Identifier
Mp00028:
Dyck paths
—reverse⟶
Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,0]=>[2,1]=>[1,2]
[1,0,1,0]=>[1,0,1,0]=>[3,1,2]=>[1,3,2]
[1,1,0,0]=>[1,1,0,0]=>[2,3,1]=>[2,1,3]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[4,1,2,3]=>[1,4,3,2]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[2,4,1,3]=>[3,1,4,2]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[3,1,4,2]=>[2,4,1,3]
[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[4,3,1,2]=>[1,2,4,3]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[2,3,4,1]=>[3,2,1,4]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>[1,5,4,3,2]
[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>[4,1,5,3,2]
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[3,5,1,4,2]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>[1,3,5,4,2]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>[4,3,1,5,2]
[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[2,5,4,1,3]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[4,2,5,1,3]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>[1,5,2,4,3]
[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>[1,2,5,4,3]
[1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>[4,1,2,5,3]
[1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[3,5,2,1,4]
[1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>[2,3,5,1,4]
[1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>[1,3,2,5,4]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[4,3,2,1,5]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[3,6,5,1,4,2]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>[1,6,3,5,4,2]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>[5,1,3,6,4,2]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[4,6,3,1,5,2]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>[3,4,6,1,5,2]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[1,4,3,6,5,2]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[2,6,5,4,1,3]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[5,2,6,4,1,3]
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>[2,4,6,5,1,3]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>[1,6,5,2,4,3]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>[5,1,6,2,4,3]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>[1,6,2,5,4,3]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>[5,1,2,6,4,3]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>[4,6,1,2,5,3]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>[1,4,6,2,5,3]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>[1,4,2,6,5,3]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>[5,4,1,2,6,3]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[3,6,5,2,1,4]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[5,3,6,2,1,4]
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>[2,6,3,5,1,4]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>[2,3,6,5,1,4]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>[5,2,3,6,1,4]
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>[1,6,3,2,5,4]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>[1,3,6,2,5,4]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>[5,1,3,2,6,4]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[4,6,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>[3,4,6,2,1,5]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>[2,4,3,6,1,5]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>[1,4,3,2,6,5]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[5,7,1,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>[6,5,1,7,4,3,2]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[4,7,6,1,5,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[6,4,7,1,5,3,2]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>[6,1,4,7,5,3,2]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[5,7,4,1,6,3,2]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>[4,5,7,1,6,3,2]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>[6,5,4,1,7,3,2]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[3,7,6,5,1,4,2]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[6,3,7,5,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[5,7,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>[3,5,7,6,1,4,2]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[6,5,3,7,1,4,2]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>[6,1,7,3,5,4,2]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>[3,1,7,6,5,4,2]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>[6,1,3,7,5,4,2]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>[5,7,1,3,6,4,2]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>[1,5,7,3,6,4,2]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>[1,5,3,7,6,4,2]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>[6,5,1,3,7,4,2]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[4,7,6,3,1,5,2]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[6,4,7,3,1,5,2]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>[3,7,4,6,1,5,2]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>[3,4,7,6,1,5,2]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>[6,3,4,7,1,5,2]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>[1,7,4,3,6,5,2]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>[1,4,7,3,6,5,2]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>[6,1,4,3,7,5,2]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[5,7,4,3,1,6,2]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>[4,5,7,3,1,6,2]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>[3,5,4,7,1,6,2]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>[6,5,4,3,1,7,2]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[2,7,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[6,2,7,5,4,1,3]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[5,7,2,6,4,1,3]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>[2,5,7,6,4,1,3]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[6,5,2,7,4,1,3]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[4,7,6,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[6,4,7,2,5,1,3]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>[2,7,4,6,5,1,3]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>[2,4,7,6,5,1,3]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>[6,2,4,7,5,1,3]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[5,7,4,2,6,1,3]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>[4,5,7,2,6,1,3]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>[2,5,4,7,6,1,3]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[6,5,4,2,7,1,3]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>[6,1,7,5,2,4,3]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>[5,7,1,6,2,4,3]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>[6,5,1,7,2,4,3]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>[6,1,7,2,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]=>[2,7,1,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>[5,7,1,2,6,4,3]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>[1,5,7,2,6,4,3]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>[2,5,1,7,6,4,3]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>[6,5,1,2,7,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>[4,7,6,1,2,5,3]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>[6,4,7,1,2,5,3]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>[1,7,4,6,2,5,3]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>[1,4,7,6,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>[6,1,4,7,2,5,3]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>[1,7,4,2,6,5,3]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>[1,4,7,2,6,5,3]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>[6,1,4,2,7,5,3]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>[5,7,4,1,2,6,3]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>[4,5,7,1,2,6,3]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>[1,5,4,7,2,6,3]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>[1,5,4,2,7,6,3]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>[6,5,4,1,2,7,3]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[3,7,6,5,2,1,4]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[6,3,7,5,2,1,4]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[5,7,3,6,2,1,4]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>[3,5,7,6,2,1,4]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[6,5,3,7,2,1,4]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>[2,7,6,3,5,1,4]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>[6,2,7,3,5,1,4]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>[2,7,3,6,5,1,4]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>[3,2,7,6,5,1,4]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>[6,2,3,7,5,1,4]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>[5,7,2,3,6,1,4]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>[2,5,7,3,6,1,4]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>[2,5,3,7,6,1,4]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>[6,5,2,3,7,1,4]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>[1,7,6,3,2,5,4]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>[6,1,7,3,2,5,4]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>[1,7,3,6,2,5,4]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>[3,1,7,6,2,5,4]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>[6,1,3,7,2,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>[2,1,7,3,6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>[6,1,2,3,7,5,4]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>[5,7,1,3,2,6,4]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>[1,5,7,3,2,6,4]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>[1,5,3,7,2,6,4]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>[1,5,2,3,7,6,4]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>[6,5,1,3,2,7,4]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[4,7,6,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[6,4,7,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>[3,7,4,6,2,1,5]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>[3,4,7,6,2,1,5]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>[6,3,4,7,2,1,5]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>[2,7,4,3,6,1,5]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>[2,4,7,3,6,1,5]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>[2,3,4,7,6,1,5]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>[6,2,4,3,7,1,5]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>[1,7,4,3,2,6,5]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>[1,4,7,3,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>[1,3,4,7,2,6,5]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>[6,1,4,3,2,7,5]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[5,7,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>[4,5,7,3,2,1,6]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>[3,5,4,7,2,1,6]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>[2,5,4,3,7,1,6]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]
[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]=>[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,8,1,3,4,5,6,7]=>[7,1,8,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[6,8,1,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,3,1,2,4,5,6,7]=>[1,6,8,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>[7,6,1,8,5,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>[5,8,7,1,6,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>[7,5,8,1,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,1,4,2,3,5,6,7]=>[1,8,5,7,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,4,1,2,3,5,6,7]=>[1,5,8,7,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,8,4,1,3,5,6,7]=>[7,1,5,8,6,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>[6,8,5,1,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,3,1,8,2,5,6,7]=>[5,6,8,1,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,3,4,1,2,5,6,7]=>[1,6,5,8,7,4,3,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>[7,6,5,1,8,4,3,2]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[5,1,2,3,8,4,6,7]=>[4,8,7,6,1,5,3,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,5,1,3,8,4,6,7]=>[7,4,8,6,1,5,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[6,8,4,7,1,5,3,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,3,1,2,8,4,6,7]=>[4,6,8,7,1,5,3,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>[7,6,4,8,1,5,3,2]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,1,2,5,3,4,6,7]=>[1,8,7,4,6,5,3,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,8,1,5,3,4,6,7]=>[7,1,8,4,6,5,3,2]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,1,5,2,3,4,6,7]=>[1,8,4,7,6,5,3,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[5,8,1,2,3,4,6,7]=>[4,1,8,7,6,5,3,2]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,8,5,1,3,4,6,7]=>[7,1,4,8,6,5,3,2]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,8,5,2,4,6,7]=>[6,8,1,4,7,5,3,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,3,1,5,2,4,6,7]=>[1,6,8,4,7,5,3,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,3,5,1,2,4,6,7]=>[1,6,4,8,7,5,3,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,8,5,1,4,6,7]=>[7,6,1,4,8,5,3,2]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,2,5,8,3,6,7]=>[5,8,7,4,1,6,3,2]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>[7,5,8,4,1,6,3,2]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,4,2,8,3,6,7]=>[4,8,5,7,1,6,3,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,8,3,6,7]=>[4,5,8,7,1,6,3,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,5,4,1,8,3,6,7]=>[7,4,5,8,1,6,3,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,1,4,5,2,3,6,7]=>[1,8,5,4,7,6,3,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,4,1,5,2,3,6,7]=>[1,5,8,4,7,6,3,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,5,4,1,2,3,6,7]=>[1,4,5,8,7,6,3,2]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,8,4,5,1,3,6,7]=>[7,1,5,4,8,6,3,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,5,8,2,6,7]=>[6,8,5,4,1,7,3,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,1,5,8,2,6,7]=>[5,6,8,4,1,7,3,2]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,3,4,1,8,2,6,7]=>[4,6,5,8,1,7,3,2]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,3,4,5,1,2,6,7]=>[1,6,5,4,8,7,3,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>[7,6,5,4,1,8,3,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,1,2,3,4,8,5,7]=>[3,8,7,6,5,1,4,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,6,1,3,4,8,5,7]=>[7,3,8,6,5,1,4,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>[6,8,3,7,5,1,4,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,3,1,2,4,8,5,7]=>[3,6,8,7,5,1,4,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>[7,6,3,8,5,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[5,8,7,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[7,5,8,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]=>[3,8,5,7,6,1,4,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,1,2,3,8,5,7]=>[3,5,8,7,6,1,4,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,6,4,1,3,8,5,7]=>[7,3,5,8,6,1,4,2]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[6,8,5,3,7,1,4,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,3,1,6,2,8,5,7]=>[5,6,8,3,7,1,4,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,3,4,1,2,8,5,7]=>[3,6,5,8,7,1,4,2]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>[7,6,5,3,8,1,4,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,1,2,3,6,4,5,7]=>[1,8,7,6,3,5,4,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,8,1,3,6,4,5,7]=>[7,1,8,6,3,5,4,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,8,2,6,4,5,7]=>[6,8,1,7,3,5,4,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,3,1,2,6,4,5,7]=>[1,6,8,7,3,5,4,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,3,8,1,6,4,5,7]=>[7,6,1,8,3,5,4,2]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,1,2,6,3,4,5,7]=>[1,8,7,3,6,5,4,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,8,1,6,3,4,5,7]=>[7,1,8,3,6,5,4,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,1,8,2,3,4,5,7]=>[3,8,1,7,6,5,4,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[1,3,8,7,6,5,4,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,6,8,1,3,4,5,7]=>[7,3,1,8,6,5,4,2]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,8,6,2,4,5,7]=>[6,8,1,3,7,5,4,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,3,1,6,2,4,5,7]=>[1,6,8,3,7,5,4,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,3,8,1,2,4,5,7]=>[3,6,1,8,7,5,4,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,8,6,1,4,5,7]=>[7,6,1,3,8,5,4,2]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[4,1,2,8,6,3,5,7]=>[5,8,7,1,3,6,4,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1,8,6,3,5,7]=>[7,5,8,1,3,6,4,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,1,4,2,6,3,5,7]=>[1,8,5,7,3,6,4,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,4,1,2,6,3,5,7]=>[1,5,8,7,3,6,4,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,8,4,1,6,3,5,7]=>[7,1,5,8,3,6,4,2]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,1,4,6,2,3,5,7]=>[1,8,5,3,7,6,4,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,4,1,6,2,3,5,7]=>[1,5,8,3,7,6,4,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,8,4,1,2,3,5,7]=>[3,1,5,8,7,6,4,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,8,4,6,1,3,5,7]=>[7,1,5,3,8,6,4,2]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,8,6,2,5,7]=>[6,8,5,1,3,7,4,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,1,8,6,2,5,7]=>[5,6,8,1,3,7,4,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,3,4,1,6,2,5,7]=>[1,6,5,8,3,7,4,2]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,3,4,6,1,2,5,7]=>[1,6,5,3,8,7,4,2]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,3,4,8,6,1,5,7]=>[7,6,5,1,3,8,4,2]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[4,8,7,6,3,1,5,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>[7,4,8,6,3,1,5,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>[6,8,4,7,3,1,5,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[5,3,1,2,6,8,4,7]=>[4,6,8,7,3,1,5,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>[7,6,4,8,3,1,5,2]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,1,2,5,3,8,4,7]=>[3,8,7,4,6,1,5,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,6,1,5,3,8,4,7]=>[7,3,8,4,6,1,5,2]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,5,2,3,8,4,7]=>[3,8,4,7,6,1,5,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[5,6,1,2,3,8,4,7]=>[4,3,8,7,6,1,5,2]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,6,5,1,3,8,4,7]=>[7,3,4,8,6,1,5,2]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,6,5,2,8,4,7]=>[6,8,3,4,7,1,5,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,1,5,2,8,4,7]=>[3,6,8,4,7,1,5,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,5,1,2,8,4,7]=>[3,6,4,8,7,1,5,2]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,6,5,1,8,4,7]=>[7,6,3,4,8,1,5,2]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,1,2,5,6,3,4,7]=>[1,8,7,4,3,6,5,2]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,8,1,5,6,3,4,7]=>[7,1,8,4,3,6,5,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,1,5,2,6,3,4,7]=>[1,8,4,7,3,6,5,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[5,8,1,2,6,3,4,7]=>[4,1,8,7,3,6,5,2]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,8,5,1,6,3,4,7]=>[7,1,4,8,3,6,5,2]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,1,6,5,2,3,4,7]=>[1,8,3,4,7,6,5,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,8,1,5,2,3,4,7]=>[3,1,8,4,7,6,5,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,8,5,1,2,3,4,7]=>[3,1,4,8,7,6,5,2]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,8,6,5,1,3,4,7]=>[7,1,3,4,8,6,5,2]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,8,5,6,2,4,7]=>[6,8,1,4,3,7,5,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,3,1,5,6,2,4,7]=>[1,6,8,4,3,7,5,2]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,3,5,1,6,2,4,7]=>[1,6,4,8,3,7,5,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,3,6,5,1,2,4,7]=>[1,6,3,4,8,7,5,2]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,3,8,5,6,1,4,7]=>[7,6,1,4,3,8,5,2]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[5,8,7,4,3,1,6,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>[7,5,8,4,3,1,6,2]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,4,2,6,8,3,7]=>[4,8,5,7,3,1,6,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[5,4,1,2,6,8,3,7]=>[4,5,8,7,3,1,6,2]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,1,6,8,3,7]=>[7,4,5,8,3,1,6,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,1,4,5,2,8,3,7]=>[3,8,5,4,7,1,6,2]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,4,1,5,2,8,3,7]=>[3,5,8,4,7,1,6,2]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,5,4,1,2,8,3,7]=>[3,4,5,8,7,1,6,2]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,6,4,5,1,8,3,7]=>[7,3,5,4,8,1,6,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,1,4,5,6,2,3,7]=>[1,8,5,4,3,7,6,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,1,5,6,2,3,7]=>[1,5,8,4,3,7,6,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,5,4,1,6,2,3,7]=>[1,4,5,8,3,7,6,2]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,6,4,5,1,2,3,7]=>[1,3,5,4,8,7,6,2]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,8,4,5,6,1,3,7]=>[7,1,5,4,3,8,6,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>[6,8,5,4,3,1,7,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,3,1,5,6,8,2,7]=>[5,6,8,4,3,1,7,2]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[5,3,4,1,6,8,2,7]=>[4,6,5,8,3,1,7,2]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,4,5,1,8,2,7]=>[3,6,5,4,8,1,7,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[1,6,5,4,3,8,7,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>[7,6,5,4,3,1,8,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,1,2,3,4,5,8,6]=>[2,8,7,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>[7,2,8,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,7,2,4,5,8,6]=>[6,8,2,7,5,4,1,3]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,3,1,2,4,5,8,6]=>[2,6,8,7,5,4,1,3]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>[7,6,2,8,5,4,1,3]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>[5,8,7,2,6,4,1,3]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>[7,5,8,2,6,4,1,3]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,1,4,2,3,5,8,6]=>[2,8,5,7,6,4,1,3]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,4,1,2,3,5,8,6]=>[2,5,8,7,6,4,1,3]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,7,4,1,3,5,8,6]=>[7,2,5,8,6,4,1,3]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