Identifier
Mp00229: Dyck paths Delest-ViennotDyck paths
Mp00023: Dyck paths to non-crossing permutationPermutations
Mp00151: Permutations to cycle typeSet partitions
Mp00115: Set partitions Kasraoui-Zeng Set partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0009;cc-rep-3Cc0009;cc-rep-4
[1,0]=>[1,0]=>[1]=>{{1}}=>{{1}} [1,0,1,0]=>[1,1,0,0]=>[2,1]=>{{1,2}}=>{{1,2}} [1,1,0,0]=>[1,0,1,0]=>[1,2]=>{{1},{2}}=>{{1},{2}} [1,0,1,0,1,0]=>[1,1,0,1,0,0]=>[2,3,1]=>{{1,2,3}}=>{{1,2,3}} [1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[2,1,3]=>{{1,2},{3}}=>{{1,2},{3}} [1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[1,3,2]=>{{1},{2,3}}=>{{1},{2,3}} [1,1,0,1,0,0]=>[1,1,1,0,0,0]=>[3,2,1]=>{{1,3},{2}}=>{{1,3},{2}} [1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[1,2,3]=>{{1},{2},{3}}=>{{1},{2},{3}} [1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>{{1,2,3},{4}}=>{{1,2,3},{4}} [1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>{{1,2},{3,4}}=>{{1,2},{3,4}} [1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>{{1,2,4},{3}}=>{{1,2,4},{3}} [1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>{{1,2},{3},{4}}=>{{1,2},{3},{4}} [1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>{{1},{2,3,4}}=>{{1},{2,3,4}} [1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>{{1},{2,3},{4}}=>{{1},{2,3},{4}} [1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>{{1,3,4},{2}}=>{{1,3,4},{2}} [1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>{{1,4},{2,3}}=>{{1,3},{2,4}} [1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>{{1,3},{2},{4}}=>{{1,3},{2},{4}} [1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>{{1},{2},{3,4}}=>{{1},{2},{3,4}} [1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>{{1},{2,4},{3}}=>{{1},{2,4},{3}} [1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[4,2,3,1]=>{{1,4},{2},{3}}=>{{1,4},{2},{3}} [1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>{{1},{2},{3},{4}}=>{{1},{2},{3},{4}} [1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}=>{{1,2,3,4},{5}} [1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>{{1,2,3},{4,5}}=>{{1,2,3},{4,5}} [1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>{{1,2,3,5},{4}}=>{{1,2,3,5},{4}} [1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}=>{{1,2,3},{4},{5}} [1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>{{1,2},{3,4,5}}=>{{1,2},{3,4,5}} [1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}}=>{{1,2},{3,4},{5}} [1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>{{1,2,4,5},{3}}=>{{1,2,4,5},{3}} [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>{{1,2,5},{3,4}}=>{{1,2,4},{3,5}} [1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>{{1,2,4},{3},{5}}=>{{1,2,4},{3},{5}} [1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}}=>{{1,2},{3},{4,5}} [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>{{1,2},{3,5},{4}}=>{{1,2},{3,5},{4}} [1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>{{1,2,5},{3},{4}}=>{{1,2,5},{3},{4}} [1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}}=>{{1,2},{3},{4},{5}} [1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}=>{{1},{2,3,4,5}} [1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}=>{{1},{2,3,4},{5}} [1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}=>{{1},{2,3},{4,5}} [1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}=>{{1},{2,3,5},{4}} [1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}=>{{1},{2,3},{4},{5}} [1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>{{1,3,4,5},{2}}=>{{1,3,4,5},{2}} [1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}}=>{{1,3,4},{2},{5}} [1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>{{1,4,5},{2,3}}=>{{1,3},{2,4,5}} [1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>{{1,5},{2,3,4}}=>{{1,3,5},{2,4}} [1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}}=>{{1,3},{2,4},{5}} [1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>{{1,3},{2},{4,5}}=>{{1,3},{2},{4,5}} [1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>{{1,3,5},{2},{4}}=>{{1,3,5},{2},{4}} [1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}}=>{{1,3},{2,5},{4}} [1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}}=>{{1,3},{2},{4},{5}} [1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}=>{{1},{2},{3,4,5}} [1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}=>{{1},{2},{3,4},{5}} [1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}=>{{1},{2,4,5},{3}} [1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}}=>{{1},{2,4},{3,5}} [1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}}=>{{1},{2,4},{3},{5}} [1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}}=>{{1,4,5},{2},{3}} [1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>{{1,5},{2},{3,4}}=>{{1,4},{2},{3,5}} [1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}}=>{{1,4},{2,5},{3}} [1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}}=>{{1,4},{2},{3},{5}} [1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}=>{{1},{2},{3},{4,5}} [1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}}=>{{1},{2},{3,5},{4}} [1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}}=>{{1},{2,5},{3},{4}} [1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}}=>{{1,5},{2},{3},{4}} [1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4},{5,6}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}}=>{{1,2,3,4,6},{5}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}=>{{1,2,3},{4,5},{6}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}}=>{{1,2,3,5,6},{4}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}}=>{{1,2,3,5},{4,6}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}}=>{{1,2,3,5},{4},{6}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}=>{{1,2,3},{4},{5,6}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}}=>{{1,2,3},{4,6},{5}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}}=>{{1,2,3,6},{4},{5}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}=>{{1,2},{3,4,5,6}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}=>{{1,2},{3,4,5},{6}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}}=>{{1,2},{3,4,6},{5}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}=>{{1,2},{3,4},{5},{6}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}}=>{{1,2,4,5,6},{3}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}}=>{{1,2,4,5},{3},{6}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}}=>{{1,2,4},{3,5,6}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}}=>{{1,2,4,6},{3,5}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}}=>{{1,2,4},{3,5},{6}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}}=>{{1,2,4},{3},{5,6}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}}=>{{1,2,4,6},{3},{5}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>{{1,2,6},{3,4},{5}}=>{{1,2,4},{3,6},{5}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}}=>{{1,2,4},{3},{5},{6}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}=>{{1,2},{3},{4,5,6}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}=>{{1,2},{3},{4,5},{6}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}}=>{{1,2},{3,5,6},{4}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}}=>{{