,6},{4},{5},{8}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2},{3,6},{4},{5},{7}}
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,6},{4},{5}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,3,7},{2},{4},{5},{6},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4},{5},{6}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,8},{2},{4},{5},{6},{7}}
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4},{5},{6}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,3,6,7},{2},{4},{5},{8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,6,7},{4},{5}}
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,3,8},{2},{4},{5},{6,7}}
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,3,6,8},{2},{4},{5},{7}}
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,3,6,7,8},{2},{4},{5}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,3,5,6},{2},{4},{7},{8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,3,5,6},{2},{4},{7,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3,5,6},{4},{8}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2},{3,5,6},{4},{7}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,5,6},{4}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4},{5,6},{8}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4},{5,6}}
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,3,8},{2},{4},{5,6},{7}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4},{5,6}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,5,7},{2},{4},{6},{8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2},{3,5,7},{4},{6}}
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,3,8},{2},{4},{5,7},{6}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,3,5,8},{2},{4},{6},{7}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,3,5,7,8},{2},{4},{6}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,3,5,6,7},{2},{4},{8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,5,6,7},{4}}
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4},{5,6,7}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,3,5,8},{2},{4},{6,7}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,3,5,6,8},{2},{4},{7}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,3,5,6,7,8},{2},{4}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,3,4,5},{2},{6},{7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,3,4,5},{2},{6,7},{8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,4,5},{2},{6,8},{7}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,3,4,5},{2},{6,7,8}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,4,5},{7},{8}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,4,5},{7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2},{3,4,5},{6},{8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,4,5},{6},{7}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,5},{6}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3,4,5},{8}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2},{3,4,5},{6,7}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,4,5},{7}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,4,5}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,3,6},{2},{4,5},{7},{8}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,3,6},{2},{4,5},{7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3,6},{4,5},{8}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2},{3,6},{4,5},{7}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,6},{4,5}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,5},{6},{8}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4,5},{6}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,3,8},{2},{4,5},{6},{7}}
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,5},{6}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,3,6,7},{2},{4,5},{8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,6,7},{4,5}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,5},{6,7}}
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,3,6,8},{2},{4,5},{7}}
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,3,6,7,8},{2},{4,5}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,3,4,6},{2},{5},{7},{8}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,3,4,6},{2},{5},{7,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3,4,6},{5},{8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2},{3,4,6},{5},{7}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,6},{5}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,6},{5},{8}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4,6},{5}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,3,8},{2},{4,6},{5},{7}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,6},{5}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,3,4,7},{2},{5},{6},{8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2},{3,4,7},{5},{6}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,7},{5},{6}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,8},{2},{5},{6},{7}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,3,4,7,8},{2},{5},{6}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,3,4,6,7},{2},{5},{8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,6,7},{5}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,6,7},{5}}
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,3,4,8},{2},{5},{6,7}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,3,4,6,8},{2},{5},{7}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,3,4,6,7,8},{2},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,3,4,5,6},{2},{7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,3,4,5,6},{2},{7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2},{3,4,5,6},{8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2},{3,4,5,6},{7}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,5,6}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,5,6},{8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2},{3,7},{4,5,6}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,3,8},{2},{4,5,6},{7}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,5,6}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,3,4,7},{2},{5,6},{8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2},{3,4,7},{5,6}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,7},{5,6}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,6},{7}}
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,3,4,7,8},{2},{5,6}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,4,5,7},{2},{6},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,5,7},{6}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,5,7},{6}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,7},{6}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,3,4,5,8},{2},{6},{7}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,3,4,5,7,8},{2},{6}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7},{2},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,5,6,7}}
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,5,6,7}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,6,7}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,3,4,5,8},{2},{6,7}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,8},{2},{7}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8},{2}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5},{6,7},{8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5},{6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4},{5,6},{7},{8}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4},{5,7},{6},{8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4},{5,8},{6},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4},{5,7,8},{6}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4},{5,6,7},{8}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4},{5,8},{6,7}}
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4},{5,6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7},{8}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2,3},{4,5},{6},{7,8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2,3},{4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5},{6,7,8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2,3},{4,6},{5},{7},{8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2,3},{4,6},{5},{7,8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2,3},{4,7},{5},{6},{8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2,3},{4,8},{5},{6},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2,3},{4,7,8},{5},{6}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2,3},{4,6,7},{5},{8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2,3},{4,8},{5},{6,7}}
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2,3},{4,6,8},{5},{7}}
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2,3},{4,6,7,8},{5}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2,3},{4,7},{5,6},{8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2,3},{4,8},{5,6},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2,3},{4,7,8},{5,6}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2,3},{4,5,7},{6},{8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2,3},{4,8},{5,7},{6}}
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2,3},{4,5,8},{6},{7}}
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2,3},{4,5,7,8},{6}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2,3},{4,8},{5,6,7}}
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2,3},{4,5,8},{6,7}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2,3},{4,5,6,8},{7}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7},{8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6},{7,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,4},{2,3},{5},{6,7},{8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,4},{2,3},{5},{6,8},{7}}
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,4},{2,3},{5},{6,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,4},{2,3},{5,6},{7},{8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,4},{2,3},{5,7},{6},{8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,4},{2,3},{5,8},{6},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,4},{2,3},{5,7,8},{6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,4},{2,3},{5,6,7},{8}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,8},{6,7}}
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,4},{2,3},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,4},{2,3},{5,6,7,8}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7},{8}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2,3},{4},{6},{7,8}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,3},{4},{6,7},{8}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,3},{4},{6,8},{7}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,3},{4},{6,7,8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2,3},{4},{5},{7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4},{5},{7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,3},{4},{5},{6},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,3},{4},{5},{6},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3},{4},{5},{6}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3},{4},{5},{8}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,3},{4},{5},{6,7}}
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3},{4},{5},{7}}
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3},{4},{5}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2,3},{4},{7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,3},{4},{7,8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,3},{4},{5,6},{8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2,3},{4},{5,6},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4},{5,6}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,3},{4},{6},{8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,3},{4},{5,7},{6}}
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2,3},{4},{6},{7}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,3},{4},{6}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,3},{4},{8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,3},{4},{5,6,7}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,3},{4},{6,7}}
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,3},{4},{7}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,3},{4}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7},{8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,4,5},{2,3},{6},{7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,4,5},{2,3},{6,7},{8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,4,5},{2,3},{6,8},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,4,5},{2,3},{6,7,8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,3},{4,5},{7},{8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3},{4,5},{6},{8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,3},{4,5},{6},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,5},{6}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3},{4,5},{8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3},{4,5},{6,7}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3},{4,5},{7}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3},{4,5}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,4,6},{2,3},{5},{7},{8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,4,6},{2,3},{5},{7,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,3},{4,6},{5},{8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2,3},{4,6},{5},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,6},{5}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,4,7},{2,3},{5},{6},{8}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,3},{4,7},{5},{6}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,4,8},{2,3},{5},{6},{7}}
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,4,7,8},{2,3},{5},{6}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,4,6,7},{2,3},{5},{8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,3},{4,6,7},{5}}
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,4,8},{2,3},{5},{6,7}}
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,4,6,8},{2,3},{5},{7}}
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,4,6,7,8},{2,3},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,4,5,6},{2,3},{7},{8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,4,5,6},{2,3},{7,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2,3},{4,5,6},{8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3},{4,5,6},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,5,6}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,4,7},{2,3},{5,6},{8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,3},{4,7},{5,6}}
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,4,8},{2,3},{5,6},{7}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,4,7,8},{2,3},{5,6}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,4,5,7},{2,3},{6},{8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3},{4,5,7},{6}}
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,4,8},{2,3},{5,7},{6}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,4,5,8},{2,3},{6},{7}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,4,5,7,8},{2,3},{6}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,4,5,6,7},{2,3},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3},{4,5,6,7}}
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,4,8},{2,3},{5,6,7}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,4,5,8},{2,3},{6,7}}
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,4,5,6,8},{2,3},{7}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2,3}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6},{7,8}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,4},{3},{5},{6,7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,4},{3},{5},{6,8},{7}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,4},{3},{5},{6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,4},{3},{5,6},{7},{8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,4},{3},{5,6},{7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,4},{3},{5,7},{6},{8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,4},{3},{5,8},{6},{7}}
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,4},{3},{5,7,8},{6}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,4},{3},{5,6,7},{8}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,4},{3},{5,8},{6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,4},{3},{5,6,8},{7}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,4},{3},{5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7},{8}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2,4},{3},{6},{7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,4},{3},{6,7},{8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,4},{3},{6,8},{7}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,4},{3},{6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2,4},{3},{5},{7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,4},{3},{5},{7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,4},{3},{5},{6},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,4},{3},{5},{6},{7}}
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2,4},{3},{5},{6}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2,4},{3},{5},{8}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,4},{3},{5},{6,7}}
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,4},{3},{5},{7}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,4},{3},{5}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2,4},{3},{7},{8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,4},{3},{7,8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,4},{3},{5,6},{8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2,4},{3},{5,6},{7}}
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,4},{3},{5,6}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,4},{3},{6},{8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,4},{3},{5,7},{6}}
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2,4},{3},{6},{7}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,4},{3},{6}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,4},{3},{8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,4},{3},{5,6,7}}
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,4},{3},{6,7}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,4},{3},{7}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7},{8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,5},{3},{4},{6},{7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,5},{3},{4},{6,7},{8}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,5},{3},{4},{6,8},{7}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,5},{3},{4},{6,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,5},{3},{4},{7},{8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3},{4},{7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,5},{3},{4},{6},{8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,5},{3},{4},{6},{7}}
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,5},{3},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,5},{3},{4},{8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,5},{3},{4},{6,7}}
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,5},{3},{4},{7}}
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,5},{3},{4}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3},{4},{5},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3},{4},{5},{7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3},{4},{5},{8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3},{4},{5},{6},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3},{4},{5},{6},{7}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3},{4},{5},{8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3},{4},{5}}
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3},{4},{5},{6,7}}
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3},{4},{5}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,5,6},{3},{4},{7},{8}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,5,6},{3},{4},{7,8}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2,5,6},{3},{4},{8}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2,5,6},{3},{4},{7}}
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,5,6},{3},{4}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3},{4},{5,6},{8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4},{5,6}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3},{4},{5,6},{7}}
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4},{5,6}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,5,7},{3},{4},{6},{8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,5,7},{3},{4},{6}}
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3},{4},{5,7},{6}}
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,5,8},{3},{4},{6},{7}}
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,5,7,8},{3},{4},{6}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,5,6,7},{3},{4},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,5,6,7},{3},{4}}
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4},{5,6,7}}
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,5,8},{3},{4},{6,7}}
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,5,6,8},{3},{4},{7}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,5,6,7,8},{3},{4}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,4,5},{3},{6},{7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,4,5},{3},{6,7},{8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,4,5},{3},{6,8},{7}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,4,5},{3},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2,4,5},{3},{7},{8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,4,5},{3},{7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,4,5},{3},{6},{8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2,4,5},{3},{6},{7}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,4,5},{3},{6}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,4,5},{3},{8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,4,5},{3},{6,7}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,4,5},{3},{7}}
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,4,5},{3}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3},{4,5},{7},{8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3},{4,5},{7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3},{4,5},{8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3},{4,5},{7}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3},{4,5}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3},{4,5},{6},{8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,5},{6}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3},{4,5},{6},{7}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,5},{6}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3},{4,5},{8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3},{4,5}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,5},{6,7}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3},{4,5},{7}}
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3},{4,5}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,4,6},{3},{5},{7},{8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,4,6},{3},{5},{7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2,4,6},{3},{5},{8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,4,6},{3},{5},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,4,6},{3},{5}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3},{4,6},{5},{8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,6},{5}}
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3},{4,6},{5},{7}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,6},{5}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,4,7},{3},{5},{6},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,4,7},{3},{5},{6}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,7},{5},{6}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,4,8},{3},{5},{6},{7}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,4,7,8},{3},{5},{6}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,4,6,7},{3},{5},{8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,4,6,7},{3},{5}}
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,6,7},{5}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5},{6,7}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,4,6,8},{3},{5},{7}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,4,6,7,8},{3},{5}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,4,5,6},{3},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,4,5,6},{3},{7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,4,5,6},{3},{8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,4,5,6},{3},{7}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,4,5,6},{3}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3},{4,5,6},{8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,5,6}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3},{4,5,6},{7}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,5,6}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,4,7},{3},{5,6},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,4,7},{3},{5,6}}
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,7},{5,6}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,6},{7}}
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,4,7,8},{3},{5,6}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,4,5,7},{3},{6},{8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,4,5,7},{3},{6}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,5,7},{6}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,7},{6}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,4,5,8},{3},{6},{7}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,4,5,7,8},{3},{6}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,4,5,6,7},{3},{8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,4,5,6,7},{3}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,5,6,7}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,6,7}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,4,5,8},{3},{6,7}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,4,5,6,8},{3},{7}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8},{3}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6},{7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4},{5},{6,7},{8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3,4},{5},{6,8},{7}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3,4},{5},{6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3,4},{5,7},{6},{8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3,4},{5,8},{6},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3,4},{5,7,8},{6}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3,4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3,4},{5,6,8},{7}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7},{8}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2,3,4},{6},{7,8}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,3,4},{6,7},{8}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,3,4},{6,8},{7}}
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,3,4},{6,7,8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2,3,4},{5},{7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,3,4},{5},{7,8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,3,4},{5},{6},{8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,3,4},{5},{6},{7}}
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3,4},{5},{6}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3,4},{5},{8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,3,4},{5},{6,7}}
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,4},{5},{7}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,4},{5}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2,3,4},{7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,3,4},{7,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,3,4},{5,6},{8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2,3,4},{5,6},{7}}
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,3,4},{6},{8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,3,4},{5,7},{6}}
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2,3,4},{6},{7}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,3,4},{6}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,3,4},{8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,3,4},{6,7}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,3,4},{7}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,3,4}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7},{8}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,5},{3,4},{6},{7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,5},{3,4},{6,7},{8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,5},{3,4},{6,8},{7}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,5},{3,4},{6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,5},{3,4},{7},{8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,5},{3,4},{6},{8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,5},{3,4},{6},{7}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,5},{3,4},{6}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,5},{3,4},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,5},{3,4},{6,7}}
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,5},{3,4},{7}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,5},{3,4}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3,4},{5},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,4},{5},{7,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,4},{5},{8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,4},{5},{7}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,4},{5}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3,4},{5},{6},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5},{6}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3,4},{5},{6},{7}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4},{5},{6}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3,4},{5},{8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,4},{5}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,4},{5},{6,7}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,4},{5},{7}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,4},{5}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,5,6},{3,4},{7},{8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,5,6},{3,4},{7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2,5,6},{3,4},{8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2,5,6},{3,4},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,5,6},{3,4}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4},{5,6},{8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5,6}}
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4},{5,6},{7}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4},{5,6}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,5,7},{3,4},{6},{8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,5,7},{3,4},{6}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,4},{5,7},{6}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,5,8},{3,4},{6},{7}}
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,5,7,8},{3,4},{6}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,5,6,7},{3,4},{8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,5,6,7},{3,4}}
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4},{5,6,7}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,5,8},{3,4},{6,7}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,5,6,8},{3,4},{7}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,5,6,7,8},{3,4}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,5},{4},{6},{7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,5},{4},{6,7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,5},{4},{6,8},{7}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,5},{4},{6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2,3,5},{4},{7},{8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3,5},{4},{7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3,5},{4},{6},{8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2,3,5},{4},{6},{7}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3,5},{4},{6}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3,5},{4},{8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3,5},{4},{6,7}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,5},{4},{7}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,5},{4}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3,5},{4},{7},{8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,5},{4},{7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,5},{4},{8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,5},{4},{7}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,5},{4}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3,5},{4},{6},{8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,5},{4},{6}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3,5},{4},{6},{7}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,5},{4},{6}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3,5},{4},{8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,5},{4}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,5},{4},{6,7}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,5},{4},{7}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,5},{4}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,6},{4},{5},{7},{8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,6},{4},{5},{7,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2,3,6},{4},{5},{8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3,6},{4},{5},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,6},{4},{5}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,6},{4},{5},{8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4},{5}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,6},{4},{5},{7}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,6},{4},{5}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4},{5},{6},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4},{5},{6}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4},{5},{6}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4},{5},{6},{7}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4},{5},{6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,6,7},{4},{5},{8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3,6,7},{4},{5}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3,6,7},{4},{5}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5},{6,7}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,6,8},{4},{5},{7}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4},{5}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,5,6},{4},{7},{8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,5,6},{4},{7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,5,6},{4},{8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,5,6},{4},{7}}
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,5,6},{4}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,5,6},{4},{8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,5,6},{4}}
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,5,6},{4},{7}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,5,6},{4}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4},{5,6},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4},{5,6}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4},{5,6}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,6},{7}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4},{5,6}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,5,7},{4},{6},{8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,5,7},{4},{6}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,5,7},{4},{6}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,7},{6}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,5,8},{4},{6},{7}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,5,7,8},{4},{6}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,5,6,7},{4}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,5,6,7},{4}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,6,7}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,5,8},{4},{6,7}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,5,6,8},{4},{7}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8},{4}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4,5},{6},{7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4,5},{6,8},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2,3,4,5},{7},{8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3,4,5},{7,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3,4,5},{6},{8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2,3,4,5},{6},{7}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3,4,5},{6}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3,4,5},{8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,4,5},{7}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,4,5}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3,4,5},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,4,5},{7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,4,5},{8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,4,5},{7}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,4,5}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3,4,5},{6},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,5},{6}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3,4,5},{6},{7}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,5},{6}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => {{1,2,6,7},{3,4,5},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,4,5}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,4,5},{7}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,4,5}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,6},{4,5},{7},{8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,6},{4,5},{7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2,3,6},{4,5},{8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3,6},{4,5},{7}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,6},{4,5}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,6},{4,5},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4,5}}
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,6},{4,5},{7}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,6},{4,5}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5},{6},{8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,5},{6}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,5},{6}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,5},{6},{7}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,5},{6}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,6,7},{4,5},{8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3,6,7},{4,5}}
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3,6,7},{4,5}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5},{6,7}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,6,8},{4,5},{7}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4,5}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,6},{5},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,6},{5},{7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,4,6},{5},{8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,4,6},{5},{7}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,4,6},{5}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4,6},{5},{8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,6},{5}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4,6},{5},{7}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,6},{5}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,6},{5},{8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,6},{5}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,6},{5}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,6},{5},{7}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,6},{5}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,4,7},{5},{6}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4,7},{5},{6}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,7},{5},{6}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5},{6},{7}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,7,8},{5},{6}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,6,7},{5}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,6,7},{5}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,6,7},{5}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5},{6,7}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,6,8},{5},{7}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,4,5,6},{8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,4,5,6}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4,5,6},{8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,5,6}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,5,6}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,5,6}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,5,6}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,5,6}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,4,7},{5,6}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4,7},{5,6}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,7},{5,6}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6},{7}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,7,8},{5,6}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,7},{6}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,7},{6}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,7},{6}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,7},{6}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6},{7}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6,7}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6,7}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{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] => {{1,2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,9},{8}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}}
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9},{7,8}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8,9},{7}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,8},{5,6,7},{9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6},{7},{9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7,8},{5},{9}}
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,9},{6,7,8}}
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9},{7},{8}}
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8,9},{6}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,8},{4,5,6,7},{9}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,8},{5,7},{6},{9}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,7,8},{5,6},{9}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,8},{5},{7},{9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7,8},{4},{9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1},{2,3,4,9},{5,6,7,8}}
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,9},{6,8},{7}}
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,8,9},{6,7}}
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,9},{6},{8}}
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8,9},{5}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => {{1,2,8},{3,4,5,6,7},{9}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,8},{4,5,7},{6},{9}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,8},{5,6},{7},{9}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,8},{5},{6,7},{9}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,7,8},{5},{6},{9}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,8},{4},{7},{9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,4,5,6,7,8},{3},{9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1},{2,3,9},{4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,9},{5,6,8},{7}}
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,9},{6,7},{8}}
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,9},{6},{7,8}}
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,8,9},{6},{7}}
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,9},{5},{8}}
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8,9},{4}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => {{1,8},{2,3,4,5,6,7},{9}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,8},{4,7},{5,6},{9}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,7,8},{4,5,6},{9}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,8},{5},{6},{7},{9}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,7,8},{4},{6},{9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7,8},{2},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1},{2,9},{3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => {{1},{2,3,4,9},{5,8},{6,7}}
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => {{1},{2,3,4,8,9},{5,6,7}}
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,9},{6},{7},{8}}
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,8,9},{5},{7}}
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,5,6,7,9},{4},{8}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8,9},{3}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,7},{8},{9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => {{1,8},{2,3,4,5,7},{6},{9}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,8},{4,7},{5},{6},{9}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,8},{4},{5,6,7},{9}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,7,8},{4,6},{5},{9}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,6,8},{4,5},{7},{9}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,5,8},{4},{6},{7},{9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,7},{6},{8,9}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1},{2,9},{3,4,5,6,8},{7}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => {{1},{2,3,9},{4,5,8},{6,7}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => {{1},{2,3,4,9},{5,6,7},{8}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => {{1},{2,3,4,9},{5,8},{6},{7}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,9},{5},{6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => {{1},{2,3,4,8,9},{5,7},{6}}
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,7,9},{5,6},{8}}
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,6,9},{5},{7},{8}}
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,7,8,9},{5},{6}}
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,9},{8}}
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,9},{3},{8}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,7},{6},{8},{9}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => {{1,2,8},{3,7},{4,5,6},{9}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,2,8},{3,4,7},{5},{6},{9}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,4,5,8},{3},{6},{7},{9}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,3,4,5,7,8},{2},{6},{9}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,8},{7},{9}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,7},{5,6},{8,9}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,6,7},{5},{8,9}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1},{2,3,9},{4,5,8},{6},{7}}
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => {{1},{2,3,4,8,9},{5},{6,7}}
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,5,6,9},{4},{7},{8}}
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2},{3,4,5,6,9},{7,8}}
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,4,5,6,9},{3},{7,8}}
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,8,9},{7}}
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,9},{8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,7},{5,6},{8},{9}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,6,7},{5},{8},{9}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,8},{2,3,4,7},{5},{6},{9}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => {{1,2,8},{3,4,5,6},{7},{9}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => {{1,2,8},{3},{4,5,6,7},{9}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,8},{4,5},{6},{7},{9}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,6,7,8},{3,4,5},{9}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,7,8},{4},{5},{6},{9}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,8},{6,7},{9}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,7,8},{6},{9}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,7},{4,5,6},{8,9}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,7},{5},{6},{8,9}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,5,6,7},{4},{8,9}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => {{1},{2,3,9},{4,5,6,7},{8}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,3,9},{4,6,8},{5},{7}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => {{1},{2,3,9},{4},{5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,9},{5,6},{7},{8}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => {{1},{2,3,4,9},{5},{6,7},{8}}
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => {{1},{2,3,7,8,9},{4,5,6}}
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,8,9},{5},{6},{7}}
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2},{3,4,5,6,9},{7},{8}}
