Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00066: Permutations —inverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1]=>
[1,0,1,0]=>[2,1]=>[2,1]=>[2,1]=>1
[1,1,0,0]=>[1,2]=>[1,2]=>[1,2]=>0
[1,0,1,0,1,0]=>[3,2,1]=>[3,2,1]=>[3,2,1]=>11
[1,0,1,1,0,0]=>[2,3,1]=>[3,1,2]=>[1,3,2]=>01
[1,1,0,0,1,0]=>[3,1,2]=>[2,3,1]=>[3,1,2]=>10
[1,1,0,1,0,0]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>10
[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>00
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[4,3,2,1]=>[4,3,2,1]=>111
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[4,3,1,2]=>[1,4,3,2]=>011
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[4,2,3,1]=>[4,1,3,2]=>101
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[4,2,1,3]=>[3,1,4,2]=>101
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[1,2,4,3]=>001
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[3,4,2,1]=>[4,3,1,2]=>110
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[3,4,1,2]=>[1,4,2,3]=>010
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[3,2,4,1]=>[4,2,1,3]=>110
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[3,2,1,4]=>[3,2,1,4]=>110
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,1,2,4]=>[1,3,2,4]=>010
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[2,3,4,1]=>[4,1,2,3]=>100
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[2,3,1,4]=>[3,1,2,4]=>100
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>100
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>000
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>1111
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,5,4,3,2]=>0111
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[5,1,4,3,2]=>1011
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[4,1,5,3,2]=>1011
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[1,2,5,4,3]=>0011
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[5,4,1,3,2]=>1101
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[5,3,4,1,2]=>[1,5,2,4,3]=>0101
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[5,3,1,4,2]=>1101
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[4,3,1,5,2]=>1101
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,4,2,5,3]=>0101
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[5,2,3,4,1]=>[5,1,2,4,3]=>1001
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[5,2,3,1,4]=>[4,1,2,5,3]=>1001
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[3,1,2,5,4]=>1001
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,2,3,5,4]=>0001
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[4,5,3,2,1]=>[5,4,3,1,2]=>1110
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[1,5,4,2,3]=>0110
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[4,5,2,3,1]=>[5,1,4,2,3]=>1010
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[4,5,2,1,3]=>[4,1,5,2,3]=>1010
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[4,5,1,2,3]=>[1,2,5,3,4]=>0010
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[4,3,5,2,1]=>[5,4,2,1,3]=>1110
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[4,3,5,1,2]=>[1,5,3,2,4]=>0110
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>1110
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>1110
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[1,4,3,2,5]=>0110
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[4,2,3,5,1]=>[5,1,3,2,4]=>1010
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[4,2,3,1,5]=>[4,1,3,2,5]=>1010
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[3,1,4,2,5]=>1010
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[1,2,4,3,5]=>0010
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[3,4,5,2,1]=>[5,4,1,2,3]=>1100
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[3,4,5,1,2]=>[1,5,2,3,4]=>0100
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[3,4,2,5,1]=>[5,3,1,2,4]=>1100
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[3,4,2,1,5]=>[4,3,1,2,5]=>1100
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[3,4,1,2,5]=>[1,4,2,3,5]=>0100
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[3,2,4,5,1]=>[5,2,1,3,4]=>1100
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[3,2,4,1,5]=>[4,2,1,3,5]=>1100
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]=>1100
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[1,3,2,4,5]=>0100
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[5,1,2,3,4]=>1000
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[4,1,2,3,5]=>1000
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[3,1,2,4,5]=>1000
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>01111
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[6,1,5,4,3,2]=>10111
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[5,1,6,4,3,2]=>10111
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>00111
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>11011
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,6,2,5,4,3]=>01011
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[6,4,1,5,3,2]=>11011
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[5,4,1,6,3,2]=>11011
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,5,2,6,4,3]=>01011
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[6,5,2,3,4,1]=>[6,1,2,5,4,3]=>10011
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[6,5,2,3,1,4]=>[5,1,2,6,4,3]=>10011
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[4,1,2,6,5,3]=>10011
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>00011
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[6,5,4,1,3,2]=>11101
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,6,5,2,4,3]=>01101
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[6,1,5,2,4,3]=>10101
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[5,1,6,2,4,3]=>10101
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[6,4,5,1,2,3]=>[1,2,6,3,5,4]=>00101
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[6,5,3,1,4,2]=>11101
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,6,4,2,5,3]=>01101
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[6,4,3,1,5,2]=>11101
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[5,4,3,1,6,2]=>11101
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,5,4,2,6,3]=>01101
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[6,1,4,2,5,3]=>10101
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[5,1,4,2,6,3]=>10101
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[4,1,5,2,6,3]=>10101
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[1,2,5,3,6,4]=>00101
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[6,3,4,5,2,1]=>[6,5,1,2,4,3]=>11001
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[6,3,4,5,1,2]=>[1,6,2,3,5,4]=>01001
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[6,3,4,2,5,1]=>[6,4,1,2,5,3]=>11001
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[6,3,4,2,1,5]=>[5,4,1,2,6,3]=>11001
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[6,3,4,1,2,5]=>[1,5,2,3,6,4]=>01001
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[6,3,2,4,5,1]=>[6,3,1,2,5,4]=>11001
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[6,3,2,4,1,5]=>[5,3,1,2,6,4]=>11001
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[4,3,1,2,6,5]=>11001
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[1,4,2,3,6,5]=>01001
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>10001
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[6,2,3,4,1,5]=>[5,1,2,3,6,4]=>10001
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[6,2,3,1,4,5]=>[4,1,2,3,6,5]=>10001
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[3,1,2,4,6,5]=>10001
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>00001
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>11110
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[1,6,5,4,2,3]=>01110
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[5,6,4,2,3,1]=>[6,1,5,4,2,3]=>10110
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[5,6,4,2,1,3]=>[5,1,6,4,2,3]=>10110
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[5,6,4,1,2,3]=>[1,2,6,5,3,4]=>00110
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[5,6,3,4,2,1]=>[6,5,1,4,2,3]=>11010
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[1,6,2,5,3,4]=>01010
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[5,6,3,2,4,1]=>[6,4,1,5,2,3]=>11010
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[5,6,3,2,1,4]=>[5,4,1,6,2,3]=>11010
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[5,6,3,1,2,4]=>[1,5,2,6,3,4]=>01010
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[5,6,2,3,4,1]=>[6,1,2,5,3,4]=>10010
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[5,6,2,3,1,4]=>[5,1,2,6,3,4]=>10010
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[5,6,2,1,3,4]=>[4,1,2,6,3,5]=>10010
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[5,6,1,2,3,4]=>[1,2,3,6,4,5]=>00010
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>11110
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[5,4,6,3,1,2]=>[1,6,5,3,2,4]=>01110
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[5,4,6,2,3,1]=>[6,1,5,3,2,4]=>10110
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[5,1,6,3,2,4]=>10110
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[5,4,6,1,2,3]=>[1,2,6,4,3,5]=>00110
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>11110
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[5,4,3,6,1,2]=>[1,6,4,3,2,5]=>01110
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>11110
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[1,5,4,3,2,6]=>01110
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[5,4,2,3,6,1]=>[6,1,4,3,2,5]=>10110
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[5,4,2,3,1,6]=>[5,1,4,3,2,6]=>10110
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[4,1,5,3,2,6]=>10110
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[1,2,5,4,3,6]=>00110
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[5,3,4,6,2,1]=>[6,5,1,3,2,4]=>11010
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[5,3,4,6,1,2]=>[1,6,2,4,3,5]=>01010
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[5,3,4,2,6,1]=>[6,4,1,3,2,5]=>11010
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[5,3,4,2,1,6]=>[5,4,1,3,2,6]=>11010
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[5,3,4,1,2,6]=>[1,5,2,4,3,6]=>01010
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[5,3,2,4,6,1]=>[6,3,1,4,2,5]=>11010
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[5,3,2,4,1,6]=>[5,3,1,4,2,6]=>11010
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[4,3,1,5,2,6]=>11010
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[1,4,2,5,3,6]=>01010
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[5,2,3,4,6,1]=>[6,1,2,4,3,5]=>10010
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>10010
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[5,2,3,1,4,6]=>[4,1,2,5,3,6]=>10010
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[3,1,2,5,4,6]=>10010
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[1,2,3,5,4,6]=>00010
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>11100
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[4,5,6,3,1,2]=>[1,6,5,2,3,4]=>01100
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[4,5,6,2,3,1]=>[6,1,5,2,3,4]=>10100
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[4,5,6,2,1,3]=>[5,1,6,2,3,4]=>10100
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[4,5,6,1,2,3]=>[1,2,6,3,4,5]=>00100
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>11100
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[4,5,3,6,1,2]=>[1,6,4,2,3,5]=>01100
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>11100
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>11100
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[4,5,3,1,2,6]=>[1,5,4,2,3,6]=>01100
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[4,5,2,3,6,1]=>[6,1,4,2,3,5]=>10100
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[4,5,2,3,1,6]=>[5,1,4,2,3,6]=>10100
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[4,5,2,1,3,6]=>[4,1,5,2,3,6]=>10100
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[4,5,1,2,3,6]=>[1,2,5,3,4,6]=>00100
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>11100
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[4,3,5,6,1,2]=>[1,6,3,2,4,5]=>01100
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>11100
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>11100
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[4,3,5,1,2,6]=>[1,5,3,2,4,6]=>01100
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>11100
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>11100
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[1,4,3,2,5,6]=>01100
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[4,2,3,5,6,1]=>[6,1,3,2,4,5]=>10100
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[4,2,3,5,1,6]=>[5,1,3,2,4,6]=>10100
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>10100
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>10100
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[1,2,4,3,5,6]=>00100
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>11000
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[3,4,5,6,1,2]=>[1,6,2,3,4,5]=>01000
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>11000
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>11000
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[3,4,5,1,2,6]=>[1,5,2,3,4,6]=>01000
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>11000
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>11000
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>11000
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[3,4,1,2,5,6]=>[1,4,2,3,5,6]=>01000
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>11000
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>11000
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>11000
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[1,3,2,4,5,6]=>01000
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>10000
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>10000
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>10000
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>10000
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>011111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[7,1,6,5,4,3,2]=>101111
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[6,1,7,5,4,3,2]=>101111
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>001111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[7,6,1,5,4,3,2]=>110111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,7,2,6,5,4,3]=>010111
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[7,5,1,6,4,3,2]=>110111
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[6,5,1,7,4,3,2]=>110111
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,6,2,7,5,4,3]=>010111
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[7,6,5,2,3,4,1]=>[7,1,2,6,5,4,3]=>100111
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>[6,1,2,7,5,4,3]=>100111
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[5,1,2,7,6,4,3]=>100111
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>000111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[7,6,5,1,4,3,2]=>111011
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,7,6,2,5,4,3]=>011011
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[7,1,6,2,5,4,3]=>101011
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[6,1,7,2,5,4,3]=>101011
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[7,6,4,5,1,2,3]=>[1,2,7,3,6,5,4]=>001011
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,1,5,3,2]=>111011
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,7,5,2,6,4,3]=>011011
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[7,5,4,1,6,3,2]=>111011
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[6,5,4,1,7,3,2]=>111011
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,6,5,2,7,4,3]=>011011
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[7,1,5,2,6,4,3]=>101011
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[6,1,5,2,7,4,3]=>101011
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[5,1,6,2,7,4,3]=>101011
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[1,2,6,3,7,5,4]=>001011
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[7,6,3,4,5,2,1]=>[7,6,1,2,5,4,3]=>110011
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[7,6,3,4,5,1,2]=>[1,7,2,3,6,5,4]=>010011
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[7,6,3,4,2,5,1]=>[7,5,1,2,6,4,3]=>110011
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[7,6,3,4,2,1,5]=>[6,5,1,2,7,4,3]=>110011
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[7,6,3,4,1,2,5]=>[1,6,2,3,7,5,4]=>010011
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[7,6,3,2,4,5,1]=>[7,4,1,2,6,5,3]=>110011
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[7,6,3,2,4,1,5]=>[6,4,1,2,7,5,3]=>110011
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[5,4,1,2,7,6,3]=>110011
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[1,5,2,3,7,6,4]=>010011
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[7,6,2,3,4,5,1]=>[7,1,2,3,6,5,4]=>100011
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[7,6,2,3,4,1,5]=>[6,1,2,3,7,5,4]=>100011
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>[5,1,2,3,7,6,4]=>100011
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[4,1,2,3,7,6,5]=>100011
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>000011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>111101
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,7,6,5,2,4,3]=>011101
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[7,1,6,5,2,4,3]=>101101
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[6,1,7,5,2,4,3]=>101101
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[7,5,6,4,1,2,3]=>[1,2,7,6,3,5,4]=>001101
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[7,6,1,5,2,4,3]=>110101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,7,2,6,3,5,4]=>010101
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[7,5,1,6,2,4,3]=>110101
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[6,5,1,7,2,4,3]=>110101
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,6,2,7,3,5,4]=>010101
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[7,5,6,2,3,4,1]=>[7,1,2,6,3,5,4]=>100101
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[7,5,6,2,3,1,4]=>[6,1,2,7,3,5,4]=>100101
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[7,5,6,2,1,3,4]=>[5,1,2,7,3,6,4]=>100101
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[7,5,6,1,2,3,4]=>[1,2,3,7,4,6,5]=>000101
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>111101
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,7,6,4,2,5,3]=>011101
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[7,1,6,4,2,5,3]=>101101
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[6,1,7,4,2,5,3]=>101101
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[7,5,4,6,1,2,3]=>[1,2,7,5,3,6,4]=>001101
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>111101
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,7,5,4,2,6,3]=>011101
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>111101
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[6,5,4,3,1,7,2]=>111101
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,6,5,4,2,7,3]=>011101
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[7,1,5,4,2,6,3]=>101101
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[6,1,5,4,2,7,3]=>101101
