Identifier
Mp00031: Dyck paths to 312-avoiding permutationPermutations
Mp00064: Permutations reversePermutations
Mp00151: Permutations to cycle type Set partitions
Images
=>
Cc0005;cc-rep-0Cc0009;cc-rep-3
[1,0]=>[1]=>[1]=>{{1}} [1,0,1,0]=>[1,2]=>[2,1]=>{{1,2}} [1,1,0,0]=>[2,1]=>[1,2]=>{{1},{2}} [1,0,1,0,1,0]=>[1,2,3]=>[3,2,1]=>{{1,3},{2}} [1,0,1,1,0,0]=>[1,3,2]=>[2,3,1]=>{{1,2,3}} [1,1,0,0,1,0]=>[2,1,3]=>[3,1,2]=>{{1,2,3}} [1,1,0,1,0,0]=>[2,3,1]=>[1,3,2]=>{{1},{2,3}} [1,1,1,0,0,0]=>[3,2,1]=>[1,2,3]=>{{1},{2},{3}} [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[4,3,2,1]=>{{1,4},{2,3}} [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[3,4,2,1]=>{{1,2,3,4}} [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[4,2,3,1]=>{{1,4},{2},{3}} [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,3,1]=>{{1,2,4},{3}} [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[2,3,4,1]=>{{1,2,3,4}} [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[4,3,1,2]=>{{1,2,3,4}} [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,4,1,2]=>{{1,3},{2,4}} [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[4,1,3,2]=>{{1,2,4},{3}} [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[1,4,3,2]=>{{1},{2,4},{3}} [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[1,3,4,2]=>{{1},{2,3,4}} [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[4,1,2,3]=>{{1,2,3,4}} [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[1,4,2,3]=>{{1},{2,3,4}} [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[1,2,4,3]=>{{1},{2},{3,4}} [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,2,3,4]=>{{1},{2},{3},{4}} [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}} [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[4,5,3,2,1]=>{{1,2,4,5},{3}} [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[5,3,4,2,1]=>{{1,5},{2,3,4}} [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[3,5,4,2,1]=>{{1,2,3,4,5}} [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1]=>{{1,3,5},{2,4}} [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[5,4,2,3,1]=>{{1,5},{2,3,4}} [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[4,5,2,3,1]=>{{1,2,3,4,5}} [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[5,2,4,3,1]=>{{1,5},{2},{3,4}} [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,5,4,3,1]=>{{1,2,5},{3,4}} [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[2,4,5,3,1]=>{{1,2,3,4,5}} [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}} [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[2,5,3,4,1]=>{{1,2,5},{3},{4}} [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[2,3,5,4,1]=>{{1,2,3,5},{4}} [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>{{1,2,4,5},{3}} [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[4,5,3,1,2]=>{{1,4},{2,5},{3}} [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[5,3,4,1,2]=>{{1,2,3,4,5}} [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,5,4,1,2]=>{{1,3,4},{2,5}} [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[3,4,5,1,2]=>{{1,2,3,4,5}} [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[5,4,1,3,2]=>{{1,2,3,4,5}} [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,5,1,3,2]=>{{1,3,4},{2,5}} [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[5,1,4,3,2]=>{{1,2,5},{3,4}} [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}} [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[1,4,5,3,2]=>{{1},{2,3,4,5}} [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[5,1,3,4,2]=>{{1,2,5},{3},{4}} [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}} [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}} [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[1,3,4,5,2]=>{{1},{2,3,4,5}} [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[5,4,1,2,3]=>{{1,3,5},{2,4}} [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,5,1,2,3]=>{{1,2,3,4,5}} [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[5,1,4,2,3]=>{{1,2,3,4,5}} [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[1,5,4,2,3]=>{{1},{2,3,4,5}} [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}} [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[5,1,2,4,3]=>{{1,2,3,5},{4}} [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[1,5,2,4,3]=>{{1},{2,3,5},{4}} [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}} [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}} [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[5,1,2,3,4]=>{{1,2,3,4,5}} [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[1,5,2,3,4]=>{{1},{2,3,4,5}} [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[1,2,5,3,4]=>{{1},{2},{3,4,5}} [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}} [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>{{1,2,5,6},{3,4}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>{{1,3,4,6},{2,5}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>{{1,2,5,6},{3},{4}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>{{1,2,3,5,6},{4}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>{{1,3,6},{2,5},{4}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>{{1,3,6},{2,4,5}