,4,7,2,5,8,6]=>[6,8,5,2,7,4,1,3]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,3,1,7,2,5,8,6]=>[5,6,8,2,7,4,1,3]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,3,4,1,2,5,8,6]=>[2,6,5,8,7,4,1,3]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>[7,6,5,2,8,4,1,3]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[4,8,7,6,2,5,1,3]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[7,4,8,6,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[6,8,4,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,3,1,2,7,4,8,6]=>[4,6,8,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[7,6,4,8,2,5,1,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,1,2,5,3,4,8,6]=>[2,8,7,4,6,5,1,3]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,7,1,5,3,4,8,6]=>[7,2,8,4,6,5,1,3]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,1,5,2,3,4,8,6]=>[2,8,4,7,6,5,1,3]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,7,1,2,3,4,8,6]=>[4,2,8,7,6,5,1,3]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,7,5,1,3,4,8,6]=>[7,2,4,8,6,5,1,3]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,7,5,2,4,8,6]=>[6,8,2,4,7,5,1,3]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,3,1,5,2,4,8,6]=>[2,6,8,4,7,5,1,3]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]=>[2,6,4,8,7,5,1,3]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,7,5,1,4,8,6]=>[7,6,2,4,8,5,1,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[5,8,7,4,2,6,1,3]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[7,5,8,4,2,6,1,3]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,1,4,2,7,3,8,6]=>[4,8,5,7,2,6,1,3]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,4,1,2,7,3,8,6]=>[4,5,8,7,2,6,1,3]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,5,4,1,7,3,8,6]=>[7,4,5,8,2,6,1,3]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,1,4,5,2,3,8,6]=>[2,8,5,4,7,6,1,3]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,4,1,5,2,3,8,6]=>[2,5,8,4,7,6,1,3]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,5,4,1,2,3,8,6]=>[2,4,5,8,7,6,1,3]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,7,4,5,1,3,8,6]=>[7,2,5,4,8,6,1,3]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>[6,8,5,4,2,7,1,3]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,1,5,7,2,8,6]=>[5,6,8,4,2,7,1,3]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,3,4,1,7,2,8,6]=>[4,6,5,8,2,7,1,3]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,3,4,5,1,2,8,6]=>[2,6,5,4,8,7,1,3]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>[7,6,5,4,2,8,1,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,1,2,3,4,7,5,6]=>[1,8,7,6,5,2,4,3]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,8,1,3,4,7,5,6]=>[7,1,8,6,5,2,4,3]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,8,2,4,7,5,6]=>[6,8,1,7,5,2,4,3]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[8,3,1,2,4,7,5,6]=>[1,6,8,7,5,2,4,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,3,8,1,4,7,5,6]=>[7,6,1,8,5,2,4,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[4,1,2,8,3,7,5,6]=>[5,8,7,1,6,2,4,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,7,5,6]=>[7,5,8,1,6,2,4,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[8,1,4,2,3,7,5,6]=>[1,8,5,7,6,2,4,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[8,4,1,2,3,7,5,6]=>[1,5,8,7,6,2,4,3]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,8,4,1,3,7,5,6]=>[7,1,5,8,6,2,4,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,4,8,2,7,5,6]=>[6,8,5,1,7,2,4,3]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,1,8,2,7,5,6]=>[5,6,8,1,7,2,4,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[8,3,4,1,2,7,5,6]=>[1,6,5,8,7,2,4,3]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,8,1,7,5,6]=>[7,6,5,1,8,2,4,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,1,2,3,7,4,5,6]=>[1,8,7,6,2,5,4,3]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,8,1,3,7,4,5,6]=>[7,1,8,6,2,5,4,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,8,2,7,4,5,6]=>[6,8,1,7,2,5,4,3]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[8,3,1,2,7,4,5,6]=>[1,6,8,7,2,5,4,3]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,3,8,1,7,4,5,6]=>[7,6,1,8,2,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,1,2,8,3,4,5,6]=>[2,8,7,1,6,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>[7,2,8,1,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,1,7,2,3,4,5,6]=>[1,8,2,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,1,2,3,4,5,6]=>[1,2,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,8,7,1,3,4,5,6]=>[7,1,2,8,6,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,7,8,2,4,5,6]=>[6,8,2,1,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,3,1,8,2,4,5,6]=>[2,6,8,1,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,3,7,1,2,4,5,6]=>[1,6,2,8,7,5,4,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,7,8,1,4,5,6]=>[7,6,2,1,8,5,4,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[4,1,2,8,7,3,5,6]=>[5,8,7,1,2,6,4,3]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,8,7,3,5,6]=>[7,5,8,1,2,6,4,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[8,1,4,2,7,3,5,6]=>[1,8,5,7,2,6,4,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[8,4,1,2,7,3,5,6]=>[1,5,8,7,2,6,4,3]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,8,4,1,7,3,5,6]=>[7,1,5,8,2,6,4,3]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,1,4,8,2,3,5,6]=>[2,8,5,1,7,6,4,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,4,1,8,2,3,5,6]=>[2,5,8,1,7,6,4,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,4,1,2,3,5,6]=>[1,2,5,8,7,6,4,3]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,7,4,8,1,3,5,6]=>[7,2,5,1,8,6,4,3]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,4,8,7,2,5,6]=>[6,8,5,1,2,7,4,3]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,1,8,7,2,5,6]=>[5,6,8,1,2,7,4,3]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,3,4,1,7,2,5,6]=>[1,6,5,8,2,7,4,3]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,3,4,8,1,2,5,6]=>[2,6,5,1,8,7,4,3]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,4,8,7,1,5,6]=>[7,6,5,1,2,8,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,1,2,3,8,7,4,6]=>[4,8,7,6,1,2,5,3]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,5,1,3,8,7,4,6]=>[7,4,8,6,1,2,5,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,5,2,8,7,4,6]=>[6,8,4,7,1,2,5,3]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,1,2,8,7,4,6]=>[4,6,8,7,1,2,5,3]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,5,1,8,7,4,6]=>[7,6,4,8,1,2,5,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[8,1,2,5,3,7,4,6]=>[1,8,7,4,6,2,5,3]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,8,1,5,3,7,4,6]=>[7,1,8,4,6,2,5,3]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[8,1,5,2,3,7,4,6]=>[1,8,4,7,6,2,5,3]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,8,1,2,3,7,4,6]=>[4,1,8,7,6,2,5,3]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,8,5,1,3,7,4,6]=>[7,1,4,8,6,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,8,5,2,7,4,6]=>[6,8,1,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,3,1,5,2,7,4,6]=>[1,6,8,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[8,3,5,1,2,7,4,6]=>[1,6,4,8,7,2,5,3]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,8,5,1,7,4,6]=>[7,6,1,4,8,2,5,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[8,1,2,5,7,3,4,6]=>[1,8,7,4,2,6,5,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,8,1,5,7,3,4,6]=>[7,1,8,4,2,6,5,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]=>[1,8,4,7,2,6,5,3]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,8,1,2,7,3,4,6]=>[4,1,8,7,2,6,5,3]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,8,5,1,7,3,4,6]=>[7,1,4,8,2,6,5,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,1,8,5,2,3,4,6]=>[2,8,1,4,7,6,5,3]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[8,7,1,5,2,3,4,6]=>[1,2,8,4,7,6,5,3]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]=>[1,2,4,8,7,6,5,3]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,7,8,5,1,3,4,6]=>[7,2,1,4,8,6,5,3]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,8,5,7,2,4,6]=>[6,8,1,4,2,7,5,3]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]=>[1,6,8,4,2,7,5,3]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[8,3,5,1,7,2,4,6]=>[1,6,4,8,2,7,5,3]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,3,8,5,1,2,4,6]=>[2,6,1,4,8,7,5,3]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,8,5,7,1,4,6]=>[7,6,1,4,2,8,5,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,8,7,3,6]=>[5,8,7,4,1,2,6,3]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,8,7,3,6]=>[7,5,8,4,1,2,6,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,1,4,2,8,7,3,6]=>[4,8,5,7,1,2,6,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,4,1,2,8,7,3,6]=>[4,5,8,7,1,2,6,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,1,8,7,3,6]=>[7,4,5,8,1,2,6,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[8,1,4,5,2,7,3,6]=>[1,8,5,4,7,2,6,3]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[8,4,1,5,2,7,3,6]=>[1,5,8,4,7,2,6,3]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]=>[1,4,5,8,7,2,6,3]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,8,4,5,1,7,3,6]=>[7,1,5,4,8,2,6,3]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[8,1,4,5,7,2,3,6]=>[1,8,5,4,2,7,6,3]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[8,4,1,5,7,2,3,6]=>[1,5,8,4,2,7,6,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[8,5,4,1,7,2,3,6]=>[1,4,5,8,2,7,6,3]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,8,4,5,1,2,3,6]=>[2,1,5,4,8,7,6,3]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,8,4,5,7,1,3,6]=>[7,1,5,4,2,8,6,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,4,5,8,7,2,6]=>[6,8,5,4,1,2,7,3]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[4,3,1,5,8,7,2,6]=>[5,6,8,4,1,2,7,3]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,3,4,1,8,7,2,6]=>[4,6,5,8,1,2,7,3]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[8,3,4,5,1,7,2,6]=>[1,6,5,4,8,2,7,3]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[8,3,4,5,7,1,2,6]=>[1,6,5,4,2,8,7,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,4,5,8,7,1,6]=>[7,6,5,4,1,2,8,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>[3,8,7,6,5,2,1,4]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,6,1,3,4,7,8,5]=>[7,3,8,6,5,2,1,4]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[6,8,3,7,5,2,1,4]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,3,1,2,4,7,8,5]=>[3,6,8,7,5,2,1,4]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[7,6,3,8,5,2,1,4]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[5,8,7,3,6,2,1,4]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[7,5,8,3,6,2,1,4]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,1,4,2,3,7,8,5]=>[3,8,5,7,6,2,1,4]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,4,1,2,3,7,8,5]=>[3,5,8,7,6,2,1,4]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,4,1,3,7,8,5]=>[7,3,5,8,6,2,1,4]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>[6,8,5,3,7,2,1,4]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,1,6,2,7,8,5]=>[5,6,8,3,7,2,1,4]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,3,4,1,2,7,8,5]=>[3,6,5,8,7,2,1,4]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>[7,6,5,3,8,2,1,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[7,1,2,3,6,4,8,5]=>[2,8,7,6,3,5,1,4]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,7,1,3,6,4,8,5]=>[7,2,8,6,3,5,1,4]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]=>[6,8,2,7,3,5,1,4]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[7,3,1,2,6,4,8,5]=>[2,6,8,7,3,5,1,4]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,3,7,1,6,4,8,5]=>[7,6,2,8,3,5,1,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[7,1,2,6,3,4,8,5]=>[2,8,7,3,6,5,1,4]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,7,1,6,3,4,8,5]=>[7,2,8,3,6,5,1,4]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,1,7,2,3,4,8,5]=>[3,8,2,7,6,5,1,4]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,6,1,2,3,4,8,5]=>[2,3,8,7,6,5,1,4]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[7,3,2,8,6,5,1,4]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,7,6,2,4,8,5]=>[6,8,2,3,7,5,1,4]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7,3,1,6,2,4,8,5]=>[2,6,8,3,7,5,1,4]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,3,7,1,2,4,8,5]=>[3,6,2,8,7,5,1,4]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,7,6,1,4,8,5]=>[7,6,2,3,8,5,1,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,1,2,7,6,3,8,5]=>[5,8,7,2,3,6,1,4]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,1,7,6,3,8,5]=>[7,5,8,2,3,6,1,4]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,1,4,2,6,3,8,5]=>[2,8,5,7,3,6,1,4]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7,4,1,2,6,3,8,5]=>[2,5,8,7,3,6,1,4]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,7,4,1,6,3,8,5]=>[7,2,5,8,3,6,1,4]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[7,1,4,6,2,3,8,5]=>[2,8,5,3,7,6,1,4]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7,4,1,6,2,3,8,5]=>[2,5,8,3,7,6,1,4]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,1,2,3,8,5]=>[3,2,5,8,7,6,1,4]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,7,4,6,1,3,8,5]=>[7,2,5,3,8,6,1,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,4,7,6,2,8,5]=>[6,8,5,2,3,7,1,4]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,1,7,6,2,8,5]=>[5,6,8,2,3,7,1,4]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[7,3,4,1,6,2,8,5]=>[2,6,5,8,3,7,1,4]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[7,3,4,6,1,2,8,5]=>[2,6,5,3,8,7,1,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,4,7,6,1,8,5]=>[7,6,5,2,3,8,1,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[8,1,2,3,6,7,4,5]=>[1,8,7,6,3,2,5,4]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,8,1,3,6,7,4,5]=>[7,1,8,6,3,2,5,4]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,8,2,6,7,4,5]=>[6,8,1,7,3,2,5,4]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[8,3,1,2,6,7,4,5]=>[1,6,8,7,3,2,5,4]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,3,8,1,6,7,4,5]=>[7,6,1,8,3,2,5,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[8,1,2,6,3,7,4,5]=>[1,8,7,3,6,2,5,4]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,8,1,6,3,7,4,5]=>[7,1,8,3,6,2,5,4]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,1,8,2,3,7,4,5]=>[3,8,1,7,6,2,5,4]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,6,1,2,3,7,4,5]=>[1,3,8,7,6,2,5,4]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,6,8,1,3,7,4,5]=>[7,3,1,8,6,2,5,4]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,8,6,2,7,4,5]=>[6,8,1,3,7,2,5,4]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[8,3,1,6,2,7,4,5]=>[1,6,8,3,7,2,5,4]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,3,8,1,2,7,4,5]=>[3,6,1,8,7,2,5,4]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,8,6,1,7,4,5]=>[7,6,1,3,8,2,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[8,1,2,7,6,3,4,5]=>[1,8,7,2,3,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,8,1,7,6,3,4,5]=>[7,1,8,2,3,6,5,4]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[7,1,8,2,6,3,4,5]=>[2,8,1,7,3,6,5,4]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,1,2,6,3,4,5]=>[1,2,8,7,3,6,5,4]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,7,8,1,6,3,4,5]=>[7,2,1,8,3,6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,6,2,3,4,5]=>[2,8,1,3,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]=>[1,2,8,3,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[3,2,1,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,7,8,6,1,3,4,5]=>[7,2,1,3,8,6,5,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,8,7,6,2,4,5]=>[6,8,1,2,3,7,5,4]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8,3,1,7,6,2,4,5]=>[1,6,8,2,3,7,5,4]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,3,8,1,6,2,4,5]=>[2,6,1,8,3,7,5,4]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,8,6,1,2,4,5]=>[2,6,1,3,8,7,5,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,8,7,6,1,4,5]=>[7,6,1,2,3,8,5,4]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,1,2,8,6,7,3,5]=>[5,8,7,1,3,2,6,4]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1,8,6,7,3,5]=>[7,5,8,1,3,2,6,4]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[8,1,4,2,6,7,3,5]=>[1,8,5,7,3,2,6,4]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8,4,1,2,6,7,3,5]=>[1,5,8,7,3,2,6,4]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,8,4,1,6,7,3,5]=>[7,1,5,8,3,2,6,4]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[8,1,4,6,2,7,3,5]=>[1,8,5,3,7,2,6,4]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[8,4,1,6,2,7,3,5]=>[1,5,8,3,7,2,6,4]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,8,4,1,2,7,3,5]=>[3,1,5,8,7,2,6,4]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,8,4,6,1,7,3,5]=>[7,1,5,3,8,2,6,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[8,1,4,7,6,2,3,5]=>[1,8,5,2,3,7,6,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[8,4,1,7,6,2,3,5]=>[1,5,8,2,3,7,6,4]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]=>[2,1,5,8,3,7,6,4]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,8,4,6,1,2,3,5]=>[2,1,5,3,8,7,6,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,8,4,7,6,1,3,5]=>[7,1,5,2,3,8,6,4]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,4,8,6,7,2,5]=>[6,8,5,1,3,2,7,4]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,3,1,8,6,7,2,5]=>[5,6,8,1,3,2,7,4]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[8,3,4,1,6,7,2,5]=>[1,6,5,8,3,2,7,4]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[8,3,4,6,1,7,2,5]=>[1,6,5,3,8,2,7,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[8,3,4,7,6,1,2,5]=>[1,6,5,2,3,8,7,4]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,8,6,7,1,5]=>[7,6,5,1,3,2,8,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[4,8,7,6,3,2,1,5]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>[7,4,8,6,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[6,8,4,7,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,3,1,2,6,7,8,4]=>[4,6,8,7,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[7,6,4,8,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[6,1,2,5,3,7,8,4]=>[3,8,7,4,6,2,1,5]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,6,1,5,3,7,8,4]=>[7,3,8,4,6,2,1,5]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,1,5,2,3,7,8,4]=>[3,8,4,7,6,2,1,5]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,1,2,3,7,8,4]=>[4,3,8,7,6,2,1,5]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,6,5,1,3,7,8,4]=>[7,3,4,8,6,2,1,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,5,2,7,8,4]=>[6,8,3,4,7,2,1,5]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[6,3,1,5,2,7,8,4]=>[3,6,8,4,7,2,1,5]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[6,3,5,1,2,7,8,4]=>[3,6,4,8,7,2,1,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,6,5,1,7,8,4]=>[7,6,3,4,8,2,1,5]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[7,1,2,5,6,3,8,4]=>[2,8,7,4,3,6,1,5]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,7,1,5,6,3,8,4]=>[7,2,8,4,3,6,1,5]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[7,1,5,2,6,3,8,4]=>[2,8,4,7,3,6,1,5]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,7,1,2,6,3,8,4]=>[4,2,8,7,3,6,1,5]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,7,5,1,6,3,8,4]=>[7,2,4,8,3,6,1,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[7,1,6,5,2,3,8,4]=>[2,8,3,4,7,6,1,5]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[6,7,1,5,2,3,8,4]=>[3,2,8,4,7,6,1,5]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,5,1,2,3,8,4]=>[3,2,4,8,7,6,1,5]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,7,6,5,1,3,8,4]=>[7,2,3,4,8,6,1,5]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,7,5,6,2,8,4]=>[6,8,2,4,3,7,1,5]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7,3,1,5,6,2,8,4]=>[2,6,8,4,3,7,1,5]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,3,5,1,6,2,8,4]=>[2,6,4,8,3,7,1,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,6,5,1,2,8,4]=>[2,6,3,4,8,7,1,5]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,7,5,6,1,8,4]=>[7,6,2,4,3,8,1,5]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[8,1,2,5,6,7,3,4]=>[1,8,7,4,3,2,6,5]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,8,1,5,6,7,3,4]=>[7,1,8,4,3,2,6,5]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[8,1,5,2,6,7,3,4]=>[1,8,4,7,3,2,6,5]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,8,1,2,6,7,3,4]=>[4,1,8,7,3,2,6,5]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,8,5,1,6,7,3,4]=>[7,1,4,8,3,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[8,1,6,5,2,7,3,4]=>[1,8,3,4,7,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,8,1,5,2,7,3,4]=>[3,1,8,4,7,2,6,5]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[6,8,5,1,2,7,3,4]=>[3,1,4,8,7,2,6,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,8,6,5,1,7,3,4]=>[7,1,3,4,8,2,6,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[8,1,7,5,6,2,3,4]=>[1,8,2,4,3,7,6,5]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7,8,1,5,6,2,3,4]=>[2,1,8,4,3,7,6,5]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,8,5,1,6,2,3,4]=>[2,1,4,8,3,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]=>[2,1,3,4,8,7,6,5]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,8,7,5,6,1,3,4]=>[7,1,2,4,3,8,6,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,8,5,6,7,2,4]=>[6,8,1,4,3,2,7,5]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[8,3,1,5,6,7,2,4]=>[1,6,8,4,3,2,7,5]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[8,3,5,1,6,7,2,4]=>[1,6,4,8,3,2,7,5]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[8,3,6,5,1,7,2,4]=>[1,6,3,4,8,2,7,5]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,3,7,5,6,1,2,4]=>[1,6,2,4,3,8,7,5]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,8,5,6,7,1,4]=>[7,6,1,4,3,2,8,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[5,8,7,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[7,5,8,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[5,1,4,2,6,7,8,3]=>[4,8,5,7,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,4,1,2,6,7,8,3]=>[4,5,8,7,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,5,4,1,6,7,8,3]=>[7,4,5,8,3,2,1,6]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[6,1,4,5,2,7,8,3]=>[3,8,5,4,7,2,1,6]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[6,4,1,5,2,7,8,3]=>[3,5,8,4,7,2,1,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[6,5,4,1,2,7,8,3]=>[3,4,5,8,7,2,1,6]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,6,4,5,1,7,8,3]=>[7,3,5,4,8,2,1,6]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[7,1,4,5,6,2,8,3]=>[2,8,5,4,3,7,1,6]