Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]
[1,0,1,0]=>[1,2]=>[2,1]
[1,1,0,0]=>[2,1]=>[1,2]
[1,0,1,0,1,0]=>[1,2,3]=>[2,3,1]
[1,0,1,1,0,0]=>[1,3,2]=>[2,1,3]
[1,1,0,0,1,0]=>[2,1,3]=>[3,2,1]
[1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]
[1,1,1,0,0,0]=>[3,2,1]=>[1,2,3]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[2,3,4,1]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[2,3,1,4]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[2,4,3,1]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,1,3]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[2,1,3,4]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[3,2,4,1]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,2,1,4]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,4,2,1]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[3,4,1,2]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[3,1,2,4]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[4,3,2,1]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,3,1,2]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,1,2,3]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,2,3,4]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[2,3,4,5,1]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[2,3,4,1,5]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[2,3,5,4,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[2,3,5,1,4]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[2,3,1,4,5]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[2,4,3,5,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[2,4,3,1,5]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[2,4,5,3,1]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,4,5,1,3]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[2,4,1,3,5]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[2,5,4,3,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[2,5,4,1,3]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[2,5,1,3,4]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[2,1,3,4,5]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[3,2,4,5,1]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[3,2,4,1,5]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[3,2,5,4,1]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,2,5,1,4]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[3,2,1,4,5]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,4,2,5,1]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,4,2,1,5]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[3,4,5,2,1]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[3,4,5,1,2]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[3,4,1,2,5]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[3,5,4,2,1]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[3,5,4,1,2]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[3,5,1,2,4]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[3,1,2,4,5]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[4,3,2,5,1]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,3,2,1,5]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,3,5,2,1]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[4,3,5,1,2]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[4,3,1,2,5]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,5,3,2,1]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[4,5,3,1,2]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[4,5,1,2,3]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[4,1,2,3,5]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,4,3,1,2]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,4,1,2,3]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,1,2,3,4]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,2,3,4,5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[2,3,4,5,6,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[2,3,4,5,1,6]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[2,3,4,6,5,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[2,3,4,1,5,6]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[2,3,5,4,6,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[2,3,5,4,1,6]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[2,3,5,6,4,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[2,3,5,6,1,4]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[2,3,5,1,4,6]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[2,3,6,5,4,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[2,3,6,5,1,4]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[2,3,6,1,4,5]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[2,3,1,4,5,6]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[2,4,3,5,6,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[2,4,3,5,1,6]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[2,4,3,6,5,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[2,4,3,6,1,5]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[2,4,3,1,5,6]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[2,4,5,3,6,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[2,4,5,3,1,6]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[2,4,5,6,3,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,4,5,6,1,3]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[2,4,5,1,3,6]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[2,4,6,5,3,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[2,4,6,5,1,3]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[2,4,6,1,3,5]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[2,4,1,3,5,6]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[2,5,4,3,6,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[2,5,4,3,1,6]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[2,5,4,6,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[2,5,4,6,1,3]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[2,5,4,1,3,6]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[2,5,6,4,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[2,5,6,4,1,3]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[2,5,6,1,3,4]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[2,5,1,3,4,6]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[2,6,5,4,3,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[2,6,5,4,1,3]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[2,6,5,1,3,4]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[2,6,1,3,4,5]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[2,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[3,2,4,5,6,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[3,2,4,5,1,6]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[3,2,4,6,5,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[3,2,4,1,5,6]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[3,2,5,4,6,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[3,2,5,4,1,6]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[3,2,5,6,4,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,2,5,6,1,4]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[3,2,5,1,4,6]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[3,2,6,5,4,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[3,2,6,5,1,4]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[3,2,6,1,4,5]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[3,2,1,4,5,6]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,4,2,5,6,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,4,2,5,1,6]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,4,2,6,5,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,4,2,6,1,5]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[3,4,2,1,5,6]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[3,4,5,2,6,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[3,4,5,2,1,6]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[3,4,5,6,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[3,4,5,6,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[3,4,5,1,2,6]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[3,4,6,5,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[3,4,6,5,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[3,4,6,1,2,5]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[3,4,1,2,5,6]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[3,5,4,2,6,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[3,5,4,2,1,6]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[3,5,4,6,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[3,5,4,6,1,2]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[3,5,4,1,2,6]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[3,5,6,4,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[3,5,6,4,1,2]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[3,5,6,1,2,4]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[3,5,1,2,4,6]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[3,6,5,4,2,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[3,6,5,4,1,2]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[3,6,5,1,2,4]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[3,6,1,2,4,5]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[3,1,2,4,5,6]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[4,3,2,5,6,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[4,3,2,5,1,6]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[4,3,2,6,5,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[4,3,2,1,5,6]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,3,5,2,6,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[4,3,5,2,1,6]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[4,3,5,6,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[4,3,5,6,1,2]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[4,3,5,1,2,6]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[4,3,6,5,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[4,3,6,5,1,2]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[4,3,6,1,2,5]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[4,3,1,2,5,6]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,5,3,2,6,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[4,5,3,2,1,6]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[4,5,3,6,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[4,5,3,6,1,2]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[4,5,3,1,2,6]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[4,5,6,3,2,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[4,5,6,3,1,2]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[4,5,6,1,2,3]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[4,5,1,2,3,6]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[4,6,5,3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[4,6,5,3,1,2]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[4,6,5,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[4,6,1,2,3,5]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[4,1,2,3,5,6]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[5,4,3,2,6,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,4,3,2,1,6]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,4,3,6,2,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[5,4,3,6,1,2]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[5,4,3,1,2,6]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,4,6,3,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[5,4,6,3,1,2]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[5,4,6,1,2,3]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[5,4,1,2,3,6]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,6,4,3,2,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[5,6,4,3,1,2]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[5,6,4,1,2,3]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[5,6,1,2,3,4]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[5,1,2,3,4,6]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[6,5,4,3,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,5,4,3,1,2]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,5,4,1,2,3]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,5,1,2,3,4]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,1,2,3,4,5]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[2,3,4,5,6,1,7]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[2,3,4,5,7,6,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[2,3,4,5,7,1,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[2,3,4,5,1,6,7]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[2,3,4,6,5,7,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[2,3,4,6,5,1,7]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[2,3,4,6,7,5,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[2,3,4,6,7,1,5]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[2,3,4,6,1,5,7]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[2,3,4,7,6,5,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[2,3,4,7,6,1,5]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[2,3,4,7,1,5,6]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[2,3,4,1,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[2,3,5,4,6,7,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[2,3,5,4,6,1,7]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[2,3,5,4,7,6,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[2,3,5,4,7,1,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[2,3,5,4,1,6,7]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[2,3,5,6,4,7,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[2,3,5,6,4,1,7]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[2,3,5,6,7,4,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[2,3,5,6,7,1,4]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[2,3,5,6,1,4,7]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[2,3,5,7,6,4,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[2,3,5,7,6,1,4]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[2,3,5,7,1,4,6]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[2,3,5,1,4,6,7]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[2,3,6,5,4,7,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[2,3,6,5,4,1,7]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[2,3,6,5,7,4,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[2,3,6,5,7,1,4]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[2,3,6,5,1,4,7]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[2,3,6,7,5,4,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[2,3,6,7,5,1,4]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[2,3,6,7,1,4,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[2,3,6,1,4,5,7]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[2,3,7,6,5,4,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[2,3,7,6,5,1,4]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[2,3,7,6,1,4,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[2,3,7,1,4,5,6]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[2,3,1,4,5,6,7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[2,4,3,5,6,7,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[2,4,3,5,6,1,7]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[2,4,3,5,7,6,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[2,4,3,5,7,1,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[2,4,3,5,1,6,7]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[2,4,3,6,5,7,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[2,4,3,6,5,1,7]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[2,4,3,6,7,5,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[2,4,3,6,7,1,5]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[2,4,3,6,1,5,7]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[2,4,3,7,6,5,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[2,4,3,7,6,1,5]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[2,4,3,7,1,5,6]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[2,4,3,1,5,6,7]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[2,4,5,3,6,7,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[2,4,5,3,6,1,7]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[2,4,5,3,7,6,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[2,4,5,3,7,1,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[2,4,5,3,1,6,7]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[2,4,5,6,3,7,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[2,4,5,6,3,1,7]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[2,4,5,6,7,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[2,4,5,6,7,1,3]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[2,4,5,6,1,3,7]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[2,4,5,7,6,3,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[2,4,5,7,6,1,3]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[2,4,5,7,1,3,6]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[2,4,5,1,3,6,7]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[2,4,6,5,3,7,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[2,4,6,5,3,1,7]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[2,4,6,5,7,3,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[2,4,6,5,7,1,3]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[2,4,6,5,1,3,7]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[2,4,6,7,5,3,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[2,4,6,7,5,1,3]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[2,4,6,7,1,3,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[2,4,6,1,3,5,7]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[2,4,7,6,5,3,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[2,4,7,6,5,1,3]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[2,4,7,6,1,3,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[2,4,7,1,3,5,6]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[2,4,1,3,5,6,7]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[2,5,4,3,6,7,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[2,5,4,3,6,1,7]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[2,5,4,3,7,6,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[2,5,4,3,7,1,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[2,5,4,3,1,6,7]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[2,5,4,6,3,7,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[2,5,4,6,3,1,7]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[2,5,4,6,7,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[2,5,4,6,7,1,3]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[2,5,4,6,1,3,7]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[2,5,4,7,6,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[2,5,4,7,6,1,3]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[2,5,4,7,1,3,6]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[2,5,4,1,3,6,7]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[2,5,6,4,3,7,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[2,5,6,4,3,1,7]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[2,5,6,4,7,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[2,5,6,4,7,1,3]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[2,5,6,4,1,3,7]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[2,5,6,7,4,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[2,5,6,7,4,1,3]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[2,5,6,7,1,3,4]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[2,5,6,1,3,4,7]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[2,5,7,6,4,3,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[2,5,7,6,4,1,3]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[2,5,7,6,1,3,4]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[2,5,7,1,3,4,6]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[2,5,1,3,4,6,7]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[2,6,5,4,3,7,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[2,6,5,4,3,1,7]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[2,6,5,4,7,3,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[2,6,5,4,7,1,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[2,6,5,4,1,3,7]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[2,6,5,7,4,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[2,6,5,7,4,1,3]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[2,6,5,7,1,3,4]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[2,6,5,1,3,4,7]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[2,6,7,5,4,3,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[2,6,7,5,4,1,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[2,6,7,5,1,3,4]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[2,6,7,1,3,4,5]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[2,6,1,3,4,5,7]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[2,7,6,5,4,3,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[2,7,6,5,4,1,3]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[2,7,6,5,1,3,4]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[2,7,6,1,3,4,5]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[2,7,1,3,4,5,6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[2,1,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[3,2,4,5,6,7,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[3,2,4,5,6,1,7]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[3,2,4,5,7,6,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[3,2,4,5,7,1,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[3,2,4,5,1,6,7]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[3,2,4,6,5,7,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[3,2,4,6,5,1,7]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[3,2,4,6,7,5,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[3,2,4,6,7,1,5]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[3,2,4,6,1,5,7]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[3,2,4,7,6,5,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[3,2,4,7,6,1,5]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[3,2,4,7,1,5,6]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[3,2,4,1,5,6,7]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[3,2,5,4,6,7,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[3,2,5,4,6,1,7]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[3,2,5,4,7,6,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[3,2,5,4,7,1,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[3,2,5,4,1,6,7]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[3,2,5,6,4,7,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[3,2,5,6,4,1,7]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[3,2,5,6,7,4,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[3,2,5,6,7,1,4]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[3,2,5,6,1,4,7]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[3,2,5,7,6,4,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[3,2,5,7,6,1,4]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[3,2,5,7,1,4,6]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[3,2,5,1,4,6,7]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[3,2,6,5,4,7,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[3,2,6,5,4,1,7]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[3,2,6,5,7,4,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[3,2,6,5,7,1,4]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[3,2,6,5,1,4,7]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[3,2,6,7,5,4,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[3,2,6,7,5,1,4]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[3,2,6,7,1,4,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[3,2,6,1,4,5,7]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[3,2,7,6,5,4,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[3,2,7,6,5,1,4]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[3,2,7,6,1,4,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