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>{{1,2,3,4,5,6}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>{{1,6},{2,3,4,5}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>{{1,2,3,4,5,6}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>{{1,6},{2,4},{3,5}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>{{1,2,4,6},{3,5}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>{{1,6},{2,3,5},{4}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>{{1,2,3,5,6},{4}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>{{1,2,3,5,6},{4}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>{{1,6},{2},{3,4,5}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>{{1,2,6},{3,4,5}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>{{1,2,6},{3},{4,5}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>{{1,2,3,4,5,6}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>{{1,2,5,6},{3,4}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>{{1,5},{2,6},{3,4}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>{{1,2,3,4,5,6}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>{{1,3,4,5},{2,6}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>{{1,2,5,6},{3},{4}} [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>{{1,5},{2,6},{3},{4}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>{{1,2,3,5,6},{4}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>{{1,3,5},{2,6},{4}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>{{1,2,3,5,6},{4}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>{{1,3,4,5},{2,6}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>{{1,2,3,4,5,6}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>{{1,3,4,5},{2,6}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>{{1,2,4,6},{3,5}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>{{1,4},{2,6},{3,5}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>{{1,4},{2,3,5,6}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>{{1,2,3,5,6},{4}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>{{1,3,5},{2,6},{4}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>{{1,2,6},{3,5},{4}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>{{1,2,6},{3,4,5}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>{{1},{2,4,6},{3,5}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>{{1,2,3,4,5,6}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>{{1,3,4,5},{2,6}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>{{1,2,6},{3,4,5}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>{{1},{2,6},{3,4,5}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>{{1},{2,3,4,5,6}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[6,1,3,5,4,2]=>{{1,2,6},{3},{4,5}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>{{1,2,6},{3},{4},{5}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>{{1,3,4,6},{2,5}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>{{1,2,3,4,5,6}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>{{1,2,3,4,5,6}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>{{1,4},{2,3,5,6}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>{{1,3,6},{2,5},{4}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>{{1,2,3,5,6},{4}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>{{1,2,3,5,6},{4}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>{{1},{2,3,5,6},{4}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>{{1,2,3,4,5,6}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>{{1},{2,3,4,5,6}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>{{1},{2,3,4,5,6}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>{{1,3,6},{2,4,5}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>{{1},{2,3,4,5,6}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>{{1},{2,4,5},{3,6}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>{{1,2,3,6},{4,5}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>{{1},{2,3,6},{4,5}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>{{1,2,3,6},{4},{5}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>{{1},{2,3,6},{4},{5}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>{{1,3,5},{2,4,6}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>{{1,2,4,6},{3,5}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>{{1},{2,4,6},{3,5}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>{{1},{2,3,4,5,6}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>{{1},{2,3,4,5,6}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>{{1},{2},{3,4,5,6}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>{{1,2,3,4,6},{5}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>{{1},{2,3,4,6},{5}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>{{1},{2},{3,4,6},{5}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>{{1},{2,3,4,5,6}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>{{1},{2},{3,4,5,6}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>{{1},{2},{3},{4,5,6}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>{{1,2,6,7},{3,5},{4}} [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>{{1,7},{2,3,5,6},{4}} [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