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[7,4,1,5,6,2,8,3]=>[2,5,8,4,3,7,1,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,5,4,1,6,2,8,3]=>[2,4,5,8,3,7,1,6]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,6,4,5,1,2,8,3]=>[2,3,5,4,8,7,1,6]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,7,4,5,6,1,8,3]=>[7,2,5,4,3,8,1,6]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]=>[1,8,5,4,3,2,7,6]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[8,4,1,5,6,7,2,3]=>[1,5,8,4,3,2,7,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[8,5,4,1,6,7,2,3]=>[1,4,5,8,3,2,7,6]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[8,6,4,5,1,7,2,3]=>[1,3,5,4,8,2,7,6]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,7,4,5,6,1,2,3]=>[1,2,5,4,3,8,7,6]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,4,5,6,7,1,3]=>[7,1,5,4,3,2,8,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[6,8,5,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,2]=>[5,6,8,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,2]=>[4,6,5,8,3,2,1,7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,2]=>[3,6,5,4,8,2,1,7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,2]=>[2,6,5,4,3,8,1,7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,2]=>[1,6,5,4,3,2,8,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[7,6,5,4,3,2,1,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,9,1,3,4,5,6,7,8]=>[8,1,9,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,9,2,4,5,6,7,8]=>[7,9,1,8,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[1,7,9,8,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,9,1,4,5,6,7,8]=>[8,7,1,9,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,9,3,5,6,7,8]=>[6,9,8,1,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,9,3,5,6,7,8]=>[8,6,9,1,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,1,4,2,3,5,6,7,8]=>[1,9,6,8,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,4,1,2,3,5,6,7,8]=>[1,6,9,8,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,9,4,1,3,5,6,7,8]=>[8,1,6,9,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,9,2,5,6,7,8]=>[7,9,6,1,8,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,1,9,2,5,6,7,8]=>[6,7,9,1,8,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,3,4,1,2,5,6,7,8]=>[1,7,6,9,8,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,9,1,5,6,7,8]=>[8,7,6,1,9,5,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[5,1,2,3,9,4,6,7,8]=>[5,9,8,7,1,6,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,5,1,3,9,4,6,7,8]=>[8,5,9,7,1,6,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,9,4,6,7,8]=>[7,9,5,8,1,6,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[5,3,1,2,9,4,6,7,8]=>[5,7,9,8,1,6,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,5,1,9,4,6,7,8]=>[8,7,5,9,1,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[9,1,2,5,3,4,6,7,8]=>[1,9,8,5,7,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,9,1,5,3,4,6,7,8]=>[8,1,9,5,7,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,1,5,2,3,4,6,7,8]=>[1,9,5,8,7,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,9,1,2,3,4,6,7,8]=>[5,1,9,8,7,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,9,5,1,3,4,6,7,8]=>[8,1,5,9,7,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[9,3,1,5,2,4,6,7,8]=>[1,7,9,5,8,6,4,3,2]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[2,3,9,5,1,4,6,7,8]=>[8,7,1,5,9,6,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,9,3,6,7,8]=>[6,9,8,5,1,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>[8,6,9,5,1,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,4,2,9,3,6,7,8]=>[5,9,6,8,1,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,1,2,9,3,6,7,8]=>[5,6,9,8,1,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,5,4,1,9,3,6,7,8]=>[8,5,6,9,1,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,1,4,5,2,3,6,7,8]=>[1,9,6,5,8,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,4,1,5,2,3,6,7,8]=>[1,6,9,5,8,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,5,4,1,2,3,6,7,8]=>[1,5,6,9,8,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[2,9,4,5,1,3,6,7,8]=>[8,1,6,5,9,7,4,3,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,4,5,9,2,6,7,8]=>[7,9,6,5,1,8,4,3,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,1,5,9,2,6,7,8]=>[6,7,9,5,1,8,4,3,2]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[9,3,4,5,1,2,6,7,8]=>[1,7,6,5,9,8,4,3,2]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,9,1,6,7,8]=>[8,7,6,5,1,9,4,3,2]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,1,2,3,4,9,5,7,8]=>[4,9,8,7,6,1,5,3,2]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,6,1,3,4,9,5,7,8]=>[8,4,9,7,6,1,5,3,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[6,3,1,2,4,9,5,7,8]=>[4,7,9,8,6,1,5,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,6,3,9,5,7,8]=>[6,9,8,4,7,1,5,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,6,3,9,5,7,8]=>[8,6,9,4,7,1,5,3,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[6,4,1,2,3,9,5,7,8]=>[4,6,9,8,7,1,5,3,2]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,6,1,9,5,7,8]=>[8,7,6,4,9,1,5,3,2]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[9,1,2,3,6,4,5,7,8]=>[1,9,8,7,4,6,5,3,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[9,3,1,2,6,4,5,7,8]=>[1,7,9,8,4,6,5,3,2]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[9,1,2,6,3,4,5,7,8]=>[1,9,8,4,7,6,5,3,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,1,9,2,3,4,5,7,8]=>[4,9,1,8,7,6,5,3,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,6,1,2,3,4,5,7,8]=>[1,4,9,8,7,6,5,3,2]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,6,9,1,3,4,5,7,8]=>[8,4,1,9,7,6,5,3,2]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[2,3,9,6,1,4,5,7,8]=>[8,7,1,4,9,6,5,3,2]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,9,4,1,6,3,5,7,8]=>[8,1,6,9,4,7,5,3,2]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,9,4,1,2,3,5,7,8]=>[4,1,6,9,8,7,5,3,2]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[2,3,4,9,6,1,5,7,8]=>[8,7,6,1,4,9,5,3,2]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[5,1,2,3,6,9,4,7,8]=>[5,9,8,7,4,1,6,3,2]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,9,4,7,8]=>[8,5,9,7,4,1,6,3,2]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,6,9,4,7,8]=>[7,9,5,8,4,1,6,3,2]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[5,3,1,2,6,9,4,7,8]=>[5,7,9,8,4,1,6,3,2]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,2,5,3,9,4,7,8]=>[4,9,8,5,7,1,6,3,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,5,2,3,9,4,7,8]=>[4,9,5,8,7,1,6,3,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,6,1,2,3,9,4,7,8]=>[5,4,9,8,7,1,6,3,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[9,1,2,5,6,3,4,7,8]=>[1,9,8,5,4,7,6,3,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[5,9,1,2,6,3,4,7,8]=>[5,1,9,8,4,7,6,3,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[9,1,6,5,2,3,4,7,8]=>[1,9,4,5,8,7,6,3,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,9,1,5,2,3,4,7,8]=>[4,1,9,5,8,7,6,3,2]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,9,5,1,2,3,4,7,8]=>[4,1,5,9,8,7,6,3,2]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[2,9,6,5,1,3,4,7,8]=>[8,1,4,5,9,7,6,3,2]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[9,3,1,5,6,2,4,7,8]=>[1,7,9,5,4,8,6,3,2]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[9,3,6,5,1,2,4,7,8]=>[1,7,4,5,9,8,6,3,2]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[2,3,9,5,6,1,4,7,8]=>[8,7,1,5,4,9,6,3,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,5,6,9,3,7,8]=>[6,9,8,5,4,1,7,3,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,5,6,9,3,7,8]=>[8,6,9,5,4,1,7,3,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[5,4,1,2,6,9,3,7,8]=>[5,6,9,8,4,1,7,3,2]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[9,4,1,5,6,2,3,7,8]=>[1,6,9,5,4,8,7,3,2]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[9,6,4,5,1,2,3,7,8]=>[1,4,6,5,9,8,7,3,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,5,6,9,2,7,8]=>[7,9,6,5,4,1,8,3,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,3,1,5,6,9,2,7,8]=>[6,7,9,5,4,1,8,3,2]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[6,3,4,5,1,9,2,7,8]=>[4,7,6,5,9,1,8,3,2]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[9,3,4,5,6,1,2,7,8]=>[1,7,6,5,4,9,8,3,2]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]=>[8,7,6,5,4,1,9,3,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,1,2,3,4,5,9,6,8]=>[3,9,8,7,6,5,1,4,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,7,1,3,4,5,9,6,8]=>[8,3,9,7,6,5,1,4,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,7,2,4,5,9,6,8]=>[7,9,3,8,6,5,1,4,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,3,1,2,4,5,9,6,8]=>[3,7,9,8,6,5,1,4,2]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,7,1,5,9,6,8]=>[8,7,6,3,9,5,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,9,6,8]=>[8,5,9,7,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>[7,9,5,8,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,9,6,8]=>[5,7,9,8,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,9,6,8]=>[8,7,5,9,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[5,7,1,2,3,4,9,6,8]=>[5,3,9,8,7,6,1,4,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,7,5,2,4,9,6,8]=>[7,9,3,5,8,6,1,4,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,3,1,5,2,4,9,6,8]=>[3,7,9,5,8,6,1,4,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,1,4,2,7,3,9,6,8]=>[5,9,6,8,3,7,1,4,2]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,5,4,1,7,3,9,6,8]=>[8,5,6,9,3,7,1,4,2]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,5,7,1,9,6,8]=>[8,7,6,5,3,9,1,4,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,1,2,3,4,7,5,6,8]=>[1,9,8,7,6,3,5,4,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,9,1,3,4,7,5,6,8]=>[8,1,9,7,6,3,5,4,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[9,3,1,2,4,7,5,6,8]=>[1,7,9,8,6,3,5,4,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[9,1,4,2,3,7,5,6,8]=>[1,9,6,8,7,3,5,4,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[9,4,1,2,3,7,5,6,8]=>[1,6,9,8,7,3,5,4,2]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,9,1,7,5,6,8]=>[8,7,6,1,9,3,5,4,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,1,2,9,3,4,5,6,8]=>[3,9,8,1,7,6,5,4,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1,7,2,3,4,5,6,8]=>[1,9,3,8,7,6,5,4,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[1,3,9,8,7,6,5,4,2]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,9,7,1,3,4,5,6,8]=>[8,1,3,9,7,6,5,4,2]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,3,7,1,2,4,5,6,8]=>[1,7,3,9,8,6,5,4,2]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[2,3,7,9,1,4,5,6,8]=>[8,7,3,1,9,6,5,4,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1,4,9,2,3,5,6,8]=>[3,9,6,1,8,7,5,4,2]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[9,7,4,1,2,3,5,6,8]=>[1,3,6,9,8,7,5,4,2]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[2,3,4,9,7,1,5,6,8]=>[8,7,6,1,3,9,5,4,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,9,7,4,6,8]=>[5,7,9,8,1,3,6,4,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,9,5,2,7,4,6,8]=>[7,9,1,5,8,3,6,4,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[9,3,1,5,2,7,4,6,8]=>[1,7,9,5,8,3,6,4,2]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[2,3,9,5,1,7,4,6,8]=>[8,7,1,5,9,3,6,4,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[9,1,5,2,7,3,4,6,8]=>[1,9,5,8,3,7,6,4,2]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[9,7,5,1,2,3,4,6,8]=>[1,3,5,9,8,7,6,4,2]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,3,9,5,1,2,4,6,8]=>[3,7,1,5,9,8,6,4,2]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[2,3,9,5,7,1,4,6,8]=>[8,7,1,5,3,9,6,4,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[9,1,4,5,2,7,3,6,8]=>[1,9,6,5,8,3,7,4,2]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[9,5,4,1,7,2,3,6,8]=>[1,5,6,9,3,8,7,4,2]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[2,3,4,5,9,7,1,6,8]=>[8,7,6,5,1,3,9,4,2]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,1,2,3,4,7,9,5,8]=>[4,9,8,7,6,3,1,5,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,1,2,4,7,9,5,8]=>[4,7,9,8,6,3,1,5,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,6,3,7,9,5,8]=>[8,6,9,4,7,3,1,5,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,4,1,2,3,7,9,5,8]=>[4,6,9,8,7,3,1,5,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,7,9,5,8]=>[7,9,6,4,8,3,1,5,2]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,6,1,7,9,5,8]=>[8,7,6,4,9,3,1,5,2]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,1,2,3,6,4,9,5,8]=>[3,9,8,7,4,6,1,5,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,7,2,6,4,9,5,8]=>[7,9,3,8,4,6,1,5,2]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,7,1,6,4,9,5,8]=>[8,7,3,9,4,6,1,5,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,7,2,3,4,9,5,8]=>[4,9,3,8,7,6,1,5,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,6,1,2,3,4,9,5,8]=>[3,4,9,8,7,6,1,5,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,1,4,2,6,3,9,5,8]=>[3,9,6,8,4,7,1,5,2]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,7,4,1,6,3,9,5,8]=>[8,3,6,9,4,7,1,5,2]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,1,7,6,2,9,5,8]=>[6,7,9,3,4,8,1,5,2]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[9,1,2,3,6,7,4,5,8]=>[1,9,8,7,4,3,6,5,2]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,9,1,6,7,4,5,8]=>[8,7,1,9,4,3,6,5,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,1,9,2,3,7,4,5,8]=>[4,9,1,8,7,3,6,5,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[9,6,1,2,3,7,4,5,8]=>[1,4,9,8,7,3,6,5,2]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,9,1,2,7,4,5,8]=>[4,7,1,9,8,3,6,5,2]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[9,1,2,7,6,3,4,5,8]=>[1,9,8,3,4,7,6,5,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[9,7,1,2,6,3,4,5,8]=>[1,3,9,8,4,7,6,5,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1,9,6,2,3,4,5,8]=>[3,9,1,4,8,7,6,5,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,7,1,6,2,3,4,5,8]=>[1,3,9,4,8,7,6,5,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,7,9,1,2,3,4,5,8]=>[4,3,1,9,8,7,6,5,2]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[9,3,1,7,6,2,4,5,8]=>[1,7,9,3,4,8,6,5,2]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,3,9,6,1,2,4,5,8]=>[3,7,1,4,9,8,6,5,2]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[2,3,9,7,6,1,4,5,8]=>[8,7,1,3,4,9,6,5,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[9,1,4,2,6,7,3,5,8]=>[1,9,6,8,4,3,7,5,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[9,4,1,2,6,7,3,5,8]=>[1,6,9,8,4,3,7,5,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[9,4,1,7,6,2,3,5,8]=>[1,6,9,3,4,8,7,5,2]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,3,1,9,6,7,2,5,8]=>[6,7,9,1,4,3,8,5,2]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[9,3,4,6,1,7,2,5,8]=>[1,7,6,4,9,3,8,5,2]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[2,3,4,9,6,7,1,5,8]=>[8,7,6,1,4,3,9,5,2]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,9,4,8]=>[5,9,8,7,4,3,1,6,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,5,2,6,7,9,4,8]=>[7,9,5,8,4,3,1,6,2]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>[8,7,5,9,4,3,1,6,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,9,4,8]=>[5,4,9,8,7,3,1,6,2]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,7,5,1,2,3,9,4,8]=>[4,3,5,9,8,7,1,6,2]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,7,5,6,2,9,4,8]=>[7,9,3,5,4,8,1,6,2]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[2,3,7,5,6,1,9,4,8]=>[8,7,3,5,4,9,1,6,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,9,1,5,6,7,3,4,8]=>[8,1,9,5,4,3,7,6,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,9,1,5,2,7,3,4,8]=>[4,1,9,5,8,3,7,6,2]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,9,5,1,2,7,3,4,8]=>[4,1,5,9,8,3,7,6,2]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,9,1,5,6,2,3,4,8]=>[3,1,9,5,4,8,7,6,2]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,9,6,5,1,2,3,4,8]=>[3,1,4,5,9,8,7,6,2]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[2,3,9,5,6,7,1,4,8]=>[8,7,1,5,4,3,9,6,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,9,3,8]=>[6,9,8,5,4,3,1,7,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>[8,6,9,5,4,3,1,7,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,1,2,6,7,9,3,8]=>[5,6,9,8,4,3,1,7,2]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,5,4,1,2,7,9,3,8]=>[4,5,6,9,8,3,1,7,2]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,4,1,5,6,2,9,3,8]=>[3,6,9,5,4,8,1,7,2]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,6,4,5,1,2,9,3,8]=>[3,4,6,5,9,8,1,7,2]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[2,7,4,5,6,1,9,3,8]=>[8,3,6,5,4,9,1,7,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[9,1,4,5,6,7,2,3,8]=>[1,9,6,5,4,3,8,7,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[9,6,4,5,1,7,2,3,8]=>[1,4,6,5,9,3,8,7,2]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[9,7,4,5,6,1,2,3,8]=>[1,3,6,5,4,9,8,7,2]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[2,9,4,5,6,7,1,3,8]=>[8,1,6,5,4,3,9,7,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]=>[7,9,6,5,4,3,1,8,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1,5,6,7,9,2,8]=>[6,7,9,5,4,3,1,8,2]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[5,3,4,1,6,7,9,2,8]=>[5,7,6,9,4,3,1,8,2]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[6,3,4,5,1,7,9,2,8]=>[4,7,6,5,9,3,1,8,2]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,3,4,5,6,1,9,2,8]=>[3,7,6,5,4,9,1,8,2]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,1,2,8]=>[1,7,6,5,4,3,9,8,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>[8,7,6,5,4,3,1,9,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,1,2,3,4,5,6,9,7]=>[2,9,8,7,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,8,1,3,4,5,6,9,7]=>[8,2,9,7,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,8,2,4,5,6,9,7]=>[7,9,2,8,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[8,3,1,2,4,5,6,9,7]=>[2,7,9,8,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,8,1,4,5,6,9,7]=>[8,7,2,9,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,8,3,5,6,9,7]=>[6,9,8,2,7,5,4,1,3]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[8,1,4,2,3,5,6,9,7]=>[2,9,6,8,7,5,4,1,3]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[8,4,1,2,3,5,6,9,7]=>[2,6,9,8,7,5,4,1,3]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,8,1,5,6,9,7]=>[8,7,6,2,9,5,4,1,3]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,1,2,3,8,4,6,9,7]=>[5,9,8,7,2,6,4,1,3]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,5,2,8,4,6,9,7]=>[7,9,5,8,2,6,4,1,3]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[8,1,2,5,3,4,6,9,7]=>[2,9,8,5,7,6,4,1,3]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,8,1,2,3,4,6,9,7]=>[5,2,9,8,7,6,4,1,3]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[8,3,1,5,2,4,6,9,7]=>[2,7,9,5,8,6,4,1,3]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,5,4,1,8,3,6,9,7]=>[8,5,6,9,2,7,4,1,3]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[8,5,4,1,2,3,6,9,7]=>[2,5,6,9,8,7,4,1,3]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[8,3,4,5,1,2,6,9,7]=>[2,7,6,5,9,8,4,1,3]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,5,8,1,6,9,7]=>[8,7,6,5,2,9,4,1,3]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,1,2,3,4,8,5,9,7]=>[4,9,8,7,6,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,8,5,9,7]=>[6,9,8,4,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>[8,6,9,4,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,6,4,1,3,8,5,9,7]=>[8,4,6,9,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,6,2,8,5,9,7]=>[7,9,6,4,8,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,1,6,2,8,5,9,7]=>[6,7,9,4,8,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,3,4,1,2,8,5,9,7]=>[4,7,6,9,8,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,6,1,8,5,9,7]=>[8,7,6,4,9,2,5,1,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[8,1,2,3,6,4,5,9,7]=>[2,9,8,7,4,6,5,1,3]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,6,1,2,3,4,5,9,7]=>[2,4,9,8,7,6,5,1,3]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[2,3,8,6,1,4,5,9,7]=>[8,7,2,4,9,6,5,1,3]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,8,4,1,6,3,5,9,7]=>[8,2,6,9,4,7,5,1,3]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,8,4,1,2,3,5,9,7]=>[4,2,6,9,8,7,5,1,3]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[8,3,4,1,6,2,5,9,7]=>[2,7,6,9,4,8,5,1,3]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[2,3,4,8,6,1,5,9,7]=>[8,7,6,2,4,9,5,1,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[5,1,2,3,6,8,4,9,7]=>[5,9,8,7,4,2,6,1,3]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,8,4,9,7]=>[5,4,9,8,7,2,6,1,3]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,3,1,5,2,8,4,9,7]=>[4,7,9,5,8,2,6,1,3]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,8,1,5,6,3,4,9,7]=>[8,2,9,5,4,7,6,1,3]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,8,5,1,2,3,4,9,7]=>[4,2,5,9,8,7,6,1,3]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[8,3,1,5,6,2,4,9,7]=>[2,7,9,5,4,8,6,1,3]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[8,3,5,1,6,2,4,9,7]=>[2,7,5,9,4,8,6,1,3]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[2,3,8,5,6,1,4,9,7]=>[8,7,2,5,4,9,6,1,3]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,5,6,8,3,9,7]=>[6,9,8,5,4,2,7,1,3]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,5,6,8,3,9,7]=>[8,6,9,5,4,2,7,1,3]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,5,4,1,2,8,3,9,7]=>[4,5,6,9,8,2,7,1,3]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[8,1,4,5,6,2,3,9,7]=>[2,9,6,5,4,8,7,1,3]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[8,6,4,5,1,2,3,9,7]=>[2,4,6,5,9,8,7,1,3]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[2,8,4,5,6,1,3,9,7]=>[8,2,6,5,4,9,7,1,3]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>[7,9,6,5,4,2,8,1,3]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,3,1,5,6,8,2,9,7]=>[6,7,9,5,4,2,8,1,3]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,3,4,1,6,8,2,9,7]=>[5,7,6,9,4,2,8,1,3]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,3,4,5,1,8,2,9,7]=>[4,7,6,5,9,2,8,1,3]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[8,3,4,5,6,1,2,9,7]=>[2,7,6,5,4,9,8,1,3]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>[8,7,6,5,4,2,9,1,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,1,2,3,4,5,8,6,7]=>[1,9,8,7,6,5,2,4,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,9,1,3,4,5,8,6,7]=>[8,1,9,7,6,5,2,4,3]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,9,2,4,5,8,6,7]=>[7,9,1,8,6,5,2,4,3]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[9,3,1,2,4,5,8,6,