[3,2,7,1,4,5,6]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[3,2,1,4,5,6,7]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,4,2,5,6,7,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,4,2,5,6,1,7]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,4,2,5,7,6,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,4,2,5,7,1,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[3,4,2,5,1,6,7]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,4,2,6,5,7,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,4,2,6,5,1,7]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,4,2,6,7,5,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,4,2,6,7,1,5]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[3,4,2,6,1,5,7]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[3,4,2,7,6,5,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[3,4,2,7,6,1,5]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[3,4,2,7,1,5,6]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[3,4,2,1,5,6,7]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[3,4,5,2,6,7,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[3,4,5,2,6,1,7]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[3,4,5,2,7,6,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[3,4,5,2,7,1,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[3,4,5,2,1,6,7]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[3,4,5,6,2,7,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[3,4,5,6,2,1,7]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[3,4,5,6,7,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[3,4,5,6,7,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[3,4,5,6,1,2,7]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[3,4,5,7,6,2,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[3,4,5,7,6,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[3,4,5,7,1,2,6]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[3,4,5,1,2,6,7]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[3,4,6,5,2,7,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[3,4,6,5,2,1,7]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[3,4,6,5,7,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[3,4,6,5,7,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[3,4,6,5,1,2,7]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[3,4,6,7,5,2,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[3,4,6,7,5,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[3,4,6,7,1,2,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[3,4,6,1,2,5,7]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[3,4,7,6,5,2,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[3,4,7,6,5,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[3,4,7,6,1,2,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[3,4,7,1,2,5,6]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[3,4,1,2,5,6,7]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[3,5,4,2,6,7,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[3,5,4,2,6,1,7]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[3,5,4,2,7,6,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[3,5,4,2,7,1,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[3,5,4,2,1,6,7]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[3,5,4,6,2,7,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[3,5,4,6,2,1,7]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[3,5,4,6,7,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[3,5,4,6,7,1,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[3,5,4,6,1,2,7]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[3,5,4,7,6,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[3,5,4,7,6,1,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[3,5,4,7,1,2,6]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[3,5,4,1,2,6,7]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[3,5,6,4,2,7,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[3,5,6,4,2,1,7]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[3,5,6,4,7,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[3,5,6,4,7,1,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[3,5,6,4,1,2,7]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[3,5,6,7,4,2,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[3,5,6,7,4,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[3,5,6,7,1,2,4]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[3,5,6,1,2,4,7]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[3,5,7,6,4,2,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[3,5,7,6,4,1,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[3,5,7,6,1,2,4]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[3,5,7,1,2,4,6]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[3,5,1,2,4,6,7]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[3,6,5,4,2,7,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[3,6,5,4,2,1,7]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[3,6,5,4,7,2,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[3,6,5,4,7,1,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[3,6,5,4,1,2,7]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[3,6,5,7,4,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[3,6,5,7,4,1,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[3,6,5,7,1,2,4]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[3,6,5,1,2,4,7]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[3,6,7,5,4,2,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[3,6,7,5,4,1,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[3,6,7,5,1,2,4]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[3,6,7,1,2,4,5]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[3,6,1,2,4,5,7]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[3,7,6,5,4,2,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[3,7,6,5,4,1,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[3,7,6,5,1,2,4]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[3,7,6,1,2,4,5]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[3,7,1,2,4,5,6]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[3,1,2,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[4,3,2,5,6,7,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[4,3,2,5,6,1,7]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[4,3,2,5,7,6,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[4,3,2,5,7,1,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[4,3,2,5,1,6,7]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[4,3,2,6,5,7,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[4,3,2,6,5,1,7]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[4,3,2,6,7,5,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[4,3,2,6,7,1,5]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[4,3,2,6,1,5,7]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[4,3,2,7,6,5,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[4,3,2,7,6,1,5]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[4,3,2,7,1,5,6]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[4,3,2,1,5,6,7]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,3,5,2,6,7,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[4,3,5,2,6,1,7]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[4,3,5,2,7,6,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[4,3,5,2,7,1,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[4,3,5,2,1,6,7]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[4,3,5,6,2,7,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[4,3,5,6,2,1,7]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[4,3,5,6,7,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[4,3,5,6,7,1,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[4,3,5,6,1,2,7]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[4,3,5,7,6,2,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[4,3,5,7,6,1,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[4,3,5,7,1,2,6]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[4,3,5,1,2,6,7]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[4,3,6,5,2,7,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[4,3,6,5,2,1,7]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[4,3,6,5,7,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[4,3,6,5,7,1,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[4,3,6,5,1,2,7]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[4,3,6,7,5,2,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[4,3,6,7,5,1,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[4,3,6,7,1,2,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[4,3,6,1,2,5,7]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[4,3,7,6,5,2,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[4,3,7,6,5,1,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[4,3,7,6,1,2,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[4,3,7,1,2,5,6]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[4,3,1,2,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[4,5,3,2,6,7,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[4,5,3,2,6,1,7]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[4,5,3,2,7,6,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[4,5,3,2,7,1,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[4,5,3,2,1,6,7]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[4,5,3,6,2,7,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[4,5,3,6,2,1,7]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[4,5,3,6,7,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[4,5,3,6,7,1,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[4,5,3,6,1,2,7]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[4,5,3,7,6,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[4,5,3,7,6,1,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[4,5,3,7,1,2,6]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[4,5,3,1,2,6,7]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[4,5,6,3,2,7,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[4,5,6,3,2,1,7]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[4,5,6,3,7,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[4,5,6,3,7,1,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[4,5,6,3,1,2,7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[4,5,6,7,3,2,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[4,5,6,7,3,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[4,5,6,7,1,2,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[4,5,6,1,2,3,7]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[4,5,7,6,3,2,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[4,5,7,6,3,1,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[4,5,7,6,1,2,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[4,5,7,1,2,3,6]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[4,5,1,2,3,6,7]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[4,6,5,3,2,7,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[4,6,5,3,2,1,7]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[4,6,5,3,7,2,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[4,6,5,3,7,1,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[4,6,5,3,1,2,7]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[4,6,5,7,3,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[4,6,5,7,3,1,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[4,6,5,7,1,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[4,6,5,1,2,3,7]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[4,6,7,5,3,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[4,6,7,5,3,1,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[4,6,7,5,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[4,6,7,1,2,3,5]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[4,6,1,2,3,5,7]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[4,7,6,5,3,2,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[4,7,6,5,3,1,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[4,7,6,5,1,2,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[4,7,6,1,2,3,5]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[4,7,1,2,3,5,6]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[4,1,2,3,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[5,4,3,2,6,7,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[5,4,3,2,6,1,7]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[5,4,3,2,7,6,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[5,4,3,2,7,1,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[5,4,3,2,1,6,7]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,4,3,6,2,7,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[5,4,3,6,2,1,7]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[5,4,3,6,7,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[5,4,3,6,7,1,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[5,4,3,6,1,2,7]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[5,4,3,7,6,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[5,4,3,7,6,1,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[5,4,3,7,1,2,6]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[5,4,3,1,2,6,7]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[5,4,6,3,2,7,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[5,4,6,3,2,1,7]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[5,4,6,3,7,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[5,4,6,3,7,1,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[5,4,6,3,1,2,7]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[5,4,6,7,3,2,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[5,4,6,7,3,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[5,4,6,7,1,2,3]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[5,4,6,1,2,3,7]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[5,4,7,6,3,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[5,4,7,6,3,1,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[5,4,7,6,1,2,3]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[5,4,7,1,2,3,6]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[5,4,1,2,3,6,7]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[5,6,4,3,2,7,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[5,6,4,3,2,1,7]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[5,6,4,3,7,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[5,6,4,3,7,1,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[5,6,4,3,1,2,7]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[5,6,4,7,3,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[5,6,4,7,3,1,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[5,6,4,7,1,2,3]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[5,6,4,1,2,3,7]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[5,6,7,4,3,2,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[5,6,7,4,3,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[5,6,7,4,1,2,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[5,6,7,1,2,3,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[5,6,1,2,3,4,7]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[5,7,6,4,3,2,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[5,7,6,4,3,1,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[5,7,6,4,1,2,3]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[5,7,6,1,2,3,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[5,7,1,2,3,4,6]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[5,1,2,3,4,6,7]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[6,5,4,3,2,7,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[6,5,4,3,2,1,7]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,5,4,3,7,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[6,5,4,3,7,1,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[6,5,4,3,1,2,7]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[6,5,4,7,3,2,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[6,5,4,7,3,1,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[6,5,4,7,1,2,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[6,5,4,1,2,3,7]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[6,5,7,4,3,2,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[6,5,7,4,3,1,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[6,5,7,4,1,2,3]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[6,5,7,1,2,3,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[6,5,1,2,3,4,7]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[6,7,5,4,3,2,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[6,7,5,4,3,1,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[6,7,5,4,1,2,3]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[6,7,5,1,2,3,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[6,7,1,2,3,4,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[6,1,2,3,4,5,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[7,6,5,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,6,5,4,3,1,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[7,6,5,4,1,2,3]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,6,5,1,2,3,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[7,6,1,2,3,4,5]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[7,1,2,3,4,5,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[2,3,4,5,6,7,1,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[2,3,4,5,6,8,7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[2,3,4,5,6,8,1,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[2,3,4,5,6,1,7,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[2,3,4,5,7,6,8,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[2,3,4,5,7,6,1,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[2,3,4,5,7,8,6,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[2,3,4,5,7,8,1,6]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>[2,3,4,5,7,1,6,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>[2,3,4,5,8,7,6,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[2,3,4,5,8,7,1,6]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>[2,3,4,5,8,1,6,7]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[2,3,4,5,1,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[2,3,4,6,5,7,8,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>[2,3,4,6,5,7,1,8]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[2,3,4,6,5,8,7,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[2,3,4,6,5,8,1,7]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[2,3,4,6,5,1,7,8]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[2,3,4,6,7,5,8,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[2,3,4,6,7,5,1,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[2,3,4,6,7,8,5,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[2,3,4,6,7,8,1,5]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[2,3,4,6,7,1,5,8]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>[2,3,4,6,8,7,5,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[2,3,4,6,8,7,1,5]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[2,3,4,6,8,1,5,7]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[2,3,4,6,1,5,7,8]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,5,4,7,8]=>[2,3,4,7,6,5,8,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>[2,3,4,7,6,5,1,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>[2,3,4,7,6,8,5,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[2,3,4,7,6,8,1,5]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[2,3,4,7,6,1,5,8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,5,4,8]=>[2,3,4,7,8,6,5,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>[2,3,4,7,8,6,1,5]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[2,3,4,7,8,1,5,6]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>[2,3,4,7,1,5,6,8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[2,3,4,8,7,6,5,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[2,3,4,8,7,6,1,5]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[2,3,4,8,7,1,5,6]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>[2,3,4,8,1,5,6,7]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[2,3,4,1,5,6,7,8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[2,3,5,4,6,7,8,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[2,3,5,4,6,7,1,8]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>[2,3,5,4,6,8,7,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>[2,3,5,4,6,8,1,7]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,7,6]=>[2,3,5,4,6,1,7,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[2,3,5,4,7,6,8,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[2,3,5,4,7,6,1,8]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>[2,3,5,4,7,8,6,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[2,3,5,4,7,8,1,6]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>[2,3,5,4,7,1,6,8]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[2,3,5,4,8,7,1,6]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,6,5]=>[2,3,5,4,8,1,6,7]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[2,3,5,4,1,6,7,8]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8]=>[2,3,5,6,4,7,8,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6,8]=>[2,3,5,6,4,8,7,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,4,5,3,7,8,6]=>[2,3,5,6,4,8,1,7]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>[2,3,5,6,4,1,7,8]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>[2,3,5,6,7,4,8,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,6,3,8,7]=>[2,3,5,6,7,4,1,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,7,3,8]=>[2,3,5,6,7,8,4,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[2,3,5,6,7,8,1,4]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,7,3]=>[2,3,5,6,7,1,4,8]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,7,8,6,3]=>[2,3,5,6,8,1,4,7]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,4,5,8,7,6,3]=>[2,3,5,6,1,4,7,8]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,5,3,7,8]=>[2,3,5,7,6,4,8,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,4,6,5,7,3,8]=>[2,3,5,7,6,8,4,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,4,6,5,7,8,3]=>[2,3,5,7,6,8,1,4]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,5,8,7,3]=>[2,3,5,7,6,1,4,8]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,4,6,7,5,3,8]=>[2,3,5,7,8,6,4,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,5,3]=>[2,3,5,7,8,1,4,6]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,7,5,3]=>[2,3,5,7,1,4,6,8]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,6,5,8,3]=>[2,3,5,8,7,6,1,4]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,6,8,5,3]=>[2,3,5,8,7,1,4,6]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>[2,3,5,8,1,4,6,7]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[2,3,5,1,4,6,7,8]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,4,3,6,7,8]=>[2,3,6,5,4,7,8,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>[2,3,6,5,4,7,1,8]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>[2,3,6,5,4,8,1,7]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,4,3,8,7,6]=>[2,3,6,5,4,1,7,8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>[2,3,6,5,7,8,4,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,3]=>[2,3,6,5,7,8,1,4]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>[2,3,6,5,7,1,4,8]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,4,7,6,8,3]=>[2,3,6,5,8,7,1,4]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,4,7,8,6,3]=>[2,3,6,5,8,1,4,7]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>[2,3,6,5,1,4,7,8]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,4,3,7,8]=>[2,3,6,7,5,4,8,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,4,7,3,8]=>[2,3,6,7,5,8,4,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,4,7,8,3]=>[2,3,6,7,5,8,1,4]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,5,6,7,4,3,8]=>[2,3,6,7,8,5,4,