Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0009;cc-rep-3
[1,0]=>[1]=>[1]=>{{1}} [1,0,1,0]=>[1,2]=>[1,2]=>{{1},{2}} [1,1,0,0]=>[2,1]=>[2,1]=>{{1,2}} [1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}} [1,0,1,1,0,0]=>[1,3,2]=>[3,1,2]=>{{1,2,3}} [1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>{{1,2},{3}} [1,1,0,1,0,0]=>[2,3,1]=>[2,3,1]=>{{1,2,3}} [1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>{{1,3},{2}} [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}} [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[4,1,2,3]=>{{1,2,3,4}} [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[3,1,2,4]=>{{1,2,3},{4}} [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[3,1,4,2]=>{{1,2,3,4}} [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[4,3,1,2]=>{{1,2,3,4}} [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>{{1,2},{3},{4}} [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[4,2,1,3]=>{{1,3,4},{2}} [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[2,3,1,4]=>{{1,2,3},{4}} [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[2,3,4,1]=>{{1,2,3,4}} [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>{{1,4},{2},{3}} [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>{{1,3},{2},{4}} [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[3,2,4,1]=>{{1,3,4},{2}} [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[3,4,2,1]=>{{1,2,3,4}} [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>{{1,4},{2,3}} [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}} [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[5,1,2,3,4]=>{{1,2,3,4,5}} [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[4,1,2,3,5]=>{{1,2,3,4},{5}} [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[4,1,2,5,3]=>{{1,2,3,4,5}} [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[5,4,1,2,3]=>{{1,3,5},{2,4}} [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[3,1,2,4,5]=>{{1,2,3},{4},{5}} [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[5,3,1,2,4]=>{{1,2,3,4,5}} [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[3,1,4,2,5]=>{{1,2,3,4},{5}} [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[3,1,4,5,2]=>{{1,2,3,4,5}} [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[5,3,1,4,2]=>{{1,2,3,5},{4}} [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[4,3,1,2,5]=>{{1,2,3,4},{5}} [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[4,3,1,5,2]=>{{1,2,3,4,5}} [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[4,5,1,3,2]=>{{1,3,4},{2,5}} [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[5,4,3,1,2]=>{{1,2,4,5},{3}} [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}} [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[5,2,1,3,4]=>{{1,3,4,5},{2}} [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[4,2,1,3,5]=>{{1,3,4},{2},{5}} [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[4,2,1,5,3]=>{{1,3,4,5},{2}} [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[5,4,2,1,3]=>{{1,2,3,4,5}} [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}} [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[5,2,3,1,4]=>{{1,4,5},{2},{3}} [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}} [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}} [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}} [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}} [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[4,2,5,3,1]=>{{1,3,4,5},{2}} [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,4,2,3,1]=>{{1,5},{2,3,4}} [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}} [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[5,3,2,1,4]=>{{1,4,5},{2,3}} [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}} [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[3,2,4,5,1]=>{{1,3,4,5},{2}} [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}} [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[3,4,2,1,5]=>{{1,2,3,4},{5}} [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[3,4,2,5,1]=>{{1,2,3,4,5}} [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[3,4,5,2,1]=>{{1,3,5},{2,4}} [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,3,4,2,1]=>{{1,5},{2,3,4}} [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}} [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[4,3,2,5,1]=>{{1,4,5},{2,3}} [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[4,3,5,2,1]=>{{1,2,3,4,5}} [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[4,5,3,2,1]=>{{1,2,4,5},{3}} [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]=>{{1,3,5,6},{2,4}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[4,1,2,5,3,6]=>{{1,2,3,4,5},{6}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>{{1,3,6},{2,4},{5}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