Identifier
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>
[1,0,1,0]=>[1,2]=>[1,2]=>1
[1,1,0,0]=>[2,1]=>[2,1]=>0
[1,0,1,0,1,0]=>[1,2,3]=>[1,3,2]=>10
[1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>10
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>01
[1,1,0,1,0,0]=>[2,3,1]=>[2,3,1]=>00
[1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>00
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,4,3,2]=>100
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,4,3,2]=>100
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,4,3,2]=>100
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,3,2]=>100
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,4,3,2]=>100
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,4,3]=>010
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>010
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[2,4,1,3]=>000
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[2,4,3,1]=>000
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[2,4,3,1]=>000
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>001
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[3,2,4,1]=>000
[1,1,1,0,1,0,0,0]=>[4,2,3,1]=>[4,2,3,1]=>000
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>000
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,5,4,3,2]=>1000
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,5,4,3,2]=>1000
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,5,4,3,2]=>1000
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,5,4,3,2]=>1000
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,5,4,3,2]=>1000
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,5,4,3,2]=>1000
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,5,4,3,2]=>1000
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,5,4,3,2]=>1000
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,4,3,2]=>1000
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,5,4,3,2]=>1000
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,5,4,3,2]=>1000
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,5,4,3,2]=>1000
[1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>[1,5,4,3,2]=>1000
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,5,4,3,2]=>1000
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,5,4,3]=>0100
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,5,4,3]=>0100
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,5,4,3]=>0100
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>0100
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,5,4,3]=>0100
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[2,5,1,4,3]=>0000
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[2,5,1,4,3]=>0000
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[2,5,4,1,3]=>0000
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[2,5,4,3,1]=>0000
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[2,5,4,3,1]=>0000
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[2,5,4,1,3]=>0000
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[2,5,4,3,1]=>0000
[1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>[2,5,4,3,1]=>0000
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[2,5,4,3,1]=>0000
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,5,4]=>0010
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[3,2,1,5,4]=>0010
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[3,2,5,1,4]=>0000
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[3,2,5,4,1]=>0000
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[3,2,5,4,1]=>0000
[1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>[4,2,5,1,3]=>0000
[1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>[4,2,5,3,1]=>0000
[1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>[5,2,4,3,1]=>0000
[1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>[5,2,4,3,1]=>0000
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>0001
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[4,3,2,5,1]=>0000
[1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>[5,3,2,4,1]=>0000
[1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>[5,3,4,2,1]=>0000
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>[1,6,5,4,3,2]=>10000
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>[1,6,5,4,3,2]=>10000
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>10000
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>[2,1,6,5,4,3]=>01000
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>01000
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[2,6,1,5,4,3]=>00000
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[2,6,1,5,4,3]=>00000
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[2,6,1,5,4,3]=>00000
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[2,6,1,5,4,3]=>00000
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[2,6,1,5,4,3]=>00000
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[2,6,5,1,4,3]=>00000
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[2,6,5,1,4,3]=>00000
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[2,6,5,4,1,3]=>00000
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[2,6,5,4,1,3]=>00000
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[2,6,5,1,4,3]=>00000
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[2,6,5,1,4,3]=>00000
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[2,6,5,4,1,3]=>00000
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>[2,6,5,4,1,3]=>00000
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[2,6,5,4,1,3]=>00000
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>[2,6,5,4,3,1]=>00000
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[2,6,5,4,3,1]=>00000
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,6,5,4]=>00100
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[3,2,1,6,5,4]=>00100
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[3,2,1,6,5,4]=>00100
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[3,2,1,6,5,4]=>00100
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>00100
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[3,2,6,1,5,4]=>00000
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[3,2,6,1,5,4]=>00000
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[3,2,6,5,1,4]=>00000
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[3,2,6,5,4,1]=>00000
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[3,2,6,5,4,1]=>00000
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[3,2,6,5,1,4]=>00000
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[3,2,6,5,4,1]=>00000
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>[3,2,6,5,4,1]=>00000
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[3,2,6,5,4,1]=>00000
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>[4,2,6,1,5,3]=>00000
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>[4,2,6,1,5,3]=>00000
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>[4,2,6,5,1,3]=>00000
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>[4,2,6,5,3,1]=>00000