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[5,1,6,4,2,7,3]=>101101
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[1,2,6,5,3,7,4]=>001101
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[7,6,1,4,2,5,3]=>110101
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,7,2,5,3,6,4]=>010101
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[7,5,1,4,2,6,3]=>110101
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[6,5,1,4,2,7,3]=>110101
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,6,2,5,3,7,4]=>010101
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[7,4,1,5,2,6,3]=>110101
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[6,4,1,5,2,7,3]=>110101
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[5,4,1,6,2,7,3]=>110101
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,5,2,6,3,7,4]=>010101
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[7,5,2,3,4,6,1]=>[7,1,2,5,3,6,4]=>100101
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[7,5,2,3,4,1,6]=>[6,1,2,5,3,7,4]=>100101
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>[5,1,2,6,3,7,4]=>100101
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[4,1,2,6,3,7,5]=>100101
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[1,2,3,6,4,7,5]=>000101
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[7,4,5,6,3,2,1]=>[7,6,5,1,2,4,3]=>111001
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[7,4,5,6,3,1,2]=>[1,7,6,2,3,5,4]=>011001
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[7,4,5,6,2,3,1]=>[7,1,6,2,3,5,4]=>101001
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[7,4,5,6,2,1,3]=>[6,1,7,2,3,5,4]=>101001
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[7,4,5,6,1,2,3]=>[1,2,7,3,4,6,5]=>001001
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[7,4,5,3,6,2,1]=>[7,6,4,1,2,5,3]=>111001
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[7,4,5,3,6,1,2]=>[1,7,5,2,3,6,4]=>011001
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[7,4,5,3,2,6,1]=>[7,5,4,1,2,6,3]=>111001
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[7,4,5,3,2,1,6]=>[6,5,4,1,2,7,3]=>111001
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[7,4,5,3,1,2,6]=>[1,6,5,2,3,7,4]=>011001
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[7,4,5,2,3,6,1]=>[7,1,5,2,3,6,4]=>101001
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[7,4,5,2,3,1,6]=>[6,1,5,2,3,7,4]=>101001
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[7,4,5,2,1,3,6]=>[5,1,6,2,3,7,4]=>101001
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[7,4,5,1,2,3,6]=>[1,2,6,3,4,7,5]=>001001
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[7,4,3,5,6,2,1]=>[7,6,3,1,2,5,4]=>111001
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[7,4,3,5,6,1,2]=>[1,7,4,2,3,6,5]=>011001
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[7,4,3,5,2,6,1]=>[7,5,3,1,2,6,4]=>111001
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[7,4,3,5,2,1,6]=>[6,5,3,1,2,7,4]=>111001
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[7,4,3,5,1,2,6]=>[1,6,4,2,3,7,5]=>011001
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[7,4,3,2,5,6,1]=>[7,4,3,1,2,6,5]=>111001
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[7,4,3,2,5,1,6]=>[6,4,3,1,2,7,5]=>111001
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[5,4,3,1,2,7,6]=>111001
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[1,5,4,2,3,7,6]=>011001
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[7,4,2,3,5,6,1]=>[7,1,4,2,3,6,5]=>101001
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[7,4,2,3,5,1,6]=>[6,1,4,2,3,7,5]=>101001
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>[5,1,4,2,3,7,6]=>101001
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[4,1,5,2,3,7,6]=>101001
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[1,2,5,3,4,7,6]=>001001
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[7,3,4,5,6,2,1]=>[7,6,1,2,3,5,4]=>110001
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[7,3,4,5,6,1,2]=>[1,7,2,3,4,6,5]=>010001
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[7,3,4,5,2,6,1]=>[7,5,1,2,3,6,4]=>110001
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[7,3,4,5,2,1,6]=>[6,5,1,2,3,7,4]=>110001
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[7,3,4,5,1,2,6]=>[1,6,2,3,4,7,5]=>010001
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[7,3,4,2,5,6,1]=>[7,4,1,2,3,6,5]=>110001
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[7,3,4,2,5,1,6]=>[6,4,1,2,3,7,5]=>110001
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[7,3,4,2,1,5,6]=>[5,4,1,2,3,7,6]=>110001
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[7,3,4,1,2,5,6]=>[1,5,2,3,4,7,6]=>010001
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[7,3,2,4,5,6,1]=>[7,3,1,2,4,6,5]=>110001
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[7,3,2,4,5,1,6]=>[6,3,1,2,4,7,5]=>110001
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[7,3,2,4,1,5,6]=>[5,3,1,2,4,7,6]=>110001
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[4,3,1,2,5,7,6]=>110001
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[1,4,2,3,5,7,6]=>010001
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[7,2,3,4,5,6,1]=>[7,1,2,3,4,6,5]=>100001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[7,2,3,4,5,1,6]=>[6,1,2,3,4,7,5]=>100001
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[7,2,3,4,1,5,6]=>[5,1,2,3,4,7,6]=>100001
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>[4,1,2,3,5,7,6]=>100001
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[3,1,2,4,5,7,6]=>100001
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>111110
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[1,7,6,5,4,2,3]=>011110
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[6,7,5,4,2,3,1]=>[7,1,6,5,4,2,3]=>101110
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[6,7,5,4,2,1,3]=>[6,1,7,5,4,2,3]=>101110
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[6,7,5,4,1,2,3]=>[1,2,7,6,5,3,4]=>001110
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[6,7,5,3,4,2,1]=>[7,6,1,5,4,2,3]=>110110
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[6,7,5,3,4,1,2]=>[1,7,2,6,5,3,4]=>010110
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[6,7,5,3,2,4,1]=>[7,5,1,6,4,2,3]=>110110
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[6,7,5,3,2,1,4]=>[6,5,1,7,4,2,3]=>110110
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[6,7,5,3,1,2,4]=>[1,6,2,7,5,3,4]=>010110
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[6,7,5,2,3,4,1]=>[7,1,2,6,5,3,4]=>100110
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[6,7,5,2,3,1,4]=>[6,1,2,7,5,3,4]=>100110
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[6,7,5,2,1,3,4]=>[5,1,2,7,6,3,4]=>100110
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[6,7,5,1,2,3,4]=>[1,2,3,7,6,4,5]=>000110
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[6,7,4,5,3,2,1]=>[7,6,5,1,4,2,3]=>111010
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[6,7,4,5,3,1,2]=>[1,7,6,2,5,3,4]=>011010
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[6,7,4,5,2,3,1]=>[7,1,6,2,5,3,4]=>101010
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[6,7,4,5,2,1,3]=>[6,1,7,2,5,3,4]=>101010
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[6,7,4,5,1,2,3]=>[1,2,7,3,6,4,5]=>001010
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[6,7,4,3,5,2,1]=>[7,6,4,1,5,2,3]=>111010
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[1,7,5,2,6,3,4]=>011010
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[6,7,4,3,2,5,1]=>[7,5,4,1,6,2,3]=>111010
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[6,7,4,3,2,1,5]=>[6,5,4,1,7,2,3]=>111010
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[6,7,4,3,1,2,5]=>[1,6,5,2,7,3,4]=>011010
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[6,7,4,2,3,5,1]=>[7,1,5,2,6,3,4]=>101010
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[6,7,4,2,3,1,5]=>[6,1,5,2,7,3,4]=>101010
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[6,7,4,2,1,3,5]=>[5,1,6,2,7,3,4]=>101010
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[6,7,4,1,2,3,5]=>[1,2,6,3,7,4,5]=>001010
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[6,7,3,4,5,2,1]=>[7,6,1,2,5,3,4]=>110010
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[6,7,3,4,5,1,2]=>[1,7,2,3,6,4,5]=>010010
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[6,7,3,4,2,5,1]=>[7,5,1,2,6,3,4]=>110010
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[6,7,3,4,2,1,5]=>[6,5,1,2,7,3,4]=>110010
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[6,7,3,4,1,2,5]=>[1,6,2,3,7,4,5]=>010010
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[6,7,3,2,4,5,1]=>[7,4,1,2,6,3,5]=>110010
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[6,7,3,2,4,1,5]=>[6,4,1,2,7,3,5]=>110010
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[6,7,3,2,1,4,5]=>[5,4,1,2,7,3,6]=>110010
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[6,7,3,1,2,4,5]=>[1,5,2,3,7,4,6]=>010010
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[6,7,2,3,4,5,1]=>[7,1,2,3,6,4,5]=>100010
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[6,7,2,3,4,1,5]=>[6,1,2,3,7,4,5]=>100010
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[6,7,2,3,1,4,5]=>[5,1,2,3,7,4,6]=>100010
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[6,7,2,1,3,4,5]=>[4,1,2,3,7,5,6]=>100010
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[6,7,1,2,3,4,5]=>[1,2,3,4,7,5,6]=>000010
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>111110
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[6,5,7,4,3,1,2]=>[1,7,6,5,3,2,4]=>011110
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[6,5,7,4,2,3,1]=>[7,1,6,5,3,2,4]=>101110
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[6,1,7,5,3,2,4]=>101110
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[6,5,7,4,1,2,3]=>[1,2,7,6,4,3,5]=>001110
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[6,5,7,3,4,2,1]=>[7,6,1,5,3,2,4]=>110110
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[6,5,7,3,4,1,2]=>[1,7,2,6,4,3,5]=>010110
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[6,5,7,3,2,4,1]=>[7,5,1,6,3,2,4]=>110110
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[6,5,7,3,2,1,4]=>[6,5,1,7,3,2,4]=>110110
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[6,5,7,3,1,2,4]=>[1,6,2,7,4,3,5]=>010110
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[6,5,7,2,3,4,1]=>[7,1,2,6,4,3,5]=>100110
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[6,5,7,2,3,1,4]=>[6,1,2,7,4,3,5]=>100110
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[6,5,7,2,1,3,4]=>[5,1,2,7,4,3,6]=>100110
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[6,5,7,1,2,3,4]=>[1,2,3,7,5,4,6]=>000110
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>111110
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[6,5,4,7,3,1,2]=>[1,7,6,4,3,2,5]=>011110
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[6,5,4,7,2,3,1]=>[7,1,6,4,3,2,5]=>101110
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[6,5,4,7,2,1,3]=>[6,1,7,4,3,2,5]=>101110
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[6,5,4,7,1,2,3]=>[1,2,7,5,4,3,6]=>001110
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>111110
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[6,5,4,3,7,1,2]=>[1,7,5,4,3,2,6]=>011110
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[1,6,5,4,3,2,7]=>011110
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[6,5,4,2,3,7,1]=>[7,1,5,4,3,2,6]=>101110
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>[6,1,5,4,3,2,7]=>101110
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[5,1,6,4,3,2,7]=>101110
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[1,2,6,5,4,3,7]=>001110
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[6,5,3,4,7,2,1]=>[7,6,1,4,3,2,5]=>110110
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[6,5,3,4,7,1,2]=>[1,7,2,5,4,3,6]=>010110
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[6,5,3,4,2,7,1]=>[7,5,1,4,3,2,6]=>110110
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[6,5,3,4,2,1,7]=>[6,5,1,4,3,2,7]=>110110
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[6,5,3,4,1,2,7]=>[1,6,2,5,4,3,7]=>010110
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[6,5,3,2,4,7,1]=>[7,4,1,5,3,2,6]=>110110
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[6,5,3,2,4,1,7]=>[6,4,1,5,3,2,7]=>110110
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[5,4,1,6,3,2,7]=>110110
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[1,5,2,6,4,3,7]=>010110
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[6,5,2,3,4,7,1]=>[7,1,2,5,4,3,6]=>100110
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[6,5,2,3,4,1,7]=>[6,1,2,5,4,3,7]=>100110
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>[5,1,2,6,4,3,7]=>100110
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[4,1,2,6,5,3,7]=>100110
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[1,2,3,6,5,4,7]=>000110
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[6,4,5,7,3,2,1]=>[7,6,5,1,3,2,4]=>111010
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[6,4,5,7,3,1,2]=>[1,7,6,2,4,3,5]=>011010
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[6,4,5,7,2,3,1]=>[7,1,6,2,4,3,5]=>101010
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[6,4,5,7,2,1,3]=>[6,1,7,2,4,3,5]=>101010
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[6,4,5,7,1,2,3]=>[1,2,7,3,5,4,6]=>001010
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[6,4,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>111010
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[6,4,5,3,7,1,2]=>[1,7,5,2,4,3,6]=>011010
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[6,4,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>111010
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[6,4,5,3,2,1,7]=>[6,5,4,1,3,2,7]=>111010
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[6,4,5,3,1,2,7]=>[1,6,5,2,4,3,7]=>011010
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[6,4,5,2,3,7,1]=>[7,1,5,2,4,3,6]=>101010
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[6,4,5,2,3,1,7]=>[6,1,5,2,4,3,7]=>101010
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[6,4,5,2,1,3,7]=>[5,1,6,2,4,3,7]=>101010
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[6,4,5,1,2,3,7]=>[1,2,6,3,5,4,7]=>001010
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[6,4,3,5,7,2,1]=>[7,6,3,1,4,2,5]=>111010
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[6,4,3,5,7,1,2]=>[1,7,4,2,5,3,6]=>011010
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[6,4,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>111010
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[6,4,3,5,2,1,7]=>[6,5,3,1,4,2,7]=>111010
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[6,4,3,5,1,2,7]=>[1,6,4,2,5,3,7]=>011010
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[6,4,3,2,5,7,1]=>[7,4,3,1,5,2,6]=>111010
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,1,5,2,7]=>111010
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[5,4,3,1,6,2,7]=>111010
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[1,5,4,2,6,3,7]=>011010
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[6,4,2,3,5,7,1]=>[7,1,4,2,5,3,6]=>101010
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[6,4,2,3,5,1,7]=>[6,1,4,2,5,3,7]=>101010
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>[5,1,4,2,6,3,7]=>101010
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[4,1,5,2,6,3,7]=>101010
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[1,2,5,3,6,4,7]=>001010
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[6,3,4,5,7,2,1]=>[7,6,1,2,4,3,5]=>110010
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[6,3,4,5,7,1,2]=>[1,7,2,3,5,4,6]=>010010
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[6,3,4,5,2,7,1]=>[7,5,1,2,4,3,6]=>110010
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[6,3,4,5,2,1,7]=>[6,5,1,2,4,3,7]=>110010
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[6,3,4,5,1,2,7]=>[1,6,2,3,5,4,7]=>010010
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[6,3,4,2,5,7,1]=>[7,4,1,2,5,3,6]=>110010
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[6,3,4,2,5,1,7]=>[6,4,1,2,5,3,7]=>110010
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[6,3,4,2,1,5,7]=>[5,4,1,2,6,3,7]=>110010
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[6,3,4,1,2,5,7]=>[1,5,2,3,6,4,7]=>010010
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[6,3,2,4,5,7,1]=>[7,3,1,2,5,4,6]=>110010
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[6,3,2,4,5,1,7]=>[6,3,1,2,5,4,7]=>110010
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[6,3,2,4,1,5,7]=>[5,3,1,2,6,4,7]=>110010
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[4,3,1,2,6,5,7]=>110010
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[1,4,2,3,6,5,7]=>010010
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[6,2,3,4,5,7,1]=>[7,1,2,3,5,4,6]=>100010
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[6,2,3,4,5,1,7]=>[6,1,2,3,5,4,7]=>100010
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[6,2,3,4,1,5,7]=>[5,1,2,3,6,4,7]=>100010
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>[4,1,2,3,6,5,7]=>100010
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[3,1,2,4,6,5,7]=>100010
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,5,7]=>000010
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>111100
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[5,6,7,4,3,1,2]=>[1,7,6,5,2,3,4]=>011100
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[5,6,7,4,2,3,1]=>[7,1,6,5,2,3,4]=>101100
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[5,6,7,4,2,1,3]=>[6,1,7,5,2,3,4]=>101100
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[5,6,7,4,1,2,3]=>[1,2,7,6,3,4,5]=>001100
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[5,6,7,3,4,2,1]=>[7,6,1,5,2,3,4]=>110100
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[5,6,7,3,4,1,2]=>[1,7,2,6,3,4,5]=>010100
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[5,6,7,3,2,4,1]=>[7,5,1,6,2,3,4]=>110100
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[5,6,7,3,2,1,4]=>[6,5,1,7,2,3,4]=>110100
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[5,6,7,3,1,2,4]=>[1,6,2,7,3,4,5]=>010100
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[5,6,7,2,3,4,1]=>[7,1,2,6,3,4,5]=>100100
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[5,6,7,2,3,1,4]=>[6,1,2,7,3,4,5]=>100100
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[5,6,7,2,1,3,4]=>[5,1,2,7,3,4,6]=>100100
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[5,6,7,1,2,3,4]=>[1,2,3,7,4,5,6]=>000100
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>111100
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[5,6,4,7,3,1,2]=>[1,7,6,4,2,3,5]=>011100
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[5,6,4,7,2,3,1]=>[7,1,6,4,2,3,5]=>101100
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[5,6,4,7,2,1,3]=>[6,1,7,4,2,3,5]=>101100
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[5,6,4,7,1,2,3]=>[1,2,7,5,3,4,6]=>001100
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>111100
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[5,6,4,3,7,1,2]=>[1,7,5,4,2,3,6]=>011100
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>111100
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>111100
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[5,6,4,3,1,2,7]=>[1,6,5,4,2,3,7]=>011100
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[5,6,4,2,3,7,1]=>[7,1,5,4,2,3,6]=>101100