>{{1,3,5},{2,4},{6}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>{{1,3,5,6},{2,4}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[5,6,1,2,4,3]=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>{{1,3,4,6},{2,5}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]=>{{1,2,3,4,5,6}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]=>{{1,2,3,4,5},{6}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>{{1,2,3,4,5,6}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>{{1,4,6},{2,5},{3}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[3,1,4,2,5,6]=>{{1,2,3,4},{5},{6}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>{{1,2,3,5,6},{4}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[3,1,4,5,2,6]=>{{1,2,3,4,5},{6}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>{{1,2,3,6},{4},{5}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[5,3,1,4,2,6]=>{{1,2,3,5},{4},{6}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>{{1,2,3,5,6},{4}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[5,3,1,6,4,2]=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>{{1,2,4,5,6},{3}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>{{1,2,3,4},{5},{6}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>{{1,2,4,5,6},{3}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[4,3,1,5,2,6]=>{{1,2,3,4,5},{6}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>{{1,2,4,6},{3},{5}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[4,5,1,3,2,6]=>{{1,3,4},{2,5},{6}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[4,5,1,3,6,2]=>{{1,3,4},{2,5,6}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[4,5,1,6,3,2]=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[6,4,5,1,3,2]=>{{1,2,4,6},{3,5}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>{{1,2,4,5},{3},{6}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>{{1,2,4,5,6},{3}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[5,4,6,1,3,2]=>{{1,2,3,4,5,6}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[5,6,4,1,3,2]=>{{1,3,4,5},{2,6}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>{{1,2,5,6},{3,4}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]=>{{1,3,4,5,6},{2}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]=>{{1,3,4,5},{2},{6}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>{{1,3,4,5,6},{2}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>{{1,4,6},{2,3,5}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[4,2,1,3,5,6]=>{{1,3,4},{2},{5},{6}} [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[4,2,1,5,3,6]=>{{1,3,4,5},{2},{6}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>{{1,3,4,5,6},{2}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>{{1,2,3,4,6},{5}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]=>{{1,2,3,4,5},{6}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[5,6,2,1,4,3]=>{{1,4,5},{2,3,6}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>{{1,2,3,4,5,6}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[6,2,3,1,4,5]=>{{1,4,5,6},{2},{3}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[5,2,3,1,4,6]=>{{1,4,5},{2},{3},{6}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>{{1,4,5,6},{2},{3}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>{{1,2,3,4,5,6}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>{{1,5,6},{2},{3},{4}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[5,2,3,6,4,1]=>{{1,4,5,6},{2},{3}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>{{1,5,6},{2,3,4}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>{{1,6},{2,3,4},{5}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[4,2,5,3,1,6]=>{{1,3,4,5},{2},{6}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[4,2,5,3,6,1]=>{{1,3,4,5,6},{2}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[4,2,5,6,3,1]=>{{1,4,6},{2},{3,5}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,4,2,5,3,1]=>{{1,6},{2,3,4,5}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>{{1,5},{2,3,4},{6}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>{{1,5,6},{2,3,4}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[5,4,2,6,3,1]=>{{1,2,3,4,5,6}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[5,6,2,4,3,1]=>{{1,2,3,5,6},{4}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>{{1,6},{2,3,4,5}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]=>{{1,4,5,6},{2,3}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]=>{{1,4,5},{2,3},{6}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>{{1,4,5,6},{2,3}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>{{1,2,4,5,6},{3}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>{{1,5,6},{2,3},{4}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[5,3,2,6,4,1]=>{{1,4,5,6},{2,3}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