Identifier
Mp00024: Dyck paths to 321-avoiding permutationPermutations
Mp00151: Permutations to cycle typeSet partitions
Mp00115: Set partitions Kasraoui-Zeng Set partitions
Images
=>
Cc0005;cc-rep-0Cc0009;cc-rep-2Cc0009;cc-rep-3
[1,0]=>[1]=>{{1}}=>{{1}} [1,0,1,0]=>[2,1]=>{{1,2}}=>{{1,2}} [1,1,0,0]=>[1,2]=>{{1},{2}}=>{{1},{2}} [1,0,1,0,1,0]=>[2,1,3]=>{{1,2},{3}}=>{{1,2},{3}} [1,0,1,1,0,0]=>[2,3,1]=>{{1,2,3}}=>{{1,2,3}} [1,1,0,0,1,0]=>[3,1,2]=>{{1,2,3}}=>{{1,2,3}} [1,1,0,1,0,0]=>[1,3,2]=>{{1},{2,3}}=>{{1},{2,3}} [1,1,1,0,0,0]=>[1,2,3]=>{{1},{2},{3}}=>{{1},{2},{3}} [1,0,1,0,1,0,1,0]=>[2,1,4,3]=>{{1,2},{3,4}}=>{{1,2},{3,4}} [1,0,1,0,1,1,0,0]=>[2,4,1,3]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,0,1,1,0,0,1,0]=>[2,1,3,4]=>{{1,2},{3},{4}}=>{{1,2},{3},{4}} [1,0,1,1,0,1,0,0]=>[2,3,1,4]=>{{1,2,3},{4}}=>{{1,2,3},{4}} [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,1,0,0,1,0,1,0]=>[3,1,4,2]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>{{1,3},{2,4}}=>{{1,4},{2,3}} [1,1,0,1,0,0,1,0]=>[3,1,2,4]=>{{1,2,3},{4}}=>{{1,2,3},{4}} [1,1,0,1,0,1,0,0]=>[1,3,2,4]=>{{1},{2,3},{4}}=>{{1},{2,3},{4}} [1,1,0,1,1,0,0,0]=>[1,3,4,2]=>{{1},{2,3,4}}=>{{1},{2,3,4}} [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,1,1,0,0,1,0,0]=>[1,4,2,3]=>{{1},{2,3,4}}=>{{1},{2,3,4}} [1,1,1,0,1,0,0,0]=>[1,2,4,3]=>{{1},{2},{3,4}}=>{{1},{2},{3,4}} [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]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}}=>{{1,2},{3,4},{5}} [1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>{{1,2,3,4},{5}}=>{{1,2,3,4},{5}} [1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>{{1,2},{3,4,5}}=>{{1,2},{3,4,5}} [1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>{{1,2,4},{3,5}}=>{{1,2,5},{3,4}} [1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>{{1,2},{3,4,5}}=>{{1,2},{3,4,5}} [1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}}=>{{1,2},{3},{4,5}} [1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>{{1,2,3},{4,5}}=>{{1,2,3},{4,5}} [1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}}=>{{1,2},{3},{4},{5}} [1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}=>{{1,2,3},{4},{5}} [1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}=>{{1,2,3,4},{5}} [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>{{1,2,3,4},{5}}=>{{1,2,3,4},{5}} [1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>{{1,3},{2,4},{5}}=>{{1,4},{2,3},{5}} [1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>{{1,3},{2,4,5}}=>{{1,4,5},{2,3}} [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>{{1,3},{2,4,5}}=>{{1,4,5},{2,3}} [1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>{{1,2,3},{4,5}}=>{{1,2,3},{4,5}} [1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}=>{{1},{2,3},{4,5}} [1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>{{1},{2,3,4,5}}=>{{1},{2,3,4,5}} [1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>{{1,2,3},{4},{5}}=>{{1,2,3},{4},{5}} [1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}=>{{1},{2,3},{4},{5}} [1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}=>{{1},{2,3,4},{5}} [1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}=>{{1},{2,3,4,5}} [1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>{{1,2,4},{3,5}}=>{{1,2,5},{3,4}} [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>{{1},{2,3,4,5}}=>{{1},{2,3,4,5}} [1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}=>{{1},{2,5},{3,4}} [1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>{{1,2,3,4},{5}}=>{{1,2,3,4},{5}} [1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>{{1},{2,3,4},{5}}=>{{1},{2,3,4},{5}} [1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}=>{{1},{2},{3,4},{5}} [1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}=>{{1},{2},{3,4,5}} [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>{{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},{2,3,4,5}}=>{{1},{2,3,4,5}} [1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>{{1},{2},{3,4,5}}=>{{1},{2},{3,4,5}} [1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}=>{{1},{2},{3},{4,5}} [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]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4},{5,6}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>{{1,2},{3,4,5,6}}=>{{1,2},{3,4,5,6}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>{{1,2,4},{3,5,6}}=>{{1,2,5,6},{3,4}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}=>{{1,2},{3,4},{5},{6}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}=>{{1,2},{3,4,5},{6}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>{{1,2,4},{3,5},{6}}=>{{1,2,5},{3,4},{6}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}=>{{1,2},{3,4,5,6}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>{{1,2,4},{3,5,6}}=>{{1,2,5,6},{3,4}