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,4,5,6,9},{3},{7},{8}}
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,9},{7,8}}
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,6,7,8,9},{4},{5}}
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,7,8,9},{6}}
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,8,9},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,8,9},{2},{3},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6},{7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2},{3},{4},{5},{6},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2},{3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6,7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,8,9},{2},{3},{4},{5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6,8},{7}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,6,9},{2},{3},{4},{5},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,6,8,9},{2},{3},{4},{5},{7}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,6,9},{2},{3},{4},{5},{7,8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,6,7,9},{2},{3},{4},{5},{8}}
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2},{3},{4},{5}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,9},{2},{3},{4},{5,6},{7},{8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,8,9},{2},{3},{4},{5,6},{7}}
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2},{3},{4},{5,6}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,9},{2},{3},{4},{5,7},{6},{8}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,5,9},{2},{3},{4},{6},{7},{8}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,5,8,9},{2},{3},{4},{6},{7}}
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,5,7,8,9},{2},{3},{4},{6}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,9},{2},{3},{4},{5,6,7},{8}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,5,9},{2},{3},{4},{6,7},{8}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,9},{2},{3},{4},{5,6,8},{7}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,5,9},{2},{3},{4},{6,8},{7}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,5,6,9},{2},{3},{4},{7},{8}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,9},{2},{3},{4},{5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,5,9},{2},{3},{4},{6,7,8}}
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,5,6,7,9},{2},{3},{4},{8}}
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,5,6,7,8,9},{2},{3},{4}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2},{3},{4,5},{6},{7},{8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,8,9},{2},{3},{4,5},{6},{7}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,9},{2},{3},{4,5},{6},{7,8}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2},{3},{4,5},{6},{8}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,9},{2},{3},{4,5},{6,7},{8}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,9},{2},{3},{4,5},{6,8},{7}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,6,9},{2},{3},{4,5},{7},{8}}
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2},{3},{4,5}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,9},{2},{3},{4,6},{5},{7},{8}}
[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2},{3},{4,6},{5}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,9},{2},{3},{4,7},{5},{6},{8}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,4,9},{2},{3},{5},{6},{7},{8}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,4,8,9},{2},{3},{5},{6},{7}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,9},{2},{3},{4,6,7},{5},{8}}
[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,4,6,9},{2},{3},{5},{7},{8}}
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,4,6,7,8,9},{2},{3},{5}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2},{3},{4,5,6},{7},{8}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,9},{2},{3},{4,7},{5,6},{8}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,4,9},{2},{3},{5,6},{7},{8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,9},{2},{3},{4,5,7},{6},{8}}
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,4,9},{2},{3},{5,7},{6},{8}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,4,9},{2},{3},{5,8},{6},{7}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,4,5,9},{2},{3},{6},{7},{8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2},{3},{4,5,6,7}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,4,9},{2},{3},{5,6,7},{8}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,4,8,9},{2},{3},{5,6,7}}
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,4,5,9},{2},{3},{6,7},{8}}
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,4,5,6,9},{2},{3},{7},{8}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,9},{2},{3},{4,5,6,7,8}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,4,5,9},{2},{3},{6,7,8}}
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,4,5,6,9},{2},{3},{7,8}}
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,4,5,6,7,9},{2},{3},{8}}
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9},{2},{3}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2},{3,4},{5},{6},{7},{8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,8,9},{2},{3,4},{5},{6},{7}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2},{3,4},{5},{6},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,9},{2},{3,4},{5},{6,7},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,9},{2},{3,4},{5},{6,8},{7}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,6,9},{2},{3,4},{5},{7},{8}}
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,9},{2},{3,4},{5},{6,7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,9},{2},{3,4},{5,6},{7},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,8,9},{2},{3,4},{5,6},{7}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,9},{2},{3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,7,9},{2},{3,4},{5,6},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2},{3,4},{5,6}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,5,9},{2},{3,4},{6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,5,7,9},{2},{3,4},{6},{8}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,9},{2},{3,4},{5,8},{6,7}}
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,5,9},{2},{3,4},{6,8},{7}}
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,5,6,8,9},{2},{3,4},{7}}
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,5,6,7,8,9},{2},{3,4}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2},{3,5},{4},{6},{7},{8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,8,9},{2},{3,5},{4},{6},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2},{3,5},{4},{6},{8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,9},{2},{3,5},{4},{6,7},{8}}
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,9},{2},{3,5},{4},{6,8},{7}}
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2},{3,5},{4}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,9},{2},{3,6},{4},{5},{7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,9},{2},{3,8},{4},{5},{6},{7}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,9},{2},{4},{5},{6},{7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,3,8,9},{2},{4},{5},{6},{7}}
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,3,7,9},{2},{4},{5},{6},{8}}
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,3,7,8,9},{2},{4},{5},{6}}
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,9},{2},{3,6,7,8},{4},{5}}
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,3,6,7,8,9},{2},{4},{5}}
[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,3,8,9},{2},{4},{5,6},{7}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,5,9},{2},{4},{6},{7},{8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,3,5,9},{2},{4},{6},{7,8}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,3,5,7,9},{2},{4},{6},{8}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,3,9},{2},{4},{5,8},{6,7}}
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,3,5,6,7,8,9},{2},{4}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2},{3,4,5},{6},{7},{8}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2},{3,4,5},{6},{8}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => {{1,6,9},{2},{3,4,5},{7},{8}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => {{1,6,7,9},{2},{3,4,5},{8}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,7,9},{2},{3,6},{4,5},{8}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,9},{2},{4,5},{6},{7},{8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2},{3,4,6},{5},{7},{8}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2},{3,4,6},{5}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => {{1,9},{2},{3,8},{4,6},{5},{7}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => {{1,3,9},{2},{4,6},{5},{7},{8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => {{1,9},{2},{3,4,7},{5},{6},{8}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => {{1,3,9},{2},{4,7},{5},{6},{8}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => {{1,9},{2},{3,4,8},{5},{6},{7}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => {{1,3,9},{2},{4,8},{5},{6},{7}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,9},{2},{5},{6},{7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2},{3,4,5,6},{7},{8}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2},{3,4,5,6}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => {{1,3,9},{2},{4,5,6},{7},{8}}
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => {{1,3,7,8,9},{2},{4,5,6}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,9},{2},{3,8},{4,7},{5,6}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => {{1,3,9},{2},{4,7},{5,6},{8}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,9},{2},{5,6},{7},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2},{3,4,5,7},{6}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => {{1,3,4,9},{2},{5,7},{6},{8}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,3,9},{2},{4,5,8},{6},{7}}
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,3,4,5,9},{2},{6},{7},{8}}
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,3,4,5,7,9},{2},{6},{8}}
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,3,4,5,7,8,9},{2},{6}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => {{1,9},{2},{3,4,5,6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2},{3,4,5,6,7}}
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,3,8,9},{2},{4,5,6,7}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => {{1,3,9},{2},{4,8},{5,6,7}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => {{1,3,4,9},{2},{5,6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => {{1,3,4,8,9},{2},{5,6,7}}
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => {{1,3,4,5,9},{2},{6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,3,4,5,8,9},{2},{6,7}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,9},{2},{3,4,5,6,8},{7}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1,3,4,9},{2},{5,6,8},{7}}
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => {{1,3,4,5,9},{2},{6,8},{7}}
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,9},{2},{7},{8}}
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,8,9},{2},{7}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,9},{2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,3,9},{2},{4,5,6,7,8}}
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => {{1,3,4,5,9},{2},{6,7,8}}
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,9},{2},{7,8}}
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,9},{2},{8}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9},{2}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,3},{4},{5},{6},{7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,8,9},{2,3},{4},{5},{6},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,9},{2,3},{4},{5},{6},{7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2,3},{4},{5},{6},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3},{4},{5},{6}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,9},{2,3},{4},{5},{6,7},{8}}
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,6,9},{2,3},{4},{5},{7},{8}}
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,5,9},{2,3},{4},{6},{7},{8}}
[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,5,6,9},{2,3},{4},{7},{8}}
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,5,6,8,9},{2,3},{4},{7}}
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,5,6,7,9},{2,3},{4},{8}}
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,5,6,7,8,9},{2,3},{4}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,3},{4,5},{6},{7},{8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,9},{2,3},{4,5},{6,7},{8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,8,9},{2,3},{4,5},{6,7}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,9},{2,3},{4,5},{6,8},{7}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,6,8,9},{2,3},{4,5},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,9},{2,3},{4,6},{5},{7},{8}}
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,7,9},{2,3},{4,6},{5},{8}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,4,9},{2,3},{5},{6},{7},{8}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,4,8,9},{2,3},{5},{6},{7}}
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,4,7,8,9},{2,3},{5},{6}}
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,4,6,8,9},{2,3},{5},{7}}
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,4,6,7,8,9},{2,3},{5}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2,3},{4,5,6},{7},{8}}
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,4,9},{2,3},{5,6},{7},{8}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,4,5,9},{2,3},{6},{7},{8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,9},{2,3},{4,5,6,7},{8}}
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,4,5,6,9},{2,3},{7},{8}}
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,4,5,6,8,9},{2,3},{7}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,9},{2,3},{4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,4,9},{2,3},{5,6,7,8}}
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,4,5,6,7,9},{2,3},{8}}
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9},{2,3}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,4},{3},{5},{6},{7},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,8,9},{2,4},{3},{5},{6},{7}}
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2,4},{3},{5},{6},{8}}
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,6,9},{2,4},{3},{5},{7},{8}}
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2,4},{3},{5}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,9},{2,4},{3},{5,6},{7},{8}}
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,9},{2,4},{3},{5,8},{6,7}}
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,5,6,7,9},{2,4},{3},{8}}
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,5,6,7,8,9},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,5},{3},{4},{6},{7},{8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,8,9},{2,5},{3},{4},{6},{7}}
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2,5},{3},{4},{6},{8}}
[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,5},{3},{4},{6}}
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,6,9},{2,5},{3},{4},{7},{8}}
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2,5},{3},{4}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,9},{2,6},{3},{4},{5},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,8,9},{2,6},{3},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,6},{3},{4},{5}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,9},{2,7},{3},{4},{5},{6},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,8,9},{2,7},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,9},{2,8},{3},{4},{5},{6},{7}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3},{4},{5},{6},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,8,9},{3},{4},{5},{6},{7}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,9},{2,7,8},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,9},{3},{4},{5},{6},{7,8}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,7,9},{3},{4},{5},{6},{8}}
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,7,8,9},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,9},{2,6,7},{3},{4},{5},{8}}
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,9},{3},{4},{5},{6,7},{8}}
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,9},{2,6,8},{3},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,6,9},{3},{4},{5},{7},{8}}
[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,6,8,9},{3},{4},{5},{7}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,9},{2,6,7,8},{3},{4},{5}}
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,6,7,9},{3},{4},{5},{8}}
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,6,7,8,9},{3},{4},{5}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2,5,6},{3},{4},{7},{8}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3},{4},{5,6},{7},{8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,9},{2,5,7},{3},{4},{6},{8}}
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,9},{3},{4},{5,8},{6},{7}}
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,5,9},{3},{4},{6},{7},{8}}
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,5,7,9},{3},{4},{6},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,9},{2,5,6,7},{3},{4},{8}}
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,9},{3},{4},{5,6,7},{8}}
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,9},{3},{4},{5,6,8},{7}}
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,5,6,9},{3},{4},{7},{8}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,9},{2,5,6,7,8},{3},{4}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,9},{3},{4},{5,6,7,8}}
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,5,6,7,8,9},{3},{4}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,4,5},{3},{6},{7},{8}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3},{4,5},{6},{7},{8}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,9},{3},{4,5},{6},{7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,9},{2,8},{3},{4,5},{6,7}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,8,9},{3},{4,5},{6,7}}
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,6,8,9},{3},{4,5},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2,4,6},{3},{5},{7},{8}}
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3},{4,6},{5},{7},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => {{1,9},{2,4,7},{3},{5},{6},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,9},{3},{4,7},{5},{6},{8}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,8,9},{3},{4,7},{5},{6}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => {{1,9},{2,4,8},{3},{5},{6},{7}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,9},{3},{4,8},{5},{6},{7}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,4,9},{3},{5},{6},{7},{8}}
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,4,8,9},{3},{5},{6},{7}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => {{1,9},{2,4,8},{3},{5},{6,7}}
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,4,6,9},{3},{5},{7},{8}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,9},{2,4,6,7,8},{3},{5}}
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,4,6,7,8,9},{3},{5}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2,4,5,6},{3},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => {{1,8,9},{2,4,5,6},{3},{7}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3},{4,5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => {{1,2,7,9},{3},{4,5,6},{8}}
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => {{1,2,7,8,9},{3},{4,5,6}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => {{1,8,9},{2,4,7},{3},{5,6}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => {{1,2,9},{3},{4,5,7},{6},{8}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1,2,9},{3},{4,8},{5,7},{6}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2,9},{3},{4,5,8},{6},{7}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,4,9},{3},{5,8},{6},{7}}
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,4,5,9},{3},{6},{7},{8}}
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,4,5,8,9},{3},{6},{7}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => {{1,9},{2,4,5,7,8},{3},{6}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => {{1,2,4,9},{3},{5,7,8},{6}}
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,4,5,7,8,9},{3},{6}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2,4,5,6,7},{3}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => {{1,2,9},{3},{4,5,6,7},{8}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,2,8,9},{3},{4,5,6,7}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => {{1,2,4,9},{3},{5,6,7},{8}}
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => {{1,2,4,8,9},{3},{5,6,7}}
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => {{1,2,4,5,9},{3},{6,7},{8}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => {{1,2,9},{3},{4,5,6,8},{7}}
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,4,5,6,9},{3},{7},{8}}
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,8,9},{3},{7}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,9},{2,4,5,6,7,8},{3}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,9},{3},{4,5,6,7,8}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,2,4,9},{3},{5,6,7,8}}
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => {{1,2,4,5,9},{3},{6,7,8}}
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,4,5,6,9},{3},{7,8}}
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,9},{3},{8}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8,9},{3}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,3,4},{5},{6},{7},{8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,8,9},{2,3,4},{5},{6},{7}}
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2,3,4},{5},{6},{8}}
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3,4},{5},{6}}
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,6,9},{2,3,4},{5},{7},{8}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,6,9},{2,3,4},{5},{7,8}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,6,7,9},{2,3,4},{5},{8}}
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2,3,4},{5}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,9},{2,3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,9},{2,3,4},{5,6},{7,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3,4},{5,6}}
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,5,7,8,9},{2,3,4},{6}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,8,9},{2,3,4},{5,6,7}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,5,6,9},{2,3,4},{7},{8}}
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,5,6,8,9},{2,3,4},{7}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,9},{2,3,4},{5,6,7,8}}
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,5,6,7,9},{2,3,4},{8}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,5,6,7,8,9},{2,3,4}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,5},{3,4},{6},{7},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,8,9},{2,5},{3,4},{6,7}}
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2,5},{3,4}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,9},{2,6},{3,4},{5},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,9},{2,7},{3,4},{5},{6},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,8,9},{2,7},{3,4},{5},{6}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,4},{5},{6},{7}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3,4},{5},{6},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,8,9},{3,4},{5},{6},{7}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,7,9},{3,4},{5},{6},{8}}
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,7,8,9},{3,4},{5},{6}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,8,9},{3,4},{5},{6,7}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,9},{3,4},{5},{6,8},{7}}
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,6,8,9},{3,4},{5},{7}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,9},{3,4},{5},{6,7,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3,4},{5,6},{7},{8}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,5,9},{3,4},{6},{7},{8}}
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,5,6,9},{3,4},{7},{8}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,9},{3,4},{5,6,7,8}}
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,5,6,9},{3,4},{7,8}}
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,5,6,7,9},{3,4},{8}}
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,5,6,7,8,9},{3,4}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,3,5},{4},{6},{7},{8}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0] => {{1,6,7,9},{2,3,5},{4},{8}}
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2,3,5},{4}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,9},{2,6},{3,5},{4},{7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,5},{4},{6},{7}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3,5},{4},{6},{7},{8}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,7,9},{3,5},{4},{6},{8}}
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,6,7,8,9},{3,5},{4}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2,3,6},{4},{5},{7},{8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0] => {{1,8,9},{2,3,6},{4},{5},{7}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,7,9},{2,3,6},{4},{5},{8}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3,6},{4},{5}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0] => {{1,9},{2,7},{3,6},{4},{5},{8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => {{1,8,9},{2,7},{3,6},{4},{5}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,6},{4},{5},{7}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3,6},{4},{5},{7},{8}}
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,7,8,9},{3,6},{4},{5}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => {{1,9},{2,3,7},{4},{5},{6},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,8,9},{2,3,7},{4},{5},{6}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,7},{4},{5},{6}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,9},{3,7},{4},{5},{6},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,8,9},{3,7},{4},{5},{6}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => {{1,9},{2,3,8},{4},{5},{6},{7}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,9},{3,8},{4},{5},{6},{7}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4},{5},{6},{7},{8}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4},{5},{6},{7}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => {{1,9},{2,3,7,8},{4},{5},{6}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,9},{4},{5},{6},{7,8}}
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,7,9},{4},{5},{6},{8}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,7,8,9},{4},{5},{6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => {{1,9},{2,3,6,7},{4},{5},{8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2,3,6,7},{4},{5}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4},{5},{6,7},{8}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,9},{2,3,6,8},{4},{5},{7}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,9},{4},{5},{6,8},{7}}
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,6,9},{4},{5},{7},{8}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,9},{2,3,6,7,8},{4},{5}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,6,7,9},{4},{5},{8}}
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,6,7,8,9},{4},{5}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2,3,5,6},{4},{7},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,7},{4},{5,6}}
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4},{5,6},{7}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4},{5,7},{6},{8}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2,9},{3,5,8},{4},{6},{7}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,5,9},{4},{6},{7},{8}}
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,5,8,9},{4},{6},{7}}
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,5,7,9},{4},{6},{8}}
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,5,7,8,9},{4},{6}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => {{1,9},{2,3,5,6,7},{4},{8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2,3,5,6,7},{4}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => {{1,2,9},{3,5,6,7},{4},{8}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => {{1,9},{2,3,8},{4},{5,6,7}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4},{5,6,7},{8}}
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4},{5,6,7}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => {{1,2,9},{3,5,8},{4},{6,7}}
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,5,9},{4},{6,7},{8}}
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,5,8,9},{4},{6,7}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,9},{2,3,5,6,8},{4},{7}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1,2,3,9},{4},{5,6,8},{7}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,5,6,9},{4},{7},{8}}
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,5,6,8,9},{4},{7}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,9},{2,3,5,6,7,8},{4}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,9},{3,5,6,7,8},{4}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,2,3,9},{4},{5,6,7,8}}
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,5,6,9},{4},{7,8}}
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,9},{4},{8}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8,9},{4}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2,3,4,5},{6},{8}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3,4,5},{6}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0] => {{1,9},{2,3,4,5},{6,7},{8}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => {{1,6,7,9},{2,3,4,5},{8}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2,3,4,5}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => {{1,9},{2,6},{3,4,5},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0] => {{1,9},{2,7},{3,4,5},{6},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,4,5},{6},{7}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3,4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,8,9},{3,4,5},{6},{7}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,9},{3,4,5},{6},{7,8}}
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,7,8,9},{3,4,5},{6}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,8,9},{3,4,5},{6,7}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,9},{3,4,5},{6,7,8}}
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,6,7,9},{3,4,5},{8}}
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,6,7,8,9},{3,4,5}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2,3,6},{4,5},{7},{8}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3,6},{4,5}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => {{1,9},{2,7},{3,6},{4,5},{8}}
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3,6},{4,5},{7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,9},{3,8},{4,5},{6},{7}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4,5},{6},{7}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,9},{3,7,8},{4,5},{6}}
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4,5},{6,7}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,6,9},{4,5},{7},{8}}
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,6,8,9},{4,5},{7}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,9},{4,5},{6,7,8}}
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,6,7,9},{4,5},{8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2,3,4,6},{5},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0] => {{1,8,9},{2,3,4,6},{5},{7}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3,4,6},{5}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3,4,6},{5},{7},{8}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,7},{4,6},{5}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => {{1,2,9},{3,7},{4,6},{5},{8}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4,6},{5},{7},{8}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => {{1,2,9},{3,7,8},{4,6},{5}}
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,7,9},{4,6},{5},{8}}
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,7,8,9},{4,6},{5}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,4,7},{5},{6}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => {{1,2,9},{3,4,7},{5},{6},{8}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4,7},{5},{6},{8}}
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4,7},{5},{6}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2,9},{3,4,8},{5},{6},{7}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,9},{4,8},{5},{6},{7}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5},{6},{7},{8}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,8,9},{5},{6},{7}}
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5},{6},{7,8}}
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,7,9},{5},{6},{8}}
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,7,8,9},{5},{6}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => {{1,9},{2,3,4,6,7},{5},{8}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => {{1,2,9},{3,4,6,7},{5},{8}}
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5},{6,7},{8}}
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,8,9},{5},{6,7}}
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5},{6,8},{7}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,6,9},{5},{7},{8}}
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,6,8,9},{5},{7}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,6,7,8},{5}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,9},{3,4,6,7,8},{5}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,2,3,9},{4,6,7,8},{5}}
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5},{6,7,8}}
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,6,9},{5},{7,8}}
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,9},{5},{8}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8,9},{5}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => {{1,9},{2,3,4,5,6},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => {{1,8,9},{2,3,4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => {{1,9},{2,3,4,5,6},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => {{1,7,9},{2,3,4,5,6},{8}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3,4,5,6}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => {{1,9},{2,7},{3,4,5,6},{8}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => {{1,2,7,9},{3,4,5,6},{8}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => {{1,2,7,8,9},{3,4,5,6}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0] => {{1,9},{2,3,7},{4,5,6},{8}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,7},{4,5,6}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4,5,6},{7},{8}}
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4,5,6},{7}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => {{1,2,9},{3,7,8},{4,5,6}}
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,7,9},{4,5,6},{8}}
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,7,8,9},{4,5,6}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2,3,4,7},{5,6}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => {{1,2,9},{3,8},{4,7},{5,6}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4,7},{5,6},{8}}
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4,7},{5,6}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,9},{4,8},{5,6},{7}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,6},{7},{8}}
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,8,9},{5,6},{7}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,7,8},{5,6}}
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,6},{7,8}}
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,7,9},{5,6},{8}}
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,7,8,9},{5,6}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => {{1,9},{2,3,4,5,7},{6},{8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2,3,4,5,7},{6}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => {{1,2,9},{3,4,5,7},{6},{8}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4,5,7},{6},{8}}
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4,5,7},{6}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => {{1,2,9},{3,4,8},{5,7},{6}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => {{1,2,3,9},{4,8},{5,7},{6}}
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,7},{6},{8}}
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,8,9},{5,7},{6}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,5,8},{6},{7}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => {{1,2,9},{3,4,5,8},{6},{7}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => {{1,2,3,9},{4,5,8},{6},{7}}
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,8},{6},{7}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,9},{6},{7},{8}}
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,8,9},{6},{7}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,5,7,8},{6}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,9},{3,4,5,7,8},{6}}
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,7,8},{6}}
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,9},{6},{7,8}}
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,9},{6},{8}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8,9},{6}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => {{1,9},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2,3,4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => {{1,9},{2,8},{3,4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => {{1,2,9},{3,4,5,6,7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => {{1,2,8,9},{3,4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => {{1,9},{2,3,8},{4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4,5,6,7}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => {{1,9},{2,3,4,8},{5,6,7}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0] => {{1,2,9},{3,4,8},{5,6,7}}
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,6,7},{8}}
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,8,9},{5,6,7}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,5,8},{6,7}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => {{1,2,9},{3,4,5,8},{6,7}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => {{1,2,3,9},{4,5,8},{6,7}}
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,8},{6,7}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,9},{6,7},{8}}
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,8,9},{6,7}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,5,6,8},{7}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => {{1,2,9},{3,4,5,6,8},{7}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => {{1,2,3,9},{4,5,6,8},{7}}
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,6,8},{7}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,9},{6,8},{7}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,9},{7},{8}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8,9},{7}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => {{1,2,9},{3,4,5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => {{1,2,3,9},{4,5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,9},{6,7,8}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,9},{7,8}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,9},{8}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,9},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,9},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,9},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,9},{5},{6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,9},{4},{5},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,9},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5},{6,9},{7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,9},{6,7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,9},{5,6},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,9},{4,5},{6},{7},{8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,9},{3,4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,9},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3},{4},{5,9},{6,8},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4,9},{5,7},{6},{8}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3},{4},{5,9},{6,7,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3,9},{4,6},{5},{7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2},{3},{4,9},{5,6,7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2,9},{3,5},{4},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4},{5,6,9},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2},{3},{4,9},{5,8},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,8,9},{7}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,9},{4,7},{5},{6},{8}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,9},{8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1},{2,9},{3,6},{4},{5},{7},{8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1},{2},{3,9},{4,6,7},{5},{8}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2},{3},{4,9},{5,6,8},{7}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1},{2},{3,9},{4,5,7},{6},{8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1},{2,9},{3,4,6},{5},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4,5,9},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2},{3},{4,5,8,9},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2},{3},{4,5,7,9},{6},{8}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => {{1},{2,9},{3,6,7},{4},{5},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1},{2},{3,9},{4,5,6,7},{8}}
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2},{3,9},{4,6,8},{5},{7}}
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1},{2},{3,9},{4,5,8},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,9},{5},{6},{7},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1},{2,9},{3,8},{4},{5},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,8,9},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2},{3},{4,5,6,9},{7,8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => {{1},{2,9},{3,5,6,7},{4},{8}}
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,9},{3,6,8},{4},{5},{7}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2},{3,9},{4,5,8},{6,7}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => {{1},{2,9},{3,4,8},{5},{6},{7}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,9},{4},{5},{6},{7},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,8,9},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,9},{8}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2},{3,9},{4,5,6,8},{7}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8,9}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2,9},{3,5,8},{4},{6,7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => {{1},{2,9},{3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,5,9},{4},{6},{7},{8}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,9},{5},{6},{7},{8}}
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3,4,6,7,9},{5},{8}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2},{3,4,5,9},{6,7,8}}
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,9},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5,6},{7},{8},{9}}
[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},{8,9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7,8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6},{7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6,7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7,8},{9}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6},{7,8},{9}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8},{9}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7},{8,9}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5},{6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5,6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5,6},{7,8},{9}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6},{7,8,9}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3},{4,5,6,7,8},{9}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6},{7},{8,9}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5},{6},{7,8},{9}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5},{6},{7,8,9}}
[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},{8,9}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8},{9}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6},{7,8,9}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6,7},{8,9}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4},{5,6,7,8},{9}}
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4},{5,6,7,8,9}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8},{9}}
[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},{8,9}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5,6},{7},{8},{9}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1},{2},{3,4,5,6},{7,8,9}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2},{3,4,5,6,7},{8},{9}}
[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},{8,9}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7,8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7},{8,9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6},{7,8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6},{7,8,9}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5},{6,7},{8},{9}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5,6},{7},{8},{9}}
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4},{5,6,7,8,9}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[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},{8,9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6,7},{8},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5},{6,7,8},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5},{6,7,8,9}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5,6},{7},{8},{9}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6},{7,8,9}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3},{4,5,6,7,8},{9}}
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8,9}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7,8},{9}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5,6,7},{8},{9}}
[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},{8,9}}
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4},{5,6,7,8,9}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7},{8},{9}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4,5},{6},{7,8,9}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3,4,5},{6,7},{8},{9}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5},{6,7,8,9}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8},{9}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4,5,6},{7,8,9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6,7},{8},{9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6},{7,8},{9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5},{6},{7,8,9}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4},{5},{6,7},{8},{9}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7},{8,9}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4},{5},{6,7,8},{9}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5},{6,7,8,9}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5,6},{7},{8},{9}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6},{7,8,9}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4},{5,6,7,8},{9}}
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8,9}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8},{9}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7},{8,9}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6},{7,8,9}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7,8},{9}}
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8,9}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6},{7},{8,9}}
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5},{6,7,8,9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5,6},{7},{8},{9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6},{7,8,9}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4},{5,6,7},{8},{9}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4},{5,6,7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4},{5,6,7,8,9}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7},{8},{9}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6,7,8},{9}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5},{6,7,8,9}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2},{3,4,5,6},{7},{8},{9}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5,6},{7,8,9}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2},{3,4,5,6,7},{8},{9}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6,7},{8,9}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8},{9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7},{8,9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5},{6},{7,8},{9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5},{6},{7,8,9}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7},{8,9}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7,8},{9}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4},{5,6,7,8},{9}}
