Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1]
[1,0,1,0]=>[2,1]=>[1,2]=>[1,2]
[1,1,0,0]=>[1,2]=>[2,1]=>[2,1]
[1,0,1,0,1,0]=>[3,2,1]=>[1,2,3]=>[1,2,3]
[1,0,1,1,0,0]=>[2,3,1]=>[2,1,3]=>[2,1,3]
[1,1,0,0,1,0]=>[3,1,2]=>[1,3,2]=>[1,3,2]
[1,1,0,1,0,0]=>[2,1,3]=>[2,3,1]=>[3,2,1]
[1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>[2,3,1]
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,2,3,4]=>[1,2,3,4]
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[2,1,3,4]=>[2,1,3,4]
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[1,3,2,4]=>[1,3,2,4]
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[2,3,1,4]=>[3,2,1,4]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[3,2,1,4]=>[2,3,1,4]
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[1,2,4,3]=>[1,2,4,3]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,1,4,3]=>[2,1,4,3]
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[1,3,4,2]=>[1,4,3,2]
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[2,3,4,1]=>[4,2,3,1]
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,2,4,1]=>[4,3,2,1]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[1,4,3,2]=>[1,3,4,2]
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[2,4,3,1]=>[3,2,4,1]
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[3,4,2,1]=>[2,4,3,1]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4,3,2,1]=>[2,3,4,1]
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[1,2,3,4,5]
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[2,1,3,4,5]=>[2,1,3,4,5]
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[2,3,1,4,5]=>[3,2,1,4,5]
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[3,2,1,4,5]=>[2,3,1,4,5]
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[1,2,4,3,5]=>[1,2,4,3,5]
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[2,1,4,3,5]=>[2,1,4,3,5]
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[1,3,4,2,5]=>[1,4,3,2,5]
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[2,3,4,1,5]=>[4,2,3,1,5]
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[3,2,4,1,5]=>[4,3,2,1,5]
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,3,4,2,5]
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[2,4,3,1,5]=>[3,2,4,1,5]
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[3,4,2,1,5]=>[2,4,3,1,5]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[4,3,2,1,5]=>[2,3,4,1,5]
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[1,2,3,5,4]
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[2,1,3,5,4]
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[2,3,1,5,4]=>[3,2,1,5,4]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[3,2,1,5,4]=>[2,3,1,5,4]
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[1,2,5,4,3]
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[2,1,4,5,3]=>[2,1,5,4,3]
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[1,5,3,4,2]
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[5,2,3,4,1]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[3,2,4,5,1]=>[5,3,2,4,1]
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[1,4,3,5,2]=>[1,5,4,3,2]
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[2,4,3,5,1]=>[5,2,4,3,1]
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[3,4,2,5,1]=>[5,4,3,2,1]
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[5,3,4,2,1]
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[1,2,4,5,3]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[2,1,5,4,3]=>[2,1,4,5,3]
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[1,4,3,5,2]
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[4,2,3,5,1]
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[3,2,5,4,1]=>[4,3,2,5,1]
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[1,3,5,4,2]
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[3,2,5,4,1]
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[2,5,3,4,1]
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[2,5,4,3,1]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[1,3,4,5,2]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[3,2,4,5,1]
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[2,4,3,5,1]
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[2,3,5,4,1]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[2,3,4,5,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>[3,2,4,1,5,6]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>[1,4,3,5,2,6]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>[4,2,3,5,1,6]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[3,2,5,4,1,6]=>[4,3,2,5,1,6]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>[1,3,5,4,2,6]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>[3,2,5,4,1,6]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>[3,2,4,5,1,6]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>[2,4,3,5,1,6]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[2,4,3,1,6,5]=>[3,2,4,1,6,5]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[3,4,2,1,6,5]=>[2,4,3,1,6,5]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>[1,6,4,5,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>[6,2,4,5,3,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>[6,4,3,5,2,1]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[1,2,5,4,6,3]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[2,1,4,6,5,3]=>[2,1,5,4,6,3]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[1,5,3,4,6,2]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[5,2,3,4,6,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[3,2,4,6,5,1]=>[5,3,2,4,6,1]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>[1,5,4,3,6,2]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[2,4,3,6,5,1]=>[5,2,4,3,6,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>[5,4,3,2,6,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>[5,3,4,2,6,1]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[1,2,4,6,5,3]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[2,1,5,6,4,3]=>[2,1,4,6,5,3]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[1,4,3,6,5,2]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[4,2,3,6,5,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[3,2,5,6,4,1]=>[4,3,2,6,5,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[1,3,6,4,5,2]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[3,2,6,4,5,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>[1,3,6,5,4,2]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>[3,2,6,5,4,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>[2,6,3,5,4,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[1,4,3,5,6,2]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[4,2,3,5,6,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>[4,3,2,5,6,1]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[1,3,5,4,6,2]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[3,2,5,4,6,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[2,5,3,4,6,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[2,5,4,3,6,1]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[1,3,4,6,5,2]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[3,2,4,6,5,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[2,4,3,6,5,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[3,2,4,5,6,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[2,4,3,5,6,1]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[2,3,5,4,6,1]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>[1,3,5,4,2,6,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>[3,2,5,4,1,6,7]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>[2,4,3,5,1,6,7]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[3,4,2,1,6,5,7]=>[2,4,3,1,6,5,7]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>[1,6,4,5,3,2,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>[6,2,4,5,3,1,7]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>[6,4,3,5,2,1,7]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[3,2,4,6,5,1,7]=>[5,3,2,4,6,1,7]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[1,4,3,6,5,2,7]=>[1,5,4,3,6,2,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[2,4,3,6,5,1,7]=>[5,2,4,3,6,1,7]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[3,4,2,6,5,1,7]=>[5,4,3,2,6,1,7]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[4,3,2,6,5,1,7]=>[5,3,4,2,6,1,7]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>[1,2,4,6,5,3,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[2,1,5,6,4,3,7]=>[2,1,4,6,5,3,7]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>[1,4,3,6,5,2,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>[4,2,3,6,5,1,7]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[3,2,5,6,4,1,7]=>[4,3,2,6,5,1,7]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>[1,3,6,4,5,2,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>[3,2,6,4,5,1,7]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>[1,3,6,5,4,2,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[2,5,4,6,3,1,7]=>[3,2,6,5,4,1,7]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>[2,6,3,5,4,1,7]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>[1,4,3,5,6,2,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[2,3,6,5,4,1,7]=>[4,2,3,5,6,1,7]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[3,2,6,5,4,1,7]=>[4,3,2,5,6,1,7]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>[1,3,5,4,6,2,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>[3,2,5,4,6,1,7]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>[2,5,3,4,6,1,7]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[4,3,6,5,2,1,7]=>[2,5,4,3,6,1,7]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>[1,3,4,6,5,2,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>[3,2,4,6,5,1,7]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>[2,4,3,6,5,1,7]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>[3,2,4,5,6,1,7]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>[2,4,3,5,6,1,7]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>[2,3,5,4,6,1,7]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[3,4,2,1,5,7,6]=>[2,4,3,1,5,7,6]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[4,3,2,5,1,7,6]=>[5,3,4,2,1,7,6]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[3,2,5,4,1,7,6]=>[4,3,2,5,1,7,6]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[1,4,5,3,2,7,6]=>[1,3,5,4,2,7,6]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[2,4,5,3,1,7,6]=>[3,2,5,4,1,7,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[3,4,5,2,1,7,6]=>[2,5,3,4,1,7,6]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[4,3,5,2,1,7,6]=>[2,5,4,3,1,7,6]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[2,5,4,3,1,7,6]=>[3,2,4,5,1,7,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[3,5,4,2,1,7,6]=>[2,4,3,5,1,7,6]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[4,5,3,2,1,7,6]=>[2,3,5,4,1,7,6]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[3,4,2,1,6,7,5]=>[2,4,3,1,7,6,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>[7,4,3,5,2,6,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>[1,7,5,4,6,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>[7,2,5,4,6,3,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>[7,5,3,4,6,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[4,3,6,5,2,7,1]=>[7,5,4,3,6,2,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>[1,7,4,6,5,3,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>[7,2,4,6,5,3,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>[7,4,3,6,5,2,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>[7,4,3,5,6,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>[7,3,5,4,6,2,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[3,2,4,1,7,6,5]=>[4,3,2,1,6,7,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[3,4,2,1,7,6,5]=>[2,4,3,1,6,7,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[3,4,2,5,7,6,1]=>[6,4,3,2,5,7,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[1,4,5,3,7,6,2]=>[1,6,5,4,3,7,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>[6,2,5,4,3,7,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>[6,5,3,4,2,7,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[4,3,5,2,7,6,1]=>[6,5,4,3,2,7,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[3,5,4,2,7,6,1]=>[6,4,3,5,2,7,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[4,5,3,2,7,6,1]=>[6,3,5,4,2,7,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>[1,2,3,5,7,6,4]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[2,1,3,6,7,5,4]=>[2,1,3,5,7,6,4]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[1,3,2,6,7,5,4]=>[1,3,2,5,7,6,4]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[2,3,1,6,7,5,4]=>[3,2,1,5,7,6,4]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[3,2,1,6,7,5,4]=>[2,3,1,5,7,6,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[1,2,5,4,7,6,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[2,1,4,6,7,5,3]=>[2,1,5,4,7,6,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>[1,5,3,4,7,6,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[5,2,3,4,7,6,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[3,2,4,6,7,5,1]=>[5,3,2,4,7,6,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[1,4,3,6,7,5,2]=>[1,5,4,3,7,6,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[2,4,3,6,7,5,1]=>[5,2,4,3,7,6,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[3,4,2,6,7,5,1]=>[5,4,3,2,7,6,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[4,3,2,6,7,5,1]=>[5,3,4,2,7,6,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>[1,2,4,7,5,6,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[2,1,5,6,7,4,3]=>[2,1,4,7,5,6,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>[1,4,3,7,5,6,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[4,2,3,7,5,6,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[3,2,5,6,7,4,1]=>[4,3,2,7,5,6,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>[1,3,7,4,5,6,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[3,2,7,4,5,6,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>[1,3,7,5,4,6,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>[3,2,7,5,4,6,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>[2,7,3,5,4,6,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>[1,2,4,7,6,5,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[2,1,6,5,7,4,3]=>[2,1,4,7,6,5,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>[1,4,3,7,6,5,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>[4,2,3,7,6,5,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[3,2,6,5,7,4,1]=>[4,3,2,7,6,5,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>[1,3,7,4,6,5,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>[3,2,7,4,6,5,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>[2,7,3,4,6,5,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[4,3,6,5,7,2,1]=>[2,7,4,3,6,5,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>[1,3,7,6,5,4,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>[3,2,7,6,5,4,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>[2,7,3,6,5,4,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>[1,3,7,5,6,4,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>[3,2,7,5,6,4,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>[2,7,3,5,6,4,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>[2,7,5,4,6,3,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>[5,4,3,2,6,7,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[1,2,4,6,5,7,3]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[2,1,5,7,6,4,3]=>[2,1,4,6,5,7,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[1,4,3,6,5,7,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[4,2,3,6,5,7,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[3,2,5,7,6,4,1]=>[4,3,2,6,5,7,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[1,3,6,4,5,7,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[3,2,6,4,5,7,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[2,6,3,4,5,7,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[4,3,5,7,6,2,1]=>[2,6,4,3,5,7,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>[1,3,6,5,4,7,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>[3,2,6,5,4,7,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>[2,6,3,5,4,7,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>[2,6,5,4,3,7,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]=>[2,6,4,5,3,7,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[1,2,4,5,7,6,3]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[2,1,6,7,5,4,3]=>[2,1,4,5,7,6,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>[1,4,3,5,7,6,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[4,2,3,5,7,6,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[3,2,6,7,5,4,1]=>[4,3,2,5,7,6,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>[1,3,5,4,7,6,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[3,2,5,4,7,6,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[2,5,3,4,7,6,