Identifier
Mp00235:
Permutations
—descent views to invisible inversion bottoms⟶
Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
=>
[1]=>[1]=>[1]=>
[1,2]=>[1,2]=>[1,2]=>0
[2,1]=>[2,1]=>[2,1]=>1
[1,2,3]=>[1,2,3]=>[1,2,3]=>00
[1,3,2]=>[1,3,2]=>[1,3,2]=>01
[2,1,3]=>[2,1,3]=>[2,1,3]=>10
[2,3,1]=>[3,2,1]=>[2,3,1]=>01
[3,1,2]=>[3,1,2]=>[3,1,2]=>01
[3,2,1]=>[2,3,1]=>[3,2,1]=>11
[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>000
[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]=>001
[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>010
[1,3,4,2]=>[1,4,3,2]=>[1,3,4,2]=>001
[1,4,2,3]=>[1,4,2,3]=>[1,4,2,3]=>001
[1,4,3,2]=>[1,3,4,2]=>[1,4,3,2]=>011
[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>100
[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]=>101
[2,3,1,4]=>[3,2,1,4]=>[2,3,1,4]=>010
[2,3,4,1]=>[4,2,3,1]=>[2,3,4,1]=>001
[2,4,1,3]=>[4,2,1,3]=>[2,4,1,3]=>001
[2,4,3,1]=>[3,2,4,1]=>[2,4,3,1]=>011
[3,1,2,4]=>[3,1,2,4]=>[3,1,2,4]=>010
[3,1,4,2]=>[3,4,1,2]=>[4,1,3,2]=>011
[3,2,1,4]=>[2,3,1,4]=>[3,2,1,4]=>110
[3,2,4,1]=>[4,3,2,1]=>[3,2,4,1]=>011
[3,4,1,2]=>[4,1,3,2]=>[3,4,1,2]=>001
[3,4,2,1]=>[2,4,3,1]=>[3,4,2,1]=>101
[4,1,2,3]=>[4,1,2,3]=>[4,1,2,3]=>001
[4,1,3,2]=>[4,3,1,2]=>[3,1,4,2]=>011
[4,2,1,3]=>[2,4,1,3]=>[4,2,1,3]=>101
[4,2,3,1]=>[3,4,2,1]=>[4,2,3,1]=>011
[4,3,1,2]=>[3,1,4,2]=>[4,3,1,2]=>011
[4,3,2,1]=>[2,3,4,1]=>[4,3,2,1]=>111
[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000
[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]=>0001
[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>0010
[1,2,4,5,3]=>[1,2,5,4,3]=>[1,2,4,5,3]=>0001
[1,2,5,3,4]=>[1,2,5,3,4]=>[1,2,5,3,4]=>0001
[1,2,5,4,3]=>[1,2,4,5,3]=>[1,2,5,4,3]=>0011
[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>0100
[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]=>0101
[1,3,4,2,5]=>[1,4,3,2,5]=>[1,3,4,2,5]=>0010
[1,3,4,5,2]=>[1,5,3,4,2]=>[1,3,4,5,2]=>0001
[1,3,5,2,4]=>[1,5,3,2,4]=>[1,3,5,2,4]=>0001
[1,3,5,4,2]=>[1,4,3,5,2]=>[1,3,5,4,2]=>0011
[1,4,2,3,5]=>[1,4,2,3,5]=>[1,4,2,3,5]=>0010
[1,4,2,5,3]=>[1,4,5,2,3]=>[1,5,2,4,3]=>0011
[1,4,3,2,5]=>[1,3,4,2,5]=>[1,4,3,2,5]=>0110
[1,4,3,5,2]=>[1,5,4,3,2]=>[1,4,3,5,2]=>0011
[1,4,5,2,3]=>[1,5,2,4,3]=>[1,4,5,2,3]=>0001
[1,4,5,3,2]=>[1,3,5,4,2]=>[1,4,5,3,2]=>0101
[1,5,2,3,4]=>[1,5,2,3,4]=>[1,5,2,3,4]=>0001
[1,5,2,4,3]=>[1,5,4,2,3]=>[1,4,2,5,3]=>0011
[1,5,3,2,4]=>[1,3,5,2,4]=>[1,5,3,2,4]=>0101
[1,5,3,4,2]=>[1,4,5,3,2]=>[1,5,3,4,2]=>0011
[1,5,4,2,3]=>[1,4,2,5,3]=>[1,5,4,2,3]=>0011
[1,5,4,3,2]=>[1,3,4,5,2]=>[1,5,4,3,2]=>0111
[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000
[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]=>1001
[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]=>1010
[2,1,4,5,3]=>[2,1,5,4,3]=>[2,1,4,5,3]=>1001
[2,1,5,3,4]=>[2,1,5,3,4]=>[2,1,5,3,4]=>1001
[2,1,5,4,3]=>[2,1,4,5,3]=>[2,1,5,4,3]=>1011
[2,3,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]=>0100
[2,3,1,5,4]=>[3,2,1,5,4]=>[2,3,1,5,4]=>0101
[2,3,4,1,5]=>[4,2,3,1,5]=>[2,3,4,1,5]=>0010
[2,3,4,5,1]=>[5,2,3,4,1]=>[2,3,4,5,1]=>0001
[2,3,5,1,4]=>[5,2,3,1,4]=>[2,3,5,1,4]=>0001
[2,3,5,4,1]=>[4,2,3,5,1]=>[2,3,5,4,1]=>0011
[2,4,1,3,5]=>[4,2,1,3,5]=>[2,4,1,3,5]=>0010
[2,4,1,5,3]=>[4,2,5,1,3]=>[2,5,1,4,3]=>0011
[2,4,3,1,5]=>[3,2,4,1,5]=>[2,4,3,1,5]=>0110
[2,4,3,5,1]=>[5,2,4,3,1]=>[2,4,3,5,1]=>0011
[2,4,5,1,3]=>[5,2,1,4,3]=>[2,4,5,1,3]=>0001
[2,4,5,3,1]=>[3,2,5,4,1]=>[2,4,5,3,1]=>0101
[2,5,1,3,4]=>[5,2,1,3,4]=>[2,5,1,3,4]=>0001
[2,5,1,4,3]=>[5,2,4,1,3]=>[2,4,1,5,3]=>0011
[2,5,3,1,4]=>[3,2,5,1,4]=>[2,5,3,1,4]=>0101
[2,5,3,4,1]=>[4,2,5,3,1]=>[2,5,3,4,1]=>0011
[2,5,4,1,3]=>[4,2,1,5,3]=>[2,5,4,1,3]=>0011
[2,5,4,3,1]=>[3,2,4,5,1]=>[2,5,4,3,1]=>0111
[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]=>0100
[3,1,2,5,4]=>[3,1,2,5,4]=>[3,1,2,5,4]=>0101
[3,1,4,2,5]=>[3,4,1,2,5]=>[4,1,3,2,5]=>0110
[3,1,4,5,2]=>[3,5,1,4,2]=>[4,5,1,3,2]=>0101
[3,1,5,2,4]=>[3,5,1,2,4]=>[5,1,3,2,4]=>0101
[3,1,5,4,2]=>[3,4,1,5,2]=>[5,4,1,3,2]=>0111
[3,2,1,4,5]=>[2,3,1,4,5]=>[3,2,1,4,5]=>1100
[3,2,1,5,4]=>[2,3,1,5,4]=>[3,2,1,5,4]=>1101
[3,2,4,1,5]=>[4,3,2,1,5]=>[3,2,4,1,5]=>0110
[3,2,4,5,1]=>[5,3,2,4,1]=>[3,2,4,5,1]=>0101
[3,2,5,1,4]=>[5,3,2,1,4]=>[3,2,5,1,4]=>0101
[3,2,5,4,1]=>[4,3,2,5,1]=>[3,2,5,4,1]=>0111
[3,4,1,2,5]=>[4,1,3,2,5]=>[3,4,1,2,5]=>0010
[3,4,1,5,2]=>[4,5,3,1,2]=>[3,5,1,4,2]=>0011
[3,4,2,1,5]=>[2,4,3,1,5]=>[3,4,2,1,5]=>1010
[3,4,2,5,1]=>[5,4,3,2,1]=>[3,4,2,5,1]=>0011
[3,4,5,1,2]=>[5,1,3,4,2]=>[3,4,5,1,2]=>0001
[3,4,5,2,1]=>[2,5,3,4,1]=>[3,4,5,2,1]=>1001
[3,5,1,2,4]=>[5,1,3,2,4]=>[3,5,1,2,4]=>0001
[3,5,1,4,2]=>[5,4,3,1,2]=>[3,4,1,5,2]=>0011
[3,5,2,1,4]=>[2,5,3,1,4]=>[3,5,2,1,4]=>1001
[3,5,2,4,1]=>[4,5,3,2,1]=>[3,5,2,4,1]=>0011
[3,5,4,1,2]=>[4,1,3,5,2]=>[3,5,4,1,2]=>0011
[3,5,4,2,1]=>[2,4,3,5,1]=>[3,5,4,2,1]=>1011
[4,1,2,3,5]=>[4,1,2,3,5]=>[4,1,2,3,5]=>0010
[4,1,2,5,3]=>[4,1,5,2,3]=>[5,1,2,4,3]=>0011
[4,1,3,2,5]=>[4,3,1,2,5]=>[3,1,4,2,5]=>0110
[4,1,3,5,2]=>[4,5,1,3,2]=>[5,1,3,4,2]=>0011
[4,1,5,2,3]=>[4,5,2,1,3]=>[5,2,4,1,3]=>0011
[4,1,5,3,2]=>[4,3,5,1,2]=>[5,3,1,4,2]=>0111
[4,2,1,3,5]=>[2,4,1,3,5]=>[4,2,1,3,5]=>1010
[4,2,1,5,3]=>[2,4,5,1,3]=>[5,2,1,4,3]=>1011
[4,2,3,1,5]=>[3,4,2,1,5]=>[4,2,3,1,5]=>0110
[4,2,3,5,1]=>[5,4,2,3,1]=>[4,2,3,5,1]=>0011
[4,2,5,1,3]=>[5,4,1,2,3]=>[4,1,5,2,3]=>0011
[4,2,5,3,1]=>[3,5,4,1,2]=>[4,1,5,3,2]=>0111
[4,3,1,2,5]=>[3,1,4,2,5]=>[4,3,1,2,5]=>0110
[4,3,1,5,2]=>[3,4,5,2,1]=>[5,2,4,3,1]=>0111
[4,3,2,1,5]=>[2,3,4,1,5]=>[4,3,2,1,5]=>1110
[4,3,2,5,1]=>[5,3,4,2,1]=>[4,3,2,5,1]=>0111
[4,3,5,1,2]=>[5,1,4,3,2]=>[4,3,5,1,2]=>0011
[4,3,5,2,1]=>[2,5,4,3,1]=>[4,3,5,2,1]=>1011
[4,5,1,2,3]=>[5,1,2,4,3]=>[4,5,1,2,3]=>0001
[4,5,1,3,2]=>[5,3,1,4,2]=>[3,1,4,5,2]=>0101
[4,5,2,1,3]=>[2,5,1,4,3]=>[4,5,2,1,3]=>1001
[4,5,2,3,1]=>[3,5,2,4,1]=>[4,5,2,3,1]=>0101
[4,5,3,1,2]=>[3,1,5,4,2]=>[4,5,3,1,2]=>0101
[4,5,3,2,1]=>[2,3,5,4,1]=>[4,5,3,2,1]=>1101
[5,1,2,3,4]=>[5,1,2,3,4]=>[5,1,2,3,4]=>0001
[5,1,2,4,3]=>[5,1,4,2,3]=>[4,1,2,5,3]=>0011
[5,1,3,2,4]=>[5,3,1,2,4]=>[3,1,5,2,4]=>0101
[5,1,3,4,2]=>[5,4,1,3,2]=>[4,1,3,5,2]=>0011
[5,1,4,2,3]=>[5,4,2,1,3]=>[4,2,5,1,3]=>0011
[5,1,4,3,2]=>[5,3,4,1,2]=>[4,3,1,5,2]=>0111
[5,2,1,3,4]=>[2,5,1,3,4]=>[5,2,1,3,4]=>1001
[5,2,1,4,3]=>[2,5,4,1,3]=>[4,2,1,5,3]=>1011
[5,2,3,1,4]=>[3,5,2,1,4]=>[5,2,3,1,4]=>0101
[5,2,3,4,1]=>[4,5,2,3,1]=>[5,2,3,4,1]=>0011
[5,2,4,1,3]=>[4,5,1,2,3]=>[5,1,4,2,3]=>0011
[5,2,4,3,1]=>[3,4,5,1,2]=>[5,1,4,3,2]=>0111
[5,3,1,2,4]=>[3,1,5,2,4]=>[5,3,1,2,4]=>0101
[5,3,1,4,2]=>[3,5,4,2,1]=>[4,2,5,3,1]=>0111
[5,3,2,1,4]=>[2,3,5,1,4]=>[5,3,2,1,4]=>1101
[5,3,2,4,1]=>[4,3,5,2,1]=>[5,3,2,4,1]=>0111
[5,3,4,1,2]=>[4,1,5,3,2]=>[5,3,4,1,2]=>0011
[5,3,4,2,1]=>[2,4,5,3,1]=>[5,3,4,2,1]=>1011
[5,4,1,2,3]=>[4,1,2,5,3]=>[5,4,1,2,3]=>0011
[5,4,1,3,2]=>[4,3,1,5,2]=>[3,1,5,4,2]=>0111
[5,4,2,1,3]=>[2,4,1,5,3]=>[5,4,2,1,3]=>1011
[5,4,2,3,1]=>[3,4,2,5,1]=>[5,4,2,3,1]=>0111
[5,4,3,1,2]=>[3,1,4,5,2]=>[5,4,3,1,2]=>0111
[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]=>1111
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>00001
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>00010
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>00001
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>00001
[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>00011
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>00100
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>00101
[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>00010
[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[1,2,4,5,6,3]=>00001
[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>00001
[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>[1,2,4,6,5,3]=>00011
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>00010
[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[1,2,6,3,5,4]=>00011
[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>00110
[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[1,2,5,4,6,3]=>00011
[1,2,5,6,3,4]=>[1,2,6,3,5,4]=>[1,2,5,6,3,4]=>00001
[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>[1,2,5,6,4,3]=>00101
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>00001
[1,2,6,3,5,4]=>[1,2,6,5,3,4]=>[1,2,5,3,6,4]=>00011
[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>00101
[1,2,6,4,5,3]=>[1,2,5,6,4,3]=>[1,2,6,4,5,3]=>00011
[1,2,6,5,3,4]=>[1,2,5,3,6,4]=>[1,2,6,5,3,4]=>00011
[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>[1,2,6,5,4,3]=>00111
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>01000
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>01001
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>01010
[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>01001
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>01001
[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>01011
[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>00100
[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>00101
[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[1,3,4,5,2,6]=>00010
[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[1,3,4,5,6,2]=>00001
[1,3,4,6,2,5]=>[1,6,3,4,2,5]=>[1,3,4,6,2,5]=>00001
[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>[1,3,4,6,5,2]=>00011
[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>00010
[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[1,3,6,2,5,4]=>00011
[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>[1,3,5,4,2,6]=>00110
[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[1,3,5,4,6,2]=>00011
[1,3,5,6,2,4]=>[1,6,3,2,5,4]=>[1,3,5,6,2,4]=>00001
[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>[1,3,5,6,4,2]=>00101
[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>00001
[1,3,6,2,5,4]=>[1,6,3,5,2,4]=>[1,3,5,2,6,4]=>00011
[1,3,6,4,2,5]=>[1,4,3,6,2,5]=>[1,3,6,4,2,5]=>00101
[1,3,6,4,5,2]=>[1,5,3,6,4,2]=>[1,3,6,4,5,2]=>00011
[1,3,6,5,2,4]=>[1,5,3,2,6,4]=>[1,3,6,5,2,4]=>00011
[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>[1,3,6,5,4,2]=>00111
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>00100
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>00101
[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[1,5,2,4,3,6]=>00110
[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[1,5,6,2,4,3]=>00101
[1,4,2,6,3,5]=>[1,4,6,2,3,5]=>[1,6,2,4,3,5]=>00101
[1,4,2,6,5,3]=>[1,4,5,2,6,3]=>[1,6,5,2,4,3]=>00111
[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>01100
[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>01101
[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[1,4,3,5,2,6]=>00110
[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[1,4,3,5,6,2]=>00101
[1,4,3,6,2,5]=>[1,6,4,3,2,5]=>[1,4,3,6,2,5]=>00101
[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>[1,4,3,6,5,2]=>00111
[1,4,5,2,3,6]=>[1,5,2,4,3,6]=>[1,4,5,2,3,6]=>00010
[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[1,4,6,2,5,3]=>00011
[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>[1,4,5,3,2,6]=>01010
[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[1,4,5,3,6,2]=>00011
[1,4,5,6,2,3]=>[1,6,2,4,5,3]=>[1,4,5,6,2,3]=>00001
[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>[1,4,5,6,3,2]=>01001
[1,4,6,2,3,5]=>[1,6,2,4,3,5]=>[1,4,6,2,3,5]=>00001
[1,4,6,2,5,3]=>[1,6,5,4,2,3]=>[1,4,5,2,6,3]=>00011
[1,4,6,3,2,5]=>[1,3,6,4,2,5]=>[1,4,6,3,2,5]=>01001
[1,4,6,3,5,2]=>[1,5,6,4,3,2]=>[1,4,6,3,5,2]=>00011
[1,4,6,5,2,3]=>[1,5,2,4,6,3]=>[1,4,6,5,2,3]=>00011
[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>[1,4,6,5,3,2]=>01011
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>00010
[1,5,2,3,6,4]=>[1,5,2,6,3,4]=>[1,6,2,3,5,4]=>00011
[1,5,2,4,3,6]=>[1,5,4,2,3,6]=>[1,4,2,5,3,6]=>00110
[1,5,2,4,6,3]=>[1,5,6,2,4,3]=>[1,6,2,4,5,3]=>00011
[1,5,2,6,3,4]=>[1,5,6,3,2,4]=>[1,6,3,5,2,4]=>00011
[1,5,2,6,4,3]=>[1,5,4,6,2,3]=>[1,6,4,2,5,3]=>00111
[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>01010
[1,5,3,2,6,4]=>[1,3,5,6,2,4]=>[1,6,3,2,5,4]=>01011
[1,5,3,4,2,6]=>[1,4,5,3,2,6]=>[1,5,3,4,2,6]=>00110
[1,5,3,4,6,2]=>[1,6,5,3,4,2]=>[1,5,3,4,6,2]=>00011
[1,5,3,6,2,4]=>[1,6,5,2,3,4]=>[1,5,2,6,3,4]=>00011
[1,5,3,6,4,2]=>[1,4,6,5,2,3]=>[1,5,2,6,4,3]=>00111
[1,5,4,2,3,6]=>[1,4,2,5,3,6]=>[1,5,4,2,3,6]=>00110
[1,5,4,2,6,3]=>[1,4,5,6,3,2]=>[1,6,3,5,4,2]=>00111
[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>[1,5,4,3,2,6]=>01110
[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>[1,5,4,3,6,2]=>00111
[1,5,4,6,2,3]=>[1,6,2,5,4,3]=>[1,5,4,6,2,3]=>00011
[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>[1,5,4,6,3,2]=>01011
[1,5,6,2,3,4]=>[1,6,2,3,5,4]=>[1,5,6,2,3,4]=>00001
[1,5,6,2,4,3]=>[1,6,4,2,5,3]=>[1,4,2,5,6,3]=>00101
[1,5,6,3,2,4]=>[1,3,6,2,5,4]=>[1,5,6,3,2,4]=>01001
[1,5,6,3,4,2]=>[1,4,6,3,5,2]=>[1,5,6,3,4,2]=>00101
[1,5,6,4,2,3]=>[1,4,2,6,5,3]=>[1,5,6,4,2,3]=>00101
[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>[1,5,6,4,3,2]=>01101
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>00001
[1,6,2,3,5,4]=>[1,6,2,5,3,4]=>[1,5,2,3,6,4]=>00011
[1,6,2,4,3,5]=>[1,6,4,2,3,5]=>[1,4,2,6,3,5]=>00101
[1,6,2,4,5,3]=>[1,6,5,2,4,3]=>[1,5,2,4,6,3]=>00011
[1,6,2,5,3,4]=>[1,6,5,3,2,4]=>[1,5,3,6,2,4]=>00011
[1,6,2,5,4,3]=>[1,6,4,5,2,3]=>[1,5,4,2,6,3]=>00111
[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>01001
[1,6,3,2,5,4]=>[1,3,6,5,2,4]=>[1,5,3,2,6,4]=>01011
[1,6,3,4,2,5]=>[1,4,6,3,2,5]=>[1,6,3,4,2,5]=>00101
[1,6,3,4,5,2]=>[1,5,6,3,4,2]=>[1,6,3,4,5,2]=>00011
[1,6,3,5,2,4]=>[1,5,6,2,3,4]=>[1,6,2,5,3,4]=>00011
[1,6,3,5,4,2]=>[1,4,5,6,2,3]=>[1,6,2,5,4,3]=>00111
[1,6,4,2,3,5]=>[1,4,2,6,3,5]=>[1,6,4,2,3,5]=>00101
[1,6,4,2,5,3]=>[1,4,6,5,3,2]=>[1,5,3,6,4,2]=>00111
[1,6,4,3,2,5]=>[1,3,4,6,2,5]=>[1,6,4,3,2,5]=>01101
[1,6,4,3,5,2]=>[1,5,4,6,3,2]=>[1,6,4,3,5,2]=>00111
[1,6,4,5,2,3]=>[1,5,2,6,4,3]=>[1,6,4,5,2,3]=>00011
[1,6,4,5,3,2]=>[1,3,5,6,4,2]=>[1,6,4,5,3,2]=>01011
[1,6,5,2,3,4]=>[1,5,2,3,6,4]=>[1,6,5,2,3,4]=>00011
[1,6,5,2,4,3]=>[1,5,4,2,6,3]=>[1,4,2,6,5,3]=>00111
[1,6,5,3,2,4]=>[1,3,5,2,6,4]=>[1,6,5,3,2,4]=>01011
[1,6,5,3,4,2]=>[1,4,5,3,6,2]=>[1,6,5,3,4,2]=>00111
[1,6,5,4,2,3]=>[1,4,2,5,6,3]=>[1,6,5,4,2,3]=>00111
[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>[1,6,5,4,3,2]=>01111
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>10001
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>10010
[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>10001
[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>10001
[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>10011
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>10100
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>10101
[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>10010
[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[2,1,4,5,6,3]=>10001
[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>10001
[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>[2,1,4,6,5,3]=>10011
[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>10010
[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>10011
[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>10110
[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[2,1,5,4,6,3]=>10011
[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>[2,1,5,6,3,4]=>10001
[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>[2,1,5,6,4,3]=>10101
[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>10001
[2,1,6,3,5,4]=>[2,1,6,5,3,4]=>[2,1,5,3,6,4]=>10011
[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>10101
[2,1,6,4,5,3]=>[2,1,5,6,4,3]=>[2,1,6,4,5,3]=>10011
[2,1,6,5,3,4]=>[2,1,5,3,6,4]=>[2,1,6,5,3,4]=>10011
[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>[2,1,6,5,4,3]=>10111
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>01000
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>01001
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>01010
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>01001
[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>01001
[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>01011
[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[2,3,4,1,5,6]=>00100
[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[2,3,4,1,6,5]=>00101
[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[2,3,4,5,1,6]=>00010
[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[2,3,4,5,6,1]=>00001
[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[2,3,4,6,1,5]=>00001
[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>[2,3,4,6,5,1]=>00011
[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[2,3,5,1,4,6]=>00010
[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[2,3,6,1,5,4]=>00011
[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>[2,3,5,4,1,6]=>00110
[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[2,3,5,4,6,1]=>00011
[2,3,5,6,1,4]=>[6,2,3,1,5,4]=>[2,3,5,6,1,4]=>00001
[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>[2,3,5,6,4,1]=>00101
[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[2,3,6,1,4,5]=>00001
[2,3,6,1,5,4]=>[6,2,3,5,1,4]=>[2,3,5,1,6,4]=>00011
[2,3,6,4,1,5]=>[4,2,3,6,1,5]=>[2,3,6,4,1,5]=>00101
[2,3,6,4,5,1]=>[5,2,3,6,4,1]=>[2,3,6,4,5,1]=>00011
[2,3,6,5,1,4]=>[5,2,3,1,6,4]=>[2,3,6,5,1,4]=>00011
[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>[2,3,6,5,4,1]=>00111
[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>00100
[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>00101
[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[2,5,1,4,3,6]=>00110
[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[2,5,6,1,4,3]=>00101
[2,4,1,6,3,5]=>[4,2,6,1,3,5]=>[2,6,1,4,3,5]=>00101
[2,4,1,6,5,3]=>[4,2,5,1,6,3]=>[2,6,5,1,4,3]=>00111
[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>[2,4,3,1,5,6]=>01100
[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>[2,4,3,1,6,5]=>01101
[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>[2,4,3,5,1,6]=>00110
[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[2,4,3,5,6,1]=>00101
[2,4,3,6,1,5]=>[6,2,4,3,1,5]=>[2,4,3,6,1,5]=>00101
[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>[2,4,3,6,5,1]=>00111
[2,4,5,1,3,6]=>[5,2,1,4,3,6]=>[2,4,5,1,3,6]=>00010
[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[2,4,6,1,5,3]=>00011
[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>[2,4,5,3,1,6]=>01010
[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[2,4,5,3,6,1]=>00011
[2,4,5,6,1,3]=>[6,2,1,4,5,3]=>[2,4,5,6,1,3]=>00001
[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>[2,4,5,6,3,1]=>01001
[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[2,4,6,1,3,5]=>00001
[2,4,6,1,5,3]=>[6,2,5,4,1,3]=>[2,4,5,1,6,3]=>00011
[2,4,6,3,1,5]=>[3,2,6,4,1,5]=>[2,4,6,3,1,5]=>01001
[2,4,6,3,5,1]=>[5,2,6,4,3,1]=>[2,4,6,3,5,1]=>00011
[2,4,6,5,1,3]=>[5,2,1,4,6,3]=>[2,4,6,5,1,3]=>00011
[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>[2,4,6,5,3,1]=>01011
[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>00010
[2,5,1,3,6,4]=>[5,2,1,6,3,4]=>[2,6,1,3,5,4]=>00011
[2,5,1,4,3,6]=>[5,2,4,1,3,6]=>[2,4,1,5,3,6]=>00110
[2,5,1,4,6,3]=>[5,2,6,1,4,3]=>[2,6,1,4,5,3]=>00011
[2,5,1,6,3,4]=>[5,2,6,3,1,4]=>[2,6,3,5,1,4]=>00011
[2,5,1,6,4,3]=>[5,2,4,6,1,3]=>[2,6,4,1,5,3]=>00111
[2,5,3,1,4,6]=>[3,2,5,1,4,6]=>[2,5,3,1,4,6]=>01010
[2,5,3,1,6,4]=>[3,2,5,6,1,4]=>[2,6,3,1,5,4]=>01011
[2,5,3,4,1,6]=>[4,2,5,3,1,6]=>[2,5,3,4,1,6]=>00110
[2,5,3,4,6,1]=>[6,2,5,3,4,1]=>[2,5,3,4,6,1]=>00011
[2,5,3,6,1,4]=>[6,2,5,1,3,4]=>[2,5,1,6,3,4]=>00011
[2,5,3,6,4,1]=>[4,2,6,5,1,3]=>[2,5,1,6,4,3]=>00111
[2,5,4,1,3,6]=>[4,2,1,5,3,6]=>[2,5,4,1,3,6]=>00110
[2,5,4,1,6,3]=>[4,2,5,6,3,1]=>[2,6,3,5,4,1]=>00111
[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>[2,5,4,3,1,6]=>01110
[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>[2,5,4,3,6,1]=>00111
[2,5,4,6,1,3]=>[6,2,1,5,4,3]=>[2,5,4,6,1,3]=>00011
[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>[2,5,4,6,3,1]=>01011
[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[2,5,6,1,3,4]=>00001
[2,5,6,1,4,3]=>[6,2,4,1,5,3]=>[2,4,1,5,6,3]=>00101
[2,5,6,3,1,4]=>[3,2,6,1,5,4]=>[2,5,6,3,1,4]=>01001
[2,5,6,3,4,1]=>[4,2,6,3,5,1]=>[2,5,6,3,4,1]=>00101
[2,5,6,4,1,3]=>[4,2,1,6,5,3]=>[2,5,6,4,1,3]=>00101
[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>[2,5,6,4,3,1]=>01101
[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>00001
[2,6,1,3,5,4]=>[6,2,1,5,3,4]=>[2,5,1,3,6,4]=>00011
[2,6,1,4,3,5]=>[6,2,4,1,3,5]=>[2,4,1,6,3,5]=>00101
[2,6,1,4,5,3]=>[6,2,5,1,4,3]=>[2,5,1,4,6,3]=>00011
[2,6,1,5,3,4]=>[6,2,5,3,1,4]=>[2,5,3,6,1,4]=>00011
[2,6,1,5,4,3]=>[6,2,4,5,1,3]=>[2,5,4,1,6,3]=>00111
[2,6,3,1,4,5]=>[3,2,6,1,4,5]=>[2,6,3,1,4,5]=>01001
[2,6,3,1,5,4]=>[3,2,6,5,1,4]=>[2,5,3,1,6,4]=>01011
[2,6,3,4,1,5]=>[4,2,6,3,1,5]=>[2,6,3,4,1,5]=>00101
[2,6,3,4,5,1]=>[5,2,6,3,4,1]=>[2,6,3,4,5,1]=>00011
[2,6,3,5,1,4]=>[5,2,6,1,3,4]=>[2,6,1,5,3,4]=>00011
[2,6,3,5,4,1]=>[4,2,5,6,1,3]=>[2,6,1,5,4,3]=>00111
[2,6,4,1,3,5]=>[4,2,1,6,3,5]=>[2,6,4,1,3,5]=>00101
[2,6,4,1,5,3]=>[4,2,6,5,3,1]=>[2,5,3,6,4,1]=>00111
[2,6,4,3,1,5]=>[3,2,4,6,1,5]=>[2,6,4,3,1,5]=>01101
[2,6,4,3,5,1]=>[5,2,4,6,3,1]=>[2,6,4,3,5,1]=>00111
[2,6,4,5,1,3]=>[5,2,1,6,4,3]=>[2,6,4,5,1,3]=>00011
[2,6,4,5,3,1]=>[3,2,5,6,4,1]=>[2,6,4,5,3,1]=>01011
[2,6,5,1,3,4]=>[5,2,1,3,6,4]=>[2,6,5,1,3,4]=>00011
[2,6,5,1,4,3]=>[5,2,4,1,6,3]=>[2,4,1,6,5,3]=>00111
[2,6,5,3,1,4]=>[3,2,5,1,6,4]=>[2,6,5,3,1,4]=>01011
[2,6,5,3,4,1]=>[4,2,5,3,6,1]=>[2,6,5,3,4,1]=>00111
[2,6,5,4,1,3]=>[4,2,1,5,6,3]=>[2,6,5,4,1,3]=>00111
[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>[2,6,5,4,3,1]=>01111
[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>01000
[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>01001
[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>01010
[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>[3,1,2,5,6,4]=>01001
[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>01001
[3,1,2,6,5,4]=>[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>01011
[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>01100
[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>01101
[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[4,5,1,3,2,6]=>01010
[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[4,5,6,1,3,2]=>01001
[3,1,4,6,2,5]=>[3,6,1,4,2,5]=>[4,6,1,3,2,5]=>01001
[3,1,4,6,5,2]=>[3,5,1,4,6,2]=>[4,6,5,1,3,2]=>01011
[3,1,5,2,4,6]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>01010
[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[6,1,3,2,5,4]=>01011
[3,1,5,4,2,6]=>[3,4,1,5,2,6]=>[5,4,1,3,2,6]=>01110
[3,1,5,4,6,2]=>[3,6,1,5,4,2]=>[5,4,6,1,3,2]=>01011
[3,1,5,6,2,4]=>[3,6,1,2,5,4]=>[5,6,1,3,2,4]=>01001
[3,1,5,6,4,2]=>[3,4,1,6,5,2]=>[5,6,4,1,3,2]=>01101
[3,1,6,2,4,5]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>01001
[3,1,6,2,5,4]=>[3,6,1,5,2,4]=>[5,1,3,2,6,4]=>01011
[3,1,6,4,2,5]=>[3,4,1,6,2,5]=>[6,4,1,3,2,5]=>01101
[3,1,6,4,5,2]=>[3,5,1,6,4,2]=>[6,4,5,1,3,2]=>01011
[3,1,6,5,2,4]=>[3,5,1,2,6,4]=>[6,5,1,3,2,4]=>01011
[3,1,6,5,4,2]=>[3,4,1,5,6,2]=>[6,5,4,1,3,2]=>01111
[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>11000
[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>11001
[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>11010
[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>11001
[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>11001
[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>11011
[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[3,2,4,1,5,6]=>01100
[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[3,2,4,1,6,5]=>01101
[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[3,2,4,5,1,6]=>01010
[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[3,2,4,5,6,1]=>01001
[3,2,4,6,1,5]=>[6,3,2,4,1,5]=>[3,2,4,6,1,5]=>01001
[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>[3,2,4,6,5,1]=>01011
[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>[3,2,5,1,4,6]=>01010
[3,2,5,1,6,4]=>[5,3,2,6,1,4]=>[3,2,6,1,5,4]=>01011
[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>[3,2,5,4,1,6]=>01110
[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[3,2,5,4,6,1]=>01011
[3,2,5,6,1,4]=>[6,3,2,1,5,4]=>[3,2,5,6,1,4]=>01001
[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>[3,2,5,6,4,1]=>01101
[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>[3,2,6,1,4,5]=>01001
[3,2,6,1,5,4]=>[6,3,2,5,1,4]=>[3,2,5,1,6,4]=>01011
[3,2,6,4,1,5]=>[4,3,2,6,1,5]=>[3,2,6,4,1,5]=>01101
[3,2,6,4,5,1]=>[5,3,2,6,4,1]=>[3,2,6,4,5,1]=>01011
[3,2,6,5,1,4]=>[5,3,2,1,6,4]=>[3,2,6,5,1,4]=>01011
[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>[3,2,6,5,4,1]=>01111
[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[3,4,1,2,5,6]=>00100
[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>[3,4,1,2,6,5]=>00101
[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[3,5,1,4,2,6]=>00110
[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[3,5,6,1,4,2]=>00101
[3,4,1,6,2,5]=>[4,6,3,1,2,5]=>[3,6,1,4,2,5]=>00101
[3,4,1,6,5,2]=>[4,5,3,1,6,2]=>[3,6,5,1,4,2]=>00111
[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[3,4,2,1,5,6]=>10100
[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>[3,4,2,1,6,5]=>10101
[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[3,4,2,5,1,6]=>00110
[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[3,4,2,5,6,1]=>00101
[3,4,2,6,1,5]=>[6,4,3,2,1,5]=>[3,4,2,6,1,5]=>00101
[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>[3,4,2,6,5,1]=>00111
[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[3,4,5,1,2,6]=>00010
[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[3,4,6,1,5,2]=>00011
[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[3,4,5,2,1,6]=>10010
[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[3,4,5,2,6,1]=>00011
[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[3,4,5,6,1,2]=>00001
[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[3,4,5,6,2,1]=>10001
[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[3,4,6,1,2,5]=>00001
[3,4,6,1,5,2]=>[6,5,3,4,1,2]=>[3,4,5,1,6,2]=>00011
[3,4,6,2,1,5]=>[2,6,3,4,1,5]=>[3,4,6,2,1,5]=>10001
[3,4,6,2,5,1]=>[5,6,3,4,2,1]=>[3,4,6,2,5,1]=>00011
[3,4,6,5,1,2]=>[5,1,3,4,6,2]=>[3,4,6,5,1,2]=>00011
[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>[3,4,6,5,2,1]=>10011
[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[3,5,1,2,4,6]=>00010
[3,5,1,2,6,4]=>[5,1,3,6,2,4]=>[3,6,1,2,5,4]=>00011
[3,5,1,4,2,6]=>[5,4,3,1,2,6]=>[3,4,1,5,2,6]=>00110
[3,5,1,4,6,2]=>[5,6,3,1,4,2]=>[3,6,1,4,5,2]=>00011
[3,5,1,6,2,4]=>[5,6,3,2,1,4]=>[3,6,2,5,1,4]=>00011
[3,5,1,6,4,2]=>[5,4,3,6,1,2]=>[3,6,4,1,5,2]=>00111
[3,5,2,1,4,6]=>[2,5,3,1,4,6]=>[3,5,2,1,4,6]=>10010
[3,5,2,1,6,4]=>[2,5,3,6,1,4]=>[3,6,2,1,5,4]=>10011
[3,5,2,4,1,6]=>[4,5,3,2,1,6]=>[3,5,2,4,1,6]=>00110
[3,5,2,4,6,1]=>[6,5,3,2,4,1]=>[3,5,2,4,6,1]=>00011
[3,5,2,6,1,4]=>[6,5,3,1,2,4]=>[3,5,1,6,2,4]=>00011
[3,5,2,6,4,1]=>[4,6,3,5,1,2]=>[3,5,1,6,4,2]=>00111
[3,5,4,1,2,6]=>[4,1,3,5,2,6]=>[3,5,4,1,2,6]=>00110
[3,5,4,1,6,2]=>[4,5,3,6,2,1]=>[3,6,2,5,4,1]=>00111
[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>[3,5,4,2,1,6]=>10110
[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>[3,5,4,2,6,1]=>00111
[3,5,4,6,1,2]=>[6,1,3,5,4,2]=>[3,5,4,6,1,2]=>00011
[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>[3,5,4,6,2,1]=>10011
[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[3,5,6,1,2,4]=>00001
[3,5,6,1,4,2]=>[6,4,3,1,5,2]=>[3,4,1,5,6,2]=>00101
[3,5,6,2,1,4]=>[2,6,3,1,5,4]=>[3,5,6,2,1,4]=>10001
[3,5,6,2,4,1]=>[4,6,3,2,5,1]=>[3,5,6,2,4,1]=>00101
[3,5,6,4,1,2]=>[4,1,3,6,5,2]=>[3,5,6,4,1,2]=>00101
[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>[3,5,6,4,2,1]=>10101
[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[3,6,1,2,4,5]=>00001
[3,6,1,2,5,4]=>[6,1,3,5,2,4]=>[3,5,1,2,6,4]=>00011
[3,6,1,4,2,5]=>[6,4,3,1,2,5]=>[3,4,1,6,2,5]=>00101
[3,6,1,4,5,2]=>[6,5,3,1,4,2]=>[3,5,1,4,6,2]=>00011
[3,6,1,5,2,4]=>[6,5,3,2,1,4]=>[3,5,2,6,1,4]=>00011
[3,6,1,5,4,2]=>[6,4,3,5,1,2]=>[3,5,4,1,6,2]=>00111
[3,6,2,1,4,5]=>[2,6,3,1,4,5]=>[3,6,2,1,4,5]=>10001
[3,6,2,1,5,4]=>[2,6,3,5,1,4]=>[3,5,2,1,6,4]=>10011
[3,6,2,4,1,5]=>[4,6,3,2,1,5]=>[3,6,2,4,1,5]=>00101
[3,6,2,4,5,1]=>[5,6,3,2,4,1]=>[3,6,2,4,5,1]=>00011
[3,6,2,5,1,4]=>[5,6,3,1,2,4]=>[3,6,1,5,2,4]=>00011
[3,6,2,5,4,1]=>[4,5,3,6,1,2]=>[3,6,1,5,4,2]=>00111
[3,6,4,1,2,5]=>[4,1,3,6,2,5]=>[3,6,4,1,2,5]=>00101
[3,6,4,1,5,2]=>[4,6,3,5,2,1]=>[3,5,2,6,4,1]=>00111
[3,6,4,2,1,5]=>[2,4,3,6,1,5]=>[3,6,4,2,1,5]=>10101
[3,6,4,2,5,1]=>[5,4,3,6,2,1]=>[3,6,4,2,5,1]=>00111
[3,6,4,5,1,2]=>[5,1,3,6,4,2]=>[3,6,4,5,1,2]=>00011
[3,6,4,5,2,1]=>[2,5,3,6,4,1]=>[3,6,4,5,2,1]=>10011
[3,6,5,1,2,4]=>[5,1,3,2,6,4]=>[3,6,5,1,2,4]=>00011
[3,6,5,1,4,2]=>[5,4,3,1,6,2]=>[3,4,1,6,5,2]=>00111
[3,6,5,2,1,4]=>[2,5,3,1,6,4]=>[3,6,5,2,1,4]=>10011
[3,6,5,2,4,1]=>[4,5,3,2,6,1]=>[3,6,5,2,4,1]=>00111
[3,6,5,4,1,2]=>[4,1,3,5,6,2]=>[3,6,5,4,1,2]=>00111
[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>[3,6,5,4,2,1]=>10111
[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>00100
[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>00101
[4,1,2,5,3,6]=>[4,1,5,2,3,6]=>[5,1,2,4,3,6]=>00110
[4,1,2,5,6,3]=>[4,1,6,2,5,3]=>[5,6,1,2,4,3]=>00101
[4,1,2,6,3,5]=>[4,1,6,2,3,5]=>[6,1,2,4,3,5]=>00101
[4,1,2,6,5,3]=>[4,1,5,2,6,3]=>[6,5,1,2,4,3]=>00111
[4,1,3,2,5,6]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>01100
[4,1,3,2,6,5]=>[4,3,1,2,6,5]=>[3,1,4,2,6,5]=>01101
[4,1,3,5,2,6]=>[4,5,1,3,2,6]=>[5,1,3,4,2,6]=>00110
[4,1,3,5,6,2]=>[4,6,1,3,5,2]=>[5,6,1,3,4,2]=>00101
[4,1,3,6,2,5]=>[4,6,1,3,2,5]=>[6,1,3,4,2,5]=>00101
[4,1,3,6,5,2]=>[4,5,1,3,6,2]=>[6,5,1,3,4,2]=>00111
[4,1,5,2,3,6]=>[4,5,2,1,3,6]=>[5,2,4,1,3,6]=>00110
[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[6,1,5,2,4,3]=>00111
[4,1,5,3,2,6]=>[4,3,5,1,2,6]=>[5,3,1,4,2,6]=>01110
[4,1,5,3,6,2]=>[4,6,5,1,3,2]=>[5,1,6,3,4,2]=>00111
[4,1,5,6,2,3]=>[4,6,2,1,5,3]=>[5,6,2,4,1,3]=>00101
[4,1,5,6,3,2]=>[4,3,6,1,5,2]=>[5,6,3,1,4,2]=>01101
[4,1,6,2,3,5]=>[4,6,2,1,3,5]=>[6,2,4,1,3,5]=>00101
[4,1,6,2,5,3]=>[4,6,5,1,2,3]=>[5,1,6,2,4,3]=>00111
[4,1,6,3,2,5]=>[4,3,6,1,2,5]=>[6,3,1,4,2,5]=>01101
[4,1,6,3,5,2]=>[4,5,6,1,3,2]=>[6,1,5,3,4,2]=>00111
[4,1,6,5,2,3]=>[4,5,2,1,6,3]=>[6,5,2,4,1,3]=>00111
[4,1,6,5,3,2]=>[4,3,5,1,6,2]=>[6,5,3,1,4,2]=>01111
[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>10100
[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>10101
[4,2,1,5,3,6]=>[2,4,5,1,3,6]=>[5,2,1,4,3,6]=>10110
[4,2,1,5,6,3]=>[2,4,6,1,5,3]=>[5,6,2,1,4,3]=>10101
[4,2,1,6,3,5]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>10101
[4,2,1,6,5,3]=>[2,4,5,1,6,3]=>[6,5,2,1,4,3]=>10111
[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,2,3,1,5,6]=>01100
[4,2,3,1,6,5]=>[3,4,2,1,6,5]=>[4,2,3,1,6,5]=>01101
[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[4,2,3,5,1,6]=>00110
[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[4,2,3,5,6,1]=>00101
[4,2,3,6,1,5]=>[6,4,2,3,1,5]=>[4,2,3,6,1,5]=>00101
[4,2,3,6,5,1]=>[5,4,2,3,6,1]=>[4,2,3,6,5,1]=>00111
[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[4,1,5,2,3,6]=>00110
[4,2,5,1,6,3]=>[5,4,6,2,1,3]=>[6,2,4,1,5,3]=>00111
[4,2,5,3,1,6]=>[3,5,4,1,2,6]=>[4,1,5,3,2,6]=>01110
[4,2,5,3,6,1]=>[6,4,5,2,3,1]=>[5,2,4,3,6,1]=>00111
[4,2,5,6,1,3]=>[6,4,1,2,5,3]=>[4,1,5,6,2,3]=>00101
[4,2,5,6,3,1]=>[3,6,4,1,5,2]=>[4,1,5,6,3,2]=>01101
[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>[4,1,6,2,3,5]=>00101
[4,2,6,1,5,3]=>[6,4,5,2,1,3]=>[5,2,4,1,6,3]=>00111
[4,2,6,3,1,5]=>[3,6,4,1,2,5]=>[4,1,6,3,2,5]=>01101
[4,2,6,3,5,1]=>[5,4,6,2,3,1]=>[6,2,4,3,5,1]=>00111
[4,2,6,5,1,3]=>[5,4,1,2,6,3]=>[4,1,6,5,2,3]=>00111
[4,2,6,5,3,1]=>[3,5,4,1,6,2]=>[4,1,6,5,3,2]=>01111
[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[4,3,1,2,5,6]=>01100
[4,3,1,2,6,5]=>[3,1,4,2,6,5]=>[4,3,1,2,6,5]=>01101
[4,3,1,5,2,6]=>[3,4,5,2,1,6]=>[5,2,4,3,1,6]=>01110
[4,3,1,5,6,2]=>[3,4,6,2,5,1]=>[5,6,2,4,3,1]=>01101
[4,3,1,6,2,5]=>[3,4,6,2,1,5]=>[6,2,4,3,1,5]=>01101
[4,3,1,6,5,2]=>[3,4,5,2,6,1]=>[6,5,2,4,3,1]=>01111
[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,3,2,1,5,6]=>11100
[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>[4,3,2,1,6,5]=>11101
[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[4,3,2,5,1,6]=>01110
[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[4,3,2,5,6,1]=>01101
[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>[4,3,2,6,1,5]=>01101
[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>[4,3,2,6,5,1]=>01111
[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[4,3,5,1,2,6]=>00110
[4,3,5,1,6,2]=>[5,6,4,3,1,2]=>[4,3,6,1,5,2]=>00111
[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[4,3,5,2,1,6]=>10110
[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[4,3,5,2,6,1]=>00111
[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[4,3,5,6,1,2]=>00101
[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[4,3,5,6,2,1]=>10101
[4,3,6,1,2,5]=>[6,1,4,3,2,5]=>[4,3,6,1,2,5]=>00101
[4,3,6,1,5,2]=>[6,5,4,3,1,2]=>[4,3,5,1,6,2]=>00111
[4,3,6,2,1,5]=>[2,6,4,3,1,5]=>[4,3,6,2,1,5]=>10101
[4,3,6,2,5,1]=>[5,6,4,3,2,1]=>[4,3,6,2,5,1]=>00111
[4,3,6,5,1,2]=>[5,1,4,3,6,2]=>[4,3,6,5,1,2]=>00111
[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>[4,3,6,5,2,1]=>10111
[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[4,5,1,2,3,6]=>00010
[4,5,1,2,6,3]=>[5,1,6,4,2,3]=>[4,6,1,2,5,3]=>00011
[4,5,1,3,2,6]=>[5,3,1,4,2,6]=>[3,1,4,5,2,6]=>01010
[4,5,1,3,6,2]=>[5,6,1,4,3,2]=>[4,6,1,3,5,2]=>00011
[4,5,1,6,2,3]=>[5,6,2,4,1,3]=>[4,6,2,5,1,3]=>00011
[4,5,1,6,3,2]=>[5,3,6,4,1,2]=>[4,6,3,1,5,2]=>01011
[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>[4,5,2,1,3,6]=>10010
[4,5,2,1,6,3]=>[2,5,6,4,1,3]=>[4,6,2,1,5,3]=>10011
[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[4,5,2,3,1,6]=>01010
[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[4,5,2,3,6,1]=>00011
[4,5,2,6,1,3]=>[6,5,1,4,2,3]=>[4,5,1,6,2,3]=>00011
[4,5,2,6,3,1]=>[3,6,5,4,1,2]=>[4,5,1,6,3,2]=>01011
[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>[4,5,3,1,2,6]=>01010
[4,5,3,1,6,2]=>[3,5,6,4,2,1]=>[4,6,2,5,3,1]=>01011
[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[4,5,3,2,1,6]=>11010
[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[4,5,3,2,6,1]=>01011
[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[4,5,3,6,1,2]=>00011
[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[4,5,3,6,2,1]=>10011
[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[4,5,6,1,2,3]=>00001
[4,5,6,1,3,2]=>[6,3,1,4,5,2]=>[3,1,4,5,6,2]=>01001
[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[4,5,6,2,1,3]=>10001
[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[4,5,6,2,3,1]=>01001
[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[4,5,6,3,1,2]=>01001
[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[4,5,6,3,2,1]=>11001
[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[4,6,1,2,3,5]=>00001
[4,6,1,2,5,3]=>[6,1,5,4,2,3]=>[4,5,1,2,6,3]=>00011
[4,6,1,3,2,5]=>[6,3,1,4,2,5]=>[3,1,4,6,2,5]=>01001
[4,6,1,3,5,2]=>[6,5,1,4,3,2]=>[4,5,1,3,6,2]=>00011
[4,6,1,5,2,3]=>[6,5,2,4,1,3]=>[4,5,2,6,1,3]=>00011
[4,6,1,5,3,2]=>[6,3,5,4,1,2]=>[4,5,3,1,6,2]=>01011
[4,6,2,1,3,5]=>[2,6,1,4,3,5]=>[4,6,2,1,3,5]=>10001
[4,6,2,1,5,3]=>[2,6,5,4,1,3]=>[4,5,2,1,6,3]=>10011
[4,6,2,3,1,5]=>[3,6,2,4,1,5]=>[4,6,2,3,1,5]=>01001
[4,6,2,3,5,1]=>[5,6,2,4,3,1]=>[4,6,2,3,5,1]=>00011
[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>[4,6,1,5,2,3]=>00011
[4,6,2,5,3,1]=>[3,5,6,4,1,2]=>[4,6,1,5,3,2]=>01011
[4,6,3,1,2,5]=>[3,1,6,4,2,5]=>[4,6,3,1,2,5]=>01001
[4,6,3,1,5,2]=>[3,6,5,4,2,1]=>[4,5,2,6,3,1]=>01011
[4,6,3,2,1,5]=>[2,3,6,4,1,5]=>[4,6,3,2,1,5]=>11001
[4,6,3,2,5,1]=>[5,3,6,4,2,1]=>[4,6,3,2,5,1]=>01011
[4,6,3,5,1,2]=>[5,1,6,4,3,2]=>[4,6,3,5,1,2]=>00011
[4,6,3,5,2,1]=>[2,5,6,4,3,1]=>[4,6,3,5,2,1]=>10011
[4,6,5,1,2,3]=>[5,1,2,4,6,3]=>[4,6,5,1,2,3]=>00011
[4,6,5,1,3,2]=>[5,3,1,4,6,2]=>[3,1,4,6,5,2]=>01011
[4,6,5,2,1,3]=>[2,5,1,4,6,3]=>[4,6,5,2,1,3]=>10011
[4,6,5,2,3,1]=>[3,5,2,4,6,1]=>[4,6,5,2,3,1]=>01011
[4,6,5,3,1,2]=>[3,1,5,4,6,2]=>[4,6,5,3,1,2]=>01011
[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>[4,6,5,3,2,1]=>11011
[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>00010
[5,1,2,3,6,4]=>[5,1,2,6,3,4]=>[6,1,2,3,5,4]=>00011
[5,1,2,4,3,6]=>[5,1,4,2,3,6]=>[4,1,2,5,3,6]=>00110
[5,1,2,4,6,3]=>[5,1,6,2,4,3]=>[6,1,2,4,5,3]=>00011
[5,1,2,6,3,4]=>[5,1,6,3,2,4]=>[6,3,5,1,2,4]=>00011
[5,1,2,6,4,3]=>[5,1,4,6,2,3]=>[6,4,1,2,5,3]=>00111
[5,1,3,2,4,6]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>01010
[5,1,3,2,6,4]=>[5,3,1,6,2,4]=>[3,1,6,2,5,4]=>01011
[5,1,3,4,2,6]=>[5,4,1,3,2,6]=>[4,1,3,5,2,6]=>00110
[5,1,3,4,6,2]=>[5,6,1,3,4,2]=>[6,1,3,4,5,2]=>00011
[5,1,3,6,2,4]=>[5,6,1,2,3,4]=>[6,1,5,2,3,4]=>00011
[5,1,3,6,4,2]=>[5,4,1,6,3,2]=>[6,4,1,3,5,2]=>00111
[5,1,4,2,3,6]=>[5,4,2,1,3,6]=>[4,2,5,1,3,6]=>00110
[5,1,4,2,6,3]=>[5,4,6,1,2,3]=>[6,1,4,2,5,3]=>00111
[5,1,4,3,2,6]=>[5,3,4,1,2,6]=>[4,3,1,5,2,6]=>01110
[5,1,4,3,6,2]=>[5,6,4,1,3,2]=>[4,1,6,3,5,2]=>00111
[5,1,4,6,2,3]=>[5,6,2,1,4,3]=>[6,2,4,5,1,3]=>00011
[5,1,4,6,3,2]=>[5,3,6,1,4,2]=>[6,3,1,4,5,2]=>01011
[5,1,6,2,3,4]=>[5,6,2,3,1,4]=>[6,2,3,5,1,4]=>00011
[5,1,6,2,4,3]=>[5,6,4,2,1,3]=>[4,2,6,1,5,3]=>00111
[5,1,6,3,2,4]=>[5,3,6,2,1,4]=>[6,3,2,5,1,4]=>01011
[5,1,6,3,4,2]=>[5,4,6,3,1,2]=>[6,3,4,1,5,2]=>00111
[5,1,6,4,2,3]=>[5,4,2,6,1,3]=>[6,4,2,5,1,3]=>00111
[5,1,6,4,3,2]=>[5,3,4,6,1,2]=>[6,4,3,1,5,2]=>01111
[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>10010
[5,2,1,3,6,4]=>[2,5,1,6,3,4]=>[6,2,1,3,5,4]=>10011
[5,2,1,4,3,6]=>[2,5,4,1,3,6]=>[4,2,1,5,3,6]=>10110
[5,2,1,4,6,3]=>[2,5,6,1,4,3]=>[6,2,1,4,5,3]=>10011
[5,2,1,6,3,4]=>[2,5,6,3,1,4]=>[6,3,5,2,1,4]=>10011
[5,2,1,6,4,3]=>[2,5,4,6,1,3]=>[6,4,2,1,5,3]=>10111
[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[5,2,3,1,4,6]=>01010
[5,2,3,1,6,4]=>[3,5,2,6,1,4]=>[6,2,3,1,5,4]=>01011
[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,2,3,4,1,6]=>00110
[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[5,2,3,4,6,1]=>00011
[5,2,3,6,1,4]=>[6,5,2,1,3,4]=>[5,2,6,1,3,4]=>00011
[5,2,3,6,4,1]=>[4,6,1,5,3,2]=>[5,1,3,6,4,2]=>00111
[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>[5,1,4,2,3,6]=>00110
[5,2,4,1,6,3]=>[4,5,6,2,1,3]=>[6,2,5,1,4,3]=>00111
[5,2,4,3,1,6]=>[3,4,5,1,2,6]=>[5,1,4,3,2,6]=>01110
[5,2,4,3,6,1]=>[6,5,4,2,3,1]=>[4,2,5,3,6,1]=>00111
[5,2,4,6,1,3]=>[6,5,1,2,4,3]=>[5,1,4,6,2,3]=>00011
[5,2,4,6,3,1]=>[3,6,5,1,4,2]=>[5,1,4,6,3,2]=>01011
[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>[5,1,3,6,2,4]=>00011
[5,2,6,1,4,3]=>[6,5,4,1,2,3]=>[4,1,5,2,6,3]=>00111
[5,2,6,3,1,4]=>[3,6,5,2,1,4]=>[5,2,6,3,1,4]=>01011
[5,2,6,3,4,1]=>[4,5,6,3,2,1]=>[6,3,5,2,4,1]=>00111
[5,2,6,4,1,3]=>[4,6,2,5,1,3]=>[5,2,6,4,1,3]=>00111
[5,2,6,4,3,1]=>[3,4,6,5,2,1]=>[5,2,6,4,3,1]=>01111
[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[5,3,1,2,4,6]=>01010
[5,3,1,2,6,4]=>[3,1,5,6,2,4]=>[6,3,1,2,5,4]=>01011
[5,3,1,4,2,6]=>[3,5,4,2,1,6]=>[4,2,5,3,1,6]=>01110
[5,3,1,4,6,2]=>[3,5,6,2,4,1]=>[6,2,4,5,3,1]=>01011
[5,3,1,6,2,4]=>[3,5,6,1,2,4]=>[6,1,5,3,2,4]=>01011
[5,3,1,6,4,2]=>[3,5,4,6,2,1]=>[6,4,2,5,3,1]=>01111
[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[5,3,2,1,4,6]=>11010
[5,3,2,1,6,4]=>[2,3,5,6,1,4]=>[6,3,2,1,5,4]=>11011
[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[5,3,2,4,1,6]=>01110
[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[5,3,2,4,6,1]=>01011
[5,3,2,6,1,4]=>[6,3,5,1,2,4]=>[5,3,1,6,2,4]=>01011
[5,3,2,6,4,1]=>[4,3,6,5,1,2]=>[5,3,1,6,4,2]=>01111
[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[5,3,4,1,2,6]=>00110
[5,3,4,1,6,2]=>[4,6,5,3,1,2]=>[5,3,6,1,4,2]=>00111
[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[5,3,4,2,1,6]=>10110
[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[5,3,4,2,6,1]=>00111
[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[5,3,4,6,1,2]=>00011
[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[5,3,4,6,2,1]=>10011
[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[5,1,2,6,3,4]=>00011
[5,3,6,1,4,2]=>[6,4,5,1,3,2]=>[5,1,4,3,6,2]=>00111
[5,3,6,2,1,4]=>[2,6,5,1,3,4]=>[5,2,1,6,3,4]=>10011
[5,3,6,2,4,1]=>[4,6,5,2,3,1]=>[5,2,6,3,4,1]=>00111
[5,3,6,4,1,2]=>[4,1,6,5,2,3]=>[5,1,2,6,4,3]=>00111
[5,3,6,4,2,1]=>[2,4,6,5,1,3]=>[5,2,1,6,4,3]=>10111
[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[5,4,1,2,3,6]=>00110
[5,4,1,2,6,3]=>[4,1,5,6,3,2]=>[6,3,5,4,1,2]=>00111
[5,4,1,3,2,6]=>[4,3,1,5,2,6]=>[3,1,5,4,2,6]=>01110
[5,4,1,3,6,2]=>[4,5,2,6,3,1]=>[6,2,3,5,4,1]=>00111
[5,4,1,6,2,3]=>[4,5,1,6,2,3]=>[6,1,5,4,2,3]=>00111
[5,4,1,6,3,2]=>[4,3,5,6,2,1]=>[6,3,2,5,4,1]=>01111
[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[5,4,2,1,3,6]=>10110
[5,4,2,1,6,3]=>[2,4,5,6,3,1]=>[6,3,5,4,2,1]=>10111
[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[5,4,2,3,1,6]=>01110
[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[5,4,2,3,6,1]=>00111
[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>[5,4,1,6,2,3]=>00111
[5,4,2,6,3,1]=>[3,6,4,5,1,2]=>[5,4,1,6,3,2]=>01111
[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[5,4,3,1,2,6]=>01110
[5,4,3,1,6,2]=>[3,4,5,6,1,2]=>[6,1,5,4,3,2]=>01111
[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]=>11110
[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[5,4,3,2,6,1]=>01111
[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[5,4,3,6,1,2]=>00111
[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[5,4,3,6,2,1]=>10111
[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[5,4,6,1,2,3]=>00011
[5,4,6,1,3,2]=>[6,3,1,5,4,2]=>[3,1,5,4,6,2]=>01011
[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[5,4,6,2,1,3]=>10011
[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[5,4,6,2,3,1]=>01011
[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[5,4,6,3,1,2]=>01011
[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[5,4,6,3,2,1]=>11011
[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[5,6,1,2,3,4]=>00001
[5,6,1,2,4,3]=>[6,1,4,2,5,3]=>[4,1,2,5,6,3]=>00101
[5,6,1,3,2,4]=>[6,3,1,2,5,4]=>[3,1,5,6,2,4]=>01001
[5,6,1,3,4,2]=>[6,4,1,3,5,2]=>[4,1,3,5,6,2]=>00101
[5,6,1,4,2,3]=>[6,4,2,1,5,3]=>[4,2,5,6,1,3]=>00101
[5,6,1,4,3,2]=>[6,3,4,1,5,2]=>[4,3,1,5,6,2]=>01101
[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[5,6,2,1,3,4]=>10001
[5,6,2,1,4,3]=>[2,6,4,1,5,3]=>[4,2,1,5,6,3]=>10101
[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[5,6,2,3,1,4]=>01001
[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[5,6,2,3,4,1]=>00101
[5,6,2,4,1,3]=>[4,6,1,2,5,3]=>[5,6,1,4,2,3]=>00101
[5,6,2,4,3,1]=>[3,4,6,1,5,2]=>[5,6,1,4,3,2]=>01101
[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[5,6,3,1,2,4]=>01001
[5,6,3,1,4,2]=>[3,6,4,2,5,1]=>[4,2,5,6,3,1]=>01101
[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[5,6,3,2,1,4]=>11001
[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[5,6,3,2,4,1]=>01101
[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[5,6,3,4,1,2]=>00101
[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[5,6,3,4,2,1]=>10101
[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[5,6,4,1,2,3]=>00101
[5,6,4,1,3,2]=>[4,3,1,6,5,2]=>[3,1,5,6,4,2]=>01101
[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[5,6,4,2,1,3]=>10101
[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[5,6,4,2,3,1]=>01101
[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[5,6,4,3,1,2]=>01101
[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[5,6,4,3,2,1]=>11101
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>00001
[6,1,2,3,5,4]=>[6,1,2,5,3,4]=>[5,1,2,3,6,4]=>00011
[6,1,2,4,3,5]=>[6,1,4,2,3,5]=>[4,1,2,6,3,5]=>00101
[6,1,2,4,5,3]=>[6,1,5,2,4,3]=>[5,1,2,4,6,3]=>00011
[6,1,2,5,3,4]=>[6,1,5,3,2,4]=>[5,3,6,1,2,4]=>00011
[6,1,2,5,4,3]=>[6,1,4,5,2,3]=>[5,4,1,2,6,3]=>00111
[6,1,3,2,4,5]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>01001
[6,1,3,2,5,4]=>[6,3,1,5,2,4]=>[3,1,5,2,6,4]=>01011
[6,1,3,4,2,5]=>[6,4,1,3,2,5]=>[4,1,3,6,2,5]=>00101
[6,1,3,4,5,2]=>[6,5,1,3,4,2]=>[5,1,3,4,6,2]=>00011
[6,1,3,5,2,4]=>[6,5,1,2,3,4]=>[5,1,6,2,3,4]=>00011
[6,1,3,5,4,2]=>[6,4,1,5,3,2]=>[5,4,1,3,6,2]=>00111
[6,1,4,2,3,5]=>[6,4,2,1,3,5]=>[4,2,6,1,3,5]=>00101
[6,1,4,2,5,3]=>[6,4,5,1,2,3]=>[5,1,4,2,6,3]=>00111
[6,1,4,3,2,5]=>[6,3,4,1,2,5]=>[4,3,1,6,2,5]=>01101
[6,1,4,3,5,2]=>[6,5,4,1,3,2]=>[4,1,5,3,6,2]=>00111
[6,1,4,5,2,3]=>[6,5,2,1,4,3]=>[5,2,4,6,1,3]=>00011
[6,1,4,5,3,2]=>[6,3,5,1,4,2]=>[5,3,1,4,6,2]=>01011
[6,1,5,2,3,4]=>[6,5,2,3,1,4]=>[5,2,3,6,1,4]=>00011
[6,1,5,2,4,3]=>[6,5,4,2,1,3]=>[4,2,5,1,6,3]=>00111
[6,1,5,3,2,4]=>[6,3,5,2,1,4]=>[5,3,2,6,1,4]=>01011
[6,1,5,3,4,2]=>[6,4,5,3,1,2]=>[5,3,4,1,6,2]=>00111
[6,1,5,4,2,3]=>[6,4,2,5,1,3]=>[5,4,2,6,1,3]=>00111
[6,1,5,4,3,2]=>[6,3,4,5,1,2]=>[5,4,3,1,6,2]=>01111
[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>10001
[6,2,1,3,5,4]=>[2,6,1,5,3,4]=>[5,2,1,3,6,4]=>10011
[6,2,1,4,3,5]=>[2,6,4,1,3,5]=>[4,2,1,6,3,5]=>10101
[6,2,1,4,5,3]=>[2,6,5,1,4,3]=>[5,2,1,4,6,3]=>10011
[6,2,1,5,3,4]=>[2,6,5,3,1,4]=>[5,3,6,2,1,4]=>10011
[6,2,1,5,4,3]=>[2,6,4,5,1,3]=>[5,4,2,1,6,3]=>10111
[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[6,2,3,1,4,5]=>01001
[6,2,3,1,5,4]=>[3,6,2,5,1,4]=>[5,2,3,1,6,4]=>01011
[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[6,2,3,4,1,5]=>00101
[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6,2,3,4,5,1]=>00011
[6,2,3,5,1,4]=>[5,6,2,1,3,4]=>[6,2,5,1,3,4]=>00011
[6,2,3,5,4,1]=>[4,5,1,6,3,2]=>[6,1,3,5,4,2]=>00111
[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>[6,1,4,2,3,5]=>00101
[6,2,4,1,5,3]=>[4,6,5,2,1,3]=>[5,2,6,1,4,3]=>00111
[6,2,4,3,1,5]=>[3,4,6,1,2,5]=>[6,1,4,3,2,5]=>01101
[6,2,4,3,5,1]=>[5,6,4,2,3,1]=>[4,2,6,3,5,1]=>00111
[6,2,4,5,1,3]=>[5,6,1,2,4,3]=>[6,1,4,5,2,3]=>00011
[6,2,4,5,3,1]=>[3,5,6,1,4,2]=>[6,1,4,5,3,2]=>01011
[6,2,5,1,3,4]=>[5,6,1,3,2,4]=>[6,1,3,5,2,4]=>00011
[6,2,5,1,4,3]=>[5,6,4,1,2,3]=>[4,1,6,2,5,3]=>00111
[6,2,5,3,1,4]=>[3,5,6,2,1,4]=>[6,2,5,3,1,4]=>01011
[6,2,5,3,4,1]=>[4,6,5,3,2,1]=>[5,3,6,2,4,1]=>00111
[6,2,5,4,1,3]=>[4,5,2,6,1,3]=>[6,2,5,4,1,3]=>00111
[6,2,5,4,3,1]=>[3,4,5,6,2,1]=>[6,2,5,4,3,1]=>01111
[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[6,3,1,2,4,5]=>01001
[6,3,1,2,5,4]=>[3,1,6,5,2,4]=>[5,3,1,2,6,4]=>01011
[6,3,1,4,2,5]=>[3,6,4,2,1,5]=>[4,2,6,3,1,5]=>01101
[6,3,1,4,5,2]=>[3,6,5,2,4,1]=>[5,2,4,6,3,1]=>01011
[6,3,1,5,2,4]=>[3,6,5,1,2,4]=>[5,1,6,3,2,4]=>01011
[6,3,1,5,4,2]=>[3,6,4,5,2,1]=>[5,4,2,6,3,1]=>01111
[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[6,3,2,1,4,5]=>11001
[6,3,2,1,5,4]=>[2,3,6,5,1,4]=>[5,3,2,1,6,4]=>11011
[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[6,3,2,4,1,5]=>01101
[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[6,3,2,4,5,1]=>01011
[6,3,2,5,1,4]=>[5,3,6,1,2,4]=>[6,3,1,5,2,4]=>01011
[6,3,2,5,4,1]=>[4,3,5,6,1,2]=>[6,3,1,5,4,2]=>01111
[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[6,3,4,1,2,5]=>00101
[6,3,4,1,5,2]=>[4,5,6,3,1,2]=>[6,3,5,1,4,2]=>00111
[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[6,3,4,2,1,5]=>10101
[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[6,3,4,2,5,1]=>00111
[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[6,3,4,5,1,2]=>00011
[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[6,3,4,5,2,1]=>10011
[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>[6,1,2,5,3,4]=>00011
[6,3,5,1,4,2]=>[5,4,6,1,3,2]=>[6,1,4,3,5,2]=>00111
[6,3,5,2,1,4]=>[2,5,6,1,3,4]=>[6,2,1,5,3,4]=>10011
[6,3,5,2,4,1]=>[4,5,6,2,3,1]=>[6,2,5,3,4,1]=>00111
[6,3,5,4,1,2]=>[4,1,5,6,2,3]=>[6,1,2,5,4,3]=>00111
[6,3,5,4,2,1]=>[2,4,5,6,1,3]=>[6,2,1,5,4,3]=>10111
[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[6,4,1,2,3,5]=>00101
[6,4,1,2,5,3]=>[4,1,6,5,3,2]=>[5,3,6,4,1,2]=>00111
[6,4,1,3,2,5]=>[4,3,1,6,2,5]=>[3,1,6,4,2,5]=>01101
[6,4,1,3,5,2]=>[4,6,2,5,3,1]=>[5,2,3,6,4,1]=>00111
[6,4,1,5,2,3]=>[4,6,1,5,2,3]=>[5,1,6,4,2,3]=>00111
[6,4,1,5,3,2]=>[4,3,6,5,2,1]=>[5,3,2,6,4,1]=>01111
[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[6,4,2,1,3,5]=>10101
[6,4,2,1,5,3]=>[2,4,6,5,3,1]=>[5,3,6,4,2,1]=>10111
[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[6,4,2,3,1,5]=>01101
[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[6,4,2,3,5,1]=>00111
[6,4,2,5,1,3]=>[5,4,1,6,2,3]=>[6,4,1,5,2,3]=>00111
[6,4,2,5,3,1]=>[3,5,4,6,1,2]=>[6,4,1,5,3,2]=>01111
[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[6,4,3,1,2,5]=>01101
[6,4,3,1,5,2]=>[3,4,6,5,1,2]=>[5,1,6,4,3,2]=>01111
[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[6,4,3,2,1,5]=>11101
[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]=>01111
[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[6,4,3,5,1,2]=>00111
[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[6,4,3,5,2,1]=>10111
[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[6,4,5,1,2,3]=>00011
[6,4,5,1,3,2]=>[5,3,1,6,4,2]=>[3,1,6,4,5,2]=>01011
[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[6,4,5,2,1,3]=>10011
[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[6,4,5,2,3,1]=>01011
[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[6,4,5,3,1,2]=>01011
[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[6,4,5,3,2,1]=>11011
[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[6,5,1,2,3,4]=>00011
[6,5,1,2,4,3]=>[5,1,4,2,6,3]=>[4,1,2,6,5,3]=>00111
[6,5,1,3,2,4]=>[5,3,1,2,6,4]=>[3,1,6,5,2,4]=>01011
[6,5,1,3,4,2]=>[5,4,1,3,6,2]=>[4,1,3,6,5,2]=>00111
[6,5,1,4,2,3]=>[5,4,2,1,6,3]=>[4,2,6,5,1,3]=>00111
[6,5,1,4,3,2]=>[5,3,4,1,6,2]=>[4,3,1,6,5,2]=>01111
[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[6,5,2,1,3,4]=>10011
[6,5,2,1,4,3]=>[2,5,4,1,6,3]=>[4,2,1,6,5,3]=>10111
[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[6,5,2,3,1,4]=>01011
[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[6,5,2,3,4,1]=>00111
[6,5,2,4,1,3]=>[4,5,1,2,6,3]=>[6,5,1,4,2,3]=>00111
[6,5,2,4,3,1]=>[3,4,5,1,6,2]=>[6,5,1,4,3,2]=>01111
[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[6,5,3,1,2,4]=>01011
[6,5,3,1,4,2]=>[3,5,4,2,6,1]=>[4,2,6,5,3,1]=>01111
[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[6,5,3,2,1,4]=>11011
[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[6,5,3,2,4,1]=>01111
[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[6,5,3,4,1,2]=>00111
[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]=>10111
[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[6,5,4,1,2,3]=>00111
[6,5,4,1,3,2]=>[4,3,1,5,6,2]=>[3,1,6,5,4,2]=>01111
[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[6,5,4,2,1,3]=>10111
[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[6,5,4,2,3,1]=>01111
[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[6,5,4,3,1,2]=>01111
[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]=>11111
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>000001
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>000010
[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>000001
[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>000001
[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>000011
[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>000100
[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>000101
[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>000010
[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[1,2,3,5,6,7,4]=>000001
[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>[1,2,3,5,7,4,6]=>000001
[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>[1,2,3,5,7,6,4]=>000011
[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>000010
[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]=>000011
[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>000110
[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>[1,2,3,6,5,7,4]=>000011
[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,4,5]=>000001
[1,2,3,6,7,5,4]=>[1,2,3,5,7,6,4]=>[1,2,3,6,7,5,4]=>000101
[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>000001
[1,2,3,7,4,6,5]=>[1,2,3,7,6,4,5]=>[1,2,3,6,4,7,5]=>000011
[1,2,3,7,5,4,6]=>[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>000101
[1,2,3,7,5,6,4]=>[1,2,3,6,7,5,4]=>[1,2,3,7,5,6,4]=>000011
[1,2,3,7,6,4,5]=>[1,2,3,6,4,7,5]=>[1,2,3,7,6,4,5]=>000011
[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>[1,2,3,7,6,5,4]=>000111
[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000
[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>001001
[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>001010
[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>001001
[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>001001
[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>001011
[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>000100
[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>000101
[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[1,2,4,5,6,3,7]=>000010
[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[1,2,4,5,6,7,3]=>000001
[1,2,4,5,7,3,6]=>[1,2,7,4,5,3,6]=>[1,2,4,5,7,3,6]=>000001
[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>[1,2,4,5,7,6,3]=>000011
[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>[1,2,4,6,3,5,7]=>000010
[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[1,2,4,7,3,6,5]=>000011
[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>[1,2,4,6,5,3,7]=>000110
[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>[1,2,4,6,5,7,3]=>000011
[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]=>[1,2,4,6,7,3,5]=>000001
[1,2,4,6,7,5,3]=>[1,2,5,4,7,6,3]=>[1,2,4,6,7,5,3]=>000101
[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>[1,2,4,7,3,5,6]=>000001
[1,2,4,7,3,6,5]=>[1,2,7,4,6,3,5]=>[1,2,4,6,3,7,5]=>000011
[1,2,4,7,5,3,6]=>[1,2,5,4,7,3,6]=>[1,2,4,7,5,3,6]=>000101
[1,2,4,7,5,6,3]=>[1,2,6,4,7,5,3]=>[1,2,4,7,5,6,3]=>000011
[1,2,4,7,6,3,5]=>[1,2,6,4,3,7,5]=>[1,2,4,7,6,3,5]=>000011
[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]=>[1,2,4,7,6,5,3]=>000111
[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>000100
[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>000101
[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]=>000110
[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[1,2,6,7,3,5,4]=>000101
[1,2,5,3,7,4,6]=>[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]=>000101
[1,2,5,3,7,6,4]=>[1,2,5,6,3,7,4]=>[1,2,7,6,3,5,4]=>000111
[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>001100
[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>001101
[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>[1,2,5,4,6,3,7]=>000110
[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>[1,2,5,4,6,7,3]=>000101
[1,2,5,4,7,3,6]=>[1,2,7,5,4,3,6]=>[1,2,5,4,7,3,6]=>000101
[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]=>[1,2,5,4,7,6,3]=>000111
[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]=>[1,2,5,6,3,4,7]=>000010
[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[1,2,5,7,3,6,4]=>000011
[1,2,5,6,4,3,7]=>[1,2,4,6,5,3,7]=>[1,2,5,6,4,3,7]=>001010
[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>[1,2,5,6,4,7,3]=>000011
[1,2,5,6,7,3,4]=>[1,2,7,3,5,6,4]=>[1,2,5,6,7,3,4]=>000001
[1,2,5,6,7,4,3]=>[1,2,4,7,5,6,3]=>[1,2,5,6,7,4,3]=>001001
[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]=>[1,2,5,7,3,4,6]=>000001
[1,2,5,7,3,6,4]=>[1,2,7,6,5,3,4]=>[1,2,5,6,3,7,4]=>000011
[1,2,5,7,4,3,6]=>[1,2,4,7,5,3,6]=>[1,2,5,7,4,3,6]=>001001
[1,2,5,7,4,6,3]=>[1,2,6,7,5,4,3]=>[1,2,5,7,4,6,3]=>000011
[1,2,5,7,6,3,4]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>000011
[1,2,5,7,6,4,3]=>[1,2,4,6,5,7,3]=>[1,2,5,7,6,4,3]=>001011
[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>000010
[1,2,6,3,4,7,5]=>[1,2,6,3,7,4,5]=>[1,2,7,3,4,6,5]=>000011
[1,2,6,3,5,4,7]=>[1,2,6,5,3,4,7]=>[1,2,5,3,6,4,7]=>000110
[1,2,6,3,5,7,4]=>[1,2,6,7,3,5,4]=>[1,2,7,3,5,6,4]=>000011
[1,2,6,3,7,4,5]=>[1,2,6,7,4,3,5]=>[1,2,7,4,6,3,5]=>000011
[1,2,6,3,7,5,4]=>[1,2,6,5,7,3,4]=>[1,2,7,5,3,6,4]=>000111
[1,2,6,4,3,5,7]=>[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>001010
[1,2,6,4,3,7,5]=>[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]=>001011
[1,2,6,4,5,3,7]=>[1,2,5,6,4,3,7]=>[1,2,6,4,5,3,7]=>000110
[1,2,6,4,5,7,3]=>[1,2,7,6,4,5,3]=>[1,2,6,4,5,7,3]=>000011
[1,2,6,4,7,3,5]=>[1,2,7,6,3,4,5]=>[1,2,6,3,7,4,5]=>000011
[1,2,6,4,7,5,3]=>[1,2,5,7,6,3,4]=>[1,2,6,3,7,5,4]=>000111
[1,2,6,5,3,4,7]=>[1,2,5,3,6,4,7]=>[1,2,6,5,3,4,7]=>000110
[1,2,6,5,3,7,4]=>[1,2,5,6,7,4,3]=>[1,2,7,4,6,5,3]=>000111
[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>[1,2,6,5,4,3,7]=>001110
[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]=>[1,2,6,5,4,7,3]=>000111
[1,2,6,5,7,3,4]=>[1,2,7,3,6,5,4]=>[1,2,6,5,7,3,4]=>000011
[1,2,6,5,7,4,3]=>[1,2,4,7,6,5,3]=>[1,2,6,5,7,4,3]=>001011
[1,2,6,7,3,4,5]=>[1,2,7,3,4,6,5]=>[1,2,6,7,3,4,5]=>000001
[1,2,6,7,3,5,4]=>[1,2,7,5,3,6,4]=>[1,2,5,3,6,7,4]=>000101
[1,2,6,7,4,3,5]=>[1,2,4,7,3,6,5]=>[1,2,6,7,4,3,5]=>001001
[1,2,6,7,4,5,3]=>[1,2,5,7,4,6,3]=>[1,2,6,7,4,5,3]=>000101
[1,2,6,7,5,3,4]=>[1,2,5,3,7,6,4]=>[1,2,6,7,5,3,4]=>000101
[1,2,6,7,5,4,3]=>[1,2,4,5,7,6,3]=>[1,2,6,7,5,4,3]=>001101
[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>000001
[1,2,7,3,4,6,5]=>[1,2,7,3,6,4,5]=>[1,2,6,3,4,7,5]=>000011
[1,2,7,3,5,4,6]=>[1,2,7,5,3,4,6]=>[1,2,5,3,7,4,6]=>000101
[1,2,7,3,5,6,4]=>[1,2,7,6,3,5,4]=>[1,2,6,3,5,7,4]=>000011
[1,2,7,3,6,4,5]=>[1,2,7,6,4,3,5]=>[1,2,6,4,7,3,5]=>000011
[1,2,7,3,6,5,4]=>[1,2,7,5,6,3,4]=>[1,2,6,5,3,7,4]=>000111
[1,2,7,4,3,5,6]=>[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>001001
[1,2,7,4,3,6,5]=>[1,2,4,7,6,3,5]=>[1,2,6,4,3,7,5]=>001011
[1,2,7,4,5,3,6]=>[1,2,5,7,4,3,6]=>[1,2,7,4,5,3,6]=>000101
[1,2,7,4,5,6,3]=>[1,2,6,7,4,5,3]=>[1,2,7,4,5,6,3]=>000011
[1,2,7,4,6,3,5]=>[1,2,6,7,3,4,5]=>[1,2,7,3,6,4,5]=>000011
[1,2,7,4,6,5,3]=>[1,2,5,6,7,3,4]=>[1,2,7,3,6,5,4]=>000111
[1,2,7,5,3,4,6]=>[1,2,5,3,7,4,6]=>[1,2,7,5,3,4,6]=>000101
[1,2,7,5,3,6,4]=>[1,2,5,7,6,4,3]=>[1,2,6,4,7,5,3]=>000111
[1,2,7,5,4,3,6]=>[1,2,4,5,7,3,6]=>[1,2,7,5,4,3,6]=>001101
[1,2,7,5,4,6,3]=>[1,2,6,5,7,4,3]=>[1,2,7,5,4,6,3]=>000111
[1,2,7,5,6,3,4]=>[1,2,6,3,7,5,4]=>[1,2,7,5,6,3,4]=>000011
[1,2,7,5,6,4,3]=>[1,2,4,6,7,5,3]=>[1,2,7,5,6,4,3]=>001011
[1,2,7,6,3,4,5]=>[1,2,6,3,4,7,5]=>[1,2,7,6,3,4,5]=>000011
[1,2,7,6,3,5,4]=>[1,2,6,5,3,7,4]=>[1,2,5,3,7,6,4]=>000111
[1,2,7,6,4,3,5]=>[1,2,4,6,3,7,5]=>[1,2,7,6,4,3,5]=>001011
[1,2,7,6,4,5,3]=>[1,2,5,6,4,7,3]=>[1,2,7,6,4,5,3]=>000111
[1,2,7,6,5,3,4]=>[1,2,5,3,6,7,4]=>[1,2,7,6,5,3,4]=>000111
[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]=>[1,2,7,6,5,4,3]=>001111
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000
[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>010001
[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>010010
[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>010001
[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>010001
[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>010011
[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>010100
[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>010101
[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>010010
[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[1,3,2,5,6,7,4]=>010001
[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>[1,3,2,5,7,4,6]=>010001
[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>[1,3,2,5,7,6,4]=>010011
[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>010010
[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]=>010011
[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>010110
[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>[1,3,2,6,5,7,4]=>010011
[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,4,5]=>010001
[1,3,2,6,7,5,4]=>[1,3,2,5,7,6,4]=>[1,3,2,6,7,5,4]=>010101
[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>010001
[1,3,2,7,4,6,5]=>[1,3,2,7,6,4,5]=>[1,3,2,6,4,7,5]=>010011
[1,3,2,7,5,4,6]=>[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>010101
[1,3,2,7,5,6,4]=>[1,3,2,6,7,5,4]=>[1,3,2,7,5,6,4]=>010011
[1,3,2,7,6,4,5]=>[1,3,2,6,4,7,5]=>[1,3,2,7,6,4,5]=>010011
[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]=>[1,3,2,7,6,5,4]=>010111
[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>001000
[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>001001
[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>001010
[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>001001
[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>[1,3,4,2,7,5,6]=>001001
[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>001011
[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[1,3,4,5,2,6,7]=>000100
[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[1,3,4,5,2,7,6]=>000101
[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[1,3,4,5,6,2,7]=>000010
[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[1,3,4,5,6,7,2]=>000001
[1,3,4,5,7,2,6]=>[1,7,3,4,5,2,6]=>[1,3,4,5,7,2,6]=>000001
[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>[1,3,4,5,7,6,2]=>000011
[1,3,4,6,2,5,7]=>[1,6,3,4,2,5,7]=>[1,3,4,6,2,5,7]=>000010
[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[1,3,4,7,2,6,5]=>000011
[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]=>[1,3,4,6,5,2,7]=>000110
[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>[1,3,4,6,5,7,2]=>000011
[1,3,4,6,7,2,5]=>[1,7,3,4,2,6,5]=>[1,3,4,6,7,2,5]=>000001
[1,3,4,6,7,5,2]=>[1,5,3,4,7,6,2]=>[1,3,4,6,7,5,2]=>000101
[1,3,4,7,2,5,6]=>[1,7,3,4,2,5,6]=>[1,3,4,7,2,5,6]=>000001
[1,3,4,7,2,6,5]=>[1,7,3,4,6,2,5]=>[1,3,4,6,2,7,5]=>000011
[1,3,4,7,5,2,6]=>[1,5,3,4,7,2,6]=>[1,3,4,7,5,2,6]=>000101
[1,3,4,7,5,6,2]=>[1,6,3,4,7,5,2]=>[1,3,4,7,5,6,2]=>000011
[1,3,4,7,6,2,5]=>[1,6,3,4,2,7,5]=>[1,3,4,7,6,2,5]=>000011
[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]=>[1,3,4,7,6,5,2]=>000111
[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>[1,3,5,2,4,6,7]=>000100
[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>[1,3,5,2,4,7,6]=>000101
[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[1,3,6,2,5,4,7]=>000110
[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[1,3,6,7,2,5,4]=>000101
[1,3,5,2,7,4,6]=>[1,5,3,7,2,4,6]=>[1,3,7,2,5,4,6]=>000101
[1,3,5,2,7,6,4]=>[1,5,3,6,2,7,4]=>[1,3,7,6,2,5,4]=>000111
[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>[1,3,5,4,2,6,7]=>001100
[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]=>[1,3,5,4,2,7,6]=>001101
[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>[1,3,5,4,6,2,7]=>000110
[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>[1,3,5,4,6,7,2]=>000101
[1,3,5,4,7,2,6]=>[1,7,3,5,4,2,6]=>[1,3,5,4,7,2,6]=>000101
[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]=>[1,3,5,4,7,6,2]=>000111
[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]=>[1,3,5,6,2,4,7]=>000010
[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[1,3,5,7,2,6,4]=>000011
[1,3,5,6,4,2,7]=>[1,4,3,6,5,2,7]=>[1,3,5,6,4,2,7]=>001010
[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>[1,3,5,6,4,7,2]=>000011
[1,3,5,6,7,2,4]=>[1,7,3,2,5,6,4]=>[1,3,5,6,7,2,4]=>000001
[1,3,5,6,7,4,2]=>[1,4,3,7,5,6,2]=>[1,3,5,6,7,4,2]=>001001
[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]=>[1,3,5,7,2,4,6]=>000001
[1,3,5,7,2,6,4]=>[1,7,3,6,5,2,4]=>[1,3,5,6,2,7,4]=>000011
[1,3,5,7,4,2,6]=>[1,4,3,7,5,2,6]=>[1,3,5,7,4,2,6]=>001001
[1,3,5,7,4,6,2]=>[1,6,3,7,5,4,2]=>[1,3,5,7,4,6,2]=>000011
[1,3,5,7,6,2,4]=>[1,6,3,2,5,7,4]=>[1,3,5,7,6,2,4]=>000011
[1,3,5,7,6,4,2]=>[1,4,3,6,5,7,2]=>[1,3,5,7,6,4,2]=>001011
[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>[1,3,6,2,4,5,7]=>000010
[1,3,6,2,4,7,5]=>[1,6,3,2,7,4,5]=>[1,3,7,2,4,6,5]=>000011
[1,3,6,2,5,4,7]=>[1,6,3,5,2,4,7]=>[1,3,5,2,6,4,7]=>000110
[1,3,6,2,5,7,4]=>[1,6,3,7,2,5,4]=>[1,3,7,2,5,6,4]=>000011
[1,3,6,2,7,4,5]=>[1,6,3,7,4,2,5]=>[1,3,7,4,6,2,5]=>000011
[1,3,6,2,7,5,4]=>[1,6,3,5,7,2,4]=>[1,3,7,5,2,6,4]=>000111
[1,3,6,4,2,5,7]=>[1,4,3,6,2,5,7]=>[1,3,6,4,2,5,7]=>001010
[1,3,6,4,2,7,5]=>[1,4,3,6,7,2,5]=>[1,3,7,4,2,6,5]=>001011
[1,3,6,4,5,2,7]=>[1,5,3,6,4,2,7]=>[1,3,6,4,5,2,7]=>000110
[1,3,6,4,5,7,2]=>[1,7,3,6,4,5,2]=>[1,3,6,4,5,7,2]=>000011
[1,3,6,4,7,2,5]=>[1,7,3,6,2,4,5]=>[1,3,6,2,7,4,5]=>000011
[1,3,6,4,7,5,2]=>[1,5,3,7,6,2,4]=>[1,3,6,2,7,5,4]=>000111
[1,3,6,5,2,4,7]=>[1,5,3,2,6,4,7]=>[1,3,6,5,2,4,7]=>000110
[1,3,6,5,2,7,4]=>[1,5,3,6,7,4,2]=>[1,3,7,4,6,5,2]=>000111
[1,3,6,5,4,2,7]=>[1,4,3,5,6,2,7]=>[1,3,6,5,4,2,7]=>001110
[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]=>[1,3,6,5,4,7,2]=>000111
[1,3,6,5,7,2,4]=>[1,7,3,2,6,5,4]=>[1,3,6,5,7,2,4]=>000011
[1,3,6,5,7,4,2]=>[1,4,3,7,6,5,2]=>[1,3,6,5,7,4,2]=>001011
[1,3,6,7,2,4,5]=>[1,7,3,2,4,6,5]=>[1,3,6,7,2,4,5]=>000001
[1,3,6,7,2,5,4]=>[1,7,3,5,2,6,4]=>[1,3,5,2,6,7,4]=>000101
[1,3,6,7,4,2,5]=>[1,4,3,7,2,6,5]=>[1,3,6,7,4,2,5]=>001001
[1,3,6,7,4,5,2]=>[1,5,3,7,4,6,2]=>[1,3,6,7,4,5,2]=>000101
[1,3,6,7,5,2,4]=>[1,5,3,2,7,6,4]=>[1,3,6,7,5,2,4]=>000101
[1,3,6,7,5,4,2]=>[1,4,3,5,7,6,2]=>[1,3,6,7,5,4,2]=>001101
[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>[1,3,7,2,4,5,6]=>000001
[1,3,7,2,4,6,5]=>[1,7,3,2,6,4,5]=>[1,3,6,2,4,7,5]=>000011
[1,3,7,2,5,4,6]=>[1,7,3,5,2,4,6]=>[1,3,5,2,7,4,6]=>000101
[1,3,7,2,5,6,4]=>[1,7,3,6,2,5,4]=>[1,3,6,2,5,7,4]=>000011
[1,3,7,2,6,4,5]=>[1,7,3,6,4,2,5]=>[1,3,6,4,7,2,5]=>000011
[1,3,7,2,6,5,4]=>[1,7,3,5,6,2,4]=>[1,3,6,5,2,7,4]=>000111
[1,3,7,4,2,5,6]=>[1,4,3,7,2,5,6]=>[1,3,7,4,2,5,6]=>001001
[1,3,7,4,2,6,5]=>[1,4,3,7,6,2,5]=>[1,3,6,4,2,7,5]=>001011
[1,3,7,4,5,2,6]=>[1,5,3,7,4,2,6]=>[1,3,7,4,5,2,6]=>000101
[1,3,7,4,5,6,2]=>[1,6,3,7,4,5,2]=>[1,3,7,4,5,6,2]=>000011
[1,3,7,4,6,2,5]=>[1,6,3,7,2,4,5]=>[1,3,7,2,6,4,5]=>000011
[1,3,7,4,6,5,2]=>[1,5,3,6,7,2,4]=>[1,3,7,2,6,5,4]=>000111
[1,3,7,5,2,4,6]=>[1,5,3,2,7,4,6]=>[1,3,7,5,2,4,6]=>000101
[1,3,7,5,2,6,4]=>[1,5,3,7,6,4,2]=>[1,3,6,4,7,5,2]=>000111
[1,3,7,5,4,2,6]=>[1,4,3,5,7,2,6]=>[1,3,7,5,4,2,6]=>001101
[1,3,7,5,4,6,2]=>[1,6,3,5,7,4,2]=>[1,3,7,5,4,6,2]=>000111
[1,3,7,5,6,2,4]=>[1,6,3,2,7,5,4]=>[1,3,7,5,6,2,4]=>000011
[1,3,7,5,6,4,2]=>[1,4,3,6,7,5,2]=>[1,3,7,5,6,4,2]=>001011
[1,3,7,6,2,4,5]=>[1,6,3,2,4,7,5]=>[1,3,7,6,2,4,5]=>000011
[1,3,7,6,2,5,4]=>[1,6,3,5,2,7,4]=>[1,3,5,2,7,6,4]=>000111
[1,3,7,6,4,2,5]=>[1,4,3,6,2,7,5]=>[1,3,7,6,4,2,5]=>001011
[1,3,7,6,4,5,2]=>[1,5,3,6,4,7,2]=>[1,3,7,6,4,5,2]=>000111
[1,3,7,6,5,2,4]=>[1,5,3,2,6,7,4]=>[1,3,7,6,5,2,4]=>000111
[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]=>[1,3,7,6,5,4,2]=>001111
[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>001000
[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>001001
[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>001010
[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>[1,4,2,3,6,7,5]=>001001
[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>001001
[1,4,2,3,7,6,5]=>[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>001011
[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]=>001100
[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]=>001101
[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[1,5,6,2,4,3,7]=>001010
[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[1,5,6,7,2,4,3]=>001001
[1,4,2,5,7,3,6]=>[1,4,7,2,5,3,6]=>[1,5,7,2,4,3,6]=>001001
[1,4,2,5,7,6,3]=>[1,4,6,2,5,7,3]=>[1,5,7,6,2,4,3]=>001011
[1,4,2,6,3,5,7]=>[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]=>001010
[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[1,7,2,4,3,6,5]=>001011
[1,4,2,6,5,3,7]=>[1,4,5,2,6,3,7]=>[1,6,5,2,4,3,7]=>001110
[1,4,2,6,5,7,3]=>[1,4,7,2,6,5,3]=>[1,6,5,7,2,4,3]=>001011
[1,4,2,6,7,3,5]=>[1,4,7,2,3,6,5]=>[1,6,7,2,4,3,5]=>001001
[1,4,2,6,7,5,3]=>[1,4,5,2,7,6,3]=>[1,6,7,5,2,4,3]=>001101
[1,4,2,7,3,5,6]=>[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]=>001001
[1,4,2,7,3,6,5]=>[1,4,7,2,6,3,5]=>[1,6,2,4,3,7,5]=>001011
[1,4,2,7,5,3,6]=>[1,4,5,2,7,3,6]=>[1,7,5,2,4,3,6]=>001101
[1,4,2,7,5,6,3]=>[1,4,6,2,7,5,3]=>[1,7,5,6,2,4,3]=>001011
[1,4,2,7,6,3,5]=>[1,4,6,2,3,7,5]=>[1,7,6,2,4,3,5]=>001011
[1,4,2,7,6,5,3]=>[1,4,5,2,6,7,3]=>[1,7,6,5,2,4,3]=>001111
[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>011000
[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>011001
[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>011010
[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>011001
[1,4,3,2,7,5,6]=>[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>011001
[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>011011
[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>[1,4,3,5,2,6,7]=>001100
[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>[1,4,3,5,2,7,6]=>001101
[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>[1,4,3,5,6,2,7]=>001010
[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>[1,4,3,5,6,7,2]=>001001
[1,4,3,5,7,2,6]=>[1,7,4,3,5,2,6]=>[1,4,3,5,7,2,6]=>001001
[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]=>[1,4,3,5,7,6,2]=>001011
[1,4,3,6,2,5,7]=>[1,6,4,3,2,5,7]=>[1,4,3,6,2,5,7]=>001010
[1,4,3,6,2,7,5]=>[1,6,4,3,7,2,5]=>[1,4,3,7,2,6,5]=>001011
[1,4,3,6,5,2,7]=>[1,5,4,3,6,2,7]=>[1,4,3,6,5,2,7]=>001110
[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>[1,4,3,6,5,7,2]=>001011
[1,4,3,6,7,2,5]=>[1,7,4,3,2,6,5]=>[1,4,3,6,7,2,5]=>001001
[1,4,3,6,7,5,2]=>[1,5,4,3,7,6,2]=>[1,4,3,6,7,5,2]=>001101
[1,4,3,7,2,5,6]=>[1,7,4,3,2,5,6]=>[1,4,3,7,2,5,6]=>001001
[1,4,3,7,2,6,5]=>[1,7,4,3,6,2,5]=>[1,4,3,6,2,7,5]=>001011
[1,4,3,7,5,2,6]=>[1,5,4,3,7,2,6]=>[1,4,3,7,5,2,6]=>001101
[1,4,3,7,5,6,2]=>[1,6,4,3,7,5,2]=>[1,4,3,7,5,6,2]=>001011
[1,4,3,7,6,2,5]=>[1,6,4,3,2,7,5]=>[1,4,3,7,6,2,5]=>001011
[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]=>[1,4,3,7,6,5,2]=>001111
[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]=>[1,4,5,2,3,6,7]=>000100
[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]=>[1,4,5,2,3,7,6]=>000101
[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[1,4,6,2,5,3,7]=>000110
[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[1,4,6,7,2,5,3]=>000101
[1,4,5,2,7,3,6]=>[1,5,7,4,2,3,6]=>[1,4,7,2,5,3,6]=>000101
[1,4,5,2,7,6,3]=>[1,5,6,4,2,7,3]=>[1,4,7,6,2,5,3]=>000111
[1,4,5,3,2,6,7]=>[1,3,5,4,2,6,7]=>[1,4,5,3,2,6,7]=>010100
[1,4,5,3,2,7,6]=>[1,3,5,4,2,7,6]=>[1,4,5,3,2,7,6]=>010101
[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>[1,4,5,3,6,2,7]=>000110
[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>[1,4,5,3,6,7,2]=>000101
[1,4,5,3,7,2,6]=>[1,7,5,4,3,2,6]=>[1,4,5,3,7,2,6]=>000101
[1,4,5,3,7,6,2]=>[1,6,5,4,3,7,2]=>[1,4,5,3,7,6,2]=>000111
[1,4,5,6,2,3,7]=>[1,6,2,4,5,3,7]=>[1,4,5,6,2,3,7]=>000010
[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[1,4,5,7,2,6,3]=>000011
[1,4,5,6,3,2,7]=>[1,3,6,4,5,2,7]=>[1,4,5,6,3,2,7]=>010010
[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>[1,4,5,6,3,7,2]=>000011
[1,4,5,6,7,2,3]=>[1,7,2,4,5,6,3]=>[1,4,5,6,7,2,3]=>000001
[1,4,5,6,7,3,2]=>[1,3,7,4,5,6,2]=>[1,4,5,6,7,3,2]=>010001
[1,4,5,7,2,3,6]=>[1,7,2,4,5,3,6]=>[1,4,5,7,2,3,6]=>000001
[1,4,5,7,2,6,3]=>[1,7,6,4,5,2,3]=>[1,4,5,6,2,7,3]=>000011
[1,4,5,7,3,2,6]=>[1,3,7,4,5,2,6]=>[1,4,5,7,3,2,6]=>010001
[1,4,5,7,3,6,2]=>[1,6,7,4,5,3,2]=>[1,4,5,7,3,6,2]=>000011
[1,4,5,7,6,2,3]=>[1,6,2,4,5,7,3]=>[1,4,5,7,6,2,3]=>000011
[1,4,5,7,6,3,2]=>[1,3,6,4,5,7,2]=>[1,4,5,7,6,3,2]=>010011
[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]=>[1,4,6,2,3,5,7]=>000010
[1,4,6,2,3,7,5]=>[1,6,2,4,7,3,5]=>[1,4,7,2,3,6,5]=>000011
[1,4,6,2,5,3,7]=>[1,6,5,4,2,3,7]=>[1,4,5,2,6,3,7]=>000110
[1,4,6,2,5,7,3]=>[1,6,7,4,2,5,3]=>[1,4,7,2,5,6,3]=>000011
[1,4,6,2,7,3,5]=>[1,6,7,4,3,2,5]=>[1,4,7,3,6,2,5]=>000011
[1,4,6,2,7,5,3]=>[1,6,5,4,7,2,3]=>[1,4,7,5,2,6,3]=>000111
[1,4,6,3,2,5,7]=>[1,3,6,4,2,5,7]=>[1,4,6,3,2,5,7]=>010010
[1,4,6,3,2,7,5]=>[1,3,6,4,7,2,5]=>[1,4,7,3,2,6,5]=>010011
[1,4,6,3,5,2,7]=>[1,5,6,4,3,2,7]=>[1,4,6,3,5,2,7]=>000110
[1,4,6,3,5,7,2]=>[1,7,6,4,3,5,2]=>[1,4,6,3,5,7,2]=>000011
[1,4,6,3,7,2,5]=>[1,7,6,4,2,3,5]=>[1,4,6,2,7,3,5]=>000011
[1,4,6,3,7,5,2]=>[1,5,7,4,6,2,3]=>[1,4,6,2,7,5,3]=>000111
[1,4,6,5,2,3,7]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>000110
[1,4,6,5,2,7,3]=>[1,5,6,4,7,3,2]=>[1,4,7,3,6,5,2]=>000111
[1,4,6,5,3,2,7]=>[1,3,5,4,6,2,7]=>[1,4,6,5,3,2,7]=>010110
[1,4,6,5,3,7,2]=>[1,7,5,4,6,3,2]=>[1,4,6,5,3,7,2]=>000111
[1,4,6,5,7,2,3]=>[1,7,2,4,6,5,3]=>[1,4,6,5,7,2,3]=>000011
[1,4,6,5,7,3,2]=>[1,3,7,4,6,5,2]=>[1,4,6,5,7,3,2]=>010011
[1,4,6,7,2,3,5]=>[1,7,2,4,3,6,5]=>[1,4,6,7,2,3,5]=>000001
[1,4,6,7,2,5,3]=>[1,7,5,4,2,6,3]=>[1,4,5,2,6,7,3]=>000101
[1,4,6,7,3,2,5]=>[1,3,7,4,2,6,5]=>[1,4,6,7,3,2,5]=>010001
[1,4,6,7,3,5,2]=>[1,5,7,4,3,6,2]=>[1,4,6,7,3,5,2]=>000101
[1,4,6,7,5,2,3]=>[1,5,2,4,7,6,3]=>[1,4,6,7,5,2,3]=>000101
[1,4,6,7,5,3,2]=>[1,3,5,4,7,6,2]=>[1,4,6,7,5,3,2]=>010101
[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]=>[1,4,7,2,3,5,6]=>000001
[1,4,7,2,3,6,5]=>[1,7,2,4,6,3,5]=>[1,4,6,2,3,7,5]=>000011
[1,4,7,2,5,3,6]=>[1,7,5,4,2,3,6]=>[1,4,5,2,7,3,6]=>000101
[1,4,7,2,5,6,3]=>[1,7,6,4,2,5,3]=>[1,4,6,2,5,7,3]=>000011
[1,4,7,2,6,3,5]=>[1,7,6,4,3,2,5]=>[1,4,6,3,7,2,5]=>000011
[1,4,7,2,6,5,3]=>[1,7,5,4,6,2,3]=>[1,4,6,5,2,7,3]=>000111
[1,4,7,3,2,5,6]=>[1,3,7,4,2,5,6]=>[1,4,7,3,2,5,6]=>010001
[1,4,7,3,2,6,5]=>[1,3,7,4,6,2,5]=>[1,4,6,3,2,7,5]=>010011
[1,4,7,3,5,2,6]=>[1,5,7,4,3,2,6]=>[1,4,7,3,5,2,6]=>000101
[1,4,7,3,5,6,2]=>[1,6,7,4,3,5,2]=>[1,4,7,3,5,6,2]=>000011
[1,4,7,3,6,2,5]=>[1,6,7,4,2,3,5]=>[1,4,7,2,6,3,5]=>000011
[1,4,7,3,6,5,2]=>[1,5,6,4,7,2,3]=>[1,4,7,2,6,5,3]=>000111
[1,4,7,5,2,3,6]=>[1,5,2,4,7,3,6]=>[1,4,7,5,2,3,6]=>000101
[1,4,7,5,2,6,3]=>[1,5,7,4,6,3,2]=>[1,4,6,3,7,5,2]=>000111
[1,4,7,5,3,2,6]=>[1,3,5,4,7,2,6]=>[1,4,7,5,3,2,6]=>010101
[1,4,7,5,3,6,2]=>[1,6,5,4,7,3,2]=>[1,4,7,5,3,6,2]=>000111
[1,4,7,5,6,2,3]=>[1,6,2,4,7,5,3]=>[1,4,7,5,6,2,3]=>000011
[1,4,7,5,6,3,2]=>[1,3,6,4,7,5,2]=>[1,4,7,5,6,3,2]=>010011
[1,4,7,6,2,3,5]=>[1,6,2,4,3,7,5]=>[1,4,7,6,2,3,5]=>000011
[1,4,7,6,2,5,3]=>[1,6,5,4,2,7,3]=>[1,4,5,2,7,6,3]=>000111
[1,4,7,6,3,2,5]=>[1,3,6,4,2,7,5]=>[1,4,7,6,3,2,5]=>010011
[1,4,7,6,3,5,2]=>[1,5,6,4,3,7,2]=>[1,4,7,6,3,5,2]=>000111
[1,4,7,6,5,2,3]=>[1,5,2,4,6,7,3]=>[1,4,7,6,5,2,3]=>000111
[1,4,7,6,5,3,2]=>[1,3,5,4,6,7,2]=>[1,4,7,6,5,3,2]=>010111
[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>000100
[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>000101
[1,5,2,3,6,4,7]=>[1,5,2,6,3,4,7]=>[1,6,2,3,5,4,7]=>000110
[1,5,2,3,6,7,4]=>[1,5,2,7,3,6,4]=>[1,6,7,2,3,5,4]=>000101
[1,5,2,3,7,4,6]=>[1,5,2,7,3,4,6]=>[1,7,2,3,5,4,6]=>000101
[1,5,2,3,7,6,4]=>[1,5,2,6,3,7,4]=>[1,7,6,2,3,5,4]=>000111
[1,5,2,4,3,6,7]=>[1,5,4,2,3,6,7]=>[1,4,2,5,3,6,7]=>001100
[1,5,2,4,3,7,6]=>[1,5,4,2,3,7,6]=>[1,4,2,5,3,7,6]=>001101
[1,5,2,4,6,3,7]=>[1,5,6,2,4,3,7]=>[1,6,2,4,5,3,7]=>000110
[1,5,2,4,6,7,3]=>[1,5,7,2,4,6,3]=>[1,6,7,2,4,5,3]=>000101
[1,5,2,4,7,3,6]=>[1,5,7,2,4,3,6]=>[1,7,2,4,5,3,6]=>000101
[1,5,2,4,7,6,3]=>[1,5,6,2,4,7,3]=>[1,7,6,2,4,5,3]=>000111
[1,5,2,6,3,4,7]=>[1,5,6,3,2,4,7]=>[1,6,3,5,2,4,7]=>000110
[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[1,7,2,6,3,5,4]=>000111
[1,5,2,6,4,3,7]=>[1,5,4,6,2,3,7]=>[1,6,4,2,5,3,7]=>001110
[1,5,2,6,4,7,3]=>[1,5,7,6,2,4,3]=>[1,6,2,7,4,5,3]=>000111
[1,5,2,6,7,3,4]=>[1,5,7,3,2,6,4]=>[1,6,7,3,5,2,4]=>000101
[1,5,2,6,7,4,3]=>[1,5,4,7,2,6,3]=>[1,6,7,4,2,5,3]=>001101
[1,5,2,7,3,4,6]=>[1,5,7,3,2,4,6]=>[1,7,3,5,2,4,6]=>000101
[1,5,2,7,3,6,4]=>[1,5,7,6,2,3,4]=>[1,6,2,7,3,5,4]=>000111
[1,5,2,7,4,3,6]=>[1,5,4,7,2,3,6]=>[1,7,4,2,5,3,6]=>001101
[1,5,2,7,4,6,3]=>[1,5,6,7,2,4,3]=>[1,7,2,6,4,5,3]=>000111
[1,5,2,7,6,3,4]=>[1,5,6,3,2,7,4]=>[1,7,6,3,5,2,4]=>000111
[1,5,2,7,6,4,3]=>[1,5,4,6,2,7,3]=>[1,7,6,4,2,5,3]=>001111
[1,5,3,2,4,6,7]=>[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>010100
[1,5,3,2,4,7,6]=>[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>010101
[1,5,3,2,6,4,7]=>[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]=>010110
[1,5,3,2,6,7,4]=>[1,3,5,7,2,6,4]=>[1,6,7,3,2,5,4]=>010101
[1,5,3,2,7,4,6]=>[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]=>010101
[1,5,3,2,7,6,4]=>[1,3,5,6,2,7,4]=>[1,7,6,3,2,5,4]=>010111
[1,5,3,4,2,6,7]=>[1,4,5,3,2,6,7]=>[1,5,3,4,2,6,7]=>001100
[1,5,3,4,2,7,6]=>[1,4,5,3,2,7,6]=>[1,5,3,4,2,7,6]=>001101
[1,5,3,4,6,2,7]=>[1,6,5,3,4,2,7]=>[1,5,3,4,6,2,7]=>000110
[1,5,3,4,6,7,2]=>[1,7,5,3,4,6,2]=>[1,5,3,4,6,7,2]=>000101
[1,5,3,4,7,2,6]=>[1,7,5,3,4,2,6]=>[1,5,3,4,7,2,6]=>000101
[1,5,3,4,7,6,2]=>[1,6,5,3,4,7,2]=>[1,5,3,4,7,6,2]=>000111
[1,5,3,6,2,4,7]=>[1,6,5,2,3,4,7]=>[1,5,2,6,3,4,7]=>000110
[1,5,3,6,2,7,4]=>[1,6,5,7,3,2,4]=>[1,7,3,5,2,6,4]=>000111
[1,5,3,6,4,2,7]=>[1,4,6,5,2,3,7]=>[1,5,2,6,4,3,7]=>001110
[1,5,3,6,4,7,2]=>[1,7,5,6,3,4,2]=>[1,6,3,5,4,7,2]=>000111
[1,5,3,6,7,2,4]=>[1,7,5,2,3,6,4]=>[1,5,2,6,7,3,4]=>000101
[1,5,3,6,7,4,2]=>[1,4,7,5,2,6,3]=>[1,5,2,6,7,4,3]=>001101
[1,5,3,7,2,4,6]=>[1,7,5,2,3,4,6]=>[1,5,2,7,3,4,6]=>000101
[1,5,3,7,2,6,4]=>[1,7,5,6,3,2,4]=>[1,6,3,5,2,7,4]=>000111
[1,5,3,7,4,2,6]=>[1,4,7,5,2,3,6]=>[1,5,2,7,4,3,6]=>001101
[1,5,3,7,4,6,2]=>[1,6,5,7,3,4,2]=>[1,7,3,5,4,6,2]=>000111
[1,5,3,7,6,2,4]=>[1,6,5,2,3,7,4]=>[1,5,2,7,6,3,4]=>000111
[1,5,3,7,6,4,2]=>[1,4,6,5,2,7,3]=>[1,5,2,7,6,4,3]=>001111
[1,5,4,2,3,6,7]=>[1,4,2,5,3,6,7]=>[1,5,4,2,3,6,7]=>001100
[1,5,4,2,3,7,6]=>[1,4,2,5,3,7,6]=>[1,5,4,2,3,7,6]=>001101
[1,5,4,2,6,3,7]=>[1,4,5,6,3,2,7]=>[1,6,3,5,4,2,7]=>001110
[1,5,4,2,6,7,3]=>[1,4,5,7,3,6,2]=>[1,6,7,3,5,4,2]=>001101
[1,5,4,2,7,3,6]=>[1,4,5,7,3,2,6]=>[1,7,3,5,4,2,6]=>001101
[1,5,4,2,7,6,3]=>[1,4,5,6,3,7,2]=>[1,7,6,3,5,4,2]=>001111
[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]=>[1,5,4,3,2,6,7]=>011100
[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]=>[1,5,4,3,2,7,6]=>011101
[1,5,4,3,6,2,7]=>[1,6,4,5,3,2,7]=>[1,5,4,3,6,2,7]=>001110
[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]=>[1,5,4,3,6,7,2]=>001101
[1,5,4,3,7,2,6]=>[1,7,4,5,3,2,6]=>[1,5,4,3,7,2,6]=>001101
[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]=>[1,5,4,3,7,6,2]=>001111
[1,5,4,6,2,3,7]=>[1,6,2,5,4,3,7]=>[1,5,4,6,2,3,7]=>000110
[1,5,4,6,2,7,3]=>[1,6,7,5,4,2,3]=>[1,5,4,7,2,6,3]=>000111
[1,5,4,6,3,2,7]=>[1,3,6,5,4,2,7]=>[1,5,4,6,3,2,7]=>010110
[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>[1,5,4,6,3,7,2]=>000111
[1,5,4,6,7,2,3]=>[1,7,2,5,4,6,3]=>[1,5,4,6,7,2,3]=>000101
[1,5,4,6,7,3,2]=>[1,3,7,5,4,6,2]=>[1,5,4,6,7,3,2]=>010101
[1,5,4,7,2,3,6]=>[1,7,2,5,4,3,6]=>[1,5,4,7,2,3,6]=>000101
[1,5,4,7,2,6,3]=>[1,7,6,5,4,2,3]=>[1,5,4,6,2,7,3]=>000111
[1,5,4,7,3,2,6]=>[1,3,7,5,4,2,6]=>[1,5,4,7,3,2,6]=>010101
[1,5,4,7,3,6,2]=>[1,6,7,5,4,3,2]=>[1,5,4,7,3,6,2]=>000111
[1,5,4,7,6,2,3]=>[1,6,2,5,4,7,3]=>[1,5,4,7,6,2,3]=>000111
[1,5,4,7,6,3,2]=>[1,3,6,5,4,7,2]=>[1,5,4,7,6,3,2]=>010111
[1,5,6,2,3,4,7]=>[1,6,2,3,5,4,7]=>[1,5,6,2,3,4,7]=>000010
[1,5,6,2,3,7,4]=>[1,6,2,7,5,3,4]=>[1,5,7,2,3,6,4]=>000011
[1,5,6,2,4,3,7]=>[1,6,4,2,5,3,7]=>[1,4,2,5,6,3,7]=>001010
[1,5,6,2,4,7,3]=>[1,6,7,2,5,4,3]=>[1,5,7,2,4,6,3]=>000011
[1,5,6,2,7,3,4]=>[1,6,7,3,5,2,4]=>[1,5,7,3,6,2,4]=>000011
[1,5,6,2,7,4,3]=>[1,6,4,7,5,2,3]=>[1,5,7,4,2,6,3]=>001011
[1,5,6,3,2,4,7]=>[1,3,6,2,5,4,7]=>[1,5,6,3,2,4,7]=>010010
[1,5,6,3,2,7,4]=>[1,3,6,7,5,2,4]=>[1,5,7,3,2,6,4]=>010011
[1,5,6,3,4,2,7]=>[1,4,6,3,5,2,7]=>[1,5,6,3,4,2,7]=>001010
[1,5,6,3,4,7,2]=>[1,7,6,3,5,4,2]=>[1,5,6,3,4,7,2]=>000011
[1,5,6,3,7,2,4]=>[1,7,6,2,5,3,4]=>[1,5,6,2,7,3,4]=>000011
[1,5,6,3,7,4,2]=>[1,4,7,6,5,2,3]=>[1,5,6,2,7,4,3]=>001011
[1,5,6,4,2,3,7]=>[1,4,2,6,5,3,7]=>[1,5,6,4,2,3,7]=>001010
[1,5,6,4,2,7,3]=>[1,4,6,7,5,3,2]=>[1,5,7,3,6,4,2]=>001011
[1,5,6,4,3,2,7]=>[1,3,4,6,5,2,7]=>[1,5,6,4,3,2,7]=>011010
[1,5,6,4,3,7,2]=>[1,7,4,6,5,3,2]=>[1,5,6,4,3,7,2]=>001011
[1,5,6,4,7,2,3]=>[1,7,2,6,5,4,3]=>[1,5,6,4,7,2,3]=>000011
[1,5,6,4,7,3,2]=>[1,3,7,6,5,4,2]=>[1,5,6,4,7,3,2]=>010011
[1,5,6,7,2,3,4]=>[1,7,2,3,5,6,4]=>[1,5,6,7,2,3,4]=>000001
[1,5,6,7,2,4,3]=>[1,7,4,2,5,6,3]=>[1,4,2,5,6,7,3]=>001001
[1,5,6,7,3,2,4]=>[1,3,7,2,5,6,4]=>[1,5,6,7,3,2,4]=>010001
[1,5,6,7,3,4,2]=>[1,4,7,3,5,6,2]=>[1,5,6,7,3,4,2]=>001001
[1,5,6,7,4,2,3]=>[1,4,2,7,5,6,3]=>[1,5,6,7,4,2,3]=>001001
[1,5,6,7,4,3,2]=>[1,3,4,7,5,6,2]=>[1,5,6,7,4,3,2]=>011001
[1,5,7,2,3,4,6]=>[1,7,2,3,5,4,6]=>[1,5,7,2,3,4,6]=>000001
[1,5,7,2,3,6,4]=>[1,7,2,6,5,3,4]=>[1,5,6,2,3,7,4]=>000011
[1,5,7,2,4,3,6]=>[1,7,4,2,5,3,6]=>[1,4,2,5,7,3,6]=>001001
[1,5,7,2,4,6,3]=>[1,7,6,2,5,4,3]=>[1,5,6,2,4,7,3]=>000011
[1,5,7,2,6,3,4]=>[1,7,6,3,5,2,4]=>[1,5,6,3,7,2,4]=>000011
[1,5,7,2,6,4,3]=>[1,7,4,6,5,2,3]=>[1,5,6,4,2,7,3]=>001011
[1,5,7,3,2,4,6]=>[1,3,7,2,5,4,6]=>[1,5,7,3,2,4,6]=>010001
[1,5,7,3,2,6,4]=>[1,3,7,6,5,2,4]=>[1,5,6,3,2,7,4]=>010011
[1,5,7,3,4,2,6]=>[1,4,7,3,5,2,6]=>[1,5,7,3,4,2,6]=>001001
[1,5,7,3,4,6,2]=>[1,6,7,3,5,4,2]=>[1,5,7,3,4,6,2]=>000011
[1,5,7,3,6,2,4]=>[1,6,7,2,5,3,4]=>[1,5,7,2,6,3,4]=>000011
[1,5,7,3,6,4,2]=>[1,4,6,7,5,2,3]=>[1,5,7,2,6,4,3]=>001011
[1,5,7,4,2,3,6]=>[1,4,2,7,5,3,6]=>[1,5,7,4,2,3,6]=>001001
[1,5,7,4,2,6,3]=>[1,4,7,6,5,3,2]=>[1,5,6,3,7,4,2]=>001011
[1,5,7,4,3,2,6]=>[1,3,4,7,5,2,6]=>[1,5,7,4,3,2,6]=>011001
[1,5,7,4,3,6,2]=>[1,6,4,7,5,3,2]=>[1,5,7,4,3,6,2]=>001011
[1,5,7,4,6,2,3]=>[1,6,2,7,5,4,3]=>[1,5,7,4,6,2,3]=>000011
[1,5,7,4,6,3,2]=>[1,3,6,7,5,4,2]=>[1,5,7,4,6,3,2]=>010011
[1,5,7,6,2,3,4]=>[1,6,2,3,5,7,4]=>[1,5,7,6,2,3,4]=>000011
[1,5,7,6,2,4,3]=>[1,6,4,2,5,7,3]=>[1,4,2,5,7,6,3]=>001011
[1,5,7,6,3,2,4]=>[1,3,6,2,5,7,4]=>[1,5,7,6,3,2,4]=>010011
[1,5,7,6,3,4,2]=>[1,4,6,3,5,7,2]=>[1,5,7,6,3,4,2]=>001011
[1,5,7,6,4,2,3]=>[1,4,2,6,5,7,3]=>[1,5,7,6,4,2,3]=>001011
[1,5,7,6,4,3,2]=>[1,3,4,6,5,7,2]=>[1,5,7,6,4,3,2]=>011011
[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>000010
[1,6,2,3,4,7,5]=>[1,6,2,3,7,4,5]=>[1,7,2,3,4,6,5]=>000011
[1,6,2,3,5,4,7]=>[1,6,2,5,3,4,7]=>[1,5,2,3,6,4,7]=>000110
[1,6,2,3,5,7,4]=>[1,6,2,7,3,5,4]=>[1,7,2,3,5,6,4]=>000011
[1,6,2,3,7,4,5]=>[1,6,2,7,4,3,5]=>[1,7,4,6,2,3,5]=>000011
[1,6,2,3,7,5,4]=>[1,6,2,5,7,3,4]=>[1,7,5,2,3,6,4]=>000111
[1,6,2,4,3,5,7]=>[1,6,4,2,3,5,7]=>[1,4,2,6,3,5,7]=>001010
[1,6,2,4,3,7,5]=>[1,6,4,2,7,3,5]=>[1,4,2,7,3,6,5]=>001011
[1,6,2,4,5,3,7]=>[1,6,5,2,4,3,7]=>[1,5,2,4,6,3,7]=>000110
[1,6,2,4,5,7,3]=>[1,6,7,2,4,5,3]=>[1,7,2,4,5,6,3]=>000011
[1,6,2,4,7,3,5]=>[1,6,7,2,3,4,5]=>[1,7,2,6,3,4,5]=>000011
[1,6,2,4,7,5,3]=>[1,6,5,2,7,4,3]=>[1,7,5,2,4,6,3]=>000111
[1,6,2,5,3,4,7]=>[1,6,5,3,2,4,7]=>[1,5,3,6,2,4,7]=>000110
[1,6,2,5,3,7,4]=>[1,6,5,7,2,3,4]=>[1,7,2,5,3,6,4]=>000111
[1,6,2,5,4,3,7]=>[1,6,4,5,2,3,7]=>[1,5,4,2,6,3,7]=>001110
[1,6,2,5,4,7,3]=>[1,6,7,5,2,4,3]=>[1,5,2,7,4,6,3]=>000111
[1,6,2,5,7,3,4]=>[1,6,7,3,2,5,4]=>[1,7,3,5,6,2,4]=>000011
[1,6,2,5,7,4,3]=>[1,6,4,7,2,5,3]=>[1,7,4,2,5,6,3]=>001011
[1,6,2,7,3,4,5]=>[1,6,7,3,4,2,5]=>[1,7,3,4,6,2,5]=>000011
[1,6,2,7,3,5,4]=>[1,6,7,5,3,2,4]=>[1,5,3,7,2,6,4]=>000111
[1,6,2,7,4,3,5]=>[1,6,4,7,3,2,5]=>[1,7,4,3,6,2,5]=>001011
[1,6,2,7,4,5,3]=>[1,6,5,7,4,2,3]=>[1,7,4,5,2,6,3]=>000111
[1,6,2,7,5,3,4]=>[1,6,5,3,7,2,4]=>[1,7,5,3,6,2,4]=>000111
[1,6,2,7,5,4,3]=>[1,6,4,5,7,2,3]=>[1,7,5,4,2,6,3]=>001111
[1,6,3,2,4,5,7]=>[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>010010
[1,6,3,2,4,7,5]=>[1,3,6,2,7,4,5]=>[1,7,3,2,4,6,5]=>010011
[1,6,3,2,5,4,7]=>[1,3,6,5,2,4,7]=>[1,5,3,2,6,4,7]=>010110
[1,6,3,2,5,7,4]=>[1,3,6,7,2,5,4]=>[1,7,3,2,5,6,4]=>010011
[1,6,3,2,7,4,5]=>[1,3,6,7,4,2,5]=>[1,7,4,6,3,2,5]=>010011
[1,6,3,2,7,5,4]=>[1,3,6,5,7,2,4]=>[1,7,5,3,2,6,4]=>010111
[1,6,3,4,2,5,7]=>[1,4,6,3,2,5,7]=>[1,6,3,4,2,5,7]=>001010
[1,6,3,4,2,7,5]=>[1,4,6,3,7,2,5]=>[1,7,3,4,2,6,5]=>001011
[1,6,3,4,5,2,7]=>[1,5,6,3,4,2,7]=>[1,6,3,4,5,2,7]=>000110
[1,6,3,4,5,7,2]=>[1,7,6,3,4,5,2]=>[1,6,3,4,5,7,2]=>000011
[1,6,3,4,7,2,5]=>[1,7,6,3,2,4,5]=>[1,6,3,7,2,4,5]=>000011
[1,6,3,4,7,5,2]=>[1,5,7,2,6,4,3]=>[1,6,2,4,7,5,3]=>000111
[1,6,3,5,2,4,7]=>[1,5,6,2,3,4,7]=>[1,6,2,5,3,4,7]=>000110
[1,6,3,5,2,7,4]=>[1,5,6,7,3,2,4]=>[1,7,3,6,2,5,4]=>000111
[1,6,3,5,4,2,7]=>[1,4,5,6,2,3,7]=>[1,6,2,5,4,3,7]=>001110
[1,6,3,5,4,7,2]=>[1,7,6,5,3,4,2]=>[1,5,3,6,4,7,2]=>000111
[1,6,3,5,7,2,4]=>[1,7,6,2,3,5,4]=>[1,6,2,5,7,3,4]=>000011
[1,6,3,5,7,4,2]=>[1,4,7,6,2,5,3]=>[1,6,2,5,7,4,3]=>001011
[1,6,3,7,2,4,5]=>[1,7,6,2,4,3,5]=>[1,6,2,4,7,3,5]=>000011
[1,6,3,7,2,5,4]=>[1,7,6,5,2,3,4]=>[1,5,2,6,3,7,4]=>000111
[1,6,3,7,4,2,5]=>[1,4,7,6,3,2,5]=>[1,6,3,7,4,2,5]=>001011
[1,6,3,7,4,5,2]=>[1,5,6,7,4,3,2]=>[1,7,4,6,3,5,2]=>000111
[1,6,3,7,5,2,4]=>[1,5,7,3,6,2,4]=>[1,6,3,7,5,2,4]=>000111
[1,6,3,7,5,4,2]=>[1,4,5,7,6,3,2]=>[1,6,3,7,5,4,2]=>001111
[1,6,4,2,3,5,7]=>[1,4,2,6,3,5,7]=>[1,6,4,2,3,5,7]=>001010
[1,6,4,2,3,7,5]=>[1,4,2,6,7,3,5]=>[1,7,4,2,3,6,5]=>001011
[1,6,4,2,5,3,7]=>[1,4,6,5,3,2,7]=>[1,5,3,6,4,2,7]=>001110
[1,6,4,2,5,7,3]=>[1,4,6,7,3,5,2]=>[1,7,3,5,6,4,2]=>001011
[1,6,4,2,7,3,5]=>[1,4,6,7,2,3,5]=>[1,7,2,6,4,3,5]=>001011
[1,6,4,2,7,5,3]=>[1,4,6,5,7,3,2]=>[1,7,5,3,6,4,2]=>001111
[1,6,4,3,2,5,7]=>[1,3,4,6,2,5,7]=>[1,6,4,3,2,5,7]=>011010
[1,6,4,3,2,7,5]=>[1,3,4,6,7,2,5]=>[1,7,4,3,2,6,5]=>011011
[1,6,4,3,5,2,7]=>[1,5,4,6,3,2,7]=>[1,6,4,3,5,2,7]=>001110
[1,6,4,3,5,7,2]=>[1,7,4,6,3,5,2]=>[1,6,4,3,5,7,2]=>001011
[1,6,4,3,7,2,5]=>[1,7,4,6,2,3,5]=>[1,6,4,2,7,3,5]=>001011
[1,6,4,3,7,5,2]=>[1,5,4,7,6,2,3]=>[1,6,4,2,7,5,3]=>001111
[1,6,4,5,2,3,7]=>[1,5,2,6,4,3,7]=>[1,6,4,5,2,3,7]=>000110
[1,6,4,5,2,7,3]=>[1,5,7,6,4,2,3]=>[1,6,4,7,2,5,3]=>000111
[1,6,4,5,3,2,7]=>[1,3,5,6,4,2,7]=>[1,6,4,5,3,2,7]=>010110
[1,6,4,5,3,7,2]=>[1,7,5,6,4,3,2]=>[1,6,4,5,3,7,2]=>000111
[1,6,4,5,7,2,3]=>[1,7,2,6,4,5,3]=>[1,6,4,5,7,2,3]=>000011
[1,6,4,5,7,3,2]=>[1,3,7,6,4,5,2]=>[1,6,4,5,7,3,2]=>010011
[1,6,4,7,2,3,5]=>[1,7,2,6,3,4,5]=>[1,6,2,3,7,4,5]=>000011
[1,6,4,7,2,5,3]=>[1,7,5,6,2,4,3]=>[1,6,2,5,4,7,3]=>000111
[1,6,4,7,3,2,5]=>[1,3,7,6,2,4,5]=>[1,6,3,2,7,4,5]=>010011
[1,6,4,7,3,5,2]=>[1,5,7,6,3,4,2]=>[1,6,3,7,4,5,2]=>000111
[1,6,4,7,5,2,3]=>[1,5,2,7,6,3,4]=>[1,6,2,3,7,5,4]=>000111
[1,6,4,7,5,3,2]=>[1,3,5,7,6,2,4]=>[1,6,3,2,7,5,4]=>010111
[1,6,5,2,3,4,7]=>[1,5,2,3,6,4,7]=>[1,6,5,2,3,4,7]=>000110
[1,6,5,2,3,7,4]=>[1,5,2,6,7,4,3]=>[1,7,4,6,5,2,3]=>000111
[1,6,5,2,4,3,7]=>[1,5,4,2,6,3,7]=>[1,4,2,6,5,3,7]=>001110
[1,6,5,2,4,7,3]=>[1,5,6,3,7,4,2]=>[1,7,3,4,6,5,2]=>000111
[1,6,5,2,7,3,4]=>[1,5,6,2,7,3,4]=>[1,7,2,6,5,3,4]=>000111
[1,6,5,2,7,4,3]=>[1,5,4,6,7,3,2]=>[1,7,4,3,6,5,2]=>001111
[1,6,5,3,2,4,7]=>[1,3,5,2,6,4,7]=>[1,6,5,3,2,4,7]=>010110
[1,6,5,3,2,7,4]=>[1,3,5,6,7,4,2]=>[1,7,4,6,5,3,2]=>010111
[1,6,5,3,4,2,7]=>[1,4,5,3,6,2,7]=>[1,6,5,3,4,2,7]=>001110
[1,6,5,3,4,7,2]=>[1,7,5,3,6,4,2]=>[1,6,5,3,4,7,2]=>000111
[1,6,5,3,7,2,4]=>[1,7,5,2,6,3,4]=>[1,6,5,2,7,3,4]=>000111
[1,6,5,3,7,4,2]=>[1,4,7,5,6,2,3]=>[1,6,5,2,7,4,3]=>001111
[1,6,5,4,2,3,7]=>[1,4,2,5,6,3,7]=>[1,6,5,4,2,3,7]=>001110
[1,6,5,4,2,7,3]=>[1,4,5,6,7,2,3]=>[1,7,2,6,5,4,3]=>001111
[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]=>[1,6,5,4,3,2,7]=>011110
[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]=>[1,6,5,4,3,7,2]=>001111
[1,6,5,4,7,2,3]=>[1,7,2,5,6,4,3]=>[1,6,5,4,7,2,3]=>000111
[1,6,5,4,7,3,2]=>[1,3,7,5,6,4,2]=>[1,6,5,4,7,3,2]=>010111
[1,6,5,7,2,3,4]=>[1,7,2,3,6,5,4]=>[1,6,5,7,2,3,4]=>000011
[1,6,5,7,2,4,3]=>[1,7,4,2,6,5,3]=>[1,4,2,6,5,7,3]=>001011
[1,6,5,7,3,2,4]=>[1,3,7,2,6,5,4]=>[1,6,5,7,3,2,4]=>010011
[1,6,5,7,3,4,2]=>[1,4,7,3,6,5,2]=>[1,6,5,7,3,4,2]=>001011
[1,6,5,7,4,2,3]=>[1,4,2,7,6,5,3]=>[1,6,5,7,4,2,3]=>001011
[1,6,5,7,4,3,2]=>[1,3,4,7,6,5,2]=>[1,6,5,7,4,3,2]=>011011
[1,6,7,2,3,4,5]=>[1,7,2,3,4,6,5]=>[1,6,7,2,3,4,5]=>000001
[1,6,7,2,3,5,4]=>[1,7,2,5,3,6,4]=>[1,5,2,3,6,7,4]=>000101
[1,6,7,2,4,3,5]=>[1,7,4,2,3,6,5]=>[1,4,2,6,7,3,5]=>001001
[1,6,7,2,4,5,3]=>[1,7,5,2,4,6,3]=>[1,5,2,4,6,7,3]=>000101
[1,6,7,2,5,3,4]=>[1,7,5,3,2,6,4]=>[1,5,3,6,7,2,4]=>000101
[1,6,7,2,5,4,3]=>[1,7,4,5,2,6,3]=>[1,5,4,2,6,7,3]=>001101
[1,6,7,3,2,4,5]=>[1,3,7,2,4,6,5]=>[1,6,7,3,2,4,5]=>010001
[1,6,7,3,2,5,4]=>[1,3,7,5,2,6,4]=>[1,5,3,2,6,7,4]=>010101
[1,6,7,3,4,2,5]=>[1,4,7,3,2,6,5]=>[1,6,7,3,4,2,5]=>001001
[1,6,7,3,4,5,2]=>[1,5,7,3,4,6,2]=>[1,6,7,3,4,5,2]=>000101
[1,6,7,3,5,2,4]=>[1,5,7,2,3,6,4]=>[1,6,7,2,5,3,4]=>000101
[1,6,7,3,5,4,2]=>[1,4,5,7,2,6,3]=>[1,6,7,2,5,4,3]=>001101
[1,6,7,4,2,3,5]=>[1,4,2,7,3,6,5]=>[1,6,7,4,2,3,5]=>001001
[1,6,7,4,2,5,3]=>[1,4,7,5,3,6,2]=>[1,5,3,6,7,4,2]=>001101
[1,6,7,4,3,2,5]=>[1,3,4,7,2,6,5]=>[1,6,7,4,3,2,5]=>011001
[1,6,7,4,3,5,2]=>[1,5,4,7,3,6,2]=>[1,6,7,4,3,5,2]=>001101
[1,6,7,4,5,2,3]=>[1,5,2,7,4,6,3]=>[1,6,7,4,5,2,3]=>000101
[1,6,7,4,5,3,2]=>[1,3,5,7,4,6,2]=>[1,6,7,4,5,3,2]=>010101
[1,6,7,5,2,3,4]=>[1,5,2,3,7,6,4]=>[1,6,7,5,2,3,4]=>000101
[1,6,7,5,2,4,3]=>[1,5,4,2,7,6,3]=>[1,4,2,6,7,5,3]=>001101
[1,6,7,5,3,2,4]=>[1,3,5,2,7,6,4]=>[1,6,7,5,3,2,4]=>010101
[1,6,7,5,3,4,2]=>[1,4,5,3,7,6,2]=>[1,6,7,5,3,4,2]=>001101
[1,6,7,5,4,2,3]=>[1,4,2,5,7,6,3]=>[1,6,7,5,4,2,3]=>001101
[1,6,7,5,4,3,2]=>[1,3,4,5,7,6,2]=>[1,6,7,5,4,3,2]=>011101
[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>000001
[1,7,2,3,4,6,5]=>[1,7,2,3,6,4,5]=>[1,6,2,3,4,7,5]=>000011
[1,7,2,3,5,4,6]=>[1,7,2,5,3,4,6]=>[1,5,2,3,7,4,6]=>000101
[1,7,2,3,5,6,4]=>[1,7,2,6,3,5,4]=>[1,6,2,3,5,7,4]=>000011
[1,7,2,3,6,4,5]=>[1,7,2,6,4,3,5]=>[1,6,4,7,2,3,5]=>000011
[1,7,2,3,6,5,4]=>[1,7,2,5,6,3,4]=>[1,6,5,2,3,7,4]=>000111
[1,7,2,4,3,5,6]=>[1,7,4,2,3,5,6]=>[1,4,2,7,3,5,6]=>001001
[1,7,2,4,3,6,5]=>[1,7,4,2,6,3,5]=>[1,4,2,6,3,7,5]=>001011
[1,7,2,4,5,3,6]=>[1,7,5,2,4,3,6]=>[1,5,2,4,7,3,6]=>000101
[1,7,2,4,5,6,3]=>[1,7,6,2,4,5,3]=>[1,6,2,4,5,7,3]=>000011
[1,7,2,4,6,3,5]=>[1,7,6,2,3,4,5]=>[1,6,2,7,3,4,5]=>000011
[1,7,2,4,6,5,3]=>[1,7,5,2,6,4,3]=>[1,6,5,2,4,7,3]=>000111
[1,7,2,5,3,4,6]=>[1,7,5,3,2,4,6]=>[1,5,3,7,2,4,6]=>000101
[1,7,2,5,3,6,4]=>[1,7,5,6,2,3,4]=>[1,6,2,5,3,7,4]=>000111
[1,7,2,5,4,3,6]=>[1,7,4,5,2,3,6]=>[1,5,4,2,7,3,6]=>001101
[1,7,2,5,4,6,3]=>[1,7,6,5,2,4,3]=>[1,5,2,6,4,7,3]=>000111
[1,7,2,5,6,3,4]=>[1,7,6,3,2,5,4]=>[1,6,3,5,7,2,4]=>000011
[1,7,2,5,6,4,3]=>[1,7,4,6,2,5,3]=>[1,6,4,2,5,7,3]=>001011
[1,7,2,6,3,4,5]=>[1,7,6,3,4,2,5]=>[1,6,3,4,7,2,5]=>000011
[1,7,2,6,3,5,4]=>[1,7,6,5,3,2,4]=>[1,5,3,6,2,7,4]=>000111
[1,7,2,6,4,3,5]=>[1,7,4,6,3,2,5]=>[1,6,4,3,7,2,5]=>001011
[1,7,2,6,4,5,3]=>[1,7,5,6,4,2,3]=>[1,6,4,5,2,7,3]=>000111
[1,7,2,6,5,3,4]=>[1,7,5,3,6,2,4]=>[1,6,5,3,7,2,4]=>000111
[1,7,2,6,5,4,3]=>[1,7,4,5,6,2,3]=>[1,6,5,4,2,7,3]=>001111
[1,7,3,2,4,5,6]=>[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>010001
[1,7,3,2,4,6,5]=>[1,3,7,2,6,4,5]=>[1,6,3,2,4,7,5]=>010011
[1,7,3,2,5,4,6]=>[1,3,7,5,2,4,6]=>[1,5,3,2,7,4,6]=>010101
[1,7,3,2,5,6,4]=>[1,3,7,6,2,5,4]=>[1,6,3,2,5,7,4]=>010011
[1,7,3,2,6,4,5]=>[1,3,7,6,4,2,5]=>[1,6,4,7,3,2,5]=>010011
[1,7,3,2,6,5,4]=>[1,3,7,5,6,2,4]=>[1,6,5,3,2,7,4]=>010111
[1,7,3,4,2,5,6]=>[1,4,7,3,2,5,6]=>[1,7,3,4,2,5,6]=>001001
[1,7,3,4,2,6,5]=>[1,4,7,3,6,2,5]=>[1,6,3,4,2,7,5]=>001011
[1,7,3,4,5,2,6]=>[1,5,7,3,4,2,6]=>[1,7,3,4,5,2,6]=>000101
[1,7,3,4,5,6,2]=>[1,6,7,3,4,5,2]=>[1,7,3,4,5,6,2]=>000011
[1,7,3,4,6,2,5]=>[1,6,7,3,2,4,5]=>[1,7,3,6,2,4,5]=>000011
[1,7,3,4,6,5,2]=>[1,5,6,2,7,4,3]=>[1,7,2,4,6,5,3]=>000111
[1,7,3,5,2,4,6]=>[1,5,7,2,3,4,6]=>[1,7,2,5,3,4,6]=>000101
[1,7,3,5,2,6,4]=>[1,5,7,6,3,2,4]=>[1,6,3,7,2,5,4]=>000111
[1,7,3,5,4,2,6]=>[1,4,5,7,2,3,6]=>[1,7,2,5,4,3,6]=>001101
[1,7,3,5,4,6,2]=>[1,6,7,5,3,4,2]=>[1,5,3,7,4,6,2]=>000111
[1,7,3,5,6,2,4]=>[1,6,7,2,3,5,4]=>[1,7,2,5,6,3,4]=>000011
[1,7,3,5,6,4,2]=>[1,4,6,7,2,5,3]=>[1,7,2,5,6,4,3]=>001011
[1,7,3,6,2,4,5]=>[1,6,7,2,4,3,5]=>[1,7,2,4,6,3,5]=>000011
[1,7,3,6,2,5,4]=>[1,6,7,5,2,3,4]=>[1,5,2,7,3,6,4]=>000111
[1,7,3,6,4,2,5]=>[1,4,6,7,3,2,5]=>[1,7,3,6,4,2,5]=>001011
[1,7,3,6,4,5,2]=>[1,5,7,6,4,3,2]=>[1,6,4,7,3,5,2]=>000111
[1,7,3,6,5,2,4]=>[1,5,6,3,7,2,4]=>[1,7,3,6,5,2,4]=>000111
[1,7,3,6,5,4,2]=>[1,4,5,6,7,3,2]=>[1,7,3,6,5,4,2]=>001111
[1,7,4,2,3,5,6]=>[1,4,2,7,3,5,6]=>[1,7,4,2,3,5,6]=>001001
[1,7,4,2,3,6,5]=>[1,4,2,7,6,3,5]=>[1,6,4,2,3,7,5]=>001011
[1,7,4,2,5,3,6]=>[1,4,7,5,3,2,6]=>[1,5,3,7,4,2,6]=>001101
[1,7,4,2,5,6,3]=>[1,4,7,6,3,5,2]=>[1,6,3,5,7,4,2]=>001011
[1,7,4,2,6,3,5]=>[1,4,7,6,2,3,5]=>[1,6,2,7,4,3,5]=>001011
[1,7,4,2,6,5,3]=>[1,4,7,5,6,3,2]=>[1,6,5,3,7,4,2]=>001111
[1,7,4,3,2,5,6]=>[1,3,4,7,2,5,6]=>[1,7,4,3,2,5,6]=>011001
[1,7,4,3,2,6,5]=>[1,3,4,7,6,2,5]=>[1,6,4,3,2,7,5]=>011011
[1,7,4,3,5,2,6]=>[1,5,4,7,3,2,6]=>[1,7,4,3,5,2,6]=>001101
[1,7,4,3,5,6,2]=>[1,6,4,7,3,5,2]=>[1,7,4,3,5,6,2]=>001011
[1,7,4,3,6,2,5]=>[1,6,4,7,2,3,5]=>[1,7,4,2,6,3,5]=>001011
[1,7,4,3,6,5,2]=>[1,5,4,6,7,2,3]=>[1,7,4,2,6,5,3]=>001111
[1,7,4,5,2,3,6]=>[1,5,2,7,4,3,6]=>[1,7,4,5,2,3,6]=>000101
[1,7,4,5,2,6,3]=>[1,5,6,7,4,2,3]=>[1,7,4,6,2,5,3]=>000111
[1,7,4,5,3,2,6]=>[1,3,5,7,4,2,6]=>[1,7,4,5,3,2,6]=>010101
[1,7,4,5,3,6,2]=>[1,6,5,7,4,3,2]=>[1,7,4,5,3,6,2]=>000111
[1,7,4,5,6,2,3]=>[1,6,2,7,4,5,3]=>[1,7,4,5,6,2,3]=>000011
[1,7,4,5,6,3,2]=>[1,3,6,7,4,5,2]=>[1,7,4,5,6,3,2]=>010011
[1,7,4,6,2,3,5]=>[1,6,2,7,3,4,5]=>[1,7,2,3,6,4,5]=>000011
[1,7,4,6,2,5,3]=>[1,6,5,7,2,4,3]=>[1,7,2,5,4,6,3]=>000111
[1,7,4,6,3,2,5]=>[1,3,6,7,2,4,5]=>[1,7,3,2,6,4,5]=>010011
[1,7,4,6,3,5,2]=>[1,5,6,7,3,4,2]=>[1,7,3,6,4,5,2]=>000111
[1,7,4,6,5,2,3]=>[1,5,2,6,7,3,4]=>[1,7,2,3,6,5,4]=>000111
[1,7,4,6,5,3,2]=>[1,3,5,6,7,2,4]=>[1,7,3,2,6,5,4]=>010111
[1,7,5,2,3,4,6]=>[1,5,2,3,7,4,6]=>[1,7,5,2,3,4,6]=>000101
[1,7,5,2,3,6,4]=>[1,5,2,7,6,4,3]=>[1,6,4,7,5,2,3]=>000111
[1,7,5,2,4,3,6]=>[1,5,4,2,7,3,6]=>[1,4,2,7,5,3,6]=>001101
[1,7,5,2,4,6,3]=>[1,5,7,3,6,4,2]=>[1,6,3,4,7,5,2]=>000111
[1,7,5,2,6,3,4]=>[1,5,7,2,6,3,4]=>[1,6,2,7,5,3,4]=>000111
[1,7,5,2,6,4,3]=>[1,5,4,7,6,3,2]=>[1,6,4,3,7,5,2]=>001111
[1,7,5,3,2,4,6]=>[1,3,5,2,7,4,6]=>[1,7,5,3,2,4,6]=>010101
[1,7,5,3,2,6,4]=>[1,3,5,7,6,4,2]=>[1,6,4,7,5,3,2]=>010111
[1,7,5,3,4,2,6]=>[1,4,5,3,7,2,6]=>[1,7,5,3,4,2,6]=>001101
[1,7,5,3,4,6,2]=>[1,6,5,3,7,4,2]=>[1,7,5,3,4,6,2]=>000111
[1,7,5,3,6,2,4]=>[1,6,5,2,7,3,4]=>[1,7,5,2,6,3,4]=>000111
[1,7,5,3,6,4,2]=>[1,4,6,5,7,2,3]=>[1,7,5,2,6,4,3]=>001111
[1,7,5,4,2,3,6]=>[1,4,2,5,7,3,6]=>[1,7,5,4,2,3,6]=>001101
[1,7,5,4,2,6,3]=>[1,4,5,7,6,2,3]=>[1,6,2,7,5,4,3]=>001111
[1,7,5,4,3,2,6]=>[1,3,4,5,7,2,6]=>[1,7,5,4,3,2,6]=>011101
[1,7,5,4,3,6,2]=>[1,6,4,5,7,3,2]=>[1,7,5,4,3,6,2]=>001111
[1,7,5,4,6,2,3]=>[1,6,2,5,7,4,3]=>[1,7,5,4,6,2,3]=>000111
[1,7,5,4,6,3,2]=>[1,3,6,5,7,4,2]=>[1,7,5,4,6,3,2]=>010111
[1,7,5,6,2,3,4]=>[1,6,2,3,7,5,4]=>[1,7,5,6,2,3,4]=>000011
[1,7,5,6,2,4,3]=>[1,6,4,2,7,5,3]=>[1,4,2,7,5,6,3]=>001011
[1,7,5,6,3,2,4]=>[1,3,6,2,7,5,4]=>[1,7,5,6,3,2,4]=>010011
[1,7,5,6,3,4,2]=>[1,4,6,3,7,5,2]=>[1,7,5,6,3,4,2]=>001011
[1,7,5,6,4,2,3]=>[1,4,2,6,7,5,3]=>[1,7,5,6,4,2,3]=>001011
[1,7,5,6,4,3,2]=>[1,3,4,6,7,5,2]=>[1,7,5,6,4,3,2]=>011011
[1,7,6,2,3,4,5]=>[1,6,2,3,4,7,5]=>[1,7,6,2,3,4,5]=>000011
[1,7,6,2,3,5,4]=>[1,6,2,5,3,7,4]=>[1,5,2,3,7,6,4]=>000111
[1,7,6,2,4,3,5]=>[1,6,4,2,3,7,5]=>[1,4,2,7,6,3,5]=>001011
[1,7,6,2,4,5,3]=>[1,6,5,2,4,7,3]=>[1,5,2,4,7,6,3]=>000111
[1,7,6,2,5,3,4]=>[1,6,5,3,2,7,4]=>[1,5,3,7,6,2,4]=>000111
[1,7,6,2,5,4,3]=>[1,6,4,5,2,7,3]=>[1,5,4,2,7,6,3]=>001111
[1,7,6,3,2,4,5]=>[1,3,6,2,4,7,5]=>[1,7,6,3,2,4,5]=>010011
[1,7,6,3,2,5,4]=>[1,3,6,5,2,7,4]=>[1,5,3,2,7,6,4]=>010111
[1,7,6,3,4,2,5]=>[1,4,6,3,2,7,5]=>[1,7,6,3,4,2,5]=>001011
[1,7,6,3,4,5,2]=>[1,5,6,3,4,7,2]=>[1,7,6,3,4,5,2]=>000111
[1,7,6,3,5,2,4]=>[1,5,6,2,3,7,4]=>[1,7,6,2,5,3,4]=>000111
[1,7,6,3,5,4,2]=>[1,4,5,6,2,7,3]=>[1,7,6,2,5,4,3]=>001111
[1,7,6,4,2,3,5]=>[1,4,2,6,3,7,5]=>[1,7,6,4,2,3,5]=>001011
[1,7,6,4,2,5,3]=>[1,4,6,5,3,7,2]=>[1,5,3,7,6,4,2]=>001111
[1,7,6,4,3,2,5]=>[1,3,4,6,2,7,5]=>[1,7,6,4,3,2,5]=>011011
[1,7,6,4,3,5,2]=>[1,5,4,6,3,7,2]=>[1,7,6,4,3,5,2]=>001111
[1,7,6,4,5,2,3]=>[1,5,2,6,4,7,3]=>[1,7,6,4,5,2,3]=>000111
[1,7,6,4,5,3,2]=>[1,3,5,6,4,7,2]=>[1,7,6,4,5,3,2]=>010111
[1,7,6,5,2,3,4]=>[1,5,2,3,6,7,4]=>[1,7,6,5,2,3,4]=>000111
[1,7,6,5,2,4,3]=>[1,5,4,2,6,7,3]=>[1,4,2,7,6,5,3]=>001111
[1,7,6,5,3,2,4]=>[1,3,5,2,6,7,4]=>[1,7,6,5,3,2,4]=>010111
[1,7,6,5,3,4,2]=>[1,4,5,3,6,7,2]=>[1,7,6,5,3,4,2]=>001111
[1,7,6,5,4,2,3]=>[1,4,2,5,6,7,3]=>[1,7,6,5,4,2,3]=>001111
[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]=>[1,7,6,5,4,3,2]=>011111
[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>100001
[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>100010
[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>100001
[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>100001
[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>100011
[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>100100
[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>100101
[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>100010
[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[2,1,3,5,6,7,4]=>100001
[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>[2,1,3,5,7,4,6]=>100001
[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>[2,1,3,5,7,6,4]=>100011
[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>100010
[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]=>100011
[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>100110
[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>[2,1,3,6,5,7,4]=>100011
[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]=>[2,1,3,6,7,4,5]=>100001
[2,1,3,6,7,5,4]=>[2,1,3,5,7,6,4]=>[2,1,3,6,7,5,4]=>100101
[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>100001
[2,1,3,7,4,6,5]=>[2,1,3,7,6,4,5]=>[2,1,3,6,4,7,5]=>100011
[2,1,3,7,5,4,6]=>[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>100101
[2,1,3,7,5,6,4]=>[2,1,3,6,7,5,4]=>[2,1,3,7,5,6,4]=>100011
[2,1,3,7,6,4,5]=>[2,1,3,6,4,7,5]=>[2,1,3,7,6,4,5]=>100011
[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]=>[2,1,3,7,6,5,4]=>100111
[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>101000
[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>101001
[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>101010
[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>101001
[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>101001
[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>101011
[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>100100
[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>100101
[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[2,1,4,5,6,3,7]=>100010
[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[2,1,4,5,6,7,3]=>100001
[2,1,4,5,7,3,6]=>[2,1,7,4,5,3,6]=>[2,1,4,5,7,3,6]=>100001
[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>[2,1,4,5,7,6,3]=>100011
[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>[2,1,4,6,3,5,7]=>100010
[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[2,1,4,7,3,6,5]=>100011
[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>[2,1,4,6,5,3,7]=>100110
[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>[2,1,4,6,5,7,3]=>100011
[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]=>[2,1,4,6,7,3,5]=>100001
[2,1,4,6,7,5,3]=>[2,1,5,4,7,6,3]=>[2,1,4,6,7,5,3]=>100101
[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>[2,1,4,7,3,5,6]=>100001
[2,1,4,7,3,6,5]=>[2,1,7,4,6,3,5]=>[2,1,4,6,3,7,5]=>100011
[2,1,4,7,5,3,6]=>[2,1,5,4,7,3,6]=>[2,1,4,7,5,3,6]=>100101
[2,1,4,7,5,6,3]=>[2,1,6,4,7,5,3]=>[2,1,4,7,5,6,3]=>100011
[2,1,4,7,6,3,5]=>[2,1,6,4,3,7,5]=>[2,1,4,7,6,3,5]=>100011
[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]=>[2,1,4,7,6,5,3]=>100111
[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>100100
[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>100101
[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]=>100110
[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[2,1,6,7,3,5,4]=>100101
[2,1,5,3,7,4,6]=>[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]=>100101
[2,1,5,3,7,6,4]=>[2,1,5,6,3,7,4]=>[2,1,7,6,3,5,4]=>100111
[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>101100
[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>101101
[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>[2,1,5,4,6,3,7]=>100110
[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>[2,1,5,4,6,7,3]=>100101
