- FindStat

Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Images
=>
            
              Cc0005;cc-rep-0
            

            [1,0]=>[1]=>[1]=>[1]
[1,0,1,0]=>[1,2]=>[1,2]=>[1,2]
[1,1,0,0]=>[2,1]=>[2,1]=>[2,1]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[1,2,3]
[1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[1,3,2]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[2,1,3]
[1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[3,1,2]
[1,1,1,0,0,0]=>[3,2,1]=>[2,3,1]=>[3,2,1]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,2,3]=>[1,4,2,3]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,3,4,2]=>[1,4,3,2]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[3,1,2,4]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[4,1,2,3]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[3,4,1,2]=>[4,1,3,2]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[2,3,1,4]=>[3,2,1,4]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[2,4,1,3]=>[4,2,1,3]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,1,3,2]=>[4,3,1,2]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[3,2,4,1]=>[4,3,2,1]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,3,4]=>[1,2,5,3,4]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,2,4,5,3]=>[1,2,5,4,3]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,2,3,5]=>[1,4,2,3,5]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,2,3,4]=>[1,5,2,3,4]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,4,5,2,3]=>[1,5,2,4,3]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,3,4,2,5]=>[1,4,3,2,5]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,3,5,2,4]=>[1,5,3,2,4]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[1,5,2,4,3]=>[1,5,4,2,3]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,4,3,5,2]=>[1,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,3,4]=>[2,1,5,3,4]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,4,5,3]=>[2,1,5,4,3]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,1,2,5,4]=>[3,1,2,5,4]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[4,1,2,3,5]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[5,1,2,3,4]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[4,5,1,2,3]=>[5,1,2,4,3]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[3,4,1,2,5]=>[4,1,3,2,5]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[3,5,1,2,4]=>[5,1,3,2,4]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,1,2,4,3]=>[5,1,4,2,3]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[4,3,5,1,2]=>[5,1,4,3,2]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[3,2,1,4,5]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[2,3,1,5,4]=>[3,2,1,5,4]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[2,4,1,3,5]=>[4,2,1,3,5]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[2,5,1,3,4]=>[5,2,1,3,4]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[2,4,5,1,3]=>[5,2,1,4,3]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,1,3,2,5]=>[4,3,1,2,5]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,1,3,2,4]=>[5,3,1,2,4]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[4,2,5,1,3]=>[5,4,1,2,3]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,1,3,4,2]=>[5,4,1,3,2]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[3,2,4,1,5]=>[4,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[3,2,5,1,4]=>[5,3,2,1,4]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,1,4,2,3]=>[5,4,2,1,3]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[3,5,1,4,2]=>[5,4,3,1,2]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[3,4,2,5,1]=>[5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,2,5,6,3,4]=>[1,2,6,3,5,4]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,2,4,6,3,5]=>[1,2,6,4,3,5]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[1,2,6,3,5,4]=>[1,2,6,5,3,4]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>[1,6,2,3,5,4]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,4,5,2,3,6]=>[1,5,2,4,3,6]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>[1,6,2,4,3,5]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[1,6,2,3,5,4]=>[1,6,2,5,3,4]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,5,4,6,2,3]=>[1,6,2,5,4,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,3,5,2,4,6]=>[1,5,3,2,4,6]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>[1,6,3,2,4,5]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,3,5,6,2,4]=>[1,6,3,2,5,4]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[1,5,2,4,3,6]=>[1,5,4,2,3,6]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[1,6,2,4,3,5]=>[1,6,4,2,3,5]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[1,5,3,6,2,4]=>[1,6,5,2,3,4]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[1,6,2,4,5,3]=>[1,6,5,2,4,3]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,4,3,6,2,5]=>[1,6,4,3,2,5]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[1,6,2,5,3,4]=>[1,6,5,3,2,4]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[1,4,6,2,5,3]=>[1,6,5,4,2,3]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,5,6,3,4]=>[2,1,6,3,5,4]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,4,6,3,5]=>[2,1,6,4,3,5]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[2,1,6,3,5,4]=>[2,1,6,5,3,4]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[3,1,2,5,6,4]=>[3,1,2,6,5,4]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,1,2,3,5,4]=>[6,1,2,5,3,4]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[3,4,1,2,6,5]=>[4,1,3,2,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,1,2,4,3,6]=>[5,1,4,2,3,6]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,1,2,4,3,5]=>[6,1,4,2,3,5]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,1,2,4,5,3]=>[6,1,5,2,4,3]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>[6,1,4,3,2,5]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,1,2,5,3,4]=>[6,1,5,3,2,4]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[4,6,1,2,5,3]=>[6,1,5,4,2,3]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[2,3,1,6,4,5]=>[3,2,1,6,4,5]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[2,4,1,3,6,5]=>[4,2,1,3,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[2,4,5,1,3,6]=>[5,2,1,4,3,6]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[2,6,1,3,5,4]=>[6,2,1,5,3,4]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[2,5,4,6,1,3]=>[6,2,1,5,4,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>[4,3,1,2,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[4,1,3,2,6,5]=>[4,3,1,2,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,1,3,2,4,6]=>[5,3,1,2,4,6]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,1,3,2,4,5]=>[6,3,1,2,4,5]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[5,6,1,3,2,4]=>[6,3,1,2,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[4,2,6,1,3,5]=>[6,4,1,2,3,5]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,1,3,5,2,4]=>[6,5,1,2,3,4]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[5,2,4,6,1,3]=>[6,5,1,2,4,3]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,1,3,4,2,6]=>[5,4,1,3,2,6]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,1,3,4,2,5]=>[6,4,1,3,2,5]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[4,5,2,6,1,3]=>[6,5,1,4,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[4,6,1,3,5,2]=>[6,5,1,4,3,2]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[3,2,5,1,4,6]=>[5,3,2,1,4,6]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>[6,3,2,1,4,5]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[3,2,5,6,1,4]=>[6,3,2,1,5,4]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,1,4,2,3,6]=>[5,4,2,1,3,6]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,1,4,2,3,5]=>[6,4,2,1,3,5]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[5,2,3,6,1,4]=>[6,5,2,1,3,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,1,4,5,2,3]=>[6,5,2,1,4,3]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[3,5,1,4,2,6]=>[5,4,3,1,2,6]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[3,6,1,4,2,5]=>[6,4,3,1,2,5]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[3,5,2,6,1,4]=>[6,5,3,1,2,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[5,2,6,1,4,3]=>[6,5,4,1,2,3]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,1,4,3,5,2]=>[6,5,4,1,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[3,4,2,6,1,5]=>[6,4,3,2,1,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[3,6,1,5,2,4]=>[6,5,3,2,1,4]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,1,5,2,4,3]=>[6,5,4,2,1,3]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[4,3,6,1,5,2]=>[6,5,4,3,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[1,2,3,7,4,6,5]=>[1,2,3,7,6,4,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,2,6,7,3,4,5]=>[1,2,7,3,4,6,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[1,2,7,3,4,6,5]=>[1,2,7,3,6,4,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,2,6,5,7,3,4]=>[1,2,7,3,6,5,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[1,2,6,3,5,4,7]=>[1,2,6,5,3,4,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[1,2,7,3,5,4,6]=>[1,2,7,5,3,4,6]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[1,2,6,4,7,3,5]=>[1,2,7,6,3,4,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[1,2,7,3,5,6,4]=>[1,2,7,6,3,5,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,2,5,4,7,3,6]=>[1,2,7,5,4,3,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[1,2,7,3,6,4,5]=>[1,2,7,6,4,3,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[1,2,5,7,3,6,4]=>[1,2,7,6,5,3,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[1,3,2,7,4,6,5]=>[1,3,2,7,6,4,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>[1,7,2,3,4,6,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,5,6,2,3,4,7]=>[1,6,2,3,5,4,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>[1,7,2,3,5,4,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[1,7,2,3,4,6,5]=>[1,7,2,3,6,4,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,6,5,7,2,3,4]=>[1,7,2,3,6,5,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,4,6,7,2,3,5]=>[1,7,2,4,3,6,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[1,6,2,3,5,4,7]=>[1,6,2,5,3,4,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[1,7,2,3,5,4,6]=>[1,7,2,5,3,4,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[1,6,4,7,2,3,5]=>[1,7,2,6,3,4,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[1,7,2,3,5,6,4]=>[1,7,2,6,3,5,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,5,4,6,2,3,7]=>[1,6,2,5,4,3,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,5,4,7,2,3,6]=>[1,7,2,5,4,3,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[1,7,2,3,6,4,5]=>[1,7,2,6,4,3,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[1,5,7,2,3,6,4]=>[1,7,2,6,5,3,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,5,6,4,7,2,3]=>[1,7,2,6,5,4,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,3,6,7,2,4,5]=>[1,7,3,2,4,6,5]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[1,3,7,2,4,6,5]=>[1,7,3,2,6,4,5]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,3,6,5,7,2,4]=>[1,7,3,2,6,5,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[1,5,2,4,3,6,7]=>[1,5,4,2,3,6,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[1,5,2,4,3,7,6]=>[1,5,4,2,3,7,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[1,6,2,4,3,5,7]=>[1,6,4,2,3,5,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[1,7,2,4,3,5,6]=>[1,7,4,2,3,5,6]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[1,6,7,2,4,3,5]=>[1,7,4,2,3,6,5]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[1,5,3,6,2,4,7]=>[1,6,5,2,3,4,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[1,5,3,7,2,4,6]=>[1,7,5,2,3,4,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[1,7,2,4,6,3,5]=>[1,7,6,2,3,4,5]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[1,6,3,5,7,2,4]=>[1,7,6,2,3,5,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[1,6,2,4,5,3,7]=>[1,6,5,2,4,3,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[1,7,2,4,5,3,6]=>[1,7,5,2,4,3,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[1,6,3,7,2,4,5]=>[1,7,6,2,4,3,5]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[1,5,6,3,7,2,4]=>[1,7,6,2,5,3,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[1,5,7,2,4,6,3]=>[1,7,6,2,5,4,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,4,3,6,2,5,7]=>[1,6,4,3,2,5,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,4,3,7,2,5,6]=>[1,7,4,3,2,5,6]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,4,3,6,7,2,5]=>[1,7,4,3,2,6,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[1,6,2,5,3,4,7]=>[1,6,5,3,2,4,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[1,7,2,5,3,4,6]=>[1,7,5,3,2,4,6]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[1,6,3,4,7,2,5]=>[1,7,6,3,2,4,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[1,7,2,5,6,3,4]=>[1,7,6,3,2,5,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[1,4,6,2,5,3,7]=>[1,6,5,4,2,3,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[1,4,7,2,5,3,6]=>[1,7,5,4,2,3,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[1,4,6,3,7,2,5]=>[1,7,6,4,2,3,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[1,6,3,7,2,5,4]=>[1,7,6,5,2,3,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[1,7,2,5,4,6,3]=>[1,7,6,5,2,4,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,4,5,3,7,2,6]=>[1,7,5,4,3,2,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[1,4,7,2,6,3,5]=>[1,7,6,4,3,2,5]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[1,7,2,6,3,5,4]=>[1,7,6,5,3,2,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[1,5,4,7,2,6,3]=>[1,7,6,5,4,2,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[2,1,3,7,4,6,5]=>[2,1,3,7,6,4,5]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,6,7,3,4,5]=>[2,1,7,3,4,6,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[2,1,7,3,4,6,5]=>[2,1,7,3,6,4,5]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,6,5,7,3,4]=>[2,1,7,3,6,5,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[2,1,6,3,5,4,7]=>[2,1,6,5,3,4,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[2,1,7,3,5,4,6]=>[2,1,7,5,3,4,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[2,1,6,4,7,3,5]=>[2,1,7,6,3,4,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[2,1,7,3,5,6,4]=>[2,1,7,6,3,5,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,5,4,7,3,6]=>[2,1,7,5,4,3,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[2,1,7,3,6,4,5]=>[2,1,7,6,4,3,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[2,1,5,7,3,6,4]=>[2,1,7,6,5,3,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[3,1,2,7,4,6,5]=>[3,1,2,7,6,4,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[3,1,2,6,5,7,4]=>[3,1,2,7,6,5,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[7,1,2,3,4,6,5]=>[7,1,2,3,6,4,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[4,5,1,2,3,7,6]=>[5,1,2,4,3,7,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[6,1,2,3,5,4,7]=>[6,1,2,5,3,4,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[7,1,2,3,5,4,6]=>[7,1,2,5,3,4,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[6,4,7,1,2,3,5]=>[7,1,2,6,3,4,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,1,2,3,5,6,4]=>[7,1,2,6,3,5,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[5,4,7,1,2,3,6]=>[7,1,2,5,4,3,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[7,1,2,3,6,4,5]=>[7,1,2,6,4,3,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[5,7,1,2,3,6,4]=>[7,1,2,6,5,3,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[3,7,1,2,4,6,5]=>[7,1,3,2,6,4,5]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[3,6,5,7,1,2,4]=>[7,1,3,2,6,5,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[5,1,2,4,3,6,7]=>[5,1,4,2,3,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[5,1,2,4,3,7,6]=>[5,1,4,2,3,7,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[6,1,2,4,3,5,7]=>[6,1,4,2,3,5,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[7,1,2,4,3,5,6]=>[7,1,4,2,3,5,6]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[6,7,1,2,4,3,5]=>[7,1,4,2,3,6,5]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[5,3,6,1,2,4,7]=>[6,1,5,2,3,4,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[5,3,7,1,2,4,6]=>[7,1,5,2,3,4,6]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[7,1,2,4,6,3,5]=>[7,1,6,2,3,4,5]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[6,3,5,7,1,2,4]=>[7,1,6,2,3,5,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,1,2,4,5,3,7]=>[6,1,5,2,4,3,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[7,1,2,4,5,3,6]=>[7,1,5,2,4,3,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[6,3,7,1,2,4,5]=>[7,1,6,2,4,3,5]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[5,6,3,7,1,2,4]=>[7,1,6,2,5,3,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[5,7,1,2,4,6,3]=>[7,1,6,2,5,4,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[4,3,5,1,2,7,6]=>[5,1,4,3,2,7,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[4,3,6,1,2,5,7]=>[6,1,4,3,2,5,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[4,3,7,1,2,5,6]=>[7,1,4,3,2,5,6]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[4,3,6,7,1,2,5]=>[7,1,4,3,2,6,5]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[6,1,2,5,3,4,7]=>[6,1,5,3,2,4,7]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[7,1,2,5,3,4,6]=>[7,1,5,3,2,4,6]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>[7,1,6,3,2,4,5]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,1,2,5,6,3,4]=>[7,1,6,3,2,5,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[4,6,1,2,5,3,7]=>[6,1,5,4,2,3,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[4,7,1,2,5,3,6]=>[7,1,5,4,2,3,6]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[4,6,3,7,1,2,5]=>[7,1,6,4,2,3,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[6,3,7,1,2,5,4]=>[7,1,6,5,2,3,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,1,2,5,4,6,3]=>[7,1,6,5,2,4,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[4,5,3,7,1,2,6]=>[7,1,5,4,3,2,6]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[4,7,1,2,6,3,5]=>[7,1,6,4,3,2,5]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[7,1,2,6,3,5,4]=>[7,1,6,5,3,2,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[5,4,7,1,2,6,3]=>[7,1,6,5,4,2,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[2,3,1,7,4,6,5]=>[3,2,1,7,6,4,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[2,7,1,3,4,6,5]=>[7,2,1,3,6,4,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[2,6,5,7,1,3,4]=>[7,2,1,3,6,5,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[2,4,6,7,1,3,5]=>[7,2,1,4,3,6,5]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[2,6,1,3,5,4,7]=>[6,2,1,5,3,4,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[2,7,1,3,5,4,6]=>[7,2,1,5,3,4,6]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[2,6,4,7,1,3,5]=>[7,2,1,6,3,4,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[2,7,1,3,5,6,4]=>[7,2,1,6,3,5,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[2,5,4,6,1,3,7]=>[6,2,1,5,4,3,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[2,5,4,7,1,3,6]=>[7,2,1,5,4,3,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[2,7,1,3,6,4,5]=>[7,2,1,6,4,3,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[2,5,7,1,3,6,4]=>[7,2,1,6,5,3,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[2,5,6,4,7,1,3]=>[7,2,1,6,5,4,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[4,1,3,2,5,6,7]=>[4,3,1,2,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[4,1,3,2,5,7,6]=>[4,3,1,2,5,7,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[4,1,3,2,6,5,7]=>[4,3,1,2,6,5,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[4,1,3,2,7,5,6]=>[4,3,1,2,7,5,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[4,1,3,2,6,7,5]=>[4,3,1,2,7,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[5,1,3,2,4,6,7]=>[5,3,1,2,4,6,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[5,1,3,2,4,7,6]=>[5,3,1,2,4,7,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[6,1,3,2,4,5,7]=>[6,3,1,2,4,5,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[7,1,3,2,4,5,6]=>[7,3,1,2,4,5,6]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[6,7,1,3,2,4,5]=>[7,3,1,2,4,6,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[5,6,1,3,2,4,7]=>[6,3,1,2,5,4,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[5,7,1,3,2,4,6]=>[7,3,1,2,5,4,6]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[7,1,3,2,4,6,5]=>[7,3,1,2,6,4,5]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[6,5,7,1,3,2,4]=>[7,3,1,2,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[4,2,5,1,3,6,7]=