Identifier
Mp00227: Dyck paths Delest-Viennot-inverseDyck paths
Mp00129: Dyck paths to 321-avoiding permutation (Billey-Jockusch-Stanley)Permutations
Mp00240: Permutations weak exceedance partition Set partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0009;cc-rep-3
[1,0]=>[1,0]=>[1]=>{{1}} [1,0,1,0]=>[1,1,0,0]=>[1,2]=>{{1},{2}} [1,1,0,0]=>[1,0,1,0]=>[2,1]=>{{1,2}} [1,0,1,0,1,0]=>[1,1,1,0,0,0]=>[1,2,3]=>{{1},{2},{3}} [1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[1,3,2]=>{{1},{2,3}} [1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[2,1,3]=>{{1,2},{3}} [1,1,0,1,0,0]=>[1,0,1,0,1,0]=>[2,3,1]=>{{1,2,3}} [1,1,1,0,0,0]=>[1,1,0,1,0,0]=>[3,1,2]=>{{1,3},{2}} [1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>{{1},{2},{3},{4}} [1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>{{1},{2},{3,4}} [1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>{{1},{2,3},{4}} [1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>{{1},{2,3,4}} [1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>{{1},{2,4},{3}} [1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>{{1,2},{3},{4}} [1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>{{1,2},{3,4}} [1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>{{1,2,3},{4}} [1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>{{1,2,3,4}} [1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>{{1,2,4},{3}} [1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>{{1,3},{2},{4}} [1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>{{1,3,4},{2}} [1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>{{1,4},{2},{3}} [1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>{{1,3},{2,4}} [1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}} [1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}} [1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}} [1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}} [1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>{{1},{2},{3,5},{4}} [1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>{{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]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}} [1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}} [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>{{1},{2,3,4,5}} [1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>{{1},{2,3,5},{4}} [1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>{{1},{2,4},{3},{5}} [1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>{{1},{2,4,5},{3}} [1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>{{1},{2,5},{3},{4}} [1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}} [1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}} [1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>{{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]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}} [1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>{{1,2},{3,4,5}} [1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>{{1,2},{3,5},{4}} [1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}} [1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>{{1,2,3},{4,5}} [1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>{{1,2,3,4},{5}} [1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>{{1,2,3,5},{4}} [1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>{{1,2,4},{3},{5}} [1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>{{1,2,4,5},{3}} [1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>{{1,2,5},{3},{4}} [1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>{{1,2,4},{3,5}} [1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>{{1,3},{2},{4},{5}} [1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>{{1,3},{2},{4,5}} [1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>{{1,3,4},{2},{5}} [1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>{{1,3,4,5},{2}} [1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>{{1,3,5},{2},{4}} [1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>{{1,4},{2},{3},{5}} [1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>{{1,4,5},{2},{3}} [1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>{{1,5},{2},{3},{4}} [1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>{{1,4},{2},{3,5}} [1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>{{1,3},{2,4},{5}} [1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>{{1,3},{2,4,5}} [1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>{{1,3},{2,5},{4}} [1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>{{1,3,5},{2,4}} [1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>{{1,4},{2,5},{3}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>{{1},{2},{3},{4,6},{5}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>{{1},{2},{3,4,6},{5}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>{{1},{2},{3,5},{4},{6}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>{{1},{2},{3,5,6},{4}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>{{1},{2},{3,6},{4},{5}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>{{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]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>{{1},{2,3},{4,6},{5}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>{{1},{2,3,4,6},{5}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>{{1},{2,3,5},{4},{6}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>{{1},{2,3,5,6},{4}