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[5,6,4,2,3,1,7]=>[6,1,5,4,2,3,7]=>101100
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[5,6,4,2,1,3,7]=>[5,1,6,4,2,3,7]=>101100
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[5,6,4,1,2,3,7]=>[1,2,6,5,3,4,7]=>001100
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[5,6,3,4,7,2,1]=>[7,6,1,4,2,3,5]=>110100
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[5,6,3,4,7,1,2]=>[1,7,2,5,3,4,6]=>010100
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[5,6,3,4,2,7,1]=>[7,5,1,4,2,3,6]=>110100
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[5,6,3,4,2,1,7]=>[6,5,1,4,2,3,7]=>110100
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[5,6,3,4,1,2,7]=>[1,6,2,5,3,4,7]=>010100
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[5,6,3,2,4,7,1]=>[7,4,1,5,2,3,6]=>110100
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[5,6,3,2,4,1,7]=>[6,4,1,5,2,3,7]=>110100
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[5,6,3,2,1,4,7]=>[5,4,1,6,2,3,7]=>110100
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[5,6,3,1,2,4,7]=>[1,5,2,6,3,4,7]=>010100
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[5,6,2,3,4,7,1]=>[7,1,2,5,3,4,6]=>100100
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[5,6,2,3,4,1,7]=>[6,1,2,5,3,4,7]=>100100
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[5,6,2,3,1,4,7]=>[5,1,2,6,3,4,7]=>100100
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[5,6,2,1,3,4,7]=>[4,1,2,6,3,5,7]=>100100
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[5,6,1,2,3,4,7]=>[1,2,3,6,4,5,7]=>000100
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>111100
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[5,4,6,7,3,1,2]=>[1,7,6,3,2,4,5]=>011100
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[5,4,6,7,2,3,1]=>[7,1,6,3,2,4,5]=>101100
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[5,4,6,7,2,1,3]=>[6,1,7,3,2,4,5]=>101100
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[5,4,6,7,1,2,3]=>[1,2,7,4,3,5,6]=>001100
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>111100
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[5,4,6,3,7,1,2]=>[1,7,5,3,2,4,6]=>011100
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>111100
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>111100
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[5,4,6,3,1,2,7]=>[1,6,5,3,2,4,7]=>011100
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[5,4,6,2,3,7,1]=>[7,1,5,3,2,4,6]=>101100
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[5,4,6,2,3,1,7]=>[6,1,5,3,2,4,7]=>101100
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[5,4,6,2,1,3,7]=>[5,1,6,3,2,4,7]=>101100
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[5,4,6,1,2,3,7]=>[1,2,6,4,3,5,7]=>001100
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>111100
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[5,4,3,6,7,1,2]=>[1,7,4,3,2,5,6]=>011100
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>111100
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>111100
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[5,4,3,6,1,2,7]=>[1,6,4,3,2,5,7]=>011100
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>111100
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>111100
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>111100
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[1,5,4,3,2,6,7]=>011100
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[5,4,2,3,6,7,1]=>[7,1,4,3,2,5,6]=>101100
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[5,4,2,3,6,1,7]=>[6,1,4,3,2,5,7]=>101100
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>[5,1,4,3,2,6,7]=>101100
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[4,1,5,3,2,6,7]=>101100
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[1,2,5,4,3,6,7]=>001100
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[5,3,4,6,7,2,1]=>[7,6,1,3,2,4,5]=>110100
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[5,3,4,6,7,1,2]=>[1,7,2,4,3,5,6]=>010100
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[5,3,4,6,2,7,1]=>[7,5,1,3,2,4,6]=>110100
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[5,3,4,6,2,1,7]=>[6,5,1,3,2,4,7]=>110100
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[5,3,4,6,1,2,7]=>[1,6,2,4,3,5,7]=>010100
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[5,3,4,2,6,7,1]=>[7,4,1,3,2,5,6]=>110100
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[5,3,4,2,6,1,7]=>[6,4,1,3,2,5,7]=>110100
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[5,3,4,2,1,6,7]=>[5,4,1,3,2,6,7]=>110100
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[5,3,4,1,2,6,7]=>[1,5,2,4,3,6,7]=>010100
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[5,3,2,4,6,7,1]=>[7,3,1,4,2,5,6]=>110100
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[5,3,2,4,6,1,7]=>[6,3,1,4,2,5,7]=>110100
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[5,3,2,4,1,6,7]=>[5,3,1,4,2,6,7]=>110100
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[4,3,1,5,2,6,7]=>110100
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[1,4,2,5,3,6,7]=>010100
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[5,2,3,4,6,7,1]=>[7,1,2,4,3,5,6]=>100100
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[5,2,3,4,6,1,7]=>[6,1,2,4,3,5,7]=>100100
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[5,2,3,4,1,6,7]=>[5,1,2,4,3,6,7]=>100100
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>[4,1,2,5,3,6,7]=>100100
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[3,1,2,5,4,6,7]=>100100
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[1,2,3,5,4,6,7]=>000100
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>111000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[4,5,6,7,3,1,2]=>[1,7,6,2,3,4,5]=>011000
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[4,5,6,7,2,3,1]=>[7,1,6,2,3,4,5]=>101000
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[4,5,6,7,2,1,3]=>[6,1,7,2,3,4,5]=>101000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[4,5,6,7,1,2,3]=>[1,2,7,3,4,5,6]=>001000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>111000
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[4,5,6,3,7,1,2]=>[1,7,5,2,3,4,6]=>011000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>111000
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>111000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[4,5,6,3,1,2,7]=>[1,6,5,2,3,4,7]=>011000
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[4,5,6,2,3,7,1]=>[7,1,5,2,3,4,6]=>101000
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[4,5,6,2,3,1,7]=>[6,1,5,2,3,4,7]=>101000
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[4,5,6,2,1,3,7]=>[5,1,6,2,3,4,7]=>101000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[4,5,6,1,2,3,7]=>[1,2,6,3,4,5,7]=>001000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>111000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[4,5,3,6,7,1,2]=>[1,7,4,2,3,5,6]=>011000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>111000
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>111000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[4,5,3,6,1,2,7]=>[1,6,4,2,3,5,7]=>011000
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>111000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>111000
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>111000
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[4,5,3,1,2,6,7]=>[1,5,4,2,3,6,7]=>011000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[4,5,2,3,6,7,1]=>[7,1,4,2,3,5,6]=>101000
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[4,5,2,3,6,1,7]=>[6,1,4,2,3,5,7]=>101000
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[4,5,2,3,1,6,7]=>[5,1,4,2,3,6,7]=>101000
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[4,5,2,1,3,6,7]=>[4,1,5,2,3,6,7]=>101000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[4,5,1,2,3,6,7]=>[1,2,5,3,4,6,7]=>001000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>111000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[4,3,5,6,7,1,2]=>[1,7,3,2,4,5,6]=>011000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>111000
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>111000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[4,3,5,6,1,2,7]=>[1,6,3,2,4,5,7]=>011000
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>111000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>111000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>111000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[4,3,5,1,2,6,7]=>[1,5,3,2,4,6,7]=>011000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>111000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>111000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>111000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[1,4,3,2,5,6,7]=>011000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[4,2,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>101000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[4,2,3,5,6,1,7]=>[6,1,3,2,4,5,7]=>101000
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[4,2,3,5,1,6,7]=>[5,1,3,2,4,6,7]=>101000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>101000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>101000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>110000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[3,4,5,6,7,1,2]=>[1,7,2,3,4,5,6]=>010000
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>110000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>110000
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[3,4,5,6,1,2,7]=>[1,6,2,3,4,5,7]=>010000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>110000
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>110000
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>110000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[3,4,5,1,2,6,7]=>[1,5,2,3,4,6,7]=>010000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>110000
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>110000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>110000
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>110000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[3,4,1,2,5,6,7]=>[1,4,2,3,5,6,7]=>010000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>110000
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>110000
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>110000
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>110000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>100000
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>100000
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>100000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>100000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>100000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,8,7,6,5,4,3,2]=>0111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[8,1,7,6,5,4,3,2]=>1011111
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[7,1,8,6,5,4,3,2]=>1011111
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>[1,2,8,7,6,5,4,3]=>0011111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[8,7,1,6,5,4,3,2]=>1101111
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>[1,8,2,7,6,5,4,3]=>0101111
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[8,6,1,7,5,4,3,2]=>1101111
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[7,6,1,8,5,4,3,2]=>1101111
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,2,3,4,1]=>[8,1,2,7,6,5,4,3]=>1001111
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,2,3,1,4]=>[7,1,2,8,6,5,4,3]=>1001111
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>[1,2,3,8,7,6,5,4]=>0001111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>1110111
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,2,1]=>[8,7,6,4,5,3,1,2]=>[1,8,7,2,6,5,4,3]=>0110111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[8,1,7,2,6,5,4,3]=>1010111
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>[7,1,8,2,6,5,4,3]=>1010111
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,2,1]=>[8,7,6,4,5,1,2,3]=>[1,2,8,3,7,6,5,4]=>0010111
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>1110111
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>1110111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[7,6,5,1,8,4,3,2]=>1110111
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,7,6,2,8,5,4,3]=>0110111
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[7,1,6,2,8,5,4,3]=>1010111
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[6,1,7,2,8,5,4,3]=>1010111
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>[1,2,7,3,8,6,5,4]=>0010111
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,2,1]=>[8,7,6,3,4,5,2,1]=>[8,7,1,2,6,5,4,3]=>1100111
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,2,1]=>[8,7,6,3,4,5,1,2]=>[1,8,2,3,7,6,5,4]=>0100111
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,2,1]=>[8,7,6,3,4,2,5,1]=>[8,6,1,2,7,5,4,3]=>1100111
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[8,7,6,3,4,2,1,5]=>[7,6,1,2,8,5,4,3]=>1100111
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>[8,7,6,3,4,1,2,5]=>[1,7,2,3,8,6,5,4]=>0100111
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,2,1]=>[8,7,6,3,2,4,5,1]=>[8,5,1,2,7,6,4,3]=>1100111
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,2,4,1,5]=>[7,5,1,2,8,6,4,3]=>1100111
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>[6,5,1,2,8,7,4,3]=>1100111
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,3,2,1]=>[8,7,6,2,3,4,5,1]=>[8,1,2,3,7,6,5,4]=>1000111
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[8,7,6,2,3,4,1,5]=>[7,1,2,3,8,6,5,4]=>1000111
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[8,7,6,2,3,1,4,5]=>[6,1,2,3,8,7,5,4]=>1000111
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>[5,1,2,3,8,7,6,4]=>1000111
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>[1,2,3,4,8,7,6,5]=>0000111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>1111011
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,8,7,6,2,5,4,3]=>0111011
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,2,1]=>[8,7,5,6,4,2,3,1]=>[8,1,7,6,2,5,4,3]=>1011011
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>[8,7,5,6,4,2,1,3]=>[7,1,8,6,2,5,4,3]=>1011011
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,1,6,2,5,4,3]=>1101011
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[8,7,5,6,3,4,1,2]=>[1,8,2,7,3,6,5,4]=>0101011
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[8,6,1,7,2,5,4,3]=>1101011
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[7,6,1,8,2,5,4,3]=>1101011
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>[8,7,5,6,3,1,2,4]=>[1,7,2,8,3,6,5,4]=>0101011
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>[8,7,5,6,2,3,4,1]=>[8,1,2,7,3,6,5,4]=>1001011
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,2,1]=>[8,7,5,6,2,3,1,4]=>[7,1,2,8,3,6,5,4]=>1001011
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[8,7,5,6,1,2,3,4]=>[1,2,3,8,4,7,6,5]=>0001011
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,1,5,3,2]=>1111011
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>[8,7,5,4,6,1,2,3]=>[1,2,8,6,3,7,5,4]=>0011011
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,1,6,3,2]=>1111011
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,1,8,3,2]=>1111011
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,7,6,5,2,8,4,3]=>0111011
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[8,1,6,5,2,7,4,3]=>1011011
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>[1,2,7,6,3,8,5,4]=>0011011
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[8,6,1,5,2,7,4,3]=>1101011
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,2,1]=>[8,7,5,3,4,1,2,6]=>[1,7,2,6,3,8,5,4]=>0101011
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[7,5,1,6,2,8,4,3]=>1101011
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[6,5,1,7,2,8,4,3]=>1101011
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,2,1]=>[8,7,5,3,1,2,4,6]=>[1,6,2,7,3,8,5,4]=>0101011
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,2,1]=>[8,7,5,2,3,1,4,6]=>[6,1,2,7,3,8,5,4]=>1001011
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>[5,1,2,7,3,8,6,4]=>1001011
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>[1,2,3,7,4,8,6,5]=>0001011
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[8,7,4,5,6,3,2,1]=>[8,7,6,1,2,5,4,3]=>1110011
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[8,7,4,5,6,2,3,1]=>[8,1,7,2,3,6,5,4]=>1010011
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>[8,7,4,5,6,2,1,3]=>[7,1,8,2,3,6,5,4]=>1010011
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[8,7,4,5,6,1,2,3]=>[1,2,8,3,4,7,6,5]=>0010011
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,6,2,1]=>[8,7,4,5,3,6,2,1]=>[8,7,5,1,2,6,4,3]=>1110011
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,2,1]=>[8,7,4,5,3,2,1,6]=>[7,6,5,1,2,8,4,3]=>1110011
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,2,1]=>[8,7,4,5,2,3,1,6]=>[7,1,6,2,3,8,5,4]=>1010011
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,8,2,1]=>[8,7,4,5,1,2,3,6]=>[1,2,7,3,4,8,6,5]=>0010011
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,1,2,6,5,3]=>1110011
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,2,1]=>[8,7,4,3,5,6,1,2]=>[1,8,5,2,3,7,6,4]=>0110011
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,7,2,1]=>[8,7,4,3,5,2,6,1]=>[8,6,4,1,2,7,5,3]=>1110011
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,2,1]=>[8,7,4,3,2,5,6,1]=>[8,5,4,1,2,7,6,3]=>1110011
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>[1,2,6,3,4,8,7,5]=>0010011
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[8,7,3,4,5,6,2,1]=>[8,7,1,2,3,6,5,4]=>1100011
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,2,1]=>[8,7,3,4,5,6,1,2]=>[1,8,2,3,4,7,6,5]=>0100011
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[8,7,3,4,5,2,1,6]=>[7,6,1,2,3,8,5,4]=>1100011
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,8,2,1]=>[8,7,3,4,5,1,2,6]=>[1,7,2,3,4,8,6,5]=>0100011
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,2,1]=>[8,7,3,4,2,5,1,6]=>[7,5,1,2,3,8,6,4]=>1100011
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,2,1]=>[8,7,3,4,1,2,5,6]=>[1,6,2,3,4,8,7,5]=>0100011
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,2,1]=>[8,7,3,2,4,1,5,6]=>[6,4,1,2,3,8,7,5]=>1100011
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>[5,4,1,2,3,8,7,6]=>1100011
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,2,1]=>[8,7,2,3,4,5,6,1]=>[8,1,2,3,4,7,6,5]=>1000011
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,2,1]=>[8,7,2,3,4,5,1,6]=>[7,1,2,3,4,8,6,5]=>1000011
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,2,1]=>[8,7,2,3,4,1,5,6]=>[6,1,2,3,4,8,7,5]=>1000011
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,2,1]=>[8,7,2,3,1,4,5,6]=>[5,1,2,3,4,8,7,6]=>1000011
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>[4,1,2,3,5,8,7,6]=>1000011
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,8,7,6]=>0000011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>1111101
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,3,1]=>[8,6,7,5,4,3,1,2]=>[1,8,7,6,5,2,4,3]=>0111101
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[8,1,7,6,5,2,4,3]=>1011101
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[8,6,7,5,4,2,1,3]=>[7,1,8,6,5,2,4,3]=>1011101
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,3,1]=>[8,6,7,5,3,4,2,1]=>[8,7,1,6,5,2,4,3]=>1101101
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,3,1]=>[8,6,7,5,3,2,4,1]=>[8,6,1,7,5,2,4,3]=>1101101
