Identifier
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0009;cc-rep-4
[1,0]=>[1]=>[1]=>[1]=>{{1}} [1,0,1,0]=>[2,1]=>[1,2]=>[1,2]=>{{1},{2}} [1,1,0,0]=>[1,2]=>[2,1]=>[2,1]=>{{1,2}} [1,0,1,0,1,0]=>[3,2,1]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}} [1,0,1,1,0,0]=>[2,3,1]=>[2,1,3]=>[2,1,3]=>{{1,2},{3}} [1,1,0,0,1,0]=>[3,1,2]=>[1,3,2]=>[1,3,2]=>{{1},{2,3}} [1,1,0,1,0,0]=>[2,1,3]=>[2,3,1]=>[3,2,1]=>{{1,3},{2}} [1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>[2,3,1]=>{{1,2,3}} [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}} [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[2,1,3,4]=>[2,1,3,4]=>{{1,2},{3},{4}} [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[1,3,2,4]=>[1,3,2,4]=>{{1},{2,3},{4}} [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[2,3,1,4]=>[3,2,1,4]=>{{1,3},{2},{4}} [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[3,2,1,4]=>[2,3,1,4]=>{{1,2,3},{4}} [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[1,2,4,3]=>[1,2,4,3]=>{{1},{2},{3,4}} [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,1,4,3]=>[2,1,4,3]=>{{1,2},{3,4}} [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[1,3,4,2]=>[1,4,3,2]=>{{1},{2,4},{3}} [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[2,3,4,1]=>[4,2,3,1]=>{{1,4},{2},{3}} [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,2,4,1]=>[4,3,2,1]=>{{1,4},{2,3}} [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[1,4,3,2]=>[1,3,4,2]=>{{1},{2,3,4}} [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[2,4,3,1]=>[3,2,4,1]=>{{1,3,4},{2}} [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[3,4,2,1]=>[2,4,3,1]=>{{1,2,4},{3}} [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4,3,2,1]=>[2,3,4,1]=>{{1,2,3,4}} [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}} [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[2,1,3,4,5]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}} [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}} [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[2,3,1,4,5]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}} [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[3,2,1,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}} [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}} [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[2,1,4,3,5]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}} [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[1,3,4,2,5]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}} [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[2,3,4,1,5]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}} [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[3,2,4,1,5]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}} [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}} [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[2,4,3,1,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}} [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[3,4,2,1,5]=>[2,4,3,1,5]=>{{1,2,4},{3},{5}} [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[4,3,2,1,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}} [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}} [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}} [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[1,3,2,5,4]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}} [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[2,3,1,5,4]=>[3,2,1,5,4]=>{{1,3},{2},{4,5}} [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[3,2,1,5,4]=>[2,3,1,5,4]=>{{1,2,3},{4,5}} [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}} [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[2,1,4,5,3]=>[2,1,5,4,3]=>{{1,2},{3,5},{4}} [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}} [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}} [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[3,2,4,5,1]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}} [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[1,4,3,5,2]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}} [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[2,4,3,5,1]=>[5,2,4,3,1]=>{{1,5},{2},{3,4}} [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[3,4,2,5,1]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}} [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[5,3,4,2,1]=>{{1,5},{2,3,4}} [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}} [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[2,1,5,4,3]=>[2,1,4,5,3]=>{{1,2},{3,4,5}} [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}} [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}} [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[3,2,5,4,1]=>[4,3,2,5,1]=>{{1,4,5},{2,3}} [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}} [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[3,2,5,4,1]=>{{1,3,5},{2},{4}} [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[2,5,3,4,1]=>{{1,2,5},{3},{4}} [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[2,5,4,3,1]=>{{1,2,5},{3,4}} [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[1,3,4,5,2]=>{{1},{2,3,4,5}} [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[3,2,4,5,1]=>{{1,3,4,5},{2}} [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[2,4,3,5,1]=>{{1,2,4,5},{3}} [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[2,3,5,4,1]=>{{1,2,3,5},{4}} [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>{{1,5},{2},{3,4},{6}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>{{1,2,5},{3},{4},{6}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}} [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>{{1,6},{2},{3,4},{5}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>{{1,4,6},{2},{3},{5}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>{{1,3,6},{2},{4},{5}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>{{1,2,6},{3,4},{5}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>{{1,2,6},{3},{4,5}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}} [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}} [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}} [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}} [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>{{1,2,4},{3},{5},{6},{7}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}} [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}} [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}} [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>{{1,2},{3,5},{4},{6},{7}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>{{1},{2,5},{3,4},{6},{7}} [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>{{1,5},{2},{3,4},{6},{7}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}} [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>[3,2,5,4,1,6,7]=>{{1,3,5},{2},{4},{6},{7}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>{{1,2,5},{3},{4},{6},{7}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>{{1,2,5},{3,4},{6},{7}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}} [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>[2,4,3,5,1,6,7]=>{{1,2,4,5},{3},{6},{7}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}} [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}} [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>{{1,4},{2},{3},{5,6},{7}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>{{1,4},{2,3},{5,6},{7}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}} [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>{{1,3,4},{2},{5,6},{7}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[3,4,2,1,6,5,7]=>[2,4,3,1,6,5,7]=>{{1,2,4},{3},{5,6},{7}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>{{1,2},{3},{4,6},{5},{7}} [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>{{1,3},{2},{4,6},{5},{7}} [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>{{1,2},{3,6},{4},{5},{7}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>{{1},{2,6},{3,4},{5},{7}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>{{1,6},{2},{3,4},{5},{7}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>{{1,6},{2,4},{3},{5},{7}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>{{1},{2},{3,6},{4,5},{7}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>{{1,2},{3,6},{4,5},{7}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>{{1},{2,6},{3},{4,5},{7}} [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>{{1,6},{2},{3},{4,5},{7}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>{{1,6},{2,3},{4,5},{7}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>{{1},{2,6},{3,5},{4},{7}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>{{1,6},{2},{3,5},{4},{7}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>{{1,6},{2,5},{3},{4},{7}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}} [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>[1,6,4,5,3,2,7]=>{{1},{2,6},{3,4,5},{7}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>[6,2,4,5,3,1,7]=>{{1,6},{2},{3,4,5},{7}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>[6,4,3,5,2,1,7]=>{{1,6},{2,4,5},{3},{7}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>{{1,6},{2,3,5},{4},{7}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}} [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}} [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}} [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>{{1,2},{3,5,6},{4},{7}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{7}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[3,2,4,6,5,1,7]=>[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[1,4,3,6,5,2,7]=>[1,5,4,3,6,2,7]=>{{1},{2,5,6},{3,4},{7}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[2,4,3,6,5,1,7]=>[5,2,4,3,6,1,7]=>{{1,5,6},{2},{3,4},{7}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[3,4,2,6,5,1,7]=>[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}} [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[4,3,2,6,5,1,7]=>[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[2,1,5,6,4,3,7]=>[2,1,4,6,5,3,7]=>{{1,2},{3,4,6},{5},{7}} [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}} [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>[4,2,3,6,5,1,7]=>{{1,4,6},{2},{3},{5},{7}} [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[3,2,5,6,4,1,7]=>[4,3,2,6,5,1,7]=>{{1,4,6},{2,3},{5},{7}} [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>[3,2,6,4,5,1,7]=>{{1,3,6},{2},{4},{5},{7}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>{{1,2,6},{3},{4},{5},{7}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>{{1,2,6},{3,4},{5},{7}} [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>[1,3,6,5,4,2,7]=>{{1},{2,3,6},{4,5},{7}} [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[2,5,4,6,3,1,7]=>[3,2,6,5,4,1,7]=>{{1,3,6},{2},{4,5},{7}} [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>[2,6,3,5,4,1,7]=>{{1,2,6},{3},{4,5},{7}} [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>{{1,2,6},{3,5},{4},{7}} [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>{{1,2,6},{3,4,5},{7}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}} [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}} [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}} [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[2,3,6,5,4,1,7]=>[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[3,2,6,5,4,1,7]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}} [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>[3,2,5,4,6,1,7]=>{{1,3,5,6},{2},{4},{7}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>[2,5,3,4,6,1,7]=>{{1,2,5,6},{3},{4},{7}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[4,3,6,5,2,1,7]=>[2,5,4,3,6,1,7]=>{{1,2,5,6},{3,4},{7}} [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>[3,2,4,6,5,1,7]=>{{1,3,4,6},{2},{5},{7}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>[2,4,3,6,5,1,7]=>{{1,2,4,6},{3},{5},{7}} [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}} [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>{{1,2,3,6},{4,5},{7}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}} [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>[2,4,3,5,6,1,7]=>{{1,2,4,5,6},{3},{7}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>[2,3,5,4,6,1,7]=>{{1,2,3,5,6},{4},{7}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>{{1,2,3,4,6},{5},{7}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}} [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}} [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}} [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}} [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>{{1,4},{2},{3},{5},{6,7}} [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>{{1,4},{2,3},{5},{6,7}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}} [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]=>{{1,3,4},{2},{5},{6,7}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[3,4,2,1,5,7,6]=>[2,4,3,1,5,7,6]=>{{1,2,4},{3},{5},{6,7}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}} [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}} [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}} [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>{{1,2},{3,5},{4},{6,7}} [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>{{1,5},{2},{3},{4},{6,7}} [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>{{1,5},{2,3},{4},{6,7}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>{{1},{2,5},{3,4},{6,7}} [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>{{1,5},{2},{3,4},{6,7}} [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>{{1,5},{2,4},{3},{6,7}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[4,3,2,5,1,7,6]=>[5,3,4,2,1,7,6]=>{{1,5},{2,3,4},{6,7}} [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}} [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]=>{{1,4,5},{2},{3},{6,7}} [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[3,2,5,4,1,7,6]=>[4,3,2,5,1,7,6]=>{{1,4,5},{2,3},{6,7}} [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[1,4,5,3,2,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}} [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[2,4,5,3,1,7,6]=>[3,2,5,4,1,7,6]=>{{1,3,5},{2},{4},{6,7}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[3,4,5,2,1,7,6]=>[2,5,3,4,1,7,6]=>{{1,2,5},{3},{4},{6,7}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[4,3,5,2,1,7,6]=>[2,5,4,3,1,7,6]=>{{1,2,5},{3,4},{6,7}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}} [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[2,5,4,3,1,7,6]=>[3,2,4,5,1,7,6]=>{{1,3,4,5},{2},{6,7}} [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[3,5,4,2,1,7,6]=>[2,4,3,5,1,7,6]=>{{1,2,4,5},{3},{6,7}} [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[4,5,3,2,1,7,6]=>[2,3,5,4,1,7,6]=>{{1,2,3,5},{4},{6,7}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>{{1,2},{3},{4},{5,7},{6}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}} [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>{{1,3},{2},{4},{5,7},{6}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>{{1,2},{3,4},{5,7},{6}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>{{1,4},{2},{3},{5,7},{6}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>{{1,4},{2,3},{5,7},{6}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}} [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]=>{{1,3,4},{2},{5,7},{6}} [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[3,4,2,1,6,7,5]=>[2,4,3,1,7,6,5]=>{{1,2,4},{3},{5,7},{6}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]=>{{1,2,3,4},{5,7},{6}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}} [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>{{1,2},{3},{4,7},{5},{6}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>{{1,3},{2},{4,7},{5},{6}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}} [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>{{1,2},{3,7},{4},{5},{6}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>{{1},{2,7},{3,4},{5},{6}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>{{1,7},{2},{3,4},{5},{6}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>{{1},{2},{3,7},{4,5},{6}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>{{1,2},{3,7},{4,5},{6}} [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>{{1},{2,7},{3},{4,5},{6}} [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>{{1,7},{2},{3},{4,5},{6}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>{{1,7},{2,3},{4,5},{6}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>{{1},{2,7},{3,5},{4},{6}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>{{1,7},{2},{3,5},{4},{6}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]=>{{1},{2,7},{3,4,5},{6}} [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]=>{{1,7},{2},{3,4,5},{6}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>{{1,7},{2,3,5},{4},{6}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>{{1,2},{3},{4,7},{5,6}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>{{1},{2,3},{4,7},{5,6}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]=>{{1,2,3},{4,7},{5,6}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>{{1},{2},{3,7},{4},{5,6}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>{{1,2},{3,7},{4},{5,6}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>{{1},{2,7},{3},{4},{5,6}} [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>{{1,7},{2},{3},{4},{5,6}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>{{1,7},{2,3},{4},{5,6}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>{{1},{2,7},{3,4},{5,6}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>{{1,7},{2},{3,4},{5,6}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>{{1,7},{2,4},{3},{5,6}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]=>{{1,7},{2,3,4},{5,6}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>{{1},{2},{3,7},{4,6},{5}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>{{1,2},{3,7},{4,6},{5}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>{{1},{2,7},{3},{4,6},{5}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>{{1,7},{2},{3},{4,6},{5}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>{{1,7},{2,3},{4,6},{5}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>{{1},{2,7},{3,6},{4},{5}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>{{1,7},{2},{3,6},{4},{5}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>{{1},{2,7},{3,6},{4,5}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>{{1,7},{2},{3,6},{4,5}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>{{1,7},{2,6},{3},{4,5}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]=>{{1},{2},{3,7},{4,5,6}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]=>{{1,2},{3,7},{4,5,6}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]=>{{1},{2,7},{3},{4,5,6}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]=>{{1,7},{2},{3},{4,5,6}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]=>{{1,7},{2,3},{4,5,6}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>[1,7,5,4,6,3,2]=>{{1},{2,7},{3,5,6},{4}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>[7,2,5,4,6,3,1]=>{{1,7},{2},{3,5,6},{4}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[4,3,6,5,2,7,1]=>[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}} [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>[1,7,4,6,5,3,2]=>{{1},{2,7},{3,4,6},{5}} [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>[7,2,4,6,5,3,1]=>{{1,7},{2},{3,4,6},{5}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>[7,4,3,6,5,2,1]=>{{1,7},{2,4,6},{3},{5}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>{{1,7},{2,3,6},{4},{5}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>{{1,7},{2,3,6},{4,5}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]=>{{1},{2,7},{3,4,5,6}} [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]=>{{1,7},{2},{3,4,5,6}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>[7,3,5,4,6,2,1]=>{{1,7},{2,3,5,6},{4}} [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>{{1,7},{2,3,4,6},{5}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}} [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}} [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}} [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}} [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]=>{{1,4},{2},{3},{5,6,7}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[3,2,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>{{1,4},{2,3},{5,6,7}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}} [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>{{1,3,4},{2},{5,6,7}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[3,4,2,1,7,6,5]=>[2,4,3,1,6,7,5]=>{{1,2,4},{3},{5,6,7}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>{{1,2},{3},{4,6,7},{5}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>{{1,2,3},{4,6,7},{5}