7]=>[1,7,9,8,6,5,2,4,3]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,9,1,4,5,8,6,7]=>[8,7,1,9,6,5,2,4,3]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,9,3,5,8,6,7]=>[6,9,8,1,7,5,2,4,3]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[9,1,4,2,3,5,8,6,7]=>[1,9,6,8,7,5,2,4,3]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[9,4,1,2,3,5,8,6,7]=>[1,6,9,8,7,5,2,4,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,9,2,5,8,6,7]=>[7,9,6,1,8,5,2,4,3]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[9,3,4,1,2,5,8,6,7]=>[1,7,6,9,8,5,2,4,3]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,9,1,5,8,6,7]=>[8,7,6,1,9,5,2,4,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[5,1,2,3,9,4,8,6,7]=>[5,9,8,7,1,6,2,4,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,5,2,9,4,8,6,7]=>[7,9,5,8,1,6,2,4,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[9,1,2,5,3,4,8,6,7]=>[1,9,8,5,7,6,2,4,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,9,1,2,3,4,8,6,7]=>[5,1,9,8,7,6,2,4,3]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[9,3,5,1,2,4,8,6,7]=>[1,7,5,9,8,6,2,4,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,9,3,8,6,7]=>[6,9,8,5,1,7,2,4,3]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,1,4,2,9,3,8,6,7]=>[5,9,6,8,1,7,2,4,3]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,5,4,1,9,3,8,6,7]=>[8,5,6,9,1,7,2,4,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[9,4,1,5,2,3,8,6,7]=>[1,6,9,5,8,7,2,4,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[2,9,4,5,1,3,8,6,7]=>[8,1,6,5,9,7,2,4,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[9,3,4,5,1,2,8,6,7]=>[1,7,6,5,9,8,2,4,3]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,5,9,1,8,6,7]=>[8,7,6,5,1,9,2,4,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,1,2,3,4,8,5,6,7]=>[1,9,8,7,6,2,5,4,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,9,1,3,4,8,5,6,7]=>[8,1,9,7,6,2,5,4,3]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[9,3,1,2,4,8,5,6,7]=>[1,7,9,8,6,2,5,4,3]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,9,1,4,8,5,6,7]=>[8,7,1,9,6,2,5,4,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,9,3,8,5,6,7]=>[6,9,8,1,7,2,5,4,3]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[9,1,4,2,3,8,5,6,7]=>[1,9,6,8,7,2,5,4,3]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[9,4,1,2,3,8,5,6,7]=>[1,6,9,8,7,2,5,4,3]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,9,2,8,5,6,7]=>[7,9,6,1,8,2,5,4,3]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,9,1,8,5,6,7]=>[8,7,6,1,9,2,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,1,2,3,9,4,5,6,7]=>[2,9,8,7,1,6,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,8,1,3,9,4,5,6,7]=>[8,2,9,7,1,6,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,8,2,9,4,5,6,7]=>[7,9,2,8,1,6,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[8,3,1,2,9,4,5,6,7]=>[2,7,9,8,1,6,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,8,1,9,4,5,6,7]=>[8,7,2,9,1,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,2,8,3,4,5,6,7]=>[1,9,8,2,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,9,1,8,3,4,5,6,7]=>[8,1,9,2,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,8,2,3,4,5,6,7]=>[1,9,2,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[2,1,9,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,9,8,1,3,4,5,6,7]=>[8,1,2,9,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,9,8,2,4,5,6,7]=>[7,9,1,2,8,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,3,1,8,2,4,5,6,7]=>[1,7,9,2,8,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,3,8,1,2,4,5,6,7]=>[1,7,2,9,8,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,9,8,1,4,5,6,7]=>[8,7,1,2,9,6,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[4,1,2,8,9,3,5,6,7]=>[6,9,8,2,1,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,8,9,3,5,6,7]=>[8,6,9,2,1,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8,1,4,2,9,3,5,6,7]=>[2,9,6,8,1,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8,4,1,2,9,3,5,6,7]=>[2,6,9,8,1,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,8,4,1,9,3,5,6,7]=>[8,2,6,9,1,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,1,4,8,2,3,5,6,7]=>[1,9,6,2,8,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,4,1,8,2,3,5,6,7]=>[1,6,9,2,8,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,8,4,1,2,3,5,6,7]=>[1,2,6,9,8,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[2,9,4,8,1,3,5,6,7]=>[8,1,6,2,9,7,5,4,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,4,8,9,2,5,6,7]=>[7,9,6,2,1,8,5,4,3]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[8,3,4,1,9,2,5,6,7]=>[2,7,6,9,1,8,5,4,3]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[9,3,4,8,1,2,5,6,7]=>[1,7,6,2,9,8,5,4,3]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[2,3,4,8,9,1,5,6,7]=>[8,7,6,2,1,9,5,4,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,1,2,3,9,8,4,6,7]=>[5,9,8,7,1,2,6,4,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[9,1,5,2,3,8,4,6,7]=>[1,9,5,8,7,2,6,4,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[5,9,1,2,3,8,4,6,7]=>[5,1,9,8,7,2,6,4,3]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[9,3,1,5,2,8,4,6,7]=>[1,7,9,5,8,2,6,4,3]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[8,1,2,5,9,3,4,6,7]=>[2,9,8,5,1,7,6,4,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[5,8,1,2,9,3,4,6,7]=>[5,2,9,8,1,7,6,4,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,1,8,5,2,3,4,6,7]=>[1,9,2,5,8,7,6,4,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,8,1,5,2,3,4,6,7]=>[1,2,9,5,8,7,6,4,3]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,8,5,1,2,3,4,6,7]=>[1,2,5,9,8,7,6,4,3]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[9,3,8,5,1,2,4,6,7]=>[1,7,2,5,9,8,6,4,3]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[2,3,8,5,9,1,4,6,7]=>[8,7,2,5,1,9,6,4,3]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,9,8,3,6,7]=>[6,9,8,5,1,2,7,4,3]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[9,1,4,5,2,8,3,6,7]=>[1,9,6,5,8,2,7,4,3]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[9,5,4,1,2,8,3,6,7]=>[1,5,6,9,8,2,7,4,3]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[8,5,4,1,9,2,3,6,7]=>[2,5,6,9,1,8,7,4,3]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[9,8,4,5,1,2,3,6,7]=>[1,2,6,5,9,8,7,4,3]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[2,8,4,5,9,1,3,6,7]=>[8,2,6,5,1,9,7,4,3]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,4,5,9,8,2,6,7]=>[7,9,6,5,1,2,8,4,3]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,3,1,5,9,8,2,6,7]=>[6,7,9,5,1,2,8,4,3]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,3,4,1,9,8,2,6,7]=>[5,7,6,9,1,2,8,4,3]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[8,3,4,5,9,1,2,6,7]=>[2,7,6,5,1,9,8,4,3]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[2,3,4,5,9,8,1,6,7]=>[8,7,6,5,1,2,9,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,1,2,3,4,9,8,5,7]=>[4,9,8,7,6,1,2,5,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,3,9,8,5,7]=>[8,6,9,4,7,1,2,5,3]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1,6,2,9,8,5,7]=>[6,7,9,4,8,1,2,5,3]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,6,1,9,8,5,7]=>[8,7,6,4,9,1,2,5,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[9,1,2,3,6,4,8,5,7]=>[1,9,8,7,4,6,2,5,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,9,1,3,6,4,8,5,7]=>[8,1,9,7,4,6,2,5,3]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,9,2,6,4,8,5,7]=>[7,9,1,8,4,6,2,5,3]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,9,1,6,4,8,5,7]=>[8,7,1,9,4,6,2,5,3]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,1,9,2,3,4,8,5,7]=>[4,9,1,8,7,6,2,5,3]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[9,6,1,2,3,4,8,5,7]=>[1,4,9,8,7,6,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,9,6,3,8,5,7]=>[8,6,9,1,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[9,1,4,2,6,3,8,5,7]=>[1,9,6,8,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[9,4,1,2,6,3,8,5,7]=>[1,6,9,8,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,9,4,1,6,3,8,5,7]=>[8,1,6,9,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,1,9,6,2,8,5,7]=>[6,7,9,1,4,8,2,5,3]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[9,3,4,1,6,2,8,5,7]=>[1,7,6,9,4,8,2,5,3]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[9,3,4,6,1,2,8,5,7]=>[1,7,6,4,9,8,2,5,3]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[2,3,4,9,6,1,8,5,7]=>[8,7,6,1,4,9,2,5,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[9,1,2,3,6,8,4,5,7]=>[1,9,8,7,4,2,6,5,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[9,3,1,2,6,8,4,5,7]=>[1,7,9,8,4,2,6,5,3]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[9,6,1,2,3,8,4,5,7]=>[1,4,9,8,7,2,6,5,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[8,1,2,9,6,3,4,5,7]=>[2,9,8,1,4,7,6,5,3]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[9,8,1,2,6,3,4,5,7]=>[1,2,9,8,4,7,6,5,3]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,1,8,6,2,3,4,5,7]=>[1,9,2,4,8,7,6,5,3]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,8,1,6,2,3,4,5,7]=>[1,2,9,4,8,7,6,5,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,9,8,1,2,3,4,5,7]=>[4,1,2,9,8,7,6,5,3]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[2,9,8,6,1,3,4,5,7]=>[8,1,2,4,9,7,6,5,3]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[2,3,8,9,6,1,4,5,7]=>[8,7,2,1,4,9,6,5,3]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[9,4,1,6,2,8,3,5,7]=>[1,6,9,4,8,2,7,5,3]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[8,1,4,9,6,2,3,5,7]=>[2,9,6,1,4,8,7,5,3]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[9,8,4,6,1,2,3,5,7]=>[1,2,6,4,9,8,7,5,3]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[8,3,4,9,6,1,2,5,7]=>[2,7,6,1,4,9,8,5,3]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[2,3,4,9,6,8,1,5,7]=>[8,7,6,1,4,2,9,5,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,1,2,3,6,9,8,4,7]=>[5,9,8,7,4,1,2,6,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,6,1,2,3,9,8,4,7]=>[5,4,9,8,7,1,2,6,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,1,5,2,9,8,4,7]=>[4,7,9,5,8,1,2,6,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[9,1,2,5,6,3,8,4,7]=>[1,9,8,5,4,7,2,6,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,9,1,5,6,3,8,4,7]=>[8,1,9,5,4,7,2,6,3]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,9,5,1,6,3,8,4,7]=>[8,1,5,9,4,7,2,6,3]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[9,1,6,5,2,3,8,4,7]=>[1,9,4,5,8,7,2,6,3]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,9,5,1,2,3,8,4,7]=>[4,1,5,9,8,7,2,6,3]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[9,3,1,5,6,2,8,4,7]=>[1,7,9,5,4,8,2,6,3]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[9,3,5,1,6,2,8,4,7]=>[1,7,5,9,4,8,2,6,3]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[2,3,9,5,6,1,8,4,7]=>[8,7,1,5,4,9,2,6,3]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[9,1,2,5,6,8,3,4,7]=>[1,9,8,5,4,2,7,6,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[9,1,6,5,2,8,3,4,7]=>[1,9,4,5,8,2,7,6,3]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,9,5,1,2,8,3,4,7]=>[4,1,5,9,8,2,7,6,3]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[8,1,9,5,6,2,3,4,7]=>[2,9,1,5,4,8,7,6,3]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[9,8,5,1,6,2,3,4,7]=>[1,2,5,9,4,8,7,6,3]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[9,8,6,5,1,2,3,4,7]=>[1,2,4,5,9,8,7,6,3]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,1,9,5,6,8,2,4,7]=>[7,9,1,5,4,2,8,6,3]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[9,3,5,1,6,8,2,4,7]=>[1,7,5,9,4,2,8,6,3]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[8,3,9,5,6,1,2,4,7]=>[2,7,1,5,4,9,8,6,3]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[2,3,9,5,6,8,1,4,7]=>[8,7,1,5,4,2,9,6,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,5,6,9,8,3,7]=>[6,9,8,5,4,1,2,7,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,5,6,9,8,3,7]=>[8,6,9,5,4,1,2,7,3]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,1,2,6,9,8,3,7]=>[5,6,9,8,4,1,2,7,3]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,4,1,6,9,8,3,7]=>[8,5,6,9,4,1,2,7,3]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,1,4,5,2,9,8,3,7]=>[4,9,6,5,8,1,2,7,3]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,5,4,1,2,9,8,3,7]=>[4,5,6,9,8,1,2,7,3]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[2,9,4,5,6,1,8,3,7]=>[8,1,6,5,4,9,2,7,3]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[9,4,1,5,6,8,2,3,7]=>[1,6,9,5,4,2,8,7,3]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[9,5,4,1,6,8,2,3,7]=>[1,5,6,9,4,2,8,7,3]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[9,6,4,5,1,8,2,3,7]=>[1,4,6,5,9,2,8,7,3]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[8,9,4,5,6,1,2,3,7]=>[2,1,6,5,4,9,8,7,3]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[2,9,4,5,6,8,1,3,7]=>[8,1,6,5,4,2,9,7,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,4,5,6,9,8,2,7]=>[7,9,6,5,4,1,2,8,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1,5,6,9,8,2,7]=>[6,7,9,5,4,1,2,8,3]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[5,3,4,1,6,9,8,2,7]=>[5,7,6,9,4,1,2,8,3]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,3,4,5,1,9,8,2,7]=>[4,7,6,5,9,1,2,8,3]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[9,3,4,5,6,1,8,2,7]=>[1,7,6,5,4,9,2,8,3]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[9,3,4,5,6,8,1,2,7]=>[1,7,6,5,4,2,9,8,3]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,9,8,1,7]=>[8,7,6,5,4,1,2,9,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,1,2,3,4,5,8,9,6]=>[3,9,8,7,6,5,2,1,4]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,7,1,3,4,5,8,9,6]=>[8,3,9,7,6,5,2,1,4]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[7,3,1,2,4,5,8,9,6]=>[3,7,9,8,6,5,2,1,4]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,7,1,4,5,8,9,6]=>[8,7,3,9,6,5,2,1,4]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[7,4,1,2,3,5,8,9,6]=>[3,6,9,8,7,5,2,1,4]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,7,2,5,8,9,6]=>[7,9,6,3,8,5,2,1,4]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[7,3,4,1,2,5,8,9,6]=>[3,7,6,9,8,5,2,1,4]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,7,1,5,8,9,6]=>[8,7,6,3,9,5,2,1,4]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,7,4,8,9,6]=>[7,9,5,8,3,6,2,1,4]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,7,1,2,3,4,8,9,6]=>[5,3,9,8,7,6,2,1,4]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[7,3,1,5,2,4,8,9,6]=>[3,7,9,5,8,6,2,1,4]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,7,3,8,9,6]=>[6,9,8,5,3,7,2,1,4]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[7,1,4,5,2,3,8,9,6]=>[3,9,6,5,8,7,2,1,4]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[7,5,4,1,2,3,8,9,6]=>[3,5,6,9,8,7,2,1,4]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[2,7,4,5,1,3,8,9,6]=>[8,3,6,5,9,7,2,1,4]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,1,4,5,7,2,8,9,6]=>[7,9,6,5,3,8,2,1,4]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[7,3,4,5,1,2,8,9,6]=>[3,7,6,5,9,8,2,1,4]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>[8,7,6,5,3,9,2,1,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[8,1,2,3,4,7,5,9,6]=>[2,9,8,7,6,3,5,1,4]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,8,4,1,3,7,5,9,6]=>[8,2,6,9,7,3,5,1,4]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,8,1,7,5,9,6]=>[8,7,6,2,9,3,5,1,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[8,1,2,3,7,4,5,9,6]=>[2,9,8,7,3,6,5,1,4]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[7,1,2,8,3,4,5,9,6]=>[3,9,8,2,7,6,5,1,4]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,1,7,2,3,4,5,9,6]=>[2,9,3,8,7,6,5,1,4]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,7,1,2,3,4,5,9,6]=>[2,3,9,8,7,6,5,1,4]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,3,1,2,8,7,4,9,6]=>[5,7,9,8,2,3,6,1,4]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,8,1,2,3,7,4,9,6]=>[5,2,9,8,7,3,6,1,4]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[8,3,1,5,2,7,4,9,6]=>[2,7,9,5,8,3,6,1,4]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,8,1,2,7,3,4,9,6]=>[5,2,9,8,3,7,6,1,4]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,8,5,1,7,3,4,9,6]=>[8,2,5,9,3,7,6,1,4]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[8,7,5,1,2,3,4,9,6]=>[2,3,5,9,8,7,6,1,4]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[2,3,8,5,7,1,4,9,6]=>[8,7,2,5,3,9,6,1,4]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,4,1,2,8,7,3,9,6]=>[5,6,9,8,2,3,7,1,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,3,1,5,8,7,2,9,6]=>[6,7,9,5,2,3,8,1,4]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[8,3,4,5,7,1,2,9,6]=>[2,7,6,5,3,9,8,1,4]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,3,4,5,8,7,1,9,6]=>[8,7,6,5,2,3,9,1,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[9,1,2,3,4,7,8,5,6]=>[1,9,8,7,6,3,2,5,4]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[9,3,1,2,4,7,8,5,6]=>[1,7,9,8,6,3,2,5,4]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,9,1,4,7,8,5,6]=>[8,7,1,9,6,3,2,5,4]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,9,3,7,8,5,6]=>[8,6,9,1,7,3,2,5,4]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[9,3,4,1,2,7,8,5,6]=>[1,7,6,9,8,3,2,5,4]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,9,1,7,8,5,6]=>[8,7,6,1,9,3,2,5,4]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[9,3,1,2,7,4,8,5,6]=>[1,7,9,8,3,6,2,5,4]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9,1,7,2,3,4,8,5,6]=>[1,9,3,8,7,6,2,5,4]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9,7,1,2,3,4,8,5,6]=>[1,3,9,8,7,6,2,5,4]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,9,4,1,7,3,8,5,6]=>[8,1,6,9,3,7,2,5,4]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[7,1,4,9,2,3,8,5,6]=>[3,9,6,1,8,7,2,5,4]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[2,3,4,9,7,1,8,5,6]=>[8,7,6,1,3,9,2,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[9,1,2,3,8,7,4,5,6]=>[1,9,8,7,2,3,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,9,1,3,8,7,4,5,6]=>[8,1,9,7,2,3,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,9,1,8,7,4,5,6]=>[8,7,1,9,2,3,6,5,4]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[8,1,2,9,3,7,4,5,6]=>[2,9,8,1,7,3,6,5,4]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,8,1,9,3,7,4,5,6]=>[8,2,9,1,7,3,6,5,4]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,1,8,2,3,7,4,5,6]=>[1,9,2,8,7,3,6,5,4]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,8,1,2,3,7,4,5,6]=>[1,2,9,8,7,3,6,5,4]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[9,3,8,1,2,7,4,5,6]=>[1,7,2,9,8,3,6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[8,1,2,9,7,3,4,5,6]=>[2,9,8,1,3,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,8,1,9,7,3,4,5,6]=>[8,2,9,1,3,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[9,1,8,2,7,3,4,5,6]=>[1,9,2,8,3,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[9,8,1,2,7,3,4,5,6]=>[1,2,9,8,3,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,9,8,1,7,3,4,5,6]=>[8,1,2,9,3,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,9,2,3,4,5,6]=>[3,9,2,1,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,9,2,3,4,5,6]=>[2,3,9,1,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,7,8,1,2,3,4,5,6]=>[1,3,2,9,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,7,8,9,1,3,4,5,6]=>[8,3,2,1,9,7,6,5,4]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,1,8,9,7,2,4,5,6]=>[7,9,2,1,3,8,6,5,4]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[8,3,1,9,7,2,4,5,6]=>[2,7,9,1,3,8,6,5,4]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[9,3,8,1,7,2,4,5,6]=>[1,7,2,9,3,8,6,5,4]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,8,9,1,2,4,5,6]=>[3,7,2,1,9,8,6,5,4]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[2,3,8,9,7,1,4,5,6]=>[8,7,2,1,3,9,6,5,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,9,8,7,3,5,6]=>[8,6,9,1,2,3,7,5,4]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[9,4,1,2,8,7,3,5,6]=>[1,6,9,8,2,3,7,5,4]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[9,8,4,1,2,7,3,5,6]=>[1,2,6,9,8,3,7,5,4]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[2,8,4,9,1,7,3,5,6]=>[8,2,6,1,9,3,7,5,4]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[8,1,4,9,7,2,3,5,6]=>[2,9,6,1,3,8,7,5,4]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[8,4,1,9,7,2,3,5,6]=>[2,6,9,1,3,8,7,5,4]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[9,8,4,1,7,2,3,5,6]=>[1,2,6,9,3,8,7,5,4]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[7,8,4,9,1,2,3,5,6]=>[3,2,6,1,9,8,7,5,4]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[2,8,4,9,7,1,3,5,6]=>[8,2,6,1,3,9,7,5,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,1,4,9,8,7,2,5,6]=>[7,9,6,1,2,3,8,5,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3,1,9,8,7,2,5,6]=>[6,7,9,1,2,3,8,5,4]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[9,3,4,1,8,7,2,5,6]=>[1,7,6,9,2,3,8,5,4]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[8,3,4,9,1,7,2,5,6]=>[2,7,6,1,9,3,8,5,4]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[8,3,4,9,7,1,2,5,6]=>[2,7,6,1,3,9,8,5,4]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[2,3,4,9,8,7,1,5,6]=>[8,7,6,1,2,3,9,5,4]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,9,1,2,3,7,8,4,6]=>[5,1,9,8,7,3,2,6,4]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[9,3,1,5,2,7,8,4,6]=>[1,7,9,5,8,3,2,6,4]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,9,1,5,7,3,8,4,6]=>[8,1,9,5,3,7,2,6,4]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,9,5,1,7,3,8,4,6]=>[8,1,5,9,3,7,2,6,4]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[9,7,5,1,2,3,8,4,6]=>[1,3,5,9,8,7,2,6,4]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[2,7,9,5,1,3,8,4,6]=>[8,3,1,5,9,7,2,6,4]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[9,3,1,5,7,2,8,4,6]=>[1,7,9,5,3,8,2,6,4]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[9,3,5,1,7,2,8,4,6]=>[1,7,5,9,3,8,2,6,4]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,9,5,1,2,8,4,6]=>[3,7,1,5,9,8,2,6,4]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[2,3,9,5,7,1,8,4,6]=>[8,7,1,5,3,9,2,6,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[9,1,5,2,8,7,3,4,6]=>[1,9,5,8,2,3,7,6,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,9,1,2,8,7,3,4,6]=>[5,1,9,8,2,3,7,6,4]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[9,8,5,1,2,7,3,4,6]=>[1,2,5,9,8,3,7,6,4]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[2,8,9,5,1,7,3,4,6]=>[8,2,1,5,9,3,7,6,4]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[9,8,1,5,7,2,3,4,6]=>[1,2,9,5,3,8,7,6,4]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[9,8,5,1,7,2,3,4,6]=>[1,2,5,9,3,8,7,6,4]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