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,4,8,3]=>[2,3,6,7,8,5,1,4]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[2,3,6,7,8,1,4,5]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,7,4,3]=>[2,3,6,7,1,4,5,8]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,5,7,6,4,3,8]=>[2,3,6,8,7,5,4,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,6,4,8,3]=>[2,3,6,8,7,5,1,4]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,6,8,4,3]=>[2,3,6,8,7,1,4,5]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,8,7,6,4,3]=>[2,3,6,1,4,5,7,8]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>[2,3,7,6,5,4,8,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>[2,3,7,6,5,8,1,4]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>[2,3,7,6,5,1,4,8]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,5,7,8,4,3]=>[2,3,7,6,8,1,4,5]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,5,8,7,4,3]=>[2,3,7,6,1,4,5,8]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,6,7,5,4,3,8]=>[2,3,7,8,6,5,4,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>[2,3,7,8,1,4,5,6]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>[2,3,8,7,6,5,4,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,6,5,4,8,3]=>[2,3,8,7,6,5,1,4]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,6,5,8,4,3]=>[2,3,8,7,6,1,4,5]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,6,8,5,4,3]=>[2,3,8,7,1,4,5,6]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,6,5,4,3]=>[2,3,8,1,4,5,6,7]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[2,3,1,4,5,6,7,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[2,4,3,5,6,7,8,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[2,4,3,5,6,7,1,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[2,4,3,5,6,8,7,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[2,4,3,5,6,8,1,7]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,7,6]=>[2,4,3,5,6,1,7,8]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[2,4,3,5,7,6,8,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[2,4,3,5,7,6,1,8]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,2,4,6,7,5,8]=>[2,4,3,5,7,8,6,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[2,4,3,5,7,8,1,6]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>[2,4,3,5,7,1,6,8]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>[2,4,3,5,8,7,6,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[2,4,3,5,8,7,1,6]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[2,4,3,5,1,6,7,8]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[2,4,3,6,5,7,8,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[2,4,3,6,5,8,7,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[2,4,3,6,5,8,1,7]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>[2,4,3,6,5,1,7,8]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>[2,4,3,6,7,5,8,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2,5,6,4,8,7]=>[2,4,3,6,7,5,1,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,5,6,7,4,8]=>[2,4,3,6,7,8,5,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,8,4]=>[2,4,3,6,7,8,1,5]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,2,5,6,8,7,4]=>[2,4,3,6,7,1,5,8]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,6,4,8]=>[2,4,3,6,8,7,5,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,6,8,4]=>[2,4,3,6,8,7,1,5]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,6,4]=>[2,4,3,6,8,1,5,7]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,7,6,4]=>[2,4,3,6,1,5,7,8]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,5,4,7,8]=>[2,4,3,7,6,5,8,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,6,5,4,8,7]=>[2,4,3,7,6,5,1,8]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>[2,4,3,7,6,8,5,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>[2,4,3,7,6,8,1,5]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>[2,4,3,7,6,1,5,8]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,2,6,7,5,4,8]=>[2,4,3,7,8,6,5,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,5,8,4]=>[2,4,3,7,8,6,1,5]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,2,6,7,8,5,4]=>[2,4,3,7,8,1,5,6]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,6,8,7,5,4]=>[2,4,3,7,1,5,6,8]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,6,5,4,8]=>[2,4,3,8,7,6,5,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,6,5,8,4]=>[2,4,3,8,7,6,1,5]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,6,8,5,4]=>[2,4,3,8,7,1,5,6]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[2,4,3,1,5,6,7,8]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[2,4,5,3,6,7,8,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>[2,4,5,3,6,7,1,8]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>[2,4,5,3,6,8,7,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[2,4,5,3,6,8,1,7]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,7,6]=>[2,4,5,3,6,1,7,8]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7]=>[2,4,5,3,7,6,1,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[2,4,5,3,7,8,6,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[2,4,5,3,7,8,1,6]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>[2,4,5,3,7,1,6,8]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[2,4,5,3,8,7,1,6]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,6,5]=>[2,4,5,3,8,1,6,7]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[2,4,5,3,1,6,7,8]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>[2,4,5,6,3,7,8,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,5,2,6,8,7]=>[2,4,5,6,3,7,1,8]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,8]=>[2,4,5,6,3,8,7,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>[2,4,5,6,3,8,1,7]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,5,2,8,7,6]=>[2,4,5,6,3,1,7,8]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,7,8]=>[2,4,5,6,7,3,8,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,2,8,7]=>[2,4,5,6,7,3,1,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>[2,4,5,6,7,8,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[2,4,5,6,7,8,1,3]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[2,4,5,6,7,1,3,8]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,5,7,6,2,8]=>[2,4,5,6,8,7,3,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,7,6,8,2]=>[2,4,5,6,8,7,1,3]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,6,2]=>[2,4,5,6,8,1,3,7]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,7,6,2]=>[2,4,5,6,1,3,7,8]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,4,6,5,7,2,8]=>[2,4,5,7,6,8,3,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,4,6,5,7,8,2]=>[2,4,5,7,6,8,1,3]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,4,6,7,5,2,8]=>[2,4,5,7,8,6,3,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,5,8,2]=>[2,4,5,7,8,6,1,3]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,5,2]=>[2,4,5,7,8,1,3,6]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>[2,4,5,8,7,6,1,3]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,7,6,8,5,2]=>[2,4,5,8,7,1,3,6]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[2,4,5,1,3,6,7,8]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,4,2,6,7,8]=>[2,4,6,5,3,7,8,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,4,2,6,8,7]=>[2,4,6,5,3,7,1,8]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,4,2,7,6,8]=>[2,4,6,5,3,8,7,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,4,2,7,8,6]=>[2,4,6,5,3,8,1,7]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,5,4,6,2,7,8]=>[2,4,6,5,7,3,8,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,5,4,6,7,2,8]=>[2,4,6,5,7,8,3,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,5,4,6,7,8,2]=>[2,4,6,5,7,8,1,3]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>[2,4,6,5,8,7,3,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,4,7,6,8,2]=>[2,4,6,5,8,7,1,3]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,4,7,8,6,2]=>[2,4,6,5,8,1,3,7]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,4,8,7,6,2]=>[2,4,6,5,1,3,7,8]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,4,2,7,8]=>[2,4,6,7,5,3,8,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,4,7,2,8]=>[2,4,6,7,5,8,3,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,5,6,4,7,8,2]=>[2,4,6,7,5,8,1,3]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,5,6,7,4,2,8]=>[2,4,6,7,8,5,3,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,5,6,7,4,8,2]=>[2,4,6,7,8,5,1,3]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[2,4,6,7,8,1,3,5]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,8,7,4,2]=>[2,4,6,7,1,3,5,8]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,6,4,2,8]=>[2,4,6,8,7,5,3,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,6,4,8,2]=>[2,4,6,8,7,5,1,3]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,7,6,8,4,2]=>[2,4,6,8,7,1,3,5]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[2,4,6,8,1,3,5,7]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,7,6,4,2]=>[2,4,6,1,3,5,7,8]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,6,5,4,2,8,7]=>[2,4,7,6,5,3,1,8]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,5,4,7,2,8]=>[2,4,7,6,5,8,3,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>[2,4,7,6,5,1,3,8]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,6,5,7,4,2,8]=>[2,4,7,6,8,5,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,5,7,4,8,2]=>[2,4,7,6,8,5,1,3]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,5,7,8,4,2]=>[2,4,7,6,8,1,3,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,6,7,5,4,2,8]=>[2,4,7,8,6,5,3,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,6,7,5,8,4,2]=>[2,4,7,8,6,1,3,5]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,6,7,8,5,4,2]=>[2,4,7,8,1,3,5,6]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,6,8,7,5,4,2]=>[2,4,7,1,3,5,6,8]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,7,6,5,4,2,8]=>[2,4,8,7,6,5,3,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,7,8,6,5,4,2]=>[2,4,8,1,3,5,6,7]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>[2,4,1,3,5,6,7,8]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>[2,5,4,3,6,7,8,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>[2,5,4,3,6,7,1,8]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>[2,5,4,3,6,8,7,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,3,2,5,7,8,6]=>[2,5,4,3,6,8,1,7]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>[2,5,4,3,6,1,7,8]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,3,2,6,7,5,8]=>[2,5,4,3,7,8,6,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[2,5,4,3,7,8,1,6]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,3,2,6,8,7,5]=>[2,5,4,3,7,1,6,8]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[2,5,4,3,8,7,6,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>[2,5,4,3,8,7,1,6]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[2,5,4,3,1,6,7,8]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,3,5,2,6,7,8]=>[2,5,4,6,3,7,8,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,3,5,2,7,6,8]=>[2,5,4,6,3,8,7,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3,5,2,7,8,6]=>[2,5,4,6,3,8,1,7]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,3,5,2,8,7,6]=>[2,5,4,6,3,1,7,8]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,3,5,6,2,7,8]=>[2,5,4,6,7,3,8,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,7,2,8]=>[2,5,4,6,7,8,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,2]=>[2,5,4,6,7,8,1,3]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,3,5,7,6,2,8]=>[2,5,4,6,8,7,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,3,5,7,8,6,2]=>[2,5,4,6,8,1,3,7]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>[2,5,4,6,1,3,7,8]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>[2,5,4,7,6,3,8,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>[2,5,4,7,6,8,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,3,6,5,7,8,2]=>[2,5,4,7,6,8,1,3]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[2,5,4,7,6,1,3,8]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,3,6,7,5,8,2]=>[2,5,4,7,8,6,1,3]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,6,7,8,5,2]=>[2,5,4,7,8,1,3,6]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,6,8,7,5,2]=>[2,5,4,7,1,3,6,8]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,3,7,6,8,5,2]=>[2,5,4,8,7,1,3,6]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,7,8,6,5,2]=>[2,5,4,8,1,3,6,7]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[2,5,4,1,3,6,7,8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,5,3,2,6,7,8]=>[2,5,6,4,3,7,8,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,5,3,2,6,8,7]=>[2,5,6,4,3,7,1,8]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,3,2,7,6,8]=>[2,5,6,4,3,8,7,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,5,3,2,7,8,6]=>[2,5,6,4,3,8,1,7]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,5,3,2,8,7,6]=>[2,5,6,4,3,1,7,8]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,4,5,3,6,2,7,8]=>[2,5,6,4,7,3,8,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,3,6,7,2,8]=>[2,5,6,4,7,8,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,3,6,7,8,2]=>[2,5,6,4,7,8,1,3]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,3,6,8,7,2]=>[2,5,6,4,7,1,3,8]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,3,7,8,6,2]=>[2,5,6,4,8,1,3,7]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,3,8,7,6,2]=>[2,5,6,4,1,3,7,8]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,6,3,2,7,8]=>[2,5,6,7,4,3,8,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,6,3,7,2,8]=>[2,5,6,7,4,8,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,6,3,8,7,2]=>[2,5,6,7,4,1,3,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,3,2,8]=>[2,5,6,7,8,4,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,3,8,2]=>[2,5,6,7,8,4,1,3]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,3,2]=>[2,5,6,7,8,1,3,4]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,7,8,6,3,2]=>[2,5,6,8,1,3,4,7]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,8,7,6,3,2]=>[2,5,6,1,3,4,7,8]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,4,6,5,3,2,7,8]=>[2,5,7,6,4,3,8,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,5,3,8,7,2]=>[2,5,7,6,4,1,3,8]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,5,7,3,2,8]=>[2,5,7,6,8,4,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,6,5,7,3,8,2]=>[2,5,7,6,8,4,1,3]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,5,8,7,3,2]=>[2,5,7,6,1,3,4,8]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,4,6,7,5,3,2,8]=>[2,5,7,8,6,4,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,6,7,5,3,8,2]=>[2,5,7,8,6,4,1,3]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,5,8,3,2]=>[2,5,7,8,6,1,3,4]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,4,6,7,8,5,3,2]=>[2,5,7,8,1,3,4,6]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,7,5,3,2]=>[2,5,7,1,3,4,6,8]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,4,7,6,5,3,2,8]=>[2,5,8,7,6,4,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,4,7,6,5,8,3,2]=>[2,5,8,7,6,1,3,4]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,4,7,8,6,5,3,2]=>[2,5,8,1,3,4,6,7]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>[2,5,1,3,4,6,7,8]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8]=>[2,6,5,4,3,7,8,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,4,3,2,7,6,8]=>[2,6,5,4,3,8,7,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,4,3,2,7,8,6]=>[2,6,5,4,3,8,1,7]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,4,3,2,8,7,6]=>[2,6,5,4,3,1,7,8]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>[2,6,5,4,7,3,8,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,5,4,3,6,7,2,8]=>[2,6,5,4,7,8,3,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>[2,6,5,4,7,8,1,3]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>[2,6,5,4,7,1,3,8]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,4,3,8,7,6,2]=>[2,6,5,4,1,3,7,8]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,4,6,3,2,7,8]=>[2,6,5,7,4,3,8,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,4,6,3,2,8,7]=>[2,6,5,7,4,3,1,8]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,4,6,3,7,2,8]=>[2,6,5,7,4,8,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,4,6,3,7,8,2]=>[2,6,5,7,4,8,1,3]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,4,6,7,3,2,8]=>[2,6,5,7,8,4,3,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,4,6,7,3,8,2]=>[2,6,5,7,8,4,1,3]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,3,2]=>[2,6,5,7,8,1,3,4]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,4,6,8,7,3,2]=>[2,6,5,7,1,3,4,8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,4,7,6,3,2,8]=>[2,6,5,8,7,4,3,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,4,7,8,6,3,2]=>[2,6,5,8,1,3,4,7]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,6,4,3,2,7,8]=>[2,6,7,5,4,3,8,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,6,4,3,2,8,7]=>[2,6,7,5,4,3,1,8]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,4,3,8,7,2]=>[2,6,7,5,4,1,3,8]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,5,6,4,7,3,2,8]=>[2,6,7,5,8,4,3,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,4,7,3,8,2]=>[2,6,7,5,8,4,1,3]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,5,6,4,7,8,3,2]=>[2,6,7,5,8,1,3,4]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,5,6,7,4,3,2,8]=>[2,6,7,8,5,4,3,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,6,7,4,3,8,2]=>[2,6,7,8,5,4,1,3]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[2,6,7,8,1,3,4,5]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,6,8,4,3,2]=>[2,6,8,7,1,3,4,5]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,7,6,4,3,2]=>[2,6,1,3,4,5,7,8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,5,4,3,2,7,8]=>[2,7,6,5,4,3,8,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,5,4,3,2,8,7]=>[2,7,6,5,4,3,1,8]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,5,4,3,7,8,2]=>[2,7,6,5,4,8,1,3]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[2,7,6,5,4,1,3,8]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,6,5,4,7,8,3,2]=>[2,7,6,5,8,1,3,4]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,6,5,4,8,7,3,2]=>[2,7,6,5,1,3,4,8]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,5,7,4,3,2,8]=>[2,7,6,8,5,4,3,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,5,7,4,3,8,2]=>[2,7,6,8,5,4,1,3]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,4,3,2]=>[2,7,6,8,1,3,4,5]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,5,8,7,4,3,2]=>[2,7,6,1,3,4,5,8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,7,5,4,3,2,8]=>[2,7,8,6,5,4,3,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,5,4,3,8,2]=>[2,7,8,6,5,4,1,3]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,5,8,4,3,2]=>[2,7,8,6,1,3,4,5]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[2,7,8,1,3,4,5,6]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>[2,7,1,3,4,5,6,8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,6,5,4,3,2,8]=>[2,8,7,6,5,4,3,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,6,5,4,3,8,2]=>[2,8,7,6,5,4,1,3]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7,6,5,4,8,3,2]=>[2,8,7,6,5,1,3,4]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[2,8,7,6,1,3,4,5]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>[2,8,7,1,3,4,5,6]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>[2,8,1,3,4,5,6,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[2,1,3,4,5,6,7,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[3,2,4,5,6,7,1,8]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[3,2,4,5,6,8,7,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,7,8,6]=>[3,2,4,5,6,8,1,7]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,7,6]=>[3,2,4,5,6,1,7,8]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[3,2,4,5,7,6,8,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[3,2,4,5,7,6,1,8]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,4,6,7,5,8]=>[3,2,4,5,7,8,6,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[3,2,4,5,7,8,1,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[3,2,4,5,8,7,1,6]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,6,5]=>[3,2,4,5,8,1,6,7]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[3,2,4,5,1,6,7,8]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,3,5,4,6,7,8]=>[3,2,4,6,5,7,8,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[3,2,4,6,5,7,1,8]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,3,5,4,7,8,6]=>[3,2,4,6,5,8,1,7]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>[3,2,4,6,5,1,7,8]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,5,6,4,8,7]=>[3,2,4,6,7,5,1,8]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,4]=>[3,2,4,6,7,8,1,5]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,3,5,7,6,8,4]=>[3,2,4,6,8,7,1,5]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>[3,2,4,7,6,5,1,8]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,6,5,8,7,4]=>[3,2,4,7,6,1,5,8]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,5,4,8]=>[3,2,4,7,8,6,5,1]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,6,7,8,5,4]=>[3,2,4,7,8,1,5,6]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,6,8,7,5,4]=>[3,2,4,7,1,5,6,8]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,3,7,8,6,5,4]=>[3,2,4,8,1,5,6,7]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[3,2,4,1,5,6,7,8]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[3,2,5,4,6,7,8,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[3,2,5,4,6,7,1,8]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,3,5,7,8,6]=>[3,2,5,4,6,8,1,7]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,7,6]=>[3,2,5,4,6,1,7,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[3,2,5,4,7,6,8,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[3,2,5,4,7,6,1,8]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,3,6,7,5,8]=>[3,2,5,4,7,8,6,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[3,2,5,4,7,8,1,6]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[3,2,5,4,7,1,6,8]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[3,2,5,4,8,7,1,6]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[3,2,5,4,8,1,6,7]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[3,2,5,4,1,6,7,8]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8]=>[3,2,5,6,4,7,8,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[3,2,5,6,4,7,1,8]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,4,5,3,8,7,6]=>[3,2,5,6,4,1,7,8]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[3,2,5,6,7,4,1,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,7,3,8]=>[3,2,5,6,7,8,4,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[3,2,5,6,7,8,1,4]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>[3,2,5,6,7,1,4,8]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,6,3]=>[3,2,5,6,8,1,4,7]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[3,2,5,6,1,4,7,8]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>[3,2,5,7,6,4,8,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[3,2,5,7,6,4,1,8]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>[3,2,5,7,6,1,4,8]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,5,3,8]=>[3,2,5,7,8,6,4,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,5,8,3]=>[3,2,5,7,8,6,1,4]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,4,6,7,8,5,3]=>[3,2,5,7,8,1,4,6]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,7,5,3]=>[3,2,5,7,1,4,6,8]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>[3,2,5,8,7,6,1,4]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,7,6,8,5,3]=>[3,2,5,8,7,1,4,6]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,6,5,3]=>[3,2,5,8,1,4,6,7]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[3,2,5,1,4,6,7,8]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