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>{{1,2},{3,6,7},{4},{5}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]=>{{1},{2,6,7},{3,4},{5}} [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]=>{{1,6,7},{2},{3,4},{5}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[3,4,2,5,7,6,1]=>[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]=>{{1},{2},{3,6,7},{4,5}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]=>{{1,2},{3,6,7},{4,5}} [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]=>{{1},{2,6,7},{3},{4,5}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]=>{{1,6,7},{2},{3},{4,5}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]=>{{1,6,7},{2,3},{4,5}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[1,4,5,3,7,6,2]=>[1,6,5,4,3,7,2]=>{{1},{2,6,7},{3,5},{4}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>[6,2,5,4,3,7,1]=>{{1,6,7},{2},{3,5},{4}} [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[4,3,5,2,7,6,1]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}} [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]=>{{1},{2,6,7},{3,4,5}} [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]=>{{1,6,7},{2},{3,4,5}} [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[3,5,4,2,7,6,1]=>[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}} [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[4,5,3,2,7,6,1]=>[6,3,5,4,2,7,1]=>{{1,6,7},{2,3,5},{4}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[2,1,3,6,7,5,4]=>[2,1,3,5,7,6,4]=>{{1,2},{3},{4,5,7},{6}} [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[1,3,2,6,7,5,4]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[2,3,1,6,7,5,4]=>[3,2,1,5,7,6,4]=>{{1,3},{2},{4,5,7},{6}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[3,2,1,6,7,5,4]=>[2,3,1,5,7,6,4]=>{{1,2,3},{4,5,7},{6}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[2,1,4,6,7,5,3]=>[2,1,5,4,7,6,3]=>{{1,2},{3,5,7},{4},{6}} [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[5,2,3,4,7,6,1]=>{{1,5,7},{2},{3},{4},{6}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[3,2,4,6,7,5,1]=>[5,3,2,4,7,6,1]=>{{1,5,7},{2,3},{4},{6}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[1,4,3,6,7,5,2]=>[1,5,4,3,7,6,2]=>{{1},{2,5,7},{3,4},{6}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[2,4,3,6,7,5,1]=>[5,2,4,3,7,6,1]=>{{1,5,7},{2},{3,4},{6}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[3,4,2,6,7,5,1]=>[5,4,3,2,7,6,1]=>{{1,5,7},{2,4},{3},{6}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[4,3,2,6,7,5,1]=>[5,3,4,2,7,6,1]=>{{1,5,7},{2,3,4},{6}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}} [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[2,1,5,6,7,4,3]=>[2,1,4,7,5,6,3]=>{{1,2},{3,4,7},{5},{6}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[4,2,3,7,5,6,1]=>{{1,4,7},{2},{3},{5},{6}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[3,2,5,6,7,4,1]=>[4,3,2,7,5,6,1]=>{{1,4,7},{2,3},{5},{6}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[3,2,7,4,5,6,1]=>{{1,3,7},{2},{4},{5},{6}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>{{1,2,7},{3},{4},{5},{6}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>{{1,2,7},{3,4},{5},{6}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>[1,3,7,5,4,6,2]=>{{1},{2,3,7},{4,5},{6}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>[3,2,7,5,4,6,1]=>{{1,3,7},{2},{4,5},{6}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>[2,7,3,5,4,6,1]=>{{1,2,7},{3},{4,5},{6}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>{{1,2,7},{3,5},{4},{6}} [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>{{1,2,7},{3,4,5},{6}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>[1,2,4,7,6,5,3]=>{{1},{2},{3,4,7},{5,6}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[2,1,6,5,7,4,3]=>[2,1,4,7,6,5,3]=>{{1,2},{3,4,7},{5,6}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>[1,4,3,7,6,5,2]=>{{1},{2,4,7},{3},{5,6}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>[4,2,3,7,6,5,1]=>{{1,4,7},{2},{3},{5,6}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[3,2,6,5,7,4,1]=>[4,3,2,7,6,5,1]=>{{1,4,7},{2,3},{5,6}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>[1,3,7,4,6,5,2]=>{{1},{2,3,7},{4},{5,6}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>[3,2,7,4,6,5,1]=>{{1,3,7},{2},{4},{5,6}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>[2,7,3,4,6,5,1]=>{{1,2,7},{3},{4},{5,6}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[4,3,6,5,7,2,1]=>[2,7,4,3,6,5,1]=>{{1,2,7},{3,4},{5,6}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>[1,3,7,6,5,4,2]=>{{1},{2,3,7},{4,6},{5}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>[3,2,7,6,5,4,1]=>{{1,3,7},{2},{4,6},{5}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>[2,7,3,6,5,4,1]=>{{1,2,7},{3},{4,6},{5}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>{{1,2,7},{3,6},{4},{5}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>{{1,2,7},{3,6},{4,5}} [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>[1,3,7,5,6,4,2]=>{{1},{2,3,7},{4,5,6}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>[3,2,7,5,6,4,1]=>{{1,3,7},{2},{4,5,6}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>[2,7,3,5,6,4,1]=>{{1,2,7},{3},{4,5,6}} [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>[2,7,5,4,6,3,1]=>{{1,2,7},{3,5,6},{4}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>{{1,2,7},{3,4,6},{5}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>{{1,2,7},{3,4,5,6}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]=>{{1,3},{2},{4,5,6,7}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}} [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]=>{{1,2},{3,5,6,7},{4}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}} [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]=>{{1},{2,5,6,7},{3,4}} [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]=>{{1,5,6,7},{2},{3,4}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}} [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[2,1,5,7,6,4,3]=>[2,1,4,6,5,7,3]=>{{1,2},{3,4,6,7},{5}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[4,2,3,6,5,7,1]=>{{1,4,6,7},{2},{3},{5}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[3,2,5,7,6,4,1]=>[4,3,2,6,5,7,1]=>{{1,4,6,7},{2,3},{5}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[3,2,6,4,5,7,1]=>{{1,3,6,7},{2},{4},{5}} [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[2,6,3,4,5,7,1]=>{{1,2,6,7},{3},{4},{5}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[4,3,5,7,6,2,1]=>[2,6,4,3,5,7,1]=>{{1,2,6,7},{3,4},{5}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>[1,3,6,5,4,7,2]=>{{1},{2,3,6,7},{4,5}} [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>[3,2,6,5,4,7,1]=>{{1,3,6,7},{2},{4,5}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>[2,6,3,5,4,7,1]=>{{1,2,6,7},{3},{4,5}} [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>[2,6,5,4,3,7,1]=>{{1,2,6,7},{3,5},{4}} [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]=>[2,6,4,5,3,7,1]=>{{1,2,6,7},{3,4,5}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}} [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[2,1,6,7,5,4,3]=>[2,1,4,5,7,6,3]=>{{1,2},{3,4,5,7},{6}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}} [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[4,2,3,5,7,6,1]=>{{1,4,5,7},{2},{3},{6}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[3,2,6,7,5,4,1]=>[4,3,2,5,7,6,1]=>{{1,4,5,7},{2,3},{6}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[3,2,5,4,7,6,1]=>{{1,3,5,7},{2},{4},{6}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[2,5,3,4,7,6,1]=>{{1,2,5,7},{3},{4},{6}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[4,3,6,7,5,2,1]=>[2,5,4,3,7,6,1]=>{{1,2,5,7},{3,4},{6}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[3,2,4,7,5,6,1]=>{{1,3,4,7},{2},{5},{6}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[2,4,3,7,5,6,1]=>{{1,2,4,7},{3},{5},{6}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}} [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>{{1,2,3,7},{4,5},{6}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>[1,3,4,7,6,5,2]=>{{1},{2,3,4,7},{5,6}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>[3,2,4,7,6,5,1]=>{{1,3,4,7},{2},{5,6}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>[2,4,3,7,6,5,1]=>{{1,2,4,7},{3},{5,6}} [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>[2,3,7,4,6,5,1]=>{{1,2,3,7},{4},{5,6}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>{{1,2,3,7},{4,6},{5}} [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}} [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[3,2,5,4,6,7,1]=>{{1,3,5,6,7},{2},{4}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[2,5,3,4,6,7,1]=>{{1,2,5,6,7},{3},{4}} [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>[2,5,4,3,6,7,1]=>{{1,2,5,6,7},{3,4}} [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}} [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[2,4,3,6,5,7,1]=>{{1,2,4,6,7},{3},{5}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[2,3,6,4,5,7,1]=>{{1,2,3,6,7},{4},{5}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>[2,3,6,5,4,7,1]=>{{1,2,3,6,7},{4,5}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}} [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[2,4,3,5,7,6,1]=>{{1,2,4,5,7},{3},{6}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[2,3,5,4,7,6,1]=>{{1,2,3,5,7},{4},{6}} [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[2,4,3,5,6,7,1]=>{{1,2,4,5,6,7},{3}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[2,3,5,4,6,7,1]=>{{1,2,3,5,6,7},{4}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>[2,3,4,6,5,7,1]=>{{1,2,3,4,6,7},{5}} [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>{{1,2},{3},{4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>{{1,3},{2},{4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>{{1,2,3},{4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>{{1,2},{3,4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>{{1,4},{2},{3},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>{{1,4},{2,3},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[2,4,3,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>{{1,3,4},{2},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>{{1,2,4},{3},{5},{6},{7},{8}} [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,2,1]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>{{1,2},{3},{4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>{{1,3},{2},{4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,2,1]=>[3,2,1,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>{{1,2,3},{4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>{{1},{2},{3,5},{4},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,3,2,1]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>{{1,2},{3,5},{4},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>{{1},{2,5},{3},{4},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>{{1,5},{2},{3},{4},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>{{1,5},{2,3},{4},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,2,1]=>[1,4,3,5,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>{{1},{2,5},{3,4},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[2,4,3,5,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>{{1,5},{2},{3,4},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>{{1,5},{2,4},{3},{6},{7},{8}} [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>{{1,5},{2,3,4},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,2,1]=>[2,1,5,4,3,6,7,8]=>[2,1,4,5,3,6,7,8]=>{{1,2},{3,4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[2,3,5,4,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>{{1,4,5},{2},{3},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>[3,2,5,4,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>{{1,4,5},{2,3},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[2,4,5,3,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>{{1,3,5},{2},{4},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>{{1,2,5},{3},{4},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>{{1,2,5},{3,4},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,3,2,1]=>[1,5,4,3,2,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[2,5,4,3,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[3,5,4,2,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>{{1,2,4,5},{3},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>{{1,2,3,5},{4},{6},{7},{8}} [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>{{1,2},{3},{4},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,2,1]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>{{1},{2,3},{4},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>{{1,2},{3,4},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>{{1,4},{2},{3},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>{{1,4},{2,3},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,2,1]=>[2,4,3,1,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>{{1,3,4},{2},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,2,1]=>[3,4,2,1,6,5,7,8]=>[2,4,3,1,6,5,7,8]=>{{1,2,4},{3},{5,6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,2,1]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>{{1},{2},{3},{4,6},{5},{7},{8}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,5,2,1]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>{{1},{2,3},{4,6},{5},{7},{8}} [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>{{1,3},{2},{4,6},{5},{7},{8}} [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>[3,2,1,5,6,4,7,8]=>[2,3,1,6,5,4,7,8]=>{{1,2,3},{4,6},{5},{7},{8}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>{{1},{2},{3,6},{4},{5},{7},{8}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,2,1]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>{{1},{2,6},{3},{4},{5},{7},{8}} [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>{{1,6},{2},{3},{4},{5},{7},{8}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,7,2,1]=>[1,4,3,5,6,2,7,8]=>[1,6,4,3,5,2,7,8]=>{{1},{2,6},{3,4},{5},{7},{8}} [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[3,4,2,5,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>{{1,6},{2,4},{3},{5},{7},{8}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,2,1]=>[1,2,5,4,6,3,7,8]=>[1,2,6,5,4,3,7,8]=>{{1},{2},{3,6},{4,5},{7},{8}} [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,7,2,1]=>[1,3,5,4,6,2,7,8]=>[1,6,3,5,4,2,7,8]=>{{1},{2,6},{3},{4,5},{7},{8}} [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,8,2,1]=>[2,3,5,4,6,1,7,8]=>[6,2,3,5,4,1,7,8]=>{{1,6},{2},{3},{4,5},{7},{8}} [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,2,1]=>[3,2,5,4,6,1,7,8]=>[6,3,2,5,4,1,7,8]=>{{1,6},{2,3},{4,5},{7},{8}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,2,1]=>[1,4,5,3,6,2,7,8]=>[1,6,5,4,3,2,7,8]=>{{1},{2,6},{3,5},{4},{7},{8}} [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]=>{{1,6},{2,5},{3},{4},{7},{8}} [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,2,1]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>{{1,6},{2,5},{3,4},{7},{8}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,7,2,1]=>[1,5,4,3,6,2,7,8]=>[1,6,4,5,3,2,7,8]=>{{1},{2,6},{3,4,5},{7},{8}} [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,2,1]=>[2,5,4,3,6,1,7,8]=>[6,2,4,5,3,1,7,8]=>{{1,6},{2},{3,4,5},{7},{8}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}} [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>[2,3,1,6,5,4,7,8]=>[3,2,1,5,6,4,7,8]=>{{1,3},{2},{4,5,6},{7},{8}} [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[3,2,1,6,5,4,7,8]=>[2,3,1,5,6,4,7,8]=>{{1,2,3},{4,5,6},{7},{8}} [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,2,1]=>[2,3,4,6,5,1,7,8]=>[5,2,3,4,6,1,7,8]=>{{1,5,6},{2},{3},{4},{7},{8}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,7,2,1]=>[1,4,3,6,5,2,7,8]=>[1,5,4,3,6,2,7,8]=>{{1},{2,5,6},{3,4},{7},{8}} [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,2,1]=>[2,4,3,6,5,1,7,8]=>[5,2,4,3,6,1,7,8]=>{{1,5,6},{2},{3,4},{7},{8}} [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,8,2,1]=>[3,4,2,6,5,1,7,8]=>[5,4,3,2,6,1,7,8]=>{{1,5,6},{2,4},{3},{7},{8}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[1,2,5,6,4,3,7,8]=>[1,2,4,6,5,3,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}} [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,2,1]=>[2,1,5,6,4,3,7,8]=>[2,1,4,6,5,3,7,8]=>{{1,2},{3,4,6},{5},{7},{8}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,7,2,1]=>[1,3,5,6,4,2,7,8]=>[1,4,3,6,5,2,7,8]=>{{1},{2,4,6},{3},{5},{7},{8}} [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[3,4,5,6,2,1,7,8]=>[2,6,3,4,5,1,7,8]=>{{1,2,6},{3},{4},{5},{7},{8}} [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,2,1]=>[5,4,3,6,2,1,7,8]=>[2,6,4,5,3,1,7,8]=>{{1,2,6},{3,4,5},{7},{8}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,7,2,1]=>[1,3,6,5,4,2,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}} [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[2,3,6,5,4,1,7,8]=>[4,2,3,5,6,1,7,8]=>{{1,4,5,6},{2},{3},{7},{8}} [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,2,1]=>[3,5,6,4,2,1,7,8]=>[2,4,3,6,5,1,7,8]=>{{1,2,4,6},{3},{5},{7},{8}} [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,2,1]=>[4,5,6,3,2,1,7,8]=>[2,3,6,4,5,1,7,8]=>{{1,2,3,6},{4},{5},{7},{8}} [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,2,1]=>[5,4,6,3,2,1,7,8]=>[2,3,6,5,4,1,7,8]=>{{1,2,3,6},{4,5},{7},{8}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,2,1]=>[1,6,5,4,3,2,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}} [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[5,6,4,3,2,1,7,8]=>[2,3,4,6,5,1,7,8]=>{{1,2,3,4,6},{5},{7},{8}} [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[6,5,4,3,2,1,7,8]=>[2,3,4,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,3,1]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>{{1,2},{3},{4},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>{{1,3},{2},{4},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,3,1]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]=>{{1,2,3},{4},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,3,1]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>{{1},{2},{3,4},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,3,1]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>{{1},{2,4},{3},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>{{1,4},{2},{3},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>{{1,4},{2,3},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,3,1]=>[2,4,3,1,5,7,6,8]=>[3,2,4,1,5,7,6,8]=>{{1,3,4},{2},{5},{6,7},{8}} [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>{{1,2,3,4},{5},{6,7},{8}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}} [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>{{1,3},{2},{4,5},{6,7},{8}} [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>{{1,2,3},{4,5},{6,7},{8}} [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,3,1]=>[3,2,4,5,1,7,6,8]=>[5,3,2,4,1,7,6,8]=>{{1,5},{2,3},{4},{6,7},{8}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[1,4,3,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>{{1},{2,5},{3,4},{6,7},{8}} [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[2,4,3,5,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>{{1,5},{2},{3,4},{6,7},{8}} [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>{{1,5},{2,4},{3},{6,7},{8}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>[1,2,5,4,3,7,6,8]=>[1,2,4,5,3,7,6,8]=>{{1},{2},{3,4,5},{6,7},{8}} [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>[1,3,5,4,2,7,6,8]=>[1,4,3,5,2,7,6,8]=>{{1},{2,4,5},{3},{6,7},{8}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,2,3,1]=>[1,4,5,3,2,7,6,8]=>[1,3,5,4,2,7,6,8]=>{{1},{2,3,5},{4},{6,7},{8}} [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,2,3,1]=>[2,4,5,3,1,7,6,8]=>[3,2,5,4,1,7,6,8]=>{{1,3,5},{2},{4},{6,7},{8}} [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,2,3,1]=>[4,3,5,2,1,7,6,8]=>[2,5,4,3,1,7,6,8]=>{{1,2,5},{3,4},{6,7},{8}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,3,1]=>[1,5,4,3,2,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}} [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,2,3,1]=>[3,5,4,2,1,7,6,8]=>[2,4,3,5,1,7,6,8]=>{{1,2,4,5},{3},{6,7},{8}} [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,2,3,1]=>[4,5,3,2,1,7,6,8]=>[2,3,5,4,1,7,6,8]=>{{1,2,3,5},{4},{6,7},{8}} [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[5,4,3,2,1,7,6,8]=>[2,3,4,5,1,7,6,8]=>{{1,2,3,4,5},{6,7},{8}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>{{1},{2},{3},{4},{5,7},{6},{8}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>{{1},{2,3},{4},{5,7},{6},{8}} [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>{{1,3},{2},{4},{5,7},{6},{8}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>{{1},{2,4},{3},{5,7},{6},{8}} [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>{{1,4},{2},{3},{5,7},{6},{8}} [