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[4,3,6,7,5,2,1]=>[2,5,4,3,7,6,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>[1,3,4,7,5,6,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[3,2,4,7,5,6,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[2,4,3,7,5,6,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>[1,3,4,7,6,5,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>[3,2,4,7,6,5,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>[2,4,3,7,6,5,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>[2,3,7,4,6,5,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[1,3,5,4,6,7,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[3,2,5,4,6,7,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[2,5,3,4,6,7,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>[2,5,4,3,6,7,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[1,3,4,6,5,7,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[3,2,4,6,5,7,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[2,4,3,6,5,7,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[2,3,6,4,5,7,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>[2,3,6,5,4,7,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[1,3,4,5,7,6,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[3,2,4,5,7,6,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[2,4,3,5,7,6,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[2,3,5,4,7,6,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[2,4,3,5,6,7,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[2,3,5,4,6,7,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>[2,3,4,6,5,7,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[2,4,3,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,2,1]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,2,1]=>[3,2,1,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,3,2,1]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,2,1]=>[1,4,3,5,2,6,7,8]=>[1,5,4,3,2,6,7,8]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[2,4,3,5,1,6,7,8]=>[5,2,4,3,1,6,7,8]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,2,1]=>[1,2,5,4,3,6,7,8]=>[1,2,4,5,3,6,7,8]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,2,1]=>[2,1,5,4,3,6,7,8]=>[2,1,4,5,3,6,7,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,2,1]=>[1,3,5,4,2,6,7,8]=>[1,4,3,5,2,6,7,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[2,3,5,4,1,6,7,8]=>[4,2,3,5,1,6,7,8]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>[3,2,5,4,1,6,7,8]=>[4,3,2,5,1,6,7,8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,2,1]=>[1,4,5,3,2,6,7,8]=>[1,3,5,4,2,6,7,8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[2,4,5,3,1,6,7,8]=>[3,2,5,4,1,6,7,8]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,3,2,1]=>[1,5,4,3,2,6,7,8]=>[1,3,4,5,2,6,7,8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[2,5,4,3,1,6,7,8]=>[3,2,4,5,1,6,7,8]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[3,5,4,2,1,6,7,8]=>[2,4,3,5,1,6,7,8]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,2,1]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,2,1]=>[2,4,3,1,6,5,7,8]=>[3,2,4,1,6,5,7,8]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,2,1]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,5,2,1]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>[3,2,1,5,6,4,7,8]=>[2,3,1,6,5,4,7,8]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,2,1]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[3,2,4,5,6,1,7,8]=>[6,3,2,4,5,1,7,8]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,7,2,1]=>[1,4,3,5,6,2,7,8]=>[1,6,4,3,5,2,7,8]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,2,1]=>[4,3,2,5,6,1,7,8]=>[6,3,4,2,5,1,7,8]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,7,2,1]=>[1,3,5,4,6,2,7,8]=>[1,6,3,5,4,2,7,8]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,8,2,1]=>[2,3,5,4,6,1,7,8]=>[6,2,3,5,4,1,7,8]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,2,1]=>[1,4,5,3,6,2,7,8]=>[1,6,5,4,3,2,7,8]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,2,1]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,7,2,1]=>[1,5,4,3,6,2,7,8]=>[1,6,4,5,3,2,7,8]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,2,1]=>[3,5,4,2,6,1,7,8]=>[6,4,3,5,2,1,7,8]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>[4,5,3,2,6,1,7,8]=>[6,3,5,4,2,1,7,8]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>[5,4,3,2,6,1,7,8]=>[6,3,4,5,2,1,7,8]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>[2,3,1,6,5,4,7,8]=>[3,2,1,5,6,4,7,8]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[3,2,1,6,5,4,7,8]=>[2,3,1,5,6,4,7,8]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,6,2,1]=>[1,2,4,6,5,3,7,8]=>[1,2,5,4,6,3,7,8]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>[2,1,4,6,5,3,7,8]=>[2,1,5,4,6,3,7,8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,2,1]=>[2,3,4,6,5,1,7,8]=>[5,2,3,4,6,1,7,8]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,7,2,1]=>[1,4,3,6,5,2,7,8]=>[1,5,4,3,6,2,7,8]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,2,1]=>[2,4,3,6,5,1,7,8]=>[5,2,4,3,6,1,7,8]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,8,2,1]=>[4,3,2,6,5,1,7,8]=>[5,3,4,2,6,1,7,8]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[1,2,5,6,4,3,7,8]=>[1,2,4,6,5,3,7,8]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,2,1]=>[2,1,5,6,4,3,7,8]=>[2,1,4,6,5,3,7,8]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,7,2,1]=>[1,3,5,6,4,2,7,8]=>[1,4,3,6,5,2,7,8]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,2,1]=>[2,3,5,6,4,1,7,8]=>[4,2,3,6,5,1,7,8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,2,1]=>[1,4,5,6,3,2,7,8]=>[1,3,6,4,5,2,7,8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,2,1]=>[2,4,5,6,3,1,7,8]=>[3,2,6,4,5,1,7,8]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[3,4,5,6,2,1,7,8]=>[2,6,3,4,5,1,7,8]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,7,2,1]=>[1,5,4,6,3,2,7,8]=>[1,3,6,5,4,2,7,8]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,2,1]=>[5,4,3,6,2,1,7,8]=>[2,6,4,5,3,1,7,8]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>[1,2,4,5,6,3,7,8]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[2,3,6,5,4,1,7,8]=>[4,2,3,5,6,1,7,8]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,2,1]=>[1,4,6,5,3,2,7,8]=>[1,3,5,4,6,2,7,8]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,2,1]=>[2,4,6,5,3,1,7,8]=>[3,2,5,4,6,1,7,8]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,2,1]=>[4,3,6,5,2,1,7,8]=>[2,5,4,3,6,1,7,8]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,2,1]=>[1,5,6,4,3,2,7,8]=>[1,3,4,6,5,2,7,8]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,2,1]=>[4,5,6,3,2,1,7,8]=>[2,3,6,4,5,1,7,8]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,2,1]=>[5,4,6,3,2,1,7,8]=>[2,3,6,5,4,1,7,8]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,2,1]=>[1,6,5,4,3,2,7,8]=>[1,3,4,5,6,2,7,8]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,2,1]=>[3,6,5,4,2,1,7,8]=>[2,4,3,5,6,1,7,8]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[5,6,4,3,2,1,7,8]=>[2,3,4,6,5,1,7,8]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[6,5,4,3,2,1,7,8]=>[2,3,4,5,6,1,7,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,3,1]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,3,1]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,3,1]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,3,1]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,3,1]=>[1,2,4,5,3,7,6,8]=>[1,2,5,4,3,7,6,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,3,1]=>[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,3,1]=>[2,3,4,5,1,7,6,8]=>[5,2,3,4,1,7,6,8]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[1,4,3,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[2,4,3,5,1,7,6,8]=>[5,2,4,3,1,7,6,8]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,3,1]=>[2,1,5,4,3,7,6,8]=>[2,1,4,5,3,7,6,8]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>[1,3,5,4,2,7,6,8]=>[1,4,3,5,2,7,6,8]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,3,1]=>[2,3,5,4,1,7,6,8]=>[4,2,3,5,1,7,6,8]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,2,3,1]=>[3,2,5,4,1,7,6,8]=>[4,3,2,5,1,7,6,8]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,2,3,1]=>[1,4,5,3,2,7,6,8]=>[1,3,5,4,2,7,6,8]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,2,3,1]=>[2,4,5,3,1,7,6,8]=>[3,2,5,4,1,7,6,8]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,2,3,1]=>[3,4,5,2,1,7,6,8]=>[2,5,3,4,1,7,6,8]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,3,1]=>[1,5,4,3,2,7,6,8]=>[1,3,4,5,2,7,6,8]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,2,3,1]=>[2,5,4,3,1,7,6,8]=>[3,2,4,5,1,7,6,8]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,2,3,1]=>[3,5,4,2,1,7,6,8]=>[2,4,3,5,1,7,6,8]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,2,3,1]=>[4,5,3,2,1,7,6,8]=>[2,3,5,4,1,7,6,8]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[5,4,3,2,1,7,6,8]=>[2,3,4,5,1,7,6,8]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>[2,1,3,4,6,7,5,8]=>[2,1,3,4,7,6,5,8]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,4,1]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,4,1]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>[1,4,3,2,6,7,5,8]=>[1,3,4,2,7,6,5,8]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[4,3,2,1,6,7,5,8]=>[2,3,4,1,7,6,5,8]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,5,1]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,5,6,4,8]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,5,1]=>[3,2,1,5,6,7,4,8]=>[2,3,1,7,5,6,4,8]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,6,1]=>[1,2,4,5,6,7,3,8]=>[1,2,7,4,5,6,3,8]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,6,1]=>[2,1,4,5,6,7,3,8]=>[2,1,7,4,5,6,3,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,8,1]=>[3,2,4,5,6,7,1,8]=>[7,3,2,4,5,6,1,8]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,7,1]=>[1,4,3,5,6,7,2,8]=>[1,7,4,3,5,6,2,8]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,8,1]=>[2,4,3,5,6,7,1,8]=>[7,2,4,3,5,6,1,8]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,8,1]=>[3,4,2,5,6,7,1,8]=>[7,4,3,2,5,6,1,8]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,8,1]=>[4,3,2,5,6,7,1,8]=>[7,3,4,2,5,6,1,8]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,2,6,1]=>[1,2,5,4,6,7,3,8]=>[1,2,7,5,4,6,3,8]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,2,6,1]=>[2,1,5,4,6,7,3,8]=>[2,1,7,5,4,6,3,8]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,7,1]=>[1,3,5,4,6,7,2,8]=>[1,7,3,5,4,6,2,8]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,8,1]=>[2,3,5,4,6,7,1,8]=>[7,2,3,5,4,6,1,8]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,7,1]=>[1,4,5,3,6,7,2,8]=>[1,7,5,4,3,6,2,8]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,8,1]=>[2,4,5,3,6,7,1,8]=>[7,2,5,4,3,6,1,8]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,7,1]=>[1,5,4,3,6,7,2,8]=>[1,7,4,5,3,6,2,8]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>[2,5,4,3,6,7,1,8]=>[7,2,4,5,3,6,1,8]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,8,1]=>[3,5,4,2,6,7,1,8]=>[7,4,3,5,2,6,1,8]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[5,4,3,2,6,7,1,8]=>[7,3,4,5,2,6,1,8]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[1,2,3,6,5,7,4,8]=>[1,2,3,7,6,5,4,8]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[1,3,2,6,5,7,4,8]=>[1,3,2,7,6,5,4,8]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[2,3,1,6,5,7,4,8]=>[3,2,1,7,6,5,4,8]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,5,1]=>[3,2,1,6,5,7,4,8]=>[2,3,1,7,6,5,4,8]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[1,2,4,6,5,7,3,8]=>[1,2,7,4,6,5,3,8]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,7,1]=>[1,3,4,6,5,7,2,8]=>[1,7,3,4,6,5,2,8]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,8,1]=>[2,3,4,6,5,7,1,8]=>[7,2,3,4,6,5,1,8]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[1,4,3,6,5,7,2,8]=>[1,7,4,3,6,5,2,8]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[2,4,3,6,5,7,1,8]=>[7,2,4,3,6,5,1,8]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[3,4,2,6,5,7,1,8]=>[7,4,3,2,6,5,1,8]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,8,1]=>[4,3,2,6,5,7,1,8]=>[7,3,4,2,6,5,1,8]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,2,6,1]=>[1,2,5,6,4,7,3,8]=>[1,2,7,6,5,4,3,8]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[1,3,5,6,4,7,2,8]=>[1,7,3,6,5,4,2,8]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,8,1]=>[2,3,5,6,4,7,1,8]=>[7,2,3,6,5,4,1,8]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,2,7,1]=>[1,4,5,6,3,7,2,8]=>[1,7,6,4,5,3,2,8]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,8,1]=>[2,4,5,6,3,7,1,8]=>[7,2,6,4,5,3,1,8]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[1,5,4,6,3,7,2,8]=>[1,7,6,5,4,3,2,8]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[2,5,4,6,3,7,1,8]=>[7,2,6,5,4,3,1,8]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[3,5,4,6,2,7,1,8]=>[7,6,3,5,4,2,1,8]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>[1,3,6,5,4,7,2,8]=>[1,7,3,5,6,4,2,8]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,2,8,1]=>[3,2,6,5,4,7,1,8]=>[7,3,2,5,6,4,1,8]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[3,4,6,5,2,7,1,8]=>[7,5,3,4,6,2,1,8]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,2,8,1]=>[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,8,1]=>[3,6,5,4,2,7,1,8]=>[7,4,3,5,6,2,1,8]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,1]=>[6,5,4,3,2,7,1,8]=>[7,3,4,5,6,2,1,8]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>[2,3,4,1,7,6,5,8]=>[4,2,3,1,6,7,5,8]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,5,1]=>[1,2,3,5,7,6,4,8]=>[1,2,3,6,5,7,4,8]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,3,5,1]=>[1,3,2,5,7,6,4,8]=>[1,3,2,6,5,7,4,8]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[3,2,1,5,7,6,4,8]=>[2,3,1,6,5,7,4,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,7,1]=>[1,3,4,5,7,6,2,8]=>[1,6,3,4,5,7,2,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,8,1]=>[2,3,4,5,7,6,1,8]=>[6,2,3,4,5,7,1,8]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,7,1]=>[1,4,3,5,7,6,2,8]=>[1,6,4,3,5,7,2,8]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,8,1]=>[3,4,2,5,7,6,1,8]=>[6,4,3,2,5,7,1,8]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,8,1]=>[4,3,2,5,7,6,1,8]=>[6,3,4,2,5,7,1,8]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,3,7,1]=>[1,3,5,4,7,6,2,8]=>[1,6,3,5,4,7,2,8]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[3,2,5,4,7,6,1,8]=>[6,3,2,5,4,7,1,8]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>[3,4,5,2,7,6,1,8]=>[6,5,3,4,2,7,1,8]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,8,1]=>[4,3,5,2,7,6,1,8]=>[6,5,4,3,2,7,1,8]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,2,3,8,1]=>[3,5,4,2,7,6,1,8]=>[6,4,3,5,2,7,1,8]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>[4,5,3,2,7,6,1,8]=>[6,3,5,4,2,7,1,8]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[5,4,3,2,7,6,1,8]=>[6,3,4,5,2,7,1,8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,5,1]=>[1,2,3,6,7,5,4,8]=>[1,2,3,5,7,6,4,8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,4,5,1]=>[2,1,3,6,7,5,4,8]=>[2,1,3,5,7,6,4,8]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>[1,3,2,6,7,5,4,8]=>[1,3,2,5,7,6,4,8]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,4,5,1]=>[2,3,1,6,7,5,4,8]=>[3,2,1,5,7,6,4,8]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>[3,2,1,6,7,5,4,8]=>[2,3,1,5,7,6,4,8]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,6,1]=>[1,2,4,6,7,5,3,8]=>[1,2,5,4,7,6,3,8]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,4,6,1]=>[2,1,4,6,7,5,3,8]=>[2,1,5,4,7,6,3,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,7,1]=>[1,3,4,6,7,5,2,8]=>[1,5,3,4,7,6,2,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,8,1]=>[2,3,4,6,7,5,1,8]=>[5,2,3,4,7,6,1,8]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,8,1]=>[3,2,4,6,7,5,1,8]=>[5,3,2,4,7,6,1,8]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,8,1]=>[4,3,2,6,7,5,1,8]=>[5,3,4,2,7,6,1,8]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,6,1]=>[1,2,5,6,7,4,3,8]=>[1,2,4,7,5,6,3,8]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[2,1,5,6,7,4,3,8]=>[2,1,4,7,5,6,3,8]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,5,7,1]=>[1,3,5,6,7,4,2,8]=>[1,4,3,7,5,6,2,8]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,8,1]=>[2,3,5,6,7,4,1,8]=>[4,2,3,7,5,6,1,8]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>[3,2,5,6,7,4,1,8]=>[4,3,2,7,5,6,1,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,8,1]=>[2,4,5,6,7,3,1,8]=>[3,2,7,4,5,6,1,8]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[3,4,5,6,7,2,1,8]=>[2,7,3,4,5,6,1,8]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,7,1]=>[1,5,4,6,7,3,2,8]=>[1,3,7,5,4,6,2,8]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,8,1]=>[2,5,4,6,7