Identifier
Mp00023: to non-crossing permutationPermutations
Mp00087: Permutations inverse first fundamental transformationPermutations
Mp00127: Permutations left-to-right-maxima to Dyck pathDyck paths
Mp00138: to noncrossing partition
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-3Cc0009;cc-rep-4
[1,0]=>[1]=>[1]=>[1,0]=>{{1}} [1,0,1,0]=>[1,2]=>[1,2]=>[1,0,1,0]=>{{1},{2}} [1,1,0,0]=>[2,1]=>[2,1]=>[1,1,0,0]=>{{1,2}} [1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[1,0,1,0,1,0]=>{{1},{2},{3}} [1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[1,0,1,1,0,0]=>{{1},{2,3}} [1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[1,1,0,0,1,0]=>{{1,2},{3}} [1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[1,1,1,0,0,0]=>{{1,2,3}} [1,1,1,0,0,0]=>[3,2,1]=>[2,3,1]=>[1,1,0,1,0,0]=>{{1,3},{2}} [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4}} [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}} [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>{{1},{2,3},{4}} [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,2,3]=>[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}} [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>{{1},{2,4},{3}} [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[1,1,0,0,1,0,1,0]=>{{1,2},{3},{4}} [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}} [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[1,1,1,0,0,0,1,0]=>{{1,2,3},{4}} [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[1,1,1,1,0,0,0,0]=>{{1,2,3,4}} [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[3,4,1,2]=>[1,1,1,0,1,0,0,0]=>{{1,2,4},{3}} [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>{{1,3},{2},{4}} [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>{{1,3,4},{2}} [1,1,1,0,1,0,0,0]=>[4,2,3,1]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>{{1,4},{2},{3}} [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>{{1,4},{2,3}} [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5}} [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}} [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}} [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,3,4]=>[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}} [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3,5},{4}} [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5}} [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}} [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}} [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,2,3,4]=>[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}} [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>{{1},{2,3,5},{4}} [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>{{1},{2,4},{3},{5}} [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>{{1},{2,4,5},{3}} [1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>{{1},{2,5},{3},{4}} [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>{{1},{2,5},{3,4}} [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5}} [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5}} [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}} [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,3,4]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}} [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,5},{4}} [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4},{5}} [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,1,2,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}} [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5}} [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}} [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]=>{{1,2,3,5},{4}} [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>{{1,2,4},{3},{5}} [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[3,5,1,2,4]=>[1,1,1,0,1,1,0,0,0,0]=>{{1,2,4,5},{3}} [1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>{{1,2,5},{3},{4}} [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>{{1,2,5},{3,4}} [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>{{1,3},{2},{4},{5}} [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[2,3,1,5,4]=>[1,1,0,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5}} [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[2,4,1,3,5]=>[1,1,0,1,1,0,0,0,1,0]=>{{1,3,4},{2},{5}} [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[2,5,1,3,4]=>[1,1,0,1,1,1,0,0,0,0]=>{{1,3,4,5},{2}} [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>{{1,3,5},{2},{4}} [1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>{{1,4},{2},{3},{5}} [1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>{{1,4,5},{2},{3}} [1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>{{1,5},{2},{3},{4}} [1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>{{1,5},{2},{3,4}} [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>{{1,4},{2,3},{5}} [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[3,2,5,1,4]=>[1,1,1,0,0,1,1,0,0,0]=>{{1,4,5},{2,3}} [1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]=>{{1,5},{2,3},{4}} [1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>{{1,5},{2,3,4}} [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>{{1,5},{2,4},{3}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4,6},{5}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,2,5,6,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3,4,6},{5}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3,5},{4},{6}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3,5,6},{4}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3,6},{4},{5}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,2,5,4,6,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3,6},{4,5}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2,3},{4,6},{5}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2,3,4,6},{5}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,4,5,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2,3,5},{4},{6}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2,3,5,6},{4}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2,3,6},{4},{5}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2,3,6},{4,5}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2,4},{3},{5,6}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2,4,5},{3},{6}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2,4,5,6},{3}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,3,5,6,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2,4,6},{3},{5}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2,5},{3},{4},{6}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2,5,6},{3},{4}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2,6},{3},{4},{5}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>[1,3,5,4,6,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2,6},{3},{4,5}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2,5},{3,4},{6}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,4,3,6,2,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2,5,6},{3,4}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>[1,4,3,5,6,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2,6},{3,4},{5}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2,6},{3,4,5}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,4,5,3,6,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2,6},{3,5},{4}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5,6}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4,6},{5}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}} [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,5,6,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>{{1,2},{3,4,6},{5}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>{{1,2},{3,5},{4},{6}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,4,6,3,5]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>{{1,2},{3,5,6},{4}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>{{1,2},{3,6},{4},{5}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,5,4,6,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[3,1,2,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>{{1,2,3},{4,6},{5}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>{