1,2},{3,5},{4,6}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}}=>{{1,2},{3,5},{4},{6}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}}=>{{1,2,5,6},{3},{4}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>{{1,2,6},{3},{4,5}}=>{{1,2,5},{3},{4,6}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}}=>{{1,2,5},{3,6},{4}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>{{1,2,5},{3},{4},{6}}=>{{1,2,5},{3},{4},{6}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5,6}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}}=>{{1,2},{3},{4,6},{5}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}}=>{{1,2},{3,6},{4},{5}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}}=>{{1,2,6},{3},{4},{5}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}=>{{1},{2,3,4},{5,6}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}=>{{1},{2,3,4,6},{5}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}=>{{1},{2,3,4},{5},{6}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}=>{{1},{2,3},{4,5,6}} [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}=>{{1},{2,3},{4,5},{6}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}=>{{1},{2,3,5,6},{4}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}}=>{{1},{2,3,5},{4,6}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}=>{{1},{2,3,5},{4},{6}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}=>{{1},{2,3},{4},{5,6}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}=>{{1},{2,3},{4,6},{5}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}=>{{1},{2,3,6},{4},{5}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}}=>{{1,3,4,5,6},{2}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}=>{{1,3,4,5},{2},{6}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}}=>{{1,3,4},{2},{5,6}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}}=>{{1,3,4,6},{2},{5}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}}=>{{1,3,4},{2},{5},{6}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}=>{{1,3},{2,4,5,6}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}=>{{1,3},{2,4,5},{6}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}}=>{{1,3,5,6},{2,4}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}}=>{{1,3,5},{2,4,6}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}}=>{{1,3,5},{2,4},{6}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}}=>{{1,3},{2,4},{5,6}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}}=>{{1,3},{2,4,6},{5}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}}=>{{1,3,6},{2,4},{5}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}=>{{1,3},{2,4},{5},{6}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}}=>{{1,3},{2},{4,5,6}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}}=>{{1,3},{2},{4,5},{6}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}}=>{{1,3,5,6},{2},{4}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}}=>{{1,3,5},{2},{4,6}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}}=>{{1,3,5},{2},{4},{6}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}}=>{{1,3},{2,5,6},{4}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}}=>{{1,3},{2,5},{4,6}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}}=>{{1,3,6},{2,5},{4}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}}=>{{1,3},{2,5},{4},{6}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}}=>{{1,3},{2},{4},{5,6}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}}=>{{1,3},{2},{4,6},{5}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>{{1,3,6},{2},{4},{5}}=>{{1,3,6},{2},{4},{5}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}}=>{{1,3},{2,6},{4},{5}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}=>{{1,3},{2},{4},{5},{6}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}=>{{1},{2},{3,4,5,6}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}=>{{1},{2},{3,4,5},{6}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}=>{{1},{2},{3,4},{5,6}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}=>{{1},{2},{3,4,6},{5}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5},{6}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}=>{{1},{2,4,5,6},{3}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}=>{{1},{2,4,5},{3},{6}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}}=>{{1},{2,4},{3,5,6}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}}=>{{1},{2,4,6},{3,5}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}}=>{{1},{2,4},{3,5},{6}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}=>{{1},{2,4},{3},{5,6}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}=>{{1},{2,4,6},{3},{5}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}}=>{{1},{2,4},{3,6},{5}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}=>{{1},{2,4},{3},{5},{6}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}}=>{{1,4,5,6},{2},{3}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}}=>{{1,4,5},{2},{3},{6}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}}=>{{1,4},{2},{3,5,6}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}}=>{{1,4,6},{2},{3,5}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>{{1,5},{2},{3,4},{6}}=>{{1,4},{2},{3,5},{6}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}=>{{1,4},{2,5,6},{3}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}}=>{{1,4,6},{2,5},{3}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}=>{{1,4},{2,5},{3,6}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}=>{{1,4},{2,5},{3},{6}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}}=>{{1,4},{2},{3},{5,6}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>{{1,4,6},{2},{3},{5}}=>{{1,4,6},{2},{3},{5}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>{{1,6},{2},{3,4},{5}}=>{{1,4},{2},{3,6},{5}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}}=>{{1,4},{2,6},{3},{5}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}}=>{{1,4},{2},{3},{5},{6}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}=>{{1},{2},{3},{4,5,6}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}=>{{1},{2},{3},{4,5},{6}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}=>{{1},{2},{3,5,6},{4}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}}=>{{1},{2},{3,5},{4,6}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}=>{{1},{2},{3,5},{4},{6}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}=>{{1},{2,5,6},{3},{4}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}}=>{{1},{2,5},{3},{4,6}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}}=>{{1},{2,5},{3,6},{4}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}=>{{1},{2,5},{3},{4},{6}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}}=>{{1,5,6},{2},{3},{4}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}}=>{{1,5},{2},{3},{4,6}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}}=>{{1,5},{2},{3,6},{4}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}}=>{{1,5},{2,6},{3},{4}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}}=>{{1,5},{2},{3},{4},{6}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}=>{{1},{2},{3},{4},{5,6}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}=>{{1},{2},{3},{4,6},{5}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}=>{{1},{2},{3,6},{4},{5}