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>{{1,4},{2,3},{5,7},{6},{8}} [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[4,3,2,1,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>{{1,2,3,4},{5,7},{6},{8}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>{{1},{2},{3},{4,7},{5},{6},{8}} [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>{{1,3},{2},{4,7},{5},{6},{8}} [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,5,1]=>[3,2,1,5,6,7,4,8]=>[2,3,1,7,5,6,4,8]=>{{1,2,3},{4,7},{5},{6},{8}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>{{1},{2,7},{3},{4},{5},{6},{8}} [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>{{1,7},{2},{3},{4},{5},{6},{8}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,2,6,1]=>[1,2,5,4,6,7,3,8]=>[1,2,7,5,4,6,3,8]=>{{1},{2},{3,7},{4,5},{6},{8}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,7,1]=>[1,3,5,4,6,7,2,8]=>[1,7,3,5,4,6,2,8]=>{{1},{2,7},{3},{4,5},{6},{8}} [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,8,1]=>[2,3,5,4,6,7,1,8]=>[7,2,3,5,4,6,1,8]=>{{1,7},{2},{3},{4,5},{6},{8}} [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,8,1]=>[3,2,5,4,6,7,1,8]=>[7,3,2,5,4,6,1,8]=>{{1,7},{2,3},{4,5},{6},{8}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,7,1]=>[1,4,5,3,6,7,2,8]=>[1,7,5,4,3,6,2,8]=>{{1},{2,7},{3,5},{4},{6},{8}} [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,8,1]=>[2,4,5,3,6,7,1,8]=>[7,2,5,4,3,6,1,8]=>{{1,7},{2},{3,5},{4},{6},{8}} [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,8,1]=>[3,4,5,2,6,7,1,8]=>[7,5,3,4,2,6,1,8]=>{{1,7},{2,5},{3},{4},{6},{8}} [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,8,1]=>[4,3,5,2,6,7,1,8]=>[7,5,4,3,2,6,1,8]=>{{1,7},{2,5},{3,4},{6},{8}} [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>[2,5,4,3,6,7,1,8]=>[7,2,4,5,3,6,1,8]=>{{1,7},{2},{3,4,5},{6},{8}} [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,8,1]=>[3,5,4,2,6,7,1,8]=>[7,4,3,5,2,6,1,8]=>{{1,7},{2,4,5},{3},{6},{8}} [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,8,1]=>[4,5,3,2,6,7,1,8]=>[7,3,5,4,2,6,1,8]=>{{1,7},{2,3,5},{4},{6},{8}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[1,2,3,6,5,7,4,8]=>[1,2,3,7,6,5,4,8]=>{{1},{2},{3},{4,7},{5,6},{8}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[1,3,2,6,5,7,4,8]=>[1,3,2,7,6,5,4,8]=>{{1},{2,3},{4,7},{5,6},{8}} [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[2,3,1,6,5,7,4,8]=>[3,2,1,7,6,5,4,8]=>{{1,3},{2},{4,7},{5,6},{8}} [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,8,1]=>[2,3,4,6,5,7,1,8]=>[7,2,3,4,6,5,1,8]=>{{1,7},{2},{3},{4},{5,6},{8}} [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[2,4,3,6,5,7,1,8]=>[7,2,4,3,6,5,1,8]=>{{1,7},{2},{3,4},{5,6},{8}} [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[3,4,2,6,5,7,1,8]=>[7,4,3,2,6,5,1,8]=>{{1,7},{2,4},{3},{5,6},{8}} [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,8,1]=>[4,3,2,6,5,7,1,8]=>[7,3,4,2,6,5,1,8]=>{{1,7},{2,3,4},{5,6},{8}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,2,6,1]=>[1,2,5,6,4,7,3,8]=>[1,2,7,6,5,4,3,8]=>{{1},{2},{3,7},{4,6},{5},{8}} [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>[2,1,5,6,4,7,3,8]=>[2,1,7,6,5,4,3,8]=>{{1,2},{3,7},{4,6},{5},{8}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[1,3,5,6,4,7,2,8]=>[1,7,3,6,5,4,2,8]=>{{1},{2,7},{3},{4,6},{5},{8}} [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,8,1]=>[2,3,5,6,4,7,1,8]=>[7,2,3,6,5,4,1,8]=>{{1,7},{2},{3},{4,6},{5},{8}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,2,7,1]=>[1,4,5,6,3,7,2,8]=>[1,7,6,4,5,3,2,8]=>{{1},{2,7},{3,6},{4},{5},{8}} [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,8,1]=>[2,4,5,6,3,7,1,8]=>[7,2,6,4,5,3,1,8]=>{{1,7},{2},{3,6},{4},{5},{8}} [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>{{1,7},{2,6},{3},{4},{5},{8}} [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,8,1]=>[4,3,5,6,2,7,1,8]=>[7,6,4,3,5,2,1,8]=>{{1,7},{2,6},{3,4},{5},{8}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[1,5,4,6,3,7,2,8]=>[1,7,6,5,4,3,2,8]=>{{1},{2,7},{3,6},{4,5},{8}} [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[2,5,4,6,3,7,1,8]=>[7,2,6,5,4,3,1,8]=>{{1,7},{2},{3,6},{4,5},{8}} [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[3,5,4,6,2,7,1,8]=>[7,6,3,5,4,2,1,8]=>{{1,7},{2,6},{3},{4,5},{8}} [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>{{1,7},{2,6},{3,5},{4},{8}} [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>{{1,7},{2,6},{3,4,5},{8}} [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>[4,3,6,5,2,7,1,8]=>[7,5,4,3,6,2,1,8]=>{{1,7},{2,5,6},{3,4},{8}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,7,1]=>[1,5,6,4,3,7,2,8]=>[1,7,4,6,5,3,2,8]=>{{1},{2,7},{3,4,6},{5},{8}} [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,2,8,1]=>[3,5,6,4,2,7,1,8]=>[7,4,3,6,5,2,1,8]=>{{1,7},{2,4,6},{3},{5},{8}} [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,2,8,1]=>[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]=>{{1,7},{2,3,6},{4,5},{8}} [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,2,8,1]=>[5,6,4,3,2,7,1,8]=>[7,3,4,6,5,2,1,8]=>{{1,7},{2,3,4,6},{5},{8}} [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,1]=>[6,5,4,3,2,7,1,8]=>[7,3,4,5,6,2,1,8]=>{{1,7},{2,3,4,5,6},{8}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}} [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>{{1,2,3},{4},{5,6,7},{8}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[1,2,4,3,7,6,5,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}} [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>[2,1,4,3,7,6,5,8]=>[2,1,4,3,6,7,5,8]=>{{1,2},{3,4},{5,6,7},{8}} [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>[1,3,4,2,7,6,5,8]=>[1,4,3,2,6,7,5,8]=>{{1},{2,4},{3},{5,6,7},{8}} [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>{{1,4},{2,3},{5,6,7},{8}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}} [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>{{1,2,3,4},{5,6,7},{8}} [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,5,1]=>[1,2,3,5,7,6,4,8]=>[1,2,3,6,5,7,4,8]=>{{1},{2},{3},{4,6,7},{5},{8}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,3,5,1]=>[1,3,2,5,7,6,4,8]=>[1,3,2,6,5,7,4,8]=>{{1},{2,3},{4,6,7},{5},{8}} [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[3,2,1,5,7,6,4,8]=>[2,3,1,6,5,7,4,8]=>{{1,2,3},{4,6,7},{5},{8}} [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,8,1]=>[2,3,4,5,7,6,1,8]=>[6,2,3,4,5,7,1,8]=>{{1,6,7},{2},{3},{4},{5},{8}} [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>[3,2,4,5,7,6,1,8]=>[6,3,2,4,5,7,1,8]=>{{1,6,7},{2,3},{4},{5},{8}} [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,8,1]=>[2,3,5,4,7,6,1,8]=>[6,2,3,5,4,7,1,8]=>{{1,6,7},{2},{3},{4,5},{8}} [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[3,2,5,4,7,6,1,8]=>[6,3,2,5,4,7,1,8]=>{{1,6,7},{2,3},{4,5},{8}} [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,8,1]=>[4,3,5,2,7,6,1,8]=>[6,5,4,3,2,7,1,8]=>{{1,6,7},{2,5},{3,4},{8}} [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>[4,5,3,2,7,6,1,8]=>[6,3,5,4,2,7,1,8]=>{{1,6,7},{2,3,5},{4},{8}} [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[5,4,3,2,7,6,1,8]=>[6,3,4,5,2,7,1,8]=>{{1,6,7},{2,3,4,5},{8}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,5,1]=>[1,2,3,6,7,5,4,8]=>[1,2,3,5,7,6,4,8]=>{{1},{2},{3},{4,5,7},{6},{8}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>[1,3,2,6,7,5,4,8]=>[1,3,2,5,7,6,4,8]=>{{1},{2,3},{4,5,7},{6},{8}} [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,4,5,1]=>[2,3,1,6,7,5,4,8]=>[3,2,1,5,7,6,4,8]=>{{1,3},{2},{4,5,7},{6},{8}} [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,8,1]=>[2,3,4,6,7,5,1,8]=>[5,2,3,4,7,6,1,8]=>{{1,5,7},{2},{3},{4},{6},{8}} [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,8,1]=>[3,2,4,6,7,5,1,8]=>[5,3,2,4,7,6,1,8]=>{{1,5,7},{2,3},{4},{6},{8}} [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,8,1]=>[3,4,2,6,7,5,1,8]=>[5,4,3,2,7,6,1,8]=>{{1,5,7},{2,4},{3},{6},{8}} [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,8,1]=>[4,3,2,6,7,5,1,8]=>[5,3,4,2,7,6,1,8]=>{{1,5,7},{2,3,4},{6},{8}} [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,8,1]=>[2,3,5,6,7,4,1,8]=>[4,2,3,7,5,6,1,8]=>{{1,4,7},{2},{3},{5},{6},{8}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,7,1]=>[1,4,5,6,7,3,2,8]=>[1,3,7,4,5,6,2,8]=>{{1},{2,3,7},{4},{5},{6},{8}} [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,8,1]=>[2,4,5,6,7,3,1,8]=>[3,2,7,4,5,6,1,8]=>{{1,3,7},{2},{4},{5},{6},{8}} [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[3,4,5,6,7,2,1,8]=>[2,7,3,4,5,6,1,8]=>{{1,2,7},{3},{4},{5},{6},{8}} [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,8,1]=>[2,5,4,6,7,3,1,8]=>[3,2,7,5,4,6,1,8]=>{{1,3,7},{2},{4,5},{6},{8}} [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,8,1]=>[2,5,6,4,7,3,1,8]=>[3,2,7,6,5,4,1,8]=>{{1,3,7},{2},{4,6},{5},{8}} [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,7,8,1]=>[3,5,6,4,7,2,1,8]=>[2,7,3,6,5,4,1,8]=>{{1,2,7},{3},{4,6},{5},{8}} [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,8,1]=>[5,4,6,3,7,2,1,8]=>[2,7,6,5,4,3,1,8]=>{{1,2,7},{3,6},{4,5},{8}} [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,8,1]=>[5,6,4,3,7,2,1,8]=>[2,7,4,6,5,3,1,8]=>{{1,2,7},{3,4,6},{5},{8}} [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]=>{{1,2,7},{3,4,5,6},{8}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[1,2,3,7,6,5,4,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}} [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[1,3,2,7,6,5,4,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}} [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[3,2,1,7,6,5,4,8]=>[2,3,1,5,6,7,4,8]=>{{1,2,3},{4,5,6,7},{8}} [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,4,6,1]=>[1,2,4,7,6,5,3,8]=>[1,2,5,4,6,7,3,8]=>{{1},{2},{3,5,6,7},{4},{8}} [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,6,1]=>[2,1,4,7,6,5,3,8]=>[2,1,5,4,6,7,3,8]=>{{1,2},{3,5,6,7},{4},{8}} [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[2,3,4,7,6,5,1,8]=>[5,2,3,4,6,7,1,8]=>{{1,5,6,7},{2},{3},{4},{8}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,4,7,1]=>[1,4,3,7,6,5,2,8]=>[1,5,4,3,6,7,2,8]=>{{1},{2,5,6,7},{3,4},{8}} [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,8,1]=>[2,4,3,7,6,5,1,8]=>[5,2,4,3,6,7,1,8]=>{{1,5,6,7},{2},{3,4},{8}} [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,8,1]=>[3,4,2,7,6,5,1,8]=>[5,4,3,2,6,7,1,8]=>{{1,5,6,7},{2,4},{3},{8}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[1,3,5,7,6,4,2,8]=>[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}} [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,8,1]=>[3,2,5,7,6,4,1,8]=>[4,3,2,6,5,7,1,8]=>{{1,4,6,7},{2,3},{5},{8}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,7,1]=>[1,4,5,7,6,3,2,8]=>[1,3,6,4,5,7,2,8]=>{{1},{2,3,6,7},{4},{5},{8}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,6,7,1]=>[1,5,4,7,6,3,2,8]=>[1,3,6,5,4,7,2,8]=>{{1},{2,3,6,7},{4,5},{8}} [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,8,1]=>[2,5,4,7,6,3,1,8]=>[3,2,6,5,4,7,1,8]=>{{1,3,6,7},{2},{4,5},{8}} [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,8,1]=>[3,2,6,7,5,4,1,8]=>[4,3,2,5,7,6,1,8]=>{{1,4,5,7},{2,3},{6},{8}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,6,7,1]=>[1,4,6,7,5,3,2,8]=>[1,3,5,4,7,6,2,8]=>{{1},{2,3,5,7},{4},{6},{8}} [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,8,1]=>[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]=>{{1,3,5,7},{2},{4},{6},{8}} [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,7,8,1]=>[5,4,6,7,3,2,1,8]=>[2,3,7,5,4,6,1,8]=>{{1,2,3,7},{4,5},{6},{8}} [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,8,1]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>{{1,2,3,7},{4,6},{5},{8}} [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,1]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]=>{{1,2,3,7},{4,5,6},{8}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,6,1]=>[1,2,7,6,5,4,3,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}} [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,6,1]=>[2,1,7,6,5,4,3,8]=>[2,1,4,5,6,7,3,8]=>{{1,2},{3,4,5,6,7},{8}} [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,8,1]=>[2,3,7,6,5,4,1,8]=>[4,2,3,5,6,7,1,8]=>{{1,4,5,6,7},{2},{3},{8}} [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>[3,2,7,6,5,4,1,8]=>[4,3,2,5,6,7,1,8]=>{{1,4,5,6,7},{2,3},{8}} [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>[3,4,7,6,5,2,1,8]=>[2,5,3,4,6,7,1,8]=>{{1,2,5,6,7},{3},{4},{8}} [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,7,8,1]=>[4,3,7,6,5,2,1,8]=>[2,5,4,3,6,7,1,8]=>{{1,2,5,6,7},{3,4},{8}} [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,8,1]=>[3,5,7,6,4,2,1,8]=>[2,4,3,6,5,7,1,8]=>{{1,2,4,6,7},{3},{5},{8}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,7,1]=>[1,6,7,5,4,3,2,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}} [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}} [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>{{1,2,3,4,7},{5,6},{8}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}} [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,8,1]=>[2,7,6,5,4,3,1,8]=>[3,2,4,5,6,7,1,8]=>{{1,3,4,5,6,7},{2},{8}} [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[4,7,6,5,3,2,1,8]=>[2,3,5,4,6,7,1,8]=>{{1,2,3,5,6,7},{4},{8}} [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,8,1]=>[5,7,6,4,3,2,1,8]=>[2,3,4,6,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}} [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[6,7,5,4,3,2,1,8]=>[2,3,4,5,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}} [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>{{1,2},{3},{4},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,1,2]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>{{1},{2,3},{4},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,1,2]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>{{1,3},{2},{4},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]=>{{1,2,3},{4},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>{{1,2},{3,4},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,1,2]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>{{1},{2,4},{3},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>{{1,4},{2,3},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,1,2]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,1,2]=>[2,4,3,1,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>{{1,3,4},{2},{5},{6},{7,8}} [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>{{1,2,3,4},{5},{6},{7,8}} [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,1,2]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>{{1},{2},{3},{4,5},{6},{7,8}} [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>{{1,2},{3},{4,5},{6},{7,8}} [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>{{1},{2},{3,5},{4},{6},{7,8}} [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,3,1,2]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>{{1,2},{3,5},{4},{6},{7,8}} [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,1,2]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>{{1,5},{2},{3},{4},{6},{7,8}} [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,1,2]=>[3,2,4,5,1,6,8,7]=>[5,3,2,4,1,6,8,7]=>{{1,5},{2,3},{4},{6},{7,8}} [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,1,2]=>[2,4,3,5,1,6,8,7]=>[5,2,4,3,1,6,8,7]=>{{1,5},{2},{3,4},{6},{7,8}} [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>[3,4,2,5,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>{{1,5},{2,4},{3},{6},{7,8}} [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,1,2]=>[4,3,2,5,1,6,8,7]=>[5,3,4,2,1,6,8,7]=>{{1,5},{2,3,4},{6},{7,8}} [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>{{1,2},{3,4,5},{6},{7,8}} [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[2,3,5,4,1,6,8,7]=>[4,2,3,5,1,6,8,7]=>{{1,4,5},{2},{3},{6},{7,8}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,1,2]=>[1,4,5,3,2,6,8,7]=>[1,3,5,4,2,6,8,7]=>{{1},{2,3,5},{4},{6},{7,8}} [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,1,2]=>[2,4,5,3,1,6,8,7]=>[3,2,5,4,1,6,8,7]=>{{1,3,5},{2},{4},{6},{7,8}} [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>[4,3,5,2,1,6,8,7]=>[2,5,4,3,1,6,8,7]=>{{1,2,5},{3,4},{6},{7,8}} [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,1,2]=>[4,5,3,2,1,6,8,7]=>[2,3,5,4,1,6,8,7]=>{{1,2,3,5},{4},{6},{7,8}} [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[5,4,3,2,1,6,8,7]=>[2,3,4,5,1,6,8,7]=>{{1,2,3,4,5},{6},{7,8}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>{{1},{2},{3},{4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>{{1,2},{3},{4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,1,2]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>{{1},{2,3},{4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[3,2,1,4,6,5,8,7]=>[2,3,1,4,6,5,8,7]=>{{1,2,3},{4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>{{1},{2},{3,4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>{{1,4},{2},{3},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>{{1,4},{2,3},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[1,4,3,2,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}} [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}} [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,1,2]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>{{1},{2},{3},{4,6},{5},{7,8}} [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,1,2]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>{{1,2},{3},{4,6},{5},{7,8}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,5,1,2]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>{{1},{2,3},{4,6},{5},{7,8}} [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,1,2]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]=>{{1,3},{2},{4,6},{5},{7,8}} [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,1,2]=>[3,2,1,5,6,4,8,7]=>[2,3,1,6,5,4,8,7]=>{{1,2,3},{4,6},{5},{7,8}} [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>{{1,2},{3,6},{4},{5},{7,8}} [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>{{1,6},{2},{3},{4},{5},{7,8}} [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,1,2]=>[2,4,3,5,6,1,8,7]=>[6,2,4,3,5,1,8,7]=>{{1,6},{2},{3,4},{5},{7,8}} [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,1,2]=>[3,4,2,5,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>{{1,6},{2,4},{3},{5},{7,8}} [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>[4,3,2,5,6,1,8,7]=>[6,3,4,2,5,1,8,7]=>{{1,6},{2,3,4},{5},{7,8}} [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>{{1,2},{3,6},{4,5},{7,8}} [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>{{1,6},{2,3},{4,5},{7,8}} [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,1,2]=>[2,4,5,3,6,1,8,7]=>[6,2,5,4,3,1,8,7]=>{{1,6},{2},{3,5},{4},{7,8}} [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>[3,4,5,2,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>{{1,6},{2,5},{3},{4},{7,8}} [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>{{1,6},{2,5},{3,4},{7,8}} [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,1,2]=>[3,5,4,2,6,1,8,7]=>[6,4,3,5,2,1,8,7]=>{{1,6},{2,4,5},{3},{7,8}} [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,1,2]=>[4,5,3,2,6,1,8,7]=>[6,3,5,4,2,1,8,7]=>{{1,6},{2,3,5},{4},{7,8}} [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>[5,4,3,2,6,1,8,7]=>[6,3,4,5,2,1,8,7]=>{{1,6},{2,3,4,5},{7,8}} [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}} [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]=>{{1,2},{3},{4,5,6},{7,8}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,1,2]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]=>{{1},{2,3},{4,5,6},{7,8}} [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[2,1,4,6,5,3,8,7]=>[2,1,5,4,6,3,8,7]=>{{1,2},{3,5,6},{4},{7,8}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,7,1,2]=>[1,3,4,6,5,2,8,7]=>[1,5,3,4,6,2,8,7]=>{{1},{2,5,6},{3},{4},{7,8}} [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,1,2]=>[2,3,4,6,5,1,8,7]=>[5,2,3,4,6,1,8,7]=>{{1,5,6},{2},{3},{4},{7,8}} [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,8,1,2]=>[3,2,4,6,5,1,8,7]=>[5,3,2,4,6,1,8,7]=>{{1,5,6},{2,3},{4},{7,8}} [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,1,2]=>[2,4,3,6,5,1,8,7]=>[5,2,4,3,6,1,8,7]=>{{1,5,6},{2},{3,4},{7,8}} [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,8,1,2]=>[3,4,2,6,5,1,8,7]=>[5,4,3,2,6,1,8,7]=>{{1,5,6},{2,4},{3},{7,8}} [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,8,1,2]=>[4,3,2,6,5,1,8,7]=>[5,3,4,2,6,1,8,7]=>{{1,5,6},{2,3,4},{7,8}} [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>{{1,2},{3,4,6},{5},{7,8}} [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,8,1,2]=>[3,2,5,6,4,1,8,7]=>[4,3,2,6,5,1,8,7]=>{{1,4,6},{2,3},{5},{7,8}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,1,2]=>[1,4,5,6,3,2,8,7]=>[1,3,6,4,5,2,8,7]=>{{1},{2,3,6},{4},{5},{7,8}} [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,1,2]=>[2,4,5,6,3,1,8,7]=>[3,2,6,4,5,1,8,7]=>{{1,3,6},{2},{4},{5},{7,8}} [