{1,2,3,4,6},{5}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>{{1,2,3,5},{4},{6}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>{{1,2,3,5,6},{4}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>{{1,2,3,6},{4},{5}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>{{1,2,3,6},{4,5}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[3,4,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>{{1,2,4},{3},{5},{6}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[3,4,1,2,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>{{1,2,4},{3},{5,6}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>{{1,2,4,5},{3},{6}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>{{1,2,4,5,6},{3}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>{{1,2,4,6},{3},{5}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>{{1,2,5},{3},{4},{6}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>{{1,2,5,6},{3},{4}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>{{1,2,6},{3},{4},{5}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>{{1,2,6},{3},{4,5}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>{{1,2,5},{3,4},{6}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>{{1,2,5,6},{3,4}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>{{1,2,6},{3,4},{5}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>{{1,2,6},{3,4,5}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>{{1,2,6},{3,5},{4}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5,6}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>{{1,3},{2},{4,5},{6}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[2,3,1,6,4,5]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>{{1,3},{2},{4,5,6}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>{{1,3},{2},{4,6},{5}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[2,4,1,3,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>{{1,3,4},{2},{5},{6}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[2,4,1,3,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>{{1,3,4},{2},{5,6}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>{{1,3,4,5},{2},{6}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>{{1,3,4,6},{2},{5}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[2,4,5,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>{{1,3,5},{2},{4},{6}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>{{1,3,5,6},{2},{4}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>{{1,3,6},{2},{4},{5}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>{{1,3,6},{2},{4,5}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>[2,3,4,1,6,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>{{1,4},{2},{3},{5,6}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>[2,3,5,1,4,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>{{1,4,5},{2},{3},{6}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>[2,3,6,1,4,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2},{3}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>[2,3,5,6,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>{{1,4,6},{2},{3},{5}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>{{1,5},{2},{3},{4},{6}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>{{1,5,6},{2},{3},{4}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>{{1,6},{2},{3},{4},{5}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>{{1,6},{2},{3},{4,5}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>[2,4,3,5,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>{{1,5},{2},{3,4},{6}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>[2,4,3,6,1,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>{{1,5,6},{2},{3,4}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>{{1,6},{2},{3,4},{5}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>{{1,6},{2},{3,4,5}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>{{1,6},{2},{3,5},{4}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>{{1,4},{2,3},{5},{6}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[3,2,4,1,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[3,2,5,1,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>{{1,4,5},{2,3},{6}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2,3}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[3,2,5,6,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>{{1,4,6},{2,3},{5}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>{{1,5},{2,3},{4},{6}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[3,2,4,6,1,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>{{1,5,6},{2,3},{4}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>{{1,6},{2,3},{4},{5}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>{{1,5},{2,3,4},{6}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>[4,2,3,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>{{1,5,6},{2,3,4}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>{{1,6},{2,3,4},{5}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>{{1,6},{2,3,5},{4}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[3,4,2,5,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>{{1,5},{2,4},{3},{6}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[3,4,2,6,1,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>{{1,5,6},{2,4},{3}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>{{1,6},{2,4},{3},{5}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>{{1,6},{2,4,5},{3}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3},{4}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3,4}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7}} [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5,6},{7}} [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,5,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6,7}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4},{5,7},{6}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}} [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,4,5,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{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]=>[1,2,3,6,7,4,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3},{4,5,7},{6}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3},{4,6},{5},{7}} [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,2,3,5,7,4,6]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3},{4,6,7},{5}} [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>[1,2,3,5,6,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3},{4,7},{5},{6}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,2,3,6,5,7,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3},{4,7},{5,6}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7}} [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}} [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,5,6]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{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]=>[1,2,4,3,6,7,5]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2},{3,4},{5,7},{6}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,3,4,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,3,4,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,3,4,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,2,6,7,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2},{3,4,5,7},{6}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,2,5,6,3,4,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2},{3,4,6},{5},{7}} [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,2,5,7,3,4,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2},{3,4,6,7},{5}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>[1,2,5,6,7,3,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2},{3,4,7},{5},{6}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,2,6,5,7,3,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2},{3,4,7},{5,6}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2},{3,5},{4},{6},{7}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2},{3,5},{4},{6,7}} [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,2,4,6,3,5,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2},{3,5,6},{4},{7}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,2,4,7,3,5