[2,1,5,4,7,3,6]=>[2,1,7,5,4,3,6]=>[2,1,5,4,7,3,6]=>100101
[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]=>[2,1,5,4,7,6,3]=>100111
[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]=>[2,1,5,6,3,4,7]=>100010
[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[2,1,5,7,3,6,4]=>100011
[2,1,5,6,4,3,7]=>[2,1,4,6,5,3,7]=>[2,1,5,6,4,3,7]=>101010
[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>[2,1,5,6,4,7,3]=>100011
[2,1,5,6,7,3,4]=>[2,1,7,3,5,6,4]=>[2,1,5,6,7,3,4]=>100001
[2,1,5,6,7,4,3]=>[2,1,4,7,5,6,3]=>[2,1,5,6,7,4,3]=>101001
[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]=>[2,1,5,7,3,4,6]=>100001
[2,1,5,7,3,6,4]=>[2,1,7,6,5,3,4]=>[2,1,5,6,3,7,4]=>100011
[2,1,5,7,4,3,6]=>[2,1,4,7,5,3,6]=>[2,1,5,7,4,3,6]=>101001
[2,1,5,7,4,6,3]=>[2,1,6,7,5,4,3]=>[2,1,5,7,4,6,3]=>100011
[2,1,5,7,6,3,4]=>[2,1,6,3,5,7,4]=>[2,1,5,7,6,3,4]=>100011
[2,1,5,7,6,4,3]=>[2,1,4,6,5,7,3]=>[2,1,5,7,6,4,3]=>101011
[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>100010
[2,1,6,3,4,7,5]=>[2,1,6,3,7,4,5]=>[2,1,7,3,4,6,5]=>100011
[2,1,6,3,5,4,7]=>[2,1,6,5,3,4,7]=>[2,1,5,3,6,4,7]=>100110
[2,1,6,3,5,7,4]=>[2,1,6,7,3,5,4]=>[2,1,7,3,5,6,4]=>100011
[2,1,6,3,7,4,5]=>[2,1,6,7,4,3,5]=>[2,1,7,4,6,3,5]=>100011
[2,1,6,3,7,5,4]=>[2,1,6,5,7,3,4]=>[2,1,7,5,3,6,4]=>100111
[2,1,6,4,3,5,7]=>[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>101010
[2,1,6,4,3,7,5]=>[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]=>101011
[2,1,6,4,5,3,7]=>[2,1,5,6,4,3,7]=>[2,1,6,4,5,3,7]=>100110
[2,1,6,4,5,7,3]=>[2,1,7,6,4,5,3]=>[2,1,6,4,5,7,3]=>100011
[2,1,6,4,7,3,5]=>[2,1,7,6,3,4,5]=>[2,1,6,3,7,4,5]=>100011
[2,1,6,4,7,5,3]=>[2,1,5,7,6,3,4]=>[2,1,6,3,7,5,4]=>100111
[2,1,6,5,3,4,7]=>[2,1,5,3,6,4,7]=>[2,1,6,5,3,4,7]=>100110
[2,1,6,5,3,7,4]=>[2,1,5,6,7,4,3]=>[2,1,7,4,6,5,3]=>100111
[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]=>[2,1,6,5,4,3,7]=>101110
[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]=>[2,1,6,5,4,7,3]=>100111
[2,1,6,5,7,3,4]=>[2,1,7,3,6,5,4]=>[2,1,6,5,7,3,4]=>100011
[2,1,6,5,7,4,3]=>[2,1,4,7,6,5,3]=>[2,1,6,5,7,4,3]=>101011
[2,1,6,7,3,4,5]=>[2,1,7,3,4,6,5]=>[2,1,6,7,3,4,5]=>100001
[2,1,6,7,3,5,4]=>[2,1,7,5,3,6,4]=>[2,1,5,3,6,7,4]=>100101
[2,1,6,7,4,3,5]=>[2,1,4,7,3,6,5]=>[2,1,6,7,4,3,5]=>101001
[2,1,6,7,4,5,3]=>[2,1,5,7,4,6,3]=>[2,1,6,7,4,5,3]=>100101
[2,1,6,7,5,3,4]=>[2,1,5,3,7,6,4]=>[2,1,6,7,5,3,4]=>100101
[2,1,6,7,5,4,3]=>[2,1,4,5,7,6,3]=>[2,1,6,7,5,4,3]=>101101
[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>100001
[2,1,7,3,4,6,5]=>[2,1,7,3,6,4,5]=>[2,1,6,3,4,7,5]=>100011
[2,1,7,3,5,4,6]=>[2,1,7,5,3,4,6]=>[2,1,5,3,7,4,6]=>100101
[2,1,7,3,5,6,4]=>[2,1,7,6,3,5,4]=>[2,1,6,3,5,7,4]=>100011
[2,1,7,3,6,4,5]=>[2,1,7,6,4,3,5]=>[2,1,6,4,7,3,5]=>100011
[2,1,7,3,6,5,4]=>[2,1,7,5,6,3,4]=>[2,1,6,5,3,7,4]=>100111
[2,1,7,4,3,5,6]=>[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>101001
[2,1,7,4,3,6,5]=>[2,1,4,7,6,3,5]=>[2,1,6,4,3,7,5]=>101011
[2,1,7,4,5,3,6]=>[2,1,5,7,4,3,6]=>[2,1,7,4,5,3,6]=>100101
[2,1,7,4,5,6,3]=>[2,1,6,7,4,5,3]=>[2,1,7,4,5,6,3]=>100011
[2,1,7,4,6,3,5]=>[2,1,6,7,3,4,5]=>[2,1,7,3,6,4,5]=>100011
[2,1,7,4,6,5,3]=>[2,1,5,6,7,3,4]=>[2,1,7,3,6,5,4]=>100111
[2,1,7,5,3,4,6]=>[2,1,5,3,7,4,6]=>[2,1,7,5,3,4,6]=>100101
[2,1,7,5,3,6,4]=>[2,1,5,7,6,4,3]=>[2,1,6,4,7,5,3]=>100111
[2,1,7,5,4,3,6]=>[2,1,4,5,7,3,6]=>[2,1,7,5,4,3,6]=>101101
[2,1,7,5,4,6,3]=>[2,1,6,5,7,4,3]=>[2,1,7,5,4,6,3]=>100111
[2,1,7,5,6,3,4]=>[2,1,6,3,7,5,4]=>[2,1,7,5,6,3,4]=>100011
[2,1,7,5,6,4,3]=>[2,1,4,6,7,5,3]=>[2,1,7,5,6,4,3]=>101011
[2,1,7,6,3,4,5]=>[2,1,6,3,4,7,5]=>[2,1,7,6,3,4,5]=>100011
[2,1,7,6,3,5,4]=>[2,1,6,5,3,7,4]=>[2,1,5,3,7,6,4]=>100111
[2,1,7,6,4,3,5]=>[2,1,4,6,3,7,5]=>[2,1,7,6,4,3,5]=>101011
[2,1,7,6,4,5,3]=>[2,1,5,6,4,7,3]=>[2,1,7,6,4,5,3]=>100111
[2,1,7,6,5,3,4]=>[2,1,5,3,6,7,4]=>[2,1,7,6,5,3,4]=>100111
[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]=>[2,1,7,6,5,4,3]=>101111
[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>010000
[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>010001
[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>010010
[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>010001
[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>[2,3,1,4,7,5,6]=>010001
[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>010011
[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>010100
[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>010101
[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>010010
[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[2,3,1,5,6,7,4]=>010001
[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>[2,3,1,5,7,4,6]=>010001
[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>[2,3,1,5,7,6,4]=>010011
[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>[2,3,1,6,4,5,7]=>010010
[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[2,3,1,7,4,6,5]=>010011
[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>010110
[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>[2,3,1,6,5,7,4]=>010011
[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]=>[2,3,1,6,7,4,5]=>010001
[2,3,1,6,7,5,4]=>[3,2,1,5,7,6,4]=>[2,3,1,6,7,5,4]=>010101
[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>[2,3,1,7,4,5,6]=>010001
[2,3,1,7,4,6,5]=>[3,2,1,7,6,4,5]=>[2,3,1,6,4,7,5]=>010011
[2,3,1,7,5,4,6]=>[3,2,1,5,7,4,6]=>[2,3,1,7,5,4,6]=>010101
[2,3,1,7,5,6,4]=>[3,2,1,6,7,5,4]=>[2,3,1,7,5,6,4]=>010011
[2,3,1,7,6,4,5]=>[3,2,1,6,4,7,5]=>[2,3,1,7,6,4,5]=>010011
[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]=>[2,3,1,7,6,5,4]=>010111
[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[2,3,4,1,5,6,7]=>001000
[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[2,3,4,1,5,7,6]=>001001
[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[2,3,4,1,6,5,7]=>001010
[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[2,3,4,1,6,7,5]=>001001
[2,3,4,1,7,5,6]=>[4,2,3,1,7,5,6]=>[2,3,4,1,7,5,6]=>001001
[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]=>[2,3,4,1,7,6,5]=>001011
[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[2,3,4,5,1,6,7]=>000100
[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[2,3,4,5,1,7,6]=>000101
[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[2,3,4,5,6,1,7]=>000010
[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,7,1]=>000001
[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>[2,3,4,5,7,1,6]=>000001
[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>[2,3,4,5,7,6,1]=>000011
[2,3,4,6,1,5,7]=>[6,2,3,4,1,5,7]=>[2,3,4,6,1,5,7]=>000010
[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[2,3,4,7,1,6,5]=>000011
[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]=>[2,3,4,6,5,1,7]=>000110
[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>[2,3,4,6,5,7,1]=>000011
[2,3,4,6,7,1,5]=>[7,2,3,4,1,6,5]=>[2,3,4,6,7,1,5]=>000001
[2,3,4,6,7,5,1]=>[5,2,3,4,7,6,1]=>[2,3,4,6,7,5,1]=>000101
[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>[2,3,4,7,1,5,6]=>000001
[2,3,4,7,1,6,5]=>[7,2,3,4,6,1,5]=>[2,3,4,6,1,7,5]=>000011
[2,3,4,7,5,1,6]=>[5,2,3,4,7,1,6]=>[2,3,4,7,5,1,6]=>000101
[2,3,4,7,5,6,1]=>[6,2,3,4,7,5,1]=>[2,3,4,7,5,6,1]=>000011
[2,3,4,7,6,1,5]=>[6,2,3,4,1,7,5]=>[2,3,4,7,6,1,5]=>000011
[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]=>[2,3,4,7,6,5,1]=>000111
[2,3,5,1,4,6,7]=>[5,2,3,1,4,6,7]=>[2,3,5,1,4,6,7]=>000100
[2,3,5,1,4,7,6]=>[5,2,3,1,4,7,6]=>[2,3,5,1,4,7,6]=>000101
[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[2,3,6,1,5,4,7]=>000110
[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[2,3,6,7,1,5,4]=>000101
[2,3,5,1,7,4,6]=>[5,2,3,7,1,4,6]=>[2,3,7,1,5,4,6]=>000101
[2,3,5,1,7,6,4]=>[5,2,3,6,1,7,4]=>[2,3,7,6,1,5,4]=>000111
[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>[2,3,5,4,1,6,7]=>001100
[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]=>[2,3,5,4,1,7,6]=>001101
[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>[2,3,5,4,6,1,7]=>000110
[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>[2,3,5,4,6,7,1]=>000101
[2,3,5,4,7,1,6]=>[7,2,3,5,4,1,6]=>[2,3,5,4,7,1,6]=>000101
[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]=>[2,3,5,4,7,6,1]=>000111
[2,3,5,6,1,4,7]=>[6,2,3,1,5,4,7]=>[2,3,5,6,1,4,7]=>000010
[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[2,3,5,7,1,6,4]=>000011
[2,3,5,6,4,1,7]=>[4,2,3,6,5,1,7]=>[2,3,5,6,4,1,7]=>001010
[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>[2,3,5,6,4,7,1]=>000011
[2,3,5,6,7,1,4]=>[7,2,3,1,5,6,4]=>[2,3,5,6,7,1,4]=>000001
[2,3,5,6,7,4,1]=>[4,2,3,7,5,6,1]=>[2,3,5,6,7,4,1]=>001001
[2,3,5,7,1,4,6]=>[7,2,3,1,5,4,6]=>[2,3,5,7,1,4,6]=>000001
[2,3,5,7,1,6,4]=>[7,2,3,6,5,1,4]=>[2,3,5,6,1,7,4]=>000011
[2,3,5,7,4,1,6]=>[4,2,3,7,5,1,6]=>[2,3,5,7,4,1,6]=>001001
[2,3,5,7,4,6,1]=>[6,2,3,7,5,4,1]=>[2,3,5,7,4,6,1]=>000011
[2,3,5,7,6,1,4]=>[6,2,3,1,5,7,4]=>[2,3,5,7,6,1,4]=>000011
[2,3,5,7,6,4,1]=>[4,2,3,6,5,7,1]=>[2,3,5,7,6,4,1]=>001011
[2,3,6,1,4,5,7]=>[6,2,3,1,4,5,7]=>[2,3,6,1,4,5,7]=>000010
[2,3,6,1,4,7,5]=>[6,2,3,1,7,4,5]=>[2,3,7,1,4,6,5]=>000011
[2,3,6,1,5,4,7]=>[6,2,3,5,1,4,7]=>[2,3,5,1,6,4,7]=>000110
[2,3,6,1,5,7,4]=>[6,2,3,7,1,5,4]=>[2,3,7,1,5,6,4]=>000011
[2,3,6,1,7,4,5]=>[6,2,3,7,4,1,5]=>[2,3,7,4,6,1,5]=>000011
[2,3,6,1,7,5,4]=>[6,2,3,5,7,1,4]=>[2,3,7,5,1,6,4]=>000111
[2,3,6,4,1,5,7]=>[4,2,3,6,1,5,7]=>[2,3,6,4,1,5,7]=>001010
[2,3,6,4,1,7,5]=>[4,2,3,6,7,1,5]=>[2,3,7,4,1,6,5]=>001011
[2,3,6,4,5,1,7]=>[5,2,3,6,4,1,7]=>[2,3,6,4,5,1,7]=>000110
[2,3,6,4,5,7,1]=>[7,2,3,6,4,5,1]=>[2,3,6,4,5,7,1]=>000011
[2,3,6,4,7,1,5]=>[7,2,3,6,1,4,5]=>[2,3,6,1,7,4,5]=>000011
[2,3,6,4,7,5,1]=>[5,2,3,7,6,1,4]=>[2,3,6,1,7,5,4]=>000111
[2,3,6,5,1,4,7]=>[5,2,3,1,6,4,7]=>[2,3,6,5,1,4,7]=>000110
[2,3,6,5,1,7,4]=>[5,2,3,6,7,4,1]=>[2,3,7,4,6,5,1]=>000111
[2,3,6,5,4,1,7]=>[4,2,3,5,6,1,7]=>[2,3,6,5,4,1,7]=>001110
[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]=>[2,3,6,5,4,7,1]=>000111
[2,3,6,5,7,1,4]=>[7,2,3,1,6,5,4]=>[2,3,6,5,7,1,4]=>000011
[2,3,6,5,7,4,1]=>[4,2,3,7,6,5,1]=>[2,3,6,5,7,4,1]=>001011
[2,3,6,7,1,4,5]=>[7,2,3,1,4,6,5]=>[2,3,6,7,1,4,5]=>000001
[2,3,6,7,1,5,4]=>[7,2,3,5,1,6,4]=>[2,3,5,1,6,7,4]=>000101
[2,3,6,7,4,1,5]=>[4,2,3,7,1,6,5]=>[2,3,6,7,4,1,5]=>001001
[2,3,6,7,4,5,1]=>[5,2,3,7,4,6,1]=>[2,3,6,7,4,5,1]=>000101
[2,3,6,7,5,1,4]=>[5,2,3,1,7,6,4]=>[2,3,6,7,5,1,4]=>000101
[2,3,6,7,5,4,1]=>[4,2,3,5,7,6,1]=>[2,3,6,7,5,4,1]=>001101
[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>[2,3,7,1,4,5,6]=>000001
[2,3,7,1,4,6,5]=>[7,2,3,1,6,4,5]=>[2,3,6,1,4,7,5]=>000011
[2,3,7,1,5,4,6]=>[7,2,3,5,1,4,6]=>[2,3,5,1,7,4,6]=>000101
[2,3,7,1,5,6,4]=>[7,2,3,6,1,5,4]=>[2,3,6,1,5,7,4]=>000011
[2,3,7,1,6,4,5]=>[7,2,3,6,4,1,5]=>[2,3,6,4,7,1,5]=>000011
[2,3,7,1,6,5,4]=>[7,2,3,5,6,1,4]=>[2,3,6,5,1,7,4]=>000111
[2,3,7,4,1,5,6]=>[4,2,3,7,1,5,6]=>[2,3,7,4,1,5,6]=>001001
[2,3,7,4,1,6,5]=>[4,2,3,7,6,1,5]=>[2,3,6,4,1,7,5]=>001011
[2,3,7,4,5,1,6]=>[5,2,3,7,4,1,6]=>[2,3,7,4,5,1,6]=>000101
[2,3,7,4,5,6,1]=>[6,2,3,7,4,5,1]=>[2,3,7,4,5,6,1]=>000011
[2,3,7,4,6,1,5]=>[6,2,3,7,1,4,5]=>[2,3,7,1,6,4,5]=>000011
[2,3,7,4,6,5,1]=>[5,2,3,6,7,1,4]=>[2,3,7,1,6,5,4]=>000111
[2,3,7,5,1,4,6]=>[5,2,3,1,7,4,6]=>[2,3,7,5,1,4,6]=>000101
[2,3,7,5,1,6,4]=>[5,2,3,7,6,4,1]=>[2,3,6,4,7,5,1]=>000111
[2,3,7,5,4,1,6]=>[4,2,3,5,7,1,6]=>[2,3,7,5,4,1,6]=>001101
[2,3,7,5,4,6,1]=>[6,2,3,5,7,4,1]=>[2,3,7,5,4,6,1]=>000111
[2,3,7,5,6,1,4]=>[6,2,3,1,7,5,4]=>[2,3,7,5,6,1,4]=>000011
[2,3,7,5,6,4,1]=>[4,2,3,6,7,5,1]=>[2,3,7,5,6,4,1]=>001011
[2,3,7,6,1,4,5]=>[6,2,3,1,4,7,5]=>[2,3,7,6,1,4,5]=>000011
[2,3,7,6,1,5,4]=>[6,2,3,5,1,7,4]=>[2,3,5,1,7,6,4]=>000111
[2,3,7,6,4,1,5]=>[4,2,3,6,1,7,5]=>[2,3,7,6,4,1,5]=>001011
[2,3,7,6,4,5,1]=>[5,2,3,6,4,7,1]=>[2,3,7,6,4,5,1]=>000111
[2,3,7,6,5,1,4]=>[5,2,3,1,6,7,4]=>[2,3,7,6,5,1,4]=>000111
[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]=>[2,3,7,6,5,4,1]=>001111
[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>001000
[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>[2,4,1,3,5,7,6]=>001001
[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>[2,4,1,3,6,5,7]=>001010
[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>[2,4,1,3,6,7,5]=>001001
[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>[2,4,1,3,7,5,6]=>001001
[2,4,1,3,7,6,5]=>[4,2,1,3,6,7,5]=>[2,4,1,3,7,6,5]=>001011
[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[2,5,1,4,3,6,7]=>001100
[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[2,5,1,4,3,7,6]=>001101
[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[2,5,6,1,4,3,7]=>001010
[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[2,5,6,7,1,4,3]=>001001
[2,4,1,5,7,3,6]=>[4,2,7,1,5,3,6]=>[2,5,7,1,4,3,6]=>001001
[2,4,1,5,7,6,3]=>[4,2,6,1,5,7,3]=>[2,5,7,6,1,4,3]=>001011
[2,4,1,6,3,5,7]=>[4,2,6,1,3,5,7]=>[2,6,1,4,3,5,7]=>001010
[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[2,7,1,4,3,6,5]=>001011
[2,4,1,6,5,3,7]=>[4,2,5,1,6,3,7]=>[2,6,5,1,4,3,7]=>001110
[2,4,1,6,5,7,3]=>[4,2,7,1,6,5,3]=>[2,6,5,7,1,4,3]=>001011
[2,4,1,6,7,3,5]=>[4,2,7,1,3,6,5]=>[2,6,7,1,4,3,5]=>001001
[2,4,1,6,7,5,3]=>[4,2,5,1,7,6,3]=>[2,6,7,5,1,4,3]=>001101
[2,4,1,7,3,5,6]=>[4,2,7,1,3,5,6]=>[2,7,1,4,3,5,6]=>001001
[2,4,1,7,3,6,5]=>[4,2,7,1,6,3,5]=>[2,6,1,4,3,7,5]=>001011
[2,4,1,7,5,3,6]=>[4,2,5,1,7,3,6]=>[2,7,5,1,4,3,6]=>001101
[2,4,1,7,5,6,3]=>[4,2,6,1,7,5,3]=>[2,7,5,6,1,4,3]=>001011
[2,4,1,7,6,3,5]=>[4,2,6,1,3,7,5]=>[2,7,6,1,4,3,5]=>001011
[2,4,1,7,6,5,3]=>[4,2,5,1,6,7,3]=>[2,7,6,5,1,4,3]=>001111
[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>[2,4,3,1,5,6,7]=>011000
[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]=>[2,4,3,1,5,7,6]=>011001
[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>[2,4,3,1,6,5,7]=>011010
[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]=>[2,4,3,1,6,7,5]=>011001
[2,4,3,1,7,5,6]=>[3,2,4,1,7,5,6]=>[2,4,3,1,7,5,6]=>011001
[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>[2,4,3,1,7,6,5]=>011011
[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>[2,4,3,5,1,6,7]=>001100
[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>[2,4,3,5,1,7,6]=>001101
[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>[2,4,3,5,6,1,7]=>001010
[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>[2,4,3,5,6,7,1]=>001001
[2,4,3,5,7,1,6]=>[7,2,4,3,5,1,6]=>[2,4,3,5,7,1,6]=>001001
[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]=>[2,4,3,5,7,6,1]=>001011
[2,4,3,6,1,5,7]=>[6,2,4,3,1,5,7]=>[2,4,3,6,1,5,7]=>001010
[2,4,3,6,1,7,5]=>[6,2,4,3,7,1,5]=>[2,4,3,7,1,6,5]=>001011
[2,4,3,6,5,1,7]=>[5,2,4,3,6,1,7]=>[2,4,3,6,5,1,7]=>001110
[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>[2,4,3,6,5,7,1]=>001011
[2,4,3,6,7,1,5]=>[7,2,4,3,1,6,5]=>[2,4,3,6,7,1,5]=>001001
[2,4,3,6,7,5,1]=>[5,2,4,3,7,6,1]=>[2,4,3,6,7,5,1]=>001101
[2,4,3,7,1,5,6]=>[7,2,4,3,1,5,6]=>[2,4,3,7,1,5,6]=>001001
[2,4,3,7,1,6,5]=>[7,2,4,3,6,1,5]=>[2,4,3,6,1,7,5]=>001011
[2,4,3,7,5,1,6]=>[5,2,4,3,7,1,6]=>[2,4,3,7,5,1,6]=>001101
[2,4,3,7,5,6,1]=>[6,2,4,3,7,5,1]=>[2,4,3,7,5,6,1]=>001011
[2,4,3,7,6,1,5]=>[6,2,4,3,1,7,5]=>[2,4,3,7,6,1,5]=>001011
[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]=>[2,4,3,7,6,5,1]=>001111
[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]=>[2,4,5,1,3,6,7]=>000100
[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]=>[2,4,5,1,3,7,6]=>000101
[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[2,4,6,1,5,3,7]=>000110
[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[2,4,6,7,1,5,3]=>000101
[2,4,5,1,7,3,6]=>[5,2,7,4,1,3,6]=>[2,4,7,1,5,3,6]=>000101
[2,4,5,1,7,6,3]=>[5,2,6,4,1,7,3]=>[2,4,7,6,1,5,3]=>000111
[2,4,5,3,1,6,7]=>[3,2,5,4,1,6,7]=>[2,4,5,3,1,6,7]=>010100
[2,4,5,3,1,7,6]=>[3,2,5,4,1,7,6]=>[2,4,5,3,1,7,6]=>010101
[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>[2,4,5,3,6,1,7]=>000110
[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>[2,4,5,3,6,7,1]=>000101
[2,4,5,3,7,1,6]=>[7,2,5,4,3,1,6]=>[2,4,5,3,7,1,6]=>000101
[2,4,5,3,7,6,1]=>[6,2,5,4,3,7,1]=>[2,4,5,3,7,6,1]=>000111
[2,4,5,6,1,3,7]=>[6,2,1,4,5,3,7]=>[2,4,5,6,1,3,7]=>000010
[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[2,4,5,7,1,6,3]=>000011
[2,4,5,6,3,1,7]=>[3,2,6,4,5,1,7]=>[2,4,5,6,3,1,7]=>010010
[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>[2,4,5,6,3,7,1]=>000011
[2,4,5,6,7,1,3]=>[7,2,1,4,5,6,3]=>[2,4,5,6,7,1,3]=>000001
[2,4,5,6,7,3,1]=>[3,2,7,4,5,6,1]=>[2,4,5,6,7,3,1]=>010001
[2,4,5,7,1,3,6]=>[7,2,1,4,5,3,6]=>[2,4,5,7,1,3,6]=>000001
[2,4,5,7,1,6,3]=>[7,2,6,4,5,1,3]=>[2,4,5,6,1,7,3]=>000011
[2,4,5,7,3,1,6]=>[3,2,7,4,5,1,6]=>[2,4,5,7,3,1,6]=>010001
[2,4,5,7,3,6,1]=>[6,2,7,4,5,3,1]=>[2,4,5,7,3,6,1]=>000011
[2,4,5,7,6,1,3]=>[6,2,1,4,5,7,3]=>[2,4,5,7,6,1,3]=>000011
[2,4,5,7,6,3,1]=>[3,2,6,4,5,7,1]=>[2,4,5,7,6,3,1]=>010011
[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>[2,4,6,1,3,5,7]=>000010
[2,4,6,1,3,7,5]=>[6,2,1,4,7,3,5]=>[2,4,7,1,3,6,5]=>000011
[2,4,6,1,5,3,7]=>[6,2,5,4,1,3,7]=>[2,4,5,1,6,3,7]=>000110
[2,4,6,1,5,7,3]=>[6,2,7,4,1,5,3]=>[2,4,7,1,5,6,3]=>000011
[2,4,6,1,7,3,5]=>[6,2,7,4,3,1,5]=>[2,4,7,3,6,1,5]=>000011
[2,4,6,1,7,5,3]=>[6,2,5,4,7,1,3]=>[2,4,7,5,1,6,3]=>000111
[2,4,6,3,1,5,7]=>[3,2,6,4,1,5,7]=>[2,4,6,3,1,5,7]=>010010
[2,4,6,3,1,7,5]=>[3,2,6,4,7,1,5]=>[2,4,7,3,1,6,5]=>010011
[2,4,6,3,5,1,7]=>[5,2,6,4,3,1,7]=>[2,4,6,3,5,1,7]=>000110
[2,4,6,3,5,7,1]=>[7,2,6,4,3,5,1]=>[2,4,6,3,5,7,1]=>000011
[2,4,6,3,7,1,5]=>[7,2,6,4,1,3,5]=>[2,4,6,1,7,3,5]=>000011
[2,4,6,3,7,5,1]=>[5,2,7,4,6,1,3]=>[2,4,6,1,7,5,3]=>000111
[2,4,6,5,1,3,7]=>[5,2,1,4,6,3,7]=>[2,4,6,5,1,3,7]=>000110
[2,4,6,5,1,7,3]=>[5,2,6,4,7,3,1]=>[2,4,7,3,6,5,1]=>000111
[2,4,6,5,3,1,7]=>[3,2,5,4,6,1,7]=>[2,4,6,5,3,1,7]=>010110
[2,4,6,5,3,7,1]=>[7,2,5,4,6,3,1]=>[2,4,6,5,3,7,1]=>000111
[2,4,6,5,7,1,3]=>[7,2,1,4,6,5,3]=>[2,4,6,5,7,1,3]=>000011
[2,4,6,5,7,3,1]=>[3,2,7,4,6,5,1]=>[2,4,6,5,7,3,1]=>010011
[2,4,6,7,1,3,5]=>[7,2,1,4,3,6,5]=>[2,4,6,7,1,3,5]=>000001
[2,4,6,7,1,5,3]=>[7,2,5,4,1,6,3]=>[2,4,5,1,6,7,3]=>000101
[2,4,6,7,3,1,5]=>[3,2,7,4,1,6,5]=>[2,4,6,7,3,1,5]=>010001
[2,4,6,7,3,5,1]=>[5,2,7,4,3,6,1]=>[2,4,6,7,3,5,1]=>000101
[2,4,6,7,5,1,3]=>[5,2,1,4,7,6,3]=>[2,4,6,7,5,1,3]=>000101
[2,4,6,7,5,3,1]=>[3,2,5,4,7,6,1]=>[2,4,6,7,5,3,1]=>010101
[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>[2,4,7,1,3,5,6]=>000001
[2,4,7,1,3,6,5]=>[7,2,1,4,6,3,5]=>[2,4,6,1,3,7,5]=>000011
[2,4,7,1,5,3,6]=>[7,2,5,4,1,3,6]=>[2,4,5,1,7,3,6]=>000101
[2,4,7,1,5,6,3]=>[7,2,6,4,1,5,3]=>[2,4,6,1,5,7,3]=>000011
[2,4,7,1,6,3,5]=>[7,2,6,4,3,1,5]=>[2,4,6,3,7,1,5]=>000011
[2,4,7,1,6,5,3]=>[7,2,5,4,6,1,3]=>[2,4,6,5,1,7,3]=>000111
[2,4,7,3,1,5,6]=>[3,2,7,4,1,5,6]=>[2,4,7,3,1,5,6]=>010001
[2,4,7,3,1,6,5]=>[3,2,7,4,6,1,5]=>[2,4,6,3,1,7,5]=>010011
[2,4,7,3,5,1,6]=>[5,2,7,4,3,1,6]=>[2,4,7,3,5,1,6]=>000101
[2,4,7,3,5,6,1]=>[6,2,7,4,3,5,1]=>[2,4,7,3,5,6,1]=>000011
[2,4,7,3,6,1,5]=>[6,2,7,4,1,3,5]=>[2,4,7,1,6,3,5]=>000011
[2,4,7,3,6,5,1]=>[5,2,6,4,7,1,3]=>[2,4,7,1,6,5,3]=>000111
[2,4,7,5,1,3,6]=>[5,2,1,4,7,3,6]=>[2,4,7,5,1,3,6]=>000101
[2,4,7,5,1,6,3]=>[5,2,7,4,6,3,1]=>[2,4,6,3,7,5,1]=>000111
[2,4,7,5,3,1,6]=>[3,2,5,4,7,1,6]=>[2,4,7,5,3,1,6]=>010101
[2,4,7,5,3,6,1]=>[6,2,5,4,7,3,1]=>[2,4,7,5,3,6,1]=>000111
[2,4,7,5,6,1,3]=>[6,2,1,4,7,5,3]=>[2,4,7,5,6,1,3]=>000011
[2,4,7,5,6,3,1]=>[3,2,6,4,7,5,1]=>[2,4,7,5,6,3,1]=>010011
[2,4,7,6,1,3,5]=>[6,2,1,4,3,7,5]=>[2,4,7,6,1,3,5]=>000011
[2,4,7,6,1,5,3]=>[6,2,5,4,1,7,3]=>[2,4,5,1,7,6,3]=>000111
[2,4,7,6,3,1,5]=>[3,2,6,4,1,7,5]=>[2,4,7,6,3,1,5]=>010011
[2,4,7,6,3,5,1]=>[5,2,6,4,3,7,1]=>[2,4,7,6,3,5,1]=>000111
[2,4,7,6,5,1,3]=>[5,2,1,4,6,7,3]=>[2,4,7,6,5,1,3]=>000111
[2,4,7,6,5,3,1]=>[3,2,5,4,6,7,1]=>[2,4,7,6,5,3,1]=>010111
[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>000100
[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>[2,5,1,3,4,7,6]=>000101
[2,5,1,3,6,4,7]=>[5,2,1,6,3,4,7]=>[2,6,1,3,5,4,7]=>000110
[2,5,1,3,6,7,4]=>[5,2,1,7,3,6,4]=>[2,6,7,1,3,5,4]=>000101
[2,5,1,3,7,4,6]=>[5,2,1,7,3,4,6]=>[2,7,1,3,5,4,6]=>000101
[2,5,1,3,7,6,4]=>[5,2,1,6,3,7,4]=>[2,7,6,1,3,5,4]=>000111
[2,5,1,4,3,6,7]=>[5,2,4,1,3,6,7]=>[2,4,1,5,3,6,7]=>001100
[2,5,1,4,3,7,6]=>[5,2,4,1,3,7,6]=>[2,4,1,5,3,7,6]=>001101
[2,5,1,4,6,3,7]=>[5,2,6,1,4,3,7]=>[2,6,1,4,5,3,7]=>000110
[2,5,1,4,6,7,3]=>[5,2,7,1,4,6,3]=>[2,6,7,1,4,5,3]=>000101
[2,5,1,4,7,3,6]=>[5,2,7,1,4,3,6]=>[2,7,1,4,5,3,6]=>000101
[2,5,1,4,7,6,3]=>[5,2,6,1,4,7,3]=>[2,7,6,1,4,5,3]=>000111
[2,5,1,6,3,4,7]=>[5,2,6,3,1,4,7]=>[2,6,3,5,1,4,7]=>000110
[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[2,7,1,6,3,5,4]=>000111
[2,5,1,6,4,3,7]=>[5,2,4,6,1,3,7]=>[2,6,4,1,5,3,7]=>001110
[2,5,1,6,4,7,3]=>[5,2,7,6,1,4,3]=>[2,6,1,7,4,5,3]=>000111
[2,5,1,6,7,3,4]=>[5,2,7,3,1,6,4]=>[2,6,7,3,5,1,4]=>000101
[2,5,1,6,7,4,3]=>[5,2,4,7,1,6,3]=>[2,6,7,4,1,5,3]=>001101
[2,5,1,7,3,4,6]=>[5,2,7,3,1,4,6]=>[2,7,3,5,1,4,6]=>000101
[2,5,1,7,3,6,4]=>[5,2,7,6,1,3,4]=>[2,6,1,7,3,5,4]=>000111
[2,5,1,7,4,3,6]=>[5,2,4,7,1,3,6]=>[2,7,4,1,5,3,6]=>001101
[2,5,1,7,4,6,3]=>[5,2,6,7,1,4,3]=>[2,7,1,6,4,5,3]=>000111
[2,5,1,7,6,3,4]=>[5,2,6,3,1,7,4]=>[2,7,6,3,5,1,4]=>000111
[2,5,1,7,6,4,3]=>[5,2,4,6,1,7,3]=>[2,7,6,4,1,5,3]=>001111
[2,5,3,1,4,6,7]=>[3,2,5,1,4,6,7]=>[2,5,3,1,4,6,7]=>010100
[2,5,3,1,4,7,6]=>[3,2,5,1,4,7,6]=>[2,5,3,1,4,7,6]=>010101
[2,5,3,1,6,4,7]=>[3,2,5,6,1,4,7]=>[2,6,3,1,5,4,7]=>010110
[2,5,3,1,6,7,4]=>[3,2,5,7,1,6,4]=>[2,6,7,3,1,5,4]=>010101
[2,5,3,1,7,4,6]=>[3,2,5,7,1,4,6]=>[2,7,3,1,5,4,6]=>010101
[2,5,3,1,7,6,4]=>[3,2,5,6,1,7,4]=>[2,7,6,3,1,5,4]=>010111
[2,5,3,4,1,6,7]=>[4,2,5,3,1,6,7]=>[2,5,3,4,1,6,7]=>001100
[2,5,3,4,1,7,6]=>[4,2,5,3,1,7,6]=>[2,5,3,4,1,7,6]=>001101
[2,5,3,4,6,1,7]=>[6,2,5,3,4,1,7]=>[2,5,3,4,6,1,7]=>000110
[2,5,3,4,6,7,1]=>[7,2,5,3,4,6,1]=>[2,5,3,4,6,7,1]=>000101
[2,5,3,4,7,1,6]=>[7,2,5,3,4,1,6]=>[2,5,3,4,7,1,6]=>000101
[2,5,3,4,7,6,1]=>[6,2,5,3,4,7,1]=>[2,5,3,4,7,6,1]=>000111
[2,5,3,6,1,4,7]=>[6,2,5,1,3,4,7]=>[2,5,1,6,3,4,7]=>000110
[2,5,3,6,1,7,4]=>[6,2,5,7,3,1,4]=>[2,7,3,5,1,6,4]=>000111
[2,5,3,6,4,1,7]=>[4,2,6,5,1,3,7]=>[2,5,1,6,4,3,7]=>001110
[2,5,3,6,4,7,1]=>[7,2,5,6,3,4,1]=>[2,6,3,5,4,7,1]=>000111
[2,5,3,6,7,1,4]=>[7,2,5,1,3,6,4]=>[2,5,1,6,7,3,4]=>000101
[2,5,3,6,7,4,1]=>[4,2,7,5,1,6,3]=>[2,5,1,6,7,4,3]=>001101
[2,5,3,7,1,4,6]=>[7,2,5,1,3,4,6]=>[2,5,1,7,3,4,6]=>000101
[2,5,3,7,1,6,4]=>[7,2,5,6,3,1,4]=>[2,6,3,5,1,7,4]=>000111
[2,5,3,7,4,1,6]=>[4,2,7,5,1,3,6]=>[2,5,1,7,4,3,6]=>001101
[2,5,3,7,4,6,1]=>[6,2,5,7,3,4,1]=>[2,7,3,5,4,6,1]=>000111
[2,5,3,7,6,1,4]=>[6,2,5,1,3,7,4]=>[2,5,1,7,6,3,4]=>000111
[2,5,3,7,6,4,1]=>[4,2,6,5,1,7,3]=>[2,5,1,7,6,4,3]=>001111
[2,5,4,1,3,6,7]=>[4,2,1,5,3,6,7]=>[2,5,4,1,3,6,7]=>001100
[2,5,4,1,3,7,6]=>[4,2,1,5,3,7,6]=>[2,5,4,1,3,7,6]=>001101
[2,5,4,1,6,3,7]=>[4,2,5,6,3,1,7]=>[2,6,3,5,4,1,7]=>001110
[2,5,4,1,6,7,3]=>[4,2,5,7,3,6,1]=>[2,6,7,3,5,4,1]=>001101
[2,5,4,1,7,3,6]=>[4,2,5,7,3,1,6]=>[2,7,3,5,4,1,6]=>001101
[2,5,4,1,7,6,3]=>[4,2,5,6,3,7,1]=>[2,7,6,3,5,4,1]=>001111
[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]=>[2,5,4,3,1,6,7]=>011100
[2,5,4,3,1,7,6]=>[3,2,4,5,1,7,6]=>[2,5,4,3,1,7,6]=>011101
[2,5,4,3,6,1,7]=>[6,2,4,5,3,1,7]=>[2,5,4,3,6,1,7]=>001110
[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]=>[2,5,4,3,6,7,1]=>001101
[2,5,4,3,7,1,6]=>[7,2,4,5,3,1,6]=>[2,5,4,3,7,1,6]=>001101
[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]=>[2,5,4,3,7,6,1]=>001111
[2,5,4,6,1,3,7]=>[6,2,1,5,4,3,7]=>[2,5,4,6,1,3,7]=>000110
[2,5,4,6,1,7,3]=>[6,2,7,5,4,1,3]=>[2,5,4,7,1,6,3]=>000111
[2,5,4,6,3,1,7]=>[3,2,6,5,4,1,7]=>[2,5,4,6,3,1,7]=>010110
[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>[2,5,4,6,3,7,1]=>000111
[2,5,4,6,7,1,3]=>[7,2,1,5,4,6,3]=>[2,5,4,6,7,1,3]=>000101
[2,5,4,6,7,3,1]=>[3,2,7,5,4,6,1]=>[2,5,4,6,7,3,1]=>010101
[2,5,4,7,1,3,6]=>[7,2,1,5,4,3,6]=>[2,5,4,7,1,3,6]=>000101
[2,5,4,7,1,6,3]=>[7,2,6,5,4,1,3]=>[2,5,4,6,1,7,3]=>000111
[2,5,4,7,3,1,6]=>[3,2,7,5,4,1,6]=>[2,5,4,7,3,1,6]=>010101
[2,5,4,7,3,6,1]=>[6,2,7,5,4,3,1]=>[2,5,4,7,3,6,1]=>000111
[2,5,4,7,6,1,3]=>[6,2,1,5,4,7,3]=>[2,5,4,7,6,1,3]=>000111
[2,5,4,7,6,3,1]=>[3,2,6,5,4,7,1]=>[2,5,4,7,6,3,1]=>010111
[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[2,5,6,1,3,4,7]=>000010
[2,5,6,1,3,7,4]=>[6,2,1,7,5,3,4]=>[2,5,7,1,3,6,4]=>000011
[2,5,6,1,4,3,7]=>[6,2,4,1,5,3,7]=>[2,4,1,5,6,3,7]=>001010
[2,5,6,1,4,7,3]=>[6,2,7,1,5,4,3]=>[2,5,7,1,4,6,3]=>000011
[2,5,6,1,7,3,4]=>[6,2,7,3,5,1,4]=>[2,5,7,3,6,1,4]=>000011
[2,5,6,1,7,4,3]=>[6,2,4,7,5,1,3]=>[2,5,7,4,1,6,3]=>001011
[2,5,6,3,1,4,7]=>[3,2,6,1,5,4,7]=>[2,5,6,3,1,4,7]=>010010
[2,5,6,3,1,7,4]=>[3,2,6,7,5,1,4]=>[2,5,7,3,1,6,4]=>010011
[2,5,6,3,4,1,7]=>[4,2,6,3,5,1,7]=>[2,5,6,3,4,1,7]=>001010
[2,5,6,3,4,7,1]=>[7,2,6,3,5,4,1]=>[2,5,6,3,4,7,1]=>000011
[2,5,6,3,7,1,4]=>[7,2,6,1,5,3,4]=>[2,5,6,1,7,3,4]=>000011
[2,5,6,3,7,4,1]=>[4,2,7,6,5,1,3]=>[2,5,6,1,7,4,3]=>001011
[2,5,6,4,1,3,7]=>[4,2,1,6,5,3,7]=>[2,5,6,4,1,3,7]=>001010
[2,5,6,4,1,7,3]=>[4,2,6,7,5,3,1]=>[2,5,7,3,6,4,1]=>001011
[2,5,6,4,3,1,7]=>[3,2,4,6,5,1,7]=>[2,5,6,4,3,1,7]=>011010
[2,5,6,4,3,7,1]=>[7,2,4,6,5,3,1]=>[2,5,6,4,3,7,1]=>001011
[2,5,6,4,7,1,3]=>[7,2,1,6,5,4,3]=>[2,5,6,4,7,1,3]=>000011
[2,5,6,4,7,3,1]=>[3,2,7,6,5,4,1]=>[2,5,6,4,7,3,1]=>010011
[2,5,6,7,1,3,4]=>[7,2,1,3,5,6,4]=>[2,5,6,7,1,3,4]=>000001
[2,5,6,7,1,4,3]=>[7,2,4,1,5,6,3]=>[2,4,1,5,6,7,3]=>001001
[2,5,6,7,3,1,4]=>[3,2,7,1,5,6,4]=>[2,5,6,7,3,1,4]=>010001
[2,5,6,7,3,4,1]=>[4,2,7,3,5,6,1]=>[2,5,6,7,3,4,1]=>001001
[2,5,6,7,4,1,3]=>[4,2,1,7,5,6,3]=>[2,5,6,7,4,1,3]=>001001
[2,5,6,7,4,3,1]=>[3,2,4,7,5,6,1]=>[2,5,6,7,4,3,1]=>011001
[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>[2,5,7,1,3,4,6]=>000001
[2,5,7,1,3,6,4]=>[7,2,1,6,5,3,4]=>[2,5,6,1,3,7,4]=>000011
[2,5,7,1,4,3,6]=>[7,2,4,1,5,3,6]=>[2,4,1,5,7,3,6]=>001001
[2,5,7,1,4,6,3]=>[7,2,6,1,5,4,3]=>[2,5,6,1,4,7,3]=>000011
[2,5,7,1,6,3,4]=>[7,2,6,3,5,1,4]=>[2,5,6,3,7,1,4]=>000011
[2,5,7,1,6,4,3]=>[7,2,4,6,5,1,3]=>[2,5,6,4,1,7,3]=>001011
[2,5,7,3,1,4,6]=>[3,2,7,1,5,4,6]=>[2,5,7,3,1,4,6]=>010001
[2,5,7,3,1,6,4]=>[3,2,7,6,5,1,4]=>[2,5,6,3,1,7,4]=>010011
[2,5,7,3,4,1,6]=>[4,2,7,3,5,1,6]=>[2,5,7,3,4,1,6]=>001001
[2,5,7,3,4,6,1]=>[6,2,7,3,5,4,1]=>[2,5,7,3,4,6,1]=>000011
[2,5,7,3,6,1,4]=>[6,2,7,1,5,3,4]=>[2,5,7,1,6,3,4]=>000011
[2,5,7,3,6,4,1]=>[4,2,6,7,5,1,3]=>[2,5,7,1,6,4,3]=>001011
[2,5,7,4,1,3,6]=>[4,2,1,7,5,3,6]=>[2,5,7,4,1,3,6]=>001001
[2,5,7,4,1,6,3]=>[4,2,7,6,5,3,1]=>[2,5,6,3,7,4,1]=>001011
[2,5,7,4,3,1,6]=>[3,2,4,7,5,1,6]=>[2,5,7,4,3,1,6]=>011001
[2,5,7,4,3,6,1]=>[6,2,4,7,5,3,1]=>[2,5,7,4,3,6,1]=>001011
[2,5,7,4,6,1,3]=>[6,2,1,7,5,4,3]=>[2,5,7,4,6,1,3]=>000011
[2,5,7,4,6,3,1]=>[3,2,6,7,5,4,1]=>[2,5,7,4,6,3,1]=>010011
[2,5,7,6,1,3,4]=>[6,2,1,3,5,7,4]=>[2,5,7,6,1,3,4]=>000011
[2,5,7,6,1,4,3]=>[6,2,4,1,5,7,3]=>[2,4,1,5,7,6,3]=>001011
[2,5,7,6,3,1,4]=>[3,2,6,1,5,7,4]=>[2,5,7,6,3,1,4]=>010011
[2,5,7,6,3,4,1]=>[4,2,6,3,5,7,1]=>[2,5,7,6,3,4,1]=>001011
[2,5,7,6,4,1,3]=>[4,2,1,6,5,7,3]=>[2,5,7,6,4,1,3]=>001011
[2,5,7,6,4,3,1]=>[3,2,4,6,5,7,1]=>[2,5,7,6,4,3,1]=>011011
[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>000010
[2,6,1,3,4,7,5]=>[6,2,1,3,7,4,5]=>[2,7,1,3,4,6,5]=>000011
[2,6,1,3,5,4,7]=>[6,2,1,5,3,4,7]=>[2,5,1,3,6,4,7]=>000110
[2,6,1,3,5,7,4]=>[6,2,1,7,3,5,4]=>[2,7,1,3,5,6,4]=>000011
[2,6,1,3,7,4,5]=>[6,2,1,7,4,3,5]=>[2,7,4,6,1,3,5]=>000011
[2,6,1,3,7,5,4]=>[6,2,1,5,7,3,4]=>[2,7,5,1,3,6,4]=>000111
[2,6,1,4,3,5,7]=>[6,2,4,1,3,5,7]=>[2,4,1,6,3,5,7]=>001010
[2,6,1,4,3,7,5]=>[6,2,4,1,7,3,5]=>[2,4,1,7,3,6,5]=>001011
[2,6,1,4,5,3,7]=>[6,2,5,1,4,3,7]=>[2,5,1,4,6,3,7]=>000110
[2,6,1,4,5,7,3]=>[6,2,7,1,4,5,3]=>[2,7,1,4,5,6,3]=>000011
[2,6,1,4,7,3,5]=>[6,2,7,1,3,4,5]=>[2,7,1,6,3,4,5]=>000011
[2,6,1,4,7,5,3]=>[6,2,5,1,7,4,3]=>[2,7,5,1,4,6,3]=>000111
[2,6,1,5,3,4,7]=>[6,2,5,3,1,4,7]=>[2,5,3,6,1,4,7]=>000110
[2,6,1,5,3,7,4]=>[6,2,5,7,1,3,4]=>[2,7,1,5,3,6,4]=>000111
[2,6,1,5,4,3,7]=>[6,2,4,5,1,3,7]=>[2,5,4,1,6,3,7]=>001110
[2,6,1,5,4,7,3]=>[6,2,7,5,1,4,3]=>[2,5,1,7,4,6,3]=>000111
[2,6,1,5,7,3,4]=>[6,2,7,3,1,5,4]=>[2,7,3,5,6,1,4]=>000011
[2,6,1,5,7,4,3]=>[6,2,4,7,1,5,3]=>[2,7,4,1,5,6,3]=>001011
[2,6,1,7,3,4,5]=>[6,2,7,3,4,1,5]=>[2,7,3,4,6,1,5]=>000011
[2,6,1,7,3,5,4]=>[6,2,7,5,3,1,4]=>[2,5,3,7,1,6,4]=>000111
[2,6,1,7,4,3,5]=>[6,2,4,7,3,1,5]=>[2,7,4,3,6,1,5]=>001011
[2,6,1,7,4,5,3]=>[6,2,5,7,4,1,3]=>[2,7,4,5,1,6,3]=>000111
[2,6,1,7,5,3,4]=>[6,2,5,3,7,1,4]=>[2,7,5,3,6,1,4]=>000111
[2,6,1,7,5,4,3]=>[6,2,4,5,7,1,3]=>[2,7,5,4,1,6,3]=>001111
[2,6,3,1,4,5,7]=>[3,2,6,1,4,5,7]=>[2,6,3,1,4,5,7]=>010010
[2,6,3,1,4,7,5]=>[3,2,6,1,7,4,5]=>[2,7,3,1,4,6,5]=>010011
[2,6,3,1,5,4,7]=>[3,2,6,5,1,4,7]=>[2,5,3,1,6,4,7]=>010110
[2,6,3,1,5,7,4]=>[3,2,6,7,1,5,4]=>[2,7,3,1,5,6,4]=>010011
[2,6,3,1,7,4,5]=>[3,2,6,7,4,1,5]=>[2,7,4,6,3,1,5]=>010011
[2,6,3,1,7,5,4]=>[3,2,6,5,7,1,4]=>[2,7,5,3,1,6,4]=>010111
[2,6,3,4,1,5,7]=>[4,2,6,3,1,5,7]=>[2,6,3,4,1,5,7]=>001010
[2,6,3,4,1,7,5]=>[4,2,6,3,7,1,5]=>[2,7,3,4,1,6,5]=>001011
[2,6,3,4,5,1,7]=>[5,2,6,3,4,1,7]=>[2,6,3,4,5,1,7]=>000110
[2,6,3,4,5,7,1]=>[7,2,6,3,4,5,1]=>[2,6,3,4,5,7,1]=>000011
[2,6,3,4,7,1,5]=>[7,2,6,3,1,4,5]=>[2,6,3,7,1,4,5]=>000011
[2,6,3,4,7,5,1]=>[5,2,7,1,6,4,3]=>[2,6,1,4,7,5,3]=>000111
[2,6,3,5,1,4,7]=>[5,2,6,1,3,4,7]=>[2,6,1,5,3,4,7]=>000110
[2,6,3,5,1,7,4]=>[5,2,6,7,3,1,4]=>[2,7,3,6,1,5,4]=>000111
[2,6,3,5,4,1,7]=>[4,2,5,6,1,3,7]=>[2,6,1,5,4,3,7]=>001110
[2,6,3,5,4,7,1]=>[7,2,6,5,3,4,1]=>[2,5,3,6,4,7,1]=>000111
[2,6,3,5,7,1,4]=>[7,2,6,1,3,5,4]=>[2,6,1,5,7,3,4]=>000011
[2,6,3,5,7,4,1]=>[4,2,7,6,1,5,3]=>[2,6,1,5,7,4,3]=>001011
[2,6,3,7,1,4,5]=>[7,2,6,1,4,3,5]=>[2,6,1,4,7,3,5]=>000011
[2,6,3,7,1,5,4]=>[7,2,6,5,1,3,4]=>[2,5,1,6,3,7,4]=>000111
[2,6,3,7,4,1,5]=>[4,2,7,6,3,1,5]=>[2,6,3,7,4,1,5]=>001011
[2,6,3,7,4,5,1]=>[5,2,6,7,4,3,1]=>[2,7,4,6,3,5,1]=>000111
[2,6,3,7,5,1,4]=>[5,2,7,3,6,1,4]=>[2,6,3,7,5,1,4]=>000111
[2,6,3,7,5,4,1]=>[4,2,5,7,6,3,1]=>[2,6,3,7,5,4,1]=>001111
[2,6,4,1,3,5,7]=>[4,2,1,6,3,5,7]=>[2,6,4,1,3,5,7]=>001010
[2,6,4,1,3,7,5]=>[4,2,1,6,7,3,5]=>[2,7,4,1,3,6,5]=>001011
[2,6,4,1,5,3,7]=>[4,2,6,5,3,1,7]=>[2,5,3,6,4,1,7]=>001110
[2,6,4,1,5,7,3]=>[4,2,6,7,3,5,1]=>[2,7,3,5,6,4,1]=>001011
[2,6,4,1,7,3,5]=>[4,2,6,7,1,3,5]=>[2,7,1,6,4,3,5]=>001011
[2,6,4,1,7,5,3]=>[4,2,6,5,7,3,1]=>[2,7,5,3,6,4,1]=>001111
[2,6,4,3,1,5,7]=>[3,2,4,6,1,5,7]=>[2,6,4,3,1,5,7]=>011010
[2,6,4,3,1,7,5]=>[3,2,4,6,7,1,5]=>[2,7,4,3,1,6,5]=>011011
[2,6,4,3,5,1,7]=>[5,2,4,6,3,1,7]=>[2,6,4,3,5,1,7]=>001110
[2,6,4,3,5,7,1]=>[7,2,4,6,3,5,1]=>[2,6,4,3,5,7,1]=>001011
[2,6,4,3,7,1,5]=>[7,2,4,6,1,3,5]=>[2,6,4,1,7,3,5]=>001011
[2,6,4,3,7,5,1]=>[5,2,4,7,6,1,3]=>[2,6,4,1,7,5,3]=>001111
[2,6,4,5,1,3,7]=>[5,2,1,6,4,3,7]=>[2,6,4,5,1,3,7]=>000110
[2,6,4,5,1,7,3]=>[5,2,7,6,4,1,3]=>[2,6,4,7,1,5,3]=>000111
[2,6,4,5,3,1,7]=>[3,2,5,6,4,1,7]=>[2,6,4,5,3,1,7]=>010110
[2,6,4,5,3,7,1]=>[7,2,5,6,4,3,1]=>[2,6,4,5,3,7,1]=>000111
[2,6,4,5,7,1,3]=>[7,2,1,6,4,5,3]=>[2,6,4,5,7,1,3]=>000011
[2,6,4,5,7,3,1]=>[3,2,7,6,4,5,1]=>[2,6,4,5,7,3,1]=>010011
[2,6,4,7,1,3,5]=>[7,2,1,6,3,4,5]=>[2,6,1,3,7,4,5]=>000011
[2,6,4,7,1,5,3]=>[7,2,5,6,1,4,3]=>[2,6,1,5,4,7,3]=>000111
[2,6,4,7,3,1,5]=>[3,2,7,6,1,4,5]=>[2,6,3,1,7,4,5]=>010011
[2,6,4,7,3,5,1]=>[5,2,7,6,3,4,1]=>[2,6,3,7,4,5,1]=>000111
[2,6,4,7,5,1,3]=>[5,2,1,7,6,3,4]=>[2,6,1,3,7,5,4]=>000111
[2,6,4,7,5,3,1]=>[3,2,5,7,6,1,4]=>[2,6,3,1,7,5,4]=>010111
[2,6,5,1,3,4,7]=>[5,2,1,3,6,4,7]=>[2,6,5,1,3,4,7]=>000110
[2,6,5,1,3,7,4]=>[5,2,1,6,7,4,3]=>[2,7,4,6,5,1,3]=>000111
[2,6,5,1,4,3,7]=>[5,2,4,1,6,3,7]=>[2,4,1,6,5,3,7]=>001110
[2,6,5,1,4,7,3]=>[5,2,6,3,7,4,1]=>[2,7,3,4,6,5,1]=>000111
[2,6,5,1,7,3,4]=>[5,2,6,1,7,3,4]=>[2,7,1,6,5,3,4]=>000111
[2,6,5,1,7,4,3]=>[5,2,4,6,7,3,1]=>[2,7,4,3,6,5,1]=>001111
[2,6,5,3,1,4,7]=>[3,2,5,1,6,4,7]=>[2,6,5,3,1,4,7]=>010110
[2,6,5,3,1,7,4]=>[3,2,5,6,7,4,1]=>[2,7,4,6,5,3,1]=>010111
[2,6,5,3,4,1,7]=>[4,2,5,3,6,1,7]=>[2,6,5,3,4,1,7]=>001110
[2,6,5,3,4,7,1]=>[7,2,5,3,6,4,1]=>[2,6,5,3,4,7,1]=>000111
[2,6,5,3,7,1,4]=>[7,2,5,1,6,3,4]=>[2,6,5,1,7,3,4]=>000111
[2,6,5,3,7,4,1]=>[4,2,7,5,6,1,3]=>[2,6,5,1,7,4,3]=>001111
[2,6,5,4,1,3,7]=>[4,2,1,5,6,3,7]=>[2,6,5,4,1,3,7]=>001110
[2,6,5,4,1,7,3]=>[4,2,5,6,7,1,3]=>[2,7,1,6,5,4,3]=>001111
[2,6,5,4,3,1,7]=>[3,2,4,5,6,1,7]=>[2,6,5,4,3,1,7]=>011110
[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]=>[2,6,5,4,3,7,1]=>001111
[2,6,5,4,7,1,3]=>[7,2,1,5,6,4,3]=>[2,6,5,4,7,1,3]=>000111
[2,6,5,4,7,3,1]=>[3,2,7,5,6,4,1]=>[2,6,5,4,7,3,1]=>010111
[2,6,5,7,1,3,4]=>[7,2,1,3,6,5,4]=>[2,6,5,7,1,3,4]=>000011
[2,6,5,7,1,4,3]=>[7,2,4,1,6,5,3]=>[2,4,1,6,5,7,3]=>001011
[2,6,5,7,3,1,4]=>[3,2,7,1,6,5,4]=>[2,6,5,7,3,1,4]=>010011
[2,6,5,7,3,4,1]=>[4,2,7,3,6,5,1]=>[2,6,5,7,3,4,1]=>001011
[2,6,5,7,4,1,3]=>[4,2,1,7,6,5,3]=>[2,6,5,7,4,1,3]=>001011
[2,6,5,7,4,3,1]=>[3,2,4,7,6,5,1]=>[2,6,5,7,4,3,1]=>011011
[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[2,6,7,1,3,4,5]=>000001
[2,6,7,1,3,5,4]=>[7,2,1,5,3,6,4]=>[2,5,1,3,6,7,4]=>000101
[2,6,7,1,4,3,5]=>[7,2,4,1,3,6,5]=>[2,4,1,6,7,3,5]=>001001
[2,6,7,1,4,5,3]=>[7,2,5,1,4,6,3]=>[2,5,1,4,6,7,3]=>000101
[2,6,7,1,5,3,4]=>[7,2,5,3,1,6,4]=>[2,5,3,6,7,1,4]=>000101
[2,6,7,1,5,4,3]=>[7,2,4,5,1,6,3]=>[2,5,4,1,6,7,3]=>001101
[2,6,7,3,1,4,5]=>[3,2,7,1,4,6,5]=>[2,6,7,3,1,4,5]=>010001
[2,6,7,3,1,5,4]=>[3,2,7,5,1,6,4]=>[2,5,3,1,6,7,4]=>010101
[2,6,7,3,4,1,5]=>[4,2,7,3,1,6,5]=>[2,6,7,3,4,1,5]=>001001
[2,6,7,3,4,5,1]=>[5,2,7,3,4,6,1]=>[2,6,7,3,4,5,1]=>000101
[2,6,7,3,5,1,4]=>[5,2,7,1,3,6,4]=>[2,6,7,1,5,3,4]=>000101
[2,6,7,3,5,4,1]=>[4,2,5,7,1,6,3]=>[2,6,7,1,5,4,3]=>001101
[2,6,7,4,1,3,5]=>[4,2,1,7,3,6,5]=>[2,6,7,4,1,3,5]=>001001
[2,6,7,4,1,5,3]=>[4,2,7,5,3,6,1]=>[2,5,3,6,7,4,1]=>001101
[2,6,7,4,3,1,5]=>[3,2,4,7,1,6,5]=>[2,6,7,4,3,1,5]=>011001
[2,6,7,4,3,5,1]=>[5,2,4,7,3,6,1]=>[2,6,7,4,3,5,1]=>001101
[2,6,7,4,5,1,3]=>[5,2,1,7,4,6,3]=>[2,6,7,4,5,1,3]=>000101
[2,6,7,4,5,3,1]=>[3,2,5,7,4,6,1]=>[2,6,7,4,5,3,1]=>010101
[2,6,7,5,1,3,4]=>[5,2,1,3,7,6,4]=>[2,6,7,5,1,3,4]=>000101
[2,6,7,5,1,4,3]=>[5,2,4,1,7,6,3]=>[2,4,1,6,7,5,3]=>001101
[2,6,7,5,3,1,4]=>[3,2,5,1,7,6,4]=>[2,6,7,5,3,1,4]=>010101
[2,6,7,5,3,4,1]=>[4,2,5,3,7,6,1]=>[2,6,7,5,3,4,1]=>001101
[2,6,7,5,4,1,3]=>[4,2,1,5,7,6,3]=>[2,6,7,5,4,1,3]=>001101
[2,6,7,5,4,3,1]=>[3,2,4,5,7,6,1]=>[2,6,7,5,4,3,1]=>011101
[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>000001
[2,7,1,3,4,6,5]=>[7,2,1,3,6,4,5]=>[2,6,1,3,4,7,5]=>000011
[2,7,1,3,5,4,6]=>[7,2,1,5,3,4,6]=>[2,5,1,3,7,4,6]=>000101
[2,7,1,3,5,6,4]=>[7,2,1,6,3,5,4]=>[2,6,1,3,5,7,4]=>000011
[2,7,1,3,6,4,5]=>[7,2,1,6,4,3,5]=>[2,6,4,7,1,3,5]=>000011
[2,7,1,3,6,5,4]=>[7,2,1,5,6,3,4]=>[2,6,5,1,3,7,4]=>000111
[2,7,1,4,3,5,6]=>[7,2,4,1,3,5,6]=>[2,4,1,7,3,5,6]=>001001
[2,7,1,4,3,6,5]=>[7,2,4,1,6,3,5]=>[2,4,1,6,3,7,5]=>001011
[2,7,1,4,5,3,6]=>[7,2,5,1,4,3,6]=>[2,5,1,4,7,3,6]=>000101
[2,7,1,4,5,6,3]=>[7,2,6,1,4,5,3]=>[2,6,1,4,5,7,3]=>000011
[2,7,1,4,6,3,5]=>[7,2,6,1,3,4,5]=>[2,6,1,7,3,4,5]=>000011
[2,7,1,4,6,5,3]=>[7,2,5,1,6,4,3]=>[2,6,5,1,4,7,3]=>000111
[2,7,1,5,3,4,6]=>[7,2,5,3,1,4,6]=>[2,5,3,7,1,4,6]=>000101
[2,7,1,5,3,6,4]=>[7,2,5,6,1,3,4]=>[2,6,1,5,3,7,4]=>000111
[2,7,1,5,4,3,6]=>[7,2,4,5,1,3,6]=>[2,5,4,1,7,3,6]=>001101
[2,7,1,5,4,6,3]=>[7,2,6,5,1,4,3]=>[2,5,1,6,4,7,3]=>000111
[2,7,1,5,6,3,4]=>[7,2,6,3,1,5,4]=>[2,6,3,5,7,1,4]=>000011
[2,7,1,5,6,4,3]=>[7,2,4,6,1,5,3]=>[2,6,4,1,5,7,3]=>001011
[2,7,1,6,3,4,5]=>[7,2,6,3,4,1,5]=>[2,6,3,4,7,1,5]=>000011
[2,7,1,6,3,5,4]=>[7,2,6,5,3,1,4]=>[2,5,3,6,1,7,4]=>000111
[2,7,1,6,4,3,5]=>[7,2,4,6,3,1,5]=>[2,6,4,3,7,1,5]=>001011
[2,7,1,6,4,5,3]=>[7,2,5,6,4,1,3]=>[2,6,4,5,1,7,3]=>000111
[2,7,1,6,5,3,4]=>[7,2,5,3,6,1,4]=>[2,6,5,3,7,1,4]=>000111
[2,7,1,6,5,4,3]=>[7,2,4,5,6,1,3]=>[2,6,5,4,1,7,3]=>001111
[2,7,3,1,4,5,6]=>[3,2,7,1,4,5,6]=>[2,7,3,1,4,5,6]=>010001
[2,7,3,1,4,6,5]=>[3,2,7,1,6,4,5]=>[2,6,3,1,4,7,5]=>010011
[2,7,3,1,5,4,6]=>[3,2,7,5,1,4,6]=>[2,5,3,1,7,4,6]=>010101
[2,7,3,1,5,6,4]=>[3,2,7,6,1,5,4]=>[2,6,3,1,5,7,4]=>010011
[2,7,3,1,6,4,5]=>[3,2,7,6,4,1,5]=>[2,6,4,7,3,1,5]=>010011
[2,7,3,1,6,5,4]=>[3,2,7,5,6,1,4]=>[2,6,5,3,1,7,4]=>010111
[2,7,3,4,1,5,6]=>[4,2,7,3,1,5,6]=>[2,7,3,4,1,5,6]=>001001
[2,7,3,4,1,6,5]=>[4,2,7,3,6,1,5]=>[2,6,3,4,1,7,5]=>001011
[2,7,3,4,5,1,6]=>[5,2,7,3,4,1,6]=>[2,7,3,4,5,1,6]=>000101
[2,7,3,4,5,6,1]=>[6,2,7,3,4,5,1]=>[2,7,3,4,5,6,1]=>000011
[2,7,3,4,6,1,5]=>[6,2,7,3,1,4,5]=>[2,7,3,6,1,4,5]=>000011
[2,7,3,4,6,5,1]=>[5,2,6,1,7,4,3]=>[2,7,1,4,6,5,3]=>000111
[2,7,3,5,1,4,6]=>[5,2,7,1,3,4,6]=>[2,7,1,5,3,4,6]=>000101
[2,7,3,5,1,6,4]=>[5,2,7,6,3,1,4]=>[2,6,3,7,1,5,4]=>000111
[2,7,3,5,4,1,6]=>[4,2,5,7,1,3,6]=>[2,7,1,5,4,3,6]=>001101
[2,7,3,5,4,6,1]=>[6,2,7,5,3,4,1]=>[2,5,3,7,4,6,1]=>000111
[2,7,3,5,6,1,4]=>[6,2,7,1,3,5,4]=>[2,7,1,5,6,3,4]=>000011
[2,7,3,5,6,4,1]=>[4,2,6,7,1,5,3]=>[2,7,1,5,6,4,3]=>001011
[2,7,3,6,1,4,5]=>[6,2,7,1,4,3,5]=>[2,7,1,4,6,3,5]=>000011
[2,7,3,6,1,5,4]=>[6,2,7,5,1,3,4]=>[2,5,1,7,3,6,4]=>000111
[2,7,3,6,4,1,5]=>[4,2,6,7,3,1,5]=>[2,7,3,6,4,1,5]=>001011
[2,7,3,6,4,5,1]=>[5,2,7,6,4,3,1]=>[2,6,4,7,3,5,1]=>000111
[2,7,3,6,5,1,4]=>[5,2,6,3,7,1,4]=>[2,7,3,6,5,1,4]=>000111
[2,7,3,6,5,4,1]=>[4,2,5,6,7,3,1]=>[2,7,3,6,5,4,1]=>001111
[2,7,4,1,3,5,6]=>[4,2,1,7,3,5,6]=>[2,7,4,1,3,5,6]=>001001
[2,7,4,1,3,6,5]=>[4,2,1,7,6,3,5]=>[2,6,4,1,3,7,5]=>001011
[2,7,4,1,5,3,6]=>[4,2,7,5,3,1,6]=>[2,5,3,7,4,1,6]=>001101
[2,7,4,1,5,6,3]=>[4,2,7,6,3,5,1]=>[2,6,3,5,7,4,1]=>001011
[2,7,4,1,6,3,5]=>[4,2,7,6,1,3,5]=>[2,6,1,7,4,3,5]=>001011
[2,7,4,1,6,5,3]=>[4,2,7,5,6,3,1]=>[2,6,5,3,7,4,1]=>001111
[2,7,4,3,1,5,6]=>[3,2,4,7,1,5,6]=>[2,7,4,3,1,5,6]=>011001
[2,7,4,3,1,6,5]=>[3,2,4,7,6,1,5]=>[2,6,4,3,1,7,5]=>011011
[2,7,4,3,5,1,6]=>[5,2,4,7,3,1,6]=>[2,7,4,3,5,1,6]=>001101
[2,7,4,3,5,6,1]=>[6,2,4,7,3,5,1]=>[2,7,4,3,5,6,1]=>001011
[2,7,4,3,6,1,5]=>[6,2,4,7,1,3,5]=>[2,7,4,1,6,3,5]=>001011
[2,7,4,3,6,5,1]=>[5,2,4,6,7,1,3]=>[2,7,4,1,6,5,3]=>001111
[2,7,4,5,1,3,6]=>[5,2,1,7,4,3,6]=>[2,7,4,5,1,3,6]=>000101
[2,7,4,5,1,6,3]=>[5,2,6,7,4,1,3]=>[2,7,4,6,1,5,3]=>000111
[2,7,4,5,3,1,6]=>[3,2,5,7,4,1,6]=>[2,7,4,5,3,1,6]=>010101
[2,7,4,5,3,6,1]=>[6,2,5,7,4,3,1]=>[2,7,4,5,3,6,1]=>000111
[2,7,4,5,6,1,3]=>[6,2,1,7,4,5,3]=>[2,7,4,5,6,1,3]=>000011
[2,7,4,5,6,3,1]=>[3,2,6,7,4,5,1]=>[2,7,4,5,6,3,1]=>010011
[2,7,4,6,1,3,5]=>[6,2,1,7,3,4,5]=>[2,7,1,3,6,4,5]=>000011
[2,7,4,6,1,5,3]=>[6,2,5,7,1,4,3]=>[2,7,1,5,4,6,3]=>000111
[2,7,4,6,3,1,5]=>[3,2,6,7,1,4,5]=>[2,7,3,1,6,4,5]=>010011
[2,7,4,6,3,5,1]=>[5,2,6,7,3,4,1]=>[2,7,3,6,4,5,1]=>000111
[2,7,4,6,5,1,3]=>[5,2,1,6,7,3,4]=>[2,7,1,3,6,5,4]=>000111
[2,7,4,6,5,3,1]=>[3,2,5,6,7,1,4]=>[2,7,3,1,6,5,4]=>010111
[2,7,5,1,3,4,6]=>[5,2,1,3,7,4,6]=>[2,7,5,1,3,4,6]=>000101
[2,7,5,1,3,6,4]=>[5,2,1,7,6,4,3]=>[2,6,4,7,5,1,3]=>000111
[2,7,5,1,4,3,6]=>[5,2,4,1,7,3,6]=>[2,4,1,7,5,3,6]=>001101
[2,7,5,1,4,6,3]=>[5,2,7,3,6,4,1]=>[2,6,3,4,7,5,1]=>000111
[2,7,5,1,6,3,4]=>[5,2,7,1,6,3,4]=>[2,6,1,7,5,3,4]=>000111
[2,7,5,1,6,4,3]=>[5,2,4,7,6,3,1]=>[2,6,4,3,7,5,1]=>001111
[2,7,5,3,1,4,6]=>[3,2,5,1,7,4,6]=>[2,7,5,3,1,4,6]=>010101
[2,7,5,3,1,6,4]=>[3,2,5,7,6,4,1]=>[2,6,4,7,5,3,1]=>010111
[2,7,5,3,4,1,6]=>[4,2,5,3,7,1,6]=>[2,7,5,3,4,1,6]=>001101
[2,7,5,3,4,6,1]=>[6,2,5,3,7,4,1]=>[2,7,5,3,4,6,1]=>000111
[2,7,5,3,6,1,4]=>[6,2,5,1,7,3,4]=>[2,7,5,1,6,3,4]=>000111
[2,7,5,3,6,4,1]=>[4,2,6,5,7,1,3]=>[2,7,5,1,6,4,3]=>001111
[2,7,5,4,1,3,6]=>[4,2,1,5,7,3,6]=>[2,7,5,4,1,3,6]=>001101
[2,7,5,4,1,6,3]=>[4,2,5,7,6,1,3]=>[2,6,1,7,5,4,3]=>001111
[2,7,5,4,3,1,6]=>[3,2,4,5,7,1,6]=>[2,7,5,4,3,1,6]=>011101
[2,7,5,4,3,6,1]=>[6,2,4,5,7,3,1]=>[2,7,5,4,3,6,1]=>001111
[2,7,5,4,6,1,3]=>[6,2,1,5,7,4,3]=>[2,7,5,4,6,1,3]=>000111
[2,7,5,4,6,3,1]=>[3,2,6,5,7,4,1]=>[2,7,5,4,6,3,1]=>010111
[2,7,5,6,1,3,4]=>[6,2,1,3,7,5,4]=>[2,7,5,6,1,3,4]=>000011
[2,7,5,6,1,4,3]=>[6,2,4,1,7,5,3]=>[2,4,1,7,5,6,3]=>001011
[2,7,5,6,3,1,4]=>[3,2,6,1,7,5,4]=>[2,7,5,6,3,1,4]=>010011
[2,7,5,6,3,4,1]=>[4,2,6,3,7,5,1]=>[2,7,5,6,3,4,1]=>001011
[2,7,5,6,4,1,3]=>[4,2,1,6,7,5,3]=>[2,7,5,6,4,1,3]=>001011
[2,7,5,6,4,3,1]=>[3,2,4,6,7,5,1]=>[2,7,5,6,4,3,1]=>011011
[2,7,6,1,3,4,5]=>[6,2,1,3,4,7,5]=>[2,7,6,1,3,4,5]=>000011
[2,7,6,1,3,5,4]=>[6,2,1,5,3,7,4]=>[2,5,1,3,7,6,4]=>000111
[2,7,6,1,4,3,5]=>[6,2,4,1,3,7,5]=>[2,4,1,7,6,3,5]=>001011
[2,7,6,1,4,5,3]=>[6,2,5,1,4,7,3]=>[2,5,1,4,7,6,3]=>000111
[2,7,6,1,5,3,4]=>[6,2,5,3,1,7,4]=>[2,5,3,7,6,1,4]=>000111
[2,7,6,1,5,4,3]=>[6,2,4,5,1,7,3]=>[2,5,4,1,7,6,3]=>001111
[2,7,6,3,1,4,5]=>[3,2,6,1,4,7,5]=>[2,7,6,3,1,4,5]=>010011
[2,7,6,3,1,5,4]=>[3,2,6,5,1,7,4]=>[2,5,3,1,7,6,4]=>010111
[2,7,6,3,4,1,5]=>[4,2,6,3,1,7,5]=>[2,7,6,3,4,1,5]=>001011
[2,7,6,3,4,5,1]=>[5,2,6,3,4,7,1]=>[2,7,6,3,4,5,1]=>000111
[2,7,6,3,5,1,4]=>[5,2,6,1,3,7,4]=>[2,7,6,1,5,3,4]=>000111
[2,7,6,3,5,4,1]=>[4,2,5,6,1,7,3]=>[2,7,6,1,5,4,3]=>001111
[2,7,6,4,1,3,5]=>[4,2,1,6,3,7,5]=>[2,7,6,4,1,3,5]=>001011
[2,7,6,4,1,5,3]=>[4,2,6,5,3,7,1]=>[2,5,3,7,6,4,1]=>001111
[2,7,6,4,3,1,5]=>[3,2,4,6,1,7,5]=>[2,7,6,4,3,1,5]=>011011
[2,7,6,4,3,5,1]=>[5,2,4,6,3,7,1]=>[2,7,6,4,3,5,1]=>001111
[2,7,6,4,5,1,3]=>[5,2,1,6,4,7,3]=>[2,7,6,4,5,1,3]=>000111
[2,7,6,4,5,3,1]=>[3,2,5,6,4,7,1]=>[2,7,6,4,5,3,1]=>010111
[2,7,6,5,1,3,4]=>[5,2,1,3,6,7,4]=>[2,7,6,5,1,3,4]=>000111
[2,7,6,5,1,4,3]=>[5,2,4,1,6,7,3]=>[2,4,1,7,6,5,3]=>001111
[2,7,6,5,3,1,4]=>[3,2,5,1,6,7,4]=>[2,7,6,5,3,1,4]=>010111
[2,7,6,5,3,4,1]=>[4,2,5,3,6,7,1]=>[2,7,6,5,3,4,1]=>001111
[2,7,6,5,4,1,3]=>[4,2,1,5,6,7,3]=>[2,7,6,5,4,1,3]=>001111
[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]=>[2,7,6,5,4,3,1]=>011111
[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>010000
[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>010001
[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>010010
[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>[3,1,2,4,6,7,5]=>010001
[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>010001
[3,1,2,4,7,6,5]=>[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>010011
[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>010100
[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>010101
[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>[3,1,2,5,6,4,7]=>010010
[3,1,2,5,6,7,4]=>[3,1,2,7,5,6,4]=>[3,1,2,5,6,7,4]=>010001
[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>[3,1,2,5,7,4,6]=>010001
[3,1,2,5,7,6,4]=>[3,1,2,6,5,7,4]=>[3,1,2,5,7,6,4]=>010011
[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>010010
[3,1,2,6,4,7,5]=>[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]=>010011
[3,1,2,6,5,4,7]=>[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>010110
[3,1,2,6,5,7,4]=>[3,1,2,7,6,5,4]=>[3,1,2,6,5,7,4]=>010011
[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]=>[3,1,2,6,7,4,5]=>010001
[3,1,2,6,7,5,4]=>[3,1,2,5,7,6,4]=>[3,1,2,6,7,5,4]=>010101
[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>010001
[3,1,2,7,4,6,5]=>[3,1,2,7,6,4,5]=>[3,1,2,6,4,7,5]=>010011
[3,1,2,7,5,4,6]=>[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>010101
[3,1,2,7,5,6,4]=>[3,1,2,6,7,5,4]=>[3,1,2,7,5,6,4]=>010011
[3,1,2,7,6,4,5]=>[3,1,2,6,4,7,5]=>[3,1,2,7,6,4,5]=>010011
[3,1,2,7,6,5,4]=>[3,1,2,5,6,7,4]=>[3,1,2,7,6,5,4]=>010111
[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>011000
[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]=>011001
[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]=>011010
[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[4,1,3,2,6,7,5]=>011001
[3,1,4,2,7,5,6]=>[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]=>011001
[3,1,4,2,7,6,5]=>[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]=>011011
[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[4,5,1,3,2,6,7]=>010100
[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[4,5,1,3,2,7,6]=>010101
[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[4,5,6,1,3,2,7]=>010010
[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[4,5,6,7,1,3,2]=>010001
[3,1,4,5,7,2,6]=>[3,7,1,4,5,2,6]=>[4,5,7,1,3,2,6]=>010001
[3,1,4,5,7,6,2]=>[3,6,1,4,5,7,2]=>[4,5,7,6,1,3,2]=>010011
[3,1,4,6,2,5,7]=>[3,6,1,4,2,5,7]=>[4,6,1,3,2,5,7]=>010010
[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[4,7,1,3,2,6,5]=>010011
[3,1,4,6,5,2,7]=>[3,5,1,4,6,2,7]=>[4,6,5,1,3,2,7]=>010110
[3,1,4,6,5,7,2]=>[3,7,1,4,6,5,2]=>[4,6,5,7,1,3,2]=>010011
[3,1,4,6,7,2,5]=>[3,7,1,4,2,6,5]=>[4,6,7,1,3,2,5]=>010001
[3,1,4,6,7,5,2]=>[3,5,1,4,7,6,2]=>[4,6,7,5,1,3,2]=>010101
[3,1,4,7,2,5,6]=>[3,7,1,4,2,5,6]=>[4,7,1,3,2,5,6]=>010001
[3,1,4,7,2,6,5]=>[3,7,1,4,6,2,5]=>[4,6,1,3,2,7,5]=>010011
[3,1,4,7,5,2,6]=>[3,5,1,4,7,2,6]=>[4,7,5,1,3,2,6]=>010101
[3,1,4,7,5,6,2]=>[3,6,1,4,7,5,2]=>[4,7,5,6,1,3,2]=>010011
[3,1,4,7,6,2,5]=>[3,6,1,4,2,7,5]=>[4,7,6,1,3,2,5]=>010011
[3,1,4,7,6,5,2]=>[3,5,1,4,6,7,2]=>[4,7,6,5,1,3,2]=>010111
[3,1,5,2,4,6,7]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>010100
[3,1,5,2,4,7,6]=>[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]=>010101
[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[6,1,3,2,5,4,7]=>010110
[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[6,7,1,3,2,5,4]=>010101
[3,1,5,2,7,4,6]=>[3,5,1,7,2,4,6]=>[7,1,3,2,5,4,6]=>010101
[3,1,5,2,7,6,4]=>[3,5,1,6,2,7,4]=>[7,6,1,3,2,5,4]=>010111
[3,1,5,4,2,6,7]=>[3,4,1,5,2,6,7]=>[5,4,1,3,2,6,7]=>011100
[3,1,5,4,2,7,6]=>[3,4,1,5,2,7,6]=>[5,4,1,3,2,7,6]=>011101
[3,1,5,4,6,2,7]=>[3,6,1,5,4,2,7]=>[5,4,6,1,3,2,7]=>010110
[3,1,5,4,6,7,2]=>[3,7,1,5,4,6,2]=>[5,4,6,7,1,3,2]=>010101
[3,1,5,4,7,2,6]=>[3,7,1,5,4,2,6]=>[5,4,7,1,3,2,6]=>010101
[3,1,5,4,7,6,2]=>[3,6,1,5,4,7,2]=>[5,4,7,6,1,3,2]=>010111
[3,1,5,6,2,4,7]=>[3,6,1,2,5,4,7]=>[5,6,1,3,2,4,7]=>010010
[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[5,7,1,3,2,6,4]=>010011
[3,1,5,6,4,2,7]=>[3,4,1,6,5,2,7]=>[5,6,4,1,3,2,7]=>011010
[3,1,5,6,4,7,2]=>[3,7,1,6,5,4,2]=>[5,6,4,7,1,3,2]=>010011
[3,1,5,6,7,2,4]=>[3,7,1,2,5,6,4]=>[5,6,7,1,3,2,4]=>010001
[3,1,5,6,7,4,2]=>[3,4,1,7,5,6,2]=>[5,6,7,4,1,3,2]=>011001
[3,1,5,7,2,4,6]=>[3,7,1,2,5,4,6]=>[5,7,1,3,2,4,6]=>010001
[3,1,5,7,2,6,4]=>[3,7,1,6,5,2,4]=>[5,6,1,3,2,7,4]=>010011
[3,1,5,7,4,2,6]=>[3,4,1,7,5,2,6]=>[5,7,4,1,3,2,6]=>011001
[3,1,5,7,4,6,2]=>[3,6,1,7,5,4,2]=>[5,7,4,6,1,3,2]=>010011
[3,1,5,7,6,2,4]=>[3,6,1,2,5,7,4]=>[5,7,6,1,3,2,4]=>010011
[3,1,5,7,6,4,2]=>[3,4,1,6,5,7,2]=>[5,7,6,4,1,3,2]=>011011
[3,1,6,2,4,5,7]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>010010
[3,1,6,2,4,7,5]=>[3,6,1,2,7,4,5]=>[7,1,3,2,4,6,5]=>010011
[3,1,6,2,5,4,7]=>[3,6,1,5,2,4,7]=>[5,1,3,2,6,4,7]=>010110
[3,1,6,2,5,7,4]=>[3,6,1,7,2,5,4]=>[7,1,3,2,5,6,4]=>010011
[3,1,6,2,7,4,5]=>[3,6,1,7,4,2,5]=>[7,4,6,1,3,2,5]=>010011
[3,1,6,2,7,5,4]=>[3,6,1,5,7,2,4]=>[7,5,1,3,2,6,4]=>010111
[3,1,6,4,2,5,7]=>[3,4,1,6,2,5,7]=>[6,4,1,3,2,5,7]=>011010
[3,1,6,4,2,7,5]=>[3,4,1,6,7,2,5]=>[7,4,1,3,2,6,5]=>011011
[3,1,6,4,5,2,7]=>[3,5,1,6,4,2,7]=>[6,4,5,1,3,2,7]=>010110
[3,1,6,4,5,7,2]=>[3,7,1,6,4,5,2]=>[6,4,5,7,1,3,2]=>010011
[3,1,6,4,7,2,5]=>[3,7,1,6,2,4,5]=>[6,1,3,2,7,4,5]=>010011
[3,1,6,4,7,5,2]=>[3,5,1,7,6,2,4]=>[6,1,3,2,7,5,4]=>010111
[3,1,6,5,2,4,7]=>[3,5,1,2,6,4,7]=>[6,5,1,3,2,4,7]=>010110
[3,1,6,5,2,7,4]=>[3,5,1,6,7,4,2]=>[7,4,6,5,1,3,2]=>010111
[3,1,6,5,4,2,7]=>[3,4,1,5,6,2,7]=>[6,5,4,1,3,2,7]=>011110
[3,1,6,5,4,7,2]=>[3,7,1,5,6,4,2]=>[6,5,4,7,1,3,2]=>010111
[3,1,6,5,7,2,4]=>[3,7,1,2,6,5,4]=>[6,5,7,1,3,2,4]=>010011
[3,1,6,5,7,4,2]=>[3,4,1,7,6,5,2]=>[6,5,7,4,1,3,2]=>011011
[3,1,6,7,2,4,5]=>[3,7,1,2,4,6,5]=>[6,7,1,3,2,4,5]=>010001
[3,1,6,7,2,5,4]=>[3,7,1,5,2,6,4]=>[5,1,3,2,6,7,4]=>010101
[3,1,6,7,4,2,5]=>[3,4,1,7,2,6,5]=>[6,7,4,1,3,2,5]=>011001
[3,1,6,7,4,5,2]=>[3,5,1,7,4,6,2]=>[6,7,4,5,1,3,2]=>010101
[3,1,6,7,5,2,4]=>[3,5,1,2,7,6,4]=>[6,7,5,1,3,2,4]=>010101
[3,1,6,7,5,4,2]=>[3,4,1,5,7,6,2]=>[6,7,5,4,1,3,2]=>011101
[3,1,7,2,4,5,6]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>010001
[3,1,7,2,4,6,5]=>[3,7,1,2,6,4,5]=>[6,1,3,2,4,7,5]=>010011
[3,1,7,2,5,4,6]=>[3,7,1,5,2,4,6]=>[5,1,3,2,7,4,6]=>010101
[3,1,7,2,5,6,4]=>[3,7,1,6,2,5,4]=>[6,1,3,2,5,7,4]=>010011
[3,1,7,2,6,4,5]=>[3,7,1,6,4,2,5]=>[6,4,7,1,3,2,5]=>010011
[3,1,7,2,6,5,4]=>[3,7,1,5,6,2,4]=>[6,5,1,3,2,7,4]=>010111
[3,1,7,4,2,5,6]=>[3,4,1,7,2,5,6]=>[7,4,1,3,2,5,6]=>011001
[3,1,7,4,2,6,5]=>[3,4,1,7,6,2,5]=>[6,4,1,3,2,7,5]=>011011
[3,1,7,4,5,2,6]=>[3,5,1,7,4,2,6]=>[7,4,5,1,3,2,6]=>010101
[3,1,7,4,5,6,2]=>[3,6,1,7,4,5,2]=>[7,4,5,6,1,3,2]=>010011
[3,1,7,4,6,2,5]=>[3,6,1,7,2,4,5]=>[7,1,3,2,6,4,5]=>010011
[3,1,7,4,6,5,2]=>[3,5,1,6,7,2,4]=>[7,1,3,2,6,5,4]=>010111
[3,1,7,5,2,4,6]=>[3,5,1,2,7,4,6]=>[7,5,1,3,2,4,6]=>010101
[3,1,7,5,2,6,4]=>[3,5,1,7,6,4,2]=>[6,4,7,5,1,3,2]=>010111
[3,1,7,5,4,2,6]=>[3,4,1,5,7,2,6]=>[7,5,4,1,3,2,6]=>011101
[3,1,7,5,4,6,2]=>[3,6,1,5,7,4,2]=>[7,5,4,6,1,3,2]=>010111
[3,1,7,5,6,2,4]=>[3,6,1,2,7,5,4]=>[7,5,6,1,3,2,4]=>010011
[3,1,7,5,6,4,2]=>[3,4,1,6,7,5,2]=>[7,5,6,4,1,3,2]=>011011
[3,1,7,6,2,4,5]=>[3,6,1,2,4,7,5]=>[7,6,1,3,2,4,5]=>010011
[3,1,7,6,2,5,4]=>[3,6,1,5,2,7,4]=>[5,1,3,2,7,6,4]=>010111
[3,1,7,6,4,2,5]=>[3,4,1,6,2,7,5]=>[7,6,4,1,3,2,5]=>011011
[3,1,7,6,4,5,2]=>[3,5,1,6,4,7,2]=>[7,6,4,5,1,3,2]=>010111
[3,1,7,6,5,2,4]=>[3,5,1,2,6,7,4]=>[7,6,5,1,3,2,4]=>010111
[3,1,7,6,5,4,2]=>[3,4,1,5,6,7,2]=>[7,6,5,4,1,3,2]=>011111
[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>110001
[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>110010
[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>110001
[3,2,1,4,7,5,6]=>[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>110001
[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>110011
[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>110100
[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>110101
[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>110010
[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>[3,2,1,5,6,7,4]=>110001
[3,2,1,5,7,4,6]=>[2,3,1,7,5,4,6]=>[3,2,1,5,7,4,6]=>110001
[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>[3,2,1,5,7,6,4]=>110011
[3,2,1,6,4,5,7]=>[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>110010
[3,2,1,6,4,7,5]=>[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]=>110011
[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>110110
[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]=>[3,2,1,6,5,7,4]=>110011
[3,2,1,6,7,4,5]=>[2,3,1,7,4,6,5]=>[3,2,1,6,7,4,5]=>110001
[3,2,1,6,7,5,4]=>[2,3,1,5,7,6,4]=>[3,2,1,6,7,5,4]=>110101
[3,2,1,7,4,5,6]=>[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>110001
[3,2,1,7,4,6,5]=>[2,3,1,7,6,4,5]=>[3,2,1,6,4,7,5]=>110011
[3,2,1,7,5,4,6]=>[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>110101
[3,2,1,7,5,6,4]=>[2,3,1,6,7,5,4]=>[3,2,1,7,5,6,4]=>110011
[3,2,1,7,6,4,5]=>[2,3,1,6,4,7,5]=>[3,2,1,7,6,4,5]=>110011
[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]=>[3,2,1,7,6,5,4]=>110111
[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[3,2,4,1,5,6,7]=>011000
[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>[3,2,4,1,5,7,6]=>011001
[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>[3,2,4,1,6,5,7]=>011010
[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>[3,2,4,1,6,7,5]=>011001
[3,2,4,1,7,5,6]=>[4,3,2,1,7,5,6]=>[3,2,4,1,7,5,6]=>011001
[3,2,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>[3,2,4,1,7,6,5]=>011011
[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[3,2,4,5,1,6,7]=>010100
[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>[3,2,4,5,1,7,6]=>010101
[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[3,2,4,5,6,1,7]=>010010
[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[3,2,4,5,6,7,1]=>010001
[3,2,4,5,7,1,6]=>[7,3,2,4,5,1,6]=>[3,2,4,5,7,1,6]=>010001
[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]=>[3,2,4,5,7,6,1]=>010011
[3,2,4,6,1,5,7]=>[6,3,2,4,1,5,7]=>[3,2,4,6,1,5,7]=>010010
[3,2,4,6,1,7,5]=>[6,3,2,4,7,1,5]=>[3,2,4,7,1,6,5]=>010011
[3,2,4,6,5,1,7]=>[5,3,2,4,6,1,7]=>[3,2,4,6,5,1,7]=>010110
[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>[3,2,4,6,5,7,1]=>010011
[3,2,4,6,7,1,5]=>[7,3,2,4,1,6,5]=>[3,2,4,6,7,1,5]=>010001
[3,2,4,6,7,5,1]=>[5,3,2,4,7,6,1]=>[3,2,4,6,7,5,1]=>010101
[3,2,4,7,1,5,6]=>[7,3,2,4,1,5,6]=>[3,2,4,7,1,5,6]=>010001
[3,2,4,7,1,6,5]=>[7,3,2,4,6,1,5]=>[3,2,4,6,1,7,5]=>010011
[3,2,4,7,5,1,6]=>[5,3,2,4,7,1,6]=>[3,2,4,7,5,1,6]=>010101
[3,2,4,7,5,6,1]=>[6,3,2,4,7,5,1]=>[3,2,4,7,5,6,1]=>010011
[3,2,4,7,6,1,5]=>[6,3,2,4,1,7,5]=>[3,2,4,7,6,1,5]=>010011
[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]=>[3,2,4,7,6,5,1]=>010111
[3,2,5,1,4,6,7]=>[5,3,2,1,4,6,7]=>[3,2,5,1,4,6,7]=>010100
[3,2,5,1,4,7,6]=>[5,3,2,1,4,7,6]=>[3,2,5,1,4,7,6]=>010101
[3,2,5,1,6,4,7]=>[5,3,2,6,1,4,7]=>[3,2,6,1,5,4,7]=>010110
[3,2,5,1,6,7,4]=>[5,3,2,7,1,6,4]=>[3,2,6,7,1,5,4]=>010101
[3,2,5,1,7,4,6]=>[5,3,2,7,1,4,6]=>[3,2,7,1,5,4,6]=>010101
[3,2,5,1,7,6,4]=>[5,3,2,6,1,7,4]=>[3,2,7,6,1,5,4]=>010111
[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]=>[3,2,5,4,1,6,7]=>011100
[3,2,5,4,1,7,6]=>[4,3,2,5,1,7,6]=>[3,2,5,4,1,7,6]=>011101
[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>[3,2,5,4,6,1,7]=>010110
[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>[3,2,5,4,6,7,1]=>010101
[3,2,5,4,7,1,6]=>[7,3,2,5,4,1,6]=>[3,2,5,4,7,1,6]=>010101
[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]=>[3,2,5,4,7,6,1]=>010111
[3,2,5,6,1,4,7]=>[6,3,2,1,5,4,7]=>[3,2,5,6,1,4,7]=>010010
[3,2,5,6,1,7,4]=>[6,3,2,7,5,1,4]=>[3,2,5,7,1,6,4]=>010011
[3,2,5,6,4,1,7]=>[4,3,2,6,5,1,7]=>[3,2,5,6,4,1,7]=>011010
[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>[3,2,5,6,4,7,1]=>010011
[3,2,5,6,7,1,4]=>[7,3,2,1,5,6,4]=>[3,2,5,6,7,1,4]=>010001
[3,2,5,6,7,4,1]=>[4,3,2,7,5,6,1]=>[3,2,5,6,7,4,1]=>011001
[3,2,5,7,1,4,6]=>[7,3,2,1,5,4,6]=>[3,2,5,7,1,4,6]=>010001
[3,2,5,7,1,6,4]=>[7,3,2,6,5,1,4]=>[3,2,5,6,1,7,4]=>010011
[3,2,5,7,4,1,6]=>[4,3,2,7,5,1,6]=>[3,2,5,7,4,1,6]=>011001
[3,2,5,7,4,6,1]=>[6,3,2,7,5,4,1]=>[3,2,5,7,4,6,1]=>010011
[3,2,5,7,6,1,4]=>[6,3,2,1,5,7,4]=>[3,2,5,7,6,1,4]=>010011
[3,2,5,7,6,4,1]=>[4,3,2,6,5,7,1]=>[3,2,5,7,6,4,1]=>011011
[3,2,6,1,4,5,7]=>[6,3,2,1,4,5,7]=>[3,2,6,1,4,5,7]=>010010
[3,2,6,1,4,7,5]=>[6,3,2,1,7,4,5]=>[3,2,7,1,4,6,5]=>010011
[3,2,6,1,5,4,7]=>[6,3,2,5,1,4,7]=>[3,2,5,1,6,4,7]=>010110
[3,2,6,1,5,7,4]=>[6,3,2,7,1,5,4]=>[3,2,7,1,5,6,4]=>010011
[3,2,6,1,7,4,5]=>[6,3,2,7,4,1,5]=>[3,2,7,4,6,1,5]=>010011
[3,2,6,1,7,5,4]=>[6,3,2,5,7,1,4]=>[3,2,7,5,1,6,4]=>010111
[3,2,6,4,1,5,7]=>[4,3,2,6,1,5,7]=>[3,2,6,4,1,5,7]=>011010
[3,2,6,4,1,7,5]=>[4,3,2,6,7,1,5]=>[3,2,7,4,1,6,5]=>011011
[3,2,6,4,5,1,7]=>[5,3,2,6,4,1,7]=>[3,2,6,4,5,1,7]=>010110
[3,2,6,4,5,7,1]=>[7,3,2,6,4,5,1]=>[3,2,6,4,5,7,1]=>010011
[3,2,6,4,7,1,5]=>[7,3,2,6,1,4,5]=>[3,2,6,1,7,4,5]=>010011
[3,2,6,4,7,5,1]=>[5,3,2,7,6,1,4]=>[3,2,6,1,7,5,4]=>010111
[3,2,6,5,1,4,7]=>[5,3,2,1,6,4,7]=>[3,2,6,5,1,4,7]=>010110
[3,2,6,5,1,7,4]=>[5,3,2,6,7,4,1]=>[3,2,7,4,6,5,1]=>010111
[3,2,6,5,4,1,7]=>[4,3,2,5,6,1,7]=>[3,2,6,5,4,1,7]=>011110
[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]=>[3,2,6,5,4,7,1]=>010111
[3,2,6,5,7,1,4]=>[7,3,2,1,6,5,4]=>[3,2,6,5,7,1,4]=>010011
[3,2,6,5,7,4,1]=>[4,3,2,7,6,5,1]=>[3,2,6,5,7,4,1]=>011011
[3,2,6,7,1,4,5]=>[7,3,2,1,4,6,5]=>[3,2,6,7,1,4,5]=>010001
[3,2,6,7,1,5,4]=>[7,3,2,5,1,6,4]=>[3,2,5,1,6,7,4]=>010101
[3,2,6,7,4,1,5]=>[4,3,2,7,1,6,5]=>[3,2,6,7,4,1,5]=>011001
[3,2,6,7,4,5,1]=>[5,3,2,7,4,6,1]=>[3,2,6,7,4,5,1]=>010101
[3,2,6,7,5,1,4]=>[5,3,2,1,7,6,4]=>[3,2,6,7,5,1,4]=>010101
[3,2,6,7,5,4,1]=>[4,3,2,5,7,6,1]=>[3,2,6,7,5,4,1]=>011101
[3,2,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>[3,2,7,1,4,5,6]=>010001
[3,2,7,1,4,6,5]=>[7,3,2,1,6,4,5]=>[3,2,6,1,4,7,5]=>010011
[3,2,7,1,5,4,6]=>[7,3,2,5,1,4,6]=>[3,2,5,1,7,4,6]=>010101
[3,2,7,1,5,6,4]=>[7,3,2,6,1,5,4]=>[3,2,6,1,5,7,4]=>010011
[3,2,7,1,6,4,5]=>[7,3,2,6,4,1,5]=>[3,2,6,4,7,1,5]=>010011
[3,2,7,1,6,5,4]=>[7,3,2,5,6,1,4]=>[3,2,6,5,1,7,4]=>010111
[3,2,7,4,1,5,6]=>[4,3,2,7,1,5,6]=>[3,2,7,4,1,5,6]=>011001
[3,2,7,4,1,6,5]=>[4,3,2,7,6,1,5]=>[3,2,6,4,1,7,5]=>011011
[3,2,7,4,5,1,6]=>[5,3,2,7,4,1,6]=>[3,2,7,4,5,1,6]=>010101
[3,2,7,4,5,6,1]=>[6,3,2,7,4,5,1]=>[3,2,7,4,5,6,1]=>010011
[3,2,7,4,6,1,5]=>[6,3,2,7,1,4,5]=>[3,2,7,1,6,4,5]=>010011
[3,2,7,4,6,5,1]=>[5,3,2,6,7,1,4]=>[3,2,7,1,6,5,4]=>010111
[3,2,7,5,1,4,6]=>[5,3,2,1,7,4,6]=>[3,2,7,5,1,4,6]=>010101
[3,2,7,5,1,6,4]=>[5,3,2,7,6,4,1]=>[3,2,6,4,7,5,1]=>010111
[3,2,7,5,4,1,6]=>[4,3,2,5,7,1,6]=>[3,2,7,5,4,1,6]=>011101
[3,2,7,5,4,6,1]=>[6,3,2,5,7,4,1]=>[3,2,7,5,4,6,1]=>010111
[3,2,7,5,6,1,4]=>[6,3,2,1,7,5,4]=>[3,2,7,5,6,1,4]=>010011
[3,2,7,5,6,4,1]=>[4,3,2,6,7,5,1]=>[3,2,7,5,6,4,1]=>011011
[3,2,7,6,1,4,5]=>[6,3,2,1,4,7,5]=>[3,2,7,6,1,4,5]=>010011
[3,2,7,6,1,5,4]=>[6,3,2,5,1,7,4]=>[3,2,5,1,7,6,4]=>010111
[3,2,7,6,4,1,5]=>[4,3,2,6,1,7,5]=>[3,2,7,6,4,1,5]=>011011
[3,2,7,6,4,5,1]=>[5,3,2,6,4,7,1]=>[3,2,7,6,4,5,1]=>010111
[3,2,7,6,5,1,4]=>[5,3,2,1,6,7,4]=>[3,2,7,6,5,1,4]=>010111
[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]=>[3,2,7,6,5,4,1]=>011111
[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[3,4,1,2,5,6,7]=>001000
[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]=>[3,4,1,2,5,7,6]=>001001
[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]=>[3,4,1,2,6,5,7]=>001010
[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]=>[3,4,1,2,6,7,5]=>001001
[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]=>[3,4,1,2,7,5,6]=>001001
[3,4,1,2,7,6,5]=>[4,1,3,2,6,7,5]=>[3,4,1,2,7,6,5]=>001011
[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[3,5,1,4,2,6,7]=>001100
[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[3,5,1,4,2,7,6]=>001101
[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[3,5,6,1,4,2,7]=>001010
[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[3,5,6,7,1,4,2]=>001001
[3,4,1,5,7,2,6]=>[4,7,3,1,5,2,6]=>[3,5,7,1,4,2,6]=>001001
[3,4,1,5,7,6,2]=>[4,6,3,1,5,7,2]=>[3,5,7,6,1,4,2]=>001011
[3,4,1,6,2,5,7]=>[4,6,3,1,2,5,7]=>[3,6,1,4,2,5,7]=>001010
[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[3,7,1,4,2,6,5]=>001011
[3,4,1,6,5,2,7]=>[4,5,3,1,6,2,7]=>[3,6,5,1,4,2,7]=>001110
[3,4,1,6,5,7,2]=>[4,7,3,1,6,5,2]=>[3,6,5,7,1,4,2]=>001011
[3,4,1,6,7,2,5]=>[4,7,3,1,2,6,5]=>[3,6,7,1,4,2,5]=>001001
[3,4,1,6,7,5,2]=>[4,5,3,1,7,6,2]=>[3,6,7,5,1,4,2]=>001101
[3,4,1,7,2,5,6]=>[4,7,3,1,2,5,6]=>[3,7,1,4,2,5,6]=>001001
[3,4,1,7,2,6,5]=>[4,7,3,1,6,2,5]=>[3,6,1,4,2,7,5]=>001011
[3,4,1,7,5,2,6]=>[4,5,3,1,7,2,6]=>[3,7,5,1,4,2,6]=>001101
[3,4,1,7,5,6,2]=>[4,6,3,1,7,5,2]=>[3,7,5,6,1,4,2]=>001011
[3,4,1,7,6,2,5]=>[4,6,3,1,2,7,5]=>[3,7,6,1,4,2,5]=>001011
[3,4,1,7,6,5,2]=>[4,5,3,1,6,7,2]=>[3,7,6,5,1,4,2]=>001111
[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>101000
[3,4,2,1,5,7,6]=>[2,4,3,1,5,7,6]=>[3,4,2,1,5,7,6]=>101001
[3,4,2,1,6,5,7]=>[2,4,3,1,6,5,7]=>[3,4,2,1,6,5,7]=>101010
[3,4,2,1,6,7,5]=>[2,4,3,1,7,6,5]=>[3,4,2,1,6,7,5]=>101001
[3,4,2,1,7,5,6]=>[2,4,3,1,7,5,6]=>[3,4,2,1,7,5,6]=>101001
[3,4,2,1,7,6,5]=>[2,4,3,1,6,7,5]=>[3,4,2,1,7,6,5]=>101011
[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[3,4,2,5,1,6,7]=>001100
[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>[3,4,2,5,1,7,6]=>001101
[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[3,4,2,5,6,1,7]=>001010
[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[3,4,2,5,6,7,1]=>001001
[3,4,2,5,7,1,6]=>[7,4,3,2,5,1,6]=>[3,4,2,5,7,1,6]=>001001
[3,4,2,5,7,6,1]=>[6,4,3,2,5,7,1]=>[3,4,2,5,7,6,1]=>001011
[3,4,2,6,1,5,7]=>[6,4,3,2,1,5,7]=>[3,4,2,6,1,5,7]=>001010
[3,4,2,6,1,7,5]=>[6,4,3,2,7,1,5]=>[3,4,2,7,1,6,5]=>001011
[3,4,2,6,5,1,7]=>[5,4,3,2,6,1,7]=>[3,4,2,6,5,1,7]=>001110
[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>[3,4,2,6,5,7,1]=>001011
[3,4,2,6,7,1,5]=>[7,4,3,2,1,6,5]=>[3,4,2,6,7,1,5]=>001001
[3,4,2,6,7,5,1]=>[5,4,3,2,7,6,1]=>[3,4,2,6,7,5,1]=>001101
[3,4,2,7,1,5,6]=>[7,4,3,2,1,5,6]=>[3,4,2,7,1,5,6]=>001001
[3,4,2,7,1,6,5]=>[7,4,3,2,6,1,5]=>[3,4,2,6,1,7,5]=>001011
[3,4,2,7,5,1,6]=>[5,4,3,2,7,1,6]=>[3,4,2,7,5,1,6]=>001101
[3,4,2,7,5,6,1]=>[6,4,3,2,7,5,1]=>[3,4,2,7,5,6,1]=>001011
[3,4,2,7,6,1,5]=>[6,4,3,2,1,7,5]=>[3,4,2,7,6,1,5]=>001011
[3,4,2,7,6,5,1]=>[5,4,3,2,6,7,1]=>[3,4,2,7,6,5,1]=>001111
[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[3,4,5,1,2,6,7]=>000100
[3,4,5,1,2,7,6]=>[5,1,3,4,2,7,6]=>[3,4,5,1,2,7,6]=>000101
[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[3,4,6,1,5,2,7]=>000110
[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[3,4,6,7,1,5,2]=>000101
[3,4,5,1,7,2,6]=>[5,7,3,4,1,2,6]=>[3,4,7,1,5,2,6]=>000101
[3,4,5,1,7,6,2]=>[5,6,3,4,1,7,2]=>[3,4,7,6,1,5,2]=>000111
[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[3,4,5,2,1,6,7]=>100100
[3,4,5,2,1,7,6]=>[2,5,3,4,1,7,6]=>[3,4,5,2,1,7,6]=>100101
[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[3,4,5,2,6,1,7]=>000110
[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[3,4,5,2,6,7,1]=>000101
[3,4,5,2,7,1,6]=>[7,5,3,4,2,1,6]=>[3,4,5,2,7,1,6]=>000101
[3,4,5,2,7,6,1]=>[6,5,3,4,2,7,1]=>[3,4,5,2,7,6,1]=>000111
[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[3,4,5,6,1,2,7]=>000010
[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[3,4,5,7,1,6,2]=>000011
[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[3,4,5,6,2,1,7]=>100010
[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[3,4,5,6,2,7,1]=>000011
[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[3,4,5,6,7,1,2]=>000001
[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[3,4,5,6,7,2,1]=>100001
[3,4,5,7,1,2,6]=>[7,1,3,4,5,2,6]=>[3,4,5,7,1,2,6]=>000001
[3,4,5,7,1,6,2]=>[7,6,3,4,5,1,2]=>[3,4,5,6,1,7,2]=>000011
[3,4,5,7,2,1,6]=>[2,7,3,4,5,1,6]=>[3,4,5,7,2,1,6]=>100001
[3,4,5,7,2,6,1]=>[6,7,3,4,5,2,1]=>[3,4,5,7,2,6,1]=>000011
[3,4,5,7,6,1,2]=>[6,1,3,4,5,7,2]=>[3,4,5,7,6,1,2]=>000011
[3,4,5,7,6,2,1]=>[2,6,3,4,5,7,1]=>[3,4,5,7,6,2,1]=>100011
[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[3,4,6,1,2,5,7]=>000010
[3,4,6,1,2,7,5]=>[6,1,3,4,7,2,5]=>[3,4,7,1,2,6,5]=>000011
[3,4,6,1,5,2,7]=>[6,5,3,4,1,2,7]=>[3,4,5,1,6,2,7]=>000110
[3,4,6,1,5,7,2]=>[6,7,3,4,1,5,2]=>[3,4,7,1,5,6,2]=>000011
[3,4,6,1,7,2,5]=>[6,7,3,4,2,1,5]=>[3,4,7,2,6,1,5]=>000011
[3,4,6,1,7,5,2]=>[6,5,3,4,7,1,2]=>[3,4,7,5,1,6,2]=>000111
[3,4,6,2,1,5,7]=>[2,6,3,4,1,5,7]=>[3,4,6,2,1,5,7]=>100010
[3,4,6,2,1,7,5]=>[2,6,3,4,7,1,5]=>[3,4,7,2,1,6,5]=>100011
[3,4,6,2,5,1,7]=>[5,6,3,4,2,1,7]=>[3,4,6,2,5,1,7]=>000110
[3,4,6,2,5,7,1]=>[7,6,3,4,2,5,1]=>[3,4,6,2,5,7,1]=>000011
[3,4,6,2,7,1,5]=>[7,6,3,4,1,2,5]=>[3,4,6,1,7,2,5]=>000011
[3,4,6,2,7,5,1]=>[5,7,3,4,6,1,2]=>[3,4,6,1,7,5,2]=>000111
[3,4,6,5,1,2,7]=>[5,1,3,4,6,2,7]=>[3,4,6,5,1,2,7]=>000110
[3,4,6,5,1,7,2]=>[5,6,3,4,7,2,1]=>[3,4,7,2,6,5,1]=>000111
[3,4,6,5,2,1,7]=>[2,5,3,4,6,1,7]=>[3,4,6,5,2,1,7]=>100110
[3,4,6,5,2,7,1]=>[7,5,3,4,6,2,1]=>[3,4,6,5,2,7,1]=>000111
[3,4,6,5,7,1,2]=>[7,1,3,4,6,5,2]=>[3,4,6,5,7,1,2]=>000011
[3,4,6,5,7,2,1]=>[2,7,3,4,6,5,1]=>[3,4,6,5,7,2,1]=>100011
[3,4,6,7,1,2,5]=>[7,1,3,4,2,6,5]=>[3,4,6,7,1,2,5]=>000001
[3,4,6,7,1,5,2]=>[7,5,3,4,1,6,2]=>[3,4,5,1,6,7,2]=>000101
[3,4,6,7,2,1,5]=>[2,7,3,4,1,6,5]=>[3,4,6,7,2,1,5]=>100001
[3,4,6,7,2,5,1]=>[5,7,3,4,2,6,1]=>[3,4,6,7,2,5,1]=>000101
[3,4,6,7,5,1,2]=>[5,1,3,4,7,6,2]=>[3,4,6,7,5,1,2]=>000101
[3,4,6,7,5,2,1]=>[2,5,3,4,7,6,1]=>[3,4,6,7,5,2,1]=>100101
[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[3,4,7,1,2,5,6]=>000001
[3,4,7,1,2,6,5]=>[7,1,3,4,6,2,5]=>[3,4,6,1,2,7,5]=>000011
[3,4,7,1,5,2,6]=>[7,5,3,4,1,2,6]=>[3,4,5,1,7,2,6]=>000101
[3,4,7,1,5,6,2]=>[7,6,3,4,1,5,2]=>[3,4,6,1,5,7,2]=>000011
[3,4,7,1,6,2,5]=>[7,6,3,4,2,1,5]=>[3,4,6,2,7,1,5]=>000011
[3,4,7,1,6,5,2]=>[7,5,3,4,6,1,2]=>[3,4,6,5,1,7,2]=>000111
[3,4,7,2,1,5,6]=>[2,7,3,4,1,5,6]=>[3,4,7,2,1,5,6]=>100001
[3,4,7,2,1,6,5]=>[2,7,3,4,6,1,5]=>[3,4,6,2,1,7,5]=>100011
[3,4,7,2,5,1,6]=>[5,7,3,4,2,1,6]=>[3,4,7,2,5,1,6]=>000101
[3,4,7,2,5,6,1]=>[6,7,3,4,2,5,1]=>[3,4,7,2,5,6,1]=>000011
[3,4,7,2,6,1,5]=>[6,7,3,4,1,2,5]=>[3,4,7,1,6,2,5]=>000011
[3,4,7,2,6,5,1]=>[5,6,3,4,7,1,2]=>[3,4,7,1,6,5,2]=>000111
[3,4,7,5,1,2,6]=>[5,1,3,4,7,2,6]=>[3,4,7,5,1,2,6]=>000101
[3,4,7,5,1,6,2]=>[5,7,3,4,6,2,1]=>[3,4,6,2,7,5,1]=>000111
[3,4,7,5,2,1,6]=>[2,5,3,4,7,1,6]=>[3,4,7,5,2,1,6]=>100101
[3,4,7,5,2,6,1]=>[6,5,3,4,7,2,1]=>[3,4,7,5,2,6,1]=>000111
[3,4,7,5,6,1,2]=>[6,1,3,4,7,5,2]=>[3,4,7,5,6,1,2]=>000011
[3,4,7,5,6,2,1]=>[2,6,3,4,7,5,1]=>[3,4,7,5,6,2,1]=>100011
[3,4,7,6,1,2,5]=>[6,1,3,4,2,7,5]=>[3,4,7,6,1,2,5]=>000011
[3,4,7,6,1,5,2]=>[6,5,3,4,1,7,2]=>[3,4,5,1,7,6,2]=>000111
[3,4,7,6,2,1,5]=>[2,6,3,4,1,7,5]=>[3,4,7,6,2,1,5]=>100011
[3,4,7,6,2,5,1]=>[5,6,3,4,2,7,1]=>[3,4,7,6,2,5,1]=>000111
[3,4,7,6,5,1,2]=>[5,1,3,4,6,7,2]=>[3,4,7,6,5,1,2]=>000111
[3,4,7,6,5,2,1]=>[2,5,3,4,6,7,1]=>[3,4,7,6,5,2,1]=>100111
[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>[3,5,1,2,4,6,7]=>000100
[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]=>[3,5,1,2,4,7,6]=>000101
[3,5,1,2,6,4,7]=>[5,1,3,6,2,4,7]=>[3,6,1,2,5,4,7]=>000110
[3,5,1,2,6,7,4]=>[5,1,3,7,2,6,4]=>[3,6,7,1,2,5,4]=>000101
[3,5,1,2,7,4,6]=>[5,1,3,7,2,4,6]=>[3,7,1,2,5,4,6]=>000101
[3,5,1,2,7,6,4]=>[5,1,3,6,2,7,4]=>[3,7,6,1,2,5,4]=>000111
[3,5,1,4,2,6,7]=>[5,4,3,1,2,6,7]=>[3,4,1,5,2,6,7]=>001100
[3,5,1,4,2,7,6]=>[5,4,3,1,2,7,6]=>[3,4,1,5,2,7,6]=>001101
[3,5,1,4,6,2,7]=>[5,6,3,1,4,2,7]=>[3,6,1,4,5,2,7]=>000110
[3,5,1,4,6,7,2]=>[5,7,3,1,4,6,2]=>[3,6,7,1,4,5,2]=>000101
[3,5,1,4,7,2,6]=>[5,7,3,1,4,2,6]=>[3,7,1,4,5,2,6]=>000101
[3,5,1,4,7,6,2]=>[5,6,3,1,4,7,2]=>[3,7,6,1,4,5,2]=>000111
[3,5,1,6,2,4,7]=>[5,6,3,2,1,4,7]=>[3,6,2,5,1,4,7]=>000110
[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[3,7,1,6,2,5,4]=>000111
[3,5,1,6,4,2,7]=>[5,4,3,6,1,2,7]=>[3,6,4,1,5,2,7]=>001110
[3,5,1,6,4,7,2]=>[5,7,3,6,1,4,2]=>[3,6,1,7,4,5,2]=>000111
[3,5,1,6,7,2,4]=>[5,7,3,2,1,6,4]=>[3,6,7,2,5,1,4]=>000101
[3,5,1,6,7,4,2]=>[5,4,3,7,1,6,2]=>[3,6,7,4,1,5,2]=>001101
[3,5,1,7,2,4,6]=>[5,7,3,2,1,4,6]=>[3,7,2,5,1,4,6]=>000101
[3,5,1,7,2,6,4]=>[5,7,3,6,1,2,4]=>[3,6,1,7,2,5,4]=>000111
[3,5,1,7,4,2,6]=>[5,4,3,7,1,2,6]=>[3,7,4,1,5,2,6]=>001101
[3,5,1,7,4,6,2]=>[5,6,3,7,1,4,2]=>[3,7,1,6,4,5,2]=>000111
[3,5,1,7,6,2,4]=>[5,6,3,2,1,7,4]=>[3,7,6,2,5,1,4]=>000111
[3,5,1,7,6,4,2]=>[5,4,3,6,1,7,2]=>[3,7,6,4,1,5,2]=>001111
[3,5,2,1,4,6,7]=>[2,5,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>100100
[3,5,2,1,4,7,6]=>[2,5,3,1,4,7,6]=>[3,5,2,1,4,7,6]=>100101
[3,5,2,1,6,4,7]=>[2,5,3,6,1,4,7]=>[3,6,2,1,5,4,7]=>100110
[3,5,2,1,6,7,4]=>[2,5,3,7,1,6,4]=>[3,6,7,2,1,5,4]=>100101
[3,5,2,1,7,4,6]=>[2,5,3,7,1,4,6]=>[3,7,2,1,5,4,6]=>100101
[3,5,2,1,7,6,4]=>[2,5,3,6,1,7,4]=>[3,7,6,2,1,5,4]=>100111
[3,5,2,4,1,6,7]=>[4,5,3,2,1,6,7]=>[3,5,2,4,1,6,7]=>001100
[3,5,2,4,1,7,6]=>[4,5,3,2,1,7,6]=>[3,5,2,4,1,7,6]=>001101
[3,5,2,4,6,1,7]=>[6,5,3,2,4,1,7]=>[3,5,2,4,6,1,7]=>000110
[3,5,2,4,6,7,1]=>[7,5,3,2,4,6,1]=>[3,5,2,4,6,7,1]=>000101
[3,5,2,4,7,1,6]=>[7,5,3,2,4,1,6]=>[3,5,2,4,7,1,6]=>000101
[3,5,2,4,7,6,1]=>[6,5,3,2,4,7,1]=>[3,5,2,4,7,6,1]=>000111
[3,5,2,6,1,4,7]=>[6,5,3,1,2,4,7]=>[3,5,1,6,2,4,7]=>000110
[3,5,2,6,1,7,4]=>[6,5,3,7,2,1,4]=>[3,7,2,5,1,6,4]=>000111
[3,5,2,6,4,1,7]=>[4,6,3,5,1,2,7]=>[3,5,1,6,4,2,7]=>001110
[3,5,2,6,4,7,1]=>[7,5,3,6,2,4,1]=>[3,6,2,5,4,7,1]=>000111
[3,5,2,6,7,1,4]=>[7,5,3,1,2,6,4]=>[3,5,1,6,7,2,4]=>000101
[3,5,2,6,7,4,1]=>[4,7,3,5,1,6,2]=>[3,5,1,6,7,4,2]=>001101
[3,5,2,7,1,4,6]=>[7,5,3,1,2,4,6]=>[3,5,1,7,2,4,6]=>000101
[3,5,2,7,1,6,4]=>[7,5,3,6,2,1,4]=>[3,6,2,5,1,7,4]=>000111
[3,5,2,7,4,1,6]=>[4,7,3,5,1,2,6]=>[3,5,1,7,4,2,6]=>001101
[3,5,2,7,4,6,1]=>[6,5,3,7,2,4,1]=>[3,7,2,5,4,6,1]=>000111
[3,5,2,7,6,1,4]=>[6,5,3,1,2,7,4]=>[3,5,1,7,6,2,4]=>000111
[3,5,2,7,6,4,1]=>[4,6,3,5,1,7,2]=>[3,5,1,7,6,4,2]=>001111
[3,5,4,1,2,6,7]=>[4,1,3,5,2,6,7]=>[3,5,4,1,2,6,7]=>001100
[3,5,4,1,2,7,6]=>[4,1,3,5,2,7,6]=>[3,5,4,1,2,7,6]=>001101
[3,5,4,1,6,2,7]=>[4,5,3,6,2,1,7]=>[3,6,2,5,4,1,7]=>001110
[3,5,4,1,6,7,2]=>[4,5,3,7,2,6,1]=>[3,6,7,2,5,4,1]=>001101
[3,5,4,1,7,2,6]=>[4,5,3,7,2,1,6]=>[3,7,2,5,4,1,6]=>001101
[3,5,4,1,7,6,2]=>[4,5,3,6,2,7,1]=>[3,7,6,2,5,4,1]=>001111
[3,5,4,2,1,6,7]=>[2,4,3,5,1,6,7]=>[3,5,4,2,1,6,7]=>101100
[3,5,4,2,1,7,6]=>[2,4,3,5,1,7,6]=>[3,5,4,2,1,7,6]=>101101
[3,5,4,2,6,1,7]=>[6,4,3,5,2,1,7]=>[3,5,4,2,6,1,7]=>001110
[3,5,4,2,6,7,1]=>[7,4,3,5,2,6,1]=>[3,5,4,2,6,7,1]=>001101
[3,5,4,2,7,1,6]=>[7,4,3,5,2,1,6]=>[3,5,4,2,7,1,6]=>001101
[3,5,4,2,7,6,1]=>[6,4,3,5,2,7,1]=>[3,5,4,2,7,6,1]=>001111
[3,5,4,6,1,2,7]=>[6,1,3,5,4,2,7]=>[3,5,4,6,1,2,7]=>000110
[3,5,4,6,1,7,2]=>[6,7,3,5,4,1,2]=>[3,5,4,7,1,6,2]=>000111
[3,5,4,6,2,1,7]=>[2,6,3,5,4,1,7]=>[3,5,4,6,2,1,7]=>100110
[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>[3,5,4,6,2,7,1]=>000111
[3,5,4,6,7,1,2]=>[7,1,3,5,4,6,2]=>[3,5,4,6,7,1,2]=>000101
[3,5,4,6,7,2,1]=>[2,7,3,5,4,6,1]=>[3,5,4,6,7,2,1]=>100101
[3,5,4,7,1,2,6]=>[7,1,3,5,4,2,6]=>[3,5,4,7,1,2,6]=>000101
[3,5,4,7,1,6,2]=>[7,6,3,5,4,1,2]=>[3,5,4,6,1,7,2]=>000111
[3,5,4,7,2,1,6]=>[2,7,3,5,4,1,6]=>[3,5,4,7,2,1,6]=>100101
[3,5,4,7,2,6,1]=>[6,7,3,5,4,2,1]=>[3,5,4,7,2,6,1]=>000111
[3,5,4,7,6,1,2]=>[6,1,3,5,4,7,2]=>[3,5,4,7,6,1,2]=>000111
[3,5,4,7,6,2,1]=>[2,6,3,5,4,7,1]=>[3,5,4,7,6,2,1]=>100111
[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[3,5,6,1,2,4,7]=>000010
[3,5,6,1,2,7,4]=>[6,1,3,7,5,2,4]=>[3,5,7,1,2,6,4]=>000011
[3,5,6,1,4,2,7]=>[6,4,3,1,5,2,7]=>[3,4,1,5,6,2,7]=>001010
[3,5,6,1,4,7,2]=>[6,7,3,1,5,4,2]=>[3,5,7,1,4,6,2]=>000011
[3,5,6,1,7,2,4]=>[6,7,3,2,5,1,4]=>[3,5,7,2,6,1,4]=>000011
[3,5,6,1,7,4,2]=>[6,4,3,7,5,1,2]=>[3,5,7,4,1,6,2]=>001011
[3,5,6,2,1,4,7]=>[2,6,3,1,5,4,7]=>[3,5,6,2,1,4,7]=>100010
[3,5,6,2,1,7,4]=>[2,6,3,7,5,1,4]=>[3,5,7,2,1,6,4]=>100011
[3,5,6,2,4,1,7]=>[4,6,3,2,5,1,7]=>[3,5,6,2,4,1,7]=>001010
[3,5,6,2,4,7,1]=>[7,6,3,2,5,4,1]=>[3,5,6,2,4,7,1]=>000011
[3,5,6,2,7,1,4]=>[7,6,3,1,5,2,4]=>[3,5,6,1,7,2,4]=>000011
[3,5,6,2,7,4,1]=>[4,7,3,6,5,1,2]=>[3,5,6,1,7,4,2]=>001011
[3,5,6,4,1,2,7]=>[4,1,3,6,5,2,7]=>[3,5,6,4,1,2,7]=>001010
[3,5,6,4,1,7,2]=>[4,6,3,7,5,2,1]=>[3,5,7,2,6,4,1]=>001011
[3,5,6,4,2,1,7]=>[2,4,3,6,5,1,7]=>[3,5,6,4,2,1,7]=>101010
[3,5,6,4,2,7,1]=>[7,4,3,6,5,2,1]=>[3,5,6,4,2,7,1]=>001011
[3,5,6,4,7,1,2]=>[7,1,3,6,5,4,2]=>[3,5,6,4,7,1,2]=>000011
[3,5,6,4,7,2,1]=>[2,7,3,6,5,4,1]=>[3,5,6,4,7,2,1]=>100011
[3,5,6,7,1,2,4]=>[7,1,3,2,5,6,4]=>[3,5,6,7,1,2,4]=>000001
[3,5,6,7,1,4,2]=>[7,4,3,1,5,6,2]=>[3,4,1,5,6,7,2]=>001001
[3,5,6,7,2,1,4]=>[2,7,3,1,5,6,4]=>[3,5,6,7,2,1,4]=>100001
[3,5,6,7,2,4,1]=>[4,7,3,2,5,6,1]=>[3,5,6,7,2,4,1]=>001001
[3,5,6,7,4,1,2]=>[4,1,3,7,5,6,2]=>[3,5,6,7,4,1,2]=>001001
[3,5,6,7,4,2,1]=>[2,4,3,7,5,6,1]=>[3,5,6,7,4,2,1]=>101001
[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>[3,5,7,1,2,4,6]=>000001
[3,5,7,1,2,6,4]=>[7,1,3,6,5,2,4]=>[3,5,6,1,2,7,4]=>000011
[3,5,7,1,4,2,6]=>[7,4,3,1,5,2,6]=>[3,4,1,5,7,2,6]=>001001
[3,5,7,1,4,6,2]=>[7,6,3,1,5,4,2]=>[3,5,6,1,4,7,2]=>000011
[3,5,7,1,6,2,4]=>[7,6,3,2,5,1,4]=>[3,5,6,2,7,1,4]=>000011
[3,5,7,1,6,4,2]=>[7,4,3,6,5,1,2]=>[3,5,6,4,1,7,2]=>001011
[3,5,7,2,1,4,6]=>[2,7,3,1,5,4,6]=>[3,5,7,2,1,4,6]=>100001
[3,5,7,2,1,6,4]=>[2,7,3,6,5,1,4]=>[3,5,6,2,1,7,4]=>100011
[3,5,7,2,4,1,6]=>[4,7,3,2,5,1,6]=>[3,5,7,2,4,1,6]=>001001
[3,5,7,2,4,6,1]=>[6,7,3,2,5,4,1]=>[3,5,7,2,4,6,1]=>000011
[3,5,7,2,6,1,4]=>[6,7,3,1,5,2,4]=>[3,5,7,1,6,2,4]=>000011
[3,5,7,2,6,4,1]=>[4,6,3,7,5,1,2]=>[3,5,7,1,6,4,2]=>001011
[3,5,7,4,1,2,6]=>[4,1,3,7,5,2,6]=>[3,5,7,4,1,2,6]=>001001
[3,5,7,4,1,6,2]=>[4,7,3,6,5,2,1]=>[3,5,6,2,7,4,1]=>001011
[3,5,7,4,2,1,6]=>[2,4,3,7,5,1,6]=>[3,5,7,4,2,1,6]=>101001
[3,5,7,4,2,6,1]=>[6,4,3,7,5,2,1]=>[3,5,7,4,2,6,1]=>001011
[3,5,7,4,6,1,2]=>[6,1,3,7,5,4,2]=>[3,5,7,4,6,1,2]=>000011
[3,5,7,4,6,2,1]=>[2,6,3,7,5,4,1]=>[3,5,7,4,6,2,1]=>100011
[3,5,7,6,1,2,4]=>[6,1,3,2,5,7,4]=>[3,5,7,6,1,2,4]=>000011
[3,5,7,6,1,4,2]=>[6,4,3,1,5,7,2]=>[3,4,1,5,7,6,2]=>001011
[3,5,7,6,2,1,4]=>[2,6,3,1,5,7,4]=>[3,5,7,6,2,1,4]=>100011
[3,5,7,6,2,4,1]=>[4,6,3,2,5,7,1]=>[3,5,7,6,2,4,1]=>001011
[3,5,7,6,4,1,2]=>[4,1,3,6,5,7,2]=>[3,5,7,6,4,1,2]=>001011
[3,5,7,6,4,2,1]=>[2,4,3,6,5,7,1]=>[3,5,7,6,4,2,1]=>101011
[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>[3,6,1,2,4,5,7]=>000010
[3,6,1,2,4,7,5]=>[6,1,3,2,7,4,5]=>[3,7,1,2,4,6,5]=>000011
[3,6,1,2,5,4,7]=>[6,1,3,5,2,4,7]=>[3,5,1,2,6,4,7]=>000110
[3,6,1,2,5,7,4]=>[6,1,3,7,2,5,4]=>[3,7,1,2,5,6,4]=>000011
[3,6,1,2,7,4,5]=>[6,1,3,7,4,2,5]=>[3,7,4,6,1,2,5]=>000011
[3,6,1,2,7,5,4]=>[6,1,3,5,7,2,4]=>[3,7,5,1,2,6,4]=>000111
[3,6,1,4,2,5,7]=>[6,4,3,1,2,5,7]=>[3,4,1,6,2,5,7]=>001010
[3,6,1,4,2,7,5]=>[6,4,3,1,7,2,5]=>[3,4,1,7,2,6,5]=>001011
[3,6,1,4,5,2,7]=>[6,5,3,1,4,2,7]=>[3,5,1,4,6,2,7]=>000110
[3,6,1,4,5,7,2]=>[6,7,3,1,4,5,2]=>[3,7,1,4,5,6,2]=>000011
[3,6,1,4,7,2,5]=>[6,7,3,1,2,4,5]=>[3,7,1,6,2,4,5]=>000011
[3,6,1,4,7,5,2]=>[6,5,3,1,7,4,2]=>[3,7,5,1,4,6,2]=>000111
[3,6,1,5,2,4,7]=>[6,5,3,2,1,4,7]=>[3,5,2,6,1,4,7]=>000110
[3,6,1,5,2,7,4]=>[6,5,3,7,1,2,4]=>[3,7,1,5,2,6,4]=>000111
[3,6,1,5,4,2,7]=>[6,4,3,5,1,2,7]=>[3,5,4,1,6,2,7]=>001110
[3,6,1,5,4,7,2]=>[6,7,3,5,1,4,2]=>[3,5,1,7,4,6,2]=>000111
[3,6,1,5,7,2,4]=>[6,7,3,2,1,5,4]=>[3,7,2,5,6,1,4]=>000011
[3,6,1,5,7,4,2]=>[6,4,3,7,1,5,2]=>[3,7,4,1,5,6,2]=>001011
[3,6,1,7,2,4,5]=>[6,7,3,2,4,1,5]=>[3,7,2,4,6,1,5]=>000011
[3,6,1,7,2,5,4]=>[6,7,3,5,2,1,4]=>[3,5,2,7,1,6,4]=>000111
[3,6,1,7,4,2,5]=>[6,4,3,7,2,1,5]=>[3,7,4,2,6,1,5]=>001011
[3,6,1,7,4,5,2]=>[6,5,3,7,4,1,2]=>[3,7,4,5,1,6,2]=>000111
[3,6,1,7,5,2,4]=>[6,5,3,2,7,1,4]=>[3,7,5,2,6,1,4]=>000111
[3,6,1,7,5,4,2]=>[6,4,3,5,7,1,2]=>[3,7,5,4,1,6,2]=>001111
[3,6,2,1,4,5,7]=>[2,6,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>100010
[3,6,2,1,4,7,5]=>[2,6,3,1,7,4,5]=>[3,7,2,1,4,6,5]=>100011
[3,6,2,1,5,4,7]=>[2,6,3,5,1,4,7]=>[3,5,2,1,6,4,7]=>100110
[3,6,2,1,5,7,4]=>[2,6,3,7,1,5,4]=>[3,7,2,1,5,6,4]=>100011
[3,6,2,1,7,4,5]=>[2,6,3,7,4,1,5]=>[3,7,4,6,2,1,5]=>100011
[3,6,2,1,7,5,4]=>[2,6,3,5,7,1,4]=>[3,7,5,2,1,6,4]=>100111
[3,6,2,4,1,5,7]=>[4,6,3,2,1,5,7]=>[3,6,2,4,1,5,7]=>001010
[3,6,2,4,1,7,5]=>[4,6,3,2,7,1,5]=>[3,7,2,4,1,6,5]=>001011
[3,6,2,4,5,1,7]=>[5,6,3,2,4,1,7]=>[3,6,2,4,5,1,7]=>000110
[3,6,2,4,5,7,1]=>[7,6,3,2,4,5,1]=>[3,6,2,4,5,7,1]=>000011
[3,6,2,4,7,1,5]=>[7,6,3,2,1,4,5]=>[3,6,2,7,1,4,5]=>000011
[3,6,2,4,7,5,1]=>[5,7,3,1,6,4,2]=>[3,6,1,4,7,5,2]=>000111
[3,6,2,5,1,4,7]=>[5,6,3,1,2,4,7]=>[3,6,1,5,2,4,7]=>000110
[3,6,2,5,1,7,4]=>[5,6,3,7,2,1,4]=>[3,7,2,6,1,5,4]=>000111
[3,6,2,5,4,1,7]=>[4,5,3,6,1,2,7]=>[3,6,1,5,4,2,7]=>001110
[3,6,2,5,4,7,1]=>[7,6,3,5,2,4,1]=>[3,5,2,6,4,7,1]=>000111
[3,6,2,5,7,1,4]=>[7,6,3,1,2,5,4]=>[3,6,1,5,7,2,4]=>000011
[3,6,2,5,7,4,1]=>[4,7,3,6,1,5,2]=>[3,6,1,5,7,4,2]=>001011
[3,6,2,7,1,4,5]=>[7,6,3,1,4,2,5]=>[3,6,1,4,7,2,5]=>000011
[3,6,2,7,1,5,4]=>[7,6,3,5,1,2,4]=>[3,5,1,6,2,7,4]=>000111
[3,6,2,7,4,1,5]=>[4,7,3,6,2,1,5]=>[3,6,2,7,4,1,5]=>001011
[3,6,2,7,4,5,1]=>[5,6,3,7,4,2,1]=>[3,7,4,6,2,5,1]=>000111
[3,6,2,7,5,1,4]=>[5,7,3,2,6,1,4]=>[3,6,2,7,5,1,4]=>000111
[3,6,2,7,5,4,1]=>[4,5,3,7,6,2,1]=>[3,6,2,7,5,4,1]=>001111
[3,6,4,1,2,5,7]=>[4,1,3,6,2,5,7]=>[3,6,4,1,2,5,7]=>001010
[3,6,4,1,2,7,5]=>[4,1,3,6,7,2,5]=>[3,7,4,1,2,6,5]=>001011
[3,6,4,1,5,2,7]=>[4,6,3,5,2,1,7]=>[3,5,2,6,4,1,7]=>001110
[3,6,4,1,5,7,2]=>[4,6,3,7,2,5,1]=>[3,7,2,5,6,4,1]=>001011
[3,6,4,1,7,2,5]=>[4,6,3,7,1,2,5]=>[3,7,1,6,4,2,5]=>001011
[3,6,4,1,7,5,2]=>[4,6,3,5,7,2,1]=>[3,7,5,2,6,4,1]=>001111
[3,6,4,2,1,5,7]=>[2,4,3,6,1,5,7]=>[3,6,4,2,1,5,7]=>101010
[3,6,4,2,1,7,5]=>[2,4,3,6,7,1,5]=>[3,7,4,2,1,6,5]=>101011
[3,6,4,2,5,1,7]=>[5,4,3,6,2,1,7]=>[3,6,4,2,5,1,7]=>001110
[3,6,4,2,5,7,1]=>[7,4,3,6,2,5,1]=>[3,6,4,2,5,7,1]=>001011
[3,6,4,2,7,1,5]=>[7,4,3,6,1,2,5]=>[3,6,4,1,7,2,5]=>001011
[3,6,4,2,7,5,1]=>[5,4,3,7,6,1,2]=>[3,6,4,1,7,5,2]=>001111
[3,6,4,5,1,2,7]=>[5,1,3,6,4,2,7]=>[3,6,4,5,1,2,7]=>000110
[3,6,4,5,1,7,2]=>[5,7,3,6,4,1,2]=>[3,6,4,7,1,5,2]=>000111
[3,6,4,5,2,1,7]=>[2,5,3,6,4,1,7]=>[3,6,4,5,2,1,7]=>100110
[3,6,4,5,2,7,1]=>[7,5,3,6,4,2,1]=>[3,6,4,5,2,7,1]=>000111
[3,6,4,5,7,1,2]=>[7,1,3,6,4,5,2]=>[3,6,4,5,7,1,2]=>000011
[3,6,4,5,7,2,1]=>[2,7,3,6,4,5,1]=>[3,6,4,5,7,2,1]=>100011
[3,6,4,7,1,2,5]=>[7,1,3,6,2,4,5]=>[3,6,1,2,7,4,5]=>000011
[3,6,4,7,1,5,2]=>[7,5,3,6,1,4,2]=>[3,6,1,5,4,7,2]=>000111
[3,6,4,7,2,1,5]=>[2,7,3,6,1,4,5]=>[3,6,2,1,7,4,5]=>100011
[3,6,4,7,2,5,1]=>[5,7,3,6,2,4,1]=>[3,6,2,7,4,5,1]=>000111
[3,6,4,7,5,1,2]=>[5,1,3,7,6,2,4]=>[3,6,1,2,7,5,4]=>000111
[3,6,4,7,5,2,1]=>[2,5,3,7,6,1,4]=>[3,6,2,1,7,5,4]=>100111
[3,6,5,1,2,4,7]=>[5,1,3,2,6,4,7]=>[3,6,5,1,2,4,7]=>000110
[3,6,5,1,2,7,4]=>[5,1,3,6,7,4,2]=>[3,7,4,6,5,1,2]=>000111
[3,6,5,1,4,2,7]=>[5,4,3,1,6,2,7]=>[3,4,1,6,5,2,7]=>001110
[3,6,5,1,4,7,2]=>[5,6,3,2,7,4,1]=>[3,7,2,4,6,5,1]=>000111
[3,6,5,1,7,2,4]=>[5,6,3,1,7,2,4]=>[3,7,1,6,5,2,4]=>000111
[3,6,5,1,7,4,2]=>[5,4,3,6,7,2,1]=>[3,7,4,2,6,5,1]=>001111
[3,6,5,2,1,4,7]=>[2,5,3,1,6,4,7]=>[3,6,5,2,1,4,7]=>100110
[3,6,5,2,1,7,4]=>[2,5,3,6,7,4,1]=>[3,7,4,6,5,2,1]=>100111
[3,6,5,2,4,1,7]=>[4,5,3,2,6,1,7]=>[3,6,5,2,4,1,7]=>001110
[3,6,5,2,4,7,1]=>[7,5,3,2,6,4,1]=>[3,6,5,2,4,7,1]=>000111
[3,6,5,2,7,1,4]=>[7,5,3,1,6,2,4]=>[3,6,5,1,7,2,4]=>000111
[3,6,5,2,7,4,1]=>[4,7,3,5,6,1,2]=>[3,6,5,1,7,4,2]=>001111
[3,6,5,4,1,2,7]=>[4,1,3,5,6,2,7]=>[3,6,5,4,1,2,7]=>001110
[3,6,5,4,1,7,2]=>[4,5,3,6,7,1,2]=>[3,7,1,6,5,4,2]=>001111
[3,6,5,4,2,1,7]=>[2,4,3,5,6,1,7]=>[3,6,5,4,2,1,7]=>101110
[3,6,5,4,2,7,1]=>[7,4,3,5,6,2,1]=>[3,6,5,4,2,7,1]=>001111
[3,6,5,4,7,1,2]=>[7,1,3,5,6,4,2]=>[3,6,5,4,7,1,2]=>000111
[3,6,5,4,7,2,1]=>[2,7,3,5,6,4,1]=>[3,6,5,4,7,2,1]=>100111
[3,6,5,7,1,2,4]=>[7,1,3,2,6,5,4]=>[3,6,5,7,1,2,4]=>000011
[3,6,5,7,1,4,2]=>[7,4,3,1,6,5,2]=>[3,4,1,6,5,7,2]=>001011
[3,6,5,7,2,1,4]=>[2,7,3,1,6,5,4]=>[3,6,5,7,2,1,4]=>100011
[3,6,5,7,2,4,1]=>[4,7,3,2,6,5,1]=>[3,6,5,7,2,4,1]=>001011
[3,6,5,7,4,1,2]=>[4,1,3,7,6,5,2]=>[3,6,5,7,4,1,2]=>001011
[3,6,5,7,4,2,1]=>[2,4,3,7,6,5,1]=>[3,6,5,7,4,2,1]=>101011
[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[3,6,7,1,2,4,5]=>000001
[3,6,7,1,2,5,4]=>[7,1,3,5,2,6,4]=>[3,5,1,2,6,7,4]=>000101
[3,6,7,1,4,2,5]=>[7,4,3,1,2,6,5]=>[3,4,1,6,7,2,5]=>001001
[3,6,7,1,4,5,2]=>[7,5,3,1,4,6,2]=>[3,5,1,4,6,7,2]=>000101
[3,6,7,1,5,2,4]=>[7,5,3,2,1,6,4]=>[3,5,2,6,7,1,4]=>000101
[3,6,7,1,5,4,2]=>[7,4,3,5,1,6,2]=>[3,5,4,1,6,7,2]=>001101
[3,6,7,2,1,4,5]=>[2,7,3,1,4,6,5]=>[3,6,7,2,1,4,5]=>100001
[3,6,7,2,1,5,4]=>[2,7,3,5,1,6,4]=>[3,5,2,1,6,7,4]=>100101
[3,6,7,2,4,1,5]=>[4,7,3,2,1,6,5]=>[3,6,7,2,4,1,5]=>001001
[3,6,7,2,4,5,1]=>[5,7,3,2,4,6,1]=>[3,6,7,2,4,5,1]=>000101
[3,6,7,2,5,1,4]=>[5,7,3,1,2,6,4]=>[3,6,7,1,5,2,4]=>000101
[3,6,7,2,5,4,1]=>[4,5,3,7,1,6,2]=>[3,6,7,1,5,4,2]=>001101
[3,6,7,4,1,2,5]=>[4,1,3,7,2,6,5]=>[3,6,7,4,1,2,5]=>001001
[3,6,7,4,1,5,2]=>[4,7,3,5,2,6,1]=>[3,5,2,6,7,4,1]=>001101
[3,6,7,4,2,1,5]=>[2,4,3,7,1,6,5]=>[3,6,7,4,2,1,5]=>101001
[3,6,7,4,2,5,1]=>[5,4,3,7,2,6,1]=>[3,6,7,4,2,5,1]=>001101
[3,6,7,4,5,1,2]=>[5,1,3,7,4,6,2]=>[3,6,7,4,5,1,2]=>000101
[3,6,7,4,5,2,1]=>[2,5,3,7,4,6,1]=>[3,6,7,4,5,2,1]=>100101
[3,6,7,5,1,2,4]=>[5,1,3,2,7,6,4]=>[3,6,7,5,1,2,4]=>000101
[3,6,7,5,1,4,2]=>[5,4,3,1,7,6,2]=>[3,4,1,6,7,5,2]=>001101
[3,6,7,5,2,1,4]=>[2,5,3,1,7,6,4]=>[3,6,7,5,2,1,4]=>100101
[3,6,7,5,2,4,1]=>[4,5,3,2,7,6,1]=>[3,6,7,5,2,4,1]=>001101
[3,6,7,5,4,1,2]=>[4,1,3,5,7,6,2]=>[3,6,7,5,4,1,2]=>001101
[3,6,7,5,4,2,1]=>[2,4,3,5,7,6,1]=>[3,6,7,5,4,2,1]=>101101
[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>[3,7,1,2,4,5,6]=>000001
[3,7,1,2,4,6,5]=>[7,1,3,2,6,4,5]=>[3,6,1,2,4,7,5]=>000011
[3,7,1,2,5,4,6]=>[7,1,3,5,2,4,6]=>[3,5,1,2,7,4,6]=>000101
[3,7,1,2,5,6,4]=>[7,1,3,6,2,5,4]=>[3,6,1,2,5,7,4]=>000011
[3,7,1,2,6,4,5]=>[7,1,3,6,4,2,5]=>[3,6,4,7,1,2,5]=>000011
[3,7,1,2,6,5,4]=>[7,1,3,5,6,2,4]=>[3,6,5,1,2,7,4]=>000111
[3,7,1,4,2,5,6]=>[7,4,3,1,2,5,6]=>[3,4,1,7,2,5,6]=>001001
[3,7,1,4,2,6,5]=>[7,4,3,1,6,2,5]=>[3,4,1,6,2,7,5]=>001011
[3,7,1,4,5,2,6]=>[7,5,3,1,4,2,6]=>[3,5,1,4,7,2,6]=>000101
[3,7,1,4,5,6,2]=>[7,6,3,1,4,5,2]=>[3,6,1,4,5,7,2]=>000011
[3,7,1,4,6,2,5]=>[7,6,3,1,2,4,5]=>[3,6,1,7,2,4,5]=>000011
[3,7,1,4,6,5,2]=>[7,5,3,1,6,4,2]=>[3,6,5,1,4,7,2]=>000111
[3,7,1,5,2,4,6]=>[7,5,3,2,1,4,6]=>[3,5,2,7,1,4,6]=>000101
[3,7,1,5,2,6,4]=>[7,5,3,6,1,2,4]=>[3,6,1,5,2,7,4]=>000111
[3,7,1,5,4,2,6]=>[7,4,3,5,1,2,6]=>[3,5,4,1,7,2,6]=>001101
[3,7,1,5,4,6,2]=>[7,6,3,5,1,4,2]=>[3,5,1,6,4,7,2]=>000111
[3,7,1,5,6,2,4]=>[7,6,3,2,1,5,4]=>[3,6,2,5,7,1,4]=>000011
[3,7,1,5,6,4,2]=>[7,4,3,6,1,5,2]=>[3,6,4,1,5,7,2]=>001011
[3,7,1,6,2,4,5]=>[7,6,3,2,4,1,5]=>[3,6,2,4,7,1,5]=>000011
[3,7,1,6,2,5,4]=>[7,6,3,5,2,1,4]=>[3,5,2,6,1,7,4]=>000111
[3,7,1,6,4,2,5]=>[7,4,3,6,2,1,5]=>[3,6,4,2,7,1,5]=>001011
[3,7,1,6,4,5,2]=>[7,5,3,6,4,1,2]=>[3,6,4,5,1,7,2]=>000111
[3,7,1,6,5,2,4]=>[7,5,3,2,6,1,4]=>[3,6,5,2,7,1,4]=>000111
[3,7,1,6,5,4,2]=>[7,4,3,5,6,1,2]=>[3,6,5,4,1,7,2]=>001111
[3,7,2,1,4,5,6]=>[2,7,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>100001
[3,7,2,1,4,6,5]=>[2,7,3,1,6,4,5]=>[3,6,2,1,4,7,5]=>100011
[3,7,2,1,5,4,6]=>[2,7,3,5,1,4,6]=>[3,5,2,1,7,4,6]=>100101
[3,7,2,1,5,6,4]=>[2,7,3,6,1,5,4]=>[3,6,2,1,5,7,4]=>100011
[3,7,2,1,6,4,5]=>[2,7,3,6,4,1,5]=>[3,6,4,7,2,1,5]=>100011
[3,7,2,1,6,5,4]=>[2,7,3,5,6,1,4]=>[3,6,5,2,1,7,4]=>100111
[3,7,2,4,1,5,6]=>[4,7,3,2,1,5,6]=>[3,7,2,4,1,5,6]=>001001
[3,7,2,4,1,6,5]=>[4,7,3,2,6,1,5]=>[3,6,2,4,1,7,5]=>001011
[3,7,2,4,5,1,6]=>[5,7,3,2,4,1,6]=>[3,7,2,4,5,1,6]=>000101
[3,7,2,4,5,6,1]=>[6,7,3,2,4,5,1]=>[3,7,2,4,5,6,1]=>000011
[3,7,2,4,6,1,5]=>[6,7,3,2,1,4,5]=>[3,7,2,6,1,4,5]=>000011
[3,7,2,4,6,5,1]=>[5,6,3,1,7,4,2]=>[3,7,1,4,6,5,2]=>000111
[3,7,2,5,1,4,6]=>[5,7,3,1,2,4,6]=>[3,7,1,5,2,4,6]=>000101
[3,7,2,5,1,6,4]=>[5,7,3,6,2,1,4]=>[3,6,2,7,1,5,4]=>000111
[3,7,2,5,4,1,6]=>[4,5,3,7,1,2,6]=>[3,7,1,5,4,2,6]=>001101
[3,7,2,5,4,6,1]=>[6,7,3,5,2,4,1]=>[3,5,2,7,4,6,1]=>000111
[3,7,2,5,6,1,4]=>[6,7,3,1,2,5,4]=>[3,7,1,5,6,2,4]=>000011
[3,7,2,5,6,4,1]=>[4,6,3,7,1,5,2]=>[3,7,1,5,6,4,2]=>001011
[3,7,2,6,1,4,5]=>[6,7,3,1,4,2,5]=>[3,7,1,4,6,2,5]=>000011
[3,7,2,6,1,5,4]=>[6,7,3,5,1,2,4]=>[3,5,1,7,2,6,4]=>000111
[3,7,2,6,4,1,5]=>[4,6,3,7,2,1,5]=>[3,7,2,6,4,1,5]=>001011
[3,7,2,6,4,5,1]=>[5,7,3,6,4,2,1]=>[3,6,4,7,2,5,1]=>000111
[3,7,2,6,5,1,4]=>[5,6,3,2,7,1,4]=>[3,7,2,6,5,1,4]=>000111
[3,7,2,6,5,4,1]=>[4,5,3,6,7,2,1]=>[3,7,2,6,5,4,1]=>001111
[3,7,4,1,2,5,6]=>[4,1,3,7,2,5,6]=>[3,7,4,1,2,5,6]=>001001
[3,7,4,1,2,6,5]=>[4,1,3,7,6,2,5]=>[3,6,4,1,2,7,5]=>001011
[3,7,4,1,5,2,6]=>[4,7,3,5,2,1,6]=>[3,5,2,7,4,1,6]=>001101
[3,7,4,1,5,6,2]=>[4,7,3,6,2,5,1]=>[3,6,2,5,7,4,1]=>001011
[3,7,4,1,6,2,5]=>[4,7,3,6,1,2,5]=>[3,6,1,7,4,2,5]=>001011
[3,7,4,1,6,5,2]=>[4,7,3,5,6,2,1]=>[3,6,5,2,7,4,1]=>001111
[3,7,4,2,1,5,6]=>[2,4,3,7,1,5,6]=>[3,7,4,2,1,5,6]=>101001
[3,7,4,2,1,6,5]=>[2,4,3,7,6,1,5]=>[3,6,4,2,1,7,5]=>101011
[3,7,4,2,5,1,6]=>[5,4,3,7,2,1,6]=>[3,7,4,2,5,1,6]=>001101
[3,7,4,2,5,6,1]=>[6,4,3,7,2,5,1]=>[3,7,4,2,5,6,1]=>001011
[3,7,4,2,6,1,5]=>[6,4,3,7,1,2,5]=>[3,7,4,1,6,2,5]=>001011
[3,7,4,2,6,5,1]=>[5,4,3,6,7,1,2]=>[3,7,4,1,6,5,2]=>001111
[3,7,4,5,1,2,6]=>[5,1,3,7,4,2,6]=>[3,7,4,5,1,2,6]=>000101
[3,7,4,5,1,6,2]=>[5,6,3,7,4,1,2]=>[3,7,4,6,1,5,2]=>000111
[3,7,4,5,2,1,6]=>[2,5,3,7,4,1,6]=>[3,7,4,5,2,1,6]=>100101
[3,7,4,5,2,6,1]=>[6,5,3,7,4,2,1]=>[3,7,4,5,2,6,1]=>000111
[3,7,4,5,6,1,2]=>[6,1,3,7,4,5,2]=>[3,7,4,5,6,1,2]=>000011
[3,7,4,5,6,2,1]=>[2,6,3,7,4,5,1]=>[3,7,4,5,6,2,1]=>100011
[3,7,4,6,1,2,5]=>[6,1,3,7,2,4,5]=>[3,7,1,2,6,4,5]=>000011
[3,7,4,6,1,5,2]=>[6,5,3,7,1,4,2]=>[3,7,1,5,4,6,2]=>000111
[3,7,4,6,2,1,5]=>[2,6,3,7,1,4,5]=>[3,7,2,1,6,4,5]=>100011
[3,7,4,6,2,5,1]=>[5,6,3,7,2,4,1]=>[3,7,2,6,4,5,1]=>000111
[3,7,4,6,5,1,2]=>[5,1,3,6,7,2,4]=>[3,7,1,2,6,5,4]=>000111
[3,7,4,6,5,2,1]=>[2,5,3,6,7,1,4]=>[3,7,2,1,6,5,4]=>100111
[3,7,5,1,2,4,6]=>[5,1,3,2,7,4,6]=>[3,7,5,1,2,4,6]=>000101
[3,7,5,1,2,6,4]=>[5,1,3,7,6,4,2]=>[3,6,4,7,5,1,2]=>000111
[3,7,5,1,4,2,6]=>[5,4,3,1,7,2,6]=>[3,4,1,7,5,2,6]=>001101
[3,7,5,1,4,6,2]=>[5,7,3,2,6,4,1]=>[3,6,2,4,7,5,1]=>000111
[3,7,5,1,6,2,4]=>[5,7,3,1,6,2,4]=>[3,6,1,7,5,2,4]=>000111
[3,7,5,1,6,4,2]=>[5,4,3,7,6,2,1]=>[3,6,4,2,7,5,1]=>001111
[3,7,5,2,1,4,6]=>[2,5,3,1,7,4,6]=>[3,7,5,2,1,4,6]=>100101
[3,7,5,2,1,6,4]=>[2,5,3,7,6,4,1]=>[3,6,4,7,5,2,1]=>100111
[3,7,5,2,4,1,6]=>[4,5,3,2,7,1,6]=>[3,7,5,2,4,1,6]=>001101
[3,7,5,2,4,6,1]=>[6,5,3,2,7,4,1]=>[3,7,5,2,4,6,1]=>000111
[3,7,5,2,6,1,4]=>[6,5,3,1,7,2,4]=>[3,7,5,1,6,2,4]=>000111
[3,7,5,2,6,4,1]=>[4,6,3,5,7,1,2]=>[3,7,5,1,6,4,2]=>001111
[3,7,5,4,1,2,6]=>[4,1,3,5,7,2,6]=>[3,7,5,4,1,2,6]=>001101
[3,7,5,4,1,6,2]=>[4,5,3,7,6,1,2]=>[3,6,1,7,5,4,2]=>001111
[3,7,5,4,2,1,6]=>[2,4,3,5,7,1,6]=>[3,7,5,4,2,1,6]=>101101
[3,7,5,4,2,6,1]=>[6,4,3,5,7,2,1]=>[3,7,5,4,2,6,1]=>001111
[3,7,5,4,6,1,2]=>[6,1,3,5,7,4,2]=>[3,7,5,4,6,1,2]=>000111
[3,7,5,4,6,2,1]=>[2,6,3,5,7,4,1]=>[3,7,5,4,6,2,1]=>100111
[3,7,5,6,1,2,4]=>[6,1,3,2,7,5,4]=>[3,7,5,6,1,2,4]=>000011
[3,7,5,6,1,4,2]=>[6,4,3,1,7,5,2]=>[3,4,1,7,5,6,2]=>001011
[3,7,5,6,2,1,4]=>[2,6,3,1,7,5,4]=>[3,7,5,6,2,1,4]=>100011
[3,7,5,6,2,4,1]=>[4,6,3,2,7,5,1]=>[3,7,5,6,2,4,1]=>001011
[3,7,5,6,4,1,2]=>[4,1,3,6,7,5,2]=>[3,7,5,6,4,1,2]=>001011
[3,7,5,6,4,2,1]=>[2,4,3,6,7,5,1]=>[3,7,5,6,4,2,1]=>101011
[3,7,6,1,2,4,5]=>[6,1,3,2,4,7,5]=>[3,7,6,1,2,4,5]=>000011
[3,7,6,1,2,5,4]=>[6,1,3,5,2,7,4]=>[3,5,1,2,7,6,4]=>000111
[3,7,6,1,4,2,5]=>[6,4,3,1,2,7,5]=>[3,4,1,7,6,2,5]=>001011
[3,7,6,1,4,5,2]=>[6,5,3,1,4,7,2]=>[3,5,1,4,7,6,2]=>000111
[3,7,6,1,5,2,4]=>[6,5,3,2,1,7,4]=>[3,5,2,7,6,1,4]=>000111
[3,7,6,1,5,4,2]=>[6,4,3,5,1,7,2]=>[3,5,4,1,7,6,2]=>001111
[3,7,6,2,1,4,5]=>[2,6,3,1,4,7,5]=>[3,7,6,2,1,4,5]=>100011
[3,7,6,2,1,5,4]=>[2,6,3,5,1,7,4]=>[3,5,2,1,7,6,4]=>100111
[3,7,6,2,4,1,5]=>[4,6,3,2,1,7,5]=>[3,7,6,2,4,1,5]=>001011
[3,7,6,2,4,5,1]=>[5,6,3,2,4,7,1]=>[3,7,6,2,4,5,1]=>000111
[3,7,6,2,5,1,4]=>[5,6,3,1,2,7,4]=>[3,7,6,1,5,2,4]=>000111
[3,7,6,2,5,4,1]=>[4,5,3,6,1,7,2]=>[3,7,6,1,5,4,2]=>001111
[3,7,6,4,1,2,5]=>[4,1,3,6,2,7,5]=>[3,7,6,4,1,2,5]=>001011
[3,7,6,4,1,5,2]=>[4,6,3,5,2,7,1]=>[3,5,2,7,6,4,1]=>001111
[3,7,6,4,2,1,5]=>[2,4,3,6,1,7,5]=>[3,7,6,4,2,1,5]=>101011
[3,7,6,4,2,5,1]=>[5,4,3,6,2,7,1]=>[3,7,6,4,2,5,1]=>001111
[3,7,6,4,5,1,2]=>[5,1,3,6,4,7,2]=>[3,7,6,4,5,1,2]=>000111
[3,7,6,4,5,2,1]=>[2,5,3,6,4,7,1]=>[3,7,6,4,5,2,1]=>100111
[3,7,6,5,1,2,4]=>[5,1,3,2,6,7,4]=>[3,7,6,5,1,2,4]=>000111
[3,7,6,5,1,4,2]=>[5,4,3,1,6,7,2]=>[3,4,1,7,6,5,2]=>001111
[3,7,6,5,2,1,4]=>[2,5,3,1,6,7,4]=>[3,7,6,5,2,1,4]=>100111
[3,7,6,5,2,4,1]=>[4,5,3,2,6,7,1]=>[3,7,6,5,2,4,1]=>001111
[3,7,6,5,4,1,2]=>[4,1,3,5,6,7,2]=>[3,7,6,5,4,1,2]=>001111
[3,7,6,5,4,2,1]=>[2,4,3,5,6,7,1]=>[3,7,6,5,4,2,1]=>101111
[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>001000
[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>001001
[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>001010
[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>[4,1,2,3,6,7,5]=>001001
[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>001001
[4,1,2,3,7,6,5]=>[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>001011
[4,1,2,5,3,6,7]=>[4,1,5,2,3,6,7]=>[5,1,2,4,3,6,7]=>001100
[4,1,2,5,3,7,6]=>[4,1,5,2,3,7,6]=>[5,1,2,4,3,7,6]=>001101
[4,1,2,5,6,3,7]=>[4,1,6,2,5,3,7]=>[5,6,1,2,4,3,7]=>001010
[4,1,2,5,6,7,3]=>[4,1,7,2,5,6,3]=>[5,6,7,1,2,4,3]=>001001
[4,1,2,5,7,3,6]=>[4,1,7,2,5,3,6]=>[5,7,1,2,4,3,6]=>001001
[4,1,2,5,7,6,3]=>[4,1,6,2,5,7,3]=>[5,7,6,1,2,4,3]=>001011
[4,1,2,6,3,5,7]=>[4,1,6,2,3,5,7]=>[6,1,2,4,3,5,7]=>001010
[4,1,2,6,3,7,5]=>[4,1,6,2,7,3,5]=>[7,1,2,4,3,6,5]=>001011
[4,1,2,6,5,3,7]=>[4,1,5,2,6,3,7]=>[6,5,1,2,4,3,7]=>001110
[4,1,2,6,5,7,3]=>[4,1,7,2,6,5,3]=>[6,5,7,1,2,4,3]=>001011
[4,1,2,6,7,3,5]=>[4,1,7,2,3,6,5]=>[6,7,1,2,4,3,5]=>001001
[4,1,2,6,7,5,3]=>[4,1,5,2,7,6,3]=>[6,7,5,1,2,4,3]=>001101
[4,1,2,7,3,5,6]=>[4,1,7,2,3,5,6]=>[7,1,2,4,3,5,6]=>001001
[4,1,2,7,3,6,5]=>[4,1,7,2,6,3,5]=>[6,1,2,4,3,7,5]=>001011
[4,1,2,7,5,3,6]=>[4,1,5,2,7,3,6]=>[7,5,1,2,4,3,6]=>001101
[4,1,2,7,5,6,3]=>[4,1,6,2,7,5,3]=>[7,5,6,1,2,4,3]=>001011
[4,1,2,7,6,3,5]=>[4,1,6,2,3,7,5]=>[7,6,1,2,4,3,5]=>001011
[4,1,2,7,6,5,3]=>[4,1,5,2,6,7,3]=>[7,6,5,1,2,4,3]=>001111
[4,1,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>011000
[4,1,3,2,5,7,6]=>[4,3,1,2,5,7,6]=>[3,1,4,2,5,7,6]=>011001
[4,1,3,2,6,5,7]=>[4,3,1,2,6,5,7]=>[3,1,4,2,6,5,7]=>011010
[4,1,3,2,6,7,5]=>[4,3,1,2,7,6,5]=>[3,1,4,2,6,7,5]=>011001
[4,1,3,2,7,5,6]=>[4,3,1,2,7,5,6]=>[3,1,4,2,7,5,6]=>011001
[4,1,3,2,7,6,5]=>[4,3,1,2,6,7,5]=>[3,1,4,2,7,6,5]=>011011
[4,1,3,5,2,6,7]=>[4,5,1,3,2,6,7]=>[5,1,3,4,2,6,7]=>001100
[4,1,3,5,2,7,6]=>[4,5,1,3,2,7,6]=>[5,1,3,4,2,7,6]=>001101
[4,1,3,5,6,2,7]=>[4,6,1,3,5,2,7]=>[5,6,1,3,4,2,7]=>001010
[4,1,3,5,6,7,2]=>[4,7,1,3,5,6,2]=>[5,6,7,1,3,4,2]=>001001
[4,1,3,5,7,2,6]=>[4,7,1,3,5,2,6]=>[5,7,1,3,4,2,6]=>001001
[4,1,3,5,7,6,2]=>[4,6,1,3,5,7,2]=>[5,7,6,1,3,4,2]=>001011
[4,1,3,6,2,5,7]=>[4,6,1,3,2,5,7]=>[6,1,3,4,2,5,7]=>001010
[4,1,3,6,2,7,5]=>[4,6,1,3,7,2,5]=>[7,1,3,4,2,6,5]=>001011
[4,1,3,6,5,2,7]=>[4,5,1,3,6,2,7]=>[6,5,1,3,4,2,7]=>001110
[4,1,3,6,5,7,2]=>[4,7,1,3,6,5,2]=>[6,5,7,1,3,4,2]=>001011
[4,1,3,6,7,2,5]=>[4,7,1,3,2,6,5]=>[6,7,1,3,4,2,5]=>001001
[4,1,3,6,7,5,2]=>[4,5,1,3,7,6,2]=>[6,7,5,1,3,4,2]=>001101
[4,1,3,7,2,5,6]=>[4,7,1,3,2,5,6]=>[7,1,3,4,2,5,6]=>001001
[4,1,3,7,2,6,5]=>[4,7,1,3,6,2,5]=>[6,1,3,4,2,7,5]=>001011
[4,1,3,7,5,2,6]=>[4,5,1,3,7,2,6]=>[7,5,1,3,4,2,6]=>001101
[4,1,3,7,5,6,2]=>[4,6,1,3,7,5,2]=>[7,5,6,1,3,4,2]=>001011
[4,1,3,7,6,2,5]=>[4,6,1,3,2,7,5]=>[7,6,1,3,4,2,5]=>001011
[4,1,3,7,6,5,2]=>[4,5,1,3,6,7,2]=>[7,6,5,1,3,4,2]=>001111
[4,1,5,2,3,6,7]=>[4,5,2,1,3,6,7]=>[5,2,4,1,3,6,7]=>001100
[4,1,5,2,3,7,6]=>[4,5,2,1,3,7,6]=>[5,2,4,1,3,7,6]=>001101
[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[6,1,5,2,4,3,7]=>001110
[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[6,7,1,5,2,4,3]=>001101
[4,1,5,2,7,3,6]=>[4,5,7,1,2,3,6]=>[7,1,5,2,4,3,6]=>001101
[4,1,5,2,7,6,3]=>[4,5,6,1,2,7,3]=>[7,6,1,5,2,4,3]=>001111
[4,1,5,3,2,6,7]=>[4,3,5,1,2,6,7]=>[5,3,1,4,2,6,7]=>011100
[4,1,5,3,2,7,6]=>[4,3,5,1,2,7,6]=>[5,3,1,4,2,7,6]=>011101
[4,1,5,3,6,2,7]=>[4,6,5,1,3,2,7]=>[5,1,6,3,4,2,7]=>001110
[4,1,5,3,6,7,2]=>[4,7,5,1,3,6,2]=>[5,1,6,7,3,4,2]=>001101
[4,1,5,3,7,2,6]=>[4,7,5,1,3,2,6]=>[5,1,7,3,4,2,6]=>001101
[4,1,5,3,7,6,2]=>[4,6,5,1,3,7,2]=>[5,1,7,6,3,4,2]=>001111
[4,1,5,6,2,3,7]=>[4,6,2,1,5,3,7]=>[5,6,2,4,1,3,7]=>001010
[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[5,7,1,6,2,4,3]=>001011
[4,1,5,6,3,2,7]=>[4,3,6,1,5,2,7]=>[5,6,3,1,4,2,7]=>011010
[4,1,5,6,3,7,2]=>[4,7,6,1,5,3,2]=>[5,6,1,7,3,4,2]=>001011
[4,1,5,6,7,2,3]=>[4,7,2,1,5,6,3]=>[5,6,7,2,4,1,3]=>001001
[4,1,5,6,7,3,2]=>[4,3,7,1,5,6,2]=>[5,6,7,3,1,4,2]=>011001
[4,1,5,7,2,3,6]=>[4,7,2,1,5,3,6]=>[5,7,2,4,1,3,6]=>001001
[4,1,5,7,2,6,3]=>[4,7,6,1,5,2,3]=>[5,6,1,7,2,4,3]=>001011
[4,1,5,7,3,2,6]=>[4,3,7,1,5,2,6]=>[5,7,3,1,4,2,6]=>011001
[4,1,5,7,3,6,2]=>[4,6,7,1,5,3,2]=>[5,7,1,6,3,4,2]=>001011
[4,1,5,7,6,2,3]=>[4,6,2,1,5,7,3]=>[5,7,6,2,4,1,3]=>001011
[4,1,5,7,6,3,2]=>[4,3,6,1,5,7,2]=>[5,7,6,3,1,4,2]=>011011
[4,1,6,2,3,5,7]=>[4,6,2,1,3,5,7]=>[6,2,4,1,3,5,7]=>001010
[4,1,6,2,3,7,5]=>[4,6,2,1,7,3,5]=>[7,2,4,1,3,6,5]=>001011
[4,1,6,2,5,3,7]=>[4,6,5,1,2,3,7]=>[5,1,6,2,4,3,7]=>001110
[4,1,6,2,5,7,3]=>[4,6,7,1,2,5,3]=>[7,1,5,6,2,4,3]=>001011
[4,1,6,2,7,3,5]=>[4,6,7,1,3,2,5]=>[7,1,6,3,4,2,5]=>001011
[4,1,6,2,7,5,3]=>[4,6,5,1,7,2,3]=>[7,5,1,6,2,4,3]=>001111
[4,1,6,3,2,5,7]=>[4,3,6,1,2,5,7]=>[6,3,1,4,2,5,7]=>011010
[4,1,6,3,2,7,5]=>[4,3,6,1,7,2,5]=>[7,3,1,4,2,6,5]=>011011
[4,1,6,3,5,2,7]=>[4,5,6,1,3,2,7]=>[6,1,5,3,4,2,7]=>001110
[4,1,6,3,5,7,2]=>[4,7,6,1,3,5,2]=>[6,1,5,7,3,4,2]=>001011
[4,1,6,3,7,2,5]=>[4,7,6,1,2,3,5]=>[6,1,7,2,4,3,5]=>001011
[4,1,6,3,7,5,2]=>[4,5,7,1,6,2,3]=>[6,1,7,5,2,4,3]=>001111
[4,1,6,5,2,3,7]=>[4,5,2,1,6,3,7]=>[6,5,2,4,1,3,7]=>001110
[4,1,6,5,2,7,3]=>[4,5,6,1,7,3,2]=>[7,1,6,5,3,4,2]=>001111
[4,1,6,5,3,2,7]=>[4,3,5,1,6,2,7]=>[6,5,3,1,4,2,7]=>011110
[4,1,6,5,3,7,2]=>[4,7,5,1,6,3,2]=>[6,5,1,7,3,4,2]=>001111
[4,1,6,5,7,2,3]=>[4,7,2,1,6,5,3]=>[6,5,7,2,4,1,3]=>001011
[4,1,6,5,7,3,2]=>[4,3,7,1,6,5,2]=>[6,5,7,3,1,4,2]=>011011
[4,1,6,7,2,3,5]=>[4,7,2,1,3,6,5]=>[6,7,2,4,1,3,5]=>001001
[4,1,6,7,2,5,3]=>[4,7,5,1,2,6,3]=>[5,1,6,7,2,4,3]=>001101
[4,1,6,7,3,2,5]=>[4,3,7,1,2,6,5]=>[6,7,3,1,4,2,5]=>011001
[4,1,6,7,3,5,2]=>[4,5,7,1,3,6,2]=>[6,7,1,5,3,4,2]=>001101
[4,1,6,7,5,2,3]=>[4,5,2,1,7,6,3]=>[6,7,5,2,4,1,3]=>001101
[4,1,6,7,5,3,2]=>[4,3,5,1,7,6,2]=>[6,7,5,3,1,4,2]=>011101
[4,1,7,2,3,5,6]=>[4,7,2,1,3,5,6]=>[7,2,4,1,3,5,6]=>001001
[4,1,7,2,3,6,5]=>[4,7,2,1,6,3,5]=>[6,2,4,1,3,7,5]=>001011
[4,1,7,2,5,3,6]=>[4,7,5,1,2,3,6]=>[5,1,7,2,4,3,6]=>001101
[4,1,7,2,5,6,3]=>[4,7,6,1,2,5,3]=>[6,1,5,7,2,4,3]=>001011
[4,1,7,2,6,3,5]=>[4,7,6,1,3,2,5]=>[6,1,7,3,4,2,5]=>001011
[4,1,7,2,6,5,3]=>[4,7,5,1,6,2,3]=>[6,5,1,7,2,4,3]=>001111
[4,1,7,3,2,5,6]=>[4,3,7,1,2,5,6]=>[7,3,1,4,2,5,6]=>011001
[4,1,7,3,2,6,5]=>[4,3,7,1,6,2,5]=>[6,3,1,4,2,7,5]=>011011
[4,1,7,3,5,2,6]=>[4,5,7,1,3,2,6]=>[7,1,5,3,4,2,6]=>001101
[4,1,7,3,5,6,2]=>[4,6,7,1,3,5,2]=>[7,1,5,6,3,4,2]=>001011
[4,1,7,3,6,2,5]=>[4,6,7,1,2,3,5]=>[7,1,6,2,4,3,5]=>001011
[4,1,7,3,6,5,2]=>[4,5,6,1,7,2,3]=>[7,1,6,5,2,4,3]=>001111
[4,1,7,5,2,3,6]=>[4,5,2,1,7,3,6]=>[7,5,2,4,1,3,6]=>001101
[4,1,7,5,2,6,3]=>[4,5,7,1,6,3,2]=>[6,1,7,5,3,4,2]=>001111
[4,1,7,5,3,2,6]=>[4,3,5,1,7,2,6]=>[7,5,3,1,4,2,6]=>011101
[4,1,7,5,3,6,2]=>[4,6,5,1,7,3,2]=>[7,5,1,6,3,4,2]=>001111
[4,1,7,5,6,2,3]=>[4,6,2,1,7,5,3]=>[7,5,6,2,4,1,3]=>001011
[4,1,7,5,6,3,2]=>[4,3,6,1,7,5,2]=>[7,5,6,3,1,4,2]=>011011
[4,1,7,6,2,3,5]=>[4,6,2,1,3,7,5]=>[7,6,2,4,1,3,5]=>001011
[4,1,7,6,2,5,3]=>[4,6,5,1,2,7,3]=>[5,1,7,6,2,4,3]=>001111
[4,1,7,6,3,2,5]=>[4,3,6,1,2,7,5]=>[7,6,3,1,4,2,5]=>011011
[4,1,7,6,3,5,2]=>[4,5,6,1,3,7,2]=>[7,6,1,5,3,4,2]=>001111
[4,1,7,6,5,2,3]=>[4,5,2,1,6,7,3]=>[7,6,5,2,4,1,3]=>001111
[4,1,7,6,5,3,2]=>[4,3,5,1,6,7,2]=>[7,6,5,3,1,4,2]=>011111
[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>101000
[4,2,1,3,5,7,6]=>[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>101001
[4,2,1,3,6,5,7]=>[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>101010
[4,2,1,3,6,7,5]=>[2,4,1,3,7,6,5]=>[4,2,1,3,6,7,5]=>101001
[4,2,1,3,7,5,6]=>[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>101001
[4,2,1,3,7,6,5]=>[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>101011
[4,2,1,5,3,6,7]=>[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]=>101100
[4,2,1,5,3,7,6]=>[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]=>101101
[4,2,1,5,6,3,7]=>[2,4,6,1,5,3,7]=>[5,6,2,1,4,3,7]=>101010
[4,2,1,5,6,7,3]=>[2,4,7,1,5,6,3]=>[5,6,7,2,1,4,3]=>101001
[4,2,1,5,7,3,6]=>[2,4,7,1,5,3,6]=>[5,7,2,1,4,3,6]=>101001
[4,2,1,5,7,6,3]=>[2,4,6,1,5,7,3]=>[5,7,6,2,1,4,3]=>101011
[4,2,1,6,3,5,7]=>[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>101010
[4,2,1,6,3,7,5]=>[2,4,6,1,7,3,5]=>[7,2,1,4,3,6,5]=>101011
[4,2,1,6,5,3,7]=>[2,4,5,1,6,3,7]=>[6,5,2,1,4,3,7]=>101110
[4,2,1,6,5,7,3]=>[2,4,7,1,6,5,3]=>[6,5,7,2,1,4,3]=>101011
[4,2,1,6,7,3,5]=>[2,4,7,1,3,6,5]=>[6,7,2,1,4,3,5]=>101001
[4,2,1,6,7,5,3]=>[2,4,5,1,7,6,3]=>[6,7,5,2,1,4,3]=>101101
[4,2,1,7,3,5,6]=>[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>101001
[4,2,1,7,3,6,5]=>[2,4,7,1,6,3,5]=>[6,2,1,4,3,7,5]=>101011
[4,2,1,7,5,3,6]=>[2,4,5,1,7,3,6]=>[7,5,2,1,4,3,6]=>101101
[4,2,1,7,5,6,3]=>[2,4,6,1,7,5,3]=>[7,5,6,2,1,4,3]=>101011
[4,2,1,7,6,3,5]=>[2,4,6,1,3,7,5]=>[7,6,2,1,4,3,5]=>101011
[4,2,1,7,6,5,3]=>[2,4,5,1,6,7,3]=>[7,6,5,2,1,4,3]=>101111
[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,2,3,1,5,6,7]=>011000
[4,2,3,1,5,7,6]=>[3,4,2,1,5,7,6]=>[4,2,3,1,5,7,6]=>011001
[4,2,3,1,6,5,7]=>[3,4,2,1,6,5,7]=>[4,2,3,1,6,5,7]=>011010
[4,2,3,1,6,7,5]=>[3,4,2,1,7,6,5]=>[4,2,3,1,6,7,5]=>011001
[4,2,3,1,7,5,6]=>[3,4,2,1,7,5,6]=>[4,2,3,1,7,5,6]=>011001
[4,2,3,1,7,6,5]=>[3,4,2,1,6,7,5]=>[4,2,3,1,7,6,5]=>011011
[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>[4,2,3,5,1,6,7]=>001100
[4,2,3,5,1,7,6]=>[5,4,2,3,1,7,6]=>[4,2,3,5,1,7,6]=>001101
[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>[4,2,3,5,6,1,7]=>001010
[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>[4,2,3,5,6,7,1]=>001001
[4,2,3,5,7,1,6]=>[7,4,2,3,5,1,6]=>[4,2,3,5,7,1,6]=>001001
[4,2,3,5,7,6,1]=>[6,4,2,3,5,7,1]=>[4,2,3,5,7,6,1]=>001011
[4,2,3,6,1,5,7]=>[6,4,2,3,1,5,7]=>[4,2,3,6,1,5,7]=>001010
[4,2,3,6,1,7,5]=>[6,4,2,3,7,1,5]=>[4,2,3,7,1,6,5]=>001011
[4,2,3,6,5,1,7]=>[5,4,2,3,6,1,7]=>[4,2,3,6,5,1,7]=>001110
[4,2,3,6,5,7,1]=>[7,4,2,3,6,5,1]=>[4,2,3,6,5,7,1]=>001011
[4,2,3,6,7,1,5]=>[7,4,2,3,1,6,5]=>[4,2,3,6,7,1,5]=>001001
[4,2,3,6,7,5,1]=>[5,4,2,3,7,6,1]=>[4,2,3,6,7,5,1]=>001101
[4,2,3,7,1,5,6]=>[7,4,2,3,1,5,6]=>[4,2,3,7,1,5,6]=>001001
[4,2,3,7,1,6,5]=>[7,4,2,3,6,1,5]=>[4,2,3,6,1,7,5]=>001011
[4,2,3,7,5,1,6]=>[5,4,2,3,7,1,6]=>[4,2,3,7,5,1,6]=>001101
[4,2,3,7,5,6,1]=>[6,4,2,3,7,5,1]=>[4,2,3,7,5,6,1]=>001011
[4,2,3,7,6,1,5]=>[6,4,2,3,1,7,5]=>[4,2,3,7,6,1,5]=>001011
[4,2,3,7,6,5,1]=>[5,4,2,3,6,7,1]=>[4,2,3,7,6,5,1]=>001111
[4,2,5,1,3,6,7]=>[5,4,1,2,3,6,7]=>[4,1,5,2,3,6,7]=>001100
[4,2,5,1,3,7,6]=>[5,4,1,2,3,7,6]=>[4,1,5,2,3,7,6]=>001101
[4,2,5,1,6,3,7]=>[5,4,6,2,1,3,7]=>[6,2,4,1,5,3,7]=>001110
[4,2,5,1,6,7,3]=>[5,4,7,2,1,6,3]=>[6,7,2,4,1,5,3]=>001101
[4,2,5,1,7,3,6]=>[5,4,7,2,1,3,6]=>[7,2,4,1,5,3,6]=>001101
[4,2,5,1,7,6,3]=>[5,4,6,2,1,7,3]=>[7,6,2,4,1,5,3]=>001111
[4,2,5,3,1,6,7]=>[3,5,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>011100
[4,2,5,3,1,7,6]=>[3,5,4,1,2,7,6]=>[4,1,5,3,2,7,6]=>011101
[4,2,5,3,6,1,7]=>[6,4,5,2,3,1,7]=>[5,2,4,3,6,1,7]=>001110
[4,2,5,3,6,7,1]=>[7,4,5,2,3,6,1]=>[5,2,4,3,6,7,1]=>001101
[4,2,5,3,7,1,6]=>[7,4,5,2,3,1,6]=>[5,2,4,3,7,1,6]=>001101
[4,2,5,3,7,6,1]=>[6,4,5,2,3,7,1]=>[5,2,4,3,7,6,1]=>001111
[4,2,5,6,1,3,7]=>[6,4,1,2,5,3,7]=>[4,1,5,6,2,3,7]=>001010
[4,2,5,6,1,7,3]=>[6,4,7,2,5,1,3]=>[5,7,2,4,1,6,3]=>001011
[4,2,5,6,3,1,7]=>[3,6,4,1,5,2,7]=>[4,1,5,6,3,2,7]=>011010
[4,2,5,6,3,7,1]=>[7,4,6,2,5,3,1]=>[5,6,2,4,3,7,1]=>001011
[4,2,5,6,7,1,3]=>[7,4,1,2,5,6,3]=>[4,1,5,6,7,2,3]=>001001
[4,2,5,6,7,3,1]=>[3,7,4,1,5,6,2]=>[4,1,5,6,7,3,2]=>011001
[4,2,5,7,1,3,6]=>[7,4,1,2,5,3,6]=>[4,1,5,7,2,3,6]=>001001
[4,2,5,7,1,6,3]=>[7,4,6,2,5,1,3]=>[5,6,2,4,1,7,3]=>001011
[4,2,5,7,3,1,6]=>[3,7,4,1,5,2,6]=>[4,1,5,7,3,2,6]=>011001
[4,2,5,7,3,6,1]=>[6,4,7,2,5,3,1]=>[5,7,2,4,3,6,1]=>001011
[4,2,5,7,6,1,3]=>[6,4,1,2,5,7,3]=>[4,1,5,7,6,2,3]=>001011
[4,2,5,7,6,3,1]=>[3,6,4,1,5,7,2]=>[4,1,5,7,6,3,2]=>011011
[4,2,6,1,3,5,7]=>[6,4,1,2,3,5,7]=>[4,1,6,2,3,5,7]=>001010
[4,2,6,1,3,7,5]=>[6,4,1,2,7,3,5]=>[4,1,7,2,3,6,5]=>001011
[4,2,6,1,5,3,7]=>[6,4,5,2,1,3,7]=>[5,2,4,1,6,3,7]=>001110
[4,2,6,1,5,7,3]=>[6,4,7,2,1,5,3]=>[7,2,4,1,5,6,3]=>001011
[4,2,6,1,7,3,5]=>[6,4,7,2,3,1,5]=>[7,2,4,3,6,1,5]=>001011
[4,2,6,1,7,5,3]=>[6,4,5,2,7,1,3]=>[7,5,2,4,1,6,3]=>001111
[4,2,6,3,1,5,7]=>[3,6,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>011010
[4,2,6,3,1,7,5]=>[3,6,4,1,7,2,5]=>[4,1,7,3,2,6,5]=>011011
[4,2,6,3,5,1,7]=>[5,4,6,2,3,1,7]=>[6,2,4,3,5,1,7]=>001110
[4,2,6,3,5,7,1]=>[7,4,6,2,3,5,1]=>[6,2,4,3,5,7,1]=>001011
[4,2,6,3,7,1,5]=>[7,4,6,2,1,3,5]=>[6,2,4,1,7,3,5]=>001011
[4,2,6,3,7,5,1]=>[5,4,7,2,6,1,3]=>[6,2,4,1,7,5,3]=>001111
[4,2,6,5,1,3,7]=>[5,4,1,2,6,3,7]=>[4,1,6,5,2,3,7]=>001110
[4,2,6,5,1,7,3]=>[5,4,6,2,7,3,1]=>[7,2,4,3,6,5,1]=>001111
[4,2,6,5,3,1,7]=>[3,5,4,1,6,2,7]=>[4,1,6,5,3,2,7]=>011110
[4,2,6,5,3,7,1]=>[7,4,5,2,6,3,1]=>[6,5,2,4,3,7,1]=>001111
[4,2,6,5,7,1,3]=>[7,4,1,2,6,5,3]=>[4,1,6,5,7,2,3]=>001011
[4,2,6,5,7,3,1]=>[3,7,4,1,6,5,2]=>[4,1,6,5,7,3,2]=>011011
[4,2,6,7,1,3,5]=>[7,4,1,2,3,6,5]=>[4,1,6,7,2,3,5]=>001001
[4,2,6,7,1,5,3]=>[7,4,5,2,1,6,3]=>[5,2,4,1,6,7,3]=>001101
[4,2,6,7,3,1,5]=>[3,7,4,1,2,6,5]=>[4,1,6,7,3,2,5]=>011001
[4,2,6,7,3,5,1]=>[5,4,7,2,3,6,1]=>[6,7,2,4,3,5,1]=>001101
[4,2,6,7,5,1,3]=>[5,4,1,2,7,6,3]=>[4,1,6,7,5,2,3]=>001101
[4,2,6,7,5,3,1]=>[3,5,4,1,7,6,2]=>[4,1,6,7,5,3,2]=>011101
[4,2,7,1,3,5,6]=>[7,4,1,2,3,5,6]=>[4,1,7,2,3,5,6]=>001001
[4,2,7,1,3,6,5]=>[7,4,1,2,6,3,5]=>[4,1,6,2,3,7,5]=>001011
[4,2,7,1,5,3,6]=>[7,4,5,2,1,3,6]=>[5,2,4,1,7,3,6]=>001101
[4,2,7,1,5,6,3]=>[7,4,6,2,1,5,3]=>[6,2,4,1,5,7,3]=>001011
[4,2,7,1,6,3,5]=>[7,4,6,2,3,1,5]=>[6,2,4,3,7,1,5]=>001011
[4,2,7,1,6,5,3]=>[7,4,5,2,6,1,3]=>[6,5,2,4,1,7,3]=>001111
[4,2,7,3,1,5,6]=>[3,7,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>011001
[4,2,7,3,1,6,5]=>[3,7,4,1,6,2,5]=>[4,1,6,3,2,7,5]=>011011
[4,2,7,3,5,1,6]=>[5,4,7,2,3,1,6]=>[7,2,4,3,5,1,6]=>001101
[4,2,7,3,5,6,1]=>[6,4,7,2,3,5,1]=>[7,2,4,3,5,6,1]=>001011
[4,2,7,3,6,1,5]=>[6,4,7,2,1,3,5]=>[7,2,4,1,6,3,5]=>001011
[4,2,7,3,6,5,1]=>[5,4,6,2,7,1,3]=>[7,2,4,1,6,5,3]=>001111
[4,2,7,5,1,3,6]=>[5,4,1,2,7,3,6]=>[4,1,7,5,2,3,6]=>001101
[4,2,7,5,1,6,3]=>[5,4,7,2,6,3,1]=>[6,2,4,3,7,5,1]=>001111
