Identifier
Mp00138: Dyck paths to noncrossing partitionSet partitions
Mp00215: Set partitions Wachs-WhiteSet partitions
Mp00115: Set partitions Kasraoui-Zeng Set partitions
Images
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Cc0005;cc-rep-0Cc0009;cc-rep-1Cc0009;cc-rep-2Cc0009;cc-rep-3
[1,0]=>{{1}}=>{{1}}=>{{1}} [1,0,1,0]=>{{1},{2}}=>{{1},{2}}=>{{1},{2}} [1,1,0,0]=>{{1,2}}=>{{1,2}}=>{{1,2}} [1,0,1,0,1,0]=>{{1},{2},{3}}=>{{1},{2},{3}}=>{{1},{2},{3}} [1,0,1,1,0,0]=>{{1},{2,3}}=>{{1,2},{3}}=>{{1,2},{3}} [1,1,0,0,1,0]=>{{1,2},{3}}=>{{1},{2,3}}=>{{1},{2,3}} [1,1,0,1,0,0]=>{{1,3},{2}}=>{{1,3},{2}}=>{{1,3},{2}} [1,1,1,0,0,0]=>{{1,2,3}}=>{{1,2,3}}=>{{1,2,3}} [1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4}}=>{{1},{2},{3},{4}}=>{{1},{2},{3},{4}} [1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}}=>{{1,2},{3},{4}}=>{{1,2},{3},{4}} [1,0,1,1,0,0,1,0]=>{{1},{2,3},{4}}=>{{1},{2,3},{4}}=>{{1},{2,3},{4}} [1,0,1,1,0,1,0,0]=>{{1},{2,4},{3}}=>{{1,3},{2},{4}}=>{{1,3},{2},{4}} [1,0,1,1,1,0,0,0]=>{{1},{2,3,4}}=>{{1,2,3},{4}}=>{{1,2,3},{4}} [1,1,0,0,1,0,1,0]=>{{1,2},{3},{4}}=>{{1},{2},{3,4}}=>{{1},{2},{3,4}} [1,1,0,0,1,1,0,0]=>{{1,2},{3,4}}=>{{1,2},{3,4}}=>{{1,2},{3,4}} [1,1,0,1,0,0,1,0]=>{{1,3},{2},{4}}=>{{1},{2,4},{3}}=>{{1},{2,4},{3}} [1,1,0,1,0,1,0,0]=>{{1,4},{2},{3}}=>{{1,4},{2},{3}}=>{{1,4},{2},{3}} [1,1,0,1,1,0,0,0]=>{{1,3,4},{2}}=>{{1,2,4},{3}}=>{{1,2,4},{3}} [1,1,1,0,0,0,1,0]=>{{1,2,3},{4}}=>{{1},{2,3,4}}=>{{1},{2,3,4}} [1,1,1,0,0,1,0,0]=>{{1,4},{2,3}}=>{{1,4},{2,3}}=>{{1,3},{2,4}} [1,1,1,0,1,0,0,0]=>{{1,2,4},{3}}=>{{1,3},{2,4}}=>{{1,4},{2,3}} [1,1,1,1,0,0,0,0]=>{{1,2,3,4}}=>{{1,2,3,4}}=>{{1,2,3,4}} [1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5}} [1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}}=>{{1,2},{3},{4},{5}}=>{{1,2},{3},{4},{5}} [1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}}=>{{1},{2,3},{4},{5}}=>{{1},{2,3},{4},{5}} [1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3,5},{4}}=>{{1,3},{2},{4},{5}}=>{{1,3},{2},{4},{5}} [1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}}=>{{1,2,3},{4},{5}}=>{{1,2,3},{4},{5}} [1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5}}=>{{1},{2},{3,4},{5}}=>{{1},{2},{3,4},{5}} [1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>{{1,2},{3,4},{5}}=>{{1,2},{3,4},{5}} [1,0,1,1,0,1,0,0,1,0]=>{{1},{2,4},{3},{5}}=>{{1},{2,4},{3},{5}}=>{{1},{2,4},{3},{5}} [1,0,1,1,0,1,0,1,0,0]=>{{1},{2,5},{3},{4}}=>{{1,4},{2},{3},{5}}=>{{1,4},{2},{3},{5}} [1,0,1,1,0,1,1,0,0,0]=>{{1},{2,4,5},{3}}=>{{1,2,4},{3},{5}}=>{{1,2,4},{3},{5}} [1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}}=>{{1},{2,3,4},{5}}=>{{1},{2,3,4},{5}} [1,0,1,1,1,0,0,1,0,0]=>{{1},{2,5},{3,4}}=>{{1,4},{2,3},{5}}=>{{1,3},{2,4},{5}} [1,0,1,1,1,0,1,0,0,0]=>{{1},{2,3,5},{4}}=>{{1,3},{2,4},{5}}=>{{1,4},{2,3},{5}} [1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}}=>{{1,2,3,4},{5}}=>{{1,2,3,4},{5}} [1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5}}=>{{1},{2},{3},{4,5}}=>{{1},{2},{3},{4,5}} [1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5}}=>{{1,2},{3},{4,5}}=>{{1,2},{3},{4,5}} [1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}}=>{{1},{2,3},{4,5}}=>{{1},{2,3},{4,5}} [1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,5},{4}}=>{{1,3},{2},{4,5}}=>{{1,3},{2},{4,5}} [1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>{{1,2,3},{4,5}}=>{{1,2,3},{4,5}} [1,1,0,1,0,0,1,0,1,0]=>{{1,3},{2},{4},{5}}=>{{1},{2},{3,5},{4}}=>{{1},{2},{3,5},{4}} [1,1,0,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5}}=>{{1,2},{3,5},{4}}=>{{1,2},{3,5},{4}} [1,1,0,1,0,1,0,0,1,0]=>{{1,4},{2},{3},{5}}=>{{1},{2,5},{3},{4}}=>{{1},{2,5},{3},{4}} [1,1,0,1,0,1,0,1,0,0]=>{{1,5},{2},{3},{4}}=>{{1,5},{2},{3},{4}}=>{{1,5},{2},{3},{4}} [1,1,0,1,0,1,1,0,0,0]=>{{1,4,5},{2},{3}}=>{{1,2,5},{3},{4}}=>{{1,2,5},{3},{4}} [1,1,0,1,1,0,0,0,1,0]=>{{1,3,4},{2},{5}}=>{{1},{2,3,5},{4}}=>{{1},{2,3,5},{4}} [1,1,0,1,1,0,0,1,0,0]=>{{1,5},{2},{3,4}}=>{{1,5},{2,3},{4}}=>{{1,3},{2,5},{4}} [1,1,0,1,1,0,1,0,0,0]=>{{1,3,5},{2},{4}}=>{{1,3},{2,5},{4}}=>{{1,5},{2,3},{4}} [1,1,0,1,1,1,0,0,0,0]=>{{1,3,4,5},{2}}=>{{1,2,3,5},{4}}=>{{1,2,3,5},{4}} [1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4},{5}}=>{{1},{2},{3,4,5}}=>{{1},{2},{3,4,5}} [1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}}=>{{1,2},{3,4,5}}=>{{1,2},{3,4,5}} [1,1,1,0,0,1,0,0,1,0]=>{{1,4},{2,3},{5}}=>{{1},{2,5},{3,4}}=>{{1},{2,4},{3,5}} [1,1,1,0,0,1,0,1,0,0]=>{{1,5},{2,3},{4}}=>{{1,5},{2},{3,4}}=>{{1,4},{2},{3,5}} [1,1,1,0,0,1,1,0,0,0]=>{{1,4,5},{2,3}}=>{{1,2,5},{3,4}}=>{{1,2,4},{3,5}} [1,1,1,0,1,0,0,0,1,0]=>{{1,2,4},{3},{5}}=>{{1},{2,4},{3,5}}=>{{1},{2,5},{3,4}} [1,1,1,0,1,0,0,1,0,0]=>{{1,5},{2,4},{3}}=>{{1,5},{2,4},{3}}=>{{1,4},{2,5},{3}} [1,1,1,0,1,0,1,0,0,0]=>{{1,2,5},{3},{4}}=>{{1,4},{2},{3,5}}=>{{1,5},{2},{3,4}} [1,1,1,0,1,1,0,0,0,0]=>{{1,2,4,5},{3}}=>{{1,2,4},{3,5}}=>{{1,2,5},{3,4}} [1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5}}=>{{1},{2,3,4,5}}=>{{1},{2,3,4,5}} [1,1,1,1,0,0,0,1,0,0]=>{{1,5},{2,3,4}}=>{{1,5},{2,3,4}}=>{{1,3,5},{2,4}} [1,1,1,1,0,0,1,0,0,0]=>{{1,2,5},{3,4}}=>{{1,4},{2,3,5}}=>{{1,3,4},{2,5}} [1,1,1,1,0,1,0,0,0,0]=>{{1,2,3,5},{4}}=>{{1,3},{2,4,5}}=>{{1,4,5},{2,3}} [1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6}} [1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6}} [1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}}=>{{1},{2,3},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6}} [1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4,6},{5}}=>{{1,3},{2},{4},{5},{6}}=>{{1,3},{2},{4},{5},{6}} [1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}}=>{{1,2,3},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}} [1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5},{6}} [1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>{{1,2},{3,4},{5},{6}}=>{{1,2},{3,4},{5},{6}} [1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3,5},{4},{6}}=>{{1},{2,4},{3},{5},{6}}=>{{1},{2,4},{3},{5},{6}} [1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3,6},{4},{5}}=>{{1,4},{2},{3},{5},{6}}=>{{1,4},{2},{3},{5},{6}} [1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3,5,6},{4}}=>{{1,2,4},{3},{5},{6}}=>{{1,2,4},{3},{5},{6}} [1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}}=>{{1},{2,3,4},{5},{6}}=>{{1},{2,3,4},{5},{6}} [1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3,6},{4,5}}=>{{1,4},{2,3},{5},{6}}=>{{1,3},{2,4},{5},{6}} [1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3,4,6},{5}}=>{{1,3},{2,4},{5},{6}}=>{{1,4},{2,3},{5},{6}} [1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}}=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}} [1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6}}=>{{1},{2},{3},{4,5},{6}}=>{{1},{2},{3},{4,5},{6}} [1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}}=>{{1,2},{3},{4,5},{6}}=>{{1,2},{3},{4,5},{6}} [1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>{{1},{2,3},{4,5},{6}}=>{{1},{2,3},{4,5},{6}} [1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2,3},{4,6},{5}}=>{{1,3},{2},{4,5},{6}}=>{{1,3},{2},{4,5},{6}} [1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,2,3},{4,5},{6}}=>{{1,2,3},{4,5},{6}} [1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6}}=>{{1},{2},{3,5},{4},{6}}=>{{1},{2},{3,5},{4},{6}} [1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2,4},{3},{5,6}}=>{{1,2},{3,5},{4},{6}}=>{{1,2},{3,5},{4},{6}} [1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2,5},{3},{4},{6}}=>{{1},{2,5},{3},{4},{6}}=>{{1},{2,5},{3},{4},{6}} [1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2,6},{3},{4},{5}}=>{{1,5},{2},{3},{4},{6}}=>{{1,5},{2},{3},{4},{6}} [1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2,5,6},{3},{4}}=>{{1,2,5},{3},{4},{6}}=>{{1,2,5},{3},{4},{6}} [1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2,4,5},{3},{6}}=>{{1},{2,3,5},{4},{6}}=>{{1},{2,3,5},{4},{6}} [1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2,6},{3},{4,5}}=>{{1,5},{2,3},{4},{6}}=>{{1,3},{2,5},{4},{6}} [1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2,4,6},{3},{5}}=>{{1,3},{2,5},{4},{6}}=>{{1,5},{2,3},{4},{6}} [1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2,4,5,6},{3}}=>{{1,2,3,5},{4},{6}}=>{{1,2,3,5},{4},{6}} [1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}}=>{{1},{2},{3,4,5},{6}}=>{{1},{2},{3,4,5},{6}} [1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,2},{3,4,5},{6}}=>{{1,2},{3,4,5},{6}} [1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2,5},{3,4},{6}}=>{{1},{2,5},{3,4},{6}}=>{{1},{2,4},{3,5},{6}} [1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2,6},{3,4},{5}}=>{{1,5},{2},{3,4},{6}}=>{{1,4},{2},{3,5},{6}} [1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2,5,6},{3,4}}=>{{1,2,5},{3,4},{6}}=>{{1,2,4},{3,5},{6}} [1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2,3,5},{4},{6}}=>{{1},{2,4},{3,5},{6}}=>{{1},{2,5},{3,4},{6}} [1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2,6},{3,5},{4}}=>{{1,5},{2,4},{3},{6}}=>{{1,4},{2,5},{3},{6}} [1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2,3,6},{4},{5}}=>{{1,4},{2},{3,5},{6}}=>{{1,5},{2},{3,4},{6}} [1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2,3,5,6},{4}}=>{{1,2,4},{3,5},{6}}=>{{1,2,5},{3,4},{6}} [1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}} [1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2,6},{3,4,5}}=>{{1,5},{2,3,4},{6}}=>{{1,3,5},{2,4},{6}} [1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2,3,6},{4,5}}=>{{1,4},{2,3,5},{6}}=>{{1,3,4},{2,5},{6}} [1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2,3,4,6},{5}}=>{{1,3},{2,4,5},{6}}=>{{1,4,5},{2,3},{6}} [1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5,6}}=>{{1},{2},{3},{4},{5,6}} [1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5,6}} [1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6}}=>{{1},{2,3},{4},{5,6}}=>{{1},{2,3},{4},{5,6}} [1,1,0,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4,6},{5}}=>{{1,3},{2},{4},{5,6}}=>{{1,3},{2},{4},{5,6}} [1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}}=>{{1,2,3},{4},{5,6}}=>{{1,2,3},{4},{5,6}} [1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5,6}}=>{{1},{2},{3,4},{5,6}} [1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}} [1,1,0,0,1,1,0,1,0,0,1,0]=>{{1,2},{3,5},{4},{6}}=>{{1},{2,4},{3},{5,6}}=>{{1},{2,4},{3},{5,6}} [1,1,0,0,1,1,0,1,0,1,0,0]=>{{1,2},{3,6},{4},{5}}=>{{1,4},{2},{3},{5,6}}=>{{1,4},{2},{3},{5,6}} [1,1,0,0,1,1,0,1,1,0,0,0]=>{{1,2},{3,5,6},{4}}=>{{1,2,4},{3},{5,6}}=>{{1,2,4},{3},{5,6}} [1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>{{1},{2,3,4},{5,6}}=>{{1},{2,3,4},{5,6}} [1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5}}=>{{1,4},{2,3},{5,6}}=>{{1,3},{2,4},{5,6}} [1,1,0,0,1,1,1,0,1,0,0,0]=>{{1,2},{3,4,6},{5}}=>{{1,3},{2,4},{5,6}}=>{{1,4},{2,3},{5,6}} [1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,3,4},{5,6}}=>{{1,2,3,4},{5,6}} [1,1,0,1,0,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6}}=>{{1},{2},{3},{4,6},{5}}=>{{1},{2},{3},{4,6},{5}} [1,1,0,1,0,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5,6}}=>{{1,2},{3},{4,6},{5}}=>{{1,2},{3},{4,6},{5}} [1,1,0,1,0,0,1,1,0,0,1,0]=>{{1,3},{2},{4,5},{6}}=>{{1},{2,3},{4,6},{5}}=>{{1},{2,3},{4,6},{5}} [1,1,0,1,0,0,1,1,0,1,0,0]=>{{1,3},{2},{4,6},{5}}=>{{1,3},{2},{4,6},{5}}=>{{1,3},{2},{4,6},{5}} [1,1,0,1,0,0,1,1,1,0,0,0]=>{{1,3},{2},{4,5,6}}=>{{1,2,3},{4,6},{5}}=>{{1,2,3},{4,6},{5}} [1,1,0,1,0,1,0,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6}}=>{{1},{2},{3,6},{4},{5}}=>{{1},{2},{3,6},{4},{5}} [1,1,0,1,0,1,0,0,1,1,0,0]=>{{1,4},{2},{3},{5,6}}=>{{1,2},{3,6},{4},{5}}=>{{1,2},{3,6},{4},{5}} [1,1,0,1,0,1,0,1,0,0,1,0]=>{{1,5},{2},{3},{4},{6}}=>{{1},{2,6},{3},{4},{5}}=>{{1},{2,6},{3},{4},{5}} [1,1,0,1,0,1,0,1,0,1,0,0]=>{{1,6},{2},{3},{4},{5}}=>{{1,6},{2},{3},{4},{5}}=>{{1,6},{2},{3},{4},{5}} [1,1,0,1,0,1,0,1,1,0,0,0]=>{{1,5,6},{2},{3},{4}}=>{{1,2,6},{3},{4},{5}}=>{{1,2,6},{3},{4},{5}} [1,1,0,1,0,1,1,0,0,0,1,0]=>{{1,4,5},{2},{3},{6}}=>{{1},{2,3,6},{4},{5}}=>{{1},{2,3,6},{4},{5}} [1,1,0,1,0,1,1,0,0,1,0,0]=>{{1,6},{2},{3},{4,5}}=>{{1,6},{2,3},{4},{5}}=>{{1,3},{2,6},{4},{5}} [1,1,0,1,0,1,1,0,1,0,0,0]=>{{1,4,6},{2},{3},{5}}=>{{1,3},{2,6},{4},{5}}=>{{1,6},{2,3},{4},{5}} [1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2},{3}}=>{{1,2,3,6},{4},{5}}=>{{1,2,3,6},{4},{5}} [1,1,0,1,1,0,0,0,1,0,1,0]=>{{1,3,4},{2},{5},{6}}=>{{1},{2},{3,4,6},{5}}=>{{1},{2},{3,4,6},{5}} [1,1,0,1,1,0,0,0,1,1,0,0]=>{{1,3,4},{2},{5,6}}=>{{1,2},{3,4,6},{5}}=>{{1,2},{3,4,6},{5}} [1,1,0,1,1,0,0,1,0,0,1,0]=>{{1,5},{2},{3,4},{6}}=>{{1},{2,6},{3,4},{5}}=>{{1},{2,4},{3,6},{5}} [1,1,0,1,1,0,0,1,0,1,0,0]=>{{1,6},{2},{3,4},{5}}=>{{1,6},{2},{3,4},{5}}=>{{1,4},{2},{3,6},{5}} [1,1,0,1,1,0,0,1,1,0,0,0]=>{{1,5,6},{2},{3,