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4},{5,6,7,8,9}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7},{8},{9}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8},{9}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6},{7,8,9}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6,7},{8,9}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7,8},{9}}
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6},{7},{8,9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2,3,4},{5},{6},{7,8,9}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5},{6,7,8},{9}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5},{6,7,8,9}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8},{9}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7,8},{9}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6},{7,8,9}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3,4},{5,6,7},{8},{9}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6,7},{8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5,6,7,8},{9}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3,4,5},{6},{7},{8,9}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6},{7,8},{9}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6},{7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4,5},{6,7},{8},{9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5},{6,7,8},{9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4,5,6},{7},{8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6},{7,8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,8},{2},{3},{4},{5},{6},{7},{9}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,5,6},{2},{3},{4},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,6,7},{2},{3},{4},{5},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,7,8},{2},{3},{4},{5},{6},{9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5},{6},{7,9},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5},{6},{7,9},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5},{6},{7,9},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6},{7},{8,9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,8},{3},{4},{5},{6},{7},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,7},{3},{4},{5},{6},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,6},{3},{4},{5},{7},{8},{9}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7},{8},{9}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => {{1,7},{2,3,4,5,6},{8},{9}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2,3,4,5},{7},{8},{9}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7},{8},{9}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,7},{3},{4},{5},{6},{8,9}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2},{3,4,9},{5},{6},{7},{8}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,3,8},{2},{4},{5},{6},{7},{9}}
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,3},{2},{4,5,6,7,8,9}}
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,4},{3},{5,6,7,8,9}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,5},{4},{6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,6},{5},{7,8,9}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7},{8},{9}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,5},{2},{3},{4},{6},{7},{8,9}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7},{8},{9}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,9},{4,5},{6},{7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,8},{2,3},{4},{5},{6},{7},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,8,9},{3},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,7},{2},{3},{4},{5},{6},{8,9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,9},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,6},{2},{3},{4},{5},{7,8,9}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,5},{2},{3},{4},{6,7,8,9}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,4},{2},{3},{5,6,7,9},{8}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1,3},{2},{4,5,6,9},{7},{8}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,5,9},{6},{7},{8}}
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,5,6,7,8,9},{4}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,4,5,6,7},{3},{8,9}}
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,7,8,9},{6}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,5,6},{4},{7,8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2,3,4},{5,6,7,9},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4,5,6},{7,9},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3,4,5},{6,7,9},{8}}
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,9},{8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,4},{5},{6,9},{7},{8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => {{1,7},{2,3,4,5,6},{8,9}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2},{3,4,9},{5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,6},{3,4,5},{7,8,9}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3},{4,5,6,9},{7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5,8},{6},{7},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,7},{6},{8},{9}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3},{4},{5,9},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,7},{6},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7,8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6,7},{8},{9}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5,6},{7},{8},{9}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7},{8},{9}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7,8},{9}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,5,6},{2},{3,4},{7,8},{9}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,7,8},{2},{3,4},{5,6},{9}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,7},{2},{3,4},{5,6},{8,9}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7},{8,9}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7},{8,9}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => {{1,3,6},{2},{4,5},{7,8},{9}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,5,8},{2},{3,4},{6,7},{9}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,7},{2},{3,4},{5,6},{8},{9}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,5},{2},{3,4},{6,9},{7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,7},{5,6},{8,9}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7},{8,9}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,4},{2},{3},{5},{6,9},{7},{8}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,8},{4},{5},{6},{7},{9}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,7,8},{3},{4},{5},{6},{9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5},{6},{7,8},{9}}
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,5,6,7,8,9},{4}}
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,6,7,8,9},{5}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,7,8,9},{6}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,8,9},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1,2,3},{4,9},{5},{6},{7},{8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2,3,4},{5,9},{6},{7},{8}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3,5},{4},{6,9},{7},{8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,6},{4},{5},{7,9},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,7},{4},{5},{6},{8,9}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,4,7},{2},{3},{5},{6},{8},{9}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6,7},{8},{9}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3},{4,5,6,9},{7},{8}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,3},{4,5,9},{6,8},{7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2,3,4},{5,8},{6},{7},{9}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,3,4},{5,9},{6},{7},{8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,6},{5},{7},{8},{9}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7},{8},{9}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4,6},{5},{7,9},{8}}
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,5,6,7,8,9},{3,4}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6},{7},{8,9}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3,5},{4},{6},{7},{8,9}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4,6},{5},{7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,8},{7},{9}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,9},{3},{4},{5},{6,7},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,7},{5},{6},{8},{9}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3,9},{4},{5,6},{7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7},{8},{9}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1,3},{2},{4,9},{5},{6},{7},{8}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,8,9},{4,5},{6},{7}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,8,9},{5,6},{7}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2},{3},{4,5,8,9},{6,7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,6},{4},{5},{7},{8},{9}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,6},{5},{7},{8},{9}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,5},{3},{4},{6,7,9},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,8},{7},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4,8,9},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,6},{2},{3},{4},{5},{7},{8,9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,7},{3},{4},{5},{6},{8,9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,8,9},{4},{5},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7},{8},{9}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1},{2},{3,8,9},{4,5,6,7}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,4,5,6,7},{3},{8,9}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,2},{3,8},{4,5,6,7},{9}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,4,5,6,7},{2,3},{8},{9}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,2},{3,5,6},{4},{7},{8},{9}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,4},{5,7,8},{6},{9}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7},{8,9}}
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1,3},{2},{4,5,6,7,9},{8}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,8},{7},{9}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,7,8},{3,4},{5},{6},{9}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,2},{3,9},{4,5,6,7,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1,3},{2},{4,7,8,9},{5},{6}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,2},{3,8,9},{4},{5},{6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,8},{3},{4},{5},{6},{7},{9}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,5},{4},{6,9},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,6},{3},{4},{5},{7,9},{8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,6},{3},{4},{5},{7,8,9}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,5},{3},{4},{6,7,8,9}}
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,4},{2},{3},{5,6,7,8,9}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,5},{4},{6,7,8,9}}
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3,5,6,7,9},{4},{8}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,5,6,7,8},{4},{9}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,8},{2},{3},{4},{5},{6,7},{9}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,6,8},{2},{3},{4},{5},{7},{9}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6,8},{7},{9}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,6,7,8},{2},{3},{4},{5},{9}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => {{1},{2,8},{3,6},{4},{5},{7},{9}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,8},{5},{6},{7},{9}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3},{4,9},{5},{6},{7},{8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4},{5},{6,8},{7},{9}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4},{5},{6,8},{7},{9}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4},{5},{6,8},{7},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5,7,9},{6},{8}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4,6,9},{5},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2},{3,5,9},{4},{6},{7},{8}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,4,9},{3},{5},{6},{7},{8}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2,4},{3},{5},{6,7,9},{8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,6},{2},{3},{4},{5},{7,9},{8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,5,6},{4},{7},{8,9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2,3,4},{5},{6},{7,9},{8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => {{1,7},{2,3,4,6},{5},{8},{9}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => {{1,7},{2,3,5,6},{4},{8},{9}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => {{1,7},{2,3,4,5},{6},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,7},{4},{5},{6},{8},{9}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0] => {{1,7},{2,3,6},{4},{5},{8},{9}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2,3,5},{4},{7},{8},{9}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1,3,8},{2},{4,6,7},{5},{9}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5},{6},{7,8},{9}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,7},{4,5},{6},{8},{9}}
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,9},{8}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3},{4},{5,6,7,9},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4},{5},{6,7,9},{8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,6},{7,9},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,4},{5,7},{6},{8},{9}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7},{8,9}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7,8},{9}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,4,5},{2,3},{6,7,8,9}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1,2,3},{4,9},{5,6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5,9},{6},{7,8}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2},{3},{4,6,9},{5},{7,8}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2},{3,5,6,9},{4},{7,8}}
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,5,6,7,8,9},{3},{4}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,5,6},{2},{3},{4},{7,8,9}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,5,6,7},{2},{3},{4},{8,9}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,5,6,7,8},{2},{3},{4},{9}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,8},{3,7},{4},{5},{6},{9}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,4,8},{3},{5},{6},{7},{9}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,7},{4,5,6},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,7,8},{6},{9}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4,6},{5},{7},{8},{9}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4},{5},{6,9},{7},{8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7},{8},{9}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,5,6},{4},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4,6,7},{5},{8},{9}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,6},{4,5},{7,8,9}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5,6},{7},{8},{9}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2,3},{4},{5},{7},{8},{9}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,7},{2},{3},{4,5},{6},{8},{9}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1,2},{3},{4,9},{5,6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1,2,3},{4},{5,9},{6,8},{7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2,3,4},{5},{6,9},{7},{8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,4},{2},{3},{5,9},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3},{4},{5,8,9},{6,7}}
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1},{2},{3,7,8,9},{4,5,6}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2},{3},{4,8,9},{5,6,7}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,5,6},{3,4},{7},{8},{9}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2},{3,4,7},{5,6},{8},{9}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4},{5,6,8},{7},{9}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7},{8},{9}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,6,7},{3},{4},{5},{8},{9}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => {{1},{2,7,8,9},{3,4,5,6}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5,6},{7},{8},{9}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4,6},{5},{7},{8},{9}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4,6},{5},{7},{8},{9}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => {{1,6,7,8},{2,3,4,5},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,7,9},{3},{4},{5},{6},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,7},{4},{5},{6},{8},{9}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,8},{4,5},{6},{7},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4,7},{5},{6},{8},{9}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4,8},{5,6},{7},{9}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,7},{4},{5},{6},{8},{9}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,3},{4,7},{5},{6},{8},{9}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,8},{4,5},{6},{7},{9}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,3,4},{5,8},{6},{7},{9}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,5,6},{2,3,4},{7,8,9}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,8,9},{3,4,5},{6,7}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7},{8,9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => {{1},{2,8,9},{3,4,5,6,7}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,7,8,9},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1,3},{2},{4},{5,6,7,9},{8}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,9},{8}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,3},{4,5,9},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,6},{3},{4},{5},{7},{8,9}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => {{1,3,4,8},{2},{5},{6},{7},{9}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0] => {{1,8},{2,3,7},{4},{5},{6},{9}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,4,5,9},{3},{6},{7},{8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7,8},{9}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7,8},{9}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,8},{2,3},{4,5},{6,7},{9}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,6,7},{2,3},{4,5},{8,9}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7},{8,9}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7,8},{9}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,8},{2,3},{4,6,7},{5},{9}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,6,7},{2,3},{4,5},{8},{9}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,4,5},{2,3},{6,8,9},{7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,6,7},{5},{8,9}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7},{8,9}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => {{1,3,4,6,7},{2},{5},{8},{9}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => {{1,3,8},{2},{4,6},{5},{7},{9}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => {{1,3,7},{2},{4,6},{5},{8},{9}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => {{1,3,4,6},{2},{5},{7},{8},{9}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,4,8},{2},{3},{5,6,7},{9}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,4,5,6,7},{2},{3},{8},{9}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,4,8},{2},{3},{5,6},{7},{9}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,4,7},{2},{3},{5,6},{8},{9}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,4,5,6},{2},{3},{7},{8},{9}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,5,8},{2},{3},{4},{6},{7},{9}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,5,7},{2},{3},{4},{6},{8},{9}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,7,8,9},{6}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,8},{2,4},{3},{5},{6},{7},{9}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,8},{2},{3,4},{5},{6},{7},{9}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4,6,7,8},{5},{9}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,4,5,6,7,8},{3},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,7,8},{3},{4},{5},{6},{9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6},{7},{8,9}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,9},{5,6},{7},{8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,5},{2},{3},{4},{6},{7,8},{9}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5},{6,8},{7},{9}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1,3},{2},{4},{5,8},{6},{7},{9}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1,2},{3},{4,8},{5},{6},{7},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,8},{4},{5},{6},{7},{9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5},{6},{7,9},{8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4},{5},{6,9},{7},{8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2,5},{3},{4},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,7},{2,6},{3},{4},{5},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,8},{2,7},{3},{4},{5},{6},{9}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,5,6},{4},{7},{8},{9}}
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,3},{2},{4},{5,6,7,8,9}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,4,5,6,7,8},{2},{3},{9}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => {{1,7,8},{2,3,4,5,6},{9}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => {{1},{2,3,9},{4,8},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3},{4},{5,8},{6,7},{9}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4,5,7},{6},{8},{9}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2},{3},{4,5,8},{6,7},{9}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,4,5,6},{3},{7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3,4,5},{6,9},{7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3,4,5},{6,9},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,9},{3},{4},{5},{6},{7,8}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,4,5,6,7,8},{2,3},{9}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => {{1},{2,3,9},{4,7},{5},{6},{8}}
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,2},{3,7,8,9},{4,5,6}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,3,4,5},{2},{6,7,8,9}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => {{1,6,7,8},{2},{3,4,5},{9}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,5,6},{7,9},{8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,2},{3,8},{4},{5},{6},{7},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,5},{6,9},{7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,3},{4,9},{5,6},{7,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,9},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,9},{4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,9},{6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,3},{4,9},{5,7,8},{6}}
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => {{1},{2,9},{3,5,6},{4},{7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2},{3,9},{4},{5,6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,3,4},{2},{5,9},{6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,2},{3,5,6},{4},{7,9},{8}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3},{4},{5,6,9},{7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2},{3},{4,5,9},{6,7},{8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3,4,5},{6},{7,9},{8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5},{6},{7,9},{8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,6},{4},{5},{7,8,9}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0] => {{1,8},{2,3,5},{4},{6},{7},{9}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2,9},{3},{4,5},{6},{7},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,4},{5,9},{6},{7},{8}}
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3},{4,5,9},{6},{7},{8}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,7,8},{3,5},{4},{6},{9}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4},{5},{6,7,9},{8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2,4},{3},{5},{6},{7,8},{9}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2},{3,5,7},{4},{6},{8},{9}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6,7},{8},{9}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,7},{2,3,4},{5},{6},{8},{9}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1,3},{2},{4},{5,9},{6},{7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,3},{4,9},{5},{6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,4},{5,9},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,5},{6,9},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,6},{7,9},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2},{3},{4,7,8},{5,6},{9}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2},{3,5,6},{4},{7,8},{9}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,3},{4,7},{5,6},{8},{9}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,5,6},{3,4},{7},{8},{9}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,3},{4},{5,9},{6},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,7},{3},{4},{5},{6},{8},{9}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,5},{2},{3,4},{6,8,9},{7}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3},{2},{4,6,8,9},{5},{7}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1},{2,4,6,8,9},{3},{5},{7}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,5,6},{2},{3,4},{7},{8},{9}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1,3},{2},{4,8,9},{5,6},{7}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,6,8,9},{3,4},{5},{7}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1},{2,9},{3},{4,5,6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,6},{4},{5},{7},{8,9}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,4,5},{3},{6,7,8,9}}
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,3,4},{2},{5,6,7,8,9}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,8},{3,4},{5},{6},{7},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5,8,9},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,8},{2,5},{3},{4},{6},{7},{9}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1},{2,8,9},{3},{4,5,6,7}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => {{1},{2,3,8,9},{4},{5,6,7}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,7},{6},{8,9}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,2},{3,9},{4,5,6,8},{7}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,8},{7},{9}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,7},{6},{8},{9}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => {{1,3,4,5,7},{2},{6},{8,9}}
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,9},{4,5},{6,7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3,5},{4},{6,7,9},{8}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,3},{4},{5,8,9},{6,7}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,8,9},{4,5},{6,7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,3},{4,7},{5,6},{8,9}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,4},{2},{3},{5},{6,7,8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,7},{2,3},{4},{5},{6},{8},{9}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,5,6},{3},{4},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4,6,7},{5},{8,9}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2},{3},{4,7},{5,6},{8,9}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,7},{5,6},{8,9}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,6,7},{4},{5},{8,9}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1},{2},{3,7},{4,6},{5},{8,9}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1},{2},{3,7},{4,5,6},{8,9}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,8},{4},{5},{6},{7},{9}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,8},{5},{6},{7},{9}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,2,8},{3},{4,5,7},{6},{9}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5},{6,8},{7},{9}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,4},{5},{6,8},{7},{9}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5},{6},{7,8},{9}}
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,3},{4,5,9},{6},{7},{8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,7},{3,4},{5},{6},{8},{9}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,6},{5},{7,8,9}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,2},{3,7},{4,5,6},{8,9}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,2},{3,6},{4,5},{7,8,9}}
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,5},{4},{6,7,8,9}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1},{2},{3,4,6},{5},{7,8,9}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => {{1},{2,3,7},{4,5,6},{8,9}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,6},{4,5},{7,8,9}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,5},{4},{6,7,8,9}}
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,4},{2},{3},{5,6,9},{7},{8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5,8},{6},{7},{9}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1,3},{2},{4,8},{5},{6},{7},{9}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,5},{2},{3},{4},{6,7,8},{9}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,4},{2},{3},{5,8},{6,7},{9}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1,3},{2},{4,8},{5,6},{7},{9}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,2},{3,8},{4,5},{6},{7},{9}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,8},{3,4},{5},{6},{7},{9}}
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,4},{2},{3},{5,6,8},{7},{9}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1,3},{2},{4,8},{5,7},{6},{9}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,4},{2},{3},{5,6,7,8},{9}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,2},{3,8},{4,6},{5},{7},{9}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1,3},{2},{4,8},{5,6,7},{9}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => {{1},{2,8},{3,5},{4},{6},{7},{9}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,2},{3,8},{4,5,6},{7},{9}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => {{1},{2,8},{3,4,5},{6},{7},{9}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,6},{3},{4,5},{7,8},{9}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,8},{3},{4,5},{6,7},{9}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => {{1,8},{2,6,7},{3},{4,5},{9}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,8,9},{3},{4},{5},{6,7}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,8,9},{3,4},{5},{6,7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,6,7},{2},{3},{4},{5},{8,9}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,8,9},{4},{5},{6,7}}
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,7,8},{4},{5},{6},{9}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2,3,4},{5,9},{6,7,8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7},{8},{9}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4},{5},{6,7,8,9}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,5,6},{2,3,4},{7,8},{9}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,5,6},{3,4},{7,8},{9}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,3,5,6},{2},{4},{7,8},{9}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7,8},{9}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7,8},{9}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,7},{4},{5},{6},{8,9}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,6},{3},{4},{5},{7},{8,9}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,7},{2,4},{3},{5},{6},{8},{9}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,8},{2},{3},{4,7},{5},{6},{9}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,8},{2},{3},{4},{5,6},{7},{9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,2},{3,7},{4},{5},{6},{8},{9}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,3},{2},{4,5,6,7,8},{9}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,4},{3},{5,6,7,8},{9}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,5},{4},{6,7,8},{9}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,6},{5},{7,8},{9}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,4},{2,3},{5,6,7,8},{9}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,5},{3,4},{6,7,8},{9}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,4},{3},{5,6,7,8},{9}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,6},{4,5},{7,8},{9}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6,7,8},{9}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4,6},{5},{7,8},{9}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4},{6,9},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,6},{3},{4},{5},{7,8},{9}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,7,9},{4,5},{6},{8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1,2,3},{4},{5,9},{6},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4},{5},{6,9},{7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,7,8,9},{3},{4},{5},{6}}
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,6,9},{3},{4},{5},{7},{8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,7},{4},{5,6},{8,9}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,2},{3,5,6},{4},{7,8},{9}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => {{1,7,8},{2,6},{3},{4,5},{9}}
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,4,8},{2,3},{5},{6,7},{9}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,2},{3,8},{4},{5,6},{7},{9}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,4},{2,3},{5,7,8},{6},{9}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,5,6},{2,3},{4},{7,8},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,7,9},{4},{5},{6},{8}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,9},{3},{4,5,6,8},{7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,5,6,7},{2,3,4},{8},{9}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,3,4,5,6},{2},{7,8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,7},{2,3},{4},{5},{6},{8,9}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,7},{2},{3,4},{5},{6},{8},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,5},{6,8,9},{7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,3},{4,8,9},{5},{6,7}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,8,9},{3},{4,5},{6,7}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,8,9},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,4},{5,8,9},{6,7}}
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,3},{4,6,9},{5},{7,8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1},{2,8,9},{3},{4,7},{5,6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,4},{2,3},{5,8,9},{6,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,4},{5,8},{6,7},{9}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,7},{2},{3},{4},{5,6},{8},{9}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2},{3},{4,5},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2},{3},{4,6,7,9},{5},{8}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,6,9},{4,5},{7},{8}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1},{2,3,9},{4,8},{5,6},{7}}
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,6,8,9},{4,5},{7}}
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,2,3},{4,6,8,9},{5},{7}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => {{1},{2,8,9},{3,7},{4},{5},{6}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2,4,8,9},{3},{5},{6},{7}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => {{1},{2,9},{3,8},{4,5},{6},{7}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,5,9},{3,4},{6},{7},{8}}
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,2},{3,7,8},{4,5,6},{9}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7},{8,9}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,7},{6},{8,9}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,7},{3,4},{5,6},{8,9}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,7},{3,6},{4},{5},{8},{9}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,8},{3,6},{4},{5},{7},{9}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,5,7,8},{2},{3,4},{6},{9}}
[1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1,3},{2},{4,5,8,9},{6},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,3,5},{2},{4},{6,7,8,9}}
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,7,8},{2,3},{4,5},{6},{9}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,7,8},{2,5},{3,4},{6},{9}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,8,9},{3,5},{4},{6,7}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,8},{2,6,7},{3,4},{5},{9}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3},{4},{5,6,8,9},{7}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,2},{3,8},{4,6,7},{5},{9}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1},{2,6,7},{3},{4,5},{8,9}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1},{2,8},{3},{4,5},{6,7},{9}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7,8},{9}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7,8},{9}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1},{2,4,7},{3},{5,6},{8,9}}
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1},{2,6,9},{3},{4,5},{7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1},{2,9},{3},{4,5},{6,7},{8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1},{2,6},{3},{4,5},{7,8,9}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,4},{3},{5,8},{6,7},{9}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7,8},{9}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1},{2,4,9},{3},{5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2,4,9},{3},{5,7,8},{6}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,7,8},{2,6},{3},{4},{5},{9}}
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,3,7,8},{2},{4},{5},{6},{9}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,8},{2,7},{3,4},{5},{6},{9}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,4,8},{2,3},{5},{6},{7},{9}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,6},{4},{5},{7},{8},{9}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,7},{2,3},{4,6},{5},{8,9}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,6},{2,3},{4,5},{7,8,9}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5,8},{6,7},{9}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7,8},{9}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,6,7},{5},{8,9}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,6,7},{4},{5},{8},{9}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2},{3,5},{4},{6},{7},{8,9}}
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,4,8},{2,3},{5,7},{6},{9}}
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,5,8},{2,3},{4},{6},{7},{9}}
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,5,8},{2,3,4},{6},{7},{9}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,4,5,7},{2,3},{6},{8},{9}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,5,7},{2,3},{4},{6},{8},{9}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,5,7},{2,3,4},{6},{8},{9}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => {{1,2,7},{3,4,5,6},{8},{9}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2,3,4},{5},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,8},{2,6},{3},{4},{5},{7},{9}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,7},{2,6},{3},{4},{5},{8,9}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,2},{3,9},{4,6},{5},{7},{8}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2},{3,4,9},{5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,8},{2,4,7},{3},{5,6},{9}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => {{1,8},{2,4,5},{3},{6,7},{9}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => {{1},{2,6,7},{3,5},{4},{8,9}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,5},{3},{4},{6,8,9},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,4},{3},{5},{6,8,9},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4},{5},{6,8,9},{7}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,4,7,8},{3},{5},{6},{9}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,7,8},{3,6},{4},{5},{9}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1},{2},{3,4,5,7},{6},{8},{9}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,8},{2,7},{3,6},{4,5},{9}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,6},{2,5},{3,4},{7,9},{8}}
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,9},{6,8},{7}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,9},{4,8},{5,7},{6}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,9},{3,8},{4,7},{5,6}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,9},{5,8},{6,7}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6,9},{7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,7},{2,6},{3,5},{4},{8,9}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,9},{6},{7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,9},{4,8},{5},{6,7}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,9},{3,8},{4,7},{5},{6}}
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2,3},{4,9},{5,8},{6,7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,7},{2,4},{3},{5,6},{8,9}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7},{8,9}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => {{1,8},{2},{3,4,5,6,7},{9}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5,7,8},{6},{9}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => {{1},{2,8},{3,7},{4},{5},{6},{9}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => {{1},{2,3,9},{4},{5,6,7},{8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1},{2,9},{3},{4,5,6,7},{8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7,8},{9}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4},{5},{6,9},{7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2,4},{3},{5,9},{6},{7},{8}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1},{2,9},{3},{4,7,8},{5,6}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1},{2,7},{3},{4,5,6},{8,9}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7},{8,9}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => {{1,2,7},{3,5,6},{4},{8,9}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,7},{2,3,6},{4},{5},{8,9}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7},{8,9}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7,8},{9}}
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1,2,3},{4,7,9},{5},{6},{8}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,5},{2,3},{4},{6,7,9},{8}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4},{5},{6,7,9},{8}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2,3,4},{5},{6,7,9},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,6,7},{2},{3,4},{5},{8,9}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,5,6},{2},{3,4},{7,9},{8}}
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,9},{3},{4},{5,6,8},{7}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1},{2,9},{3},{4,5,8},{6},{7}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2},{3,4,5,9},{6,7},{8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,9},{4,5},{6},{7},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0] => {{1,8},{2,7},{3,4,5},{6},{9}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0] => {{1,8},{2,3,6},{4,5},{7},{9}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0] => {{1,8},{2,6},{3,4,5},{7},{9}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0] => {{1,8},{2,3,4,5},{6},{7},{9}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,7},{3,6},{4,5},{8},{9}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,7},{3,4,5},{6},{8},{9}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0] => {{1,7},{2,3,6},{4,5},{8},{9}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => {{1,7},{2,6},{3,4,5},{8},{9}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,6},{4,5},{7},{8},{9}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,6},{3,4,5},{7},{8},{9}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,7,9},{5,6},{8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,8},{2,3,5,7},{4},{6},{9}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4,7},{5},{6},{8},{9}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,4,5,6},{2},{3},{7,9},{8}}
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,4},{2},{3},{5,7,8,9},{6}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,5,6,7},{2},{3,4},{8,9}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => {{1,7},{2},{3,4,5,6},{8,9}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,2},{3,9},{4},{5,6,7},{8}}
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,2},{3,7,8,9},{4},{5},{6}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,2},{3,9},{4,5},{6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,2},{3,9},{4,5,6,7},{8}}
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,2},{3,6,7,8,9},{4},{5}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2,4},{3},{5,6,9},{7},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1},{2,4,6,7},{3},{5},{8,9}}
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1},{2,6,8,9},{3},{4,5},{7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,5},{6},{7,9},{8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,6},{3,4,5},{7,8},{9}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7,8},{9}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => {{1,7},{2,6},{3,5},{4},{8},{9}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2,4,9},{3},{5,8},{6,7}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1},{2,4,6,9},{3},{5},{7,8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2},{3,8},{4,7},{5,6},{9}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,3,8},{2},{4,7},{5,6},{9}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,6},{2,3,5},{4},{7,9},{8}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,5},{2,3,4},{6,9},{7},{8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,4},{2,3},{5,9},{6},{7},{8}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7},{8,9}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7},{8,9}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,6,7},{4},{5},{8},{9}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,5,6},{4},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2},{3},{4,7,9},{5},{6},{8}}
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,6,7,9},{4},{5},{8}}
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,5,6,7,9},{3},{4},{8}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,3,4,5},{2},{6,7,8},{9}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,5,6},{4},{7,8,9}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => {{1,6,7},{2},{3,4,5},{8},{9}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,5},{6,8,9},{7}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,2},{3,7,8},{4},{5,6},{9}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6,7},{8,9}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4},{5},{6,8},{7},{9}}
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,9},{4},{5},{6,7,8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1},{2,4,5,6},{3},{7,9},{8}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,5,6},{3},{4},{7,9},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2},{3},{4,5,8},{6},{7},{9}}
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,4},{2,3},{5,6,7,8,9}}
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,5},{2,3,4},{6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => {{1,6},{2,3,4,5},{7,8,9}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,8},{2,7},{3,5,6},{4},{9}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => {{1,8},{2},{3,6,7},{4,5},{9}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => {{1},{2,7,8},{3,6},{4,5},{9}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6,7},{8},{9}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2,3,4},{5,7,8,9},{6}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,4,5,6},{2,3},{7,8,9}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,6,7},{3,4,5},{8,9}}
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2},{3,4,5,8,9},{6,7}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2,4,8},{3},{5},{6},{7},{9}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5},{6},{7,9},{8}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,5},{2},{3},{4},{6,9},{7,8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,6},{3},{4},{5},{7,8,9}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,5},{3},{4},{6},{7,8,9}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1},{2,8,9},{3,4,7},{5},{6}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5},{6},{7,8,9}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3,5},{4},{6,8,9},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,3,4},{5},{6,8,9},{7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,8},{2},{3,4,5,7},{6},{9}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,5},{2},{3,4},{6},{7,8},{9}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,4,5,7},{2},{3},{6},{8},{9}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => {{1},{2,3,9},{4,6,7},{5},{8}}
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => {{1},{2,3,9},{4,6},{5},{7},{8}}
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,6,7,8,9},{3},{5}}