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,1,2]=>[4,3,5,6,2,1,8,7]=>[2,6,4,3,5,1,8,7]=>{{1,2,6},{3,4},{5},{7,8}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,7,1,2]=>[1,5,4,6,3,2,8,7]=>[1,3,6,5,4,2,8,7]=>{{1},{2,3,6},{4,5},{7,8}} [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,8,1,2]=>[3,5,4,6,2,1,8,7]=>[2,6,3,5,4,1,8,7]=>{{1,2,6},{3},{4,5},{7,8}} [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[4,5,3,6,2,1,8,7]=>[2,6,5,4,3,1,8,7]=>{{1,2,6},{3,5},{4},{7,8}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,1,2]=>[1,2,6,5,4,3,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}} [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]=>{{1,2},{3,4,5,6},{7,8}} [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>[2,3,6,5,4,1,8,7]=>[4,2,3,5,6,1,8,7]=>{{1,4,5,6},{2},{3},{7,8}} [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,8,1,2]=>[3,2,6,5,4,1,8,7]=>[4,3,2,5,6,1,8,7]=>{{1,4,5,6},{2,3},{7,8}} [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>[2,4,6,5,3,1,8,7]=>[3,2,5,4,6,1,8,7]=>{{1,3,5,6},{2},{4},{7,8}} [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[4,3,6,5,2,1,8,7]=>[2,5,4,3,6,1,8,7]=>{{1,2,5,6},{3,4},{7,8}} [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[3,5,6,4,2,1,8,7]=>[2,4,3,6,5,1,8,7]=>{{1,2,4,6},{3},{5},{7,8}} [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]=>{{1,2,3,6},{4},{5},{7,8}} [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[5,4,6,3,2,1,8,7]=>[2,3,6,5,4,1,8,7]=>{{1,2,3,6},{4,5},{7,8}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}} [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[3,6,5,4,2,1,8,7]=>[2,4,3,5,6,1,8,7]=>{{1,2,4,5,6},{3},{7,8}} [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[6,5,4,3,2,1,8,7]=>[2,3,4,5,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,1,3]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>{{1,2},{3},{4},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,1,3]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>{{1},{2,3},{4},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>{{1,3},{2},{4},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>{{1},{2},{3,4},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>{{1,2},{3,4},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,1,3]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>{{1},{2,4},{3},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>{{1,4},{2},{3},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>{{1,4},{2,3},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>[2,4,3,1,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>{{1,3,4},{2},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>[3,4,2,1,5,7,8,6]=>[2,4,3,1,5,8,7,6]=>{{1,2,4},{3},{5},{6,8},{7}} [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[4,3,2,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>{{1,2,3,4},{5},{6,8},{7}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,1,3]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>{{1},{2},{3},{4,5},{6,8},{7}} [1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,2,1,3]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>{{1,2},{3},{4,5},{6,8},{7}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,1,3]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>{{1},{2,3},{4,5},{6,8},{7}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,1,3]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>{{1},{2},{3,5},{4},{6,8},{7}} [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,2,1,3]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]=>{{1,2},{3,5},{4},{6,8},{7}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,1,3]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>{{1},{2,5},{3},{4},{6,8},{7}} [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,1,3]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>{{1,5},{2},{3},{4},{6,8},{7}} [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,1,3]=>[3,2,4,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>{{1,5},{2,3},{4},{6,8},{7}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,1,3]=>[1,4,3,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>{{1},{2,5},{3,4},{6,8},{7}} [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,1,3]=>[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>{{1,5},{2},{3,4},{6,8},{7}} [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,1,3]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>{{1,5},{2,4},{3},{6,8},{7}} [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,2,1,3]=>[4,3,2,5,1,7,8,6]=>[5,3,4,2,1,8,7,6]=>{{1,5},{2,3,4},{6,8},{7}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,1,3]=>[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,7,6]=>{{1},{2},{3,4,5},{6,8},{7}} [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,1,3]=>[2,1,5,4,3,7,8,6]=>[2,1,4,5,3,8,7,6]=>{{1,2},{3,4,5},{6,8},{7}} [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,1,3]=>[2,3,5,4,1,7,8,6]=>[4,2,3,5,1,8,7,6]=>{{1,4,5},{2},{3},{6,8},{7}} [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,2,1,3]=>[3,2,5,4,1,7,8,6]=>[4,3,2,5,1,8,7,6]=>{{1,4,5},{2,3},{6,8},{7}} [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,2,1,3]=>[2,4,5,3,1,7,8,6]=>[3,2,5,4,1,8,7,6]=>{{1,3,5},{2},{4},{6,8},{7}} [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,2,1,3]=>[3,4,5,2,1,7,8,6]=>[2,5,3,4,1,8,7,6]=>{{1,2,5},{3},{4},{6,8},{7}} [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,2,1,3]=>[4,3,5,2,1,7,8,6]=>[2,5,4,3,1,8,7,6]=>{{1,2,5},{3,4},{6,8},{7}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,1,3]=>[1,5,4,3,2,7,8,6]=>[1,3,4,5,2,8,7,6]=>{{1},{2,3,4,5},{6,8},{7}} [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,2,1,3]=>[2,5,4,3,1,7,8,6]=>[3,2,4,5,1,8,7,6]=>{{1,3,4,5},{2},{6,8},{7}} [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,2,1,3]=>[3,5,4,2,1,7,8,6]=>[2,4,3,5,1,8,7,6]=>{{1,2,4,5},{3},{6,8},{7}} [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,2,1,3]=>[4,5,3,2,1,7,8,6]=>[2,3,5,4,1,8,7,6]=>{{1,2,3,5},{4},{6,8},{7}} [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[5,4,3,2,1,7,8,6]=>[2,3,4,5,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>{{1},{2},{3},{4},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>{{1,2},{3},{4},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>{{1},{2,3},{4},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>{{1,3},{2},{4},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>{{1},{2},{3,4},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>{{1,2},{3,4},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>{{1},{2,4},{3},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>{{1,4},{2},{3},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>{{1,4},{2,3},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>{{1},{2,3,4},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>{{1,3,4},{2},{5,8},{6},{7}} [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[4,3,2,1,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>{{1,2,3,4},{5,8},{6},{7}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]=>{{1,2},{3},{4,8},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>{{1,3},{2},{4,8},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[3,2,1,5,6,7,8,4]=>[2,3,1,8,5,6,7,4]=>{{1,2,3},{4,8},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>{{1},{2},{3,8},{4},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>{{1,2},{3,8},{4},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>{{1},{2,8},{3},{4},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>{{1,8},{2},{3},{4},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>{{1,8},{2,3},{4},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[1,4,3,5,6,7,8,2]=>[1,8,4,3,5,6,7,2]=>{{1},{2,8},{3,4},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>{{1,8},{2,4},{3},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[4,3,2,5,6,7,8,1]=>[8,3,4,2,5,6,7,1]=>{{1,8},{2,3,4},{5},{6},{7}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,2,1,6]=>[1,2,5,4,6,7,8,3]=>[1,2,8,5,4,6,7,3]=>{{1},{2},{3,8},{4,5},{6},{7}} [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,2,1,6]=>[2,1,5,4,6,7,8,3]=>[2,1,8,5,4,6,7,3]=>{{1,2},{3,8},{4,5},{6},{7}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,1,7]=>[1,3,5,4,6,7,8,2]=>[1,8,3,5,4,6,7,2]=>{{1},{2,8},{3},{4,5},{6},{7}} [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[2,3,5,4,6,7,8,1]=>[8,2,3,5,4,6,7,1]=>{{1,8},{2},{3},{4,5},{6},{7}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,1,7]=>[1,4,5,3,6,7,8,2]=>[1,8,5,4,3,6,7,2]=>{{1},{2,8},{3,5},{4},{6},{7}} [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,1,8]=>[2,4,5,3,6,7,8,1]=>[8,2,5,4,3,6,7,1]=>{{1,8},{2},{3,5},{4},{6},{7}} [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>{{1,8},{2,5},{3},{4},{6},{7}} [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>{{1,8},{2,5},{3,4},{6},{7}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[1,5,4,3,6,7,8,2]=>[1,8,4,5,3,6,7,2]=>{{1},{2,8},{3,4,5},{6},{7}} [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1,8]=>[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>{{1,8},{2,3,5},{4},{6},{7}} [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>[5,4,3,2,6,7,8,1]=>[8,3,4,5,2,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>{{1},{2},{3},{4,8},{5,6},{7}} [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,1,5]=>[2,1,3,6,5,7,8,4]=>[2,1,3,8,6,5,7,4]=>{{1,2},{3},{4,8},{5,6},{7}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,1,5]=>[1,3,2,6,5,7,8,4]=>[1,3,2,8,6,5,7,4]=>{{1},{2,3},{4,8},{5,6},{7}} [1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,1,5]=>[2,3,1,6,5,7,8,4]=>[3,2,1,8,6,5,7,4]=>{{1,3},{2},{4,8},{5,6},{7}} [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,1,6]=>[2,1,4,6,5,7,8,3]=>[2,1,8,4,6,5,7,3]=>{{1,2},{3,8},{4},{5,6},{7}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[1,4,3,6,5,7,8,2]=>[1,8,4,3,6,5,7,2]=>{{1},{2,8},{3,4},{5,6},{7}} [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[2,4,3,6,5,7,8,1]=>[8,2,4,3,6,5,7,1]=>{{1,8},{2},{3,4},{5,6},{7}} [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,1,8]=>[3,4,2,6,5,7,8,1]=>[8,4,3,2,6,5,7,1]=>{{1,8},{2,4},{3},{5,6},{7}} [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>[4,3,2,6,5,7,8,1]=>[8,3,4,2,6,5,7,1]=>{{1,8},{2,3,4},{5,6},{7}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,2,1,6]=>[1,2,5,6,4,7,8,3]=>[1,2,8,6,5,4,7,3]=>{{1},{2},{3,8},{4,6},{5},{7}} [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,1,6]=>[2,1,5,6,4,7,8,3]=>[2,1,8,6,5,4,7,3]=>{{1,2},{3,8},{4,6},{5},{7}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,1,7]=>[1,3,5,6,4,7,8,2]=>[1,8,3,6,5,4,7,2]=>{{1},{2,8},{3},{4,6},{5},{7}} [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,1,8]=>[2,3,5,6,4,7,8,1]=>[8,2,3,6,5,4,7,1]=>{{1,8},{2},{3},{4,6},{5},{7}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,2,1,7]=>[1,4,5,6,3,7,8,2]=>[1,8,6,4,5,3,7,2]=>{{1},{2,8},{3,6},{4},{5},{7}} [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,1,8]=>[2,4,5,6,3,7,8,1]=>[8,2,6,4,5,3,7,1]=>{{1,8},{2},{3,6},{4},{5},{7}} [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>{{1,8},{2,6},{3},{4},{5},{7}} [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,1,8]=>[4,3,5,6,2,7,8,1]=>[8,6,4,3,5,2,7,1]=>{{1,8},{2,6},{3,4},{5},{7}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>[1,5,4,6,3,7,8,2]=>[1,8,6,5,4,3,7,2]=>{{1},{2,8},{3,6},{4,5},{7}} [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,1,8]=>[2,5,4,6,3,7,8,1]=>[8,2,6,5,4,3,7,1]=>{{1,8},{2},{3,6},{4,5},{7}} [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,1,8]=>[3,5,4,6,2,7,8,1]=>[8,6,3,5,4,2,7,1]=>{{1,8},{2,6},{3},{4,5},{7}} [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>[4,5,3,6,2,7,8,1]=>[8,6,5,4,3,2,7,1]=>{{1,8},{2,6},{3,5},{4},{7}} [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,1,8]=>[5,4,3,6,2,7,8,1]=>[8,6,4,5,3,2,7,1]=>{{1,8},{2,6},{3,4,5},{7}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[1,2,6,5,4,7,8,3]=>[1,2,8,5,6,4,7,3]=>{{1},{2},{3,8},{4,5,6},{7}} [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>[2,1,6,5,4,7,8,3]=>[2,1,8,5,6,4,7,3]=>{{1,2},{3,8},{4,5,6},{7}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,2,1,7]=>[1,4,6,5,3,7,8,2]=>[1,8,5,4,6,3,7,2]=>{{1},{2,8},{3,5,6},{4},{7}} [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,1,8]=>[4,3,6,5,2,7,8,1]=>[8,5,4,3,6,2,7,1]=>{{1,8},{2,5,6},{3,4},{7}} [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>[4,5,6,3,2,7,8,1]=>[8,3,6,4,5,2,7,1]=>{{1,8},{2,3,6},{4},{5},{7}} [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,2,1,8]=>[5,4,6,3,2,7,8,1]=>[8,3,6,5,4,2,7,1]=>{{1,8},{2,3,6},{4,5},{7}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[1,6,5,4,3,7,8,2]=>[1,8,4,5,6,3,7,2]=>{{1},{2,8},{3,4,5,6},{7}} [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,1,8]=>[3,6,5,4,2,7,8,1]=>[8,4,3,5,6,2,7,1]=>{{1,8},{2,4,5,6},{3},{7}} [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8]=>[6,5,4,3,2,7,8,1]=>[8,3,4,5,6,2,7,1]=>{{1,8},{2,3,4,5,6},{7}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>{{1},{2},{3},{4},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>{{1,2},{3},{4},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>{{1},{2,3},{4},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>{{1,3},{2},{4},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>{{1},{2},{3,4},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>{{1,2},{3,4},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>{{1},{2,4},{3},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>{{1,4},{2},{3},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>{{1,4},{2,3},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,1,4]=>[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]=>{{1},{2,3,4},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]=>{{1,3,4},{2},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]=>{{1,2,4},{3},{5,8},{6,7}} [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[4,3,2,1,7,6,8,5]=>[2,3,4,1,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>{{1},{2},{3},{4,8},{5},{6,7}} [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,3,1,5]=>[2,1,3,5,7,6,8,4]=>[2,1,3,8,5,7,6,4]=>{{1,2},{3},{4,8},{5},{6,7}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,3,1,5]=>[1,3,2,5,7,6,8,4]=>[1,3,2,8,5,7,6,4]=>{{1},{2,3},{4,8},{5},{6,7}} [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>[2,3,1,5,7,6,8,4]=>[3,2,1,8,5,7,6,4]=>{{1,3},{2},{4,8},{5},{6,7}} [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,3,1,6]=>[2,1,4,5,7,6,8,3]=>[2,1,8,4,5,7,6,3]=>{{1,2},{3,8},{4},{5},{6,7}} [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,1,8]=>[2,3,4,5,7,6,8,1]=>[8,2,3,4,5,7,6,1]=>{{1,8},{2},{3},{4},{5},{6,7}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,1,7]=>[1,4,3,5,7,6,8,2]=>[1,8,4,3,5,7,6,2]=>{{1},{2,8},{3,4},{5},{6,7}} [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,1,8]=>[3,4,2,5,7,6,8,1]=>[8,4,3,2,5,7,6,1]=>{{1,8},{2,4},{3},{5},{6,7}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[1,2,5,4,7,6,8,3]=>[1,2,8,5,4,7,6,3]=>{{1},{2},{3,8},{4,5},{6,7}} [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>{{1,2},{3,8},{4,5},{6,7}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,3,1,7]=>[1,3,5,4,7,6,8,2]=>[1,8,3,5,4,7,6,2]=>{{1},{2,8},{3},{4,5},{6,7}} [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[2,3,5,4,7,6,8,1]=>[8,2,3,5,4,7,6,1]=>{{1,8},{2},{3},{4,5},{6,7}} [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>{{1,8},{2,3},{4,5},{6,7}} [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,1,8]=>[2,4,5,3,7,6,8,1]=>[8,2,5,4,3,7,6,1]=>{{1,8},{2},{3,5},{4},{6,7}} [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>[3,4,5,2,7,6,8,1]=>[8,5,3,4,2,7,6,1]=>{{1,8},{2,5},{3},{4},{6,7}} [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>{{1,8},{2,5},{3,4},{6,7}} [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,1,8]=>[2,5,4,3,7,6,8,1]=>[8,2,4,5,3,7,6,1]=>{{1,8},{2},{3,4,5},{6,7}} [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,1,8]=>[5,4,3,2,7,6,8,1]=>[8,3,4,5,2,7,6,1]=>{{1,8},{2,3,4,5},{6,7}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>{{1},{2},{3},{4,8},{5,7},{6}} [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,4,1,5]=>[2,1,3,6,7,5,8,4]=>[2,1,3,8,7,6,5,4]=>{{1,2},{3},{4,8},{5,7},{6}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>[1,3,2,6,7,5,8,4]=>[1,3,2,8,7,6,5,4]=>{{1},{2,3},{4,8},{5,7},{6}} [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,4,1,5]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]=>{{1,3},{2},{4,8},{5,7},{6}} [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,6,5,4]=>{{1,2,3},{4,8},{5,7},{6}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[1,2,4,6,7,5,8,3]=>[1,2,8,4,7,6,5,3]=>{{1},{2},{3,8},{4},{5,7},{6}} [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,4,1,6]=>[2,1,4,6,7,5,8,3]=>[2,1,8,4,7,6,5,3]=>{{1,2},{3,8},{4},{5,7},{6}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>[1,3,4,6,7,5,8,2]=>[1,8,3,4,7,6,5,2]=>{{1},{2,8},{3},{4},{5,7},{6}} [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,1,8]=>[2,3,4,6,7,5,8,1]=>[8,2,3,4,7,6,5,1]=>{{1,8},{2},{3},{4},{5,7},{6}} [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,1,8]=>[3,2,4,6,7,5,8,1]=>[8,3,2,4,7,6,5,1]=>{{1,8},{2,3},{4},{5,7},{6}} [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,2,4,1,8]=>[2,4,3,6,7,5,8,1]=>[8,2,4,3,7,6,5,1]=>{{1,8},{2},{3,4},{5,7},{6}} [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[3,4,2,6,7,5,8,1]=>[8,4,3,2,7,6,5,1]=>{{1,8},{2,4},{3},{5,7},{6}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,1,6]=>[1,2,5,6,7,4,8,3]=>[1,2,8,7,5,6,4,3]=>{{1},{2},{3,8},{4,7},{5},{6}} [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>{{1,2},{3,8},{4,7},{5},{6}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,5,1,7]=>[1,3,5,6,7,4,8,2]=>[1,8,3,7,5,6,4,2]=>{{1},{2,8},{3},{4,7},{5},{6}} [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,1,8]=>[2,3,5,6,7,4,8,1]=>[8,2,3,7,5,6,4,1]=>{{1,8},{2},{3},{4,7},{5},{6}} [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>[3,2,5,6,7,4,8,1]=>[8,3,2,7,5,6,4,1]=>{{1,8},{2,3},{4,7},{5},{6}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,1,7]=>[1,4,5,6,7,3,8,2]=>[1,8,7,4,5,6,3,2]=>{{1},{2,8},{3,7},{4},{5},{6}} [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,1,8]=>[2,4,5,6,7,3,8,1]=>[8,2,7,4,5,6,3,1]=>{{1,8},{2},{3,7},{4},{5},{6}} [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,1,8]=>[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]=>{{1,8},{2,7},{3},{4},{5},{6}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,1,7]=>[1,5,4,6,7,3,8,2]=>[1,8,7,5,4,6,3,2]=>{{1},{2,8},{3,7},{4,5},{6}} [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,1,8]=>[2,5,4,6,7,3,8,1]=>[8,2,7,5,4,6,3,1]=>{{1,8},{2},{3,7},{4,5},{6}} [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,2,7,1,8]=>[3,5,4,6,7,2,8,1]=>[8,7,3,5,4,6,2,1]=>{{1,8},{2,7},{3},{4,5},{6}} [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,1,8]=>[4,5,3,6,7,2,8,1]=>[8,7,5,4,3,6,2,1]=>{{1,8},{2,7},{3,5},{4},{6}} [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,1,8]=>[5,4,3,6,7,2,8,1]=>[8,7,4,5,3,6,2,1]=>{{1,8},{2,7},{3,4,5},{6}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>[1,2,6,5,7,4,8,3]=>[1,2,8,7,6,5,4,3]=>{{1},{2},{3,8},{4,7},{5,6}} [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>{{1,2},{3,8},{4,7},{5,6}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,5,1,7]=>[1,3,6,5,7,4,8,2]=>[1,8,3,7,6,5,4,2]=>{{1},{2,8},{3},{4,7},{5,6}} [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>{{1,8},{2,3},{4,7},{5,6}} [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>[2,4,6,5,7,3,8,1]=>[8,2,7,4,6,5,3,1]=>{{1,8},{2},{3,7},{4},{5,6}} [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,7,1,8]=>[3,4,6,5,7,2,8,1]=>[8,7,3,4,6,5,2,1]=>{{1,8},{2,7},{3},{4},{5,6}} [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>{{1,8},{2,7},{3,4},{5,6}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,6,1,7]=>[1,5,6,4,7,3,8,2]=>[1,8,7,6,5,4,3,2]=>{{1},{2,8},{3,7},{4,6},{5}} [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>[2,5,6,4,7,3,8,1]=>[8,2,7,6,5,4,3,1]=>{{1,8},{2},{3,7},{4,6},{5}} [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,7,1,8]=>[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>{{1,8},{2,7},{3},{4,6},{5}} [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>{{1,8},{2,7},{3,6},{4},{5}} [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}} [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>[3,6,5,4,7,2,8,1]=>[8,7,3,5,6,4,2,1]=>{{1,8},{2,7},{3},{4,5,6}} [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,1,8]=>[4,6,5,3,7,2,8,1]=>[8,7,5,4,6,3,2,1]=>{{1,8},{2,7},{3,5,6},{4}} [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,1,8]=>[5,6,4,3,7,2,8,1]=>[8,7,4,6,5,3,2,1]=>{{1,8},{2,7},{3,4,6},{5}} [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[6,5,4,3,7,2,8,1]=>[8,7,4,5,6,3,2,1]=>{{1,8},{2,7},{3,4,5,6}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