[7,8,9,5,1,2,3,4,6]=>[3,2,1,5,9,8,7,6,4]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[2,8,9,5,7,1,3,4,6]=>[8,2,1,5,3,9,7,6,4]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[9,3,5,1,8,7,2,4,6]=>[1,7,5,9,2,3,8,6,4]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[8,3,9,5,1,7,2,4,6]=>[2,7,1,5,9,3,8,6,4]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[8,3,9,5,7,1,2,4,6]=>[2,7,1,5,3,9,8,6,4]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[2,3,9,5,8,7,1,4,6]=>[8,7,1,5,2,3,9,6,4]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,5,9,7,8,3,6]=>[6,9,8,5,1,3,2,7,4]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1,5,9,7,8,3,6]=>[8,6,9,5,1,3,2,7,4]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,1,2,9,7,8,3,6]=>[5,6,9,8,1,3,2,7,4]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[9,5,4,1,2,7,8,3,6]=>[1,5,6,9,8,3,2,7,4]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[2,9,4,5,1,7,8,3,6]=>[8,1,6,5,9,3,2,7,4]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[9,4,1,5,7,2,8,3,6]=>[1,6,9,5,3,8,2,7,4]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[9,5,4,1,7,2,8,3,6]=>[1,5,6,9,3,8,2,7,4]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[7,9,4,5,1,2,8,3,6]=>[3,1,6,5,9,8,2,7,4]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[2,9,4,5,7,1,8,3,6]=>[8,1,6,5,3,9,2,7,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[9,4,1,5,8,7,2,3,6]=>[1,6,9,5,2,3,8,7,4]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[9,5,4,1,8,7,2,3,6]=>[1,5,6,9,2,3,8,7,4]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[8,9,4,5,1,7,2,3,6]=>[2,1,6,5,9,3,8,7,4]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[8,9,4,5,7,1,2,3,6]=>[2,1,6,5,3,9,8,7,4]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[2,9,4,5,8,7,1,3,6]=>[8,1,6,5,2,3,9,7,4]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,4,5,9,7,8,2,6]=>[7,9,6,5,1,3,2,8,4]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1,5,9,7,8,2,6]=>[6,7,9,5,1,3,2,8,4]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,3,4,1,9,7,8,2,6]=>[5,7,6,9,1,3,2,8,4]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[9,3,4,5,1,7,8,2,6]=>[1,7,6,5,9,3,2,8,4]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[9,3,4,5,7,1,8,2,6]=>[1,7,6,5,3,9,2,8,4]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[9,3,4,5,8,7,1,2,6]=>[1,7,6,5,2,3,9,8,4]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,9,7,8,1,6]=>[8,7,6,5,1,3,2,9,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,1,2,3,4,7,8,9,5]=>[4,9,8,7,6,3,2,1,5]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,6,1,3,4,7,8,9,5]=>[8,4,9,7,6,3,2,1,5]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,6,2,4,7,8,9,5]=>[7,9,4,8,6,3,2,1,5]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[6,3,1,2,4,7,8,9,5]=>[4,7,9,8,6,3,2,1,5]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,6,1,4,7,8,9,5]=>[8,7,4,9,6,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,6,3,7,8,9,5]=>[6,9,8,4,7,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,6,3,7,8,9,5]=>[8,6,9,4,7,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[6,1,4,2,3,7,8,9,5]=>[4,9,6,8,7,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[6,4,1,2,3,7,8,9,5]=>[4,6,9,8,7,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,6,4,1,3,7,8,9,5]=>[8,4,6,9,7,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,6,2,7,8,9,5]=>[7,9,6,4,8,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,1,6,2,7,8,9,5]=>[6,7,9,4,8,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[6,3,4,1,2,7,8,9,5]=>[4,7,6,9,8,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>[8,7,6,4,9,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[7,1,2,3,6,4,8,9,5]=>[3,9,8,7,4,6,2,1,5]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,7,1,6,4,8,9,5]=>[8,7,3,9,4,6,2,1,5]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[7,1,2,6,3,4,8,9,5]=>[3,9,8,4,7,6,2,1,5]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,7,1,6,3,4,8,9,5]=>[8,3,9,4,7,6,2,1,5]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,1,7,2,3,4,8,9,5]=>[4,9,3,8,7,6,2,1,5]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7,6,1,2,3,4,8,9,5]=>[3,4,9,8,7,6,2,1,5]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[2,3,7,6,1,4,8,9,5]=>[8,7,3,4,9,6,2,1,5]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[7,4,1,2,6,3,8,9,5]=>[3,6,9,8,4,7,2,1,5]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,7,4,1,6,3,8,9,5]=>[8,3,6,9,4,7,2,1,5]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[7,4,1,6,2,3,8,9,5]=>[3,6,9,4,8,7,2,1,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,1,7,6,2,8,9,5]=>[6,7,9,3,4,8,2,1,5]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[7,3,4,6,1,2,8,9,5]=>[3,7,6,4,9,8,2,1,5]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,1,8,9,5]=>[8,7,6,3,4,9,2,1,5]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[8,1,2,3,6,7,4,9,5]=>[2,9,8,7,4,3,6,1,5]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[8,3,1,2,6,7,4,9,5]=>[2,7,9,8,4,3,6,1,5]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,8,1,6,7,4,9,5]=>[8,7,2,9,4,3,6,1,5]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[8,6,1,2,3,7,4,9,5]=>[2,4,9,8,7,3,6,1,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[8,1,2,7,6,3,4,9,5]=>[2,9,8,3,4,7,6,1,5]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[8,7,1,6,2,3,4,9,5]=>[2,3,9,4,8,7,6,1,5]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,8,1,2,3,4,9,5]=>[4,3,2,9,8,7,6,1,5]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[2,7,8,6,1,3,4,9,5]=>[8,3,2,4,9,7,6,1,5]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,8,1,6,2,4,9,5]=>[3,7,2,9,4,8,6,1,5]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,8,6,1,2,4,9,5]=>[3,7,2,4,9,8,6,1,5]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[2,3,8,7,6,1,4,9,5]=>[8,7,2,3,4,9,6,1,5]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[6,8,4,1,2,7,3,9,5]=>[4,2,6,9,8,3,7,1,5]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[2,8,4,6,1,7,3,9,5]=>[8,2,6,4,9,3,7,1,5]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,8,4,1,6,2,3,9,5]=>[3,2,6,9,4,8,7,1,5]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[7,8,4,6,1,2,3,9,5]=>[3,2,6,4,9,8,7,1,5]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[2,8,4,7,6,1,3,9,5]=>[8,2,6,3,4,9,7,1,5]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[8,3,4,1,6,7,2,9,5]=>[2,7,6,9,4,3,8,1,5]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[8,3,4,6,1,7,2,9,5]=>[2,7,6,4,9,3,8,1,5]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[8,3,4,7,6,1,2,9,5]=>[2,7,6,3,4,9,8,1,5]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,3,4,8,6,7,1,9,5]=>[8,7,6,2,4,3,9,1,5]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[9,1,2,3,6,7,8,4,5]=>[1,9,8,7,4,3,2,6,5]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,9,1,3,6,7,8,4,5]=>[8,1,9,7,4,3,2,6,5]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[9,3,1,2,6,7,8,4,5]=>[1,7,9,8,4,3,2,6,5]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,9,1,6,7,8,4,5]=>[8,7,1,9,4,3,2,6,5]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[9,6,1,2,3,7,8,4,5]=>[1,4,9,8,7,3,2,6,5]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[9,3,1,6,2,7,8,4,5]=>[1,7,9,4,8,3,2,6,5]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,9,6,1,7,8,4,5]=>[8,7,1,4,9,3,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[9,1,2,7,6,3,8,4,5]=>[1,9,8,3,4,7,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[7,1,9,2,6,3,8,4,5]=>[3,9,1,8,4,7,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[9,7,1,2,6,3,8,4,5]=>[1,3,9,8,4,7,2,6,5]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,1,9,6,2,3,8,4,5]=>[3,9,1,4,8,7,2,6,5]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[9,7,1,6,2,3,8,4,5]=>[1,3,9,4,8,7,2,6,5]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[6,7,9,1,2,3,8,4,5]=>[4,3,1,9,8,7,2,6,5]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[2,7,9,6,1,3,8,4,5]=>[8,3,1,4,9,7,2,6,5]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,9,1,6,2,8,4,5]=>[3,7,1,9,4,8,2,6,5]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,9,6,1,2,8,4,5]=>[3,7,1,4,9,8,2,6,5]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[2,3,9,7,6,1,8,4,5]=>[8,7,1,3,4,9,2,6,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[9,1,2,8,6,7,3,4,5]=>[1,9,8,2,4,3,7,6,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,9,1,8,6,7,3,4,5]=>[8,1,9,2,4,3,7,6,5]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[9,8,1,2,6,7,3,4,5]=>[1,2,9,8,4,3,7,6,5]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[9,8,1,6,2,7,3,4,5]=>[1,2,9,4,8,3,7,6,5]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[6,8,9,1,2,7,3,4,5]=>[4,2,1,9,8,3,7,6,5]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[2,8,9,6,1,7,3,4,5]=>[8,2,1,4,9,3,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[8,1,9,7,6,2,3,4,5]=>[2,9,1,3,4,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[9,8,1,7,6,2,3,4,5]=>[1,2,9,3,4,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,9,1,6,2,3,4,5]=>[3,2,1,9,4,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,9,6,1,2,3,4,5]=>[3,2,1,4,9,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,8,9,7,6,1,3,4,5]=>[8,2,1,3,4,9,7,6,5]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,1,9,8,6,7,2,4,5]=>[7,9,1,2,4,3,8,6,5]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[8,3,9,1,6,7,2,4,5]=>[2,7,1,9,4,3,8,6,5]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[8,3,9,6,1,7,2,4,5]=>[2,7,1,4,9,3,8,6,5]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[8,3,9,7,6,1,2,4,5]=>[2,7,1,3,4,9,8,6,5]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[2,3,9,8,6,7,1,4,5]=>[8,7,1,2,4,3,9,6,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,1,2,9,6,7,8,3,5]=>[6,9,8,1,4,3,2,7,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1,9,6,7,8,3,5]=>[8,6,9,1,4,3,2,7,5]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[9,1,4,6,2,7,8,3,5]=>[1,9,6,4,8,3,2,7,5]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[6,9,4,1,2,7,8,3,5]=>[4,1,6,9,8,3,2,7,5]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[2,9,4,6,1,7,8,3,5]=>[8,1,6,4,9,3,2,7,5]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,9,4,1,6,2,8,3,5]=>[3,1,6,9,4,8,2,7,5]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[7,9,4,6,1,2,8,3,5]=>[3,1,6,4,9,8,2,7,5]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[2,9,4,7,6,1,8,3,5]=>[8,1,6,3,4,9,2,7,5]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[9,1,4,8,6,7,2,3,5]=>[1,9,6,2,4,3,8,7,5]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[9,4,1,8,6,7,2,3,5]=>[1,6,9,2,4,3,8,7,5]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,9,4,1,6,7,2,3,5]=>[2,1,6,9,4,3,8,7,5]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[8,9,4,6,1,7,2,3,5]=>[2,1,6,4,9,3,8,7,5]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[8,9,4,7,6,1,2,3,5]=>[2,1,6,3,4,9,8,7,5]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[2,9,4,8,6,7,1,3,5]=>[8,1,6,2,4,3,9,7,5]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,1,4,9,6,7,8,2,5]=>[7,9,6,1,4,3,2,8,5]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1,9,6,7,8,2,5]=>[6,7,9,1,4,3,2,8,5]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[9,3,4,1,6,7,8,2,5]=>[1,7,6,9,4,3,2,8,5]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[9,3,4,6,1,7,8,2,5]=>[1,7,6,4,9,3,2,8,5]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[9,3,4,7,6,1,8,2,5]=>[1,7,6,3,4,9,2,8,5]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[9,3,4,8,6,7,1,2,5]=>[1,7,6,2,4,3,9,8,5]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[2,3,4,9,6,7,8,1,5]=>[8,7,6,1,4,3,2,9,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,4]=>[5,9,8,7,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,1,3,6,7,8,9,4]=>[8,5,9,7,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5,2,6,7,8,9,4]=>[7,9,5,8,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,3,1,2,6,7,8,9,4]=>[5,7,9,8,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>[8,7,5,9,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[6,1,2,5,3,7,8,9,4]=>[4,9,8,5,7,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,5,3,7,8,9,4]=>[8,4,9,5,7,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[6,1,5,2,3,7,8,9,4]=>[4,9,5,8,7,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,6,1,2,3,7,8,9,4]=>[5,4,9,8,7,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[6,3,1,5,2,7,8,9,4]=>[4,7,9,5,8,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[6,3,5,1,2,7,8,9,4]=>[4,7,5,9,8,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,6,5,1,7,8,9,4]=>[8,7,4,5,9,3,2,1,6]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[7,1,2,5,6,3,8,9,4]=>[3,9,8,5,4,7,2,1,6]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,1,5,6,3,8,9,4]=>[8,3,9,5,4,7,2,1,6]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[7,1,5,2,6,3,8,9,4]=>[3,9,5,8,4,7,2,1,6]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[5,7,1,2,6,3,8,9,4]=>[5,3,9,8,4,7,2,1,6]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,5,1,6,3,8,9,4]=>[8,3,5,9,4,7,2,1,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,1,6,5,2,3,8,9,4]=>[3,9,4,5,8,7,2,1,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[6,7,1,5,2,3,8,9,4]=>[4,3,9,5,8,7,2,1,6]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[6,7,5,1,2,3,8,9,4]=>[4,3,5,9,8,7,2,1,6]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[2,7,6,5,1,3,8,9,4]=>[8,3,4,5,9,7,2,1,6]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,1,7,5,6,2,8,9,4]=>[7,9,3,5,4,8,2,1,6]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,1,5,6,2,8,9,4]=>[3,7,9,5,4,8,2,1,6]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,5,1,6,2,8,9,4]=>[3,7,5,9,4,8,2,1,6]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,6,5,1,2,8,9,4]=>[3,7,4,5,9,8,2,1,6]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[2,3,7,5,6,1,8,9,4]=>[8,7,3,5,4,9,2,1,6]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,8,1,5,6,7,3,9,4]=>[8,2,9,5,4,3,7,1,6]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[5,8,1,2,6,7,3,9,4]=>[5,2,9,8,4,3,7,1,6]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,8,5,1,6,7,3,9,4]=>[8,2,5,9,4,3,7,1,6]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[6,8,5,1,2,7,3,9,4]=>[4,2,5,9,8,3,7,1,6]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[2,8,6,5,1,7,3,9,4]=>[8,2,4,5,9,3,7,1,6]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,5,1,6,2,3,9,4]=>[3,2,5,9,4,8,7,1,6]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,6,5,1,2,3,9,4]=>[3,2,4,5,9,8,7,1,6]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[2,8,7,5,6,1,3,9,4]=>[8,2,3,5,4,9,7,1,6]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,1,8,5,6,7,2,9,4]=>[7,9,2,5,4,3,8,1,6]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[8,3,1,5,6,7,2,9,4]=>[2,7,9,5,4,3,8,1,6]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[8,3,5,1,6,7,2,9,4]=>[2,7,5,9,4,3,8,1,6]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[8,3,6,5,1,7,2,9,4]=>[2,7,4,5,9,3,8,1,6]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[8,3,7,5,6,1,2,9,4]=>[2,7,3,5,4,9,8,1,6]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,3,8,5,6,7,1,9,4]=>[8,7,2,5,4,3,9,1,6]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[9,1,2,5,6,7,8,3,4]=>[1,9,8,5,4,3,2,7,6]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,9,1,5,6,7,8,3,4]=>[8,1,9,5,4,3,2,7,6]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[5,9,1,2,6,7,8,3,4]=>[5,1,9,8,4,3,2,7,6]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,9,5,1,6,7,8,3,4]=>[8,1,5,9,4,3,2,7,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[6,9,1,5,2,7,8,3,4]=>[4,1,9,5,8,3,2,7,6]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[6,9,5,1,2,7,8,3,4]=>[4,1,5,9,8,3,2,7,6]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[2,9,6,5,1,7,8,3,4]=>[8,1,4,5,9,3,2,7,6]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,9,1,5,6,2,8,3,4]=>[3,1,9,5,4,8,2,7,6]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,9,5,1,6,2,8,3,4]=>[3,1,5,9,4,8,2,7,6]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[7,9,6,5,1,2,8,3,4]=>[3,1,4,5,9,8,2,7,6]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,9,7,5,6,1,8,3,4]=>[8,1,3,5,4,9,2,7,6]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[9,1,8,5,6,7,2,3,4]=>[1,9,2,5,4,3,8,7,6]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,9,1,5,6,7,2,3,4]=>[2,1,9,5,4,3,8,7,6]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,9,5,1,6,7,2,3,4]=>[2,1,5,9,4,3,8,7,6]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[8,9,6,5,1,7,2,3,4]=>[2,1,4,5,9,3,8,7,6]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[8,9,7,5,6,1,2,3,4]=>[2,1,3,5,4,9,8,7,6]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,9,8,5,6,7,1,3,4]=>[8,1,2,5,4,3,9,7,6]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,9,5,6,7,8,2,4]=>[7,9,1,5,4,3,2,8,6]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[9,3,1,5,6,7,8,2,4]=>[1,7,9,5,4,3,2,8,6]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[9,3,5,1,6,7,8,2,4]=>[1,7,5,9,4,3,2,8,6]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[9,3,6,5,1,7,8,2,4]=>[1,7,4,5,9,3,2,8,6]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[9,3,7,5,6,1,8,2,4]=>[1,7,3,5,4,9,2,8,6]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[9,3,8,5,6,7,1,2,4]=>[1,7,2,5,4,3,9,8,6]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,3,9,5,6,7,8,1,4]=>[8,7,1,5,4,3,2,9,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,3]=>[6,9,8,5,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>[8,6,9,5,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,1,4,2,6,7,8,9,3]=>[5,9,6,8,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,4,1,2,6,7,8,9,3]=>[5,6,9,8,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5,4,1,6,7,8,9,3]=>[8,5,6,9,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[6,1,4,5,2,7,8,9,3]=>[4,9,6,5,8,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[6,4,1,5,2,7,8,9,3]=>[4,6,9,5,8,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,1,2,7,8,9,3]=>[4,5,6,9,8,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,6,4,5,1,7,8,9,3]=>[8,4,6,5,9,3,2,1,7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,1,4,5,6,2,8,9,3]=>[3,9,6,5,4,8,2,1,7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,4,1,5,6,2,8,9,3]=>[3,6,9,5,4,8,2,1,7]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,5,4,1,6,2,8,9,3]=>[3,5,6,9,4,8,2,1,7]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[7,6,4,5,1,2,8,9,3]=>[3,4,6,5,9,8,2,1,7]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,7,4,5,6,1,8,9,3]=>[8,3,6,5,4,9,2,1,7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[8,1,4,5,6,7,2,9,3]=>[2,9,6,5,4,3,8,1,7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[8,4,1,5,6,7,2,9,3]=>[2,6,9,5,4,3,8,1,7]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[8,5,4,1,6,7,2,9,3]=>[2,5,6,9,4,3,8,1,7]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[8,6,4,5,1,7,2,9,3]=>[2,4,6,5,9,3,8,1,7]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[8,7,4,5,6,1,2,9,3]=>[2,3,6,5,4,9,8,1,7]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,8,4,5,6,7,1,9,3]=>[8,2,6,5,4,3,9,1,7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[9,1,4,5,6,7,8,2,3]=>[1,9,6,5,4,3,2,8,7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[9,4,1,5,6,7,8,2,3]=>[1,6,9,5,4,3,2,8,7]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[9,5,4,1,6,7,8,2,3]=>[1,5,6,9,4,3,2,8,7]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[9,6,4,5,1,7,8,2,3]=>[1,4,6,5,9,3,2,8,7]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[9,7,4,5,6,1,8,2,3]=>[1,3,6,5,4,9,2,8,7]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9,8,4,5,6,7,1,2,3]=>[1,2,6,5,4,3,9,8,7]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,9,4,5,6,7,8,1,3]=>[8,1,6,5,4,3,2,9,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,2]=>[7,9,6,5,4,3,2,1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,2]=>[6,7,9,5,4,3,2,1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,9,2]=>[5,7,6,9,4,3,2,1,8]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,9,2]=>[4,7,6,5,9,3,2,1,8]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,9,2]=>[3,7,6,5,4,9,2,1,8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,9,2]=>[2,7,6,5,4,3,9,1,8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,2]=>[1,7,6,5,4,3,2,9,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[8,7,6,5,4,3,2,1,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,2]=>[8,10,7,6,5,4,3,2,1,9]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>[9,8,7,6,5,4,3,1,10,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[9,11,8,7,6,5,4,3,2,1,10]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[10,1,4,5,6,7,8,9,2,3]=>[1,10,7,6,5,4,3,2,9,8]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,1,2,9]=>[1,8,7,6,5,4,3,10,9,2]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[10,9,8,7,6,5,4,3,1,11,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,12,2]=>[10,12,9,8,7,6,5,4,3,2,1,11]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[11,1,4,5,6,7,8,9,10,2,3]=>[1,11,8,7,6,5,4,3,2,10,9]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9,1,4,5,6,7,8,2,10,3]=>[2,10,7,6,5,4,3,9,1,8]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,10,5,6,7,8,9,2,4]=>[8,10,1,6,5,4,3,2,9,7]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,10,2,9]=>[3,8,7,6,5,4,10,1,9,2]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[2,10,4,5,6,7,8,1,3,9]=>[9,1,7,6,5,4,3,10,8,2]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[11,3,4,5,6,7,8,9,1,2,10]=>[1,9,8,7,6,5,4,3,11,10,2]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>[11,10,9,8,7,6,5,4,3,1,12,2]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[12,1,4,5,6,7,8,9,10,11,2,3]=>[1,12,9,8,7,6,5,4,3,2,11,10]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,11,5,6,7,8,9,10,2,4]=>[9,11,1,7,6,5,4,3,2,10,8]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[10,1,9,5,6,7,8,2,3,4]=>[1,10,2,6,5,4,3,9,8,7]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3,1,4,10,6,7,8,9,2,5]=>[8,10,7,1,5,4,3,2,9,6]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,3,4,5,6,1,8,10,2,9]=>[4,8,7,6,5,10,3,1,9,2]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[10,8,4,5,6,7,1,2,3,9]=>[1,3,7,6,5,4,10,9,8,2]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,1,11,2,10]=>[3,9,8,7,6,5,4,11,1,10,2]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[11,1,10,5,6,7,8,9,2,3,4]=>[1,11,2,7,6,5,4,3,10,9,8]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,1,9,5,6,7,8,2,10,4]=>[8,10,2,6,5,4,3,9,1,7]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[3,1,4,5,10,7,8,9,2,6]=>[8,10,7,6,1,4,3,2,9,5]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[2,8,4,5,6,7,1,10,3,9]=>[9,3,7,6,5,4,10,1,8,2]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[11,9,4,5,6,7,8,1,2,3,10]=>[1,3,8,7,6,5,4,11,10,9,2]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[2,3,4,10,6,7,8,1,5,9]=>[9,8,7,1,5,4,3,10,6,2]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,1,10,9,6,7,8,2,4,5]=>[8,10,1,2,5,4,3,9,7,6]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[3,1,4,5,6,10,8,9,2,7]=>[8,10,7,6,5,1,3,2,9,4]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,7,4,5,6,1,2,10,3,9]=>[3,4,7,6,5,10,9,1,8,2]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[2,3,4,5,10,7,8,1,6,9]=>[9,8,7,6,1,4,3,10,5,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,4,2,6,7,8,9,10,3]=>[6,10,7,9,5,4,3,2,1,8]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[9,1,10,8,6,7,2,3,4,5]=>[2,10,1,3,5,4,9,8,7,6]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,1,4,5,6,7,10,9,2,8]=>[8,10,7,6,5,4,1,2,9,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>[9,7,10,6,5,4,3,2,1,8]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,3,1,5,6,7,8,10,2,9]=>[7,8,10,6,5,4,3,1,9,2]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,10,7,5,6,1,2,3,4,9]=>[3,1,4,6,5,10,9,8,7,2]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>[9,8,7,6,5,4,2,10,1,3]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[2,3,4,5,6,10,8,1,7,9]=>[9,8,7,6,5,1,3,10,4,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[10,1,11,9,6,7,8,2,3,4,5]=>[2,11,1,3,6,5,4,10,9,8,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,10,3]=>[7,10,9,6,5,4,3,2,1,8]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>[8,10,7,6,5,4,3,1,9,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,10,1,5,6,7,8,9,3,4]=>[9,1,10,6,5,4,3,2,8,7]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,11,8,5,6,7,1,2,3,4,10]=>[3,1,4,7,6,5,11,10,9,8,2]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[9,3,4,5,6,7,1,2,10,8]=>[2,8,7,6,5,4,10,9,1,3]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>[9,8,7,6,5,4,1,10,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,3]=>[10,8,11,7,6,5,4,3,2,1,9]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,9,1,5,6,7,8,3,10,4]=>[9,2,10,6,5,4,3,8,1,7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,4,1,10,6,7,8,9,3,5]=>[9,7,10,1,5,4,3,2,8,6]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,3,4,5,6,1,9,2,10,8]=>[4,8,7,6,5,10,2,9,1,3]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[2,9,4,5,6,7,1,3,10,8]=>[9,2,7,6,5,4,10,8,1,3]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>[10,9,8,7,6,5,4,2,11,1,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,10,11,3]=>[8,11,10,7,6,5,4,3,2,1,9]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>[9,11,8,7,6,5,4,3,1,10,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,11,1,5,6,7,8,9,10,3,4]=>[10,1,11,7,6,5,4,3,2,9,8]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[3,1,9,10,8,7,2,4,5,6]=>[8,10,2,1,3,4,9,7,6,5]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,8,6,5,1,2,3,10,4,9]=>[4,3,5,6,10,9,8,1,7,2]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[10,3,4,5,6,7,8,1,2,11,9]=>[2,9,8,7,6,5,4,11,10,1,3]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>[10,9,8,7,6,5,4,1,11,3,2]