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>{{1,2},{3,4,5,6}}=>{{1,2},{3,4,5,6}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}=>{{1,2},{3,6},{4,5}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>{{1,2,3,5},{4,6}}=>{{1,2,3,6},{4,5}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>{{1,2},{3,4,5},{6}}=>{{1,2},{3,4,5},{6}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}=>{{1,2},{3},{4,5},{6}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}=>{{1,2,3},{4,5},{6}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}=>{{1,2},{3},{4,5,6}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>{{1,2,3,5},{4,6}}=>{{1,2,3,6},{4,5}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>{{1,2},{3,4,5,6}}=>{{1,2},{3,4,5,6}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>{{1,2},{3},{4,5,6}}=>{{1,2},{3},{4,5,6}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5,6}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}=>{{1,2,3},{4},{5,6}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4},{5,6}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4},{5,6}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}=>{{1,4},{2,3},{5,6}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>{{1,3},{2,4,5,6}}=>{{1,4,5,6},{2,3}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}} [1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>{{1,3},{2,4},{5},{6}}=>{{1,4},{2,3},{5},{6}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>{{1,3},{2,4,5},{6}}=>{{1,4,5},{2,3},{6}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>{{1,3},{2,4,5,6}}=>{{1,4,5,6},{2,3}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}}=>{{1,6},{2,3,4,5}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>{{1,3},{2,4,5,6}}=>{{1,4,5,6},{2,3}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>{{1,2,3,5},{4,6}}=>{{1,2,3,6},{4,5}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3},{4,5}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>{{1,3,4,6},{2,5}}=>{{1,4,5},{2,3,6}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>{{1,3},{2,4,5},{6}}=>{{1,4,5},{2,3},{6}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>{{1,2,3},{4,5},{6}}=>{{1,2,3},{4,5},{6}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}=>{{1},{2,3},{4,5},{6}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}=>{{1},{2,3},{4,5,6}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}=>{{1},{2,3,6},{4,5}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>{{1,3},{2,4,5,6}}=>{{1,4,5,6},{2,3}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>{{1},{2,3},{4,5,6}}=>{{1},{2,3},{4,5,6}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>{{1,2,3},{4},{5,6}}=>{{1,2,3},{4},{5,6}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}=>{{1},{2,3},{4},{5,6}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}=>{{1},{2,3,4},{5,6}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}=>{{1},{2,3,4},{5},{6}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>{{1,2,4},{3,5,6}}=>{{1,2,5,6},{3,4}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>{{1,3,4,6},{2,5}}=>{{1,4,5},{2,3,6}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>{{1,2,4},{3,5},{6}}=>{{1,2,5},{3,4},{6}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}=>{{1},{2,5},{3,4},{6}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}=>{{1},{2,5,6},{3,4}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>{{1,2,4},{3,5,6}}=>{{1,2,5,6},{3,4}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>{{1},{2,4},{3,5,6}}=>{{1},{2,5,6},{3,4}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4},{5,6}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>{{1},{2,3,4},{5,6}}=>{{1},{2,3,4},{5,6}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}=>{{1},{2},{3,4},{5,6}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>{{1},{2},{3,4,5,6}}=>{{1},{2},{3,4,5,6}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>{{1},{2,3,4},{5},{6}}=>{{1},{2,3,4},{5},{6}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5},{6}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}=>{{1},{2},{3,4,5},{6}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}=>{{1},{2},{3,4,5,6}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>{{1,3,5},{2,4,6}}=>{{1,6},{2,3,4,5}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>{{1,2,3,5},{4,6}}=>{{1,2,3,6},{4,5}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>{{1},{2,3,5},{4,6}}=>{{1},{2,3,6},{4,5}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>{{1},{2},{3,4,5,6}}=>{{1},{2},{3,4,5,6}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}=>{{1},{2},{3,6},{4,5}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>{{1},{2},{3,4,5},{6}}=>{{1},{2},{3,4,5},{6}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}=>{{1},{2},{3},{4,5},{6}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}=>