Identifier
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00277: Permutations —catalanization⟶ Permutations
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1] [1,0,1,0]=>[1,2]=>[2,1]=>[2,1] [1,1,0,0]=>[2,1]=>[1,2]=>[1,2] [1,0,1,0,1,0]=>[1,2,3]=>[2,3,1]=>[2,3,1] [1,0,1,1,0,0]=>[1,3,2]=>[2,1,3]=>[2,1,3] [1,1,0,0,1,0]=>[2,1,3]=>[3,2,1]=>[3,2,1] [1,1,0,1,0,0]=>[2,3,1]=>[1,2,3]=>[1,2,3] [1,1,1,0,0,0]=>[3,2,1]=>[1,3,2]=>[1,3,2] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[2,3,4,1]=>[2,3,4,1] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[2,3,1,4]=>[2,3,1,4] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[2,4,3,1]=>[2,4,3,1] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,1,3,4]=>[2,1,3,4] [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[2,1,4,3]=>[2,1,4,3] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[3,2,4,1]=>[3,2,4,1] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,2,1,4]=>[3,2,1,4] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[4,2,3,1]=>[3,4,2,1] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[1,2,3,4]=>[1,2,3,4] [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[1,2,4,3]=>[1,2,4,3] [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[4,3,2,1]=>[4,3,2,1] [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[1,3,2,4]=>[1,3,2,4] [1,1,1,0,1,0,0,0]=>[4,2,3,1]=>[1,3,4,2]=>[1,3,4,2] [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,4,3,2]=>[1,4,3,2] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[2,3,4,5,1]=>[2,3,4,5,1] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[2,3,4,1,5]=>[2,3,4,1,5] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[2,3,5,4,1]=>[2,3,5,4,1] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[2,3,1,4,5]=>[2,3,1,4,5] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[2,3,1,5,4]=>[2,3,1,5,4] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[2,4,3,5,1]=>[2,4,3,5,1] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[2,4,3,1,5]=>[2,4,3,1,5] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[2,5,3,4,1]=>[2,4,5,3,1] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,1,3,4,5]=>[2,1,3,4,5] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[2,1,3,5,4]=>[2,1,3,5,4] [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[2,5,4,3,1]=>[2,5,4,3,1] [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[2,1,4,3,5]=>[2,1,4,3,5] [1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>[2,1,4,5,3]=>[2,1,4,5,3] [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[2,1,5,4,3]=>[2,1,5,4,3] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[3,2,4,5,1]=>[3,2,4,5,1] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[3,2,4,1,5]=>[3,2,4,1,5] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[3,2,5,4,1]=>[3,2,5,4,1] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,2,1,4,5]=>[3,2,1,4,5] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[3,2,1,5,4]=>[3,2,1,5,4] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[4,2,3,5,1]=>[3,4,2,5,1] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,2,3,1,5]=>[3,4,2,1,5] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[5,2,3,4,1]=>[3,4,5,2,1] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[1,2,3,4,5]=>[1,2,3,4,5] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[1,2,3,5,4]=>[1,2,3,5,4] [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[5,2,4,3,1]=>[3,5,4,2,1] [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[1,2,4,3,5]=>[1,2,4,3,5] [1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>[1,2,4,5,3]=>[1,2,4,5,3] [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[1,2,5,4,3]=>[1,2,5,4,3] [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[4,3,2,5,1]=>[4,3,2,5,1] [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,3,2,1,5]=>[4,3,2,1,5] [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[5,3,2,4,1]=>[4,3,5,2,1] [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[1,3,2,4,5]=>[1,3,2,4,5] [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[1,3,2,5,4]=>[1,3,2,5,4] [1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>[5,3,4,2,1]=>[4,5,3,2,1] [1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>[1,3,4,2,5]=>[1,3,4,2,5] [1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>[1,3,4,5,2]=>[1,3,4,5,2] [1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>[1,3,5,4,2]=>[1,3,5,4,2] [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[5,4,3,2,1]=>[5,4,3,2,1] [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[1,4,3,2,5]=>[1,4,3,2,5] [1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>[1,4,3,5,2]=>[1,4,3,5,2] [1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>[1,5,3,4,2]=>[1,4,5,3,2] [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,5,4,3,2]=>[1,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[2,3,4,6,5,1]=>[2,3,4,6,5,1] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[2,3,4,1,6,5]=>[2,3,4,1,6,5] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[2,3,5,4,6,1]=>[2,3,5,4,6,1] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[2,3,5,4,1,6]=>[2,3,5,4,1,6] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[2,3,6,4,5,1]=>[2,3,5,6,4,1] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[2,3,1,4,6,5]=>[2,3,1,4,6,5] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[2,3,6,5,4,1]=>[2,3,6,5,4,1] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[2,3,1,5,4,6]=>[2,3,1,5,4,6] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>[2,3,1,5,6,4]=>[2,3,1,5,6,4] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[2,3,1,6,5,4]=>[2,3,1,6,5,4] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[2,4,3,5,6,1]=>[2,4,3,5,6,1] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[2,4,3,5,1,6]=>[2,4,3,5,1,6] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[2,4,3,6,5,1]=>[2,4,3,6,5,1] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[2,4,3,1,5,6]=>[2,4,3,1,5,6] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[2,4,3,1,6,5]=>[2,4,3,1,6,5] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[2,5,3,4,6,1]=>[2,4,5,3,6,1] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[2,5,3,4,1,6]=>[2,4,5,3,1,6] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[2,6,3,4,5,1]=>[2,4,5,6,3,1] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[2,6,3,5,4,1]=>[2,4,6,5,3,1] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>[2,1,3,5,6,4]=>[2,1,3,5,6,4] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[2,5,4,3,6,1]=>[2,5,4,3,6,1] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[2,5,4,3,1,6]=>[2,5,4,3,1,6] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[2,6,4,3,5,1]=>[2,5,4,6,3,1] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>[2,6,4,5,3,1]=>[2,5,6,4,3,1] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>[2,1,4,5,3,6]=>[2,1,4,5,3,6] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>[2,1,4,5,6,3]=>[2,1,4,5,6,3] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>[2,1,4,6,5,3]=>[2,1,4,6,5,3] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[2,6,5,4,3,1]=>[2,6,5,4,3,1] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>[2,1,5,4,6,3]=>[2,1,5,4,6,3] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>[2,1,6,4,5,3]=>[2,1,5,6,4,3] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[3,2,4,6,5,1]=>[3,2,4,6,5,1] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[3,2,4,1,6,5]=>[3,2,4,1,6,5] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[3,2,5,4,6,1]=>[3,2,5,4,6,1] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[3,2,5,4,1,6]=>[3,2,5,4,1,6] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[3,2,6,4,5,1]=>[3,2,5,6,4,1] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[3,2,6,5,4,1]=>[3,2,6,5,4,1] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>[3,2,1,5,6,4]=>[3,2,1,5,6,4] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[4,2,3,5,6,1]=>[3,4,2,5,6,1] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[4,2,3,5,1,6]=>[3,4,2,5,1,6] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[4,2,3,6,5,1]=>[3,4,2,6,5,1] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[4,2,3,1,6,5]=>[3,4,2,1,6,5] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[5,2,3,4,6,1]=>[3,4,5,2,6,1] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,2,3,4,1,6]=>[3,4,5,2,1,6] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[6,2,3,4,5,1]=>[3,4,5,6,2,1] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[6,2,3,5,4,1]=>[3,4,6,5,2,1] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>[1,2,3,5,6,4]=>[1,2,3,5,6,4] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[5,2,4,3,6,1]=>[3,5,4,2,6,1] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,2,4,3,1,6]=>[3,5,4,2,1,6] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[6,2,4,3,5,1]=>[3,5,4,6,2,1] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>[6,2,4,5,3,1]=>[3,5,6,4,2,1] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>[1,2,4,5,3,6]=>[1,2,4,5,3,6] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>[1,2,4,5,6,3]=>[1,2,4,5,6,3] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>[1,2,4,6,5,3]=>[1,2,4,6,5,3] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[6,2,5,4,3,1]=>[3,6,5,4,2,1] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>[1,2,5,4,6,3]=>[1,2,5,4,6,3] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>[1,2,6,4,5,3]=>[1,2,5,6,4,3] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[4,3,2,6,5,1]=>[4,3,2,6,5,1] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[5,3,2,4,6,1]=>[4,3,5,2,6,1] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[6,3,2,4,5,1]=>[4,3,5,6,2,1] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[6,3,2,5,4,1]=>[4,3,6,5,2,1] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>[1,3,2,5,6,4]=>[1,3,2,5,6,4] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4] [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>[5,3,4,2,6,1]=>[4,5,3,2,6,1] [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>[5,3,4,2,1,6]=>[4,5,3,2,1,6] [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>[6,3,4,2,5,1]=>[4,5,3,6,2,1] [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>[1,3,4,2,5,6]=>[1,3,4,2,5,6] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>[1,3,4,2,6,5]=>[1,3,4,2,6,5] [1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>[6,3,4,5,2,1]=>[4,5,6,3,2,1] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>[1,3,4,5,2,6]=>[1,3,4,5,2,6] [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>[1,3,4,5,6,2]=>[1,3,4,5,6,2] [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>[1,3,4,6,5,2]=>[1,3,4,6,5,2] [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>[6,3,5,4,2,1]=>[4,6,5,3,2,1] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>[1,3,5,4,2,6]=>[1,3,5,4,2,6] [1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>[1,3,5,4,6,2]=>[1,3,5,4,6,2] [1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>[1,3,6,4,5,2]=>[1,3,5,6,4,2] [1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>[1,3,6,5,4,2]=>[1,3,6,5,4,2] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[6,4,3,2,5,1]=>[5,4,3,6,2,1] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5] [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>[6,4,3,5,2,1]=>[5,4,6,3,2,1] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[1,4,3,5,2,6]=>[1,4,3,5,2,6] [1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>[1,4,3,5,6,2]=>[1,4,3,5,6,2] [1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>[1,4,3,6,5,2]=>[1,4,3,6,5,2] [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>[6,5,3,4,2,1]=>[5,6,4,3,2,1] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>[1,5,3,4,2,6]=>[1,4,5,3,2,6] [1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>[1,5,3,4,6,2]=>[1,4,5,3,6,2] [1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>[1,6,3,4,5,2]=>[1,4,5,6,3,2] [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>[1,6,3,5,4,2]=>[1,4,6,5,3,2] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6] [1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>[1,5,4,3,6,2]=>[1,5,4,3,6,2] [1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>[1,6,4,3,5,2]=>[1,5,4,6,3,2] [1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>[1,6,4,5,3,2]=>[1,5,6,4,3,2] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[2,3,4,5,7,6,1]=>[2,3,4,5,7,6,1] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[2,3,4,5,1,7,6]=>[2,3,4,5,1,7,6] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[2,3,4,6,5,7,1]=>[2,3,4,6,5,7,1] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[2,3,4,6,5,1,7]=>[2,3,4,6,5,1,7] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[2,3,4,7,5,6,1]=>[2,3,4,6,7,5,1] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[2,3,4,1,5,7,6]=>[2,3,4,1,5,7,6] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[2,3,4,7,6,5,1]=>[2,3,4,7,6,5,1] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[2,3,4,1,6,5,7]=>[2,3,4,1,6,5,7] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>[2,3,4,1,6,7,5]=>[2,3,4,1,6,7,5] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[2,3,4,1,7,6,5]=>[2,3,4,1,7,6,5] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[2,3,5,4,6,7,1]=>[2,3,5,4,6,7,1] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[2,3,5,4,6,1,7]=>[2,3,5,4,6,1,7] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[2,3,5,4,7,6,1]=>[2,3,5,4,7,6,1] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[2,3,5,4,1,6,7]=>[2,3,5,4,1,6,7] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[2,3,5,4,1,7,6]=>[2,3,5,4,1,7,6] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[2,3,6,4,5,7,1]=>[2,3,5,6,4,7,1] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[2,3,6,4,5,1,7]=>[2,3,5,6,4,1,7] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[2,3,7,4,5,6,1]=>[2,3,5,6,7,4,1] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[2,3,1,4,5,7,6]=>[2,3,1,4,5,7,6] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[2,3,7,4,6,5,1]=>[2,3,5,7,6,4,1] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[2,3,1,4,6,5,7]=>[2,3,1,4,6,5,7] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>[2,3,1,4,6,7,5]=>[2,3,1,4,6,7,5] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[2,3,1,4,7,6,5]=>[2,3,1,4,7,6,5] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[2,3,6,5,4,7,1]=>[2,3,6,5,4,7,1] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[2,3,6,5,4,1,7]=>[2,3,6,5,4,1,7] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[2,3,7,5,4,6,1]=>[2,3,6,5,7,4,1] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[2,3,1,5,4,6,7]=>[2,3,1,5,4,6,7] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[2,3,1,5,4,7,6]=>[2,3,1,5,4,7,6] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>[2,3,7,5,6,4,1]=>[2,3,6,7,5,4,1] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>[2,3,1,5,6,4,7]=>[2,3,1,5,6,4,7] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>[2,3,1,5,6,7,4]=>[2,3,1,5,6,7,4] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>[2,3,1,5,7,6,4]=>[2,3,1,5,7,6,4] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[2,3,7,6,5,4,1]=>[2,3,7,6,5,4,1] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[2,3,1,6,5,4,7]=>[2,3,1,6,5,4,7] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>[2,3,1,6,5,7,4]=>[2,3,1,6,5,7,4] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>[2,3,1,7,5,6,4]=>[2,3,1,6,7,5,4] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[2,3,1,7,6,5,4]=>[2,3,1,7,6,5,4] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[2,4,3,5,6,7,1]=>[2,4,3,5,6,7,1] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[2,4,3,5,6,1,7]=>[2,4,3,5,6,1,7] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[2,4,3,5,7,6,1]=>[2,4,3,5,7,6,1] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[2,4,3,5,1,6,7]=>[2,4,3,5,1,6,7] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[2,4,3,5,1,7,6]=>[2,4,3,5,1,7,6] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[2,4,3,6,5,7,1]=>[2,4,3,6,5,7,1] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[2,4,3,6,5,1,7]=>[2,4,3,6,5,1,7] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[2,4,3,7,5,6,1]=>[2,4,3,6,7,5,1] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[2,4,3,1,5,6,7]=>[2,4,3,1,5,6,7] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[2,4,3,1,5,7,6]=>[2,4,3,1,5,7,6] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[2,4,3,7,6,5,1]=>[2,4,3,7,6,5,1] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[2,4,3,1,6,5,7]=>[2,4,3,1,6,5,7] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>[2,4,3,1,6,7,5]=>[2,4,3,1,6,7,5] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[2,4,3,1,7,6,5]=>[2,4,3,1,7,6,5] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[2,5,3,4,6,7,1]=>[2,4,5,3,6,7,1] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[2,5,3,4,6,1,7]=>[2,4,5,3,6,1,7] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[2,5,3,4,7,6,1]=>[2,4,5,3,7,6,1] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[2,5,3,4,1,6,7]=>[2,4,5,3,1,6,7] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[2,5,3,4,1,7,6]=>[2,4,5,3,1,7,6] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[2,6,3,4,5,7,1]=>[2,4,5,6,3,7,1] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[2,6,3,4,5,1,7]=>[2,4,5,6,3,1,7] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[2,7,3,4,5,6,1]=>[2,4,5,6,7,3,1] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[2,7,3,4,6,5,1]=>[2,4,5,7,6,3,1] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>[2,1,3,4,6,7,5]=>[2,1,3,4,6,7,5] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[2,6,3,5,4,7,1]=>[2,4,6,5,3,7,1] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[2,6,3,5,4,1,7]=>[2,4,6,5,3,1,7] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[2,7,3,5,4,6,1]=>[2,4,6,5,7,3,1] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>[2,7,3,5,6,4,1]=>[2,4,6,7,5,3,1] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>[2,1,3,5,6,4,7]=>[2,1,3,5,6,4,7] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>[2,1,3,5,6,7,4]=>[2,1,3,5,6,7,4] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>[2,1,3,5,7,6,4]=>[2,1,3,5,7,6,4] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[2,7,3,6,5,4,1]=>[2,4,7,6,5,3,1] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>[2,1,3,6,5,7,4]=>[2,1,3,6,5,7,4] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>[2,1,3,7,5,6,4]=>[2,1,3,6,7,5,4] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[2,5,4,3,6,7,1]=>[2,5,4,3,6,7,1] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[2,5,4,3,6,1,7]=>[2,5