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>[4,2,6,5,3,1]=>00000
[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>[5,2,6,4,1,3]=>00000
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>[5,2,6,4,3,1]=>00000
[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>[6,2,5,4,3,1]=>00000
[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>00000
[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>[5,2,6,4,1,3]=>00000
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>[5,2,6,4,3,1]=>00000
[1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>00000
[1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>[6,2,5,4,3,1]=>00000
[1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>00000
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,6,5]=>00010
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>00010
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[4,3,2,6,1,5]=>00000
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[4,3,2,6,5,1]=>00000
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[4,3,2,6,5,1]=>00000
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>[5,3,2,6,1,4]=>00000
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[5,3,2,6,4,1]=>00000
[1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>00000
[1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>00000
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>[5,3,6,2,1,4]=>00000
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>[5,3,6,2,4,1]=>00000
[1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>[6,3,5,2,4,1]=>00000
[1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>[6,3,5,4,2,1]=>00000
[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>[6,3,5,4,2,1]=>00000
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>00000
[1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>00000
[1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>[6,4,3,5,2,1]=>00000
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>00000
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>[1,7,6,5,4,3,2]=>100000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>100000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>010000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[2,7,1,6,5,4,3]=>000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[2,7,6,1,5,4,3]=>000000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[2,7,6,1,5,4,3]=>000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[2,7,6,1,5,4,3]=>000000
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[2,7,6,1,5,4,3]=>000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[2,7,6,1,5,4,3]=>000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[2,7,6,5,1,4,3]=>000000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[2,7,6,5,1,4,3]=>000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[2,7,6,5,1,4,3]=>000000
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[2,7,6,5,1,4,3]=>000000
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[2,7,6,1,5,4,3]=>000000
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[2,7,6,1,5,4,3]=>000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[2,7,6,1,5,4,3]=>000000
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[2,7,6,1,5,4,3]=>000000
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[2,7,6,1,5,4,3]=>000000
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[2,7,6,5,1,4,3]=>000000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[2,7,6,5,1,4,3]=>000000
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>[2,7,6,5,1,4,3]=>000000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>[2,7,6,5,1,4,3]=>000000
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[2,7,6,5,1,4,3]=>000000
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[2,7,6,5,1,4,3]=>000000
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[2,7,6,5,4,1,3]=>000000
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[2,7,6,5,4,3,1]=>000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>001000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[3,2,7,1,6,5,4]=>000000
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[3,2,7,1,6,5,4]=>000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[3,2,7,1,6,5,4]=>000000
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[3,2,7,1,6,5,4]=>000000
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[3,2,7,1,6,5,4]=>000000
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[3,2,7,6,1,5,4]=>000000
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[3,2,7,6,1,5,4]=>000000
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[3,2,7,6,5,1,4]=>000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[3,2,7,6,5,1,4]=>000000
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[3,2,7,6,1,5,4]=>000000
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[3,2,7,6,1,5,4]=>000000
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[3,2,7,6,5,1,4]=>000000
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>[3,2,7,6,5,1,4]=>000000
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[3,2,7,6,5,1,4]=>000000
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[3,2,7,6,5,4,1]=>000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>[4,2,7,1,6,5,3]=>000000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>[4,2,7,1,6,5,3]=>000000
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>[4,2,7,1,6,5,3]=>000000
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>[4,2,7,1,6,5,3]=>000000
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>000000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>[4,2,7,6,1,5,3]=>000000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>[4,2,7,6,1,5,3]=>000000
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>[4,2,7,6,5,1,3]=>000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>[4,2,7,6,5,3,1]=>000000
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>[4,2,7,6,5,3,1]=>000000
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>[4,2,7,6,5,1,3]=>000000
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>[4,2,7,6,5,3,1]=>000000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>[4,2,7,6,5,3,1]=>000000
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>[4,2,7,6,5,3,1]=>000000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>[5,2,7,6,1,4,3]=>000000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>[5,2,7,6,1,4,3]=>000000
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>[5,2,7,6,4,1,3]=>000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>[5,2,7,6,4,3,1]=>000000
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>[5,2,7,6,4,3,1]=>000000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>[6,2,7,5,4,1,3]=>000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[6,2,7,5,4,3,1]=>000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>000000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>[6,2,7,5,4,3,1]=>000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>[5,2,7,6,1,4,3]=>000000
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>[5,2,7,6,1,4,3]=>000000