>{{1,2,3,5,6,7},{4}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>{{1,3,5,7},{2,6},{4}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>{{1,2,6,7},{3,4,5}} [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>{{1,7},{2,3,4,5,6}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1]=>{{1,3,4,5,7},{2,6}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>{{1,7},{2,4,6},{3,5}} [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1]=>{{1,2,4,6,7},{3,5}} [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>{{1,4,7},{2,3,5,6}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>{{1,7},{2,6},{3,4,5}} [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>{{1,2,6,7},{3,4,5}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>{{1,7},{2,3,4,5,6}} [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>{{1,3,4,5,7},{2,6}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>{{1,7},{2,6},{3},{4,5}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>{{1,2,6,7},{3},{4,5}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>{{1,7},{2,3,6},{4,5}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>{{1,2,3,6,7},{4,5}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[3,6,7,5,4,2,1]=>{{1,3,7},{2,6},{4,5}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1]=>{{1,7},{2,3,4,5,6}} [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1]=>{{1,3,7},{2,4,5,6}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>{{1,2,6,7},{3},{4},{5}} [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1]=>{{1,7},{2,3,6},{4},{5}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[3,7,6,4,5,2,1]=>{{1,2,3,6,7},{4},{5}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[3,6,7,4,5,2,1]=>{{1,3,7},{2,6},{4},{5}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1]=>{{1,7},{2,3,4,6},{5}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[3,7,4,6,5,2,1]=>{{1,2,3,4,6,7},{5}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1]=>{{1,3,7},{2,4,6},{5}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[3,4,6,7,5,2,1]=>{{1,2,3,4,6,7},{5}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[3,7,4,5,6,2,1]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1]=>{{1,3,7},{2,4,5,6}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[3,4,5,7,6,2,1]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>{{1,7},{2,3,5,6},{4}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>{{1,2,3,5,6,7},{4}} [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>{{1,7},{2,5},{3,6},{4}} [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>{{1,2,5,7},{3,6},{4}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>{{1,2,3,5,6,7},{4}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>{{1,7},{2,3,4,5,6}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>{{1,7},{2,4,5},{3,6}} [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>{{1,2,4,5,7},{3,6}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[4,6,7,5,2,3,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>{{1,7},{2,3,4,5,6}} [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[4,7,5,6,2,3,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[4,5,7,6,2,3,1]=>{{1,3,4,6,7},{2,5}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>{{1,4,7},{2,5},{3,6}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>{{1,7},{2,3,4,5,6}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>{{1,7},{2,4,5},{3,6}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>{{1,2,4,5,7},{3,6}} [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[5,6,7,2,4,3,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>{{1,7},{2,3,6},{4,5}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>{{1,2,3,6,7},{4,5}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>{{1,7},{2},{3,6},{4,5}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>{{1,2,7},{3,6},{4,5}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[2,6,7,5,4,3,1]=>{{1,2,3,6,7},{4,5}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[7,2,5,6,4,3,1]=>{{1,7},{2},{3,4,5,6}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[2,7,5,6,4,3,1]=>{{1,2,7},{3,4,5,6}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[2,5,7,6,4,3,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[2,5,6,7,4,3,1]=>{{1,2,4,5,7},{3,6}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[7,6,2,4,5,3,1]=>{{1,7},{2,3,6},{4},{5}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[6,7,2,4,5,3,1]=>{{1,2,3,6,7},{4},{5}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[7,2,6,4,5,3,1]=>{{1,7},{2},{3,6},{4},{5}} [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[2,7,6,4,5,3,1]=>{{1,2,7},{3,6},{4},{5}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[2,6,7,4,5,3,1]=>{{1,2,3,6,7},{4},{5}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[7,2,4,6,5,3,1]=>{{1,7},{2},{3,4,6},{5}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[2,7,4,6,5,3,1]=>{{1,2,7},{3,4,6},{5}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[2,4,7,6,5,3,1]=>{{1,2,3,4,6,7},{5}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1]=>{{1,2,4,7},{3,6},{5}} [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[7,2