,4,3,6,7,8]=>[3,2,6,5,4,7,8,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[3,2,6,5,4,7,1,8]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,4,3,7,6,8]=>[3,2,6,5,4,8,7,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,5,4,3,8,7,6]=>[3,2,6,5,4,1,7,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>[3,2,6,5,7,4,1,8]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,4,6,7,3,8]=>[3,2,6,5,7,8,4,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,4,6,7,8,3]=>[3,2,6,5,7,8,1,4]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,4,6,8,7,3]=>[3,2,6,5,7,1,4,8]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>[3,2,6,5,8,7,1,4]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,4,7,8,6,3]=>[3,2,6,5,8,1,4,7]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,4,8,7,6,3]=>[3,2,6,5,1,4,7,8]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,6,4,3,7,8]=>[3,2,6,7,5,4,8,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[3,2,6,7,5,4,1,8]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,4,7,8,3]=>[3,2,6,7,5,8,1,4]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,5,6,4,8,7,3]=>[3,2,6,7,5,1,4,8]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,4,3,8]=>[3,2,6,7,8,5,4,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,4,8,3]=>[3,2,6,7,8,5,1,4]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>[3,2,6,7,8,1,4,5]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,5,6,8,7,4,3]=>[3,2,6,7,1,4,5,8]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,6,4,8,3]=>[3,2,6,8,7,5,1,4]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,6,8,4,3]=>[3,2,6,8,7,1,4,5]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,6,4,3]=>[3,2,6,8,1,4,5,7]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,5,8,7,6,4,3]=>[3,2,6,1,4,5,7,8]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[3,2,7,6,5,4,1,8]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,6,5,4,8,7,3]=>[3,2,7,6,5,1,4,8]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>[3,2,7,6,8,5,1,4]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>[3,2,7,6,8,1,4,5]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>[3,2,7,6,1,4,5,8]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,6,7,5,4,3,8]=>[3,2,7,8,6,5,4,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,5,4,8,3]=>[3,2,7,8,6,5,1,4]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[3,2,7,8,6,1,4,5]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[3,2,7,8,1,4,5,6]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,6,8,7,5,4,3]=>[3,2,7,1,4,5,6,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,6,5,4,3,8]=>[3,2,8,7,6,5,4,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,7,6,5,4,8,3]=>[3,2,8,7,6,5,1,4]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[3,2,8,7,6,1,4,5]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,6,8,5,4,3]=>[3,2,8,7,1,4,5,6]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,6,5,4,3]=>[3,2,8,1,4,5,6,7]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[3,2,1,4,5,6,7,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[3,4,2,5,6,7,8,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,8,7]=>[3,4,2,5,6,7,1,8]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,5,7,6,8]=>[3,4,2,5,6,8,7,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,4,2,5,6,8,1,7]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,4,6,5,8,7]=>[3,4,2,5,7,6,1,8]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[3,4,2,5,7,8,6,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,4,2,5,7,8,1,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[3,4,2,5,8,7,1,6]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,6,5]=>[3,4,2,5,8,1,6,7]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[3,4,2,5,1,6,7,8]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8]=>[3,4,2,6,5,7,8,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[3,4,2,6,5,8,7,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,5,6,4,7,8]=>[3,4,2,6,7,5,8,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[3,4,2,6,7,8,5,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[3,4,2,6,7,8,1,5]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,6,8,4]=>[3,4,2,6,8,7,1,5]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,5,7,8,6,4]=>[3,4,2,6,8,1,5,7]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,6,5,4,7,8]=>[3,4,2,7,6,5,8,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>[3,4,2,7,6,5,1,8]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>[3,4,2,7,6,8,5,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>[3,4,2,7,6,1,5,8]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,6,7,5,4,8]=>[3,4,2,7,8,6,5,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,5,8,4]=>[3,4,2,7,8,6,1,5]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,5,4]=>[3,4,2,7,8,1,5,6]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,7,5,4]=>[3,4,2,7,1,5,6,8]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,6,5,8,4]=>[3,4,2,8,7,6,1,5]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,6,8,5,4]=>[3,4,2,8,7,1,5,6]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,6,5,4]=>[3,4,2,8,1,5,6,7]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[3,4,2,1,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[3,4,5,2,6,7,8,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[3,4,5,2,6,7,1,8]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[3,4,5,2,6,8,7,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[3,4,5,2,6,8,1,7]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[3,4,5,2,6,1,7,8]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[3,4,5,2,7,6,8,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[3,4,5,2,7,6,1,8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[3,4,5,2,7,8,6,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[3,4,5,2,7,8,1,6]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[3,4,5,2,7,1,6,8]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>[3,4,5,2,8,7,6,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[3,4,5,2,8,7,1,6]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[3,4,5,2,8,1,6,7]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[3,4,5,2,1,6,7,8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[3,4,5,6,2,7,8,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,8,7]=>[3,4,5,6,2,7,1,8]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,8]=>[3,4,5,6,2,8,7,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,1,7,8,6]=>[3,4,5,6,2,8,1,7]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[3,4,5,6,2,1,7,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[3,4,5,6,7,2,8,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[3,4,5,6,7,2,1,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[3,4,5,6,7,8,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[3,4,5,6,7,8,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[3,4,5,6,7,1,2,8]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,6,1,8]=>[3,4,5,6,8,7,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>[3,4,5,6,8,7,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,6,1]=>[3,4,5,6,8,1,2,7]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>[3,4,5,6,1,2,7,8]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,6,5,1,7,8]=>[3,4,5,7,6,2,8,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,4,6,5,7,1,8]=>[3,4,5,7,6,8,2,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>[3,4,5,7,6,8,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>[3,4,5,7,6,1,2,8]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,4,6,7,5,1,8]=>[3,4,5,7,8,6,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,5,8,1]=>[3,4,5,7,8,6,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]=>[3,4,5,7,8,1,2,6]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,8,7,5,1]=>[3,4,5,7,1,2,6,8]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>[3,4,5,8,7,6,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>[3,4,5,8,7,6,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,7,6,8,5,1]=>[3,4,5,8,7,1,2,6]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,6,5,1]=>[3,4,5,8,1,2,6,7]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[3,4,5,1,2,6,7,8]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>[3,4,6,5,2,7,8,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,5,4,1,6,8,7]=>[3,4,6,5,2,7,1,8]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,4,1,7,6,8]=>[3,4,6,5,2,8,7,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>[3,4,6,5,2,1,7,8]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,5,4,6,1,7,8]=>[3,4,6,5,7,2,8,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,5,4,6,7,1,8]=>[3,4,6,5,7,8,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>[3,4,6,5,7,8,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>[3,4,6,5,8,7,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,4,7,8,6,1]=>[3,4,6,5,8,1,2,7]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>[3,4,6,5,1,2,7,8]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,5,6,4,1,7,8]=>[3,4,6,7,5,2,8,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,4,1,8,7]=>[3,4,6,7,5,2,1,8]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,4,7,1,8]=>[3,4,6,7,5,8,2,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]=>[3,4,6,7,5,8,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,5,6,4,8,7,1]=>[3,4,6,7,5,1,2,8]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,5,6,7,4,1,8]=>[3,4,6,7,8,5,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,4,8,1]=>[3,4,6,7,8,5,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[3,4,6,7,8,1,2,5]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[3,4,6,7,1,2,5,8]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,5,7,6,4,1,8]=>[3,4,6,8,7,5,2,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,5,7,6,4,8,1]=>[3,4,6,8,7,5,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,6,8,4,1]=>[3,4,6,8,7,1,2,5]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]=>[3,4,6,8,1,2,5,7]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,8,7,6,4,1]=>[3,4,6,1,2,5,7,8]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,6,5,4,1,7,8]=>[3,4,7,6,5,2,8,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[3,4,7,6,5,2,1,8]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]=>[3,4,7,6,5,8,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,6,5,7,4,1,8]=>[3,4,7,6,8,5,2,1]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,5,8,7,4,1]=>[3,4,7,6,1,2,5,8]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,6,7,5,4,1,8]=>[3,4,7,8,6,5,2,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,5,4,1]=>[3,4,7,8,1,2,5,6]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>[3,4,8,7,6,5,2,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>[3,4,8,7,6,5,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,6,5,8,4,1]=>[3,4,8,7,6,1,2,5]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>[3,4,1,2,5,6,7,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>[3,5,4,2,6,7,8,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,4,3,1,5,8,7,6]=>[3,5,4,2,6,1,7,8]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,4,3,1,6,5,7,8]=>[3,5,4,2,7,6,8,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[3,5,4,2,7,6,1,8]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>[3,5,4,2,7,8,1,6]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[3,5,4,2,7,1,6,8]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[3,5,4,2,8,7,1,6]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,3,1,7,8,6,5]=>[3,5,4,2,8,1,6,7]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[3,5,4,2,1,6,7,8]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>[3,5,4,6,2,7,8,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,4,3,5,1,6,8,7]=>[3,5,4,6,2,7,1,8]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>[3,5,4,6,2,8,7,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,3,5,1,7,8,6]=>[3,5,4,6,2,8,1,7]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>[3,5,4,6,2,1,7,8]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,4,3,5,6,1,8,7]=>[3,5,4,6,7,2,1,8]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,7,1,8]=>[3,5,4,6,7,8,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>[3,5,4,6,7,8,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>[3,5,4,6,7,1,2,8]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>[3,5,4,6,8,7,1,2]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,4,3,5,8,7,6,1]=>[3,5,4,6,1,2,7,8]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,6,5,1,7,8]=>[3,5,4,7,6,2,8,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[3,5,4,7,6,2,1,8]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>[3,5,4,7,6,8,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>[3,5,4,7,6,8,1,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[3,5,4,7,6,1,2,8]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,3,6,7,5,8,1]=>[3,5,4,7,8,6,1,2]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,3,6,7,8,5,1]=>[3,5,4,7,8,1,2,6]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,3,6,8,7,5,1]=>[3,5,4,7,1,2,6,8]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[3,5,4,8,7,6,1,2]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>[3,5,4,1,2,6,7,8]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,4,5,3,1,6,7,8]=>[3,5,6,4,2,7,8,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,4,5,3,1,6,8,7]=>[3,5,6,4,2,7,1,8]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,4,5,3,1,7,6,8]=>[3,5,6,4,2,8,7,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,3,1,7,8,6]=>[3,5,6,4,2,8,1,7]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[3,5,6,4,2,1,7,8]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,4,5,3,6,1,8,7]=>[3,5,6,4,7,2,1,8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,4,5,3,6,7,1,8]=>[3,5,6,4,7,8,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]=>[3,5,6,4,7,8,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,3,6,8,7,1]=>[3,5,6,4,7,1,2,8]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,3,7,8,6,1]=>[3,5,6,4,8,1,2,7]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,3,8,7,6,1]=>[3,5,6,4,1,2,7,8]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,3,1,7,8]=>[3,5,6,7,4,2,8,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,6,3,7,1,8]=>[3,5,6,7,4,8,2,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,1]=>[3,5,6,7,4,8,1,2]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,3,8,7,1]=>[3,5,6,7,4,1,2,8]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,3,1,8]=>[3,5,6,7,8,4,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,3,8,1]=>[3,5,6,7,8,4,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,3,1]=>[3,5,6,7,8,1,2,4]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,8,7,3,1]=>[3,5,6,7,1,2,4,8]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,6,3,1]=>[3,5,6,8,1,2,4,7]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,4,6,5,3,1,7,8]=>[3,5,7,6,4,2,8,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,5,3,1,8,7]=>[3,5,7,6,4,2,1,8]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,5,3,7,8,1]=>[3,5,7,6,4,8,1,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,5,3,8,7,1]=>[3,5,7,6,4,1,2,8]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]=>[3,5,7,6,8,4,1,2]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,5,7,8,3,1]=>[3,5,7,6,8,1,2,4]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,5,8,7,3,1]=>[3,5,7,6,1,2,4,8]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,5,3,1,8]=>[3,5,7,8,6,4,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,6,7,5,3,8,1]=>[3,5,7,8,6,4,1,2]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,6,7,5,8,3,1]=>[3,5,7,8,6,1,2,4]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,5,3,1]=>[3,5,7,8,1,2,4,6]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>[3,5,7,1,2,4,6,8]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,6,5,8,3,1]=>[3,5,8,7,6,1,2,4]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]=>[3,5,8,1,2,4,6,7]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[3,5,1,2,4,6,7,8]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>[3,6,5,4,2,7,8,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,5,4,3,1,6,8,7]=>[3,6,5,4,2,7,1,8]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,5,4,3,1,7,6,8]=>[3,6,5,4,2,8,7,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,4,3,1,7,8,6]=>[3,6,5,4,2,8,1,7]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>[3,6,5,4,2,1,7,8]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,4,3,6,1,8,7]=>[3,6,5,4,7,2,1,8]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>[3,6,5,4,7,8,2,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[3,6,5,4,7,8,1,2]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[3,6,5,4,7,1,2,8]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>[3,6,5,4,8,7,1,2]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>[3,6,5,4,8,1,2,7]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[3,6,5,4,1,2,7,8]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,4,6,3,7,1,8]=>[3,6,5,7,4,8,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,4,6,3,7,8,1]=>[3,6,5,7,4,8,1,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,4,6,7,3,1,8]=>[3,6,5,7,8,4,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]=>[3,6,5,7,8,4,1,2]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,3,1]=>[3,6,5,7,8,1,2,4]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,5,4,7,6,3,1,8]=>[3,6,5,8,7,4,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]=>[3,6,5,8,7,4,1,2]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,4,7,6,8,3,1]=>[3,6,5,8,7,1,2,4]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,4,7,8,6,3,1]=>[3,6,5,8,1,2,4,7]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,4,8,7,6,3,1]=>[3,6,5,1,2,4,7,8]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,5,6,4,3,1,8,7]=>[3,6,7,5,4,2,1,8]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,4,3,7,8,1]=>[3,6,7,5,4,8,1,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,5,6,4,7,3,1,8]=>[3,6,7,5,8,4,2,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,4,7,8,3,1]=>[3,6,7,5,8,1,2,4]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,4,8,7,3,1]=>[3,6,7,5,1,2,4,8]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,5,6,7,4,3,1,8]=>[3,6,7,8,5,4,2,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,4,3,8,1]=>[3,6,7,8,5,4,1,2]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,4,8,3,1]=>[3,6,7,8,5,1,2,4]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[3,6,7,8,1,2,4,5]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,5,7,6,4,3,1,8]=>[3,6,8,7,5,4,2,1]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,5,8,7,6,4,3,1]=>[3,6,1,2,4,5,7,8]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,6,5,4,3,1,8,7]=>[3,7,6,5,4,2,1,8]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>[3,7,6,5,4,8,1,2]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,6,5,4,3,8,7,1]=>[3,7,6,5,4,1,2,8]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,3,1]=>[3,7,6,5,8,1,2,4]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,6,5,4,8,7,3,1]=>[3,7,6,5,1,2,4,8]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,6,5,7,4,3,8,1]=>[3,7,6,8,5,4,1,2]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,6,5,7,8,4,3,1]=>[3,7,6,8,1,2,4,5]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,6,7,5,4,3,1,8]=>[3,7,8,6,5,4,2,1]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,6,7,5,4,8,3,1]=>[3,7,8,6,5,1,2,4]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,7,5,8,4,3,1]=>[3,7,8,6,1,2,4,5]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,5,4,3,1]=>[3,7,8,1,2,4,5,6]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>[3,7,1,2,4,5,6,8]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,7,6,5,4,3,1,8]=>[3,8,7,6,5,4,2,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,6,5,4,3,8,1]=>[3,8,7,6,5,4,1,2]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>[3,8,7,6,5,1,2,4]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,6,8,5,4,3,1]=>[3,8,7,1,2,4,5,6]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>[3,8,1,2,4,5,6,7]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>[3,1,2,4,5,6,7,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[4,3,2,5,6,7,8,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>[4,3,2,5,6,7,1,8]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,5,7,6,8]=>[4,3,2,5,6,8,7,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>[4,3,2,5,6,8,1,7]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[4,3,2,5,6,1,7,8]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[4,3,2,5,7,8,1,6]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>[4,3,2,5,7,1,6,8]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[4,3,2,5,8,7,6,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[4,3,2,5,8,7,1,6]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,7,8,6,5]=>[4,3,2,5,8,1,6,7]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[4,3,2,5,1,6,7,8]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8]=>[4,3,2,6,5,7,8,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[4,3,2,6,5,8,7,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>[4,3,2,6,7,5,8,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,5,6,7,4,8]=>[4,3,2,6,7,8,5,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[4,3,2,6,7,8,1,5]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>[4,3,2,6,7,1,5,8]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>[4,3,2,6,8,7,5,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>[4,3,2,6,8,7,1,5]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[4,3,2,6,8,1,5,7]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[4,3,2,6,1,5,7,8]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,2,1,6,5,4,7,8]=>[4,3,2,7,6,5,8,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7]=>[4,3,2,7,6,5,1,8]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,2,1,6,5,7,4,8]=>[4,3,2,7,6,8,5,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[4,3,2,7,6,8,1,5]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[4,3,2,7,6,1,5,8]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,2,1,6,7,5,4,8]=>[4,3,2,7,8,6,5,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>[4,3,2,7,8,6,1,5]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,6,7,8,5,4]=>[4,3,2,7,8,1,5,6]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>[4,3,2,7,1,5,6,8]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,2,1,7,6,5,4,8]=>[4,3,2,8,7,6,5,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[4,3,2,8,7,6,1,5]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>[4,3,2,8,7,1,5,6]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>[4,3,2,8,1,5,6,7]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[4,3,2,1,5,6,7,8]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[4,3,5,2,6,7,8,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>[4,3,5,2,6,7,1,8]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>[4,3,5,2,6,8,7,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>[4,3,5,2,6,8,1,7]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>[4,3,5,2,6,1,7,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>[4,3,5,2,7,6,8,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[4,3,5,2,7,6,1,8]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>[4,3,5,2,7,8,6,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>[4,3,5,2,7,8,1,6]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[4,3,5,2,7,1,6,8]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>[4,3,5,2,8,7,6,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[4,3,5,2,8,7,1,6]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[4,3,5,2,8,1,6,7]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[4,3,5,2,1,6,7,8]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