[]=>[]=>[1]=>[1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,10,9,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,9,10,1,3,4,5,6,7,8]=>[9,2,1,10,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,3,1,9,2,4,5,6,7,8]=>[1,8,10,2,9,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,3,10,1,2,4,5,6,7,8]=>[2,8,1,10,9,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,10,9,1,4,5,6,7,8]=>[9,8,1,2,10,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[10,4,1,2,9,3,5,6,7,8]=>[1,7,10,9,2,8,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10,4,1,9,2,3,5,6,7,8]=>[1,7,10,2,9,8,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,10,4,1,2,3,5,6,7,8]=>[2,1,7,10,9,8,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,10,4,9,1,3,5,6,7,8]=>[9,1,7,2,10,8,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,1,10,9,2,5,6,7,8]=>[7,8,10,1,2,9,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[10,3,4,1,9,2,5,6,7,8]=>[1,8,7,10,2,9,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[10,3,4,9,1,2,5,6,7,8]=>[1,8,7,2,10,9,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,10,9,1,5,6,7,8]=>[9,8,7,1,2,10,6,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[5,9,1,2,3,10,4,6,7,8]=>[6,2,10,9,8,1,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,10,5,1,2,3,4,6,7,8]=>[2,1,6,10,9,8,7,5,4,3]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[9,5,4,1,2,10,3,6,7,8]=>[2,6,7,10,9,1,8,5,4,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[10,6,1,2,3,4,9,5,7,8]=>[1,5,10,9,8,7,2,6,4,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,10,1,2,6,3,4,5,7,8]=>[2,1,10,9,5,8,7,6,4,3]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,10,9,1,2,3,4,5,7,8]=>[5,1,2,10,9,8,7,6,4,3]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[10,9,6,5,1,2,3,4,7,8]=>[1,2,5,6,10,9,8,7,4,3]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[10,7,1,2,3,4,5,9,6,8]=>[1,4,10,9,8,7,6,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,3,1,5,2,7,4,9,6,8]=>[1,8,10,6,9,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,10,5,1,7,4,9,6,8]=>[9,8,1,6,10,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[2,3,4,5,10,7,1,9,6,8]=>[9,8,7,6,1,4,10,2,5,3]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[10,7,1,2,3,4,9,5,6,8]=>[1,4,10,9,8,7,2,6,5,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10,7,1,9,2,3,4,5,6,8]=>[1,4,10,2,9,8,7,6,5,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10,7,9,1,2,3,4,5,6,8]=>[1,4,2,10,9,8,7,6,5,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,6,1,2,3,4,10,9,5,8]=>[4,5,10,9,8,7,1,2,6,3]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,10,9,6,1,2,3,4,5,8]=>[4,1,2,5,10,9,8,7,6,3]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,7,5,1,2,3,10,9,4,8]=>[5,4,6,10,9,8,1,2,7,3]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[2,3,10,5,6,7,9,1,4,8]=>[9,8,1,6,5,4,2,10,7,3]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[9,10,4,5,6,7,1,2,3,8]=>[2,1,7,6,5,4,10,9,8,3]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[2,10,4,5,6,7,9,1,3,8]=>[9,1,7,6,5,4,2,10,8,3]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[4,3,1,5,6,7,10,9,2,8]=>[7,8,10,6,5,4,1,2,9,3]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,3,4,5,6,1,10,9,2,8]=>[4,8,7,6,5,10,1,2,9,3]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[10,3,4,5,6,7,1,9,2,8]=>[1,8,7,6,5,4,10,2,9,3]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[10,3,4,5,6,7,9,1,2,8]=>[1,8,7,6,5,4,2,10,9,3]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,7,10,9,1,8]=>[9,8,7,6,5,4,1,2,10,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,10,7]=>[3,2,10,9,8,7,6,5,1,4]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[9,6,1,2,3,4,8,5,10,7]=>[2,5,10,9,8,7,3,6,1,4]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,9,4,1,6,3,8,5,10,7]=>[9,2,7,10,5,8,3,6,1,4]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,10,1,2,3,4,5,9,6,7]=>[3,1,10,9,8,7,6,2,5,4]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,10,1,2,3,4,8,5,6,7]=>[2,1,10,9,8,7,3,6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[9,10,1,2,3,8,4,5,6,7]=>[2,1,10,9,8,3,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,1,2,10,3,4,5,6,7]=>[2,3,10,9,1,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,8,1,9,2,3,4,5,6,7]=>[1,3,10,2,9,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,10,9,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,10,8,9,1,3,4,5,6,7]=>[9,1,3,2,10,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[8,3,1,9,10,2,4,5,6,7]=>[3,8,10,2,1,9,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[10,3,8,9,1,2,4,5,6,7]=>[1,8,3,2,10,9,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,8,9,10,1,4,5,6,7]=>[9,8,3,2,1,10,7,6,5,4]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[9,4,1,2,10,8,3,5,6,7]=>[2,7,10,9,1,3,8,6,5,4]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[8,4,1,9,10,2,3,5,6,7]=>[3,7,10,2,1,9,8,6,5,4]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[10,8,4,9,1,2,3,5,6,7]=>[1,3,7,2,10,9,8,6,5,4]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[4,3,1,9,10,8,2,5,6,7]=>[7,8,10,2,1,3,9,6,5,4]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,10,1,2,3,9,8,4,6,7]=>[6,1,10,9,8,2,3,7,5,4]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,9,1,2,10,8,3,4,6,7]=>[6,2,10,9,1,3,8,7,5,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,10,9,8,3,6,7]=>[6,7,10,9,1,2,3,8,5,4]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[8,9,4,5,10,1,2,3,6,7]=>[3,2,7,6,1,10,9,8,5,4]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[10,6,1,2,3,4,8,9,5,7]=>[1,5,10,9,8,7,3,2,6,4]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[2,8,9,10,6,1,3,4,5,7]=>[9,3,2,1,5,10,8,7,6,4]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,10,5,6,1,8,9,4,7]=>[9,8,1,6,5,10,3,2,7,4]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5,3,4,1,6,10,8,9,2,7]=>[6,8,7,10,5,1,3,2,9,4]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,6,10,8,9,1,7]=>[9,8,7,6,5,1,3,2,10,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[8,7,1,2,3,4,5,9,10,6]=>[3,4,10,9,8,7,6,2,1,5]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[8,3,1,5,2,7,4,9,10,6]=>[3,8,10,6,9,4,7,2,1,5]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,3,1,5,8,7,2,9,10,6]=>[7,8,10,6,3,4,9,2,1,5]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[9,7,1,2,3,4,8,5,10,6]=>[2,4,10,9,8,7,3,6,1,5]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,9,4,1,7,3,8,5,10,6]=>[9,2,7,10,4,8,3,6,1,5]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9,7,8,1,2,3,4,5,10,6]=>[2,4,3,10,9,8,7,6,1,5]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[7,8,9,5,1,2,3,4,10,6]=>[4,3,2,6,10,9,8,7,1,5]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[10,7,1,2,3,4,8,9,5,6]=>[1,4,10,9,8,7,3,2,6,5]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[10,7,8,1,2,3,4,9,5,6]=>[1,4,3,10,9,8,7,2,6,5]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[10,9,1,2,3,7,8,4,5,6]=>[1,2,10,9,8,4,3,7,6,5]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[10,7,9,1,2,3,8,4,5,6]=>[1,4,2,10,9,8,3,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[10,9,1,2,8,7,3,4,5,6]=>[1,2,10,9,3,4,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,8,9,10,1,7,3,4,5,6]=>[9,3,2,1,10,4,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9,8,1,10,7,2,3,4,5,6]=>[2,3,10,1,4,9,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[4,3,2,1,10,9,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,8,9,10,7,1,3,4,5,6]=>[9,3,2,1,4,10,8,7,6,5]
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[9,10,4,5,1,7,8,2,3,6]=>[2,1,7,6,10,4,3,9,8,5]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[10,3,4,5,1,7,8,9,2,6]=>[1,8,7,6,10,4,3,2,9,5]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,10,7,8,9,1,6]=>[9,8,7,6,1,4,3,2,10,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[7,6,1,2,3,4,8,9,10,5]=>[4,5,10,9,8,7,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,7,6,1,8,9,10,5]=>[9,8,7,4,5,10,3,2,1,6]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,9,10,5]=>[5,4,3,10,9,8,7,2,1,6]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[8,3,4,1,6,7,2,9,10,5]=>[3,8,7,10,5,4,9,2,1,6]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[2,3,4,8,6,7,1,9,10,5]=>[9,8,7,3,5,4,10,2,1,6]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,9,1,6,2,3,4,10,5]=>[4,3,2,10,5,9,8,7,1,6]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,9,6,1,2,3,4,10,5]=>[4,3,2,5,10,9,8,7,1,6]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[9,3,4,6,1,7,8,2,10,5]=>[2,8,7,5,10,4,3,9,1,6]
[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[2,3,4,9,6,7,8,1,10,5]=>[9,8,7,2,5,4,3,10,1,6]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[8,9,10,1,6,7,2,3,4,5]=>[3,2,1,10,5,4,9,8,7,6]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[2,9,10,8,6,7,1,3,4,5]=>[9,2,1,3,5,4,10,8,7,6]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[2,10,4,9,6,7,8,1,3,5]=>[9,1,7,2,5,4,3,10,8,6]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,3,1,10,6,7,8,9,2,5]=>[7,8,10,1,5,4,3,2,9,6]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[10,3,4,7,6,1,8,9,2,5]=>[1,8,7,4,5,10,3,2,9,6]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[10,3,4,9,6,7,8,1,2,5]=>[1,8,7,2,5,4,3,10,9,6]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[2,3,4,10,6,7,8,9,1,5]=>[9,8,7,1,5,4,3,2,10,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,1,2,3,7,8,9,10,4]=>[6,5,10,9,8,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[6,3,1,5,2,7,8,9,10,4]=>[5,8,10,6,9,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,7,5,6,1,8,9,10,4]=>[9,8,4,6,5,10,3,2,1,7]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[2,3,8,5,6,7,1,9,10,4]=>[9,8,3,6,5,4,10,2,1,7]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[8,9,7,5,6,1,2,3,10,4]=>[3,2,4,6,5,10,9,8,1,7]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[9,3,7,5,6,1,8,2,10,4]=>[2,8,4,6,5,10,3,9,1,7]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[9,3,8,5,6,7,1,2,10,4]=>[2,8,3,6,5,4,10,9,1,7]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[2,3,9,5,6,7,8,1,10,4]=>[9,8,2,6,5,4,3,10,1,7]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[2,10,8,5,6,7,1,9,3,4]=>[9,1,3,6,5,4,10,2,8,7]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9,10,1,5,6,7,8,2,3,4]=>[2,1,10,6,5,4,3,9,8,7]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[2,10,9,5,6,7,8,1,3,4]=>[9,1,2,6,5,4,3,10,8,7]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[10,3,1,5,6,7,8,9,2,4]=>[1,8,10,6,5,4,3,2,9,7]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[10,3,8,5,6,7,1,9,2,4]=>[1,8,3,6,5,4,10,2,9,7]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[10,3,9,5,6,7,8,1,2,4]=>[1,8,2,6,5,4,3,10,9,7]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[2,3,10,5,6,7,8,9,1,4]=>[9,8,1,6,5,4,3,2,10,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,4,1,2,6,7,8,9,10,3]=>[6,7,10,9,5,4,3,2,1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,5,4,1,6,7,8,9,10,3]=>[9,6,7,10,5,4,3,2,1,8]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[8,4,1,5,6,7,2,9,10,3]=>[3,7,10,6,5,4,9,2,1,8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9,4,1,5,6,7,8,2,10,3]=>[2,7,10,6,5,4,3,9,1,8]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[9,7,4,5,6,1,8,2,10,3]=>[2,4,7,6,5,10,3,9,1,8]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[9,8,4,5,6,7,1,2,10,3]=>[2,3,7,6,5,4,10,9,1,8]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,9,4,5,6,7,8,1,10,3]=>[9,2,7,6,5,4,3,10,1,8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[10,4,1,5,6,7,8,9,2,3]=>[1,7,10,6,5,4,3,2,9,8]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[10,7,4,5,6,1,8,9,2,3]=>[1,4,7,6,5,10,3,2,9,8]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[10,8,4,5,6,7,1,9,2,3]=>[1,3,7,6,5,4,10,2,9,8]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[10,9,4,5,6,7,8,1,2,3]=>[1,2,7,6,5,4,3,10,9,8]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,10,4,5,6,7,8,9,1,3]=>[9,1,7,6,5,4,3,2,10,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,10,2]=>[7,8,10,6,5,4,3,2,1,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,9,10,2]=>[6,8,7,10,5,4,3,2,1,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,9,10,2]=>[5,8,7,6,10,4,3,2,1,9]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,9,10,2]=>[4,8,7,6,5,10,3,2,1,9]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,9,10,2]=>[3,8,7,6,5,4,10,2,1,9]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,10,2]=>[2,8,7,6,5,4,3,10,1,9]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10,3,4,5,6,7,8,9,1,2]=>[1,8,7,6,5,4,3,2,10,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[9,8,7,6,5,4,3,2,1,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,10,1,3,4,5,6,7,8,9]=>[9,1,10,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,3,1,2,4,5,6,7,8,9]=>[1,8,10,9,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,4,1,2,3,5,6,7,8,9]=>[1,7,10,9,8,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,10,1,2,3,4,6,7,8,9]=>[6,1,10,9,8,7,5,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[10,6,1,2,3,4,5,7,8,9]=>[1,5,10,9,8,7,6,4,3,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,7,1,2,3,4,5,6,8,9]=>[1,4,10,9,8,7,6,5,3,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,10,1,2,3,4,5,6,7,9]=>[3,1,10,9,8,7,6,5,4,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[10,1,11,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,10,1,4,5,6,7,8,9]=>[9,8,1,10,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,3,1,2,4,5,6,7,8,9,10]=>[1,9,11,10,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,1,10,2,5,6,7,8,9]=>[7,8,10,1,9,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,4,1,2,3,5,6,7,8,9,10]=>[1,8,11,10,9,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,1,2,10,3,6,7,8,9]=>[6,7,10,9,1,8,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,11,1,2,3,4,6,7,8,9,10]=>[7,1,11,10,9,8,6,5,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,6,1,2,3,10,4,7,8,9]=>[6,5,10,9,8,1,7,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[11,6,1,2,3,4,5,7,8,9,10]=>[1,6,11,10,9,8,7,5,4,3,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,10,5,8,9]=>[4,5,10,9,8,7,1,6,3,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[11,7,1,2,3,4,5,6,8,9,10]=>[1,5,11,10,9,8,7,6,4,3,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,7,1,2,3,4,5,10,6,9]=>[3,4,10,9,8,7,6,1,5,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,11,1,2,3,4,5,6,7,9,10]=>[4,1,11,10,9,8,7,6,5,3,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,1,2,3,4,5,6,7,8,10]=>[1,3,11,10,9,8,7,6,5,4,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,10,1,2,3,4,5,6,7,8,9]=>[1,2,11,10,9,8,7,6,5,4,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[1,12,11,10,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,12,1,3,4,5,6,7,8,9,10,11]=>[11,1,12,10,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,11,1,4,5,6,7,8,9,10]=>[10,9,1,11,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[12,3,1,2,4,5,6,7,8,9,10,11]=>[1,10,12,11,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,3,4,1,2,5,6,7,8,9]=>[1,8,7,10,9,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,10,1,5,6,7,8,9]=>[9,8,7,1,10,6,5,4,3,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[10,6,1,2,3,7,4,5,8,9]=>[1,5,10,9,8,4,7,6,3,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,4,1,2,6,10,3,7,8,9]=>[6,7,10,9,5,1,8,4,3,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[10,9,1,2,3,4,5,6,7,11,8]=>[2,3,11,10,9,8,7,6,5,1,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>[2,1,12,11,10,9,8,7,6,5,4,3]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[10,5,4,1,2,3,6,7,8,9]=>[1,6,7,10,9,8,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,11,1,5,6,7,8,9,10]=>[10,9,8,1,11,7,6,5,4,3,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[10,7,1,2,6,3,4,5,8,9]=>[1,4,10,9,5,8,7,6,3,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[10,8,1,2,3,7,4,5,6,9]=>[1,3,10,9,8,4,7,6,5,2]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[10,4,1,2,6,7,3,5,8,9]=>[1,7,10,9,5,4,8,6,3,2]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[10,4,1,5,6,2,3,7,8,9]=>[1,7,10,6,5,9,8,4,3,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[11,9,1,2,3,4,5,6,10,7,8]=>[1,3,11,10,9,8,7,6,2,5,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[8,9,1,2,3,4,5,6,10,11,7]=>[4,3,11,10,9,8,7,6,2,1,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[11,10,1,2,3,4,5,6,7,8,12,9]=>[2,3,12,11,10,9,8,7,6,5,1,4]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,10,5,1,2,3,4,7,8,9]=>[5,1,6,10,9,8,7,4,3,2]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,10,1,6,7,8,9]=>[9,8,7,6,1,10,5,4,3,2]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[10,4,1,2,8,7,3,5,6,9]=>[1,7,10,9,3,4,8,6,5,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,1,2,6,7,10,3,8,9]=>[6,7,10,9,5,4,1,8,3,2]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[10,4,1,7,6,2,3,5,8,9]=>[1,7,10,4,5,9,8,6,3,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[11,10,1,2,3,4,5,9,6,7,8]=>[1,2,11,10,9,8,7,3,6,5,4]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[11,7,1,2,3,4,5,9,10,6,8]=>[1,5,11,10,9,8,7,3,2,6,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[8,11,1,2,3,4,5,9,10,6,7]=>[4,1,11,10,9,8,7,3,2,6,5]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,7,10,1,2,3,4,5,8,9]=>[5,4,1,10,9,8,7,6,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,11,1,6,7,8,9,10]=>[10,9,8,7,1,11,6,5,4,3,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,7,1,10,2,3,4,5,6,9]=>[3,4,10,1,9,8,7,6,5,2]
[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[2,3,10,5,6,1,4,7,8,9]=>[9,8,1,6,5,10,7,4,3,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[11,10,1,2,3,4,9,5,6,7,8]=>[1,2,11,10,9,8,3,7,6,5,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,1,2,10,7,8,3,6,9]=>[6,7,10,9,1,4,3,8,5,2]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,4,1,10,7,2,3,5,6,9]=>[3,7,10,1,4,9,8,6,5,2]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,4,1,5,6,2,10,3,8,9]=>[4,7,10,6,5,9,1,8,3,2]
[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[7,10,6,5,1,2,3,4,8,9]=>[4,1,5,6,10,9,8,7,3,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[8,7,1,2,3,4,5,9,10,11,6]=>[4,5,11,10,9,8,7,3,2,1,6]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[10,11,1,2,3,4,8,9,5,6,7]=>[2,1,11,10,9,8,4,3,7,6,5]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[10,7,8,1,2,3,4,5,6,9]=>[1,4,3,10,9,8,7,6,5,2]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,10,1,7,8,9]=>[9,8,7,6,5,1,10,4,3,2]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,10,1,2,3,11,9,4,6,7,8]=>[7,2,11,10,9,1,3,8,6,5,4]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[10,4,1,5,7,2,8,3,6,9]=>[1,7,10,6,4,9,3,8,5,2]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,8,10,6,1,2,3,4,5,9]=>[4,3,1,5,10,9,8,7,6,2]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[10,11,1,2,3,9,8,4,5,6,7]=>[2,1,11,10,9,3,4,8,7,6,5]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,11,1,7,8,9,10]=>[10,9,8,7,6,1,11,5,4,3,2]