[4,2,7,5,3,1,6]=>[3,5,4,1,7,2,6]=>[4,1,7,5,3,2,6]=>011101
[4,2,7,5,3,6,1]=>[6,4,5,2,7,3,1]=>[7,5,2,4,3,6,1]=>001111
[4,2,7,5,6,1,3]=>[6,4,1,2,7,5,3]=>[4,1,7,5,6,2,3]=>001011
[4,2,7,5,6,3,1]=>[3,6,4,1,7,5,2]=>[4,1,7,5,6,3,2]=>011011
[4,2,7,6,1,3,5]=>[6,4,1,2,3,7,5]=>[4,1,7,6,2,3,5]=>001011
[4,2,7,6,1,5,3]=>[6,4,5,2,1,7,3]=>[5,2,4,1,7,6,3]=>001111
[4,2,7,6,3,1,5]=>[3,6,4,1,2,7,5]=>[4,1,7,6,3,2,5]=>011011
[4,2,7,6,3,5,1]=>[5,4,6,2,3,7,1]=>[7,6,2,4,3,5,1]=>001111
[4,2,7,6,5,1,3]=>[5,4,1,2,6,7,3]=>[4,1,7,6,5,2,3]=>001111
[4,2,7,6,5,3,1]=>[3,5,4,1,6,7,2]=>[4,1,7,6,5,3,2]=>011111
[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[4,3,1,2,5,6,7]=>011000
[4,3,1,2,5,7,6]=>[3,1,4,2,5,7,6]=>[4,3,1,2,5,7,6]=>011001
[4,3,1,2,6,5,7]=>[3,1,4,2,6,5,7]=>[4,3,1,2,6,5,7]=>011010
[4,3,1,2,6,7,5]=>[3,1,4,2,7,6,5]=>[4,3,1,2,6,7,5]=>011001
[4,3,1,2,7,5,6]=>[3,1,4,2,7,5,6]=>[4,3,1,2,7,5,6]=>011001
[4,3,1,2,7,6,5]=>[3,1,4,2,6,7,5]=>[4,3,1,2,7,6,5]=>011011
[4,3,1,5,2,6,7]=>[3,4,5,2,1,6,7]=>[5,2,4,3,1,6,7]=>011100
[4,3,1,5,2,7,6]=>[3,4,5,2,1,7,6]=>[5,2,4,3,1,7,6]=>011101
[4,3,1,5,6,2,7]=>[3,4,6,2,5,1,7]=>[5,6,2,4,3,1,7]=>011010
[4,3,1,5,6,7,2]=>[3,4,7,2,5,6,1]=>[5,6,7,2,4,3,1]=>011001
[4,3,1,5,7,2,6]=>[3,4,7,2,5,1,6]=>[5,7,2,4,3,1,6]=>011001
[4,3,1,5,7,6,2]=>[3,4,6,2,5,7,1]=>[5,7,6,2,4,3,1]=>011011
[4,3,1,6,2,5,7]=>[3,4,6,2,1,5,7]=>[6,2,4,3,1,5,7]=>011010
[4,3,1,6,2,7,5]=>[3,4,6,2,7,1,5]=>[7,2,4,3,1,6,5]=>011011
[4,3,1,6,5,2,7]=>[3,4,5,2,6,1,7]=>[6,5,2,4,3,1,7]=>011110
[4,3,1,6,5,7,2]=>[3,4,7,2,6,5,1]=>[6,5,7,2,4,3,1]=>011011
[4,3,1,6,7,2,5]=>[3,4,7,2,1,6,5]=>[6,7,2,4,3,1,5]=>011001
[4,3,1,6,7,5,2]=>[3,4,5,2,7,6,1]=>[6,7,5,2,4,3,1]=>011101
[4,3,1,7,2,5,6]=>[3,4,7,2,1,5,6]=>[7,2,4,3,1,5,6]=>011001
[4,3,1,7,2,6,5]=>[3,4,7,2,6,1,5]=>[6,2,4,3,1,7,5]=>011011
[4,3,1,7,5,2,6]=>[3,4,5,2,7,1,6]=>[7,5,2,4,3,1,6]=>011101
[4,3,1,7,5,6,2]=>[3,4,6,2,7,5,1]=>[7,5,6,2,4,3,1]=>011011
[4,3,1,7,6,2,5]=>[3,4,6,2,1,7,5]=>[7,6,2,4,3,1,5]=>011011
[4,3,1,7,6,5,2]=>[3,4,5,2,6,7,1]=>[7,6,5,2,4,3,1]=>011111
[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>111001
[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>111010
[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>111001
[4,3,2,1,7,5,6]=>[2,3,4,1,7,5,6]=>[4,3,2,1,7,5,6]=>111001
[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>111011
[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[4,3,2,5,1,6,7]=>011100
[4,3,2,5,1,7,6]=>[5,3,4,2,1,7,6]=>[4,3,2,5,1,7,6]=>011101
[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[4,3,2,5,6,1,7]=>011010
[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[4,3,2,5,6,7,1]=>011001
[4,3,2,5,7,1,6]=>[7,3,4,2,5,1,6]=>[4,3,2,5,7,1,6]=>011001
[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]=>[4,3,2,5,7,6,1]=>011011
[4,3,2,6,1,5,7]=>[6,3,4,2,1,5,7]=>[4,3,2,6,1,5,7]=>011010
[4,3,2,6,1,7,5]=>[6,3,4,2,7,1,5]=>[4,3,2,7,1,6,5]=>011011
[4,3,2,6,5,1,7]=>[5,3,4,2,6,1,7]=>[4,3,2,6,5,1,7]=>011110
[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]=>[4,3,2,6,5,7,1]=>011011
[4,3,2,6,7,1,5]=>[7,3,4,2,1,6,5]=>[4,3,2,6,7,1,5]=>011001
[4,3,2,6,7,5,1]=>[5,3,4,2,7,6,1]=>[4,3,2,6,7,5,1]=>011101
[4,3,2,7,1,5,6]=>[7,3,4,2,1,5,6]=>[4,3,2,7,1,5,6]=>011001
[4,3,2,7,1,6,5]=>[7,3,4,2,6,1,5]=>[4,3,2,6,1,7,5]=>011011
[4,3,2,7,5,1,6]=>[5,3,4,2,7,1,6]=>[4,3,2,7,5,1,6]=>011101
[4,3,2,7,5,6,1]=>[6,3,4,2,7,5,1]=>[4,3,2,7,5,6,1]=>011011
[4,3,2,7,6,1,5]=>[6,3,4,2,1,7,5]=>[4,3,2,7,6,1,5]=>011011
[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]=>[4,3,2,7,6,5,1]=>011111
[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[4,3,5,1,2,6,7]=>001100
[4,3,5,1,2,7,6]=>[5,1,4,3,2,7,6]=>[4,3,5,1,2,7,6]=>001101
[4,3,5,1,6,2,7]=>[5,6,4,3,1,2,7]=>[4,3,6,1,5,2,7]=>001110
[4,3,5,1,6,7,2]=>[5,7,4,3,1,6,2]=>[4,3,6,7,1,5,2]=>001101
[4,3,5,1,7,2,6]=>[5,7,4,3,1,2,6]=>[4,3,7,1,5,2,6]=>001101
[4,3,5,1,7,6,2]=>[5,6,4,3,1,7,2]=>[4,3,7,6,1,5,2]=>001111
[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[4,3,5,2,1,6,7]=>101100
[4,3,5,2,1,7,6]=>[2,5,4,3,1,7,6]=>[4,3,5,2,1,7,6]=>101101
[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[4,3,5,2,6,1,7]=>001110
[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[4,3,5,2,6,7,1]=>001101
[4,3,5,2,7,1,6]=>[7,5,4,3,2,1,6]=>[4,3,5,2,7,1,6]=>001101
[4,3,5,2,7,6,1]=>[6,5,4,3,2,7,1]=>[4,3,5,2,7,6,1]=>001111
[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>[4,3,5,6,1,2,7]=>001010
[4,3,5,6,1,7,2]=>[6,7,4,3,5,1,2]=>[4,3,5,7,1,6,2]=>001011
[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[4,3,5,6,2,1,7]=>101010
[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[4,3,5,6,2,7,1]=>001011
[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>[4,3,5,6,7,1,2]=>001001
[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[4,3,5,6,7,2,1]=>101001
[4,3,5,7,1,2,6]=>[7,1,4,3,5,2,6]=>[4,3,5,7,1,2,6]=>001001
[4,3,5,7,1,6,2]=>[7,6,4,3,5,1,2]=>[4,3,5,6,1,7,2]=>001011
[4,3,5,7,2,1,6]=>[2,7,4,3,5,1,6]=>[4,3,5,7,2,1,6]=>101001
[4,3,5,7,2,6,1]=>[6,7,4,3,5,2,1]=>[4,3,5,7,2,6,1]=>001011
[4,3,5,7,6,1,2]=>[6,1,4,3,5,7,2]=>[4,3,5,7,6,1,2]=>001011
[4,3,5,7,6,2,1]=>[2,6,4,3,5,7,1]=>[4,3,5,7,6,2,1]=>101011
[4,3,6,1,2,5,7]=>[6,1,4,3,2,5,7]=>[4,3,6,1,2,5,7]=>001010
[4,3,6,1,2,7,5]=>[6,1,4,3,7,2,5]=>[4,3,7,1,2,6,5]=>001011
[4,3,6,1,5,2,7]=>[6,5,4,3,1,2,7]=>[4,3,5,1,6,2,7]=>001110
[4,3,6,1,5,7,2]=>[6,7,4,3,1,5,2]=>[4,3,7,1,5,6,2]=>001011
[4,3,6,1,7,2,5]=>[6,7,4,3,2,1,5]=>[4,3,7,2,6,1,5]=>001011
[4,3,6,1,7,5,2]=>[6,5,4,3,7,1,2]=>[4,3,7,5,1,6,2]=>001111
[4,3,6,2,1,5,7]=>[2,6,4,3,1,5,7]=>[4,3,6,2,1,5,7]=>101010
[4,3,6,2,1,7,5]=>[2,6,4,3,7,1,5]=>[4,3,7,2,1,6,5]=>101011
[4,3,6,2,5,1,7]=>[5,6,4,3,2,1,7]=>[4,3,6,2,5,1,7]=>001110
[4,3,6,2,5,7,1]=>[7,6,4,3,2,5,1]=>[4,3,6,2,5,7,1]=>001011
[4,3,6,2,7,1,5]=>[7,6,4,3,1,2,5]=>[4,3,6,1,7,2,5]=>001011
[4,3,6,2,7,5,1]=>[5,7,4,3,6,1,2]=>[4,3,6,1,7,5,2]=>001111
[4,3,6,5,1,2,7]=>[5,1,4,3,6,2,7]=>[4,3,6,5,1,2,7]=>001110
[4,3,6,5,1,7,2]=>[5,6,4,3,7,2,1]=>[4,3,7,2,6,5,1]=>001111
[4,3,6,5,2,1,7]=>[2,5,4,3,6,1,7]=>[4,3,6,5,2,1,7]=>101110
[4,3,6,5,2,7,1]=>[7,5,4,3,6,2,1]=>[4,3,6,5,2,7,1]=>001111
[4,3,6,5,7,1,2]=>[7,1,4,3,6,5,2]=>[4,3,6,5,7,1,2]=>001011
[4,3,6,5,7,2,1]=>[2,7,4,3,6,5,1]=>[4,3,6,5,7,2,1]=>101011
[4,3,6,7,1,2,5]=>[7,1,4,3,2,6,5]=>[4,3,6,7,1,2,5]=>001001
[4,3,6,7,1,5,2]=>[7,5,4,3,1,6,2]=>[4,3,5,1,6,7,2]=>001101
[4,3,6,7,2,1,5]=>[2,7,4,3,1,6,5]=>[4,3,6,7,2,1,5]=>101001
[4,3,6,7,2,5,1]=>[5,7,4,3,2,6,1]=>[4,3,6,7,2,5,1]=>001101
[4,3,6,7,5,1,2]=>[5,1,4,3,7,6,2]=>[4,3,6,7,5,1,2]=>001101
[4,3,6,7,5,2,1]=>[2,5,4,3,7,6,1]=>[4,3,6,7,5,2,1]=>101101
[4,3,7,1,2,5,6]=>[7,1,4,3,2,5,6]=>[4,3,7,1,2,5,6]=>001001
[4,3,7,1,2,6,5]=>[7,1,4,3,6,2,5]=>[4,3,6,1,2,7,5]=>001011
[4,3,7,1,5,2,6]=>[7,5,4,3,1,2,6]=>[4,3,5,1,7,2,6]=>001101
[4,3,7,1,5,6,2]=>[7,6,4,3,1,5,2]=>[4,3,6,1,5,7,2]=>001011
[4,3,7,1,6,2,5]=>[7,6,4,3,2,1,5]=>[4,3,6,2,7,1,5]=>001011
[4,3,7,1,6,5,2]=>[7,5,4,3,6,1,2]=>[4,3,6,5,1,7,2]=>001111
[4,3,7,2,1,5,6]=>[2,7,4,3,1,5,6]=>[4,3,7,2,1,5,6]=>101001
[4,3,7,2,1,6,5]=>[2,7,4,3,6,1,5]=>[4,3,6,2,1,7,5]=>101011
[4,3,7,2,5,1,6]=>[5,7,4,3,2,1,6]=>[4,3,7,2,5,1,6]=>001101
[4,3,7,2,5,6,1]=>[6,7,4,3,2,5,1]=>[4,3,7,2,5,6,1]=>001011
[4,3,7,2,6,1,5]=>[6,7,4,3,1,2,5]=>[4,3,7,1,6,2,5]=>001011
[4,3,7,2,6,5,1]=>[5,6,4,3,7,1,2]=>[4,3,7,1,6,5,2]=>001111
[4,3,7,5,1,2,6]=>[5,1,4,3,7,2,6]=>[4,3,7,5,1,2,6]=>001101
[4,3,7,5,1,6,2]=>[5,7,4,3,6,2,1]=>[4,3,6,2,7,5,1]=>001111
[4,3,7,5,2,1,6]=>[2,5,4,3,7,1,6]=>[4,3,7,5,2,1,6]=>101101
[4,3,7,5,2,6,1]=>[6,5,4,3,7,2,1]=>[4,3,7,5,2,6,1]=>001111
[4,3,7,5,6,1,2]=>[6,1,4,3,7,5,2]=>[4,3,7,5,6,1,2]=>001011
[4,3,7,5,6,2,1]=>[2,6,4,3,7,5,1]=>[4,3,7,5,6,2,1]=>101011
[4,3,7,6,1,2,5]=>[6,1,4,3,2,7,5]=>[4,3,7,6,1,2,5]=>001011
[4,3,7,6,1,5,2]=>[6,5,4,3,1,7,2]=>[4,3,5,1,7,6,2]=>001111
[4,3,7,6,2,1,5]=>[2,6,4,3,1,7,5]=>[4,3,7,6,2,1,5]=>101011
[4,3,7,6,2,5,1]=>[5,6,4,3,2,7,1]=>[4,3,7,6,2,5,1]=>001111
[4,3,7,6,5,1,2]=>[5,1,4,3,6,7,2]=>[4,3,7,6,5,1,2]=>001111
[4,3,7,6,5,2,1]=>[2,5,4,3,6,7,1]=>[4,3,7,6,5,2,1]=>101111
[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[4,5,1,2,3,6,7]=>000100
[4,5,1,2,3,7,6]=>[5,1,2,4,3,7,6]=>[4,5,1,2,3,7,6]=>000101
[4,5,1,2,6,3,7]=>[5,1,6,4,2,3,7]=>[4,6,1,2,5,3,7]=>000110
[4,5,1,2,6,7,3]=>[5,1,7,4,2,6,3]=>[4,6,7,1,2,5,3]=>000101
[4,5,1,2,7,3,6]=>[5,1,7,4,2,3,6]=>[4,7,1,2,5,3,6]=>000101
[4,5,1,2,7,6,3]=>[5,1,6,4,2,7,3]=>[4,7,6,1,2,5,3]=>000111
[4,5,1,3,2,6,7]=>[5,3,1,4,2,6,7]=>[3,1,4,5,2,6,7]=>010100
[4,5,1,3,2,7,6]=>[5,3,1,4,2,7,6]=>[3,1,4,5,2,7,6]=>010101
[4,5,1,3,6,2,7]=>[5,6,1,4,3,2,7]=>[4,6,1,3,5,2,7]=>000110
[4,5,1,3,6,7,2]=>[5,7,1,4,3,6,2]=>[4,6,7,1,3,5,2]=>000101
[4,5,1,3,7,2,6]=>[5,7,1,4,3,2,6]=>[4,7,1,3,5,2,6]=>000101
[4,5,1,3,7,6,2]=>[5,6,1,4,3,7,2]=>[4,7,6,1,3,5,2]=>000111
[4,5,1,6,2,3,7]=>[5,6,2,4,1,3,7]=>[4,6,2,5,1,3,7]=>000110
[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[4,7,1,6,2,5,3]=>000111
[4,5,1,6,3,2,7]=>[5,3,6,4,1,2,7]=>[4,6,3,1,5,2,7]=>010110
[4,5,1,6,3,7,2]=>[5,7,6,4,1,3,2]=>[4,6,1,7,3,5,2]=>000111
[4,5,1,6,7,2,3]=>[5,7,2,4,1,6,3]=>[4,6,7,2,5,1,3]=>000101
[4,5,1,6,7,3,2]=>[5,3,7,4,1,6,2]=>[4,6,7,3,1,5,2]=>010101
[4,5,1,7,2,3,6]=>[5,7,2,4,1,3,6]=>[4,7,2,5,1,3,6]=>000101
[4,5,1,7,2,6,3]=>[5,7,6,4,1,2,3]=>[4,6,1,7,2,5,3]=>000111
[4,5,1,7,3,2,6]=>[5,3,7,4,1,2,6]=>[4,7,3,1,5,2,6]=>010101
[4,5,1,7,3,6,2]=>[5,6,7,4,1,3,2]=>[4,7,1,6,3,5,2]=>000111
[4,5,1,7,6,2,3]=>[5,6,2,4,1,7,3]=>[4,7,6,2,5,1,3]=>000111
[4,5,1,7,6,3,2]=>[5,3,6,4,1,7,2]=>[4,7,6,3,1,5,2]=>010111
[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>[4,5,2,1,3,6,7]=>100100
[4,5,2,1,3,7,6]=>[2,5,1,4,3,7,6]=>[4,5,2,1,3,7,6]=>100101
[4,5,2,1,6,3,7]=>[2,5,6,4,1,3,7]=>[4,6,2,1,5,3,7]=>100110
[4,5,2,1,6,7,3]=>[2,5,7,4,1,6,3]=>[4,6,7,2,1,5,3]=>100101
[4,5,2,1,7,3,6]=>[2,5,7,4,1,3,6]=>[4,7,2,1,5,3,6]=>100101
[4,5,2,1,7,6,3]=>[2,5,6,4,1,7,3]=>[4,7,6,2,1,5,3]=>100111
[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>[4,5,2,3,1,6,7]=>010100
[4,5,2,3,1,7,6]=>[3,5,2,4,1,7,6]=>[4,5,2,3,1,7,6]=>010101
[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>[4,5,2,3,6,1,7]=>000110
[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>[4,5,2,3,6,7,1]=>000101
[4,5,2,3,7,1,6]=>[7,5,2,4,3,1,6]=>[4,5,2,3,7,1,6]=>000101
[4,5,2,3,7,6,1]=>[6,5,2,4,3,7,1]=>[4,5,2,3,7,6,1]=>000111
[4,5,2,6,1,3,7]=>[6,5,1,4,2,3,7]=>[4,5,1,6,2,3,7]=>000110
[4,5,2,6,1,7,3]=>[6,5,7,4,2,1,3]=>[4,7,2,5,1,6,3]=>000111
[4,5,2,6,3,1,7]=>[3,6,5,4,1,2,7]=>[4,5,1,6,3,2,7]=>010110
[4,5,2,6,3,7,1]=>[7,5,6,4,2,3,1]=>[4,6,2,5,3,7,1]=>000111
[4,5,2,6,7,1,3]=>[7,5,1,4,2,6,3]=>[4,5,1,6,7,2,3]=>000101
[4,5,2,6,7,3,1]=>[3,7,5,4,1,6,2]=>[4,5,1,6,7,3,2]=>010101
[4,5,2,7,1,3,6]=>[7,5,1,4,2,3,6]=>[4,5,1,7,2,3,6]=>000101
[4,5,2,7,1,6,3]=>[7,5,6,4,2,1,3]=>[4,6,2,5,1,7,3]=>000111
[4,5,2,7,3,1,6]=>[3,7,5,4,1,2,6]=>[4,5,1,7,3,2,6]=>010101
[4,5,2,7,3,6,1]=>[6,5,7,4,2,3,1]=>[4,7,2,5,3,6,1]=>000111
[4,5,2,7,6,1,3]=>[6,5,1,4,2,7,3]=>[4,5,1,7,6,2,3]=>000111
[4,5,2,7,6,3,1]=>[3,6,5,4,1,7,2]=>[4,5,1,7,6,3,2]=>010111
[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>[4,5,3,1,2,6,7]=>010100
[4,5,3,1,2,7,6]=>[3,1,5,4,2,7,6]=>[4,5,3,1,2,7,6]=>010101
[4,5,3,1,6,2,7]=>[3,5,6,4,2,1,7]=>[4,6,2,5,3,1,7]=>010110
[4,5,3,1,6,7,2]=>[3,5,7,4,2,6,1]=>[4,6,7,2,5,3,1]=>010101
[4,5,3,1,7,2,6]=>[3,5,7,4,2,1,6]=>[4,7,2,5,3,1,6]=>010101
[4,5,3,1,7,6,2]=>[3,5,6,4,2,7,1]=>[4,7,6,2,5,3,1]=>010111
[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[4,5,3,2,1,6,7]=>110100
[4,5,3,2,1,7,6]=>[2,3,5,4,1,7,6]=>[4,5,3,2,1,7,6]=>110101
[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[4,5,3,2,6,1,7]=>010110
[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[4,5,3,2,6,7,1]=>010101
[4,5,3,2,7,1,6]=>[7,3,5,4,2,1,6]=>[4,5,3,2,7,1,6]=>010101
[4,5,3,2,7,6,1]=>[6,3,5,4,2,7,1]=>[4,5,3,2,7,6,1]=>010111
[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>[4,5,3,6,1,2,7]=>000110
[4,5,3,6,1,7,2]=>[6,7,5,4,3,1,2]=>[4,5,3,7,1,6,2]=>000111
[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[4,5,3,6,2,1,7]=>100110
[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[4,5,3,6,2,7,1]=>000111
[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>[4,5,3,6,7,1,2]=>000101
[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[4,5,3,6,7,2,1]=>100101
[4,5,3,7,1,2,6]=>[7,1,5,4,3,2,6]=>[4,5,3,7,1,2,6]=>000101
[4,5,3,7,1,6,2]=>[7,6,5,4,3,1,2]=>[4,5,3,6,1,7,2]=>000111
[4,5,3,7,2,1,6]=>[2,7,5,4,3,1,6]=>[4,5,3,7,2,1,6]=>100101
[4,5,3,7,2,6,1]=>[6,7,5,4,3,2,1]=>[4,5,3,7,2,6,1]=>000111
[4,5,3,7,6,1,2]=>[6,1,5,4,3,7,2]=>[4,5,3,7,6,1,2]=>000111
[4,5,3,7,6,2,1]=>[2,6,5,4,3,7,1]=>[4,5,3,7,6,2,1]=>100111
[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[4,5,6,1,2,3,7]=>000010
[4,5,6,1,2,7,3]=>[6,1,7,4,5,2,3]=>[4,5,7,1,2,6,3]=>000011
[4,5,6,1,3,2,7]=>[6,3,1,4,5,2,7]=>[3,1,4,5,6,2,7]=>010010
[4,5,6,1,3,7,2]=>[6,7,1,4,5,3,2]=>[4,5,7,1,3,6,2]=>000011
[4,5,6,1,7,2,3]=>[6,7,2,4,5,1,3]=>[4,5,7,2,6,1,3]=>000011
[4,5,6,1,7,3,2]=>[6,3,7,4,5,1,2]=>[4,5,7,3,1,6,2]=>010011
[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>[4,5,6,2,1,3,7]=>100010
[4,5,6,2,1,7,3]=>[2,6,7,4,5,1,3]=>[4,5,7,2,1,6,3]=>100011
[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>[4,5,6,2,3,1,7]=>010010
[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>[4,5,6,2,3,7,1]=>000011
[4,5,6,2,7,1,3]=>[7,6,1,4,5,2,3]=>[4,5,6,1,7,2,3]=>000011
[4,5,6,2,7,3,1]=>[3,7,6,4,5,1,2]=>[4,5,6,1,7,3,2]=>010011
[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>[4,5,6,3,1,2,7]=>010010
[4,5,6,3,1,7,2]=>[3,6,7,4,5,2,1]=>[4,5,7,2,6,3,1]=>010011
[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[4,5,6,3,2,1,7]=>110010
[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[4,5,6,3,2,7,1]=>010011
[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>[4,5,6,3,7,1,2]=>000011
[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[4,5,6,3,7,2,1]=>100011
[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[4,5,6,7,1,2,3]=>000001
[4,5,6,7,1,3,2]=>[7,3,1,4,5,6,2]=>[3,1,4,5,6,7,2]=>010001
[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>[4,5,6,7,2,1,3]=>100001
[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>[4,5,6,7,2,3,1]=>010001
[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>[4,5,6,7,3,1,2]=>010001
[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[4,5,6,7,3,2,1]=>110001
[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[4,5,7,1,2,3,6]=>000001
[4,5,7,1,2,6,3]=>[7,1,6,4,5,2,3]=>[4,5,6,1,2,7,3]=>000011
[4,5,7,1,3,2,6]=>[7,3,1,4,5,2,6]=>[3,1,4,5,7,2,6]=>010001
[4,5,7,1,3,6,2]=>[7,6,1,4,5,3,2]=>[4,5,6,1,3,7,2]=>000011
[4,5,7,1,6,2,3]=>[7,6,2,4,5,1,3]=>[4,5,6,2,7,1,3]=>000011
[4,5,7,1,6,3,2]=>[7,3,6,4,5,1,2]=>[4,5,6,3,1,7,2]=>010011
[4,5,7,2,1,3,6]=>[2,7,1,4,5,3,6]=>[4,5,7,2,1,3,6]=>100001
[4,5,7,2,1,6,3]=>[2,7,6,4,5,1,3]=>[4,5,6,2,1,7,3]=>100011
[4,5,7,2,3,1,6]=>[3,7,2,4,5,1,6]=>[4,5,7,2,3,1,6]=>010001
[4,5,7,2,3,6,1]=>[6,7,2,4,5,3,1]=>[4,5,7,2,3,6,1]=>000011
[4,5,7,2,6,1,3]=>[6,7,1,4,5,2,3]=>[4,5,7,1,6,2,3]=>000011
[4,5,7,2,6,3,1]=>[3,6,7,4,5,1,2]=>[4,5,7,1,6,3,2]=>010011
[4,5,7,3,1,2,6]=>[3,1,7,4,5,2,6]=>[4,5,7,3,1,2,6]=>010001
[4,5,7,3,1,6,2]=>[3,7,6,4,5,2,1]=>[4,5,6,2,7,3,1]=>010011
[4,5,7,3,2,1,6]=>[2,3,7,4,5,1,6]=>[4,5,7,3,2,1,6]=>110001
[4,5,7,3,2,6,1]=>[6,3,7,4,5,2,1]=>[4,5,7,3,2,6,1]=>010011
[4,5,7,3,6,1,2]=>[6,1,7,4,5,3,2]=>[4,5,7,3,6,1,2]=>000011
[4,5,7,3,6,2,1]=>[2,6,7,4,5,3,1]=>[4,5,7,3,6,2,1]=>100011
[4,5,7,6,1,2,3]=>[6,1,2,4,5,7,3]=>[4,5,7,6,1,2,3]=>000011
[4,5,7,6,1,3,2]=>[6,3,1,4,5,7,2]=>[3,1,4,5,7,6,2]=>010011
[4,5,7,6,2,1,3]=>[2,6,1,4,5,7,3]=>[4,5,7,6,2,1,3]=>100011
[4,5,7,6,2,3,1]=>[3,6,2,4,5,7,1]=>[4,5,7,6,2,3,1]=>010011
[4,5,7,6,3,1,2]=>[3,1,6,4,5,7,2]=>[4,5,7,6,3,1,2]=>010011
[4,5,7,6,3,2,1]=>[2,3,6,4,5,7,1]=>[4,5,7,6,3,2,1]=>110011
[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>[4,6,1,2,3,5,7]=>000010
[4,6,1,2,3,7,5]=>[6,1,2,4,7,3,5]=>[4,7,1,2,3,6,5]=>000011
[4,6,1,2,5,3,7]=>[6,1,5,4,2,3,7]=>[4,5,1,2,6,3,7]=>000110
[4,6,1,2,5,7,3]=>[6,1,7,4,2,5,3]=>[4,7,1,2,5,6,3]=>000011
[4,6,1,2,7,3,5]=>[6,1,7,4,3,2,5]=>[4,7,3,6,1,2,5]=>000011
[4,6,1,2,7,5,3]=>[6,1,5,4,7,2,3]=>[4,7,5,1,2,6,3]=>000111
[4,6,1,3,2,5,7]=>[6,3,1,4,2,5,7]=>[3,1,4,6,2,5,7]=>010010
[4,6,1,3,2,7,5]=>[6,3,1,4,7,2,5]=>[3,1,4,7,2,6,5]=>010011
[4,6,1,3,5,2,7]=>[6,5,1,4,3,2,7]=>[4,5,1,3,6,2,7]=>000110
[4,6,1,3,5,7,2]=>[6,7,1,4,3,5,2]=>[4,7,1,3,5,6,2]=>000011
[4,6,1,3,7,2,5]=>[6,7,1,4,2,3,5]=>[4,7,1,6,2,3,5]=>000011
[4,6,1,3,7,5,2]=>[6,5,1,4,7,3,2]=>[4,7,5,1,3,6,2]=>000111
[4,6,1,5,2,3,7]=>[6,5,2,4,1,3,7]=>[4,5,2,6,1,3,7]=>000110
[4,6,1,5,2,7,3]=>[6,5,7,4,1,2,3]=>[4,7,1,5,2,6,3]=>000111
[4,6,1,5,3,2,7]=>[6,3,5,4,1,2,7]=>[4,5,3,1,6,2,7]=>010110
[4,6,1,5,3,7,2]=>[6,7,5,4,1,3,2]=>[4,5,1,7,3,6,2]=>000111
[4,6,1,5,7,2,3]=>[6,7,2,4,1,5,3]=>[4,7,2,5,6,1,3]=>000011
[4,6,1,5,7,3,2]=>[6,3,7,4,1,5,2]=>[4,7,3,1,5,6,2]=>010011
[4,6,1,7,2,3,5]=>[6,7,2,4,3,1,5]=>[4,7,2,3,6,1,5]=>000011
[4,6,1,7,2,5,3]=>[6,7,5,4,2,1,3]=>[4,5,2,7,1,6,3]=>000111
[4,6,1,7,3,2,5]=>[6,3,7,4,2,1,5]=>[4,7,3,2,6,1,5]=>010011
[4,6,1,7,3,5,2]=>[6,5,7,4,3,1,2]=>[4,7,3,5,1,6,2]=>000111
[4,6,1,7,5,2,3]=>[6,5,2,4,7,1,3]=>[4,7,5,2,6,1,3]=>000111
[4,6,1,7,5,3,2]=>[6,3,5,4,7,1,2]=>[4,7,5,3,1,6,2]=>010111
[4,6,2,1,3,5,7]=>[2,6,1,4,3,5,7]=>[4,6,2,1,3,5,7]=>100010
[4,6,2,1,3,7,5]=>[2,6,1,4,7,3,5]=>[4,7,2,1,3,6,5]=>100011
[4,6,2,1,5,3,7]=>[2,6,5,4,1,3,7]=>[4,5,2,1,6,3,7]=>100110
[4,6,2,1,5,7,3]=>[2,6,7,4,1,5,3]=>[4,7,2,1,5,6,3]=>100011
[4,6,2,1,7,3,5]=>[2,6,7,4,3,1,5]=>[4,7,3,6,2,1,5]=>100011
[4,6,2,1,7,5,3]=>[2,6,5,4,7,1,3]=>[4,7,5,2,1,6,3]=>100111
[4,6,2,3,1,5,7]=>[3,6,2,4,1,5,7]=>[4,6,2,3,1,5,7]=>010010
[4,6,2,3,1,7,5]=>[3,6,2,4,7,1,5]=>[4,7,2,3,1,6,5]=>010011
[4,6,2,3,5,1,7]=>[5,6,2,4,3,1,7]=>[4,6,2,3,5,1,7]=>000110
[4,6,2,3,5,7,1]=>[7,6,2,4,3,5,1]=>[4,6,2,3,5,7,1]=>000011
[4,6,2,3,7,1,5]=>[7,6,2,4,1,3,5]=>[4,6,2,7,1,3,5]=>000011
[4,6,2,3,7,5,1]=>[5,7,1,4,6,3,2]=>[4,6,1,3,7,5,2]=>000111
[4,6,2,5,1,3,7]=>[5,6,1,4,2,3,7]=>[4,6,1,5,2,3,7]=>000110
[4,6,2,5,1,7,3]=>[5,6,7,4,2,1,3]=>[4,7,2,6,1,5,3]=>000111
[4,6,2,5,3,1,7]=>[3,5,6,4,1,2,7]=>[4,6,1,5,3,2,7]=>010110
[4,6,2,5,3,7,1]=>[7,6,5,4,2,3,1]=>[4,5,2,6,3,7,1]=>000111
[4,6,2,5,7,1,3]=>[7,6,1,4,2,5,3]=>[4,6,1,5,7,2,3]=>000011
[4,6,2,5,7,3,1]=>[3,7,6,4,1,5,2]=>[4,6,1,5,7,3,2]=>010011
[4,6,2,7,1,3,5]=>[7,6,1,4,3,2,5]=>[4,6,1,3,7,2,5]=>000011
[4,6,2,7,1,5,3]=>[7,6,5,4,1,2,3]=>[4,5,1,6,2,7,3]=>000111
[4,6,2,7,3,1,5]=>[3,7,6,4,2,1,5]=>[4,6,2,7,3,1,5]=>010011
[4,6,2,7,3,5,1]=>[5,6,7,4,3,2,1]=>[4,7,3,6,2,5,1]=>000111
[4,6,2,7,5,1,3]=>[5,7,2,4,6,1,3]=>[4,6,2,7,5,1,3]=>000111
[4,6,2,7,5,3,1]=>[3,5,7,4,6,2,1]=>[4,6,2,7,5,3,1]=>010111
[4,6,3,1,2,5,7]=>[3,1,6,4,2,5,7]=>[4,6,3,1,2,5,7]=>010010
[4,6,3,1,2,7,5]=>[3,1,6,4,7,2,5]=>[4,7,3,1,2,6,5]=>010011
[4,6,3,1,5,2,7]=>[3,6,5,4,2,1,7]=>[4,5,2,6,3,1,7]=>010110
[4,6,3,1,5,7,2]=>[3,6,7,4,2,5,1]=>[4,7,2,5,6,3,1]=>010011
[4,6,3,1,7,2,5]=>[3,6,7,4,1,2,5]=>[4,7,1,6,3,2,5]=>010011
[4,6,3,1,7,5,2]=>[3,6,5,4,7,2,1]=>[4,7,5,2,6,3,1]=>010111
[4,6,3,2,1,5,7]=>[2,3,6,4,1,5,7]=>[4,6,3,2,1,5,7]=>110010
[4,6,3,2,1,7,5]=>[2,3,6,4,7,1,5]=>[4,7,3,2,1,6,5]=>110011
[4,6,3,2,5,1,7]=>[5,3,6,4,2,1,7]=>[4,6,3,2,5,1,7]=>010110
[4,6,3,2,5,7,1]=>[7,3,6,4,2,5,1]=>[4,6,3,2,5,7,1]=>010011
[4,6,3,2,7,1,5]=>[7,3,6,4,1,2,5]=>[4,6,3,1,7,2,5]=>010011
[4,6,3,2,7,5,1]=>[5,3,7,4,6,1,2]=>[4,6,3,1,7,5,2]=>010111
[4,6,3,5,1,2,7]=>[5,1,6,4,3,2,7]=>[4,6,3,5,1,2,7]=>000110
[4,6,3,5,1,7,2]=>[5,7,6,4,3,1,2]=>[4,6,3,7,1,5,2]=>000111
[4,6,3,5,2,1,7]=>[2,5,6,4,3,1,7]=>[4,6,3,5,2,1,7]=>100110
[4,6,3,5,2,7,1]=>[7,5,6,4,3,2,1]=>[4,6,3,5,2,7,1]=>000111
[4,6,3,5,7,1,2]=>[7,1,6,4,3,5,2]=>[4,6,3,5,7,1,2]=>000011
[4,6,3,5,7,2,1]=>[2,7,6,4,3,5,1]=>[4,6,3,5,7,2,1]=>100011
[4,6,3,7,1,2,5]=>[7,1,6,4,2,3,5]=>[4,6,1,2,7,3,5]=>000011
[4,6,3,7,1,5,2]=>[7,5,6,4,1,3,2]=>[4,6,1,5,3,7,2]=>000111
[4,6,3,7,2,1,5]=>[2,7,6,4,1,3,5]=>[4,6,2,1,7,3,5]=>100011
[4,6,3,7,2,5,1]=>[5,7,6,4,2,3,1]=>[4,6,2,7,3,5,1]=>000111
[4,6,3,7,5,1,2]=>[5,1,7,4,6,2,3]=>[4,6,1,2,7,5,3]=>000111
[4,6,3,7,5,2,1]=>[2,5,7,4,6,1,3]=>[4,6,2,1,7,5,3]=>100111
[4,6,5,1,2,3,7]=>[5,1,2,4,6,3,7]=>[4,6,5,1,2,3,7]=>000110
[4,6,5,1,2,7,3]=>[5,1,6,4,7,3,2]=>[4,7,3,6,5,1,2]=>000111
[4,6,5,1,3,2,7]=>[5,3,1,4,6,2,7]=>[3,1,4,6,5,2,7]=>010110
[4,6,5,1,3,7,2]=>[5,6,2,4,7,3,1]=>[4,7,2,3,6,5,1]=>000111
[4,6,5,1,7,2,3]=>[5,6,1,4,7,2,3]=>[4,7,1,6,5,2,3]=>000111
[4,6,5,1,7,3,2]=>[5,3,6,4,7,2,1]=>[4,7,3,2,6,5,1]=>010111
[4,6,5,2,1,3,7]=>[2,5,1,4,6,3,7]=>[4,6,5,2,1,3,7]=>100110
[4,6,5,2,1,7,3]=>[2,5,6,4,7,3,1]=>[4,7,3,6,5,2,1]=>100111
[4,6,5,2,3,1,7]=>[3,5,2,4,6,1,7]=>[4,6,5,2,3,1,7]=>010110
[4,6,5,2,3,7,1]=>[7,5,2,4,6,3,1]=>[4,6,5,2,3,7,1]=>000111
[4,6,5,2,7,1,3]=>[7,5,1,4,6,2,3]=>[4,6,5,1,7,2,3]=>000111
[4,6,5,2,7,3,1]=>[3,7,5,4,6,1,2]=>[4,6,5,1,7,3,2]=>010111
[4,6,5,3,1,2,7]=>[3,1,5,4,6,2,7]=>[4,6,5,3,1,2,7]=>010110
[4,6,5,3,1,7,2]=>[3,5,6,4,7,1,2]=>[4,7,1,6,5,3,2]=>010111
[4,6,5,3,2,1,7]=>[2,3,5,4,6,1,7]=>[4,6,5,3,2,1,7]=>110110
[4,6,5,3,2,7,1]=>[7,3,5,4,6,2,1]=>[4,6,5,3,2,7,1]=>010111
[4,6,5,3,7,1,2]=>[7,1,5,4,6,3,2]=>[4,6,5,3,7,1,2]=>000111
[4,6,5,3,7,2,1]=>[2,7,5,4,6,3,1]=>[4,6,5,3,7,2,1]=>100111
[4,6,5,7,1,2,3]=>[7,1,2,4,6,5,3]=>[4,6,5,7,1,2,3]=>000011
[4,6,5,7,1,3,2]=>[7,3,1,4,6,5,2]=>[3,1,4,6,5,7,2]=>010011
[4,6,5,7,2,1,3]=>[2,7,1,4,6,5,3]=>[4,6,5,7,2,1,3]=>100011
[4,6,5,7,2,3,1]=>[3,7,2,4,6,5,1]=>[4,6,5,7,2,3,1]=>010011
[4,6,5,7,3,1,2]=>[3,1,7,4,6,5,2]=>[4,6,5,7,3,1,2]=>010011
[4,6,5,7,3,2,1]=>[2,3,7,4,6,5,1]=>[4,6,5,7,3,2,1]=>110011
[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[4,6,7,1,2,3,5]=>000001
[4,6,7,1,2,5,3]=>[7,1,5,4,2,6,3]=>[4,5,1,2,6,7,3]=>000101
[4,6,7,1,3,2,5]=>[7,3,1,4,2,6,5]=>[3,1,4,6,7,2,5]=>010001
[4,6,7,1,3,5,2]=>[7,5,1,4,3,6,2]=>[4,5,1,3,6,7,2]=>000101
[4,6,7,1,5,2,3]=>[7,5,2,4,1,6,3]=>[4,5,2,6,7,1,3]=>000101
[4,6,7,1,5,3,2]=>[7,3,5,4,1,6,2]=>[4,5,3,1,6,7,2]=>010101
[4,6,7,2,1,3,5]=>[2,7,1,4,3,6,5]=>[4,6,7,2,1,3,5]=>100001
[4,6,7,2,1,5,3]=>[2,7,5,4,1,6,3]=>[4,5,2,1,6,7,3]=>100101
[4,6,7,2,3,1,5]=>[3,7,2,4,1,6,5]=>[4,6,7,2,3,1,5]=>010001
[4,6,7,2,3,5,1]=>[5,7,2,4,3,6,1]=>[4,6,7,2,3,5,1]=>000101
[4,6,7,2,5,1,3]=>[5,7,1,4,2,6,3]=>[4,6,7,1,5,2,3]=>000101
[4,6,7,2,5,3,1]=>[3,5,7,4,1,6,2]=>[4,6,7,1,5,3,2]=>010101
[4,6,7,3,1,2,5]=>[3,1,7,4,2,6,5]=>[4,6,7,3,1,2,5]=>010001
[4,6,7,3,1,5,2]=>[3,7,5,4,2,6,1]=>[4,5,2,6,7,3,1]=>010101
[4,6,7,3,2,1,5]=>[2,3,7,4,1,6,5]=>[4,6,7,3,2,1,5]=>110001
[4,6,7,3,2,5,1]=>[5,3,7,4,2,6,1]=>[4,6,7,3,2,5,1]=>010101
[4,6,7,3,5,1,2]=>[5,1,7,4,3,6,2]=>[4,6,7,3,5,1,2]=>000101
[4,6,7,3,5,2,1]=>[2,5,7,4,3,6,1]=>[4,6,7,3,5,2,1]=>100101
[4,6,7,5,1,2,3]=>[5,1,2,4,7,6,3]=>[4,6,7,5,1,2,3]=>000101
[4,6,7,5,1,3,2]=>[5,3,1,4,7,6,2]=>[3,1,4,6,7,5,2]=>010101
[4,6,7,5,2,1,3]=>[2,5,1,4,7,6,3]=>[4,6,7,5,2,1,3]=>100101
[4,6,7,5,2,3,1]=>[3,5,2,4,7,6,1]=>[4,6,7,5,2,3,1]=>010101
[4,6,7,5,3,1,2]=>[3,1,5,4,7,6,2]=>[4,6,7,5,3,1,2]=>010101
[4,6,7,5,3,2,1]=>[2,3,5,4,7,6,1]=>[4,6,7,5,3,2,1]=>110101
[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[4,7,1,2,3,5,6]=>000001
[4,7,1,2,3,6,5]=>[7,1,2,4,6,3,5]=>[4,6,1,2,3,7,5]=>000011
[4,7,1,2,5,3,6]=>[7,1,5,4,2,3,6]=>[4,5,1,2,7,3,6]=>000101
[4,7,1,2,5,6,3]=>[7,1,6,4,2,5,3]=>[4,6,1,2,5,7,3]=>000011
[4,7,1,2,6,3,5]=>[7,1,6,4,3,2,5]=>[4,6,3,7,1,2,5]=>000011
[4,7,1,2,6,5,3]=>[7,1,5,4,6,2,3]=>[4,6,5,1,2,7,3]=>000111
[4,7,1,3,2,5,6]=>[7,3,1,4,2,5,6]=>[3,1,4,7,2,5,6]=>010001
[4,7,1,3,2,6,5]=>[7,3,1,4,6,2,5]=>[3,1,4,6,2,7,5]=>010011
[4,7,1,3,5,2,6]=>[7,5,1,4,3,2,6]=>[4,5,1,3,7,2,6]=>000101
[4,7,1,3,5,6,2]=>[7,6,1,4,3,5,2]=>[4,6,1,3,5,7,2]=>000011
[4,7,1,3,6,2,5]=>[7,6,1,4,2,3,5]=>[4,6,1,7,2,3,5]=>000011
[4,7,1,3,6,5,2]=>[7,5,1,4,6,3,2]=>[4,6,5,1,3,7,2]=>000111
[4,7,1,5,2,3,6]=>[7,5,2,4,1,3,6]=>[4,5,2,7,1,3,6]=>000101
[4,7,1,5,2,6,3]=>[7,5,6,4,1,2,3]=>[4,6,1,5,2,7,3]=>000111
[4,7,1,5,3,2,6]=>[7,3,5,4,1,2,6]=>[4,5,3,1,7,2,6]=>010101
[4,7,1,5,3,6,2]=>[7,6,5,4,1,3,2]=>[4,5,1,6,3,7,2]=>000111
[4,7,1,5,6,2,3]=>[7,6,2,4,1,5,3]=>[4,6,2,5,7,1,3]=>000011
[4,7,1,5,6,3,2]=>[7,3,6,4,1,5,2]=>[4,6,3,1,5,7,2]=>010011
[4,7,1,6,2,3,5]=>[7,6,2,4,3,1,5]=>[4,6,2,3,7,1,5]=>000011
[4,7,1,6,2,5,3]=>[7,6,5,4,2,1,3]=>[4,5,2,6,1,7,3]=>000111
[4,7,1,6,3,2,5]=>[7,3,6,4,2,1,5]=>[4,6,3,2,7,1,5]=>010011
[4,7,1,6,3,5,2]=>[7,5,6,4,3,1,2]=>[4,6,3,5,1,7,2]=>000111
[4,7,1,6,5,2,3]=>[7,5,2,4,6,1,3]=>[4,6,5,2,7,1,3]=>000111
[4,7,1,6,5,3,2]=>[7,3,5,4,6,1,2]=>[4,6,5,3,1,7,2]=>010111
[4,7,2,1,3,5,6]=>[2,7,1,4,3,5,6]=>[4,7,2,1,3,5,6]=>100001
[4,7,2,1,3,6,5]=>[2,7,1,4,6,3,5]=>[4,6,2,1,3,7,5]=>100011
[4,7,2,1,5,3,6]=>[2,7,5,4,1,3,6]=>[4,5,2,1,7,3,6]=>100101
[4,7,2,1,5,6,3]=>[2,7,6,4,1,5,3]=>[4,6,2,1,5,7,3]=>100011
[4,7,2,1,6,3,5]=>[2,7,6,4,3,1,5]=>[4,6,3,7,2,1,5]=>100011
[4,7,2,1,6,5,3]=>[2,7,5,4,6,1,3]=>[4,6,5,2,1,7,3]=>100111
[4,7,2,3,1,5,6]=>[3,7,2,4,1,5,6]=>[4,7,2,3,1,5,6]=>010001
[4,7,2,3,1,6,5]=>[3,7,2,4,6,1,5]=>[4,6,2,3,1,7,5]=>010011
[4,7,2,3,5,1,6]=>[5,7,2,4,3,1,6]=>[4,7,2,3,5,1,6]=>000101
[4,7,2,3,5,6,1]=>[6,7,2,4,3,5,1]=>[4,7,2,3,5,6,1]=>000011
[4,7,2,3,6,1,5]=>[6,7,2,4,1,3,5]=>[4,7,2,6,1,3,5]=>000011
[4,7,2,3,6,5,1]=>[5,6,1,4,7,3,2]=>[4,7,1,3,6,5,2]=>000111
[4,7,2,5,1,3,6]=>[5,7,1,4,2,3,6]=>[4,7,1,5,2,3,6]=>000101
[4,7,2,5,1,6,3]=>[5,7,6,4,2,1,3]=>[4,6,2,7,1,5,3]=>000111
[4,7,2,5,3,1,6]=>[3,5,7,4,1,2,6]=>[4,7,1,5,3,2,6]=>010101
[4,7,2,5,3,6,1]=>[6,7,5,4,2,3,1]=>[4,5,2,7,3,6,1]=>000111
[4,7,2,5,6,1,3]=>[6,7,1,4,2,5,3]=>[4,7,1,5,6,2,3]=>000011
[4,7,2,5,6,3,1]=>[3,6,7,4,1,5,2]=>[4,7,1,5,6,3,2]=>010011
[4,7,2,6,1,3,5]=>[6,7,1,4,3,2,5]=>[4,7,1,3,6,2,5]=>000011
[4,7,2,6,1,5,3]=>[6,7,5,4,1,2,3]=>[4,5,1,7,2,6,3]=>000111
[4,7,2,6,3,1,5]=>[3,6,7,4,2,1,5]=>[4,7,2,6,3,1,5]=>010011
[4,7,2,6,3,5,1]=>[5,7,6,4,3,2,1]=>[4,6,3,7,2,5,1]=>000111
[4,7,2,6,5,1,3]=>[5,6,2,4,7,1,3]=>[4,7,2,6,5,1,3]=>000111
[4,7,2,6,5,3,1]=>[3,5,6,4,7,2,1]=>[4,7,2,6,5,3,1]=>010111
[4,7,3,1,2,5,6]=>[3,1,7,4,2,5,6]=>[4,7,3,1,2,5,6]=>010001
[4,7,3,1,2,6,5]=>[3,1,7,4,6,2,5]=>[4,6,3,1,2,7,5]=>010011
[4,7,3,1,5,2,6]=>[3,7,5,4,2,1,6]=>[4,5,2,7,3,1,6]=>010101
[4,7,3,1,5,6,2]=>[3,7,6,4,2,5,1]=>[4,6,2,5,7,3,1]=>010011
[4,7,3,1,6,2,5]=>[3,7,6,4,1,2,5]=>[4,6,1,7,3,2,5]=>010011
[4,7,3,1,6,5,2]=>[3,7,5,4,6,2,1]=>[4,6,5,2,7,3,1]=>010111
[4,7,3,2,1,5,6]=>[2,3,7,4,1,5,6]=>[4,7,3,2,1,5,6]=>110001
[4,7,3,2,1,6,5]=>[2,3,7,4,6,1,5]=>[4,6,3,2,1,7,5]=>110011
[4,7,3,2,5,1,6]=>[5,3,7,4,2,1,6]=>[4,7,3,2,5,1,6]=>010101
[4,7,3,2,5,6,1]=>[6,3,7,4,2,5,1]=>[4,7,3,2,5,6,1]=>010011
[4,7,3,2,6,1,5]=>[6,3,7,4,1,2,5]=>[4,7,3,1,6,2,5]=>010011
[4,7,3,2,6,5,1]=>[5,3,6,4,7,1,2]=>[4,7,3,1,6,5,2]=>010111
[4,7,3,5,1,2,6]=>[5,1,7,4,3,2,6]=>[4,7,3,5,1,2,6]=>000101
[4,7,3,5,1,6,2]=>[5,6,7,4,3,1,2]=>[4,7,3,6,1,5,2]=>000111
[4,7,3,5,2,1,6]=>[2,5,7,4,3,1,6]=>[4,7,3,5,2,1,6]=>100101
[4,7,3,5,2,6,1]=>[6,5,7,4,3,2,1]=>[4,7,3,5,2,6,1]=>000111
[4,7,3,5,6,1,2]=>[6,1,7,4,3,5,2]=>[4,7,3,5,6,1,2]=>000011
[4,7,3,5,6,2,1]=>[2,6,7,4,3,5,1]=>[4,7,3,5,6,2,1]=>100011
[4,7,3,6,1,2,5]=>[6,1,7,4,2,3,5]=>[4,7,1,2,6,3,5]=>000011
[4,7,3,6,1,5,2]=>[6,5,7,4,1,3,2]=>[4,7,1,5,3,6,2]=>000111
[4,7,3,6,2,1,5]=>[2,6,7,4,1,3,5]=>[4,7,2,1,6,3,5]=>100011
[4,7,3,6,2,5,1]=>[5,6,7,4,2,3,1]=>[4,7,2,6,3,5,1]=>000111
[4,7,3,6,5,1,2]=>[5,1,6,4,7,2,3]=>[4,7,1,2,6,5,3]=>000111
[4,7,3,6,5,2,1]=>[2,5,6,4,7,1,3]=>[4,7,2,1,6,5,3]=>100111
[4,7,5,1,2,3,6]=>[5,1,2,4,7,3,6]=>[4,7,5,1,2,3,6]=>000101
[4,7,5,1,2,6,3]=>[5,1,7,4,6,3,2]=>[4,6,3,7,5,1,2]=>000111
[4,7,5,1,3,2,6]=>[5,3,1,4,7,2,6]=>[3,1,4,7,5,2,6]=>010101
[4,7,5,1,3,6,2]=>[5,7,2,4,6,3,1]=>[4,6,2,3,7,5,1]=>000111
[4,7,5,1,6,2,3]=>[5,7,1,4,6,2,3]=>[4,6,1,7,5,2,3]=>000111
[4,7,5,1,6,3,2]=>[5,3,7,4,6,2,1]=>[4,6,3,2,7,5,1]=>010111
[4,7,5,2,1,3,6]=>[2,5,1,4,7,3,6]=>[4,7,5,2,1,3,6]=>100101
[4,7,5,2,1,6,3]=>[2,5,7,4,6,3,1]=>[4,6,3,7,5,2,1]=>100111
[4,7,5,2,3,1,6]=>[3,5,2,4,7,1,6]=>[4,7,5,2,3,1,6]=>010101
[4,7,5,2,3,6,1]=>[6,5,2,4,7,3,1]=>[4,7,5,2,3,6,1]=>000111
[4,7,5,2,6,1,3]=>[6,5,1,4,7,2,3]=>[4,7,5,1,6,2,3]=>000111
[4,7,5,2,6,3,1]=>[3,6,5,4,7,1,2]=>[4,7,5,1,6,3,2]=>010111
[4,7,5,3,1,2,6]=>[3,1,5,4,7,2,6]=>[4,7,5,3,1,2,6]=>010101
[4,7,5,3,1,6,2]=>[3,5,7,4,6,1,2]=>[4,6,1,7,5,3,2]=>010111
[4,7,5,3,2,1,6]=>[2,3,5,4,7,1,6]=>[4,7,5,3,2,1,6]=>110101
[4,7,5,3,2,6,1]=>[6,3,5,4,7,2,1]=>[4,7,5,3,2,6,1]=>010111
[4,7,5,3,6,1,2]=>[6,1,5,4,7,3,2]=>[4,7,5,3,6,1,2]=>000111
[4,7,5,3,6,2,1]=>[2,6,5,4,7,3,1]=>[4,7,5,3,6,2,1]=>100111
[4,7,5,6,1,2,3]=>[6,1,2,4,7,5,3]=>[4,7,5,6,1,2,3]=>000011
[4,7,5,6,1,3,2]=>[6,3,1,4,7,5,2]=>[3,1,4,7,5,6,2]=>010011
[4,7,5,6,2,1,3]=>[2,6,1,4,7,5,3]=>[4,7,5,6,2,1,3]=>100011
[4,7,5,6,2,3,1]=>[3,6,2,4,7,5,1]=>[4,7,5,6,2,3,1]=>010011
[4,7,5,6,3,1,2]=>[3,1,6,4,7,5,2]=>[4,7,5,6,3,1,2]=>010011
[4,7,5,6,3,2,1]=>[2,3,6,4,7,5,1]=>[4,7,5,6,3,2,1]=>110011
[4,7,6,1,2,3,5]=>[6,1,2,4,3,7,5]=>[4,7,6,1,2,3,5]=>000011
[4,7,6,1,2,5,3]=>[6,1,5,4,2,7,3]=>[4,5,1,2,7,6,3]=>000111
[4,7,6,1,3,2,5]=>[6,3,1,4,2,7,5]=>[3,1,4,7,6,2,5]=>010011
[4,7,6,1,3,5,2]=>[6,5,1,4,3,7,2]=>[4,5,1,3,7,6,2]=>000111
[4,7,6,1,5,2,3]=>[6,5,2,4,1,7,3]=>[4,5,2,7,6,1,3]=>000111
[4,7,6,1,5,3,2]=>[6,3,5,4,1,7,2]=>[4,5,3,1,7,6,2]=>010111
[4,7,6,2,1,3,5]=>[2,6,1,4,3,7,5]=>[4,7,6,2,1,3,5]=>100011
[4,7,6,2,1,5,3]=>[2,6,5,4,1,7,3]=>[4,5,2,1,7,6,3]=>100111
[4,7,6,2,3,1,5]=>[3,6,2,4,1,7,5]=>[4,7,6,2,3,1,5]=>010011
[4,7,6,2,3,5,1]=>[5,6,2,4,3,7,1]=>[4,7,6,2,3,5,1]=>000111
[4,7,6,2,5,1,3]=>[5,6,1,4,2,7,3]=>[4,7,6,1,5,2,3]=>000111
[4,7,6,2,5,3,1]=>[3,5,6,4,1,7,2]=>[4,7,6,1,5,3,2]=>010111
[4,7,6,3,1,2,5]=>[3,1,6,4,2,7,5]=>[4,7,6,3,1,2,5]=>010011
[4,7,6,3,1,5,2]=>[3,6,5,4,2,7,1]=>[4,5,2,7,6,3,1]=>010111
[4,7,6,3,2,1,5]=>[2,3,6,4,1,7,5]=>[4,7,6,3,2,1,5]=>110011
[4,7,6,3,2,5,1]=>[5,3,6,4,2,7,1]=>[4,7,6,3,2,5,1]=>010111
[4,7,6,3,5,1,2]=>[5,1,6,4,3,7,2]=>[4,7,6,3,5,1,2]=>000111
[4,7,6,3,5,2,1]=>[2,5,6,4,3,7,1]=>[4,7,6,3,5,2,1]=>100111
[4,7,6,5,1,2,3]=>[5,1,2,4,6,7,3]=>[4,7,6,5,1,2,3]=>000111
[4,7,6,5,1,3,2]=>[5,3,1,4,6,7,2]=>[3,1,4,7,6,5,2]=>010111
[4,7,6,5,2,1,3]=>[2,5,1,4,6,7,3]=>[4,7,6,5,2,1,3]=>100111
[4,7,6,5,2,3,1]=>[3,5,2,4,6,7,1]=>[4,7,6,5,2,3,1]=>010111
[4,7,6,5,3,1,2]=>[3,1,5,4,6,7,2]=>[4,7,6,5,3,1,2]=>010111
[4,7,6,5,3,2,1]=>[2,3,5,4,6,7,1]=>[4,7,6,5,3,2,1]=>110111
[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>000100
[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>000101
[5,1,2,3,6,4,7]=>[5,1,2,6,3,4,7]=>[6,1,2,3,5,4,7]=>000110
[5,1,2,3,6,7,4]=>[5,1,2,7,3,6,4]=>[6,7,1,2,3,5,4]=>000101
[5,1,2,3,7,4,6]=>[5,1,2,7,3,4,6]=>[7,1,2,3,5,4,6]=>000101
[5,1,2,3,7,6,4]=>[5,1,2,6,3,7,4]=>[7,6,1,2,3,5,4]=>000111
[5,1,2,4,3,6,7]=>[5,1,4,2,3,6,7]=>[4,1,2,5,3,6,7]=>001100
[5,1,2,4,3,7,6]=>[5,1,4,2,3,7,6]=>[4,1,2,5,3,7,6]=>001101
[5,1,2,4,6,3,7]=>[5,1,6,2,4,3,7]=>[6,1,2,4,5,3,7]=>000110
[5,1,2,4,6,7,3]=>[5,1,7,2,4,6,3]=>[6,7,1,2,4,5,3]=>000101
[5,1,2,4,7,3,6]=>[5,1,7,2,4,3,6]=>[7,1,2,4,5,3,6]=>000101
[5,1,2,4,7,6,3]=>[5,1,6,2,4,7,3]=>[7,6,1,2,4,5,3]=>000111
[5,1,2,6,3,4,7]=>[5,1,6,3,2,4,7]=>[6,3,5,1,2,4,7]=>000110
[5,1,2,6,3,7,4]=>[5,1,6,7,2,3,4]=>[7,1,2,6,3,5,4]=>000111
[5,1,2,6,4,3,7]=>[5,1,4,6,2,3,7]=>[6,4,1,2,5,3,7]=>001110
[5,1,2,6,4,7,3]=>[5,1,7,6,2,4,3]=>[6,1,2,7,4,5,3]=>000111
[5,1,2,6,7,3,4]=>[5,1,7,3,2,6,4]=>[6,7,3,5,1,2,4]=>000101
[5,1,2,6,7,4,3]=>[5,1,4,7,2,6,3]=>[6,7,4,1,2,5,3]=>001101
[5,1,2,7,3,4,6]=>[5,1,7,3,2,4,6]=>[7,3,5,1,2,4,6]=>000101
[5,1,2,7,3,6,4]=>[5,1,7,6,2,3,4]=>[6,1,2,7,3,5,4]=>000111
[5,1,2,7,4,3,6]=>[5,1,4,7,2,3,6]=>[7,4,1,2,5,3,6]=>001101
[5,1,2,7,4,6,3]=>[5,1,6,7,2,4,3]=>[7,1,2,6,4,5,3]=>000111
[5,1,2,7,6,3,4]=>[5,1,6,3,2,7,4]=>[7,6,3,5,1,2,4]=>000111
[5,1,2,7,6,4,3]=>[5,1,4,6,2,7,3]=>[7,6,4,1,2,5,3]=>001111
[5,1,3,2,4,6,7]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>010100
[5,1,3,2,4,7,6]=>[5,3,1,2,4,7,6]=>[3,1,5,2,4,7,6]=>010101
[5,1,3,2,6,4,7]=>[5,3,1,6,2,4,7]=>[3,1,6,2,5,4,7]=>010110
[5,1,3,2,6,7,4]=>[5,3,1,7,2,6,4]=>[3,1,6,7,2,5,4]=>010101
[5,1,3,2,7,4,6]=>[5,3,1,7,2,4,6]=>[3,1,7,2,5,4,6]=>010101
[5,1,3,2,7,6,4]=>[5,3,1,6,2,7,4]=>[3,1,7,6,2,5,4]=>010111
[5,1,3,4,2,6,7]=>[5,4,1,3,2,6,7]=>[4,1,3,5,2,6,7]=>001100
[5,1,3,4,2,7,6]=>[5,4,1,3,2,7,6]=>[4,1,3,5,2,7,6]=>001101
[5,1,3,4,6,2,7]=>[5,6,1,3,4,2,7]=>[6,1,3,4,5,2,7]=>000110
[5,1,3,4,6,7,2]=>[5,7,1,3,4,6,2]=>[6,7,1,3,4,5,2]=>000101
[5,1,3,4,7,2,6]=>[5,7,1,3,4,2,6]=>[7,1,3,4,5,2,6]=>000101
[5,1,3,4,7,6,2]=>[5,6,1,3,4,7,2]=>[7,6,1,3,4,5,2]=>000111
[5,1,3,6,2,4,7]=>[5,6,1,2,3,4,7]=>[6,1,5,2,3,4,7]=>000110
[5,1,3,6,2,7,4]=>[5,6,1,7,3,2,4]=>[7,1,3,6,2,5,4]=>000111
[5,1,3,6,4,2,7]=>[5,4,1,6,3,2,7]=>[6,4,1,3,5,2,7]=>001110
[5,1,3,6,4,7,2]=>[5,7,1,6,3,4,2]=>[6,1,3,7,4,5,2]=>000111
[5,1,3,6,7,2,4]=>[5,7,1,2,3,6,4]=>[6,7,1,5,2,3,4]=>000101
[5,1,3,6,7,4,2]=>[5,4,1,7,3,6,2]=>[6,7,4,1,3,5,2]=>001101
[5,1,3,7,2,4,6]=>[5,7,1,2,3,4,6]=>[7,1,5,2,3,4,6]=>000101
[5,1,3,7,2,6,4]=>[5,7,1,6,3,2,4]=>[6,1,3,7,2,5,4]=>000111
[5,1,3,7,4,2,6]=>[5,4,1,7,3,2,6]=>[7,4,1,3,5,2,6]=>001101
[5,1,3,7,4,6,2]=>[5,6,1,7,3,4,2]=>[7,1,3,6,4,5,2]=>000111
[5,1,3,7,6,2,4]=>[5,6,1,2,3,7,4]=>[7,6,1,5,2,3,4]=>000111
[5,1,3,7,6,4,2]=>[5,4,1,6,3,7,2]=>[7,6,4,1,3,5,2]=>001111
[5,1,4,2,3,6,7]=>[5,4,2,1,3,6,7]=>[4,2,5,1,3,6,7]=>001100
[5,1,4,2,3,7,6]=>[5,4,2,1,3,7,6]=>[4,2,5,1,3,7,6]=>001101
[5,1,4,2,6,3,7]=>[5,4,6,1,2,3,7]=>[6,1,4,2,5,3,7]=>001110
[5,1,4,2,6,7,3]=>[5,4,7,1,2,6,3]=>[6,7,1,4,2,5,3]=>001101
[5,1,4,2,7,3,6]=>[5,4,7,1,2,3,6]=>[7,1,4,2,5,3,6]=>001101
[5,1,4,2,7,6,3]=>[5,4,6,1,2,7,3]=>[7,6,1,4,2,5,3]=>001111
[5,1,4,3,2,6,7]=>[5,3,4,1,2,6,7]=>[4,3,1,5,2,6,7]=>011100
[5,1,4,3,2,7,6]=>[5,3,4,1,2,7,6]=>[4,3,1,5,2,7,6]=>011101
[5,1,4,3,6,2,7]=>[5,6,4,1,3,2,7]=>[4,1,6,3,5,2,7]=>001110
[5,1,4,3,6,7,2]=>[5,7,4,1,3,6,2]=>[4,1,6,7,3,5,2]=>001101
[5,1,4,3,7,2,6]=>[5,7,4,1,3,2,6]=>[4,1,7,3,5,2,6]=>001101
[5,1,4,3,7,6,2]=>[5,6,4,1,3,7,2]=>[4,1,7,6,3,5,2]=>001111
[5,1,4,6,2,3,7]=>[5,6,2,1,4,3,7]=>[6,2,4,5,1,3,7]=>000110
[5,1,4,6,2,7,3]=>[5,6,7,1,4,2,3]=>[7,1,4,6,2,5,3]=>000111
[5,1,4,6,3,2,7]=>[5,3,6,1,4,2,7]=>[6,3,1,4,5,2,7]=>010110
[5,1,4,6,3,7,2]=>[5,7,6,1,4,3,2]=>[6,1,4,7,3,5,2]=>000111
[5,1,4,6,7,2,3]=>[5,7,2,1,4,6,3]=>[6,7,2,4,5,1,3]=>000101
[5,1,4,6,7,3,2]=>[5,3,7,1,4,6,2]=>[6,7,3,1,4,5,2]=>010101
[5,1,4,7,2,3,6]=>[5,7,2,1,4,3,6]=>[7,2,4,5,1,3,6]=>000101
[5,1,4,7,2,6,3]=>[5,7,6,1,4,2,3]=>[6,1,4,7,2,5,3]=>000111
[5,1,4,7,3,2,6]=>[5,3,7,1,4,2,6]=>[7,3,1,4,5,2,6]=>010101
[5,1,4,7,3,6,2]=>[5,6,7,1,4,3,2]=>[7,1,4,6,3,5,2]=>000111
[5,1,4,7,6,2,3]=>[5,6,2,1,4,7,3]=>[7,6,2,4,5,1,3]=>000111
[5,1,4,7,6,3,2]=>[5,3,6,1,4,7,2]=>[7,6,3,1,4,5,2]=>010111
[5,1,6,2,3,4,7]=>[5,6,2,3,1,4,7]=>[6,2,3,5,1,4,7]=>000110
[5,1,6,2,3,7,4]=>[5,6,2,7,1,3,4]=>[7,2,6,1,3,5,4]=>000111
[5,1,6,2,4,3,7]=>[5,6,4,2,1,3,7]=>[4,2,6,1,5,3,7]=>001110
[5,1,6,2,4,7,3]=>[5,6,7,2,1,4,3]=>[7,2,6,1,4,5,3]=>000111
[5,1,6,2,7,3,4]=>[5,6,7,3,1,2,4]=>[7,3,6,1,5,2,4]=>000111
[5,1,6,2,7,4,3]=>[5,6,4,7,1,2,3]=>[7,4,1,6,2,5,3]=>001111
[5,1,6,3,2,4,7]=>[5,3,6,2,1,4,7]=>[6,3,2,5,1,4,7]=>010110
[5,1,6,3,2,7,4]=>[5,3,6,7,1,2,4]=>[7,3,1,6,2,5,4]=>010111
[5,1,6,3,4,2,7]=>[5,4,6,3,1,2,7]=>[6,3,4,1,5,2,7]=>001110
[5,1,6,3,4,7,2]=>[5,7,6,3,1,4,2]=>[6,3,7,1,4,5,2]=>000111
[5,1,6,3,7,2,4]=>[5,7,6,2,1,3,4]=>[6,2,7,1,5,3,4]=>000111
[5,1,6,3,7,4,2]=>[5,4,7,6,1,2,3]=>[6,1,7,4,2,5,3]=>001111
[5,1,6,4,2,3,7]=>[5,4,2,6,1,3,7]=>[6,4,2,5,1,3,7]=>001110
[5,1,6,4,2,7,3]=>[5,4,6,7,1,3,2]=>[7,1,6,4,3,5,2]=>001111
[5,1,6,4,3,2,7]=>[5,3,4,6,1,2,7]=>[6,4,3,1,5,2,7]=>011110
[5,1,6,4,3,7,2]=>[5,7,4,6,1,3,2]=>[6,4,1,7,3,5,2]=>001111
[5,1,6,4,7,2,3]=>[5,7,2,6,1,4,3]=>[6,2,7,4,5,1,3]=>000111
[5,1,6,4,7,3,2]=>[5,3,7,6,1,4,2]=>[6,3,1,7,4,5,2]=>010111
[5,1,6,7,2,3,4]=>[5,7,2,3,1,6,4]=>[6,7,2,3,5,1,4]=>000101
[5,1,6,7,2,4,3]=>[5,7,4,2,1,6,3]=>[4,2,6,7,1,5,3]=>001101
[5,1,6,7,3,2,4]=>[5,3,7,2,1,6,4]=>[6,7,3,2,5,1,4]=>010101
[5,1,6,7,3,4,2]=>[5,4,7,3,1,6,2]=>[6,7,3,4,1,5,2]=>001101
[5,1,6,7,4,2,3]=>[5,4,2,7,1,6,3]=>[6,7,4,2,5,1,3]=>001101
[5,1,6,7,4,3,2]=>[5,3,4,7,1,6,2]=>[6,7,4,3,1,5,2]=>011101
[5,1,7,2,3,4,6]=>[5,7,2,3,1,4,6]=>[7,2,3,5,1,4,6]=>000101
[5,1,7,2,3,6,4]=>[5,7,2,6,1,3,4]=>[6,2,7,1,3,5,4]=>000111
[5,1,7,2,4,3,6]=>[5,7,4,2,1,3,6]=>[4,2,7,1,5,3,6]=>001101
[5,1,7,2,4,6,3]=>[5,7,6,2,1,4,3]=>[6,2,7,1,4,5,3]=>000111
[5,1,7,2,6,3,4]=>[5,7,6,3,1,2,4]=>[6,3,7,1,5,2,4]=>000111
[5,1,7,2,6,4,3]=>[5,7,4,6,1,2,3]=>[6,4,1,7,2,5,3]=>001111
[5,1,7,3,2,4,6]=>[5,3,7,2,1,4,6]=>[7,3,2,5,1,4,6]=>010101
[5,1,7,3,2,6,4]=>[5,3,7,6,1,2,4]=>[6,3,1,7,2,5,4]=>010111
[5,1,7,3,4,2,6]=>[5,4,7,3,1,2,6]=>[7,3,4,1,5,2,6]=>001101
[5,1,7,3,4,6,2]=>[5,6,7,3,1,4,2]=>[7,3,6,1,4,5,2]=>000111
[5,1,7,3,6,2,4]=>[5,6,7,2,1,3,4]=>[7,2,6,1,5,3,4]=>000111
[5,1,7,3,6,4,2]=>[5,4,6,7,1,2,3]=>[7,1,6,4,2,5,3]=>001111
[5,1,7,4,2,3,6]=>[5,4,2,7,1,3,6]=>[7,4,2,5,1,3,6]=>001101
[5,1,7,4,2,6,3]=>[5,4,7,6,1,3,2]=>[6,1,7,4,3,5,2]=>001111
[5,1,7,4,3,2,6]=>[5,3,4,7,1,2,6]=>[7,4,3,1,5,2,6]=>011101
[5,1,7,4,3,6,2]=>[5,6,4,7,1,3,2]=>[7,4,1,6,3,5,2]=>001111
[5,1,7,4,6,2,3]=>[5,6,2,7,1,4,3]=>[7,2,6,4,5,1,3]=>000111
[5,1,7,4,6,3,2]=>[5,3,6,7,1,4,2]=>[7,3,1,6,4,5,2]=>010111
[5,1,7,6,2,3,4]=>[5,6,2,3,1,7,4]=>[7,6,2,3,5,1,4]=>000111
[5,1,7,6,2,4,3]=>[5,6,4,2,1,7,3]=>[4,2,7,6,1,5,3]=>001111
[5,1,7,6,3,2,4]=>[5,3,6,2,1,7,4]=>[7,6,3,2,5,1,4]=>010111
[5,1,7,6,3,4,2]=>[5,4,6,3,1,7,2]=>[7,6,3,4,1,5,2]=>001111
[5,1,7,6,4,2,3]=>[5,4,2,6,1,7,3]=>[7,6,4,2,5,1,3]=>001111
[5,1,7,6,4,3,2]=>[5,3,4,6,1,7,2]=>[7,6,4,3,1,5,2]=>011111
[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>100100
[5,2,1,3,4,7,6]=>[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>100101
[5,2,1,3,6,4,7]=>[2,5,1,6,3,4,7]=>[6,2,1,3,5,4,7]=>100110
[5,2,1,3,6,7,4]=>[2,5,1,7,3,6,4]=>[6,7,2,1,3,5,4]=>100101
[5,2,1,3,7,4,6]=>[2,5,1,7,3,4,6]=>[7,2,1,3,5,4,6]=>100101
[5,2,1,3,7,6,4]=>[2,5,1,6,3,7,4]=>[7,6,2,1,3,5,4]=>100111
[5,2,1,4,3,6,7]=>[2,5,4,1,3,6,7]=>[4,2,1,5,3,6,7]=>101100
[5,2,1,4,3,7,6]=>[2,5,4,1,3,7,6]=>[4,2,1,5,3,7,6]=>101101
[5,2,1,4,6,3,7]=>[2,5,6,1,4,3,7]=>[6,2,1,4,5,3,7]=>100110
[5,2,1,4,6,7,3]=>[2,5,7,1,4,6,3]=>[6,7,2,1,4,5,3]=>100101
[5,2,1,4,7,3,6]=>[2,5,7,1,4,3,6]=>[7,2,1,4,5,3,6]=>100101
[5,2,1,4,7,6,3]=>[2,5,6,1,4,7,3]=>[7,6,2,1,4,5,3]=>100111
[5,2,1,6,3,4,7]=>[2,5,6,3,1,4,7]=>[6,3,5,2,1,4,7]=>100110
[5,2,1,6,3,7,4]=>[2,5,6,7,1,3,4]=>[7,2,1,6,3,5,4]=>100111
[5,2,1,6,4,3,7]=>[2,5,4,6,1,3,7]=>[6,4,2,1,5,3,7]=>101110
[5,2,1,6,4,7,3]=>[2,5,7,6,1,4,3]=>[6,2,1,7,4,5,3]=>100111
[5,2,1,6,7,3,4]=>[2,5,7,3,1,6,4]=>[6,7,3,5,2,1,4]=>100101
[5,2,1,6,7,4,3]=>[2,5,4,7,1,6,3]=>[6,7,4,2,1,5,3]=>101101
[5,2,1,7,3,4,6]=>[2,5,7,3,1,4,6]=>[7,3,5,2,1,4,6]=>100101
[5,2,1,7,3,6,4]=>[2,5,7,6,1,3,4]=>[6,2,1,7,3,5,4]=>100111
[5,2,1,7,4,3,6]=>[2,5,4,7,1,3,6]=>[7,4,2,1,5,3,6]=>101101
[5,2,1,7,4,6,3]=>[2,5,6,7,1,4,3]=>[7,2,1,6,4,5,3]=>100111
[5,2,1,7,6,3,4]=>[2,5,6,3,1,7,4]=>[7,6,3,5,2,1,4]=>100111
[5,2,1,7,6,4,3]=>[2,5,4,6,1,7,3]=>[7,6,4,2,1,5,3]=>101111
[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[5,2,3,1,4,6,7]=>010100
[5,2,3,1,4,7,6]=>[3,5,2,1,4,7,6]=>[5,2,3,1,4,7,6]=>010101
[5,2,3,1,6,4,7]=>[3,5,2,6,1,4,7]=>[6,2,3,1,5,4,7]=>010110
[5,2,3,1,6,7,4]=>[3,5,2,7,1,6,4]=>[6,7,2,3,1,5,4]=>010101
[5,2,3,1,7,4,6]=>[3,5,2,7,1,4,6]=>[7,2,3,1,5,4,6]=>010101
[5,2,3,1,7,6,4]=>[3,5,2,6,1,7,4]=>[7,6,2,3,1,5,4]=>010111
[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,2,3,4,1,6,7]=>001100
[5,2,3,4,1,7,6]=>[4,5,2,3,1,7,6]=>[5,2,3,4,1,7,6]=>001101
[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>[5,2,3,4,6,1,7]=>000110
[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>[5,2,3,4,6,7,1]=>000101
[5,2,3,4,7,1,6]=>[7,5,2,3,4,1,6]=>[5,2,3,4,7,1,6]=>000101
[5,2,3,4,7,6,1]=>[6,5,2,3,4,7,1]=>[5,2,3,4,7,6,1]=>000111
[5,2,3,6,1,4,7]=>[6,5,2,1,3,4,7]=>[5,2,6,1,3,4,7]=>000110
[5,2,3,6,1,7,4]=>[6,5,2,7,3,1,4]=>[7,2,3,5,1,6,4]=>000111
[5,2,3,6,4,1,7]=>[4,6,1,5,3,2,7]=>[5,1,3,6,4,2,7]=>001110
[5,2,3,6,4,7,1]=>[7,5,2,6,3,4,1]=>[6,2,3,5,4,7,1]=>000111
[5,2,3,6,7,1,4]=>[7,5,2,1,3,6,4]=>[5,2,6,7,1,3,4]=>000101
[5,2,3,6,7,4,1]=>[4,7,1,5,3,6,2]=>[5,1,3,6,7,4,2]=>001101
[5,2,3,7,1,4,6]=>[7,5,2,1,3,4,6]=>[5,2,7,1,3,4,6]=>000101
[5,2,3,7,1,6,4]=>[7,5,2,6,3,1,4]=>[6,2,3,5,1,7,4]=>000111
[5,2,3,7,4,1,6]=>[4,7,1,5,3,2,6]=>[5,1,3,7,4,2,6]=>001101
[5,2,3,7,4,6,1]=>[6,5,2,7,3,4,1]=>[7,2,3,5,4,6,1]=>000111
[5,2,3,7,6,1,4]=>[6,5,2,1,3,7,4]=>[5,2,7,6,1,3,4]=>000111
[5,2,3,7,6,4,1]=>[4,6,1,5,3,7,2]=>[5,1,3,7,6,4,2]=>001111
[5,2,4,1,3,6,7]=>[4,5,1,2,3,6,7]=>[5,1,4,2,3,6,7]=>001100
[5,2,4,1,3,7,6]=>[4,5,1,2,3,7,6]=>[5,1,4,2,3,7,6]=>001101
[5,2,4,1,6,3,7]=>[4,5,6,2,1,3,7]=>[6,2,5,1,4,3,7]=>001110
[5,2,4,1,6,7,3]=>[4,5,7,2,1,6,3]=>[6,7,2,5,1,4,3]=>001101
[5,2,4,1,7,3,6]=>[4,5,7,2,1,3,6]=>[7,2,5,1,4,3,6]=>001101
[5,2,4,1,7,6,3]=>[4,5,6,2,1,7,3]=>[7,6,2,5,1,4,3]=>001111
[5,2,4,3,1,6,7]=>[3,4,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>011100
[5,2,4,3,1,7,6]=>[3,4,5,1,2,7,6]=>[5,1,4,3,2,7,6]=>011101
[5,2,4,3,6,1,7]=>[6,5,4,2,3,1,7]=>[4,2,5,3,6,1,7]=>001110
[5,2,4,3,6,7,1]=>[7,5,4,2,3,6,1]=>[4,2,5,3,6,7,1]=>001101
[5,2,4,3,7,1,6]=>[7,5,4,2,3,1,6]=>[4,2,5,3,7,1,6]=>001101
[5,2,4,3,7,6,1]=>[6,5,4,2,3,7,1]=>[4,2,5,3,7,6,1]=>001111
[5,2,4,6,1,3,7]=>[6,5,1,2,4,3,7]=>[5,1,4,6,2,3,7]=>000110
[5,2,4,6,1,7,3]=>[6,5,7,2,4,1,3]=>[7,2,4,5,1,6,3]=>000111
[5,2,4,6,3,1,7]=>[3,6,5,1,4,2,7]=>[5,1,4,6,3,2,7]=>010110
[5,2,4,6,3,7,1]=>[7,5,6,2,4,3,1]=>[6,2,4,5,3,7,1]=>000111
[5,2,4,6,7,1,3]=>[7,5,1,2,4,6,3]=>[5,1,4,6,7,2,3]=>000101
[5,2,4,6,7,3,1]=>[3,7,5,1,4,6,2]=>[5,1,4,6,7,3,2]=>010101
[5,2,4,7,1,3,6]=>[7,5,1,2,4,3,6]=>[5,1,4,7,2,3,6]=>000101
[5,2,4,7,1,6,3]=>[7,5,6,2,4,1,3]=>[6,2,4,5,1,7,3]=>000111
[5,2,4,7,3,1,6]=>[3,7,5,1,4,2,6]=>[5,1,4,7,3,2,6]=>010101
[5,2,4,7,3,6,1]=>[6,5,7,2,4,3,1]=>[7,2,4,5,3,6,1]=>000111
[5,2,4,7,6,1,3]=>[6,5,1,2,4,7,3]=>[5,1,4,7,6,2,3]=>000111
[5,2,4,7,6,3,1]=>[3,6,5,1,4,7,2]=>[5,1,4,7,6,3,2]=>010111
[5,2,6,1,3,4,7]=>[6,5,1,3,2,4,7]=>[5,1,3,6,2,4,7]=>000110
[5,2,6,1,3,7,4]=>[6,5,1,7,2,3,4]=>[7,1,5,2,3,6,4]=>000111
[5,2,6,1,4,3,7]=>[6,5,4,1,2,3,7]=>[4,1,5,2,6,3,7]=>001110
[5,2,6,1,4,7,3]=>[6,5,7,1,2,4,3]=>[7,1,5,2,4,6,3]=>000111
[5,2,6,1,7,3,4]=>[6,5,7,3,2,1,4]=>[7,3,5,2,6,1,4]=>000111
[5,2,6,1,7,4,3]=>[6,5,4,7,2,1,3]=>[7,4,2,5,1,6,3]=>001111
[5,2,6,3,1,4,7]=>[3,6,5,2,1,4,7]=>[5,2,6,3,1,4,7]=>010110
[5,2,6,3,1,7,4]=>[3,6,5,7,1,2,4]=>[7,1,5,3,2,6,4]=>010111
[5,2,6,3,4,1,7]=>[4,5,6,3,2,1,7]=>[6,3,5,2,4,1,7]=>001110
[5,2,6,3,4,7,1]=>[7,5,6,3,2,4,1]=>[6,3,5,2,4,7,1]=>000111
[5,2,6,3,7,1,4]=>[7,5,6,1,2,3,4]=>[6,1,5,2,7,3,4]=>000111
[5,2,6,3,7,4,1]=>[4,7,5,6,3,1,2]=>[6,3,5,1,7,4,2]=>001111
[5,2,6,4,1,3,7]=>[4,6,2,5,1,3,7]=>[5,2,6,4,1,3,7]=>001110
[5,2,6,4,1,7,3]=>[4,6,5,7,3,2,1]=>[7,3,5,2,6,4,1]=>001111
[5,2,6,4,3,1,7]=>[3,4,6,5,2,1,7]=>[5,2,6,4,3,1,7]=>011110
[5,2,6,4,3,7,1]=>[7,5,4,6,2,3,1]=>[6,4,2,5,3,7,1]=>001111
[5,2,6,4,7,1,3]=>[7,5,1,6,2,4,3]=>[6,1,5,4,7,2,3]=>000111
[5,2,6,4,7,3,1]=>[3,7,5,6,1,4,2]=>[6,1,5,4,7,3,2]=>010111
[5,2,6,7,1,3,4]=>[7,5,1,3,2,6,4]=>[5,1,3,6,7,2,4]=>000101
[5,2,6,7,1,4,3]=>[7,5,4,1,2,6,3]=>[4,1,5,2,6,7,3]=>001101
[5,2,6,7,3,1,4]=>[3,7,5,2,1,6,4]=>[5,2,6,7,3,1,4]=>010101
[5,2,6,7,3,4,1]=>[4,5,7,3,2,6,1]=>[6,7,3,5,2,4,1]=>001101
[5,2,6,7,4,1,3]=>[4,7,2,5,1,6,3]=>[5,2,6,7,4,1,3]=>001101
[5,2,6,7,4,3,1]=>[3,4,7,5,2,6,1]=>[5,2,6,7,4,3,1]=>011101
[5,2,7,1,3,4,6]=>[7,5,1,3,2,4,6]=>[5,1,3,7,2,4,6]=>000101
[5,2,7,1,3,6,4]=>[7,5,1,6,2,3,4]=>[6,1,5,2,3,7,4]=>000111
[5,2,7,1,4,3,6]=>[7,5,4,1,2,3,6]=>[4,1,5,2,7,3,6]=>001101
[5,2,7,1,4,6,3]=>[7,5,6,1,2,4,3]=>[6,1,5,2,4,7,3]=>000111
[5,2,7,1,6,3,4]=>[7,5,6,3,2,1,4]=>[6,3,5,2,7,1,4]=>000111
[5,2,7,1,6,4,3]=>[7,5,4,6,2,1,3]=>[6,4,2,5,1,7,3]=>001111
[5,2,7,3,1,4,6]=>[3,7,5,2,1,4,6]=>[5,2,7,3,1,4,6]=>010101
[5,2,7,3,1,6,4]=>[3,7,5,6,1,2,4]=>[6,1,5,3,2,7,4]=>010111
[5,2,7,3,4,1,6]=>[4,5,7,3,2,1,6]=>[7,3,5,2,4,1,6]=>001101
[5,2,7,3,4,6,1]=>[6,5,7,3,2,4,1]=>[7,3,5,2,4,6,1]=>000111
[5,2,7,3,6,1,4]=>[6,5,7,1,2,3,4]=>[7,1,5,2,6,3,4]=>000111
[5,2,7,3,6,4,1]=>[4,6,5,7,3,1,2]=>[7,3,5,1,6,4,2]=>001111
[5,2,7,4,1,3,6]=>[4,7,2,5,1,3,6]=>[5,2,7,4,1,3,6]=>001101
[5,2,7,4,1,6,3]=>[4,7,5,6,3,2,1]=>[6,3,5,2,7,4,1]=>001111
[5,2,7,4,3,1,6]=>[3,4,7,5,2,1,6]=>[5,2,7,4,3,1,6]=>011101
[5,2,7,4,3,6,1]=>[6,5,4,7,2,3,1]=>[7,4,2,5,3,6,1]=>001111
[5,2,7,4,6,1,3]=>[6,5,1,7,2,4,3]=>[7,1,5,4,6,2,3]=>000111
[5,2,7,4,6,3,1]=>[3,6,5,7,1,4,2]=>[7,1,5,4,6,3,2]=>010111
[5,2,7,6,1,3,4]=>[6,5,1,3,2,7,4]=>[5,1,3,7,6,2,4]=>000111
[5,2,7,6,1,4,3]=>[6,5,4,1,2,7,3]=>[4,1,5,2,7,6,3]=>001111
[5,2,7,6,3,1,4]=>[3,6,5,2,1,7,4]=>[5,2,7,6,3,1,4]=>010111
[5,2,7,6,3,4,1]=>[4,5,6,3,2,7,1]=>[7,6,3,5,2,4,1]=>001111
[5,2,7,6,4,1,3]=>[4,6,2,5,1,7,3]=>[5,2,7,6,4,1,3]=>001111
[5,2,7,6,4,3,1]=>[3,4,6,5,2,7,1]=>[5,2,7,6,4,3,1]=>011111
[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[5,3,1,2,4,6,7]=>010100
[5,3,1,2,4,7,6]=>[3,1,5,2,4,7,6]=>[5,3,1,2,4,7,6]=>010101
[5,3,1,2,6,4,7]=>[3,1,5,6,2,4,7]=>[6,3,1,2,5,4,7]=>010110
[5,3,1,2,6,7,4]=>[3,1,5,7,2,6,4]=>[6,7,3,1,2,5,4]=>010101
[5,3,1,2,7,4,6]=>[3,1,5,7,2,4,6]=>[7,3,1,2,5,4,6]=>010101
[5,3,1,2,7,6,4]=>[3,1,5,6,2,7,4]=>[7,6,3,1,2,5,4]=>010111
[5,3,1,4,2,6,7]=>[3,5,4,2,1,6,7]=>[4,2,5,3,1,6,7]=>011100
[5,3,1,4,2,7,6]=>[3,5,4,2,1,7,6]=>[4,2,5,3,1,7,6]=>011101
[5,3,1,4,6,2,7]=>[3,5,6,2,4,1,7]=>[6,2,4,5,3,1,7]=>010110
[5,3,1,4,6,7,2]=>[3,5,7,2,4,6,1]=>[6,7,2,4,5,3,1]=>010101
[5,3,1,4,7,2,6]=>[3,5,7,2,4,1,6]=>[7,2,4,5,3,1,6]=>010101
[5,3,1,4,7,6,2]=>[3,5,6,2,4,7,1]=>[7,6,2,4,5,3,1]=>010111
[5,3,1,6,2,4,7]=>[3,5,6,1,2,4,7]=>[6,1,5,3,2,4,7]=>010110
[5,3,1,6,2,7,4]=>[3,5,6,7,2,1,4]=>[7,2,6,3,1,5,4]=>010111
[5,3,1,6,4,2,7]=>[3,5,4,6,2,1,7]=>[6,4,2,5,3,1,7]=>011110
[5,3,1,6,4,7,2]=>[3,5,7,6,2,4,1]=>[6,2,7,4,5,3,1]=>010111
[5,3,1,6,7,2,4]=>[3,5,7,1,2,6,4]=>[6,7,1,5,3,2,4]=>010101
[5,3,1,6,7,4,2]=>[3,5,4,7,2,6,1]=>[6,7,4,2,5,3,1]=>011101
[5,3,1,7,2,4,6]=>[3,5,7,1,2,4,6]=>[7,1,5,3,2,4,6]=>010101
[5,3,1,7,2,6,4]=>[3,5,7,6,2,1,4]=>[6,2,7,3,1,5,4]=>010111
[5,3,1,7,4,2,6]=>[3,5,4,7,2,1,6]=>[7,4,2,5,3,1,6]=>011101
[5,3,1,7,4,6,2]=>[3,5,6,7,2,4,1]=>[7,2,6,4,5,3,1]=>010111
[5,3,1,7,6,2,4]=>[3,5,6,1,2,7,4]=>[7,6,1,5,3,2,4]=>010111
[5,3,1,7,6,4,2]=>[3,5,4,6,2,7,1]=>[7,6,4,2,5,3,1]=>011111
[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[5,3,2,1,4,6,7]=>110100
[5,3,2,1,4,7,6]=>[2,3,5,1,4,7,6]=>[5,3,2,1,4,7,6]=>110101
[5,3,2,1,6,4,7]=>[2,3,5,6,1,4,7]=>[6,3,2,1,5,4,7]=>110110
[5,3,2,1,6,7,4]=>[2,3,5,7,1,6,4]=>[6,7,3,2,1,5,4]=>110101
[5,3,2,1,7,4,6]=>[2,3,5,7,1,4,6]=>[7,3,2,1,5,4,6]=>110101
[5,3,2,1,7,6,4]=>[2,3,5,6,1,7,4]=>[7,6,3,2,1,5,4]=>110111
[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[5,3,2,4,1,6,7]=>011100
[5,3,2,4,1,7,6]=>[4,3,5,2,1,7,6]=>[5,3,2,4,1,7,6]=>011101
[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>[5,3,2,4,6,1,7]=>010110
[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>[5,3,2,4,6,7,1]=>010101
[5,3,2,4,7,1,6]=>[7,3,5,2,4,1,6]=>[5,3,2,4,7,1,6]=>010101
[5,3,2,4,7,6,1]=>[6,3,5,2,4,7,1]=>[5,3,2,4,7,6,1]=>010111
[5,3,2,6,1,4,7]=>[6,3,5,1,2,4,7]=>[5,3,1,6,2,4,7]=>010110
[5,3,2,6,1,7,4]=>[6,3,5,7,2,1,4]=>[7,3,2,5,1,6,4]=>010111
[5,3,2,6,4,1,7]=>[4,3,6,5,1,2,7]=>[5,3,1,6,4,2,7]=>011110
[5,3,2,6,4,7,1]=>[7,3,5,6,2,4,1]=>[6,3,2,5,4,7,1]=>010111
[5,3,2,6,7,1,4]=>[7,3,5,1,2,6,4]=>[5,3,1,6,7,2,4]=>010101
[5,3,2,6,7,4,1]=>[4,3,7,5,1,6,2]=>[5,3,1,6,7,4,2]=>011101
[5,3,2,7,1,4,6]=>[7,3,5,1,2,4,6]=>[5,3,1,7,2,4,6]=>010101
[5,3,2,7,1,6,4]=>[7,3,5,6,2,1,4]=>[6,3,2,5,1,7,4]=>010111
[5,3,2,7,4,1,6]=>[4,3,7,5,1,2,6]=>[5,3,1,7,4,2,6]=>011101
[5,3,2,7,4,6,1]=>[6,3,5,7,2,4,1]=>[7,3,2,5,4,6,1]=>010111
[5,3,2,7,6,1,4]=>[6,3,5,1,2,7,4]=>[5,3,1,7,6,2,4]=>010111
[5,3,2,7,6,4,1]=>[4,3,6,5,1,7,2]=>[5,3,1,7,6,4,2]=>011111
[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[5,3,4,1,2,6,7]=>001100
[5,3,4,1,2,7,6]=>[4,1,5,3,2,7,6]=>[5,3,4,1,2,7,6]=>001101
[5,3,4,1,6,2,7]=>[4,6,5,3,1,2,7]=>[5,3,6,1,4,2,7]=>001110
[5,3,4,1,6,7,2]=>[4,7,5,3,1,6,2]=>[5,3,6,7,1,4,2]=>001101
[5,3,4,1,7,2,6]=>[4,7,5,3,1,2,6]=>[5,3,7,1,4,2,6]=>001101
[5,3,4,1,7,6,2]=>[4,6,5,3,1,7,2]=>[5,3,7,6,1,4,2]=>001111
[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>[5,3,4,2,1,6,7]=>101100
[5,3,4,2,1,7,6]=>[2,4,5,3,1,7,6]=>[5,3,4,2,1,7,6]=>101101
[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>[5,3,4,2,6,1,7]=>001110
[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>[5,3,4,2,6,7,1]=>001101
[5,3,4,2,7,1,6]=>[7,4,5,3,2,1,6]=>[5,3,4,2,7,1,6]=>001101
[5,3,4,2,7,6,1]=>[6,4,5,3,2,7,1]=>[5,3,4,2,7,6,1]=>001111
[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>[5,3,4,6,1,2,7]=>000110
[5,3,4,6,1,7,2]=>[6,7,5,3,4,1,2]=>[5,3,4,7,1,6,2]=>000111
[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>[5,3,4,6,2,1,7]=>100110
[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>[5,3,4,6,2,7,1]=>000111
[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>[5,3,4,6,7,1,2]=>000101
[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>[5,3,4,6,7,2,1]=>100101
[5,3,4,7,1,2,6]=>[7,1,5,3,4,2,6]=>[5,3,4,7,1,2,6]=>000101
[5,3,4,7,1,6,2]=>[7,6,5,3,4,1,2]=>[5,3,4,6,1,7,2]=>000111
[5,3,4,7,2,1,6]=>[2,7,5,3,4,1,6]=>[5,3,4,7,2,1,6]=>100101
[5,3,4,7,2,6,1]=>[6,7,5,3,4,2,1]=>[5,3,4,7,2,6,1]=>000111
[5,3,4,7,6,1,2]=>[6,1,5,3,4,7,2]=>[5,3,4,7,6,1,2]=>000111
[5,3,4,7,6,2,1]=>[2,6,5,3,4,7,1]=>[5,3,4,7,6,2,1]=>100111
[5,3,6,1,2,4,7]=>[6,1,5,2,3,4,7]=>[5,1,2,6,3,4,7]=>000110
[5,3,6,1,2,7,4]=>[6,1,5,7,3,2,4]=>[7,3,5,1,2,6,4]=>000111
[5,3,6,1,4,2,7]=>[6,4,5,1,3,2,7]=>[5,1,4,3,6,2,7]=>001110
[5,3,6,1,4,7,2]=>[6,7,5,1,3,4,2]=>[5,1,7,3,4,6,2]=>000111
[5,3,6,1,7,2,4]=>[6,7,5,2,3,1,4]=>[5,2,7,3,6,1,4]=>000111
[5,3,6,1,7,4,2]=>[6,4,7,5,2,1,3]=>[5,2,7,4,1,6,3]=>001111
[5,3,6,2,1,4,7]=>[2,6,5,1,3,4,7]=>[5,2,1,6,3,4,7]=>100110
[5,3,6,2,1,7,4]=>[2,6,5,7,3,1,4]=>[7,3,5,2,1,6,4]=>100111
[5,3,6,2,4,1,7]=>[4,6,5,2,3,1,7]=>[5,2,6,3,4,1,7]=>001110
[5,3,6,2,4,7,1]=>[7,6,5,2,3,4,1]=>[5,2,6,3,4,7,1]=>000111
[5,3,6,2,7,1,4]=>[7,6,5,1,3,2,4]=>[5,1,6,3,7,2,4]=>000111
[5,3,6,2,7,4,1]=>[4,7,6,5,1,3,2]=>[5,1,6,3,7,4,2]=>001111
[5,3,6,4,1,2,7]=>[4,1,6,5,2,3,7]=>[5,1,2,6,4,3,7]=>001110
[5,3,6,4,1,7,2]=>[4,6,7,5,1,2,3]=>[5,1,7,2,6,4,3]=>001111
[5,3,6,4,2,1,7]=>[2,4,6,5,1,3,7]=>[5,2,1,6,4,3,7]=>101110
[5,3,6,4,2,7,1]=>[7,4,6,5,2,3,1]=>[5,2,6,4,3,7,1]=>001111
[5,3,6,4,7,1,2]=>[7,1,5,6,3,4,2]=>[6,3,5,4,7,1,2]=>000111
[5,3,6,4,7,2,1]=>[2,7,5,6,3,4,1]=>[6,3,5,4,7,2,1]=>100111
[5,3,6,7,1,2,4]=>[7,1,5,2,3,6,4]=>[5,1,2,6,7,3,4]=>000101
[5,3,6,7,1,4,2]=>[7,4,5,1,3,6,2]=>[5,1,4,3,6,7,2]=>001101
[5,3,6,7,2,1,4]=>[2,7,5,1,3,6,4]=>[5,2,1,6,7,3,4]=>100101
[5,3,6,7,2,4,1]=>[4,7,5,2,3,6,1]=>[5,2,6,7,3,4,1]=>001101
[5,3,6,7,4,1,2]=>[4,1,7,5,2,6,3]=>[5,1,2,6,7,4,3]=>001101
[5,3,6,7,4,2,1]=>[2,4,7,5,1,6,3]=>[5,2,1,6,7,4,3]=>101101
[5,3,7,1,2,4,6]=>[7,1,5,2,3,4,6]=>[5,1,2,7,3,4,6]=>000101
[5,3,7,1,2,6,4]=>[7,1,5,6,3,2,4]=>[6,3,5,1,2,7,4]=>000111
[5,3,7,1,4,2,6]=>[7,4,5,1,3,2,6]=>[5,1,4,3,7,2,6]=>001101
[5,3,7,1,4,6,2]=>[7,6,5,1,3,4,2]=>[5,1,6,3,4,7,2]=>000111
[5,3,7,1,6,2,4]=>[7,6,5,2,3,1,4]=>[5,2,6,3,7,1,4]=>000111
[5,3,7,1,6,4,2]=>[7,4,6,5,2,1,3]=>[5,2,6,4,1,7,3]=>001111
[5,3,7,2,1,4,6]=>[2,7,5,1,3,4,6]=>[5,2,1,7,3,4,6]=>100101
[5,3,7,2,1,6,4]=>[2,7,5,6,3,1,4]=>[6,3,5,2,1,7,4]=>100111
[5,3,7,2,4,1,6]=>[4,7,5,2,3,1,6]=>[5,2,7,3,4,1,6]=>001101
[5,3,7,2,4,6,1]=>[6,7,5,2,3,4,1]=>[5,2,7,3,4,6,1]=>000111
[5,3,7,2,6,1,4]=>[6,7,5,1,3,2,4]=>[5,1,7,3,6,2,4]=>000111
[5,3,7,2,6,4,1]=>[4,6,7,5,1,3,2]=>[5,1,7,3,6,4,2]=>001111
[5,3,7,4,1,2,6]=>[4,1,7,5,2,3,6]=>[5,1,2,7,4,3,6]=>001101
[5,3,7,4,1,6,2]=>[4,7,6,5,1,2,3]=>[5,1,6,2,7,4,3]=>001111
[5,3,7,4,2,1,6]=>[2,4,7,5,1,3,6]=>[5,2,1,7,4,3,6]=>101101
[5,3,7,4,2,6,1]=>[6,4,7,5,2,3,1]=>[5,2,7,4,3,6,1]=>001111
[5,3,7,4,6,1,2]=>[6,1,5,7,3,4,2]=>[7,3,5,4,6,1,2]=>000111
[5,3,7,4,6,2,1]=>[2,6,5,7,3,4,1]=>[7,3,5,4,6,2,1]=>100111
[5,3,7,6,1,2,4]=>[6,1,5,2,3,7,4]=>[5,1,2,7,6,3,4]=>000111
[5,3,7,6,1,4,2]=>[6,4,5,1,3,7,2]=>[5,1,4,3,7,6,2]=>001111
[5,3,7,6,2,1,4]=>[2,6,5,1,3,7,4]=>[5,2,1,7,6,3,4]=>100111
[5,3,7,6,2,4,1]=>[4,6,5,2,3,7,1]=>[5,2,7,6,3,4,1]=>001111
[5,3,7,6,4,1,2]=>[4,1,6,5,2,7,3]=>[5,1,2,7,6,4,3]=>001111
[5,3,7,6,4,2,1]=>[2,4,6,5,1,7,3]=>[5,2,1,7,6,4,3]=>101111
[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[5,4,1,2,3,6,7]=>001100
[5,4,1,2,3,7,6]=>[4,1,2,5,3,7,6]=>[5,4,1,2,3,7,6]=>001101
[5,4,1,2,6,3,7]=>[4,1,5,6,3,2,7]=>[6,3,5,4,1,2,7]=>001110
[5,4,1,2,6,7,3]=>[4,1,5,7,3,6,2]=>[6,7,3,5,4,1,2]=>001101
[5,4,1,2,7,3,6]=>[4,1,5,7,3,2,6]=>[7,3,5,4,1,2,6]=>001101
[5,4,1,2,7,6,3]=>[4,1,5,6,3,7,2]=>[7,6,3,5,4,1,2]=>001111
[5,4,1,3,2,6,7]=>[4,3,1,5,2,6,7]=>[3,1,5,4,2,6,7]=>011100
[5,4,1,3,2,7,6]=>[4,3,1,5,2,7,6]=>[3,1,5,4,2,7,6]=>011101
[5,4,1,3,6,2,7]=>[4,5,2,6,3,1,7]=>[6,2,3,5,4,1,7]=>001110
[5,4,1,3,6,7,2]=>[4,5,2,7,3,6,1]=>[6,7,2,3,5,4,1]=>001101
[5,4,1,3,7,2,6]=>[4,5,2,7,3,1,6]=>[7,2,3,5,4,1,6]=>001101
[5,4,1,3,7,6,2]=>[4,5,2,6,3,7,1]=>[7,6,2,3,5,4,1]=>001111
[5,4,1,6,2,3,7]=>[4,5,1,6,2,3,7]=>[6,1,5,4,2,3,7]=>001110
[5,4,1,6,2,7,3]=>[4,5,6,7,2,3,1]=>[7,2,6,3,5,4,1]=>001111
[5,4,1,6,3,2,7]=>[4,3,5,6,2,1,7]=>[6,3,2,5,4,1,7]=>011110
[5,4,1,6,3,7,2]=>[4,5,7,6,2,1,3]=>[6,2,7,1,5,4,3]=>001111
[5,4,1,6,7,2,3]=>[4,5,1,7,2,6,3]=>[6,7,1,5,4,2,3]=>001101
[5,4,1,6,7,3,2]=>[4,3,5,7,2,6,1]=>[6,7,3,2,5,4,1]=>011101
[5,4,1,7,2,3,6]=>[4,5,1,7,2,3,6]=>[7,1,5,4,2,3,6]=>001101
[5,4,1,7,2,6,3]=>[4,5,7,6,2,3,1]=>[6,2,7,3,5,4,1]=>001111
[5,4,1,7,3,2,6]=>[4,3,5,7,2,1,6]=>[7,3,2,5,4,1,6]=>011101
[5,4,1,7,3,6,2]=>[4,5,6,7,2,1,3]=>[7,2,6,1,5,4,3]=>001111
[5,4,1,7,6,2,3]=>[4,5,1,6,2,7,3]=>[7,6,1,5,4,2,3]=>001111
[5,4,1,7,6,3,2]=>[4,3,5,6,2,7,1]=>[7,6,3,2,5,4,1]=>011111
[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[5,4,2,1,3,6,7]=>101100
[5,4,2,1,3,7,6]=>[2,4,1,5,3,7,6]=>[5,4,2,1,3,7,6]=>101101
[5,4,2,1,6,3,7]=>[2,4,5,6,3,1,7]=>[6,3,5,4,2,1,7]=>101110
[5,4,2,1,6,7,3]=>[2,4,5,7,3,6,1]=>[6,7,3,5,4,2,1]=>101101
[5,4,2,1,7,3,6]=>[2,4,5,7,3,1,6]=>[7,3,5,4,2,1,6]=>101101
[5,4,2,1,7,6,3]=>[2,4,5,6,3,7,1]=>[7,6,3,5,4,2,1]=>101111
[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>[5,4,2,3,1,6,7]=>011100
[5,4,2,3,1,7,6]=>[3,4,2,5,1,7,6]=>[5,4,2,3,1,7,6]=>011101
[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>[5,4,2,3,6,1,7]=>001110
[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>[5,4,2,3,6,7,1]=>001101
[5,4,2,3,7,1,6]=>[7,4,2,5,3,1,6]=>[5,4,2,3,7,1,6]=>001101
[5,4,2,3,7,6,1]=>[6,4,2,5,3,7,1]=>[5,4,2,3,7,6,1]=>001111
[5,4,2,6,1,3,7]=>[6,4,1,5,2,3,7]=>[5,4,1,6,2,3,7]=>001110
[5,4,2,6,1,7,3]=>[6,4,5,7,3,1,2]=>[7,3,5,4,1,6,2]=>001111
[5,4,2,6,3,1,7]=>[3,6,4,5,1,2,7]=>[5,4,1,6,3,2,7]=>011110
[5,4,2,6,3,7,1]=>[7,4,5,6,3,2,1]=>[6,3,5,4,2,7,1]=>001111
[5,4,2,6,7,1,3]=>[7,4,1,5,2,6,3]=>[5,4,1,6,7,2,3]=>001101
[5,4,2,6,7,3,1]=>[3,7,4,5,1,6,2]=>[5,4,1,6,7,3,2]=>011101
[5,4,2,7,1,3,6]=>[7,4,1,5,2,3,6]=>[5,4,1,7,2,3,6]=>001101
[5,4,2,7,1,6,3]=>[7,4,5,6,3,1,2]=>[6,3,5,4,1,7,2]=>001111
[5,4,2,7,3,1,6]=>[3,7,4,5,1,2,6]=>[5,4,1,7,3,2,6]=>011101
[5,4,2,7,3,6,1]=>[6,4,5,7,3,2,1]=>[7,3,5,4,2,6,1]=>001111
[5,4,2,7,6,1,3]=>[6,4,1,5,2,7,3]=>[5,4,1,7,6,2,3]=>001111
[5,4,2,7,6,3,1]=>[3,6,4,5,1,7,2]=>[5,4,1,7,6,3,2]=>011111
[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[5,4,3,1,2,6,7]=>011100
[5,4,3,1,2,7,6]=>[3,1,4,5,2,7,6]=>[5,4,3,1,2,7,6]=>011101
[5,4,3,1,6,2,7]=>[3,4,5,6,1,2,7]=>[6,1,5,4,3,2,7]=>011110
[5,4,3,1,6,7,2]=>[3,4,5,7,1,6,2]=>[6,7,1,5,4,3,2]=>011101
[5,4,3,1,7,2,6]=>[3,4,5,7,1,2,6]=>[7,1,5,4,3,2,6]=>011101
[5,4,3,1,7,6,2]=>[3,4,5,6,1,7,2]=>[7,6,1,5,4,3,2]=>011111
[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]=>111100
[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]=>[5,4,3,2,1,7,6]=>111101
[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[5,4,3,2,6,1,7]=>011110
[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[5,4,3,2,6,7,1]=>011101
[5,4,3,2,7,1,6]=>[7,3,4,5,2,1,6]=>[5,4,3,2,7,1,6]=>011101
[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]=>[5,4,3,2,7,6,1]=>011111
[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[5,4,3,6,1,2,7]=>001110
[5,4,3,6,1,7,2]=>[6,7,4,5,3,1,2]=>[5,4,3,7,1,6,2]=>001111
[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[5,4,3,6,2,1,7]=>101110
[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[5,4,3,6,2,7,1]=>001111
[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>[5,4,3,6,7,1,2]=>001101
[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[5,4,3,6,7,2,1]=>101101
[5,4,3,7,1,2,6]=>[7,1,4,5,3,2,6]=>[5,4,3,7,1,2,6]=>001101
[5,4,3,7,1,6,2]=>[7,6,4,5,3,1,2]=>[5,4,3,6,1,7,2]=>001111
[5,4,3,7,2,1,6]=>[2,7,4,5,3,1,6]=>[5,4,3,7,2,1,6]=>101101
[5,4,3,7,2,6,1]=>[6,7,4,5,3,2,1]=>[5,4,3,7,2,6,1]=>001111
[5,4,3,7,6,1,2]=>[6,1,4,5,3,7,2]=>[5,4,3,7,6,1,2]=>001111
[5,4,3,7,6,2,1]=>[2,6,4,5,3,7,1]=>[5,4,3,7,6,2,1]=>101111
[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[5,4,6,1,2,3,7]=>000110
[5,4,6,1,2,7,3]=>[6,1,7,5,4,2,3]=>[5,4,7,1,2,6,3]=>000111
[5,4,6,1,3,2,7]=>[6,3,1,5,4,2,7]=>[3,1,5,4,6,2,7]=>010110
[5,4,6,1,3,7,2]=>[6,7,1,5,4,3,2]=>[5,4,7,1,3,6,2]=>000111
[5,4,6,1,7,2,3]=>[6,7,2,5,4,1,3]=>[5,4,7,2,6,1,3]=>000111
[5,4,6,1,7,3,2]=>[6,3,7,5,4,1,2]=>[5,4,7,3,1,6,2]=>010111
[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>[5,4,6,2,1,3,7]=>100110
[5,4,6,2,1,7,3]=>[2,6,7,5,4,1,3]=>[5,4,7,2,1,6,3]=>100111
[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>[5,4,6,2,3,1,7]=>010110
[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>[5,4,6,2,3,7,1]=>000111
[5,4,6,2,7,1,3]=>[7,6,1,5,4,2,3]=>[5,4,6,1,7,2,3]=>000111
[5,4,6,2,7,3,1]=>[3,7,6,5,4,1,2]=>[5,4,6,1,7,3,2]=>010111
[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>[5,4,6,3,1,2,7]=>010110
[5,4,6,3,1,7,2]=>[3,6,7,5,4,2,1]=>[5,4,7,2,6,3,1]=>010111
[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[5,4,6,3,2,1,7]=>110110
[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[5,4,6,3,2,7,1]=>010111
[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>[5,4,6,3,7,1,2]=>000111
[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[5,4,6,3,7,2,1]=>100111
[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[5,4,6,7,1,2,3]=>000101
[5,4,6,7,1,3,2]=>[7,3,1,5,4,6,2]=>[3,1,5,4,6,7,2]=>010101
[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>[5,4,6,7,2,1,3]=>100101
[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>[5,4,6,7,2,3,1]=>010101
[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>[5,4,6,7,3,1,2]=>010101
[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[5,4,6,7,3,2,1]=>110101
[5,4,7,1,2,3,6]=>[7,1,2,5,4,3,6]=>[5,4,7,1,2,3,6]=>000101
[5,4,7,1,2,6,3]=>[7,1,6,5,4,2,3]=>[5,4,6,1,2,7,3]=>000111
[5,4,7,1,3,2,6]=>[7,3,1,5,4,2,6]=>[3,1,5,4,7,2,6]=>010101
[5,4,7,1,3,6,2]=>[7,6,1,5,4,3,2]=>[5,4,6,1,3,7,2]=>000111
[5,4,7,1,6,2,3]=>[7,6,2,5,4,1,3]=>[5,4,6,2,7,1,3]=>000111
[5,4,7,1,6,3,2]=>[7,3,6,5,4,1,2]=>[5,4,6,3,1,7,2]=>010111
[5,4,7,2,1,3,6]=>[2,7,1,5,4,3,6]=>[5,4,7,2,1,3,6]=>100101
[5,4,7,2,1,6,3]=>[2,7,6,5,4,1,3]=>[5,4,6,2,1,7,3]=>100111
[5,4,7,2,3,1,6]=>[3,7,2,5,4,1,6]=>[5,4,7,2,3,1,6]=>010101
[5,4,7,2,3,6,1]=>[6,7,2,5,4,3,1]=>[5,4,7,2,3,6,1]=>000111
[5,4,7,2,6,1,3]=>[6,7,1,5,4,2,3]=>[5,4,7,1,6,2,3]=>000111
[5,4,7,2,6,3,1]=>[3,6,7,5,4,1,2]=>[5,4,7,1,6,3,2]=>010111
[5,4,7,3,1,2,6]=>[3,1,7,5,4,2,6]=>[5,4,7,3,1,2,6]=>010101
[5,4,7,3,1,6,2]=>[3,7,6,5,4,2,1]=>[5,4,6,2,7,3,1]=>010111
[5,4,7,3,2,1,6]=>[2,3,7,5,4,1,6]=>[5,4,7,3,2,1,6]=>110101
[5,4,7,3,2,6,1]=>[6,3,7,5,4,2,1]=>[5,4,7,3,2,6,1]=>010111
[5,4,7,3,6,1,2]=>[6,1,7,5,4,3,2]=>[5,4,7,3,6,1,2]=>000111
[5,4,7,3,6,2,1]=>[2,6,7,5,4,3,1]=>[5,4,7,3,6,2,1]=>100111
[5,4,7,6,1,2,3]=>[6,1,2,5,4,7,3]=>[5,4,7,6,1,2,3]=>000111
[5,4,7,6,1,3,2]=>[6,3,1,5,4,7,2]=>[3,1,5,4,7,6,2]=>010111
[5,4,7,6,2,1,3]=>[2,6,1,5,4,7,3]=>[5,4,7,6,2,1,3]=>100111
[5,4,7,6,2,3,1]=>[3,6,2,5,4,7,1]=>[5,4,7,6,2,3,1]=>010111
[5,4,7,6,3,1,2]=>[3,1,6,5,4,7,2]=>[5,4,7,6,3,1,2]=>010111
[5,4,7,6,3,2,1]=>[2,3,6,5,4,7,1]=>[5,4,7,6,3,2,1]=>110111
[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[5,6,1,2,3,4,7]=>000010
[5,6,1,2,3,7,4]=>[6,1,2,7,5,3,4]=>[5,7,1,2,3,6,4]=>000011
[5,6,1,2,4,3,7]=>[6,1,4,2,5,3,7]=>[4,1,2,5,6,3,7]=>001010
[5,6,1,2,4,7,3]=>[6,1,7,2,5,4,3]=>[5,7,1,2,4,6,3]=>000011
[5,6,1,2,7,3,4]=>[6,1,7,3,5,2,4]=>[5,7,3,6,1,2,4]=>000011
[5,6,1,2,7,4,3]=>[6,1,4,7,5,2,3]=>[5,7,4,1,2,6,3]=>001011
[5,6,1,3,2,4,7]=>[6,3,1,2,5,4,7]=>[3,1,5,6,2,4,7]=>010010
[5,6,1,3,2,7,4]=>[6,3,1,7,5,2,4]=>[3,1,5,7,2,6,4]=>010011
[5,6,1,3,4,2,7]=>[6,4,1,3,5,2,7]=>[4,1,3,5,6,2,7]=>001010
[5,6,1,3,4,7,2]=>[6,7,1,3,5,4,2]=>[5,7,1,3,4,6,2]=>000011
[5,6,1,3,7,2,4]=>[6,7,1,2,5,3,4]=>[5,7,1,6,2,3,4]=>000011
[5,6,1,3,7,4,2]=>[6,4,1,7,5,3,2]=>[5,7,4,1,3,6,2]=>001011
[5,6,1,4,2,3,7]=>[6,4,2,1,5,3,7]=>[4,2,5,6,1,3,7]=>001010
[5,6,1,4,2,7,3]=>[6,4,7,1,5,2,3]=>[5,7,1,4,2,6,3]=>001011
[5,6,1,4,3,2,7]=>[6,3,4,1,5,2,7]=>[4,3,1,5,6,2,7]=>011010
[5,6,1,4,3,7,2]=>[6,7,4,1,5,3,2]=>[4,1,5,7,3,6,2]=>001011
[5,6,1,4,7,2,3]=>[6,7,2,1,5,4,3]=>[5,7,2,4,6,1,3]=>000011
[5,6,1,4,7,3,2]=>[6,3,7,1,5,4,2]=>[5,7,3,1,4,6,2]=>010011
[5,6,1,7,2,3,4]=>[6,7,2,3,5,1,4]=>[5,7,2,3,6,1,4]=>000011
[5,6,1,7,2,4,3]=>[6,7,4,2,5,1,3]=>[4,2,5,7,1,6,3]=>001011
[5,6,1,7,3,2,4]=>[6,3,7,2,5,1,4]=>[5,7,3,2,6,1,4]=>010011
[5,6,1,7,3,4,2]=>[6,4,7,3,5,1,2]=>[5,7,3,4,1,6,2]=>001011
[5,6,1,7,4,2,3]=>[6,4,2,7,5,1,3]=>[5,7,4,2,6,1,3]=>001011
[5,6,1,7,4,3,2]=>[6,3,4,7,5,1,2]=>[5,7,4,3,1,6,2]=>011011
[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>[5,6,2,1,3,4,7]=>100010
[5,6,2,1,3,7,4]=>[2,6,1,7,5,3,4]=>[5,7,2,1,3,6,4]=>100011
[5,6,2,1,4,3,7]=>[2,6,4,1,5,3,7]=>[4,2,1,5,6,3,7]=>101010
[5,6,2,1,4,7,3]=>[2,6,7,1,5,4,3]=>[5,7,2,1,4,6,3]=>100011
[5,6,2,1,7,3,4]=>[2,6,7,3,5,1,4]=>[5,7,3,6,2,1,4]=>100011
[5,6,2,1,7,4,3]=>[2,6,4,7,5,1,3]=>[5,7,4,2,1,6,3]=>101011
[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>[5,6,2,3,1,4,7]=>010010
[5,6,2,3,1,7,4]=>[3,6,2,7,5,1,4]=>[5,7,2,3,1,6,4]=>010011
[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>[5,6,2,3,4,1,7]=>001010
[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>[5,6,2,3,4,7,1]=>000011
[5,6,2,3,7,1,4]=>[7,6,2,1,5,3,4]=>[5,6,2,7,1,3,4]=>000011
[5,6,2,3,7,4,1]=>[4,7,1,6,5,3,2]=>[5,6,1,3,7,4,2]=>001011
[5,6,2,4,1,3,7]=>[4,6,1,2,5,3,7]=>[5,6,1,4,2,3,7]=>001010
[5,6,2,4,1,7,3]=>[4,6,7,2,5,1,3]=>[5,7,2,6,1,4,3]=>001011
[5,6,2,4,3,1,7]=>[3,4,6,1,5,2,7]=>[5,6,1,4,3,2,7]=>011010
[5,6,2,4,3,7,1]=>[7,6,4,2,5,3,1]=>[4,2,5,6,3,7,1]=>001011
[5,6,2,4,7,1,3]=>[7,6,1,2,5,4,3]=>[5,6,1,4,7,2,3]=>000011
[5,6,2,4,7,3,1]=>[3,7,6,1,5,4,2]=>[5,6,1,4,7,3,2]=>010011
[5,6,2,7,1,3,4]=>[7,6,1,3,5,2,4]=>[5,6,1,3,7,2,4]=>000011
[5,6,2,7,1,4,3]=>[7,6,4,1,5,2,3]=>[4,1,5,6,2,7,3]=>001011
[5,6,2,7,3,1,4]=>[3,7,6,2,5,1,4]=>[5,6,2,7,3,1,4]=>010011
[5,6,2,7,3,4,1]=>[4,6,7,3,5,2,1]=>[5,7,3,6,2,4,1]=>001011
[5,6,2,7,4,1,3]=>[4,7,2,6,5,1,3]=>[5,6,2,7,4,1,3]=>001011
[5,6,2,7,4,3,1]=>[3,4,7,6,5,2,1]=>[5,6,2,7,4,3,1]=>011011
[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>[5,6,3,1,2,4,7]=>010010
[5,6,3,1,2,7,4]=>[3,1,6,7,5,2,4]=>[5,7,3,1,2,6,4]=>010011
[5,6,3,1,4,2,7]=>[3,6,4,2,5,1,7]=>[4,2,5,6,3,1,7]=>011010
[5,6,3,1,4,7,2]=>[3,6,7,2,5,4,1]=>[5,7,2,4,6,3,1]=>010011
[5,6,3,1,7,2,4]=>[3,6,7,1,5,2,4]=>[5,7,1,6,3,2,4]=>010011
[5,6,3,1,7,4,2]=>[3,6,4,7,5,2,1]=>[5,7,4,2,6,3,1]=>011011
[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>[5,6,3,2,1,4,7]=>110010
[5,6,3,2,1,7,4]=>[2,3,6,7,5,1,4]=>[5,7,3,2,1,6,4]=>110011
[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>[5,6,3,2,4,1,7]=>011010
[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>[5,6,3,2,4,7,1]=>010011
[5,6,3,2,7,1,4]=>[7,3,6,1,5,2,4]=>[5,6,3,1,7,2,4]=>010011
[5,6,3,2,7,4,1]=>[4,3,7,6,5,1,2]=>[5,6,3,1,7,4,2]=>011011
[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[5,6,3,4,1,2,7]=>001010
[5,6,3,4,1,7,2]=>[4,7,6,3,5,1,2]=>[5,6,3,7,1,4,2]=>001011
[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>[5,6,3,4,2,1,7]=>101010
[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>[5,6,3,4,2,7,1]=>001011
[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>[5,6,3,4,7,1,2]=>000011
[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>[5,6,3,4,7,2,1]=>100011
[5,6,3,7,1,2,4]=>[7,1,6,2,5,3,4]=>[5,6,1,2,7,3,4]=>000011
[5,6,3,7,1,4,2]=>[7,4,6,1,5,3,2]=>[5,6,1,4,3,7,2]=>001011
[5,6,3,7,2,1,4]=>[2,7,6,1,5,3,4]=>[5,6,2,1,7,3,4]=>100011
[5,6,3,7,2,4,1]=>[4,7,6,2,5,3,1]=>[5,6,2,7,3,4,1]=>001011
[5,6,3,7,4,1,2]=>[4,1,7,6,5,2,3]=>[5,6,1,2,7,4,3]=>001011
[5,6,3,7,4,2,1]=>[2,4,7,6,5,1,3]=>[5,6,2,1,7,4,3]=>101011
[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>[5,6,4,1,2,3,7]=>001010
[5,6,4,1,2,7,3]=>[4,1,6,7,5,3,2]=>[5,7,3,6,4,1,2]=>001011
[5,6,4,1,3,2,7]=>[4,3,1,6,5,2,7]=>[3,1,5,6,4,2,7]=>011010
[5,6,4,1,3,7,2]=>[4,6,2,7,5,3,1]=>[5,7,2,3,6,4,1]=>001011
[5,6,4,1,7,2,3]=>[4,6,1,7,5,2,3]=>[5,7,1,6,4,2,3]=>001011
[5,6,4,1,7,3,2]=>[4,3,6,7,5,2,1]=>[5,7,3,2,6,4,1]=>011011
[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>[5,6,4,2,1,3,7]=>101010
[5,6,4,2,1,7,3]=>[2,4,6,7,5,3,1]=>[5,7,3,6,4,2,1]=>101011
[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>[5,6,4,2,3,1,7]=>011010
[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>[5,6,4,2,3,7,1]=>001011
[5,6,4,2,7,1,3]=>[7,4,1,6,5,2,3]=>[5,6,4,1,7,2,3]=>001011
[5,6,4,2,7,3,1]=>[3,7,4,6,5,1,2]=>[5,6,4,1,7,3,2]=>011011
[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>[5,6,4,3,1,2,7]=>011010
[5,6,4,3,1,7,2]=>[3,4,6,7,5,1,2]=>[5,7,1,6,4,3,2]=>011011
[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[5,6,4,3,2,1,7]=>111010
[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[5,6,4,3,2,7,1]=>011011
[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>[5,6,4,3,7,1,2]=>001011
[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[5,6,4,3,7,2,1]=>101011
[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[5,6,4,7,1,2,3]=>000011
[5,6,4,7,1,3,2]=>[7,3,1,6,5,4,2]=>[3,1,5,6,4,7,2]=>010011
[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>[5,6,4,7,2,1,3]=>100011
[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>[5,6,4,7,2,3,1]=>010011
[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>[5,6,4,7,3,1,2]=>010011
[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[5,6,4,7,3,2,1]=>110011
[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[5,6,7,1,2,3,4]=>000001
[5,6,7,1,2,4,3]=>[7,1,4,2,5,6,3]=>[4,1,2,5,6,7,3]=>001001
[5,6,7,1,3,2,4]=>[7,3,1,2,5,6,4]=>[3,1,5,6,7,2,4]=>010001
[5,6,7,1,3,4,2]=>[7,4,1,3,5,6,2]=>[4,1,3,5,6,7,2]=>001001
[5,6,7,1,4,2,3]=>[7,4,2,1,5,6,3]=>[4,2,5,6,7,1,3]=>001001
[5,6,7,1,4,3,2]=>[7,3,4,1,5,6,2]=>[4,3,1,5,6,7,2]=>011001
[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[5,6,7,2,1,3,4]=>100001
[5,6,7,2,1,4,3]=>[2,7,4,1,5,6,3]=>[4,2,1,5,6,7,3]=>101001
[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>[5,6,7,2,3,1,4]=>010001
[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>[5,6,7,2,3,4,1]=>001001
[5,6,7,2,4,1,3]=>[4,7,1,2,5,6,3]=>[5,6,7,1,4,2,3]=>001001
[5,6,7,2,4,3,1]=>[3,4,7,1,5,6,2]=>[5,6,7,1,4,3,2]=>011001
[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[5,6,7,3,1,2,4]=>010001
[5,6,7,3,1,4,2]=>[3,7,4,2,5,6,1]=>[4,2,5,6,7,3,1]=>011001
[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[5,6,7,3,2,1,4]=>110001
[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>[5,6,7,3,2,4,1]=>011001
[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>[5,6,7,3,4,1,2]=>001001
[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>[5,6,7,3,4,2,1]=>101001
[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>[5,6,7,4,1,2,3]=>001001
[5,6,7,4,1,3,2]=>[4,3,1,7,5,6,2]=>[3,1,5,6,7,4,2]=>011001
[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>[5,6,7,4,2,1,3]=>101001
[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>[5,6,7,4,2,3,1]=>011001
[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>[5,6,7,4,3,1,2]=>011001
[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[5,6,7,4,3,2,1]=>111001
[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>[5,7,1,2,3,4,6]=>000001
[5,7,1,2,3,6,4]=>[7,1,2,6,5,3,4]=>[5,6,1,2,3,7,4]=>000011
[5,7,1,2,4,3,6]=>[7,1,4,2,5,3,6]=>[4,1,2,5,7,3,6]=>001001
[5,7,1,2,4,6,3]=>[7,1,6,2,5,4,3]=>[5,6,1,2,4,7,3]=>000011
[5,7,1,2,6,3,4]=>[7,1,6,3,5,2,4]=>[5,6,3,7,1,2,4]=>000011
[5,7,1,2,6,4,3]=>[7,1,4,6,5,2,3]=>[5,6,4,1,2,7,3]=>001011
[5,7,1,3,2,4,6]=>[7,3,1,2,5,4,6]=>[3,1,5,7,2,4,6]=>010001
[5,7,1,3,2,6,4]=>[7,3,1,6,5,2,4]=>[3,1,5,6,2,7,4]=>010011
[5,7,1,3,4,2,6]=>[7,4,1,3,5,2,6]=>[4,1,3,5,7,2,6]=>001001
[5,7,1,3,4,6,2]=>[7,6,1,3,5,4,2]=>[5,6,1,3,4,7,2]=>000011
[5,7,1,3,6,2,4]=>[7,6,1,2,5,3,4]=>[5,6,1,7,2,3,4]=>000011
[5,7,1,3,6,4,2]=>[7,4,1,6,5,3,2]=>[5,6,4,1,3,7,2]=>001011
[5,7,1,4,2,3,6]=>[7,4,2,1,5,3,6]=>[4,2,5,7,1,3,6]=>001001
[5,7,1,4,2,6,3]=>[7,4,6,1,5,2,3]=>[5,6,1,4,2,7,3]=>001011
[5,7,1,4,3,2,6]=>[7,3,4,1,5,2,6]=>[4,3,1,5,7,2,6]=>011001
[5,7,1,4,3,6,2]=>[7,6,4,1,5,3,2]=>[4,1,5,6,3,7,2]=>001011
[5,7,1,4,6,2,3]=>[7,6,2,1,5,4,3]=>[5,6,2,4,7,1,3]=>000011
[5,7,1,4,6,3,2]=>[7,3,6,1,5,4,2]=>[5,6,3,1,4,7,2]=>010011
[5,7,1,6,2,3,4]=>[7,6,2,3,5,1,4]=>[5,6,2,3,7,1,4]=>000011
[5,7,1,6,2,4,3]=>[7,6,4,2,5,1,3]=>[4,2,5,6,1,7,3]=>001011
[5,7,1,6,3,2,4]=>[7,3,6,2,5,1,4]=>[5,6,3,2,7,1,4]=>010011
[5,7,1,6,3,4,2]=>[7,4,6,3,5,1,2]=>[5,6,3,4,1,7,2]=>001011
[5,7,1,6,4,2,3]=>[7,4,2,6,5,1,3]=>[5,6,4,2,7,1,3]=>001011
[5,7,1,6,4,3,2]=>[7,3,4,6,5,1,2]=>[5,6,4,3,1,7,2]=>011011
[5,7,2,1,3,4,6]=>[2,7,1,3,5,4,6]=>[5,7,2,1,3,4,6]=>100001
[5,7,2,1,3,6,4]=>[2,7,1,6,5,3,4]=>[5,6,2,1,3,7,4]=>100011
[5,7,2,1,4,3,6]=>[2,7,4,1,5,3,6]=>[4,2,1,5,7,3,6]=>101001
[5,7,2,1,4,6,3]=>[2,7,6,1,5,4,3]=>[5,6,2,1,4,7,3]=>100011
[5,7,2,1,6,3,4]=>[2,7,6,3,5,1,4]=>[5,6,3,7,2,1,4]=>100011
[5,7,2,1,6,4,3]=>[2,7,4,6,5,1,3]=>[5,6,4,2,1,7,3]=>101011
[5,7,2,3,1,4,6]=>[3,7,2,1,5,4,6]=>[5,7,2,3,1,4,6]=>010001
[5,7,2,3,1,6,4]=>[3,7,2,6,5,1,4]=>[5,6,2,3,1,7,4]=>010011
[5,7,2,3,4,1,6]=>[4,7,2,3,5,1,6]=>[5,7,2,3,4,1,6]=>001001
[5,7,2,3,4,6,1]=>[6,7,2,3,5,4,1]=>[5,7,2,3,4,6,1]=>000011
[5,7,2,3,6,1,4]=>[6,7,2,1,5,3,4]=>[5,7,2,6,1,3,4]=>000011
[5,7,2,3,6,4,1]=>[4,6,1,7,5,3,2]=>[5,7,1,3,6,4,2]=>001011
[5,7,2,4,1,3,6]=>[4,7,1,2,5,3,6]=>[5,7,1,4,2,3,6]=>001001
[5,7,2,4,1,6,3]=>[4,7,6,2,5,1,3]=>[5,6,2,7,1,4,3]=>001011
[5,7,2,4,3,1,6]=>[3,4,7,1,5,2,6]=>[5,7,1,4,3,2,6]=>011001
[5,7,2,4,3,6,1]=>[6,7,4,2,5,3,1]=>[4,2,5,7,3,6,1]=>001011
[5,7,2,4,6,1,3]=>[6,7,1,2,5,4,3]=>[5,7,1,4,6,2,3]=>000011
[5,7,2,4,6,3,1]=>[3,6,7,1,5,4,2]=>[5,7,1,4,6,3,2]=>010011
[5,7,2,6,1,3,4]=>[6,7,1,3,5,2,4]=>[5,7,1,3,6,2,4]=>000011
[5,7,2,6,1,4,3]=>[6,7,4,1,5,2,3]=>[4,1,5,7,2,6,3]=>001011
[5,7,2,6,3,1,4]=>[3,6,7,2,5,1,4]=>[5,7,2,6,3,1,4]=>010011
[5,7,2,6,3,4,1]=>[4,7,6,3,5,2,1]=>[5,6,3,7,2,4,1]=>001011
[5,7,2,6,4,1,3]=>[4,6,2,7,5,1,3]=>[5,7,2,6,4,1,3]=>001011
[5,7,2,6,4,3,1]=>[3,4,6,7,5,2,1]=>[5,7,2,6,4,3,1]=>011011
[5,7,3,1,2,4,6]=>[3,1,7,2,5,4,6]=>[5,7,3,1,2,4,6]=>010001
[5,7,3,1,2,6,4]=>[3,1,7,6,5,2,4]=>[5,6,3,1,2,7,4]=>010011
[5,7,3,1,4,2,6]=>[3,7,4,2,5,1,6]=>[4,2,5,7,3,1,6]=>011001
[5,7,3,1,4,6,2]=>[3,7,6,2,5,4,1]=>[5,6,2,4,7,3,1]=>010011
[5,7,3,1,6,2,4]=>[3,7,6,1,5,2,4]=>[5,6,1,7,3,2,4]=>010011
[5,7,3,1,6,4,2]=>[3,7,4,6,5,2,1]=>[5,6,4,2,7,3,1]=>011011
[5,7,3,2,1,4,6]=>[2,3,7,1,5,4,6]=>[5,7,3,2,1,4,6]=>110001
[5,7,3,2,1,6,4]=>[2,3,7,6,5,1,4]=>[5,6,3,2,1,7,4]=>110011
[5,7,3,2,4,1,6]=>[4,3,7,2,5,1,6]=>[5,7,3,2,4,1,6]=>011001
[5,7,3,2,4,6,1]=>[6,3,7,2,5,4,1]=>[5,7,3,2,4,6,1]=>010011
[5,7,3,2,6,1,4]=>[6,3,7,1,5,2,4]=>[5,7,3,1,6,2,4]=>010011
[5,7,3,2,6,4,1]=>[4,3,6,7,5,1,2]=>[5,7,3,1,6,4,2]=>011011
[5,7,3,4,1,2,6]=>[4,1,7,3,5,2,6]=>[5,7,3,4,1,2,6]=>001001
[5,7,3,4,1,6,2]=>[4,6,7,3,5,1,2]=>[5,7,3,6,1,4,2]=>001011
[5,7,3,4,2,1,6]=>[2,4,7,3,5,1,6]=>[5,7,3,4,2,1,6]=>101001
[5,7,3,4,2,6,1]=>[6,4,7,3,5,2,1]=>[5,7,3,4,2,6,1]=>001011
[5,7,3,4,6,1,2]=>[6,1,7,3,5,4,2]=>[5,7,3,4,6,1,2]=>000011
[5,7,3,4,6,2,1]=>[2,6,7,3,5,4,1]=>[5,7,3,4,6,2,1]=>100011
[5,7,3,6,1,2,4]=>[6,1,7,2,5,3,4]=>[5,7,1,2,6,3,4]=>000011
[5,7,3,6,1,4,2]=>[6,4,7,1,5,3,2]=>[5,7,1,4,3,6,2]=>001011
[5,7,3,6,2,1,4]=>[2,6,7,1,5,3,4]=>[5,7,2,1,6,3,4]=>100011
[5,7,3,6,2,4,1]=>[4,6,7,2,5,3,1]=>[5,7,2,6,3,4,1]=>001011
[5,7,3,6,4,1,2]=>[4,1,6,7,5,2,3]=>[5,7,1,2,6,4,3]=>001011
[5,7,3,6,4,2,1]=>[2,4,6,7,5,1,3]=>[5,7,2,1,6,4,3]=>101011
[5,7,4,1,2,3,6]=>[4,1,2,7,5,3,6]=>[5,7,4,1,2,3,6]=>001001
[5,7,4,1,2,6,3]=>[4,1,7,6,5,3,2]=>[5,6,3,7,4,1,2]=>001011
[5,7,4,1,3,2,6]=>[4,3,1,7,5,2,6]=>[3,1,5,7,4,2,6]=>011001
[5,7,4,1,3,6,2]=>[4,7,2,6,5,3,1]=>[5,6,2,3,7,4,1]=>001011
[5,7,4,1,6,2,3]=>[4,7,1,6,5,2,3]=>[5,6,1,7,4,2,3]=>001011
[5,7,4,1,6,3,2]=>[4,3,7,6,5,2,1]=>[5,6,3,2,7,4,1]=>011011
[5,7,4,2,1,3,6]=>[2,4,1,7,5,3,6]=>[5,7,4,2,1,3,6]=>101001
[5,7,4,2,1,6,3]=>[2,4,7,6,5,3,1]=>[5,6,3,7,4,2,1]=>101011
[5,7,4,2,3,1,6]=>[3,4,2,7,5,1,6]=>[5,7,4,2,3,1,6]=>011001
[5,7,4,2,3,6,1]=>[6,4,2,7,5,3,1]=>[5,7,4,2,3,6,1]=>001011
[5,7,4,2,6,1,3]=>[6,4,1,7,5,2,3]=>[5,7,4,1,6,2,3]=>001011
[5,7,4,2,6,3,1]=>[3,6,4,7,5,1,2]=>[5,7,4,1,6,3,2]=>011011
[5,7,4,3,1,2,6]=>[3,1,4,7,5,2,6]=>[5,7,4,3,1,2,6]=>011001
[5,7,4,3,1,6,2]=>[3,4,7,6,5,1,2]=>[5,6,1,7,4,3,2]=>011011
[5,7,4,3,2,1,6]=>[2,3,4,7,5,1,6]=>[5,7,4,3,2,1,6]=>111001
[5,7,4,3,2,6,1]=>[6,3,4,7,5,2,1]=>[5,7,4,3,2,6,1]=>011011
[5,7,4,3,6,1,2]=>[6,1,4,7,5,3,2]=>[5,7,4,3,6,1,2]=>001011
[5,7,4,3,6,2,1]=>[2,6,4,7,5,3,1]=>[5,7,4,3,6,2,1]=>101011
[5,7,4,6,1,2,3]=>[6,1,2,7,5,4,3]=>[5,7,4,6,1,2,3]=>000011
[5,7,4,6,1,3,2]=>[6,3,1,7,5,4,2]=>[3,1,5,7,4,6,2]=>010011
[5,7,4,6,2,1,3]=>[2,6,1,7,5,4,3]=>[5,7,4,6,2,1,3]=>100011
[5,7,4,6,2,3,1]=>[3,6,2,7,5,4,1]=>[5,7,4,6,2,3,1]=>010011
[5,7,4,6,3,1,2]=>[3,1,6,7,5,4,2]=>[5,7,4,6,3,1,2]=>010011
[5,7,4,6,3,2,1]=>[2,3,6,7,5,4,1]=>[5,7,4,6,3,2,1]=>110011
[5,7,6,1,2,3,4]=>[6,1,2,3,5,7,4]=>[5,7,6,1,2,3,4]=>000011
[5,7,6,1,2,4,3]=>[6,1,4,2,5,7,3]=>[4,1,2,5,7,6,3]=>001011
[5,7,6,1,3,2,4]=>[6,3,1,2,5,7,4]=>[3,1,5,7,6,2,4]=>010011
[5,7,6,1,3,4,2]=>[6,4,1,3,5,7,2]=>[4,1,3,5,7,6,2]=>001011
[5,7,6,1,4,2,3]=>[6,4,2,1,5,7,3]=>[4,2,5,7,6,1,3]=>001011
[5,7,6,1,4,3,2]=>[6,3,4,1,5,7,2]=>[4,3,1,5,7,6,2]=>011011
[5,7,6,2,1,3,4]=>[2,6,1,3,5,7,4]=>[5,7,6,2,1,3,4]=>100011
[5,7,6,2,1,4,3]=>[2,6,4,1,5,7,3]=>[4,2,1,5,7,6,3]=>101011
[5,7,6,2,3,1,4]=>[3,6,2,1,5,7,4]=>[5,7,6,2,3,1,4]=>010011
[5,7,6,2,3,4,1]=>[4,6,2,3,5,7,1]=>[5,7,6,2,3,4,1]=>001011
[5,7,6,2,4,1,3]=>[4,6,1,2,5,7,3]=>[5,7,6,1,4,2,3]=>001011
[5,7,6,2,4,3,1]=>[3,4,6,1,5,7,2]=>[5,7,6,1,4,3,2]=>011011
[5,7,6,3,1,2,4]=>[3,1,6,2,5,7,4]=>[5,7,6,3,1,2,4]=>010011
[5,7,6,3,1,4,2]=>[3,6,4,2,5,7,1]=>[4,2,5,7,6,3,1]=>011011
[5,7,6,3,2,1,4]=>[2,3,6,1,5,7,4]=>[5,7,6,3,2,1,4]=>110011
[5,7,6,3,2,4,1]=>[4,3,6,2,5,7,1]=>[5,7,6,3,2,4,1]=>011011
[5,7,6,3,4,1,2]=>[4,1,6,3,5,7,2]=>[5,7,6,3,4,1,2]=>001011
[5,7,6,3,4,2,1]=>[2,4,6,3,5,7,1]=>[5,7,6,3,4,2,1]=>101011
[5,7,6,4,1,2,3]=>[4,1,2,6,5,7,3]=>[5,7,6,4,1,2,3]=>001011
[5,7,6,4,1,3,2]=>[4,3,1,6,5,7,2]=>[3,1,5,7,6,4,2]=>011011
[5,7,6,4,2,1,3]=>[2,4,1,6,5,7,3]=>[5,7,6,4,2,1,3]=>101011
[5,7,6,4,2,3,1]=>[3,4,2,6,5,7,1]=>[5,7,6,4,2,3,1]=>011011
[5,7,6,4,3,1,2]=>[3,1,4,6,5,7,2]=>[5,7,6,4,3,1,2]=>011011
[5,7,6,4,3,2,1]=>[2,3,4,6,5,7,1]=>[5,7,6,4,3,2,1]=>111011
[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>000010
[6,1,2,3,4,7,5]=>[6,1,2,3,7,4,5]=>[7,1,2,3,4,6,5]=>000011
[6,1,2,3,5,4,7]=>[6,1,2,5,3,4,7]=>[5,1,2,3,6,4,7]=>000110
[6,1,2,3,5,7,4]=>[6,1,2,7,3,5,4]=>[7,1,2,3,5,6,4]=>000011
[6,1,2,3,7,4,5]=>[6,1,2,7,4,3,5]=>[7,4,6,1,2,3,5]=>000011
[6,1,2,3,7,5,4]=>[6,1,2,5,7,3,4]=>[7,5,1,2,3,6,4]=>000111
[6,1,2,4,3,5,7]=>[6,1,4,2,3,5,7]=>[4,1,2,6,3,5,7]=>001010
[6,1,2,4,3,7,5]=>[6,1,4,2,7,3,5]=>[4,1,2,7,3,6,5]=>001011
[6,1,2,4,5,3,7]=>[6,1,5,2,4,3,7]=>[5,1,2,4,6,3,7]=>000110
[6,1,2,4,5,7,3]=>[6,1,7,2,4,5,3]=>[7,1,2,4,5,6,3]=>000011
[6,1,2,4,7,3,5]=>[6,1,7,2,3,4,5]=>[7,1,2,6,3,4,5]=>000011
[6,1,2,4,7,5,3]=>[6,1,5,2,7,4,3]=>[7,5,1,2,4,6,3]=>000111
[6,1,2,5,3,4,7]=>[6,1,5,3,2,4,7]=>[5,3,6,1,2,4,7]=>000110
[6,1,2,5,3,7,4]=>[6,1,5,7,2,3,4]=>[7,1,2,5,3,6,4]=>000111
[6,1,2,5,4,3,7]=>[6,1,4,5,2,3,7]=>[5,4,1,2,6,3,7]=>001110
[6,1,2,5,4,7,3]=>[6,1,7,5,2,4,3]=>[5,1,2,7,4,6,3]=>000111
[6,1,2,5,7,3,4]=>[6,1,7,3,2,5,4]=>[7,3,5,6,1,2,4]=>000011
[6,1,2,5,7,4,3]=>[6,1,4,7,2,5,3]=>[7,4,1,2,5,6,3]=>001011
[6,1,2,7,3,4,5]=>[6,1,7,3,4,2,5]=>[7,3,4,6,1,2,5]=>000011
[6,1,2,7,3,5,4]=>[6,1,7,5,3,2,4]=>[5,3,7,1,2,6,4]=>000111
[6,1,2,7,4,3,5]=>[6,1,4,7,3,2,5]=>[7,4,3,6,1,2,5]=>001011
[6,1,2,7,4,5,3]=>[6,1,5,7,4,2,3]=>[7,4,5,1,2,6,3]=>000111
[6,1,2,7,5,3,4]=>[6,1,5,3,7,2,4]=>[7,5,3,6,1,2,4]=>000111
[6,1,2,7,5,4,3]=>[6,1,4,5,7,2,3]=>[7,5,4,1,2,6,3]=>001111
[6,1,3,2,4,5,7]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>010010
[6,1,3,2,4,7,5]=>[6,3,1,2,7,4,5]=>[3,1,7,2,4,6,5]=>010011
[6,1,3,2,5,4,7]=>[6,3,1,5,2,4,7]=>[3,1,5,2,6,4,7]=>010110
[6,1,3,2,5,7,4]=>[6,3,1,7,2,5,4]=>[3,1,7,2,5,6,4]=>010011
[6,1,3,2,7,4,5]=>[6,3,1,7,4,2,5]=>[3,1,7,4,6,2,5]=>010011
[6,1,3,2,7,5,4]=>[6,3,1,5,7,2,4]=>[3,1,7,5,2,6,4]=>010111
[6,1,3,4,2,5,7]=>[6,4,1,3,2,5,7]=>[4,1,3,6,2,5,7]=>001010
[6,1,3,4,2,7,5]=>[6,4,1,3,7,2,5]=>[4,1,3,7,2,6,5]=>001011
[6,1,3,4,5,2,7]=>[6,5,1,3,4,2,7]=>[5,1,3,4,6,2,7]=>000110
[6,1,3,4,5,7,2]=>[6,7,1,3,4,5,2]=>[7,1,3,4,5,6,2]=>000011
[6,1,3,4,7,2,5]=>[6,7,1,3,2,4,5]=>[7,1,3,6,2,4,5]=>000011
[6,1,3,4,7,5,2]=>[6,5,1,3,7,4,2]=>[7,5,1,3,4,6,2]=>000111
[6,1,3,5,2,4,7]=>[6,5,1,2,3,4,7]=>[5,1,6,2,3,4,7]=>000110
[6,1,3,5,2,7,4]=>[6,5,1,7,3,2,4]=>[7,1,3,5,2,6,4]=>000111
[6,1,3,5,4,2,7]=>[6,4,1,5,3,2,7]=>[5,4,1,3,6,2,7]=>001110
[6,1,3,5,4,7,2]=>[6,7,1,5,3,4,2]=>[5,1,3,7,4,6,2]=>000111
[6,1,3,5,7,2,4]=>[6,7,1,2,3,5,4]=>[7,1,5,6,2,3,4]=>000011
[6,1,3,5,7,4,2]=>[6,4,1,7,3,5,2]=>[7,4,1,3,5,6,2]=>001011
[6,1,3,7,2,4,5]=>[6,7,1,2,4,3,5]=>[7,1,4,6,2,3,5]=>000011
[6,1,3,7,2,5,4]=>[6,7,1,5,2,3,4]=>[5,1,7,2,3,6,4]=>000111
[6,1,3,7,4,2,5]=>[6,4,1,7,2,3,5]=>[7,4,1,6,2,3,5]=>001011
[6,1,3,7,4,5,2]=>[6,5,1,7,4,3,2]=>[7,4,5,1,3,6,2]=>000111
[6,1,3,7,5,2,4]=>[6,5,1,2,7,3,4]=>[7,5,1,6,2,3,4]=>000111
[6,1,3,7,5,4,2]=>[6,4,1,5,7,3,2]=>[7,5,4,1,3,6,2]=>001111
[6,1,4,2,3,5,7]=>[6,4,2,1,3,5,7]=>[4,2,6,1,3,5,7]=>001010
[6,1,4,2,3,7,5]=>[6,4,2,1,7,3,5]=>[4,2,7,1,3,6,5]=>001011
[6,1,4,2,5,3,7]=>[6,4,5,1,2,3,7]=>[5,1,4,2,6,3,7]=>001110
[6,1,4,2,5,7,3]=>[6,4,7,1,2,5,3]=>[7,1,4,2,5,6,3]=>001011
[6,1,4,2,7,3,5]=>[6,4,7,1,3,2,5]=>[7,1,4,3,6,2,5]=>001011
[6,1,4,2,7,5,3]=>[6,4,5,1,7,2,3]=>[7,5,1,4,2,6,3]=>001111
[6,1,4,3,2,5,7]=>[6,3,4,1,2,5,7]=>[4,3,1,6,2,5,7]=>011010
[6,1,4,3,2,7,5]=>[6,3,4,1,7,2,5]=>[4,3,1,7,2,6,5]=>011011
[6,1,4,3,5,2,7]=>[6,5,4,1,3,2,7]=>[4,1,5,3,6,2,7]=>001110
[6,1,4,3,5,7,2]=>[6,7,4,1,3,5,2]=>[4,1,7,3,5,6,2]=>001011
[6,1,4,3,7,2,5]=>[6,7,4,1,2,3,5]=>[4,1,7,2,6,3,5]=>001011
[6,1,4,3,7,5,2]=>[6,5,4,1,7,3,2]=>[4,1,7,5,3,6,2]=>001111
[6,1,4,5,2,3,7]=>[6,5,2,1,4,3,7]=>[5,2,4,6,1,3,7]=>000110
[6,1,4,5,2,7,3]=>[6,5,7,1,4,2,3]=>[7,1,4,5,2,6,3]=>000111
[6,1,4,5,3,2,7]=>[6,3,5,1,4,2,7]=>[5,3,1,4,6,2,7]=>010110
[6,1,4,5,3,7,2]=>[6,7,5,1,4,3,2]=>[5,1,4,7,3,6,2]=>000111
[6,1,4,5,7,2,3]=>[6,7,2,1,4,5,3]=>[7,2,4,5,6,1,3]=>000011
[6,1,4,5,7,3,2]=>[6,3,7,1,4,5,2]=>[7,3,1,4,5,6,2]=>010011
[6,1,4,7,2,3,5]=>[6,7,2,1,3,4,5]=>[7,2,6,1,3,4,5]=>000011
[6,1,4,7,2,5,3]=>[6,7,5,1,2,4,3]=>[5,1,7,2,4,6,3]=>000111
[6,1,4,7,3,2,5]=>[6,3,7,1,2,4,5]=>[7,3,1,6,2,4,5]=>010011
[6,1,4,7,3,5,2]=>[6,5,7,1,3,4,2]=>[7,1,5,3,4,6,2]=>000111
[6,1,4,7,5,2,3]=>[6,5,2,1,7,4,3]=>[7,5,2,4,6,1,3]=>000111
[6,1,4,7,5,3,2]=>[6,3,5,1,7,4,2]=>[7,5,3,1,4,6,2]=>010111
[6,1,5,2,3,4,7]=>[6,5,2,3,1,4,7]=>[5,2,3,6,1,4,7]=>000110
[6,1,5,2,3,7,4]=>[6,5,2,7,1,3,4]=>[7,2,5,1,3,6,4]=>000111
[6,1,5,2,4,3,7]=>[6,5,4,2,1,3,7]=>[4,2,5,1,6,3,7]=>001110
[6,1,5,2,4,7,3]=>[6,5,7,2,1,4,3]=>[7,2,5,1,4,6,3]=>000111
[6,1,5,2,7,3,4]=>[6,5,7,3,1,2,4]=>[7,3,5,1,6,2,4]=>000111
[6,1,5,2,7,4,3]=>[6,5,4,7,1,2,3]=>[7,4,1,5,2,6,3]=>001111
[6,1,5,3,2,4,7]=>[6,3,5,2,1,4,7]=>[5,3,2,6,1,4,7]=>010110
[6,1,5,3,2,7,4]=>[6,3,5,7,1,2,4]=>[7,3,1,5,2,6,4]=>010111
[6,1,5,3,4,2,7]=>[6,4,5,3,1,2,7]=>[5,3,4,1,6,2,7]=>001110
[6,1,5,3,4,7,2]=>[6,7,5,3,1,4,2]=>[5,3,7,1,4,6,2]=>000111
[6,1,5,3,7,2,4]=>[6,7,5,2,1,3,4]=>[5,2,7,1,6,3,4]=>000111
[6,1,5,3,7,4,2]=>[6,4,7,5,1,2,3]=>[5,1,7,4,2,6,3]=>001111
[6,1,5,4,2,3,7]=>[6,4,2,5,1,3,7]=>[5,4,2,6,1,3,7]=>001110
[6,1,5,4,2,7,3]=>[6,4,5,7,1,3,2]=>[7,1,5,4,3,6,2]=>001111
[6,1,5,4,3,2,7]=>[6,3,4,5,1,2,7]=>[5,4,3,1,6,2,7]=>011110
[6,1,5,4,3,7,2]=>[6,7,4,5,1,3,2]=>[5,4,1,7,3,6,2]=>001111
[6,1,5,4,7,2,3]=>[6,7,2,5,1,4,3]=>[5,2,7,4,6,1,3]=>000111
[6,1,5,4,7,3,2]=>[6,3,7,5,1,4,2]=>[5,3,1,7,4,6,2]=>010111
[6,1,5,7,2,3,4]=>[6,7,2,3,1,5,4]=>[7,2,3,5,6,1,4]=>000011
[6,1,5,7,2,4,3]=>[6,7,4,2,1,5,3]=>[4,2,7,1,5,6,3]=>001011
[6,1,5,7,3,2,4]=>[6,3,7,2,1,5,4]=>[7,3,2,5,6,1,4]=>010011
[6,1,5,7,3,4,2]=>[6,4,7,3,1,5,2]=>[7,3,4,1,5,6,2]=>001011
[6,1,5,7,4,2,3]=>[6,4,2,7,1,5,3]=>[7,4,2,5,6,1,3]=>001011
[6,1,5,7,4,3,2]=>[6,3,4,7,1,5,2]=>[7,4,3,1,5,6,2]=>011011
[6,1,7,2,3,4,5]=>[6,7,2,3,4,1,5]=>[7,2,3,4,6,1,5]=>000011
[6,1,7,2,3,5,4]=>[6,7,2,5,3,1,4]=>[5,2,3,7,1,6,4]=>000111
[6,1,7,2,4,3,5]=>[6,7,4,2,3,1,5]=>[4,2,7,3,6,1,5]=>001011
[6,1,7,2,4,5,3]=>[6,7,5,2,4,1,3]=>[5,2,4,7,1,6,3]=>000111
[6,1,7,2,5,3,4]=>[6,7,5,3,2,1,4]=>[5,3,7,2,6,1,4]=>000111
[6,1,7,2,5,4,3]=>[6,7,4,5,2,1,3]=>[5,4,2,7,1,6,3]=>001111
[6,1,7,3,2,4,5]=>[6,3,7,2,4,1,5]=>[7,3,2,4,6,1,5]=>010011
[6,1,7,3,2,5,4]=>[6,3,7,5,2,1,4]=>[5,3,2,7,1,6,4]=>010111
[6,1,7,3,4,2,5]=>[6,4,7,3,2,1,5]=>[7,3,4,2,6,1,5]=>001011
[6,1,7,3,4,5,2]=>[6,5,7,3,4,1,2]=>[7,3,4,5,1,6,2]=>000111
[6,1,7,3,5,2,4]=>[6,5,7,2,3,1,4]=>[7,2,5,3,6,1,4]=>000111
[6,1,7,3,5,4,2]=>[6,4,5,7,2,1,3]=>[7,2,5,4,1,6,3]=>001111
[6,1,7,4,2,3,5]=>[6,4,2,7,3,1,5]=>[7,4,2,3,6,1,5]=>001011
[6,1,7,4,2,5,3]=>[6,4,7,5,3,1,2]=>[5,3,7,4,1,6,2]=>001111
[6,1,7,4,3,2,5]=>[6,3,4,7,2,1,5]=>[7,4,3,2,6,1,5]=>011011
[6,1,7,4,3,5,2]=>[6,5,4,7,3,1,2]=>[7,4,3,5,1,6,2]=>001111
[6,1,7,4,5,2,3]=>[6,5,2,7,4,1,3]=>[7,4,5,2,6,1,3]=>000111
[6,1,7,4,5,3,2]=>[6,3,5,7,4,1,2]=>[7,4,5,3,1,6,2]=>010111
[6,1,7,5,2,3,4]=>[6,5,2,3,7,1,4]=>[7,5,2,3,6,1,4]=>000111
[6,1,7,5,2,4,3]=>[6,5,4,2,7,1,3]=>[4,2,7,5,1,6,3]=>001111
[6,1,7,5,3,2,4]=>[6,3,5,2,7,1,4]=>[7,5,3,2,6,1,4]=>010111
[6,1,7,5,3,4,2]=>[6,4,5,3,7,1,2]=>[7,5,3,4,1,6,2]=>001111
[6,1,7,5,4,2,3]=>[6,4,2,5,7,1,3]=>[7,5,4,2,6,1,3]=>001111
[6,1,7,5,4,3,2]=>[6,3,4,5,7,1,2]=>[7,5,4,3,1,6,2]=>011111
[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>100010
[6,2,1,3,4,7,5]=>[2,6,1,3,7,4,5]=>[7,2,1,3,4,6,5]=>100011
[6,2,1,3,5,4,7]=>[2,6,1,5,3,4,7]=>[5,2,1,3,6,4,7]=>100110
[6,2,1,3,5,7,4]=>[2,6,1,7,3,5,4]=>[7,2,1,3,5,6,4]=>100011
[6,2,1,3,7,4,5]=>[2,6,1,7,4,3,5]=>[7,4,6,2,1,3,5]=>100011
[6,2,1,3,7,5,4]=>[2,6,1,5,7,3,4]=>[7,5,2,1,3,6,4]=>100111
[6,2,1,4,3,5,7]=>[2,6,4,1,3,5,7]=>[4,2,1,6,3,5,7]=>101010
[6,2,1,4,3,7,5]=>[2,6,4,1,7,3,5]=>[4,2,1,7,3,6,5]=>101011
[6,2,1,4,5,3,7]=>[2,6,5,1,4,3,7]=>[5,2,1,4,6,3,7]=>100110
[6,2,1,4,5,7,3]=>[2,6,7,1,4,5,3]=>[7,2,1,4,5,6,3]=>100011
[6,2,1,4,7,3,5]=>[2,6,7,1,3,4,5]=>[7,2,1,6,3,4,5]=>100011
[6,2,1,4,7,5,3]=>[2,6,5,1,7,4,3]=>[7,5,2,1,4,6,3]=>100111
[6,2,1,5,3,4,7]=>[2,6,5,3,1,4,7]=>[5,3,6,2,1,4,7]=>100110
[6,2,1,5,3,7,4]=>[2,6,5,7,1,3,4]=>[7,2,1,5,3,6,4]=>100111
[6,2,1,5,4,3,7]=>[2,6,4,5,1,3,7]=>[5,4,2,1,6,3,7]=>101110
[6,2,1,5,4,7,3]=>[2,6,7,5,1,4,3]=>[5,2,1,7,4,6,3]=>100111
[6,2,1,5,7,3,4]=>[2,6,7,3,1,5,4]=>[7,3,5,6,2,1,4]=>100011
[6,2,1,5,7,4,3]=>[2,6,4,7,1,5,3]=>[7,4,2,1,5,6,3]=>101011
[6,2,1,7,3,4,5]=>[2,6,7,3,4,1,5]=>[7,3,4,6,2,1,5]=>100011
[6,2,1,7,3,5,4]=>[2,6,7,5,3,1,4]=>[5,3,7,2,1,6,4]=>100111
[6,2,1,7,4,3,5]=>[2,6,4,7,3,1,5]=>[7,4,3,6,2,1,5]=>101011
[6,2,1,7,4,5,3]=>[2,6,5,7,4,1,3]=>[7,4,5,2,1,6,3]=>100111
[6,2,1,7,5,3,4]=>[2,6,5,3,7,1,4]=>[7,5,3,6,2,1,4]=>100111
[6,2,1,7,5,4,3]=>[2,6,4,5,7,1,3]=>[7,5,4,2,1,6,3]=>101111
[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[6,2,3,1,4,5,7]=>010010
[6,2,3,1,4,7,5]=>[3,6,2,1,7,4,5]=>[7,2,3,1,4,6,5]=>010011
[6,2,3,1,5,4,7]=>[3,6,2,5,1,4,7]=>[5,2,3,1,6,4,7]=>010110
[6,2,3,1,5,7,4]=>[3,6,2,7,1,5,4]=>[7,2,3,1,5,6,4]=>010011
[6,2,3,1,7,4,5]=>[3,6,2,7,4,1,5]=>[7,4,6,2,3,1,5]=>010011
[6,2,3,1,7,5,4]=>[3,6,2,5,7,1,4]=>[7,5,2,3,1,6,4]=>010111
[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[6,2,3,4,1,5,7]=>001010
[6,2,3,4,1,7,5]=>[4,6,2,3,7,1,5]=>[7,2,3,4,1,6,5]=>001011
[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,2,3,4,5,1,7]=>000110
[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>[6,2,3,4,5,7,1]=>000011
[6,2,3,4,7,1,5]=>[7,6,2,3,1,4,5]=>[6,2,3,7,1,4,5]=>000011
[6,2,3,4,7,5,1]=>[5,7,1,3,6,4,2]=>[6,1,3,4,7,5,2]=>000111
[6,2,3,5,1,4,7]=>[5,6,2,1,3,4,7]=>[6,2,5,1,3,4,7]=>000110
[6,2,3,5,1,7,4]=>[5,6,2,7,3,1,4]=>[7,2,3,6,1,5,4]=>000111
[6,2,3,5,4,1,7]=>[4,5,1,6,3,2,7]=>[6,1,3,5,4,2,7]=>001110
[6,2,3,5,4,7,1]=>[7,6,2,5,3,4,1]=>[5,2,3,6,4,7,1]=>000111
[6,2,3,5,7,1,4]=>[7,6,2,1,3,5,4]=>[6,2,5,7,1,3,4]=>000011
[6,2,3,5,7,4,1]=>[4,7,1,6,3,5,2]=>[6,1,3,5,7,4,2]=>001011
[6,2,3,7,1,4,5]=>[7,6,2,1,4,3,5]=>[6,2,4,7,1,3,5]=>000011
[6,2,3,7,1,5,4]=>[7,6,2,5,1,3,4]=>[5,2,6,1,3,7,4]=>000111
[6,2,3,7,4,1,5]=>[4,7,1,6,2,3,5]=>[6,1,7,4,2,3,5]=>001011
[6,2,3,7,4,5,1]=>[5,6,2,7,4,3,1]=>[7,4,6,2,3,5,1]=>000111
[6,2,3,7,5,1,4]=>[5,7,1,2,6,3,4]=>[6,1,7,5,2,3,4]=>000111
[6,2,3,7,5,4,1]=>[4,5,2,7,6,3,1]=>[6,2,3,7,5,4,1]=>001111
[6,2,4,1,3,5,7]=>[4,6,1,2,3,5,7]=>[6,1,4,2,3,5,7]=>001010
[6,2,4,1,3,7,5]=>[4,6,1,2,7,3,5]=>[7,1,4,2,3,6,5]=>001011
[6,2,4,1,5,3,7]=>[4,6,5,2,1,3,7]=>[5,2,6,1,4,3,7]=>001110
[6,2,4,1,5,7,3]=>[4,6,7,2,1,5,3]=>[7,2,5,6,1,4,3]=>001011
[6,2,4,1,7,3,5]=>[4,6,7,2,3,1,5]=>[7,2,6,3,4,1,5]=>001011
[6,2,4,1,7,5,3]=>[4,6,5,2,7,1,3]=>[7,5,2,6,1,4,3]=>001111
[6,2,4,3,1,5,7]=>[3,4,6,1,2,5,7]=>[6,1,4,3,2,5,7]=>011010
[6,2,4,3,1,7,5]=>[3,4,6,1,7,2,5]=>[7,1,4,3,2,6,5]=>011011
[6,2,4,3,5,1,7]=>[5,6,4,2,3,1,7]=>[4,2,6,3,5,1,7]=>001110
[6,2,4,3,5,7,1]=>[7,6,4,2,3,5,1]=>[4,2,6,3,5,7,1]=>001011
[6,2,4,3,7,1,5]=>[7,6,4,2,1,3,5]=>[4,2,6,1,7,3,5]=>001011
[6,2,4,3,7,5,1]=>[5,7,4,1,6,3,2]=>[4,1,6,3,7,5,2]=>001111
[6,2,4,5,1,3,7]=>[5,6,1,2,4,3,7]=>[6,1,4,5,2,3,7]=>000110
[6,2,4,5,1,7,3]=>[5,6,7,2,4,1,3]=>[7,2,4,6,1,5,3]=>000111
[6,2,4,5,3,1,7]=>[3,5,6,1,4,2,7]=>[6,1,4,5,3,2,7]=>010110
[6,2,4,5,3,7,1]=>[7,6,5,2,4,3,1]=>[5,2,4,6,3,7,1]=>000111
[6,2,4,5,7,1,3]=>[7,6,1,2,4,5,3]=>[6,1,4,5,7,2,3]=>000011
[6,2,4,5,7,3,1]=>[3,7,6,1,4,5,2]=>[6,1,4,5,7,3,2]=>010011
[6,2,4,7,1,3,5]=>[7,6,1,2,3,4,5]=>[6,1,7,2,3,4,5]=>000011
[6,2,4,7,1,5,3]=>[7,6,5,2,1,4,3]=>[5,2,6,1,4,7,3]=>000111
[6,2,4,7,3,1,5]=>[3,7,6,1,2,4,5]=>[6,1,7,3,2,4,5]=>010011
[6,2,4,7,3,5,1]=>[5,6,7,2,3,4,1]=>[7,2,6,3,4,5,1]=>000111
[6,2,4,7,5,1,3]=>[5,7,2,1,6,4,3]=>[6,2,4,7,5,1,3]=>000111
[6,2,4,7,5,3,1]=>[3,5,7,2,6,4,1]=>[6,2,4,7,5,3,1]=>010111
[6,2,5,1,3,4,7]=>[5,6,1,3,2,4,7]=>[6,1,3,5,2,4,7]=>000110
[6,2,5,1,3,7,4]=>[5,6,1,7,2,3,4]=>[7,1,6,2,3,5,4]=>000111
[6,2,5,1,4,3,7]=>[5,6,4,1,2,3,7]=>[4,1,6,2,5,3,7]=>001110
[6,2,5,1,4,7,3]=>[5,6,7,1,2,4,3]=>[7,1,6,2,4,5,3]=>000111
[6,2,5,1,7,3,4]=>[5,6,7,3,2,1,4]=>[7,3,6,2,5,1,4]=>000111
[6,2,5,1,7,4,3]=>[5,6,4,7,2,1,3]=>[7,4,2,6,1,5,3]=>001111
[6,2,5,3,1,4,7]=>[3,5,6,2,1,4,7]=>[6,2,5,3,1,4,7]=>010110
[6,2,5,3,1,7,4]=>[3,5,6,7,1,2,4]=>[7,1,6,3,2,5,4]=>010111
[6,2,5,3,4,1,7]=>[4,6,5,3,2,1,7]=>[5,3,6,2,4,1,7]=>001110
[6,2,5,3,4,7,1]=>[7,6,5,3,2,4,1]=>[5,3,6,2,4,7,1]=>000111
[6,2,5,3,7,1,4]=>[7,6,5,1,2,3,4]=>[5,1,6,2,7,3,4]=>000111
[6,2,5,3,7,4,1]=>[4,7,6,5,3,1,2]=>[5,3,6,1,7,4,2]=>001111
[6,2,5,4,1,3,7]=>[4,5,2,6,1,3,7]=>[6,2,5,4,1,3,7]=>001110
[6,2,5,4,1,7,3]=>[4,5,6,7,3,2,1]=>[7,3,6,2,5,4,1]=>001111
[6,2,5,4,3,1,7]=>[3,4,5,6,2,1,7]=>[6,2,5,4,3,1,7]=>011110
[6,2,5,4,3,7,1]=>[7,6,4,5,2,3,1]=>[5,4,2,6,3,7,1]=>001111
[6,2,5,4,7,1,3]=>[7,6,1,5,2,4,3]=>[5,1,6,4,7,2,3]=>000111
[6,2,5,4,7,3,1]=>[3,7,6,5,1,4,2]=>[5,1,6,4,7,3,2]=>010111
[6,2,5,7,1,3,4]=>[7,6,1,3,2,5,4]=>[6,1,3,5,7,2,4]=>000011
[6,2,5,7,1,4,3]=>[7,6,4,1,2,5,3]=>[4,1,6,2,5,7,3]=>001011
[6,2,5,7,3,1,4]=>[3,7,6,2,1,5,4]=>[6,2,5,7,3,1,4]=>010011
[6,2,5,7,3,4,1]=>[4,6,7,3,2,5,1]=>[7,3,5,6,2,4,1]=>001011
[6,2,5,7,4,1,3]=>[4,7,2,6,1,5,3]=>[6,2,5,7,4,1,3]=>001011
[6,2,5,7,4,3,1]=>[3,4,7,6,2,5,1]=>[6,2,5,7,4,3,1]=>011011
[6,2,7,1,3,4,5]=>[7,6,1,3,4,2,5]=>[6,1,3,4,7,2,5]=>000011
[6,2,7,1,3,5,4]=>[7,6,1,5,3,2,4]=>[5,1,3,6,2,7,4]=>000111
[6,2,7,1,4,3,5]=>[7,6,4,1,3,2,5]=>[4,1,6,3,7,2,5]=>001011
[6,2,7,1,4,5,3]=>[7,6,5,1,4,2,3]=>[5,1,4,6,2,7,3]=>000111
[6,2,7,1,5,3,4]=>[7,6,5,3,1,2,4]=>[5,3,6,1,7,2,4]=>000111
[6,2,7,1,5,4,3]=>[7,6,4,5,1,2,3]=>[5,4,1,6,2,7,3]=>001111
[6,2,7,3,1,4,5]=>[3,7,6,2,4,1,5]=>[6,2,4,7,3,1,5]=>010011
[6,2,7,3,1,5,4]=>[3,7,6,5,2,1,4]=>[5,2,6,3,1,7,4]=>010111
[6,2,7,3,4,1,5]=>[4,6,7,3,1,2,5]=>[7,3,6,1,4,2,5]=>001011
[6,2,7,3,4,5,1]=>[5,6,7,3,4,2,1]=>[7,3,4,6,2,5,1]=>000111
[6,2,7,3,5,1,4]=>[5,6,7,1,3,2,4]=>[7,1,6,3,5,2,4]=>000111
[6,2,7,3,5,4,1]=>[4,5,6,7,1,3,2]=>[7,1,6,3,5,4,2]=>001111
[6,2,7,4,1,3,5]=>[4,7,2,6,3,1,5]=>[6,2,3,7,4,1,5]=>001011
[6,2,7,4,1,5,3]=>[4,7,6,5,2,3,1]=>[5,2,6,3,7,4,1]=>001111
[6,2,7,4,3,1,5]=>[3,4,7,6,1,2,5]=>[6,1,7,4,3,2,5]=>011011
[6,2,7,4,3,5,1]=>[5,6,4,7,3,2,1]=>[7,4,3,6,2,5,1]=>001111
[6,2,7,4,5,1,3]=>[5,6,1,7,4,2,3]=>[7,4,6,1,5,2,3]=>000111
[6,2,7,4,5,3,1]=>[3,5,6,7,4,1,2]=>[7,4,6,1,5,3,2]=>010111
[6,2,7,5,1,3,4]=>[5,7,2,3,6,1,4]=>[6,2,3,7,5,1,4]=>000111
[6,2,7,5,1,4,3]=>[5,7,4,2,6,1,3]=>[4,2,6,1,7,5,3]=>001111
[6,2,7,5,3,1,4]=>[3,5,7,1,6,2,4]=>[6,1,7,5,3,2,4]=>010111
[6,2,7,5,3,4,1]=>[4,6,5,3,7,2,1]=>[7,5,3,6,2,4,1]=>001111
[6,2,7,5,4,1,3]=>[4,5,1,7,6,2,3]=>[6,1,7,5,4,2,3]=>001111
[6,2,7,5,4,3,1]=>[3,4,5,7,6,1,2]=>[6,1,7,5,4,3,2]=>011111
[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[6,3,1,2,4,5,7]=>010010
[6,3,1,2,4,7,5]=>[3,1,6,2,7,4,5]=>[7,3,1,2,4,6,5]=>010011
[6,3,1,2,5,4,7]=>[3,1,6,5,2,4,7]=>[5,3,1,2,6,4,7]=>010110
[6,3,1,2,5,7,4]=>[3,1,6,7,2,5,4]=>[7,3,1,2,5,6,4]=>010011
[6,3,1,2,7,4,5]=>[3,1,6,7,4,2,5]=>[7,4,6,3,1,2,5]=>010011
[6,3,1,2,7,5,4]=>[3,1,6,5,7,2,4]=>[7,5,3,1,2,6,4]=>010111
[6,3,1,4,2,5,7]=>[3,6,4,2,1,5,7]=>[4,2,6,3,1,5,7]=>011010
[6,3,1,4,2,7,5]=>[3,6,4,2,7,1,5]=>[4,2,7,3,1,6,5]=>011011
[6,3,1,4,5,2,7]=>[3,6,5,2,4,1,7]=>[5,2,4,6,3,1,7]=>010110
[6,3,1,4,5,7,2]=>[3,6,7,2,4,5,1]=>[7,2,4,5,6,3,1]=>010011
[6,3,1,4,7,2,5]=>[3,6,7,2,1,4,5]=>[7,2,6,3,1,4,5]=>010011
[6,3,1,4,7,5,2]=>[3,6,5,2,7,4,1]=>[7,5,2,4,6,3,1]=>010111
[6,3,1,5,2,4,7]=>[3,6,5,1,2,4,7]=>[5,1,6,3,2,4,7]=>010110
[6,3,1,5,2,7,4]=>[3,6,5,7,2,1,4]=>[7,2,5,3,1,6,4]=>010111
[6,3,1,5,4,2,7]=>[3,6,4,5,2,1,7]=>[5,4,2,6,3,1,7]=>011110
[6,3,1,5,4,7,2]=>[3,6,7,5,2,4,1]=>[5,2,7,4,6,3,1]=>010111
[6,3,1,5,7,2,4]=>[3,6,7,1,2,5,4]=>[7,1,5,6,3,2,4]=>010011
[6,3,1,5,7,4,2]=>[3,6,4,7,2,5,1]=>[7,4,2,5,6,3,1]=>011011
[6,3,1,7,2,4,5]=>[3,6,7,1,4,2,5]=>[7,1,4,6,3,2,5]=>010011
[6,3,1,7,2,5,4]=>[3,6,7,5,1,2,4]=>[5,1,7,3,2,6,4]=>010111
[6,3,1,7,4,2,5]=>[3,6,4,7,1,2,5]=>[7,4,1,6,3,2,5]=>011011
[6,3,1,7,4,5,2]=>[3,6,5,7,4,2,1]=>[7,4,5,2,6,3,1]=>010111
[6,3,1,7,5,2,4]=>[3,6,5,1,7,2,4]=>[7,5,1,6,3,2,4]=>010111
[6,3,1,7,5,4,2]=>[3,6,4,5,7,2,1]=>[7,5,4,2,6,3,1]=>011111
[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[6,3,2,1,4,5,7]=>110010
[6,3,2,1,4,7,5]=>[2,3,6,1,7,4,5]=>[7,3,2,1,4,6,5]=>110011
[6,3,2,1,5,4,7]=>[2,3,6,5,1,4,7]=>[5,3,2,1,6,4,7]=>110110
[6,3,2,1,5,7,4]=>[2,3,6,7,1,5,4]=>[7,3,2,1,5,6,4]=>110011
[6,3,2,1,7,4,5]=>[2,3,6,7,4,1,5]=>[7,4,6,3,2,1,5]=>110011
[6,3,2,1,7,5,4]=>[2,3,6,5,7,1,4]=>[7,5,3,2,1,6,4]=>110111
[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>[6,3,2,4,1,5,7]=>011010
[6,3,2,4,1,7,5]=>[4,3,6,2,7,1,5]=>[7,3,2,4,1,6,5]=>011011
[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[6,3,2,4,5,1,7]=>010110
[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>[6,3,2,4,5,7,1]=>010011
[6,3,2,4,7,1,5]=>[7,3,6,2,1,4,5]=>[6,3,2,7,1,4,5]=>010011
[6,3,2,4,7,5,1]=>[5,3,7,1,6,4,2]=>[6,3,1,4,7,5,2]=>010111
[6,3,2,5,1,4,7]=>[5,3,6,1,2,4,7]=>[6,3,1,5,2,4,7]=>010110
[6,3,2,5,1,7,4]=>[5,3,6,7,2,1,4]=>[7,3,2,6,1,5,4]=>010111
[6,3,2,5,4,1,7]=>[4,3,5,6,1,2,7]=>[6,3,1,5,4,2,7]=>011110
[6,3,2,5,4,7,1]=>[7,3,6,5,2,4,1]=>[5,3,2,6,4,7,1]=>010111
[6,3,2,5,7,1,4]=>[7,3,6,1,2,5,4]=>[6,3,1,5,7,2,4]=>010011
[6,3,2,5,7,4,1]=>[4,3,7,6,1,5,2]=>[6,3,1,5,7,4,2]=>011011
[6,3,2,7,1,4,5]=>[7,3,6,1,4,2,5]=>[6,3,1,4,7,2,5]=>010011
[6,3,2,7,1,5,4]=>[7,3,6,5,1,2,4]=>[5,3,1,6,2,7,4]=>010111
[6,3,2,7,4,1,5]=>[4,3,7,6,2,1,5]=>[6,3,2,7,4,1,5]=>011011
[6,3,2,7,4,5,1]=>[5,3,6,7,4,2,1]=>[7,4,6,3,2,5,1]=>010111
[6,3,2,7,5,1,4]=>[5,3,7,2,6,1,4]=>[6,3,2,7,5,1,4]=>010111
[6,3,2,7,5,4,1]=>[4,3,5,7,6,2,1]=>[6,3,2,7,5,4,1]=>011111
[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[6,3,4,1,2,5,7]=>001010
[6,3,4,1,2,7,5]=>[4,1,6,3,7,2,5]=>[7,3,4,1,2,6,5]=>001011
[6,3,4,1,5,2,7]=>[4,5,6,3,1,2,7]=>[6,3,5,1,4,2,7]=>001110
[6,3,4,1,5,7,2]=>[4,7,6,3,1,5,2]=>[6,3,5,7,1,4,2]=>001011
[6,3,4,1,7,2,5]=>[4,7,6,3,2,1,5]=>[6,3,7,2,4,1,5]=>001011
[6,3,4,1,7,5,2]=>[4,5,7,2,6,1,3]=>[6,2,7,5,1,4,3]=>001111
[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>[6,3,4,2,1,5,7]=>101010
[6,3,4,2,1,7,5]=>[2,4,6,3,7,1,5]=>[7,3,4,2,1,6,5]=>101011
[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>[6,3,4,2,5,1,7]=>001110
[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>[6,3,4,2,5,7,1]=>001011
[6,3,4,2,7,1,5]=>[7,4,6,3,1,2,5]=>[6,3,4,1,7,2,5]=>001011
[6,3,4,2,7,5,1]=>[5,4,7,1,6,2,3]=>[6,1,4,2,7,5,3]=>001111
[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>[6,3,4,5,1,2,7]=>000110
[6,3,4,5,1,7,2]=>[5,7,6,3,4,1,2]=>[6,3,4,7,1,5,2]=>000111
[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>[6,3,4,5,2,1,7]=>100110
[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>[6,3,4,5,2,7,1]=>000111
[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>[6,3,4,5,7,1,2]=>000011
[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>[6,3,4,5,7,2,1]=>100011
[6,3,4,7,1,2,5]=>[7,1,6,3,2,4,5]=>[6,3,7,1,2,4,5]=>000011
[6,3,4,7,1,5,2]=>[7,5,6,3,1,4,2]=>[6,3,5,1,4,7,2]=>000111
[6,3,4,7,2,1,5]=>[2,7,6,3,1,4,5]=>[6,3,7,2,1,4,5]=>100011
[6,3,4,7,2,5,1]=>[5,7,6,3,2,4,1]=>[6,3,7,2,4,5,1]=>000111
[6,3,4,7,5,1,2]=>[5,1,7,2,6,4,3]=>[6,1,2,4,7,5,3]=>000111
[6,3,4,7,5,2,1]=>[2,5,7,1,6,4,3]=>[6,2,1,4,7,5,3]=>100111
[6,3,5,1,2,4,7]=>[5,1,6,2,3,4,7]=>[6,1,2,5,3,4,7]=>000110
[6,3,5,1,2,7,4]=>[5,1,6,7,3,2,4]=>[7,3,6,1,2,5,4]=>000111
[6,3,5,1,4,2,7]=>[5,4,6,1,3,2,7]=>[6,1,4,3,5,2,7]=>001110
[6,3,5,1,4,7,2]=>[5,7,6,1,3,4,2]=>[6,1,7,3,4,5,2]=>000111
[6,3,5,1,7,2,4]=>[5,7,6,2,3,1,4]=>[6,2,7,3,5,1,4]=>000111
[6,3,5,1,7,4,2]=>[5,4,7,6,2,1,3]=>[6,2,7,4,1,5,3]=>001111
[6,3,5,2,1,4,7]=>[2,5,6,1,3,4,7]=>[6,2,1,5,3,4,7]=>100110
[6,3,5,2,1,7,4]=>[2,5,6,7,3,1,4]=>[7,3,6,2,1,5,4]=>100111
[6,3,5,2,4,1,7]=>[4,5,6,2,3,1,7]=>[6,2,5,3,4,1,7]=>001110
[6,3,5,2,4,7,1]=>[7,5,6,2,3,4,1]=>[6,2,5,3,4,7,1]=>000111
[6,3,5,2,7,1,4]=>[7,5,6,1,3,2,4]=>[6,1,5,3,7,2,4]=>000111
[6,3,5,2,7,4,1]=>[4,7,5,6,1,3,2]=>[6,1,5,3,7,4,2]=>001111
[6,3,5,4,1,2,7]=>[4,1,5,6,2,3,7]=>[6,1,2,5,4,3,7]=>001110
[6,3,5,4,1,7,2]=>[4,5,7,6,1,2,3]=>[6,1,7,2,5,4,3]=>001111
[6,3,5,4,2,1,7]=>[2,4,5,6,1,3,7]=>[6,2,1,5,4,3,7]=>101110
[6,3,5,4,2,7,1]=>[7,4,5,6,2,3,1]=>[6,2,5,4,3,7,1]=>001111
[6,3,5,4,7,1,2]=>[7,1,6,5,3,4,2]=>[5,3,6,4,7,1,2]=>000111
[6,3,5,4,7,2,1]=>[2,7,6,5,3,4,1]=>[5,3,6,4,7,2,1]=>100111
[6,3,5,7,1,2,4]=>[7,1,6,2,3,5,4]=>[6,1,2,5,7,3,4]=>000011
[6,3,5,7,1,4,2]=>[7,4,6,1,3,5,2]=>[6,1,4,3,5,7,2]=>001011
[6,3,5,7,2,1,4]=>[2,7,6,1,3,5,4]=>[6,2,1,5,7,3,4]=>100011
[6,3,5,7,2,4,1]=>[4,7,6,2,3,5,1]=>[6,2,5,7,3,4,1]=>001011
[6,3,5,7,4,1,2]=>[4,1,7,6,2,5,3]=>[6,1,2,5,7,4,3]=>001011
[6,3,5,7,4,2,1]=>[2,4,7,6,1,5,3]=>[6,2,1,5,7,4,3]=>101011
[6,3,7,1,2,4,5]=>[7,1,6,2,4,3,5]=>[6,1,2,4,7,3,5]=>000011
[6,3,7,1,2,5,4]=>[7,1,6,5,2,3,4]=>[5,1,2,6,3,7,4]=>000111
[6,3,7,1,4,2,5]=>[7,4,6,1,2,3,5]=>[6,1,4,2,7,3,5]=>001011
[6,3,7,1,4,5,2]=>[7,5,6,1,4,3,2]=>[6,1,4,5,3,7,2]=>000111
[6,3,7,1,5,2,4]=>[7,5,6,2,1,3,4]=>[6,2,5,1,7,3,4]=>000111
[6,3,7,1,5,4,2]=>[7,4,5,6,1,2,3]=>[6,1,5,4,2,7,3]=>001111
[6,3,7,2,1,4,5]=>[2,7,6,1,4,3,5]=>[6,2,1,4,7,3,5]=>100011
[6,3,7,2,1,5,4]=>[2,7,6,5,1,3,4]=>[5,2,1,6,3,7,4]=>100111
[6,3,7,2,4,1,5]=>[4,7,6,2,1,3,5]=>[6,2,7,1,4,3,5]=>001011
[6,3,7,2,4,5,1]=>[5,7,6,2,4,3,1]=>[6,2,4,7,3,5,1]=>000111
[6,3,7,2,5,1,4]=>[5,7,6,1,2,3,4]=>[6,1,7,2,5,3,4]=>000111
[6,3,7,2,5,4,1]=>[4,5,7,6,3,1,2]=>[6,3,7,1,5,4,2]=>001111
[6,3,7,4,1,2,5]=>[4,1,7,6,3,2,5]=>[6,3,7,4,1,2,5]=>001011
[6,3,7,4,1,5,2]=>[4,7,5,6,2,1,3]=>[6,2,5,1,7,4,3]=>001111
[6,3,7,4,2,1,5]=>[2,4,7,6,3,1,5]=>[6,3,7,4,2,1,5]=>101011
[6,3,7,4,2,5,1]=>[5,4,7,6,3,2,1]=>[6,3,7,4,2,5,1]=>001111
[6,3,7,4,5,1,2]=>[5,1,6,7,4,3,2]=>[7,4,6,3,5,1,2]=>000111
[6,3,7,4,5,2,1]=>[2,5,6,7,4,3,1]=>[7,4,6,3,5,2,1]=>100111
[6,3,7,5,1,2,4]=>[5,1,7,3,6,2,4]=>[6,3,7,5,1,2,4]=>000111
[6,3,7,5,1,4,2]=>[5,4,7,3,6,1,2]=>[6,3,4,1,7,5,2]=>001111
[6,3,7,5,2,1,4]=>[2,5,7,3,6,1,4]=>[6,3,7,5,2,1,4]=>100111
[6,3,7,5,2,4,1]=>[4,5,7,3,6,2,1]=>[6,3,7,5,2,4,1]=>001111
[6,3,7,5,4,1,2]=>[4,1,5,7,6,3,2]=>[6,3,7,5,4,1,2]=>001111
[6,3,7,5,4,2,1]=>[2,4,5,7,6,3,1]=>[6,3,7,5,4,2,1]=>101111
[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[6,4,1,2,3,5,7]=>001010
[6,4,1,2,3,7,5]=>[4,1,2,6,7,3,5]=>[7,4,1,2,3,6,5]=>001011
[6,4,1,2,5,3,7]=>[4,1,6,5,3,2,7]=>[5,3,6,4,1,2,7]=>001110
[6,4,1,2,5,7,3]=>[4,1,6,7,3,5,2]=>[7,3,5,6,4,1,2]=>001011
[6,4,1,2,7,3,5]=>[4,1,6,7,2,3,5]=>[7,1,2,6,4,3,5]=>001011
[6,4,1,2,7,5,3]=>[4,1,6,5,7,3,2]=>[7,5,3,6,4,1,2]=>001111
[6,4,1,3,2,5,7]=>[4,3,1,6,2,5,7]=>[3,1,6,4,2,5,7]=>011010
[6,4,1,3,2,7,5]=>[4,3,1,6,7,2,5]=>[3,1,7,4,2,6,5]=>011011
[6,4,1,3,5,2,7]=>[4,6,2,5,3,1,7]=>[5,2,3,6,4,1,7]=>001110
[6,4,1,3,5,7,2]=>[4,6,2,7,3,5,1]=>[7,2,3,5,6,4,1]=>001011
[6,4,1,3,7,2,5]=>[4,6,2,7,1,3,5]=>[7,2,6,4,1,3,5]=>001011
[6,4,1,3,7,5,2]=>[4,6,2,5,7,3,1]=>[7,5,2,3,6,4,1]=>001111
[6,4,1,5,2,3,7]=>[4,6,1,5,2,3,7]=>[5,1,6,4,2,3,7]=>001110
[6,4,1,5,2,7,3]=>[4,6,5,7,2,3,1]=>[7,2,5,3,6,4,1]=>001111
[6,4,1,5,3,2,7]=>[4,3,6,5,2,1,7]=>[5,3,2,6,4,1,7]=>011110
[6,4,1,5,3,7,2]=>[4,6,7,5,2,1,3]=>[5,2,7,1,6,4,3]=>001111
[6,4,1,5,7,2,3]=>[4,6,1,7,2,5,3]=>[7,1,5,6,4,2,3]=>001011
[6,4,1,5,7,3,2]=>[4,3,6,7,2,5,1]=>[7,3,2,5,6,4,1]=>011011
[6,4,1,7,2,3,5]=>[4,6,1,7,3,2,5]=>[7,1,3,6,4,2,5]=>001011
[6,4,1,7,2,5,3]=>[4,6,7,5,3,2,1]=>[5,3,7,2,6,4,1]=>001111
[6,4,1,7,3,2,5]=>[4,3,6,7,1,2,5]=>[7,3,1,6,4,2,5]=>011011
[6,4,1,7,3,5,2]=>[4,6,5,7,1,2,3]=>[7,1,5,2,6,4,3]=>001111
[6,4,1,7,5,2,3]=>[4,6,1,5,7,2,3]=>[7,5,1,6,4,2,3]=>001111
[6,4,1,7,5,3,2]=>[4,3,6,5,7,2,1]=>[7,5,3,2,6,4,1]=>011111
[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[6,4,2,1,3,5,7]=>101010
[6,4,2,1,3,7,5]=>[2,4,1,6,7,3,5]=>[7,4,2,1,3,6,5]=>101011
[6,4,2,1,5,3,7]=>[2,4,6,5,3,1,7]=>[5,3,6,4,2,1,7]=>101110
[6,4,2,1,5,7,3]=>[2,4,6,7,3,5,1]=>[7,3,5,6,4,2,1]=>101011
[6,4,2,1,7,3,5]=>[2,4,6,7,1,3,5]=>[7,2,1,6,4,3,5]=>101011
[6,4,2,1,7,5,3]=>[2,4,6,5,7,3,1]=>[7,5,3,6,4,2,1]=>101111
[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>[6,4,2,3,1,5,7]=>011010
[6,4,2,3,1,7,5]=>[3,4,2,6,7,1,5]=>[7,4,2,3,1,6,5]=>011011
[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>[6,4,2,3,5,1,7]=>001110
[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>[6,4,2,3,5,7,1]=>001011
[6,4,2,3,7,1,5]=>[7,4,2,6,1,3,5]=>[6,4,2,7,1,3,5]=>001011
[6,4,2,3,7,5,1]=>[5,4,1,7,6,3,2]=>[6,4,1,3,7,5,2]=>001111
[6,4,2,5,1,3,7]=>[5,4,1,6,2,3,7]=>[6,4,1,5,2,3,7]=>001110
[6,4,2,5,1,7,3]=>[5,4,6,7,3,1,2]=>[7,3,6,4,1,5,2]=>001111
[6,4,2,5,3,1,7]=>[3,5,4,6,1,2,7]=>[6,4,1,5,3,2,7]=>011110
[6,4,2,5,3,7,1]=>[7,4,6,5,3,2,1]=>[5,3,6,4,2,7,1]=>001111
[6,4,2,5,7,1,3]=>[7,4,1,6,2,5,3]=>[6,4,1,5,7,2,3]=>001011
[6,4,2,5,7,3,1]=>[3,7,4,6,1,5,2]=>[6,4,1,5,7,3,2]=>011011
[6,4,2,7,1,3,5]=>[7,4,1,6,3,2,5]=>[6,4,1,3,7,2,5]=>001011
[6,4,2,7,1,5,3]=>[7,4,6,5,1,3,2]=>[5,1,6,4,3,7,2]=>001111
[6,4,2,7,3,1,5]=>[3,7,4,6,2,1,5]=>[6,4,2,7,3,1,5]=>011011
[6,4,2,7,3,5,1]=>[5,4,6,7,2,3,1]=>[7,2,6,4,3,5,1]=>001111
[6,4,2,7,5,1,3]=>[5,4,2,7,6,1,3]=>[6,4,2,7,5,1,3]=>001111
[6,4,2,7,5,3,1]=>[3,5,4,7,6,2,1]=>[6,4,2,7,5,3,1]=>011111
[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[6,4,3,1,2,5,7]=>011010
[6,4,3,1,2,7,5]=>[3,1,4,6,7,2,5]=>[7,4,3,1,2,6,5]=>011011
[6,4,3,1,5,2,7]=>[3,4,6,5,1,2,7]=>[5,1,6,4,3,2,7]=>011110
[6,4,3,1,5,7,2]=>[3,4,6,7,1,5,2]=>[7,1,5,6,4,3,2]=>011011
[6,4,3,1,7,2,5]=>[3,4,6,7,2,1,5]=>[7,2,6,4,3,1,5]=>011011
[6,4,3,1,7,5,2]=>[3,4,6,5,7,1,2]=>[7,5,1,6,4,3,2]=>011111
[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[6,4,3,2,1,5,7]=>111010
[6,4,3,2,1,7,5]=>[2,3,4,6,7,1,5]=>[7,4,3,2,1,6,5]=>111011
[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]=>011110
[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>[6,4,3,2,5,7,1]=>011011
[6,4,3,2,7,1,5]=>[7,3,4,6,1,2,5]=>[6,4,3,1,7,2,5]=>011011