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1},{2,4,7,8,9},{3},{5},{6}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1},{2,4,6,9},{3},{5},{7},{8}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}}
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,10},{9}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,9},{7,8},{10}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8,9},{7},{10}}
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,10},{8,9}}
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,9,10},{8}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,9},{6,7,8},{10}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,9},{7},{8},{10}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8,9},{6},{10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,10},{7,8,9}}
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,10},{8},{9}}
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8,9,10},{7}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,9},{5,6,7,8},{10}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,9},{6,8},{7},{10}}
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,9},{6},{8},{10}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7,8,9},{5},{10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,10},{6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,10},{7,9},{8}}
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9,10},{7,8}}
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8,10},{7},{9}}
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8,9,10},{6}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,9},{4,5,6,7,8},{10}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,9},{6,7},{8},{10}}
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8,9},{6},{7},{10}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7,8,9},{4},{10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => {{1},{2,3,4,10},{5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,10},{7,8},{9}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,10},{7},{8,9}}
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9,10},{7},{8}}
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8,9,10},{5}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => {{1,2,9},{3,4,5,6,7,8},{10}}
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,8,9},{5,6,7},{10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,9},{6},{7},{8},{10}}
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,7,8,9},{5,6},{10}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,4,5,6,7,8,9},{3},{10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => {{1},{2,3,10},{4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,9,10},{6,7,8}}
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,10},{7},{8},{9}}
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,7,9,10},{6},{8}}
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8,9,10},{4}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => {{1,9},{2,3,4,5,6,7,8},{10}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7,8,9},{2},{10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8},{9,10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => {{1},{2,10},{3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,10},{6},{7,8,9}}
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,8,9,10},{6},{7}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8,9,10},{3}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,7,8},{9},{10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => {{1,9},{2,3,4,5,6,8},{7},{10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,8},{7},{9,10}}
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,10},{9}}
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8,10},{3},{9}}
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,10},{8,9}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,10},{3,4},{5},{6},{7},{8},{9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,10},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3},{4},{5},{6,10},{7,9},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,10},{6,8},{7},{9}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,10},{5,7},{6},{8},{9}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,10},{4,6},{5},{7},{8},{9}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,10},{3,5},{4},{6},{7},{8},{9}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,4},{3},{5},{6},{7},{8},{9}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,3,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,10},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6,7,9,10},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8,10},{9}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,5},{3},{4},{6},{7},{8},{9}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,4,5},{3},{6},{7},{8},{9}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,3,5},{4},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4},{5,6,10},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,9,10},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,6},{3},{4},{5},{7},{8},{9}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,5,6},{3},{4},{7},{8},{9}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,3,4,5},{6},{7},{8},{9}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,3,6},{4},{5},{7},{8},{9}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2},{3},{4,5,10},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2},{3},{4,5,9,10},{6},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,10},{2,7},{3},{4},{5},{6},{8},{9}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,10},{2,6,7},{3},{4},{5},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,10},{2,3,7},{4},{5},{6},{8},{9}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,10},{5},{6},{7},{8},{9}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,9,10},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8,10},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,10},{2,8},{3},{4},{5},{6},{7},{9}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,10},{2,7,8},{3},{4},{5},{6},{9}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2},{3,10},{4,6,9},{5},{7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,3,4,6},{5},{7},{8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,3,4,5,6},{7},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => {{1,10},{2,3,8},{4},{5},{6},{7},{9}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,10},{4},{5},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,10},{2,9},{3},{4},{5},{6},{7},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,9,10},{4},{5},{6},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,10},{2,8,9},{3},{4},{5},{6},{7}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,10},{2,6,7,8},{3},{4},{5},{9}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => {{1,10},{2,4,9},{3},{5},{6},{7},{8}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,10},{5},{6},{7},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => {{1,10},{2,3,9},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7,8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7,8,9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8,9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7,8,9},{10}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5,6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7,8,9},{10}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7},{8},{9,10}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6,7},{8,9},{10}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5,6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5,6,7},{8,9},{10}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2},{3},{4,5,6,7,8,9},{10}}
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8},{9},{10}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4,5,6},{7},{8},{9},{10}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6},{7,8,9,10}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5,6,7},{8},{9},{10}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6,7,8},{9,10}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7,8,9},{10}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7},{8},{9,10}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8,9},{10}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5},{6},{7},{8,9,10}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6,7},{8},{9,10}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8},{9},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6,7},{8},{9},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7},{8,9,10}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8},{9,10}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6},{7,8,9,10}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3},{4,5,6,7},{8},{9},{10}}
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8,9,10}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8},{9},{10}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7},{8,9,10}}
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4},{5,6,7,8,9,10}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7},{8},{9},{10}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5},{6,7,8,9,10}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8},{9},{10}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5,6},{7,8,9,10}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4,5,6,7},{8},{9},{10}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6,7,8},{9},{10}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7,8},{9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8,9},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5},{6},{7},{8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7,8},{9},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4},{5},{6},{7,8,9},{10}}
[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},{6},{7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4},{5},{6,7,8,9,10}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8},{9},{10}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5,6,7},{8},{9,10}}
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7,8,9},{10}}
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8,9,10}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5},{6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5,6},{7},{8},{9},{10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7},{8,9},{10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5,6},{7,8},{9},{10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4},{5,6},{7,8,9},{10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5,6,7},{8},{9},{10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7},{8,9,10}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7},{8},{9},{10}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7,8},{9,10}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5,6},{7,8,9},{10}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6},{7,8,9,10}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{1,2},{3,4,5,6,7,8},{9},{10}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6,7,8},{9,10}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8,9},{10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7},{8},{9,10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8,9},{10}}
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3},{4},{5,6,7,8,9},{10}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7},{8},{9},{10}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6,7},{8,9},{10}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5},{6,7},{8,9,10}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8},{9,10}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6},{7,8,9,10}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6,7},{8,9,10}}
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7,8,9},{10}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6},{7},{8},{9,10}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5},{6},{7,8,9,10}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5},{6,7,8,9},{10}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6},{7,8,9,10}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7},{8,9,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5,6,7,8},{9},{10}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6,7,8},{9,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4},{5,6,7,8,9},{10}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3,4,5},{6},{7},{8},{9,10}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5},{6},{7,8,9},{10}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6},{7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8,9},{10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4,5},{6,7,8,9},{10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8},{9},{10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3,4,5,6},{7},{8},{9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4,5,6},{7},{8,9},{10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7},{8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5,6},{7,8,9},{10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5,6,7},{8},{9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8},{9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6,7},{8,9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,8},{2},{3},{4},{5},{6},{7},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,9,10},{5},{6},{7},{8}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5,6},{7},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,9,10},{4},{5},{6},{7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4,5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,9,10},{8}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,10},{8,9}}
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,9,10},{7},{8}}
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,10},{7,8},{9}}
[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},{7},{8,10},{9}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9,10},{2}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => {{1,10},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => {{1,10},{2,3,4,5,6,7,9},{8}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,10},{9}}
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8,9,10},{7}}
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8,9,10},{6}}
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8,9,10},{5}}
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8,9,10},{4}}
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8,9,10},{3}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,10},{2},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6,8},{7},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,9},{7},{8},{10}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3,6},{4},{5},{7},{8},{9}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4,6},{5},{7},{8},{9}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4},{5,6},{7},{8},{9}}
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,10},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2},{3},{4},{5},{6},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,7,8,10},{2},{3},{4},{5},{6},{9}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,6,7,10},{2},{3},{4},{5},{8},{9}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,5,6,10},{2},{3},{4},{7},{8},{9}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,4,5,10},{2},{3},{6},{7},{8},{9}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,10},{2},{5},{6},{7},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => {{1,2,10},{3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => {{1,2,3,10},{4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,10},{6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,10},{7,8,9}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7},{8},{9},{10}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,6,10},{2},{3},{4},{5},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,10},{2},{3},{4},{5},{6,9},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,10},{2},{3},{4},{5},{6,8},{7},{9}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4},{5},{6,7},{8},{9}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => {{1,10},{2,3,4,5,6,9},{7},{8}}
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,10},{2},{8},{9}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,3,4},{2},{5,6},{7,8},{9,10}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,5,6},{2},{3,4},{7,8},{9,10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,7,8},{2},{3,4},{5,6},{9,10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,9,10},{2},{3,4},{5,6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,9},{2},{3,4},{5,6},{7,8},{10}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,7},{2},{3,4},{5,6},{8,9},{10}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,5},{2},{3,4},{6,7},{8,9},{10}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6,7},{8,9},{10}}
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9,10},{2},{3}}
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,5,6,7,8,9,10},{2},{3},{4}}
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,6,7,8,9,10},{2},{3},{4},{5}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,7,8,9,10},{2},{3},{4},{5},{6}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,8,10},{2},{3},{4},{5},{6},{7},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,7,10},{2},{3},{4},{5},{6},{8},{9}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,5,10},{2},{3},{4},{6},{7},{8},{9}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,4,10},{2},{3},{5},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,7,10},{2},{3},{4},{5},{6},{8,9}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,6,10},{2},{3},{4},{5},{7,8},{9}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,5,10},{2},{3},{4},{6,7},{8},{9}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,4,10},{2},{3},{5,6},{7},{8},{9}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,10},{2},{4,5},{6},{7},{8},{9}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,10},{3,4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,9,10},{7,8}}
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,9,10},{6,7,8}}
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,8,9,10},{5,6,7}}
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,8,9,10},{4,5,6,7}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,7,8,9,10},{3,4,5,6}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,7,8,9,10},{2,3,4,5,6}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,4,6,8,10},{3},{5},{7},{9}}
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,4,6,10},{3},{5},{7,9},{8}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,4,8,10},{3},{5,7},{6},{9}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,4,10},{3},{5,7,9},{6},{8}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1},{2,4,10},{3},{5,9},{6,8},{7}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,6,8,10},{3,5},{4},{7},{9}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,6,10},{3,5},{4},{7,9},{8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,8,10},{3,5,7},{4},{6},{9}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,8,10},{3,7},{4,6},{5},{9}}
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,10},{3,5,7,9},{4},{6},{8}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,10},{3,5,9},{4},{6,8},{7}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,10},{3,7,9},{4,6},{5},{8}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,10},{3,9},{4,6,8},{5},{7}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,10},{3,9},{4,8},{5,7},{6}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,6,8,10},{5},{7},{9}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3},{2},{4,6,10},{5},{7,9},{8}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,8,10},{5,7},{6},{9}}
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,3},{2},{4,10},{5,7,9},{6},{8}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,10},{5,9},{6,8},{7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4},{6,8,10},{7},{9}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3,5},{2},{4},{6,10},{7,9},{8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,5},{2,4},{3},{6,8,10},{7},{9}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6,10},{7,9},{8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,5,7},{2},{4},{6},{8,10},{9}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,7},{2},{4,6},{5},{8,10},{9}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,5,7},{2,4},{3},{6},{8,10},{9}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,7},{2,4,6},{3},{5},{8,10},{9}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,7},{2,6},{3,5},{4},{8,10},{9}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,5,7,9},{2},{4},{6},{8},{10}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,3,5,9},{2},{4},{6,8},{7},{10}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,7,9},{2},{4,6},{5},{8},{10}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,3,9},{2},{4,6,8},{5},{7},{10}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,3,9},{2},{4,8},{5,7},{6},{10}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,5,7,9},{2,4},{3},{6},{8},{10}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,5,9},{2,4},{3},{6,8},{7},{10}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,7,9},{2,4,6},{3},{5},{8},{10}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,7,9},{2,6},{3,5},{4},{8},{10}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,9},{2,4,6,8},{3},{5},{7},{10}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,9},{2,4,8},{3},{5,7},{6},{10}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,9},{2,6,8},{3,5},{4},{7},{10}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3,5,7},{4},{6},{10}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3,7},{4,6},{5},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,9},{3},{4},{5},{6},{7},{8},{10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,9},{5},{6},{7},{8},{10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,9},{4},{5},{6},{7},{8},{10}}
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8,10},{7},{9}}
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,10},{2},{9}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => {{1,10},{2,3,4,5,6,9},{7,8}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => {{1,10},{2,3,4,5,6,8,9},{7}}
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,10},{2},{8,9}}
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,9,10},{2},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6},{7},{8},{9,10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,10},{6,7},{8},{9}}
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,10},{8},{9}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,3,4},{5,6,10},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,10},{7,9},{8}}
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,3,4,5,10},{2},{6},{7},{8},{9}}
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,10},{2},{7},{8},{9}}
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,10},{9}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8,10},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2,3,4,5,6,7}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => {{1,2,9,10},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8,10},{4},{9}}
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,10},{4},{8,9}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => {{1,2,3,5,6,10},{4},{7,8,9}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => {{1,2,3,5,10},{4},{6,7,8,9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => {{1,10},{2},{3,4,5,6,7,8},{9}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4,5,6,7},{8},{9}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4,5},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,10},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,10},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,9,10},{3},{4},{5},{6},{7},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,10},{2},{3},{4},{5},{6},{7,8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,10},{2},{3},{4},{5},{6},{7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5},{7,10},{8},{9}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,10},{2},{3,4,7},{5},{6},{8},{9}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4,5,7},{6},{8},{9}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4},{5,6,7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7,9},{8},{10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,8},{3},{4},{5},{6},{7},{9},{10}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,9},{4},{5},{6},{7},{8},{10}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3,5},{4},{6},{7},{8},{9,10}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,5},{3},{4},{6},{7},{8},{9,10}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,5},{2},{3},{4},{6},{7},{8},{9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,10},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,10},{7},{8},{9}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => {{1,2,10},{3,4,5,6,9},{7},{8}}
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,10},{3},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,8,9,10},{4},{5},{6},{7}}
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,7,8,9,10},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,6,7,8,9,10},{3},{4},{5}}
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,5,6,7,8,9,10},{3},{4}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => {{1,9,10},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,6,7,8,9,10},{2,3,4,5}}
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,5,6,7,8,9,10},{2,3,4}}
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9,10},{2,3}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,10},{2},{7,8,9}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => {{1,2,4,5,10},{3},{6,7,8,9}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => {{1,2,3,10},{4},{5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => {{1,2,10},{3,4,6,7,8,9},{5}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => {{1,10},{2,3,4,5,7,8,9},{6}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,9},{2,6},{3},{4},{5},{7},{8},{10}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,9},{2},{3,6},{4},{5},{7},{8},{10}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,9},{2},{3},{4,6},{5},{7},{8},{10}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,9},{2},{3},{4},{5,6},{7},{8},{10}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,5,10},{4},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5,9},{6},{7},{8}}
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,4,5,10},{3},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5,8},{6},{7},{9}}
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5,7},{6},{8},{9}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,10},{6,9},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4},{5},{6},{7,9},{8},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,8},{3},{4},{5},{6},{7},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,7},{3},{4},{5},{6},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,6},{3},{4},{5},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7},{8},{9},{10}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,8},{2},{3},{4},{5},{6},{7},{9,10}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,6},{5},{7},{8},{9},{10}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5,7},{6},{8},{9},{10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,8},{4},{5},{6},{7},{9},{10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,10},{3,8},{4},{5},{6},{7},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,8,10},{4},{5},{6},{7},{9}}
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,6,7,8,9,10},{4},{5}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7,9},{8},{10}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2,4},{3},{5,6},{7,8},{9,10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,10},{4,9},{5},{6},{7},{8}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => {{1,2,3,10},{4,5,9},{6},{7},{8}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,5,6,10},{4},{7},{8},{9}}
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,7,8,9,10},{5},{6}}
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,6,7,8,9,10},{4},{5}}
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,5,6,7,8,9,10},{3},{4}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5,7},{6},{8},{9},{10}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4,6},{5},{7},{8},{9},{10}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,6},{5},{7,8,9,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,9},{3},{4},{5},{6},{7},{8},{10}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,6},{3},{4},{5},{7},{8},{9},{10}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,6},{4},{5},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,9,10},{8}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,8,10},{5},{6},{7},{9}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0] => {{1,10},{2,3,4,9},{5},{6},{7},{8}}
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,7,10},{5},{6},{8},{9}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2,10},{3,4,9},{5},{6},{7},{8}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,6,10},{5},{7},{8},{9}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7},{8},{9},{10}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,9,10},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4,8},{5},{6},{7},{9},{10}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4,9},{5,6},{7},{8},{10}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,8},{4},{5},{6},{7},{9},{10}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,9},{4,5},{6},{7},{8},{10}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,5,6,7},{2,3,4},{8,9,10}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,8,9,10},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,8,9,10},{6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,8},{3},{4},{5},{6},{7},{9,10}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6,8},{7},{9},{10}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,8},{6,7},{9,10}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,3},{4,5},{6,7},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,3},{4,5},{6,7},{8,9}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,8,9},{2,3},{4,5},{6,7},{10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,6,7},{2,3},{4,5},{8,9},{10}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,4,5},{2,3},{6,7},{8,9},{10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,9},{2,3},{4},{5},{6},{7},{8},{10}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,5,6},{4},{7},{8},{9},{10}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,5,6},{3},{4},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,5,6},{2},{3},{4},{7},{8},{9},{10}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,10},{5,6},{7},{8},{9}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,10},{2},{5,6,7},{8},{9}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => {{1,4,10},{2},{3},{5,6,7},{8},{9}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => {{1,2,10},{3},{4},{5,6,7,8},{9}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,10},{2,3,7,8,9},{4},{5},{6}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,8,9},{4},{5},{6},{7},{10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8,9},{10}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6},{7,9},{8},{10}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5},{6,9},{7},{8},{10}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1,3},{2},{4},{5,9},{6},{7},{8},{10}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,2},{3},{4,9},{5},{6},{7},{8},{10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,8},{7},{9},{10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => {{1,10},{2,3,4,5,6,8},{7},{9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => {{1,2,10},{3,4,5,6,8},{7},{9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4,5,6,8},{7},{9}}
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5,6,8},{7},{9}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,10},{6,8},{7},{9}}
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,8,9,10},{6,7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => {{1},{2,8,9,10},{3,4,5,6,7}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => {{1},{2,3,9,10},{4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,6,10},{4,5},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,9},{7,8},{10}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2},{3,4,10},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,7,8,9,10},{4,5,6}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4,6},{5},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,8,10},{3},{4},{5},{6},{7},{9}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,10},{3,5},{4},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,10},{2},{3},{4},{5},{6},{7},{8,9}}
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,5,6,7,8,9,10},{3,4}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,3,4},{5,6,9,10},{7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2,3,4,5},{6,7,10},{8,9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,9,10},{8}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,3},{4,5,9,10},{6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,9,10},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => {{1,2,10},{3,4,5,6,7,9},{8}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => {{1,2,3,10},{4,5,6,7,9},{8}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5,6,7,9},{8}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,10},{6,7,9},{8}}
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8,10},{6},{9}}
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8,10},{5},{9}}
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8,10},{3},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => {{1,10},{2,3,4,5,6,7,8},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => {{1,10},{2,3,4,5,6,7},{8},{9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,6},{7,10},{8,9}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,10},{6,7},{8,9}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,10},{4,5},{6,7},{8,9}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,10},{3},{4,5},{6,7},{8,9}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,3},{4,10},{5},{6,7},{8,9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,3},{4,5},{6,10},{7},{8,9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5},{6,7},{8,10},{9}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4,6},{5},{7},{8},{9},{10}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4,6},{5},{7},{8},{9},{10}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4,5,6},{7},{8},{9}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4},{5,6},{7},{8},{9}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,6,10},{3,5},{4},{7},{8},{9}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,6,7,10},{2,3,5},{4},{8},{9}}
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,8,10},{6},{7},{9}}
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,10},{2,3},{9}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,10},{2},{3},{4},{5,6,7},{8,9}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,10},{2},{3,4},{5,6,7},{8},{9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,2},{3,9},{4},{5},{6},{7},{8},{10}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7},{8},{9},{10}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2},{3,5,7,9,10},{4},{6},{8}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,4},{2},{5,7,9,10},{6},{8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,5,6},{2},{3,4},{7,9,10},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,7,8},{2},{3,4},{5,6},{9},{10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,10},{2},{3,4},{5,6},{7,8},{9}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,8,10},{2},{3,4},{5,6},{7},{9}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,6,8,10},{2},{3,4},{5},{7},{9}}
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,4,6,8,10},{2},{3},{5},{7},{9}}
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,4,6,8,10},{3},{5},{7},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,8,9},{2},{3},{4},{5},{6},{7},{10}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,9},{3,4},{5},{6},{7},{8},{10}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => {{1,2,10},{3,9},{4,8},{5,7},{6}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,10},{3},{4,5},{6},{7},{8},{9}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3,4,5},{6},{7},{8},{9}}
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,9},{8},{10}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,8},{7},{9,10}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,7,10},{3},{4},{5},{6},{8},{9}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,4,10},{3},{5},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,8,9,10},{3},{4},{5},{6},{7}}
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,7,8,10},{3},{4},{5},{6},{9}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,9,10},{3,4},{5,6},{7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,3},{4,9,10},{5,6},{7,8}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,3},{4,5},{6,9,10},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3},{4},{5},{6,10},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,7,8},{6},{9,10}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,8},{6,7},{9,10}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,6,7},{5},{8,9},{10}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4,7},{5,6},{8,9},{10}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => {{1,10},{2},{3,4,5,6,7,8,9}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,9},{4},{5},{6},{7},{8},{10}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,9},{5},{6},{7},{8},{10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4},{5},{6},{7,9},{8},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,9,10},{2,8},{3},{4},{5},{6},{7}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,4,10},{2,3},{5},{6},{7},{8},{9}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8},{9,10}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,8},{4,7},{5,6},{9,10}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,3},{4,7},{5,6},{9,10}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,7},{3,4},{5,6},{9,10}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,7},{3,6},{4,5},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,8},{6,7},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,8},{6,7},{9,10}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,5},{3,4},{6,7},{9,10}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,8},{4,5},{6,7},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,4},{5,10},{6,9},{7,8}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,10},{6,9},{7,8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,10},{2,5},{3,4},{6,9},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,10},{4,5},{6,9},{7,8}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,10},{2,3},{4,5},{6,9},{7,8}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,4},{5,6},{7,8}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,6},{4,5},{7,8}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,4},{5,8},{6,7}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,8},{4,5},{6,7}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,10},{4,9},{5,6},{7,8}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,10},{2,3},{4,9},{5,6},{7,8}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,8},{4,7},{5,6}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,10},{4,9},{5,8},{6,7}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,3},{4,9},{5,8},{6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,6},{7,10},{8,9}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,6},{2,5},{3,4},{7,10},{8,9}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5},{7,10},{8,9}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5},{7,10},{8,9}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,10},{4,7},{5,6},{8,9}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,3},{4,7},{5,6},{8,9}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,7},{3,4},{5,6},{8,9}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,7},{3,6},{4,5},{8,9}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,10},{6,7},{8,9}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,5},{3,4},{6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8,9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7,9},{8},{10}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6,9},{7},{8},{10}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5,9},{6},{7},{8},{10}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,3},{2},{4,9},{5},{6},{7},{8},{10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7,8,9},{10}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6,9},{7,8},{10}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5,9},{6,7},{8},{10}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,3},{2},{4,9},{5,6},{7},{8},{10}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,2},{3,9},{4,5},{6},{7},{8},{10}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,9},{3,4},{5},{6},{7},{8},{10}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3,4},{5},{6},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,9,10},{3},{4},{5},{6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,9,10},{3,4},{5},{6},{7,8}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,9,10},{3,4},{5,6},{7,8}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,7,8},{6},{9,10}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,10},{4},{5,9},{6},{7},{8}}
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2,10},{3,6,9},{4},{5},{7},{8}}
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,10},{2,3,7,9},{4},{5},{6},{8}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => {{1,2,10},{3,6,7,9},{4},{5},{8}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => {{1,2,3,10},{4},{5,6,9},{7},{8}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0] => {{1,10},{2,8},{3,4,5,6,7},{9}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0] => {{1,10},{2,7},{3,4,5,6},{8},{9}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,6},{3,4,5},{7},{8},{9}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,5},{3,4},{6},{7},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,8},{4},{5},{6},{7}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,8},{4,7},{5},{6}}
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,10},{3},{8,9}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => {{1,10},{2,4,5,6,7,8,9},{3}}
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,10},{7},{8,9}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,10},{6},{7,8,9}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5},{6,7,8,9}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,5,6},{2,3,4},{7,8},{9,10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,10},{3,9},{4},{5},{6},{7},{8}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,8},{3},{4},{5},{6},{7},{9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => {{1,10},{2,3,4,5,9},{6},{7},{8}}
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,10},{2,3},{4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => {{1,9,10},{2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,9,10},{3,4},{5},{6},{7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6},{7,8},{9,10}}
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,3},{2},{4,5,6,7,8,9},{10}}
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,4},{3},{5,6,7,8,9},{10}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6,7,8,9},{10}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,6},{5},{7,8,9},{10}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,7},{6},{8,9},{10}}
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,10},{2},{7,8},{9}}
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => {{1,3,4,5,10},{2},{6,7},{8},{9}}
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,10},{2},{5,6},{7},{8},{9}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,4},{5},{6},{7},{8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,8},{2,3},{4},{5},{6},{7},{9,10}}
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2,3,5,7,9},{4},{6},{8},{10}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3},{4},{5,6,8,10},{7},{9}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,10},{3},{4,5,7,9},{6},{8}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1},{2,9},{3,4,6,8},{5},{7},{10}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,7,8,10},{3},{4,5},{6},{9}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,6,7,9},{3,4},{5},{8},{10}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,4,5,7},{3},{6},{8},{9,10}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3,4,6},{5},{7},{8,9},{10}}
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,4,10},{3},{5},{6,7,9},{8}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1},{2,3,9},{4},{5,6,8},{7},{10}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,3},{4},{5,10},{6,7,9},{8}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,10},{3},{4,9},{5,6,8},{7}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1},{2,9},{3,8},{4,5,7},{6},{10}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1},{2,4,9,10},{3},{5},{6,7},{8}}
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,8,9},{4},{5,6},{7},{10}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,3},{4},{5,9,10},{6,7},{8}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => {{1},{2,10},{3},{4,8,9},{5,6},{7}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => {{1},{2,9},{3,7,8},{4,5},{6},{10}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3},{6},{7,9,10},{8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,3,4},{5},{6,8,9},{7},{10}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,6},{3},{4,5},{7},{8,9,10}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2,5},{3,4},{6},{7,8,9},{10}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1},{2,9,10},{3},{4,6,7},{5},{8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => {{1},{2,8,9},{3,5,6},{4},{7},{10}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => {{1},{2,10},{3},{4,5,6},{7},{8,9}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,9},{3,4,5},{6},{7,8},{10}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => {{1},{2,4,6,10},{3},{5},{7},{8,9}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => {{1},{2,3,5,9},{4},{6},{7,8},{10}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3},{4},{5,6,10},{7},{8,9}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2,10},{3},{4,5,9},{6},{7,8}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => {{1},{2,9},{3,4,8},{5},{6,7},{10}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,7,10},{3},{4,5},{6},{8,9}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,6,9},{3,4},{5},{7,8},{10}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => {{1},{2,4,7},{3},{5,6},{8},{9,10}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3,6},{4,5},{7},{8,9},{10}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2,4,10},{3},{5},{6,9},{7,8}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => {{1},{2,3,9},{4},{5,8},{6,7},{10}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,3},{4},{5,10},{6,9},{7,8}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,10},{3},{4,9},{5,8},{6,7}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2,9},{3,8},{4,7},{5,6},{10}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => {{1,3,10},{2},{4,9},{5},{6},{7},{8}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => {{1,4,10},{2},{3},{5,8},{6},{7},{9}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,7,10},{2},{3},{4,5},{6},{8},{9}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,8,10},{2},{3,4},{5},{6},{7},{9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,9,10},{2,3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4,5,6,7},{8,10},{9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3,4,5,6},{7,10},{8},{9}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2,3,4,5},{6,10},{7},{8},{9}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1,2,3,4},{5,10},{6},{7},{8},{9}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,2,3},{4,10},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,9,10},{6},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5},{6},{7},{8,10},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,10},{3},{4},{5},{6},{7},{8,9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,8,10},{3},{4},{5},{6},{7},{9}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,5,6},{4},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4},{5,7,8},{6},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,4},{5,6},{7,9,10},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1,2},{3,4},{5,9},{6},{7,8},{10}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,2},{3,7},{4},{5,6},{8,9},{10}}