4}}=>{{1,2,6},{3,4},{5}}=>{{1,2,4},{3,6},{5}} [1,1,0,1,1,0,1,0,0,0,1,0]=>{{1,3,5},{2},{4},{6}}=>{{1},{2,4},{3,6},{5}}=>{{1},{2,6},{3,4},{5}} [1,1,0,1,1,0,1,0,0,1,0,0]=>{{1,6},{2},{3,5},{4}}=>{{1,6},{2,4},{3},{5}}=>{{1,4},{2,6},{3},{5}} [1,1,0,1,1,0,1,0,1,0,0,0]=>{{1,3,6},{2},{4},{5}}=>{{1,4},{2},{3,6},{5}}=>{{1,6},{2},{3,4},{5}} [1,1,0,1,1,0,1,1,0,0,0,0]=>{{1,3,5,6},{2},{4}}=>{{1,2,4},{3,6},{5}}=>{{1,2,6},{3,4},{5}} [1,1,0,1,1,1,0,0,0,0,1,0]=>{{1,3,4,5},{2},{6}}=>{{1},{2,3,4,6},{5}}=>{{1},{2,3,4,6},{5}} [1,1,0,1,1,1,0,0,0,1,0,0]=>{{1,6},{2},{3,4,5}}=>{{1,6},{2,3,4},{5}}=>{{1,3,6},{2,4},{5}} [1,1,0,1,1,1,0,0,1,0,0,0]=>{{1,3,6},{2},{4,5}}=>{{1,4},{2,3,6},{5}}=>{{1,3,4},{2,6},{5}} [1,1,0,1,1,1,0,1,0,0,0,0]=>{{1,3,4,6},{2},{5}}=>{{1,3},{2,4,6},{5}}=>{{1,4,6},{2,3},{5}} [1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}}=>{{1,2,3,4,6},{5}}=>{{1,2,3,4,6},{5}} [1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6}}=>{{1},{2},{3},{4,5,6}}=>{{1},{2},{3},{4,5,6}} [1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}}=>{{1,2},{3},{4,5,6}}=>{{1,2},{3},{4,5,6}} [1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}}=>{{1},{2,3},{4,5,6}}=>{{1},{2,3},{4,5,6}} [1,1,1,0,0,0,1,1,0,1,0,0]=>{{1,2,3},{4,6},{5}}=>{{1,3},{2},{4,5,6}}=>{{1,3},{2},{4,5,6}} [1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}} [1,1,1,0,0,1,0,0,1,0,1,0]=>{{1,4},{2,3},{5},{6}}=>{{1},{2},{3,6},{4,5}}=>{{1},{2},{3,5},{4,6}} [1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6}}=>{{1,2},{3,6},{4,5}}=>{{1,2},{3,5},{4,6}} [1,1,1,0,0,1,0,1,0,0,1,0]=>{{1,5},{2,3},{4},{6}}=>{{1},{2,6},{3},{4,5}}=>{{1},{2,5},{3},{4,6}} [1,1,1,0,0,1,0,1,0,1,0,0]=>{{1,6},{2,3},{4},{5}}=>{{1,6},{2},{3},{4,5}}=>{{1,5},{2},{3},{4,6}} [1,1,1,0,0,1,0,1,1,0,0,0]=>{{1,5,6},{2,3},{4}}=>{{1,2,6},{3},{4,5}}=>{{1,2,5},{3},{4,6}} [1,1,1,0,0,1,1,0,0,0,1,0]=>{{1,4,5},{2,3},{6}}=>{{1},{2,3,6},{4,5}}=>{{1},{2,3,5},{4,6}} [1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5}}=>{{1,6},{2,3},{4,5}}=>{{1,3},{2,5},{4,6}} [1,1,1,0,0,1,1,0,1,0,0,0]=>{{1,4,6},{2,3},{5}}=>{{1,3},{2,6},{4,5}}=>{{1,5},{2,3},{4,6}} [1,1,1,0,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2,3}}=>{{1,2,3,6},{4,5}}=>{{1,2,3,5},{4,6}} [1,1,1,0,1,0,0,0,1,0,1,0]=>{{1,2,4},{3},{5},{6}}=>{{1},{2},{3,5},{4,6}}=>{{1},{2},{3,6},{4,5}} [1,1,1,0,1,0,0,0,1,1,0,0]=>{{1,2,4},{3},{5,6}}=>{{1,2},{3,5},{4,6}}=>{{1,2},{3,6},{4,5}} [1,1,1,0,1,0,0,1,0,0,1,0]=>{{1,5},{2,4},{3},{6}}=>{{1},{2,6},{3,5},{4}}=>{{1},{2,5},{3,6},{4}} [1,1,1,0,1,0,0,1,0,1,0,0]=>{{1,6},{2,4},{3},{5}}=>{{1,6},{2},{3,5},{4}}=>{{1,5},{2},{3,6},{4}} [1,1,1,0,1,0,0,1,1,0,0,0]=>{{1,5,6},{2,4},{3}}=>{{1,2,6},{3,5},{4}}=>{{1,2,5},{3,6},{4}} [1,1,1,0,1,0,1,0,0,0,1,0]=>{{1,2,5},{3},{4},{6}}=>{{1},{2,5},{3},{4,6}}=>{{1},{2,6},{3},{4,5}} [1,1,1,0,1,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3},{4}}=>{{1,6},{2,5},{3},{4}}=>{{1,5},{2,6},{3},{4}} [1,1,1,0,1,0,1,0,1,0,0,0]=>{{1,2,6},{3},{4},{5}}=>{{1,5},{2},{3},{4,6}}=>{{1,6},{2},{3},{4,5}} [1,1,1,0,1,0,1,1,0,0,0,0]=>{{1,2,5,6},{3},{4}}=>{{1,2,5},{3},{4,6}}=>{{1,2,6},{3},{4,5}} [1,1,1,0,1,1,0,0,0,0,1,0]=>{{1,2,4,5},{3},{6}}=>{{1},{2,3,5},{4,6}}=>{{1},{2,3,6},{4,5}} [1,1,1,0,1,1,0,0,0,1,0,0]=>{{1,6},{2,4,5},{3}}=>{{1,6},{2,3,5},{4}}=>{{1,3,6},{2,5},{4}} [1,1,1,0,1,1,0,0,1,0,0,0]=>{{1,2,6},{3},{4,5}}=>{{1,5},{2,3},{4,6}}=>{{1,3},{2,6},{4,5}} [1,1,1,0,1,1,0,1,0,0,0,0]=>{{1,2,4,6},{3},{5}}=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3},{4,5}} [1,1,1,0,1,1,1,0,0,0,0,0]=>{{1,2,4,5,6},{3}}=>{{1,2,3,5},{4,6}}=>{{1,2,3,6},{4,5}} [1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}}=>{{1},{2},{3,4,5,6}}=>{{1},{2},{3,4,5,6}} [1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>{{1,2},{3,4,5,6}}=>{{1,2},{3,4,5,6}} [1,1,1,1,0,0,0,1,0,0,1,0]=>{{1,5},{2,3,4},{6}}=>{{1},{2,6},{3,4,5}}=>{{1},{2,4,6},{3,5}} [1,1,1,1,0,0,0,1,0,1,0,0]=>{{1,6},{2,3,4},{5}}=>{{1,6},{2},{3,4,5}}=>{{1,4,6},{2},{3,5}} [1,1,1,1,0,0,0,1,1,0,0,0]=>{{1,5,6},{2,3,4}}=>{{1,2,6},{3,4,5}}=>{{1,2,4,6},{3,5}} [1,1,1,1,0,0,1,0,0,0,1,0]=>{{1,2,5},{3,4},{6}}=>{{1},{2,5},{3,4,6}}=>{{1},{2,4,5},{3,6}} [1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3,4}}=>{{1,6},{2,5},{3,4}}=>{{1,4},{2,5},{3,6}} [1,1,1,1,0,0,1,0,1,0,0,0]=>{{1,2,6},{3,4},{5}}=>{{1,5},{2},{3,4,6}}=>{{1,4,5},{2},{3,6}} [1,1,1,1,0,0,1,1,0,0,0,0]=>{{1,2,5,6},{3,4}}=>{{1,2,5},{3,4,6}}=>{{1,2,4,5},{3,6}} [1,1,1,1,0,1,0,0,0,0,1,0]=>{{1,2,3,5},{4},{6}}=>{{1},{2,4},{3,5,6}}=>{{1},{2,5,6},{3,4}} [1,1,1,1,0,1,0,0,0,1,0,0]=>{{1,6},{2,3,5},{4}}=>{{1,6},{2,4},{3,5}}=>{{1,5},{2,4},{3,6}} [1,1,1,1,0,1,0,0,1,0,0,0]=>{{1,2,6},{3,5},{4}}=>{{1,5},{2,4},{3,6}}=>{{1,6},{2,4},{3,5}} [1,1,1,1,0,1,0,1,0,0,0,0]=>{{1,2,3,6},{4},{5}}=>{{1,4},{2},{3,5,6}}=>{{1,5,6},{2},{3,4}} [1,1,1,1,0,1,1,0,0,0,0,0]=>{{1,2,3,5,6},{4}}=>{{1,2,4},{3,5,6}}=>{{1,2,5,6},{3,4}} [1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}}=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}}=>{{1,6},{2,3,4,5}}=>{{1,3,5},{2,4,6}} [1,1,1,1,1,0,0,0,1,0,0,0]=>{{1,2,6},{3,4,5}}=>{{1,5},{2,3,4,6}}=>{{1,3,6},{2,4,5}} [1,1,1,1,1,0,0,1,0,0,0,0]=>{{1,2,3,6},{4,5}}=>{{1,4},{2,3,5,6}}=>{{1,3,4},{2,5,6}} [1,1,1,1,1,0,1,0,0,0,0,0]=>{{1,2,3,4,6},{5}}=>{{1,3},{2,4,5,6}}=>{{1,4,5,6},{2,3}} [1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4},{5,7},{6}}=>{{1,3},{2},{4},{5},{6},{7}}=>{{1,3},{2},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6,7}}=>{{1,2,3},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7}}=>{{1},{2},{3,4},{5},{6},{7}}=>{{1},{2},{3,4},{5},{6},{7}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>{{1,2},{3,4},{5},{6},{7}}=>{{1,2},{3,4},{5},{6},{7}} [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3},{4,6},{5},{7}}=>{{1},{2,4},{3},{5},{6},{7}}=>{{1},{2,4},{3},{5},{6},{7}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3},{4,7},{5},{6}}=>{{1,4},{2},{3},{5},{6},{7}}=>{{1,4},{2},{3},{5},{6},{7}} [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3},{4,6,7},{5}}=>{{1,2,4},{3},{5},{6},{7}}=>{{1,2,4},{3},{5},{6},{7}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}}=>{{1},{2,3,4},{5},{6},{7}}=>{{1},{2,3,4},{5},{6},{7}} [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3},{4,7},{5,6}}=>{{1,4},{2,3},{5},{6},{7}}=>{{1,3},{2,4},{5},{6},{7}} [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3},{4,5,7},{6}}=>{{1,3},{2,4},{5},{6},{7}}=>{{1,4},{2,3},{5},{6},{7}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}}=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7}} [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}}=>{{1,2},{3},{4,5},{6},{7}}=>{{1,2},{3},{4,5},{6},{7}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>{{1},{2,3},{4,5},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}} [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2},{3,4},{5,7},{6}}=>{{1,3},{2},{4,5},{6},{7}}=>{{1,3},{2},{4,5},{6},{7}} [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3},{4,5},{6},{7}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2},{3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4},{6},{7}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2},{3,5},{4},{6,7}}=>{{1,2},{3,5},{4},{6},{7}}=>{{1,2},{3,5},{4},{6},{7}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2},{3,6},{4},{5},{7}}=>{{1},{2,5},{3},{4},{6},{7}}=>{{1},{2,5},{3},{4},{6},{7}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2},{3,7},{4},{5},{6}}=>{{1,5},{2},{3},{4},{6},{7}}=>{{1,5},{2},{3},{4},{6},{7}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4},{5}}=>{{1,2,5},{3},{4},{6},{7}}=>{{1,2,5},{3},{4},{6},{7}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2},{3,5,6},{4},{7}}=>{{1},{2,3,5},{4},{6},{7}}=>{{1},{2,3,5},{4},{6},{7}} [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2},{3,7},{4},{5,6}}=>{{1,5},{2,3},{4},{6},{7}}=>{{1,3},{2,5},{4},{6},{7}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2},{3,5,7},{4},{6}}=>{{1,3},{2,5},{4},{6},{7}}=>{{1,5},{2,3},{4},{6},{7}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2},{3,5,6,7},{4}}=>{{1,2,3,5},{4},{6},{7}}=>{{1,2,3,5},{4},{6},{7}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6},{7}}=>{{1,2},{3,4,5},{6},{7}} [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2},{3,6},{4,5},{7}}=>{{1},{2,5},{3,4},{6},{7}}=>{{1},{2,4},{3,5},{6},{7}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2},{3,7},{4,5},{6}}=>{{1,5},{2},{3,4},{6},{7}}=>{{1,4},{2},{3,5},{6},{7}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4,5}}=>{{1,2,5},{3,4},{6},{7}}=>{{1,2,4},{3,5},{6},{7}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2},{3,4,6},{5},{7}}=>{{1},{2,4},{3,5},{6},{7}}=>{{1},{2,5},{3,4},{6},{7}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2},{3,7},{4,6},{5}}=>{{1,5},{2,4},{3},{6},{7}}=>{{1,4},{2,5},{3},{6},{7}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2},{3,4,7},{5},{6}}=>{{1,4},{2},{3,5},{6},{7}}=>{{1,5},{2},{3,4},{6},{7}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2},{3,4,6,7},{5}}=>{{1,2,4},{3,5},{6},{7}}=>{{1,2,5},{3,4},{6},{7}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}}=>{{1},{2,3,4,5},{6},{7}}=>{{1},{2,3,4,5},{6},{7}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2},{3,7},{4,5,6}}=>{{1,5},{2,3,4},{6},{7}}=>{{1,3,5},{2,4},{6},{7}} [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2},{3,4,7},{5,6}}=>{{1,4},{2,3,5},{6},{7}}=>{{1,3,4},{2,5},{6},{7}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2},{3,4,5,7},{6}}=>{{1,3},{2,4,5},{6},{7}}=>{{1,4,5},{2,3},{6},{7}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5,6},{7}}=>{{1},{2},{3},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5,6},{7}}=>{{1,2},{3},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>{{1},{2,3},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,6},{7}}=>{{1,3},{2},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6},{7}}=>{{1,2,3},{4},{5,6},{7}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>{{1},{2},{3,4},{5,6},{7}}=>{{1},{2},{3,4},{5,6},{7}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,2},{3,4},{5,6},{7}}=>{{1,2},{3,4},{5,6},{7}} [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>{{1},{2,3},{4,6},{5},{7}}=>{{1},{2,4},{3},{5,6},{7}}=>{{1},{2,4},{3},{5,6},{7}} [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>{{1},{2,3},{4,7},{5},{6}}=>{{1,4},{2},{3},{5,6},{7}}=>{{1,4},{2},{3},{5,6},{7}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>{{1},{2,3},{4,6,7},{5}}=>{{1,2,4},{3},{5,6},{7}}=>{{1,2,4},{3},{5,6},{7}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1},{2,3,4},{5,6},{7}}=>{{1},{2,3,4},{5,6},{7}} [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1},{2,3},{4,7},{5,6}}=>{{1,4},{2,3},{5,6},{7}}=>{{1,3},{2,4},{5,6},{7}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>{{1},{2,3},{4,5,7},{6}}=>{{1,3},{2,4},{5,6},{7}}=>{{1,4},{2,3},{5,6},{7}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4},{5,6},{7}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6},{7}}=>{{1},{2},{3},{4,6},{5},{7}}=>{{1},{2},{3},{4,6},{5},{7}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>{{1},{2,4},{3},{5},{6,7}}=>{{1,2},{3},{4,6},{5},{7}}=>{{1,2},{3},{4,6},{5},{7}} [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>{{1},{2,4},{3},{5,6},{7}}=>{{1},{2,3},{4,6},{5},{7}}=>{{1},{2,3},{4,6},{5},{7}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>{{1},{2,4},{3},{5,7},{6}}=>{{1,3},{2},{4,6},{5},{7}}=>{{1,3},{2},{4,6},{5},{7}} [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>{{1},{2,4},{3},{5,6,7}}=>{{1,2,3},{4,6},{5},{7}}=>{{1,2,3},{4,6},{5},{7}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3},{4},{6},{7}}=>{{1},{2},{3,6},{4},{5},{7}}=>{{1},{2},{3,6},{4},{5},{7}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3},{4},{6,7}}=>{{1,2},{3,6},{4},{5},{7}}=>{{1,2},{3,6},{4},{5},{7}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3},{4},{5},{7}}=>{{1},{2,6},{3},{4},{5},{7}}=>{{1},{2,6},{3},{4},{5},{7}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3},{4},{5},{6}}=>{{1,6},{2},{3},{4},{5},{7}}=>{{1,6},{2},{3},{4},{5},{7}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4},{5}}=>{{1,2,6},{3},{4},{5},{7}}=>{{1,2,6},{3},{4},{5},{7}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3},{4},{7}}=>{{1},{2,3,6},{4},{5},{7}}=>{{1},{2,3,6},{4},{5},{7}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3},{4},{5,6}}=>{{1,6},{2,3},{4},{5},{7}}=>{{1,3},{2,6},{4},{5},{7}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3},{4},{6}}=>{{1,3},{2,6},{4},{5},{7}}=>{{1,6},{2,3},{4},{5},{7}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3},{4}}=>{{1,2,3,6},{4},{5},{7}}=>{{1,2,3,6},{4},{5},{7}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>{{1},{2,4,5},{3},{6},{7}}=>{{1},{2},{3,4,6},{5},{7}}=>{{1},{2},{3,4,6},{5},{7}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>{{1},{2,4,5},{3},{6,7}}