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>{{1},{2,3,6},{4},{5}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>{{1},{2,4},{3},{5},{6}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>{{1},{2,4},{3},{5,6}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>{{1},{2,4,5},{3},{6}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>{{1},{2,4,5,6},{3}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>{{1},{2,4,6},{3},{5}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>{{1},{2,5},{3},{4},{6}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>{{1},{2,5,6},{3},{4}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>{{1},{2,6},{3},{4},{5}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>{{1},{2,5},{3},{4,6}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>{{1},{2,4},{3,6},{5}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>{{1},{2,4,6},{3,5}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>{{1},{2,5},{3,6},{4}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>{{1,2},{3},{4,6},{5}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>{{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]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>{{1,2},{3,4,6},{5}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>{{1,2},{3,5},{4},{6}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>{{1,2},{3,5,6},{4}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>{{1,2},{3,6},{4},{5}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>{{1,2,3},{4,6},{5}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,6},{5}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>{{1,2,3,5},{4},{6}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>{{1,2,3,5,6},{4}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>{{1,2,3,6},{4},{5}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>{{1,2,3,5},{4,6}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>{{1,2,4},{3},{5},{6}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>{{1,2,4},{3},{5,6}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>{{1,2,4,5},{3},{6}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>{{1,2,4,5,6},{3}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>{{1,2,4,6},{3},{5}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>{{1,2,5},{3},{4},{6}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>{{1,2,5,6},{3},{4}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>{{1,2,6},{3},{4},{5}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>{{1,2,5},{3},{4,6}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>{{1,2,4},{3,5},{6}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>{{1,2,4},{3,5,6}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>{{1,2,4},{3,6},{5}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>{{1,2,4,6},{3,5}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>{{1,2,5},{3,6},{4}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>{{1,3},{2},{4},{5},{6}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>{{1,3},{2},{4},{5,6}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>{{1,3},{2},{4,5},{6}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>{{1,3},{2},{4,5,6}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>{{1,3},{2},{4,6},{5}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>{{1,3,4},{2},{5},{6}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>{{1,3,4},{2},{5,6}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>{{1,3,4,5},{2},{6}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>{{1,3,4,5,6},{2}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>{{1,3,4,6},{2},{5}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>{{1,3,5},{2},{4},{6}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>{{1,3,5,6},{2},{4}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>{{1,3,6},{2},{4},{5}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>{{1,3,5},{2},{4,6}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>{{1,4},{2},{3},{5},{6}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>{{1,4},{2},{3},{5,6}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>{{1,4,5},{2},{3},{6}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>{{1,4,5,6},{2},{3}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>{{1,4,6},{2},{3},{5}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>{{1,5},{2},{3},{4},{6}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>{{1,5,6},{2},{3},{4}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>{{1,6},{2},{3},{4},{5}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>{{1,5},{2},{3},{4,6}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>{{1,4},{2},{3,5},{6}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>{{1,4},{2},{3,5,6}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>{{1,4},{2},{3,6},{5}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>{{1,4,6},{2},{3,5}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>{{1,5},{2},{3,6},{4}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>{{1,3},{2,4},{5},{6}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>{{1,3},{2,4,5},{6}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>{{1,3},{2,4,5,6}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>{{1,3},{2,4,6},{5}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>{{1,3},{2,5},{4},{6}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>{{1,3},{2,5,6},{4}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