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}}=>{{1},{2,6},{3},{4},{5}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}}=>{{1,6},{2},{3},{4},{5}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>{{1},{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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>{{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]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>{{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]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>{{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]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}}=>{{1,2,3,4,5,7},{6}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>{{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]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>{{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]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>{{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]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>{{1,2,3,4,6,7},{5}}=>{{1,2,3,4,6,7},{5}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}}=>{{1,2,3,4,6},{5,7}} [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>{{1,2,3,4,6},{5},{7}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>{{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]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>{{1,2,3,4},{5,7},{6}}=>{{1,2,3,4},{5,7},{6}} [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>{{1,2,3,4,7},{5},{6}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>{{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]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>{{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]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>{{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]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>{{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]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>{{1,2,3},{4,5,7},{6}}=>{{1,2,3},{4,5,7},{6}} [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>{{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]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>{{1,2,3,5,6,7},{4}}=>{{1,2,3,5,6,7},{4}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}=>{{1,2,3,5,6},{4},{7}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>{{1,2,3,6,7},{4,5}}=>{{1,2,3,5},{4,6,7}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}}=>{{1,2,3,5,7},{4,6}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}=>{{1,2,3,5},{4,6},{7}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>{{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]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>{{1,2,3,5,7},{4},{6}}=>{{1,2,3,5,7},{4},{6}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}=>{{1,2,3,5},{4,7},{6}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>{{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]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>{{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]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>{{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]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>{{1,2,3},{4,6,7},{5}}=>{{1,2,3},{4,6,7},{5}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>{{1,2,3},{4,7},{5,6}}=>{{1,2,3},{4,6},{5,7}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}}=>{{1,2,3},{4,6},{5},{7}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>{{1,2,3,6,7},{4},{5}}=>{{1,2,3,6,7},{4},{5}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>{{1,2,3,7},{4},{5,6}}=>{{1,2,3,6},{4},{5,7}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}=>{{1,2,3,6},{4,7},{5}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}=>{{1,2,3,6},{4},{5},{7}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>{{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]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}}=>{{1,2,3},{4},{5,7},{6}} [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}}=>{{1,2,3},{4,7},{5},{6}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}=>{{1,2,3,7},{4},{5},{6}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>{{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]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>{{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]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>{{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]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>{{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]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>{{1,2},{3,4,5,7},{6}}=>{{1,2},{3,4,5,7},{6}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>{{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]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>{{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]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>{{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]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>{{1,2},{3,4,6,7},{5}}=>{{1,2},{3,4,6,7},{5}} [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>{{1,2},{3,4,7},{5,6}}=>{{1,2},{3,4,6},{5,7}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>{{1,2},{3,4,6},{5},{7}}=>{{1,2},{3,4,6},{5},{7}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>{{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]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>{{1,2},{3,4},{5,7},{6}}=>{{1,2},{3,4},{5,7},{6}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>{{1,2},{3,4,7},{5},{6}}=>{{1,2},{3,4,7},{5},{6}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>{{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]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>{{1,2,4,5,6,7},{3}}=>{{1,2,4,5,6,7},{3}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>{{1,2,4,5,6},{3},{7}}=>{{1,2,4,5,6},{3},{7}} [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>{{1,2,4,5},{3},{6,7}}=>{{1,2,4,5},{3},{6,7}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>{{1,2,4,5,7},{3},{6}}=>{{1,2,4,5,7},{3},{6}} [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>{{1,2,4,5},{3},{6},{7}}=>{{1,2,4,5},{3},{6},{7}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>{{1,2,5,6,7},{3,4}}=>{{1,2,4},{3,5,6,7}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>{{1,2,5,6},{3,4},{7}}=>{{1,2,4},{3,5,6},{7}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>{{1,2,6,7},{3,4,5}}=>{{1,2,4,6,7},{3,5}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>{{1,2,7},{3,4,5,6}}=>{{1,2,4,6},{3,5,7}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>{{1,2,6},{3,4,5},{7}}=>{{1,2,4,6},{3,5},{7}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>{{1,2,5},{3,4},{6,7}}=>{{1,2,4},{3,5},{6,7}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>{{1,2,5,7},{3,4},{6}}=>{{1,2,4},{3,5,7},{6}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>{{1,2,7},{3,4,5},{6}}=>{{1,2,4,7},{3,5},{6}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>{{1,2,5},{3,4},{6},{7}}=>{{1,2,4},{3,5},{6},{7}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