=>{{1,2},{3,4,6},{5},{7}}=>{{1,2},{3,4,6},{5},{7}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3},{4,5},{7}}=>{{1},{2,6},{3,4},{5},{7}}=>{{1},{2,4},{3,6},{5},{7}} [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3},{4,5},{6}}=>{{1,6},{2},{3,4},{5},{7}}=>{{1,4},{2},{3,6},{5},{7}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4,5}}=>{{1,2,6},{3,4},{5},{7}}=>{{1,2,4},{3,6},{5},{7}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>{{1},{2,4,6},{3},{5},{7}}=>{{1},{2,4},{3,6},{5},{7}}=>{{1},{2,6},{3,4},{5},{7}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3},{4,6},{5}}=>{{1,6},{2,4},{3},{5},{7}}=>{{1,4},{2,6},{3},{5},{7}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>{{1},{2,4,7},{3},{5},{6}}=>{{1,4},{2},{3,6},{5},{7}}=>{{1,6},{2},{3,4},{5},{7}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>{{1},{2,4,6,7},{3},{5}}=>{{1,2,4},{3,6},{5},{7}}=>{{1,2,6},{3,4},{5},{7}} [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>{{1},{2,4,5,6},{3},{7}}=>{{1},{2,3,4,6},{5},{7}}=>{{1},{2,3,4,6},{5},{7}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3},{4,5,6}}=>{{1,6},{2,3,4},{5},{7}}=>{{1,3,6},{2,4},{5},{7}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>{{1},{2,4,7},{3},{5,6}}=>{{1,4},{2,3,6},{5},{7}}=>{{1,3,4},{2,6},{5},{7}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>{{1},{2,4,5,7},{3},{6}}=>{{1,3},{2,4,6},{5},{7}}=>{{1,4,6},{2,3},{5},{7}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}}=>{{1,2,3,4,6},{5},{7}}=>{{1,2,3,4,6},{5},{7}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}}=>{{1},{2},{3},{4,5,6},{7}}=>{{1},{2},{3},{4,5,6},{7}} [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>{{1,2},{3},{4,5,6},{7}}=>{{1,2},{3},{4,5,6},{7}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1},{2,3},{4,5,6},{7}}=>{{1},{2,3},{4,5,6},{7}} [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>{{1},{2,3,4},{5,7},{6}}=>{{1,3},{2},{4,5,6},{7}}=>{{1,3},{2},{4,5,6},{7}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3},{4,5,6},{7}} [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3,4},{6},{7}}=>{{1},{2},{3,6},{4,5},{7}}=>{{1},{2},{3,5},{4,6},{7}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3,4},{6,7}}=>{{1,2},{3,6},{4,5},{7}}=>{{1,2},{3,5},{4,6},{7}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3,4},{5},{7}}=>{{1},{2,6},{3},{4,5},{7}}=>{{1},{2,5},{3},{4,6},{7}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3,4},{5},{6}}=>{{1,6},{2},{3},{4,5},{7}}=>{{1,5},{2},{3},{4,6},{7}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4},{5}}=>{{1,2,6},{3},{4,5},{7}}=>{{1,2,5},{3},{4,6},{7}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3,4},{7}}=>{{1},{2,3,6},{4,5},{7}}=>{{1},{2,3,5},{4,6},{7}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3,4},{5,6}}=>{{1,6},{2,3},{4,5},{7}}=>{{1,3},{2,5},{4,6},{7}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3,4},{6}}=>{{1,3},{2,6},{4,5},{7}}=>{{1,5},{2,3},{4,6},{7}} [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3,4}}=>{{1,2,3,6},{4,5},{7}}=>{{1,2,3,5},{4,6},{7}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>{{1},{2,3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4,6},{7}}=>{{1},{2},{3,6},{4,5},{7}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>{{1},{2,3,5},{4},{6,7}}=>{{1,2},{3,5},{4,6},{7}}=>{{1,2},{3,6},{4,5},{7}} [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3,5},{4},{7}}=>{{1},{2,6},{3,5},{4},{7}}=>{{1},{2,5},{3,6},{4},{7}} [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3,5},{4},{6}}=>{{1,6},{2},{3,5},{4},{7}}=>{{1,5},{2},{3,6},{4},{7}} [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,5},{4}}=>{{1,2,6},{3,5},{4},{7}}=>{{1,2,5},{3,6},{4},{7}} [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4},{5},{7}}=>{{1},{2,5},{3},{4,6},{7}}=>{{1},{2,6},{3},{4,5},{7}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4},{5}}=>{{1,6},{2,5},{3},{4},{7}}=>{{1,5},{2,6},{3},{4},{7}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4},{5},{6}}=>{{1,5},{2},{3},{4,6},{7}}=>{{1,6},{2},{3},{4,5},{7}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4},{5}}=>{{1,2,5},{3},{4,6},{7}}=>{{1,2,6},{3},{4,5},{7}} [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>{{1},{2,3,5,6},{4},{7}}=>{{1},{2,3,5},{4,6},{7}}=>{{1},{2,3,6},{4,5},{7}} [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3,5,6},{4}}=>{{1,6},{2,3,5},{4},{7}}=>{{1,3,6},{2,5},{4},{7}} [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4},{5,6}}=>{{1,5},{2,3},{4,6},{7}}=>{{1,3},{2,6},{4,5},{7}} [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>{{1},{2,3,5,7},{4},{6}}=>{{1,3},{2,5},{4,6},{7}}=>{{1,6},{2,3},{4,5},{7}} [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>{{1},{2,3,5,6,7},{4}}=>{{1,2,3,5},{4,6},{7}}=>{{1,2,3,6},{4,5},{7}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}}=>{{1},{2},{3,4,5,6},{7}}=>{{1},{2},{3,4,5,6},{7}} [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,2},{3,4,5,6},{7}}=>{{1,2},{3,4,5,6},{7}} [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>{{1},{2,6},{3,4,5},{7}}=>{{1},{2,6},{3,4,5},{7}}=>{{1},{2,4,6},{3,5},{7}} [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>{{1},{2,7},{3,4,5},{6}}=>{{1,6},{2},{3,4,5},{7}}=>{{1,4,6},{2},{3,5},{7}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4,5}}=>{{1,2,6},{3,4,5},{7}}=>{{1,2,4,6},{3,5},{7}} [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4,5},{7}}=>{{1},{2,5},{3,4,6},{7}}=>{{1},{2,4,5},{3,6},{7}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4,5}}=>{{1,6},{2,5},{3,4},{7}}=>{{1,4},{2,5},{3,6},{7}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4,5},{6}}=>{{1,5},{2},{3,4,6},{7}}=>{{1,4,5},{2},{3,6},{7}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4,5}}=>{{1,2,5},{3,4,6},{7}}=>{{1,2,4,5},{3,6},{7}} [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>{{1},{2,3,4,6},{5},{7}}=>{{1},{2,4},{3,5,6},{7}}=>{{1},{2,5,6},{3,4},{7}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>{{1},{2,7},{3,4,6},{5}}=>{{1,6},{2,4},{3,5},{7}}=>{{1,5},{2,4},{3,6},{7}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4,6},{5}}=>{{1,5},{2,4},{3,6},{7}}=>{{1,6},{2,4},{3,5},{7}} [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5},{6}}=>{{1,4},{2},{3,5,6},{7}}=>{{1,5,6},{2},{3,4},{7}} [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>{{1},{2,3,4,6,7},{5}}=>{{1,2,4},{3,5,6},{7}}=>{{1,2,5,6},{3,4},{7}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1},{2,7},{3,4,5,6}}=>{{1,6},{2,3,4,5},{7}}=>{{1,3,5},{2,4,6},{7}} [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>{{1},{2,3,7},{4,5,6}}=>{{1,5},{2,3,4,6},{7}}=>{{1,3,6},{2,4,5},{7}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5,6}}=>{{1,4},{2,3,5,6},{7}}=>{{1,3,4},{2,5,6},{7}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>{{1},{2,3,4,5,7},{6}}=>{{1,3},{2,4,5,6},{7}}=>{{1,4,5,6},{2,3},{7}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6,7}}=>{{1},{2},{3},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5},{6,7}}=>{{1},{2,3},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4},{5,7},{6}}=>{{1,3},{2},{4},{5},{6,7}}=>{{1,3},{2},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}}=>{{1,2,3},{4},{5},{6,7}}=>{{1,2,3},{4},{5},{6,7}} [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7}}=>{{1},{2},{3,4},{5},{6,7}}=>{{1},{2},{3,4},{5},{6,7}} [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2},{3,4},{5},{6,7}}=>{{1,2},{3,4},{5},{6,7}} [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>{{1,2},{3},{4,6},{5},{7}}=>{{1},{2,4},{3},{5},{6,7}}=>{{1},{2,4},{3},{5},{6,7}} [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>{{1,2},{3},{4,7},{5},{6}}=>{{1,4},{2},{3},{5},{6,7}}=>{{1,4},{2},{3},{5},{6,7}} [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>{{1,2},{3},{4,6,7},{5}}=>{{1,2,4},{3},{5},{6,7}}=>{{1,2,4},{3},{5},{6,7}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4,5,6},{7}}=>{{1},{2,3,4},{5},{6,7}}=>{{1},{2,3,4},{5},{6,7}} [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>{{1,2},{3},{4,7},{5,6}}=>{{1,4},{2,3},{5},{6,7}}=>{{1,3},{2,4},{5},{6,7}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>{{1,2},{3},{4,5,7},{6}}=>{{1,3},{2,4},{5},{6,7}}=>{{1,4},{2,3},{5},{6,7}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}}=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4},{5},{6,7}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7}}=>{{1},{2},{3},{4,5},{6,7}}=>{{1},{2},{3},{4,5},{6,7}} [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2},{3},{4,5},{6,7}}=>{{1,2},{3},{4,5},{6,7}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1},{2,3},{4,5},{6,7}}=>{{1},{2,3},{4,5},{6,7}} [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,4},{5,7},{6}}=>{{1,3},{2},{4,5},{6,7}}=>{{1,3},{2},{4,5},{6,7}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3},{4,5},{6,7}} [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>{{1,2},{3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4},{6,7}}=>{{1},{2},{3,5},{4},{6,7}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>{{1,2},{3,5},{4},{6,7}}=>{{1,2},{3,5},{4},{6,7}}=>{{1,2},{3,5},{4},{6,7}} [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>{{1,2},{3,6},{4},{5},{7}}=>{{1},{2,5},{3},{4},{6,7}}=>{{1},{2,5},{3},{4},{6,7}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>{{1,2},{3,7},{4},{5},{6}}=>{{1,5},{2},{3},{4},{6,7}}=>{{1,5},{2},{3},{4},{6,7}} [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4},{5}}=>{{1,2,5},{3},{4},{6,7}}=>{{1,2,5},{3},{4},{6,7}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>{{1,2},{3,5,6},{4},{7}}=>{{1},{2,3,5},{4},{6,7}}=>{{1},{2,3,5},{4},{6,7}} [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>{{1,2},{3,7},{4},{5,6}}=>{{1,5},{2,3},{4},{6,7}}=>{{1,3},{2,5},{4},{6,7}} [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>{{1,2},{3,5,7},{4},{6}}=>{{1,3},{2,5},{4},{6,7}}=>{{1,5},{2,3},{4},{6,7}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,5,6,7},{4}}=>{{1,2,3,5},{4},{6,7}}=>{{1,2,3,5},{4},{6,7}} [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6,7}}=>{{1},{2},{3,4,5},{6,7}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6,7}} [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>{{1,2},{3,6},{4,5},{7}}=>{{1},{2,5},{3,4},{6,7}}=>{{1},{2,4},{3,5},{6,7}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>{{1,2},{3,7},{4,5},{6}}=>{{1,5},{2},{3,4},{6,7}}=>{{1,4},{2},{3,5},{6,7}} [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4,5}}=>{{1,2,5},{3,4},{6,7}}=>{{1,2,4},{3,5},{6,7}} [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>{{1,2},{3,4,6},{5},{7}}=>{{1},{2,4},{3,5},{6,7}}=>{{1},{2,5},{3,4},{6,7}} [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>{{1,2},{3,7},{4,6},{5}}=>{{1,5},{2,4},{3},{6,7}}=>{{1,4},{2,5},{3},{6,7}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>{{1,2},{3,4,7},{5},{6}}=>{{1,4},{2},{3,5},{6,7}}=>{{1,5},{2},{3,4},{6,7}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>{{1,2},{3,4,6,7},{5}}=>{{1,2,4},{3,5},{6,7}}=>{{1,2,5},{3,4},{6,7}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1},{2,3,4,5},{6,7}}=>{{1},{2,3,4,5},{6,7}} [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>{{1,2},{3,7},{4,5,6}}=>{{1,5},{2,3,4},{6,7}}=>{{1,3,5},{2,4},{6,7}} [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>{{1,2},{3,4,7},{5,6}}=>{{1,4},{2,3,5},{6,7}}=>{{1,3,4},{2,5},{6,7}} [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>{{1,2},{3,4,5,7},{6}}=>{{1,3},{2,4,5},{6,7}}=>{{1,4,5},{2,3},{6,7}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5,7},{6}}=>{{1},{2},{3},{4},{5,7},{6}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5},{6,7}}=>{{1,2},{3},{4},{5,7},{6}}=>{{1,2},{3},{4},{5,7},{6}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>{{1,3},{2},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,7},{6}}=>{{1},{2,3},{4},{5,7},{6}} [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>{{1,3},{2},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,7},{6}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>{{1,3},{2},{4},{5,6,7}}=>{{1,2,3},{4},{5,7},{6}}=>{{1,2,3},{4},{5,7},{6}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>{{1,3},{2},{4,5},{6},{7}}=>{{1},{2},{3,4},{5,7},{6}}=>{{1},{2},{3,4},{5,7},{6}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5},{6,7}}=>{{1,2},{3,4},{5,7},{6}}=>{{1,2},{3,4},{5,7},{6}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>{{1,3},{2},{4,6},{5},{7}}=>{{1},{2,4},{3},{5,7},{6}}=>{{1},{2,4},{3},{5,7},{6}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>{{1,3},{2},{4,7},{5},{6}}=>{{1,4},{2},{3},{5,7},{6}}=>{{1,4},{2},{3},{5,7},{6}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>{{1,3},{2},{4,6,7},{5}}=>{{1,2,4},{3},{5,7},{6}}=>{{1,2,4},{3},{5,7},{6}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>{{1,3},{2},