>[5,4,1,2,3,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[4,2,5,1,3,7,6]=>[5,4,1,2,3,7,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[4,2,6,1,3,5,7]=>[6,4,1,2,3,5,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[4,2,7,1,3,5,6]=>[7,4,1,2,3,5,6]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[4,2,6,7,1,3,5]=>[7,4,1,2,3,6,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[6,1,3,5,2,4,7]=>[6,5,1,2,3,4,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,1,3,5,2,4,6]=>[7,5,1,2,3,4,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[6,2,4,7,1,3,5]=>[7,6,1,2,3,4,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,1,3,5,6,2,4]=>[7,6,1,2,3,5,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[5,2,4,6,1,3,7]=>[6,5,1,2,4,3,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[5,2,4,7,1,3,6]=>[7,5,1,2,4,3,6]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[7,1,3,6,2,4,5]=>[7,6,1,2,4,3,5]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[5,7,1,3,6,2,4]=>[7,6,1,2,5,3,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[5,6,2,4,7,1,3]=>[7,6,1,2,5,4,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,1,3,4,2,6,7]=>[5,4,1,3,2,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[5,1,3,4,2,7,6]=>[5,4,1,3,2,7,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[6,1,3,4,2,5,7]=>[6,4,1,3,2,5,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[7,1,3,4,2,5,6]=>[7,4,1,3,2,5,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[6,7,1,3,4,2,5]=>[7,4,1,3,2,6,5]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[5,2,6,1,3,4,7]=>[6,5,1,3,2,4,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[5,2,7,1,3,4,6]=>[7,5,1,3,2,4,6]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[7,1,3,4,6,2,5]=>[7,6,1,3,2,4,5]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[6,2,5,7,1,3,4]=>[7,6,1,3,2,5,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[4,5,2,6,1,3,7]=>[6,5,1,4,2,3,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[4,5,2,7,1,3,6]=>[7,5,1,4,2,3,6]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[4,7,1,3,6,2,5]=>[7,6,1,4,2,3,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[7,1,3,6,2,5,4]=>[7,6,1,5,2,3,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[6,2,5,4,7,1,3]=>[7,6,1,5,2,4,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[4,6,1,3,5,2,7]=>[6,5,1,4,3,2,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[4,7,1,3,5,2,6]=>[7,5,1,4,3,2,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[4,6,2,7,1,3,5]=>[7,6,1,4,3,2,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[6,2,7,1,3,5,4]=>[7,6,1,5,3,2,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[5,4,6,2,7,1,3]=>[7,6,1,5,4,2,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[5,4,7,1,3,6,2]=>[7,6,1,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[3,2,4,1,7,5,6]=>[4,3,2,1,7,5,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[3,2,5,1,4,6,7]=>[5,3,2,1,4,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[3,2,5,1,4,7,6]=>[5,3,2,1,4,7,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[3,2,6,1,4,5,7]=>[6,3,2,1,4,5,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[3,2,7,1,4,5,6]=>[7,3,2,1,4,5,6]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[3,2,6,7,1,4,5]=>[7,3,2,1,4,6,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[3,2,5,6,1,4,7]=>[6,3,2,1,5,4,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[3,2,5,7,1,4,6]=>[7,3,2,1,5,4,6]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[3,2,7,1,4,6,5]=>[7,3,2,1,6,4,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[3,2,6,5,7,1,4]=>[7,3,2,1,6,5,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[5,1,4,2,3,6,7]=>[5,4,2,1,3,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[5,1,4,2,3,7,6]=>[5,4,2,1,3,7,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[6,1,4,2,3,5,7]=>[6,4,2,1,3,5,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[7,1,4,2,3,5,6]=>[7,4,2,1,3,5,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[6,7,1,4,2,3,5]=>[7,4,2,1,3,6,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[5,2,3,6,1,4,7]=>[6,5,2,1,3,4,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[5,2,3,7,1,4,6]=>[7,5,2,1,3,4,6]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[7,1,4,6,2,3,5]=>[7,6,2,1,3,4,5]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[6,2,3,5,7,1,4]=>[7,6,2,1,3,5,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,1,4,5,2,3,7]=>[6,5,2,1,4,3,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,1,4,5,2,3,6]=>[7,5,2,1,4,3,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[6,2,3,7,1,4,5]=>[7,6,2,1,4,3,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[5,6,2,3,7,1,4]=>[7,6,2,1,5,3,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[5,7,1,4,6,2,3]=>[7,6,2,1,5,4,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[3,5,1,4,2,6,7]=>[5,4,3,1,2,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[3,5,1,4,2,7,6]=>[5,4,3,1,2,7,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[3,6,1,4,2,5,7]=>[6,4,3,1,2,5,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[3,7,1,4,2,5,6]=>[7,4,3,1,2,5,6]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[3,6,7,1,4,2,5]=>[7,4,3,1,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[3,5,2,6,1,4,7]=>[6,5,3,1,2,4,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[3,5,2,7,1,4,6]=>[7,5,3,1,2,4,6]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[3,7,1,4,6,2,5]=>[7,6,3,1,2,4,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[3,6,2,5,7,1,4]=>[7,6,3,1,2,5,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[5,2,6,1,4,3,7]=>[6,5,4,1,2,3,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[5,2,7,1,4,3,6]=>[7,5,4,1,2,3,6]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[7,1,4,3,6,2,5]=>[7,6,4,1,2,3,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[6,2,5,3,7,1,4]=>[7,6,5,1,2,3,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,1,4,6,2,5,3]=>[7,6,5,1,2,4,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,1,4,3,5,2,7]=>[6,5,4,1,3,2,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,1,4,3,5,2,6]=>[7,5,4,1,3,2,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[6,2,7,1,4,3,5]=>[7,6,4,1,3,2,5]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[5,3,6,2,7,1,4]=>[7,6,5,1,3,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[6,2,7,1,4,5,3]=>[7,6,5,1,4,2,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,1,4,5,3,6,2]=>[7,6,5,1,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[3,4,2,6,1,5,7]=>[6,4,3,2,1,5,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[3,4,2,7,1,5,6]=>[7,4,3,2,1,5,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[3,4,2,6,7,1,5]=>[7,4,3,2,1,6,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[3,6,1,5,2,4,7]=>[6,5,3,2,1,4,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[3,7,1,5,2,4,6]=>[7,5,3,2,1,4,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[3,6,2,4,7,1,5]=>[7,6,3,2,1,4,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[3,7,1,5,6,2,4]=>[7,6,3,2,1,5,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[6,1,5,2,4,3,7]=>[6,5,4,2,1,3,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,1,5,2,4,3,6]=>[7,5,4,2,1,3,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[6,2,4,3,7,1,5]=>[7,6,4,2,1,3,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[7,1,5,3,6,2,4]=>[7,6,5,2,1,3,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[6,2,4,7,1,5,3]=>[7,6,5,2,1,4,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[4,3,6,1,5,2,7]=>[6,5,4,3,1,2,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[4,3,7,1,5,2,6]=>[7,5,4,3,1,2,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[4,3,6,2,7,1,5]=>[7,6,4,3,1,2,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[6,2,7,1,5,3,4]=>[7,6,5,3,1,2,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[4,6,2,7,1,5,3]=>[7,6,5,4,1,2,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[4,7,1,5,3,6,2]=>[7,6,5,4,1,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[4,3,5,2,7,1,6]=>[7,5,4,3,2,1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[4,3,7,1,6,2,5]=>[7,6,4,3,2,1,5]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,1,6,2,5,3,4]=>[7,6,5,3,2,1,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[4,7,1,6,2,5,3]=>[7,6,5,4,2,1,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[4,5,3,7,1,6,2]=>[7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,5,6,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,5,7,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,8,6,5,7]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,8,7,5,6]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,4,5,8,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,8,4,5,6]=>[1,2,3,8,4,5,7,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>[1,2,3,6,7,4,5,8]=>[1,2,3,7,4,6,5,8]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[1,2,3,6,8,4,5,7]=>[1,2,3,8,4,6,5,7]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,4,5,7,6]=>[1,2,3,8,4,7,5,6]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[1,2,3,7,6,8,4,5]=>[1,2,3,8,4,7,6,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>[1,2,3,5,7,4,6,8]=>[1,2,3,7,5,4,6,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[1,2,3,5,8,4,6,7]=>[1,2,3,8,5,4,6,7]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[1,2,3,5,7,8,4,6]=>[1,2,3,8,5,4,7,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,5,4,8]=>[1,2,3,7,4,6,5,8]=>[1,2,3,7,6,4,5,8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,4,6,5,7]=>[1,2,3,8,6,4,5,7]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[1,2,3,7,5,8,4,6]=>[1,2,3,8,7,4,5,6]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,4,6,7,5]=>[1,2,3,8,7,4,6,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[1,2,3,6,5,7,4,8]=>[1,2,3,7,6,5,4,8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[1,2,3,6,5,8,4,7]=>[1,2,3,8,6,5,4,7]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,4,7,5,6]=>[1,2,3,8,7,5,4,6]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>[1,2,3,6,8,4,7,5]=>[1,2,3,8,7,6,4,5]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,7,5,6,8]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,8,5,7,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,7,6,5,8]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,6,8,5,7]=>[1,2,4,3,8,6,5,7]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,6,5]=>[1,2,4,3,8,5,7,6]=>[1,2,4,3,8,7,5,6]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>[1,2,5,3,4,6,7,8]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,3,4,6,8,7]=>[1,2,5,3,4,6,8,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6,8]=>[1,2,5,3,4,7,6,8]=>[1,2,5,3,4,7,6,8]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,4,5,3,7,8,6]=>[1,2,5,3,4,8,6,7]=>[1,2,5,3,4,8,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>[1,2,5,3,4,7,8,6]=>[1,2,5,3,4,8,7,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>[1,2,6,3,4,5,7,8]=>[1,2,6,3,4,5,7,8]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,6,3,8,7]=>[1,2,6,3,4,5,8,7]=>[1,2,6,3,4,5,8,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,7,3,8]=>[1,2,7,3,4,5,6,8]=>[1,2,7,3,4,5,6,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,7,3]=>[1,2,7,8,3,4,5,6]=>[1,2,8,3,4,5,7,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,4,5,7,6,3,8]=>[1,2,6,7,3,4,5,8]=>[1,2,7,3,4,6,5,8]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,7,8,6,3]=>[1,2,8,3,4,5,7,6]=>[1,2,8,3,4,7,5,6]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,4,5,8,7,6,3]=>[1,2,7,6,8,3,4,5]=>[1,2,8,3,4,7,6,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,5,3,7,8]=>[1,2,5,6,3,4,7,8]=>[1,2,6,3,5,4,7,8]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,4,6,5,3,8,7]=>[1,2,5,6,3,4,8,7]=>[1,2,6,3,5,4,8,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,4,6,5,7,3,8]=>[1,2,5,7,3,4,6,8]=>[1,2,7,3,5,4,6,8]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,4,6,5,7,8,3]=>[1,2,5,8,3,4,6,7]=>[1,2,8,3,5,4,6,7]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,5,8,7,3]=>[1,2,5,7,8,3,4,6]=>[1,2,8,3,5,4,7,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,4,6,7,5,3,8]=>[1,2,7,3,4,6,5,8]=>[1,2,7,3,6,4,5,8]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,4,6,7,5,8,3]=>[1,2,8,3,4,6,5,7]=>[1,2,8,3,6,4,5,7]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,5,3]=>[1,2,7,5,8,3,4,6]=>[1,2,8,3,7,4,5,6]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,7,5,3]=>[1,2,8,3,4,6,7,5]=>[1,2,8,3,7,4,6,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,4,7,6,5,3,8]=>[1,2,6,5,7,3,4,8]=>[1,2,7,3,6,5,4,8]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,6,5,8,3]=>[1,2,6,5,8,3,4,7]=>[1,2,8,3,6,5,4,7]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,6,8,5,3]=>[1,2,8,3,4,7,5,6]=>[1,2,8,3,7,5,4,6]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>[1,2,6,8,3,4,7,5]=>[1,2,8,3,7,6,4,5]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[1,2,6,7,5,8,3,4]=>[1,2,8,3,7,6,5,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,4,3,6,7,8]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,5,4,3,7,6,8]=>[1,2,4,5,3,7,6,8]=>[1,2,5,4,3,7,6,8]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,5,4,6,3,7,8]=>[1,2,4,6,3,5,7,8]=>[1,2,6,4,3,5,7,8]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,5,4,6,3,8,7]=>[1,2,4,6,3,5,8,7]=>[1,2,6,4,3,5,8,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>[1,2,4,7,3,5,6,8]=>[1,2,7,4,3,5,6,8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,3]=>[1,2,4,8,3,5,6,7]=>[1,2,8,4,3,5,6,7]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>[1,2,4,7,8,3,5,6]=>[1,2,8,4,3,5,7,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,5,4,7,6,3,8]=>[1,2,4,6,7,3,5,8]=>[1,2,7,4,3,6,5,8]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,4,7,6,8,3]=>[1,2,4,6,8,3,5,7]=>[1,2,8,4,3,6,5,7]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,4,7,8,6,3]=>[1,2,4,8,3,5,7,6]=>[1,2,8,4,3,7,5,6]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>[1,2,4,7,6,8,3,5]=>[1,2,8,4,3,7,6,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,4,3,7,8]=>[1,2,6,3,5,4,7,8]=>[1,2,6,5,3,4,7,8]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,4,7,3,8]=>[1,2,7,3,5,4,6,8]=>[1,2,7,5,3,4,6,8]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,4,7,8,3]=>[1,2,8,3,5,4,6,7]=>[1,2,8,5,3,4,6,7]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,5,6,4,8,7,3]=>[1,2,7,8,3,5,4,6]=>[1,2,8,5,3,4,7,6]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,5,6,7,4,3,8]=>[1,2,6,4,7,3,5,8]=>[1,2,7,6,3,4,5,8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,4,8,3]=>[1,2,6,4,8,3,5,7]=>[1,2,8,6,3,4,5,7]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[1,2,8,3,5,7,4,6]=>[1,2,8,7,3,4,5,6]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,7,4,3]=>[1,2,7,4,6,8,3,5]=>[1,2,8,7,3,4,6,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,6,4,8,3]=>[1,2,8,3,5,6,4,7]=>[1,2,8,6,3,5,4,7]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,6,8,4,3]=>[1,2,7,4,8,3,5,6]=>[1,2,8,7,3,5,4,6]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,8,6,4,3]=>[1,2,6,7,4,8,3,5]=>[1,2,8,7,3,6,4,5]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>[1,2,5,4,6,3,7,8]=>[1,2,6,5,4,3,7,8]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,6,5,4,3,8,7]=>[1,2,5,4,6,3,8,7]=>[1,2,6,5,4,3,8,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>[1,2,5,4,8,3,6,7]=>[1,2,8,5,4,3,6,7]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>[1,2,5,4,7,8,3,6]=>[1,2,8,5,4,3,7,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,6,5,7,4,8,3]=>[1,2,8,3,6,4,5,7]=>[1,2,8,6,4,3,5,7]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,5,7,8,4,3]=>[1,2,7,4,5,8,3,6]=>[1,2,8,7,4,3,5,6]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,5,8,7,4,3]=>[1,2,8,3,6,7,4,5]=>[1,2,8,7,4,3,6,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,6,7,5,4,3,8]=>[1,2,5,7,3,6,4,8]=>[1,2,7,6,5,3,4,8]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,6,7,5,4,8,3]=>[1,2,5,8,3,6,4,7]=>[1,2,8,6,5,3,4,7]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,6,7,5,8,4,3]=>[1,2,5,7,4,8,3,6]=>[1,2,8,7,5,3,4,6]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>[1,2,7,4,8,3,6,5]=>[1,2,8,7,6,3,4,5]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,6,8,7,5,4,3]=>[1,2,8,3,6,5,7,4]=>[1,2,8,7,6,3,5,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>[1,2,5,6,4,7,3,8]=>[1,2,7,6,5,4,3,8]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,6,5,4,8,3]=>[1,2,5,6,4,8,3,7]=>[1,2,8,6,5,4,3,7]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,6,5,8,4,3]=>[1,2,5,8,3,7,4,6]=>[1,2,8,7,5,4,3,6]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,6,8,5,4,3]=>[1,2,8,3,7,4,6,5]=>[1,2,8,7,6,4,3,5]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,6,5,4,3]=>[1,2,6,5,8,3,7,4]=>[1,2,8,7,6,5,3,4]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[1,2,6,5,7,4,8,3]=>[1,2,8,7,6,5,4,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,5,6,8]=>[1,3,2,4,7,5,6,8]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,8,5,7,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,6,8,5,7]=>[1,3,2,4,8,6,5,7]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,2,4,7,8,6,5]=>[1,3,2,4,8,5,7,6]=>[1,3,2,4,8,7,5,6]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,4,6,8,7]=>[1,3,2,5,4,6,8,7]=>[1,3,2,5,4,6,8,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,2,5,6,8,7,4]=>[1,3,2,7,8,4,5,6]=>[1,3,2,8,4,5,7,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,6,4,8]=>[1,3,2,6,7,4,5,8]=>[1,3,2,7,4,6,5,8]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,6,8,4]=>[1,3,2,6,8,4,5,7]=>[1,3,2,8,4,6,5,7]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,6,4]=>[1,3,2,8,4,5,7,6]=>[1,3,2,8,4,7,5,6]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,7,6,4]=>[1,3,2,7,6,8,4,5]=>[1,3,2,8,4,7,6,5]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>[1,3,2,5,7,4,6,8]=>[1,3,2,7,5,4,6,8]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>[1,3,2,5,8,4,6,7]=>[1,3,2,8,5,4,6,7]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>[1,3,2,5,7,8,4,6]=>[1,3,2,8,5,4,7,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,2,6,7,5,4,8]=>[1,3,2,7,4,6,5,8]=>[1,3,2,7,6,4,5,8]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,5,8,4]=>[1,3,2,8,4,6,5,7]=>[1,3,2,8,6,4,5,7]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,2,6,7,8,5,4]=>[1,3,2,7,5,8,4,6]=>[1,3,2,8,7,4,5,6]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,6,8,7,5,4]=>[1,3,2,8,4,6,7,5]=>[1,3,2,8,7,4,6,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,6,5,4,8]=>[1,3,2,6,5,7,4,8]=>[1,3,2,7,6,5,4,8]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,6,5,8,4]=>[1,3,2,6,5,8,4,7]=>[1,3,2,8,6,5,4,7]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,6,8,5,4]=>[1,3,2,8,4,7,5,6]=>[1,3,2,8,7,5,4,6]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,2,7,8,6,5,4]=>[1,3,2,6,8,4,7,5]=>[1,3,2,8,7,6,4,5]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[1,3,2,6,7,5,8,4]=>[1,3,2,8,7,6,5,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>[1,4,2,3,5,6,8,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,7,6]=>[1,4,2,3,5,7,8,6]=>[1,4,2,3,5,8,7,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>[1,4,2,3,6,5,8,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>[1,4,2,3,7,8,5,6]=>[1,4,2,3,8,5,7,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,7,6,5,8]=>[1,4,2,3,6,7,5,8]=>[1,4,2,3,7,6,5,8]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[1,4,2,3,6,8,5,7]=>[1,4,2,3,8,6,5,7]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,6,5]=>[1,4,2,3,8,5,7,6]=>[1,4,2,3,8,7,5,6]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[1,4,2,3,7,6,8,5]=>[1,4,2,3,8,7,6,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,5,2,6,8,7]=>[1,5,2,3,4,6,8,7]=>[1,5,2,3,4,6,8,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,8]=>[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,5,2,8,7,6]=>[1,5,2,3,4,7,8,6]=>[1,5,2,3,4,8,7,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,7,8]=>[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,2,8,7]=>[1,6,2,3,4,5,8,7]=>[1,6,2,3,4,5,8,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>[1,8,2,3,4,5,7,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>[1,7,2,3,4,6,5,8]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>[1,8,2,3,4,6,5,7]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,6,2]=>[1,8,2,3,4,5,7,6]=>[1,8,2,3,4,7,5,6]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,7,6,2]=>[1,7,6,8,2,3,4,5]