>{{1,6},{2,4,5},{3}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>{{1,2,3,4},{5},{6}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[6,3,4,2,1,5]=>{{1,5,6},{2,3,4}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>{{1,2,3,4,5},{6}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>{{1,2,3,4,5,6}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[5,3,6,4,2,1]=>{{1,2,3,5,6},{4}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>{{1,5,6},{2,4},{3}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>{{1,2,4,5},{3},{6}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>{{1,2,4,5,6},{3}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>{{1,3,4,6},{2,5}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>{{1,2,4,5,6},{3}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>{{1,2,5,6},{3,4}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>{{1,3,5,7},{2,4,6}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[5,1,2,3,6,4,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[7,5,1,2,3,6,4]=>{{1,2,3,4,5,7},{6}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[6,5,1,2,3,7,4]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[6,7,1,2,3,5,4]=>{{1,3,5,6},{2,4,7}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>{{1,4,7},{2,3,5,6}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]=>{{1,3,5,6,7},{2,4}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]=>{{1,3,5,6},{2,4},{7}} [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[6,4,1,2,3,7,5]=>{{1,3,5,6,7},{2,4}} [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[4,1,2,5,3,6,7]=>{{1,2,3,4,5},{6},{7}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[7,4,1,2,5,3,6]=>{{1,3,6,7},{2,4},{5}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[4,1,2,5,6,3,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[7,4,1,2,5,6,3]=>{{1,3,7},{2,4},{5},{6}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[6,4,1,2,5,3,7]=>{{1,3,6},{2,4},{5},{7}} [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[6,4,1,2,5,7,3]=>{{1,3,6,7},{2,4},{5}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[6,4,1,2,7,5,3]=>{{1,3,5,6,7},{2,4}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,5,3]=>{{1,3,4,7},{2,5,6}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>{{1,3,5},{2,4},{6},{7}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]=>{{1,3,4,6,7},{2,5}} [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[5,4,1,2,6,3,7]=>{{1,3,5,6},{2,4},{7}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[5,4,1,2,6,7,3]=>{{1,3,5,6,7},{2,4}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[7,5,4,1,2,6,3]=>{{1,3,4,7},{2,5},{6}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[5,6,1,2,4,3,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[5,6,1,2,4,7,3]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[5,6,1,2,7,4,3]=>{{1,3,5,7},{2,4,6}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[7,5,6,1,2,4,3]=>{{1,3,4,6,7},{2,5}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>{{1,3,4,6},{2,5},{7}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[6,5,4,1,2,7,3]=>{{1,3,4,6,7},{2,5}} [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[6,5,7,1,2,4,3]=>{{1,4,6},{2,5},{3,7}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[6,7,5,1,2,4,3]=>{{1,4,6},{2,3,5,7}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>{{1,3,5,7},{2,6},{4}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[7,3,1,2,4,5,6]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[6,3,1,2,4,7,5]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]=>{{1,2,4,5,6,7},{3}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]=>{{1,2,3,4,5},{6},{7}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]=>{{1,4,6,7},{2,5},{3}} [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[5,3,1,2,6,4,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[5,3,1,2,6,7,4]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[7,5,3,1,2,6,4]=>{{1,4,7},{2,5},{3},{6}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]=>{{1,4,6},{2,5},{3},{7}} [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[6,5,3,1,2,7,4]=>{{1,4,6,7},{2,5},{3}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[6,7,3,1,2,5,4]=>{{1,2,4,5,6,7},{3}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]=>{{1,3,4,5,7},{2,6}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[3,1,4,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[7,3,1,4,2,5,6]=>{{1,2,3,5,6,7},{4}} [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[6,3,1,4,2,5,7]=>{{1,2,3,5,6},{4},{7}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[6,3,1,4,2,7,5]=>{{1,2,3,5,6,7},{4}} [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[7,6,3,1,4,2,5]=>{{1,4,5,7},{2,6},{3}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