Identifier
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-2Cc0009;cc-rep-3
[1,0]=>[1]=>[1,0]=>{{1}} [1,0,1,0]=>[1,2]=>[1,0,1,0]=>{{1},{2}} [1,1,0,0]=>[2,1]=>[1,1,0,0]=>{{1,2}} [1,0,1,0,1,0]=>[1,2,3]=>[1,0,1,0,1,0]=>{{1},{2},{3}} [1,0,1,1,0,0]=>[1,3,2]=>[1,0,1,1,0,0]=>{{1},{2,3}} [1,1,0,0,1,0]=>[2,1,3]=>[1,1,0,0,1,0]=>{{1,2},{3}} [1,1,0,1,0,0]=>[2,3,1]=>[1,1,0,1,0,0]=>{{1,3},{2}} [1,1,1,0,0,0]=>[3,2,1]=>[1,1,1,0,0,0]=>{{1,2,3}} [1,0,1,0,1,0,1,0]=>[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]=>[1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}} [1,0,1,1,0,0,1,0]=>[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]=>[1,0,1,1,0,1,0,0]=>{{1},{2,4},{3}} [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}} [1,1,0,0,1,0,1,0]=>[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]=>[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}} [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>{{1,3},{2},{4}} [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>{{1,4},{2},{3}} [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[1,1,0,1,1,0,0,0]=>{{1,3,4},{2}} [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[1,1,1,0,0,0,1,0]=>{{1,2,3},{4}} [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>{{1,4},{2,3}} [1,1,1,0,1,0,0,0]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]=>{{1,2,3,4}} [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]=>{{1,2,3,4}} [1,0,1,0,1,0,1,0,1,0]=>[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]=>[1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}} [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}} [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3,5},{4}} [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}} [1,0,1,1,0,0,1,0,1,0]=>[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]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}} [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>{{1},{2,4},{3},{5}} [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>{{1},{2,5},{3},{4}} [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,0,1,1,0,1,1,0,0,0]=>{{1},{2,4,5},{3}} [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}} [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>{{1},{2,5},{3,4}} [1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}} [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}} [1,1,0,0,1,0,1,0,1,0]=>[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]=>[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]=>[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]=>[1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,5},{4}} [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}} [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>{{1,3},{2},{4},{5}} [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[1,1,0,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5}} [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>{{1,4},{2},{3},{5}} [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>{{1,5},{2},{3},{4}} [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[1,1,0,1,0,1,1,0,0,0]=>{{1,4,5},{2},{3}} [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>{{1,3,4},{2},{5}} [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>{{1,5},{2},{3,4}} [1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]=>{{1,3,4,5},{2}} [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]=>{{1,3,4,5},{2}} [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4},{5}} [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}} [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>{{1,4},{2,3},{5}} [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]=>{{1,5},{2,3},{4}} [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>{{1,4,5},{2,3}} [1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5}} [1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>{{1,5},{2,3,4}} [1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}} [1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}} [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5}} [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>{{1,5},{2,3,4}} [1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}} [1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}} [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4,6},{5}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[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]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3,5},{4},{6}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3,6},{4},{5}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3,5,6},{4}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3,6},{4,5}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[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]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2,3},{4,6},{5}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2,4},{3},{5,6}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2,5},{3},{4},{6}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2,6},{3},{4},{5}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2,5,6},{3},{4}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2,4,5},{3},{6}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2,6},{3},{4,5}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2,4,5,6},{3}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2,4,5,6},{3}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2,5},{3,4},{6}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2,6},{3,4},{5}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2,5,6},{3,4}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2,6},{3,4,5}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2,6},{3,4,5}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[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]=>[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]=>[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]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4,6},{5}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[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]=>[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]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>{{1,2},{3,5},{4},{6}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>{{1,2},{3,6},{4},{5}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>{{1,2},{3,5,6},{4}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5,6}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>{{1,3},{2},{4,5},{6}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>{{1,3},{2},{4,6},{5}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>{{1,3},{2},{4,5,6}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>{{1,4},{2},{3},{5,6}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>{{1,5},{2},{3},{4},{6}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>{{1,6},{2},{3},{4},{5}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>{{1,5,6},{2},{3},{4}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>{{1,4,5},{2},{3},{6}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>{{1,6},{2},{3},{4,5}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2},{3}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2},{3}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>{{1,3,4},{2},{5},{6}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>{{1,3,4},{2},{5,6}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>{{1,5},{2},{3,4},{6}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>{{1,6},{2},{3,4},{5}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>{{1,5,6},{2},{3,4}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>{{1,3,4,5},{2},{6}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>{{1,6},{2},{3,4,5}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>{{1,3,4,5},{2},{6}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>{{1,6},{2},{3,4,5}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>{{1,2,3},{4,6},{5}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>{{1,4},{2,3},{5},{6}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>{{1,5},{2,3},{4},{6}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>{{1,6},{2,3},{4},{5}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>{{1,5,6},{2,3},{4}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>{{1,4,5},{2,3},{6}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2,3}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2,3}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>{{1,5},{2,3,4},{6}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>{{1,6},{2,3,4},{5}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>{{1,5,6},{2,3,4}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>{{1,5},{2,3,4},{6}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>{{1,6},{2,3,4},{5}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>{{1,5,6},{2,3,4}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{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]=>[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]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{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]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{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]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4},{5,7},{6}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6,7}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[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]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{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]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3},{4,6},{5},{7}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[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}} [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3},{4,6,7},{5}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}} [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[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}} [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[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]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{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]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{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]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2},{3,4},{5,7},{6}} [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[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}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[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}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[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}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[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}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4},{5}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2},{3,5,6},{4},{7}} [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[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}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2},{3,5,6,7},{4}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2},{3,5,6,7},{4}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}} [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[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}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[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}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4,5}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[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}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2},{3,7},{4,5,6}} [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[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]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{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]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{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