{{1},{2},{3},{4,5,6}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>{{1},{2},{3,4,5,6}}=>{{1},{2},{3,4,5,6}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>{{1},{2},{3},{4,5,6}}=>{{1},{2},{3},{4,5,6}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}=>{{1},{2},{3},{4},{5,6}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,6,5,7]=>{{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]=>[2,4,1,3,6,5,7]=>{{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]=>[2,1,4,6,3,5,7]=>{{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]=>[2,4,1,6,3,5,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>{{1,2,4},{3,5,6},{7}}=>{{1,2,5,6},{3,4},{7}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}}=>{{1,2},{3,4},{5,6,7}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4},{5,6,7}} [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>{{1,2},{3,4,5,6,7}}=>{{1,2},{3,4,5,6,7}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>{{1,2},{3,4,6},{5,7}}=>{{1,2},{3,4,7},{5,6}} [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}} [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>{{1,2,4},{3,6},{5,7}}=>{{1,2,7},{3,4},{5,6}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>{{1,2,4,5,7},{3,6}}=>{{1,2,5,6},{3,4,7}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>{{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]=>[2,4,1,3,7,5,6]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4},{5,6,7}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>{{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]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2},{3,4},{5},{6,7}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4},{5},{6,7}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6,7}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>{{1,2,4},{3,5},{6,7}}=>{{1,2,5},{3,4},{6,7}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>{{1,2},{3,4,5,6,7}}=>{{1,2},{3,4,5,6,7}} [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}}=>{{1,2},{3,4},{5},{6},{7}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>{{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]=>[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2},{3,4,5},{6},{7}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>{{1,2,4},{3,5},{6},{7}}=>{{1,2,5},{3,4},{6},{7}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}}=>{{1,2},{3,4,5,6},{7}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>{{1,2,4},{3,5,6},{7}}=>{{1,2,5,6},{3,4},{7}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}}=>{{1,2},{3,4,5,6,7}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>{{1,2,4,6},{3,5,7}}=>{{1,2,7},{3,4,5,6}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>{{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]=>[2,5,1,3,6,4,7]=>{{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]=>[2,1,5,6,3,4,7]=>{{1,2},{3,5},{4,6},{7}}=>{{1,2},{3,6},{4,5},{7}} [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>{{1,2,3,5},{4,6},{7}}=>{{1,2,3,6},{4,5},{7}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>{{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]=>[2,1,5,3,6,7,4]=>{{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]=>[2,5,1,3,6,7,4]=>{{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]=>[2,1,5,6,3,7,4]=>{{1,2},{3,5},{4,6,7}}=>{{1,2},{3,6,7},{4,5}} [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>{{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]=>[2,5,1,6,7,3,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>{{1,2,4,5,7},{3,6}}=>{{1,2,5,6},{3,4,7}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>{{1,2,5},{3,6},{4,7}}=>{{1,2,7},{3,6},{4,5}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>{{1,2},{3,4,5,6,7}}=>{{1,2},{3,4,5,6,7}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>{{1,2},{3,5},{4,6,7}}=>{{1,2},{3,6,7},{4,5}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}} [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>{{1,2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6,7}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2},{3},{4,5},{6,7}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3},{4,5},{6,7}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>{{1,2},{3},{4,5,6,7}}=>{{1,2},{3},{4,5,6,7}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2},{3,4,5},{6},{7}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}}=>{{1,2},{3},{4,5},{6},{7}} [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3},{4,5},{6},{7}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}}=>{{1,2},{3},{4,5,6},{7}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3},{4,5,6},{7}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}=>{{1,2,3,6},{4,5},{7}} [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}}=>{{1,2},{3},{4,5,6,7}