[3,1,4,5,2,6,7]=>{{1,2,3,4,5},{6},{7}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[7,3,1,4,5,2,6]=>{{1,2,3,6,7},{4},{5}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[3,1,4,5,6,2,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[7,3,1,4,5,6,2]=>{{1,2,3,7},{4},{5},{6}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[6,3,1,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[6,3,1,4,5,7,2]=>{{1,2,3,6,7},{4},{5}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[6,3,1,4,7,5,2]=>{{1,2,3,5,6,7},{4}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[7,6,3,1,4,5,2]=>{{1,2,4,5,6,7},{3}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[5,3,1,4,2,6,7]=>{{1,2,3,5},{4},{6},{7}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[7,5,3,1,4,2,6]=>{{1,2,4,5,6,7},{3}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[5,3,1,4,6,2,7]=>{{1,2,3,5,6},{4},{7}} [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[5,3,1,4,6,7,2]=>{{1,2,3,5,6,7},{4}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[7,5,3,1,4,6,2]=>{{1,2,4,5,7},{3},{6}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[5,3,1,6,4,2,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[5,3,1,6,4,7,2]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[5,3,1,6,7,4,2]=>{{1,2,3,5,7},{4,6}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[7,5,3,1,6,4,2]=>{{1,2,4,5,6,7},{3}} [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[6,5,3,1,4,2,7]=>{{1,2,4,5,6},{3},{7}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[6,5,3,1,4,7,2]=>{{1,2,4,5,6,7},{3}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[6,5,3,1,7,4,2]=>{{1,4,6},{2,5,7},{3}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[6,7,3,1,5,4,2]=>{{1,4,6},{2,7},{3},{5}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]=>{{1,2,4,5,6,7},{3}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]=>{{1,2,4,5,6},{3},{7}} [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[6,4,3,1,2,7,5]=>{{1,2,4,5,6,7},{3}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]=>{{1,5,7},{2,6},{3,4}} [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[4,3,1,5,2,6,7]=>{{1,2,3,4,5},{6},{7}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[7,4,3,1,5,2,6]=>{{1,2,4,6,7},{3},{5}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[4,3,1,5,6,2,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[4,3,1,5,6,7,2]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[7,4,3,1,5,6,2]=>{{1,2,4,7},{3},{5},{6}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[6,4,3,1,5,2,7]=>{{1,2,4,6},{3},{5},{7}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[6,4,3,1,5,7,2]=>{{1,2,4,6,7},{3},{5}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[6,4,3,1,7,5,2]=>{{1,2,4,5,6,7},{3}} [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[7,6,4,3,1,5,2]=>{{1,2,5,6,7},{3,4}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[4,5,1,3,2,6,7]=>{{1,3,4},{2,5},{6},{7}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[7,4,5,1,3,2,6]=>{{1,2,4,6,7},{3,5}} [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[4,5,1,3,6,2,7]=>{{1,3,4},{2,5,6},{7}} [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[4,5,1,3,6,7,2]=>{{1,3,4},{2,5,6,7}} [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[7,4,5,1,3,6,2]=>{{1,2,4,7},{3,5},{6}} [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[4,5,1,6,3,2,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[4,5,1,6,3,7,2]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[4,5,1,6,7,3,2]=>{{1,3,4,6},{2,5,7}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[7,4,5,1,6,3,2]=>{{1,2,4,7},{3,5,6}} [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[6,4,5,1,3,2,7]=>{{1,2,4,6},{3,5},{7}} [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[6,4,5,1,3,7,2]=>{{1,2,4,6,7},{3,5}} [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[6,4,5,1,7,3,2]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[6,4,7,1,5,3,2]=>{{1,2,3,4,6,7},{5}} [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[7,6,4,5,1,3,2]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>{{1,2,4,5},{3},{6},{7}} [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]=>{{1,2,5,6,7},{3,4}} [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[5,4,3,1,6,2,7]=>{{1,2,4,5,6},{3},{7}} [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[5,4,3,1,6,7,2]=>{{1,2,4,5,6,7},{3}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[7,5,4,3,1,6,2]=>{{1,2,5,7},{3,4},{6}} [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[5,4,6,1,3,2,7]=>{{1,2,3,4,5,6},{7}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[5,4,6,1,3,7,2]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[5,4,6,1,7,3,2]=>{{1,2,4,5,7},{3,6}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[7,5,4,6,1,3,2]=>{{1,2,5,