,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2},{3,5,6,7},{4}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,2,4,6,7,3,5]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2},{3,5,7},{4},{6}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>[1,2,4,5,6,3,7]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2},{3,6},{4},{5},{7}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>[1,2,4,5,7,3,6]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4},{5}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>[1,2,4,5,6,7,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2},{3,7},{4},{5},{6}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>[1,2,4,6,5,7,3]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2},{3,7},{4},{5,6}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,2,5,4,6,3,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2},{3,6},{4,5},{7}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,2,5,4,7,3,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4,5}} [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>[1,2,5,4,6,7,3]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2},{3,7},{4,5},{6}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>[1,2,6,4,5,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2},{3,7},{4,5,6}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,2,5,6,4,7,3]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2},{3,7},{4,6},{5}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}} [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,5,6]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>{{1},{2,3},{4},{5,7},{6}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{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]=>[1,3,2,6,4,5,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}} [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,4,5,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,3,2,6,7,4,5]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>{{1},{2,3},{4,5,7},{6}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>{{1},{2,3},{4,6},{5},{7}} [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,3,2,5,7,4,6]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>{{1},{2,3},{4,6,7},{5}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>[1,3,2,5,6,7,4]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>{{1},{2,3},{4,7},{5},{6}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,3,2,6,5,7,4]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1},{2,3},{4,7},{5,6}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,2,3,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,2,3,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{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]=>[1,4,2,3,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,2,3,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}} [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,4,2,3,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>{{1},{2,3,4},{5,7},{6}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,2,3,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,2,3,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>{{1},{2,3,4,5,7},{6}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,5,6,2,3,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>{{1},{2,3,4,6},{5},{7}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>{{1},{2,3,4,6,7},{5}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>[1,5,6,7,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5},{6}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,6,5,7,2,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5,6}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,4,5,2,3,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>{{1},{2,3,5},{4},{6},{7}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,4,5,2,3,7,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>{{1},{2,3,5},{4},{6,7}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,4,6,2,3,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>{{1},{2,3,5,6},{4},{7}} [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>{{1},{2,3,5,6,7},{4}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,4,6,7,2,3,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>{{1},{2,3,5,7},{4},{6}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>[1,4,5,6,2,3,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4},{5},{7}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>[1,4,5,7,2,3,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4},{5}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>[1,4,5,6,7,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4},{5},{6}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>[1,4,6,5,7,2,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4},{5,6}} [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,5,4,6,2,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4,5},{7}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,5,4,7,2,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4,5}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>[1,5,4,6,7,2,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4,5},{6}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>[1,6,4,5,7,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>{{1},{2,3,7},{4,5,6}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,5,6,4,7,2,3]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4,6},{5}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6},{7}} [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>{{1},{2,4},{3},{5},{6,7}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>{{1},{2,4},{3},{5,6},{7}} [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,5,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>{{1},{2,4},{3},{5,6,7}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>{{1},{2,4},{3},{5,7},{6}} [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,3,5,2,4,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>{{1},{2,4,5},{3},{6},{7}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,3,5,2,4,7,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>{{1},{2,4,5},{3},{6,7}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,3,6,2,4,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>{{1},{2,4,5,6},{3},{7}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,3,6,7,2,4,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>{{1},{2,4,5,7},{3},{6}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,3,5,6,2,4,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>{{1},{2,4,6},{3},{5},{7}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,3,5,7,2,4,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>{{1},{2,4,6,7},{3},{5}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>[1,3,5,6,7,2,4]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>{{1},{2,4,7},{3},{5},{6}} [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,3,6,5,7,2,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>{{1},{2,4,7},{3},{5,6}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>[1,3,4,5,2,6,7]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3},{4},{6},{7}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>[1,3,4,5,2,7,6]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3},{4},{6,7}} [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>[1,3,4,6,2,5,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3},{4},{7}} [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>[1,3,4,7,2,5,6]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3},{4}} [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>[1,3,4,6,7,2,5]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3},{4},{6}} [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>[1,3,4,5,6,2,7]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3},{4},{5},{7}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>[1,3,4,5,7,2,6]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4},{5}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>[1,3,4,5,6,7,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3},{4},{5},{6}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>[1,3,4,6,5,7,2]