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[8,6,7,5,3,1,2,4]=>[1,7,2,8,6,3,5,4]=>0101101
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[8,6,7,5,2,3,4,1]=>[8,1,2,7,6,3,5,4]=>1001101
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[8,6,7,5,1,2,3,4]=>[1,2,3,8,7,4,6,5]=>0001101
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[8,7,6,1,5,2,4,3]=>1110101
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,2,3,1]=>[8,6,7,4,5,3,1,2]=>[1,8,7,2,6,3,5,4]=>0110101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[8,1,7,2,6,3,5,4]=>1010101
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[8,6,7,4,5,2,1,3]=>[7,1,8,2,6,3,5,4]=>1010101
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[8,6,7,4,5,1,2,3]=>[1,2,8,3,7,4,6,5]=>0010101
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[8,6,5,1,7,2,4,3]=>1110101
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[7,6,5,1,8,2,4,3]=>1110101
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[8,6,7,4,2,3,5,1]=>[8,1,6,2,7,3,5,4]=>1010101
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[8,6,7,4,2,3,1,5]=>[7,1,6,2,8,3,5,4]=>1010101
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[6,1,7,2,8,3,5,4]=>1010101
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>[8,6,7,3,4,2,5,1]=>[8,6,1,2,7,3,5,4]=>1100101
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,2,3,1]=>[8,6,7,3,2,1,4,5]=>[6,5,1,2,8,3,7,4]=>1100101
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,2,3,1]=>[8,6,7,2,3,1,4,5]=>[6,1,2,3,8,4,7,5]=>1000101
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,2,3,1]=>[8,6,7,2,1,3,4,5]=>[5,1,2,3,8,4,7,6]=>1000101
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[8,6,7,1,2,3,4,5]=>[1,2,3,4,8,5,7,6]=>0000101
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>1111101
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,8,7,6,4,2,5,3]=>0111101
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>[8,6,5,7,4,2,3,1]=>[8,1,7,6,4,2,5,3]=>1011101
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[8,6,5,7,4,1,2,3]=>[1,2,8,7,5,3,6,4]=>0011101
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,4,1]=>[8,6,5,7,3,4,1,2]=>[1,8,2,7,5,3,6,4]=>0101101
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[8,6,1,7,4,2,5,3]=>1101101
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[7,6,1,8,4,2,5,3]=>1101101
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[8,6,5,7,3,1,2,4]=>[1,7,2,8,5,3,6,4]=>0101101
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,4,1]=>[8,6,5,7,2,1,3,4]=>[6,1,2,8,5,3,7,4]=>1001101
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[8,6,5,7,1,2,3,4]=>[1,2,3,8,6,4,7,5]=>0001101
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>1111101
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[8,1,7,5,4,2,6,3]=>1011101
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>1111101
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>1111101
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,1,8,2]=>1111101
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,7,6,5,4,2,8,3]=>0111101
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[6,1,7,5,4,2,8,3]=>1011101
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>[1,2,7,6,5,3,8,4]=>0011101
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[7,6,1,5,4,2,8,3]=>1101101
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[8,5,1,6,4,2,7,3]=>1101101
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[6,5,1,7,4,2,8,3]=>1101101
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>[8,6,5,2,3,4,1,7]=>[7,1,2,6,5,3,8,4]=>1001101
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,8,1]=>[8,6,5,2,3,1,4,7]=>[6,1,2,7,5,3,8,4]=>1001101
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>[1,2,3,7,6,4,8,5]=>0001101
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[8,7,6,1,4,2,5,3]=>1110101
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[8,6,4,5,7,2,3,1]=>[8,1,7,2,5,3,6,4]=>1010101
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[8,6,4,5,7,2,1,3]=>[7,1,8,2,5,3,6,4]=>1010101
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,5,1]=>[8,6,4,5,7,1,2,3]=>[1,2,8,3,6,4,7,5]=>0010101
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[7,6,5,1,4,2,8,3]=>1110101
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,7,6,2,5,3,8,4]=>0110101
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[8,6,4,5,2,3,7,1]=>[8,1,6,2,5,3,7,4]=>1010101
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[8,6,4,5,2,3,1,7]=>[7,1,6,2,5,3,8,4]=>1010101
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[8,6,4,5,2,1,3,7]=>[6,1,7,2,5,3,8,4]=>1010101
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,8,1]=>[8,6,4,5,1,2,3,7]=>[1,2,7,3,6,4,8,5]=>0010101
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[8,7,4,1,5,2,6,3]=>1110101
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,1,5,2,7,3]=>1110101
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,8,1]=>[8,6,4,3,5,2,1,7]=>[7,6,4,1,5,2,8,3]=>1110101
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[8,5,4,1,6,2,7,3]=>1110101
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,8,1]=>[8,6,4,3,2,5,1,7]=>[7,5,4,1,6,2,8,3]=>1110101
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[6,5,4,1,7,2,8,3]=>1110101
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,6,5,2,7,3,8,4]=>0110101
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[8,1,5,2,6,3,7,4]=>1010101
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[7,1,5,2,6,3,8,4]=>1010101
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[6,1,5,2,7,3,8,4]=>1010101
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[5,1,6,2,7,3,8,4]=>1010101
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>[1,2,6,3,7,4,8,5]=>0010101
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>[8,6,3,4,5,2,7,1]=>[8,6,1,2,5,3,7,4]=>1100101
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,2,8,1]=>[8,6,3,4,5,1,2,7]=>[1,7,2,3,6,4,8,5]=>0100101
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[8,6,3,4,2,1,5,7]=>[6,5,1,2,7,3,8,4]=>1100101
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>[8,6,3,4,1,2,5,7]=>[1,6,2,3,7,4,8,5]=>0100101
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,6,2,8,1]=>[8,6,3,2,4,5,1,7]=>[7,4,1,2,6,3,8,5]=>1100101
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,2,8,1]=>[8,6,3,2,4,1,5,7]=>[6,4,1,2,7,3,8,5]=>1100101
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,8,1]=>[8,6,3,2,1,4,5,7]=>[5,4,1,2,7,3,8,6]=>1100101
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,7,1]=>[8,6,2,3,4,5,7,1]=>[8,1,2,3,6,4,7,5]=>1000101
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,8,1]=>[8,6,2,3,4,1,5,7]=>[6,1,2,3,7,4,8,5]=>1000101
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>[1,2,3,4,7,5,8,6]=>0000101
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,1,2,4,3]=>1111001
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[8,5,6,7,4,1,2,3]=>[1,2,8,7,3,4,6,5]=>0011001
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[8,5,6,7,3,4,2,1]=>[8,7,1,6,2,3,5,4]=>1101001
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>[8,5,6,7,3,4,1,2]=>[1,8,2,7,3,4,6,5]=>0101001
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>[8,5,6,7,3,2,4,1]=>[8,6,1,7,2,3,5,4]=>1101001
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>[8,5,6,7,3,2,1,4]=>[7,6,1,8,2,3,5,4]=>1101001
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[8,5,6,7,2,3,4,1]=>[8,1,2,7,3,4,6,5]=>1001001
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,4,1]=>[8,5,6,7,2,1,3,4]=>[6,1,2,8,3,4,7,5]=>1001001
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[8,5,6,7,1,2,3,4]=>[1,2,3,8,4,5,7,6]=>0001001
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,5,1]=>[8,5,6,4,7,3,2,1]=>[8,7,6,4,1,2,5,3]=>1111001
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[8,5,6,4,7,1,2,3]=>[1,2,8,6,3,4,7,5]=>0011001
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,7,1]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,1,2,7,3]=>1111001
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,8,1]=>[8,5,6,4,3,2,1,7]=>[7,6,5,4,1,2,8,3]=>1111001
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,7,1]=>[8,5,6,4,2,3,7,1]=>[8,1,6,5,2,3,7,4]=>1011001
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,8,1]=>[8,5,6,4,2,3,1,7]=>[7,1,6,5,2,3,8,4]=>1011001
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,8,1]=>[8,5,6,4,1,2,3,7]=>[1,2,7,6,3,4,8,5]=>0011001
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,8,1]=>[8,5,6,3,4,2,1,7]=>[7,6,1,5,2,3,8,4]=>1101001
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[8,5,6,3,4,1,2,7]=>[1,7,2,6,3,4,8,5]=>0101001
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>[8,5,6,3,2,1,4,7]=>[6,5,1,7,2,3,8,4]=>1101001
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,8,1]=>[8,5,6,3,1,2,4,7]=>[1,6,2,7,3,4,8,5]=>0101001
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,8,1]=>[8,5,6,2,3,4,1,7]=>[7,1,2,6,3,4,8,5]=>1001001
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,2,3,8,1]=>[8,5,6,2,3,1,4,7]=>[6,1,2,7,3,4,8,5]=>1001001
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>[8,5,6,2,1,3,4,7]=>[5,1,2,7,3,4,8,6]=>1001001
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[8,5,6,1,2,3,4,7]=>[1,2,3,7,4,5,8,6]=>0001001
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,4,5,1]=>[8,5,4,6,7,3,1,2]=>[1,8,7,4,2,3,6,5]=>0111001
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,6,1]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>1111001
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,7,1]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>1111001
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,8,1]=>[8,5,4,6,3,2,1,7]=>[7,6,5,3,1,2,8,4]=>1111001
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[8,5,4,3,6,7,1,2]=>[1,8,5,4,2,3,7,6]=>0111001
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,1,2,8,7]=>1111001
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>[5,1,6,4,2,3,8,7]=>1011001
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,6,1]=>[8,5,3,4,6,7,1,2]=>[1,8,2,5,3,4,7,6]=>0101001
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,8,1]=>[8,5,3,4,6,1,2,7]=>[1,7,2,5,3,4,8,6]=>0101001
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[8,5,3,4,2,6,7,1]=>[8,5,1,4,2,3,7,6]=>1101001
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,8,1]=>[8,5,3,4,1,2,6,7]=>[1,6,2,5,3,4,8,7]=>0101001
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,8,1]=>[8,5,3,2,4,6,1,7]=>[7,4,1,5,2,3,8,6]=>1101001
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>[5,4,1,6,2,3,8,7]=>1101001
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,8,1]=>[8,5,3,1,2,4,6,7]=>[1,5,2,6,3,4,8,7]=>0101001
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,6,7,1]=>[8,5,2,3,4,6,7,1]=>[8,1,2,5,3,4,7,6]=>1001001
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,6,8,1]=>[8,5,2,3,4,6,1,7]=>[7,1,2,5,3,4,8,6]=>1001001
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>[4,1,2,6,3,5,8,7]=>1001001
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>[1,2,3,6,4,5,8,7]=>0001001
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[8,4,5,6,7,3,2,1]=>[8,7,6,1,2,3,5,4]=>1110001
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[8,4,5,6,7,1,2,3]=>[1,2,8,3,4,5,7,6]=>0010001
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[8,4,5,6,3,2,1,7]=>[7,6,5,1,2,3,8,4]=>1110001
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,8,1]=>[8,4,5,6,2,1,3,7]=>[6,1,7,2,3,4,8,5]=>1010001
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,8,1]=>[8,4,5,6,1,2,3,7]=>[1,2,7,3,4,5,8,6]=>0010001
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[8,4,5,3,6,2,7,1]=>[8,6,4,1,2,3,7,5]=>1110001
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>[8,4,5,3,6,2,1,7]=>[7,6,4,1,2,3,8,5]=>1110001
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,8,1]=>[8,4,5,3,6,1,2,7]=>[1,7,5,2,3,4,8,6]=>0110001
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,7,1]=>[8,4,5,3,2,6,7,1]=>[8,5,4,1,2,3,7,6]=>1110001
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,8,1]=>[8,4,5,2,3,6,1,7]=>[7,1,5,2,3,4,8,6]=>1010001
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,8,1]=>[8,4,5,2,3,1,6,7]=>[6,1,5,2,3,4,8,7]=>1010001
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,8,1]=>[8,4,5,1,2,3,6,7]=>[1,2,6,3,4,5,8,7]=>0010001
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,5,6,1]=>[8,4,3,5,6,7,2,1]=>[8,7,3,1,2,4,6,5]=>1110001
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[8,4,3,5,6,7,1,2]=>[1,8,4,2,3,5,7,6]=>0110001
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,7,1]=>[8,4,3,5,6,2,7,1]=>[8,6,3,1,2,4,7,5]=>1110001
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,8,1]=>[8,4,3,5,6,2,1,7]=>[7,6,3,1,2,4,8,5]=>1110001
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,8,1]=>[8,4,3,5,6,1,2,7]=>[1,7,4,2,3,5,8,6]=>0110001
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,8,1]=>[8,4,3,5,2,6,1,7]=>[7,5,3,1,2,4,8,6]=>1110001
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,1,2,5,7,6]=>1110001
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,7,1]=>[8,4,2,3,5,6,7,1]=>[8,1,4,2,3,5,7,6]=>1010001
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,5,7,8,1]=>[8,4,2,3,5,1,6,7]=>[6,1,4,2,3,5,8,7]=>1010001
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>[1,2,5,3,4,6,8,7]=>0010001
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,6,1]=>[8,3,4,5,6,7,2,1]=>[8,7,1,2,3,4,6,5]=>1100001
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,6,1]=>[8,3,4,5,6,7,1,2]=>[1,8,2,3,4,5,7,6]=>0100001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,5,7,1]=>[8,3,4,5,6,2,7,1]=>[8,6,1,2,3,4,7,5]=>1100001
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,8,1]=>[8,3,4,5,6,2,1,7]=>[7,6,1,2,3,4,8,5]=>1100001
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>[8,3,4,5,6,1,2,7]=>[1,7,2,3,4,5,8,6]=>0100001
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>[8,3,4,5,2,1,6,7]=>[6,5,1,2,3,4,8,7]=>1100001
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,7,8,1]=>[8,3,4,5,1,2,6,7]=>[1,6,2,3,4,5,8,7]=>0100001
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,8,1]=>[8,3,4,2,5,6,1,7]=>[7,4,1,2,3,5,8,6]=>1100001
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,8,1]=>[8,3,4,1,2,5,6,7]=>[1,5,2,3,4,6,8,7]=>0100001
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,7,1]=>[8,3,2,4,5,6,7,1]=>[8,3,1,2,4,5,7,6]=>1100001
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,6,8,1]=>[8,3,2,4,5,6,1,7]=>[7,3,1,2,4,5,8,6]=>1100001
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>[4,3,1,2,5,6,8,7]=>1100001
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>[1,4,2,3,5,6,8,7]=>0100001
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,7,1]=>[8,2,3,4,5,6,7,1]=>[8,1,2,3,4,5,7,6]=>1000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,8,1]=>[8,2,3,4,5,6,1,7]=>[7,1,2,3,4,5,8,6]=>1000001
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,8,1]=>[8,2,3,4,5,1,6,7]=>[6,1,2,3,4,5,8,7]=>1000001
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[8,2,3,4,1,5,6,7]=>[5,1,2,3,4,6,8,7]=>1000001
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,8,1]=>[8,2,3,1,4,5,6,7]=>[4,1,2,3,5,6,8,7]=>1000001
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>[3,1,2,4,5,6,8,7]=>1000001
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,8,7]=>0000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>1111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[1,8,7,6,5,4,2,3]=>0111110
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,1,2]=>[7,8,6,5,4,2,3,1]=>[8,1,7,6,5,4,2,3]=>1011110
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,1,2]=>[7,8,6,5,4,2,1,3]=>[7,1,8,6,5,4,2,3]=>1011110
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[7,8,6,5,4,1,2,3]=>[1,2,8,7,6,5,3,4]=>0011110
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,1,2]=>[7,8,6,5,3,2,4,1]=>[8,6,1,7,5,4,2,3]=>1101110
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>[7,8,6,5,3,2,1,4]=>[7,6,1,8,5,4,2,3]=>1101110
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[7,8,6,5,3,1,2,4]=>[1,7,2,8,6,5,3,4]=>0101110
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,1,2]=>[7,8,6,5,2,1,3,4]=>[6,1,2,8,7,5,3,4]=>1001110
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[7,8,6,5,1,2,3,4]=>[1,2,3,8,7,6,4,5]=>0001110
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,1,2]=>[7,8,6,4,5,3,2,1]=>[8,7,6,1,5,4,2,3]=>1110110
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[1,8,7,2,6,5,3,4]=>0110110
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[7,8,6,4,3,5,2,1]=>[8,7,5,1,6,4,2,3]=>1110110
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,1,2]=>[7,8,6,4,3,2,5,1]=>[8,6,5,1,7,4,2,3]=>1110110
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,1,2]=>[7,8,6,4,3,2,1,5]=>[7,6,5,1,8,4,2,3]=>1110110
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,1,2]=>[7,8,6,4,1,2,3,5]=>[1,2,7,3,8,6,4,5]=>0010110
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,1,2]=>[7,8,6,3,4,5,2,1]=>[8,7,1,2,6,5,3,4]=>1100110
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[7,8,6,3,4,5,1,2]=>[1,8,2,3,7,6,4,5]=>0100110
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,1,2]=>[7,8,6,3,4,2,5,1]=>[8,6,1,2,7,5,3,4]=>1100110
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>[7,8,6,3,4,1,2,5]=>[1,7,2,3,8,6,4,5]=>0100110
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,1,2]=>[7,8,6,3,2,4,5,1]=>[8,5,1,2,7,6,3,4]=>1100110
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,1,2]=>[7,8,6,3,2,1,4,5]=>[6,5,1,2,8,7,3,4]=>1100110
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>[7,8,6,3,1,2,4,5]=>[1,6,2,3,8,7,4,5]=>0100110
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,1,2]=>[7,8,6,2,3,1,4,5]=>[6,1,2,3,8,7,4,5]=>1000110
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,1,2]=>[7,8,6,2,1,3,4,5]=>[5,1,2,3,8,7,4,6]=>1000110
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[7,8,6,1,2,3,4,5]=>[1,2,3,4,8,7,5,6]=>0000110
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,1,4,2,3]=>1111010
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,1,2]=>[7,8,5,6,4,2,1,3]=>[7,1,8,6,2,5,3,4]=>1011010
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[7,8,5,6,3,4,2,1]=>[8,7,1,6,2,5,3,4]=>1101010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[1,8,2,7,3,6,4,5]=>0101010
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[7,8,5,6,3,2,1,4]=>[7,6,1,8,2,5,3,4]=>1101010
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[7,8,5,6,3,1,2,4]=>[1,7,2,8,3,6,4,5]=>0101010
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[7,8,5,6,2,3,4,1]=>[8,1,2,7,3,6,4,5]=>1001010
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[7,8,5,6,2,3,1,4]=>[7,1,2,8,3,6,4,5]=>1001010
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[7,8,5,6,2,1,3,4]=>[6,1,2,8,3,7,4,5]=>1001010
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[7,8,5,6,1,2,3,4]=>[1,2,3,8,4,7,5,6]=>0001010
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,1,2]=>[7,8,5,4,6,1,2,3]=>[1,2,8,6,3,7,4,5]=>0011010
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,1,2]=>[7,8,5,4,3,6,2,1]=>[8,7,5,4,1,6,2,3]=>1111010
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[1,8,6,5,2,7,3,4]=>0111010
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,1,2]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,1,7,2,3]=>1111010
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,1,8,2,3]=>1111010
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,8,1,2]=>[7,8,5,4,3,1,2,6]=>[1,7,6,5,2,8,3,4]=>0111010
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,1,2]=>[7,8,5,4,2,1,3,6]=>[6,1,7,5,2,8,3,4]=>1011010
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>[7,8,5,4,1,2,3,6]=>[1,2,7,6,3,8,4,5]=>0011010