,3,1,8]=>[3,2,7,5,4,6,1,8]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,8,1]=>[5,4,3,6,7,2,1,8]=>[2,7,4,5,3,6,1,8]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,5,7,1]=>[1,3,6,5,7,4,2,8]=>[1,4,3,7,6,5,2,8]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,2,5,8,1]=>[2,3,6,5,7,4,1,8]=>[4,2,3,7,6,5,1,8]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,8,1]=>[3,2,6,5,7,4,1,8]=>[4,3,2,7,6,5,1,8]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[1,4,6,5,7,3,2,8]=>[1,3,7,4,6,5,2,8]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,8,1]=>[4,3,6,5,7,2,1,8]=>[2,7,4,3,6,5,1,8]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,6,7,1]=>[1,5,6,4,7,3,2,8]=>[1,3,7,6,5,4,2,8]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,8,1]=>[2,5,6,4,7,3,1,8]=>[3,2,7,6,5,4,1,8]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,7,8,1]=>[3,5,6,4,7,2,1,8]=>[2,7,3,6,5,4,1,8]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,8,1]=>[5,4,6,3,7,2,1,8]=>[2,7,6,5,4,3,1,8]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,8,1]=>[3,6,5,4,7,2,1,8]=>[2,7,3,5,6,4,1,8]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,8,1]=>[5,6,4,3,7,2,1,8]=>[2,7,4,6,5,3,1,8]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[1,2,3,7,6,5,4,8]=>[1,2,3,5,6,7,4,8]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[1,3,2,7,6,5,4,8]=>[1,3,2,5,6,7,4,8]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[3,2,1,7,6,5,4,8]=>[2,3,1,5,6,7,4,8]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[2,3,4,7,6,5,1,8]=>[5,2,3,4,6,7,1,8]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,8,1]=>[3,4,2,7,6,5,1,8]=>[5,4,3,2,6,7,1,8]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,2,3,5,6,1]=>[1,2,5,7,6,4,3,8]=>[1,2,4,6,5,7,3,8]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[1,3,5,7,6,4,2,8]=>[1,4,3,6,5,7,2,8]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>[2,3,5,7,6,4,1,8]=>[4,2,3,6,5,7,1,8]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,8,1]=>[3,2,5,7,6,4,1,8]=>[4,3,2,6,5,7,1,8]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,7,8,1]=>[4,3,5,7,6,2,1,8]=>[2,6,4,3,5,7,1,8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,6,7,1]=>[1,5,4,7,6,3,2,8]=>[1,3,6,5,4,7,2,8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,8,1]=>[2,5,4,7,6,3,1,8]=>[3,2,6,5,4,7,1,8]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,8,1]=>[3,5,4,7,6,2,1,8]=>[2,6,3,5,4,7,1,8]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,8,1]=>[4,5,3,7,6,2,1,8]=>[2,6,5,4,3,7,1,8]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,8,1]=>[5,4,3,7,6,2,1,8]=>[2,6,4,5,3,7,1,8]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,5,6,1]=>[1,2,6,7,5,4,3,8]=>[1,2,4,5,7,6,3,8]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[2,1,6,7,5,4,3,8]=>[2,1,4,5,7,6,3,8]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,8,1]=>[2,3,6,7,5,4,1,8]=>[4,2,3,5,7,6,1,8]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,8,1]=>[3,2,6,7,5,4,1,8]=>[4,3,2,5,7,6,1,8]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,6,7,1]=>[1,4,6,7,5,3,2,8]=>[1,3,5,4,7,6,2,8]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,8,1]=>[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,5,6,7,1]=>[1,5,6,7,4,3,2,8]=>[1,3,4,7,5,6,2,8]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,6,8,1]=>[2,5,6,7,4,3,1,8]=>[3,2,4,7,5,6,1,8]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,7,8,1]=>[3,5,6,7,4,2,1,8]=>[2,4,3,7,5,6,1,8]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>[4,5,6,7,3,2,1,8]=>[2,3,7,4,5,6,1,8]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,7,1]=>[1,6,5,7,4,3,2,8]=>[1,3,4,7,6,5,2,8]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,8,1]=>[4,6,5,7,3,2,1,8]=>[2,3,7,4,6,5,1,8]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,8,1]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,1]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,6,1]=>[1,2,7,6,5,4,3,8]=>[1,2,4,5,6,7,3,8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,6,1]=>[2,1,7,6,5,4,3,8]=>[2,1,4,5,6,7,3,8]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,5,7,1]=>[1,3,7,6,5,4,2,8]=>[1,4,3,5,6,7,2,8]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,8,1]=>[2,3,7,6,5,4,1,8]=>[4,2,3,5,6,7,1,8]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>[3,2,7,6,5,4,1,8]=>[4,3,2,5,6,7,1,8]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,7,1]=>[1,4,7,6,5,3,2,8]=>[1,3,5,4,6,7,2,8]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>[3,4,7,6,5,2,1,8]=>[2,5,3,4,6,7,1,8]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,7,8,1]=>[4,3,7,6,5,2,1,8]=>[2,5,4,3,6,7,1,8]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,8,1]=>[2,5,7,6,4,3,1,8]=>[3,2,4,6,5,7,1,8]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,8,1]=>[3,5,7,6,4,2,1,8]=>[2,4,3,6,5,7,1,8]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>[4,5,7,6,3,2,1,8]=>[2,3,6,4,5,7,1,8]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,8,1]=>[5,4,7,6,3,2,1,8]=>[2,3,6,5,4,7,1,8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,7,1]=>[1,6,7,5,4,3,2,8]=>[1,3,4,5,7,6,2,8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,6,8,1]=>[2,6,7,5,4,3,1,8]=>[3,2,4,5,7,6,1,8]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,7,8,1]=>[4,6,7,5,3,2,1,8]=>[2,3,5,4,7,6,1,8]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,8]=>[1,3,4,5,6,7,2,8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,8,1]=>[2,7,6,5,4,3,1,8]=>[3,2,4,5,6,7,1,8]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[4,7,6,5,3,2,1,8]=>[2,3,5,4,6,7,1,8]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,8,1]=>[5,7,6,4,3,2,1,8]=>[2,3,4,6,5,7,1,8]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[6,7,5,4,3,2,1,8]=>[2,3,4,5,7,6,1,8]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,1,2]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,1,2]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,1,2]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>[2,3,4,1,5,6,8,7]=>[4,2,3,1,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,1,2]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,1,2]=>[3,4,2,1,5,6,8,7]=>[2,4,3,1,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,1,2]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,3,1,2]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,1,2]=>[1,3,4,5,2,6,8,7]=>[1,5,3,4,2,6,8,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,1,2]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,1,2]=>[2,4,3,5,1,6,8,7]=>[5,2,4,3,1,6,8,7]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,1,2]=>[1,2,5,4,3,6,8,7]=>[1,2,4,5,3,6,8,7]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,1,2]=>[1,3,5,4,2,6,8,7]=>[1,4,3,5,2,6,8,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[2,3,5,4,1,6,8,7]=>[4,2,3,5,1,6,8,7]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>[3,2,5,4,1,6,8,7]=>[4,3,2,5,1,6,8,7]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,1,2]=>[1,4,5,3,2,6,8,7]=>[1,3,5,4,2,6,8,7]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,1,2]=>[2,4,5,3,1,6,8,7]=>[3,2,5,4,1,6,8,7]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,1,2]=>[3,4,5,2,1,6,8,7]=>[2,5,3,4,1,6,8,7]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>[4,3,5,2,1,6,8,7]=>[2,5,4,3,1,6,8,7]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,1,2]=>[2,5,4,3,1,6,8,7]=>[3,2,4,5,1,6,8,7]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,1,2]=>[4,5,3,2,1,6,8,7]=>[2,3,5,4,1,6,8,7]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[5,4,3,2,1,6,8,7]=>[2,3,4,5,1,6,8,7]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,1,2]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,1,2]=>[2,3,1,4,6,5,8,7]=>[3,2,1,4,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,4,1,2]=>[1,3,4,2,6,5,8,7]=>[1,4,3,2,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,1,2]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,1,2]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,5,1,2]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,1,2]=>[1,2,4,5,6,3,8,7]=>[1,2,6,4,5,3,8,7]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,1,2]=>[1,3,4,5,6,2,8,7]=>[1,6,3,4,5,2,8,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,1,2]=>[2,4,3,5,6,1,8,7]=>[6,2,4,3,5,1,8,7]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,1,2]=>[3,4,2,5,6,1,8,7]=>[6,4,3,2,5,1,8,7]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>[4,3,2,5,6,1,8,7]=>[6,3,4,2,5,1,8,7]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,1,2]=>[2,4,5,3,6,1,8,7]=>[6,2,5,4,3,1,8,7]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>[3,4,5,2,6,1,8,7]=>[6,5,3,4,2,1,8,7]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,1,2]=>[2,5,4,3,6,1,8,7]=>[6,2,4,5,3,1,8,7]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,1,2]=>[3,5,4,2,6,1,8,7]=>[6,4,3,5,2,1,8,7]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,1,2]=>[4,5,3,2,6,1,8,7]=>[6,3,5,4,2,1,8,7]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>[5,4,3,2,6,1,8,7]=>[6,3,4,5,2,1,8,7]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,1,2]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,1,2]=>[2,3,1,6,5,4,8,7]=>[3,2,1,5,6,4,8,7]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,1,2]=>[3,2,1,6,5,4,8,7]=>[2,3,1,5,6,4,8,7]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[2,1,4,6,5,3,8,7]=>[2,1,5,4,6,3,8,7]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,1,2]=>[2,4,3,6,5,1,8,7]=>[5,2,4,3,6,1,8,7]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,8,1,2]=>[3,4,2,6,5,1,8,7]=>[5,4,3,2,6,1,8,7]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,8,1,2]=>[4,3,2,6,5,1,8,7]=>[5,3,4,2,6,1,8,7]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,1,2]=>[2,3,5,6,4,1,8,7]=>[4,2,3,6,5,1,8,7]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,8,1,2]=>[3,2,5,6,4,1,8,7]=>[4,3,2,6,5,1,8,7]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[3,4,5,6,2,1,8,7]=>[2,6,3,4,5,1,8,7]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,1,2]=>[4,3,5,6,2,1,8,7]=>[2,6,4,3,5,1,8,7]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,7,1,2]=>[1,5,4,6,3,2,8,7]=>[1,3,6,5,4,2,8,7]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[4,5,3,6,2,1,8,7]=>[2,6,5,4,3,1,8,7]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>[5,4,3,6,2,1,8,7]=>[2,6,4,5,3,1,8,7]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,7,1,2]=>[1,3,6,5,4,2,8,7]=>[1,4,3,5,6,2,8,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>[2,3,6,5,4,1,8,7]=>[4,2,3,5,6,1,8,7]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,8,1,2]=>[3,2,6,5,4,1,8,7]=>[4,3,2,5,6,1,8,7]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>[2,4,6,5,3,1,8,7]=>[3,2,5,4,6,1,8,7]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,8,1,2]=>[3,4,6,5,2,1,8,7]=>[2,5,3,4,6,1,8,7]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[4,3,6,5,2,1,8,7]=>[2,5,4,3,6,1,8,7]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[1,5,6,4,3,2,8,7]=>[1,3,4,6,5,2,8,7]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[3,5,6,4,2,1,8,7]=>[2,4,3,6,5,1,8,7]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[5,4,6,3,2,1,8,7]=>[2,3,6,5,4,1,8,7]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,1,2]=>[2,6,5,4,3,1,8,7]=>[3,2,4,5,6,1,8,7]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[3,6,5,4,2,1,8,7]=>[2,4,3,5,6,1,8,7]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>[4,6,5,3,2,1,8,7]=>[2,3,5,4,6,1,8,7]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>[5,6,4,3,2,1,8,7]=>[2,3,4,6,5,1,8,7]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[6,5,4,3,2,1,8,7]=>[2,3,4,5,6,1,8,7]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,1,3]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,1,3]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,1,3]=>[3,2,1,4,5,7,8,6]=>[2,3,1,4,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,1,3]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,1,3]=>[1,4,3,2,5,7,8,6]=>[1,3,4,2,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[4,3,2,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,1,3]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,2,1,3]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,1,3]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,1,3]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,1,3]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,1,3]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,1,3]=>[1,4,3,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,1,3]=>[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,1,3]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,2,1,3]=>[4,3,2,5,1,7,8,6]=>[5,3,4,2,1,8,7,6]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,1,3]=>[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,7,6]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,1,3]=>[1,3,5,4,2,7,8,6]=>[1,4,3,5,2,8,7,6]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,2,1,3]=>[3,2,5,4,1,7,8,6]=>[4,3,2,5,1,8,7,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,2,1,3]=>[1,4,5,3,2,7,8,6]=>[1,3,5,4,2,8,7,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,2,1,3]=>[2,4,5,3,1,7,8,6]=>[3,2,5,4,1,8,7,6]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,2,1,3]=>[3,4,5,2,1,7,8,6]=>[2,5,3,4,1,8,7,6]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,1,3]=>[1,5,4,3,2,7,8,6]=>[1,3,4,5,2,8,7,6]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,2,1,3]=>[2,5,4,3,1,7,8,6]=>[3,2,4,5,1,8,7,6]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,2,1,3]=>[3,5,4,2,1,7,8,6]=>[2,4,3,5,1,8,7,6]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[5,4,3,2,1,7,8,6]=>[2,3,4,5,1,8,7,6]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>[3,2,1,4,6,7,8,5]=>[2,3,1,4,8,6,7,5]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,6,7,5]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>[3,4,2,1,6,7,8,5]=>[2,4,3,1,8,6,7,5]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[4,3,2,1,6,7,8,5]=>[2,3,4,1,8,6,7,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,5,6,7,4]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[3,2,1,5,6,7,8,4]=>[2,3,1,8,5,6,7,4]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[1,4,3,5,6,7,8,2]=>[1,8,4,3,5,6,7,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>[2,4,3,5,6,7,8,1]=>[8,2,4,3,5,6,7,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[4,3,2,5,6,7,8,1]=>[8,3,4,2,5,6,7,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,2,1,6]=>[1,2,5,4,6,7,8,3]=>[1,2,8,5,4,6,7,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,2,1,6]=>[2,1,5,4,6,7,8,3]=>[2,1,8,5,4,6,7,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,1,7]=>[1,3,5,4,6,7,8,2]=>[1,8,3,5,4,6,7,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[2,3,5,4,6,7,8,1]=>[8,2,3,5,4,6,7,1]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,1,8]=>[3,2,5,4,6,7,8,1]=>[8,3,2,5,4,6,7,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,1,7]=>[1,4,5,3,6,7,8,2]=>[1,8,5,4,3,6,7,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,1,8]=>[2,4,5,3,6,7,8,1]=>[8,2,5,4,3,6,7,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[1,5,4,3,6,7,8,2]=>[1,8,4,5,3,6,7,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,1,8]=>[2,5,4,3,6,7,8,1]=>[8,2,4,5,3,6,7,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,1,8]=>[3,5,4,2,6,7,8,1]=>[8,4,3,5,2,6,7,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1,8]=>[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>[5,4,3,2,6,7,8,1]=>[8,3,4,5,2,6,7,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,1,5]=>[1,3,2,6,5,7,8,4]=>[1,3,2,8,6,5,7,4]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,1,5]=>[3,2,1,6,5,7,8,4]=>[2,3,1,8,6,5,7,4]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[1,2,4,6,5,7,8,3]=>[1,2,8,4,6,5,7,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[1,3,4,6,5,7,8,2]=>[1,8,3,4,6,5,7,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,1,8]=>[2,3,4,6,5,7,8,1]=>[8,2,3,4,6,5,7,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[1,4,3,6,5,7,8,2]=>[1,8,4,3,6,5,7,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[2,4,3,6,5,7,8,1]=>[8,2,4,3,6,5,7,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,1,8]=>[3,4,2,6,5,7,8,1]=>[8,4,3,2,6,5,7,1]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>[4,3,2,6,5,7,8,1]=>[8,3,4,2,6,5,7,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,1,6]=>[2,1,5,6,4,7,8,3]=>[2,1,8,6,5,4,7,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,1,7]=>[1,3,5,6,4,7,8,2]=>[1,8,3,6,5,4,7,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,1,8]=>[2,3,5,6,4,7,8,1]=>[8,2,3,6,5,4,7,1]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,2,1,8]=>[3,2,5,6,4,7,8,1]=>[8,3,2,6,5,4,7,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,1,8]=>[2,4,5,6,3,7,8,1]=>[8,2,6,4,5,3,7,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,1,8]=>[4,3,5,6,2,7,8,1]=>[8,6,4,3,5,2,7,