>{{1,3},{2,6},{4},{5}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>{{1,3,5},{2,4},{6}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>{{1,3,5,6},{2,4}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>{{1,3,6},{2,4},{5}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>{{1,3,6},{2,5},{4}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>{{1,4},{2,5},{3},{6}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>{{1,4},{2,5,6},{3}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>{{1,4},{2,6},{3},{5}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>{{1,4,6},{2,5},{3}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>{{1,5},{2,6},{3},{4}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}} [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}} [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,3,4,7,5,6]=>{{1},{2},{3},{4},{5,7},{6}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}} [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}} [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,5,7,4,6]=>{{1},{2},{3},{4,5,7},{6}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,3,6,4,5,7]=>{{1},{2},{3},{4,6},{5},{7}} [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]=>{{1},{2},{3},{4,6,7},{5}} [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,3,7,4,5,6]=>{{1},{2},{3},{4,7},{5},{6}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}} [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}} [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}} [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,6]=>{{1},{2},{3,4},{5,7},{6}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,7,3,6]=>{{1},{2},{3,4,5,7},{6}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5,7]=>{{1},{2},{3,4,6},{5},{7}} [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,6,3,7,5]=>{{1},{2},{3,4,6,7},{5}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,7,3,5,6]=>{{1},{2},{3,4,7},{5},{6}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,4,6,7]=>{{1},{2},{3,5},{4},{6},{7}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,4,7,6]=>{{1},{2},{3,5},{4},{6,7}} [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,7]=>{{1},{2},{3,5,6},{4},{7}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,7,4]=>{{1},{2},{3,5,6,7},{4}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,6]=>{{1},{2},{3,5,7},{4},{6}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,3,4,5,7]=>{{1},{2},{3,6},{4},{5},{7}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]=>{{1},{2},{3,6,7},{4},{5}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,7,3,4,5,6]=>{{1},{2},{3,7},{4},{5},{6}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,5]=>{{1},{2},{3,6},{4},{5,7}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}} [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,2,5,7,3,4,6]=>{{1},{2},{3,5},{4,7},{6}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,3,4]=>{{1},{2},{3,5,7},{4,6}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,7,3,4,5]=>{{1},{2},{3,6},{4,7},{5}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}} [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>{{1},{2,3},{4},{5,7},{6}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]=>{{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]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}} [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}} [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,7,4,6]=>{{1},{2,3},{4,5,7},{6}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,5,7]=>{{1},{2,3},{4,6},{5},{7}} [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5]=>{{1},{2,3},{4,6,7},{5}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,5,6]=>{{1},{2,3},{4,7},{5},{6}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}} [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}} [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,6]=>{{1},{2,3,4},{5,7},{6}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,7,2,6]=>{{1},{2,3,4,5,7},{6}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,6,2,5,7]=>{{1},{2,3,4,6},{5},{7}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,6,2,7,5]=>{{1},{2,3,4,6,7},{5}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,7,2,5,6]=>{{1},{2,3,4,7},{5},{6}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,5,2,4,6,7]=>{{1},{2,3,5},{4},{6},{7}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,7,6]=>{{1},{2,3,5},{4},{6,7}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,7]=>{{1},{2,3,5,6},{4},{7}} [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,7,4]=>{{1},{2,3,5,6,7},{4}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,6]=>{{1},{2,3,5,7},{4},{6}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,6,2,4,5,7]=>{{1},{2,3,6},{4},{5},{7}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,6,2,4,7,5]=>{{1},{2,3,6,7},{4},{5}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]=>{{1},{2,3,7},{4},{5},{6}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,5]=>{{1},{2,3,6},{4},{5,7}} [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,7,2,4,6]=>{{1},{2,3,5},{4,7},{6}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,2,4]=>{{1},{2,3,5,7},{4,6}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,6,7,2,4,5]=>{{1},{2,3,6},{4,7},{5}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,3,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}} [