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>{{1,2},{3,4,6},{5,7}}=>{{1,2},{3,4,7},{5,6}} [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>{{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]=>[2,6,1,7,3,4,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>{{1,2,4,6},{3,5,7}}=>{{1,2,7},{3,4,5,6}} [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>{{1,2},{3,4,5,6,7}}=>{{1,2},{3,4,5,6,7}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>{{1,2},{3},{4,5,6,7}}=>{{1,2},{3},{4,5,6,7}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>{{1,2},{3},{4,6},{5,7}}=>{{1,2},{3},{4,7},{5,6}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>{{1,2,3},{4,6},{5,7}}=>{{1,2,3},{4,7},{5,6}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}} [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>{{1,2},{3,4,5,6},{7}}=>{{1,2},{3,4,5,6},{7}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>{{1,2},{3},{4,5,6},{7}}=>{{1,2},{3},{4,5,6},{7}} [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3},{4,5,6},{7}} [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}}=>{{1,2},{3},{4},{5,6},{7}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}=>{{1,2,3},{4},{5,6},{7}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4},{5,6},{7}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}}=>{{1,2},{3},{4},{5,6,7}} [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}} [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4},{5,6,7}} [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>{{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]=>[2,7,1,3,4,5,6]=>{{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]=>[2,1,3,7,4,5,6]=>{{1,2},{3},{4,5,6,7}}=>{{1,2},{3},{4,5,6,7}} [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>{{1,2},{3},{4},{5,6,7}}=>{{1,2},{3},{4},{5,6,7}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4},{5,6,7}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5},{6,7}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}=>{{1,2,3},{4},{5},{6,7}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4},{5},{6,7}} [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7}} [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}} [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>{{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]=>[3,1,4,2,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4},{5,6},{7}} [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>{{1,3},{2,4},{5,6},{7}}=>{{1,4},{2,3},{5,6},{7}} [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>{{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]=>[3,4,1,6,2,5,7]=>{{1,3},{2,4,5,6},{7}}=>{{1,4,5,6},{2,3},{7}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>{{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]=>[3,4,1,2,6,7,5]=>{{1,3},{2,4},{5,6,7}}=>{{1,4},{2,3},{5,6,7}} [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}} [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>{{1,3},{2,4,6},{5,7}}=>{{1,4,7},{2,3},{5,6}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>{{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]=>[3,1,4,2,7,5,6]=>{{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]=>[3,4,1,2,7,5,6]=>{{1,3},{2,4},{5,6,7}}=>{{1,4},{2,3},{5,6,7}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>{{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]=>[3,4,1,7,2,5,6]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>{{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]=>[3,1,4,2,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4},{5},{6,7}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>{{1,3},{2,4},{5},{6,7}}=>{{1,4},{2,3},{5},{6,7}} [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>{{1,3},{2,4,5},{6,7}}=>{{1,4,5},{2,3},{6,7}} [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>{{1,3,5},{2,4,6,7}}=>{{1,6,7},{2,3,4,5}} [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>{{1,3},{2,4},{5},{6},{7}}=>{{1,4},{2,3},{5},{6},{7}} [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>{{1,3},{2,4,5},{6},{7}}=>{{1,4,5},{2,3},{6},{7}} [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>{{1,3},{2,4,5,6},{7}}=>{{1,4,5,6},{2,3},{7}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>{{1,3,5},{2,4,6},{7}}=>{{1,6},{2,3,4,5},{7}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>{{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]=>[3,4,1,5,6,7,2]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>{{1,3,5},{2,4,6,7}}=>{{1,6,7},{2,3,4,5}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>{{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]=>[3,1,5,2,6,4,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>{{1,3},{2,4,5,6},{7}}=>{{1,4,5,6},{2,3},{7}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>{{1,2,3,5},{4,6},{7}}=>{{1,2,3,6},{4,5},{7}} [