,4,3,6,1,7] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[2,5,4,3,7,6,1]=>[2,5,4,3,7,6,1] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[2,5,4,3,1,6,7]=>[2,5,4,3,1,6,7] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[2,5,4,3,1,7,6]=>[2,5,4,3,1,7,6] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[2,6,4,3,5,7,1]=>[2,5,4,6,3,7,1] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[2,6,4,3,5,1,7]=>[2,5,4,6,3,1,7] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[2,7,4,3,5,6,1]=>[2,5,4,6,7,3,1] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[2,7,4,3,6,5,1]=>[2,5,4,7,6,3,1] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>[2,1,4,3,6,7,5]=>[2,1,4,3,6,7,5] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>[2,6,4,5,3,7,1]=>[2,5,6,4,3,7,1] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>[2,6,4,5,3,1,7]=>[2,5,6,4,3,1,7] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>[2,7,4,5,3,6,1]=>[2,5,6,4,7,3,1] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>[2,1,4,5,3,6,7]=>[2,1,4,5,3,6,7] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>[2,1,4,5,3,7,6]=>[2,1,4,5,3,7,6] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>[2,7,4,5,6,3,1]=>[2,5,6,7,4,3,1] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>[2,1,4,5,6,3,7]=>[2,1,4,5,6,3,7] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>[2,1,4,5,6,7,3]=>[2,1,4,5,6,7,3] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>[2,1,4,5,7,6,3]=>[2,1,4,5,7,6,3] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>[2,7,4,6,5,3,1]=>[2,5,7,6,4,3,1] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>[2,1,4,6,5,3,7]=>[2,1,4,6,5,3,7] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>[2,1,4,6,5,7,3]=>[2,1,4,6,5,7,3] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>[2,1,4,7,5,6,3]=>[2,1,4,6,7,5,3] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>[2,1,4,7,6,5,3]=>[2,1,4,7,6,5,3] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[2,6,5,4,3,7,1]=>[2,6,5,4,3,7,1] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[2,6,5,4,3,1,7]=>[2,6,5,4,3,1,7] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[2,7,5,4,3,6,1]=>[2,6,5,4,7,3,1] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>[2,7,5,4,6,3,1]=>[2,6,5,7,4,3,1] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>[2,1,5,4,6,3,7]=>[2,1,5,4,6,3,7] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>[2,1,5,4,6,7,3]=>[2,1,5,4,6,7,3] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>[2,1,5,4,7,6,3]=>[2,1,5,4,7,6,3] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>[2,7,6,4,5,3,1]=>[2,6,7,5,4,3,1] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>[2,1,6,4,5,3,7]=>[2,1,5,6,4,3,7] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>[2,1,6,4,5,7,3]=>[2,1,5,6,4,7,3] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>[2,1,7,4,5,6,3]=>[2,1,5,6,7,4,3] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>[2,1,7,4,6,5,3]=>[2,1,5,7,6,4,3] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[2,7,6,5,4,3,1]=>[2,7,6,5,4,3,1] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>[2,1,6,5,4,7,3]=>[2,1,6,5,4,7,3] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>[2,1,7,5,4,6,3]=>[2,1,6,5,7,4,3] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>[2,1,7,5,6,4,3]=>[2,1,6,7,5,4,3] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[3,2,4,5,7,6,1]=>[3,2,4,5,7,6,1] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[3,2,4,5,1,7,6]=>[3,2,4,5,1,7,6] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[3,2,4,6,5,7,1]=>[3,2,4,6,5,7,1] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[3,2,4,6,5,1,7]=>[3,2,4,6,5,1,7] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[3,2,4,7,5,6,1]=>[3,2,4,6,7,5,1] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[3,2,4,1,5,7,6]=>[3,2,4,1,5,7,6] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[3,2,4,7,6,5,1]=>[3,2,4,7,6,5,1] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[3,2,4,1,6,5,7]=>[3,2,4,1,6,5,7] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>[3,2,4,1,6,7,5]=>[3,2,4,1,6,7,5] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[3,2,4,1,7,6,5]=>[3,2,4,1,7,6,5] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[3,2,5,4,6,7,1]=>[3,2,5,4,6,7,1] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[3,2,5,4,6,1,7]=>[3,2,5,4,6,1,7] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[3,2,5,4,7,6,1]=>[3,2,5,4,7,6,1] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[3,2,5,4,1,6,7]=>[3,2,5,4,1,6,7] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[3,2,5,4,1,7,6]=>[3,2,5,4,1,7,6] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[3,2,6,4,5,7,1]=>[3,2,5,6,4,7,1] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[3,2,6,4,5,1,7]=>[3,2,5,6,4,1,7] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[3,2,7,4,5,6,1]=>[3,2,5,6,7,4,1] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[3,2,7,4,6,5,1]=>[3,2,5,7,6,4,1] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>[3,2,1,4,6,7,5]=>[3,2,1,4,6,7,5] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[3,2,6,5,4,7,1]=>[3,2,6,5,4,7,1] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[3,2,6,5,4,1,7]=>[3,2,6,5,4,1,7] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[3,2,7,5,4,6,1]=>[3,2,6,5,7,4,1] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>[3,2,7,5,6,4,1]=>[3,2,6,7,5,4,1] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>[3,2,1,5,6,4,7]=>[3,2,1,5,6,4,7] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>[3,2,1,5,6,7,4]=>[3,2,1,5,6,7,4] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>[3,2,1,5,7,6,4]=>[3,2,1,5,7,6,4] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[3,2,7,6,5,4,1]=>[3,2,7,6,5,4,1] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>[3,2,1,6,5,7,4]=>[3,2,1,6,5,7,4] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>[3,2,1,7,5,6,4]=>[3,2,1,6,7,5,4] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[4,2,3,5,6,7,1]=>[3,4,2,5,6,7,1] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[4,2,3,5,6,1,7]=>[3,4,2,5,6,1,7] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[4,2,3,5,7,6,1]=>[3,4,2,5,7,6,1] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[4,2,3,5,1,6,7]=>[3,4,2,5,1,6,7] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[4,2,3,5,1,7,6]=>[3,4,2,5,1,7,6] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[4,2,3,6,5,7,1]=>[3,4,2,6,5,7,1] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[4,2,3,6,5,1,7]=>[3,4,2,6,5,1,7] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[4,2,3,7,5,6,1]=>[3,4,2,6,7,5,1] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[4,2,3,1,5,7,6]=>[3,4,2,1,5,7,6] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[4,2,3,7,6,5,1]=>[3,4,2,7,6,5,1] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[4,2,3,1,6,5,7]=>[3,4,2,1,6,5,7] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>[4,2,3,1,6,7,5]=>[3,4,2,1,6,7,5] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[4,2,3,1,7,6,5]=>[3,4,2,1,7,6,5] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[5,2,3,4,6,7,1]=>[3,4,5,2,6,7,1] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[5,2,3,4,6,1,7]=>[3,4,5,2,6,1,7] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[5,2,3,4,7,6,1]=>[3,4,5,2,7,6,1] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[5,2,3,4,1,6,7]=>[3,4,5,2,1,6,7] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[5,2,3,4,1,7,6]=>[3,4,5,2,1,7,6] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[6,2,3,4,5,7,1]=>[3,4,5,6,2,7,1] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[6,2,3,4,5,1,7]=>[3,4,5,6,2,1,7] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[7,2,3,4,5,6,1]=>[3,4,5,6,7,2,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>[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]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[7,2,3,4,6,5,1]=>[3,4,5,7,6,2,1] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>[1,2,3,4,6,7,5]=>[1,2,3,4,6,7,5] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[6,2,3,5,4,7,1]=>[3,4,6,5,2,7,1] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[6,2,3,5,4,1,7]=>[3,4,6,5,2,1,7] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[7,2,3,5,4,6,1]=>[3,4,6,5,7,2,1] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>[7,2,3,5,6,4,1]=>[3,4,6,7,5,2,1] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>[1,2,3,5,6,4,7]=>[1,2,3,5,6,4,7] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>[1,2,3,5,6,7,4]=>[1,2,3,5,6,7,4] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>[1,2,3,5,7,6,4]=>[1,2,3,5,7,6,4] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[7,2,3,6,5,4,1]=>[3,4,7,6,5,2,1] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>[1,2,3,6,5,7,4]=>[1,2,3,6,5,7,4] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>[1,2,3,7,5,6,4]=>[1,2,3,6,7,5,4] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[5,2,4,3,6,7,1]=>[3,5,4,2,6,7,1] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[5,2,4,3,6,1,7]=>[3,5,4,2,6,1,7] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[5,2,4,3,7,6,1]=>[3,5,4,2,7,6,1] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[5,2,4,3,1,6,7]=>[3,5,4,2,1,6,7] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[5,2,4,3,1,7,6]=>[3,5,4,2,1,7,6] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[6,2,4,3,5,7,1]=>[3,5,4,6,2,7,1] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[6,2,4,3,5,1,7]=>[3,5,4,6,2,1,7] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[7,2,4,3,5,6,1]=>[3,5,4,6,7,2,1] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[7,2,4,3,6,5,1]=>[3,5,4,7,6,2,1] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>[1,2,4,3,6,7,5]=>[1,2,4,3,6,7,5] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>[6,2,4,5,3,7,1]=>[3,5,6,4,2,7,1] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>[6,2,4,5,3,1,7]=>[3,5,6,4,2,1,7] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>[7,2,4,5,3,6,1]=>[3,5,6,4,7,2,1] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>[1,2,4,5,3,6,7]=>[1,2,4,5,3,6,7] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>[1,2,4,5,3,7,6]=>[1,2,4,5,3,7,6] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>[7,2,4,5,6,3,1]=>[3,5,6,7,4,2,1] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>[1,2,4,5,6,3,7]=>[1,2,4,5,6,3,7] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>[1,2,4,5,6,7,3]=>[1,2,4,5,6,7,3] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>[1,2,4,5,7,6,3]=>[1,2,4,5,7,6,3] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>[7,2,4,6,5,3,1]=>[3,5,7,6,4,2,1] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>[1,2,4,6,5,3,7]=>[1,2,4,6,5,3,7] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>[1,2,4,6,5,7,3]=>[1,2,4,6,5,7,3] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>[1,2,4,7,5,6,3]=>[1,2,4,6,7,5,3] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>[1,2,4,7,6,5,3]=>[1,2,4,7,6,5,3] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[6,2,5,4,3,7,1]=>[3,6,5,4,2,7,1] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[6,2,5,4,3,1,7]=>[3,6,5,4,2,1,7] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[7,2,5,4,3,6,1]=>[3,6,5,4,7,2,1] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[1,2,5,4,3,7,6]=>[1,2,5,4,3,7,6] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>[7,2,5,4,6,3,1]=>[3,6,5,7,4,2,1] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>[1,2,5,4,6,3,7]=>[1,2,5,4,6,3,7] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>[1,2,5,4,6,7,3]=>[1,2,5,4,6,7,3] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>[1,2,5,4,7,6,3]=>[1,2,5,4,7,6,3] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>[7,2,6,4,5,3,1]=>[3,6,7,5,4,2,1] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>[1,2,6,4,5,3,7]=>[1,2,5,6,4,3,7] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>[1,2,6,4,5,7,3]=>[1,2,5,6,4,7,3] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>[1,2,7,4,5,6,3]=>[1,2,5,6,7,4,3] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>[1,2,7,4,6,5,3]=>[1,2,5,7,6,4,3] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[7,2,6,5,4,3,1]=>[3,7,6,5,4,2,1] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[1,2,6,5,4,3,7]=>[1,2,6,5,4,3,7] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>[1,2,6,5,4,7,3]=>[1,2,6,5,4,7,3] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