,7,5,4]=>{{1},{2},{3},{4,8},{5,6,7}} [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,4,1,5]=>[2,1,3,7,6,5,8,4]=>[2,1,3,8,6,7,5,4]=>{{1,2},{3},{4,8},{5,6,7}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,1,5]=>[1,3,2,7,6,5,8,4]=>[1,3,2,8,6,7,5,4]=>{{1},{2,3},{4,8},{5,6,7}} [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,1,5]=>[2,3,1,7,6,5,8,4]=>[3,2,1,8,6,7,5,4]=>{{1,3},{2},{4,8},{5,6,7}} [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>[3,2,1,7,6,5,8,4]=>[2,3,1,8,6,7,5,4]=>{{1,2,3},{4,8},{5,6,7}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,4,1,6]=>[1,2,4,7,6,5,8,3]=>[1,2,8,4,6,7,5,3]=>{{1},{2},{3,8},{4},{5,6,7}} [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,1,6]=>[2,1,4,7,6,5,8,3]=>[2,1,8,4,6,7,5,3]=>{{1,2},{3,8},{4},{5,6,7}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[1,3,4,7,6,5,8,2]=>[1,8,3,4,6,7,5,2]=>{{1},{2,8},{3},{4},{5,6,7}} [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>[3,2,4,7,6,5,8,1]=>[8,3,2,4,6,7,5,1]=>{{1,8},{2,3},{4},{5,6,7}} [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>[2,4,3,7,6,5,8,1]=>[8,2,4,3,6,7,5,1]=>{{1,8},{2},{3,4},{5,6,7}} [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>[3,4,2,7,6,5,8,1]=>[8,4,3,2,6,7,5,1]=>{{1,8},{2,4},{3},{5,6,7}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,2,3,5,1,6]=>[1,2,5,7,6,4,8,3]=>[1,2,8,6,5,7,4,3]=>{{1},{2},{3,8},{4,6,7},{5}} [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,5,1,6]=>[2,1,5,7,6,4,8,3]=>[2,1,8,6,5,7,4,3]=>{{1,2},{3,8},{4,6,7},{5}} [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,1,8]=>[3,2,5,7,6,4,8,1]=>[8,3,2,6,5,7,4,1]=>{{1,8},{2,3},{4,6,7},{5}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,1,7]=>[1,4,5,7,6,3,8,2]=>[1,8,6,4,5,7,3,2]=>{{1},{2,8},{3,6,7},{4},{5}} [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,6,1,8]=>[2,4,5,7,6,3,8,1]=>[8,2,6,4,5,7,3,1]=>{{1,8},{2},{3,6,7},{4},{5}} [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,7,1,8]=>[4,3,5,7,6,2,8,1]=>[8,6,4,3,5,7,2,1]=>{{1,8},{2,6,7},{3,4},{5}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,6,1,7]=>[1,5,4,7,6,3,8,2]=>[1,8,6,5,4,7,3,2]=>{{1},{2,8},{3,6,7},{4,5}} [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>[2,5,4,7,6,3,8,1]=>[8,2,6,5,4,7,3,1]=>{{1,8},{2},{3,6,7},{4,5}} [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,1,8]=>[4,5,3,7,6,2,8,1]=>[8,6,5,4,3,7,2,1]=>{{1,8},{2,6,7},{3,5},{4}} [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,1,6]=>[2,1,6,7,5,4,8,3]=>[2,1,8,5,7,6,4,3]=>{{1,2},{3,8},{4,5,7},{6}} [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,1,8]=>[2,3,6,7,5,4,8,1]=>[8,2,3,5,7,6,4,1]=>{{1,8},{2},{3},{4,5,7},{6}} [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,1,8]=>[3,2,6,7,5,4,8,1]=>[8,3,2,5,7,6,4,1]=>{{1,8},{2,3},{4,5,7},{6}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,6,1,7]=>[1,4,6,7,5,3,8,2]=>[1,8,5,4,7,6,3,2]=>{{1},{2,8},{3,5,7},{4},{6}} [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[2,4,6,7,5,3,8,1]=>[8,2,5,4,7,6,3,1]=>{{1,8},{2},{3,5,7},{4},{6}} [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[3,4,6,7,5,2,8,1]=>[8,5,3,4,7,6,2,1]=>{{1,8},{2,5,7},{3},{4},{6}} [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,7,1,8]=>[4,3,6,7,5,2,8,1]=>[8,5,4,3,7,6,2,1]=>{{1,8},{2,5,7},{3,4},{6}} [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,6,1,8]=>[2,5,6,7,4,3,8,1]=>[8,2,4,7,5,6,3,1]=>{{1,8},{2},{3,4,7},{5},{6}} [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,7,1,8]=>[3,5,6,7,4,2,8,1]=>[8,4,3,7,5,6,2,1]=>{{1,8},{2,4,7},{3},{5},{6}} [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>{{1,8},{2,3,7},{4},{5},{6}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,1,7]=>[1,6,5,7,4,3,8,2]=>[1,8,4,7,6,5,3,2]=>{{1},{2,8},{3,4,7},{5,6}} [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,2,5,6,1,8]=>[2,6,5,7,4,3,8,1]=>[8,2,4,7,6,5,3,1]=>{{1,8},{2},{3,4,7},{5,6}} [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,1,8]=>[4,6,5,7,3,2,8,1]=>[8,3,7,4,6,5,2,1]=>{{1,8},{2,3,7},{4},{5,6}} [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,1,8]=>[5,6,4,7,3,2,8,1]=>[8,3,7,6,5,4,2,1]=>{{1,8},{2,3,7},{4,6},{5}} [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,1,8]=>[6,5,4,7,3,2,8,1]=>[8,3,7,5,6,4,2,1]=>{{1,8},{2,3,7},{4,5,6}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,1,6]=>[1,2,7,6,5,4,8,3]=>[1,2,8,5,6,7,4,3]=>{{1},{2},{3,8},{4,5,6,7}} [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,1,6]=>[2,1,7,6,5,4,8,3]=>[2,1,8,5,6,7,4,3]=>{{1,2},{3,8},{4,5,6,7}} [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>[2,3,7,6,5,4,8,1]=>[8,2,3,5,6,7,4,1]=>{{1,8},{2},{3},{4,5,6,7}} [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,1,8]=>[3,2,7,6,5,4,8,1]=>[8,3,2,5,6,7,4,1]=>{{1,8},{2,3},{4,5,6,7}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,1,7]=>[1,4,7,6,5,3,8,2]=>[1,8,5,4,6,7,3,2]=>{{1},{2,8},{3,5,6,7},{4}} [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,1,8]=>[3,4,7,6,5,2,8,1]=>[8,5,3,4,6,7,2,1]=>{{1,8},{2,5,6,7},{3},{4}} [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,7,1,8]=>[4,3,7,6,5,2,8,1]=>[8,5,4,3,6,7,2,1]=>{{1,8},{2,5,6,7},{3,4}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,6,1,7]=>[1,5,7,6,4,3,8,2]=>[1,8,4,6,5,7,3,2]=>{{1},{2,8},{3,4,6,7},{5}} [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,1,8]=>[5,4,7,6,3,2,8,1]=>[8,3,6,5,4,7,2,1]=>{{1,8},{2,3,6,7},{4,5}} [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,7,1,8]=>[3,6,7,5,4,2,8,1]=>[8,4,3,5,7,6,2,1]=>{{1,8},{2,4,5,7},{3},{6}} [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,7,1,8]=>[4,6,7,5,3,2,8,1]=>[8,3,5,4,7,6,2,1]=>{{1,8},{2,3,5,7},{4},{6}} [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,1,8]=>[6,5,7,4,3,2,8,1]=>[8,3,4,7,6,5,2,1]=>{{1,8},{2,3,4,7},{5,6}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,1,7]=>[1,7,6,5,4,3,8,2]=>[1,8,4,5,6,7,3,2]=>{{1},{2,8},{3,4,5,6,7}} [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,1,8]=>[2,7,6,5,4,3,8,1]=>[8,2,4,5,6,7,3,1]=>{{1,8},{2},{3,4,5,6,7}} [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>[3,7,6,5,4,2,8,1]=>[8,4,3,5,6,7,2,1]=>{{1,8},{2,4,5,6,7},{3}} [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,1,8]=>[4,7,6,5,3,2,8,1]=>[8,3,5,4,6,7,2,1]=>{{1,8},{2,3,5,6,7},{4}} [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,1,8]=>[6,7,5,4,3,2,8,1]=>[8,3,4,5,7,6,2,1]=>{{1,8},{2,3,4,5,7},{6}} [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,2,1]=>{{1,8},{2,3,4,5,6,7}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,1,2,3]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]=>{{1,2},{3},{4},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,1,2,3]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,1,2,3]=>[2,3,1,4,5,8,7,6]=>[3,2,1,4,5,7,8,6]=>{{1,3},{2},{4},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>{{1,2,3},{4},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,1,2,3]=>[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[2,1,4,3,5,8,7,6]=>[2,1,4,3,5,7,8,6]=>{{1,2},{3,4},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,1,2,3]=>[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,7,8,6]=>{{1},{2,4},{3},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,7,8,6]=>{{1,4},{2},{3},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>{{1,4},{2,3},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,1,2,3]=>[2,4,3,1,5,8,7,6]=>[3,2,4,1,5,7,8,6]=>{{1,3,4},{2},{5},{6,7,8}} [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>{{1,2,3,4},{5},{6,7,8}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,1,2,3]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}} [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,1,2,3]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]=>{{1,2},{3},{4,5},{6,7,8}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>{{1},{2,3},{4,5},{6,7,8}} [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,7,8,6]=>{{1},{2},{3,5},{4},{6,7,8}} [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,1,2,3]=>[1,3,4,5,2,8,7,6]=>[1,5,3,4,2,7,8,6]=>{{1},{2,5},{3},{4},{6,7,8}} [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[2,3,4,5,1,8,7,6]=>[5,2,3,4,1,7,8,6]=>{{1,5},{2},{3},{4},{6,7,8}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[1,4,3,5,2,8,7,6]=>[1,5,4,3,2,7,8,6]=>{{1},{2,5},{3,4},{6,7,8}} [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]=>{{1,5},{2,4},{3},{6,7,8}} [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,1,2,3]=>[4,3,2,5,1,8,7,6]=>[5,3,4,2,1,7,8,6]=>{{1,5},{2,3,4},{6,7,8}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}} [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[2,3,5,4,1,8,7,6]=>[4,2,3,5,1,7,8,6]=>{{1,4,5},{2},{3},{6,7,8}} [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[3,2,5,4,1,8,7,6]=>[4,3,2,5,1,7,8,6]=>{{1,4,5},{2,3},{6,7,8}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,1,2,3]=>[1,4,5,3,2,8,7,6]=>[1,3,5,4,2,7,8,6]=>{{1},{2,3,5},{4},{6,7,8}} [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[2,4,5,3,1,8,7,6]=>[3,2,5,4,1,7,8,6]=>{{1,3,5},{2},{4},{6,7,8}} [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[4,3,5,2,1,8,7,6]=>[2,5,4,3,1,7,8,6]=>{{1,2,5},{3,4},{6,7,8}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,1,2,3]=>[1,5,4,3,2,8,7,6]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}} [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[3,5,4,2,1,8,7,6]=>[2,4,3,5,1,7,8,6]=>{{1,2,4,5},{3},{6,7,8}} [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[5,4,3,2,1,8,7,6]=>[2,3,4,5,1,7,8,6]=>{{1,2,3,4,5},{6,7,8}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,6,8,5]=>{{1},{2},{3},{4},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,1,2,4]=>[2,1,3,4,6,8,7,5]=>[2,1,3,4,7,6,8,5]=>{{1,2},{3},{4},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,1,2,4]=>[1,3,2,4,6,8,7,5]=>[1,3,2,4,7,6,8,5]=>{{1},{2,3},{4},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,1,2,4]=>[2,3,1,4,6,8,7,5]=>[3,2,1,4,7,6,8,5]=>{{1,3},{2},{4},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,1,2,4]=>[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,6,8,5]=>{{1,2,3},{4},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,1,2,4]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,6,8,5]=>{{1},{2},{3,4},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]=>{{1,2},{3,4},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,1,2,4]=>[1,3,4,2,6,8,7,5]=>[1,4,3,2,7,6,8,5]=>{{1},{2,4},{3},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[2,3,4,1,6,8,7,5]=>[4,2,3,1,7,6,8,5]=>{{1,4},{2},{3},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>{{1,4},{2,3},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,1,2,4]=>[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,6,8,5]=>{{1},{2,3,4},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]=>{{1,3,4},{2},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[3,4,2,1,6,8,7,5]=>[2,4,3,1,7,6,8,5]=>{{1,2,4},{3},{5,7,8},{6}} [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[4,3,2,1,6,8,7,5]=>[2,3,4,1,7,6,8,5]=>{{1,2,3,4},{5,7,8},{6}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,1,2,5]=>[1,3,2,5,6,8,7,4]=>[1,3,2,7,5,6,8,4]=>{{1},{2,3},{4,7,8},{5},{6}} [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,1,2,5]=>[2,3,1,5,6,8,7,4]=>[3,2,1,7,5,6,8,4]=>{{1,3},{2},{4,7,8},{5},{6}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[1,2,4,5,6,8,7,3]=>[1,2,7,4,5,6,8,3]=>{{1},{2},{3,7,8},{4},{5},{6}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1,2,7]=>[1,3,4,5,6,8,7,2]=>[1,7,3,4,5,6,8,2]=>{{1},{2,7,8},{3},{4},{5},{6}} [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[2,3,4,5,6,8,7,1]=>[7,2,3,4,5,6,8,1]=>{{1,7,8},{2},{3},{4},{5},{6}} [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,1,2,8]=>[3,2,4,5,6,8,7,1]=>[7,3,2,4,5,6,8,1]=>{{1,7,8},{2,3},{4},{5},{6}} [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,1,2,8]=>[3,4,2,5,6,8,7,1]=>[7,4,3,2,5,6,8,1]=>{{1,7,8},{2,4},{3},{5},{6}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,1,2,6]=>[1,2,5,4,6,8,7,3]=>[1,2,7,5,4,6,8,3]=>{{1},{2},{3,7,8},{4,5},{6}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,1,2,7]=>[1,4,5,3,6,8,7,2]=>[1,7,5,4,3,6,8,2]=>{{1},{2,7,8},{3,5},{4},{6}} [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,1,2,8]=>[4,3,5,2,6,8,7,1]=>[7,5,4,3,2,6,8,1]=>{{1,7,8},{2,5},{3,4},{6}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,1,2,7]=>[1,5,4,3,6,8,7,2]=>[1,7,4,5,3,6,8,2]=>{{1},{2,7,8},{3,4,5},{6}} [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,1,2,8]=>[2,5,4,3,6,8,7,1]=>[7,2,4,5,3,6,8,1]=>{{1,7,8},{2},{3,4,5},{6}} [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,1,2,8]=>[3,5,4,2,6,8,7,1]=>[7,4,3,5,2,6,8,1]=>{{1,7,8},{2,4,5},{3},{6}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[1,2,3,6,5,8,7,4]=>[1,2,3,7,6,5,8,4]=>{{1},{2},{3},{4,7,8},{5,6}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,1,2,5]=>[1,3,2,6,5,8,7,4]=>[1,3,2,7,6,5,8,4]=>{{1},{2,3},{4,7,8},{5,6}} [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,1,2,5]=>[2,3,1,6,5,8,7,4]=>[3,2,1,7,6,5,8,4]=>{{1,3},{2},{4,7,8},{5,6}} [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[3,2,1,6,5,8,7,4]=>[2,3,1,7,6,5,8,4]=>{{1,2,3},{4,7,8},{5,6}} [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,1,2,6]=>[2,1,4,6,5,8,7,3]=>[2,1,7,4,6,5,8,3]=>{{1,2},{3,7,8},{4},{5,6}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[1,4,3,6,5,8,7,2]=>[1,7,4,3,6,5,8,2]=>{{1},{2,7,8},{3,4},{5,6}} [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,1,2,8]=>[2,4,3,6,5,8,7,1]=>[7,2,4,3,6,5,8,1]=>{{1,7,8},{2},{3,4},{5,6}} [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>[3,4,2,6,5,8,7,1]=>[7,4,3,2,6,5,8,1]=>{{1,7,8},{2,4},{3},{5,6}} [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,1,2,8]=>[4,3,2,6,5,8,7,1]=>[7,3,4,2,6,5,8,1]=>{{1,7,8},{2,3,4},{5,6}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,1,2,6]=>[1,2,5,6,4,8,7,3]=>[1,2,7,6,5,4,8,3]=>{{1},{2},{3,7,8},{4,6},{5}} [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,1,2,6]=>[2,1,5,6,4,8,7,3]=>[2,1,7,6,5,4,8,3]=>{{1,2},{3,7,8},{4,6},{5}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,1,2,7]=>[1,3,5,6,4,8,7,2]=>[1,7,3,6,5,4,8,2]=>{{1},{2,7,8},{3},{4,6},{5}} [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,1,2,8]=>[2,4,5,6,3,8,7,1]=>[7,2,6,4,5,3,8,1]=>{{1,7,8},{2},{3,6},{4},{5}} [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,1,2,8]=>[3,4,5,6,2,8,7,1]=>[7,6,3,4,5,2,8,1]=>{{1,7,8},{2,6},{3},{4},{5}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,1,2,7]=>[1,5,4,6,3,8,7,2]=>[1,7,6,5,4,3,8,2]=>{{1},{2,7,8},{3,6},{4,5}} [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>[3,5,4,6,2,8,7,1]=>[7,6,3,5,4,2,8,1]=>{{1,7,8},{2,6},{3},{4,5}} [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,1,2,8]=>[4,5,3,6,2,8,7,1]=>[7,6,5,4,3,2,8,1]=>{{1,7,8},{2,6},{3,5},{4}} [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,1,2,8]=>[5,4,3,6,2,8,7,1]=>[7,6,4,5,3,2,8,1]=>{{1,7,8},{2,6},{3,4,5}} [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,1,2,6]=>[2,1,6,5,4,8,7,3]=>[2,1,7,5,6,4,8,3]=>{{1,2},{3,7,8},{4,5,6}} [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>[3,2,6,5,4,8,7,1]=>[7,3,2,5,6,4,8,1]=>{{1,7,8},{2,3},{4,5,6}} [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,1,2,8]=>[4,3,6,5,2,8,7,1]=>[7,5,4,3,6,2,8,1]=>{{1,7,8},{2,5,6},{3,4}} [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,1,2,8]=>[3,5,6,4,2,8,7,1]=>[7,4,3,6,5,2,8,1]=>{{1,7,8},{2,4,6},{3},{5}} [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,1,2,8]=>[4,5,6,3,2,8,7,1]=>[7,3,6,4,5,2,8,1]=>{{1,7,8},{2,3,6},{4},{5}} [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,1,2,8]=>[5,4,6,3,2,8,7,1]=>[7,3,6,5,4,2,8,1]=>{{1,7,8},{2,3,6},{4,5}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[1,6,5,4,3,8,7,2]=>[1,7,4,5,6,3,8,2]=>{{1},{2,7,8},{3,4,5,6}} [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,1,2,8]=>[4,6,5,3,2,8,7,1]=>[7,3,5,4,6,2,8,1]=>{{1,7,8},{2,3,5,6},{4}} [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[6,5,4,3,2,8,7,1]=>[7,3,4,5,6,2,8,1]=>{{1,7,8},{2,3,4,5,6}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,6,8,7,5]=>{{1},{2},{3},{4},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,1,3,4]=>[1,3,2,4,7,8,6,5]=>[1,3,2,4,6,8,7,5]=>{{1},{2,3},{4},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,1,3,4]=>[2,3,1,4,7,8,6,5]=>[3,2,1,4,6,8,7,5]=>{{1,3},{2},{4},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,1,3,4]=>[1,2,4,3,7,8,6,5]=>[1,2,4,3,6,8,7,5]=>{{1},{2},{3,4},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]=>{{1,2},{3,4},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[1,3,4,2,7,8,6,5]=>[1,4,3,2,6,8,7,5]=>{{1},{2,4},{3},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>[2,3,4,1,7,8,6,5]=>[4,2,3,1,6,8,7,5]=>{{1,4},{2},{3},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>{{1,4},{2,3},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,1,3,4]=>[1,4,3,2,7,8,6,5]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>[2,4,3,1,7,8,6,5]=>[3,2,4,1,6,8,7,5]=>{{1,3,4},{2},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]=>{{1,2,4},{3},{5,6,8},{7}} [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[4,3,2,1,7,8,6,5]=>[2,3,4,1,6,8,7,5]=>{{1,2,3,4},{5,6,8},{7}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[1,2,3,5,7,8,6,4]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}} [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,1,3,5]=>[2,1,3,5,7,8,6,4]=>[2,1,3,6,5,8,7,4]=>{{1,2},{3},{4,6,8},{5},{7}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[1,3,2,5,7,8,6,4]=>[1,3,2,6,5,8,7,4]=>{{1},{2,3},{4,6,8},{5},{7}} [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,1,3,5]=>[2,3,1,5,7,8,6,4]=>[3,2,1,6,5,8,7,4]=>{{1,3},{2},{4,6,8},{5},{7}} [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[3,2,1,5,7,8,6,4]=>[2,3,1,6,5,8,7,4]=>{{1,2,3},{4,6,8},{5},{7}} [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[2,1,4,5,7,8,6,3]=>[2,1,6,4,5,8,7,3]=>{{1,2},{3,6,8},{4},{5},{7}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[1,3,4,5,7,8,6,2]=>[1,6,3,4,5,8,7,2]=>{{1},{2,6,8},{3},{4},{5},{7}} [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,3,8]=>[2,3,4,5,7,8,6,1]=>[6,2,3,4,5,8,7,1]=>{{1,6,8},{2},{3},{4},{5},{7}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>[1,4,3,5,7,8,6,2]=>[1,6,4,3,5,8,7,2]=>{{1},{2,6,8},{3,4},{5},{7}} [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,1,3,8]=>[3,4,2,5,7,8,6,1]=>[6,4,3,2,5,8,7,1]=>{{1,6,8},{2,4},{3},{5},{7}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,1,3,6]=>[1,2,5,4,7,8,6,3]=>[1,2,6,5,4,8,7,3]=>{{1},{2},{3,6,8},{4,5},{7}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,1,3,7]=>[1,3,5,4,7,8,6,2]=>[1,6,3,5,4,8,7,2]=>{{1},{2,6,8},{3},{4,5},{7}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,2,1,3,7]=>[1,4,5,3,7,8,6,2]=>[1,6,5,4,3,8,7,2]=>{{1},{2,6,8},{3,5},{4},{7}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,1,3,7]=>[1,5,4,3,7,8,6,2]=>[1,6,4,5,3,8,7,2]=>{{1},{2,6,8},{3,4,5},{7}} [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,1,3,8]=>[5,4,3,2,7,8,6,1]=>[6,3,4,5,2,8,7,1]=>{{1,6,8},{2,3,4,5},{7}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[1,2,3,6,7,8,5,4]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}} [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,1,4,5]=>[2,1,3,6,7,8,5,4]=>[2,1,3,5,8,6,7,4]=>{{1,2},{3},{4,5,8},{6},{7}} [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>[2,3,1,6,7,8,5,4]=>[3,2,1,5,8,6,7,4]=>{{1,3},{2},{4,5,8},{6},{7}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[1,2,4,6,7,8,5,3]=>[1,2,5,4,8,6,7,3]=>{{1},{2},{3,5,8},{4},{6},{7}} [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[2,1,4,6,7,8,5,3]=>[2,1,5,4,8,6,7,3]=>{{1,2},{3,5,8},{4},{6},{7}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[1,3,4,6,7,8,5,2]=>[1,5,3,4,8,6,7,2]=>{{1},{2,5,8},{3},{4},{6},{7}} [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1,4,8]=>[2,3,4,6,7,8,5,1]=>[5,2,3,4,8,6,7,1]=>{{1,5,8},{2},{3},{4},{6},{7}} [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,1,4,8]=>[3,4,2,6,7,8,5,1]=>[5,4,3,2,8,6,7,1]=>{{1,5,8},{2,4},{3},{6},{7}} [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,1,4,8]=>[4,3,2,6,7,8,5,1]=>[5,3,4,2,8,6,7,1]=>{{1,5,8},{2,3,4},{6},{7}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[1,2,5,6,7,8,4,3]=>[1,2,4,8,5,6,7,3]=>{{1},{2},{3,4,8},{5},{6},{7}} [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[2,1,5,6,7,8,4,3]=>[2,1,4,8,5,6,7,3]=>{{1,2},{3,4,8},{5},{6},{7}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[1,3,5,6,7,8,4,2]=>[1,4,3,8,5,6,7,2]=>{{1},{2,4,8},{3},{5},{6},{7}} [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[2,3,5,6,7,8,4,1]=>[4,2,3,8,5,6,7,1]=>{{1,4,8},{2},{3},{5},{6},{7}} [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>[3,2,5,6,7,8,4,1]=>[4,3,2,8,5,6,7,1]=>{{1,4,8},{2,3},{5},{6},{7}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,6,7]=>[1,4,5,6,7,8,3,2]=>[1,3,8,4,5,6,7,2]=>{{1},{2,3,8},{4},{5},{6},{7}} [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1,6,8]=>[2,4,5,6,7,8