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,3,5,7,6]=>{{1},{2,4},{3},{5},{6,7}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5,7]=>{{1},{2,4},{3},{5,6},{7}} [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,6,7,5]=>{{1},{2,4},{3},{5,6,7}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>{{1},{2,4},{3},{5,7},{6}} [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,6,7]=>{{1},{2,4,5},{3},{6},{7}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6]=>{{1},{2,4,5},{3},{6,7}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,6,3,7]=>{{1},{2,4,5,6},{3},{7}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,3]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,7,3,6]=>{{1},{2,4,5,7},{3},{6}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5,7]=>{{1},{2,4,6},{3},{5},{7}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5]=>{{1},{2,4,6,7},{3},{5}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,5,6]=>{{1},{2,4,7},{3},{5},{6}} [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,7,3,5]=>{{1},{2,4,6},{3},{5,7}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,3,4,6,7]=>{{1},{2,5},{3},{4},{6},{7}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]=>{{1},{2,5},{3},{4},{6,7}} [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,3,6,4,7]=>{{1},{2,5,6},{3},{4},{7}} [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,3,6,7,4]=>{{1},{2,5,6,7},{3},{4}} [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>{{1},{2,5,7},{3},{4},{6}} [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,3,4,5,7]=>{{1},{2,6},{3},{4},{5},{7}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,3,4,7,5]=>{{1},{2,6,7},{3},{4},{5}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>{{1},{2,7},{3},{4},{5},{6}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>{{1},{2,6},{3},{4},{5,7}} [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,4,7]=>{{1},{2,5},{3},{4,6},{7}} [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4]=>{{1},{2,5},{3},{4,6,7}} [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]=>{{1},{2,5},{3},{4,7},{6}} [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,7,3,4]=>{{1},{2,5,7},{3},{4,6}} [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]=>{{1},{2,6},{3},{4,7},{5}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}} [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}} [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}} [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,6]=>{{1},{2,4},{3,5,7},{6}} [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5,7]=>{{1},{2,4},{3,6},{5},{7}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,6,2,3,7,5]=>{{1},{2,4},{3,6,7},{5}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]=>{{1},{2,4},{3,7},{5},{6}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}} [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,2,3,7]=>{{1},{2,4,6},{3,5},{7}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,2,7,3]=>{{1},{2,4,6,7},{3,5}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,7,2,3,6]=>{{1},{2,4,7},{3,5},{6}} [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}} [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]=>{{1},{2,4,7},{3,6},{5}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,6,2,3,4,7]=>{{1},{2,5},{3,6},{4},{7}} [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,6,2,3,7,4]=>{{1},{2,5},{3,6,7},{4}} [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]=>{{1},{2,5},{3,7},{4},{6}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]=>{{1},{2,5,7},{3,6},{4}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]=>{{1},{2,6},{3,7},{4},{5}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}} [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}} [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]=>{{1,2},{3},{4},{5,7},{6}} [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}} [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}} [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}} [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}} [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,5,7,4,6]=>{{1,2},{3},{4,5,7},{6}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,6,4,5,7]=>{{1,2},{3},{4,6},{5},{7}} [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>{{1,2},{3},{4,6,7},{5}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]=>{{1,2},{3},{4,7},{5},{6}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,6,7,4,5]=>{{1,2},{3},{4,6},{5,7}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}} [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>{{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]=>[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}} [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,6]=>{{1,2},{3,4},{5,7},{6}} [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}} [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}} [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,7,3,6]=>{{1,2},{3,4,5,7},{6}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5,7]=>{{1,2},{3,4,6},{5},{7}} [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>{{1,2},{3,4,6,7},{5}} [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,7,3,5,6]=>{{1,2},{3,4,7},{5},{6}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,6,7,3,5]=>{{1,2},{3,4,6},{5,7}} [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,4,6,7]=>{{1,2},{3,5},{4},{6},{7}