[6,4,3,2,7,5,1]=>[5,3,4,7,6,1,2]=>[6,4,3,1,7,5,2]=>011111
[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[6,4,3,5,1,2,7]=>001110
[6,4,3,5,1,7,2]=>[5,7,4,6,3,1,2]=>[6,4,3,7,1,5,2]=>001111
[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>[6,4,3,5,2,1,7]=>101110
[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>[6,4,3,5,2,7,1]=>001111
[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>[6,4,3,5,7,1,2]=>001011
[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>[6,4,3,5,7,2,1]=>101011
[6,4,3,7,1,2,5]=>[7,1,4,6,2,3,5]=>[6,4,1,2,7,3,5]=>001011
[6,4,3,7,1,5,2]=>[7,5,4,6,1,3,2]=>[6,4,1,5,3,7,2]=>001111
[6,4,3,7,2,1,5]=>[2,7,4,6,1,3,5]=>[6,4,2,1,7,3,5]=>101011
[6,4,3,7,2,5,1]=>[5,7,4,6,2,3,1]=>[6,4,2,7,3,5,1]=>001111
[6,4,3,7,5,1,2]=>[5,1,4,7,6,2,3]=>[6,4,1,2,7,5,3]=>001111
[6,4,3,7,5,2,1]=>[2,5,4,7,6,1,3]=>[6,4,2,1,7,5,3]=>101111
[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[6,4,5,1,2,3,7]=>000110
[6,4,5,1,2,7,3]=>[5,1,7,6,4,2,3]=>[6,4,7,1,2,5,3]=>000111
[6,4,5,1,3,2,7]=>[5,3,1,6,4,2,7]=>[3,1,6,4,5,2,7]=>010110
[6,4,5,1,3,7,2]=>[5,7,1,6,4,3,2]=>[6,4,7,1,3,5,2]=>000111
[6,4,5,1,7,2,3]=>[5,7,2,6,4,1,3]=>[6,4,7,2,5,1,3]=>000111
[6,4,5,1,7,3,2]=>[5,3,7,6,4,1,2]=>[6,4,7,3,1,5,2]=>010111
[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>[6,4,5,2,1,3,7]=>100110
[6,4,5,2,1,7,3]=>[2,5,7,6,4,1,3]=>[6,4,7,2,1,5,3]=>100111
[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>[6,4,5,2,3,1,7]=>010110
[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>[6,4,5,2,3,7,1]=>000111
[6,4,5,2,7,1,3]=>[7,5,1,6,4,2,3]=>[6,4,5,1,7,2,3]=>000111
[6,4,5,2,7,3,1]=>[3,7,5,6,4,1,2]=>[6,4,5,1,7,3,2]=>010111
[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>[6,4,5,3,1,2,7]=>010110
[6,4,5,3,1,7,2]=>[3,5,7,6,4,2,1]=>[6,4,7,2,5,3,1]=>010111
[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>[6,4,5,3,2,1,7]=>110110
[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>[6,4,5,3,2,7,1]=>010111
[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>[6,4,5,3,7,1,2]=>000111
[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>[6,4,5,3,7,2,1]=>100111
[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[6,4,5,7,1,2,3]=>000011
[6,4,5,7,1,3,2]=>[7,3,1,6,4,5,2]=>[3,1,6,4,5,7,2]=>010011
[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>[6,4,5,7,2,1,3]=>100011
[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>[6,4,5,7,2,3,1]=>010011
[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>[6,4,5,7,3,1,2]=>010011
[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>[6,4,5,7,3,2,1]=>110011
[6,4,7,1,2,3,5]=>[7,1,2,6,3,4,5]=>[6,1,2,3,7,4,5]=>000011
[6,4,7,1,2,5,3]=>[7,1,5,6,2,4,3]=>[6,1,2,5,4,7,3]=>000111
[6,4,7,1,3,2,5]=>[7,3,1,6,2,4,5]=>[3,1,6,2,7,4,5]=>010011
[6,4,7,1,3,5,2]=>[7,5,1,6,3,4,2]=>[6,1,3,5,4,7,2]=>000111
[6,4,7,1,5,2,3]=>[7,5,2,6,1,4,3]=>[6,2,5,4,7,1,3]=>000111
[6,4,7,1,5,3,2]=>[7,3,5,6,1,4,2]=>[6,3,1,5,4,7,2]=>010111
[6,4,7,2,1,3,5]=>[2,7,1,6,3,4,5]=>[6,2,1,3,7,4,5]=>100011
[6,4,7,2,1,5,3]=>[2,7,5,6,1,4,3]=>[6,2,1,5,4,7,3]=>100111
[6,4,7,2,3,1,5]=>[3,7,2,6,1,4,5]=>[6,2,3,1,7,4,5]=>010011
[6,4,7,2,3,5,1]=>[5,7,2,6,3,4,1]=>[6,2,3,7,4,5,1]=>000111
[6,4,7,2,5,1,3]=>[5,7,1,6,2,4,3]=>[6,1,7,4,5,2,3]=>000111
[6,4,7,2,5,3,1]=>[3,5,7,6,1,4,2]=>[6,1,7,4,5,3,2]=>010111
[6,4,7,3,1,2,5]=>[3,1,7,6,2,4,5]=>[6,3,1,2,7,4,5]=>010011
[6,4,7,3,1,5,2]=>[3,7,5,6,2,4,1]=>[6,2,5,4,7,3,1]=>010111
[6,4,7,3,2,1,5]=>[2,3,7,6,1,4,5]=>[6,3,2,1,7,4,5]=>110011
[6,4,7,3,2,5,1]=>[5,3,7,6,2,4,1]=>[6,3,2,7,4,5,1]=>010111
[6,4,7,3,5,1,2]=>[5,1,7,6,3,4,2]=>[6,3,7,4,5,1,2]=>000111
[6,4,7,3,5,2,1]=>[2,5,7,6,3,4,1]=>[6,3,7,4,5,2,1]=>100111
[6,4,7,5,1,2,3]=>[5,1,2,7,6,3,4]=>[6,1,2,3,7,5,4]=>000111
[6,4,7,5,1,3,2]=>[5,3,1,7,6,2,4]=>[3,1,6,2,7,5,4]=>010111
[6,4,7,5,2,1,3]=>[2,5,1,7,6,3,4]=>[6,2,1,3,7,5,4]=>100111
[6,4,7,5,2,3,1]=>[3,5,2,7,6,1,4]=>[6,2,3,1,7,5,4]=>010111
[6,4,7,5,3,1,2]=>[3,1,5,7,6,2,4]=>[6,3,1,2,7,5,4]=>010111
[6,4,7,5,3,2,1]=>[2,3,5,7,6,1,4]=>[6,3,2,1,7,5,4]=>110111
[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[6,5,1,2,3,4,7]=>000110
[6,5,1,2,3,7,4]=>[5,1,2,6,7,4,3]=>[7,4,6,5,1,2,3]=>000111
[6,5,1,2,4,3,7]=>[5,1,4,2,6,3,7]=>[4,1,2,6,5,3,7]=>001110
[6,5,1,2,4,7,3]=>[5,1,6,3,7,4,2]=>[7,3,4,6,5,1,2]=>000111
[6,5,1,2,7,3,4]=>[5,1,6,2,7,3,4]=>[7,1,2,6,5,3,4]=>000111
[6,5,1,2,7,4,3]=>[5,1,4,6,7,3,2]=>[7,4,3,6,5,1,2]=>001111
[6,5,1,3,2,4,7]=>[5,3,1,2,6,4,7]=>[3,1,6,5,2,4,7]=>010110
[6,5,1,3,2,7,4]=>[5,3,1,6,7,4,2]=>[3,1,7,4,6,5,2]=>010111
[6,5,1,3,4,2,7]=>[5,4,1,3,6,2,7]=>[4,1,3,6,5,2,7]=>001110
[6,5,1,3,4,7,2]=>[5,6,2,3,7,4,1]=>[7,2,3,4,6,5,1]=>000111
[6,5,1,3,7,2,4]=>[5,6,2,1,7,3,4]=>[7,2,6,5,1,3,4]=>000111
[6,5,1,3,7,4,2]=>[5,4,2,6,7,3,1]=>[7,4,2,3,6,5,1]=>001111
[6,5,1,4,2,3,7]=>[5,4,2,1,6,3,7]=>[4,2,6,5,1,3,7]=>001110
[6,5,1,4,2,7,3]=>[5,4,6,3,7,2,1]=>[7,3,4,2,6,5,1]=>001111
[6,5,1,4,3,2,7]=>[5,3,4,1,6,2,7]=>[4,3,1,6,5,2,7]=>011110
[6,5,1,4,3,7,2]=>[5,6,4,2,7,3,1]=>[4,2,7,3,6,5,1]=>001111
[6,5,1,4,7,2,3]=>[5,6,1,2,7,4,3]=>[7,1,4,6,5,2,3]=>000111
[6,5,1,4,7,3,2]=>[5,3,6,2,7,4,1]=>[7,3,2,4,6,5,1]=>010111
[6,5,1,7,2,3,4]=>[5,6,1,3,7,2,4]=>[7,1,3,6,5,2,4]=>000111
[6,5,1,7,2,4,3]=>[5,6,4,1,7,2,3]=>[4,1,7,2,6,5,3]=>001111
[6,5,1,7,3,2,4]=>[5,3,6,1,7,2,4]=>[7,3,1,6,5,2,4]=>010111
[6,5,1,7,3,4,2]=>[5,4,6,1,7,3,2]=>[7,1,4,3,6,5,2]=>001111
[6,5,1,7,4,2,3]=>[5,4,1,6,7,2,3]=>[7,4,1,6,5,2,3]=>001111
[6,5,1,7,4,3,2]=>[5,3,4,6,7,2,1]=>[7,4,3,2,6,5,1]=>011111
[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[6,5,2,1,3,4,7]=>100110
[6,5,2,1,3,7,4]=>[2,5,1,6,7,4,3]=>[7,4,6,5,2,1,3]=>100111
[6,5,2,1,4,3,7]=>[2,5,4,1,6,3,7]=>[4,2,1,6,5,3,7]=>101110
[6,5,2,1,4,7,3]=>[2,5,6,3,7,4,1]=>[7,3,4,6,5,2,1]=>100111
[6,5,2,1,7,3,4]=>[2,5,6,1,7,3,4]=>[7,2,1,6,5,3,4]=>100111
[6,5,2,1,7,4,3]=>[2,5,4,6,7,3,1]=>[7,4,3,6,5,2,1]=>101111
[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>[6,5,2,3,1,4,7]=>010110
[6,5,2,3,1,7,4]=>[3,5,2,6,7,4,1]=>[7,4,6,5,2,3,1]=>010111
[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>[6,5,2,3,4,1,7]=>001110
[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>[6,5,2,3,4,7,1]=>000111
[6,5,2,3,7,1,4]=>[7,5,2,1,6,3,4]=>[6,5,2,7,1,3,4]=>000111
[6,5,2,3,7,4,1]=>[4,7,1,5,6,3,2]=>[6,5,1,3,7,4,2]=>001111
[6,5,2,4,1,3,7]=>[4,5,1,2,6,3,7]=>[6,5,1,4,2,3,7]=>001110
[6,5,2,4,1,7,3]=>[4,5,6,3,7,1,2]=>[7,3,6,5,1,4,2]=>001111
[6,5,2,4,3,1,7]=>[3,4,5,1,6,2,7]=>[6,5,1,4,3,2,7]=>011110
[6,5,2,4,3,7,1]=>[7,5,4,2,6,3,1]=>[4,2,6,5,3,7,1]=>001111
[6,5,2,4,7,1,3]=>[7,5,1,2,6,4,3]=>[6,5,1,4,7,2,3]=>000111
[6,5,2,4,7,3,1]=>[3,7,5,1,6,4,2]=>[6,5,1,4,7,3,2]=>010111
[6,5,2,7,1,3,4]=>[7,5,1,3,6,2,4]=>[6,5,1,3,7,2,4]=>000111
[6,5,2,7,1,4,3]=>[7,5,4,1,6,2,3]=>[4,1,6,5,2,7,3]=>001111
[6,5,2,7,3,1,4]=>[3,7,5,2,6,1,4]=>[6,5,2,7,3,1,4]=>010111
[6,5,2,7,3,4,1]=>[4,5,6,2,7,3,1]=>[7,2,6,5,3,4,1]=>001111
[6,5,2,7,4,1,3]=>[4,7,2,5,6,1,3]=>[6,5,2,7,4,1,3]=>001111
[6,5,2,7,4,3,1]=>[3,4,7,5,6,2,1]=>[6,5,2,7,4,3,1]=>011111
[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[6,5,3,1,2,4,7]=>010110
[6,5,3,1,2,7,4]=>[3,1,5,6,7,4,2]=>[7,4,6,5,3,1,2]=>010111
[6,5,3,1,4,2,7]=>[3,5,4,2,6,1,7]=>[4,2,6,5,3,1,7]=>011110
[6,5,3,1,4,7,2]=>[3,5,6,1,7,4,2]=>[7,1,4,6,5,3,2]=>010111
[6,5,3,1,7,2,4]=>[3,5,6,2,7,1,4]=>[7,2,6,5,3,1,4]=>010111
[6,5,3,1,7,4,2]=>[3,5,4,6,7,1,2]=>[7,4,1,6,5,3,2]=>011111
[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[6,5,3,2,1,4,7]=>110110
[6,5,3,2,1,7,4]=>[2,3,5,6,7,4,1]=>[7,4,6,5,3,2,1]=>110111
[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>[6,5,3,2,4,1,7]=>011110
[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>[6,5,3,2,4,7,1]=>010111
[6,5,3,2,7,1,4]=>[7,3,5,1,6,2,4]=>[6,5,3,1,7,2,4]=>010111
[6,5,3,2,7,4,1]=>[4,3,7,5,6,1,2]=>[6,5,3,1,7,4,2]=>011111
[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[6,5,3,4,1,2,7]=>001110
[6,5,3,4,1,7,2]=>[4,7,5,3,6,1,2]=>[6,5,3,7,1,4,2]=>001111
[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]=>101110
[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>[6,5,3,4,2,7,1]=>001111
[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>[6,5,3,4,7,1,2]=>000111
[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>[6,5,3,4,7,2,1]=>100111
[6,5,3,7,1,2,4]=>[7,1,5,2,6,3,4]=>[6,5,1,2,7,3,4]=>000111
[6,5,3,7,1,4,2]=>[7,4,5,1,6,3,2]=>[6,5,1,4,3,7,2]=>001111
[6,5,3,7,2,1,4]=>[2,7,5,1,6,3,4]=>[6,5,2,1,7,3,4]=>100111
[6,5,3,7,2,4,1]=>[4,7,5,2,6,3,1]=>[6,5,2,7,3,4,1]=>001111
[6,5,3,7,4,1,2]=>[4,1,7,5,6,2,3]=>[6,5,1,2,7,4,3]=>001111
[6,5,3,7,4,2,1]=>[2,4,7,5,6,1,3]=>[6,5,2,1,7,4,3]=>101111
[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[6,5,4,1,2,3,7]=>001110
[6,5,4,1,2,7,3]=>[4,1,5,6,7,2,3]=>[7,1,2,6,5,4,3]=>001111
[6,5,4,1,3,2,7]=>[4,3,1,5,6,2,7]=>[3,1,6,5,4,2,7]=>011110
[6,5,4,1,3,7,2]=>[4,5,1,6,7,3,2]=>[7,1,3,6,5,4,2]=>001111
[6,5,4,1,7,2,3]=>[4,5,2,6,7,1,3]=>[7,2,6,5,4,1,3]=>001111
[6,5,4,1,7,3,2]=>[4,3,5,6,7,1,2]=>[7,3,1,6,5,4,2]=>011111
[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[6,5,4,2,1,3,7]=>101110
[6,5,4,2,1,7,3]=>[2,4,5,6,7,1,3]=>[7,2,1,6,5,4,3]=>101111
[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>[6,5,4,2,3,1,7]=>011110
[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>[6,5,4,2,3,7,1]=>001111
[6,5,4,2,7,1,3]=>[7,4,1,5,6,2,3]=>[6,5,4,1,7,2,3]=>001111
[6,5,4,2,7,3,1]=>[3,7,4,5,6,1,2]=>[6,5,4,1,7,3,2]=>011111
[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[6,5,4,3,1,2,7]=>011110
[6,5,4,3,1,7,2]=>[3,4,5,6,7,2,1]=>[7,2,6,5,4,3,1]=>011111
[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]=>111110
[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[6,5,4,3,2,7,1]=>011111
[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[6,5,4,3,7,1,2]=>001111
[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[6,5,4,3,7,2,1]=>101111
[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[6,5,4,7,1,2,3]=>000111
[6,5,4,7,1,3,2]=>[7,3,1,5,6,4,2]=>[3,1,6,5,4,7,2]=>010111
[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>[6,5,4,7,2,1,3]=>100111
[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>[6,5,4,7,2,3,1]=>010111
[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>[6,5,4,7,3,1,2]=>010111
[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[6,5,4,7,3,2,1]=>110111
[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[6,5,7,1,2,3,4]=>000011
[6,5,7,1,2,4,3]=>[7,1,4,2,6,5,3]=>[4,1,2,6,5,7,3]=>001011
[6,5,7,1,3,2,4]=>[7,3,1,2,6,5,4]=>[3,1,6,5,7,2,4]=>010011
[6,5,7,1,3,4,2]=>[7,4,1,3,6,5,2]=>[4,1,3,6,5,7,2]=>001011
[6,5,7,1,4,2,3]=>[7,4,2,1,6,5,3]=>[4,2,6,5,7,1,3]=>001011
[6,5,7,1,4,3,2]=>[7,3,4,1,6,5,2]=>[4,3,1,6,5,7,2]=>011011
[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[6,5,7,2,1,3,4]=>100011
[6,5,7,2,1,4,3]=>[2,7,4,1,6,5,3]=>[4,2,1,6,5,7,3]=>101011
[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>[6,5,7,2,3,1,4]=>010011
[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>[6,5,7,2,3,4,1]=>001011
[6,5,7,2,4,1,3]=>[4,7,1,2,6,5,3]=>[6,5,7,1,4,2,3]=>001011
[6,5,7,2,4,3,1]=>[3,4,7,1,6,5,2]=>[6,5,7,1,4,3,2]=>011011
[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[6,5,7,3,1,2,4]=>010011
[6,5,7,3,1,4,2]=>[3,7,4,2,6,5,1]=>[4,2,6,5,7,3,1]=>011011
[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[6,5,7,3,2,1,4]=>110011
[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>[6,5,7,3,2,4,1]=>011011
[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[6,5,7,3,4,1,2]=>001011
[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>[6,5,7,3,4,2,1]=>101011
[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>[6,5,7,4,1,2,3]=>001011
[6,5,7,4,1,3,2]=>[4,3,1,7,6,5,2]=>[3,1,6,5,7,4,2]=>011011
[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>[6,5,7,4,2,1,3]=>101011
[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>[6,5,7,4,2,3,1]=>011011
[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>[6,5,7,4,3,1,2]=>011011
[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[6,5,7,4,3,2,1]=>111011
[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[6,7,1,2,3,4,5]=>000001
[6,7,1,2,3,5,4]=>[7,1,2,5,3,6,4]=>[5,1,2,3,6,7,4]=>000101
[6,7,1,2,4,3,5]=>[7,1,4,2,3,6,5]=>[4,1,2,6,7,3,5]=>001001
[6,7,1,2,4,5,3]=>[7,1,5,2,4,6,3]=>[5,1,2,4,6,7,3]=>000101
[6,7,1,2,5,3,4]=>[7,1,5,3,2,6,4]=>[5,3,6,7,1,2,4]=>000101
[6,7,1,2,5,4,3]=>[7,1,4,5,2,6,3]=>[5,4,1,2,6,7,3]=>001101
[6,7,1,3,2,4,5]=>[7,3,1,2,4,6,5]=>[3,1,6,7,2,4,5]=>010001
[6,7,1,3,2,5,4]=>[7,3,1,5,2,6,4]=>[3,1,5,2,6,7,4]=>010101
[6,7,1,3,4,2,5]=>[7,4,1,3,2,6,5]=>[4,1,3,6,7,2,5]=>001001
[6,7,1,3,4,5,2]=>[7,5,1,3,4,6,2]=>[5,1,3,4,6,7,2]=>000101
[6,7,1,3,5,2,4]=>[7,5,1,2,3,6,4]=>[5,1,6,7,2,3,4]=>000101
[6,7,1,3,5,4,2]=>[7,4,1,5,3,6,2]=>[5,4,1,3,6,7,2]=>001101
[6,7,1,4,2,3,5]=>[7,4,2,1,3,6,5]=>[4,2,6,7,1,3,5]=>001001
[6,7,1,4,2,5,3]=>[7,4,5,1,2,6,3]=>[5,1,4,2,6,7,3]=>001101
[6,7,1,4,3,2,5]=>[7,3,4,1,2,6,5]=>[4,3,1,6,7,2,5]=>011001
[6,7,1,4,3,5,2]=>[7,5,4,1,3,6,2]=>[4,1,5,3,6,7,2]=>001101
[6,7,1,4,5,2,3]=>[7,5,2,1,4,6,3]=>[5,2,4,6,7,1,3]=>000101
[6,7,1,4,5,3,2]=>[7,3,5,1,4,6,2]=>[5,3,1,4,6,7,2]=>010101
[6,7,1,5,2,3,4]=>[7,5,2,3,1,6,4]=>[5,2,3,6,7,1,4]=>000101
[6,7,1,5,2,4,3]=>[7,5,4,2,1,6,3]=>[4,2,5,1,6,7,3]=>001101
[6,7,1,5,3,2,4]=>[7,3,5,2,1,6,4]=>[5,3,2,6,7,1,4]=>010101
[6,7,1,5,3,4,2]=>[7,4,5,3,1,6,2]=>[5,3,4,1,6,7,2]=>001101
[6,7,1,5,4,2,3]=>[7,4,2,5,1,6,3]=>[5,4,2,6,7,1,3]=>001101
[6,7,1,5,4,3,2]=>[7,3,4,5,1,6,2]=>[5,4,3,1,6,7,2]=>011101
[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[6,7,2,1,3,4,5]=>100001
[6,7,2,1,3,5,4]=>[2,7,1,5,3,6,4]=>[5,2,1,3,6,7,4]=>100101
[6,7,2,1,4,3,5]=>[2,7,4,1,3,6,5]=>[4,2,1,6,7,3,5]=>101001
[6,7,2,1,4,5,3]=>[2,7,5,1,4,6,3]=>[5,2,1,4,6,7,3]=>100101
[6,7,2,1,5,3,4]=>[2,7,5,3,1,6,4]=>[5,3,6,7,2,1,4]=>100101
[6,7,2,1,5,4,3]=>[2,7,4,5,1,6,3]=>[5,4,2,1,6,7,3]=>101101
[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[6,7,2,3,1,4,5]=>010001
[6,7,2,3,1,5,4]=>[3,7,2,5,1,6,4]=>[5,2,3,1,6,7,4]=>010101
[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>[6,7,2,3,4,1,5]=>001001
[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>[6,7,2,3,4,5,1]=>000101
[6,7,2,3,5,1,4]=>[5,7,2,1,3,6,4]=>[6,7,2,5,1,3,4]=>000101
[6,7,2,3,5,4,1]=>[4,5,1,7,3,6,2]=>[6,7,1,3,5,4,2]=>001101
[6,7,2,4,1,3,5]=>[4,7,1,2,3,6,5]=>[6,7,1,4,2,3,5]=>001001
[6,7,2,4,1,5,3]=>[4,7,5,2,1,6,3]=>[5,2,6,7,1,4,3]=>001101
[6,7,2,4,3,1,5]=>[3,4,7,1,2,6,5]=>[6,7,1,4,3,2,5]=>011001
[6,7,2,4,3,5,1]=>[5,7,4,2,3,6,1]=>[4,2,6,7,3,5,1]=>001101
[6,7,2,4,5,1,3]=>[5,7,1,2,4,6,3]=>[6,7,1,4,5,2,3]=>000101
[6,7,2,4,5,3,1]=>[3,5,7,1,4,6,2]=>[6,7,1,4,5,3,2]=>010101
[6,7,2,5,1,3,4]=>[5,7,1,3,2,6,4]=>[6,7,1,3,5,2,4]=>000101
[6,7,2,5,1,4,3]=>[5,7,4,1,2,6,3]=>[4,1,6,7,2,5,3]=>001101
[6,7,2,5,3,1,4]=>[3,5,7,2,1,6,4]=>[6,7,2,5,3,1,4]=>010101
[6,7,2,5,3,4,1]=>[4,7,5,3,2,6,1]=>[5,3,6,7,2,4,1]=>001101
[6,7,2,5,4,1,3]=>[4,5,2,7,1,6,3]=>[6,7,2,5,4,1,3]=>001101
[6,7,2,5,4,3,1]=>[3,4,5,7,2,6,1]=>[6,7,2,5,4,3,1]=>011101
[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[6,7,3,1,2,4,5]=>010001
[6,7,3,1,2,5,4]=>[3,1,7,5,2,6,4]=>[5,3,1,2,6,7,4]=>010101
[6,7,3,1,4,2,5]=>[3,7,4,2,1,6,5]=>[4,2,6,7,3,1,5]=>011001
[6,7,3,1,4,5,2]=>[3,7,5,2,4,6,1]=>[5,2,4,6,7,3,1]=>010101
[6,7,3,1,5,2,4]=>[3,7,5,1,2,6,4]=>[5,1,6,7,3,2,4]=>010101
[6,7,3,1,5,4,2]=>[3,7,4,5,2,6,1]=>[5,4,2,6,7,3,1]=>011101
[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[6,7,3,2,1,4,5]=>110001
[6,7,3,2,1,5,4]=>[2,3,7,5,1,6,4]=>[5,3,2,1,6,7,4]=>110101
[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[6,7,3,2,4,1,5]=>011001
[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>[6,7,3,2,4,5,1]=>010101
[6,7,3,2,5,1,4]=>[5,3,7,1,2,6,4]=>[6,7,3,1,5,2,4]=>010101
[6,7,3,2,5,4,1]=>[4,3,5,7,1,6,2]=>[6,7,3,1,5,4,2]=>011101
[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[6,7,3,4,1,2,5]=>001001
[6,7,3,4,1,5,2]=>[4,5,7,3,1,6,2]=>[6,7,3,5,1,4,2]=>001101
[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>[6,7,3,4,2,1,5]=>101001
[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>[6,7,3,4,2,5,1]=>001101
[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>[6,7,3,4,5,1,2]=>000101
[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>[6,7,3,4,5,2,1]=>100101
[6,7,3,5,1,2,4]=>[5,1,7,2,3,6,4]=>[6,7,1,2,5,3,4]=>000101
[6,7,3,5,1,4,2]=>[5,4,7,1,3,6,2]=>[6,7,1,4,3,5,2]=>001101
[6,7,3,5,2,1,4]=>[2,5,7,1,3,6,4]=>[6,7,2,1,5,3,4]=>100101
[6,7,3,5,2,4,1]=>[4,5,7,2,3,6,1]=>[6,7,2,5,3,4,1]=>001101
[6,7,3,5,4,1,2]=>[4,1,5,7,2,6,3]=>[6,7,1,2,5,4,3]=>001101
[6,7,3,5,4,2,1]=>[2,4,5,7,1,6,3]=>[6,7,2,1,5,4,3]=>101101
[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[6,7,4,1,2,3,5]=>001001
[6,7,4,1,2,5,3]=>[4,1,7,5,3,6,2]=>[5,3,6,7,4,1,2]=>001101
[6,7,4,1,3,2,5]=>[4,3,1,7,2,6,5]=>[3,1,6,7,4,2,5]=>011001
[6,7,4,1,3,5,2]=>[4,7,2,5,3,6,1]=>[5,2,3,6,7,4,1]=>001101
[6,7,4,1,5,2,3]=>[4,7,1,5,2,6,3]=>[5,1,6,7,4,2,3]=>001101
[6,7,4,1,5,3,2]=>[4,3,7,5,2,6,1]=>[5,3,2,6,7,4,1]=>011101
[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[6,7,4,2,1,3,5]=>101001
[6,7,4,2,1,5,3]=>[2,4,7,5,3,6,1]=>[5,3,6,7,4,2,1]=>101101
[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>[6,7,4,2,3,1,5]=>011001
[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>[6,7,4,2,3,5,1]=>001101
[6,7,4,2,5,1,3]=>[5,4,1,7,2,6,3]=>[6,7,4,1,5,2,3]=>001101
[6,7,4,2,5,3,1]=>[3,5,4,7,1,6,2]=>[6,7,4,1,5,3,2]=>011101
[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[6,7,4,3,1,2,5]=>011001
[6,7,4,3,1,5,2]=>[3,4,7,5,1,6,2]=>[5,1,6,7,4,3,2]=>011101
[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[6,7,4,3,2,1,5]=>111001
[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>[6,7,4,3,2,5,1]=>011101
[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>[6,7,4,3,5,1,2]=>001101
[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>[6,7,4,3,5,2,1]=>101101
[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[6,7,4,5,1,2,3]=>000101
[6,7,4,5,1,3,2]=>[5,3,1,7,4,6,2]=>[3,1,6,7,4,5,2]=>010101
[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>[6,7,4,5,2,1,3]=>100101
[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>[6,7,4,5,2,3,1]=>010101
[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>[6,7,4,5,3,1,2]=>010101
[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>[6,7,4,5,3,2,1]=>110101
[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[6,7,5,1,2,3,4]=>000101
[6,7,5,1,2,4,3]=>[5,1,4,2,7,6,3]=>[4,1,2,6,7,5,3]=>001101
[6,7,5,1,3,2,4]=>[5,3,1,2,7,6,4]=>[3,1,6,7,5,2,4]=>010101
[6,7,5,1,3,4,2]=>[5,4,1,3,7,6,2]=>[4,1,3,6,7,5,2]=>001101
[6,7,5,1,4,2,3]=>[5,4,2,1,7,6,3]=>[4,2,6,7,5,1,3]=>001101
[6,7,5,1,4,3,2]=>[5,3,4,1,7,6,2]=>[4,3,1,6,7,5,2]=>011101
[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[6,7,5,2,1,3,4]=>100101
[6,7,5,2,1,4,3]=>[2,5,4,1,7,6,3]=>[4,2,1,6,7,5,3]=>101101
[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>[6,7,5,2,3,1,4]=>010101
[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>[6,7,5,2,3,4,1]=>001101
[6,7,5,2,4,1,3]=>[4,5,1,2,7,6,3]=>[6,7,5,1,4,2,3]=>001101
[6,7,5,2,4,3,1]=>[3,4,5,1,7,6,2]=>[6,7,5,1,4,3,2]=>011101
[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[6,7,5,3,1,2,4]=>010101
[6,7,5,3,1,4,2]=>[3,5,4,2,7,6,1]=>[4,2,6,7,5,3,1]=>011101
[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[6,7,5,3,2,1,4]=>110101
[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>[6,7,5,3,2,4,1]=>011101
[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>[6,7,5,3,4,1,2]=>001101
[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>[6,7,5,3,4,2,1]=>101101
[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>[6,7,5,4,1,2,3]=>001101
[6,7,5,4,1,3,2]=>[4,3,1,5,7,6,2]=>[3,1,6,7,5,4,2]=>011101
[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>[6,7,5,4,2,1,3]=>101101
[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>[6,7,5,4,2,3,1]=>011101
[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>[6,7,5,4,3,1,2]=>011101
[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[6,7,5,4,3,2,1]=>111101
[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>000001
[7,1,2,3,4,6,5]=>[7,1,2,3,6,4,5]=>[6,1,2,3,4,7,5]=>000011
[7,1,2,3,5,4,6]=>[7,1,2,5,3,4,6]=>[5,1,2,3,7,4,6]=>000101
[7,1,2,3,5,6,4]=>[7,1,2,6,3,5,4]=>[6,1,2,3,5,7,4]=>000011
[7,1,2,3,6,4,5]=>[7,1,2,6,4,3,5]=>[6,4,7,1,2,3,5]=>000011
[7,1,2,3,6,5,4]=>[7,1,2,5,6,3,4]=>[6,5,1,2,3,7,4]=>000111
[7,1,2,4,3,5,6]=>[7,1,4,2,3,5,6]=>[4,1,2,7,3,5,6]=>001001
[7,1,2,4,3,6,5]=>[7,1,4,2,6,3,5]=>[4,1,2,6,3,7,5]=>001011
[7,1,2,4,5,3,6]=>[7,1,5,2,4,3,6]=>[5,1,2,4,7,3,6]=>000101
[7,1,2,4,5,6,3]=>[7,1,6,2,4,5,3]=>[6,1,2,4,5,7,3]=>000011
[7,1,2,4,6,3,5]=>[7,1,6,2,3,4,5]=>[6,1,2,7,3,4,5]=>000011
[7,1,2,4,6,5,3]=>[7,1,5,2,6,4,3]=>[6,5,1,2,4,7,3]=>000111
[7,1,2,5,3,4,6]=>[7,1,5,3,2,4,6]=>[5,3,7,1,2,4,6]=>000101
[7,1,2,5,3,6,4]=>[7,1,5,6,2,3,4]=>[6,1,2,5,3,7,4]=>000111
[7,1,2,5,4,3,6]=>[7,1,4,5,2,3,6]=>[5,4,1,2,7,3,6]=>001101
[7,1,2,5,4,6,3]=>[7,1,6,5,2,4,3]=>[5,1,2,6,4,7,3]=>000111
[7,1,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[6,3,5,7,1,2,4]=>000011
[7,1,2,5,6,4,3]=>[7,1,4,6,2,5,3]=>[6,4,1,2,5,7,3]=>001011
[7,1,2,6,3,4,5]=>[7,1,6,3,4,2,5]=>[6,3,4,7,1,2,5]=>000011
[7,1,2,6,3,5,4]=>[7,1,6,5,3,2,4]=>[5,3,6,1,2,7,4]=>000111
[7,1,2,6,4,3,5]=>[7,1,4,6,3,2,5]=>[6,4,3,7,1,2,5]=>001011
[7,1,2,6,4,5,3]=>[7,1,5,6,4,2,3]=>[6,4,5,1,2,7,3]=>000111
[7,1,2,6,5,3,4]=>[7,1,5,3,6,2,4]=>[6,5,3,7,1,2,4]=>000111
[7,1,2,6,5,4,3]=>[7,1,4,5,6,2,3]=>[6,5,4,1,2,7,3]=>001111
[7,1,3,2,4,5,6]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>010001
[7,1,3,2,4,6,5]=>[7,3,1,2,6,4,5]=>[3,1,6,2,4,7,5]=>010011
[7,1,3,2,5,4,6]=>[7,3,1,5,2,4,6]=>[3,1,5,2,7,4,6]=>010101
[7,1,3,2,5,6,4]=>[7,3,1,6,2,5,4]=>[3,1,6,2,5,7,4]=>010011
[7,1,3,2,6,4,5]=>[7,3,1,6,4,2,5]=>[3,1,6,4,7,2,5]=>010011
[7,1,3,2,6,5,4]=>[7,3,1,5,6,2,4]=>[3,1,6,5,2,7,4]=>010111
[7,1,3,4,2,5,6]=>[7,4,1,3,2,5,6]=>[4,1,3,7,2,5,6]=>001001
[7,1,3,4,2,6,5]=>[7,4,1,3,6,2,5]=>[4,1,3,6,2,7,5]=>001011
[7,1,3,4,5,2,6]=>[7,5,1,3,4,2,6]=>[5,1,3,4,7,2,6]=>000101
[7,1,3,4,5,6,2]=>[7,6,1,3,4,5,2]=>[6,1,3,4,5,7,2]=>000011
[7,1,3,4,6,2,5]=>[7,6,1,3,2,4,5]=>[6,1,3,7,2,4,5]=>000011
[7,1,3,4,6,5,2]=>[7,5,1,3,6,4,2]=>[6,5,1,3,4,7,2]=>000111
[7,1,3,5,2,4,6]=>[7,5,1,2,3,4,6]=>[5,1,7,2,3,4,6]=>000101
[7,1,3,5,2,6,4]=>[7,5,1,6,3,2,4]=>[6,1,3,5,2,7,4]=>000111
[7,1,3,5,4,2,6]=>[7,4,1,5,3,2,6]=>[5,4,1,3,7,2,6]=>001101
[7,1,3,5,4,6,2]=>[7,6,1,5,3,4,2]=>[5,1,3,6,4,7,2]=>000111
[7,1,3,5,6,2,4]=>[7,6,1,2,3,5,4]=>[6,1,5,7,2,3,4]=>000011
[7,1,3,5,6,4,2]=>[7,4,1,6,3,5,2]=>[6,4,1,3,5,7,2]=>001011
[7,1,3,6,2,4,5]=>[7,6,1,2,4,3,5]=>[6,1,4,7,2,3,5]=>000011
[7,1,3,6,2,5,4]=>[7,6,1,5,2,3,4]=>[5,1,6,2,3,7,4]=>000111
[7,1,3,6,4,2,5]=>[7,4,1,6,2,3,5]=>[6,4,1,7,2,3,5]=>001011
[7,1,3,6,4,5,2]=>[7,5,1,6,4,3,2]=>[6,4,5,1,3,7,2]=>000111
[7,1,3,6,5,2,4]=>[7,5,1,2,6,3,4]=>[6,5,1,7,2,3,4]=>000111
[7,1,3,6,5,4,2]=>[7,4,1,5,6,3,2]=>[6,5,4,1,3,7,2]=>001111
[7,1,4,2,3,5,6]=>[7,4,2,1,3,5,6]=>[4,2,7,1,3,5,6]=>001001
[7,1,4,2,3,6,5]=>[7,4,2,1,6,3,5]=>[4,2,6,1,3,7,5]=>001011
[7,1,4,2,5,3,6]=>[7,4,5,1,2,3,6]=>[5,1,4,2,7,3,6]=>001101
[7,1,4,2,5,6,3]=>[7,4,6,1,2,5,3]=>[6,1,4,2,5,7,3]=>001011
[7,1,4,2,6,3,5]=>[7,4,6,1,3,2,5]=>[6,1,4,3,7,2,5]=>001011
[7,1,4,2,6,5,3]=>[7,4,5,1,6,2,3]=>[6,5,1,4,2,7,3]=>001111
[7,1,4,3,2,5,6]=>[7,3,4,1,2,5,6]=>[4,3,1,7,2,5,6]=>011001
[7,1,4,3,2,6,5]=>[7,3,4,1,6,2,5]=>[4,3,1,6,2,7,5]=>011011
[7,1,4,3,5,2,6]=>[7,5,4,1,3,2,6]=>[4,1,5,3,7,2,6]=>001101
[7,1,4,3,5,6,2]=>[7,6,4,1,3,5,2]=>[4,1,6,3,5,7,2]=>001011
[7,1,4,3,6,2,5]=>[7,6,4,1,2,3,5]=>[4,1,6,2,7,3,5]=>001011
[7,1,4,3,6,5,2]=>[7,5,4,1,6,3,2]=>[4,1,6,5,3,7,2]=>001111
[7,1,4,5,2,3,6]=>[7,5,2,1,4,3,6]=>[5,2,4,7,1,3,6]=>000101
[7,1,4,5,2,6,3]=>[7,5,6,1,4,2,3]=>[6,1,4,5,2,7,3]=>000111
[7,1,4,5,3,2,6]=>[7,3,5,1,4,2,6]=>[5,3,1,4,7,2,6]=>010101
[7,1,4,5,3,6,2]=>[7,6,5,1,4,3,2]=>[5,1,4,6,3,7,2]=>000111
[7,1,4,5,6,2,3]=>[7,6,2,1,4,5,3]=>[6,2,4,5,7,1,3]=>000011
[7,1,4,5,6,3,2]=>[7,3,6,1,4,5,2]=>[6,3,1,4,5,7,2]=>010011
[7,1,4,6,2,3,5]=>[7,6,2,1,3,4,5]=>[6,2,7,1,3,4,5]=>000011
[7,1,4,6,2,5,3]=>[7,6,5,1,2,4,3]=>[5,1,6,2,4,7,3]=>000111
[7,1,4,6,3,2,5]=>[7,3,6,1,2,4,5]=>[6,3,1,7,2,4,5]=>010011
[7,1,4,6,3,5,2]=>[7,5,6,1,3,4,2]=>[6,1,5,3,4,7,2]=>000111
[7,1,4,6,5,2,3]=>[7,5,2,1,6,4,3]=>[6,5,2,4,7,1,3]=>000111
[7,1,4,6,5,3,2]=>[7,3,5,1,6,4,2]=>[6,5,3,1,4,7,2]=>010111
[7,1,5,2,3,4,6]=>[7,5,2,3,1,4,6]=>[5,2,3,7,1,4,6]=>000101
[7,1,5,2,3,6,4]=>[7,5,2,6,1,3,4]=>[6,2,5,1,3,7,4]=>000111
[7,1,5,2,4,3,6]=>[7,5,4,2,1,3,6]=>[4,2,5,1,7,3,6]=>001101
[7,1,5,2,4,6,3]=>[7,5,6,2,1,4,3]=>[6,2,5,1,4,7,3]=>000111
[7,1,5,2,6,3,4]=>[7,5,6,3,1,2,4]=>[6,3,5,1,7,2,4]=>000111
[7,1,5,2,6,4,3]=>[7,5,4,6,1,2,3]=>[6,4,1,5,2,7,3]=>001111
[7,1,5,3,2,4,6]=>[7,3,5,2,1,4,6]=>[5,3,2,7,1,4,6]=>010101
[7,1,5,3,2,6,4]=>[7,3,5,6,1,2,4]=>[6,3,1,5,2,7,4]=>010111
[7,1,5,3,4,2,6]=>[7,4,5,3,1,2,6]=>[5,3,4,1,7,2,6]=>001101
[7,1,5,3,4,6,2]=>[7,6,5,3,1,4,2]=>[5,3,6,1,4,7,2]=>000111
[7,1,5,3,6,2,4]=>[7,6,5,2,1,3,4]=>[5,2,6,1,7,3,4]=>000111
[7,1,5,3,6,4,2]=>[7,4,6,5,1,2,3]=>[5,1,6,4,2,7,3]=>001111
[7,1,5,4,2,3,6]=>[7,4,2,5,1,3,6]=>[5,4,2,7,1,3,6]=>001101
[7,1,5,4,2,6,3]=>[7,4,5,6,1,3,2]=>[6,1,5,4,3,7,2]=>001111
[7,1,5,4,3,2,6]=>[7,3,4,5,1,2,6]=>[5,4,3,1,7,2,6]=>011101
[7,1,5,4,3,6,2]=>[7,6,4,5,1,3,2]=>[5,4,1,6,3,7,2]=>001111
[7,1,5,4,6,2,3]=>[7,6,2,5,1,4,3]=>[5,2,6,4,7,1,3]=>000111
[7,1,5,4,6,3,2]=>[7,3,6,5,1,4,2]=>[5,3,1,6,4,7,2]=>010111
[7,1,5,6,2,3,4]=>[7,6,2,3,1,5,4]=>[6,2,3,5,7,1,4]=>000011
[7,1,5,6,2,4,3]=>[7,6,4,2,1,5,3]=>[4,2,6,1,5,7,3]=>001011
[7,1,5,6,3,2,4]=>[7,3,6,2,1,5,4]=>[6,3,2,5,7,1,4]=>010011
[7,1,5,6,3,4,2]=>[7,4,6,3,1,5,2]=>[6,3,4,1,5,7,2]=>001011
[7,1,5,6,4,2,3]=>[7,4,2,6,1,5,3]=>[6,4,2,5,7,1,3]=>001011
[7,1,5,6,4,3,2]=>[7,3,4,6,1,5,2]=>[6,4,3,1,5,7,2]=>011011
[7,1,6,2,3,4,5]=>[7,6,2,3,4,1,5]=>[6,2,3,4,7,1,5]=>000011
[7,1,6,2,3,5,4]=>[7,6,2,5,3,1,4]=>[5,2,3,6,1,7,4]=>000111
[7,1,6,2,4,3,5]=>[7,6,4,2,3,1,5]=>[4,2,6,3,7,1,5]=>001011
[7,1,6,2,4,5,3]=>[7,6,5,2,4,1,3]=>[5,2,4,6,1,7,3]=>000111
[7,1,6,2,5,3,4]=>[7,6,5,3,2,1,4]=>[5,3,6,2,7,1,4]=>000111
[7,1,6,2,5,4,3]=>[7,6,4,5,2,1,3]=>[5,4,2,6,1,7,3]=>001111
[7,1,6,3,2,4,5]=>[7,3,6,2,4,1,5]=>[6,3,2,4,7,1,5]=>010011
[7,1,6,3,2,5,4]=>[7,3,6,5,2,1,4]=>[5,3,2,6,1,7,4]=>010111
[7,1,6,3,4,2,5]=>[7,4,6,3,2,1,5]=>[6,3,4,2,7,1,5]=>001011
[7,1,6,3,4,5,2]=>[7,5,6,3,4,1,2]=>[6,3,4,5,1,7,2]=>000111
[7,1,6,3,5,2,4]=>[7,5,6,2,3,1,4]=>[6,2,5,3,7,1,4]=>000111
[7,1,6,3,5,4,2]=>[7,4,5,6,2,1,3]=>[6,2,5,4,1,7,3]=>001111
[7,1,6,4,2,3,5]=>[7,4,2,6,3,1,5]=>[6,4,2,3,7,1,5]=>001011
[7,1,6,4,2,5,3]=>[7,4,6,5,3,1,2]=>[5,3,6,4,1,7,2]=>001111
[7,1,6,4,3,2,5]=>[7,3,4,6,2,1,5]=>[6,4,3,2,7,1,5]=>011011
[7,1,6,4,3,5,2]=>[7,5,4,6,3,1,2]=>[6,4,3,5,1,7,2]=>001111
[7,1,6,4,5,2,3]=>[7,5,2,6,4,1,3]=>[6,4,5,2,7,1,3]=>000111
[7,1,6,4,5,3,2]=>[7,3,5,6,4,1,2]=>[6,4,5,3,1,7,2]=>010111
[7,1,6,5,2,3,4]=>[7,5,2,3,6,1,4]=>[6,5,2,3,7,1,4]=>000111
[7,1,6,5,2,4,3]=>[7,5,4,2,6,1,3]=>[4,2,6,5,1,7,3]=>001111
[7,1,6,5,3,2,4]=>[7,3,5,2,6,1,4]=>[6,5,3,2,7,1,4]=>010111
[7,1,6,5,3,4,2]=>[7,4,5,3,6,1,2]=>[6,5,3,4,1,7,2]=>001111
[7,1,6,5,4,2,3]=>[7,4,2,5,6,1,3]=>[6,5,4,2,7,1,3]=>001111
[7,1,6,5,4,3,2]=>[7,3,4,5,6,1,2]=>[6,5,4,3,1,7,2]=>011111
[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>100001
[7,2,1,3,4,6,5]=>[2,7,1,3,6,4,5]=>[6,2,1,3,4,7,5]=>100011
[7,2,1,3,5,4,6]=>[2,7,1,5,3,4,6]=>[5,2,1,3,7,4,6]=>100101
[7,2,1,3,5,6,4]=>[2,7,1,6,3,5,4]=>[6,2,1,3,5,7,4]=>100011
[7,2,1,3,6,4,5]=>[2,7,1,6,4,3,5]=>[6,4,7,2,1,3,5]=>100011
[7,2,1,3,6,5,4]=>[2,7,1,5,6,3,4]=>[6,5,2,1,3,7,4]=>100111
[7,2,1,4,3,5,6]=>[2,7,4,1,3,5,6]=>[4,2,1,7,3,5,6]=>101001
[7,2,1,4,3,6,5]=>[2,7,4,1,6,3,5]=>[4,2,1,6,3,7,5]=>101011
[7,2,1,4,5,3,6]=>[2,7,5,1,4,3,6]=>[5,2,1,4,7,3,6]=>100101
[7,2,1,4,5,6,3]=>[2,7,6,1,4,5,3]=>[6,2,1,4,5,7,3]=>100011
[7,2,1,4,6,3,5]=>[2,7,6,1,3,4,5]=>[6,2,1,7,3,4,5]=>100011
[7,2,1,4,6,5,3]=>[2,7,5,1,6,4,3]=>[6,5,2,1,4,7,3]=>100111
[7,2,1,5,3,4,6]=>[2,7,5,3,1,4,6]=>[5,3,7,2,1,4,6]=>100101
[7,2,1,5,3,6,4]=>[2,7,5,6,1,3,4]=>[6,2,1,5,3,7,4]=>100111
[7,2,1,5,4,3,6]=>[2,7,4,5,1,3,6]=>[5,4,2,1,7,3,6]=>101101
[7,2,1,5,4,6,3]=>[2,7,6,5,1,4,3]=>[5,2,1,6,4,7,3]=>100111
[7,2,1,5,6,3,4]=>[2,7,6,3,1,5,4]=>[6,3,5,7,2,1,4]=>100011
[7,2,1,5,6,4,3]=>[2,7,4,6,1,5,3]=>[6,4,2,1,5,7,3]=>101011
[7,2,1,6,3,4,5]=>[2,7,6,3,4,1,5]=>[6,3,4,7,2,1,5]=>100011
[7,2,1,6,3,5,4]=>[2,7,6,5,3,1,4]=>[5,3,6,2,1,7,4]=>100111
[7,2,1,6,4,3,5]=>[2,7,4,6,3,1,5]=>[6,4,3,7,2,1,5]=>101011
[7,2,1,6,4,5,3]=>[2,7,5,6,4,1,3]=>[6,4,5,2,1,7,3]=>100111
[7,2,1,6,5,3,4]=>[2,7,5,3,6,1,4]=>[6,5,3,7,2,1,4]=>100111
[7,2,1,6,5,4,3]=>[2,7,4,5,6,1,3]=>[6,5,4,2,1,7,3]=>101111
[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[7,2,3,1,4,5,6]=>010001
[7,2,3,1,4,6,5]=>[3,7,2,1,6,4,5]=>[6,2,3,1,4,7,5]=>010011
[7,2,3,1,5,4,6]=>[3,7,2,5,1,4,6]=>[5,2,3,1,7,4,6]=>010101
[7,2,3,1,5,6,4]=>[3,7,2,6,1,5,4]=>[6,2,3,1,5,7,4]=>010011
[7,2,3,1,6,4,5]=>[3,7,2,6,4,1,5]=>[6,4,7,2,3,1,5]=>010011
[7,2,3,1,6,5,4]=>[3,7,2,5,6,1,4]=>[6,5,2,3,1,7,4]=>010111
[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[7,2,3,4,1,5,6]=>001001
[7,2,3,4,1,6,5]=>[4,7,2,3,6,1,5]=>[6,2,3,4,1,7,5]=>001011
[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[7,2,3,4,5,1,6]=>000101
[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7,2,3,4,5,6,1]=>000011
[7,2,3,4,6,1,5]=>[6,7,2,3,1,4,5]=>[7,2,3,6,1,4,5]=>000011
[7,2,3,4,6,5,1]=>[5,6,1,3,7,4,2]=>[7,1,3,4,6,5,2]=>000111
[7,2,3,5,1,4,6]=>[5,7,2,1,3,4,6]=>[7,2,5,1,3,4,6]=>000101
[7,2,3,5,1,6,4]=>[5,7,2,6,3,1,4]=>[6,2,3,7,1,5,4]=>000111
[7,2,3,5,4,1,6]=>[4,5,1,7,3,2,6]=>[7,1,3,5,4,2,6]=>001101
[7,2,3,5,4,6,1]=>[6,7,2,5,3,4,1]=>[5,2,3,7,4,6,1]=>000111
[7,2,3,5,6,1,4]=>[6,7,2,1,3,5,4]=>[7,2,5,6,1,3,4]=>000011
[7,2,3,5,6,4,1]=>[4,6,1,7,3,5,2]=>[7,1,3,5,6,4,2]=>001011
[7,2,3,6,1,4,5]=>[6,7,2,1,4,3,5]=>[7,2,4,6,1,3,5]=>000011
[7,2,3,6,1,5,4]=>[6,7,2,5,1,3,4]=>[5,2,7,1,3,6,4]=>000111
[7,2,3,6,4,1,5]=>[4,6,1,7,2,3,5]=>[7,1,6,4,2,3,5]=>001011
[7,2,3,6,4,5,1]=>[5,7,2,6,4,3,1]=>[6,4,7,2,3,5,1]=>000111
[7,2,3,6,5,1,4]=>[5,6,1,2,7,3,4]=>[7,1,6,5,2,3,4]=>000111
[7,2,3,6,5,4,1]=>[4,5,2,6,7,3,1]=>[7,2,3,6,5,4,1]=>001111
[7,2,4,1,3,5,6]=>[4,7,1,2,3,5,6]=>[7,1,4,2,3,5,6]=>001001
[7,2,4,1,3,6,5]=>[4,7,1,2,6,3,5]=>[6,1,4,2,3,7,5]=>001011
[7,2,4,1,5,3,6]=>[4,7,5,2,1,3,6]=>[5,2,7,1,4,3,6]=>001101
[7,2,4,1,5,6,3]=>[4,7,6,2,1,5,3]=>[6,2,5,7,1,4,3]=>001011
[7,2,4,1,6,3,5]=>[4,7,6,2,3,1,5]=>[6,2,7,3,4,1,5]=>001011
[7,2,4,1,6,5,3]=>[4,7,5,2,6,1,3]=>[6,5,2,7,1,4,3]=>001111
[7,2,4,3,1,5,6]=>[3,4,7,1,2,5,6]=>[7,1,4,3,2,5,6]=>011001
[7,2,4,3,1,6,5]=>[3,4,7,1,6,2,5]=>[6,1,4,3,2,7,5]=>011011
[7,2,4,3,5,1,6]=>[5,7,4,2,3,1,6]=>[4,2,7,3,5,1,6]=>001101
[7,2,4,3,5,6,1]=>[6,7,4,2,3,5,1]=>[4,2,7,3,5,6,1]=>001011
[7,2,4,3,6,1,5]=>[6,7,4,2,1,3,5]=>[4,2,7,1,6,3,5]=>001011
[7,2,4,3,6,5,1]=>[5,6,4,1,7,3,2]=>[4,1,7,3,6,5,2]=>001111
[7,2,4,5,1,3,6]=>[5,7,1,2,4,3,6]=>[7,1,4,5,2,3,6]=>000101
[7,2,4,5,1,6,3]=>[5,7,6,2,4,1,3]=>[6,2,4,7,1,5,3]=>000111
[7,2,4,5,3,1,6]=>[3,5,7,1,4,2,6]=>[7,1,4,5,3,2,6]=>010101
[7,2,4,5,3,6,1]=>[6,7,5,2,4,3,1]=>[5,2,4,7,3,6,1]=>000111
[7,2,4,5,6,1,3]=>[6,7,1,2,4,5,3]=>[7,1,4,5,6,2,3]=>000011
[7,2,4,5,6,3,1]=>[3,6,7,1,4,5,2]=>[7,1,4,5,6,3,2]=>010011
[7,2,4,6,1,3,5]=>[6,7,1,2,3,4,5]=>[7,1,6,2,3,4,5]=>000011
[7,2,4,6,1,5,3]=>[6,7,5,2,1,4,3]=>[5,2,7,1,4,6,3]=>000111
[7,2,4,6,3,1,5]=>[3,6,7,1,2,4,5]=>[7,1,6,3,2,4,5]=>010011
[7,2,4,6,3,5,1]=>[5,7,6,2,3,4,1]=>[6,2,7,3,4,5,1]=>000111
[7,2,4,6,5,1,3]=>[5,6,2,1,7,4,3]=>[7,2,4,6,5,1,3]=>000111
[7,2,4,6,5,3,1]=>[3,5,6,2,7,4,1]=>[7,2,4,6,5,3,1]=>010111
[7,2,5,1,3,4,6]=>[5,7,1,3,2,4,6]=>[7,1,3,5,2,4,6]=>000101
[7,2,5,1,3,6,4]=>[5,7,1,6,2,3,4]=>[6,1,7,2,3,5,4]=>000111
[7,2,5,1,4,3,6]=>[5,7,4,1,2,3,6]=>[4,1,7,2,5,3,6]=>001101
[7,2,5,1,4,6,3]=>[5,7,6,1,2,4,3]=>[6,1,7,2,4,5,3]=>000111
[7,2,5,1,6,3,4]=>[5,7,6,3,2,1,4]=>[6,3,7,2,5,1,4]=>000111
[7,2,5,1,6,4,3]=>[5,7,4,6,2,1,3]=>[6,4,2,7,1,5,3]=>001111
[7,2,5,3,1,4,6]=>[3,5,7,2,1,4,6]=>[7,2,5,3,1,4,6]=>010101
[7,2,5,3,1,6,4]=>[3,5,7,6,1,2,4]=>[6,1,7,3,2,5,4]=>010111
[7,2,5,3,4,1,6]=>[4,7,5,3,2,1,6]=>[5,3,7,2,4,1,6]=>001101
[7,2,5,3,4,6,1]=>[6,7,5,3,2,4,1]=>[5,3,7,2,4,6,1]=>000111
[7,2,5,3,6,1,4]=>[6,7,5,1,2,3,4]=>[5,1,7,2,6,3,4]=>000111
[7,2,5,3,6,4,1]=>[4,6,7,5,3,1,2]=>[5,3,7,1,6,4,2]=>001111
[7,2,5,4,1,3,6]=>[4,5,2,7,1,3,6]=>[7,2,5,4,1,3,6]=>001101
[7,2,5,4,1,6,3]=>[4,5,7,6,3,2,1]=>[6,3,7,2,5,4,1]=>001111
[7,2,5,4,3,1,6]=>[3,4,5,7,2,1,6]=>[7,2,5,4,3,1,6]=>011101
[7,2,5,4,3,6,1]=>[6,7,4,5,2,3,1]=>[5,4,2,7,3,6,1]=>001111
[7,2,5,4,6,1,3]=>[6,7,1,5,2,4,3]=>[5,1,7,4,6,2,3]=>000111
[7,2,5,4,6,3,1]=>[3,6,7,5,1,4,2]=>[5,1,7,4,6,3,2]=>010111
[7,2,5,6,1,3,4]=>[6,7,1,3,2,5,4]=>[7,1,3,5,6,2,4]=>000011
[7,2,5,6,1,4,3]=>[6,7,4,1,2,5,3]=>[4,1,7,2,5,6,3]=>001011
[7,2,5,6,3,1,4]=>[3,6,7,2,1,5,4]=>[7,2,5,6,3,1,4]=>010011
[7,2,5,6,3,4,1]=>[4,7,6,3,2,5,1]=>[6,3,5,7,2,4,1]=>001011
[7,2,5,6,4,1,3]=>[4,6,2,7,1,5,3]=>[7,2,5,6,4,1,3]=>001011
[7,2,5,6,4,3,1]=>[3,4,6,7,2,5,1]=>[7,2,5,6,4,3,1]=>011011
[7,2,6,1,3,4,5]=>[6,7,1,3,4,2,5]=>[7,1,3,4,6,2,5]=>000011
[7,2,6,1,3,5,4]=>[6,7,1,5,3,2,4]=>[5,1,3,7,2,6,4]=>000111
[7,2,6,1,4,3,5]=>[6,7,4,1,3,2,5]=>[4,1,7,3,6,2,5]=>001011
[7,2,6,1,4,5,3]=>[6,7,5,1,4,2,3]=>[5,1,4,7,2,6,3]=>000111
[7,2,6,1,5,3,4]=>[6,7,5,3,1,2,4]=>[5,3,7,1,6,2,4]=>000111
[7,2,6,1,5,4,3]=>[6,7,4,5,1,2,3]=>[5,4,1,7,2,6,3]=>001111
[7,2,6,3,1,4,5]=>[3,6,7,2,4,1,5]=>[7,2,4,6,3,1,5]=>010011
[7,2,6,3,1,5,4]=>[3,6,7,5,2,1,4]=>[5,2,7,3,1,6,4]=>010111
[7,2,6,3,4,1,5]=>[4,7,6,3,1,2,5]=>[6,3,7,1,4,2,5]=>001011
[7,2,6,3,4,5,1]=>[5,7,6,3,4,2,1]=>[6,3,4,7,2,5,1]=>000111
[7,2,6,3,5,1,4]=>[5,7,6,1,3,2,4]=>[6,1,7,3,5,2,4]=>000111
[7,2,6,3,5,4,1]=>[4,5,7,6,1,3,2]=>[6,1,7,3,5,4,2]=>001111
[7,2,6,4,1,3,5]=>[4,6,2,7,3,1,5]=>[7,2,3,6,4,1,5]=>001011
[7,2,6,4,1,5,3]=>[4,6,7,5,2,3,1]=>[5,2,7,3,6,4,1]=>001111
[7,2,6,4,3,1,5]=>[3,4,6,7,1,2,5]=>[7,1,6,4,3,2,5]=>011011
[7,2,6,4,3,5,1]=>[5,7,4,6,3,2,1]=>[6,4,3,7,2,5,1]=>001111
[7,2,6,4,5,1,3]=>[5,7,1,6,4,2,3]=>[6,4,7,1,5,2,3]=>000111
[7,2,6,4,5,3,1]=>[3,5,7,6,4,1,2]=>[6,4,7,1,5,3,2]=>010111
[7,2,6,5,1,3,4]=>[5,6,2,3,7,1,4]=>[7,2,3,6,5,1,4]=>000111
[7,2,6,5,1,4,3]=>[5,6,4,2,7,1,3]=>[4,2,7,1,6,5,3]=>001111
[7,2,6,5,3,1,4]=>[3,5,6,1,7,2,4]=>[7,1,6,5,3,2,4]=>010111
[7,2,6,5,3,4,1]=>[4,7,5,3,6,2,1]=>[6,5,3,7,2,4,1]=>001111
[7,2,6,5,4,1,3]=>[4,5,1,6,7,2,3]=>[7,1,6,5,4,2,3]=>001111
[7,2,6,5,4,3,1]=>[3,4,5,6,7,1,2]=>[7,1,6,5,4,3,2]=>011111
[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[7,3,1,2,4,5,6]=>010001
[7,3,1,2,4,6,5]=>[3,1,7,2,6,4,5]=>[6,3,1,2,4,7,5]=>010011
[7,3,1,2,5,4,6]=>[3,1,7,5,2,4,6]=>[5,3,1,2,7,4,6]=>010101
[7,3,1,2,5,6,4]=>[3,1,7,6,2,5,4]=>[6,3,1,2,5,7,4]=>010011
[7,3,1,2,6,4,5]=>[3,1,7,6,4,2,5]=>[6,4,7,3,1,2,5]=>010011
[7,3,1,2,6,5,4]=>[3,1,7,5,6,2,4]=>[6,5,3,1,2,7,4]=>010111
[7,3,1,4,2,5,6]=>[3,7,4,2,1,5,6]=>[4,2,7,3,1,5,6]=>011001
[7,3,1,4,2,6,5]=>[3,7,4,2,6,1,5]=>[4,2,6,3,1,7,5]=>011011
[7,3,1,4,5,2,6]=>[3,7,5,2,4,1,6]=>[5,2,4,7,3,1,6]=>010101
[7,3,1,4,5,6,2]=>[3,7,6,2,4,5,1]=>[6,2,4,5,7,3,1]=>010011
[7,3,1,4,6,2,5]=>[3,7,6,2,1,4,5]=>[6,2,7,3,1,4,5]=>010011
[7,3,1,4,6,5,2]=>[3,7,5,2,6,4,1]=>[6,5,2,4,7,3,1]=>010111
[7,3,1,5,2,4,6]=>[3,7,5,1,2,4,6]=>[5,1,7,3,2,4,6]=>010101
[7,3,1,5,2,6,4]=>[3,7,5,6,2,1,4]=>[6,2,5,3,1,7,4]=>010111
[7,3,1,5,4,2,6]=>[3,7,4,5,2,1,6]=>[5,4,2,7,3,1,6]=>011101
[7,3,1,5,4,6,2]=>[3,7,6,5,2,4,1]=>[5,2,6,4,7,3,1]=>010111
[7,3,1,5,6,2,4]=>[3,7,6,1,2,5,4]=>[6,1,5,7,3,2,4]=>010011
[7,3,1,5,6,4,2]=>[3,7,4,6,2,5,1]=>[6,4,2,5,7,3,1]=>011011
[7,3,1,6,2,4,5]=>[3,7,6,1,4,2,5]=>[6,1,4,7,3,2,5]=>010011
[7,3,1,6,2,5,4]=>[3,7,6,5,1,2,4]=>[5,1,6,3,2,7,4]=>010111
[7,3,1,6,4,2,5]=>[3,7,4,6,1,2,5]=>[6,4,1,7,3,2,5]=>011011
[7,3,1,6,4,5,2]=>[3,7,5,6,4,2,1]=>[6,4,5,2,7,3,1]=>010111
[7,3,1,6,5,2,4]=>[3,7,5,1,6,2,4]=>[6,5,1,7,3,2,4]=>010111
[7,3,1,6,5,4,2]=>[3,7,4,5,6,2,1]=>[6,5,4,2,7,3,1]=>011111
[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>110001
[7,3,2,1,4,6,5]=>[2,3,7,1,6,4,5]=>[6,3,2,1,4,7,5]=>110011
[7,3,2,1,5,4,6]=>[2,3,7,5,1,4,6]=>[5,3,2,1,7,4,6]=>110101
[7,3,2,1,5,6,4]=>[2,3,7,6,1,5,4]=>[6,3,2,1,5,7,4]=>110011
[7,3,2,1,6,4,5]=>[2,3,7,6,4,1,5]=>[6,4,7,3,2,1,5]=>110011
[7,3,2,1,6,5,4]=>[2,3,7,5,6,1,4]=>[6,5,3,2,1,7,4]=>110111
[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[7,3,2,4,1,5,6]=>011001
[7,3,2,4,1,6,5]=>[4,3,7,2,6,1,5]=>[6,3,2,4,1,7,5]=>011011
[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[7,3,2,4,5,1,6]=>010101
[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[7,3,2,4,5,6,1]=>010011
[7,3,2,4,6,1,5]=>[6,3,7,2,1,4,5]=>[7,3,2,6,1,4,5]=>010011
[7,3,2,4,6,5,1]=>[5,3,6,1,7,4,2]=>[7,3,1,4,6,5,2]=>010111
[7,3,2,5,1,4,6]=>[5,3,7,1,2,4,6]=>[7,3,1,5,2,4,6]=>010101
[7,3,2,5,1,6,4]=>[5,3,7,6,2,1,4]=>[6,3,2,7,1,5,4]=>010111
[7,3,2,5,4,1,6]=>[4,3,5,7,1,2,6]=>[7,3,1,5,4,2,6]=>011101
[7,3,2,5,4,6,1]=>[6,3,7,5,2,4,1]=>[5,3,2,7,4,6,1]=>010111
[7,3,2,5,6,1,4]=>[6,3,7,1,2,5,4]=>[7,3,1,5,6,2,4]=>010011
[7,3,2,5,6,4,1]=>[4,3,6,7,1,5,2]=>[7,3,1,5,6,4,2]=>011011
[7,3,2,6,1,4,5]=>[6,3,7,1,4,2,5]=>[7,3,1,4,6,2,5]=>010011
[7,3,2,6,1,5,4]=>[6,3,7,5,1,2,4]=>[5,3,1,7,2,6,4]=>010111
[7,3,2,6,4,1,5]=>[4,3,6,7,2,1,5]=>[7,3,2,6,4,1,5]=>011011
[7,3,2,6,4,5,1]=>[5,3,7,6,4,2,1]=>[6,4,7,3,2,5,1]=>010111
[7,3,2,6,5,1,4]=>[5,3,6,2,7,1,4]=>[7,3,2,6,5,1,4]=>010111
[7,3,2,6,5,4,1]=>[4,3,5,6,7,2,1]=>[7,3,2,6,5,4,1]=>011111
[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[7,3,4,1,2,5,6]=>001001
[7,3,4,1,2,6,5]=>[4,1,7,3,6,2,5]=>[6,3,4,1,2,7,5]=>001011
[7,3,4,1,5,2,6]=>[4,5,7,3,1,2,6]=>[7,3,5,1,4,2,6]=>001101
[7,3,4,1,5,6,2]=>[4,6,7,3,1,5,2]=>[7,3,5,6,1,4,2]=>001011
[7,3,4,1,6,2,5]=>[4,6,7,3,2,1,5]=>[7,3,6,2,4,1,5]=>001011
[7,3,4,1,6,5,2]=>[4,5,6,2,7,1,3]=>[7,2,6,5,1,4,3]=>001111
[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[7,3,4,2,1,5,6]=>101001
[7,3,4,2,1,6,5]=>[2,4,7,3,6,1,5]=>[6,3,4,2,1,7,5]=>101011
[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>[7,3,4,2,5,1,6]=>001101
[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>[7,3,4,2,5,6,1]=>001011
[7,3,4,2,6,1,5]=>[6,4,7,3,1,2,5]=>[7,3,4,1,6,2,5]=>001011
[7,3,4,2,6,5,1]=>[5,4,6,1,7,2,3]=>[7,1,4,2,6,5,3]=>001111
[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>[7,3,4,5,1,2,6]=>000101
[7,3,4,5,1,6,2]=>[5,6,7,3,4,1,2]=>[7,3,4,6,1,5,2]=>000111
[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[7,3,4,5,2,1,6]=>100101
[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>[7,3,4,5,2,6,1]=>000111
[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>[7,3,4,5,6,1,2]=>000011
[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>[7,3,4,5,6,2,1]=>100011
[7,3,4,6,1,2,5]=>[6,1,7,3,2,4,5]=>[7,3,6,1,2,4,5]=>000011
[7,3,4,6,1,5,2]=>[6,5,7,3,1,4,2]=>[7,3,5,1,4,6,2]=>000111
[7,3,4,6,2,1,5]=>[2,6,7,3,1,4,5]=>[7,3,6,2,1,4,5]=>100011
[7,3,4,6,2,5,1]=>[5,6,7,3,2,4,1]=>[7,3,6,2,4,5,1]=>000111
[7,3,4,6,5,1,2]=>[5,1,6,2,7,4,3]=>[7,1,2,4,6,5,3]=>000111
[7,3,4,6,5,2,1]=>[2,5,6,1,7,4,3]=>[7,2,1,4,6,5,3]=>100111
[7,3,5,1,2,4,6]=>[5,1,7,2,3,4,6]=>[7,1,2,5,3,4,6]=>000101
[7,3,5,1,2,6,4]=>[5,1,7,6,3,2,4]=>[6,3,7,1,2,5,4]=>000111
[7,3,5,1,4,2,6]=>[5,4,7,1,3,2,6]=>[7,1,4,3,5,2,6]=>001101
[7,3,5,1,4,6,2]=>[5,6,7,1,3,4,2]=>[7,1,6,3,4,5,2]=>000111
[7,3,5,1,6,2,4]=>[5,6,7,2,3,1,4]=>[7,2,6,3,5,1,4]=>000111
[7,3,5,1,6,4,2]=>[5,4,6,7,2,1,3]=>[7,2,6,4,1,5,3]=>001111
[7,3,5,2,1,4,6]=>[2,5,7,1,3,4,6]=>[7,2,1,5,3,4,6]=>100101
[7,3,5,2,1,6,4]=>[2,5,7,6,3,1,4]=>[6,3,7,2,1,5,4]=>100111
[7,3,5,2,4,1,6]=>[4,5,7,2,3,1,6]=>[7,2,5,3,4,1,6]=>001101
[7,3,5,2,4,6,1]=>[6,5,7,2,3,4,1]=>[7,2,5,3,4,6,1]=>000111
[7,3,5,2,6,1,4]=>[6,5,7,1,3,2,4]=>[7,1,5,3,6,2,4]=>000111
[7,3,5,2,6,4,1]=>[4,6,5,7,1,3,2]=>[7,1,5,3,6,4,2]=>001111
[7,3,5,4,1,2,6]=>[4,1,5,7,2,3,6]=>[7,1,2,5,4,3,6]=>001101
[7,3,5,4,1,6,2]=>[4,5,6,7,1,2,3]=>[7,1,6,2,5,4,3]=>001111
[7,3,5,4,2,1,6]=>[2,4,5,7,1,3,6]=>[7,2,1,5,4,3,6]=>101101
[7,3,5,4,2,6,1]=>[6,4,5,7,2,3,1]=>[7,2,5,4,3,6,1]=>001111
[7,3,5,4,6,1,2]=>[6,1,7,5,3,4,2]=>[5,3,7,4,6,1,2]=>000111
[7,3,5,4,6,2,1]=>[2,6,7,5,3,4,1]=>[5,3,7,4,6,2,1]=>100111
[7,3,5,6,1,2,4]=>[6,1,7,2,3,5,4]=>[7,1,2,5,6,3,4]=>000011
[7,3,5,6,1,4,2]=>[6,4,7,1,3,5,2]=>[7,1,4,3,5,6,2]=>001011
[7,3,5,6,2,1,4]=>[2,6,7,1,3,5,4]=>[7,2,1,5,6,3,4]=>100011
[7,3,5,6,2,4,1]=>[4,6,7,2,3,5,1]=>[7,2,5,6,3,4,1]=>001011
[7,3,5,6,4,1,2]=>[4,1,6,7,2,5,3]=>[7,1,2,5,6,4,3]=>001011
[7,3,5,6,4,2,1]=>[2,4,6,7,1,5,3]=>[7,2,1,5,6,4,3]=>101011
[7,3,6,1,2,4,5]=>[6,1,7,2,4,3,5]=>[7,1,2,4,6,3,5]=>000011
[7,3,6,1,2,5,4]=>[6,1,7,5,2,3,4]=>[5,1,2,7,3,6,4]=>000111
[7,3,6,1,4,2,5]=>[6,4,7,1,2,3,5]=>[7,1,4,2,6,3,5]=>001011
[7,3,6,1,4,5,2]=>[6,5,7,1,4,3,2]=>[7,1,4,5,3,6,2]=>000111
[7,3,6,1,5,2,4]=>[6,5,7,2,1,3,4]=>[7,2,5,1,6,3,4]=>000111
[7,3,6,1,5,4,2]=>[6,4,5,7,1,2,3]=>[7,1,5,4,2,6,3]=>001111
[7,3,6,2,1,4,5]=>[2,6,7,1,4,3,5]=>[7,2,1,4,6,3,5]=>100011
[7,3,6,2,1,5,4]=>[2,6,7,5,1,3,4]=>[5,2,1,7,3,6,4]=>100111
[7,3,6,2,4,1,5]=>[4,6,7,2,1,3,5]=>[7,2,6,1,4,3,5]=>001011
[7,3,6,2,4,5,1]=>[5,6,7,2,4,3,1]=>[7,2,4,6,3,5,1]=>000111
[7,3,6,2,5,1,4]=>[5,6,7,1,2,3,4]=>[7,1,6,2,5,3,4]=>000111
[7,3,6,2,5,4,1]=>[4,5,6,7,3,1,2]=>[7,3,6,1,5,4,2]=>001111
[7,3,6,4,1,2,5]=>[4,1,6,7,3,2,5]=>[7,3,6,4,1,2,5]=>001011
[7,3,6,4,1,5,2]=>[4,6,5,7,2,1,3]=>[7,2,5,1,6,4,3]=>001111
[7,3,6,4,2,1,5]=>[2,4,6,7,3,1,5]=>[7,3,6,4,2,1,5]=>101011
[7,3,6,4,2,5,1]=>[5,4,6,7,3,2,1]=>[7,3,6,4,2,5,1]=>001111
[7,3,6,4,5,1,2]=>[5,1,7,6,4,3,2]=>[6,4,7,3,5,1,2]=>000111
[7,3,6,4,5,2,1]=>[2,5,7,6,4,3,1]=>[6,4,7,3,5,2,1]=>100111
[7,3,6,5,1,2,4]=>[5,1,6,3,7,2,4]=>[7,3,6,5,1,2,4]=>000111
[7,3,6,5,1,4,2]=>[5,4,6,3,7,1,2]=>[7,3,4,1,6,5,2]=>001111
[7,3,6,5,2,1,4]=>[2,5,6,3,7,1,4]=>[7,3,6,5,2,1,4]=>100111
[7,3,6,5,2,4,1]=>[4,5,6,3,7,2,1]=>[7,3,6,5,2,4,1]=>001111
[7,3,6,5,4,1,2]=>[4,1,5,6,7,3,2]=>[7,3,6,5,4,1,2]=>001111
[7,3,6,5,4,2,1]=>[2,4,5,6,7,3,1]=>[7,3,6,5,4,2,1]=>101111
[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[7,4,1,2,3,5,6]=>001001
[7,4,1,2,3,6,5]=>[4,1,2,7,6,3,5]=>[6,4,1,2,3,7,5]=>001011
[7,4,1,2,5,3,6]=>[4,1,7,5,3,2,6]=>[5,3,7,4,1,2,6]=>001101
[7,4,1,2,5,6,3]=>[4,1,7,6,3,5,2]=>[6,3,5,7,4,1,2]=>001011
[7,4,1,2,6,3,5]=>[4,1,7,6,2,3,5]=>[6,1,2,7,4,3,5]=>001011
[7,4,1,2,6,5,3]=>[4,1,7,5,6,3,2]=>[6,5,3,7,4,1,2]=>001111
[7,4,1,3,2,5,6]=>[4,3,1,7,2,5,6]=>[3,1,7,4,2,5,6]=>011001
[7,4,1,3,2,6,5]=>[4,3,1,7,6,2,5]=>[3,1,6,4,2,7,5]=>011011
[7,4,1,3,5,2,6]=>[4,7,2,5,3,1,6]=>[5,2,3,7,4,1,6]=>001101
[7,4,1,3,5,6,2]=>[4,7,2,6,3,5,1]=>[6,2,3,5,7,4,1]=>001011
[7,4,1,3,6,2,5]=>[4,7,2,6,1,3,5]=>[6,2,7,4,1,3,5]=>001011
[7,4,1,3,6,5,2]=>[4,7,2,5,6,3,1]=>[6,5,2,3,7,4,1]=>001111
[7,4,1,5,2,3,6]=>[4,7,1,5,2,3,6]=>[5,1,7,4,2,3,6]=>001101
[7,4,1,5,2,6,3]=>[4,7,5,6,2,3,1]=>[6,2,5,3,7,4,1]=>001111
[7,4,1,5,3,2,6]=>[4,3,7,5,2,1,6]=>[5,3,2,7,4,1,6]=>011101
[7,4,1,5,3,6,2]=>[4,7,6,5,2,1,3]=>[5,2,6,1,7,4,3]=>001111
[7,4,1,5,6,2,3]=>[4,7,1,6,2,5,3]=>[6,1,5,7,4,2,3]=>001011
[7,4,1,5,6,3,2]=>[4,3,7,6,2,5,1]=>[6,3,2,5,7,4,1]=>011011
[7,4,1,6,2,3,5]=>[4,7,1,6,3,2,5]=>[6,1,3,7,4,2,5]=>001011
[7,4,1,6,2,5,3]=>[4,7,6,5,3,2,1]=>[5,3,6,2,7,4,1]=>001111
[7,4,1,6,3,2,5]=>[4,3,7,6,1,2,5]=>[6,3,1,7,4,2,5]=>011011
[7,4,1,6,3,5,2]=>[4,7,5,6,1,2,3]=>[6,1,5,2,7,4,3]=>001111
[7,4,1,6,5,2,3]=>[4,7,1,5,6,2,3]=>[6,5,1,7,4,2,3]=>001111
[7,4,1,6,5,3,2]=>[4,3,7,5,6,2,1]=>[6,5,3,2,7,4,1]=>011111
[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[7,4,2,1,3,5,6]=>101001
[7,4,2,1,3,6,5]=>[2,4,1,7,6,3,5]=>[6,4,2,1,3,7,5]=>101011
[7,4,2,1,5,3,6]=>[2,4,7,5,3,1,6]=>[5,3,7,4,2,1,6]=>101101
[7,4,2,1,5,6,3]=>[2,4,7,6,3,5,1]=>[6,3,5,7,4,2,1]=>101011
[7,4,2,1,6,3,5]=>[2,4,7,6,1,3,5]=>[6,2,1,7,4,3,5]=>101011
[7,4,2,1,6,5,3]=>[2,4,7,5,6,3,1]=>[6,5,3,7,4,2,1]=>101111
[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>[7,4,2,3,1,5,6]=>011001
[7,4,2,3,1,6,5]=>[3,4,2,7,6,1,5]=>[6,4,2,3,1,7,5]=>011011
[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>[7,4,2,3,5,1,6]=>001101
[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>[7,4,2,3,5,6,1]=>001011
[7,4,2,3,6,1,5]=>[6,4,2,7,1,3,5]=>[7,4,2,6,1,3,5]=>001011
[7,4,2,3,6,5,1]=>[5,4,1,6,7,3,2]=>[7,4,1,3,6,5,2]=>001111
[7,4,2,5,1,3,6]=>[5,4,1,7,2,3,6]=>[7,4,1,5,2,3,6]=>001101
[7,4,2,5,1,6,3]=>[5,4,7,6,3,1,2]=>[6,3,7,4,1,5,2]=>001111
[7,4,2,5,3,1,6]=>[3,5,4,7,1,2,6]=>[7,4,1,5,3,2,6]=>011101
[7,4,2,5,3,6,1]=>[6,4,7,5,3,2,1]=>[5,3,7,4,2,6,1]=>001111
[7,4,2,5,6,1,3]=>[6,4,1,7,2,5,3]=>[7,4,1,5,6,2,3]=>001011
[7,4,2,5,6,3,1]=>[3,6,4,7,1,5,2]=>[7,4,1,5,6,3,2]=>011011
[7,4,2,6,1,3,5]=>[6,4,1,7,3,2,5]=>[7,4,1,3,6,2,5]=>001011
[7,4,2,6,1,5,3]=>[6,4,7,5,1,3,2]=>[5,1,7,4,3,6,2]=>001111
[7,4,2,6,3,1,5]=>[3,6,4,7,2,1,5]=>[7,4,2,6,3,1,5]=>011011
[7,4,2,6,3,5,1]=>[5,4,7,6,2,3,1]=>[6,2,7,4,3,5,1]=>001111
[7,4,2,6,5,1,3]=>[5,4,2,6,7,1,3]=>[7,4,2,6,5,1,3]=>001111
[7,4,2,6,5,3,1]=>[3,5,4,6,7,2,1]=>[7,4,2,6,5,3,1]=>011111
[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[7,4,3,1,2,5,6]=>011001
[7,4,3,1,2,6,5]=>[3,1,4,7,6,2,5]=>[6,4,3,1,2,7,5]=>011011
[7,4,3,1,5,2,6]=>[3,4,7,5,1,2,6]=>[5,1,7,4,3,2,6]=>011101
[7,4,3,1,5,6,2]=>[3,4,7,6,1,5,2]=>[6,1,5,7,4,3,2]=>011011
[7,4,3,1,6,2,5]=>[3,4,7,6,2,1,5]=>[6,2,7,4,3,1,5]=>011011
[7,4,3,1,6,5,2]=>[3,4,7,5,6,1,2]=>[6,5,1,7,4,3,2]=>011111
[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[7,4,3,2,1,5,6]=>111001
[7,4,3,2,1,6,5]=>[2,3,4,7,6,1,5]=>[6,4,3,2,1,7,5]=>111011
[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[7,4,3,2,5,1,6]=>011101
[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]=>011011
[7,4,3,2,6,1,5]=>[6,3,4,7,1,2,5]=>[7,4,3,1,6,2,5]=>011011
[7,4,3,2,6,5,1]=>[5,3,4,6,7,1,2]=>[7,4,3,1,6,5,2]=>011111
[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[7,4,3,5,1,2,6]=>001101
[7,4,3,5,1,6,2]=>[5,6,4,7,3,1,2]=>[7,4,3,6,1,5,2]=>001111
[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[7,4,3,5,2,1,6]=>101101
[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>[7,4,3,5,2,6,1]=>001111
[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>[7,4,3,5,6,1,2]=>001011
[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>[7,4,3,5,6,2,1]=>101011
[7,4,3,6,1,2,5]=>[6,1,4,7,2,3,5]=>[7,4,1,2,6,3,5]=>001011
[7,4,3,6,1,5,2]=>[6,5,4,7,1,3,2]=>[7,4,1,5,3,6,2]=>001111
[7,4,3,6,2,1,5]=>[2,6,4,7,1,3,5]=>[7,4,2,1,6,3,5]=>101011
[7,4,3,6,2,5,1]=>[5,6,4,7,2,3,1]=>[7,4,2,6,3,5,1]=>001111
[7,4,3,6,5,1,2]=>[5,1,4,6,7,2,3]=>[7,4,1,2,6,5,3]=>001111
[7,4,3,6,5,2,1]=>[2,5,4,6,7,1,3]=>[7,4,2,1,6,5,3]=>101111
[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[7,4,5,1,2,3,6]=>000101
[7,4,5,1,2,6,3]=>[5,1,6,7,4,2,3]=>[7,4,6,1,2,5,3]=>000111
[7,4,5,1,3,2,6]=>[5,3,1,7,4,2,6]=>[3,1,7,4,5,2,6]=>010101
[7,4,5,1,3,6,2]=>[5,6,1,7,4,3,2]=>[7,4,6,1,3,5,2]=>000111
[7,4,5,1,6,2,3]=>[5,6,2,7,4,1,3]=>[7,4,6,2,5,1,3]=>000111
[7,4,5,1,6,3,2]=>[5,3,6,7,4,1,2]=>[7,4,6,3,1,5,2]=>010111
[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>[7,4,5,2,1,3,6]=>100101
[7,4,5,2,1,6,3]=>[2,5,6,7,4,1,3]=>[7,4,6,2,1,5,3]=>100111
[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>[7,4,5,2,3,1,6]=>010101
[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>[7,4,5,2,3,6,1]=>000111
[7,4,5,2,6,1,3]=>[6,5,1,7,4,2,3]=>[7,4,5,1,6,2,3]=>000111
[7,4,5,2,6,3,1]=>[3,6,5,7,4,1,2]=>[7,4,5,1,6,3,2]=>010111
[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>[7,4,5,3,1,2,6]=>010101
[7,4,5,3,1,6,2]=>[3,5,6,7,4,2,1]=>[7,4,6,2,5,3,1]=>010111
[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[7,4,5,3,2,1,6]=>110101
[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>[7,4,5,3,2,6,1]=>010111
[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>[7,4,5,3,6,1,2]=>000111
[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>[7,4,5,3,6,2,1]=>100111
[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[7,4,5,6,1,2,3]=>000011
[7,4,5,6,1,3,2]=>[6,3,1,7,4,5,2]=>[3,1,7,4,5,6,2]=>010011
[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>[7,4,5,6,2,1,3]=>100011
[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>[7,4,5,6,2,3,1]=>010011
[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>[7,4,5,6,3,1,2]=>010011
[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>[7,4,5,6,3,2,1]=>110011
[7,4,6,1,2,3,5]=>[6,1,2,7,3,4,5]=>[7,1,2,3,6,4,5]=>000011
[7,4,6,1,2,5,3]=>[6,1,5,7,2,4,3]=>[7,1,2,5,4,6,3]=>000111
[7,4,6,1,3,2,5]=>[6,3,1,7,2,4,5]=>[3,1,7,2,6,4,5]=>010011
[7,4,6,1,3,5,2]=>[6,5,1,7,3,4,2]=>[7,1,3,5,4,6,2]=>000111
[7,4,6,1,5,2,3]=>[6,5,2,7,1,4,3]=>[7,2,5,4,6,1,3]=>000111
[7,4,6,1,5,3,2]=>[6,3,5,7,1,4,2]=>[7,3,1,5,4,6,2]=>010111
[7,4,6,2,1,3,5]=>[2,6,1,7,3,4,5]=>[7,2,1,3,6,4,5]=>100011
[7,4,6,2,1,5,3]=>[2,6,5,7,1,4,3]=>[7,2,1,5,4,6,3]=>100111
[7,4,6,2,3,1,5]=>[3,6,2,7,1,4,5]=>[7,2,3,1,6,4,5]=>010011
[7,4,6,2,3,5,1]=>[5,6,2,7,3,4,1]=>[7,2,3,6,4,5,1]=>000111
[7,4,6,2,5,1,3]=>[5,6,1,7,2,4,3]=>[7,1,6,4,5,2,3]=>000111
[7,4,6,2,5,3,1]=>[3,5,6,7,1,4,2]=>[7,1,6,4,5,3,2]=>010111
[7,4,6,3,1,2,5]=>[3,1,6,7,2,4,5]=>[7,3,1,2,6,4,5]=>010011
[7,4,6,3,1,5,2]=>[3,6,5,7,2,4,1]=>[7,2,5,4,6,3,1]=>010111
[7,4,6,3,2,1,5]=>[2,3,6,7,1,4,5]=>[7,3,2,1,6,4,5]=>110011
[7,4,6,3,2,5,1]=>[5,3,6,7,2,4,1]=>[7,3,2,6,4,5,1]=>010111
[7,4,6,3,5,1,2]=>[5,1,6,7,3,4,2]=>[7,3,6,4,5,1,2]=>000111
[7,4,6,3,5,2,1]=>[2,5,6,7,3,4,1]=>[7,3,6,4,5,2,1]=>100111
[7,4,6,5,1,2,3]=>[5,1,2,6,7,3,4]=>[7,1,2,3,6,5,4]=>000111
[7,4,6,5,1,3,2]=>[5,3,1,6,7,2,4]=>[3,1,7,2,6,5,4]=>010111
[7,4,6,5,2,1,3]=>[2,5,1,6,7,3,4]=>[7,2,1,3,6,5,4]=>100111
[7,4,6,5,2,3,1]=>[3,5,2,6,7,1,4]=>[7,2,3,1,6,5,4]=>010111
[7,4,6,5,3,1,2]=>[3,1,5,6,7,2,4]=>[7,3,1,2,6,5,4]=>010111
[7,4,6,5,3,2,1]=>[2,3,5,6,7,1,4]=>[7,3,2,1,6,5,4]=>110111
[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[7,5,1,2,3,4,6]=>000101
[7,5,1,2,3,6,4]=>[5,1,2,7,6,4,3]=>[6,4,7,5,1,2,3]=>000111
[7,5,1,2,4,3,6]=>[5,1,4,2,7,3,6]=>[4,1,2,7,5,3,6]=>001101
[7,5,1,2,4,6,3]=>[5,1,7,3,6,4,2]=>[6,3,4,7,5,1,2]=>000111
[7,5,1,2,6,3,4]=>[5,1,7,2,6,3,4]=>[6,1,2,7,5,3,4]=>000111
[7,5,1,2,6,4,3]=>[5,1,4,7,6,3,2]=>[6,4,3,7,5,1,2]=>001111
[7,5,1,3,2,4,6]=>[5,3,1,2,7,4,6]=>[3,1,7,5,2,4,6]=>010101
[7,5,1,3,2,6,4]=>[5,3,1,7,6,4,2]=>[3,1,6,4,7,5,2]=>010111
[7,5,1,3,4,2,6]=>[5,4,1,3,7,2,6]=>[4,1,3,7,5,2,6]=>001101
[7,5,1,3,4,6,2]=>[5,7,2,3,6,4,1]=>[6,2,3,4,7,5,1]=>000111
[7,5,1,3,6,2,4]=>[5,7,2,1,6,3,4]=>[6,2,7,5,1,3,4]=>000111
[7,5,1,3,6,4,2]=>[5,4,2,7,6,3,1]=>[6,4,2,3,7,5,1]=>001111
[7,5,1,4,2,3,6]=>[5,4,2,1,7,3,6]=>[4,2,7,5,1,3,6]=>001101
[7,5,1,4,2,6,3]=>[5,4,7,3,6,2,1]=>[6,3,4,2,7,5,1]=>001111
[7,5,1,4,3,2,6]=>[5,3,4,1,7,2,6]=>[4,3,1,7,5,2,6]=>011101
[7,5,1,4,3,6,2]=>[5,7,4,2,6,3,1]=>[4,2,6,3,7,5,1]=>001111
[7,5,1,4,6,2,3]=>[5,7,1,2,6,4,3]=>[6,1,4,7,5,2,3]=>000111
[7,5,1,4,6,3,2]=>[5,3,7,2,6,4,1]=>[6,3,2,4,7,5,1]=>010111
[7,5,1,6,2,3,4]=>[5,7,1,3,6,2,4]=>[6,1,3,7,5,2,4]=>000111
[7,5,1,6,2,4,3]=>[5,7,4,1,6,2,3]=>[4,1,6,2,7,5,3]=>001111
[7,5,1,6,3,2,4]=>[5,3,7,1,6,2,4]=>[6,3,1,7,5,2,4]=>010111
[7,5,1,6,3,4,2]=>[5,4,7,1,6,3,2]=>[6,1,4,3,7,5,2]=>001111
[7,5,1,6,4,2,3]=>[5,4,1,7,6,2,3]=>[6,4,1,7,5,2,3]=>001111
[7,5,1,6,4,3,2]=>[5,3,4,7,6,2,1]=>[6,4,3,2,7,5,1]=>011111
[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[7,5,2,1,3,4,6]=>100101
[7,5,2,1,3,6,4]=>[2,5,1,7,6,4,3]=>[6,4,7,5,2,1,3]=>100111
[7,5,2,1,4,3,6]=>[2,5,4,1,7,3,6]=>[4,2,1,7,5,3,6]=>101101
[7,5,2,1,4,6,3]=>[2,5,7,3,6,4,1]=>[6,3,4,7,5,2,1]=>100111
[7,5,2,1,6,3,4]=>[2,5,7,1,6,3,4]=>[6,2,1,7,5,3,4]=>100111
[7,5,2,1,6,4,3]=>[2,5,4,7,6,3,1]=>[6,4,3,7,5,2,1]=>101111
[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>[7,5,2,3,1,4,6]=>010101
[7,5,2,3,1,6,4]=>[3,5,2,7,6,4,1]=>[6,4,7,5,2,3,1]=>010111
[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>[7,5,2,3,4,1,6]=>001101
[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>[7,5,2,3,4,6,1]=>000111
[7,5,2,3,6,1,4]=>[6,5,2,1,7,3,4]=>[7,5,2,6,1,3,4]=>000111
[7,5,2,3,6,4,1]=>[4,6,1,5,7,3,2]=>[7,5,1,3,6,4,2]=>001111
[7,5,2,4,1,3,6]=>[4,5,1,2,7,3,6]=>[7,5,1,4,2,3,6]=>001101
[7,5,2,4,1,6,3]=>[4,5,7,3,6,1,2]=>[6,3,7,5,1,4,2]=>001111
[7,5,2,4,3,1,6]=>[3,4,5,1,7,2,6]=>[7,5,1,4,3,2,6]=>011101
[7,5,2,4,3,6,1]=>[6,5,4,2,7,3,1]=>[4,2,7,5,3,6,1]=>001111
[7,5,2,4,6,1,3]=>[6,5,1,2,7,4,3]=>[7,5,1,4,6,2,3]=>000111
[7,5,2,4,6,3,1]=>[3,6,5,1,7,4,2]=>[7,5,1,4,6,3,2]=>010111
[7,5,2,6,1,3,4]=>[6,5,1,3,7,2,4]=>[7,5,1,3,6,2,4]=>000111
[7,5,2,6,1,4,3]=>[6,5,4,1,7,2,3]=>[4,1,7,5,2,6,3]=>001111
[7,5,2,6,3,1,4]=>[3,6,5,2,7,1,4]=>[7,5,2,6,3,1,4]=>010111
[7,5,2,6,3,4,1]=>[4,5,7,2,6,3,1]=>[6,2,7,5,3,4,1]=>001111
[7,5,2,6,4,1,3]=>[4,6,2,5,7,1,3]=>[7,5,2,6,4,1,3]=>001111
[7,5,2,6,4,3,1]=>[3,4,6,5,7,2,1]=>[7,5,2,6,4,3,1]=>011111
[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[7,5,3,1,2,4,6]=>010101
[7,5,3,1,2,6,4]=>[3,1,5,7,6,4,2]=>[6,4,7,5,3,1,2]=>010111
[7,5,3,1,4,2,6]=>[3,5,4,2,7,1,6]=>[4,2,7,5,3,1,6]=>011101
[7,5,3,1,4,6,2]=>[3,5,7,1,6,4,2]=>[6,1,4,7,5,3,2]=>010111
[7,5,3,1,6,2,4]=>[3,5,7,2,6,1,4]=>[6,2,7,5,3,1,4]=>010111
[7,5,3,1,6,4,2]=>[3,5,4,7,6,1,2]=>[6,4,1,7,5,3,2]=>011111
[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[7,5,3,2,1,4,6]=>110101
[7,5,3,2,1,6,4]=>[2,3,5,7,6,4,1]=>[6,4,7,5,3,2,1]=>110111
[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>[7,5,3,2,4,1,6]=>011101
[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>[7,5,3,2,4,6,1]=>010111
[7,5,3,2,6,1,4]=>[6,3,5,1,7,2,4]=>[7,5,3,1,6,2,4]=>010111
[7,5,3,2,6,4,1]=>[4,3,6,5,7,1,2]=>[7,5,3,1,6,4,2]=>011111
[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[7,5,3,4,1,2,6]=>001101
[7,5,3,4,1,6,2]=>[4,6,5,3,7,1,2]=>[7,5,3,6,1,4,2]=>001111
[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>[7,5,3,4,2,1,6]=>101101
[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]=>001111
[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>[7,5,3,4,6,1,2]=>000111
[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>[7,5,3,4,6,2,1]=>100111
[7,5,3,6,1,2,4]=>[6,1,5,2,7,3,4]=>[7,5,1,2,6,3,4]=>000111
[7,5,3,6,1,4,2]=>[6,4,5,1,7,3,2]=>[7,5,1,4,3,6,2]=>001111
[7,5,3,6,2,1,4]=>[2,6,5,1,7,3,4]=>[7,5,2,1,6,3,4]=>100111
[7,5,3,6,2,4,1]=>[4,6,5,2,7,3,1]=>[7,5,2,6,3,4,1]=>001111
[7,5,3,6,4,1,2]=>[4,1,6,5,7,2,3]=>[7,5,1,2,6,4,3]=>001111
[7,5,3,6,4,2,1]=>[2,4,6,5,7,1,3]=>[7,5,2,1,6,4,3]=>101111
[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[7,5,4,1,2,3,6]=>001101
[7,5,4,1,2,6,3]=>[4,1,5,7,6,2,3]=>[6,1,2,7,5,4,3]=>001111
[7,5,4,1,3,2,6]=>[4,3,1,5,7,2,6]=>[3,1,7,5,4,2,6]=>011101
[7,5,4,1,3,6,2]=>[4,5,1,7,6,3,2]=>[6,1,3,7,5,4,2]=>001111
[7,5,4,1,6,2,3]=>[4,5,2,7,6,1,3]=>[6,2,7,5,4,1,3]=>001111
[7,5,4,1,6,3,2]=>[4,3,5,7,6,1,2]=>[6,3,1,7,5,4,2]=>011111
[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[7,5,4,2,1,3,6]=>101101
[7,5,4,2,1,6,3]=>[2,4,5,7,6,1,3]=>[6,2,1,7,5,4,3]=>101111
[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>[7,5,4,2,3,1,6]=>011101
[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>[7,5,4,2,3,6,1]=>001111
[7,5,4,2,6,1,3]=>[6,4,1,5,7,2,3]=>[7,5,4,1,6,2,3]=>001111
[7,5,4,2,6,3,1]=>[3,6,4,5,7,1,2]=>[7,5,4,1,6,3,2]=>011111
[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[7,5,4,3,1,2,6]=>011101
[7,5,4,3,1,6,2]=>[3,4,5,7,6,2,1]=>[6,2,7,5,4,3,1]=>011111
[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[7,5,4,3,2,1,6]=>111101
[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]=>011111
[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[7,5,4,3,6,1,2]=>001111
[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>[7,5,4,3,6,2,1]=>101111
[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[7,5,4,6,1,2,3]=>000111
[7,5,4,6,1,3,2]=>[6,3,1,5,7,4,2]=>[3,1,7,5,4,6,2]=>010111
[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>[7,5,4,6,2,1,3]=>100111
[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>[7,5,4,6,2,3,1]=>010111
[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>[7,5,4,6,3,1,2]=>010111
[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>[7,5,4,6,3,2,1]=>110111
[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[7,5,6,1,2,3,4]=>000011
[7,5,6,1,2,4,3]=>[6,1,4,2,7,5,3]=>[4,1,2,7,5,6,3]=>001011
[7,5,6,1,3,2,4]=>[6,3,1,2,7,5,4]=>[3,1,7,5,6,2,4]=>010011
[7,5,6,1,3,4,2]=>[6,4,1,3,7,5,2]=>[4,1,3,7,5,6,2]=>001011
[7,5,6,1,4,2,3]=>[6,4,2,1,7,5,3]=>[4,2,7,5,6,1,3]=>001011
[7,5,6,1,4,3,2]=>[6,3,4,1,7,5,2]=>[4,3,1,7,5,6,2]=>011011
[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[7,5,6,2,1,3,4]=>100011
[7,5,6,2,1,4,3]=>[2,6,4,1,7,5,3]=>[4,2,1,7,5,6,3]=>101011
[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>[7,5,6,2,3,1,4]=>010011
[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>[7,5,6,2,3,4,1]=>001011
[7,5,6,2,4,1,3]=>[4,6,1,2,7,5,3]=>[7,5,6,1,4,2,3]=>001011
[7,5,6,2,4,3,1]=>[3,4,6,1,7,5,2]=>[7,5,6,1,4,3,2]=>011011
[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[7,5,6,3,1,2,4]=>010011
[7,5,6,3,1,4,2]=>[3,6,4,2,7,5,1]=>[4,2,7,5,6,3,1]=>011011
[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[7,5,6,3,2,1,4]=>110011
[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>[7,5,6,3,2,4,1]=>011011
[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[7,5,6,3,4,1,2]=>001011
[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>[7,5,6,3,4,2,1]=>101011
[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>[7,5,6,4,1,2,3]=>001011
[7,5,6,4,1,3,2]=>[4,3,1,6,7,5,2]=>[3,1,7,5,6,4,2]=>011011
[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>[7,5,6,4,2,1,3]=>101011
[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>[7,5,6,4,2,3,1]=>011011
[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>[7,5,6,4,3,1,2]=>011011
[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>[7,5,6,4,3,2,1]=>111011
[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[7,6,1,2,3,4,5]=>000011
[7,6,1,2,3,5,4]=>[6,1,2,5,3,7,4]=>[5,1,2,3,7,6,4]=>000111
[7,6,1,2,4,3,5]=>[6,1,4,2,3,7,5]=>[4,1,2,7,6,3,5]=>001011
[7,6,1,2,4,5,3]=>[6,1,5,2,4,7,3]=>[5,1,2,4,7,6,3]=>000111
[7,6,1,2,5,3,4]=>[6,1,5,3,2,7,4]=>[5,3,7,6,1,2,4]=>000111
[7,6,1,2,5,4,3]=>[6,1,4,5,2,7,3]=>[5,4,1,2,7,6,3]=>001111
[7,6,1,3,2,4,5]=>[6,3,1,2,4,7,5]=>[3,1,7,6,2,4,5]=>010011
[7,6,1,3,2,5,4]=>[6,3,1,5,2,7,4]=>[3,1,5,2,7,6,4]=>010111
[7,6,1,3,4,2,5]=>[6,4,1,3,2,7,5]=>[4,1,3,7,6,2,5]=>001011
[7,6,1,3,4,5,2]=>[6,5,1,3,4,7,2]=>[5,1,3,4,7,6,2]=>000111
[7,6,1,3,5,2,4]=>[6,5,1,2,3,7,4]=>[5,1,7,6,2,3,4]=>000111
[7,6,1,3,5,4,2]=>[6,4,1,5,3,7,2]=>[5,4,1,3,7,6,2]=>001111
[7,6,1,4,2,3,5]=>[6,4,2,1,3,7,5]=>[4,2,7,6,1,3,5]=>001011
[7,6,1,4,2,5,3]=>[6,4,5,1,2,7,3]=>[5,1,4,2,7,6,3]=>001111
[7,6,1,4,3,2,5]=>[6,3,4,1,2,7,5]=>[4,3,1,7,6,2,5]=>011011
[7,6,1,4,3,5,2]=>[6,5,4,1,3,7,2]=>[4,1,5,3,7,6,2]=>001111
[7,6,1,4,5,2,3]=>[6,5,2,1,4,7,3]=>[5,2,4,7,6,1,3]=>000111
[7,6,1,4,5,3,2]=>[6,3,5,1,4,7,2]=>[5,3,1,4,7,6,2]=>010111
[7,6,1,5,2,3,4]=>[6,5,2,3,1,7,4]=>[5,2,3,7,6,1,4]=>000111
[7,6,1,5,2,4,3]=>[6,5,4,2,1,7,3]=>[4,2,5,1,7,6,3]=>001111
[7,6,1,5,3,2,4]=>[6,3,5,2,1,7,4]=>[5,3,2,7,6,1,4]=>010111
[7,6,1,5,3,4,2]=>[6,4,5,3,1,7,2]=>[5,3,4,1,7,6,2]=>001111
[7,6,1,5,4,2,3]=>[6,4,2,5,1,7,3]=>[5,4,2,7,6,1,3]=>001111
[7,6,1,5,4,3,2]=>[6,3,4,5,1,7,2]=>[5,4,3,1,7,6,2]=>011111
[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[7,6,2,1,3,4,5]=>100011
[7,6,2,1,3,5,4]=>[2,6,1,5,3,7,4]=>[5,2,1,3,7,6,4]=>100111
[7,6,2,1,4,3,5]=>[2,6,4,1,3,7,5]=>[4,2,1,7,6,3,5]=>101011
[7,6,2,1,4,5,3]=>[2,6,5,1,4,7,3]=>[5,2,1,4,7,6,3]=>100111
[7,6,2,1,5,3,4]=>[2,6,5,3,1,7,4]=>[5,3,7,6,2,1,4]=>100111
[7,6,2,1,5,4,3]=>[2,6,4,5,1,7,3]=>[5,4,2,1,7,6,3]=>101111
[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[7,6,2,3,1,4,5]=>010011
[7,6,2,3,1,5,4]=>[3,6,2,5,1,7,4]=>[5,2,3,1,7,6,4]=>010111
[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[7,6,2,3,4,1,5]=>001011
[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>[7,6,2,3,4,5,1]=>000111
[7,6,2,3,5,1,4]=>[5,6,2,1,3,7,4]=>[7,6,2,5,1,3,4]=>000111
[7,6,2,3,5,4,1]=>[4,5,1,6,3,7,2]=>[7,6,1,3,5,4,2]=>001111
[7,6,2,4,1,3,5]=>[4,6,1,2,3,7,5]=>[7,6,1,4,2,3,5]=>001011
[7,6,2,4,1,5,3]=>[4,6,5,2,1,7,3]=>[5,2,7,6,1,4,3]=>001111
[7,6,2,4,3,1,5]=>[3,4,6,1,2,7,5]=>[7,6,1,4,3,2,5]=>011011
[7,6,2,4,3,5,1]=>[5,6,4,2,3,7,1]=>[4,2,7,6,3,5,1]=>001111
[7,6,2,4,5,1,3]=>[5,6,1,2,4,7,3]=>[7,6,1,4,5,2,3]=>000111
[7,6,2,4,5,3,1]=>[3,5,6,1,4,7,2]=>[7,6,1,4,5,3,2]=>010111
[7,6,2,5,1,3,4]=>[5,6,1,3,2,7,4]=>[7,6,1,3,5,2,4]=>000111
[7,6,2,5,1,4,3]=>[5,6,4,1,2,7,3]=>[4,1,7,6,2,5,3]=>001111
[7,6,2,5,3,1,4]=>[3,5,6,2,1,7,4]=>[7,6,2,5,3,1,4]=>010111
[7,6,2,5,3,4,1]=>[4,6,5,3,2,7,1]=>[5,3,7,6,2,4,1]=>001111
[7,6,2,5,4,1,3]=>[4,5,2,6,1,7,3]=>[7,6,2,5,4,1,3]=>001111
[7,6,2,5,4,3,1]=>[3,4,5,6,2,7,1]=>[7,6,2,5,4,3,1]=>011111
[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[7,6,3,1,2,4,5]=>010011
[7,6,3,1,2,5,4]=>[3,1,6,5,2,7,4]=>[5,3,1,2,7,6,4]=>010111
[7,6,3,1,4,2,5]=>[3,6,4,2,1,7,5]=>[4,2,7,6,3,1,5]=>011011
[7,6,3,1,4,5,2]=>[3,6,5,2,4,7,1]=>[5,2,4,7,6,3,1]=>010111
[7,6,3,1,5,2,4]=>[3,6,5,1,2,7,4]=>[5,1,7,6,3,2,4]=>010111
[7,6,3,1,5,4,2]=>[3,6,4,5,2,7,1]=>[5,4,2,7,6,3,1]=>011111
[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[7,6,3,2,1,4,5]=>110011
[7,6,3,2,1,5,4]=>[2,3,6,5,1,7,4]=>[5,3,2,1,7,6,4]=>110111
[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[7,6,3,2,4,1,5]=>011011
[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>[7,6,3,2,4,5,1]=>010111
[7,6,3,2,5,1,4]=>[5,3,6,1,2,7,4]=>[7,6,3,1,5,2,4]=>010111
[7,6,3,2,5,4,1]=>[4,3,5,6,1,7,2]=>[7,6,3,1,5,4,2]=>011111
[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[7,6,3,4,1,2,5]=>001011
[7,6,3,4,1,5,2]=>[4,5,6,3,1,7,2]=>[7,6,3,5,1,4,2]=>001111
[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[7,6,3,4,2,1,5]=>101011
[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>[7,6,3,4,2,5,1]=>001111
[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>[7,6,3,4,5,1,2]=>000111
[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]=>100111
[7,6,3,5,1,2,4]=>[5,1,6,2,3,7,4]=>[7,6,1,2,5,3,4]=>000111
[7,6,3,5,1,4,2]=>[5,4,6,1,3,7,2]=>[7,6,1,4,3,5,2]=>001111
[7,6,3,5,2,1,4]=>[2,5,6,1,3,7,4]=>[7,6,2,1,5,3,4]=>100111
[7,6,3,5,2,4,1]=>[4,5,6,2,3,7,1]=>[7,6,2,5,3,4,1]=>001111
[7,6,3,5,4,1,2]=>[4,1,5,6,2,7,3]=>[7,6,1,2,5,4,3]=>001111
[7,6,3,5,4,2,1]=>[2,4,5,6,1,7,3]=>[7,6,2,1,5,4,3]=>101111
[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[7,6,4,1,2,3,5]=>001011
[7,6,4,1,2,5,3]=>[4,1,6,5,3,7,2]=>[5,3,7,6,4,1,2]=>001111
[7,6,4,1,3,2,5]=>[4,3,1,6,2,7,5]=>[3,1,7,6,4,2,5]=>011011
[7,6,4,1,3,5,2]=>[4,6,2,5,3,7,1]=>[5,2,3,7,6,4,1]=>001111
[7,6,4,1,5,2,3]=>[4,6,1,5,2,7,3]=>[5,1,7,6,4,2,3]=>001111
[7,6,4,1,5,3,2]=>[4,3,6,5,2,7,1]=>[5,3,2,7,6,4,1]=>011111
[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>101011
[7,6,4,2,1,5,3]=>[2,4,6,5,3,7,1]=>[5,3,7,6,4,2,1]=>101111
[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>[7,6,4,2,3,1,5]=>011011
[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>[7,6,4,2,3,5,1]=>001111
[7,6,4,2,5,1,3]=>[5,4,1,6,2,7,3]=>[7,6,4,1,5,2,3]=>001111
[7,6,4,2,5,3,1]=>[3,5,4,6,1,7,2]=>[7,6,4,1,5,3,2]=>011111
[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>011011
[7,6,4,3,1,5,2]=>[3,4,6,5,1,7,2]=>[5,1,7,6,4,3,2]=>011111
[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[7,6,4,3,2,1,5]=>111011
[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>[7,6,4,3,2,5,1]=>011111
[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[7,6,4,3,5,1,2]=>001111
[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]=>101111
[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[7,6,4,5,1,2,3]=>000111
[7,6,4,5,1,3,2]=>[5,3,1,6,4,7,2]=>[3,1,7,6,4,5,2]=>010111
[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>[7,6,4,5,2,1,3]=>100111
[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>[7,6,4,5,2,3,1]=>010111
[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>[7,6,4,5,3,1,2]=>010111
[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>[7,6,4,5,3,2,1]=>110111
[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[7,6,5,1,2,3,4]=>000111
[7,6,5,1,2,4,3]=>[5,1,4,2,6,7,3]=>[4,1,2,7,6,5,3]=>001111
[7,6,5,1,3,2,4]=>[5,3,1,2,6,7,4]=>[3,1,7,6,5,2,4]=>010111
[7,6,5,1,3,4,2]=>[5,4,1,3,6,7,2]=>[4,1,3,7,6,5,2]=>001111
[7,6,5,1,4,2,3]=>[5,4,2,1,6,7,3]=>[4,2,7,6,5,1,3]=>001111
[7,6,5,1,4,3,2]=>[5,3,4,1,6,7,2]=>[4,3,1,7,6,5,2]=>011111
[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[7,6,5,2,1,3,4]=>100111
[7,6,5,2,1,4,3]=>[2,5,4,1,6,7,3]=>[4,2,1,7,6,5,3]=>101111
[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>[7,6,5,2,3,1,4]=>010111
[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>[7,6,5,2,3,4,1]=>001111
[7,6,5,2,4,1,3]=>[4,5,1,2,6,7,3]=>[7,6,5,1,4,2,3]=>001111
[7,6,5,2,4,3,1]=>[3,4,5,1,6,7,2]=>[7,6,5,1,4,3,2]=>011111
[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>010111
[7,6,5,3,1,4,2]=>[3,5,4,2,6,7,1]=>[4,2,7,6,5,3,1]=>011111
[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>110111
[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>[7,6,5,3,2,4,1]=>011111
[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[7,6,5,3,4,1,2]=>001111
[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>[7,6,5,3,4,2,1]=>101111
[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[7,6,5,4,1,2,3]=>001111
[7,6,5,4,1,3,2]=>[4,3,1,5,6,7,2]=>[3,1,7,6,5,4,2]=>011111
[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>101111
[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>[7,6,5,4,2,3,1]=>011111
[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[7,6,5,4,3,1,2]=>011111
[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]=>111111
[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]=>1111111
[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>[7,8,6,5,4,3,2,1]=>1111101
[8,6,7,5,4,3,2,1]=>[2,3,4,5,7,8,6,1]=>[8,6,7,5,4,3,2,1]=>1111011
[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>[7,6,8,5,4,3,2,1]=>1111011
[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>[6,7,8,5,4,3,2,1]=>1111001
[8,7,5,6,4,3,2,1]=>[2,3,4,6,7,5,8,1]=>[8,7,5,6,4,3,2,1]=>1110111
[7,8,5,6,4,3,2,1]=>[2,3,4,6,8,5,7,1]=>[7,8,5,6,4,3,2,1]=>1110101
[8,6,5,7,4,3,2,1]=>[2,3,4,7,6,8,5,1]=>[8,6,5,7,4,3,2,1]=>1110111
[8,5,6,7,4,3,2,1]=>[2,3,4,7,8,5,6,1]=>[8,5,6,7,4,3,2,1]=>1110011
[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>[7,6,5,8,4,3,2,1]=>1110111
[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>[6,7,5,8,4,3,2,1]=>1110011
[7,5,6,8,4,3,2,1]=>[2,3,4,8,7,5,6,1]=>[7,5,6,8,4,3,2,1]=>1110011
[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>[6,5,7,8,4,3,2,1]=>1110101
[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,4,3,2,1]=>1110001
[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]=>1101111
[7,8,6,4,5,3,2,1]=>[2,3,5,6,4,8,7,1]=>[7,8,6,4,5,3,2,1]=>1101101
[8,6,7,4,5,3,2,1]=>[2,3,5,7,4,8,6,1]=>[8,6,7,4,5,3,2,1]=>1101011
[6,7,8,4,5,3,2,1]=>[2,3,5,8,4,6,7,1]=>[6,7,8,4,5,3,2,1]=>1101001
[8,7,4,5,6,3,2,1]=>[2,3,6,7,4,5,8,1]=>[8,7,4,5,6,3,2,1]=>1100111
[8,6,5,4,7,3,2,1]=>[2,3,7,5,6,8,4,1]=>[8,6,5,4,7,3,2,1]=>1101111
[8,5,4,6,7,3,2,1]=>[2,3,7,5,8,4,6,1]=>[8,5,4,6,7,3,2,1]=>1101011
[8,4,5,6,7,3,2,1]=>[2,3,7,8,4,5,6,1]=>[8,4,5,6,7,3,2,1]=>1100011
[7,6,5,4,8,3,2,1]=>[2,3,8,5,6,7,4,1]=>[7,6,5,4,8,3,2,1]=>1101111
[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>[6,7,5,4,8,3,2,1]=>1101011
[7,5,6,4,8,3,2,1]=>[2,3,8,6,7,5,4,1]=>[7,5,6,4,8,3,2,1]=>1100111
[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>[6,5,7,4,8,3,2,1]=>1100111
[7,4,5,6,8,3,2,1]=>[2,3,8,7,4,5,6,1]=>[7,4,5,6,8,3,2,1]=>1100011
[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]=>[6,5,4,7,8,3,2,1]=>1101101
[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]=>[5,6,4,7,8,3,2,1]=>1100101
[6,4,5,7,8,3,2,1]=>[2,3,8,6,4,5,7,1]=>[6,4,5,7,8,3,2,1]=>1100101
[5,4,6,7,8,3,2,1]=>[2,3,8,5,4,6,7,1]=>[5,4,6,7,8,3,2,1]=>1101001
[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>[4,5,6,7,8,3,2,1]=>1100001
[8,7,6,5,3,4,2,1]=>[2,4,5,3,6,7,8,1]=>[8,7,6,5,3,4,2,1]=>1011111
[7,8,6,5,3,4,2,1]=>[2,4,5,3,6,8,7,1]=>[7,8,6,5,3,4,2,1]=>1011101
[8,6,7,5,3,4,2,1]=>[2,4,5,3,7,8,6,1]=>[8,6,7,5,3,4,2,1]=>1011011
[7,6,8,5,3,4,2,1]=>[2,4,5,3,8,7,6,1]=>[7,6,8,5,3,4,2,1]=>1011011
[8,7,5,6,3,4,2,1]=>[2,4,6,3,7,5,8,1]=>[8,7,5,6,3,4,2,1]=>1010111
[7,8,5,6,3,4,2,1]=>[2,4,6,3,8,5,7,1]=>[7,8,5,6,3,4,2,1]=>1010101
[8,5,6,7,3,4,2,1]=>[2,4,7,3,8,5,6,1]=>[8,5,6,7,3,4,2,1]=>1010011
[6,7,5,8,3,4,2,1]=>[2,4,8,3,7,6,5,1]=>[6,7,5,8,3,4,2,1]=>1010011
[6,5,7,8,3,4,2,1]=>[2,4,8,3,6,5,7,1]=>[6,5,7,8,3,4,2,1]=>1010101
[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>[5,6,7,8,3,4,2,1]=>1010001
[8,7,6,4,3,5,2,1]=>[2,5,4,6,3,7,8,1]=>[8,7,6,4,3,5,2,1]=>1011111
[8,6,7,4,3,5,2,1]=>[2,5,4,7,3,8,6,1]=>[8,6,7,4,3,5,2,1]=>1011011
[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]=>[7,6,8,4,3,5,2,1]=>1011011
[6,7,8,4,3,5,2,1]=>[2,5,4,8,3,6,7,1]=>[6,7,8,4,3,5,2,1]=>1011001
[8,7,6,3,4,5,2,1]=>[2,5,6,3,4,7,8,1]=>[8,7,6,3,4,5,2,1]=>1001111
[7,8,6,3,4,5,2,1]=>[2,5,6,3,4,8,7,1]=>[7,8,6,3,4,5,2,1]=>1001101
[8,6,7,3,4,5,2,1]=>[2,5,7,3,4,8,6,1]=>[8,6,7,3,4,5,2,1]=>1001011
[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]=>[6,7,8,3,4,5,2,1]=>1001001
[8,7,5,4,3,6,2,1]=>[2,6,4,5,7,3,8,1]=>[8,7,5,4,3,6,2,1]=>1011111
[7,8,5,4,3,6,2,1]=>[2,6,4,5,8,3,7,1]=>[7,8,5,4,3,6,2,1]=>1011101
[8,7,4,5,3,6,2,1]=>[2,6,5,7,4,3,8,1]=>[8,7,4,5,3,6,2,1]=>1001111
[8,7,5,3,4,6,2,1]=>[2,6,5,3,7,4,8,1]=>[8,7,5,3,4,6,2,1]=>1001111
[7,8,5,3,4,6,2,1]=>[2,6,5,3,8,4,7,1]=>[7,8,5,3,4,6,2,1]=>1001101
[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]=>1010111
[7,8,3,4,5,6,2,1]=>[2,6,8,3,4,5,7,1]=>[7,8,3,4,5,6,2,1]=>1000101
[8,6,5,4,3,7,2,1]=>[2,7,4,5,6,8,3,1]=>[8,6,5,4,3,7,2,1]=>1011111
[8,6,4,3,5,7,2,1]=>[2,7,4,6,3,8,5,1]=>[8,6,4,3,5,7,2,1]=>1010111
[8,5,4,3,6,7,2,1]=>[2,7,4,5,8,3,6,1]=>[8,5,4,3,6,7,2,1]=>1011011
[8,4,3,5,6,7,2,1]=>[2,7,4,8,3,5,6,1]=>[8,4,3,5,6,7,2,1]=>1010011
[8,3,4,5,6,7,2,1]=>[2,7,8,3,4,5,6,1]=>[8,3,4,5,6,7,2,1]=>1000011
[7,6,5,4,3,8,2,1]=>[2,8,4,5,6,7,3,1]=>[7,6,5,4,3,8,2,1]=>1011111
[7,5,6,4,3,8,2,1]=>[2,8,4,6,7,5,3,1]=>[7,5,6,4,3,8,2,1]=>1010111
[6,5,7,4,3,8,2,1]=>[2,8,4,7,6,5,3,1]=>[6,5,7,4,3,8,2,1]=>1010111
[6,7,4,5,3,8,2,1]=>[2,8,5,7,4,6,3,1]=>[6,7,4,5,3,8,2,1]=>1001011
[7,5,4,6,3,8,2,1]=>[2,8,6,5,7,4,3,1]=>[7,5,4,6,3,8,2,1]=>1001111
[7,4,5,6,3,8,2,1]=>[2,8,6,7,4,5,3,1]=>[7,4,5,6,3,8,2,1]=>1000111
[6,5,4,7,3,8,2,1]=>[2,8,7,5,6,4,3,1]=>[6,5,4,7,3,8,2,1]=>1001111
[6,4,5,7,3,8,2,1]=>[2,8,7,6,4,5,3,1]=>[6,4,5,7,3,8,2,1]=>1000111
[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>[5,4,6,7,3,8,2,1]=>1001011
[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]=>[4,5,6,7,3,8,2,1]=>1000011
[7,6,4,3,5,8,2,1]=>[2,8,4,6,3,7,5,1]=>[7,6,4,3,5,8,2,1]=>1010111
[7,5,4,3,6,8,2,1]=>[2,8,4,5,7,3,6,1]=>[7,5,4,3,6,8,2,1]=>1011011
[7,3,4,5,6,8,2,1]=>[2,8,7,3,4,5,6,1]=>[7,3,4,5,6,8,2,1]=>1000011
[6,5,4,3,7,8,2,1]=>[2,8,4,5,6,3,7,1]=>[6,5,4,3,7,8,2,1]=>1011101
[6,5,3,4,7,8,2,1]=>[2,8,5,3,6,4,7,1]=>[6,5,3,4,7,8,2,1]=>1001101
[6,3,4,5,7,8,2,1]=>[2,8,6,3,4,5,7,1]=>[6,3,4,5,7,8,2,1]=>1000101
[5,4,3,6,7,8,2,1]=>[2,8,4,5,3,6,7,1]=>[5,4,3,6,7,8,2,1]=>1011001
[5,3,4,6,7,8,2,1]=>[2,8,5,3,4,6,7,1]=>[5,3,4,6,7,8,2,1]=>1001001
[4,3,5,6,7,8,2,1]=>[2,8,4,3,5,6,7,1]=>[4,3,5,6,7,8,2,1]=>1010001
[3,4,5,6,7,8,2,1]=>[2,8,3,4,5,6,7,1]=>[3,4,5,6,7,8,2,1]=>1000001
[8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,1]=>[8,7,6,5,4,2,3,1]=>0111111
[7,8,6,5,4,2,3,1]=>[3,4,2,5,6,8,7,1]=>[7,8,6,5,4,2,3,1]=>0111101
[8,6,7,5,4,2,3,1]=>[3,4,2,5,7,8,6,1]=>[8,6,7,5,4,2,3,1]=>0111011
[7,6,8,5,4,2,3,1]=>[3,4,2,5,8,7,6,1]=>[7,6,8,5,4,2,3,1]=>0111011
[8,7,5,6,4,2,3,1]=>[3,4,2,6,7,5,8,1]=>[8,7,5,6,4,2,3,1]=>0110111
[7,6,5,8,4,2,3,1]=>[3,4,2,8,6,7,5,1]=>[7,6,5,8,4,2,3,1]=>0110111
[6,7,5,8,4,2,3,1]=>[3,4,2,8,7,6,5,1]=>[6,7,5,8,4,2,3,1]=>0110011
[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>[5,6,7,8,4,2,3,1]=>0110001
[8,7,6,4,5,2,3,1]=>[3,5,2,6,4,7,8,1]=>[8,7,6,4,5,2,3,1]=>0101111
[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>[8,6,7,4,5,2,3,1]=>0101011
[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]=>[7,6,8,4,5,2,3,1]=>0101011
[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]=>[6,7,8,4,5,2,3,1]=>0101001
[8,7,5,4,6,2,3,1]=>[3,6,2,5,7,4,8,1]=>[8,7,5,4,6,2,3,1]=>0101111
[8,7,4,5,6,2,3,1]=>[3,6,2,7,4,5,8,1]=>[8,7,4,5,6,2,3,1]=>0100111
[7,8,4,5,6,2,3,1]=>[3,6,2,8,4,5,7,1]=>[7,8,4,5,6,2,3,1]=>0100101
[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]=>[8,5,6,4,7,2,3,1]=>0100111
[8,4,5,6,7,2,3,1]=>[3,7,2,8,4,5,6,1]=>[8,4,5,6,7,2,3,1]=>0100011
[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]=>[7,5,6,4,8,2,3,1]=>0100111
[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>[6,5,7,4,8,2,3,1]=>0100111
[4,5,6,7,8,2,3,1]=>[3,8,2,4,5,6,7,1]=>[4,5,6,7,8,2,3,1]=>0100001
[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]=>[8,7,6,5,3,2,4,1]=>0111111
[7,6,8,5,3,2,4,1]=>[4,3,5,2,8,7,6,1]=>[7,6,8,5,3,2,4,1]=>0111011
[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]=>[6,7,8,5,3,2,4,1]=>0111001
[8,7,5,6,3,2,4,1]=>[4,3,6,2,7,5,8,1]=>[8,7,5,6,3,2,4,1]=>0110111
[8,6,5,7,3,2,4,1]=>[4,3,7,2,6,8,5,1]=>[8,6,5,7,3,2,4,1]=>0110111
[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>[8,5,6,7,3,2,4,1]=>0110011
[7,6,5,8,3,2,4,1]=>[4,3,8,2,6,7,5,1]=>[7,6,5,8,3,2,4,1]=>0110111
[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]=>[6,7,5,8,3,2,4,1]=>0110011
[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>[5,6,7,8,3,2,4,1]=>0110001
[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]=>[8,7,6,5,2,3,4,1]=>0011111
[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]=>[6,7,8,5,2,3,4,1]=>0011001
[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]=>[8,7,5,6,2,3,4,1]=>0010111
[8,5,6,7,2,3,4,1]=>[4,7,2,3,8,5,6,1]=>[8,5,6,7,2,3,4,1]=>0010011
[7,6,5,8,2,3,4,1]=>[4,8,2,3,6,7,5,1]=>[7,6,5,8,2,3,4,1]=>0010111
[6,5,7,8,2,3,4,1]=>[4,8,2,3,6,5,7,1]=>[6,5,7,8,2,3,4,1]=>0010101
[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[5,6,7,8,2,3,4,1]=>0010001
[7,8,6,4,3,2,5,1]=>[5,3,4,6,2,8,7,1]=>[7,8,6,4,3,2,5,1]=>0111101
[7,6,8,4,3,2,5,1]=>[5,3,4,8,2,7,6,1]=>[7,6,8,4,3,2,5,1]=>0111011
[6,7,8,4,3,2,5,1]=>[5,3,4,8,2,6,7,1]=>[6,7,8,4,3,2,5,1]=>0111001
[8,7,6,3,4,2,5,1]=>[5,4,6,3,2,7,8,1]=>[8,7,6,3,4,2,5,1]=>0011111
[7,8,6,3,4,2,5,1]=>[5,4,6,3,2,8,7,1]=>[7,8,6,3,4,2,5,1]=>0011101
[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>[8,6,7,3,4,2,5,1]=>0011011
[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>[7,6,8,3,4,2,5,1]=>0011011
[6,7,8,3,4,2,5,1]=>[5,4,8,3,2,6,7,1]=>[6,7,8,3,4,2,5,1]=>0011001
[8,7,6,4,2,3,5,1]=>[5,4,2,6,3,7,8,1]=>[8,7,6,4,2,3,5,1]=>0011111
[8,6,7,4,2,3,5,1]=>[5,4,2,7,3,8,6,1]=>[8,6,7,4,2,3,5,1]=>0011011
[6,7,8,4,2,3,5,1]=>[5,4,2,8,3,6,7,1]=>[6,7,8,4,2,3,5,1]=>0011001
[8,7,6,3,2,4,5,1]=>[5,3,6,2,4,7,8,1]=>[8,7,6,3,2,4,5,1]=>0101111
[7,8,6,3,2,4,5,1]=>[5,3,6,2,4,8,7,1]=>[7,8,6,3,2,4,5,1]=>0101101
[8,6,7,3,2,4,5,1]=>[5,3,7,2,4,8,6,1]=>[8,6,7,3,2,4,5,1]=>0101011
[6,7,8,3,2,4,5,1]=>[5,3,8,2,4,6,7,1]=>[6,7,8,3,2,4,5,1]=>0101001
[8,7,6,2,3,4,5,1]=>[5,6,2,3,4,7,8,1]=>[8,7,6,2,3,4,5,1]=>0001111
[8,6,7,2,3,4,5,1]=>[5,7,2,3,4,8,6,1]=>[8,6,7,2,3,4,5,1]=>0001011
[7,6,8,2,3,4,5,1]=>[5,8,2,3,4,7,6,1]=>[7,6,8,2,3,4,5,1]=>0001011
[6,7,8,2,3,4,5,1]=>[5,8,2,3,4,6,7,1]=>[6,7,8,2,3,4,5,1]=>0001001
[8,7,5,4,3,2,6,1]=>[6,3,4,5,7,2,8,1]=>[8,7,5,4,3,2,6,1]=>0111111
[7,8,5,4,3,2,6,1]=>[6,3,4,5,8,2,7,1]=>[7,8,5,4,3,2,6,1]=>0111101
[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]=>[8,7,5,3,4,2,6,1]=>0011111
[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>[7,8,5,3,4,2,6,1]=>0011101
[8,7,4,3,5,2,6,1]=>[6,5,4,7,3,2,8,1]=>[8,7,4,3,5,2,6,1]=>0011111
[7,8,4,3,5,2,6,1]=>[6,5,4,8,3,2,7,1]=>[7,8,4,3,5,2,6,1]=>0011101
[8,7,5,4,2,3,6,1]=>[6,4,2,5,7,3,8,1]=>[8,7,5,4,2,3,6,1]=>0011111
[8,7,5,3,2,4,6,1]=>[6,3,5,2,7,4,8,1]=>[8,7,5,3,2,4,6,1]=>0101111
[7,8,4,3,2,5,6,1]=>[6,3,4,8,2,5,7,1]=>[7,8,4,3,2,5,6,1]=>0110101
[7,8,4,2,3,5,6,1]=>[6,4,2,8,3,5,7,1]=>[7,8,4,2,3,5,6,1]=>0010101
[7,8,3,2,4,5,6,1]=>[6,3,8,2,4,5,7,1]=>[7,8,3,2,4,5,6,1]=>0100101
[8,7,2,3,4,5,6,1]=>[6,7,2,3,4,5,8,1]=>[8,7,2,3,4,5,6,1]=>0000111
[8,6,5,4,3,2,7,1]=>[7,3,4,5,6,8,2,1]=>[8,6,5,4,3,2,7,1]=>0111111
[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>[8,5,6,3,4,2,7,1]=>0010111
[8,6,4,3,5,2,7,1]=>[7,5,4,6,3,8,2,1]=>[8,6,4,3,5,2,7,1]=>0011111
[8,5,4,3,6,2,7,1]=>[7,6,4,5,8,3,2,1]=>[8,5,4,3,6,2,7,1]=>0011111
[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>[8,4,5,3,6,2,7,1]=>0001111
[8,4,3,5,6,2,7,1]=>[7,6,4,8,3,5,2,1]=>[8,4,3,5,6,2,7,1]=>0010111
[8,3,4,5,6,2,7,1]=>[7,6,8,3,4,5,2,1]=>[8,3,4,5,6,2,7,1]=>0000111
[8,5,6,4,2,3,7,1]=>[7,4,2,6,8,5,3,1]=>[8,5,6,4,2,3,7,1]=>0010111
[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]=>0111011
[8,4,5,3,2,6,7,1]=>[7,3,5,8,4,2,6,1]=>[8,4,5,3,2,6,7,1]=>0101011
[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[8,5,3,4,2,6,7,1]=>0011011
[8,3,4,5,2,6,7,1]=>[7,5,8,3,4,2,6,1]=>[8,3,4,5,2,6,7,1]=>0001011
[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>[8,5,4,2,3,6,7,1]=>0011011
[8,5,2,3,4,6,7,1]=>[7,5,2,3,8,4,6,1]=>[8,5,2,3,4,6,7,1]=>0001011
[8,3,4,2,5,6,7,1]=>[7,4,8,3,2,5,6,1]=>[8,3,4,2,5,6,7,1]=>0010011
[8,3,2,4,5,6,7,1]=>[7,3,8,2,4,5,6,1]=>[8,3,2,4,5,6,7,1]=>0100011
[8,2,3,4,5,6,7,1]=>[7,8,2,3,4,5,6,1]=>[8,2,3,4,5,6,7,1]=>0000011
[7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,2,1]=>[7,6,5,4,3,2,8,1]=>0111111
[6,7,5,4,3,2,8,1]=>[8,3,4,5,7,6,2,1]=>[6,7,5,4,3,2,8,1]=>0111011
[6,5,7,4,3,2,8,1]=>[8,3,4,7,6,5,2,1]=>[6,5,7,4,3,2,8,1]=>0110111
[7,6,4,5,3,2,8,1]=>[8,3,5,6,4,7,2,1]=>[7,6,4,5,3,2,8,1]=>0101111
[6,5,4,7,3,2,8,1]=>[8,3,7,5,6,4,2,1]=>[6,5,4,7,3,2,8,1]=>0101111
[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>[4,5,6,7,3,2,8,1]=>0100011
[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]=>[7,5,6,3,4,2,8,1]=>0010111
[6,5,7,3,4,2,8,1]=>[8,4,7,3,6,5,2,1]=>[6,5,7,3,4,2,8,1]=>0010111
[5,6,7,3,4,2,8,1]=>[8,4,7,3,5,6,2,1]=>[5,6,7,3,4,2,8,1]=>0010011
[7,6,4,3,5,2,8,1]=>[8,5,4,6,3,7,2,1]=>[7,6,4,3,5,2,8,1]=>0011111
[7,5,4,3,6,2,8,1]=>[8,6,4,5,7,3,2,1]=>[7,5,4,3,6,2,8,1]=>0011111
[7,4,5,3,6,2,8,1]=>[8,6,5,7,4,3,2,1]=>[7,4,5,3,6,2,8,1]=>0001111
[7,5,3,4,6,2,8,1]=>[8,6,5,3,7,4,2,1]=>[7,5,3,4,6,2,8,1]=>0001111
[7,3,4,5,6,2,8,1]=>[8,6,7,3,4,5,2,1]=>[7,3,4,5,6,2,8,1]=>0000111
[6,5,4,3,7,2,8,1]=>[8,7,4,5,6,3,2,1]=>[6,5,4,3,7,2,8,1]=>0011111
[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]=>[6,4,5,3,7,2,8,1]=>0001111
[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[5,4,6,3,7,2,8,1]=>0001111
[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[4,5,6,3,7,2,8,1]=>0000111
[6,5,3,4,7,2,8,1]=>[8,7,5,3,6,4,2,1]=>[6,5,3,4,7,2,8,1]=>0001111
[5,6,3,4,7,2,8,1]=>[8,7,6,3,5,4,2,1]=>[5,6,3,4,7,2,8,1]=>0000111
[6,4,3,5,7,2,8,1]=>[8,7,4,6,3,5,2,1]=>[6,4,3,5,7,2,8,1]=>0010111
[6,3,4,5,7,2,8,1]=>[8,7,6,3,4,5,2,1]=>[6,3,4,5,7,2,8,1]=>0000111
[5,4,3,6,7,2,8,1]=>[8,7,4,5,3,6,2,1]=>[5,4,3,6,7,2,8,1]=>0011011
[4,5,3,6,7,2,8,1]=>[8,7,5,4,3,6,2,1]=>[4,5,3,6,7,2,8,1]=>0001011
[4,3,5,6,7,2,8,1]=>[8,7,4,3,5,6,2,1]=>[4,3,5,6,7,2,8,1]=>0010011
[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]=>[3,4,5,6,7,2,8,1]=>0000011
[7,6,5,4,2,3,8,1]=>[8,4,2,5,6,7,3,1]=>[7,6,5,4,2,3,8,1]=>0011111
[6,7,5,4,2,3,8,1]=>[8,4,2,5,7,6,3,1]=>[6,7,5,4,2,3,8,1]=>0011011
[7,5,6,4,2,3,8,1]=>[8,4,2,6,7,5,3,1]=>[7,5,6,4,2,3,8,1]=>0010111
[6,5,7,4,2,3,8,1]=>[8,4,2,7,6,5,3,1]=>[6,5,7,4,2,3,8,1]=>0010111
[7,6,4,5,2,3,8,1]=>[8,5,2,6,4,7,3,1]=>[7,6,4,5,2,3,8,1]=>0001111
[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]=>[6,7,4,5,2,3,8,1]=>0001011
[7,5,4,6,2,3,8,1]=>[8,6,2,5,7,4,3,1]=>[7,5,4,6,2,3,8,1]=>0001111
[7,4,5,6,2,3,8,1]=>[8,6,2,7,4,5,3,1]=>[7,4,5,6,2,3,8,1]=>0000111
[6,5,4,7,2,3,8,1]=>[8,7,2,5,6,4,3,1]=>[6,5,4,7,2,3,8,1]=>0001111
[5,6,4,7,2,3,8,1]=>[8,7,2,6,5,4,3,1]=>[5,6,4,7,2,3,8,1]=>0000111
[6,4,5,7,2,3,8,1]=>[8,7,2,6,4,5,3,1]=>[6,4,5,7,2,3,8,1]=>0000111
[4,5,6,7,2,3,8,1]=>[8,7,2,4,5,6,3,1]=>[4,5,6,7,2,3,8,1]=>0000011
[6,5,7,3,2,4,8,1]=>[8,3,7,2,6,5,4,1]=>[6,5,7,3,2,4,8,1]=>0100111
[7,6,5,2,3,4,8,1]=>[8,5,2,3,6,7,4,1]=>[7,6,5,2,3,4,8,1]=>0001111
[7,5,6,2,3,4,8,1]=>[8,6,2,3,7,5,4,1]=>[7,5,6,2,3,4,8,1]=>0000111
[6,7,4,3,2,5,8,1]=>[8,3,4,7,2,6,5,1]=>[6,7,4,3,2,5,8,1]=>0110011
[7,6,4,2,3,5,8,1]=>[8,4,2,6,3,7,5,1]=>[7,6,4,2,3,5,8,1]=>0010111
[7,6,3,2,4,5,8,1]=>[8,3,6,2,4,7,5,1]=>[7,6,3,2,4,5,8,1]=>0100111
[7,5,4,2,3,6,8,1]=>[8,4,2,5,7,3,6,1]=>[7,5,4,2,3,6,8,1]=>0011011
[7,5,3,2,4,6,8,1]=>[8,3,5,2,7,4,6,1]=>[7,5,3,2,4,6,8,1]=>0101011
[7,5,2,3,4,6,8,1]=>[8,5,2,3,7,4,6,1]=>[7,5,2,3,4,6,8,1]=>0001011
[7,4,3,2,5,6,8,1]=>[8,3,4,7,2,5,6,1]=>[7,4,3,2,5,6,8,1]=>0110011
[7,4,2,3,5,6,8,1]=>[8,4,2,7,3,5,6,1]=>[7,4,2,3,5,6,8,1]=>0010011
[7,3,2,4,5,6,8,1]=>[8,3,7,2,4,5,6,1]=>[7,3,2,4,5,6,8,1]=>0100011
[7,2,3,4,5,6,8,1]=>[8,7,2,3,4,5,6,1]=>[7,2,3,4,5,6,8,1]=>0000011
[6,5,4,3,2,7,8,1]=>[8,3,4,5,6,2,7,1]=>[6,5,4,3,2,7,8,1]=>0111101
[5,4,6,3,2,7,8,1]=>[8,3,6,5,4,2,7,1]=>[5,4,6,3,2,7,8,1]=>0101101
[4,5,6,3,2,7,8,1]=>[8,3,6,4,5,2,7,1]=>[4,5,6,3,2,7,8,1]=>0100101
[6,5,3,4,2,7,8,1]=>[8,4,5,3,6,2,7,1]=>[6,5,3,4,2,7,8,1]=>0011101
[6,3,4,5,2,7,8,1]=>[8,5,6,3,4,2,7,1]=>[6,3,4,5,2,7,8,1]=>0001101
[5,4,3,6,2,7,8,1]=>[8,6,4,5,3,2,7,1]=>[5,4,3,6,2,7,8,1]=>0011101
[4,3,5,6,2,7,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,5,6,2,7,8,1]=>0010101
[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>[3,4,5,6,2,7,8,1]=>0000101
[6,5,4,2,3,7,8,1]=>[8,4,2,5,6,3,7,1]=>[6,5,4,2,3,7,8,1]=>0011101
[5,6,4,2,3,7,8,1]=>[8,4,2,6,5,3,7,1]=>[5,6,4,2,3,7,8,1]=>0010101
[5,4,6,2,3,7,8,1]=>[8,6,2,5,4,3,7,1]=>[5,4,6,2,3,7,8,1]=>0001101
[4,5,6,2,3,7,8,1]=>[8,6,2,4,5,3,7,1]=>[4,5,6,2,3,7,8,1]=>0000101
[6,2,3,4,5,7,8,1]=>[8,6,2,3,4,5,7,1]=>[6,2,3,4,5,7,8,1]=>0000101
[5,4,3,2,6,7,8,1]=>[8,3,4,5,2,6,7,1]=>[5,4,3,2,6,7,8,1]=>0111001
[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>[4,5,3,2,6,7,8,1]=>0101001
[5,3,4,2,6,7,8,1]=>[8,4,5,3,2,6,7,1]=>[5,3,4,2,6,7,8,1]=>0011001
[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>[4,3,5,2,6,7,8,1]=>0011001
[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>[3,4,5,2,6,7,8,1]=>0001001
[5,4,2,3,6,7,8,1]=>[8,4,2,5,3,6,7,1]=>[5,4,2,3,6,7,8,1]=>0011001
[4,3,2,5,6,7,8,1]=>[8,3,4,2,5,6,7,1]=>[4,3,2,5,6,7,8,1]=>0110001
[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[3,4,2,5,6,7,8,1]=>0010001
[4,2,3,5,6,7,8,1]=>[8,4,2,3,5,6,7,1]=>[4,2,3,5,6,7,8,1]=>0010001
[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>[3,2,4,5,6,7,8,1]=>0100001
[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[2,3,4,5,6,7,8,1]=>0000001
[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]=>[8,7,6,5,4,3,1,2]=>0111111
[7,8,6,5,4,3,1,2]=>[3,1,4,5,6,8,7,2]=>[7,8,6,5,4,3,1,2]=>0111101
[8,6,7,5,4,3,1,2]=>[3,1,4,5,7,8,6,2]=>[8,6,7,5,4,3,1,2]=>0111011
[6,7,8,5,4,3,1,2]=>[3,1,4,5,8,6,7,2]=>[6,7,8,5,4,3,1,2]=>0111001
[8,7,5,6,4,3,1,2]=>[3,1,4,6,7,5,8,2]=>[8,7,5,6,4,3,1,2]=>0110111
[7,8,5,6,4,3,1,2]=>[3,1,4,6,8,5,7,2]=>[7,8,5,6,4,3,1,2]=>0110101
[8,6,5,7,4,3,1,2]=>[3,1,4,7,6,8,5,2]=>[8,6,5,7,4,3,1,2]=>0110111
[6,7,5,8,4,3,1,2]=>[3,1,4,8,7,6,5,2]=>[6,7,5,8,4,3,1,2]=>0110011
[6,5,7,8,4,3,1,2]=>[3,1,4,8,6,5,7,2]=>[6,5,7,8,4,3,1,2]=>0110101
[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>[5,6,7,8,4,3,1,2]=>0110001
[8,7,6,4,5,3,1,2]=>[3,1,5,6,4,7,8,2]=>[8,7,6,4,5,3,1,2]=>0101111
[7,8,6,4,5,3,1,2]=>[3,1,5,6,4,8,7,2]=>[7,8,6,4,5,3,1,2]=>0101101
[8,6,7,4,5,3,1,2]=>[3,1,5,7,4,8,6,2]=>[8,6,7,4,5,3,1,2]=>0101011
[8,7,5,4,6,3,1,2]=>[3,1,6,5,7,4,8,2]=>[8,7,5,4,6,3,1,2]=>0101111
[7,8,4,5,6,3,1,2]=>[3,1,6,8,4,5,7,2]=>[7,8,4,5,6,3,1,2]=>0100101
[8,5,6,4,7,3,1,2]=>[3,1,7,6,8,5,4,2]=>[8,5,6,4,7,3,1,2]=>0100111
[8,6,4,5,7,3,1,2]=>[3,1,7,6,4,8,5,2]=>[8,6,4,5,7,3,1,2]=>0100111
[7,5,6,4,8,3,1,2]=>[3,1,8,6,7,5,4,2]=>[7,5,6,4,8,3,1,2]=>0100111
[6,5,7,4,8,3,1,2]=>[3,1,8,7,6,5,4,2]=>[6,5,7,4,8,3,1,2]=>0100111
[7,6,4,5,8,3,1,2]=>[3,1,8,6,4,7,5,2]=>[7,6,4,5,8,3,1,2]=>0100111
[5,4,6,7,8,3,1,2]=>[3,1,8,5,4,6,7,2]=>[5,4,6,7,8,3,1,2]=>0101001
[4,5,6,7,8,3,1,2]=>[3,1,8,4,5,6,7,2]=>[4,5,6,7,8,3,1,2]=>0100001
[8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,2]=>[8,7,6,5,3,4,1,2]=>0011111
[7,8,6,5,3,4,1,2]=>[4,1,5,3,6,8,7,2]=>[7,8,6,5,3,4,1,2]=>0011101
[7,6,8,5,3,4,1,2]=>[4,1,5,3,8,7,6,2]=>[7,6,8,5,3,4,1,2]=>0011011
[6,7,8,5,3,4,1,2]=>[4,1,5,3,8,6,7,2]=>[6,7,8,5,3,4,1,2]=>0011001
[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>[8,7,5,6,3,4,1,2]=>0010111
[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>[7,8,5,6,3,4,1,2]=>0010101
[8,6,5,7,3,4,1,2]=>[4,1,7,3,6,8,5,2]=>[8,6,5,7,3,4,1,2]=>0010111
[8,5,6,7,3,4,1,2]=>[4,1,7,3,8,5,6,2]=>[8,5,6,7,3,4,1,2]=>0010011
[7,6,5,8,3,4,1,2]=>[4,1,8,3,6,7,5,2]=>[7,6,5,8,3,4,1,2]=>0010111
[7,5,6,8,3,4,1,2]=>[4,1,8,3,7,5,6,2]=>[7,5,6,8,3,4,1,2]=>0010011
[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]=>[6,5,7,8,3,4,1,2]=>0010101
[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>[5,6,7,8,3,4,1,2]=>0010001
[8,7,6,3,4,5,1,2]=>[5,1,6,3,4,7,8,2]=>[8,7,6,3,4,5,1,2]=>0001111
[8,6,7,3,4,5,1,2]=>[5,1,7,3,4,8,6,2]=>[8,6,7,3,4,5,1,2]=>0001011
[6,7,8,3,4,5,1,2]=>[5,1,8,3,4,6,7,2]=>[6,7,8,3,4,5,1,2]=>0001001
[7,8,5,4,3,6,1,2]=>[6,1,4,5,8,3,7,2]=>[7,8,5,4,3,6,1,2]=>0011101
[7,8,5,3,4,6,1,2]=>[6,1,5,3,8,4,7,2]=>[7,8,5,3,4,6,1,2]=>0001101
[7,8,4,3,5,6,1,2]=>[6,1,4,8,3,5,7,2]=>[7,8,4,3,5,6,1,2]=>0010101
[8,7,3,4,5,6,1,2]=>[6,1,7,3,4,5,8,2]=>[8,7,3,4,5,6,1,2]=>0000111
[7,8,3,4,5,6,1,2]=>[6,1,8,3,4,5,7,2]=>[7,8,3,4,5,6,1,2]=>0000101
[8,6,5,4,3,7,1,2]=>[7,1,4,5,6,8,3,2]=>[8,6,5,4,3,7,1,2]=>0011111
[8,5,4,6,3,7,1,2]=>[7,1,6,5,8,4,3,2]=>[8,5,4,6,3,7,1,2]=>0001111
[8,5,4,3,6,7,1,2]=>[7,1,4,5,8,3,6,2]=>[8,5,4,3,6,7,1,2]=>0011011
[8,5,3,4,6,7,1,2]=>[7,1,5,3,8,4,6,2]=>[8,5,3,4,6,7,1,2]=>0001011
[8,4,3,5,6,7,1,2]=>[7,1,4,8,3,5,6,2]=>[8,4,3,5,6,7,1,2]=>0010011
[8,3,4,5,6,7,1,2]=>[7,1,8,3,4,5,6,2]=>[8,3,4,5,6,7,1,2]=>0000011
[7,6,5,4,3,8,1,2]=>[8,1,4,5,6,7,3,2]=>[7,6,5,4,3,8,1,2]=>0011111
[6,5,7,4,3,8,1,2]=>[8,1,4,7,6,5,3,2]=>[6,5,7,4,3,8,1,2]=>0010111
[6,7,4,5,3,8,1,2]=>[8,1,5,7,4,6,3,2]=>[6,7,4,5,3,8,1,2]=>0001011
[7,5,4,6,3,8,1,2]=>[8,1,6,5,7,4,3,2]=>[7,5,4,6,3,8,1,2]=>0001111
[6,5,4,7,3,8,1,2]=>[8,1,7,5,6,4,3,2]=>[6,5,4,7,3,8,1,2]=>0001111
[5,6,4,7,3,8,1,2]=>[8,1,7,6,5,4,3,2]=>[5,6,4,7,3,8,1,2]=>0000111
[7,5,6,3,4,8,1,2]=>[8,1,6,3,7,5,4,2]=>[7,5,6,3,4,8,1,2]=>0000111
[5,6,7,3,4,8,1,2]=>[8,1,7,3,5,6,4,2]=>[5,6,7,3,4,8,1,2]=>0000011
[7,6,4,3,5,8,1,2]=>[8,1,4,6,3,7,5,2]=>[7,6,4,3,5,8,1,2]=>0010111
[7,5,4,3,6,8,1,2]=>[8,1,4,5,7,3,6,2]=>[7,5,4,3,6,8,1,2]=>0011011
[7,5,3,4,6,8,1,2]=>[8,1,5,3,7,4,6,2]=>[7,5,3,4,6,8,1,2]=>0001011
[7,3,4,5,6,8,1,2]=>[8,1,7,3,4,5,6,2]=>[7,3,4,5,6,8,1,2]=>0000011
[6,5,4,3,7,8,1,2]=>[8,1,4,5,6,3,7,2]=>[6,5,4,3,7,8,1,2]=>0011101
[5,6,4,3,7,8,1,2]=>[8,1,4,6,5,3,7,2]=>[5,6,4,3,7,8,1,2]=>0010101
[6,5,3,4,7,8,1,2]=>[8,1,5,3,6,4,7,2]=>[6,5,3,4,7,8,1,2]=>0001101
[5,6,3,4,7,8,1,2]=>[8,1,6,3,5,4,7,2]=>[5,6,3,4,7,8,1,2]=>0000101
[6,4,3,5,7,8,1,2]=>[8,1,4,6,3,5,7,2]=>[6,4,3,5,7,8,1,2]=>0010101
[6,3,4,5,7,8,1,2]=>[8,1,6,3,4,5,7,2]=>[6,3,4,5,7,8,1,2]=>0000101
[5,4,3,6,7,8,1,2]=>[8,1,4,5,3,6,7,2]=>[5,4,3,6,7,8,1,2]=>0011001
[4,5,3,6,7,8,1,2]=>[8,1,5,4,3,6,7,2]=>[4,5,3,6,7,8,1,2]=>0001001
[4,3,5,6,7,8,1,2]=>[8,1,4,3,5,6,7,2]=>[4,3,5,6,7,8,1,2]=>0010001
[3,4,5,6,7,8,1,2]=>[8,1,3,4,5,6,7,2]=>[3,4,5,6,7,8,1,2]=>0000001
[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>1011111
[7,6,8,5,4,2,1,3]=>[2,4,1,5,8,7,6,3]=>[7,6,8,5,4,2,1,3]=>1011011
[8,7,5,6,4,2,1,3]=>[2,4,1,6,7,5,8,3]=>[8,7,5,6,4,2,1,3]=>1010111
[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>[7,8,5,6,4,2,1,3]=>1010101
[8,6,5,7,4,2,1,3]=>[2,4,1,7,6,8,5,3]=>[8,6,5,7,4,2,1,3]=>1010111
[7,6,5,8,4,2,1,3]=>[2,4,1,8,6,7,5,3]=>[7,6,5,8,4,2,1,3]=>1010111
[6,7,5,8,4,2,1,3]=>[2,4,1,8,7,6,5,3]=>[6,7,5,8,4,2,1,3]=>1010011
[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>[5,6,7,8,4,2,1,3]=>1010001
[8,6,7,4,5,2,1,3]=>[2,5,1,7,4,8,6,3]=>[8,6,7,4,5,2,1,3]=>1001011
[7,6,8,4,5,2,1,3]=>[2,5,1,8,4,7,6,3]=>[7,6,8,4,5,2,1,3]=>1001011
[8,6,5,4,7,2,1,3]=>[2,7,1,5,6,8,4,3]=>[8,6,5,4,7,2,1,3]=>1001111
[8,4,5,6,7,2,1,3]=>[2,7,1,8,4,5,6,3]=>[8,4,5,6,7,2,1,3]=>1000011
[6,5,7,4,8,2,1,3]=>[2,8,1,7,6,5,4,3]=>[6,5,7,4,8,2,1,3]=>1000111
[5,6,7,4,8,2,1,3]=>[2,8,1,7,5,6,4,3]=>[5,6,7,4,8,2,1,3]=>1000011
[7,6,4,5,8,2,1,3]=>[2,8,1,6,4,7,5,3]=>[7,6,4,5,8,2,1,3]=>1000111
[5,4,6,7,8,2,1,3]=>[2,8,1,5,4,6,7,3]=>[5,4,6,7,8,2,1,3]=>1001001
[4,5,6,7,8,2,1,3]=>[2,8,1,4,5,6,7,3]=>[4,5,6,7,8,2,1,3]=>1000001
[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>[8,7,6,5,4,1,2,3]=>0011111
[7,8,6,5,4,1,2,3]=>[4,1,2,5,6,8,7,3]=>[7,8,6,5,4,1,2,3]=>0011101
[7,6,8,5,4,1,2,3]=>[4,1,2,5,8,7,6,3]=>[7,6,8,5,4,1,2,3]=>0011011
[6,7,8,5,4,1,2,3]=>[4,1,2,5,8,6,7,3]=>[6,7,8,5,4,1,2,3]=>0011001
[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]=>[7,8,5,6,4,1,2,3]=>0010101
[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>[8,5,6,7,4,1,2,3]=>0010011
[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]=>[6,7,5,8,4,1,2,3]=>0010011
[7,5,6,8,4,1,2,3]=>[4,1,2,8,7,5,6,3]=>[7,5,6,8,4,1,2,3]=>0010011
[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>[5,6,7,8,4,1,2,3]=>0010001
[8,7,6,4,5,1,2,3]=>[5,1,2,6,4,7,8,3]=>[8,7,6,4,5,1,2,3]=>0001111
[8,6,7,4,5,1,2,3]=>[5,1,2,7,4,8,6,3]=>[8,6,7,4,5,1,2,3]=>0001011
[6,7,8,4,5,1,2,3]=>[5,1,2,8,4,6,7,3]=>[6,7,8,4,5,1,2,3]=>0001001
[8,7,5,4,6,1,2,3]=>[6,1,2,5,7,4,8,3]=>[8,7,5,4,6,1,2,3]=>0001111
[7,8,5,4,6,1,2,3]=>[6,1,2,5,8,4,7,3]=>[7,8,5,4,6,1,2,3]=>0001101
[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>[8,7,4,5,6,1,2,3]=>0000111
[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>[7,8,4,5,6,1,2,3]=>0000101
[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]=>[8,5,6,4,7,1,2,3]=>0000111
[8,5,4,6,7,1,2,3]=>[7,1,2,5,8,4,6,3]=>[8,5,4,6,7,1,2,3]=>0001011
[8,4,5,6,7,1,2,3]=>[7,1,2,8,4,5,6,3]=>[8,4,5,6,7,1,2,3]=>0000011
[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>[7,6,5,4,8,1,2,3]=>0001111
[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]=>[7,5,6,4,8,1,2,3]=>0000111
[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]=>[6,5,7,4,8,1,2,3]=>0000111
[7,6,4,5,8,1,2,3]=>[8,1,2,6,4,7,5,3]=>[7,6,4,5,8,1,2,3]=>0000111
[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>[6,7,4,5,8,1,2,3]=>0000011
[7,5,4,6,8,1,2,3]=>[8,1,2,5,7,4,6,3]=>[7,5,4,6,8,1,2,3]=>0001011
[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>[7,4,5,6,8,1,2,3]=>0000011
[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]=>[6,4,5,7,8,1,2,3]=>0000101
[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[4,5,6,7,8,1,2,3]=>0000001
[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>1101111
[7,6,8,5,3,2,1,4]=>[2,3,5,1,8,7,6,4]=>[7,6,8,5,3,2,1,4]=>1101011
[8,7,5,6,3,2,1,4]=>[2,3,6,1,7,5,8,4]=>[8,7,5,6,3,2,1,4]=>1100111
[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]=>[7,8,5,6,3,2,1,4]=>1100101
[8,6,5,7,3,2,1,4]=>[2,3,7,1,6,8,5,4]=>[8,6,5,7,3,2,1,4]=>1100111
[8,5,6,7,3,2,1,4]=>[2,3,7,1,8,5,6,4]=>[8,5,6,7,3,2,1,4]=>1100011
[7,6,5,8,3,2,1,4]=>[2,3,8,1,6,7,5,4]=>[7,6,5,8,3,2,1,4]=>1100111
[6,7,5,8,3,2,1,4]=>[2,3,8,1,7,6,5,4]=>[6,7,5,8,3,2,1,4]=>1100011
[6,5,7,8,3,2,1,4]=>[2,3,8,1,6,5,7,4]=>[6,5,7,8,3,2,1,4]=>1100101
[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>[5,6,7,8,3,2,1,4]=>1100001
[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>[8,7,6,5,2,3,1,4]=>0101111
[7,8,6,5,2,3,1,4]=>[3,5,2,1,6,8,7,4]=>[7,8,6,5,2,3,1,4]=>0101101
[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]=>[8,6,7,5,2,3,1,4]=>0101011
[7,6,8,5,2,3,1,4]=>[3,5,2,1,8,7,6,4]=>[7,6,8,5,2,3,1,4]=>0101011
[8,7,5,6,2,3,1,4]=>[3,6,2,1,7,5,8,4]=>[8,7,5,6,2,3,1,4]=>0100111
[8,5,6,7,2,3,1,4]=>[3,7,2,1,8,5,6,4]=>[8,5,6,7,2,3,1,4]=>0100011
[7,6,5,8,2,3,1,4]=>[3,8,2,1,6,7,5,4]=>[7,6,5,8,2,3,1,4]=>0100111
[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>[6,7,5,8,2,3,1,4]=>0100011
[7,5,6,8,2,3,1,4]=>[3,8,2,1,7,5,6,4]=>[7,5,6,8,2,3,1,4]=>0100011
[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>[5,6,7,8,2,3,1,4]=>0100001
[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>0101111
[8,6,7,5,3,1,2,4]=>[3,1,5,2,7,8,6,4]=>[8,6,7,5,3,1,2,4]=>0101011
[7,6,8,5,3,1,2,4]=>[3,1,5,2,8,7,6,4]=>[7,6,8,5,3,1,2,4]=>0101011
[8,7,5,6,3,1,2,4]=>[3,1,6,2,7,5,8,4]=>[8,7,5,6,3,1,2,4]=>0100111
[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>[7,8,5,6,3,1,2,4]=>0100101
[7,6,5,8,3,1,2,4]=>[3,1,8,2,6,7,5,4]=>[7,6,5,8,3,1,2,4]=>0100111
[6,7,5,8,3,1,2,4]=>[3,1,8,2,7,6,5,4]=>[6,7,5,8,3,1,2,4]=>0100011
[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]=>[7,5,6,8,3,1,2,4]=>0100011
[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]=>[6,5,7,8,3,1,2,4]=>0100101
[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>[5,6,7,8,3,1,2,4]=>0100001
[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]=>[8,7,6,5,2,1,3,4]=>1001111
[7,8,6,5,2,1,3,4]=>[2,5,1,3,6,8,7,4]=>[7,8,6,5,2,1,3,4]=>1001101
[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]=>[6,7,8,5,2,1,3,4]=>1001001
[7,8,5,6,2,1,3,4]=>[2,6,1,3,8,5,7,4]=>[7,8,5,6,2,1,3,4]=>1000101
[8,6,5,7,2,1,3,4]=>[2,7,1,3,6,8,5,4]=>[8,6,5,7,2,1,3,4]=>1000111
[8,5,6,7,2,1,3,4]=>[2,7,1,3,8,5,6,4]=>[8,5,6,7,2,1,3,4]=>1000011
[7,6,5,8,2,1,3,4]=>[2,8,1,3,6,7,5,4]=>[7,6,5,8,2,1,3,4]=>1000111
[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]=>[6,7,5,8,2,1,3,4]=>1000011
[7,5,6,8,2,1,3,4]=>[2,8,1,3,7,5,6,4]=>[7,5,6,8,2,1,3,4]=>1000011
[6,5,7,8,2,1,3,4]=>[2,8,1,3,6,5,7,4]=>[6,5,7,8,2,1,3,4]=>1000101
[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[5,6,7,8,2,1,3,4]=>1000001
[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[8,7,6,5,1,2,3,4]=>0001111
[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>[7,8,6,5,1,2,3,4]=>0001101
[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>[8,6,7,5,1,2,3,4]=>0001011
[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>[7,6,8,5,1,2,3,4]=>0001011
[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>[6,7,8,5,1,2,3,4]=>0001001
[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[8,7,5,6,1,2,3,4]=>0000111
[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[7,8,5,6,1,2,3,4]=>0000101
[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>[8,6,5,7,1,2,3,4]=>0000111
[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[8,5,6,7,1,2,3,4]=>0000011
[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[7,6,5,8,1,2,3,4]=>0000111
[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>[6,7,5,8,1,2,3,4]=>0000011
[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[7,5,6,8,1,2,3,4]=>0000011
[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>[6,5,7,8,1,2,3,4]=>0000101
[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[5,6,7,8,1,2,3,4]=>0000001
[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]=>[8,7,6,4,3,2,1,5]=>1110111
[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]=>[7,8,6,4,3,2,1,5]=>1110101
[8,6,7,4,3,2,1,5]=>[2,3,4,7,1,8,6,5]=>[8,6,7,4,3,2,1,5]=>1110011
[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]=>[7,6,8,4,3,2,1,5]=>1110011
[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]=>[6,7,8,4,3,2,1,5]=>1110001
[8,7,6,3,4,2,1,5]=>[2,4,6,3,1,7,8,5]=>[8,7,6,3,4,2,1,5]=>1010111
[7,8,6,3,4,2,1,5]=>[2,4,6,3,1,8,7,5]=>[7,8,6,3,4,2,1,5]=>1010101
[6,7,8,3,4,2,1,5]=>[2,4,8,3,1,6,7,5]=>[6,7,8,3,4,2,1,5]=>1010001
[7,6,8,4,2,3,1,5]=>[3,4,2,8,1,7,6,5]=>[7,6,8,4,2,3,1,5]=>0110011
[6,7,8,4,2,3,1,5]=>[3,4,2,8,1,6,7,5]=>[6,7,8,4,2,3,1,5]=>0110001
[8,6,7,3,2,4,1,5]=>[4,3,7,2,1,8,6,5]=>[8,6,7,3,2,4,1,5]=>0110011
[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]=>[6,7,8,3,2,4,1,5]=>0110001
[8,6,7,2,3,4,1,5]=>[4,7,2,3,1,8,6,5]=>[8,6,7,2,3,4,1,5]=>0010011
[6,7,8,2,3,4,1,5]=>[4,8,2,3,1,6,7,5]=>[6,7,8,2,3,4,1,5]=>0010001
[8,7,6,4,3,1,2,5]=>[3,1,4,6,2,7,8,5]=>[8,7,6,4,3,1,2,5]=>0110111
[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>[6,7,8,4,3,1,2,5]=>0110001
[8,7,6,3,4,1,2,5]=>[4,1,6,3,2,7,8,5]=>[8,7,6,3,4,1,2,5]=>0010111
[8,6,7,3,4,1,2,5]=>[4,1,7,3,2,8,6,5]=>[8,6,7,3,4,1,2,5]=>0010011
[6,7,8,3,4,1,2,5]=>[4,1,8,3,2,6,7,5]=>[6,7,8,3,4,1,2,5]=>0010001
[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>1010111
[7,8,6,4,2,1,3,5]=>[2,4,1,6,3,8,7,5]=>[7,8,6,4,2,1,3,5]=>1010101
[8,6,7,4,2,1,3,5]=>[2,4,1,7,3,8,6,5]=>[8,6,7,4,2,1,3,5]=>1010011
[6,7,8,4,2,1,3,5]=>[2,4,1,8,3,6,7,5]=>[6,7,8,4,2,1,3,5]=>1010001
[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>0010111
[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[7,8,6,4,1,2,3,5]=>0010101
[7,6,8,4,1,2,3,5]=>[4,1,2,8,3,7,6,5]=>[7,6,8,4,1,2,3,5]=>0010011
[6,7,8,4,1,2,3,5]=>[4,1,2,8,3,6,7,5]=>[6,7,8,4,1,2,3,5]=>0010001
[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]=>[8,7,6,3,2,1,4,5]=>1100111
[7,8,6,3,2,1,4,5]=>[2,3,6,1,4,8,7,5]=>[7,8,6,3,2,1,4,5]=>1100101
[8,6,7,3,2,1,4,5]=>[2,3,7,1,4,8,6,5]=>[8,6,7,3,2,1,4,5]=>1100011
[7,6,8,3,2,1,4,5]=>[2,3,8,1,4,7,6,5]=>[7,6,8,3,2,1,4,5]=>1100011
[6,7,8,3,2,1,4,5]=>[2,3,8,1,4,6,7,5]=>[6,7,8,3,2,1,4,5]=>1100001
[8,7,6,2,3,1,4,5]=>[3,6,2,1,4,7,8,5]=>[8,7,6,2,3,1,4,5]=>0100111
[7,8,6,2,3,1,4,5]=>[3,6,2,1,4,8,7,5]=>[7,8,6,2,3,1,4,5]=>0100101
[8,6,7,2,3,1,4,5]=>[3,7,2,1,4,8,6,5]=>[8,6,7,2,3,1,4,5]=>0100011
[6,7,8,2,3,1,4,5]=>[3,8,2,1,4,6,7,5]=>[6,7,8,2,3,1,4,5]=>0100001
[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>[8,7,6,3,1,2,4,5]=>0100111
[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[7,8,6,3,1,2,4,5]=>0100101
[7,6,8,3,1,2,4,5]=>[3,1,8,2,4,7,6,5]=>[7,6,8,3,1,2,4,5]=>0100011
[8,7,6,2,1,3,4,5]=>[2,6,1,3,4,7,8,5]=>[8,7,6,2,1,3,4,5]=>1000111
[8,6,7,2,1,3,4,5]=>[2,7,1,3,4,8,6,5]=>[8,6,7,2,1,3,4,5]=>1000011
[6,7,8,2,1,3,4,5]=>[2,8,1,3,4,6,7,5]=>[6,7,8,2,1,3,4,5]=>1000001
[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>[8,7,6,1,2,3,4,5]=>0000111
[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>[7,8,6,1,2,3,4,5]=>0000101
[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[8,6,7,1,2,3,4,5]=>0000011
[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[7,6,8,1,2,3,4,5]=>0000011
[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[6,7,8,1,2,3,4,5]=>0000001
[8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,6]=>[8,7,5,4,3,2,1,6]=>1111011
[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>[7,8,5,4,3,2,1,6]=>1111001
[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[8,7,5,3,4,2,1,6]=>1011011
[8,7,4,3,5,2,1,6]=>[2,5,4,7,3,1,8,6]=>[8,7,4,3,5,2,1,6]=>1011011
[8,7,4,5,2,3,1,6]=>[3,5,2,7,4,1,8,6]=>[8,7,4,5,2,3,1,6]=>0101011
[8,7,5,3,2,4,1,6]=>[4,3,5,2,7,1,8,6]=>[8,7,5,3,2,4,1,6]=>0111011
[7,8,5,2,3,4,1,6]=>[4,5,2,3,8,1,7,6]=>[7,8,5,2,3,4,1,6]=>0011001
[7,8,3,4,2,5,1,6]=>[5,4,8,3,2,1,7,6]=>[7,8,3,4,2,5,1,6]=>0011001
[8,7,2,3,4,5,1,6]=>[5,7,2,3,4,1,8,6]=>[8,7,2,3,4,5,1,6]=>0001011
[8,7,5,4,3,1,2,6]=>[3,1,4,5,7,2,8,6]=>[8,7,5,4,3,1,2,6]=>0111011
[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[8,7,5,3,4,1,2,6]=>0011011
[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>[7,8,5,3,4,1,2,6]=>0011001
[8,7,3,4,5,1,2,6]=>[5,1,7,3,4,2,8,6]=>[8,7,3,4,5,1,2,6]=>0001011
[7,8,3,4,5,1,2,6]=>[5,1,8,3,4,2,7,6]=>[7,8,3,4,5,1,2,6]=>0001001
[7,8,5,4,2,1,3,6]=>[2,4,1,5,8,3,7,6]=>[7,8,5,4,2,1,3,6]=>1011001
[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>0011011
[7,8,5,4,1,2,3,6]=>[4,1,2,5,8,3,7,6]=>[7,8,5,4,1,2,3,6]=>0011001
[7,8,4,5,1,2,3,6]=>[5,1,2,8,4,3,7,6]=>[7,8,4,5,1,2,3,6]=>0001001
[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>1101011
[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]=>[7,8,5,3,2,1,4,6]=>1101001
[8,7,5,2,3,1,4,6]=>[3,5,2,1,7,4,8,6]=>[8,7,5,2,3,1,4,6]=>0101011
[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>0101011
[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[7,8,5,3,1,2,4,6]=>0101001
[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]=>[8,7,5,2,1,3,4,6]=>1001011
[7,8,5,2,1,3,4,6]=>[2,5,1,3,8,4,7,6]=>[7,8,5,2,1,3,4,6]=>1001001
[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[8,7,5,1,2,3,4,6]=>0001011
[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>[7,8,5,1,2,3,4,6]=>0001001
[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[8,7,4,3,2,1,5,6]=>1110011
[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]=>[7,8,4,3,2,1,5,6]=>1110001
[8,7,3,4,2,1,5,6]=>[2,4,7,3,1,5,8,6]=>[8,7,3,4,2,1,5,6]=>1010011