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3},{4},{5,6}} [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>[1,3,5,4,6,2,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3},{4,5},{7}} [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>[1,3,5,4,7,2,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4,5}} [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>[1,3,5,4,6,7,2]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3},{4,5},{6}} [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>[1,3,6,4,5,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3},{4,5,6}} [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>[1,3,5,6,4,7,2]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3},{4,6},{5}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,4,3,5,2,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3,4},{6},{7}} [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,4,3,5,2,7,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3,4},{6,7}} [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,4,3,6,2,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3,4},{7}} [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,4,3,7,2,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3,4}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,4,3,6,7,2,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3,4},{6}} [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>[1,4,3,5,6,2,7]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3,4},{5},{7}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>[1,4,3,5,7,2,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4},{5}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>[1,4,3,5,6,7,2]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3,4},{5},{6}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>[1,4,3,6,5,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3,4},{5,6}} [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>[1,5,3,4,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>{{1},{2,6},{3,4,5},{7}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>[1,5,3,4,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4,5}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>[1,5,3,4,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>{{1},{2,7},{3,4,5},{6}} [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>[1,6,3,4,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1},{2,7},{3,4,5,6}} [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>[1,5,6,3,4,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>{{1},{2,7},{3,4,6},{5}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,4,5,3,6,2,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3,5},{4},{7}} [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,4,5,3,7,2,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,5},{4}} [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>[1,4,5,3,6,7,2]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3,5},{4},{6}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>[1,4,6,3,5,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3,5,6},{4}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>[1,4,5,6,3,7,2]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4},{5}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,5,4,6,3,7,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4,5}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7}} [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5,6},{7}} [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4},{5,7},{6}} [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7}} [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}} [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,4,5,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{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]=>[2,1,3,7,4,5,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}} [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,3,6,7,4,5]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>{{1,2},{3},{4,5,7},{6}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>{{1,2},{3},{4,6},{5},{7}} [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,3,5,7,4,6]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>{{1,2},{3},{4,6,7},{5}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>[2,1,3,5,6,7,4]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>{{1,2},{3},{4,7},{5},{6}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,3,6,5,7,4]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>{{1,2},{3},{4,7},{5,6}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7}} [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{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]=>[2,1,4,3,7,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,4},{5,7},{6}} [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,3,4,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,3,4,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}} [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}} [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,6,7,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>{{1,2},{3,4,5,7},{6}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,5,6,3,4,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>{{1,2},{3,4,6},{5},{7}} [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,5,7,3,4,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>{{1,2},{3,4,6,7},{5}} [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>[2,1,5,6,7,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>{{1,2},{3,4,7},{5},{6}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,6,5,7,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>{{1,2},{3,4,7},{5,6}} [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>{{1,2},{3,5},{4},{6},{7}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>{{1,2},{3,5},{4},{6,7}} [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,4,6,3,5,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>{{1,2},{3,5,6},{4},{7}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,4,7,3,5,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,5,6,7},{4}} [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,4,6,7,3,5]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>{{1,2},{3,5,7},{4},{6}} [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>[2,1,4,5,6,3,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>{{1,2},{3,6},{4},{5},{7}} [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>[2,1,4,5,7,3,6]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4},{5}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>[2,1,4,5,6,7,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>{{1,2},{3,7},{4},{5},{6}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>[2,1,4,6,5,7,3]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>{{1,2},{3,7},{4},{5,6}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,5,4,6,3,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>{{1,2},{3,6},{4,5},{7}} [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,5,4,7,3,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4,5}} [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>[2,1,5,4,6,7,3]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>{{1,2},{3,7},{4,5},{6}} [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>[2,1,6,4,5,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>{{1,2},{3,7},{4,5,6}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,5,6,4,7,3]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>{{1,2},{3,7},{4,6},{5}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5,6},{7}} [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,1,2,4,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[3,1,2,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>{{1,2,3},{4},{5,7},{6}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{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]=>[3,1,2,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,1,2,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,1,2,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[3,1,2,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>{{1,2,3},