=>[1,8,2,3,4,7,6,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,4,6,5,2,7,8]=>[1,5,6,2,3,4,7,8]=>[1,6,2,3,5,4,7,8]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,4,6,5,2,8,7]=>[1,5,6,2,3,4,8,7]=>[1,6,2,3,5,4,8,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,4,6,5,7,2,8]=>[1,5,7,2,3,4,6,8]=>[1,7,2,3,5,4,6,8]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>[1,8,2,3,5,4,6,7]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,4,6,5,8,7,2]=>[1,5,7,8,2,3,4,6]=>[1,8,2,3,5,4,7,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,4,6,7,5,2,8]=>[1,7,2,3,4,6,5,8]=>[1,7,2,3,6,4,5,8]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,5,8,2]=>[1,8,2,3,4,6,5,7]=>[1,8,2,3,6,4,5,7]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,5,2]=>[1,7,5,8,2,3,4,6]=>[1,8,2,3,7,4,5,6]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,8,7,5,2]=>[1,8,2,3,4,6,7,5]=>[1,8,2,3,7,4,6,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>[1,6,5,8,2,3,4,7]=>[1,8,2,3,6,5,4,7]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,7,6,8,5,2]=>[1,8,2,3,4,7,5,6]=>[1,8,2,3,7,5,4,6]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,7,8,6,5,2]=>[1,6,8,2,3,4,7,5]=>[1,8,2,3,7,6,4,5]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[1,6,7,5,8,2,3,4]=>[1,8,2,3,7,6,5,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,4,2,6,7,8]=>[1,4,5,2,3,6,7,8]=>[1,5,2,4,3,6,7,8]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,4,2,7,6,8]=>[1,4,5,2,3,7,6,8]=>[1,5,2,4,3,7,6,8]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,4,2,7,8,6]=>[1,4,5,2,3,8,6,7]=>[1,5,2,4,3,8,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,5,4,2,8,7,6]=>[1,4,5,2,3,7,8,6]=>[1,5,2,4,3,8,7,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,5,4,6,2,7,8]=>[1,4,6,2,3,5,7,8]=>[1,6,2,4,3,5,7,8]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,5,4,6,7,2,8]=>[1,4,7,2,3,5,6,8]=>[1,7,2,4,3,5,6,8]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,5,4,6,7,8,2]=>[1,4,8,2,3,5,6,7]=>[1,8,2,4,3,5,6,7]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,5,4,6,8,7,2]=>[1,4,7,8,2,3,5,6]=>[1,8,2,4,3,5,7,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>[1,4,6,7,2,3,5,8]=>[1,7,2,4,3,6,5,8]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,4,7,6,8,2]=>[1,4,6,8,2,3,5,7]=>[1,8,2,4,3,6,5,7]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,4,7,8,6,2]=>[1,4,8,2,3,5,7,6]=>[1,8,2,4,3,7,5,6]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,4,8,7,6,2]=>[1,4,7,6,8,2,3,5]=>[1,8,2,4,3,7,6,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,4,2,7,8]=>[1,6,2,3,5,4,7,8]=>[1,6,2,5,3,4,7,8]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,5,6,4,2,8,7]=>[1,6,2,3,5,4,8,7]=>[1,6,2,5,3,4,8,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,4,7,2,8]=>[1,7,2,3,5,4,6,8]=>[1,7,2,5,3,4,6,8]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,5,6,4,7,8,2]=>[1,8,2,3,5,4,6,7]=>[1,8,2,5,3,4,6,7]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,5,6,7,4,8,2]=>[1,6,4,8,2,3,5,7]=>[1,8,2,6,3,4,5,7]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[1,8,2,3,5,7,4,6]=>[1,8,2,7,3,4,5,6]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,6,4,2,8]=>[1,7,2,3,5,6,4,8]=>[1,7,2,6,3,5,4,8]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,6,4,8,2]=>[1,8,2,3,5,6,4,7]=>[1,8,2,6,3,5,4,7]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[1,6,7,4,8,2,3,5]=>[1,8,2,7,3,6,4,5]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,7,6,4,2]=>[1,6,8,2,3,5,7,4]=>[1,8,2,7,3,6,5,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,6,5,4,2,7,8]=>[1,5,4,6,2,3,7,8]=>[1,6,2,5,4,3,7,8]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,6,5,4,2,8,7]=>[1,5,4,6,2,3,8,7]=>[1,6,2,5,4,3,8,7]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,5,7,4,8,2]=>[1,8,2,3,6,4,5,7]=>[1,8,2,6,4,3,5,7]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,5,7,8,4,2]=>[1,7,4,5,8,2,3,6]=>[1,8,2,7,4,3,5,6]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,6,5,8,7,4,2]=>[1,8,2,3,6,7,4,5]=>[1,8,2,7,4,3,6,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,6,7,5,4,2,8]=>[1,5,7,2,3,6,4,8]=>[1,7,2,6,5,3,4,8]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,6,7,5,8,4,2]=>[1,5,7,4,8,2,3,6]=>[1,8,2,7,5,3,4,6]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,6,8,7,5,4,2]=>[1,8,2,3,6,5,7,4]=>[1,8,2,7,6,3,5,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,7,6,5,4,2,8]=>[1,5,6,4,7,2,3,8]=>[1,7,2,6,5,4,3,8]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,7,6,5,8,4,2]=>[1,5,8,2,3,7,4,6]=>[1,8,2,7,5,4,3,6]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,7,6,8,5,4,2]=>[1,8,2,3,7,4,6,5]=>[1,8,2,7,6,4,3,5]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,7,8,6,5,4,2]=>[1,6,5,8,2,3,7,4]=>[1,8,2,7,6,5,3,4]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>[1,6,5,7,4,8,2,3]=>[1,8,2,7,6,5,4,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,3,2,5,7,8,6]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,8,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,3,2,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>[1,4,3,2,6,5,8,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,3,2,6,7,5,8]=>[1,3,4,2,7,5,6,8]=>[1,4,3,2,7,5,6,8]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,8,5,6]=>[1,4,3,2,8,5,7,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>[1,3,4,2,6,8,5,7]=>[1,4,3,2,8,6,5,7]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,4,3,2,7,8,6,5]=>[1,3,4,2,8,5,7,6]=>[1,4,3,2,8,7,5,6]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,3,5,2,6,7,8]=>[1,3,5,2,4,6,7,8]=>[1,5,3,2,4,6,7,8]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,3,5,2,6,8,7]=>[1,3,5,2,4,6,8,7]=>[1,5,3,2,4,6,8,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,3,5,2,7,6,8]=>[1,3,5,2,4,7,6,8]=>[1,5,3,2,4,7,6,8]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3,5,2,7,8,6]=>[1,3,5,2,4,8,6,7]=>[1,5,3,2,4,8,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,3,5,2,8,7,6]=>[1,3,5,2,4,7,8,6]=>[1,5,3,2,4,8,7,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,3,5,6,2,7,8]=>[1,3,6,2,4,5,7,8]=>[1,6,3,2,4,5,7,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,7,2,8]=>[1,3,7,2,4,5,6,8]=>[1,7,3,2,4,5,6,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,2]=>[1,3,8,2,4,5,6,7]=>[1,8,3,2,4,5,6,7]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,3,5,6,8,7,2]=>[1,3,7,8,2,4,5,6]=>[1,8,3,2,4,5,7,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,3,5,7,6,2,8]=>[1,3,6,7,2,4,5,8]=>[1,7,3,2,4,6,5,8]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,3,5,7,6,8,2]=>[1,3,6,8,2,4,5,7]=>[1,8,3,2,4,6,5,7]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,3,5,7,8,6,2]=>[1,3,8,2,4,5,7,6]=>[1,8,3,2,4,7,5,6]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>[1,3,5,6,2,4,7,8]=>[1,6,3,2,5,4,7,8]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>[1,3,5,7,2,4,6,8]=>[1,7,3,2,5,4,6,8]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>[1,8,3,2,5,4,6,7]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[1,3,5,7,8,2,4,6]=>[1,8,3,2,5,4,7,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,3,6,7,5,8,2]=>[1,3,8,2,4,6,5,7]=>[1,8,3,2,6,4,5,7]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,6,7,8,5,2]=>[1,3,7,5,8,2,4,6]=>[1,8,3,2,7,4,5,6]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,6,8,7,5,2]=>[1,3,8,2,4,6,7,5]=>[1,8,3,2,7,4,6,5]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,3,7,6,5,2,8]=>[1,3,6,5,7,2,4,8]=>[1,7,3,2,6,5,4,8]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,3,7,6,8,5,2]=>[1,3,8,2,4,7,5,6]=>[1,8,3,2,7,5,4,6]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,7,8,6,5,2]=>[1,3,6,8,2,4,7,5]=>[1,8,3,2,7,6,4,5]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[1,3,6,7,5,8,2,4]=>[1,8,3,2,7,6,5,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,5,3,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>[1,5,4,2,3,6,7,8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,5,3,2,6,8,7]=>[1,5,2,4,3,6,8,7]=>[1,5,4,2,3,6,8,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,3,2,7,6,8]=>[1,5,2,4,3,7,6,8]=>[1,5,4,2,3,7,6,8]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,4,5,3,6,2,7,8]=>[1,6,2,4,3,5,7,8]=>[1,6,4,2,3,5,7,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,3,6,7,2,8]=>[1,7,2,4,3,5,6,8]=>[1,7,4,2,3,5,6,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,3,6,7,8,2]=>[1,8,2,4,3,5,6,7]=>[1,8,4,2,3,5,6,7]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,3,6,8,7,2]=>[1,7,8,2,4,3,5,6]=>[1,8,4,2,3,5,7,6]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,4,5,3,7,6,2,8]=>[1,6,7,2,4,3,5,8]=>[1,7,4,2,3,6,5,8]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,3,7,8,6,2]=>[1,8,2,4,3,5,7,6]=>[1,8,4,2,3,7,5,6]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,3,8,7,6,2]=>[1,7,6,8,2,4,3,5]=>[1,8,4,2,3,7,6,5]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,6,3,2,7,8]=>[1,5,3,6,2,4,7,8]=>[1,6,5,2,3,4,7,8]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,6,3,7,2,8]=>[1,5,3,7,2,4,6,8]=>[1,7,5,2,3,4,6,8]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,6,3,7,8,2]=>[1,5,3,8,2,4,6,7]=>[1,8,5,2,3,4,6,7]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,6,3,8,7,2]=>[1,5,3,7,8,2,4,6]=>[1,8,5,2,3,4,7,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,3,2,8]=>[1,7,2,4,6,3,5,8]=>[1,7,6,2,3,4,5,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,3,8,2]=>[1,8,2,4,6,3,5,7]=>[1,8,6,2,3,4,5,7]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,5,7,6,3,8,2]=>[1,6,3,5,8,2,4,7]=>[1,8,6,2,3,5,4,7]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,7,6,8,3,2]=>[1,8,2,4,7,3,5,6]=>[1,8,7,2,3,5,4,6]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,8,7,6,3,2]=>[1,6,7,3,5,8,2,4]=>[1,8,7,2,3,6,5,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,4,6,5,3,2,7,8]=>[1,6,2,4,5,3,7,8]=>[1,6,5,2,4,3,7,8]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,4,6,5,3,7,2,8]=>[1,7,2,4,5,3,6,8]=>[1,7,5,2,4,3,6,8]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,6,5,3,7,8,2]=>[1,8,2,4,5,3,6,7]=>[1,8,5,2,4,3,6,7]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,5,3,8,7,2]=>[1,7,8,2,4,5,3,6]=>[1,8,5,2,4,3,7,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,5,7,3,2,8]=>[1,6,3,7,2,4,5,8]=>[1,7,6,2,4,3,5,8]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,6,5,7,3,8,2]=>[1,6,3,8,2,4,5,7]=>[1,8,6,2,4,3,5,7]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,4,6,7,5,3,2,8]=>[1,5,6,3,7,2,4,8]=>[1,7,6,2,5,3,4,8]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,6,7,5,3,8,2]=>[1,5,6,3,8,2,4,7]=>[1,8,6,2,5,3,4,7]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,5,8,3,2]=>[1,5,8,2,4,7,3,6]=>[1,8,7,2,5,3,4,6]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,4,6,7,8,5,3,2]=>[1,8,2,4,7,3,6,5]=>[1,8,7,2,6,3,4,5]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,7,5,3,2]=>[1,7,3,6,5,8,2,4]=>[1,8,7,2,6,3,5,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,7,6,5,3,8,2]=>[1,5,8,2,4,6,3,7]=>[1,8,6,2,5,4,3,7]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,4,7,6,5,8,3,2]=>[1,5,7,3,8,2,4,6]=>[1,8,7,2,5,4,3,6]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,4,7,6,8,5,3,2]=>[1,7,3,8,2,4,6,5]=>[1,8,7,2,6,4,3,5]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,4,7,8,6,5,3,2]=>[1,6,5,7,3,8,2,4]=>[1,8,7,2,6,5,3,4]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>[1,6,5,8,2,4,7,3]=>[1,8,7,2,6,5,4,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8]=>[1,4,3,5,2,6,7,8]=>[1,5,4,3,2,6,7,8]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,5,4,3,2,6,8,7]=>[1,4,3,5,2,6,8,7]=>[1,5,4,3,2,6,8,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,4,3,2,7,6,8]=>[1,4,3,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,4,3,2,7,8,6]=>[1,4,3,5,2,8,6,7]=>[1,5,4,3,2,8,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,4,3,2,8,7,6]=>[1,4,3,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>[1,4,3,6,2,5,7,8]=>[1,6,4,3,2,5,7,8]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>[1,4,3,8,2,5,6,7]=>[1,8,4,3,2,5,6,7]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>[1,4,3,7,8,2,5,6]=>[1,8,4,3,2,5,7,6]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,4,3,7,6,8,2]=>[1,4,3,6,8,2,5,7]=>[1,8,4,3,2,6,5,7]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,4,3,7,8,6,2]=>[1,4,3,8,2,5,7,6]=>[1,8,4,3,2,7,5,6]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,4,3,8,7,6,2]=>[1,4,3,7,6,8,2,5]=>[1,8,4,3,2,7,6,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,4,6,3,2,7,8]=>[1,6,2,5,3,4,7,8]=>[1,6,5,3,2,4,7,8]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,4,6,3,2,8,7]=>[1,6,2,5,3,4,8,7]=>[1,6,5,3,2,4,8,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,4,6,3,7,2,8]=>[1,7,2,5,3,4,6,8]=>[1,7,5,3,2,4,6,8]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,4,6,3,7,8,2]=>[1,8,2,5,3,4,6,7]=>[1,8,5,3,2,4,6,7]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,4,6,3,8,7,2]=>[1,7,8,2,5,3,4,6]=>[1,8,5,3,2,4,7,6]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,3,2]=>[1,8,2,5,7,3,4,6]=>[1,8,7,3,2,4,5,6]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,4,6,8,7,3,2]=>[1,7,3,4,6,8,2,5]=>[1,8,7,3,2,4,6,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,4,7,6,3,2,8]=>[1,7,2,5,6,3,4,8]=>[1,7,6,3,2,5,4,8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,4,7,6,3,8,2]=>[1,8,2,5,6,3,4,7]=>[1,8,6,3,2,5,4,7]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,4,7,6,8,3,2]=>[1,7,3,4,8,2,5,6]=>[1,8,7,3,2,5,4,6]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,4,7,8,6,3,2]=>[1,6,7,3,4,8,2,5]=>[1,8,7,3,2,6,4,5]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,4,8,7,6,3,2]=>[1,6,8,2,5,7,3,4]=>[1,8,7,3,2,6,5,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,6,4,3,2,7,8]=>[1,4,6,2,5,3,7,8]=>[1,6,5,4,2,3,7,8]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,6,4,3,2,8,7]=>[1,4,6,2,5,3,8,7]=>[1,6,5,4,2,3,8,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,5,6,4,3,7,2,8]=>[1,4,7,2,5,3,6,8]=>[1,7,5,4,2,3,6,8]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,4,3,8,7,2]=>[1,4,7,8,2,5,3,6]=>[1,8,5,4,2,3,7,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,5,6,4,7,3,2,8]=>[1,4,6,3,7,2,5,8]=>[1,7,6,4,2,3,5,8]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,4,7,3,8,2]=>[1,4,6,3,8,2,5,7]=>[1,8,6,4,2,3,5,7]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,5,6,4,7,8,3,2]=>[1,4,8,2,5,7,3,6]=>[1,8,7,4,2,3,5,6]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,5,6,7,4,3,2,8]=>[1,6,3,7,2,5,4,8]=>[1,7,6,5,2,3,4,8]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,6,7,4,3,8,2]=>[1,6,3,8,2,5,4,7]=>[1,8,6,5,2,3,4,7]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,5,6,7,4,8,3,2]=>[1,8,2,5,4,7,3,6]=>[1,8,7,5,2,3,4,6]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[1,7,3,6,4,8,2,5]=>[1,8,7,6,2,3,4,5]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,5,7,6,4,3,2,8]=>[1,7,2,5,4,6,3,8]=>[1,7,6,5,2,4,3,8]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,7,6,4,3,8,2]=>[1,8,2,5,4,6,3,7]=>[1,8,6,5,2,4,3,7]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,6,8,4,3,2]=>[1,6,4,7,3,8,2,5]=>[1,8,7,6,2,4,3,5]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,5,7,8,6,4,3,2]=>[1,7,3,8,2,5,6,4]=>[1,8,7,6,2,5,3,4]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,7,6,4,3,2]=>[1,8,2,5,6,4,7,3]=>[1,8,7,6,2,5,4,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,5,4,3,2,7,8]=>[1,4,5,3,6,2,7,8]=>[1,6,5,4,3,2,7,8]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,6,5,4,3,7,2,8]=>[1,4,5,3,7,2,6,8]=>[1,7,5,4,3,2,6,8]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,5,4,3,7,8,2]=>[1,4,5,3,8,2,6,7]=>[1,8,5,4,3,2,6,7]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[1,4,5,3,7,8,2,6]=>[1,8,5,4,3,2,7,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,5,4,7,3,8,2]=>[1,4,8,2,6,3,5,7]=>[1,8,6,4,3,2,5,7]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,6,5,4,7,8,3,2]=>[1,4,7,3,5,8,2,6]=>[1,8,7,4,3,2,5,6]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,6,5,4,8,7,3,2]=>[1,4,8,2,6,7,3,5]=>[1,8,7,4,3,2,6,5]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,5,7,4,3,2,8]=>[1,7,2,6,3,5,4,8]=>[1,7,6,5,3,2,4,8]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,5,7,4,3,8,2]=>[1,8,2,6,3,5,4,7]=>[1,8,6,5,3,2,4,7]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,5,7,4,8,3,2]=>[1,7,3,5,4,8,2,6]=>[1,8,7,5,3,2,4,6]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,4,3,2]=>[1,8,2,6,4,7,3,5]=>[1,8,7,6,3,2,4,5]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,5,8,7,4,3,2]=>[1,7,3,5,8,2,6,4]=>[1,8,7,6,3,2,5,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,7,5,4,3,2,8]=>[1,5,4,7,2,6,3,8]=>[1,7,6,5,4,2,3,8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,5,4,3,8,2]=>[1,5,4,8,2,6,3,7]=>[1,8,6,5,4,2,3,7]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,6,7,5,4,8,3,2]=>[1,5,4,7,3,8,2,6]=>[1,8,7,5,4,2,3,6]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,5,8,4,3,2]=>[1,7,3,8,2,6,4,5]=>[1,8,7,6,4,2,3,5]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[1,5,7,3,8,2,6,4]=>[1,8,7,6,5,2,3,4]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>[1,5,8,2,6,4,7,3]=>[1,8,7,6,5,2,4,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,6,5,4,3,2,8]=>[1,5,4,6,3,7,2,8]=>[1,7,6,5,4,3,2,8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,6,5,4,3,8,2]=>[1,5,4,6,3,8,2,7]=>[1,8,6,5,4,3,2,7]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7,6,5,4,8,3,2]=>[1,5,4,8,2,7,3,6]=>[1,8,7,5,4,3,2,6]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[1,8,2,7,3,6,4,5]=>[1,8,7,6,4,3,2,5]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>[1,5,8,2,7,3,6,4]=>[1,8,7,6,5,3,2,4]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>[1,5,6,4,8,2,7,3]=>[1,8,7,6,5,4,2,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[1,5,6,4,7,3,8,2]=>[1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,4,6,7,5,8]=>[2,1,3,4,7,5,6,8]=>[2,1,3,4,7,5,6,8]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,4,6,8,7,5]=>[2,1,3,4,7,8,5,6]=>[2,1,3,4,8,5,7,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,6,8,5,7]=>[2,1,3,4,8,6,5,7]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,6,5]=>[2,1,3,4,8,5,7,6]=>[2,1,3,4,8,7,5,6]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,6,7]=>[2,1,3,5,4,8,6,7]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,4,5,7,8]=>[2,1,3,6,4,5,7,8]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,4,5,8,7]=>[2,1,3,6,4,5,8,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,3,5,6,8,7,4]=>[2,1,3,7,8,4,5,6]=>[2,1,3,8,4,5,7,6]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,3,5,7,8,6,4]=>[2,1,3,8,4,5,7,6]=>[2,1,3,8,4,7,5,6]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,6,5,4,7,8]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,5,4,7,8]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,5,7,4,8]=>[2,1,3,5,7,4,6,8]=>[2,1,3,7,5,4,6,8]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,6,5,7,8,4]=>[2,1,3,5,8,4,6,7]=>[2,1,3,8,5,4,6,7]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,6,5,8,7,4]=>[2,1,3,5,7,8,4,6]=>[2,1,3,8,5,4,7,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,6,7,5,8,4]=>[2,1,3,8,4,6,5,7]=>[2,1,3,8,6,4,5,7]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,6,7,8,5,4]=>[2,1,3,7,5,8,4,6]=>[2,1,3,8,7,4,5,6]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,6,8,7,5,4]=>[2,1,3,8,4,6,7,5]=>[2,1,3,8,7,4,6,5]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,7,6,5,4,8]=>[2,1,3,6,5,7,4,8]=>[2,1,3,7,6,5,4,8]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,7,6,5,8,4]=>[2,1,3,6,5,8,4,7]=>[2,1,3,8,6,5,4,7]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,3,7,6,8,5,4]=>[2,1,3,8,4,7,5,6]=>[2,1,3,8,7,5,4,6]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,3,7,8,6,5,4]=>[2,1,3,6,8,4,7,5]=>[2,1,3,8,7,6,4,5]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[2,1,3,6,7,5,8,4]=>[2,1,3,8,7,6,5,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,6,7]=>[2,1,4,3,5,8,6,7]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,7,6]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,7,6,5,8]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,7,5,6]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,3,4,6,7,8]=>[2,1,5,3,4,6,7,8]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,3,4,6,8,7]=>[2,1,5,3,4,6,8,7]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,6,3,7,8]=>[2,1,6,3,4,5,7,8]=>[2,1,6,3,4,5,7,8]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