{4,5,6},{7}}=>{{1},{2,3,4},{5,7},{6}}=>{{1},{2,3,4},{5,7},{6}} [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,3},{2},{4,7},{5,6}}=>{{1,4},{2,3},{5,7},{6}}=>{{1,3},{2,4},{5,7},{6}} [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>{{1,3},{2},{4,5,7},{6}}=>{{1,3},{2,4},{5,7},{6}}=>{{1,4},{2,3},{5,7},{6}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,3},{2},{4,5,6,7}}=>{{1,2,3,4},{5,7},{6}}=>{{1,2,3,4},{5,7},{6}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6},{7}}=>{{1},{2},{3},{4,7},{5},{6}}=>{{1},{2},{3},{4,7},{5},{6}} [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2},{3},{5},{6,7}}=>{{1,2},{3},{4,7},{5},{6}}=>{{1,2},{3},{4,7},{5},{6}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2},{3},{5,6},{7}}=>{{1},{2,3},{4,7},{5},{6}}=>{{1},{2,3},{4,7},{5},{6}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2},{3},{5,7},{6}}=>{{1,3},{2},{4,7},{5},{6}}=>{{1,3},{2},{4,7},{5},{6}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2},{3},{5,6,7}}=>{{1,2,3},{4,7},{5},{6}}=>{{1,2,3},{4,7},{5},{6}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3},{4},{6},{7}}=>{{1},{2},{3,7},{4},{5},{6}}=>{{1},{2},{3,7},{4},{5},{6}} [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3},{4},{6,7}}=>{{1,2},{3,7},{4},{5},{6}}=>{{1,2},{3,7},{4},{5},{6}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3},{4},{5},{7}}=>{{1},{2,7},{3},{4},{5},{6}}=>{{1},{2,7},{3},{4},{5},{6}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3},{4},{5},{6}}=>{{1,7},{2},{3},{4},{5},{6}}=>{{1,7},{2},{3},{4},{5},{6}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4},{5}}=>{{1,2,7},{3},{4},{5},{6}}=>{{1,2,7},{3},{4},{5},{6}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3},{4},{7}}=>{{1},{2,3,7},{4},{5},{6}}=>{{1},{2,3,7},{4},{5},{6}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3},{4},{5,6}}=>{{1,7},{2,3},{4},{5},{6}}=>{{1,3},{2,7},{4},{5},{6}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3},{4},{6}}=>{{1,3},{2,7},{4},{5},{6}}=>{{1,7},{2,3},{4},{5},{6}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3},{4}}=>{{1,2,3,7},{4},{5},{6}}=>{{1,2,3,7},{4},{5},{6}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2},{3},{6},{7}}=>{{1},{2},{3,4,7},{5},{6}}=>{{1},{2},{3,4,7},{5},{6}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2},{3},{6,7}}=>{{1,2},{3,4,7},{5},{6}}=>{{1,2},{3,4,7},{5},{6}} [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3},{4,5},{7}}=>{{1},{2,7},{3,4},{5},{6}}=>{{1},{2,4},{3,7},{5},{6}} [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3},{4,5},{6}}=>{{1,7},{2},{3,4},{5},{6}}=>{{1,4},{2},{3,7},{5},{6}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4,5}}=>{{1,2,7},{3,4},{5},{6}}=>{{1,2,4},{3,7},{5},{6}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2},{3},{5},{7}}=>{{1},{2,4},{3,7},{5},{6}}=>{{1},{2,7},{3,4},{5},{6}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3},{4,6},{5}}=>{{1,7},{2,4},{3},{5},{6}}=>{{1,4},{2,7},{3},{5},{6}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2},{3},{5},{6}}=>{{1,4},{2},{3,7},{5},{6}}=>{{1,7},{2},{3,4},{5},{6}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2},{3},{5}}=>{{1,2,4},{3,7},{5},{6}}=>{{1,2,7},{3,4},{5},{6}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2},{3},{7}}=>{{1},{2,3,4,7},{5},{6}}=>{{1},{2,3,4,7},{5},{6}} [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3},{4,5,6}}=>{{1,7},{2,3,4},{5},{6}}=>{{1,3,7},{2,4},{5},{6}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2},{3},{5,6}}=>{{1,4},{2,3,7},{5},{6}}=>{{1,3,4},{2,7},{5},{6}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2},{3},{6}}=>{{1,3},{2,4,7},{5},{6}}=>{{1,4,7},{2,3},{5},{6}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}}=>{{1,2,3,4,7},{5},{6}}=>{{1,2,3,4,7},{5},{6}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>{{1,3,4},{2},{5},{6},{7}}=>{{1},{2},{3},{4,5,7},{6}}=>{{1},{2},{3},{4,5,7},{6}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>{{1,3,4},{2},{5},{6,7}}=>{{1,2},{3},{4,5,7},{6}}=>{{1,2},{3},{4,5,7},{6}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>{{1,3,4},{2},{5,6},{7}}=>{{1},{2,3},{4,5,7},{6}}=>{{1},{2,3},{4,5,7},{6}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>{{1,3,4},{2},{5,7},{6}}=>{{1,3},{2},{4,5,7},{6}}=>{{1,3},{2},{4,5,7},{6}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>{{1,3,4},{2},{5,6,7}}=>{{1,2,3},{4,5,7},{6}}=>{{1,2,3},{4,5,7},{6}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3,4},{6},{7}}=>{{1},{2},{3,7},{4,5},{6}}=>{{1},{2},{3,5},{4,7},{6}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3,4},{6,7}}=>{{1,2},{3,7},{4,5},{6}}=>{{1,2},{3,5},{4,7},{6}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3,4},{5},{7}}=>{{1},{2,7},{3},{4,5},{6}}=>{{1},{2,5},{3},{4,7},{6}} [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3,4},{5},{6}}=>{{1,7},{2},{3},{4,5},{6}}=>{{1,5},{2},{3},{4,7},{6}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4},{5}}=>{{1,2,7},{3},{4,5},{6}}=>{{1,2,5},{3},{4,7},{6}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3,4},{7}}=>{{1},{2,3,7},{4,5},{6}}=>{{1},{2,3,5},{4,7},{6}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3,4},{5,6}}=>{{1,7},{2,3},{4,5},{6}}=>{{1,3},{2,5},{4,7},{6}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3,4},{6}}=>{{1,3},{2,7},{4,5},{6}}=>{{1,5},{2,3},{4,7},{6}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3,4}}=>{{1,2,3,7},{4,5},{6}}=>{{1,2,3,5},{4,7},{6}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>{{1,3,5},{2},{4},{6},{7}}=>{{1},{2},{3,5},{4,7},{6}}=>{{1},{2},{3,7},{4,5},{6}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>{{1,3,5},{2},{4},{6,7}}=>{{1,2},{3,5},{4,7},{6}}=>{{1,2},{3,7},{4,5},{6}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3,5},{4},{7}}=>{{1},{2,7},{3,5},{4},{6}}=>{{1},{2,5},{3,7},{4},{6}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3,5},{4},{6}}=>{{1,7},{2},{3,5},{4},{6}}=>{{1,5},{2},{3,7},{4},{6}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,5},{4}}=>{{1,2,7},{3,5},{4},{6}}=>{{1,2,5},{3,7},{4},{6}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4},{5},{7}}=>{{1},{2,5},{3},{4,7},{6}}=>{{1},{2,7},{3},{4,5},{6}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4},{5}}=>{{1,7},{2,5},{3},{4},{6}}=>{{1,5},{2,7},{3},{4},{6}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4},{5},{6}}=>{{1,5},{2},{3},{4,7},{6}}=>{{1,7},{2},{3},{4,5},{6}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4},{5}}=>{{1,2,5},{3},{4,7},{6}}=>{{1,2,7},{3},{4,5},{6}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3,5},{4,7},{6}}=>{{1},{2,3,7},{4,5},{6}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3,5,6},{4}}=>{{1,7},{2,3,5},{4},{6}}=>{{1,3,7},{2,5},{4},{6}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4},{5,6}}=>{{1,5},{2,3},{4,7},{6}}=>{{1,3},{2,7},{4,5},{6}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>{{1,3,5,7},{2},{4},{6}}=>{{1,3},{2,5},{4,7},{6}}=>{{1,7},{2,3},{4,5},{6}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>{{1,3,5,6,7},{2},{4}}=>{{1,2,3,5},{4,7},{6}}=>{{1,2,3,7},{4,5},{6}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>{{1,3,4,5},{2},{6},{7}}=>{{1},{2},{3,4,5,7},{6}}=>{{1},{2},{3,4,5,7},{6}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,3,4,5},{2},{6,7}}=>{{1,2},{3,4,5,7},{6}}=>{{1,2},{3,4,5,7},{6}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2},{3,4,5},{7}}=>{{1},{2,7},{3,4,5},{6}}=>{{1},{2,4,7},{3,5},{6}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2},{3,4,5},{6}}=>{{1,7},{2},{3,4,5},{6}}=>{{1,4,7},{2},{3,5},{6}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4,5}}=>{{1,2,7},{3,4,5},{6}}=>{{1,2,4,7},{3,5},{6}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4,5},{7}}=>{{1},{2,5},{3,4,7},{6}}=>{{1},{2,4,5},{3,7},{6}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4,5}}=>{{1,7},{2,5},{3,4},{6}}=>{{1,4},{2,5},{3,7},{6}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4,5},{6}}=>{{1,5},{2},{3,4,7},{6}}=>{{1,4,5},{2},{3,7},{6}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4,5}}=>{{1,2,5},{3,4,7},{6}}=>{{1,2,4,5},{3,7},{6}} [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,4},{3,5,7},{6}}=>{{1},{2,5,7},{3,4},{6}} [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2},{3,4,6},{5}}=>{{1,7},{2,4},{3,5},{6}}=>{{1,5},{2,4},{3,7},{6}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4,6},{5}}=>{{1,5},{2,4},{3,7},{6}}=>{{1,7},{2,4},{3,5},{6}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5},{6}}=>{{1,4},{2},{3,5,7},{6}}=>{{1,5,7},{2},{3,4},{6}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>{{1,3,4,6,7},{2},{5}}=>{{1,2,4},{3,5,7},{6}}=>{{1,2,5,7},{3,4},{6}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}}=>{{1},{2,3,4,5,7},{6}}=>{{1},{2,3,4,5,7},{6}} [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2},{3,4,5,6}}=>{{1,7},{2,3,4,5},{6}}=>{{1,3,5},{2,4,7},{6}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>{{1,3,7},{2},{4,5,6}}=>{{1,5},{2,3,4,7},{6}}=>{{1,3,7},{2,4,5},{6}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5,6}}=>{{1,4},{2,3,5,7},{6}}=>{{1,3,4},{2,5,7},{6}} [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>{{1,3,4,5,7},{2},{6}}=>{{1,3},{2,4,5,7},{6}}=>{{1,4,5,7},{2,3},{6}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}}=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5,7},{6}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5,6,7}}=>{{1},{2},{3},{4},{5,6,7}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5,6,7}}=>{{1,2},{3},{4},{5,6,7}} [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,6,7}}=>{{1},{2,3},{4},{5,6,7}} [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>{{1,2,3},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,6,7}}=>{{1,3},{2},{4},{5,6,7}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7}}=>{{1},{2},{3,4},{5,6,7}}=>{{1},{2},{3,4},{5,6,7}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2},{3,4},{5,6,7}}=>{{1,2},{3,4},{5,6,7}} [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>{{1,2,3},{4,6},{5},{7}}=>{{1},{2,4},{3},{5,6,7}}=>{{1},{2,4},{3},{5,6,7}} [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>{{1,2,3},{4,7},{5},{6}}=>{{1,4},{2},{3},{5,6,7}}=>{{1,4},{2},{3},{5,6,7}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>{{1,2,3},{4,6,7},{5}}=>{{1,2,4},{3},{5,6,7}}=>{{1,2,4},{3},{5,6,7}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1},{2,3,4},{5,6,7}}=>{{1},{2,3,4},{5,6,7}} [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,3},{4,7},{5,6}}=>{{1,4},{2,3},{5,6,7}}=>{{1,3},{2,4},{5,6,7}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>{{1,2,3},{4,5,7},{6}}=>{{1,3},{2,4},{5,6,7}}=>{{1,4},{2,3},{5,6,7}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4},{5,6,7}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2,3},{5},{6},{7}}=>{{1},{2},{3},{4,7},{5,6}}=>{{1},{2},{3},{4,6},{5,7}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2,3},{5},{6,7}}=>{{1,2},{3},{4,7},{5,6}}=>{{1,2},{3},{4,6},{5,7}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2,3},{5,6},{7}}=>{{1},{2,3},{4,7},{5,6}}=>{{1},{2,3},{4,6},{5,7}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2,3},{5,7},{6}}=>{{1,3},{2},{4,7},{5,6}}=>{{1,3},{2},{4,6},{5,7}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2,3},{5,6,7}}=>{{1,2,3},{4,7},{5,6}}=>{{1,2,3},{4,6},{5,7}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2,3},{4},{6},{7}}=>{{1},{2},{3,7},{4},{5,6}}=>{{1},{2},{3,6},{4},{5,7}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2,3},{4},{6,7}}=>{{1,2},{3,7},{4},{5,6}}=>{{1,2},{3,6},{4},{5,7}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2,3},{4},{5},{7}}=>{{1},{2,7},{3},{4},{5,6}}=>{{1},{2,6},{3},{4},{5,7}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2,3},{4},{5},{6}}=>{{1,7},{2},{3},{4},{5,6}}=>{{1,6},{2},{3},{4},{5,7}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4},{5}}=>{{1,2,7},{3},{4},{5,6}}=>{{1,2,6},{3},{4},{5,7}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3},{4},{7}}=>{{1},{2,3,7},{4},{5,6}}=>{{1},{2,3,6},{4},{5,7}} [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2,3},{4},{5,6}}=>{{1,7},{2,3},{4},{5,6}}=>{{1,3},{2,6},{4},{5,7}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3},{4},{6}}=>{{1,3},{2,7},{4},{5,6}}=>{{1,6},{2,3},{4},{5,7}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3},{4}}=>{{1,2,3,7},{4},{5,6}}=>{{1,2,3,6},{4},{5,7}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2,3},{6},{7}}=>{{1},{2},{3,4,7},{5,6}}=>{{1},{2},{3,4,6},{5,7}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2,3},{6,7}}=>{{1,2},{3,4,7},{5,6}}=>{{1,2},{3,4,6},{5,7}} [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2,3},{4,5},{7}}=>{{1},{2,7},{3,4},{5,6}}=>{{1},{2,4},{3,6},{5,7}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2,3},{4,5},{6}}=>{{1,7},{2