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>{{1,3},{2,5},{4,6},{7}}=>{{1,6},{2,3},{4,5},{7}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>{{1,3,4,6},{2,5},{7}}=>{{1,4,5},{2,3,6},{7}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>{{1,3},{2,5},{4,6,7}}=>{{1,6,7},{2,3},{4,5}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>{{1,3,4,6,7},{2,5}}=>{{1,4,5},{2,3,6,7}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>{{1,2,3,5,6},{4,7}}=>{{1,2,3,6},{4,5,7}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>{{1,3},{2,5},{4,6,7}}=>{{1,6,7},{2,3},{4,5}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>{{1,3,4,6,7},{2,5}}=>{{1,4,5},{2,3,6,7}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>{{1,3},{2,4,5},{6,7}}=>{{1,4,5},{2,3},{6,7}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3},{4,5},{6,7}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}=>{{1},{2,3},{4,5},{6,7}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>{{1},{2,3,4,5},{6,7}}=>{{1},{2,3,4,5},{6,7}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>{{1},{2,3},{4,5,6,7}}=>{{1},{2,3},{4,5,6,7}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>{{1},{2,3,5},{4,6,7}}=>{{1},{2,3,6,7},{4,5}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>{{1,3},{2,4,5},{6},{7}}=>{{1,4,5},{2,3},{6},{7}} [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3},{4,5},{6},{7}} [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>{{1},{2,3,4,5},{6},{7}}=>{{1},{2,3,4,5},{6},{7}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3},{4,5,6},{7}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}=>{{1},{2,3},{4,5,6},{7}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}=>{{1},{2,3,6},{4,5},{7}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}} [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}=>{{1},{2,3},{4,5,6,7}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}=>{{1},{2,3,6,7},{4,5}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>{{1,3},{2,4,6},{5,7}}=>{{1,4,7},{2,3},{5,6}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}} [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>{{1},{2,3},{4,5,6,7}}=>{{1},{2,3},{4,5,6,7}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>{{1,2,3},{4,6},{5,7}}=>{{1,2,3},{4,7},{5,6}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}=>{{1},{2,3},{4,7},{5,6}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>{{1},{2,3,4,6},{5,7}}=>{{1},{2,3,4,7},{5,6}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>{{1,3},{2,4,5,6},{7}}=>{{1,4,5,6},{2,3},{7}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3},{4,5,6},{7}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>{{1},{2,3},{4,5,6},{7}}=>{{1},{2,3},{4,5,6},{7}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}=>{{1,2,3},{4},{5,6},{7}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,6},{7}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}=>{{1},{2,3,4},{5,6},{7}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}=>{{1},{2,3},{4},{5,6,7}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}=>{{1},{2,3,4},{5,6,7}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}=>{{1},{2,3,4,7},{5,6}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>{{1,3},{2,4,5,6,7}}=>{{1,4,5,6,7},{2,3}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>{{1},{2,3},{4,5,6,7}}=>{{1},{2,3},{4,5,6,7}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>{{1},{2,3},{4},{5,6,7}}=>{{1},{2,3},{4},{5,6,7}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>{{1},{2,3,4},{5,6,7}}=>{{1},{2,3,4},{5,6,7}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}=>{{1,2,3},{4},{5},{6,7}} [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}=>{{1},{2,3},{4},{5},{6,7}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}=>{{1},{2,3,4},{5},{6,7}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}=>{{1},{2,3,4,5},{6,7}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}} [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}=>{{1},{2,3,4},{5},{6},{7}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}=>{{1},{2,3,4,5},{6},{7}} [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>{{1,2,4},{3,5,6},{7}}=>{{1,2,5,6},{3,4},{7}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>{{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]=>[4,1,5,6,2,3,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>{{1,3,4,6},{2,5},{7}}=>{{1,4,5},{2,3,6},{7}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>{{1,4},{2,5},{3,6},{7}}=>{{1,6},{2,5},{3,4},{7}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>{{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]=>[4,1,5,6,2,7,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>{{1,3,4,6,7},{2,5}}=>{{1,4,5},{2,3,6,7}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>{{1,4},{2,5},{3,6,7}}=>{{1,6