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>[5,2,7,6,4,1,3]=>000000
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>[5,2,7,6,4,3,1]=>000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>[5,2,7,6,4,3,1]=>000000
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>000000
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>[6,2,7,5,4,3,1]=>000000
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>[6,2,7,5,4,1,3]=>000000
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>[6,2,7,5,4,3,1]=>000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>000000
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>[6,2,7,5,4,3,1]=>000000
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,7,6,5]=>000100
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[4,3,2,1,7,6,5]=>000100
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[4,3,2,1,7,6,5]=>000100
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[4,3,2,1,7,6,5]=>000100
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>000100
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[4,3,2,7,1,6,5]=>000000
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[4,3,2,7,1,6,5]=>000000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[4,3,2,7,6,1,5]=>000000
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[4,3,2,7,6,5,1]=>000000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[4,3,2,7,6,5,1]=>000000
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[4,3,2,7,6,1,5]=>000000
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[4,3,2,7,6,5,1]=>000000
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>[4,3,2,7,6,5,1]=>000000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[4,3,2,7,6,5,1]=>000000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>[5,3,2,7,1,6,4]=>000000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>[5,3,2,7,1,6,4]=>000000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>[5,3,2,7,6,1,4]=>000000
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>[5,3,2,7,6,4,1]=>000000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>[5,3,2,7,6,4,1]=>000000
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>000000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[6,3,2,7,5,4,1]=>000000
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>000000
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>000000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>000000
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>[6,3,2,7,5,4,1]=>000000
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>000000
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>[7,3,2,6,5,4,1]=>000000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>000000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>[5,3,7,2,1,6,4]=>000000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>[5,3,7,2,1,6,4]=>000000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>[5,3,7,2,6,1,4]=>000000
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>[5,3,7,2,6,4,1]=>000000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>[5,3,7,2,6,4,1]=>000000
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>[6,3,7,2,5,1,4]=>000000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[6,3,7,2,5,4,1]=>000000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>[7,3,6,2,5,4,1]=>000000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>[7,3,6,2,5,4,1]=>000000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>[6,3,7,5,2,1,4]=>000000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[6,3,7,5,2,4,1]=>000000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>[7,3,6,5,2,4,1]=>000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>[7,3,6,5,4,2,1]=>000000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>[7,3,6,5,4,2,1]=>000000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>[6,3,7,5,2,1,4]=>000000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>[6,3,7,5,2,4,1]=>000000
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>[7,3,6,5,2,4,1]=>000000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>[7,3,6,5,4,2,1]=>000000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>[7,3,6,5,4,2,1]=>000000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>[7,3,6,5,4,2,1]=>000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>000010
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>000010
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[5,4,3,2,7,1,6]=>000000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[5,4,3,2,7,6,1]=>000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[5,4,3,2,7,6,1]=>000000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>000000
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[6,4,3,2,7,5,1]=>000000
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>000000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>000000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>[6,4,3,7,2,1,5]=>000000
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[6,4,3,7,2,5,1]=>000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>[7,4,3,6,2,5,1]=>000000
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>[7,4,3,6,5,2,1]=>000000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>[7,4,3,6,5,2,1]=>000000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>000000
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>[6,5,3,7,2,4,1]=>000000
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>000000
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>[7,5,3,6,4,2,1]=>000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1]=>000000
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>000000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>[7,5,4,3,6,2,1]=>000000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>000000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>[7,6,4,5,3,2,1]=>000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,8,6,7,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,7,5,6,4,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,7,5,6,8,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,8,5,6,7,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,8,6,7,5,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,8,6,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,5,8,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,8,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,8,6,5,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,4,8,6,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,6,4,5,3,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,6,4,5,8,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,8,4,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,8,4,6,7,5,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,7,5,4,6,8,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,8,5,4,6,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,8,5,4,7,6,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,6,4,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,6,8,