,4,5,6,3,1]=>{{1,7},{2},{3,4,5,6}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[2,7,4,5,6,3,1]=>{{1,2,7},{3,4,5,6}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[2,4,7,5,6,3,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[2,4,5,7,6,3,1]=>{{1,2,4,7},{3,5,6}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[2,4,5,6,7,3,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>{{1,7},{2,4,6},{3,5}} [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>{{1,2,4,6,7},{3,5}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>{{1,7},{2,3,4,5,6}} [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[5,7,6,2,3,4,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>{{1,3,5,7},{2,4,6}} [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[7,6,2,5,3,4,1]=>{{1,7},{2,3,4,5,6}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[6,7,2,5,3,4,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[7,2,6,5,3,4,1]=>{{1,7},{2},{3,4,5,6}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[2,7,6,5,3,4,1]=>{{1,2,7},{3,4,5,6}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[2,6,7,5,3,4,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[7,2,5,6,3,4,1]=>{{1,7},{2},{3,5},{4,6}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[2,7,5,6,3,4,1]=>{{1,2,7},{3,5},{4,6}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[2,5,7,6,3,4,1]=>{{1,2,3,5,7},{4,6}} [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[2,5,6,7,3,4,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[7,6,2,3,5,4,1]=>{{1,7},{2,3,4,6},{5}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[6,7,2,3,5,4,1]=>{{1,2,3,4,6,7},{5}} [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[7,2,6,3,5,4,1]=>{{1,7},{2},{3,4,6},{5}} [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[2,7,6,3,5,4,1]=>{{1,2,7},{3,4,6},{5}} [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[2,6,7,3,5,4,1]=>{{1,2,3,4,6,7},{5}} [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[7,2,3,6,5,4,1]=>{{1,7},{2},{3},{4,6},{5}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[2,7,3,6,5,4,1]=>{{1,2,7},{3},{4,6},{5}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[2,3,7,6,5,4,1]=>{{1,2,3,7},{4,6},{5}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[2,3,6,7,5,4,1]=>{{1,2,3,4,6,7},{5}} [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[7,2,3,5,6,4,1]=>{{1,7},{2},{3},{4,5,6}} [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[2,7,3,5,6,4,1]=>{{1,2,7},{3},{4,5,6}} [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}} [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[2,3,5,7,6,4,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1]=>{{1,2,3,5,7},{4,6}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}} [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[7,2,6,3,4,5,1]=>{{1,7},{2},{3,4,5,6}} [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[2,7,6,3,4,5,1]=>{{1,2,7},{3,4,5,6}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[2,6,7,3,4,5,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[7,2,3,6,4,5,1]=>{{1,7},{2},{3},{4,5,6}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[2,7,3,6,4,5,1]=>{{1,2,7},{3},{4,5,6}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[2,3,7,6,4,5,1]=>{{1,2,3,7},{4,5,6}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[2,3,6,7,4,5,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[7,2,3,4,6,5,1]=>{{1,7},{2},{3},{4},{5,6}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[2,7,3,4,6,5,1]=>{{1,2,7},{3},{4},{5,6}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[2,3,7,4,6,5,1]=>{{1,2,3,7},{4},{5,6}} [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}} [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[2,3,4,6,7,5,1]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}} [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[2,7,3,4,5,6,1]=>{{1,2,7},{3},{4},{5},{6}} [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[2,3,7,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>{{1,2,6,7},{3,5},{4}} [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>{{1,6},{2,7},{3,5},{4}} [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>{{1,2,3,5,6,7},{4}} [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[5,7,6,4,3,1,2]=>{{1,3,5,6},{2,7},{4}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>{{1,2,3,5,6,7},{4}} [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>{{1,2,6,7},{3,4,5}} [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>{{1,6},{2,7},{3,4,5}} [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[7,4,6,5,3,1,2]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[4,7,6,5,3,1,2]=>{{1,3,4,5,6},{2,7}} [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[4,6,7,5,3,1,2]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>{{1,2,4,6,7},{3,5}} [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[4,7,5,6,3,1,2]=>{{1,4,6},{2,7},{3,5}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[4,5,7,6,3,1,2]=>{{1,4,6},{2,3,5,7}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>{{1,2,6,7},{3,4,5}} [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>{{1,6},{2,7},{3,4,5}