>[4,3,5,6,2,7,8,1]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>[4,3,5,6,2,1,7,8]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,6,1,7,8]=>[4,3,5,6,7,2,8,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,1,8]=>[4,3,5,6,7,8,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[4,3,5,6,7,8,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,8,7,1]=>[4,3,5,6,7,1,2,8]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>[4,3,5,6,8,7,1,2]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,7,8,6,1]=>[4,3,5,6,8,1,2,7]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,2,4,6,5,8,7,1]=>[4,3,5,7,6,1,2,8]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,2,4,6,7,5,1,8]=>[4,3,5,7,8,6,2,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>[4,3,5,8,7,6,1,2]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,7,8,6,5,1]=>[4,3,5,8,1,2,6,7]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[4,3,5,1,2,6,7,8]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>[4,3,6,5,2,7,8,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,5,4,1,6,8,7]=>[4,3,6,5,2,7,1,8]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>[4,3,6,5,2,8,7,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>[4,3,6,5,2,8,1,7]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[4,3,6,5,2,1,7,8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>[4,3,6,5,7,2,1,8]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,5,4,6,7,8,1]=>[4,3,6,5,7,8,1,2]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,5,4,6,8,7,1]=>[4,3,6,5,7,1,2,8]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[4,3,6,5,8,7,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[4,3,6,5,8,7,1,2]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,4,7,8,6,1]=>[4,3,6,5,8,1,2,7]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,5,6,4,1,8,7]=>[4,3,6,7,5,2,1,8]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,5,6,4,7,8,1]=>[4,3,6,7,5,8,1,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,5,6,7,4,1,8]=>[4,3,6,7,8,5,2,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,5,6,7,4,8,1]=>[4,3,6,7,8,5,1,2]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]=>[4,3,6,7,8,1,2,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,5,7,6,4,1,8]=>[4,3,6,8,7,5,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,5,7,6,4,8,1]=>[4,3,6,8,7,5,1,2]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,5,7,6,8,4,1]=>[4,3,6,8,7,1,2,5]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,5,7,8,6,4,1]=>[4,3,6,8,1,2,5,7]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,2,6,5,4,1,8,7]=>[4,3,7,6,5,2,1,8]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,2,6,5,4,7,1,8]=>[4,3,7,6,5,8,2,1]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]=>[4,3,7,6,5,1,2,8]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,2,6,5,7,4,1,8]=>[4,3,7,6,8,5,2,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>[4,3,7,6,8,5,1,2]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,2,6,5,8,7,4,1]=>[4,3,7,6,1,2,5,8]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[4,3,7,8,6,5,2,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]=>[4,3,7,8,6,5,1,2]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,2,6,7,5,8,4,1]=>[4,3,7,8,6,1,2,5]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,6,8,7,5,4,1]=>[4,3,7,1,2,5,6,8]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[4,3,8,7,6,5,2,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,2,7,6,5,4,8,1]=>[4,3,8,7,6,5,1,2]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,7,8,6,5,4,1]=>[4,3,8,1,2,5,6,7]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>[4,3,1,2,5,6,7,8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8]=>[4,5,3,2,6,7,8,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,4,2,1,5,6,8,7]=>[4,5,3,2,6,7,1,8]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,4,2,1,5,8,7,6]=>[4,5,3,2,6,1,7,8]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[4,5,3,2,7,6,1,8]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>[4,5,3,2,7,8,1,6]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>[4,5,3,2,7,1,6,8]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[4,5,3,2,8,7,1,6]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[4,5,3,2,8,1,6,7]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[4,5,3,2,1,6,7,8]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8]=>[4,5,3,6,2,7,8,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,2,5,1,7,6,8]=>[4,5,3,6,2,8,7,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,2,5,1,7,8,6]=>[4,5,3,6,2,8,1,7]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>[4,5,3,6,2,1,7,8]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,2,5,6,1,7,8]=>[4,5,3,6,7,2,8,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,4,2,5,6,1,8,7]=>[4,5,3,6,7,2,1,8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,7,1,8]=>[4,5,3,6,7,8,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>[4,5,3,6,7,8,1,2]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,8,7,1]=>[4,5,3,6,7,1,2,8]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,4,2,5,7,6,1,8]=>[4,5,3,6,8,7,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,2,5,7,6,8,1]=>[4,5,3,6,8,7,1,2]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>[4,5,3,6,8,1,2,7]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,4,2,5,8,7,6,1]=>[4,5,3,6,1,2,7,8]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,4,2,6,5,1,8,7]=>[4,5,3,7,6,2,1,8]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,2,6,5,7,1,8]=>[4,5,3,7,6,8,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,2,6,5,7,8,1]=>[4,5,3,7,6,8,1,2]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,8,7,1]=>[4,5,3,7,6,1,2,8]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,4,2,6,7,5,1,8]=>[4,5,3,7,8,6,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>[4,5,3,7,8,6,1,2]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,4,2,7,6,5,1,8]=>[4,5,3,8,7,6,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,2,7,6,5,8,1]=>[4,5,3,8,7,6,1,2]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,4,2,7,8,6,5,1]=>[4,5,3,8,1,2,6,7]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[4,5,3,1,2,6,7,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8]=>[4,5,6,3,2,7,8,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,5,2,1,6,8,7]=>[4,5,6,3,2,7,1,8]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,5,2,1,7,6,8]=>[4,5,6,3,2,8,7,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,5,2,1,7,8,6]=>[4,5,6,3,2,8,1,7]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>[4,5,6,3,2,1,7,8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,2,6,1,7,8]=>[4,5,6,3,7,2,8,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,2,6,1,8,7]=>[4,5,6,3,7,2,1,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,5,2,6,7,1,8]=>[4,5,6,3,7,8,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>[4,5,6,3,7,8,1,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,5,2,7,6,1,8]=>[4,5,6,3,8,7,2,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,2,7,6,8,1]=>[4,5,6,3,8,7,1,2]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,2,7,8,6,1]=>[4,5,6,3,8,1,2,7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,2,1,7,8]=>[4,5,6,7,3,2,8,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,2,1,8,7]=>[4,5,6,7,3,2,1,8]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,2,7,1,8]=>[4,5,6,7,3,8,2,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]=>[4,5,6,7,3,8,1,2]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,2,8,7,1]=>[4,5,6,7,3,1,2,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,2,1,8]=>[4,5,6,7,8,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,2,8,1]=>[4,5,6,7,8,3,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,2,1]=>[4,5,6,7,8,1,2,3]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,7,2,1]=>[4,5,6,7,1,2,3,8]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,7,6,2,8,1]=>[4,5,6,8,7,3,1,2]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,6,8,2,1]=>[4,5,6,8,7,1,2,3]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]=>[4,5,6,8,1,2,3,7]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[4,5,6,1,2,3,7,8]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,4,6,5,2,1,8,7]=>[4,5,7,6,3,2,1,8]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,5,2,7,1,8]=>[4,5,7,6,3,8,2,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,6,5,2,7,8,1]=>[4,5,7,6,3,8,1,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,5,7,2,8,1]=>[4,5,7,6,8,3,1,2]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,5,7,8,2,1]=>[4,5,7,6,8,1,2,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,6,7,5,2,8,1]=>[4,5,7,8,6,3,1,2]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,5,8,2,1]=>[4,5,7,8,6,1,2,3]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,5,2,1]=>[4,5,7,8,1,2,3,6]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,6,5,2,1,8]=>[4,5,8,7,6,3,2,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,6,5,2,8,1]=>[4,5,8,7,6,3,1,2]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,7,6,5,8,2,1]=>[4,5,8,7,6,1,2,3]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[4,5,1,2,3,6,7,8]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,4,2,1,6,7,8]=>[4,6,5,3,2,7,8,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,4,2,1,6,8,7]=>[4,6,5,3,2,7,1,8]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,4,2,1,7,6,8]=>[4,6,5,3,2,8,7,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,4,2,1,7,8,6]=>[4,6,5,3,2,8,1,7]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[4,6,5,3,2,1,7,8]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,5,4,2,6,1,7,8]=>[4,6,5,3,7,2,8,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,5,4,2,6,1,8,7]=>[4,6,5,3,7,2,1,8]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>[4,6,5,3,7,8,2,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,4,2,6,7,8,1]=>[4,6,5,3,7,8,1,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,4,2,7,6,1,8]=>[4,6,5,3,8,7,2,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,5,4,2,7,6,8,1]=>[4,6,5,3,8,7,1,2]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,4,2,7,8,6,1]=>[4,6,5,3,8,1,2,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,4,6,2,7,1,8]=>[4,6,5,7,3,8,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,4,6,2,7,8,1]=>[4,6,5,7,3,8,1,2]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,5,4,6,2,8,7,1]=>[4,6,5,7,3,1,2,8]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,4,6,7,2,8,1]=>[4,6,5,7,8,3,1,2]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,4,6,7,8,2,1]=>[4,6,5,7,8,1,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,5,4,7,6,2,1,8]=>[4,6,5,8,7,3,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,4,7,6,2,8,1]=>[4,6,5,8,7,3,1,2]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,4,7,6,8,2,1]=>[4,6,5,8,7,1,2,3]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,4,7,8,6,2,1]=>[4,6,5,8,1,2,3,7]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,4,2,1,8,7]=>[4,6,7,5,3,2,1,8]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,5,6,4,2,7,1,8]=>[4,6,7,5,3,8,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,4,2,7,8,1]=>[4,6,7,5,3,8,1,2]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,4,2,8,7,1]=>[4,6,7,5,3,1,2,8]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,4,7,2,1,8]=>[4,6,7,5,8,3,2,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]=>[4,6,7,5,8,3,1,2]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,4,7,8,2,1]=>[4,6,7,5,8,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,5,6,7,4,2,1,8]=>[4,6,7,8,5,3,2,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>[4,6,7,8,5,3,1,2]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,4,8,2,1]=>[4,6,7,8,5,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[4,6,7,8,1,2,3,5]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,7,4,2,1]=>[4,6,7,1,2,3,5,8]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,6,4,2,1,8]=>[4,6,8,7,5,3,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,6,4,2,8,1]=>[4,6,8,7,5,3,1,2]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,5,7,6,4,8,2,1]=>[4,6,8,7,5,1,2,3]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,5,7,6,8,4,2,1]=>[4,6,8,7,1,2,3,5]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]=>[4,6,8,1,2,3,5,7]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[4,6,1,2,3,5,7,8]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,6,5,4,2,1,7,8]=>[4,7,6,5,3,2,8,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>[4,7,6,5,3,2,1,8]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,6,5,4,2,7,1,8]=>[4,7,6,5,3,8,2,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,5,4,2,7,8,1]=>[4,7,6,5,3,8,1,2]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,6,5,4,2,8,7,1]=>[4,7,6,5,3,1,2,8]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,6,5,4,7,2,1,8]=>[4,7,6,5,8,3,2,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]=>[4,7,6,5,8,3,1,2]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,6,5,4,7,8,2,1]=>[4,7,6,5,8,1,2,3]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,6,5,4,8,7,2,1]=>[4,7,6,5,1,2,3,8]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,5,8,4,2,1]=>[4,7,8,6,1,2,3,5]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,7,5,4,2,1]=>[4,7,1,2,3,5,6,8]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,6,5,4,8,2,1]=>[4,8,7,6,5,1,2,3]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,6,5,8,4,2,1]=>[4,8,7,6,1,2,3,5]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]=>[4,8,7,1,2,3,5,6]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,6,5,4,2,1]=>[4,8,1,2,3,5,6,7]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]=>[4,1,2,3,5,6,7,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[5,4,3,2,6,7,8,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[5,4,3,2,6,7,1,8]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[5,4,3,2,6,8,7,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[5,4,3,2,6,8,1,7]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[5,4,3,2,6,1,7,8]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[5,4,3,2,7,6,8,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[5,4,3,2,7,6,1,8]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[5,4,3,2,7,8,6,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[5,4,3,2,7,8,1,6]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[5,4,3,2,7,1,6,8]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[5,4,3,2,8,7,6,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[5,4,3,2,8,7,1,6]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[5,4,3,2,8,1,6,7]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>[5,4,3,6,2,7,8,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,3,2,5,1,7,8,6]=>[5,4,3,6,2,8,1,7]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[5,4,3,6,2,1,7,8]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,3,2,5,6,1,7,8]=>[5,4,3,6,7,2,8,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,3,2,5,6,1,8,7]=>[5,4,3,6,7,2,1,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,7,1,8]=>[5,4,3,6,7,8,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[5,4,3,6,7,8,1,2]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]=>[5,4,3,6,7,1,2,8]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,3,2,5,7,6,1,8]=>[5,4,3,6,8,7,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,3,2,5,7,6,8,1]=>[5,4,3,6,8,7,1,2]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,2,5,7,8,6,1]=>[5,4,3,6,8,1,2,7]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>[5,4,3,6,1,2,7,8]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,3,2,6,5,1,7,8]=>[5,4,3,7,6,2,8,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,3,2,6,5,1,8,7]=>[5,4,3,7,6,2,1,8]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,3,2,6,5,7,1,8]=>[5,4,3,7,6,8,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>[5,4,3,7,6,8,1,2]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]=>[5,4,3,7,6,1,2,8]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,3,2,6,7,5,1,8]=>[5,4,3,7,8,6,2,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,6,7,5,8,1]=>[5,4,3,7,8,6,1,2]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,3,2,6,8,7,5,1]=>[5,4,3,7,1,2,6,8]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[5,4,3,8,7,6,1,2]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,7,8,6,5,1]=>[5,4,3,8,1,2,6,7]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[5,4,3,1,2,6,7,8]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,3,5,2,1,6,7,8]=>[5,4,6,3,2,7,8,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,3,5,2,1,6,8,7]=>[5,4,6,3,2,7,1,8]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>[5,4,6,3,2,1,7,8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,3,5,2,6,1,7,8]=>[5,4,6,3,7,2,8,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>[5,4,6,3,7,2,1,8]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]=>[5,4,6,3,7,8,1,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,3,5,2,7,6,1,8]=>[5,4,6,3,8,7,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>[5,4,6,3,8,7,1,2]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,3,5,2,8,7,6,1]=>[5,4,6,3,1,2,7,8]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,3,5,6,2,1,8,7]=>[5,4,6,7,3,2,1,8]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,3,5,6,2,7,1,8]=>[5,4,6,7,3,8,2,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,1]=>[5,4,6,7,3,8,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,7,2,8,1]=>[5,4,6,7,8,3,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,2,1]=>[5,4,6,7,8,1,2,3]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,8,7,2,1]=>[5,4,6,7,1,2,3,8]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,3,5,7,6,2,1,8]=>[5,4,6,8,7,3,2,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,3,5,7,6,8,2,1]=>[5,4,6,8,7,1,2,3]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,7,8,6,2,1]=>[5,4,6,8,1,2,3,7]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,3,6,5,2,1,7,8]=>[5,4,7,6,3,2,8,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,3,6,5,2,1,8,7]=>[5,4,7,6,3,2,1,8]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>[5,4,7,6,3,1,2,8]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,3,6,5,7,2,1,8]=>[5,4,7,6,8,3,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>[5,4,7,6,8,3,1,2]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,2,1]=>[5,4,7,6,8,1,2,3]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>[5,4,7,6,1,2,3,8]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,6,7,5,2,8,1]=>[5,4,7,8,6,3,1,2]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,5,2,1]=>[5,4,7,8,1,2,3,6]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,7,6,5,2,1,8]=>[5,4,8,7,6,3,2,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,7,6,5,2,8,1]=>[5,4,8,7,6,3,1,2]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,7,6,5,8,2,1]=>[5,4,8,7,6,1,2,3]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,7,8,6,5,2,1]=>[5,4,8,1,2,3,6,7]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,3,8,7,6,5,2,1]=>[5,4,1,2,3,6,7,8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8]=>[5,6,4,3,2,7,8,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,3,2,1,6,8,7]=>[5,6,4,3,2,7,1,8]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,5,3,2,1,7,6,8]=>[5,6,4,3,2,8,7,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>[5,6,4,3,2,1,7,8]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,5,3,2,6,1,7,8]=>[5,6,4,3,7,2,8,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,3,2,6,1,8,7]=>[5,6,4,3,7,2,1,8]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,3,2,6,7,8,1]=>[5,6,4,3,7,8,1,2]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,8,7,1]=>[5,6,4,3,7,1,2,8]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,3,2,7,6,1,8]=>[5,6,4,3,8,7,2,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,3,2,8,7,6,1]=>[5,6,4,3,1,2,7,8]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[5,6,4,7,3,2,1,8]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>[5,6,4,7,3,8,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,3,6,2,8,7,1]=>[5,6,4,7,3,1,2,8]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,3,6,7,2,8,1]=>[5,6,4,7,8,3,1,2]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,6,8,7,2,1]=>[5,6,4,7,1,2,3,8]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,3,7,6,2,1,8]=>[5,6,4,8,7,3,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,5,3,7,6,2,8,1]=>[5,6,4,8,7,3,1,2]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,3,7,6,8,2,1]=>[5,6,4,8,7,1,2,3]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,3,7,8,6,2,1]=>[5,6,4,8,1,2,3,7]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,6,3,2,1,7,8]=>[5,6,7,4,3,2,8,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[5,6,7,4,3,2,1,8]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,3,2,7,8,1]=>[5,6,7,4,3,8,1,2]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,3,2,8,7,1]=>[5,6,7,4,3,1,2,8]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>[5,6,7,4,8,3,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,6,3,7,8,2,1]=>[5,6,7,4,8,1,2,3]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,3,8,7,2,1]=>[5,6,7,4,1,2,3,8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>[5,6,7,8,4,3,2,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[5,6,7,8,4,3,1,2]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[5,6,7,8,4,1,2,3]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[5,6,7,8,1,2,3,4]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,7,3,2,1]=>[5,6,7,1,2,3,4,8]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,5,7,6,3,2,1,8]=>[5,6,8,7,4,3,2,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,6,8,3,2,1]=>[5,6,8,7,1,2,3,4]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,6,3,2,1]=>[5,6,8,1,2,3,4,7]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]=>[5,6,1,2,3,4,7,8]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,6,5,3,2,1,8,7]=>[5,7,6,4,3,2,1,8]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,5,3,2,8,7,1]=>[5,7,6,4,3,1,2,8]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,5,3,7,2,8,1]=>[5,7,6,4,8,3,1,2]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,6,5,7,3,2,1,8]=>[5,7,6,8,4,3,2,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,5,7,3,2,8,1]=>[5,7,6,8,4,3,1,2]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,3,2,1]=>[5,7,6,8,1,2,3,4]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]=>[5,7,6,1,2,3,4,8]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,6,7,5,3,2,1,8]=>[5,7,8,6,4,3,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,5,3,2,8,1]=>[5,7,8,6,4,3,1,2]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,5,8,3,2,1]=>[5,7,8,6,1,2,3,4]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,5,3,2,1]=>[5,7,8,1,2,3,4,6]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>[5,7,1,2,3,4,6,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>[5,8,7,6,4,3,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,6,5,3,2,8,1]=>[5,8,7,6,4,3,1,2]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,6,5,3,8,2,1]=>[5,8,7,6,4,1,2,3]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>[5,8,7,6,1,2,3,4]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,6,8,5,3,2,1]=>[5,8,7,1,2,3,4,6]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,6,5,3,2,1]=>[5,8,1,2,3,4,6,7]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[5,1,2,3,4,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[6,5,4,3,2,7,8,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[6,5,4,3,2,7,1,8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[6,5,4,3,2,8,7,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[6,5,4,3,2,8,1,7]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[6,5,4,3,2,1,7,8]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[6,5,4,3,