>{{1,2,4},{3},{5,6,7}}=>{{1,2,4},{3},{5,6,7}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>{{1,2,4},{3},{5,6},{7}}=>{{1,2,4},{3},{5,6},{7}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>{{1,2,4,6,7},{3},{5}}=>{{1,2,4,6,7},{3},{5}} [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>{{1,2,4,7},{3},{5,6}}=>{{1,2,4,6},{3},{5,7}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>{{1,2,4,6},{3},{5},{7}}=>{{1,2,4,6},{3},{5},{7}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>{{1,2,6,7},{3,4},{5}}=>{{1,2,4},{3,6,7},{5}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>{{1,2,7},{3,4},{5,6}}=>{{1,2,4},{3,6},{5,7}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>{{1,2,7},{3,4,6},{5}}=>{{1,2,4,7},{3,6},{5}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>{{1,2,6},{3,4},{5},{7}}=>{{1,2,4},{3,6},{5},{7}} [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>{{1,2,4},{3},{5},{6,7}}=>{{1,2,4},{3},{5},{6,7}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>{{1,2,4},{3},{5,7},{6}}=>{{1,2,4},{3},{5,7},{6}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>{{1,2,4,7},{3},{5},{6}}=>{{1,2,4,7},{3},{5},{6}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>{{1,2,7},{3,4},{5},{6}}=>{{1,2,4},{3,7},{5},{6}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}=>{{1,2,4},{3},{5},{6},{7}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>{{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]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>{{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]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>{{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]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>{{1,2},{3},{4,5,7},{6}}=>{{1,2},{3},{4,5,7},{6}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>{{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]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>{{1,2},{3,5,6,7},{4}}=>{{1,2},{3,5,6,7},{4}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>{{1,2},{3,5,6},{4},{7}}=>{{1,2},{3,5,6},{4},{7}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>{{1,2},{3,6,7},{4,5}}=>{{1,2},{3,5},{4,6,7}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>{{1,2},{3,7},{4,5,6}}=>{{1,2},{3,5,7},{4,6}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>{{1,2},{3,6},{4,5},{7}}=>{{1,2},{3,5},{4,6},{7}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>{{1,2},{3,5},{4},{6,7}}=>{{1,2},{3,5},{4},{6,7}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>{{1,2},{3,5,7},{4},{6}}=>{{1,2},{3,5,7},{4},{6}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>{{1,2},{3,7},{4,5},{6}}=>{{1,2},{3,5},{4,7},{6}} [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>{{1,2},{3,5},{4},{6},{7}}=>{{1,2},{3,5},{4},{6},{7}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>{{1,2,5,6,7},{3},{4}}=>{{1,2,5,6,7},{3},{4}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>{{1,2,5,6},{3},{4},{7}}=>{{1,2,5,6},{3},{4},{7}} [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>{{1,2,6,7},{3},{4,5}}=>{{1,2,5},{3},{4,6,7}} [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>{{1,2,7},{3},{4,5,6}}=>{{1,2,5,7},{3},{4,6}} [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>{{1,2,6},{3},{4,5},{7}}=>{{1,2,5},{3},{4,6},{7}} [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>{{1,2,6,7},{3,5},{4}}=>{{1,2,5},{3,6,7},{4}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>{{1,2,7},{3,5,6},{4}}=>{{1,2,5,7},{3,6},{4}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>{{1,2,7},{3,6},{4,5}}=>{{1,2,5},{3,6},{4,7}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>{{1,2,6},{3,5},{4},{7}}=>{{1,2,5},{3,6},{4},{7}} [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>{{1,2,5},{3},{4},{6,7}}=>{{1,2,5},{3},{4},{6,7}} [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>{{1,2,5,7},{3},{4},{6}}=>{{1,2,5,7},{3},{4},{6}} [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>{{1,2,7},{3},{4,5},{6}}=>{{1,2,5},{3},{4,7},{6}} [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>{{1,2,7},{3,5},{4},{6}}=>{{1,2,5},{3,7},{4},{6}} [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>{{1,2,5},{3},{4},{6},{7}}=>{{1,2,5},{3},{4},{6},{7}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>{{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]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>{{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]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>{{1,2},{3},{4,6,7},{5}}=>{{1,2},{3},{4,6,7},{5}} [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>{{1,2},{3},{4,7},{5,6}}=>{{1,2},{3},{4,6},{5,7}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>{{1,2},{3},{4,6},{5},{7}}=>{{1,2},{3},{4,6},{5},{7}} [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>{{1,2},{3,6,7},{4},{5}}=>{{1,2},{3,6,7},{4},{5}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>{{1,2},{3,7},{4},{5,6}}=>{{1,2},{3,6},{4},{5,7}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>{{1,2},{3,7},{4,6},{5}}=>{{1,2},{3,6},{4,7},{5}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>{{1,2},{3,6},{4},{5},{7}}=>{{1,2},{3,6},{4},{5},{7}} [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>{{1,2,6,7},{3},{4},{5}}=>{{1,2,6,7},{3},{4},{5}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>{{1,2,7},{3},{4},{5,6}}=>{{1,2,6},{3},{4},{5,7}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>{{1,2,7},{3},{4,6},{5}}=>{{1,2,6},{3},{4,7},{5}} [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>{{1,2,7},{3,6},{4},{5}}=>{{1,2,6},{3,7},{4},{5}} [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>{{1,2,6},{3},{4},{5},{7}}=>{{1,2,6},{3},{4},{5},{7}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>{{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]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>{{1,2},{3},{4},{5,7},{6}}=>{{1,2},{3},{4},{5,7},{6}} [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>{{1,2},{3},{4,7},{5},{6}}=>{{1,2},{3},{4,7},{5},{6}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>{{1,2},{3,7},{4},{5},{6}}=>{{1,2},{3,7},{4},{5},{6}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>{{1,2,7},{3},{4},{5},{6}}=>{{1,2,7},{3},{4},{5},{6}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>{{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]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>{{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]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>{{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]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>{{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]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}=>{{1},{2,3,4,5,7},{6}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>{{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]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>{{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]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>{{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]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}=>{{1},{2,3,4,6,7},{5}} [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