,7,3,8]=>[2,1,7,3,4,5,6,8]=>[2,1,7,3,4,5,6,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>[2,1,7,8,3,4,5,6]=>[2,1,8,3,4,5,7,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,6,3,8]=>[2,1,6,7,3,4,5,8]=>[2,1,7,3,4,6,5,8]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,4,5,7,6,8,3]=>[2,1,6,8,3,4,5,7]=>[2,1,8,3,4,6,5,7]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,6,3]=>[2,1,8,3,4,5,7,6]=>[2,1,8,3,4,7,5,6]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[2,1,7,6,8,3,4,5]=>[2,1,8,3,4,7,6,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>[2,1,5,6,3,4,7,8]=>[2,1,6,3,5,4,7,8]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,4,6,5,7,3,8]=>[2,1,5,7,3,4,6,8]=>[2,1,7,3,5,4,6,8]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,4,6,5,7,8,3]=>[2,1,5,8,3,4,6,7]=>[2,1,8,3,5,4,6,7]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>[2,1,5,7,8,3,4,6]=>[2,1,8,3,5,4,7,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,5,3,8]=>[2,1,7,3,4,6,5,8]=>[2,1,7,3,6,4,5,8]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,4,6,7,8,5,3]=>[2,1,7,5,8,3,4,6]=>[2,1,8,3,7,4,5,6]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,7,5,3]=>[2,1,8,3,4,6,7,5]=>[2,1,8,3,7,4,6,5]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,4,7,6,5,3,8]=>[2,1,6,5,7,3,4,8]=>[2,1,7,3,6,5,4,8]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>[2,1,6,5,8,3,4,7]=>[2,1,8,3,6,5,4,7]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,7,6,8,5,3]=>[2,1,8,3,4,7,5,6]=>[2,1,8,3,7,5,4,6]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,6,5,3]=>[2,1,6,8,3,4,7,5]=>[2,1,8,3,7,6,4,5]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[2,1,6,7,5,8,3,4]=>[2,1,8,3,7,6,5,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,4,3,6,7,8]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,5,4,3,7,8,6]=>[2,1,4,5,3,8,6,7]=>[2,1,5,4,3,8,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,5,4,3,8,7,6]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,4,6,3,7,8]=>[2,1,4,6,3,5,7,8]=>[2,1,6,4,3,5,7,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,4,6,7,3,8]=>[2,1,4,7,3,5,6,8]=>[2,1,7,4,3,5,6,8]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,4,6,7,8,3]=>[2,1,4,8,3,5,6,7]=>[2,1,8,4,3,5,6,7]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,4,6,8,7,3]=>[2,1,4,7,8,3,5,6]=>[2,1,8,4,3,5,7,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,4,7,6,3,8]=>[2,1,4,6,7,3,5,8]=>[2,1,7,4,3,6,5,8]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>[2,1,4,6,8,3,5,7]=>[2,1,8,4,3,6,5,7]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,4,7,8,6,3]=>[2,1,4,8,3,5,7,6]=>[2,1,8,4,3,7,5,6]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,4,8,7,6,3]=>[2,1,4,7,6,8,3,5]=>[2,1,8,4,3,7,6,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,6,4,3,7,8]=>[2,1,6,3,5,4,7,8]=>[2,1,6,5,3,4,7,8]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[2,1,6,3,5,4,8,7]=>[2,1,6,5,3,4,8,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,5,6,4,7,3,8]=>[2,1,7,3,5,4,6,8]=>[2,1,7,5,3,4,6,8]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,5,6,4,8,7,3]=>[2,1,7,8,3,5,4,6]=>[2,1,8,5,3,4,7,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,4,8,3]=>[2,1,6,4,8,3,5,7]=>[2,1,8,6,3,4,5,7]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>[2,1,8,3,5,7,4,6]=>[2,1,8,7,3,4,5,6]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,5,6,8,7,4,3]=>[2,1,7,4,6,8,3,5]=>[2,1,8,7,3,4,6,5]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,6,8,4,3]=>[2,1,7,4,8,3,5,6]=>[2,1,8,7,3,5,4,6]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,6,4,3]=>[2,1,6,7,4,8,3,5]=>[2,1,8,7,3,6,4,5]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,5,8,7,6,4,3]=>[2,1,6,8,3,5,7,4]=>[2,1,8,7,3,6,5,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,6,5,4,7,3,8]=>[2,1,5,4,7,3,6,8]=>[2,1,7,5,4,3,6,8]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,6,5,4,7,8,3]=>[2,1,5,4,8,3,6,7]=>[2,1,8,5,4,3,6,7]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,6,5,4,8,7,3]=>[2,1,5,4,7,8,3,6]=>[2,1,8,5,4,3,7,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>[2,1,8,3,6,4,5,7]=>[2,1,8,6,4,3,5,7]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>[2,1,7,4,5,8,3,6]=>[2,1,8,7,4,3,5,6]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>[2,1,8,3,6,7,4,5]=>[2,1,8,7,4,3,6,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,6,7,5,4,3,8]=>[2,1,5,7,3,6,4,8]=>[2,1,7,6,5,3,4,8]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,5,4,8,3]=>[2,1,5,8,3,6,4,7]=>[2,1,8,6,5,3,4,7]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[2,1,5,7,4,8,3,6]=>[2,1,8,7,5,3,4,6]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[2,1,7,4,8,3,6,5]=>[2,1,8,7,6,3,4,5]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,6,8,7,5,4,3]=>[2,1,8,3,6,5,7,4]=>[2,1,8,7,6,3,5,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,6,5,4,3,8]=>[2,1,5,6,4,7,3,8]=>[2,1,7,6,5,4,3,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,7,6,5,4,8,3]=>[2,1,5,6,4,8,3,7]=>[2,1,8,6,5,4,3,7]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[2,1,5,8,3,7,4,6]=>[2,1,8,7,5,4,3,6]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,6,8,5,4,3]=>[2,1,8,3,7,4,6,5]=>[2,1,8,7,6,4,3,5]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,6,5,4,3]=>[2,1,6,5,8,3,7,4]=>[2,1,8,7,6,5,3,4]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,8,7]=>[3,1,2,4,5,6,8,7]=>[3,1,2,4,5,6,8,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,5,7,6,8]=>[3,1,2,4,5,7,6,8]=>[3,1,2,4,5,7,6,8]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5,8,7,6]=>[3,1,2,4,5,7,8,6]=>[3,1,2,4,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,4,6,5,8,7]=>[3,1,2,4,6,5,8,7]=>[3,1,2,4,6,5,8,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[3,1,2,4,7,5,6,8]=>[3,1,2,4,7,5,6,8]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,1,4,6,8,7,5]=>[3,1,2,4,7,8,5,6]=>[3,1,2,4,8,5,7,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[3,1,2,4,6,8,5,7]=>[3,1,2,4,8,6,5,7]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,6,5]=>[3,1,2,4,8,5,7,6]=>[3,1,2,4,8,7,5,6]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[3,1,2,4,7,6,8,5]=>[3,1,2,4,8,7,6,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8]=>[3,1,2,5,4,6,7,8]=>[3,1,2,5,4,6,7,8]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,5,6,4,7,8]=>[3,1,2,6,4,5,7,8]=>[3,1,2,6,4,5,7,8]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,6,4,8,7]=>[3,1,2,6,4,5,8,7]=>[3,1,2,6,4,5,8,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[3,1,2,7,4,5,6,8]=>[3,1,2,7,4,5,6,8]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[3,1,2,8,4,5,6,7]=>[3,1,2,8,4,5,6,7]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,1,5,6,8,7,4]=>[3,1,2,7,8,4,5,6]=>[3,1,2,8,4,5,7,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,6,8,4]=>[3,1,2,6,8,4,5,7]=>[3,1,2,8,4,6,5,7]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,5,7,8,6,4]=>[3,1,2,8,4,5,7,6]=>[3,1,2,8,4,7,5,6]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,6,5,4,7,8]=>[3,1,2,5,6,4,7,8]=>[3,1,2,6,5,4,7,8]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>[3,1,2,5,7,4,6,8]=>[3,1,2,7,5,4,6,8]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,5,7,8,4]=>[3,1,2,5,8,4,6,7]=>[3,1,2,8,5,4,6,7]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>[3,1,2,5,7,8,4,6]=>[3,1,2,8,5,4,7,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,5,8,4]=>[3,1,2,8,4,6,5,7]=>[3,1,2,8,6,4,5,7]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,5,4]=>[3,1,2,7,5,8,4,6]=>[3,1,2,8,7,4,5,6]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,7,5,4]=>[3,1,2,8,4,6,7,5]=>[3,1,2,8,7,4,6,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,6,5,8,4]=>[3,1,2,6,5,8,4,7]=>[3,1,2,8,6,5,4,7]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,6,8,5,4]=>[3,1,2,8,4,7,5,6]=>[3,1,2,8,7,5,4,6]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,6,5,4]=>[3,1,2,6,8,4,7,5]=>[3,1,2,8,7,6,4,5]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[3,1,2,6,7,5,8,4]=>[3,1,2,8,7,6,5,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,5,7,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[4,1,2,3,8,5,7,6]=>[4,1,2,3,8,7,5,6]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[4,1,2,3,7,6,8,5]=>[4,1,2,3,8,7,6,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,8,7]=>[5,1,2,3,4,6,8,7]=>[5,1,2,3,4,6,8,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,8]=>[5,1,2,3,4,7,6,8]=>[5,1,2,3,4,7,6,8]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,1,7,8,6]=>[5,1,2,3,4,8,6,7]=>[5,1,2,3,4,8,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[5,1,2,3,4,7,8,6]=>[5,1,2,3,4,8,7,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>[6,8,1,2,3,4,5,7]=>[8,1,2,3,4,6,5,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,6,1]=>[8,1,2,3,4,5,7,6]=>[8,1,2,3,4,7,5,6]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,6,5,1,7,8]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,4,6,5,1,8,7]=>[5,6,1,2,3,4,8,7]=>[6,1,2,3,5,4,8,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>[7,1,2,3,5,4,6,8]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>[5,8,1,2,3,4,6,7]=>[8,1,2,3,5,4,6,7]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>[5,7,8,1,2,3,4,6]=>[8,1,2,3,5,4,7,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,4,6,7,5,1,8]=>[7,1,2,3,4,6,5,8]=>[7,1,2,3,6,4,5,8]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,5,8,1]=>[8,1,2,3,4,6,5,7]=>[8,1,2,3,6,4,5,7]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]=>[7,5,8,1,2,3,4,6]=>[8,1,2,3,7,4,5,6]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,8,7,5,1]=>[8,1,2,3,4,6,7,5]=>[8,1,2,3,7,4,6,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>[6,5,8,1,2,3,4,7]=>[8,1,2,3,6,5,4,7]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,7,6,8,5,1]=>[8,1,2,3,4,7,5,6]=>[8,1,2,3,7,5,4,6]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,6,5,1]=>[6,8,1,2,3,4,7,5]=>[8,1,2,3,7,6,4,5]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,5,4,1,6,8,7]=>[4,5,1,2,3,6,8,7]=>[5,1,2,4,3,6,8,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,4,1,7,6,8]=>[4,5,1,2,3,7,6,8]=>[5,1,2,4,3,7,6,8]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,5,4,1,7,8,6]=>[4,5,1,2,3,8,6,7]=>[5,1,2,4,3,8,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>[4,5,1,2,3,7,8,6]=>[5,1,2,4,3,8,7,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,5,4,6,1,7,8]=>[4,6,1,2,3,5,7,8]=>[6,1,2,4,3,5,7,8]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>[7,1,2,4,3,5,6,8]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>[4,8,1,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,5,4,7,6,1,8]=>[4,6,7,1,2,3,5,8]=>[7,1,2,4,3,6,5,8]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>[4,6,8,1,2,3,5,7]=>[8,1,2,4,3,6,5,7]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,4,7,8,6,1]=>[4,8,1,2,3,5,7,6]=>[8,1,2,4,3,7,5,6]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>[4,7,6,8,1,2,3,5]=>[8,1,2,4,3,7,6,5]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,5,6,4,1,7,8]=>[6,1,2,3,5,4,7,8]=>[6,1,2,5,3,4,7,8]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,4,1,8,7]=>[6,1,2,3,5,4,8,7]=>[6,1,2,5,3,4,8,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,4,7,1,8]=>[7,1,2,3,5,4,6,8]=>[7,1,2,5,3,4,6,8]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]=>[8,1,2,3,5,4,6,7]=>[8,1,2,5,3,4,6,7]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,5,6,4,8,7,1]=>[7,8,1,2,3,5,4,6]=>[8,1,2,5,3,4,7,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,5,6,7,4,1,8]=>[6,4,7,1,2,3,5,8]=>[7,1,2,6,3,4,5,8]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,4,8,1]=>[6,4,8,1,2,3,5,7]=>[8,1,2,6,3,4,5,7]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[8,1,2,3,5,7,4,6]=>[8,1,2,7,3,4,5,6]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[7,4,6,8,1,2,3,5]=>[8,1,2,7,3,4,6,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,5,7,6,4,1,8]=>[7,1,2,3,5,6,4,8]=>[7,1,2,6,3,5,4,8]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,5,7,6,4,8,1]=>[8,1,2,3,5,6,4,7]=>[8,1,2,6,3,5,4,7]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,6,8,4,1]=>[7,4,8,1,2,3,5,6]=>[8,1,2,7,3,5,4,6]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]=>[6,7,4,8,1,2,3,5]=>[8,1,2,7,3,6,4,5]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,8,7,6,4,1]=>[6,8,1,2,3,5,7,4]=>[8,1,2,7,3,6,5,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,6,5,4,1,7,8]=>[5,4,6,1,2,3,7,8]=>[6,1,2,5,4,3,7,8]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[5,4,6,1,2,3,8,7]=>[6,1,2,5,4,3,8,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]=>[5,4,8,1,2,3,6,7]=>[8,1,2,5,4,3,6,7]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,6,5,7,4,1,8]=>[7,1,2,3,6,4,5,8]=>[7,1,2,6,4,3,5,8]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,6,5,7,8,4,1]=>[7,4,5,8,1,2,3,6]=>[8,1,2,7,4,3,5,6]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,5,8,7,4,1]=>[8,1,2,3,6,7,4,5]=>[8,1,2,7,4,3,6,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,6,7,5,4,1,8]=>[5,7,1,2,3,6,4,8]=>[7,1,2,6,5,3,4,8]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,6,7,5,4,8,1]=>[5,8,1,2,3,6,4,7]=>[8,1,2,6,5,3,4,7]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,7,5,8,4,1]=>[5,7,4,8,1,2,3,6]=>[8,1,2,7,5,3,4,6]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,5,4,1]=>[7,4,8,1,2,3,6,5]=>[8,1,2,7,6,3,4,5]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,6,8,7,5,4,1]=>[8,1,2,3,6,5,7,4]=>[8,1,2,7,6,3,5,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>[5,6,4,8,1,2,3,7]=>[8,1,2,6,5,4,3,7]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,6,5,8,4,1]=>[5,8,1,2,3,7,4,6]=>[8,1,2,7,5,4,3,6]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,7,6,8,5,4,1]=>[8,1,2,3,7,4,6,5]=>[8,1,2,7,6,4,3,5]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,7,8,6,5,4,1]=>[6,5,8,1,2,3,7,4]=>[8,1,2,7,6,5,3,4]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,4,3,1,5,6,8,7]=>[3,4,1,2,5,6,8,7]=>[4,1,3,2,5,6,8,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,4,3,1,5,7,6,8]=>[3,4,1,2,5,7,6,8]=>[4,1,3,2,5,7,6,8]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,4,3,1,5,7,8,6]=>[3,4,1,2,5,8,6,7]=>[4,1,3,2,5,8,6,7]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,4,3,1,5,8,7,6]=>[3,4,1,2,5,7,8,6]=>[4,1,3,2,5,8,7,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,4,3,1,6,5,7,8]=>[3,4,1,2,6,5,7,8]=>[4,1,3,2,6,5,7,8]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[3,4,1,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,3,1,7,8,6,5]=>[3,4,1,2,8,5,7,6]=>[4,1,3,2,8,7,5,6]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[3,4,1,2,7,6,8,5]=>[4,1,3,2,8,7,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>[3,5,1,2,4,6,7,8]=>[5,1,3,2,4,6,7,8]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,4,3,5,1,6,8,7]=>[3,5,1,2,4,6,8,7]=>[5,1,3,2,4,6,8,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>[3,5,1,2,4,7,6,8]=>[5,1,3,2,4,7,6,8]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,3,5,1,7,8,6]=>[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>[3,5,1,2,4,7,8,6]=>[5,1,3,2,4,8,7,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,4,3,5,6,1,7,8]=>[3,6,1,2,4,5,7,8]=>[6,1,3,2,4,5,7,8]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,4,3,5,6,1,8,7]=>[3,6,1,2,4,5,8,7]=>[6,1,3,2,4,5,8,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,7,1,8]=>[3,7,1,2,4,5,6,8]=>[7,1,3,2,4,5,6,8]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>[3,8,1,2,4,5,6,7]=>[8,1,3,2,4,5,6,7]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>[3,7,8,1,2,4,5,6]=>[8,1,3,2,4,5,7,6]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,4,3,5,7,6,1,8]=>[3,6,7,1,2,4,5,8]=>[7,1,3,2,4,6,5,8]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>[3,6,8,1,2,4,5,7]=>[8,1,3,2,4,6,5,7]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,4,3,5,7,8,6,1]=>[3,8,1,2,4,5,7,6]=>[8,1,3,2,4,7,5,6]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,6,5,1,7,8]=>[3,5,6,1,2,4,7,8]=>[6,1,3,2,5,4,7,8]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[3,5,6,1,2,4,8,7]=>[6,1,3,2,5,4,8,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>[3,5,7,1,2,4,6,8]=>[7,1,3,2,5,4,6,8]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>[3,5,8,1,2,4,6,7]=>[8,1,3,2,5,4,6,7]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>[8,1,3,2,5,4,7,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,3,6,7,5,8,1]=>[3,8,1,2,4,6,5,7]=>[8,1,3,2,6,4,5,7]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,3,6,7,8,5,1]=>[3,7,5,8,1,2,4,6]=>[8,1,3,2,7,4,5,6]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,3,6,8,7,5,1]=>[3,8,1,2,4,6,7,5]=>[8,1,3,2,7,4,6,5]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,4,3,7,6,5,1,8]=>[3,6,5,7,1,2,4,8]=>[7,1,3,2,6,5,4,8]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[3,6,5,8,1,2,4,7]=>[8,1,3,2,6,5,4,7]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,4,3,7,6,8,5,1]=>[3,8,1,2,4,7,5,6]=>[8,1,3,2,7,5,4,6]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,4,3,7,8,6,5,1]=>[3,6,8,1,2,4,7,5]=>[8,1,3,2,7,6,4,5]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>[3,6,7,5,8,1,2,4]=>[8,1,3,2,7,6,5,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,4,5,3,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>[5,1,4,2,3,6,7,8]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,4,5,3,1,6,8,7]=>[5,1,2,4,3,6,8,7]=>[5,1,4,2,3,6,8,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,4,5,3,1,7,6,8]=>[5,1,2,4,3,7,6,8]=>[5,1,4,2,3,7,6,8]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,3,1,7,8,6]=>[5,1,2,4,3,8,6,7]=>[5,1,4,2,3,8,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[5,1,2,4,3,7,8,6]=>[5,1,4,2,3,8,7,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,4,5,3,6,1,8,7]=>[6,1,2,4,3,5,8,7]=>[6,1,4,2,3,5,8,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,4,5,3,6,7,1,8]=>[7,1,2,4,3,5,6,8]=>[7,1,4,2,3,5,6,8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]=>[8,1,2,4,3,5,6,7]=>[8,1,4,2,3,5,6,7]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,3,6,8,7,1]=>[7,8,1,2,4,3,5,6]=>[8,1,4,2,3,5,7,6]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,4,5,3,7,6,8,1]=>[6,8,1,2,4,3,5,7]=>[8,1,4,2,3,6,5,7]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,3,7,8,6,1]=>[8,1,2,4,3,5,7,6]=>[8,1,4,2,3,7,5,6]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,3,8,7,6,1]=>[7,6,8,1,2,4,3,5]=>[8,1,4,2,3,7,6,5]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,3,1,7,8]=>[5,3,6,1,2,4,7,8]=>[6,1,5,2,3,4,7,8]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,6,3,1,8,7]=>[5,3,6,1,2,4,8,7]=>[6,1,5,2,3,4,8,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,6,3,7,1,8]=>[5,3,7,1,2,4,6,8]=>[7,1,5,2,3,4,6,8]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,1]=>[5,3,8,1,2,4,6,7]=>[8,1,5,2,3,4,6,7]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,3,8,7,1]=>[5,3,7,8,1,2,4,6]=>[8,1,5,2,3,4,7,6]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,3,1,8]=>[7,1,2,4,6,3,5,8]=>[7,1,6,2,3,4,5,8]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,3,8,1]=>[8,1,2,4,6,3,5,7]=>[8,1,6,2,3,4,5,7]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,3,1]=>[7,3,5,8,1,2,4,6]=>[8,1,7,2,3,4,5,6]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,8,7,3,1]=>[8,1,2,4,6,7,3,5]=>[8,1,7,2,3,4,6,5]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,4,5,7,6,3,1,8]=>[6,3,5,7,1,2,4,8]=>[7,1,6,2,3,5,4,8]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,6,3,1]=>[6,8,1,2,4,7,3,5]=>[8,1,7,2,3,6,4,5]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,4,6,5,3,1,7,8]=>[6,1,2,4,5,3,7,8]=>[6,1,5,2,4,3,7,8]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,5,3,1,8,7]=>[6,1,2,4,5,3,8,7]=>[6,1,5,2,4,3,8,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,4,6,5,3,7,1,8]=>[7,1,2,4,5,3,6,8]=>[7,1,5,2,4,3,6,8]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,5,3,7,8,1]=>[8,1,2,4,5,3,6,7]=>[8,1,5,2,4,3,6,7]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,5,3,8,7,1]=>[7,8,1,2,4,5,3,6]=>[8,1,5,2,4,3,7,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]=>[6,3,8,1,2,4,5,7]=>[8,1,6,2,4,3,5,7]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,5,8,7,3,1]=>[7,3,6,8,1,2,4,5]=>[8,1,7,2,4,3,6,5]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,5,3,1,8]=>[5,6,3,7,1,2,4,8]=>[7,1,6,2,5,3,4,8]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,6,7,5,3,8,1]=>[5,6,3,8,1,2,4,7]=>[8,1,6,2,5,3,4,7]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,6,7,5,8,3,1]=>[5,8,1,2,4,7,3,6]=>[8,1,7,2,5,3,4,