},{3,4},{5,6}}=>{{1,4},{2},{3,6},{5,7}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4,5}}=>{{1,2,7},{3,4},{5,6}}=>{{1,2,4},{3,6},{5,7}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2,3},{5},{7}}=>{{1},{2,4},{3,7},{5,6}}=>{{1},{2,6},{3,4},{5,7}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2,3},{4,6},{5}}=>{{1,7},{2,4},{3},{5,6}}=>{{1,4},{2,6},{3},{5,7}} [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2,3},{5},{6}}=>{{1,4},{2},{3,7},{5,6}}=>{{1,6},{2},{3,4},{5,7}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2,3},{5}}=>{{1,2,4},{3,7},{5,6}}=>{{1,2,6},{3,4},{5,7}} [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2,3},{7}}=>{{1},{2,3,4,7},{5,6}}=>{{1},{2,3,4,6},{5,7}} [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2,3},{4,5,6}}=>{{1,7},{2,3,4},{5,6}}=>{{1,3,6},{2,4},{5,7}} [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2,3},{5,6}}=>{{1,4},{2,3,7},{5,6}}=>{{1,3,4},{2,6},{5,7}} [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2,3},{6}}=>{{1,3},{2,4,7},{5,6}}=>{{1,4,6},{2,3},{5,7}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}}=>{{1,2,3,4,7},{5,6}}=>{{1,2,3,4,6},{5,7}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>{{1,2,4},{3},{5},{6},{7}}=>{{1},{2},{3},{4,6},{5,7}}=>{{1},{2},{3},{4,7},{5,6}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>{{1,2,4},{3},{5},{6,7}}=>{{1,2},{3},{4,6},{5,7}}=>{{1,2},{3},{4,7},{5,6}} [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>{{1,2,4},{3},{5,6},{7}}=>{{1},{2,3},{4,6},{5,7}}=>{{1},{2,3},{4,7},{5,6}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>{{1,2,4},{3},{5,7},{6}}=>{{1,3},{2},{4,6},{5,7}}=>{{1,3},{2},{4,7},{5,6}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>{{1,2,4},{3},{5,6,7}}=>{{1,2,3},{4,6},{5,7}}=>{{1,2,3},{4,7},{5,6}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,4},{3},{6},{7}}=>{{1},{2},{3,7},{4,6},{5}}=>{{1},{2},{3,6},{4,7},{5}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,4},{3},{6,7}}=>{{1,2},{3,7},{4,6},{5}}=>{{1,2},{3,6},{4,7},{5}} [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,4},{3},{5},{7}}=>{{1},{2,7},{3},{4,6},{5}}=>{{1},{2,6},{3},{4,7},{5}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,4},{3},{5},{6}}=>{{1,7},{2},{3},{4,6},{5}}=>{{1,6},{2},{3},{4,7},{5}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,4},{3},{5}}=>{{1,2,7},{3},{4,6},{5}}=>{{1,2,6},{3},{4,7},{5}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,4},{3},{7}}=>{{1},{2,3,7},{4,6},{5}}=>{{1},{2,3,6},{4,7},{5}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,4},{3},{5,6}}=>{{1,7},{2,3},{4,6},{5}}=>{{1,3},{2,6},{4,7},{5}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,4},{3},{6}}=>{{1,3},{2,7},{4,6},{5}}=>{{1,6},{2,3},{4,7},{5}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,4},{3}}=>{{1,2,3,7},{4,6},{5}}=>{{1,2,3,6},{4,7},{5}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3},{4},{6},{7}}=>{{1},{2},{3,6},{4},{5,7}}=>{{1},{2},{3,7},{4},{5,6}} [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3},{4},{6,7}}=>{{1,2},{3,6},{4},{5,7}}=>{{1,2},{3,7},{4},{5,6}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3},{4},{7}}=>{{1},{2,7},{3,6},{4},{5}}=>{{1},{2,6},{3,7},{4},{5}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3},{4},{6}}=>{{1,7},{2},{3,6},{4},{5}}=>{{1,6},{2},{3,7},{4},{5}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3},{4}}=>{{1,2,7},{3,6},{4},{5}}=>{{1,2,6},{3,7},{4},{5}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4},{5},{7}}=>{{1},{2,6},{3},{4},{5,7}}=>{{1},{2,7},{3},{4},{5,6}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4},{5}}=>{{1,7},{2,6},{3},{4},{5}}=>{{1,6},{2,7},{3},{4},{5}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4},{5},{6}}=>{{1,6},{2},{3},{4},{5,7}}=>{{1,7},{2},{3},{4},{5,6}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4},{5}}=>{{1,2,6},{3},{4},{5,7}}=>{{1,2,7},{3},{4},{5,6}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3},{4},{7}}=>{{1},{2,3,6},{4},{5,7}}=>{{1},{2,3,7},{4},{5,6}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3},{4}}=>{{1,7},{2,3,6},{4},{5}}=>{{1,3,7},{2,6},{4},{5}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4},{5,6}}=>{{1,6},{2,3},{4},{5,7}}=>{{1,3},{2,7},{4},{5,6}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3},{4},{6}}=>{{1,3},{2,6},{4},{5,7}}=>{{1,7},{2,3},{4},{5,6}} [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3},{4}}=>{{1,2,3,6},{4},{5,7}}=>{{1,2,3,7},{4},{5,6}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>{{1,2,4,5},{3},{6},{7}}=>{{1},{2},{3,4,6},{5,7}}=>{{1},{2},{3,4,7},{5,6}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>{{1,2,4,5},{3},{6,7}}=>{{1,2},{3,4,6},{5,7}}=>{{1,2},{3,4,7},{5,6}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,4,5},{3},{7}}=>{{1},{2,7},{3,4,6},{5}}=>{{1},{2,4,7},{3,6},{5}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,4,5},{3},{6}}=>{{1,7},{2},{3,4,6},{5}}=>{{1,4,7},{2},{3,6},{5}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,4,5},{3}}=>{{1,2,7},{3,4,6},{5}}=>{{1,2,4,7},{3,6},{5}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4,5},{7}}=>{{1},{2,6},{3,4},{5,7}}=>{{1},{2,4},{3,7},{5,6}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4,5}}=>{{1,7},{2,6},{3,4},{5}}=>{{1,4},{2,6},{3,7},{5}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4,5},{6}}=>{{1,6},{2},{3,4},{5,7}}=>{{1,4},{2},{3,7},{5,6}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4,5}}=>{{1,2,6},{3,4},{5,7}}=>{{1,2,4},{3,7},{5,6}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>{{1,2,4,6},{3},{5},{7}}=>{{1},{2,4},{3,6},{5,7}}=>{{1},{2,7},{3,4},{5,6}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,4,6},{3},{5}}=>{{1,7},{2,4},{3,6},{5}}=>{{1,6},{2,4},{3,7},{5}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4,6},{5}}=>{{1,6},{2,4},{3},{5,7}}=>{{1,4},{2,7},{3},{5,6}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5},{6}}=>{{1,4},{2},{3,6},{5,7}}=>{{1,7},{2},{3,4},{5,6}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>{{1,2,4,6,7},{3},{5}}=>{{1,2,4},{3,6},{5,7}}=>{{1,2,7},{3,4},{5,6}} [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>{{1,2,4,5,6},{3},{7}}=>{{1},{2,3,4,6},{5,7}}=>{{1},{2,3,4,7},{5,6}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,4,5,6},{3}}=>{{1,7},{2,3,4,6},{5}}=>{{1,3,6},{2,4,7},{5}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3},{4,5,6}}=>{{1,6},{2,3,4},{5,7}}=>{{1,3,7},{2,4},{5,6}} [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5,6}}=>{{1,4},{2,3,6},{5,7}}=>{{1,3,4},{2,7},{5,6}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>{{1,2,4,5,7},{3},{6}}=>{{1,3},{2,4,6},{5,7}}=>{{1,4,7},{2,3},{5,6}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,4,5,6,7},{3}}=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7}}=>{{1},{2},{3},{4,5,6,7}}=>{{1},{2},{3},{4,5,6,7}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}}=>{{1,2},{3},{4,5,6,7}}=>{{1,2},{3},{4,5,6,7}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>{{1},{2,3},{4,5,6,7}}=>{{1},{2,3},{4,5,6,7}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>{{1,2,3,4},{5,7},{6}}=>{{1,3},{2},{4,5,6,7}}=>{{1,3},{2},{4,5,6,7}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}} [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,3,4},{6},{7}}=>{{1},{2},{3,7},{4,5,6}}=>{{1},{2},{3,5,7},{4,6}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,3,4},{6,7}}=>{{1,2},{3,7},{4,5,6}}=>{{1,2},{3,5,7},{4,6}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,3,4},{5},{7}}=>{{1},{2,7},{3},{4,5,6}}=>{{1},{2,5,7},{3},{4,6}} [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,3,4},{5},{6}}=>{{1,7},{2},{3},{4,5,6}}=>{{1,5,7},{2},{3},{4,6}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3,4},{5}}=>{{1,2,7},{3},{4,5,6}}=>{{1,2,5,7},{3},{4,6}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3,4},{7}}=>{{1},{2,3,7},{4,5,6}}=>{{1},{2,3,5,7},{4,6}} [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,3,4},{5,6}}=>{{1,7},{2,3},{4,5,6}}=>{{1,3},{2,5,7},{4,6}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3,4},{6}}=>{{1,3},{2,7},{4,5,6}}=>{{1,5,7},{2,3},{4,6}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3,4}}=>{{1,2,3,7},{4,5,6}}=>{{1,2,3,5,7},{4,6}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3,4},{6},{7}}=>{{1},{2},{3,6},{4,5,7}}=>{{1},{2},{3,5,6},{4,7}} [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3,4},{6,7}}=>{{1,2},{3,6},{4,5,7}}=>{{1,2},{3,5,6},{4,7}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3,4},{7}}=>{{1},{2,7},{3,6},{4,5}}=>{{1},{2,5},{3,6},{4,7}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3,4},{6}}=>{{1,7},{2},{3,6},{4,5}}=>{{1,5},{2},{3,6},{4,7}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3,4}}=>{{1,2,7},{3,6},{4,5}}=>{{1,2,5},{3,6},{4,7}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3,4},{5},{7}}=>{{1},{2,6},{3},{4,5,7}}=>{{1},{2,5,6},{3},{4,7}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4},{5}}=>{{1,7},{2,6},{3},{4,5}}=>{{1,5},{2,6},{3},{4,7}} [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3,4},{5},{6}}=>{{1,6},{2},{3},{4,5,7}}=>{{1,5,6},{2},{3},{4,7}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4},{5}}=>{{1,2,6},{3},{4,5,7}}=>{{1,2,5,6},{3},{4,7}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3,4},{7}}=>{{1},{2,3,6},{4,5,7}}=>{{1},{2,3,5,6},{4,7}} [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3,4}}=>{{1,7},{2,3,6},{4,5}}=>{{1,3,6},{2,5},{4,7}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3,4},{5,6}}=>{{1,6},{2,3},{4,5,7}}=>{{1,3},{2,5,6},{4,7}} [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3,4},{6}}=>{{1,3},{2,6},{4,5,7}}=>{{1,5,6},{2,3},{4,7}} [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3,4}}=>{{1,2,3,6},{4,5,7}}=>{{1,2,3,5,6},{4,7}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>{{1,2,3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4,6,7}}=>{{1},{2},{3,6,7},{4,5}} [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>{{1,2,3,5},{4},{6,7}}=>{{1,2},{3,5},{4,6,7}}=>{{1,2},{3,6,7},{4,5}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,5},{4},{7}}=>{{1},{2,7},{3,5},{4,6}}=>{{1},{2,6},{3,5},{4,7}} [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,5},{4},{6}}=>{{1,7},{2},{3,5},{4,6}}=>{{1,6},{2},{3,5},{4,7}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,5},{4}}=>{{1,2,7},{3,5},{4,6}}=>{{1,2,6},{3,5},{4,7}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,5},{4},{7}}=>{{1},{2,6},{3,5},{4,7}}=>{{1},{2,7},{3,5},{4,6}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,5},{4}}=>{{1,7},{2,6},{3,5},{4}}=>{{1,5},{2,6},{3,7},{4}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,5},{4},{6}}=>{{1,6},{2},{3,5},{4,7}}=>{{1,7},{2},{3,5},{4,6}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,5},{4}}=>{{1,2,6},{3,5},{4,7}}=>{{1,2,7},{3,5},{4,6}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4},{5},{7}}=>{{1},{2,5},{3},{4,6,7}}=>{{1},{2,6,7},{3},{4,5}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4},{5}}=>{{1,7},{2,5},{3},{4,6}}=>{{1,6},{2,5},{3},{4,7}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4},{5}}=>{{1,6},{2,5},{3},{4,7}}=>{{1,7},{2,5},{3},{4,6}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5},{6}}=>{{1,5},{2},{3},{4,6,7}}=>{{1,6,7},{2},{3},{4,5}} [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4},{5}}=>{{1,2,5},{3},{4,6,7}}=>{{1,2,6,7},{3},{4,5}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>{{1,2,3,5,6},{4},{7}}=>{{1},{2,3,5},{4,6,7}}=>{{1},{2,3,6,7},{4,5}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,5,6},{4}}=>{{1,7},{2,3,5},{4,6}}=>{{1,3,5},{2,6},{4,7}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,5,6},{4}}=>{{1,6},{2,3,5},{4,7}}=>{{1,3,5},{2,7},{4,6}} [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5,6}}=>{{1,5},{2,3},{4,6,7}}=>{{1,3},{2,6,7},{4,5}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>{{1,2,3,5,7},{4},{6}}=>{{1,3},{2,5},{4,6,7}}=>{{1,6,7},{2,3},{4,5}} [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,5,6,7},{4}}=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}}=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>{{1,2},{3,4,5,6,7}}=>{{1,2},{3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,4,5},{7}}=>{{1},{2,7},{3,4,5,6}}=>{{1},{2,4,6},{3,5,7}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,4,5},{6}}=>{{1,7},{2},{3,4,5,6}}=>{{1,4,6},{2},{3,5,7}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}}=>{{1,2,7},{3,4,5,6}}=>{{1,2,4,6},{3,5,7}} [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,4,5},{7}}=>{{1},{2,6},{3,4,5,7}}=>{{1},{2,4,7},{3,5,6}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4,5}}=>{{1,7},{2,6},{3,4,5}}=>{{1,4,7},{2,5},{3,6}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,4,5},{6}}=>{{1,6},{2},{3,4,5,7}}=>{{1,4,7},{2},{3,5,6}} [