7,2,8,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[6,5,4,3,7,2,1,8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>[6,5,4,3,7,8,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[6,5,4,3,7,8,1,2]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>[6,5,4,3,7,1,2,8]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[6,5,4,3,8,7,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>[6,5,4,3,8,7,1,2]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>[6,5,4,3,8,1,2,7]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[6,5,4,3,1,2,7,8]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,4,3,6,2,1,7,8]=>[6,5,4,7,3,2,8,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,4,3,6,2,1,8,7]=>[6,5,4,7,3,2,1,8]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,4,3,6,2,7,1,8]=>[6,5,4,7,3,8,2,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,1]=>[6,5,4,7,3,8,1,2]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,4,3,6,2,8,7,1]=>[6,5,4,7,3,1,2,8]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,4,3,6,7,2,1,8]=>[6,5,4,7,8,3,2,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,4,3,6,7,2,8,1]=>[6,5,4,7,8,3,1,2]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,2,1]=>[6,5,4,7,8,1,2,3]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,4,3,6,8,7,2,1]=>[6,5,4,7,1,2,3,8]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,4,3,7,6,2,1,8]=>[6,5,4,8,7,3,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,4,3,7,6,2,8,1]=>[6,5,4,8,7,3,1,2]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,3,7,8,6,2,1]=>[6,5,4,8,1,2,3,7]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,4,3,8,7,6,2,1]=>[6,5,4,1,2,3,7,8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,4,6,3,2,1,7,8]=>[6,5,7,4,3,2,8,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,4,6,3,2,1,8,7]=>[6,5,7,4,3,2,1,8]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,4,6,3,2,7,1,8]=>[6,5,7,4,3,8,2,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,4,6,3,2,7,8,1]=>[6,5,7,4,3,8,1,2]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,4,6,3,2,8,7,1]=>[6,5,7,4,3,1,2,8]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,4,6,3,7,2,1,8]=>[6,5,7,4,8,3,2,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[6,5,7,4,8,3,1,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,4,6,7,3,2,1,8]=>[6,5,7,8,4,3,2,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[6,5,7,8,4,1,2,3]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[6,5,7,8,1,2,3,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,4,7,6,3,2,1,8]=>[6,5,8,7,4,3,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,4,7,6,3,8,2,1]=>[6,5,8,7,4,1,2,3]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,4,7,6,8,3,2,1]=>[6,5,8,7,1,2,3,4]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,4,7,8,6,3,2,1]=>[6,5,8,1,2,3,4,7]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,4,3,2,1,7,8]=>[6,7,5,4,3,2,8,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,6,4,3,2,1,8,7]=>[6,7,5,4,3,2,1,8]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,6,4,3,2,7,1,8]=>[6,7,5,4,3,8,2,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,6,4,3,7,2,1,8]=>[6,7,5,4,8,3,2,1]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,4,3,8,7,2,1]=>[6,7,5,4,1,2,3,8]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,6,4,7,3,2,1,8]=>[6,7,5,8,4,3,2,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[6,7,5,8,1,2,3,4]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,4,8,7,3,2,1]=>[6,7,5,1,2,3,4,8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[6,7,8,5,4,3,2,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,4,3,2,8,1]=>[6,7,8,5,4,3,1,2]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,4,3,8,2,1]=>[6,7,8,5,4,1,2,3]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[6,7,8,5,1,2,3,4]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[6,7,8,1,2,3,4,5]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]=>[6,7,1,2,3,4,5,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>[6,8,7,5,4,3,2,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,6,4,3,2,8,1]=>[6,8,7,5,4,3,1,2]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]=>[6,8,7,5,4,1,2,3]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,6,4,8,3,2,1]=>[6,8,7,5,1,2,3,4]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>[6,8,7,1,2,3,4,5]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]=>[6,8,1,2,3,4,5,7]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[6,1,2,3,4,5,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[7,6,5,4,3,2,8,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[7,6,5,4,3,2,1,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,5,4,3,2,7,1,8]=>[7,6,5,4,3,8,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>[7,6,5,4,3,8,1,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>[7,6,5,4,3,1,2,8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,5,4,3,7,2,1,8]=>[7,6,5,4,8,3,2,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>[7,6,5,4,8,3,1,2]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[7,6,5,4,8,1,2,3]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,5,4,3,8,7,2,1]=>[7,6,5,4,1,2,3,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>[7,6,5,8,4,3,2,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,5,4,7,3,2,8,1]=>[7,6,5,8,4,3,1,2]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[7,6,5,8,4,1,2,3]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]=>[7,6,5,8,1,2,3,4]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,5,4,8,7,3,2,1]=>[7,6,5,1,2,3,4,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>[7,6,8,5,4,3,2,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>[7,6,8,5,4,3,1,2]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[7,6,8,5,4,1,2,3]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>[7,6,8,5,1,2,3,4]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>[7,6,8,1,2,3,4,5]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>[7,6,1,2,3,4,5,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>[7,8,6,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]=>[7,8,6,5,4,3,1,2]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[7,8,6,5,4,1,2,3]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,5,4,8,3,2,1]=>[7,8,6,5,1,2,3,4]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>[7,8,6,1,2,3,4,5]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[7,8,1,2,3,4,5,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>[7,1,2,3,4,5,6,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>[8,7,6,5,4,1,2,3]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>[8,7,6,5,1,2,3,4]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>[8,7,6,1,2,3,4,5]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>[8,7,1,2,3,4,5,6]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>[8,1,2,3,4,5,6,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,2,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,8,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,6,5,4,3,2,1,9]=>[8,9,7,6,5,4,3,2,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,7,6,5,4,3,2]=>[2,9,1,3,4,5,6,7,8]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[11,10,9,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,9,7,6,5,4,3,2,1,10]=>[9,10,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,6,8,5,4,3,2,1,9]=>[8,7,9,6,5,4,3,2,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,8,7,5,4,3,2,1,9]=>[7,9,8,6,5,4,3,2,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,7,9,6,5,4,3,2]=>[2,9,8,1,3,4,5,6,7]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,7,9,8,6,5,4,3,2]=>[2,8,1,3,4,5,6,7,9]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9,10,8,7,6,5,4,3,2]=>[2,10,1,3,4,5,6,7,8,9]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[8,7,9,6,5,4,3,2,1,10]=>[9,8,10,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[7,6,5,8,4,3,2,1,9]=>[8,7,6,9,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,8,5,4,3,2,1,9]=>[7,8,9,6,5,4,3,2,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,7,8,9,6,5,4,3,2]=>[2,8,9,1,3,4,5,6,7]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,8,10,7,6,5,4,3,2]=>[2,10,9,1,3,4,5,6,7,8]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,6,9,8,7,5,4,3,2]=>[2,7,1,3,4,5,6,8,9]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,8,10,9,7,6,5,4,3,2]=>[2,9,1,3,4,5,6,7,8,10]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,8,10,7,6,5,4,3,2,1,11]=>[10,9,11,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[8,7,6,9,5,4,3,2,1,10]=>[9,8,7,10,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,9,6,5,4,3,2,1,10]=>[8,9,10,7,6,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[6,7,5,8,4,3,2,1,9]=>[7,8,6,9,5,4,3,2,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[6,5,8,7,4,3,2,1,9]=>[7,6,9,8,5,4,3,2,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,8,7,6,5,3,2,1,9]=>[5,9,8,7,6,4,3,2,1]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,7,6,9,8,5,4,3,2]=>[2,8,7,1,3,4,5,6,9]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,10,7,6,5,4,3,2]=>[2,9,10,1,3,4,5,6,7,8]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,7,10,9,8,6,5,4,3,2]=>[2,8,1,3,4,5,6,7,9,10]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,9,11,10,8,7,6,5,4,3,2]=>[2,10,1,3,4,5,6,7,8,9,11]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[5,9,8,7,6,4,3,2,1,10]=>[6,10,9,8,7,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[7,6,5,4,3,8,2,1,9]=>[8,7,6,5,4,9,3,2,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[6,5,7,8,4,3,2,1,9]=>[7,6,8,9,5,4,3,2,1]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,6,8,9,5,4,3,2]=>[2,8,7,9,1,3,4,5,6]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,9,8,7,6,5,3,2]=>[2,5,1,3,4,6,7,8,9]
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,8,11,10,9,7,6,5,4,3,2]=>[2,9,1,3,4,5,6,7,8,10,11]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[8,7,6,5,4,9,3,2,1,10]=>[9,8,7,6,5,10,4,3,2,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,6,8,9,5,4,3,2,1,10]=>[8,7,9,10,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,6,5,4,3,2,8,1,9]=>[8,7,6,5,4,3,9,2,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,8,7,6,5,4,3,1,9]=>[3,9,8,7,6,5,4,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,6,5,4,3,2,1,9,8]=>[8,7,6,5,4,3,2,1,9]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,9,5,4,3,2]=>[2,7,8,9,1,3,4,5,6]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,9,8,7,6,5,4,3]=>[3,2,1,4,5,6,7,8,9]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,9,8,7,6,5,4,2]=>[2,4,1,3,5,6,7,8,9]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,5,10,9,8,7,6,4,3,2]=>[2,6,1,3,4,5,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[8,7,6,5,4,3,9,2,1,10]=>[9,8,7,6,5,4,10,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>[8,7,6,5,4,3,2,9,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,8,7,6,5,4,3,2,9]=>[2,9,8,7,6,5,4,3,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,7,5,4,3,2,1,9,8]=>[7,8,6,5,4,3,2,1,9]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,7,8,9,10,6,5,4,3,2]=>[2,8,9,10,1,3,4,5,6,7]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,8,9,7,6,5,4,3]=>[3,2,9,1,4,5,6,7,8]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,9,8,7,6,5,4,3]=>[2,3,1,4,5,6,7,8,9]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,4,10,9,8,7,6,5,3,2]=>[2,5,1,3,4,6,7,8,9,10]
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,6,11,10,9,8,7,5,4,3,2]=>[2,7,1,3,4,5,6,8,9,10,11]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[8,7,6,5,4,3,2,9,1,10]=>[9,8,7,6,5,4,3,10,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>[9,8,7,6,5,4,3,2,1,10]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9]=>[7,8,6,5,4,3,2,9,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,7,8,6,5,4,3,2,9]=>[2,8,9,7,6,5,4,3,1]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,9,8,7,6,5,4,3]=>[3,2,1,4,5,6,7,8,9,10]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,10,9,8,7,6,5,4,2]=>[2,4,1,3,5,6,7,8,9,10]
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,5,11,10,9,8,7,6,4,3,2]=>[2,6,1,3,4,5,7,8,9,10,11]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>[9,8,7,6,5,4,3,2,10,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,9,8,7,6,5,4,3,2,10]=>[2,10,9,8,7,6,5,4,3,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[6,5,4,3,7,8,2,1,9]=>[7,6,5,4,8,9,3,2,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,9,4,3,2]=>[2,7,6,8,9,1,3,4,5]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,10,9,8,7,6,5,4,3]=>[2,3,1,4,5,6,7,8,9,10]
[]=>[]=>[]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>[3,4,5,6,7,8,9,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,9,8,1]=>[3,4,5,6,7,8,1,2,9]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,6,8,7,9,1]=>[3,4,5,6,7,9,8,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,7,1]=>[3,4,5,6,7,9,1,2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,9,8,7,1]=>[3,4,5,6,7,1,2,8,9]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,1]=>[3,4,5,6,8,7,9,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,5,7,8,6,9,1]=>[3,4,5,6,8,9,7,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,6,1]=>[3,4,5,6,8,9,1,2,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,5,7,9,8,6,1]=>[3,4,5,6,8,1,2,7,9]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,5,8,7,6,9,1]=>[3,4,5,6,9,8,7,1,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,8,7,9,6,1]=>[3,4,5,6,9,8,1,2,7]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,8,9,7,6,1]=>[3,4,5,6,9,1,2,7,8]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,1]=>[3,4,5,7,6,8,9,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,4,6,7,5,8,9,1]=>[3,4,5,7,8,6,9,1,2]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,7,8,9,6,5,1]=>[3,4,5,8,9,1,2,6,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,9,1]=>[3,4,6,7,5,8,9,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,4,1]=>[3,4,6,7,8,9,1,2,5]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,6,5,7,8,9,4,1]=>[3,4,7,6,8,9,1,2,5]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,9,5,4,1]=>[3,4,7,8,9,1,2,5,6]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,9,8,7,6,5,4,1]=>[3,4,1,2,5,6,7,8,9]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,9,1]=>[3,5,4,6,7,8,9,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,3,1]=>[3,5,6,7,8,9,1,2,4]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,9,4,3,1]=>[3,6,7,8,9,1,2,4,5]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,8,7,6,5,4,3,9,1]=>[3,9,8,7,6,5,4,1,2]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,8,7,9,6,5,4,3,1]=>[3,9,8,1,2,4,5,6,7]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,8,9,7,6,5,4,3,1]=>[3,9,1,2,4,5,6,7,8]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,9,8,7,6,5,4,3,1]=>[3,1,2,4,5,6,7,8,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]=>[4,3,5,6,7,8,9,1,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,9,8,1]=>[4,3,6,5,8,7,1,2,9]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,9,8,7,6,5,4,1]=>[4,3,1,2,5,6,7,8,9]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,1]=>[4,5,3,6,7,8,9,1,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,9,1]=>[4,5,6,3,7,8,9,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,2,8,9,1]=>[4,5,6,7,8,3,9,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,2,9,1]=>[4,5,6,7,8,9,3,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[4,5,6,7,8,9,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,9,4,2,1]=>[4,6,7,8,9,1,2,3,5]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,7,9,8,4,2,1]=>[4,6,7,8,1,2,3,5,9]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[3,8,7,6,5,4,9,2,1]=>[4,9,8,7,6,5,1,2,3]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,9,8,7,6,5,4,2,1]=>[4,1,2,3,5,6,7,8,9]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,1]=>[5,4,3,6,7,8,9,1,2]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,9,5,2,1]=>[5,4,7,8,9,1,2,3,6]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,6,3,7,8,9,2,1]=>[5,6,7,4,8,9,1,2,3]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,7,3,9,8,2,1]=>[5,6,7,8,4,1,2,3,9]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[5,6,7,8,9,1,2,3,4]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,7,9,8,3,2,1]=>[5,6,7,8,1,2,3,4,9]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4,8,7,6,5,9,3,2,1]=>[5,9,8,7,6,1,2,3,4]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,9,8,7,6,5,3,2,1]=>[5,1,2,3,4,6,7,8,9]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,9,1]=>[6,5,4,3,7,8,9,1,2]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,9,8,7,6,1]=>[6,5,4,3,1,2,7,8,9]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,8,3,9,2,1]=>[6,5,7,8,9,4,1,2,3]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,9,3,2,1]=>[6,5,7,8,9,1,2,3,4]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,9,8,3,2,1]=>[6,5,8,7,1,2,3,4,9]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,6,4,7,3,8,2,9,1]=>[6,7,5,8,4,9,3,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[6,7,8,9,1,2,3,4,5]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,9,8,4,3,2,1]=>[6,7,8,1,2,3,4,5,9]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[5,7,9,8,6,4,3,2,1]=>[6,8,1,2,3,4,5,7,9]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,8,7,6,9,4,3,2,1]=>[6,9,8,7,1,2,3,4,5]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,9,8,7,6,4,3,2,1]=>[6,1,2,3,4,5,7,8,9]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,9,1]=>[7,6,5,4,3,8,9,1,2]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,5,4,9,8,7,3,2,1]=>[7,6,5,1,2,3,4,8,9]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,4,3,2,1]=>[7,6,8,9,1,2,3,4,5]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[6,5,8,9,7,4,3,2,1]=>[7,6,9,1,2,3,4,5,8]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[6,7,5,9,8,4,3,2,1]=>[7,8,6,1,2,3,4,5,9]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[7,8,9,1,2,3,4,5,6]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,9,8,5,4,3,2,1]=>[7,8,1,2,3,4,5,6,9]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[6,8,7,5,4,3,2,9,1]=>[7,9,8,6,5,4,3,1,2]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[6,8,7,9,5,4,3,2,1]=>[7,9,8,1,2,3,4,5,6]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,9,8,7,5,4,3,2,1]=>[7,1,2,3,4,5,6,8,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,9,1]=>[8,7,6,5,4,3,9,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,6,5,4,3,2,9,8,1]=>[8,7,6,5,4,3,1,2,9]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,6,8,5,4,3,2,9,1]=>[8,7,9,6,5,4,3,1,2]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[7,6,8,5,9,4,3,2,1]=>[8,7,9,6,1,2,3,4,5]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>[8,7,9,1,2,3,4,5,6]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,6,9,8,5,4,3,2,1]=>[8,7,1,2,3,4,5,6,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,8,6,5,4,3,2,9,1]=>[8,9,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[8,9,1,2,3,4,5,6,7]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,9,8,6,5,4,3,2,1]=>[8,1,2,3,4,5,6,7,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1]=>[9,8,7,6,5,4,1,2,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,6,5,1,2,3,4]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,1,2,3,4,5,6]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,7,9,6,5,4,3,2,1]=>[9,8,1,2,3,4,5,6,7]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,7,6,5,4,3,2,1]=>[9,1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8]=>[2,3,4,5,6,7,8,1,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,7]=>[2,3,4,5,6,7,9,1,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,6]=>[2,3,4,5,6,8,9,1,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,5]=>[2,3,4,5,7,8,9,1,6]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,4]=>[2,3,4,6,7,8,9,1,5]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,3]=>[2,3,5,6,7,8,9,1,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,2]=>[2,4,5,6,7,8,9,1,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[2,3,4,5,6,7,8,9,1,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,9,8,7]=>[2,3,4,5,6,7,1,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[2,3,4,5,6,7,8,10,1,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,5,8,7,9,6]=>[2,3,4,5,6,9,8,1,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[2,3,4,5,6,7,9,10,1,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,4,7,6,8,9,5]=>[2,3,4,5,8,7,9,1,6]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[2,3,4,5,6,8,9,10,1,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,9,4]=>[2,3,4,7,6,8,9,1,5]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[2,3,4,5,7,8,9,10,1,6]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,9,3]=>[2,3,6,5,7,8,9,1,4]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[2,3,4,6,7,8,9,10,1,5]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,9,2]=>[2,5,4,6,7,8,9,1,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[2,3,5,6,7,8,9,10,1,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[2,4,5,6,7,8,9,10,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[3,4,5,6,7,8,9,10,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[2,3,4,5,6,7,8,9,10,11,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[2,3,4,5,6,7,8,9,10,1,11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,10,9,8]=>[2,3,4,5,6,7,8,1,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[2,3,4,5,6,7,8,9,11,1,10]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,5,8,9,7,6]=>[2,3,4,5,6,9,1,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,9,8,7,6]=>[2,3,4,5,6,1,7,8,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[4,3,5,6,7,8,9,10,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,11,2]=>[2,4,5,6,7,8,9,10,11,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[3,4,5,6,7,8,9,10,11,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,8,11,10,9]=>[2,3,4,5,6,7,8,9,1,10,11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,6,10,9,8,7]=>[2,3,4,5,6,7,1,8,9,10]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,7,4,8,9,3]=>[2,3,6,7,8,5,9,1,4]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,10,1]=>[4,5,3,6,7,8,9,10,1,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,10,1]=>[5,4,3,6,7,8,9,10,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,11,1]=>[4,3,5,6,7,8,9,10,11,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[2,4,5,6,7,8,9,10,11,12,1,3]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,9,8,7,6,5]=>[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]=>[3,4,5,2,6,7,8,9,10,1]=>[4,5,6,3,7,8,9,10,1,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,10,11,1]=>[4,5,3,6,7,8,9,10,11,1,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5,10,9,8,7,6]=>[2,3,4,5,6,1,7,8,9,10]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,8,3,9,2]=>[2,5,6,7,8,9,4,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,9,10,1]=>[4,5,6,7,3,8,9,10,1,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,9,10,11,1]=>[4,5,6,3,7,8,9,10,11,1,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,9,10,1]=>[6,5,4,3,7,8,9,10,1,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,9,3,2]=>[2,5,6,7,8,9,1,3,4]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,2,8,9,10,1]=>[4,5,6,7,8,3,9,10,1,2]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,9,8,7,6,5,4]=>[2,3,4,1,5,6,7,8,9]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,9,4,3,2]=>[2,6,7,8,9,1,3,4,5]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,8,2,9,10,1]=>[4,5,6,7,8,9,3,10,1,2]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,10,9,8,7,6,5]=>[2,3,4,5,1,6,7,8,9,10]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,2,8,9,10,11,1]=>[4,5,6,7,8,3,9,10,11,1,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