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,7,5,6,8,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,8,6,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,7,6,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,8,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,4,2,7,6,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,4,2,7,8,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,4,7,6,8,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,6,4,5,2,8,7]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,4,5,7,2,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,4,5,8,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,8,4,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,8,4,6,5,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,8,4,6,7,5,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,6,5,4,2,8,7]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,5,4,7,2,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,8,5,4,6,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,8,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,8,5,6,7,4,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,8,6,5,7,4,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,3,2,6,7,5,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,3,5,2,7,6,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,3,5,7,6,2,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,3,6,5,7,8,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,8,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,8,5,7,6,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,8,6,7,5,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,5,3,4,2,7,8,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,3,4,8,6,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,8,3,4,6,7,5,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,6,3,5,4,8,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,8,3,5,6,4,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,6,4,3,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,8,4,3,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,7,4,3,6,5,8,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,8,4,3,6,7,5,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,6,4,5,3,8,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,8,4,5,6,3,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,8,4,5,6,7,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,8,4,6,5,7,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,8,4,7,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,7,5,4,3,6,8,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,8,5,4,6,3,7,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,8,5,4,6,7,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,8,5,4,7,6,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,8,6,4,5,7,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,8,6,5,4,7,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,8,7,5,6,4,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>1000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,3,6,7,5,8]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,8,6,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,4,8,5,6,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,8,5,7,6,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,8,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,8,6,7,5,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,4,8,6,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,6,4,5,3,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,6,4,5,7,8,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,6,4,5,8,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,8,4,5,6,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,8,4,5,7,6,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,8,4,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,8,4,6,7,5,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,8,5,4,6,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,8,5,4,7,6,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,7,5,6,4,8,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,8,5,6,4,7,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,8,5,7,6,4,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>0100000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,6,8,4]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,5,8,6,7,4]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,6,5,4,7,8]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,8,5,6,7,4]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,8,6,7,5,4]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[2,8,1,7,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,8,6,7,5]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,8,6,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,4,7,5,6,1,8]=>[2,8,7,6,5,4,1,3]=>0000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,7,5,6,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,8,5,6,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,8,5,7,6,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>[2,8,7,6,5,4,1,3]=>0000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,8,6,5,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,8,6,7,5,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,6,4,5,1,8,7]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,6,4,5,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,7,4,5,6,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,8,4,5,6,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,7,4,6,5,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,6,5,4,1,7,8]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,7,5,4,6,1,8]=>[2,8,7,6,5,4,1,3]=>0000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,7,5,4,6,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,7,5,6,4,1,8]=>[2,8,7,6,5,4,1,3]=>0000000
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,7,5,6,4,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,8,5,7,6,4,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>[2,8,7,6,5,4,1,3]=>0000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,3,1,8,6,7,5]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[2,8,7,1,6,5,4,3]=>0000000
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,3,5,1,7,8,6]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,4,3,5,8,6,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,4,3,5,8,7,6,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>[2,8,7,6,5,4,1,3]=>0000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,3,8,5,6,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,4,3,8,6,7,5,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,3,4,1,6,7,8]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,5,3,4,1,8,7,6]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,3,4,6,7,1,8]=>[2,8,7,6,5,4,1,3]=>0000000