{4,5,7},{6}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[3,1,2,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>{{1,2,3},{4,6},{5},{7}} [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[3,1,2,5,7,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>{{1,2,3},{4,6,7},{5}} [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>[3,1,2,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>{{1,2,3},{4,7},{5},{6}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[3,1,2,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,3},{4,7},{5,6}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{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]=>[4,1,2,3,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,1,2,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,1,2,3,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[4,1,2,3,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>{{1,2,3,4},{5,7},{6}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}} [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,7},{6}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>{{1,2,3,4,6},{5},{7}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[5,7,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>{{1,2,3,4,6,7},{5}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5},{6}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[6,5,7,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5,6}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[4,5,1,2,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>{{1,2,3,5},{4},{6},{7}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[4,5,1,2,3,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>{{1,2,3,5},{4},{6,7}} [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>{{1,2,3,5,6},{4},{7}} [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[4,7,1,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,5,6,7},{4}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[4,6,7,1,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>{{1,2,3,5,7},{4},{6}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>[4,5,6,1,2,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4},{5},{7}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>[4,5,7,1,2,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4},{5}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>[4,5,6,7,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5},{6}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>[4,6,5,7,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5,6}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[5,4,6,1,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4,5},{7}} [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[5,4,7,1,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4,5}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>[5,4,6,7,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4,5},{6}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,5,6}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[5,6,4,7,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,6},{5}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[3,4,1,2,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>{{1,2,4},{3},{5},{6},{7}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[3,4,1,2,5,7,6]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>{{1,2,4},{3},{5},{6,7}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[3,4,1,2,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>{{1,2,4},{3},{5,6},{7}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[3,4,1,2,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>{{1,2,4},{3},{5,6,7}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[3,4,1,2,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>{{1,2,4},{3},{5,7},{6}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[3,5,1,2,4,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>{{1,2,4,5},{3},{6},{7}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[3,5,1,2,4,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>{{1,2,4,5},{3},{6,7}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>{{1,2,4,5,6},{3},{7}} [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[3,7,1,2,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,4,5,6,7},{3}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[3,6,7,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>{{1,2,4,5,7},{3},{6}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[3,5,6,1,2,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>{{1,2,4,6},{3},{5},{7}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[3,5,7,1,2,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>{{1,2,4,6,7},{3},{5}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>[3,5,6,7,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5},{6}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[3,6,5,7,1,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5,6}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>[3,4,5,1,2,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3},{4},{6},{7}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>[3,4,5,1,2,7,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3},{4},{6,7}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>[3,4,6,1,2,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3},{4},{7}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>[3,4,7,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3},{4}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>[3,4,6,7,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3},{4},{6}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>[3,4,5,6,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4},{5},{7}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>[3,4,5,7,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4},{5}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>[3,4,5,6,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4},{5},{6}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>[3,4,6,5,7,1,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4},{5,6}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>[3,5,4,6,1,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4,5},{7}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>[3,5,4,7,1,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4,5}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>[3,5,4,6,7,1,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4,5},{6}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>[3,6,4,5,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3},{4,5,6}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>[3,5,6,4,7,1,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4,6},{5}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[4,3,5,1,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3,4},{6},{7}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[4,3,5,1,2,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3,4},{6,7}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[4,3,6,1,2,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3,4},{7}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[4,3,7,1,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3,4}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[4,3,6,7,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3,4},{6}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>[4,3,5,6,1,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3,4},{5},{7}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>[4,3,5,7,1,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4},{5}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>[4,3,5,6,7,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3,4},{5},{6}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>[4,3,6,5,7,1,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3,4},{5,6}} [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>[5,3,4,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,4,5},{7}} [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>[5,3,4,7,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4,5}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>[5,3