[1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[2,3,4,10,6,7,1,5,8,9]=>[9,8,7,1,5,4,10,6,3,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[7,6,1,2,3,4,8,9,10,11,5]=>[5,6,11,10,9,8,4,3,2,1,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[10,9,1,2,11,8,3,4,5,6,7]=>[2,3,11,10,1,4,9,8,7,6,5]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[11,9,8,1,2,3,4,5,6,7,10]=>[1,3,4,11,10,9,8,7,6,5,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,11,1,9,2,3,4,5,6,7,8]=>[2,1,11,3,10,9,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[11,3,1,9,10,2,4,5,6,7,8]=>[1,9,11,3,2,10,8,7,6,5,4]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,8,9,11,1,2,3,4,5,6,10]=>[5,4,3,1,11,10,9,8,7,6,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9,8,1,10,11,2,3,4,5,6,7]=>[3,4,11,2,1,10,9,8,7,6,5]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,10,2,4,5,6,7,8,9]=>[8,10,1,9,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,10,3,5,6,7,8,9]=>[7,10,9,1,8,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,1,10,3,5,6,7,8,9]=>[9,7,10,1,8,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,10,2,5,6,7,8,9]=>[8,10,7,1,9,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,10,4,6,7,8,9]=>[6,10,9,8,1,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,5,1,3,10,4,6,7,8,9]=>[9,6,10,8,1,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,10,4,6,7,8,9]=>[8,10,6,9,1,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,10,3,6,7,8,9]=>[7,10,9,6,1,8,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,10,3,6,7,8,9]=>[9,7,10,6,1,8,5,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[6,1,2,3,4,10,5,7,8,9]=>[5,10,9,8,7,1,6,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,6,3,10,5,7,8,9]=>[9,7,10,5,8,1,6,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,6,10,4,7,8,9]=>[6,10,9,8,5,1,7,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,10,4,7,8,9]=>[8,10,6,9,5,1,7,4,3,2]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,1,2,3,4,5,10,6,8,9]=>[4,10,9,8,7,6,1,5,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,7,4,10,6,8,9]=>[8,10,6,9,4,7,1,5,3,2]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[6,1,2,3,4,7,10,5,8,9]=>[5,10,9,8,7,4,1,6,3,2]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,6,3,7,10,5,8,9]=>[9,7,10,5,8,4,1,6,3,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,1,2,3,4,5,6,10,7,9]=>[3,10,9,8,7,6,5,1,4,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,8,1,3,4,5,6,10,7,9]=>[9,3,10,8,7,6,5,1,4,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[4,1,2,8,3,5,6,10,7,9]=>[7,10,9,3,8,6,5,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[6,1,2,3,4,8,5,10,7,9]=>[5,10,9,8,7,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,10,7,9]=>[7,10,9,5,8,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>[9,7,10,5,8,3,6,1,4,2]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,5,6,8,1,10,7,9]=>[9,8,7,6,5,3,10,1,4,2]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,1,2,3,4,5,8,10,6,9]=>[4,10,9,8,7,6,3,1,5,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,7,4,8,10,6,9]=>[8,10,6,9,4,7,3,1,5,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,8,10,3,9]=>[9,7,10,6,5,4,3,1,8,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,1,2,3,4,5,6,7,10,8]=>[2,10,9,8,7,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,9,1,3,4,5,6,7,10,8]=>[9,2,10,8,7,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,9,2,4,5,6,7,10,8]=>[8,10,2,9,7,6,5,4,1,3]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,5,6,9,1,7,10,8]=>[9,8,7,6,5,2,10,4,1,3]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,1,2,3,4,5,9,6,10,8]=>[4,10,9,8,7,6,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,9,6,10,8]=>[6,10,9,8,4,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>[8,10,6,9,4,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,9,6,10,8]=>[9,8,6,10,4,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,5,7,3,9,6,10,8]=>[7,10,9,6,4,8,2,5,1,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,1,2,3,4,7,9,5,10,8]=>[5,10,9,8,7,4,2,6,1,3]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,5,1,6,7,9,4,10,8]=>[9,8,6,10,5,4,2,7,1,3]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,7,9,2,10,8]=>[8,10,7,6,5,4,2,9,1,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,1,2,3,4,5,6,9,10,7]=>[3,10,9,8,7,6,5,2,1,4]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,8,5,9,10,7]=>[9,7,10,5,8,3,6,2,1,4]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,8,4,9,10,7]=>[9,8,6,10,5,3,7,2,1,4]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>[9,8,7,6,5,3,10,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,1,2,3,4,5,8,9,10,6]=>[4,10,9,8,7,6,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,7,2,8,9,10,6]=>[8,10,7,6,4,9,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>[9,8,7,6,4,10,3,2,1,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,1,2,3,4,7,8,9,10,5]=>[5,10,9,8,7,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>[9,8,7,5,10,4,3,2,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,10,4]=>[6,10,9,8,5,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,5,2,6,7,8,9,10,4]=>[8,10,6,9,5,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,4]=>[9,8,6,10,5,4,3,2,1,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,11,2,4,5,6,7,8,9,10]=>[9,11,1,10,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,11,3,5,6,7,8,9,10]=>[8,11,10,1,9,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,1,11,3,5,6,7,8,9,10]=>[10,8,11,1,9,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,11,4,6,7,8,9,10]=>[7,11,10,9,1,8,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,11,4,6,7,8,9,10]=>[9,11,7,10,1,8,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,11,5,7,8,9,10]=>[6,11,10,9,8,1,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,6,3,11,5,7,8,9,10]=>[10,8,11,6,9,1,7,5,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,11,6,8,9,10]=>[5,11,10,9,8,7,1,6,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,11,6,8,9,10]=>[9,11,7,10,5,8,1,6,4,3,2]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,11,1,8,9,10]=>[10,9,8,7,6,5,1,11,4,3,2]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,1,2,3,4,5,6,11,7,9,10]=>[4,11,10,9,8,7,6,1,5,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,6,3,8,5,11,7,9,10]=>[10,8,11,6,9,4,7,1,5,3,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,1,2,3,4,5,6,7,11,8,10]=>[3,11,10,9,8,7,6,5,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,11,8,10]=>[9,11,7,10,5,8,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,9,6,11,8,10]=>[10,9,7,11,5,8,3,6,1,4,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[2,11,10,9,8,7,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,10,1,3,4,5,6,7,8,11,9]=>[10,2,11,9,8,7,6,5,4,1,3]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,1,2,3,4,5,6,10,7,11,9]=>[4,11,10,9,8,7,6,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,1,2,3,4,8,5,10,7,11,9]=>[6,11,10,9,8,4,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,8,5,10,7,11,9]=>[8,11,10,6,9,4,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,10,7,11,9]=>[10,8,11,6,9,4,7,2,5,1,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[9,1,2,3,4,5,6,7,10,11,8]=>[3,11,10,9,8,7,6,5,2,1,4]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>[10,9,8,7,6,5,3,11,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[8,1,2,3,4,5,6,9,10,11,7]=>[4,11,10,9,8,7,6,3,2,1,5]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>[10,9,8,7,6,4,11,3,2,1,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[7,1,2,3,4,5,8,9,10,11,6]=>[5,11,10,9,8,7,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>[10,9,8,7,5,11,4,3,2,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,7,8,9,10,11,5]=>[6,11,10,9,8,5,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>[10,9,8,6,11,5,4,3,2,1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,10,11,4]=>[7,11,10,9,6,5,4,3,2,1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>[10,9,7,11,6,5,4,3,2,1,8]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[10,9,8,7,6,5,4,3,2,1,11]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,1,2,3,4,5,6,9,7,8]=>[1,10,9,8,7,6,5,2,4,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[10,1,2,3,4,5,9,6,7,8]=>[1,10,9,8,7,6,2,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,1,2,3,4,10,5,6,7,8]=>[2,10,9,8,7,1,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,3,9,4,5,6,7,8]=>[1,10,9,8,2,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,9,3,4,5,6,7,8]=>[1,10,9,2,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,10,2,3,4,5,6,7,8]=>[2,10,1,9,8,7,6,5,4,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[11,1,2,3,4,5,6,7,10,8,9]=>[1,11,10,9,8,7,6,5,2,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,1,2,3,4,5,10,9,6,8]=>[4,10,9,8,7,6,1,2,5,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[11,1,2,3,4,5,6,10,7,8,9]=>[1,11,10,9,8,7,6,2,5,4,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,1,2,3,4,10,9,5,7,8]=>[5,10,9,8,7,1,2,6,4,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[10,1,2,3,4,5,11,6,7,8,9]=>[2,11,10,9,8,7,1,6,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[5,1,2,3,9,10,4,6,7,8]=>[6,10,9,8,2,1,7,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,2,3,4,10,5,6,7,8,9]=>[1,11,10,9,8,2,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,2,10,9,3,5,6,7,8]=>[7,10,9,1,2,8,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,2,3,10,4,5,6,7,8,9]=>[1,11,10,9,2,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,10,9,2,4,5,6,7,8]=>[8,10,1,2,9,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,11,3,4,5,6,7,8,9]=>[2,11,10,1,9,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,10,2,3,4,5,6,7,8,9]=>[1,11,2,10,9,8,7,6,5,4,3]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,9,10,11,8,7,1,3,4,5,6]=>[10,3,2,1,4,5,11,9,8,7,6]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[8,9,10,7,6,1,2,3,4,11,5]=>[4,3,2,5,6,11,10,9,8,1,7]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,9,10,11,12,8,1,3,4,5,6,7]=>[11,4,3,2,1,5,12,10,9,8,7,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,8,9,10,11,1,3,4,5,6,7]=>[10,4,3,2,1,11,9,8,7,6,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,11,6]=>[5,4,3,2,11,10,9,8,7,1,6]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[11,1,2,3,4,5,6,7,8,9,12,10]=>[2,12,11,10,9,8,7,6,5,4,1,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,3,1,2,4,5,6,7,10,8]=>[2,8,10,9,7,6,5,4,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,11,10,1,3,4,5,6,7,8,9]=>[10,1,2,11,9,8,7,6,5,4,3]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2,11,4,5,6,7,8,9,10,1,3]=>[10,1,8,7,6,5,4,3,2,11,9]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[10,3,4,5,6,7,8,9,1,11,2]=>[2,9,8,7,6,5,4,3,11,1,10]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[2,12,4,5,6,7,8,9,10,11,1,3]=>[11,1,9,8,7,6,5,4,3,2,12,10]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[2,11,10,5,6,7,8,9,1,3,4]=>[10,1,2,7,6,5,4,3,11,9,8]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[10,9,4,5,6,7,8,1,2,11,3]=>[2,3,8,7,6,5,4,11,10,1,9]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[11,3,4,5,6,7,8,9,10,1,12,2]=>[2,10,9,8,7,6,5,4,3,12,1,11]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,3,1,2,4,5,6,7,8,11,9]=>[2,9,11,10,8,7,6,5,4,1,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,3,1,2,4,5,6,9,7,8]=>[1,8,10,9,7,6,5,2,4,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,3,1,2,4,5,6,10,7,9]=>[3,8,10,9,7,6,5,1,4,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,10,1,3,4,5,6,9,7,8]=>[9,1,10,8,7,6,5,2,4,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,1,8,9,2,3,4,5,6,7]=>[1,10,3,2,9,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,1,2,9,10,3,4,5,6,7]=>[3,10,9,2,1,8,7,6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[9,1,2,3,10,8,4,5,6,7]=>[2,10,9,8,1,3,7,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[10,1,2,3,4,9,8,5,6,7]=>[1,10,9,8,7,2,3,6,5,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[10,1,2,3,4,5,8,9,6,7]=>[1,10,9,8,7,6,3,2,5,4]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,7,8,11,10,1,9]=>[10,9,8,7,6,5,4,1,2,11,3]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,10,11,2]=>[8,9,11,7,6,5,4,3,2,1,10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,10,11,12,2]=>[9,10,12,8,7,6,5,4,3,2,1,11]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[11,4,1,5,6,7,8,9,10,2,3]=>[1,8,11,7,6,5,4,3,2,10,9]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,5,3,7,8,9,10,4]=>[5,10,9,6,8,4,3,2,1,7]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[7,1,2,3,6,4,8,9,10,5]=>[4,10,9,8,5,7,3,2,1,6]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[8,1,2,3,4,7,5,9,10,6]=>[3,10,9,8,7,4,6,2,1,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[9,1,2,3,4,5,8,6,10,7]=>[2,10,9,8,7,6,3,5,1,4]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[11,3,4,5,6,7,8,9,10,1,2]=>[1,9,8,7,6,5,4,3,2,11,10]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[2,3,11,5,6,7,8,9,10,1,4]=>[10,9,1,7,6,5,4,3,2,11,8]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[2,3,4,11,6,7,8,9,10,1,5]=>[10,9,8,1,6,5,4,3,2,11,7]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[2,3,4,5,11,7,8,9,10,1,6]=>[10,9,8,7,1,5,4,3,2,11,6]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,6,11,8,9,10,1,7]=>[10,9,8,7,6,1,4,3,2,11,5]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,6,7,11,9,10,1,8]=>[10,9,8,7,6,5,1,3,2,11,4]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,8,1,9,10,3,4,5,6,7]=>[9,3,10,2,1,8,7,6,5,4]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,9,1,2,3,4,5,10,8]=>[5,4,2,10,9,8,7,6,1,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,1,10,9,2,3,4,5,6,8]=>[4,10,1,2,9,8,7,6,5,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10,11,8,1,2,3,4,5,6,7,9]=>[2,1,4,11,10,9,8,7,6,5,3]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[12,3,4,5,6,7,8,9,10,11,1,2]=>[1,10,9,8,7,6,5,4,3,2,12,11]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,10,1,9,7,8]=>[9,8,7,6,5,1,10,2,4,3]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,10,1,8,9,6,7]=>[9,8,7,6,1,10,3,2,5,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,10,1,7,8,9,5,6]=>[9,8,7,1,10,4,3,2,6,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,10,1,6,7,8,9,4,5]=>[9,8,1,10,5,4,3,2,7,6]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[10,1,2,3,4,8,5,6,7,9]=>[1,10,9,8,7,3,6,5,4,2]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[10,1,2,3,4,7,5,6,8,9]=>[1,10,9,8,7,4,6,5,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[11,1,2,5,3,4,6,7,8,9,10]=>[1,11,10,7,9,8,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[11,1,5,2,3,4,6,7,8,9,10]=>[1,11,7,10,9,8,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,9,1,3,4,10,5,6,7,8]=>[9,2,10,8,7,1,6,5,4,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[9,1,2,3,4,7,5,6,10,8]=>[2,10,9,8,7,4,6,5,1,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[10,6,1,2,3,4,11,5,7,8,9]=>[2,6,11,10,9,8,1,7,5,4,3]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,9,11,7,6,1,2,3,4,5,10]=>[4,3,1,5,6,11,10,9,8,7,2]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,7,8,1,2,3,4,10,5,9]=>[5,4,3,10,9,8,7,1,6,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[9,1,8,2,3,4,5,6,10,7]=>[2,10,3,9,8,7,6,5,1,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,10,8,1,3,4,5,6,7,9]=>[9,1,3,10,8,7,6,5,4,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,10,1,9,3,4,5,6,7,8]=>[9,1,10,2,8,7,6,5,4,3]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[9,7,1,2,3,4,5,6,10,8]=>[2,4,10,9,8,7,6,5,1,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,10,1,9,4,5,6,7,8]=>[9,8,1,10,2,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,10,11,1,4,5,6,7,8,9]=>[10,9,2,1,11,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,9,1,10,5,6,7,8]=>[9,8,7,2,10,1,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,3,4,11,1,2,5,6,7,8,9]=>[2,9,8,1,11,10,7,6,5,4,3]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[10,3,4,5,1,2,9,6,7,8]=>[1,8,7,6,10,9,2,5,4,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[10,6,4,5,1,2,3,9,7,8]=>[1,5,7,6,10,9,8,2,4,3]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[10,11,6,5,1,2,3,4,7,8,9]=>[2,1,6,7,11,10,9,8,5,4,3]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,9,6,5,1,2,3,4,10,8]=>[4,2,5,6,10,9,8,7,1,3]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,8,11,10,1,2,3,4,5,6,9]=>[5,4,1,2,11,10,9,8,7,6,3]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[11,8,9,10,1,2,3,4,5,6,7]=>[1,4,3,2,11,10,9,8,7,6,5]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[2,3,4,5,9,7,1,6,10,8]=>[9,8,7,6,2,4,10,5,1,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,4,1,5,6,10,8,9,3,7]=>[9,7,10,6,5,1,3,2,8,4]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[2,3,8,5,6,1,4,9,10,7]=>[9,8,3,6,5,10,7,2,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,5,1,10,7,8,9,4,6]=>[9,8,6,10,1,4,3,2,7,5]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,3,4,5,1,2,8,9,10,6]=>[4,8,7,6,10,9,3,2,1,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,3,1,2,6,7,8,9,10,4]=>[6,8,10,9,5,4,3,2,1,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,9,10,11,2]=>[7,9,8,11,6,5,4,3,2,1,10]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,3,4,1,2,7,8,9,10,5]=>[5,8,7,10,9,4,3,2,1,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,9,10,11,2]=>[6,9,8,7,11,5,4,3,2,1,10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,9,10,11,2]=>[5,9,8,7,6,11,4,3,2,1,10]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[8,3,4,5,6,1,2,9,10,7]=>[3,8,7,6,5,10,9,2,1,4]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,9,10,11,2]=>[4,9,8,7,6,5,11,3,2,1,10]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,10,11,2]=>[3,9,8,7,6,5,4,11,2,1,10]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,10,6,8,9]=>[4,7,10,9,8,6,1,5,3,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,6,1,5,3,7,8,9,10,4]=>[9,5,10,6,8,4,3,2,1,7]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,3,4,1,6,7,9,2,10,8]=>[6,8,7,10,5,4,2,9,1,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,8,1,6,7,4,9,10,5]=>[9,8,3,10,5,4,7,2,1,6]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3,4,5,1,8,2,9,10,7]=>[5,8,7,6,10,3,9,2,1,4]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,1,5,2,3,4,6,7,8,9]=>[1,10,6,9,8,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,1,2,5,3,4,6,7,8,9]=>[1,10,9,6,8,7,5,4,3,2]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[11,1,2,3,4,5,8,6,7,9,10]=>[1,11,10,9,8,7,4,6,5,3,2]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[11,1,2,3,4,5,9,6,7,8,10]=>[1,11,10,9,8,7,3,6,5,4,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[5,9,1,2,3,4,6,7,10,8]=>[6,2,10,9,8,7,5,4,1,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,10,1,5,3,4,6,7,8,9]=>[9,1,10,6,8,7,5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,11,1,2,3,10,4,6,7,8,9]=>[7,1,11,10,9,2,8,6,5,4,3]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[12,4,1,5,6,7,8,9,10,11,2,3]=>[1,9,12,8,7,6,5,4,3,2,11,10]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[10,11,1,5,6,7,8,9,2,3,4]=>[2,1,11,7,6,5,4,3,10,9,8]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[10,11,4,5,6,7,8,1,2,3,9]=>[2,1,8,7,6,5,4,11,10,9,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,10,2,9,4,5,6,7,8]=>[8,10,1,9,2,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,1,2,9,3,10,5,6,7,8]=>[7,10,9,2,8,1,6,5,4,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[5,1,2,3,10,4,9,6,7,8]=>[6,10,9,8,1,7,2,5,4,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,1,2,3,4,10,5,9,7,8]=>[5,10,9,8,7,1,6,2,4,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,10,9,6,8]=>[8,10,6,9,4,7,1,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,10,7,4,9,6,8]=>[8,10,6,9,1,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,10,5,2,7,4,9,6,8]=>[8,10,1,6,9,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,10,1,5,3,7,4,9,6,8]=>[9,1,10,6,8,4,7,2,5,3]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,10,3,7,5,9,6,8]=>[9,7,10,1,8,4,6,2,5,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,6,3,10,5,9,7,8]=>[9,7,10,5,8,1,6,2,4,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,11,10,7,9]=>[10,8,11,6,9,4,7,1,2,5,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[3,1,10,2,6,7,4,9,5,8]=>[8,10,1,9,5,4,7,2,6,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,11,8,5,10,7,9]=>[10,8,11,6,9,1,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[10,1,4,5,2,7,3,9,6,8]=>[1,10,7,6,9,4,8,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,11,6,3,8,5,10,7,9]=>[10,8,11,1,6,9,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,11,4,1,6,3,8,5,10,7,9]=>[10,1,8,11,6,9,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,1,2,5,3,7,4,9,6,8]=>[1,10,9,6,8,4,7,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[11,1,4,2,6,3,8,5,10,7,9]=>[1,11,8,10,6,9,4,7,2,5,3]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[4,3,1,10,2,7,5,9,6,8]=>[7,8,10,1,9,4,6,2,5,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,11,2,6,4,8,5,10,7,9]=>[9,11,1,10,6,8,4,7,2,5,3]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,10,4,9,7,8]=>[9,5,10,6,8,1,7,2,4,3]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,11,4,8,6,10,7,9]=>[9,11,7,10,1,8,4,6,2,5,3]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,8,3,7,5,10,6,9]=>[9,7,10,3,8,4,6,1,5,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,5,2,7,4,11,6,10,8,9]=>[9,11,7,10,5,8,1,6,2,4,3]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[10,4,1,2,3,5,9,6,7,8]=>[1,7,10,9,8,6,2,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,3,10,1,2,4,5,6,7,8,9]=>[1,9,2,11,10,8,7,6,5,4,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,11,9,1,2,3,4,5,6,7,8]=>[2,1,3,11,10,9,8,7,6,5,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,12,11,1,3,4,5,6,7,8,9,10]=>[11,1,2,12,10,9,8,7,6,5,4,3]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[10,9,8,1,2,3,4,5,6,11,7]=>[2,3,4,11,10,9,8,7,6,1,5]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,11,12,1,2,3,4,5,6,7,8,9]=>[3,2,1,12,11,10,9,8,7,6,5,4]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,10,4,5,6,7,8,9,1,11,3]=>[10,2,8,7,6,5,4,3,11,1,9]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,9,5,6,7,8,1,10,11,4]=>[10,9,3,7,6,5,4,11,2,1,8]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,8,6,7,1,9,10,11,5]=>[10,9,8,4,6,5,11,3,2,1,7]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[11,3,9,5,7,1,2,4,6,8,10]=>[1,9,3,7,5,11,10,8,6,4,2]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[11,9,4,5,1,7,2,3,6,8,10]=>[1,3,8,7,11,5,10,9,6,4,2]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,3,11,6,1,2,9,4,5,8,10]=>[5,9,1,6,11,10,3,8,7,4,2]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,11,5,1,6,2,9,3,4,8,10]=>[5,1,7,11,6,10,3,9,8,4,2]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[11,3,8,5,1,2,4,9,6,7,10]=>[1,9,4,7,11,10,8,3,6,5,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,11,1,2,9,8,4,5,7,10]=>[6,9,1,11,10,3,4,8,7,5,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