>[1,2,7,5,4,6,3]=>[1,2,6,5,7,4,3] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>[1,2,7,5,6,4,3]=>[1,2,6,7,5,4,3] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[4,3,2,5,7,6,1]=>[4,3,2,5,7,6,1] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[4,3,2,5,1,7,6]=>[4,3,2,5,1,7,6] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[4,3,2,6,5,7,1]=>[4,3,2,6,5,7,1] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[4,3,2,6,5,1,7]=>[4,3,2,6,5,1,7] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[4,3,2,7,5,6,1]=>[4,3,2,6,7,5,1] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[4,3,2,7,6,5,1]=>[4,3,2,7,6,5,1] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>[4,3,2,1,6,7,5]=>[4,3,2,1,6,7,5] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[5,3,2,4,6,7,1]=>[4,3,5,2,6,7,1] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[5,3,2,4,6,1,7]=>[4,3,5,2,6,1,7] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[5,3,2,4,7,6,1]=>[4,3,5,2,7,6,1] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[5,3,2,4,1,7,6]=>[4,3,5,2,1,7,6] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[6,3,2,4,5,7,1]=>[4,3,5,6,2,7,1] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[6,3,2,4,5,1,7]=>[4,3,5,6,2,1,7] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[7,3,2,4,5,6,1]=>[4,3,5,6,7,2,1] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[7,3,2,4,6,5,1]=>[4,3,5,7,6,2,1] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>[1,3,2,4,6,7,5]=>[1,3,2,4,6,7,5] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[6,3,2,5,4,7,1]=>[4,3,6,5,2,7,1] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[6,3,2,5,4,1,7]=>[4,3,6,5,2,1,7] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[7,3,2,5,4,6,1]=>[4,3,6,5,7,2,1] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>[7,3,2,5,6,4,1]=>[4,3,6,7,5,2,1] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>[1,3,2,5,6,4,7]=>[1,3,2,5,6,4,7] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>[1,3,2,5,6,7,4]=>[1,3,2,5,6,7,4] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>[1,3,2,5,7,6,4]=>[1,3,2,5,7,6,4] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[7,3,2,6,5,4,1]=>[4,3,7,6,5,2,1] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[1,3,2,6,5,4,7]=>[1,3,2,6,5,4,7] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>[1,3,2,6,5,7,4]=>[1,3,2,6,5,7,4] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>[1,3,2,7,5,6,4]=>[1,3,2,6,7,5,4] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>[5,3,4,2,6,7,1]=>[4,5,3,2,6,7,1] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>[5,3,4,2,6,1,7]=>[4,5,3,2,6,1,7] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>[5,3,4,2,7,6,1]=>[4,5,3,2,7,6,1] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>[5,3,4,2,1,6,7]=>[4,5,3,2,1,6,7] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>[5,3,4,2,1,7,6]=>[4,5,3,2,1,7,6] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>[6,3,4,2,5,7,1]=>[4,5,3,6,2,7,1] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>[6,3,4,2,5,1,7]=>[4,5,3,6,2,1,7] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>[7,3,4,2,5,6,1]=>[4,5,3,6,7,2,1] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>[1,3,4,2,5,6,7]=>[1,3,4,2,5,6,7] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>[1,3,4,2,5,7,6]=>[1,3,4,2,5,7,6] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>[7,3,4,2,6,5,1]=>[4,5,3,7,6,2,1] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>[1,3,4,2,6,5,7]=>[1,3,4,2,6,5,7] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>[1,3,4,2,6,7,5]=>[1,3,4,2,6,7,5] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>[1,3,4,2,7,6,5]=>[1,3,4,2,7,6,5] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>[6,3,4,5,2,7,1]=>[4,5,6,3,2,7,1] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>[6,3,4,5,2,1,7]=>[4,5,6,3,2,1,7] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>[7,3,4,5,2,6,1]=>[4,5,6,3,7,2,1] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>[1,3,4,5,2,6,7]=>[1,3,4,5,2,6,7] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>[1,3,4,5,2,7,6]=>[1,3,4,5,2,7,6] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>[7,3,4,5,6,2,1]=>[4,5,6,7,3,2,1] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[1,3,4,5,6,2,7]=>[1,3,4,5,6,2,7] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>[1,3,4,5,6,7,2]=>[1,3,4,5,6,7,2] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>[1,3,4,5,7,6,2]=>[1,3,4,5,7,6,2] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>[7,3,4,6,5,2,1]=>[4,5,7,6,3,2,1] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>[1,3,4,6,5,2,7]=>[1,3,4,6,5,2,7] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>[1,3,4,6,5,7,2]=>[1,3,4,6,5,7,2] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>[1,3,4,7,5,6,2]=>[1,3,4,6,7,5,2] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>[1,3,4,7,6,5,2]=>[1,3,4,7,6,5,2] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>[6,3,5,4,2,7,1]=>[4,6,5,3,2,7,1] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>[6,3,5,4,2,1,7]=>[4,6,5,3,2,1,7] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>[7,3,5,4,2,6,1]=>[4,6,5,3,7,2,1] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>[1,3,5,4,2,6,7]=>[1,3,5,4,2,6,7] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>[1,3,5,4,2,7,6]=>[1,3,5,4,2,7,6] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>[7,3,5,4,6,2,1]=>[4,6,5,7,3,2,1] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>[1,3,5,4,6,2,7]=>[1,3,5,4,6,2,7] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>[1,3,5,4,6,7,2]=>[1,3,5,4,6,7,2] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>[1,3,5,4,7,6,2]=>[1,3,5,4,7,6,2] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>[7,3,6,4,5,2,1]=>[4,6,7,5,3,2,1] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>[1,3,6,4,5,2,7]=>[1,3,5,6,4,2,7] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>[1,3,6,4,5,7,2]=>[1,3,5,6,4,7,2] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>[1,3,7,4,5,6,2]=>[1,3,5,6,7,4,2] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>[1,3,7,4,6,5,2]=>[1,3,5,7,6,4,2] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