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => {{1,10},{2},{3,4,5,6,7,9},{8}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6,8},{7},{9},{10}}
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7,9},{8},{10}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,9},{8},{10}}
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,9,10},{8}}
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,5,6,7,8,9,10},{2,4},{3}}
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,6,7,8,9,10},{2,3,5},{4}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,7,8,9,10},{2,3,4,6},{5}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2,3,4,5,7},{6}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0] => {{1,9,10},{2,3,4,5,6,8},{7}}
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,9,10},{6},{8}}
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,10},{6},{8},{9}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2,4,5},{3},{7,8},{9,10}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0] => {{1,10},{2,8,9},{3},{4,5,6,7}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,10},{2,8,9},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,4},{5,9,10},{6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,9,10},{4},{5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2},{3,4,10},{5},{6},{7,8},{9}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,10},{2,6},{3,4},{5},{7,8,9}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,8},{3},{4},{5,6},{7},{9,10}}
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,10},{6,7},{8},{9}}
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,5,7,9,10},{4},{6},{8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,6},{2},{3},{4},{5},{7},{8,10},{9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,6},{2},{3},{4},{5},{7},{8},{9,10}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,6},{4},{5},{7},{8},{9},{10}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,9,10},{5},{6},{7},{8}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,10},{4,5},{6},{7},{8},{9}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3,4},{6,7},{8,9},{10}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1,8,10},{2,4,6,7},{3},{5},{9}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => {{1,8},{2,4,6,7},{3},{5},{9},{10}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => {{1,3,8,10},{2},{4,6,7},{5},{9}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => {{1,3,8},{2},{4,6,7},{5},{9},{10}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1},{2,9},{3,8},{4,6,7},{5},{10}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,5,6},{2,4},{3},{7,9},{8},{10}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,5,6},{2,4},{3},{7},{8,10},{9}}
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,3,5,8,10},{2},{4},{6,7},{9}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,3},{2},{4,7,9},{5,6},{8},{10}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => {{1,3,5,8},{2},{4},{6,7},{9},{10}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => {{1},{2,9},{3,5,8},{4},{6,7},{10}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,7},{5,6},{8,10},{9}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => {{1},{2,4,9},{3},{5,8},{6,7},{10}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2},{3,10},{4,9},{5,8},{6,7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0] => {{1,3,4,6},{2},{5},{7,9},{8},{10}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => {{1,3,4,6},{2},{5},{7},{8,10},{9}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1},{2,7,9},{3,4,6},{5},{8},{10}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1},{2,7},{3,4,6},{5},{8,10},{9}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,8},{4,5,7},{6}}
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => {{1,3,5,7,8,10},{2},{4},{6},{9}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3},{2},{4,6,7,9},{5},{8},{10}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,6,7,9},{3,5},{4},{8},{10}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1,3},{2},{4},{5,10},{6,7,9},{8}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,4},{3},{5,10},{6,7,9},{8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => {{1,3,5,7,8},{2},{4},{6},{9},{10}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => {{1},{2,9},{3,5,7,8},{4},{6},{10}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6,7},{5},{8,10},{9}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1},{2,4,9},{3},{5,7,8},{6},{10}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => {{1},{2},{3,10},{4,9},{5,7,8},{6}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,6,7},{3,5},{4},{8,10},{9}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,7,8},{4,6},{5}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1,3},{2},{4},{5,8,10},{6,7},{9}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,4},{3},{5,8,10},{6,7},{9}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => {{1},{2,4,6,9},{3},{5},{7,8},{10}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,10},{2,6,9},{3,5},{4},{7,8}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2},{3,5,10},{4},{6,9},{7,8}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,5,10},{2,4},{3},{6,9},{7,8}}
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,6,7,10},{3},{4},{5},{8},{9}}
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,5,6,10},{3},{4},{7},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2,7},{3},{4},{5},{6}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,7,8,9,10},{2,6},{3},{4},{5}}
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,6,7,8,10},{2,5},{3},{4},{9}}
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,5,6,7,10},{2,4},{3},{8},{9}}
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,4,5,6,10},{2,3},{7},{8},{9}}
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => {{1,3,10},{2},{4,6,9},{5},{7,8}}
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,3,4,8,10},{2},{5},{6,7},{9}}
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,3,10},{2},{4,5},{6,7,8,9}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,3,4,9,10},{2},{5},{6,8},{7}}
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,3,6,7,9,10},{2},{4,5},{8}}
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,3,10},{2},{4},{5,8,9},{6},{7}}
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => {{1,3,8,9,10},{2},{4},{5,7},{6}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,3,10},{2},{4,5,6},{7,9},{8}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,3,10},{2},{4},{5,9},{6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0] => {{1,3,9,10},{2},{4,5,8},{6,7}}
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0] => {{1,3,4,10},{2},{5,6},{7,9},{8}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,3,9,10},{2},{4},{5,6,7,8}}
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0] => {{1,3,4,10},{2},{5,7},{6},{8,9}}
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => {{1,3,5,10},{2},{4},{6,8,9},{7}}
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,5,10},{2,3},{4},{6,8,9},{7}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,5,8,9,10},{2,3},{4},{6,7}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,5,10},{2,3},{4},{6},{7,9},{8}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,5,9,10},{2,3},{4},{6,7,8}}
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,5,7,10},{2,3},{4},{6},{8,9}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,7,10},{2,5},{3,4},{6},{8,9}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,7,9,10},{2,5},{3,4},{6},{8}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,7,10},{2,4,5},{3},{6},{8,9}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,7,9,10},{2,4,5},{3},{6},{8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,9,10},{2,7},{3,5,6},{4},{8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => {{1,9,10},{2,5,6,7},{3,4},{8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,9,10},{2,7},{3},{4,6},{5},{8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,9,10},{2,6,7},{3,4,5},{8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => {{1,9,10},{2,4,7},{3},{5,6},{8}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,5,8},{4},{6,7}}
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,10},{2,3,7,9},{4},{5,6},{8}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,4},{5,6,7,8}}
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0] => {{1,10},{2,3,8,9},{4},{5,7},{6}}
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => {{1,10},{2,5,6,8,9},{3,4},{7}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3},{4,7,8},{5},{6}}
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => {{1,10},{2,7,8,9},{3},{4,6},{5}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,4,5},{6,8},{7}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3},{4,8},{5,6},{7}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0] => {{1,10},{2,8,9},{3,4,7},{5,6}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,10},{2,3,9},{4,5},{6,8},{7}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0] => {{1,10},{2,3,9},{4,6},{5},{7,8}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => {{1,10},{2,4,9},{3},{5,7,8},{6}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,9,10},{3,6},{4,5},{7,8}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,6,9,10},{3,4},{5},{7,8}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,9,10},{3,4},{5},{6,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,9,10},{3,4},{5},{6},{7,8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,9,10},{3,4},{5},{6,7},{8}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,10},{3,4},{5},{6,8,9},{7}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6},{7,8},{9,10}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6},{7,8},{9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,9,10},{2},{3},{4},{5},{6},{7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0] => {{1,8,10},{2,3,4,5,6,7},{9}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0] => {{1,7,8,10},{2,3,4,5,6},{9}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,6,7,8,10},{2,3,4,5},{9}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,5,6,7,8,10},{2,3,4},{9}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4},{5,7,9,10},{6},{8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4},{7,9,10},{8}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,7,8},{4},{5,6},{9,10}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,5,7,8},{4},{6},{9,10}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,7,9,10},{4},{5,6},{8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,2},{3,9,10},{4},{5,7,8},{6}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2},{3,5,9,10},{4},{6},{7,8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,3,4},{2},{5,6},{7,9,10},{8}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,7,8},{6},{9,10}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,3,4},{2},{5,9,10},{6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,3,5,6},{2},{4},{7,8},{9,10}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => {{1,3,5,6},{2},{4},{7,9,10},{8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,5,7,8},{2},{3,4},{6},{9,10}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => {{1,7,8},{2},{3,5,6},{4},{9,10}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => {{1,3,7,8},{2},{4},{5,6},{9,10}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => {{1,3,5,7,8},{2},{4},{6},{9,10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,7,9,10},{2},{3,4},{5,6},{8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,9,10},{2},{3,4},{5,7,8},{6}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,5,9,10},{2},{3,4},{6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,5,7,9,10},{2},{3,4},{6},{8}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => {{1,9,10},{2},{3,5,6},{4},{7,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => {{1,7,9,10},{2},{3,5,6},{4},{8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,9,10},{2},{3,7,8},{4},{5,6}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => {{1,9,10},{2},{3,5,7,8},{4},{6}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,3,9,10},{2},{4},{5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,3,7,9,10},{2},{4},{5,6},{8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,3,9,10},{2},{4},{5,7,8},{6}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,3,5,9,10},{2},{4},{6},{7,8}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,3,5,7,9,10},{2},{4},{6},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,4,5},{3},{6,7},{8,9},{10}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,6,7},{3},{4,5},{8,9},{10}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,8,9},{3},{4,5},{6,7},{10}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,8},{3},{4,5},{6,7},{9,10}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,6},{3},{4,5},{7,8},{9,10}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => {{1},{2,4,7},{3},{5,6},{8,9},{10}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,9},{4,5},{6},{7},{8},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,8,9},{3},{4},{5},{6},{7},{10}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2,3,4},{5,6,7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,7},{2},{3},{4},{5},{6},{8,10},{9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,8},{2,3},{4},{5},{6},{7},{9},{10}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,9},{2,4},{3},{5},{6},{7},{8},{10}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2},{3,5,7,10},{4},{6},{8},{9}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2},{3,5,10},{4},{6,9},{7},{8}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,2},{3,10},{4,6,9},{5},{7},{8}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,10},{4,9},{5,8},{6},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,7,10},{2,3},{4},{5,6},{8},{9}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,10},{2,3},{4},{5,9},{6,7},{8}}
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,10},{2,3},{4,7,8},{5},{6},{9}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,10},{2,6},{3,4},{5},{7,8},{9}}
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,4,6,9},{2,3},{5},{7},{8},{10}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => {{1,4,9},{2,3},{5,8},{6},{7},{10}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,9},{3,4},{5},{6,7},{8},{10}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => {{1,9},{2,5,8},{3,4},{6},{7},{10}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3,7},{4,5},{6},{10}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4},{5,7,10},{6},{8},{9}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2},{3,4},{5,10},{6,9},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,10},{4,5},{6},{7,8},{9}}
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2},{3,6,9},{4,5},{7},{8},{10}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => {{1},{2},{3,9},{4,8},{5,6},{7},{10}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1},{2,5,6},{3},{4},{7,10},{8},{9}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1},{2,9},{3},{4},{5,6,7},{8},{10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1,4},{2},{3},{5,6},{7,10},{8},{9}}
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => {{1},{2,4,7,8},{3},{5},{6},{9},{10}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => {{1},{2,7,8},{3,6},{4},{5},{9},{10}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,7,8},{2},{3},{4,5},{6},{9},{10}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,3,6},{2},{4},{5},{7,8},{9},{10}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,6},{2,5},{3},{4},{7,8},{9},{10}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,4,6,9,10},{3},{5},{7},{8}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => {{1},{2,4,9,10},{3},{5,8},{6},{7}}
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1},{2,3,9,10},{4},{5},{6,7},{8}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1},{2,9,10},{3,5,8},{4},{6},{7}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => {{1},{2,9,10},{3,8},{4,7},{5},{6}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,6,9,10},{2},{3},{4,5},{7},{8}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => {{1,9,10},{2},{3},{4,8},{5,6},{7}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,9,10},{2},{3,6,7},{4},{5},{8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,9,10},{2,5},{3},{4},{6,7},{8}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,3,5,8},{2},{4},{6},{7},{9,10}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0] => {{1,3,8},{2},{4,7},{5},{6},{9,10}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,8},{2,4,7},{3},{5},{6},{9,10}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,7},{3,6},{4},{5},{9,10}}
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,4,6,7,8,9,10},{2,3},{5}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => {{1,9,10},{2,3,5,6,7,8},{4}}
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,5,6,8,9,10},{2,3,4},{7}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2,3,4,6,7},{5}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,10},{2},{3},{4},{5},{6},{7,9},{8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,7,9,10},{2},{3},{4},{5},{6},{8}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,10},{3,7},{4},{5},{6},{8},{9}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,6},{4},{5},{7},{8},{9},{10}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4,6},{5},{7},{8},{9},{10}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3},{4,5},{6,7},{10}}
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,4,5,7,8,10},{3},{6},{9}}
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,4,5,7,10},{3},{6},{8,9}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,8},{2,4,7},{3},{5,6},{9,10}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,7,8,10},{4},{5},{6},{9}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,6,7,10},{4},{5},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,8,10},{2,3,7},{4},{5},{6},{9}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,7,8,9,10},{2,3,6},{4},{5}}
[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,4,5,6,7,10},{2,3},{8},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,9,10},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4,9,10},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5,9,10},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,9,10},{7},{8}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,8,9},{5},{6},{7},{10}}
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,9,10},{6,8},{7}}
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,8,10},{6,7},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,8,9,10},{3},{4},{5},{6},{7}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,5,9},{4},{6},{7},{8},{10}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,9},{4,8},{5},{6},{7},{10}}
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,6,10},{5},{7},{8},{9}}
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => {{1},{2,3,4,10},{5,9},{6},{7},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,4},{5,10},{6},{7},{8},{9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,4},{5,6},{7,10},{8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,10},{3},{4},{5},{6},{7,8},{9}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,10},{3},{4},{5},{6},{7,9},{8}}
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,10},{3},{4},{5},{6},{7,8,9}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,7,9,10},{3},{4},{5},{6},{8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,9,10},{2,6},{3},{4},{5},{7},{8}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4,7},{5},{6},{8},{9}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,3},{4,6},{5},{7},{8},{9}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3,4},{5,6},{7},{8},{9}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2},{3,4,6,10},{5},{7,8},{9}}
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,2},{3,4,10},{5,8,9},{6},{7}}
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2},{3,4,5,6,10},{7},{8},{9}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2,4},{3},{5,6},{7,8,10},{9}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,4,8},{3},{5,6},{7},{9,10}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => {{1,2,8},{3,6,7},{4},{5},{9,10}}
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,5,6,7,8,9,10},{2,3},{4}}
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,6,7,8,10},{2,4},{3},{5},{9}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,7,8,9,10},{2,3,4,5},{6}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => {{1,8,10},{2,3,4,6},{5},{7},{9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0] => {{1,9,10},{2,3,4,5,6,7},{8}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,9,10},{4,8},{5},{6},{7}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4,8},{5},{6},{7},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3},{4},{5},{6},{7},{10}}
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1},{2,3,4,10},{5},{6,7,8,9}}
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1},{2,3,10},{4},{5,6,7,8,9}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1},{2,10},{3},{4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,5},{2},{3},{4},{6,7},{8,9},{10}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,10},{3,4,5},{6},{7},{8},{9}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => {{1},{2,4,9},{3},{5,6},{7,8},{10}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1},{2,4,9,10},{3},{5,6},{7,8}}
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => {{1},{2,9},{3},{4,7,8},{5,6},{10}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2,7},{3},{4,5,6},{8,9},{10}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3},{4},{6,7},{8,9},{10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,10},{2,3},{4},{5},{6},{7},{8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,8,10},{2,3},{4},{5},{6},{7},{9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,10},{3},{4},{5},{6},{7},{8,9}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0] => {{1,2,10},{3,8},{4,5},{6,7},{9}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => {{1,10},{2,5,9},{3,4},{6,7},{8}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,10},{3,6},{4,5},{7,9},{8}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,7,10},{3,4},{5,6},{8},{9}}
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,10},{2,3},{4,9},{5,6,8},{7}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => {{1,4,10},{2,3},{5,7,8},{6},{9}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,10},{2,6,9},{3,4},{5},{7,8}}
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,10},{2,3},{4,6,7,9},{5},{8}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,10},{3,7},{4,5},{6},{8,9}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,8,10},{3,4},{5,7},{6},{9}}
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,4,10},{2,3},{5,8,9},{6},{7}}
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,6,10},{3,4},{5},{7},{8,9}}
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,4,6,8,10},{2,3},{5},{7},{9}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2},{3,9},{4,8},{5,6,7}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0] => {{1,3,10},{2},{4,5,6},{7,8},{9}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,10},{2},{3,4,5},{6,7,9},{8}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,3,10},{2},{4,5,6},{7},{8,9}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,6,8,10},{2},{3,4,5},{7},{9}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,10},{2,4},{3},{5,9},{6,7,8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,8,10},{2,4},{3},{5,6,7},{9}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => {{1,10},{2},{3,9},{4},{5,6,7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1,8,10},{2},{3,5,6,7},{4},{9}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,10},{2,6},{3,5},{4},{7,8,9}}
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,10},{2,7,8,9},{3},{4,5},{6}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => {{1,10},{2},{3,4,6},{5},{7,8,9}}
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => {{1,10},{2,7,8,9},{3},{4},{5,6}}
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,10},{2},{3,5,7,8,9},{4},{6}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => {{1,9,10},{2,8},{3,7},{4,6},{5}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,9,10},{3,7},{4},{5,6},{8}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,9,10},{2,4,8},{3},{5,6},{7}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,9,10},{3,5},{4},{6,8},{7}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,6,9,10},{3},{4,5},{7},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => {{1,9,10},{2},{3,8},{4,5,7},{6}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => {{1,3,9,10},{2},{4,6,7},{5},{8}}
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => {{1,9,10},{2,5,8},{3},{4},{6,7}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => {{1,9,10},{2},{3,5,6,8},{4},{7}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,9,10},{3,6},{4},{5},{7,8}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,7,9,10},{3},{4,6},{5},{8}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,3,9,10},{2},{4,7,8},{5},{6}}
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,5,9,10},{3},{4},{6},{7,8}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,10},{8,9}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,10},{7,8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4},{5},{6},{7,10},{8},{9}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,8,10},{2,4},{3},{5},{6},{7},{9}}
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,10},{8},{9}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,5,10},{6},{7},{8},{9}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,5,9,10},{4},{6},{7},{8}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,2},{3,10},{4,5,9},{6,8},{7}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,2},{3,10},{4},{5},{6,8},{7},{9}}
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2},{3,5,6,8,10},{4},{7},{9}}
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,10},{2,8},{3,4},{5,6,7},{9}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => {{1,8,10},{2,5,6},{3,4},{7},{9}}
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,5,10},{2,3},{4},{6},{7,8,9}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => {{1,2,5,9},{3,4},{6,7},{8},{10}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,9},{2,3,8},{4,7},{5,6},{10}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,9},{2,3},{4},{5,7},{6},{8},{10}}
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,4,5,7,9},{2,3},{6},{8},{10}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,9},{3,7,8},{4,5},{6},{10}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,4},{5,10},{6,8},{7},{9}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,4},{5,8,10},{6},{7},{9}}
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,4,10},{5,6},{7,8,9}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => {{1},{2},{3,9},{4,7},{5,6},{8},{10}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,7,9},{4,5},{6},{8},{10}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5,6},{4},{7,8,10},{9}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => {{1},{2,3,9},{4},{5,6,7,8},{10}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,4},{3},{5,6,9},{7,8},{10}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,7,8},{3,5},{4},{6},{9},{10}}
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1},{2,5,7,8},{3},{4},{6},{9},{10}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,7,8},{3},{4,5,6},{9},{10}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,6},{2,4},{3},{5},{7,8},{9},{10}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,4,6},{2},{3},{5},{7,8},{9},{10}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,5,9,10},{4},{6,7},{8}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => {{1},{2,9,10},{3,4,8},{5,7},{6}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1},{2,9,10},{3},{4},{5,7},{6},{8}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,4,5,7,9,10},{3},{6},{8}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1},{2,3,9,10},{4,7,8},{5},{6}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,9,10},{2,7},{3},{4,5,6},{8}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,6,9,10},{2,4},{3},{5},{7,8}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,4,9,10},{2},{3},{5},{6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,8},{2,3,7},{4,6},{5},{9,10}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,8},{2},{3},{4,6},{5},{7},{9,10}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0] => {{1,3,4,6,8},{2},{5},{7},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1,4},{2,3},{5,6,7,8},{9},{10}}
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3},{4,6,7,8},{5},{9,10}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,5},{2,3},{4},{6,7,8,9},{10}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3},{2},{4,6,7,8},{5},{9,10}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,4},{3},{5},{6,7,8,9},{10}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,3,5},{2},{4},{6,7,8,9},{10}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,2,3},{4},{5,10},{6},{7,8,9}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1,2,4},{3},{5},{6,10},{7,8,9}}
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,6,7,8},{2},{3,4},{5},{9,10}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3},{4},{6,10},{7,8,9}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,6,7,8},{2},{3,5},{4},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1,4},{2,3},{5,10},{6,7,8},{9}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,5,6,7},{2,4},{3},{8,10},{9}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,6},{4,5},{7},{8,9},{10}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => {{1,3,4,7},{2},{5,6},{8,9},{10}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3,6},{4,5},{7},{8,10},{9}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,8},{2},{3,4,7},{5,6},{9,10}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,7},{2,3,6},{4,5},{8,10},{9}}
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2},{3},{4,5,9,10},{6,7},{8}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,3},{2},{4,5,9,10},{6,7},{8}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2},{3},{4,5,9,10},{6,8},{7}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,3},{2},{4,5,9,10},{6,8},{7}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,9},{3,4,5},{6},{7,8},{10}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,9},{3,5,6},{4},{7,8},{10}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,7,9},{3,4,5},{6},{8},{10}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,8,9},{3,7},{4},{5,6},{10}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,7,9},{3,6},{4,5},{8},{10}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,9,10},{2,3},{4},{5,6,7},{8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,10},{2,5},{3,4},{6,7,8},{9}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,9,10},{2,3},{4},{5,7,8},{6}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,9,10},{2,4},{3},{5,7,8},{6}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,10},{2,3,5},{4},{6},{7,8,9}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => {{1,10},{2,4,6},{3},{5},{7,8,9}}
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,6,10},{2,3,4},{5},{7},{8,9}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,7,10},{2,3,5},{4},{6},{8,9}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,9,10},{2,7,8},{3},{4,5},{6}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,7,10},{2,6},{3,4},{5},{8,9}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,9,10},{2,7,8},{3},{4,6},{5}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,6,10},{2,5},{3,4},{7,8},{9}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,8,10},{2,6,7},{3,5},{4},{9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0] => {{1,10},{2,3,4,5,7,8},{6},{9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => {{1,2,10},{3,4,6,7,8},{5},{9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4},{5,6,7,8},{9}}
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => {{1,2,4,5,10},{3},{6,7,8},{9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => {{1,2,3,9,10},{4,5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,9,10},{5,6,7,8}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0] => {{1,2,10},{3,4,5,6,9},{7,8}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0] => {{1,2,10},{3,4,5,6,8,9},{7}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5,9},{6,8},{7}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => {{1,3,10},{2},{4,9},{5,8},{6,7}}
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => {{1,3,5,10},{2},{4},{6,9},{7,8}}
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => {{1,3,5,7,10},{2},{4},{6},{8,9}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,7,8},{3},{4},{5},{6},{9},{10}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,6,7},{3},{4},{5},{8},{9},{10}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,5,6},{3},{4},{7},{8},{9},{10}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5},{6,8,10},{7},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2},{3},{4},{5,7,8,10},{6},{9}}
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3},{4,6,7,8,10},{5},{9}}
[1,0,1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2},{3,5,6,7,8,10},{4},{9}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,10},{4,9},{5,6},{7},{8}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,6,7,8},{2,3,4,5},{9},{10}}
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => {{1,2},{3,7,8,9},{4,5,6},{10}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1,2},{3,4},{5,9,10},{6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,5,6},{3,4},{7,8},{9,10}}
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,8},{6,7},{9,10}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,6},{7,8,10},{9}}
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,8,9,10},{6},{7}}
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,9,10},{6,7},{8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4},{5},{6},{7,9},{8},{10}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4},{5},{6},{7,9},{8},{10}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8,9},{10}}
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,5,6,7,8,9,10},{4}}
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1},{2},{3,5,6,10},{4},{7},{8,9}}
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,4,10},{5},{6,8,9},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,5},{4},{6,7,10},{8,9}}
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,4},{3},{5,6,10},{7},{8,9}}
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1},{2},{3,10},{4},{5,7,8,9},{6}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1},{2},{3},{4,10},{5,6},{7,8,9}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,4},{3},{5,10},{6},{7,8,9}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1},{2},{3},{4,10},{5,6,7},{8,9}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,4},{5,6},{7,10},{8,9}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1,3},{2},{4},{5,6,10},{7},{8,9}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,3},{2},{4},{5,10},{6},{7,8,9}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4},{5,6},{7,10},{8,9}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,3,5},{2},{4},{6},{7,10},{8,9}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6},{7,10},{8,9}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => {{1},{2,4,6,8,9},{3},{5},{7},{10}}
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,8,9},{5},{6,7},{10}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,6,8,9},{3,5},{4},{7},{10}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7,8,9},{10}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,4},{3},{5,6},{7,8,9},{10}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3},{2},{4,6,8,9},{5},{7},{10}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,6},{5},{7,8,9},{10}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6,8,9},{7},{10}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,5},{2,4},{3},{6,8,9},{7},{10}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => {{1},{2,3,5,7},{4},{6},{8,9},{10}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => {{1},{2},{3,4,7},{5,6},{8,9},{10}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5,7},{6},{8,9},{10}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,7},{4,5,6},{8,9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7,9},{8},{10}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,9},{7},{8},{10}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2},{3},{4,5,9},{6},{7},{8},{10}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3,5},{2},{4},{6,7},{8,10},{9}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,5},{2,4},{3},{6,7},{8,10},{9}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,9,10},{2,4},{3},{5},{6},{7},{8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,9,10},{2},{3,4},{5},{6},{7},{8}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,8},{4,6,7},{5}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => {{1,10},{2,9},{3,7,8},{4},{5,6}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3,7},{4},{5,6},{10}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,4,10},{3},{5},{6},{7},{8},{9}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2},{3,9},{4,8},{5,7},{6}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2},{3},{4},{5},{7,8},{9,10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6},{7,8},{9,10}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => {{1},{2,9,10},{3,8},{4},{5},{6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,6},{3},{4},{5},{7,9,10},{8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,5},{3},{4},{6},{7,9,10},{8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,4},{3},{5},{6},{7,9,10},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4},{5},{6},{7,9,10},{8}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => {{1,2,10},{3},{4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,9,10},{2,3,8},{4},{5},{6},{7}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,4,5,10},{2,3},{6},{7},{8},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3},{4,5},{6,10},{7,9},{8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5,7},{6},{8,10},{9}}
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,3},{4,10},{5,7,9},{6},{8}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,3},{4,10},{5,9},{6,8},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3,5},{4},{6,7},{8,10},{9}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3,5},{4},{6,10},{7,9},{8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1},{2,3,5,7},{4},{6},{8,10},{9}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,7},{4,6},{5},{8,10},{9}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5},{6,7},{8,10},{9}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3},{2},{4,5},{6,10},{7,9},{8}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5,7},{6},{8,10},{9}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,10},{2},{3,5,7,9},{4},{6},{8}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,10},{2},{3,5,9},{4},{6,8},{7}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,10},{2},{3,7,9},{4,6},{5},{8}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,10},{2},{3,9},{4,6,8},{5},{7}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,10},{2,4},{3},{5,7,9},{6},{8}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,10},{2,4},{3},{5,9},{6,8},{7}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => {{1,10},{2,4,6},{3},{5},{7,9},{8}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,10},{2,6},{3,5},{4},{7,9},{8}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => {{1,10},{2,4,6,8},{3},{5},{7},{9}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => {{1,10},{2,4,8},{3},{5,7},{6},{9}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,10},{2,6,8},{3,5},{4},{7},{9}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,10},{2,8},{3,5,7},{4},{6},{9}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => {{1,10},{2,8},{3,7},{4,6},{5},{9}}
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,4,6,7,8,9,10},{3},{5}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,4,6,8,9,10},{3},{5},{7}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,3,9,10},{2},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,10},{9},{11}}
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,11},{10}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,10},{8,9},{11}}
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9,10},{8},{11}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,11},{9,10}}
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,10,11},{9}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,10},{8},{9},{11}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,11},{8,9,10}}
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,11},{9},{10}}
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,9,10,11},{8}}
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8,9,10,11},{7}}
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8,9,10,11},{6}}
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8,9,10,11},{5}}
[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8,9,10,11},{4}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,11},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,11},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,11},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,11},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,11},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,11},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,11},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9,11},{10}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2,4},{3},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2,3,4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9,11},{10}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2,5},{3},{4},{6},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2,6},{3},{4},{5},{7},{8},{9},{10}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2,3,4,5},{6},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2,7},{3},{4},{5},{6},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8,9,11},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,11},{2,8},{3},{4},{5},{6},{7},{9},{10}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2,3,4,5,6},{7},{8},{9},{10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,10,11},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,11},{5,6},{7},{8},{9},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,10,11},{9}}
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,11},{9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => {{1,11},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,11},{10}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => {{1,11},{2,3,4,5,6,7,8,10},{9}}
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9,11},{2},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,9,11},{2},{3},{4},{5},{6},{7},{8},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,8,11},{2},{3},{4},{5},{6},{7},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,7,11},{2},{3},{4},{5},{6},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,6,11},{2},{3},{4},{5},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,5,11},{2},{3},{4},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,4,11},{2},{3},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,11},{2},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,11},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10,11}}
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9,10,11},{2}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8,9},{10,11}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,11},{2},{3},{4},{5},{6},{7,8},{9},{10}}
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,11},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10},{11}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7,8,9,10},{2},{11}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => {{1},{2,11},{3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9},{11}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,11},{8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0] => {{1,2,11},{3,4,5,6,7,10},{8},{9}}
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8,11},{3},{9},{10}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8,9,11},{10}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7,8,9,10},{11}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,11},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,11},{8,10},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9},{11}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4,5,6,7},{8},{9},{10},{11}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5,7},{6},{8},{9},{10},{11}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10,11}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,11},{10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,11},{5,10},{6},{7},{8},{9}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,6,11},{5},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,10},{3},{4},{5},{6},{7},{8},{9},{11}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,11},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10},{11}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,10},{5},{6},{7},{8},{9},{11}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,11},{2,9},{3},{4},{5},{6},{7},{8},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,11},{2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10,11}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2},{3},{4},{5,6},{7},{8},{9},{10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,11},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4,9},{5},{6},{7},{8},{10},{11}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4,10},{5,6},{7},{8},{9},{11}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9,10},{11}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,10},{6},{7},{8},{9},{11}}
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,11},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,11},{2},{3},{4},{5},{6},{7,9},{8},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4},{5},{6},{7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10},{11}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,9,11},{4},{5},{6},{7},{8},{10}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,11},{4,6},{5},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,9,11},{8},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,7,8,9,10,11},{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] => {{1,2,3,4,5,6},{7},{8},{9},{10},{11}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => {{1,11},{2},{3},{4},{5,6,7,8},{9,10}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => {{1,11},{2},{3,4},{5,6,7,8},{9},{10}}
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,11},{6},{7},{8},{9},{10}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,11},{3,4},{5},{6},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,10,11},{3},{4},{5},{6},{7},{8},{9}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,4,11},{3},{5},{6},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,9,10,11},{3},{4},{5},{6},{7},{8}}
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,9,10,11},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,7,8},{6},{9,10},{11}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,8},{6,7},{9,10},{11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8,10},{9},{11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10},{11}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10},{11}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,8},{2},{3},{4},{5},{6},{7},{9,10},{11}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8,10},{9},{11}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7,10},{8},{9},{11}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6,10},{7},{8},{9},{11}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5,10},{6},{7},{8},{9},{11}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,3},{2},{4,10},{5},{6},{7},{8},{9},{11}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,2},{3,10},{4},{5},{6},{7},{8},{9},{11}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9},{11}}
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0] => {{1,11},{2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,0] => {{1,11},{2,3,4,5,6,7,8},{9},{10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2,3,4,5,6,7},{8},{9},{10}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,11},{2},{9,10}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,5,6},{2},{3,4},{7,8},{9,10},{11}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7,8},{9,10},{11}}