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4,5}}=>{{1,2,6},{3,4,5,7}}=>{{1,2,4,7},{3,5,6}} [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4,5},{7}}=>{{1},{2,5},{3,4,6,7}}=>{{1},{2,4,5},{3,6,7}} [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4,5}}=>{{1,7},{2,5},{3,4,6}}=>{{1,4,7},{2,6},{3,5}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4,5}}=>{{1,6},{2,5},{3,4,7}}=>{{1,4,6},{2,7},{3,5}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4,5},{6}}=>{{1,5},{2},{3,4,6,7}}=>{{1,4,5},{2},{3,6,7}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4,5}}=>{{1,2,5},{3,4,6,7}}=>{{1,2,4,5},{3,6,7}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>{{1,2,3,4,6},{5},{7}}=>{{1},{2,4},{3,5,6,7}}=>{{1},{2,5,6,7},{3,4}} [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,6},{5}}=>{{1,7},{2,4},{3,5,6}}=>{{1,5,7},{2,4},{3,6}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,6},{5}}=>{{1,6},{2,4},{3,5,7}}=>{{1,5,6},{2,4},{3,7}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,6},{5}}=>{{1,5},{2,4},{3,6,7}}=>{{1,6,7},{2,4},{3,5}} [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5},{6}}=>{{1,4},{2},{3,5,6,7}}=>{{1,5,6,7},{2},{3,4}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>{{1,2,3,4,6,7},{5}}=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}}=>{{1,7},{2,3,4,5,6}}=>{{1,3,5,7},{2,4,6}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,5,6}}=>{{1,6},{2,3,4,5,7}}=>{{1,3,5,6},{2,4,7}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,5,6}}=>{{1,5},{2,3,4,6,7}}=>{{1,3,6,7},{2,4,5}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5,6}}=>{{1,4},{2,3,5,6,7}}=>{{1,3,4},{2,5,6,7}} [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,7},{6}}=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8}}=>{{1,2},{3},{4},{5},{6},{7},{8}}=>{{1,2},{3},{4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7},{8}}=>{{1},{2,3},{4},{5},{6},{7},{8}}=>{{1},{2,3},{4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8}}=>{{1,2,3},{4},{5},{6},{7},{8}}=>{{1,2,3},{4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1,2},{3,4},{5},{6},{7},{8}}=>{{1,2},{3,4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3},{4},{5,8},{6,7}}=>{{1,4},{2,3},{5},{6},{7},{8}}=>{{1,3},{2,4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1,2,3,4},{5},{6},{7},{8}}=>{{1,2,3,4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,2,3},{4,5},{6},{7},{8}}=>{{1,2,3},{4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2},{3},{4,8},{5,7},{6}}=>{{1,5},{2,4},{3},{6},{7},{8}}=>{{1,4},{2,5},{3},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3},{4,5,6,7},{8}}=>{{1},{2,3,4,5},{6},{7},{8}}=>{{1},{2,3,4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8}}=>{{1,2,3,4,5},{6},{7},{8}}=>{{1,2,3,4,5},{6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7},{8}}=>{{1,2},{3,4},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3,4},{5,8},{6,7}}=>{{1,4},{2,3},{5,6},{7},{8}}=>{{1,3},{2,4},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6},{7},{8}}=>{{1,2,3,4},{5,6},{7},{8}} [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,5,6,7,8},{4}}=>{{1,2,3,4,6},{5},{7},{8}}=>{{1,2,3,4,6},{5},{7},{8}} [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5},{6,7,8}}=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3},{4,5,6},{7},{8}} [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>{{1},{2},{3,4,6,8},{5},{7}}=>{{1,3},{2,5},{4,6},{7},{8}}=>{{1,6},{2,3},{4,5},{7},{8}} [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,6,7,8},{5}}=>{{1,2,3,5},{4,6},{7},{8}}=>{{1,2,3,6},{4,5},{7},{8}} [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>{{1},{2},{3,4,8},{5,6,7}}=>{{1,5},{2,3,4,6},{7},{8}}=>{{1,3,6},{2,4,5},{7},{8}} [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>{{1,2,3,4,5,6},{7},{8}}=>{{1,2,3,4,5,6},{7},{8}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6,7},{8}}=>{{1},{2},{3},{4},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1},{2,3},{4},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2,3},{4},{5,8},{6,7}}=>{{1,4},{2,3},{5},{6,7},{8}}=>{{1,3},{2,4},{5},{6,7},{8}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6,7},{8}} [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3},{4,5},{6,7},{8}} [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2,3},{4,6,7,8},{5}}=>{{1,2,3,5},{4},{6,7},{8}}=>{{1,2,3,5},{4},{6,7},{8}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3},{4,5,6,7},{8}}=>{{1},{2,3,4,5},{6,7},{8}}=>{{1},{2,3,4,5},{6,7},{8}} [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,2,3,4,5},{6,7},{8}}=>{{1,2,3,4,5},{6,7},{8}} [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1},{2,4},{3},{5,8},{6,7}}=>{{1,4},{2,3},{5,7},{6},{8}}=>{{1,3},{2,4},{5,7},{6},{8}} [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,4,5,6,7,8},{3}}=>{{1,2,3,4,5,7},{6},{8}}=>{{1,2,3,4,5,7},{6},{8}} [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1},{2,3,4},{5,8},{6,7}}=>{{1,4},{2,3},{5,6,7},{8}}=>{{1,3},{2,4},{5,6,7},{8}} [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4},{5,6,7},{8}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5,6,7},{8}}=>{{1},{2},{3},{4,5,6,7},{8}} [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4,5},{6,7},{8}}=>{{1},{2,3},{4,5,6,7},{8}}=>{{1},{2,3},{4,5,6,7},{8}} [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>{{1},{2,8},{3,7},{4,6},{5}}=>{{1,7},{2,6},{3,5},{4},{8}}=>{{1,5},{2,6},{3,7},{4},{8}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>{{1},{2,3,4,5,6,7},{8}}=>{{1},{2,3,4,5,6,7},{8}} [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1},{2,8},{3,4,5,6,7}}=>{{1,7},{2,3,4,5,6},{8}}=>{{1,3,5,7},{2,4,6},{8}} [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7},{8}}=>{{1,2,3,4,5,6,7},{8}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6},{7,8}}=>{{1},{2},{3},{4},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>{{1,2},{3},{4},{5,8},{6,7}}=>{{1,4},{2,3},{5},{6},{7,8}}=>{{1,3},{2,4},{5},{6},{7,8}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1},{2},{3},{4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5,6},{7},{8}}=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1},{2},{3,4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>{{1,2},{3,4},{5,8},{6},{7}}=>{{1,4},{2},{3},{5,6},{7,8}}=>{{1,4},{2},{3},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>{{1,2},{3,4},{5,7,8},{6}}=>{{1,2,4},{3},{5,6},{7,8}}=>{{1,2,4},{3},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,8},{6,7}}=>{{1,4},{2,3},{5,6},{7,8}}=>{{1,3},{2,4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>{{1,2},{3,4},{5,6,8},{7}}=>{{1,3},{2,4},{5,6},{7,8}}=>{{1,4},{2,3},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4},{5,6},{7,8}} [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>{{1,2},{3,6},{4},{5},{7,8}}=>{{1,2},{3,6},{4},{5},{7,8}}=>{{1,2},{3,6},{4},{5},{7,8}} [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>{{1,2},{3,6,8},{4},{5},{7}}=>{{1,3},{2,6},{4},{5},{7,8}}=>{{1,6},{2,3},{4},{5},{7,8}} [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,6,7,8},{4},{5}}=>{{1,2,3,6},{4},{5},{7,8}}=>{{1,2,3,6},{4},{5},{7,8}} [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,5,6},{4},{7,8}}=>{{1,2},{3,4,6},{5},{7,8}}=>{{1,2},{3,4,6},{5},{7,8}} [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>{{1,2},{3,5,8},{4},{6,7}}=>{{1,4},{2,3,6},{5},{7,8}}=>{{1,3,4},{2,6},{5},{7,8}} [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,5,6,7,8},{4}}=>{{1,2,3,4,6},{5},{7,8}}=>{{1,2,3,4,6},{5},{7,8}} [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3},{4,5,6},{7,8}} [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,6},{4,5},{7,8}}=>{{1,2},{3,6},{4,5},{7,8}}=>{{1,2},{3,5},{4,6},{7,8}} [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,8},{4,5},{6,7}}=>{{1,6},{2,3},{4,5},{7,8}}=>{{1,3},{2,5},{4,6},{7,8}} [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>{{1,2},{3,6,7,8},{4,5}}=>{{1,2,3,6},{4,5},{7,8}}=>{{1,2,3,5},{4,6},{7,8}} [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,6},{5},{7,8}}=>{{1,2},{3,5},{4,6},{7,8}}=>{{1,2},{3,6},{4,5},{7,8}} [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>{{1,2},{3,7,8},{4,6},{5}}=>{{1,2,6},{3,5},{4},{7,8}}=>{{1,2,5},{3,6},{4},{7,8}} [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>{{1,2},{3,8},{4,7},{5},{6}}=>{{1,6},{2,5},{3},{4},{7,8}}=>{{1,5},{2,6},{3},{4},{7,8}} [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>{{1,2},{3,8},{4,6,7},{5}}=>{{1,6},{2,3,5},{4},{7,8}}=>{{1,3,6},{2,5},{4},{7,8}} [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>{{1,2},{3,4,8},{5},{6,7}}=>{{1,5},{2,3},{4,6},{7,8}}=>{{1,3},{2,6},{4,5},{7,8}} [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>{{1,2},{3,4,6,8},{5},{7}}=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3},{4,5},{7,8}} [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,6,7,8},{5}}=>{{1,2,3,5},{4,6},{7,8}}=>{{1,2,3,6},{4,5},{7,8}} [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2},{3,4,5,6},{7,8}} [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,8},{4,7},{5,6}}=>{{1,6},{2,5},{3,4},{7,8}}=>{{1,4},{2,5},{3,6},{7,8}} [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>{{1,2},{3,4,7,8},{5,6}}=>{{1,2,5},{3,4,6},{7,8}}=>{{1,2,4,5},{3,6},{7,8}} [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,7,8},{6}}=>{{1,2,4},{3,5,6},{7,8}}=>{{1,2,5,6},{3,4},{7,8}} [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,2},{3,8},{4,5,6,7}}=>{{1,6},{2,3,4,5},{7,8}}=>{{1,3,5},{2,4,6},{7,8}} [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>{{1,2},{3,4,8},{5,6,7}}=>{{1,5},{2,3,4,6},{7,8}}=>{{1,3,6},{2,4,5},{7,8}} [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>{{1,2},{3,4,5,8},{6,7}}=>{{1,4},{2,3,5,6},{7,8}}=>{{1,3,4},{2,5,6},{7,8}} [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,8},{7}}=>{{1,3},{2,4,5,6},{7,8}}=>{{1,4,5,6},{2,3},{7,8}} [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6},{7,8}} [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>{{1,3},{2},{4},{5,8},{6,7}}=>{{1,4},{2,3},{5},{6,8},{7}}=>{{1,3},{2,4},{5},{6,8},{7}} [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>{{1,3},{2},{4,8},{5,7},{6}}=>{{1,5},{2,4},{3},{6,8},{7}}=>{{1,4},{2,5},{3},{6,8},{7}} [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,3},{2},{4,5,6,7,8}}=>{{1,2,3,4,5},{6,8},{7}}=>{{1,2,3,4,5},{6,8},{7}} [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2},{3},{5,6},{7,8}}=>{{1,2},{3,4},{5,8},{6},{7}}=>{{1,2},{3,4},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>{{1,4},{2},{3},{5,8},{6},{7}}=>{{1,4},{2},{3},{5,8},{6},{7}}=>{{1,4},{2},{3},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,4},{2},{3},{5,8},{6,7}}=>{{1,4},{2,3},{5,8},{6},{7}}=>{{1,3},{2,4},{5,8},{6},{7}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,8},{2},{3},{4},{5},{6},{7}}=>{{1,8},{2},{3},{4},{5},{6},{7}}=>{{1,8},{2},{3},{4},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,7,8},{2},{3},{4},{5},{6}}=>{{1,2,8},{3},{4},{5},{6},{7}}=>{{1,2,8},{3},{4},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,6,7,8},{2},{3},{4},{5}}=>{{1,2,3,8},{4},{5},{6},{7}}=>{{1,2,3,8},{4},{5},{6},{7}} [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,5,6,7,8},{2},{3},{4}}=>{{1,2,3,4,8},{5},{6},{7}}=>{{1,2,3,4,8},{5},{6},{7}} [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>{{1,4,6},{2},{3},{5},{7,8}}=>{{1,2},{3,5},{4,8},{6},{7}}=>{{1,2},{3,8},{4,5},{6},{7}} [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,4,5,6},{2},{3},{7,8}}=>{{1,2},{3,4,5,8},{6},{7}}=>{{1,2},{3,4,5,8},{6},{7}} [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,4,5,6,7,8},{2},{3}}=>{{1,2,3,4,5,8},{6},{7}}=>{{1,2,3,4,5,8},{6},{7}} [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,3,4},{2},{5,6},{7,8}}=>{{1,2},{3,4},{5,6,8},{7}}=>{{1,2},{3,4},{5,6,8},{7}} [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>{{1,3,4},{2},{5,7,8},{6}}=>{{1,2,4},{3},{5,6,8},{7}}=>{{1,2,4},{3},{5,6,8},{7}} [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1,3,4},{2},{5,8},{6,7}}=>{{1,4},{2,3},{5,6,8},{7}}=>{{1,3},{2,4},{5,6,8},{7}} [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,3,4},{2},{5,6,7,8}}=>{{1,2,3,4},{5,6,8},{7}}=>{{1,2,3,4},{5,6,8},{7}} [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>{{1,3,5,6,8},{2},{4},{7}}=>{{1,3},{2,4,6},{5,8},{7}}=>{{1,4,8},{2,3},{5,6},{7}} [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,3,5,6,7,8},{2},{4}}=>{{1,2,3,4,6},{5,8},{7}}=>{{1,2,3,4,8},{5,6},{7}} [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>{{1,3,6},{2},{4,5},{7,8}}=>{{1,2},{3,6},{4,5,8},{7}}=>{{1,2},{3,5,6},{4,8},{7}} [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>{{1,3,8},{2},{4,5},{6,7}}=>{{1,6},{2,3},{4,5,8},{7}}=>{{1,3},{2,5,6},{4,8},{7}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>{{1,3,4,6,7},{2},{5},{8}}=>{{1},{2,3,5},{4,6,8},{