]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>{{1},{2,3},{4},{5,7},{6}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[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]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{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]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>{{1},{2,3},{4,6},{5},{7}} [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[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}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>{{1},{2,3},{4,6,7},{5}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}} [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[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}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[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}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[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}} [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[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}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[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}} [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>{{1},{2,4},{3},{5,6,7}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[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}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[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}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[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}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[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}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4},{5}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3},{4},{7}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[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}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3},{4}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3},{4}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>{{1},{2,4,5},{3},{6},{7}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>{{1},{2,4,5},{3},{6,7}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[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}} [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[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}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4,5}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>{{1},{2,4,5,6},{3},{7}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[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}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>{{1},{2,4,5,6},{3},{7}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3},{4,5,6}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}} [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}} [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>{{1},{2,3,4},{5,7},{6}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}} [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[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}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[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}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[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}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[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}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4},{5}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3,4},{7}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[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}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3,4}} [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3,4}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}} [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[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}} [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[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}} [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4,5}} [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[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}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1},{2,7},{3,4,5,6}} [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}} [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}} [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>{{1},{2,6},{3,4,5},{7}} [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>{{1},{2,7},{3,4,5},{6}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4,5}} [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1},{2,7},{3,4,5,6}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1},{2,7},{3,4,5,6}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1},{2,7},{3,4,5,6}} [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{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]=>[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]=>[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]=>[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]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4},{5,7},{6}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}} [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[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]=>[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]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>{{1,2},{3},{4,6},{5},{7}} [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[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}} [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>{{1,2},{3},{4,6,7},{5}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4,5,6},{7}} [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[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}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[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]=>[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]=>[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]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,4},{5,7},{6}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}} [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[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}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[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}} [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[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}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[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}} [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4},{5}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>{{1,2},{3,5,6},{4},{7}} [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[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}} [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,5,6,7},{4}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,5,6,7},{4}} [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}} [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[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}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[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}} [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4,5}} [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}} [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[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}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}} [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>{{1,2},{3,7},{4,5,6}} [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{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]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{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]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>{{1,3},{2},{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]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>{{1,3},{2},{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]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>{{1,3},{2},{4},{5,7},{6}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>{{1,3},{2},{4},{5,6,7}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[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}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[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}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[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}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[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}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>{{1,3},{2},{4,6,7},{5}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>{{1,3},{2},{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]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,3},{2},{4,7},{5,6}} [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,3},{2},{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]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,3},{2},{4,5,6,7}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[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}} [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[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}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[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}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[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}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2},{3},{5,6,7}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[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}} [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[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}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[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}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4},{5}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3},{4},{7}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[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}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3},{4}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3},{4}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2},{3},{6},{7}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2},{3},{6,7}} [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[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}} [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[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}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4,5}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2},{3},{7}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[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}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2},{3},{7}} [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3},{4,5,6}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>{{1,3,4},{2},{5},{6},{7}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>{{1,3,4},{2},{5},{6,7}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>{{1,3,4},{2},{5,6},{7}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>{{1,3,4},{2},{5,7},{6}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>{{1,3,4},{2},{5,6,7}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[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}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[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}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[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}} [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[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}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4},{5}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3,4},{7}