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,1,2]=>[7,8,5,3,4,6,2,1]=>[8,7,1,5,2,6,3,4]=>1101010
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[7,8,5,3,4,6,1,2]=>[1,8,2,6,3,7,4,5]=>0101010
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[7,8,5,3,4,1,2,6]=>[1,7,2,6,3,8,4,5]=>0101010
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>[7,8,5,3,2,1,4,6]=>[6,5,1,7,2,8,3,4]=>1101010
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[7,8,5,3,1,2,4,6]=>[1,6,2,7,3,8,4,5]=>0101010
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,1,2]=>[7,8,5,2,3,4,1,6]=>[7,1,2,6,3,8,4,5]=>1001010
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,1,2]=>[7,8,5,2,1,3,4,6]=>[5,1,2,7,3,8,4,6]=>1001010
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>[7,8,5,1,2,3,4,6]=>[1,2,3,7,4,8,5,6]=>0001010
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[7,8,4,5,6,3,1,2]=>[1,8,7,2,3,6,4,5]=>0110010
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,1,2]=>[7,8,4,5,6,2,3,1]=>[8,1,7,2,3,6,4,5]=>1010010
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[7,8,4,5,3,6,1,2]=>[1,8,6,2,3,7,4,5]=>0110010
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,1,2]=>[7,8,4,5,3,2,1,6]=>[7,6,5,1,2,8,3,4]=>1110010
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,1,2]=>[7,8,4,5,2,3,1,6]=>[7,1,6,2,3,8,4,5]=>1010010
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,8,1,2]=>[7,8,4,5,1,2,3,6]=>[1,2,7,3,4,8,5,6]=>0010010
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,5,6,1,2]=>[1,8,5,2,3,7,4,6]=>0110010
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,7,1,2]=>[7,8,4,3,5,2,6,1]=>[8,6,4,1,2,7,3,5]=>1110010
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,1,2]=>[7,8,4,3,2,5,6,1]=>[8,5,4,1,2,7,3,6]=>1110010
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,1,2]=>[7,8,4,3,2,5,1,6]=>[7,5,4,1,2,8,3,6]=>1110010
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[7,8,4,3,2,1,5,6]=>[6,5,4,1,2,8,3,7]=>1110010
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,1,2]=>[7,8,4,3,1,2,5,6]=>[1,6,5,2,3,8,4,7]=>0110010
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,7,1,2]=>[7,8,4,2,3,5,6,1]=>[8,1,5,2,3,7,4,6]=>1010010
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[7,8,4,2,1,3,5,6]=>[5,1,6,2,3,8,4,7]=>1010010
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>[7,8,4,1,2,3,5,6]=>[1,2,6,3,4,8,5,7]=>0010010
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,1,2]=>[7,8,3,4,5,6,2,1]=>[8,7,1,2,3,6,4,5]=>1100010
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[7,8,3,4,5,6,1,2]=>[1,8,2,3,4,7,5,6]=>0100010
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>[7,8,3,4,5,2,1,6]=>[7,6,1,2,3,8,4,5]=>1100010
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,8,1,2]=>[7,8,3,4,5,1,2,6]=>[1,7,2,3,4,8,5,6]=>0100010
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>[7,8,3,4,2,5,6,1]=>[8,5,1,2,3,7,4,6]=>1100010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>[7,8,3,4,2,5,1,6]=>[7,5,1,2,3,8,4,6]=>1100010
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,8,1,2]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,3,8,4,7]=>1100010
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[7,8,3,4,1,2,5,6]=>[1,6,2,3,4,8,5,7]=>0100010
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[7,8,3,2,4,5,6,1]=>[8,4,1,2,3,7,5,6]=>1100010
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[7,8,3,2,4,1,5,6]=>[6,4,1,2,3,8,5,7]=>1100010
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[7,8,3,2,1,4,5,6]=>[5,4,1,2,3,8,6,7]=>1100010
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[7,8,3,1,2,4,5,6]=>[1,5,2,3,4,8,6,7]=>0100010
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[7,8,2,3,4,5,6,1]=>[8,1,2,3,4,7,5,6]=>1000010
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,1,2]=>[7,8,2,3,4,5,1,6]=>[7,1,2,3,4,8,5,6]=>1000010
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[7,8,2,3,4,1,5,6]=>[6,1,2,3,4,8,5,7]=>1000010
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>[7,8,2,3,1,4,5,6]=>[5,1,2,3,4,8,6,7]=>1000010
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>[7,8,2,1,3,4,5,6]=>[4,1,2,3,5,8,6,7]=>1000010
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[7,8,1,2,3,4,5,6]=>[1,2,3,4,5,8,6,7]=>0000010
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>1111110
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,1,3]=>[7,6,8,5,4,3,1,2]=>[1,8,7,6,5,3,2,4]=>0111110
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,1,3]=>[7,6,8,5,4,2,3,1]=>[8,1,7,6,5,3,2,4]=>1011110
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[7,1,8,6,5,3,2,4]=>1011110
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,1,3]=>[7,6,8,5,4,1,2,3]=>[1,2,8,7,6,4,3,5]=>0011110
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[7,6,8,5,3,4,2,1]=>[8,7,1,6,5,3,2,4]=>1101110
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[7,6,8,5,3,4,1,2]=>[1,8,2,7,6,4,3,5]=>0101110
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[7,6,8,5,3,2,1,4]=>[7,6,1,8,5,3,2,4]=>1101110
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>[7,6,8,5,2,3,1,4]=>[7,1,2,8,6,4,3,5]=>1001110
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>[7,6,8,5,2,1,3,4]=>[6,1,2,8,7,4,3,5]=>1001110
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[7,6,8,5,1,2,3,4]=>[1,2,3,8,7,5,4,6]=>0001110
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,1,3]=>[7,6,8,4,5,3,2,1]=>[8,7,6,1,5,3,2,4]=>1110110
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,1,3]=>[7,6,8,4,5,2,3,1]=>[8,1,7,2,6,4,3,5]=>1010110
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[7,1,8,2,6,4,3,5]=>1010110
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,1,3]=>[7,6,8,4,3,5,2,1]=>[8,7,5,1,6,3,2,4]=>1110110
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,1,3]=>[7,6,8,4,3,2,5,1]=>[8,6,5,1,7,3,2,4]=>1110110
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,1,3]=>[7,6,8,4,3,2,1,5]=>[7,6,5,1,8,3,2,4]=>1110110
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,1,3]=>[7,6,8,4,2,3,5,1]=>[8,1,6,2,7,4,3,5]=>1010110
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,1,3]=>[7,6,8,4,2,3,1,5]=>[7,1,6,2,8,4,3,5]=>1010110
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,2,1,3]=>[7,6,8,4,1,2,3,5]=>[1,2,7,3,8,5,4,6]=>0010110
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,1,3]=>[7,6,8,3,4,2,5,1]=>[8,6,1,2,7,4,3,5]=>1100110
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,2,1,3]=>[7,6,8,3,2,1,4,5]=>[6,5,1,2,8,4,3,7]=>1100110
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,2,1,3]=>[7,6,8,3,1,2,4,5]=>[1,6,2,3,8,5,4,7]=>0100110
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,1,3]=>[7,6,8,2,3,4,5,1]=>[8,1,2,3,7,5,4,6]=>1000110
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,2,1,3]=>[7,6,8,2,3,4,1,5]=>[7,1,2,3,8,5,4,6]=>1000110
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,2,1,3]=>[7,6,8,2,3,1,4,5]=>[6,1,2,3,8,5,4,7]=>1000110
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[7,6,8,1,2,3,4,5]=>[1,2,3,4,8,6,5,7]=>0000110
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>1111110
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[7,6,5,8,4,3,1,2]=>[1,8,7,6,4,3,2,5]=>0111110
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>[7,6,5,8,4,2,3,1]=>[8,1,7,6,4,3,2,5]=>1011110
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[7,6,5,8,4,2,1,3]=>[7,1,8,6,4,3,2,5]=>1011110
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>[7,6,5,8,4,1,2,3]=>[1,2,8,7,5,4,3,6]=>0011110
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[7,6,5,8,3,4,2,1]=>[8,7,1,6,4,3,2,5]=>1101110
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[7,6,5,8,3,4,1,2]=>[1,8,2,7,5,4,3,6]=>0101110
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[7,6,5,8,3,2,4,1]=>[8,6,1,7,4,3,2,5]=>1101110
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[7,6,1,8,4,3,2,5]=>1101110
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[7,6,5,8,3,1,2,4]=>[1,7,2,8,5,4,3,6]=>0101110
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[7,6,5,8,2,3,4,1]=>[8,1,2,7,5,4,3,6]=>1001110
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[7,6,5,8,1,2,3,4]=>[1,2,3,8,6,5,4,7]=>0001110
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>1111110
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[7,6,5,4,8,3,1,2]=>[1,8,7,5,4,3,2,6]=>0111110
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>[7,6,5,4,8,2,3,1]=>[8,1,7,5,4,3,2,6]=>1011110
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[7,6,5,4,8,2,1,3]=>[7,1,8,5,4,3,2,6]=>1011110
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[7,6,5,4,8,1,2,3]=>[1,2,8,6,5,4,3,7]=>0011110
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>1111110
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,3,8,1,2]=>[1,8,6,5,4,3,2,7]=>0111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>1111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>1111110
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>[1,7,6,5,4,3,2,8]=>0111110
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[7,6,5,4,2,3,8,1]=>[8,1,6,5,4,3,2,7]=>1011110
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,2,3,1,8]=>[7,1,6,5,4,3,2,8]=>1011110
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>[1,2,7,6,5,4,3,8]=>0011110
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,1,7]=>[7,6,5,3,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>1101110
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,1,8]=>[7,6,5,3,4,1,2,8]=>[1,7,2,6,5,4,3,8]=>0101110
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,1,7]=>[7,6,5,3,2,4,8,1]=>[8,5,1,6,4,3,2,7]=>1101110
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,1,8]=>[7,6,5,3,2,4,1,8]=>[7,5,1,6,4,3,2,8]=>1101110
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[6,5,1,7,4,3,2,8]=>1101110
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[7,6,5,2,3,4,8,1]=>[8,1,2,6,5,4,3,7]=>1001110
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,1,8]=>[7,6,5,2,3,4,1,8]=>[7,1,2,6,5,4,3,8]=>1001110
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,1,8]=>[7,6,5,2,3,1,4,8]=>[6,1,2,7,5,4,3,8]=>1001110
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>[1,2,3,7,6,5,4,8]=>0001110
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[7,6,4,5,8,3,2,1]=>[8,7,6,1,4,3,2,5]=>1110110
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,1,5]=>[7,6,4,5,8,3,1,2]=>[1,8,7,2,5,4,3,6]=>0110110
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,1,5]=>[7,6,4,5,8,2,3,1]=>[8,1,7,2,5,4,3,6]=>1010110
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,1,5]=>[7,6,4,5,8,2,1,3]=>[7,1,8,2,5,4,3,6]=>1010110
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,1,5]=>[7,6,4,5,8,1,2,3]=>[1,2,8,3,6,5,4,7]=>0010110
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[7,6,4,5,3,8,2,1]=>[8,7,5,1,4,3,2,6]=>1110110
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>1110110
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,1,8]=>[7,6,4,5,3,2,1,8]=>[7,6,5,1,4,3,2,8]=>1110110
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[7,6,4,5,2,3,1,8]=>[7,1,6,2,5,4,3,8]=>1010110
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,1,7]=>[7,6,4,3,5,2,8,1]=>[8,6,4,1,5,3,2,7]=>1110110
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,2,5,1,8]=>[7,5,4,1,6,3,2,8]=>1110110
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>[1,6,5,2,7,4,3,8]=>0110110
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>[7,6,4,2,3,5,8,1]=>[8,1,5,2,6,4,3,7]=>1010110
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,1,8]=>[7,6,4,2,3,5,1,8]=>[7,1,5,2,6,4,3,8]=>1010110
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>[5,1,6,2,7,4,3,8]=>1010110
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[7,6,3,4,5,8,2,1]=>[8,7,1,2,5,4,3,6]=>1100110
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>[7,6,3,4,5,8,1,2]=>[1,8,2,3,6,5,4,7]=>0100110
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,1,7]=>[7,6,3,4,5,2,8,1]=>[8,6,1,2,5,4,3,7]=>1100110
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,1,2,5,4,3,8]=>1100110
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,1,7]=>[7,6,3,2,4,5,8,1]=>[8,4,1,2,6,5,3,7]=>1100110
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,6,2,1,8]=>[7,6,3,2,4,5,1,8]=>[7,4,1,2,6,5,3,8]=>1100110
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>[5,4,1,2,7,6,3,8]=>1100110
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[7,6,2,3,4,5,8,1]=>[8,1,2,3,6,5,4,7]=>1000110
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,1,8]=>[7,6,2,3,4,5,1,8]=>[7,1,2,3,6,5,4,8]=>1000110
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,1,8]=>[7,6,2,3,4,1,5,8]=>[6,1,2,3,7,5,4,8]=>1000110
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,2,1,8]=>[7,6,2,3,1,4,5,8]=>[5,1,2,3,7,6,4,8]=>1000110
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>[1,2,3,4,7,6,5,8]=>0000110
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,1,3,2,4]=>1111010
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[7,5,6,8,4,3,1,2]=>[1,8,7,6,2,4,3,5]=>0111010
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[7,5,6,8,4,2,3,1]=>[8,1,7,6,2,4,3,5]=>1011010
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[7,5,6,8,4,2,1,3]=>[7,1,8,6,2,4,3,5]=>1011010
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,1,4]=>[7,5,6,8,4,1,2,3]=>[1,2,8,7,3,5,4,6]=>0011010
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[7,5,6,8,3,4,1,2]=>[1,8,2,7,3,5,4,6]=>0101010
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[7,5,6,8,3,1,2,4]=>[1,7,2,8,3,5,4,6]=>0101010
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[7,5,6,8,2,3,1,4]=>[7,1,2,8,3,5,4,6]=>1001010
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>[7,5,6,8,2,1,3,4]=>[6,1,2,8,3,5,4,7]=>1001010
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[7,5,6,8,1,2,3,4]=>[1,2,3,8,4,6,5,7]=>0001010
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>1111010
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,3,1,5]=>[7,5,6,4,8,2,3,1]=>[8,1,7,5,2,4,3,6]=>1011010
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,2,3,1,6]=>[7,5,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>1111010
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>1111010
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,1,8]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,1,3,2,8]=>1111010
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,1,8]=>[7,5,6,4,3,1,2,8]=>[1,7,6,5,2,4,3,8]=>0111010
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>[7,5,6,4,2,3,1,8]=>[7,1,6,5,2,4,3,8]=>1011010
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[7,5,6,3,4,8,1,2]=>[1,8,2,6,3,5,4,7]=>0101010
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,3,1,7]=>[7,5,6,3,4,2,8,1]=>[8,6,1,5,2,4,3,7]=>1101010
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[7,5,6,3,4,2,1,8]=>[7,6,1,5,2,4,3,8]=>1101010
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[7,5,6,3,4,1,2,8]=>[1,7,2,6,3,5,4,8]=>0101010
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[7,5,6,3,1,2,4,8]=>[1,6,2,7,3,5,4,8]=>0101010
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,1,8]=>[7,5,6,2,3,4,1,8]=>[7,1,2,6,3,5,4,8]=>1001010
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,1,8]=>[7,5,6,2,1,3,4,8]=>[5,1,2,7,3,6,4,8]=>1001010
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,1,8]=>[7,5,6,1,2,3,4,8]=>[1,2,3,7,4,6,5,8]=>0001010
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,1,4,2,5]=>1111010
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,4,1,5]=>[7,5,4,6,8,2,1,3]=>[7,1,8,4,2,5,3,6]=>1011010
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[7,5,4,6,8,1,2,3]=>[1,2,8,5,3,6,4,7]=>0011010
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>1111010
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,1,8]=>[7,5,4,6,3,2,1,8]=>[7,6,5,3,1,4,2,8]=>1111010
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,4,1,7]=>[7,5,4,6,2,3,8,1]=>[8,1,6,4,2,5,3,7]=>1011010
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,2,4,1,8]=>[7,5,4,6,2,3,1,8]=>[7,1,6,4,2,5,3,8]=>1011010
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[7,5,4,6,2,1,3,8]=>[6,1,7,4,2,5,3,8]=>1011010
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>[7,5,4,6,1,2,3,8]=>[1,2,7,5,3,6,4,8]=>0011010
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,1,6]=>[7,5,4,3,6,8,2,1]=>[8,7,4,3,1,5,2,6]=>1111010
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[7,5,4,3,6,8,1,2]=>[1,8,5,4,2,6,3,7]=>0111010
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,1,8]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,1,5,2,8]=>1111010
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,1,7]=>[7,5,4,2,3,6,8,1]=>[8,1,5,4,2,6,3,7]=>1011010
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,1,8]=>[7,5,4,2,3,6,1,8]=>[7,1,5,4,2,6,3,8]=>1011010
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,2,7,1,8]=>[7,5,4,2,3,1,6,8]=>[6,1,5,4,2,7,3,8]=>1011010
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>[7,5,3,4,6,8,2,1]=>[8,7,1,4,2,5,3,6]=>1101010
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[7,5,3,4,6,8,1,2]=>[1,8,2,5,3,6,4,7]=>0101010
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,5,1,7]=>[7,5,3,4,6,2,8,1]=>[8,6,1,4,2,5,3,7]=>1101010
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>[7,5,3,4,6,1,2,8]=>[1,7,2,5,3,6,4,8]=>0101010
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,1,4,2,6,3,8]=>1101010
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[7,5,3,4,1,2,6,8]=>[1,6,2,5,3,7,4,8]=>0101010
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,6,1,7]=>[7,5,3,2,4,6,8,1]=>[8,4,1,5,2,6,3,7]=>1101010
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>[7,5,3,2,4,6,1,8]=>[7,4,1,5,2,6,3,8]=>1101010
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,7,1,8]=>[7,5,3,2,4,1,6,8]=>[6,4,1,5,2,7,3,8]=>1101010
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>[5,4,1,6,2,7,3,8]=>1101010
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>[1,5,2,6,3,7,4,8]=>0101010
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,1,8]=>[7,5,2,3,1,4,6,8]=>[5,1,2,6,3,7,4,8]=>1001010
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>[1,2,3,6,4,7,5,8]=>0001010
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[7,4,5,6,8,3,2,1]=>[8,7,6,1,2,4,3,5]=>1110010
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>[7,4,5,6,8,1,2,3]=>[1,2,8,3,4,6,5,7]=>0010010
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,4,1,6]=>[7,4,5,6,3,8,2,1]=>[8,7,5,1,2,4,3,6]=>1110010
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[7,4,5,6,3,2,8,1]=>[8,6,5,1,2,4,3,7]=>1110010
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[7,4,5,6,3,2,1,8]=>[7,6,5,1,2,4,3,8]=>1110010
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,4,1,7]=>[7,4,5,6,2,3,8,1]=>[8,1,6,2,3,5,4,7]=>1010010
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[7,4,5,6,1,2,3,8]=>[1,2,7,3,4,6,5,8]=>0010010
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,1,2,5,3,7]=>1110010
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>[7,4,5,3,6,2,1,8]=>[7,6,4,1,2,5,3,8]=>1110010
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>[7,4,5,2,3,6,1,8]=>[7,1,5,2,3,6,4,8]=>1010010
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,1,8]=>[7,4,5,2,1,3,6,8]=>[5,1,6,2,3,7,4,8]=>1010010
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,1,8]=>[7,4,5,1,2,3,6,8]=>[1,2,6,3,4,7,5,8]=>0010010
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[7,4,3,5,2,6,1,8]=>[7,5,3,1,2,6,4,8]=>1110010
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[7,4,3,5,2,1,6,8]=>[6,5,3,1,2,7,4,8]=>1110010
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,5,6,1,7]=>[7,4,3,2,5,6,8,1]=>[8,4,3,1,2,6,5,7]=>1110010