7}}=>{{1},{2,3,6,8},{4,5},{7}} [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>{{1,3,8},{2},{4,6,7},{5}}=>{{1,6},{2,3,5},{4,8},{7}}=>{{1,3,5},{2,8},{4,6},{7}} [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>{{1,3,4,6,8},{2},{5},{7}}=>{{1,3},{2,5},{4,6,8},{7}}=>{{1,6,8},{2,3},{4,5},{7}} [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,3,4,5,6},{2},{7,8}}=>{{1,2},{3,4,5,6,8},{7}}=>{{1,2},{3,4,5,6,8},{7}} [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,8},{2},{3,4,5,6},{7}}=>{{1,8},{2},{3,4,5,6},{7}}=>{{1,4,6},{2},{3,5,8},{7}} [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>{{1,3,8},{2},{4,7},{5,6}}=>{{1,6},{2,5},{3,4,8},{7}}=>{{1,4,6},{2,8},{3,5},{7}} [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>{{1,3,4,5,7,8},{2},{6}}=>{{1,2,4},{3,5,6,8},{7}}=>{{1,2,5,6,8},{3,4},{7}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,3,4,5,6,7},{2},{8}}=>{{1},{2,3,4,5,6,8},{7}}=>{{1},{2,3,4,5,6,8},{7}} [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1,3,4,5,6,8},{2},{7}}=>{{1,3},{2,4,5,6,8},{7}}=>{{1,4,5,6,8},{2,3},{7}} [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,3,4,5,6,7,8},{2}}=>{{1,2,3,4,5,6,8},{7}}=>{{1,2,3,4,5,6,8},{7}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6,7,8}}=>{{1},{2},{3},{4},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>{{1,2,3},{4},{5,8},{6,7}}=>{{1,4},{2,3},{5},{6,7,8}}=>{{1,3},{2,4},{5},{6,7,8}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1},{2},{3},{4,5},{6,7,8}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6,7,8}}=>{{1},{2,3},{4,5},{6,7,8}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1},{2},{3,4,5},{6,7,8}}=>{{1},{2},{3,4,5},{6,7,8}} [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2},{3,4,5},{6,7,8}} [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>{{1,2,3},{4,8},{5,6,7}}=>{{1,5},{2,3,4},{6,7,8}}=>{{1,3,5},{2,4},{6,7,8}} [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5},{6,7,8}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,4},{2,3},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5,8},{6,7}}=>{{1},{2},{3},{4},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>{{1,4},{2,3},{5},{6},{7,8}}=>{{1,2},{3},{4},{5,8},{6,7}}=>{{1,2},{3},{4},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>{{1,4},{2,3},{5},{6,7},{8}}=>{{1},{2,3},{4},{5,8},{6,7}}=>{{1},{2,3},{4},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>{{1,4},{2,3},{5},{6,8},{7}}=>{{1,3},{2},{4},{5,8},{6,7}}=>{{1,3},{2},{4},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>{{1,4},{2,3},{5},{6,7,8}}=>{{1,2,3},{4},{5,8},{6,7}}=>{{1,2,3},{4},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>{{1,4},{2,3},{5,6},{7},{8}}=>{{1},{2},{3,4},{5,8},{6,7}}=>{{1},{2},{3,4},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6},{7,8}}=>{{1,2},{3,4},{5,8},{6,7}}=>{{1,2},{3,4},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>{{1,4},{2,3},{5,7},{6},{8}}=>{{1},{2,4},{3},{5,8},{6,7}}=>{{1},{2,4},{3},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>{{1,4},{2,3},{5,8},{6},{7}}=>{{1,4},{2},{3},{5,8},{6,7}}=>{{1,4},{2},{3},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>{{1,4},{2,3},{5,7,8},{6}}=>{{1,2,4},{3},{5,8},{6,7}}=>{{1,2,4},{3},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>{{1,4},{2,3},{5,6,7},{8}}=>{{1},{2,3,4},{5,8},{6,7}}=>{{1},{2,3,4},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,8},{6,7}}=>{{1,4},{2,3},{5,8},{6,7}}=>{{1,3},{2,4},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>{{1,4},{2,3},{5,6,8},{7}}=>{{1,3},{2,4},{5,8},{6,7}}=>{{1,4},{2,3},{5,7},{6,8}} [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,4},{2,3},{5,6,7,8}}=>{{1,2,3,4},{5,8},{6,7}}=>{{1,2,3,4},{5,7},{6,8}} [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,3},{4,5},{7,8}}=>{{1,2},{3,8},{4,5},{6,7}}=>{{1,2},{3,5},{4,7},{6,8}} [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,3},{4,5},{6,7}}=>{{1,8},{2,3},{4,5},{6,7}}=>{{1,3},{2,5},{4,7},{6,8}} [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,6,7,8},{2,3},{4,5}}=>{{1,2,3,8},{4,5},{6,7}}=>{{1,2,3,5},{4,7},{6,8}} [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>{{1,4,7,8},{2,3},{5},{6}}=>{{1,2,5},{3},{4,8},{6,7}}=>{{1,2,7},{3},{4,5},{6,8}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>{{1,4,6,7},{2,3},{5},{8}}=>{{1},{2,3,5},{4,8},{6,7}}=>{{1},{2,3,7},{4,5},{6,8}} [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>{{1,8},{2,3},{4,6,7},{5}}=>{{1,8},{2,3,5},{4},{6,7}}=>{{1,3,7},{2,5},{4},{6,8}} [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>{{1,4,6,8},{2,3},{5},{7}}=>{{1,3},{2,5},{4,8},{6,7}}=>{{1,7},{2,3},{4,5},{6,8}} [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>{{1,4,6,7,8},{2,3},{5}}=>{{1,2,3,5},{4,8},{6,7}}=>{{1,2,3,7},{4,5},{6,8}} [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,4,5,6},{2,3},{7,8}}=>{{1,2},{3,4,5,8},{6,7}}=>{{1,2},{3,4,5,7},{6,8}} [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,3},{4,7},{5,6}}=>{{1,8},{2,5},{3,4},{6,7}}=>{{1,4},{2,5},{3,7},{6,8}} [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>{{1,4,7,8},{2,3},{5,6}}=>{{1,2,5},{3,4,8},{6,7}}=>{{1,2,4,5},{3,7},{6,8}} [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>{{1,4,5,7,8},{2,3},{6}}=>{{1,2,4},{3,5,8},{6,7}}=>{{1,2,5,7},{3,4},{6,8}} [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,8},{2,3},{4,5,6,7}}=>{{1,8},{2,3,4,5},{6,7}}=>{{1,3,5},{2,4,7},{6,8}} [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>{{1,4,8},{2,3},{5,6,7}}=>{{1,5},{2,3,4,8},{6,7}}=>{{1,3,7},{2,4,5},{6,8}} [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>{{1,4,5,8},{2,3},{6,7}}=>{{1,4},{2,3,5,8},{6,7}}=>{{1,3,4},{2,5,7},{6,8}} [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,4,5,6,7,8},{2,3}}=>{{1,2,3,4,5,8},{6,7}}=>{{1,2,3,4,5,7},{6,8}} [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,4},{3},{5,6},{7,8}}=>{{1,2},{3,4},{5,7},{6,8}}=>{{1,2},{3,4},{5,8},{6,7}} [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,4},{3},{5,8},{6,7}}=>{{1,4},{2,3},{5,7},{6,8}}=>{{1,3},{2,4},{5,8},{6,7}} [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>{{1,2,4},{3},{5,6,8},{7}}=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4},{2,3},{5,8},{6,7}} [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,4},{3},{5,6,7,8}}=>{{1,2,3,4},{5,7},{6,8}}=>{{1,2,3,4},{5,8},{6,7}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>{{1,5},{2,4},{3},{6},{7},{8}}=>{{1},{2},{3},{4,8},{5,7},{6}}=>{{1},{2},{3},{4,7},{5,8},{6}} [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>{{1,5},{2,4},{3},{6,8},{7}}=>{{1,3},{2},{4,8},{5,7},{6}}=>{{1,3},{2},{4,7},{5,8},{6}} [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>{{1,5,6},{2,4},{3},{7,8}}=>{{1,2},{3,4,8},{5,7},{6}}=>{{1,2},{3,4,7},{5,8},{6}} [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>{{1,5,8},{2,4},{3},{6,7}}=>{{1,4},{2,3,8},{5,7},{6}}=>{{1,3,4},{2,7},{5,8},{6}} [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,5},{3},{4},{7,8}}=>{{1,2},{3,8},{4,7},{5},{6}}=>{{1,2},{3,7},{4,8},{5},{6}} [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>{{1,2,8},{3},{4},{5},{6},{7}}=>{{1,7},{2},{3},{4},{5},{6,8}}=>{{1,8},{2},{3},{4},{5},{6,7}} [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,5,6,7,8},{3},{4}}=>{{1,2,3,4,7},{5},{6,8}}=>{{1,2,3,4,8},{5},{6,7}} [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,4,5},{3},{7,8}}=>{{1,2},{3,8},{4,5,7},{6}}=>{{1,2},{3,5,8},{4,7},{6}} [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,4,5},{3},{6,7}}=>{{1,8},{2,3},{4,5,7},{6}}=>{{1,3},{2,5,8},{4,7},{6}} [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>{{1,2,6},{3},{4,5},{7,8}}=>{{1,2},{3,7},{4,5},{6,8}}=>{{1,2},{3,5},{4,8},{6,7}} [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>{{1,8},{2,6,7},{3},{4,5}}=>{{1,8},{2,3,7},{4,5},{6}}=>{{1,3,7},{2,5},{4,8},{6}} [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>{{1,2,8},{3},{4,5},{6,7}}=>{{1,7},{2,3},{4,5},{6,8}}=>{{1,3},{2,5},{4,8},{6,7}} [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>{{1,2,4,6},{3},{5},{7,8}}=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2},{3,8},{4,5},{6,7}} [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}} [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2,3,5},{4,7},{6,8}}=>{{1,2,3,8},{4,5},{6,7}} [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,4,5,6},{3},{7,8}}=>{{1,2},{3,4,5,7},{6,8}}=>{{1,2},{3,4,5,8},{6,7}} [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>{{1,8},{2,4,7},{3},{5,6}}=>{{1,8},{2,5},{3,4,7},{6}}=>{{1,4,8},{2,7},{3,5},{6}} [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>{{1,2,4,5,7,8},{3},{6}}=>{{1,2,4},{3,5,7},{6,8}}=>{{1,2,5,8},{3,4},{6,7}} [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1,2,4,5,6,8},{3},{7}}=>{{1,3},{2,4,5,7},{6,8}}=>{{1,4,5,8},{2,3},{6,7}} [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,4,5,6,7,8},{3}}=>{{1,2,3,4,5,7},{6,8}}=>{{1,2,3,4,5,8},{6,7}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1},{2},{3},{4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3,4},{5,6},{7},{8}}=>{{1},{2},{3,4},{5,6,7,8}}=>{{1},{2},{3,4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2},{3,4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>{{1,2,3,4},{5,7,8},{6}}=>{{1,2,4},{3},{5,6,7,8}}=>{{1,2,4},{3},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1},{2,3,4},{5,6,7,8}}=>{{1},{2,3,4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,3,4},{5,8},{6,7}}=>{{1,4},{2,3},{5,6,7,8}}=>{{1,3},{2,4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>{{1,2,3,4},{5,6,8},{7}}=>{{1,3},{2,4},{5,6,7,8}}=>{{1,4},{2,3},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6,7,8}} [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>{{1,5},{2,3,4},{6,7,8}}=>{{1,2,3},{4,8},{5,6,7}}=>{{1,2,3},{4,6,8},{5,7}} [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>{{1,6,8},{2,3,4},{5},{7}}=>{{1,3},{2,8},{4},{5,6,7}}=>{{1,6,8},{2,3},{4},{5,7}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>{{1,5,7},{2,3,4},{6},{8}}=>{{1},{2,4},{3,8},{5,6,7}}=>{{1},{2,6,8},{3,4},{5,7}} [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>{{1,5,6,7,8},{2,3,4}}=>{{1,2,3,4,8},{5,6,7}}=>{{1,2,3,4,6,8},{5,7}} [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,5},{3,4},{7,8}}=>{{1,2},{3,8},{4,7},{5,6}}=>{{1,2},{3,6},{4,7},{5,8}} [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,5},{3,4},{6,7}}=>{{1,8},{2,3},{4,7},{5,6}}=>{{1,3},{2,6},{4,7},{5,8}} [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>{{1,6,8},{2,5},{3,4},{7}}=>{{1,3},{2,8},{4,7},{5,6}}=>{{1,6},{2,3},{4,7},{5,8}} [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>{{1,6,7,8},{2,5},{3,4}}=>{{1,2,3,8},{4,7},{5,6}}=>{{1,2,3,6},{4,7},{5,8}} [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>{{1,2,5,6},{3,4},{7,8}}=>{{1,2},{3,4,7},{5,6,8}}=>{{1,2},{3,4,6,7},{5,8}} [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>{{1,7,8},{2,5,6},{3,4}}=>{{1,2,8},{3,4,7},{5,6}}=>{{1,2,4,7},{3,6},{5,8}} [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,4},{5,6}}=>{{1,8},{2,7},{3,4},{5,6}}=>{{1,4},{2,6},{3,7},{5,8}} [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>{{1,8},{2,5,6,7},{3,4}}=>{{1,8},{2,3,4,7},{5,6}}=>{{1,3,6},{2,4,7},{5,8}} [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,5,6,7,8},{3,4}}=>{{1,2,3,4,7},{5,6,8}}=>{{1,2,3,4,6,7},{5,8}} [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,5},{4},{6,7,8}}=>{{1,2,3},{4,6},{5,7,8}}=>{{1,2,3},{4,7,8},{5,6}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>{{1,7},{2,6},{3,5},{4},{8}}=>{{1},{2,8},{3,7},{4,6},{5}}=>{{1},{2,6},{3,7},{4,8},{5}} [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>{{1,7,8},{2,6},{3,5},{4}}=>{{1,2,8},{3,7},{4,6},{5}}=>{{1,2,6},{3,7},{4,8},{5}} [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>{{1,8},{2,6,7},{3,5},{4}}=>{{1,8},{2,3,7},{4,6},{5}}=>{{1,3,7},{2,6},{4,8},{5}} [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,6},{4},{5}}=>{{1,8},{2,7},{3,6},{4},{5}}=>{{1,6},{2,7},{3,8},{4},{5}} [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>{{1,2,8},{3,6,7},{4},{5}}=>{{1,7},{2,3,6},{4},{5,8}}=>{{1,3,6},{2,8},{4},{5,7}} [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,5,6},{4},{7,8}}=>{{1,2},{3,4,6},{5,7,8}}=>{{1,2},{3,4,7,8},{5,6}} [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,5,6},{4}}=>{{1,8},{2,7},{3,4,6},{5}}=>{{1,4,8},{2,6},{3,7},{5}} [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>{{1,2,3,5,7,8},{4},{6}}=>{{1,2,4},{3,6},{5,7,8}}=>{{1,2,7,8},{3,4},{5,6}} [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>{{1,8},{2,3,5,6,7},{4}}=>{{1,8},{2,3,4,6},{5,7}}=>{{1,3,7},{2,4,6},{5,8}} [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>{{1,2,8},{3,5,6,7},{4}}=>{{1,7},{2,3,4,6},{5,8}}=>{{1,3,8},{2,4,6},{5,7}} [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,5,6,7,8