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8,9,10,11},{3}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0] => {{1,2,11},{3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,9,10,11},{4},{5},{6},{7},{8}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,10,11},{4,5},{6},{7},{8},{9}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8,9,10},{11}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7,8,9,10},{11}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4},{5,6,7,8,9,10},{11}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6,7,8,9,10},{11}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7,8,9,10},{11}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8,9,10},{11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9,10},{11}}
[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,11},{2},{9},{10}}
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,11},{2},{8},{9},{10}}
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,11},{2},{7},{8},{9},{10}}
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,3,4,5,11},{2},{6},{7},{8},{9},{10}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,11},{2},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10,11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10,11}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,10,11},{3},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10,11}}
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9,11},{10}}
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9,10,11},{2,3}}
[1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,5,6,7,8,9,10,11},{2,3,4}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,6,7,8,9,10,11},{2,3,4,5}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,7,8,9,10,11},{2,3,4,5,6}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,8,9,10,11},{2,3,4,5,6,7}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0] => {{1,9,10,11},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0] => {{1,10,11},{2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,10,11},{8,9}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,11},{6},{7},{8},{9},{10}}
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,11},{6,7},{8},{9},{10}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,10,11},{5},{6},{7},{8},{9}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,11},{5,6},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,8,9,11},{3},{4},{5},{6},{7},{10}}
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,7,8,11},{3},{4},{5},{6},{9},{10}}
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,6,7,11},{3},{4},{5},{8},{9},{10}}
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,5,6,11},{3},{4},{7},{8},{9},{10}}
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,4,5,11},{3},{6},{7},{8},{9},{10}}
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8,9,10,11},{3}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0] => {{1,2,3,11},{4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,11},{5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,11},{6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,11},{7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,9,10},{4},{5},{6},{7},{8},{11}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,10},{4,5},{6},{7},{8},{9},{11}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7,8},{9,10},{11}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7,8},{9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7,8},{9},{10},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7,9},{8},{10},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9},{11}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2},{3,7},{4},{5},{6},{8},{9},{10}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2},{3},{4,7},{5},{6},{8},{9},{10}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2},{3},{4},{5,7},{6},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,10},{4},{5},{6},{7},{8},{9},{11}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,11},{3,10},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,10,11},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,8,9,11},{4},{5},{6},{7},{10}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,7,8,11},{4},{5},{6},{9},{10}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,6,7,11},{4},{5},{8},{9},{10}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,5,6,11},{4},{7},{8},{9},{10}}
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,10,11},{7,8,9}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,9,10},{5},{6},{7},{8},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,10,11},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,10,11},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,10,11},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5,10,11},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3},{4,10,11},{5},{6},{7},{8},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,10,11},{4},{5},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,10,11},{8},{9}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,11},{8,9},{10}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => {{1,11},{2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,11},{2},{3},{4},{5},{6},{7,10},{8},{9}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,11},{3,7},{4},{5},{6},{8},{9},{10}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,11},{3},{4,7},{5},{6},{8},{9},{10}}
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,11},{3},{4},{5,7},{6},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,11},{3},{4},{5},{6,7},{8},{9},{10}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,10,11},{2,3},{4},{5},{6},{7},{8},{9}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7,8,9},{10,11}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => {{1,2,11},{3,4,5,6,7,8,10},{9}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => {{1,2,3,11},{4,5,6,7,8,10},{9}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,11},{5,6,7,8,10},{9}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,11},{6,7,8,10},{9}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,11},{7,8,10},{9}}
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8,9,11},{10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,10,11},{6},{7},{8},{9}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,11},{6,7},{8},{9},{10}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6},{7,8,9,10,11}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6},{7,8,9,10,11}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6,7},{8,9,10,11}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7},{8,9,10,11}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7,8,9},{10,11}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7},{8,9,10,11}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7},{8,9,10,11}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,9,11},{2,3},{4},{5},{6},{7},{8},{10}}
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8,9,10,11},{7}}
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8,9,10,11},{6}}
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8,9,10,11},{5}}
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8,9,10,11},{4}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10,11},{12}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,11},{10},{12}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,12},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,12},{11}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,12},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11,12}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,12},{2,3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1},{2,4,6,8,10,12},{3},{5},{7},{9},{11}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => {{1},{2,4,6,8,12},{3},{5},{7},{9,11},{10}}
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => {{1},{2,4,6,10,12},{3},{5},{7,9},{8},{11}}
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => {{1},{2,4,6,12},{3},{5},{7,9,11},{8},{10}}
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => {{1},{2,4,6,12},{3},{5},{7,11},{8,10},{9}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,4,8,10,12},{3},{5,7},{6},{9},{11}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,4,8,12},{3},{5,7},{6},{9,11},{10}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => {{1},{2,4,10,12},{3},{5,7,9},{6},{8},{11}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,4,10,12},{3},{5,9},{6,8},{7},{11}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,7,9,11},{6},{8},{10}}
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,7,11},{6},{8,10},{9}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,9,11},{6,8},{7},{10}}
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,11},{6,8,10},{7},{9}}
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,11},{6,10},{7,9},{8}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,6,8,10,12},{3,5},{4},{7},{9},{11}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,6,8,12},{3,5},{4},{7},{9,11},{10}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,6,10,12},{3,5},{4},{7,9},{8},{11}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,6,12},{3,5},{4},{7,9,11},{8},{10}}
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1},{2,6,12},{3,5},{4},{7,11},{8,10},{9}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,8,10,12},{3,5,7},{4},{6},{9},{11}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,8,12},{3,5,7},{4},{6},{9,11},{10}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,8,10,12},{3,7},{4,6},{5},{9},{11}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,8,12},{3,7},{4,6},{5},{9,11},{10}}
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,5,7,9},{4},{6},{8},{11}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,5,9},{4},{6,8},{7},{11}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,7,9},{4,6},{5},{8},{11}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,9},{4,6,8},{5},{7},{11}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,9},{4,8},{5,7},{6},{11}}
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => {{1},{2,12},{3,5,7,9,11},{4},{6},{8},{10}}
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3,5,7,11},{4},{6},{8,10},{9}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3,5,9,11},{4},{6,8},{7},{10}}
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,5,11},{4},{6,8,10},{7},{9}}
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,5,11},{4},{6,10},{7,9},{8}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3,7,9,11},{4,6},{5},{8},{10}}
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,7,11},{4,6},{5},{8,10},{9}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,9,11},{4,6,8},{5},{7},{10}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,9,11},{4,8},{5,7},{6},{10}}
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,6,8,10},{5},{7},{9}}
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,6,10},{5},{7,9},{8}}
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,8,10},{5,7},{6},{9}}
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,10},{5,7,9},{6},{8}}
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,3},{2},{4,6,8,10,12},{5},{7},{9},{11}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,3},{2},{4,6,8,12},{5},{7},{9,11},{10}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,6,10,12},{5},{7,9},{8},{11}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,3},{2},{4,6,12},{5},{7,9,11},{8},{10}}
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1,3},{2},{4,6,12},{5},{7,11},{8,10},{9}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,8,10,12},{5,7},{6},{9},{11}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3},{2},{4,8,12},{5,7},{6},{9,11},{10}}
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,10,12},{5,7,9},{6},{8},{11}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,10,12},{5,9},{6,8},{7},{11}}
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,3},{2},{4,12},{5,7,9,11},{6},{8},{10}}
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,3},{2},{4,12},{5,7,11},{6},{8,10},{9}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,3},{2},{4,12},{5,9,11},{6,8},{7},{10}}
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,12},{5,11},{6,8,10},{7},{9}}
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,12},{5,11},{6,10},{7,9},{8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5},{2},{4},{6,8,10,12},{7},{9},{11}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,5},{2},{4},{6,8,12},{7},{9,11},{10}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4},{6,10,12},{7,9},{8},{11}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,3,5},{2},{4},{6,12},{7,9,11},{8},{10}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,3,5},{2},{4},{6,12},{7,11},{8,10},{9}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,5},{2,4},{3},{6,8,10,12},{7},{9},{11}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,5},{2,4},{3},{6,8,12},{7},{9,11},{10}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5},{2,4},{3},{6,10,12},{7,9},{8},{11}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,5},{2,4},{3},{6,12},{7,9,11},{8},{10}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6,12},{7,11},{8,10},{9}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3,5,7},{2},{4},{6},{8,10,12},{9},{11}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3,5,7},{2},{4},{6},{8,12},{9,11},{10}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5},{8,10,12},{9},{11}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3,7},{2},{4,6},{5},{8,12},{9,11},{10}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6},{8,10,12},{9},{11}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,5,7},{2,4},{3},{6},{8,12},{9,11},{10}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,7},{2,4,6},{3},{5},{8,10,12},{9},{11}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5},{8,12},{9,11},{10}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,7},{2,6},{3,5},{4},{8,10,12},{9},{11}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4},{8,12},{9,11},{10}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => {{1,3,5,7,9},{2},{4},{6},{8},{10,12},{11}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,5,9},{2},{4},{6,8},{7},{10,12},{11}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,7,9},{2},{4,6},{5},{8},{10,12},{11}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,9},{2},{4,6,8},{5},{7},{10,12},{11}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,9},{2},{4,8},{5,7},{6},{10,12},{11}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,5,7,9},{2,4},{3},{6},{8},{10,12},{11}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,5,9},{2,4},{3},{6,8},{7},{10,12},{11}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,7,9},{2,4,6},{3},{5},{8},{10,12},{11}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,7,9},{2,6},{3,5},{4},{8},{10,12},{11}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,4,6,8},{3},{5},{7},{10,12},{11}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,4,8},{3},{5,7},{6},{10,12},{11}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,6,8},{3,5},{4},{7},{10,12},{11}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,8},{3,5,7},{4},{6},{10,12},{11}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,8},{3,7},{4,6},{5},{10,12},{11}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,3,5,7,9,11},{2},{4},{6},{8},{10},{12}}
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => {{1,3,5,7,11},{2},{4},{6},{8,10},{9},{12}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,5,9,11},{2},{4},{6,8},{7},{10},{12}}
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => {{1,3,5,11},{2},{4},{6,8,10},{7},{9},{12}}
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => {{1,3,5,11},{2},{4},{6,10},{7,9},{8},{12}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,7,9,11},{2},{4,6},{5},{8},{10},{12}}
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,3,7,11},{2},{4,6},{5},{8,10},{9},{12}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,9,11},{2},{4,6,8},{5},{7},{10},{12}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,9,11},{2},{4,8},{5,7},{6},{10},{12}}
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,6,8,10},{5},{7},{9},{12}}
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,6,10},{5},{7,9},{8},{12}}
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,8,10},{5,7},{6},{9},{12}}
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,10},{5,7,9},{6},{8},{12}}
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,10},{5,9},{6,8},{7},{12}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,5,7,9,11},{2,4},{3},{6},{8},{10},{12}}
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,5,7,11},{2,4},{3},{6},{8,10},{9},{12}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,5,9,11},{2,4},{3},{6,8},{7},{10},{12}}
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,5,11},{2,4},{3},{6,8,10},{7},{9},{12}}
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,5,11},{2,4},{3},{6,10},{7,9},{8},{12}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,7,9,11},{2,4,6},{3},{5},{8},{10},{12}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,7,11},{2,4,6},{3},{5},{8,10},{9},{12}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,7,9,11},{2,6},{3,5},{4},{8},{10},{12}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,7,11},{2,6},{3,5},{4},{8,10},{9},{12}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,4,6,8},{3},{5},{7},{10},{12}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,4,8},{3},{5,7},{6},{10},{12}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,6,8},{3,5},{4},{7},{10},{12}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,8},{3,5,7},{4},{6},{10},{12}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,8},{3,7},{4,6},{5},{10},{12}}
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => {{1,11},{2,4,6,8,10},{3},{5},{7},{9},{12}}
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => {{1,11},{2,4,6,10},{3},{5},{7,9},{8},{12}}
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,11},{2,4,8,10},{3},{5,7},{6},{9},{12}}
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,4,10},{3},{5,7,9},{6},{8},{12}}
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,4,10},{3},{5,9},{6,8},{7},{12}}
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,11},{2,6,8,10},{3,5},{4},{7},{9},{12}}
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,6,10},{3,5},{4},{7,9},{8},{12}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,8,10},{3,5,7},{4},{6},{9},{12}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,8,10},{3,7},{4,6},{5},{9},{12}}
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,5,7,9},{4},{6},{8},{12}}
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,5,9},{4},{6,8},{7},{12}}
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,7,9},{4,6},{5},{8},{12}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,9},{4,6,8},{5},{7},{12}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => {{1,12},{2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9,10,11,12},{2}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,12},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,11,12},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11},{12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}}
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}}
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}}
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}}
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}}
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}}
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}}
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}}
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}}
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}}
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}}
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}}
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}}
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}}
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}}
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}}
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}}
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}}
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,12},{10,11}}
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,10,12},{11}}
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => {{1},{2,3,5,7,9,11},{4},{6},{8},{10},{12}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,3},{4},{5,6,8,10,12},{7},{9},{11}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => {{1},{2,12},{3},{4,5,7,9,11},{6},{8},{10}}
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,4,6,8,10},{5},{7},{9},{12}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,7,8,10,12},{3},{4,5},{6},{9},{11}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2,6,7,9,11},{3,4},{5},{8},{10},{12}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => {{1},{2,4,5,7,9},{3},{6},{8},{10},{11,12}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3,4,6,8},{5},{7},{9},{10,11},{12}}
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5},{6,7,9,11},{8},{10}}
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => {{1},{2,3,11},{4},{5,6,8,10},{7},{9},{12}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,3},{4},{5,12},{6,7,9,11},{8},{10}}
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3},{4,11},{5,6,8,10},{7},{9}}
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => {{1},{2,11},{3,10},{4,5,7,9},{6},{8},{12}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0] => {{1},{2,4,9,10,12},{3},{5},{6,7},{8},{11}}
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2,3,8,9,11},{4},{5,6},{7},{10},{12}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,3},{4},{5,9,10,12},{6,7},{8},{11}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3},{4,8,9,11},{5,6},{7},{10}}
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,7,8,10},{4,5},{6},{9},{12}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5},{3},{6},{7,9,10,12},{8},{11}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4},{5},{6,8,9,11},{7},{10},{12}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,6},{3},{4,5},{7},{8,9,10,12},{11}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,5},{3,4},{6},{7,8,9,11},{10},{12}}
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0] => {{1},{2,11,12},{3},{4,6,7,9},{5},{8},{10}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,0] => {{1},{2,10,11},{3,5,6,8},{4},{7},{9},{12}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6,7,9},{8},{10},{11,12}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0] => {{1},{2,12},{3},{4,5,6,8},{7},{9},{10,11}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,11},{3,4,5,7},{6},{8},{9,10},{12}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1},{2,4,6,12},{3},{5},{7},{8,9,11},{10}}
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => {{1},{2,3,5,11},{4},{6},{7,8,10},{9},{12}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,3},{4},{5,6,12},{7},{8,9,11},{10}}
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3},{4,5,11},{6},{7,8,10},{9}}
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,4,10},{5},{6,7,9},{8},{12}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,7,12},{3},{4,5},{6},{8,9,11},{10}}
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1},{2,6,11},{3,4},{5},{7,8,10},{9},{12}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0] => {{1},{2,4,9},{3},{5,6,8},{7},{10},{11,12}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3,8},{4,5,7},{6},{9},{10,11},{12}}
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5},{6,11},{7,8,10},{9}}
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => {{1},{2,3,11},{4},{5,10},{6,7,9},{8},{12}}
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,3},{4},{5,12},{6,11},{7,8,10},{9}}
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,12},{3},{4,11},{5,10},{6,7,9},{8}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2,11},{3,10},{4,9},{5,6,8},{7},{12}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => {{1},{2,4,6,11,12},{3},{5},{7},{8,9},{10}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0] => {{1},{2,3,5,10,11},{4},{6},{7,8},{9},{12}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1},{2,3},{4},{5,6,11,12},{7},{8,9},{10}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0] => {{1},{2,12},{3},{4,5,10,11},{6},{7,8},{9}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,4,9,10},{5},{6,7},{8},{12}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1},{2,7,11,12},{3},{4,5},{6},{8,9},{10}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => {{1},{2,6,10,11},{3,4},{5},{7,8},{9},{12}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,4,8,9},{3},{5,6},{7},{10},{11,12}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3,7,8},{4,5},{6},{9},{10,11},{12}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5},{6,10,11},{7,8},{9}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1},{2,3,11},{4},{5,9,10},{6,7},{8},{12}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => {{1},{2,3},{4},{5,12},{6,10,11},{7,8},{9}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3},{4,11},{5,9,10},{6,7},{8}}
[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1},{2,11},{3,10},{4,8,9},{5,6},{7},{12}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,9,11,12},{3},{4,6,7},{5},{8},{10}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,8,10,11},{3,5,6},{4},{7},{9},{12}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7},{8},{9,11,12},{10}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,12},{3},{4,5,6},{7},{8,10,11},{9}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,4,5},{6},{7,9,10},{8},{12}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0] => {{1},{2,10,11,12},{3},{4,8},{5},{6,7},{9}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,9,10,11},{3,7},{4},{5,6},{8},{12}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,8},{6,7},{9},{10,11,12}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,12},{3},{4,7},{5,6},{8},{9,10,11}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,6},{4,5},{7},{8,9,10},{12}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,6,7},{3},{5},{8},{9,11,12},{10}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,8},{3},{4,6,7},{5},{9},{10,11,12}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7},{8,10,11},{9},{12}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2,7},{3,5,6},{4},{8},{9,10,11},{12}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,4,5},{3},{6},{7,8},{9},{10,11,12}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5},{6,7},{8},{9,10,11},{12}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,4,5,6},{3},{7},{8,12},{9},{10,11}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6},{8},{9,12},{10,11}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,3,4,5},{6},{7,11},{8},{9,10},{12}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7},{8,11},{9,10},{12}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => {{1},{2,4,11,12},{3},{5},{6,8,9},{7},{10}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,10,11},{4},{5,7,8},{6},{9},{12}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1},{2,3},{4},{5,11,12},{6,8,9},{7},{10}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0] => {{1},{2,12},{3},{4,10,11},{5,7,8},{6},{9}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,9,10},{4,6,7},{5},{8},{12}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1},{2,11,12},{3},{4,5},{6},{7,8,9},{10}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => {{1},{2,10,11},{3,4},{5},{6,7,8},{9},{12}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,8,9},{3},{4,5,6},{7},{10},{11,12}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,7,8},{3,4,5},{6},{9},{10,11},{12}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5},{6,7,8},{9},{10,11}}
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,11},{4},{5,6,7},{8},{9,10},{12}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => {{1},{2,3},{4},{5,12},{6,7,8},{9},{10,11}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0] => {{1},{2,12},{3},{4,11},{5,6,7},{8},{9,10}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2,11},{3,10},{4,5,6},{7},{8,9},{12}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => {{1},{2,4,6,8,12},{3},{5},{7},{9},{10,11}}
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => {{1},{2,3,5,7,11},{4},{6},{8},{9,10},{12}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => {{1},{2,3},{4},{5,6,8,12},{7},{9},{10,11}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3},{4,5,7,11},{6},{8},{9,10}}
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,4,6,10},{5},{7},{8,9},{12}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1},{2,7,8,12},{3},{4,5},{6},{9},{10,11}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => {{1},{2,6,7,11},{3,4},{5},{8},{9,10},{12}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0] => {{1},{2,4,5,9},{3},{6},{7,8},{10},{11,12}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3,4,8},{5},{6,7},{9},{10,11},{12}}
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5},{6,7,11},{8},{9,10}}
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0] => {{1},{2,3,11},{4},{5,6,10},{7},{8,9},{12}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2,3},{4},{5,12},{6,7,11},{8},{9,10}}
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3},{4,11},{5,6,10},{7},{8,9}}
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1},{2,11},{3,10},{4,5,9},{6},{7,8},{12}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0] => {{1},{2,4,9,12},{3},{5},{6,7},{8},{10,11}}
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => {{1},{2,3,8,11},{4},{5,6},{7},{9,10},{12}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,3},{4},{5,9,12},{6,7},{8},{10,11}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3},{4,8,11},{5,6},{7},{9,10}}
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,7,10},{4,5},{6},{8,9},{12}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,5},{3},{6},{7,9,12},{8},{10,11}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,4},{5},{6,8,11},{7},{9,10},{12}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,6},{3},{4,5},{7},{8,9,12},{10,11}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,5},{3,4},{6},{7,8,11},{9,10},{12}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => {{1},{2,11,12},{3},{4,6,9},{5},{7,8},{10}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0,1,0] => {{1},{2,10,11},{3,5,8},{4},{6,7},{9},{12}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6,9},{7,8},{10},{11,12}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0] => {{1},{2,12},{3},{4,5,8},{6,7},{9},{10,11}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,11},{3,4,7},{5,6},{8},{9,10},{12}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0] => {{1},{2,4,6,12},{3},{5},{7},{8,11},{9,10}}
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => {{1},{2,3,5,11},{4},{6},{7,10},{8,9},{12}}
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2,3},{4},{5,6,12},{7},{8,11},{9,10}}
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3},{4,5,11},{6},{7,10},{8,9}}
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,4,10},{5},{6,9},{7,8},{12}}
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2,7,12},{3},{4,5},{6},{8,11},{9,10}}
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => {{1},{2,6,11},{3,4},{5},{7,10},{8,9},{12}}
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0] => {{1},{2,4,9},{3},{5,8},{6,7},{10},{11,12}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3,8},{4,7},{5,6},{9},{10,11},{12}}
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5},{6,11},{7,10},{8,9}}
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1},{2,3,11},{4},{5,10},{6,9},{7,8},{12}}
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,3},{4},{5,12},{6,11},{7,10},{8,9}}
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,12},{3},{4,11},{5,10},{6,9},{7,8}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2,11},{3,10},{4,9},{5,8},{6,7},{12}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10},{11},{12}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,5,12},{2,4},{3},{6,9,11},{7,8},{10}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,8,11,12},{2},{3,6,7},{4},{5},{9},{10}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => {{1},{2},{3,4},{5,6,12},{7},{8},{9,10},{11}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,8},{3},{4},{5,6},{7},{9,10},{11},{12}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,12},{2,6},{3,4},{5},{7,11},{8,9},{10}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0,1,0] => {{1,3,5,7,8},{2},{4},{6},{9,11},{10},{12}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => {{1,3,5,7,8},{2},{4},{6},{9},{10,12},{11}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => {{1},{2,9,11},{3,5,7,8},{4},{6},{10},{12}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => {{1},{2,9},{3,5,7,8},{4},{6},{10,12},{11}}
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,6,8,9},{5},{7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3},{2},{4,6,7},{5},{8,12},{9,11},{10}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,6,7},{5},{8,10,12},{9},{11}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => {{1},{2,4,9,11},{3},{5,7,8},{6},{10},{12}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2},{3,12},{4,9,11},{5,7,8},{6},{10}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,4,9},{3},{5,7,8},{6},{10,12},{11}}
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,5,10},{4},{6,8,9},{7}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2},{3,10,12},{4,9},{5,7,8},{6},{11}}
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2,4,11},{3},{5,10},{6,8,9},{7}}
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0] => {{1,3,12},{2},{4,11},{5,10},{6,8,9},{7}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6,7},{3,5},{4},{8,12},{9,11},{10}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,6,7},{3,5},{4},{8,10,12},{9},{11}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2,9,11},{3,7,8},{4,6},{5},{10}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2,9},{3,7,8},{4,6},{5},{11}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => {{1,10},{2,9},{3,7,8},{4,6},{5},{11},{12}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3},{2},{4},{5,8,12},{6,7},{9,11},{10}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4},{5,8,10,12},{6,7},{9},{11}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,4},{3},{5,8,12},{6,7},{9,11},{10}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,4},{3},{5,8,10,12},{6,7},{9},{11}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2,4,6,9,11},{3},{5},{7,8},{10},{12}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2},{3,12},{4,6,9,11},{5},{7,8},{10}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2,6,9,11},{3,5},{4},{7,8},{10}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2},{3,5,12},{4},{6,9,11},{7,8},{10}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => {{1},{2,4,6,9},{3},{5},{7,8},{10,12},{11}}
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,5,7,10},{4},{6},{8,9}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2},{3,10,12},{4,6,9},{5},{7,8},{11}}
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0] => {{1,12},{2,4,11},{3},{5,7,10},{6},{8,9}}
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0] => {{1,3,12},{2},{4,11},{5,7,10},{6},{8,9}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2,6,9},{3,5},{4},{7,8},{11}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0] => {{1,10},{2,6,9},{3,5},{4},{7,8},{11},{12}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2},{3,5,10,12},{4},{6,9},{7,8},{11}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,5,10,12},{2,4},{3},{6,9},{7,8},{11}}
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0] => {{1,12},{2,4,6,11},{3},{5},{7,10},{8,9}}
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0] => {{1,3,12},{2},{4,6,11},{5},{7,10},{8,9}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0] => {{1,5,10},{2,4},{3},{6,9},{7,8},{11},{12}}
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0] => {{1,3,5,12},{2},{4},{6,11},{7,10},{8,9}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,3},{2},{4,11},{5,10},{6,9},{7,8},{12}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,4,5,7},{3},{6},{8,12},{9,11},{10}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,5,7},{3},{6},{8,10,12},{9},{11}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2,9,11},{3,5,6,8},{4},{7},{10}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2,9},{3,5,6,8},{4},{7},{11}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0] => {{1,10},{2,9},{3,5,6,8},{4},{7},{11},{12}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2},{3,8,12},{4,5,7},{6},{9,11},{10}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2},{3,8,10,12},{4,5,7},{6},{9},{11}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2,4,9,11},{3},{5,6,8},{7},{10}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,3,12},{2},{4,9,11},{5,6,8},{7},{10}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2,4,9},{3},{5,6,8},{7},{11}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0] => {{1,10},{2,4,9},{3},{5,6,8},{7},{11},{12}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,3,10,12},{2},{4,9},{5,6,8},{7},{11}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0] => {{1,3,10},{2},{4,9},{5,6,8},{7},{11},{12}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,8,12},{2,3,7},{4,6},{5},{9,11},{10}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,8,10,12},{2,3,7},{4,6},{5},{9},{11}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,8,10},{2,3,7},{4,6},{5},{9},{11},{12}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,8},{2,3,7},{4,6},{5},{9,11},{10},{12}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,8},{2,3,7},{4,6},{5},{9},{10,12},{11}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,8,12},{2,3,5,7},{4},{6},{9,11},{10}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,8,10,12},{2,3,5,7},{4},{6},{9},{11}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,8,10},{2,3,5,7},{4},{6},{9},{11},{12}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,8},{2,3,5,7},{4},{6},{9,11},{10},{12}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,8},{2,3,5,7},{4},{6},{9},{10,12},{11}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,3},{2},{4},{5,7,8,12},{6},{9,11},{10}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,3},{2},{4},{5,7,8,10,12},{6},{9},{11}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,4},{3},{5,7,8,12},{6},{9,11},{10}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,4},{3},{5,7,8,10,12},{6},{9},{11}}
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2},{3,7,8,12},{4,6},{5},{9,11},{10}}
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2},{3,7,8,10,12},{4,6},{5},{9},{11}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,7,8,12},{2,6},{3,5},{4},{9,11},{10}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,7,8,10,12},{2,6},{3,5},{4},{9},{11}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,7,8,12},{2,4,6},{3},{5},{9,11},{10}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,7,8,10,12},{2,4,6},{3},{5},{9},{11}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1},{2,4,6,8,9,11},{3},{5},{7},{10},{12}}
[1,0,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1},{2},{3,12},{4,6,8,9,11},{5},{7},{10}}
[1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,12},{2,6,8,9,11},{3,5},{4},{7},{10}}
[1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => {{1},{2},{3,5,12},{4},{6,8,9,11},{7},{10}}
[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => {{1,5,12},{2,4},{3},{6,8,9,11},{7},{10}}
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,12},{2,4,8,9,11},{3},{5,7},{6},{10}}
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => {{1,3,12},{2},{4,8,9,11},{5,7},{6},{10}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,7,8,10},{2,6},{3,5},{4},{9},{11},{12}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,7,8,10},{2,4,6},{3},{5},{9},{11},{12}}
[1,0,1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1},{2},{3,5,7,12},{4},{6},{8,9,11},{10}}
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1,5,7,12},{2,4},{3},{6},{8,9,11},{10}}
[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1,3,7,12},{2},{4,6},{5},{8,9,11},{10}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6,11},{7,8,10},{9},{12}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,3,5},{2},{4},{6,11},{7,8,10},{9},{12}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0] => {{1},{2,4,6,8,9},{3},{5},{7},{10,12},{11}}
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,5,7,9,10},{4},{6},{8}}
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1},{2},{3,10,12},{4,6,8,9},{5},{7},{11}}
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0] => {{1,12},{2,4,11},{3},{5,7,9,10},{6},{8}}
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0] => {{1,3,12},{2},{4,11},{5,7,9,10},{6},{8}}
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2,6,8,9},{3,5},{4},{7},{11}}
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => {{1,10},{2,6,8,9},{3,5},{4},{7},{11},{12}}
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => {{1},{2},{3,5,10,12},{4},{6,8,9},{7},{11}}
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => {{1,5,10,12},{2,4},{3},{6,8,9},{7},{11}}
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0] => {{1,12},{2,4,6,11},{3},{5},{7,9,10},{8}}
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] => {{1,3,12},{2},{4,6,11},{5},{7,9,10},{8}}
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => {{1,5,10},{2,4},{3},{6,8,9},{7},{11},{12}}
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0] => {{1,3,5,12},{2},{4},{6,11},{7,9,10},{8}}
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,3},{2},{4,11},{5,10},{6,8,9},{7},{12}}
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2,4,8,9},{3},{5,7},{6},{11}}
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => {{1,10},{2,4,8,9},{3},{5,7},{6},{11},{12}}
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => {{1,3,10,12},{2},{4,8,9},{5,7},{6},{11}}
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => {{1,3,10},{2},{4,8,9},{5,7},{6},{11},{12}}
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1},{2,11},{3,10},{4,8,9},{5,7},{6},{12}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,7,8},{2,6},{3,5},{4},{9,11},{10},{12}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,7,8},{2,6},{3,5},{4},{9},{10,12},{11}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,7,8},{2,4,6},{3},{5},{9,11},{10},{12}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,7,8},{2,4,6},{3},{5},{9},{10,12},{11}}
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1},{2},{3,5,7,10,12},{4},{6},{8,9},{11}}
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,5,7,10,12},{2,4},{3},{6},{8,9},{11}}
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,3,7,10,12},{2},{4,6},{5},{8,9},{11}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,5},{2,4},{3},{6,9,11},{7,8},{10},{12}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6,9,11},{7,8},{10},{12}}
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => {{1,12},{2,4,6,8,11},{3},{5},{7},{9,10}}
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => {{1,3,12},{2},{4,6,8,11},{5},{7},{9,10}}
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => {{1,5,7,10},{2,4},{3},{6},{8,9},{11},{12}}
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => {{1,3,5,12},{2},{4},{6,8,11},{7},{9,10}}
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,3},{2},{4,11},{5,7,10},{6},{8,9},{12}}
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => {{1,3,7,10},{2},{4,6},{5},{8,9},{11},{12}}
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => {{1},{2,11},{3,7,10},{4,6},{5},{8,9},{12}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,4},{3},{6,9},{7,8},{10,12},{11}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,3,5},{2},{4},{6,9},{7,8},{10,12},{11}}
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => {{1,3,5,7,12},{2},{4},{6},{8,11},{9,10}}
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,3},{2},{4,6,11},{5},{7,10},{8,9},{12}}
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => {{1},{2,6,11},{3,5},{4},{7,10},{8,9},{12}}
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4},{5,12},{6,11},{7,10},{8,9}}
[1,0,1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,4},{3},{5,12},{6,11},{7,10},{8,9}}
[1,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0,0] => {{1,3,4,6,12},{2},{5},{7,8},{9,10},{11}}
[1,1,0,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,3,12},{2},{4,8,9,10,11},{5},{6,7}}
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,0] => {{1,3,4,6,12},{2},{5},{7,8},{9},{10,11}}
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,3,4,8,10,11,12},{2},{5},{6,7},{9}}
[1,1,0,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => {{1,3,12},{2},{4,5},{6,7,11},{8,10},{9}}
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => {{1,3,6,10,12},{2},{4,5},{7,8,9},{11}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,0] => {{1,3,12},{2},{4,9,10,11},{5},{6,8},{7}}
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => {{1,3,12},{2},{4,5},{6,7,9,11},{8},{10}}
[1,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,0] => {{1,3,4,11,12},{2},{5},{6,10},{7,8,9}}
[1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => {{1,3,4,6,11,12},{2},{5},{7},{8,9},{10}}
[1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => {{1,3,6,11,12},{2},{4,5},{7,8,9,10}}
[1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,3,4,6,11,12},{2},{5},{7},{8},{9,10}}
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,3,6,7,9,12},{2},{4,5},{8},{10,11}}
[1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => {{1,3,12},{2},{4},{5,8,11},{6},{7},{9,10}}
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,3,5,10,12},{2},{4},{6},{7},{8,9},{11}}
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,3,12},{2},{4},{5,7},{6},{8,9,10,11}}
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,3,5,11,12},{2},{4},{6},{7},{8,10},{9}}
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,3,8,9,11,12},{2},{4},{5,7},{6},{10}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,3,12},{2},{4,5,6},{7,10,11},{8},{9}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => {{1,3,10,11,12},{2},{4,5,6},{7,9},{8}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,3,12},{2},{4},{5,10,11},{6,7},{8},{9}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => {{1,3,10,11,12},{2},{4},{5,9},{6,7},{8}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,3,12},{2},{4,5,8},{6,7},{9,11},{10}}
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,3,12},{2},{4,11},{5,6},{7,9},{8},{10}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,3,12},{2},{4},{5,6,7,8},{9,11},{10}}
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,3,12},{2},{4,11},{5,7},{6},{8,9},{10}}
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,0] => {{1,3,12},{2},{4},{5,11},{6,8,9},{7},{10}}
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4,5,10},{6,8,9},{7}}
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => {{1,3,4,12},{2},{5,11},{6,7},{8,9},{10}}
[1,1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4,7,8,9,10},{5,6}}
[1,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,0] => {{1,3,4,12},{2},{5,11},{6,7},{8},{9,10}}
[1,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,3,4,12},{2},{5,6},{7,9,10,11},{8}}
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4},{5,6,10},{7,9},{8}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,0] => {{1,3,5,12},{2},{4},{6,7,8},{9,11},{10}}
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4,8,9,10},{5,7},{6}}
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4},{5,6,8,10},{7},{9}}
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0] => {{1,3,4,12},{2},{5,9},{6,7,8},{10,11}}
[1,1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,0] => {{1,3,4,12},{2},{5,10,11},{6},{7,8},{9}}
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0] => {{1,3,5,12},{2},{4},{6,7,8,9},{10,11}}
[1,1,0,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,0] => {{1,3,4,12},{2},{5,10,11},{6},{7},{8,9}}
[1,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => {{1,5,12},{2,3},{4},{6,8,11},{7},{9,10}}
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,5,6,10,12},{2,3},{4},{7},{8,9},{11}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,5,12},{2,3},{4},{6,7},{8,9,10,11}}
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,5,6,11,12},{2,3},{4},{7},{8,10},{9}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,5,8,9,11,12},{2,3},{4},{6,7},{10}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,5,12},{2,3},{4},{6},{7,10,11},{8},{9}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => {{1,5,10,11,12},{2,3},{4},{6},{7,9},{8}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,5,12},{2,3},{4},{6,7,8},{9,11},{10}}
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,5,12},{2,3},{4},{6},{7,11},{8,9},{10}}