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,4,7,6]=>{{1,2},{3,5},{4},{6,7}} [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,7]=>{{1,2},{3,5,6},{4},{7}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>{{1,2},{3,5,6,7},{4}} [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,6]=>{{1,2},{3,5,7},{4},{6}} [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]=>{{1,2},{3,6},{4},{5},{7}} [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,4,7,5]=>{{1,2},{3,6,7},{4},{5}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]=>{{1,2},{3,7},{4},{5},{6}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,5]=>{{1,2},{3,6},{4},{5,7}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,6,3,4,7]=>{{1,2},{3,5},{4,6},{7}} [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>{{1,2},{3,5},{4,6,7}} [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,7,3,4,6]=>{{1,2},{3,5},{4,7},{6}} [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,3,4]=>{{1,2},{3,5,7},{4,6}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,7,3,4,5]=>{{1,2},{3,6},{4,7},{5}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}} [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>{{1,2,3},{4},{5,7},{6}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,7,4,6]=>{{1,2,3},{4,5,7},{6}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,5,7]=>{{1,2,3},{4,6},{5},{7}} [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5]=>{{1,2,3},{4,6,7},{5}} [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,5,6]=>{{1,2,3},{4,7},{5},{6}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,7,4,5]=>{{1,2,3},{4,6},{5,7}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,6]=>{{1,2,3,4},{5,7},{6}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}} [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,7},{6}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,6,1,5,7]=>{{1,2,3,4,6},{5},{7}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,6,7},{5}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,7},{5},{6}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]=>{{1,2,3,4,6},{5,7}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,1,4,6,7]=>{{1,2,3,5},{4},{6},{7}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,7,6]=>{{1,2,3,5},{4},{6,7}} [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,7]=>{{1,2,3,5,6},{4},{7}} [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,5,6,7},{4}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,5,7},{4},{6}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,6,1,4,5,7]=>{{1,2,3,6},{4},{5},{7}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,6,1,4,7,5]=>{{1,2,3,6,7},{4},{5}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,7,1,4,5,6]=>{{1,2,3,7},{4},{5},{6}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,5]=>{{1,2,3,6},{4},{5,7}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,1,4,7]=>{{1,2,3,5},{4,6},{7}} [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,1,7,4]=>{{1,2,3,5},{4,6,7}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,7,1,4,6]=>{{1,2,3,5},{4,7},{6}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]=>{{1,2,3,5,7},{4,6}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,6,7,1,4,5]=>{{1,2,3,6},{4,7},{5}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]=>{{1,2,4},{3},{5},{6},{7}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,3,5,7,6]=>{{1,2,4},{3},{5},{6,7}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>{{1,2,4},{3},{5,6},{7}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,6,7,5]=>{{1,2,4},{3},{5,6,7}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,3,7,5,6]=>{{1,2,4},{3},{5,7},{6}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,6,7]=>{{1,2,4,5},{3},{6},{7}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6]=>{{1,2,4,5},{3},{6,7}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,6,3,7]=>{{1,2,4,5,6},{3},{7}} [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,3]=>{{1,2,4,5,6,7},{3}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,7,3,6]=>{{1,2,4,5,7},{3},{6}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5,7]=>{{1,2,4,6},{3},{5},{7}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5]=>{{1,2,4,6,7},{3},{5}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,5,6]=>{{1,2,4,7},{3},{5},{6}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,7,3,5]=>{{1,2,4,6},{3},{5,7}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]=>{{1,2,5},{3},{4},{6},{7}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,7,6]=>{{1,2,5},{3},{4},{6,7}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>{{1,2,5,6},{3},{4},{7}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,7,4]=>{{1,2,5,6,7},{3},{4}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,5,1,3,7,4,6]=>{{1,2,5,7},{3},{4},{6}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]=>{{1,2,6},{3},{4},{5},{7}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,1,3,4,7,5]=>{{1,2,6,7},{3},{4},{5}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>{{1,2,7},{3},{4},{5},{6}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,1,3,7,4,5]=>{{1,2,6},{3},{4},{5,7}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,4,7]=>{{1,2,5},{3},{4,6},{7}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4]=>{{1,2,5},{3},{4,6,7}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,4,6]=>{{1,2,5},{3},{4,7},{6}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,7,3,4]=>{{1,2,