[11,3,8,1,2,7,4,9,5,6,10]=>[1,9,4,11,10,5,8,3,7,6,2]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[9,4,1,11,6,8,2,3,5,7,10]=>[3,8,11,1,6,4,10,9,7,5,2]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[11,9,1,5,6,2,8,3,4,7,10]=>[1,3,11,7,6,10,4,9,8,5,2]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,1,11,7,2,3,9,5,6,10]=>[4,8,11,1,5,10,9,3,7,6,2]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[11,9,1,5,2,7,8,3,4,6,10]=>[1,3,11,7,10,5,4,9,8,6,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[11,8,1,6,2,7,3,9,4,5,10]=>[1,4,11,6,10,5,9,3,8,7,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,3,11,5,1,2,4,6,10,8,9]=>[5,9,1,7,11,10,8,6,2,4,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,3,11,1,2,7,4,5,10,8,9]=>[6,9,1,11,10,5,8,7,2,4,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[11,4,1,7,6,2,3,5,10,8,9]=>[1,8,11,5,6,10,9,7,2,4,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[6,11,1,5,2,7,3,4,10,8,9]=>[6,1,11,7,10,5,9,8,2,4,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[11,3,5,1,2,4,8,10,6,7,9]=>[1,9,7,11,10,8,4,2,6,5,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[11,4,1,5,2,3,8,10,6,7,9]=>[1,8,11,7,10,9,4,2,6,5,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[11,3,5,1,2,4,9,6,10,7,8]=>[1,9,7,11,10,8,3,6,2,5,4]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[11,4,1,5,2,3,9,6,10,7,8]=>[1,8,11,7,10,9,3,6,2,5,4]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[10,3,1,2,6,11,8,4,5,7,9]=>[2,9,11,10,6,1,4,8,7,5,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[11,3,1,2,8,7,4,10,5,6,9]=>[1,9,11,10,4,5,8,2,7,6,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[9,3,1,2,6,11,4,5,10,7,8]=>[3,9,11,10,6,1,8,7,2,5,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[11,3,1,2,7,4,10,9,5,6,8]=>[1,9,11,10,5,8,2,3,7,6,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[9,3,1,2,11,4,8,5,10,6,7]=>[3,9,11,10,1,8,4,7,2,6,5]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[11,1,4,10,6,8,2,3,5,7,9]=>[1,11,8,2,6,4,10,9,7,5,3]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[11,1,10,5,2,7,8,3,4,6,9]=>[1,11,2,7,10,5,4,9,8,6,3]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[8,1,11,6,2,7,3,10,4,5,9]=>[4,11,1,6,10,5,9,2,8,7,3]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[9,1,6,5,2,11,3,4,10,7,8]=>[3,11,6,7,10,1,9,8,2,5,4]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[7,1,4,11,2,3,10,9,5,6,8]=>[5,11,8,1,10,9,2,3,7,6,4]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[11,1,4,9,2,3,8,5,10,6,7]=>[1,11,8,3,10,9,4,7,2,6,5]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[10,1,5,2,11,7,9,3,4,6,8]=>[2,11,7,10,1,5,3,9,8,6,4]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[11,1,10,2,6,3,8,9,4,5,7]=>[1,11,2,10,6,9,4,3,8,7,5]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[11,1,9,2,7,3,8,4,10,5,6]=>[1,11,3,10,5,9,4,8,2,7,6]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,3,13,5,11,7,1,2,4,6,8,10,12]=>[5,11,1,9,3,7,13,12,10,8,6,4,2]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[13,3,11,7,6,1,2,9,4,5,8,10,12]=>[1,11,3,7,8,13,12,5,10,9,6,4,2]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,3,9,5,13,1,2,4,11,6,7,10,12]=>[6,11,5,9,1,13,12,10,3,8,7,4,2]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[13,3,11,6,1,2,8,9,4,5,7,10,12]=>[1,11,3,8,13,12,6,5,10,9,7,4,2]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,3,9,13,1,2,8,4,11,5,6,10,12]=>[7,11,5,1,13,12,6,10,3,9,8,4,2]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[13,3,10,5,7,1,2,4,6,11,8,9,12]=>[1,11,4,9,7,13,12,10,8,3,6,5,2]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,3,10,6,1,2,13,4,5,11,8,9,12]=>[7,11,4,8,13,12,1,10,9,3,6,5,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[13,3,8,5,1,2,4,11,10,6,7,9,12]=>[1,11,6,9,13,12,10,3,4,8,7,5,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[13,3,10,5,1,2,4,9,6,11,7,8,12]=>[1,11,4,9,13,12,10,5,8,3,7,6,2]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[6,3,11,1,2,13,8,10,4,5,7,9,12]=>[8,11,3,13,12,1,6,4,10,9,7,5,2]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[13,3,11,1,2,7,8,4,10,5,6,9,12]=>[1,11,3,13,12,7,6,10,4,9,8,5,2]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[6,3,10,1,2,13,9,4,5,11,7,8,12]=>[8,11,4,13,12,1,5,10,9,3,7,6,2]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[13,3,11,1,2,7,4,9,10,5,6,8,12]=>[1,11,3,13,12,7,10,5,4,9,8,6,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[13,3,10,1,2,8,4,9,5,11,6,7,12]=>[1,11,4,13,12,6,10,5,9,3,8,7,2]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[10,4,1,11,6,13,8,2,3,5,7,9,12]=>[4,10,13,3,8,1,6,12,11,9,7,5,2]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[13,11,1,5,6,8,2,10,3,4,7,9,12]=>[1,3,13,9,8,6,12,4,11,10,7,5,2]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[13,4,1,11,8,7,2,3,10,5,6,9,12]=>[1,10,13,3,6,7,12,11,4,9,8,5,2]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[13,11,1,5,7,2,8,10,3,4,6,9,12]=>[1,3,13,9,7,12,6,4,11,10,8,5,2]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[13,11,1,7,6,2,8,3,10,4,5,9,12]=>[1,3,13,7,8,12,6,11,4,10,9,5,2]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[9,4,1,10,6,13,2,3,5,11,7,8,12]=>[5,10,13,4,8,1,12,11,9,3,7,6,2]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[13,10,1,5,6,2,9,3,4,11,7,8,12]=>[1,4,13,9,8,12,5,11,10,3,7,6,2]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[13,4,1,11,7,2,3,9,10,5,6,8,12]=>[1,10,13,3,7,12,11,5,4,9,8,6,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[8,4,1,10,13,2,3,9,5,11,6,7,12]=>[6,10,13,4,1,12,11,5,9,3,8,7,2]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[13,11,1,5,2,7,10,9,3,4,6,8,12]=>[1,3,13,9,12,7,4,5,11,10,8,6,2]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[13,11,1,6,2,7,9,3,10,4,5,8,12]=>[1,3,13,8,12,7,5,11,4,10,9,6,2]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[13,10,1,5,2,9,8,3,4,11,6,7,12]=>[1,4,13,9,12,5,6,11,10,3,8,7,2]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[13,11,1,6,2,8,3,9,10,4,5,7,12]=>[1,3,13,8,12,6,11,5,4,10,9,7,2]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[10,8,1,13,2,7,3,9,4,11,5,6,12]=>[4,6,13,1,12,7,11,5,10,3,9,8,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[13,3,9,5,7,1,2,4,6,8,12,10,11]=>[1,11,5,9,7,13,12,10,8,6,2,4,3]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,3,13,6,1,2,9,4,5,8,12,10,11]=>[7,11,1,8,13,12,5,10,9,6,2,4,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[13,3,8,5,1,2,4,9,6,7,12,10,11]=>[1,11,6,9,13,12,10,5,8,7,2,4,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[6,3,13,1,2,9,8,4,5,7,12,10,11]=>[8,11,1,13,12,5,6,10,9,7,2,4,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[13,3,8,1,2,7,4,9,5,6,12,10,11]=>[1,11,6,13,12,7,10,5,9,8,2,4,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[9,4,1,13,6,8,2,3,5,7,12,10,11]=>[5,10,13,1,8,6,12,11,9,7,2,4,3]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[13,9,1,5,6,2,8,3,4,7,12,10,11]=>[1,5,13,9,8,12,6,11,10,7,2,4,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[8,4,1,13,7,2,3,9,5,6,12,10,11]=>[6,10,13,1,7,12,11,5,9,8,2,4,3]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[13,9,1,5,2,7,8,3,4,6,12,10,11]=>[1,5,13,9,12,7,6,11,10,8,2,4,3]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[13,8,1,6,2,7,3,9,4,5,12,10,11]=>[1,6,13,8,12,7,11,5,10,9,2,4,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,3,13,5,1,2,4,6,10,12,8,9,11]=>[7,11,1,9,13,12,10,8,4,2,6,5,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,3,13,1,2,7,4,5,10,12,8,9,11]=>[8,11,1,13,12,7,10,9,4,2,6,5,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[13,4,1,7,6,2,3,5,10,12,8,9,11]=>[1,10,13,7,8,12,11,9,4,2,6,5,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,13,1,5,2,7,3,4,10,12,8,9,11]=>[8,1,13,9,12,7,11,10,4,2,6,5,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[7,3,13,5,1,2,4,6,11,8,12,9,10]=>[7,11,1,9,13,12,10,8,3,6,2,5,4]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,3,13,1,2,7,4,5,11,8,12,9,10]=>[8,11,1,13,12,7,10,9,3,6,2,5,4]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[13,4,1,7,6,2,3,5,11,8,12,9,10]=>[1,10,13,7,8,12,11,9,3,6,2,5,4]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,13,1,5,2,7,3,4,11,8,12,9,10]=>[8,1,13,9,12,7,11,10,3,6,2,5,4]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[12,3,5,1,2,4,8,13,10,6,7,9,11]=>[2,11,9,13,12,10,6,1,4,8,7,5,3]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[12,4,1,5,2,3,8,13,10,6,7,9,11]=>[2,10,13,9,12,11,6,1,4,8,7,5,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[13,3,5,1,2,4,10,9,6,12,7,8,11]=>[1,11,9,13,12,10,4,5,8,2,7,6,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[13,4,1,5,2,3,10,9,6,12,7,8,11]=>[1,10,13,9,12,11,4,5,8,2,7,6,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[11,3,5,1,2,4,8,13,6,7,12,9,10]=>[3,11,9,13,12,10,6,1,8,7,2,5,4]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[11,4,1,5,2,3,8,13,6,7,12,9,10]=>[3,10,13,9,12,11,6,1,8,7,2,5,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[13,3,5,1,2,4,9,6,12,11,7,8,10]=>[1,11,9,13,12,10,5,8,2,3,7,6,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[13,4,1,5,2,3,9,6,12,11,7,8,10]=>[1,10,13,9,12,11,5,8,2,3,7,6,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[11,3,5,1,2,4,13,6,10,7,12,8,9]=>[3,11,9,13,12,10,1,8,4,7,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[11,4,1,5,2,3,13,6,10,7,12,8,9]=>[3,10,13,9,12,11,1,8,4,7,2,6,5]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[13,3,1,2,6,12,8,10,4,5,7,9,11]=>[1,11,13,12,8,2,6,4,10,9,7,5,3]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[13,3,1,2,12,7,8,4,10,5,6,9,11]=>[1,11,13,12,2,7,6,10,4,9,8,5,3]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[10,3,1,2,6,13,9,4,5,12,7,8,11]=>[4,11,13,12,8,1,5,10,9,2,7,6,3]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[13,3,1,2,12,7,4,9,10,5,6,8,11]=>[1,11,13,12,2,7,10,5,4,9,8,6,3]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[10,3,1,2,13,8,4,9,5,12,6,7,11]=>[4,11,13,12,1,6,10,5,9,2,8,7,3]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[13,3,1,2,6,11,8,4,5,7,12,9,10]=>[1,11,13,12,8,3,6,10,9,7,2,5,4]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[11,3,1,2,8,7,4,13,5,6,12,9,10]=>[3,11,13,12,6,7,10,1,9,8,2,5,4]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[9,3,1,2,6,13,4,5,12,11,7,8,10]=>[5,11,13,12,8,1,10,9,2,3,7,6,4]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[13,3,1,2,6,11,4,5,10,7,12,8,9]=>[1,11,13,12,8,3,10,9,4,7,2,6,5]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[12,3,1,2,7,4,13,9,11,5,6,8,10]=>[2,11,13,12,7,10,1,5,3,9,8,6,4]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[13,3,1,2,12,4,8,9,5,11,6,7,10]=>[1,11,13,12,2,10,6,5,9,3,8,7,4]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[11,3,1,2,7,4,13,10,5,6,12,8,9]=>[3,11,13,12,7,10,1,4,9,8,2,6,5]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[13,3,1,2,12,4,8,5,10,11,6,7,9]=>[1,11,13,12,2,10,6,9,4,3,8,7,5]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[13,3,1,2,11,4,9,5,10,6,12,7,8]=>[1,11,13,12,3,10,5,9,4,8,2,7,6]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[13,1,12,6,2,7,9,3,10,4,5,8,11]=>[1,13,2,8,12,7,5,11,4,10,9,6,3]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[13,1,10,5,2,9,8,3,4,12,6,7,11]=>[1,13,4,9,12,5,6,11,10,2,8,7,3]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[13,1,12,6,2,8,3,9,10,4,5,7,11]=>[1,13,2,8,12,6,11,5,4,10,9,7,3]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[8,1,10,13,2,7,3,9,4,12,5,6,11]=>[6,13,4,1,12,7,11,5,10,2,9,8,3]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[8,1,11,6,2,7,3,13,4,5,12,9,10]=>[6,13,3,8,12,7,11,1,10,9,2,5,4]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[9,1,6,5,2,13,3,4,12,11,7,8,10]=>[5,13,8,9,12,1,11,10,2,3,7,6,4]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[13,1,6,5,2,11,3,4,10,7,12,8,9]=>[1,13,8,9,12,3,11,10,4,7,2,6,5]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[13,1,4,12,2,3,8,9,5,11,6,7,10]=>[1,13,10,2,12,11,6,5,9,3,8,7,4]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[7,1,4,11,2,3,13,10,5,6,12,8,9]=>[7,13,10,3,12,11,1,4,9,8,2,6,5]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[13,1,4,12,2,3,8,5,10,11,6,7,9]=>[1,13,10,2,12,11,6,9,4,3,8,7,5]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[13,1,4,11,2,3,9,5,10,6,12,7,8]=>[1,13,10,3,12,11,5,9,4,8,2,7,6]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[13,1,12,2,6,8,3,9,11,4,5,7,10]=>[1,13,2,12,8,6,11,5,3,10,9,7,4]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[11,1,9,2,13,3,8,4,10,5,12,6,7]=>[3,13,5,12,1,11,6,10,4,9,2,8,7]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[11,10,9,8,7,6,5,4,3,2,1,12]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,11,1,12,10]=>[11,10,9,8,7,6,5,4,2,12,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[11,1,10,9,2,3,4,5,6,7,8]=>[1,11,2,3,10,9,8,7,6,5,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[8,1,9,10,7,2,3,4,5,6]=>[3,10,2,1,4,9,8,7,6,5]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[9,1,10,11,8,7,2,3,4,5,6]=>[3,11,2,1,4,5,10,9,8,7,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,8,9,10,2,4,5,6,7]=>[8,10,3,2,1,9,7,6,5,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[8,1,9,10,11,2,3,4,5,6,7]=>[4,11,3,2,1,10,9,8,7,6,5]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[11,3,10,5,6,7,8,9,1,2,4]=>[1,9,2,7,6,5,4,3,11,10,8]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[11,3,4,5,6,7,8,10,1,2,9]=>[1,9,8,7,6,5,4,2,11,10,3]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,7,8,9,12,11,1,10]=>[11,10,9,8,7,6,5,4,1,2,12,3]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[11,3,1,5,6,7,8,9,10,2,4]=>[1,9,11,7,6,5,4,3,2,10,8]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[11,3,4,5,6,7,8,1,10,2,9]=>[1,9,8,7,6,5,4,11,2,10,3]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[2,11,4,5,6,7,8,10,1,3,9]=>[10,1,8,7,6,5,4,2,11,9,3]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,13,12,1,11]=>[12,11,10,9,8,7,6,5,4,1,2,13,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[12,1,2,3,4,5,6,7,8,11,9,10]=>[1,12,11,10,9,8,7,6,5,2,4,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,11,1,3,4,5,6,7,10,8,9]=>[10,1,11,9,8,7,6,5,2,4,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,10,2,4,5,6,9,7,8]=>[8,10,1,9,7,6,5,2,4,3]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[2,3,4,5,10,7,1,6,8,9]=>[9,8,7,6,1,4,10,5,3,2]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,10,6,1,5,7,8,9]=>[9,8,7,1,5,10,6,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,10,5,1,4,6,7,8,9]=>[9,8,1,6,10,7,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,10,4,1,3,5,6,7,8,9]=>[9,1,7,10,8,6,5,4,3,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[8,6,1,2,3,4,5,9,10,7]=>[3,5,10,9,8,7,6,2,1,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,7,1,2,3,4,8,9,10,6]=>[6,4,10,9,8,7,3,2,1,5]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[10,4,1,2,3,7,8,9,5,6]=>[1,7,10,9,8,4,3,2,6,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[10,3,1,2,9,7,8,4,5,6]=>[1,8,10,9,2,4,3,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,9,1,10,8,7,3,4,5,6]=>[9,2,10,1,3,4,8,7,6,5]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,12,3]=>[11,9,12,8,7,6,5,4,3,2,1,10]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[10,1,2,9,6,3,4,5,7,8]=>[1,10,9,2,5,8,7,6,4,3]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,1,2,10,3,5,9,6,7,8]=>[7,10,9,1,8,6,2,5,4,3]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[11,9,4,5,6,7,8,1,10,2,3]=>[1,3,8,7,6,5,4,11,2,10,9]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[10,1,4,5,2,3,6,7,8,9]=>[1,10,7,6,9,8,5,4,3,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[10,1,2,3,4,5,8,6,7,9]=>[1,10,9,8,7,6,3,5,4,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,11,10,9,1,3,4,5,6,7,8]=>[10,1,2,3,11,9,8,7,6,5,4]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[10,1,2,3,6,7,4,5,8,9]=>[1,10,9,8,5,4,7,6,3,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[11,1,8,2,3,4,5,6,7,9,10]=>[1,11,4,10,9,8,7,6,5,3,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[12,1,11,2,3,4,5,6,7,8,9,10]=>[1,12,2,11,10,9,8,7,6,5,4,3]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,7,5,2,4,9,6,10,8]=>[8,10,4,6,9,7,2,5,1,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,1,8,2,3,4,5,6,7,9]=>[1,10,3,9,8,7,6,5,4,2]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,8,7,1,9,10,11,6]=>[10,9,8,7,4,5,11,3,2,1,6]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,1,2,3,4,7,5,10,6,9]=>[3,10,9,8,7,4,6,1,5,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[5,3,1,2,7,4,9,6,10,8]=>[6,8,10,9,4,7,2,5,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[12,11,1,10,2,3,4,5,6,7,8,9]=>[1,2,12,3,11,10,9,8,7,6,5,4]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[10,1,2,3,6,4,5,7,8,9]=>[1,10,9,8,5,7,6,4,3,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[11,1,2,3,4,5,6,9,7,8,10]=>[1,11,10,9,8,7,6,3,5,4,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,12,6]=>[11,10,9,8,6,12,5,4,3,2,1,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1,11,2,3,4,5,6,7,8,10]=>[3,11,1,10,9,8,7,6,5,4,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[8,9,10,11,12,1,2,3,4,5,6,7]=>[5,4,3,2,1,12,11,10,9,8,7,6]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,2,10,3,4,5,6,8,9]=>[4,10,9,1,8,7,6,5,3,2]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,10,12,2,11]=>[10,12,9,8,7,6,5,4,3,1,11,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[10,3,1,5,2,7,4,9,6,11,8]=>[2,9,11,7,10,5,8,3,6,1,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[4,1,2,10,6,7,9,3,5,8]=>[7,10,9,1,5,4,2,8,6,3]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,1,10,6,2,3,9,4,5,8]=>[4,10,1,5,9,8,2,7,6,3]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[10,1,2,3,6,7,9,4,5,8]=>[1,10,9,8,5,4,2,7,6,3]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,5,6,10,9,3,7,8]=>[7,10,9,6,5,1,2,8,4,3]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,1,2,3,6,10,9,4,7,8]=>[6,10,9,8,5,1,2,7,4,3]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[10,1,9,5,2,3,4,6,7,8]=>[1,10,2,6,9,8,7,5,4,3]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[10,1,2,5,9,3,4,6,7,8]=>[1,10,9,6,2,8,7,5,4,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,1,8,2,10,3,4,5,6,7]=>[2,10,3,9,1,8,7,6,5,4]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[2,3,10,5,6,7,8,9,1,11,4]=>[10,9,2,7,6,5,4,3,11,1,8]
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,9,6,7,8,1,10,11,5]=>[10,9,8,3,6,5,4,11,2,1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,4,1,2,6,7,8,9,10,11,3]=>[7,8,11,10,6,5,4,3,2,1,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,6,1,2,3,7,8,9,10,11,4]=>[7,6,11,10,9,5,4,3,2,1,8]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,3,1,6,2,8,5,10,7,9]=>[7,8,10,5,9,3,6,1,4,2]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,3,1,5,2,8,4,10,7,9]=>[5,8,10,6,9,3,7,1,4,2]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,3,1,5,2,7,4,10,6,9]=>[3,8,10,6,9,4,7,1,5,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[9,3,1,5,2,7,4,6,10,8]=>[2,8,10,6,9,4,7,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,3,1,5,2,4,9,6,10,8]=>[4,8,10,6,9,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,1,6,2,8,5,10,7,11,9]=>[8,9,11,6,10,4,7,2,5,1,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,3,1,5,2,8,4,10,7,11,9]=>[6,9,11,7,10,4,8,2,5,1,3]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[10,3,1,5,2,7,8,4,6,9]=>[1,8,10,6,9,4,3,7,5,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[8,3,1,5,2,7,4,10,6,11,9]=>[4,9,11,7,10,5,8,2,6,1,3]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[11,3,1,5,2,7,4,9,6,8,10]=>[1,9,11,7,10,5,8,3,6,4,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,3,1,5,2,4,10,9,6,8]=>[4,8,10,6,9,7,1,2,5,3]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[9,3,1,5,2,7,4,6,11,8,10]=>[3,9,11,7,10,5,8,6,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,3,1,5,2,4,9,6,11,8,10]=>[5,9,11,7,10,8,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,9,6,11,8,10]=>[7,9,11,10,5,8,3,6,1,4,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,1,2,3,4,5,10,7,9]=>[3,5,10,9,8,7,6,1,4,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,7,1,2,3,4,10,6,8,9]=>[6,4,10,9,8,7,1,5,3,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[6,4,1,2,3,10,5,7,8,9]=>[5,7,10,9,8,1,6,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[5,3,1,2,10,4,6,7,8,9]=>[6,8,10,9,1,7,5,4,3,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,1,2,8,3,4,5,6,7,9]=>[1,10,9,3,8,7,6,5,4,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[10,1,2,5,6,7,8,3,4,9]=>[1,10,9,6,5,4,3,8,7,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,7,4,1,6,3,10,5,8,9]=>[9,4,7,10,5,8,1,6,3,2]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,9,4,1,6,3,8,5,11,7,10]=>[10,3,8,11,6,9,4,7,1,5,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,7,1,6,4,9,5,10,8]=>[9,8,4,10,5,7,2,6,1,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,1,10,2,3,4,5,9,7,8]=>[5,10,1,9,8,7,6,2,4,3]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[11,10,6,5,1,9,8,2,3,4,7]=>[1,2,6,7,11,3,4,10,9,8,5]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[10,1,2,3,4,7,8,5,6,9]=>[1,10,9,8,7,4,3,6,5,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[9,4,1,2,3,10,5,6,7,8]=>[2,7,10,9,8,1,6,5,4,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,6,4,1,3,8,5,10,7,11,9]=>[10,6,8,11,9,4,7,2,5,1,3]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,8,7,1,9,10,11,12,6]=>[11,10,9,8,5,6,12,4,3,2,1,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,6,4,1,3,8,5,10,7,9]=>[9,5,7,10,8,3,6,1,4,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,10,4,1,6,3,8,5,7,9]=>[9,1,7,10,5,8,3,6,4,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,7,4,1,6,3,9,5,10,8]=>[9,4,7,10,5,8,2,6,1,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,5,4,1,7,3,9,6,10,8]=>[9,6,7,10,4,8,2,5,1,3]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[8,3,4,1,6,2,5,10,7,9]=>[3,8,7,10,5,9,6,1,4,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,8,4,1,6,3,5,10,7,11,9]=>[10,4,8,11,6,9,7,2,5,1,3]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,10,4,1,6,3,8,5,7,11,9]=>[10,2,8,11,6,9,4,7,5,1,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,1,4,2,7,3,9,6,10,8]=>[6,10,7,9,4,8,2,5,1,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[6,1,11,2,3,4,5,7,8,9,10]=>[6,11,1,10,9,8,7,5,4,3,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,9,10,11,12,2]=>[5,10,9,8,7,6,12,4,3,2,1,11]
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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