6]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,5,3,1]=>[8,1,2,4,7,3,6,5]=>[8,1,7,2,6,3,4,5]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>[7,3,6,5,8,1,2,4]=>[8,1,7,2,6,3,5,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,4,7,6,5,3,8,1]=>[5,8,1,2,4,6,3,7]=>[8,1,6,2,5,4,3,7]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,6,5,8,3,1]=>[5,7,3,8,1,2,4,6]=>[8,1,7,2,5,4,3,6]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]=>[6,5,7,3,8,1,2,4]=>[8,1,7,2,6,5,3,4]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[6,5,8,1,2,4,7,3]=>[8,1,7,2,6,5,4,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>[4,3,5,1,2,6,7,8]=>[5,1,4,3,2,6,7,8]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,5,4,3,1,7,6,8]=>[4,3,5,1,2,7,6,8]=>[5,1,4,3,2,7,6,8]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>[4,3,5,1,2,7,8,6]=>[5,1,4,3,2,8,7,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,4,3,6,1,8,7]=>[4,3,6,1,2,5,8,7]=>[6,1,4,3,2,5,8,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[4,3,8,1,2,5,6,7]=>[8,1,4,3,2,5,6,7]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[4,3,7,8,1,2,5,6]=>[8,1,4,3,2,5,7,6]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,5,4,3,7,6,1,8]=>[4,3,6,7,1,2,5,8]=>[7,1,4,3,2,6,5,8]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>[4,3,6,8,1,2,5,7]=>[8,1,4,3,2,6,5,7]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>[4,3,8,1,2,5,7,6]=>[8,1,4,3,2,7,5,6]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[4,3,7,6,8,1,2,5]=>[8,1,4,3,2,7,6,5]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,5,4,6,3,1,7,8]=>[6,1,2,5,3,4,7,8]=>[6,1,5,3,2,4,7,8]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,4,6,3,7,1,8]=>[7,1,2,5,3,4,6,8]=>[7,1,5,3,2,4,6,8]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,4,6,3,7,8,1]=>[8,1,2,5,3,4,6,7]=>[8,1,5,3,2,4,6,7]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,4,6,7,3,1,8]=>[6,3,4,7,1,2,5,8]=>[7,1,6,3,2,4,5,8]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]=>[6,3,4,8,1,2,5,7]=>[8,1,6,3,2,4,5,7]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,3,1]=>[8,1,2,5,7,3,4,6]=>[8,1,7,3,2,4,5,6]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,5,4,7,6,3,1,8]=>[7,1,2,5,6,3,4,8]=>[7,1,6,3,2,5,4,8]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]=>[8,1,2,5,6,3,4,7]=>[8,1,6,3,2,5,4,7]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,4,7,6,8,3,1]=>[7,3,4,8,1,2,5,6]=>[8,1,7,3,2,5,4,6]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,4,7,8,6,3,1]=>[6,7,3,4,8,1,2,5]=>[8,1,7,3,2,6,4,5]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,4,8,7,6,3,1]=>[6,8,1,2,5,7,3,4]=>[8,1,7,3,2,6,5,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,5,6,4,3,1,8,7]=>[4,6,1,2,5,3,8,7]=>[6,1,5,4,2,3,8,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,4,3,7,8,1]=>[4,8,1,2,5,3,6,7]=>[8,1,5,4,2,3,6,7]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,5,6,4,7,3,1,8]=>[4,6,3,7,1,2,5,8]=>[7,1,6,4,2,3,5,8]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,5,6,4,7,3,8,1]=>[4,6,3,8,1,2,5,7]=>[8,1,6,4,2,3,5,7]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,4,7,8,3,1]=>[4,8,1,2,5,7,3,6]=>[8,1,7,4,2,3,5,6]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,4,8,7,3,1]=>[4,7,3,6,8,1,2,5]=>[8,1,7,4,2,3,6,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,4,3,8,1]=>[6,3,8,1,2,5,4,7]=>[8,1,6,5,2,3,4,7]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[7,3,6,4,8,1,2,5]=>[8,1,7,6,2,3,4,5]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,5,6,8,7,4,3,1]=>[8,1,2,5,7,3,6,4]=>[8,1,7,6,2,3,5,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,5,7,6,4,3,1,8]=>[7,1,2,5,4,6,3,8]=>[7,1,6,5,2,4,3,8]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,5,7,6,4,3,8,1]=>[8,1,2,5,4,6,3,7]=>[8,1,6,5,2,4,3,7]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,5,7,6,4,8,3,1]=>[7,3,8,1,2,5,4,6]=>[8,1,7,5,2,4,3,6]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,5,7,6,8,4,3,1]=>[6,4,7,3,8,1,2,5]=>[8,1,7,6,2,4,3,5]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,5,7,8,6,4,3,1]=>[7,3,8,1,2,5,6,4]=>[8,1,7,6,2,5,3,4]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,5,8,7,6,4,3,1]=>[8,1,2,5,6,4,7,3]=>[8,1,7,6,2,5,4,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,6,5,4,3,1,8,7]=>[4,5,3,6,1,2,8,7]=>[6,1,5,4,3,2,8,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,6,5,4,3,7,1,8]=>[4,5,3,7,1,2,6,8]=>[7,1,5,4,3,2,6,8]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>[4,5,3,8,1,2,6,7]=>[8,1,5,4,3,2,6,7]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,6,5,4,3,8,7,1]=>[4,5,3,7,8,1,2,6]=>[8,1,5,4,3,2,7,6]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,3,1]=>[4,7,3,5,8,1,2,6]=>[8,1,7,4,3,2,5,6]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,6,5,4,8,7,3,1]=>[4,8,1,2,6,7,3,5]=>[8,1,7,4,3,2,6,5]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,6,5,7,4,3,1,8]=>[7,1,2,6,3,5,4,8]=>[7,1,6,5,3,2,4,8]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,6,5,7,4,3,8,1]=>[8,1,2,6,3,5,4,7]=>[8,1,6,5,3,2,4,7]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,6,5,7,4,8,3,1]=>[7,3,5,4,8,1,2,6]=>[8,1,7,5,3,2,4,6]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,6,5,8,7,4,3,1]=>[7,3,5,8,1,2,6,4]=>[8,1,7,6,3,2,5,4]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,6,7,5,4,8,3,1]=>[5,4,7,3,8,1,2,6]=>[8,1,7,5,4,2,3,6]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,7,5,8,4,3,1]=>[7,3,8,1,2,6,4,5]=>[8,1,7,6,4,2,3,5]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,5,4,3,1]=>[5,7,3,8,1,2,6,4]=>[8,1,7,6,5,2,3,4]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>[5,8,1,2,6,4,7,3]=>[8,1,7,6,5,2,4,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,7,6,5,4,3,1,8]=>[5,4,6,3,7,1,2,8]=>[7,1,6,5,4,3,2,8]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,6,5,4,3,8,1]=>[5,4,6,3,8,1,2,7]=>[8,1,6,5,4,3,2,7]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>[5,4,8,1,2,7,3,6]=>[8,1,7,5,4,3,2,6]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,7,6,5,8,4,3,1]=>[8,1,2,7,3,6,4,5]=>[8,1,7,6,4,3,2,5]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,6,8,5,4,3,1]=>[5,8,1,2,7,3,6,4]=>[8,1,7,6,5,3,2,4]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>[5,6,4,8,1,2,7,3]=>[8,1,7,6,5,4,2,3]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>[5,6,4,7,3,8,1,2]=>[8,1,7,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>[2,3,1,4,5,8,6,7]=>[3,2,1,4,5,8,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,2,1,4,6,5,7,8]=>[2,3,1,4,6,5,7,8]=>[3,2,1,4,6,5,7,8]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,2,1,4,6,5,8,7]=>[2,3,1,4,6,5,8,7]=>[3,2,1,4,6,5,8,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,2,1,4,6,7,5,8]=>[2,3,1,4,7,5,6,8]=>[3,2,1,4,7,5,6,8]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,8,5,6]=>[3,2,1,4,8,5,7,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[2,3,1,4,6,8,5,7]=>[3,2,1,4,8,6,5,7]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,7,8,6,5]=>[2,3,1,4,8,5,7,6]=>[3,2,1,4,8,7,5,6]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,1,5,4,8,7,6]=>[2,3,1,5,4,7,8,6]=>[3,2,1,5,4,8,7,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>[2,3,1,6,4,5,7,8]=>[3,2,1,6,4,5,7,8]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,5,6,4,8,7]=>[2,3,1,6,4,5,8,7]=>[3,2,1,6,4,5,8,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,5,6,7,4,8]=>[2,3,1,7,4,5,6,8]=>[3,2,1,7,4,5,6,8]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[2,3,1,8,4,5,6,7]=>[3,2,1,8,4,5,6,7]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>[2,3,1,7,8,4,5,6]=>[3,2,1,8,4,5,7,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>[2,3,1,6,7,4,5,8]=>[3,2,1,7,4,6,5,8]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>[2,3,1,6,8,4,5,7]=>[3,2,1,8,4,6,5,7]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[2,3,1,8,4,5,7,6]=>[3,2,1,8,4,7,5,6]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[2,3,1,7,6,8,4,5]=>[3,2,1,8,4,7,6,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,2,1,6,5,4,7,8]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,2,1,6,5,7,4,8]=>[2,3,1,5,7,4,6,8]=>[3,2,1,7,5,4,6,8]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[2,3,1,5,8,4,6,7]=>[3,2,1,8,5,4,6,7]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[2,3,1,5,7,8,4,6]=>[3,2,1,8,5,4,7,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,2,1,6,7,5,4,8]=>[2,3,1,7,4,6,5,8]=>[3,2,1,7,6,4,5,8]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>[2,3,1,8,4,6,5,7]=>[3,2,1,8,6,4,5,7]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,6,7,8,5,4]=>[2,3,1,7,5,8,4,6]=>[3,2,1,8,7,4,5,6]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>[2,3,1,8,4,6,7,5]=>[3,2,1,8,7,4,6,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,2,1,7,6,5,4,8]=>[2,3,1,6,5,7,4,8]=>[3,2,1,7,6,5,4,8]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[2,3,1,6,5,8,4,7]=>[3,2,1,8,6,5,4,7]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>[2,3,1,8,4,7,5,6]=>[3,2,1,8,7,5,4,6]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>[2,3,1,6,8,4,7,5]=>[3,2,1,8,7,6,4,5]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>[2,4,1,3,5,6,8,7]=>[4,2,1,3,5,6,8,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>[2,4,1,3,5,7,6,8]=>[4,2,1,3,5,7,6,8]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>[2,4,1,3,5,8,6,7]=>[4,2,1,3,5,8,6,7]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>[2,4,1,3,5,7,8,6]=>[4,2,1,3,5,8,7,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>[2,4,1,3,6,5,7,8]=>[4,2,1,3,6,5,7,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>[2,4,1,3,7,5,6,8]=>[4,2,1,3,7,5,6,8]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[2,4,1,3,7,8,5,6]=>[4,2,1,3,8,5,7,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>[2,4,1,3,6,7,5,8]=>[4,2,1,3,7,6,5,8]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[2,4,1,3,8,5,7,6]=>[4,2,1,3,8,7,5,6]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[2,4,1,3,7,6,8,5]=>[4,2,1,3,8,7,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,5,1,7,6,8]=>[2,5,1,3,4,7,6,8]=>[5,2,1,3,4,7,6,8]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,5,1,7,8,6]=>[2,5,1,3,4,8,6,7]=>[5,2,1,3,4,8,6,7]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>[2,5,1,3,4,7,8,6]=>[5,2,1,3,4,8,7,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>[6,2,1,3,4,5,7,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>[7,2,1,3,4,5,6,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>[8,2,1,3,4,5,7,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,5,7,6,1,8]=>[2,6,7,1,3,4,5,8]=>[7,2,1,3,4,6,5,8]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>[2,6,8,1,3,4,5,7]=>[8,2,1,3,4,6,5,7]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,7,8,6,1]=>[2,8,1,3,4,5,7,6]=>[8,2,1,3,4,7,5,6]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,2,4,6,5,1,8,7]=>[2,5,6,1,3,4,8,7]=>[6,2,1,3,5,4,8,7]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,2,4,6,7,5,8,1]=>[2,8,1,3,4,6,5,7]=>[8,2,1,3,6,4,5,7]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,4,6,7,8,5,1]=>[2,7,5,8,1,3,4,6]=>[8,2,1,3,7,4,5,6]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,2,4,7,6,5,1,8]=>[2,6,5,7,1,3,4,8]=>[7,2,1,3,6,5,4,8]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>[2,6,5,8,1,3,4,7]=>[8,2,1,3,6,5,4,7]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,7,8,6,5,1]=>[2,6,8,1,3,4,7,5]=>[8,2,1,3,7,6,4,5]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[2,6,7,5,8,1,3,4]=>[8,2,1,3,7,6,5,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>[2,4,5,1,3,6,7,8]=>[5,2,1,4,3,6,7,8]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>[2,4,5,1,3,7,6,8]=>[5,2,1,4,3,7,6,8]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[2,4,5,1,3,7,8,6]=>[5,2,1,4,3,8,7,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,5,4,6,1,7,8]=>[2,4,6,1,3,5,7,8]=>[6,2,1,4,3,5,7,8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>[2,4,6,1,3,5,8,7]=>[6,2,1,4,3,5,8,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,5,4,6,7,1,8]=>[2,4,7,1,3,5,6,8]=>[7,2,1,4,3,5,6,8]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,5,4,6,7,8,1]=>[2,4,8,1,3,5,6,7]=>[8,2,1,4,3,5,6,7]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>[8,2,1,4,3,5,7,6]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[2,4,6,7,1,3,5,8]=>[7,2,1,4,3,6,5,8]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>[8,2,1,4,3,6,5,7]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,4,7,8,6,1]=>[2,4,8,1,3,5,7,6]=>[8,2,1,4,3,7,5,6]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,5,6,4,1,8,7]=>[2,6,1,3,5,4,8,7]=>[6,2,1,5,3,4,8,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,5,6,4,7,8,1]=>[2,8,1,3,5,4,6,7]=>[8,2,1,5,3,4,6,7]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,5,6,7,4,8,1]=>[2,6,4,8,1,3,5,7]=>[8,2,1,6,3,4,5,7]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]=>[2,8,1,3,5,7,4,6]=>[8,2,1,7,3,4,5,6]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,5,6,8,7,4,1]=>[2,7,4,6,8,1,3,5]=>[8,2,1,7,3,4,6,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,5,7,6,4,1,8]=>[2,7,1,3,5,6,4,8]=>[7,2,1,6,3,5,4,8]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,5,7,6,4,8,1]=>[2,8,1,3,5,6,4,7]=>[8,2,1,6,3,5,4,7]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,5,7,6,8,4,1]=>[2,7,4,8,1,3,5,6]=>[8,2,1,7,3,5,4,6]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,5,7,8,6,4,1]=>[2,6,7,4,8,1,3,5]=>[8,2,1,7,3,6,4,5]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,5,8,7,6,4,1]=>[2,6,8,1,3,5,7,4]=>[8,2,1,7,3,6,5,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,2,6,5,4,1,8,7]=>[2,5,4,6,1,3,8,7]=>[6,2,1,5,4,3,8,7]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]=>[2,5,4,7,8,1,3,6]=>[8,2,1,5,4,3,7,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,2,6,5,7,4,1,8]=>[2,7,1,3,6,4,5,8]=>[7,2,1,6,4,3,5,8]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>[2,8,1,3,6,4,5,7]=>[8,2,1,6,4,3,5,7]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,2,6,5,7,8,4,1]=>[2,7,4,5,8,1,3,6]=>[8,2,1,7,4,3,5,6]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,2,6,5,8,7,4,1]=>[2,8,1,3,6,7,4,5]=>[8,2,1,7,4,3,6,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[2,5,7,1,3,6,4,8]=>[7,2,1,6,5,3,4,8]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]=>[2,5,8,1,3,6,4,7]=>[8,2,1,6,5,3,4,7]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,2,6,7,5,8,4,1]=>[2,5,7,4,8,1,3,6]=>[8,2,1,7,5,3,4,6]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,6,8,7,5,4,1]=>[2,8,1,3,6,5,7,4]=>[8,2,1,7,6,3,5,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[2,5,6,4,7,1,3,8]=>[7,2,1,6,5,4,3,8]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,2,7,6,5,4,8,1]=>[2,5,6,4,8,1,3,7]=>[8,2,1,6,5,4,3,7]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,2,7,6,5,8,4,1]=>[2,5,8,1,3,7,4,6]=>[8,2,1,7,5,4,3,6]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,2,7,6,8,5,4,1]=>[2,8,1,3,7,4,6,5]=>[8,2,1,7,6,4,3,5]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,7,8,6,5,4,1]=>[2,6,5,8,1,3,7,4]=>[8,2,1,7,6,5,3,4]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>[2,6,5,7,4,8,1,3]=>[8,2,1,7,6,5,4,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,4,2,1,5,6,8,7]=>[4,1,3,2,5,6,8,7]=>[4,3,1,2,5,6,8,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,4,2,1,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>[4,3,1,2,5,7,6,8]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,4,2,1,5,7,8,6]=>[4,1,3,2,5,8,6,7]=>[4,3,1,2,5,8,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,4,2,1,5,8,7,6]=>[4,1,3,2,5,7,8,6]=>[4,3,1,2,5,8,7,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>[4,1,3,2,8,5,6,7]=>[4,3,1,2,8,5,6,7]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>[4,1,3,2,7,8,5,6]=>[4,3,1,2,8,5,7,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[4,1,3,2,6,8,5,7]=>[4,3,1,2,8,6,5,7]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[4,1,3,2,8,5,7,6]=>[4,3,1,2,8,7,5,6]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[4,1,3,2,7,6,8,5]=>[4,3,1,2,8,7,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>[5,3,1,2,4,6,7,8]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,4,2,5,1,6,8,7]=>[5,1,3,2,4,6,8,7]=>[5,3,1,2,4,6,8,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,2,5,1,7,6,8]=>[5,1,3,2,4,7,6,8]=>[5,3,1,2,4,7,6,8]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,2,5,1,7,8,6]=>[5,1,3,2,4,8,6,7]=>[5,3,1,2,4,8,6,7]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>[5,1,3,2,4,7,8,6]=>[5,3,1,2,4,8,7,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,4,2,5,6,1,8,7]=>[6,1,3,2,4,5,8,7]=>[6,3,1,2,4,5,8,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>[7,3,1,2,4,5,6,8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>[8,3,1,2,4,5,6,7]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,8,7,1]=>[7,8,1,3,2,4,5,6]=>[8,3,1,2,4,5,7,6]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,2,5,7,6,8,1]=>[6,8,1,3,2,4,5,7]=>[8,3,1,2,4,6,5,7]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>[8,1,3,2,4,5,7,6]=>[8,3,1,2,4,7,5,6]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,4,2,5,8,7,6,1]=>[7,6,8,1,3,2,4,5]=>[8,3,1,2,4,7,6,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,4,2,6,5,1,7,8]=>[5,6,1,3,2,4,7,8]=>[6,3,1,2,5,4,7,8]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,4,2,6,5,1,8,7]=>[5,6,1,3,2,4,8,7]=>[6,3,1,2,5,4,8,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,2,6,5,7,1,8]=>[5,7,1,3,2,4,6,8]=>[7,3,1,2,5,4,6,8]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,2,6,5,7,8,1]=>[5,8,1,3,2,4,6,7]=>[8,3,1,2,5,4,6,7]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,8,7,1]=>[5,7,8,1,3,2,4,6]=>[8,3,1,2,5,4,7,6]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,4,2,6,7,5,1,8]=>[7,1,3,2,4,6,5,8]=>[7,3,1,2,6,4,5,8]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>[8,1,3,2,4,6,5,7]=>[8,3,1,2,6,4,5,7]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,4,2,6,7,8,5,1]=>[7,5,8,1,3,2,4,6]=>[8,3,1,2,7,4,5,6]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,6,8,7,5,1]=>[8,1,3,2,4,6,7,5]=>[8,3,1,2,7,4,6,5]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,4,2,7,6,5,1,8]=>[6,5,7,1,3,2,4,8]=>[7,3,1,2,6,5,4,8]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,2,7,6,5,8,1]=>[6,5,8,1,3,2,4,7]=>[8,3,1,2,6,5,4,7]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,4,2,7,8,6,5,1]=>[6,8,1,3,2,4,7,5]=>[8,3,1,2,7,6,4,5]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[6,7,5,8,1,3,2,4]=>[8,3,1,2,7,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8]=>[4,2,5,1,3,6,7,8]=>[5,4,1,2,3,6,7,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,5,2,1,6,8,7]=>[4,2,5,1,3,6,8,7]=>[5,4,1,2,3,6,8,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,5,2,1,7,6,8]=>[4,2,5,1,3,7,6,8]=>[5,4,1,2,3,7,6,8]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,5,2,1,7,8,6]=>[4,2,5,1,3,8,6,7]=>[5,4,1,2,3,8,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>[4,2,5,1,3,7,8,6]=>[5,4,1,2,3,8,7,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,2,6,1,7,8]=>[4,2,6,1,3,5,7,8]=>[6,4,1,2,3,5,7,8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,2,6,1,8,7]=>[4,2,6,1,3,5,8,7]=>[6,4,1,2,3,5,8,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,5,2,6,7,1,8]=>[4,2,7,1,3,5,6,8]=>[7,4,1,2,3,5,6,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>[4,2,8,1,3,5,6,7]=>[8,4,1,2,3,5,6,7]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,2,6,8,7,1]=>[4,2,7,8,1,3,5,6]=>[8,4,1,2,3,5,7,6]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,5,2,7,6,1,8]=>[4,2,6,7,1,3,5,8]=>[7,4,1,2,3,6,5,8]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,2,7,6,8,1]=>[4,2,6,8,1,3,5,7]=>[8,4,1,2,3,6,5,7]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,2,7,8,6,1]=>[4,2,8,1,3,5,7,6]=>[8,4,1,2,3,7,5,6]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,2,8,7,6,1]=>[4,2,7,6,8,1,3,5]=>[8,4,1,2,3,7,6,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,2,1,7,8]=>[6,1,3,5,2,4,7,8]=>[6,5,1,2,3,4,7,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,2,1,8,7]=>[6,1,3,5,2,4,8,7]=>[6,5,1,2,3,4,8,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,2,7,1,8]=>[7,1,3,5,2,4,6,8]=>[7,5,1,2,3,4,6,8]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]=>[8,1,3,5,2,4,6,7]=>[8,5,1,2,3,4,6,7]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,2,8,7,1]=>[7,8,1,3,5,2,4,6]=>[8,5,1,2,3,4,7,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,2,1,8]=>[6,2,4,7,1,3,5,8]=>[7,6,1,2,3,4,5,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