>[7,3,6,5,4,2,1]=>[4,7,6,5,3,2,1] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>[1,3,6,5,4,2,7]=>[1,3,6,5,4,2,7] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>[1,3,6,5,4,7,2]=>[1,3,6,5,4,7,2] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>[1,3,7,5,4,6,2]=>[1,3,6,5,7,4,2] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>[1,3,7,5,6,4,2]=>[1,3,6,7,5,4,2] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>[1,3,7,6,5,4,2]=>[1,3,7,6,5,4,2] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1,7] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[5,4,3,2,7,6,1]=>[5,4,3,2,7,6,1] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[6,4,3,2,5,7,1]=>[5,4,3,6,2,7,1] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[6,4,3,2,5,1,7]=>[5,4,3,6,2,1,7] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[7,4,3,2,5,6,1]=>[5,4,3,6,7,2,1] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[1,4,3,2,5,7,6]=>[1,4,3,2,5,7,6] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[7,4,3,2,6,5,1]=>[5,4,3,7,6,2,1] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[1,4,3,2,6,5,7]=>[1,4,3,2,6,5,7] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>[1,4,3,2,6,7,5]=>[1,4,3,2,6,7,5] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>[6,4,3,5,2,7,1]=>[5,4,6,3,2,7,1] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>[6,4,3,5,2,1,7]=>[5,4,6,3,2,1,7] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>[7,4,3,5,2,6,1]=>[5,4,6,3,7,2,1] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>[1,4,3,5,2,6,7]=>[1,4,3,5,2,6,7] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>[1,4,3,5,2,7,6]=>[1,4,3,5,2,7,6] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>[7,4,3,5,6,2,1]=>[5,4,6,7,3,2,1] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[1,4,3,5,6,2,7]=>[1,4,3,5,6,2,7] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>[1,4,3,5,6,7,2]=>[1,4,3,5,6,7,2] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>[1,4,3,5,7,6,2]=>[1,4,3,5,7,6,2] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>[7,4,3,6,5,2,1]=>[5,4,7,6,3,2,1] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>[1,4,3,6,5,2,7]=>[1,4,3,6,5,2,7] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>[1,4,3,6,5,7,2]=>[1,4,3,6,5,7,2] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>[1,4,3,7,5,6,2]=>[1,4,3,6,7,5,2] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>[1,4,3,7,6,5,2]=>[1,4,3,7,6,5,2] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>[6,5,3,4,2,7,1]=>[5,6,4,3,2,7,1] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>[6,5,3,4,2,1,7]=>[5,6,4,3,2,1,7] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>[7,5,3,4,2,6,1]=>[5,6,4,3,7,2,1] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>[1,5,3,4,2,6,7]=>[1,4,5,3,2,6,7] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>[1,5,3,4,2,7,6]=>[1,4,5,3,2,7,6] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>[7,5,3,4,6,2,1]=>[5,6,4,7,3,2,1] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[1,5,3,4,6,2,7]=>[1,4,5,3,6,2,7] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>[1,5,3,4,6,7,2]=>[1,4,5,3,6,7,2] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>[1,5,3,4,7,6,2]=>[1,4,5,3,7,6,2] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>[7,6,3,4,5,2,1]=>[5,6,7,4,3,2,1] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[1,6,3,4,5,2,7]=>[1,4,5,6,3,2,7] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>[1,6,3,4,5,7,2]=>[1,4,5,6,3,7,2] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>[1,7,3,4,5,6,2]=>[1,4,5,6,7,3,2] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>[1,7,3,4,6,5,2]=>[1,4,5,7,6,3,2] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>[7,6,3,5,4,2,1]=>[5,7,6,4,3,2,1] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>[1,6,3,5,4,2,7]=>[1,4,6,5,3,2,7] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>[1,6,3,5,4,7,2]=>[1,4,6,5,3,7,2] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>[1,7,3,5,4,6,2]=>[1,4,6,5,7,3,2] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>[1,7,3,5,6,4,2]=>[1,4,6,7,5,3,2] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>[1,7,3,6,5,4,2]=>[1,4,7,6,5,3,2] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[7,5,4,3,2,6,1]=>[6,5,4,3,7,2,1] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>[7,5,4,3,6,2,1]=>[6,5,4,7,3,2,1] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[1,5,4,3,6,2,7]=>[1,5,4,3,6,2,7] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>[1,5,4,3,6,7,2]=>[1,5,4,3,6,7,2] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>[1,5,4,3,7,6,2]=>[1,5,4,3,7,6,2] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>[7,6,4,3,5,2,1]=>[6,5,7,4,3,2,1] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[1,6,4,3,5,2,7]=>[1,5,4,6,3,2,7] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>[1,6,4,3,5,7,2]=>[1,5,4,6,3,7,2] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>[1,7,4,3,5,6,2]=>[1,5,4,6,7,3,2] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>[1,7,4,3,6,5,2]=>[1,5,4,7,6,3,2] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>[7,6,4,5,3,2,1]=>[6,7,5,4,3,2,1] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>[1,6,4,5,3,2,7]=>[1,5,6,4,3,2,7] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>[1,6,4,5,3,7,2]=>[1,5,6,4,3,7,2] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>[1,7,4,5,3,6,2]=>[1,5,6,4,7,3,2] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>[1,7,4,5,6,3,2]=>[1,5,6,7,4,3,2] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>[1,7,4,6,5,3,2]=>[1,5,7,6,4,3,2] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>[1,6,5,4,3,7,2]=>[1,6,5,4,3,7,2] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>[1,7,5,4,3,6,2]=>[1,6,5,4,7,3,2] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>[1,7,5,4,6,3,2]=>[1,6,5,7,4,3,2] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>[1,7,6,4,5,3,2]=>[1,6,7,5,4,3,2] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,1] [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[2,3,4,5,6,1,8,7]=>[2,3,4,5,6,1,8,7] [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[2,3,4,8,5,6,7,1]=>[2,3,4,6,7,8,5,1] [