,7},{2,5},{3,4}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>{{1,2,4,6},{3,5,7}}=>{{1,2,7},{3,4,5,6}} [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>{{1,4},{2,3,5,6,7}}=>{{1,3,4},{2,5,6,7}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>{{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]=>[4,1,5,2,7,3,6]=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>{{1,3,4,6,7},{2,5}}=>{{1,4,5},{2,3,6,7}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>{{1,4},{2,5},{3,6,7}}=>{{1,6,7},{2,5},{3,4}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>{{1,2,4},{3,5},{6,7}}=>{{1,2,5},{3,4},{6,7}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>{{1},{2,3,4,5},{6,7}}=>{{1},{2,3,4,5},{6,7}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}=>{{1},{2,5},{3,4},{6,7}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>{{1},{2,4},{3,5,6,7}}=>{{1},{2,5,6,7},{3,4}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>{{1,2,4},{3,5},{6},{7}}=>{{1,2,5},{3,4},{6},{7}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>{{1},{2,3,4,5},{6},{7}}=>{{1},{2,3,4,5},{6},{7}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}=>{{1},{2,5},{3,4},{6},{7}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}=>{{1},{2,5,6},{3,4},{7}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}=>{{1},{2,5,6,7},{3,4}} [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}=>{{1},{2,7},{3,4,5,6}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>{{1,2,4},{3,6},{5,7}}=>{{1,2,7},{3,4},{5,6}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>{{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]=>[4,1,6,7,2,3,5]=>{{1,2,4,5,7},{3,6}}=>{{1,2,5,6},{3,4,7}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>{{1,4},{2,3,5,6,7}}=>{{1,3,4},{2,5,6,7}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>{{1},{2,4},{3,5,6,7}}=>{{1},{2,5,6,7},{3,4}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>{{1},{2,3,4,6},{5,7}}=>{{1},{2,3,4,7},{5,6}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}=>{{1},{2,7},{3,4},{5,6}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>{{1},{2,4,5,7},{3,6}}=>{{1},{2,5,6},{3,4,7}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>{{1,2,4},{3,5,6},{7}}=>{{1,2,5,6},{3,4},{7}} [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>{{1},{2,4},{3,5,6},{7}}=>{{1},{2,5,6},{3,4},{7}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4},{5,6},{7}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>{{1},{2,3,4},{5,6},{7}}=>{{1},{2,3,4},{5,6},{7}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}=>{{1},{2},{3,4},{5,6},{7}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>{{1},{2},{3,4,5,6},{7}}=>{{1},{2},{3,4,5,6},{7}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4},{5,6,7}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>{{1},{2,3,4},{5,6,7}}=>{{1},{2,3,4},{5,6,7}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}=>{{1},{2},{3,4},{5,6,7}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}=>{{1},{2},{3,4,7},{5,6}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>{{1,2,4},{3,5,6,7}}=>{{1,2,5,6,7},{3,4}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>{{1},{2,4},{3,5,6,7}}=>{{1},{2,5,6,7},{3,4}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4},{5,6,7}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>{{1},{2,3,4},{5,6,7}}=>{{1},{2,3,4},{5,6,7}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>{{1},{2},{3,4},{5,6,7}}=>{{1},{2},{3,4},{5,6,7}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4},{5},{6,7}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>{{1},{2,3,4},{5},{6,7}}=>{{1},{2,3,4},{5},{6,7}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}=>{{1},{2},{3,4},{5},{6,7}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}=>{{1},{2},{3,4,5},{6,7}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}=>{{1},{2,3,4},{5},{6},{7}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}=>{{1},{2},{3,4},{5},{6},{7}} [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}=>{{1},{2},{3,4,5,6},{7}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>{{1,2,4,5,7},{3,6}}=>{{1,2,5,6},{3,4,7}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>{{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]=>[5,1,6,7,2,3,4]=>{{1,2,5},{3,6},{4,7}}=>{{1,2,7},{3,6},{4,5}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>{{1,2,3,5,6},{4,7}}=>{{1,2,3,6},{4,5,7}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>{{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]=>[5,1,6,2,3,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>{{1,3,5},{2,4,6,7}}=>{{1,6,7},{2,3,4,5}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}} [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>{{1},{2,3,5},{4,6,7}}=>{{1},{2,3,6,7},{4,5}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