>{{1},{2,3,4,7},{5,6}}=>{{1},{2,3,4,6},{5,7}} [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}=>{{1},{2,3,4,6},{5},{7}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>{{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]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}=>{{1},{2,3,4},{5,7},{6}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}=>{{1},{2,3,4,7},{5},{6}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>{{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]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>{{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]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>{{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]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>{{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]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}=>{{1},{2,3},{4,5,7},{6}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>{{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]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}=>{{1},{2,3,5,6,7},{4}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}=>{{1},{2,3,5,6},{4},{7}} [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>{{1},{2,3,6,7},{4,5}}=>{{1},{2,3,5},{4,6,7}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>{{1},{2,3,7},{4,5,6}}=>{{1},{2,3,5,7},{4,6}} [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>{{1},{2,3,6},{4,5},{7}}=>{{1},{2,3,5},{4,6},{7}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>{{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]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}=>{{1},{2,3,5,7},{4},{6}} [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>{{1},{2,3,7},{4,5},{6}}=>{{1},{2,3,5},{4,7},{6}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>{{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]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>{{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]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>{{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]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}=>{{1},{2,3},{4,6,7},{5}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>{{1},{2,3},{4,7},{5,6}}=>{{1},{2,3},{4,6},{5,7}} [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}=>{{1},{2,3},{4,6},{5},{7}} [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}=>{{1},{2,3,6,7},{4},{5}} [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>{{1},{2,3,7},{4},{5,6}}=>{{1},{2,3,6},{4},{5,7}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>{{1},{2,3,7},{4,6},{5}}=>{{1},{2,3,6},{4,7},{5}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}=>{{1},{2,3,6},{4},{5},{7}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>{{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]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}=>{{1},{2,3},{4},{5,7},{6}} [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}}=>{{1},{2,3},{4,7},{5},{6}} [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}=>{{1},{2,3,7},{4},{5},{6}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>{{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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}}=>{{1,3,4,5,6,7},{2}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}}=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>{{1,3,4,5},{2},{6,7}}=>{{1,3,4,5},{2},{6,7}} [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}}=>{{1,3,4,5,7},{2},{6}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}}=>{{1,3,4,5},{2},{6},{7}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>{{1,3,4},{2},{5,6,7}}=>{{1,3,4},{2},{5,6,7}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>{{1,3,4},{2},{5,6},{7}}=>{{1,3,4},{2},{5,6},{7}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}}=>{{1,3,4,6,7},{2},{5}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>{{1,3,4,7},{2},{5,6}}=>{{1,3,4,6},{2},{5,7}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>{{1,3,4,6},{2},{5},{7}}=>{{1,3,4,6},{2},{5},{7}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>{{1,3,4},{2},{5},{6,7}}=>{{1,3,4},{2},{5},{6,7}} [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>{{1,3,4},{2},{5,7},{6}}=>{{1,3,4},{2},{5,7},{6}} [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>{{1,3,4,7},{2},{5},{6}}=>{{1,3,4,7},{2},{5},{6}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}=>{{1,3,4},{2},{5},{6},{7}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}}=>{{1,3},{2,4,5,6,7}} [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}}=>{{1,3},{2,4,5,6},{7}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>{{1,4,5},{2,3},{6,7}}=>{{1,3},{2,4,5},{6,7}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>{{1,4,5,7},{2,3},{6}}=>{{1,3},{2,4,5,7},{6}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}}=>{{1,3},{2,4,5},{6},{7}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}}=>{{1,3,5,6,7},{2,4}} [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}}=>{{1,3,5,6},{2,4},{7}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}}=>{{1,3,5},{2,4,6,7}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}}=>{{1,3,5,7},{2,4,6}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}}=>{{1,3,5},{2,4,6},{7}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>{{1,5},{2,3,4},{6,7}}=>{{1,3,5},{2,4},{6,7}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>{{1,5,7},{2,3,4},{6}}=>{{1,3,5,7},{2,4},{6}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}}=>{{1,3,5},{2,4,7},{6}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}}=>{{1,3,5},{2,4},{6},{7}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>{{1,4},{2,3},{5,6,7}}=>{{1,3},{2,4},{5,6,7}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>{{1,4},{2,3},{5,6},{7}}=>{{1,3},{2,4},{5,6},{7}} [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>{{1,4,6,7},{2,3},{5}}=>{{1,3},{2,4,6,7},{5}} [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>{{1,4,7},{2,3},{5,6}}=>{{1,3},{2,4,6},{5,7}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>{{1,4,6},{2,3},{5},{7}}=>{{1,3},{2,4,6},{5},{7}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}}=>{{1,3,6,7},{2,4},{5}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>{{1,7},{2,3,4},{5,6}}=>{{1,3,6},{2,4},{5,7}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>{{1,7},{2,3,4,6},{5}}=>{{1,3,6},{2,4,7},{5}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}}=>{{1,3,6},{2,4},{5},{7}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>{{1,4},{2,3},{5},{6,7}}=>{{1,3},{2,4},{5},{6,7}} [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>{{1,4},{2,3},{5,7},{6}}=>{{1,3},{2,4},{5,7},{6}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>{{1,4,7},{2,3},{5},{6}}=>{{1,3},{2,4,7},{5},{6}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}}=>{{1,3,7},{2,4},{5},{6}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}}=>{{1,3},{2,4},{5},{6},{7}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>{{1,3},{2},{4,5,6,7}}=>{{1,3},{2},{4,5,6,7}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}}=>{{1,3},{2},{4,5,6},{7}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}}=>{{1,3},{2},{