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[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}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3,4}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3,4}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>{{1,3,4,5},{2},{6},{7}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,3,4,5},{2},{6,7}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[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}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[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}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4,5}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[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}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2},{3,4,5,6}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>{{1,3,4,5},{2},{6},{7}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,3,4,5},{2},{6,7}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2},{3,4,5},{7}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2},{3,4,5},{6}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4,5}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2},{3,4,5,6}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2},{3,4,5,6}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2},{3,4,5,6}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}} [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5,6},{7}} [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>{{1,2,3},{4},{5,7},{6}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}} [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>{{1,2,3},{4,6},{5},{7}} [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>{{1,2,3},{4,7},{5},{6}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>{{1,2,3},{4,6,7},{5}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}} [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,3},{4,7},{5,6}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{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]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2,3},{5},{6},{7}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[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}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[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}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[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}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2,3},{5,6,7}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[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}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[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}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[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}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[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}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4},{5}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3},{4},{7}} [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[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}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3},{4}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3},{4}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2,3},{6},{7}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2,3},{6,7}} [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[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}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[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}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4,5}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2,3},{7}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[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}} [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2,3},{7}} [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2,3},{4,5,6}} [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}} [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>{{1,2,3,4},{5,7},{6}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[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}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[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}} [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[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}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[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}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3,4},{5}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3,4},{7}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[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}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3,4}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3,4}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}} [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[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}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[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}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[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}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,4,5},{7}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,4,5},{6}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>{{1,2,3,4},{5,7},{6}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{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]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,3,4},{6},{7}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,3,4},{6,7}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,3,4},{5},{7}} [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,3,4},{5},{6}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3,4},{5}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3,4},{7}} [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,3,4},{5,6}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3,4}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3,4}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}} [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,4,5},{7}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,4,5},{6}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}} [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,4,5},{7}} [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,4,5},{6}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,4,5},{7}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,4,5},{6}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}} [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{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]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{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]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2},{3},{4,8},{5},{6},{7}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{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]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{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]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>{{1},{2,4},{3},{5,7},{6},{8}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5,6,7},{8}} [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>{{1},{2,7,8},{3,4},{5,6}} [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,5,6,7,8},{3,4}} [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1},{2,7,8},{3,4,5,6}} [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,8,5,4,7,6,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}} [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}} [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]=>[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]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>{{1,2},{3,4},{5,8},{6},{7}} [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>{{1,2},{3,4},{5,7,8},{6}} [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[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}} [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}} [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>{{1,2},{3,6},{4},{5},{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]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>{{1,2},{3,8},{4},{5},{6},{7}} [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,8,6,7,3]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,6,7,8},{4},{5}} [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,5,6},{4},{7,8}} [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[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}} [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[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}} [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}} [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,8,5,4,7,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}} [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}} [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[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}} [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,4},{2},{3},{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]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>{{1,4},{2},{3},{5,8},{6},{7}} [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>{{1,6},{2},{3},{4},{5},{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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,8},{2},{3},{4},{5},{6},{7}} [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,8,5,6,7,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,5,6,7,8},{2},{3},{4}} [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,6,4,5,1,8,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,4,5,6},{2},{3},{7,8}} [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,3,4},{2},{5,6},{7,8}} [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>{{1,3,4},{2},{5,7,8},{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]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1,3,4},{2},{5,8},{6,7}} [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5},{6,7,8}} [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>{{1,2,3},{4,7,8},{5,6}} [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}} [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[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}} [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>{{1,4},{2,3},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[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}} [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>{{1,4,5},{2,3},{6,7,8}} [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[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}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>{{1,6,7},{2,3},{4,5},{8}} [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[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}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,4,5,6,7},{2,3},{8}} [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,2,3,1,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}} [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}} [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,3,2,5,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}} [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>{{1,6,7},{2,3,4,5},{8}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,4,3,6,5,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7},{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]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}} [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7},{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]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}}
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
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.