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>[5,4,3,1,2,7,6,8]=>1110010
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,7,1,8]=>[7,4,3,1,2,5,6,8]=>[1,5,4,2,3,7,6,8]=>0110010
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,1,7]=>[7,4,2,3,5,6,8,1]=>[8,1,4,2,3,6,5,7]=>1010010
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>[1,2,5,3,4,7,6,8]=>0010010
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,1,6]=>[7,3,4,5,6,8,1,2]=>[1,8,2,3,4,6,5,7]=>0100010
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,5,1,7]=>[7,3,4,5,6,2,8,1]=>[8,6,1,2,3,5,4,7]=>1100010
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>[7,3,4,5,6,2,1,8]=>[7,6,1,2,3,5,4,8]=>1100010
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,1,8]=>[7,3,4,1,2,5,6,8]=>[1,5,2,3,4,7,6,8]=>0100010
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,1,7]=>[7,3,2,4,5,6,8,1]=>[8,3,1,2,4,6,5,7]=>1100010
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>[4,3,1,2,5,7,6,8]=>1100010
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>[1,4,2,3,5,7,6,8]=>0100010
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,1,7]=>[7,2,3,4,5,6,8,1]=>[8,1,2,3,4,6,5,7]=>1000010
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,1,8]=>[7,2,3,4,5,6,1,8]=>[7,1,2,3,4,6,5,8]=>1000010
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>[7,2,3,4,5,1,6,8]=>[6,1,2,3,4,7,5,8]=>1000010
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,1,8]=>[7,2,3,1,4,5,6,8]=>[4,1,2,3,5,7,6,8]=>1000010
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>[3,1,2,4,5,7,6,8]=>1000010
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,6,8]=>0000010
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>1111100
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,1,2,3]=>[6,7,8,5,4,3,1,2]=>[1,8,7,6,5,2,3,4]=>0111100
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,1,2,3]=>[6,7,8,5,4,2,1,3]=>[7,1,8,6,5,2,3,4]=>1011100
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[6,7,8,5,4,1,2,3]=>[1,2,8,7,6,3,4,5]=>0011100
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[6,7,8,5,3,4,1,2]=>[1,8,2,7,6,3,4,5]=>0101100
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,1,2,3]=>[6,7,8,5,3,2,4,1]=>[8,6,1,7,5,2,3,4]=>1101100
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[6,7,8,5,3,2,1,4]=>[7,6,1,8,5,2,3,4]=>1101100
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[6,7,8,5,2,3,4,1]=>[8,1,2,7,6,3,4,5]=>1001100
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>[6,7,8,5,2,1,3,4]=>[6,1,2,8,7,3,4,5]=>1001100
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[6,7,8,5,1,2,3,4]=>[1,2,3,8,7,4,5,6]=>0001100
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,1,2,3]=>[6,7,8,4,5,3,2,1]=>[8,7,6,1,5,2,3,4]=>1110100
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,1,2,3]=>[6,7,8,4,5,3,1,2]=>[1,8,7,2,6,3,4,5]=>0110100
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[6,7,8,4,5,2,3,1]=>[8,1,7,2,6,3,4,5]=>1010100
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,1,2,3]=>[6,7,8,4,5,1,2,3]=>[1,2,8,3,7,4,5,6]=>0010100
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[6,7,8,4,3,5,2,1]=>[8,7,5,1,6,2,3,4]=>1110100
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,1,2,3]=>[6,7,8,4,3,5,1,2]=>[1,8,6,2,7,3,4,5]=>0110100
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[6,7,8,4,3,2,1,5]=>[7,6,5,1,8,2,3,4]=>1110100
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,1,2,3]=>[6,7,8,4,3,1,2,5]=>[1,7,6,2,8,3,4,5]=>0110100
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[6,7,8,4,2,3,5,1]=>[8,1,6,2,7,3,4,5]=>1010100
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[6,7,8,4,2,3,1,5]=>[7,1,6,2,8,3,4,5]=>1010100
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[6,7,8,4,2,1,3,5]=>[6,1,7,2,8,3,4,5]=>1010100
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,1,2,3]=>[6,7,8,4,1,2,3,5]=>[1,2,7,3,8,4,5,6]=>0010100
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[6,7,8,3,4,5,2,1]=>[8,7,1,2,6,3,4,5]=>1100100
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>[6,7,8,3,4,2,5,1]=>[8,6,1,2,7,3,4,5]=>1100100
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[6,7,8,3,4,1,2,5]=>[1,7,2,3,8,4,5,6]=>0100100
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,1,2,3]=>[6,7,8,3,2,4,5,1]=>[8,5,1,2,7,3,4,6]=>1100100
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[6,7,8,3,2,4,1,5]=>[7,5,1,2,8,3,4,6]=>1100100
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>[6,7,8,3,2,1,4,5]=>[6,5,1,2,8,3,4,7]=>1100100
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[6,7,8,3,1,2,4,5]=>[1,6,2,3,8,4,5,7]=>0100100
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,1,2,3]=>[6,7,8,2,3,4,5,1]=>[8,1,2,3,7,4,5,6]=>1000100
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[6,7,8,2,3,4,1,5]=>[7,1,2,3,8,4,5,6]=>1000100
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[6,7,8,2,3,1,4,5]=>[6,1,2,3,8,4,5,7]=>1000100
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>[6,7,8,2,1,3,4,5]=>[5,1,2,3,8,4,6,7]=>1000100
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[6,7,8,1,2,3,4,5]=>[1,2,3,4,8,5,6,7]=>0000100
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>1111100
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,1,2,4]=>[6,7,5,8,4,3,1,2]=>[1,8,7,6,4,2,3,5]=>0111100
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,1,2,4]=>[6,7,5,8,4,2,3,1]=>[8,1,7,6,4,2,3,5]=>1011100
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,1,2,4]=>[6,7,5,8,4,2,1,3]=>[7,1,8,6,4,2,3,5]=>1011100
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,1,2,4]=>[6,7,5,8,3,4,2,1]=>[8,7,1,6,4,2,3,5]=>1101100
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[6,7,5,8,3,4,1,2]=>[1,8,2,7,5,3,4,6]=>0101100
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,1,2,4]=>[6,7,5,8,3,2,4,1]=>[8,6,1,7,4,2,3,5]=>1101100
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[6,7,5,8,3,2,1,4]=>[7,6,1,8,4,2,3,5]=>1101100
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[6,7,5,8,3,1,2,4]=>[1,7,2,8,5,3,4,6]=>0101100
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,1,2,4]=>[6,7,5,8,2,3,4,1]=>[8,1,2,7,5,3,4,6]=>1001100
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[6,7,5,8,2,3,1,4]=>[7,1,2,8,5,3,4,6]=>1001100
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[6,7,5,8,2,1,3,4]=>[6,1,2,8,5,3,4,7]=>1001100
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[6,7,5,8,1,2,3,4]=>[1,2,3,8,6,4,5,7]=>0001100
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>1111100
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,1,2,5]=>[6,7,5,4,8,2,1,3]=>[7,1,8,5,4,2,3,6]=>1011100
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>1111100
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1,2,7]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>1111100
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>1111100
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,1,2,8]=>[6,7,5,4,3,1,2,8]=>[1,7,6,5,4,2,3,8]=>0111100
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,1,2,8]=>[6,7,5,4,2,3,1,8]=>[7,1,6,5,4,2,3,8]=>1011100
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,1,2,7]=>[6,7,5,3,2,4,8,1]=>[8,5,1,6,4,2,3,7]=>1101100
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,1,2,8]=>[6,7,5,2,3,4,1,8]=>[7,1,2,6,5,3,4,8]=>1001100
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,1,2,8]=>[6,7,5,2,1,3,4,8]=>[5,1,2,7,6,3,4,8]=>1001100
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,1,2,8]=>[6,7,5,1,2,3,4,8]=>[1,2,3,7,6,4,5,8]=>0001100
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[6,7,4,5,8,3,2,1]=>[8,7,6,1,4,2,3,5]=>1110100
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,1,2,5]=>[6,7,4,5,8,3,1,2]=>[1,8,7,2,5,3,4,6]=>0110100
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,1,2,5]=>[6,7,4,5,8,2,3,1]=>[8,1,7,2,5,3,4,6]=>1010100
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[6,7,4,5,8,1,2,3]=>[1,2,8,3,6,4,5,7]=>0010100
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[6,7,4,5,3,8,2,1]=>[8,7,5,1,4,2,3,6]=>1110100
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,1,2,6]=>[6,7,4,5,3,8,1,2]=>[1,8,6,2,5,3,4,7]=>0110100
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,1,2,8]=>[6,7,4,5,3,2,1,8]=>[7,6,5,1,4,2,3,8]=>1110100
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[6,7,4,5,2,3,8,1]=>[8,1,6,2,5,3,4,7]=>1010100
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,1,2,8]=>[6,7,4,5,2,3,1,8]=>[7,1,6,2,5,3,4,8]=>1010100
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,1,2,8]=>[6,7,4,3,5,2,1,8]=>[7,6,4,1,5,2,3,8]=>1110100
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,1,2,7]=>[6,7,4,3,2,5,8,1]=>[8,5,4,1,6,2,3,7]=>1110100
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,1,2,8]=>[6,7,4,3,2,5,1,8]=>[7,5,4,1,6,2,3,8]=>1110100
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,1,2,8]=>[6,7,4,3,2,1,5,8]=>[6,5,4,1,7,2,3,8]=>1110100
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,1,2,8]=>[6,7,4,2,3,5,1,8]=>[7,1,5,2,6,3,4,8]=>1010100
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>[6,7,4,2,3,1,5,8]=>[6,1,5,2,7,3,4,8]=>1010100
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>[6,7,3,4,5,1,2,8]=>[1,7,2,3,6,4,5,8]=>0100100
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,1,2,8]=>[6,7,3,4,1,2,5,8]=>[1,6,2,3,7,4,5,8]=>0100100
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>[6,7,3,2,4,5,8,1]=>[8,4,1,2,6,3,5,7]=>1100100
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,1,2,8]=>[6,7,3,2,4,1,5,8]=>[6,4,1,2,7,3,5,8]=>1100100
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,1,2,8]=>[6,7,3,1,2,4,5,8]=>[1,5,2,3,7,4,6,8]=>0100100
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[6,7,2,3,4,5,8,1]=>[8,1,2,3,6,4,5,7]=>1000100
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,1,2,8]=>[6,7,2,3,4,5,1,8]=>[7,1,2,3,6,4,5,8]=>1000100
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,1,2,8]=>[6,7,2,3,4,1,5,8]=>[6,1,2,3,7,4,5,8]=>1000100
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[6,7,1,2,3,4,5,8]=>[1,2,3,4,7,5,6,8]=>0000100
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>1111100
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,1,3,4]=>[6,5,7,8,4,3,1,2]=>[1,8,7,6,3,2,4,5]=>0111100
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,1,3,4]=>[6,5,7,8,4,2,1,3]=>[7,1,8,6,3,2,4,5]=>1011100
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[6,5,7,8,3,4,1,2]=>[1,8,2,7,4,3,5,6]=>0101100
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>[6,5,7,8,3,2,1,4]=>[7,6,1,8,3,2,4,5]=>1101100
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[6,5,7,8,3,1,2,4]=>[1,7,2,8,4,3,5,6]=>0101100
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[6,5,7,8,2,1,3,4]=>[6,1,2,8,4,3,5,7]=>1001100
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[6,5,7,8,1,2,3,4]=>[1,2,3,8,5,4,6,7]=>0001100
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>1111100
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,1,3,5]=>[6,5,7,4,8,3,1,2]=>[1,8,7,5,3,2,4,6]=>0111100
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[6,5,7,4,8,2,3,1]=>[8,1,7,5,3,2,4,6]=>1011100
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,1,3,5]=>[6,5,7,4,8,2,1,3]=>[7,1,8,5,3,2,4,6]=>1011100
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[6,5,7,4,8,1,2,3]=>[1,2,8,6,4,3,5,7]=>0011100
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[6,5,7,4,3,8,1,2]=>[1,8,6,5,3,2,4,7]=>0111100
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>1111100
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,3,8]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>1111100
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,1,3,8]=>[6,5,7,4,2,1,3,8]=>[6,1,7,5,3,2,4,8]=>1011100
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,1,3,7]=>[6,5,7,3,4,2,8,1]=>[8,6,1,5,3,2,4,7]=>1101100
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,1,3,8]=>[6,5,7,3,4,1,2,8]=>[1,7,2,6,4,3,5,8]=>0101100
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,2,1,3,7]=>[6,5,7,3,2,4,8,1]=>[8,5,1,6,3,2,4,7]=>1101100
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,1,3,8]=>[6,5,7,3,2,4,1,8]=>[7,5,1,6,3,2,4,8]=>1101100
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,1,3,8]=>[6,5,7,2,3,4,1,8]=>[7,1,2,6,4,3,5,8]=>1001100
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,1,3,8]=>[6,5,7,1,2,3,4,8]=>[1,2,3,7,5,4,6,8]=>0001100
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>1111100
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,1,4,5]=>[6,5,4,7,8,3,1,2]=>[1,8,7,4,3,2,5,6]=>0111100
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[6,5,4,7,8,1,2,3]=>[1,2,8,5,4,3,6,7]=>0011100
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>1111100
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>1111100
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1,4,8]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>1111100
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>1111100
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[6,5,4,3,7,8,1,2]=>[1,8,5,4,3,2,6,7]=>0111100
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>1111100
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>1111100
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>[6,5,4,3,7,1,2,8]=>[1,7,5,4,3,2,6,8]=>0111100
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>1111100
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1,6,8]=>[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,1,6,8]=>1111100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>[1,6,5,4,3,2,7,8]=>0111100
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,1,6,7]=>[6,5,4,2,3,7,8,1]=>[8,1,5,4,3,2,6,7]=>1011100
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>[5,1,6,4,3,2,7,8]=>1011100
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>[1,2,6,5,4,3,7,8]=>0011100
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[6,5,3,4,7,8,2,1]=>[8,7,1,4,3,2,5,6]=>1101100
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[6,5,3,4,7,2,8,1]=>[8,6,1,4,3,2,5,7]=>1101100
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,1,4,3,2,7,8]=>1101100
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,1,6,7]=>[6,5,3,2,4,7,8,1]=>[8,4,1,5,3,2,6,7]=>1101100
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,1,6,8]=>[6,5,3,2,4,7,1,8]=>[7,4,1,5,3,2,6,8]=>1101100
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>[5,4,1,6,3,2,7,8]=>1101100
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[6,5,2,3,4,7,8,1]=>[8,1,2,5,4,3,6,7]=>1001100
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[6,5,1,2,3,4,7,8]=>[1,2,3,6,5,4,7,8]=>0001100
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[6,4,5,7,8,3,2,1]=>[8,7,6,1,3,2,4,5]=>1110100
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[6,4,5,7,8,1,2,3]=>[1,2,8,3,5,4,6,7]=>0010100
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,1,4,6]=>[6,4,5,7,3,8,1,2]=>[1,8,6,2,4,3,5,7]=>0110100
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[6,4,5,7,3,2,8,1]=>[8,6,5,1,3,2,4,7]=>1110100
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[6,4,5,7,2,3,8,1]=>[8,1,6,2,4,3,5,7]=>1010100
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>[6,4,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>1110100
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,1,7,8]=>[6,4,5,2,1,3,7,8]=>[5,1,6,2,4,3,7,8]=>1010100
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[6,4,3,5,7,8,1,2]=>[1,8,4,2,5,3,6,7]=>0110100
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[6,4,3,5,7,2,8,1]=>[8,6,3,1,4,2,5,7]=>1110100
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,1,5,8]=>[6,4,3,5,7,1,2,8]=>[1,7,4,2,5,3,6,8]=>0110100
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>[6,4,3,5,1,2,7,8]=>[1,6,4,2,5,3,7,8]=>0110100
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,1,5,2,7,8]=>1110100
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>[5,4,3,1,6,2,7,8]=>1110100
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>[1,5,4,2,6,3,7,8]=>0110100
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,2,5,1,6,8]=>[6,4,2,3,5,7,1,8]=>[7,1,4,2,5,3,6,8]=>1010100
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>[4,1,5,2,6,3,7,8]=>1010100
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>[1,2,5,3,6,4,7,8]=>0010100
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,1,5,6]=>[6,3,4,5,7,8,2,1]=>[8,7,1,2,4,3,5,6]=>1100100
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[6,3,4,5,7,8,1,2]=>[1,8,2,3,5,4,6,7]=>0100100
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,1,5,7]=>[6,3,4,5,7,2,8,1]=>[8,6,1,2,4,3,5,7]=>1100100
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,1,5,8]=>[6,3,4,5,7,1,2,8]=>[1,7,2,3,5,4,6,8]=>0100100
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[6,3,4,5,2,7,8,1]=>[8,5,1,2,4,3,6,7]=>1100100
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>[6,3,4,5,2,7,1,8]=>[7,5,1,2,4,3,6,8]=>1100100
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,1,6,8]=>[6,3,2,4,5,7,1,8]=>[7,3,1,2,5,4,6,8]=>1100100
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,1,7,8]=>[6,3,2,1,4,5,7,8]=>[4,3,1,2,6,5,7,8]=>1100100
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,1,7,8]=>[6,3,1,2,4,5,7,8]=>[1,4,2,3,6,5,7,8]=>0100100
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,1,6,7]=>[6,2,3,4,5,7,8,1]=>[8,1,2,3,5,4,6,7]=>1000100
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[6,2,3,4,5,7,1,8]=>[7,1,2,3,5,4,6,8]=>1000100
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,1,7,8]=>[6,2,3,4,5,1,7,8]=>[6,1,2,3,5,4,7,8]=>1000100
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,1,7,8]=>[6,2,3,1,4,5,7,8]=>[4,1,2,3,6,5,7,8]=>1000100
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>0000100
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>1111000
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[5,6,7,8,4,3,1,2]=>[1,8,7,6,2,3,4,5]=>0111000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[5,6,7,8,4,2,3,1]=>[8,1,7,6,2,3,4,5]=>1011000
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[5,6,7,8,4,2,1,3]=>[7,1,8,6,2,3,4,5]=>1011000
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[5,6,7,8,4,1,2,3]=>[1,2,8,7,3,4,5,6]=>0011000
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[5,6,7,8,3,4,2,1]=>[8,7,1,6,2,3,4,5]=>1101000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[5,6,7,8,3,4,1,2]=>[1,8,2,7,3,4,5,6]=>0101000
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[5,6,7,8,3,2,4,1]=>[8,6,1,7,2,3,4,5]=>1101000
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[5,6,7,8,3,2,1,4]=>[7,6,1,8,2,3,4,5]=>1101000
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[5,6,7,8,3,1,2,4]=>[1,7,2,8,3,4,5,6]=>0101000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[5,6,7,8,2,3,4,1]=>[8,1,2,7,3,4,5,6]=>1001000
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[5,6,7,8,2,3,1,4]=>[7,1,2,8,3,4,5,6]=>1001000
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[5,6,7,8,2,1,3,4]=>[6,1,2,8,3,4,5,7]=>1001000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4]=>[1,2,3,8,4,5,6,7]=>0001000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>1111000
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>[5,6,7,4,8,2,1,3]=>[7,1,8,5,2,3,4,6]=>1011000
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>[5,6,7,4,8,1,2,3]=>[1,2,8,6,3,4,5,7]=>0011000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,1,2,3,6]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>1111000
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,1,2,3,7]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>1111000
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>1111000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[5,6,7,4,2,3,8,1]=>[8,1,6,5,2,3,4,7]=>1011000