4,5},{6,7}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>{{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]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}}=>{{1,3},{2},{4,5},{6},{7}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>{{1,3,5,6,7},{2},{4}}=>{{1,3,5,6,7},{2},{4}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>{{1,3,5,6},{2},{4},{7}}=>{{1,3,5,6},{2},{4},{7}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>{{1,3,6,7},{2},{4,5}}=>{{1,3,5},{2},{4,6,7}} [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>{{1,3,7},{2},{4,5,6}}=>{{1,3,5,7},{2},{4,6}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>{{1,3,6},{2},{4,5},{7}}=>{{1,3,5},{2},{4,6},{7}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>{{1,3,5},{2},{4},{6,7}}=>{{1,3,5},{2},{4},{6,7}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>{{1,3,5,7},{2},{4},{6}}=>{{1,3,5,7},{2},{4},{6}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>{{1,3,7},{2},{4,5},{6}}=>{{1,3,5},{2},{4,7},{6}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>{{1,3,5},{2},{4},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}}=>{{1,3},{2,5,6,7},{4}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}}=>{{1,3},{2,5,6},{4},{7}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>{{1,6,7},{2,3},{4,5}}=>{{1,3},{2,5},{4,6,7}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>{{1,7},{2,3},{4,5,6}}=>{{1,3},{2,5,7},{4,6}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>{{1,6},{2,3},{4,5},{7}}=>{{1,3},{2,5},{4,6},{7}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>{{1,6,7},{2,3,5},{4}}=>{{1,3,6,7},{2,5},{4}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>{{1,7},{2,3,5,6},{4}}=>{{1,3,6},{2,5,7},{4}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>{{1,7},{2,3,6},{4,5}}=>{{1,3,6},{2,5},{4,7}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>{{1,6},{2,3,5},{4},{7}}=>{{1,3,6},{2,5},{4},{7}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>{{1,5},{2,3},{4},{6,7}}=>{{1,3},{2,5},{4},{6,7}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>{{1,5,7},{2,3},{4},{6}}=>{{1,3},{2,5,7},{4},{6}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>{{1,7},{2,3},{4,5},{6}}=>{{1,3},{2,5},{4,7},{6}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>{{1,7},{2,3,5},{4},{6}}=>{{1,3,7},{2,5},{4},{6}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}}=>{{1,3},{2,5},{4},{6},{7}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}}=>{{1,3},{2},{4},{5,6,7}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}}=>{{1,3},{2},{4},{5,6},{7}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}}=>{{1,3},{2},{4,6,7},{5}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}}=>{{1,3},{2},{4,6},{5,7}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>{{1,3},{2},{4,6},{5},{7}}=>{{1,3},{2},{4,6},{5},{7}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>{{1,3,6,7},{2},{4},{5}}=>{{1,3,6,7},{2},{4},{5}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>{{1,3,7},{2},{4},{5,6}}=>{{1,3,6},{2},{4},{5,7}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>{{1,3,7},{2},{4,6},{5}}=>{{1,3,6},{2},{4,7},{5}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>{{1,3,6},{2},{4},{5},{7}}=>{{1,3,6},{2},{4},{5},{7}} [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}}=>{{1,3},{2,6,7},{4},{5}} [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>{{1,7},{2,3},{4},{5,6}}=>{{1,3},{2,6},{4},{5,7}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>{{1,7},{2,3},{4,6},{5}}=>{{1,3},{2,6},{4,7},{5}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>{{1,7},{2,3,6},{4},{5}}=>{{1,3,7},{2,6},{4},{5}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}}=>{{1,3},{2,6},{4},{5},{7}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}}=>{{1,3},{2},{4},{5},{6,7}} [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>{{1,3},{2},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,7},{6}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>{{1,3},{2},{4,7},{5},{6}}=>{{1,3},{2},{4,7},{5},{6}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>{{1,3,7},{2},{4},{5},{6}}=>{{1,3,7},{2},{4},{5},{6}} [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}}=>{{1,3},{2,7},{4},{5},{6}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}=>{{1,3},{2},{4},{5},{6},{7}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>{{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]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>{{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]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>{{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]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}=>{{1},{2},{3,4,5,7},{6}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>{{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]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>{{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]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>{{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]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}=>{{1},{2},{3,4,6,7},{5}} [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>{{1},{2},{3,4,7},{5,6}}=>{{1},{2},{3,4,6},{5,7}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}=>{{1},{2},{3,4,6},{5},{7}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>{{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]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}=>{{1},{2},{3,4},{5,7},{6}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}=>{{1},{2},{3,4,7},{5},{6}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>{{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]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}=>{{1},{2,4,5,6,7},{3}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}=>{{1},{2,4,5,6},{3},{7}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}=>{{1},{2,4,5},{3},{6,7}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}=>{{1},{2,4,5,7},{3},{6}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}=>{{1},{2,4,5},{3},{6},{7}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>{{1},{2,5,6,7},{3,4}}=>{{1},{2,4},{3,5,6,7}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>{{1},{2,5,6},{3,4},{7}}=>{{1},{2,4},{3,5,6},{7}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>{{1},{2,6,7},{3,4,5}}=>{{1},{2,4,6,7},{3,5}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>{{1},{2,7},{3,4,5,6}}=>{{1},{2,4,6},{3,5,7}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>{{1},{2,6},{3,4,5},{7}}=>{{1},{2,4,6},{3,5},{7}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>{{1},{2,5},{3,4},{6,7}}=>{{1},{2,4},{3,5},{6,7}} [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>{{1},{2,5,7},{3,4},{6}}=>{{1},{2,4},{3,5,7},{6}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>{{1},{2,7},{3,4,5},{6}}=>{{1},{2,4,7},{3,5},{6}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>{{1},{2,5},{3,4},{6},{7}}=>{{1},{2,4},{3,5},{6},{7}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}=>{{1},{2,4},{3},{5,6,7}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}=>{{1},{2,4},{3},{5,6},{7}} [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