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0] => {{1,5,11,12},{2,3},{4},{6,7,10},{8,9}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0] => {{1,5,6,12},{2,3},{4},{7,8},{9,11},{10}}
[1,1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,5,11,12},{2,3},{4},{6},{7,8,9,10}}
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0] => {{1,5,6,12},{2,3},{4},{7,9},{8},{10,11}}
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => {{1,5,7,12},{2,3},{4},{6},{8,10,11},{9}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,7,12},{2,5},{3,4},{6},{8,10,11},{9}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,7,10,11,12},{2,5},{3,4},{6},{8,9}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,7,12},{2,5},{3,4},{6},{8},{9,11},{10}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,7,11,12},{2,5},{3,4},{6},{8,9,10}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,7,9,12},{2,5},{3,4},{6},{8},{10,11}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,7,12},{2,4,5},{3},{6},{8,10,11},{9}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,7,10,11,12},{2,4,5},{3},{6},{8,9}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,7,12},{2,4,5},{3},{6},{8},{9,11},{10}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,7,11,12},{2,4,5},{3},{6},{8,9,10}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,7,9,12},{2,4,5},{3},{6},{8},{10,11}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,9,12},{2,7},{3,5,6},{4},{8},{10,11}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,7},{3,5,6},{4},{8},{10}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,9,12},{2,5,6,7},{3,4},{8},{10,11}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,5,6,7},{3,4},{8},{10}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,9,12},{2,7},{3},{4,6},{5},{8},{10,11}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,7},{3},{4,6},{5},{8},{10}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,9,12},{2,6,7},{3,4,5},{8},{10,11}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,6,7},{3,4,5},{8},{10}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,9,12},{2,4,7},{3},{5,6},{8},{10,11}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,4,7},{3},{5,6},{8},{10}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,9},{3,5,8},{4},{6,7},{10}}
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,3,7,9},{4},{5,6},{8},{10}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,9},{3,4},{5,6,7,8},{10}}
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,3,8,9},{4},{5,7},{6},{10}}
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,5,6,8,9},{3,4},{7},{10}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,9},{3},{4,7,8},{5},{6},{10}}
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,7,8,9},{3},{4,6},{5},{10}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,9},{3,4,5},{6,8},{7},{10}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,9},{3},{4,8},{5,6},{7},{10}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,8,9},{3,4,7},{5,6},{10}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,3,9},{4,5},{6,8},{7},{10}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,8,9},{3},{4,5,6,7},{10}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,3,9},{4,6},{5},{7,8},{10}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,4,9},{3},{5,7,8},{6},{10}}
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2,3,5,11},{4},{6,7},{8,9},{10}}
[1,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,7,8,9,10},{4},{5,6}}
[1,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => {{1,12},{2,3,5,11},{4},{6,7},{8},{9,10}}
[1,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,12},{2,3,7,9,10,11},{4},{5,6},{8}}
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,6,10},{7,9},{8}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2,5,9,11},{3,4},{6,7,8},{10}}
[1,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,8,9,10},{4},{5,7},{6}}
[1,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,6,8,10},{7},{9}}
[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,1,0,0] => {{1,12},{2,3,10,11},{4},{5,9},{6,7,8}}
[1,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,0] => {{1,12},{2,3,5,10,11},{4},{6},{7,8},{9}}
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,0,0] => {{1,12},{2,5,10,11},{3,4},{6,7,8,9}}
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => {{1,12},{2,3,5,10,11},{4},{6},{7},{8,9}}
[1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => {{1,12},{2,5,6,8,11},{3,4},{7},{9,10}}
[1,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3},{4,7,10},{5},{6},{8,9}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2,4,9,11},{3},{5},{6},{7,8},{10}}
[1,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3},{4,6},{5},{7,8,9,10}}
[1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0] => {{1,12},{2,4,10,11},{3},{5},{6},{7,9},{8}}
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => {{1,12},{2,7,8,10,11},{3},{4,6},{5},{9}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4,5},{6,9,10},{7},{8}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => {{1,12},{2,9,10,11},{3,4,5},{6,8},{7}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3},{4,9,10},{5,6},{7},{8}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => {{1,12},{2,9,10,11},{3},{4,8},{5,6},{7}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4,7},{5,6},{8,10},{9}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,5},{6,8},{7},{9}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3},{4,5,6,7},{8,10},{9}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,10},{4,6},{5},{7,8},{9}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3},{4,10},{5,7,8},{6},{9}}
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0] => {{1,12},{2,10,11},{3,4,9},{5,7,8},{6}}
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2,3,11},{4,10},{5,6},{7,8},{9}}
[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0,0] => {{1,12},{2,10,11},{3,6,7,8,9},{4,5}}
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2,3,11},{4,10},{5,6},{7},{8,9}}
[1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => {{1,12},{2,3,11},{4,5},{6,8,9,10},{7}}
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0] => {{1,12},{2,10,11},{3},{4,5,9},{6,8},{7}}
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2,4,11},{3},{5,6,7},{8,10},{9}}
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0] => {{1,12},{2,10,11},{3,7,8,9},{4,6},{5}}
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0,0] => {{1,12},{2,10,11},{3},{4,5,7,9},{6},{8}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2,3,11},{4,8},{5,6,7},{9,10}}
[1,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => {{1,12},{2,3,11},{4,9,10},{5},{6,7},{8}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2,4,11},{3},{5,6,7,8},{9,10}}
[1,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0] => {{1,12},{2,3,11},{4,9,10},{5},{6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,11,12},{10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,9,10},{8},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,4},{5,6},{7,11,12},{8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4},{5,6},{7,9,11,12},{8},{10}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,7,8},{6},{9,10},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,4},{5,7,8},{6},{9,11,12},{10}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4},{5,9,10},{6},{7,8},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4},{5,7,9,10},{6},{8},{11,12}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,4},{5,11,12},{6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4},{5,9,11,12},{6},{7,8},{10}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,2},{3,4},{5,11,12},{6},{7,9,10},{8}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2},{3,4},{5,7,11,12},{6},{8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2},{3,4},{5,7,9,11,12},{6},{8},{10}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,5,6},{4},{7,8},{9,10},{11,12}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4},{7,8},{9,11,12},{10}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,5,6},{4},{7,9,10},{8},{11,12}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,5,6},{4},{7,11,12},{8},{9,10}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,5,6},{4},{7,9,11,12},{8},{10}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,7,8},{4},{5,6},{9,10},{11,12}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,7,8},{4},{5,6},{9,11,12},{10}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,5,7,8},{4},{6},{9,10},{11,12}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,7,8},{4},{6},{9,11,12},{10}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,9,10},{4},{5,6},{7,8},{11,12}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,7,9,10},{4},{5,6},{8},{11,12}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,9,10},{4},{5,7,8},{6},{11,12}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,5,9,10},{4},{6},{7,8},{11,12}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => {{1,2},{3,5,7,9,10},{4},{6},{8},{11,12}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,11,12},{4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,9,11,12},{4},{5,6},{7,8},{10}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,2},{3,11,12},{4},{5,6},{7,9,10},{8}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2},{3,7,11,12},{4},{5,6},{8},{9,10}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2},{3,7,9,11,12},{4},{5,6},{8},{10}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,11,12},{4},{5,7,8},{6},{9,10}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,9,11,12},{4},{5,7,8},{6},{10}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,2},{3,11,12},{4},{5,9,10},{6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => {{1,2},{3,11,12},{4},{5,7,9,10},{6},{8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,2},{3,5,11,12},{4},{6},{7,8},{9,10}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,2},{3,5,9,11,12},{4},{6},{7,8},{10}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,2},{3,5,11,12},{4},{6},{7,9,10},{8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,2},{3,5,7,11,12},{4},{6},{8},{9,10}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,2},{3,5,7,9,11,12},{4},{6},{8},{10}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,3,4},{2},{5,6},{7,8},{9,10},{11,12}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,3,4},{2},{5,6},{7,8},{9,11,12},{10}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6},{7,9,10},{8},{11,12}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,3,4},{2},{5,6},{7,11,12},{8},{9,10}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,4},{2},{5,6},{7,9,11,12},{8},{10}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,3,4},{2},{5,7,8},{6},{9,10},{11,12}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,3,4},{2},{5,7,8},{6},{9,11,12},{10}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,9,10},{6},{7,8},{11,12}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,7,9,10},{6},{8},{11,12}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,3,4},{2},{5,11,12},{6},{7,8},{9,10}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,3,4},{2},{5,9,11,12},{6},{7,8},{10}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,3,4},{2},{5,11,12},{6},{7,9,10},{8}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,3,4},{2},{5,7,11,12},{6},{8},{9,10}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,3,4},{2},{5,7,9,11,12},{6},{8},{10}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,5,6},{2},{3,4},{7,8},{9,10},{11,12}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,5,6},{2},{3,4},{7,8},{9,11,12},{10}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2},{3,4},{7,9,10},{8},{11,12}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4},{7,11,12},{8},{9,10}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,6},{2},{3,4},{7,9,11,12},{8},{10}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,3,5,6},{2},{4},{7,8},{9,10},{11,12}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,3,5,6},{2},{4},{7,8},{9,11,12},{10}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,5,6},{2},{4},{7,9,10},{8},{11,12}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,3,5,6},{2},{4},{7,11,12},{8},{9,10}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4},{7,9,11,12},{8},{10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,7,8},{2},{3,4},{5,6},{9,10},{11,12}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,4},{5,6},{9,11,12},{10}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,5,7,8},{2},{3,4},{6},{9,10},{11,12}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => {{1,5,7,8},{2},{3,4},{6},{9,11,12},{10}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,7,8},{2},{3,5,6},{4},{9,10},{11,12}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,5,6},{4},{9,11,12},{10}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,3,7,8},{2},{4},{5,6},{9,10},{11,12}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => {{1,3,7,8},{2},{4},{5,6},{9,11,12},{10}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,3,5,7,8},{2},{4},{6},{9,10},{11,12}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0] => {{1,3,5,7,8},{2},{4},{6},{9,11,12},{10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,9,10},{2},{3,4},{5,6},{7,8},{11,12}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,7,9,10},{2},{3,4},{5,6},{8},{11,12}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => {{1,9,10},{2},{3,4},{5,7,8},{6},{11,12}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => {{1,5,9,10},{2},{3,4},{6},{7,8},{11,12}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => {{1,5,7,9,10},{2},{3,4},{6},{8},{11,12}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,9,10},{2},{3,5,6},{4},{7,8},{11,12}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,7,9,10},{2},{3,5,6},{4},{8},{11,12}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => {{1,9,10},{2},{3,7,8},{4},{5,6},{11,12}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0] => {{1,9,10},{2},{3,5,7,8},{4},{6},{11,12}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => {{1,3,9,10},{2},{4},{5,6},{7,8},{11,12}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => {{1,3,7,9,10},{2},{4},{5,6},{8},{11,12}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => {{1,3,9,10},{2},{4},{5,7,8},{6},{11,12}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0] => {{1,3,5,9,10},{2},{4},{6},{7,8},{11,12}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,3,5,7,9,10},{2},{4},{6},{8},{11,12}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2},{3,4},{5,6},{7,8},{10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,4},{5,6},{7,9,10},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,7,11,12},{2},{3,4},{5,6},{8},{9,10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,7,9,11,12},{2},{3,4},{5,6},{8},{10}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,4},{5,7,8},{6},{9,10}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2},{3,4},{5,7,8},{6},{10}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,4},{5,9,10},{6},{7,8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,4},{5,7,9,10},{6},{8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,5,11,12},{2},{3,4},{6},{7,8},{9,10}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,5,9,11,12},{2},{3,4},{6},{7,8},{10}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,5,11,12},{2},{3,4},{6},{7,9,10},{8}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,5,7,11,12},{2},{3,4},{6},{8},{9,10}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,5,7,9,11,12},{2},{3,4},{6},{8},{10}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,5,6},{4},{7,8},{9,10}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2},{3,5,6},{4},{7,8},{10}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,5,6},{4},{7,9,10},{8}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,7,11,12},{2},{3,5,6},{4},{8},{9,10}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,7,9,11,12},{2},{3,5,6},{4},{8},{10}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,7,8},{4},{5,6},{9,10}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2},{3,7,8},{4},{5,6},{10}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,5,7,8},{4},{6},{9,10}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2},{3,5,7,8},{4},{6},{10}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,9,10},{4},{5,6},{7,8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,7,9,10},{4},{5,6},{8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,9,10},{4},{5,7,8},{6}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,5,9,10},{4},{6},{7,8}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,5,7,9,10},{4},{6},{8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4},{5,6},{7,8},{9,10}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,3,9,11,12},{2},{4},{5,6},{7,8},{10}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4},{5,6},{7,9,10},{8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,3,7,11,12},{2},{4},{5,6},{8},{9,10}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,3,7,9,11,12},{2},{4},{5,6},{8},{10}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4},{5,7,8},{6},{9,10}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,3,9,11,12},{2},{4},{5,7,8},{6},{10}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4},{5,9,10},{6},{7,8}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4},{5,7,9,10},{6},{8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,3,5,11,12},{2},{4},{6},{7,8},{9,10}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,3,5,9,11,12},{2},{4},{6},{7,8},{10}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0] => {{1,3,5,11,12},{2},{4},{6},{7,9,10},{8}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,3,5,7,11,12},{2},{4},{6},{8},{9,10}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,3,5,7,9,11,12},{2},{4},{6},{8},{10}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10},{11},{12}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => {{1,2},{3,5,7,9,12},{4},{6},{8},{10},{11}}
[1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2},{3,5,7,12},{4},{6},{8,11},{9},{10}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => {{1,2},{3,5,6,12},{4},{7},{8},{9,10},{11}}
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2},{3,5,12},{4},{6,8,11},{7},{9},{10}}
[1,1,0,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0] => {{1,2},{3,5,12},{4},{6,11},{7,10},{8},{9}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,9,12},{5},{6},{7,8},{10},{11}}
[1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,2},{3,4,12},{5},{6},{7,11},{8,9},{10}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0] => {{1,2},{3,4,12},{5},{6,9,10},{7},{8},{11}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0] => {{1,2},{3,4,12},{5,8},{6},{7},{9,10},{11}}
[1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0] => {{1,2},{3,12},{4,6,8,11},{5},{7},{9},{10}}
[1,1,0,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,2},{3,12},{4,6,11},{5},{7,10},{8},{9}}
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0] => {{1,2},{3,12},{4,5,11},{6},{7},{8,9},{10}}
[1,1,0,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,7,10},{6},{8},{9}}
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,10},{6,9},{7},{8}}
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,7,9,12},{2,3},{4},{5,6},{8},{10},{11}}
[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,7,12},{2,3},{4},{5,6},{8,11},{9},{10}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,5,12},{2,3},{4},{6,7},{8},{9,10},{11}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,12},{2,3},{4},{5,8,11},{6,7},{9},{10}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4},{5,11},{6,10},{7,8},{9}}
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => {{1,9,12},{2,3},{4,7,8},{5},{6},{10},{11}}
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5},{6},{7,8,9},{10}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,9,12},{2,6},{3,4},{5},{7,8},{10},{11}}
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => {{1,12},{2,3},{4,6,9,10},{5},{7},{8},{11}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0] => {{1,12},{2,3},{4,9,10},{5,8},{6},{7},{11}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,12},{2,9,10},{3,4},{5},{6,7},{8},{11}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0,0] => {{1,12},{2,5,8},{3,4},{6},{7},{9,10},{11}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,12},{2,8},{3,7},{4,5},{6},{9,10},{11}}
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,4,6,8,11},{2,3},{5},{7},{9},{10},{12}}
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,4,6,11},{2,3},{5},{7,10},{8},{9},{12}}
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0] => {{1,4,5,11},{2,3},{6},{7},{8,9},{10},{12}}
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,4,11},{2,3},{5,7,10},{6},{8},{9},{12}}
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,4,11},{2,3},{5,10},{6,9},{7},{8},{12}}
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,8,11},{3,4},{5},{6,7},{9},{10},{12}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,11},{3,4},{5},{6,10},{7,8},{9},{12}}
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0] => {{1,2,11},{3,4},{5,8,9},{6},{7},{10},{12}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,11},{3,7},{4,5},{6},{8,9},{10},{12}}
[1,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,11},{2,5,7,10},{3,4},{6},{8},{9},{12}}
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,5,10},{3,4},{6,9},{7},{8},{12}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,3,10},{4,5},{6},{7,8},{9},{12}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,6,9},{4,5},{7},{8},{12}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,9},{4,8},{5,6},{7},{12}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1},{2},{3,4},{5,7,9,12},{6},{8},{10},{11}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1},{2},{3,4},{5,7,12},{6},{8,11},{9},{10}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => {{1},{2},{3,4},{5,12},{6,8,11},{7},{9},{10}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2},{3,4},{5,12},{6,11},{7,10},{8},{9}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,9,12},{4,5},{6},{7,8},{10},{11}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1},{2},{3,12},{4,5},{6},{7,11},{8,9},{10}}
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => {{1},{2},{3,12},{4,5},{6,9,10},{7},{8},{11}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,12},{4,8},{5,6},{7},{9,10},{11}}
[1,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => {{1},{2},{3,6,8,11},{4,5},{7},{9},{10},{12}}
[1,0,1,0,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => {{1},{2},{3,6,11},{4,5},{7,10},{8},{9},{12}}
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,11},{5,6},{7},{8,9},{10},{12}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => {{1},{2},{3,11},{4,7,10},{5,6},{8},{9},{12}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2},{3,11},{4,10},{5,9},{6,7},{8},{12}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,5,6},{3},{4},{7,9,12},{8},{10},{11}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,5,6},{3},{4},{7,12},{8,11},{9},{10}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,12},{3},{4},{5,6,7},{8},{9,10},{11}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,8,11},{3},{4},{5,6,7},{9},{10},{12}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0] => {{1},{2,11},{3},{4},{5,10},{6,7,8},{9},{12}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1,4},{2},{3},{5,6},{7,9,12},{8},{10},{11}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1,4},{2},{3},{5,6},{7,12},{8,11},{9},{10}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,4},{2},{3},{5,12},{6,7},{8},{9,10},{11}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,4},{2},{3},{5,8,11},{6,7},{9},{10},{12}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => {{1,4},{2},{3},{5,11},{6,10},{7,8},{9},{12}}
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => {{1},{2,4,7,8},{3},{5},{6},{9,12},{10},{11}}
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => {{1},{2,11},{3},{4,7,8,9},{5},{6},{10},{12}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1},{2,7,8},{3,6},{4},{5},{9,12},{10},{11}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1},{2,11},{3,6},{4},{5},{7,8,9},{10},{12}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,7,8},{2},{3},{4,5},{6},{9,12},{10},{11}}
[1,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,11},{2},{3},{4,5},{6},{7,8,9},{10},{12}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1,3,6},{2},{4},{5},{7,8},{9,12},{10},{11}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1,3,6},{2},{4},{5},{7,11},{8,9},{10},{12}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1,6},{2,5},{3},{4},{7,8},{9,12},{10},{11}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7,11},{8,9},{10},{12}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,4,6,9,10},{3},{5},{7},{8},{11},{12}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0,1,0] => {{1},{2,4,9,10},{3},{5,8},{6},{7},{11},{12}}
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,9,10},{4},{5},{6,7},{8},{11},{12}}
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0] => {{1},{2,9,10},{3,5,8},{4},{6},{7},{11},{12}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,0] => {{1},{2,9,10},{3,8},{4,7},{5},{6},{11},{12}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,6,9,10},{2},{3},{4,5},{7},{8},{11},{12}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,9,10},{2},{3},{4,8},{5,6},{7},{11},{12}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,9,10},{2},{3,6,7},{4},{5},{8},{11},{12}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,9,10},{2,5},{3},{4},{6,7},{8},{11},{12}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,3,5,8},{2},{4},{6},{7},{9,10},{11},{12}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,3,8},{2},{4,7},{5},{6},{9,10},{11},{12}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,8},{2,4,7},{3},{5},{6},{9,10},{11},{12}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,8},{2,7},{3,6},{4},{5},{9,10},{11},{12}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => {{1},{2,4,6,8,11,12},{3},{5},{7},{9},{10}}
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => {{1},{2,4,6,11,12},{3},{5},{7,10},{8},{9}}
[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => {{1},{2,4,5,11,12},{3},{6},{7},{8,9},{10}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,0] => {{1},{2,4,11,12},{3},{5,7,10},{6},{8},{9}}
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0] => {{1},{2,4,11,12},{3},{5,10},{6,9},{7},{8}}
[1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,8,11,12},{4},{5},{6,7},{9},{10}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0] => {{1},{2,3,11,12},{4},{5},{6,10},{7,8},{9}}
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => {{1},{2,3,11,12},{4},{5,8,9},{6},{7},{10}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1},{2,3,11,12},{4,7},{5},{6},{8,9},{10}}
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0] => {{1},{2,11,12},{3,5,7,10},{4},{6},{8},{9}}
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => {{1},{2,11,12},{3,5,10},{4},{6,9},{7},{8}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => {{1},{2,11,12},{3,4,10},{5},{6},{7,8},{9}}
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => {{1},{2,11,12},{3,10},{4,6,9},{5},{7},{8}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => {{1},{2,11,12},{3,10},{4,9},{5,8},{6},{7}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,6,8,11,12},{2},{3},{4,5},{7},{9},{10}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => {{1,6,11,12},{2},{3},{4,5},{7,10},{8},{9}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,4,11,12},{2},{3},{5,6},{7},{8,9},{10}}
[1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3},{4,7,10},{5,6},{8},{9}}
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => {{1,11,12},{2},{3},{4,10},{5,9},{6,7},{8}}
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,10},{4},{5},{6,7,8},{9}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,8,11,12},{2,5},{3},{4},{6,7},{9},{10}}
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => {{1,11,12},{2,5},{3},{4},{6,10},{7,8},{9}}
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2},{3,5,8,9},{4},{6},{7},{10}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2},{3,8,9},{4,7},{5},{6},{10}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,8,9},{3},{4},{5,6},{7},{10}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,4,7},{3},{5},{6},{8,9},{10}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,7},{3,6},{4},{5},{8,9},{10}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => {{1,3,5,7,10},{2},{4},{6},{8},{9},{11,12}}
[1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,1,0,0] => {{1,3,5,10},{2},{4},{6,9},{7},{8},{11,12}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,3,4,10},{2},{5},{6},{7,8},{9},{11,12}}
[1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,1,0,0] => {{1,3,10},{2},{4,6,9},{5},{7},{8},{11,12}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,0] => {{1,3,10},{2},{4,9},{5,8},{6},{7},{11,12}}
[1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,7,10},{3},{4},{5,6},{8},{9},{11,12}}
[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,10},{3},{4},{5,9},{6,7},{8},{11,12}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,10},{3},{4,7,8},{5},{6},{9},{11,12}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,10},{3,6},{4},{5},{7,8},{9},{11,12}}
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,1,0,0] => {{1,10},{2,4,6,9},{3},{5},{7},{8},{11,12}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,10},{2,4,9},{3},{5,8},{6},{7},{11,12}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3,9},{4},{5},{6,7},{8},{11,12}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,5,8},{4},{6},{7},{11,12}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,8},{4,7},{5},{6},{11,12}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10,11},{12}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,12},{9,10,11}}
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,11,12},{10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,11},{6},{7},{8},{9},{10},{12}}
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,12},{7},{8},{9},{10},{11}}
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0] => {{1,2,12},{3,10},{4,9},{5,6},{7,8},{11}}
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0] => {{1,12},{2,3,11},{4,5},{6,9},{7,8},{10}}
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,2,12},{3,11},{4,7},{5,6},{8,9},{10}}
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,12},{4,5},{6,7},{8,9},{10},{11}}
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5,6,10},{7,8},{9}}
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0] => {{1,2,12},{3,4},{5,8,10},{6,7},{9},{11}}
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2,7,11},{3,6},{4,5},{8,10},{9}}
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2,7,8,11},{3,4},{5,6},{9},{10}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,12},{3,11},{4,7},{5,6},{8},{9,10}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,12},{4,5},{6,7},{8},{9,10},{11}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,12},{3,4},{5,9,11},{6,7},{8},{10}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,7,12},{3,6},{4,5},{8},{9,11},{10}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,7,9,12},{3,4},{5,6},{8},{10},{11}}
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5,10},{6,7,9},{8}}
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,0] => {{1,4,12},{2,3},{5,10},{6,8,9},{7},{11}}
[1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0] => {{1,12},{2,3},{4,5,11},{6},{7,8,9},{10}}
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,4,12},{2,3},{5,6,8},{7},{9,11},{10}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0,0] => {{1,4,9,12},{2,3},{5,7,8},{6},{10},{11}}
[1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3,4},{5},{6,7,10},{8,9}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,12},{3,4},{5},{6,9,10},{7,8},{11}}
[1,1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2,3},{4,11},{5},{6,7,8,10},{9}}
[1,1,1,0,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => {{1,4,12},{2,3},{5},{6,7,9,10},{8},{11}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2,8,11},{3,7},{4,5},{6},{9,10}}
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2,8,9,11},{3,4},{5,7},{6},{10}}
[1,1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => {{1,12},{2,3},{4,5,11},{6},{7},{8,9,10}}
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0] => {{1,12},{2,6,8,11},{3,4},{5},{7},{9,10}}
[1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,12},{2,3},{4,6,8,9,11},{5},{7},{10}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,12},{3,9},{4,8},{5,6},{7},{10,11}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,10,12},{3,9},{4,5},{6,8},{7},{11}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,12},{3,4},{5,10,11},{6,8},{7},{9}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,12},{4,5},{6},{7,8},{9},{10,11}}
[1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,5,10,12},{3,4},{6},{7,8},{9},{11}}
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0,0] => {{1,4,12},{2,3},{5,6,9},{7},{8},{10,11}}
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => {{1,4,10,12},{2,3},{5,7,9},{6},{8},{11}}
[1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => {{1,2,12},{3,4},{5},{6,10,11},{7,9},{8}}
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0] => {{1,4,12},{2,3},{5},{6,7,10,11},{8},{9}}
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,12},{4,5},{6},{7},{8,9},{10,11}}
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,2,5,10,12},{3,4},{6},{7},{8,9},{11}}
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0] => {{1,4,5,12},{2,3},{6},{7},{8,10,11},{9}}
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => {{1,2,6,8,12},{3,4},{5},{7},{9},{10,11}}
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,4,6,8,10,12},{2,3},{5},{7},{9},{11}}
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2},{3,11},{4,10},{5,9},{6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0] => {{1,3,12},{2},{4,10},{5,6,7},{8,9},{11}}
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => {{1,12},{2},{3,7,11},{4,5,6},{8,9},{10}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,3,12},{2},{4,8},{5,6,7},{9,11},{10}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => {{1,3,9,12},{2},{4,5,6},{7,8},{10},{11}}
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2},{3,4,5},{6,11},{7,8,10},{9}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => {{1,6,12},{2},{3,4,5},{7,9,10},{8},{11}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2},{3,8,11},{4,5,6},{7},{9,10}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2},{3,4,5},{6,8,9,11},{7},{10}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0] => {{1,3,12},{2},{4,9},{5,6,7},{8},{10,11}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,3,10,12},{2},{4,5,6},{7,9},{8},{11}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,6,12},{2},{3,4,5},{7,10,11},{8},{9}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,3,8,12},{2},{4,5,6},{7},{9},{10,11}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,6,8,10,12},{2},{3,4,5},{7},{9},{11}}
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,4},{3},{5,11},{6,10},{7,8,9}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0] => {{1,5,12},{2,4},{3},{6,7,8},{9,10},{11}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2,4},{3},{5,6,7},{8,9,11},{10}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,5,12},{2,4},{3},{6,7,8},{9},{10,11}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,8,10,12},{2,4},{3},{5,6,7},{9},{11}}
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2},{3,11},{4},{5,10},{6,7,8,9}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0] => {{1,3,12},{2},{4},{5,6,7,8},{9,10},{11}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2},{3,5,6,7},{4},{8,9,11},{10}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,3,12},{2},{4},{5,6,7,8},{9},{10,11}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,8,10,12},{2},{3,5,6,7},{4},{9},{11}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2,6},{3,5},{4},{7,11},{8,9,10}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2,6},{3,5},{4},{7,8,9},{11}}
[1,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3},{4,5},{6},{7,8,9,10}}
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2,7,8,9},{3},{4,5},{6},{11}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2},{3,4,6},{5},{7,11},{8,9,10}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2},{3,4,6},{5},{7,8,9},{11}}
[1,1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2,11},{3},{4},{5,6},{7,8,9,10}}
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2,7,8,9},{3},{4},{5,6},{11}}
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2},{3,11},{4},{5,7,8,9,10},{6}}
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2},{3,5,7,8,9},{4},{6},{11}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,12},{2,8},{3,7},{4,6},{5},{9,10,11}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,12},{2,9,10,11},{3,7},{4},{5,6},{8}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => {{1,12},{2,4,8},{3},{5,6},{7},{9,10,11}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => {{1,12},{2,9,10,11},{3,5},{4},{6,8},{7}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,12},{2,6,9,10,11},{3},{4,5},{7},{8}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,12},{2},{3,8},{4,5,7},{6},{9,10,11}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,12},{2},{3,9,10,11},{4,6,7},{5},{8}}
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => {{1,12},{2,5,8},{3},{4},{6,7},{9,10,11}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0] => {{1,12},{2},{3,5,6,8},{4},{7},{9,10,11}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => {{1,12},{2,9,10,11},{3,6},{4},{5},{7,8}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,12},{2,7,9,10,11},{3},{4,6},{5},{8}}
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0] => {{1,12},{2},{3,9,10,11},{4,7,8},{5},{6}}
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,12},{2,5,9,10,11},{3},{4},{6},{7,8}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,12},{2},{3,5,7,9,10,11},{4},{6},{8}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => {{1,11,12},{2,10},{3,9},{4,8},{5,7},{6}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,11,12},{3,9},{4,8},{5},{6,7},{10}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2,3,10},{4},{5,8},{6,7},{9}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,11,12},{3,10},{4,6},{5},{7,8},{9}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,11,12},{4},{5,6},{7,8},{9},{10}}
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => {{1,11,12},{2,10},{3},{4,5,9},{6,7},{8}}
[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0,0,0] => {{1,2,11,12},{3},{4,7,9},{5,6},{8},{10}}
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2,6,10},{3,5},{4},{7,9},{8}}
[1,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0] => {{1,11,12},{2,6,7,10},{3},{4,5},{8},{9}}
[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0] => {{1,2,11,12},{3,10},{4,6},{5},{7},{8,9}}
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,11,12},{4},{5,6},{7},{8,9},{10}}
[1,1,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0] => {{1,2,11,12},{3},{4,8,10},{5,6},{7},{9}}
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,2,6,11,12},{3,5},{4},{7},{8,10},{9}}
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,6,8,11,12},{3},{4,5},{7},{9},{10}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,10},{4,9},{5,6,8},{7}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4,9},{5,7,8},{6},{10}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,4,10},{5},{6,7,8},{9}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4,5,7},{6},{8,10},{9}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,3,8,11,12},{2},{4,6,7},{5},{9},{10}}
[1,1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,0] => {{1,11,12},{2,10},{3},{4},{5,6,9},{7,8}}
[1,1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => {{1,2,11,12},{3},{4},{5,8,9},{6,7},{10}}
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,10},{4},{5,6,7,9},{8}}
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4},{5,6,8,9},{7},{10}}
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2,7,10},{3,6},{4},{5},{8,9}}
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => {{1,11,12},{2,7,8,10},{3},{4,6},{5},{9}}
[1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,4,10},{5},{6},{7,8,9}}
[1,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => {{1,11,12},{2,5,7,10},{3},{4},{6},{8,9}}
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => {{1,11,12},{2},{3,5,7,8,10},{4},{6},{9}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,11,12},{3,8},{4,7},{5},{6},{9,10}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,9,11,12},{3,8},{4},{5,7},{6},{10}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,11,12},{3},{4,9,10},{5,7},{6},{8}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,11,12},{4},{5},{6,7},{8},{9,10}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,4,9,11,12},{3},{5},{6,7},{8},{10}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4,5,8},{6},{7},{9,10}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0] => {{1,3,9,11,12},{2},{4,6,8},{5},{7},{10}}
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,11,12},{3},{4},{5,9,10},{6,8},{7}}
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4},{5,6,9,10},{7},{8}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,11,12},{4},{5},{6},{7,8},{9,10}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,4,9,11,12},{3},{5},{6},{7,8},{10}}
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0] => {{1,3,4,11,12},{2},{5},{6},{7,9,10},{8}}
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,2,5,7,11,12},{3},{4},{6},{8},{9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,11,12},{6},{7},{8},{9},{10}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0] => {{1,2},{3,4,12},{5},{6,10},{7,8},{9},{11}}
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,9,12},{5},{6,7},{8},{10},{11}}
[1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => {{1,2},{3,4,5,12},{6,8,11},{7},{9,10}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0] => {{1,2},{3,12},{4,11},{5,9},{6,8},{7},{10}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,2},{3,12},{4,8,11},{5,7},{6},{9},{10}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2},{3,6,8,12},{4},{5},{7},{9,10},{11}}
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,2},{3,12},{4},{5},{6,7,11},{8,10},{9}}
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => {{1,2},{3,12},{4},{5,6,8,10},{7},{9},{11}}
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,2},{3,12},{4,10},{5,8,9},{6},{7},{11}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,2},{3,5,10,12},{4},{6,9},{7},{8},{11}}
[1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2},{3,5,8,10,12},{4},{6},{7},{9},{11}}
[1,1,0,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => {{1,2},{3,4,5,7,12},{6},{8,10,11},{9}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,2},{3,4,12},{5,8},{6},{7},{9},{10,11}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,2},{3,4,12},{5},{6},{7,10,11},{8},{9}}
[1,1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,8,12},{3,4},{5,6,7},{9,10},{11}}
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2,5,11},{3,4},{6,10},{7,8,9}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,12},{2,5,6},{3,4},{7},{8,10},{9},{11}}
[1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,7,8,10,12},{2,5,6},{3,4},{9},{11}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,12},{3,4},{5,10,11},{6,7,8},{9}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,12},{2,5},{3,4},{6},{7,10},{8,9},{11}}
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,10,12},{2,5},{3,4},{6},{7,8},{9},{11}}
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,12},{2,3},{4},{5,10},{6},{7,8,9},{11}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => {{1,10,12},{2,3},{4},{5,7,8},{6},{9},{11}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,12},{3,4},{5,9,10,11},{6,7},{8}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0,0] => {{1,9,12},{2,3,8},{4,7},{5,6},{10,11}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,9,12},{2,3},{4},{5,7},{6},{8},{10,11}}
[1,1,1,0,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,4,12},{2,3},{5,7,9,10,11},{6},{8}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,12},{3,7,8},{4,5},{6},{9,10,11}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,11},{3,4},{5,9},{6,7},{8},{10},{12}}
[1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,8,11},{3,4},{5,6},{7},{9},{10},{12}}
[1,1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,11},{4,7,10},{5,6},{8,9},{12}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,8},{4,7},{5,6},{9},{12}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,7,10},{3,6},{4,5},{8},{9},{12}}
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => {{1,5,7,11},{2,3},{4},{6},{8,9},{10},{12}}
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,3},{4},{5,6,10},{7,9},{8},{12}}
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0] => {{1,11},{2,3},{4,5,7,9},{6},{8},{10},{12}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0] => {{1,11},{2,9},{3,7,8},{4,5},{6},{10},{12}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,4,9,11},{2,3},{5,8},{6},{7},{10},{12}}
[1,1,1,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,4,7,9,11},{2,3},{5},{6},{8},{10},{12}}
[1,1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,6,11},{4,5},{7,9,10},{8},{12}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,11},{3,7},{4,5},{6},{8},{9,10},{12}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,11},{3,4},{5},{6,9,10},{7},{8},{12}}
[1,0,1,0,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => {{1},{2},{3,4},{5,6,8,12},{7},{9,10},{11}}
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2},{3,4},{5,12},{6,7,11},{8,10},{9}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,4},{5,12},{6},{7},{8,10},{9},{11}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2},{3,4},{5,7,8,10,12},{6},{9},{11}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,4},{5,6,12},{7,10,11},{8},{9}}
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,12},{4,10},{5,6},{7,8,9},{11}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,10,12},{4,7,8},{5,6},{9},{11}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,9,12},{4,7},{5,6},{8},{10,11}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,7,12},{4,5},{6},{8},{9,10,11}}
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => {{1},{2},{3,4,7,11},{5,6},{8,9},{10},{12}}
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1},{2},{3,11},{4,5,10},{6,9},{7,8},{12}}
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1},{2},{3,11},{4,5},{6},{7,9},{8},{10},{12}}
[1,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2},{3,6,7,9,11},{4,5},{8},{10},{12}}
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1},{2},{3,4,11},{5,9,10},{6,7},{8},{12}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,3,5,6},{4},{7,12},{8,10},{9},{11}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,3,5,6},{4},{7,10,12},{8},{9},{11}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,12},{4},{5,6,7,8},{9,10,11}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,1,0] => {{1},{2,11},{3,9},{4},{5,6,7,8},{10},{12}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,9,11},{3,5,6,7},{4},{8},{10},{12}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1,2,4},{3},{5,6},{7,12},{8,10},{9},{11}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1,2,4},{3},{5,6},{7,10,12},{8},{9},{11}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,4},{3},{5,6,12},{7,8},{9,10,11}}
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => {{1,2,4},{3},{5,11},{6,9},{7,8},{10},{12}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5,9,11},{6,7},{8},{10},{12}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1},{2,7,8},{3,5},{4},{6},{9,10,12},{11}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1},{2,7,11},{3,5},{4},{6},{8,9,10},{12}}
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => {{1},{2,5,7,8},{3},{4},{6},{9,10,12},{11}}
[1,0,1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => {{1},{2,5,11},{3},{4},{6},{7,8,9,10},{12}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,7,8},{3},{4,5,6},{9,10,12},{11}}