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>[1,5,4,6,3,7,8,2]=>[1,8,6,5,4,3,7,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,1,8]=>[2,5,4,6,3,7,8,1]=>[8,2,6,5,4,3,7,1]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,1,8]=>[3,5,4,6,2,7,8,1]=>[8,6,3,5,4,2,7,1]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,1,8]=>[5,4,3,6,2,7,8,1]=>[8,6,4,5,3,2,7,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[1,2,6,5,4,7,8,3]=>[1,2,8,5,6,4,7,3]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[2,3,6,5,4,7,8,1]=>[8,2,3,5,6,4,7,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,2,1,8]=>[2,4,6,5,3,7,8,1]=>[8,2,5,4,6,3,7,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,1,8]=>[3,4,6,5,2,7,8,1]=>[8,5,3,4,6,2,7,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,6,2,1,8]=>[2,5,6,4,3,7,8,1]=>[8,2,4,6,5,3,7,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,2,1,8]=>[3,5,6,4,2,7,8,1]=>[8,4,3,6,5,2,7,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>[4,5,6,3,2,7,8,1]=>[8,3,6,4,5,2,7,1]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,2,1,8]=>[5,4,6,3,2,7,8,1]=>[8,3,6,5,4,2,7,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[1,6,5,4,3,7,8,2]=>[1,8,4,5,6,3,7,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,1,8]=>[2,6,5,4,3,7,8,1]=>[8,2,4,5,6,3,7,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,1,8]=>[3,6,5,4,2,7,8,1]=>[8,4,3,5,6,2,7,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8]=>[6,5,4,3,2,7,8,1]=>[8,3,4,5,6,2,7,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,1,4]=>[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[4,3,2,1,7,6,8,5]=>[2,3,4,1,8,7,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,3,1,5]=>[2,1,3,5,7,6,8,4]=>[2,1,3,8,5,7,6,4]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,3,1,5]=>[1,3,2,5,7,6,8,4]=>[1,3,2,8,5,7,6,4]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>[2,3,1,5,7,6,8,4]=>[3,2,1,8,5,7,6,4]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>[3,2,1,5,7,6,8,4]=>[2,3,1,8,5,7,6,4]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[1,3,4,5,7,6,8,2]=>[1,8,3,4,5,7,6,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,1,8]=>[2,3,4,5,7,6,8,1]=>[8,2,3,4,5,7,6,1]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,1,8]=>[3,2,4,5,7,6,8,1]=>[8,3,2,4,5,7,6,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>[2,4,3,5,7,6,8,1]=>[8,2,4,3,5,7,6,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,1,8]=>[3,4,2,5,7,6,8,1]=>[8,4,3,2,5,7,6,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>[4,3,2,5,7,6,8,1]=>[8,3,4,2,5,7,6,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[1,2,5,4,7,6,8,3]=>[1,2,8,5,4,7,6,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,3,1,7]=>[1,3,5,4,7,6,8,2]=>[1,8,3,5,4,7,6,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[2,3,5,4,7,6,8,1]=>[8,2,3,5,4,7,6,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>[3,4,5,2,7,6,8,1]=>[8,5,3,4,2,7,6,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,1,8]=>[2,5,4,3,7,6,8,1]=>[8,2,4,5,3,7,6,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,2,3,1,8]=>[3,5,4,2,7,6,8,1]=>[8,4,3,5,2,7,6,1]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,1,8]=>[5,4,3,2,7,6,8,1]=>[8,3,4,5,2,7,6,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>[1,3,2,6,7,5,8,4]=>[1,3,2,8,7,6,5,4]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,4,1,5]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,6,5,4]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,4,1,6]=>[2,1,4,6,7,5,8,3]=>[2,1,8,4,7,6,5,3]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>[1,3,4,6,7,5,8,2]=>[1,8,3,4,7,6,5,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,1,8]=>[2,3,4,6,7,5,8,1]=>[8,2,3,4,7,6,5,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,4,1,7]=>[1,4,3,6,7,5,8,2]=>[1,8,4,3,7,6,5,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,2,4,1,8]=>[2,4,3,6,7,5,8,1]=>[8,2,4,3,7,6,5,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[3,4,2,6,7,5,8,1]=>[8,4,3,2,7,6,5,1]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>[4,3,2,6,7,5,8,1]=>[8,3,4,2,7,6,5,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,1,6]=>[1,2,5,6,7,4,8,3]=>[1,2,8,7,5,6,4,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,5,1,7]=>[1,3,5,6,7,4,8,2]=>[1,8,3,7,5,6,4,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,1,8]=>[2,3,5,6,7,4,8,1]=>[8,2,3,7,5,6,4,1]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>[3,2,5,6,7,4,8,1]=>[8,3,2,7,5,6,4,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,1,8]=>[2,4,5,6,7,3,8,1]=>[8,2,7,4,5,6,3,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,1,8]=>[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,1,7]=>[1,5,4,6,7,3,8,2]=>[1,8,7,5,4,6,3,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,1,8]=>[2,5,4,6,7,3,8,1]=>[8,2,7,5,4,6,3,1]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,2,7,1,8]=>[3,5,4,6,7,2,8,1]=>[8,7,3,5,4,6,2,1]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,1,8]=>[4,5,3,6,7,2,8,1]=>[8,7,5,4,3,6,2,1]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,1,8]=>[5,4,3,6,7,2,8,1]=>[8,7,4,5,3,6,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,5,1,7]=>[1,3,6,5,7,4,8,2]=>[1,8,3,7,6,5,4,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>[2,4,6,5,7,3,8,1]=>[8,2,7,4,6,5,3,1]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,7,1,8]=>[3,4,6,5,7,2,8,1]=>[8,7,3,4,6,5,2,1]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,6,1,7]=>[1,5,6,4,7,3,8,2]=>[1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,7,1,8]=>[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>[3,6,5,4,7,2,8,1]=>[8,7,3,5,6,4,2,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,1,8]=>[4,6,5,3,7,2,8,1]=>[8,7,5,4,6,3,2,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[6,5,4,3,7,2,8,1]=>[8,7,4,5,6,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,7,5,4]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,1,5]=>[1,3,2,7,6,5,8,4]=>[1,3,2,8,6,7,5,4]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,1,5]=>[2,3,1,7,6,5,8,4]=>[3,2,1,8,6,7,5,4]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>[3,2,1,7,6,5,8,4]=>[2,3,1,8,6,7,5,4]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,4,1,6]=>[1,2,4,7,6,5,8,3]=>[1,2,8,4,6,7,5,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,1,6]=>[2,1,4,7,6,5,8,3]=>[2,1,8,4,6,7,5,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[1,3,4,7,6,5,8,2]=>[1,8,3,4,6,7,5,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[2,3,4,7,6,5,8,1]=>[8,2,3,4,6,7,5,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>[3,2,4,7,6,5,8,1]=>[8,3,2,4,6,7,5,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>[2,4,3,7,6,5,8,1]=>[8,2,4,3,6,7,5,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>[3,4,2,7,6,5,8,1]=>[8,4,3,2,6,7,5,1]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[4,3,2,7,6,5,8,1]=>[8,3,4,2,6,7,5,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,2,3,5,1,6]=>[1,2,5,7,6,4,8,3]=>[1,2,8,6,5,7,4,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,5,1,6]=>[2,1,5,7,6,4,8,3]=>[2,1,8,6,5,7,4,3]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>[1,3,5,7,6,4,8,2]=>[1,8,3,6,5,7,4,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>[2,3,5,7,6,4,8,1]=>[8,2,3,6,5,7,4,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,1,8]=>[3,2,5,7,6,4,8,1]=>[8,3,2,6,5,7,4,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,1,8]=>[3,4,5,7,6,2,8,1]=>[8,6,3,4,5,7,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>[2,5,4,7,6,3,8,1]=>[8,2,6,5,4,7,3,1]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,1,8]=>[3,5,4,7,6,2,8,1]=>[8,6,3,5,4,7,2,1]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,1,8]=>[4,5,3,7,6,2,8,1]=>[8,6,5,4,3,7,2,1]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,1,8]=>[5,4,3,7,6,2,8,1]=>[8,6,4,5,3,7,2,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,1,6]=>[2,1,6,7,5,4,8,3]=>[2,1,8,5,7,6,4,3]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,1,8]=>[3,2,6,7,5,4,8,1]=>[8,3,2,5,7,6,4,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,6,1,7]=>[1,4,6,7,5,3,8,2]=>[1,8,5,4,7,6,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[2,4,6,7,5,3,8,1]=>[8,2,5,4,7,6,3,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[3,4,6,7,5,2,8,1]=>[8,5,3,4,7,6,2,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,7,1,8]=>[4,3,6,7,5,2,8,1]=>[8,5,4,3,7,6,2,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,6,1,8]=>[2,5,6,7,4,3,8,1]=>[8,2,4,7,5,6,3,1]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,7,1,8]=>[3,5,6,7,4,2,8,1]=>[8,4,3,7,5,6,2,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,1,7]=>[1,6,5,7,4,3,8,2]=>[1,8,4,7,6,5,3,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,2,5,6,1,8]=>[2,6,5,7,4,3,8,1]=>[8,2,4,7,6,5,3,1]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,1,8]=>[4,6,5,7,3,2,8,1]=>[8,3,7,4,6,5,2,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,1,6]=>[1,2,7,6,5,4,8,3]=>[1,2,8,5,6,7,4,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,1,6]=>[2,1,7,6,5,4,8,3]=>[2,1,8,5,6,7,4,3]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>[2,3,7,6,5,4,8,1]=>[8,2,3,5,6,7,4,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,1,8]=>[3,2,7,6,5,4,8,1]=>[8,3,2,5,6,7,4,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,1,8]=>[3,4,7,6,5,2,8,1]=>[8,5,3,4,6,7,2,1]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,7,1,8]=>[4,3,7,6,5,2,8,1]=>[8,5,4,3,6,7,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,1,8]=>[3,5,7,6,4,2,8,1]=>[8,4,3,6,5,7,2,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,1,7]=>[1,6,7,5,4,3,8,2]=>[1,8,4,5,7,6,3,2]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,7,1,8]=>[4,6,7,5,3,2,8,1]=>[8,3,5,4,7,6,2,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,1,8]=>[6,5,7,4,3,2,8,1]=>[8,3,4,7,6,5,2,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,1,7]=>[1,7,6,5,4,3,8,2]=>[1,8,4,5,6,7,3,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,1,8]=>[2,7,6,5,4,3,8,1]=>[8,2,4,5,6,7,3,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,1,8]=>[4,7,6,5,3,2,8,1]=>[8,3,5,4,6,7,2,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,1,8]=>[5,7,6,4,3,2,8,1]=>[8,3,4,6,5,7,2,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,1,8]=>[6,7,5,4,3,2,8,1]=>[8,3,4,5,7,6,2,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,1,2,3]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,1,2,3]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,1,2,3]=>[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,7,8,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[2,1,4,3,5,8,7,6]=>[2,1,4,3,5,7,8,6]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,1,2,3]=>[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,7,8,6]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,7,8,6]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,1,2,3]=>[2,4,3,1,5,8,7,6]=>[3,2,4,1,5,7,8,6]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>[3,4,2,1,5,8,7,6]=>[2,4,3,1,5,7,8,6]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,1,2,3]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,1,2,3]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,7,8,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,1,2,3]=>[2,1,4,5,3,8,7,6]=>[2,1,5,4,3,7,8,6]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,1,2,3]=>[1,3,4,5,2,8,7,6]=>[1,5,3,4,2,7,8,6]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[2,3,4,5,1,8,7,6]=>[5,2,3,4,1,7,8,6]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,1,2,3]=>[3,2,4,5,1,8,7,6]=>[5,3,2,4,1,7,8,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[1,4,3,5,2,8,7,6]=>[1,5,4,3,2,7,8,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[2,4,3,5,1,8,7,6]=>[5,2,4,3,1,7,8,6]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,1,2,3]=>[4,3,2,5,1,8,7,6]=>[5,3,4,2,1,7,8,6]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,1,2,3]=>[2,1,5,4,3,8,7,6]=>[2,1,4,5,3,7,8,6]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[2,3,5,4,1,8,7,6]=>[4,2,3,5,1,7,8,6]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[3,2,5,4,1,8,7,6]=>[4,3,2,5,1,7,8,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,1,2,3]=>[1,4,5,3,2,8,7,6]=>[1,3,5,4,2,7,8,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[2,4,5,3,1,8,7,6]=>[3,2,5,4,1,7,8,6]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>[3,4,5,2,1,8,7,6]=>[2,5,3,4,1,7,8,6]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[4,3,5,2,1,8,7,6]=>[2,5,4,3,1,7,8,6]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,1,2,3]=>[1,5,4,3,2,8,7,6]=>[1,3,4,5,2,7,8,6]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[2,5,4,3,1,8,7,6]=>[3,2,4,5,1,7,8,6]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[3,5,4,2,1,8,7,6]=>[2,4,3,5,1,7,8,6]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>[4,5,3,2,1,8,7,6]=>[2,3,5,4,1,7,8,6]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[5,4,3,2,1,8,7,6]=>[2,3,4,5,1,7,8,6]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,6,8,5]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,1,2,4]=>[1,3,2,4,6,8,7,5]=>[1,3,2,4,7,6,8,5]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,1,2,4]=>[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,6,8,5]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,1,2,4]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,6,8,5]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,1,2,4]=>[1,3,4,2,6,8,7,5]=>[1,4,3,2,7,6,8,5]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[2,3,4,1,6,8,7,5]=>[4,2,3,1,7,6,8,5]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,1,2,4]=>[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,6,8,5]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[3,4,2,1,6,8,7,5]=>[2,4,3,1,7,6,8,5]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[4,3,2,1,6,8,7,5]=>[2,3,4,1,7,6,8,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,5,6,8,4]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,1,2,5]=>[1,3,2,5,6,8,7,4]=>[1,3,2,7,5,6,8,4]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[3,2,1,5,6,8,7,4]=>[2,3,1,7,5,6,8,4]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[1,2,4,5,6,8,7,3]=>[1,2,7,4,5,6,8,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,1,2,6]=>[2,1,4,5,6,8,7,3]=>[2,1,7,4,5,6,8,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1,2,7]=>[1,3,4,5,6,8,7,2]=>[1,7,3,4,5,6,8,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[2,3,4,5,6,8,7,1]=>[7,2,3,4,5,6,8,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,1,2,8]=>[3,2,4,5,6,8,7,1]=>[7,3,2,4,5,6,8,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,1,2,8]=>[2,4,3,5,6,8,7,1]=>[7,2,4,3,5,6,8,1]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,1,2,8]=>[3,4,2,5,6,8,7,1]=>[7,4,3,2,5,6,8,1]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,1,2,8]=>[4,3,2,5,6,8,7,1]=>[7,3,4,2,5,6,8,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,1,2,6]=>[1,2,5,4,6,8,7,3]=>[1,2,7,5,4,6,8,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,1,2,6]=>[2,1,5,4,6,8,7,3]=>[2,1,7,5,4,6,8,3]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,1,2,8]=>[3,2,5,4,6,8,7,1]=>[7,3,2,5,4,6,8,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,1,2,7]=>[1,4,5,3,6,8,7,2]=>[1,7,5,4,3,6,8,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,1,2,8]=>[2,4,5,3,6,8,7,1]=>[7,2,5,4,3,6,8,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,1,2,7]=>[1,5,4,3,6,8,7,2]=>[1,7,4,5,3,6,8,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,1,2,8]=>[2,5,4,3,6,8,7,1]=>[7,2,4,5,3,6,8,1]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,1,2,8]=>[4,5,3,2,6,8,7,1]=>[7,3,5,4,2,6,8,1]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,1,2,8]=>[5,4,3,2,6,8,7,1]=>[7,3,4,5,2,6,8,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[1,2,3,6,5,8,7,4]=>[1,2,3,7,6,5,8,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,1,2,5]=>[2,1,3,6,5,8,7,4]=>[2,1,3,7,6,5,8,4]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,1,2,5]=>[1,3,2,6,5,8,7,4]=>[1,3,2,7,6,5,8,4]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,1,2,5]=>[2,3,1,6,5,8,7,4]=>[3,2,1,7,6,5,8,4]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[3,2,1,6,5,8,7,4]=>[2,3,1,7,6,5,8,4]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[1,2,4,6,5,8,7,3]=>[1,2,7,4,6,5,8,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,1,2,6]=>[2,1,4,6,5,8,7,3]=>[2,1,7,4,6,5,8,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,1,2,8]=>[2,3,4,6,5,8,7,1]=>[7,2,3,4,6,5,8,1]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,1,2,8]=>[3,2,4,6,5,8,7,1]=>[7,3,2,4,6,5,8,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[1,4,3,6,5,8,7,2]=>[1,7,4,3,6,5,8,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,1,2,8]=>[2,4,3,6,5,8,7,1]=>[7,2,4,3,6,5,8,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>[3,4,2,6,5,8,7,1]=>[7,4,3,2,6,5,8,1]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