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,5,3,4,8,7,6,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,6,3,4,5,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,6,3,4,5,8,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,6,3,5,4,1,7,8]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,6,3,5,4,1,8,7]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,6,3,5,4,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,7,3,5,4,6,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,7,3,5,6,4,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,8,3,5,7,6,4,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,7,3,6,5,4,1,8]=>[2,8,7,6,5,4,1,3]=>0000000
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,8,3,7,5,6,4,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,5,4,3,1,6,8,7]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,5,4,3,1,7,6,8]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,4,3,1,7,8,6]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>[2,8,7,6,1,5,4,3]=>0000000
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,4,3,6,1,8,7]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>[2,8,7,6,5,4,1,3]=>0000000
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,8,6,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,6,4,3,5,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,8,4,3,5,6,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,8,4,3,7,6,5,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,6,4,5,3,1,7,8]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,6,4,5,3,1,8,7]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,6,4,5,3,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,6,4,5,3,8,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,7,4,5,6,3,1,8]=>[2,8,7,6,5,4,1,3]=>0000000
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,7,4,5,6,3,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,6,5,4,3,1,8,7]=>[2,8,7,6,5,1,4,3]=>0000000
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,7,5,4,3,6,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,8,5,4,3,6,7,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,8,5,4,3,7,6,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,7,5,4,6,3,8,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,8,5,4,7,6,3,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,7,5,4,6,3,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,7,5,6,4,3,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>[2,8,7,6,5,4,3,1]=>0000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,5,6,7,4,8]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,8,6,7,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,2,1,6,5,7,4,8]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,7,5,6,8,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,8,6,7,5,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>0010000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,8,6,7,5]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[3,2,8,1,7,6,5,4]=>0000000
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>[3,2,8,7,1,6,5,4]=>0000000
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>[3,2,8,7,1,6,5,4]=>0000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,4,8,5,6,7,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>[3,2,8,7,1,6,5,4]=>0000000
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,5,4,1,6,8,7]=>[3,2,8,7,1,6,5,4]=>0000000
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>[3,2,8,7,1,6,5,4]=>0000000
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>[3,2,8,7,1,6,5,4]=>0000000
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[3,2,8,7,1,6,5,4]=>0000000
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>[3,2,8,7,6,1,5,4]=>0000000
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,5,4,6,7,8,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[3,2,8,7,6,5,1,4]=>0000000
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,4,8,6,7,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,2,6,4,5,1,7,8]=>[3,2,8,7,6,1,5,4]=>0000000
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,6,4,5,1,8,7]=>[3,2,8,7,6,1,5,4]=>0000000
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,2,6,4,5,7,1,8]=>[3,2,8,7,6,5,1,4]=>0000000
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,7,4,6,5,1,8]=>[3,2,8,7,6,5,1,4]=>0000000
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,7,4,6,5,8,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,2,6,5,4,7,1,8]=>[3,2,8,7,6,5,1,4]=>0000000
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,2,8,5,4,6,7,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,7,5,6,4,1,8]=>[3,2,8,7,6,5,1,4]=>0000000
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,7,5,6,4,8,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,2,8,5,6,4,7,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,8,5,7,6,4,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[3,2,8,7,6,5,1,4]=>0000000
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>[3,2,8,7,6,5,4,1]=>0000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7,8]=>[4,2,8,1,7,6,5,3]=>0000000
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,3,1,6,5,8,7]=>[4,2,8,1,7,6,5,3]=>0000000
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,3,1,6,7,8,5]=>[4,2,8,1,7,6,5,3]=>0000000
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,3,1,6,8,7,5]=>[4,2,8,1,7,6,5,3]=>0000000
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,2,3,1,7,6,8,5]=>[4,2,8,1,7,6,5,3]=>0000000
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>0000000
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>0000000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,2,3,5,1,6,7,8]=>[4,2,8,7,1,6,5,3]=>0000000
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,2,3,5,1,7,8,6]=>[4,2,8,7,1,6,5,3]=>0000000
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,2,3,5,1,8,7,6]=>[4,2,8,7,1,6,5,3]=>0000000
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,2,3,5,6,8,7,1]=>[4,2,8,7,6,5,3,1]=>0000000
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,8,7,1]=>[4,2,8,7,6,5,3,1]=>0000000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,3,7,5,6,1,8]=>[4,2,8,7,6,5,1,3]=>0000000
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,3,8,5,6,7,1]=>[4,2,8,7,6,5,3,1]=>0000000
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[4,2,3,7,6,5,8,1]=>[4,2,8,7,6,5,3,1]=>0000000
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,2,3,8,6,7,5,1]=>[4,2,8,7,6,5,3,1]=>0000000
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,2,3,8,7,6,5,1]=>[4,2,8,7,6,5,3,1]=>0000000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,2,3,4,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>0000000
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>0000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[5,2,3,4,6,7,8,1]=>[5,2,8,7,6,4,3,1]=>0000000
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,2,3,4,8,7,6,1]=>[5,2,8,7,6,4,3,1]=>0000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,2,3,4,5,7,1,8]=>[6,2,8,7,5,4,1,3]=>0000000
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,2,3,5,4,1,7,8]=>[6,2,8,7,5,1,4,3]=>0000000