7},{3,4,6}} [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[5,6,4,1,3,2,7]=>{{1,3,4,5},{2,6},{7}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[5,6,4,1,3,7,2]=>{{1,3,4,5},{2,6,7}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[5,6,4,1,7,3,2]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[5,6,7,1,4,3,2]=>{{1,4,5},{2,3,6,7}} [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[7,5,6,4,1,3,2]=>{{1,2,5,7},{3,6},{4}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>{{1,2,5,6},{3,4},{7}} [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[6,5,4,3,1,7,2]=>{{1,2,5,6,7},{3,4}} [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[6,5,4,7,1,3,2]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[6,5,7,4,1,3,2]=>{{1,2,3,5,6,7},{4}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[6,7,5,4,1,3,2]=>{{1,3,5,6},{2,7},{4}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>{{1,2,6,7},{3,5},{4}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}} [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[7,2,1,3,4,5,6]=>{{1,3,4,5,6,7},{2}} [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]=>{{1,3,4,5,6},{2},{7}} [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[6,2,1,3,4,7,5]=>{{1,3,4,5,6,7},{2}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]=>{{1,3,4,5},{2},{6},{7}} [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]=>{{1,4,6,7},{2,3,5}} [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[5,2,1,3,6,4,7]=>{{1,3,4,5,6},{2},{7}} [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[5,2,1,3,6,7,4]=>{{1,3,4,5,6,7},{2}} [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[7,5,2,1,3,6,4]=>{{1,4,7},{2,3,5},{6}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]=>{{1,4,6},{2,3,5},{7}} [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[6,5,2,1,3,7,4]=>{{1,4,6,7},{2,3,5}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[6,7,2,1,3,5,4]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[4,2,1,3,5,6,7]=>{{1,3,4},{2},{5},{6},{7}} [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]=>{{1,2,3,4,5,6},{7}} [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[6,4,2,1,3,7,5]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]=>{{1,5,7},{2,3,4,6}} [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[4,2,1,5,3,6,7]=>{{1,3,4,5},{2},{6},{7}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[7,4,2,1,5,3,6]=>{{1,2,3,4,6,7},{5}} [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[4,2,1,5,6,3,7]=>{{1,3,4,5,6},{2},{7}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[4,2,1,5,6,7,3]=>{{1,3,4,5,6,7},{2}} [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[7,4,2,1,5,6,3]=>{{1,2,3,4,7},{5},{6}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[6,4,2,1,5,3,7]=>{{1,2,3,4,6},{5},{7}} [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[6,4,2,1,5,7,3]=>{{1,2,3,4,6,7},{5}} [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[7,6,4,2,1,5,3]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]=>{{1,2,3,4,5},{6},{7}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[5,4,2,1,6,3,7]=>{{1,2,3,4,5,6},{7}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[5,4,2,1,6,7,3]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[7,5,4,2,1,6,3]=>{{1,2,3,4,5,7},{6}} [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[5,6,2,1,4,3,7]=>{{1,4,5},{2,3,6},{7}} [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[5,6,2,1,4,7,3]=>{{1,4,5},{2,3,6,7}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[5,6,2,1,7,4,3]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]=>{{1,2,3,4,5,6},{7}} [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[6,5,4,2,1,7,3]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[6,5,7,2,1,4,3]=>{{1,2,4,5,6},{3,7}} [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]=>{{1,2,3,5,6,7},{4}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[7,2,3,1,4,5,6]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[6,2,3,1,4,5,7]=>{{1,4,5,6},{2},{3},{7}} [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[6,2,3,1,4,7,5]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[7,6,2,3,1,4,5]=>{{1,5,7},{2,3,4,6}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[5,2,3,1,4,6,7]=>{{1,4,5},{2},{3},{6},{7}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[7,5,2,3,1,4,6]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[5,2,3,1,6,4,7]=>{{1,4,5,6},{2},{3},{7}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[5,2,3,1,6,7,4]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[7,5,2,3,1,6,4]=>{{1,2,3,4,5,7},{6}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[6,5,2,3,1,4,7]=>{{1,2,3,4,5,6},{7}} [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[6,5,2,3,1,7,4]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[6,7,2