[7,8,3,4,2,1,5,6]=>[2,4,8,3,1,5,7,6]=>[7,8,3,4,2,1,5,6]=>1010001
[8,7,3,2,4,1,5,6]=>[4,3,7,2,1,5,8,6]=>[8,7,3,2,4,1,5,6]=>0110011
[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>[7,8,3,2,4,1,5,6]=>0110001
[8,7,2,3,4,1,5,6]=>[4,7,2,3,1,5,8,6]=>[8,7,2,3,4,1,5,6]=>0010011
[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>[7,8,2,3,4,1,5,6]=>0010001
[7,8,4,3,1,2,5,6]=>[3,1,4,8,2,5,7,6]=>[7,8,4,3,1,2,5,6]=>0110001
[8,7,3,4,1,2,5,6]=>[4,1,7,3,2,5,8,6]=>[8,7,3,4,1,2,5,6]=>0010011
[8,7,4,2,1,3,5,6]=>[2,4,1,7,3,5,8,6]=>[8,7,4,2,1,3,5,6]=>1010011
[7,8,4,2,1,3,5,6]=>[2,4,1,8,3,5,7,6]=>[7,8,4,2,1,3,5,6]=>1010001
[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>[8,7,4,1,2,3,5,6]=>0010011
[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]=>[8,7,3,2,1,4,5,6]=>1100011
[7,8,3,2,1,4,5,6]=>[2,3,8,1,4,5,7,6]=>[7,8,3,2,1,4,5,6]=>1100001
[8,7,2,3,1,4,5,6]=>[3,7,2,1,4,5,8,6]=>[8,7,2,3,1,4,5,6]=>0100011
[7,8,2,3,1,4,5,6]=>[3,8,2,1,4,5,7,6]=>[7,8,2,3,1,4,5,6]=>0100001
[7,8,3,1,2,4,5,6]=>[3,1,8,2,4,5,7,6]=>[7,8,3,1,2,4,5,6]=>0100001
[8,7,2,1,3,4,5,6]=>[2,7,1,3,4,5,8,6]=>[8,7,2,1,3,4,5,6]=>1000011
[7,8,2,1,3,4,5,6]=>[2,8,1,3,4,5,7,6]=>[7,8,2,1,3,4,5,6]=>1000001
[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,6]=>[8,7,1,2,3,4,5,6]=>0000011
[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]=>[7,8,1,2,3,4,5,6]=>0000001
[8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,7]=>[8,6,5,4,3,2,1,7]=>1111101
[8,5,6,4,3,2,1,7]=>[2,3,4,6,8,5,1,7]=>[8,5,6,4,3,2,1,7]=>1110101
[8,5,4,6,3,2,1,7]=>[2,3,6,5,8,4,1,7]=>[8,5,4,6,3,2,1,7]=>1101101
[8,4,5,6,3,2,1,7]=>[2,3,6,8,4,5,1,7]=>[8,4,5,6,3,2,1,7]=>1100101
[8,6,5,3,4,2,1,7]=>[2,4,5,3,6,8,1,7]=>[8,6,5,3,4,2,1,7]=>1011101
[8,5,6,3,4,2,1,7]=>[2,4,6,3,8,5,1,7]=>[8,5,6,3,4,2,1,7]=>1010101
[8,4,3,5,6,2,1,7]=>[2,6,4,8,3,5,1,7]=>[8,4,3,5,6,2,1,7]=>1010101
[8,3,4,5,6,2,1,7]=>[2,6,8,3,4,5,1,7]=>[8,3,4,5,6,2,1,7]=>1000101
[8,6,5,4,2,3,1,7]=>[3,4,2,5,6,8,1,7]=>[8,6,5,4,2,3,1,7]=>0111101
[8,6,4,5,2,3,1,7]=>[3,5,2,6,4,8,1,7]=>[8,6,4,5,2,3,1,7]=>0101101
[8,4,5,6,2,3,1,7]=>[3,6,2,8,4,5,1,7]=>[8,4,5,6,2,3,1,7]=>0100101
[8,6,5,3,2,4,1,7]=>[4,3,5,2,6,8,1,7]=>[8,6,5,3,2,4,1,7]=>0111101
[8,5,6,2,3,4,1,7]=>[4,6,2,3,8,5,1,7]=>[8,5,6,2,3,4,1,7]=>0010101
[8,6,4,3,2,5,1,7]=>[5,3,4,6,2,8,1,7]=>[8,6,4,3,2,5,1,7]=>0111101
[8,6,3,2,4,5,1,7]=>[5,3,6,2,4,8,1,7]=>[8,6,3,2,4,5,1,7]=>0101101
[8,5,4,3,2,6,1,7]=>[6,3,4,5,8,2,1,7]=>[8,5,4,3,2,6,1,7]=>0111101
[8,4,3,5,2,6,1,7]=>[6,5,4,8,3,2,1,7]=>[8,4,3,5,2,6,1,7]=>0011101
[8,5,4,2,3,6,1,7]=>[6,4,2,5,8,3,1,7]=>[8,5,4,2,3,6,1,7]=>0011101
[8,4,5,2,3,6,1,7]=>[6,5,2,8,4,3,1,7]=>[8,4,5,2,3,6,1,7]=>0001101
[8,3,2,4,5,6,1,7]=>[6,3,8,2,4,5,1,7]=>[8,3,2,4,5,6,1,7]=>0100101
[8,2,3,4,5,6,1,7]=>[6,8,2,3,4,5,1,7]=>[8,2,3,4,5,6,1,7]=>0000101
[8,6,5,4,3,1,2,7]=>[3,1,4,5,6,8,2,7]=>[8,6,5,4,3,1,2,7]=>0111101
[8,6,5,3,4,1,2,7]=>[4,1,5,3,6,8,2,7]=>[8,6,5,3,4,1,2,7]=>0011101
[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]=>[8,5,6,3,4,1,2,7]=>0010101
[8,6,3,4,5,1,2,7]=>[5,1,6,3,4,8,2,7]=>[8,6,3,4,5,1,2,7]=>0001101
[8,5,4,3,6,1,2,7]=>[6,1,4,5,8,3,2,7]=>[8,5,4,3,6,1,2,7]=>0011101
[8,4,5,3,6,1,2,7]=>[6,1,5,8,4,3,2,7]=>[8,4,5,3,6,1,2,7]=>0001101
[8,5,3,4,6,1,2,7]=>[6,1,5,3,8,4,2,7]=>[8,5,3,4,6,1,2,7]=>0001101
[8,3,4,5,6,1,2,7]=>[6,1,8,3,4,5,2,7]=>[8,3,4,5,6,1,2,7]=>0000101
[8,6,5,4,2,1,3,7]=>[2,4,1,5,6,8,3,7]=>[8,6,5,4,2,1,3,7]=>1011101
[8,5,6,4,2,1,3,7]=>[2,4,1,6,8,5,3,7]=>[8,5,6,4,2,1,3,7]=>1010101
[8,6,4,5,2,1,3,7]=>[2,5,1,6,4,8,3,7]=>[8,6,4,5,2,1,3,7]=>1001101
[8,4,5,6,2,1,3,7]=>[2,6,1,8,4,5,3,7]=>[8,4,5,6,2,1,3,7]=>1000101
[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>[8,6,5,4,1,2,3,7]=>0011101
[8,5,6,4,1,2,3,7]=>[4,1,2,6,8,5,3,7]=>[8,5,6,4,1,2,3,7]=>0010101
[8,6,4,5,1,2,3,7]=>[5,1,2,6,4,8,3,7]=>[8,6,4,5,1,2,3,7]=>0001101
[8,4,5,6,1,2,3,7]=>[6,1,2,8,4,5,3,7]=>[8,4,5,6,1,2,3,7]=>0000101
[8,6,5,3,2,1,4,7]=>[2,3,5,1,6,8,4,7]=>[8,6,5,3,2,1,4,7]=>1101101
[8,5,6,3,2,1,4,7]=>[2,3,6,1,8,5,4,7]=>[8,5,6,3,2,1,4,7]=>1100101
[8,6,5,2,3,1,4,7]=>[3,5,2,1,6,8,4,7]=>[8,6,5,2,3,1,4,7]=>0101101
[8,5,6,2,3,1,4,7]=>[3,6,2,1,8,5,4,7]=>[8,5,6,2,3,1,4,7]=>0100101
[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]=>[8,6,5,2,1,3,4,7]=>1001101
[8,5,6,2,1,3,4,7]=>[2,6,1,3,8,5,4,7]=>[8,5,6,2,1,3,4,7]=>1000101
[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>[8,6,5,1,2,3,4,7]=>0001101
[8,5,6,1,2,3,4,7]=>[6,1,2,3,8,5,4,7]=>[8,5,6,1,2,3,4,7]=>0000101
[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>[8,6,4,3,2,1,5,7]=>1110101
[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]=>[8,6,3,4,2,1,5,7]=>1010101
[8,6,3,2,4,1,5,7]=>[4,3,6,2,1,8,5,7]=>[8,6,3,2,4,1,5,7]=>0110101
[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>0110101
[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>1010101
[8,6,3,2,1,4,5,7]=>[2,3,6,1,4,8,5,7]=>[8,6,3,2,1,4,5,7]=>1100101
[8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,7]=>[8,6,1,2,3,4,5,7]=>0000101
[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]=>[8,5,4,3,2,1,6,7]=>1111001
[8,4,3,5,2,1,6,7]=>[2,5,4,8,3,1,6,7]=>[8,4,3,5,2,1,6,7]=>1011001
[8,3,4,5,2,1,6,7]=>[2,5,8,3,4,1,6,7]=>[8,3,4,5,2,1,6,7]=>1001001
[8,4,5,2,3,1,6,7]=>[3,5,2,8,4,1,6,7]=>[8,4,5,2,3,1,6,7]=>0101001
[8,5,2,3,4,1,6,7]=>[4,5,2,3,8,1,6,7]=>[8,5,2,3,4,1,6,7]=>0011001
[8,4,2,3,5,1,6,7]=>[5,4,2,8,3,1,6,7]=>[8,4,2,3,5,1,6,7]=>0011001
[8,2,3,4,5,1,6,7]=>[5,8,2,3,4,1,6,7]=>[8,2,3,4,5,1,6,7]=>0001001
[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>[8,5,3,4,1,2,6,7]=>0011001
[8,3,4,5,1,2,6,7]=>[5,1,8,3,4,2,6,7]=>[8,3,4,5,1,2,6,7]=>0001001
[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]=>[8,5,4,2,1,3,6,7]=>1011001
[8,5,4,1,2,3,6,7]=>[4,1,2,5,8,3,6,7]=>[8,5,4,1,2,3,6,7]=>0011001
[8,4,5,1,2,3,6,7]=>[5,1,2,8,4,3,6,7]=>[8,4,5,1,2,3,6,7]=>0001001
[8,5,3,2,1,4,6,7]=>[2,3,5,1,8,4,6,7]=>[8,5,3,2,1,4,6,7]=>1101001
[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>[8,5,3,1,2,4,6,7]=>0101001
[8,5,2,1,3,4,6,7]=>[2,5,1,3,8,4,6,7]=>[8,5,2,1,3,4,6,7]=>1001001
[8,5,1,2,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>[8,5,1,2,3,4,6,7]=>0001001
[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>[8,4,3,2,1,5,6,7]=>1110001
[8,3,4,2,1,5,6,7]=>[2,4,8,3,1,5,6,7]=>[8,3,4,2,1,5,6,7]=>1010001
[8,4,2,3,1,5,6,7]=>[3,4,2,8,1,5,6,7]=>[8,4,2,3,1,5,6,7]=>0110001
[8,2,3,4,1,5,6,7]=>[4,8,2,3,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>0010001
[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>[8,3,4,1,2,5,6,7]=>0010001
[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>[8,4,2,1,3,5,6,7]=>1010001
[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>[8,4,1,2,3,5,6,7]=>0010001
[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>[8,3,2,1,4,5,6,7]=>1100001
[8,2,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]=>[8,2,3,1,4,5,6,7]=>0100001
[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>[8,3,1,2,4,5,6,7]=>0100001
[8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]=>1000001
[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>0000001
[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]=>[7,6,5,4,3,2,1,8]=>1111110
[6,7,5,4,3,2,1,8]=>[2,3,4,5,7,6,1,8]=>[6,7,5,4,3,2,1,8]=>1111010
[7,5,6,4,3,2,1,8]=>[2,3,4,6,7,5,1,8]=>[7,5,6,4,3,2,1,8]=>1110110
[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>[6,5,7,4,3,2,1,8]=>1110110
[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>[5,6,7,4,3,2,1,8]=>1110010
[7,6,4,5,3,2,1,8]=>[2,3,5,6,4,7,1,8]=>[7,6,4,5,3,2,1,8]=>1101110
[7,5,4,6,3,2,1,8]=>[2,3,6,5,7,4,1,8]=>[7,5,4,6,3,2,1,8]=>1101110
[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]=>[6,5,4,7,3,2,1,8]=>1101110
[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[5,6,4,7,3,2,1,8]=>1100110
[5,4,6,7,3,2,1,8]=>[2,3,7,5,4,6,1,8]=>[5,4,6,7,3,2,1,8]=>1101010
[7,6,5,3,4,2,1,8]=>[2,4,5,3,6,7,1,8]=>[7,6,5,3,4,2,1,8]=>1011110
[7,5,6,3,4,2,1,8]=>[2,4,6,3,7,5,1,8]=>[7,5,6,3,4,2,1,8]=>1010110
[5,6,7,3,4,2,1,8]=>[2,4,7,3,5,6,1,8]=>[5,6,7,3,4,2,1,8]=>1010010
[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>[7,6,4,3,5,2,1,8]=>1011110
[6,7,4,3,5,2,1,8]=>[2,5,4,7,3,6,1,8]=>[6,7,4,3,5,2,1,8]=>1011010
[7,6,3,4,5,2,1,8]=>[2,5,6,3,4,7,1,8]=>[7,6,3,4,5,2,1,8]=>1001110
[7,5,4,3,6,2,1,8]=>[2,6,4,5,7,3,1,8]=>[7,5,4,3,6,2,1,8]=>1011110
[7,3,4,5,6,2,1,8]=>[2,6,7,3,4,5,1,8]=>[7,3,4,5,6,2,1,8]=>1000110
[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]=>[6,5,4,3,7,2,1,8]=>1011110
[5,6,4,3,7,2,1,8]=>[2,7,4,6,5,3,1,8]=>[5,6,4,3,7,2,1,8]=>1010110
[5,4,6,3,7,2,1,8]=>[2,7,6,5,4,3,1,8]=>[5,4,6,3,7,2,1,8]=>1001110
[3,4,5,6,7,2,1,8]=>[2,7,3,4,5,6,1,8]=>[3,4,5,6,7,2,1,8]=>1000010
[7,6,5,4,2,3,1,8]=>[3,4,2,5,6,7,1,8]=>[7,6,5,4,2,3,1,8]=>0111110
[6,7,5,4,2,3,1,8]=>[3,4,2,5,7,6,1,8]=>[6,7,5,4,2,3,1,8]=>0111010
[7,5,6,4,2,3,1,8]=>[3,4,2,6,7,5,1,8]=>[7,5,6,4,2,3,1,8]=>0110110
[5,6,7,4,2,3,1,8]=>[3,4,2,7,5,6,1,8]=>[5,6,7,4,2,3,1,8]=>0110010
[7,6,4,5,2,3,1,8]=>[3,5,2,6,4,7,1,8]=>[7,6,4,5,2,3,1,8]=>0101110
[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>[6,7,4,5,2,3,1,8]=>0101010
[7,4,5,6,2,3,1,8]=>[3,6,2,7,4,5,1,8]=>[7,4,5,6,2,3,1,8]=>0100110
[6,5,4,7,2,3,1,8]=>[3,7,2,5,6,4,1,8]=>[6,5,4,7,2,3,1,8]=>0101110
[5,6,4,7,2,3,1,8]=>[3,7,2,6,5,4,1,8]=>[5,6,4,7,2,3,1,8]=>0100110
[5,4,6,7,2,3,1,8]=>[3,7,2,5,4,6,1,8]=>[5,4,6,7,2,3,1,8]=>0101010
[4,5,6,7,2,3,1,8]=>[3,7,2,4,5,6,1,8]=>[4,5,6,7,2,3,1,8]=>0100010
[6,5,7,3,2,4,1,8]=>[4,3,7,2,6,5,1,8]=>[6,5,7,3,2,4,1,8]=>0110110
[5,6,7,3,2,4,1,8]=>[4,3,7,2,5,6,1,8]=>[5,6,7,3,2,4,1,8]=>0110010
[7,6,5,2,3,4,1,8]=>[4,5,2,3,6,7,1,8]=>[7,6,5,2,3,4,1,8]=>0011110
[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>[6,7,5,2,3,4,1,8]=>0011010
[7,5,6,2,3,4,1,8]=>[4,6,2,3,7,5,1,8]=>[7,5,6,2,3,4,1,8]=>0010110
[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]=>[6,5,7,2,3,4,1,8]=>0010110
[5,6,7,2,3,4,1,8]=>[4,7,2,3,5,6,1,8]=>[5,6,7,2,3,4,1,8]=>0010010
[7,6,4,3,2,5,1,8]=>[5,3,4,6,2,7,1,8]=>[7,6,4,3,2,5,1,8]=>0111110
[6,7,4,3,2,5,1,8]=>[5,3,4,7,2,6,1,8]=>[6,7,4,3,2,5,1,8]=>0111010
[7,6,4,2,3,5,1,8]=>[5,4,2,6,3,7,1,8]=>[7,6,4,2,3,5,1,8]=>0011110
[6,7,4,2,3,5,1,8]=>[5,4,2,7,3,6,1,8]=>[6,7,4,2,3,5,1,8]=>0011010
[7,6,3,2,4,5,1,8]=>[5,3,6,2,4,7,1,8]=>[7,6,3,2,4,5,1,8]=>0101110
[6,7,3,2,4,5,1,8]=>[5,3,7,2,4,6,1,8]=>[6,7,3,2,4,5,1,8]=>0101010
[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]=>[7,4,3,5,2,6,1,8]=>0011110
[7,5,4,2,3,6,1,8]=>[6,4,2,5,7,3,1,8]=>[7,5,4,2,3,6,1,8]=>0011110
[7,4,5,2,3,6,1,8]=>[6,5,2,7,4,3,1,8]=>[7,4,5,2,3,6,1,8]=>0001110
[7,5,3,2,4,6,1,8]=>[6,3,5,2,7,4,1,8]=>[7,5,3,2,4,6,1,8]=>0101110
[7,2,3,4,5,6,1,8]=>[6,7,2,3,4,5,1,8]=>[7,2,3,4,5,6,1,8]=>0000110
[6,5,4,3,2,7,1,8]=>[7,3,4,5,6,2,1,8]=>[6,5,4,3,2,7,1,8]=>0111110
[5,6,4,3,2,7,1,8]=>[7,3,4,6,5,2,1,8]=>[5,6,4,3,2,7,1,8]=>0110110
[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]=>[5,4,6,3,2,7,1,8]=>0101110
[5,6,3,4,2,7,1,8]=>[7,4,6,3,5,2,1,8]=>[5,6,3,4,2,7,1,8]=>0010110
[6,3,4,5,2,7,1,8]=>[7,5,6,3,4,2,1,8]=>[6,3,4,5,2,7,1,8]=>0001110
[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>[5,4,3,6,2,7,1,8]=>0011110
[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[4,5,3,6,2,7,1,8]=>0001110
[5,3,4,6,2,7,1,8]=>[7,6,5,3,4,2,1,8]=>[5,3,4,6,2,7,1,8]=>0001110
[4,3,5,6,2,7,1,8]=>[7,6,4,3,5,2,1,8]=>[4,3,5,6,2,7,1,8]=>0010110
[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>[3,4,5,6,2,7,1,8]=>0000110
[5,4,6,2,3,7,1,8]=>[7,6,2,5,4,3,1,8]=>[5,4,6,2,3,7,1,8]=>0001110
[6,5,3,2,4,7,1,8]=>[7,3,5,2,6,4,1,8]=>[6,5,3,2,4,7,1,8]=>0101110
[6,2,3,4,5,7,1,8]=>[7,6,2,3,4,5,1,8]=>[6,2,3,4,5,7,1,8]=>0000110
[3,4,5,2,6,7,1,8]=>[7,5,3,4,2,6,1,8]=>[3,4,5,2,6,7,1,8]=>0001010
[5,4,2,3,6,7,1,8]=>[7,4,2,5,3,6,1,8]=>[5,4,2,3,6,7,1,8]=>0011010
[4,2,3,5,6,7,1,8]=>[7,4,2,3,5,6,1,8]=>[4,2,3,5,6,7,1,8]=>0010010
[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[2,3,4,5,6,7,1,8]=>0000010
[7,6,5,4,3,1,2,8]=>[3,1,4,5,6,7,2,8]=>[7,6,5,4,3,1,2,8]=>0111110
[6,7,5,4,3,1,2,8]=>[3,1,4,5,7,6,2,8]=>[6,7,5,4,3,1,2,8]=>0111010
[7,4,5,6,3,1,2,8]=>[3,1,6,7,4,5,2,8]=>[7,4,5,6,3,1,2,8]=>0100110
[4,5,6,7,3,1,2,8]=>[3,1,7,4,5,6,2,8]=>[4,5,6,7,3,1,2,8]=>0100010
[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]=>[7,5,6,3,4,1,2,8]=>0010110
[6,5,7,3,4,1,2,8]=>[4,1,7,3,6,5,2,8]=>[6,5,7,3,4,1,2,8]=>0010110
[6,4,5,3,7,1,2,8]=>[7,1,5,6,4,3,2,8]=>[6,4,5,3,7,1,2,8]=>0001110
[5,6,3,4,7,1,2,8]=>[7,1,6,3,5,4,2,8]=>[5,6,3,4,7,1,2,8]=>0000110
[3,4,5,6,7,1,2,8]=>[7,1,3,4,5,6,2,8]=>[3,4,5,6,7,1,2,8]=>0000010
[7,6,5,4,2,1,3,8]=>[2,4,1,5,6,7,3,8]=>[7,6,5,4,2,1,3,8]=>1011110
[7,6,4,5,2,1,3,8]=>[2,5,1,6,4,7,3,8]=>[7,6,4,5,2,1,3,8]=>1001110
[7,5,4,6,2,1,3,8]=>[2,6,1,5,7,4,3,8]=>[7,5,4,6,2,1,3,8]=>1001110
[7,6,5,4,1,2,3,8]=>[4,1,2,5,6,7,3,8]=>[7,6,5,4,1,2,3,8]=>0011110
[7,5,6,4,1,2,3,8]=>[4,1,2,6,7,5,3,8]=>[7,5,6,4,1,2,3,8]=>0010110
[5,6,7,4,1,2,3,8]=>[4,1,2,7,5,6,3,8]=>[5,6,7,4,1,2,3,8]=>0010010
[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]=>[5,6,4,7,1,2,3,8]=>0000110
[5,4,6,7,1,2,3,8]=>[7,1,2,5,4,6,3,8]=>[5,4,6,7,1,2,3,8]=>0001010
[4,5,6,7,1,2,3,8]=>[7,1,2,4,5,6,3,8]=>[4,5,6,7,1,2,3,8]=>0000010
[7,5,6,2,3,1,4,8]=>[3,6,2,1,7,5,4,8]=>[7,5,6,2,3,1,4,8]=>0100110
[5,6,7,2,3,1,4,8]=>[3,7,2,1,5,6,4,8]=>[5,6,7,2,3,1,4,8]=>0100010
[5,6,7,3,1,2,4,8]=>[3,1,7,2,5,6,4,8]=>[5,6,7,3,1,2,4,8]=>0100010
[6,7,5,2,1,3,4,8]=>[2,5,1,3,7,6,4,8]=>[6,7,5,2,1,3,4,8]=>1001010
[7,5,6,2,1,3,4,8]=>[2,6,1,3,7,5,4,8]=>[7,5,6,2,1,3,4,8]=>1000110
[5,6,7,2,1,3,4,8]=>[2,7,1,3,5,6,4,8]=>[5,6,7,2,1,3,4,8]=>1000010
[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>[7,6,5,1,2,3,4,8]=>0001110
[6,7,5,1,2,3,4,8]=>[5,1,2,3,7,6,4,8]=>[6,7,5,1,2,3,4,8]=>0001010
[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>[7,5,6,1,2,3,4,8]=>0000110
[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>[6,5,7,1,2,3,4,8]=>0000110
[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[5,6,7,1,2,3,4,8]=>0000010
[7,6,4,3,2,1,5,8]=>[2,3,4,6,1,7,5,8]=>[7,6,4,3,2,1,5,8]=>1110110
[6,7,4,3,2,1,5,8]=>[2,3,4,7,1,6,5,8]=>[6,7,4,3,2,1,5,8]=>1110010
[7,6,3,4,2,1,5,8]=>[2,4,6,3,1,7,5,8]=>[7,6,3,4,2,1,5,8]=>1010110
[7,6,4,2,3,1,5,8]=>[3,4,2,6,1,7,5,8]=>[7,6,4,2,3,1,5,8]=>0110110
[7,6,3,2,4,1,5,8]=>[4,3,6,2,1,7,5,8]=>[7,6,3,2,4,1,5,8]=>0110110
[6,7,3,2,4,1,5,8]=>[4,3,7,2,1,6,5,8]=>[6,7,3,2,4,1,5,8]=>0110010
[7,6,2,3,4,1,5,8]=>[4,6,2,3,1,7,5,8]=>[7,6,2,3,4,1,5,8]=>0010110
[6,7,3,4,1,2,5,8]=>[4,1,7,3,2,6,5,8]=>[6,7,3,4,1,2,5,8]=>0010010
[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>[7,6,4,2,1,3,5,8]=>1010110
[7,6,3,2,1,4,5,8]=>[2,3,6,1,4,7,5,8]=>[7,6,3,2,1,4,5,8]=>1100110
[7,6,2,3,1,4,5,8]=>[3,6,2,1,4,7,5,8]=>[7,6,2,3,1,4,5,8]=>0100110
[7,6,1,2,3,4,5,8]=>[6,1,2,3,4,7,5,8]=>[7,6,1,2,3,4,5,8]=>0000110
[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]=>[6,7,1,2,3,4,5,8]=>0000010
[7,5,4,3,2,1,6,8]=>[2,3,4,5,7,1,6,8]=>[7,5,4,3,2,1,6,8]=>1111010
[7,3,4,5,2,1,6,8]=>[2,5,7,3,4,1,6,8]=>[7,3,4,5,2,1,6,8]=>1001010
[7,5,3,2,4,1,6,8]=>[4,3,5,2,7,1,6,8]=>[7,5,3,2,4,1,6,8]=>0111010
[7,5,2,3,4,1,6,8]=>[4,5,2,3,7,1,6,8]=>[7,5,2,3,4,1,6,8]=>0011010
[7,4,2,3,5,1,6,8]=>[5,4,2,7,3,1,6,8]=>[7,4,2,3,5,1,6,8]=>0011010
[7,2,3,4,5,1,6,8]=>[5,7,2,3,4,1,6,8]=>[7,2,3,4,5,1,6,8]=>0001010
[7,4,5,2,1,3,6,8]=>[2,5,1,7,4,3,6,8]=>[7,4,5,2,1,3,6,8]=>1001010
[7,5,2,3,1,4,6,8]=>[3,5,2,1,7,4,6,8]=>[7,5,2,3,1,4,6,8]=>0101010
[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>[7,5,3,1,2,4,6,8]=>0101010
[7,5,1,2,3,4,6,8]=>[5,1,2,3,7,4,6,8]=>[7,5,1,2,3,4,6,8]=>0001010
[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>[7,4,3,2,1,5,6,8]=>1110010
[7,3,4,1,2,5,6,8]=>[4,1,7,3,2,5,6,8]=>[7,3,4,1,2,5,6,8]=>0010010
[7,4,1,2,3,5,6,8]=>[4,1,2,7,3,5,6,8]=>[7,4,1,2,3,5,6,8]=>0010010
[7,3,2,1,4,5,6,8]=>[2,3,7,1,4,5,6,8]=>[7,3,2,1,4,5,6,8]=>1100010
[7,3,1,2,4,5,6,8]=>[3,1,7,2,4,5,6,8]=>[7,3,1,2,4,5,6,8]=>0100010
[7,2,1,3,4,5,6,8]=>[2,7,1,3,4,5,6,8]=>[7,2,1,3,4,5,6,8]=>1000010
[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>0000010
[6,5,4,3,2,1,7,8]=>[2,3,4,5,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100
[5,6,4,3,2,1,7,8]=>[2,3,4,6,5,1,7,8]=>[5,6,4,3,2,1,7,8]=>1110100
[5,4,6,3,2,1,7,8]=>[2,3,6,5,4,1,7,8]=>[5,4,6,3,2,1,7,8]=>1101100
[4,5,6,3,2,1,7,8]=>[2,3,6,4,5,1,7,8]=>[4,5,6,3,2,1,7,8]=>1100100
[5,6,3,4,2,1,7,8]=>[2,4,6,3,5,1,7,8]=>[5,6,3,4,2,1,7,8]=>1010100
[5,4,3,6,2,1,7,8]=>[2,6,4,5,3,1,7,8]=>[5,4,3,6,2,1,7,8]=>1011100
[3,4,5,6,2,1,7,8]=>[2,6,3,4,5,1,7,8]=>[3,4,5,6,2,1,7,8]=>1000100
[5,4,6,2,3,1,7,8]=>[3,6,2,5,4,1,7,8]=>[5,4,6,2,3,1,7,8]=>0101100
[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>[5,6,3,2,4,1,7,8]=>0110100
[5,6,2,3,4,1,7,8]=>[4,6,2,3,5,1,7,8]=>[5,6,2,3,4,1,7,8]=>0010100
[6,2,3,4,5,1,7,8]=>[5,6,2,3,4,1,7,8]=>[6,2,3,4,5,1,7,8]=>0001100
[5,4,3,2,6,1,7,8]=>[6,3,4,5,2,1,7,8]=>[5,4,3,2,6,1,7,8]=>0111100
[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>[4,3,5,2,6,1,7,8]=>0011100
[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]=>[3,4,5,2,6,1,7,8]=>0001100
[5,3,2,4,6,1,7,8]=>[6,3,5,2,4,1,7,8]=>[5,3,2,4,6,1,7,8]=>0101100
[5,2,3,4,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>[5,2,3,4,6,1,7,8]=>0001100
[3,4,2,5,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[3,4,2,5,6,1,7,8]=>0010100
[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[2,3,4,5,6,1,7,8]=>0000100
[6,5,4,3,1,2,7,8]=>[3,1,4,5,6,2,7,8]=>[6,5,4,3,1,2,7,8]=>0111100
[5,6,4,3,1,2,7,8]=>[3,1,4,6,5,2,7,8]=>[5,6,4,3,1,2,7,8]=>0110100
[6,4,5,3,1,2,7,8]=>[3,1,5,6,4,2,7,8]=>[6,4,5,3,1,2,7,8]=>0101100
[5,4,6,3,1,2,7,8]=>[3,1,6,5,4,2,7,8]=>[5,4,6,3,1,2,7,8]=>0101100
[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>[5,6,3,4,1,2,7,8]=>0010100
[5,4,3,6,1,2,7,8]=>[6,1,4,5,3,2,7,8]=>[5,4,3,6,1,2,7,8]=>0011100
[3,4,5,6,1,2,7,8]=>[6,1,3,4,5,2,7,8]=>[3,4,5,6,1,2,7,8]=>0000100
[6,5,4,2,1,3,7,8]=>[2,4,1,5,6,3,7,8]=>[6,5,4,2,1,3,7,8]=>1011100
[5,6,4,2,1,3,7,8]=>[2,4,1,6,5,3,7,8]=>[5,6,4,2,1,3,7,8]=>1010100
[6,4,5,2,1,3,7,8]=>[2,5,1,6,4,3,7,8]=>[6,4,5,2,1,3,7,8]=>1001100
[5,4,6,2,1,3,7,8]=>[2,6,1,5,4,3,7,8]=>[5,4,6,2,1,3,7,8]=>1001100
[4,5,6,2,1,3,7,8]=>[2,6,1,4,5,3,7,8]=>[4,5,6,2,1,3,7,8]=>1000100
[6,5,4,1,2,3,7,8]=>[4,1,2,5,6,3,7,8]=>[6,5,4,1,2,3,7,8]=>0011100
[4,5,6,1,2,3,7,8]=>[6,1,2,4,5,3,7,8]=>[4,5,6,1,2,3,7,8]=>0000100
[6,5,3,2,1,4,7,8]=>[2,3,5,1,6,4,7,8]=>[6,5,3,2,1,4,7,8]=>1101100
[5,6,3,2,1,4,7,8]=>[2,3,6,1,5,4,7,8]=>[5,6,3,2,1,4,7,8]=>1100100
[5,6,2,1,3,4,7,8]=>[2,6,1,3,5,4,7,8]=>[5,6,2,1,3,4,7,8]=>1000100
[6,4,3,2,1,5,7,8]=>[2,3,4,6,1,5,7,8]=>[6,4,3,2,1,5,7,8]=>1110100
[6,4,2,1,3,5,7,8]=>[2,4,1,6,3,5,7,8]=>[6,4,2,1,3,5,7,8]=>1010100
[6,4,1,2,3,5,7,8]=>[4,1,2,6,3,5,7,8]=>[6,4,1,2,3,5,7,8]=>0010100
[6,3,2,1,4,5,7,8]=>[2,3,6,1,4,5,7,8]=>[6,3,2,1,4,5,7,8]=>1100100
[6,3,1,2,4,5,7,8]=>[3,1,6,2,4,5,7,8]=>[6,3,1,2,4,5,7,8]=>0100100
[6,2,1,3,4,5,7,8]=>[2,6,1,3,4,5,7,8]=>[6,2,1,3,4,5,7,8]=>1000100
[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>0000100
[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000
[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[4,5,3,2,1,6,7,8]=>1101000
[5,3,4,2,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>1011000
[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>1011000
[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>[3,4,5,2,1,6,7,8]=>1001000
[5,4,2,3,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>0111000
[4,5,2,3,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>0101000
[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>0111000
[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>0011000
[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>0111000
[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>0011000
[4,2,3,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>0011000
[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>0101000
[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>0001000
[5,4,3,1,2,6,7,8]=>[3,1,4,5,2,6,7,8]=>[5,4,3,1,2,6,7,8]=>0111000
[4,3,5,1,2,6,7,8]=>[5,1,4,3,2,6,7,8]=>[4,3,5,1,2,6,7,8]=>0011000
[3,4,5,1,2,6,7,8]=>[5,1,3,4,2,6,7,8]=>[3,4,5,1,2,6,7,8]=>0001000
[5,4,2,1,3,6,7,8]=>[2,4,1,5,3,6,7,8]=>[5,4,2,1,3,6,7,8]=>1011000
[4,5,2,1,3,6,7,8]=>[2,5,1,4,3,6,7,8]=>[4,5,2,1,3,6,7,8]=>1001000
[5,4,1,2,3,6,7,8]=>[4,1,2,5,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>0011000
[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[4,5,1,2,3,6,7,8]=>0001000
[5,3,2,1,4,6,7,8]=>[2,3,5,1,4,6,7,8]=>[5,3,2,1,4,6,7,8]=>1101000
[5,2,3,1,4,6,7,8]=>[3,5,2,1,4,6,7,8]=>[5,2,3,1,4,6,7,8]=>0101000
[5,3,1,2,4,6,7,8]=>[3,1,5,2,4,6,7,8]=>[5,3,1,2,4,6,7,8]=>0101000
[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>1001000
[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>0001000
[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000
[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>1010000
[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>0110000
[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>0110000
[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>0010000
[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>0110000
[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>0010000
[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>1010000
[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>0010000
[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000
[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>0100000
[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>0100000
[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
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[6,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,1]=>[6,8,7,5,4,3,2,1]=>1111011
[5,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,1]=>[5,8,7,6,4,3,2,1]=>1110111
[5,7,8,6,4,3,2,1]=>[2,3,4,6,5,8,7,1]=>[5,7,8,6,4,3,2,1]=>1110101
[6,5,8,7,4,3,2,1]=>[2,3,4,7,6,5,8,1]=>[6,5,8,7,4,3,2,1]=>1110111
[5,6,8,7,4,3,2,1]=>[2,3,4,7,5,6,8,1]=>[5,6,8,7,4,3,2,1]=>1110011
[5,7,6,8,4,3,2,1]=>[2,3,4,8,5,7,6,1]=>[5,7,6,8,4,3,2,1]=>1110011
[4,8,7,6,5,3,2,1]=>[2,3,5,4,6,7,8,1]=>[4,8,7,6,5,3,2,1]=>1101111
[4,6,8,7,5,3,2,1]=>[2,3,5,4,7,6,8,1]=>[4,6,8,7,5,3,2,1]=>1101011
[4,7,6,8,5,3,2,1]=>[2,3,5,4,8,7,6,1]=>[4,7,6,8,5,3,2,1]=>1101011
[4,6,7,8,5,3,2,1]=>[2,3,5,4,8,6,7,1]=>[4,6,7,8,5,3,2,1]=>1101001
[4,5,8,7,6,3,2,1]=>[2,3,6,4,5,7,8,1]=>[4,5,8,7,6,3,2,1]=>1100111
[4,5,7,8,6,3,2,1]=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,6,3,2,1]=>1100101
[6,5,4,8,7,3,2,1]=>[2,3,7,5,6,4,8,1]=>[6,5,4,8,7,3,2,1]=>1101111
[5,6,4,8,7,3,2,1]=>[2,3,7,6,5,4,8,1]=>[5,6,4,8,7,3,2,1]=>1100111
[4,6,5,8,7,3,2,1]=>[2,3,7,4,6,5,8,1]=>[4,6,5,8,7,3,2,1]=>1100111
[4,5,6,8,7,3,2,1]=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,7,3,2,1]=>1100011
[4,7,6,5,8,3,2,1]=>[2,3,8,4,6,7,5,1]=>[4,7,6,5,8,3,2,1]=>1100111
[3,8,7,6,5,4,2,1]=>[2,4,3,5,6,7,8,1]=>[3,8,7,6,5,4,2,1]=>1011111
[3,7,8,6,5,4,2,1]=>[2,4,3,5,6,8,7,1]=>[3,7,8,6,5,4,2,1]=>1011101
[3,6,8,7,5,4,2,1]=>[2,4,3,5,7,6,8,1]=>[3,6,8,7,5,4,2,1]=>1011011
[3,7,6,8,5,4,2,1]=>[2,4,3,5,8,7,6,1]=>[3,7,6,8,5,4,2,1]=>1011011
[3,5,8,7,6,4,2,1]=>[2,4,3,6,5,7,8,1]=>[3,5,8,7,6,4,2,1]=>1010111
[3,5,7,8,6,4,2,1]=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,6,4,2,1]=>1010101
[3,5,6,8,7,4,2,1]=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,7,4,2,1]=>1010011
[3,7,6,5,8,4,2,1]=>[2,4,3,8,6,7,5,1]=>[3,7,6,5,8,4,2,1]=>1010111
[3,6,7,5,8,4,2,1]=>[2,4,3,8,7,6,5,1]=>[3,6,7,5,8,4,2,1]=>1010011
[3,5,7,6,8,4,2,1]=>[2,4,3,8,5,7,6,1]=>[3,5,7,6,8,4,2,1]=>1010011
[3,5,6,7,8,4,2,1]=>[2,4,3,8,5,6,7,1]=>[3,5,6,7,8,4,2,1]=>1010001
[4,3,8,7,6,5,2,1]=>[2,5,4,3,6,7,8,1]=>[4,3,8,7,6,5,2,1]=>1011111
[4,3,7,8,6,5,2,1]=>[2,5,4,3,6,8,7,1]=>[4,3,7,8,6,5,2,1]=>1011101
[4,3,6,7,8,5,2,1]=>[2,5,4,3,8,6,7,1]=>[4,3,6,7,8,5,2,1]=>1011001
[3,4,8,7,6,5,2,1]=>[2,5,3,4,6,7,8,1]=>[3,4,8,7,6,5,2,1]=>1001111
[3,4,6,7,8,5,2,1]=>[2,5,3,4,8,6,7,1]=>[3,4,6,7,8,5,2,1]=>1001001
[5,4,3,8,7,6,2,1]=>[2,6,4,5,3,7,8,1]=>[5,4,3,8,7,6,2,1]=>1011111
[5,4,3,7,8,6,2,1]=>[2,6,4,5,3,8,7,1]=>[5,4,3,7,8,6,2,1]=>1011101
[4,5,3,7,8,6,2,1]=>[2,6,5,4,3,8,7,1]=>[4,5,3,7,8,6,2,1]=>1001101
[3,5,4,7,8,6,2,1]=>[2,6,3,5,4,8,7,1]=>[3,5,4,7,8,6,2,1]=>1001101
[4,3,5,7,8,6,2,1]=>[2,6,4,3,5,8,7,1]=>[4,3,5,7,8,6,2,1]=>1010101
[3,4,5,8,7,6,2,1]=>[2,6,3,4,5,7,8,1]=>[3,4,5,8,7,6,2,1]=>1000111
[3,4,5,7,8,6,2,1]=>[2,6,3,4,5,8,7,1]=>[3,4,5,7,8,6,2,1]=>1000101
[6,5,4,3,8,7,2,1]=>[2,7,4,5,6,3,8,1]=>[6,5,4,3,8,7,2,1]=>1011111
[5,6,4,3,8,7,2,1]=>[2,7,4,6,5,3,8,1]=>[5,6,4,3,8,7,2,1]=>1010111
[4,5,6,3,8,7,2,1]=>[2,7,6,4,5,3,8,1]=>[4,5,6,3,8,7,2,1]=>1000111
[3,6,5,4,8,7,2,1]=>[2,7,3,5,6,4,8,1]=>[3,6,5,4,8,7,2,1]=>1001111
[4,3,6,5,8,7,2,1]=>[2,7,4,3,6,5,8,1]=>[4,3,6,5,8,7,2,1]=>1010111
[4,5,3,6,8,7,2,1]=>[2,7,5,4,3,6,8,1]=>[4,5,3,6,8,7,2,1]=>1001011
[4,3,5,6,8,7,2,1]=>[2,7,4,3,5,6,8,1]=>[4,3,5,6,8,7,2,1]=>1010011
[4,7,6,5,3,8,2,1]=>[2,8,5,4,6,7,3,1]=>[4,7,6,5,3,8,2,1]=>1001111
[3,7,6,5,4,8,2,1]=>[2,8,3,5,6,7,4,1]=>[3,7,6,5,4,8,2,1]=>1001111
[3,5,6,7,4,8,2,1]=>[2,8,3,7,5,6,4,1]=>[3,5,6,7,4,8,2,1]=>1000011
[4,3,7,6,5,8,2,1]=>[2,8,4,3,6,7,5,1]=>[4,3,7,6,5,8,2,1]=>1010111
[4,5,3,7,6,8,2,1]=>[2,8,5,4,3,7,6,1]=>[4,5,3,7,6,8,2,1]=>1001011
[3,5,4,7,6,8,2,1]=>[2,8,3,5,4,7,6,1]=>[3,5,4,7,6,8,2,1]=>1001011
[4,3,5,7,6,8,2,1]=>[2,8,4,3,5,7,6,1]=>[4,3,5,7,6,8,2,1]=>1010011
[3,4,5,7,6,8,2,1]=>[2,8,3,4,5,7,6,1]=>[3,4,5,7,6,8,2,1]=>1000011
[4,3,6,5,7,8,2,1]=>[2,8,4,3,6,5,7,1]=>[4,3,6,5,7,8,2,1]=>1010101
[2,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,1]=>[2,8,7,6,5,4,3,1]=>0111111
[2,7,8,6,5,4,3,1]=>[3,2,4,5,6,8,7,1]=>[2,7,8,6,5,4,3,1]=>0111101
[2,6,8,7,5,4,3,1]=>[3,2,4,5,7,6,8,1]=>[2,6,8,7,5,4,3,1]=>0111011
[2,6,7,8,5,4,3,1]=>[3,2,4,5,8,6,7,1]=>[2,6,7,8,5,4,3,1]=>0111001
[2,6,7,5,8,4,3,1]=>[3,2,4,8,7,6,5,1]=>[2,6,7,5,8,4,3,1]=>0110011
[2,5,6,7,8,4,3,1]=>[3,2,4,8,5,6,7,1]=>[2,5,6,7,8,4,3,1]=>0110001
[2,4,8,7,6,5,3,1]=>[3,2,5,4,6,7,8,1]=>[2,4,8,7,6,5,3,1]=>0101111
[2,4,7,8,6,5,3,1]=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,6,5,3,1]=>0101101
[2,4,6,8,7,5,3,1]=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,7,5,3,1]=>0101011
[2,4,6,7,8,5,3,1]=>[3,2,5,4,8,6,7,1]=>[2,4,6,7,8,5,3,1]=>0101001
[2,5,4,7,8,6,3,1]=>[3,2,6,5,4,8,7,1]=>[2,5,4,7,8,6,3,1]=>0101101
[2,6,5,4,8,7,3,1]=>[3,2,7,5,6,4,8,1]=>[2,6,5,4,8,7,3,1]=>0101111
[2,5,6,4,8,7,3,1]=>[3,2,7,6,5,4,8,1]=>[2,5,6,4,8,7,3,1]=>0100111
[2,4,6,5,8,7,3,1]=>[3,2,7,4,6,5,8,1]=>[2,4,6,5,8,7,3,1]=>0100111
[2,6,7,5,4,8,3,1]=>[3,2,8,5,7,6,4,1]=>[2,6,7,5,4,8,3,1]=>0101011
[2,5,6,7,4,8,3,1]=>[3,2,8,7,5,6,4,1]=>[2,5,6,7,4,8,3,1]=>0100011
[2,5,4,7,6,8,3,1]=>[3,2,8,5,4,7,6,1]=>[2,5,4,7,6,8,3,1]=>0101011
[2,6,5,4,7,8,3,1]=>[3,2,8,5,6,4,7,1]=>[2,6,5,4,7,8,3,1]=>0101101
[2,4,6,5,7,8,3,1]=>[3,2,8,4,6,5,7,1]=>[2,4,6,5,7,8,3,1]=>0100101
[2,5,4,6,7,8,3,1]=>[3,2,8,5,4,6,7,1]=>[2,5,4,6,7,8,3,1]=>0101001
[2,4,5,6,7,8,3,1]=>[3,2,8,4,5,6,7,1]=>[2,4,5,6,7,8,3,1]=>0100001
[3,2,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,1]=>[3,2,8,7,6,5,4,1]=>0111111
[3,2,7,8,6,5,4,1]=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,6,5,4,1]=>0111101
[3,2,6,8,7,5,4,1]=>[4,3,2,5,7,6,8,1]=>[3,2,6,8,7,5,4,1]=>0111011
[3,2,5,7,8,6,4,1]=>[4,3,2,6,5,8,7,1]=>[3,2,5,7,8,6,4,1]=>0110101
[3,2,6,5,8,7,4,1]=>[4,3,2,7,6,5,8,1]=>[3,2,6,5,8,7,4,1]=>0110111
[3,2,5,7,6,8,4,1]=>[4,3,2,8,5,7,6,1]=>[3,2,5,7,6,8,4,1]=>0110011
[3,2,5,6,7,8,4,1]=>[4,3,2,8,5,6,7,1]=>[3,2,5,6,7,8,4,1]=>0110001
[2,3,8,7,6,5,4,1]=>[4,2,3,5,6,7,8,1]=>[2,3,8,7,6,5,4,1]=>0011111
[2,3,5,7,8,6,4,1]=>[4,2,3,6,5,8,7,1]=>[2,3,5,7,8,6,4,1]=>0010101
[2,3,6,5,8,7,4,1]=>[4,2,3,7,6,5,8,1]=>[2,3,6,5,8,7,4,1]=>0010111
[2,3,5,6,8,7,4,1]=>[4,2,3,7,5,6,8,1]=>[2,3,5,6,8,7,4,1]=>0010011
[2,3,7,6,5,8,4,1]=>[4,2,3,8,6,7,5,1]=>[2,3,7,6,5,8,4,1]=>0010111
[2,3,5,7,6,8,4,1]=>[4,2,3,8,5,7,6,1]=>[2,3,5,7,6,8,4,1]=>0010011
[2,3,5,6,7,8,4,1]=>[4,2,3,8,5,6,7,1]=>[2,3,5,6,7,8,4,1]=>0010001
[4,3,2,8,7,6,5,1]=>[5,3,4,2,6,7,8,1]=>[4,3,2,8,7,6,5,1]=>0111111
[4,3,2,6,8,7,5,1]=>[5,3,4,2,7,6,8,1]=>[4,3,2,6,8,7,5,1]=>0111011
[3,4,2,8,7,6,5,1]=>[5,4,3,2,6,7,8,1]=>[3,4,2,8,7,6,5,1]=>0011111
[3,4,2,7,8,6,5,1]=>[5,4,3,2,6,8,7,1]=>[3,4,2,7,8,6,5,1]=>0011101
[2,4,3,6,8,7,5,1]=>[5,2,4,3,7,6,8,1]=>[2,4,3,6,8,7,5,1]=>0011011
[3,2,4,8,7,6,5,1]=>[5,3,2,4,6,7,8,1]=>[3,2,4,8,7,6,5,1]=>0101111
[2,3,4,8,7,6,5,1]=>[5,2,3,4,6,7,8,1]=>[2,3,4,8,7,6,5,1]=>0001111
[2,3,4,7,6,8,5,1]=>[5,2,3,4,8,7,6,1]=>[2,3,4,7,6,8,5,1]=>0001011
[2,3,4,6,7,8,5,1]=>[5,2,3,4,8,6,7,1]=>[2,3,4,6,7,8,5,1]=>0001001
[5,4,3,2,8,7,6,1]=>[6,3,4,5,2,7,8,1]=>[5,4,3,2,8,7,6,1]=>0111111
[5,4,3,2,7,8,6,1]=>[6,3,4,5,2,8,7,1]=>[5,4,3,2,7,8,6,1]=>0111101
[4,5,3,2,8,7,6,1]=>[6,3,5,4,2,7,8,1]=>[4,5,3,2,8,7,6,1]=>0101111
[4,3,5,2,8,7,6,1]=>[6,5,4,3,2,7,8,1]=>[4,3,5,2,8,7,6,1]=>0011111
[2,5,4,3,7,8,6,1]=>[6,2,4,5,3,8,7,1]=>[2,5,4,3,7,8,6,1]=>0011101
[2,4,5,3,8,7,6,1]=>[6,2,5,4,3,7,8,1]=>[2,4,5,3,8,7,6,1]=>0001111
[3,2,5,4,7,8,6,1]=>[6,3,2,5,4,8,7,1]=>[3,2,5,4,7,8,6,1]=>0101101
[2,3,5,4,8,7,6,1]=>[6,2,3,5,4,7,8,1]=>[2,3,5,4,8,7,6,1]=>0001111
[3,4,2,5,7,8,6,1]=>[6,4,3,2,5,8,7,1]=>[3,4,2,5,7,8,6,1]=>0010101
[2,3,4,5,8,7,6,1]=>[6,2,3,4,5,7,8,1]=>[2,3,4,5,8,7,6,1]=>0000111
[2,3,4,5,7,8,6,1]=>[6,2,3,4,5,8,7,1]=>[2,3,4,5,7,8,6,1]=>0000101
[6,5,4,3,2,8,7,1]=>[7,3,4,5,6,2,8,1]=>[6,5,4,3,2,8,7,1]=>0111111
[4,6,5,3,2,8,7,1]=>[7,3,5,4,6,2,8,1]=>[4,6,5,3,2,8,7,1]=>0101111
[5,4,6,3,2,8,7,1]=>[7,3,6,5,4,2,8,1]=>[5,4,6,3,2,8,7,1]=>0101111
[4,5,6,3,2,8,7,1]=>[7,3,6,4,5,2,8,1]=>[4,5,6,3,2,8,7,1]=>0100111
[3,5,6,4,2,8,7,1]=>[7,4,3,6,5,2,8,1]=>[3,5,6,4,2,8,7,1]=>0010111
[4,3,6,5,2,8,7,1]=>[7,5,4,3,6,2,8,1]=>[4,3,6,5,2,8,7,1]=>0011111
[5,4,3,6,2,8,7,1]=>[7,6,4,5,3,2,8,1]=>[5,4,3,6,2,8,7,1]=>0011111
[4,5,3,6,2,8,7,1]=>[7,6,5,4,3,2,8,1]=>[4,5,3,6,2,8,7,1]=>0001111
[3,5,4,6,2,8,7,1]=>[7,6,3,5,4,2,8,1]=>[3,5,4,6,2,8,7,1]=>0001111
[3,4,5,6,2,8,7,1]=>[7,6,3,4,5,2,8,1]=>[3,4,5,6,2,8,7,1]=>0000111
[2,4,6,5,3,8,7,1]=>[7,2,5,4,6,3,8,1]=>[2,4,6,5,3,8,7,1]=>0001111
[2,4,5,6,3,8,7,1]=>[7,2,6,4,5,3,8,1]=>[2,4,5,6,3,8,7,1]=>0000111
[3,2,6,5,4,8,7,1]=>[7,3,2,5,6,4,8,1]=>[3,2,6,5,4,8,7,1]=>0101111
[4,3,2,6,5,8,7,1]=>[7,3,4,2,6,5,8,1]=>[4,3,2,6,5,8,7,1]=>0110111
[3,4,2,6,5,8,7,1]=>[7,4,3,2,6,5,8,1]=>[3,4,2,6,5,8,7,1]=>0010111
[2,4,3,6,5,8,7,1]=>[7,2,4,3,6,5,8,1]=>[2,4,3,6,5,8,7,1]=>0010111
[2,5,4,3,6,8,7,1]=>[7,2,4,5,3,6,8,1]=>[2,5,4,3,6,8,7,1]=>0011011
[3,4,2,5,6,8,7,1]=>[7,4,3,2,5,6,8,1]=>[3,4,2,5,6,8,7,1]=>0010011
[3,2,4,5,6,8,7,1]=>[7,3,2,4,5,6,8,1]=>[3,2,4,5,6,8,7,1]=>0100011
[2,3,4,5,6,8,7,1]=>[7,2,3,4,5,6,8,1]=>[2,3,4,5,6,8,7,1]=>0000011
[4,7,6,5,3,2,8,1]=>[8,3,5,4,6,7,2,1]=>[4,7,6,5,3,2,8,1]=>0101111
[4,6,7,5,3,2,8,1]=>[8,3,5,4,7,6,2,1]=>[4,6,7,5,3,2,8,1]=>0101011
[4,6,5,7,3,2,8,1]=>[8,3,7,4,6,5,2,1]=>[4,6,5,7,3,2,8,1]=>0100111
[3,5,6,7,4,2,8,1]=>[8,4,3,7,5,6,2,1]=>[3,5,6,7,4,2,8,1]=>0010011
[4,3,7,6,5,2,8,1]=>[8,5,4,3,6,7,2,1]=>[4,3,7,6,5,2,8,1]=>0011111
[4,3,6,7,5,2,8,1]=>[8,5,4,3,7,6,2,1]=>[4,3,6,7,5,2,8,1]=>0011011
[3,4,7,6,5,2,8,1]=>[8,5,3,4,6,7,2,1]=>[3,4,7,6,5,2,8,1]=>0001111
[3,4,6,7,5,2,8,1]=>[8,5,3,4,7,6,2,1]=>[3,4,6,7,5,2,8,1]=>0001011
[5,4,3,7,6,2,8,1]=>[8,6,4,5,3,7,2,1]=>[5,4,3,7,6,2,8,1]=>0011111
[4,5,3,7,6,2,8,1]=>[8,6,5,4,3,7,2,1]=>[4,5,3,7,6,2,8,1]=>0001111
[3,5,4,7,6,2,8,1]=>[8,6,3,5,4,7,2,1]=>[3,5,4,7,6,2,8,1]=>0001111
[4,6,5,3,7,2,8,1]=>[8,7,5,4,6,3,2,1]=>[4,6,5,3,7,2,8,1]=>0001111
[3,6,5,4,7,2,8,1]=>[8,7,3,5,6,4,2,1]=>[3,6,5,4,7,2,8,1]=>0001111
[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>[3,5,6,4,7,2,8,1]=>0000111
[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>[4,3,6,5,7,2,8,1]=>0010111
[3,4,6,5,7,2,8,1]=>[8,7,3,4,6,5,2,1]=>[3,4,6,5,7,2,8,1]=>0000111
[3,5,4,6,7,2,8,1]=>[8,7,3,5,4,6,2,1]=>[3,5,4,6,7,2,8,1]=>0001011
[2,7,6,5,4,3,8,1]=>[8,2,4,5,6,7,3,1]=>[2,7,6,5,4,3,8,1]=>0011111
[2,6,5,7,4,3,8,1]=>[8,2,4,7,6,5,3,1]=>[2,6,5,7,4,3,8,1]=>0010111
[2,5,6,7,4,3,8,1]=>[8,2,4,7,5,6,3,1]=>[2,5,6,7,4,3,8,1]=>0010011
[2,4,6,7,5,3,8,1]=>[8,2,5,4,7,6,3,1]=>[2,4,6,7,5,3,8,1]=>0001011
[2,5,4,7,6,3,8,1]=>[8,2,6,5,4,7,3,1]=>[2,5,4,7,6,3,8,1]=>0001111
[2,4,6,5,7,3,8,1]=>[8,2,7,4,6,5,3,1]=>[2,4,6,5,7,3,8,1]=>0000111
[2,5,4,6,7,3,8,1]=>[8,2,7,5,4,6,3,1]=>[2,5,4,6,7,3,8,1]=>0001011
[2,4,5,6,7,3,8,1]=>[8,2,7,4,5,6,3,1]=>[2,4,5,6,7,3,8,1]=>0000011
[3,2,7,6,5,4,8,1]=>[8,3,2,5,6,7,4,1]=>[3,2,7,6,5,4,8,1]=>0101111
[3,2,6,7,5,4,8,1]=>[8,3,2,5,7,6,4,1]=>[3,2,6,7,5,4,8,1]=>0101011
[3,2,5,7,6,4,8,1]=>[8,3,2,6,5,7,4,1]=>[3,2,5,7,6,4,8,1]=>0100111
[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>[3,2,6,5,7,4,8,1]=>0100111
[3,2,5,6,7,4,8,1]=>[8,3,2,7,5,6,4,1]=>[3,2,5,6,7,4,8,1]=>0100011
[2,3,7,6,5,4,8,1]=>[8,2,3,5,6,7,4,1]=>[2,3,7,6,5,4,8,1]=>0001111
[2,3,5,6,7,4,8,1]=>[8,2,3,7,5,6,4,1]=>[2,3,5,6,7,4,8,1]=>0000011
[3,4,2,7,6,5,8,1]=>[8,4,3,2,6,7,5,1]=>[3,4,2,7,6,5,8,1]=>0010111
[3,4,2,6,7,5,8,1]=>[8,4,3,2,7,6,5,1]=>[3,4,2,6,7,5,8,1]=>0010011
[2,4,3,7,6,5,8,1]=>[8,2,4,3,6,7,5,1]=>[2,4,3,7,6,5,8,1]=>0010111
[2,4,3,6,7,5,8,1]=>[8,2,4,3,7,6,5,1]=>[2,4,3,6,7,5,8,1]=>0010011
[3,2,4,7,6,5,8,1]=>[8,3,2,4,6,7,5,1]=>[3,2,4,7,6,5,8,1]=>0100111
[2,3,4,6,7,5,8,1]=>[8,2,3,4,7,6,5,1]=>[2,3,4,6,7,5,8,1]=>0000011
[5,4,3,2,7,6,8,1]=>[8,3,4,5,2,7,6,1]=>[5,4,3,2,7,6,8,1]=>0111011
[3,5,4,2,7,6,8,1]=>[8,4,3,5,2,7,6,1]=>[3,5,4,2,7,6,8,1]=>0011011
[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>[4,3,5,2,7,6,8,1]=>0011011
[3,4,5,2,7,6,8,1]=>[8,5,3,4,2,7,6,1]=>[3,4,5,2,7,6,8,1]=>0001011
[2,5,4,3,7,6,8,1]=>[8,2,4,5,3,7,6,1]=>[2,5,4,3,7,6,8,1]=>0011011
[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[3,2,5,4,7,6,8,1]=>0101011
[2,3,5,4,7,6,8,1]=>[8,2,3,5,4,7,6,1]=>[2,3,5,4,7,6,8,1]=>0001011
[3,4,2,5,7,6,8,1]=>[8,4,3,2,5,7,6,1]=>[3,4,2,5,7,6,8,1]=>0010011
[2,3,4,5,7,6,8,1]=>[8,2,3,4,5,7,6,1]=>[2,3,4,5,7,6,8,1]=>0000011
[3,6,5,4,2,7,8,1]=>[8,4,3,5,6,2,7,1]=>[3,6,5,4,2,7,8,1]=>0011101
[3,5,4,6,2,7,8,1]=>[8,6,3,5,4,2,7,1]=>[3,5,4,6,2,7,8,1]=>0001101
[2,6,5,4,3,7,8,1]=>[8,2,4,5,6,3,7,1]=>[2,6,5,4,3,7,8,1]=>0011101
[2,5,4,6,3,7,8,1]=>[8,2,6,5,4,3,7,1]=>[2,5,4,6,3,7,8,1]=>0001101
[2,4,5,6,3,7,8,1]=>[8,2,6,4,5,3,7,1]=>[2,4,5,6,3,7,8,1]=>0000101
[2,3,5,6,4,7,8,1]=>[8,2,3,6,5,4,7,1]=>[2,3,5,6,4,7,8,1]=>0000101
[4,3,2,6,5,7,8,1]=>[8,3,4,2,6,5,7,1]=>[4,3,2,6,5,7,8,1]=>0110101
[3,4,2,6,5,7,8,1]=>[8,4,3,2,6,5,7,1]=>[3,4,2,6,5,7,8,1]=>0010101
[2,4,3,6,5,7,8,1]=>[8,2,4,3,6,5,7,1]=>[2,4,3,6,5,7,8,1]=>0010101
[2,4,5,3,6,7,8,1]=>[8,2,5,4,3,6,7,1]=>[2,4,5,3,6,7,8,1]=>0001001
[2,3,5,4,6,7,8,1]=>[8,2,3,5,4,6,7,1]=>[2,3,5,4,6,7,8,1]=>0001001
[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]=>[1,8,7,6,5,4,3,2]=>0111111
[1,7,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,2]=>[1,7,8,6,5,4,3,2]=>0111101
[1,6,8,7,5,4,3,2]=>[1,3,4,5,7,6,8,2]=>[1,6,8,7,5,4,3,2]=>0111011
[1,7,6,8,5,4,3,2]=>[1,3,4,5,8,7,6,2]=>[1,7,6,8,5,4,3,2]=>0111011
[1,6,7,8,5,4,3,2]=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,5,4,3,2]=>0111001
[1,5,8,7,6,4,3,2]=>[1,3,4,6,5,7,8,2]=>[1,5,8,7,6,4,3,2]=>0110111
[1,6,5,8,7,4,3,2]=>[1,3,4,7,6,5,8,2]=>[1,6,5,8,7,4,3,2]=>0110111
[1,6,7,5,8,4,3,2]=>[1,3,4,8,7,6,5,2]=>[1,6,7,5,8,4,3,2]=>0110011
[1,6,5,7,8,4,3,2]=>[1,3,4,8,6,5,7,2]=>[1,6,5,7,8,4,3,2]=>0110101
[1,5,6,7,8,4,3,2]=>[1,3,4,8,5,6,7,2]=>[1,5,6,7,8,4,3,2]=>0110001
[1,4,8,7,6,5,3,2]=>[1,3,5,4,6,7,8,2]=>[1,4,8,7,6,5,3,2]=>0101111
[1,4,6,8,7,5,3,2]=>[1,3,5,4,7,6,8,2]=>[1,4,6,8,7,5,3,2]=>0101011
[1,5,4,7,8,6,3,2]=>[1,3,6,5,4,8,7,2]=>[1,5,4,7,8,6,3,2]=>0101101
[1,4,5,8,7,6,3,2]=>[1,3,6,4,5,7,8,2]=>[1,4,5,8,7,6,3,2]=>0100111
[1,4,5,7,8,6,3,2]=>[1,3,6,4,5,8,7,2]=>[1,4,5,7,8,6,3,2]=>0100101
[1,7,6,5,4,8,3,2]=>[1,3,8,5,6,7,4,2]=>[1,7,6,5,4,8,3,2]=>0101111
[1,4,7,6,5,8,3,2]=>[1,3,8,4,6,7,5,2]=>[1,4,7,6,5,8,3,2]=>0100111
[1,5,4,6,7,8,3,2]=>[1,3,8,5,4,6,7,2]=>[1,5,4,6,7,8,3,2]=>0101001
[1,4,5,6,7,8,3,2]=>[1,3,8,4,5,6,7,2]=>[1,4,5,6,7,8,3,2]=>0100001
[1,3,8,7,6,5,4,2]=>[1,4,3,5,6,7,8,2]=>[1,3,8,7,6,5,4,2]=>0011111
[1,3,6,7,8,5,4,2]=>[1,4,3,5,8,6,7,2]=>[1,3,6,7,8,5,4,2]=>0011001
[1,3,5,8,7,6,4,2]=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,7,6,4,2]=>0010111
[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]=>[1,3,5,7,8,6,4,2]=>0010101
[1,3,6,7,5,8,4,2]=>[1,4,3,8,7,6,5,2]=>[1,3,6,7,5,8,4,2]=>0010011
[1,3,5,7,6,8,4,2]=>[1,4,3,8,5,7,6,2]=>[1,3,5,7,6,8,4,2]=>0010011
[1,3,6,5,7,8,4,2]=>[1,4,3,8,6,5,7,2]=>[1,3,6,5,7,8,4,2]=>0010101
[1,3,5,6,7,8,4,2]=>[1,4,3,8,5,6,7,2]=>[1,3,5,6,7,8,4,2]=>0010001
[1,4,3,8,7,6,5,2]=>[1,5,4,3,6,7,8,2]=>[1,4,3,8,7,6,5,2]=>0011111
[1,4,3,7,8,6,5,2]=>[1,5,4,3,6,8,7,2]=>[1,4,3,7,8,6,5,2]=>0011101
[1,4,3,7,6,8,5,2]=>[1,5,4,3,8,7,6,2]=>[1,4,3,7,6,8,5,2]=>0011011
[1,3,4,8,7,6,5,2]=>[1,5,3,4,6,7,8,2]=>[1,3,4,8,7,6,5,2]=>0001111
[1,3,4,6,7,8,5,2]=>[1,5,3,4,8,6,7,2]=>[1,3,4,6,7,8,5,2]=>0001001
[1,4,5,3,8,7,6,2]=>[1,6,5,4,3,7,8,2]=>[1,4,5,3,8,7,6,2]=>0001111
[1,4,5,3,7,8,6,2]=>[1,6,5,4,3,8,7,2]=>[1,4,5,3,7,8,6,2]=>0001101
[1,3,5,4,7,8,6,2]=>[1,6,3,5,4,8,7,2]=>[1,3,5,4,7,8,6,2]=>0001101
[1,4,3,5,7,8,6,2]=>[1,6,4,3,5,8,7,2]=>[1,4,3,5,7,8,6,2]=>0010101
[1,3,4,5,7,8,6,2]=>[1,6,3,4,5,8,7,2]=>[1,3,4,5,7,8,6,2]=>0000101
[1,6,5,4,3,8,7,2]=>[1,7,4,5,6,3,8,2]=>[1,6,5,4,3,8,7,2]=>0011111
[1,4,3,6,5,8,7,2]=>[1,7,4,3,6,5,8,2]=>[1,4,3,6,5,8,7,2]=>0010111
[1,5,4,3,6,8,7,2]=>[1,7,4,5,3,6,8,2]=>[1,5,4,3,6,8,7,2]=>0011011
[1,4,5,3,6,8,7,2]=>[1,7,5,4,3,6,8,2]=>[1,4,5,3,6,8,7,2]=>0001011
[1,3,4,5,6,8,7,2]=>[1,7,3,4,5,6,8,2]=>[1,3,4,5,6,8,7,2]=>0000011
[1,7,6,5,4,3,8,2]=>[1,8,4,5,6,7,3,2]=>[1,7,6,5,4,3,8,2]=>0011111
[1,6,5,7,4,3,8,2]=>[1,8,4,7,6,5,3,2]=>[1,6,5,7,4,3,8,2]=>0010111
[1,4,6,7,5,3,8,2]=>[1,8,5,4,7,6,3,2]=>[1,4,6,7,5,3,8,2]=>0001011
[1,5,6,4,7,3,8,2]=>[1,8,7,6,5,4,3,2]=>[1,5,6,4,7,3,8,2]=>0000111
[1,5,4,6,7,3,8,2]=>[1,8,7,5,4,6,3,2]=>[1,5,4,6,7,3,8,2]=>0001011
[1,4,5,6,7,3,8,2]=>[1,8,7,4,5,6,3,2]=>[1,4,5,6,7,3,8,2]=>0000011
[1,3,6,5,7,4,8,2]=>[1,8,3,7,6,5,4,2]=>[1,3,6,5,7,4,8,2]=>0000111
[1,3,5,6,7,4,8,2]=>[1,8,3,7,5,6,4,2]=>[1,3,5,6,7,4,8,2]=>0000011
[1,3,4,7,6,5,8,2]=>[1,8,3,4,6,7,5,2]=>[1,3,4,7,6,5,8,2]=>0000111
[1,3,4,6,7,5,8,2]=>[1,8,3,4,7,6,5,2]=>[1,3,4,6,7,5,8,2]=>0000011
[1,3,5,4,7,6,8,2]=>[1,8,3,5,4,7,6,2]=>[1,3,5,4,7,6,8,2]=>0001011
[1,6,5,4,3,7,8,2]=>[1,8,4,5,6,3,7,2]=>[1,6,5,4,3,7,8,2]=>0011101
[1,5,4,6,3,7,8,2]=>[1,8,6,5,4,3,7,2]=>[1,5,4,6,3,7,8,2]=>0001101
[1,3,5,6,4,7,8,2]=>[1,8,3,6,5,4,7,2]=>[1,3,5,6,4,7,8,2]=>0000101
[1,4,3,6,5,7,8,2]=>[1,8,4,3,6,5,7,2]=>[1,4,3,6,5,7,8,2]=>0010101
[1,5,4,3,6,7,8,2]=>[1,8,4,5,3,6,7,2]=>[1,5,4,3,6,7,8,2]=>0011001
[1,4,5,3,6,7,8,2]=>[1,8,5,4,3,6,7,2]=>[1,4,5,3,6,7,8,2]=>0001001
[1,3,5,4,6,7,8,2]=>[1,8,3,5,4,6,7,2]=>[1,3,5,4,6,7,8,2]=>0001001
[1,4,3,5,6,7,8,2]=>[1,8,4,3,5,6,7,2]=>[1,4,3,5,6,7,8,2]=>0010001
[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>[1,3,4,5,6,7,8,2]=>0000001
[2,1,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,3]=>[2,1,8,7,6,5,4,3]=>1011111
[2,1,7,8,6,5,4,3]=>[2,1,4,5,6,8,7,3]=>[2,1,7,8,6,5,4,3]=>1011101
[2,1,7,6,8,5,4,3]=>[2,1,4,5,8,7,6,3]=>[2,1,7,6,8,5,4,3]=>1011011
[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]=>[2,1,6,7,8,5,4,3]=>1011001
[2,1,5,7,8,6,4,3]=>[2,1,4,6,5,8,7,3]=>[2,1,5,7,8,6,4,3]=>1010101
[2,1,6,5,8,7,4,3]=>[2,1,4,7,6,5,8,3]=>[2,1,6,5,8,7,4,3]=>1010111
[2,1,7,6,5,8,4,3]=>[2,1,4,8,6,7,5,3]=>[2,1,7,6,5,8,4,3]=>1010111
[2,1,6,7,5,8,4,3]=>[2,1,4,8,7,6,5,3]=>[2,1,6,7,5,8,4,3]=>1010011
[2,1,5,7,6,8,4,3]=>[2,1,4,8,5,7,6,3]=>[2,1,5,7,6,8,4,3]=>1010011
[2,1,6,5,7,8,4,3]=>[2,1,4,8,6,5,7,3]=>[2,1,6,5,7,8,4,3]=>1010101
[2,1,5,6,7,8,4,3]=>[2,1,4,8,5,6,7,3]=>[2,1,5,6,7,8,4,3]=>1010001
[2,1,4,8,7,6,5,3]=>[2,1,5,4,6,7,8,3]=>[2,1,4,8,7,6,5,3]=>1001111
[2,1,4,7,8,6,5,3]=>[2,1,5,4,6,8,7,3]=>[2,1,4,7,8,6,5,3]=>1001101
[2,1,4,6,8,7,5,3]=>[2,1,5,4,7,6,8,3]=>[2,1,4,6,8,7,5,3]=>1001011
[2,1,4,7,6,8,5,3]=>[2,1,5,4,8,7,6,3]=>[2,1,4,7,6,8,5,3]=>1001011
[2,1,4,6,7,8,5,3]=>[2,1,5,4,8,6,7,3]=>[2,1,4,6,7,8,5,3]=>1001001
[2,1,5,4,7,8,6,3]=>[2,1,6,5,4,8,7,3]=>[2,1,5,4,7,8,6,3]=>1001101
[2,1,4,5,8,7,6,3]=>[2,1,6,4,5,7,8,3]=>[2,1,4,5,8,7,6,3]=>1000111
[2,1,4,5,7,8,6,3]=>[2,1,6,4,5,8,7,3]=>[2,1,4,5,7,8,6,3]=>1000101
[2,1,6,5,4,8,7,3]=>[2,1,7,5,6,4,8,3]=>[2,1,6,5,4,8,7,3]=>1001111
[2,1,5,6,4,8,7,3]=>[2,1,7,6,5,4,8,3]=>[2,1,5,6,4,8,7,3]=>1000111
[2,1,4,6,5,8,7,3]=>[2,1,7,4,6,5,8,3]=>[2,1,4,6,5,8,7,3]=>1000111
[2,1,5,4,6,8,7,3]=>[2,1,7,5,4,6,8,3]=>[2,1,5,4,6,8,7,3]=>1001011
[2,1,7,6,5,4,8,3]=>[2,1,8,5,6,7,4,3]=>[2,1,7,6,5,4,8,3]=>1001111
[2,1,6,7,5,4,8,3]=>[2,1,8,5,7,6,4,3]=>[2,1,6,7,5,4,8,3]=>1001011
[2,1,5,7,6,4,8,3]=>[2,1,8,6,5,7,4,3]=>[2,1,5,7,6,4,8,3]=>1000111
[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[2,1,6,5,7,4,8,3]=>1000111
[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>[2,1,5,6,7,4,8,3]=>1000011
[2,1,4,7,6,5,8,3]=>[2,1,8,4,6,7,5,3]=>[2,1,4,7,6,5,8,3]=>1000111
[2,1,4,6,7,5,8,3]=>[2,1,8,4,7,6,5,3]=>[2,1,4,6,7,5,8,3]=>1000011
[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[2,1,5,4,7,6,8,3]=>1001011
[2,1,5,6,4,7,8,3]=>[2,1,8,6,5,4,7,3]=>[2,1,5,6,4,7,8,3]=>1000101
[2,1,5,4,6,7,8,3]=>[2,1,8,5,4,6,7,3]=>[2,1,5,4,6,7,8,3]=>1001001
[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[2,1,4,5,6,7,8,3]=>1000001
[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]=>[1,2,8,7,6,5,4,3]=>0011111
[1,2,7,8,6,5,4,3]=>[1,2,4,5,6,8,7,3]=>[1,2,7,8,6,5,4,3]=>0011101
[1,2,7,6,8,5,4,3]=>[1,2,4,5,8,7,6,3]=>[1,2,7,6,8,5,4,3]=>0011011
[1,2,6,7,8,5,4,3]=>[1,2,4,5,8,6,7,3]=>[1,2,6,7,8,5,4,3]=>0011001
[1,2,5,8,7,6,4,3]=>[1,2,4,6,5,7,8,3]=>[1,2,5,8,7,6,4,3]=>0010111
[1,2,6,5,8,7,4,3]=>[1,2,4,7,6,5,8,3]=>[1,2,6,5,8,7,4,3]=>0010111
[1,2,5,6,8,7,4,3]=>[1,2,4,7,5,6,8,3]=>[1,2,5,6,8,7,4,3]=>0010011
[1,2,6,5,7,8,4,3]=>[1,2,4,8,6,5,7,3]=>[1,2,6,5,7,8,4,3]=>0010101
[1,2,5,6,7,8,4,3]=>[1,2,4,8,5,6,7,3]=>[1,2,5,6,7,8,4,3]=>0010001
[1,2,4,8,7,6,5,3]=>[1,2,5,4,6,7,8,3]=>[1,2,4,8,7,6,5,3]=>0001111
[1,2,4,7,8,6,5,3]=>[1,2,5,4,6,8,7,3]=>[1,2,4,7,8,6,5,3]=>0001101
[1,2,4,6,8,7,5,3]=>[1,2,5,4,7,6,8,3]=>[1,2,4,6,8,7,5,3]=>0001011
[1,2,4,7,6,8,5,3]=>[1,2,5,4,8,7,6,3]=>[1,2,4,7,6,8,5,3]=>0001011
[1,2,4,6,7,8,5,3]=>[1,2,5,4,8,6,7,3]=>[1,2,4,6,7,8,5,3]=>0001001
[1,2,5,4,8,7,6,3]=>[1,2,6,5,4,7,8,3]=>[1,2,5,4,8,7,6,3]=>0001111
[1,2,5,4,7,8,6,3]=>[1,2,6,5,4,8,7,3]=>[1,2,5,4,7,8,6,3]=>0001101
[1,2,4,5,8,7,6,3]=>[1,2,6,4,5,7,8,3]=>[1,2,4,5,8,7,6,3]=>0000111
[1,2,4,5,7,8,6,3]=>[1,2,6,4,5,8,7,3]=>[1,2,4,5,7,8,6,3]=>0000101
[1,2,5,4,6,8,7,3]=>[1,2,7,5,4,6,8,3]=>[1,2,5,4,6,8,7,3]=>0001011
[1,2,4,5,6,8,7,3]=>[1,2,7,4,5,6,8,3]=>[1,2,4,5,6,8,7,3]=>0000011
[1,2,7,6,5,4,8,3]=>[1,2,8,5,6,7,4,3]=>[1,2,7,6,5,4,8,3]=>0001111
[1,2,5,7,6,4,8,3]=>[1,2,8,6,5,7,4,3]=>[1,2,5,7,6,4,8,3]=>0000111
[1,2,5,6,7,4,8,3]=>[1,2,8,7,5,6,4,3]=>[1,2,5,6,7,4,8,3]=>0000011
[1,2,4,7,6,5,8,3]=>[1,2,8,4,6,7,5,3]=>[1,2,4,7,6,5,8,3]=>0000111
[1,2,5,4,7,6,8,3]=>[1,2,8,5,4,7,6,3]=>[1,2,5,4,7,6,8,3]=>0001011
[1,2,6,5,4,7,8,3]=>[1,2,8,5,6,4,7,3]=>[1,2,6,5,4,7,8,3]=>0001101
[1,2,5,6,4,7,8,3]=>[1,2,8,6,5,4,7,3]=>[1,2,5,6,4,7,8,3]=>0000101
[1,2,5,4,6,7,8,3]=>[1,2,8,5,4,6,7,3]=>[1,2,5,4,6,7,8,3]=>0001001
[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>[1,2,4,5,6,7,8,3]=>0000001
[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,7,6,5,4]=>1101111
[3,2,1,6,8,7,5,4]=>[2,3,1,5,7,6,8,4]=>[3,2,1,6,8,7,5,4]=>1101011
[3,2,1,6,7,8,5,4]=>[2,3,1,5,8,6,7,4]=>[3,2,1,6,7,8,5,4]=>1101001
[3,2,1,5,7,8,6,4]=>[2,3,1,6,5,8,7,4]=>[3,2,1,5,7,8,6,4]=>1100101
[3,2,1,6,5,8,7,4]=>[2,3,1,7,6,5,8,4]=>[3,2,1,6,5,8,7,4]=>1100111
[3,2,1,7,6,5,8,4]=>[2,3,1,8,6,7,5,4]=>[3,2,1,7,6,5,8,4]=>1100111
[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,6,5,4]=>[3,2,1,6,7,5,8,4]=>1100011
[3,2,1,5,6,7,8,4]=>[2,3,1,8,5,6,7,4]=>[3,2,1,5,6,7,8,4]=>1100001
[2,3,1,8,7,6,5,4]=>[3,2,1,5,6,7,8,4]=>[2,3,1,8,7,6,5,4]=>0101111
[2,3,1,7,8,6,5,4]=>[3,2,1,5,6,8,7,4]=>[2,3,1,7,8,6,5,4]=>0101101
[2,3,1,6,8,7,5,4]=>[3,2,1,5,7,6,8,4]=>[2,3,1,6,8,7,5,4]=>0101011
[2,3,1,7,6,8,5,4]=>[3,2,1,5,8,7,6,4]=>[2,3,1,7,6,8,5,4]=>0101011
[2,3,1,6,7,8,5,4]=>[3,2,1,5,8,6,7,4]=>[2,3,1,6,7,8,5,4]=>0101001
[2,3,1,5,7,8,6,4]=>[3,2,1,6,5,8,7,4]=>[2,3,1,5,7,8,6,4]=>0100101
[2,3,1,6,5,8,7,4]=>[3,2,1,7,6,5,8,4]=>[2,3,1,6,5,8,7,4]=>0100111
[2,3,1,7,6,5,8,4]=>[3,2,1,8,6,7,5,4]=>[2,3,1,7,6,5,8,4]=>0100111
[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]=>[2,3,1,6,7,5,8,4]=>0100011
[2,3,1,5,7,6,8,4]=>[3,2,1,8,5,7,6,4]=>[2,3,1,5,7,6,8,4]=>0100011
[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[2,3,1,5,6,7,8,4]=>0100001
[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,7,6,5,4]=>0101111
[1,3,2,6,8,7,5,4]=>[1,3,2,5,7,6,8,4]=>[1,3,2,6,8,7,5,4]=>0101011
[1,3,2,7,6,8,5,4]=>[1,3,2,5,8,7,6,4]=>[1,3,2,7,6,8,5,4]=>0101011
[1,3,2,5,8,7,6,4]=>[1,3,2,6,5,7,8,4]=>[1,3,2,5,8,7,6,4]=>0100111
[1,3,2,5,7,8,6,4]=>[1,3,2,6,5,8,7,4]=>[1,3,2,5,7,8,6,4]=>0100101
[1,3,2,6,5,8,7,4]=>[1,3,2,7,6,5,8,4]=>[1,3,2,6,5,8,7,4]=>0100111
[1,3,2,5,6,8,7,4]=>[1,3,2,7,5,6,8,4]=>[1,3,2,5,6,8,7,4]=>0100011
[1,3,2,7,6,5,8,4]=>[1,3,2,8,6,7,5,4]=>[1,3,2,7,6,5,8,4]=>0100111
[1,3,2,6,7,5,8,4]=>[1,3,2,8,7,6,5,4]=>[1,3,2,6,7,5,8,4]=>0100011
[1,3,2,5,7,6,8,4]=>[1,3,2,8,5,7,6,4]=>[1,3,2,5,7,6,8,4]=>0100011
[1,3,2,6,5,7,8,4]=>[1,3,2,8,6,5,7,4]=>[1,3,2,6,5,7,8,4]=>0100101
[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,7,6,5,4]=>1001111
[2,1,3,6,8,7,5,4]=>[2,1,3,5,7,6,8,4]=>[2,1,3,6,8,7,5,4]=>1001011
[2,1,3,6,7,8,5,4]=>[2,1,3,5,8,6,7,4]=>[2,1,3,6,7,8,5,4]=>1001001
[2,1,3,5,7,6,8,4]=>[2,1,3,8,5,7,6,4]=>[2,1,3,5,7,6,8,4]=>1000011
[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]=>[2,1,3,5,6,7,8,4]=>1000001
[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,7,6,5,4]=>0001111
[1,2,3,7,8,6,5,4]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,8,6,5,4]=>0001101
[1,2,3,6,8,7,5,4]=>[1,2,3,5,7,6,8,4]=>[1,2,3,6,8,7,5,4]=>0001011
[1,2,3,7,6,8,5,4]=>[1,2,3,5,8,7,6,4]=>[1,2,3,7,6,8,5,4]=>0001011
[1,2,3,6,7,8,5,4]=>[1,2,3,5,8,6,7,4]=>[1,2,3,6,7,8,5,4]=>0001001
[1,2,3,5,8,7,6,4]=>[1,2,3,6,5,7,8,4]=>[1,2,3,5,8,7,6,4]=>0000111
[1,2,3,5,7,8,6,4]=>[1,2,3,6,5,8,7,4]=>[1,2,3,5,7,8,6,4]=>0000101
[1,2,3,6,5,8,7,4]=>[1,2,3,7,6,5,8,4]=>[1,2,3,6,5,8,7,4]=>0000111
[1,2,3,5,6,8,7,4]=>[1,2,3,7,5,6,8,4]=>[1,2,3,5,6,8,7,4]=>0000011
[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,7,5,4]=>[1,2,3,7,6,5,8,4]=>0000111
[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>[1,2,3,6,7,5,8,4]=>0000011
[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>[1,2,3,5,7,6,8,4]=>0000011
[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>[1,2,3,6,5,7,8,4]=>0000101
[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[1,2,3,5,6,7,8,4]=>0000001
[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]=>[4,3,2,1,8,7,6,5]=>1110111
[4,3,2,1,7,8,6,5]=>[2,3,4,1,6,8,7,5]=>[4,3,2,1,7,8,6,5]=>1110101
[4,3,2,1,6,8,7,5]=>[2,3,4,1,7,6,8,5]=>[4,3,2,1,6,8,7,5]=>1110011
[4,3,2,1,7,6,8,5]=>[2,3,4,1,8,7,6,5]=>[4,3,2,1,7,6,8,5]=>1110011
[4,3,2,1,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>[4,3,2,1,6,7,8,5]=>1110001
[3,4,2,1,8,7,6,5]=>[2,4,3,1,6,7,8,5]=>[3,4,2,1,8,7,6,5]=>1010111
[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]=>[3,4,2,1,7,8,6,5]=>1010101
[3,4,2,1,6,8,7,5]=>[2,4,3,1,7,6,8,5]=>[3,4,2,1,6,8,7,5]=>1010011
[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]=>[3,4,2,1,7,6,8,5]=>1010011
[3,4,2,1,6,7,8,5]=>[2,4,3,1,8,6,7,5]=>[3,4,2,1,6,7,8,5]=>1010001
[2,4,3,1,8,7,6,5]=>[3,2,4,1,6,7,8,5]=>[2,4,3,1,8,7,6,5]=>0110111
[2,4,3,1,7,8,6,5]=>[3,2,4,1,6,8,7,5]=>[2,4,3,1,7,8,6,5]=>0110101
[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]=>[2,4,3,1,6,8,7,5]=>0110011
[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]=>[2,4,3,1,7,6,8,5]=>0110011
[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>[2,4,3,1,6,7,8,5]=>0110001
[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]=>[3,2,4,1,8,7,6,5]=>0110111
[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>[3,2,4,1,7,8,6,5]=>0110101
[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>[3,2,4,1,6,8,7,5]=>0110011
[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[3,2,4,1,7,6,8,5]=>0110011
[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[3,2,4,1,6,7,8,5]=>0110001
[2,3,4,1,8,7,6,5]=>[4,2,3,1,6,7,8,5]=>[2,3,4,1,8,7,6,5]=>0010111
[2,3,4,1,7,8,6,5]=>[4,2,3,1,6,8,7,5]=>[2,3,4,1,7,8,6,5]=>0010101
[2,3,4,1,6,8,7,5]=>[4,2,3,1,7,6,8,5]=>[2,3,4,1,6,8,7,5]=>0010011
[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>[2,3,4,1,7,6,8,5]=>0010011
[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[2,3,4,1,6,7,8,5]=>0010001
[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,7,6,5]=>0110111
[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,6,8,7,5]=>0110011
[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,7,6,8,5]=>0110011
[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>[1,4,3,2,6,7,8,5]=>0110001
[1,3,4,2,8,7,6,5]=>[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,7,6,5]=>0010111
[1,3,4,2,7,8,6,5]=>[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,8,6,5]=>0010101
[1,3,4,2,6,8,7,5]=>[1,4,3,2,7,6,8,5]=>[1,3,4,2,6,8,7,5]=>0010011
[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,7,6,8,5]=>0010011
[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[1,3,4,2,6,7,8,5]=>0010001
[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,7,6,5]=>1010111
[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,8,6,5]=>1010101
[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,6,8,7,5]=>1010011
[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,6,8,5]=>1010011
[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,1,4,3,6,7,8,5]=>1010001
[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,7,6,5]=>0010111
[1,2,4,3,7,8,6,5]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,8,6,5]=>0010101
[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,6,8,7,5]=>0010011
[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,7,6,8,5]=>0010011
[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[1,2,4,3,6,7,8,5]=>0010001
[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,7,6,5]=>1100111
[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,6,8,7,5]=>1100011
[3,2,1,4,7,6,8,5]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,7,6,8,5]=>1100011
[2,3,1,4,8,7,6,5]=>[3,2,1,4,6,7,8,5]=>[2,3,1,4,8,7,6,5]=>0100111
[2,3,1,4,7,8,6,5]=>[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,8,6,5]=>0100101
[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,7,6,8,5]=>0100011
[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[2,3,1,4,6,7,8,5]=>0100001
[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,7,6,5]=>0100111
[1,3,2,4,6,8,7,5]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,6,8,7,5]=>0100011
[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,7,6,8,5]=>0100011
[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>[1,3,2,4,6,7,8,5]=>0100001
[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,7,6,5]=>1000111
[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,7,6,8,5]=>1000011
[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[2,1,3,4,6,7,8,5]=>1000001
[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,7,6,5]=>0000111
[1,2,3,4,7,8,6,5]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,8,6,5]=>0000101
[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,6,8,7,5]=>0000011
[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,7,6,8,5]=>0000011
[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[1,2,3,4,6,7,8,5]=>0000001
[5,4,3,2,1,8,7,6]=>[2,3,4,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>1111011
[5,4,3,2,1,7,8,6]=>[2,3,4,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]=>1111001
[3,5,4,2,1,8,7,6]=>[2,4,3,5,1,7,8,6]=>[3,5,4,2,1,8,7,6]=>1011011
[3,5,4,2,1,7,8,6]=>[2,4,3,5,1,8,7,6]=>[3,5,4,2,1,7,8,6]=>1011001
[4,3,5,2,1,8,7,6]=>[2,5,4,3,1,7,8,6]=>[4,3,5,2,1,8,7,6]=>1011011
[3,4,5,2,1,7,8,6]=>[2,5,3,4,1,8,7,6]=>[3,4,5,2,1,7,8,6]=>1001001
[2,5,4,3,1,7,8,6]=>[3,2,4,5,1,8,7,6]=>[2,5,4,3,1,7,8,6]=>0111001
[2,4,5,3,1,8,7,6]=>[3,2,5,4,1,7,8,6]=>[2,4,5,3,1,8,7,6]=>0101011
[2,4,5,3,1,7,8,6]=>[3,2,5,4,1,8,7,6]=>[2,4,5,3,1,7,8,6]=>0101001
[3,2,5,4,1,8,7,6]=>[4,3,2,5,1,7,8,6]=>[3,2,5,4,1,8,7,6]=>0111011
[3,2,5,4,1,7,8,6]=>[4,3,2,5,1,8,7,6]=>[3,2,5,4,1,7,8,6]=>0111001
[2,3,5,4,1,8,7,6]=>[4,2,3,5,1,7,8,6]=>[2,3,5,4,1,8,7,6]=>0011011
[4,3,2,5,1,8,7,6]=>[5,3,4,2,1,7,8,6]=>[4,3,2,5,1,8,7,6]=>0111011
[4,3,2,5,1,7,8,6]=>[5,3,4,2,1,8,7,6]=>[4,3,2,5,1,7,8,6]=>0111001
[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]=>[3,4,2,5,1,8,7,6]=>0011011
[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[3,4,2,5,1,7,8,6]=>0011001
[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>[2,4,3,5,1,7,8,6]=>0011001
[2,3,4,5,1,8,7,6]=>[5,2,3,4,1,7,8,6]=>[2,3,4,5,1,8,7,6]=>0001011
[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>[2,3,4,5,1,7,8,6]=>0001001
[1,5,4,3,2,8,7,6]=>[1,3,4,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>0111011
[1,5,4,3,2,7,8,6]=>[1,3,4,5,2,8,7,6]=>[1,5,4,3,2,7,8,6]=>0111001
[1,4,5,3,2,8,7,6]=>[1,3,5,4,2,7,8,6]=>[1,4,5,3,2,8,7,6]=>0101011
[1,3,5,4,2,7,8,6]=>[1,4,3,5,2,8,7,6]=>[1,3,5,4,2,7,8,6]=>0011001
[1,4,3,5,2,8,7,6]=>[1,5,4,3,2,7,8,6]=>[1,4,3,5,2,8,7,6]=>0011011
[1,4,3,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>[1,4,3,5,2,7,8,6]=>0011001
[1,3,4,5,2,8,7,6]=>[1,5,3,4,2,7,8,6]=>[1,3,4,5,2,8,7,6]=>0001011
[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[1,3,4,5,2,7,8,6]=>0001001
[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>0011011
[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,7,8,6]=>0011001
[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,7,6]=>0001011
[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]=>0001001
[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>0101011
[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>0101001
[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>1001011
[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]=>1001001
[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>0001011
[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>0001001
[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>1110011
[4,3,2,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>1110001
[2,4,3,1,5,8,7,6]=>[3,2,4,1,5,7,8,6]=>[2,4,3,1,5,8,7,6]=>0110011
[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>0110011
[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[3,2,4,1,5,7,8,6]=>0110001
[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>0010011
[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>0010001
[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>0110011
[1,4,3,2,5,7,8,6]=>[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,7,8,6]=>0110001
[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,7,8,6]=>[1,3,4,2,5,8,7,6]=>0010011
[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>0010001
[2,1,4,3,5,8,7,6]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>1010011
[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>[2,1,4,3,5,7,8,6]=>1010001
[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>0010011
[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,7,8,6]=>0010001
[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>1100011
[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>0100001
[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>0100011
[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]=>0100001
[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>1000011
[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]=>1000001
[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>0000011
[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>0000001
[6,5,4,3,2,1,8,7]=>[2,3,4,5,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>1111101
[5,4,6,3,2,1,8,7]=>[2,3,6,5,4,1,8,7]=>[5,4,6,3,2,1,8,7]=>1101101
[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]=>[4,5,6,3,2,1,8,7]=>1100101
[3,6,5,4,2,1,8,7]=>[2,4,3,5,6,1,8,7]=>[3,6,5,4,2,1,8,7]=>1011101
[3,5,6,4,2,1,8,7]=>[2,4,3,6,5,1,8,7]=>[3,5,6,4,2,1,8,7]=>1010101
[4,3,6,5,2,1,8,7]=>[2,5,4,3,6,1,8,7]=>[4,3,6,5,2,1,8,7]=>1011101
[5,4,3,6,2,1,8,7]=>[2,6,4,5,3,1,8,7]=>[5,4,3,6,2,1,8,7]=>1011101
[4,5,3,6,2,1,8,7]=>[2,6,5,4,3,1,8,7]=>[4,5,3,6,2,1,8,7]=>1001101
[4,3,5,6,2,1,8,7]=>[2,6,4,3,5,1,8,7]=>[4,3,5,6,2,1,8,7]=>1010101
[2,4,6,5,3,1,8,7]=>[3,2,5,4,6,1,8,7]=>[2,4,6,5,3,1,8,7]=>0101101
[3,2,6,5,4,1,8,7]=>[4,3,2,5,6,1,8,7]=>[3,2,6,5,4,1,8,7]=>0111101
[3,2,5,6,4,1,8,7]=>[4,3,2,6,5,1,8,7]=>[3,2,5,6,4,1,8,7]=>0110101
[2,3,6,5,4,1,8,7]=>[4,2,3,5,6,1,8,7]=>[2,3,6,5,4,1,8,7]=>0011101
[2,3,5,6,4,1,8,7]=>[4,2,3,6,5,1,8,7]=>[2,3,5,6,4,1,8,7]=>0010101
[4,3,2,6,5,1,8,7]=>[5,3,4,2,6,1,8,7]=>[4,3,2,6,5,1,8,7]=>0111101
[3,4,2,6,5,1,8,7]=>[5,4,3,2,6,1,8,7]=>[3,4,2,6,5,1,8,7]=>0011101
[2,4,3,6,5,1,8,7]=>[5,2,4,3,6,1,8,7]=>[2,4,3,6,5,1,8,7]=>0011101
[5,4,3,2,6,1,8,7]=>[6,3,4,5,2,1,8,7]=>[5,4,3,2,6,1,8,7]=>0111101
[4,5,3,2,6,1,8,7]=>[6,3,5,4,2,1,8,7]=>[4,5,3,2,6,1,8,7]=>0101101
[3,5,4,2,6,1,8,7]=>[6,4,3,5,2,1,8,7]=>[3,5,4,2,6,1,8,7]=>0011101
[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[4,3,5,2,6,1,8,7]=>0011101
[3,4,5,2,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>[3,4,5,2,6,1,8,7]=>0001101
[2,5,4,3,6,1,8,7]=>[6,2,4,5,3,1,8,7]=>[2,5,4,3,6,1,8,7]=>0011101
[2,4,5,3,6,1,8,7]=>[6,2,5,4,3,1,8,7]=>[2,4,5,3,6,1,8,7]=>0001101
[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>[3,2,5,4,6,1,8,7]=>0101101
[4,3,2,5,6,1,8,7]=>[6,3,4,2,5,1,8,7]=>[4,3,2,5,6,1,8,7]=>0110101
[3,4,2,5,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[3,4,2,5,6,1,8,7]=>0010101
[2,4,3,5,6,1,8,7]=>[6,2,4,3,5,1,8,7]=>[2,4,3,5,6,1,8,7]=>0010101
[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[2,3,4,5,6,1,8,7]=>0000101
[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]=>[1,6,5,4,3,2,8,7]=>0111101
[1,5,4,6,3,2,8,7]=>[1,3,6,5,4,2,8,7]=>[1,5,4,6,3,2,8,7]=>0101101
[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>1011101
[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>[2,1,5,6,4,3,8,7]=>1010101
[2,1,4,6,5,3,8,7]=>[2,1,5,4,6,3,8,7]=>[2,1,4,6,5,3,8,7]=>1001101
[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,5,4,6,3,8,7]=>1001101
[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,4,5,6,3,8,7]=>1000101
[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>0101101
[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]=>0100101
[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>1001101
[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]=>1000101
[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>0001101
[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>0000101
[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>1110101
[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>1010101
[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>0110101
[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>0110101
[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>0010101
[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>1010101
[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>0010101
[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>0100101
[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>1000101
[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>0000101
[5,4,3,2,1,6,8,7]=>[2,3,4,5,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>1111001
[4,5,3,2,1,6,8,7]=>[2,3,5,4,1,6,8,7]=>[4,5,3,2,1,6,8,7]=>1101001
[3,5,4,2,1,6,8,7]=>[2,4,3,5,1,6,8,7]=>[3,5,4,2,1,6,8,7]=>1011001
[4,3,5,2,1,6,8,7]=>[2,5,4,3,1,6,8,7]=>[4,3,5,2,1,6,8,7]=>1011001
[2,4,5,3,1,6,8,7]=>[3,2,5,4,1,6,8,7]=>[2,4,5,3,1,6,8,7]=>0101001
[2,3,5,4,1,6,8,7]=>[4,2,3,5,1,6,8,7]=>[2,3,5,4,1,6,8,7]=>0011001
[2,4,3,5,1,6,8,7]=>[5,2,4,3,1,6,8,7]=>[2,4,3,5,1,6,8,7]=>0011001
[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>[2,3,4,5,1,6,8,7]=>0001001
[1,4,5,3,2,6,8,7]=>[1,3,5,4,2,6,8,7]=>[1,4,5,3,2,6,8,7]=>0101001
[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>1011001
[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>1001001
[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>1001001
[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>0001001
[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>1110001
[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>0110001
[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>0110001
[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>0010001
[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>1010001
[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>0010001
[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>1100001
[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]=>0100001
[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>0100001
[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>1000001
[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>0000001
[5,7,6,4,3,2,1,8]=>[2,3,4,6,5,7,1,8]=>[5,7,6,4,3,2,1,8]=>1110110
[4,7,6,5,3,2,1,8]=>[2,3,5,4,6,7,1,8]=>[4,7,6,5,3,2,1,8]=>1101110
[3,5,7,6,4,2,1,8]=>[2,4,3,6,5,7,1,8]=>[3,5,7,6,4,2,1,8]=>1010110
[4,3,7,6,5,2,1,8]=>[2,5,4,3,6,7,1,8]=>[4,3,7,6,5,2,1,8]=>1011110
[3,4,7,6,5,2,1,8]=>[2,5,3,4,6,7,1,8]=>[3,4,7,6,5,2,1,8]=>1001110
[3,5,6,4,7,2,1,8]=>[2,7,3,6,5,4,1,8]=>[3,5,6,4,7,2,1,8]=>1000110
[2,7,6,5,4,3,1,8]=>[3,2,4,5,6,7,1,8]=>[2,7,6,5,4,3,1,8]=>0111110
[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]=>[2,4,6,7,5,3,1,8]=>0101010
[2,5,4,7,6,3,1,8]=>[3,2,6,5,4,7,1,8]=>[2,5,4,7,6,3,1,8]=>0101110
[2,5,6,4,7,3,1,8]=>[3,2,7,6,5,4,1,8]=>[2,5,6,4,7,3,1,8]=>0100110
[2,5,4,6,7,3,1,8]=>[3,2,7,5,4,6,1,8]=>[2,5,4,6,7,3,1,8]=>0101010
[2,4,5,6,7,3,1,8]=>[3,2,7,4,5,6,1,8]=>[2,4,5,6,7,3,1,8]=>0100010
[3,2,7,6,5,4,1,8]=>[4,3,2,5,6,7,1,8]=>[3,2,7,6,5,4,1,8]=>0111110
[3,2,6,7,5,4,1,8]=>[4,3,2,5,7,6,1,8]=>[3,2,6,7,5,4,1,8]=>0111010
[3,2,5,7,6,4,1,8]=>[4,3,2,6,5,7,1,8]=>[3,2,5,7,6,4,1,8]=>0110110
[2,3,7,6,5,4,1,8]=>[4,2,3,5,6,7,1,8]=>[2,3,7,6,5,4,1,8]=>0011110
[2,3,6,7,5,4,1,8]=>[4,2,3,5,7,6,1,8]=>[2,3,6,7,5,4,1,8]=>0011010
[2,3,5,6,7,4,1,8]=>[4,2,3,7,5,6,1,8]=>[2,3,5,6,7,4,1,8]=>0010010
[4,3,2,6,7,5,1,8]=>[5,3,4,2,7,6,1,8]=>[4,3,2,6,7,5,1,8]=>0111010
[3,4,2,7,6,5,1,8]=>[5,4,3,2,6,7,1,8]=>[3,4,2,7,6,5,1,8]=>0011110
[3,4,2,6,7,5,1,8]=>[5,4,3,2,7,6,1,8]=>[3,4,2,6,7,5,1,8]=>0011010
[3,2,4,6,7,5,1,8]=>[5,3,2,4,7,6,1,8]=>[3,2,4,6,7,5,1,8]=>0101010
[2,3,4,7,6,5,1,8]=>[5,2,3,4,6,7,1,8]=>[2,3,4,7,6,5,1,8]=>0001110
[2,3,4,6,7,5,1,8]=>[5,2,3,4,7,6,1,8]=>[2,3,4,6,7,5,1,8]=>0001010
[5,4,3,2,7,6,1,8]=>[6,3,4,5,2,7,1,8]=>[5,4,3,2,7,6,1,8]=>0111110
[4,5,3,2,7,6,1,8]=>[6,3,5,4,2,7,1,8]=>[4,5,3,2,7,6,1,8]=>0101110
[4,3,5,2,7,6,1,8]=>[6,5,4,3,2,7,1,8]=>[4,3,5,2,7,6,1,8]=>0011110
[3,2,5,4,7,6,1,8]=>[6,3,2,5,4,7,1,8]=>[3,2,5,4,7,6,1,8]=>0101110
[2,3,4,5,7,6,1,8]=>[6,2,3,4,5,7,1,8]=>[2,3,4,5,7,6,1,8]=>0000110
[3,5,6,4,2,7,1,8]=>[7,4,3,6,5,2,1,8]=>[3,5,6,4,2,7,1,8]=>0010110
[3,5,4,6,2,7,1,8]=>[7,6,3,5,4,2,1,8]=>[3,5,4,6,2,7,1,8]=>0001110
[2,5,4,6,3,7,1,8]=>[7,2,6,5,4,3,1,8]=>[2,5,4,6,3,7,1,8]=>0001110
[2,3,5,6,4,7,1,8]=>[7,2,3,6,5,4,1,8]=>[2,3,5,6,4,7,1,8]=>0000110
[4,3,2,6,5,7,1,8]=>[7,3,4,2,6,5,1,8]=>[4,3,2,6,5,7,1,8]=>0110110
[3,4,2,6,5,7,1,8]=>[7,4,3,2,6,5,1,8]=>[3,4,2,6,5,7,1,8]=>0010110
[2,4,3,6,5,7,1,8]=>[7,2,4,3,6,5,1,8]=>[2,4,3,6,5,7,1,8]=>0010110
[2,3,4,6,5,7,1,8]=>[7,2,3,4,6,5,1,8]=>[2,3,4,6,5,7,1,8]=>0000110
[3,5,4,2,6,7,1,8]=>[7,4,3,5,2,6,1,8]=>[3,5,4,2,6,7,1,8]=>0011010
[2,5,4,3,6,7,1,8]=>[7,2,4,5,3,6,1,8]=>[2,5,4,3,6,7,1,8]=>0011010
[2,4,5,3,6,7,1,8]=>[7,2,5,4,3,6,1,8]=>[2,4,5,3,6,7,1,8]=>0001010
[2,3,5,4,6,7,1,8]=>[7,2,3,5,4,6,1,8]=>[2,3,5,4,6,7,1,8]=>0001010
[1,7,6,5,4,3,2,8]=>[1,3,4,5,6,7,2,8]=>[1,7,6,5,4,3,2,8]=>0111110
[1,6,7,5,4,3,2,8]=>[1,3,4,5,7,6,2,8]=>[1,6,7,5,4,3,2,8]=>0111010
[1,4,7,6,5,3,2,8]=>[1,3,5,4,6,7,2,8]=>[1,4,7,6,5,3,2,8]=>0101110
[1,4,6,7,5,3,2,8]=>[1,3,5,4,7,6,2,8]=>[1,4,6,7,5,3,2,8]=>0101010
[1,5,4,7,6,3,2,8]=>[1,3,6,5,4,7,2,8]=>[1,5,4,7,6,3,2,8]=>0101110
[1,5,6,4,7,3,2,8]=>[1,3,7,6,5,4,2,8]=>[1,5,6,4,7,3,2,8]=>0100110
[1,4,5,6,7,3,2,8]=>[1,3,7,4,5,6,2,8]=>[1,4,5,6,7,3,2,8]=>0100010
[1,3,7,6,5,4,2,8]=>[1,4,3,5,6,7,2,8]=>[1,3,7,6,5,4,2,8]=>0011110
[1,3,6,7,5,4,2,8]=>[1,4,3,5,7,6,2,8]=>[1,3,6,7,5,4,2,8]=>0011010
[1,3,5,7,6,4,2,8]=>[1,4,3,6,5,7,2,8]=>[1,3,5,7,6,4,2,8]=>0010110
[1,3,4,6,7,5,2,8]=>[1,5,3,4,7,6,2,8]=>[1,3,4,6,7,5,2,8]=>0001010
[1,5,4,6,3,7,2,8]=>[1,7,6,5,4,3,2,8]=>[1,5,4,6,3,7,2,8]=>0001110
[1,4,5,6,3,7,2,8]=>[1,7,6,4,5,3,2,8]=>[1,4,5,6,3,7,2,8]=>0000110
[1,3,5,6,4,7,2,8]=>[1,7,3,6,5,4,2,8]=>[1,3,5,6,4,7,2,8]=>0000110
[1,4,5,3,6,7,2,8]=>[1,7,5,4,3,6,2,8]=>[1,4,5,3,6,7,2,8]=>0001010
[1,3,5,4,6,7,2,8]=>[1,7,3,5,4,6,2,8]=>[1,3,5,4,6,7,2,8]=>0001010
[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>[1,3,4,5,6,7,2,8]=>0000010
[2,1,7,6,5,4,3,8]=>[2,1,4,5,6,7,3,8]=>[2,1,7,6,5,4,3,8]=>1011110
[1,2,7,6,5,4,3,8]=>[1,2,4,5,6,7,3,8]=>[1,2,7,6,5,4,3,8]=>0011110
[1,2,5,7,6,4,3,8]=>[1,2,4,6,5,7,3,8]=>[1,2,5,7,6,4,3,8]=>0010110
[1,2,5,6,4,7,3,8]=>[1,2,7,6,5,4,3,8]=>[1,2,5,6,4,7,3,8]=>0000110
[1,2,5,4,6,7,3,8]=>[1,2,7,5,4,6,3,8]=>[1,2,5,4,6,7,3,8]=>0001010
[3,2,1,7,6,5,4,8]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,6,5,4,8]=>1101110
[3,2,1,5,7,6,4,8]=>[2,3,1,6,5,7,4,8]=>[3,2,1,5,7,6,4,8]=>1100110
[3,2,1,5,6,7,4,8]=>[2,3,1,7,5,6,4,8]=>[3,2,1,5,6,7,4,8]=>1100010
[2,3,1,6,7,5,4,8]=>[3,2,1,5,7,6,4,8]=>[2,3,1,6,7,5,4,8]=>0101010
[2,3,1,6,5,7,4,8]=>[3,2,1,7,6,5,4,8]=>[2,3,1,6,5,7,4,8]=>0100110
[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[2,3,1,5,6,7,4,8]=>0100010
[1,3,2,7,6,5,4,8]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,6,5,4,8]=>0101110
[1,3,2,6,7,5,4,8]=>[1,3,2,5,7,6,4,8]=>[1,3,2,6,7,5,4,8]=>0101010
[1,3,2,5,7,6,4,8]=>[1,3,2,6,5,7,4,8]=>[1,3,2,5,7,6,4,8]=>0100110
[1,3,2,6,5,7,4,8]=>[1,3,2,7,6,5,4,8]=>[1,3,2,6,5,7,4,8]=>0100110
[1,2,3,7,6,5,4,8]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,6,5,4,8]=>0001110
[1,2,3,6,7,5,4,8]=>[1,2,3,5,7,6,4,8]=>[1,2,3,6,7,5,4,8]=>0001010
[1,2,3,5,7,6,4,8]=>[1,2,3,6,5,7,4,8]=>[1,2,3,5,7,6,4,8]=>0000110
[1,2,3,6,5,7,4,8]=>[1,2,3,7,6,5,4,8]=>[1,2,3,6,5,7,4,8]=>0000110
[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[1,2,3,5,6,7,4,8]=>0000010
[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>1110110
[4,3,2,1,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>1110010
[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>[3,2,4,1,7,6,5,8]=>0110110
[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[3,2,4,1,6,7,5,8]=>0110010
[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>0010010
[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>0110110
[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>0010010
[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>1100110
[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>0100010
[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>0100110
[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>0000110
[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>0000010
[5,4,3,2,1,7,6,8]=>[2,3,4,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>1111010
[4,5,3,2,1,7,6,8]=>[2,3,5,4,1,7,6,8]=>[4,5,3,2,1,7,6,8]=>1101010
[3,5,4,2,1,7,6,8]=>[2,4,3,5,1,7,6,8]=>[3,5,4,2,1,7,6,8]=>1011010
[2,4,5,3,1,7,6,8]=>[3,2,5,4,1,7,6,8]=>[2,4,5,3,1,7,6,8]=>0101010
[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[3,4,2,5,1,7,6,8]=>0011010
[2,4,3,5,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>[2,4,3,5,1,7,6,8]=>0011010
[1,5,4,3,2,7,6,8]=>[1,3,4,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>0111010
[1,4,5,3,2,7,6,8]=>[1,3,5,4,2,7,6,8]=>[1,4,5,3,2,7,6,8]=>0101010
[1,3,5,4,2,7,6,8]=>[1,4,3,5,2,7,6,8]=>[1,3,5,4,2,7,6,8]=>0011010
[1,4,3,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>[1,4,3,5,2,7,6,8]=>0011010
[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>1101010
[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>0101010
[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>0101010
[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>0001010
[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>1110010
[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[3,2,4,1,5,7,6,8]=>0110010
[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>0010010
[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>0110010
[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>0010010
[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>0010010
[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>1100010
[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]=>0100010
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>0100010
[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>1000010
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>0000010
[2,4,5,6,3,1,7,8]=>[3,2,6,4,5,1,7,8]=>[2,4,5,6,3,1,7,8]=>0100100
[2,3,6,5,4,1,7,8]=>[4,2,3,5,6,1,7,8]=>[2,3,6,5,4,1,7,8]=>0011100
[2,3,5,6,4,1,7,8]=>[4,2,3,6,5,1,7,8]=>[2,3,5,6,4,1,7,8]=>0010100
[2,4,3,6,5,1,7,8]=>[5,2,4,3,6,1,7,8]=>[2,4,3,6,5,1,7,8]=>0011100
[2,3,4,6,5,1,7,8]=>[5,2,3,4,6,1,7,8]=>[2,3,4,6,5,1,7,8]=>0001100
[2,3,5,4,6,1,7,8]=>[6,2,3,5,4,1,7,8]=>[2,3,5,4,6,1,7,8]=>0001100
[1,6,5,4,3,2,7,8]=>[1,3,4,5,6,2,7,8]=>[1,6,5,4,3,2,7,8]=>0111100
[1,4,6,5,3,2,7,8]=>[1,3,5,4,6,2,7,8]=>[1,4,6,5,3,2,7,8]=>0101100
[1,3,5,6,4,2,7,8]=>[1,4,3,6,5,2,7,8]=>[1,3,5,6,4,2,7,8]=>0010100
[1,4,3,6,5,2,7,8]=>[1,5,4,3,6,2,7,8]=>[1,4,3,6,5,2,7,8]=>0011100
[1,5,4,3,6,2,7,8]=>[1,6,4,5,3,2,7,8]=>[1,5,4,3,6,2,7,8]=>0011100
[1,4,5,3,6,2,7,8]=>[1,6,5,4,3,2,7,8]=>[1,4,5,3,6,2,7,8]=>0001100
[1,3,5,4,6,2,7,8]=>[1,6,3,5,4,2,7,8]=>[1,3,5,4,6,2,7,8]=>0001100
[1,4,3,5,6,2,7,8]=>[1,6,4,3,5,2,7,8]=>[1,4,3,5,6,2,7,8]=>0010100
[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[1,3,4,5,6,2,7,8]=>0000100
[2,1,5,6,4,3,7,8]=>[2,1,4,6,5,3,7,8]=>[2,1,5,6,4,3,7,8]=>1010100
[1,2,6,5,4,3,7,8]=>[1,2,4,5,6,3,7,8]=>[1,2,6,5,4,3,7,8]=>0011100
[1,2,5,6,4,3,7,8]=>[1,2,4,6,5,3,7,8]=>[1,2,5,6,4,3,7,8]=>0010100
[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>[1,2,4,5,6,3,7,8]=>0000100
[3,2,1,6,5,4,7,8]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>1101100
[3,2,1,5,6,4,7,8]=>[2,3,1,6,5,4,7,8]=>[3,2,1,5,6,4,7,8]=>1100100
[2,3,1,6,5,4,7,8]=>[3,2,1,5,6,4,7,8]=>[2,3,1,6,5,4,7,8]=>0101100
[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[2,3,1,5,6,4,7,8]=>0100100
[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>0101100
[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]=>0100100
[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>0001100
[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>0000100
[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>1110100
[2,4,3,1,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>[2,4,3,1,6,5,7,8]=>0110100
[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>0110100
[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>0010100
[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>1010100
[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>0010100
[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>0100100
[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>1000100
[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>0000100
[3,5,4,2,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>[3,5,4,2,1,6,7,8]=>1011000
[2,5,4,3,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>0111000
[2,4,5,3,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>0101000
[3,2,5,4,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>0111000
[2,3,5,4,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>0011000
[2,4,3,5,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>0011000
[1,5,4,3,2,6,7,8]=>[1,3,4,5,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>0111000
[1,4,5,3,2,6,7,8]=>[1,3,5,4,2,6,7,8]=>[1,4,5,3,2,6,7,8]=>0101000
[1,3,5,4,2,6,7,8]=>[1,4,3,5,2,6,7,8]=>[1,3,5,4,2,6,7,8]=>0011000
[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[1,3,4,5,2,6,7,8]=>0001000
[2,1,5,4,3,6,7,8]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>1011000
[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[2,1,4,5,3,6,7,8]=>1001000
[1,2,5,4,3,6,7,8]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>0011000
[3,2,1,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>1101000
[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>0101000
[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>0101000
[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>1001000
[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000
[2,4,3,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>0110000
[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000
[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>0010000
[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>1010000
[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000
[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000
[1,2,3,4,8,6,7,5]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,6,7,5]=>0000011
[1,2,3,5,8,6,7,4]=>[1,2,3,7,5,8,6,4]=>[1,2,3,5,8,6,7,4]=>0000011
[1,2,3,7,5,6,4,8]=>[1,2,3,6,7,5,4,8]=>[1,2,3,7,5,6,4,8]=>0000110
[1,2,3,7,5,6,8,4]=>[1,2,3,8,7,5,6,4]=>[1,2,3,7,5,6,8,4]=>0000011
[1,2,3,8,5,6,7,4]=>[1,2,3,7,8,5,6,4]=>[1,2,3,8,5,6,7,4]=>0000011
[1,2,3,8,5,7,6,4]=>[1,2,3,6,7,8,4,5]=>[1,2,3,8,4,7,6,5]=>0000111
[1,2,3,8,6,5,7,4]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,6,5,7,4]=>0000111
[1,2,3,8,6,7,5,4]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,6,7,5,4]=>0001011
[1,2,4,3,8,6,7,5]=>[1,2,4,3,7,8,6,5]=>[1,2,4,3,8,6,7,5]=>0010011
[1,2,4,8,5,6,7,3]=>[1,2,7,4,8,5,6,3]=>[1,2,4,8,5,6,7,3]=>0000011
[1,2,4,8,5,7,6,3]=>[1,2,6,4,7,8,3,5]=>[1,2,4,8,3,7,6,5]=>0000111
[1,2,4,8,6,5,7,3]=>[1,2,7,4,6,8,5,3]=>[1,2,4,8,6,5,7,3]=>0000111
[1,2,5,4,8,6,7,3]=>[1,2,7,5,4,8,6,3]=>[1,2,5,4,8,6,7,3]=>0001011
[1,2,6,4,5,3,7,8]=>[1,2,5,6,4,3,7,8]=>[1,2,6,4,5,3,7,8]=>0001100
[1,2,6,4,5,7,8,3]=>[1,2,8,6,4,5,7,3]=>[1,2,6,4,5,7,8,3]=>0000101
[1,2,6,4,5,8,7,3]=>[1,2,7,6,4,5,8,3]=>[1,2,6,4,5,8,7,3]=>0000111
[1,2,7,4,5,6,8,3]=>[1,2,8,7,4,5,6,3]=>[1,2,7,4,5,6,8,3]=>0000011
[1,2,8,4,5,6,7,3]=>[1,2,7,8,4,5,6,3]=>[1,2,8,4,5,6,7,3]=>0000011
[1,2,8,4,5,7,6,3]=>[1,2,6,7,3,8,5,4]=>[1,2,8,3,5,7,6,4]=>0000111
[1,2,8,4,7,6,5,3]=>[1,2,5,6,7,8,4,3]=>[1,2,8,4,7,6,5,3]=>0001111
[1,2,7,5,4,6,8,3]=>[1,2,8,5,7,4,6,3]=>[1,2,7,5,4,6,8,3]=>0001011
[1,2,8,5,6,4,7,3]=>[1,2,7,6,8,5,4,3]=>[1,2,8,5,6,4,7,3]=>0000111
[1,2,8,5,6,7,4,3]=>[1,2,4,7,8,5,6,3]=>[1,2,8,5,6,7,4,3]=>0010011
[1,2,8,5,7,6,4,3]=>[1,2,4,6,7,8,3,5]=>[1,2,8,4,3,7,6,5]=>0010111
[1,2,8,6,5,4,7,3]=>[1,2,7,5,6,8,4,3]=>[1,2,8,6,5,4,7,3]=>0001111
[1,2,8,6,5,7,4,3]=>[1,2,4,7,6,8,5,3]=>[1,2,8,6,5,7,4,3]=>0010111
[1,3,2,8,6,5,7,4]=>[1,3,2,7,6,8,5,4]=>[1,3,2,8,6,5,7,4]=>0100111
[1,3,2,8,6,7,5,4]=>[1,3,2,5,7,8,6,4]=>[1,3,2,8,6,7,5,4]=>0101011
[1,3,4,8,6,5,7,2]=>[1,7,3,4,6,8,5,2]=>[1,3,4,8,6,5,7,2]=>0000111
[1,3,4,8,6,7,5,2]=>[1,5,3,4,7,8,6,2]=>[1,3,4,8,6,7,5,2]=>0001011
[1,3,6,4,5,7,8,2]=>[1,8,3,6,4,5,7,2]=>[1,3,6,4,5,7,8,2]=>0000101
[1,3,6,4,5,8,7,2]=>[1,7,3,6,4,5,8,2]=>[1,3,6,4,5,8,7,2]=>0000111
[1,3,7,4,5,6,2,8]=>[1,6,3,7,4,5,2,8]=>[1,3,7,4,5,6,2,8]=>0000110
[1,3,7,4,5,6,8,2]=>[1,8,3,7,4,5,6,2]=>[1,3,7,4,5,6,8,2]=>0000011
[1,3,8,4,5,6,7,2]=>[1,7,3,8,4,5,6,2]=>[1,3,8,4,5,6,7,2]=>0000011
[1,3,8,4,6,5,7,2]=>[1,7,3,8,6,4,5,2]=>[1,3,6,4,8,5,7,2]=>0000111
[1,3,8,5,4,6,7,2]=>[1,7,3,5,8,4,6,2]=>[1,3,8,5,4,6,7,2]=>0001011
[1,3,8,5,4,7,6,2]=>[1,6,3,5,7,8,2,4]=>[1,3,8,5,2,7,6,4]=>0001111
[1,3,8,5,6,7,4,2]=>[1,4,3,7,8,5,6,2]=>[1,3,8,5,6,7,4,2]=>0010011
[1,3,8,6,5,7,4,2]=>[1,4,3,7,6,8,5,2]=>[1,3,8,6,5,7,4,2]=>0010111
[1,3,8,7,5,6,4,2]=>[1,4,3,6,7,5,8,2]=>[1,3,8,7,5,6,4,2]=>0010111
[1,4,3,2,8,6,7,5]=>[1,3,4,2,7,8,6,5]=>[1,4,3,2,8,6,7,5]=>0110011
[1,4,3,8,6,5,7,2]=>[1,7,4,3,6,8,5,2]=>[1,4,3,8,6,5,7,2]=>0010111
[1,5,3,4,2,6,7,8]=>[1,4,5,3,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>0011000
[1,5,3,4,2,7,8,6]=>[1,4,5,3,2,8,7,6]=>[1,5,3,4,2,7,8,6]=>0011001
[1,5,3,4,2,8,7,6]=>[1,4,5,3,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>0011011
[1,5,3,4,6,7,8,2]=>[1,8,5,3,4,6,7,2]=>[1,5,3,4,6,7,8,2]=>0001001
[1,5,3,4,8,6,7,2]=>[1,7,5,3,4,8,6,2]=>[1,5,3,4,8,6,7,2]=>0001011
[1,6,3,4,5,2,7,8]=>[1,5,6,3,4,2,7,8]=>[1,6,3,4,5,2,7,8]=>0001100
[1,6,3,4,5,8,7,2]=>[1,7,6,3,4,5,8,2]=>[1,6,3,4,5,8,7,2]=>0000111
[1,7,3,4,5,6,8,2]=>[1,8,7,3,4,5,6,2]=>[1,7,3,4,5,6,8,2]=>0000011
[1,8,3,4,5,6,7,2]=>[1,7,8,3,4,5,6,2]=>[1,8,3,4,5,6,7,2]=>0000011
[1,8,3,4,5,7,6,2]=>[1,6,7,2,4,8,5,3]=>[1,8,2,4,5,7,6,3]=>0000111
[1,8,3,4,6,7,5,2]=>[1,5,7,2,8,4,6,3]=>[1,8,2,4,6,7,5,3]=>0001011
[1,8,3,4,7,6,5,2]=>[1,5,6,3,7,8,4,2]=>[1,8,3,4,7,6,5,2]=>0001111
[1,7,3,5,6,4,8,2]=>[1,8,7,6,3,5,4,2]=>[1,6,3,5,7,4,8,2]=>0000111
[1,8,3,5,7,6,4,2]=>[1,4,6,7,3,8,5,2]=>[1,8,3,5,7,6,4,2]=>0010111
[1,7,3,6,5,4,2,8]=>[1,4,5,6,7,3,2,8]=>[1,7,3,6,5,4,2,8]=>0011110
[1,8,3,6,5,4,7,2]=>[1,7,8,5,6,3,4,2]=>[1,6,5,3,8,4,7,2]=>0001111
[1,8,3,7,6,5,4,2]=>[1,4,5,6,7,8,2,3]=>[1,8,2,7,6,5,4,3]=>0011111
[1,6,4,3,5,2,7,8]=>[1,5,4,6,3,2,7,8]=>[1,6,4,3,5,2,7,8]=>0011100
[1,8,4,3,5,6,7,2]=>[1,7,4,8,3,5,6,2]=>[1,8,4,3,5,6,7,2]=>0010011
[1,7,4,3,6,5,2,8]=>[1,5,4,6,7,2,3,8]=>[1,7,4,2,6,5,3,8]=>0011110
[1,7,4,3,6,5,8,2]=>[1,8,4,7,6,3,5,2]=>[1,6,4,3,7,5,8,2]=>0010111
[1,8,4,3,6,5,7,2]=>[1,7,4,8,6,3,5,2]=>[1,6,4,3,8,5,7,2]=>0010111
[1,6,4,5,3,2,7,8]=>[1,3,5,6,4,2,7,8]=>[1,6,4,5,3,2,7,8]=>0101100
[1,7,4,5,3,6,8,2]=>[1,8,5,7,4,3,6,2]=>[1,7,4,5,3,6,8,2]=>0001011
[1,8,4,5,3,6,7,2]=>[1,7,5,8,4,3,6,2]=>[1,8,4,5,3,6,7,2]=>0001011
[1,8,4,5,3,7,6,2]=>[1,6,5,7,2,8,3,4]=>[1,8,2,5,3,7,6,4]=>0001111
[1,7,4,5,6,3,8,2]=>[1,8,6,7,4,5,3,2]=>[1,7,4,5,6,3,8,2]=>0000111
[1,8,4,5,6,3,7,2]=>[1,7,6,8,4,5,3,2]=>[1,8,4,5,6,3,7,2]=>0000111
[1,8,4,5,6,7,3,2]=>[1,3,7,8,4,5,6,2]=>[1,8,4,5,6,7,3,2]=>0100011
[1,7,4,6,5,3,8,2]=>[1,8,5,6,7,3,4,2]=>[1,7,3,6,5,4,8,2]=>0001111
[1,8,4,6,5,3,7,2]=>[1,7,5,6,8,3,4,2]=>[1,8,3,6,5,4,7,2]=>0001111
[1,8,4,7,5,6,3,2]=>[1,3,6,8,7,5,4,2]=>[1,7,5,8,4,6,3,2]=>0100111
[1,8,4,7,6,5,3,2]=>[1,3,5,6,7,8,4,2]=>[1,8,4,7,6,5,3,2]=>0101111
[1,7,5,4,3,6,2,8]=>[1,6,4,5,7,3,2,8]=>[1,7,5,4,3,6,2,8]=>0011110
[1,8,5,4,3,6,7,2]=>[1,7,4,5,8,3,6,2]=>[1,8,5,4,3,6,7,2]=>0011011
[1,8,5,4,3,7,6,2]=>[1,6,4,5,7,8,2,3]=>[1,8,5,4,2,7,6,3]=>0011111
[1,8,5,4,6,3,7,2]=>[1,7,6,5,8,4,3,2]=>[1,8,5,4,6,3,7,2]=>0001111
[1,8,5,4,6,7,3,2]=>[1,3,7,5,8,4,6,2]=>[1,8,5,4,6,7,3,2]=>0101011
[1,8,5,4,7,6,3,2]=>[1,3,6,5,7,8,2,4]=>[1,8,5,3,2,7,6,4]=>0101111
[1,7,6,4,5,3,2,8]=>[1,3,5,6,4,7,2,8]=>[1,7,6,4,5,3,2,8]=>0101110
[1,8,6,4,5,3,7,2]=>[1,7,5,6,4,8,3,2]=>[1,8,6,4,5,3,7,2]=>0001111
[1,8,6,4,5,7,3,2]=>[1,3,7,6,4,8,5,2]=>[1,8,6,4,5,7,3,2]=>0100111
[1,8,7,4,5,6,3,2]=>[1,3,6,7,4,5,8,2]=>[1,8,7,4,5,6,3,2]=>0100111
[1,8,6,5,4,3,7,2]=>[1,7,4,5,6,8,3,2]=>[1,8,6,5,4,3,7,2]=>0011111
[1,8,6,5,4,7,3,2]=>[1,3,7,5,6,8,4,2]=>[1,8,6,5,4,7,3,2]=>0101111
[1,8,7,5,4,6,3,2]=>[1,3,6,5,7,4,8,2]=>[1,8,7,5,4,6,3,2]=>0101111
[1,8,7,5,6,4,3,2]=>[1,3,4,6,7,5,8,2]=>[1,8,7,5,6,4,3,2]=>0110111
[2,1,3,4,8,6,7,5]=>[2,1,3,4,7,8,6,5]=>[2,1,3,4,8,6,7,5]=>1000011
[2,1,3,8,5,6,7,4]=>[2,1,3,7,8,5,6,4]=>[2,1,3,8,5,6,7,4]=>1000011
[2,1,3,8,5,7,6,4]=>[2,1,3,6,7,8,4,5]=>[2,1,3,8,4,7,6,5]=>1000111
[2,1,4,3,8,6,7,5]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,6,7,5]=>1010011
[2,1,4,5,8,6,7,3]=>[2,1,7,4,5,8,6,3]=>[2,1,4,5,8,6,7,3]=>1000011
[2,1,4,8,5,6,7,3]=>[2,1,7,4,8,5,6,3]=>[2,1,4,8,5,6,7,3]=>1000011
[2,1,4,8,6,7,5,3]=>[2,1,5,4,7,8,6,3]=>[2,1,4,8,6,7,5,3]=>1001011
[2,1,6,4,5,3,8,7]=>[2,1,5,6,4,3,8,7]=>[2,1,6,4,5,3,8,7]=>1001101
[2,1,6,4,5,7,8,3]=>[2,1,8,6,4,5,7,3]=>[2,1,6,4,5,7,8,3]=>1000101
[2,1,6,4,5,8,7,3]=>[2,1,7,6,4,5,8,3]=>[2,1,6,4,5,8,7,3]=>1000111
[2,1,8,4,5,6,7,3]=>[2,1,7,8,4,5,6,3]=>[2,1,8,4,5,6,7,3]=>1000011
[2,1,8,4,5,7,6,3]=>[2,1,6,7,3,8,5,4]=>[2,1,8,3,5,7,6,4]=>1000111
[2,1,7,4,6,5,8,3]=>[2,1,8,7,6,4,5,3]=>[2,1,6,4,7,5,8,3]=>1000111
[2,1,8,4,6,5,7,3]=>[2,1,7,8,6,4,5,3]=>[2,1,6,4,8,5,7,3]=>1000111
[2,1,8,4,6,7,5,3]=>[2,1,5,7,8,3,6,4]=>[2,1,8,3,6,7,5,4]=>1001011
[2,1,8,4,7,6,5,3]=>[2,1,5,6,7,8,4,3]=>[2,1,8,4,7,6,5,3]=>1001111
[2,1,7,5,4,6,8,3]=>[2,1,8,5,7,4,6,3]=>[2,1,7,5,4,6,8,3]=>1001011
[2,1,8,5,4,6,7,3]=>[2,1,7,5,8,4,6,3]=>[2,1,8,5,4,6,7,3]=>1001011
[2,1,8,5,4,7,6,3]=>[2,1,6,5,7,8,3,4]=>[2,1,8,5,3,7,6,4]=>1001111
[2,1,7,5,6,4,8,3]=>[2,1,8,6,7,5,4,3]=>[2,1,7,5,6,4,8,3]=>1000111
[2,1,8,5,6,7,4,3]=>[2,1,4,7,8,5,6,3]=>[2,1,8,5,6,7,4,3]=>1010011
[2,1,8,5,7,6,4,3]=>[2,1,4,6,7,8,3,5]=>[2,1,8,4,3,7,6,5]=>1010111
[2,1,8,6,5,4,7,3]=>[2,1,7,5,6,8,4,3]=>[2,1,8,6,5,4,7,3]=>1001111
[2,1,8,6,5,7,4,3]=>[2,1,4,7,6,8,5,3]=>[2,1,8,6,5,7,4,3]=>1010111
[2,1,8,7,5,6,4,3]=>[2,1,4,6,7,5,8,3]=>[2,1,8,7,5,6,4,3]=>1010111
[2,3,1,5,8,6,7,4]=>[3,2,1,7,5,8,6,4]=>[2,3,1,5,8,6,7,4]=>0100011
[2,3,1,7,5,6,4,8]=>[3,2,1,6,7,5,4,8]=>[2,3,1,7,5,6,4,8]=>0100110
[2,3,1,8,5,6,7,4]=>[3,2,1,7,8,5,6,4]=>[2,3,1,8,5,6,7,4]=>0100011
[2,3,1,8,5,7,6,4]=>[3,2,1,6,7,8,4,5]=>[2,3,1,8,4,7,6,5]=>0100111
[2,3,1,8,6,7,5,4]=>[3,2,1,5,7,8,6,4]=>[2,3,1,8,6,7,5,4]=>0101011
[2,3,4,1,8,6,7,5]=>[4,2,3,1,7,8,6,5]=>[2,3,4,1,8,6,7,5]=>0010011
[2,3,4,5,8,6,7,1]=>[7,2,3,4,5,8,6,1]=>[2,3,4,5,8,6,7,1]=>0000011
[2,3,4,8,5,6,7,1]=>[7,2,3,4,8,5,6,1]=>[2,3,4,8,5,6,7,1]=>0000011
[2,3,4,8,5,7,6,1]=>[6,2,3,4,7,8,1,5]=>[2,3,4,8,1,7,6,5]=>0000111
[2,3,4,8,6,5,7,1]=>[7,2,3,4,6,8,5,1]=>[2,3,4,8,6,5,7,1]=>0000111
[2,3,4,8,6,7,5,1]=>[5,2,3,4,7,8,6,1]=>[2,3,4,8,6,7,5,1]=>0001011
[2,3,5,4,8,6,7,1]=>[7,2,3,5,4,8,6,1]=>[2,3,5,4,8,6,7,1]=>0001011
[2,3,6,4,5,1,8,7]=>[5,2,3,6,4,1,8,7]=>[2,3,6,4,5,1,8,7]=>0001101
[2,3,7,4,5,6,8,1]=>[8,2,3,7,4,5,6,1]=>[2,3,7,4,5,6,8,1]=>0000011
[2,3,8,4,5,6,7,1]=>[7,2,3,8,4,5,6,1]=>[2,3,8,4,5,6,7,1]=>0000011
[2,3,7,4,6,5,8,1]=>[8,2,3,7,6,4,5,1]=>[2,3,6,4,7,5,8,1]=>0000111
[2,3,8,4,6,7,5,1]=>[5,2,3,7,8,1,6,4]=>[2,3,8,1,6,7,5,4]=>0001011
[2,3,7,5,4,6,1,8]=>[6,2,3,5,7,4,1,8]=>[2,3,7,5,4,6,1,8]=>0001110
[2,3,7,5,6,4,1,8]=>[4,2,3,6,7,5,1,8]=>[2,3,7,5,6,4,1,8]=>0010110
[2,3,8,5,6,4,7,1]=>[7,2,3,6,8,5,4,1]=>[2,3,8,5,6,4,7,1]=>0000111
[2,3,8,5,7,6,4,1]=>[4,2,3,6,7,8,1,5]=>[2,3,8,4,1,7,6,5]=>0010111
[2,3,8,6,5,4,7,1]=>[7,2,3,5,6,8,4,1]=>[2,3,8,6,5,4,7,1]=>0001111
[2,4,3,1,8,6,7,5]=>[3,2,4,1,7,8,6,5]=>[2,4,3,1,8,6,7,5]=>0110011
[2,4,3,7,5,6,8,1]=>[8,2,4,3,7,5,6,1]=>[2,4,3,7,5,6,8,1]=>0010011
[2,4,3,8,5,6,7,1]=>[7,2,4,3,8,5,6,1]=>[2,4,3,8,5,6,7,1]=>0010011
[2,5,3,4,1,6,7,8]=>[4,2,5,3,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>0011000
[2,5,3,4,1,8,7,6]=>[4,2,5,3,1,7,8,6]=>[2,5,3,4,1,8,7,6]=>0011011
[2,5,3,4,6,7,1,8]=>[7,2,5,3,4,6,1,8]=>[2,5,3,4,6,7,1,8]=>0001010
[2,5,3,4,7,6,8,1]=>[8,2,5,3,4,7,6,1]=>[2,5,3,4,7,6,8,1]=>0001011
[2,6,3,4,5,1,7,8]=>[5,2,6,3,4,1,7,8]=>[2,6,3,4,5,1,7,8]=>0001100
[2,6,3,4,5,7,8,1]=>[8,2,6,3,4,5,7,1]=>[2,6,3,4,5,7,8,1]=>0000101
[2,6,3,4,5,8,7,1]=>[7,2,6,3,4,5,8,1]=>[2,6,3,4,5,8,7,1]=>0000111
[2,7,3,4,5,6,1,8]=>[6,2,7,3,4,5,1,8]=>[2,7,3,4,5,6,1,8]=>0000110
[2,8,3,4,5,6,7,1]=>[7,2,8,3,4,5,6,1]=>[2,8,3,4,5,6,7,1]=>0000011
[2,8,3,4,5,7,6,1]=>[6,2,7,1,4,8,5,3]=>[2,8,1,4,5,7,6,3]=>0000111
[2,6,3,5,4,1,8,7]=>[4,2,5,6,1,3,8,7]=>[2,6,1,5,4,3,8,7]=>0011101
[2,8,3,5,7,6,4,1]=>[4,2,6,7,3,8,5,1]=>[2,8,3,5,7,6,4,1]=>0010111
[2,8,3,6,5,4,7,1]=>[7,2,8,5,6,3,4,1]=>[2,6,5,3,8,4,7,1]=>0001111
[2,8,3,6,5,7,4,1]=>[4,2,7,8,6,1,5,3]=>[2,6,1,8,5,7,4,3]=>0010111
[2,8,3,7,6,5,4,1]=>[4,2,5,6,7,8,1,3]=>[2,8,1,7,6,5,4,3]=>0011111
[2,7,4,3,5,6,8,1]=>[8,2,4,7,3,5,6,1]=>[2,7,4,3,5,6,8,1]=>0010011
[2,8,4,3,5,7,6,1]=>[6,2,4,7,1,8,5,3]=>[2,8,4,1,5,7,6,3]=>0010111
[2,7,4,3,6,5,1,8]=>[5,2,4,6,7,1,3,8]=>[2,7,4,1,6,5,3,8]=>0011110
[2,8,4,3,6,5,7,1]=>[7,2,4,8,6,3,5,1]=>[2,6,4,3,8,5,7,1]=>0010111
[2,8,4,3,6,7,5,1]=>[5,2,4,7,8,1,6,3]=>[2,8,4,1,6,7,5,3]=>0011011
[2,6,4,5,3,1,8,7]=>[3,2,5,6,4,1,8,7]=>[2,6,4,5,3,1,8,7]=>0101101
[2,7,4,5,6,3,1,8]=>[3,2,6,7,4,5,1,8]=>[2,7,4,5,6,3,1,8]=>0100110
[2,7,4,5,6,3,8,1]=>[8,2,6,7,4,5,3,1]=>[2,7,4,5,6,3,8,1]=>0000111
[2,8,4,5,6,3,7,1]=>[7,2,6,8,4,5,3,1]=>[2,8,4,5,6,3,7,1]=>0000111
[2,8,4,6,5,7,3,1]=>[3,2,7,8,6,4,5,1]=>[2,6,4,8,5,7,3,1]=>0100111
[2,8,4,7,5,6,3,1]=>[3,2,6,8,7,5,4,1]=>[2,7,5,8,4,6,3,1]=>0100111
[2,8,4,7,6,5,3,1]=>[3,2,5,6,7,8,4,1]=>[2,8,4,7,6,5,3,1]=>0101111
[2,7,5,4,3,6,8,1]=>[8,2,4,5,7,3,6,1]=>[2,7,5,4,3,6,8,1]=>0011011
[2,8,5,4,3,6,7,1]=>[7,2,4,5,8,3,6,1]=>[2,8,5,4,3,6,7,1]=>0011011
[2,8,5,4,3,7,6,1]=>[6,2,4,5,7,8,1,3]=>[2,8,5,4,1,7,6,3]=>0011111
[2,7,5,4,6,3,8,1]=>[8,2,6,5,7,4,3,1]=>[2,7,5,4,6,3,8,1]=>0001111
[2,8,5,4,6,7,3,1]=>[3,2,7,5,8,4,6,1]=>[2,8,5,4,6,7,3,1]=>0101011
[2,8,5,4,7,6,3,1]=>[3,2,6,5,7,8,1,4]=>[2,8,5,3,1,7,6,4]=>0101111
[2,8,7,5,4,6,3,1]=>[3,2,6,5,7,4,8,1]=>[2,8,7,5,4,6,3,1]=>0101111
[3,2,1,4,8,6,7,5]=>[2,3,1,4,7,8,6,5]=>[3,2,1,4,8,6,7,5]=>1100011
[3,2,1,5,8,6,7,4]=>[2,3,1,7,5,8,6,4]=>[3,2,1,5,8,6,7,4]=>1100011
[3,2,1,7,5,6,4,8]=>[2,3,1,6,7,5,4,8]=>[3,2,1,7,5,6,4,8]=>1100110
[3,2,1,7,5,6,8,4]=>[2,3,1,8,7,5,6,4]=>[3,2,1,7,5,6,8,4]=>1100011
[3,2,1,8,5,6,7,4]=>[2,3,1,7,8,5,6,4]=>[3,2,1,8,5,6,7,4]=>1100011
[3,2,1,8,5,7,6,4]=>[2,3,1,6,7,8,4,5]=>[3,2,1,8,4,7,6,5]=>1100111
[3,2,1,8,6,5,7,4]=>[2,3,1,7,6,8,5,4]=>[3,2,1,8,6,5,7,4]=>1100111
[3,2,1,8,6,7,5,4]=>[2,3,1,5,7,8,6,4]=>[3,2,1,8,6,7,5,4]=>1101011
[3,2,4,1,8,6,7,5]=>[4,3,2,1,7,8,6,5]=>[3,2,4,1,8,6,7,5]=>0110011
[3,2,4,8,6,7,5,1]=>[5,3,2,4,7,8,6,1]=>[3,2,4,8,6,7,5,1]=>0101011
[3,2,5,4,8,6,7,1]=>[7,3,2,5,4,8,6,1]=>[3,2,5,4,8,6,7,1]=>0101011
[3,2,7,4,5,6,1,8]=>[6,3,2,7,4,5,1,8]=>[3,2,7,4,5,6,1,8]=>0100110
[3,2,7,4,6,5,8,1]=>[8,3,2,7,6,4,5,1]=>[3,2,6,4,7,5,8,1]=>0100111
[3,2,8,4,6,5,7,1]=>[7,3,2,8,6,4,5,1]=>[3,2,6,4,8,5,7,1]=>0100111
[3,2,7,5,4,6,1,8]=>[6,3,2,5,7,4,1,8]=>[3,2,7,5,4,6,1,8]=>0101110
[3,2,8,5,4,6,7,1]=>[7,3,2,5,8,4,6,1]=>[3,2,8,5,4,6,7,1]=>0101011
[3,2,7,5,6,4,1,8]=>[4,3,2,6,7,5,1,8]=>[3,2,7,5,6,4,1,8]=>0110110
[3,2,7,5,6,4,8,1]=>[8,3,2,6,7,5,4,1]=>[3,2,7,5,6,4,8,1]=>0100111
[3,2,8,5,7,6,4,1]=>[4,3,2,6,7,8,1,5]=>[3,2,8,4,1,7,6,5]=>0110111
[3,2,8,7,5,6,4,1]=>[4,3,2,6,7,5,8,1]=>[3,2,8,7,5,6,4,1]=>0110111
[4,2,3,1,5,7,8,6]=>[3,4,2,1,5,8,7,6]=>[4,2,3,1,5,7,8,6]=>0110001
[4,2,3,1,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>0110101
[4,2,3,1,6,7,8,5]=>[3,4,2,1,8,6,7,5]=>[4,2,3,1,6,7,8,5]=>0110001
[4,2,3,1,6,8,7,5]=>[3,4,2,1,7,6,8,5]=>[4,2,3,1,6,8,7,5]=>0110011
[4,2,3,1,7,6,8,5]=>[3,4,2,1,8,7,6,5]=>[4,2,3,1,7,6,8,5]=>0110011
[4,2,3,1,8,6,7,5]=>[3,4,2,1,7,8,6,5]=>[4,2,3,1,8,6,7,5]=>0110011
[4,2,3,1,8,7,6,5]=>[3,4,2,1,6,7,8,5]=>[4,2,3,1,8,7,6,5]=>0110111
[4,2,3,5,1,6,8,7]=>[5,4,2,3,1,6,8,7]=>[4,2,3,5,1,6,8,7]=>0011001
[4,2,3,5,1,7,8,6]=>[5,4,2,3,1,8,7,6]=>[4,2,3,5,1,7,8,6]=>0011001
[4,2,3,5,1,8,7,6]=>[5,4,2,3,1,7,8,6]=>[4,2,3,5,1,8,7,6]=>0011011
[4,2,3,5,6,1,8,7]=>[6,4,2,3,5,1,8,7]=>[4,2,3,5,6,1,8,7]=>0010101
[4,2,3,5,6,8,7,1]=>[7,4,2,3,5,6,8,1]=>[4,2,3,5,6,8,7,1]=>0010011
[4,2,3,5,7,6,1,8]=>[6,4,2,3,5,7,1,8]=>[4,2,3,5,7,6,1,8]=>0010110
[4,2,3,6,5,1,8,7]=>[5,4,2,3,6,1,8,7]=>[4,2,3,6,5,1,8,7]=>0011101
[4,2,3,7,5,6,8,1]=>[8,4,2,3,7,5,6,1]=>[4,2,3,7,5,6,8,1]=>0010011
[4,2,3,7,6,5,8,1]=>[8,4,2,3,6,7,5,1]=>[4,2,3,7,6,5,8,1]=>0010111
[4,2,3,8,6,7,5,1]=>[5,4,2,3,7,8,6,1]=>[4,2,3,8,6,7,5,1]=>0011011
[4,2,3,8,7,6,5,1]=>[5,4,2,3,6,7,8,1]=>[4,2,3,8,7,6,5,1]=>0011111
[5,2,3,4,1,6,8,7]=>[4,5,2,3,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>0011001
[5,2,3,4,1,7,8,6]=>[4,5,2,3,1,8,7,6]=>[5,2,3,4,1,7,8,6]=>0011001
[5,2,3,4,1,8,7,6]=>[4,5,2,3,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>0011011
[5,2,3,4,8,6,7,1]=>[7,5,2,3,4,8,6,1]=>[5,2,3,4,8,6,7,1]=>0001011
[5,2,3,4,8,7,6,1]=>[6,5,2,3,4,7,8,1]=>[5,2,3,4,8,7,6,1]=>0001111
[6,2,3,4,5,8,7,1]=>[7,6,2,3,4,5,8,1]=>[6,2,3,4,5,8,7,1]=>0000111
[8,2,3,4,5,7,6,1]=>[6,7,1,3,4,8,5,2]=>[8,1,3,4,5,7,6,2]=>0000111
[8,2,3,4,6,7,5,1]=>[5,7,1,3,8,4,6,2]=>[8,1,3,4,6,7,5,2]=>0001011
[6,2,3,5,4,1,7,8]=>[4,5,1,6,3,2,7,8]=>[6,1,3,5,4,2,7,8]=>0011100
[6,2,3,5,4,1,8,7]=>[4,5,1,6,3,2,8,7]=>[6,1,3,5,4,2,8,7]=>0011101
[7,2,3,5,4,6,1,8]=>[6,7,2,5,3,4,1,8]=>[5,2,3,7,4,6,1,8]=>0001110
[7,2,3,5,6,4,1,8]=>[4,6,1,7,3,5,2,8]=>[7,1,3,5,6,4,2,8]=>0010110
[8,2,3,5,7,6,4,1]=>[4,6,2,7,3,8,5,1]=>[8,2,3,5,7,6,4,1]=>0010111
[7,2,3,6,5,4,1,8]=>[4,5,2,6,7,3,1,8]=>[7,2,3,6,5,4,1,8]=>0011110
[8,2,3,7,5,6,4,1]=>[4,6,1,8,7,5,3,2]=>[7,5,8,1,3,6,4,2]=>0010111
[8,2,3,7,6,5,4,1]=>[4,5,1,6,7,8,3,2]=>[8,1,3,7,6,5,4,2]=>0011111
[5,2,4,3,1,6,7,8]=>[3,4,5,1,2,6,7,8]=>[5,1,4,3,2,6,7,8]=>0111000
[5,2,4,3,1,6,8,7]=>[3,4,5,1,2,6,8,7]=>[5,1,4,3,2,6,8,7]=>0111001
[5,2,4,3,1,7,8,6]=>[3,4,5,1,2,8,7,6]=>[5,1,4,3,2,7,8,6]=>0111001
[5,2,4,3,1,8,7,6]=>[3,4,5,1,2,7,8,6]=>[5,1,4,3,2,8,7,6]=>0111011
[5,2,4,3,6,1,8,7]=>[6,5,4,2,3,1,8,7]=>[4,2,5,3,6,1,8,7]=>0011101
[5,2,4,3,6,7,8,1]=>[8,5,4,2,3,6,7,1]=>[4,2,5,3,6,7,8,1]=>0011001
[5,2,4,3,7,6,8,1]=>[8,5,4,2,3,7,6,1]=>[4,2,5,3,7,6,8,1]=>0011011
[5,2,4,3,8,7,6,1]=>[6,5,4,2,3,7,8,1]=>[4,2,5,3,8,7,6,1]=>0011111
[6,2,4,3,5,1,8,7]=>[5,6,4,2,3,1,8,7]=>[4,2,6,3,5,1,8,7]=>0011101
[6,2,4,3,5,8,7,1]=>[7,6,4,2,3,5,8,1]=>[4,2,6,3,5,8,7,1]=>0010111
[7,2,4,3,6,5,8,1]=>[8,7,4,2,6,3,5,1]=>[4,2,6,3,7,5,8,1]=>0010111
[8,2,4,3,6,5,7,1]=>[7,8,4,2,6,3,5,1]=>[4,2,6,3,8,5,7,1]=>0010111
[8,2,4,3,7,6,5,1]=>[5,6,4,2,7,8,3,1]=>[4,2,8,3,7,6,5,1]=>0011111
[6,2,4,5,3,1,7,8]=>[3,5,6,1,4,2,7,8]=>[6,1,4,5,3,2,7,8]=>0101100
[7,2,4,5,3,6,8,1]=>[8,7,5,2,4,3,6,1]=>[5,2,4,7,3,6,8,1]=>0001011
[8,2,4,5,3,7,6,1]=>[6,7,5,1,4,8,3,2]=>[5,1,4,8,3,7,6,2]=>0001111
[7,2,4,5,6,3,8,1]=>[8,7,6,2,4,5,3,1]=>[6,2,4,5,7,3,8,1]=>0000111
[8,2,4,5,7,6,3,1]=>[3,6,7,2,4,8,5,1]=>[8,2,4,5,7,6,3,1]=>0100111
[7,2,4,6,5,3,1,8]=>[3,5,6,2,7,4,1,8]=>[7,2,4,6,5,3,1,8]=>0101110
[8,2,4,7,5,6,3,1]=>[3,6,8,1,7,5,4,2]=>[7,5,8,1,4,6,3,2]=>0100111
[8,2,4,7,6,5,3,1]=>[3,5,6,1,7,8,4,2]=>[8,1,4,7,6,5,3,2]=>0101111
[6,2,5,4,3,1,7,8]=>[3,4,5,6,2,1,7,8]=>[6,2,5,4,3,1,7,8]=>0111100
[6,2,5,4,3,1,8,7]=>[3,4,5,6,2,1,8,7]=>[6,2,5,4,3,1,8,7]=>0111101
[6,2,5,4,3,7,1,8]=>[7,6,4,5,2,3,1,8]=>[5,4,2,6,3,7,1,8]=>0011110
[6,2,5,4,3,7,8,1]=>[8,6,4,5,2,3,7,1]=>[5,4,2,6,3,7,8,1]=>0011101
[6,2,5,4,3,8,7,1]=>[7,6,4,5,2,3,8,1]=>[5,4,2,6,3,8,7,1]=>0011111
[7,2,5,4,3,6,1,8]=>[6,7,4,5,2,3,1,8]=>[5,4,2,7,3,6,1,8]=>0011110
[7,2,5,4,6,3,8,1]=>[8,7,6,5,2,4,3,1]=>[5,2,6,4,7,3,8,1]=>0001111
[8,2,5,4,6,3,7,1]=>[7,8,6,5,2,4,3,1]=>[5,2,6,4,8,3,7,1]=>0001111
[8,2,5,4,6,7,3,1]=>[3,7,8,5,1,4,6,2]=>[5,1,8,4,6,7,3,2]=>0101011
[7,2,6,4,5,3,8,1]=>[8,7,5,6,4,2,3,1]=>[6,4,5,2,7,3,8,1]=>0001111
[8,2,6,4,5,7,3,1]=>[3,7,8,6,4,1,5,2]=>[6,4,8,1,5,7,3,2]=>0100111
[7,2,6,5,4,3,1,8]=>[3,4,5,6,7,1,2,8]=>[7,1,6,5,4,3,2,8]=>0111110
[8,2,6,5,4,3,7,1]=>[7,8,4,5,6,2,3,1]=>[6,5,4,2,8,3,7,1]=>0011111
[8,2,6,5,4,7,3,1]=>[3,7,8,5,6,1,4,2]=>[6,5,1,8,4,7,3,2]=>0101111
[8,2,7,5,4,6,3,1]=>[3,6,8,5,7,4,1,2]=>[7,5,4,8,1,6,3,2]=>0101111
[8,2,7,6,5,4,3,1]=>[3,4,5,6,7,8,2,1]=>[8,2,7,6,5,4,3,1]=>0111111
[4,3,2,1,8,6,7,5]=>[2,3,4,1,7,8,6,5]=>[4,3,2,1,8,6,7,5]=>1110011
[4,3,2,7,5,6,8,1]=>[8,3,4,2,7,5,6,1]=>[4,3,2,7,5,6,8,1]=>0110011
[4,3,2,8,5,6,7,1]=>[7,3,4,2,8,5,6,1]=>[4,3,2,8,5,6,7,1]=>0110011
[4,3,2,8,5,7,6,1]=>[6,3,4,2,7,8,1,5]=>[4,3,2,8,1,7,6,5]=>0110111
[5,3,2,4,1,6,8,7]=>[4,3,5,2,1,6,8,7]=>[5,3,2,4,1,6,8,7]=>0111001
[5,3,2,4,6,1,8,7]=>[6,3,5,2,4,1,8,7]=>[5,3,2,4,6,1,8,7]=>0101101
[8,3,2,4,5,7,6,1]=>[6,3,7,1,4,8,5,2]=>[8,3,1,4,5,7,6,2]=>0100111
[7,3,2,4,6,5,8,1]=>[8,3,7,2,6,4,5,1]=>[6,3,2,4,7,5,8,1]=>0100111
[8,3,2,4,7,6,5,1]=>[5,3,6,2,7,8,4,1]=>[8,3,2,4,7,6,5,1]=>0101111
[6,3,2,5,4,1,7,8]=>[4,3,5,6,1,2,7,8]=>[6,3,1,5,4,2,7,8]=>0111100
[6,3,2,5,4,1,8,7]=>[4,3,5,6,1,2,8,7]=>[6,3,1,5,4,2,8,7]=>0111101
[7,3,2,5,4,6,1,8]=>[6,3,7,5,2,4,1,8]=>[5,3,2,7,4,6,1,8]=>0101110
[7,3,2,5,4,6,8,1]=>[8,3,7,5,2,4,6,1]=>[5,3,2,7,4,6,8,1]=>0101011
[8,3,2,5,4,7,6,1]=>[6,3,7,5,1,8,4,2]=>[5,3,1,8,4,7,6,2]=>0101111
[7,3,2,5,6,4,8,1]=>[8,3,7,6,2,5,4,1]=>[6,3,2,5,7,4,8,1]=>0100111
[8,3,2,5,7,6,4,1]=>[4,3,6,7,2,8,5,1]=>[8,3,2,5,7,6,4,1]=>0110111
[7,3,2,6,5,4,8,1]=>[8,3,7,5,6,2,4,1]=>[6,5,3,2,7,4,8,1]=>0101111
[8,3,2,7,5,6,4,1]=>[4,3,6,8,7,5,1,2]=>[7,5,8,3,1,6,4,2]=>0110111
[8,3,2,7,6,5,4,1]=>[4,3,5,6,7,8,1,2]=>[8,3,1,7,6,5,4,2]=>0111111
[5,3,4,2,1,6,8,7]=>[2,4,5,3,1,6,8,7]=>[5,3,4,2,1,6,8,7]=>1011001
[5,3,4,2,1,7,8,6]=>[2,4,5,3,1,8,7,6]=>[5,3,4,2,1,7,8,6]=>1011001
[5,3,4,2,1,8,7,6]=>[2,4,5,3,1,7,8,6]=>[5,3,4,2,1,8,7,6]=>1011011
[8,3,4,2,5,7,6,1]=>[6,4,7,1,2,8,5,3]=>[8,1,4,2,5,7,6,3]=>0010111
[6,3,4,5,2,1,8,7]=>[2,5,6,3,4,1,8,7]=>[6,3,4,5,2,1,8,7]=>1001101
[6,3,4,5,2,8,7,1]=>[7,5,6,3,4,2,8,1]=>[6,3,4,5,2,8,7,1]=>0001111
[7,3,4,6,5,2,8,1]=>[8,5,6,2,7,4,3,1]=>[7,2,4,6,5,3,8,1]=>0001111
[8,3,4,7,6,5,2,1]=>[2,5,6,3,7,8,4,1]=>[8,3,4,7,6,5,2,1]=>1001111
[6,3,5,4,2,1,7,8]=>[2,4,5,6,1,3,7,8]=>[6,2,1,5,4,3,7,8]=>1011100
[6,3,5,4,2,1,8,7]=>[2,4,5,6,1,3,8,7]=>[6,2,1,5,4,3,8,7]=>1011101
[6,3,5,4,2,7,1,8]=>[7,4,5,6,2,3,1,8]=>[6,2,5,4,3,7,1,8]=>0011110
[7,3,5,4,6,2,1,8]=>[2,6,7,5,3,4,1,8]=>[5,3,7,4,6,2,1,8]=>1001110
[7,3,5,4,6,2,8,1]=>[8,6,7,5,3,4,2,1]=>[5,3,7,4,6,2,8,1]=>0001111
[8,3,5,4,6,2,7,1]=>[7,6,8,5,3,4,2,1]=>[5,3,8,4,6,2,7,1]=>0001111
[7,3,6,4,5,2,1,8]=>[2,5,7,6,4,3,1,8]=>[6,4,7,3,5,2,1,8]=>1001110
[7,3,6,4,5,2,8,1]=>[8,5,7,6,4,3,2,1]=>[6,4,7,3,5,2,8,1]=>0001111
[8,3,6,4,5,2,7,1]=>[7,5,8,6,4,3,2,1]=>[6,4,8,3,5,2,7,1]=>0001111
[8,3,7,4,5,6,2,1]=>[2,6,8,7,4,5,3,1]=>[7,4,5,8,3,6,2,1]=>1000111
[8,3,7,4,6,5,2,1]=>[2,5,6,8,7,1,4,3]=>[7,2,1,8,4,6,5,3]=>1001111
[7,3,6,5,4,2,1,8]=>[2,4,5,6,7,3,1,8]=>[7,3,6,5,4,2,1,8]=>1011110
[7,3,6,5,4,2,8,1]=>[8,4,5,6,7,3,2,1]=>[7,3,6,5,4,2,8,1]=>0011111
[8,3,6,5,4,2,7,1]=>[7,4,5,6,8,3,2,1]=>[8,3,6,5,4,2,7,1]=>0011111
[8,3,6,5,4,7,2,1]=>[2,7,8,5,6,3,4,1]=>[6,5,3,8,4,7,2,1]=>1001111
[8,3,7,5,4,6,2,1]=>[2,6,8,5,7,4,3,1]=>[7,5,4,8,3,6,2,1]=>1001111
[8,3,7,5,6,4,2,1]=>[2,4,6,8,7,5,1,3]=>[7,5,8,2,1,6,4,3]=>1010111
[8,3,7,6,5,4,2,1]=>[2,4,5,6,7,8,1,3]=>[8,2,1,7,6,5,4,3]=>1011111
[8,4,3,2,7,6,5,1]=>[5,3,4,6,7,8,2,1]=>[8,4,3,2,7,6,5,1]=>0111111
[8,4,3,5,2,7,6,1]=>[6,5,4,7,1,8,2,3]=>[8,4,1,5,2,7,6,3]=>0011111
[7,4,3,6,5,2,1,8]=>[2,5,4,6,7,1,3,8]=>[7,4,2,1,6,5,3,8]=>1011110
[8,4,3,7,5,6,2,1]=>[2,6,4,8,7,5,3,1]=>[7,5,8,4,3,6,2,1]=>1010111
[8,4,3,7,6,5,2,1]=>[2,5,4,6,7,8,3,1]=>[8,4,3,7,6,5,2,1]=>1011111
[6,5,3,4,2,1,8,7]=>[2,4,5,3,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>1011101
[8,5,3,4,7,6,2,1]=>[2,6,5,1,7,8,4,3]=>[8,5,2,1,4,7,6,3]=>1001111
[7,6,3,5,4,2,1,8]=>[2,4,5,6,1,7,3,8]=>[7,6,2,1,5,4,3,8]=>1011110
[8,7,3,5,4,6,2,1]=>[2,6,7,5,3,4,8,1]=>[5,3,8,7,4,6,2,1]=>1001111
[8,7,3,6,5,4,2,1]=>[2,4,5,6,7,3,8,1]=>[8,7,3,6,5,4,2,1]=>1011111
[8,5,4,3,2,7,6,1]=>[6,3,4,5,7,8,1,2]=>[8,5,4,3,1,7,6,2]=>0111111
[8,5,4,3,7,6,2,1]=>[2,6,4,5,7,8,1,3]=>[8,5,4,2,1,7,6,3]=>1011111
[8,7,4,6,5,3,2,1]=>[2,3,5,6,7,1,8,4]=>[8,7,3,2,1,6,5,4]=>1101111
[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>0010101
[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]=>[2,1,4,6,3,5,8,7]=>1000101
[2,4,1,6,3,5,8,7]=>[4,2,6,1,3,5,8,7]=>[2,6,1,4,3,5,8,7]=>0010101
[2,4,6,1,3,5,8,7]=>[6,2,1,4,3,5,8,7]=>[2,4,6,1,3,5,8,7]=>0000101
[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,5,7]=>1010001
[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]=>[2,4,1,3,6,8,5,7]=>0010001
[2,1,4,6,3,8,5,7]=>[2,1,6,4,8,3,5,7]=>[2,1,4,8,3,6,5,7]=>1000101
[2,4,1,6,3,8,5,7]=>[4,2,6,1,8,3,5,7]=>[2,8,1,4,3,6,5,7]=>0010101
[2,4,6,1,3,8,5,7]=>[6,2,1,4,8,3,5,7]=>[2,4,8,1,3,6,5,7]=>0000101
[2,1,4,6,8,3,5,7]=>[2,1,8,4,3,6,5,7]=>[2,1,4,6,8,3,5,7]=>1000001
[2,4,1,6,8,3,5,7]=>[4,2,8,1,3,6,5,7]=>[2,6,8,1,4,3,5,7]=>0010001
[2,4,6,1,8,3,5,7]=>[6,2,8,4,3,1,5,7]=>[2,4,8,3,6,1,5,7]=>0000101
[2,4,6,8,1,3,5,7]=>[8,2,1,4,3,6,5,7]=>[2,4,6,8,1,3,5,7]=>0000001
[2,4,1,3,6,5,7,8]=>[4,2,1,3,6,5,7,8]=>[2,4,1,3,6,5,7,8]=>0010100
[2,1,4,6,3,5,7,8]=>[2,1,6,4,3,5,7,8]=>[2,1,4,6,3,5,7,8]=>1000100
[2,4,1,6,3,5,7,8]=>[4,2,6,1,3,5,7,8]=>[2,6,1,4,3,5,7,8]=>0010100
[2,4,6,1,3,5,7,8]=>[6,2,1,4,3,5,7,8]=>[2,4,6,1,3,5,7,8]=>0000100
[2,4,1,6,3,7,5,8]=>[4,2,6,1,7,3,5,8]=>[2,7,1,4,3,6,5,8]=>0010110
[2,4,6,7,1,3,5,8]=>[7,2,1,4,3,6,5,8]=>[2,4,6,7,1,3,5,8]=>0000010
[2,4,1,3,6,7,8,5]=>[4,2,1,3,8,6,7,5]=>[2,4,1,3,6,7,8,5]=>0010001
[2,4,1,6,3,7,8,5]=>[4,2,6,1,8,3,7,5]=>[2,7,8,1,4,3,6,5]=>0010101
[2,4,6,1,3,7,8,5]=>[6,2,1,4,8,3,7,5]=>[2,4,7,8,1,3,6,5]=>0000101
[2,1,4,6,7,3,8,5]=>[2,1,7,4,8,6,3,5]=>[2,1,4,6,8,3,7,5]=>1000011
[2,4,1,6,7,3,8,5]=>[4,2,7,1,8,6,3,5]=>[2,6,8,1,4,3,7,5]=>0010011
[2,4,6,1,7,3,8,5]=>[6,2,7,4,8,1,3,5]=>[2,4,8,1,7,3,6,5]=>0000111
[2,4,1,6,7,8,3,5]=>[4,2,8,1,3,6,7,5]=>[2,6,7,8,1,4,3,5]=>0010001
[2,4,6,7,1,8,3,5]=>[7,2,8,4,3,6,1,5]=>[2,4,6,8,3,7,1,5]=>0000011
[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>1010011
[2,4,1,3,7,5,8,6]=>[4,2,1,3,7,8,5,6]=>[2,4,1,3,8,5,7,6]=>0010011
[2,1,4,7,3,5,8,6]=>[2,1,7,4,3,8,5,6]=>[2,1,4,8,3,5,7,6]=>1000011
[2,4,1,7,3,5,8,6]=>[4,2,7,1,3,8,5,6]=>[2,8,1,4,3,5,7,6]=>0010011
[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,7,8,5,6]=>1010001
[2,4,1,3,7,8,5,6]=>[4,2,1,3,8,5,7,6]=>[2,4,1,3,7,8,5,6]=>0010001
[2,1,4,7,3,8,5,6]=>[2,1,7,4,8,5,3,6]=>[2,1,4,8,5,7,3,6]=>1000011
[2,4,1,7,3,8,5,6]=>[4,2,7,1,8,5,3,6]=>[2,8,5,7,1,4,3,6]=>0010011
[2,1,4,7,8,3,5,6]=>[2,1,8,4,3,5,7,6]=>[2,1,4,7,8,3,5,6]=>1000001
[2,4,7,1,8,3,5,6]=>[7,2,8,4,3,5,1,6]=>[2,4,8,3,5,7,1,6]=>0000011
[2,4,7,8,1,3,5,6]=>[8,2,1,4,3,5,7,6]=>[2,4,7,8,1,3,5,6]=>0000001
[2,4,1,5,3,7,6,8]=>[4,2,5,1,3,7,6,8]=>[2,5,1,4,3,7,6,8]=>0011010
[2,4,5,1,3,7,6,8]=>[5,2,1,4,3,7,6,8]=>[2,4,5,1,3,7,6,8]=>0001010
[2,4,5,1,7,3,6,8]=>[5,2,7,4,1,3,6,8]=>[2,4,7,1,5,3,6,8]=>0001010
[2,4,1,3,5,7,8,6]=>[4,2,1,3,5,8,7,6]=>[2,4,1,3,5,7,8,6]=>0010001
[2,4,1,5,3,7,8,6]=>[4,2,5,1,3,8,7,6]=>[2,5,1,4,3,7,8,6]=>0011001
[2,4,5,1,3,7,8,6]=>[5,2,1,4,3,8,7,6]=>[2,4,5,1,3,7,8,6]=>0001001
[2,1,4,5,7,3,8,6]=>[2,1,7,4,5,8,3,6]=>[2,1,4,5,8,3,7,6]=>1000011
[2,4,1,5,7,3,8,6]=>[4,2,7,1,5,8,3,6]=>[2,5,8,1,4,3,7,6]=>0010011
[2,4,5,1,7,3,8,6]=>[5,2,7,4,1,8,3,6]=>[2,4,8,1,5,3,7,6]=>0001011
[2,4,5,7,1,3,8,6]=>[7,2,1,4,5,8,3,6]=>[2,4,5,8,1,3,7,6]=>0000011
[2,1,4,5,7,8,3,6]=>[2,1,8,4,5,3,7,6]=>[2,1,4,5,7,8,3,6]=>1000001
[2,4,5,1,7,8,3,6]=>[5,2,8,4,1,3,7,6]=>[2,4,7,8,1,5,3,6]=>0001001
[2,4,5,7,1,8,3,6]=>[7,2,8,4,5,3,1,6]=>[2,4,5,8,3,7,1,6]=>0000011
[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>1010001
[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]=>[2,4,1,3,8,5,6,7]=>0010001
[2,1,4,3,5,8,6,7]=>[2,1,4,3,5,8,6,7]=>[2,1,4,3,5,8,6,7]=>1010001
[2,4,1,5,3,8,6,7]=>[4,2,5,1,3,8,6,7]=>[2,5,1,4,3,8,6,7]=>0011001
[2,1,4,5,8,3,6,7]=>[2,1,8,4,5,3,6,7]=>[2,1,4,5,8,3,6,7]=>1000001
[2,4,5,1,6,3,8,7]=>[5,2,6,4,1,3,8,7]=>[2,4,6,1,5,3,8,7]=>0001101
[2,4,5,1,6,8,3,7]=>[5,2,8,4,1,6,3,7]=>[2,4,6,8,1,5,3,7]=>0001001
[2,4,5,6,1,8,3,7]=>[6,2,8,4,5,1,3,7]=>[2,4,5,8,1,6,3,7]=>0000101
[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>0010000
[2,4,5,1,3,6,7,8]=>[5,2,1,4,3,6,7,8]=>[2,4,5,1,3,6,7,8]=>0001000
[2,4,1,5,6,3,7,8]=>[4,2,6,1,5,3,7,8]=>[2,5,6,1,4,3,7,8]=>0010100
[2,4,5,1,6,3,7,8]=>[5,2,6,4,1,3,7,8]=>[2,4,6,1,5,3,7,8]=>0001100
[2,4,5,6,1,3,7,8]=>[6,2,1,4,5,3,7,8]=>[2,4,5,6,1,3,7,8]=>0000100
[2,4,5,6,7,1,3,8]=>[7,2,1,4,5,6,3,8]=>[2,4,5,6,7,1,3,8]=>0000010
[2,4,1,5,6,7,8,3]=>[4,2,8,1,5,6,7,3]=>[2,5,6,7,8,1,4,3]=>0010001
[2,4,5,1,6,7,8,3]=>[5,2,8,4,1,6,7,3]=>[2,4,6,7,8,1,5,3]=>0001001
[2,4,5,6,1,7,8,3]=>[6,2,8,4,5,1,7,3]=>[2,4,5,7,8,1,6,3]=>0000101
[2,4,5,6,7,1,8,3]=>[7,2,8,4,5,6,1,3]=>[2,4,5,6,8,1,7,3]=>0000011
[2,4,5,6,7,8,1,3]=>[8,2,1,4,5,6,7,3]=>[2,4,5,6,7,8,1,3]=>0000001
[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>1001101
[2,5,1,3,6,4,8,7]=>[5,2,1,6,3,4,8,7]=>[2,6,1,3,5,4,8,7]=>0001101
[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>[2,1,5,6,3,4,8,7]=>1000101
[2,5,6,8,1,3,4,7]=>[8,2,1,3,5,6,4,7]=>[2,5,6,8,1,3,4,7]=>0000001
[2,5,1,3,6,4,7,8]=>[5,2,1,6,3,4,7,8]=>[2,6,1,3,5,4,7,8]=>0001100
[2,5,1,3,6,7,4,8]=>[5,2,1,7,3,6,4,8]=>[2,6,7,1,3,5,4,8]=>0001010
[2,5,1,6,3,7,4,8]=>[5,2,6,7,1,3,4,8]=>[2,7,1,6,3,5,4,8]=>0001110
[2,5,6,1,3,7,4,8]=>[6,2,1,7,5,3,4,8]=>[2,5,7,1,3,6,4,8]=>0000110
[2,1,5,3,6,7,8,4]=>[2,1,5,8,3,6,7,4]=>[2,1,6,7,8,3,5,4]=>1001001