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,2,3,5,4,1,8,7]=>[6,2,8,7,5,1,4,3]=>0000000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,2,3,5,4,7,1,8]=>[6,2,8,7,5,4,1,3]=>0000000
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,2,3,5,6,4,1,8]=>[7,2,8,6,5,4,1,3]=>0000000
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[8,2,3,5,6,7,4,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>0000000
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,2,4,3,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>0000000
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,2,4,3,1,6,8,7]=>[5,2,8,7,1,6,4,3]=>0000000
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,4,3,1,7,6,8]=>[5,2,8,7,1,6,4,3]=>0000000
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>0000000
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,2,4,3,6,1,7,8]=>[5,2,8,7,6,1,4,3]=>0000000
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,2,4,3,6,1,8,7]=>[5,2,8,7,6,1,4,3]=>0000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,2,4,3,7,6,1,8]=>[5,2,8,7,6,4,1,3]=>0000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,2,4,3,7,6,8,1]=>[5,2,8,7,6,4,3,1]=>0000000
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>0000000
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,2,4,3,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>0000000
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,2,4,3,6,5,8,1]=>[7,2,8,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,2,4,5,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>0000000
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,2,4,5,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>0000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,2,4,5,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>0000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,2,4,5,3,6,8,1]=>[7,2,8,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[8,2,4,7,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[8,2,4,7,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>0000000
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>0000000
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[8,2,5,4,7,6,3,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,2,6,4,5,7,3,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>0000000
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[8,2,7,5,6,4,3,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>0000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>0001000
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,3,2,5,7,6,1,8]=>[4,3,2,8,7,6,1,5]=>0000000
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,3,2,5,7,6,8,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,7,5,6,8,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,8,5,6,7,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,8,6,7,5,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[4,3,2,8,7,6,5,1]=>0000000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,3,2,4,1,6,7,8]=>[5,3,2,8,1,7,6,4]=>0000000
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,3,2,4,1,6,8,7]=>[5,3,2,8,1,7,6,4]=>0000000
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>0000000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,3,2,4,6,1,7,8]=>[5,3,2,8,7,1,6,4]=>0000000
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,3,2,4,6,1,8,7]=>[5,3,2,8,7,1,6,4]=>0000000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>0000000
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,3,2,5,4,1,8,7]=>[6,3,2,8,7,1,5,4]=>0000000
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>0000000
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[8,3,2,5,6,4,7,1]=>[8,3,2,7,6,5,4,1]=>0000000
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[8,3,2,5,7,6,4,1]=>[8,3,2,7,6,5,4,1]=>0000000
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>0000000
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>0000000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,3,4,2,1,6,7,8]=>[5,3,8,2,1,7,6,4]=>0000000
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,3,4,2,1,7,8,6]=>[5,3,8,2,1,7,6,4]=>0000000
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,3,4,2,1,8,7,6]=>[5,3,8,2,1,7,6,4]=>0000000
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,3,4,2,6,1,8,7]=>[5,3,8,2,7,1,6,4]=>0000000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,3,4,2,7,6,1,8]=>[5,3,8,2,7,6,1,4]=>0000000
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,4,2,7,6,8,1]=>[5,3,8,2,7,6,4,1]=>0000000
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,3,4,2,8,6,7,1]=>[5,3,8,2,7,6,4,1]=>0000000
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,3,4,2,5,1,8,7]=>[6,3,8,2,7,1,5,4]=>0000000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[6,3,4,5,2,7,1,8]=>[6,3,8,7,2,5,1,4]=>0000000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[6,3,5,4,2,7,1,8]=>[6,3,8,7,2,5,1,4]=>0000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>0000100
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>0000100
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>0000100
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>0000100
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>0000100
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,8,1,7,6]=>0000000
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[5,4,3,2,8,1,7,6]=>0000000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>[5,4,3,2,8,7,1,6]=>0000000
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,8,7,6,1]=>0000000
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>[5,4,3,2,8,7,6,1]=>0000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[5,4,3,2,8,7,1,6]=>0000000
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>[5,4,3,2,8,7,6,1]=>0000000
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,8,6,7,1]=>[5,4,3,2,8,7,6,1]=>0000000
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[5,4,3,2,8,7,6,1]=>0000000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>0000000
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,4,3,5,2,1,8,7]=>[6,4,3,8,2,1,7,5]=>0000000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,4,3,6,5,2,1,8]=>[7,4,3,8,6,2,1,5]=>0000000
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,4,3,6,5,2,8,1]=>[7,4,3,8,6,2,5,1]=>0000000
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>0000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>0000000
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>0000000
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[8,7,3,5,6,4,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>0000010
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>[6,5,4,3,2,8,7,1]=>0000000
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>0000000
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>0000000
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>0000000
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>0000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>0000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
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