5,7},{3},{4,6}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]=>{{1,2,6},{3},{4,7},{5}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,1,3,6,7]=>{{1,2,4},{3,5},{6},{7}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,1,3,7,6]=>{{1,2,4},{3,5},{6,7}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,7]=>{{1,2,4},{3,5,6},{7}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,7,3]=>{{1,2,4},{3,5,6,7}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,6]=>{{1,2,4},{3,5,7},{6}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5,7]=>{{1,2,4},{3,6},{5},{7}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,6,1,3,7,5]=>{{1,2,4},{3,6,7},{5}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,7,1,3,5,6]=>{{1,2,4},{3,7},{5},{6}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,5]=>{{1,2,4},{3,6},{5,7}} [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,1,3,7]=>{{1,2,4,6},{3,5},{7}} [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,1,7,3]=>{{1,2,4,6,7},{3,5}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,7,1,3,6]=>{{1,2,4,7},{3,5},{6}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,1,3]=>{{1,2,4,6},{3,5,7}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,6,7,1,3,5]=>{{1,2,4,7},{3,6},{5}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,1,3,4,7]=>{{1,2,5},{3,6},{4},{7}} [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,1,3,7,4]=>{{1,2,5},{3,6,7},{4}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]=>{{1,2,5},{3,7},{4},{6}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,4]=>{{1,2,5,7},{3,6},{4}} [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]=>{{1,2,6},{3,7},{4},{5}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,1,3,4]=>{{1,2,5},{3,6},{4,7}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}} [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}} [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,2,4,7,5,6]=>{{1,3},{2},{4},{5,7},{6}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}} [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}} [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,4]=>{{1,3},{2},{4,5,6,7}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,7,4,6]=>{{1,3},{2},{4,5,7},{6}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,6,4,5,7]=>{{1,3},{2},{4,6},{5},{7}} [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>{{1,3},{2},{4,6,7},{5}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,7,4,5,6]=>{{1,3},{2},{4,7},{5},{6}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,6,7,4,5]=>{{1,3},{2},{4,6},{5,7}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,5,6,7]=>{{1,3,4},{2},{5},{6},{7}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,5,7,6]=>{{1,3,4},{2},{5},{6,7}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,7]=>{{1,3,4},{2},{5,6},{7}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>{{1,3,4},{2},{5,6,7}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,6]=>{{1,3,4},{2},{5,7},{6}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,2,6,7]=>{{1,3,4,5},{2},{6},{7}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>{{1,3,4,5},{2},{6,7}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,2,7]=>{{1,3,4,5,6},{2},{7}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,2]=>{{1,3,4,5,6,7},{2}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,7,2,6]=>{{1,3,4,5,7},{2},{6}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,6,2,5,7]=>{{1,3,4,6},{2},{5},{7}} [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>{{1,3,4,6,7},{2},{5}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,7,2,5,6]=>{{1,3,4,7},{2},{5},{6}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,6,7,2,5]=>{{1,3,4,6},{2},{5,7}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,4,6,7]=>{{1,3,5},{2},{4},{6},{7}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,7,6]=>{{1,3,5},{2},{4},{6,7}} [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,7]=>{{1,3,5,6},{2},{4},{7}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>{{1,3,5,6,7},{2},{4}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,6]=>{{1,3,5,7},{2},{4},{6}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,4,5,7]=>{{1,3,6},{2},{4},{5},{7}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,4,7,5]=>{{1,3,6,7},{2},{4},{5}} [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,4,5,6]=>{{1,3,7},{2},{4},{5},{6}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,5]=>{{1,3,6},{2},{4},{5,7}} [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,6,2,4,7]=>{{1,3,5},{2},{4,6},{7}} [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>{{1,3,5},{2},{4,6,7}} [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,7,2,4,6]=>{{1,3,5},{2},{4,7},{6}} [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,2,4]=>{{1,3,5,7},{2},{4,6}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,7,2,4,5]=>{{1,3,6},{2},{4,7},{5}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>{{1,4},{2},{3},{5},{6,7}} [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5,7]=>{{1,4},{2},{3},{5,6},{7}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,6,7,5]=>{{1,4},{2},{3},{5,6,7}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,3,7,5,6]=>{{1,4},{2},{3},{5,7},{6}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,6,7]=>{{1,4,5},{2},{3},{6},{7}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>{{1,4,5},{2},{3},{6,7}} [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