,1,2,8]=>[4,3,2,6,5,8,7,1]=>[7,3,4,2,6,5,8,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,1,2,6]=>[2,1,5,6,4,8,7,3]=>[2,1,7,6,5,4,8,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,1,2,8]=>[2,3,5,6,4,8,7,1]=>[7,2,3,6,5,4,8,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,1,2,7]=>[1,4,5,6,3,8,7,2]=>[1,7,6,4,5,3,8,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,1,2,8]=>[2,4,5,6,3,8,7,1]=>[7,2,6,4,5,3,8,1]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>[3,5,4,6,2,8,7,1]=>[7,6,3,5,4,2,8,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,1,2,8]=>[4,5,3,6,2,8,7,1]=>[7,6,5,4,3,2,8,1]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,1,2,8]=>[5,4,3,6,2,8,7,1]=>[7,6,4,5,3,2,8,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,1,2,6]=>[1,2,6,5,4,8,7,3]=>[1,2,7,5,6,4,8,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,1,2,6]=>[2,1,6,5,4,8,7,3]=>[2,1,7,5,6,4,8,3]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,1,2,7]=>[1,3,6,5,4,8,7,2]=>[1,7,3,5,6,4,8,2]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>[3,2,6,5,4,8,7,1]=>[7,3,2,5,6,4,8,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,1,2,7]=>[1,4,6,5,3,8,7,2]=>[1,7,5,4,6,3,8,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,1,2,8]=>[2,4,6,5,3,8,7,1]=>[7,2,5,4,6,3,8,1]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,1,2,8]=>[4,3,6,5,2,8,7,1]=>[7,5,4,3,6,2,8,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>[1,5,6,4,3,8,7,2]=>[1,7,4,6,5,3,8,2]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,1,2,8]=>[3,5,6,4,2,8,7,1]=>[7,4,3,6,5,2,8,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,1,2,8]=>[4,5,6,3,2,8,7,1]=>[7,3,6,4,5,2,8,1]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,1,2,8]=>[5,4,6,3,2,8,7,1]=>[7,3,6,5,4,2,8,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[1,6,5,4,3,8,7,2]=>[1,7,4,5,6,3,8,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,1,2,8]=>[2,6,5,4,3,8,7,1]=>[7,2,4,5,6,3,8,1]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,1,2,8]=>[3,6,5,4,2,8,7,1]=>[7,4,3,5,6,2,8,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,1,2,8]=>[4,6,5,3,2,8,7,1]=>[7,3,5,4,6,2,8,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[6,5,4,3,2,8,7,1]=>[7,3,4,5,6,2,8,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,6,8,7,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,1,3,4]=>[2,1,3,4,7,8,6,5]=>[2,1,3,4,6,8,7,5]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,1,3,4]=>[2,3,1,4,7,8,6,5]=>[3,2,1,4,6,8,7,5]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[3,2,1,4,7,8,6,5]=>[2,3,1,4,6,8,7,5]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,1,3,4]=>[1,2,4,3,7,8,6,5]=>[1,2,4,3,6,8,7,5]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[1,3,4,2,7,8,6,5]=>[1,4,3,2,6,8,7,5]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>[2,3,4,1,7,8,6,5]=>[4,2,3,1,6,8,7,5]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>[2,4,3,1,7,8,6,5]=>[3,2,4,1,6,8,7,5]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[4,3,2,1,7,8,6,5]=>[2,3,4,1,6,8,7,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[1,2,3,5,7,8,6,4]=>[1,2,3,6,5,8,7,4]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[1,3,2,5,7,8,6,4]=>[1,3,2,6,5,8,7,4]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[3,2,1,5,7,8,6,4]=>[2,3,1,6,5,8,7,4]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,2,1,3,6]=>[1,2,4,5,7,8,6,3]=>[1,2,6,4,5,8,7,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[2,1,4,5,7,8,6,3]=>[2,1,6,4,5,8,7,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[1,3,4,5,7,8,6,2]=>[1,6,3,4,5,8,7,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,3,8]=>[2,3,4,5,7,8,6,1]=>[6,2,3,4,5,8,7,1]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,1,3,8]=>[3,2,4,5,7,8,6,1]=>[6,3,2,4,5,8,7,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>[1,4,3,5,7,8,6,2]=>[1,6,4,3,5,8,7,2]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,1,3,8]=>[3,4,2,5,7,8,6,1]=>[6,4,3,2,5,8,7,1]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,1,3,8]=>[4,3,2,5,7,8,6,1]=>[6,3,4,2,5,8,7,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,1,3,6]=>[1,2,5,4,7,8,6,3]=>[1,2,6,5,4,8,7,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,1,3,6]=>[2,1,5,4,7,8,6,3]=>[2,1,6,5,4,8,7,3]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,1,3,7]=>[1,3,5,4,7,8,6,2]=>[1,6,3,5,4,8,7,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,1,3,8]=>[2,3,5,4,7,8,6,1]=>[6,2,3,5,4,8,7,1]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,1,3,8]=>[3,2,5,4,7,8,6,1]=>[6,3,2,5,4,8,7,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,1,3,8]=>[2,4,5,3,7,8,6,1]=>[6,2,5,4,3,8,7,1]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,1,3,8]=>[3,4,5,2,7,8,6,1]=>[6,5,3,4,2,8,7,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,1,3,8]=>[2,5,4,3,7,8,6,1]=>[6,2,4,5,3,8,7,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,1,3,8]=>[5,4,3,2,7,8,6,1]=>[6,3,4,5,2,8,7,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[1,2,3,6,7,8,5,4]=>[1,2,3,5,8,6,7,4]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,1,4,5]=>[1,3,2,6,7,8,5,4]=>[1,3,2,5,8,6,7,4]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>[2,3,1,6,7,8,5,4]=>[3,2,1,5,8,6,7,4]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[3,2,1,6,7,8,5,4]=>[2,3,1,5,8,6,7,4]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[1,2,4,6,7,8,5,3]=>[1,2,5,4,8,6,7,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[2,1,4,6,7,8,5,3]=>[2,1,5,4,8,6,7,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[1,3,4,6,7,8,5,2]=>[1,5,3,4,8,6,7,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1,4,8]=>[2,3,4,6,7,8,5,1]=>[5,2,3,4,8,6,7,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>[1,4,3,6,7,8,5,2]=>[1,5,4,3,8,6,7,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,2,1,4,8]=>[2,4,3,6,7,8,5,1]=>[5,2,4,3,8,6,7,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[1,2,5,6,7,8,4,3]=>[1,2,4,8,5,6,7,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[2,1,5,6,7,8,4,3]=>[2,1,4,8,5,6,7,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[1,3,5,6,7,8,4,2]=>[1,4,3,8,5,6,7,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[2,3,5,6,7,8,4,1]=>[4,2,3,8,5,6,7,1]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>[3,2,5,6,7,8,4,1]=>[4,3,2,8,5,6,7,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,6,7]=>[1,4,5,6,7,8,3,2]=>[1,3,8,4,5,6,7,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1,6,8]=>[2,4,5,6,7,8,3,1]=>[3,2,8,4,5,6,7,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[3,4,5,6,7,8,2,1]=>[2,8,3,4,5,6,7,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[4,3,5,6,7,8,2,1]=>[2,8,4,3,5,6,7,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,1,6,7]=>[1,5,4,6,7,8,3,2]=>[1,3,8,5,4,6,7,2]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,1,6,8]=>[2,5,4,6,7,8,3,1]=>[3,2,8,5,4,6,7,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,2,1,7,8]=>[3,5,4,6,7,8,2,1]=>[2,8,3,5,4,6,7,1]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[5,4,3,6,7,8,2,1]=>[2,8,4,5,3,6,7,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[1,2,6,5,7,8,4,3]=>[1,2,4,8,6,5,7,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[2,1,6,5,7,8,4,3]=>[2,1,4,8,6,5,7,3]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[1,3,6,5,7,8,4,2]=>[1,4,3,8,6,5,7,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,1,6,8]=>[2,4,6,5,7,8,3,1]=>[3,2,8,4,6,5,7,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,1,7,8]=>[3,4,6,5,7,8,2,1]=>[2,8,3,4,6,5,7,1]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,1,7,8]=>[4,3,6,5,7,8,2,1]=>[2,8,4,3,6,5,7,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,1,6,8]=>[2,5,6,4,7,8,3,1]=>[3,2,8,6,5,4,7,1]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,1,7,8]=>[3,5,6,4,7,8,2,1]=>[2,8,3,6,5,4,7,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,1,7,8]=>[4,5,6,3,7,8,2,1]=>[2,8,6,4,5,3,7,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[1,6,5,4,7,8,3,2]=>[1,3,8,5,6,4,7,2]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,1,6,8]=>[2,6,5,4,7,8,3,1]=>[3,2,8,5,6,4,7,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,1,7,8]=>[3,6,5,4,7,8,2,1]=>[2,8,3,5,6,4,7,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[6,5,4,3,7,8,2,1]=>[2,8,4,5,6,3,7,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[1,2,3,7,6,8,5,4]=>[1,2,3,5,8,7,6,4]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,1,4,5]=>[1,3,2,7,6,8,5,4]=>[1,3,2,5,8,7,6,4]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>[2,3,1,7,6,8,5,4]=>[3,2,1,5,8,7,6,4]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[3,2,1,7,6,8,5,4]=>[2,3,1,5,8,7,6,4]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,1,4,6]=>[1,2,4,7,6,8,5,3]=>[1,2,5,4,8,7,6,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,1,4,6]=>[2,1,4,7,6,8,5,3]=>[2,1,5,4,8,7,6,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[1,3,4,7,6,8,5,2]=>[1,5,3,4,8,7,6,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,1,4,8]=>[2,3,4,7,6,8,5,1]=>[5,2,3,4,8,7,6,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[1,4,3,7,6,8,5,2]=>[1,5,4,3,8,7,6,2]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,1,5,6]=>[2,1,5,7,6,8,4,3]=>[2,1,4,8,5,7,6,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>[1,3,5,7,6,8,4,2]=>[1,4,3,8,5,7,6,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>[2,3,5,7,6,8,4,1]=>[4,2,3,8,5,7,6,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,1,5,8]=>[3,2,5,7,6,8,4,1]=>[4,3,2,8,5,7,6,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,1,7,8]=>[3,4,5,7,6,8,2,1]=>[2,8,3,4,5,7,6,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,1,7,8]=>[4,3,5,7,6,8,2,1]=>[2,8,4,3,5,7,6,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,1,6,8]=>[2,5,4,7,6,8,3,1]=>[3,2,8,5,4,7,6,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,1,7,8]=>[3,5,4,7,6,8,2,1]=>[2,8,3,5,4,7,6,1]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,1,7,8]=>[4,5,3,7,6,8,2,1]=>[2,8,5,4,3,7,6,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[2,1,6,7,5,8,4,3]=>[2,1,4,8,7,6,5,3]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,1,5,8]=>[3,2,6,7,5,8,4,1]=>[4,3,2,8,7,6,5,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,1,6,7]=>[1,4,6,7,5,8,3,2]=>[1,3,8,4,7,6,5,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,1,6,8]=>[2,4,6,7,5,8,3,1]=>[3,2,8,4,7,6,5,1]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,1,7,8]=>[3,4,6,7,5,8,2,1]=>[2,8,3,4,7,6,5,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,1,6,8]=>[2,5,6,7,4,8,3,1]=>[3,2,8,7,5,6,4,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>[3,5,6,7,4,8,2,1]=>[2,8,3,7,5,6,4,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,1,7,8]=>[6,5,4,7,3,8,2,1]=>[2,8,7,5,6,4,3,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,1,5,6]=>[1,2,7,6,5,8,4,3]=>[1,2,4,8,6,7,5,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[2,1,7,6,5,8,4,3]=>[2,1,4,8,6,7,5,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>[2,3,7,6,5,8,4,1]=>[4,2,3,8,6,7,5,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[1,4,7,6,5,8,3,2]=>[1,3,8,4,6,7,5,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>[2,4,7,6,5,8,3,1]=>[3,2,8,4,6,7,5,1]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,1,7,8]=>[3,4,7,6,5,8,2,1]=>[2,8,3,4,6,7,5,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>[4,3,7,6,5,8,2,1]=>[2,8,4,3,6,7,5,1]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,1,7,8]=>[3,5,7,6,4,8,2,1]=>[2,8,3,6,5,7,4,1]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,1,7,8]=>[5,4,7,6,3,8,2,1]=>[2,8,6,5,4,7,3,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,1,6,8]=>[2,6,7,5,4,8,3,1]=>[3,2,8,5,7,6,4,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,1,7,8]=>[5,6,7,4,3,8,2,1]=>[2,8,4,7,5,6,3,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,1,6,7]=>[1,7,6,5,4,8,3,2]=>[1,3,8,5,6,7,4,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[2,7,6,5,4,8,3,1]=>[3,2,8,5,6,7,4,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,1,7,8]=>[3,7,6,5,4,8,2,1]=>[2,8,3,5,6,7,4,1]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,1,7,8]=>[4,7,6,5,3,8,2,1]=>[2,8,5,4,6,7,3,1]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,1,7,8]=>[5,7,6,4,3,8,2,1]=>[2,8,4,6,5,7,3,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,1,7,8]=>[6,7,5,4,3,8,2,1]=>[2,8,4,5,7,6,3,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[7,6,5,4,3,8,2,1]=>[2,8,4,5,6,7,3,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,6,7,8,5]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,6,7,8,5]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[2,3,4,1,8,7,6,5]=>[4,2,3,1,6,7,8,5]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[2,4,3,1,8,7,6,5]=>[3,2,4,1,6,7,8,5]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[3,4,2,1,8,7,6,5]=>[2,4,3,1,6,7,8,5]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[1,2,3,5,8,7,6,4]=>[1,2,3,6,5,7,8,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,1,2,3,5]=>[1,3,2,5,8,7,6,4]=>[1,3,2,6,5,7,8,4]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>[3,2,1,5,8,7,6,4]=>[2,3,1,6,5,7,8,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,1,2,3,6]=>[1,2,4,5,8,7,6,3]=>[1,2,6,4,5,7,8,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[2,1,4,5,8,7,6,3]=>[2,1,6,4,5,7,8,3]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,1,2,3,7]=>[1,3,4,5,8,7,6,2]=>[1,6,3,4,5,7,8,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[2,3,4,5,8,7,6,1]=>[6,2,3,4,5,7,8,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[1,4,3,5,8,7,6,2]=>[1,6,4,3,5,7,8,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,1,2,3,8]=>[2,4,3,5,8,7,6,1]=>[6,2,4,3,5,7,8,1]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,1,2,3,8]=>[3,4,2,5,8,7,6,1]=>[6,4,3,2,5,7,8,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>[4,3,2,5,8,7,6,1]=>[6,3,4,2,5,7,8,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,1,2,3,6]=>[1,2,5,4,8,7,6,3]=>[1,2,6,5,4,7,8,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,1,2,3,6]=>[2,1,5,4,8,7,6,3]=>[2,1,6,5,4,7,8,3]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,1,2,3,7]=>[1,3,5,4,8,7,6,2]=>[1,6,3,5,4,7,8,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,1,2,3,8]=>[2,3,5,4,8,7,6,1]=>[6,2,3,5,4,7,8,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,1,2,3,7]=>[1,4,5,3,8,7,6,2]=>[1,6,5,4,3,7,8,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,1,2,3,8]=>[2,4,5,3,8,7,6,1]=>[6,2,5,4,3,7,8,1]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[4,3,5,2,8,7,6,1]=>[6,5,4,3,2,7,8,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>[1,5,4,3,8,7,6,2]=>[1,6,4,5,3,7,8,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,1,2,3,8]=>[2,5,4,3,8,7,6,1]=>[6,2,4,5,3,7,8,1]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[4,5,3,2,8,7,6,1]=>[6,3,5,4,2,7,8,1]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[5,4,3,2,8,7,6,1]=>[6,3,4,5,2,7,8,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[1,2,3,6,8,7,5,4]=>[1,2,3,5,7,6,8,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[2,1,3,6,8,7,5,4]=>[2,1,3,5,7,6,8,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,1,2,4,5]=>[1,3,2,6,8,7,5,4]=>[1,3,2,5,7,6,8,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,1,2,4,5]=>[2,3,1,6,8,7,5,4]=>[3,2,1,5,7,6,8,4]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>[3,2,1,6,8,7,5,4]=>[2,3,1,5,7,6,8,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[1,2,4,6,8,7,5,3]=>[1,2,5,4,7,6,8,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[2,1,4,6,8,7,5,3]=>[2,1,5,4,7,6,8,3]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,1,2,4,8]=>[2,3,4,6,8,7,5,1]=>[5,2,3,4,7,6,8,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>[1,4,3,6,8,7,5,2]=>[1,5,4,3,7,6,8,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,1,2,4,8]=>[2,4,3,6,8,7,5,1]=>[5,2,4,3,7,6,8,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[4,3,2,6,8,7,5,1]=>[5,3,4,2,7,6,8,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,1,2,5,6]=>[1,2,5,6,8,7,4,3]=>[1,2,4,7,5,6,8,3]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>[2,1,5,6,8,7,4,3]=>[2,1,4,7,5,6,8,3]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,1,2,5,7]=>[1,3,5,6,8,7,4,2]=>[1,4,3,7,5,6,8,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,1,2,5,8]=>[2,3,5,6,8,7,4,1]=>[4,2,3,7,5,6,8,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,2,7,8]=>[3,4,5,6,8,7,2,1]=>[2,7,3,4,5,6,8,1]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>[4,3,5,6,8,7,2,1]=>[2,7,4,3,5,6,8,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,1,2,6,7]=>[1,5,4,6,8,7,3,2]=>[1,3,7,5,4,6,8,2]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[4,5,3,6,8,7,2,1]=>[2,7,5,4,3,6,8,1]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,1,2,7,8]=>[5,4,3,6,8,7,2,1]=>[2,7,4,5,3,6,8,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>[1,2,6,5,8,7,4,3]=>[1,2,4,7,6,5,8,3]