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>[5,6,7,4,1,2,3,8]=>[1,2,7,6,3,4,5,8]=>0011000
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,1,2,3,6]=>[5,6,7,3,4,8,1,2]=>[1,8,2,6,3,4,5,7]=>0101000
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,1,2,3,7]=>[5,6,7,3,4,2,8,1]=>[8,6,1,5,2,3,4,7]=>1101000
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[5,6,7,3,1,2,4,8]=>[1,6,2,7,3,4,5,8]=>0101000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>[5,6,7,2,3,4,8,1]=>[8,1,2,6,3,4,5,7]=>1001000
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,1,2,3,8]=>[5,6,7,2,3,4,1,8]=>[7,1,2,6,3,4,5,8]=>1001000
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,1,2,3,8]=>[5,6,7,2,3,1,4,8]=>[6,1,2,7,3,4,5,8]=>1001000
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[5,6,7,2,1,3,4,8]=>[5,1,2,7,3,4,6,8]=>1001000
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[5,6,7,1,2,3,4,8]=>[1,2,3,7,4,5,6,8]=>0001000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>1111000
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[5,6,4,7,8,3,1,2]=>[1,8,7,4,2,3,5,6]=>0111000
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>[5,6,4,7,8,1,2,3]=>[1,2,8,5,3,4,6,7]=>0011000
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[5,6,4,7,3,8,1,2]=>[1,8,6,4,2,3,5,7]=>0111000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>[5,6,4,7,2,3,8,1]=>[8,1,6,4,2,3,5,7]=>1011000
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,1,2,4,8]=>[5,6,4,7,2,3,1,8]=>[7,1,6,4,2,3,5,8]=>1011000
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[5,6,4,7,1,2,3,8]=>[1,2,7,5,3,4,6,8]=>0011000
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>[5,6,4,3,7,8,1,2]=>[1,8,5,4,2,3,6,7]=>0111000
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,1,2,5,8]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>1111000
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,2,7,8]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>1111000
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,1,2,6,7]=>[5,6,4,2,3,7,8,1]=>[8,1,5,4,2,3,6,7]=>1011000
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[5,6,4,2,1,3,7,8]=>[5,1,6,4,2,3,7,8]=>1011000
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[5,6,3,4,7,8,1,2]=>[1,8,2,5,3,4,6,7]=>0101000
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>[5,6,3,4,7,2,8,1]=>[8,6,1,4,2,3,5,7]=>1101000
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,1,2,5,8]=>[5,6,3,4,7,1,2,8]=>[1,7,2,5,3,4,6,8]=>0101000
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,1,2,6,8]=>[5,6,3,4,2,7,1,8]=>[7,5,1,4,2,3,6,8]=>1101000
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7,8]=>[1,6,2,5,3,4,7,8]=>0101000
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,1,2,7,8]=>[5,6,3,2,4,1,7,8]=>[6,4,1,5,2,3,7,8]=>1101000
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[5,6,3,2,1,4,7,8]=>[5,4,1,6,2,3,7,8]=>1101000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,1,2,6,7]=>[5,6,2,3,4,7,8,1]=>[8,1,2,5,3,4,6,7]=>1001000
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,1,2,7,8]=>[5,6,2,3,4,1,7,8]=>[6,1,2,5,3,4,7,8]=>1001000
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[5,6,1,2,3,4,7,8]=>[1,2,3,6,4,5,7,8]=>0001000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>1111000
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>[5,4,6,7,8,3,1,2]=>[1,8,7,3,2,4,5,6]=>0111000
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>[5,4,6,7,8,1,2,3]=>[1,2,8,4,3,5,6,7]=>0011000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>1111000
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[5,4,6,7,3,8,1,2]=>[1,8,6,3,2,4,5,7]=>0111000
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1,3,4,8]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>1111000
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,1,3,4,8]=>[5,4,6,7,3,1,2,8]=>[1,7,6,3,2,4,5,8]=>0111000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[5,4,6,7,2,3,8,1]=>[8,1,6,3,2,4,5,7]=>1011000
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,1,3,4,8]=>[5,4,6,7,2,1,3,8]=>[6,1,7,3,2,4,5,8]=>1011000
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[5,4,6,7,1,2,3,8]=>[1,2,7,4,3,5,6,8]=>0011000
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[5,4,6,3,7,8,1,2]=>[1,8,5,3,2,4,6,7]=>0111000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>1111000
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>1111000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>1111000
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,1,3,7,8]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>1111000
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[5,4,6,3,1,2,7,8]=>[1,6,5,3,2,4,7,8]=>0111000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,1,3,6,7]=>[5,4,6,2,3,7,8,1]=>[8,1,5,3,2,4,6,7]=>1011000
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,1,3,6,8]=>[5,4,6,2,3,7,1,8]=>[7,1,5,3,2,4,6,8]=>1011000
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[5,4,6,2,1,3,7,8]=>[5,1,6,3,2,4,7,8]=>1011000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>1111000
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[5,4,3,6,7,8,1,2]=>[1,8,4,3,2,5,6,7]=>0111000
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>1111000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>1111000
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>1111000
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,1,4,7,8]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>1111000
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[5,4,3,6,1,2,7,8]=>[1,6,4,3,2,5,7,8]=>0111000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>1111000
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>1111000
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>1111000
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>0111000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,1,5,6,7]=>[5,4,2,3,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>1011000
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,2,1,5,6,8]=>[5,4,2,3,6,7,1,8]=>[7,1,4,3,2,5,6,8]=>1011000
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>1011000
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>0011000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,1,4,5,6]=>[5,3,4,6,7,8,2,1]=>[8,7,1,3,2,4,5,6]=>1101000
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[5,3,4,6,7,8,1,2]=>[1,8,2,4,3,5,6,7]=>0101000
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,1,4,6,8]=>[5,3,4,6,2,7,1,8]=>[7,5,1,3,2,4,6,8]=>1101000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,1,5,6,7]=>[5,3,4,2,6,7,8,1]=>[8,4,1,3,2,5,6,7]=>1101000
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>1101000
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[5,3,4,1,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>0101000
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,1,4,2,6,7,8]=>1101000
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>[1,4,2,5,3,6,7,8]=>0101000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[5,2,3,4,6,7,8,1]=>[8,1,2,4,3,5,6,7]=>1001000
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,1,5,6,8]=>[5,2,3,4,6,7,1,8]=>[7,1,2,4,3,5,6,8]=>1001000
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,1,5,7,8]=>[5,2,3,4,6,1,7,8]=>[6,1,2,4,3,5,7,8]=>1001000
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>1001000
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>[5,2,3,1,4,6,7,8]=>[4,1,2,5,3,6,7,8]=>1001000
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>1110000
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[4,5,6,7,8,3,1,2]=>[1,8,7,2,3,4,5,6]=>0110000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[4,5,6,7,8,2,3,1]=>[8,1,7,2,3,4,5,6]=>1010000
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[4,5,6,7,8,2,1,3]=>[7,1,8,2,3,4,5,6]=>1010000
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[4,5,6,7,8,1,2,3]=>[1,2,8,3,4,5,6,7]=>0010000
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>1110000
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[4,5,6,7,3,8,1,2]=>[1,8,6,2,3,4,5,7]=>0110000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>1110000
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>1110000
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[4,5,6,7,3,1,2,8]=>[1,7,6,2,3,4,5,8]=>0110000
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[4,5,6,7,2,3,8,1]=>[8,1,6,2,3,4,5,7]=>1010000
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[4,5,6,7,2,3,1,8]=>[7,1,6,2,3,4,5,8]=>1010000
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[4,5,6,7,2,1,3,8]=>[6,1,7,2,3,4,5,8]=>1010000
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[4,5,6,7,1,2,3,8]=>[1,2,7,3,4,5,6,8]=>0010000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,1,2,3,5,6]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>1110000
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>1110000
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,1,2,3,6,7]=>[4,5,6,3,2,7,8,1]=>[8,5,4,1,2,3,6,7]=>1110000
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3,7,8]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>1110000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,1,2,3,6,7]=>[4,5,6,2,3,7,8,1]=>[8,1,5,2,3,4,6,7]=>1010000
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,1,2,3,7,8]=>[4,5,6,2,1,3,7,8]=>[5,1,6,2,3,4,7,8]=>1010000
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[4,5,6,1,2,3,7,8]=>[1,2,6,3,4,5,7,8]=>0010000
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>[4,5,3,6,7,8,1,2]=>[1,8,4,2,3,5,6,7]=>0110000
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>1110000
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>1110000
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>1110000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[4,5,2,3,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>1010000
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,1,2,5,6,8]=>[4,5,2,3,6,7,1,8]=>[7,1,4,2,3,5,6,8]=>1010000
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,1,2,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>1010000
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[4,5,1,2,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>0010000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>1110000
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[4,3,5,6,7,8,1,2]=>[1,8,3,2,4,5,6,7]=>0110000
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,1,3,4,5,8]=>[4,3,5,6,7,1,2,8]=>[1,7,3,2,4,5,6,8]=>0110000
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,1,3,4,6,7]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>1110000
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>1110000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>1110000
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>1110000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>1110000
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,1,4,5,6,8]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>1110000
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1,4,5,7,8]=>[4,3,2,5,6,1,7,8]=>[6,3,2,1,4,5,7,8]=>1110000
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>1110000
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[4,2,3,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>1010000
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,1,4,5,6,8]=>[4,2,3,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>1010000
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>1010000
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>1010000
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>1010000
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,2,3,4,5,6]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>1100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[3,4,5,6,7,8,1,2]=>[1,8,2,3,4,5,6,7]=>0100000
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>1100000
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,2,3,4,5,8]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>1100000
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[3,4,5,6,7,1,2,8]=>[1,7,2,3,4,5,6,8]=>0100000
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,5,1,2,3,4,6,7]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>1100000
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>1100000
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[5,6,1,2,3,4,7,8]=>[3,4,5,6,1,2,7,8]=>[1,6,2,3,4,5,7,8]=>0100000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,2,3,5,6,7]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>1100000
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[7,4,1,2,3,5,6,8]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>1100000
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,4,1,2,3,5,7,8]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>1100000
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>1100000
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[3,4,5,1,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>0100000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>1100000
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>1100000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>1100000
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>1100000
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>0100000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>1100000
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>1100000
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,2,1,3,4,5,7,8]=>[3,2,4,5,6,1,7,8]=>[6,2,1,3,4,5,7,8]=>1100000
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>1100000
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>1100000
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>1000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>1000000
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>1000000
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>1000000
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>1000000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>1000000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>10000000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,9,8]=>00000001
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>100000000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>11000000
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>[3,1,2,4,5,6,7,9,8]=>10000001
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>000000001
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,10,1]=>[10,2,1,3,4,5,6,7,8,9]=>110000000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[3,4,2,5,6,7,8,9,1]=>[9,3,1,2,4,5,6,7,8]=>11000000
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,1,4,5,6,7,8]=>[4,2,3,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>10100000
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>10000000000
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[11,2,1,3,4,5,6,7,8,9,10]=>[3,2,4,5,6,7,8,9,10,11,1]=>[11,2,1,3,4,5,6,7,8,9,10]=>1100000000
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,1,2,4,5,6,7,8,9]=>[3,4,2,5,6,7,8,9,10,1]=>[10,3,1,2,4,5,6,7,8,9]=>110000000
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[9,4,1,2,3,5,6,7,8]=>[3,4,5,2,6,7,8,9,1]=>[9,4,1,2,3,5,6,7,8]=>11000000
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[11,3,1,2,4,5,6,7,8,9,10]=>[3,4,2,5,6,7,8,9,10,11,1]=>[11,3,1,2,4,5,6,7,8,9,10]=>1100000000
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[10,4,1,2,3,5,6,7,8,9]=>[3,4,5,2,6,7,8,9,10,1]=>[10,4,1,2,3,5,6,7,8,9]=>110000000
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,1,6,7,8,9]=>[6,2,3,4,5,7,8,9,10,1]=>[10,1,2,3,5,4,6,7,8,9]=>100010000
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[9,6,1,2,3,4,5,7,8]=>[3,4,5,6,7,2,8,9,1]=>[9,6,1,2,3,4,5,7,8]=>11000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,2,3,4,5,6,8,9,1]=>[9,2,3,4,5,6,1,7,8]=>[7,1,2,3,4,5,6,9,8]=>10000001
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,9,1]=>[9,6,1,2,3,4,5,7,8]=>[1,2,3,4,7,5,6,9,8]=>00001001
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[10,6,1,2,3,4,5,7,8,9]=>[3,4,5,6,7,2,8,9,10,1]=>[10,6,1,2,3,4,5,7,8,9]=>110000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>11000000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,1,8]=>[8,2,3,4,5,6,7,9,1]=>[9,1,2,3,4,5,7,6,8]=>10000010
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,1,2]=>[1,9,2,3,4,5,6,7,8]=>01000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,9,1]=>[9,2,3,4,5,6,7,1,8]=>[8,1,2,3,4,5,6,9,7]=>10000001
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,7,8]=>00000010
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>[1,2,3,4,5,8,6,9,7]=>00000101
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[10,7,1,2,3,4,5,6,8,9]=>[3,4,5,6,7,8,2,9,10,1]=>[10,7,1,2,3,4,5,6,8,9]=>110000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>11000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,8,1]=>[9,2,3,4,5,6,7,8,1]=>[9,1,2,3,4,5,6,8,7]=>10000001
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,1,3,4,5,6,7]=>[4,3,5,6,7,8,9,1,2]=>[1,9,3,2,4,5,6,7,8]=>01100000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,2,3,4,5,6,7,9,10,1]=>[10,2,3,4,5,6,7,1,8,9]=>[8,1,2,3,4,5,6,7,10,9]=>100000001
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,8,7]=>00000011
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,1,2]=>[1,10,2,3,4,5,6,7,8,9]=>010000000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,10,1]=>[10,2,3,4,5,6,7,8,1,9]=>[9,1,2,3,4,5,6,7,10,8]=>100000001
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[9,10,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,8,9]=>000000010
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>110000000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,3,4,5,6,7,8,9,1]=>[10,1,2,3,4,5,6,7,9,8]=>100000001
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,9,8]=>000000011
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>11111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>[1,8,7,6,5,4,3,2,9]=>01111110
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,4,6,3,7,2,8,1,9]=>[8,6,4,2,1,3,5,7,9]=>[5,1,6,2,7,3,8,4,9]=>10101010
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,1,9]=>[8,2,3,4,5,6,7,1,9]=>[8,1,2,3,4,5,7,6,9]=>10000010
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,1,9]=>[8,2,3,1,4,5,6,7,9]=>[4,1,2,3,5,6,8,7,9]=>10000010
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,8,7,9]=>00000010
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,1,2,9]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>11111100
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,1,3,9]=>[7,6,8,5,4,3,2,1,9]=>[8,7,6,5,4,2,1,3,9]=>11111100
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,3,2,1,4,9]=>[7,6,5,8,4,3,2,1,9]=>[8,7,6,5,3,2,1,4,9]=>11111100
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,3,2,1,6,9]=>[7,6,5,4,3,8,2,1,9]=>[8,7,5,4,3,2,1,6,9]=>11111100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,1,7,9]=>[7,6,5,4,3,2,8,1,9]=>[8,6,5,4,3,2,1,7,9]=>11111100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>11111100
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>00000100
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,1,2,3,9]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>11111000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>11111000
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>00001000