},{4}}=>{{1,2,3,4,6},{5,7,8}}=>{{1,2,3,4,7,8},{5,6}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5,6,7,8}}=>{{1},{2},{3},{4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5},{6,7},{8}}=>{{1},{2,3},{4,5,6,7,8}}=>{{1},{2,3},{4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>{{1,2,3,4,5},{6,8},{7}}=>{{1,3},{2},{4,5,6,7,8}}=>{{1,3},{2},{4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3},{4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,3,4,5},{7,8}}=>{{1,2},{3,8},{4,5,6,7}}=>{{1,2},{3,5,7},{4,6,8}} [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,3,4,5},{6,7}}=>{{1,8},{2,3},{4,5,6,7}}=>{{1,3},{2,5,7},{4,6,8}} [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>{{1,6,8},{2,3,4,5},{7}}=>{{1,3},{2,8},{4,5,6,7}}=>{{1,5,7},{2,3},{4,6,8}} [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>{{1,6,7,8},{2,3,4,5}}=>{{1,2,3,8},{4,5,6,7}}=>{{1,2,3,5,7},{4,6,8}} [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>{{1,2,6},{3,4,5},{7,8}}=>{{1,2},{3,7},{4,5,6,8}}=>{{1,2},{3,5,8},{4,6,7}} [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>{{1,7,8},{2,6},{3,4,5}}=>{{1,2,8},{3,7},{4,5,6}}=>{{1,2,5,8},{3,6},{4,7}} [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>{{1,2,8},{3,4,5},{6,7}}=>{{1,7},{2,3},{4,5,6,8}}=>{{1,3},{2,5,8},{4,6,7}} [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>{{1,2,6,7,8},{3,4,5}}=>{{1,2,3,7},{4,5,6,8}}=>{{1,2,3,5,8},{4,6,7}} [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>{{1,2,3,6},{4,5},{7,8}}=>{{1,2},{3,6},{4,5,7,8}}=>{{1,2},{3,5,6},{4,7,8}} [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>{{1,7,8},{2,3,6},{4,5}}=>{{1,2,8},{3,6},{4,5,7}}=>{{1,2,5,8},{3,7},{4,6}} [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,6},{4,5}}=>{{1,8},{2,7},{3,6},{4,5}}=>{{1,5},{2,6},{3,7},{4,8}} [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>{{1,8},{2,3,6,7},{4,5}}=>{{1,8},{2,3,6},{4,5,7}}=>{{1,3,7},{2,5,8},{4,6}} [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>{{1,2,3,8},{4,5},{6,7}}=>{{1,6},{2,3},{4,5,7,8}}=>{{1,3},{2,5,6},{4,7,8}} [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,6,7,8},{4,5}}=>{{1,2,3,6},{4,5,7,8}}=>{{1,2,3,5,6},{4,7,8}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,6},{5},{7},{8}}=>{{1},{2},{3,5},{4,6,7,8}}=>{{1},{2},{3,6,7,8},{4,5}} [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,6},{5},{7,8}}=>{{1,2},{3,5},{4,6,7,8}}=>{{1,2},{3,6,7,8},{4,5}} [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,4,6},{5}}=>{{1,8},{2,7},{3,5},{4,6}}=>{{1,6},{2,5},{3,7},{4,8}} [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>{{1,8},{2,3,7},{4,6},{5}}=>{{1,8},{2,6},{3,5},{4,7}}=>{{1,7},{2,5},{3,6},{4,8}} [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>{{1,2,8},{3,7},{4,6},{5}}=>{{1,7},{2,6},{3,5},{4,8}}=>{{1,8},{2,5},{3,6},{4,7}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,6,7},{5},{8}}=>{{1},{2,3,5},{4,6,7,8}}=>{{1},{2,3,6,7,8},{4,5}} [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,6,8},{5},{7}}=>{{1,3},{2,5},{4,6,7,8}}=>{{1,6,7,8},{2,3},{4,5}} [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,6,7,8},{5}}=>{{1,2,3,5},{4,6,7,8}}=>{{1,2,3,6,7,8},{4,5}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5,6},{7},{8}}=>{{1},{2},{3,4,5,6,7,8}}=>{{1},{2},{3,4,5,6,7,8}} [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>{{1,2},{3,4,5,6,7,8}}=>{{1,2},{3,4,5,6,7,8}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>{{1,7},{2,3,4,5,6},{8}}=>{{1},{2,8},{3,4,5,6,7}}=>{{1},{2,4,6,8},{3,5,7}} [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,4,5,6}}=>{{1,8},{2,7},{3,4,5,6}}=>{{1,4,7},{2,5,8},{3,6}} [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>{{1,2,7,8},{3,4,5,6}}=>{{1,2,7},{3,4,5,6,8}}=>{{1,2,4,6,7},{3,5,8}} [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>{{1,2,8},{3,7},{4,5,6}}=>{{1,7},{2,6},{3,4,5,8}}=>{{1,4,6},{2,5,7},{3,8}} [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>{{1,2,3,8},{4,5,6},{7}}=>{{1,6},{2},{3,4,5,7,8}}=>{{1,4,7,8},{2},{3,5,6}} [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>{{1,2,3,7,8},{4,5,6}}=>{{1,2,6},{3,4,5,7,8}}=>{{1,2,4,7,8},{3,5,6}} [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>{{1,8},{2,3,4,7},{5,6}}=>{{1,8},{2,5},{3,4,6,7}}=>{{1,4,7},{2,6,8},{3,5}} [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>{{1,2,8},{3,4,7},{5,6}}=>{{1,7},{2,5},{3,4,6,8}}=>{{1,4,8},{2,6,7},{3,5}} [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>{{1,2,3,8},{4,7},{5,6}}=>{{1,6},{2,5},{3,4,7,8}}=>{{1,4,6},{2,7,8},{3,5}} [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>{{1,2,3,4,7,8},{5,6}}=>{{1,2,5},{3,4,6,7,8}}=>{{1,2,4,5},{3,6,7,8}} [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>{{1,2,8},{3,4,5,7},{6}}=>{{1,7},{2,4},{3,5,6,8}}=>{{1,5,8},{2,4},{3,6,7}} [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>{{1,2,3,8},{4,5,7},{6}}=>{{1,6},{2,4},{3,5,7,8}}=>{{1,5,6},{2,4},{3,7,8}} [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,8},{6},{7}}=>{{1,4},{2},{3,5,6,7,8}}=>{{1,5,6,7,8},{2},{3,4}} [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,7,8},{6}}=>{{1,2,4},{3,5,6,7,8}}=>{{1,2,5,6,7,8},{3,4}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7},{8}}=>{{1},{2,3,4,5,6,7,8}}=>{{1},{2,3,4,5,6,7,8}} [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>{{1,8},{2,3,4,5,6,7}}=>{{1,8},{2,3,4,5,6,7}}=>{{1,3,5,7},{2,4,6,8}} [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>{{1,2,8},{3,4,5,6,7}}=>{{1,7},{2,3,4,5,6,8}}=>{{1,3,5,8},{2,4,6,7}} [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>{{1,2,3,8},{4,5,6,7}}=>{{1,6},{2,3,4,5,7,8}}=>{{1,3,5,6},{2,4,7,8}} [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>{{1,2,3,4,8},{5,6,7}}=>{{1,5},{2,3,4,6,7,8}}=>{{1,3,6,7,8},{2,4,5}} [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,8},{6,7}}=>{{1,4},{2,3,5,6,7,8}}=>{{1,3,4},{2,5,6,7,8}} [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,8},{7}}=>{{1,3},{2,4,5,6,7,8}}=>{{1,4,5,6,7,8},{2,3}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7,8},{9}}=>{{1},{2,3,4,5,6,7,8,9}}=>{{1},{2,3,4,5,6,7,8,9}} [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8,9}}=>{{1,2,3,4,5,6,7,8},{9}}=>{{1,2,3,4,5,6,7,8},{9}} [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7,8,9},{10}}=>{{1},{2,3,4,5,6,7,8,9,10}}=>{{1},{2,3,4,5,6,7,8,9,10}} [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7,8,9},{10}}=>{{1,2,3,4,5,6,7,8,9},{10}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2},{3,4,5,6,7,8,9}}=>{{1,2},{3,4,5,6,7,8,9}} [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8,9}}=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7},{8,9}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5,6,7},{8},{9}}=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1},{2},{3,4,5,6,7,8,9}} [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1,2,3,4,5,6,7},{8},{9}}=>{{1,2,3,4,5,6,7},{8},{9}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2},{3,4,5,6,7,8,9,10}}=>{{1,2},{3,4,5,6,7,8,9,10}} [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2,3,4,5,6,7,8},{9,10}} [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7,8},{9},{10}}=>{{1,2,3,4,5,6,7,8},{9},{10}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}=>{{1,9},{2},{3},{4},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>{{1,2,9},{3},{4},{5},{6},{7},{8}}=>{{1,2,9},{3},{4},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,7,8,9},{2},{3},{4},{5},{6}}=>{{1,2,3,9},{4},{5},{6},{7},{8}}=>{{1,2,3,9},{4},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,6,7,8,9},{2},{3},{4},{5}}=>{{1,2,3,4,9},{5},{6},{7},{8}}=>{{1,2,3,4,9},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,5,6,7,8,9},{2},{3},{4}}=>{{1,2,3,4,5,9},{6},{7},{8}}=>{{1,2,3,4,5,9},{6},{7},{8}} [1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,4,5,6,7,8,9},{2},{3}}=>{{1,2,3,4,5,6,9},{7},{8}}=>{{1,2,3,4,5,6,9},{7},{8}} [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,3,4,5,6,7,8,9},{2}}=>{{1,2,3,4,5,6,7,9},{8}}=>{{1,2,3,4,5,6,7,9},{8}} [1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>{{1,6,7,8,9},{2,3,4,5}}=>{{1,2,3,4,9},{5,6,7,8}}=>{{1,2,3,4,6,8},{5,7,9}} [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8,9}}=>{{1,2,3,4,5,6,7,8,9}}=>{{1,2,3,4,5,6,7,8,9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}=>{{1,2,3},{4},{5},{6},{7},{8},{9}}=>{{1,2,3},{4},{5},{6},{7},{8},{9}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8,9}}=>{{1,2,3,4},{5},{6},{7},{8},{9}}=>{{1,2,3,4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8,9}}=>{{1,2,3,4,5},{6},{7},{8},{9}}=>{{1,2,3,4,5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}=>{{1,2,3,4,5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8,9}}=>{{1,2,3,4,5,6},{7},{8},{9}}=>{{1,2,3,4,5,6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}=>{{1,2,3,4,5,6},{7},{8},{9},{10}}=>{{1,2,3,4,5,6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7},{8,9}}=>{{1,2},{3,4},{5},{6},{7},{8},{9}}=>{{1,2},{3,4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,2,3},{4,5},{6},{7},{8},{9}}=>{{1,2,3},{4,5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8,9}}=>{{1,2,3,4},{5,6},{7},{8},{9}}=>{{1,2,3,4},{5,6},{7},{8},{9}} [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4},{5,6,7,8,9}}=>{{1,2,3,4,5},{6,7},{8},{9}}=>{{1,2,3,4,5},{6,7},{8},{9}} [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8,9}}=>{{1,2,3,4,5,6},{7,8},{9}}=>{{1,2,3,4,5,6},{7,8},{9}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}=>{{1},{2},{3},{4},{5},{6},{7},{8,9}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8},{9}}=>{{1},{2},{3},{4},{5},{6,7},{8,9}}=>{{1},{2},{3},{4},{5},{6,7},{8,9}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}=>{{1},{2},{3},{4},{5},{6},{7,8,9}}=>{{1},{2},{3},{4},{5},{6},{7,8,9}} [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8,9}}=>{{1,2,3,4,5,6},{7,8,9}}=>{{1,2,3,4,5,6},{7,8,9}} [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4},{5,6,7,8,9}}=>{{1,2,3,4,5},{6,7,8,9}}=>{{1,2,3,4,5},{6,7,8,9}} [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4,5},{6,7,8,9}}=>{{1,2,3,4},{5,6,7,8,9}}=>{{1,2,3,4},{5,6,7,8,9}} [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5,6},{7,8,9}}=>{{1,2,3},{4,5,6,7,8,9}}=>{{1,2,3},{4,5,6,7,8,9}} [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7},{8},{9},{10}}=>{{1,2,3,4,5,6,7},{8},{9},{10}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7},{8,9,10}}=>{{1,2,3,4,5,6,7},{8,9,10}} [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4},{5,6,7,8,9,10}}=>{{1,2,3,4,5,6},{7,8,9,10}}=>{{1,2,3,4,5,6},{7,8,9,10}} [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5},{6,7,8,9,10}}=>{{1,2,3,4,5},{6,7,8,9,10}}=>{{1,2,3,4,5},{6,7,8,9,10}} [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4,5,6},{7,8,9,10}}=>{{1,2,3,4},{5,6,7,8,9,10}}=>{{1,2,3,4},{5,6,7,8,9,10}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5,6,7},{8,9,10}}=>{{1,2,3},{4,5,6,7,8,9,10}}=>{{1,2,3},{4,5,6,7,8,9,10}} [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7,8,9,10}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}=>{{1,2,10},{3},{4},{5},{6},{7},{8},{9}}=>{{1,2,10},{3},{4},{5},{6},{7},{8},{9}} [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{1,3,4,5,6,7,8,9,10},{2}}=>{{1,2,3,4,5,6,7,8,10},{9}}=>{{1,2,3,4,5,6,7,8,10},{9}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}=>{{1,2,3,10},{4},{5},{6},{7},{8},{9}}=>{{1,2,3,10},{4},{5},{6},{7},{8},{9}} [1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,4,5,6,7,8,9,10},{2},{3}}=>{{1,2,3,4,5,6,7,10},{8},{9}}=>{{1,2,3,4,5,6,7,10},{8},{9}} [1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,5,6,7,8,9,10},{2},{3},{4}}=>{{1,2,3,4,5,6,10},{7},{8},{9}}=>{{1,2,3,4,5,6,10},{7},{8},{9}} [1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,6,7,8,9,10},{2},{3},{4},{5}}=>{{1,2,3,4,5,10},{6},{7},{8},{9}}=>{{1,2,3,4,5,10},{6},{7},{8},{9}} [1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,7,8,9,10},{2},{3},{4},{5},{6}}=>{{1,2,3,4,10},{5},{6},{7},{8},{9}}=>{{1,2,3,4,10},{5},{6},{7},{8},{9}} [1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,7,8,9,10},{3,4,5,6}}=>{{1,2,3,4,9},{5,6,7,8,10}}=>{{1,2,3,4,6,8,9},{5,7,10}} [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8,9,10,11}}=>{{1,2,3,4,5,6,7,8,9,10,11}}=>{{1,2,3,4,5,6,7,8,9,10,11}}
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
Wachs-White
Description
A transformation of set partitions due to Wachs and White.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection $\gamma$.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with $(i,j)$ to the cell in the $i$-th column from the right and the $j$-th row from the top.
Map
Kasraoui-Zeng
Description
The Kasraoui-Zeng involution.
This is defined in [1] and yields the set partition with the number of nestings and crossings exchanged.