[1,1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => {{1,2,11},{3},{4,5,6},{7,8,9,10},{12}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1,6},{2,4},{3},{5},{7,8},{9,10,12},{11}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1,6},{2,4},{3},{5},{7,8,11},{9,10},{12}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5},{7,8},{9,10,12},{11}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7,8,11},{9,10},{12}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,5,9,10},{4},{6,7},{8},{11},{12}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,0] => {{1},{2,9,10},{3,4,8},{5,7},{6},{11},{12}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,9,10},{3},{4},{5,7},{6},{8},{11},{12}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => {{1},{2,4,5,7,9,10},{3},{6},{8},{11},{12}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,9,10},{4,7,8},{5},{6},{11},{12}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,9,10},{2,7},{3},{4,5,6},{8},{11},{12}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,7,9,10},{2,4,5},{3},{6},{8},{11},{12}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => {{1,6,9,10},{2,4},{3},{5},{7,8},{11},{12}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0] => {{1,4,9,10},{2},{3},{5},{6,7,8},{11},{12}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,4,8},{3},{5,6},{7},{9,10},{11},{12}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,8},{2,3,7},{4,6},{5},{9,10},{11},{12}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,8},{2},{3},{4,6},{5},{7},{9,10},{11},{12}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,3,4,6,8},{2},{5},{7},{9,10},{11},{12}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,8},{3,6,7},{4},{5},{9,10},{11},{12}}
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,0,0] => {{1},{2,3,11,12},{4},{5,9},{6,7},{8},{10}}
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,8,11,12},{4},{5,6},{7},{9},{10}}
[1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0,0] => {{1},{2,3,4,11,12},{5,7,10},{6},{8,9}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,0,0] => {{1},{2,11,12},{3,10},{4,8},{5,7},{6},{9}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1},{2,11,12},{3,7,10},{4,6},{5},{8},{9}}
[1,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => {{1},{2,5,7,11,12},{3},{4},{6},{8,9},{10}}
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => {{1},{2,11,12},{3},{4},{5,6,10},{7,9},{8}}
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0] => {{1},{2,11,12},{3},{4,5,7,9},{6},{8},{10}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => {{1},{2,11,12},{3,9},{4,7,8},{5},{6},{10}}
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0] => {{1},{2,4,9,11,12},{3},{5,8},{6},{7},{10}}
[1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,4,7,9,11,12},{3},{5},{6},{8},{10}}
[1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,11,12},{5},{7,9,10},{8}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,11,12},{4,7},{5},{6},{8},{9,10}}
[1,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1},{2,3,11,12},{4},{5},{6,9,10},{7},{8}}
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => {{1,2,7,11,12},{3},{4,5,6},{8,9},{10}}
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2,4,10},{3},{5,9},{6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,4,5},{3},{6},{7,9},{8},{10}}
[1,1,1,0,1,1,0,0,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,6,7,9,11,12},{2,4,5},{3},{8},{10}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,11,12},{3},{4,9,10},{5,6,7},{8}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2,4},{3},{5},{6,9},{7,8},{10}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,4},{3},{5},{6,7},{8},{10}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,11,12},{2},{3},{4,9},{5},{6,7,8},{10}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2},{3},{4,6,7},{5},{8},{10}}
[1,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,2,11,12},{3},{4,8,9,10},{5,6},{7}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,8,11,12},{2,3,7},{4,6},{5},{9,10}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,8,11,12},{2},{3},{4,6},{5},{7},{9,10}}
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => {{1,3,11,12},{2},{4,6,8,9,10},{5},{7}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,11,12},{3,6,7},{4},{5},{8,9,10}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,10},{3},{4,8},{5,6},{7},{9},{11,12}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,7,10},{3},{4,5},{6},{8},{9},{11,12}}
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,10},{4,6,9},{5},{7,8},{11,12}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,9},{3,7},{4,6},{5},{8},{11,12}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,10},{2,6,9},{3,5},{4},{7},{8},{11,12}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,4,6,10},{2},{3},{5},{7,8},{9},{11,12}}
[1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,10},{2},{3},{4,5,9},{6,8},{7},{11,12}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,1,0,0] => {{1,10},{2},{3,4,6,8},{5},{7},{9},{11,12}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,10},{2,8},{3,6,7},{4},{5},{9},{11,12}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,3,8,10},{2},{4,7},{5},{6},{9},{11,12}}
[1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0] => {{1,3,6,8,10},{2},{4},{5},{7},{9},{11,12}}
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,5,10},{4},{6,8,9},{7},{11,12}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,10},{3,6},{4},{5},{7},{8,9},{11,12}}
[1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => {{1,2,10},{3},{4},{5,8,9},{6},{7},{11,12}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4},{5,6},{7},{8,9,10,11},{12}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,3,4},{2},{5,6},{7},{8},{9,10,11,12}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4,7},{5,6},{8,9,10,11},{12}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,4,5},{2},{3},{6,7},{8},{9,10,11,12}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,3},{2},{4,7},{5,6},{8,9,10,11},{12}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,6},{7},{8,10,11,12},{9}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,7,8},{2,4,5,6},{3},{9,10},{11},{12}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,8},{5,6},{7},{9,10,11,12}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,7},{6},{8,10,11,12},{9}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,9},{2,3,4,5},{6},{7,8},{10,11},{12}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,4,5},{2},{3},{6,8},{7},{9,10,11,12}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,9},{2,4,5,6},{3},{7,8},{10,11},{12}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3,4},{2},{5,8},{6},{7},{9,10,11,12}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,4},{2,3},{5,7},{6},{8,10,11,12},{9}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,7},{6},{8},{9,10,11,12}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1,6},{2,3,4,5},{7,8,10},{9},{11},{12}}
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,6,8},{5},{7},{9,10,11,12}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,7},{2,3,4,5},{6},{8,9,11},{10},{12}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,6,8},{5},{7},{9,10,11,12}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2,7},{3},{4,5,6},{8},{9,10,11},{12}}
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,3,8},{2},{4},{5,6,7},{9,10,11},{12}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7},{8,9,11},{10},{12}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,5,6},{8,9,11},{10},{12}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,10,11,12},{6},{7,8},{9}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1,2,6},{3,4,5},{7},{8,12},{9,10},{11}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,2,3},{4},{5,10,11,12},{6},{7,9},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2,7},{3,4,5},{6},{8},{9,12},{10,11}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,2,4},{3},{5},{6,10,11,12},{7,9},{8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,8},{2},{3,4},{5},{6,7},{9,10,11,12}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,6,7},{2,3},{4},{5},{8,10,11,12},{9}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2},{3,7},{4,5,6},{8,9},{11,12}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1,5,6},{2,3},{4},{7,10,11,12},{8},{9}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,6},{3,4,5},{7,8},{10,12},{11}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,6,8},{2},{3,4},{5},{7},{9,10,11,12}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,5},{2,3},{4},{6,10,11,12},{7,9},{8}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,9,10},{2},{3,8},{4,5,6},{7},{11,12}}
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,6,8},{2},{3,5},{4},{7},{9,10,11,12}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,7},{8},{9,10,11}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1,5,6},{2,4},{3},{7,10,11,12},{8},{9}}
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,4},{2,3},{5,12},{6,8},{7},{9,10,11}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,6,7},{2,5},{3},{4},{8,10,11,12},{9}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,5,7},{2,4},{3},{6},{8,12},{9,10,11}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5,6,9},{7,8},{10},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => {{1,4},{2,3},{5,6,7,10},{8,9},{11},{12}}
[1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => {{1,2},{3},{4,6,7,10},{5},{8,9},{11,12}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,5},{2,3},{4},{6,7,8,11},{9,10},{12}}
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => {{1,3},{2},{4,6,7,10},{5},{8,9},{11,12}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,4},{3},{5},{6,7,8,11},{9,10},{12}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,3,5},{2},{4},{6,7,8,11},{9,10},{12}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,2,3},{4},{5,12},{6},{7,8,11},{9,10}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,2,4},{3},{5},{6,12},{7,8,11},{9,10}}
[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => {{1,6,7,10},{2},{3,4},{5},{8,9},{11,12}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,5},{2,3},{4},{6,12},{7,8,11},{9,10}}
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => {{1,6,7,10},{2},{3,5},{4},{8,9},{11,12}}
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => {{1,4},{2,3},{5,12},{6,7,10},{8,9},{11}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,5,6,9},{2,4},{3},{7,8},{10,12},{11}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,7,8},{4,5},{6},{9},{10,11},{12}}
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,3,4,8,9},{2},{5,6},{7},{10,11},{12}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3,7,8},{4,5},{6},{9},{10,12},{11}}
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,0] => {{1,10},{2},{3,4,8,9},{5,6},{7},{11,12}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,3,7,8},{4,5},{6},{10,12},{11}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,7,8},{4,6},{5},{9},{10,11},{12}}
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,3,4,8,9},{2},{5,7},{6},{10,11},{12}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3,7,8},{4,6},{5},{9},{10,12},{11}}
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0] => {{1,10},{2},{3,4,8,9},{5,7},{6},{11,12}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,3,7,8},{4,6},{5},{10,12},{11}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,2},{3},{4,5,12},{6,7,8},{9},{10,11}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,3},{2},{4,5,12},{6,7,8},{9},{10,11}}
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0] => {{1,2},{3},{4,5,12},{6,8,9},{7},{10,11}}
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0] => {{1,3},{2},{4,5,12},{6,8,9},{7},{10,11}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0] => {{1,2},{3},{4,5,10,12},{6,7,8},{9},{11}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,5,10,12},{6,7,8},{9},{11}}
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0] => {{1,2},{3},{4,5,11,12},{6,10},{7},{8,9}}
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0] => {{1,3},{2},{4,5,11,12},{6,10},{7},{8,9}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,2},{3},{4,5,10,12},{6,9},{7,8},{11}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,5,10,12},{6,9},{7,8},{11}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,10,11},{3,4},{5},{6,7,8},{9},{12}}
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => {{1,2,11},{3,6},{4,5},{7,8,9},{10},{12}}
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => {{1,2,10,11},{3,4},{5},{6,8,9},{7},{12}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,11},{3,7},{4,5},{6},{8,9,10},{12}}
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => {{1,2,10,11},{3,5},{4},{6,8,9},{7},{12}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,11},{3,4,6},{5},{7},{8,9,10},{12}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,11},{3,5,7},{4},{6},{8,9,10},{12}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,7,11},{3,4,5},{6},{8},{9,10},{12}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,8,11},{3,4,6},{5},{7},{9,10},{12}}
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => {{1,2,10,11},{3,8,9},{4},{5,6},{7},{12}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,8,11},{3,7},{4,5},{6},{9,10},{12}}
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => {{1,2,10,11},{3,8,9},{4},{5,7},{6},{12}}
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => {{1,2,7,11},{3,6},{4,5},{8,9},{10},{12}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,9,11},{3,7,8},{4,6},{5},{10},{12}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,12},{2,3,4},{5},{6,7},{8},{9,10,11}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,4,5},{3},{6,7},{8},{9}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,12},{2,3},{4},{5,8},{6,7},{9,10,11}}
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,5,6},{3},{4},{7,8},{9}}
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,12},{2,4},{3},{5,8},{6,7},{9,10,11}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,3,4},{5},{6,7},{8},{10}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => {{1,12},{2,7,8},{3,5,6},{4},{9,10},{11}}
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,3},{4},{5,9},{6,7},{8}}
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,3,4},{5},{6,8},{7},{10}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,4,5},{6},{7,8},{10,11}}
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,5,6},{3},{4},{7,9},{8}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,5,6},{4},{7,8},{10,11}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,4,5},{3},{6,9},{7},{8}}
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,5},{3,4},{6,8},{7},{10}}
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,3},{4},{5,6,8},{7},{9}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,12},{2,6},{3,4,5},{7,8,10},{9},{11}}
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,3},{4},{5,7,9},{6},{8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2,7},{3,4,5},{6},{8,9,11},{10}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,4},{3},{5,7,9},{6},{8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,12},{2,3,7},{4},{5,6},{8},{9,10,11}}
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => {{1,12},{2,4,8},{3},{5},{6,7},{9,10,11}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2,3,6},{4,5},{7},{8,9,11},{10}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2,4,7},{3},{5,6},{8,9,11},{10}}
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,6,11,12},{2,3,4},{5},{7},{8,9},{10}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,8,12},{2,3,6},{4,5},{7},{9,10},{11}}
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,6,11,12},{2,3,4},{5},{7},{8,10},{9}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,9,12},{2,3,7},{4,5},{6},{8},{10,11}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,7,11,12},{2,3,5},{4},{6},{8,10},{9}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,9},{3},{4,5},{6},{7,8}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,7,8},{3,4},{5},{6},{10}}
[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,11,12},{2,10},{3},{4,7},{5,6},{8,9}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,8,11,12},{2,6,7},{3,4},{5},{9},{10}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,10,12},{2,9},{3,6},{4,5},{7,8},{11}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,7,9},{3},{4,5},{6},{8}}
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,7,11,12},{2,6},{3,4},{5},{8,10},{9}}
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,11,12},{2,9,10},{3},{4,8},{5,6},{7}}
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,10,11,12},{2,7,9},{3},{4,6},{5},{8}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,6,12},{2,5},{3,4},{7,8},{9},{10,11}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,8,11,12},{2,6,7},{3,5},{4},{9},{10}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => {{1,6,12},{2,5},{3,4},{7,9},{8},{10,11}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => {{1,9,11,12},{2,7,8},{3,6},{4},{5},{10}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,0] => {{1,9,12},{2,6,8},{3,5},{4},{7},{10,11}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0] => {{1,2,12},{3,4,5,6,7,8,9,10,11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11},{12}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,12},{6,7},{8},{9},{10},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10},{12}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11},{12}}
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => {{1},{2},{3,5,7,8,12},{4},{6},{9},{10,11}}
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0] => {{1},{2},{3,5,6,12},{4},{7},{8,10,11},{9}}
[1,0,1,0,1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0] => {{1},{2},{3},{4,5,6,12},{7},{8,9},{10,11}}
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1},{2},{3,7,8,12},{4,6},{5},{9},{10,11}}
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0] => {{1},{2},{3,4,12},{5},{6,8,10,11},{7},{9}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => {{1},{2},{3},{4,5,12},{6},{7,8},{9,10,11}}
[1,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,4,12},{5,7},{6},{8,10,11},{9}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6},{8,9,12},{10,11}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,5},{4},{6,7},{8,9,12},{10,11}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1},{2,4},{3},{5,7,8,12},{6},{9},{10,11}}
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2,4},{3},{5,6,12},{7},{8,10,11},{9}}
[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},{2,4},{3},{5,7},{6},{8,9,12},{10,11}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,4,6},{3},{5},{7,8,12},{9},{10,11}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,6},{3,5},{4},{7,8,12},{9},{10,11}}
[1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1},{2},{3,12},{4},{5,7,9,10,11},{6},{8}}
[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => {{1},{2},{3},{4,12},{5,7,10,11},{6},{8,9}}
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1},{2},{3,12},{4,6},{5},{7,9,10,11},{8}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => {{1},{2},{3},{4,12},{5},{6,7,8},{9,10,11}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1},{2},{3},{4,5},{6,12},{7,10,11},{8,9}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1},{2,4},{3},{5,12},{6},{7,9,10,11},{8}}
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1},{2,4},{3},{5},{6,12},{7,8},{9,10,11}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,4,6},{3},{5},{7,12},{8},{9,10,11}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,5},{4},{7,12},{8},{9,10,11}}
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => {{1},{2},{3},{4,12},{5},{6,7,8,9},{10,11}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,5,8},{6,7},{9,12},{10,11}}
[1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1},{2,4},{3},{5},{6,12},{7,8,9},{10,11}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,6,7},{9,12},{10,11}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,4},{5,6},{7,8},{9,12},{10,11}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,3},{2},{4},{5,7,8,12},{6},{9},{10,11}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,3},{2},{4},{5,6,12},{7},{8,10,11},{9}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,3},{2},{4},{5,7},{6},{8,9,12},{10,11}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1,3},{2},{4,6},{5},{7,8,12},{9},{10,11}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,3},{2},{4},{5,12},{6},{7,9,10,11},{8}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,3},{2},{4},{5},{6,12},{7,8},{9,10,11}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,3},{2},{4,6},{5},{7,12},{8},{9,10,11}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,3},{2},{4},{5},{6,12},{7,8,9},{10,11}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4},{5,6},{7,8},{9,12},{10,11}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1,3,5},{2},{4},{6},{7,8,12},{9},{10,11}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,3,5},{2},{4},{6},{7,12},{8},{9,10,11}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,3,5},{2},{4},{6},{7,8},{9,12},{10,11}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1,5},{2,4},{3},{6},{7,8,12},{9},{10,11}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,5},{2,4},{3},{6},{7,12},{8},{9,10,11}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6},{7,8},{9,12},{10,11}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,3,5,7},{2},{4},{6},{8},{9,12},{10,11}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,3,7},{2},{4,6},{5},{8},{9,12},{10,11}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,5,7},{2,4},{3},{6},{8},{9,12},{10,11}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5},{8},{9,12},{10,11}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4},{8},{9,12},{10,11}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1},{2,4,6,8,10,11},{3},{5},{7},{9},{12}}
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,5,6,10,11},{4},{7},{8,9},{12}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0] => {{1},{2,4,8,10,11},{3},{5,7},{6},{9},{12}}
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,10,11},{5},{6,8,9},{7},{12}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,7},{4},{5,6},{8,9,10,11},{12}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => {{1},{2,6,8,10,11},{3,5},{4},{7},{9},{12}}
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => {{1},{2,4},{3},{5,6,10,11},{7},{8,9},{12}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,8,10,11},{3,5,7},{4},{6},{9},{12}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,8,10,11},{3,7},{4,6},{5},{9},{12}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1},{2,4,6,8},{3},{5},{7},{9,10,11},{12}}
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,8},{5},{6,7},{9,10,11},{12}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1},{2,6,8},{3,5},{4},{7},{9,10,11},{12}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7,8},{9,10,11},{12}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,4},{3},{5,6},{7,8},{9,10,11},{12}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,3},{2},{4,6,8,10,11},{5},{7},{9},{12}}
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,3},{2},{4},{5,6,10,11},{7},{8,9},{12}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3},{2},{4,8,10,11},{5,7},{6},{9},{12}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,6,8},{5},{7},{9,10,11},{12}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,6},{5},{7,8},{9,10,11},{12}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5},{2},{4},{6,8,10,11},{7},{9},{12}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6,8},{7},{9,10,11},{12}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,5},{2,4},{3},{6,8,10,11},{7},{9},{12}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,5},{2,4},{3},{6,8},{7},{9,10,11},{12}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,3,5,7},{2},{4},{6},{8,10,11},{9},{12}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,3,7},{2},{4,6},{5},{8,10,11},{9},{12}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,5,7},{2,4},{3},{6},{8,10,11},{9},{12}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,7},{2,4,6},{3},{5},{8,10,11},{9},{12}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,7},{2,6},{3,5},{4},{8,10,11},{9},{12}}
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => {{1},{2,3,5,7,9},{4},{6},{8},{10,11},{12}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => {{1},{2},{3,5,8,9},{4},{6,7},{10,11},{12}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => {{1},{2,3,7,9},{4,6},{5},{8},{10,11},{12}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => {{1},{2},{3,4,9},{5},{6,7,8},{10,11},{12}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,8,9},{6,7},{10,11},{12}}
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5,7,9},{6},{8},{10,11},{12}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6,9},{7,8},{10,11},{12}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,3,5},{2},{4},{6,7,9},{8},{10,11},{12}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,5},{2,4},{3},{6,7,9},{8},{10,11},{12}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,9},{4},{5,6,7,8},{10,11},{12}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4,7},{5,6},{8,9},{10,11},{12}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,9},{6,7,8},{10,11},{12}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,7},{4,5,6},{8,9},{10,11},{12}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3,5,7},{2},{4},{6},{8,9},{10,12},{11}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3,7},{2},{4,6},{5},{8,9},{10,12},{11}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,5,7},{2,4},{3},{6},{8,9},{10,12},{11}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,7},{2,4,6},{3},{5},{8,9},{10,12},{11}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,7},{2,6},{3,5},{4},{8,9},{10,12},{11}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,10,12},{2},{3},{4},{5},{6},{7},{8},{9},{11}}
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2},{3,11},{4,10},{5,9},{6,8},{7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10},{12}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5},{6,7},{8,9},{10,12},{11}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3},{4,5},{6,7},{8,12},{9,11},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5},{6,7,9},{8},{10,12},{11}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,3},{4,5},{6,12},{7,9,11},{8},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,3},{4,5},{6,12},{7,11},{8,10},{9}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5,7},{6},{8,9},{10,12},{11}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3},{4,5,7},{6},{8,12},{9,11},{10}}
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5,7,9},{6},{8},{10,12},{11}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5,9},{6,8},{7},{10,12},{11}}
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,3},{4,12},{5,7,9,11},{6},{8},{10}}
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,3},{4,12},{5,7,11},{6},{8,10},{9}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,3},{4,12},{5,9,11},{6,8},{7},{10}}
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,3},{4,12},{5,11},{6,8,10},{7},{9}}
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,3},{4,12},{5,11},{6,10},{7,9},{8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3,5},{4},{6,7},{8,9},{10,12},{11}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3,5},{4},{6,7},{8,12},{9,11},{10}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,5},{4},{6,7,9},{8},{10,12},{11}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,3,5},{4},{6,12},{7,9,11},{8},{10}}
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,3,5},{4},{6,12},{7,11},{8,10},{9}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3,5,7},{4},{6},{8,9},{10,12},{11}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3,5,7},{4},{6},{8,12},{9,11},{10}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3,7},{4,6},{5},{8,9},{10,12},{11}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3,7},{4,6},{5},{8,12},{9,11},{10}}
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => {{1},{2,3,5,7,9},{4},{6},{8},{10,12},{11}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => {{1},{2,3,5,9},{4},{6,8},{7},{10,12},{11}}
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1},{2,3,7,9},{4,6},{5},{8},{10,12},{11}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,9},{4,6,8},{5},{7},{10,12},{11}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,9},{4,8},{5,7},{6},{10,12},{11}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5},{6,7},{8,9},{10,12},{11}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3},{2},{4,5},{6,7},{8,12},{9,11},{10}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5},{6,7,9},{8},{10,12},{11}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,3},{2},{4,5},{6,12},{7,9,11},{8},{10}}
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,5},{6,12},{7,11},{8,10},{9}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5,7},{6},{8,9},{10,12},{11}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3},{2},{4,5,7},{6},{8,12},{9,11},{10}}
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5,7,9},{6},{8},{10,12},{11}}
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5,9},{6,8},{7},{10,12},{11}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3,5},{2},{4},{6,7},{8,9},{10,12},{11}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3,5},{2},{4},{6,7},{8,12},{9,11},{10}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,5},{2},{4},{6,7,9},{8},{10,12},{11}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,5},{2,4},{3},{6,7},{8,9},{10,12},{11}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6,7},{8,12},{9,11},{10}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,5},{2,4},{3},{6,7,9},{8},{10,12},{11}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,12},{2},{3,5,7,9,11},{4},{6},{8},{10}}
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => {{1,12},{2},{3,5,7,11},{4},{6},{8,10},{9}}
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2},{3,5,9,11},{4},{6,8},{7},{10}}
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => {{1,12},{2},{3,5,11},{4},{6,8,10},{7},{9}}
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2},{3,5,11},{4},{6,10},{7,9},{8}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2},{3,7,9,11},{4,6},{5},{8},{10}}
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2},{3,7,11},{4,6},{5},{8,10},{9}}
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2},{3,9,11},{4,6,8},{5},{7},{10}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2},{3,9,11},{4,8},{5,7},{6},{10}}
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => {{1,12},{2},{3,11},{4,6,8,10},{5},{7},{9}}
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2},{3,11},{4,6,10},{5},{7,9},{8}}
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2},{3,11},{4,8,10},{5,7},{6},{9}}
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2},{3,11},{4,10},{5,7,9},{6},{8}}
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,12},{2,4},{3},{5,7,9,11},{6},{8},{10}}
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,12},{2,4},{3},{5,7,11},{6},{8,10},{9}}
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2,4},{3},{5,9,11},{6,8},{7},{10}}
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,12},{2,4},{3},{5,11},{6,8,10},{7},{9}}
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,4},{3},{5,11},{6,10},{7,9},{8}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2,4,6},{3},{5},{7,9,11},{8},{10}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,4,6},{3},{5},{7,11},{8,10},{9}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,12},{2,6},{3,5},{4},{7,9,11},{8},{10}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,12},{2,6},{3,5},{4},{7,11},{8,10},{9}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0] => {{1,12},{2,4,6,8},{3},{5},{7},{9,11},{10}}
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => {{1,12},{2,4,8},{3},{5,7},{6},{9,11},{10}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => {{1,12},{2,6,8},{3,5},{4},{7},{9,11},{10}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,12},{2,8},{3,5,7},{4},{6},{9,11},{10}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,12},{2,8},{3,7},{4,6},{5},{9,11},{10}}
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => {{1,12},{2,4,6,8,10},{3},{5},{7},{9},{11}}
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0] => {{1,12},{2,4,6,10},{3},{5},{7,9},{8},{11}}
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => {{1,12},{2,4,8,10},{3},{5,7},{6},{9},{11}}
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0] => {{1,12},{2,4,10},{3},{5,7,9},{6},{8},{11}}
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0] => {{1,12},{2,4,10},{3},{5,9},{6,8},{7},{11}}
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => {{1,12},{2,6,8,10},{3,5},{4},{7},{9},{11}}
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => {{1,12},{2,6,10},{3,5},{4},{7,9},{8},{11}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,12},{2,8,10},{3,5,7},{4},{6},{9},{11}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,12},{2,8,10},{3,7},{4,6},{5},{9},{11}}
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0] => {{1,12},{2,10},{3,5,7,9},{4},{6},{8},{11}}
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,12},{2,10},{3,5,9},{4},{6,8},{7},{11}}
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,12},{2,10},{3,7,9},{4,6},{5},{8},{11}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0] => {{1,12},{2,10},{3,9},{4,6,8},{5},{7},{11}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => {{1,12},{2,10},{3,9},{4,8},{5,7},{6},{11}}
Identities
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Inverses
Mp00128to composition ∘ Mp00138to noncrossing partition ∘ Mp00231bounce path = id : Integer compositions ⟶ Integer compositions
Intertwining relations
Mp00138to noncrossing partition ∘ Mp00327inverse Kreweras complement = Mp00112complement ∘ Mp00221conjugate ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00112complement ∘ Mp00138to noncrossing partition ∘ Mp00231bounce path = Mp00138to noncrossing partition ∘ Mp00231bounce path ∘ Mp00038reverse : Integer compositions ⟶ Set partitions
Mp00215Wachs-White ∘ Mp00138to noncrossing partition ∘ Mp00231bounce path = Mp00138to noncrossing partition ∘ Mp00231bounce path ∘ Mp00038reverse : Integer compositions ⟶ Set partitions
Mp00216inverse Wachs-White ∘ Mp00138to noncrossing partition ∘ Mp00231bounce path = Mp00138to noncrossing partition ∘ Mp00231bounce path ∘ Mp00038reverse : Integer compositions ⟶ Set partitions
Absorbing relations
Mp00164Chen Deng Du Stanley Yan ∘ Mp00115Kasraoui-Zeng ∘ Mp00138to noncrossing partition = Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00217Wachs-White-rho ∘ Mp00115Kasraoui-Zeng ∘ Mp00138to noncrossing partition = Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00124Adin-Bagno-Roichman transformation = Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00132switch returns and last double rise = Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00164Chen Deng Du Stanley Yan ∘ Mp00115Kasraoui-Zeng ∘ Mp00112complement ∘ Mp00138to noncrossing partition = Mp00112complement ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00217Wachs-White-rho ∘ Mp00115Kasraoui-Zeng ∘ Mp00112complement ∘ Mp00138to noncrossing partition = Mp00112complement ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00217Wachs-White-rho ∘ Mp00138to noncrossing partition ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00115Kasraoui-Zeng ∘ Mp00138to noncrossing partition ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00164Chen Deng Du Stanley Yan ∘ Mp00115Kasraoui-Zeng ∘ Mp00221conjugate ∘ Mp00138to noncrossing partition = Mp00221conjugate ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00217Wachs-White-rho ∘ Mp00115Kasraoui-Zeng ∘ Mp00221conjugate ∘ Mp00138to noncrossing partition = Mp00221conjugate ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00217Wachs-White-rho ∘ Mp00115Kasraoui-Zeng ∘ Mp00215Wachs-White ∘ Mp00138to noncrossing partition = Mp00215Wachs-White ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00115Kasraoui-Zeng ∘ Mp00138to noncrossing partition ∘ Mp00231bounce path = Mp00138to noncrossing partition ∘ Mp00231bounce path : Integer compositions ⟶ Set partitions
Mp00217Wachs-White-rho ∘ Mp00138to noncrossing partition ∘ Mp00231bounce path = Mp00138to noncrossing partition ∘ Mp00231bounce path : Integer compositions ⟶ Set partitions
Mp00164Chen Deng Du Stanley Yan ∘ Mp00115Kasraoui-Zeng ∘ Mp00176rotate decreasing ∘ Mp00138to noncrossing partition = Mp00176rotate decreasing ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00217Wachs-White-rho ∘ Mp00115Kasraoui-Zeng ∘ Mp00176rotate decreasing ∘ Mp00138to noncrossing partition = Mp00176rotate decreasing ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00217Wachs-White-rho ∘ Mp00115Kasraoui-Zeng ∘ Mp00091rotate increasing ∘ Mp00138to noncrossing partition = Mp00091rotate increasing ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00164Chen Deng Du Stanley Yan ∘ Mp00115Kasraoui-Zeng ∘ Mp00091rotate increasing ∘ Mp00138to noncrossing partition = Mp00091rotate increasing ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00174dual major index to intertwining number ∘ Mp00220Yip ∘ Mp00138to noncrossing partition ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Other relations
Mp00164Chen Deng Du Stanley Yan ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00218inverse Wachs-White-rho ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00080to permutation ∘ Mp00138to noncrossing partition = Mp00235descent views to invisible inversion bottoms ∘ Mp00031to 312-avoiding permutation : Dyck paths ⟶ Permutations
Mp00164Chen Deng Du Stanley Yan ∘ Mp00112complement ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00112complement ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00218inverse Wachs-White-rho ∘ Mp00112complement ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00112complement ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00112complement ∘ Mp00115Kasraoui-Zeng ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00112complement ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00040to partition ∘ Mp00102rise composition ∘ Mp00028reverse = Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00028reverse = Mp00040to partition ∘ Mp00102rise composition : Dyck paths ⟶ Integer partitions
Mp00128to composition ∘ Mp00112complement ∘ Mp00138to noncrossing partition = Mp00102rise composition ∘ Mp00028reverse : Dyck paths ⟶ Integer compositions
Mp00112complement ∘ Mp00115Kasraoui-Zeng ∘ Mp00112complement ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00218inverse Wachs-White-rho ∘ Mp00215Wachs-White ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00215Wachs-White ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00112complement ∘ Mp00138to noncrossing partition ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00028reverse ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00164Chen Deng Du Stanley Yan ∘ Mp00221conjugate ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00221conjugate ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00218inverse Wachs-White-rho ∘ Mp00221conjugate ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00221conjugate ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00127left-to-right-maxima to Dyck path = Mp00108cycle type ∘ Mp00086first fundamental transformation : Permutations ⟶ Integer partitions
Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00099bounce path = Mp00204LLPS ∘ Mp00023to non-crossing permutation ∘ Mp00099bounce path : Dyck paths ⟶ Integer partitions
Mp00108cycle type ∘ Mp00235descent views to invisible inversion bottoms ∘ Mp00031to 312-avoiding permutation = Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00108cycle type ∘ Mp00086first fundamental transformation ∘ Mp00031to 312-avoiding permutation = Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00108cycle type ∘ Mp00235descent views to invisible inversion bottoms ∘ Mp00119to 321-avoiding permutation (Krattenthaler) = Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00108cycle type ∘ Mp00086first fundamental transformation ∘ Mp00119to 321-avoiding permutation (Krattenthaler) = Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00108cycle type ∘ Mp00002to left key permutation ∘ Mp00035to alternating sign matrix = Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00204LLPS ∘ Mp00002to left key permutation ∘ Mp00137to symmetric ASM = Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00040to partition ∘ Mp00102rise composition ∘ Mp00101decomposition reverse = Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00030zeta map : Dyck paths ⟶ Integer partitions
Mp00079shape ∘ Mp00221conjugate ∘ Mp00138to noncrossing partition = Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00030zeta map : Dyck paths ⟶ Integer partitions
Mp00060Robinson-Schensted tableau shape ∘ Mp00002to left key permutation ∘ Mp00137to symmetric ASM = Mp00044conjugate ∘ Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00101decomposition reverse = Mp00040to partition ∘ Mp00071descent composition ∘ Mp00031to 312-avoiding permutation : Dyck paths ⟶ Integer partitions
Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00120Lalanne-Kreweras involution = Mp00040to partition ∘ Mp00039complement ∘ Mp00102rise composition : Dyck paths ⟶ Integer partitions
Mp00102rise composition ∘ Mp00028reverse ∘ Mp00327inverse Kreweras complement = Mp00128to composition ∘ Mp00221conjugate ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer compositions
Mp00128to composition ∘ Mp00138to noncrossing partition ∘ Mp00099bounce path = Mp00100touch composition ∘ Mp00099bounce path : Dyck paths ⟶ Integer compositions
Mp00176rotate decreasing ∘ Mp00138to noncrossing partition ∘ Mp00199prime Dyck path = Mp00138to noncrossing partition ∘ Mp00124Adin-Bagno-Roichman transformation ∘ Mp00199prime Dyck path : Dyck paths ⟶ Set partitions
Mp00218inverse Wachs-White-rho ∘ Mp00176rotate decreasing ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00176rotate decreasing ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00164Chen Deng Du Stanley Yan ∘ Mp00176rotate decreasing ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00176rotate decreasing ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00216inverse Wachs-White ∘ Mp00138to noncrossing partition ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00028reverse ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00215Wachs-White ∘ Mp00138to noncrossing partition ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00028reverse ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00151to cycle type ∘ Mp00235descent views to invisible inversion bottoms ∘ Mp00031to 312-avoiding permutation = Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00151to cycle type ∘ Mp00086first fundamental transformation ∘ Mp00031to 312-avoiding permutation = Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00138to noncrossing partition ∘ Mp00127left-to-right-maxima to Dyck path ∘ Mp00023to non-crossing permutation = Mp00151to cycle type ∘ Mp00086first fundamental transformation ∘ Mp00023to non-crossing permutation : Dyck paths ⟶ Set partitions
Mp00112complement ∘ Mp00138to noncrossing partition ∘ Mp00028reverse ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00151to cycle type ∘ Mp00119to 321-avoiding permutation (Krattenthaler) ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00164Chen Deng Du Stanley Yan ∘ Mp00091rotate increasing ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00091rotate increasing ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00218inverse Wachs-White-rho ∘ Mp00091rotate increasing ∘ Mp00138to noncrossing partition = Mp00115Kasraoui-Zeng ∘ Mp00091rotate increasing ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00171intertwining number to dual major index ∘ Mp00138to noncrossing partition ∘ Mp00099bounce path = Mp00220Yip ∘ Mp00138to noncrossing partition ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00138to noncrossing partition ∘ Mp00127left-to-right-maxima to Dyck path ∘ Mp00025to 132-avoiding permutation = Mp00151to cycle type ∘ Mp00086first fundamental transformation ∘ Mp00025to 132-avoiding permutation : Dyck paths ⟶ Set partitions
Mp00151to cycle type ∘ Mp00129to 321-avoiding permutation (Billey-Jockusch-Stanley) ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00120Lalanne-Kreweras involution ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00020to Tamari-corresponding Dyck path = Mp00108cycle type ∘ Mp00086first fundamental transformation ∘ Mp00017to 312-avoiding permutation : Binary trees ⟶ Integer partitions
Mp00138to noncrossing partition ∘ Mp00127left-to-right-maxima to Dyck path ∘ Mp00014to 132-avoiding permutation = Mp00151to cycle type ∘ Mp00086first fundamental transformation ∘ Mp00014to 132-avoiding permutation : Binary trees ⟶ Set partitions
Mp00151to cycle type ∘ Mp00235descent views to invisible inversion bottoms ∘ Mp00017to 312-avoiding permutation = Mp00138to noncrossing partition ∘ Mp00020to Tamari-corresponding Dyck path : Binary trees ⟶ Set partitions
Mp00151to cycle type ∘ Mp00086first fundamental transformation ∘ Mp00017to 312-avoiding permutation = Mp00138to noncrossing partition ∘ Mp00020to Tamari-corresponding Dyck path : Binary trees ⟶ Set partitions
Mp00071descent composition ∘ Mp00241invert Laguerre heap ∘ Mp00031to 312-avoiding permutation = Mp00039complement ∘ Mp00128to composition ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer compositions
Mp00215Wachs-White ∘ Mp00138to noncrossing partition ∘ Mp00028reverse ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00216inverse Wachs-White ∘ Mp00138to noncrossing partition ∘ Mp00028reverse ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00240weak exceedance partition ∘ Mp00235descent views to invisible inversion bottoms ∘ Mp00031to 312-avoiding permutation = Mp00138to noncrossing partition : Dyck paths ⟶ Set partitions
Mp00151to cycle type ∘ Mp00235descent views to invisible inversion bottoms ∘ Mp00069complement ∘ Mp00025to 132-avoiding permutation = Mp00138to noncrossing partition ∘ Mp00028reverse : Dyck paths ⟶ Set partitions
Mp00151to cycle type ∘ Mp00086first fundamental transformation ∘ Mp00069complement ∘ Mp00025to 132-avoiding permutation = Mp00138to noncrossing partition ∘ Mp00028reverse : Dyck paths ⟶ Set partitions
Mp00240weak exceedance partition ∘ Mp00235descent views to invisible inversion bottoms ∘ Mp00017to 312-avoiding permutation = Mp00138to noncrossing partition ∘ Mp00020to Tamari-corresponding Dyck path : Binary trees ⟶ Set partitions
Mp00204LLPS ∘ Mp00087inverse first fundamental transformation ∘ Mp00235descent views to invisible inversion bottoms ∘ Mp00119to 321-avoiding permutation (Krattenthaler) = Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00030zeta map ∘ Mp00101decomposition reverse = Mp00040to partition ∘ Mp00102rise composition : Dyck paths ⟶ Integer partitions
Mp00071descent composition ∘ Mp00326weak order rowmotion ∘ Mp00031to 312-avoiding permutation = Mp00038reverse ∘ Mp00128to composition ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer compositions
Mp00071descent composition ∘ Mp00069complement ∘ Mp00241invert Laguerre heap ∘ Mp00031to 312-avoiding permutation = Mp00128to composition ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer compositions
Mp00102rise composition ∘ Mp00101decomposition reverse ∘ Mp00028reverse ∘ Mp00327inverse Kreweras complement = Mp00128to composition ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer compositions
Mp00240weak exceedance partition ∘ Mp00235descent views to invisible inversion bottoms ∘ Mp00069complement ∘ Mp00025to 132-avoiding permutation = Mp00138to noncrossing partition ∘ Mp00028reverse : Dyck paths ⟶ Set partitions
Mp00138to noncrossing partition ∘ Mp00127left-to-right-maxima to Dyck path ∘ Mp00087inverse first fundamental transformation ∘ Mp00023to non-crossing permutation = Mp00151to cycle type ∘ Mp00023to non-crossing permutation : Dyck paths ⟶ Set partitions
Mp00240weak exceedance partition ∘ Mp00129to 321-avoiding permutation (Billey-Jockusch-Stanley) ∘ Mp00099bounce path = Mp00138to noncrossing partition ∘ Mp00120Lalanne-Kreweras involution ∘ Mp00099bounce path : Dyck paths ⟶ Set partitions
Mp00079shape ∘ Mp00138to noncrossing partition ∘ Mp00231bounce path = Mp00040to partition : Integer compositions ⟶ Integer partitions
Mp00151to cycle type ∘ Mp00129to 321-avoiding permutation (Billey-Jockusch-Stanley) ∘ Mp00231bounce path = Mp00138to noncrossing partition ∘ Mp00231bounce path ∘ Mp00039complement : Integer compositions ⟶ Set partitions
Mp00171intertwining number to dual major index ∘ Mp00138to noncrossing partition ∘ Mp00231bounce path = Mp00220Yip ∘ Mp00138to noncrossing partition ∘ Mp00231bounce path : Integer compositions ⟶ Set partitions
Mp00151to cycle type ∘ Mp00119to 321-avoiding permutation (Krattenthaler) ∘ Mp00231bounce path = Mp00138to noncrossing partition ∘ Mp00231bounce path : Integer compositions ⟶ Set partitions
Description
Biane's map to noncrossing set partitions.
Properties
injective, graded
Sage code
def mapping(D):
return SetPartition(D.to_noncrossing_partition())
Weight
26
Created
Jan 29, 2020 at 13:26 by FindStatCrew
Updated
Jan 29, 2020 at 13:26 by Martin Rubey
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