,3,1]=>[3,2,8,4,5,6,7,1]=>{{1,3,8},{2},{4},{5},{6},{7}} [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[3,4,5,6,7,8,2,1]=>[2,8,3,4,5,6,7,1]=>{{1,2,8},{3},{4},{5},{6},{7}} [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[4,3,5,6,7,8,2,1]=>[2,8,4,3,5,6,7,1]=>{{1,2,8},{3,4},{5},{6},{7}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,1,6,7]=>[1,5,4,6,7,8,3,2]=>[1,3,8,5,4,6,7,2]=>{{1},{2,3,8},{4,5},{6},{7}} [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,1,6,8]=>[2,5,4,6,7,8,3,1]=>[3,2,8,5,4,6,7,1]=>{{1,3,8},{2},{4,5},{6},{7}} [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>[4,5,3,6,7,8,2,1]=>[2,8,5,4,3,6,7,1]=>{{1,2,8},{3,5},{4},{6},{7}} [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[5,4,3,6,7,8,2,1]=>[2,8,4,5,3,6,7,1]=>{{1,2,8},{3,4,5},{6},{7}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[1,2,6,5,7,8,4,3]=>[1,2,4,8,6,5,7,3]=>{{1},{2},{3,4,8},{5,6},{7}} [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[2,1,6,5,7,8,4,3]=>[2,1,4,8,6,5,7,3]=>{{1,2},{3,4,8},{5,6},{7}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[1,3,6,5,7,8,4,2]=>[1,4,3,8,6,5,7,2]=>{{1},{2,4,8},{3},{5,6},{7}} [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,1,6,8]=>[2,4,6,5,7,8,3,1]=>[3,2,8,4,6,5,7,1]=>{{1,3,8},{2},{4},{5,6},{7}} [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,1,7,8]=>[4,3,6,5,7,8,2,1]=>[2,8,4,3,6,5,7,1]=>{{1,2,8},{3,4},{5,6},{7}} [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,1,6,8]=>[2,6,5,4,7,8,3,1]=>[3,2,8,5,6,4,7,1]=>{{1,3,8},{2},{4,5,6},{7}} [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,1,7,8]=>[5,6,4,3,7,8,2,1]=>[2,8,4,6,5,3,7,1]=>{{1,2,8},{3,4,6},{5},{7}} [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[6,5,4,3,7,8,2,1]=>[2,8,4,5,6,3,7,1]=>{{1,2,8},{3,4,5,6},{7}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[1,2,3,7,6,8,5,4]=>[1,2,3,5,8,7,6,4]=>{{1},{2},{3},{4,5,8},{6,7}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,1,4,5]=>[1,3,2,7,6,8,5,4]=>[1,3,2,5,8,7,6,4]=>{{1},{2,3},{4,5,8},{6,7}} [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>[2,3,1,7,6,8,5,4]=>[3,2,1,5,8,7,6,4]=>{{1,3},{2},{4,5,8},{6,7}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,1,4,6]=>[1,2,4,7,6,8,5,3]=>[1,2,5,4,8,7,6,3]=>{{1},{2},{3,5,8},{4},{6,7}} [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,1,4,6]=>[2,1,4,7,6,8,5,3]=>[2,1,5,4,8,7,6,3]=>{{1,2},{3,5,8},{4},{6,7}} [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,1,4,8]=>[2,3,4,7,6,8,5,1]=>[5,2,3,4,8,7,6,1]=>{{1,5,8},{2},{3},{4},{6,7}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[1,4,3,7,6,8,5,2]=>[1,5,4,3,8,7,6,2]=>{{1},{2,5,8},{3,4},{6,7}} [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,1,4,8]=>[3,4,2,7,6,8,5,1]=>[5,4,3,2,8,7,6,1]=>{{1,5,8},{2,4},{3},{6,7}} [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,1,5,6]=>[2,1,5,7,6,8,4,3]=>[2,1,4,8,5,7,6,3]=>{{1,2},{3,4,8},{5},{6,7}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>[1,3,5,7,6,8,4,2]=>[1,4,3,8,5,7,6,2]=>{{1},{2,4,8},{3},{5},{6,7}} [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>[2,3,5,7,6,8,4,1]=>[4,2,3,8,5,7,6,1]=>{{1,4,8},{2},{3},{5},{6,7}} [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,1,5,8]=>[3,2,5,7,6,8,4,1]=>[4,3,2,8,5,7,6,1]=>{{1,4,8},{2,3},{5},{6,7}} [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,1,7,8]=>[3,4,5,7,6,8,2,1]=>[2,8,3,4,5,7,6,1]=>{{1,2,8},{3},{4},{5},{6,7}} [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,1,7,8]=>[4,3,5,7,6,8,2,1]=>[2,8,4,3,5,7,6,1]=>{{1,2,8},{3,4},{5},{6,7}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,1,6,7]=>[1,5,4,7,6,8,3,2]=>[1,3,8,5,4,7,6,2]=>{{1},{2,3,8},{4,5},{6,7}} [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,1,6,8]=>[2,5,4,7,6,8,3,1]=>[3,2,8,5,4,7,6,1]=>{{1,3,8},{2},{4,5},{6,7}} [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,1,7,8]=>[3,5,4,7,6,8,2,1]=>[2,8,3,5,4,7,6,1]=>{{1,2,8},{3},{4,5},{6,7}} [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,1,7,8]=>[4,5,3,7,6,8,2,1]=>[2,8,5,4,3,7,6,1]=>{{1,2,8},{3,5},{4},{6,7}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,1,5,6]=>[1,2,6,7,5,8,4,3]=>[1,2,4,8,7,6,5,3]=>{{1},{2},{3,4,8},{5,7},{6}} [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[2,1,6,7,5,8,4,3]=>[2,1,4,8,7,6,5,3]=>{{1,2},{3,4,8},{5,7},{6}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[1,3,6,7,5,8,4,2]=>[1,4,3,8,7,6,5,2]=>{{1},{2,4,8},{3},{5,7},{6}} [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,1,5,8]=>[2,3,6,7,5,8,4,1]=>[4,2,3,8,7,6,5,1]=>{{1,4,8},{2},{3},{5,7},{6}} [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,1,5,8]=>[3,2,6,7,5,8,4,1]=>[4,3,2,8,7,6,5,1]=>{{1,4,8},{2,3},{5,7},{6}} [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>[4,3,6,7,5,8,2,1]=>[2,8,4,3,7,6,5,1]=>{{1,2,8},{3,4},{5,7},{6}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,5,1,6,7]=>[1,5,6,7,4,8,3,2]=>[1,3,8,7,5,6,4,2]=>{{1},{2,3,8},{4,7},{5},{6}} [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,1,6,8]=>[2,5,6,7,4,8,3,1]=>[3,2,8,7,5,6,4,1]=>{{1,3,8},{2},{4,7},{5},{6}} [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>[3,5,6,7,4,8,2,1]=>[2,8,3,7,5,6,4,1]=>{{1,2,8},{3},{4,7},{5},{6}} [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]=>{{1,2,8},{3,7},{4},{5},{6}} [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>{{1,2,8},{3,7},{4,5},{6}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,1,6,7]=>[1,6,5,7,4,8,3,2]=>[1,3,8,7,6,5,4,2]=>{{1},{2,3,8},{4,7},{5,6}} [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,2,5,1,6,8]=>[2,6,5,7,4,8,3,1]=>[3,2,8,7,6,5,4,1]=>{{1,3,8},{2},{4,7},{5,6}} [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,5,1,7,8]=>[3,6,5,7,4,8,2,1]=>[2,8,3,7,6,5,4,1]=>{{1,2,8},{3},{4,7},{5,6}} [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,1,7,8]=>[4,6,5,7,3,8,2,1]=>[2,8,7,4,6,5,3,1]=>{{1,2,8},{3,7},{4},{5,6}} [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,1,7,8]=>[5,6,4,7,3,8,2,1]=>[2,8,7,6,5,4,3,1]=>{{1,2,8},{3,7},{4,6},{5}} [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,1,7,8]=>[6,5,4,7,3,8,2,1]=>[2,8,7,5,6,4,3,1]=>{{1,2,8},{3,7},{4,5,6}} [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[2,1,7,6,5,8,4,3]=>[2,1,4,8,6,7,5,3]=>{{1,2},{3,4,8},{5,6,7}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,1,5,7]=>[1,3,7,6,5,8,4,2]=>[1,4,3,8,6,7,5,2]=>{{1},{2,4,8},{3},{5,6,7}} [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,1,5,8]=>[3,2,7,6,5,8,4,1]=>[4,3,2,8,6,7,5,1]=>{{1,4,8},{2,3},{5,6,7}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[1,4,7,6,5,8,3,2]=>[1,3,8,4,6,7,5,2]=>{{1},{2,3,8},{4},{5,6,7}} [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>[4,3,7,6,5,8,2,1]=>[2,8,4,3,6,7,5,1]=>{{1,2,8},{3,4},{5,6,7}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,1,6,7]=>[1,6,7,5,4,8,3,2]=>[1,3,8,5,7,6,4,2]=>{{1},{2,3,8},{4,5,7},{6}} [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,1,6,8]=>[2,6,7,5,4,8,3,1]=>[3,2,8,5,7,6,4,1]=>{{1,3,8},{2},{4,5,7},{6}} [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,1,7,8]=>[3,6,7,5,4,8,2,1]=>[2,8,3,5,7,6,4,1]=>{{1,2,8},{3},{4,5,7},{6}} [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,1,7,8]=>[4,6,7,5,3,8,2,1]=>[2,8,5,4,7,6,3,1]=>{{1,2,8},{3,5,7},{4},{6}} [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,1,7,8]=>[6,5,7,4,3,8,2,1]=>[2,8,4,7,6,5,3,1]=>{{1,2,8},{3,4,7},{5,6}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,1,6,7]=>[1,7,6,5,4,8,3,2]=>[1,3,8,5,6,7,4,2]=>{{1},{2,3,8},{4,5,6,7}} [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,1,7,8]=>[3,7,6,5,4,8,2,1]=>[2,8,3,5,6,7,4,1]=>{{1,2,8},{3},{4,5,6,7}} [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,1,7,8]=>[4,7,6,5,3,8,2,1]=>[2,8,5,4,6,7,3,1]=>{{1,2,8},{3,5,6,7},{4}} [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[7,6,5,4,3,8,2,1]=>[2,8,4,5,6,7,3,1]=>{{1,2,8},{3,4,5,6,7}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]=>{{1,2},{3},{4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,6,7,8,5]=>{{1,3},{2},{4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]=>{{1,2,3},{4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]=>{{1,2},{3,4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[2,3,4,1,8,7,6,5]=>[4,2,3,1,6,7,8,5]=>{{1,4},{2},{3},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]=>{{1,4},{2,3},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[2,4,3,1,8,7,6,5]=>[3,2,4,1,6,7,8,5]=>{{1,3,4},{2},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[3,4,2,1,8,7,6,5]=>[2,4,3,1,6,7,8,5]=>{{1,2,4},{3},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}} [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[1,2,3,5,8,7,6,4]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,1,2,3,5]=>[1,3,2,5,8,7,6,4]=>[1,3,2,6,5,7,8,4]=>{{1},{2,3},{4,6,7,8},{5}} [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>[2,3,1,5,8,7,6,4]=>[3,2,1,6,5,7,8,4]=>{{1,3},{2},{4,6,7,8},{5}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,1,2,3,6]=>[1,2,4,5,8,7,6,3]=>[1,2,6,4,5,7,8,3]=>{{1},{2},{3,6,7,8},{4},{5}} [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[2,1,4,5,8,7,6,3]=>[2,1,6,4,5,7,8,3]=>{{1,2},{3,6,7,8},{4},{5}} [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[2,3,4,5,8,7,6,1]=>[6,2,3,4,5,7,8,1]=>{{1,6,7,8},{2},{3},{4},{5}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,1,2,3,6]=>[1,2,5,4,8,7,6,3]=>[1,2,6,5,4,7,8,3]=>{{1},{2},{3,6,7,8},{4,5}} [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[4,3,5,2,8,7,6,1]=>[6,5,4,3,2,7,8,1]=>{{1,6,7,8},{2,5},{3,4}} [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[4,5,3,2,8,7,6,1]=>[6,3,5,4,2,7,8,1]=>{{1,6,7,8},{2,3,5},{4}} [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[5,4,3,2,8,7,6,1]=>[6,3,4,5,2,7,8,1]=>{{1,6,7,8},{2,3,4,5}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[1,2,3,6,8,7,5,4]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}} [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,1,2,4,5]=>[2,3,1,6,8,7,5,4]=>[3,2,1,5,7,6,8,4]=>{{1,3},{2},{4,5,7,8},{6}} [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>[3,2,1,6,8,7,5,4]=>[2,3,1,5,7,6,8,4]=>{{1,2,3},{4,5,7,8},{6}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[1,2,4,6,8,7,5,3]=>[1,2,5,4,7,6,8,3]=>{{1},{2},{3,5,7,8},{4},{6}} [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[2,1,4,6,8,7,5,3]=>[2,1,5,4,7,6,8,3]=>{{1,2},{3,5,7,8},{4},{6}} [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,1,2,4,8]=>[2,4,3,6,8,7,5,1]=>[5,2,4,3,7,6,8,1]=>{{1,5,7,8},{2},{3,4},{6}} [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,1,2,4,8]=>[3,4,2,6,8,7,5,1]=>[5,4,3,2,7,6,8,1]=>{{1,5,7,8},{2,4},{3},{6}} [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[4,3,2,6,8,7,5,1]=>[5,3,4,2,7,6,8,1]=>{{1,5,7,8},{2,3,4},{6}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,1,2,5,6]=>[1,2,5,6,8,7,4,3]=>[1,2,4,7,5,6,8,3]=>{{1},{2},{3,4,7,8},{5},{6}} [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,1,2,5,8]=>[2,3,5,6,8,7,4,1]=>[4,2,3,7,5,6,8,1]=>{{1,4,7,8},{2},{3},{5},{6}} [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,1,2,5,8]=>[3,2,5,6,8,7,4,1]=>[4,3,2,7,5,6,8,1]=>{{1,4,7,8},{2,3},{5},{6}} [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>[4,3,5,6,8,7,2,1]=>[2,7,4,3,5,6,8,1]=>{{1,2,7,8},{3,4},{5},{6}} [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,1,2,7,8]=>[3,5,4,6,8,7,2,1]=>[2,7,3,5,4,6,8,1]=>{{1,2,7,8},{3},{4,5},{6}} [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[4,5,3,6,8,7,2,1]=>[2,7,5,4,3,6,8,1]=>{{1,2,7,8},{3,5},{4},{6}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>[1,2,6,5,8,7,4,3]=>[1,2,4,7,6,5,8,3]=>{{1},{2},{3,4,7,8},{5,6}} [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[2,1,6,5,8,7,4,3]=>[2,1,4,7,6,5,8,3]=>{{1,2},{3,4,7,8},{5,6}} [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,1,2,5,8]=>[2,3,6,5,8,7,4,1]=>[4,2,3,7,6,5,8,1]=>{{1,4,7,8},{2},{3},{5,6}} [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,1,2,5,8]=>[3,2,6,5,8,7,4,1]=>[4,3,2,7,6,5,8,1]=>{{1,4,7,8},{2,3},{5,6}} [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,1,2,6,8]=>[2,4,6,5,8,7,3,1]=>[3,2,7,4,6,5,8,1]=>{{1,3,7,8},{2},{4},{5,6}} [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[4,3,6,5,8,7,2,1]=>[2,7,4,3,6,5,8,1]=>{{1,2,7,8},{3,4},{5,6}} [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,1,2,6,8]=>[2,5,6,4,8,7,3,1]=>[3,2,7,6,5,4,8,1]=>{{1,3,7,8},{2},{4,6},{5}} [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[4,5,6,3,8,7,2,1]=>[2,7,6,4,5,3,8,1]=>{{1,2,7,8},{3,6},{4},{5}} [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,1,2,7,8]=>[5,4,6,3,8,7,2,1]=>[2,7,6,5,4,3,8,1]=>{{1,2,7,8},{3,6},{4,5}} [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,1,2,6,8]=>[2,6,5,4,8,7,3,1]=>[3,2,7,5,6,4,8,1]=>{{1,3,7,8},{2},{4,5,6}} [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,1,2,7,8]=>[3,6,5,4,8,7,2,1]=>[2,7,3,5,6,4,8,1]=>{{1,2,7,8},{3},{4,5,6}} [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,1,2,7,8]=>[4,6,5,3,8,7,2,1]=>[2,7,5,4,6,3,8,1]=>{{1,2,7,8},{3,5,6},{4}} [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,1,2,7,8]=>[5,6,4,3,8,7,2,1]=>[2,7,4,6,5,3,8,1]=>{{1,2,7,8},{3,4,6},{5}} [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[6,5,4,3,8,7,2,1]=>[2,7,4,5,6,3,8,1]=>{{1,2,7,8},{3,4,5,6}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[1,2,3,7,8,6,5,4]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}} [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,1,3,4,5]=>[2,3,1,7,8,6,5,4]=>[3,2,1,5,6,8,7,4]=>{{1,3},{2},{4,5,6,8},{7}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[1,2,4,7,8,6,5,3]=>[1,2,5,4,6,8,7,3]=>{{1},{2},{3,5,6,8},{4},{7}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[1,4,3,7,8,6,5,2]=>[1,5,4,3,6,8,7,2]=>{{1},{2,5,6,8},{3,4},{7}} [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,1,3,4,8]=>[3,4,2,7,8,6,5,1]=>[5,4,3,2,6,8,7,1]=>{{1,5,6,8},{2,4},{3},{7}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,2,1,3,5,6]=>[1,2,5,7,8,6,4,3]=>[1,2,4,6,5,8,7,3]=>{{1},{2},{3,4,6,8},{5},{7}} [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[2,1,5,7,8,6,4,3]=>[2,1,4,6,5,8,7,3]=>{{1,2},{3,4,6,8},{5},{7}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]=>{{1},{2,4,6,8},{3},{5},{7}} [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[2,3,5,7,8,6,4,1]=>[4,2,3,6,5,8,7,1]=>{{1,4,6,8},{2},{3},{5},{7}} [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,1,3,5,8]=>[3,2,5,7,8,6,4,1]=>[4,3,2,6,5,8,7,1]=>{{1,4,6,8},{2,3},{5},{7}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>[1,4,5,7,8,6,3,2]=>[1,3,6,4,5,8,7,2]=>{{1},{2,3,6,8},{4},{5},{7}} [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,1,3,7,8]=>[3,4,5,7,8,6,2,1]=>[2,6,3,4,5,8,7,1]=>{{1,2,6,8},{3},{4},{5},{7}} [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[4,3,5,7,8,6,2,1]=>[2,6,4,3,5,8,7,1]=>{{1,2,6,8},{3,4},{5},{7}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,1,3,6,7]=>[1,5,4,7,8,6,3,2]=>[1,3,6,5,4,8,7,2]=>{{1},{2,3,6,8},{4,5},{7}} [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,1,3,6,8]=>[2,5,4,7,8,6,3,1]=>[3,2,6,5,4,8,7,1]=>{{1,3,6,8},{2},{4,5},{7}} [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[4,5,3,7,8,6,2,1]=>[2,6,5,4,3,8,7,1]=>{{1,2,6,8},{3,5},{4},{7}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[1,2,6,7,8,5,4,3]=>[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}} [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]=>{{1,2},{3,4,5,8},{6},{7}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>[1,3,6,7,8,5,4,2]=>[1,4,3,5,8,6,7,2]=>{{1},{2,4,5,8},{3},{6},{7}} [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>[2,4,6,7,8,5,3,1]=>[3,2,5,4,8,6,7,1]=>{{1,3,5,8},{2},{4},{6},{7}} [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,1,4,7,8]=>[3,4,6,7,8,5,2,1]=>[2,5,3,4,8,6,7,1]=>{{1,2,5,8},{3},{4},{6},{7}} [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[4,3,6,7,8,5,2,1]=>[2,5,4,3,8,6,7,1]=>{{1,2,5,8},{3,4},{6},{7}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[1,5,6,7,8,4,3,2]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}} [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[2,5,6,7,8,4,3,1]=>[3,2,4,8,5,6,7,1]=>{{1,3,4,8},{2},{5},{6},{7}} [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[3,5,6,7,8,4,2,1]=>[2,4,3,8,5,6,7,1]=>{{1,2,4,8},{3},{5},{6},{7}} [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>{{1,2,3,8},{4},{5},{6},{7}} [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[5,4,6,7,8,3,2,1]=>[2,3,8,5,4,6,7,1]=>{{1,2,3,8},{4,5},{6},{7}} [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,1,5,7,8]=>[3,6,5,7,8,4,2,1]=>[2,4,3,8,6,5,7,1]=>{{1,2,4,8},{3},{5,6},{7}} [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]=>{{1,2,3,8},{4,6},{5},{7}} [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]=>{{1,2,3,8},{4,5,6},{7}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,1,4,5,6]=>[1,2,7,6,8,5,4,3]=>[1,2,4,5,8,7,6,3]=>{{1},{2},{3,4,5,8},{6,7}} [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[2,1,7,6,8,5,4,3]=>[2,1,4,5,8,7,6,3]=>{{1,2},{3,4,5,8},{6,7}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,1,4,5,7]=>[1,3,7,6,8,5,4,2]=>[1,4,3,5,8,7,6,2]=>{{1},{2,4,5,8},{3},{6,7}} [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,1,4,5,8]=>[3,2,7,6,8,5,4,1]=>[4,3,2,5,8,7,6,1]=>{{1,4,5,8},{2,3},{6,7}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,1,4,6,7]=>[1,4,7,6,8,5,3,2]=>[1,3,5,4,8,7,6,2]=>{{1},{2,3,5,8},{4},{6,7}} [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,1,4,7,8]=>[3,4,7,6,8,5,2,1]=>[2,5,3,4,8,7,6,1]=>{{1,2,5,8},{3},{4},{6,7}} [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,1,4,7,8]=>[4,3,7,6,8,5,2,1]=>[2,5,4,3,8,7,6,1]=>{{1,2,5,8},{3,4},{6,7}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,1,5,6,7]=>[1,6,7,5,8,4,3,2]=>[1,3,4,8,7,6,5,2]=>{{1},{2,3,4,8},{5,7},{6}} [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,1,5,6,8]=>[2,6,7,5,8,4,3,1]=>[3,2,4,8,7,6,5,1]=>{{1,3,4,8},{2},{5,7},{6}} [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,1,5,7,8]=>[3,6,7,5,8,4,2,1]=>[2,4,3,8,7,6,5,1]=>{{1,2,4,8},{3},{5,7},{6}} [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>{{1,2,3,8},{4,7},{5,6}} [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,1,5,6,8]=>[2,7,6,5,8,4,3,1]=>[3,2,4,8,6,7,5,1]=>{{1,3,4,8},{2},{5,6,7}} [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[4,7,6,5,8,3,2,1]=>[2,3,8,4,6,7,5,1]=>{{1,2,3,8},{4},{5,6,7}} [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>{{1,2,3,8},{4,5,7},{6}} [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[7,6,5,4,8,3,2,1]=>[2,3,8,5,6,7,4,1]=>{{1,2,3,8},{4,5,6,7}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]=>{{1,2},{3},{4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[2,3,1,8,7,6,5,4]=>[3,2,1,5,6,7,8,4]=>{{1,3},{2},{4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]=>{{1,2,3},{4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[1,2,4,8,7,6,5,3]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}} [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[2,1,4,8,7,6,5,3]=>[2,1,5,4,6,7,8,3]=>{{1,2},{3,5,6,7,8},{4}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[1,3,4,8,7,6,5,2]=>[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}} [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[2,3,4,8,7,6,5,1]=>[5,2,3,4,6,7,8,1]=>{{1,5,6,7,8},{2},{3},{4}} [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[3,2,4,8,7,6,5,1]=>[5,3,2,4,6,7,8,1]=>{{1,5,6,7,8},{2,3},{4}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[1,4,3,8,7,6,5,2]=>[1,5,4,3,6,7,8,2]=>{{1},{2,5,6,7,8},{3,4}} [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[3,4,2,8,7,6,5,1]=>[5,4,3,2,6,7,8,1]=>{{1,5,6,7,8},{2,4},{3}} [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[4,3,2,8,7,6,5,1]=>[5,3,4,2,6,7,8,1]=>{{1,5,6,7,8},{2,3,4}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[1,3,5,8,7,6,4,2]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}} [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,1,2,3,5,8]=>[3,2,5,8,7,6,4,1]=>[4,3,2,6,5,7,8,1]=>{{1,4,6,7,8},{2,3},{5}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,1,2,3,6,7]=>[1,4,5,8,7,6,3,2]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}} [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3,7,8]=>[3,4,5,8,7,6,2,1]=>[2,6,3,4,5,7,8,1]=>{{1,2,6,7,8},{3},{4},{5}} [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,1,2,3,7,8]=>[4,3,5,8,7,6,2,1]=>[2,6,4,3,5,7,8,1]=>{{1,2,6,7,8},{3,4},{5}} [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,1,2,3,7,8]=>[3,5,4,8,7,6,2,1]=>[2,6,3,5,4,7,8,1]=>{{1,2,6,7,8},{3},{4,5}} [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,1,2,3,7,8]=>[4,5,3,8,7,6,2,1]=>[2,6,5,4,3,7,8,1]=>{{1,2,6,7,8},{3,5},{4}} [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[5,4,3,8,7,6,2,1]=>[2,6,4,5,3,7,8,1]=>{{1,2,6,7,8},{3,4,5}} [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,1,2,4,5,8]=>[3,2,6,8,7,5,4,1]=>[4,3,2,5,7,6,8,1]=>{{1,4,5,7,8},{2,3},{6}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,2,4,6,7]=>[1,4,6,8,7,5,3,2]=>[1,3,5,4,7,6,8,2]=>{{1},{2,3,5,7,8},{4},{6}} [