,9,10,1]=>[7,6,5,4,3,8,9,10,1,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,9,10,3,2]=>[2,5,6,7,8,9,10,1,3,4]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,2,10,1]=>[4,5,6,7,8,9,10,3,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,2,9,10,11,1]=>[4,5,6,7,8,9,3,10,11,1,2]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,9,10,4,3,2]=>[2,6,7,8,9,10,1,3,4,5]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,9]=>[2,3,4,5,6,7,9,8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9]=>[2,3,4,5,6,8,7,9,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,9,8]=>[2,3,4,5,6,8,7,1,9]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9]=>[2,3,4,5,7,6,8,9,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,9]=>[2,3,4,5,7,6,9,8,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,9,8,7]=>[2,3,4,5,7,6,1,8,9]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9]=>[2,3,4,6,5,7,8,9,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8]=>[2,3,4,6,5,8,7,1,9]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,9,8,7,6]=>[2,3,4,6,5,1,7,8,9]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,3,6,5,4,9,8,7]=>[2,3,4,7,6,5,1,8,9]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9]=>[2,3,5,4,6,7,8,9,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,9]=>[2,3,5,4,7,6,9,8,1]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,9,8,7,6,5]=>[2,3,5,4,1,6,7,8,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9]=>[2,4,3,5,6,7,8,9,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>[2,4,3,5,6,7,8,1,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,6,9,8,7]=>[2,4,3,5,6,7,1,8,9]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8,9]=>[2,4,3,6,5,7,8,9,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[2,4,3,6,5,8,7,1,9]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,9,8,7,6,5,4]=>[2,4,3,1,5,6,7,8,9]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8,9]=>[2,5,4,3,6,7,8,9,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2,9,8,7,6]=>[2,6,5,4,3,1,7,8,9]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,7,6,5,4,3,2,9,8]=>[2,8,7,6,5,4,3,1,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,9,8]=>[3,2,4,5,6,7,8,1,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,6,8,7,9]=>[3,2,4,5,6,7,9,8,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[3,2,5,4,6,7,8,9,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[3,2,5,4,7,6,9,8,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,9,8,7]=>[3,2,5,4,7,6,1,8,9]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,9,8,7,6,5]=>[3,2,5,4,1,6,7,8,9]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,8,7,6,5,4,3,9]=>[3,2,9,8,7,6,5,4,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9]=>[4,3,2,5,6,7,8,9,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8,9]=>[4,3,2,6,5,7,8,9,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6,9,8]=>[4,3,2,6,5,8,7,1,9]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,6,5,4,7,8,9]=>[4,3,2,7,6,5,8,9,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4,9,8,7]=>[4,3,2,7,6,5,1,8,9]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,1,9,8,7,6,5,4]=>[4,3,2,1,5,6,7,8,9]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>[5,4,3,2,6,7,8,9,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,3,2,1,6,5,7,8,9]=>[5,4,3,2,7,6,8,9,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,8,7,9]=>[5,4,3,2,7,6,9,8,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,3,2,1,7,6,5,8,9]=>[5,4,3,2,8,7,6,9,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,3,2,1,7,6,5,9,8]=>[5,4,3,2,8,7,6,1,9]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,8,7,6,5,9]=>[5,4,3,2,9,8,7,6,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,3,2,1,9,8,7,6,5]=>[5,4,3,2,1,6,7,8,9]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>[6,5,4,3,2,7,8,9,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,4,3,2,1,7,6,8,9]=>[6,5,4,3,2,8,7,9,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,4,3,2,1,8,7,6,9]=>[6,5,4,3,2,9,8,7,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4,3,2,1,9,8,7,6]=>[6,5,4,3,2,1,7,8,9]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>[7,6,5,4,3,2,8,9,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,5,4,3,2,1,8,7,9]=>[7,6,5,4,3,2,9,8,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,5,4,3,2,1,9,8,7]=>[7,6,5,4,3,2,1,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,9,8,10]=>[2,3,4,5,6,7,8,10,9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,7,9,10]=>[2,3,4,5,6,7,9,8,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,10,9]=>[2,3,4,5,6,7,9,8,1,10]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9,10]=>[2,3,4,5,6,8,7,9,10,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9,10]=>[2,3,4,5,7,6,8,9,10,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9,10]=>[2,3,4,6,5,7,8,9,10,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8,10]=>[2,3,4,6,5,8,7,10,9,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,10,9,8,7,6,5,4]=>[2,3,4,1,5,6,7,8,9,10]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9,10]=>[2,3,5,4,6,7,8,9,10,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>[2,3,5,4,7,6,9,8,1,10]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3,10,9,8,7]=>[2,3,7,6,5,4,1,8,9,10]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9,10]=>[2,4,3,5,6,7,8,9,10,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,10]=>[2,4,3,6,5,8,7,10,9,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,7,6,10,9,8]=>[2,4,3,6,5,8,7,1,9,10]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,10,9,8,7,6,5,4]=>[2,4,3,1,5,6,7,8,9,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[3,2,4,5,6,7,8,9,10,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,8,10,9]=>[3,2,4,5,6,7,8,9,1,10]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9,10]=>[3,2,5,4,6,7,8,9,10,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>[3,2,5,4,7,6,9,8,1,10]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5,10,9,8]=>[3,2,5,4,8,7,6,1,9,10]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3,10,9,8,7]=>[3,2,7,6,5,4,1,8,9,10]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,8,7,6,5,4,3,10,9]=>[3,2,9,8,7,6,5,4,1,10]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10]=>[4,3,2,5,6,7,8,9,10,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8,9,10]=>[4,3,2,6,5,7,8,9,10,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,9,8,10]=>[4,3,2,6,5,8,7,10,9,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7,10,9]=>[4,3,2,7,6,5,9,8,1,10]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,6,5,4,10,9,8,7]=>[4,3,2,7,6,5,1,8,9,10]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,1,10,9,8,7,6,5,4]=>[4,3,2,1,5,6,7,8,9,10]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9,10]=>[5,4,3,2,6,7,8,9,10,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7,10,9]=>[5,4,3,2,7,6,9,8,1,10]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,6,5,10,9,8,7]=>[5,4,3,2,7,6,1,8,9,10]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5,10,9,8]=>[5,4,3,2,8,7,6,1,9,10]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,8,7,6,5,9,10]=>[5,4,3,2,9,8,7,6,10,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,8,7,6,5,10,9]=>[5,4,3,2,9,8,7,6,1,10]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,1,10,9,8,7,6,5]=>[5,4,3,2,1,6,7,8,9,10]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9,10]=>[6,5,4,3,2,7,8,9,10,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,9,8,10]=>[6,5,4,3,2,8,7,10,9,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,3,2,1,9,8,7,6,10]=>[6,5,4,3,2,10,9,8,7,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1,10,9,8,7,6]=>[6,5,4,3,2,1,7,8,9,10]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9,10]=>[7,6,5,4,3,2,8,9,10,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[6,5,4,3,2,1,9,8,7,10]=>[7,6,5,4,3,2,10,9,8,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,5,4,3,2,1,10,9,8,7]=>[7,6,5,4,3,2,1,8,9,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9,10]=>[8,7,6,5,4,3,2,9,10,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[7,6,5,4,3,2,1,9,8,10]=>[8,7,6,5,4,3,2,10,9,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,6,5,4,3,2,1,10,9,8]=>[8,7,6,5,4,3,2,1,9,10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9]=>[3,4,2,5,6,7,8,9,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9]=>[3,4,5,2,6,7,8,9,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9]=>[3,4,5,6,2,7,8,9,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9]=>[3,4,5,6,7,2,8,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9]=>[3,4,5,6,7,8,2,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,9]=>[3,4,5,6,7,8,9,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,4,2,5,6,7,8,9,10,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9]=>[3,5,4,2,6,7,8,9,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9,10]=>[3,4,5,2,6,7,8,9,10,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8,9]=>[3,4,6,5,2,7,8,9,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9,10]=>[3,4,5,6,2,7,8,9,10,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,4,6,5,1,7,8,9]=>[3,4,5,7,6,2,8,9,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9,10]=>[3,4,5,6,7,2,8,9,10,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,5,7,6,1,8,9]=>[3,4,5,6,8,7,2,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9,10]=>[3,4,5,6,7,8,2,9,10,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,6,8,7,1,9]=>[3,4,5,6,7,9,8,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,1,9,10]=>[3,4,5,6,7,8,9,2,10,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>[3,4,5,6,7,8,9,10,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,8,10,9,4,3,2,1]=>[6,7,8,9,1,2,3,4,5,10]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,10,4,3,2,1]=>[7,6,8,9,10,1,2,3,4,5]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,11,10,4,3,2,1]=>[6,7,8,9,10,1,2,3,4,5,11]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,7,8,10,9,3,2,1]=>[5,6,7,8,9,1,2,3,4,10]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,9,10,3,2,1]=>[6,5,7,8,9,10,1,2,3,4]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,10,11,4,3,2,1]=>[7,6,8,9,10,11,1,2,3,4,5]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[3,2,4,5,6,7,8,9,10,11,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,6,8,9,7]=>[3,2,4,5,6,7,9,1,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,10,9,1]=>[3,4,5,6,7,8,9,1,2,10]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[8,10,9,7,6,5,4,3,2,1]=>[9,1,2,3,4,5,6,7,8,10]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[9,11,10,8,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,7,8,9,11]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,8,10,9,6,5,4,3,2,1]=>[8,9,1,2,3,4,5,6,7,10]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[8,7,9,10,6,5,4,3,2,1]=>[9,8,10,1,2,3,4,5,6,7]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[10,9,11,8,7,6,5,4,3,2,1]=>[11,10,1,2,3,4,5,6,7,8,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,6,7,9,10,8]=>[3,2,4,5,6,7,8,10,1,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,6,8,9,7]=>[3,4,2,5,6,7,9,1,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,6,8,9,7]=>[2,4,3,5,6,7,9,1,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,7,9,8]=>[3,4,2,5,6,7,8,1,9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,8,2,1,9]=>[4,5,6,7,8,9,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,7,2,1,8,9]=>[4,5,6,7,8,3,2,9,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,6,2,1,7,8,9]=>[4,5,6,7,3,2,8,9,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8,9]=>[4,5,6,3,2,7,8,9,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8,9]=>[4,5,3,2,6,7,8,9,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,10,9,8,7,6,5,4,3,1]=>[3,1,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[10,9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,10,9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,9,7,6,5,4,3,2,10,1]=>[9,10,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[6,5,4,3,2,7,1,8,9]=>[7,6,5,4,3,8,2,9,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,2,6,1,7,8,9]=>[6,5,4,3,7,2,8,9,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8,9]=>[5,4,3,6,2,7,8,9,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8,9]=>[4,3,5,2,6,7,8,9,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,10,9,8,6,5,4,3,2,1]=>[8,1,2,3,4,5,6,7,9,10]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,10,9,8,7,5,4,3,2,1]=>[7,1,2,3,4,5,6,8,9,10]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,10,9,8,7,6,4,3,2,1]=>[6,1,2,3,4,5,7,8,9,10]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,10,9,8,7,6,5,3,2,1]=>[5,1,2,3,4,6,7,8,9,10]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,10,9,8,7,6,5,4,2,1]=>[4,1,2,3,5,6,7,8,9,10]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,7,2,1,9,8]=>[4,5,6,7,8,3,2,1,9]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,9,4,3]=>[3,2,6,7,8,9,1,4,5]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,8,3,1,9]=>[3,5,6,7,8,9,4,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,10,3,1]=>[3,5,6,7,8,9,10,1,2,4]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,1,2,3,4,5,6,7,8,9,10]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,9,8,7,6,5,4]=>[3,4,2,1,5,6,7,8,9]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,2,1,9,8,7,6,5]=>[4,5,3,2,1,6,7,8,9]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,3,2,1,9,8,7,6]=>[5,6,4,3,2,1,7,8,9]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,6,4,3,2,1,9,8,7]=>[6,7,5,4,3,2,1,8,9]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8,9]=>[2,4,5,6,3,7,8,9,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8,9]=>[2,3,5,6,4,7,8,9,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6,9,10]=>[2,3,4,5,6,8,9,7,10,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,4,5,7,8,9,6,10]=>[2,3,4,5,6,8,9,10,7,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,7,9,8]=>[3,4,5,6,2,7,8,1,9]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8,9]=>[3,2,5,6,4,7,8,9,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,9,10,1]=>[3,5,6,7,4,8,9,10,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,9,10,1]=>[3,4,6,7,5,8,9,10,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,10,1]=>[3,4,5,7,6,8,9,10,1,2]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,9,10,5,4,3,2]=>[2,7,8,9,10,1,3,4,5,6]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,9,3,2]=>[2,6,5,7,8,9,1,3,4]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,8,1,9]=>[4,3,5,6,7,8,9,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,7,9,8,2]=>[2,4,5,6,7,8,1,3,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8]=>[3,4,5,6,7,8,2,1,9]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,3]=>[3,2,5,6,7,8,9,1,4]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,9,8,7]=>[3,4,5,6,7,2,1,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,10,9,8,1]=>[3,4,5,6,7,8,1,2,9,10]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,9,8,7,6]=>[3,4,5,6,2,1,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,6,9,10,8,7,1]=>[3,4,5,6,7,10,1,2,8,9]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,1,8,9,7,6,5]=>[3,4,5,2,9,1,6,7,8]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,8,9,10,7,6,1]=>[3,4,5,6,9,10,1,2,7,8]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,7,8,9,6,5,4]=>[3,4,2,8,9,1,5,6,7]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,7,8,9,10,6,5,1]=>[3,4,5,8,9,10,1,2,6,7]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,9,5,4,3]=>[3,2,7,8,9,1,4,5,6]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,9,10,5,4,1]=>[3,4,7,8,9,10,1,2,5,6]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,9,10,4,3,1]=>[3,6,7,8,9,10,1,2,4,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[5,6,7,8,9,10,1,2,3,4]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,9,8,7,6,5,3]=>[3,2,5,1,4,6,7,8,9]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,7,6,5,4,2,1,9,8]=>[4,8,7,6,5,3,2,1,9]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,1,6,9,8,7,5,4]=>[4,3,2,7,1,5,6,8,9]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[4,6,5,3,2,1,9,8,7]=>[5,7,6,4,3,2,1,8,9]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,2,1,8,9,7,6,5]=>[5,4,3,2,9,1,6,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,4,3,2,1,8,9,7]=>[7,6,5,4,3,2,9,1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,8,7,6,5,4,1,2,3]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,3,2,1,8,9,7,6]=>[6,5,4,3,2,9,1,7,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,1,8,9,7,6,5,4]=>[4,3,2,9,1,5,6,7,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,5,7,8,9,6]=>[2,3,5,4,6,8,9,1,7]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,10,1]=>[3,4,5,6,8,7,9,10,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7,9]=>[3,4,5,6,7,2,9,8,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,6,8,9]=>[3,4,5,6,2,8,7,9,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,5,7,8,9]=>[3,4,5,2,7,6,8,9,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8,9]=>[3,4,2,6,5,7,8,9,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,8,7,1,9]=>[3,5,4,7,6,9,8,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>[3,4,2,6,5,8,7,1,9]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7,10,9]=>[3,5,4,2,7,6,9,8,1,10]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,10,9,1]=>[3,5,4,7,6,9,8,1,2,10]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,4,2,6,5,8,7,10,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,9,10,8,1]=>[3,4,5,6,7,8,10,1,2,9]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,10,7,1]=>[3,4,5,6,7,9,10,1,2,8]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,10,5,1]=>[3,4,5,7,8,9,10,1,2,6]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,10,4,1]=>[3,4,6,7,8,9,10,1,2,5]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[4,5,6,7,8,9,10,1,2,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,9,11,10,1]=>[3,4,5,6,7,8,9,10,1,2,11]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,8,10,11,9,1]=>[3,4,5,6,7,8,9,11,1,2,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,6,9,8,10,7,1]=>[3,4,5,6,7,10,9,1,2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,7,9,10,11,8,1]=>[3,4,5,6,7,8,10,11,1,2,9]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,10,11,6,1]=>[3,4,5,6,8,9,10,11,1,2,7]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,10,11,5,1]=>[3,4,5,7,8,9,10,11,1,2,6]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,10,11,3,1]=>[3,5,6,7,8,9,10,11,1,2,4]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[4,5,6,7,8,9,10,11,1,2,3]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[8,7,10,9,6,5,4,3,2,1]=>[9,8,1,2,3,4,5,6,7,10]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,10,9,8,4,3,2,1]=>[8,7,6,1,2,3,4,5,9,10]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,10,9,8,7,2,1]=>[7,6,5,4,1,2,3,8,9,10]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,5,7,9,10,8,6,4,2]=>[2,4,6,8,10,1,3,5,7,9]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,7,5,8,4,9,3,10,2]=>[2,7,8,6,9,5,10,4,1,3]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,6,4,7,3,8,2,9,1,10]=>[6,7,5,8,4,9,3,10,2,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,11,10,9,8,7,6,5,4,3]=>[3,2,1,4,5,6,7,8,9,10,11]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,11,10,9,8,7,6,5,4,3,1]=>[3,1,2,4,5,6,7,8,9,10,11]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9,10,11]=>[3,4,2,5,6,7,8,9,10,11,1]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,9,8,7,6,5,3]=>[2,3,5,1,4,6,7,8,9]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,9,8,7,6,4]=>[2,3,4,6,1,5,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,4,6,9,8,7,5]=>[2,3,4,5,7,1,6,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,7,9,8,6]=>[2,3,4,5,6,8,1,7,9]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,9,4]=>[4,3,2,6,7,8,9,1,5]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,9,5]=>[5,4,3,2,7,8,9,1,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,8,7,6,5,4,3,2,1,11,10]=>[10,9,8,7,6,5,4,3,2,1,11]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[6,7,8,9,10,1,2,3,4,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,6,4,3,2,1,7,8,9]=>[6,7,5,4,3,2,8,9,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8,9]=>[5,6,4,3,2,7,8,9,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9]=>[2,4,5,3,6,7,8,9,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,10,3]=>[3,2,5,6,7,8,9,10,1,4]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,9,4]=>[3,4,2,6,7,8,9,1,5]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[9,10,1,2,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[2,3,4,5,6,7,8,9,11,10,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,1,8,9,10,7]=>[3,4,5,6,7,2,9,10,1,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,5,7,8,6,9]=>[2,3,4,5,6,8,9,7,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,7,9,8,4]=>[2,3,4,6,7,8,1,5,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,5,6,8,9,7,10]=>[2,3,4,5,6,7,9,10,8,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,7,2,9,8]=>[2,4,5,6,7,8,3,1,9]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8,9]=>[4,5,3,6,2,7,8,9,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[7,8,9,10,1,2,3,4,5,6]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[8,9,10,1,2,3,4,5,6,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[3,4,5,6,7,8,9,10,11,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,8,2,9]=>[2,4,5,6,7,8,9,3,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,7,6,5,4,3,2,10,9,1]=>[9,8,7,6,5,4,3,1,2,10]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,2,10,9,8,7,6,5,4,1]=>[4,3,1,2,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,4,5,7,6,8,1,9]=>[3,4,5,6,8,7,9,2,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,5,8,7,6,1,9]=>[3,4,5,6,9,8,7,2,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,9,4]=>[3,2,4,6,7,8,9,1,5]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,4,6,8,9,7,5]=>[2,3,4,5,7,9,1,6,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8,9,10]=>[4,5,6,3,2,7,8,9,10,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8,9,10]=>[4,5,3,2,6,7,8,9,10,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,10,9]=>[3,4,5,6,7,8,9,2,1,10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,1,8,9,7]=>[3,4,5,6,7,2,9,1,8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,6,4,3,2,1,7,8,9,10]=>[6,7,5,4,3,2,8,9,10,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,6,4,3,2,7,1,8,9]=>[6,7,5,4,3,8,2,9,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9,10]=>[7,8,6,5,4,3,2,9,10,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9,10,11]=>[7,8,6,5,4,3,2,9,10,11,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,10]=>[2,4,3,6,5,8,7,10,9,1,11]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7,10,9]=>[4,5,3,2,7,6,9,8,1,10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1,10,11]=>[10,9,8,7,6,5,4,3,2,11,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,10,2,11,1]=>[4,5,6,7,8,9,10,11,3,1,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9,10]=>[2,4,5,3,6,7,8,9,10,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,8,9,2,10]=>[2,4,5,6,7,8,9,10,3,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,3,7,8,9,10]=>[2,3,5,6,7,4,8,9,10,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,9,5]=>[3,4,5,2,7,8,9,1,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,6,8,10,9,7]=>[2,3,4,5,6,7,9,1,8,10]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,7,8,4,9,10]=>[2,3,4,6,7,8,9,5,10,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,6,5,4,3,9,8,2]=>[2,8,7,6,5,4,1,3,9]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,3,