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,1,2,7,8,9]=>[5,6,4,3,2,1,7,8,9]=>[6,5,4,3,1,2,7,8,9]=>11110000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,1,3,5,7,9]=>[5,4,6,3,7,2,8,1,9]=>[8,6,4,2,1,3,5,7,9]=>11110000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>00010000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[7,5,3,1,2,4,6,8,9]=>[4,5,3,6,2,7,1,8,9]=>[7,5,3,1,2,4,6,8,9]=>11100000
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,1,2,6,7,8,9]=>[4,5,3,2,1,6,7,8,9]=>[5,4,3,1,2,6,7,8,9]=>11100000
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>10100000
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>00100000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[3,4,5,6,7,8,1,2,9]=>[1,8,2,3,4,5,6,7,9]=>01000000
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[6,7,1,2,3,4,5,8,9]=>[3,4,5,6,7,1,2,8,9]=>[1,7,2,3,4,5,6,8,9]=>01000000
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1,2,3,6,7,8,9]=>[3,4,5,2,1,6,7,8,9]=>[5,4,1,2,3,6,7,8,9]=>11000000
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[5,3,1,2,4,6,7,8,9]=>[3,4,2,5,1,6,7,8,9]=>[5,3,1,2,4,6,7,8,9]=>11000000
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,2,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>11000000
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]=>01000000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1,3,4,5,6,7,9]=>[3,2,4,5,6,7,8,1,9]=>[8,2,1,3,4,5,6,7,9]=>11000000
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>01000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>10000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>10000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>10000000
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>10000000
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>10000000
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>10000000
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,3,2]=>01111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[8,1,9,7,6,5,4,3,2]=>10111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>[8,7,1,9,6,5,4,3,2]=>11011111
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>[8,7,6,1,9,5,4,3,2]=>11101111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>[8,7,6,5,1,9,4,3,2]=>11110111
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>[8,7,6,5,4,1,9,3,2]=>11111011
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,1,9,2]=>11111101
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>[1,2,9,8,7,6,5,4,3]=>00111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>[9,1,10,8,7,6,5,4,3,2]=>101111111
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[8,6,7,9,5,4,3,2,1]=>[9,8,7,6,5,2,3,1,4]=>[8,1,2,9,7,6,5,4,3]=>10011111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,1,10,7,6,5,4,3,2]=>110111111
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[8,7,5,6,9,4,3,2,1]=>[9,8,7,6,3,4,2,1,5]=>[8,7,1,2,9,6,5,4,3]=>11001111
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,1,10,3,2]=>111111011
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,1,10,2]=>111111101
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>1111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,10,9,8,7,6,5,4,3]=>001111111
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,9,8,7,6,5,4]=>00011111
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,1,2,10]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>111111100
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,9,8,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,3,1,11,2]=>1111111101
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[11,10,12,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,2,1,3]=>[11,1,12,10,9,8,7,6,5,4,3,2]=>10111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,10,9,8,7,6,5,4]=>000111111
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,2,1,3,10]=>[8,7,9,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,2,1,3,10]=>111111100
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,10,9,8,7,6,5,4,3,2,12,1]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[11,10,9,8,7,6,5,4,3,1,12,2]=>11111111101
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>00001111
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,3,2,1,4,10]=>[8,7,6,9,5,4,3,2,1,10]=>[9,8,7,6,5,3,2,1,4,10]=>111111100
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,2,1,3,11]=>[9,8,10,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,2,1,3,11]=>1111111100
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,10,9,8,7,6,5]=>000011111
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,3,2,1,4,11]=>[9,8,7,10,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,3,2,1,4,11]=>1111111100
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,9,1]=>[9,6,5,4,3,2,1,7,8]=>[7,6,5,4,3,1,2,9,8]=>11111001
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,8,7,5,4,3,2,1,6,10]=>[8,7,6,5,4,9,3,2,1,10]=>[9,8,7,5,4,3,2,1,6,10]=>111111100
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,9,8,7,6]=>00000111
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,8,6,5,4,3,2,1,7,10]=>[8,7,6,5,4,3,9,2,1,10]=>[9,8,6,5,4,3,2,1,7,10]=>111111100
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,10,9,8,7,6]=>000001111
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,5,4,3,2,1,6,11]=>[9,8,7,6,5,10,4,3,2,1,11]=>[10,9,8,7,5,4,3,2,1,6,11]=>1111111100
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,9,10,1]=>[10,7,6,5,4,3,2,1,8,9]=>[8,7,6,5,4,3,1,2,10,9]=>111111001
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,7,6,5,4,3,2,1,8,10]=>[8,7,6,5,4,3,2,9,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>111111100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[10,9,8,6,5,4,3,2,1,7,11]=>[9,8,7,6,5,4,10,3,2,1,11]=>[10,9,8,6,5,4,3,2,1,7,11]=>1111111100
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,3,1]=>[9,1,8,7,6,5,4,3,2]=>10111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,5,4,3,2,1]=>[9,8,7,6,5,3,4,2,1]=>[9,8,1,7,6,5,4,3,2]=>11011111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,5,4,3,2,1]=>[9,8,7,6,5,3,4,1,2]=>[1,9,2,8,7,6,5,4,3]=>01011111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,1,6,5,4,3,2]=>11101111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,1,5,4,3,2]=>11110111
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,2,1]=>[9,8,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,7,6]=>10000011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,3,1]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,3,2]=>11111101
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,3,1]=>[9,7,8,6,5,4,3,1,2]=>[1,9,8,7,6,5,2,4,3]=>01111101
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,3,1]=>[9,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,9,6,8,7]=>00000101
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,3,4,1]=>[9,6,7,8,1,2,3,4,5]=>[1,2,3,4,9,5,6,8,7]=>00001001
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,6,7,1]=>[9,3,4,5,6,7,8,1,2]=>[1,9,2,3,4,5,6,8,7]=>01000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>11111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,2,3]=>01111110
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,3,4,1,2]=>[8,9,6,7,4,5,2,3,1]=>[9,1,8,2,7,3,6,4,5]=>10101010
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,1,2]=>[8,9,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,6,7]=>10000010
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,2,3]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>11111100
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,6,7,8]=>00000100
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,2,3,4]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>11111000
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[6,7,8,9,1,2,3,4,5]=>[1,2,3,4,9,5,6,7,8]=>00001000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,2,3,4,5]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>11110000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,1,2,3,4,5]=>[5,6,7,8,9,3,4,2,1]=>[9,8,1,7,2,3,4,5,6]=>11010000
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,1,2,3,4,5]=>[5,6,7,8,9,2,3,4,1]=>[9,1,2,8,3,4,5,6,7]=>10010000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[5,6,7,8,9,1,2,3,4]=>[1,2,3,9,4,5,6,7,8]=>00010000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,2,3,4,5,6]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>11100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[9,7,8,1,2,3,4,5,6]=>[4,5,6,7,8,9,2,3,1]=>[9,1,8,2,3,4,5,6,7]=>10100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[4,5,6,7,8,9,1,2,3]=>[1,2,9,3,4,5,6,7,8]=>00100000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,3,1]=>[10,1,9,8,7,6,5,4,3,2]=>101111111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,1,6,5,4,3,2]=>111101111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,5,3,2,1]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,1,5,4,3,2]=>111110111
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,9,8,7]=>000000111
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,9,2,1]=>[10,9,2,3,4,5,6,7,8,1]=>[10,1,2,3,4,5,6,9,8,7]=>100000011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,3,1]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,3,2]=>111111101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,3,1]=>[10,8,9,6,7,4,5,2,3,1]=>[10,1,9,2,8,3,7,4,6,5]=>101010101
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,2,3,4,1]=>[10,7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,10,6,7,9,8]=>000001001
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,2,3,4,5,1]=>[10,6,7,8,9,1,2,3,4,5]=>[1,2,3,4,10,5,6,7,9,8]=>000010001
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,2,3,4,5,6,7,8,1]=>[10,3,4,5,6,7,8,9,1,2]=>[1,10,2,3,4,5,6,7,9,8]=>010000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>111111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,2,3]=>011111110
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,1,2,3]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>111111100
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[8,9,10,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,7,8,9]=>000000100
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,1,2,3,4]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>111111000
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[7,8,9,10,1,2,3,4,5,6]=>[1,2,3,4,5,10,6,7,8,9]=>000001000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,1,2,3,4,5]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>111110000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,1,2,3,4,5]=>[6,7,8,9,10,4,5,2,3,1]=>[10,1,9,2,8,3,4,5,6,7]=>101010000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[10,6,7,8,9,1,2,3,4,5]=>[6,7,8,9,10,2,3,4,5,1]=>[10,1,2,3,9,4,5,6,7,8]=>100010000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[6,7,8,9,10,1,2,3,4,5]=>[1,2,3,4,10,5,6,7,8,9]=>000010000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,2,3,4,5,6]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>111100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[10,7,8,9,1,2,3,4,5,6]=>[5,6,7,8,9,10,2,3,4,1]=>[10,1,2,9,3,4,5,6,7,8]=>100100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[5,6,7,8,9,10,1,2,3,4]=>[1,2,3,10,4,5,6,7,8,9]=>000100000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>111000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,1,2,3]=>[1,2,10,3,4,5,6,7,8,9]=>001000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1,3]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>11111110
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,1,4]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>11111110
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,1,5]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>11111110
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,3,2,1,6]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>11111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>11111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>11111110
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,1,3]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>111111110
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>111111110
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,3,2,1,5]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>111111110
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>111111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>111111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>111111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>111111110
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,1,2,7,8,9,10]=>[5,6,4,3,2,1,7,8,9,10]=>[6,5,4,3,1,2,7,8,9,10]=>111100000
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,1,2,8,9,10]=>[6,7,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,1,2,8,9,10]=>111110000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1,2]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>1111111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>[1,9,8,7,6,5,4,3,2,10]=>011111110
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>010000000
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>100000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,1,3]=>[8,7,9,6,5,4,3,1,2]=>[1,9,8,7,6,5,3,2,4]=>01111110
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,1,7,8]=>[7,6,5,4,3,2,8,9,1]=>[9,6,5,4,3,2,1,7,8]=>11111100
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,1,3,4]=>[7,6,8,9,5,4,3,2,1]=>[9,8,7,6,5,2,1,3,4]=>11111100
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>000000010
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>100000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>1000000000
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>001000000
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>000100000
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>000010000
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>000001000
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>000000100
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,1,3]=>[8,7,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,7,6,8]=>00000110
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,1,3,4]=>[7,6,8,9,1,2,3,4,5]=>[1,2,3,4,9,6,5,7,8]=>00001100
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,2,1,3,4,5]=>[6,5,7,8,9,1,2,3,4]=>[1,2,3,9,5,4,6,7,8]=>00011000
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,1,3,4,5,6]=>[5,4,6,7,8,9,1,2,3]=>[1,2,9,4,3,5,6,7,8]=>00110000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,1,2,8]=>[7,8,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,1,2,8]=>11111100
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,9,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,9,1,2]=>[1,9,7,6,5,4,3,2,8]=>01111110
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>111111000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[8,7,9,1,2,3,4,5,6]=>[4,5,6,7,8,9,2,1,3]=>[8,1,9,2,3,4,5,6,7]=>10100000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>100000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>100000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>100000000
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,9,1,2,3]=>[7,8,9,2,1,3,4,5,6]=>[5,1,2,3,4,9,6,7,8]=>10000100
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>100000000
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>100000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,7,4,3,2,1]=>[9,8,7,6,4,3,5,2,1]=>[9,8,6,1,7,5,4,3,2]=>11101111
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>111111100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,4,3,2,1,10,11]=>[9,8,7,6,5,4,3,2,1,10,11]=>[9,8,7,6,5,4,3,2,1,10,11]=>1111111100
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>[6,1,7,2,8,3,9,4,10,5]=>101010101
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[10,8,6,4,2,1,3,5,7,9]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>111110000
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>10101010101
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[10,11,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,11,9,10]=>0000000010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[10,7,6,5,4,3,2,1,8,9]=>[8,7,6,5,4,3,2,9,10,1]=>[10,7,6,5,4,3,2,1,8,9]=>111111100
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,5,4,3,2,1,6,7,8]=>[6,5,4,3,2,7,8,9,1]=>[9,5,4,3,2,1,6,7,8]=>11111000
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>0000000010
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,2,1,3]=>[9,8,10,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,3,2,4]=>011111110
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[3,4,5,6,7,8,9,10,11,1,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>0100000000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>111110000
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,7,6,8,5,4,3,2,1]=>[9,8,7,6,5,3,2,4,1]=>[9,7,1,8,6,5,4,3,2]=>11011111
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>111100000
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>111000000
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[10,2,3,4,5,6,7,8,9,11,1]=>[11,2,3,4,5,6,7,8,9,1,10]=>[10,1,2,3,4,5,6,7,8,11,9]=>1000000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,8,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,9,8,7,6,5,4,3,2,1,10]=>1111111110
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[8,3,4,5,6,7,9,1,2]=>[8,9,2,3,4,5,6,1,7]=>[8,1,2,3,4,5,9,6,7]=>10000010
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,1,8,2]=>11111101
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[3,4,5,6,7,8,9,1,2,10]=>[1,9,2,3,4,5,6,7,8,10]=>010000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[11,10,1,2,3,4,5,6,7,8,9]=>[3,4,5,6,7,8,9,10,11,2,1]=>[11,10,1,2,3,4,5,6,7,8,9]=>1100000000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[9,8,4,1,2,3,5,6,7]=>[4,5,6,3,7,8,9,2,1]=>[9,8,4,1,2,3,5,6,7]=>11100000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10,8,7,6,5,4,3,2,1,9,11]=>[9,8,7,6,5,4,3,2,10,1,11]=>[10,8,7,6,5,4,3,2,1,9,11]=>1111111100
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,1,6,4,3,2]=>11110111
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,1,2,9]=>[8,9,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,1,2,9]=>111111100
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,1,2,3,4,5]=>[5,6,7,8,9,3,2,1,4]=>[8,7,1,9,2,3,4,5,6]=>11010000
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,1,2,8]=>[7,8,2,3,4,5,6,9,1]=>[9,1,2,3,4,7,5,6,8]=>10000100
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1]=>[9,7,5,3,1,2,4,6,8]=>[1,6,2,7,3,8,4,9,5]=>01010101
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[9,1,2,3,4,5,6,8,7,10]=>100000010
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,3,1,2,4,6,8,10]=>[5,6,4,7,3,8,2,9,1,10]=>[9,7,5,3,1,2,4,6,8,10]=>111100000
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[8,5,6,7,9,1,2,3,4]=>[6,7,8,9,2,3,4,1,5]=>[8,1,2,3,9,4,5,6,7]=>10001000
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[11,10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>0000000011
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[9,8,10,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,2,1,3]=>[9,1,10,2,3,4,5,6,7,8]=>101000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,3,1,2,4,6,8]=>[5,6,4,7,3,8,2,9,1]=>[9,7,5,3,1,2,4,6,8]=>11110000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,2,3,4,5,6,7,8,9,1]=>[11,3,4,5,6,7,8,9,10,1,2]=>[1,11,2,3,4,5,6,7,8,10,9]=>0100000001
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
inverse
Description
Sends a permutation to its inverse.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
searching the database
Sorry, this map was not found in the database.