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[5,7,6,3,4,1,2]=>{{1,3,4,5,6},{2,7}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[7,6,3,5,4,1,2]=>{{1,2,6,7},{3},{4,5}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[6,7,3,5,4,1,2]=>{{1,6},{2,7},{3},{4,5}} [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[7,3,6,5,4,1,2]=>{{1,2,3,6,7},{4,5}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[3,7,6,5,4,1,2]=>{{1,3,6},{2,7},{4,5}} [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[3,6,7,5,4,1,2]=>{{1,2,3,6,7},{4,5}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[7,3,5,6,4,1,2]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[3,7,5,6,4,1,2]=>{{1,3,4,5,6},{2,7}} [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[3,5,7,6,4,1,2]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[3,5,6,7,4,1,2]=>{{1,3,6},{2,4,5,7}} [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>{{1,2,6,7},{3},{4},{5}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>{{1,6},{2,7},{3},{4},{5}} [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[7,3,6,4,5,1,2]=>{{1,2,3,6,7},{4},{5}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[3,7,6,4,5,1,2]=>{{1,3,6},{2,7},{4},{5}} [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[3,6,7,4,5,1,2]=>{{1,2,3,6,7},{4},{5}} [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[7,3,4,6,5,1,2]=>{{1,2,3,4,6,7},{5}} [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[3,7,4,6,5,1,2]=>{{1,3,4,6},{2,7},{5}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[3,4,7,6,5,1,2]=>{{1,2,3,4,6,7},{5}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[3,4,6,7,5,1,2]=>{{1,3,6},{2,4,7},{5}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[3,7,4,5,6,1,2]=>{{1,3,4,5,6},{2,7}} [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[3,4,7,5,6,1,2]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[3,4,5,7,6,1,2]=>{{1,3,5,6},{2,4,7}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>{{1,2,3,5,6,7},{4}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>{{1,3,5,6},{2,7},{4}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2]=>{{1,2,5,7},{3,6},{4}} [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[5,7,6,4,1,3,2]=>{{1,5},{2,7},{3,6},{4}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[5,6,7,4,1,3,2]=>{{1,5},{2,3,6,7},{4}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[7,6,4,5,1,3,2]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2]=>{{1,3,4,5,6},{2,7}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[7,4,6,5,1,3,2]=>{{1,2,4,5,7},{3,6}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[4,7,6,5,1,3,2]=>{{1,4,5},{2,7},{3,6}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[4,6,7,5,1,3,2]=>{{1,4,5},{2,3,6,7}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[7,4,5,6,1,3,2]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[4,7,5,6,1,3,2]=>{{1,3,4,5,6},{2,7}} [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[4,5,7,6,1,3,2]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[4,5,6,7,1,3,2]=>{{1,2,4,5,7},{3,6}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>{{1,3,4,5,6},{2,7}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2]=>{{1,2,4,5,7},{3,6}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2]=>{{1,4,5},{2,7},{3,6}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[5,6,7,1,4,3,2]=>{{1,4,5},{2,3,6,7}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>{{1,2,3,6,7},{4,5}} [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>{{1,3,6},{2,7},{4,5}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>{{1,2,7},{3,6},{4,5}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>{{1},{2,7},{3,6},{4,5}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[1,6,7,5,4,3,2]=>{{1},{2,3,6,7},{4,5}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[7,1,5,6,4,3,2]=>{{1,2,7},{3,4,5,6}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[1,7,5,6,4,3,2]=>{{1},{2,7},{3,4,5,6}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[1,5,7,6,4,3,2]=>{{1},{2,3,4,5,6,7}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2]=>{{1},{2,4,5,7},{3,6}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[7,6,1,4,5,3,2]=>{{1,2,3,6,7},{4},{5}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[6,7,1,4,5,3,2]=>{{1,3,6},{2,7},{4},{5}} [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[7,1,6,4,5,3,2]=>{{1,2,7},{3,6},{4},{5}} [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>{{1},{2,7},{3,6},{4},{5}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[1,6,7,4,5,3,2]=>{{1},{2,3,6,7},{4},{5}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[7,1,4,6,5,3,2]=>{{1,2,7},{3,4,6},{5}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[1,7,4,6,5,3,2]=>{{1},{2,7},{3,4,6},{5}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[1,4,6,7,5,3,2]=>{{1},{2,4,7},{3,6},{5}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[7,1,4,5,6,3,2]=>{{1,2,7},{3,4,5,6}} [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[1,7,4,5,6,3,2]=>{{1},{2,7},{3,4,5,6}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[1,4,5,7,6,3,2]=>{{1},{2,4,7},{3,5,6}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