,4,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,4,5},{6}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>[6,3,4,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,5,6}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>[5,6,3,4,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,6},{5}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[4,5,3,6,1,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,5},{4},{7}} [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[4,5,3,7,1,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,5},{4}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>[4,5,3,6,7,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,5},{4},{6}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>[4,6,3,5,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,5,6},{4}} [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>[4,5,6,3,7,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4},{5}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[5,4,6,3,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4,5}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6},{7}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5},{6,7}} [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>{{1,3},{2},{4},{5,6},{7}} [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,5,6]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>{{1,3},{2},{4},{5,6,7}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>{{1,3},{2},{4},{5,7},{6}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>{{1,3},{2},{4,5},{6},{7}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,3},{2},{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]=>[2,3,1,6,4,5,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>{{1,3},{2},{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]=>[2,3,1,7,4,5,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,3},{2},{4,5,6,7}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[2,3,1,6,7,4,5]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>{{1,3},{2},{4,5,7},{6}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>{{1,3},{2},{4,6},{5},{7}} [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[2,3,1,5,7,4,6]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>{{1,3},{2},{4,6,7},{5}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>[2,3,1,5,6,7,4]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>{{1,3},{2},{4,7},{5},{6}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[2,3,1,6,5,7,4]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,3},{2},{4,7},{5,6}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[2,4,1,3,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>{{1,3,4},{2},{5},{6},{7}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[2,4,1,3,5,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>{{1,3,4},{2},{5},{6,7}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[2,4,1,3,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>{{1,3,4},{2},{5,6},{7}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[2,4,1,3,7,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>{{1,3,4},{2},{5,6,7}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[2,4,1,3,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>{{1,3,4},{2},{5,7},{6}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[2,5,1,3,4,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>{{1,3,4,5},{2},{6},{7}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[2,5,1,3,4,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,3,4,5},{2},{6,7}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>{{1,3,4,5,7},{2},{6}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[2,5,6,1,3,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>{{1,3,4,6},{2},{5},{7}} [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>{{1,3,4,6,7},{2},{5}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>[2,5,6,7,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5},{6}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[2,6,5,7,1,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5,6}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[2,4,5,1,3,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>{{1,3,5},{2},{4},{6},{7}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[2,4,5,1,3,7,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>{{1,3,5},{2},{4},{6,7}} [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[2,4,6,1,3,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>{{1,3,5,6},{2},{4},{7}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[2,4,7,1,3,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>{{1,3,5,6,7},{2},{4}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[2,4,6,7,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>{{1,3,5,7},{2},{4},{6}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>[2,4,5,6,1,3,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4},{5},{7}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>[2,4,5,7,1,3,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4},{5}} [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>[2,4,5,6,7,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4},{5},{6}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>[2,4,6,5,7,1,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4},{5,6}} [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[2,5,4,6,1,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4,5},{7}} [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[2,5,4,7,1,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4,5}} [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>[2,5,4,6,7,1,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4,5},{6}} [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>[2,6,4,5,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>{{1,3,7},{2},{4,5,6}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[2,5,6,4,7,1,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4,6},{5}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>[2,3,4,1,5,6,7]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6},{7}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>[2,3,4,1,5,7,6]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2},{3},{5},{6,7}} [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>[2,3,4,1,6,5,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2},{3},{5,6},{7}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>[2,3,4,1,7,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2},{3},{5,6,7}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>[2,3,4,1,6,7,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2},{3},{5,7},{6}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>[2,3,5,1,4,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2},{3},{6},{7}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>[2,3,5,1,4,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2},{3},{6,7}} [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>[2,3,6,1,4,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2},{3},{7}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>[2,3,7,1,4,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>[2,3,6,7,1,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2},{3},{6}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>[2,3,5,6,1,4,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2},{3},{5},{7}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>[2,3,5,7,1,4,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2},{3},{5}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>[2,3,5,6,7,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2},{3},{5},{6}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>[2,3,6,5,7,1,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2},{3},{5,6}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>[2,3,4,5,1,6,7]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3},{4},{6},{7}} [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>[2,3,4,5,1,7,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3},{4},{6,7}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>[2,3,4,6,1,5,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3},{4},{7}