,3,1,5,4]=>{{1,5,6},{2,3,4,7}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[7,6,5,2,3,1,4]=>{{1,2,4,6,7},{3,5}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[7,2,3,4,1,5,6]=>{{1,5,6,7},{2},{3},{4}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[6,2,3,4,1,5,7]=>{{1,5,6},{2},{3},{4},{7}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[6,2,3,4,1,7,5]=>{{1,5,6,7},{2},{3},{4}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}} [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[7,2,3,4,5,1,6]=>{{1,6,7},{2},{3},{4},{5}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[6,2,3,4,7,5,1]=>{{1,5,6,7},{2},{3},{4}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[7,5,2,3,4,1,6]=>{{1,6,7},{2,3,4,5}} [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{7}} [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,5,2,3,4,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[5,2,3,6,4,1,7]=>{{1,4,5,6},{2},{3},{7}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[5,2,3,6,4,7,1]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[5,2,3,6,7,4,1]=>{{1,5,7},{2},{3},{4,6}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,5,2,3,6,4,1]=>{{1,7},{2,3,4,5,6}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,1,7]=>{{1,6},{2,3,4,5},{7}} [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[6,5,2,3,7,4,1]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[6,7,2,3,5,4,1]=>{{1,2,3,4,6,7},{5}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,6,5,2,3,4,1]=>{{1,7},{2,4,6},{3,5}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[7,4,2,3,1,5,6]=>{{1,5,6,7},{2,3,4}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[6,4,2,3,1,5,7]=>{{1,5,6},{2,3,4},{7}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[6,4,2,3,1,7,5]=>{{1,5,6,7},{2,3,4}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[7,6,4,2,3,1,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[7,4,2,3,5,1,6]=>{{1,6,7},{2,3,4},{5}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}} [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,4,2,3,5,6,1]=>{{1,7},{2,3,4},{5},{6}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,4,2,3,5,1,7]=>{{1,6},{2,3,4},{5},{7}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[6,4,2,3,5,7,1]=>{{1,6,7},{2,3,4},{5}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[6,4,2,3,7,5,1]=>{{1,5,6,7},{2,3,4}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,6,4,2,3,5,1]=>{{1,7},{2,3,4,5,6}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[4,2,5,3,1,6,7]=>{{1,3,4,5},{2},{6},{7}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[7,4,2,5,3,1,6]=>{{1,6,7},{2,3,4,5}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[4,2,5,3,6,1,7]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[4,2,5,3,6,7,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,4,2,5,3,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[4,2,5,6,3,1,7]=>{{1,4,6},{2},{3,5},{7}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[4,2,5,6,3,7,1]=>{{1,4,6,7},{2},{3,5}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[4,2,5,6,7,3,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,4,2,5,6,3,1]=>{{1,7},{2,3,4,5,6}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,4,2,5,3,1,7]=>{{1,6},{2,3,4,5},{7}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[6,4,2,5,3,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[6,4,2,5,7,3,1]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[6,4,2,7,5,3,1]=>{{1,2,3,4,6,7},{5}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,6,4,2,5,3,1]=>{{1,7},{2,3,4,6},{5}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,4,2,3,1,6,7]=>{{1,5},{2,3,4},{6},{7}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[7,5,4,2,3,1,6]=>{{1,6,7},{2,3,4,5}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[5,4,2,3,6,1,7]=>{{1,5,6},{2,3,4},{7}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[5,4,2,3,6,7,1]=>{{1,5,6,7},{2,3,4}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,5,4,2,3,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[5,4,2,6,3,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[5,4,2,6,3,7,1]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[5,4,2,6,7,3,1]=>{{1,5,7},{2,3,4,6}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,5,4,2,6,3,1]=>{{1,7},{2,3,4,5,6}} [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[5,6,2,4,3,1,7]=>{{1,2,3,5,6},{4},{7}} [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[5,6,2,4,3,7,1]=>{{1,2,3,5,6,7},{4}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[5,6,2,4,7,3,1]=>{{1,5,7},{2,3,6},{4}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[5,6,2,7,4,3,1]=>{{1,4,5,7},{2,3,6}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,5,6,2,4,3,1]=>{{1,7},{2,4,5},{3,6}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