[7,6,5,1,3,4,2]=>{{1,2,4,6,7},{3,5}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[6,7,5,1,3,4,2]=>{{1,4,6},{2,7},{3,5}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[7,5,6,1,3,4,2]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[5,7,6,1,3,4,2]=>{{1,3,4,5,6},{2,7}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[5,6,7,1,3,4,2]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[7,6,1,5,3,4,2]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[6,7,1,5,3,4,2]=>{{1,3,4,5,6},{2,7}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[7,1,6,5,3,4,2]=>{{1,2,7},{3,4,5,6}} [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[1,7,6,5,3,4,2]=>{{1},{2,7},{3,4,5,6}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[1,6,7,5,3,4,2]=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[7,1,5,6,3,4,2]=>{{1,2,7},{3,5},{4,6}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2]=>{{1},{2,7},{3,5},{4,6}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[1,5,7,6,3,4,2]=>{{1},{2,3,5,7},{4,6}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[7,6,1,3,5,4,2]=>{{1,2,3,4,6,7},{5}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[6,7,1,3,5,4,2]=>{{1,3,4,6},{2,7},{5}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[7,1,6,3,5,4,2]=>{{1,2,7},{3,4,6},{5}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[1,7,6,3,5,4,2]=>{{1},{2,7},{3,4,6},{5}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[1,6,7,3,5,4,2]=>{{1},{2,3,4,6,7},{5}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[7,1,3,6,5,4,2]=>{{1,2,7},{3},{4,6},{5}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[1,7,3,6,5,4,2]=>{{1},{2,7},{3},{4,6},{5}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[1,3,7,6,5,4,2]=>{{1},{2,3,7},{4,6},{5}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[7,1,3,5,6,4,2]=>{{1,2,7},{3},{4,5,6}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[1,7,3,5,6,4,2]=>{{1},{2,7},{3},{4,5,6}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[1,3,7,5,6,4,2]=>{{1},{2,3,7},{4,5,6}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2]=>{{1},{2,3,5,7},{4,6}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[7,6,1,3,4,5,2]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[6,7,1,3,4,5,2]=>{{1,3,4,5,6},{2,7}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[7,1,6,3,4,5,2]=>{{1,2,7},{3,4,5,6}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[1,7,6,3,4,5,2]=>{{1},{2,7},{3,4,5,6}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[1,6,7,3,4,5,2]=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[7,1,3,6,4,5,2]=>{{1,2,7},{3},{4,5,6}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[1,7,3,6,4,5,2]=>{{1},{2,7},{3},{4,5,6}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[1,3,7,6,4,5,2]=>{{1},{2,3,7},{4,5,6}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[1,3,6,7,4,5,2]=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[7,1,3,4,6,5,2]=>{{1,2,7},{3},{4},{5,6}} [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[1,7,3,4,6,5,2]=>{{1},{2,7},{3},{4},{5,6}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[1,3,7,4,6,5,2]=>{{1},{2,3,7},{4},{5,6}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[1,3,4,7,6,5,2]=>{{1},{2,3,4,7},{5,6}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[7,1,3,4,5,6,2]=>{{1,2,7},{3},{4},{5},{6}} [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}} [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>{{1,3,5,7},{2,6},{4}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>{{1,2,3,5,6,7},{4}} [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>{{1,2,3,5,6,7},{4}} [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[5,7,6,4,1,2,3]=>{{1,5},{2,3,6,7},{4}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>{{1,5},{2,6},{3,7},{4}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>{{1,3,4,5,7},{2,6}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[7,4,6,5,1,2,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[4,7,6,5,1,2,3]=>{{1,4,5},{2,3,6,7}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[4,6,7,5,1,2,3]=>{{1,4,5},{2,6},{3,7}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>{{1,3,5,7},{2,4,6}} [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[4,7,5,6,1,2,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[4,5,7,6,1,2,3]=>{{1,2,4,5,6},{3,7}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>{{1,3,4,5,7},{2,6}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[6,7,5,1,4,2,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[7,5,6,1,4,2,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[5,7,6,1,4,2,3]=>{{1,4,5},{2,3,6,7}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[5,6,7,1,4,2,3]=>{{1,4,5},{2,6},{3,7}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>{{1,3,7},{2,6},{4,5}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[6,7,1,5,4,2,3]=>{{1,2,3,6,7},{4,5}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>{{1,2,3,6,7},{4,5}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>{{1},{2,3,6,7},{4,5}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[1,6,7,5,4,2,3]=>{{1},{2,6},{3,7},{