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>[2,3,4,7,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3},{4}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>[2,3,4,6,7,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3},{4},{6}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>[2,3,4,5,6,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3},{4},{5},{7}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[2,3,4,5,7,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4},{5}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3},{4},{5},{6}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>[2,3,4,6,5,7,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3},{4},{5,6}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>[2,3,5,4,6,1,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3},{4,5},{7}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>[2,3,5,4,7,1,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4,5}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>[2,3,5,4,6,7,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3},{4,5},{6}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>[2,3,6,4,5,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3},{4,5,6}} [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>[2,3,5,6,4,7,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3},{4,6},{5}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>[2,4,3,5,1,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3,4},{6},{7}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>[2,4,3,5,1,7,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3,4},{6,7}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>[2,4,3,6,1,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3,4},{7}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>[2,4,3,7,1,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3,4}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>[2,4,3,6,7,1,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3,4},{6}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>[2,4,3,5,6,1,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3,4},{5},{7}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>[2,4,3,5,7,1,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4},{5}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>[2,4,3,5,6,7,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3,4},{5},{6}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>[2,4,3,6,5,7,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3,4},{5,6}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>[2,5,3,4,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2},{3,4,5},{7}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>[2,5,3,4,7,1,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4,5}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>[2,5,3,4,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2},{3,4,5},{6}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>[2,6,3,4,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2},{3,4,5,6}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>[2,5,6,3,4,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2},{3,4,6},{5}} [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>[2,4,5,3,6,1,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3,5},{4},{7}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>[2,4,5,3,7,1,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,5},{4}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>[2,4,5,3,6,7,1]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3,5},{4},{6}} [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>[2,4,6,3,5,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3,5,6},{4}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>[2,4,5,6,3,7,1]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4},{5}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>[2,5,4,6,3,7,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4,5}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[3,2,4,1,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2,3},{5},{6},{7}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[3,2,4,1,5,7,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2,3},{5},{6,7}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[3,2,4,1,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2,3},{5,6},{7}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[3,2,4,1,7,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2,3},{5,6,7}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[3,2,4,1,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2,3},{5,7},{6}} [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[3,2,5,1,4,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2,3},{6},{7}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[3,2,5,1,4,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2,3},{6,7}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[3,2,6,1,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2,3},{7}} [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[3,2,7,1,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[3,2,6,7,1,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2,3},{6}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[3,2,5,6,1,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2,3},{5},{7}} [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[3,2,5,7,1,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2,3},{5}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>[3,2,5,6,7,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2,3},{5},{6}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[3,2,6,5,7,1,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2,3},{5,6}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>[3,2,4,5,1,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2,3},{4},{6},{7}} [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>[3,2,4,5,1,7,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2,3},{4},{6,7}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>[3,2,4,6,1,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3},{4},{7}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>[3,2,4,7,1,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3},{4}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>[3,2,4,6,7,1,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3},{4},{6}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>[3,2,4,5,6,1,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2,3},{4},{5},{7}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[3,2,4,5,7,1,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4},{5}} [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>[3,2,4,5,6,7,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2,3},{4},{5},{6}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>[3,2,4,6,5,7,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2,3},{4},{5,6}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>[3,2,5,4,6,1,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2,3},{4,5},{7}} [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>[3,2,5,4,7,1,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4,5}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>[3,2,5,4,6,7,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2,3},{4,5},{6}} [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>[3,2,6,4,5,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2,3},{4,5,6}} [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>[3,2,5,6,4,7,1]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2,3},{4,6},{5}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>[4,2,3,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,3,4},{6},{7}} [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>[4,2,3,5,1,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,3,4},{6,7}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>[4,2,3,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3,4},{7}} [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>[4,2,3,7,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3,4}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>[4,2,3,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3,4},{6}