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[2,4,6,8,7,5,3,1]=>[3,2,5,4,7,6,8,1]=>{{1,3,5,7,8},{2},{4},{6}} [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,1,2,4,7,8]=>[3,4,6,8,7,5,2,1]=>[2,5,3,4,7,6,8,1]=>{{1,2,5,7,8},{3},{4},{6}} [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,1,2,4,7,8]=>[4,3,6,8,7,5,2,1]=>[2,5,4,3,7,6,8,1]=>{{1,2,5,7,8},{3,4},{6}} [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,1,2,5,6,8]=>[2,5,6,8,7,4,3,1]=>[3,2,4,7,5,6,8,1]=>{{1,3,4,7,8},{2},{5},{6}} [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>[3,5,6,8,7,4,2,1]=>[2,4,3,7,5,6,8,1]=>{{1,2,4,7,8},{3},{5},{6}} [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[4,5,6,8,7,3,2,1]=>[2,3,7,4,5,6,8,1]=>{{1,2,3,7,8},{4},{5},{6}} [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,1,2,6,7,8]=>[5,4,6,8,7,3,2,1]=>[2,3,7,5,4,6,8,1]=>{{1,2,3,7,8},{4,5},{6}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[1,6,5,8,7,4,3,2]=>[1,3,4,7,6,5,8,2]=>{{1},{2,3,4,7,8},{5,6}} [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,1,2,5,6,8]=>[2,6,5,8,7,4,3,1]=>[3,2,4,7,6,5,8,1]=>{{1,3,4,7,8},{2},{5,6}} [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,1,2,5,7,8]=>[3,6,5,8,7,4,2,1]=>[2,4,3,7,6,5,8,1]=>{{1,2,4,7,8},{3},{5,6}} [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,1,2,6,7,8]=>[4,6,5,8,7,3,2,1]=>[2,3,7,4,6,5,8,1]=>{{1,2,3,7,8},{4},{5,6}} [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,1,2,6,7,8]=>[5,6,4,8,7,3,2,1]=>[2,3,7,6,5,4,8,1]=>{{1,2,3,7,8},{4,6},{5}} [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[6,5,4,8,7,3,2,1]=>[2,3,7,5,6,4,8,1]=>{{1,2,3,7,8},{4,5,6}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[1,2,7,8,6,5,4,3]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}} [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[2,1,7,8,6,5,4,3]=>[2,1,4,5,6,8,7,3]=>{{1,2},{3,4,5,6,8},{7}} [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,1,3,4,5,8]=>[2,3,7,8,6,5,4,1]=>[4,2,3,5,6,8,7,1]=>{{1,4,5,6,8},{2},{3},{7}} [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,1,3,4,5,8]=>[3,2,7,8,6,5,4,1]=>[4,3,2,5,6,8,7,1]=>{{1,4,5,6,8},{2,3},{7}} [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,1,3,4,6,8]=>[2,4,7,8,6,5,3,1]=>[3,2,5,4,6,8,7,1]=>{{1,3,5,6,8},{2},{4},{7}} [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,1,3,4,7,8]=>[3,4,7,8,6,5,2,1]=>[2,5,3,4,6,8,7,1]=>{{1,2,5,6,8},{3},{4},{7}} [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,1,3,5,6,8]=>[2,5,7,8,6,4,3,1]=>[3,2,4,6,5,8,7,1]=>{{1,3,4,6,8},{2},{5},{7}} [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[3,5,7,8,6,4,2,1]=>[2,4,3,6,5,8,7,1]=>{{1,2,4,6,8},{3},{5},{7}} [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[4,5,7,8,6,3,2,1]=>[2,3,6,4,5,8,7,1]=>{{1,2,3,6,8},{4},{5},{7}} [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[1,6,7,8,5,4,3,2]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}} [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,1,4,5,6,8]=>[2,6,7,8,5,4,3,1]=>[3,2,4,5,8,6,7,1]=>{{1,3,4,5,8},{2},{6},{7}} [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1,4,5,7,8]=>[3,6,7,8,5,4,2,1]=>[2,4,3,5,8,6,7,1]=>{{1,2,4,5,8},{3},{6},{7}} [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[4,6,7,8,5,3,2,1]=>[2,3,5,4,8,6,7,1]=>{{1,2,3,5,8},{4},{6},{7}} [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}} [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>{{1,2,3,4,8},{5,6},{7}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[1,7,6,8,5,4,3,2]=>[1,3,4,5,8,7,6,2]=>{{1},{2,3,4,5,8},{6,7}} [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[4,7,6,8,5,3,2,1]=>[2,3,5,4,8,7,6,1]=>{{1,2,3,5,8},{4},{6,7}} [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[5,7,6,8,4,3,2,1]=>[2,3,4,8,5,7,6,1]=>{{1,2,3,4,8},{5},{6,7}} [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}} [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>{{1,2,3,4,8},{5,6,7}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,2,3,4,5,6]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}} [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[2,1,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,3]=>{{1,2},{3,4,5,6,7,8}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[1,3,8,7,6,5,4,2]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}} [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,2,3,4,5,8]=>[2,3,8,7,6,5,4,1]=>[4,2,3,5,6,7,8,1]=>{{1,4,5,6,7,8},{2},{3}} [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[3,2,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,1]=>{{1,4,5,6,7,8},{2,3}} [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[2,4,8,7,6,5,3,1]=>[3,2,5,4,6,7,8,1]=>{{1,3,5,6,7,8},{2},{4}} [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,1,2,3,4,7,8]=>[3,4,8,7,6,5,2,1]=>[2,5,3,4,6,7,8,1]=>{{1,2,5,6,7,8},{3},{4}} [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[5,6,1,2,3,4,7,8]=>[4,3,8,7,6,5,2,1]=>[2,5,4,3,6,7,8,1]=>{{1,2,5,6,7,8},{3,4}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,2,3,5,6,7]=>[1,5,8,7,6,4,3,2]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}} [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,4,1,2,3,5,7,8]=>[3,5,8,7,6,4,2,1]=>[2,4,3,6,5,7,8,1]=>{{1,2,4,6,7,8},{3},{5}} [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[4,5,8,7,6,3,2,1]=>[2,3,6,4,5,7,8,1]=>{{1,2,3,6,7,8},{4},{5}} [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[5,4,8,7,6,3,2,1]=>[2,3,6,5,4,7,8,1]=>{{1,2,3,6,7,8},{4,5}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[1,6,8,7,5,4,3,2]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}} [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[2,6,8,7,5,4,3,1]=>[3,2,4,5,7,6,8,1]=>{{1,3,4,5,7,8},{2},{6}} [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,3,1,2,4,5,7,8]=>[3,6,8,7,5,4,2,1]=>[2,4,3,5,7,6,8,1]=>{{1,2,4,5,7,8},{3},{6}} [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[4,6,8,7,5,3,2,1]=>[2,3,5,4,7,6,8,1]=>{{1,2,3,5,7,8},{4},{6}} [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[5,6,8,7,4,3,2,1]=>[2,3,4,7,5,6,8,1]=>{{1,2,3,4,7,8},{5},{6}} [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[6,5,8,7,4,3,2,1]=>[2,3,4,7,6,5,8,1]=>{{1,2,3,4,7,8},{5,6}} [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,3,4,5,6,7]=>[1,7,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}} [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[2,7,8,6,5,4,3,1]=>[3,2,4,5,6,8,7,1]=>{{1,3,4,5,6,8},{2},{7}} [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,2,1,3,4,5,7,8]=>[3,7,8,6,5,4,2,1]=>[2,4,3,5,6,8,7,1]=>{{1,2,4,5,6,8},{3},{7}} [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[5,7,8,6,4,3,2,1]=>[2,3,4,6,5,8,7,1]=>{{1,2,3,4,6,8},{5},{7}} [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}} [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>{{1,2,3,4,5,8},{6,7}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}} [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[2,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,1]=>{{1,3,4,5,6,7,8},{2}} [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,5,7,8]=>[3,8,7,6,5,4,2,1]=>[2,4,3,5,6,7,8,1]=>{{1,2,4,5,6,7,8},{3}} [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[4,8,7,6,5,3,2,1]=>[2,3,5,4,6,7,8,1]=>{{1,2,3,5,6,7,8},{4}} [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[5,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}} [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[6,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,1]=>{{1,2,3,4,5,7,8},{6}} [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{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]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}} [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,1,9]=>{{1,2,3,4,5,6,7,8},{9}} [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}} [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1,3,4,5,6,7,8]=>[1,8,9,7,6,5,4,3,2]=>[1,3,4,5,6,7,9,8,2]=>{{1},{2,3,4,5,6,7,9},{8}} [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1]=>[7,8,6,5,4,3,2,1,9]=>[2,3,4,5,6,8,7,1,9]=>{{1,2,3,4,5,6,8},{7},{9}} [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}} [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,11,2]=>{{1},{2,3,4,5,6,7,8,9,10,11}} [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,1,3,4,5,6,7,8,9]=>[1,9,10,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,10,9,2]=>{{1},{2,3,4,5,6,7,8,10},{9}} [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[1,7,9,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,9,2]=>{{1},{2,3,4,5,6,8,9},{7}} [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,9,1]=>[6,8,7,5,4,3,2,1,9]=>[2,3,4,5,7,6,8,1,9]=>{{1,2,3,4,5,7,8},{6},{9}} [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[8,9,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,9,8,1,10]=>{{1,2,3,4,5,6,7,9},{8},{10}} [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>{{1,2,3,4,5,6,7,8,9,10},{11}} [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}} [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[1,3,9,8,7,6,5,4,2]=>[1,4,3,5,6,7,8,9,2]=>{{1},{2,4,5,6,7,8,9},{3}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[2,1,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,3]=>{{1,2},{3,4,5,6,7,8,9}} [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,9,1]=>[2,8,7,6,5,4,3,1,9]=>[3,2,4,5,6,7,8,1,9]=>{{1,3,4,5,6,7,8},{2},{9}} [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,6,7,8,9,1]=>[5,6,7,8,4,3,2,1,9]=>[2,3,4,8,5,6,7,1,9]=>{{1,2,3,4,8},{5},{6},{7},{9}} [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[7,6,5,4,3,2,1,9,8]=>[2,3,4,5,6,7,1,9,8]=>{{1,2,3,4,5,6,7},{8,9}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,2,3,4,5,6,7]=>[1,2,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,3]=>{{1},{2},{3,4,5,6,7,8,9}} [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2,9]=>[1,3,4,5,6,7,8,2,9]=>{{1},{2,3,4,5,6,7,8},{9}} [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>{{1,2,3,4,5,6,7},{8},{9}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,3]=>{{1,2},{3,4,5,6,7,8,9,10}} [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,6,7,8,9,2,1]=>[6,7,5,4,3,2,1,8,9]=>[2,3,4,5,7,6,1,8,9]=>{{1,2,3,4,5,7},{6},{8},{9}} [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[8,7,6,5,4,3,2,1,10,9]=>[2,3,4,5,6,7,8,1,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,10,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,10,3]=>{{1},{2},{3,4,5,6,7,8,9,10}} [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2,10]=>[1,3,4,5,6,7,8,9,2,10]=>{{1},{2,3,4,5,6,7,8,9},{10}} [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>{{1,2,3,4,5,6,7,8},{9},{10}} []=>[]=>[]=>[]=>{} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,1,9]=>[3,2,4,5,6,7,8,9,1]=>[9,3,2,4,5,6,7,8,1]=>{{1,9},{2,3},{4},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,4,3,2,1,9]=>[3,4,2,5,6,7,8,9,1]=>[9,4,3,2,5,6,7,8,1]=>{{1,9},{2,4},{3},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,7,8,5,4,3,2,1,9]=>[4,3,2,5,6,7,8,9,1]=>[9,3,4,2,5,6,7,8,1]=>{{1,9},{2,3,4},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1,9]=>[5,4,3,2,6,7,8,9,1]=>[9,3,4,5,2,6,7,8,1]=>{{1,9},{2,3,4,5},{6},{7},{8}} [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,4,6,3,7,2,8,1,9]=>[5,6,4,7,3,8,2,9,1]=>[9,8,7,6,5,4,3,2,1]=>{{1,9},{2,8},{3,7},{4,6},{5}} [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1,9]=>[7,8,6,5,4,3,2,9,1]=>[9,3,4,5,6,8,7,2,1]=>{{1,9},{2,3,4,5,6,8},{7}} [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,7,6,5,4,3,2,9,1]=>[9,3,4,5,6,7,8,2,1]=>{{1,9},{2,3,4,5,6,7,8}} [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,1,2,9]=>[2,3,4,5,6,7,9,8,1]=>[8,2,3,4,5,6,7,9,1]=>{{1,8,9},{2},{3},{4},{5},{6},{7}} [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,1,3,9]=>[2,3,4,5,6,8,9,7,1]=>[7,2,3,4,5,6,9,8,1]=>{{1,7,9},{2},{3},{4},{5},{6},{8}} [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,3,2,1,4,9]=>[2,3,4,5,7,8,9,6,1]=>[6,2,3,4,5,9,7,8,1]=>{{1,6,9},{2},{3},{4},{5},{7},{8}} [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,3,2,1,5,9]=>[2,3,4,6,7,8,9,5,1]=>[5,2,3,4,9,6,7,8,1]=>{{1,5,9},{2},{3},{4},{6},{7},{8}} [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,3,2,1,6,9]=>[2,3,5,6,7,8,9,4,1]=>[4,2,3,9,5,6,7,8,1]=>{{1,4,9},{2},{3},{5},{6},{7},{8}} [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,1,7,9]=>[2,4,5,6,7,8,9,3,1]=>[3,2,9,4,5,6,7,8,1]=>{{1,3,9},{2},{4},{5},{6},{7},{8}} [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,8,9]=>[3,4,5,6,7,8,9,2,1]=>[2,9,3,4,5,6,7,8,1]=>{{1,2,9},{3},{4},{5},{6},{7},{8}} [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,5,4,3,2,1,8,9]=>[4,3,5,6,7,8,9,2,1]=>[2,9,4,3,5,6,7,8,1]=>{{1,2,9},{3,4},{5},{6},{7},{8}} [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[8,7,6,5,4,3,9,2,1]=>[2,9,4,5,6,7,8,3,1]=>{{1,2,9},{3,4,5,6,7,8}} [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,7,8,9]=>[4,5,6,7,8,9,3,2,1]=>[2,3,9,4,5,6,7,8,1]=>{{1,2,3,9},{4},{5},{6},{7},{8}} [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,4,3,2,1,7,8,9]=>[5,4,6,7,8,9,3,2,1]=>[2,3,9,5,4,6,7,8,1]=>{{1,2,3,9},{4,5},{6},{7},{8}} [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[8,7,6,5,4,9,3,2,1]=>[2,3,9,5,6,7,8,4,1]=>{{1,2,3,9},{4,5,6,7,8}} [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[5,6,7,8,9,4,3,2,1]=>[2,3,4,9,5,6,7,8,1]=>{{1,2,3,4,9},{5},{6},{7},{8}} [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,5,3,2,1,6,7,8,9]=>[6,5,7,8,9,4,3,2,1]=>[2,3,4,9,6,5,7,8,1]=>{{1,2,3,4,9},{5,6},{7},{8}} [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[8,7,6,5,9,4,3,2,1]=>[2,3,4,9,6,7,8,5,1]=>{{1,2,3,4,9},{5,6,7,8}} [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9]=>[6,7,8,9,5,4,3,2,1]=>[2,3,4,5,9,6,7,8,1]=>{{1,2,3,4,5,9},{6},{7},{8}} [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8,9]=>[7,6,8,9,5,4,3,2,1]=>[2,3,4,5,9,7,6,8,1]=>{{1,2,3,4,5,9},{6,7},{8}} [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,1,5,6,7,8,9]=>[6,8,7,9,5,4,3,2,1]=>[2,3,4,5,9,6,8,7,1]=>{{1,2,3,4,5,9},{6},{7,8}} [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[8,7,6,9,5,4,3,2,1]=>[2,3,4,5,9,7,8,6,1]=>{{1,2,3,4,5,9},{6,7,8}} [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[8,7,1,2,3,4,5,6,9]=>[2,3,9,8,7,6,5,4,1]=>[4,2,3,5,6,7,8,9,1]=>{{1,4,5,6,7,8,9},{2},{3}} [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[3,2,9,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,9,1]=>{{1,4,5,6,7,8,9},{2,3}} [1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1,2,3,6,7,8,9]=>[5,6,9,8,7,4,3,2,1]=>[2,3,4,7,5,6,8,9,1]=>{{1,2,3,4,7,8,9},{5},{6}} [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,2,5,6,7,8,9]=>[6,7,9,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,9,1]=>{{1,2,3,4,5,8,9},{6},{7}} [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[7,6,9,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,9,1]=>{{1,2,3,4,5,8,9},{6,7}} [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[7,8,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,7,8,1]=>{{1,2,3,4,5,6,9},{7},{8}} [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[8,7,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,8,7,1]=>{{1,2,3,4,5,6,9},{7,8}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[2,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,1]=>{{1,3,4,5,6,7,8,9},{2}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[3,9,8,7,6,5,4,2,1]=>[2,4,3,5,6,7,8,9,1]=>{{1,2,4,5,6,7,8,9},{3}} [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[5,9,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,9,1]=>{{1,2,3,4,6,7,8,9},{5}} [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[6,9,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,9,1]=>{{1,2,3,4,5,7,8,9},{6}} [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[7,9,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,9,1]=>{{1,2,3,4,5,6,8,9},{7}} [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[8,9,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,9,8,1]=>{{1,2,3,4,5,6,7,9},{8}} [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>{{1,3},{2},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,5,4,3,2,1]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>{{1,4},{2},{3},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,4,3,2,1]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>{{1,5},{2},{3},{4},{6},{7},{8},{9}} [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,3,2,1]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>{{1,6},{2},{3},{4},{5},{7},{8},{9}} [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,2,1]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>{{1,7},{2},{3},{4},{5},{6},{8},{9}} [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>{{1,8},{2},{3},{4},{5},{6},{7},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>{{1,2,3},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[8,6,7,9,5,4,3,2,1]=>[2,4,3,1,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>{{1,3,4},{2},{5},{6},{7},{8},{9}} [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>[3,4,2,1,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>{{1,2,4},{3},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[4,3,2,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}} [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,1,2,10]=>[2,3,4,5,6,7,8,10,9,1]=>[9,2,3,4,5,6,7,8,10,1]=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>{{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,9,4,3,2,1]=>[4,5,3,2,1,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>{{1,2,3,5},{4},{6},{7},{8},{9}} [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,2,1,3,10]=>[2,3,4,5,6,7,9,10,8,1]=>[8,2,3,4,5,6,7,10,9,1]=>{{1,8,10},{2},{3},{4},{5},{6},{7},{9}} [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,1,2,11]=>[2,3,4,5,6,7,8,9,11,10,1]=>[10,2,3,4,5,6,7,8,9,11,1]=>{{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[5,4,3,2,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}} [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,3,2,1,4,10]=>[2,3,4,5,6,8,9,10,7,1]=>[7,2,3,4,5,6,10,8,9,1]=>{{1,7,10},{2},{3},{4},{5},{6},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}} [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,9,1]=>[3,4,5,6,7,8,2,1,9]=>[2,8,3,4,5,6,7,1,9]=>{{1,2,8},{3},{4},{5},{6},{7},{9}} [1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,9,3,2,1]=>[5,6,4,3,2,1,7,8,9]=>[2,3,4,6,5,1,7,8,9]=>{{1,2,3,4,6},{5},{7},{8},{9}} [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,8,7,5,4,3,2,1,6,10]=>[2,3,4,6,7,8,9,10,5,1]=>[5,2,3,4,10,6,7,8,9,1]=>{{1,5,10},{2},{3},{4},{6},{7},{8},{9}} [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}} [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,8,6,5,4,3,2,1,7,10]=>[2,3,5,6,7,8,9,10,4,1]=>[4,2,3,10,5,6,7,8,9,1]=>{{1,4,10},{2},{3},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}} [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,7,6,5,4,3,2,1,8,10]=>[2,4,5,6,7,8,9,10,3,1]=>[3,2,10,4,5,6,7,8,9,1]=>{{1,3,10},{2},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,2,1]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>{{1},{2,3},{4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,5,4,3,2,1]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>{{1},{2},{3,4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,5,4,3,2,1]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>{{1,2},{3,4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,5,4,3,2,1]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]=>{{1},{2,3,4},{5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,4,3,2,1]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>{{1},{2},{3},{4,5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,4,3,2,1]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>{{1},{2,3},{4,5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,6,4,3,2,1]=>[3,2,1,5,4,6,7,8,9]=>[2,3,1,5,4,6,7,8,9]=>{{1,2,3},{4,5},{6},{7},{8},{9}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,3,2,1]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>{{1},{2},{3},{4},{5,6},{7},{8},{9}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,3,2,1]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>{{1,2},{3,4},{5,6},{7},{8},{9}} [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,4,5,3,2,1]=>[4,3,2,1,6,5,7,8,9]=>[2,3,4,1,6,5,7,8,9]=>{{1,2,3,4},{5,6},{7},{8},{9}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,2,1]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>{{1},{2},{3},{4},{5},{6,7},{8},{9}} [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,4,2,1]=>[5,4,3,2,1,7,6,8,9]=>[2,3,4,5,1,7,6,8,9]=>{{1,2,3,4,5},{6,7},{8},{9}} [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,2,1]=>[1,7,6,5,4,3,2,8,9]=>[1,3,4,5,6,7,2,8,9]=>{{1},{2,3,4,5,6,7},{8},{9}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>{{1},{2},{3},{4},{5},{6},{7,8},{9}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,3,1]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>{{1,2},{3},{4},{5},{6},{7,8},{9}