4,6,7,10,9,8,5]=>[2,3,4,5,7,8,1,6,9,10]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,8,7,9]=>[4,3,5,2,7,6,9,8,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,5,4,6,1,8,7,9]=>[4,3,6,5,7,2,9,8,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7,10,9]=>[4,3,5,2,7,6,9,8,1,10]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7,10,9]=>[4,3,6,5,7,2,9,8,1,10]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,7,6,8,1,10,9]=>[4,3,6,5,8,7,9,2,1,10]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,9,8,10,1]=>[4,3,6,5,8,7,10,9,1,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,9,8,1,10]=>[4,3,6,5,8,7,10,9,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,2,1,7,8,9,6]=>[6,5,4,3,2,8,9,1,7]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,6,8,7,9,2]=>[2,4,5,6,7,9,8,1,3]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,2,8,7,6,5,4,1,9]=>[4,3,9,8,7,6,5,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,7,8,10,9,2]=>[2,4,5,6,7,8,9,1,3,10]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,7,8,3,9]=>[3,2,5,6,7,8,9,4,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,10,1]=>[9,8,7,6,5,4,3,10,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,9,10,1]=>[8,7,6,5,4,3,9,10,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,9,8,10,7]=>[3,2,5,4,7,6,10,9,1,8]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,9,8,10,5]=>[3,2,5,4,8,7,10,9,1,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,9,8,10,3]=>[3,2,6,5,8,7,10,9,1,4]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>[2,4,3,6,5,8,7,10,1,9]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9,10]=>[3,5,4,2,6,7,8,9,10,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,9,5]=>[3,2,5,4,7,8,9,1,6]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8,9,10]=>[4,3,5,2,6,7,8,9,10,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,7,2,8,9]=>[2,4,5,6,7,8,3,9,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,7,9,8,6,4,2]=>[2,4,6,8,1,3,5,7,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,6,7,9,8,1,10]=>[3,4,5,6,7,8,10,9,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,4,6,7,9,8,5]=>[2,3,4,5,7,8,1,6,9]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,9,8,3]=>[2,3,6,5,8,7,1,4,9]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,10,9,2]=>[2,5,4,7,6,9,8,1,3,10]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,4,5,7,8,9,10,6]=>[3,2,4,5,6,8,9,10,1,7]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7,10,9]=>[5,4,6,3,7,2,9,8,1,10]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7,10,9]=>[3,2,6,5,7,4,9,8,1,10]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,6,5,7,4,8,3,10,9]=>[3,2,7,6,8,5,9,4,1,10]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,6,5,7,4,8,1,10,9]=>[4,3,7,6,8,5,9,2,1,10]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,6,5,7,2,8,1,10,9]=>[5,4,7,6,8,3,9,2,1,10]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,4,6,3,7,2,8,1,10,9]=>[6,5,7,4,8,3,9,2,1,10]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,7,6,8,5,10,9]=>[3,2,5,4,8,7,9,6,1,10]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,7,6,8,5,10,9]=>[4,3,5,2,8,7,9,6,1,10]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,7,6,8,1,10,9]=>[5,4,6,3,8,7,9,2,1,10]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,7,6,8,3,10,9]=>[3,2,6,5,8,7,9,4,1,10]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,8,7,9,6,10,5]=>[3,2,5,4,9,8,10,7,1,6]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,8,7,9,6,10,5]=>[4,3,5,2,9,8,10,7,1,6]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,8,7,9,6,10,1]=>[5,4,6,3,9,8,10,7,1,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,8,7,9,6,10,3]=>[3,2,6,5,9,8,10,7,1,4]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,8,7,9,6,10,1]=>[4,3,6,5,9,8,10,7,1,2]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,8,7,9,2,10,1]=>[5,4,7,6,9,8,10,3,1,2]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,8,7,9,2,10,1]=>[6,5,7,4,9,8,10,3,1,2]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,7,6,8,5,9,2,10,1]=>[5,4,8,7,9,6,10,3,1,2]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,7,6,8,3,9,2,10,1]=>[6,5,8,7,9,4,10,3,1,2]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,8,7,9,4,10,3]=>[3,2,7,6,9,8,10,5,1,4]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,8,7,9,4,10,1]=>[4,3,7,6,9,8,10,5,1,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[7,6,8,5,9,4,10,3,1,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,7,6,8,5,9,4,10,3]=>[3,2,8,7,9,6,10,5,1,4]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,7,6,8,5,9,4,10,1]=>[4,3,8,7,9,6,10,5,1,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,6,5,9,8,10,7]=>[4,3,5,2,7,6,10,9,1,8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,5,2,6,1,9,8,10,7]=>[5,4,6,3,7,2,10,9,1,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3,9,8,10,7]=>[3,2,6,5,7,4,10,9,1,8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,5,4,6,1,9,8,10,7]=>[4,3,6,5,7,2,10,9,1,8]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,6,5,7,4,9,8,10,3]=>[3,2,7,6,8,5,10,9,1,4]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,6,5,7,4,9,8,10,1]=>[4,3,7,6,8,5,10,9,1,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,6,5,7,2,9,8,10,1]=>[5,4,7,6,8,3,10,9,1,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,4,6,3,7,2,9,8,10,1]=>[6,5,7,4,8,3,10,9,1,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,9,8,10,5]=>[4,3,5,2,8,7,10,9,1,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,9,8,10,1]=>[5,4,6,3,8,7,10,9,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[3,2,5,4,7,6,9,8,11,10,1,12]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7,10,9,12,11]=>[4,3,5,2,7,6,9,8,11,10,1,12]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7,10,9,12,11]=>[5,4,6,3,7,2,9,8,11,10,1,12]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7,10,9,12,11]=>[3,2,6,5,7,4,9,8,11,10,1,12]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7,10,9,12,11]=>[4,3,6,5,7,2,9,8,11,10,1,12]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,6,5,7,4,8,3,10,9,12,11]=>[3,2,7,6,8,5,9,4,11,10,1,12]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,6,5,7,4,8,1,10,9,12,11]=>[4,3,7,6,8,5,9,2,11,10,1,12]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,6,5,7,2,8,1,10,9,12,11]=>[5,4,7,6,8,3,9,2,11,10,1,12]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,4,6,3,7,2,8,1,10,9,12,11]=>[6,5,7,4,8,3,9,2,11,10,1,12]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,7,6,8,5,10,9,12,11]=>[3,2,5,4,8,7,9,6,11,10,1,12]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,7,6,8,5,10,9,12,11]=>[4,3,5,2,8,7,9,6,11,10,1,12]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,5,2,7,6,8,1,10,9,12,11]=>[5,4,6,3,8,7,9,2,11,10,1,12]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,5,4,7,6,8,3,10,9,12,11]=>[3,2,6,5,8,7,9,4,11,10,1,12]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,5,4,7,6,8,1,10,9,12,11]=>[4,3,6,5,8,7,9,2,11,10,1,12]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,8,7,9,6,10,5,12,11]=>[3,2,5,4,9,8,10,7,11,6,1,12]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,8,7,9,6,10,5,12,11]=>[4,3,5,2,9,8,10,7,11,6,1,12]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,8,7,9,6,10,1,12,11]=>[5,4,6,3,9,8,10,7,11,2,1,12]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,8,7,9,6,10,3,12,11]=>[3,2,6,5,9,8,10,7,11,4,1,12]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,8,7,9,6,10,1,12,11]=>[4,3,6,5,9,8,10,7,11,2,1,12]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,6,5,8,7,9,2,10,1,12,11]=>[5,4,7,6,9,8,10,3,11,2,1,12]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,4,6,3,8,7,9,2,10,1,12,11]=>[6,5,7,4,9,8,10,3,11,2,1,12]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,7,6,8,5,9,2,10,1,12,11]=>[5,4,8,7,9,6,10,3,11,2,1,12]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,4,7,6,8,3,9,2,10,1,12,11]=>[6,5,8,7,9,4,10,3,11,2,1,12]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,6,5,8,7,9,4,10,3,12,11]=>[3,2,7,6,9,8,10,5,11,4,1,12]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,6,5,8,7,9,4,10,1,12,11]=>[4,3,7,6,9,8,10,5,11,2,1,12]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[6,5,7,4,8,3,9,2,10,1,12,11]=>[7,6,8,5,9,4,10,3,11,2,1,12]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,7,6,8,5,9,4,10,3,12,11]=>[3,2,8,7,9,6,10,5,11,4,1,12]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,7,6,8,5,9,4,10,1,12,11]=>[4,3,8,7,9,6,10,5,11,2,1,12]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,9,8,10,7,12,11]=>[3,2,5,4,7,6,10,9,11,8,1,12]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,9,8,10,7,12,11]=>[4,3,5,2,7,6,10,9,11,8,1,12]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,9,8,10,7,12,11]=>[5,4,6,3,7,2,10,9,11,8,1,12]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,9,8,10,7,12,11]=>[3,2,6,5,7,4,10,9,11,8,1,12]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,9,8,10,7,12,11]=>[4,3,6,5,7,2,10,9,11,8,1,12]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,6,5,7,4,9,8,10,3,12,11]=>[3,2,7,6,8,5,10,9,11,4,1,12]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,6,5,7,4,9,8,10,1,12,11]=>[4,3,7,6,8,5,10,9,11,2,1,12]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,6,5,7,2,9,8,10,1,12,11]=>[5,4,7,6,8,3,10,9,11,2,1,12]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,4,6,3,7,2,9,8,10,1,12,11]=>[6,5,7,4,8,3,10,9,11,2,1,12]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,7,6,9,8,10,5,12,11]=>[3,2,5,4,8,7,10,9,11,6,1,12]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,7,6,9,8,10,5,12,11]=>[4,3,5,2,8,7,10,9,11,6,1,12]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,7,6,9,8,10,1,12,11]=>[5,4,6,3,8,7,10,9,11,2,1,12]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,7,6,9,8,10,3,12,11]=>[3,2,6,5,8,7,10,9,11,4,1,12]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,7,6,9,8,10,1,12,11]=>[4,3,6,5,8,7,10,9,11,2,1,12]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,6,5,10,9,11,8,12,7]=>[3,2,5,4,7,6,11,10,12,9,1,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,6,5,10,9,11,8,12,7]=>[4,3,5,2,7,6,11,10,12,9,1,8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1,10,9,11,8,12,7]=>[5,4,6,3,7,2,11,10,12,9,1,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,6,3,10,9,11,8,12,7]=>[3,2,6,5,7,4,11,10,12,9,1,8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,6,1,10,9,11,8,12,7]=>[4,3,6,5,7,2,11,10,12,9,1,8]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,10,9,11,8,12,3]=>[3,2,7,6,8,5,11,10,12,9,1,4]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,10,9,11,8,12,1]=>[4,3,7,6,8,5,11,10,12,9,1,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,10,9,11,8,12,1]=>[5,4,7,6,8,3,11,10,12,9,1,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,10,9,11,8,12,1]=>[6,5,7,4,8,3,11,10,12,9,1,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,7,6,10,9,11,8,12,5]=>[3,2,5,4,8,7,11,10,12,9,1,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,7,6,10,9,11,8,12,5]=>[4,3,5,2,8,7,11,10,12,9,1,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,7,6,10,9,11,8,12,1]=>[5,4,6,3,8,7,11,10,12,9,1,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,7,6,10,9,11,8,12,3]=>[3,2,6,5,8,7,11,10,12,9,1,4]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,7,6,10,9,11,8,12,1]=>[4,3,6,5,8,7,11,10,12,9,1,2]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,8,7,10,9,11,4,12,3]=>[3,2,7,6,9,8,11,10,12,5,1,4]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,8,7,10,9,11,4,12,1]=>[4,3,7,6,9,8,11,10,12,5,1,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,8,3,10,9,11,2,12,1]=>[7,6,8,5,9,4,11,10,12,3,1,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,7,6,8,5,10,9,11,4,12,3]=>[3,2,8,7,9,6,11,10,12,5,1,4]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,7,6,8,5,10,9,11,4,12,1]=>[4,3,8,7,9,6,11,10,12,5,1,2]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,9,8,10,7,11,4,12,3]=>[3,2,7,6,10,9,11,8,12,5,1,4]
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,9,8,10,7,11,4,12,1]=>[4,3,7,6,10,9,11,8,12,5,1,2]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,9,8,10,3,11,2,12,1]=>[7,6,8,5,10,9,11,4,12,3,1,2]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,7,6,9,8,10,5,11,4,12,3]=>[3,2,8,7,10,9,11,6,12,5,1,4]
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,7,6,9,8,10,5,11,4,12,1]=>[4,3,8,7,10,9,11,6,12,5,1,2]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,8,7,10,9,11,2,12,1]=>[5,4,7,6,9,8,11,10,12,3,1,2]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,7,6,8,5,10,9,11,2,12,1]=>[5,4,8,7,9,6,11,10,12,3,1,2]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,8,7,10,9,11,2,12,1]=>[6,5,7,4,9,8,11,10,12,3,1,2]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,4,7,6,8,3,10,9,11,2,12,1]=>[6,5,8,7,9,4,11,10,12,3,1,2]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,8,7,9,4,10,3,11,2,12,1]=>[7,6,9,8,10,5,11,4,12,3,1,2]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[8,7,9,6,10,5,11,4,12,3,1,2]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,9,8,10,7,11,2,12,1]=>[5,4,7,6,10,9,11,8,12,3,1,2]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,7,6,9,8,10,5,11,2,12,1]=>[5,4,8,7,10,9,11,6,12,3,1,2]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,9,8,10,7,11,2,12,1]=>[6,5,7,4,10,9,11,8,12,3,1,2]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,7,6,9,8,10,3,11,2,12,1]=>[6,5,8,7,10,9,11,4,12,3,1,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,8,7,10,9,11,6,12,5]=>[3,2,5,4,9,8,11,10,12,7,1,6]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,8,7,10,9,11,6,12,5]=>[4,3,5,2,9,8,11,10,12,7,1,6]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,8,7,10,9,11,6,12,1]=>[5,4,6,3,9,8,11,10,12,7,1,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,8,7,10,9,11,6,12,3]=>[3,2,6,5,9,8,11,10,12,7,1,4]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,8,7,10,9,11,6,12,1]=>[4,3,6,5,9,8,11,10,12,7,1,2]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,8,7,9,6,10,5,11,4,12,3]=>[3,2,9,8,10,7,11,6,12,5,1,4]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,8,7,9,6,10,5,11,4,12,1]=>[4,3,9,8,10,7,11,6,12,5,1,2]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,8,7,9,6,10,5,11,2,12,1]=>[5,4,9,8,10,7,11,6,12,3,1,2]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,8,7,9,6,10,3,11,2,12,1]=>[6,5,9,8,10,7,11,4,12,3,1,2]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,9,8,10,7,11,6,12,5]=>[3,2,5,4,10,9,11,8,12,7,1,6]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,9,8,10,7,11,6,12,5]=>[4,3,5,2,10,9,11,8,12,7,1,6]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,9,8,10,7,11,6,12,1]=>[5,4,6,3,10,9,11,8,12,7,1,2]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,9,8,10,7,11,6,12,3]=>[3,2,6,5,10,9,11,8,12,7,1,4]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,9,8,10,7,11,6,12,1]=>[4,3,6,5,10,9,11,8,12,7,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,8,7,11,10,12,9]=>[3,2,5,4,7,6,9,8,12,11,1,10]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,6,5,8,7,11,10,12,9]=>[4,3,5,2,7,6,9,8,12,11,1,10]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,5,2,6,1,8,7,11,10,12,9]=>[5,4,6,3,7,2,9,8,12,11,1,10]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3,8,7,11,10,12,9]=>[3,2,6,5,7,4,9,8,12,11,1,10]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,5,4,6,1,8,7,11,10,12,9]=>[4,3,6,5,7,2,9,8,12,11,1,10]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3,11,10,12,9]=>[3,2,7,6,8,5,9,4,12,11,1,10]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1,11,10,12,9]=>[4,3,7,6,8,5,9,2,12,11,1,10]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1,11,10,12,9]=>[5,4,7,6,8,3,9,2,12,11,1,10]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1,11,10,12,9]=>[6,5,7,4,8,3,9,2,12,11,1,10]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5,11,10,12,9]=>[3,2,5,4,8,7,9,6,12,11,1,10]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5,11,10,12,9]=>[4,3,5,2,8,7,9,6,12,11,1,10]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1,11,10,12,9]=>[5,4,6,3,8,7,9,2,12,11,1,10]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3,11,10,12,9]=>[3,2,6,5,8,7,9,4,12,11,1,10]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1,11,10,12,9]=>[4,3,6,5,8,7,9,2,12,11,1,10]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,8,7,9,6,11,10,12,5]=>[3,2,5,4,9,8,10,7,12,11,1,6]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,8,7,9,6,11,10,12,5]=>[4,3,5,2,9,8,10,7,12,11,1,6]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,8,7,9,6,11,10,12,1]=>[5,4,6,3,9,8,10,7,12,11,1,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,8,7,9,6,11,10,12,3]=>[3,2,6,5,9,8,10,7,12,11,1,4]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,8,7,9,6,11,10,12,1]=>[4,3,6,5,9,8,10,7,12,11,1,2]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,6,5,8,7,9,2,11,10,12,1]=>[5,4,7,6,9,8,10,3,12,11,1,2]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,4,6,3,8,7,9,2,11,10,12,1]=>[6,5,7,4,9,8,10,3,12,11,1,2]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,7,6,8,5,9,2,11,10,12,1]=>[5,4,8,7,9,6,10,3,12,11,1,2]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,4,7,6,8,3,9,2,11,10,12,1]=>[6,5,8,7,9,4,10,3,12,11,1,2]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,6,5,8,7,9,4,11,10,12,3]=>[3,2,7,6,9,8,10,5,12,11,1,4]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,6,5,8,7,9,4,11,10,12,1]=>[4,3,7,6,9,8,10,5,12,11,1,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,5,7,4,8,3,9,2,11,10,12,1]=>[7,6,8,5,9,4,10,3,12,11,1,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,7,6,8,5,9,4,11,10,12,3]=>[3,2,8,7,9,6,10,5,12,11,1,4]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,7,6,8,5,9,4,11,10,12,1]=>[4,3,8,7,9,6,10,5,12,11,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,9,8,11,10,12,7]=>[3,2,5,4,7,6,10,9,12,11,1,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,6,5,9,8,11,10,12,7]=>[4,3,5,2,7,6,10,9,12,11,1,8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,6,1,9,8,11,10,12,7]=>[5,4,6,3,7,2,10,9,12,11,1,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,6,3,9,8,11,10,12,7]=>[3,2,6,5,7,4,10,9,12,11,1,8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1,9,8,11,10,12,7]=>[4,3,6,5,7,2,10,9,12,11,1,8]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,6,5,7,4,9,8,11,10,12,3]=>[3,2,7,6,8,5,10,9,12,11,1,4]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,6,5,7,4,9,8,11,10,12,1]=>[4,3,7,6,8,5,10,9,12,11,1,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,6,5,7,2,9,8,11,10,12,1]=>[5,4,7,6,8,3,10,9,12,11,1,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,4,6,3,7,2,9,8,11,10,12,1]=>[6,5,7,4,8,3,10,9,12,11,1,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,9,8,11,10,12,5]=>[3,2,5,4,8,7,10,9,12,11,1,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,9,8,11,10,12,5]=>[4,3,5,2,8,7,10,9,12,11,1,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,9,8,11,10,12,1]=>[5,4,6,3,8,7,10,9,12,11,1,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,9,8,11,10,12,3]=>[3,2,6,5,8,7,10,9,12,11,1,4]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>[4,3,6,5,8,7,10,9,12,11,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8,10]=>[3,4,5,6,7,8,2,10,9,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,10,9,2,1]=>[5,4,7,6,9,8,1,2,3,10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[11,10,9,8,7,6,5,4,3,2,1,12]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,11,10,9,8,7,6,5,4,3]=>[2,3,1,4,5,6,7,8,9,10,11]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7,10,9]=>[2,4,5,3,7,6,9,8,1,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,11,10]=>[3,4,5,6,7,8,9,10,2,1,11]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,1,7,8,9,6]=>[3,4,5,6,2,8,9,1,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,7,8,10,9,1]=>[4,3,5,6,7,8,9,1,2,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,5,4,3,2,1,9,10,8]=>[8,7,6,5,4,3,2,10,1,9]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,8,9,10,7]=>[7,6,5,4,3,2,9,10,1,8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,7,8,9,10,6]=>[6,5,4,3,2,8,9,10,1,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,9,10,5]=>[5,4,3,2,7,8,9,10,1,6]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,9,10,4]=>[4,3,2,6,7,8,9,10,1,5]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,6,9,8,7,2]=>[2,4,5,6,7,1,3,8,9]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7,10,9]=>[3,2,5,7,6,4,9,8,1,10]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,3,6,8,7,5,10,9]=>[3,2,5,4,7,9,8,6,1,10]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,5,8,10,9,7]=>[3,2,5,4,7,6,9,1,8,10]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,5,8,9,7,10,4,3,1]=>[3,7,6,9,10,8,1,2,4,5]
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,11,10,9,8,7,6,5,4,2]=>[2,4,1,3,5,6,7,8,9,10,11]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7,9]=>[2,4,5,3,7,6,9,8,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,10,9,8,1]=>[5,4,3,8,7,6,1,2,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,1,9,10,8]=>[3,4,5,6,7,8,2,10,1,9]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,5,8,9,10,7]=>[3,4,5,2,7,6,9,10,1,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,3,4,6,7,8,10,9,5]=>[2,3,4,5,7,8,9,1,6,10]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,4,5,7,8,10,9,6]=>[2,3,4,5,6,8,9,1,7,10]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,4,6,3,7,2,8,1,9]=>[6,5,7,4,8,3,9,2,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,5,7,4,8,3,9,2]=>[2,7,6,8,5,9,4,1,3]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,7,4,8,3,9,2]=>[2,6,7,8,5,9,4,1,3]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,9,10,5]=>[3,2,5,4,7,8,9,10,1,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,5,8,9,10,7]=>[3,2,5,4,7,6,9,10,1,8]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,1,7,8,9,10,6,5,4,3]=>[3,2,8,9,10,1,4,5,6,7]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,6,5,9,10,8,7]=>[4,5,3,2,7,6,10,1,8,9]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7,9]=>[3,4,5,2,7,6,9,8,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,9,8,10]=>[3,4,5,6,2,8,7,10,9,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,9,8]=>[2,4,5,6,3,8,7,1,9]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,9,8]=>[3,4,5,6,2,8,7,1,9]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,9,8,10]=>[2,4,5,6,3,8,7,10,9,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,8,7,9]=>[3,4,2,5,7,6,9,8,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,3,6,2,7,1,8,9]=>[5,6,4,7,3,8,2,9,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,4,5,7,9,10,8,6]=>[2,3,4,5,6,8,10,1,7,9]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,6,8,9,7,4]=>[2,3,4,6,7,9,1,5,8]
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,10,9,8,7,6,5,3]=>[2,3,5,1,4,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,10,9]=>[3,4,5,6,7,2,9,8,1,10]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7,10,9]=>[3,4,5,2,7,6,9,8,1,10]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,12,10]=>[2,4,3,6,5,8,7,10,9,12,1,11]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,9,8,7,6,4,2]=>[2,4,6,1,3,5,7,8,9]
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5,10,9,8,7,6,4,2]=>[2,4,6,1,3,5,7,8,9,10]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,5,7,10,9,8,6,4,2]=>[2,4,6,8,1,3,5,7,9,10]
Map
to 312-avoiding permutation
Description
Map
Lehmer code rotation
Description
Sends a permutation $\pi$ to the unique permutation $\tau$ (of the same length) such that every entry in the Lehmer code of $\tau$ is cyclically one larger than the Lehmer code of $\pi$.
searching the database
Sorry, this map was not found in the database.