4,5}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[7,1,5,6,4,2,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[1,7,5,6,4,2,3]=>{{1},{2,3,4,5,6,7}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[1,5,7,6,4,2,3]=>{{1},{2,4,5,6},{3,7}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3]=>{{1},{2,3,4,5,6,7}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[7,6,1,4,5,2,3]=>{{1,3,7},{2,6},{4},{5}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[6,7,1,4,5,2,3]=>{{1,2,3,6,7},{4},{5}} [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[7,1,6,4,5,2,3]=>{{1,2,3,6,7},{4},{5}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[1,7,6,4,5,2,3]=>{{1},{2,3,6,7},{4},{5}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[7,1,4,6,5,2,3]=>{{1,2,3,4,6,7},{5}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[1,7,4,6,5,2,3]=>{{1},{2,3,4,6,7},{5}} [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[1,4,6,7,5,2,3]=>{{1},{2,3,4,6,7},{5}} [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[7,1,4,5,6,2,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[1,7,4,5,6,2,3]=>{{1},{2,3,4,5,6,7}} [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}} [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[1,4,5,7,6,2,3]=>{{1},{2,3,4,5,6,7}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[6,7,5,1,2,4,3]=>{{1,4,6},{2,3,5,7}} [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[7,5,6,1,2,4,3]=>{{1,3,4,6,7},{2,5}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[5,7,6,1,2,4,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[5,6,7,1,2,4,3]=>{{1,2,4,5,6},{3,7}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>{{1,3,7},{2,4,5,6}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[6,7,1,5,2,4,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>{{1},{2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[1,6,7,5,2,4,3]=>{{1},{2,4,5,6},{3,7}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[7,1,5,6,2,4,3]=>{{1,2,3,5,7},{4,6}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[1,7,5,6,2,4,3]=>{{1},{2,3,5,7},{4,6}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[1,5,7,6,2,4,3]=>{{1},{2,5},{3,7},{4,6}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>{{1,3,7},{2,4,6},{5}} [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[6,7,1,2,5,4,3]=>{{1,2,3,4,6,7},{5}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>{{1,2,3,4,6,7},{5}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>{{1},{2,3,4,6,7},{5}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[1,6,7,2,5,4,3]=>{{1},{2,4,6},{3,7},{5}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>{{1,2,3,7},{4,6},{5}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>{{1},{2,3,7},{4,6},{5}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>{{1},{2},{3,7},{4,6},{5}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>{{1,2,3,7},{4,5,6}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[1,7,2,5,6,4,3]=>{{1},{2,3,7},{4,5,6}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[1,2,7,5,6,4,3]=>{{1},{2},{3,7},{4,5,6}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}} [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3]=>{{1},{2},{3,5,7},{4,6}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[7,6,1,2,4,5,3]=>{{1,3,7},{2,4,5,6}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[6,7,1,2,4,5,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[7,1,6,2,4,5,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[1,7,6,2,4,5,3]=>{{1},{2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[1,6,7,2,4,5,3]=>{{1},{2,4,5,6},{3,7}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[7,1,2,6,4,5,3]=>{{1,2,3,7},{4,5,6}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[1,7,2,6,4,5,3]=>{{1},{2,3,7},{4,5,6}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[1,2,7,6,4,5,3]=>{{1},{2},{3,7},{4,5,6}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[1,2,6,7,4,5,3]=>{{1},{2},{3,4,5,6,7}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[7,1,2,4,6,5,3]=>{{1,2,3,7},{4},{5,6}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[1,7,2,4,6,5,3]=>{{1},{2,3,7},{4},{5,6}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[1,2,7,4,6,5,3]=>{{1},{2},{3,7},{4},{5,6}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[1,2,4,7,6,5,3]=>{{1},{2},{3,4,7},{5,6}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}} [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[7,1,2,4,5,6,3]=>{{1,2,3,7},{4},{5},{6}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[1,7,2,4,5,6,3]=>{{1},{2,3,7},{4},{5},{6}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}} [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>{{1,4,7},{2,3,5,6}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>{{1,4,7},{2,5},{3,6}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[5,7,6,1,2,3,4]=>{{1,2,4,5,7},{3,6}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[6,7,1,5,2,3,4]=>{{1,3,6},{2,4,5,7}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>{{1,2,4,5,7},{3,6}} [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>{{1},{2,4,5,7},{3,6}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