[2,5,1,3,6,7,8,4]=>[5,2,1,8,3,6,7,4]=>[2,6,7,8,1,3,5,4]=>0001001
[2,1,5,6,3,7,8,4]=>[2,1,6,8,5,3,7,4]=>[2,1,5,7,8,3,6,4]=>1000101
[2,1,5,6,7,3,8,4]=>[2,1,7,8,5,6,3,4]=>[2,1,5,6,8,3,7,4]=>1000011
[2,5,6,1,7,3,8,4]=>[6,2,7,8,5,1,3,4]=>[2,5,8,1,7,3,6,4]=>0000111
[2,1,5,6,7,8,3,4]=>[2,1,8,3,5,6,7,4]=>[2,1,5,6,7,8,3,4]=>1000001
[2,5,6,1,7,8,3,4]=>[6,2,8,3,5,1,7,4]=>[2,5,7,8,3,6,1,4]=>0000101
[2,5,6,7,8,1,3,4]=>[8,2,1,3,5,6,7,4]=>[2,5,6,7,8,1,3,4]=>0000001
[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[2,1,8,3,5,4,7,6]=>1001011
[2,5,1,3,7,4,8,6]=>[5,2,1,7,3,8,4,6]=>[2,8,1,3,5,4,7,6]=>0001011
[2,5,1,7,3,4,8,6]=>[5,2,7,3,1,8,4,6]=>[2,8,3,5,1,4,7,6]=>0001011
[2,5,7,1,3,4,8,6]=>[7,2,1,3,5,8,4,6]=>[2,5,8,1,3,4,7,6]=>0000011
[2,5,1,3,7,8,4,6]=>[5,2,1,8,3,4,7,6]=>[2,7,8,1,3,5,4,6]=>0001001
[2,1,5,7,3,8,4,6]=>[2,1,7,8,5,4,3,6]=>[2,1,5,8,4,7,3,6]=>1000011
[2,5,1,7,3,8,4,6]=>[5,2,7,8,1,4,3,6]=>[2,8,1,7,4,5,3,6]=>0001011
[2,1,5,7,8,3,4,6]=>[2,1,8,3,5,4,7,6]=>[2,1,5,7,8,3,4,6]=>1000001
[2,5,7,8,1,3,4,6]=>[8,2,1,3,5,4,7,6]=>[2,5,7,8,1,3,4,6]=>0000001
[2,3,5,1,7,4,8,6]=>[5,2,3,7,1,8,4,6]=>[2,3,8,1,5,4,7,6]=>0001011
[2,3,1,5,7,8,4,6]=>[3,2,1,8,5,4,7,6]=>[2,3,1,5,7,8,4,6]=>0100001
[2,3,5,1,7,8,4,6]=>[5,2,3,8,1,4,7,6]=>[2,3,7,8,1,5,4,6]=>0001001
[2,3,5,7,8,1,4,6]=>[8,2,3,1,5,4,7,6]=>[2,3,5,7,8,1,4,6]=>0000001
[2,5,1,3,8,4,6,7]=>[5,2,1,8,3,4,6,7]=>[2,8,1,3,5,4,6,7]=>0001001
[2,3,5,1,4,8,6,7]=>[5,2,3,1,4,8,6,7]=>[2,3,5,1,4,8,6,7]=>0001001
[2,1,3,5,8,4,6,7]=>[2,1,3,8,5,4,6,7]=>[2,1,3,5,8,4,6,7]=>1000001
[2,1,5,3,4,6,8,7]=>[2,1,5,3,4,6,8,7]=>[2,1,5,3,4,6,8,7]=>1001001
[2,3,5,1,6,4,8,7]=>[5,2,3,6,1,4,8,7]=>[2,3,6,1,5,4,8,7]=>0001101
[2,3,5,6,1,4,8,7]=>[6,2,3,1,5,4,8,7]=>[2,3,5,6,1,4,8,7]=>0000101
[2,3,1,5,6,8,4,7]=>[3,2,1,8,5,6,4,7]=>[2,3,1,5,6,8,4,7]=>0100001
[2,3,5,6,8,1,4,7]=>[8,2,3,1,5,6,4,7]=>[2,3,5,6,8,1,4,7]=>0000001
[2,1,5,3,4,6,7,8]=>[2,1,5,3,4,6,7,8]=>[2,1,5,3,4,6,7,8]=>1001000
[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>0001000
[2,3,5,1,4,6,7,8]=>[5,2,3,1,4,6,7,8]=>[2,3,5,1,4,6,7,8]=>0001000
[2,3,5,1,6,4,7,8]=>[5,2,3,6,1,4,7,8]=>[2,3,6,1,5,4,7,8]=>0001100
[2,3,5,6,1,4,7,8]=>[6,2,3,1,5,4,7,8]=>[2,3,5,6,1,4,7,8]=>0000100
[2,3,5,1,6,7,4,8]=>[5,2,3,7,1,6,4,8]=>[2,3,6,7,1,5,4,8]=>0001010
[2,3,5,6,1,7,4,8]=>[6,2,3,7,5,1,4,8]=>[2,3,5,7,1,6,4,8]=>0000110
[2,3,5,6,7,1,4,8]=>[7,2,3,1,5,6,4,8]=>[2,3,5,6,7,1,4,8]=>0000010
[2,3,5,1,6,7,8,4]=>[5,2,3,8,1,6,7,4]=>[2,3,6,7,8,1,5,4]=>0001001
[2,3,5,6,1,7,8,4]=>[6,2,3,8,5,1,7,4]=>[2,3,5,7,8,1,6,4]=>0000101
[2,3,5,6,7,1,8,4]=>[7,2,3,8,5,6,1,4]=>[2,3,5,6,8,1,7,4]=>0000011
[2,3,5,6,7,8,1,4]=>[8,2,3,1,5,6,7,4]=>[2,3,5,6,7,8,1,4]=>0000001
[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[2,1,8,3,7,4,6,5]=>1000111
[2,1,6,7,3,4,8,5]=>[2,1,7,3,8,6,4,5]=>[2,1,6,8,3,4,7,5]=>1000011
[2,6,1,7,3,4,8,5]=>[6,2,7,3,8,1,4,5]=>[2,8,3,7,1,4,6,5]=>0000111
[2,6,1,3,7,8,4,5]=>[6,2,1,8,4,3,7,5]=>[2,7,8,4,6,1,3,5]=>0000101
[2,1,6,7,3,8,4,5]=>[2,1,7,8,4,6,3,5]=>[2,1,6,8,4,7,3,5]=>1000011
[2,6,1,7,3,8,4,5]=>[6,2,7,8,4,1,3,5]=>[2,8,4,7,1,6,3,5]=>0000111
[2,1,6,7,8,3,4,5]=>[2,1,8,3,4,6,7,5]=>[2,1,6,7,8,3,4,5]=>1000001
[2,6,7,1,8,3,4,5]=>[7,2,8,3,4,6,1,5]=>[2,6,8,3,4,7,1,5]=>0000011
[2,6,7,8,1,3,4,5]=>[8,2,1,3,4,6,7,5]=>[2,6,7,8,1,3,4,5]=>0000001
[2,3,6,7,1,4,5,8]=>[7,2,3,1,4,6,5,8]=>[2,3,6,7,1,4,5,8]=>0000010
[2,1,6,3,4,7,8,5]=>[2,1,6,3,8,4,7,5]=>[2,1,7,8,3,4,6,5]=>1000101
[2,3,6,1,4,7,8,5]=>[6,2,3,1,8,4,7,5]=>[2,3,7,8,1,4,6,5]=>0000101
[2,3,1,6,7,4,8,5]=>[3,2,1,7,8,6,4,5]=>[2,3,1,6,8,4,7,5]=>0100011
[2,3,6,7,1,4,8,5]=>[7,2,3,1,8,6,4,5]=>[2,3,6,8,1,4,7,5]=>0000011
[2,1,3,6,7,8,4,5]=>[2,1,3,8,4,6,7,5]=>[2,1,3,6,7,8,4,5]=>1000001
[2,3,1,6,7,8,4,5]=>[3,2,1,8,4,6,7,5]=>[2,3,1,6,7,8,4,5]=>0100001
[2,3,6,1,7,8,4,5]=>[6,2,3,8,4,1,7,5]=>[2,3,7,8,4,6,1,5]=>0000101
[2,3,6,7,1,8,4,5]=>[7,2,3,8,4,6,1,5]=>[2,3,6,8,4,7,1,5]=>0000011
[2,1,6,3,8,4,5,7]=>[2,1,6,8,4,3,5,7]=>[2,1,8,4,6,3,5,7]=>1000101
[2,6,1,3,8,4,5,7]=>[6,2,1,8,4,3,5,7]=>[2,8,4,6,1,3,5,7]=>0000101
[2,6,8,1,3,4,5,7]=>[8,2,1,3,4,6,5,7]=>[2,6,8,1,3,4,5,7]=>0000001
[2,3,1,6,4,8,5,7]=>[3,2,1,6,8,4,5,7]=>[2,3,1,8,4,6,5,7]=>0100101
[2,3,1,6,8,4,5,7]=>[3,2,1,8,4,6,5,7]=>[2,3,1,6,8,4,5,7]=>0100001
[2,3,6,8,1,4,5,7]=>[8,2,3,1,4,6,5,7]=>[2,3,6,8,1,4,5,7]=>0000001
[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>1000101
[2,1,3,6,4,5,8,7]=>[2,1,3,6,4,5,8,7]=>[2,1,3,6,4,5,8,7]=>1000101
[2,3,6,1,4,5,8,7]=>[6,2,3,1,4,5,8,7]=>[2,3,6,1,4,5,8,7]=>0000101
[2,3,4,1,6,8,5,7]=>[4,2,3,1,8,6,5,7]=>[2,3,4,1,6,8,5,7]=>0010001
[2,3,4,6,1,8,5,7]=>[6,2,3,4,8,1,5,7]=>[2,3,4,8,1,6,5,7]=>0000101
[2,6,1,3,4,5,7,8]=>[6,2,1,3,4,5,7,8]=>[2,6,1,3,4,5,7,8]=>0000100
[2,1,3,6,4,5,7,8]=>[2,1,3,6,4,5,7,8]=>[2,1,3,6,4,5,7,8]=>1000100
[2,3,1,6,4,5,7,8]=>[3,2,1,6,4,5,7,8]=>[2,3,1,6,4,5,7,8]=>0100100
[2,3,6,1,4,5,7,8]=>[6,2,3,1,4,5,7,8]=>[2,3,6,1,4,5,7,8]=>0000100
[2,3,4,6,7,1,5,8]=>[7,2,3,4,1,6,5,8]=>[2,3,4,6,7,1,5,8]=>0000010
[2,3,4,6,1,7,8,5]=>[6,2,3,4,8,1,7,5]=>[2,3,4,7,8,1,6,5]=>0000101
[2,3,4,6,7,1,8,5]=>[7,2,3,4,8,6,1,5]=>[2,3,4,6,8,1,7,5]=>0000011
[2,3,4,6,7,8,1,5]=>[8,2,3,4,1,6,7,5]=>[2,3,4,6,7,8,1,5]=>0000001
[2,1,7,3,8,4,5,6]=>[2,1,7,8,4,5,3,6]=>[2,1,8,4,5,7,3,6]=>1000011
[2,7,1,3,8,4,5,6]=>[7,2,1,8,4,5,3,6]=>[2,8,4,5,7,1,3,6]=>0000011
[2,7,8,1,3,4,5,6]=>[8,2,1,3,4,5,7,6]=>[2,7,8,1,3,4,5,6]=>0000001
[2,1,7,3,4,8,5,6]=>[2,1,7,3,8,5,4,6]=>[2,1,8,5,7,3,4,6]=>1000011
[2,7,1,3,4,8,5,6]=>[7,2,1,3,8,5,4,6]=>[2,8,5,7,1,3,4,6]=>0000011
[2,1,3,7,8,4,5,6]=>[2,1,3,8,4,5,7,6]=>[2,1,3,7,8,4,5,6]=>1000001
[2,3,1,7,8,4,5,6]=>[3,2,1,8,4,5,7,6]=>[2,3,1,7,8,4,5,6]=>0100001
[2,3,7,8,1,4,5,6]=>[8,2,3,1,4,5,7,6]=>[2,3,7,8,1,4,5,6]=>0000001
[2,1,3,7,4,5,8,6]=>[2,1,3,7,4,8,5,6]=>[2,1,3,8,4,5,7,6]=>1000011
[2,3,1,7,4,5,8,6]=>[3,2,1,7,4,8,5,6]=>[2,3,1,8,4,5,7,6]=>0100011
[2,1,3,4,7,5,8,6]=>[2,1,3,4,7,8,5,6]=>[2,1,3,4,8,5,7,6]=>1000011
[2,3,4,1,7,5,8,6]=>[4,2,3,1,7,8,5,6]=>[2,3,4,1,8,5,7,6]=>0010011
[2,3,4,7,1,5,8,6]=>[7,2,3,4,1,8,5,6]=>[2,3,4,8,1,5,7,6]=>0000011
[2,1,3,4,7,8,5,6]=>[2,1,3,4,8,5,7,6]=>[2,1,3,4,7,8,5,6]=>1000001
[2,3,1,4,7,8,5,6]=>[3,2,1,4,8,5,7,6]=>[2,3,1,4,7,8,5,6]=>0100001
[2,3,4,1,7,8,5,6]=>[4,2,3,1,8,5,7,6]=>[2,3,4,1,7,8,5,6]=>0010001
[2,3,4,7,1,8,5,6]=>[7,2,3,4,8,5,1,6]=>[2,3,4,8,5,7,1,6]=>0000011
[2,3,4,7,8,1,5,6]=>[8,2,3,4,1,5,7,6]=>[2,3,4,7,8,1,5,6]=>0000001
[2,1,7,3,4,5,6,8]=>[2,1,7,3,4,5,6,8]=>[2,1,7,3,4,5,6,8]=>1000010
[2,7,1,3,4,5,6,8]=>[7,2,1,3,4,5,6,8]=>[2,7,1,3,4,5,6,8]=>0000010
[2,3,7,1,4,5,6,8]=>[7,2,3,1,4,5,6,8]=>[2,3,7,1,4,5,6,8]=>0000010
[2,1,3,4,7,5,6,8]=>[2,1,3,4,7,5,6,8]=>[2,1,3,4,7,5,6,8]=>1000010
[2,3,4,7,1,5,6,8]=>[7,2,3,4,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>0000010
[2,3,4,5,7,1,6,8]=>[7,2,3,4,5,1,6,8]=>[2,3,4,5,7,1,6,8]=>0000010
[2,3,4,5,7,1,8,6]=>[7,2,3,4,5,8,1,6]=>[2,3,4,5,8,1,7,6]=>0000011
[2,3,4,5,7,8,1,6]=>[8,2,3,4,5,1,7,6]=>[2,3,4,5,7,8,1,6]=>0000001
[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>1000001
[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,7]=>0000001
[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>1000001
[2,3,1,8,4,5,6,7]=>[3,2,1,8,4,5,6,7]=>[2,3,1,8,4,5,6,7]=>0100001
[2,3,8,1,4,5,6,7]=>[8,2,3,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>0000001
[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>1000001
[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,5,6,7]=>0100001
[2,3,4,1,8,5,6,7]=>[4,2,3,1,8,5,6,7]=>[2,3,4,1,8,5,6,7]=>0010001
[2,3,4,8,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>0000001
[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,6,7]=>1000001
[2,3,1,4,5,8,6,7]=>[3,2,1,4,5,8,6,7]=>[2,3,1,4,5,8,6,7]=>0100001
[2,3,4,1,5,8,6,7]=>[4,2,3,1,5,8,6,7]=>[2,3,4,1,5,8,6,7]=>0010001
[2,3,4,5,1,8,6,7]=>[5,2,3,4,1,8,6,7]=>[2,3,4,5,1,8,6,7]=>0001001
[2,3,4,5,8,1,6,7]=>[8,2,3,4,5,1,6,7]=>[2,3,4,5,8,1,6,7]=>0000001
[2,3,4,5,6,8,1,7]=>[8,2,3,4,5,6,1,7]=>[2,3,4,5,6,8,1,7]=>0000001
[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>0110101
[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>0010101
[3,4,6,1,2,5,8,7]=>[6,1,3,4,2,5,8,7]=>[3,4,6,1,2,5,8,7]=>0000101
[3,4,1,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]=>[3,4,1,2,6,8,5,7]=>0010001
[3,4,6,8,1,2,5,7]=>[8,1,3,4,2,6,5,7]=>[3,4,6,8,1,2,5,7]=>0000001
[3,1,4,6,2,7,5,8]=>[3,6,1,4,7,2,5,8]=>[4,7,1,3,2,6,5,8]=>0100110
[3,4,1,6,2,7,5,8]=>[4,6,3,1,7,2,5,8]=>[3,7,1,4,2,6,5,8]=>0010110
[3,4,6,1,2,7,5,8]=>[6,1,3,4,7,2,5,8]=>[3,4,7,1,2,6,5,8]=>0000110
[3,1,4,6,7,2,5,8]=>[3,7,1,4,2,6,5,8]=>[4,6,7,1,3,2,5,8]=>0100010
[3,4,1,6,7,2,5,8]=>[4,7,3,1,2,6,5,8]=>[3,6,7,1,4,2,5,8]=>0010010
[3,1,4,2,6,7,8,5]=>[3,4,1,2,8,6,7,5]=>[4,1,3,2,6,7,8,5]=>0110001
[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[3,4,1,2,6,7,8,5]=>0010001
[3,4,1,6,2,7,8,5]=>[4,6,3,1,8,2,7,5]=>[3,7,8,1,4,2,6,5]=>0010101
[3,4,1,6,7,2,8,5]=>[4,7,3,1,8,6,2,5]=>[3,6,8,1,4,2,7,5]=>0010011
[3,4,6,1,7,2,8,5]=>[6,7,3,4,8,1,2,5]=>[3,4,8,1,7,2,6,5]=>0000111
[3,4,1,6,7,8,2,5]=>[4,8,3,1,2,6,7,5]=>[3,6,7,8,1,4,2,5]=>0010001
[3,4,6,1,7,8,2,5]=>[6,8,3,4,2,1,7,5]=>[3,4,7,8,2,6,1,5]=>0000101
[3,4,6,7,1,8,2,5]=>[7,8,3,4,2,6,1,5]=>[3,4,6,8,2,7,1,5]=>0000011
[3,4,6,7,8,1,2,5]=>[8,1,3,4,2,6,7,5]=>[3,4,6,7,8,1,2,5]=>0000001
[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>0110011
[3,4,1,2,7,5,8,6]=>[4,1,3,2,7,8,5,6]=>[3,4,1,2,8,5,7,6]=>0010011
[3,1,4,7,2,5,8,6]=>[3,7,1,4,2,8,5,6]=>[4,8,1,3,2,5,7,6]=>0100011
[3,4,1,7,2,5,8,6]=>[4,7,3,1,2,8,5,6]=>[3,8,1,4,2,5,7,6]=>0010011
[3,4,7,1,2,5,8,6]=>[7,1,3,4,2,8,5,6]=>[3,4,8,1,2,5,7,6]=>0000011
[3,1,4,2,7,8,5,6]=>[3,4,1,2,8,5,7,6]=>[4,1,3,2,7,8,5,6]=>0110001
[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>[3,4,1,2,7,8,5,6]=>0010001
[3,4,1,7,2,8,5,6]=>[4,7,3,1,8,5,2,6]=>[3,8,5,7,1,4,2,6]=>0010011
[3,4,7,8,1,2,5,6]=>[8,1,3,4,2,5,7,6]=>[3,4,7,8,1,2,5,6]=>0000001
[3,1,4,2,5,7,6,8]=>[3,4,1,2,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>0110010
[3,4,1,2,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>[3,4,1,2,5,7,6,8]=>0010010
[3,1,4,5,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[4,5,1,3,2,7,6,8]=>0101010
[3,4,5,1,7,2,6,8]=>[5,7,3,4,1,2,6,8]=>[3,4,7,1,5,2,6,8]=>0001010
[3,1,4,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>[4,1,3,2,5,7,8,6]=>0110001
[3,1,4,5,2,7,8,6]=>[3,5,1,4,2,8,7,6]=>[4,5,1,3,2,7,8,6]=>0101001
[3,4,1,5,2,7,8,6]=>[4,5,3,1,2,8,7,6]=>[3,5,1,4,2,7,8,6]=>0011001
[3,4,5,1,2,7,8,6]=>[5,1,3,4,2,8,7,6]=>[3,4,5,1,2,7,8,6]=>0001001
[3,4,5,1,7,2,8,6]=>[5,7,3,4,1,8,2,6]=>[3,4,8,1,5,2,7,6]=>0001011
[3,4,5,7,1,2,8,6]=>[7,1,3,4,5,8,2,6]=>[3,4,5,8,1,2,7,6]=>0000011
[3,4,1,5,7,8,2,6]=>[4,8,3,1,5,2,7,6]=>[3,5,7,8,1,4,2,6]=>0010001
[3,4,5,7,1,8,2,6]=>[7,8,3,4,5,2,1,6]=>[3,4,5,8,2,7,1,6]=>0000011
[3,1,4,2,8,5,6,7]=>[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>0110001
[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[3,4,1,2,8,5,6,7]=>0010001
[3,4,1,5,2,8,6,7]=>[4,5,3,1,2,8,6,7]=>[3,5,1,4,2,8,6,7]=>0011001
[3,4,5,1,2,8,6,7]=>[5,1,3,4,2,8,6,7]=>[3,4,5,1,2,8,6,7]=>0001001
[3,4,5,1,8,2,6,7]=>[5,8,3,4,1,2,6,7]=>[3,4,8,1,5,2,6,7]=>0001001
[3,4,5,8,1,2,6,7]=>[8,1,3,4,5,2,6,7]=>[3,4,5,8,1,2,6,7]=>0000001
[3,4,1,5,2,6,8,7]=>[4,5,3,1,2,6,8,7]=>[3,5,1,4,2,6,8,7]=>0011001
[3,4,5,1,2,6,8,7]=>[5,1,3,4,2,6,8,7]=>[3,4,5,1,2,6,8,7]=>0001001
[3,1,4,5,6,2,8,7]=>[3,6,1,4,5,2,8,7]=>[4,5,6,1,3,2,8,7]=>0100101
[3,1,4,5,6,8,2,7]=>[3,8,1,4,5,6,2,7]=>[4,5,6,8,1,3,2,7]=>0100001
[3,4,5,1,6,8,2,7]=>[5,8,3,4,1,6,2,7]=>[3,4,6,8,1,5,2,7]=>0001001
[3,1,4,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>0110000
[3,1,4,5,2,6,7,8]=>[3,5,1,4,2,6,7,8]=>[4,5,1,3,2,6,7,8]=>0101000
[3,1,4,5,6,2,7,8]=>[3,6,1,4,5,2,7,8]=>[4,5,6,1,3,2,7,8]=>0100100
[3,4,1,5,6,2,7,8]=>[4,6,3,1,5,2,7,8]=>[3,5,6,1,4,2,7,8]=>0010100
[3,4,5,1,6,2,7,8]=>[5,6,3,4,1,2,7,8]=>[3,4,6,1,5,2,7,8]=>0001100
[3,1,4,5,6,7,2,8]=>[3,7,1,4,5,6,2,8]=>[4,5,6,7,1,3,2,8]=>0100010
[3,1,4,5,6,7,8,2]=>[3,8,1,4,5,6,7,2]=>[4,5,6,7,8,1,3,2]=>0100001
[3,4,1,5,6,7,8,2]=>[4,8,3,1,5,6,7,2]=>[3,5,6,7,8,1,4,2]=>0010001
[3,4,5,1,6,7,8,2]=>[5,8,3,4,1,6,7,2]=>[3,4,6,7,8,1,5,2]=>0001001
[3,4,5,6,1,7,8,2]=>[6,8,3,4,5,1,7,2]=>[3,4,5,7,8,1,6,2]=>0000101
[3,4,5,6,7,1,8,2]=>[7,8,3,4,5,6,1,2]=>[3,4,5,6,8,1,7,2]=>0000011
[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>0101101
[3,5,1,6,2,4,8,7]=>[5,6,3,2,1,4,8,7]=>[3,6,2,5,1,4,8,7]=>0001101
[3,5,6,1,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>[3,5,6,1,2,4,8,7]=>0000101
[3,1,5,2,6,8,4,7]=>[3,5,1,8,2,6,4,7]=>[6,8,1,3,2,5,4,7]=>0101001
[3,5,1,2,6,8,4,7]=>[5,1,3,8,2,6,4,7]=>[3,6,8,1,2,5,4,7]=>0001001
[3,1,5,6,2,8,4,7]=>[3,6,1,8,5,2,4,7]=>[5,8,1,3,2,6,4,7]=>0100101
[3,5,6,1,2,8,4,7]=>[6,1,3,8,5,2,4,7]=>[3,5,8,1,2,6,4,7]=>0000101
[3,1,5,6,8,2,4,7]=>[3,8,1,2,5,6,4,7]=>[5,6,8,1,3,2,4,7]=>0100001
[3,5,1,6,8,2,4,7]=>[5,8,3,2,1,6,4,7]=>[3,6,8,2,5,1,4,7]=>0001001
[3,5,6,1,8,2,4,7]=>[6,8,3,2,5,1,4,7]=>[3,5,8,2,6,1,4,7]=>0000101
[3,5,6,8,1,2,4,7]=>[8,1,3,2,5,6,4,7]=>[3,5,6,8,1,2,4,7]=>0000001
[3,5,1,6,2,4,7,8]=>[5,6,3,2,1,4,7,8]=>[3,6,2,5,1,4,7,8]=>0001100
[3,1,5,6,2,7,4,8]=>[3,6,1,7,5,2,4,8]=>[5,7,1,3,2,6,4,8]=>0100110
[3,5,1,6,2,7,4,8]=>[5,6,3,7,1,2,4,8]=>[3,7,1,6,2,5,4,8]=>0001110
[3,5,6,1,2,7,4,8]=>[6,1,3,7,5,2,4,8]=>[3,5,7,1,2,6,4,8]=>0000110
[3,1,5,6,7,2,4,8]=>[3,7,1,2,5,6,4,8]=>[5,6,7,1,3,2,4,8]=>0100010
[3,5,1,6,7,2,4,8]=>[5,7,3,2,1,6,4,8]=>[3,6,7,2,5,1,4,8]=>0001010
[3,5,6,1,7,2,4,8]=>[6,7,3,2,5,1,4,8]=>[3,5,7,2,6,1,4,8]=>0000110
[3,5,6,7,1,2,4,8]=>[7,1,3,2,5,6,4,8]=>[3,5,6,7,1,2,4,8]=>0000010
[3,1,5,6,2,7,8,4]=>[3,6,1,8,5,2,7,4]=>[5,7,8,1,3,2,6,4]=>0100101
[3,5,6,1,2,7,8,4]=>[6,1,3,8,5,2,7,4]=>[3,5,7,8,1,2,6,4]=>0000101
[3,1,5,6,7,2,8,4]=>[3,7,1,8,5,6,2,4]=>[5,6,8,1,3,2,7,4]=>0100011
[3,5,1,6,7,2,8,4]=>[5,7,3,8,1,6,2,4]=>[3,6,8,1,7,2,5,4]=>0001011
[3,5,6,7,1,2,8,4]=>[7,1,3,8,5,6,2,4]=>[3,5,6,8,1,2,7,4]=>0000011
[3,1,5,6,7,8,2,4]=>[3,8,1,2,5,6,7,4]=>[5,6,7,8,1,3,2,4]=>0100001
[3,5,1,6,7,8,2,4]=>[5,8,3,2,1,6,7,4]=>[3,6,7,8,2,5,1,4]=>0001001
[3,5,6,1,7,8,2,4]=>[6,8,3,2,5,1,7,4]=>[3,5,7,8,2,6,1,4]=>0000101
[3,5,6,7,1,8,2,4]=>[7,8,3,2,5,6,1,4]=>[3,5,6,8,2,7,1,4]=>0000011
[3,5,6,7,8,1,2,4]=>[8,1,3,2,5,6,7,4]=>[3,5,6,7,8,1,2,4]=>0000001
[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[8,1,3,2,5,4,7,6]=>0101011
[3,5,1,2,7,4,8,6]=>[5,1,3,7,2,8,4,6]=>[3,8,1,2,5,4,7,6]=>0001011
[3,1,5,7,2,4,8,6]=>[3,7,1,2,5,8,4,6]=>[5,8,1,3,2,4,7,6]=>0100011
[3,5,7,1,2,4,8,6]=>[7,1,3,2,5,8,4,6]=>[3,5,8,1,2,4,7,6]=>0000011
[3,1,5,2,7,8,4,6]=>[3,5,1,8,2,4,7,6]=>[7,8,1,3,2,5,4,6]=>0101001
[3,1,5,7,8,2,4,6]=>[3,8,1,2,5,4,7,6]=>[5,7,8,1,3,2,4,6]=>0100001
[3,5,7,8,1,2,4,6]=>[8,1,3,2,5,4,7,6]=>[3,5,7,8,1,2,4,6]=>0000001
[3,1,5,2,7,4,6,8]=>[3,5,1,7,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>0101010
[3,5,1,2,7,4,6,8]=>[5,1,3,7,2,4,6,8]=>[3,7,1,2,5,4,6,8]=>0001010
[3,1,5,7,2,4,6,8]=>[3,7,1,2,5,4,6,8]=>[5,7,1,3,2,4,6,8]=>0100010
[3,5,1,7,2,4,6,8]=>[5,7,3,2,1,4,6,8]=>[3,7,2,5,1,4,6,8]=>0001010
[3,5,7,1,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>[3,5,7,1,2,4,6,8]=>0000010
[3,1,5,2,4,7,6,8]=>[3,5,1,2,4,7,6,8]=>[5,1,3,2,4,7,6,8]=>0101010
[3,5,1,2,4,7,6,8]=>[5,1,3,2,4,7,6,8]=>[3,5,1,2,4,7,6,8]=>0001010
[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>0101010
[1,3,5,2,4,7,6,8]=>[1,5,3,2,4,7,6,8]=>[1,3,5,2,4,7,6,8]=>0001010
[3,1,2,5,7,4,6,8]=>[3,1,2,7,5,4,6,8]=>[3,1,2,5,7,4,6,8]=>0100010
[1,3,2,5,7,4,6,8]=>[1,3,2,7,5,4,6,8]=>[1,3,2,5,7,4,6,8]=>0100010
[1,3,5,2,7,4,6,8]=>[1,5,3,7,2,4,6,8]=>[1,3,7,2,5,4,6,8]=>0001010
[1,3,5,7,2,4,6,8]=>[1,7,3,2,5,4,6,8]=>[1,3,5,7,2,4,6,8]=>0000010
[3,1,5,2,4,7,8,6]=>[3,5,1,2,4,8,7,6]=>[5,1,3,2,4,7,8,6]=>0101001
[3,5,1,2,4,7,8,6]=>[5,1,3,2,4,8,7,6]=>[3,5,1,2,4,7,8,6]=>0001001
[1,3,5,2,4,7,8,6]=>[1,5,3,2,4,8,7,6]=>[1,3,5,2,4,7,8,6]=>0001001
[1,3,5,2,7,4,8,6]=>[1,5,3,7,2,8,4,6]=>[1,3,8,2,5,4,7,6]=>0001011
[1,3,5,7,2,4,8,6]=>[1,7,3,2,5,8,4,6]=>[1,3,5,8,2,4,7,6]=>0000011
[3,1,2,5,7,8,4,6]=>[3,1,2,8,5,4,7,6]=>[3,1,2,5,7,8,4,6]=>0100001
[1,3,2,5,7,8,4,6]=>[1,3,2,8,5,4,7,6]=>[1,3,2,5,7,8,4,6]=>0100001
[1,3,5,2,7,8,4,6]=>[1,5,3,8,2,4,7,6]=>[1,3,7,8,2,5,4,6]=>0001001
[1,3,5,7,2,8,4,6]=>[1,7,3,8,5,4,2,6]=>[1,3,5,8,4,7,2,6]=>0000011
[1,3,5,7,8,2,4,6]=>[1,8,3,2,5,4,7,6]=>[1,3,5,7,8,2,4,6]=>0000001
[3,1,5,2,8,4,6,7]=>[3,5,1,8,2,4,6,7]=>[8,1,3,2,5,4,6,7]=>0101001
[3,1,5,2,4,8,6,7]=>[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>0101001
[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>[3,5,1,2,4,8,6,7]=>0001001
[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>0101001
[1,3,5,2,4,8,6,7]=>[1,5,3,2,4,8,6,7]=>[1,3,5,2,4,8,6,7]=>0001001
[1,3,2,5,8,4,6,7]=>[1,3,2,8,5,4,6,7]=>[1,3,2,5,8,4,6,7]=>0100001
[1,3,5,2,8,4,6,7]=>[1,5,3,8,2,4,6,7]=>[1,3,8,2,5,4,6,7]=>0001001
[1,3,5,8,2,4,6,7]=>[1,8,3,2,5,4,6,7]=>[1,3,5,8,2,4,6,7]=>0000001
[3,1,5,2,4,6,8,7]=>[3,5,1,2,4,6,8,7]=>[5,1,3,2,4,6,8,7]=>0101001
[3,5,1,2,4,6,8,7]=>[5,1,3,2,4,6,8,7]=>[3,5,1,2,4,6,8,7]=>0001001
[3,1,2,5,4,6,8,7]=>[3,1,2,5,4,6,8,7]=>[3,1,2,5,4,6,8,7]=>0101001
[1,3,5,2,4,6,8,7]=>[1,5,3,2,4,6,8,7]=>[1,3,5,2,4,6,8,7]=>0001001
[3,1,2,5,6,8,4,7]=>[3,1,2,8,5,6,4,7]=>[3,1,2,5,6,8,4,7]=>0100001
[1,3,5,2,6,8,4,7]=>[1,5,3,8,2,6,4,7]=>[1,3,6,8,2,5,4,7]=>0001001
[1,3,5,6,8,2,4,7]=>[1,8,3,2,5,6,4,7]=>[1,3,5,6,8,2,4,7]=>0000001
[3,1,5,2,4,6,7,8]=>[3,5,1,2,4,6,7,8]=>[5,1,3,2,4,6,7,8]=>0101000
[3,5,1,2,4,6,7,8]=>[5,1,3,2,4,6,7,8]=>[3,5,1,2,4,6,7,8]=>0001000
[1,3,5,2,4,6,7,8]=>[1,5,3,2,4,6,7,8]=>[1,3,5,2,4,6,7,8]=>0001000
[1,3,5,6,2,4,7,8]=>[1,6,3,2,5,4,7,8]=>[1,3,5,6,2,4,7,8]=>0000100
[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>[1,3,6,7,2,5,4,8]=>0001010
[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>[1,3,5,7,2,6,4,8]=>0000110
[1,3,5,6,7,2,4,8]=>[1,7,3,2,5,6,4,8]=>[1,3,5,6,7,2,4,8]=>0000010
[3,1,2,5,6,7,8,4]=>[3,1,2,8,5,6,7,4]=>[3,1,2,5,6,7,8,4]=>0100001
[1,3,5,6,2,7,8,4]=>[1,6,3,8,5,2,7,4]=>[1,3,5,7,8,2,6,4]=>0000101
[1,3,5,6,7,8,2,4]=>[1,8,3,2,5,6,7,4]=>[1,3,5,6,7,8,2,4]=>0000001
[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[8,1,3,2,7,4,6,5]=>0100111
[3,6,7,1,2,4,8,5]=>[7,1,3,2,8,6,4,5]=>[3,6,8,1,2,4,7,5]=>0000011
[3,1,6,7,2,8,4,5]=>[3,7,1,8,4,6,2,5]=>[6,8,4,7,1,3,2,5]=>0100011
[3,6,1,7,2,8,4,5]=>[6,7,3,8,4,1,2,5]=>[3,8,4,7,1,6,2,5]=>0000111
[3,6,1,7,8,2,4,5]=>[6,8,3,2,4,1,7,5]=>[3,7,8,2,4,6,1,5]=>0000101
[3,6,7,1,8,2,4,5]=>[7,8,3,2,4,6,1,5]=>[3,6,8,2,4,7,1,5]=>0000011
[3,6,7,8,1,2,4,5]=>[8,1,3,2,4,6,7,5]=>[3,6,7,8,1,2,4,5]=>0000001
[3,1,6,2,7,4,5,8]=>[3,6,1,7,4,2,5,8]=>[7,4,6,1,3,2,5,8]=>0100110
[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>[1,3,2,7,4,6,5,8]=>0100110
[1,3,6,2,4,7,5,8]=>[1,6,3,2,7,4,5,8]=>[1,3,7,2,4,6,5,8]=>0000110
[1,3,2,6,7,4,5,8]=>[1,3,2,7,4,6,5,8]=>[1,3,2,6,7,4,5,8]=>0100010
[1,3,6,2,7,4,5,8]=>[1,6,3,7,4,2,5,8]=>[1,3,7,4,6,2,5,8]=>0000110
[3,6,1,2,4,7,8,5]=>[6,1,3,2,8,4,7,5]=>[3,7,8,1,2,4,6,5]=>0000101
[3,1,2,6,4,7,8,5]=>[3,1,2,6,8,4,7,5]=>[3,1,2,7,8,4,6,5]=>0100101
[1,3,2,6,4,7,8,5]=>[1,3,2,6,8,4,7,5]=>[1,3,2,7,8,4,6,5]=>0100101
[3,1,2,6,7,4,8,5]=>[3,1,2,7,8,6,4,5]=>[3,1,2,6,8,4,7,5]=>0100011
[1,3,6,2,7,4,8,5]=>[1,6,3,7,8,2,4,5]=>[1,3,8,2,7,4,6,5]=>0000111
[1,3,6,7,2,4,8,5]=>[1,7,3,2,8,6,4,5]=>[1,3,6,8,2,4,7,5]=>0000011
[3,1,2,6,7,8,4,5]=>[3,1,2,8,4,6,7,5]=>[3,1,2,6,7,8,4,5]=>0100001
[1,3,2,6,7,8,4,5]=>[1,3,2,8,4,6,7,5]=>[1,3,2,6,7,8,4,5]=>0100001
[1,3,6,2,7,8,4,5]=>[1,6,3,8,4,2,7,5]=>[1,3,7,8,4,6,2,5]=>0000101
[1,3,6,7,8,2,4,5]=>[1,8,3,2,4,6,7,5]=>[1,3,6,7,8,2,4,5]=>0000001
[3,1,6,2,8,4,5,7]=>[3,6,1,8,4,2,5,7]=>[8,4,6,1,3,2,5,7]=>0100101
[3,6,8,1,2,4,5,7]=>[8,1,3,2,4,6,5,7]=>[3,6,8,1,2,4,5,7]=>0000001
[3,1,6,2,4,8,5,7]=>[3,6,1,2,8,4,5,7]=>[8,1,3,2,4,6,5,7]=>0100101
[1,3,2,6,4,8,5,7]=>[1,3,2,6,8,4,5,7]=>[1,3,2,8,4,6,5,7]=>0100101
[1,3,6,2,4,8,5,7]=>[1,6,3,2,8,4,5,7]=>[1,3,8,2,4,6,5,7]=>0000101
[1,3,2,6,8,4,5,7]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,8,4,5,7]=>0100001
[1,3,6,2,8,4,5,7]=>[1,6,3,8,4,2,5,7]=>[1,3,8,4,6,2,5,7]=>0000101
[3,1,6,2,4,5,8,7]=>[3,6,1,2,4,5,8,7]=>[6,1,3,2,4,5,8,7]=>0100101
[3,6,1,2,4,5,8,7]=>[6,1,3,2,4,5,8,7]=>[3,6,1,2,4,5,8,7]=>0000101
[3,1,2,6,4,5,8,7]=>[3,1,2,6,4,5,8,7]=>[3,1,2,6,4,5,8,7]=>0100101
[3,1,2,4,6,5,8,7]=>[3,1,2,4,6,5,8,7]=>[3,1,2,4,6,5,8,7]=>0100101
[1,3,4,6,2,5,8,7]=>[1,6,3,4,2,5,8,7]=>[1,3,4,6,2,5,8,7]=>0000101
[3,1,2,4,6,8,5,7]=>[3,1,2,4,8,6,5,7]=>[3,1,2,4,6,8,5,7]=>0100001
[1,3,2,4,6,8,5,7]=>[1,3,2,4,8,6,5,7]=>[1,3,2,4,6,8,5,7]=>0100001
[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>0100100
[1,3,6,2,4,5,7,8]=>[1,6,3,2,4,5,7,8]=>[1,3,6,2,4,5,7,8]=>0000100
[1,3,4,6,2,5,7,8]=>[1,6,3,4,2,5,7,8]=>[1,3,4,6,2,5,7,8]=>0000100
[1,3,4,6,7,2,5,8]=>[1,7,3,4,2,6,5,8]=>[1,3,4,6,7,2,5,8]=>0000010
[3,1,2,4,6,7,8,5]=>[3,1,2,4,8,6,7,5]=>[3,1,2,4,6,7,8,5]=>0100001
[1,3,4,6,2,7,8,5]=>[1,6,3,4,8,2,7,5]=>[1,3,4,7,8,2,6,5]=>0000101
[1,3,4,6,7,8,2,5]=>[1,8,3,4,2,6,7,5]=>[1,3,4,6,7,8,2,5]=>0000001
[3,7,1,2,8,4,5,6]=>[7,1,3,8,4,5,2,6]=>[3,8,4,5,7,1,2,6]=>0000011
[3,1,7,8,2,4,5,6]=>[3,8,1,2,4,5,7,6]=>[7,8,1,3,2,4,5,6]=>0100001
[3,7,8,1,2,4,5,6]=>[8,1,3,2,4,5,7,6]=>[3,7,8,1,2,4,5,6]=>0000001
[3,7,1,2,4,8,5,6]=>[7,1,3,2,8,5,4,6]=>[3,8,5,7,1,2,4,6]=>0000011
[1,3,2,7,4,8,5,6]=>[1,3,2,7,8,5,4,6]=>[1,3,2,8,5,7,4,6]=>0100011
[3,1,2,7,8,4,5,6]=>[3,1,2,8,4,5,7,6]=>[3,1,2,7,8,4,5,6]=>0100001
[1,3,7,2,8,4,5,6]=>[1,7,3,8,4,5,2,6]=>[1,3,8,4,5,7,2,6]=>0000011
[1,3,7,8,2,4,5,6]=>[1,8,3,2,4,5,7,6]=>[1,3,7,8,2,4,5,6]=>0000001
[3,1,7,2,4,5,8,6]=>[3,7,1,2,4,8,5,6]=>[8,1,3,2,4,5,7,6]=>0100011
[3,7,1,2,4,5,8,6]=>[7,1,3,2,4,8,5,6]=>[3,8,1,2,4,5,7,6]=>0000011
[3,1,2,7,4,5,8,6]=>[3,1,2,7,4,8,5,6]=>[3,1,2,8,4,5,7,6]=>0100011
[1,3,2,7,4,5,8,6]=>[1,3,2,7,4,8,5,6]=>[1,3,2,8,4,5,7,6]=>0100011
[1,3,7,2,4,5,8,6]=>[1,7,3,2,4,8,5,6]=>[1,3,8,2,4,5,7,6]=>0000011
[3,1,2,4,7,5,8,6]=>[3,1,2,4,7,8,5,6]=>[3,1,2,4,8,5,7,6]=>0100011
[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,8,5,7,6]=>0100011
[1,3,4,2,7,5,8,6]=>[1,4,3,2,7,8,5,6]=>[1,3,4,2,8,5,7,6]=>0010011
[1,3,4,7,2,5,8,6]=>[1,7,3,4,2,8,5,6]=>[1,3,4,8,2,5,7,6]=>0000011
[3,1,2,4,7,8,5,6]=>[3,1,2,4,8,5,7,6]=>[3,1,2,4,7,8,5,6]=>0100001
[1,3,2,4,7,8,5,6]=>[1,3,2,4,8,5,7,6]=>[1,3,2,4,7,8,5,6]=>0100001
[1,3,4,7,2,8,5,6]=>[1,7,3,4,8,5,2,6]=>[1,3,4,8,5,7,2,6]=>0000011
[3,1,7,2,4,5,6,8]=>[3,7,1,2,4,5,6,8]=>[7,1,3,2,4,5,6,8]=>0100010
[3,7,1,2,4,5,6,8]=>[7,1,3,2,4,5,6,8]=>[3,7,1,2,4,5,6,8]=>0000010
[3,1,2,7,4,5,6,8]=>[3,1,2,7,4,5,6,8]=>[3,1,2,7,4,5,6,8]=>0100010
[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>0100010
[1,3,7,2,4,5,6,8]=>[1,7,3,2,4,5,6,8]=>[1,3,7,2,4,5,6,8]=>0000010
[3,1,2,4,7,5,6,8]=>[3,1,2,4,7,5,6,8]=>[3,1,2,4,7,5,6,8]=>0100010
[1,3,4,7,2,5,6,8]=>[1,7,3,4,2,5,6,8]=>[1,3,4,7,2,5,6,8]=>0000010
[3,1,2,4,5,7,6,8]=>[3,1,2,4,5,7,6,8]=>[3,1,2,4,5,7,6,8]=>0100010
[1,3,4,5,7,2,8,6]=>[1,7,3,4,5,8,2,6]=>[1,3,4,5,8,2,7,6]=>0000011
[1,3,4,5,7,8,2,6]=>[1,8,3,4,5,2,7,6]=>[1,3,4,5,7,8,2,6]=>0000001
[3,1,8,2,4,5,6,7]=>[3,8,1,2,4,5,6,7]=>[8,1,3,2,4,5,6,7]=>0100001
[3,8,1,2,4,5,6,7]=>[8,1,3,2,4,5,6,7]=>[3,8,1,2,4,5,6,7]=>0000001
[3,1,2,8,4,5,6,7]=>[3,1,2,8,4,5,6,7]=>[3,1,2,8,4,5,6,7]=>0100001
[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>0100001
[1,3,8,2,4,5,6,7]=>[1,8,3,2,4,5,6,7]=>[1,3,8,2,4,5,6,7]=>0000001
[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>0100001
[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>0100001
[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]=>0010001
[1,3,4,8,2,5,6,7]=>[1,8,3,4,2,5,6,7]=>[1,3,4,8,2,5,6,7]=>0000001
[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>0100001
[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>0100001
[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,8,6,7]=>[1,3,4,2,5,8,6,7]=>0010001
[1,3,4,5,8,2,6,7]=>[1,8,3,4,5,2,6,7]=>[1,3,4,5,8,2,6,7]=>0000001
[3,1,2,4,5,6,8,7]=>[3,1,2,4,5,6,8,7]=>[3,1,2,4,5,6,8,7]=>0100001
[1,3,4,5,6,8,2,7]=>[1,8,3,4,5,6,2,7]=>[1,3,4,5,6,8,2,7]=>0000001
[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[6,1,5,2,4,3,8,7]=>0011101
[4,5,6,1,2,3,8,7]=>[6,1,2,4,5,3,8,7]=>[4,5,6,1,2,3,8,7]=>0000101
[4,1,5,2,6,8,3,7]=>[4,5,8,1,2,6,3,7]=>[6,8,1,5,2,4,3,7]=>0011001
[4,5,1,2,6,8,3,7]=>[5,1,8,4,2,6,3,7]=>[4,6,8,1,2,5,3,7]=>0001001
[4,5,1,6,2,8,3,7]=>[5,6,8,4,1,2,3,7]=>[4,8,1,6,2,5,3,7]=>0001101
[4,5,6,1,2,8,3,7]=>[6,1,8,4,5,2,3,7]=>[4,5,8,1,2,6,3,7]=>0000101
[4,1,5,6,8,2,3,7]=>[4,8,2,1,5,6,3,7]=>[5,6,8,2,4,1,3,7]=>0010001
[4,5,1,6,8,2,3,7]=>[5,8,2,4,1,6,3,7]=>[4,6,8,2,5,1,3,7]=>0001001
[4,5,6,8,1,2,3,7]=>[8,1,2,4,5,6,3,7]=>[4,5,6,8,1,2,3,7]=>0000001
[4,1,5,6,2,3,7,8]=>[4,6,2,1,5,3,7,8]=>[5,6,2,4,1,3,7,8]=>0010100
[4,5,1,6,2,3,7,8]=>[5,6,2,4,1,3,7,8]=>[4,6,2,5,1,3,7,8]=>0001100
[4,1,5,6,2,7,3,8]=>[4,6,7,1,5,2,3,8]=>[5,7,1,6,2,4,3,8]=>0010110
[4,5,1,6,2,7,3,8]=>[5,6,7,4,1,2,3,8]=>[4,7,1,6,2,5,3,8]=>0001110
[4,5,6,1,2,7,3,8]=>[6,1,7,4,5,2,3,8]=>[4,5,7,1,2,6,3,8]=>0000110
[4,5,1,6,7,2,3,8]=>[5,7,2,4,1,6,3,8]=>[4,6,7,2,5,1,3,8]=>0001010
[4,1,5,2,6,7,8,3]=>[4,5,8,1,2,6,7,3]=>[6,7,8,1,5,2,4,3]=>0011001
[4,5,1,6,7,2,8,3]=>[5,7,8,4,1,6,2,3]=>[4,6,8,1,7,2,5,3]=>0001011
[4,5,6,1,7,2,8,3]=>[6,7,8,4,5,1,2,3]=>[4,5,8,1,7,2,6,3]=>0000111
[4,1,5,6,7,8,2,3]=>[4,8,2,1,5,6,7,3]=>[5,6,7,8,2,4,1,3]=>0010001
[4,5,6,1,7,8,2,3]=>[6,8,2,4,5,1,7,3]=>[4,5,7,8,2,6,1,3]=>0000101
[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[8,1,5,2,4,3,7,6]=>0011011
[4,1,5,2,7,8,3,6]=>[4,5,8,1,2,3,7,6]=>[7,8,1,5,2,4,3,6]=>0011001
[4,5,1,2,7,8,3,6]=>[5,1,8,4,2,3,7,6]=>[4,7,8,1,2,5,3,6]=>0001001
[4,5,1,7,2,8,3,6]=>[5,7,8,4,1,3,2,6]=>[4,8,1,7,3,5,2,6]=>0001011
[4,5,1,7,8,2,3,6]=>[5,8,2,4,1,3,7,6]=>[4,7,8,2,5,1,3,6]=>0001001
[4,5,7,8,1,2,3,6]=>[8,1,2,4,5,3,7,6]=>[4,5,7,8,1,2,3,6]=>0000001
[4,5,1,2,7,3,6,8]=>[5,1,7,4,2,3,6,8]=>[4,7,1,2,5,3,6,8]=>0001010
[4,1,5,7,2,3,6,8]=>[4,7,2,1,5,3,6,8]=>[5,7,2,4,1,3,6,8]=>0010010
[4,5,1,2,3,7,6,8]=>[5,1,2,4,3,7,6,8]=>[4,5,1,2,3,7,6,8]=>0001010
[4,1,2,5,3,7,6,8]=>[4,1,5,2,3,7,6,8]=>[5,1,2,4,3,7,6,8]=>0011010
[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>0011010
[1,4,5,2,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>0001010
[1,4,2,5,7,3,6,8]=>[1,4,7,2,5,3,6,8]=>[1,5,7,2,4,3,6,8]=>0010010
[1,4,5,2,7,3,6,8]=>[1,5,7,4,2,3,6,8]=>[1,4,7,2,5,3,6,8]=>0001010
[1,4,5,7,2,3,6,8]=>[1,7,2,4,5,3,6,8]=>[1,4,5,7,2,3,6,8]=>0000010
[4,1,5,2,3,7,8,6]=>[4,5,2,1,3,8,7,6]=>[5,2,4,1,3,7,8,6]=>0011001
[4,1,2,5,3,7,8,6]=>[4,1,5,2,3,8,7,6]=>[5,1,2,4,3,7,8,6]=>0011001
[1,4,5,2,3,7,8,6]=>[1,5,2,4,3,8,7,6]=>[1,4,5,2,3,7,8,6]=>0001001
[4,1,2,5,7,3,8,6]=>[4,1,7,2,5,8,3,6]=>[5,8,1,2,4,3,7,6]=>0010011
[1,4,2,5,7,3,8,6]=>[1,4,7,2,5,8,3,6]=>[1,5,8,2,4,3,7,6]=>0010011
[1,4,5,7,2,3,8,6]=>[1,7,2,4,5,8,3,6]=>[1,4,5,8,2,3,7,6]=>0000011
[4,1,2,5,7,8,3,6]=>[4,1,8,2,5,3,7,6]=>[5,7,8,1,2,4,3,6]=>0010001
[4,5,1,2,8,3,6,7]=>[5,1,8,4,2,3,6,7]=>[4,8,1,2,5,3,6,7]=>0001001
[4,5,1,8,2,3,6,7]=>[5,8,2,4,1,3,6,7]=>[4,8,2,5,1,3,6,7]=>0001001
[4,5,8,1,2,3,6,7]=>[8,1,2,4,5,3,6,7]=>[4,5,8,1,2,3,6,7]=>0000001
[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>0011001
[1,4,5,2,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>[1,4,5,2,3,8,6,7]=>0001001
[4,1,2,5,6,3,8,7]=>[4,1,6,2,5,3,8,7]=>[5,6,1,2,4,3,8,7]=>0010101
[1,4,5,6,2,8,3,7]=>[1,6,8,4,5,2,3,7]=>[1,4,5,8,2,6,3,7]=>0000101
[4,1,5,2,3,6,7,8]=>[4,5,2,1,3,6,7,8]=>[5,2,4,1,3,6,7,8]=>0011000
[4,1,2,5,3,6,7,8]=>[4,1,5,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>0011000
[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>0011000
[1,4,5,2,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>0001000
[1,4,5,2,6,3,7,8]=>[1,5,6,4,2,3,7,8]=>[1,4,6,2,5,3,7,8]=>0001100
[1,4,5,6,2,3,7,8]=>[1,6,2,4,5,3,7,8]=>[1,4,5,6,2,3,7,8]=>0000100
[1,4,2,5,6,7,3,8]=>[1,4,7,2,5,6,3,8]=>[1,5,6,7,2,4,3,8]=>0010010
[1,4,5,6,2,7,3,8]=>[1,6,7,4,5,2,3,8]=>[1,4,5,7,2,6,3,8]=>0000110
[1,4,5,6,7,2,3,8]=>[1,7,2,4,5,6,3,8]=>[1,4,5,6,7,2,3,8]=>0000010
[4,1,2,5,6,7,8,3]=>[4,1,8,2,5,6,7,3]=>[5,6,7,8,1,2,4,3]=>0010001
[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>[1,5,6,7,8,2,4,3]=>0010001
[1,4,5,6,2,7,8,3]=>[1,6,8,4,5,2,7,3]=>[1,4,5,7,8,2,6,3]=>0000101
[1,4,5,6,7,2,8,3]=>[1,7,8,4,5,6,2,3]=>[1,4,5,6,8,2,7,3]=>0000011
[1,4,5,6,7,8,2,3]=>[1,8,2,4,5,6,7,3]=>[1,4,5,6,7,8,2,3]=>0000001
[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[8,1,7,2,4,3,6,5]=>0010111
[4,6,1,2,7,3,8,5]=>[6,1,7,4,8,2,3,5]=>[4,8,1,2,7,3,6,5]=>0000111
[4,1,6,7,2,8,3,5]=>[4,7,8,1,3,6,2,5]=>[6,8,1,7,3,4,2,5]=>0010011
[4,6,1,7,2,8,3,5]=>[6,7,8,4,3,1,2,5]=>[4,8,3,7,1,6,2,5]=>0000111
[4,6,7,1,2,8,3,5]=>[7,1,8,4,3,6,2,5]=>[4,6,8,3,7,1,2,5]=>0000011
[4,1,6,7,8,2,3,5]=>[4,8,2,1,3,6,7,5]=>[6,7,8,2,4,1,3,5]=>0010001
[4,6,7,8,1,2,3,5]=>[8,1,2,4,3,6,7,5]=>[4,6,7,8,1,2,3,5]=>0000001
[4,1,6,2,7,3,5,8]=>[4,6,7,1,3,2,5,8]=>[7,1,6,3,4,2,5,8]=>0010110
[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>[1,7,2,4,3,6,5,8]=>0010110
[1,4,6,2,3,7,5,8]=>[1,6,2,4,7,3,5,8]=>[1,4,7,2,3,6,5,8]=>0000110
[1,4,2,6,7,3,5,8]=>[1,4,7,2,3,6,5,8]=>[1,6,7,2,4,3,5,8]=>0010010
[1,4,6,2,7,3,5,8]=>[1,6,7,4,3,2,5,8]=>[1,4,7,3,6,2,5,8]=>0000110
[1,4,6,7,2,3,5,8]=>[1,7,2,4,3,6,5,8]=>[1,4,6,7,2,3,5,8]=>0000010
[4,1,6,2,3,7,8,5]=>[4,6,2,1,8,3,7,5]=>[7,8,2,4,1,3,6,5]=>0010101
[4,6,1,2,3,7,8,5]=>[6,1,2,4,8,3,7,5]=>[4,7,8,1,2,3,6,5]=>0000101
[4,1,2,6,3,7,8,5]=>[4,1,6,2,8,3,7,5]=>[7,8,1,2,4,3,6,5]=>0010101
[1,4,2,6,3,7,8,5]=>[1,4,6,2,8,3,7,5]=>[1,7,8,2,4,3,6,5]=>0010101
[1,4,2,6,7,3,8,5]=>[1,4,7,2,8,6,3,5]=>[1,6,8,2,4,3,7,5]=>0010011
[1,4,6,7,2,3,8,5]=>[1,7,2,4,8,6,3,5]=>[1,4,6,8,2,3,7,5]=>0000011
[1,4,2,6,7,8,3,5]=>[1,4,8,2,3,6,7,5]=>[1,6,7,8,2,4,3,5]=>0010001
[1,4,6,2,7,8,3,5]=>[1,6,8,4,3,2,7,5]=>[1,4,7,8,3,6,2,5]=>0000101
[4,1,6,8,2,3,5,7]=>[4,8,2,1,3,6,5,7]=>[6,8,2,4,1,3,5,7]=>0010001
[4,6,1,8,2,3,5,7]=>[6,8,2,4,3,1,5,7]=>[4,8,2,3,6,1,5,7]=>0000101
[4,6,8,1,2,3,5,7]=>[8,1,2,4,3,6,5,7]=>[4,6,8,1,2,3,5,7]=>0000001
[4,1,6,2,3,8,5,7]=>[4,6,2,1,8,3,5,7]=>[8,2,4,1,3,6,5,7]=>0010101
[4,6,1,2,3,8,5,7]=>[6,1,2,4,8,3,5,7]=>[4,8,1,2,3,6,5,7]=>0000101
[4,1,2,6,3,8,5,7]=>[4,1,6,2,8,3,5,7]=>[8,1,2,4,3,6,5,7]=>0010101
[1,4,2,6,3,8,5,7]=>[1,4,6,2,8,3,5,7]=>[1,8,2,4,3,6,5,7]=>0010101
[1,4,6,2,3,8,5,7]=>[1,6,2,4,8,3,5,7]=>[1,4,8,2,3,6,5,7]=>0000101
[4,1,2,6,8,3,5,7]=>[4,1,8,2,3,6,5,7]=>[6,8,1,2,4,3,5,7]=>0010001
[1,4,2,6,8,3,5,7]=>[1,4,8,2,3,6,5,7]=>[1,6,8,2,4,3,5,7]=>0010001
[1,4,6,2,8,3,5,7]=>[1,6,8,4,3,2,5,7]=>[1,4,8,3,6,2,5,7]=>0000101
[1,4,6,8,2,3,5,7]=>[1,8,2,4,3,6,5,7]=>[1,4,6,8,2,3,5,7]=>0000001
[4,1,6,2,3,5,8,7]=>[4,6,2,1,3,5,8,7]=>[6,2,4,1,3,5,8,7]=>0010101
[4,6,1,2,3,5,8,7]=>[6,1,2,4,3,5,8,7]=>[4,6,1,2,3,5,8,7]=>0000101
[4,1,2,6,3,5,8,7]=>[4,1,6,2,3,5,8,7]=>[6,1,2,4,3,5,8,7]=>0010101
[1,4,2,6,3,5,8,7]=>[1,4,6,2,3,5,8,7]=>[1,6,2,4,3,5,8,7]=>0010101
[1,4,6,2,3,5,8,7]=>[1,6,2,4,3,5,8,7]=>[1,4,6,2,3,5,8,7]=>0000101
[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>0010101
[1,4,2,3,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>0010101
[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]=>[4,1,2,3,6,8,5,7]=>0010001
[1,2,4,3,6,8,5,7]=>[1,2,4,3,8,6,5,7]=>[1,2,4,3,6,8,5,7]=>0010001
[1,2,4,6,8,3,5,7]=>[1,2,8,4,3,6,5,7]=>[1,2,4,6,8,3,5,7]=>0000001
[4,1,6,2,3,5,7,8]=>[4,6,2,1,3,5,7,8]=>[6,2,4,1,3,5,7,8]=>0010100
[4,6,1,2,3,5,7,8]=>[6,1,2,4,3,5,7,8]=>[4,6,1,2,3,5,7,8]=>0000100
[4,1,2,6,3,5,7,8]=>[4,1,6,2,3,5,7,8]=>[6,1,2,4,3,5,7,8]=>0010100
[1,4,2,6,3,5,7,8]=>[1,4,6,2,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>0010100
[1,4,6,2,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>[1,4,6,2,3,5,7,8]=>0000100
[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>0010100
[1,4,2,3,6,5,7,8]=>[1,4,2,3,6,5,7,8]=>[1,4,2,3,6,5,7,8]=>0010100
[1,2,4,6,3,5,7,8]=>[1,2,6,4,3,5,7,8]=>[1,2,4,6,3,5,7,8]=>0000100
[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>[4,1,2,3,6,7,5,8]=>0010010
[4,1,2,3,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>[4,1,2,3,6,7,8,5]=>0010001
[1,2,4,6,7,3,8,5]=>[1,2,7,4,8,6,3,5]=>[1,2,4,6,8,3,7,5]=>0000011
[1,2,4,6,7,8,3,5]=>[1,2,8,4,3,6,7,5]=>[1,2,4,6,7,8,3,5]=>0000001
[4,7,1,2,8,3,5,6]=>[7,1,8,4,3,5,2,6]=>[4,8,3,5,7,1,2,6]=>0000011
[4,1,7,8,2,3,5,6]=>[4,8,2,1,3,5,7,6]=>[7,8,2,4,1,3,5,6]=>0010001
[4,7,1,8,2,3,5,6]=>[7,8,2,4,3,5,1,6]=>[4,8,2,3,5,7,1,6]=>0000011
[4,7,8,1,2,3,5,6]=>[8,1,2,4,3,5,7,6]=>[4,7,8,1,2,3,5,6]=>0000001
[4,1,7,2,3,8,5,6]=>[4,7,2,1,8,5,3,6]=>[8,5,7,2,4,1,3,6]=>0010011
[1,4,2,7,3,8,5,6]=>[1,4,7,2,8,5,3,6]=>[1,8,5,7,2,4,3,6]=>0010011
[1,4,7,2,3,8,5,6]=>[1,7,2,4,8,5,3,6]=>[1,4,8,5,7,2,3,6]=>0000011
[4,1,2,7,8,3,5,6]=>[4,1,8,2,3,5,7,6]=>[7,8,1,2,4,3,5,6]=>0010001
[1,4,2,7,8,3,5,6]=>[1,4,8,2,3,5,7,6]=>[1,7,8,2,4,3,5,6]=>0010001
[4,1,2,7,3,5,8,6]=>[4,1,7,2,3,8,5,6]=>[8,1,2,4,3,5,7,6]=>0010011
[1,4,7,2,3,5,8,6]=>[1,7,2,4,3,8,5,6]=>[1,4,8,2,3,5,7,6]=>0000011
[4,1,2,3,7,5,8,6]=>[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,5,7,6]=>0010011
[1,4,2,3,7,5,8,6]=>[1,4,2,3,7,8,5,6]=>[1,4,2,3,8,5,7,6]=>0010011
[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,8,5,7,6]=>0010011
[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,5,7,6]=>[4,1,2,3,7,8,5,6]=>0010001
[1,4,2,3,7,8,5,6]=>[1,4,2,3,8,5,7,6]=>[1,4,2,3,7,8,5,6]=>0010001
[1,2,4,3,7,8,5,6]=>[1,2,4,3,8,5,7,6]=>[1,2,4,3,7,8,5,6]=>0010001
[1,2,4,7,3,8,5,6]=>[1,2,7,4,8,5,3,6]=>[1,2,4,8,5,7,3,6]=>0000011
[1,2,4,7,8,3,5,6]=>[1,2,8,4,3,5,7,6]=>[1,2,4,7,8,3,5,6]=>0000001
[4,7,1,2,3,5,6,8]=>[7,1,2,4,3,5,6,8]=>[4,7,1,2,3,5,6,8]=>0000010
[4,1,2,7,3,5,6,8]=>[4,1,7,2,3,5,6,8]=>[7,1,2,4,3,5,6,8]=>0010010
[1,4,2,7,3,5,6,8]=>[1,4,7,2,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>0010010
[1,4,7,2,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>[1,4,7,2,3,5,6,8]=>0000010
[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>0010010
[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>0010010
[1,2,4,3,7,5,6,8]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,7,5,6,8]=>0010010
[1,2,4,7,3,5,6,8]=>[1,2,7,4,3,5,6,8]=>[1,2,4,7,3,5,6,8]=>0000010
[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>0010010
[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>0010010
[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>[4,1,2,3,5,7,8,6]=>0010001
[1,4,2,3,5,7,8,6]=>[1,4,2,3,5,8,7,6]=>[1,4,2,3,5,7,8,6]=>0010001
[1,2,4,5,7,3,8,6]=>[1,2,7,4,5,8,3,6]=>[1,2,4,5,8,3,7,6]=>0000011
[1,2,4,5,7,8,3,6]=>[1,2,8,4,5,3,7,6]=>[1,2,4,5,7,8,3,6]=>0000001
[4,1,8,2,3,5,6,7]=>[4,8,2,1,3,5,6,7]=>[8,2,4,1,3,5,6,7]=>0010001
[4,8,1,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]=>[4,8,1,2,3,5,6,7]=>0000001
[4,1,2,8,3,5,6,7]=>[4,1,8,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]=>0010001
[1,4,2,8,3,5,6,7]=>[1,4,8,2,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>0010001
[1,4,8,2,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>[1,4,8,2,3,5,6,7]=>0000001
[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>0010001
[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>0010001
[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>0010001
[1,2,4,8,3,5,6,7]=>[1,2,8,4,3,5,6,7]=>[1,2,4,8,3,5,6,7]=>0000001
[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>0010001
[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>0010001
[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,6,7]=>0010001
[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>[1,2,4,5,3,8,6,7]=>0001001
[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>0010001
[1,4,2,3,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>0010001
[1,2,4,5,6,8,3,7]=>[1,2,8,4,5,6,3,7]=>[1,2,4,5,6,8,3,7]=>0000001
[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>0010000
[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[8,1,7,2,6,3,5,4]=>0001111
[5,6,1,2,7,3,8,4]=>[6,1,7,8,5,2,3,4]=>[5,8,1,2,7,3,6,4]=>0000111
[5,1,6,7,2,3,8,4]=>[5,7,2,8,1,6,3,4]=>[6,8,2,7,1,3,5,4]=>0001011
[5,6,1,7,2,3,8,4]=>[6,7,2,8,5,1,3,4]=>[5,8,2,7,1,3,6,4]=>0000111
[5,6,7,1,2,3,8,4]=>[7,1,2,8,5,6,3,4]=>[5,6,8,1,2,3,7,4]=>0000011
[5,1,6,2,7,8,3,4]=>[5,6,8,3,1,2,7,4]=>[7,8,3,6,1,5,2,4]=>0001101
[5,6,1,2,7,8,3,4]=>[6,1,8,3,5,2,7,4]=>[5,7,8,3,6,1,2,4]=>0000101
[5,1,6,7,2,8,3,4]=>[5,7,8,3,1,6,2,4]=>[6,8,3,7,1,5,2,4]=>0001011
[5,6,1,7,2,8,3,4]=>[6,7,8,3,5,1,2,4]=>[5,8,3,7,1,6,2,4]=>0000111
[5,6,1,7,8,2,3,4]=>[6,8,2,3,5,1,7,4]=>[5,7,8,2,3,6,1,4]=>0000101
[5,6,7,1,8,2,3,4]=>[7,8,2,3,5,6,1,4]=>[5,6,8,2,3,7,1,4]=>0000011
[5,1,6,2,7,3,4,8]=>[5,6,7,3,1,2,4,8]=>[7,3,6,1,5,2,4,8]=>0001110
[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>[1,7,2,6,3,5,4,8]=>0001110
[1,5,6,2,3,7,4,8]=>[1,6,2,7,5,3,4,8]=>[1,5,7,2,3,6,4,8]=>0000110
[1,5,6,2,3,7,8,4]=>[1,6,2,8,5,3,7,4]=>[1,5,7,8,2,3,6,4]=>0000101
[1,5,6,2,7,3,8,4]=>[1,6,7,8,5,2,3,4]=>[1,5,8,2,7,3,6,4]=>0000111
[1,5,6,7,2,3,8,4]=>[1,7,2,8,5,6,3,4]=>[1,5,6,8,2,3,7,4]=>0000011
[5,1,2,6,7,8,3,4]=>[5,1,8,3,2,6,7,4]=>[6,7,8,3,5,1,2,4]=>0001001
[1,5,6,2,7,8,3,4]=>[1,6,8,3,5,2,7,4]=>[1,5,7,8,3,6,2,4]=>0000101
[1,5,6,7,2,8,3,4]=>[1,7,8,3,5,6,2,4]=>[1,5,6,8,3,7,2,4]=>0000011
[1,5,6,7,8,2,3,4]=>[1,8,2,3,5,6,7,4]=>[1,5,6,7,8,2,3,4]=>0000001
[5,1,6,8,2,3,4,7]=>[5,8,2,3,1,6,4,7]=>[6,8,2,3,5,1,4,7]=>0001001
[5,6,8,1,2,3,4,7]=>[8,1,2,3,5,6,4,7]=>[5,6,8,1,2,3,4,7]=>0000001
[5,1,6,2,3,8,4,7]=>[5,6,2,8,1,3,4,7]=>[8,2,6,1,3,5,4,7]=>0001101
[1,5,2,6,3,8,4,7]=>[1,5,6,8,2,3,4,7]=>[1,8,2,6,3,5,4,7]=>0001101
[1,5,6,2,3,8,4,7]=>[1,6,2,8,5,3,4,7]=>[1,5,8,2,3,6,4,7]=>0000101
[5,1,2,6,8,3,4,7]=>[5,1,8,3,2,6,4,7]=>[6,8,3,5,1,2,4,7]=>0001001
[1,5,6,8,2,3,4,7]=>[1,8,2,3,5,6,4,7]=>[1,5,6,8,2,3,4,7]=>0000001
[1,5,2,3,6,8,4,7]=>[1,5,2,8,3,6,4,7]=>[1,6,8,2,3,5,4,7]=>0001001
[1,2,5,3,6,8,4,7]=>[1,2,5,8,3,6,4,7]=>[1,2,6,8,3,5,4,7]=>0001001
[1,2,5,6,3,8,4,7]=>[1,2,6,8,5,3,4,7]=>[1,2,5,8,3,6,4,7]=>0000101
[1,2,5,6,8,3,4,7]=>[1,2,8,3,5,6,4,7]=>[1,2,5,6,8,3,4,7]=>0000001
[5,1,2,6,3,4,7,8]=>[5,1,6,3,2,4,7,8]=>[6,3,5,1,2,4,7,8]=>0001100
[1,5,2,6,3,4,7,8]=>[1,5,6,3,2,4,7,8]=>[1,6,3,5,2,4,7,8]=>0001100
[5,1,2,3,6,4,7,8]=>[5,1,2,6,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>0001100
[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>[1,2,6,3,5,4,7,8]=>0001100
[1,2,5,6,3,4,7,8]=>[1,2,6,3,5,4,7,8]=>[1,2,5,6,3,4,7,8]=>0000100
[1,5,2,3,6,7,4,8]=>[1,5,2,7,3,6,4,8]=>[1,6,7,2,3,5,4,8]=>0001010
[1,2,5,3,6,7,4,8]=>[1,2,5,7,3,6,4,8]=>[1,2,6,7,3,5,4,8]=>0001010
[1,2,5,6,3,7,4,8]=>[1,2,6,7,5,3,4,8]=>[1,2,5,7,3,6,4,8]=>0000110
[5,1,2,3,6,7,8,4]=>[5,1,2,8,3,6,7,4]=>[6,7,8,1,2,3,5,4]=>0001001
[1,5,2,3,6,7,8,4]=>[1,5,2,8,3,6,7,4]=>[1,6,7,8,2,3,5,4]=>0001001
[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>[1,2,6,7,8,3,5,4]=>0001001
[1,2,5,6,3,7,8,4]=>[1,2,6,8,5,3,7,4]=>[1,2,5,7,8,3,6,4]=>0000101
[1,2,5,6,7,3,8,4]=>[1,2,7,8,5,6,3,4]=>[1,2,5,6,8,3,7,4]=>0000011
[1,2,5,6,7,8,3,4]=>[1,2,8,3,5,6,7,4]=>[1,2,5,6,7,8,3,4]=>0000001
[5,7,8,1,2,3,4,6]=>[8,1,2,3,5,4,7,6]=>[5,7,8,1,2,3,4,6]=>0000001
[5,1,2,7,3,8,4,6]=>[5,1,7,8,2,4,3,6]=>[8,1,2,7,4,5,3,6]=>0001011
[1,5,2,7,3,8,4,6]=>[1,5,7,8,2,4,3,6]=>[1,8,2,7,4,5,3,6]=>0001011
[1,5,7,2,3,8,4,6]=>[1,7,2,8,5,4,3,6]=>[1,5,8,4,7,2,3,6]=>0000011
[5,1,2,7,8,3,4,6]=>[5,1,8,3,2,4,7,6]=>[7,8,3,5,1,2,4,6]=>0001001
[1,5,2,7,8,3,4,6]=>[1,5,8,3,2,4,7,6]=>[1,7,8,3,5,2,4,6]=>0001001
[1,5,7,2,8,3,4,6]=>[1,7,8,3,5,4,2,6]=>[1,5,8,3,4,7,2,6]=>0000011
[5,7,1,2,3,4,8,6]=>[7,1,2,3,5,8,4,6]=>[5,8,1,2,3,4,7,6]=>0000011
[5,1,2,7,3,4,8,6]=>[5,1,7,3,2,8,4,6]=>[8,3,5,1,2,4,7,6]=>0001011
[1,5,7,2,3,4,8,6]=>[1,7,2,3,5,8,4,6]=>[1,5,8,2,3,4,7,6]=>0000011
[5,1,2,3,7,4,8,6]=>[5,1,2,7,3,8,4,6]=>[8,1,2,3,5,4,7,6]=>0001011
[1,2,5,3,7,4,8,6]=>[1,2,5,7,3,8,4,6]=>[1,2,8,3,5,4,7,6]=>0001011
[1,2,5,7,3,4,8,6]=>[1,2,7,3,5,8,4,6]=>[1,2,5,8,3,4,7,6]=>0000011
[1,2,5,3,7,8,4,6]=>[1,2,5,8,3,4,7,6]=>[1,2,7,8,3,5,4,6]=>0001001
[1,2,5,7,3,8,4,6]=>[1,2,7,8,5,4,3,6]=>[1,2,5,8,4,7,3,6]=>0000011
[1,2,5,7,8,3,4,6]=>[1,2,8,3,5,4,7,6]=>[1,2,5,7,8,3,4,6]=>0000001
[5,7,1,2,3,4,6,8]=>[7,1,2,3,5,4,6,8]=>[5,7,1,2,3,4,6,8]=>0000010
[5,1,2,7,3,4,6,8]=>[5,1,7,3,2,4,6,8]=>[7,3,5,1,2,4,6,8]=>0001010
[1,5,2,7,3,4,6,8]=>[1,5,7,3,2,4,6,8]=>[1,7,3,5,2,4,6,8]=>0001010
[1,5,7,2,3,4,6,8]=>[1,7,2,3,5,4,6,8]=>[1,5,7,2,3,4,6,8]=>0000010
[5,1,2,3,7,4,6,8]=>[5,1,2,7,3,4,6,8]=>[7,1,2,3,5,4,6,8]=>0001010
[1,5,2,3,7,4,6,8]=>[1,5,2,7,3,4,6,8]=>[1,7,2,3,5,4,6,8]=>0001010
[1,2,5,3,7,4,6,8]=>[1,2,5,7,3,4,6,8]=>[1,2,7,3,5,4,6,8]=>0001010
[1,2,5,7,3,4,6,8]=>[1,2,7,3,5,4,6,8]=>[1,2,5,7,3,4,6,8]=>0000010
[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>0001010
[1,2,5,3,4,7,6,8]=>[1,2,5,3,4,7,6,8]=>[1,2,5,3,4,7,6,8]=>0001010
[1,2,3,5,7,4,6,8]=>[1,2,3,7,5,4,6,8]=>[1,2,3,5,7,4,6,8]=>0000010
[5,1,2,3,4,7,8,6]=>[5,1,2,3,4,8,7,6]=>[5,1,2,3,4,7,8,6]=>0001001
[1,5,2,3,4,7,8,6]=>[1,5,2,3,4,8,7,6]=>[1,5,2,3,4,7,8,6]=>0001001
[1,2,5,3,4,7,8,6]=>[1,2,5,3,4,8,7,6]=>[1,2,5,3,4,7,8,6]=>0001001
[1,2,3,5,7,4,8,6]=>[1,2,3,7,5,8,4,6]=>[1,2,3,5,8,4,7,6]=>0000011
[1,2,3,5,7,8,4,6]=>[1,2,3,8,5,4,7,6]=>[1,2,3,5,7,8,4,6]=>0000001
[5,1,8,2,3,4,6,7]=>[5,8,2,3,1,4,6,7]=>[8,2,3,5,1,4,6,7]=>0001001
[5,8,1,2,3,4,6,7]=>[8,1,2,3,5,4,6,7]=>[5,8,1,2,3,4,6,7]=>0000001
[5,1,2,8,3,4,6,7]=>[5,1,8,3,2,4,6,7]=>[8,3,5,1,2,4,6,7]=>0001001
[1,5,8,2,3,4,6,7]=>[1,8,2,3,5,4,6,7]=>[1,5,8,2,3,4,6,7]=>0000001
[5,1,2,3,8,4,6,7]=>[5,1,2,8,3,4,6,7]=>[8,1,2,3,5,4,6,7]=>0001001
[1,5,2,3,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>[1,8,2,3,5,4,6,7]=>0001001
[1,2,5,3,8,4,6,7]=>[1,2,5,8,3,4,6,7]=>[1,2,8,3,5,4,6,7]=>0001001
[1,2,5,8,3,4,6,7]=>[1,2,8,3,5,4,6,7]=>[1,2,5,8,3,4,6,7]=>0000001
[5,1,2,3,4,8,6,7]=>[5,1,2,3,4,8,6,7]=>[5,1,2,3,4,8,6,7]=>0001001
[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>0001001
[1,2,5,3,4,8,6,7]=>[1,2,5,3,4,8,6,7]=>[1,2,5,3,4,8,6,7]=>0001001
[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>0001001
[1,2,3,5,8,4,6,7]=>[1,2,3,8,5,4,6,7]=>[1,2,3,5,8,4,6,7]=>0000001
[5,1,2,3,4,6,8,7]=>[5,1,2,3,4,6,8,7]=>[5,1,2,3,4,6,8,7]=>0001001
[1,5,2,3,4,6,8,7]=>[1,5,2,3,4,6,8,7]=>[1,5,2,3,4,6,8,7]=>0001001
[1,2,5,3,4,6,8,7]=>[1,2,5,3,4,6,8,7]=>[1,2,5,3,4,6,8,7]=>0001001
[1,2,3,5,6,8,4,7]=>[1,2,3,8,5,6,4,7]=>[1,2,3,5,6,8,4,7]=>0000001
[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>0001000
[1,2,5,3,4,6,7,8]=>[1,2,5,3,4,6,7,8]=>[1,2,5,3,4,6,7,8]=>0001000
[6,1,7,2,8,3,4,5]=>[6,7,8,3,4,1,2,5]=>[8,3,4,7,1,6,2,5]=>0000111
[6,1,7,8,2,3,4,5]=>[6,8,2,3,4,1,7,5]=>[7,8,2,3,4,6,1,5]=>0000101
[6,7,1,8,2,3,4,5]=>[7,8,2,3,4,6,1,5]=>[6,8,2,3,4,7,1,5]=>0000011
[6,1,7,2,3,8,4,5]=>[6,7,2,8,4,1,3,5]=>[8,4,7,2,6,1,3,5]=>0000111
[1,6,2,7,3,8,4,5]=>[1,6,7,8,4,2,3,5]=>[1,8,4,7,2,6,3,5]=>0000111
[1,6,7,2,3,8,4,5]=>[1,7,2,8,4,6,3,5]=>[1,6,8,4,7,2,3,5]=>0000011
[6,1,2,7,8,3,4,5]=>[6,1,8,3,4,2,7,5]=>[7,8,3,4,6,1,2,5]=>0000101
[1,6,7,8,2,3,4,5]=>[1,8,2,3,4,6,7,5]=>[1,6,7,8,2,3,4,5]=>0000001
[6,7,1,2,3,4,8,5]=>[7,1,2,3,8,6,4,5]=>[6,8,1,2,3,4,7,5]=>0000011
[6,1,2,7,3,4,8,5]=>[6,1,7,3,8,2,4,5]=>[8,3,7,1,2,4,6,5]=>0000111
[1,6,7,2,3,4,8,5]=>[1,7,2,3,8,6,4,5]=>[1,6,8,2,3,4,7,5]=>0000011
[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>[1,2,8,3,7,4,6,5]=>0000111
[1,2,6,7,3,4,8,5]=>[1,2,7,3,8,6,4,5]=>[1,2,6,8,3,4,7,5]=>0000011
[6,1,2,3,7,8,4,5]=>[6,1,2,8,4,3,7,5]=>[7,8,4,6,1,2,3,5]=>0000101
[1,6,2,3,7,8,4,5]=>[1,6,2,8,4,3,7,5]=>[1,7,8,4,6,2,3,5]=>0000101
[1,2,6,3,7,8,4,5]=>[1,2,6,8,4,3,7,5]=>[1,2,7,8,4,6,3,5]=>0000101
[1,2,6,7,3,8,4,5]=>[1,2,7,8,4,6,3,5]=>[1,2,6,8,4,7,3,5]=>0000011
[1,2,6,7,8,3,4,5]=>[1,2,8,3,4,6,7,5]=>[1,2,6,7,8,3,4,5]=>0000001
[6,1,2,7,3,4,5,8]=>[6,1,7,3,4,2,5,8]=>[7,3,4,6,1,2,5,8]=>0000110
[1,6,7,2,3,4,5,8]=>[1,7,2,3,4,6,5,8]=>[1,6,7,2,3,4,5,8]=>0000010
[1,2,6,7,3,4,5,8]=>[1,2,7,3,4,6,5,8]=>[1,2,6,7,3,4,5,8]=>0000010
[6,1,2,3,4,7,5,8]=>[6,1,2,3,7,4,5,8]=>[7,1,2,3,4,6,5,8]=>0000110
[1,6,2,3,4,7,5,8]=>[1,6,2,3,7,4,5,8]=>[1,7,2,3,4,6,5,8]=>0000110
[1,2,6,3,4,7,5,8]=>[1,2,6,3,7,4,5,8]=>[1,2,7,3,4,6,5,8]=>0000110
[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>[1,2,3,7,4,6,5,8]=>0000110
[1,2,3,6,7,4,5,8]=>[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,4,5,8]=>0000010
[6,1,2,3,4,7,8,5]=>[6,1,2,3,8,4,7,5]=>[7,8,1,2,3,4,6,5]=>0000101
[1,2,6,3,4,7,8,5]=>[1,2,6,3,8,4,7,5]=>[1,2,7,8,3,4,6,5]=>0000101
[1,2,3,6,4,7,8,5]=>[1,2,3,6,8,4,7,5]=>[1,2,3,7,8,4,6,5]=>0000101
[1,2,3,6,7,4,8,5]=>[1,2,3,7,8,6,4,5]=>[1,2,3,6,8,4,7,5]=>0000011
[1,2,3,6,7,8,4,5]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,7,8,4,5]=>0000001
[6,1,8,2,3,4,5,7]=>[6,8,2,3,4,1,5,7]=>[8,2,3,4,6,1,5,7]=>0000101
[6,8,1,2,3,4,5,7]=>[8,1,2,3,4,6,5,7]=>[6,8,1,2,3,4,5,7]=>0000001
[6,1,2,8,3,4,5,7]=>[6,1,8,3,4,2,5,7]=>[8,3,4,6,1,2,5,7]=>0000101
[1,6,8,2,3,4,5,7]=>[1,8,2,3,4,6,5,7]=>[1,6,8,2,3,4,5,7]=>0000001
[1,2,6,3,8,4,5,7]=>[1,2,6,8,4,3,5,7]=>[1,2,8,4,6,3,5,7]=>0000101
[1,2,6,8,3,4,5,7]=>[1,2,8,3,4,6,5,7]=>[1,2,6,8,3,4,5,7]=>0000001
[6,1,2,3,4,8,5,7]=>[6,1,2,3,8,4,5,7]=>[8,1,2,3,4,6,5,7]=>0000101
[1,6,2,3,4,8,5,7]=>[1,6,2,3,8,4,5,7]=>[1,8,2,3,4,6,5,7]=>0000101
[1,2,6,3,4,8,5,7]=>[1,2,6,3,8,4,5,7]=>[1,2,8,3,4,6,5,7]=>0000101
[1,2,3,6,4,8,5,7]=>[1,2,3,6,8,4,5,7]=>[1,2,3,8,4,6,5,7]=>0000101
[1,2,3,6,8,4,5,7]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,8,4,5,7]=>0000001
[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>0000101
[1,6,2,3,4,5,8,7]=>[1,6,2,3,4,5,8,7]=>[1,6,2,3,4,5,8,7]=>0000101
[1,2,6,3,4,5,8,7]=>[1,2,6,3,4,5,8,7]=>[1,2,6,3,4,5,8,7]=>0000101
[1,2,3,6,4,5,8,7]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,4,5,8,7]=>0000101
[1,2,3,4,6,8,5,7]=>[1,2,3,4,8,6,5,7]=>[1,2,3,4,6,8,5,7]=>0000001
[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>0000100
[1,2,6,3,4,5,7,8]=>[1,2,6,3,4,5,7,8]=>[1,2,6,3,4,5,7,8]=>0000100
[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>0000100
[7,1,8,2,3,4,5,6]=>[7,8,2,3,4,5,1,6]=>[8,2,3,4,5,7,1,6]=>0000011
[7,1,2,8,3,4,5,6]=>[7,1,8,3,4,5,2,6]=>[8,3,4,5,7,1,2,6]=>0000011
[1,7,2,8,3,4,5,6]=>[1,7,8,3,4,5,2,6]=>[1,8,3,4,5,7,2,6]=>0000011
[1,7,8,2,3,4,5,6]=>[1,8,2,3,4,5,7,6]=>[1,7,8,2,3,4,5,6]=>0000001
[1,7,2,3,8,4,5,6]=>[1,7,2,8,4,5,3,6]=>[1,8,4,5,7,2,3,6]=>0000011
[1,2,7,3,8,4,5,6]=>[1,2,7,8,4,5,3,6]=>[1,2,8,4,5,7,3,6]=>0000011
[1,2,7,8,3,4,5,6]=>[1,2,8,3,4,5,7,6]=>[1,2,7,8,3,4,5,6]=>0000001
[7,1,2,3,4,8,5,6]=>[7,1,2,3,8,5,4,6]=>[8,5,7,1,2,3,4,6]=>0000011
[1,7,2,3,4,8,5,6]=>[1,7,2,3,8,5,4,6]=>[1,8,5,7,2,3,4,6]=>0000011
[1,2,7,3,4,8,5,6]=>[1,2,7,3,8,5,4,6]=>[1,2,8,5,7,3,4,6]=>0000011
[1,2,3,7,4,8,5,6]=>[1,2,3,7,8,5,4,6]=>[1,2,3,8,5,7,4,6]=>0000011
[1,2,3,7,8,4,5,6]=>[1,2,3,8,4,5,7,6]=>[1,2,3,7,8,4,5,6]=>0000001
[7,1,2,3,4,5,8,6]=>[7,1,2,3,4,8,5,6]=>[8,1,2,3,4,5,7,6]=>0000011
[1,7,2,3,4,5,8,6]=>[1,7,2,3,4,8,5,6]=>[1,8,2,3,4,5,7,6]=>0000011
[1,2,7,3,4,5,8,6]=>[1,2,7,3,4,8,5,6]=>[1,2,8,3,4,5,7,6]=>0000011
[1,2,3,7,4,5,8,6]=>[1,2,3,7,4,8,5,6]=>[1,2,3,8,4,5,7,6]=>0000011
[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,5,7,6]=>0000011
[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,5,6]=>0000001
[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>0000010
[1,2,7,3,4,5,6,8]=>[1,2,7,3,4,5,6,8]=>[1,2,7,3,4,5,6,8]=>0000010
[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>0000010
[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,5,6,8]=>0000010
[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>0000001
[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]=>0000001
[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>0000001
[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>0000001
[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>0000001
[5,3,2,6,1,4,8,7]=>[6,3,5,1,2,4,8,7]=>[5,3,1,6,2,4,8,7]=>0101101
[7,3,2,5,4,8,1,6]=>[8,3,7,5,2,1,4,6]=>[5,3,2,7,1,8,4,6]=>0101011
[8,4,5,2,3,7,6,1]=>[6,5,2,7,1,8,3,4]=>[8,2,5,1,3,7,6,4]=>0001111
[7,4,5,2,3,8,1,6]=>[8,5,2,7,4,1,3,6]=>[7,4,5,2,8,1,3,6]=>0001011
[6,4,5,2,3,1,8,7]=>[3,5,2,6,4,1,8,7]=>[6,4,5,2,3,1,8,7]=>0101101
[5,4,6,2,1,3,8,7]=>[2,6,1,5,4,3,8,7]=>[5,4,6,2,1,3,8,7]=>1001101
[4,6,5,1,3,2,8,7]=>[5,3,1,4,6,2,8,7]=>[3,1,4,6,5,2,8,7]=>0101101
[5,6,4,3,1,2,8,7]=>[3,1,4,6,5,2,8,7]=>[5,6,4,3,1,2,8,7]=>0110101
[7,5,4,3,2,8,1,6]=>[8,3,4,5,7,1,2,6]=>[7,5,4,3,1,8,2,6]=>0111011
[8,6,4,3,7,2,5,1]=>[5,7,4,6,2,8,3,1]=>[8,6,4,2,7,3,5,1]=>0011111
[7,6,4,3,8,2,1,5]=>[2,8,4,6,1,7,3,5]=>[7,6,4,2,1,8,3,5]=>1010111
[5,7,4,3,1,8,2,6]=>[3,4,7,8,5,2,1,6]=>[5,8,2,7,4,3,1,6]=>0110011
[4,7,5,1,3,8,2,6]=>[5,7,2,4,8,1,3,6]=>[4,8,2,7,5,1,3,6]=>0001011
[3,7,1,5,4,8,2,6]=>[7,8,3,5,1,2,4,6]=>[3,5,1,8,2,7,4,6]=>0001011
[2,1,7,5,4,8,3,6]=>[2,1,8,5,7,3,4,6]=>[2,1,7,5,3,8,4,6]=>1001011
[4,8,5,1,3,7,6,2]=>[5,8,2,4,6,7,3,1]=>[4,7,6,2,3,8,5,1]=>0001111
[5,8,4,3,1,7,6,2]=>[3,4,8,6,5,7,1,2]=>[5,7,6,1,8,4,3,2]=>0110111
[6,8,4,3,7,1,5,2]=>[7,5,4,8,1,6,3,2]=>[6,8,4,1,5,3,7,2]=>0011011
[7,8,4,3,6,5,1,2]=>[5,1,4,6,8,2,7,3]=>[7,8,4,1,2,6,5,3]=>0011101
[6,8,5,7,3,1,4,2]=>[3,7,4,2,8,6,5,1]=>[4,2,6,8,5,7,3,1]=>0110011
[5,8,6,7,1,3,4,2]=>[7,4,1,3,5,8,6,2]=>[4,1,3,5,8,6,7,2]=>0010011
[2,1,8,6,7,4,5,3]=>[2,1,5,7,4,8,6,3]=>[2,1,8,6,7,4,5,3]=>1001011
[2,1,7,6,8,4,3,5]=>[2,1,4,8,3,7,6,5]=>[2,1,7,6,8,4,3,5]=>1010011
[5,7,6,8,1,3,2,4]=>[8,3,1,2,5,7,6,4]=>[3,1,5,7,6,8,2,4]=>0100011
[6,4,7,2,8,1,3,5]=>[8,7,1,6,3,4,2,5]=>[6,1,3,7,4,8,2,5]=>0000111
[7,4,6,2,8,3,1,5]=>[3,8,6,7,2,4,1,5]=>[7,2,6,4,8,3,1,5]=>0100111
[8,4,6,2,7,3,5,1]=>[5,6,7,8,3,4,2,1]=>[8,3,7,4,6,2,5,1]=>0001111
[7,3,2,6,8,4,1,5]=>[4,3,8,7,2,1,6,5]=>[7,3,2,6,8,4,1,5]=>0110011
[5,3,2,7,1,8,4,6]=>[7,3,5,8,2,4,1,6]=>[8,3,2,5,4,7,1,6]=>0101011
[4,3,2,1,7,8,5,6]=>[2,3,4,1,8,5,7,6]=>[4,3,2,1,7,8,5,6]=>1110001
[3,4,1,2,8,7,6,5]=>[4,1,3,2,6,7,8,5]=>[3,4,1,2,8,7,6,5]=>0010111
[8,4,7,2,6,5,3,1]=>[3,5,6,7,8,4,2,1]=>[8,4,7,2,6,5,3,1]=>0101111
[7,4,8,2,6,5,1,3]=>[5,6,2,8,7,4,1,3]=>[7,4,8,2,6,5,1,3]=>0001111
[4,5,8,1,2,7,6,3]=>[8,1,6,4,5,7,2,3]=>[4,5,7,6,1,2,8,3]=>0000111
[3,5,1,8,2,7,6,4]=>[5,8,3,6,1,7,2,4]=>[3,7,6,1,8,2,5,4]=>0001111
[2,1,5,8,3,7,6,4]=>[2,1,8,6,5,7,3,4]=>[2,1,5,7,6,3,8,4]=>1000111
[2,1,6,8,7,3,5,4]=>[2,1,7,5,3,6,8,4]=>[2,1,5,3,6,8,7,4]=>1001011
[4,6,8,1,7,2,5,3]=>[8,7,5,4,2,6,1,3]=>[4,5,2,6,7,1,8,3]=>0001011
[5,6,8,7,1,2,4,3]=>[7,1,4,2,5,6,8,3]=>[4,1,2,5,6,8,7,3]=>0010011
[6,5,8,7,2,1,4,3]=>[2,7,4,1,6,5,8,3]=>[4,2,1,6,5,8,7,3]=>1010111
[7,5,8,6,2,4,1,3]=>[4,6,1,2,8,7,3,5]=>[7,1,4,2,3,8,6,5]=>0010111
[8,5,7,6,2,4,3,1]=>[3,4,6,1,7,8,2,5]=>[8,1,4,3,2,7,6,5]=>0110111
[5,7,8,6,1,4,2,3]=>[6,4,2,1,5,8,7,3]=>[4,2,5,7,8,6,1,3]=>0010101
[4,7,8,1,6,5,2,3]=>[8,5,2,4,6,1,7,3]=>[4,6,5,2,7,8,1,3]=>0001101
[3,7,1,8,6,5,2,4]=>[7,5,3,2,6,8,1,4]=>[3,8,6,5,2,7,1,4]=>0001111
[2,1,7,8,6,5,3,4]=>[2,1,5,3,6,8,7,4]=>[2,1,7,8,6,5,3,4]=>1001101
[4,8,7,1,6,5,3,2]=>[7,3,5,4,6,1,8,2]=>[4,6,5,3,1,8,7,2]=>0101111
[6,8,7,5,4,1,3,2]=>[4,3,1,5,7,6,8,2]=>[3,1,6,8,7,5,4,2]=>0111011
[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>101010101
[3,4,1,2,6,5,8,7,10,9]=>[4,1,3,2,6,5,8,7,10,9]=>[3,4,1,2,6,5,8,7,10,9]=>001010101
[4,3,2,1,6,5,8,7,10,9]=>[2,3,4,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>111010101
[4,5,6,1,2,3,8,7,10,9]=>[6,1,2,4,5,3,8,7,10,9]=>[4,5,6,1,2,3,8,7,10,9]=>000010101
[2,1,5,6,3,4,8,7,10,9]=>[2,1,6,3,5,4,8,7,10,9]=>[2,1,5,6,3,4,8,7,10,9]=>100010101
[2,1,6,5,4,3,8,7,10,9]=>[2,1,4,5,6,3,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>101110101
[6,5,4,3,2,1,8,7,10,9]=>[2,3,4,5,6,1,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>111110101
[5,6,7,8,1,2,3,4,10,9]=>[8,1,2,3,5,6,7,4,10,9]=>[5,6,7,8,1,2,3,4,10,9]=>000000101
[2,1,6,7,8,3,4,5,10,9]=>[2,1,8,3,4,6,7,5,10,9]=>[2,1,6,7,8,3,4,5,10,9]=>100000101
[3,4,1,2,7,8,5,6,10,9]=>[4,1,3,2,8,5,7,6,10,9]=>[3,4,1,2,7,8,5,6,10,9]=>001000101
[2,1,4,3,7,8,5,6,10,9]=>[2,1,4,3,8,5,7,6,10,9]=>[2,1,4,3,7,8,5,6,10,9]=>101000101
[2,1,4,3,8,7,6,5,10,9]=>[2,1,4,3,6,7,8,5,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>101011101
[4,3,2,1,8,7,6,5,10,9]=>[2,3,4,1,6,7,8,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>111011101
[2,1,8,7,6,5,4,3,10,9]=>[2,1,4,5,6,7,8,3,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>101111101
[8,7,6,5,4,3,2,1,10,9]=>[2,3,4,5,6,7,8,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>111111101
[10,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,10,8,1]=>[10,8,9,6,7,4,5,2,3,1]=>010101011
[2,1,7,8,9,10,3,4,5,6]=>[2,1,10,3,4,5,7,8,9,6]=>[2,1,7,8,9,10,3,4,5,6]=>100000001
[6,7,8,9,10,1,2,3,4,5]=>[10,1,2,3,4,6,7,8,9,5]=>[6,7,8,9,10,1,2,3,4,5]=>000000001
[3,4,1,2,8,9,10,5,6,7]=>[4,1,3,2,10,5,6,8,9,7]=>[3,4,1,2,8,9,10,5,6,7]=>001000001
[2,1,4,3,8,9,10,5,6,7]=>[2,1,4,3,10,5,6,8,9,7]=>[2,1,4,3,8,9,10,5,6,7]=>101000001
[2,1,5,6,3,4,9,10,7,8]=>[2,1,6,3,5,4,10,7,9,8]=>[2,1,5,6,3,4,9,10,7,8]=>100010001
[4,5,6,1,2,3,9,10,7,8]=>[6,1,2,4,5,3,10,7,9,8]=>[4,5,6,1,2,3,9,10,7,8]=>000010001
[3,4,1,2,6,5,9,10,7,8]=>[4,1,3,2,6,5,10,7,9,8]=>[3,4,1,2,6,5,9,10,7,8]=>001010001
[2,1,4,3,6,5,9,10,7,8]=>[2,1,4,3,6,5,10,7,9,8]=>[2,1,4,3,6,5,9,10,7,8]=>101010001
[2,1,4,3,6,5,10,9,8,7]=>[2,1,4,3,6,5,8,9,10,7]=>[2,1,4,3,6,5,10,9,8,7]=>101010111
[4,3,2,1,6,5,10,9,8,7]=>[2,3,4,1,6,5,8,9,10,7]=>[4,3,2,1,6,5,10,9,8,7]=>111010111
[2,1,6,5,4,3,10,9,8,7]=>[2,1,4,5,6,3,8,9,10,7]=>[2,1,6,5,4,3,10,9,8,7]=>101110111
[6,5,4,3,2,1,10,9,8,7]=>[2,3,4,5,6,1,8,9,10,7]=>[6,5,4,3,2,1,10,9,8,7]=>111110111
[2,1,4,3,10,9,8,7,6,5]=>[2,1,4,3,6,7,8,9,10,5]=>[2,1,4,3,10,9,8,7,6,5]=>101011111
[4,3,2,1,10,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,10,5]=>[4,3,2,1,10,9,8,7,6,5]=>111011111
[2,1,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,3]=>[2,1,10,9,8,7,6,5,4,3]=>101111111
[10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[3,2,5,1,4,6,7,8]=>[5,3,2,1,4,6,7,8]=>[3,2,5,1,4,6,7,8]=>0101000
[4,2,5,1,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>[4,1,5,2,3,6,7,8]=>0011000
[5,2,4,1,3,6,7,8]=>[4,5,1,2,3,6,7,8]=>[5,1,4,2,3,6,7,8]=>0011000
[3,2,6,1,4,5,7,8]=>[6,3,2,1,4,5,7,8]=>[3,2,6,1,4,5,7,8]=>0100100
[4,2,6,1,3,5,7,8]=>[6,4,1,2,3,5,7,8]=>[4,1,6,2,3,5,7,8]=>0010100
[5,3,6,1,2,4,7,8]=>[6,1,5,2,3,4,7,8]=>[5,1,2,6,3,4,7,8]=>0001100
[6,2,4,1,3,5,7,8]=>[4,6,1,2,3,5,7,8]=>[6,1,4,2,3,5,7,8]=>0010100
[6,3,5,1,2,4,7,8]=>[5,1,6,2,3,4,7,8]=>[6,1,2,5,3,4,7,8]=>0001100
[4,2,7,1,3,5,6,8]=>[7,4,1,2,3,5,6,8]=>[4,1,7,2,3,5,6,8]=>0010010
[5,2,7,1,3,4,6,8]=>[7,5,1,3,2,4,6,8]=>[5,1,3,7,2,4,6,8]=>0001010
[6,2,7,1,3,4,5,8]=>[7,6,1,3,4,2,5,8]=>[6,1,3,4,7,2,5,8]=>0000110
[6,4,7,1,2,3,5,8]=>[7,1,2,6,3,4,5,8]=>[6,1,2,3,7,4,5,8]=>0000110
[7,2,5,1,3,4,6,8]=>[5,7,1,3,2,4,6,8]=>[7,1,3,5,2,4,6,8]=>0001010
[7,3,5,1,2,4,6,8]=>[5,1,7,2,3,4,6,8]=>[7,1,2,5,3,4,6,8]=>0001010
[7,4,6,1,2,3,5,8]=>[6,1,2,7,3,4,5,8]=>[7,1,2,3,6,4,5,8]=>0000110
[3,2,8,1,4,5,6,7]=>[8,3,2,1,4,5,6,7]=>[3,2,8,1,4,5,6,7]=>0100001
[4,2,8,1,3,5,6,7]=>[8,4,1,2,3,5,6,7]=>[4,1,8,2,3,5,6,7]=>0010001
[5,2,8,1,3,4,6,7]=>[8,5,1,3,2,4,6,7]=>[5,1,3,8,2,4,6,7]=>0001001
[5,3,8,1,2,4,6,7]=>[8,1,5,2,3,4,6,7]=>[5,1,2,8,3,4,6,7]=>0001001
[5,4,8,1,2,3,6,7]=>[8,1,2,5,4,3,6,7]=>[5,4,8,1,2,3,6,7]=>0001001
[6,2,8,1,3,4,5,7]=>[8,6,1,3,4,2,5,7]=>[6,1,3,4,8,2,5,7]=>0000101
[6,3,8,1,2,4,5,7]=>[8,1,6,2,4,3,5,7]=>[6,1,2,4,8,3,5,7]=>0000101
[6,4,8,1,2,3,5,7]=>[8,1,2,6,3,4,5,7]=>[6,1,2,3,8,4,5,7]=>0000101
[6,5,8,1,2,3,4,7]=>[8,1,2,3,6,5,4,7]=>[6,5,8,1,2,3,4,7]=>0000101
[7,2,8,1,3,4,5,6]=>[8,7,1,3,4,5,2,6]=>[7,1,3,4,5,8,2,6]=>0000011
[7,4,8,1,2,3,5,6]=>[8,1,2,7,3,5,4,6]=>[7,1,2,3,5,8,4,6]=>0000011
[7,5,8,1,2,3,4,6]=>[8,1,2,3,7,4,5,6]=>[7,1,2,3,4,8,5,6]=>0000011
[8,2,4,1,3,5,6,7]=>[4,8,1,2,3,5,6,7]=>[8,1,4,2,3,5,6,7]=>0010001
[8,3,5,1,2,4,6,7]=>[5,1,8,2,3,4,6,7]=>[8,1,2,5,3,4,6,7]=>0001001
[8,2,6,1,3,4,5,7]=>[6,8,1,3,4,2,5,7]=>[8,1,3,4,6,2,5,7]=>0000101
[8,3,6,1,2,4,5,7]=>[6,1,8,2,4,3,5,7]=>[8,1,2,4,6,3,5,7]=>0000101
[8,4,6,1,2,3,5,7]=>[6,1,2,8,3,4,5,7]=>[8,1,2,3,6,4,5,7]=>0000101
[8,4,7,1,2,3,5,6]=>[7,1,2,8,3,5,4,6]=>[8,1,2,3,5,7,4,6]=>0000011
[8,5,7,1,2,3,4,6]=>[7,1,2,3,8,4,5,6]=>[8,1,2,3,4,7,5,6]=>0000011
[3,2,5,7,1,4,6,8]=>[7,3,2,1,5,4,6,8]=>[3,2,5,7,1,4,6,8]=>0100010
[5,2,4,7,1,3,6,8]=>[7,5,1,2,4,3,6,8]=>[5,1,4,7,2,3,6,8]=>0001010
[5,3,6,7,1,2,4,8]=>[7,1,5,2,3,6,4,8]=>[5,1,2,6,7,3,4,8]=>0001010
[6,2,4,7,1,3,5,8]=>[7,6,1,2,3,4,5,8]=>[6,1,7,2,3,4,5,8]=>0000110
[7,2,4,6,1,3,5,8]=>[6,7,1,2,3,4,5,8]=>[7,1,6,2,3,4,5,8]=>0000110
[7,3,4,6,1,2,5,8]=>[6,1,7,3,2,4,5,8]=>[7,3,6,1,2,4,5,8]=>0000110
[3,2,5,8,1,4,6,7]=>[8,3,2,1,5,4,6,7]=>[3,2,5,8,1,4,6,7]=>0100001
[4,2,5,8,1,3,6,7]=>[8,4,1,2,5,3,6,7]=>[4,1,5,8,2,3,6,7]=>0010001
[4,3,5,8,1,2,6,7]=>[8,1,4,3,5,2,6,7]=>[4,3,5,8,1,2,6,7]=>0010001
[3,2,6,8,1,4,5,7]=>[8,3,2,1,4,6,5,7]=>[3,2,6,8,1,4,5,7]=>0100001
[4,3,6,8,1,2,5,7]=>[8,1,4,3,2,6,5,7]=>[4,3,6,8,1,2,5,7]=>0010001
[6,2,4,8,1,3,5,7]=>[8,6,1,2,3,4,5,7]=>[6,1,8,2,3,4,5,7]=>0000101
[6,3,4,8,1,2,5,7]=>[8,1,6,3,2,4,5,7]=>[6,3,8,1,2,4,5,7]=>0000101
[6,3,5,8,1,2,4,7]=>[8,1,6,2,3,5,4,7]=>[6,1,2,5,8,3,4,7]=>0000101
[6,4,5,8,1,2,3,7]=>[8,1,2,6,4,5,3,7]=>[6,4,5,8,1,2,3,7]=>0000101
[3,2,7,8,1,4,5,6]=>[8,3,2,1,4,5,7,6]=>[3,2,7,8,1,4,5,6]=>0100001
[4,3,7,8,1,2,5,6]=>[8,1,4,3,2,5,7,6]=>[4,3,7,8,1,2,5,6]=>0010001
[6,3,7,8,1,2,4,5]=>[8,1,6,2,4,3,7,5]=>[6,1,2,4,7,8,3,5]=>0000101
[7,3,4,8,1,2,5,6]=>[8,1,7,3,2,5,4,6]=>[7,3,5,8,1,2,4,6]=>0000011
[7,2,5,8,1,3,4,6]=>[8,7,1,3,2,4,5,6]=>[7,1,3,8,2,4,5,6]=>0000011
[7,3,5,8,1,2,4,6]=>[8,1,7,2,3,4,5,6]=>[7,1,2,8,3,4,5,6]=>0000011
[7,2,6,8,1,3,4,5]=>[8,7,1,3,4,2,6,5]=>[7,1,3,4,6,8,2,5]=>0000011
[7,4,6,8,1,2,3,5]=>[8,1,2,7,3,4,6,5]=>[7,1,2,3,6,8,4,5]=>0000011
[8,2,4,6,1,3,5,7]=>[6,8,1,2,3,4,5,7]=>[8,1,6,2,3,4,5,7]=>0000101
[8,3,4,6,1,2,5,7]=>[6,1,8,3,2,4,5,7]=>[8,3,6,1,2,4,5,7]=>0000101
[8,3,5,6,1,2,4,7]=>[6,1,8,2,3,5,4,7]=>[8,1,2,5,6,3,4,7]=>0000101
[8,3,4,7,1,2,5,6]=>[7,1,8,3,2,5,4,6]=>[8,3,5,7,1,2,4,6]=>0000011
[8,2,5,7,1,3,4,6]=>[7,8,1,3,2,4,5,6]=>[8,1,3,7,2,4,5,6]=>0000011
[8,3,5,7,1,2,4,6]=>[7,1,8,2,3,4,5,6]=>[8,1,2,7,3,4,5,6]=>0000011
[8,2,6,7,1,3,4,5]=>[7,8,1,3,4,2,6,5]=>[8,1,3,4,6,7,2,5]=>0000011
[8,3,6,7,1,2,4,5]=>[7,1,8,2,4,3,6,5]=>[8,1,2,4,6,7,3,5]=>0000011
[4,6,3,5,1,2,7,8]=>[5,1,6,4,3,2,7,8]=>[4,6,3,5,1,2,7,8]=>0001100
[5,6,2,4,1,3,7,8]=>[4,6,1,2,5,3,7,8]=>[5,6,1,4,2,3,7,8]=>0010100
[3,7,2,5,1,4,6,8]=>[5,7,3,1,2,4,6,8]=>[3,7,1,5,2,4,6,8]=>0001010
[5,7,2,4,1,3,6,8]=>[4,7,1,2,5,3,6,8]=>[5,7,1,4,2,3,6,8]=>0010010
[5,7,3,4,1,2,6,8]=>[4,1,7,3,5,2,6,8]=>[5,7,3,4,1,2,6,8]=>0010010
[5,7,3,6,1,2,4,8]=>[6,1,7,2,5,3,4,8]=>[5,7,1,2,6,3,4,8]=>0000110
[3,8,2,5,1,4,6,7]=>[5,8,3,1,2,4,6,7]=>[3,8,1,5,2,4,6,7]=>0001001
[4,8,2,5,1,3,6,7]=>[5,8,1,4,2,3,6,7]=>[4,8,1,5,2,3,6,7]=>0001001
[5,8,2,4,1,3,6,7]=>[4,8,1,2,5,3,6,7]=>[5,8,1,4,2,3,6,7]=>0010001
[5,8,3,4,1,2,6,7]=>[4,1,8,3,5,2,6,7]=>[5,8,3,4,1,2,6,7]=>0010001
[3,8,2,6,1,4,5,7]=>[6,8,3,1,4,2,5,7]=>[3,8,1,4,6,2,5,7]=>0000101
[5,8,3,6,1,2,4,7]=>[6,1,8,2,5,3,4,7]=>[5,8,1,2,6,3,4,7]=>0000101
[6,8,2,4,1,3,5,7]=>[4,8,1,2,3,6,5,7]=>[6,8,1,4,2,3,5,7]=>0010001
[6,8,3,4,1,2,5,7]=>[4,1,8,3,2,6,5,7]=>[6,8,3,4,1,2,5,7]=>0010001
[4,8,2,7,1,3,5,6]=>[7,8,1,4,3,5,2,6]=>[4,8,1,3,5,7,2,6]=>0000011
[4,8,3,7,1,2,5,6]=>[7,1,8,4,2,5,3,6]=>[4,8,1,2,5,7,3,6]=>0000011
[5,8,2,7,1,3,4,6]=>[7,8,1,3,5,4,2,6]=>[5,8,1,3,4,7,2,6]=>0000011
[5,8,3,7,1,2,4,6]=>[7,1,8,2,5,4,3,6]=>[5,8,1,2,4,7,3,6]=>0000011
[5,8,4,7,1,2,3,6]=>[7,1,2,8,5,3,4,6]=>[5,8,1,2,3,7,4,6]=>0000011
[6,8,3,7,1,2,4,5]=>[7,1,8,2,4,6,3,5]=>[6,8,1,2,4,7,3,5]=>0000011
[6,8,4,7,1,2,3,5]=>[7,1,2,8,3,6,4,5]=>[6,8,1,2,3,7,4,5]=>0000011
[6,8,5,7,1,2,3,4]=>[7,1,2,3,8,6,5,4]=>[6,8,5,7,1,2,3,4]=>0000011
[7,8,2,4,1,3,5,6]=>[4,8,1,2,3,5,7,6]=>[7,8,1,4,2,3,5,6]=>0010001
[7,8,2,5,1,3,4,6]=>[5,8,1,3,2,4,7,6]=>[7,8,1,3,5,2,4,6]=>0001001
[7,8,3,5,1,2,4,6]=>[5,1,8,2,3,4,7,6]=>[7,8,1,2,5,3,4,6]=>0001001
[7,8,3,6,1,2,4,5]=>[6,1,8,2,4,3,7,5]=>[7,8,1,2,4,6,3,5]=>0000101
[7,8,4,6,1,2,3,5]=>[6,1,2,8,3,4,7,5]=>[7,8,1,2,3,6,4,5]=>0000101
[4,3,2,6,1,5,7,8]=>[6,3,4,2,1,5,7,8]=>[4,3,2,6,1,5,7,8]=>0110100
[5,3,2,6,1,4,7,8]=>[6,3,5,1,2,4,7,8]=>[5,3,1,6,2,4,7,8]=>0101100
[5,4,2,6,1,3,7,8]=>[6,4,1,5,2,3,7,8]=>[5,4,1,6,2,3,7,8]=>0011100
[6,4,2,5,1,3,7,8]=>[5,4,1,6,2,3,7,8]=>[6,4,1,5,2,3,7,8]=>0011100
[5,3,2,7,1,4,6,8]=>[7,3,5,1,2,4,6,8]=>[5,3,1,7,2,4,6,8]=>0101010
[5,4,3,7,1,2,6,8]=>[7,1,4,5,3,2,6,8]=>[5,4,3,7,1,2,6,8]=>0011010
[7,3,2,5,1,4,6,8]=>[5,3,7,1,2,4,6,8]=>[7,3,1,5,2,4,6,8]=>0101010
[7,5,2,4,1,3,6,8]=>[4,5,1,2,7,3,6,8]=>[7,5,1,4,2,3,6,8]=>0011010
[4,3,2,8,1,5,6,7]=>[8,3,4,2,1,5,6,7]=>[4,3,2,8,1,5,6,7]=>0110001
[5,3,2,8,1,4,6,7]=>[8,3,5,1,2,4,6,7]=>[5,3,1,8,2,4,6,7]=>0101001
[5,4,2,8,1,3,6,7]=>[8,4,1,5,2,3,6,7]=>[5,4,1,8,2,3,6,7]=>0011001
[5,4,3,8,1,2,6,7]=>[8,1,4,5,3,2,6,7]=>[5,4,3,8,1,2,6,7]=>0011001
[6,4,3,8,1,2,5,7]=>[8,1,4,6,2,3,5,7]=>[6,4,1,2,8,3,5,7]=>0010101
[6,5,2,8,1,3,4,7]=>[8,5,1,3,6,2,4,7]=>[6,5,1,3,8,2,4,7]=>0001101
[6,5,3,8,1,2,4,7]=>[8,1,5,2,6,3,4,7]=>[6,5,1,2,8,3,4,7]=>0001101
[6,5,4,8,1,2,3,7]=>[8,1,2,5,6,4,3,7]=>[6,5,4,8,1,2,3,7]=>0001101
[7,4,3,8,1,2,5,6]=>[8,1,4,7,2,5,3,6]=>[7,4,1,2,5,8,3,6]=>0010011
[7,5,4,8,1,2,3,6]=>[8,1,2,5,7,3,4,6]=>[7,5,1,2,3,8,4,6]=>0001011
[7,6,4,8,1,2,3,5]=>[8,1,2,6,3,7,4,5]=>[7,6,1,2,3,8,4,5]=>0000111
[8,4,2,5,1,3,6,7]=>[5,4,1,8,2,3,6,7]=>[8,4,1,5,2,3,6,7]=>0011001
[8,5,2,4,1,3,6,7]=>[4,5,1,2,8,3,6,7]=>[8,5,1,4,2,3,6,7]=>0011001
[8,3,2,6,1,4,5,7]=>[6,3,8,1,4,2,5,7]=>[8,3,1,4,6,2,5,7]=>0100101
[8,4,2,6,1,3,5,7]=>[6,4,1,8,3,2,5,7]=>[8,4,1,3,6,2,5,7]=>0010101
[8,5,3,6,1,2,4,7]=>[6,1,5,2,8,3,4,7]=>[8,5,1,2,6,3,4,7]=>0001101
[8,6,2,4,1,3,5,7]=>[4,6,1,2,3,8,5,7]=>[8,6,1,4,2,3,5,7]=>0010101
[8,6,3,5,1,2,4,7]=>[5,1,6,2,3,8,4,7]=>[8,6,1,2,5,3,4,7]=>0001101
[8,3,2,7,1,4,5,6]=>[7,3,8,1,4,5,2,6]=>[8,3,1,4,5,7,2,6]=>0100011
[8,5,4,7,1,2,3,6]=>[7,1,2,5,8,3,4,6]=>[8,5,1,2,3,7,4,6]=>0001011
[8,6,3,7,1,2,4,5]=>[7,1,6,2,4,8,3,5]=>[8,6,1,2,4,7,3,5]=>0000111
[8,6,4,7,1,2,3,5]=>[7,1,2,6,3,8,4,5]=>[8,6,1,2,3,7,4,5]=>0000111
[8,7,2,4,1,3,5,6]=>[4,7,1,2,3,5,8,6]=>[8,7,1,4,2,3,5,6]=>0010011
[8,7,3,5,1,2,4,6]=>[5,1,7,2,3,4,8,6]=>[8,7,1,2,5,3,4,6]=>0001011
[8,7,3,6,1,2,4,5]=>[6,1,7,2,4,3,8,5]=>[8,7,1,2,4,6,3,5]=>0000111
[8,7,4,6,1,2,3,5]=>[6,1,2,7,3,4,8,5]=>[8,7,1,2,3,6,4,5]=>0000111
[3,6,2,5,8,1,4,7]=>[8,6,3,1,2,5,4,7]=>[3,6,1,5,8,2,4,7]=>0000101
[4,6,2,5,8,1,3,7]=>[8,6,1,4,2,5,3,7]=>[4,6,1,5,8,2,3,7]=>0000101
[4,6,3,5,8,1,2,7]=>[8,1,6,4,3,5,2,7]=>[4,6,3,5,8,1,2,7]=>0000101
[4,7,2,5,8,1,3,6]=>[8,7,1,4,2,3,5,6]=>[4,7,1,8,2,3,5,6]=>0000011
[5,7,2,4,8,1,3,6]=>[8,7,1,2,5,3,4,6]=>[5,7,1,8,2,3,4,6]=>0000011
[5,7,3,4,8,1,2,6]=>[8,1,7,3,5,2,4,6]=>[5,7,3,8,1,2,4,6]=>0000011
[3,7,2,6,8,1,4,5]=>[8,7,3,1,4,2,6,5]=>[3,7,1,4,6,8,2,5]=>0000011
[4,7,2,6,8,1,3,5]=>[8,7,1,4,3,2,6,5]=>[4,7,1,3,6,8,2,5]=>0000011
[5,7,3,6,8,1,2,4]=>[8,1,7,2,5,3,6,4]=>[5,7,1,2,6,8,3,4]=>0000011
[6,7,2,4,8,1,3,5]=>[8,7,1,2,3,6,4,5]=>[6,7,1,8,2,3,4,5]=>0000011
[6,7,3,4,8,1,2,5]=>[8,1,7,3,2,6,4,5]=>[6,7,3,8,1,2,4,5]=>0000011
[3,8,2,5,7,1,4,6]=>[7,8,3,1,2,4,5,6]=>[3,8,1,7,2,4,5,6]=>0000011
[4,8,2,5,7,1,3,6]=>[7,8,1,4,2,3,5,6]=>[4,8,1,7,2,3,5,6]=>0000011
[3,8,2,6,7,1,4,5]=>[7,8,3,1,4,2,6,5]=>[3,8,1,4,6,7,2,5]=>0000011
[4,8,3,6,7,1,2,5]=>[7,1,8,4,2,3,6,5]=>[4,8,1,2,6,7,3,5]=>0000011
[5,8,2,6,7,1,3,4]=>[7,8,1,3,5,2,6,4]=>[5,8,1,3,6,7,2,4]=>0000011
[5,8,3,6,7,1,2,4]=>[7,1,8,2,5,3,6,4]=>[5,8,1,2,6,7,3,4]=>0000011
[6,8,2,4,7,1,3,5]=>[7,8,1,2,3,6,4,5]=>[6,8,1,7,2,3,4,5]=>0000011
[6,8,2,5,7,1,3,4]=>[7,8,1,3,2,6,5,4]=>[6,8,1,3,5,7,2,4]=>0000011
[6,8,4,5,7,1,2,3]=>[7,1,2,8,4,6,5,3]=>[6,8,4,5,7,1,2,3]=>0000011
[7,8,2,4,6,1,3,5]=>[6,8,1,2,3,4,7,5]=>[7,8,1,6,2,3,4,5]=>0000101
[7,8,2,5,6,1,3,4]=>[6,8,1,3,2,5,7,4]=>[7,8,1,3,5,6,2,4]=>0000101
[7,8,3,5,6,1,2,4]=>[6,1,8,2,3,5,7,4]=>[7,8,1,2,5,6,3,4]=>0000101
[4,3,2,6,8,1,5,7]=>[8,3,4,2,1,6,5,7]=>[4,3,2,6,8,1,5,7]=>0110001
[5,4,2,6,8,1,3,7]=>[8,4,1,5,2,6,3,7]=>[5,4,1,6,8,2,3,7]=>0011001
[5,4,3,6,8,1,2,7]=>[8,1,4,5,3,6,2,7]=>[5,4,3,6,8,1,2,7]=>0011001
[6,4,3,5,8,1,2,7]=>[8,1,4,6,3,5,2,7]=>[6,4,3,5,8,1,2,7]=>0010101
[5,3,2,7,8,1,4,6]=>[8,3,5,1,2,4,7,6]=>[5,3,1,7,8,2,4,6]=>0101001
[5,4,2,7,8,1,3,6]=>[8,4,1,5,2,3,7,6]=>[5,4,1,7,8,2,3,6]=>0011001
[5,4,3,7,8,1,2,6]=>[8,1,4,5,3,2,7,6]=>[5,4,3,7,8,1,2,6]=>0011001
[6,5,3,7,8,1,2,4]=>[8,1,5,2,6,3,7,4]=>[6,5,1,2,7,8,3,4]=>0001101
[7,3,2,5,8,1,4,6]=>[8,3,7,1,2,4,5,6]=>[7,3,1,8,2,4,5,6]=>0100011
[7,4,2,5,8,1,3,6]=>[8,4,1,7,2,3,5,6]=>[7,4,1,8,2,3,5,6]=>0010011
[7,4,3,5,8,1,2,6]=>[8,1,4,7,3,2,5,6]=>[7,4,3,8,1,2,5,6]=>0010011
[7,5,3,4,8,1,2,6]=>[8,1,5,3,7,2,4,6]=>[7,5,3,8,1,2,4,6]=>0001011
[7,3,2,6,8,1,4,5]=>[8,3,7,1,4,2,6,5]=>[7,3,1,4,6,8,2,5]=>0100011
[7,4,2,6,8,1,3,5]=>[8,4,1,7,3,2,6,5]=>[7,4,1,3,6,8,2,5]=>0010011
[7,4,3,6,8,1,2,5]=>[8,1,4,7,2,3,6,5]=>[7,4,1,2,6,8,3,5]=>0010011
[7,5,3,6,8,1,2,4]=>[8,1,5,2,7,3,6,4]=>[7,5,1,2,6,8,3,4]=>0001011
[7,6,2,4,8,1,3,5]=>[8,6,1,2,3,7,4,5]=>[7,6,1,8,2,3,4,5]=>0000111
[7,6,2,5,8,1,3,4]=>[8,6,1,3,2,7,5,4]=>[7,6,1,3,5,8,2,4]=>0000111
[7,6,3,5,8,1,2,4]=>[8,1,6,2,3,7,5,4]=>[7,6,1,2,5,8,3,4]=>0000111
[8,3,2,5,7,1,4,6]=>[7,3,8,1,2,4,5,6]=>[8,3,1,7,2,4,5,6]=>0100011
[8,4,2,5,7,1,3,6]=>[7,4,1,8,2,3,5,6]=>[8,4,1,7,2,3,5,6]=>0010011
[8,5,2,4,7,1,3,6]=>[7,5,1,2,8,3,4,6]=>[8,5,1,7,2,3,4,6]=>0001011
[8,3,2,6,7,1,4,5]=>[7,3,8,1,4,2,6,5]=>[8,3,1,4,6,7,2,5]=>0100011
[8,4,2,6,7,1,3,5]=>[7,4,1,8,3,2,6,5]=>[8,4,1,3,6,7,2,5]=>0010011
[8,4,3,6,7,1,2,5]=>[7,1,4,8,2,3,6,5]=>[8,4,1,2,6,7,3,5]=>0010011
[8,5,2,6,7,1,3,4]=>[7,5,1,3,8,2,6,4]=>[8,5,1,3,6,7,2,4]=>0001011
[8,5,3,6,7,1,2,4]=>[7,1,5,2,8,3,6,4]=>[8,5,1,2,6,7,3,4]=>0001011
[8,6,3,4,7,1,2,5]=>[7,1,6,3,2,8,4,5]=>[8,6,3,7,1,2,4,5]=>0000111
[8,6,3,5,7,1,2,4]=>[7,1,6,2,3,8,5,4]=>[8,6,1,2,5,7,3,4]=>0000111
[8,7,2,4,6,1,3,5]=>[6,7,1,2,3,4,8,5]=>[8,7,1,6,2,3,4,5]=>0000111
[8,7,2,5,6,1,3,4]=>[6,7,1,3,2,5,8,4]=>[8,7,1,3,5,6,2,4]=>0000111
[5,3,7,2,6,1,4,8]=>[6,7,5,1,3,2,4,8]=>[5,1,7,3,6,2,4,8]=>0001110
[6,3,7,2,5,1,4,8]=>[5,7,6,1,2,3,4,8]=>[6,1,7,2,5,3,4,8]=>0001110
[6,4,7,2,5,1,3,8]=>[5,7,1,6,2,4,3,8]=>[6,1,7,4,5,2,3,8]=>0001110
[7,3,6,2,5,1,4,8]=>[5,6,7,1,2,3,4,8]=>[7,1,6,2,5,3,4,8]=>0001110
[7,4,6,2,5,1,3,8]=>[5,6,1,7,2,4,3,8]=>[7,1,6,4,5,2,3,8]=>0001110
[6,3,8,2,5,1,4,7]=>[5,8,6,1,2,3,4,7]=>[6,1,8,2,5,3,4,7]=>0001101
[6,4,8,2,5,1,3,7]=>[5,8,1,6,2,4,3,7]=>[6,1,8,4,5,2,3,7]=>0001101
[6,4,8,3,5,1,2,7]=>[5,1,8,6,3,4,2,7]=>[6,3,8,4,5,1,2,7]=>0001101
[6,5,8,2,4,1,3,7]=>[4,8,1,2,6,5,3,7]=>[6,5,8,1,4,2,3,7]=>0010101
[6,5,8,3,4,1,2,7]=>[4,1,8,3,6,5,2,7]=>[6,5,8,3,4,1,2,7]=>0010101
[4,3,8,2,7,1,5,6]=>[7,8,4,3,1,5,2,6]=>[4,3,8,1,5,7,2,6]=>0010011
[5,4,8,3,7,1,2,6]=>[7,1,8,5,4,2,3,6]=>[5,4,8,1,2,7,3,6]=>0001011
[6,5,8,2,7,1,3,4]=>[7,8,1,3,6,5,2,4]=>[6,5,8,1,3,7,2,4]=>0000111
[7,3,8,2,5,1,4,6]=>[5,8,7,1,2,4,3,6]=>[7,1,8,2,4,5,3,6]=>0001011
[7,4,8,2,6,1,3,5]=>[6,8,1,7,3,2,4,5]=>[7,1,3,8,2,6,4,5]=>0000111
[7,4,8,3,6,1,2,5]=>[6,1,8,7,2,3,4,5]=>[7,1,2,8,3,6,4,5]=>0000111
[7,5,8,2,6,1,3,4]=>[6,8,1,3,7,2,5,4]=>[7,1,3,8,5,6,2,4]=>0000111
[7,5,8,3,6,1,2,4]=>[6,1,8,2,7,3,5,4]=>[7,1,2,8,5,6,3,4]=>0000111
[7,5,8,4,6,1,2,3]=>[6,1,2,8,7,4,5,3]=>[7,4,8,5,6,1,2,3]=>0000111
[7,6,8,2,4,1,3,5]=>[4,8,1,2,3,7,6,5]=>[7,6,8,1,4,2,3,5]=>0010011
[8,3,6,2,5,1,4,7]=>[5,6,8,1,2,3,4,7]=>[8,1,6,2,5,3,4,7]=>0001101
[8,5,6,2,4,1,3,7]=>[4,6,1,2,8,5,3,7]=>[8,5,6,1,4,2,3,7]=>0010101
[8,3,7,2,5,1,4,6]=>[5,7,8,1,2,4,3,6]=>[8,1,7,2,4,5,3,6]=>0001011
[8,5,7,2,4,1,3,6]=>[4,7,1,2,8,3,5,6]=>[8,1,4,2,3,7,5,6]=>0010011
[8,5,7,3,4,1,2,6]=>[4,1,7,3,8,2,5,6]=>[8,3,4,1,2,7,5,6]=>0010011
[8,3,7,2,6,1,4,5]=>[6,7,8,1,4,2,3,5]=>[8,1,4,7,2,6,3,5]=>0000111
[8,4,7,2,6,1,3,5]=>[6,7,1,8,3,2,4,5]=>[8,1,3,7,2,6,4,5]=>0000111
[8,4,7,3,6,1,2,5]=>[6,1,7,8,2,3,4,5]=>[8,1,2,7,3,6,4,5]=>0000111
[8,6,7,2,4,1,3,5]=>[4,7,1,2,3,8,6,5]=>[8,6,7,1,4,2,3,5]=>0010011
[8,6,7,3,5,1,2,4]=>[5,1,7,2,3,8,6,4]=>[8,6,7,1,2,5,3,4]=>0001011
[5,4,3,2,7,1,6,8]=>[7,3,4,5,2,1,6,8]=>[5,4,3,2,7,1,6,8]=>0111010
[6,4,3,2,7,1,5,8]=>[7,3,4,6,1,2,5,8]=>[6,4,3,1,7,2,5,8]=>0110110
[6,5,3,2,7,1,4,8]=>[7,3,5,1,6,2,4,8]=>[6,5,3,1,7,2,4,8]=>0101110
[6,5,4,2,7,1,3,8]=>[7,4,1,5,6,2,3,8]=>[6,5,4,1,7,2,3,8]=>0011110
[7,5,3,2,6,1,4,8]=>[6,3,5,1,7,2,4,8]=>[7,5,3,1,6,2,4,8]=>0101110
[7,5,4,2,6,1,3,8]=>[6,4,1,5,7,2,3,8]=>[7,5,4,1,6,2,3,8]=>0011110
[7,6,3,2,5,1,4,8]=>[5,3,6,1,2,7,4,8]=>[7,6,3,1,5,2,4,8]=>0101110
[7,6,4,2,5,1,3,8]=>[5,4,1,6,2,7,3,8]=>[7,6,4,1,5,2,3,8]=>0011110
[7,6,5,2,4,1,3,8]=>[4,5,1,2,6,7,3,8]=>[7,6,5,1,4,2,3,8]=>0011110
[5,4,3,2,8,1,6,7]=>[8,3,4,5,2,1,6,7]=>[5,4,3,2,8,1,6,7]=>0111001
[6,5,3,2,8,1,4,7]=>[8,3,5,1,6,2,4,7]=>[6,5,3,1,8,2,4,7]=>0101101
[6,5,4,3,8,1,2,7]=>[8,1,4,5,6,3,2,7]=>[6,5,4,3,8,1,2,7]=>0011101
[7,5,3,2,8,1,4,6]=>[8,3,5,1,7,4,2,6]=>[7,5,3,1,4,8,2,6]=>0101011
[7,5,4,2,8,1,3,6]=>[8,4,1,5,7,3,2,6]=>[7,5,4,1,3,8,2,6]=>0011011
[7,5,4,3,8,1,2,6]=>[8,1,4,5,7,2,3,6]=>[7,5,4,1,2,8,3,6]=>0011011
[7,6,3,2,8,1,4,5]=>[8,3,6,1,4,7,2,5]=>[7,6,3,1,4,8,2,5]=>0100111
[7,6,5,2,8,1,3,4]=>[8,5,1,3,6,7,2,4]=>[7,6,5,1,3,8,2,4]=>0001111
[7,6,5,3,8,1,2,4]=>[8,1,5,2,6,7,3,4]=>[7,6,5,1,2,8,3,4]=>0001111
[8,5,3,2,6,1,4,7]=>[6,3,5,1,8,2,4,7]=>[8,5,3,1,6,2,4,7]=>0101101
[8,6,3,2,5,1,4,7]=>[5,3,6,1,2,8,4,7]=>[8,6,3,1,5,2,4,7]=>0101101
[8,6,4,2,5,1,3,7]=>[5,4,1,6,2,8,3,7]=>[8,6,4,1,5,2,3,7]=>0011101
[8,5,4,2,7,1,3,6]=>[7,4,1,5,8,3,2,6]=>[8,5,4,1,3,7,2,6]=>0011011
[8,6,3,2,7,1,4,5]=>[7,3,6,1,4,8,2,5]=>[8,6,3,1,4,7,2,5]=>0100111
[8,6,4,2,7,1,3,5]=>[7,4,1,6,3,8,2,5]=>[8,6,4,1,3,7,2,5]=>0010111
[8,7,5,2,4,1,3,6]=>[4,5,1,2,7,3,8,6]=>[8,7,5,1,4,2,3,6]=>0011011
[8,7,3,2,6,1,4,5]=>[6,3,7,1,4,2,8,5]=>[8,7,3,1,4,6,2,5]=>0100111
[8,7,4,3,6,1,2,5]=>[6,1,4,7,2,3,8,5]=>[8,7,4,1,2,6,3,5]=>0010111
[8,7,5,2,6,1,3,4]=>[6,5,1,3,7,2,8,4]=>[8,7,5,1,3,6,2,4]=>0001111
[8,7,5,3,6,1,2,4]=>[6,1,5,2,7,3,8,4]=>[8,7,5,1,2,6,3,4]=>0001111
[8,7,6,2,5,1,3,4]=>[5,6,1,3,2,7,8,4]=>[8,7,6,1,3,5,2,4]=>0001111
[8,7,6,3,5,1,2,4]=>[5,1,6,2,3,7,8,4]=>[8,7,6,1,2,5,3,4]=>0001111
[4,8,3,7,2,6,1,5]=>[6,7,8,4,1,2,3,5]=>[4,8,1,7,2,6,3,5]=>0000111
[5,8,3,7,2,6,1,4]=>[6,7,8,1,5,2,3,4]=>[5,8,1,7,2,6,3,4]=>0000111
[5,8,4,7,2,6,1,3]=>[6,7,1,8,5,2,4,3]=>[5,8,1,7,4,6,2,3]=>0000111
[5,8,4,7,3,6,1,2]=>[6,1,7,8,5,3,4,2]=>[5,8,3,7,4,6,1,2]=>0000111
[6,8,3,7,2,5,1,4]=>[5,7,8,1,2,6,3,4]=>[6,8,1,7,2,5,3,4]=>0001011
[6,8,4,7,2,5,1,3]=>[5,7,1,8,2,6,4,3]=>[6,8,1,7,4,5,2,3]=>0001011
[6,8,4,7,3,5,1,2]=>[5,1,7,8,3,6,4,2]=>[6,8,3,7,4,5,1,2]=>0001011
[6,8,5,7,2,4,1,3]=>[4,7,1,2,8,6,5,3]=>[6,8,5,7,1,4,2,3]=>0010011
[7,8,3,6,2,5,1,4]=>[5,6,8,1,2,3,7,4]=>[7,8,1,6,2,5,3,4]=>0001101
[7,8,4,6,3,5,1,2]=>[5,1,6,8,3,4,7,2]=>[7,8,3,6,4,5,1,2]=>0001101
[6,5,3,8,2,7,1,4]=>[7,8,5,1,6,3,2,4]=>[6,5,1,8,3,7,2,4]=>0001111
[6,5,4,8,2,7,1,3]=>[7,8,1,5,6,4,2,3]=>[6,5,4,8,1,7,2,3]=>0001111
[7,6,4,8,2,5,1,3]=>[5,8,1,6,2,7,4,3]=>[7,6,1,8,4,5,2,3]=>0001111
[7,6,4,8,3,5,1,2]=>[5,1,8,6,3,7,4,2]=>[7,6,3,8,4,5,1,2]=>0001111
[7,6,5,8,2,4,1,3]=>[4,8,1,2,6,7,5,3]=>[7,6,5,8,1,4,2,3]=>0010111
[8,4,3,7,2,6,1,5]=>[6,7,4,8,1,2,3,5]=>[8,4,1,7,2,6,3,5]=>0010111
[8,5,4,7,2,6,1,3]=>[6,7,1,5,8,2,4,3]=>[8,5,1,7,4,6,2,3]=>0001111
[8,6,3,7,2,5,1,4]=>[5,7,6,1,2,8,3,4]=>[8,6,1,7,2,5,3,4]=>0001111
[8,6,4,7,2,5,1,3]=>[5,7,1,6,2,8,4,3]=>[8,6,1,7,4,5,2,3]=>0001111
[8,7,3,6,2,5,1,4]=>[5,6,7,1,2,3,8,4]=>[8,7,1,6,2,5,3,4]=>0001111
[8,7,4,6,2,5,1,3]=>[5,6,1,7,2,4,8,3]=>[8,7,1,6,4,5,2,3]=>0001111
[8,7,5,6,2,4,1,3]=>[4,6,1,2,7,5,8,3]=>[8,7,5,6,1,4,2,3]=>0010111
[6,5,4,3,2,8,1,7]=>[8,3,4,5,6,2,1,7]=>[6,5,4,3,2,8,1,7]=>0111101
[7,6,4,3,2,8,1,5]=>[8,3,4,6,1,7,2,5]=>[7,6,4,3,1,8,2,5]=>0110111
[7,6,5,3,2,8,1,4]=>[8,3,5,1,6,7,2,4]=>[7,6,5,3,1,8,2,4]=>0101111
[7,6,5,4,2,8,1,3]=>[8,4,1,5,6,7,2,3]=>[7,6,5,4,1,8,2,3]=>0011111
[8,5,4,3,2,7,1,6]=>[7,3,4,5,8,1,2,6]=>[8,5,4,3,1,7,2,6]=>0111011
[8,6,5,4,2,7,1,3]=>[7,4,1,5,6,8,2,3]=>[8,6,5,4,1,7,2,3]=>0011111
[8,7,5,4,2,6,1,3]=>[6,4,1,5,7,2,8,3]=>[8,7,5,4,1,6,2,3]=>0011111
[8,7,6,3,2,5,1,4]=>[5,3,6,1,2,7,8,4]=>[8,7,6,3,1,5,2,4]=>0101111
[8,7,6,4,2,5,1,3]=>[5,4,1,6,2,7,8,3]=>[8,7,6,4,1,5,2,3]=>0011111
[8,7,6,5,2,4,1,3]=>[4,5,1,2,6,7,8,3]=>[8,7,6,5,1,4,2,3]=>0011111
[8,1,2,3,4,7,5,6]=>[8,1,2,3,7,5,4,6]=>[7,5,8,1,2,3,4,6]=>0000011
[8,1,2,3,7,4,5,6]=>[8,1,2,7,4,5,3,6]=>[7,4,5,8,1,2,3,6]=>0000011
[8,1,2,3,6,7,4,5]=>[8,1,2,7,4,3,6,5]=>[7,4,6,8,1,2,3,5]=>0000011
[7,1,2,6,3,4,8,5]=>[7,1,6,3,8,2,4,5]=>[8,3,6,1,2,4,7,5]=>0000111
[6,1,2,5,3,7,8,4]=>[6,1,5,8,2,3,7,4]=>[7,8,1,2,5,3,6,4]=>0001101
[4,1,2,8,6,3,5,7]=>[4,1,6,2,3,8,5,7]=>[8,6,1,2,4,3,5,7]=>0010101
[4,1,2,8,7,3,5,6]=>[4,1,7,2,3,5,8,6]=>[8,7,1,2,4,3,5,6]=>0010011
[4,1,2,7,6,3,8,5]=>[4,1,6,2,7,8,5,3]=>[8,5,7,6,1,2,4,3]=>0010111
[8,1,2,5,6,3,4,7]=>[8,1,6,3,2,5,4,7]=>[6,3,5,8,1,2,4,7]=>0000101
[8,1,2,5,7,3,4,6]=>[8,1,7,3,2,4,5,6]=>[7,3,8,1,2,4,5,6]=>0000011
[7,1,2,5,6,3,8,4]=>[7,1,6,8,2,5,3,4]=>[8,1,2,5,6,3,7,4]=>0000111
[4,1,2,5,8,7,3,6]=>[4,1,7,2,5,3,8,6]=>[5,8,7,1,2,4,3,6]=>0010011
[8,1,2,5,6,7,3,4]=>[8,1,7,3,2,5,6,4]=>[7,3,5,6,8,1,2,4]=>0000011
[3,1,8,2,4,7,5,6]=>[3,8,1,2,7,5,4,6]=>[7,5,8,1,3,2,4,6]=>0100011
[3,1,8,2,6,4,5,7]=>[3,8,1,6,4,2,5,7]=>[6,4,8,1,3,2,5,7]=>0100101
[3,1,7,2,6,4,8,5]=>[3,7,1,6,8,2,4,5]=>[8,1,3,2,6,4,7,5]=>0100111
[3,1,5,2,8,7,4,6]=>[3,5,1,7,2,4,8,6]=>[8,7,1,3,2,5,4,6]=>0101011
[8,1,4,2,3,5,6,7]=>[8,4,2,1,3,5,6,7]=>[4,2,8,1,3,5,6,7]=>0010001
[7,1,4,2,3,5,8,6]=>[7,4,2,1,3,8,5,6]=>[4,2,8,1,3,5,7,6]=>0010011
[6,1,4,2,3,8,5,7]=>[6,4,2,1,8,3,5,7]=>[4,2,8,1,3,6,5,7]=>0010101
[8,1,7,2,3,4,5,6]=>[8,7,2,3,4,5,1,6]=>[7,2,3,4,5,8,1,6]=>0000011
[6,1,5,2,3,8,4,7]=>[6,5,2,8,1,3,4,7]=>[8,2,5,1,3,6,4,7]=>0001101
[5,1,4,2,8,3,6,7]=>[5,4,8,1,2,3,6,7]=>[8,1,4,2,5,3,6,7]=>0011001
[5,1,4,2,7,3,8,6]=>[5,4,7,1,2,8,3,6]=>[8,1,4,2,5,3,7,6]=>0011011
[8,1,4,2,6,3,5,7]=>[8,4,6,1,3,2,5,7]=>[6,1,4,3,8,2,5,7]=>0010101
[7,1,4,2,6,3,8,5]=>[7,4,6,1,8,2,3,5]=>[8,1,4,2,6,3,7,5]=>0010111
[8,1,5,2,6,3,4,7]=>[8,5,6,3,1,2,4,7]=>[6,3,5,1,8,2,4,7]=>0001101
[8,1,5,2,7,3,4,6]=>[8,5,7,3,1,4,2,6]=>[7,3,5,1,4,8,2,6]=>0001011
[7,1,5,2,6,3,8,4]=>[7,5,6,8,1,2,3,4]=>[8,1,6,2,5,3,7,4]=>0001111
[8,1,4,2,6,7,3,5]=>[8,4,7,1,3,2,6,5]=>[7,1,4,3,6,8,2,5]=>0010011
[8,1,5,2,6,7,3,4]=>[8,5,7,3,1,2,6,4]=>[7,3,5,1,6,8,2,4]=>0001011
[5,1,4,2,6,7,8,3]=>[5,4,8,1,2,6,7,3]=>[6,7,8,1,4,2,5,3]=>0011001
[3,1,4,8,2,7,5,6]=>[3,8,1,4,7,5,2,6]=>[4,7,5,8,1,3,2,6]=>0100011
[3,1,8,5,2,4,6,7]=>[3,5,1,2,8,4,6,7]=>[8,5,1,3,2,4,6,7]=>0101001
[3,1,7,5,2,4,8,6]=>[3,5,1,2,7,8,4,6]=>[8,5,1,3,2,4,7,6]=>0101011
[3,1,8,6,2,4,5,7]=>[3,6,1,2,4,8,5,7]=>[8,6,1,3,2,4,5,7]=>0100101
[3,1,7,6,2,4,8,5]=>[3,6,1,2,7,8,5,4]=>[8,5,7,6,1,3,2,4]=>0100111
[3,1,8,5,2,7,4,6]=>[3,5,1,8,7,2,4,6]=>[7,1,3,2,8,5,4,6]=>0101011
[8,1,4,5,2,3,6,7]=>[8,5,2,1,4,3,6,7]=>[5,2,4,8,1,3,6,7]=>0001001
[7,1,4,8,2,3,5,6]=>[7,8,2,1,3,5,4,6]=>[8,2,5,7,1,3,4,6]=>0000011
[7,1,4,6,2,3,8,5]=>[7,6,2,1,8,4,3,5]=>[8,2,4,6,1,3,7,5]=>0000111
[7,1,8,6,2,3,4,5]=>[7,6,2,3,4,8,1,5]=>[8,6,2,3,4,7,1,5]=>0000111
[7,1,6,5,2,3,8,4]=>[7,5,2,6,8,1,4,3]=>[8,2,6,5,4,7,1,3]=>0001111
[8,1,4,6,2,7,3,5]=>[8,6,7,1,3,4,2,5]=>[7,1,6,3,4,8,2,5]=>0000111
[8,1,6,5,2,7,3,4]=>[8,5,6,2,7,1,3,4]=>[7,2,6,5,1,8,3,4]=>0001111
[6,1,4,5,2,7,8,3]=>[6,5,8,1,4,2,7,3]=>[7,8,1,4,5,2,6,3]=>0001101
[3,1,4,8,6,2,5,7]=>[3,6,1,4,2,8,5,7]=>[4,8,6,1,3,2,5,7]=>0100101
[3,1,4,7,6,2,8,5]=>[3,6,1,4,7,8,5,2]=>[4,8,5,7,6,1,3,2]=>0100111
[3,1,8,7,6,2,4,5]=>[3,6,1,2,4,7,8,5]=>[8,7,6,1,3,2,4,5]=>0100111
[8,1,4,5,7,2,3,6]=>[8,7,2,1,4,3,5,6]=>[7,2,4,8,1,3,5,6]=>0000011
[8,1,4,7,6,2,3,5]=>[8,6,2,1,3,7,4,5]=>[7,6,2,8,1,3,4,5]=>0000111
[7,1,4,5,6,2,8,3]=>[7,6,8,1,4,5,2,3]=>[8,1,4,5,6,2,7,3]=>0000111
[3,1,4,8,6,7,2,5]=>[3,7,1,4,2,8,6,5]=>[4,8,6,7,1,3,2,5]=>0100011
[3,1,8,5,6,7,2,4]=>[3,7,1,2,8,5,6,4]=>[8,5,6,7,1,3,2,4]=>0100011
[8,1,4,5,6,7,2,3]=>[8,7,2,1,4,5,6,3]=>[7,2,4,5,6,8,1,3]=>0000011
[2,8,1,3,6,4,5,7]=>[8,2,1,6,4,3,5,7]=>[2,6,4,8,1,3,5,7]=>0000101
[2,7,1,3,6,4,8,5]=>[7,2,1,6,8,3,4,5]=>[2,8,1,3,6,4,7,5]=>0000111
[2,8,1,3,6,7,4,5]=>[8,2,1,7,4,3,6,5]=>[2,7,4,6,8,1,3,5]=>0000011
[2,4,1,8,3,7,5,6]=>[4,2,8,1,7,5,3,6]=>[2,7,5,8,1,4,3,6]=>0010011
[2,4,1,8,6,3,5,7]=>[4,2,6,1,3,8,5,7]=>[2,8,6,1,4,3,5,7]=>0010101
[2,4,1,5,8,7,3,6]=>[4,2,7,1,5,3,8,6]=>[2,5,8,7,1,4,3,6]=>0010011
[2,4,1,8,6,7,3,5]=>[4,2,7,1,3,8,6,5]=>[2,8,6,7,1,4,3,5]=>0010011
[6,3,1,2,4,8,5,7]=>[3,1,6,2,8,4,5,7]=>[8,3,1,2,4,6,5,7]=>0100101
[8,3,1,2,4,7,5,6]=>[3,1,8,2,7,5,4,6]=>[7,5,8,3,1,2,4,6]=>0100011
[6,3,1,2,4,7,8,5]=>[3,1,6,2,8,4,7,5]=>[7,8,3,1,2,4,6,5]=>0100101
[5,3,1,2,8,4,6,7]=>[3,1,5,8,2,4,6,7]=>[8,3,1,2,5,4,6,7]=>0101001
[5,3,1,2,7,4,8,6]=>[3,1,5,7,2,8,4,6]=>[8,3,1,2,5,4,7,6]=>0101011
[7,3,1,2,6,4,8,5]=>[3,1,7,6,8,2,4,5]=>[8,3,1,2,6,4,7,5]=>0100111
[8,4,1,2,3,7,5,6]=>[4,1,2,8,7,5,3,6]=>[7,5,8,4,1,2,3,6]=>0010011
[6,4,1,2,3,7,8,5]=>[4,1,2,6,8,3,7,5]=>[7,8,4,1,2,3,6,5]=>0010101
[7,6,1,2,3,4,8,5]=>[6,1,2,3,7,8,5,4]=>[8,5,7,6,1,2,3,4]=>0000111
[5,8,1,2,3,7,4,6]=>[8,1,2,7,5,4,3,6]=>[5,7,4,8,1,2,3,6]=>0000011
[8,6,1,2,3,7,4,5]=>[6,1,2,8,3,7,4,5]=>[7,1,2,3,8,6,4,5]=>0000111
[8,4,1,2,6,3,5,7]=>[4,1,8,6,2,3,5,7]=>[6,1,2,8,4,3,5,7]=>0010101
[5,8,1,2,7,3,4,6]=>[8,1,7,3,5,4,2,6]=>[5,7,3,4,8,1,2,6]=>0000011
[8,7,1,2,6,3,4,5]=>[7,1,6,3,4,2,8,5]=>[6,3,4,8,7,1,2,5]=>0000111
[5,7,1,2,6,3,8,4]=>[7,1,6,8,5,2,3,4]=>[5,8,1,2,6,3,7,4]=>0000111
[5,4,1,2,8,7,3,6]=>[4,1,5,7,3,2,8,6]=>[8,7,3,5,4,1,2,6]=>0011011
[4,3,1,6,2,8,5,7]=>[3,4,6,2,8,1,5,7]=>[8,2,4,3,1,6,5,7]=>0110101
[4,3,1,8,2,7,5,6]=>[3,4,8,2,7,5,1,6]=>[7,5,8,2,4,3,1,6]=>0110011
[4,3,1,6,2,7,8,5]=>[3,4,6,2,8,1,7,5]=>[7,8,2,4,3,1,6,5]=>0110101
[8,3,1,5,2,4,6,7]=>[3,8,5,1,2,4,6,7]=>[5,1,8,3,2,4,6,7]=>0101001
[7,3,1,5,2,4,8,6]=>[3,7,5,1,2,8,4,6]=>[5,1,8,3,2,4,7,6]=>0101011
[7,3,1,6,2,4,8,5]=>[3,7,6,1,8,2,4,5]=>[8,1,6,3,2,4,7,5]=>0100111
[8,3,1,6,2,7,4,5]=>[3,8,6,7,4,2,1,5]=>[7,4,6,2,8,3,1,5]=>0100111
[6,3,1,5,2,7,8,4]=>[3,6,5,8,2,1,7,4]=>[7,8,2,5,3,1,6,4]=>0101101
[8,4,1,5,2,3,6,7]=>[4,8,1,5,2,3,6,7]=>[5,1,8,4,2,3,6,7]=>0011001
[7,4,1,5,2,3,8,6]=>[4,7,1,5,2,8,3,6]=>[5,1,8,4,2,3,7,6]=>0011011
[7,4,1,8,2,3,5,6]=>[4,7,1,8,3,5,2,6]=>[8,1,3,5,7,4,2,6]=>0010011
[7,4,1,6,2,3,8,5]=>[4,7,1,6,8,2,3,5]=>[8,1,6,4,2,3,7,5]=>0010111
[8,7,1,5,2,3,4,6]=>[7,5,2,3,1,4,8,6]=>[5,2,3,8,7,1,4,6]=>0001011
[8,7,1,6,2,3,4,5]=>[7,6,2,3,4,1,8,5]=>[6,2,3,4,8,7,1,5]=>0000111
[6,7,1,5,2,3,8,4]=>[7,5,2,8,1,6,3,4]=>[6,8,2,5,1,3,7,4]=>0001011
[6,4,1,5,2,8,3,7]=>[4,6,5,8,2,3,1,7]=>[8,2,5,3,6,4,1,7]=>0011101
[8,4,1,5,2,7,3,6]=>[4,8,5,7,2,1,3,6]=>[7,2,5,1,8,4,3,6]=>0011011
[8,4,1,6,2,7,3,5]=>[4,8,6,7,1,2,3,5]=>[7,1,6,2,8,4,3,5]=>0010111
[6,8,1,5,2,7,3,4]=>[8,5,7,3,1,6,2,4]=>[6,7,3,5,1,8,2,4]=>0001011
[4,3,1,5,7,2,8,6]=>[3,4,7,2,5,8,1,6]=>[5,8,2,4,3,1,7,6]=>0110011
[4,3,1,8,6,2,5,7]=>[3,4,6,2,1,8,5,7]=>[8,6,2,4,3,1,5,7]=>0110101
[4,3,1,8,7,2,5,6]=>[3,4,7,2,1,5,8,6]=>[8,7,2,4,3,1,5,6]=>0110011
[4,3,1,7,6,2,8,5]=>[3,4,6,2,7,8,5,1]=>[8,5,7,6,2,4,3,1]=>0110111
[8,3,1,5,6,2,4,7]=>[3,8,6,1,2,5,4,7]=>[6,1,5,8,3,2,4,7]=>0100101
[8,3,1,7,6,2,4,5]=>[3,8,6,1,4,7,2,5]=>[7,6,1,4,8,3,2,5]=>0100111
[7,3,1,5,6,2,8,4]=>[3,7,6,8,2,5,1,4]=>[8,2,5,6,3,1,7,4]=>0100111
[8,4,1,5,7,2,3,6]=>[4,8,1,7,2,3,5,6]=>[7,1,8,4,2,3,5,6]=>0010011
[8,4,1,7,6,2,3,5]=>[4,8,1,6,3,7,2,5]=>[7,6,1,3,8,4,2,5]=>0010111
[7,4,1,5,6,2,8,3]=>[4,7,6,8,2,5,3,1]=>[8,2,5,6,3,7,4,1]=>0010111
[4,3,1,5,8,7,2,6]=>[3,4,7,2,5,1,8,6]=>[5,8,7,2,4,3,1,6]=>0110011
[4,3,1,5,6,7,8,2]=>[3,4,8,2,5,6,7,1]=>[5,6,7,8,2,4,3,1]=>0110001
[2,3,8,1,6,4,5,7]=>[8,2,3,6,4,1,5,7]=>[2,3,6,4,8,1,5,7]=>0000101
[2,3,7,1,6,4,8,5]=>[7,2,3,6,8,1,4,5]=>[2,3,8,1,6,4,7,5]=>0000111
[2,8,4,1,3,5,6,7]=>[4,2,1,8,3,5,6,7]=>[2,8,4,1,3,5,6,7]=>0010001
[2,7,4,1,3,5,8,6]=>[4,2,1,7,3,8,5,6]=>[2,8,4,1,3,5,7,6]=>0010011
[2,6,4,1,3,8,5,7]=>[4,2,1,6,8,3,5,7]=>[2,8,4,1,3,6,5,7]=>0010101
[2,6,4,1,3,7,8,5]=>[4,2,1,6,8,3,7,5]=>[2,7,8,4,1,3,6,5]=>0010101
[2,8,5,1,3,4,6,7]=>[5,2,1,3,8,4,6,7]=>[2,8,5,1,3,4,6,7]=>0001001
[2,8,7,1,3,4,5,6]=>[7,2,1,3,4,5,8,6]=>[2,8,7,1,3,4,5,6]=>0000011
[2,8,5,1,3,7,4,6]=>[5,2,1,8,7,3,4,6]=>[2,7,1,3,8,5,4,6]=>0001011
[2,6,8,1,3,7,4,5]=>[8,2,1,7,4,6,3,5]=>[2,6,7,4,8,1,3,5]=>0000011
[2,6,5,1,3,7,8,4]=>[5,2,1,6,8,4,7,3]=>[2,7,8,4,6,5,1,3]=>0001101
[2,5,4,1,8,3,6,7]=>[4,2,5,8,3,1,6,7]=>[2,8,3,5,4,1,6,7]=>0011001
[2,5,4,1,7,3,8,6]=>[4,2,5,7,3,8,1,6]=>[2,8,3,5,4,1,7,6]=>0011011
[2,8,4,1,6,3,5,7]=>[4,2,8,6,1,3,5,7]=>[2,6,1,8,4,3,5,7]=>0010101
[2,8,4,1,7,3,5,6]=>[4,2,8,7,1,5,3,6]=>[2,7,1,5,8,4,3,6]=>0010011
[2,7,4,1,6,3,8,5]=>[4,2,7,6,8,3,1,5]=>[2,8,3,6,4,1,7,5]=>0010111
[2,7,8,1,6,3,4,5]=>[8,2,6,3,4,1,7,5]=>[2,6,3,4,7,8,1,5]=>0000101
[2,7,5,1,6,3,8,4]=>[5,2,7,6,8,3,4,1]=>[2,8,3,6,4,7,5,1]=>0001111
[2,5,4,1,8,7,3,6]=>[4,2,5,7,3,1,8,6]=>[2,8,7,3,5,4,1,6]=>0011011
[7,3,4,1,2,5,8,6]=>[4,1,7,3,2,8,5,6]=>[8,3,4,1,2,5,7,6]=>0010011
[8,3,4,1,2,7,5,6]=>[4,1,8,3,7,5,2,6]=>[7,5,8,3,4,1,2,6]=>0010011
[7,3,5,1,2,4,8,6]=>[5,1,7,2,3,8,4,6]=>[8,1,2,5,3,4,7,6]=>0001011
[8,3,5,1,2,7,4,6]=>[5,1,8,7,3,4,2,6]=>[7,3,8,4,5,1,2,6]=>0001011
[6,3,8,1,2,7,4,5]=>[8,1,6,7,4,3,2,5]=>[7,4,6,3,8,1,2,5]=>0000111
[7,5,4,1,2,3,8,6]=>[4,1,2,5,7,8,3,6]=>[8,5,4,1,2,3,7,6]=>0011011
[6,8,4,1,2,3,5,7]=>[4,1,2,8,3,6,5,7]=>[6,8,4,1,2,3,5,7]=>0010001
[6,7,4,1,2,3,8,5]=>[4,1,2,7,8,6,3,5]=>[6,8,4,1,2,3,7,5]=>0010011
[6,8,5,1,2,3,4,7]=>[5,1,2,3,8,6,4,7]=>[6,8,5,1,2,3,4,7]=>0001001
[6,7,5,1,2,3,8,4]=>[5,1,2,7,8,6,4,3]=>[6,8,4,7,5,1,2,3]=>0001011
[6,5,4,1,2,8,3,7]=>[4,1,5,6,8,2,3,7]=>[8,1,2,6,5,4,3,7]=>0011101
[8,5,4,1,2,7,3,6]=>[4,1,5,8,7,3,2,6]=>[7,3,8,5,4,1,2,6]=>0011011
[6,8,4,1,2,7,3,5]=>[4,1,8,7,2,6,3,5]=>[6,7,1,2,8,4,3,5]=>0010011
[6,8,5,1,2,7,3,4]=>[5,1,8,2,7,6,3,4]=>[6,7,1,2,8,5,3,4]=>0001011
[6,5,4,1,2,7,8,3]=>[4,1,5,6,8,2,7,3]=>[7,8,1,2,6,5,4,3]=>0011101
[5,3,4,1,8,2,6,7]=>[4,8,5,3,1,2,6,7]=>[5,3,8,1,4,2,6,7]=>0011001
[8,3,4,1,6,2,5,7]=>[4,6,8,3,2,1,5,7]=>[8,3,6,2,4,1,5,7]=>0010101
[8,3,4,1,7,2,5,6]=>[4,7,8,3,2,5,1,6]=>[8,3,5,7,2,4,1,6]=>0010011
[7,3,4,1,6,2,8,5]=>[4,6,7,3,8,1,2,5]=>[8,3,7,1,4,2,6,5]=>0010111
[8,3,5,1,6,2,4,7]=>[5,6,8,2,3,1,4,7]=>[8,2,6,3,5,1,4,7]=>0001101
[8,3,5,1,7,2,4,6]=>[5,7,8,2,3,4,1,6]=>[8,2,7,3,4,5,1,6]=>0001011
[7,3,8,1,6,2,4,5]=>[8,6,7,2,4,1,3,5]=>[7,2,4,6,1,8,3,5]=>0000111
[7,3,5,1,6,2,8,4]=>[5,6,7,8,3,1,2,4]=>[8,3,7,1,6,2,5,4]=>0001111
[8,5,4,1,6,2,3,7]=>[4,5,2,8,6,1,3,7]=>[6,2,8,5,4,1,3,7]=>0011101
[8,5,4,1,7,2,3,6]=>[4,5,2,8,7,3,1,6]=>[7,2,3,8,5,4,1,6]=>0011011
[5,3,4,1,6,8,2,7]=>[4,8,5,3,1,6,2,7]=>[5,3,6,8,1,4,2,7]=>0011001
[5,3,4,1,8,7,2,6]=>[4,7,5,3,1,2,8,6]=>[5,3,8,7,1,4,2,6]=>0011011
[8,5,4,1,6,7,2,3]=>[4,5,2,8,7,1,6,3]=>[7,2,6,8,5,4,1,3]=>0011011
[5,3,4,1,6,7,8,2]=>[4,8,5,3,1,6,7,2]=>[5,3,6,7,8,1,4,2]=>0011001
[2,3,4,8,1,7,5,6]=>[8,2,3,4,7,5,1,6]=>[2,3,4,7,5,8,1,6]=>0000011
[2,3,7,5,1,4,8,6]=>[5,2,3,1,7,8,4,6]=>[2,3,8,5,1,4,7,6]=>0001011
[2,3,8,6,1,7,4,5]=>[6,2,3,8,1,7,4,5]=>[2,3,7,1,8,6,4,5]=>0000111
[2,7,4,6,1,3,8,5]=>[6,2,1,7,8,4,3,5]=>[2,8,4,7,1,3,6,5]=>0000111
[2,7,8,5,1,3,4,6]=>[5,2,1,3,8,4,7,6]=>[2,7,8,5,1,3,4,6]=>0001001
[2,7,8,6,1,3,4,5]=>[6,2,1,3,4,8,7,5]=>[2,7,8,6,1,3,4,5]=>0000101
[2,7,6,5,1,3,8,4]=>[5,2,1,6,7,8,3,4]=>[2,8,1,3,7,6,5,4]=>0001111
[2,6,4,5,1,8,3,7]=>[5,2,8,6,4,1,3,7]=>[2,6,4,8,1,5,3,7]=>0001101
[2,8,4,6,1,7,3,5]=>[6,2,7,8,3,4,1,5]=>[2,8,3,7,4,6,1,5]=>0000111
[2,6,4,5,1,7,8,3]=>[5,2,8,6,4,1,7,3]=>[2,6,4,7,8,1,5,3]=>0001101
[7,3,4,6,1,2,8,5]=>[6,1,7,3,8,4,2,5]=>[8,3,4,7,1,2,6,5]=>0000111
[8,3,6,5,1,2,4,7]=>[5,1,6,3,8,2,4,7]=>[8,3,6,5,1,2,4,7]=>0001101
[7,3,6,5,1,2,8,4]=>[5,1,6,7,8,4,3,2]=>[8,4,7,3,6,5,1,2]=>0001111
[7,6,4,5,1,2,8,3]=>[5,1,8,6,4,7,2,3]=>[7,6,4,8,1,2,5,3]=>0001111
[8,3,4,6,1,7,2,5]=>[6,7,8,3,2,4,1,5]=>[8,3,7,2,4,6,1,5]=>0000111
[8,3,6,5,1,7,2,4]=>[5,6,7,3,8,1,2,4]=>[8,3,7,1,6,5,2,4]=>0001111
[8,6,4,5,1,7,2,3]=>[5,7,2,6,4,8,1,3]=>[8,6,4,7,2,5,1,3]=>0001111
[2,3,4,8,6,1,5,7]=>[6,2,3,4,1,8,5,7]=>[2,3,4,8,6,1,5,7]=>0000101
[2,3,4,8,7,1,5,6]=>[7,2,3,4,1,5,8,6]=>[2,3,4,8,7,1,5,6]=>0000011
[2,3,4,7,6,1,8,5]=>[6,2,3,4,7,8,5,1]=>[2,3,4,8,5,7,6,1]=>0000111
[2,3,8,5,6,1,4,7]=>[6,2,3,1,8,5,4,7]=>[2,3,8,5,6,1,4,7]=>0000101
[2,3,8,5,7,1,4,6]=>[7,2,3,1,8,4,5,6]=>[2,3,8,1,4,7,5,6]=>0000011
[2,3,8,7,6,1,4,5]=>[6,2,3,1,4,7,8,5]=>[2,3,8,7,6,1,4,5]=>0000111
[2,8,4,5,6,1,3,7]=>[6,2,1,8,4,5,3,7]=>[2,8,4,5,6,1,3,7]=>0000101
[2,8,4,5,7,1,3,6]=>[7,2,1,8,4,3,5,6]=>[2,8,4,7,1,3,5,6]=>0000011
[2,8,4,7,6,1,3,5]=>[6,2,1,7,4,8,3,5]=>[2,8,4,7,6,1,3,5]=>0000111
[2,8,7,5,6,1,3,4]=>[6,2,1,3,7,5,8,4]=>[2,8,7,5,6,1,3,4]=>0000111
[2,7,4,5,6,1,8,3]=>[6,2,8,7,4,5,1,3]=>[2,7,4,5,8,1,6,3]=>0000111
[8,3,4,7,6,1,2,5]=>[6,1,7,2,3,8,4,5]=>[8,1,2,7,6,3,4,5]=>0000111
[8,3,7,5,6,1,2,4]=>[6,1,8,2,7,5,3,4]=>[7,5,8,1,2,6,3,4]=>0000111
[7,3,4,5,6,1,8,2]=>[6,8,7,3,4,5,1,2]=>[7,3,4,5,8,1,6,2]=>0000111
[2,3,4,5,8,7,1,6]=>[7,2,3,4,5,1,8,6]=>[2,3,4,5,8,7,1,6]=>0000011
[2,3,4,8,6,7,1,5]=>[7,2,3,4,1,8,6,5]=>[2,3,4,8,6,7,1,5]=>0000011
[2,3,8,5,6,7,1,4]=>[7,2,3,1,8,5,6,4]=>[2,3,8,5,6,7,1,4]=>0000011
[2,8,4,5,6,7,1,3]=>[7,2,1,8,4,5,6,3]=>[2,8,4,5,6,7,1,3]=>0000011
[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>00000001
[8,1,2,3,4,5,6,9,7]=>[8,1,2,3,4,5,9,6,7]=>[9,1,2,3,4,5,6,8,7]=>00000011
[3,1,9,2,4,5,6,7,8]=>[3,9,1,2,4,5,6,7,8]=>[9,1,3,2,4,5,6,7,8]=>01000001
[9,1,8,2,3,4,5,6,7]=>[9,8,2,3,4,5,6,1,7]=>[8,2,3,4,5,6,9,1,7]=>00000011
[3,1,4,5,6,7,8,9,2]=>[3,9,1,4,5,6,7,8,2]=>[4,5,6,7,8,9,1,3,2]=>01000001
[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,8]=>00000001
[9,3,1,2,4,5,6,7,8]=>[3,1,9,2,4,5,6,7,8]=>[9,3,1,2,4,5,6,7,8]=>01000001
[5,9,1,2,3,4,6,7,8]=>[9,1,2,3,5,4,6,7,8]=>[5,9,1,2,3,4,6,7,8]=>00000001
[9,6,1,2,3,4,5,7,8]=>[6,1,2,3,4,9,5,7,8]=>[9,6,1,2,3,4,5,7,8]=>00001001
[9,7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,9,6,8]=>[9,7,1,2,3,4,5,6,8]=>00000101
[8,9,1,2,3,4,5,6,7]=>[9,1,2,3,4,5,6,8,7]=>[8,9,1,2,3,4,5,6,7]=>00000001
[2,3,9,1,4,5,6,7,8]=>[9,2,3,1,4,5,6,7,8]=>[2,3,9,1,4,5,6,7,8]=>00000001
[2,9,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,9,7]=>[2,9,8,1,3,4,5,6,7]=>00000011
[9,5,4,1,2,3,6,7,8]=>[4,1,2,5,9,3,6,7,8]=>[9,5,4,1,2,3,6,7,8]=>00110001
[9,8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,9,7]=>[9,8,4,1,2,3,5,6,7]=>00100011
[9,7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,9,7,6]=>[9,7,8,1,2,3,4,5,6]=>00000011
[2,3,4,9,1,5,6,7,8]=>[9,2,3,4,1,5,6,7,8]=>[2,3,4,9,1,5,6,7,8]=>00000001
[2,3,9,8,1,4,5,6,7]=>[8,2,3,1,4,5,6,9,7]=>[2,3,9,8,1,4,5,6,7]=>00000011
[2,3,4,5,9,1,6,7,8]=>[9,2,3,4,5,1,6,7,8]=>[2,3,4,5,9,1,6,7,8]=>00000001
[9,7,4,5,6,1,2,3,8]=>[6,1,2,7,4,5,9,3,8]=>[9,7,4,5,6,1,2,3,8]=>00001101
[2,3,4,5,6,9,1,7,8]=>[9,2,3,4,5,6,1,7,8]=>[2,3,4,5,6,9,1,7,8]=>00000001
[2,3,9,5,6,7,1,4,8]=>[7,2,3,1,9,5,6,4,8]=>[2,3,9,5,6,7,1,4,8]=>00000101
[2,9,4,5,6,7,1,3,8]=>[7,2,1,9,4,5,6,3,8]=>[2,9,4,5,6,7,1,3,8]=>00000101
[9,3,4,5,6,7,1,2,8]=>[7,1,9,3,4,5,6,2,8]=>[9,3,4,5,6,7,1,2,8]=>00000101
[9,8,4,5,6,7,1,2,3]=>[7,1,2,8,4,5,6,9,3]=>[9,8,4,5,6,7,1,2,3]=>00000111
[2,3,4,5,6,7,9,1,8]=>[9,2,3,4,5,6,7,1,8]=>[2,3,4,5,6,7,9,1,8]=>00000001
[2,3,4,5,9,7,8,1,6]=>[8,2,3,4,5,1,9,7,6]=>[2,3,4,5,9,7,8,1,6]=>00000011
[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,9,1]=>00000001
[]=>[]=>[]=>
[3,5,2,6,1,4,8,7]=>[6,5,3,1,2,4,8,7]=>[3,5,1,6,2,4,8,7]=>0001101
[3,5,2,6,4,1,8,7]=>[4,6,3,5,1,2,8,7]=>[3,5,1,6,4,2,8,7]=>0011101
[3,5,2,7,4,8,1,6]=>[8,5,3,7,2,1,4,6]=>[3,7,2,5,1,8,4,6]=>0001011
[3,5,2,7,4,8,6,1]=>[6,5,3,8,2,7,1,4]=>[3,7,2,5,1,8,6,4]=>0001111
[4,5,7,2,3,8,6,1]=>[6,8,1,4,5,7,3,2]=>[4,5,7,1,3,8,6,2]=>0000111
[4,5,7,2,3,8,1,6]=>[8,7,2,4,5,1,3,6]=>[4,5,7,2,8,1,3,6]=>0000011
[4,5,6,2,3,1,8,7]=>[3,6,2,4,5,1,8,7]=>[4,5,6,2,3,1,8,7]=>0100101
[4,5,6,2,1,3,8,7]=>[2,6,1,4,5,3,8,7]=>[4,5,6,2,1,3,8,7]=>1000101
[3,5,1,6,4,2,8,7]=>[5,4,3,6,1,2,8,7]=>[3,6,4,1,5,2,8,7]=>0011101
[4,5,6,1,3,2,8,7]=>[6,3,1,4,5,2,8,7]=>[3,1,4,5,6,2,8,7]=>0100101
[4,5,6,3,1,2,8,7]=>[3,1,6,4,5,2,8,7]=>[4,5,6,3,1,2,8,7]=>0100101
[4,5,7,3,2,8,1,6]=>[8,3,7,4,5,1,2,6]=>[4,5,7,3,1,8,2,6]=>0100011
[4,5,7,3,2,8,6,1]=>[6,3,8,4,5,7,1,2]=>[4,5,7,3,1,8,6,2]=>0100111
[4,6,7,3,8,2,5,1]=>[5,8,7,4,2,6,3,1]=>[4,6,7,2,8,3,5,1]=>0001011
[4,5,7,1,3,8,2,6]=>[7,8,1,4,5,2,3,6]=>[4,5,8,1,7,2,3,6]=>0000011
[2,1,5,7,4,8,3,6]=>[2,1,8,7,5,3,4,6]=>[2,1,5,7,3,8,4,6]=>1000011
[2,1,5,7,4,8,6,3]=>[2,1,6,8,5,7,3,4]=>[2,1,5,7,3,8,6,4]=>1000111
[3,5,1,7,4,8,6,2]=>[5,6,3,8,1,7,2,4]=>[3,7,1,8,6,2,5,4]=>0001111
[4,6,7,3,8,5,1,2]=>[5,1,8,4,7,6,2,3]=>[4,6,7,1,2,8,5,3]=>0001011
[5,6,7,8,3,1,4,2]=>[3,8,4,2,5,6,7,1]=>[4,2,5,6,7,8,3,1]=>0110001
[4,6,7,1,8,3,5,2]=>[7,5,8,4,3,6,1,2]=>[4,6,8,3,5,1,7,2]=>0001011
[3,6,1,7,8,4,5,2]=>[6,5,3,8,4,1,7,2]=>[3,7,8,4,5,1,6,2]=>0001101
[2,1,6,7,8,4,5,3]=>[2,1,5,8,4,6,7,3]=>[2,1,6,7,8,4,5,3]=>1001001
[2,1,6,7,8,4,3,5]=>[2,1,4,8,3,6,7,5]=>[2,1,6,7,8,4,3,5]=>1010001
[3,6,1,7,8,4,2,5]=>[6,4,3,8,2,1,7,5]=>[3,7,8,4,2,6,1,5]=>0010101
[5,6,7,8,1,3,2,4]=>[8,3,1,2,5,6,7,4]=>[3,1,5,6,7,8,2,4]=>0100001
[4,6,7,2,8,3,1,5]=>[3,8,7,4,2,6,1,5]=>[4,6,7,2,8,3,1,5]=>0100011
[4,6,7,2,8,3,5,1]=>[5,7,8,4,3,6,2,1]=>[4,6,8,3,7,2,5,1]=>0001011
[3,6,2,7,8,4,1,5]=>[4,8,3,6,2,1,7,5]=>[3,6,2,7,8,4,1,5]=>0010101
[3,4,2,1,7,8,5,6]=>[2,4,3,1,8,5,7,6]=>[3,4,2,1,7,8,5,6]=>1010001
[3,4,1,2,7,8,6,5]=>[4,1,3,2,6,8,7,5]=>[3,4,1,2,7,8,6,5]=>0010101
[3,6,2,7,8,1,5,4]=>[8,6,3,5,1,2,7,4]=>[3,5,1,6,2,7,8,4]=>0001101
[3,6,2,7,8,5,1,4]=>[5,8,3,2,6,1,7,4]=>[3,6,2,7,8,5,1,4]=>0001101
[3,6,2,7,8,5,4,1]=>[4,5,3,8,6,2,7,1]=>[3,6,2,7,8,5,4,1]=>0011101
[4,6,7,2,8,5,3,1]=>[3,5,8,4,7,6,2,1]=>[4,6,7,2,8,5,3,1]=>0101011
[4,6,7,2,8,5,1,3]=>[5,8,2,4,7,6,1,3]=>[4,6,7,2,8,5,1,3]=>0001011
[4,6,7,2,8,1,5,3]=>[8,7,5,4,1,6,2,3]=>[4,5,1,6,7,2,8,3]=>0001011
[3,5,1,7,2,8,6,4]=>[5,7,3,6,1,8,2,4]=>[3,8,6,1,7,2,5,4]=>0001111
[2,1,5,7,3,8,6,4]=>[2,1,7,6,5,8,3,4]=>[2,1,5,8,6,3,7,4]=>1000111
[2,1,6,7,8,3,5,4]=>[2,1,8,5,3,6,7,4]=>[2,1,5,3,6,7,8,4]=>1001001
[3,6,1,7,8,2,5,4]=>[6,8,3,5,2,1,7,4]=>[3,5,2,7,8,1,6,4]=>0001101
[4,6,7,1,8,2,5,3]=>[7,8,5,4,2,6,1,3]=>[4,5,2,6,8,1,7,3]=>0001011
[5,6,7,8,1,2,4,3]=>[8,1,4,2,5,6,7,3]=>[4,1,2,5,6,7,8,3]=>0010001
[5,6,7,8,2,1,4,3]=>[2,8,4,1,5,6,7,3]=>[4,2,1,5,6,7,8,3]=>1010001
[5,6,7,8,2,4,1,3]=>[4,8,1,2,5,6,7,3]=>[5,6,7,8,1,4,2,3]=>0010001
[5,6,7,8,2,4,3,1]=>[3,4,8,1,5,6,7,2]=>[5,6,7,8,1,4,3,2]=>0110001
[5,6,7,8,1,4,2,3]=>[8,4,2,1,5,6,7,3]=>[4,2,5,6,7,8,1,3]=>0010001
[4,6,7,1,8,5,2,3]=>[7,5,2,4,8,6,1,3]=>[4,6,8,5,2,7,1,3]=>0001011
[3,6,1,7,8,5,2,4]=>[6,5,3,2,8,1,7,4]=>[3,7,8,5,2,6,1,4]=>0001101
[2,1,6,7,8,5,3,4]=>[2,1,5,3,8,6,7,4]=>[2,1,6,7,8,5,3,4]=>1001001
[3,6,1,7,8,5,4,2]=>[6,4,3,5,8,1,7,2]=>[3,7,8,5,4,1,6,2]=>0011101
[5,6,7,8,1,4,3,2]=>[8,3,4,1,5,6,7,2]=>[4,3,1,5,6,7,8,2]=>0110001
[5,6,7,8,4,1,3,2]=>[4,3,1,8,5,6,7,2]=>[3,1,5,6,7,8,4,2]=>0110001
[3,4,2,1,6,5,8,7,10,9]=>[2,4,3,1,6,5,8,7,10,9]=>[3,4,2,1,6,5,8,7,10,9]=>101010101
[2,1,5,6,4,3,8,7,10,9]=>[2,1,4,6,5,3,8,7,10,9]=>[2,1,5,6,4,3,8,7,10,9]=>101010101
[4,5,6,3,2,1,8,7,10,9]=>[2,3,6,4,5,1,8,7,10,9]=>[4,5,6,3,2,1,8,7,10,9]=>110010101
[2,1,4,3,7,8,6,5,10,9]=>[2,1,4,3,6,8,7,5,10,9]=>[2,1,4,3,7,8,6,5,10,9]=>101010101
[3,4,2,1,7,8,6,5,10,9]=>[2,4,3,1,6,8,7,5,10,9]=>[3,4,2,1,7,8,6,5,10,9]=>101010101
[3,6,2,7,8,5,4,1,10,9]=>[4,5,3,8,6,2,7,1,10,9]=>[3,6,2,7,8,5,4,1,10,9]=>001110101
[2,1,6,7,8,5,4,3,10,9]=>[2,1,4,5,8,6,7,3,10,9]=>[2,1,6,7,8,5,4,3,10,9]=>101100101
[5,6,7,8,4,3,2,1,10,9]=>[2,3,4,8,5,6,7,1,10,9]=>[5,6,7,8,4,3,2,1,10,9]=>111000101
[2,1,4,3,6,5,9,10,8,7]=>[2,1,4,3,6,5,8,10,9,7]=>[2,1,4,3,6,5,9,10,8,7]=>101010101
[3,4,2,1,6,5,9,10,8,7]=>[2,4,3,1,6,5,8,10,9,7]=>[3,4,2,1,6,5,9,10,8,7]=>101010101
[2,1,5,6,4,3,9,10,8,7]=>[2,1,4,6,5,3,8,10,9,7]=>[2,1,5,6,4,3,9,10,8,7]=>101010101
[4,5,6,3,2,1,9,10,8,7]=>[2,3,6,4,5,1,8,10,9,7]=>[4,5,6,3,2,1,9,10,8,7]=>110010101
[4,5,8,3,2,9,10,7,6,1]=>[6,3,7,4,5,10,8,2,9,1]=>[4,5,8,3,2,9,10,7,6,1]=>010011101
[2,1,5,8,4,9,10,7,6,3]=>[2,1,6,7,5,10,8,4,9,3]=>[2,1,5,8,4,9,10,7,6,3]=>100011101
[4,7,8,3,9,10,6,5,2,1]=>[2,5,6,4,10,8,7,3,9,1]=>[4,7,8,3,9,10,6,5,2,1]=>100110101
[2,1,4,3,8,9,10,7,6,5]=>[2,1,4,3,6,7,10,8,9,5]=>[2,1,4,3,8,9,10,7,6,5]=>101011001
[3,4,2,1,8,9,10,7,6,5]=>[2,4,3,1,6,7,10,8,9,5]=>[3,4,2,1,8,9,10,7,6,5]=>101011001
[2,1,7,8,9,10,6,5,4,3]=>[2,1,4,5,6,10,7,8,9,3]=>[2,1,7,8,9,10,6,5,4,3]=>101110001
[6,7,8,9,10,5,4,3,2,1]=>[2,3,4,5,10,6,7,8,9,1]=>[6,7,8,9,10,5,4,3,2,1]=>111100001
[6,5,8,7,3,4,1,2]=>[4,1,7,3,6,5,8,2]=>[6,5,8,7,3,4,1,2]=>0010111
[3,6,7,4,5,8,1,2]=>[8,1,3,7,4,6,5,2]=>[3,6,7,4,5,8,1,2]=>0000011
[1,6,7,4,5,2,3,8]=>[1,5,2,7,4,6,3,8]=>[1,6,7,4,5,2,3,8]=>0001010
[1,5,4,7,6,2,3,8]=>[1,6,2,5,4,7,3,8]=>[1,5,4,7,6,2,3,8]=>0001110
[2,5,4,7,6,1,8,3]=>[6,2,7,5,4,8,3,1]=>[2,5,4,8,3,7,6,1]=>0001111
[3,5,4,7,6,8,1,2]=>[8,1,3,5,4,7,6,2]=>[3,5,4,7,6,8,1,2]=>0001011
[4,5,3,7,8,6,1,2]=>[6,1,5,4,3,8,7,2]=>[4,5,3,7,8,6,1,2]=>0001101
[5,4,3,8,7,6,1,2]=>[6,1,4,5,3,7,8,2]=>[5,4,3,8,7,6,1,2]=>0011111
[6,4,8,3,7,5,1,2]=>[5,1,7,8,6,2,4,3]=>[6,1,2,8,4,7,5,3]=>0001111
[5,3,4,8,6,7,1,2]=>[7,1,5,3,4,8,6,2]=>[5,3,4,8,6,7,1,2]=>0001011
[4,3,5,6,8,7,1,2]=>[7,1,4,3,5,6,8,2]=>[4,3,5,6,8,7,1,2]=>0010011
[3,2,5,6,1,8,7,4]=>[6,3,2,7,5,1,8,4]=>[3,2,5,8,7,1,6,4]=>0100111
[4,2,5,6,8,1,7,3]=>[8,4,7,2,5,6,1,3]=>[5,6,7,2,4,1,8,3]=>0010011
[6,2,8,4,5,1,7,3]=>[5,6,7,8,4,2,1,3]=>[8,4,7,2,6,1,5,3]=>0001111
[7,8,2,4,5,1,6,3]=>[5,8,6,2,4,1,7,3]=>[6,2,4,7,8,1,5,3]=>0001101
[7,8,1,4,5,2,3,6]=>[8,5,2,1,4,3,7,6]=>[5,2,4,7,8,1,3,6]=>0001001
[6,1,8,4,5,2,3,7]=>[6,5,2,8,4,1,3,7]=>[8,4,5,2,6,1,3,7]=>0001101
[5,1,4,8,6,2,3,7]=>[5,6,2,1,4,8,3,7]=>[8,6,2,4,5,1,3,7]=>0001101
[4,1,3,2,8,6,5,7]=>[4,3,1,2,6,8,5,7]=>[3,1,4,2,8,6,5,7]=>0110101
[5,1,3,8,2,6,4,7]=>[5,8,1,6,3,2,4,7]=>[6,1,3,8,2,5,4,7]=>0001101
[6,1,8,3,2,5,4,7]=>[6,3,8,5,2,1,4,7]=>[5,3,2,8,1,6,4,7]=>0101101
[7,8,1,3,2,5,4,6]=>[8,3,1,5,2,4,7,6]=>[3,1,5,2,7,8,4,6]=>0101001
[7,8,2,3,1,5,6,4]=>[3,8,2,6,1,5,7,4]=>[6,2,3,1,5,7,8,4]=>0100101
[7,8,3,2,1,6,5,4]=>[2,3,8,5,6,1,7,4]=>[6,5,3,2,1,7,8,4]=>1101101
[7,8,4,2,6,1,5,3]=>[6,4,8,5,1,3,7,2]=>[5,1,7,8,4,3,6,2]=>0011101
[4,5,2,7,8,1,6,3]=>[8,5,6,4,2,1,7,3]=>[4,6,2,5,1,7,8,3]=>0001101
[1,5,3,7,2,6,4,8]=>[1,7,5,6,3,2,4,8]=>[1,6,3,5,2,7,4,8]=>0001110
[1,6,7,3,2,5,4,8]=>[1,3,7,5,2,6,4,8]=>[1,5,3,2,6,7,4,8]=>0101010
[2,6,7,3,1,5,8,4]=>[3,2,7,8,1,6,5,4]=>[2,6,8,3,1,5,7,4]=>0100011
[3,6,7,2,1,8,5,4]=>[2,7,3,5,8,6,1,4]=>[3,6,8,5,2,1,7,4]=>1001011
[7,8,5,6,2,1,4,3]=>[2,6,4,1,8,5,7,3]=>[4,2,1,7,8,5,6,3]=>1010101
[6,5,8,7,1,2,3,4]=>[7,1,2,3,6,5,8,4]=>[6,5,8,7,1,2,3,4]=>0000111
[5,4,1,8,7,2,3,6]=>[4,5,1,7,2,3,8,6]=>[8,7,1,5,4,2,3,6]=>0011011
[6,4,8,1,7,2,3,5]=>[8,7,2,6,3,4,1,5]=>[6,2,3,7,4,8,1,5]=>0000111
[7,8,3,1,2,6,4,5]=>[3,1,8,6,4,2,7,5]=>[6,4,7,8,3,1,2,5]=>0100101
[5,3,1,8,2,7,4,6]=>[3,5,8,7,2,4,1,6]=>[7,2,8,4,5,3,1,6]=>0101011
[4,3,1,2,8,7,5,6]=>[3,1,4,2,7,5,8,6]=>[4,3,1,2,8,7,5,6]=>0110011
[4,2,1,3,8,5,7,6]=>[2,4,1,3,8,7,5,6]=>[4,2,1,3,7,5,8,6]=>1010011
[7,8,2,1,3,4,6,5]=>[2,8,1,3,6,4,7,5]=>[6,2,1,3,4,7,8,5]=>1000101
[4,3,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>0110101
[6,3,1,5,2,4,8,7]=>[3,6,5,1,2,4,8,7]=>[5,1,6,3,2,4,8,7]=>0101101
[7,3,1,5,2,8,4,6]=>[3,7,5,8,2,4,1,6]=>[8,2,5,4,7,3,1,6]=>0101011
[8,4,5,1,2,7,3,6]=>[5,1,7,8,4,3,2,6]=>[8,4,7,3,5,1,2,6]=>0001011
[7,4,5,1,2,8,3,6]=>[5,1,8,7,4,3,2,6]=>[7,4,8,3,5,1,2,6]=>0001011
[6,4,5,1,2,3,8,7]=>[5,1,2,6,4,3,8,7]=>[6,4,5,1,2,3,8,7]=>0001101
[5,4,6,1,2,3,8,7]=>[6,1,2,5,4,3,8,7]=>[5,4,6,1,2,3,8,7]=>0001101
[2,1,6,5,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>[2,1,6,5,3,4,8,7]=>1001101
[3,6,1,5,2,4,8,7]=>[6,5,3,2,1,4,8,7]=>[3,5,2,6,1,4,8,7]=>0001101
[4,6,5,1,2,3,8,7]=>[5,1,2,4,6,3,8,7]=>[4,6,5,1,2,3,8,7]=>0001101
[5,6,4,1,2,3,8,7]=>[4,1,2,6,5,3,8,7]=>[5,6,4,1,2,3,8,7]=>0010101
[6,5,4,1,2,3,8,7]=>[4,1,2,5,6,3,8,7]=>[6,5,4,1,2,3,8,7]=>0011101
[7,5,4,1,2,8,3,6]=>[4,1,5,7,8,3,2,6]=>[8,3,7,5,4,1,2,6]=>0011011
[8,6,4,1,7,2,3,5]=>[4,6,2,8,3,7,1,5]=>[7,2,3,8,6,4,1,5]=>0010111
[5,7,4,1,2,8,3,6]=>[4,1,7,8,5,2,3,6]=>[5,8,1,2,7,4,3,6]=>0010011
[4,7,5,1,2,8,3,6]=>[5,1,7,4,8,2,3,6]=>[4,8,1,2,7,5,3,6]=>0001011
[3,7,1,5,2,8,4,6]=>[7,5,3,8,1,4,2,6]=>[3,8,1,5,4,7,2,6]=>0001011
[2,1,7,5,3,8,4,6]=>[2,1,5,7,8,3,4,6]=>[2,1,8,3,7,5,4,6]=>1001011
[2,1,8,5,3,7,4,6]=>[2,1,5,8,7,3,4,6]=>[2,1,7,3,8,5,4,6]=>1001011
[3,8,1,5,2,7,4,6]=>[8,5,3,7,1,4,2,6]=>[3,7,1,5,4,8,2,6]=>0001011
[4,8,5,1,2,7,3,6]=>[5,1,8,4,7,2,3,6]=>[4,7,1,2,8,5,3,6]=>0001011
[6,8,4,1,7,2,3,5]=>[4,8,1,7,3,6,2,5]=>[6,7,1,3,8,4,2,5]=>0010011
[5,8,6,7,1,2,3,4]=>[7,1,2,3,5,8,6,4]=>[5,8,6,7,1,2,3,4]=>0000011
[3,8,1,6,7,2,4,5]=>[8,7,3,2,4,1,6,5]=>[3,7,2,4,6,8,1,5]=>0000011
[2,1,8,6,7,3,4,5]=>[2,1,7,3,4,8,6,5]=>[2,1,8,6,7,3,4,5]=>1000011
[2,1,7,6,8,3,4,5]=>[2,1,8,3,4,7,6,5]=>[2,1,7,6,8,3,4,5]=>1000011
[3,7,1,6,8,2,4,5]=>[7,8,3,2,4,1,6,5]=>[3,8,2,4,6,7,1,5]=>0000011
[4,7,6,1,8,2,3,5]=>[6,7,1,4,3,8,2,5]=>[4,8,1,3,7,6,2,5]=>0000111
[5,7,6,8,1,2,3,4]=>[8,1,2,3,5,7,6,4]=>[5,7,6,8,1,2,3,4]=>0000011
[5,4,7,1,2,8,3,6]=>[7,1,8,5,4,3,2,6]=>[5,4,8,3,7,1,2,6]=>0001011
[7,4,6,1,8,2,3,5]=>[6,8,2,7,3,4,1,5]=>[7,2,3,8,4,6,1,5]=>0000111
[8,4,6,1,7,2,3,5]=>[6,7,2,8,3,4,1,5]=>[8,2,3,7,4,6,1,5]=>0000111
[7,3,1,6,8,2,4,5]=>[3,7,8,1,4,2,6,5]=>[8,1,4,6,7,3,2,5]=>0100011
[6,3,1,7,8,2,4,5]=>[3,6,8,1,4,2,7,5]=>[7,8,1,4,6,3,2,5]=>0100101
[5,3,1,7,2,8,4,6]=>[3,5,7,8,2,4,1,6]=>[8,2,7,4,5,3,1,6]=>0101011
[4,3,1,2,7,8,5,6]=>[3,1,4,2,8,5,7,6]=>[4,3,1,2,7,8,5,6]=>0110001
[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,8,7,5,6]=>1010011
[3,4,1,2,8,7,5,6]=>[4,1,3,2,7,5,8,6]=>[3,4,1,2,8,7,5,6]=>0010011
[6,3,1,8,7,2,4,5]=>[3,6,7,1,4,2,8,5]=>[8,7,1,4,6,3,2,5]=>0100111
[7,3,1,8,6,2,4,5]=>[3,7,6,1,4,8,2,5]=>[8,6,1,4,7,3,2,5]=>0100111
[7,4,8,1,6,2,3,5]=>[8,6,2,7,3,1,4,5]=>[7,2,3,6,1,8,4,5]=>0000111
[5,4,8,1,2,7,3,6]=>[8,1,7,5,4,3,2,6]=>[5,4,7,3,8,1,2,6]=>0001011
[3,5,1,8,2,7,4,6]=>[5,8,3,7,1,4,2,6]=>[3,7,1,8,4,5,2,6]=>0001011
[2,1,5,8,3,7,4,6]=>[2,1,8,7,5,4,3,6]=>[2,1,5,7,4,8,3,6]=>1000011
[2,1,6,8,7,3,4,5]=>[2,1,7,3,4,6,8,5]=>[2,1,6,8,7,3,4,5]=>1000011
[3,6,1,8,7,2,4,5]=>[6,7,3,2,4,1,8,5]=>[3,8,7,2,4,6,1,5]=>0000111
[4,6,8,1,7,2,3,5]=>[8,7,2,4,3,6,1,5]=>[4,6,7,2,3,8,1,5]=>0000011
[5,6,8,7,1,2,3,4]=>[7,1,2,3,5,6,8,4]=>[5,6,8,7,1,2,3,4]=>0000011
[7,5,8,6,1,2,3,4]=>[6,1,2,3,8,7,4,5]=>[7,1,2,3,4,8,6,5]=>0000111
[8,5,7,6,1,2,3,4]=>[6,1,2,3,7,8,4,5]=>[8,1,2,3,4,7,6,5]=>0000111
[5,7,8,6,1,2,3,4]=>[6,1,2,3,5,8,7,4]=>[5,7,8,6,1,2,3,4]=>0000101
[4,7,8,1,6,2,3,5]=>[8,6,2,4,3,1,7,5]=>[4,6,2,3,7,8,1,5]=>0000101
[3,7,1,8,6,2,4,5]=>[7,6,3,2,4,8,1,5]=>[3,8,6,2,4,7,1,5]=>0000111
[2,1,7,8,6,3,4,5]=>[2,1,6,3,4,8,7,5]=>[2,1,7,8,6,3,4,5]=>1000101
[2,1,8,7,6,3,4,5]=>[2,1,6,3,4,7,8,5]=>[2,1,8,7,6,3,4,5]=>1000111
[3,8,1,7,6,2,4,5]=>[8,6,3,2,4,7,1,5]=>[3,7,6,2,4,8,1,5]=>0000111
[5,8,7,6,1,2,3,4]=>[6,1,2,3,5,7,8,4]=>[5,8,7,6,1,2,3,4]=>0000111
[6,8,7,5,1,2,3,4]=>[5,1,2,3,7,6,8,4]=>[6,8,7,5,1,2,3,4]=>0001011
[6,4,7,3,8,5,1,2]=>[5,1,8,7,6,2,4,3]=>[6,1,2,7,4,8,5,3]=>0001111
[6,4,7,3,5,8,1,2]=>[8,1,7,6,3,4,5,2]=>[6,3,7,4,5,8,1,2]=>0000111
[6,4,7,2,5,1,8,3]=>[5,7,8,6,2,4,1,3]=>[6,2,8,4,7,1,5,3]=>0001111
[5,4,2,7,6,1,8,3]=>[6,4,5,7,3,8,2,1]=>[8,3,5,4,2,7,6,1]=>0011111
[5,4,3,7,6,8,1,2]=>[8,1,4,5,3,7,6,2]=>[5,4,3,7,6,8,1,2]=>0011011
[5,4,3,7,8,6,1,2]=>[6,1,4,5,3,8,7,2]=>[5,4,3,7,8,6,1,2]=>0011101
[6,4,8,3,5,7,1,2]=>[7,1,8,6,3,4,5,2]=>[6,3,8,4,5,7,1,2]=>0000111
[5,4,3,8,6,7,1,2]=>[7,1,4,5,3,8,6,2]=>[5,4,3,8,6,7,1,2]=>0011011
[5,4,3,6,8,7,1,2]=>[7,1,4,5,3,6,8,2]=>[5,4,3,6,8,7,1,2]=>0011011
[5,4,2,6,7,1,8,3]=>[7,4,5,8,3,6,1,2]=>[6,8,3,5,4,1,7,2]=>0011011
[5,4,2,6,7,1,3,8]=>[7,4,1,5,2,6,3,8]=>[5,4,1,6,7,2,3,8]=>0011010
[5,3,2,6,1,7,4,8]=>[6,3,5,7,2,1,4,8]=>[7,3,2,5,1,6,4,8]=>0101110
[5,3,2,6,1,8,7,4]=>[6,3,5,7,2,1,8,4]=>[8,7,3,2,5,1,6,4]=>0101111
[5,4,2,8,6,1,7,3]=>[6,4,5,8,3,7,2,1]=>[7,3,5,4,2,8,6,1]=>0011111
[6,4,8,2,5,1,7,3]=>[5,8,7,6,2,4,1,3]=>[6,2,7,4,8,1,5,3]=>0001111
[7,8,4,2,5,1,6,3]=>[5,4,8,6,3,1,7,2]=>[6,3,7,8,4,1,5,2]=>0011101
[7,8,4,2,5,1,3,6]=>[5,4,1,8,2,3,7,6]=>[7,8,4,1,5,2,3,6]=>0011001
[5,3,2,6,1,8,4,7]=>[6,3,5,8,2,1,4,7]=>[8,3,2,5,1,6,4,7]=>0101101
[4,3,2,1,6,8,5,7]=>[2,3,4,1,8,6,5,7]=>[4,3,2,1,6,8,5,7]=>1110001
[4,3,2,1,8,6,5,7]=>[2,3,4,1,6,8,5,7]=>[4,3,2,1,8,6,5,7]=>1110101
[5,3,2,8,1,6,4,7]=>[8,3,5,6,2,1,4,7]=>[6,3,2,5,1,8,4,7]=>0101101
[6,3,8,2,1,5,4,7]=>[2,8,6,5,1,3,4,7]=>[5,2,1,6,3,8,4,7]=>1001101
[7,8,3,2,1,5,4,6]=>[2,3,8,5,1,4,7,6]=>[5,3,2,1,7,8,4,6]=>1101001
[6,3,8,2,1,5,7,4]=>[2,8,6,7,1,3,5,4]=>[7,2,1,6,3,5,8,4]=>1000111
[5,3,2,8,1,6,7,4]=>[8,3,5,7,2,1,6,4]=>[7,3,2,5,1,6,8,4]=>0101011
[5,4,2,7,8,1,6,3]=>[8,4,5,6,3,1,7,2]=>[6,3,5,4,1,7,8,2]=>0011101
[5,3,2,7,1,6,8,4]=>[7,3,5,8,2,1,6,4]=>[8,3,2,5,1,6,7,4]=>0101011
[5,3,2,7,1,6,4,8]=>[7,3,5,6,2,1,4,8]=>[6,3,2,5,1,7,4,8]=>0101110
[6,3,7,2,1,5,4,8]=>[2,7,6,5,1,3,4,8]=>[5,2,1,6,3,7,4,8]=>1001110
[6,3,7,2,1,5,8,4]=>[2,7,6,8,1,3,5,4]=>[8,2,1,6,3,5,7,4]=>1000111
[6,3,7,2,1,8,5,4]=>[2,7,6,5,8,3,1,4]=>[8,5,3,6,2,1,7,4]=>1001111
