Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-2
[1,0]=>[1]=>[1,0]
[1,0,1,0]=>[2,1]=>[1,1,0,0]
[1,1,0,0]=>[1,2]=>[1,0,1,0]
[1,0,1,0,1,0]=>[3,2,1]=>[1,1,1,0,0,0]
[1,0,1,1,0,0]=>[2,3,1]=>[1,1,0,1,0,0]
[1,1,0,0,1,0]=>[3,1,2]=>[1,1,1,0,0,0]
[1,1,0,1,0,0]=>[2,1,3]=>[1,1,0,0,1,0]
[1,1,1,0,0,0]=>[1,2,3]=>[1,0,1,0,1,0]
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[1,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,8,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,8,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,2,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,4,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,8,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,7,8,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,8,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,8,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,8,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,2,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,1,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,1,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,1,8]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,1,2,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,1,3,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,1,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,1,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,1,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,1,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,1,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,1,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,1,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,1,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,1,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,1,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,1,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,1,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,1,2,3,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,1,2,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,1,2,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,1,2,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,1,2,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,1,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,5,1,2,3,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,1,2,3,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,7,8,9,10,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0,0]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
left-to-right-maxima to Dyck path
searching the database
Sorry, this map was not found in the database.