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,2,3,1]=>[1,2,3,4,6,5,8,7,9]=>[1,2,3,4,6,5,8,7,9]=>{{1},{2},{3},{4},{5,6},{7,8},{9}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,4,5,2,3,1]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>{{1},{2},{3,4},{5,6},{7,8},{9}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,2,3,1]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>{{1,2},{3,4},{5,6},{7,8},{9}} [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,3,1]=>[6,5,4,3,2,1,8,7,9]=>[2,3,4,5,6,1,8,7,9]=>{{1,2,3,4,5,6},{7,8},{9}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,6,7,1]=>[2,1,8,7,6,5,4,3,9]=>[2,1,4,5,6,7,8,3,9]=>{{1,2},{3,4,5,6,7,8},{9}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>{{1,2},{3},{4},{5},{6},{7},{8,9}} [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,1,2]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>{{1},{2,3},{4},{5},{6},{7},{8,9}} [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,1,2]=>[3,2,1,4,5,6,7,9,8]=>[2,3,1,4,5,6,7,9,8]=>{{1,2,3},{4},{5},{6},{7},{8,9}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>{{1},{2},{3},{4},{5},{6,7},{8,9}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,3,4,1,2]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>{{1},{2},{3},{4,5},{6,7},{8,9}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,3,4,1,2]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>{{1},{2,3},{4,5},{6,7},{8,9}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,6,3,4,1,2]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]=>{{1,2,3},{4,5},{6,7},{8,9}} [1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,4,1,2]=>[5,4,3,2,1,7,6,9,8]=>[2,3,4,5,1,7,6,9,8]=>{{1,2,3,4,5},{6,7},{8,9}} [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,1,2]=>[1,7,6,5,4,3,2,9,8]=>[1,3,4,5,6,7,2,9,8]=>{{1},{2,3,4,5,6,7},{8,9}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,1,2,3]=>[2,1,3,4,5,6,9,8,7]=>[2,1,3,4,5,6,8,9,7]=>{{1,2},{3},{4},{5},{6},{7,8,9}} [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[6,5,4,3,2,1,9,8,7]=>[2,3,4,5,6,1,8,9,7]=>{{1,2,3,4,5,6},{7,8,9}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]=>{{1},{2},{3},{4},{5},{6,7,8,9}} [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[5,4,3,2,1,9,8,7,6]=>[2,3,4,5,1,7,8,9,6]=>{{1,2,3,4,5},{6,7,8,9}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,5]=>{{1},{2},{3},{4},{5,6,7,8,9}} [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[4,3,2,1,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,5]=>{{1,2,3,4},{5,6,7,8,9}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,9,8,7,6,5,4]=>[1,2,3,5,6,7,8,9,4]=>{{1},{2},{3},{4,5,6,7,8,9}} [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[3,2,1,9,8,7,6,5,4]=>[2,3,1,5,6,7,8,9,4]=>{{1,2,3},{4,5,6,7,8,9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,9,7,6,5,4,3,2,1]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>{{1},{2,3},{4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[10,9,7,8,6,5,4,3,2,1]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>{{1},{2},{3,4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,6,5,4,3,2,1]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>{{1,2},{3,4},{5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,7,5,4,3,2,1]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>{{1},{2},{3},{4,5},{6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>{{1},{2},{3},{4},{5,6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,4,3,2,1]=>[2,1,4,3,6,5,7,8,9,10]=>[2,1,4,3,6,5,7,8,9,10]=>{{1,2},{3,4},{5,6},{7},{8},{9},{10}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,5,3,2,1]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>{{1},{2},{3},{4},{5},{6,7},{8},{9},{10}} [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,4,2,1]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>{{1},{2},{3},{4},{5},{6},{7,8},{9},{10}} [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,2,1]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>{{1,2},{3,4},{5,6},{7,8},{9},{10}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>{{1},{2},{3},{4},{5},{6},{7},{8,9},{10}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,7,4,5,2,3,1]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>{{1},{2},{3},{4,5},{6,7},{8,9},{10}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}} [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,2,3,1]=>[7,6,5,4,3,2,1,9,8,10]=>[2,3,4,5,6,7,1,9,8,10]=>{{1,2,3,4,5,6,7},{8,9},{10}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>{{1,2},{3},{4},{5},{6},{7},{8},{9,10}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>{{1},{2},{3},{4},{5},{6},{7,8},{9,10}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,3,4,1,2]=>[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]=>{{1},{2},{3},{4},{5,6},{7,8},{9,10}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[10,9,7,8,5,6,3,4,1,2]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>{{1},{2},{3,4},{5,6},{7,8},{9,10}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10}} [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[9,10,3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,4,5,6,7,8,3,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,9,10,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,1,2,3]=>[1,3,2,5,4,7,6,10,9,8]=>[1,3,2,5,4,7,6,9,10,8]=>{{1},{2,3},{4,5},{6,7},{8,9,10}} [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[7,6,5,4,3,2,1,10,9,8]=>[2,3,4,5,6,7,1,9,10,8]=>{{1,2,3,4,5,6,7},{8,9,10}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}} [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,1,2,3,4]=>[2,1,4,3,6,5,10,9,8,7]=>[2,1,4,3,6,5,8,9,10,7]=>{{1,2},{3,4},{5,6},{7,8,9,10}} [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,5,6,1,2,3,4]=>[4,3,2,1,6,5,10,9,8,7]=>[2,3,4,1,6,5,8,9,10,7]=>{{1,2,3,4},{5,6},{7,8,9,10}} [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[9,10,5,6,7,8,1,2,3,4]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,4,5,6,3,8,9,10,7]=>{{1,2},{3,4,5,6},{7,8,9,10}} [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[6,5,4,3,2,1,10,9,8,7]=>[2,3,4,5,6,1,8,9,10,7]=>{{1,2,3,4,5,6},{7,8,9,10}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,10,9,8,7,6]=>[1,2,3,4,5,7,8,9,10,6]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}} [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>[2,3,4,5,1,7,8,9,10,6]=>{{1,2,3,4,5},{6,7,8,9,10}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,10,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,10,5]=>{{1},{2},{3},{4},{5,6,7,8,9,10}} [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[4,3,2,1,10,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,10,5]=>{{1,2,3,4},{5,6,7,8,9,10}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,10,9,8,7,6,5,4]=>[1,2,3,5,6,7,8,9,10,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[3,2,1,10,9,8,7,6,5,4]=>[2,3,1,5,6,7,8,9,10,4]=>{{1,2,3},{4,5,6,7,8,9,10}} [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>{{1},{2},{3},{4},{5},{6},{7,9},{8}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>{{1},{2},{3},{4},{5},{6,9},{7},{8}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,1,5]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>{{1},{2},{3},{4},{5,9},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,3,2,1,6]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>{{1},{2},{3},{4,9},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,2,1,7]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>{{1},{2},{3,9},{4},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1,8]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>{{1},{2,9},{3},{4},{5},{6},{7},{8}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,1,4]=>[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,9,8,7,6]=>{{1},{2},{3},{4},{5},{6,9},{7,8}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,4,2,1,5]=>[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,9,7,6,8,5]=>{{1},{2},{3},{4},{5,9},{6,7},{8}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,3,2,1,5]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>{{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,3,2,1,6]=>[1,2,3,6,5,7,8,9,4]=>[1,2,3,9,6,5,7,8,4]=>{{1},{2},{3},{4,9},{5,6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,4,3,2,1,6]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>{{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[9,8,5,6,4,3,2,1,7]=>[1,2,5,4,6,7,8,9,3]=>[1,2,9,5,4,6,7,8,3]=>{{1},{2},{3,9},{4,5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,4,3,2,1,7]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>{{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[9,6,7,5,4,3,2,1,8]=>[1,4,3,5,6,7,8,9,2]=>[1,9,4,3,5,6,7,8,2]=>{{1},{2,9},{3,4},{5},{6},{7},{8}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,2,1,8]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>{{1},{2},{3,10},{4},{5},{6},{7},{8},{9}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1,9]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,1,2,7,8,9,10]=>[5,6,7,8,10,9,4,3,2,1]=>[2,3,4,9,5,6,7,8,10,1]=>{{1,2,3,4,9,10},{5},{6},{7},{8}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,1,10]=>[3,2,4,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>{{1,10},{2,3},{4},{5},{6},{7},{8},{9}} [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[9,8,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,9,8,1]=>{{1,2,3,4,5,6,7,10},{8,9}} [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,1,7,8]=>[1,4,5,6,7,8,9,3,2]=>[1,3,9,4,5,6,7,8,2]=>{{1},{2,3,9},{4},{5},{6},{7},{8}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,1,3,4]=>[1,2,3,4,5,8,9,7,6]=>[1,2,3,4,5,7,9,8,6]=>{{1},{2},{3},{4},{5},{6,7,9},{8}} [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,8,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,8,9,2,1]=>{{1,10},{2,3,4,5,6,7,8,9}} [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[2,10,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,10,1]=>{{1,3,4,5,6,7,8,9,10},{2}} [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[2,11,10,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,10,11,1]=>{{1,3,4,5,6,7,8,9,10,11},{2}} [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,1,3,4,5,6,7,8,10]=>[2,9,10,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,10,9,1]=>{{1,3,4,5,6,7,8,10},{2},{9}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[9,8,6,1,2,3,4,5,7]=>[1,2,4,9,8,7,6,5,3]=>[1,2,5,4,6,7,8,9,3]=>{{1},{2},{3,5,6,7,8,9},{4}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,1,2,3,4,6]=>[1,2,3,5,9,8,7,6,4]=>[1,2,3,6,5,7,8,9,4]=>{{1},{2},{3},{4,6,7,8,9},{5}} [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,1,2,3,5]=>[1,2,3,4,6,9,8,7,5]=>[1,2,3,4,7,6,8,9,5]=>{{1},{2},{3},{4},{5,7,8,9},{6}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,1,2,4]=>[1,2,3,4,5,7,9,8,6]=>[1,2,3,4,5,8,7,9,6]=>{{1},{2},{3},{4},{5},{6,8,9},{7}} [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[9,10,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,10,9,1]=>{{1,2,3,4,5,6,7,8,10},{9}} [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,8,9,7,1]=>{{1,2,3,4,5,6,10},{7,8,9}} [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,10,7,8,9,6,1]=>{{1,2,3,4,5,10},{6,7,8,9}} [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,10,6,7,8,9,5,1]=>{{1,2,3,4,10},{5,6,7,8,9}} [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[9,8,7,6,5,4,10,3,2,1]=>[2,3,10,5,6,7,8,9,4,1]=>{{1,2,3,10},{4,5,6,7,8,9}} [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[9,8,7,6,5,4,3,10,2,1]=>[2,10,4,5,6,7,8,9,3,1]=>{{1,2,10},{3,4,5,6,7,8,9}} [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,7,1,8]=>[1,4,5,6,7,8,3,9,2]=>[1,9,8,4,5,6,7,3,2]=>{{1},{2,9},{3,8},{4},{5},{6},{7}} [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,11,10,1]=>{{1,2,3,4,5,6,7,8,9,11},{10}} [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,1,3]=>[6,5,4,3,2,1,8,9,7]=>[2,3,4,5,6,1,9,8,7]=>{{1,2,3,4,5,6},{7,9},{8}} [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,1,2,8]=>[1,3,4,5,6,7,9,8,2]=>[1,8,3,4,5,6,7,9,2]=>{{1},{2,8,9},{3},{4},{5},{6},{7}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,9,6,5,4,3,2,1,7]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]=>{{1,2},{3,9},{4},{5},{6},{7},{8}} [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,1,2]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]=>{{1,7},{2},{3},{4},{5},{6},{8,9}} [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[4,5,6,7,8,9,10,3,2,1]=>[2,3,10,4,5,6,7,8,9,1]=>{{1,2,3,10},{4},{5},{6},{7},{8},{9}} [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[8,7,9,1,2,3,4,5,6]=>[2,3,1,9,8,7,6,5,4]=>[3,2,1,5,6,7,8,9,4]=>{{1,3},{2},{4,5,6,7,8,9}} [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[5,10,9,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,9,10,1]=>{{1,2,3,4,6,7,8,9,10},{5}} [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[6,10,9,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,9,10,1]=>{{1,2,3,4,5,7,8,9,10},{6}} [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,2,3,1,4]=>[2,1,4,3,6,5,9,8,10,7]=>[2,1,4,3,6,5,10,9,8,7]=>{{1,2},{3,4},{5,6},{7,10},{8,9}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,1,3]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]=>{{1},{2,3},{4,5},{6,7},{8,10},{9}} [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[3,4,5,6,7,8,9,10,2,1]=>[2,10,3,4,5,6,7,8,9,1]=>{{1,2,10},{3},{4},{5},{6},{7},{8},{9}} [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>{{1,9},{2,8},{3,7},{4,6},{5},{10}} [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[9,6,4,3,5,7,2,8,10,1]=>[2,5,7,8,6,4,9,3,1,10]=>[3,2,9,6,5,8,7,4,1,10]=>{{1,3,9},{2},{4,6,8},{5},{7},{10}} [1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[9,6,5,7,3,2,4,8,10,1]=>[2,5,6,4,8,9,7,3,1,10]=>[3,2,7,6,5,4,9,8,1,10]=>{{1,3,7,9},{2},{4,6},{5},{8},{10}} [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[9,7,4,3,5,2,6,8,10,1]=>[2,4,7,8,6,9,5,3,1,10]=>[3,2,5,4,9,8,7,6,1,10]=>{{1,3,5,9},{2},{4},{6,8},{7},{10}} [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,3,2,4,6,8,10,1]=>[2,4,6,8,9,7,5,3,1,10]=>[3,2,5,4,7,6,9,8,1,10]=>{{1,3,5,7,9},{2},{4},{6},{8},{10}} [1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[7,6,8,5,9,4,10,2,1,3]=>[4,5,3,6,2,7,1,9,10,8]=>[7,6,5,4,3,2,1,10,9,8]=>{{1,7},{2,6},{3,5},{4},{8,10},{9}} [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[8,7,9,6,10,4,2,1,3,5]=>[3,4,2,5,1,7,9,10,8,6]=>[5,4,3,2,1,8,7,10,9,6]=>{{1,5},{2,4},{3},{6,8,10},{7},{9}} [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[10,8,6,4,2,1,3,5,7,9]=>[1,3,5,7,9,10,8,6,4,2]=>[1,4,3,6,5,8,7,10,9,2]=>{{1},{2,4,6,8,10},{3},{5},{7},{9}} [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>{{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}} [1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[11,8,6,4,3,5,7,9,2,10,12,1]=>[2,5,7,9,10,8,6,4,11,3,1,12]=>[3,2,11,6,5,8,7,10,9,4,1,12]=>{{1,3,11},{2},{4,6,8,10},{5},{7},{9},{12}} [1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[11,8,6,5,7,9,3,2,4,10,12,1]=>[2,5,7,8,6,4,10,11,9,3,1,12]=>[3,2,9,6,5,8,7,4,11,10,1,12]=>{{1,3,9,11},{2},{4,6,8},{5},{7},{10},{12}} [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[11,8,7,9,4,3,5,2,6,10,12,1]=>[2,5,6,4,9,10,8,11,7,3,1,12]=>[3,2,7,6,5,4,11,10,9,8,1,12]=>{{1,3,7,11},{2},{4,6},{5},{8,10},{9},{12}} [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[11,8,7,9,5,3,2,4,6,10,12,1]=>[2,5,6,4,8,10,11,9,7,3,1,12]=>[3,2,7,6,5,4,9,8,11,10,1,12]=>{{1,3,7,9,11},{2},{4,6},{5},{8},{10},{12}} [1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[11,9,6,4,3,5,7,2,8,10,12,1]=>[2,4,7,9,10,8,6,11,5,3,1,12]=>[3,2,5,4,11,8,7,10,9,6,1,12]=>{{1,3,5,11},{2},{4},{6,8,10},{7},{9},{12}} [1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[11,9,6,5,7,3,2,4,8,10,12,1]=>[2,4,7,8,6,10,11,9,5,3,1,12]=>[3,2,5,4,9,8,7,6,11,10,1,12]=>{{1,3,5,9,11},{2},{4},{6,8},{7},{10},{12}} [1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[11,9,7,4,3,5,2,6,8,10,12,1]=>[2,4,6,9,10,8,11,7,5,3,1,12]=>[3,2,5,4,7,6,11,10,9,8,1,12]=>{{1,3,5,7,11},{2},{4},{6},{8,10},{9},{12}} [1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[11,9,7,5,3,2,4,6,8,10,12,1]=>[2,4,6,8,10,11,9,7,5,3,1,12]=>[3,2,5,4,7,6,9,8,11,10,1,12]=>{{1,3,5,7,9,11},{2},{4},{6},{8},{10},{12}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[10,9,11,8,12,4,3,5,2,6,1,7]=>[3,4,2,5,1,9,10,8,11,7,12,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>{{1,5},{2,4},{3},{6,12},{7,11},{8,10},{9}} [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[11,10,12,7,4,3,5,2,6,8,1,9]=>[2,3,1,6,9,10,8,11,7,5,12,4]=>[3,2,1,12,7,6,11,10,9,8,5,4]=>{{1,3},{2},{4,12},{5,7,11},{6},{8,10},{9}} [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,11,1]=>{{1,2,3,4,5,6,7,8,9,10,11}} [1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[9,8,7,6,5,4,3,2,1,11,10]=>[2,3,4,5,6,7,8,9,1,11,10]=>{{1,2,3,4,5,6,7,8,9},{10,11}} [1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,3,4,5,6,7,8,9,10,2,1]=>{{1,11},{2,3,4,5,6,7,8,9,10}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10}} [1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[7,8,6,9,5,4,3,2,1]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>{{1,4},{2,3},{5},{6},{7},{8},{9}} [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,1,2,3]=>[2,3,4,5,6,1,9,8,7]=>[6,2,3,4,5,1,8,9,7]=>{{1,6},{2},{3},{4},{5},{7,8,9}} [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[5,6,7,8,9,10,4,3,2,1]=>[2,3,4,10,5,6,7,8,9,1]=>{{1,2,3,4,10},{5},{6},{7},{8},{9}} [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[8,9,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,8,9,1]=>{{1,2,3,4,5,6,7,10},{8},{9}} [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,7,6,8,5,4,3,2,1]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>{{1},{2,4},{3},{5},{6},{7},{8},{9}} [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[6,7,8,9,10,5,4,3,2,1]=>[2,3,4,5,10,6,7,8,9,1]=>{{1,2,3,4,5,10},{6},{7},{8},{9}} [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9,10]=>[7,8,9,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,7,8,9,1]=>{{1,2,3,4,5,6,10},{7},{8},{9}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10},{11}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[3,2,10,9,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,9,10,1]=>{{1,4,5,6,7,8,9,10},{2,3}} [1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,9,4,3,2,1]=>[3,4,2,5,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>{{1,5},{2,4},{3},{6},{7},{8},{9}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[8,7,9,5,6,3,4,1,2]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>{{1,3},{2},{4,5},{6,7},{8,9}} [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,2,1,3,4]=>[2,1,4,3,6,5,9,10,8,7]=>[2,1,4,3,6,5,8,10,9,7]=>{{1,2},{3,4},{5,6},{7,8,10},{9}} [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[8,9,7,10,6,5,4,3,2,1]=>[3,2,4,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>{{1,4},{2,3},{5},{6},{7},{8},{9},{10}} [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,1,2,4]=>[2,1,4,3,6,5,8,10,9,7]=>[2,1,4,3,6,5,9,8,10,7]=>{{1,2},{3,4},{5,6},{7,9,10},{8}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[9,8,10,6,7,4,5,2,3,1]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>{{1,3},{2},{4,5},{6,7},{8,9},{10}} [1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1]=>[5,4,6,3,7,2,8,1,9]=>[8,7,6,5,4,3,2,1,9]=>{{1,8},{2,7},{3,6},{4,5},{9}} [1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[6,7,5,8,4,9,3,10,1,2]=>[5,4,6,3,7,2,8,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>{{1,8},{2,7},{3,6},{4,5},{9,10}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,8,11,10,9]=>[1,2,3,4,5,6,7,8,10,11,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,11,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[8,9,7,10,5,6,3,4,1,2]=>[3,2,4,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>{{1,4},{2,3},{5,6},{7,8},{9,10}} [1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1,10]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,7},{5,6}} [1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}} [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,3,1,2,4,6,8]=>[1,3,5,7,9,8,6,4,2]=>[1,4,3,6,5,8,7,9,2]=>{{1},{2,4,6,8,9},{3},{5},{7}} [1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[6,5,7,4,8,3,9,1,2,10]=>[5,6,4,7,3,8,2,10,9,1]=>[9,8,7,6,5,4,3,2,10,1]=>{{1,9,10},{2,8},{3,7},{4,6},{5}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[9,8,6,4,2,1,3,5,7]=>[1,2,4,6,8,9,7,5,3]=>[1,2,5,4,7,6,9,8,3]=>{{1},{2},{3,5,7,9},{4},{6},{8}} [1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[6,4,5,7,3,8,2,9,1,10]=>[5,7,6,4,8,3,9,2,10,1]=>[10,9,8,6,5,7,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,6,7},{5}} [1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[8,7,9,6,10,5,4,3,2,1]=>[3,4,2,5,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>{{1,5},{2,4},{3},{6},{7},{8},{9},{10}}
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].