[1,6,7,5,2,3,4]=>{{1},{2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[7,1,5,6,2,3,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[1,7,5,6,2,3,4]=>{{1},{2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[1,5,7,6,2,3,4]=>{{1},{2,5},{3,4,6,7}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>{{1,2,3,4,6,7},{5}} [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[6,7,1,2,5,3,4]=>{{1,3,6},{2,4,7},{5}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>{{1,2,4,7},{3,6},{5}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>{{1},{2,4,7},{3,6},{5}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[1,6,7,2,5,3,4]=>{{1},{2,3,4,6,7},{5}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>{{1,2,3,4,6,7},{5}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>{{1},{2,3,4,6,7},{5}} [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>{{1},{2},{3,4,6,7},{5}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[7,1,2,5,6,3,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4]=>{{1},{2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[1,2,7,5,6,3,4]=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}} [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[1,2,5,6,7,3,4]=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[6,7,1,2,3,5,4]=>{{1,3,5,6},{2,4,7}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>{{1,2,4,7},{3,5,6}} [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>{{1},{2,4,7},{3,5,6}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4]=>{{1},{2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>{{1},{2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[1,2,6,7,3,5,4]=>{{1},{2},{3,5,6},{4,7}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>{{1,2,3,4,7},{5,6}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>{{1},{2,3,4,7},{5,6}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>{{1},{2},{3,4,7},{5,6}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}} [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4]=>{{1,2,3,4,7},{5},{6}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[1,7,2,3,5,6,4]=>{{1},{2,3,4,7},{5},{6}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[1,2,7,3,5,6,4]=>{{1},{2},{3,4,7},{5},{6}} [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}} [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>{{1,3,5,7},{2,4,6}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>{{1},{2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>{{1},{2,4,6},{3,5,7}} [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>{{1,2,3,5,7},{4,6}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>{{1},{2,3,5,7},{4,6}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>{{1},{2},{3,5,7},{4,6}} [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[1,2,6,7,3,4,5]=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>{{1},{2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>{{1},{2},{3},{4,5,6,7}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>{{1,2,3,4,5,7},{6}} [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>{{1},{2,3,4,5,7},{6}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>{{1},{2},{3,4,5,7},{6}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>{{1},{2},{3},{4,5,7},{6}} [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>{{1},{2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>{{1},{2},{3},{4,5,6,7}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>{{1},{2},{3},{4},{5,6,7}} [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>{{1,8},{2,7},{3,5},{4,6}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>{{1,8},{2,6},{3,7},{4,5}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>{{1,8},{2,5},{3,7},{4,6}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>{{1,8},{2,5},{3,6},{4,7}} [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>{{1,7},{2,8},{3,6},{4,5}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>{{1,7},{2,8},{3,5},{4,6}} [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2]=>{{1,3,5,7},{2,4,6,8}} [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>{{1,7},{2,8},{3},{4},{5},{6}} [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2]=>{{1,3,5,7},{2,4,6,8}} [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[6,8,7,5,4,1,3,2]=>{{1,6},{2,8},{3,7},{4,5}} [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[5,8,7,6,1,4,3,2]=>{{1,5},{2,8},{3,7},{4,6}} [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[5,8,6,7,1,3,4,2]=>{{1,5},{2,8},{3,6},{4,7}} [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>{{1,6},{2,7},{3,8},{4,5}} [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[5,7,8,6,1,4,2,3]=>{{1,5},{2,7},{3,8},{4,6}} [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[5,6,8,7,1,2,4,3]=>{{1,5},{2,6},{3,8},{4,7}} [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4]=>{{1,3,5,7},{2,4,6,8}} [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>{{1,5},{2,6},{3,7},{4,8}} [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6]=>{{1,3,5,7},{2,4,6,8}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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].