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>[4,2,3,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,3,4},{5},{7}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[4,2,3,5,7,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3,4},{5}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>[4,2,3,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,3,4},{5},{6}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>[4,2,3,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,3,4},{5,6}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>[5,2,3,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,4,5},{7}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[5,2,3,4,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>[5,2,3,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,4,5},{6}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>[5,6,2,3,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,6},{5}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>[4,5,2,3,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,5},{4},{7}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>[4,5,2,3,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,5},{4}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>[4,5,2,3,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,5},{4},{6}} [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>[4,6,2,3,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,5,6},{4}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>[4,5,6,2,3,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4},{5}} [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>[5,4,6,2,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4,5}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[3,4,2,5,1,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,4},{3},{6},{7}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[3,4,2,5,1,7,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,4},{3},{6,7}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[3,4,2,6,1,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,4},{3},{7}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[3,4,2,7,1,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,4},{3}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[3,4,2,6,7,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,4},{3},{6}} [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>[3,4,2,5,6,1,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,4},{3},{5},{7}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[3,4,2,5,7,1,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,4},{3},{5}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>[3,4,2,5,6,7,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,4},{3},{5},{6}} [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>[3,4,2,6,5,7,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,4},{3},{5,6}} [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>[3,5,2,4,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,4,5},{3},{7}} [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[3,5,2,4,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,4,5},{3}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>[3,5,2,4,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,4,5},{3},{6}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>[3,6,2,4,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,4,5,6},{3}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>[3,5,6,2,4,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,4,6},{3},{5}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>[3,4,5,2,6,1,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3},{4},{7}} [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>[3,4,5,2,7,1,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3},{4}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>[3,4,5,2,6,7,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3},{4},{6}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>[3,4,6,2,5,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3},{4}} [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>[3,4,5,6,2,7,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4},{5}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>[3,5,4,6,2,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4,5}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[4,3,5,2,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3,4},{7}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[4,3,5,2,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3,4}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>[4,3,5,2,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3,4},{6}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>[4,3,6,2,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3,4}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>[4,3,5,6,2,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4},{5}} [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>[5,3,4,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4,5}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[4,5,3,6,2,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,5},{4}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5,6},{7},{8}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5},{6,7},{8}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5,6,7},{8}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>{{1},{2,4},{3},{5,7},{6},{8}} [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[1,3,6,7,5,8,2,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>{{1},{2,4,8},{3},{5,7},{6}} [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}} [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,6,8,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,4},{5,8},{6,7}} [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}} [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}} [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[2,1,5,4,6,3,8,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,2},{3,6},{4,5},{7,8}} [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,8,5,4,7,6,3]=>[2,1,5,4,7,6,8,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,2},{3,8},{4,5},{6,7}} [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[2,1,6,5,7,4,8,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,2},{3,8},{4,7},{5,6}} [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5},{6,7,8}} [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}} [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}} [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>{{1,3},{2},{4},{5},{6,8},{7}} [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>{{1,3,5,7,8},{2},{4},{6}} [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,2,3,1,8,6,7,5]=>[2,3,4,1,6,7,8,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>{{1,4},{2},{3},{5,8},{6},{7}} [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6},{7,8}} [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[3,2,4,1,7,6,8,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,4},{2,3},{5,8},{6,7}} [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,3,2,5,4,1,8,7]=>[3,2,5,4,6,1,8,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,3},{4,5},{7,8}} [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8,3,2,5,4,7,6,1]=>[3,2,5,4,7,6,8,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,3},{4,5},{6,7}} [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>[3,2,6,5,7,4,8,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,3},{4,7},{5,6}} [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[4,3,5,2,6,1,8,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>{{1,6},{2,5},{3,4},{7,8}} [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>[4,3,5,2,7,6,8,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>{{1,8},{2,5},{3,4},{6,7}} [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8,7,4,3,6,5,2,1]=>[4,3,6,5,7,2,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,4},{5,6}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[5,4,6,3,7,2,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>{{1,8},{2,7},{3,6},{4,5}}
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.