}=>{{1},{2,4,6,7},{3},{5}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>{{1},{2,4,7},{3},{5,6}}=>{{1},{2,4,6},{3},{5,7}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}=>{{1},{2,4,6},{3},{5},{7}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>{{1},{2,6,7},{3,4},{5}}=>{{1},{2,4},{3,6,7},{5}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>{{1},{2,7},{3,4},{5,6}}=>{{1},{2,4},{3,6},{5,7}} [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>{{1},{2,7},{3,4,6},{5}}=>{{1},{2,4,7},{3,6},{5}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>{{1},{2,6},{3,4},{5},{7}}=>{{1},{2,4},{3,6},{5},{7}} [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}=>{{1},{2,4},{3},{5},{6,7}} [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}=>{{1},{2,4},{3},{5,7},{6}} [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}=>{{1},{2,4,7},{3},{5},{6}} [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>{{1},{2,7},{3,4},{5},{6}}=>{{1},{2,4},{3,7},{5},{6}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}=>{{1},{2,4},{3},{5},{6},{7}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}}=>{{1,4,5,6,7},{2},{3}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}}=>{{1,4,5,6},{2},{3},{7}} [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>{{1,4,5},{2},{3},{6,7}}=>{{1,4,5},{2},{3},{6,7}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>{{1,4,5,7},{2},{3},{6}}=>{{1,4,5,7},{2},{3},{6}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}}=>{{1,4,5},{2},{3},{6},{7}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>{{1,5,6,7},{2},{3,4}}=>{{1,4},{2},{3,5,6,7}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>{{1,5,6},{2},{3,4},{7}}=>{{1,4},{2},{3,5,6},{7}} [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>{{1,6,7},{2},{3,4,5}}=>{{1,4,6,7},{2},{3,5}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>{{1,7},{2},{3,4,5,6}}=>{{1,4,6},{2},{3,5,7}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>{{1,6},{2},{3,4,5},{7}}=>{{1,4,6},{2},{3,5},{7}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>{{1,5},{2},{3,4},{6,7}}=>{{1,4},{2},{3,5},{6,7}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>{{1,5,7},{2},{3,4},{6}}=>{{1,4},{2},{3,5,7},{6}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>{{1,7},{2},{3,4,5},{6}}=>{{1,4,7},{2},{3,5},{6}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>{{1,5},{2},{3,4},{6},{7}}=>{{1,4},{2},{3,5},{6},{7}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}}=>{{1,4},{2,5,6,7},{3}} [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}}=>{{1,4},{2,5,6},{3},{7}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}}=>{{1,4,6,7},{2,5},{3}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}}=>{{1,4,6},{2,5,7},{3}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>{{1,6},{2,4,5},{3},{7}}=>{{1,4,6},{2,5},{3},{7}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}}=>{{1,4},{2,5},{3,6,7}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}}=>{{1,4},{2,5,7},{3,6}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}}=>{{1,4,7},{2,5},{3,6}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}}=>{{1,4},{2,5},{3,6},{7}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>{{1,5},{2,4},{3},{6,7}}=>{{1,4},{2,5},{3},{6,7}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>{{1,5,7},{2,4},{3},{6}}=>{{1,4},{2,5,7},{3},{6}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}}=>{{1,4,7},{2,5},{3},{6}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}}=>{{1,4},{2,5},{3,7},{6}} [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}}=>{{1,4},{2,5},{3},{6},{7}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>{{1,4},{2},{3},{5,6,7}}=>{{1,4},{2},{3},{5,6,7}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>{{1,4},{2},{3},{5,6},{7}}=>{{1,4},{2},{3},{5,6},{7}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>{{1,4,6,7},{2},{3},{5}}=>{{1,4,6,7},{2},{3},{5}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>{{1,4,7},{2},{3},{5,6}}=>{{1,4,6},{2},{3},{5,7}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>{{1,4,6},{2},{3},{5},{7}}=>{{1,4,6},{2},{3},{5},{7}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>{{1,6,7},{2},{3,4},{5}}=>{{1,4},{2},{3,6,7},{5}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>{{1,7},{2},{3,4},{5,6}}=>{{1,4},{2},{3,6},{5,7}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>{{1,7},{2},{3,4,6},{5}}=>{{1,4,7},{2},{3,6},{5}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>{{1,6},{2},{3,4},{5},{7}}=>{{1,4},{2},{3,6},{5},{7}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}}=>{{1,4},{2,6,7},{3},{5}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>{{1,7},{2,4},{3},{5,6}}=>{{1,4},{2,6},{3},{5,7}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>{{1,7},{2,4,6},{3},{5}}=>{{1,4,7},{2,6},{3},{5}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}}=>{{1,4},{2,6},{3,7},{5}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>{{1,6},{2,4},{3},{5},{7}}=>{{1,4},{2,6},{3},{5},{7}} [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}=>{{1,4},{2},{3},{5},{6,7}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>{{1,4},{2},{3},{5,7},{6}}=>{{1,4},{2},{3},{5,7},{6}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>{{1,4,7},{2},{3},{5},{6}}=>{{1,4,7},{2},{3},{5},{6}} [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>{{1,7},{2},{3,4},{5},{6}}=>{{1,4},{2},{3,7},{5},{6}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}}=>{{1,4},{2,7},{3},{5},{6}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}=>{{1,4},{2},{3},{5},{6},{7}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>{{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]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>{{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]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>{{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]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}=>{{1},{2},{3},{4,5,7},{6}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>{{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]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}=>{{1},{2},{3,5,6,7},{4}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}=>{{1},{2},{3,5,6},{4},{7}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>{{1},{2},{3,6,7},{4,5}}=>{{1},{2},{3,5},{4,6,7}} [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>{{1},{2},{3,7},{4,5,6}}=>{{1},{2},{3,5,7},{4,6}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>{{1},{2},{3,6},{4,5},{7}}=>{{1},{2},{3,5},{4,6},{7}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}=>{{1},{2},{3,5},{4},{6,7}} [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}=>{{1},{2},{3,5,7},{4},{6}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>{{1},{2},{3,7},{4,5},{6}}=>{{1},{2},{3,5},{4,7},{6}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4},{6},{7}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}=>{{1},{2,5,6,7},{3},{4}} [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}=>{{1},{2,5,6},{3},{4},{7}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>{{1},{2,6,7},{3},{4,5}}=>{{1},{2,5},{3},{4,6,7}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>{{1