,6,3,7]=>{{1,4,5,6},{2},{3},{7}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,3]=>{{1,4,5,6,7},{2},{3}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,7,3,6]=>{{1,4,5,7},{2},{3},{6}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5,7]=>{{1,4,6},{2},{3},{5},{7}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>{{1,4,6,7},{2},{3},{5}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,7,3,5,6]=>{{1,4,7},{2},{3},{5},{6}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,6,7,3,5]=>{{1,4,6},{2},{3},{5,7}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]=>{{1,5},{2},{3},{4},{6},{7}} [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>{{1,5},{2},{3},{4},{6,7}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]=>{{1,5,6},{2},{3},{4},{7}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]=>{{1,5,6,7},{2},{3},{4}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]=>{{1,5,7},{2},{3},{4},{6}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]=>{{1,6},{2},{3},{4},{5},{7}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>{{1,6,7},{2},{3},{4},{5}} [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]=>[7,1,2,3,4,5,6]=>{{1,7},{2},{3},{4},{5},{6}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]=>{{1,6},{2},{3},{4},{5,7}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]=>{{1,5},{2},{3},{4,6},{7}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>{{1,5},{2},{3},{4,6,7}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,7,3,4,6]=>{{1,5},{2},{3},{4,7},{6}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,2,6,7,3,4]=>{{1,5,7},{2},{3},{4,6}} [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]=>{{1,6},{2},{3},{4,7},{5}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,3,6,7]=>{{1,4},{2},{3,5},{6},{7}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,3,7,6]=>{{1,4},{2},{3,5},{6,7}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,7]=>{{1,4},{2},{3,5,6},{7}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>{{1,4},{2},{3,5,6,7}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,6]=>{{1,4},{2},{3,5,7},{6}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]=>{{1,4},{2},{3,6},{5},{7}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,3,7,5]=>{{1,4},{2},{3,6,7},{5}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,3,5,6]=>{{1,4},{2},{3,7},{5},{6}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,5]=>{{1,4},{2},{3,6},{5,7}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,6,2,3,7]=>{{1,4,6},{2},{3,5},{7}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>{{1,4,6,7},{2},{3,5}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,7,2,3,6]=>{{1,4,7},{2},{3,5},{6}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,2,3]=>{{1,4,6},{2},{3,5,7}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,7,2,3,5]=>{{1,4,7},{2},{3,6},{5}} [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]=>{{1,5},{2},{3,6},{4},{7}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]=>{{1,5},{2},{3,6,7},{4}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,3,4,6]=>{{1,5},{2},{3,7},{4},{6}} [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,4]=>{{1,5,7},{2},{3,6},{4}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,3,4,5]=>{{1,6},{2},{3,7},{4},{5}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,7,2,3,4]=>{{1,5},{2},{3,6},{4,7}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>{{1,3},{2,4},{5},{6},{7}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,2,5,7,6]=>{{1,3},{2,4},{5},{6,7}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>{{1,3},{2,4},{5,6},{7}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,2,6,7,5]=>{{1,3},{2,4},{5,6,7}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,2,7,5,6]=>{{1,3},{2,4},{5,7},{6}} [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,6,7]=>{{1,3},{2,4,5},{6},{7}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6]=>{{1,3},{2,4,5},{6,7}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,6,2,7]=>{{1,3},{2,4,5,6},{7}} [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,2]=>{{1,3},{2,4,5,6,7}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,7,2,6]=>{{1,3},{2,4,5,7},{6}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5,7]=>{{1,3},{2,4,6},{5},{7}} [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5]=>{{1,3},{2,4,6,7},{5}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,5,6]=>{{1,3},{2,4,7},{5},{6}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,7,2,5]=>{{1,3},{2,4,6},{5,7}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,5,1,2,4,6,7]=>{{1,3},{2,5},{4},{6},{7}} [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,7,6]=>{{1,3},{2,5},{4},{6,7}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>{{1,3},{2,5,6},{4},{7}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,5,1,2,6,7,4]=>{{1,3},{2,5,6,7},{4}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,7,4,6]=>{{1,3},{2,5,7},{4},{6}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]=>{{1,3},{2,6},{4},{5},{7}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1,2,4,7,5]=>{{1,3},{2,6,7},{4},{5}} [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>{{1,3},{2,7},{4},{5},{6}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,2,7,4,5]=>{{1,3},{2,6},{4},{5,7}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,4,7]=>{{1,3},{2,5},{4,6},{7}} [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4]=>{{1,3},{2,