,2,8,1]=>[6,2,4,8,1,3,5,7]=>[8,6,1,2,3,4,5,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,2,1]=>[8,1,3,5,7,2,4,6]=>[8,7,1,2,3,4,5,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,7,2,1]=>[7,2,4,6,8,1,3,5]=>[8,7,1,2,3,4,6,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,7,6,2,8,1]=>[8,1,3,5,6,2,4,7]=>[8,6,1,2,3,5,4,7]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,6,8,2,1]=>[7,2,4,8,1,3,5,6]=>[8,7,1,2,3,5,4,6]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]=>[6,7,2,4,8,1,3,5]=>[8,7,1,2,3,6,4,5]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[6,8,1,3,5,7,2,4]=>[8,7,1,2,3,6,5,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,4,6,5,2,1,8,7]=>[5,2,4,6,1,3,8,7]=>[6,5,1,2,4,3,8,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,5,2,7,1,8]=>[5,2,4,7,1,3,6,8]=>[7,5,1,2,4,3,6,8]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,6,5,2,7,8,1]=>[5,2,4,8,1,3,6,7]=>[8,5,1,2,4,3,6,7]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,5,7,2,8,1]=>[8,1,3,6,2,4,5,7]=>[8,6,1,2,4,3,5,7]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,5,7,8,2,1]=>[7,2,4,5,8,1,3,6]=>[8,7,1,2,4,3,5,6]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,4,6,5,8,7,2,1]=>[8,1,3,6,7,2,4,5]=>[8,7,1,2,4,3,6,5]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,5,8,2,1]=>[5,7,2,4,8,1,3,6]=>[8,7,1,2,5,3,4,6]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,5,2,1]=>[7,2,4,8,1,3,6,5]=>[8,7,1,2,6,3,4,5]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,6,8,7,5,2,1]=>[8,1,3,6,5,7,2,4]=>[8,7,1,2,6,3,5,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,6,5,2,1,8]=>[5,6,2,4,7,1,3,8]=>[7,6,1,2,5,4,3,8]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,6,5,2,8,1]=>[5,6,2,4,8,1,3,7]=>[8,6,1,2,5,4,3,7]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,7,6,5,8,2,1]=>[5,8,1,3,7,2,4,6]=>[8,7,1,2,5,4,3,6]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,4,7,6,8,5,2,1]=>[8,1,3,7,2,4,6,5]=>[8,7,1,2,6,4,3,5]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,4,7,8,6,5,2,1]=>[6,5,8,1,3,7,2,4]=>[8,7,1,2,6,5,3,4]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[6,5,7,2,4,8,1,3]=>[8,7,1,2,6,5,4,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,4,2,1,6,7,8]=>[5,1,3,4,2,6,7,8]=>[5,4,1,3,2,6,7,8]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,4,2,1,6,8,7]=>[5,1,3,4,2,6,8,7]=>[5,4,1,3,2,6,8,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,4,2,1,7,6,8]=>[5,1,3,4,2,7,6,8]=>[5,4,1,3,2,7,6,8]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,4,2,1,7,8,6]=>[5,1,3,4,2,8,6,7]=>[5,4,1,3,2,8,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[5,1,3,4,2,7,8,6]=>[5,4,1,3,2,8,7,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,5,4,2,6,1,7,8]=>[6,1,3,4,2,5,7,8]=>[6,4,1,3,2,5,7,8]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,5,4,2,6,1,8,7]=>[6,1,3,4,2,5,8,7]=>[6,4,1,3,2,5,8,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>[7,1,3,4,2,5,6,8]=>[7,4,1,3,2,5,6,8]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,4,2,6,7,8,1]=>[8,1,3,4,2,5,6,7]=>[8,4,1,3,2,5,6,7]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,5,4,2,6,8,7,1]=>[7,8,1,3,4,2,5,6]=>[8,4,1,3,2,5,7,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,4,2,7,6,1,8]=>[6,7,1,3,4,2,5,8]=>[7,4,1,3,2,6,5,8]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,5,4,2,7,6,8,1]=>[6,8,1,3,4,2,5,7]=>[8,4,1,3,2,6,5,7]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,4,2,7,8,6,1]=>[8,1,3,4,2,5,7,6]=>[8,4,1,3,2,7,5,6]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,5,4,6,2,1,7,8]=>[5,2,6,1,3,4,7,8]=>[6,5,1,3,2,4,7,8]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,5,4,6,2,1,8,7]=>[5,2,6,1,3,4,8,7]=>[6,5,1,3,2,4,8,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,4,6,2,7,1,8]=>[5,2,7,1,3,4,6,8]=>[7,5,1,3,2,4,6,8]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,4,6,2,7,8,1]=>[5,2,8,1,3,4,6,7]=>[8,5,1,3,2,4,6,7]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,5,4,6,2,8,7,1]=>[5,2,7,8,1,3,4,6]=>[8,5,1,3,2,4,7,6]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,4,6,7,2,8,1]=>[8,1,3,4,6,2,5,7]=>[8,6,1,3,2,4,5,7]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,4,6,7,8,2,1]=>[7,2,5,8,1,3,4,6]=>[8,7,1,3,2,4,5,6]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,5,4,6,8,7,2,1]=>[8,1,3,4,6,7,2,5]=>[8,7,1,3,2,4,6,5]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,5,4,7,6,2,1,8]=>[6,2,5,7,1,3,4,8]=>[7,6,1,3,2,5,4,8]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,4,7,6,2,8,1]=>[6,2,5,8,1,3,4,7]=>[8,6,1,3,2,5,4,7]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,4,7,6,8,2,1]=>[8,1,3,4,7,2,5,6]=>[8,7,1,3,2,5,4,6]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,4,7,8,6,2,1]=>[6,8,1,3,4,7,2,5]=>[8,7,1,3,2,6,4,5]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,5,6,4,2,1,7,8]=>[4,5,2,6,1,3,7,8]=>[6,5,1,4,2,3,7,8]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,4,2,1,8,7]=>[4,5,2,6,1,3,8,7]=>[6,5,1,4,2,3,8,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,5,6,4,2,7,1,8]=>[4,5,2,7,1,3,6,8]=>[7,5,1,4,2,3,6,8]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,4,2,7,8,1]=>[4,5,2,8,1,3,6,7]=>[8,5,1,4,2,3,6,7]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,4,2,8,7,1]=>[4,5,2,7,8,1,3,6]=>[8,5,1,4,2,3,7,6]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,4,7,2,1,8]=>[4,7,1,3,6,2,5,8]=>[7,6,1,4,2,3,5,8]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]=>[4,8,1,3,6,2,5,7]=>[8,6,1,4,2,3,5,7]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,4,7,8,2,1]=>[4,7,2,5,8,1,3,6]=>[8,7,1,4,2,3,5,6]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,5,6,4,8,7,2,1]=>[4,8,1,3,6,7,2,5]=>[8,7,1,4,2,3,6,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,5,6,7,4,2,1,8]=>[7,1,3,6,2,5,4,8]=>[7,6,1,5,2,3,4,8]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>[8,1,3,6,2,5,4,7]=>[8,6,1,5,2,3,4,7]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,4,8,2,1]=>[7,2,5,4,8,1,3,6]=>[8,7,1,5,2,3,4,6]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[8,1,3,6,4,7,2,5]=>[8,7,1,6,2,3,4,5]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,7,4,2,1]=>[7,2,5,8,1,3,6,4]=>[8,7,1,6,2,3,5,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,6,4,2,1,8]=>[6,2,5,4,7,1,3,8]=>[7,6,1,5,2,4,3,8]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,6,4,2,8,1]=>[6,2,5,4,8,1,3,7]=>[8,6,1,5,2,4,3,7]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,5,7,6,8,4,2,1]=>[6,4,8,1,3,7,2,5]=>[8,7,1,6,2,4,3,5]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]=>[8,1,3,7,2,5,6,4]=>[8,7,1,6,2,5,3,4]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[7,2,5,6,4,8,1,3]=>[8,7,1,6,2,5,4,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,6,5,4,2,1,7,8]=>[4,6,1,3,5,2,7,8]=>[6,5,1,4,3,2,7,8]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>[4,6,1,3,5,2,8,7]=>[6,5,1,4,3,2,8,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,6,5,4,2,7,1,8]=>[4,7,1,3,5,2,6,8]=>[7,5,1,4,3,2,6,8]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,5,4,2,7,8,1]=>[4,8,1,3,5,2,6,7]=>[8,5,1,4,3,2,6,7]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,6,5,4,2,8,7,1]=>[4,7,8,1,3,5,2,6]=>[8,5,1,4,3,2,7,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,6,5,4,7,2,1,8]=>[4,6,2,7,1,3,5,8]=>[7,6,1,4,3,2,5,8]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]=>[4,6,2,8,1,3,5,7]=>[8,6,1,4,3,2,5,7]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,6,5,4,7,8,2,1]=>[4,8,1,3,5,7,2,6]=>[8,7,1,4,3,2,5,6]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,6,5,4,8,7,2,1]=>[4,7,2,6,8,1,3,5]=>[8,7,1,4,3,2,6,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,6,5,7,4,2,8,1]=>[6,2,8,1,3,5,4,7]=>[8,6,1,5,3,2,4,7]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,6,5,7,4,8,2,1]=>[8,1,3,5,4,7,2,6]=>[8,7,1,5,3,2,4,6]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,6,5,7,8,4,2,1]=>[7,2,6,4,8,1,3,5]=>[8,7,1,6,3,2,4,5]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,6,5,8,7,4,2,1]=>[8,1,3,5,7,2,6,4]=>[8,7,1,6,3,2,5,4]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,5,4,8,2,1]=>[5,4,8,1,3,7,2,6]=>[8,7,1,5,4,2,3,6]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,5,8,4,2,1]=>[8,1,3,7,2,6,4,5]=>[8,7,1,6,4,2,3,5]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,5,4,2,1]=>[5,8,1,3,7,2,6,4]=>[8,7,1,6,5,2,3,4]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,7,5,4,2,1]=>[5,7,2,6,4,8,1,3]=>[8,7,1,6,5,2,4,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,7,6,5,4,2,1,8]=>[5,4,7,1,3,6,2,8]=>[7,6,1,5,4,3,2,8]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,7,6,5,4,2,8,1]=>[5,4,8,1,3,6,2,7]=>[8,6,1,5,4,3,2,7]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,6,5,4,8,2,1]=>[5,4,7,2,8,1,3,6]=>[8,7,1,5,4,3,2,6]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,6,5,8,4,2,1]=>[7,2,8,1,3,6,4,5]=>[8,7,1,6,4,3,2,5]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]=>[5,7,2,8,1,3,6,4]=>[8,7,1,6,5,3,2,4]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,6,5,4,2,1]=>[5,6,4,7,2,8,1,3]=>[8,7,1,6,5,4,2,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[3,2,4,1,5,8,6,7]=>[4,3,2,1,5,8,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[3,2,4,1,7,5,6,8]=>[4,3,2,1,7,5,6,8]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[3,2,4,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[3,2,4,1,7,8,5,6]=>[4,3,2,1,8,5,7,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[3,2,4,1,6,8,5,7]=>[4,3,2,1,8,6,5,7]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[3,2,4,1,8,5,7,6]=>[4,3,2,1,8,7,5,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>[3,2,5,1,4,6,7,8]=>[5,3,2,1,4,6,7,8]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,3,2,5,1,6,8,7]=>[3,2,5,1,4,6,8,7]=>[5,3,2,1,4,6,8,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,3,2,5,1,7,6,8]=>[3,2,5,1,4,7,6,8]=>[5,3,2,1,4,7,6,8]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,3,2,5,1,7,8,6]=>[3,2,5,1,4,8,6,7]=>[5,3,2,1,4,8,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[3,2,5,1,4,7,8,6]=>[5,3,2,1,4,8,7,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,3,2,5,6,1,7,8]=>[3,2,6,1,4,5,7,8]=>[6,3,2,1,4,5,7,8]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,3,2,5,6,1,8,7]=>[3,2,6,1,4,5,8,7]=>[6,3,2,1,4,5,8,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,7,1,8]=>[3,2,7,1,4,5,6,8]=>[7,3,2,1,4,5,6,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[3,2,8,1,4,5,6,7]=>[8,3,2,1,4,5,6,7]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>[8,3,2,1,4,5,7,6]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,3,2,5,7,6,1,8]=>[3,2,6,7,1,4,5,8]=>[7,3,2,1,4,6,5,8]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,3,2,5,7,6,8,1]=>[3,2,6,8,1,4,5,7]=>[8,3,2,1,4,6,5,7]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>[3,2,7,6,8,1,4,5]=>[8,3,2,1,4,7,6,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,3,2,6,5,1,7,8]=>[3,2,5,6,1,4,7,8]=>[6,3,2,1,5,4,7,8]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,3,2,6,5,1,8,7]=>[3,2,5,6,1,4,8,7]=>[6,3,2,1,5,4,8,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,3,2,6,5,7,1,8]=>[3,2,5,7,1,4,6,8]=>[7,3,2,1,5,4,6,8]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>[3,2,5,8,1,4,6,7]=>[8,3,2,1,5,4,6,7]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,3,2,6,7,5,1,8]=>[3,2,7,1,4,6,5,8]=>[7,3,2,1,6,4,5,8]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,6,7,5,8,1]=>[3,2,8,1,4,6,5,7]=>[8,3,2,1,6,4,5,7]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,6,7,8,5,1]=>[3,2,7,5,8,1,4,6]=>[8,3,2,1,7,4,5,6]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,3,2,6,8,7,5,1]=>[3,2,8,1,4,6,7,5]=>[8,3,2,1,7,4,6,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,2,7,6,5,1,8]=>[3,2,6,5,7,1,4,8]=>[7,3,2,1,6,5,4,8]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[3,2,6,5,8,1,4,7]=>[8,3,2,1,6,5,4,7]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,7,8,6,5,1]=>[3,2,6,8,1,4,7,5]=>[8,3,2,1,7,6,4,5]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[3,2,6,7,5,8,1,4]=>[8,3,2,1,7,6,5,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,3,5,2,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>[5,4,2,1,3,6,7,8]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,3,5,2,1,6,8,7]=>[5,1,4,2,3,6,8,7]=>[5,4,2,1,3,6,8,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,3,5,2,1,7,8,6]=>[5,1,4,2,3,8,6,7]=>[5,4,2,1,3,8,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>[5,1,4,2,3,7,8,6]=>[5,4,2,1,3,8,7,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,3,5,2,6,1,7,8]=>[6,1,4,2,3,5,7,8]=>[6,4,2,1,3,5,7,8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>[6,1,4,2,3,5,8,7]=>[6,4,2,1,3,5,8,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,3,5,2,6,7,1,8]=>[7,1,4,2,3,5,6,8]=>[7,4,2,1,3,5,6,8]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>[8,4,2,1,3,5,6,7]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,3,5,2,6,8,7,1]=>[7,8,1,4,2,3,5,6]=>[8,4,2,1,3,5,7,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,3,5,2,7,6,1,8]=>[6,7,1,4,2,3,5,8]=>[7,4,2,1,3,6,5,8]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>[6,8,1,4,2,3,5,7]=>[8,4,2,1,3,6,5,7]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,3,5,2,8,7,6,1]=>[7,6,8,1,4,2,3,5]=>[8,4,2,1,3,7,6,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,3,5,6,2,1,7,8]=>[5,2,3,6,1,4,7,8]=>[6,5,2,1,3,4,7,8]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,3,5,6,2,1,8,7]=>[5,2,3,6,1,4,8,7]=>[6,5,2,1,3,4,8,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,1]=>[5,2,3,8,1,4,6,7]=>[8,5,2,1,3,4,6,7]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,7,2,1,8]=>[7,1,4,6,2,3,5,8]=>[7,6,2,1,3,4,5,8]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,7,2,8,1]=>[8,1,4,6,2,3,5,7]=>[8,6,2,1,3,4,5,7]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,2,1]=>[7,2,3,5,8,1,4,6]=>[8,7,2,1,3,4,5,6]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,8,7,2,1]=>[8,1,4,6,7,2,3,5]=>[8,7,2,1,3,4,6,5]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,3,5,7,6,2,1,8]=>[6,2,3,5,7,1,4,8]=>[7,6,2,1,3,5,4,8]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,3,5,7,6,2,8,1]=>[6,2,3,5,8,1,4,7]=>[8,6,2,1,3,5,4,7]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,3,5,7,6,8,2,1]=>[8,1,4,7,2,3,5,6]=>[8,7,2,1,3,5,4,6]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,7,8,6,2,1]=>[6,8,1,4,7,2,3,5]=>[8,7,2,1,3,6,4,5]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,3,5,8,7,6,2,1]=>[6,7,2,3,5,8,1,4]=>[8,7,2,1,3,6,5,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,3,6,5,2,1,8,7]=>[6,1,4,5,2,3,8,7]=>[6,5,2,1,4,3,8,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,3,6,5,2,7,1,8]=>[7,1,4,5,2,3,6,8]=>[7,5,2,1,4,3,6,8]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,3,6,5,2,7,8,1]=>[8,1,4,5,2,3,6,7]=>[8,5,2,1,4,3,6,7]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>[7,8,1,4,5,2,3,6]=>[8,5,2,1,4,3,7,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,3,6,5,7,2,1,8]=>[6,2,3,7,1,4,5,8]=>[7,6,2,1,4,3,5,8]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>[6,2,3,8,1,4,5,7]=>[8,6,2,1,4,3,5,7]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,2,1]=>[8,1,4,5,7,2,3,6]=>[8,7,2,1,4,3,5,6]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>[7,2,3,6,8,1,4,5]=>[8,7,2,1,4,3,6,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,6,7,5,2,8,1]=>[5,6,2,3,8,1,4,7]=>[8,6,2,1,5,3,4,7]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,3,6,7,5,8,2,1]=>[5,8,1,4,7,2,3,6]=>[8,7,2,1,5,3,4,6]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,5,2,1]=>[8,1,4,7,2,3,6,5]=>[8,7,2,1,6,3,4,5]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,3,6,8,7,5,2,1]=>[7,2,3,6,5,8,1,4]=>[8,7,2,1,6,3,5,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,7,6,5,2,8,1]=>[5,8,1,4,6,2,3,7]=>[8,6,2,1,5,4,3,7]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,7,6,5,8,2,1]=>[5,7,2,3,8,1,4,6]=>[8,7,2,1,5,4,3,6]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,7,6,8,5,2,1]=>[7,2,3,8,1,4,6,5]=>[8,7,2,1,6,4,3,5]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,7,8,6,5,2,1]=>[6,5,7,2,3,8,1,4]=>[8,7,2,1,6,5,3,4]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,3,8,7,6,5,2,1]=>[6,5,8,1,4,7,2,3]=>[8,7,2,1,6,5,4,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8]=>[3,5,1,4,2,6,7,8]=>[5,4,3,1,2,6,7,8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,3,2,1,6,8,7]=>[3,5,1,4,2,6,8,7]=>[5,4,3,1,2,6,8,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,5,3,2,1,7,6,8]=>[3,5,1,4,2,7,6,8]=>[5,4,3,1,2,7,6,8]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,5,3,2,1,7,8,6]=>[3,5,1,4,2,8,6,7]=>[5,4,3,1,2,8,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>[3,5,1,4,2,7,8,6]=>[5,4,3,1,2,8,7,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,5,3,2,6,1,7,8]=>[3,6,1,4,2,5,7,8]=>[6,4,3,1,2,5,7,8]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,3,2,6,1,8,7]=>[3,6,1,4,2,5,8,7]=>[6,4,3,1,2,5,8,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,5,3,2,6,7,1,8]=>[3,7,1,4,2,5,6,8]=>[7,4,3,1,2,5,6,8]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,3,2,6,7,8,1]=>[3,8,1,4,2,5,6,7]=>[8,4,3,1,2,5,6,7]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,3,2,7,6,1,8]=>[3,6,7,1,4,2,5,8]=>[7,4,3,1,2,6,5,8]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,5,3,2,7,6,8,1]=>[3,6,8,1,4,2,5,7]=>[8,4,3,1,2,6,5,7]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,5,3,2,7,8,6,1]=>[3,8,1,4,2,5,7,6]=>[8,4,3,1,2,7,5,6]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,3,2,8,7,6,1]=>[3,7,6,8,1,4,2,5]=>[8,4,3,1,2,7,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,5,3,6,2,1,7,8]=>[3,5,2,6,1,4,7,8]=>[6,5,3,1,2,4,7,8]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[3,5,2,6,1,4,8,7]=>[6,5,3,1,2,4,8,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>[3,5,2,7,1,4,6,8]=>[7,5,3,1,2,4,6,8]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,3,6,2,8,7,1]=>[3,5,2,7,8,1,4,6]=>[8,5,3,1,2,4,7,6]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,5,3,6,7,2,1,8]=>[3,7,1,4,6,2,5,8]=>[7,6,3,1,2,4,5,8]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,3,6,7,2,8,1]=>[3,8,1,4,6,2,5,7]=>[8,6,3,1,2,4,5,7]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,3,6,7,8,2,1]=>[3,7,2,5,8,1,4,6]=>[8,7,3,1,2,4,5,6]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,6,8,7,2,1]=>[3,8,1,4,6,7,2,5]=>[8,7,3,1,2,4,6,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,3,7,6,2,1,8]=>[3,6,2,5,7,1,4,8]=>[7,6,3,1,2,5,4,8]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,5,3,7,6,2,8,1]=>[3,6,2,5,8,1,4,7]=>[8,6,3,1,2,5,4,7]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,3,7,6,8,2,1]=>[3,8,1,4,7,2,5,6]=>[8,7,3,1,2,5,4,6]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,3,7,8,6,2,1]=>[3,6,8,1,4,7,2,5]=>[8,7,3,1,2,6,4,5]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,3,8,7,6,2,1]=>[3,6,7,2,5,8,1,4]=>[8,7,3,1,2,6,5,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,6,3,2,1,7,8]=>[5,2,6,1,4,3,7,8]=>[6,5,4,1,2,3,7,8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[5,2,6,1,4,3,8,7]=>[6,5,4,1,2,3,8,7]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,3,2,8,7,1]=>[5,2,7,8,1,4,3,6]=>[8,5,4,1,2,3,7,6]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,6,3,7,2,1,8]=>[7,1,4,3,6,2,5,8]=>[7,6,4,1,2,3,5,8]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>[8,1,4,3,6,2,5,7]=>[8,6,4,1,2,3,5,7]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,6,3,7,8,2,1]=>[7,2,5,8,1,4,3,6]=>[8,7,4,1,2,3,5,6]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,3,8,7,2,1]=>[8,1,4,3,6,7,2,5]=>[8,7,4,1,2,3,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>[6,2,5,3,7,1,4,8]=>[7,6,5,1,2,3,4,8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[6,2,5,3,8,1,4,7]=>[8,6,5,1,2,3,4,7]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[8,1,4,7,2,5,3,6]=>[8,7,5,1,2,3,4,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[6,3,8,1,4,7,2,5]=>[8,7,6,1,2,3,4,5]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,7,3,2,1]=>[6,3,7,2,5,8,1,4]=>[8,7,6,1,2,3,5,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,5,7,6,3,2,8,1]=>[8,1,4,6,2,5,3,7]=>[8,6,5,1,2,4,3,7]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,5,7,6,3,8,2,1]=>[7,2,5,3,8,1,4,6]=>[8,7,5,1,2,4,3,6]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,6,8,3,2,1]=>[8,1,4,6,3,7,2,5]=>[8,7,6,1,2,4,3,5]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,6,3,2,1]=>[7,2,5,6,3,8,1,4]=>[8,7,6,1,2,5,3,4]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