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[2,1,6,5,8,7,4,3]=>[2,1,4,7,6,5,8,3]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,1,2,5,8]=>[2,3,6,5,8,7,4,1]=>[4,2,3,7,6,5,8,1]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,1,2,5,8]=>[3,2,6,5,8,7,4,1]=>[4,3,2,7,6,5,8,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,1,2,6,7]=>[1,4,6,5,8,7,3,2]=>[1,3,7,4,6,5,8,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,1,2,6,8]=>[2,4,6,5,8,7,3,1]=>[3,2,7,4,6,5,8,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[4,3,6,5,8,7,2,1]=>[2,7,4,3,6,5,8,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,1,2,6,8]=>[2,5,6,4,8,7,3,1]=>[3,2,7,6,5,4,8,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[4,5,6,3,8,7,2,1]=>[2,7,6,4,5,3,8,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,1,2,6,7]=>[1,6,5,4,8,7,3,2]=>[1,3,7,5,6,4,8,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,1,2,6,8]=>[2,6,5,4,8,7,3,1]=>[3,2,7,5,6,4,8,1]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,1,2,7,8]=>[5,6,4,3,8,7,2,1]=>[2,7,4,6,5,3,8,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[6,5,4,3,8,7,2,1]=>[2,7,4,5,6,3,8,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[1,2,3,7,8,6,5,4]=>[1,2,3,5,6,8,7,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>[2,1,3,7,8,6,5,4]=>[2,1,3,5,6,8,7,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>[3,2,1,7,8,6,5,4]=>[2,3,1,5,6,8,7,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[1,2,4,7,8,6,5,3]=>[1,2,5,4,6,8,7,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[2,1,4,7,8,6,5,3]=>[2,1,5,4,6,8,7,3]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,1,3,4,8]=>[3,2,4,7,8,6,5,1]=>[5,3,2,4,6,8,7,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[1,4,3,7,8,6,5,2]=>[1,5,4,3,6,8,7,2]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,1,3,4,8]=>[3,4,2,7,8,6,5,1]=>[5,4,3,2,6,8,7,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[4,3,2,7,8,6,5,1]=>[5,3,4,2,6,8,7,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[2,1,5,7,8,6,4,3]=>[2,1,4,6,5,8,7,3]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[2,3,5,7,8,6,4,1]=>[4,2,3,6,5,8,7,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,1,3,5,8]=>[3,2,5,7,8,6,4,1]=>[4,3,2,6,5,8,7,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>[1,4,5,7,8,6,3,2]=>[1,3,6,4,5,8,7,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,1,3,6,8]=>[2,4,5,7,8,6,3,1]=>[3,2,6,4,5,8,7,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,1,3,7,8]=>[3,4,5,7,8,6,2,1]=>[2,6,3,4,5,8,7,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[4,3,5,7,8,6,2,1]=>[2,6,4,3,5,8,7,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,1,3,6,7]=>[1,5,4,7,8,6,3,2]=>[1,3,6,5,4,8,7,2]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,1,3,6,8]=>[2,5,4,7,8,6,3,1]=>[3,2,6,5,4,8,7,1]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,1,3,7,8]=>[3,5,4,7,8,6,2,1]=>[2,6,3,5,4,8,7,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[4,5,3,7,8,6,2,1]=>[2,6,5,4,3,8,7,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,1,3,7,8]=>[5,4,3,7,8,6,2,1]=>[2,6,4,5,3,8,7,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[1,2,6,7,8,5,4,3]=>[1,2,4,5,8,6,7,3]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>[1,3,6,7,8,5,4,2]=>[1,4,3,5,8,6,7,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[2,3,6,7,8,5,4,1]=>[4,2,3,5,8,6,7,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>[1,4,6,7,8,5,3,2]=>[1,3,5,4,8,6,7,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>[2,4,6,7,8,5,3,1]=>[3,2,5,4,8,6,7,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,1,4,7,8]=>[3,4,6,7,8,5,2,1]=>[2,5,3,4,8,6,7,1]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[4,3,6,7,8,5,2,1]=>[2,5,4,3,8,6,7,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[1,5,6,7,8,4,3,2]=>[1,3,4,8,5,6,7,2]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[2,5,6,7,8,4,3,1]=>[3,2,4,8,5,6,7,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[3,5,6,7,8,4,2,1]=>[2,4,3,8,5,6,7,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[5,4,6,7,8,3,2,1]=>[2,3,8,5,4,6,7,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,1,5,6,7]=>[1,6,5,7,8,4,3,2]=>[1,3,4,8,6,5,7,2]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,2,1,5,6,8]=>[2,6,5,7,8,4,3,1]=>[3,2,4,8,6,5,7,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[4,6,5,7,8,3,2,1]=>[2,3,8,4,6,5,7,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[2,1,7,6,8,5,4,3]=>[2,1,4,5,8,7,6,3]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,1,5,6,7]=>[1,5,7,6,8,4,3,2]=>[1,3,4,8,5,7,6,2]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,1,5,7,8]=>[3,5,7,6,8,4,2,1]=>[2,4,3,8,5,7,6,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[4,5,7,6,8,3,2,1]=>[2,3,8,4,5,7,6,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[5,4,7,6,8,3,2,1]=>[2,3,8,5,4,7,6,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,1,5,6,7]=>[1,6,7,5,8,4,3,2]=>[1,3,4,8,7,6,5,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,1,5,6,8]=>[2,6,7,5,8,4,3,1]=>[3,2,4,8,7,6,5,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,1,5,7,8]=>[3,6,7,5,8,4,2,1]=>[2,4,3,8,7,6,5,1]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[4,6,7,5,8,3,2,1]=>[2,3,8,4,7,6,5,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>[5,6,7,4,8,3,2,1]=>[2,3,8,7,5,6,4,1]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[1,7,6,5,8,4,3,2]=>[1,3,4,8,6,7,5,2]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,1,5,7,8]=>[3,7,6,5,8,4,2,1]=>[2,4,3,8,6,7,5,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[4,7,6,5,8,3,2,1]=>[2,3,8,4,6,7,5,1]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>[5,7,6,4,8,3,2,1]=>[2,3,8,6,5,7,4,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[7,6,5,4,8,3,2,1]=>[2,3,8,5,6,7,4,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[2,3,1,8,7,6,5,4]=>[3,2,1,5,6,7,8,4]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[1,2,4,8,7,6,5,3]=>[1,2,5,4,6,7,8,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[2,1,4,8,7,6,5,3]=>[2,1,5,4,6,7,8,3]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[1,3,4,8,7,6,5,2]=>[1,5,3,4,6,7,8,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[2,3,4,8,7,6,5,1]=>[5,2,3,4,6,7,8,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[3,2,4,8,7,6,5,1]=>[5,3,2,4,6,7,8,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[1,4,3,8,7,6,5,2]=>[1,5,4,3,6,7,8,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[2,4,3,8,7,6,5,1]=>[5,2,4,3,6,7,8,1]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[3,4,2,8,7,6,5,1]=>[5,4,3,2,6,7,8,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[4,3,2,8,7,6,5,1]=>[5,3,4,2,6,7,8,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,1,2,3,5,6]=>[1,2,5,8,7,6,4,3]=>[1,2,4,6,5,7,8,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,1,2,3,5,6]=>[2,1,5,8,7,6,4,3]=>[2,1,4,6,5,7,8,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[1,3,5,8,7,6,4,2]=>[1,4,3,6,5,7,8,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,1,2,3,5,8]=>[2,3,5,8,7,6,4,1]=>[4,2,3,6,5,7,8,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,1,2,3,6,7]=>[1,4,5,8,7,6,3,2]=>[1,3,6,4,5,7,8,2]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3,7,8]=>[3,4,5,8,7,6,2,1]=>[2,6,3,4,5,7,8,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,1,2,3,6,8]=>[2,5,4,8,7,6,3,1]=>[3,2,6,5,4,7,8,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[5,4,3,8,7,6,2,1]=>[2,6,4,5,3,7,8,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>[2,1,6,8,7,5,4,3]=>[2,1,4,5,7,6,8,3]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,1,2,4,5,7]=>[1,3,6,8,7,5,4,2]=>[1,4,3,5,7,6,8,2]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,1,2,4,5,8]=>[3,2,6,8,7,5,4,1]=>[4,3,2,5,7,6,8,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,2,4,6,7]=>[1,4,6,8,7,5,3,2]=>[1,3,5,4,7,6,8,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[2,4,6,8,7,5,3,1]=>[3,2,5,4,7,6,8,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>[3,5,6,8,7,4,2,1]=>[2,4,3,7,5,6,8,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[4,5,6,8,7,3,2,1]=>[2,3,7,4,5,6,8,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[1,6,5,8,7,4,3,2]=>[1,3,4,7,6,5,8,2]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,1,2,6,7,8]=>[4,6,5,8,7,3,2,1]=>[2,3,7,4,6,5,8,1]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[6,5,4,8,7,3,2,1]=>[2,3,7,5,6,4,8,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[1,2,7,8,6,5,4,3]=>[1,2,4,5,6,8,7,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[2,1,7,8,6,5,4,3]=>[2,1,4,5,6,8,7,3]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,1,3,4,5,7]=>[1,3,7,8,6,5,4,2]=>[1,4,3,5,6,8,7,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,1,3,4,6,7]=>[1,4,7,8,6,5,3,2]=>[1,3,5,4,6,8,7,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,1,3,4,6,8]=>[2,4,7,8,6,5,3,1]=>[3,2,5,4,6,8,7,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[3,5,7,8,6,4,2,1]=>[2,4,3,6,5,8,7,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[4,5,7,8,6,3,2,1]=>[2,3,6,4,5,8,7,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[1,6,7,8,5,4,3,2]=>[1,3,4,5,8,6,7,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,1,4,5,6,8]=>[2,6,7,8,5,4,3,1]=>[3,2,4,5,8,6,7,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[4,6,7,8,5,3,2,1]=>[2,3,5,4,8,6,7,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[1,7,6,8,5,4,3,2]=>[1,3,4,5,8,7,6,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,1,4,5,6,8]=>[2,7,6,8,5,4,3,1]=>[3,2,4,5,8,7,6,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,1,4,5,7,8]=>[3,7,6,8,5,4,2,1]=>[2,4,3,5,8,7,6,1]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[4,7,6,8,5,3,2,1]=>[2,3,5,4,8,7,6,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[5,7,6,8,4,3,2,1]=>[2,3,4,8,5,7,6,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,2,3,4,5,6]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[2,1,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,3]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[1,3,8,7,6,5,4,2]=>[1,4,3,5,6,7,8,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,2,3,4,5,8]=>[2,3,8,7,6,5,4,1]=>[4,2,3,5,6,7,8,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[3,2,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,5,1,2,3,4,6,7]=>[1,4,8,7,6,5,3,2]=>[1,3,5,4,6,7,8,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[2,4,8,7,6,5,3,1]=>[3,2,5,4,6,7,8,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,1,2,3,4,7,8]=>[3,4,8,7,6,5,2,1]=>[2,5,3,4,6,7,8,1]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[5,6,1,2,3,4,7,8]=>[4,3,8,7,6,5,2,1]=>[2,5,4,3,6,7,8,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,2,3,5,6,7]=>[1,5,8,7,6,4,3,2]=>[1,3,4,6,5,7,8,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[7,4,1,2,3,5,6,8]=>[2,5,8,7,6,4,3,1]=>[3,2,4,6,5,7,8,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,4,1,2,3,5,7,8]=>[3,5,8,7,6,4,2,1]=>[2,4,3,6,5,7,8,1]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[4,5,8,7,6,3,2,1]=>[2,3,6,4,5,7,8,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[1,6,8,7,5,4,3,2]=>[1,3,4,5,7,6,8,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[2,6,8,7,5,4,3,1]=>[3,2,4,5,7,6,8,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,3,1,2,4,5,7,8]=>[3,6,8,7,5,4,2,1]=>[2,4,3,5,7,6,8,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[4,6,8,7,5,3,2,1]=>[2,3,5,4,7,6,8,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[5,6,8,7,4,3,2,1]=>[2,3,4,7,5,6,8,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[6,5,8,7,4,3,2,1]=>[2,3,4,7,6,5,8,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,3,4,5,6,7]=>[1,7,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[2,7,8,6,5,4,3,1]=>[3,2,4,5,6,8,7,1]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,2,1,3,4,5,7,8]=>[3,7,8,6,5,4,2,1]=>[2,4,3,5,6,8,7,1]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[4,7,8,6,5,3,2,1]=>[2,3,5,4,6,8,7,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[5,7,8,6,4,3,2,1]=>[2,3,4,6,5,8,7,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[2,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,5,7,8]=>[3,8,7,6,5,4,2,1]=>[2,4,3,5,6,7,8,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[4,8,7,6,5,3,2,1]=>[2,3,5,4,6,7,8,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[5,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[6,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1,3,4,5,6,7,8]=>[1,8,9,7,6,5,4,3,2]=>[1,3,4,5,6,7,9,8,2]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1]=>[7,8,6,5,4,3,2,1,9]=>[2,3,4,5,6,8,7,1,9]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,1,10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,11,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[1,7,9,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,9,2]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,1]=>[7,6,8,5,4,3,2,1,9]=>[2,3,4,5,8,7,6,1,9]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[8,9,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,9,8,1,10]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,1,11]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,11,12,2]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,1,2,4,5,6,7,8,9]=>[1,8,10,9,7,6,5,4,3,2]=>[1,3,4,5,6,7,9,8,10,2]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[9,4,1,2,3,5,6,7,8]=>[1,6,9,8,7,5,4,3,2]=>[1,3,4,5,7,6,8,9,2]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,9,1]=>[7,6,5,8,4,3,2,1,9]=>[2,3,4,8,6,7,5,1,9]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,10,1]=>[8,7,9,6,5,4,3,2,1,10]=>[2,3,4,5,6,9,8,7,1,10]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[11,3,1,2,4,5,6,7,8,9,10]=>[1,9,11,10,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,10,9,11,2]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[10,4,1,2,3,5,6,7,8,9]=>[1,7,10,9,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,9,10,2]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,1,2,5,6,7,8]=>[1,7,6,9,8,5,4,3,2]=>[1,3,4,5,8,7,6,9,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[6,2,3,4,5,7,8,9,1]=>[4,8,7,6,5,3,2,1,9]=>[2,3,5,4,6,7,8,1,9]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,5,2,3,6,7,8,9,1]=>[6,5,8,7,4,3,2,1,9]=>[2,3,4,7,6,5,8,1,9]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,9,10,1]=>[8,7,6,9,5,4,3,2,1,10]=>[2,3,4,5,9,7,8,6,1,10]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,10,11,1]=>[9,8,10,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,10,9,8,1,11]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[9,6,1,2,3,4,5,7,8]=>[1,4,9,8,7,6,5,3,2]=>[1,3,5,4,6,7,8,9,2]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[6,2,3,4,5,7,8,9,10,1]=>[5,9,8,7,6,4,3,2,1,10]=>[2,3,4,6,5,7,8,9,1,10]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,9,1]=>[7,6,5,4,3,8,2,1,9]=>[2,8,4,5,6,7,3,1,9]
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,9,10,11,1]=>[9,8,7,10,6,5,4,3,2,1,11]=>[2,3,4,5,6,10,8,9,7,1,11]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[10,6,1,2,3,4,5,7,8,9]=>[1,5,10,9,8,7,6,4,3,2]=>[1,3,4,6,5,7,8,9,10,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[1,3,9,8,7,6,5,4,2]=>[1,4,3,5,6,7,8,9,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[2,1,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,9,1]=>[2,8,7,6,5,4,3,1,9]=>[3,2,4,5,6,7,8,1,9]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[5,6,2,3,4,7,8,9,1]=>[5,4,8,7,6,3,2,1,9]=>[2,3,6,5,4,7,8,1,9]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[7,6,5,4,3,2,1,9,8]=>[2,3,4,5,6,7,1,9,8]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,1]=>[7,6,5,4,3,2,8,1,9]=>[8,3,4,5,6,7,2,1,9]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,9,10,1]=>[8,7,6,5,4,9,3,2,1,10]=>[2,3,9,5,6,7,8,4,1,10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[10,7,1,2,3,4,5,6,8,9]=>[1,4,10,9,8,7,6,5,3,2]=>[1,3,5,4,6,7,8,9,10,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,2,3,4,5,6,7]=>[1,2,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2,9]=>[1,3,4,5,6,7,8,2,9]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,1,8,9]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,10,1]=>[8,7,6,5,4,3,9,2,1,10]=>[2,9,4,5,6,7,8,3,1,10]
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,9,10,11,1]=>[9,8,7,6,5,10,4,3,2,1,11]=>[2,3,4,10,6,7,8,9,5,1,11]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[10,8,1,2,3,4,5,6,7,9]=>[1,3,10,9,8,7,6,5,4,2]=>[1,4,3,5,6,7,8,9,10,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,3]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2,4,5,6,7,8,1]=>[1,7,8,6,5,4,3,2,9]=>[1,3,4,5,6,8,7,2,9]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,6,7,8,9,2,1]=>[6,7,5,4,3,2,1,8,9]=>[2,3,4,5,7,6,1,8,9]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[8,7,6,5,4,3,2,1,10,9]=>[2,3,4,5,6,7,8,1,10,9]