>{{1},{2,4,5,7},{3,6}}=>{{1},{2,5,6},{3,4,7}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}=>{{1},{2,7},{3,6},{4,5}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>{{1,3,5},{2,4,6},{7}}=>{{1,6},{2,3,4,5},{7}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>{{1,2,3,5},{4,6},{7}}=>{{1,2,3,6},{4,5},{7}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>{{1},{2,3,5},{4,6},{7}}=>{{1},{2,3,6},{4,5},{7}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>{{1},{2},{3,4,5,6},{7}}=>{{1},{2},{3,4,5,6},{7}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}=>{{1},{2},{3,6},{4,5},{7}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}=>{{1},{2},{3,6,7},{4,5}} [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>{{1,3,5},{2,4,6,7}}=>{{1,6,7},{2,3,4,5}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>{{1,2,3,5},{4,6,7}}=>{{1,2,3,6,7},{4,5}} [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>{{1},{2,3,5},{4,6,7}}=>{{1},{2,3,6,7},{4,5}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>{{1},{2},{3,5},{4,6,7}}=>{{1},{2},{3,6,7},{4,5}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5},{6,7}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>{{1},{2,3,4,5},{6,7}}=>{{1},{2,3,4,5},{6,7}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>{{1},{2},{3,4,5},{6,7}}=>{{1},{2},{3,4,5},{6,7}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}=>{{1},{2},{3},{4,5},{6,7}} [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>{{1},{2},{3},{4,5,6,7}}=>{{1},{2},{3},{4,5,6,7}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>{{1},{2,3,4,5},{6},{7}}=>{{1},{2,3,4,5},{6},{7}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>{{1},{2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}} [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}=>{{1},{2},{3},{4,5,6},{7}} [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}=>{{1},{2},{3},{4,5,6,7}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>{{1,2,4,6},{3,5,7}}=>{{1,2,7},{3,4,5,6}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>{{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]=>[6,1,2,7,3,4,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>{{1},{2,4,6},{3,5,7}}=>{{1},{2,7},{3,4,5,6}} [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>{{1,2,3,4,6},{5,7}}=>{{1,2,3,4,7},{5,6}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>{{1},{2,3,4,6},{5,7}}=>{{1},{2,3,4,7},{5,6}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>{{1},{2},{3,4,6},{5,7}}=>{{1},{2},{3,4,7},{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},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>{{1},{2},{3},{4,5,6,7}}=>{{1},{2},{3},{4,5,6,7}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}=>{{1},{2},{3},{4,7},{5,6}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>{{1},{2},{3,4,5,6},{7}}=>{{1},{2},{3,4,5,6},{7}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>{{1},{2},{3},{4,5,6},{7}}=>{{1},{2},{3},{4,5,6},{7}} [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}=>{{1},{2},{3},{4},{5,6},{7}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}=>{{1},{2},{3},{4},{5,6,7}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>{{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]=>[1,7,2,3,4,5,6]=>{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>{{1},{2},{3},{4,5,6,7}}=>{{1},{2},{3},{4,5,6,7}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>{{1},{2},{3},{4},{5,6,7}}=>{{1},{2},{3},{4},{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},{2},{3},{4},{5},{6,7}}=>{{1},{2},{3},{4},{5},{6,7}} [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]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7,8}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,7,8,5,6]=>{{1,2},{3,4},{5,7},{6,8}}=>{{1,2},{3,4},{5,8},{6,7}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>{{1,2},{3,5},{4,6},{7,8}}=>{{1,2},{3,6},{4,5},{7,8}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,7,3,8,4,6]=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2},{3,8},{4,5},{6,7}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,6,7,8,3,4,5]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2},{3,8},{4,7},{5,6}} [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}=>{{1,4},{2,3},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4},{2,3},{5,8},{6,7}} [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3},{4,5},{7,8}} [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}} [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,6,1,7,8,2,4,5]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4},{7,8}} [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [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}}
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
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.