5},{4,6,7}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,4,6]=>{{1,3},{2,5},{4,7},{6}} [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,7,2,4]=>{{1,3},{2,5,7},{4,6}} [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,4,5]=>{{1,3},{2,6},{4,7},{5}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6,7]=>{{1,3,5},{2,4},{6},{7}} [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,1,2,7,6]=>{{1,3,5},{2,4},{6,7}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,7]=>{{1,3,5,6},{2,4},{7}} [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,7,2]=>{{1,3,5,6,7},{2,4}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,6]=>{{1,3,5,7},{2,4},{6}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5,7]=>{{1,3,6},{2,4},{5},{7}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,6,1,2,7,5]=>{{1,3,6,7},{2,4},{5}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,7,1,2,5,6]=>{{1,3,7},{2,4},{5},{6}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,5]=>{{1,3,6},{2,4},{5,7}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,1,2,7]=>{{1,3,5},{2,4,6},{7}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,1,7,2]=>{{1,3,5},{2,4,6,7}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,7,1,2,6]=>{{1,3,5},{2,4,7},{6}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]=>{{1,3,5,7},{2,4,6}} [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,6,7,1,2,5]=>{{1,3,6},{2,4,7},{5}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]=>{{1,3,6},{2,5},{4},{7}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,1,2,7,4]=>{{1,3,6,7},{2,5},{4}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,7,1,2,4,6]=>{{1,3,7},{2,5},{4},{6}} [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,4]=>{{1,3,6},{2,5,7},{4}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,6,7,1,2,4,5]=>{{1,3,7},{2,6},{4},{5}} [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,1,2,4]=>{{1,3,6},{2,5},{4,7}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7]=>{{1,4},{2,5},{3},{6},{7}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,1,2,3,7,6]=>{{1,4},{2,5},{3},{6,7}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>{{1,4},{2,5,6},{3},{7}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,1,2,6,7,3]=>{{1,4},{2,5,6,7},{3}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,1,2,7,3,6]=>{{1,4},{2,5,7},{3},{6}} [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]=>{{1,4},{2,6},{3},{5},{7}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]=>{{1,4},{2,6,7},{3},{5}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>{{1,4},{2,7},{3},{5},{6}} [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,2,7,3,5]=>{{1,4},{2,6},{3},{5,7}} [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]=>{{1,4,6},{2,5},{3},{7}} [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3]=>{{1,4,6,7},{2,5},{3}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,3,6]=>{{1,4,7},{2,5},{3},{6}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,7,2,3]=>{{1,4,6},{2,5,7},{3}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,3,5]=>{{1,4,7},{2,6},{3},{5}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]=>{{1,5},{2,6},{3},{4},{7}} [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]=>{{1,5},{2,6,7},{3},{4}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>{{1,5},{2,7},{3},{4},{6}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,1,2,7,3,4]=>{{1,5,7},{2,6},{3},{4}} [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]=>[6,7,1,2,3,4,5]=>{{1,6},{2,7},{3},{4},{5}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,3,4]=>{{1,5},{2,6},{3},{4,7}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>{{1,4},{2,5},{3,6},{7}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,1,2,7,3]=>{{1,4},{2,5},{3,6,7}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,7,1,2,3,6]=>{{1,4},{2,5},{3,7},{6}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,3]=>{{1,4},{2,5,7},{3,6}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,6,7,1,2,3,5]=>{{1,4},{2,6},{3,7},{5}} [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]=>[4,5,6,7,1,2,3]=>{{1,4,7},{2,5},{3,6}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,1,2,3,4]=>{{1,5},{2,6},{3,7},{4}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]=>{{1,2},{3,4},{5,7},{6,8}} [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>{{1,2},{3,5},{4,6},{7,8}} [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]=>{{1,2},{3,5},{4,7},{6,8}} [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]=>{{1,2},{3,6},{4,7},{5,8}} [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}} [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}} [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}} [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}} [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]=>{{1,3},{2,6},{4,7},{5,8}} [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}} [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}} [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>{{1,4},{2,6},{3,7},{5,8}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>{{1,5},{2,6},{3,7},{4,8}}
Map
Delest-Viennot-inverse
Description
Return the Dyck path obtained by applying the inverse of Delest-Viennot's bijection to the corresponding parallelogram polyomino.
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 $(\beta^{(-1)}\circ\gamma)(D)$.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.