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,10,11,1]=>[9,8,7,6,5,4,10,3,2,1,11]=>[2,3,10,5,6,7,8,9,4,1,11]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,10,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,10,3]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2,10]=>[1,3,4,5,6,7,8,9,2,10]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]
[]=>[]=>[]=>[]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,1,9]=>[3,2,4,5,6,7,8,9,1]=>[9,3,2,4,5,6,7,8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[8,6,7,5,4,3,2,1,9]=>[2,4,3,5,6,7,8,9,1]=>[9,2,4,3,5,6,7,8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,4,3,2,1,9]=>[3,4,2,5,6,7,8,9,1]=>[9,4,3,2,5,6,7,8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,7,8,5,4,3,2,1,9]=>[4,3,2,5,6,7,8,9,1]=>[9,3,4,2,5,6,7,8,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7,6,5,8,4,3,2,1,9]=>[3,4,5,2,6,7,8,9,1]=>[9,5,3,4,2,6,7,8,1]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1,9]=>[5,4,3,2,6,7,8,9,1]=>[9,3,4,5,2,6,7,8,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,5,3,2,1,9]=>[2,3,4,6,5,7,8,9,1]=>[9,2,3,4,6,5,7,8,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,6,3,2,1,9]=>[2,3,5,6,4,7,8,9,1]=>[9,2,3,6,5,4,7,8,1]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,3,2,1,9]=>[6,5,4,3,2,7,8,9,1]=>[9,3,4,5,6,2,7,8,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,3,4,2,1,9]=>[2,3,4,5,7,6,8,9,1]=>[9,2,3,4,5,7,6,8,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,8,2,1,9]=>[3,4,5,6,7,2,8,9,1]=>[9,7,3,4,5,6,2,8,1]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1,9]=>[7,6,5,4,3,2,8,9,1]=>[9,3,4,5,6,7,2,8,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,3,1,9]=>[2,3,4,5,6,8,7,9,1]=>[9,2,3,4,5,6,8,7,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,1,9]=>[3,4,5,6,7,8,2,9,1]=>[9,8,3,4,5,6,7,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,4,6,3,7,2,8,1,9]=>[5,6,4,7,3,8,2,9,1]=>[9,8,7,6,5,4,3,2,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,1,9]=>[2,8,7,6,5,4,3,9,1]=>[9,2,4,5,6,7,8,3,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,7,6,5,4,3,2,9,1]=>[9,3,4,5,6,7,8,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,1,2,9]=>[2,3,4,5,6,7,9,8,1]=>[8,2,3,4,5,6,7,9,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[7,8,5,6,3,4,1,2,9]=>[3,2,5,4,7,6,9,8,1]=>[8,3,2,5,4,7,6,9,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[7,6,5,4,3,2,9,8,1]=>[8,3,4,5,6,7,2,9,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,1,3,9]=>[2,3,4,5,6,8,9,7,1]=>[7,2,3,4,5,6,9,8,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,3,2,1,4,9]=>[2,3,4,5,7,8,9,6,1]=>[6,2,3,4,5,9,7,8,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,3,2,1,6,9]=>[2,3,5,6,7,8,9,4,1]=>[4,2,3,9,5,6,7,8,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,1,7,9]=>[2,4,5,6,7,8,9,3,1]=>[3,2,9,4,5,6,7,8,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,8,9]=>[3,4,5,6,7,8,9,2,1]=>[2,9,3,4,5,6,7,8,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,2,3,4,5,6,1,8,9]=>[3,8,7,6,5,4,9,2,1]=>[2,9,3,5,6,7,8,4,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[8,7,6,5,4,3,9,2,1]=>[2,9,4,5,6,7,8,3,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,1,2,3,9]=>[2,3,4,5,6,9,8,7,1]=>[7,2,3,4,5,6,8,9,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[7,5,4,3,2,1,6,8,9]=>[3,5,6,7,8,9,4,2,1]=>[2,4,3,9,5,6,7,8,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,7,8,9]=>[4,5,6,7,8,9,3,2,1]=>[2,3,9,4,5,6,7,8,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[6,2,3,4,5,1,7,8,9]=>[4,8,7,6,5,9,3,2,1]=>[2,3,9,4,6,7,8,5,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[8,7,6,5,4,9,3,2,1]=>[2,3,9,5,6,7,8,4,1]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[5,4,3,2,9,8,7,6,1]=>[6,3,4,5,2,7,8,9,1]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,6,3,4,1,2,7,8,9]=>[5,4,7,6,9,8,3,2,1]=>[2,3,8,5,4,7,6,9,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[5,6,7,8,9,4,3,2,1]=>[2,3,4,9,5,6,7,8,1]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,2,3,4,1,6,7,8,9]=>[5,8,7,6,9,4,3,2,1]=>[2,3,4,9,5,7,8,6,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[8,7,6,5,9,4,3,2,1]=>[2,3,4,9,6,7,8,5,1]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[6,5,4,9,8,7,3,2,1]=>[2,3,7,5,6,4,8,9,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9]=>[6,7,8,9,5,4,3,2,1]=>[2,3,4,5,9,6,7,8,1]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,1,5,6,7,8,9]=>[6,8,7,9,5,4,3,2,1]=>[2,3,4,5,9,6,8,7,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[8,7,6,9,5,4,3,2,1]=>[2,3,4,5,9,7,8,6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[8,7,1,2,3,4,5,6,9]=>[2,3,9,8,7,6,5,4,1]=>[4,2,3,5,6,7,8,9,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[3,2,9,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,9,1]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[7,6,9,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,9,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[7,8,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,7,8,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[8,7,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,8,7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[2,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[3,9,8,7,6,5,4,2,1]=>[2,4,3,5,6,7,8,9,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[4,9,8,7,6,5,3,2,1]=>[2,3,5,4,6,7,8,9,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[5,9,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,9,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[6,9,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,9,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[7,9,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,9,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[8,9,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,9,8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,5,4,3,2,1]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,4,3,2,1]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,3,2,1]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,2,1]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[8,6,7,9,5,4,3,2,1]=>[2,4,3,1,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,1,5,6,7,8,9,10]=>[4,2,3,1,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[8,7,5,6,9,4,3,2,1]=>[2,3,5,4,1,6,7,8,9]=>[4,2,3,5,1,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,1,6,7,8,9,10]=>[5,2,3,4,1,6,7,8,9,10]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,5,9,3,2,1]=>[2,3,4,6,5,1,7,8,9]=>[5,2,3,4,6,1,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,5,6,1,7,8,9,10]=>[6,2,3,4,5,1,7,8,9,10]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,3,4,9,2,1]=>[2,3,4,5,7,6,1,8,9]=>[6,2,3,4,5,7,1,8,9]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[2,3,4,5,6,7,1,8,9,10]=>[7,2,3,4,5,6,1,8,9,10]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,3,9,1]=>[2,3,4,5,6,8,7,1,9]=>[7,2,3,4,5,6,8,1,9]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[2,3,4,5,6,7,8,1,9,10]=>[8,2,3,4,5,6,7,1,9,10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[4,3,2,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,1,2,10]=>[2,3,4,5,6,7,8,10,9,1]=>[9,2,3,4,5,6,7,8,10,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,2,3,4,5,6,7,8,9,1,11]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,2,1,3,10]=>[2,3,4,5,6,7,9,10,8,1]=>[8,2,3,4,5,6,7,10,9,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,1,2,3,10]=>[2,3,4,5,6,7,10,9,8,1]=>[8,2,3,4,5,6,7,9,10,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,1,2,11]=>[2,3,4,5,6,7,8,9,11,10,1]=>[10,2,3,4,5,6,7,8,9,11,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[5,4,3,2,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,3,2,1,4,10]=>[2,3,4,5,6,8,9,10,7,1]=>[7,2,3,4,5,6,10,8,9,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,2,1,3,11]=>[2,3,4,5,6,7,8,10,11,9,1]=>[9,2,3,4,5,6,7,8,11,10,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,3,2,1,4,11]=>[2,3,4,5,6,7,9,10,11,8,1]=>[8,2,3,4,5,6,7,11,9,10,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,9,1]=>[3,4,5,6,7,8,2,1,9]=>[2,8,3,4,5,6,7,1,9]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,8,7,5,4,3,2,1,6,10]=>[2,3,4,6,7,8,9,10,5,1]=>[5,2,3,4,10,6,7,8,9,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,8,6,5,4,3,2,1,7,10]=>[2,3,5,6,7,8,9,10,4,1]=>[4,2,3,10,5,6,7,8,9,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,5,4,3,2,1,6,11]=>[2,3,4,5,7,8,9,10,11,6,1]=>[6,2,3,4,5,11,7,8,9,10,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[10,9,8,6,5,4,3,2,1,7,11]=>[2,3,4,6,7,8,9,10,11,5,1]=>[5,2,3,4,11,6,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,2,1]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,5,4,3,2,1]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,5,4,3,2,1]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,5,4,3,2,1]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,4,3,2,1]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,4,3,2,1]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,6,4,3,2,1]=>[3,2,1,5,4,6,7,8,9]=>[2,3,1,5,4,6,7,8,9]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,3,2,1]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,3,2,1]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,4,5,3,2,1]=>[4,3,2,1,6,5,7,8,9]=>[2,3,4,1,6,5,7,8,9]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,2,1]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,4,2,1]=>[5,4,3,2,1,7,6,8,9]=>[2,3,4,5,1,7,6,8,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,3,1]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,2,3,1]=>[1,2,3,4,6,5,8,7,9]=>[1,2,3,4,6,5,8,7,9]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,4,5,2,3,1]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,2,3,1]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,3,1]=>[6,5,4,3,2,1,8,7,9]=>[2,3,4,5,6,1,8,7,9]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,3,4,1]=>[5,4,3,2,1,8,7,6,9]=>[2,3,4,5,1,7,8,6,9]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,2,3,4,5,1]=>[4,3,2,1,8,7,6,5,9]=>[2,3,4,1,6,7,8,5,9]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,6,7,1]=>[2,1,8,7,6,5,4,3,9]=>[2,1,4,5,6,7,8,3,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,1,2]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,3,4,1,2]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,3,4,1,2]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,6,3,4,1,2]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,4,1,2]=>[5,4,3,2,1,7,6,9,8]=>[2,3,4,5,1,7,6,9,8]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,1,2]=>[1,7,6,5,4,3,2,9,8]=>[1,3,4,5,6,7,2,9,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,1,2,3]=>[1,2,3,4,6,5,9,8,7]=>[1,2,3,4,6,5,8,9,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,1,2,3]=>[2,1,4,3,6,5,9,8,7]=>[2,1,4,3,6,5,8,9,7]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,6,1,2,3]=>[1,2,3,6,5,4,9,8,7]=>[1,2,3,5,6,4,8,9,7]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[7,8,9,4,5,6,1,2,3]=>[3,2,1,6,5,4,9,8,7]=>[2,3,1,5,6,4,8,9,7]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[6,5,4,3,2,1,9,8,7]=>[2,3,4,5,6,1,8,9,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,1,2,3,4]=>[1,2,3,5,4,9,8,7,6]=>[1,2,3,5,4,7,8,9,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,1,2,3,4]=>[1,3,2,5,4,9,8,7,6]=>[1,3,2,5,4,7,8,9,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[9,8,5,6,7,1,2,3,4]=>[1,2,5,4,3,9,8,7,6]=>[1,2,4,5,3,7,8,9,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[8,9,5,6,7,1,2,3,4]=>[2,1,5,4,3,9,8,7,6]=>[2,1,4,5,3,7,8,9,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[9,5,6,7,8,1,2,3,4]=>[1,5,4,3,2,9,8,7,6]=>[1,3,4,5,2,7,8,9,6]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[5,4,3,2,1,9,8,7,6]=>[2,3,4,5,1,7,8,9,6]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,1,2,3,4,5]=>[1,2,4,3,9,8,7,6,5]=>[1,2,4,3,6,7,8,9,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,1,2,3,4,5]=>[1,4,3,2,9,8,7,6,5]=>[1,3,4,2,6,7,8,9,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[4,3,2,1,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,9,8,7,6,5,4]=>[1,2,3,5,6,7,8,9,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[9,7,8,1,2,3,4,5,6]=>[1,3,2,9,8,7,6,5,4]=>[1,3,2,5,6,7,8,9,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[3,2,1,9,8,7,6,5,4]=>[2,3,1,5,6,7,8,9,4]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,9,7,6,5,4,3,2,1]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[10,9,7,8,6,5,4,3,2,1]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,6,5,4,3,2,1]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,7,5,4,3,2,1]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,4,3,2,1]=>[2,1,4,3,6,5,7,8,9,10]=>[2,1,4,3,6,5,7,8,9,10]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,5,3,2,1]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,4,2,1]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,2,1]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,7,4,5,2,3,1]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,2,3,1]=>[7,6,5,4,3,2,1,9,8,10]=>[2,3,4,5,6,7,1,9,8,10]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[8,9,10,5,6,7,2,3,4,1]=>[3,2,1,6,5,4,9,8,7,10]=>[2,3,1,5,6,4,8,9,7,10]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,2,3,4,1]=>[6,5,4,3,2,1,9,8,7,10]=>[2,3,4,5,6,1,8,9,7,10]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,2,3,4,5,1]=>[5,4,3,2,1,9,8,7,6,10]=>[2,3,4,5,1,7,8,9,6,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,3,4,1,2]=>[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[10,9,7,8,5,6,3,4,1,2]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[9,10,3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,4,5,6,7,8,3,10,9]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,9,10,8]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,5,1,2,3]=>[1,2,3,4,5,7,6,10,9,8]=>[1,2,3,4,5,7,6,9,10,8]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,1,2,3]=>[1,3,2,5,4,7,6,10,9,8]=>[1,3,2,5,4,7,6,9,10,8]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,4,5,6,1,2,3]=>[2,1,4,3,7,6,5,10,9,8]=>[2,1,4,3,6,7,5,9,10,8]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[7,6,5,4,3,2,1,10,9,8]=>[2,3,4,5,6,7,1,9,10,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,1,2,3,4]=>[2,1,4,3,6,5,10,9,8,7]=>[2,1,4,3,6,5,8,9,10,7]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,5,6,1,2,3,4]=>[4,3,2,1,6,5,10,9,8,7]=>[2,3,4,1,6,5,8,9,10,7]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[8,9,10,5,6,7,1,2,3,4]=>[3,2,1,6,5,4,10,9,8,7]=>[2,3,1,5,6,4,8,9,10,7]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[10,9,5,6,7,8,1,2,3,4]=>[1,2,6,5,4,3,10,9,8,7]=>[1,2,4,5,6,3,8,9,10,7]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[9,10,5,6,7,8,1,2,3,4]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,4,5,6,3,8,9,10,7]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[6,5,4,3,2,1,10,9,8,7]=>[2,3,4,5,6,1,8,9,10,7]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,10,9,8,7,6]=>[1,2,3,4,5,7,8,9,10,6]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,1,2,3,4,5]=>[1,3,2,5,4,10,9,8,7,6]=>[1,3,2,5,4,7,8,9,10,6]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[10,6,7,8,9,1,2,3,4,5]=>[1,5,4,3,2,10,9,8,7,6]=>[1,3,4,5,2,7,8,9,10,6]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>[2,3,4,5,1,7,8,9,10,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,10,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,10,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[10,7,8,9,1,2,3,4,5,6]=>[1,4,3,2,10,9,8,7,6,5]=>[1,3,4,2,6,7,8,9,10,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[4,3,2,1,10,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,10,5]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,10,9,8,7,6,5,4]=>[1,2,3,5,6,7,8,9,10,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[10,8,9,1,2,3,4,5,6,7]=>[1,3,2,10,9,8,7,6,5,4]=>[1,3,2,5,6,7,8,9,10,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[3,2,1,10,9,8,7,6,5,4]=>[2,3,1,5,6,7,8,9,10,4]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,1,5]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,3,2,1,6]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,2,1,7]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1,8]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,1,4]=>[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,9,8,7,6]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,4,2,1,5]=>[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,9,7,6,8,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,3,2,1,5]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,3,2,1,6]=>[1,2,3,6,5,7,8,9,4]=>[1,2,3,9,6,5,7,8,4]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,4,3,2,1,6]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[9,8,5,6,4,3,2,1,7]=>[1,2,5,4,6,7,8,9,3]=>[1,2,9,5,4,6,7,8,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,4,3,2,1,7]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[9,6,7,5,4,3