]=>[8,1,4,7,2,5,6,3]=>[8,7,6,1,2,5,4,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,6,5,3,2,1,8,7]=>[6,1,4,3,5,2,8,7]=>[6,5,4,1,3,2,8,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,6,5,3,2,7,8,1]=>[8,1,4,3,5,2,6,7]=>[8,5,4,1,3,2,6,7]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,5,3,2,8,7,1]=>[7,8,1,4,3,5,2,6]=>[8,5,4,1,3,2,7,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,6,5,3,7,2,1,8]=>[6,2,7,1,4,3,5,8]=>[7,6,4,1,3,2,5,8]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,5,3,7,2,8,1]=>[6,2,8,1,4,3,5,7]=>[8,6,4,1,3,2,5,7]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,6,5,3,8,7,2,1]=>[7,2,6,8,1,4,3,5]=>[8,7,4,1,3,2,6,5]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,6,5,7,3,2,1,8]=>[5,3,6,2,7,1,4,8]=>[7,6,5,1,3,2,4,8]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,5,7,3,2,8,1]=>[5,3,6,2,8,1,4,7]=>[8,6,5,1,3,2,4,7]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,6,5,7,3,8,2,1]=>[5,3,8,1,4,7,2,6]=>[8,7,5,1,3,2,4,6]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,3,2,1]=>[8,1,4,7,2,6,3,5]=>[8,7,6,1,3,2,4,5]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]=>[7,2,6,3,5,8,1,4]=>[8,7,6,1,3,2,5,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,6,7,5,3,2,1,8]=>[6,2,7,1,4,5,3,8]=>[7,6,5,1,4,2,3,8]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,5,3,2,8,1]=>[6,2,8,1,4,5,3,7]=>[8,6,5,1,4,2,3,7]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,6,7,5,3,8,2,1]=>[8,1,4,5,3,7,2,6]=>[8,7,5,1,4,2,3,6]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,5,3,2,1]=>[5,7,2,6,3,8,1,4]=>[8,7,6,1,5,2,3,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>[5,8,1,4,7,2,6,3]=>[8,7,6,1,5,2,4,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>[7,1,4,5,3,6,2,8]=>[7,6,5,1,4,3,2,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,6,5,3,2,8,1]=>[8,1,4,5,3,6,2,7]=>[8,6,5,1,4,3,2,7]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,6,5,3,8,2,1]=>[7,2,8,1,4,5,3,6]=>[8,7,5,1,4,3,2,6]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>[6,3,7,2,8,1,4,5]=>[8,7,6,1,4,3,2,5]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,6,8,5,3,2,1]=>[5,6,3,7,2,8,1,4]=>[8,7,6,1,5,3,2,4]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,6,5,3,2,1]=>[5,7,2,8,1,4,6,3]=>[8,7,6,1,5,4,2,3]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[5,8,1,4,6,3,7,2]=>[8,7,6,1,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[3,4,2,5,1,6,8,7]=>[5,4,3,2,1,6,8,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[3,4,2,5,1,8,6,7]=>[5,4,3,2,1,8,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[3,4,2,6,1,5,7,8]=>[6,4,3,2,1,5,7,8]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[3,4,2,6,1,5,8,7]=>[6,4,3,2,1,5,8,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>[3,4,2,7,1,5,6,8]=>[7,4,3,2,1,5,6,8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[3,4,2,8,1,5,6,7]=>[8,4,3,2,1,5,6,7]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>[3,4,2,7,8,1,5,6]=>[8,4,3,2,1,5,7,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[3,4,2,6,7,1,5,8]=>[7,4,3,2,1,6,5,8]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>[3,4,2,6,8,1,5,7]=>[8,4,3,2,1,6,5,7]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>[3,4,2,8,1,5,7,6]=>[8,4,3,2,1,7,5,6]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[3,4,2,7,6,8,1,5]=>[8,4,3,2,1,7,6,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,4,3,6,2,1,7,8]=>[3,6,1,5,2,4,7,8]=>[6,5,3,2,1,4,7,8]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,4,3,6,2,1,8,7]=>[3,6,1,5,2,4,8,7]=>[6,5,3,2,1,4,8,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,4,3,6,2,7,1,8]=>[3,7,1,5,2,4,6,8]=>[7,5,3,2,1,4,6,8]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,1]=>[3,8,1,5,2,4,6,7]=>[8,5,3,2,1,4,6,7]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,4,3,6,2,8,7,1]=>[3,7,8,1,5,2,4,6]=>[8,5,3,2,1,4,7,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,4,3,6,7,2,1,8]=>[3,6,2,4,7,1,5,8]=>[7,6,3,2,1,4,5,8]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,4,3,6,7,2,8,1]=>[3,6,2,4,8,1,5,7]=>[8,6,3,2,1,4,5,7]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,2,1]=>[3,8,1,5,7,2,4,6]=>[8,7,3,2,1,4,5,6]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,4,3,6,8,7,2,1]=>[3,7,2,4,6,8,1,5]=>[8,7,3,2,1,4,6,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,4,3,7,6,2,1,8]=>[3,7,1,5,6,2,4,8]=>[7,6,3,2,1,5,4,8]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,4,3,7,6,2,8,1]=>[3,8,1,5,6,2,4,7]=>[8,6,3,2,1,5,4,7]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,4,3,7,6,8,2,1]=>[3,7,2,4,8,1,5,6]=>[8,7,3,2,1,5,4,6]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,3,7,8,6,2,1]=>[3,6,7,2,4,8,1,5]=>[8,7,3,2,1,6,4,5]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,4,3,8,7,6,2,1]=>[3,6,8,1,5,7,2,4]=>[8,7,3,2,1,6,5,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,4,6,3,2,1,7,8]=>[6,1,5,2,4,3,7,8]=>[6,5,4,2,1,3,7,8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,4,6,3,2,1,8,7]=>[6,1,5,2,4,3,8,7]=>[6,5,4,2,1,3,8,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,4,6,3,2,7,1,8]=>[7,1,5,2,4,3,6,8]=>[7,5,4,2,1,3,6,8]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,4,6,3,2,7,8,1]=>[8,1,5,2,4,3,6,7]=>[8,5,4,2,1,3,6,7]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,4,6,3,2,8,7,1]=>[7,8,1,5,2,4,3,6]=>[8,5,4,2,1,3,7,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[6,2,4,3,8,1,5,7]=>[8,6,4,2,1,3,5,7]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,6,3,7,8,2,1]=>[8,1,5,7,2,4,3,6]=>[8,7,4,2,1,3,5,6]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,4,6,3,8,7,2,1]=>[7,2,4,3,6,8,1,5]=>[8,7,4,2,1,3,6,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,4,6,7,3,2,1,8]=>[7,1,5,3,6,2,4,8]=>[7,6,5,2,1,3,4,8]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[7,2,4,8,1,5,3,6]=>[8,7,5,2,1,3,4,6]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[6,3,7,2,4,8,1,5]=>[8,7,6,2,1,3,4,5]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,4,6,8,7,3,2,1]=>[6,3,8,1,5,7,2,4]=>[8,7,6,2,1,3,5,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,4,7,6,3,2,8,1]=>[6,2,4,8,1,5,3,7]=>[8,6,5,2,1,4,3,7]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,4,7,6,3,8,2,1]=>[8,1,5,3,7,2,4,6]=>[8,7,5,2,1,4,3,6]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,4,7,6,8,3,2,1]=>[7,2,4,6,3,8,1,5]=>[8,7,6,2,1,4,3,5]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,4,7,8,6,3,2,1]=>[8,1,5,6,3,7,2,4]=>[8,7,6,2,1,5,3,4]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,4,8,7,6,3,2,1]=>[7,2,4,8,1,5,6,3]=>[8,7,6,2,1,5,4,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,4,3,2,1,7,8]=>[4,3,6,1,5,2,7,8]=>[6,5,4,3,1,2,7,8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,6,4,3,2,1,8,7]=>[4,3,6,1,5,2,8,7]=>[6,5,4,3,1,2,8,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,6,4,3,2,7,1,8]=>[4,3,7,1,5,2,6,8]=>[7,5,4,3,1,2,6,8]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,6,4,3,2,8,7,1]=>[4,3,7,8,1,5,2,6]=>[8,5,4,3,1,2,7,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,6,4,3,7,2,1,8]=>[4,3,6,2,7,1,5,8]=>[7,6,4,3,1,2,5,8]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,6,4,3,7,2,8,1]=>[4,3,6,2,8,1,5,7]=>[8,6,4,3,1,2,5,7]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,6,4,3,7,8,2,1]=>[4,3,8,1,5,7,2,6]=>[8,7,4,3,1,2,5,6]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,4,3,8,7,2,1]=>[4,3,7,2,6,8,1,5]=>[8,7,4,3,1,2,6,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,6,4,7,3,2,1,8]=>[6,2,7,1,5,3,4,8]=>[7,6,5,3,1,2,4,8]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,6,4,7,3,8,2,1]=>[8,1,5,3,4,7,2,6]=>[8,7,5,3,1,2,4,6]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[7,2,6,3,4,8,1,5]=>[8,7,6,3,1,2,4,5]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,4,8,7,3,2,1]=>[8,1,5,7,2,6,3,4]=>[8,7,6,3,1,2,5,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[4,6,2,7,1,5,3,8]=>[7,6,5,4,1,2,3,8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,4,3,2,8,1]=>[4,6,2,8,1,5,3,7]=>[8,6,5,4,1,2,3,7]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,4,3,8,2,1]=>[4,8,1,5,3,7,2,6]=>[8,7,5,4,1,2,3,6]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[4,7,2,6,3,8,1,5]=>[8,7,6,4,1,2,3,5]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[7,2,6,3,8,1,5,4]=>[8,7,6,5,1,2,3,4]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]=>[8,1,5,4,7,2,6,3]=>[8,7,6,5,1,2,4,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>[4,7,1,5,3,6,2,8]=>[7,6,5,4,1,3,2,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,6,4,3,2,8,1]=>[4,8,1,5,3,6,2,7]=>[8,6,5,4,1,3,2,7]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]=>[4,7,2,8,1,5,3,6]=>[8,7,5,4,1,3,2,6]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,6,4,8,3,2,1]=>[4,6,3,7,2,8,1,5]=>[8,7,6,4,1,3,2,5]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>[6,3,7,2,8,1,5,4]=>[8,7,6,5,1,3,2,4]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]=>[7,2,8,1,5,4,6,3]=>[8,7,6,5,1,4,2,3]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[8,1,5,4,6,3,7,2]=>[8,7,6,5,1,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,5,4,3,2,7,1,8]=>[4,3,5,2,7,1,6,8]=>[7,5,4,3,2,1,6,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>[4,3,5,2,8,1,6,7]=>[8,5,4,3,2,1,6,7]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>[4,3,5,2,7,8,1,6]=>[8,5,4,3,2,1,7,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,5,4,3,7,2,1,8]=>[4,3,7,1,6,2,5,8]=>[7,6,4,3,2,1,5,8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>[4,3,8,1,6,2,5,7]=>[8,6,4,3,2,1,5,7]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[4,3,7,2,5,8,1,6]=>[8,7,4,3,2,1,5,6]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,5,4,3,8,7,2,1]=>[4,3,8,1,6,7,2,5]=>[8,7,4,3,2,1,6,5]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>[7,1,6,2,5,3,4,8]=>[7,6,5,3,2,1,4,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,5,4,7,3,2,8,1]=>[8,1,6,2,5,3,4,7]=>[8,6,5,3,2,1,4,7]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[7,2,5,3,4,8,1,6]=>[8,7,5,3,2,1,4,6]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]=>[8,1,6,3,4,7,2,5]=>[8,7,6,3,2,1,4,5]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,5,4,8,7,3,2,1]=>[7,2,5,8,1,6,3,4]=>[8,7,6,3,2,1,5,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>[4,7,1,6,2,5,3,8]=>[7,6,5,4,2,1,3,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>[4,8,1,6,2,5,3,7]=>[8,6,5,4,2,1,3,7]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[4,7,2,5,3,8,1,6]=>[8,7,5,4,2,1,3,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>[4,8,1,6,3,7,2,5]=>[8,7,6,4,2,1,3,5]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>[8,1,6,3,7,2,5,4]=>[8,7,6,5,2,1,3,4]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>[7,2,5,4,8,1,6,3]=>[8,7,6,5,2,1,4,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>[4,5,3,7,1,6,2,8]=>[7,6,5,4,3,1,2,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]=>[4,5,3,8,1,6,2,7]=>[8,6,5,4,3,1,2,7]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[4,5,3,7,2,8,1,6]=>[8,7,5,4,3,1,2,6]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,5,4,8,3,2,1]=>[4,7,2,8,1,6,3,5]=>[8,7,6,4,3,1,2,5]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>[7,2,8,1,6,3,5,4]=>[8,7,6,5,3,1,2,4]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[5,4,7,2,8,1,6,3]=>[8,7,6,5,4,1,2,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>[5,4,8,1,6,3,7,2]=>[8,7,6,5,4,1,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[4,5,3,6,2,8,1,7]=>[8,6,5,4,3,2,1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>[4,5,3,8,1,7,2,6]=>[8,7,5,4,3,2,1,6]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>[4,8,1,7,2,6,3,5]=>[8,7,6,4,3,2,1,5]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>[8,1,7,2,6,3,5,4]=>[8,7,6,5,3,2,1,4]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>[5,4,8,1,7,2,6,3]=>[8,7,6,5,4,2,1,3]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>[5,4,6,3,8,1,7,2]=>[8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>[5,4,6,3,7,2,8,1,9]=>[8,7,6,5,4,3,2,1,9]
[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]=>[1,6,5,7,4,8,3,9,2]=>[1,9,8,7,6,5,4,3,2]
[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]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]
[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]=>[1,6,7,5,8,4,9,3,10,2]=>[1,10,9,8,7,6,5,4,3,2]
[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]=>[6,5,7,4,8,3,9,2,10,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]
[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]=>[1,7,6,8,5,9,4,10,3,11,2]=>[1,11,10,9,8,7,6,5,4,3,2]
[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]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[7,6,5,8,4,3,2,1,9]=>[8,1,7,2,6,3,5,4,9]=>[8,7,6,5,3,2,1,4,9]
[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]=>[4,5,3,6,2,7,1,8,9]=>[7,6,5,4,3,2,1,8,9]
[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]=>[5,4,6,3,7,2,8,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]
[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]=>[2,1,7,6,8,5,9,4,10,3]=>[2,1,10,9,8,7,6,5,4,3]
[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]=>[5,4,6,3,7,2,8,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]
[]=>[]=>[]=>[]
[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]=>[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,9,8,1]=>[8,9,1,2,3,4,5,6,7]=>[9,1,2,3,4,5,6,8,7]
[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]=>[7,9,1,2,3,4,5,6,8]=>[9,1,2,3,4,5,7,6,8]
[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]=>[9,1,2,3,4,5,6,8,7]=>[9,1,2,3,4,5,8,6,7]
[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]=>[8,7,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,8,7,6]
[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]=>[6,9,1,2,3,4,5,7,8]=>[9,1,2,3,4,6,5,7,8]
[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]=>[9,1,2,3,4,5,7,6,8]=>[9,1,2,3,4,7,5,6,8]
[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]=>[9,1,2,3,4,5,7,8,6]=>[9,1,2,3,4,8,5,7,6]
[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]=>[7,6,9,1,2,3,4,5,8]=>[9,1,2,3,4,7,6,5,8]
[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]=>[9,1,2,3,4,5,8,6,7]=>[9,1,2,3,4,8,6,5,7]
[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]=>[7,9,1,2,3,4,5,8,6]=>[9,1,2,3,4,8,7,5,6]
[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]=>[5,9,1,2,3,4,6,7,8]=>[9,1,2,3,5,4,6,7,8]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,8,7,6,9,5,1]=>[6,9,1,2,3,4,8,5,7]=>[9,1,2,3,8,6,5,4,7]
[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]=>[9,1,2,3,5,4,6,7,8]=>[9,1,2,5,3,4,6,7,8]
[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]=>[9,1,2,3,6,8,4,5,7]=>[9,1,2,8,4,3,5,6,7]
[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]=>[3,9,1,2,4,5,6,7,8]=>[9,1,3,2,4,5,6,7,8]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,8,7,9,1]=>[3,5,7,9,1,2,4,6,8]=>[9,1,3,2,5,4,7,6,8]
[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]=>[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]
[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]=>[9,1,3,2,4,5,6,7,8]=>[9,3,1,2,4,5,6,7,8]
[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]=>[7,4,8,2,5,9,1,3,6]=>[9,8,1,7,2,3,4,5,6]
[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]=>[3,2,9,1,4,5,6,7,8]=>[9,3,2,1,4,5,6,7,8]
[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]=>[6,4,7,3,8,2,9,1,5]=>[9,8,7,6,1,4,3,2,5]
[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]=>[5,6,4,8,2,9,1,7,3]=>[9,8,7,6,5,4,1,2,3]
[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]=>[5,4,6,3,7,2,9,1,8]=>[9,7,6,5,4,3,2,1,8]
[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]=>[5,4,6,3,9,1,8,2,7]=>[9,8,6,5,4,3,2,1,7]
[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]=>[5,4,9,1,8,2,7,3,6]=>[9,8,7,5,4,3,2,1,6]
[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]=>[9,1,8,2,7,3,6,4,5]=>[9,8,7,6,4,3,2,1,5]
[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]=>[5,9,1,8,2,7,3,6,4]=>[9,8,7,6,5,3,2,1,4]
[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]=>[5,6,4,9,1,8,2,7,3]=>[9,8,7,6,5,4,2,1,3]
[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]=>[5,6,4,7,3,9,1,8,2]=>[9,8,7,6,5,4,3,1,2]
[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]=>[5,6,4,7,3,8,2,9,1]=>[9,8,7,6,5,4,3,2,1]
[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]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[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]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8]
[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]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,6,7,8]
[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]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,5,6,7,8]
[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]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,9,4,5,6,7,8]
[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]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,3,4,5,6,7,8]
[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]=>[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]
[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]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[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]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]
[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]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,8,9]
[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]=>[1,2,3,4,5,7,9,6,8]=>[1,2,3,4,5,9,7,6,8]
[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]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,7,8,9]
[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]=>[1,2,3,4,6,9,5,7,8]=>[1,2,3,4,9,6,5,7,8]
[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]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,10,6,7,8,9]
[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]=>[1,2,3,5,9,4,6,7,8]=>[1,2,3,9,5,4,6,7,8]
[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]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,10,5,6,7,8,9]
[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]=>[1,2,4,9,3,5,6,7,8]=>[1,2,9,4,3,5,6,7,8]
[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]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,10,4,5,6,7,8,9]
[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]=>[1,3,9,2,4,5,6,7,8]=>[1,9,3,2,4,5,6,7,8]
[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]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,10,3,4,5,6,7,8,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]
[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]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]
[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]=>[1,2,3,4,5,6,7,8,11,9,10]=>[1,2,3,4,5,6,7,8,11,9,10]
[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]=>[1,2,3,4,5,9,6,8,7]=>[1,2,3,4,5,9,8,6,7]
[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]=>[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,9,8,7,6]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,9,10,2]=>[1,3,10,2,4,5,6,7,8,9]=>[1,10,3,2,4,5,6,7,8,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]
[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]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,2,3,4,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,8,11,10,9]=>[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,11,10,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,12,10]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[1,2,3,4,5,6,7,8,9,12,10,11]
[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]=>[2,11,1,3,4,5,6,7,8,9,10]=>[11,2,1,3,4,5,6,7,8,9,10]
[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]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[1,12,2,3,4,5,6,7,8,9,10,11]
[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]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[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]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[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]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[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]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,9]=>[1,2,3,4,6,5,8,7,9]=>[1,2,3,4,6,5,8,7,9]
[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]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]