[6,4,7,2,8,1,5,3]=>[8,7,5,6,1,4,2,3]=>[6,1,5,4,7,2,8,3]=>0001111
[6,5,7,8,2,1,4,3]=>[2,8,4,1,6,5,7,3]=>[4,2,1,6,5,7,8,3]=>1010101
[6,5,8,7,2,1,3,4]=>[2,7,1,3,6,5,8,4]=>[6,5,8,7,2,1,3,4]=>1000111
[6,3,7,2,1,8,4,5]=>[2,7,6,8,4,3,1,5]=>[8,4,6,3,7,2,1,5]=>1000111
[5,3,2,7,1,4,8,6]=>[7,3,5,1,2,8,4,6]=>[5,3,1,8,2,4,7,6]=>0101011
[5,4,2,8,7,1,3,6]=>[7,4,1,5,2,3,8,6]=>[5,4,1,8,7,2,3,6]=>0011011
[7,8,4,2,6,1,3,5]=>[6,4,1,8,3,2,7,5]=>[7,8,4,1,3,6,2,5]=>0010101
[7,8,3,2,1,6,4,5]=>[2,3,8,6,4,1,7,5]=>[6,4,7,8,3,2,1,5]=>1100101
[6,3,8,2,1,7,4,5]=>[2,8,6,7,4,3,1,5]=>[7,4,6,3,8,2,1,5]=>1000111
[5,3,2,8,1,7,4,6]=>[8,3,5,7,2,4,1,6]=>[7,3,2,5,4,8,1,6]=>0101011
[4,3,2,1,8,7,5,6]=>[2,3,4,1,7,5,8,6]=>[4,3,2,1,8,7,5,6]=>1110011
[4,3,2,1,7,5,8,6]=>[2,3,4,1,7,8,5,6]=>[4,3,2,1,8,5,7,6]=>1110011
[4,3,2,1,7,5,6,8]=>[2,3,4,1,7,5,6,8]=>[4,3,2,1,7,5,6,8]=>1110010
[4,3,2,1,8,5,7,6]=>[2,3,4,1,8,7,5,6]=>[4,3,2,1,7,5,8,6]=>1110011
[6,3,8,2,1,4,7,5]=>[2,8,6,1,7,3,4,5]=>[7,2,1,6,3,4,8,5]=>1000111
[7,8,3,2,1,4,6,5]=>[2,3,8,1,6,4,7,5]=>[6,3,2,1,4,7,8,5]=>1100101
[6,3,8,2,1,4,5,7]=>[2,8,6,1,4,3,5,7]=>[6,2,1,4,8,3,5,7]=>1000101
[4,3,2,1,8,5,6,7]=>[2,3,4,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>1110001
[4,3,2,1,5,8,6,7]=>[2,3,4,1,5,8,6,7]=>[4,3,2,1,5,8,6,7]=>1110001
[7,8,5,6,1,2,4,3]=>[6,1,4,2,8,5,7,3]=>[4,1,2,7,8,5,6,3]=>0010101
[7,8,4,1,6,2,5,3]=>[4,8,6,5,3,2,7,1]=>[5,3,6,2,7,8,4,1]=>0011101
[7,8,1,4,6,2,5,3]=>[8,6,5,1,2,4,7,3]=>[5,1,6,2,4,7,8,3]=>0001101
[1,6,8,4,7,2,5,3]=>[1,7,5,8,2,6,4,3]=>[1,6,8,2,5,4,7,3]=>0001011
[6,1,8,3,2,7,5,4]=>[6,3,8,5,7,1,2,4]=>[7,5,3,1,8,2,6,4]=>0101111
[7,8,1,3,2,6,5,4]=>[8,3,1,5,6,2,7,4]=>[3,1,6,5,2,7,8,4]=>0101101
[7,8,3,1,2,6,5,4]=>[3,1,8,5,6,2,7,4]=>[6,5,3,1,2,7,8,4]=>0101101
[7,8,3,4,6,5,1,2]=>[5,1,6,2,8,4,7,3]=>[7,8,1,2,4,6,5,3]=>0001101
[7,8,2,4,6,1,5,3]=>[6,8,5,2,1,4,7,3]=>[5,2,7,8,1,4,6,3]=>0001101
[7,8,2,3,1,6,5,4]=>[3,8,2,5,6,1,7,4]=>[6,5,2,3,1,7,8,4]=>0101101
[7,8,2,1,3,6,5,4]=>[2,8,1,5,6,3,7,4]=>[6,5,2,1,3,7,8,4]=>1001101
[7,8,1,2,3,6,5,4]=>[8,1,2,5,6,3,7,4]=>[6,5,1,2,3,7,8,4]=>0001101
[1,6,8,2,3,7,5,4]=>[1,8,2,5,7,6,3,4]=>[1,6,7,5,2,3,8,4]=>0001011
[1,5,2,8,3,7,6,4]=>[1,5,8,6,2,7,3,4]=>[1,7,6,2,8,3,5,4]=>0001111
[5,1,2,8,3,7,6,4]=>[5,1,8,6,2,7,3,4]=>[7,6,1,2,8,3,5,4]=>0001111
[5,2,1,8,3,7,6,4]=>[2,5,8,6,1,7,3,4]=>[7,6,2,1,8,3,5,4]=>1001111
[6,2,8,1,3,7,5,4]=>[8,6,1,5,7,2,3,4]=>[7,5,1,6,2,3,8,4]=>0001111
[6,2,8,3,1,7,5,4]=>[3,8,6,5,7,1,2,4]=>[7,5,1,6,3,2,8,4]=>0101111
[6,2,8,4,7,1,5,3]=>[7,6,5,8,1,2,4,3]=>[8,1,5,2,6,4,7,3]=>0001111
[3,6,8,4,7,5,1,2]=>[5,1,3,7,8,6,2,4]=>[3,6,8,1,2,7,5,4]=>0001011
[2,6,8,4,7,1,5,3]=>[7,2,5,8,1,6,4,3]=>[2,6,8,1,5,4,7,3]=>0001011
[2,6,8,1,3,7,5,4]=>[8,2,1,5,7,6,3,4]=>[2,6,7,5,1,3,8,4]=>0001011
[2,4,1,3,8,7,6,5]=>[4,2,1,3,6,7,8,5]=>[2,4,1,3,8,7,6,5]=>0010111
[3,5,4,8,7,6,1,2]=>[6,1,3,5,4,7,8,2]=>[3,5,4,8,7,6,1,2]=>0001111
[5,3,4,8,7,6,1,2]=>[6,1,5,3,4,7,8,2]=>[5,3,4,8,7,6,1,2]=>0001111
[5,2,4,8,7,1,6,3]=>[7,5,6,2,4,1,8,3]=>[6,2,4,5,1,8,7,3]=>0001111
[4,2,1,3,8,7,6,5]=>[2,4,1,3,6,7,8,5]=>[4,2,1,3,8,7,6,5]=>1010111
[4,1,2,3,8,7,6,5]=>[4,1,2,3,6,7,8,5]=>[4,1,2,3,8,7,6,5]=>0010111
[1,4,2,3,8,7,6,5]=>[1,4,2,3,6,7,8,5]=>[1,4,2,3,8,7,6,5]=>0010111
[4,1,3,2,8,7,6,5]=>[4,3,1,2,6,7,8,5]=>[3,1,4,2,8,7,6,5]=>0110111
[4,3,1,2,8,7,6,5]=>[3,1,4,2,6,7,8,5]=>[4,3,1,2,8,7,6,5]=>0110111
[6,3,8,1,2,7,5,4]=>[8,1,6,5,7,3,2,4]=>[7,5,3,6,1,2,8,4]=>0001111
[5,1,3,8,2,7,6,4]=>[5,8,1,6,3,7,2,4]=>[7,6,1,3,8,2,5,4]=>0001111
[1,5,4,8,7,2,6,3]=>[1,7,6,5,4,2,8,3]=>[1,5,4,6,2,8,7,3]=>0001111
[5,1,4,8,7,2,6,3]=>[5,7,6,1,4,2,8,3]=>[6,1,4,8,7,2,5,3]=>0001111
[5,4,1,8,7,2,6,3]=>[4,5,7,6,2,3,8,1]=>[6,2,8,7,3,5,4,1]=>0011111
[6,4,8,1,7,2,5,3]=>[8,7,5,6,2,4,1,3]=>[6,2,5,4,7,1,8,3]=>0001111
[6,5,8,7,1,2,4,3]=>[7,1,4,2,6,5,8,3]=>[4,1,2,6,5,8,7,3]=>0010111
[5,6,8,7,3,4,1,2]=>[4,1,7,3,5,6,8,2]=>[5,6,8,7,3,4,1,2]=>0010011
[5,6,8,7,2,1,4,3]=>[2,7,4,1,5,6,8,3]=>[4,2,1,5,6,8,7,3]=>1010011
[4,5,1,8,7,2,6,3]=>[5,7,6,4,1,2,8,3]=>[4,6,1,8,7,2,5,3]=>0001111
[4,1,5,8,7,2,6,3]=>[4,7,6,1,5,2,8,3]=>[5,6,1,8,7,2,4,3]=>0010111
[1,3,5,8,2,7,6,4]=>[1,8,3,6,5,7,2,4]=>[1,3,5,7,6,2,8,4]=>0000111
[3,1,5,8,2,7,6,4]=>[3,8,1,6,5,7,2,4]=>[5,7,6,1,3,2,8,4]=>0100111
[3,6,8,1,2,7,5,4]=>[8,1,3,5,7,6,2,4]=>[3,6,7,5,1,2,8,4]=>0001011
[3,6,8,2,1,7,5,4]=>[2,8,3,5,7,6,1,4]=>[3,6,7,5,2,1,8,4]=>1001011
[4,6,8,2,7,1,5,3]=>[7,8,5,4,1,6,2,3]=>[4,5,1,6,8,2,7,3]=>0001011
[4,6,8,3,7,5,1,2]=>[5,1,7,4,8,6,2,3]=>[4,6,8,1,2,7,5,3]=>0001011
[4,5,3,8,7,6,1,2]=>[6,1,5,4,3,7,8,2]=>[4,5,3,8,7,6,1,2]=>0001111
[4,5,2,8,7,1,6,3]=>[7,5,6,4,2,1,8,3]=>[4,6,2,5,1,8,7,3]=>0001111
[3,1,4,2,8,7,6,5]=>[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,7,6,5]=>0110111
[3,1,2,4,8,7,6,5]=>[3,1,2,4,6,7,8,5]=>[3,1,2,4,8,7,6,5]=>0100111
[3,2,5,8,1,7,6,4]=>[8,3,2,6,5,7,1,4]=>[3,2,5,7,6,1,8,4]=>0100111
[4,2,5,8,7,1,6,3]=>[7,4,6,2,5,1,8,3]=>[5,6,2,4,1,8,7,3]=>0010111
[4,3,5,8,7,6,1,2]=>[6,1,4,3,5,7,8,2]=>[4,3,5,8,7,6,1,2]=>0010111
[3,4,5,8,7,6,1,2]=>[6,1,3,4,5,7,8,2]=>[3,4,5,8,7,6,1,2]=>0000111
[2,4,5,8,7,1,6,3]=>[7,2,6,4,5,1,8,3]=>[2,4,5,6,1,8,7,3]=>0000111
[2,3,5,8,1,7,6,4]=>[8,2,3,6,5,7,1,4]=>[2,3,5,7,6,1,8,4]=>0000111
[4,1,3,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>0110101
[5,1,3,2,6,4,8,7]=>[5,3,1,6,2,4,8,7]=>[3,1,6,2,5,4,8,7]=>0101101
[6,1,3,2,5,4,8,7]=>[6,3,1,5,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>0101101
[7,1,3,2,5,4,8,6]=>[7,3,1,5,2,8,4,6]=>[3,1,5,2,8,4,7,6]=>0101011
[8,1,3,2,5,4,7,6]=>[8,3,1,5,2,7,4,6]=>[3,1,5,2,7,4,8,6]=>0101011
[8,1,4,2,5,3,7,6]=>[8,4,5,1,2,7,3,6]=>[5,1,4,2,7,3,8,6]=>0011011
[7,1,4,2,5,3,8,6]=>[7,4,5,1,2,8,3,6]=>[5,1,4,2,8,3,7,6]=>0011011
[6,1,4,2,5,3,8,7]=>[6,4,5,1,2,3,8,7]=>[5,1,4,2,6,3,8,7]=>0011101
[5,1,4,2,6,3,8,7]=>[5,4,6,1,2,3,8,7]=>[6,1,4,2,5,3,8,7]=>0011101
[2,1,6,3,5,4,8,7]=>[2,1,6,5,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>1001101
[3,1,6,2,5,4,8,7]=>[3,6,1,5,2,4,8,7]=>[5,1,3,2,6,4,8,7]=>0101101
[4,1,6,2,5,3,8,7]=>[4,6,5,1,2,3,8,7]=>[5,1,6,2,4,3,8,7]=>0011101
[6,2,5,1,4,3,8,7]=>[5,6,4,1,2,3,8,7]=>[4,1,6,2,5,3,8,7]=>0011101
[5,2,6,1,4,3,8,7]=>[6,5,4,1,2,3,8,7]=>[4,1,5,2,6,3,8,7]=>0011101
[5,2,7,1,4,3,8,6]=>[7,5,4,1,2,8,3,6]=>[4,1,5,2,8,3,7,6]=>0011011
[5,2,8,1,4,3,7,6]=>[8,5,4,1,2,7,3,6]=>[4,1,5,2,7,3,8,6]=>0011011
[6,2,8,1,4,3,7,5]=>[8,6,4,1,7,2,3,5]=>[4,1,7,2,6,3,8,5]=>0010111
[6,2,7,1,4,3,8,5]=>[7,6,4,1,8,2,3,5]=>[4,1,8,2,6,3,7,5]=>0010111
[7,2,5,1,4,3,8,6]=>[5,7,4,1,2,8,3,6]=>[4,1,8,2,5,3,7,6]=>0011011
[3,1,7,2,5,4,8,6]=>[3,7,1,5,2,8,4,6]=>[5,1,3,2,8,4,7,6]=>0101011
[2,1,7,3,5,4,8,6]=>[2,1,7,5,3,8,4,6]=>[2,1,5,3,8,4,7,6]=>1001011
[2,1,8,3,5,4,7,6]=>[2,1,8,5,3,7,4,6]=>[2,1,5,3,7,4,8,6]=>1001011
[3,1,8,2,5,4,7,6]=>[3,8,1,5,2,7,4,6]=>[5,1,3,2,7,4,8,6]=>0101011
[4,1,8,2,5,3,7,6]=>[4,8,5,1,2,7,3,6]=>[5,1,7,2,4,3,8,6]=>0011011
[8,2,5,1,4,3,7,6]=>[5,8,4,1,2,7,3,6]=>[4,1,7,2,5,3,8,6]=>0011011
[8,2,6,1,4,3,7,5]=>[6,8,4,1,7,2,3,5]=>[4,1,7,2,8,3,6,5]=>0010111
[7,1,4,3,8,2,6,5]=>[7,8,4,1,6,2,3,5]=>[4,1,6,2,8,3,7,5]=>0010111
[8,1,4,3,7,2,6,5]=>[8,7,4,1,6,2,3,5]=>[4,1,6,2,7,3,8,5]=>0010111
[8,1,5,3,7,2,6,4]=>[8,7,5,6,1,2,3,4]=>[6,1,5,2,7,3,8,4]=>0001111
[7,1,5,3,8,2,6,4]=>[7,8,5,6,1,2,3,4]=>[6,1,5,2,8,3,7,4]=>0001111
[8,2,6,1,5,3,7,4]=>[6,8,5,7,1,2,3,4]=>[7,1,5,2,8,3,6,4]=>0001111
[3,1,8,2,6,4,7,5]=>[3,8,1,6,7,2,4,5]=>[7,1,3,2,6,4,8,5]=>0100111
[2,1,8,3,6,4,7,5]=>[2,1,8,6,7,3,4,5]=>[2,1,7,3,6,4,8,5]=>1000111
[2,1,7,3,6,4,8,5]=>[2,1,7,6,8,3,4,5]=>[2,1,8,3,6,4,7,5]=>1000111
[7,2,6,1,5,3,8,4]=>[6,7,5,8,1,2,3,4]=>[8,1,5,2,7,3,6,4]=>0001111
[6,2,7,1,5,3,8,4]=>[7,6,5,8,1,2,3,4]=>[8,1,5,2,6,3,7,4]=>0001111
[6,2,8,1,5,3,7,4]=>[8,6,5,7,1,2,3,4]=>[7,1,5,2,6,3,8,4]=>0001111
[6,1,4,2,7,3,8,5]=>[6,4,7,1,8,2,3,5]=>[8,1,4,2,7,3,6,5]=>0010111
[8,1,4,2,6,3,7,5]=>[8,4,6,1,7,2,3,5]=>[7,1,4,2,6,3,8,5]=>0010111
[8,1,3,2,6,4,7,5]=>[8,3,1,6,7,2,4,5]=>[3,1,7,2,6,4,8,5]=>0100111
[7,1,3,2,6,4,8,5]=>[7,3,1,6,8,2,4,5]=>[3,1,8,2,6,4,7,5]=>0100111
[6,1,3,2,7,4,8,5]=>[6,3,1,7,8,2,4,5]=>[3,1,8,2,7,4,6,5]=>0100111
[5,1,3,2,7,4,8,6]=>[5,3,1,7,2,8,4,6]=>[3,1,8,2,5,4,7,6]=>0101011
[4,1,3,2,7,5,8,6]=>[4,3,1,2,7,8,5,6]=>[3,1,4,2,8,5,7,6]=>0110011
[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,5,8,6]=>1010011
[3,1,4,2,8,5,7,6]=>[3,4,1,2,8,7,5,6]=>[4,1,3,2,7,5,8,6]=>0110011
[4,1,3,2,8,5,7,6]=>[4,3,1,2,8,7,5,6]=>[3,1,4,2,7,5,8,6]=>0110011
[5,1,3,2,8,4,7,6]=>[5,3,1,8,2,7,4,6]=>[3,1,7,2,5,4,8,6]=>0101011
[6,1,3,2,8,4,7,5]=>[6,3,1,8,7,2,4,5]=>[3,1,7,2,8,4,6,5]=>0100111
[8,4,7,1,3,2,6,5]=>[7,3,1,8,6,2,4,5]=>[3,1,6,2,8,4,7,5]=>0100111
[7,4,8,1,3,2,6,5]=>[8,3,1,7,6,2,4,5]=>[3,1,6,2,7,4,8,5]=>0100111
[7,3,8,1,4,2,6,5]=>[8,4,7,1,6,2,3,5]=>[6,1,4,2,7,3,8,5]=>0010111
[8,3,7,1,4,2,6,5]=>[7,4,8,1,6,2,3,5]=>[6,1,4,2,8,3,7,5]=>0010111
[6,1,4,2,8,3,7,5]=>[6,4,8,1,7,2,3,5]=>[7,1,4,2,8,3,6,5]=>0010111
[5,1,4,2,8,3,7,6]=>[5,4,8,1,2,7,3,6]=>[7,1,4,2,5,3,8,6]=>0011011
[3,1,5,2,8,4,7,6]=>[3,5,1,8,2,7,4,6]=>[7,1,3,2,5,4,8,6]=>0101011
[2,1,5,3,8,4,7,6]=>[2,1,5,8,3,7,4,6]=>[2,1,7,3,5,4,8,6]=>1001011
[2,1,6,3,8,4,7,5]=>[2,1,6,8,7,3,4,5]=>[2,1,7,3,8,4,6,5]=>1000111
[4,1,6,2,8,3,7,5]=>[4,6,8,1,7,2,3,5]=>[7,1,8,2,4,3,6,5]=>0010111
[6,1,5,2,8,3,7,4]=>[6,5,8,7,1,2,3,4]=>[7,1,8,2,5,3,6,4]=>0001111
[6,2,7,3,8,1,5,4]=>[8,6,7,5,1,2,3,4]=>[5,1,7,2,6,3,8,4]=>0001111
[6,2,8,3,7,1,5,4]=>[7,6,8,5,1,2,3,4]=>[5,1,8,2,6,3,7,4]=>0001111
[3,1,8,4,7,2,6,5]=>[3,7,1,8,6,2,4,5]=>[6,1,3,2,8,4,7,5]=>0100111
[2,1,8,4,7,3,6,5]=>[2,1,7,8,6,3,4,5]=>[2,1,6,3,8,4,7,5]=>1000111
[2,1,7,4,8,3,6,5]=>[2,1,8,7,6,3,4,5]=>[2,1,6,3,7,4,8,5]=>1000111
[3,1,7,4,8,2,6,5]=>[3,8,1,7,6,2,4,5]=>[6,1,3,2,7,4,8,5]=>0100111
[5,1,7,3,8,2,6,4]=>[5,8,7,6,1,2,3,4]=>[6,1,7,2,8,3,5,4]=>0001111
[7,3,8,2,6,1,5,4]=>[6,8,7,5,1,2,3,4]=>[5,1,7,2,8,3,6,4]=>0001111
[8,2,6,3,7,1,5,4]=>[7,8,6,5,1,2,3,4]=>[5,1,6,2,8,3,7,4]=>0001111
[7,2,6,3,8,1,5,4]=>[8,7,6,5,1,2,3,4]=>[5,1,6,2,7,3,8,4]=>0001111
[3,4,2,6,8,1,5,7]=>[8,4,3,2,1,6,5,7]=>[3,4,2,6,8,1,5,7]=>0010001
[5,3,6,2,8,1,4,7]=>[8,6,5,1,3,2,4,7]=>[5,1,6,3,8,2,4,7]=>0001101
[5,7,3,8,2,4,1,6]=>[4,8,7,2,5,1,3,6]=>[5,7,2,8,1,4,3,6]=>0010011
[5,7,3,8,2,4,6,1]=>[6,8,7,2,5,4,3,1]=>[5,7,2,4,8,3,6,1]=>0000111
[7,4,2,5,8,3,6,1]=>[6,4,7,8,3,2,5,1]=>[8,3,7,4,2,5,6,1]=>0010111
[7,4,2,5,8,3,1,6]=>[3,8,4,7,1,2,5,6]=>[7,4,1,8,3,2,5,6]=>0110011
[4,5,2,6,3,8,1,7]=>[8,5,6,4,2,3,1,7]=>[4,6,2,5,3,8,1,7]=>0001101
[5,3,1,6,8,2,4,7]=>[3,5,8,1,2,6,4,7]=>[6,8,1,5,3,2,4,7]=>0101001
[4,5,1,6,3,8,2,7]=>[5,8,6,4,1,3,2,7]=>[4,6,1,8,3,5,2,7]=>0001101
[4,5,6,3,2,8,1,7]=>[8,3,6,4,5,2,1,7]=>[4,5,6,3,2,8,1,7]=>0100101
[7,4,5,3,8,2,6,1]=>[6,8,5,7,4,2,3,1]=>[7,4,5,2,8,3,6,1]=>0001111
[6,7,4,8,3,2,5,1]=>[5,3,8,7,2,6,4,1]=>[6,7,3,2,8,4,5,1]=>0101011
[6,7,4,8,3,2,1,5]=>[2,3,8,7,1,6,4,5]=>[6,7,3,2,1,8,4,5]=>1100011
[7,4,5,3,1,8,2,6]=>[3,5,8,7,4,1,2,6]=>[7,4,8,1,5,3,2,6]=>0101011
[4,7,1,5,8,3,2,6]=>[7,3,8,4,1,2,5,6]=>[4,8,3,1,7,2,5,6]=>0100011
[7,5,8,2,4,6,1,3]=>[6,8,1,2,7,4,5,3]=>[7,1,4,8,5,6,2,3]=>0000111
[4,5,1,7,8,3,6,2]=>[5,6,8,4,1,3,7,2]=>[4,7,8,1,6,3,5,2]=>0001101
[6,7,4,3,8,1,5,2]=>[8,5,4,7,1,6,3,2]=>[6,7,4,1,5,3,8,2]=>0011011
[6,7,4,8,3,5,2,1]=>[2,5,8,7,3,6,4,1]=>[6,7,3,8,4,5,2,1]=>1001011
[5,6,7,3,8,4,2,1]=>[2,4,8,7,5,6,1,3]=>[5,6,7,2,1,8,4,3]=>1010011
[5,6,7,3,1,8,4,2]=>[3,7,4,8,5,6,2,1]=>[5,6,8,4,2,7,3,1]=>0110011
[5,6,1,7,3,8,4,2]=>[6,4,8,7,5,1,2,3]=>[5,7,1,8,4,2,6,3]=>0010111
[6,4,7,1,8,3,5,2]=>[7,5,8,6,3,4,1,2]=>[6,3,8,4,5,1,7,2]=>0001111
[6,7,2,8,4,5,1,3]=>[5,7,1,8,4,6,2,3]=>[6,8,4,7,1,5,2,3]=>0001011
[6,7,2,8,4,1,3,5]=>[4,8,2,7,3,6,1,5]=>[6,7,2,3,8,4,1,5]=>0010011
[6,1,7,4,8,3,2,5]=>[6,3,8,7,2,1,4,5]=>[7,3,2,8,1,6,4,5]=>0100111
[5,1,6,7,3,2,8,4]=>[5,3,7,8,1,6,2,4]=>[6,8,3,1,7,2,5,4]=>0101011
[5,6,7,3,2,1,8,4]=>[2,3,7,8,5,6,1,4]=>[5,6,8,3,2,1,7,4]=>1100011
[5,6,7,3,2,8,4,1]=>[4,3,8,7,5,6,1,2]=>[5,6,7,3,1,8,4,2]=>0110011
[5,6,2,7,3,8,4,1]=>[4,8,6,7,5,3,1,2]=>[5,7,3,6,1,8,4,2]=>0010111
[5,6,2,1,7,3,8,4]=>[2,6,7,8,5,1,3,4]=>[5,8,2,1,7,3,6,4]=>1000111
[7,5,8,2,1,3,4,6]=>[2,8,1,3,7,4,5,6]=>[7,2,1,3,4,8,5,6]=>1000011
[5,7,3,1,8,2,4,6]=>[3,7,8,1,5,4,2,6]=>[5,8,1,4,7,3,2,6]=>0100011
[4,7,1,5,2,8,3,6]=>[7,5,8,4,1,3,2,6]=>[4,8,1,5,3,7,2,6]=>0001011
[6,7,4,2,1,8,3,5]=>[2,4,7,8,1,6,3,5]=>[6,8,2,1,7,4,3,5]=>1010011
[6,7,4,2,8,3,1,5]=>[3,8,4,7,2,6,1,5]=>[6,7,4,2,8,3,1,5]=>0110011
[6,7,4,2,8,3,5,1]=>[5,4,7,8,2,6,3,1]=>[6,8,2,7,4,3,5,1]=>0011011
[3,6,7,2,8,4,5,1]=>[5,7,3,8,4,6,2,1]=>[3,6,8,4,7,2,5,1]=>0001011
[3,6,7,2,8,4,1,5]=>[4,8,3,7,2,6,1,5]=>[3,6,7,2,8,4,1,5]=>0010011
[3,6,7,2,1,8,4,5]=>[2,7,3,8,4,6,1,5]=>[3,6,8,4,7,2,1,5]=>1000011
[3,4,7,8,2,1,5,6]=>[2,8,3,4,1,5,7,6]=>[3,4,7,8,2,1,5,6]=>1000001
[3,7,8,1,4,6,2,5]=>[8,6,3,1,2,4,7,5]=>[3,6,1,7,8,2,4,5]=>0000101
[3,4,7,8,2,6,1,5]=>[6,8,3,4,1,2,7,5]=>[3,4,7,8,1,6,2,5]=>0000101
[5,7,3,8,2,6,1,4]=>[6,8,7,1,5,2,3,4]=>[5,7,1,8,2,6,3,4]=>0000111
[3,6,7,2,8,5,1,4]=>[5,8,3,2,7,6,1,4]=>[3,6,7,2,8,5,1,4]=>0001011
[3,6,7,8,5,2,1,4]=>[2,5,3,1,8,6,7,4]=>[3,6,7,8,5,2,1,4]=>1001001
[3,6,7,8,5,2,4,1]=>[4,5,3,2,8,6,7,1]=>[3,6,7,8,5,2,4,1]=>0011001
[6,4,7,8,2,5,3,1]=>[3,5,8,6,1,4,7,2]=>[6,1,7,8,4,5,3,2]=>0101101
[4,1,5,7,8,2,6,3]=>[4,8,6,1,5,2,7,3]=>[5,6,1,7,8,2,4,3]=>0010101
[6,4,1,7,8,2,5,3]=>[4,6,8,5,3,2,7,1]=>[5,3,7,8,2,6,4,1]=>0011101
[5,1,6,2,7,8,4,3]=>[5,6,4,8,1,2,7,3]=>[7,8,4,1,6,2,5,3]=>0011101
[5,6,2,7,8,4,3,1]=>[3,4,8,6,5,2,7,1]=>[5,6,2,7,8,4,3,1]=>0110101
[5,6,7,2,8,4,3,1]=>[3,4,8,7,5,6,2,1]=>[5,6,7,2,8,4,3,1]=>0110011
[5,6,7,2,1,8,4,3]=>[2,7,4,8,5,6,1,3]=>[5,6,8,4,2,1,7,3]=>1010011
[5,6,1,7,2,8,4,3]=>[6,7,4,8,5,1,2,3]=>[5,8,4,1,7,2,6,3]=>0010111
[5,1,6,7,2,8,4,3]=>[5,7,4,8,1,6,2,3]=>[6,8,4,1,7,2,5,3]=>0011011
[6,7,8,5,2,4,1,3]=>[4,5,1,2,8,6,7,3]=>[6,7,8,5,1,4,2,3]=>0011001
[6,7,8,3,5,1,4,2]=>[5,4,8,1,3,6,7,2]=>[6,7,8,1,4,3,5,2]=>0011001
[4,6,7,8,1,5,3,2]=>[8,3,5,4,1,6,7,2]=>[4,5,3,1,6,7,8,2]=>0101001
[5,1,6,7,8,4,3,2]=>[5,3,4,8,1,6,7,2]=>[6,7,8,4,3,1,5,2]=>0111001
[5,6,1,7,8,4,3,2]=>[6,3,4,8,5,1,7,2]=>[5,7,8,4,3,1,6,2]=>0110101
[5,6,7,1,8,4,3,2]=>[7,3,4,8,5,6,1,2]=>[5,6,8,4,3,1,7,2]=>0110011
[8,6,1,3,4,2,5,7]=>[6,4,1,3,2,8,5,7]=>[4,1,3,8,6,2,5,7]=>0010101
[7,5,3,8,2,4,6,1]=>[6,8,5,2,7,4,3,1]=>[7,5,2,4,8,3,6,1]=>0001111
[7,2,4,5,8,3,6,1]=>[6,7,8,2,4,3,5,1]=>[8,2,4,7,3,5,6,1]=>0000111
[2,4,5,3,7,1,8,6]=>[7,2,5,4,3,8,1,6]=>[2,4,5,3,8,1,7,6]=>0001011
[8,2,4,5,6,3,1,7]=>[3,6,8,1,4,5,2,7]=>[8,1,4,5,6,3,2,7]=>0100101
[8,2,4,5,6,1,3,7]=>[6,8,1,2,4,5,3,7]=>[8,1,4,5,6,2,3,7]=>0000101
[8,5,6,2,1,4,3,7]=>[2,6,4,1,8,5,3,7]=>[4,2,1,8,5,6,3,7]=>1010101
[8,5,3,6,4,1,2,7]=>[4,1,6,5,8,2,3,7]=>[8,5,1,2,6,4,3,7]=>0011101
[8,4,1,5,6,3,2,7]=>[4,3,8,6,2,5,1,7]=>[6,3,2,5,8,4,1,7]=>0110101
[8,1,4,5,6,3,2,7]=>[8,3,6,1,4,5,2,7]=>[6,3,1,4,5,8,2,7]=>0100101
[4,5,3,7,2,1,8,6]=>[2,7,5,4,3,8,1,6]=>[4,5,3,8,2,1,7,6]=>1001011
[7,4,5,8,3,2,6,1]=>[6,3,8,7,4,2,5,1]=>[7,4,8,3,2,5,6,1]=>0100111
[4,3,6,7,2,8,5,1]=>[5,8,4,3,7,6,1,2]=>[4,3,6,7,1,8,5,2]=>0011011
[4,3,6,7,2,8,1,5]=>[8,7,4,3,1,6,2,5]=>[4,3,6,7,1,8,2,5]=>0010011
[4,5,3,7,1,8,2,6]=>[7,8,5,4,3,2,1,6]=>[4,5,3,8,2,7,1,6]=>0001011
[4,1,5,3,7,2,8,6]=>[4,7,5,1,3,8,2,6]=>[5,1,8,3,4,2,7,6]=>0011011
[5,3,4,7,1,2,8,6]=>[7,1,5,3,4,8,2,6]=>[5,3,4,8,1,2,7,6]=>0001011
[7,5,3,8,4,1,6,2]=>[4,8,6,5,7,2,1,3]=>[7,5,2,6,1,8,4,3]=>0011111
[7,4,5,8,3,6,1,2]=>[6,1,8,7,4,3,5,2]=>[7,4,8,3,5,6,1,2]=>0000111
[4,3,6,7,8,1,5,2]=>[8,5,4,3,1,6,7,2]=>[4,3,5,1,6,7,8,2]=>0011001
[6,4,7,8,3,5,2,1]=>[2,5,8,6,3,4,7,1]=>[6,3,7,8,4,5,2,1]=>1001101
[3,5,6,7,8,4,1,2]=>[4,1,3,8,5,6,7,2]=>[3,5,6,7,8,4,1,2]=>0010001
[3,1,5,6,7,8,4,2]=>[3,4,1,8,5,6,7,2]=>[5,6,7,8,4,1,3,2]=>0110001
[4,6,1,7,8,3,5,2]=>[6,5,8,4,3,1,7,2]=>[4,7,8,3,5,1,6,2]=>0001101
[3,6,7,1,4,8,5,2]=>[7,5,3,1,8,6,4,2]=>[3,6,8,5,1,4,7,2]=>0001011
[2,6,7,1,4,8,3,5]=>[7,2,8,1,3,6,4,5]=>[2,6,8,1,7,3,4,5]=>0000011
[4,3,6,7,8,1,2,5]=>[8,1,4,3,2,6,7,5]=>[4,3,6,7,8,1,2,5]=>0010001
[1,5,3,6,7,8,2,4]=>[1,8,5,2,3,6,7,4]=>[1,5,2,6,7,8,3,4]=>0001001
[3,5,6,7,8,2,1,4]=>[2,8,3,1,5,6,7,4]=>[3,5,6,7,8,2,1,4]=>1000001
[3,5,6,7,8,2,4,1]=>[4,8,3,2,5,6,7,1]=>[3,5,6,7,8,2,4,1]=>0010001
[5,2,7,1,3,8,4,6]=>[7,5,1,8,2,4,3,6]=>[8,1,5,4,7,2,3,6]=>0001011
[5,3,1,7,8,2,4,6]=>[3,5,8,1,2,4,7,6]=>[7,8,1,5,3,2,4,6]=>0101001
[4,5,2,7,8,1,3,6]=>[8,5,1,4,2,3,7,6]=>[4,5,1,7,8,2,3,6]=>0001001
[4,2,6,7,8,3,1,5]=>[3,8,4,1,2,6,7,5]=>[4,1,6,7,8,3,2,5]=>0110001
[4,2,6,7,8,3,5,1]=>[5,4,8,2,3,6,7,1]=>[6,7,8,2,4,3,5,1]=>0011001
[3,6,2,7,4,8,1,5]=>[8,6,3,7,1,2,4,5]=>[3,7,1,6,2,8,4,5]=>0000111
[4,7,2,1,3,5,8,6]=>[2,7,1,4,3,8,5,6]=>[4,8,2,1,3,5,7,6]=>1000011
[7,8,4,2,1,3,6,5]=>[2,4,1,8,6,3,7,5]=>[6,4,2,1,3,7,8,5]=>1010101
[7,8,3,4,2,1,6,5]=>[2,4,8,3,6,1,7,5]=>[6,3,4,2,1,7,8,5]=>1010101
[6,3,2,7,1,8,5,4]=>[7,3,6,5,8,2,1,4]=>[8,5,3,2,6,1,7,4]=>0101111
[3,6,2,7,1,8,5,4]=>[7,6,3,5,8,2,1,4]=>[3,8,5,2,6,1,7,4]=>0001111
[6,4,7,8,5,2,3,1]=>[3,5,2,8,6,1,7,4]=>[6,2,3,1,7,8,5,4]=>0101101
[2,6,4,7,8,1,5,3]=>[8,2,5,6,1,4,7,3]=>[2,6,1,5,4,7,8,3]=>0001101
[4,6,2,7,8,1,5,3]=>[8,6,5,4,1,2,7,3]=>[4,5,1,6,2,7,8,3]=>0001101
[7,4,5,8,6,2,1,3]=>[2,6,1,8,3,7,5,4]=>[7,2,1,3,5,8,6,4]=>1000111
[7,5,3,8,6,1,2,4]=>[6,1,5,3,8,7,2,4]=>[7,5,3,8,6,1,2,4]=>0001111
[7,5,8,2,1,6,3,4]=>[2,8,6,3,7,1,5,4]=>[7,3,6,5,8,2,1,4]=>1000111
[6,3,1,7,8,2,5,4]=>[3,6,8,5,1,2,7,4]=>[5,1,7,8,3,2,6,4]=>0101101
[5,2,6,7,8,4,1,3]=>[4,8,2,5,1,6,7,3]=>[5,2,6,7,8,4,1,3]=>0011001
[5,2,6,7,8,4,3,1]=>[3,4,8,5,2,6,7,1]=>[5,2,6,7,8,4,3,1]=>0111001
[2,5,6,7,8,4,1,3]=>[4,2,1,8,5,6,7,3]=>[2,5,6,7,8,4,1,3]=>0010001
[1,5,2,6,7,8,4,3]=>[1,5,4,8,2,6,7,3]=>[1,6,7,8,4,2,5,3]=>0011001
[1,6,4,7,8,5,2,3]=>[1,5,2,8,6,3,7,4]=>[1,6,2,3,7,8,5,4]=>0001101
[2,6,7,1,3,8,5,4]=>[7,2,1,5,8,6,3,4]=>[2,6,8,5,1,3,7,4]=>0001011
[6,7,8,2,1,5,4,3]=>[2,8,4,5,1,6,7,3]=>[5,4,2,1,6,7,8,3]=>1011001
[6,4,7,8,5,3,1,2]=>[3,1,5,8,6,2,7,4]=>[6,3,1,2,7,8,5,4]=>0101101
[4,5,2,3,7,6,1,8]=>[6,5,2,4,3,7,1,8]=>[4,5,2,3,7,6,1,8]=>0001110
[6,4,3,7,2,5,1,8]=>[5,7,4,6,2,3,1,8]=>[6,4,2,7,3,5,1,8]=>0011110
[8,4,3,6,5,1,2,7]=>[5,1,4,6,8,2,3,7]=>[8,4,1,2,6,5,3,7]=>0011101
[1,5,6,3,4,8,7,2]=>[1,7,6,3,5,4,8,2]=>[1,5,6,3,4,8,7,2]=>0000111
[4,6,2,7,3,5,1,8]=>[5,6,7,4,3,2,1,8]=>[4,7,3,6,2,5,1,8]=>0001110
[3,2,6,7,4,5,1,8]=>[5,3,2,7,4,6,1,8]=>[3,2,6,7,4,5,1,8]=>0101010
[4,7,2,6,5,3,1,8]=>[3,5,6,4,7,2,1,8]=>[4,7,2,6,5,3,1,8]=>0101110
[5,7,6,2,4,3,1,8]=>[3,4,6,1,5,7,2,8]=>[5,7,6,1,4,3,2,8]=>0110110
[1,7,5,4,8,3,6,2]=>[1,6,8,5,7,3,4,2]=>[1,7,5,3,8,4,6,2]=>0001111
[8,7,5,4,1,3,2,6]=>[4,3,1,5,7,2,8,6]=>[3,1,8,7,5,4,2,6]=>0111011
[6,8,5,4,2,1,3,7]=>[2,4,1,5,8,6,3,7]=>[6,8,5,4,2,1,3,7]=>1011001
[4,8,2,6,5,1,3,7]=>[5,6,2,4,8,1,3,7]=>[4,8,2,6,5,1,3,7]=>0001101
[3,2,8,6,5,1,4,7]=>[5,3,2,1,6,8,4,7]=>[3,2,8,6,5,1,4,7]=>0101101
[4,1,2,6,5,8,7,3]=>[4,1,7,2,6,5,8,3]=>[6,5,8,7,1,2,4,3]=>0010111
[5,1,6,2,4,8,7,3]=>[5,6,7,2,1,4,8,3]=>[8,7,2,6,1,4,5,3]=>0001111
[7,1,5,4,8,2,6,3]=>[7,8,6,5,1,2,4,3]=>[5,1,6,2,8,4,7,3]=>0001111
[1,8,6,7,4,5,3,2]=>[1,3,5,7,4,8,6,2]=>[1,8,6,7,4,5,3,2]=>0101011
[8,1,6,7,4,5,2,3]=>[8,5,2,7,4,1,6,3]=>[7,4,5,2,6,8,1,3]=>0001011
[7,1,6,8,4,2,5,3]=>[7,4,8,5,3,1,6,2]=>[5,3,8,4,1,6,7,2]=>0011011
[6,1,7,8,2,4,5,3]=>[6,8,5,2,4,1,7,3]=>[5,2,4,7,8,1,6,3]=>0001101
[5,1,7,2,8,4,6,3]=>[5,7,6,8,1,4,2,3]=>[8,1,6,4,7,2,5,3]=>0001111
[4,1,2,7,8,5,6,3]=>[4,1,6,2,8,5,7,3]=>[7,8,5,6,1,2,4,3]=>0010101
[3,2,1,7,8,5,6,4]=>[2,3,1,6,8,5,7,4]=>[3,2,1,7,8,5,6,4]=>1100101
[3,2,8,7,1,5,4,6]=>[7,3,2,5,1,4,8,6]=>[3,2,5,1,8,7,4,6]=>0101011
[4,8,2,7,1,5,3,6]=>[7,8,5,4,1,3,2,6]=>[4,5,1,8,3,7,2,6]=>0001011
[5,8,7,2,1,4,3,6]=>[2,7,4,1,5,3,8,6]=>[4,2,1,5,8,7,3,6]=>1010011
[7,8,6,1,4,2,3,5]=>[6,4,2,1,3,8,7,5]=>[4,2,7,8,6,1,3,5]=>0010101
[1,7,6,8,4,3,5,2]=>[1,5,4,8,3,7,6,2]=>[1,7,6,8,4,3,5,2]=>0011011
[1,6,7,8,3,4,5,2]=>[1,5,8,3,4,6,7,2]=>[1,6,7,8,3,4,5,2]=>0001001
[7,6,8,1,3,2,4,5]=>[8,3,1,2,4,7,6,5]=>[3,1,7,6,8,2,4,5]=>0100011
[5,7,8,2,1,3,4,6]=>[2,8,1,3,5,4,7,6]=>[5,7,8,2,1,3,4,6]=>1000001
[3,2,6,8,4,1,5,7]=>[4,3,2,8,1,6,5,7]=>[3,2,6,8,4,1,5,7]=>0110001
[4,6,2,8,3,1,5,7]=>[3,8,6,4,2,1,5,7]=>[4,6,2,8,3,1,5,7]=>0100101
[5,6,8,2,3,1,4,7]=>[3,8,2,1,5,6,4,7]=>[5,6,8,2,3,1,4,7]=>0100001
[6,5,8,3,2,1,4,7]=>[2,3,8,1,6,5,4,7]=>[6,5,8,3,2,1,4,7]=>1100101
[8,5,7,3,1,4,2,6]=>[3,7,4,2,8,1,5,6]=>[4,2,8,3,1,7,5,6]=>0110011
[1,5,7,3,8,4,6,2]=>[1,6,7,8,5,4,3,2]=>[1,5,8,4,7,3,6,2]=>0000111
[1,4,3,7,8,5,6,2]=>[1,6,4,3,8,5,7,2]=>[1,4,3,7,8,5,6,2]=>0010101
[8,4,3,7,1,5,2,6]=>[7,5,4,8,1,2,3,6]=>[8,4,1,5,2,7,3,6]=>0011011
[6,4,3,8,2,1,5,7]=>[2,8,4,6,1,3,5,7]=>[6,4,2,1,8,3,5,7]=>1010101
[4,5,2,3,8,1,6,7]=>[8,5,2,4,3,1,6,7]=>[4,5,2,3,8,1,6,7]=>0001001
[3,2,5,4,8,1,6,7]=>[8,3,2,5,4,1,6,7]=>[3,2,5,4,8,1,6,7]=>0101001
[4,5,2,3,1,8,7,6]=>[3,5,2,4,1,7,8,6]=>[4,5,2,3,1,8,7,6]=>0101011
[7,4,3,1,8,2,6,5]=>[3,4,7,8,6,2,1,5]=>[6,2,8,4,3,1,7,5]=>0110111
[8,4,3,1,7,6,2,5]=>[3,4,8,6,2,7,1,5]=>[7,6,2,8,4,3,1,5]=>0110111
[1,5,8,3,7,6,4,2]=>[1,4,6,7,5,8,3,2]=>[1,5,8,3,7,6,4,2]=>0010111
[8,5,1,3,7,6,2,4]=>[5,8,2,1,6,7,3,4]=>[7,6,2,8,5,1,3,4]=>0001111
[3,2,6,1,4,8,7,5]=>[6,3,2,1,7,4,8,5]=>[3,2,8,7,1,4,6,5]=>0100111
[3,2,7,1,8,4,6,5]=>[7,3,2,8,6,4,1,5]=>[3,2,6,4,8,1,7,5]=>0100111
[4,7,2,1,8,3,6,5]=>[2,7,8,4,6,3,1,5]=>[4,6,3,8,2,1,7,5]=>1000111
[5,7,1,2,8,3,6,4]=>[7,1,8,6,5,3,2,4]=>[5,6,3,8,1,2,7,4]=>0000111
[7,6,1,8,3,2,5,4]=>[6,3,7,5,1,8,2,4]=>[5,3,1,8,2,7,6,4]=>0101111
[1,6,8,7,3,5,4,2]=>[1,4,5,7,2,6,8,3]=>[1,6,8,7,2,5,4,3]=>0011011
[1,7,8,6,5,3,4,2]=>[1,4,5,3,6,8,7,2]=>[1,7,8,6,5,3,4,2]=>0011101
[8,7,1,6,5,3,2,4]=>[7,3,5,2,6,1,8,4]=>[6,5,3,2,8,7,1,4]=>0101111
[7,8,1,6,5,2,3,4]=>[8,5,2,3,6,1,7,4]=>[6,5,2,3,7,8,1,4]=>0001101
[5,8,1,2,7,6,3,4]=>[8,1,6,3,5,7,2,4]=>[5,7,6,3,8,1,2,4]=>0000111
[4,8,2,1,7,6,3,5]=>[2,8,6,4,3,7,1,5]=>[4,7,6,3,8,2,1,5]=>1000111
[4,1,2,8,7,6,5,3]=>[4,1,5,2,6,7,8,3]=>[8,7,6,5,1,2,4,3]=>0011111
[5,1,8,2,7,6,4,3]=>[5,8,4,6,1,7,2,3]=>[7,6,4,1,8,2,5,3]=>0011111
[6,1,8,7,2,5,4,3]=>[6,7,4,5,2,1,8,3]=>[5,4,2,8,7,1,6,3]=>0011111
[7,1,8,6,5,2,4,3]=>[7,5,4,2,6,8,1,3]=>[4,2,8,6,5,1,7,3]=>0011111
[8,1,7,6,5,4,2,3]=>[8,4,2,5,6,7,1,3]=>[7,6,5,4,2,8,1,3]=>0011111
[3,1,2,6,5,8,7,4]=>[3,1,2,7,6,5,8,4]=>[3,1,2,6,5,8,7,4]=>0100111
[3,1,6,2,4,8,7,5]=>[3,6,1,2,7,4,8,5]=>[8,7,1,3,2,4,6,5]=>0100111
[3,1,5,2,4,8,7,6]=>[3,5,1,2,4,7,8,6]=>[5,1,3,2,4,8,7,6]=>0101011
[4,5,1,2,3,8,7,6]=>[5,1,2,4,3,7,8,6]=>[4,5,1,2,3,8,7,6]=>0001011
[4,6,1,2,3,8,7,5]=>[6,1,2,4,7,3,8,5]=>[4,8,7,1,2,3,6,5]=>0000111
[1,6,5,3,4,8,7,2]=>[1,7,5,3,6,4,8,2]=>[1,6,5,3,4,8,7,2]=>0001111
[6,1,5,2,4,8,7,3]=>[6,5,7,2,1,4,8,3]=>[8,7,2,5,1,4,6,3]=>0001111
[6,4,1,2,3,8,7,5]=>[4,1,2,6,7,3,8,5]=>[8,7,4,1,2,3,6,5]=>0010111
[5,4,1,2,3,8,7,6]=>[4,1,2,5,3,7,8,6]=>[5,4,1,2,3,8,7,6]=>0011011
[5,4,1,2,7,3,6,8]=>[4,1,5,7,3,2,6,8]=>[7,3,5,4,1,2,6,8]=>0011010
[7,4,1,2,8,3,6,5]=>[4,1,7,8,6,2,3,5]=>[6,1,2,8,4,3,7,5]=>0010111
[7,5,1,2,8,3,6,4]=>[5,1,7,8,6,4,3,2]=>[6,4,8,3,7,5,1,2]=>0001111
[1,8,5,3,7,4,6,2]=>[1,6,5,8,7,3,4,2]=>[1,7,3,8,5,4,6,2]=>0001111
[8,1,5,2,7,4,6,3]=>[8,5,6,7,1,4,2,3]=>[7,1,6,4,5,2,8,3]=>0001111
[8,5,1,2,7,3,6,4]=>[5,1,8,7,6,4,3,2]=>[6,4,7,3,8,5,1,2]=>0001111
[8,4,1,2,7,3,6,5]=>[4,1,8,7,6,2,3,5]=>[6,1,2,7,4,3,8,5]=>0010111
[8,4,1,7,2,3,5,6]=>[4,8,1,7,3,5,2,6]=>[7,1,3,5,8,4,2,6]=>0010011
[7,4,1,6,2,3,5,8]=>[4,7,1,6,3,2,5,8]=>[6,1,3,7,4,2,5,8]=>0010110
[8,6,1,7,2,3,5,4]=>[6,8,1,5,3,7,2,4]=>[5,1,3,7,2,8,6,4]=>0001111
[1,8,6,7,3,4,5,2]=>[1,5,7,3,4,8,6,2]=>[1,8,6,7,3,4,5,2]=>0001011
[1,7,6,8,3,4,5,2]=>[1,5,8,3,4,7,6,2]=>[1,7,6,8,3,4,5,2]=>0001011
[7,1,6,8,2,4,5,3]=>[7,8,5,2,4,1,6,3]=>[5,2,4,8,1,6,7,3]=>0001011
[7,6,1,8,2,3,5,4]=>[6,7,1,5,3,8,2,4]=>[5,1,3,8,2,7,6,4]=>0001111
[4,7,1,2,8,3,6,5]=>[7,1,8,4,6,3,2,5]=>[4,6,3,8,1,2,7,5]=>0000111
[3,1,7,2,8,4,6,5]=>[3,7,1,8,6,4,2,5]=>[6,4,8,1,3,2,7,5]=>0100111
[3,1,2,7,8,5,6,4]=>[3,1,2,6,8,5,7,4]=>[3,1,2,7,8,5,6,4]=>0100101
[1,4,3,8,7,5,6,2]=>[1,6,4,3,7,5,8,2]=>[1,4,3,8,7,5,6,2]=>0010111
[4,1,2,8,7,5,6,3]=>[4,1,6,2,7,5,8,3]=>[8,7,5,6,1,2,4,3]=>0010111
[3,1,2,8,7,5,6,4]=>[3,1,2,6,7,5,8,4]=>[3,1,2,8,7,5,6,4]=>0100111
[3,1,8,2,7,4,6,5]=>[3,8,1,7,6,4,2,5]=>[6,4,7,1,3,2,8,5]=>0100111
[3,1,8,7,2,4,5,6]=>[3,7,1,2,4,5,8,6]=>[8,7,1,3,2,4,5,6]=>0100011
[4,8,1,6,2,3,5,7]=>[8,6,2,4,3,1,5,7]=>[4,6,2,3,8,1,5,7]=>0000101
[4,8,1,2,7,3,6,5]=>[8,1,7,4,6,3,2,5]=>[4,6,3,7,1,2,8,5]=>0000111
[5,1,8,2,7,4,6,3]=>[5,8,6,7,1,4,2,3]=>[7,1,6,4,8,2,5,3]=>0001111
[1,5,8,3,7,4,6,2]=>[1,6,8,7,5,4,3,2]=>[1,5,7,4,8,3,6,2]=>0000111
[1,6,8,7,3,4,5,2]=>[1,5,7,3,4,6,8,2]=>[1,6,8,7,3,4,5,2]=>0001011
[6,1,8,7,2,4,5,3]=>[6,7,5,2,4,1,8,3]=>[5,2,4,8,7,1,6,3]=>0001111
[6,8,1,7,2,3,5,4]=>[8,7,2,5,3,6,1,4]=>[5,2,3,6,7,1,8,4]=>0001011
[6,8,7,1,2,3,4,5]=>[7,1,2,3,4,6,8,5]=>[6,8,7,1,2,3,4,5]=>0000011
[5,8,7,1,2,3,4,6]=>[7,1,2,3,5,4,8,6]=>[5,8,7,1,2,3,4,6]=>0000011
[5,8,6,1,2,3,4,7]=>[6,1,2,3,5,8,4,7]=>[5,8,6,1,2,3,4,7]=>0000101
[5,7,6,1,2,3,4,8]=>[6,1,2,3,5,7,4,8]=>[5,7,6,1,2,3,4,8]=>0000110
[7,8,1,6,2,3,5,4]=>[8,6,2,5,3,1,7,4]=>[5,2,3,6,1,7,8,4]=>0001101
[7,1,8,6,2,4,5,3]=>[7,6,5,2,4,8,1,3]=>[5,2,4,8,6,1,7,3]=>0001111
[1,7,8,6,3,4,5,2]=>[1,5,6,3,4,8,7,2]=>[1,7,8,6,3,4,5,2]=>0001101
[1,8,7,6,3,4,5,2]=>[1,5,6,3,4,7,8,2]=>[1,8,7,6,3,4,5,2]=>0001111
[8,7,1,6,2,3,5,4]=>[7,6,2,5,3,1,8,4]=>[5,2,3,6,1,8,7,4]=>0001111
[3,2,5,1,6,4,8,7]=>[5,3,2,6,1,4,8,7]=>[3,2,6,1,5,4,8,7]=>0101101
[3,2,5,4,7,1,8,6]=>[7,3,2,5,4,8,1,6]=>[3,2,5,4,8,1,7,6]=>0101011
[4,2,5,3,7,6,8,1]=>[8,4,5,2,3,7,6,1]=>[5,2,4,3,7,6,8,1]=>0011011
[4,2,5,3,7,1,8,6]=>[7,4,5,2,3,8,1,6]=>[5,2,4,3,8,1,7,6]=>0011011
[4,2,5,3,6,1,8,7]=>[6,4,5,2,3,1,8,7]=>[5,2,4,3,6,1,8,7]=>0011101
[4,2,5,1,6,3,8,7]=>[5,4,6,2,1,3,8,7]=>[6,2,4,1,5,3,8,7]=>0011101
[3,1,5,4,6,2,8,7]=>[3,6,1,5,4,2,8,7]=>[5,4,6,1,3,2,8,7]=>0101101
[4,1,5,3,6,2,8,7]=>[4,6,5,1,3,2,8,7]=>[5,1,6,3,4,2,8,7]=>0011101
[4,3,5,1,6,2,8,7]=>[5,6,4,3,1,2,8,7]=>[4,3,6,1,5,2,8,7]=>0011101
[4,3,5,2,7,1,8,6]=>[7,5,4,3,2,8,1,6]=>[4,3,5,2,8,1,7,6]=>0011011
[4,3,6,2,7,5,8,1]=>[8,6,4,3,7,2,5,1]=>[4,3,7,2,6,5,8,1]=>0010111
[4,3,6,2,7,1,8,5]=>[7,6,4,3,8,2,1,5]=>[4,3,8,2,6,1,7,5]=>0010111
[4,3,6,1,7,2,8,5]=>[6,7,4,3,8,1,2,5]=>[4,3,8,1,7,2,6,5]=>0010111
[4,3,5,1,7,2,8,6]=>[5,7,4,3,1,8,2,6]=>[4,3,8,1,5,2,7,6]=>0011011
[3,1,5,4,7,2,8,6]=>[3,7,1,5,4,8,2,6]=>[5,4,8,1,3,2,7,6]=>0101011
[2,1,5,4,7,3,8,6]=>[2,1,7,5,4,8,3,6]=>[2,1,5,4,8,3,7,6]=>1001011
[3,1,5,4,7,6,8,2]=>[3,8,1,5,4,7,6,2]=>[5,4,7,6,8,1,3,2]=>0101011
[4,1,5,3,7,6,8,2]=>[4,8,5,1,3,7,6,2]=>[5,1,7,6,8,3,4,2]=>0011011
[4,3,5,1,7,6,8,2]=>[5,8,4,3,1,7,6,2]=>[4,3,7,6,8,1,5,2]=>0011011
[4,3,6,1,7,5,8,2]=>[6,8,4,3,7,1,5,2]=>[4,3,7,1,8,5,6,2]=>0010111
[4,3,6,5,7,1,8,2]=>[7,8,4,3,6,5,1,2]=>[4,3,6,5,8,1,7,2]=>0010111
[5,3,6,4,7,2,8,1]=>[8,7,5,6,3,4,2,1]=>[6,3,5,4,7,2,8,1]=>0001111
[5,3,6,4,7,1,8,2]=>[7,8,5,6,3,4,1,2]=>[6,3,5,4,8,1,7,2]=>0001111
[5,3,6,1,7,4,8,2]=>[6,8,5,7,3,1,4,2]=>[7,3,5,1,8,4,6,2]=>0001111
[5,1,6,3,7,4,8,2]=>[5,8,6,7,1,3,4,2]=>[7,1,6,3,8,4,5,2]=>0001111
[4,1,6,3,7,5,8,2]=>[4,8,6,1,7,3,5,2]=>[7,1,6,5,8,3,4,2]=>0010111
[3,1,6,4,7,5,8,2]=>[3,8,1,6,7,4,5,2]=>[7,4,6,5,8,1,3,2]=>0100111
[2,1,6,4,7,5,8,3]=>[2,1,8,6,7,4,5,3]=>[2,1,7,4,6,5,8,3]=>1000111
[2,1,6,4,7,3,8,5]=>[2,1,7,6,8,4,3,5]=>[2,1,8,4,6,3,7,5]=>1000111
[3,1,6,4,7,2,8,5]=>[3,7,1,6,8,4,2,5]=>[8,4,6,1,3,2,7,5]=>0100111
[4,1,6,3,7,2,8,5]=>[4,7,6,1,8,3,2,5]=>[8,1,6,3,4,2,7,5]=>0010111
[5,1,6,3,7,2,8,4]=>[5,7,6,8,1,3,2,4]=>[8,1,6,3,7,2,5,4]=>0001111
[5,3,6,1,7,2,8,4]=>[6,7,5,8,3,1,2,4]=>[8,3,5,1,7,2,6,4]=>0001111
[5,3,6,2,7,1,8,4]=>[7,6,5,8,3,2,1,4]=>[8,3,5,2,6,1,7,4]=>0001111
[5,3,6,2,7,4,8,1]=>[8,6,5,7,3,2,4,1]=>[7,3,5,2,6,4,8,1]=>0001111
[5,2,6,3,7,4,8,1]=>[8,5,6,7,2,3,4,1]=>[7,2,6,3,5,4,8,1]=>0001111
[5,2,6,3,7,1,8,4]=>[7,5,6,8,2,3,1,4]=>[8,2,6,3,5,1,7,4]=>0001111
[5,2,6,1,7,3,8,4]=>[6,5,7,8,2,1,3,4]=>[8,2,7,1,5,3,6,4]=>0001111
[4,2,5,1,7,3,8,6]=>[5,4,7,2,1,8,3,6]=>[8,2,4,1,5,3,7,6]=>0011011
[4,2,6,1,7,3,8,5]=>[6,4,7,2,8,1,3,5]=>[8,2,4,1,7,3,6,5]=>0010111
[4,2,6,3,7,1,8,5]=>[7,4,6,2,8,3,1,5]=>[8,2,4,3,6,1,7,5]=>0010111
[4,2,6,3,7,5,8,1]=>[8,4,6,2,7,3,5,1]=>[7,2,4,3,6,5,8,1]=>0010111
[3,2,6,4,7,5,8,1]=>[8,3,2,6,7,4,5,1]=>[3,2,7,4,6,5,8,1]=>0100111
[3,2,6,4,7,1,8,5]=>[7,3,2,6,8,4,1,5]=>[3,2,8,4,6,1,7,5]=>0100111
[3,2,6,1,7,4,8,5]=>[6,3,2,7,8,1,4,5]=>[3,2,8,1,7,4,6,5]=>0100111
[3,2,5,1,7,4,8,6]=>[5,3,2,7,1,8,4,6]=>[3,2,8,1,5,4,7,6]=>0101011
[3,2,4,1,7,5,8,6]=>[4,3,2,1,7,8,5,6]=>[3,2,4,1,8,5,7,6]=>0110011
[3,1,4,2,7,6,8,5]=>[3,4,1,2,8,7,6,5]=>[4,1,3,2,7,6,8,5]=>0110011
[3,2,5,1,7,6,8,4]=>[5,3,2,8,1,7,6,4]=>[3,2,7,6,8,1,5,4]=>0101011
[3,2,6,1,7,5,8,4]=>[6,3,2,8,7,1,5,4]=>[3,2,7,1,8,5,6,4]=>0100111
[3,2,6,5,7,1,8,4]=>[7,3,2,8,6,5,1,4]=>[3,2,6,5,8,1,7,4]=>0100111
[4,2,6,5,7,3,8,1]=>[8,4,7,2,6,5,3,1]=>[6,5,7,2,4,3,8,1]=>0010111
[4,2,6,5,7,1,8,3]=>[7,4,8,2,6,5,1,3]=>[6,5,8,2,4,1,7,3]=>0010111
[4,2,6,1,7,5,8,3]=>[6,4,8,2,7,1,5,3]=>[7,2,4,1,8,5,6,3]=>0010111
[4,2,5,1,7,6,8,3]=>[5,4,8,2,1,7,6,3]=>[7,6,8,2,4,1,5,3]=>0011011
[4,1,5,2,7,6,8,3]=>[4,5,8,1,2,7,6,3]=>[7,6,8,1,5,2,4,3]=>0011011
[3,1,5,2,7,6,8,4]=>[3,5,1,8,2,7,6,4]=>[7,6,8,1,3,2,5,4]=>0101011
[2,1,5,3,7,6,8,4]=>[2,1,5,8,3,7,6,4]=>[2,1,7,6,8,3,5,4]=>1001011
[2,1,6,3,7,5,8,4]=>[2,1,6,8,7,3,5,4]=>[2,1,7,3,8,5,6,4]=>1000111
[3,1,6,2,7,5,8,4]=>[3,6,1,8,7,2,5,4]=>[7,1,3,2,8,5,6,4]=>0100111
[4,1,6,2,7,5,8,3]=>[4,6,8,1,7,2,5,3]=>[7,1,8,5,6,2,4,3]=>0010111
[5,1,6,2,7,4,8,3]=>[5,6,8,7,1,2,4,3]=>[7,1,8,2,6,4,5,3]=>0001111
[5,2,6,1,7,4,8,3]=>[6,5,8,7,2,1,4,3]=>[7,2,8,1,5,4,6,3]=>0001111
[5,2,6,4,7,1,8,3]=>[7,5,8,6,2,4,1,3]=>[6,2,8,4,5,1,7,3]=>0001111
[5,2,6,4,7,3,8,1]=>[8,5,7,6,2,4,3,1]=>[6,2,7,4,5,3,8,1]=>0001111
[5,4,6,2,7,3,8,1]=>[8,6,7,5,4,2,3,1]=>[5,4,7,2,6,3,8,1]=>0001111
[5,4,6,2,7,1,8,3]=>[7,6,8,5,4,2,1,3]=>[5,4,8,2,6,1,7,3]=>0001111
[5,4,6,1,7,2,8,3]=>[6,7,8,5,4,1,2,3]=>[5,4,8,1,7,2,6,3]=>0001111
[5,1,6,4,7,2,8,3]=>[5,7,8,6,1,4,2,3]=>[6,1,8,4,7,2,5,3]=>0001111
[4,1,6,5,7,2,8,3]=>[4,7,8,1,6,5,2,3]=>[6,5,8,1,7,2,4,3]=>0010111
[3,1,6,5,7,2,8,4]=>[3,7,1,8,6,5,2,4]=>[6,5,8,1,3,2,7,4]=>0100111
[2,1,6,5,7,3,8,4]=>[2,1,7,8,6,5,3,4]=>[2,1,6,5,8,3,7,4]=>1000111
[3,1,6,5,7,4,8,2]=>[3,8,1,7,6,5,4,2]=>[6,5,7,4,8,1,3,2]=>0100111
[4,1,6,5,7,3,8,2]=>[4,8,7,1,6,5,3,2]=>[6,5,7,1,8,3,4,2]=>0010111
[5,1,6,4,7,3,8,2]=>[5,8,7,6,1,4,3,2]=>[6,1,7,4,8,3,5,2]=>0001111
[5,4,6,1,7,3,8,2]=>[6,8,7,5,4,1,3,2]=>[5,4,7,1,8,3,6,2]=>0001111
[5,4,6,3,7,1,8,2]=>[7,8,6,5,4,3,1,2]=>[5,4,6,3,8,1,7,2]=>0001111
[8,3,5,2,1,6,4,7]=>[2,5,8,6,3,1,4,7]=>[6,3,8,2,1,5,4,7]=>1001101
[2,4,5,7,3,1,8,6]=>[3,2,7,4,5,8,1,6]=>[2,4,5,8,3,1,7,6]=>0100011
[8,2,4,6,5,3,1,7]=>[3,5,6,2,8,4,1,7]=>[8,2,4,6,5,3,1,7]=>0101101
[8,2,5,4,6,1,3,7]=>[6,8,1,5,2,4,3,7]=>[5,1,8,4,6,2,3,7]=>0001101
[8,6,3,5,1,4,2,7]=>[5,4,6,1,3,8,2,7]=>[8,6,1,4,3,5,2,7]=>0011101
[8,6,1,4,5,3,2,7]=>[6,3,5,1,4,8,2,7]=>[5,3,1,4,8,6,2,7]=>0101101
[8,1,5,6,4,3,2,7]=>[8,3,4,6,1,5,2,7]=>[6,4,3,1,5,8,2,7]=>0110101
[5,7,4,3,2,1,8,6]=>[2,3,4,7,5,8,1,6]=>[5,8,4,3,2,1,7,6]=>1110011
[8,5,7,4,3,2,6,1]=>[6,3,4,7,8,2,5,1]=>[8,4,3,2,7,5,6,1]=>0110111
[4,6,8,3,2,7,5,1]=>[5,3,7,4,8,6,1,2]=>[4,6,8,3,1,7,5,2]=>0101011
[4,7,6,3,2,8,1,5]=>[8,3,6,4,1,7,2,5]=>[4,7,6,3,1,8,2,5]=>0100111
[1,7,4,5,3,2,8,6]=>[1,3,5,7,4,8,2,6]=>[1,8,4,5,3,2,7,6]=>0101011
[3,7,5,1,4,2,8,6]=>[5,4,3,1,7,8,2,6]=>[3,4,1,8,5,2,7,6]=>0011011
[5,7,4,2,1,3,8,6]=>[2,4,1,7,5,8,3,6]=>[5,8,4,2,1,3,7,6]=>1010011
[8,5,7,4,2,1,6,3]=>[2,4,7,6,8,3,5,1]=>[8,3,6,5,7,4,2,1]=>1010111
[8,3,7,5,1,4,6,2]=>[5,7,6,2,8,4,1,3]=>[8,2,4,6,1,7,5,3]=>0001111
[8,4,1,7,5,3,6,2]=>[4,8,6,5,7,1,2,3]=>[7,5,1,6,2,8,4,3]=>0011111
[4,6,3,8,7,1,5,2]=>[7,5,6,4,1,3,8,2]=>[4,6,1,5,3,8,7,2]=>0001111
[1,7,4,8,6,3,5,2]=>[1,5,6,8,4,7,3,2]=>[1,7,4,8,6,3,5,2]=>0001111
[8,4,7,6,3,5,2,1]=>[2,5,6,7,4,8,3,1]=>[8,4,7,6,3,5,2,1]=>1001111
[3,6,5,8,7,4,1,2]=>[4,1,3,7,6,5,8,2]=>[3,6,5,8,7,4,1,2]=>0010111
[3,1,5,8,6,7,4,2]=>[3,4,1,7,5,8,6,2]=>[5,8,6,7,4,1,3,2]=>0110011
[3,6,4,1,8,7,5,2]=>[4,6,3,5,7,2,8,1]=>[3,8,7,5,2,6,4,1]=>0011111
[8,2,6,1,4,7,5,3]=>[6,8,5,1,7,2,4,3]=>[7,5,1,8,2,4,6,3]=>0001111
[1,7,3,5,6,8,2,4]=>[1,8,7,2,3,5,6,4]=>[1,7,2,5,6,8,3,4]=>0000011
[1,3,6,7,5,8,2,4]=>[1,8,3,2,7,6,5,4]=>[1,3,6,7,5,8,2,4]=>0000011
[3,7,6,5,8,2,1,4]=>[2,8,3,1,6,7,5,4]=>[3,7,6,5,8,2,1,4]=>1000111
[3,6,8,5,7,2,4,1]=>[4,7,3,2,8,6,5,1]=>[3,6,8,5,7,2,4,1]=>0010011
[2,3,5,7,6,8,1,4]=>[8,2,3,1,5,7,6,4]=>[2,3,5,7,6,8,1,4]=>0000011
[2,1,6,5,7,8,3,4]=>[2,1,8,3,6,5,7,4]=>[2,1,6,5,7,8,3,4]=>1000101
[4,2,7,6,8,3,1,5]=>[3,8,4,1,2,7,6,5]=>[4,1,7,6,8,3,2,5]=>0110011
[4,2,6,8,7,3,5,1]=>[5,4,7,2,3,6,8,1]=>[6,8,7,2,4,3,5,1]=>0011011
[3,8,2,4,6,7,5,1]=>[5,7,3,1,8,4,6,2]=>[3,8,1,4,6,7,5,2]=>0001011
[3,7,2,6,4,8,1,5]=>[8,7,3,6,1,2,4,5]=>[3,6,1,7,2,8,4,5]=>0000111
[3,2,6,1,4,7,8,5]=>[6,3,2,1,8,4,7,5]=>[3,2,7,8,1,4,6,5]=>0100101
[4,7,3,2,1,5,8,6]=>[2,3,7,4,1,8,5,6]=>[4,8,3,2,1,5,7,6]=>1100011
[8,5,7,3,2,1,6,4]=>[2,3,7,6,8,1,5,4]=>[8,3,2,1,6,5,7,4]=>1100111
[8,3,6,7,2,1,5,4]=>[2,7,8,5,1,3,6,4]=>[5,2,1,8,3,6,7,4]=>1001011
[3,7,8,6,2,1,5,4]=>[2,6,3,5,1,8,7,4]=>[3,5,2,1,7,8,6,4]=>1001101
[8,7,6,3,5,2,4,1]=>[4,5,6,2,3,7,8,1]=>[8,7,6,2,5,3,4,1]=>0011111
[2,7,4,8,1,6,5,3]=>[8,2,5,6,7,1,3,4]=>[2,7,1,6,5,3,8,4]=>0001111
[4,6,8,2,1,7,5,3]=>[2,8,5,4,7,6,1,3]=>[4,6,7,5,2,1,8,3]=>1001011
[8,5,3,7,1,6,2,4]=>[7,6,5,2,8,1,3,4]=>[8,5,2,6,1,7,3,4]=>0001111
[8,5,7,2,1,3,6,4]=>[2,7,1,6,8,3,5,4]=>[8,2,1,3,6,5,7,4]=>1000111
[8,3,6,1,7,5,2,4]=>[6,5,7,3,8,2,1,4]=>[8,3,7,5,2,6,1,4]=>0001111
[4,6,1,8,7,2,5,3]=>[6,7,5,4,2,1,8,3]=>[4,5,2,8,7,1,6,3]=>0001111
[8,1,2,5,6,7,4,3]=>[8,1,4,7,2,5,6,3]=>[7,4,1,2,5,6,8,3]=>0010011
[2,1,7,8,5,6,4,3]=>[2,1,4,6,8,5,7,3]=>[2,1,7,8,5,6,4,3]=>1010101
[2,7,6,8,5,4,1,3]=>[4,2,1,5,8,7,6,3]=>[2,7,6,8,5,4,1,3]=>0011011
[1,7,2,5,8,6,4,3]=>[1,7,4,6,2,8,5,3]=>[1,8,6,4,2,5,7,3]=>0010111
[3,7,8,1,6,5,2,4]=>[8,5,3,2,6,1,7,4]=>[3,6,5,2,7,8,1,4]=>0001101
[2,7,8,6,1,3,5,4]=>[6,2,1,5,3,8,7,4]=>[2,5,1,3,7,8,6,4]=>0001101
[8,7,6,3,5,1,4,2]=>[5,4,6,1,3,7,8,2]=>[8,7,6,1,4,3,5,2]=>0011111
[8,4,7,6,5,1,3,2]=>[5,3,1,6,7,8,4,2]=>[3,1,8,4,7,6,5,2]=>0101111
[8,7,1,5,6,4,3,2]=>[7,3,4,6,1,5,8,2]=>[6,4,3,1,5,8,7,2]=>0110111
[6,5,3,1,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>[6,5,3,1,2,4,8,7]=>0101101
[4,6,3,5,1,2,8,7]=>[5,1,6,4,3,2,8,7]=>[4,6,3,5,1,2,8,7]=>0001101
[6,8,1,4,5,7,3,2]=>[8,3,7,1,4,6,5,2]=>[6,7,3,1,4,5,8,2]=>0100011
[8,7,2,4,5,1,3,6]=>[5,7,1,2,4,3,8,6]=>[8,7,1,4,5,2,3,6]=>0001011
[3,6,2,4,5,1,8,7]=>[5,6,3,2,4,1,8,7]=>[3,6,2,4,5,1,8,7]=>0001101
[2,6,1,4,5,3,8,7]=>[6,2,5,1,4,3,8,7]=>[2,5,1,4,6,3,8,7]=>0001101
[6,1,2,4,5,3,8,7]=>[6,1,5,2,4,3,8,7]=>[5,1,2,4,6,3,8,7]=>0001101
[5,6,3,2,1,4,8,7]=>[2,3,6,1,5,4,8,7]=>[5,6,3,2,1,4,8,7]=>1100101
[5,4,3,6,1,2,8,7]=>[6,1,4,5,3,2,8,7]=>[5,4,3,6,1,2,8,7]=>0011101
[3,1,6,4,5,2,8,7]=>[3,5,1,6,4,2,8,7]=>[6,4,5,1,3,2,8,7]=>0101101
[5,8,7,4,2,6,3,1]=>[3,6,4,7,5,1,8,2]=>[5,8,7,4,1,6,3,2]=>0110111
[2,8,7,4,1,6,3,5]=>[4,2,7,6,1,3,8,5]=>[2,6,1,8,7,4,3,5]=>0010111
[8,1,7,4,2,6,3,5]=>[8,4,7,6,2,3,1,5]=>[6,2,7,4,3,8,1,5]=>0010111
[3,7,8,4,5,1,2,6]=>[5,1,3,8,4,2,7,6]=>[3,7,8,4,5,1,2,6]=>0001001
[2,1,8,7,5,3,4,6]=>[2,1,5,3,7,4,8,6]=>[2,1,8,7,5,3,4,6]=>1001011
[2,1,6,8,5,7,3,4]=>[2,1,7,3,8,6,5,4]=>[2,1,6,8,5,7,3,4]=>1000011
[5,6,3,8,1,7,2,4]=>[8,7,6,2,5,3,1,4]=>[5,6,2,7,3,8,1,4]=>0000111
[3,7,6,4,5,8,2,1]=>[2,8,3,6,4,7,5,1]=>[3,7,6,4,5,8,2,1]=>1000111
[8,5,7,4,1,6,3,2]=>[4,3,7,6,8,2,5,1]=>[8,3,2,6,5,7,4,1]=>0110111
[2,5,8,4,7,6,1,3]=>[6,2,1,7,5,8,3,4]=>[2,5,8,1,3,7,6,4]=>0000111
[2,4,8,3,5,6,7,1]=>[7,2,8,4,3,5,6,1]=>[2,4,8,3,5,6,7,1]=>0000011
[4,1,8,3,5,6,7,2]=>[4,7,8,1,3,5,6,2]=>[8,1,5,6,7,3,4,2]=>0010011
[3,8,4,2,5,6,7,1]=>[7,4,3,8,2,5,6,1]=>[3,8,4,2,5,6,7,1]=>0010011
[8,4,1,3,5,6,7,2]=>[4,8,2,7,3,5,6,1]=>[7,2,3,5,6,8,4,1]=>0010011
[7,5,8,4,3,6,1,2]=>[6,1,4,8,7,3,5,2]=>[7,4,3,8,5,6,1,2]=>0010111
[6,5,3,8,4,1,7,2]=>[4,8,7,5,6,1,2,3]=>[6,5,1,7,2,8,4,3]=>0011111
[2,1,5,8,4,6,7,3]=>[2,1,7,8,5,4,6,3]=>[2,1,5,8,4,6,7,3]=>1000011
[2,1,4,8,3,6,7,5]=>[2,1,8,4,7,3,6,5]=>[2,1,4,7,3,6,8,5]=>1000011
[6,4,3,8,2,1,7,5]=>[2,8,4,6,7,3,1,5]=>[7,4,3,6,2,1,8,5]=>1010111
[7,3,8,4,2,6,1,5]=>[6,4,8,7,1,3,2,5]=>[7,1,8,4,3,6,2,5]=>0010111
[3,1,8,2,5,6,7,4]=>[3,8,1,7,2,5,6,4]=>[7,1,3,2,5,6,8,4]=>0100011
[4,3,8,2,5,6,7,1]=>[7,8,4,3,2,5,6,1]=>[4,3,8,2,5,6,7,1]=>0010011
[4,8,2,3,5,6,7,1]=>[7,8,2,4,3,5,6,1]=>[4,8,2,3,5,6,7,1]=>0000011
[3,8,2,1,5,6,7,4]=>[2,8,3,7,1,5,6,4]=>[3,7,2,1,5,6,8,4]=>1000011
[2,8,1,3,5,6,7,4]=>[8,2,1,7,3,5,6,4]=>[2,7,1,3,5,6,8,4]=>0000011
[8,1,2,3,5,6,7,4]=>[8,1,2,7,3,5,6,4]=>[7,1,2,3,5,6,8,4]=>0000011
[7,8,2,4,3,6,1,5]=>[6,8,4,2,1,3,7,5]=>[4,2,7,8,1,6,3,5]=>0010101
[6,8,3,2,4,1,7,5]=>[4,3,8,2,7,6,1,5]=>[6,7,3,2,4,1,8,5]=>0110011
[2,1,8,3,4,6,7,5]=>[2,1,8,3,7,4,6,5]=>[2,1,7,3,4,6,8,5]=>1000011
[2,1,7,8,5,4,3,6]=>[2,1,4,5,8,3,7,6]=>[2,1,7,8,5,4,3,6]=>1011001
[2,7,8,4,5,3,1,6]=>[3,2,5,8,4,1,7,6]=>[2,7,8,4,5,3,1,6]=>0101001
[3,8,7,4,2,6,1,5]=>[6,4,3,7,1,2,8,5]=>[3,8,7,4,1,6,2,5]=>0010111
[5,7,8,4,3,6,2,1]=>[2,6,4,8,5,3,7,1]=>[5,7,8,4,3,6,2,1]=>1010101
[5,6,3,8,4,2,7,1]=>[7,4,8,6,5,2,3,1]=>[5,6,2,8,4,3,7,1]=>0010111
[8,6,3,1,4,2,7,5]=>[3,6,4,2,8,7,5,1]=>[4,2,7,5,8,6,3,1]=>0110111
[7,5,3,8,2,4,1,6]=>[4,8,5,2,7,1,3,6]=>[7,5,2,8,1,4,3,6]=>0011011
[4,1,3,2,6,8,7,5]=>[4,3,1,2,7,6,8,5]=>[3,1,4,2,6,8,7,5]=>0110011
[7,5,3,6,2,8,1,4]=>[8,6,5,1,7,3,2,4]=>[7,5,1,6,3,8,2,4]=>0001111
[8,6,3,5,1,2,7,4]=>[5,1,6,8,4,7,2,3]=>[7,4,8,6,1,2,5,3]=>0001111
[5,8,3,2,6,1,7,4]=>[6,3,8,7,5,2,1,4]=>[5,7,3,2,8,1,6,4]=>0100111
[4,5,3,8,6,2,7,1]=>[7,6,5,4,3,8,2,1]=>[4,5,3,8,6,2,7,1]=>0001111
[5,8,2,4,7,6,1,3]=>[6,7,2,1,5,8,4,3]=>[5,8,2,4,7,6,1,3]=>0000111
[8,7,5,4,1,6,2,3]=>[4,5,2,7,6,1,8,3]=>[6,2,8,7,5,4,1,3]=>0011111
[2,7,6,4,5,8,1,3]=>[8,2,1,6,4,7,5,3]=>[2,7,6,4,5,8,1,3]=>0000111
[7,1,6,4,5,8,2,3]=>[7,8,2,6,4,1,5,3]=>[6,4,8,2,5,7,1,3]=>0000111
[2,1,7,6,5,8,3,4]=>[2,1,8,3,6,7,5,4]=>[2,1,7,6,5,8,3,4]=>1000111
[6,8,3,5,2,1,7,4]=>[2,5,8,7,3,6,1,4]=>[6,7,3,8,2,1,5,4]=>1001011
[7,8,5,4,2,6,1,3]=>[6,4,1,5,8,2,7,3]=>[7,8,5,4,1,6,2,3]=>0011101
[8,1,4,2,5,6,7,3]=>[8,4,7,1,2,5,6,3]=>[7,1,4,2,5,6,8,3]=>0010011
[4,8,1,2,5,6,7,3]=>[8,1,7,4,2,5,6,3]=>[4,7,1,2,5,6,8,3]=>0000011
[3,4,8,1,5,6,7,2]=>[8,7,3,4,1,5,6,2]=>[3,4,7,1,5,6,8,2]=>0000011
[3,4,2,8,5,6,7,1]=>[7,4,3,2,8,5,6,1]=>[3,4,2,8,5,6,7,1]=>0010011
[2,4,1,8,5,6,7,3]=>[4,2,7,1,8,5,6,3]=>[2,8,5,6,7,1,4,3]=>0010011
[8,4,2,1,5,6,7,3]=>[2,4,8,7,3,5,6,1]=>[7,3,5,6,8,4,2,1]=>1010011
[7,5,2,4,8,6,1,3]=>[6,5,2,1,8,7,4,3]=>[7,5,2,4,8,6,1,3]=>0001111
[2,1,5,3,8,6,7,4]=>[2,1,5,7,3,8,6,4]=>[2,1,8,6,7,3,5,4]=>1001011
[6,4,3,5,8,1,7,2]=>[8,7,4,6,3,5,1,2]=>[6,4,3,5,7,1,8,2]=>0010111
[7,3,5,4,8,6,1,2]=>[6,1,8,5,2,7,4,3]=>[5,1,2,7,4,8,6,3]=>0001111
[4,3,1,8,5,6,7,2]=>[3,4,7,2,8,5,6,1]=>[8,5,6,7,2,4,3,1]=>0110011
[3,1,4,8,5,6,7,2]=>[3,7,1,4,8,5,6,2]=>[4,8,5,6,7,1,3,2]=>0100011
[5,1,7,4,8,6,3,2]=>[5,3,6,8,1,7,2,4]=>[7,3,1,8,6,2,5,4]=>0101111
[2,5,7,4,8,6,3,1]=>[3,2,6,8,5,7,1,4]=>[2,5,7,3,1,8,6,4]=>0100111
[5,6,3,7,1,8,4,2]=>[7,4,8,6,5,2,1,3]=>[5,6,2,8,4,1,7,3]=>0010111
[3,8,7,4,5,2,1,6]=>[2,5,3,7,4,1,8,6]=>[3,8,7,4,5,2,1,6]=>1001011
[3,7,5,4,8,6,2,1]=>[2,6,3,5,8,7,1,4]=>[3,7,5,2,1,8,6,4]=>1001111
[5,7,1,4,8,6,2,3]=>[7,6,2,1,5,8,4,3]=>[5,8,6,2,4,7,1,3]=>0000111
[4,6,3,5,8,2,7,1]=>[7,8,6,4,3,5,2,1]=>[4,6,3,5,8,2,7,1]=>0000111
[4,6,3,8,1,2,7,5]=>[8,1,6,4,7,3,2,5]=>[4,7,3,6,1,2,8,5]=>0000111
[3,7,8,4,1,6,2,5]=>[4,8,3,6,1,2,7,5]=>[3,6,1,7,8,4,2,5]=>0010101
[3,2,5,1,6,8,4,7]=>[5,3,2,8,1,6,4,7]=>[3,2,6,8,1,5,4,7]=>0101001
[3,6,2,5,4,8,1,7]=>[8,6,3,5,2,4,1,7]=>[3,5,2,6,4,8,1,7]=>0001101
[3,5,2,4,7,1,8,6]=>[7,5,3,2,4,8,1,6]=>[3,5,2,4,8,1,7,6]=>0001011
[4,2,5,8,3,7,6,1]=>[6,4,7,2,5,8,1,3]=>[5,8,2,4,1,7,6,3]=>0010111
[6,3,5,1,4,8,2,7]=>[5,8,6,1,3,4,2,7]=>[6,1,8,3,4,5,2,7]=>0001101
[4,6,1,5,3,8,2,7]=>[6,8,5,4,1,3,2,7]=>[4,5,1,8,3,6,2,7]=>0001101
[5,4,3,2,7,1,8,6]=>[7,3,4,5,2,8,1,6]=>[5,4,3,2,8,1,7,6]=>0111011
[5,4,3,8,2,7,6,1]=>[6,7,4,5,3,8,1,2]=>[5,4,3,8,1,7,6,2]=>0011111
[4,3,6,2,8,7,5,1]=>[5,7,4,3,6,1,8,2]=>[4,3,6,1,8,7,5,2]=>0011111
[4,3,7,6,2,1,8,5]=>[2,6,4,3,7,8,5,1]=>[4,3,8,5,7,6,2,1]=>1010111
[6,4,3,1,7,2,8,5]=>[3,4,6,7,8,1,2,5]=>[8,1,7,4,3,2,6,5]=>0110111
[7,5,4,3,1,8,2,6]=>[3,4,5,7,8,1,2,6]=>[8,1,7,5,4,3,2,6]=>0111011
[1,4,7,5,8,3,2,6]=>[1,3,8,4,7,2,5,6]=>[1,4,7,3,2,8,5,6]=>0100011
[7,1,3,5,8,4,2,6]=>[7,4,1,8,3,2,5,6]=>[8,4,1,3,7,2,5,6]=>0010011
[7,2,5,8,4,1,3,6]=>[4,8,2,7,1,3,5,6]=>[7,2,8,4,1,3,5,6]=>0010011
[2,8,5,7,4,6,1,3]=>[6,2,1,7,8,4,5,3]=>[2,8,4,7,5,6,1,3]=>0000111
[3,5,8,7,1,4,6,2]=>[7,6,3,1,5,4,8,2]=>[3,5,6,1,4,8,7,2]=>0000111
[1,4,5,8,7,3,6,2]=>[1,6,7,4,5,3,8,2]=>[1,4,5,8,7,3,6,2]=>0000111
[1,5,4,8,7,3,6,2]=>[1,6,7,5,4,3,8,2]=>[1,5,4,8,7,3,6,2]=>0001111
[4,8,3,7,6,5,2,1]=>[2,5,6,4,7,8,3,1]=>[4,8,3,7,6,5,2,1]=>1001111
[5,3,8,7,6,4,2,1]=>[2,4,6,5,1,7,8,3]=>[5,2,1,8,7,6,4,3]=>1011111
[7,5,3,1,8,6,4,2]=>[3,5,4,7,6,8,1,2]=>[8,6,4,1,7,5,3,2]=>0111111
[1,8,6,5,3,7,4,2]=>[1,4,7,5,6,8,2,3]=>[1,8,6,5,2,7,4,3]=>0011111
[1,5,8,6,3,7,4,2]=>[1,4,7,6,5,8,2,3]=>[1,5,8,6,2,7,4,3]=>0010111
[4,6,1,8,7,3,5,2]=>[6,5,7,4,3,1,8,2]=>[4,8,7,3,5,1,6,2]=>0001111
[6,8,7,3,1,4,5,2]=>[3,7,5,2,4,6,8,1]=>[5,2,4,6,8,7,3,1]=>0101011
[6,2,8,7,4,5,1,3]=>[5,6,1,7,4,2,8,3]=>[8,7,4,6,1,5,2,3]=>0001111
[7,6,2,8,4,1,3,5]=>[4,8,2,6,3,7,1,5]=>[7,6,2,3,8,4,1,5]=>0010111
[1,7,6,4,8,3,2,5]=>[1,3,8,6,2,7,4,5]=>[1,7,6,3,2,8,4,5]=>0100111
[5,7,1,6,3,2,8,4]=>[7,3,6,8,5,1,2,4]=>[5,8,3,1,6,2,7,4]=>0100111
[6,1,7,5,3,2,8,4]=>[6,3,5,7,8,1,4,2]=>[8,3,1,7,5,4,6,2]=>0101111
[7,6,5,3,2,1,8,4]=>[2,3,5,6,7,8,1,4]=>[8,3,2,1,7,6,5,4]=>1101111
[6,5,3,2,8,7,4,1]=>[4,3,7,5,6,1,8,2]=>[6,5,3,1,8,7,4,2]=>0111111
[5,2,7,6,3,1,8,4]=>[3,6,5,7,1,8,4,2]=>[8,1,5,4,7,6,3,2]=>0101111
[6,5,2,1,7,3,8,4]=>[2,5,6,7,8,3,4,1]=>[8,3,7,4,6,5,2,1]=>1001111
[5,2,7,4,1,8,3,6]=>[4,7,5,8,3,1,2,6]=>[8,3,5,1,7,4,2,6]=>0011011
[2,4,8,6,3,7,5,1]=>[5,2,7,4,6,8,1,3]=>[2,4,8,6,1,7,5,3]=>0001111
[3,8,6,2,4,7,5,1]=>[5,7,3,1,6,8,4,2]=>[3,8,6,1,4,7,5,2]=>0001111
[7,3,6,2,4,1,8,5]=>[4,6,7,2,8,3,1,5]=>[8,2,7,3,4,1,6,5]=>0010111
[4,3,7,8,2,1,5,6]=>[2,8,4,3,1,5,7,6]=>[4,3,7,8,2,1,5,6]=>1010001
[8,3,7,1,4,6,2,5]=>[7,6,8,1,2,4,3,5]=>[8,1,6,2,4,7,3,5]=>0000111
[3,8,2,5,7,1,6,4]=>[7,8,3,6,2,1,5,4]=>[3,6,2,8,1,5,7,4]=>0000111
[8,7,3,6,2,5,4,1]=>[4,5,6,7,3,1,8,2]=>[8,7,3,6,1,5,4,2]=>0011111
[4,7,8,2,1,6,5,3]=>[2,8,5,4,6,1,7,3]=>[4,6,5,2,1,7,8,3]=>1001101
[4,2,6,8,1,7,5,3]=>[8,4,5,2,7,6,1,3]=>[6,7,5,2,4,1,8,3]=>0011011
[5,8,3,7,1,6,2,4]=>[7,6,8,2,5,1,3,4]=>[5,8,2,6,1,7,3,4]=>0000111
[5,8,7,2,6,1,3,4]=>[6,7,1,3,5,2,8,4]=>[5,8,7,1,3,6,2,4]=>0000111
[8,6,2,7,5,1,3,4]=>[5,7,2,3,6,8,1,4]=>[8,6,2,3,7,5,1,4]=>0001111
[3,6,8,1,7,5,2,4]=>[8,5,3,2,7,6,1,4]=>[3,6,7,5,2,8,1,4]=>0001011
[5,1,6,8,2,7,4,3]=>[5,8,4,7,1,6,2,3]=>[6,7,4,1,8,2,5,3]=>0011011
[5,2,7,1,8,6,4,3]=>[7,5,4,6,2,8,1,3]=>[8,6,4,2,5,1,7,3]=>0011111
[5,8,2,7,6,4,3,1]=>[3,4,6,7,5,8,1,2]=>[5,8,1,7,6,4,3,2]=>0110111
[6,2,8,7,5,4,3,1]=>[3,4,5,7,6,1,8,2]=>[6,1,8,7,5,4,3,2]=>0111111
[7,6,2,1,8,5,4,3]=>[2,6,4,5,7,8,3,1]=>[8,5,4,3,7,6,2,1]=>1011111
[6,1,7,2,8,5,4,3]=>[6,7,4,5,8,1,2,3]=>[8,5,4,1,7,2,6,3]=>0011111
[7,5,1,8,2,6,4,3]=>[5,7,4,8,6,3,2,1]=>[6,4,3,8,2,7,5,1]=>0011111
[4,7,1,8,6,2,5,3]=>[7,6,5,4,2,8,1,3]=>[4,5,2,8,6,1,7,3]=>0001111
[6,8,1,7,5,4,3,2]=>[8,3,4,5,7,6,1,2]=>[6,7,5,4,3,1,8,2]=>0111011
[7,1,8,6,5,4,3,2]=>[7,3,4,5,6,8,1,2]=>[8,6,5,4,3,1,7,2]=>0111111
[5,4,2,3,7,6,1,8]=>[6,4,2,5,3,7,1,8]=>[5,4,2,3,7,6,1,8]=>0011110
[8,4,2,6,3,1,5,7]=>[3,6,4,8,2,1,5,7]=>[8,4,2,6,3,1,5,7]=>0110101
[3,2,7,6,4,5,1,8]=>[5,3,2,6,4,7,1,8]=>[3,2,7,6,4,5,1,8]=>0101110
[4,7,2,6,3,5,1,8]=>[5,7,6,4,3,2,1,8]=>[4,6,3,7,2,5,1,8]=>0001110
[5,7,6,2,3,4,1,8]=>[4,6,2,3,5,7,1,8]=>[5,7,6,2,3,4,1,8]=>0010110
[6,8,5,2,3,1,4,7]=>[3,5,2,1,8,6,4,7]=>[6,8,5,2,3,1,4,7]=>0101001
[5,8,6,2,3,1,4,7]=>[3,6,2,1,5,8,4,7]=>[5,8,6,2,3,1,4,7]=>0100101
[4,8,2,6,3,1,5,7]=>[3,6,8,4,2,1,5,7]=>[4,8,2,6,3,1,5,7]=>0100101
[3,2,8,6,4,1,5,7]=>[4,3,2,6,1,8,5,7]=>[3,2,8,6,4,1,5,7]=>0110101
[3,2,1,6,4,8,5,7]=>[2,3,1,6,8,4,5,7]=>[3,2,1,8,4,6,5,7]=>1100101
[7,1,5,2,8,3,4,6]=>[7,5,8,3,1,4,2,6]=>[8,3,5,1,4,7,2,6]=>0001011
[1,8,5,2,7,3,4,6]=>[1,5,8,2,7,4,3,6]=>[1,7,2,4,8,5,3,6]=>0001011
[1,8,6,7,2,3,4,5]=>[1,7,2,3,4,8,6,5]=>[1,8,6,7,2,3,4,5]=>0000011
[8,1,6,7,2,3,4,5]=>[8,7,2,3,4,1,6,5]=>[7,2,3,4,6,8,1,5]=>0000011
[7,1,6,8,2,3,4,5]=>[7,8,2,3,4,1,6,5]=>[8,2,3,4,6,7,1,5]=>0000011
[3,2,1,7,8,4,5,6]=>[2,3,1,8,4,5,7,6]=>[3,2,1,7,8,4,5,6]=>1100001
[3,2,8,7,1,4,5,6]=>[7,3,2,1,4,5,8,6]=>[3,2,8,7,1,4,5,6]=>0100011
[5,8,7,2,1,3,4,6]=>[2,7,1,3,5,4,8,6]=>[5,8,7,2,1,3,4,6]=>1000011
[1,7,6,8,2,3,4,5]=>[1,8,2,3,4,7,6,5]=>[1,7,6,8,2,3,4,5]=>0000011
[6,5,8,2,3,1,4,7]=>[3,8,2,1,6,5,4,7]=>[6,5,8,2,3,1,4,7]=>0100101
[8,5,7,2,1,3,4,6]=>[2,7,1,3,8,4,5,6]=>[8,2,1,3,4,7,5,6]=>1000011
[6,4,2,8,3,1,5,7]=>[3,8,4,6,2,1,5,7]=>[6,4,2,8,3,1,5,7]=>0110101
[5,4,2,3,8,1,6,7]=>[8,4,2,5,3,1,6,7]=>[5,4,2,3,8,1,6,7]=>0011001
[3,2,5,4,1,8,6,7]=>[4,3,2,5,1,8,6,7]=>[3,2,5,4,1,8,6,7]=>0111001
[4,5,2,3,1,8,6,7]=>[3,5,2,4,1,8,6,7]=>[4,5,2,3,1,8,6,7]=>0101001
[5,4,2,3,1,8,6,7]=>[3,4,2,5,1,8,6,7]=>[5,4,2,3,1,8,6,7]=>0111001
[6,4,2,1,3,8,5,7]=>[2,4,1,6,8,3,5,7]=>[8,4,2,1,3,6,5,7]=>1010101
[8,4,2,1,7,3,5,6]=>[2,4,8,7,1,5,3,6]=>[7,2,1,5,8,4,3,6]=>1010011
[1,5,8,2,7,3,4,6]=>[1,8,7,3,5,4,2,6]=>[1,5,7,3,4,8,2,6]=>0000011
[4,6,2,1,3,8,5,7]=>[2,6,1,4,8,3,5,7]=>[4,8,2,1,3,6,5,7]=>1000101
[3,2,6,1,4,8,5,7]=>[6,3,2,1,8,4,5,7]=>[3,2,8,1,4,6,5,7]=>0100101
[3,2,7,1,8,4,5,6]=>[7,3,2,8,4,5,1,6]=>[3,2,8,4,5,7,1,6]=>0100011
[1,6,8,7,2,3,4,5]=>[1,7,2,3,4,6,8,5]=>[1,6,8,7,2,3,4,5]=>0000011
[1,7,8,6,2,3,4,5]=>[1,6,2,3,4,8,7,5]=>[1,7,8,6,2,3,4,5]=>0000101
[7,8,1,6,2,3,4,5]=>[8,6,2,3,4,1,7,5]=>[6,2,3,4,7,8,1,5]=>0000101
[6,8,1,7,2,3,4,5]=>[8,7,2,3,4,6,1,5]=>[6,7,2,3,4,8,1,5]=>0000011
[3,2,8,1,7,4,5,6]=>[8,3,2,7,4,5,1,6]=>[3,2,7,4,5,8,1,6]=>0100011
[3,2,1,8,7,4,5,6]=>[2,3,1,7,4,5,8,6]=>[3,2,1,8,7,4,5,6]=>1100011
[5,1,8,2,7,3,4,6]=>[5,8,7,3,1,4,2,6]=>[7,3,8,1,4,5,2,6]=>0001011
[6,1,8,7,2,3,4,5]=>[6,7,2,3,4,1,8,5]=>[8,7,2,3,4,6,1,5]=>0000111
[8,1,7,6,2,3,4,5]=>[8,6,2,3,4,7,1,5]=>[7,6,2,3,4,8,1,5]=>0000111
[1,8,7,6,2,3,4,5]=>[1,6,2,3,4,7,8,5]=>[1,8,7,6,2,3,4,5]=>0000111
[4,3,5,6,1,2,8,7]=>[6,1,4,3,5,2,8,7]=>[4,3,5,6,1,2,8,7]=>0010101
[8,5,2,7,4,1,3,6]=>[4,7,2,5,8,3,1,6]=>[8,5,2,3,7,4,1,6]=>0011011
[2,6,1,5,4,3,8,7]=>[6,2,4,5,1,3,8,7]=>[2,5,4,1,6,3,8,7]=>0011101
[6,4,3,5,1,2,8,7]=>[5,1,4,6,3,2,8,7]=>[6,4,3,5,1,2,8,7]=>0011101
[5,3,1,4,6,2,8,7]=>[3,5,6,2,4,1,8,7]=>[6,2,4,5,3,1,8,7]=>0101101
[3,1,4,6,5,2,8,7]=>[3,5,1,4,6,2,8,7]=>[4,6,5,1,3,2,8,7]=>0101101
[5,7,4,6,2,8,3,1]=>[3,8,6,7,5,4,1,2]=>[5,7,4,6,1,8,3,2]=>0100111
[8,1,4,7,2,6,3,5]=>[8,7,6,1,3,2,4,5]=>[6,1,7,3,8,2,4,5]=>0000111
[3,4,7,8,5,2,1,6]=>[2,5,3,4,8,1,7,6]=>[3,4,7,8,5,2,1,6]=>1001001
[2,1,8,5,7,3,4,6]=>[2,1,7,3,8,4,5,6]=>[2,1,8,3,4,7,5,6]=>1000011
[8,6,3,5,1,7,4,2]=>[5,4,7,6,2,8,1,3]=>[8,6,2,7,4,1,5,3]=>0011111
[3,4,8,6,5,7,1,2]=>[7,1,3,4,6,8,5,2]=>[3,4,8,6,5,7,1,2]=>0000111
[7,5,4,8,1,6,3,2]=>[8,3,6,5,7,1,4,2]=>[7,5,3,1,6,4,8,2]=>0101111
[2,5,4,6,7,1,8,3]=>[7,2,8,5,4,6,1,3]=>[2,5,4,6,8,1,7,3]=>0001011
[4,1,6,3,8,5,7,2]=>[4,7,6,1,8,3,5,2]=>[8,1,6,5,7,3,4,2]=>0010111
[3,7,4,2,8,6,5,1]=>[5,4,3,6,8,7,2,1]=>[3,7,4,2,8,6,5,1]=>0011111
[7,4,1,3,5,8,6,2]=>[4,7,2,6,3,8,5,1]=>[8,6,2,3,5,7,4,1]=>0010111
[2,1,4,8,3,7,6,5]=>[2,1,8,4,6,7,3,5]=>[2,1,4,7,6,3,8,5]=>1000111
[7,4,3,8,2,1,6,5]=>[2,8,4,7,6,1,3,5]=>[6,4,2,1,7,3,8,5]=>1010111
[6,3,7,4,1,8,2,5]=>[4,7,8,6,3,1,2,5]=>[6,3,8,1,7,4,2,5]=>0010111
[3,1,8,2,7,6,5,4]=>[3,8,1,5,6,7,2,4]=>[7,6,5,1,3,2,8,4]=>0101111
[4,3,7,2,6,8,5,1]=>[5,8,4,3,7,1,6,2]=>[4,3,7,1,6,8,5,2]=>0011011
[3,8,2,1,7,5,6,4]=>[2,8,3,6,7,5,1,4]=>[3,7,5,6,2,1,8,4]=>1000111
[2,7,8,5,4,3,1,6]=>[3,2,4,5,8,1,7,6]=>[2,7,8,5,4,3,1,6]=>0111001
[3,8,6,7,2,4,1,5]=>[4,7,3,2,1,8,6,5]=>[3,8,6,7,2,4,1,5]=>0010011
[4,3,8,7,2,1,6,5]=>[2,7,4,3,6,1,8,5]=>[4,3,6,2,1,8,7,5]=>1010111
[8,3,6,1,4,2,7,5]=>[6,4,8,1,7,3,2,5]=>[7,1,4,3,8,2,6,5]=>0010111
[7,3,5,8,2,4,1,6]=>[4,8,7,2,3,1,5,6]=>[7,2,8,3,4,1,5,6]=>0010011
[2,3,4,1,8,5,7,6]=>[4,2,3,1,8,7,5,6]=>[2,3,4,1,7,5,8,6]=>0010011
[4,1,3,2,6,7,8,5]=>[4,3,1,2,8,6,7,5]=>[3,1,4,2,6,7,8,5]=>0110001
[5,3,6,1,8,7,2,4]=>[6,7,5,2,3,1,8,4]=>[5,2,8,7,3,6,1,4]=>0001111
[5,6,2,8,7,4,1,3]=>[4,7,2,6,5,1,8,3]=>[5,6,2,8,7,4,1,3]=>0010111
[7,8,5,6,1,4,2,3]=>[6,4,2,1,8,5,7,3]=>[4,2,7,8,5,6,1,3]=>0010101
[2,8,6,5,4,7,1,3]=>[7,2,1,5,6,8,4,3]=>[2,8,6,5,4,7,1,3]=>0001111
[8,1,6,4,5,7,2,3]=>[8,7,2,6,4,1,5,3]=>[6,4,7,2,5,8,1,3]=>0000111
[5,8,3,6,1,7,2,4]=>[6,7,8,2,5,3,1,4]=>[5,8,2,7,3,6,1,4]=>0000111
[2,1,8,6,5,7,3,4]=>[2,1,7,3,6,8,5,4]=>[2,1,8,6,5,7,3,4]=>1000111
[2,1,7,5,3,6,8,4]=>[2,1,5,7,8,4,6,3]=>[2,1,8,4,6,7,5,3]=>1001011
[6,7,3,5,2,1,8,4]=>[2,5,7,8,3,6,1,4]=>[6,8,3,7,2,1,5,4]=>1001011
[7,1,4,2,5,6,8,3]=>[7,4,8,1,2,5,6,3]=>[8,1,4,2,5,6,7,3]=>0010011
[4,6,1,2,8,7,3,5]=>[6,1,7,4,3,2,8,5]=>[4,8,7,3,6,1,2,5]=>0000111
[2,4,1,5,8,7,6,3]=>[4,2,6,1,5,7,8,3]=>[2,5,8,7,6,1,4,3]=>0010111
[4,1,2,5,8,6,7,3]=>[4,1,7,2,5,8,6,3]=>[5,8,6,7,1,2,4,3]=>0010011
[6,4,2,1,5,8,7,3]=>[2,4,6,7,3,5,8,1]=>[8,7,3,5,6,4,2,1]=>1010111
[8,5,2,4,6,1,7,3]=>[6,5,8,3,7,4,1,2]=>[7,3,4,8,5,1,6,2]=>0001111
[7,5,3,2,6,8,1,4]=>[8,3,5,1,7,2,6,4]=>[7,5,3,1,6,8,2,4]=>0101011
[2,1,5,3,6,8,7,4]=>[2,1,5,7,3,6,8,4]=>[2,1,6,8,7,3,5,4]=>1001011
[7,3,5,4,6,1,8,2]=>[6,8,7,5,3,4,1,2]=>[5,3,7,4,8,1,6,2]=>0001111
[6,3,4,1,5,7,8,2]=>[4,8,6,3,1,5,7,2]=>[6,3,5,7,8,1,4,2]=>0010101
[4,5,2,6,3,1,8,7]=>[3,6,5,4,1,2,8,7]=>[4,5,1,6,3,2,8,7]=>0101101
[6,5,2,1,4,3,8,7]=>[2,5,4,1,6,3,8,7]=>[4,2,1,6,5,3,8,7]=>1011101
[6,5,2,7,4,8,3,1]=>[3,8,5,6,7,4,1,2]=>[7,4,6,5,1,8,3,2]=>0101111
[8,5,2,7,4,1,6,3]=>[4,7,5,8,6,2,1,3]=>[6,2,8,5,1,7,4,3]=>0011111
[6,3,7,5,2,8,4,1]=>[4,8,5,7,6,3,1,2]=>[6,3,7,5,1,8,4,2]=>0011111
[3,1,6,5,4,2,8,7]=>[3,4,1,5,6,2,8,7]=>[6,5,4,1,3,2,8,7]=>0111101
[5,6,3,2,4,1,8,7]=>[4,3,6,2,5,1,8,7]=>[5,6,3,2,4,1,8,7]=>0110101
[3,6,2,4,1,5,8,7]=>[4,6,3,2,1,5,8,7]=>[3,6,2,4,1,5,8,7]=>0010101
[2,6,1,3,5,4,8,7]=>[6,2,1,5,3,4,8,7]=>[2,5,1,3,6,4,8,7]=>0001101
[6,7,2,3,4,8,5,1]=>[5,8,1,3,7,6,4,2]=>[6,7,1,3,4,8,5,2]=>0001011
[5,1,7,3,8,4,6,2]=>[5,6,7,8,1,4,3,2]=>[8,1,7,4,6,3,5,2]=>0001111
[2,5,7,3,8,6,4,1]=>[4,2,6,8,5,7,3,1]=>[2,5,7,3,8,6,4,1]=>0010111
[7,6,1,3,5,8,4,2]=>[6,4,2,7,3,8,5,1]=>[8,4,2,3,5,7,6,1]=>0010111
[3,6,7,4,1,8,5,2]=>[4,7,3,5,8,6,2,1]=>[3,6,8,5,2,7,4,1]=>0011011
[5,6,3,7,4,8,1,2]=>[8,1,6,7,5,3,4,2]=>[5,7,3,6,4,8,1,2]=>0000111
[2,1,6,7,4,8,5,3]=>[2,1,5,8,7,6,3,4]=>[2,1,6,7,3,8,5,4]=>1001011
[2,1,8,7,4,3,6,5]=>[2,1,4,7,6,3,8,5]=>[2,1,6,4,3,8,7,5]=>1010111
[5,8,3,7,4,2,6,1]=>[6,4,7,8,5,3,2,1]=>[5,8,3,7,4,2,6,1]=>0010111
[3,8,7,4,1,2,6,5]=>[4,1,3,7,6,2,8,5]=>[3,6,4,1,2,8,7,5]=>0010111
[8,1,6,3,2,5,4,7]=>[8,3,6,5,2,1,4,7]=>[5,3,2,6,1,8,4,7]=>0101101
[2,8,4,1,6,3,7,5]=>[4,2,8,6,7,3,1,5]=>[2,7,3,6,4,1,8,5]=>0010111
[4,8,1,2,7,6,3,5]=>[8,1,6,4,3,7,2,5]=>[4,7,6,3,8,1,2,5]=>0000111
[3,8,4,2,5,7,1,6]=>[7,4,3,8,2,1,5,6]=>[3,8,4,2,7,1,5,6]=>0010011
[2,1,5,3,8,7,6,4]=>[2,1,5,6,3,7,8,4]=>[2,1,8,7,6,3,5,4]=>1001111
[7,5,2,4,8,1,6,3]=>[8,5,7,3,6,1,4,2]=>[6,3,7,5,1,4,8,2]=>0001111
[3,4,2,8,5,7,6,1]=>[6,4,3,2,7,8,1,5]=>[3,4,2,8,1,7,6,5]=>0010111
[2,4,1,8,7,6,5,3]=>[4,2,5,1,6,7,8,3]=>[2,8,7,6,5,1,4,3]=>0011111
[8,4,2,1,7,5,3,6]=>[2,4,8,5,7,1,3,6]=>[7,5,2,1,8,4,3,6]=>1011011
[4,3,1,8,6,7,5,2]=>[3,4,5,2,7,8,6,1]=>[8,6,7,5,2,4,3,1]=>0111011
[3,1,4,8,6,5,7,2]=>[3,7,1,4,6,8,5,2]=>[4,8,6,5,7,1,3,2]=>0100111
[7,1,6,5,4,8,2,3]=>[7,8,2,5,6,1,4,3]=>[6,5,2,8,4,7,1,3]=>0001111
[3,7,5,6,8,4,2,1]=>[2,4,3,8,7,5,6,1]=>[3,7,5,6,8,4,2,1]=>1010011
[5,7,1,6,8,2,4,3]=>[7,8,4,2,5,1,6,3]=>[4,2,5,8,1,6,7,3]=>0010011
[8,6,2,5,1,7,4,3]=>[5,6,4,8,3,7,1,2]=>[7,4,3,8,6,1,5,2]=>0011111
[7,5,2,6,3,8,1,4]=>[8,5,7,1,6,3,2,4]=>[6,1,7,5,3,8,2,4]=>0001111
[4,1,2,3,6,8,7,5]=>[4,1,2,3,7,6,8,5]=>[4,1,2,3,6,8,7,5]=>0010011
[2,4,3,1,8,5,6,7]=>[3,2,4,1,8,5,6,7]=>[2,4,3,1,8,5,6,7]=>0110001
[5,6,2,8,4,3,1,7]=>[3,4,8,6,5,2,1,7]=>[5,6,2,8,4,3,1,7]=>0110101
[4,7,2,8,1,5,3,6]=>[8,7,5,4,1,3,2,6]=>[4,5,1,7,3,8,2,6]=>0001011
[5,7,8,6,3,4,1,2]=>[4,1,6,3,5,8,7,2]=>[5,7,8,6,3,4,1,2]=>0010101
[2,7,8,4,5,3,6,1]=>[6,2,5,8,4,3,7,1]=>[2,7,8,4,5,3,6,1]=>0001101
[5,7,3,8,1,4,6,2]=>[8,6,7,1,5,4,3,2]=>[5,7,1,4,6,3,8,2]=>0000111
[2,1,7,8,5,4,6,3]=>[2,1,6,5,8,4,7,3]=>[2,1,7,8,5,4,6,3]=>1001101
[2,1,5,8,4,6,3,7]=>[2,1,6,8,5,4,3,7]=>[2,1,5,8,4,6,3,7]=>1000101
[6,5,3,8,4,1,2,7]=>[4,1,8,5,6,2,3,7]=>[6,5,1,2,8,4,3,7]=>0011101
[7,5,8,4,3,6,2,1]=>[2,6,4,8,7,3,5,1]=>[7,4,3,8,5,6,2,1]=>1010111
[2,4,8,3,5,6,1,7]=>[6,2,8,4,3,5,1,7]=>[2,4,8,3,5,6,1,7]=>0000101
[3,4,8,1,7,2,5,6]=>[8,7,3,4,2,5,1,6]=>[3,4,7,2,5,8,1,6]=>0000011
[3,1,8,2,4,7,6,5]=>[3,8,1,2,6,7,4,5]=>[7,6,1,3,2,4,8,5]=>0100111
[4,3,8,2,5,1,7,6]=>[5,8,4,3,2,7,1,6]=>[4,3,7,2,5,1,8,6]=>0011011
[6,3,8,4,2,5,7,1]=>[7,4,8,6,3,2,5,1]=>[6,3,8,4,2,5,7,1]=>0010111
[7,4,3,8,2,5,1,6]=>[5,8,4,7,2,1,3,6]=>[7,4,2,8,1,5,3,6]=>0011011
[2,1,4,8,3,5,7,6]=>[2,1,8,4,3,7,5,6]=>[2,1,4,7,3,5,8,6]=>1000011
[4,8,2,3,5,1,6,7]=>[5,8,2,4,3,1,6,7]=>[4,8,2,3,5,1,6,7]=>0001001
[3,8,2,1,4,6,5,7]=>[2,8,3,1,6,4,5,7]=>[3,6,2,1,4,8,5,7]=>1000101
[2,8,1,3,4,5,7,6]=>[8,2,1,3,4,7,5,6]=>[2,7,1,3,4,5,8,6]=>0000011
[2,8,4,1,6,5,3,7]=>[4,2,8,5,6,3,1,7]=>[2,6,5,3,8,4,1,7]=>0011101
[2,8,4,1,6,5,7,3]=>[4,2,8,7,6,3,5,1]=>[2,6,3,7,5,8,4,1]=>0010111
[2,8,7,6,1,4,3,5]=>[6,2,4,1,3,7,8,5]=>[2,4,1,8,7,6,3,5]=>0010111
[2,8,5,6,7,4,3,1]=>[3,2,4,7,8,5,6,1]=>[2,8,5,6,7,4,3,1]=>0110011
[7,5,8,6,1,4,2,3]=>[6,4,2,1,8,7,3,5]=>[4,2,7,1,3,8,6,5]=>0010111
[3,5,7,6,1,4,2,8]=>[6,4,3,1,5,7,2,8]=>[3,4,1,5,7,6,2,8]=>0010110
[3,5,7,2,4,1,6,8]=>[4,7,3,2,5,1,6,8]=>[3,5,7,2,4,1,6,8]=>0010010
[2,8,5,3,4,1,6,7]=>[4,2,5,3,8,1,6,7]=>[2,8,5,3,4,1,6,7]=>0011001
[2,8,5,6,7,4,1,3]=>[4,2,1,7,8,5,6,3]=>[2,8,5,6,7,4,1,3]=>0010011
[2,8,5,3,4,6,1,7]=>[6,2,5,3,8,4,1,7]=>[2,8,5,3,4,6,1,7]=>0001101
[2,8,5,3,4,6,7,1]=>[7,2,5,3,8,4,6,1]=>[2,8,5,3,4,6,7,1]=>0001011
[3,5,7,2,4,6,1,8]=>[6,7,3,2,5,4,1,8]=>[3,5,7,2,4,6,1,8]=>0000110
[7,5,8,2,4,6,3,1]=>[3,6,8,1,7,4,5,2]=>[7,1,4,8,5,6,3,2]=>0100111
[3,5,6,2,1,8,7,4]=>[2,6,3,7,5,1,8,4]=>[3,5,8,7,2,1,6,4]=>1000111
[3,5,7,6,1,4,8,2]=>[6,7,3,2,5,8,4,1]=>[3,5,8,2,4,7,6,1]=>0000111
[3,5,7,2,4,6,8,1]=>[8,7,3,2,5,4,6,1]=>[3,5,7,2,4,6,8,1]=>0000011
[6,5,2,7,3,1,8,4]=>[3,7,5,6,8,4,2,1]=>[8,4,6,5,2,7,3,1]=>0101111
[4,5,2,6,3,1,7,8]=>[3,6,5,4,1,2,7,8]=>[4,5,1,6,3,2,7,8]=>0101100
[4,1,2,3,7,6,8,5]=>[4,1,2,3,8,7,6,5]=>[4,1,2,3,7,6,8,5]=>0010011
[5,1,2,8,6,4,7,3]=>[5,1,7,6,2,8,4,3]=>[8,6,1,2,7,4,5,3]=>0001111
[4,1,2,3,8,7,5,6]=>[4,1,2,3,7,5,8,6]=>[4,1,2,3,8,7,5,6]=>0010011
[4,1,2,3,8,6,5,7]=>[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]=>0010101
[4,1,2,3,8,6,7,5]=>[4,1,2,3,7,8,6,5]=>[4,1,2,3,8,6,7,5]=>0010011
[4,1,2,3,7,6,5,8]=>[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>0010110
[4,1,2,3,8,5,7,6]=>[4,1,2,3,8,7,5,6]=>[4,1,2,3,7,5,8,6]=>0010011
[6,1,2,8,4,5,7,3]=>[6,1,7,8,4,2,5,3]=>[8,4,7,1,2,5,6,3]=>0000111
[5,6,8,2,3,1,7,4]=>[3,8,2,7,5,6,1,4]=>[5,6,7,2,3,1,8,4]=>0100011
[6,5,8,2,4,3,7,1]=>[7,8,4,2,6,5,3,1]=>[4,2,6,5,8,3,7,1]=>0010111
[6,5,2,8,3,7,1,4]=>[7,5,6,1,8,3,2,4]=>[8,1,6,5,3,7,2,4]=>0001111
[6,5,2,7,3,4,1,8]=>[4,5,6,2,7,3,1,8]=>[7,2,6,5,3,4,1,8]=>0011110
[5,1,6,7,4,3,2,8]=>[5,3,4,7,1,6,2,8]=>[6,7,4,3,1,5,2,8]=>0111010
[7,1,6,8,4,3,2,5]=>[7,3,4,8,2,1,6,5]=>[8,4,3,2,6,7,1,5]=>0110011
[5,7,8,6,3,4,2,1]=>[2,4,6,3,5,8,7,1]=>[5,7,8,6,3,4,2,1]=>1010101
[4,1,8,3,6,2,7,5]=>[4,6,8,1,7,3,2,5]=>[7,1,8,3,4,2,6,5]=>0010111
[7,1,6,5,8,3,2,4]=>[7,3,8,2,6,1,5,4]=>[6,3,2,8,5,7,1,4]=>0100111
[4,1,6,7,8,3,2,5]=>[4,3,8,1,2,6,7,5]=>[6,7,8,3,1,4,2,5]=>0110001
[4,5,2,7,3,8,1,6]=>[8,5,7,4,2,1,3,6]=>[4,7,2,5,1,8,3,6]=>0001011
[3,7,5,6,8,4,1,2]=>[4,1,3,8,7,5,6,2]=>[3,7,5,6,8,4,1,2]=>0010011
[6,1,2,5,8,4,7,3]=>[6,1,7,8,2,5,4,3]=>[8,1,2,5,7,4,6,3]=>0000111
[7,1,6,5,8,3,4,2]=>[7,4,8,3,6,1,5,2]=>[6,3,4,1,8,5,7,2]=>0010111
[7,5,2,6,3,8,4,1]=>[4,8,5,7,6,1,3,2]=>[6,1,7,5,3,8,4,2]=>0011111
[4,1,2,3,5,8,7,6]=>[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>0010011
[4,1,2,3,7,8,6,5]=>[4,1,2,3,6,8,7,5]=>[4,1,2,3,7,8,6,5]=>0010101
[4,1,2,6,8,5,7,3]=>[4,1,7,2,8,6,5,3]=>[6,8,5,7,1,2,4,3]=>0010011
[7,8,4,2,1,5,3,6]=>[2,4,8,5,3,1,7,6]=>[5,3,7,8,4,2,1,6]=>1011001
[7,8,2,1,6,5,3,4]=>[2,8,5,3,6,1,7,4]=>[6,5,3,7,8,2,1,4]=>1001101
[2,4,8,1,5,7,3,6]=>[8,2,7,4,1,3,5,6]=>[2,4,7,1,8,3,5,6]=>0000011
[4,3,8,1,7,2,5,6]=>[8,7,4,3,2,5,1,6]=>[4,3,7,2,5,8,1,6]=>0010011
[7,8,3,4,5,1,6,2]=>[5,6,8,3,4,1,7,2]=>[7,8,3,4,6,1,5,2]=>0001101
[7,8,3,5,4,2,1,6]=>[2,4,5,8,1,3,7,6]=>[7,8,2,1,5,4,3,6]=>1011001
[7,8,4,1,2,3,6,5]=>[4,1,2,8,6,3,7,5]=>[6,4,1,2,3,7,8,5]=>0010101
[7,8,3,6,5,4,1,2]=>[4,1,5,6,8,3,7,2]=>[7,8,3,6,5,4,1,2]=>0011101
[7,8,2,1,5,3,4,6]=>[2,8,5,3,1,4,7,6]=>[5,3,7,8,2,1,4,6]=>1001001
[7,8,1,6,5,4,3,2]=>[8,3,4,5,6,1,7,2]=>[6,5,4,3,1,7,8,2]=>0111101
[6,2,1,7,5,4,3,8]=>[2,6,4,5,7,1,3,8]=>[7,5,4,2,1,6,3,8]=>1011110
[2,1,8,7,5,4,3,6]=>[2,1,4,5,7,3,8,6]=>[2,1,8,7,5,4,3,6]=>1011011
[1,3,8,2,6,4,7,5]=>[1,8,3,6,7,2,4,5]=>[1,3,7,2,6,4,8,5]=>0000111
[5,3,7,1,6,4,8,2]=>[7,8,5,6,3,1,4,2]=>[6,3,5,1,8,4,7,2]=>0001111
[6,1,2,5,8,7,4,3]=>[6,1,4,7,2,5,8,3]=>[8,7,4,1,2,5,6,3]=>0010111
[6,4,3,7,5,8,1,2]=>[8,1,4,6,7,3,5,2]=>[7,4,3,6,5,8,1,2]=>0010111
[4,3,8,7,5,6,1,2]=>[6,1,4,3,7,5,8,2]=>[4,3,8,7,5,6,1,2]=>0010111
[1,3,7,6,4,2,8,5]=>[1,4,3,6,7,8,5,2]=>[1,3,8,5,7,6,4,2]=>0010111
[2,1,7,5,6,8,4,3]=>[2,1,4,8,7,5,6,3]=>[2,1,7,5,6,8,4,3]=>1010011
[3,7,2,8,6,4,1,5]=>[4,6,3,8,1,7,2,5]=>[3,7,1,8,6,4,2,5]=>0010111
[2,7,5,8,3,6,1,4]=>[6,2,8,1,7,3,5,4]=>[2,7,1,8,5,6,3,4]=>0000111
[1,5,6,8,2,4,7,3]=>[1,8,7,2,5,6,4,3]=>[1,5,6,7,2,4,8,3]=>0000011
[2,6,8,5,3,1,4,7]=>[3,2,5,1,8,6,4,7]=>[2,6,8,5,3,1,4,7]=>0101001
[5,6,7,3,8,4,1,2]=>[4,1,8,7,5,6,2,3]=>[5,6,7,1,2,8,4,3]=>0010011
[5,2,8,1,4,7,3,6]=>[8,5,7,1,2,3,4,6]=>[7,1,5,2,8,3,4,6]=>0001011
[4,5,6,7,2,8,1,3]=>[8,7,1,4,5,6,2,3]=>[4,5,6,7,1,8,2,3]=>0000011
[4,5,7,6,1,8,3,2]=>[6,3,7,4,5,8,2,1]=>[4,5,8,3,2,7,6,1]=>0100111
[4,6,5,7,1,2,8,3]=>[7,1,8,4,6,5,2,3]=>[4,6,5,8,1,2,7,3]=>0000111
[5,7,1,4,2,3,8,6]=>[7,4,2,1,5,8,3,6]=>[4,2,5,8,1,3,7,6]=>0010011
[6,2,4,1,8,3,7,5]=>[4,6,8,2,7,1,3,5]=>[7,2,8,1,4,3,6,5]=>0010111
[6,1,3,4,5,8,7,2]=>[6,7,1,3,4,5,8,2]=>[8,7,1,3,4,5,6,2]=>0000111
[5,8,7,6,3,4,1,2]=>[4,1,6,3,5,7,8,2]=>[5,8,7,6,3,4,1,2]=>0010111
[4,8,2,1,5,6,3,7]=>[2,8,6,4,1,5,3,7]=>[4,6,2,1,5,8,3,7]=>1000101
[2,1,8,7,6,5,3,4]=>[2,1,5,3,6,7,8,4]=>[2,1,8,7,6,5,3,4]=>1001111
[4,3,7,5,6,8,1,2]=>[8,1,4,3,7,5,6,2]=>[4,3,7,5,6,8,1,2]=>0010011
[4,8,6,3,5,7,1,2]=>[7,1,6,4,3,8,5,2]=>[4,8,6,3,5,7,1,2]=>0000111
[4,8,1,2,5,3,7,6]=>[8,1,5,4,2,7,3,6]=>[4,5,1,2,7,3,8,6]=>0001011
[5,2,8,7,1,6,4,3]=>[7,5,4,6,2,1,8,3]=>[6,4,2,5,1,8,7,3]=>0011111
[3,7,8,5,1,2,4,6]=>[5,1,3,2,8,4,7,6]=>[3,7,8,5,1,2,4,6]=>0001001
[3,7,1,6,4,2,5,8]=>[7,4,3,6,2,1,5,8]=>[3,6,4,2,7,1,5,8]=>0010110
[4,1,8,6,2,3,5,7]=>[4,6,2,1,3,8,5,7]=>[8,6,2,4,1,3,5,7]=>0010101
[4,7,8,6,3,5,1,2]=>[5,1,6,4,3,8,7,2]=>[4,7,8,6,3,5,1,2]=>0001101
[3,8,7,6,5,4,1,2]=>[4,1,3,5,6,7,8,2]=>[3,8,7,6,5,4,1,2]=>0011111
[2,1,7,6,5,3,4,8]=>[2,1,5,3,6,7,4,8]=>[2,1,7,6,5,3,4,8]=>1001110
[2,7,8,6,5,4,1,3]=>[4,2,1,5,6,8,7,3]=>[2,7,8,6,5,4,1,3]=>0011101
[6,4,2,7,1,3,8,5]=>[7,4,1,6,8,2,3,5]=>[8,4,1,6,2,3,7,5]=>0010111
[7,3,6,2,4,8,1,5]=>[8,6,7,2,1,3,4,5]=>[7,2,6,1,8,3,4,5]=>0000111
[4,3,7,1,2,5,8,6]=>[7,1,4,3,2,8,5,6]=>[4,3,8,1,2,5,7,6]=>0010011
[5,3,6,7,1,2,8,4]=>[7,1,5,8,3,6,2,4]=>[6,8,3,5,1,2,7,4]=>0001011
[3,7,5,1,2,4,8,6]=>[5,1,3,2,7,8,4,6]=>[3,8,5,1,2,4,7,6]=>0001011
[5,7,4,2,3,8,1,6]=>[8,4,2,7,5,1,3,6]=>[5,7,4,2,8,1,3,6]=>0010011
[5,7,2,6,1,8,3,4]=>[6,7,8,3,5,2,1,4]=>[5,8,3,7,2,6,1,4]=>0000111
[7,4,8,5,2,6,1,3]=>[6,5,1,8,7,4,2,3]=>[7,4,8,5,1,6,2,3]=>0001111
[5,8,2,6,3,7,1,4]=>[7,8,6,1,5,2,3,4]=>[5,6,1,8,2,7,3,4]=>0000111
[6,3,7,5,8,1,2,4]=>[8,1,6,2,7,3,5,4]=>[7,1,2,6,5,8,3,4]=>0000111
[2,6,5,8,1,3,4,7]=>[8,2,1,3,6,5,4,7]=>[2,6,5,8,1,3,4,7]=>0000101
[3,6,5,8,1,2,4,7]=>[8,1,3,2,6,5,4,7]=>[3,6,5,8,1,2,4,7]=>0000101
[2,5,7,4,8,1,3,6]=>[8,2,1,7,5,3,4,6]=>[2,5,7,1,3,8,4,6]=>0000011
[5,4,6,7,2,8,1,3]=>[8,7,1,5,4,6,2,3]=>[5,4,6,7,1,8,2,3]=>0001011
[3,5,7,1,4,8,2,6]=>[7,8,3,1,5,2,4,6]=>[3,5,8,1,7,2,4,6]=>0000011
[5,4,7,3,8,1,2,6]=>[8,1,7,5,4,2,3,6]=>[5,4,7,1,2,8,3,6]=>0001011
[7,4,6,3,8,1,2,5]=>[8,1,6,7,2,4,3,5]=>[7,1,2,6,4,8,3,5]=>0000111
[5,4,1,7,8,2,3,6]=>[4,5,1,8,2,3,7,6]=>[7,8,1,5,4,2,3,6]=>0011001
[6,5,1,2,7,8,3,4]=>[5,1,6,2,8,3,7,4]=>[7,8,1,2,6,5,3,4]=>0001101
[4,7,1,5,8,6,2,3]=>[7,6,2,4,1,8,5,3]=>[4,8,6,2,5,7,1,3]=>0000111
[5,7,2,8,1,6,3,4]=>[8,7,6,3,5,1,2,4]=>[5,6,3,7,1,8,2,4]=>0000111
[2,4,8,7,1,3,5,6]=>[7,2,1,4,3,5,8,6]=>[2,4,8,7,1,3,5,6]=>0000011
[4,3,8,7,1,2,5,6]=>[7,1,4,3,2,5,8,6]=>[4,3,8,7,1,2,5,6]=>0010011
[8,3,7,6,1,2,4,5]=>[6,1,7,3,4,8,2,5]=>[8,3,4,7,6,1,2,5]=>0000111
[3,5,8,7,1,2,4,6]=>[7,1,3,2,5,4,8,6]=>[3,5,8,7,1,2,4,6]=>0000011
[2,8,7,6,1,3,4,5]=>[6,2,1,3,4,7,8,5]=>[2,8,7,6,1,3,4,5]=>0000111
[3,8,7,6,1,2,4,5]=>[6,1,3,2,4,7,8,5]=>[3,8,7,6,1,2,4,5]=>0000111
[4,8,7,6,1,2,3,5]=>[6,1,2,4,3,7,8,5]=>[4,8,7,6,1,2,3,5]=>0000111
[5,6,3,1,4,2,8,7]=>[3,6,4,2,5,1,8,7]=>[4,2,5,6,3,1,8,7]=>0110101
[6,7,1,4,5,8,2,3]=>[7,8,2,1,4,6,5,3]=>[6,8,2,4,5,7,1,3]=>0000011
[2,1,7,8,5,3,6,4]=>[2,1,5,8,6,4,7,3]=>[2,1,6,4,7,8,5,3]=>1001101
[5,7,3,8,1,2,6,4]=>[8,1,7,6,5,2,3,4]=>[5,6,1,2,7,3,8,4]=>0000111
[8,7,1,4,5,3,2,6]=>[7,3,5,1,4,2,8,6]=>[5,3,1,4,8,7,2,6]=>0101011
[2,7,8,4,1,6,5,3]=>[4,2,8,5,6,3,7,1]=>[2,6,5,3,7,8,4,1]=>0011101
[7,5,1,4,8,6,3,2]=>[5,3,7,2,6,8,4,1]=>[8,6,3,2,4,7,5,1]=>0101111
[6,5,3,1,8,4,7,2]=>[3,5,6,7,8,1,2,4]=>[8,1,7,3,2,6,5,4]=>0101111
[8,7,1,4,2,6,5,3]=>[7,4,5,1,6,2,8,3]=>[6,5,1,4,2,8,7,3]=>0011111
[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[2,3,4,5,6,7,8,1,9]=>00000010
[2,3,4,5,6,8,9,1,7]=>[9,2,3,4,5,6,1,8,7]=>[2,3,4,5,6,8,9,1,7]=>00000001
[2,3,4,5,7,8,9,1,6]=>[9,2,3,4,5,1,7,8,6]=>[2,3,4,5,7,8,9,1,6]=>00000001
[2,3,4,6,7,8,9,1,5]=>[9,2,3,4,1,6,7,8,5]=>[2,3,4,6,7,8,9,1,5]=>00000001
[2,3,5,6,7,8,9,1,4]=>[9,2,3,1,5,6,7,8,4]=>[2,3,5,6,7,8,9,1,4]=>00000001
[2,4,5,6,7,8,9,1,3]=>[9,2,1,4,5,6,7,8,3]=>[2,4,5,6,7,8,9,1,3]=>00000001
[3,4,5,6,7,8,9,1,2]=>[9,1,3,4,5,6,7,8,2]=>[3,4,5,6,7,8,9,1,2]=>00000001
[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,9,10,1]=>000000001
[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>000000010
[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>00000100
[2,3,4,5,6,7,8,10,1,9]=>[10,2,3,4,5,6,7,8,1,9]=>[2,3,4,5,6,7,8,10,1,9]=>000000001
[2,3,4,5,6,1,9,7,8]=>[6,2,3,4,5,1,9,7,8]=>[2,3,4,5,6,1,9,7,8]=>00001001
[2,3,4,5,6,7,9,10,1,8]=>[10,2,3,4,5,6,7,1,9,8]=>[2,3,4,5,6,7,9,10,1,8]=>000000001
[2,3,4,5,1,8,9,6,7]=>[5,2,3,4,1,9,6,8,7]=>[2,3,4,5,1,8,9,6,7]=>00010001
[2,3,4,5,6,8,9,10,1,7]=>[10,2,3,4,5,6,1,8,9,7]=>[2,3,4,5,6,8,9,10,1,7]=>000000001
[2,3,4,1,7,8,9,5,6]=>[4,2,3,1,9,5,7,8,6]=>[2,3,4,1,7,8,9,5,6]=>00100001
[2,3,4,5,7,8,9,10,1,6]=>[10,2,3,4,5,1,7,8,9,6]=>[2,3,4,5,7,8,9,10,1,6]=>000000001
[2,3,1,6,7,8,9,4,5]=>[3,2,1,9,4,6,7,8,5]=>[2,3,1,6,7,8,9,4,5]=>01000001
[2,3,4,6,7,8,9,10,1,5]=>[10,2,3,4,1,6,7,8,9,5]=>[2,3,4,6,7,8,9,10,1,5]=>000000001
[2,1,5,6,7,8,9,3,4]=>[2,1,9,3,5,6,7,8,4]=>[2,1,5,6,7,8,9,3,4]=>10000001
[2,3,5,6,7,8,9,10,1,4]=>[10,2,3,1,5,6,7,8,9,4]=>[2,3,5,6,7,8,9,10,1,4]=>000000001
[1,4,5,6,7,8,9,2,3]=>[1,9,2,4,5,6,7,8,3]=>[1,4,5,6,7,8,9,2,3]=>00000001
[2,4,5,6,7,8,9,10,1,3]=>[10,2,1,4,5,6,7,8,9,3]=>[2,4,5,6,7,8,9,10,1,3]=>000000001
[3,4,5,6,7,8,9,10,1,2]=>[10,1,3,4,5,6,7,8,9,2]=>[3,4,5,6,7,8,9,10,1,2]=>000000001
[3,6,4,5,7,2,8,1]=>[8,7,3,6,4,5,2,1]=>[3,6,4,5,7,2,8,1]=>0000111
[7,5,3,6,2,4,8,1]=>[8,6,5,2,7,3,4,1]=>[7,5,2,6,3,4,8,1]=>0001111
[6,3,2,5,1,8,4,7]=>[5,3,6,8,2,1,4,7]=>[8,3,2,6,1,5,4,7]=>0101101
[8,5,3,6,2,7,1,4]=>[7,6,5,1,8,3,2,4]=>[8,5,1,6,3,7,2,4]=>0001111
[8,2,6,3,4,7,1,5]=>[7,8,6,3,1,2,4,5]=>[6,3,8,1,7,2,4,5]=>0000111
[4,2,5,7,3,6,8,1]=>[8,4,7,2,5,3,6,1]=>[5,7,2,4,3,6,8,1]=>0010011
[5,4,7,6,2,3,8,1]=>[8,6,2,5,4,7,3,1]=>[5,4,7,6,2,3,8,1]=>0001111
[3,7,6,2,4,5,8,1]=>[8,6,3,2,4,7,5,1]=>[3,7,6,2,4,5,8,1]=>0000111
[2,7,6,3,4,5,8,1]=>[8,2,6,3,4,7,5,1]=>[2,7,6,3,4,5,8,1]=>0000111
[5,7,3,1,2,8,4,6]=>[3,1,7,8,5,4,2,6]=>[5,8,4,7,3,1,2,6]=>0100011
[5,6,2,3,1,8,4,7]=>[3,6,2,8,5,1,4,7]=>[5,8,2,3,1,6,4,7]=>0100101
[4,2,6,5,1,8,3,7]=>[5,4,6,2,8,3,1,7]=>[8,2,4,3,6,5,1,7]=>0011101
[5,4,8,6,2,7,1,3]=>[7,6,1,5,4,8,2,3]=>[5,4,8,6,1,7,2,3]=>0001111
[6,8,3,5,2,7,1,4]=>[7,5,8,1,3,6,2,4]=>[6,8,1,5,3,7,2,4]=>0001011
[1,8,6,3,7,2,4,5]=>[1,7,6,2,4,8,3,5]=>[1,8,6,2,4,7,3,5]=>0000111
[1,8,2,7,3,4,5,6]=>[1,8,7,3,4,5,2,6]=>[1,7,3,4,5,8,2,6]=>0000011
[2,8,1,7,3,4,5,6]=>[8,2,7,3,4,5,1,6]=>[2,7,3,4,5,8,1,6]=>0000011
[4,8,1,5,7,2,3,6]=>[8,7,2,4,1,3,5,6]=>[4,7,2,8,1,3,5,6]=>0000011
[1,7,3,8,2,4,5,6]=>[1,8,7,2,4,5,3,6]=>[1,7,2,4,5,8,3,6]=>0000011
[8,1,2,7,3,4,5,6]=>[8,1,7,3,4,5,2,6]=>[7,3,4,5,8,1,2,6]=>0000011
[6,3,7,1,2,8,4,5]=>[7,1,6,8,4,3,2,5]=>[8,4,6,3,7,1,2,5]=>0000111
[7,2,6,1,8,3,4,5]=>[6,7,8,3,4,2,1,5]=>[8,3,4,7,2,6,1,5]=>0000111
[7,3,1,5,8,2,4,6]=>[3,7,8,1,2,4,5,6]=>[8,1,7,3,2,4,5,6]=>0100011
[3,2,1,5,8,4,6,7]=>[2,3,1,8,5,4,6,7]=>[3,2,1,5,8,4,6,7]=>1100001
[1,5,3,4,6,8,2,7]=>[1,8,5,3,4,6,2,7]=>[1,5,3,4,6,8,2,7]=>0001001
[5,4,6,3,8,7,1,2]=>[7,1,6,5,4,3,8,2]=>[5,4,6,3,8,7,1,2]=>0001111
[3,6,4,5,8,7,1,2]=>[7,1,3,6,4,5,8,2]=>[3,6,4,5,8,7,1,2]=>0000111
[6,5,3,4,8,7,1,2]=>[7,1,5,3,6,4,8,2]=>[6,5,3,4,8,7,1,2]=>0001111
[5,3,2,8,7,1,4,6]=>[7,3,5,1,2,4,8,6]=>[5,3,1,8,7,2,4,6]=>0101011
[8,5,3,7,6,1,2,4]=>[6,1,5,3,7,8,2,4]=>[8,5,3,7,6,1,2,4]=>0001111
[7,6,8,2,3,5,1,4]=>[5,8,2,1,3,7,6,4]=>[7,6,8,2,5,1,3,4]=>0001011
[3,7,8,2,4,6,1,5]=>[6,8,3,2,1,4,7,5]=>[3,7,8,2,6,1,4,5]=>0000101
[6,7,3,8,2,5,1,4]=>[5,8,7,1,2,6,3,4]=>[6,7,1,8,2,5,3,4]=>0001011
[5,4,7,8,2,6,1,3]=>[6,8,1,5,4,2,7,3]=>[5,4,7,8,1,6,2,3]=>0001101
[3,6,2,8,7,1,4,5]=>[7,6,3,1,4,2,8,5]=>[3,6,1,4,8,7,2,5]=>0000111
[3,7,8,1,6,2,4,5]=>[8,6,3,2,4,1,7,5]=>[3,6,2,4,7,8,1,5]=>0000101
[2,3,8,7,1,4,5,6]=>[7,2,3,1,4,5,8,6]=>[2,3,8,7,1,4,5,6]=>0000011
[7,2,8,6,1,3,4,5]=>[6,8,2,3,4,7,1,5]=>[7,2,3,4,8,6,1,5]=>0000111
[2,1,8,7,3,4,5,6]=>[2,1,7,3,4,5,8,6]=>[2,1,8,7,3,4,5,6]=>1000011
[8,2,7,6,1,3,4,5]=>[6,7,2,3,4,8,1,5]=>[8,2,3,4,7,6,1,5]=>0000111
[1,2,8,7,3,4,5,6]=>[1,2,7,3,4,5,8,6]=>[1,2,8,7,3,4,5,6]=>0000011
[1,3,8,7,2,4,5,6]=>[1,7,3,2,4,5,8,6]=>[1,3,8,7,2,4,5,6]=>0000011
[1,7,8,3,6,2,4,5]=>[1,6,8,2,4,3,7,5]=>[1,7,8,2,4,6,3,5]=>0000101
[4,1,5,8,7,2,3,6]=>[4,7,2,1,5,3,8,6]=>[5,8,7,2,4,1,3,6]=>0010011
[5,4,8,7,6,1,2,3]=>[6,1,2,5,4,7,8,3]=>[5,4,8,7,6,1,2,3]=>0001111
[6,8,3,7,5,1,2,4]=>[5,1,7,3,8,6,2,4]=>[6,8,3,7,5,1,2,4]=>0001011
[7,8,6,2,5,1,3,4]=>[5,6,1,3,2,8,7,4]=>[7,8,6,1,3,5,2,4]=>0001101
[8,1,6,7,3,2,5,4]=>[8,3,7,5,2,1,6,4]=>[5,3,2,7,1,6,8,4]=>0101011
[8,1,6,7,3,2,4,5]=>[8,3,7,2,4,1,6,5]=>[7,3,2,4,6,8,1,5]=>0100011
[8,1,5,3,6,2,4,7]=>[8,6,5,2,1,3,4,7]=>[5,2,6,1,8,3,4,7]=>0001101
[8,1,4,3,2,6,5,7]=>[8,3,4,1,6,2,5,7]=>[4,3,1,6,2,8,5,7]=>0110101
[8,1,4,3,2,7,6,5]=>[8,3,4,1,6,7,2,5]=>[4,3,1,7,6,2,8,5]=>0110111
[8,1,5,4,6,7,2,3]=>[8,7,2,5,1,4,6,3]=>[5,2,7,4,6,8,1,3]=>0001011
[8,1,5,3,6,2,7,4]=>[8,6,5,7,1,3,2,4]=>[7,1,5,3,6,2,8,4]=>0001111
[8,1,4,3,2,5,7,6]=>[8,3,4,1,2,7,5,6]=>[4,3,1,7,2,5,8,6]=>0110011
[8,1,4,3,2,5,6,7]=>[8,3,4,1,2,5,6,7]=>[4,3,1,8,2,5,6,7]=>0110001
[7,4,8,3,2,5,6,1]=>[6,3,8,7,2,5,4,1]=>[7,3,2,5,8,4,6,1]=>0100111
[6,4,3,1,2,5,8,7]=>[3,1,4,6,2,5,8,7]=>[6,4,3,1,2,5,8,7]=>0110101
[7,4,8,3,2,5,1,6]=>[5,3,8,7,2,1,4,6]=>[7,3,2,8,1,5,4,6]=>0101011
[6,4,3,8,2,5,1,7]=>[5,8,4,6,2,3,1,7]=>[6,4,2,8,3,5,1,7]=>0011101
[6,4,3,7,2,5,8,1]=>[8,7,4,6,2,3,5,1]=>[6,4,2,7,3,5,8,1]=>0010111
[6,5,3,8,7,2,1,4]=>[2,7,5,1,6,3,8,4]=>[6,5,2,1,8,7,3,4]=>1001111
[6,5,4,1,7,8,2,3]=>[4,5,2,6,8,1,7,3]=>[7,8,2,6,5,4,1,3]=>0011101
[6,5,3,1,7,2,8,4]=>[3,5,6,7,8,1,4,2]=>[8,1,7,4,6,5,3,2]=>0101111
[6,4,3,1,2,7,8,5]=>[3,1,4,6,8,2,7,5]=>[7,8,4,3,1,2,6,5]=>0110101
[5,4,3,2,1,8,6,7]=>[2,3,4,5,1,8,6,7]=>[5,4,3,2,1,8,6,7]=>1111001
[6,5,3,1,8,2,7,4]=>[3,5,6,8,7,1,4,2]=>[7,1,8,4,6,5,3,2]=>0101111
[6,5,4,1,8,7,2,3]=>[4,5,2,6,7,1,8,3]=>[8,7,2,6,5,4,1,3]=>0011111
[7,4,1,3,2,8,6,5]=>[4,3,1,7,6,8,2,5]=>[3,1,8,6,4,2,7,5]=>0110111
[7,4,1,3,2,8,5,6]=>[4,3,1,7,8,5,2,6]=>[3,1,8,5,7,4,2,6]=>0110011
[6,4,3,1,2,8,5,7]=>[3,1,4,6,8,2,5,7]=>[8,4,3,1,2,6,5,7]=>0110101
[6,4,3,8,2,7,5,1]=>[5,7,4,8,6,1,3,2]=>[6,4,1,8,3,7,5,2]=>0011111
[6,5,3,8,7,2,4,1]=>[4,7,5,2,6,3,8,1]=>[6,5,2,8,7,3,4,1]=>0011111
[6,5,3,1,7,2,4,8]=>[3,5,6,2,7,1,4,8]=>[7,2,6,5,3,1,4,8]=>0101110
[7,6,1,8,3,2,4,5]=>[6,3,7,1,4,8,2,5]=>[8,3,1,4,7,6,2,5]=>0100111
[7,6,1,8,4,5,2,3]=>[6,5,2,7,1,8,4,3]=>[8,2,5,4,7,6,1,3]=>0001111
[7,6,8,1,4,5,2,3]=>[8,5,2,1,4,7,6,3]=>[5,2,4,7,6,8,1,3]=>0001011
[7,6,8,1,3,2,5,4]=>[8,3,1,5,2,7,6,4]=>[3,1,5,2,7,6,8,4]=>0101011
[7,4,8,3,2,1,6,5]=>[2,3,8,7,6,1,4,5]=>[6,3,2,1,7,4,8,5]=>1100111
[5,4,3,2,8,1,7,6]=>[8,3,4,5,2,7,1,6]=>[5,4,3,2,7,1,8,6]=>0111011
[6,5,4,7,1,8,2,3]=>[7,8,2,5,6,4,1,3]=>[6,5,4,8,2,7,1,3]=>0001111
[5,4,3,2,7,8,1,6]=>[8,3,4,5,2,1,7,6]=>[5,4,3,2,7,8,1,6]=>0111001
[5,6,2,1,3,4,8,7]=>[2,6,1,3,5,4,8,7]=>[5,6,2,1,3,4,8,7]=>1000101
[5,8,2,7,4,1,3,6]=>[4,7,2,8,5,3,1,6]=>[5,8,2,3,7,4,1,6]=>0010011
[2,1,7,8,4,3,5,6]=>[2,1,4,8,3,5,7,6]=>[2,1,7,8,4,3,5,6]=>1010001
[8,3,7,4,1,5,6,2]=>[4,7,6,8,2,5,1,3]=>[8,2,5,6,1,7,4,3]=>0010111
[2,6,8,3,1,4,7,5]=>[3,2,8,1,7,6,4,5]=>[2,6,7,3,1,4,8,5]=>0100011
[6,1,8,3,2,4,5,7]=>[6,3,8,2,4,1,5,7]=>[8,3,2,4,6,1,5,7]=>0100101
[8,4,1,3,7,6,2,5]=>[4,8,2,6,1,7,3,5]=>[7,6,2,8,4,1,3,5]=>0010111
[6,5,2,1,8,7,4,3]=>[2,5,4,6,7,3,8,1]=>[8,7,4,3,6,5,2,1]=>1011111
[3,4,7,1,8,2,6,5]=>[7,8,3,4,6,2,1,5]=>[3,4,6,2,8,1,7,5]=>0000111
[1,8,2,4,3,5,6,7]=>[1,8,4,2,3,5,6,7]=>[1,4,2,8,3,5,6,7]=>0010001
[1,7,2,4,3,5,6,8]=>[1,7,4,2,3,5,6,8]=>[1,4,2,7,3,5,6,8]=>0010010
[1,6,2,4,3,5,7,8]=>[1,6,4,2,3,5,7,8]=>[1,4,2,6,3,5,7,8]=>0010100
[1,5,2,4,3,6,7,8]=>[1,5,4,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>0011000
[1,6,2,5,3,4,7,8]=>[1,6,5,3,2,4,7,8]=>[1,5,3,6,2,4,7,8]=>0001100
[1,7,2,5,3,4,6,8]=>[1,7,5,3,2,4,6,8]=>[1,5,3,7,2,4,6,8]=>0001010
[1,8,2,5,3,4,6,7]=>[1,8,5,3,2,4,6,7]=>[1,5,3,8,2,4,6,7]=>0001001
[1,8,2,7,3,5,4,6]=>[1,8,7,5,3,4,2,6]=>[1,5,3,7,4,8,2,6]=>0001011
[1,7,2,8,3,5,4,6]=>[1,7,8,5,3,4,2,6]=>[1,5,3,8,4,7,2,6]=>0001011
[1,6,2,8,3,5,4,7]=>[1,6,8,5,3,2,4,7]=>[1,5,3,8,2,6,4,7]=>0001101
[1,5,2,8,3,6,4,7]=>[1,5,8,6,2,3,4,7]=>[1,6,2,8,3,5,4,7]=>0001101
[1,4,2,8,3,6,5,7]=>[1,4,8,2,6,3,5,7]=>[1,6,2,4,3,8,5,7]=>0010101
[1,3,2,8,4,6,5,7]=>[1,3,2,8,6,4,5,7]=>[1,3,2,6,4,8,5,7]=>0100101
[1,2,3,8,4,6,5,7]=>[1,2,3,8,6,4,5,7]=>[1,2,3,6,4,8,5,7]=>0000101
[1,2,3,7,4,6,5,8]=>[1,2,3,7,6,4,5,8]=>[1,2,3,6,4,7,5,8]=>0000110
[1,3,2,7,4,6,5,8]=>[1,3,2,7,6,4,5,8]=>[1,3,2,6,4,7,5,8]=>0100110
[1,4,2,7,3,6,5,8]=>[1,4,7,2,6,3,5,8]=>[1,6,2,4,3,7,5,8]=>0010110
[1,5,2,7,3,6,4,8]=>[1,5,7,6,2,3,4,8]=>[1,6,2,7,3,5,4,8]=>0001110
[1,6,2,7,3,5,4,8]=>[1,6,7,5,3,2,4,8]=>[1,5,3,7,2,6,4,8]=>0001110
[1,7,2,6,3,5,4,8]=>[1,7,6,5,3,2,4,8]=>[1,5,3,6,2,7,4,8]=>0001110
[1,8,2,5,3,6,4,7]=>[1,8,5,6,2,3,4,7]=>[1,6,2,5,3,8,4,7]=>0001101
[1,7,2,5,3,6,4,8]=>[1,7,5,6,2,3,4,8]=>[1,6,2,5,3,7,4,8]=>0001110
[1,6,2,5,3,7,4,8]=>[1,6,5,7,2,3,4,8]=>[1,7,2,5,3,6,4,8]=>0001110
[1,5,2,4,3,7,6,8]=>[1,5,4,2,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>0011010
[1,6,2,4,3,7,5,8]=>[1,6,4,2,7,3,5,8]=>[1,4,2,7,3,6,5,8]=>0010110
[1,7,2,4,3,6,5,8]=>[1,7,4,2,6,3,5,8]=>[1,4,2,6,3,7,5,8]=>0010110
[1,8,2,4,3,6,5,7]=>[1,8,4,2,6,3,5,7]=>[1,4,2,6,3,8,5,7]=>0010101
[1,8,2,3,4,6,5,7]=>[1,8,2,3,6,4,5,7]=>[1,6,2,3,4,8,5,7]=>0000101
[1,7,2,3,4,6,5,8]=>[1,7,2,3,6,4,5,8]=>[1,6,2,3,4,7,5,8]=>0000110
[1,8,2,3,4,7,5,6]=>[1,8,2,3,7,5,4,6]=>[1,7,5,8,2,3,4,6]=>0000011
[1,8,2,4,3,7,5,6]=>[1,8,4,2,7,5,3,6]=>[1,4,2,7,5,8,3,6]=>0010011
[1,7,2,4,3,8,5,6]=>[1,7,4,2,8,5,3,6]=>[1,4,2,8,5,7,3,6]=>0010011
[1,6,2,4,3,8,5,7]=>[1,6,4,2,8,3,5,7]=>[1,4,2,8,3,6,5,7]=>0010101
[1,5,2,4,3,8,6,7]=>[1,5,4,2,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>0011001
[1,6,2,5,3,8,4,7]=>[1,6,5,8,2,3,4,7]=>[1,8,2,5,3,6,4,7]=>0001101
[1,7,2,5,3,8,4,6]=>[1,7,5,8,2,4,3,6]=>[1,8,2,5,4,7,3,6]=>0001011
[1,8,2,5,3,7,4,6]=>[1,8,5,7,2,4,3,6]=>[1,7,2,5,4,8,3,6]=>0001011
[1,8,2,6,3,7,4,5]=>[1,8,6,7,4,2,3,5]=>[1,7,4,6,2,8,3,5]=>0000111
[1,7,2,6,3,8,4,5]=>[1,7,6,8,4,2,3,5]=>[1,8,4,6,2,7,3,5]=>0000111
[1,2,3,8,4,7,5,6]=>[1,2,3,8,7,5,4,6]=>[1,2,3,7,5,8,4,6]=>0000011
[1,3,2,8,4,7,5,6]=>[1,3,2,8,7,5,4,6]=>[1,3,2,7,5,8,4,6]=>0100011
[1,4,2,8,3,7,5,6]=>[1,4,8,2,7,5,3,6]=>[1,7,5,8,2,4,3,6]=>0010011
[1,5,2,8,3,7,4,6]=>[1,5,8,7,2,4,3,6]=>[1,7,2,8,4,5,3,6]=>0001011
[1,8,2,7,3,6,4,5]=>[1,8,7,6,4,3,2,5]=>[1,6,4,7,3,8,2,5]=>0000111
[4,6,3,7,2,5,1,8]=>[5,7,6,4,2,3,1,8]=>[4,6,2,7,3,5,1,8]=>0001110
[4,6,3,7,5,2,1,8]=>[2,5,7,4,6,1,3,8]=>[4,6,2,1,7,5,3,8]=>1001110
[4,6,3,8,5,1,2,7]=>[5,1,8,4,6,2,3,7]=>[4,6,1,2,8,5,3,7]=>0001101
[5,6,8,3,4,1,2,7]=>[4,1,8,3,5,6,2,7]=>[5,6,8,3,4,1,2,7]=>0010001
[5,6,8,3,4,1,7,2]=>[4,7,8,3,5,6,1,2]=>[5,6,8,3,7,1,4,2]=>0010011
[4,6,2,7,5,3,1,8]=>[3,5,7,4,6,2,1,8]=>[4,6,2,7,5,3,1,8]=>0101110
[5,6,8,4,3,1,7,2]=>[3,4,8,7,5,6,1,2]=>[5,6,7,1,8,4,3,2]=>0110011
[5,6,8,4,3,1,2,7]=>[3,1,4,8,5,6,2,7]=>[5,6,8,4,3,1,2,7]=>0110001
[5,7,8,4,1,6,2,3]=>[4,8,1,6,5,2,7,3]=>[5,6,1,7,8,4,2,3]=>0010101
[5,7,8,4,1,6,3,2]=>[4,3,8,6,5,2,7,1]=>[5,6,3,2,7,8,4,1]=>0110101
[5,6,8,4,2,1,7,3]=>[2,4,8,7,5,6,3,1]=>[5,6,7,3,8,4,2,1]=>1010011
[3,2,6,8,5,1,7,4]=>[5,3,2,8,7,6,4,1]=>[3,2,6,7,4,8,5,1]=>0101011
[3,2,6,8,5,1,4,7]=>[5,3,2,1,8,6,4,7]=>[3,2,6,8,5,1,4,7]=>0101001
[4,6,2,8,5,1,3,7]=>[5,8,2,4,6,1,3,7]=>[4,6,2,8,5,1,3,7]=>0001101
[5,6,8,2,4,1,3,7]=>[4,8,1,2,5,6,3,7]=>[5,6,8,1,4,2,3,7]=>0010001
[5,6,8,4,2,1,3,7]=>[2,4,1,8,5,6,3,7]=>[5,6,8,4,2,1,3,7]=>1010001
[5,7,8,4,1,3,2,6]=>[4,3,1,8,5,2,7,6]=>[3,1,5,7,8,4,2,6]=>0110001
[5,7,8,4,1,2,3,6]=>[4,1,2,8,5,3,7,6]=>[5,7,8,4,1,2,3,6]=>0010001
[6,7,8,1,5,2,3,4]=>[8,5,2,3,1,6,7,4]=>[5,2,3,6,7,8,1,4]=>0001001
[6,7,8,1,5,2,4,3]=>[8,5,4,2,1,6,7,3]=>[4,2,5,1,6,7,8,3]=>0011001
[6,7,8,1,3,5,2,4]=>[8,5,1,2,3,6,7,4]=>[5,1,6,7,8,2,3,4]=>0001001
[5,7,8,2,1,6,3,4]=>[2,8,6,3,5,1,7,4]=>[5,6,3,7,8,2,1,4]=>1000101
[4,7,2,8,1,6,3,5]=>[8,7,6,4,3,1,2,5]=>[4,6,3,7,1,8,2,5]=>0000111
[3,2,7,8,1,6,4,5]=>[8,3,2,6,4,1,7,5]=>[3,2,6,4,7,8,1,5]=>0100101
[3,2,7,8,1,6,5,4]=>[8,3,2,5,6,1,7,4]=>[3,2,6,5,1,7,8,4]=>0101101
[6,7,8,1,3,5,4,2]=>[8,4,1,5,3,6,7,2]=>[5,4,1,3,6,7,8,2]=>0011001
[6,7,8,1,5,3,4,2]=>[8,4,5,3,1,6,7,2]=>[5,3,4,1,6,7,8,2]=>0011001
[6,7,8,1,5,4,3,2]=>[8,3,4,5,1,6,7,2]=>[5,4,3,1,6,7,8,2]=>0111001
[6,7,8,1,5,4,2,3]=>[8,4,2,5,1,6,7,3]=>[5,4,2,6,7,8,1,3]=>0011001
[6,7,8,1,4,5,3,2]=>[8,3,5,1,4,6,7,2]=>[5,3,1,4,6,7,8,2]=>0101001
[6,7,8,1,4,3,5,2]=>[8,5,4,1,3,6,7,2]=>[4,1,5,3,6,7,8,2]=>0011001
[6,7,8,1,3,4,5,2]=>[8,5,1,3,4,6,7,2]=>[5,1,3,4,6,7,8,2]=>0001001
[5,7,8,2,1,4,6,3]=>[2,8,6,1,5,4,7,3]=>[5,6,2,1,4,7,8,3]=>1000101
[4,7,2,8,1,5,6,3]=>[8,7,6,4,1,5,2,3]=>[4,6,1,5,7,2,8,3]=>0000111
[3,2,7,8,1,5,6,4]=>[8,3,2,6,1,5,7,4]=>[3,2,6,1,5,7,8,4]=>0100101
[3,2,6,8,4,1,7,5]=>[4,3,2,8,7,6,1,5]=>[3,2,6,7,4,1,8,5]=>0110011
[4,6,2,8,3,1,7,5]=>[3,8,6,4,7,1,2,5]=>[4,7,1,6,3,2,8,5]=>0100111
[5,6,8,3,2,1,7,4]=>[2,3,8,7,5,6,1,4]=>[5,6,7,3,2,1,8,4]=>1100011
[5,7,8,3,1,4,6,2]=>[3,8,6,2,5,4,7,1]=>[5,6,2,4,7,8,3,1]=>0100101
[4,7,3,8,1,6,2,5]=>[8,6,7,4,2,1,3,5]=>[4,7,2,6,1,8,3,5]=>0000111
[4,7,3,8,1,6,5,2]=>[8,5,6,4,7,1,2,3]=>[4,7,1,6,5,2,8,3]=>0001111
[4,6,3,8,2,1,7,5]=>[2,8,6,4,7,3,1,5]=>[4,7,3,6,2,1,8,5]=>1000111
[4,5,3,2,8,1,7,6]=>[8,3,5,4,2,7,1,6]=>[4,5,3,2,7,1,8,6]=>0101011
[4,5,2,3,8,1,7,6]=>[8,5,2,4,3,7,1,6]=>[4,5,2,3,7,1,8,6]=>0001011
[3,2,5,4,8,1,7,6]=>[8,3,2,5,4,7,1,6]=>[3,2,5,4,7,1,8,6]=>0101011
[4,5,3,2,8,1,6,7]=>[8,3,5,4,2,1,6,7]=>[4,5,3,2,8,1,6,7]=>0101001
[4,6,3,8,2,1,5,7]=>[2,8,6,4,1,3,5,7]=>[4,6,2,1,8,3,5,7]=>1000101
[4,7,3,8,1,5,2,6]=>[8,5,7,4,1,2,3,6]=>[4,7,1,5,2,8,3,6]=>0001011
[5,7,8,3,1,2,4,6]=>[3,1,8,2,5,4,7,6]=>[5,7,8,3,1,2,4,6]=>0100001
[5,7,8,3,1,2,6,4]=>[3,1,8,6,5,2,7,4]=>[5,6,3,1,2,7,8,4]=>0100101
[5,6,8,3,2,1,4,7]=>[2,3,8,1,5,6,4,7]=>[5,6,8,3,2,1,4,7]=>1100001
[3,2,7,8,1,5,4,6]=>[8,3,2,5,1,4,7,6]=>[3,2,5,1,7,8,4,6]=>0101001
[5,7,8,2,1,4,3,6]=>[2,8,4,1,5,3,7,6]=>[4,2,1,5,7,8,3,6]=>1010001
[6,7,8,1,3,4,2,5]=>[8,4,1,3,2,6,7,5]=>[4,1,3,6,7,8,2,5]=>0010001
[6,7,8,1,4,3,2,5]=>[8,3,4,1,2,6,7,5]=>[4,3,1,6,7,8,2,5]=>0110001
[6,7,8,1,4,2,5,3]=>[8,4,5,1,2,6,7,3]=>[5,1,4,2,6,7,8,3]=>0011001
[6,7,8,1,4,2,3,5]=>[8,4,2,1,3,6,7,5]=>[4,2,6,7,8,1,3,5]=>0010001
[6,7,8,1,2,5,4,3]=>[8,1,4,5,2,6,7,3]=>[5,4,1,2,6,7,8,3]=>0011001
[6,7,8,1,2,4,5,3]=>[8,1,5,2,4,6,7,3]=>[5,1,2,4,6,7,8,3]=>0001001
[6,7,8,1,3,2,5,4]=>[8,3,1,5,2,6,7,4]=>[3,1,5,2,6,7,8,4]=>0101001
[3,2,7,8,1,4,6,5]=>[8,3,2,1,6,4,7,5]=>[3,2,6,1,4,7,8,5]=>0100101
[6,7,8,1,2,3,5,4]=>[8,1,2,5,3,6,7,4]=>[5,1,2,3,6,7,8,4]=>0001001
[7,2,8,5,1,6,4,3]=>[5,8,4,7,6,2,3,1]=>[6,4,2,7,3,8,5,1]=>0011111
[1,3,7,5,2,6,4,8]=>[1,5,3,7,6,4,2,8]=>[1,3,6,4,7,5,2,8]=>0001110
[2,8,4,5,6,1,7,3]=>[6,2,7,8,4,5,1,3]=>[2,8,4,5,7,1,6,3]=>0000111
[2,8,4,5,3,7,1,6]=>[7,2,5,8,4,1,3,6]=>[2,8,4,5,1,7,3,6]=>0001011
[1,6,3,7,5,2,4,8]=>[1,5,7,3,6,2,4,8]=>[1,6,3,7,5,2,4,8]=>0001110
[6,2,3,8,5,1,7,4]=>[5,8,1,6,7,4,2,3]=>[7,4,6,1,8,5,2,3]=>0001111
[6,3,2,8,5,1,4,7]=>[5,3,8,2,6,1,4,7]=>[6,3,2,8,5,1,4,7]=>0101101
[7,4,8,5,2,1,3,6]=>[2,5,1,8,7,4,3,6]=>[7,4,8,5,2,1,3,6]=>1001011
[6,4,8,5,1,3,7,2]=>[5,8,2,7,6,1,3,4]=>[6,2,7,1,3,8,5,4]=>0001111
[3,4,1,2,7,6,8,5]=>[4,1,3,2,8,7,6,5]=>[3,4,1,2,7,6,8,5]=>0010011
[3,6,5,7,1,4,8,2]=>[7,8,3,1,6,5,4,2]=>[3,6,5,8,1,4,7,2]=>0000111
[6,5,2,7,4,1,8,3]=>[4,7,5,6,8,1,2,3]=>[8,1,6,5,2,7,4,3]=>0011111
[5,3,1,8,6,4,7,2]=>[3,5,7,6,2,8,4,1]=>[8,6,2,7,4,5,3,1]=>0101111
[5,6,1,8,7,2,4,3]=>[6,7,4,2,5,1,8,3]=>[4,2,5,8,7,1,6,3]=>0010111
[6,5,8,4,2,3,7,1]=>[7,4,2,8,6,5,3,1]=>[6,5,8,4,2,3,7,1]=>0010111
[1,6,5,7,3,4,2,8]=>[1,4,7,3,6,5,2,8]=>[1,6,5,7,3,4,2,8]=>0010110
[5,2,1,8,7,6,3,4]=>[2,5,6,3,1,7,8,4]=>[8,7,6,3,5,2,1,4]=>1001111
[2,3,4,8,6,1,7,5]=>[6,2,3,4,8,7,5,1]=>[2,3,4,7,5,8,6,1]=>0000111
[2,3,4,8,6,5,1,7]=>[5,2,3,4,6,8,1,7]=>[2,3,4,8,6,5,1,7]=>0001101
[2,7,3,5,8,6,1,4]=>[6,2,8,3,1,7,5,4]=>[2,7,3,5,8,6,1,4]=>0000111
[3,2,4,7,8,6,1,5]=>[6,3,2,4,1,8,7,5]=>[3,2,4,7,8,6,1,5]=>0100101
[5,3,6,4,1,8,7,2]=>[4,6,7,5,1,2,8,3]=>[5,1,8,7,2,6,4,3]=>0011111
[5,3,6,1,4,8,2,7]=>[6,8,5,1,3,4,2,7]=>[5,1,8,3,4,6,2,7]=>0001101
[2,7,6,5,8,3,4,1]=>[4,2,8,3,6,7,5,1]=>[2,7,6,5,8,3,4,1]=>0010111
[3,2,4,1,7,8,5,6]=>[4,3,2,1,8,5,7,6]=>[3,2,4,1,7,8,5,6]=>0110001
[6,3,4,5,7,1,8,2]=>[7,8,6,3,4,5,1,2]=>[6,3,4,5,8,1,7,2]=>0000111
[2,5,4,6,1,7,8,3]=>[6,2,8,5,4,1,7,3]=>[2,5,4,7,8,1,6,3]=>0001101
[7,2,1,4,3,6,5,8]=>[2,7,4,1,6,3,5,8]=>[4,2,1,6,3,7,5,8]=>1010110
[7,3,4,1,2,6,5,8]=>[4,1,7,3,6,2,5,8]=>[6,3,4,1,2,7,5,8]=>0010110
[7,4,3,2,1,6,5,8]=>[2,3,4,7,6,1,5,8]=>[6,4,3,2,1,7,5,8]=>1110110
[6,7,3,2,5,4,8,1]=>[8,3,7,5,2,6,4,1]=>[5,3,2,6,7,4,8,1]=>0101011
[1,8,3,2,5,4,7,6]=>[1,3,8,5,2,7,4,6]=>[1,5,3,2,7,4,8,6]=>0101011
[1,8,4,5,2,3,7,6]=>[1,5,2,8,4,7,3,6]=>[1,7,4,5,2,3,8,6]=>0001011
[7,3,5,1,6,2,4,8]=>[5,6,7,2,3,1,4,8]=>[7,2,6,3,5,1,4,8]=>0001110
[1,8,5,4,3,2,7,6]=>[1,3,4,5,8,7,2,6]=>[1,7,5,4,3,2,8,6]=>0111011
[1,8,6,4,3,7,2,5]=>[1,7,4,6,2,8,3,5]=>[1,8,6,4,2,7,3,5]=>0010111
[6,5,7,4,3,1,8,2]=>[3,4,7,8,6,5,1,2]=>[6,5,8,1,7,4,3,2]=>0110111
[6,4,7,5,1,3,8,2]=>[5,7,2,8,6,1,3,4]=>[6,2,8,1,3,7,5,4]=>0001111
[1,8,7,5,6,3,4,2]=>[1,4,6,3,7,5,8,2]=>[1,8,7,5,6,3,4,2]=>0010111
[2,7,8,5,6,3,4,1]=>[4,2,6,3,8,5,7,1]=>[2,7,8,5,6,3,4,1]=>0010101
[2,6,8,5,7,3,1,4]=>[3,2,7,1,8,6,5,4]=>[2,6,8,5,7,3,1,4]=>0100011
[2,5,8,6,7,1,3,4]=>[7,2,1,3,5,8,6,4]=>[2,5,8,6,7,1,3,4]=>0000011
[3,2,1,8,6,7,4,5]=>[2,3,1,7,4,8,6,5]=>[3,2,1,8,6,7,4,5]=>1100011
[5,3,7,1,6,8,4,2]=>[7,4,8,5,2,1,6,3]=>[5,2,8,4,1,6,7,3]=>0011011
[4,6,7,5,8,3,1,2]=>[3,1,8,4,7,6,5,2]=>[4,6,7,5,8,3,1,2]=>0100011
[1,8,6,5,7,3,2,4]=>[1,3,7,2,6,8,5,4]=>[1,8,6,5,7,3,2,4]=>0100111
[5,4,6,7,1,8,2,3]=>[7,8,2,5,4,6,1,3]=>[5,4,6,8,2,7,1,3]=>0001011
[5,3,6,1,7,8,2,4]=>[6,8,5,2,3,1,7,4]=>[5,2,7,8,3,6,1,4]=>0001101
[5,2,1,6,7,8,3,4]=>[2,5,8,3,1,6,7,4]=>[6,7,8,3,5,2,1,4]=>1001001
[6,4,5,7,1,2,8,3]=>[7,1,8,6,4,5,2,3]=>[6,4,5,8,1,2,7,3]=>0000111
[1,8,4,6,2,7,3,5]=>[1,6,7,8,3,4,2,5]=>[1,8,3,7,4,6,2,5]=>0000111
[1,8,3,2,6,7,4,5]=>[1,3,8,7,4,2,6,5]=>[1,7,4,6,8,3,2,5]=>0100011
[5,7,3,2,6,8,4,1]=>[4,3,8,7,5,1,6,2]=>[5,7,3,1,6,8,4,2]=>0110011
[6,5,3,2,7,1,8,4]=>[7,3,5,6,8,4,1,2]=>[8,4,6,5,3,1,7,2]=>0101111
[6,4,3,2,1,7,8,5]=>[2,3,4,6,8,1,7,5]=>[7,8,4,3,2,1,6,5]=>1110101
[6,2,1,4,3,7,8,5]=>[2,6,4,1,8,3,7,5]=>[4,2,1,7,8,3,6,5]=>1010101
[5,3,4,1,2,8,7,6]=>[4,1,5,3,2,7,8,6]=>[5,3,4,1,2,8,7,6]=>0011011
[4,7,3,2,8,6,5,1]=>[5,3,6,4,8,7,2,1]=>[4,7,3,2,8,6,5,1]=>0101111
[1,8,3,2,7,6,5,4]=>[1,3,8,5,6,7,2,4]=>[1,7,6,5,3,2,8,4]=>0101111
[3,7,4,8,2,6,5,1]=>[5,6,3,8,7,4,1,2]=>[3,7,4,8,1,6,5,2]=>0001111
[3,6,4,8,2,7,1,5]=>[7,8,3,6,1,4,2,5]=>[3,6,1,8,4,7,2,5]=>0000111
[4,3,5,1,8,2,7,6]=>[5,8,4,3,1,7,2,6]=>[4,3,7,1,5,2,8,6]=>0011011
[4,2,1,5,8,3,7,6]=>[2,4,8,1,5,7,3,6]=>[5,7,2,1,4,3,8,6]=>1010011
[4,2,1,6,8,7,3,5]=>[2,4,7,1,3,6,8,5]=>[6,8,7,2,1,4,3,5]=>1010011
[4,3,6,1,8,7,2,5]=>[6,7,4,3,2,1,8,5]=>[4,3,8,7,2,6,1,5]=>0010111
[3,5,6,8,7,1,2,4]=>[7,1,3,2,5,6,8,4]=>[3,5,6,8,7,1,2,4]=>0000011
[3,7,5,8,6,2,4,1]=>[4,6,3,2,8,7,1,5]=>[3,7,2,4,1,8,6,5]=>0010111
[1,8,5,7,6,2,4,3]=>[1,6,4,2,7,8,3,5]=>[1,4,2,8,3,7,6,5]=>0010111
[3,6,7,8,5,4,1,2]=>[4,1,3,5,8,6,7,2]=>[3,6,7,8,5,4,1,2]=>0011001
[4,2,1,7,8,6,5,3]=>[2,4,5,1,6,8,7,3]=>[7,8,6,5,2,1,4,3]=>1011101
[2,3,8,1,7,6,5,4]=>[8,2,3,5,6,7,1,4]=>[2,3,7,6,5,1,8,4]=>0001111
[2,4,8,7,1,6,5,3]=>[7,2,5,4,6,1,8,3]=>[2,4,6,5,1,8,7,3]=>0001111
[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101
[2,1,4,3,6,5,8,7,12,11,10,9]=>[2,1,4,3,6,5,8,7,10,11,12,9]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>10101010111
[2,1,4,3,6,5,10,9,8,7,12,11]=>[2,1,4,3,6,5,8,9,10,7,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>10101011101
[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,4,3,6,5,8,9,10,11,12,7]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>10101011111
[2,1,4,3,8,7,6,5,10,9,12,11]=>[2,1,4,3,6,7,8,5,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>10101110101
[2,1,4,3,8,7,6,5,12,11,10,9]=>[2,1,4,3,6,7,8,5,10,11,12,9]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>10101110111
[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,4,3,6,7,8,9,10,5,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>10101111101
[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,4,3,6,7,8,9,10,11,12,5]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>10101111111
[2,1,6,5,4,3,8,7,10,9,12,11]=>[2,1,4,5,6,3,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>10111010101
[2,1,6,5,4,3,8,7,12,11,10,9]=>[2,1,4,5,6,3,8,7,10,11,12,9]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>10111010111
[2,1,6,5,4,3,10,9,8,7,12,11]=>[2,1,4,5,6,3,8,9,10,7,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>10111011101
[2,1,6,5,4,3,12,11,10,9,8,7]=>[2,1,4,5,6,3,8,9,10,11,12,7]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>10111011111
[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,4,5,6,7,8,3,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>10111110101
[2,1,8,7,6,5,4,3,12,11,10,9]=>[2,1,4,5,6,7,8,3,10,11,12,9]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>10111110111
[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,4,5,6,7,8,9,10,3,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>10111111101
[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,11,12,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>10111111111
[4,3,2,1,6,5,8,7,10,9,12,11]=>[2,3,4,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>11101010101
[4,3,2,1,6,5,8,7,12,11,10,9]=>[2,3,4,1,6,5,8,7,10,11,12,9]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>11101010111
[4,3,2,1,6,5,10,9,8,7,12,11]=>[2,3,4,1,6,5,8,9,10,7,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>11101011101
[4,3,2,1,6,5,12,11,10,9,8,7]=>[2,3,4,1,6,5,8,9,10,11,12,7]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>11101011111
[4,3,2,1,8,7,6,5,10,9,12,11]=>[2,3,4,1,6,7,8,5,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>11101110101
[4,3,2,1,8,7,6,5,12,11,10,9]=>[2,3,4,1,6,7,8,5,10,11,12,9]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>11101110111
[4,3,2,1,10,9,8,7,6,5,12,11]=>[2,3,4,1,6,7,8,9,10,5,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>11101111101
[4,3,2,1,12,11,10,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,10,11,12,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>11101111111
[6,5,4,3,2,1,8,7,10,9,12,11]=>[2,3,4,5,6,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>11111010101
[6,5,4,3,2,1,8,7,12,11,10,9]=>[2,3,4,5,6,1,8,7,10,11,12,9]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>11111010111
[6,5,4,3,2,1,10,9,8,7,12,11]=>[2,3,4,5,6,1,8,9,10,7,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>11111011101
[6,5,4,3,2,1,12,11,10,9,8,7]=>[2,3,4,5,6,1,8,9,10,11,12,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>11111011111
[8,7,6,5,4,3,2,1,10,9,12,11]=>[2,3,4,5,6,7,8,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>11111110101
[8,7,6,5,4,3,2,1,12,11,10,9]=>[2,3,4,5,6,7,8,1,10,11,12,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>11111110111
[10,9,8,7,6,5,4,3,2,1,12,11]=>[2,3,4,5,6,7,8,9,10,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>11111111101
[12,11,10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>11111111111
[7,4,6,1,8,3,5,2]=>[6,5,8,7,3,4,1,2]=>[7,3,8,4,5,1,6,2]=>0001111
[8,3,5,1,7,4,6,2]=>[5,6,8,7,3,4,1,2]=>[7,3,8,4,6,1,5,2]=>0001111
[8,3,4,1,7,5,6,2]=>[4,6,8,3,7,5,1,2]=>[7,5,8,3,6,1,4,2]=>0010111
[4,6,2,1,7,5,8,3]=>[2,6,8,4,7,1,5,3]=>[4,7,2,1,8,5,6,3]=>1000111
[1,4,6,2,7,5,8,3]=>[1,6,8,4,7,2,5,3]=>[1,4,7,2,8,5,6,3]=>0000111
[1,7,5,2,6,8,4,3]=>[1,5,4,7,8,3,6,2]=>[1,8,4,3,6,7,5,2]=>0011011
[6,8,4,3,1,7,5,2]=>[3,4,8,5,7,6,1,2]=>[6,7,5,1,8,4,3,2]=>0111011
[3,6,8,4,1,7,5,2]=>[4,8,3,5,7,6,2,1]=>[3,6,7,5,2,8,4,1]=>0011011
[3,6,7,5,1,8,4,2]=>[5,4,3,7,8,6,2,1]=>[3,6,8,4,2,7,5,1]=>0011011
[7,5,6,1,8,3,4,2]=>[6,4,8,3,7,5,1,2]=>[7,5,8,3,4,1,6,2]=>0010111
[3,4,6,5,7,1,8,2]=>[7,8,3,4,6,5,1,2]=>[3,4,6,5,8,1,7,2]=>0000111
[4,7,5,6,1,8,3,2]=>[6,3,8,4,7,5,1,2]=>[4,7,5,8,3,1,6,2]=>0100111
[6,8,4,1,7,5,3,2]=>[4,3,8,5,7,6,2,1]=>[6,7,5,3,2,8,4,1]=>0111011
[6,7,5,3,1,8,4,2]=>[3,5,4,7,8,6,1,2]=>[6,8,4,1,7,5,3,2]=>0111011
[8,4,2,1,6,7,5,3]=>[2,4,8,5,7,3,6,1]=>[7,5,3,6,8,4,2,1]=>1011011
[1,5,3,2,7,6,8,4]=>[1,3,5,8,2,7,6,4]=>[1,7,6,8,3,2,5,4]=>0101011
[5,3,2,1,7,6,8,4]=>[2,3,5,8,1,7,6,4]=>[7,6,8,3,2,1,5,4]=>1101011
[2,5,3,1,7,6,8,4]=>[3,2,5,8,1,7,6,4]=>[2,7,6,8,3,1,5,4]=>0101011
[2,7,5,1,6,8,4,3]=>[5,2,4,7,8,3,6,1]=>[2,8,4,3,6,7,5,1]=>0011011
[2,4,6,1,7,5,8,3]=>[6,2,8,4,7,1,5,3]=>[2,4,7,1,8,5,6,3]=>0000111
[4,7,1,6,5,8,2,3]=>[7,8,2,4,6,1,5,3]=>[4,6,2,8,5,7,1,3]=>0000111
[4,8,2,6,5,7,1,3]=>[7,8,1,4,6,2,5,3]=>[4,6,1,8,5,7,2,3]=>0000111
[4,6,1,2,7,5,8,3]=>[6,1,8,4,7,2,5,3]=>[4,7,1,2,8,5,6,3]=>0000111
[8,4,1,2,6,7,5,3]=>[4,1,8,5,7,3,6,2]=>[7,5,3,6,8,4,1,2]=>0011011
[5,3,1,2,7,6,8,4]=>[3,1,5,8,2,7,6,4]=>[7,6,8,3,1,2,5,4]=>0101011
[1,2,5,3,7,6,8,4]=>[1,2,5,8,3,7,6,4]=>[1,2,7,6,8,3,5,4]=>0001011
[4,3,1,2,7,6,8,5]=>[3,1,4,2,8,7,6,5]=>[4,3,1,2,7,6,8,5]=>0110011
[3,5,1,2,7,6,8,4]=>[5,1,3,8,2,7,6,4]=>[3,7,6,8,1,2,5,4]=>0001011
[6,7,1,5,8,2,3,4]=>[7,8,2,3,1,6,5,4]=>[6,8,2,3,5,7,1,4]=>0000011
[2,7,6,1,5,8,3,4]=>[6,2,7,1,3,8,5,4]=>[2,8,1,5,7,6,3,4]=>0000111
[2,3,5,1,7,6,8,4]=>[5,2,3,8,1,7,6,4]=>[2,3,7,6,8,1,5,4]=>0001011
[7,6,1,5,8,3,2,4]=>[6,3,7,1,2,8,5,4]=>[8,3,1,5,7,6,2,4]=>0100111
[3,6,7,1,5,8,2,4]=>[7,8,3,2,1,6,5,4]=>[3,6,8,2,5,7,1,4]=>0000011
[7,1,6,5,8,2,4,3]=>[7,8,4,2,6,1,5,3]=>[4,2,6,1,8,5,7,3]=>0010111
[7,5,1,6,8,4,2,3]=>[5,4,1,7,8,2,6,3]=>[8,4,1,6,7,5,2,3]=>0011011
[8,4,1,6,7,5,2,3]=>[4,8,1,5,7,2,6,3]=>[7,5,1,6,8,4,2,3]=>0011011
[5,2,3,1,7,6,8,4]=>[3,5,2,8,1,7,6,4]=>[7,6,8,2,3,1,5,4]=>0101011
[3,5,2,1,7,6,8,4]=>[2,5,3,8,1,7,6,4]=>[3,7,6,8,2,1,5,4]=>1001011
[1,3,5,2,7,6,8,4]=>[1,5,3,8,2,7,6,4]=>[1,3,7,6,8,2,5,4]=>0001011
[1,7,6,2,5,8,3,4]=>[1,6,7,2,3,8,5,4]=>[1,8,2,5,7,6,3,4]=>0000111
[7,6,2,1,5,8,3,4]=>[2,6,7,1,3,8,5,4]=>[8,2,1,5,7,6,3,4]=>1000111
[6,2,4,1,7,5,8,3]=>[4,6,8,2,7,1,5,3]=>[7,2,8,5,6,1,4,3]=>0010111
[6,2,5,1,7,4,8,3]=>[5,6,8,7,2,1,4,3]=>[7,2,8,1,6,4,5,3]=>0001111
[7,1,6,4,8,2,5,3]=>[7,8,5,6,2,1,4,3]=>[6,2,5,1,8,4,7,3]=>0001111
[8,2,6,4,7,1,5,3]=>[7,8,5,6,1,2,4,3]=>[6,1,5,2,8,4,7,3]=>0001111
[6,1,5,2,7,4,8,3]=>[6,5,8,7,1,2,4,3]=>[7,1,8,2,5,4,6,3]=>0001111
[8,3,5,7,6,2,1,4]=>[2,6,7,3,1,8,5,4]=>[8,3,5,7,6,2,1,4]=>1000111
[1,8,3,5,7,6,2,4]=>[1,6,7,3,2,8,5,4]=>[1,8,3,5,7,6,2,4]=>0000111
[1,5,2,3,7,6,8,4]=>[1,5,2,8,3,7,6,4]=>[1,7,6,8,2,3,5,4]=>0001011
[5,2,1,3,7,6,8,4]=>[2,5,1,8,3,7,6,4]=>[7,6,8,2,1,3,5,4]=>1001011
[7,5,2,6,8,4,1,3]=>[4,8,2,5,7,1,6,3]=>[7,5,2,6,8,4,1,3]=>0011011
[8,4,2,6,7,5,1,3]=>[5,4,2,7,8,1,6,3]=>[8,4,2,6,7,5,1,3]=>0011011
[6,1,4,2,7,5,8,3]=>[6,4,8,1,7,2,5,3]=>[7,1,4,2,8,5,6,3]=>0010111
[8,2,6,5,7,1,4,3]=>[7,8,4,1,6,2,5,3]=>[4,1,6,2,8,5,7,3]=>0010111
[3,6,8,2,5,7,1,4]=>[7,8,3,1,2,6,5,4]=>[3,6,8,1,5,7,2,4]=>0000011
[8,3,2,5,7,6,1,4]=>[6,3,7,2,1,8,5,4]=>[8,3,2,5,7,6,1,4]=>0100111
[5,1,3,2,7,6,8,4]=>[5,3,1,8,2,7,6,4]=>[3,1,7,6,8,2,5,4]=>0101011
[4,1,3,2,7,6,8,5]=>[4,3,1,2,8,7,6,5]=>[3,1,4,2,7,6,8,5]=>0110011
[4,2,1,3,7,6,8,5]=>[2,4,1,3,8,7,6,5]=>[4,2,1,3,7,6,8,5]=>1010011
[1,4,2,3,7,6,8,5]=>[1,4,2,3,8,7,6,5]=>[1,4,2,3,7,6,8,5]=>0010011
[2,4,1,3,7,6,8,5]=>[4,2,1,3,8,7,6,5]=>[2,4,1,3,7,6,8,5]=>0010011
[2,5,1,3,7,6,8,4]=>[5,2,1,8,3,7,6,4]=>[2,7,6,8,1,3,5,4]=>0001011
[2,8,3,5,7,6,1,4]=>[6,2,7,3,1,8,5,4]=>[2,8,3,5,7,6,1,4]=>0000111
[6,8,2,3,5,7,1,4]=>[7,8,2,1,3,6,5,4]=>[6,8,2,5,7,1,3,4]=>0000011
[6,7,1,3,5,8,2,4]=>[7,8,1,2,3,6,5,4]=>[6,8,1,5,7,2,3,4]=>0000011
[8,3,5,7,6,1,2,4]=>[6,1,7,3,2,8,5,4]=>[8,3,5,7,6,1,2,4]=>0000111
[5,1,2,3,7,6,8,4]=>[5,1,2,8,3,7,6,4]=>[7,6,8,1,2,3,5,4]=>0001011
[3,1,2,4,7,6,8,5]=>[3,1,2,4,8,7,6,5]=>[3,1,2,4,7,6,8,5]=>0100011
[10,8,9,5,6,7,1,2,3,4]=>[7,1,2,3,9,5,6,10,8,4]=>[10,8,9,5,6,7,1,2,3,4]=>000001011
[10,8,9,4,5,6,1,2,3,7]=>[6,1,2,9,4,5,3,10,8,7]=>[10,8,9,4,5,6,1,2,3,7]=>000010011
[10,7,8,5,6,9,1,2,3,4]=>[9,1,2,3,8,5,10,7,6,4]=>[10,7,8,5,6,9,1,2,3,4]=>000000111
[10,6,7,4,5,8,1,2,3,9]=>[8,1,2,7,4,10,6,5,3,9]=>[10,6,7,4,5,8,1,2,3,9]=>000001101
[9,8,10,5,6,7,1,2,3,4]=>[7,1,2,3,10,5,6,9,8,4]=>[9,8,10,5,6,7,1,2,3,4]=>000001011
[9,8,10,4,5,6,1,2,3,7]=>[6,1,2,10,4,5,3,9,8,7]=>[9,8,10,4,5,6,1,2,3,7]=>000010011
[8,7,9,5,6,10,1,2,3,4]=>[10,1,2,3,9,5,8,7,6,4]=>[8,7,9,5,6,10,1,2,3,4]=>000000111
[7,6,8,4,5,9,1,2,3,10]=>[9,1,2,8,4,7,6,5,3,10]=>[7,6,8,4,5,9,1,2,3,10]=>000001110
[8,1,2,4,3,6,5,7]=>[8,1,4,2,6,3,5,7]=>[4,1,2,6,3,8,5,7]=>0010101
[8,1,3,5,6,2,7,4]=>[8,6,1,7,3,5,2,4]=>[7,1,3,5,6,2,8,4]=>0000111
[8,1,3,2,4,5,7,6]=>[8,3,1,2,4,7,5,6]=>[3,1,7,2,4,5,8,6]=>0100011
[6,3,2,1,4,5,8,7]=>[2,3,6,1,4,5,8,7]=>[6,3,2,1,4,5,8,7]=>1100101
[7,4,1,5,6,8,2,3]=>[4,7,1,8,2,5,6,3]=>[8,1,5,6,7,4,2,3]=>0010011
[3,7,8,4,2,6,1,5]=>[6,4,3,8,1,2,7,5]=>[3,7,8,4,1,6,2,5]=>0010101
[3,7,8,2,4,5,1,6]=>[5,8,3,2,4,1,7,6]=>[3,7,8,2,4,5,1,6]=>0001001
[3,5,2,4,8,6,1,7]=>[6,5,3,2,4,8,1,7]=>[3,5,2,4,8,6,1,7]=>0001101
[7,4,1,2,3,8,5,6]=>[4,1,2,7,8,5,3,6]=>[8,5,7,4,1,2,3,6]=>0010011
[2,6,5,8,7,3,4,1]=>[4,2,7,3,6,5,8,1]=>[2,6,5,8,7,3,4,1]=>0010111
[2,4,6,7,3,8,5,1]=>[5,2,8,4,7,6,1,3]=>[2,4,6,7,1,8,5,3]=>0001011
[4,7,8,2,3,1,5,6]=>[3,8,2,4,1,5,7,6]=>[4,7,8,2,3,1,5,6]=>0100001
[5,6,4,8,1,7,2,3]=>[8,7,2,6,5,4,1,3]=>[5,6,4,7,2,8,1,3]=>0000111
[5,6,3,8,1,2,7,4]=>[8,1,6,7,5,3,2,4]=>[5,7,3,6,1,2,8,4]=>0000111
[5,2,7,8,6,4,1,3]=>[4,6,2,5,1,8,7,3]=>[5,2,7,8,6,4,1,3]=>0011101
[4,7,1,2,8,6,5,3]=>[7,1,5,4,6,8,2,3]=>[4,8,6,5,1,2,7,3]=>0001111
[4,6,8,1,2,7,5,3]=>[8,1,5,4,7,6,2,3]=>[4,6,7,5,1,2,8,3]=>0001011
[6,8,7,1,5,3,2,4]=>[7,3,5,2,1,6,8,4]=>[5,3,2,6,8,7,1,4]=>0101011
[7,8,1,3,6,5,2,4]=>[8,5,1,2,6,3,7,4]=>[6,5,1,7,8,2,3,4]=>0001101
[4,7,2,8,6,1,5,3]=>[6,8,5,4,2,7,1,3]=>[4,5,2,7,1,8,6,3]=>0001111
[4,2,7,1,8,6,5,3]=>[7,4,5,2,6,8,1,3]=>[8,6,5,2,4,1,7,3]=>0011111
[6,8,7,2,5,3,1,4]=>[3,5,7,2,1,6,8,4]=>[6,8,7,2,5,3,1,4]=>0101011
[1,6,8,3,7,4,5,2]=>[1,5,8,7,4,6,3,2]=>[1,6,7,4,8,3,5,2]=>0001011
[6,8,7,2,3,5,1,4]=>[5,7,2,1,3,6,8,4]=>[6,8,7,2,5,1,3,4]=>0001011
[8,7,6,2,1,4,3,5]=>[2,6,4,1,3,7,8,5]=>[4,2,1,8,7,6,3,5]=>1010111
[8,5,7,2,3,1,6,4]=>[3,7,2,6,8,1,5,4]=>[8,2,3,1,6,5,7,4]=>0100111
[5,8,4,2,7,1,6,3]=>[7,4,8,6,5,1,3,2]=>[5,6,1,8,4,3,7,2]=>0010111
[1,8,7,3,5,4,6,2]=>[1,6,7,5,3,4,8,2]=>[1,5,3,8,7,4,6,2]=>0001111
[8,2,5,4,7,1,6,3]=>[7,8,6,5,2,1,4,3]=>[5,2,6,1,8,4,7,3]=>0001111
[8,5,2,7,3,1,6,4]=>[3,7,5,8,6,2,4,1]=>[6,2,8,5,4,7,3,1]=>0101111
[8,7,6,2,4,3,1,5]=>[3,4,6,1,2,7,8,5]=>[8,7,6,1,4,3,2,5]=>0110111
[8,7,6,4,1,3,2,5]=>[4,3,1,6,2,7,8,5]=>[3,1,8,7,6,4,2,5]=>0110111
[1,8,7,5,4,3,6,2]=>[1,6,4,5,7,3,8,2]=>[1,8,7,5,4,3,6,2]=>0011111
[1,6,8,4,3,7,5,2]=>[1,5,4,7,8,6,2,3]=>[1,6,8,4,2,7,5,3]=>0011011
[6,8,1,7,3,2,5,4]=>[8,3,7,5,2,6,1,4]=>[5,3,2,6,7,1,8,4]=>0101011
[8,5,7,3,1,6,2,4]=>[3,7,6,1,8,2,5,4]=>[8,1,6,5,7,3,2,4]=>0100111
[8,5,7,1,3,2,6,4]=>[7,3,1,6,8,2,5,4]=>[3,1,8,2,6,5,7,4]=>0100111
[5,8,4,7,1,2,6,3]=>[7,1,6,8,5,2,4,3]=>[5,8,1,2,6,4,7,3]=>0000111
[5,8,4,1,7,2,6,3]=>[4,8,7,6,5,3,2,1]=>[5,6,3,7,2,8,4,1]=>0010111
[5,8,4,7,1,6,2,3]=>[7,6,2,8,5,1,4,3]=>[5,8,2,6,4,7,1,3]=>0000111
[8,1,2,6,5,7,4,3]=>[8,1,4,7,6,2,5,3]=>[6,4,1,2,7,5,8,3]=>0010111
[8,2,5,6,7,4,1,3]=>[4,7,2,8,1,5,6,3]=>[8,2,5,6,7,4,1,3]=>0010011
[4,8,5,7,1,6,2,3]=>[7,6,2,4,8,1,5,3]=>[4,8,2,6,5,7,1,3]=>0000111
[4,8,5,7,1,2,6,3]=>[7,1,6,4,8,2,5,3]=>[4,8,1,2,6,5,7,3]=>0000111
[4,8,5,1,7,2,6,3]=>[5,8,7,4,6,3,2,1]=>[4,6,3,7,2,8,5,1]=>0001111
[6,8,1,3,7,2,5,4]=>[8,7,1,5,2,6,3,4]=>[5,1,6,7,2,3,8,4]=>0001011
[1,6,4,8,3,7,5,2]=>[1,5,7,8,6,2,4,3]=>[1,6,2,8,4,7,5,3]=>0001111
[1,8,7,4,5,3,6,2]=>[1,6,5,7,4,3,8,2]=>[1,8,7,4,5,3,6,2]=>0001111
[8,7,6,3,1,4,2,5]=>[3,6,4,2,1,7,8,5]=>[4,2,8,7,6,3,1,5]=>0110111
[8,7,6,1,3,2,4,5]=>[6,3,1,2,4,7,8,5]=>[3,1,8,7,6,2,4,5]=>0100111
[8,5,3,2,7,1,6,4]=>[7,3,5,8,6,1,4,2]=>[6,3,1,8,5,4,7,2]=>0101111
[4,8,5,2,7,1,6,3]=>[7,5,8,4,6,1,3,2]=>[4,6,1,8,5,3,7,2]=>0001111
[1,8,7,3,4,5,6,2]=>[1,6,7,3,4,5,8,2]=>[1,8,7,3,4,5,6,2]=>0000111
[8,5,2,3,7,1,6,4]=>[7,5,2,8,6,1,4,3]=>[6,2,8,5,4,7,1,3]=>0001111
[6,3,1,5,4,2,8,7]=>[3,6,4,5,2,1,8,7]=>[5,4,2,6,3,1,8,7]=>0111101
[8,3,1,5,2,7,6,4]=>[3,8,5,6,2,7,1,4]=>[7,6,2,5,3,1,8,4]=>0101111
[8,5,4,2,1,7,3,6]=>[2,4,5,8,7,3,1,6]=>[7,3,8,5,4,2,1,6]=>1011011
[8,5,4,2,1,7,6,3]=>[2,4,5,8,6,7,1,3]=>[7,6,2,1,8,5,4,3]=>1011111
[6,5,4,2,1,3,8,7]=>[2,4,1,5,6,3,8,7]=>[6,5,4,2,1,3,8,7]=>1011101
[6,5,4,2,3,1,8,7]=>[3,4,2,5,6,1,8,7]=>[6,5,4,2,3,1,8,7]=>0111101
[6,3,2,5,1,4,8,7]=>[5,3,6,1,2,4,8,7]=>[6,3,1,5,2,4,8,7]=>0101101
[6,5,4,3,1,2,8,7]=>[3,1,4,5,6,2,8,7]=>[6,5,4,3,1,2,8,7]=>0111101
[6,5,4,1,3,2,8,7]=>[4,3,1,5,6,2,8,7]=>[3,1,6,5,4,2,8,7]=>0111101
[8,5,4,1,2,7,6,3]=>[4,1,5,8,6,7,2,3]=>[7,6,1,2,8,5,4,3]=>0011111
[8,7,4,1,6,3,2,5]=>[4,3,7,6,1,2,8,5]=>[6,3,1,8,7,4,2,5]=>0110111
[8,7,4,1,6,3,5,2]=>[4,7,5,6,1,2,8,3]=>[6,1,5,2,8,7,4,3]=>0011111
[8,7,4,1,6,5,3,2]=>[4,3,7,5,6,2,8,1]=>[6,5,3,2,8,7,4,1]=>0111111
[8,5,4,1,3,7,6,2]=>[4,5,1,8,6,7,3,2]=>[7,6,1,3,8,5,4,2]=>0011111
[8,3,2,5,1,7,6,4]=>[5,3,8,6,2,7,1,4]=>[7,6,3,2,8,1,5,4]=>0101111
[2,1,8,5,3,7,6,4]=>[2,1,5,8,6,7,4,3]=>[2,1,7,6,4,8,5,3]=>1001111
[8,3,2,5,1,7,4,6]=>[5,3,8,7,2,4,1,6]=>[7,3,2,8,4,5,1,6]=>0101011
[8,5,4,3,1,7,2,6]=>[3,4,5,8,7,1,2,6]=>[7,1,8,5,4,3,2,6]=>0111011
[8,5,4,1,3,7,2,6]=>[4,5,1,8,7,2,3,6]=>[7,1,8,5,4,2,3,6]=>0011011
[8,7,4,1,6,5,2,3]=>[4,7,1,5,6,2,8,3]=>[6,5,1,8,7,4,2,3]=>0011111
[8,7,4,1,6,2,5,3]=>[4,7,6,5,3,2,8,1]=>[5,3,6,2,8,7,4,1]=>0011111
[8,7,6,5,2,1,4,3]=>[2,5,4,1,6,7,8,3]=>[4,2,1,8,7,6,5,3]=>1011111
[8,7,4,3,6,2,1,5]=>[2,6,4,7,1,3,8,5]=>[8,7,4,2,1,6,3,5]=>1010111
[8,3,2,7,6,4,1,5]=>[4,3,6,7,1,8,2,5]=>[8,3,1,7,6,4,2,5]=>0110111
[2,1,8,7,6,4,3,5]=>[2,1,4,6,3,7,8,5]=>[2,1,8,7,6,4,3,5]=>1010111
[2,1,8,7,6,4,5,3]=>[2,1,5,6,4,7,8,3]=>[2,1,8,7,6,4,5,3]=>1001111
[8,3,2,7,6,4,5,1]=>[5,3,8,6,4,7,2,1]=>[7,6,4,8,3,2,5,1]=>0101111
[8,7,4,3,6,2,5,1]=>[5,6,4,7,2,3,8,1]=>[8,7,4,2,6,3,5,1]=>0011111
[8,7,6,5,2,4,3,1]=>[3,4,5,1,6,7,8,2]=>[8,7,6,5,1,4,3,2]=>0111111
[8,5,4,2,3,7,6,1]=>[6,4,1,5,7,8,3,2]=>[8,5,4,1,3,7,6,2]=>0011111
[8,7,4,2,6,5,3,1]=>[3,5,4,6,7,2,8,1]=>[8,7,4,2,6,5,3,1]=>0111111
[8,7,4,2,6,3,5,1]=>[5,4,7,6,2,3,8,1]=>[6,2,8,7,4,3,5,1]=>0011111
[8,7,4,2,6,3,1,5]=>[3,6,4,7,2,1,8,5]=>[8,7,4,2,6,3,1,5]=>0110111
[8,3,1,7,6,4,2,5]=>[3,8,4,6,1,7,2,5]=>[7,6,4,1,8,3,2,5]=>0110111
[8,3,1,7,6,5,4,2]=>[3,8,4,5,6,7,2,1]=>[7,6,5,4,2,8,3,1]=>0111111
[8,3,1,5,4,7,2,6]=>[3,8,7,5,2,1,4,6]=>[5,2,7,3,1,8,4,6]=>0101011
[8,3,1,7,6,5,2,4]=>[3,8,5,1,6,7,2,4]=>[7,6,5,1,8,3,2,4]=>0101111
[8,7,4,2,6,1,5,3]=>[6,4,7,5,1,3,8,2]=>[5,1,8,7,4,3,6,2]=>0011111
[8,7,4,2,6,5,1,3]=>[5,4,2,6,7,1,8,3]=>[8,7,4,2,6,5,1,3]=>0011111
[8,3,2,5,4,7,1,6]=>[7,3,8,5,2,1,4,6]=>[5,3,2,8,1,7,4,6]=>0101011
[2,1,8,5,4,7,3,6]=>[2,1,7,5,8,3,4,6]=>[2,1,8,5,3,7,4,6]=>1001011
[8,3,2,7,6,5,1,4]=>[5,3,6,1,7,8,2,4]=>[8,3,1,7,6,5,2,4]=>0101111
[8,7,4,3,6,5,1,2]=>[5,1,4,6,7,2,8,3]=>[8,7,4,1,2,6,5,3]=>0011111
[8,7,6,5,3,1,4,2]=>[3,5,4,2,6,7,8,1]=>[4,2,8,7,6,5,3,1]=>0111111
[8,7,6,5,1,3,2,4]=>[5,3,1,2,6,7,8,4]=>[3,1,8,7,6,5,2,4]=>0101111
[8,7,6,5,1,3,4,2]=>[5,4,1,3,6,7,8,2]=>[4,1,3,8,7,6,5,2]=>0011111
[8,7,6,5,1,4,3,2]=>[5,3,4,1,6,7,8,2]=>[4,3,1,8,7,6,5,2]=>0111111
[8,7,6,5,4,1,3,2]=>[4,3,1,5,6,7,8,2]=>[3,1,8,7,6,5,4,2]=>0111111
[8,3,2,7,6,1,5,4]=>[6,3,7,5,2,8,1,4]=>[5,3,2,8,1,7,6,4]=>0101111
[2,1,8,7,6,3,5,4]=>[2,1,6,5,3,7,8,4]=>[2,1,5,3,8,7,6,4]=>1001111
[8,3,2,7,6,1,4,5]=>[6,3,7,2,4,8,1,5]=>[8,3,2,4,7,6,1,5]=>0100111
[8,7,6,5,1,4,2,3]=>[5,4,2,1,6,7,8,3]=>[4,2,8,7,6,5,1,3]=>0011111
[8,7,6,5,1,2,4,3]=>[5,1,4,2,6,7,8,3]=>[4,1,2,8,7,6,5,3]=>0011111
[7,3,5,1,8,4,6,2]=>[5,6,7,8,3,4,1,2]=>[8,3,7,4,6,1,5,2]=>0001111
[7,3,4,1,8,5,6,2]=>[4,6,7,3,8,5,1,2]=>[8,5,7,3,6,1,4,2]=>0010111
[4,5,6,2,1,8,7,3]=>[2,6,7,4,5,1,8,3]=>[4,5,8,7,2,1,6,3]=>1000111
[7,6,5,1,8,4,3,2]=>[5,3,4,6,7,8,1,2]=>[8,4,3,1,7,6,5,2]=>0111111
[6,4,2,1,8,7,5,3]=>[2,4,6,5,7,3,8,1]=>[8,7,5,3,6,4,2,1]=>1011111
[1,5,3,2,7,6,4,8]=>[1,3,5,6,2,7,4,8]=>[1,7,6,3,2,5,4,8]=>0101110
[5,3,2,1,8,7,6,4]=>[2,3,5,6,1,7,8,4]=>[8,7,6,3,2,1,5,4]=>1101111
[2,5,3,1,7,8,6,4]=>[3,2,5,6,1,8,7,4]=>[2,7,8,6,3,1,5,4]=>0101101
[2,6,5,1,7,8,4,3]=>[5,2,4,6,8,3,7,1]=>[2,7,8,4,3,6,5,1]=>0011101
[4,5,7,1,6,8,2,3]=>[7,8,2,4,5,1,6,3]=>[4,5,8,2,6,7,1,3]=>0000011
[6,5,1,2,8,4,3,7]=>[5,1,4,6,8,3,2,7]=>[8,4,3,6,5,1,2,7]=>0011101
[6,4,1,2,8,5,3,7]=>[4,1,6,5,8,3,2,7]=>[8,5,3,6,4,1,2,7]=>0011101
[5,3,1,2,8,6,4,7]=>[3,1,5,6,2,8,4,7]=>[8,6,3,1,2,5,4,7]=>0101101
[4,3,1,2,8,6,5,7]=>[3,1,4,2,6,8,5,7]=>[4,3,1,2,8,6,5,7]=>0110101
[6,1,2,5,8,3,4,7]=>[6,1,8,3,2,5,4,7]=>[8,3,5,6,1,2,4,7]=>0000101
[7,1,3,4,8,2,5,6]=>[7,8,1,3,2,5,4,6]=>[8,1,3,5,7,2,4,6]=>0000011
[7,1,5,6,8,2,3,4]=>[7,8,2,3,1,5,6,4]=>[8,2,3,5,6,7,1,4]=>0000011
[2,6,1,5,7,8,3,4]=>[6,2,8,3,1,5,7,4]=>[2,7,8,3,5,6,1,4]=>0000101
[7,4,1,6,8,5,2,3]=>[4,7,1,5,8,2,6,3]=>[8,5,1,6,7,4,2,3]=>0011011
[5,2,3,1,8,6,7,4]=>[3,5,2,7,1,8,6,4]=>[8,6,7,2,3,1,5,4]=>0101011
[3,5,2,1,6,8,7,4]=>[2,5,3,7,1,6,8,4]=>[3,6,8,7,2,1,5,4]=>1001011
[1,6,2,5,7,3,4,8]=>[1,6,7,3,2,5,4,8]=>[1,7,3,5,6,2,4,8]=>0000110
[6,2,1,5,8,7,3,4]=>[2,6,7,3,1,5,8,4]=>[8,7,3,5,6,2,1,4]=>1000111
[6,2,4,1,8,5,7,3]=>[4,6,7,2,8,1,5,3]=>[8,2,7,5,6,1,4,3]=>0010111
[6,2,5,1,8,4,7,3]=>[5,6,7,8,2,1,4,3]=>[8,2,7,1,6,4,5,3]=>0001111
[7,3,1,4,8,6,2,5]=>[3,7,6,2,1,8,4,5]=>[8,6,2,7,3,1,4,5]=>0100111
[6,2,1,4,8,7,3,5]=>[2,6,7,1,3,4,8,5]=>[8,7,2,1,6,3,4,5]=>1000111
[1,6,2,4,7,3,5,8]=>[1,6,7,2,3,4,5,8]=>[1,7,2,6,3,4,5,8]=>0000110
[5,2,1,3,8,7,4,6]=>[2,5,1,7,3,4,8,6]=>[8,7,2,1,3,5,4,6]=>1001011
[7,4,1,3,8,5,2,6]=>[4,7,2,5,8,1,3,6]=>[8,5,2,7,4,1,3,6]=>0011011
[7,5,1,3,8,4,2,6]=>[5,4,2,7,8,1,3,6]=>[8,4,2,7,5,1,3,6]=>0011011
[3,6,7,1,4,8,2,5]=>[7,8,3,1,2,6,4,5]=>[3,6,8,1,7,2,4,5]=>0000011
[7,6,1,4,8,3,2,5]=>[6,3,7,2,1,8,4,5]=>[8,3,2,7,6,1,4,5]=>0100111
[4,2,1,3,8,7,5,6]=>[2,4,1,3,7,5,8,6]=>[4,2,1,3,8,7,5,6]=>1010011
[2,6,1,4,7,8,3,5]=>[6,2,8,1,3,4,7,5]=>[2,7,8,1,6,3,4,5]=>0000101
[7,1,4,6,8,2,3,5]=>[7,8,2,1,3,4,6,5]=>[8,2,6,7,1,3,4,5]=>0000011
[7,1,3,5,8,2,4,6]=>[7,8,1,2,3,4,5,6]=>[8,1,7,2,3,4,5,6]=>0000011
[6,1,2,4,8,3,5,7]=>[6,1,8,2,3,4,5,7]=>[8,1,2,6,3,4,5,7]=>0000101
[5,2,3,1,6,4,8,7]=>[3,5,2,6,1,4,8,7]=>[6,2,3,1,5,4,8,7]=>0101101
[7,4,5,2,3,1,8,6]=>[3,5,2,7,4,8,1,6]=>[8,4,5,2,3,1,7,6]=>0101011
[8,6,7,3,5,2,4,1]=>[4,5,7,2,3,8,6,1]=>[8,6,7,2,5,3,4,1]=>0011011
[7,3,5,2,4,1,8,6]=>[4,5,7,2,3,8,1,6]=>[8,2,5,3,4,1,7,6]=>0011011
[6,3,5,2,4,1,8,7]=>[4,5,6,2,3,1,8,7]=>[6,2,5,3,4,1,8,7]=>0011101
[5,2,4,1,6,3,8,7]=>[4,5,6,2,1,3,8,7]=>[6,2,5,1,4,3,8,7]=>0011101