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[2,3,4,1,6,5,8,7]=>[2,3,4,1,6,5,8,7] [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,8,5,6,7,4]=>[2,3,4,1,6,7,8,5]=>[2,3,4,1,6,7,8,5] [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[2,3,4,1,8,7,6,5]=>[2,3,4,1,8,7,6,5] [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>[2,3,6,4,5,1,8,7]=>[2,3,5,6,4,1,8,7] [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,8,6,7,3]=>[2,3,1,4,5,7,8,6]=>[2,3,1,4,5,7,8,6] [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[2,3,1,4,8,7,6,5]=>[2,3,1,4,8,7,6,5] [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,8,6,5,7,4]=>[2,4,3,1,7,6,8,5]=>[2,4,3,1,7,6,8,5] [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[2,4,3,1,8,7,6,5]=>[2,4,3,1,8,7,6,5] [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7] [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5] [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7] [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,8,5,6,7,2]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,6,7,8,5] [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,8,5,7,6,2]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,6,8,7,5] [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,3,8,6,5,7,2]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,7,6,8,5] [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5] [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,8,3,4,6,7,5,2]=>[2,1,4,5,8,6,7,3]=>[2,1,4,5,7,8,6,3] [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,8,4,3,6,5,7,2]=>[2,1,5,4,7,6,8,3]=>[2,1,5,4,7,6,8,3] [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7] [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,8,5,4,7,6,3,2]=>[2,1,8,5,4,7,6,3]=>[2,1,6,5,8,7,4,3] [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3] [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,6,5,8,7,4]=>[3,2,4,1,6,5,8,7]=>[3,2,4,1,6,5,8,7] [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,3,8,6,5,7,4]=>[3,2,4,1,7,6,8,5]=>[3,2,4,1,7,6,8,5] [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[3,2,4,1,8,7,6,5]=>[3,2,4,1,8,7,6,5] [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,7,6]=>[3,2,5,4,6,1,8,7]=>[3,2,5,4,6,1,8,7] [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[3,2,5,4,7,6,8,1]=>[3,2,5,4,7,6,8,1] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[3,2,5,4,7,6,1,8]=>[3,2,5,4,7,6,1,8] [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[3,2,5,4,1,8,7,6]=>[3,2,5,4,1,8,7,6] [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6] [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5] [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[3,2,7,6,5,4,1,8]=>[3,2,7,6,5,4,1,8] [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,8,5,4,7,6,3]=>[3,2,1,6,5,8,7,4]=>[3,2,1,6,5,8,7,4] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4] [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,8,6,7,5,4]=>[4,2,3,1,8,6,7,5]=>[3,4,2,1,7,8,6,5] [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[4,2,3,1,8,7,6,5]=>[3,4,2,1,8,7,6,5] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8] [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5] [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,8,4,5,6,7,1]=>[1,2,3,5,6,7,8,4]=>[1,2,3,5,6,7,8,4] [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8] [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8] [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7] [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8] [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,8,6,7,4]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,7,8,6] [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6] [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8] [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7] [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,7,5,6,8,4]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,6,7,5,8] [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,8,5,6,7,4]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,6,7,8,5] [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,8,5,7,6,4]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,6,8,7,5] [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8] [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,8,6,5,7,4]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,7,6,8,5] [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,8,6,7,5,4]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,7,8,6,5] [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5] [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5] [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[6,3,2,5,4,1,8,7]=>[4,3,6,5,2,1,8,7] [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[8,3,2,5,4,7,6,1]=>[4,3,6,5,8,7,2,1] [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[8,3,2,7,6,5,4,1]=>[4,3,8,7,6,5,2,1] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[5,4,3,2,7,6,1,8]=>[5,4,3,2,7,6,1,8] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6] [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5,8] [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5] [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,3,2,5,4,1,8,7]=>[7,4,3,6,5,2,1,8]=>[5,4,7,6,3,2,1,8] [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8,3,2,5,4,7,6,1]=>[1,4,3,6,5,8,7,2]=>[1,4,3,6,5,8,7,2] [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>[1,4,3,8,7,6,5,2]=>[1,4,3,8,7,6,5,2] [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7] [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[8,5,4,3,2,7,6,1]=>[6,5,4,3,8,7,2,1] [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,4,3,6,5,2,1,8]=>[8,7,4,3,6,5,2,1]=>[6,5,8,7,4,3,2,1] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8] [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>[1,6,5,4,3,8,7,2]=>[1,6,5,4,3,8,7,2] [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8,7,4,3,6,5,2,1]=>[1,8,5,4,7,6,3,2]=>[1,6,5,8,7,4,3,2] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
Map
catalanization
Description
The catalanization of a permutation.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.