,5,4,2,3,1,7]=>{{1,6},{2,3,4,5},{7}} [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[6,5,4,2,3,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[6,5,4,2,7,3,1]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[6,5,7,2,4,3,1]=>{{1,3,6,7},{2,4,5}} [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[6,7,5,2,4,3,1]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,6,5,4,2,3,1]=>{{1,7},{2,3,5,6},{4}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]=>{{1,4,5,6},{2,3},{7}} [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[6,3,2,1,4,7,5]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]=>{{1,5,7},{2,4,6},{3}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]=>{{1,4,5},{2,3},{6},{7}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]=>{{1,2,4,5,6,7},{3}} [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[5,3,2,1,6,4,7]=>{{1,4,5,6},{2,3},{7}} [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[5,3,2,1,6,7,4]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[7,5,3,2,1,6,4]=>{{1,2,4,5,7},{3},{6}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]=>{{1,2,4,5,6},{3},{7}} [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[6,5,3,2,1,7,4]=>{{1,2,4,5,6,7},{3}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[6,7,3,2,1,5,4]=>{{1,5,6},{2,4,7},{3}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[7,3,2,4,1,5,6]=>{{1,5,6,7},{2,3},{4}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[6,3,2,4,1,5,7]=>{{1,5,6},{2,3},{4},{7}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[6,3,2,4,1,7,5]=>{{1,5,6,7},{2,3},{4}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[7,6,3,2,4,1,5]=>{{1,2,4,5,6,7},{3}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[7,3,2,4,5,1,6]=>{{1,6,7},{2,3},{4},{5}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}} [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[6,3,2,4,7,5,1]=>{{1,5,6,7},{2,3},{4}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,6,3,2,4,5,1]=>{{1,7},{2,4,5,6},{3}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[7,5,3,2,4,1,6]=>{{1,6,7},{2,4,5},{3}} [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,5,3,2,4,6,1]=>{{1,7},{2,4,5},{3},{6}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[5,3,2,6,4,1,7]=>{{1,4,5,6},{2,3},{7}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[5,3,2,6,4,7,1]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[5,3,2,6,7,4,1]=>{{1,5,7},{2,3},{4,6}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,5,3,2,6,4,1]=>{{1,7},{2,4,5,6},{3}} [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,5,3,2,4,1,7]=>{{1,6},{2,4,5},{3},{7}} [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[6,5,3,2,4,7,1]=>{{1,6,7},{2,4,5},{3}} [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[6,5,3,2,7,4,1]=>{{1,2,4,5,6,7},{3}} [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[6,7,3,2,5,4,1]=>{{1,2,4,6,7},{3},{5}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,6,5,3,2,4,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[7,3,4,2,1,5,6]=>{{1,5,6,7},{2,3,4}} [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[6,3,4,2,1,5,7]=>{{1,5,6},{2,3,4},{7}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[6,3,4,2,1,7,5]=>{{1,5,6,7},{2,3,4}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[7,6,3,4,2,1,5]=>{{1,2,5,6,7},{3},{4}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7]=>{{1,2,3,4,5},{6},{7}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[7,3,4,2,5,1,6]=>{{1,6,7},{2,3,4},{5}} [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,7,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[6,3,4,2,7,5,1]=>{{1,5,6,7},{2,3,4}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,6,3,4,2,5,1]=>{{1,7},{2,5,6},{3},{4}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}} [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[7,3,4,5,2,1,6]=>{{1,6,7},{2,3,4,5}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1,7]=>{{1,3,5,6},{2,4},{7}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,7,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[6,3,4,5,7,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[6,3,4,7,5,2,1]=>{{1,2,3,4,6,7},{5}} [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[7,5,3,4,2,1,6]=>{{1,6,7},{2,5},{3},{4}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[5,3,4,6,2,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[5,3,4,6,2,7,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[5,3,4,6,7,2,1]=>{{1,5,7},{2,3,4,6}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[5,3,6,4,2,1,7]=>{{1,2,3,5,6},{4},{7}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[5,3,6,4,2,7,1]=>{{1,2,3,5,6,7},{4}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[5,3,6,4,7,2,1]=>{{1,5,7},{2,3,6},{4}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