},{2,7},{3},{4,5,6}}=>{{1},{2,5,7},{3},{4,6}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>{{1},{2,6},{3},{4,5},{7}}=>{{1},{2,5},{3},{4,6},{7}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>{{1},{2,6,7},{3,5},{4}}=>{{1},{2,5},{3,6,7},{4}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>{{1},{2,7},{3,5,6},{4}}=>{{1},{2,5,7},{3,6},{4}} [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>{{1},{2,7},{3,6},{4,5}}=>{{1},{2,5},{3,6},{4,7}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>{{1},{2,6},{3,5},{4},{7}}=>{{1},{2,5},{3,6},{4},{7}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}}=>{{1},{2,5},{3},{4},{6,7}} [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}=>{{1},{2,5,7},{3},{4},{6}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>{{1},{2,7},{3},{4,5},{6}}=>{{1},{2,5},{3},{4,7},{6}} [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>{{1},{2,7},{3,5},{4},{6}}=>{{1},{2,5},{3,7},{4},{6}} [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}=>{{1},{2,5},{3},{4},{6},{7}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}}=>{{1,5,6,7},{2},{3},{4}} [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{7}}=>{{1,5,6},{2},{3},{4},{7}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>{{1,6,7},{2},{3},{4,5}}=>{{1,5},{2},{3},{4,6,7}} [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>{{1,7},{2},{3},{4,5,6}}=>{{1,5,7},{2},{3},{4,6}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>{{1,6},{2},{3},{4,5},{7}}=>{{1,5},{2},{3},{4,6},{7}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>{{1,6,7},{2},{3,5},{4}}=>{{1,5},{2},{3,6,7},{4}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>{{1,7},{2},{3,5,6},{4}}=>{{1,5,7},{2},{3,6},{4}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>{{1,7},{2},{3,6},{4,5}}=>{{1,5},{2},{3,6},{4,7}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>{{1,6},{2},{3,5},{4},{7}}=>{{1,5},{2},{3,6},{4},{7}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}}=>{{1,5},{2,6,7},{3},{4}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}}=>{{1,5,7},{2,6},{3},{4}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>{{1,7},{2,6},{3},{4,5}}=>{{1,5},{2,6},{3},{4,7}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}}=>{{1,5},{2,6},{3,7},{4}} [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>{{1,6},{2,5},{3},{4},{7}}=>{{1,5},{2,6},{3},{4},{7}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>{{1,5},{2},{3},{4},{6,7}}=>{{1,5},{2},{3},{4},{6,7}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>{{1,5,7},{2},{3},{4},{6}}=>{{1,5,7},{2},{3},{4},{6}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>{{1,7},{2},{3},{4,5},{6}}=>{{1,5},{2},{3},{4,7},{6}} [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>{{1,7},{2},{3,5},{4},{6}}=>{{1,5},{2},{3,7},{4},{6}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}}=>{{1,5},{2,7},{3},{4},{6}} [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}}=>{{1,5},{2},{3},{4},{6},{7}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>{{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]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>{{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]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}=>{{1},{2},{3},{4,6,7},{5}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}}=>{{1},{2},{3},{4,6},{5,7}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}=>{{1},{2},{3},{4,6},{5},{7}} [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}=>{{1},{2},{3,6,7},{4},{5}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>{{1},{2},{3,7},{4},{5,6}}=>{{1},{2},{3,6},{4},{5,7}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>{{1},{2},{3,7},{4,6},{5}}=>{{1},{2},{3,6},{4,7},{5}} [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}=>{{1},{2},{3,6},{4},{5},{7}} [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}=>{{1},{2,6,7},{3},{4},{5}} [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>{{1},{2,7},{3},{4},{5,6}}=>{{1},{2,6},{3},{4},{5,7}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>{{1},{2,7},{3},{4,6},{5}}=>{{1},{2,6},{3},{4,7},{5}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>{{1},{2,7},{3,6},{4},{5}}=>{{1},{2,6},{3,7},{4},{5}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}}=>{{1},{2,6},{3},{4},{5},{7}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}}=>{{1,6,7},{2},{3},{4},{5}} [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>{{1,7},{2},{3},{4},{5,6}}=>{{1,6},{2},{3},{4},{5,7}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>{{1,7},{2},{3},{4,6},{5}}=>{{1,6},{2},{3},{4,7},{5}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>{{1,7},{2},{3,6},{4},{5}}=>{{1,6},{2},{3,7},{4},{5}} [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}}=>{{1,6},{2,7},{3},{4},{5}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}}=>{{1,6},{2},{3},{4},{5},{7}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>{{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]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}=>{{1},{2},{3},{4},{5,7},{6}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}=>{{1},{2},{3},{4,7},{5},{6}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}}=>{{1},{2},{3,7},{4},{5},{6}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}}=>{{1},{2,7},{3},{4},{5},{6}} [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}}=>{{1,7},{2},{3},{4},{5},{6}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7,8}} [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>{{1,2},{3,4},{5,8},{6,7}}=>{{1,2},{3,4},{5,7},{6,8}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>{{1,2},{3,6},{4,5},{7,8}}=>{{1,2},{3,5},{4,6},{7,8}} [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,8,5,4,7,6,3]=>{{1,2},{3,8},{4,5},{6,7}}=>{{1,2},{3,5},{4,7},{6,8}} [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>{{1,2},{3,8},{4,7},{5,6}}=>{{1,2},{3,6},{4,7},{5,8}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>{{1,4},{2,3},{5,6},{7,8}}=>{{1,3},{2,4},{5,6},{7,8}} [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>{{1,4},{2,3},{5,8},{6,7}}=>{{1,3},{2,4},{5,7},{6,8}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,3,2,5,4,1,8,7]=>{{1,6},{2,3},{4,5},{7,8}}=>{{1,3},{2,5},{4,6},{7,8}} [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8,3,2,5,4,7,6,1]=>{{1,8},{2,3},{4,5},{6,7}}=>{{1,3},{2,5},{4,7},{6,8}} [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>{{1,8},{2,3},{4,7},{5,6}}=>{{1,3},{2,6},{4,7},{5,8}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>{{1,6},{2,5},{3,4},{7,8}}=>{{1,4},{2,5},{3,6},{7,8}} [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>{{1,8},{2,5},{3,4},{6,7}}=>{{1,4},{2,5},{3,7},{6,8}} [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8,7,4,3,6,5,2,1]=>{{1,8},{2,7},{3,4},{5,6}}=>{{1,4},{2,6},{3,7},{5,8}} [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}=>{{1,5},{2,6},{3,7},{4,8}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6},{7},{8}}
Map
Delest-Viennot
Description
Return the Dyck path corresponding to the parallelogram polyomino obtained by applying Delest-Viennot's bijection.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
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.