,2,1,8]=>[1,4,3,5,6,7,8,9,2]=>[1,9,4,3,5,6,7,8,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,2,1,8]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1,9]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,1,2]=>[2,3,1,4,5,6,7,9,8]=>[3,2,1,4,5,6,7,9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,1,10]=>[3,2,4,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[9,8,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,9,8,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[8,10,9,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,9,8,10,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,2,1,3]=>[2,3,1,4,5,6,8,9,7]=>[3,2,1,4,5,6,9,8,7]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,1,3]=>[2,1,3,4,5,6,8,9,7]=>[2,1,3,4,5,6,9,8,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,1,7,8]=>[1,4,5,6,7,8,9,3,2]=>[1,3,9,4,5,6,7,8,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,1,3,4]=>[1,2,3,4,5,8,9,7,6]=>[1,2,3,4,5,7,9,8,6]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,8,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,8,9,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[2,10,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,10,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[2,11,10,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,10,11,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[9,8,6,1,2,3,4,5,7]=>[1,2,4,9,8,7,6,5,3]=>[1,2,5,4,6,7,8,9,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,1,2,3,4,6]=>[1,2,3,5,9,8,7,6,4]=>[1,2,3,6,5,7,8,9,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,1,2,3,5]=>[1,2,3,4,6,9,8,7,5]=>[1,2,3,4,7,6,8,9,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,1,2,4]=>[1,2,3,4,5,7,9,8,6]=>[1,2,3,4,5,8,7,9,6]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[9,10,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,10,9,1]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,8,9,7,1]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,10,7,8,9,6,1]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,10,6,7,8,9,5,1]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[9,8,7,6,5,4,10,3,2,1]=>[2,3,10,5,6,7,8,9,4,1]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[9,8,7,6,5,4,3,10,2,1]=>[2,10,4,5,6,7,8,9,3,1]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,11,10,1]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,1,3]=>[6,5,4,3,2,1,8,9,7]=>[2,3,4,5,6,1,9,8,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,1,2,8]=>[1,3,4,5,6,7,9,8,2]=>[1,8,3,4,5,6,7,9,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,9,1]=>[3,2,4,5,6,7,8,1,9]=>[8,3,2,4,5,6,7,1,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,9,6,5,4,3,2,1,7]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,1,2]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,4,3,2,1,6]=>[3,2,1,5,6,7,8,9,4]=>[2,3,1,9,5,6,7,8,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7,8,9,6,5,4,3,2,1,10]=>[4,3,2,5,6,7,8,9,10,1]=>[10,3,4,2,5,6,7,8,9,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,4,3,2,1,5]=>[4,3,2,1,6,7,8,9,5]=>[2,3,4,1,9,6,7,8,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[4,5,6,7,8,9,10,3,2,1]=>[2,3,10,4,5,6,7,8,9,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[8,7,9,1,2,3,4,5,6]=>[2,3,1,9,8,7,6,5,4]=>[3,2,1,5,6,7,8,9,4]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[3,10,9,8,7,6,5,4,2,1]=>[2,4,3,5,6,7,8,9,10,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[4,10,9,8,7,6,5,3,2,1]=>[2,3,5,4,6,7,8,9,10,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[5,10,9,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,9,10,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[6,10,9,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,9,10,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[7,10,9,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,9,10,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,7,4,3,2,1]=>[1,2,4,5,3,6,7,8,9]=>[1,2,5,4,3,6,7,8,9]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,3,2,5,1]=>[1,2,3,4,5,7,8,9,6,10]=>[1,2,3,4,5,9,7,8,6,10]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,4,3,1,2]=>[2,3,4,5,1,6,7,9,8]=>[5,2,3,4,1,6,7,9,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[8,9,6,5,7,4,3,2,1]=>[2,1,4,5,3,6,7,8,9]=>[2,1,5,4,3,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[9,8,7,5,6,4,3,2,1,10]=>[2,3,4,6,5,7,8,9,10,1]=>[10,2,3,4,6,5,7,8,9,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[9,6,7,4,5,2,3,1,8]=>[1,4,3,6,5,8,7,9,2]=>[1,9,4,3,6,5,8,7,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,2,3,1,4]=>[2,1,4,3,6,5,9,8,10,7]=>[2,1,4,3,6,5,10,9,8,7]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,4,5,2,3,1,6]=>[2,1,4,3,7,6,9,8,10,5]=>[2,1,4,3,10,7,6,9,8,5]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[9,10,6,7,4,5,2,3,1,8]=>[2,1,5,4,7,6,9,8,10,3]=>[2,1,10,5,4,7,6,9,8,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[8,9,6,7,4,5,2,3,1,10]=>[3,2,5,4,7,6,9,8,10,1]=>[10,3,2,5,4,7,6,9,8,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,1,3]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1,10]=>[8,7,6,5,4,3,2,9,10,1]=>[10,3,4,5,6,7,8,2,9,1]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1,10]=>[7,6,5,4,3,2,8,9,10,1]=>[10,3,4,5,6,7,2,8,9,1]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1,10]=>[6,5,4,3,2,7,8,9,10,1]=>[10,3,4,5,6,2,7,8,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,5,4,3,2,1,10]=>[5,4,3,2,6,7,8,9,10,1]=>[10,3,4,5,2,6,7,8,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,7,9,6,5,4,3,2,1,10]=>[3,4,2,5,6,7,8,9,10,1]=>[10,4,3,2,5,6,7,8,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,6,9,5,4,3,2,1,10]=>[3,4,5,2,6,7,8,9,10,1]=>[10,5,3,4,2,6,7,8,9,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,9,3,2,1,10]=>[3,4,5,6,7,2,8,9,10,1]=>[10,7,3,4,5,6,2,8,9,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1,10]=>[3,4,5,6,7,8,2,9,10,1]=>[10,8,3,4,5,6,7,2,9,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[3,4,5,6,7,8,9,10,2,1]=>[2,10,3,4,5,6,7,8,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[9,10,8,7,6,5,4,3,2,1,11]=>[3,2,4,5,6,7,8,9,10,11,1]=>[11,3,2,4,5,6,7,8,9,10,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9,8,10,7,6,5,4,3,2,1,11]=>[3,4,2,5,6,7,8,9,10,11,1]=>[11,4,3,2,5,6,7,8,9,10,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,8,7,10,6,5,4,3,2,1,11]=>[3,4,5,2,6,7,8,9,10,11,1]=>[11,5,3,4,2,6,7,8,9,10,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,10,4,3,2,1,11]=>[3,4,5,6,7,2,8,9,10,11,1]=>[11,7,3,4,5,6,2,8,9,10,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,4,10,3,2,1,11]=>[3,4,5,6,7,8,2,9,10,11,1]=>[11,8,3,4,5,6,7,2,9,10,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,4,3,2,10,1,11]=>[3,4,5,6,7,8,9,10,2,11,1]=>[11,10,3,4,5,6,7,8,9,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,4,3,2,1,10,11]=>[3,4,5,6,7,8,9,10,11,2,1]=>[2,11,3,4,5,6,7,8,9,10,1]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[8,7,10,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,8,7,10,1]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[7,6,5,10,9,8,4,3,2,1]=>[2,3,4,8,6,7,5,9,10,1]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[6,5,4,3,10,9,8,7,2,1]=>[2,7,4,5,6,3,8,9,10,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[10,8,6,4,2,1,3,5,7,9]=>[1,3,5,7,9,10,8,6,4,2]=>[1,4,3,6,5,8,7,10,9,2]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,11,1]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[9,8,7,6,5,4,3,2,1,11,10]=>[2,3,4,5,6,7,8,9,1,11,10]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,3,4,5,6,7,8,9,10,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,11,10,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,2,1,3]=>[2,1,3,4,5,6,7,9,10,8]=>[2,1,3,4,5,6,7,10,9,8]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,3,9,2,1]=>[6,5,4,3,2,7,1,8,9]=>[7,3,4,5,6,2,1,8,9]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,4,9,3,2,1]=>[5,4,3,2,6,1,7,8,9]=>[6,3,4,5,2,1,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[6,7,8,5,9,4,3,2,1]=>[4,3,2,5,1,6,7,8,9]=>[5,3,4,2,1,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[7,8,6,9,5,4,3,2,1]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,1,2,3]=>[2,3,4,5,6,1,9,8,7]=>[6,2,3,4,5,1,8,9,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,1,2,3,4]=>[2,3,4,5,1,9,8,7,6]=>[5,2,3,4,1,7,8,9,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,1,11,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,11,3]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[5,6,7,8,9,10,4,3,2,1]=>[2,3,4,10,5,6,7,8,9,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,4,1]=>[1,2,3,4,5,7,8,6,9]=>[1,2,3,4,5,8,7,6,9]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,10,1,2]=>[2,3,4,5,6,7,8,1,10,9]=>[8,2,3,4,5,6,7,1,10,9]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,2,1,3]=>[2,3,4,5,6,1,8,9,7]=>[6,2,3,4,5,1,9,8,7]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[8,9,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,8,9,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,5,4,3,2,1,6]=>[2,3,4,1,6,7,8,9,10,5]=>[4,2,3,1,10,6,7,8,9,5]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,7,6,8,5,4,3,2,1]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[10,8,7,9,6,5,4,3,2,1]=>[1,3,4,2,5,6,7,8,9,10]=>[1,4,3,2,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,4,3,2,1,5]=>[2,1,3,4,5,7,8,9,10,6]=>[2,1,3,4,5,10,7,8,9,6]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[6,7,8,9,10,5,4,3,2,1]=>[2,3,4,5,10,6,7,8,9,1]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9,10]=>[7,8,9,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,7,8,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,8,7,6,5,4,3,2,1,10]=>[1,3,4,5,6,7,8,9,10,11,2]=>[1,11,3,4,5,6,7,8,9,10,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,8,1]=>[1,3,4,5,6,7,8,2,9]=>[1,8,3,4,5,6,7,2,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[3,2,10,9,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,9,10,1]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2,10]=>[8,7,6,5,4,3,2,10,9,1]=>[9,3,4,5,6,7,8,2,10,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,9,4,3,2,1]=>[3,4,2,5,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[9,10,7,6,5,4,3,2,1,8]=>[2,1,4,5,6,7,8,9,10,3]=>[2,1,10,4,5,6,7,8,9,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[8,7,9,5,4,3,2,1,6]=>[2,3,1,5,6,7,8,9,4]=>[3,2,1,9,5,6,7,8,4]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,1,2,3,4,7]=>[1,2,4,5,9,8,7,6,3]=>[1,2,6,4,5,7,8,9,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[8,7,9,5,6,3,4,1,2]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[10,8,7,9,5,6,3,4,1,2]=>[1,3,4,2,6,5,8,7,10,9]=>[1,4,3,2,6,5,8,7,10,9]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,2,1,3,4]=>[2,1,4,3,6,5,9,10,8,7]=>[2,1,4,3,6,5,8,10,9,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[11,10,1,2,3,4,5,6,7,8,9]=>[1,2,11,10,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,10,11,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10,8,7,6,5,4,3,2,1,9,11]=>[2,4,5,6,7,8,9,10,11,3,1]=>[3,2,11,4,5,6,7,8,9,10,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,2,4,1]=>[1,2,3,4,5,6,8,9,7,10]=>[1,2,3,4,5,6,9,8,7,10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,9,1]=>[1,3,4,5,6,7,8,9,2,10]=>[1,9,3,4,5,6,7,8,2,10]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,3,2,1,4]=>[2,3,4,5,1,7,8,9,6]=>[5,2,3,4,1,9,7,8,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[8,9,7,10,6,5,4,3,2,1]=>[3,2,4,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,7,3,2,1]=>[1,2,4,5,6,3,7,8,9]=>[1,2,6,4,5,3,7,8,9]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,1,2,4]=>[2,1,4,3,6,5,8,10,9,7]=>[2,1,4,3,6,5,9,8,10,7]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[9,7,8,5,6,3,4,1,2,10]=>[2,4,3,6,5,8,7,10,9,1]=>[9,2,4,3,6,5,8,7,10,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[10,7,8,5,6,3,4,1,2,9]=>[1,4,3,6,5,8,7,10,9,2]=>[1,9,4,3,6,5,8,7,10,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,1,2,9]=>[1,3,4,5,6,7,8,10,9,2]=>[1,9,3,4,5,6,7,8,10,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,8,2,1]=>[1,3,4,5,6,7,2,8,9]=>[1,7,3,4,5,6,2,8,9]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,1,2,8]=>[1,7,6,5,4,3,9,8,2]=>[1,8,4,5,6,7,3,9,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,8,1,2]=>[1,3,4,5,6,7,2,9,8]=>[1,7,3,4,5,6,2,9,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[9,8,10,6,7,4,5,2,3,1]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,2,3,1]=>[2,3,4,5,6,1,8,7,9]=>[6,2,3,4,5,1,8,7,9]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,1,2,4]=>[1,2,3,4,5,6,8,10,9,7]=>[1,2,3,4,5,6,9,8,10,7]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1]=>[5,4,6,3,7,2,8,1,9]=>[8,7,6,5,4,3,2,1,9]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[6,7,5,8,4,9,3,10,1,2]=>[5,4,6,3,7,2,8,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[8,9,7,10,4,5,2,3,1,6]=>[3,2,4,1,7,6,9,8,10,5]=>[4,3,2,1,10,7,6,9,8,5]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[8,9,6,7,4,5,2,3,10,1]=>[3,2,5,4,7,6,9,8,1,10]=>[8,3,2,5,4,7,6,9,1,10]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,8,11,10,9]=>[1,2,3,4,5,6,7,8,10,11,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[11,9,10,7,8,5,6,3,4,1,2,12]=>[2,4,3,6,5,8,7,10,9,12,11,1]=>[11,2,4,3,6,5,8,7,10,9,12,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[7,8,5,6,3,4,1,2,9,10]=>[4,3,6,5,8,7,10,9,2,1]=>[2,9,4,3,6,5,8,7,10,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,11,12,3]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[9,8,7,6,5,4,3,2,1,10,11]=>[2,3,4,5,6,7,8,9,1,10,11]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,4,3,2,1,6,8,10]=>[2,4,6,7,8,9,10,5,3,1]=>[3,2,5,4,10,6,7,8,9,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,4,3,2,1,5]=>[2,3,4,1,6,7,8,9,5]=>[4,2,3,1,9,6,7,8,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,1,2,10]=>[3,2,4,5,6,7,8,10,9,1]=>[9,3,2,4,5,6,7,8,10,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,4,5,3,6,1,2]=>[2,1,4,3,7,6,8,5,10,9]=>[2,1,4,3,8,7,6,5,10,9]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[9,10,6,7,5,8,3,4,1,2]=>[2,1,5,4,6,3,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[8,9,7,10,5,6,3,4,1,2]=>[3,2,4,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[8,9,6,7,5,10,3,4,1,2]=>[3,2,5,4,6,1,8,7,10,9]=>[6,3,2,5,4,1,8,7,10,9]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[8,9,6,7,4,5,3,10,1,2]=>[3,2,5,4,7,6,8,1,10,9]=>[8,3,2,5,4,7,6,1,10,9]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,6,4,3,5,1,2]=>[2,1,4,3,5,7,8,6,10,9]=>[2,1,4,3,5,8,7,6,10,9]
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,11,1]=>[9,8,7,6,5,4,3,2,10,1,11]=>[10,3,4,5,6,7,8,9,2,1,11]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1,10]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[7,8,9,4,5,6,1,2,3,10]=>[4,3,2,7,6,5,10,9,8,1]=>[8,3,4,2,6,7,5,9,10,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[9,8,10,6,5,4,3,2,1,7]=>[2,3,1,5,6,7,8,9,10,4]=>[3,2,1,10,5,6,7,8,9,4]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,5,6,3,2,1,4]=>[2,3,4,1,6,5,8,9,10,7]=>[4,2,3,1,6,5,10,8,9,7]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,3,1,2,4,6,8]=>[1,3,5,7,9,8,6,4,2]=>[1,4,3,6,5,8,7,9,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,10,3,4,1,2]=>[2,3,4,5,6,1,8,7,10,9]=>[6,2,3,4,5,1,8,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,5,6,3,4,1,2]=>[2,3,4,1,6,5,8,7,10,9]=>[4,2,3,1,6,5,8,7,10,9]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[9,8,6,4,2,1,3,5,7]=>[1,2,4,6,8,9,7,5,3]=>[1,2,5,4,7,6,9,8,3]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[8,7,9,6,10,5,4,3,2,1]=>[3,4,2,5,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,4,3,2,1,6]=>[2,1,4,3,6,7,8,9,10,5]=>[2,1,4,3,10,6,7,8,9,5]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,2,1,4]=>[2,1,4,3,6,5,8,9,10,7]=>[2,1,4,3,6,5,10,8,9,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[1,12,3,4,5,6,7,8,9,10,11,2]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
Clarke-Steingrimsson-Zeng
Description
The Clarke-Steingrimsson-Zeng map sending descents to excedances.
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
- $des$ is the number of descents, St000021The number of descents of a permutation.,
- $exc$ is the number of (strict) excedances, St000155The number of exceedances (also excedences) of a permutation.,
- $Dbot$ is the sum of the descent bottoms, St000154The sum of the descent bottoms of a permutation.,
- $Ebot$ is the sum of the excedance bottoms,
- $Ddif$ is the sum of the descent differences, St000030The sum of the descent differences of a permutations.,
- $Edif$ is the sum of the excedance differences (or depth), St000029The depth of a permutation.,
- $Res$ is the sum of the (right) embracing numbers,
- $Ine$ is the sum of the side numbers.
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