[5,3,6,7,4,2,1]=>{{1,4,5,7},{2,3,6}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,5,3,6,4,2,1]=>{{1,7},{2,4,5,6},{3}} [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>{{1,6},{2,5},{3},{4},{7}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[6,5,3,4,7,2,1]=>{{1,2,5,6,7},{3},{4}} [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[6,5,3,7,4,2,1]=>{{1,2,4,5,6,7},{3}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[6,7,3,5,4,2,1]=>{{1,2,6,7},{3},{4,5}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,5,3,4,2,1]=>{{1,7},{2,6},{3,4,5}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]=>{{1,5,6,7},{2,4},{3}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]=>{{1,5,6},{2,4},{3},{7}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[6,4,3,2,1,7,5]=>{{1,5,6,7},{2,4},{3}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]=>{{1,2,5,6,7},{3,4}} [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[7,4,3,2,5,1,6]=>{{1,6,7},{2,4},{3},{5}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}} [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>{{1,6},{2,4},{3},{5},{7}} [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[6,4,3,2,7,5,1]=>{{1,5,6,7},{2,4},{3}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,6,4,3,2,5,1]=>{{1,7},{2,5,6},{3,4}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7]=>{{1,2,3,4,5},{6},{7}} [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[7,4,3,5,2,1,6]=>{{1,6,7},{2,4,5},{3}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1,7]=>{{1,4,6},{2,3,5},{7}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,7,1]=>{{1,4,6,7},{2,3,5}} [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,4,3,5,2,1,7]=>{{1,6},{2,4,5},{3},{7}} [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[6,4,3,5,7,2,1]=>{{1,2,4,5,6,7},{3}} [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[6,4,3,7,5,2,1]=>{{1,2,4,6,7},{3},{5}} [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7]=>{{1,2,4,5},{3},{6},{7}} [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[7,4,5,3,2,1,6]=>{{1,6,7},{2,3,4,5}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1,7]=>{{1,2,4,5,6},{3},{7}} [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1]=>{{1,2,4,5,6,7},{3}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,4,5,3,2,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1,7]=>{{1,4,6},{2,5},{3},{7}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,7,1]=>{{1,4,6,7},{2,5},{3}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1]=>{{1,2,4,5,6,7},{3}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,4,5,3,6,2,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>{{1,3,4,6},{2,5},{7}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,7,1]=>{{1,3,4,6,7},{2,5}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1]=>{{1,4,7},{2,3,5,6}} [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,4,5,6,3,2,1]=>{{1,7},{2,4,6},{3,5}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,4,5,3,2,1,7]=>{{1,6},{2,3,4,5},{7}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[6,4,5,3,2,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[6,4,5,3,7,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[6,4,5,7,3,2,1]=>{{1,2,4,6,7},{3,5}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[6,4,7,5,3,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]=>{{1,6,7},{2,5},{3,4}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}} [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1,7]=>{{1,2,4,5,6},{3},{7}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,7,1]=>{{1,2,4,5,6,7},{3}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1]=>{{1,5,7},{2,4,6},{3}} [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}} [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,7,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1]=>{{1,5,7},{2,3,4,6}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,5,4,6,3,2,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1,7]=>{{1,2,5,6},{3,4},{7}} [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,7,1]=>{{1,2,5,6,7},{3,4}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1]=>{{1,5,7},{2,6},{3,4}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1]=>{{1,3,4,5,7},{2,6}} [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1]=>{{1,3,5,7},{2,6},{4}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>{{1,7},{2,3,5,6},{4}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1]=>{{1,2,5,6,7},{3,4}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>{{1,2,3,5,6,7},{4}} [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>{{1,2,6,7},{3,5},{4}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}} [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
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].