[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]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,5,7,8,9]=>[1,2,4,3,6,5,7,8,9]=>[1,2,4,3,6,5,7,8,9]
[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]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[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]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,6,8,7,9]=>[1,3,2,4,5,6,8,7,9]=>[1,3,2,4,5,6,8,7,9]
[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]=>[1,3,2,4,5,6,8,9,7]=>[1,3,2,4,5,6,9,8,7]
[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]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,6,8,9]=>[1,3,2,5,4,7,6,8,9]=>[1,3,2,5,4,7,6,8,9]
[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]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[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]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]
[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]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,6,9,8,7]=>[2,1,3,4,5,6,8,9,7]=>[2,1,3,4,5,6,9,8,7]
[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]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[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]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[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]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,7,9,8]=>[2,3,1,4,5,6,7,9,8]=>[3,2,1,4,5,6,7,9,8]
[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]=>[2,3,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]
[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]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]
[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]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]
[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]=>[3,2,4,1,6,5,8,7,9]=>[4,3,2,1,6,5,8,7,9]
[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]=>[3,4,2,5,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]
[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]=>[4,3,5,2,6,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]
[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]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]
[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]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]
[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]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8,10]=>[1,2,3,4,5,7,6,9,8,10]=>[1,2,3,4,5,7,6,9,8,10]
[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]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,7,6,8,9,10]=>[1,2,3,5,4,7,6,8,9,10]=>[1,2,3,5,4,7,6,8,9,10]
[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]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[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]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]
[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]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,7,8,10,9]=>[1,3,2,4,5,6,7,8,10,9]=>[1,3,2,4,5,6,7,8,10,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,6,7,9,8,10]=>[1,3,2,4,5,6,7,9,8,10]=>[1,3,2,4,5,6,7,9,8,10]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8,9,10]=>[1,3,2,5,4,6,7,8,9,10]=>[1,3,2,5,4,6,7,8,9,10]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,7,6,10,9,8]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]
[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]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,5,4,6,3,9,8,10,7]=>[2,1,6,5,4,3,10,9,8,7]
[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]=>[2,1,6,5,7,4,8,3,10,9]=>[2,1,8,7,6,5,4,3,10,9]
[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]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]
[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]=>[2,3,1,7,8,6,9,5,10,4]=>[3,2,1,10,9,8,7,6,5,4]
[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]=>[3,2,4,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7,10,9]=>[3,2,4,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]
[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]=>[3,2,4,1,6,5,9,8,10,7]=>[4,3,2,1,6,5,10,9,8,7]
[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]=>[3,2,4,1,7,6,8,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]
[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]=>[3,2,4,1,8,7,9,6,10,5]=>[4,3,2,1,10,9,8,7,6,5]
[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]=>[3,4,2,5,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1,10,9,8,7,6]=>[3,4,2,5,1,8,9,7,10,6]=>[5,4,3,2,1,10,9,8,7,6]
[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]=>[4,3,5,2,6,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]
[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]=>[4,3,5,2,6,1,9,8,10,7]=>[6,5,4,3,2,1,10,9,8,7]
[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]=>[4,5,3,6,2,7,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,6,5,4,3,2,1,10,9,8]=>[4,5,3,6,2,7,1,9,10,8]=>[7,6,5,4,3,2,1,10,9,8]
[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]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]
[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]=>[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]
[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]=>[4,1,2,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]
[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]=>[5,1,2,3,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]
[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]=>[6,1,2,3,4,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]
[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]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]
[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]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]
[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]=>[3,1,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]
[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]=>[3,4,1,2,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]
[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]=>[4,1,2,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]
[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]=>[4,5,1,2,3,6,7,8,9]=>[5,1,2,4,3,6,7,8,9]
[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]=>[5,1,2,3,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]
[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]=>[5,6,1,2,3,4,7,8,9]=>[6,1,2,3,5,4,7,8,9]
[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]=>[6,1,2,3,4,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]
[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]=>[7,1,2,3,4,5,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]
[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]=>[7,8,1,2,3,4,5,6,9]=>[8,1,2,3,4,5,7,6,9]
[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]=>[8,1,2,3,4,5,6,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]
[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]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]
[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]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[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]=>[2,1,3,4,5,6,9,7,8]=>[2,1,3,4,5,6,9,7,8]
[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]=>[9,10,1,2,3,4,5,6,7,8]=>[10,1,2,3,4,5,6,7,9,8]
[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]=>[6,5,7,4,10,1,9,2,8,3]=>[10,9,8,7,6,5,4,2,1,3]
[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]=>[2,1,3,4,5,6,7,10,8,9]=>[2,1,3,4,5,6,7,10,8,9]
[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]=>[3,1,2,4,5,6,9,7,8]=>[3,1,2,4,5,6,9,7,8]
[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]=>[1,3,2,4,5,6,9,7,8]=>[1,3,2,4,5,6,9,7,8]
[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]=>[3,1,2,4,5,6,7,9,8]=>[3,1,2,4,5,6,7,9,8]
[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]=>[4,2,5,1,3,6,7,8,9]=>[5,4,1,2,3,6,7,8,9]
[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]=>[4,1,3,2,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]
[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]=>[6,7,5,8,4,9,3,10,1,2]=>[10,1,9,8,7,6,5,4,3,2]
[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]=>[5,6,4,7,3,8,2,10,1,9]=>[10,8,7,6,5,4,3,2,1,9]
[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]=>[3,2,5,1,4,6,7,8,9]=>[5,3,2,1,4,6,7,8,9]
[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]=>[2,4,1,3,5,6,7,8,9]=>[4,2,1,3,5,6,7,8,9]
[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]=>[6,5,7,4,8,3,10,1,9,2]=>[10,9,8,7,6,5,4,3,1,2]
[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]=>[1,5,2,3,4,6,7,8,9]=>[1,5,2,3,4,6,7,8,9]
[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]=>[1,2,3,4,5,8,6,7,9,10]=>[1,2,3,4,5,8,6,7,9,10]
[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]=>[10,1,2,3,5,4,6,7,8,9]=>[10,1,2,5,3,4,6,7,8,9]
[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]=>[5,10,1,2,3,4,6,7,8,9]=>[10,1,2,3,5,4,6,7,8,9]
[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]=>[2,8,1,3,4,5,6,7,9]=>[8,2,1,3,4,5,6,7,9]
[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]=>[1,8,9,2,3,4,5,6,7]=>[1,9,2,3,4,5,6,8,7]
[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]=>[7,1,2,3,4,5,6,9,8]=>[7,1,2,3,4,5,6,9,8]
[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]=>[2,1,9,3,4,5,6,7,8]=>[2,1,9,3,4,5,6,7,8]
[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]=>[6,1,2,3,4,5,8,9,7]=>[6,1,2,3,4,5,9,8,7]
[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]=>[9,8,10,1,2,3,4,5,6,7]=>[10,1,2,3,4,5,6,9,8,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[5,6,4,7,3,10,1,9,2,8]=>[10,9,7,6,5,4,3,2,1,8]
[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]=>[5,6,4,10,1,9,2,8,3,7]=>[10,9,8,6,5,4,3,2,1,7]
[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]=>[5,10,1,9,2,8,3,7,4,6]=>[10,9,8,7,5,4,3,2,1,6]
[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]=>[10,1,9,2,8,3,7,4,6,5]=>[10,9,8,7,6,4,3,2,1,5]
[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]=>[6,5,10,1,9,2,8,3,7,4]=>[10,9,8,7,6,5,3,2,1,4]
[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]=>[6,10,1,2,3,4,5,7,8,9]=>[10,1,2,3,4,6,5,7,8,9]
[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]=>[6,1,2,3,4,5,8,7,9]=>[6,1,2,3,4,5,8,7,9]
[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]=>[5,1,2,3,4,7,6,8,9]=>[5,1,2,3,4,7,6,8,9]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,8,7,9]=>[3,4,1,2,6,5,8,7,9]=>[4,1,3,2,6,5,8,7,9]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,6,5,7,1,9,8]=>[3,5,7,1,2,4,6,9,8]=>[7,1,3,2,5,4,6,9,8]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6,9,8]=>[3,5,1,2,4,7,6,9,8]=>[5,1,3,2,4,7,6,9,8]
[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]=>[3,1,2,5,4,7,6,9,8]=>[3,1,2,5,4,7,6,9,8]
[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]=>[3,4,1,2,6,5,8,7,10,9]=>[4,1,3,2,6,5,8,7,10,9]
[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]=>[3,5,7,9,10,1,2,4,6,8]=>[10,1,3,2,5,4,7,6,9,8]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,8,7,9,1,10]=>[3,5,7,9,1,2,4,6,8,10]=>[9,1,3,2,5,4,7,6,8,10]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,6,5,7,4,9,8]=>[3,1,2,5,7,4,6,9,8]=>[3,1,2,7,5,4,6,9,8]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6,9,8]=>[1,3,5,2,4,7,6,9,8]=>[1,5,3,2,4,7,6,9,8]
[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]=>[3,1,2,5,4,7,6,9,8,10]=>[3,1,2,5,4,7,6,9,8,10]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,5,7,8,9,6]=>[4,1,2,3,5,9,6,7,8]=>[4,1,2,3,5,9,6,7,8]
[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]=>[10,1,2,3,4,5,6,7,9,8]=>[10,1,2,3,4,5,6,9,7,8]
[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]=>[9,7,10,1,2,3,4,5,6,8]=>[10,1,2,3,4,5,9,6,7,8]
[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]=>[10,11,1,2,3,4,5,6,7,8,9]=>[11,1,2,3,4,5,6,7,8,10,9]
[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]=>[11,1,2,3,4,5,6,7,8,10,9]=>[11,1,2,3,4,5,6,7,10,8,9]
[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]=>[10,1,2,3,4,5,6,9,7,8]=>[10,1,2,3,4,5,9,7,6,8]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,5,8,7,9,10,6,1]=>[9,6,7,10,1,2,3,4,5,8]=>[10,1,2,3,4,9,6,5,7,8]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[2,12,11,10,9,8,7,6,5,4,3,1]=>[7,8,6,9,5,10,4,11,3,12,1,2]=>[12,1,11,10,9,8,7,6,5,4,3,2]
[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]=>[3,1,2,4,5,6,7,8,9,10,11]=>[3,1,2,4,5,6,7,8,9,10,11]
[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]=>[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,9,6,8,7]
[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]=>[2,3,1,9,4,5,6,7,8]=>[3,2,1,9,4,5,6,7,8]
[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]=>[1,4,2,3,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]
[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]=>[2,1,10,3,4,5,6,7,8,9]=>[2,1,10,3,4,5,6,7,8,9]
[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]=>[3,1,2,9,4,5,6,7,8]=>[3,1,2,9,4,5,6,7,8]
[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]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]
[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]=>[6,1,2,3,4,5,10,7,8,9]=>[6,1,2,3,4,5,10,7,8,9]
[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]=>[1,2,3,4,5,8,6,7,9]=>[1,2,3,4,5,8,6,7,9]
[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]=>[1,2,3,4,5,6,9,7,8,10]=>[1,2,3,4,5,6,9,7,8,10]
[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]=>[1,7,2,3,4,5,6,9,8]=>[1,7,2,3,4,5,6,9,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,7,8,2,9,10]=>[1,8,2,3,4,5,6,7,9,10]=>[1,8,2,3,4,5,6,7,9,10]
[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]=>[10,1,2,3,4,5,6,7,8,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]
[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]=>[1,8,2,3,4,5,6,7,9]=>[1,8,2,3,4,5,6,7,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9,10,11]=>[1,3,2,4,5,6,7,8,9,10,11]=>[1,3,2,4,5,6,7,8,9,10,11]
[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]=>[6,8,1,2,3,4,5,7,9]=>[8,1,2,3,4,6,5,7,9]
[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]=>[1,2,3,4,9,5,6,8,7]=>[1,2,3,4,9,5,8,6,7]
[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]=>[4,1,3,2,5,6,7,8,9,10]=>[4,3,1,2,5,6,7,8,9,10]
[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]=>[8,1,2,3,4,5,6,7,10,9]=>[8,1,2,3,4,5,6,7,10,9]
[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]=>[6,1,2,3,4,5,9,7,8]=>[6,1,2,3,4,5,9,7,8]
[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]=>[1,3,2,5,4,7,6,9,8,11,10]=>[1,3,2,5,4,7,6,9,8,11,10]
[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]=>[4,1,3,2,6,5,8,7,10,9]=>[4,3,1,2,6,5,8,7,10,9]
[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]=>[1,4,2,3,5,6,7,8,9,10]=>[1,4,2,3,5,6,7,8,9,10]
[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]=>[1,9,2,3,4,5,6,7,8,10]=>[1,9,2,3,4,5,6,7,8,10]
[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]=>[1,2,6,3,4,5,7,8,9,10]=>[1,2,6,3,4,5,7,8,9,10]
[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]=>[4,1,2,3,9,5,6,7,8]=>[4,1,2,3,9,5,6,7,8]
[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]=>[1,2,3,4,5,6,9,10,7,8]=>[1,2,3,4,5,6,10,7,9,8]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8,9]=>[2,5,1,3,4,6,7,8,9]=>[5,2,1,3,4,6,7,8,9]
[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]=>[1,2,3,8,4,5,6,7,9,10]=>[1,2,3,8,4,5,6,7,9,10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,7,8,2,10,9]=>[1,8,2,3,4,5,6,7,10,9]=>[1,8,2,3,4,5,6,7,10,9]
[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]=>[2,4,1,3,6,5,8,7,10,9]=>[4,2,1,3,6,5,8,7,10,9]
[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]=>[2,4,6,8,10,1,3,5,7,9]=>[10,2,1,4,3,6,5,8,7,9]
[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]=>[2,4,6,8,9,1,3,5,7,10]=>[9,2,1,4,3,6,5,8,7,10]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,8,9,1,10]=>[2,9,1,3,4,5,6,7,8,10]=>[9,2,1,3,4,5,6,7,8,10]
[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]=>[1,7,9,2,3,4,5,6,8]=>[1,9,2,3,4,5,7,6,8]
[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]=>[1,9,10,2,3,4,5,6,7,8]=>[1,10,2,3,4,5,6,7,9,8]
[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]=>[2,1,8,3,4,5,6,7,9]=>[2,1,8,3,4,5,6,7,9]
[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]=>[2,1,4,3,6,5,8,10,7,9]=>[2,1,4,3,6,5,10,8,7,9]
[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]=>[1,3,2,5,4,7,6,10,8,9]=>[1,3,2,5,4,7,6,10,8,9]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,8,9,4]=>[1,3,2,9,4,5,6,7,8]=>[1,3,2,9,4,5,6,7,8]
[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]=>[2,4,1,3,5,6,7,8,9,10]=>[4,2,1,3,5,6,7,8,9,10]
[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]=>[1,7,2,3,4,5,6,8,9]=>[1,7,2,3,4,5,6,8,9]
[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]=>[8,9,1,2,3,4,5,6,7,10]=>[9,1,2,3,4,5,6,8,7,10]
[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]=>[1,2,3,4,8,9,5,6,7]=>[1,2,3,4,9,5,6,8,7]
[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]=>[1,3,5,7,9,10,2,4,6,8]=>[1,10,3,2,5,4,7,6,9,8]
[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]=>[2,4,1,3,6,8,5,7,10,9]=>[4,2,1,3,8,6,5,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[12,2,1,4,3,6,5,8,7,10,9,11]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,8,9,10,2,11]=>[1,10,2,3,4,5,6,7,8,9,11]=>[1,10,2,3,4,5,6,7,8,9,11]
[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]=>[6,5,7,4,8,3,9,2,10,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]
[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]=>[1,4,2,3,6,5,8,7,10,9]=>[1,4,2,3,6,5,8,7,10,9]
[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]=>[9,1,2,3,4,5,6,7,8,11,10]=>[9,1,2,3,4,5,6,7,8,11,10]
[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]=>[5,1,2,3,4,9,6,7,8]=>[5,1,2,3,4,9,6,7,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,8,9,11,10]=>[2,1,3,4,5,6,7,8,9,11,10]=>[2,1,3,4,5,6,7,8,9,11,10]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9,10,11,12]=>[1,3,2,4,5,6,7,8,9,10,11,12]=>[1,3,2,4,5,6,7,8,9,10,11,12]
[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]=>[2,1,5,6,3,4,8,7,10,9]=>[2,1,6,3,5,4,8,7,10,9]
[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]=>[2,1,4,3,7,8,5,6,10,9]=>[2,1,4,3,8,5,7,6,10,9]
[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]=>[2,1,4,3,6,5,9,10,7,8]=>[2,1,4,3,6,5,10,7,9,8]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,6,8,10,9,7,1]=>[10,1,3,4,2,5,6,8,9,7]=>[10,4,1,3,2,5,9,6,8,7]
[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]=>[1,4,2,3,6,5,8,7,9]=>[1,4,2,3,6,5,8,7,9]
[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]=>[7,1,2,3,4,5,6,10,8,9]=>[7,1,2,3,4,5,6,10,8,9]
[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]=>[4,1,2,3,6,5,10,7,8,9]=>[4,1,2,3,6,5,10,7,8,9]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,11,10,12]=>[1,3,2,5,4,7,6,9,8,11,10,12]=>[1,3,2,5,4,7,6,9,8,11,10,12]
[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]=>[1,2,3,4,5,9,10,6,7,8]=>[1,2,3,4,5,10,6,7,9,8]
[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]=>[2,1,4,3,10,5,6,7,8,9]=>[2,1,4,3,10,5,6,7,8,9]
[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]=>[2,1,4,3,6,5,10,7,8,9]=>[2,1,4,3,6,5,10,7,8,9]
[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]=>[4,1,3,2,6,5,10,7,9,8]=>[4,3,1,2,6,5,10,9,7,8]
[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]=>[4,1,2,3,6,5,8,7,9]=>[4,1,2,3,6,5,8,7,9]
[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]=>[3,1,2,4,6,5,8,7,9]=>[3,1,2,4,6,5,8,7,9]
[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]=>[1,2,3,4,5,10,6,7,9,8]=>[1,2,3,4,5,10,6,9,7,8]
[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]=>[1,2,3,9,4,5,6,8,7]=>[1,2,3,9,4,5,8,6,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,8,9,11,10,12]=>[1,2,3,4,5,6,7,8,9,11,10,12]=>[1,2,3,4,5,6,7,8,9,11,10,12]
[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]=>[6,1,2,3,4,5,8,7,10,9]=>[6,1,2,3,4,5,8,7,10,9]
[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]=>[4,1,2,3,6,5,8,7,10,9]=>[4,1,2,3,6,5,8,7,10,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,11,1,12]=>[11,1,2,3,4,5,6,7,8,9,10,12]=>[11,1,2,3,4,5,6,7,8,9,10,12]
[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]=>[1,3,2,5,4,7,6,9,8,12,10,11]=>[1,3,2,5,4,7,6,9,8,12,10,11]
          
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.