[4,1,6,3,5,2,8,7]=>[4,5,6,1,3,2,8,7]=>[6,1,5,3,4,2,8,7]=>0011101
[6,3,4,1,5,2,8,7]=>[4,5,6,3,1,2,8,7]=>[6,3,5,1,4,2,8,7]=>0011101
[5,2,6,3,4,1,8,7]=>[4,5,6,3,2,1,8,7]=>[6,3,5,2,4,1,8,7]=>0011101
[5,2,7,3,4,1,8,6]=>[4,5,7,3,2,8,1,6]=>[8,3,5,2,4,1,7,6]=>0011011
[5,2,8,6,7,3,4,1]=>[4,5,7,3,2,8,6,1]=>[8,6,7,3,5,2,4,1]=>0011011
[6,2,8,5,7,3,4,1]=>[4,6,7,3,8,2,5,1]=>[8,3,7,5,6,2,4,1]=>0010111
[6,2,7,3,4,1,8,5]=>[4,6,7,3,8,2,1,5]=>[8,3,7,2,4,1,6,5]=>0010111
[7,3,4,1,5,2,8,6]=>[4,5,7,3,1,8,2,6]=>[8,3,5,1,4,2,7,6]=>0011011
[4,1,7,3,5,2,8,6]=>[4,5,7,1,3,8,2,6]=>[8,1,5,3,4,2,7,6]=>0011011
[3,1,7,4,5,2,8,6]=>[3,5,1,7,4,8,2,6]=>[8,4,5,1,3,2,7,6]=>0101011
[2,1,7,4,5,3,8,6]=>[2,1,5,7,4,8,3,6]=>[2,1,8,4,5,3,7,6]=>1001011
[3,1,8,6,7,4,5,2]=>[3,5,1,7,4,8,6,2]=>[8,6,7,4,5,1,3,2]=>0101011
[4,1,8,6,7,3,5,2]=>[4,5,7,1,3,8,6,2]=>[8,6,7,1,5,3,4,2]=>0011011
[8,6,7,3,4,1,5,2]=>[4,5,7,3,1,8,6,2]=>[8,6,7,3,5,1,4,2]=>0011011
[8,5,7,3,4,1,6,2]=>[4,6,7,3,8,1,5,2]=>[8,3,7,5,6,1,4,2]=>0010111
[8,5,6,2,7,3,4,1]=>[4,6,7,3,8,5,2,1]=>[8,5,7,3,6,2,4,1]=>0010111
[8,4,7,3,5,1,6,2]=>[5,6,7,8,3,1,4,2]=>[8,3,7,1,6,4,5,2]=>0001111
[5,1,8,4,7,3,6,2]=>[5,6,7,8,1,3,4,2]=>[8,1,7,3,6,4,5,2]=>0001111
[4,1,8,5,7,3,6,2]=>[4,6,7,1,8,3,5,2]=>[8,1,7,5,6,3,4,2]=>0010111
[3,1,8,5,7,4,6,2]=>[3,6,1,7,8,4,5,2]=>[8,4,7,5,6,1,3,2]=>0100111
[2,1,8,5,7,4,6,3]=>[2,1,6,7,8,4,5,3]=>[2,1,8,4,7,5,6,3]=>1000111
[2,1,7,4,6,3,8,5]=>[2,1,6,7,8,4,3,5]=>[2,1,8,4,7,3,6,5]=>1000111
[3,1,7,4,6,2,8,5]=>[3,6,1,7,8,4,2,5]=>[8,4,7,1,3,2,6,5]=>0100111
[4,1,7,3,6,2,8,5]=>[4,6,7,1,8,3,2,5]=>[8,1,7,3,4,2,6,5]=>0010111
[5,1,7,3,6,2,8,4]=>[5,6,7,8,1,3,2,4]=>[8,1,7,3,6,2,5,4]=>0001111
[6,2,7,3,5,1,8,4]=>[5,6,7,8,3,2,1,4]=>[8,3,7,2,6,1,5,4]=>0001111
[6,2,8,4,7,3,5,1]=>[5,6,7,8,3,2,4,1]=>[8,3,7,2,6,4,5,1]=>0001111
[8,4,7,3,6,2,5,1]=>[5,6,7,8,2,3,4,1]=>[8,2,7,3,6,4,5,1]=>0001111
[7,3,6,2,5,1,8,4]=>[5,6,7,8,2,3,1,4]=>[8,2,7,3,6,1,5,4]=>0001111
[6,2,5,1,7,3,8,4]=>[5,6,7,8,2,1,3,4]=>[8,2,7,1,6,3,5,4]=>0001111
[5,2,4,1,7,3,8,6]=>[4,5,7,2,1,8,3,6]=>[8,2,5,1,4,3,7,6]=>0011011
[6,2,4,1,7,3,8,5]=>[4,6,7,2,8,1,3,5]=>[8,2,7,1,4,3,6,5]=>0010111
[8,5,7,3,6,2,4,1]=>[4,6,7,2,8,3,5,1]=>[8,2,7,5,6,3,4,1]=>0010111
[8,5,7,4,6,2,3,1]=>[3,6,2,7,8,4,5,1]=>[8,4,7,5,6,2,3,1]=>0100111
[7,4,6,2,3,1,8,5]=>[3,6,2,7,8,4,1,5]=>[8,4,7,2,3,1,6,5]=>0100111
[6,2,3,1,7,4,8,5]=>[3,6,2,7,8,1,4,5]=>[8,2,3,1,7,4,6,5]=>0100111
[5,2,3,1,7,4,8,6]=>[3,5,2,7,1,8,4,6]=>[8,2,3,1,5,4,7,6]=>0101011
[4,2,3,1,7,5,8,6]=>[3,4,2,1,7,8,5,6]=>[4,2,3,1,8,5,7,6]=>0110011
[3,1,4,2,8,6,7,5]=>[3,4,1,2,7,8,6,5]=>[4,1,3,2,8,6,7,5]=>0110011
[6,2,3,1,8,5,7,4]=>[3,6,2,7,8,1,5,4]=>[8,2,3,1,7,5,6,4]=>0100111
[8,5,6,2,3,1,7,4]=>[3,6,2,7,8,5,1,4]=>[8,5,7,2,3,1,6,4]=>0100111
[7,4,8,5,6,2,3,1]=>[3,6,2,7,8,5,4,1]=>[8,5,7,4,6,2,3,1]=>0100111
[7,3,8,5,6,2,4,1]=>[4,6,7,2,8,5,3,1]=>[8,5,7,2,6,3,4,1]=>0010111
[8,5,6,2,4,1,7,3]=>[4,6,7,2,8,5,1,3]=>[8,5,7,2,6,1,4,3]=>0010111
[5,2,4,1,8,6,7,3]=>[4,5,7,2,1,8,6,3]=>[8,6,7,2,5,1,4,3]=>0011011
[4,1,5,2,8,6,7,3]=>[4,5,7,1,2,8,6,3]=>[8,6,7,1,5,2,4,3]=>0011011
[3,1,5,2,8,6,7,4]=>[3,5,1,7,2,8,6,4]=>[8,6,7,1,3,2,5,4]=>0101011
[2,1,6,3,8,5,7,4]=>[2,1,6,7,8,3,5,4]=>[2,1,8,3,7,5,6,4]=>1000111
[3,1,6,2,8,5,7,4]=>[3,6,1,7,8,2,5,4]=>[8,1,3,2,7,5,6,4]=>0100111
[4,1,6,2,8,5,7,3]=>[4,6,7,1,8,2,5,3]=>[8,1,7,5,6,2,4,3]=>0010111
[5,1,6,2,8,4,7,3]=>[5,6,7,8,1,2,4,3]=>[8,1,7,2,6,4,5,3]=>0001111
[8,4,6,2,5,1,7,3]=>[5,6,7,8,2,4,1,3]=>[8,2,7,4,6,1,5,3]=>0001111
[7,3,8,4,6,2,5,1]=>[5,6,7,8,2,4,3,1]=>[8,2,7,4,6,3,5,1]=>0001111
[6,2,7,3,8,4,5,1]=>[5,6,7,8,4,2,3,1]=>[8,4,7,2,6,3,5,1]=>0001111
[8,4,5,1,6,2,7,3]=>[5,6,7,8,4,1,2,3]=>[8,4,7,1,6,2,5,3]=>0001111
[5,1,8,4,6,2,7,3]=>[5,6,7,8,1,4,2,3]=>[8,1,7,4,6,2,5,3]=>0001111
[4,1,8,5,6,2,7,3]=>[4,6,7,1,8,5,2,3]=>[8,5,7,1,6,2,4,3]=>0010111
[3,1,8,5,6,2,7,4]=>[3,6,1,7,8,5,2,4]=>[8,5,7,1,3,2,6,4]=>0100111
[2,1,8,5,6,3,7,4]=>[2,1,6,7,8,5,3,4]=>[2,1,8,5,7,3,6,4]=>1000111
[2,1,7,4,8,5,6,3]=>[2,1,6,7,8,5,4,3]=>[2,1,8,5,7,4,6,3]=>1000111
[3,1,7,4,8,5,6,2]=>[3,6,1,7,8,5,4,2]=>[8,5,7,4,6,1,3,2]=>0100111
[4,1,7,3,8,5,6,2]=>[4,6,7,1,8,5,3,2]=>[8,5,7,1,6,3,4,2]=>0010111
[7,3,8,4,5,1,6,2]=>[5,6,7,8,4,1,3,2]=>[8,4,7,1,6,3,5,2]=>0001111
[8,4,5,1,7,3,6,2]=>[5,6,7,8,4,3,1,2]=>[8,4,7,3,6,1,5,2]=>0001111
[7,3,6,2,8,4,5,1]=>[5,6,7,8,4,3,2,1]=>[8,4,7,3,6,2,5,1]=>0001111
[1,3,8,4,7,2,5,6]=>[1,7,3,8,2,5,4,6]=>[1,3,8,2,5,7,4,6]=>0000011
[4,6,1,2,5,7,3,8]=>[6,1,7,4,2,5,3,8]=>[4,7,1,2,5,6,3,8]=>0000110
[1,4,8,2,5,7,3,6]=>[1,8,7,4,2,3,5,6]=>[1,4,7,2,8,3,5,6]=>0000011
[7,8,2,4,5,6,1,3]=>[6,8,1,2,4,5,7,3]=>[7,8,1,4,5,6,2,3]=>0000101
[7,8,5,1,4,2,6,3]=>[5,4,8,3,6,2,7,1]=>[6,3,4,2,7,8,5,1]=>0011101
[2,6,4,8,3,7,1,5]=>[7,2,8,6,1,4,3,5]=>[2,6,1,8,4,7,3,5]=>0000111
[1,4,6,8,3,7,5,2]=>[1,5,7,4,8,6,2,3]=>[1,4,6,8,2,7,5,3]=>0001011
[2,4,8,5,3,1,6,7]=>[3,2,5,4,8,1,6,7]=>[2,4,8,5,3,1,6,7]=>0101001
[3,5,8,4,7,6,1,2]=>[6,1,3,7,5,8,2,4]=>[3,5,8,1,2,7,6,4]=>0000111
[1,6,2,4,7,3,8,5]=>[1,6,7,2,8,4,3,5]=>[1,8,2,4,7,3,6,5]=>0000111
[5,6,2,1,4,7,8,3]=>[2,6,8,1,5,4,7,3]=>[5,7,8,2,1,4,6,3]=>1000101
[4,6,2,5,3,1,8,7]=>[3,5,6,4,1,2,8,7]=>[4,6,1,5,3,2,8,7]=>0101101
[4,7,5,1,3,6,8,2]=>[5,7,2,4,8,3,6,1]=>[4,8,2,3,6,7,5,1]=>0001011
[5,7,3,6,1,4,8,2]=>[6,8,7,1,5,3,4,2]=>[5,7,1,8,3,4,6,2]=>0000111
[5,3,6,7,2,1,8,4]=>[2,7,5,8,3,6,1,4]=>[6,8,3,5,2,1,7,4]=>1001011
[6,1,7,5,2,4,8,3]=>[6,5,7,3,8,1,4,2]=>[8,3,7,5,1,4,6,2]=>0001111
[6,3,1,2,4,5,8,7]=>[3,1,6,2,4,5,8,7]=>[6,3,1,2,4,5,8,7]=>0100101
[1,4,7,2,5,3,8,6]=>[1,7,5,4,2,8,3,6]=>[1,4,5,2,8,3,7,6]=>0001011
[3,6,1,8,4,2,5,7]=>[6,4,3,8,2,1,5,7]=>[3,8,4,2,6,1,5,7]=>0010101
[3,5,6,7,8,1,4,2]=>[8,4,3,1,5,6,7,2]=>[3,4,1,5,6,7,8,2]=>0010001
[3,6,5,7,8,2,1,4]=>[2,8,3,1,6,5,7,4]=>[3,6,5,7,8,2,1,4]=>1000101
[2,7,5,6,8,4,1,3]=>[4,2,1,8,7,5,6,3]=>[2,7,5,6,8,4,1,3]=>0010011
[2,1,6,8,4,5,3,7]=>[2,1,5,8,4,6,3,7]=>[2,1,6,8,4,5,3,7]=>1001001
[2,7,1,8,5,3,4,6]=>[7,2,5,3,8,4,1,6]=>[2,8,5,3,4,7,1,6]=>0001011
[3,7,6,8,5,4,1,2]=>[4,1,3,5,8,7,6,2]=>[3,7,6,8,5,4,1,2]=>0011011
[4,3,8,5,6,7,1,2]=>[7,1,4,3,8,5,6,2]=>[4,3,8,5,6,7,1,2]=>0010011
[4,2,8,1,6,3,7,5]=>[8,4,6,2,7,1,3,5]=>[7,2,4,1,6,3,8,5]=>0010111
[3,2,8,4,5,6,1,7]=>[6,3,2,8,4,5,1,7]=>[3,2,8,4,5,6,1,7]=>0100101
[3,4,2,8,6,1,7,5]=>[6,4,3,2,8,7,5,1]=>[3,4,2,7,5,8,6,1]=>0010111
[3,4,7,1,5,2,6,8]=>[7,5,3,4,1,2,6,8]=>[3,4,5,1,7,2,6,8]=>0001010
[4,3,7,8,1,2,6,5]=>[8,1,4,3,6,2,7,5]=>[4,3,6,1,2,7,8,5]=>0010101
[1,7,3,8,5,2,6,4]=>[1,5,8,7,6,3,4,2]=>[1,6,3,7,4,8,5,2]=>0001111
[4,1,8,3,6,2,5,7]=>[4,6,8,1,2,3,5,7]=>[8,1,6,2,4,3,5,7]=>0010101
[5,7,8,6,3,2,1,4]=>[2,3,6,1,5,8,7,4]=>[5,7,8,6,3,2,1,4]=>1100101
[5,7,8,6,1,3,4,2]=>[6,4,1,3,5,8,7,2]=>[4,1,3,5,7,8,6,2]=>0010101
[7,6,5,8,1,3,4,2]=>[8,4,1,3,6,7,5,2]=>[4,1,3,7,6,5,8,2]=>0010111
[2,4,5,1,7,8,6,3]=>[5,2,6,4,1,8,7,3]=>[2,4,7,8,6,1,5,3]=>0001101
[2,6,3,4,5,8,1,7]=>[8,2,6,3,4,5,1,7]=>[2,6,3,4,5,8,1,7]=>0000101
[2,6,4,1,8,3,7,5]=>[4,2,6,8,7,3,1,5]=>[2,7,3,8,4,1,6,5]=>0010111
[7,2,1,4,8,3,5,6]=>[2,7,8,1,3,5,4,6]=>[8,2,1,5,7,3,4,6]=>1000011
[7,2,5,6,3,8,1,4]=>[8,7,6,1,2,5,3,4]=>[6,1,5,7,2,8,3,4]=>0000111
[5,6,7,4,2,8,1,3]=>[8,4,1,7,5,6,2,3]=>[5,6,7,4,1,8,2,3]=>0010011
[5,7,6,4,1,8,3,2]=>[4,3,6,7,5,8,1,2]=>[5,8,3,1,7,6,4,2]=>0110111
[6,7,1,5,2,8,3,4]=>[7,5,8,3,1,6,2,4]=>[6,8,3,5,1,7,2,4]=>0001011
[7,1,5,3,4,2,8,6]=>[7,4,5,3,1,8,2,6]=>[5,3,4,1,8,2,7,6]=>0011011
[7,6,1,5,3,2,8,4]=>[6,3,5,7,4,8,2,1]=>[8,4,5,3,2,7,6,1]=>0101111
[7,5,6,4,1,2,8,3]=>[4,1,6,8,7,5,3,2]=>[7,5,8,3,6,4,1,2]=>0010111
[6,7,5,4,3,1,8,2]=>[3,4,5,7,8,6,2,1]=>[6,8,2,7,5,4,3,1]=>0111011
[7,4,6,1,2,5,3,8]=>[6,1,5,7,2,4,3,8]=>[7,1,2,5,4,6,3,8]=>0001110
[7,1,4,2,5,3,6,8]=>[7,4,5,1,2,3,6,8]=>[5,1,4,2,7,3,6,8]=>0011010
[7,4,2,6,5,1,3,8]=>[5,4,2,6,7,1,3,8]=>[7,4,2,6,5,1,3,8]=>0011110
[7,2,4,1,5,3,6,8]=>[4,7,5,2,1,3,6,8]=>[5,2,7,1,4,3,6,8]=>0011010
[1,5,7,2,3,8,6,4]=>[1,7,2,6,5,8,3,4]=>[1,5,8,6,2,3,7,4]=>0000111
[5,1,8,2,3,6,7,4]=>[5,8,2,7,1,3,6,4]=>[7,2,6,8,1,3,5,4]=>0001011
[5,8,2,3,7,6,4,1]=>[4,6,2,7,5,8,3,1]=>[5,8,2,3,7,6,4,1]=>0010111
[6,8,2,4,1,5,7,3]=>[4,8,7,2,1,6,5,3]=>[6,7,2,5,8,1,4,3]=>0010011
[6,8,3,1,2,4,7,5]=>[3,1,8,2,7,6,4,5]=>[6,7,3,1,2,4,8,5]=>0100011
[2,1,4,7,8,5,6,3]=>[2,1,6,4,8,5,7,3]=>[2,1,4,7,8,5,6,3]=>1000101
[2,5,7,8,1,4,6,3]=>[8,2,6,1,5,4,7,3]=>[2,5,6,1,4,7,8,3]=>0000101
[3,5,7,4,1,6,2,8]=>[4,7,3,6,5,2,1,8]=>[3,5,6,2,7,4,1,8]=>0010110
[5,2,8,4,6,1,7,3]=>[6,5,7,8,2,4,1,3]=>[8,2,7,4,5,1,6,3]=>0001111
[5,2,1,8,6,3,7,4]=>[2,5,6,8,1,7,4,3]=>[7,2,1,8,6,4,5,3]=>1001111
[4,2,8,5,7,6,3,1]=>[3,6,4,1,7,8,2,5]=>[4,1,8,3,2,7,6,5]=>0110111
[1,4,2,7,5,8,6,3]=>[1,4,6,2,8,7,3,5]=>[1,7,2,4,3,8,6,5]=>0010111
[4,1,8,6,7,5,3,2]=>[4,3,5,1,7,8,6,2]=>[8,6,7,5,3,1,4,2]=>0111011
[5,8,4,7,6,2,1,3]=>[2,6,1,7,5,8,3,4]=>[5,8,2,1,3,7,6,4]=>1000111
[5,8,7,4,3,6,1,2]=>[6,1,4,7,5,3,8,2]=>[5,8,7,4,3,6,1,2]=>0010111
[6,4,8,3,1,7,2,5]=>[3,8,7,6,1,4,2,5]=>[6,1,7,4,8,3,2,5]=>0100111
[5,1,3,8,6,7,2,4]=>[5,7,1,2,3,8,6,4]=>[8,6,7,1,5,2,3,4]=>0001011
[1,5,3,7,8,6,2,4]=>[1,6,5,2,3,8,7,4]=>[1,5,2,7,8,6,3,4]=>0001101
[6,4,8,1,2,7,3,5]=>[8,1,7,6,3,4,2,5]=>[6,3,7,4,8,1,2,5]=>0000111
[4,5,1,2,7,6,3,8]=>[5,1,6,4,2,7,3,8]=>[4,7,6,1,2,5,3,8]=>0001110
[3,5,6,1,8,4,7,2]=>[6,7,3,8,5,1,4,2]=>[3,5,8,1,7,4,6,2]=>0000111
[4,6,3,1,2,7,5,8]=>[3,1,6,4,7,2,5,8]=>[4,7,3,1,2,6,5,8]=>0100110
[3,5,2,7,8,1,6,4]=>[8,5,3,6,2,1,7,4]=>[3,6,2,5,1,7,8,4]=>0001101
[3,4,6,8,5,2,7,1]=>[7,5,3,4,8,6,2,1]=>[3,4,6,8,5,2,7,1]=>0001011
[4,2,5,6,1,8,7,3]=>[6,4,7,2,5,1,8,3]=>[5,8,7,2,4,1,6,3]=>0010111
[4,5,3,1,6,8,7,2]=>[3,5,7,4,2,6,8,1]=>[4,6,8,7,2,5,3,1]=>0101011
[2,1,7,5,8,6,4,3]=>[2,1,4,6,8,7,3,5]=>[2,1,7,4,3,8,6,5]=>1010111
[1,2,7,5,3,8,6,4]=>[1,2,5,7,6,8,4,3]=>[1,2,8,6,4,7,5,3]=>0001111
[4,1,2,7,3,8,6,5]=>[4,1,7,2,6,8,3,5]=>[8,6,1,2,4,3,7,5]=>0010111
[6,4,1,7,5,2,3,8]=>[4,6,1,5,7,2,3,8]=>[7,5,1,6,4,2,3,8]=>0011110
[3,7,1,2,5,4,8,6]=>[7,1,3,5,2,8,4,6]=>[3,5,1,2,8,4,7,6]=>0001011
[1,3,7,2,4,8,6,5]=>[1,7,3,2,6,8,4,5]=>[1,3,8,6,2,4,7,5]=>0000111
[5,2,8,1,3,7,4,6]=>[8,5,1,7,2,4,3,6]=>[7,1,5,4,8,2,3,6]=>0001011
[2,1,6,8,3,4,7,5]=>[2,1,8,3,7,6,4,5]=>[2,1,6,7,3,4,8,5]=>1000011
[2,6,8,3,1,5,7,4]=>[3,2,8,7,1,6,5,4]=>[2,6,7,3,1,5,8,4]=>0100011
[2,8,6,4,1,5,7,3]=>[4,2,6,8,1,7,5,3]=>[2,7,1,5,8,6,4,3]=>0010111
[6,3,7,4,5,1,8,2]=>[5,8,6,7,4,3,1,2]=>[7,4,6,3,8,1,5,2]=>0001111
[2,6,3,7,5,8,1,4]=>[8,2,6,1,7,3,5,4]=>[2,7,1,6,5,8,3,4]=>0000111
[5,2,7,3,6,8,1,4]=>[8,5,7,1,2,3,6,4]=>[7,1,5,2,6,8,3,4]=>0001011
[5,7,4,6,2,8,1,3]=>[8,6,1,7,5,4,2,3]=>[5,7,4,6,1,8,2,3]=>0000111
[5,3,8,4,6,1,7,2]=>[6,7,5,8,3,4,1,2]=>[8,3,5,4,7,1,6,2]=>0001111
[8,2,3,5,1,6,7,4]=>[5,8,2,7,3,1,6,4]=>[7,2,3,6,8,1,5,4]=>0001011
[4,2,8,3,6,7,1,5]=>[7,4,8,2,1,3,6,5]=>[8,2,4,1,6,7,3,5]=>0010011
[8,4,1,3,6,2,5,7]=>[4,8,2,6,1,3,5,7]=>[6,2,8,4,1,3,5,7]=>0010101
[4,8,3,1,7,2,5,6]=>[3,8,7,4,1,5,2,6]=>[4,7,1,5,8,3,2,6]=>0100011
[5,2,8,4,7,1,6,3]=>[7,5,6,8,2,1,4,3]=>[8,2,6,1,5,4,7,3]=>0001111
[5,8,4,7,3,1,6,2]=>[3,7,6,8,5,2,4,1]=>[5,8,2,6,4,7,3,1]=>0100111
[6,3,1,8,2,4,7,5]=>[3,6,8,1,7,2,4,5]=>[7,1,8,3,2,4,6,5]=>0100111
[5,3,8,1,2,6,4,7]=>[8,1,5,6,3,2,4,7]=>[6,3,5,1,2,8,4,7]=>0001101
[5,1,8,4,2,7,3,6]=>[5,4,8,7,1,2,3,6]=>[7,1,8,4,2,5,3,6]=>0011011
[1,6,2,8,5,3,7,4]=>[1,6,5,8,7,2,4,3]=>[1,7,2,8,5,4,6,3]=>0001111
[6,8,5,3,1,7,4,2]=>[3,5,4,8,7,6,1,2]=>[6,7,4,1,8,5,3,2]=>0111011
[5,6,3,7,1,2,4,8]=>[7,1,6,2,5,3,4,8]=>[5,6,1,2,7,3,4,8]=>0000110
[1,6,3,7,2,8,4,5]=>[1,7,6,8,4,3,2,5]=>[1,8,4,6,3,7,2,5]=>0000111
[6,3,2,7,8,5,1,4]=>[5,3,8,2,6,1,7,4]=>[6,3,2,7,8,5,1,4]=>0101101
[4,5,7,8,3,1,6,2]=>[3,8,6,4,5,2,7,1]=>[4,5,6,2,7,8,3,1]=>0100101
[3,8,2,4,6,7,1,5]=>[7,8,3,2,1,4,6,5]=>[3,8,2,6,7,1,4,5]=>0000011
[3,5,6,8,2,7,1,4]=>[7,8,3,1,5,6,2,4]=>[3,5,6,8,1,7,2,4]=>0000011
[4,8,3,5,6,1,7,2]=>[6,7,8,4,3,5,1,2]=>[4,8,3,5,7,1,6,2]=>0000111
[5,8,7,3,4,1,2,6]=>[4,1,7,3,5,2,8,6]=>[5,8,7,3,4,1,2,6]=>0010011
[6,8,4,7,1,5,3,2]=>[7,3,5,8,1,6,4,2]=>[6,8,3,1,5,4,7,2]=>0101011
[5,4,8,7,1,6,3,2]=>[7,3,6,5,4,1,8,2]=>[5,4,6,3,1,8,7,2]=>0101111
[5,3,8,7,6,1,2,4]=>[6,1,5,2,3,7,8,4]=>[5,1,2,8,7,6,3,4]=>0001111
[4,3,8,7,6,1,2,5]=>[6,1,4,3,2,7,8,5]=>[4,3,8,7,6,1,2,5]=>0010111
[4,8,3,7,5,1,2,6]=>[5,1,7,4,8,3,2,6]=>[4,8,3,7,5,1,2,6]=>0001011
[3,8,4,7,5,1,2,6]=>[5,1,3,7,8,4,2,6]=>[3,8,4,7,5,1,2,6]=>0001011
[3,4,8,7,6,1,2,5]=>[6,1,3,4,2,7,8,5]=>[3,4,8,7,6,1,2,5]=>0000111
[3,5,8,7,6,1,2,4]=>[6,1,3,2,5,7,8,4]=>[3,5,8,7,6,1,2,4]=>0000111
[4,5,8,7,6,1,2,3]=>[6,1,2,4,5,7,8,3]=>[4,5,8,7,6,1,2,3]=>0000111
[3,5,8,2,7,6,4,1]=>[4,6,3,7,5,8,2,1]=>[3,5,8,2,7,6,4,1]=>0010111
[8,1,4,6,2,5,3,7]=>[8,6,5,1,2,4,3,7]=>[5,1,6,2,4,8,3,7]=>0001101
[1,8,4,7,2,5,3,6]=>[1,7,5,8,2,3,4,6]=>[1,8,2,5,3,7,4,6]=>0001011
[1,4,8,7,2,6,3,5]=>[1,7,6,4,3,2,8,5]=>[1,4,6,3,8,7,2,5]=>0000111
[1,5,8,2,7,6,4,3]=>[1,8,4,6,5,7,2,3]=>[1,5,7,6,4,2,8,3]=>0010111
[2,5,8,3,7,6,4,1]=>[4,2,6,7,5,8,3,1]=>[2,5,8,3,7,6,4,1]=>0010111
[1,4,2,8,7,6,5,3]=>[1,4,5,2,6,7,8,3]=>[1,8,7,6,5,2,4,3]=>0011111
[1,3,8,2,7,6,4,5]=>[1,8,3,6,4,7,2,5]=>[1,3,7,6,4,8,2,5]=>0000111
[1,8,3,2,7,5,4,6]=>[1,3,8,5,7,4,2,6]=>[1,7,5,4,8,3,2,6]=>0101011
[8,1,3,2,6,5,4,7]=>[8,3,1,5,6,2,4,7]=>[3,1,6,5,2,8,4,7]=>0101101
[3,4,1,8,7,6,5,2]=>[4,5,3,1,6,7,8,2]=>[3,8,7,6,5,1,4,2]=>0011111
[4,3,1,8,7,6,5,2]=>[3,4,5,2,6,7,8,1]=>[8,7,6,5,2,4,3,1]=>0111111
[4,2,1,8,7,6,5,3]=>[2,4,5,1,6,7,8,3]=>[8,7,6,5,2,1,4,3]=>1011111
[5,2,8,1,7,6,4,3]=>[8,5,4,6,2,7,1,3]=>[7,6,4,2,5,1,8,3]=>0011111
[5,3,8,2,7,6,4,1]=>[4,6,7,5,1,8,2,3]=>[5,1,8,2,7,6,4,3]=>0011111
[6,8,3,2,7,5,4,1]=>[4,3,5,7,8,6,2,1]=>[6,8,3,2,7,5,4,1]=>0111011
[6,8,2,7,1,5,3,4]=>[7,8,5,3,1,6,2,4]=>[5,3,6,8,1,7,2,4]=>0001011
[6,8,7,2,1,4,3,5]=>[2,7,4,1,3,6,8,5]=>[4,2,1,6,8,7,3,5]=>1010011
[5,8,7,1,2,4,3,6]=>[7,1,4,2,5,3,8,6]=>[4,1,2,5,8,7,3,6]=>0010011
[6,8,1,2,7,5,4,3]=>[8,1,4,5,7,6,2,3]=>[6,7,5,4,1,2,8,3]=>0011011
[6,8,2,3,7,5,4,1]=>[4,5,2,7,8,6,3,1]=>[6,8,2,3,7,5,4,1]=>0011011
[5,1,8,3,7,6,4,2]=>[5,4,6,7,1,8,3,2]=>[8,1,7,6,4,3,5,2]=>0011111
[8,4,1,6,2,5,3,7]=>[4,8,6,5,3,2,1,7]=>[5,3,6,2,8,4,1,7]=>0011101
[8,3,1,2,6,5,4,7]=>[3,1,8,5,6,2,4,7]=>[6,5,3,1,2,8,4,7]=>0101101
[3,8,1,2,7,5,4,6]=>[8,1,3,5,7,4,2,6]=>[3,7,5,4,8,1,2,6]=>0001011
[3,1,2,8,7,6,5,4]=>[3,1,2,5,6,7,8,4]=>[3,1,2,8,7,6,5,4]=>0101111
[4,1,3,8,7,6,5,2]=>[4,5,1,3,6,7,8,2]=>[8,7,6,5,1,3,4,2]=>0011111
[3,1,4,8,7,6,5,2]=>[3,5,1,4,6,7,8,2]=>[4,8,7,6,5,1,3,2]=>0101111
[8,2,1,3,6,5,4,7]=>[2,8,1,5,6,3,4,7]=>[6,5,2,1,3,8,4,7]=>1001101
[8,1,2,3,6,5,4,7]=>[8,1,2,5,6,3,4,7]=>[6,5,1,2,3,8,4,7]=>0001101
[1,4,5,2,8,3,7,6]=>[1,5,8,4,2,7,3,6]=>[1,4,7,2,5,3,8,6]=>0001011
[1,4,2,6,5,8,3,7]=>[1,4,8,2,6,5,3,7]=>[1,6,5,8,2,4,3,7]=>0010101
[1,5,4,2,6,8,3,7]=>[1,4,5,8,3,6,2,7]=>[1,6,8,3,5,4,2,7]=>0011001
[1,5,2,6,4,8,3,7]=>[1,5,8,6,2,4,3,7]=>[1,6,2,8,4,5,3,7]=>0001101
[1,2,5,4,7,3,8,6]=>[1,2,7,5,4,8,3,6]=>[1,2,5,4,8,3,7,6]=>0001011
[4,1,2,6,3,8,7,5]=>[4,1,6,2,7,3,8,5]=>[8,7,1,2,4,3,6,5]=>0010111
[7,1,5,4,2,8,3,6]=>[7,4,5,8,1,2,3,6]=>[8,1,5,4,2,7,3,6]=>0011011
[1,4,7,5,2,8,3,6]=>[1,5,7,4,8,2,3,6]=>[1,4,8,2,7,5,3,6]=>0001011
[7,1,3,5,2,8,4,6]=>[7,5,1,8,3,4,2,6]=>[8,1,3,5,4,7,2,6]=>0001011
[1,4,2,8,3,7,6,5]=>[1,4,8,2,6,7,3,5]=>[1,7,6,2,4,3,8,5]=>0010111
[1,2,5,3,8,7,6,4]=>[1,2,5,6,3,7,8,4]=>[1,2,8,7,6,3,5,4]=>0001111
[1,2,8,6,5,3,7,4]=>[1,2,5,6,8,7,3,4]=>[1,2,7,3,8,6,5,4]=>0001111
[1,5,2,8,6,3,7,4]=>[1,5,6,8,2,7,4,3]=>[1,7,2,8,6,4,5,3]=>0001111
[6,2,1,8,7,3,4,5]=>[2,6,7,3,4,1,8,5]=>[8,7,3,4,6,2,1,5]=>1000111
[7,6,2,1,8,3,4,5]=>[2,6,7,1,4,8,3,5]=>[8,2,1,4,7,6,3,5]=>1000111
[7,3,1,6,2,8,4,5]=>[3,7,6,8,4,2,1,5]=>[8,4,6,2,7,3,1,5]=>0100111
[1,7,5,2,6,3,8,4]=>[1,5,7,6,8,3,4,2]=>[1,8,3,6,4,7,5,2]=>0001111
[1,6,2,7,5,3,8,4]=>[1,6,5,7,8,2,4,3]=>[1,8,2,7,5,4,6,3]=>0001111
[1,2,7,6,5,3,8,4]=>[1,2,5,6,7,8,3,4]=>[1,2,8,3,7,6,5,4]=>0001111
[1,2,6,5,3,8,7,4]=>[1,2,5,6,7,4,8,3]=>[1,2,8,7,4,6,5,3]=>0001111
[1,5,2,6,3,8,7,4]=>[1,5,6,7,2,3,8,4]=>[1,8,7,2,6,3,5,4]=>0001111
[1,5,2,7,6,3,8,4]=>[1,5,6,7,2,8,4,3]=>[1,8,2,7,6,4,5,3]=>0001111
[1,6,5,2,7,3,8,4]=>[1,5,6,7,8,3,4,2]=>[1,8,3,7,4,6,5,2]=>0001111
[1,5,7,4,2,8,3,6]=>[1,4,7,8,5,2,3,6]=>[1,5,8,2,7,4,3,6]=>0010011
[4,1,2,8,6,3,7,5]=>[4,1,6,2,8,7,5,3]=>[7,5,8,6,1,2,4,3]=>0010111
[4,3,7,1,8,2,5,6]=>[7,8,4,3,2,5,1,6]=>[4,3,8,2,5,7,1,6]=>0010011
[8,3,1,6,2,4,7,5]=>[3,8,6,1,7,2,4,5]=>[7,1,6,3,2,4,8,5]=>0100111
[1,8,7,3,2,4,6,5]=>[1,3,7,2,6,4,8,5]=>[1,6,3,2,4,8,7,5]=>0100111
[1,4,8,5,2,7,3,6]=>[1,5,8,4,7,2,3,6]=>[1,4,7,2,8,5,3,6]=>0001011
[1,5,2,7,3,8,6,4]=>[1,5,7,6,2,8,3,4]=>[1,8,6,2,7,3,5,4]=>0001111
[1,2,8,5,3,7,6,4]=>[1,2,5,8,6,7,4,3]=>[1,2,7,6,4,8,5,3]=>0001111
[1,2,6,3,8,7,5,4]=>[1,2,6,5,7,3,8,4]=>[1,2,8,7,5,3,6,4]=>0001111
[1,2,7,6,3,8,5,4]=>[1,2,6,5,7,8,4,3]=>[1,2,8,5,4,7,6,3]=>0001111
[1,6,2,7,3,8,5,4]=>[1,6,7,5,8,2,3,4]=>[1,8,5,2,7,3,6,4]=>0001111
[1,7,2,8,5,3,6,4]=>[1,7,5,8,6,4,2,3]=>[1,6,4,8,5,2,7,3]=>0001111
[1,7,4,2,8,6,3,5]=>[1,4,7,6,2,8,3,5]=>[1,8,6,2,7,4,3,5]=>0010111
[1,4,2,8,7,6,3,5]=>[1,4,6,2,3,7,8,5]=>[1,8,7,6,2,4,3,5]=>0010111
[1,2,8,7,5,3,6,4]=>[1,2,5,7,6,4,8,3]=>[1,2,6,4,8,7,5,3]=>0001111
[1,2,8,6,3,7,5,4]=>[1,2,6,5,8,7,4,3]=>[1,2,7,5,4,8,6,3]=>0001111
[1,2,7,3,8,6,5,4]=>[1,2,7,5,6,8,3,4]=>[1,2,8,6,5,3,7,4]=>0001111
[5,7,8,6,2,4,1,3]=>[4,6,1,2,5,8,7,3]=>[5,7,8,6,1,4,2,3]=>0010101
[6,4,1,5,2,7,3,8]=>[4,6,5,7,2,3,1,8]=>[7,2,5,3,6,4,1,8]=>0011110
[6,1,4,5,3,8,7,2]=>[6,7,5,1,4,3,8,2]=>[5,1,4,8,7,3,6,2]=>0001111
[6,1,4,8,3,5,7,2]=>[6,7,8,1,3,4,5,2]=>[8,1,7,3,4,5,6,2]=>0000111
[7,1,8,6,3,4,5,2]=>[7,5,6,3,4,8,1,2]=>[8,6,3,4,5,1,7,2]=>0001111
[7,1,4,5,3,8,6,2]=>[7,6,5,1,4,8,3,2]=>[5,1,4,8,6,3,7,2]=>0001111
[7,4,1,5,2,6,3,8]=>[4,7,5,6,2,3,1,8]=>[6,2,5,3,7,4,1,8]=>0011110
[6,3,5,7,2,1,4,8]=>[2,7,6,1,3,5,4,8]=>[6,2,1,5,7,3,4,8]=>1000110
[5,8,7,6,2,4,1,3]=>[4,6,1,2,5,7,8,3]=>[5,8,7,6,1,4,2,3]=>0010111
[5,4,8,6,3,1,7,2]=>[3,6,8,5,4,7,1,2]=>[5,4,7,1,8,6,3,2]=>0101111
[5,8,1,6,2,4,3,7]=>[8,6,4,2,5,1,3,7]=>[4,2,5,6,1,8,3,7]=>0010101
[6,3,5,8,2,1,4,7]=>[2,8,6,1,3,5,4,7]=>[6,2,1,5,8,3,4,7]=>1000101
[2,3,4,1,8,6,5,7]=>[4,2,3,1,6,8,5,7]=>[2,3,4,1,8,6,5,7]=>0010101
[2,8,6,7,1,3,5,4]=>[7,2,1,5,3,8,6,4]=>[2,5,1,3,8,6,7,4]=>0001011
[8,3,5,7,2,1,6,4]=>[2,7,8,6,3,1,5,4]=>[6,3,8,2,1,5,7,4]=>1000111
[2,3,8,5,6,1,7,4]=>[6,2,3,7,8,5,1,4]=>[2,3,8,5,7,1,6,4]=>0000111
[8,4,5,6,3,1,7,2]=>[3,6,7,8,4,5,2,1]=>[8,4,5,7,2,6,3,1]=>0100111
[7,3,5,6,2,1,4,8]=>[2,6,7,1,3,5,4,8]=>[7,2,1,5,6,3,4,8]=>1000110
[2,7,6,8,1,3,5,4]=>[8,2,1,5,3,7,6,4]=>[2,5,1,3,7,6,8,4]=>0001011
[2,6,4,1,8,5,7,3]=>[4,2,6,7,8,3,5,1]=>[2,8,3,7,5,6,4,1]=>0010111
[2,6,1,3,8,5,7,4]=>[6,2,1,7,8,3,5,4]=>[2,8,1,3,7,5,6,4]=>0000111
[7,3,5,1,2,8,4,6]=>[5,1,7,8,3,4,2,6]=>[8,3,7,4,5,1,2,6]=>0001011
[8,4,1,5,2,3,7,6]=>[4,8,1,5,2,7,3,6]=>[5,1,7,4,2,3,8,6]=>0011011
[7,8,1,6,3,4,2,5]=>[8,4,6,3,2,1,7,5]=>[6,3,4,2,7,8,1,5]=>0010101
[2,8,6,7,4,3,1,5]=>[3,2,4,7,1,8,6,5]=>[2,8,6,7,4,3,1,5]=>0110011
[8,3,5,7,2,4,1,6]=>[4,7,8,2,3,1,5,6]=>[8,2,7,3,4,1,5,6]=>0010011
[2,3,4,1,8,7,5,6]=>[4,2,3,1,7,5,8,6]=>[2,3,4,1,8,7,5,6]=>0010011
[2,3,8,1,6,4,7,5]=>[8,2,3,6,7,1,4,5]=>[2,3,7,1,6,4,8,5]=>0000111
[2,8,6,1,4,3,5,7]=>[6,2,4,1,3,8,5,7]=>[2,4,1,8,6,3,5,7]=>0010101
[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>00000001
[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
[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>000000001
[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
[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001
[9,1,2,3,4,5,6,7,10,8]=>[9,1,2,3,4,5,6,10,7,8]=>[10,1,2,3,4,5,6,7,9,8]=>000000011
[1,8,2,3,4,5,6,9,7]=>[1,8,2,3,4,5,9,6,7]=>[1,9,2,3,4,5,6,8,7]=>00000011
[7,1,2,3,4,5,6,9,8]=>[7,1,2,3,4,5,6,9,8]=>[7,1,2,3,4,5,6,9,8]=>00000101
[2,1,9,3,4,5,6,7,8]=>[2,1,9,3,4,5,6,7,8]=>[2,1,9,3,4,5,6,7,8]=>10000001
[2,8,1,3,4,5,6,7,9]=>[8,2,1,3,4,5,6,7,9]=>[2,8,1,3,4,5,6,7,9]=>00000010
[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]=>[2,10,1,3,4,5,6,7,8,9]=>000000001
[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
[8,4,3,6,5,1,7,2]=>[5,6,4,7,8,1,2,3]=>[8,4,1,7,2,6,5,3]=>0011111
[8,6,5,4,3,1,7,2]=>[3,4,5,6,8,7,1,2]=>[7,1,8,6,5,4,3,2]=>0111111
[1,7,6,5,4,2,3,8]=>[1,4,2,5,6,7,3,8]=>[1,7,6,5,4,2,3,8]=>0011110
[8,7,5,4,1,6,3,2]=>[4,3,5,7,6,1,8,2]=>[6,3,1,8,7,5,4,2]=>0111111
[7,8,5,4,1,3,6,2]=>[4,5,1,8,6,3,7,2]=>[6,1,3,7,8,5,4,2]=>0011101
[6,8,5,4,2,1,7,3]=>[2,4,5,8,7,6,1,3]=>[6,7,2,1,8,5,4,3]=>1011011
[5,8,6,2,4,1,7,3]=>[4,6,8,3,5,7,1,2]=>[5,7,3,8,6,1,4,2]=>0010111
[4,8,2,6,5,1,7,3]=>[5,6,8,4,7,3,2,1]=>[4,7,3,8,2,6,5,1]=>0001111
[3,2,8,6,5,1,7,4]=>[5,3,2,6,8,7,1,4]=>[3,2,7,1,8,6,5,4]=>0101111
[3,2,1,7,6,4,5,8]=>[2,3,1,6,4,7,5,8]=>[3,2,1,7,6,4,5,8]=>1100110
[4,1,3,7,6,2,5,8]=>[4,6,1,3,2,7,5,8]=>[7,6,1,3,4,2,5,8]=>0010110
[5,1,7,3,6,2,4,8]=>[5,6,7,2,1,3,4,8]=>[7,2,6,1,5,3,4,8]=>0001110
[6,1,7,5,3,2,4,8]=>[6,3,5,2,7,1,4,8]=>[7,5,3,2,6,1,4,8]=>0101110
[7,1,6,5,2,4,3,8]=>[7,5,4,2,6,1,3,8]=>[4,2,6,5,1,7,3,8]=>0011110
[1,2,7,6,3,4,5,8]=>[1,2,6,3,4,7,5,8]=>[1,2,7,6,3,4,5,8]=>0000110
[1,2,8,3,7,4,5,6]=>[1,2,8,7,4,5,3,6]=>[1,2,7,4,5,8,3,6]=>0000011
[8,1,7,2,6,3,5,4]=>[8,7,6,5,3,2,1,4]=>[5,3,6,2,7,1,8,4]=>0001111
[7,1,8,2,6,4,3,5]=>[7,8,4,6,3,2,1,5]=>[6,4,3,8,2,7,1,5]=>0010111
[6,1,8,2,4,7,3,5]=>[6,8,7,2,3,1,4,5]=>[7,2,8,3,6,1,4,5]=>0000111
[4,1,3,8,2,7,5,6]=>[4,8,1,3,7,5,2,6]=>[7,5,8,1,3,4,2,6]=>0010011
[3,2,1,8,4,7,5,6]=>[2,3,1,8,7,5,4,6]=>[3,2,1,7,5,8,4,6]=>1100011
[3,2,8,7,1,6,5,4]=>[7,3,2,5,6,1,8,4]=>[3,2,6,5,1,8,7,4]=>0101111
[6,8,7,1,3,5,4,2]=>[7,4,1,5,3,6,8,2]=>[5,4,1,3,6,8,7,2]=>0011011
[7,8,6,1,5,3,4,2]=>[6,4,5,3,1,8,7,2]=>[5,3,4,1,7,8,6,2]=>0011101
[8,7,6,1,5,4,3,2]=>[6,3,4,5,1,7,8,2]=>[5,4,3,1,8,7,6,2]=>0111111
[1,7,8,2,5,6,3,4]=>[1,8,6,3,2,5,7,4]=>[1,6,3,5,7,8,2,4]=>0000101
[8,6,7,1,4,5,3,2]=>[7,3,5,1,4,8,6,2]=>[5,3,1,4,8,6,7,2]=>0101011
[7,6,8,1,4,3,5,2]=>[8,5,4,1,3,7,6,2]=>[4,1,5,3,7,6,8,2]=>0011011
[8,5,7,3,1,6,4,2]=>[3,7,4,6,8,2,5,1]=>[8,4,2,6,5,7,3,1]=>0110111
[1,6,8,4,2,7,3,5]=>[1,4,8,7,2,6,3,5]=>[1,6,7,2,8,4,3,5]=>0010011
[1,5,4,8,2,7,3,6]=>[1,8,7,5,4,3,2,6]=>[1,5,4,7,3,8,2,6]=>0001011
[8,4,3,7,1,6,5,2]=>[7,5,4,6,8,1,2,3]=>[8,4,1,6,5,2,7,3]=>0011111
[7,4,3,8,1,5,6,2]=>[8,6,4,7,1,5,3,2]=>[7,4,1,5,6,3,8,2]=>0010111
[6,4,3,1,5,2,7,8]=>[3,4,6,5,1,2,7,8]=>[5,1,6,4,3,2,7,8]=>0111100
[7,4,3,1,2,6,5,8]=>[3,1,4,7,6,2,5,8]=>[6,4,3,1,2,7,5,8]=>0110110
[1,5,4,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[1,5,4,2,3,6,7,8]=>0011000
[6,5,1,4,3,2,7,8]=>[5,3,4,1,6,2,7,8]=>[4,3,1,6,5,2,7,8]=>0111100
[3,2,6,1,5,4,7,8]=>[6,3,2,5,1,4,7,8]=>[3,2,5,1,6,4,7,8]=>0101100
[3,2,7,1,4,6,5,8]=>[7,3,2,1,6,4,5,8]=>[3,2,6,1,4,7,5,8]=>0100110
[4,7,2,1,3,6,5,8]=>[2,7,1,4,6,3,5,8]=>[4,6,2,1,3,7,5,8]=>1000110
[7,6,1,2,5,4,3,8]=>[6,1,4,5,2,7,3,8]=>[5,4,1,2,7,6,3,8]=>0011110
[8,7,1,2,3,6,5,4]=>[7,1,2,5,6,3,8,4]=>[6,5,1,2,3,8,7,4]=>0001111
[7,8,1,2,3,5,6,4]=>[8,1,2,6,3,5,7,4]=>[6,1,2,3,5,7,8,4]=>0000101
[6,8,1,2,4,3,7,5]=>[8,1,4,2,7,6,3,5]=>[4,1,2,6,7,3,8,5]=>0010011
[5,8,1,3,2,4,7,6]=>[8,3,1,2,5,7,4,6]=>[3,1,5,7,2,4,8,6]=>0100011
[4,8,2,1,3,5,7,6]=>[2,8,1,4,3,7,5,6]=>[4,7,2,1,3,5,8,6]=>1000011
[3,2,8,1,4,5,7,6]=>[8,3,2,1,4,7,5,6]=>[3,2,7,1,4,5,8,6]=>0100011
[4,1,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>0110000
[5,1,2,4,3,6,7,8]=>[5,1,4,2,3,6,7,8]=>[4,1,2,5,3,6,7,8]=>0011000
[6,1,2,3,5,4,7,8]=>[6,1,2,5,3,4,7,8]=>[5,1,2,3,6,4,7,8]=>0001100
[7,1,2,3,4,6,5,8]=>[7,1,2,3,6,4,5,8]=>[6,1,2,3,4,7,5,8]=>0000110
[8,1,2,3,4,5,7,6]=>[8,1,2,3,4,7,5,6]=>[7,1,2,3,4,5,8,6]=>0000011
[6,7,3,8,5,1,2,4]=>[5,1,8,3,7,6,2,4]=>[6,7,3,8,5,1,2,4]=>0001011
[6,7,4,5,1,8,3,2]=>[5,3,8,7,4,6,1,2]=>[6,7,4,8,3,1,5,2]=>0101011
[4,5,6,7,1,8,3,2]=>[7,3,8,4,5,6,1,2]=>[4,5,6,8,3,1,7,2]=>0100011
[3,5,6,2,7,4,8,1]=>[8,6,3,7,5,2,4,1]=>[3,5,7,2,6,4,8,1]=>0000111
[3,5,6,1,7,8,4,2]=>[6,4,3,8,5,1,7,2]=>[3,5,7,8,4,1,6,2]=>0010101
[8,2,4,5,1,6,3,7]=>[5,8,6,2,4,1,3,7]=>[6,2,4,8,1,5,3,7]=>0001101
[1,4,8,6,2,3,7,5]=>[1,6,2,4,8,7,5,3]=>[1,4,7,5,8,6,2,3]=>0000111
[1,5,6,8,2,3,7,4]=>[1,8,2,7,5,6,3,4]=>[1,5,6,7,2,3,8,4]=>0000011
[8,1,3,2,5,4,6,7]=>[8,3,1,5,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>0101001
[2,8,3,1,5,7,4,6]=>[3,2,8,7,1,4,5,6]=>[2,7,3,1,8,4,5,6]=>0100011
[2,4,1,6,8,7,5,3]=>[4,2,5,1,7,6,8,3]=>[2,6,8,7,5,1,4,3]=>0011011
[3,4,1,6,7,8,5,2]=>[4,5,3,1,8,6,7,2]=>[3,6,7,8,5,1,4,2]=>0011001
[5,3,7,2,6,4,8,1]=>[8,7,5,6,3,2,4,1]=>[6,3,5,2,7,4,8,1]=>0001111
[6,7,3,1,5,8,4,2]=>[3,7,4,8,2,6,5,1]=>[6,8,4,2,5,7,3,1]=>0110011
[6,7,8,2,1,4,3,5]=>[2,8,4,1,3,6,7,5]=>[4,2,1,6,7,8,3,5]=>1010001
[6,7,1,2,8,4,5,3]=>[7,1,5,8,4,6,2,3]=>[6,8,4,5,1,2,7,3]=>0001011
[6,7,1,3,4,8,5,2]=>[7,5,1,3,8,6,4,2]=>[6,8,5,1,3,4,7,2]=>0001011
[5,1,7,8,2,3,6,4]=>[5,8,2,6,1,3,7,4]=>[6,2,7,8,1,3,5,4]=>0001101
[4,1,8,7,2,3,6,5]=>[4,7,2,1,6,3,8,5]=>[6,2,4,1,3,8,7,5]=>0010111
[2,1,8,3,4,7,6,5]=>[2,1,8,3,6,7,4,5]=>[2,1,7,6,3,4,8,5]=>1000111
[1,8,2,3,4,5,7,6]=>[1,8,2,3,4,7,5,6]=>[1,7,2,3,4,5,8,6]=>0000011
[4,2,1,6,5,8,7,3]=>[2,4,7,1,6,5,8,3]=>[6,5,8,7,2,1,4,3]=>1010111
[5,2,7,4,8,6,1,3]=>[6,5,1,8,2,7,3,4]=>[7,1,5,2,3,8,6,4]=>0001111
[5,7,2,3,8,1,6,4]=>[8,7,2,6,5,1,3,4]=>[5,6,2,7,1,3,8,4]=>0000111
[5,6,1,3,2,8,7,4]=>[6,3,1,7,5,2,8,4]=>[3,1,5,8,7,2,6,4]=>0100111
[5,6,3,2,1,8,7,4]=>[2,3,6,7,5,1,8,4]=>[5,8,7,3,2,1,6,4]=>1100111
[5,7,1,3,8,2,6,4]=>[7,8,1,6,5,2,3,4]=>[5,6,1,8,2,3,7,4]=>0000111
[5,1,7,4,8,2,6,3]=>[5,8,6,7,1,2,4,3]=>[7,1,6,2,8,4,5,3]=>0001111
[1,5,7,4,8,6,3,2]=>[1,3,6,8,5,7,2,4]=>[1,5,7,3,2,8,6,4]=>0100111
[5,7,1,3,8,6,2,4]=>[7,6,1,2,5,8,3,4]=>[5,8,6,1,7,2,3,4]=>0000111
[5,7,3,1,8,6,2,4]=>[3,7,6,1,5,8,2,4]=>[5,8,6,1,7,3,2,4]=>0100111
[6,7,3,8,1,5,2,4]=>[8,5,7,2,1,6,3,4]=>[6,7,2,5,1,8,3,4]=>0001011
[6,7,3,8,5,2,1,4]=>[2,5,8,3,7,6,1,4]=>[6,7,3,8,5,2,1,4]=>1001011
[6,7,8,3,1,4,2,5]=>[3,8,4,2,1,6,7,5]=>[4,2,6,7,8,3,1,5]=>0110001
[1,6,7,8,4,5,3,2]=>[1,3,5,8,4,6,7,2]=>[1,6,7,8,4,5,3,2]=>0101001
[6,1,7,8,4,2,5,3]=>[6,4,8,5,3,1,7,2]=>[5,3,7,8,4,1,6,2]=>0011101
[5,7,2,1,8,3,6,4]=>[2,7,8,6,5,3,1,4]=>[5,6,3,8,2,1,7,4]=>1000111
[5,2,7,1,8,4,6,3]=>[7,5,6,8,2,4,1,3]=>[8,2,6,4,5,1,7,3]=>0001111
[4,2,1,7,8,5,6,3]=>[2,4,6,1,8,5,7,3]=>[7,8,5,6,2,1,4,3]=>1010101
[4,1,2,7,8,6,5,3]=>[4,1,5,2,6,8,7,3]=>[7,8,6,5,1,2,4,3]=>0011101
[6,2,7,8,5,4,1,3]=>[4,5,1,8,6,2,7,3]=>[6,1,7,8,5,4,2,3]=>0011101
[6,7,2,8,5,3,1,4]=>[3,5,8,1,7,6,2,4]=>[6,7,1,8,5,3,2,4]=>0101011
[5,7,1,2,8,6,3,4]=>[7,1,6,3,5,8,2,4]=>[5,8,6,3,7,1,2,4]=>0000111
[5,1,7,2,8,6,4,3]=>[5,7,4,6,1,8,2,3]=>[8,6,4,1,7,2,5,3]=>0011111
[1,5,7,3,8,6,4,2]=>[1,4,6,8,5,7,3,2]=>[1,5,7,3,8,6,4,2]=>0010111
[6,1,7,8,2,5,4,3]=>[6,8,4,5,2,1,7,3]=>[5,4,2,7,8,1,6,3]=>0011101
[6,7,1,8,2,5,3,4]=>[7,8,5,3,2,6,1,4]=>[5,3,6,8,2,7,1,4]=>0001011
[6,7,8,2,4,3,1,5]=>[3,4,8,1,2,6,7,5]=>[6,7,8,1,4,3,2,5]=>0110001
[1,6,7,8,5,3,4,2]=>[1,4,5,3,8,6,7,2]=>[1,6,7,8,5,3,4,2]=>0011001
[6,7,8,4,1,3,2,5]=>[4,3,1,8,2,6,7,5]=>[3,1,6,7,8,4,2,5]=>0110001
[6,3,8,5,2,7,4,1]=>[4,7,5,8,6,3,1,2]=>[6,3,8,5,1,7,4,2]=>0011111
[6,3,4,5,8,7,2,1]=>[2,7,6,3,4,5,8,1]=>[6,3,4,5,8,7,2,1]=>1000111
[5,8,1,4,7,2,3,6]=>[8,7,2,1,5,3,4,6]=>[5,7,2,8,1,3,4,6]=>0000011
[5,6,1,4,8,7,3,2]=>[6,3,7,1,5,4,8,2]=>[5,8,7,3,1,4,6,2]=>0100111
[3,4,7,1,8,6,5,2]=>[7,5,3,4,6,8,1,2]=>[3,4,8,6,5,1,7,2]=>0001111
[6,3,8,4,2,7,1,5]=>[7,4,8,6,1,2,3,5]=>[6,1,8,4,2,7,3,5]=>0010111
[4,3,8,5,6,7,2,1]=>[2,7,4,3,8,5,6,1]=>[4,3,8,5,6,7,2,1]=>1010011
[5,8,1,7,6,2,4,3]=>[8,6,4,2,5,7,1,3]=>[4,2,5,7,6,1,8,3]=>0010111
[6,3,7,5,2,8,1,4]=>[8,5,7,1,6,2,3,4]=>[6,1,7,5,2,8,3,4]=>0001111
[6,5,2,7,4,8,1,3]=>[8,5,1,6,7,4,2,3]=>[7,4,6,5,1,8,2,3]=>0001111
[5,7,1,4,8,3,2,6]=>[7,3,8,1,5,2,4,6]=>[5,8,3,1,7,2,4,6]=>0100011
[7,8,3,5,1,4,6,2]=>[5,6,8,1,3,4,7,2]=>[7,8,1,6,3,4,5,2]=>0001101
[5,8,1,4,6,7,2,3]=>[8,7,2,1,5,4,6,3]=>[5,7,2,4,6,8,1,3]=>0000011
[6,5,8,4,3,7,2,1]=>[2,7,4,8,6,5,3,1]=>[6,5,8,4,3,7,2,1]=>1010111
[6,3,7,4,2,8,5,1]=>[5,4,8,7,6,1,2,3]=>[6,1,7,4,2,8,5,3]=>0011111
[4,3,8,7,1,5,6,2]=>[7,6,4,3,1,5,8,2]=>[4,3,6,1,5,8,7,2]=>0010111
[8,3,6,1,2,5,7,4]=>[6,1,8,7,2,3,5,4]=>[7,1,2,8,3,5,6,4]=>0000111
[5,6,1,8,7,3,2,4]=>[6,3,7,2,5,1,8,4]=>[5,8,7,3,2,6,1,4]=>0100111
[8,5,2,6,4,7,3,1]=>[3,7,5,8,6,4,1,2]=>[6,4,8,5,1,7,3,2]=>0101111
[8,2,6,3,4,7,5,1]=>[5,7,8,1,6,3,4,2]=>[6,1,8,3,4,7,5,2]=>0001111
[7,2,6,3,5,4,8,1]=>[8,7,6,5,3,2,4,1]=>[5,3,6,2,7,4,8,1]=>0001111
[6,2,7,4,3,5,8,1]=>[8,6,4,7,3,2,5,1]=>[7,4,3,6,2,5,8,1]=>0010111
[3,7,6,4,5,2,8,1]=>[8,5,3,6,4,7,2,1]=>[3,7,6,4,5,2,8,1]=>0001111
[2,7,6,5,3,4,8,1]=>[8,2,5,3,6,7,4,1]=>[2,7,6,5,3,4,8,1]=>0001111
[6,5,4,3,1,8,2,7]=>[3,4,5,6,8,2,1,7]=>[8,2,6,5,4,3,1,7]=>0111101
[8,5,4,1,7,2,6,3]=>[4,5,8,7,6,1,3,2]=>[6,1,7,3,8,5,4,2]=>0011111
[1,6,5,2,8,3,4,7]=>[1,5,6,2,8,3,4,7]=>[1,8,2,6,5,3,4,7]=>0001101
[5,7,4,2,1,8,3,6]=>[2,4,7,8,5,1,3,6]=>[5,8,2,1,7,4,3,6]=>1010011
[1,6,5,3,4,8,2,7]=>[1,8,5,3,6,4,2,7]=>[1,6,5,3,4,8,2,7]=>0001101
[6,5,8,4,2,7,3,1]=>[3,7,4,8,6,5,1,2]=>[6,5,8,4,1,7,3,2]=>0110111
[3,8,6,2,5,7,4,1]=>[4,7,3,6,1,8,5,2]=>[3,8,6,1,5,7,4,2]=>0010111
[7,8,5,3,2,6,4,1]=>[4,3,6,5,8,1,7,2]=>[7,8,5,3,1,6,4,2]=>0111101
[1,8,6,3,7,5,2,4]=>[1,5,7,3,6,8,2,4]=>[1,8,6,3,7,5,2,4]=>0001111
[8,7,5,2,6,4,3,1]=>[3,4,6,5,7,2,8,1]=>[8,7,5,2,6,4,3,1]=>0111111
[8,7,1,6,2,5,4,3]=>[7,6,4,5,2,1,8,3]=>[5,4,2,6,1,8,7,3]=>0011111
[4,8,1,3,7,2,6,5]=>[8,7,1,4,6,2,3,5]=>[4,6,1,7,2,3,8,5]=>0000111
[5,1,7,6,8,3,2,4]=>[5,3,8,2,1,7,6,4]=>[7,6,8,3,2,5,1,4]=>0101011
[3,7,1,5,8,4,2,6]=>[7,4,3,8,1,2,5,6]=>[3,8,4,1,7,2,5,6]=>0010011
[6,7,3,1,8,4,2,5]=>[3,7,4,8,1,6,2,5]=>[6,8,4,1,7,3,2,5]=>0110011
[1,7,3,8,4,5,2,6]=>[1,5,7,8,4,2,3,6]=>[1,8,4,7,2,5,3,6]=>0001011
[1,7,2,8,5,3,4,6]=>[1,7,5,3,8,4,2,6]=>[1,8,5,3,4,7,2,6]=>0001011
[7,6,1,8,4,3,2,5]=>[6,3,4,7,1,8,2,5]=>[8,4,3,1,7,6,2,5]=>0110111
[8,6,1,7,4,2,5,3]=>[6,4,8,5,1,7,3,2]=>[5,1,7,4,3,8,6,2]=>0011111
[7,2,6,1,8,4,3,5]=>[6,7,4,8,3,2,1,5]=>[8,4,3,7,2,6,1,5]=>0010111
[8,2,6,1,7,3,5,4]=>[6,8,7,5,3,2,1,4]=>[5,3,7,2,8,1,6,4]=>0001111
[5,4,2,7,1,8,3,6]=>[7,4,5,8,3,2,1,6]=>[8,3,5,4,2,7,1,6]=>0011011
[4,7,5,6,8,3,2,1]=>[2,3,8,4,7,5,6,1]=>[4,7,5,6,8,3,2,1]=>1100011
[6,5,1,8,7,4,2,3]=>[5,4,1,6,7,2,8,3]=>[8,7,4,1,6,5,2,3]=>0011111
[8,6,4,7,5,3,2,1]=>[2,3,5,7,6,8,1,4]=>[8,6,3,2,1,7,5,4]=>1101111
[5,4,8,1,7,2,6,3]=>[8,7,6,5,4,2,1,3]=>[5,4,6,2,7,1,8,3]=>0001111
[7,5,8,3,2,6,4,1]=>[4,3,6,8,7,1,5,2]=>[7,3,1,8,5,6,4,2]=>0110111
[3,6,8,2,4,7,5,1]=>[5,7,3,1,8,6,4,2]=>[3,6,8,1,4,7,5,2]=>0001011
[5,7,3,8,2,6,4,1]=>[4,6,8,7,5,3,1,2]=>[5,7,3,8,1,6,4,2]=>0010111
[5,2,6,8,7,3,4,1]=>[4,5,7,3,2,6,8,1]=>[6,8,7,3,5,2,4,1]=>0011011
[2,3,8,7,4,5,6,1]=>[6,2,3,7,4,5,8,1]=>[2,3,8,7,4,5,6,1]=>0000111
[7,2,8,6,4,3,5,1]=>[5,7,4,6,3,8,2,1]=>[8,6,4,3,7,2,5,1]=>0011111
[2,1,8,7,5,6,3,4]=>[2,1,6,3,7,5,8,4]=>[2,1,8,7,5,6,3,4]=>1000111
[7,1,8,6,5,3,2,4]=>[7,3,5,2,6,8,1,4]=>[8,6,5,3,2,7,1,4]=>0101111
[1,2,8,7,6,3,4,5]=>[1,2,6,3,4,7,8,5]=>[1,2,8,7,6,3,4,5]=>0000111
[5,1,6,8,7,4,2,3]=>[5,4,2,7,1,6,8,3]=>[6,8,7,4,2,5,1,3]=>0011011
[6,8,7,2,5,4,3,1]=>[3,4,5,7,2,6,8,1]=>[6,8,7,2,5,4,3,1]=>0111011
[3,8,7,6,4,5,2,1]=>[2,5,3,6,4,7,8,1]=>[3,8,7,6,4,5,2,1]=>1001111
[2,8,7,6,5,3,4,1]=>[4,2,5,3,6,7,8,1]=>[2,8,7,6,5,3,4,1]=>0011111
[1,8,7,6,5,4,2,3]=>[1,4,2,5,6,7,8,3]=>[1,8,7,6,5,4,2,3]=>0011111
[5,8,6,7,3,4,1,2]=>[4,1,7,3,5,8,6,2]=>[5,8,6,7,3,4,1,2]=>0010011
[4,8,6,7,3,5,1,2]=>[5,1,7,4,3,8,6,2]=>[4,8,6,7,3,5,1,2]=>0001011
[1,8,6,7,4,5,2,3]=>[1,5,2,7,4,8,6,3]=>[1,8,6,7,4,5,2,3]=>0001011
[1,8,5,7,4,6,2,3]=>[1,6,2,7,8,4,5,3]=>[1,8,4,7,5,6,2,3]=>0000111
[4,8,5,7,3,6,1,2]=>[6,1,7,4,8,3,5,2]=>[4,8,3,7,5,6,1,2]=>0000111
[6,8,3,7,4,5,1,2]=>[5,1,8,7,4,6,3,2]=>[6,7,4,8,3,5,1,2]=>0001011
[5,8,3,7,4,6,1,2]=>[6,1,8,7,5,4,3,2]=>[5,7,4,8,3,6,1,2]=>0000111
[3,7,4,8,5,6,1,2]=>[6,1,3,7,8,5,4,2]=>[3,8,5,7,4,6,1,2]=>0000111
[4,7,3,8,5,6,1,2]=>[6,1,7,4,8,5,3,2]=>[4,8,5,7,3,6,1,2]=>0000111
[3,7,1,8,5,6,2,4]=>[7,6,3,2,8,5,1,4]=>[3,8,5,6,2,7,1,4]=>0000111
[3,7,2,8,5,6,1,4]=>[6,7,3,1,8,5,2,4]=>[3,8,5,7,1,6,2,4]=>0000111
[2,7,3,8,5,6,1,4]=>[6,2,7,1,8,5,3,4]=>[2,8,5,7,1,6,3,4]=>0000111
[2,7,4,8,5,6,1,3]=>[6,2,1,7,8,5,4,3]=>[2,8,5,7,4,6,1,3]=>0000111
[5,8,2,7,4,6,1,3]=>[6,8,1,7,5,4,2,3]=>[5,7,4,8,1,6,2,3]=>0000111
[6,8,2,7,4,5,1,3]=>[5,8,1,7,4,6,2,3]=>[6,7,4,8,1,5,2,3]=>0001011
[6,8,1,7,4,5,2,3]=>[8,5,2,7,4,6,1,3]=>[6,7,4,5,2,8,1,3]=>0001011
[5,8,1,7,4,6,2,3]=>[8,6,2,7,5,4,1,3]=>[5,7,4,6,2,8,1,3]=>0000111
[2,8,5,6,1,7,3,4]=>[6,2,7,3,8,5,1,4]=>[2,8,5,7,3,6,1,4]=>0000111
[1,8,5,6,2,7,3,4]=>[1,6,7,3,8,5,2,4]=>[1,8,5,7,3,6,2,4]=>0000111
[1,7,3,8,4,6,2,5]=>[1,6,7,8,2,4,3,5]=>[1,8,2,7,4,6,3,5]=>0000111
[4,8,1,7,3,6,2,5]=>[8,6,7,4,2,3,1,5]=>[4,7,2,6,3,8,1,5]=>0000111
[5,8,1,7,3,6,2,4]=>[8,6,7,2,5,3,1,4]=>[5,7,2,6,3,8,1,4]=>0000111
[6,8,2,7,3,5,1,4]=>[5,8,7,1,3,6,2,4]=>[6,7,1,8,3,5,2,4]=>0001011
[5,8,2,7,3,6,1,4]=>[6,8,7,1,5,3,2,4]=>[5,7,1,8,3,6,2,4]=>0000111
[2,7,3,8,4,6,1,5]=>[6,2,7,8,1,4,3,5]=>[2,8,1,7,4,6,3,5]=>0000111
[3,7,1,8,4,6,2,5]=>[7,6,3,8,2,4,1,5]=>[3,8,2,6,4,7,1,5]=>0000111
[1,8,4,7,3,6,2,5]=>[1,6,7,8,2,3,4,5]=>[1,8,2,7,3,6,4,5]=>0000111
[2,8,4,7,3,6,1,5]=>[6,2,7,8,1,3,4,5]=>[2,8,1,7,3,6,4,5]=>0000111
[3,8,4,7,2,6,1,5]=>[6,7,3,8,1,2,4,5]=>[3,8,1,7,2,6,4,5]=>0000111
[2,8,5,7,3,6,1,4]=>[6,2,7,1,8,3,5,4]=>[2,8,1,7,5,6,3,4]=>0000111
[1,8,6,7,3,5,2,4]=>[1,5,7,2,3,8,6,4]=>[1,8,6,7,2,5,3,4]=>0001011
[2,8,6,7,3,5,1,4]=>[5,2,7,1,3,8,6,4]=>[2,8,6,7,1,5,3,4]=>0001011
[5,8,6,7,2,4,1,3]=>[4,7,1,2,5,8,6,3]=>[5,8,6,7,1,4,2,3]=>0010011
[6,8,5,7,1,4,2,3]=>[7,4,2,1,8,6,5,3]=>[4,2,6,8,5,7,1,3]=>0010011
[5,8,6,7,1,4,2,3]=>[7,4,2,1,5,8,6,3]=>[4,2,5,8,6,7,1,3]=>0010011
[1,5,2,8,6,7,3,4]=>[1,5,7,3,2,8,6,4]=>[1,8,6,7,3,5,2,4]=>0001011
[2,6,1,8,5,7,3,4]=>[6,2,7,3,8,1,5,4]=>[2,8,3,7,5,6,1,4]=>0000111
[1,6,2,8,5,7,3,4]=>[1,6,7,3,8,2,5,4]=>[1,8,3,7,5,6,2,4]=>0000111
[3,8,5,7,1,6,2,4]=>[7,6,3,2,8,1,5,4]=>[3,8,2,6,5,7,1,4]=>0000111
[6,8,4,7,1,5,2,3]=>[7,5,2,8,1,6,4,3]=>[6,8,2,5,4,7,1,3]=>0001011
[7,8,3,6,1,5,2,4]=>[6,5,8,2,1,3,7,4]=>[7,8,2,5,1,6,3,4]=>0001101
[6,8,3,7,1,5,2,4]=>[7,5,8,2,1,6,3,4]=>[6,8,2,5,1,7,3,4]=>0001011
[3,8,4,7,1,6,2,5]=>[7,6,3,8,2,1,4,5]=>[3,8,2,6,1,7,4,5]=>0000111
[1,6,2,8,4,7,3,5]=>[1,6,7,8,3,2,4,5]=>[1,8,3,7,2,6,4,5]=>0000111
[2,6,1,8,4,7,3,5]=>[6,2,7,8,3,1,4,5]=>[2,8,3,7,1,6,4,5]=>0000111
[3,7,2,6,1,8,4,5]=>[6,7,3,8,4,2,1,5]=>[3,8,4,7,2,6,1,5]=>0000111
[7,8,1,5,2,6,3,4]=>[8,5,6,3,1,2,7,4]=>[6,3,5,1,7,8,2,4]=>0001101
[7,8,2,5,1,6,3,4]=>[5,8,6,3,2,1,7,4]=>[6,3,7,8,2,5,1,4]=>0001101
[6,8,2,5,1,7,3,4]=>[5,8,7,3,2,6,1,4]=>[6,7,3,8,2,5,1,4]=>0001011
[4,8,2,6,1,7,3,5]=>[6,8,7,4,3,2,1,5]=>[4,7,3,8,2,6,1,5]=>0000111
[1,7,3,6,2,8,4,5]=>[1,6,7,8,4,3,2,5]=>[1,8,4,7,3,6,2,5]=>0000111
[2,7,3,6,1,8,4,5]=>[6,2,7,8,4,3,1,5]=>[2,8,4,7,3,6,1,5]=>0000111
[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
[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]=>00000001
[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>[1,2,3,4,5,7,8,9,6]=>00000001
[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>[1,2,3,4,6,7,8,9,5]=>00000001
[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>[1,2,3,5,6,7,8,9,4]=>00000001
[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[1,2,4,5,6,7,8,9,3]=>00000001
[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>[1,3,4,5,6,7,8,9,2]=>00000001
[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
[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>00000011
[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,9,10,8]=>000000001
[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,8,7,9,6]=>00000011
[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[1,2,3,4,5,6,8,9,10,7]=>000000001
[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,9,7,6,8,5]=>[1,2,3,4,7,6,8,9,5]=>00000101
[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>[1,2,3,4,5,7,8,9,10,6]=>000000001
[1,2,3,6,5,7,8,9,4]=>[1,2,3,9,6,5,7,8,4]=>[1,2,3,6,5,7,8,9,4]=>00001001
[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>[1,2,3,4,6,7,8,9,10,5]=>000000001
[1,2,5,4,6,7,8,9,3]=>[1,2,9,5,4,6,7,8,3]=>[1,2,5,4,6,7,8,9,3]=>00010001
[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>[1,2,3,5,6,7,8,9,10,4]=>000000001
[1,4,3,5,6,7,8,9,2]=>[1,9,4,3,5,6,7,8,2]=>[1,4,3,5,6,7,8,9,2]=>00100001
[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>[1,2,4,5,6,7,8,9,10,3]=>000000001
[3,2,4,5,6,7,8,9,1]=>[9,3,2,4,5,6,7,8,1]=>[3,2,4,5,6,7,8,9,1]=>01000001
[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>[1,3,4,5,6,7,8,9,10,2]=>000000001
[6,7,4,8,3,5,1,2]=>[5,1,8,7,3,6,4,2]=>[6,7,3,8,4,5,1,2]=>0001011
[6,7,4,5,2,8,1,3]=>[8,5,1,7,4,6,2,3]=>[6,7,4,5,1,8,2,3]=>0001011
[5,7,4,6,2,3,1,8]=>[3,6,2,7,5,4,1,8]=>[5,7,4,6,2,3,1,8]=>0100110
[5,7,4,6,3,8,1,2]=>[8,1,6,7,5,4,3,2]=>[5,7,4,6,3,8,1,2]=>0000111
[5,7,4,8,3,6,1,2]=>[6,1,8,7,5,3,4,2]=>[5,7,3,8,4,6,1,2]=>0000111
[6,8,4,5,3,7,1,2]=>[7,1,5,8,4,6,3,2]=>[6,8,4,5,3,7,1,2]=>0001011
[5,8,4,6,3,7,1,2]=>[7,1,6,8,5,4,3,2]=>[5,8,4,6,3,7,1,2]=>0000111
[5,6,4,8,3,7,1,2]=>[7,1,8,6,5,4,3,2]=>[5,6,4,8,3,7,1,2]=>0000111
[5,6,3,7,2,8,1,4]=>[8,7,6,1,5,3,2,4]=>[5,6,1,7,3,8,2,4]=>0000111
[5,6,3,8,2,7,1,4]=>[7,8,6,1,5,3,2,4]=>[5,6,1,8,3,7,2,4]=>0000111
[5,8,4,6,2,7,1,3]=>[7,6,1,8,5,4,2,3]=>[5,8,4,6,1,7,2,3]=>0000111
[6,8,4,5,2,3,1,7]=>[3,5,2,8,4,6,1,7]=>[6,8,4,5,2,3,1,7]=>0101001
[5,6,4,8,2,3,1,7]=>[3,8,2,6,5,4,1,7]=>[5,6,4,8,2,3,1,7]=>0100101
[5,6,3,8,2,4,1,7]=>[4,8,6,2,5,3,1,7]=>[5,6,2,8,3,4,1,7]=>0010101
[4,6,3,5,2,7,1,8]=>[7,5,6,4,3,2,1,8]=>[4,6,3,5,2,7,1,8]=>0001110
[4,6,3,5,2,8,1,7]=>[8,5,6,4,3,2,1,7]=>[4,6,3,5,2,8,1,7]=>0001101
[4,6,3,8,2,5,1,7]=>[5,8,6,4,2,3,1,7]=>[4,6,2,8,3,5,1,7]=>0001101
[4,8,3,6,2,5,1,7]=>[5,6,8,4,2,3,1,7]=>[4,8,2,6,3,5,1,7]=>0001101
[7,8,3,5,2,4,1,6]=>[4,5,8,2,3,1,7,6]=>[7,8,2,5,3,4,1,6]=>0011001
[7,8,3,5,2,6,1,4]=>[6,5,8,1,3,2,7,4]=>[7,8,1,5,3,6,2,4]=>0001101
[4,8,3,6,2,7,1,5]=>[7,6,8,4,1,3,2,5]=>[4,8,1,6,3,7,2,5]=>0000111
[4,6,3,8,2,7,1,5]=>[7,8,6,4,1,3,2,5]=>[4,6,1,8,3,7,2,5]=>0000111
[4,6,3,7,2,8,1,5]=>[8,7,6,4,1,3,2,5]=>[4,6,1,7,3,8,2,5]=>0000111
[4,7,3,6,2,5,1,8]=>[5,6,7,4,2,3,1,8]=>[4,7,2,6,3,5,1,8]=>0001110
[5,7,4,8,2,6,1,3]=>[6,8,1,7,5,2,4,3]=>[5,7,1,8,4,6,2,3]=>0000111
[5,7,3,6,2,8,1,4]=>[8,6,7,1,5,3,2,4]=>[5,7,1,6,3,8,2,4]=>0000111
[6,7,3,5,2,4,1,8]=>[4,5,7,2,3,6,1,8]=>[6,7,2,5,3,4,1,8]=>0011010
[6,7,4,8,2,5,1,3]=>[5,8,1,7,2,6,4,3]=>[6,7,1,8,4,5,2,3]=>0001011
[6,7,5,8,2,4,1,3]=>[4,8,1,2,7,6,5,3]=>[6,7,5,8,1,4,2,3]=>0010011
[6,7,4,8,2,3,1,5]=>[3,8,2,7,1,6,4,5]=>[6,7,2,3,1,8,4,5]=>0100011
[6,7,3,8,2,4,1,5]=>[4,8,7,2,1,6,3,5]=>[6,7,2,8,1,4,3,5]=>0010011
[6,7,3,4,2,8,1,5]=>[8,4,7,3,1,6,2,5]=>[6,7,3,4,1,8,2,5]=>0010011
[5,7,3,4,2,6,1,8]=>[6,4,7,3,5,2,1,8]=>[5,7,3,4,2,6,1,8]=>0010110
[5,7,3,4,2,8,1,6]=>[8,4,7,3,5,1,2,6]=>[5,7,3,4,1,8,2,6]=>0010011
[6,8,4,7,2,3,1,5]=>[3,7,2,8,1,6,4,5]=>[6,8,2,3,1,7,4,5]=>0100011
[5,8,3,7,2,4,1,6]=>[4,7,8,2,5,1,3,6]=>[5,8,2,7,1,4,3,6]=>0010011
[4,7,3,8,2,5,1,6]=>[5,8,7,4,2,1,3,6]=>[4,7,2,8,1,5,3,6]=>0001011
[4,7,3,5,2,6,1,8]=>[6,5,7,4,3,2,1,8]=>[4,7,3,5,2,6,1,8]=>0001110
[4,5,3,7,2,6,1,8]=>[6,7,5,4,3,2,1,8]=>[4,5,3,7,2,6,1,8]=>0001110
[4,5,3,7,2,8,1,6]=>[8,7,5,4,3,1,2,6]=>[4,5,3,7,1,8,2,6]=>0001011
[4,5,3,8,2,7,1,6]=>[7,8,5,4,3,1,2,6]=>[4,5,3,8,1,7,2,6]=>0001011
[5,8,3,4,2,7,1,6]=>[7,4,8,3,5,1,2,6]=>[5,8,3,4,1,7,2,6]=>0010011
[6,8,3,4,2,7,1,5]=>[7,4,8,3,1,6,2,5]=>[6,8,3,4,1,7,2,5]=>0010011
[6,8,3,4,2,5,1,7]=>[5,4,8,3,2,6,1,7]=>[6,8,3,4,2,5,1,7]=>0011001
[5,8,3,4,2,6,1,7]=>[6,4,8,3,5,2,1,7]=>[5,8,3,4,2,6,1,7]=>0010101
[4,8,3,5,2,6,1,7]=>[6,5,8,4,3,2,1,7]=>[4,8,3,5,2,6,1,7]=>0001101
[4,5,3,8,2,6,1,7]=>[6,8,5,4,3,2,1,7]=>[4,5,3,8,2,6,1,7]=>0001101
[4,5,3,6,2,8,1,7]=>[8,6,5,4,3,2,1,7]=>[4,5,3,6,2,8,1,7]=>0001101
[4,7,5,2,1,8,3,6]=>[2,5,7,4,8,1,3,6]=>[4,8,2,1,7,5,3,6]=>1001011
[4,8,5,2,1,7,6,3]=>[2,5,8,4,6,7,3,1]=>[4,7,6,3,8,5,2,1]=>1001111
[4,6,5,2,1,3,8,7]=>[2,5,1,4,6,3,8,7]=>[4,6,5,2,1,3,8,7]=>1001101
[5,6,4,2,3,1,8,7]=>[3,4,2,6,5,1,8,7]=>[5,6,4,2,3,1,8,7]=>0110101
[6,4,5,3,1,2,8,7]=>[3,1,5,6,4,2,8,7]=>[6,4,5,3,1,2,8,7]=>0101101
[5,4,6,1,3,2,8,7]=>[6,3,1,5,4,2,8,7]=>[3,1,5,4,6,2,8,7]=>0101101
[4,6,8,1,7,3,2,5]=>[8,3,7,4,2,6,1,5]=>[4,6,7,3,2,8,1,5]=>0100011
[4,7,8,1,6,3,5,2]=>[8,5,6,4,3,1,7,2]=>[4,6,3,5,1,7,8,2]=>0001101
[7,4,8,1,6,5,3,2]=>[8,3,5,6,7,1,2,4]=>[7,3,1,6,5,2,8,4]=>0101111
[5,6,8,7,2,1,3,4]=>[2,7,1,3,5,6,8,4]=>[5,6,8,7,2,1,3,4]=>1000011
[8,5,7,6,4,2,1,3]=>[2,4,1,6,7,8,3,5]=>[8,4,2,1,3,7,6,5]=>1010111
[8,4,6,3,7,2,1,5]=>[2,7,6,8,1,4,3,5]=>[8,2,1,6,4,7,3,5]=>1000111
[6,3,2,8,7,4,1,5]=>[4,3,7,6,2,1,8,5]=>[6,3,2,8,7,4,1,5]=>0110111
[2,1,6,8,7,4,3,5]=>[2,1,4,7,3,6,8,5]=>[2,1,6,8,7,4,3,5]=>1010011
[2,1,7,8,6,4,5,3]=>[2,1,5,6,4,8,7,3]=>[2,1,7,8,6,4,5,3]=>1001101
[7,3,2,8,6,4,5,1]=>[5,3,7,6,4,8,2,1]=>[8,6,4,7,3,2,5,1]=>0101111
[7,6,8,5,2,4,3,1]=>[3,4,5,1,8,7,6,2]=>[7,6,8,5,1,4,3,2]=>0111011
[5,7,8,6,2,3,1,4]=>[3,6,2,1,5,8,7,4]=>[5,7,8,6,2,3,1,4]=>0100101
[5,8,7,6,3,2,1,4]=>[2,3,6,1,5,7,8,4]=>[5,8,7,6,3,2,1,4]=>1100111
[6,8,7,5,3,2,4,1]=>[4,3,5,2,7,6,8,1]=>[6,8,7,5,3,2,4,1]=>0111011
[5,8,4,2,3,7,6,1]=>[6,4,1,7,5,8,3,2]=>[5,8,4,1,3,7,6,2]=>0010111
[7,8,4,2,6,5,3,1]=>[3,5,4,6,8,2,7,1]=>[7,8,4,2,6,5,3,1]=>0111101
[4,8,7,2,6,3,5,1]=>[5,7,6,4,3,2,8,1]=>[4,6,3,8,7,2,5,1]=>0001111
[4,8,6,2,7,3,1,5]=>[3,7,6,4,2,8,1,5]=>[4,8,6,2,7,3,1,5]=>0100111
[3,6,1,8,7,4,2,5]=>[6,4,3,7,2,1,8,5]=>[3,8,7,4,2,6,1,5]=>0010111
[3,7,1,8,6,4,5,2]=>[7,5,3,6,4,8,1,2]=>[3,8,6,4,5,1,7,2]=>0001111
[3,8,1,6,7,5,2,4]=>[8,5,3,2,7,1,6,4]=>[3,7,5,2,6,8,1,4]=>0001011
[3,7,1,6,8,2,5,4]=>[7,8,3,5,2,1,6,4]=>[3,5,2,8,1,6,7,4]=>0001011
[6,7,4,2,8,1,5,3]=>[8,4,7,5,1,6,3,2]=>[5,1,6,7,4,3,8,2]=>0011011
[6,8,4,2,7,5,1,3]=>[5,4,2,7,8,6,1,3]=>[6,8,4,2,7,5,1,3]=>0011011
[2,1,8,6,7,5,3,4]=>[2,1,5,3,7,8,6,4]=>[2,1,8,6,7,5,3,4]=>1001011
[8,3,2,6,7,5,1,4]=>[5,3,7,2,8,1,6,4]=>[8,3,2,6,7,5,1,4]=>0101011
[8,6,4,3,7,5,1,2]=>[5,1,4,7,6,8,2,3]=>[8,6,4,1,2,7,5,3]=>0011111
[5,8,6,7,3,1,2,4]=>[3,1,7,2,5,8,6,4]=>[5,8,6,7,3,1,2,4]=>0100011
[6,7,5,8,1,3,4,2]=>[8,4,1,3,7,6,5,2]=>[4,1,3,6,7,5,8,2]=>0010011
[7,6,5,8,1,4,3,2]=>[8,3,4,1,6,7,5,2]=>[4,3,1,7,6,5,8,2]=>0110111
[7,3,2,6,8,1,5,4]=>[8,3,7,5,1,2,6,4]=>[5,3,1,7,2,6,8,4]=>0101011
[2,1,7,6,8,3,5,4]=>[2,1,8,5,3,7,6,4]=>[2,1,5,3,7,6,8,4]=>1001011
[7,5,6,8,1,4,2,3]=>[8,4,2,1,7,5,6,3]=>[4,2,7,5,6,8,1,3]=>0010011
[6,5,7,8,1,2,4,3]=>[8,1,4,2,6,5,7,3]=>[4,1,2,6,5,7,8,3]=>0010101
[8,1,3,7,4,6,5,2]=>[8,5,1,6,7,2,3,4]=>[7,1,6,5,2,3,8,4]=>0001111
[5,2,8,7,4,6,1,3]=>[6,5,1,7,2,4,8,3]=>[8,7,1,5,4,6,2,3]=>0001111
[6,1,5,4,3,8,7,2]=>[6,7,4,5,1,3,8,2]=>[5,4,1,8,7,3,6,2]=>0011111
[7,1,5,3,4,8,6,2]=>[7,6,5,3,1,8,4,2]=>[5,3,8,6,1,4,7,2]=>0001111
[8,1,3,4,5,6,7,2]=>[8,7,1,3,4,5,6,2]=>[7,1,3,4,5,6,8,2]=>0000011
[6,5,2,8,4,1,3,7]=>[4,8,2,5,6,1,3,7]=>[6,5,2,8,4,1,3,7]=>0011101
[5,6,2,1,4,8,3,7]=>[2,6,8,1,5,4,3,7]=>[5,8,2,1,4,6,3,7]=>1000101
[1,2,6,3,5,4,7,8]=>[1,2,6,5,3,4,7,8]=>[1,2,5,3,6,4,7,8]=>0001100
[4,3,1,2,6,8,5,7]=>[3,1,4,2,8,6,5,7]=>[4,3,1,2,6,8,5,7]=>0110001
[5,8,1,6,3,2,4,7]=>[8,3,6,2,5,1,4,7]=>[5,6,3,2,8,1,4,7]=>0100101
[8,5,6,4,2,1,7,3]=>[2,4,6,7,8,5,3,1]=>[8,5,7,3,6,4,2,1]=>1010111
[6,1,2,3,8,5,7,4]=>[6,1,2,7,8,3,5,4]=>[8,1,2,3,7,5,6,4]=>0000111
[7,2,1,3,8,6,4,5]=>[2,7,1,6,4,8,3,5]=>[8,6,4,7,2,1,3,5]=>1000111
[1,5,7,3,2,4,6,8]=>[1,3,7,2,5,4,6,8]=>[1,5,7,3,2,4,6,8]=>0100010
[5,2,7,3,1,8,4,6]=>[3,7,5,8,1,4,2,6]=>[8,1,5,4,7,3,2,6]=>0101011
[5,8,2,4,1,3,7,6]=>[4,8,1,2,5,7,3,6]=>[5,7,1,4,2,3,8,6]=>0010011
[3,1,8,6,4,2,7,5]=>[3,4,1,6,8,7,5,2]=>[7,5,8,6,4,1,3,2]=>0110111
[3,5,8,7,2,4,1,6]=>[4,7,3,2,5,1,8,6]=>[3,5,8,7,2,4,1,6]=>0010011
[4,2,1,3,7,8,5,6]=>[2,4,1,3,8,5,7,6]=>[4,2,1,3,7,8,5,6]=>1010001
[2,4,1,3,8,7,5,6]=>[4,2,1,3,7,5,8,6]=>[2,4,1,3,8,7,5,6]=>0010011
[2,8,1,3,6,4,7,5]=>[8,2,1,6,7,3,4,5]=>[2,7,1,3,6,4,8,5]=>0000111
[6,8,2,3,4,1,5,7]=>[4,8,2,3,1,6,5,7]=>[6,8,2,3,4,1,5,7]=>0010001
[5,1,8,3,2,4,6,7]=>[5,3,8,2,1,4,6,7]=>[8,3,2,5,1,4,6,7]=>0101001
[9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[8,9,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,9,8,1]=>[8,9,7,6,5,4,3,2,1]=>11111101
[8,7,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,8,7,1]=>[8,7,9,6,5,4,3,2,1]=>11111011
[8,7,6,9,5,4,3,2,1]=>[2,3,4,5,9,7,8,6,1]=>[8,7,6,9,5,4,3,2,1]=>11110111
[8,7,6,5,9,4,3,2,1]=>[2,3,4,9,6,7,8,5,1]=>[8,7,6,5,9,4,3,2,1]=>11101111
[8,7,6,5,4,9,3,2,1]=>[2,3,9,5,6,7,8,4,1]=>[8,7,6,5,4,9,3,2,1]=>11011111
[8,7,6,5,4,3,9,2,1]=>[2,9,4,5,6,7,8,3,1]=>[8,7,6,5,4,3,9,2,1]=>10111111
[8,7,6,5,4,3,2,9,1]=>[9,3,4,5,6,7,8,2,1]=>[8,7,6,5,4,3,2,9,1]=>01111111
[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,1,9]=>[8,7,6,5,4,3,2,1,9]=>11111110
[9,10,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,10,9,1]=>[9,10,8,7,6,5,4,3,2,1]=>111111101
[7,8,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,7,8,1]=>[7,8,9,6,5,4,3,2,1]=>11111001
[9,8,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,9,8,1]=>[9,8,10,7,6,5,4,3,2,1]=>111111011
[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,8,9,7,1]=>[9,8,7,10,6,5,4,3,2,1]=>111110111
[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,10,7,8,9,6,1]=>[9,8,7,6,10,5,4,3,2,1]=>111101111
[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,10,6,7,8,9,5,1]=>[9,8,7,6,5,10,4,3,2,1]=>111011111
[9,8,7,6,5,4,10,3,2,1]=>[2,3,10,5,6,7,8,9,4,1]=>[9,8,7,6,5,4,10,3,2,1]=>110111111
[9,8,7,6,5,4,3,10,2,1]=>[2,10,4,5,6,7,8,9,3,1]=>[9,8,7,6,5,4,3,10,2,1]=>101111111
[8,7,6,5,4,3,1,2,9]=>[3,1,4,5,6,7,8,2,9]=>[8,7,6,5,4,3,1,2,9]=>01111110
[9,8,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,8,9,2,1]=>[9,8,7,6,5,4,3,2,10,1]=>011111111
[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[1,4,2,7,8,6,3,5]=>[1,4,6,2,3,8,7,5]=>[1,7,8,6,2,4,3,5]=>0010101
[1,6,2,4,7,5,3,8]=>[1,6,5,2,7,4,3,8]=>[1,7,5,2,4,6,3,8]=>0001110
[1,7,3,8,5,2,4,6]=>[1,5,8,3,7,4,2,6]=>[1,7,3,4,8,5,2,6]=>0001011
[1,7,3,2,8,6,4,5]=>[1,3,7,6,4,8,2,5]=>[1,8,6,4,7,3,2,5]=>0100111
[7,2,3,1,8,5,6,4]=>[3,7,2,6,8,5,1,4]=>[8,5,6,2,3,1,7,4]=>0100111
[6,2,8,3,5,1,7,4]=>[5,6,8,7,3,2,1,4]=>[7,3,8,2,6,1,5,4]=>0001111
[1,3,6,4,8,5,7,2]=>[1,7,3,6,8,4,5,2]=>[1,3,8,4,6,5,7,2]=>0000111
[6,2,4,7,5,8,1,3]=>[8,6,1,2,7,4,5,3]=>[7,1,4,6,5,8,2,3]=>0000111
[7,8,2,1,4,3,5,6]=>[2,8,4,1,3,5,7,6]=>[4,2,1,7,8,3,5,6]=>1010001
[7,5,4,2,6,8,1,3]=>[8,4,1,5,7,2,6,3]=>[7,5,4,1,6,8,2,3]=>0011011
[1,7,5,3,4,6,8,2]=>[1,8,5,3,7,4,6,2]=>[1,7,5,3,4,6,8,2]=>0001011
[8,2,5,4,6,7,1,3]=>[7,8,1,5,2,4,6,3]=>[5,1,8,4,6,7,2,3]=>0001011
[8,2,6,4,3,1,7,5]=>[3,4,6,8,7,2,1,5]=>[7,2,8,4,3,1,6,5]=>0110111
[1,2,8,4,3,5,6,7]=>[1,2,4,8,3,5,6,7]=>[1,2,8,4,3,5,6,7]=>0010001
[1,7,4,2,3,5,6,8]=>[1,4,2,7,3,5,6,8]=>[1,7,4,2,3,5,6,8]=>0010010
[6,8,4,1,3,2,5,7]=>[4,3,1,8,2,6,5,7]=>[3,1,6,8,4,2,5,7]=>0110001
[1,8,7,4,3,2,5,6]=>[1,3,4,7,2,5,8,6]=>[1,8,7,4,3,2,5,6]=>0110011
[1,6,3,8,2,4,7,5]=>[1,8,6,2,7,3,4,5]=>[1,7,2,6,3,4,8,5]=>0000111
[1,4,6,2,8,3,7,5]=>[1,6,8,4,7,2,3,5]=>[1,4,7,2,8,3,6,5]=>0000111
[5,3,6,1,2,8,4,7]=>[6,1,5,8,3,2,4,7]=>[8,3,5,1,2,6,4,7]=>0001101
[6,3,4,1,2,5,8,7]=>[4,1,6,3,2,5,8,7]=>[6,3,4,1,2,5,8,7]=>0010101
[6,3,1,4,2,7,5,8]=>[3,6,4,2,7,1,5,8]=>[4,2,7,3,1,6,5,8]=>0110110
[1,8,3,2,4,5,6,7]=>[1,3,8,2,4,5,6,7]=>[1,8,3,2,4,5,6,7]=>0100001
[8,6,3,2,4,1,7,5]=>[4,3,6,2,8,7,5,1]=>[7,5,8,6,3,2,4,1]=>0110111
[4,5,2,6,8,1,7,3]=>[8,5,7,4,2,6,1,3]=>[4,6,7,2,5,1,8,3]=>0001011
[4,2,5,6,7,8,1,3]=>[8,4,1,2,5,6,7,3]=>[4,1,5,6,7,8,2,3]=>0010001
[7,2,3,1,4,5,8,6]=>[3,7,2,1,4,8,5,6]=>[8,2,3,1,4,5,7,6]=>0100011
[8,6,1,4,3,2,5,7]=>[6,3,4,1,2,8,5,7]=>[4,3,1,8,6,2,5,7]=>0110101
[8,1,2,4,6,5,3,7]=>[8,1,5,2,6,4,3,7]=>[6,5,1,2,4,8,3,7]=>0001101
[8,1,2,6,4,5,3,7]=>[8,1,5,6,4,2,3,7]=>[6,4,5,1,2,8,3,7]=>0001101
[8,1,2,5,6,4,3,7]=>[8,1,4,6,2,5,3,7]=>[6,4,1,2,5,8,3,7]=>0010101
[8,1,2,6,5,4,3,7]=>[8,1,4,5,6,2,3,7]=>[6,5,4,1,2,8,3,7]=>0011101
[5,1,4,8,2,7,3,6]=>[5,8,7,1,4,3,2,6]=>[7,1,4,8,3,5,2,6]=>0001011
[1,4,6,8,2,7,3,5]=>[1,8,7,4,3,6,2,5]=>[1,4,6,7,3,8,2,5]=>0000011
[1,4,7,6,2,8,3,5]=>[1,6,7,4,2,8,3,5]=>[1,4,8,2,7,6,3,5]=>0000111
[1,7,4,5,2,8,3,6]=>[1,5,8,7,4,3,2,6]=>[1,7,4,8,3,5,2,6]=>0001011
[1,4,6,2,8,7,3,5]=>[1,6,7,4,3,2,8,5]=>[1,4,8,7,3,6,2,5]=>0000111
[1,4,2,8,6,7,3,5]=>[1,4,7,2,3,8,6,5]=>[1,8,6,7,2,4,3,5]=>0010011
[3,1,2,6,4,8,7,5]=>[3,1,2,6,7,4,8,5]=>[3,1,2,8,7,4,6,5]=>0100111
[3,1,2,7,4,6,8,5]=>[3,1,2,7,8,4,6,5]=>[3,1,2,8,4,6,7,5]=>0100011
[1,2,3,6,8,5,7,4]=>[1,2,3,7,8,6,5,4]=>[1,2,3,6,8,5,7,4]=>0000011
[5,1,4,2,7,8,3,6]=>[5,4,8,1,2,3,7,6]=>[7,8,1,4,2,5,3,6]=>0011001
[1,4,2,7,6,8,3,5]=>[1,4,8,2,3,7,6,5]=>[1,7,6,8,2,4,3,5]=>0010011
[3,1,2,8,4,6,7,5]=>[3,1,2,8,7,4,6,5]=>[3,1,2,7,4,6,8,5]=>0100011
[1,8,7,3,4,2,5,6]=>[1,4,7,3,2,5,8,6]=>[1,8,7,3,4,2,5,6]=>0010011
[1,4,2,7,8,3,6,5]=>[1,4,8,2,6,3,7,5]=>[1,6,2,4,3,7,8,5]=>0010101
[1,4,2,6,8,3,7,5]=>[1,4,8,2,7,6,3,5]=>[1,6,7,2,4,3,8,5]=>0010011
[1,2,3,7,8,5,6,4]=>[1,2,3,6,8,5,7,4]=>[1,2,3,7,8,5,6,4]=>0000101
[1,2,3,7,5,8,6,4]=>[1,2,3,6,8,7,4,5]=>[1,2,3,7,4,8,6,5]=>0000111
[1,4,2,7,3,8,6,5]=>[1,4,7,2,6,8,3,5]=>[1,8,6,2,4,3,7,5]=>0010111
[3,1,7,2,8,6,4,5]=>[3,7,1,6,4,8,2,5]=>[8,6,4,7,1,3,2,5]=>0100111
[2,1,7,8,3,4,6,5]=>[2,1,8,3,6,4,7,5]=>[2,1,6,3,4,7,8,5]=>1000101
[1,2,3,8,7,5,6,4]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,5,6,4]=>0000111
[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>000000001
[10,9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,10,8]=>[10,9,1,2,3,4,5,6,7,8]=>000000011
[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>0000000001
[10,1,2,11,3,4,5,6,7,8,9]=>[10,1,11,3,4,5,6,7,8,2,9]=>[11,3,4,5,6,7,8,10,1,2,9]=>0000000011
[2,9,10,1,3,4,5,6,7,8]=>[10,2,1,3,4,5,6,7,9,8]=>[2,9,10,1,3,4,5,6,7,8]=>000000001
[11,1,10,2,3,4,5,6,7,8,9]=>[11,10,2,3,4,5,6,7,8,1,9]=>[10,2,3,4,5,6,7,8,11,1,9]=>0000000011
[11,10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,11,9]=>[11,10,1,2,3,4,5,6,7,8,9]=>0000000011
[5,7,8,4,2,6,1,3]=>[6,4,1,8,5,2,7,3]=>[5,7,8,4,1,6,2,3]=>0010101
[8,6,3,7,2,1,5,4]=>[2,7,6,5,1,8,3,4]=>[5,2,1,8,6,3,7,4]=>1001111
[7,6,3,8,2,1,5,4]=>[2,8,6,5,1,7,3,4]=>[5,2,1,7,6,3,8,4]=>1001111
[6,7,8,3,2,1,5,4]=>[2,3,8,5,1,6,7,4]=>[5,3,2,1,6,7,8,4]=>1101001
[5,7,8,3,2,1,6,4]=>[2,3,8,6,5,1,7,4]=>[5,6,3,2,1,7,8,4]=>1100101
[3,7,8,4,2,5,1,6]=>[5,4,3,8,2,1,7,6]=>[3,7,8,4,2,5,1,6]=>0011001
[4,7,8,3,2,1,5,6]=>[2,3,8,4,1,5,7,6]=>[4,7,8,3,2,1,5,6]=>1100001
[5,7,8,3,2,1,4,6]=>[2,3,8,1,5,4,7,6]=>[5,7,8,3,2,1,4,6]=>1100001
[7,6,3,8,2,1,4,5]=>[2,8,6,1,4,7,3,5]=>[7,6,2,1,4,8,3,5]=>1000111
[5,6,3,8,2,1,4,7]=>[2,8,6,1,5,3,4,7]=>[5,6,2,1,8,3,4,7]=>1000101
[3,6,4,8,2,5,1,7]=>[5,8,3,6,2,4,1,7]=>[3,6,2,8,4,5,1,7]=>0001101
[2,6,4,8,3,5,7,1]=>[7,2,8,6,3,4,5,1]=>[2,6,3,8,4,5,7,1]=>0000111
[3,6,4,7,2,5,1,8]=>[5,7,3,6,2,4,1,8]=>[3,6,2,7,4,5,1,8]=>0001110
[8,4,3,2,1,6,5,7]=>[2,3,4,8,6,1,5,7]=>[6,4,3,2,1,8,5,7]=>1110101
[6,4,3,2,1,7,5,8]=>[2,3,4,6,7,1,5,8]=>[7,4,3,2,1,6,5,8]=>1110110
[4,5,3,2,7,1,6,8]=>[7,3,5,4,2,1,6,8]=>[4,5,3,2,7,1,6,8]=>0101010
[3,5,4,2,8,6,1,7]=>[6,4,3,5,2,8,1,7]=>[3,5,4,2,8,6,1,7]=>0011101
[6,4,3,2,1,8,5,7]=>[2,3,4,6,8,1,5,7]=>[8,4,3,2,1,6,5,7]=>1110101
[8,4,3,2,1,7,5,6]=>[2,3,4,8,7,5,1,6]=>[7,5,8,4,3,2,1,6]=>1110011
[8,4,3,2,1,7,6,5]=>[2,3,4,8,6,7,1,5]=>[7,6,4,3,2,1,8,5]=>1110111
[7,4,3,2,1,8,6,5]=>[2,3,4,7,6,8,1,5]=>[8,6,4,3,2,1,7,5]=>1110111
[5,6,3,8,2,1,7,4]=>[2,8,6,7,5,3,1,4]=>[5,7,3,6,2,1,8,4]=>1000111
[7,5,3,2,8,1,6,4]=>[8,3,5,7,6,1,4,2]=>[6,3,1,7,5,4,8,2]=>0101111
[6,5,4,2,8,7,1,3]=>[7,4,1,5,6,2,8,3]=>[6,5,4,1,8,7,2,3]=>0011111
[2,6,5,7,8,3,4,1]=>[4,2,8,3,6,5,7,1]=>[2,6,5,7,8,3,4,1]=>0010101
[6,5,4,2,7,8,1,3]=>[8,4,1,5,6,2,7,3]=>[6,5,4,1,7,8,2,3]=>0011101
[8,5,4,2,6,7,1,3]=>[7,4,1,5,8,2,6,3]=>[8,5,4,1,6,7,2,3]=>0011011
[8,5,3,2,6,1,7,4]=>[6,3,5,8,7,4,1,2]=>[7,4,8,5,3,1,6,2]=>0101111
[5,6,3,7,2,1,8,4]=>[2,7,6,8,5,3,1,4]=>[5,8,3,6,2,1,7,4]=>1000111
[3,6,4,7,2,8,1,5]=>[8,7,3,6,1,4,2,5]=>[3,6,1,7,4,8,2,5]=>0000111
[2,6,4,7,3,8,5,1]=>[5,2,8,7,6,1,4,3]=>[2,6,1,7,4,8,5,3]=>0001111
[3,5,4,2,7,8,1,6]=>[8,4,3,5,2,1,7,6]=>[3,5,4,2,7,8,1,6]=>0011001
[7,4,3,2,1,6,8,5]=>[2,3,4,7,8,1,6,5]=>[8,4,3,2,1,6,7,5]=>1110011
[8,4,3,2,1,6,7,5]=>[2,3,4,8,7,1,6,5]=>[7,4,3,2,1,6,8,5]=>1110011
[8,4,3,2,1,5,7,6]=>[2,3,4,8,1,7,5,6]=>[7,4,3,2,1,5,8,6]=>1110011
[7,4,3,2,1,5,8,6]=>[2,3,4,7,1,8,5,6]=>[8,4,3,2,1,5,7,6]=>1110011
[3,5,4,2,6,8,1,7]=>[8,4,3,5,2,6,1,7]=>[3,5,4,2,6,8,1,7]=>0011001
[5,6,3,4,1,2,8,7]=>[4,1,6,3,5,2,8,7]=>[5,6,3,4,1,2,8,7]=>0010101
[8,5,3,7,2,6,4,1]=>[4,6,7,5,8,3,1,2]=>[8,5,3,7,1,6,4,2]=>0011111
[7,5,8,4,2,6,1,3]=>[6,4,1,8,7,2,5,3]=>[7,4,1,8,5,6,2,3]=>0010111
[2,1,7,8,5,6,3,4]=>[2,1,6,3,8,5,7,4]=>[2,1,7,8,5,6,3,4]=>1000101
[6,8,3,7,5,1,4,2]=>[5,4,7,3,8,6,1,2]=>[6,8,3,4,1,7,5,2]=>0011011
[5,7,3,8,1,6,2,4]=>[8,6,7,2,5,1,3,4]=>[5,7,2,6,1,8,3,4]=>0000111
[3,2,5,8,4,6,1,7]=>[6,3,2,8,5,4,1,7]=>[3,2,5,8,4,6,1,7]=>0100101
[3,5,2,4,1,7,6,8]=>[4,5,3,2,1,7,6,8]=>[3,5,2,4,1,7,6,8]=>0011010
[4,5,2,3,7,1,6,8]=>[7,5,2,4,3,1,6,8]=>[4,5,2,3,7,1,6,8]=>0001010
[4,2,5,3,8,1,6,7]=>[8,4,5,2,3,1,6,7]=>[5,2,4,3,8,1,6,7]=>0011001
[4,2,5,8,3,1,6,7]=>[3,8,4,1,5,2,6,7]=>[4,1,5,8,3,2,6,7]=>0110001
[3,1,5,4,2,8,6,7]=>[3,4,1,5,2,8,6,7]=>[5,4,1,3,2,8,6,7]=>0111001
[4,1,5,3,8,2,6,7]=>[4,8,5,1,3,2,6,7]=>[5,1,8,3,4,2,6,7]=>0011001
[4,1,5,8,3,2,6,7]=>[4,3,8,1,5,2,6,7]=>[5,8,3,1,4,2,6,7]=>0110001
[4,3,8,5,2,1,6,7]=>[2,5,4,3,8,1,6,7]=>[4,3,8,5,2,1,6,7]=>1011001
[4,7,3,5,2,1,6,8]=>[2,5,7,4,3,1,6,8]=>[4,7,3,5,2,1,6,8]=>1001010
[4,3,2,7,5,1,6,8]=>[5,3,4,2,7,1,6,8]=>[4,3,2,7,5,1,6,8]=>0111010
[4,3,6,2,5,1,7,8]=>[5,6,4,3,2,1,7,8]=>[4,3,6,2,5,1,7,8]=>0011100
[4,6,3,2,5,1,7,8]=>[5,3,6,4,2,1,7,8]=>[4,6,3,2,5,1,7,8]=>0101100
[4,5,1,3,7,2,6,8]=>[5,7,1,4,3,2,6,8]=>[4,7,1,3,5,2,6,8]=>0001010
[3,5,1,4,2,7,6,8]=>[5,4,3,1,2,7,6,8]=>[3,4,1,5,2,7,6,8]=>0011010
[2,5,1,4,3,7,8,6]=>[5,2,4,1,3,8,7,6]=>[2,4,1,5,3,7,8,6]=>0011001
[5,2,1,4,3,7,8,6]=>[2,5,4,1,3,8,7,6]=>[4,2,1,5,3,7,8,6]=>1011001
[5,3,1,4,2,7,6,8]=>[3,5,4,2,1,7,6,8]=>[4,2,5,3,1,7,6,8]=>0111010
[4,3,1,7,5,2,6,8]=>[3,4,5,2,7,1,6,8]=>[7,5,2,4,3,1,6,8]=>0111010
[4,3,6,1,5,2,7,8]=>[6,5,4,3,1,2,7,8]=>[4,3,5,1,6,2,7,8]=>0011100
[4,6,3,1,5,2,7,8]=>[3,6,5,4,2,1,7,8]=>[4,5,2,6,3,1,7,8]=>0101100
[4,3,6,1,7,2,5,8]=>[6,7,4,3,2,1,5,8]=>[4,3,7,2,6,1,5,8]=>0010110
[6,3,4,1,2,7,5,8]=>[4,1,6,3,7,2,5,8]=>[7,3,4,1,2,6,5,8]=>0010110
[6,2,4,1,3,7,8,5]=>[4,6,1,2,8,3,7,5]=>[7,8,1,4,2,3,6,5]=>0010101
[3,6,4,1,2,7,5,8]=>[4,1,3,6,7,2,5,8]=>[3,7,4,1,2,6,5,8]=>0010110
[4,6,3,1,7,2,5,8]=>[3,6,7,4,1,2,5,8]=>[4,7,1,6,3,2,5,8]=>0100110
[5,3,6,2,1,4,7,8]=>[2,6,5,1,3,4,7,8]=>[5,2,1,6,3,4,7,8]=>1001100
[4,5,2,7,3,1,6,8]=>[3,7,5,4,1,2,6,8]=>[4,5,1,7,3,2,6,8]=>0101010
[4,6,7,2,3,1,5,8]=>[3,7,2,4,1,6,5,8]=>[4,6,7,2,3,1,5,8]=>0100010
[3,2,6,1,4,7,5,8]=>[6,3,2,1,7,4,5,8]=>[3,2,7,1,4,6,5,8]=>0100110
[3,6,7,2,4,5,1,8]=>[5,7,3,2,4,6,1,8]=>[3,6,7,2,4,5,1,8]=>0001010
[3,5,2,7,4,6,1,8]=>[6,5,3,7,2,4,1,8]=>[3,7,2,5,4,6,1,8]=>0001110
[3,7,2,4,8,5,1,6]=>[5,8,3,1,7,2,4,6]=>[3,7,1,8,5,2,4,6]=>0001011
[7,2,1,4,6,3,8,5]=>[2,7,6,1,8,4,3,5]=>[8,2,1,4,6,3,7,5]=>1000111
[3,6,2,1,5,7,4,8]=>[2,6,3,7,1,5,4,8]=>[3,7,2,1,5,6,4,8]=>1000110
[6,3,2,1,5,7,4,8]=>[2,3,6,7,1,5,4,8]=>[7,3,2,1,5,6,4,8]=>1100110
[6,4,2,1,5,3,7,8]=>[2,4,6,5,3,1,7,8]=>[5,3,6,4,2,1,7,8]=>1011100
[7,3,1,5,2,6,4,8]=>[3,7,5,6,2,1,4,8]=>[6,2,5,3,1,7,4,8]=>0101110
[6,2,5,1,3,7,8,4]=>[5,6,1,8,2,3,7,4]=>[7,8,1,6,2,3,5,4]=>0001101
[6,3,5,1,2,7,4,8]=>[5,1,6,7,3,2,4,8]=>[7,3,6,1,2,5,4,8]=>0001110
[6,4,5,1,7,2,3,8]=>[5,7,2,6,4,1,3,8]=>[6,4,7,2,5,1,3,8]=>0001110
[5,2,6,4,1,3,7,8]=>[4,6,2,5,1,3,7,8]=>[5,2,6,4,1,3,7,8]=>0011100
[6,5,2,1,4,7,8,3]=>[2,5,6,3,8,4,7,1]=>[7,8,3,4,6,5,2,1]=>1001101
[6,5,3,1,4,7,2,8]=>[3,5,6,1,7,4,2,8]=>[7,1,4,6,5,3,2,8]=>0101110
[2,4,1,5,8,3,7,6]=>[4,2,8,1,5,7,3,6]=>[2,5,7,1,4,3,8,6]=>0010011
[2,4,1,5,3,8,7,6]=>[4,2,5,1,3,7,8,6]=>[2,5,1,4,3,8,7,6]=>0011011
[3,4,5,1,2,8,7,6]=>[5,1,3,4,2,7,8,6]=>[3,4,5,1,2,8,7,6]=>0001011
[3,4,5,1,8,2,7,6]=>[5,8,3,4,1,7,2,6]=>[3,4,7,1,5,2,8,6]=>0001011
[1,8,4,5,3,2,7,6]=>[1,3,5,8,4,7,2,6]=>[1,7,4,5,3,2,8,6]=>0101011
[3,4,6,2,1,7,5,8]=>[2,6,3,4,7,1,5,8]=>[3,4,7,2,1,6,5,8]=>1000110
[3,5,6,2,7,1,4,8]=>[7,6,3,1,5,2,4,8]=>[3,5,6,1,7,2,4,8]=>0000110
[3,5,6,2,7,1,8,4]=>[7,6,3,8,5,2,1,4]=>[3,5,8,2,6,1,7,4]=>0000111
[3,4,6,2,8,7,1,5]=>[7,6,3,4,1,2,8,5]=>[3,4,6,1,8,7,2,5]=>0000111
[3,4,6,8,2,7,1,5]=>[7,8,3,4,1,6,2,5]=>[3,4,6,8,1,7,2,5]=>0000011
[1,8,4,6,3,7,5,2]=>[1,5,7,6,8,2,4,3]=>[1,8,2,6,4,7,5,3]=>0001111
[3,4,6,8,2,7,5,1]=>[5,7,3,4,8,6,1,2]=>[3,4,6,8,1,7,5,2]=>0001011
[3,4,6,2,8,7,5,1]=>[5,7,3,4,6,1,8,2]=>[3,4,6,1,8,7,5,2]=>0001111
[3,5,6,2,7,8,4,1]=>[4,8,3,6,5,1,7,2]=>[3,5,6,1,7,8,4,2]=>0010101
[3,5,6,2,7,4,1,8]=>[4,7,3,6,5,1,2,8]=>[3,5,6,1,7,4,2,8]=>0010110
[4,5,6,7,2,8,3,1]=>[3,8,7,4,5,6,1,2]=>[4,5,6,7,1,8,3,2]=>0100011
[3,5,6,8,7,2,4,1]=>[4,7,3,2,5,6,8,1]=>[3,5,6,8,7,2,4,1]=>0010011
[2,5,8,6,7,3,4,1]=>[4,2,7,3,5,8,6,1]=>[2,5,8,6,7,3,4,1]=>0010011
[1,8,5,6,7,3,2,4]=>[1,3,7,2,8,5,6,4]=>[1,8,5,6,7,3,2,4]=>0100011
[2,5,8,6,7,3,1,4]=>[3,2,7,1,5,8,6,4]=>[2,5,8,6,7,3,1,4]=>0100011
[3,5,6,8,7,2,1,4]=>[2,7,3,1,5,6,8,4]=>[3,5,6,8,7,2,1,4]=>1000011
[3,4,6,1,8,7,2,5]=>[6,7,3,4,2,1,8,5]=>[3,4,8,7,2,6,1,5]=>0000111
[2,5,1,6,7,4,8,3]=>[5,2,8,7,1,6,4,3]=>[2,6,7,1,8,4,5,3]=>0001011
[3,5,6,1,7,4,2,8]=>[6,4,3,7,5,1,2,8]=>[3,5,7,4,1,6,2,8]=>0010110
[3,5,6,1,7,4,8,2]=>[6,8,3,7,5,1,4,2]=>[3,5,7,1,8,4,6,2]=>0000111
[1,8,4,6,2,7,5,3]=>[1,6,5,7,8,3,2,4]=>[1,8,3,7,5,2,6,4]=>0001111
[3,5,6,8,7,1,4,2]=>[7,4,3,1,5,6,8,2]=>[3,4,1,5,6,8,7,2]=>0010011
[4,5,6,7,8,1,3,2]=>[8,3,1,4,5,6,7,2]=>[3,1,4,5,6,7,8,2]=>0100001
[4,5,6,7,1,3,8,2]=>[7,8,1,4,5,6,3,2]=>[4,5,6,8,1,3,7,2]=>0000011
[4,5,6,7,1,3,2,8]=>[7,3,1,4,5,6,2,8]=>[3,1,4,5,6,7,2,8]=>0100010
[4,5,6,7,3,1,8,2]=>[3,7,8,4,5,6,2,1]=>[4,5,6,8,2,7,3,1]=>0100011
[3,5,6,8,7,4,1,2]=>[4,1,3,7,5,6,8,2]=>[3,5,6,8,7,4,1,2]=>0010011
[1,8,5,6,7,4,2,3]=>[1,4,2,7,8,5,6,3]=>[1,8,5,6,7,4,2,3]=>0010011
[2,5,8,6,7,4,3,1]=>[3,2,4,7,5,8,6,1]=>[2,5,8,6,7,4,3,1]=>0110011
[8,2,5,3,7,1,6,4]=>[7,8,5,6,2,1,3,4]=>[6,2,5,1,8,3,7,4]=>0001111
[8,2,4,3,7,1,6,5]=>[7,8,4,2,6,1,3,5]=>[4,2,6,1,8,3,7,5]=>0010111
[5,8,2,4,3,7,1,6]=>[7,8,4,2,5,1,3,6]=>[4,2,5,8,1,7,3,6]=>0010011
[4,2,5,6,1,8,3,7]=>[6,4,8,2,5,1,3,7]=>[5,8,2,4,1,6,3,7]=>0010101
[4,2,5,6,1,7,3,8]=>[6,4,7,2,5,1,3,8]=>[5,7,2,4,1,6,3,8]=>0010110
[6,1,5,7,3,2,4,8]=>[6,3,7,2,1,5,4,8]=>[7,3,2,5,6,1,4,8]=>0100110
[6,1,5,8,3,2,4,7]=>[6,3,8,2,1,5,4,7]=>[8,3,2,5,6,1,4,7]=>0100101
[3,8,2,4,7,1,5,6]=>[7,8,3,2,1,5,4,6]=>[3,8,2,5,7,1,4,6]=>0000011
[3,6,8,2,4,7,1,5]=>[7,8,3,2,1,6,4,5]=>[3,6,8,2,7,1,4,5]=>0000011
[4,3,5,6,7,1,8,2]=>[7,8,4,3,5,6,1,2]=>[4,3,5,6,8,1,7,2]=>0010011
[3,7,1,5,6,8,2,4]=>[7,8,3,2,1,5,6,4]=>[3,8,2,5,6,7,1,4]=>0000011
[3,7,1,5,8,2,4,6]=>[7,8,3,2,1,4,5,6]=>[3,8,2,7,1,4,5,6]=>0000011
[8,3,2,4,6,1,5,7]=>[6,3,8,2,1,4,5,7]=>[8,3,2,6,1,4,5,7]=>0100101
[7,3,2,4,6,1,5,8]=>[6,3,7,2,1,4,5,8]=>[7,3,2,6,1,4,5,8]=>0100110
[3,2,5,1,7,4,6,8]=>[5,3,2,7,1,4,6,8]=>[3,2,7,1,5,4,6,8]=>0101010
[3,2,5,1,8,4,6,7]=>[5,3,2,8,1,4,6,7]=>[3,2,8,1,5,4,6,7]=>0101001
[3,2,5,1,7,8,4,6]=>[5,3,2,8,1,4,7,6]=>[3,2,7,8,1,5,4,6]=>0101001
[7,8,3,2,4,6,1,5]=>[6,3,8,2,1,4,7,5]=>[7,8,3,2,6,1,4,5]=>0100101
[6,1,5,7,8,3,2,4]=>[6,3,8,2,1,5,7,4]=>[7,8,3,2,5,6,1,4]=>0100101
[4,2,5,6,1,7,8,3]=>[6,4,8,2,5,1,7,3]=>[5,7,8,2,4,1,6,3]=>0010101
[6,1,5,8,7,3,2,4]=>[6,3,7,2,1,5,8,4]=>[8,7,3,2,5,6,1,4]=>0100111
[8,7,3,2,4,6,1,5]=>[6,3,7,2,1,4,8,5]=>[8,7,3,2,6,1,4,5]=>0100111
[3,2,5,1,8,7,4,6]=>[5,3,2,7,1,4,8,6]=>[3,2,8,7,1,5,4,6]=>0101011
[3,2,5,1,6,4,7,8]=>[5,3,2,6,1,4,7,8]=>[3,2,6,1,5,4,7,8]=>0101100
[3,2,4,1,8,7,5,6]=>[4,3,2,1,7,5,8,6]=>[3,2,4,1,8,7,5,6]=>0110011
[3,2,5,1,6,8,7,4]=>[5,3,2,7,1,6,8,4]=>[3,2,6,8,7,1,5,4]=>0101011
[3,8,6,5,1,7,4,2]=>[5,4,3,6,8,7,1,2]=>[3,7,4,1,8,6,5,2]=>0011111
[3,7,6,5,1,8,4,2]=>[5,4,3,6,7,8,1,2]=>[3,8,4,1,7,6,5,2]=>0011111
[6,5,1,7,8,4,2,3]=>[5,4,1,6,8,2,7,3]=>[7,8,4,1,6,5,2,3]=>0011101
[3,2,5,1,6,7,8,4]=>[5,3,2,8,1,6,7,4]=>[3,2,6,7,8,1,5,4]=>0101001
[3,2,4,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>[3,2,4,1,8,5,6,7]=>0110001
[3,2,4,1,7,5,6,8]=>[4,3,2,1,7,5,6,8]=>[3,2,4,1,7,5,6,8]=>0110010
[3,2,4,1,6,8,5,7]=>[4,3,2,1,8,6,5,7]=>[3,2,4,1,6,8,5,7]=>0110001
[3,2,4,1,8,5,7,6]=>[4,3,2,1,8,7,5,6]=>[3,2,4,1,7,5,8,6]=>0110011
[8,3,2,4,7,6,1,5]=>[6,3,7,1,2,8,4,5]=>[8,3,1,7,6,2,4,5]=>0100111
[3,2,5,1,8,4,7,6]=>[5,3,2,8,1,7,4,6]=>[3,2,7,1,5,4,8,6]=>0101011
[3,2,5,1,6,7,4,8]=>[5,3,2,7,1,6,4,8]=>[3,2,6,7,1,5,4,8]=>0101010
[6,5,1,7,4,2,3,8]=>[5,4,1,6,7,2,3,8]=>[7,4,1,6,5,2,3,8]=>0011110
[6,5,1,8,4,2,3,7]=>[5,4,1,6,8,2,3,7]=>[8,4,1,6,5,2,3,7]=>0011101
[8,4,2,3,7,5,1,6]=>[5,4,1,7,8,2,3,6]=>[8,4,1,7,5,2,3,6]=>0011011
[4,2,6,1,8,3,7,5]=>[6,4,8,2,7,1,3,5]=>[7,2,4,1,8,3,6,5]=>0010111
[5,2,6,1,8,3,7,4]=>[6,5,8,7,2,1,3,4]=>[7,2,8,1,5,3,6,4]=>0001111
[8,4,6,1,7,3,5,2]=>[6,5,7,8,3,4,1,2]=>[8,3,7,4,5,1,6,2]=>0001111
[5,2,6,1,8,4,7,3]=>[6,5,7,8,2,1,4,3]=>[8,2,7,1,5,4,6,3]=>0001111
[7,4,2,3,8,5,1,6]=>[5,4,1,8,7,2,3,6]=>[7,4,1,8,5,2,3,6]=>0011011
[3,2,5,1,7,6,4,8]=>[5,3,2,6,1,7,4,8]=>[3,2,7,6,1,5,4,8]=>0101110
[3,2,5,1,8,6,4,7]=>[5,3,2,6,1,8,4,7]=>[3,2,8,6,1,5,4,7]=>0101101
[7,3,2,4,8,6,1,5]=>[6,3,8,1,2,7,4,5]=>[7,3,1,8,6,2,4,5]=>0100111
[8,6,1,5,7,3,2,4]=>[6,3,8,1,2,7,5,4]=>[7,3,1,5,8,6,2,4]=>0100111
[4,2,6,1,8,5,7,3]=>[6,4,7,2,8,1,5,3]=>[8,2,4,1,7,5,6,3]=>0010111
[8,5,6,1,7,3,4,2]=>[6,4,7,3,8,5,1,2]=>[8,5,7,3,4,1,6,2]=>0010111
[3,6,8,5,1,7,4,2]=>[5,4,3,8,7,6,2,1]=>[3,6,7,4,2,8,5,1]=>0011011
[8,5,1,6,7,4,2,3]=>[5,4,1,8,7,2,6,3]=>[7,4,1,6,8,5,2,3]=>0011011
[3,2,5,1,8,6,7,4]=>[5,3,2,7,1,8,6,4]=>[3,2,8,6,7,1,5,4]=>0101011
[3,2,4,1,8,6,5,7]=>[4,3,2,1,6,8,5,7]=>[3,2,4,1,8,6,5,7]=>0110101
[3,2,4,1,5,8,6,7]=>[4,3,2,1,5,8,6,7]=>[3,2,4,1,5,8,6,7]=>0110001
[3,2,5,1,7,8,6,4]=>[5,3,2,6,1,8,7,4]=>[3,2,7,8,6,1,5,4]=>0101101
[7,8,5,1,6,4,2,3]=>[5,4,1,8,6,2,7,3]=>[6,4,1,7,8,5,2,3]=>0011101
[3,8,5,1,7,6,4,2]=>[5,4,3,8,6,7,2,1]=>[3,7,6,4,2,8,5,1]=>0011111
[3,2,5,1,8,7,6,4]=>[5,3,2,6,1,7,8,4]=>[3,2,8,7,6,1,5,4]=>0101111
[5,4,7,3,6,1,8,2]=>[6,8,7,5,4,3,1,2]=>[5,4,7,3,8,1,6,2]=>0001111
[5,4,8,3,6,1,7,2]=>[6,7,8,5,4,3,1,2]=>[5,4,8,3,7,1,6,2]=>0001111
[5,4,3,6,7,1,8,2]=>[7,8,4,5,3,6,1,2]=>[5,4,3,6,8,1,7,2]=>0011011
[2,4,1,7,5,8,6,3]=>[4,2,6,1,8,7,3,5]=>[2,7,1,4,3,8,6,5]=>0010111
[2,4,1,7,5,3,8,6]=>[4,2,5,1,7,8,3,6]=>[2,8,5,1,4,3,7,6]=>0011011
[3,2,1,6,8,5,4,7]=>[2,3,1,5,8,6,4,7]=>[3,2,1,6,8,5,4,7]=>1101001
[3,2,7,1,5,4,8,6]=>[7,3,2,5,1,8,4,6]=>[3,2,5,1,8,4,7,6]=>0101011
[3,2,7,1,5,8,6,4]=>[7,3,2,6,1,8,5,4]=>[3,2,8,6,1,5,7,4]=>0100111
[3,8,2,5,1,6,7,4]=>[5,8,3,7,2,1,6,4]=>[3,7,2,6,8,1,5,4]=>0001011
[4,8,3,2,6,7,1,5]=>[7,3,8,4,1,2,6,5]=>[4,8,3,1,6,7,2,5]=>0100011
[4,3,8,2,6,7,1,5]=>[7,8,4,3,1,2,6,5]=>[4,3,8,1,6,7,2,5]=>0010011
[4,3,2,6,7,1,5,8]=>[7,3,4,2,1,6,5,8]=>[4,3,2,6,7,1,5,8]=>0110010
[3,2,5,7,8,1,6,4]=>[8,3,2,6,5,1,7,4]=>[3,2,5,6,1,7,8,4]=>0100101
[3,2,5,7,1,6,8,4]=>[7,3,2,8,5,1,6,4]=>[3,2,5,8,1,6,7,4]=>0100011
[6,3,2,7,1,5,8,4]=>[7,3,6,8,1,2,5,4]=>[8,3,1,6,2,5,7,4]=>0100111
[4,2,6,1,7,8,5,3]=>[6,4,5,2,8,1,7,3]=>[7,8,5,2,4,1,6,3]=>0011101
[2,1,7,5,3,8,6,4]=>[2,1,5,7,6,8,4,3]=>[2,1,8,6,4,7,5,3]=>1001111
[6,3,2,7,1,4,8,5]=>[7,3,6,1,8,2,4,5]=>[8,3,1,6,2,4,7,5]=>0100111
[6,3,2,1,4,7,8,5]=>[2,3,6,1,8,4,7,5]=>[7,8,3,2,1,4,6,5]=>1100101
[3,5,2,1,7,8,4,6]=>[2,5,3,8,1,4,7,6]=>[3,7,8,2,1,5,4,6]=>1001001
[5,8,4,2,1,7,3,6]=>[2,4,8,7,5,1,3,6]=>[5,7,2,1,8,4,3,6]=>1010011
[4,3,7,2,8,1,5,6]=>[8,7,4,3,1,5,2,6]=>[4,3,7,1,5,8,2,6]=>0010011
[4,3,7,2,1,5,6,8]=>[2,7,4,3,1,5,6,8]=>[4,3,7,2,1,5,6,8]=>1010010
[3,5,2,8,1,7,4,6]=>[8,5,3,7,2,4,1,6]=>[3,7,2,5,4,8,1,6]=>0001011
[6,3,2,8,1,4,7,5]=>[8,3,6,1,7,2,4,5]=>[7,3,1,6,2,4,8,5]=>0100111
[3,2,1,4,7,5,8,6]=>[2,3,1,4,7,8,5,6]=>[3,2,1,4,8,5,7,6]=>1100011
[5,3,2,1,8,4,6,7]=>[2,3,5,8,1,4,6,7]=>[8,3,2,1,5,4,6,7]=>1101001
[4,8,3,2,1,5,6,7]=>[2,3,8,4,1,5,6,7]=>[4,8,3,2,1,5,6,7]=>1100001
[4,3,8,2,1,5,6,7]=>[2,8,4,3,1,5,6,7]=>[4,3,8,2,1,5,6,7]=>1010001
[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]=>[1,9,8,7,6,5,4,3,2]=>01111111
[8,7,6,4,5,3,2,1,9]=>[2,3,5,6,4,7,8,1,9]=>[8,7,6,4,5,3,2,1,9]=>11011110
[1,9,8,7,5,6,4,3,2]=>[1,3,4,6,7,5,8,9,2]=>[1,9,8,7,5,6,4,3,2]=>01101111
[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110
[9,8,7,5,6,4,3,2,1,10]=>[2,3,4,6,7,5,8,9,1,10]=>[9,8,7,5,6,4,3,2,1,10]=>111011110
[8,7,5,4,6,3,2,1,9]=>[2,3,6,5,7,4,8,1,9]=>[8,7,5,4,6,3,2,1,9]=>11011110
[1,9,8,6,5,7,4,3,2]=>[1,3,4,7,6,8,5,9,2]=>[1,9,8,6,5,7,4,3,2]=>01101111
[1,10,9,8,6,7,5,4,3,2]=>[1,3,4,5,7,8,6,9,10,2]=>[1,10,9,8,6,7,5,4,3,2]=>011101111
[1,11,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,11,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111
[8,4,5,2,3,1,7,6]=>[3,5,2,8,4,7,1,6]=>[7,4,5,2,3,1,8,6]=>0101011
[8,6,7,2,5,3,4,1]=>[4,7,5,3,2,8,6,1]=>[5,3,8,6,7,2,4,1]=>0011011
[8,2,5,3,4,1,7,6]=>[4,8,5,3,2,7,1,6]=>[5,3,7,2,4,1,8,6]=>0011011
[6,2,5,3,4,1,8,7]=>[4,6,5,3,2,1,8,7]=>[5,3,6,2,4,1,8,7]=>0011101
[6,1,5,2,4,3,8,7]=>[6,5,4,2,1,3,8,7]=>[4,2,5,1,6,3,8,7]=>0011101
[6,4,5,1,3,2,8,7]=>[5,3,1,6,4,2,8,7]=>[3,1,6,4,5,2,8,7]=>0101101
[6,3,5,1,4,2,8,7]=>[5,4,6,1,3,2,8,7]=>[6,1,4,3,5,2,8,7]=>0011101
[8,3,7,5,6,2,4,1]=>[4,6,8,2,7,5,3,1]=>[7,5,8,2,6,3,4,1]=>0010111
[8,3,7,2,4,1,6,5]=>[4,7,8,2,6,1,3,5]=>[6,2,8,1,4,3,7,5]=>0010111
[8,3,5,1,4,2,7,6]=>[5,4,8,1,3,7,2,6]=>[7,1,4,3,5,2,8,6]=>0011011
[8,1,5,3,4,2,7,6]=>[8,4,5,3,1,7,2,6]=>[5,3,4,1,7,2,8,6]=>0011011
[8,4,5,1,3,2,7,6]=>[5,3,1,8,4,7,2,6]=>[3,1,7,4,5,2,8,6]=>0101011
[8,6,7,4,5,1,3,2]=>[5,3,1,7,4,8,6,2]=>[3,1,8,6,7,4,5,2]=>0101011
[8,6,7,1,5,3,4,2]=>[7,4,5,3,1,8,6,2]=>[5,3,4,1,8,6,7,2]=>0011011
[8,6,7,3,5,1,4,2]=>[5,4,7,1,3,8,6,2]=>[8,6,7,1,4,3,5,2]=>0011011
[8,5,7,3,6,1,4,2]=>[6,4,7,1,8,3,5,2]=>[8,1,4,3,7,5,6,2]=>0010111
[8,3,7,4,6,1,5,2]=>[6,5,8,7,1,4,3,2]=>[7,1,8,4,5,3,6,2]=>0001111
[8,3,7,1,6,4,5,2]=>[7,5,8,6,4,1,3,2]=>[6,4,8,1,5,3,7,2]=>0001111
[8,1,7,3,6,4,5,2]=>[8,5,7,6,4,3,1,2]=>[6,4,7,3,5,1,8,2]=>0001111
[8,1,7,5,6,3,4,2]=>[8,4,6,3,7,5,1,2]=>[7,5,6,3,4,1,8,2]=>0010111
[2,1,8,4,7,5,6,3]=>[2,1,6,8,7,5,4,3]=>[2,1,7,5,8,4,6,3]=>1000111
[8,3,7,1,6,2,5,4]=>[7,6,8,5,2,1,3,4]=>[5,2,8,1,6,3,7,4]=>0001111
[8,2,7,3,6,4,5,1]=>[5,8,7,6,4,3,2,1]=>[6,4,7,3,8,2,5,1]=>0001111
[8,2,7,3,6,1,5,4]=>[6,8,7,5,1,3,2,4]=>[5,1,7,3,8,2,6,4]=>0001111
[8,2,7,1,6,3,5,4]=>[7,8,6,5,3,1,2,4]=>[5,3,6,1,8,2,7,4]=>0001111
[8,1,7,2,4,3,6,5]=>[8,7,4,2,6,3,1,5]=>[4,2,6,3,7,1,8,5]=>0010111
[8,1,3,2,7,4,6,5]=>[8,3,1,7,6,4,2,5]=>[3,1,6,4,7,2,8,5]=>0100111
[2,1,8,3,7,4,6,5]=>[2,1,8,7,6,4,3,5]=>[2,1,6,4,7,3,8,5]=>1000111
[8,1,5,2,4,3,7,6]=>[8,5,4,2,1,7,3,6]=>[4,2,5,1,7,3,8,6]=>0011011
[8,2,7,1,4,3,6,5]=>[7,8,4,1,6,3,2,5]=>[4,1,6,3,8,2,7,5]=>0010111
[8,2,7,3,4,1,6,5]=>[4,8,7,3,6,1,2,5]=>[6,3,7,1,4,2,8,5]=>0010111
[8,2,7,5,6,3,4,1]=>[4,8,6,3,7,5,2,1]=>[7,5,6,3,8,2,4,1]=>0010111
[8,4,7,5,6,2,3,1]=>[3,6,2,8,7,5,4,1]=>[7,5,8,4,6,2,3,1]=>0100111
[8,4,7,2,3,1,6,5]=>[3,7,2,8,6,1,4,5]=>[6,2,3,1,8,4,7,5]=>0100111
[8,2,3,1,7,4,6,5]=>[3,8,2,7,6,4,1,5]=>[6,4,7,2,3,1,8,5]=>0100111
[4,2,3,1,8,5,7,6]=>[3,4,2,1,8,7,5,6]=>[4,2,3,1,7,5,8,6]=>0110011
[4,1,3,2,8,6,7,5]=>[4,3,1,2,7,8,6,5]=>[3,1,4,2,8,6,7,5]=>0110011
[8,6,7,2,3,1,5,4]=>[3,7,2,5,1,8,6,4]=>[5,2,3,1,8,6,7,4]=>0101011
[8,6,7,1,5,2,4,3]=>[7,5,4,2,1,8,6,3]=>[4,2,5,1,8,6,7,3]=>0011011
[8,6,7,1,3,2,5,4]=>[7,3,1,5,2,8,6,4]=>[3,1,5,2,8,6,7,4]=>0101011
[2,1,8,6,7,3,5,4]=>[2,1,7,5,3,8,6,4]=>[2,1,5,3,8,6,7,4]=>1001011
[2,1,8,3,7,5,6,4]=>[2,1,8,6,7,5,3,4]=>[2,1,7,5,6,3,8,4]=>1000111
[8,1,3,2,7,5,6,4]=>[8,3,1,6,7,5,2,4]=>[3,1,7,5,6,2,8,4]=>0100111
[8,1,7,5,6,2,4,3]=>[8,6,4,2,7,5,1,3]=>[4,2,7,5,6,1,8,3]=>0010111
[8,1,7,2,6,4,5,3]=>[8,7,5,6,4,2,1,3]=>[6,4,5,2,7,1,8,3]=>0001111
[8,2,7,1,6,4,5,3]=>[7,8,5,6,4,1,2,3]=>[6,4,5,1,8,2,7,3]=>0001111
[8,2,7,4,6,1,5,3]=>[6,8,5,7,1,4,2,3]=>[7,1,5,4,8,2,6,3]=>0001111
[8,2,7,4,6,3,5,1]=>[5,8,6,7,3,4,2,1]=>[7,3,6,4,8,2,5,1]=>0001111
[8,4,7,2,6,1,5,3]=>[6,7,5,8,1,2,4,3]=>[8,1,5,2,7,4,6,3]=>0001111
[8,1,7,4,6,2,5,3]=>[8,6,5,7,2,4,1,3]=>[7,2,5,4,6,1,8,3]=>0001111
[8,5,7,1,6,2,4,3]=>[7,6,4,2,8,1,5,3]=>[4,2,8,1,6,5,7,3]=>0010111
[2,1,8,5,7,3,6,4]=>[2,1,7,6,8,3,5,4]=>[2,1,8,3,6,5,7,4]=>1000111
[8,5,7,1,6,3,4,2]=>[7,4,6,3,8,1,5,2]=>[8,3,4,1,6,5,7,2]=>0010111
[8,4,7,3,6,1,5,2]=>[6,5,7,8,1,3,4,2]=>[8,1,7,3,5,4,6,2]=>0001111
[6,5,8,1,3,2,7,4]=>[8,3,1,7,6,5,2,4]=>[3,1,6,5,7,2,8,4]=>0100111
[4,5,8,6,3,2,7,1]=>[7,3,6,4,5,8,2,1]=>[4,5,8,6,3,2,7,1]=>0100111
[6,5,8,7,3,1,2,4]=>[3,1,7,2,6,5,8,4]=>[6,5,8,7,3,1,2,4]=>0100111
[6,3,1,8,4,5,7,2]=>[3,6,7,8,4,2,5,1]=>[8,4,7,2,5,6,3,1]=>0100111
[1,3,7,8,4,6,5,2]=>[1,5,3,6,8,2,7,4]=>[1,3,7,8,2,6,5,4]=>0001101
[1,5,7,8,2,4,6,3]=>[1,8,6,2,5,4,7,3]=>[1,5,6,2,4,7,8,3]=>0000101
[3,6,7,8,4,2,5,1]=>[5,4,3,8,2,6,7,1]=>[3,6,7,8,4,2,5,1]=>0011001
[2,8,3,7,1,6,5,4]=>[7,2,8,5,6,1,3,4]=>[2,6,5,1,8,3,7,4]=>0001111
[7,2,1,8,4,6,5,3]=>[2,7,5,6,8,3,1,4]=>[8,3,6,5,2,1,7,4]=>1001111
[3,2,7,8,4,6,5,1]=>[5,3,2,6,8,1,7,4]=>[3,2,7,8,1,6,5,4]=>0101101
[4,2,1,3,8,5,6,7]=>[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]=>1010001
[7,2,5,8,3,4,6,1]=>[6,7,8,3,2,4,5,1]=>[8,3,7,2,4,5,6,1]=>0000111
[6,4,8,5,2,3,1,7]=>[3,5,2,8,6,1,4,7]=>[6,2,3,1,8,5,4,7]=>0101101
[7,3,5,8,2,4,6,1]=>[6,8,7,2,3,4,5,1]=>[7,2,8,3,4,5,6,1]=>0000111
[4,3,1,2,8,5,6,7]=>[3,1,4,2,8,5,6,7]=>[4,3,1,2,8,5,6,7]=>0110001
[3,4,2,1,8,5,6,7]=>[2,4,3,1,8,5,6,7]=>[3,4,2,1,8,5,6,7]=>1010001
[1,6,8,5,4,3,2,7]=>[1,3,4,5,8,6,2,7]=>[1,6,8,5,4,3,2,7]=>0111001
[4,6,8,1,5,3,2,7]=>[8,3,5,4,1,6,2,7]=>[4,5,3,1,6,8,2,7]=>0101001
[2,7,3,8,4,6,5,1]=>[5,2,6,7,8,1,4,3]=>[2,8,1,7,4,6,5,3]=>0001111
[7,1,3,8,4,6,5,2]=>[7,5,1,6,8,2,3,4]=>[8,1,6,5,2,3,7,4]=>0001111
[5,7,8,4,3,6,1,2]=>[6,1,4,8,5,3,7,2]=>[5,7,8,4,3,6,1,2]=>0010101
[2,8,5,4,3,1,6,7]=>[3,2,4,5,8,1,6,7]=>[2,8,5,4,3,1,6,7]=>0111001
[4,1,3,2,8,5,6,7]=>[4,3,1,2,8,5,6,7]=>[3,1,4,2,8,5,6,7]=>0110001
[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>0110001
[6,4,8,2,5,3,1,7]=>[3,5,8,6,1,4,2,7]=>[6,1,8,4,5,3,2,7]=>0101101
[2,8,4,3,5,1,6,7]=>[5,2,4,8,3,1,6,7]=>[2,8,4,3,5,1,6,7]=>0011001
[2,8,3,4,5,1,6,7]=>[5,2,8,3,4,1,6,7]=>[2,8,3,4,5,1,6,7]=>0001001
[4,2,3,1,8,5,6,7]=>[3,4,2,1,8,5,6,7]=>[4,2,3,1,8,5,6,7]=>0110001
[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>1100001
[5,1,3,2,4,8,6,7]=>[5,3,1,2,4,8,6,7]=>[3,1,5,2,4,8,6,7]=>0101001
[1,2,8,4,5,3,7,6]=>[1,2,5,8,4,7,3,6]=>[1,2,7,4,5,3,8,6]=>0001011
[8,1,5,3,2,4,6,7]=>[8,3,5,2,1,4,6,7]=>[5,3,2,8,1,4,6,7]=>0101001
[1,5,2,8,4,3,6,7]=>[1,5,4,8,2,3,6,7]=>[1,8,4,2,5,3,6,7]=>0011001
[1,2,8,5,4,3,6,7]=>[1,2,4,5,8,3,6,7]=>[1,2,8,5,4,3,6,7]=>0011001
[1,2,5,4,3,8,6,7]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>0011001
[1,2,7,4,8,5,3,6]=>[1,2,5,8,7,4,3,6]=>[1,2,7,4,8,5,3,6]=>0001011
[5,1,2,7,4,8,3,6]=>[5,1,8,7,2,3,4,6]=>[7,1,2,8,3,5,4,6]=>0001011
[8,3,5,1,4,7,2,6]=>[5,7,8,1,3,2,4,6]=>[8,1,7,3,5,2,4,6]=>0001011
[2,8,1,5,4,7,3,6]=>[8,2,7,5,1,3,4,6]=>[2,5,1,7,3,8,4,6]=>0001011
[1,2,8,5,7,4,3,6]=>[1,2,4,7,8,3,5,6]=>[1,2,8,4,3,7,5,6]=>0010011
[1,2,4,8,7,5,3,6]=>[1,2,5,4,7,3,8,6]=>[1,2,4,8,7,5,3,6]=>0001011
[2,8,1,4,3,7,6,5]=>[8,2,4,1,6,7,3,5]=>[2,4,1,7,6,3,8,5]=>0010111
[6,1,2,8,7,4,3,5]=>[6,1,4,7,3,2,8,5]=>[8,7,4,3,6,1,2,5]=>0010111
[3,6,4,8,1,7,2,5]=>[8,7,3,6,2,4,1,5]=>[3,6,2,7,4,8,1,5]=>0000111
[7,1,6,2,8,4,3,5]=>[7,6,4,8,3,1,2,5]=>[8,4,3,6,1,7,2,5]=>0010111
[1,6,7,2,8,4,3,5]=>[1,7,4,8,3,6,2,5]=>[1,6,8,4,3,7,2,5]=>0010011
[6,7,1,4,2,8,3,5]=>[7,4,8,1,3,6,2,5]=>[6,8,1,4,3,7,2,5]=>0010011
[6,3,7,1,4,8,2,5]=>[7,8,6,1,2,3,4,5]=>[6,1,8,2,7,3,4,5]=>0000111
[6,1,2,8,4,3,7,5]=>[6,1,4,8,7,2,3,5]=>[7,4,1,2,8,3,6,5]=>0010111
[6,4,1,2,8,3,7,5]=>[4,1,6,8,7,3,2,5]=>[7,3,8,4,1,2,6,5]=>0010111
[7,6,1,3,2,4,8,5]=>[6,3,1,2,7,8,5,4]=>[3,1,8,5,7,6,2,4]=>0100111
[6,7,1,3,2,4,8,5]=>[7,3,1,2,8,6,4,5]=>[3,1,6,8,2,4,7,5]=>0100011
[1,2,7,3,5,8,4,6]=>[1,2,7,8,3,4,5,6]=>[1,2,8,3,7,4,5,6]=>0000011
[1,2,7,5,8,3,4,6]=>[1,2,8,3,7,4,5,6]=>[1,2,7,3,4,8,5,6]=>0000011
[5,8,1,3,7,2,4,6]=>[8,7,1,2,5,4,3,6]=>[5,7,1,4,8,2,3,6]=>0000011
[1,2,5,8,7,3,4,6]=>[1,2,7,3,5,4,8,6]=>[1,2,5,8,7,3,4,6]=>0000011
[2,8,1,7,3,5,4,6]=>[8,2,7,5,3,4,1,6]=>[2,5,3,7,4,8,1,6]=>0001011
[2,8,1,7,4,3,6,5]=>[8,2,4,7,6,3,1,5]=>[2,6,4,3,7,1,8,5]=>0010111
[7,1,2,8,4,3,6,5]=>[7,1,4,8,6,3,2,5]=>[6,4,3,8,1,2,7,5]=>0010111
[1,2,8,4,7,5,3,6]=>[1,2,5,7,8,4,3,6]=>[1,2,8,4,7,5,3,6]=>0001011
[1,2,8,7,4,5,3,6]=>[1,2,5,7,4,3,8,6]=>[1,2,8,7,4,5,3,6]=>0001011
[3,8,6,1,4,7,2,5]=>[6,8,3,2,1,7,4,5]=>[3,7,2,8,6,1,4,5]=>0000111
[8,6,1,4,2,7,3,5]=>[6,4,8,3,1,7,2,5]=>[7,3,4,1,8,6,2,5]=>0010111
[7,1,2,8,6,4,3,5]=>[7,1,4,6,3,8,2,5]=>[8,6,4,3,7,1,2,5]=>0010111
[7,4,1,2,8,6,3,5]=>[4,1,7,6,2,8,3,5]=>[8,6,1,2,7,4,3,5]=>0010111
[3,7,4,8,1,6,2,5]=>[8,6,3,7,2,1,4,5]=>[3,7,2,6,1,8,4,5]=>0000111
[3,4,8,7,1,6,2,5]=>[7,6,3,4,2,1,8,5]=>[3,4,6,2,8,7,1,5]=>0000111
[4,2,8,1,7,6,3,5]=>[8,4,6,2,3,7,1,5]=>[7,6,2,4,3,8,1,5]=>0010111
[7,8,3,4,1,5,2,6]=>[4,5,8,3,1,2,7,6]=>[7,8,3,5,1,4,2,6]=>0011001
[7,8,3,4,1,6,2,5]=>[4,6,8,3,2,1,7,5]=>[7,8,3,6,2,4,1,5]=>0010101
[6,7,3,4,1,8,2,5]=>[4,8,7,3,2,6,1,5]=>[6,7,3,8,2,4,1,5]=>0010011
[5,8,3,4,1,7,2,6]=>[4,7,8,3,5,2,1,6]=>[5,8,3,7,2,4,1,6]=>0010011
[5,8,3,4,1,6,2,7]=>[4,6,8,3,5,1,2,7]=>[5,8,3,6,1,4,2,7]=>0010101
[6,7,3,4,1,5,2,8]=>[4,5,7,3,1,6,2,8]=>[6,7,3,5,1,4,2,8]=>0011010
[4,6,2,8,3,5,1,7]=>[5,6,8,4,3,2,1,7]=>[4,8,3,6,2,5,1,7]=>0001101
[4,8,3,5,1,6,2,7]=>[5,6,8,4,3,1,2,7]=>[4,8,3,6,1,5,2,7]=>0001101
[4,8,3,5,1,7,2,6]=>[5,7,8,4,3,2,1,6]=>[4,8,3,7,2,5,1,6]=>0001011
[4,7,3,5,1,8,2,6]=>[5,8,7,4,3,2,1,6]=>[4,7,3,8,2,5,1,6]=>0001011
[5,6,2,3,1,7,4,8]=>[3,6,2,7,5,1,4,8]=>[5,7,2,3,1,6,4,8]=>0100110
[5,6,2,4,1,8,3,7]=>[4,6,8,2,5,1,3,7]=>[5,8,2,6,1,4,3,7]=>0010101
[4,6,2,5,1,8,3,7]=>[5,6,8,4,2,1,3,7]=>[4,8,2,6,1,5,3,7]=>0001101
[4,5,1,8,3,7,2,6]=>[5,7,8,4,1,2,3,6]=>[4,8,1,7,2,5,3,6]=>0001011
[4,5,1,7,3,8,2,6]=>[5,8,7,4,1,2,3,6]=>[4,7,1,8,2,5,3,6]=>0001011
[5,6,2,7,3,8,1,4]=>[8,6,7,1,5,2,3,4]=>[5,7,1,6,2,8,3,4]=>0000111
[5,6,2,7,4,8,1,3]=>[8,6,1,7,5,2,4,3]=>[5,7,1,6,4,8,2,3]=>0000111
[5,6,2,8,3,7,1,4]=>[7,6,8,1,5,2,3,4]=>[5,8,1,6,2,7,3,4]=>0000111
[4,6,2,8,3,7,1,5]=>[7,6,8,4,1,2,3,5]=>[4,8,1,6,2,7,3,5]=>0000111
[4,5,1,8,3,6,2,7]=>[5,6,8,4,1,3,2,7]=>[4,8,1,6,3,5,2,7]=>0001101
[9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]=>10000001
[10,2,1,3,4,5,6,7,8,9]=>[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]=>100000001
[3,4,2,5,6,7,8,9,1]=>[9,4,3,2,5,6,7,8,1]=>[3,4,2,5,6,7,8,9,1]=>00100001
[3,2,4,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,9,10,1]=>010000001
[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>[2,3,4,5,6,7,8,9,10,11,1]=>0000000001
[6,5,3,2,1,4,8,7]=>[2,3,5,1,6,4,8,7]=>[6,5,3,2,1,4,8,7]=>1101101
[4,6,3,5,2,1,8,7]=>[2,5,6,4,3,1,8,7]=>[4,6,3,5,2,1,8,7]=>1001101
[6,8,2,4,5,7,3,1]=>[3,7,8,1,4,6,5,2]=>[6,8,1,4,5,7,3,2]=>0100011
[8,7,2,4,5,3,1,6]=>[3,5,7,1,4,2,8,6]=>[8,7,1,4,5,3,2,6]=>0101011
[3,6,1,4,5,2,8,7]=>[6,5,3,1,4,2,8,7]=>[3,5,1,4,6,2,8,7]=>0001101
[8,3,7,4,5,2,1,6]=>[2,5,8,7,4,1,3,6]=>[7,4,8,2,1,5,3,6]=>1001011
[5,8,7,4,3,6,2,1]=>[2,6,4,7,5,3,8,1]=>[5,8,7,4,3,6,2,1]=>1010111
[2,8,7,4,3,6,1,5]=>[6,2,4,7,1,3,8,5]=>[2,8,7,4,1,6,3,5]=>0010111
[8,7,3,5,1,4,2,6]=>[5,4,7,1,3,2,8,6]=>[8,7,1,4,3,5,2,6]=>0011011
[2,1,6,8,5,7,4,3]=>[2,1,4,7,8,6,5,3]=>[2,1,6,8,5,7,4,3]=>1010011
[6,8,3,5,1,7,4,2]=>[5,4,7,8,2,6,1,3]=>[6,8,2,7,4,1,5,3]=>0011011
[5,1,8,4,7,6,3,2]=>[5,3,6,7,1,8,2,4]=>[8,3,1,7,6,2,5,4]=>0101111
[2,5,8,4,7,6,3,1]=>[3,2,6,7,5,8,1,4]=>[2,5,8,3,1,7,6,4]=>0100111
[4,3,8,1,5,6,7,2]=>[8,7,4,3,1,5,6,2]=>[4,3,7,1,5,6,8,2]=>0010011
[4,8,1,3,5,6,7,2]=>[8,7,1,4,3,5,6,2]=>[4,7,1,3,5,6,8,2]=>0000011
[5,8,3,6,1,4,7,2]=>[6,7,8,1,5,3,4,2]=>[5,8,1,7,3,4,6,2]=>0000111
[4,8,3,6,1,2,7,5]=>[6,1,8,4,7,3,2,5]=>[4,7,3,8,1,2,6,5]=>0000111
[3,8,7,4,1,6,2,5]=>[4,7,3,6,1,2,8,5]=>[3,6,1,8,7,4,2,5]=>0010111
[8,7,1,4,2,6,3,5]=>[7,4,6,1,3,2,8,5]=>[6,1,4,3,8,7,2,5]=>0010111
[8,6,3,1,2,4,7,5]=>[3,1,6,2,8,7,5,4]=>[7,5,8,6,3,1,2,4]=>0100111
[8,1,7,4,5,2,3,6]=>[8,5,2,7,4,3,1,6]=>[7,4,5,2,3,8,1,6]=>0001011
[2,8,7,4,5,1,3,6]=>[5,2,1,7,4,3,8,6]=>[2,8,7,4,5,1,3,6]=>0001011
[8,6,3,2,1,4,7,5]=>[2,3,6,1,8,7,5,4]=>[7,5,8,6,3,2,1,4]=>1100111
[8,7,3,5,2,1,4,6]=>[2,5,7,1,3,4,8,6]=>[8,7,2,1,5,3,4,6]=>1001011
[5,8,3,6,2,1,7,4]=>[2,6,8,7,5,3,1,4]=>[5,7,3,8,2,1,6,4]=>1000111
[5,8,7,4,2,6,1,3]=>[6,4,1,7,5,2,8,3]=>[5,8,7,4,1,6,2,3]=>0010111
[2,6,8,4,5,7,1,3]=>[7,2,1,8,4,6,5,3]=>[2,6,8,4,5,7,1,3]=>0000011
[6,1,8,4,5,7,2,3]=>[6,7,2,8,4,1,5,3]=>[8,4,7,2,5,6,1,3]=>0000111
[6,8,3,5,1,7,2,4]=>[5,7,8,2,3,6,1,4]=>[6,8,2,7,3,5,1,4]=>0001011
[2,1,5,8,3,6,7,4]=>[2,1,8,7,5,3,6,4]=>[2,1,5,7,3,6,8,4]=>1000011
[5,8,3,6,1,2,7,4]=>[6,1,8,7,5,3,2,4]=>[5,7,3,8,1,2,6,4]=>0000111
[4,1,8,2,5,6,7,3]=>[4,8,7,1,2,5,6,3]=>[7,1,5,6,8,2,4,3]=>0010011
[2,4,8,1,5,6,7,3]=>[8,2,7,4,1,5,6,3]=>[2,4,7,1,5,6,8,3]=>0000011
[3,4,8,2,5,6,7,1]=>[7,8,3,4,2,5,6,1]=>[3,4,8,2,5,6,7,1]=>0000011
[5,8,1,4,7,6,2,3]=>[8,6,2,1,5,7,4,3]=>[5,7,6,2,4,8,1,3]=>0000111
[4,5,3,8,6,1,7,2]=>[6,8,5,4,3,7,2,1]=>[4,5,3,7,2,8,6,1]=>0001111
[2,4,6,8,10,1,3,5,7,9]=>[10,2,1,4,3,6,5,8,7,9]=>[2,4,6,8,10,1,3,5,7,9]=>000000001
[2,4,6,9,10,1,3,5,7,8]=>[10,2,1,4,3,6,5,7,9,8]=>[2,4,6,9,10,1,3,5,7,8]=>000000001
[2,4,7,8,10,1,3,5,6,9]=>[10,2,1,4,3,5,7,8,6,9]=>[2,4,7,8,10,1,3,5,6,9]=>000000001
[2,4,7,9,10,1,3,5,6,8]=>[10,2,1,4,3,5,7,6,9,8]=>[2,4,7,9,10,1,3,5,6,8]=>000000001
[2,4,8,9,10,1,3,5,6,7]=>[10,2,1,4,3,5,6,8,9,7]=>[2,4,8,9,10,1,3,5,6,7]=>000000001
[2,5,6,8,10,1,3,4,7,9]=>[10,2,1,3,5,6,4,8,7,9]=>[2,5,6,8,10,1,3,4,7,9]=>000000001
[2,5,6,9,10,1,3,4,7,8]=>[10,2,1,3,5,6,4,7,9,8]=>[2,5,6,9,10,1,3,4,7,8]=>000000001
[2,5,7,8,10,1,3,4,6,9]=>[10,2,1,3,5,4,7,8,6,9]=>[2,5,7,8,10,1,3,4,6,9]=>000000001
[2,5,7,9,10,1,3,4,6,8]=>[10,2,1,3,5,4,7,6,9,8]=>[2,5,7,9,10,1,3,4,6,8]=>000000001
[2,5,8,9,10,1,3,4,6,7]=>[10,2,1,3,5,4,6,8,9,7]=>[2,5,8,9,10,1,3,4,6,7]=>000000001
[2,6,7,8,10,1,3,4,5,9]=>[10,2,1,3,4,6,7,8,5,9]=>[2,6,7,8,10,1,3,4,5,9]=>000000001
[2,6,7,9,10,1,3,4,5,8]=>[10,2,1,3,4,6,7,5,9,8]=>[2,6,7,9,10,1,3,4,5,8]=>000000001
[2,6,8,9,10,1,3,4,5,7]=>[10,2,1,3,4,6,5,8,9,7]=>[2,6,8,9,10,1,3,4,5,7]=>000000001
[2,7,8,9,10,1,3,4,5,6]=>[10,2,1,3,4,5,7,8,9,6]=>[2,7,8,9,10,1,3,4,5,6]=>000000001
[3,4,6,8,10,1,2,5,7,9]=>[10,1,3,4,2,6,5,8,7,9]=>[3,4,6,8,10,1,2,5,7,9]=>000000001
[3,4,6,9,10,1,2,5,7,8]=>[10,1,3,4,2,6,5,7,9,8]=>[3,4,6,9,10,1,2,5,7,8]=>000000001
[3,4,7,8,10,1,2,5,6,9]=>[10,1,3,4,2,5,7,8,6,9]=>[3,4,7,8,10,1,2,5,6,9]=>000000001
[3,4,7,9,10,1,2,5,6,8]=>[10,1,3,4,2,5,7,6,9,8]=>[3,4,7,9,10,1,2,5,6,8]=>000000001
[3,4,8,9,10,1,2,5,6,7]=>[10,1,3,4,2,5,6,8,9,7]=>[3,4,8,9,10,1,2,5,6,7]=>000000001
[3,5,6,8,10,1,2,4,7,9]=>[10,1,3,2,5,6,4,8,7,9]=>[3,5,6,8,10,1,2,4,7,9]=>000000001
[3,5,6,9,10,1,2,4,7,8]=>[10,1,3,2,5,6,4,7,9,8]=>[3,5,6,9,10,1,2,4,7,8]=>000000001
[3,5,7,8,10,1,2,4,6,9]=>[10,1,3,2,5,4,7,8,6,9]=>[3,5,7,8,10,1,2,4,6,9]=>000000001
[3,5,7,9,10,1,2,4,6,8]=>[10,1,3,2,5,4,7,6,9,8]=>[3,5,7,9,10,1,2,4,6,8]=>000000001
[3,5,8,9,10,1,2,4,6,7]=>[10,1,3,2,5,4,6,8,9,7]=>[3,5,8,9,10,1,2,4,6,7]=>000000001
[3,6,7,8,10,1,2,4,5,9]=>[10,1,3,2,4,6,7,8,5,9]=>[3,6,7,8,10,1,2,4,5,9]=>000000001
[3,6,7,9,10,1,2,4,5,8]=>[10,1,3,2,4,6,7,5,9,8]=>[3,6,7,9,10,1,2,4,5,8]=>000000001
[3,6,8,9,10,1,2,4,5,7]=>[10,1,3,2,4,6,5,8,9,7]=>[3,6,8,9,10,1,2,4,5,7]=>000000001
[3,7,8,9,10,1,2,4,5,6]=>[10,1,3,2,4,5,7,8,9,6]=>[3,7,8,9,10,1,2,4,5,6]=>000000001
[4,5,6,8,10,1,2,3,7,9]=>[10,1,2,4,5,6,3,8,7,9]=>[4,5,6,8,10,1,2,3,7,9]=>000000001
[4,5,6,9,10,1,2,3,7,8]=>[10,1,2,4,5,6,3,7,9,8]=>[4,5,6,9,10,1,2,3,7,8]=>000000001
[4,5,7,8,10,1,2,3,6,9]=>[10,1,2,4,5,3,7,8,6,9]=>[4,5,7,8,10,1,2,3,6,9]=>000000001
[4,5,7,9,10,1,2,3,6,8]=>[10,1,2,4,5,3,7,6,9,8]=>[4,5,7,9,10,1,2,3,6,8]=>000000001
[4,5,8,9,10,1,2,3,6,7]=>[10,1,2,4,5,3,6,8,9,7]=>[4,5,8,9,10,1,2,3,6,7]=>000000001
[4,6,7,8,10,1,2,3,5,9]=>[10,1,2,4,3,6,7,8,5,9]=>[4,6,7,8,10,1,2,3,5,9]=>000000001
[4,6,7,9,10,1,2,3,5,8]=>[10,1,2,4,3,6,7,5,9,8]=>[4,6,7,9,10,1,2,3,5,8]=>000000001
[4,6,8,9,10,1,2,3,5,7]=>[10,1,2,4,3,6,5,8,9,7]=>[4,6,8,9,10,1,2,3,5,7]=>000000001
[4,7,8,9,10,1,2,3,5,6]=>[10,1,2,4,3,5,7,8,9,6]=>[4,7,8,9,10,1,2,3,5,6]=>000000001
[5,6,7,8,10,1,2,3,4,9]=>[10,1,2,3,5,6,7,8,4,9]=>[5,6,7,8,10,1,2,3,4,9]=>000000001
[5,6,7,9,10,1,2,3,4,8]=>[10,1,2,3,5,6,7,4,9,8]=>[5,6,7,9,10,1,2,3,4,8]=>000000001
[5,6,8,9,10,1,2,3,4,7]=>[10,1,2,3,5,6,4,8,9,7]=>[5,6,8,9,10,1,2,3,4,7]=>000000001
[5,7,8,9,10,1,2,3,4,6]=>[10,1,2,3,5,4,7,8,9,6]=>[5,7,8,9,10,1,2,3,4,6]=>000000001
[2,4,6,8,10,12,1,3,5,7,9,11]=>[12,2,1,4,3,6,5,8,7,10,9,11]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>00000000001
[2,4,6,8,11,12,1,3,5,7,9,10]=>[12,2,1,4,3,6,5,8,7,9,11,10]=>[2,4,6,8,11,12,1,3,5,7,9,10]=>00000000001
[2,4,6,9,10,12,1,3,5,7,8,11]=>[12,2,1,4,3,6,5,7,9,10,8,11]=>[2,4,6,9,10,12,1,3,5,7,8,11]=>00000000001
[2,4,6,9,11,12,1,3,5,7,8,10]=>[12,2,1,4,3,6,5,7,9,8,11,10]=>[2,4,6,9,11,12,1,3,5,7,8,10]=>00000000001
[2,4,6,10,11,12,1,3,5,7,8,9]=>[12,2,1,4,3,6,5,7,8,10,11,9]=>[2,4,6,10,11,12,1,3,5,7,8,9]=>00000000001
[2,4,7,8,10,12,1,3,5,6,9,11]=>[12,2,1,4,3,5,7,8,6,10,9,11]=>[2,4,7,8,10,12,1,3,5,6,9,11]=>00000000001
[2,4,7,8,11,12,1,3,5,6,9,10]=>[12,2,1,4,3,5,7,8,6,9,11,10]=>[2,4,7,8,11,12,1,3,5,6,9,10]=>00000000001
[2,4,7,9,10,12,1,3,5,6,8,11]=>[12,2,1,4,3,5,7,6,9,10,8,11]=>[2,4,7,9,10,12,1,3,5,6,8,11]=>00000000001
[2,4,7,9,11,12,1,3,5,6,8,10]=>[12,2,1,4,3,5,7,6,9,8,11,10]=>[2,4,7,9,11,12,1,3,5,6,8,10]=>00000000001
[2,4,7,10,11,12,1,3,5,6,8,9]=>[12,2,1,4,3,5,7,6,8,10,11,9]=>[2,4,7,10,11,12,1,3,5,6,8,9]=>00000000001
[2,4,8,9,10,12,1,3,5,6,7,11]=>[12,2,1,4,3,5,6,8,9,10,7,11]=>[2,4,8,9,10,12,1,3,5,6,7,11]=>00000000001
[2,4,8,9,11,12,1,3,5,6,7,10]=>[12,2,1,4,3,5,6,8,9,7,11,10]=>[2,4,8,9,11,12,1,3,5,6,7,10]=>00000000001
[2,4,8,10,11,12,1,3,5,6,7,9]=>[12,2,1,4,3,5,6,8,7,10,11,9]=>[2,4,8,10,11,12,1,3,5,6,7,9]=>00000000001
[2,4,9,10,11,12,1,3,5,6,7,8]=>[12,2,1,4,3,5,6,7,9,10,11,8]=>[2,4,9,10,11,12,1,3,5,6,7,8]=>00000000001
[2,5,6,8,10,12,1,3,4,7,9,11]=>[12,2,1,3,5,6,4,8,7,10,9,11]=>[2,5,6,8,10,12,1,3,4,7,9,11]=>00000000001
[2,5,6,8,11,12,1,3,4,7,9,10]=>[12,2,1,3,5,6,4,8,7,9,11,10]=>[2,5,6,8,11,12,1,3,4,7,9,10]=>00000000001
[2,5,6,9,10,12,1,3,4,7,8,11]=>[12,2,1,3,5,6,4,7,9,10,8,11]=>[2,5,6,9,10,12,1,3,4,7,8,11]=>00000000001
[2,5,6,9,11,12,1,3,4,7,8,10]=>[12,2,1,3,5,6,4,7,9,8,11,10]=>[2,5,6,9,11,12,1,3,4,7,8,10]=>00000000001
[2,5,6,10,11,12,1,3,4,7,8,9]=>[12,2,1,3,5,6,4,7,8,10,11,9]=>[2,5,6,10,11,12,1,3,4,7,8,9]=>00000000001
[2,5,7,8,10,12,1,3,4,6,9,11]=>[12,2,1,3,5,4,7,8,6,10,9,11]=>[2,5,7,8,10,12,1,3,4,6,9,11]=>00000000001
[2,5,7,8,11,12,1,3,4,6,9,10]=>[12,2,1,3,5,4,7,8,6,9,11,10]=>[2,5,7,8,11,12,1,3,4,6,9,10]=>00000000001
[2,5,7,9,10,12,1,3,4,6,8,11]=>[12,2,1,3,5,4,7,6,9,10,8,11]=>[2,5,7,9,10,12,1,3,4,6,8,11]=>00000000001
[2,5,7,9,11,12,1,3,4,6,8,10]=>[12,2,1,3,5,4,7,6,9,8,11,10]=>[2,5,7,9,11,12,1,3,4,6,8,10]=>00000000001
[2,5,7,10,11,12,1,3,4,6,8,9]=>[12,2,1,3,5,4,7,6,8,10,11,9]=>[2,5,7,10,11,12,1,3,4,6,8,9]=>00000000001
[2,5,8,9,10,12,1,3,4,6,7,11]=>[12,2,1,3,5,4,6,8,9,10,7,11]=>[2,5,8,9,10,12,1,3,4,6,7,11]=>00000000001
[2,5,8,9,11,12,1,3,4,6,7,10]=>[12,2,1,3,5,4,6,8,9,7,11,10]=>[2,5,8,9,11,12,1,3,4,6,7,10]=>00000000001
[2,5,8,10,11,12,1,3,4,6,7,9]=>[12,2,1,3,5,4,6,8,7,10,11,9]=>[2,5,8,10,11,12,1,3,4,6,7,9]=>00000000001
[2,5,9,10,11,12,1,3,4,6,7,8]=>[12,2,1,3,5,4,6,7,9,10,11,8]=>[2,5,9,10,11,12,1,3,4,6,7,8]=>00000000001
[2,6,7,8,10,12,1,3,4,5,9,11]=>[12,2,1,3,4,6,7,8,5,10,9,11]=>[2,6,7,8,10,12,1,3,4,5,9,11]=>00000000001
[2,6,7,8,11,12,1,3,4,5,9,10]=>[12,2,1,3,4,6,7,8,5,9,11,10]=>[2,6,7,8,11,12,1,3,4,5,9,10]=>00000000001
[2,6,7,9,10,12,1,3,4,5,8,11]=>[12,2,1,3,4,6,7,5,9,10,8,11]=>[2,6,7,9,10,12,1,3,4,5,8,11]=>00000000001
[2,6,7,9,11,12,1,3,4,5,8,10]=>[12,2,1,3,4,6,7,5,9,8,11,10]=>[2,6,7,9,11,12,1,3,4,5,8,10]=>00000000001
[2,6,7,10,11,12,1,3,4,5,8,9]=>[12,2,1,3,4,6,7,5,8,10,11,9]=>[2,6,7,10,11,12,1,3,4,5,8,9]=>00000000001
[2,6,8,9,10,12,1,3,4,5,7,11]=>[12,2,1,3,4,6,5,8,9,10,7,11]=>[2,6,8,9,10,12,1,3,4,5,7,11]=>00000000001
[2,6,8,9,11,12,1,3,4,5,7,10]=>[12,2,1,3,4,6,5,8,9,7,11,10]=>[2,6,8,9,11,12,1,3,4,5,7,10]=>00000000001
[2,6,8,10,11,12,1,3,4,5,7,9]=>[12,2,1,3,4,6,5,8,7,10,11,9]=>[2,6,8,10,11,12,1,3,4,5,7,9]=>00000000001
[2,6,9,10,11,12,1,3,4,5,7,8]=>[12,2,1,3,4,6,5,7,9,10,11,8]=>[2,6,9,10,11,12,1,3,4,5,7,8]=>00000000001
[2,7,8,9,10,12,1,3,4,5,6,11]=>[12,2,1,3,4,5,7,8,9,10,6,11]=>[2,7,8,9,10,12,1,3,4,5,6,11]=>00000000001
[2,7,8,9,11,12,1,3,4,5,6,10]=>[12,2,1,3,4,5,7,8,9,6,11,10]=>[2,7,8,9,11,12,1,3,4,5,6,10]=>00000000001
[2,7,8,10,11,12,1,3,4,5,6,9]=>[12,2,1,3,4,5,7,8,6,10,11,9]=>[2,7,8,10,11,12,1,3,4,5,6,9]=>00000000001
[2,7,9,10,11,12,1,3,4,5,6,8]=>[12,2,1,3,4,5,7,6,9,10,11,8]=>[2,7,9,10,11,12,1,3,4,5,6,8]=>00000000001
[2,8,9,10,11,12,1,3,4,5,6,7]=>[12,2,1,3,4,5,6,8,9,10,11,7]=>[2,8,9,10,11,12,1,3,4,5,6,7]=>00000000001
[3,4,6,8,10,12,1,2,5,7,9,11]=>[12,1,3,4,2,6,5,8,7,10,9,11]=>[3,4,6,8,10,12,1,2,5,7,9,11]=>00000000001
[3,4,6,8,11,12,1,2,5,7,9,10]=>[12,1,3,4,2,6,5,8,7,9,11,10]=>[3,4,6,8,11,12,1,2,5,7,9,10]=>00000000001
[3,4,6,9,10,12,1,2,5,7,8,11]=>[12,1,3,4,2,6,5,7,9,10,8,11]=>[3,4,6,9,10,12,1,2,5,7,8,11]=>00000000001
[3,4,6,9,11,12,1,2,5,7,8,10]=>[12,1,3,4,2,6,5,7,9,8,11,10]=>[3,4,6,9,11,12,1,2,5,7,8,10]=>00000000001
[3,4,6,10,11,12,1,2,5,7,8,9]=>[12,1,3,4,2,6,5,7,8,10,11,9]=>[3,4,6,10,11,12,1,2,5,7,8,9]=>00000000001
[3,4,7,8,10,12,1,2,5,6,9,11]=>[12,1,3,4,2,5,7,8,6,10,9,11]=>[3,4,7,8,10,12,1,2,5,6,9,11]=>00000000001
[3,4,7,8,11,12,1,2,5,6,9,10]=>[12,1,3,4,2,5,7,8,6,9,11,10]=>[3,4,7,8,11,12,1,2,5,6,9,10]=>00000000001
[3,4,7,9,10,12,1,2,5,6,8,11]=>[12,1,3,4,2,5,7,6,9,10,8,11]=>[3,4,7,9,10,12,1,2,5,6,8,11]=>00000000001
[3,4,7,9,11,12,1,2,5,6,8,10]=>[12,1,3,4,2,5,7,6,9,8,11,10]=>[3,4,7,9,11,12,1,2,5,6,8,10]=>00000000001
[3,4,7,10,11,12,1,2,5,6,8,9]=>[12,1,3,4,2,5,7,6,8,10,11,9]=>[3,4,7,10,11,12,1,2,5,6,8,9]=>00000000001
[3,4,8,9,10,12,1,2,5,6,7,11]=>[12,1,3,4,2,5,6,8,9,10,7,11]=>[3,4,8,9,10,12,1,2,5,6,7,11]=>00000000001
[3,4,8,9,11,12,1,2,5,6,7,10]=>[12,1,3,4,2,5,6,8,9,7,11,10]=>[3,4,8,9,11,12,1,2,5,6,7,10]=>00000000001
[3,4,8,10,11,12,1,2,5,6,7,9]=>[12,1,3,4,2,5,6,8,7,10,11,9]=>[3,4,8,10,11,12,1,2,5,6,7,9]=>00000000001
[3,4,9,10,11,12,1,2,5,6,7,8]=>[12,1,3,4,2,5,6,7,9,10,11,8]=>[3,4,9,10,11,12,1,2,5,6,7,8]=>00000000001
[3,5,6,8,10,12,1,2,4,7,9,11]=>[12,1,3,2,5,6,4,8,7,10,9,11]=>[3,5,6,8,10,12,1,2,4,7,9,11]=>00000000001
[3,5,6,8,11,12,1,2,4,7,9,10]=>[12,1,3,2,5,6,4,8,7,9,11,10]=>[3,5,6,8,11,12,1,2,4,7,9,10]=>00000000001
[3,5,6,9,10,12,1,2,4,7,8,11]=>[12,1,3,2,5,6,4,7,9,10,8,11]=>[3,5,6,9,10,12,1,2,4,7,8,11]=>00000000001
[3,5,6,9,11,12,1,2,4,7,8,10]=>[12,1,3,2,5,6,4,7,9,8,11,10]=>[3,5,6,9,11,12,1,2,4,7,8,10]=>00000000001
[3,5,6,10,11,12,1,2,4,7,8,9]=>[12,1,3,2,5,6,4,7,8,10,11,9]=>[3,5,6,10,11,12,1,2,4,7,8,9]=>00000000001
[3,5,7,8,10,12,1,2,4,6,9,11]=>[12,1,3,2,5,4,7,8,6,10,9,11]=>[3,5,7,8,10,12,1,2,4,6,9,11]=>00000000001
[3,5,7,8,11,12,1,2,4,6,9,10]=>[12,1,3,2,5,4,7,8,6,9,11,10]=>[3,5,7,8,11,12,1,2,4,6,9,10]=>00000000001
[3,5,7,9,10,12,1,2,4,6,8,11]=>[12,1,3,2,5,4,7,6,9,10,8,11]=>[3,5,7,9,10,12,1,2,4,6,8,11]=>00000000001
[3,5,7,9,11,12,1,2,4,6,8,10]=>[12,1,3,2,5,4,7,6,9,8,11,10]=>[3,5,7,9,11,12,1,2,4,6,8,10]=>00000000001
[3,5,7,10,11,12,1,2,4,6,8,9]=>[12,1,3,2,5,4,7,6,8,10,11,9]=>[3,5,7,10,11,12,1,2,4,6,8,9]=>00000000001
[3,5,8,9,10,12,1,2,4,6,7,11]=>[12,1,3,2,5,4,6,8,9,10,7,11]=>[3,5,8,9,10,12,1,2,4,6,7,11]=>00000000001
[3,5,8,9,11,12,1,2,4,6,7,10]=>[12,1,3,2,5,4,6,8,9,7,11,10]=>[3,5,8,9,11,12,1,2,4,6,7,10]=>00000000001
[3,5,8,10,11,12,1,2,4,6,7,9]=>[12,1,3,2,5,4,6,8,7,10,11,9]=>[3,5,8,10,11,12,1,2,4,6,7,9]=>00000000001
[3,5,9,10,11,12,1,2,4,6,7,8]=>[12,1,3,2,5,4,6,7,9,10,11,8]=>[3,5,9,10,11,12,1,2,4,6,7,8]=>00000000001
[3,6,7,8,10,12,1,2,4,5,9,11]=>[12,1,3,2,4,6,7,8,5,10,9,11]=>[3,6,7,8,10,12,1,2,4,5,9,11]=>00000000001
[3,6,7,8,11,12,1,2,4,5,9,10]=>[12,1,3,2,4,6,7,8,5,9,11,10]=>[3,6,7,8,11,12,1,2,4,5,9,10]=>00000000001
[3,6,7,9,10,12,1,2,4,5,8,11]=>[12,1,3,2,4,6,7,5,9,10,8,11]=>[3,6,7,9,10,12,1,2,4,5,8,11]=>00000000001
[3,6,7,9,11,12,1,2,4,5,8,10]=>[12,1,3,2,4,6,7,5,9,8,11,10]=>[3,6,7,9,11,12,1,2,4,5,8,10]=>00000000001
[3,6,7,10,11,12,1,2,4,5,8,9]=>[12,1,3,2,4,6,7,5,8,10,11,9]=>[3,6,7,10,11,12,1,2,4,5,8,9]=>00000000001
[3,6,8,9,10,12,1,2,4,5,7,11]=>[12,1,3,2,4,6,5,8,9,10,7,11]=>[3,6,8,9,10,12,1,2,4,5,7,11]=>00000000001
[3,6,8,9,11,12,1,2,4,5,7,10]=>[12,1,3,2,4,6,5,8,9,7,11,10]=>[3,6,8,9,11,12,1,2,4,5,7,10]=>00000000001
[3,6,8,10,11,12,1,2,4,5,7,9]=>[12,1,3,2,4,6,5,8,7,10,11,9]=>[3,6,8,10,11,12,1,2,4,5,7,9]=>00000000001
[3,6,9,10,11,12,1,2,4,5,7,8]=>[12,1,3,2,4,6,5,7,9,10,11,8]=>[3,6,9,10,11,12,1,2,4,5,7,8]=>00000000001
[3,7,8,9,10,12,1,2,4,5,6,11]=>[12,1,3,2,4,5,7,8,9,10,6,11]=>[3,7,8,9,10,12,1,2,4,5,6,11]=>00000000001
[3,7,8,9,11,12,1,2,4,5,6,10]=>[12,1,3,2,4,5,7,8,9,6,11,10]=>[3,7,8,9,11,12,1,2,4,5,6,10]=>00000000001
[3,7,8,10,11,12,1,2,4,5,6,9]=>[12,1,3,2,4,5,7,8,6,10,11,9]=>[3,7,8,10,11,12,1,2,4,5,6,9]=>00000000001
[3,7,9,10,11,12,1,2,4,5,6,8]=>[12,1,3,2,4,5,7,6,9,10,11,8]=>[3,7,9,10,11,12,1,2,4,5,6,8]=>00000000001
[3,8,9,10,11,12,1,2,4,5,6,7]=>[12,1,3,2,4,5,6,8,9,10,11,7]=>[3,8,9,10,11,12,1,2,4,5,6,7]=>00000000001
[4,5,6,8,10,12,1,2,3,7,9,11]=>[12,1,2,4,5,6,3,8,7,10,9,11]=>[4,5,6,8,10,12,1,2,3,7,9,11]=>00000000001
[4,5,6,8,11,12,1,2,3,7,9,10]=>[12,1,2,4,5,6,3,8,7,9,11,10]=>[4,5,6,8,11,12,1,2,3,7,9,10]=>00000000001
[4,5,6,9,10,12,1,2,3,7,8,11]=>[12,1,2,4,5,6,3,7,9,10,8,11]=>[4,5,6,9,10,12,1,2,3,7,8,11]=>00000000001
[4,5,6,9,11,12,1,2,3,7,8,10]=>[12,1,2,4,5,6,3,7,9,8,11,10]=>[4,5,6,9,11,12,1,2,3,7,8,10]=>00000000001
[4,5,6,10,11,12,1,2,3,7,8,9]=>[12,1,2,4,5,6,3,7,8,10,11,9]=>[4,5,6,10,11,12,1,2,3,7,8,9]=>00000000001
[4,5,7,8,10,12,1,2,3,6,9,11]=>[12,1,2,4,5,3,7,8,6,10,9,11]=>[4,5,7,8,10,12,1,2,3,6,9,11]=>00000000001
[4,5,7,8,11,12,1,2,3,6,9,10]=>[12,1,2,4,5,3,7,8,6,9,11,10]=>[4,5,7,8,11,12,1,2,3,6,9,10]=>00000000001
[4,5,7,9,10,12,1,2,3,6,8,11]=>[12,1,2,4,5,3,7,6,9,10,8,11]=>[4,5,7,9,10,12,1,2,3,6,8,11]=>00000000001
[4,5,7,9,11,12,1,2,3,6,8,10]=>[12,1,2,4,5,3,7,6,9,8,11,10]=>[4,5,7,9,11,12,1,2,3,6,8,10]=>00000000001
[4,5,7,10,11,12,1,2,3,6,8,9]=>[12,1,2,4,5,3,7,6,8,10,11,9]=>[4,5,7,10,11,12,1,2,3,6,8,9]=>00000000001
[4,5,8,9,10,12,1,2,3,6,7,11]=>[12,1,2,4,5,3,6,8,9,10,7,11]=>[4,5,8,9,10,12,1,2,3,6,7,11]=>00000000001
[4,5,8,9,11,12,1,2,3,6,7,10]=>[12,1,2,4,5,3,6,8,9,7,11,10]=>[4,5,8,9,11,12,1,2,3,6,7,10]=>00000000001
[4,5,8,10,11,12,1,2,3,6,7,9]=>[12,1,2,4,5,3,6,8,7,10,11,9]=>[4,5,8,10,11,12,1,2,3,6,7,9]=>00000000001
[4,5,9,10,11,12,1,2,3,6,7,8]=>[12,1,2,4,5,3,6,7,9,10,11,8]=>[4,5,9,10,11,12,1,2,3,6,7,8]=>00000000001
[4,6,7,8,10,12,1,2,3,5,9,11]=>[12,1,2,4,3,6,7,8,5,10,9,11]=>[4,6,7,8,10,12,1,2,3,5,9,11]=>00000000001
[4,6,7,8,11,12,1,2,3,5,9,10]=>[12,1,2,4,3,6,7,8,5,9,11,10]=>[4,6,7,8,11,12,1,2,3,5,9,10]=>00000000001
[4,6,7,9,10,12,1,2,3,5,8,11]=>[12,1,2,4,3,6,7,5,9,10,8,11]=>[4,6,7,9,10,12,1,2,3,5,8,11]=>00000000001
[4,6,7,9,11,12,1,2,3,5,8,10]=>[12,1,2,4,3,6,7,5,9,8,11,10]=>[4,6,7,9,11,12,1,2,3,5,8,10]=>00000000001
[4,6,7,10,11,12,1,2,3,5,8,9]=>[12,1,2,4,3,6,7,5,8,10,11,9]=>[4,6,7,10,11,12,1,2,3,5,8,9]=>00000000001
[4,6,8,9,10,12,1,2,3,5,7,11]=>[12,1,2,4,3,6,5,8,9,10,7,11]=>[4,6,8,9,10,12,1,2,3,5,7,11]=>00000000001
[4,6,8,9,11,12,1,2,3,5,7,10]=>[12,1,2,4,3,6,5,8,9,7,11,10]=>[4,6,8,9,11,12,1,2,3,5,7,10]=>00000000001
[4,6,8,10,11,12,1,2,3,5,7,9]=>[12,1,2,4,3,6,5,8,7,10,11,9]=>[4,6,8,10,11,12,1,2,3,5,7,9]=>00000000001
[4,6,9,10,11,12,1,2,3,5,7,8]=>[12,1,2,4,3,6,5,7,9,10,11,8]=>[4,6,9,10,11,12,1,2,3,5,7,8]=>00000000001
[4,7,8,9,10,12,1,2,3,5,6,11]=>[12,1,2,4,3,5,7,8,9,10,6,11]=>[4,7,8,9,10,12,1,2,3,5,6,11]=>00000000001
[4,7,8,9,11,12,1,2,3,5,6,10]=>[12,1,2,4,3,5,7,8,9,6,11,10]=>[4,7,8,9,11,12,1,2,3,5,6,10]=>00000000001
[4,7,8,10,11,12,1,2,3,5,6,9]=>[12,1,2,4,3,5,7,8,6,10,11,9]=>[4,7,8,10,11,12,1,2,3,5,6,9]=>00000000001
[4,7,9,10,11,12,1,2,3,5,6,8]=>[12,1,2,4,3,5,7,6,9,10,11,8]=>[4,7,9,10,11,12,1,2,3,5,6,8]=>00000000001
[4,8,9,10,11,12,1,2,3,5,6,7]=>[12,1,2,4,3,5,6,8,9,10,11,7]=>[4,8,9,10,11,12,1,2,3,5,6,7]=>00000000001
[5,6,7,8,10,12,1,2,3,4,9,11]=>[12,1,2,3,5,6,7,8,4,10,9,11]=>[5,6,7,8,10,12,1,2,3,4,9,11]=>00000000001
[5,6,7,8,11,12,1,2,3,4,9,10]=>[12,1,2,3,5,6,7,8,4,9,11,10]=>[5,6,7,8,11,12,1,2,3,4,9,10]=>00000000001
[5,6,7,9,10,12,1,2,3,4,8,11]=>[12,1,2,3,5,6,7,4,9,10,8,11]=>[5,6,7,9,10,12,1,2,3,4,8,11]=>00000000001
[5,6,7,9,11,12,1,2,3,4,8,10]=>[12,1,2,3,5,6,7,4,9,8,11,10]=>[5,6,7,9,11,12,1,2,3,4,8,10]=>00000000001
[5,6,7,10,11,12,1,2,3,4,8,9]=>[12,1,2,3,5,6,7,4,8,10,11,9]=>[5,6,7,10,11,12,1,2,3,4,8,9]=>00000000001
[5,6,8,9,10,12,1,2,3,4,7,11]=>[12,1,2,3,5,6,4,8,9,10,7,11]=>[5,6,8,9,10,12,1,2,3,4,7,11]=>00000000001
[5,6,8,9,11,12,1,2,3,4,7,10]=>[12,1,2,3,5,6,4,8,9,7,11,10]=>[5,6,8,9,11,12,1,2,3,4,7,10]=>00000000001
[5,6,8,10,11,12,1,2,3,4,7,9]=>[12,1,2,3,5,6,4,8,7,10,11,9]=>[5,6,8,10,11,12,1,2,3,4,7,9]=>00000000001
[5,6,9,10,11,12,1,2,3,4,7,8]=>[12,1,2,3,5,6,4,7,9,10,11,8]=>[5,6,9,10,11,12,1,2,3,4,7,8]=>00000000001
[5,7,8,9,10,12,1,2,3,4,6,11]=>[12,1,2,3,5,4,7,8,9,10,6,11]=>[5,7,8,9,10,12,1,2,3,4,6,11]=>00000000001
[5,7,8,9,11,12,1,2,3,4,6,10]=>[12,1,2,3,5,4,7,8,9,6,11,10]=>[5,7,8,9,11,12,1,2,3,4,6,10]=>00000000001
[5,7,8,10,11,12,1,2,3,4,6,9]=>[12,1,2,3,5,4,7,8,6,10,11,9]=>[5,7,8,10,11,12,1,2,3,4,6,9]=>00000000001
[5,7,9,10,11,12,1,2,3,4,6,8]=>[12,1,2,3,5,4,7,6,9,10,11,8]=>[5,7,9,10,11,12,1,2,3,4,6,8]=>00000000001
[5,8,9,10,11,12,1,2,3,4,6,7]=>[12,1,2,3,5,4,6,8,9,10,11,7]=>[5,8,9,10,11,12,1,2,3,4,6,7]=>00000000001
[6,7,8,9,10,12,1,2,3,4,5,11]=>[12,1,2,3,4,6,7,8,9,10,5,11]=>[6,7,8,9,10,12,1,2,3,4,5,11]=>00000000001
[6,7,8,9,11,12,1,2,3,4,5,10]=>[12,1,2,3,4,6,7,8,9,5,11,10]=>[6,7,8,9,11,12,1,2,3,4,5,10]=>00000000001
[6,7,8,10,11,12,1,2,3,4,5,9]=>[12,1,2,3,4,6,7,8,5,10,11,9]=>[6,7,8,10,11,12,1,2,3,4,5,9]=>00000000001
[6,7,9,10,11,12,1,2,3,4,5,8]=>[12,1,2,3,4,6,7,5,9,10,11,8]=>[6,7,9,10,11,12,1,2,3,4,5,8]=>00000000001
[6,8,9,10,11,12,1,2,3,4,5,7]=>[12,1,2,3,4,6,5,8,9,10,11,7]=>[6,8,9,10,11,12,1,2,3,4,5,7]=>00000000001
[7,8,9,10,11,12,1,2,3,4,5,6]=>[12,1,2,3,4,5,7,8,9,10,11,6]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>00000000001
[4,5,7,6,2,3,8,1]=>[8,6,2,4,5,7,3,1]=>[4,5,7,6,2,3,8,1]=>0000111
[3,5,7,2,6,4,8,1]=>[8,7,3,6,5,2,4,1]=>[3,5,6,2,7,4,8,1]=>0000111
[2,5,7,3,6,4,8,1]=>[8,2,7,6,5,3,4,1]=>[2,5,6,3,7,4,8,1]=>0000111
[2,8,4,7,1,6,5,3]=>[7,2,5,6,8,1,3,4]=>[2,8,1,6,5,3,7,4]=>0001111
[8,1,3,2,7,6,5,4]=>[8,3,1,5,6,7,2,4]=>[3,1,7,6,5,2,8,4]=>0101111
[2,8,3,1,7,6,5,4]=>[3,2,8,5,6,7,1,4]=>[2,7,6,5,3,1,8,4]=>0101111
[3,8,2,1,7,6,5,4]=>[2,8,3,5,6,7,1,4]=>[3,7,6,5,2,1,8,4]=>1001111
[6,7,1,2,8,5,4,3]=>[7,1,4,5,8,6,2,3]=>[6,8,5,4,1,2,7,3]=>0011011
[8,3,2,1,7,6,5,4]=>[2,3,8,5,6,7,1,4]=>[7,6,5,3,2,1,8,4]=>1101111
[3,4,1,7,6,8,5,2]=>[4,5,3,1,8,7,6,2]=>[3,7,6,8,5,1,4,2]=>0011011
[1,4,2,7,8,6,5,3]=>[1,4,5,2,6,8,7,3]=>[1,7,8,6,5,2,4,3]=>0011101
[8,4,2,7,1,6,5,3]=>[7,4,8,5,6,1,3,2]=>[6,5,1,8,4,3,7,2]=>0011111
[5,4,7,6,8,1,3,2]=>[8,3,1,5,4,7,6,2]=>[3,1,5,4,7,6,8,2]=>0101011
[8,4,1,7,2,6,5,3]=>[4,8,7,5,6,3,2,1]=>[6,5,3,7,2,8,4,1]=>0011111
[1,4,8,7,2,6,5,3]=>[1,7,5,4,6,2,8,3]=>[1,4,6,5,2,8,7,3]=>0001111
[3,4,8,7,6,1,5,2]=>[6,5,3,4,1,7,8,2]=>[3,4,5,1,8,7,6,2]=>0001111
[5,3,7,8,6,1,4,2]=>[6,4,5,1,3,8,7,2]=>[5,1,4,3,7,8,6,2]=>0011101
[6,7,2,8,1,5,4,3]=>[8,7,4,5,1,6,2,3]=>[5,4,1,6,7,2,8,3]=>0011011
[8,3,1,2,7,6,5,4]=>[3,1,8,5,6,7,2,4]=>[7,6,5,3,1,2,8,4]=>0101111
[1,2,8,3,7,6,5,4]=>[1,2,8,5,6,7,3,4]=>[1,2,7,6,5,3,8,4]=>0001111
[2,1,8,3,7,6,5,4]=>[2,1,8,5,6,7,3,4]=>[2,1,7,6,5,3,8,4]=>1001111
[4,1,8,7,2,6,5,3]=>[4,7,5,1,6,2,8,3]=>[6,5,1,8,7,2,4,3]=>0011111
[6,7,1,8,2,5,4,3]=>[7,8,4,5,2,6,1,3]=>[5,4,2,6,8,1,7,3]=>0011011
[3,8,1,2,7,6,5,4]=>[8,1,3,5,6,7,2,4]=>[3,7,6,5,1,2,8,4]=>0001111
[2,8,1,3,7,6,5,4]=>[8,2,1,5,6,7,3,4]=>[2,7,6,5,1,3,8,4]=>0001111
[8,1,2,3,7,6,5,4]=>[8,1,2,5,6,7,3,4]=>[7,6,5,1,2,3,8,4]=>0001111
[3,1,4,5,6,7,8,9,10,2]=>[3,10,1,4,5,6,7,8,9,2]=>[4,5,6,7,8,9,10,1,3,2]=>010000001
[2,3,4,5,6,7,8,9,11,1,10]=>[11,2,3,4,5,6,7,8,9,1,10]=>[2,3,4,5,6,7,8,9,11,1,10]=>0000000001
[10,3,4,5,6,7,8,1,2,9]=>[8,1,10,3,4,5,6,7,2,9]=>[10,3,4,5,6,7,8,1,2,9]=>000000101
[3,1,4,5,6,7,8,9,10,11,2]=>[3,11,1,4,5,6,7,8,9,10,2]=>[4,5,6,7,8,9,10,11,1,3,2]=>0100000001
[2,3,4,5,6,7,8,9,10,12,1,11]=>[12,2,3,4,5,6,7,8,9,10,1,11]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>00000000001
[11,3,4,5,6,7,8,9,1,2,10]=>[9,1,11,3,4,5,6,7,8,2,10]=>[11,3,4,5,6,7,8,9,1,2,10]=>0000000101
[2,10,4,5,6,7,8,1,3,9]=>[8,2,1,10,4,5,6,7,3,9]=>[2,10,4,5,6,7,8,1,3,9]=>000000101
[6,7,1,8,4,5,2,3]=>[7,5,2,8,4,6,1,3]=>[6,8,4,5,2,7,1,3]=>0001011
[2,6,5,1,8,3,7,4]=>[5,2,6,8,7,3,4,1]=>[2,7,3,8,4,6,5,1]=>0001111
[3,6,5,1,8,2,7,4]=>[5,6,3,8,7,2,4,1]=>[3,7,2,8,4,6,5,1]=>0001111
[5,6,4,1,8,7,2,3]=>[4,6,1,7,5,2,8,3]=>[5,8,7,1,6,4,2,3]=>0010111
[6,4,5,1,8,7,2,3]=>[5,7,2,6,4,1,8,3]=>[6,4,8,7,2,5,1,3]=>0001111
[4,5,6,1,8,7,2,3]=>[6,7,2,4,5,1,8,3]=>[4,5,8,7,2,6,1,3]=>0000111
[3,5,6,1,8,2,7,4]=>[6,8,3,7,5,1,2,4]=>[3,5,7,1,8,2,6,4]=>0000111
[2,5,6,1,8,3,7,4]=>[6,2,8,7,5,1,3,4]=>[2,5,7,1,8,3,6,4]=>0000111
[3,4,6,1,2,8,7,5]=>[6,1,3,4,7,2,8,5]=>[3,4,8,7,1,2,6,5]=>0000111
[5,3,6,1,8,2,7,4]=>[6,8,5,7,3,1,2,4]=>[7,3,5,1,8,2,6,4]=>0001111
[7,3,1,5,8,2,6,4]=>[3,7,8,6,2,1,5,4]=>[6,2,8,3,1,5,7,4]=>0100111
[7,2,1,5,8,3,6,4]=>[2,7,8,6,1,3,5,4]=>[6,2,1,8,3,5,7,4]=>1000111
[6,2,5,1,8,3,7,4]=>[5,6,8,7,2,1,3,4]=>[7,2,8,1,6,3,5,4]=>0001111
[4,2,6,1,3,8,7,5]=>[6,4,1,2,7,3,8,5]=>[4,1,8,7,2,3,6,5]=>0010111
[2,3,6,1,4,8,7,5]=>[6,2,3,1,7,4,8,5]=>[2,3,8,7,1,4,6,5]=>0000111
[7,2,1,4,3,8,6,5]=>[2,7,4,1,6,8,3,5]=>[4,2,1,8,6,3,7,5]=>1010111
[8,1,2,4,3,7,6,5]=>[8,1,4,2,6,7,3,5]=>[4,1,2,7,6,3,8,5]=>0010111
[8,1,3,4,2,7,6,5]=>[8,4,1,3,6,7,2,5]=>[4,1,3,7,6,2,8,5]=>0010111
[7,3,1,4,2,8,6,5]=>[3,7,4,2,6,8,1,5]=>[4,2,8,6,3,1,7,5]=>0110111
[6,3,4,1,2,8,7,5]=>[4,1,6,3,7,2,8,5]=>[8,7,3,4,1,2,6,5]=>0010111
[4,6,3,1,2,8,7,5]=>[3,1,6,4,7,2,8,5]=>[4,8,7,3,1,2,6,5]=>0100111
[3,6,4,1,2,8,7,5]=>[4,1,3,6,7,2,8,5]=>[3,8,7,4,1,2,6,5]=>0010111
[4,7,1,3,2,8,6,5]=>[7,3,1,4,6,8,2,5]=>[3,1,4,8,6,2,7,5]=>0100111
[8,1,6,7,2,3,5,4]=>[8,7,2,5,3,1,6,4]=>[5,2,3,7,1,6,8,4]=>0001011
[2,6,3,1,4,8,7,5]=>[3,2,6,1,7,4,8,5]=>[2,8,7,3,1,4,6,5]=>0100111
[3,6,2,1,4,8,7,5]=>[2,6,3,1,7,4,8,5]=>[3,8,7,2,1,4,6,5]=>1000111
[5,6,2,1,8,3,7,4]=>[2,6,8,7,5,1,3,4]=>[5,7,2,1,8,3,6,4]=>1000111
[6,4,2,1,3,8,7,5]=>[2,4,1,6,7,3,8,5]=>[8,7,4,2,1,3,6,5]=>1010111
[5,4,2,3,1,8,7,6]=>[3,4,2,5,1,7,8,6]=>[5,4,2,3,1,8,7,6]=>0111011
[7,3,1,2,4,8,6,5]=>[3,1,7,2,6,8,4,5]=>[8,6,3,1,2,4,7,5]=>0100111
[8,1,3,2,4,7,6,5]=>[8,3,1,2,6,7,4,5]=>[3,1,7,6,2,4,8,5]=>0100111
[8,1,2,3,4,7,6,5]=>[8,1,2,3,6,7,4,5]=>[7,6,1,2,3,4,8,5]=>0000111
[2,4,3,6,1,5,8,7]=>[6,2,4,3,1,5,8,7]=>[2,4,3,6,1,5,8,7]=>0010101
[2,4,3,6,5,8,1,7]=>[8,2,4,3,6,5,1,7]=>[2,4,3,6,5,8,1,7]=>0010101
[2,4,6,3,5,8,7,1]=>[7,2,6,4,3,5,8,1]=>[2,4,6,3,5,8,7,1]=>0000111
[2,4,6,3,5,8,1,7]=>[8,2,6,4,3,5,1,7]=>[2,4,6,3,5,8,1,7]=>0000101
[2,4,1,6,5,3,8,7]=>[4,2,5,1,6,3,8,7]=>[2,6,5,1,4,3,8,7]=>0011101
[4,2,6,5,1,3,8,7]=>[5,4,1,2,6,3,8,7]=>[4,1,6,5,2,3,8,7]=>0011101
[4,2,6,5,1,8,7,3]=>[5,4,6,2,7,3,8,1]=>[8,7,2,4,3,6,5,1]=>0011111
[4,2,6,5,8,1,3,7]=>[8,4,1,2,6,5,3,7]=>[4,1,6,5,8,2,3,7]=>0010101
[4,2,6,5,8,3,1,7]=>[3,8,4,1,6,5,2,7]=>[4,1,6,5,8,3,2,7]=>0110101
[2,4,6,1,5,8,3,7]=>[6,2,8,4,1,5,3,7]=>[2,4,8,1,5,6,3,7]=>0000101
[2,4,1,6,5,8,3,7]=>[4,2,8,1,6,5,3,7]=>[2,6,5,8,1,4,3,7]=>0010101
[2,1,4,6,5,8,3,7]=>[2,1,8,4,6,5,3,7]=>[2,1,4,6,5,8,3,7]=>1000101
[4,2,6,5,8,3,7,1]=>[7,4,8,2,6,5,3,1]=>[6,5,8,2,4,3,7,1]=>0010111
[4,2,6,8,5,3,7,1]=>[7,4,5,2,8,6,3,1]=>[6,8,5,2,4,3,7,1]=>0011011
[2,4,6,8,1,5,7,3]=>[8,2,7,4,1,6,5,3]=>[2,4,6,7,1,5,8,3]=>0000011
[2,4,6,1,8,5,3,7]=>[6,2,5,4,8,1,3,7]=>[2,4,8,5,1,6,3,7]=>0001101
[2,4,6,8,1,5,3,7]=>[8,2,5,4,1,6,3,7]=>[2,4,5,1,6,8,3,7]=>0001001
[4,2,6,8,5,1,7,3]=>[5,4,8,2,7,6,3,1]=>[6,7,2,4,3,8,5,1]=>0011011
[2,4,6,8,3,5,7,1]=>[7,2,8,4,3,6,5,1]=>[2,4,6,8,3,5,7,1]=>0000011
[2,4,6,8,3,1,5,7]=>[3,2,8,4,1,6,5,7]=>[2,4,6,8,3,1,5,7]=>0100001
[2,4,6,3,1,8,5,7]=>[3,2,6,4,8,1,5,7]=>[2,4,8,3,1,6,5,7]=>0100101
[2,4,6,3,8,1,5,7]=>[8,2,6,4,1,3,5,7]=>[2,4,6,1,8,3,5,7]=>0000101
[2,4,6,3,8,5,1,7]=>[5,2,8,4,6,1,3,7]=>[2,4,6,1,8,5,3,7]=>0001101
[2,4,3,6,8,5,1,7]=>[5,2,4,3,8,6,1,7]=>[2,4,3,6,8,5,1,7]=>0011001
[2,4,3,6,8,1,5,7]=>[8,2,4,3,1,6,5,7]=>[2,4,3,6,8,1,5,7]=>0010001
[2,4,3,6,1,8,5,7]=>[6,2,4,3,8,1,5,7]=>[2,4,3,8,1,6,5,7]=>0010101
[2,4,3,1,6,8,5,7]=>[3,2,4,1,8,6,5,7]=>[2,4,3,1,6,8,5,7]=>0110001
[2,4,1,3,6,8,7,5]=>[4,2,1,3,7,6,8,5]=>[2,4,1,3,6,8,7,5]=>0010011
[4,6,2,5,8,7,3,1]=>[3,7,6,4,1,5,8,2]=>[4,6,1,5,8,7,3,2]=>0100111
[2,4,6,3,8,1,7,5]=>[8,2,6,4,7,3,1,5]=>[2,4,7,3,6,1,8,5]=>0000111
[2,4,6,3,1,8,7,5]=>[3,2,6,4,7,1,8,5]=>[2,4,8,7,3,1,6,5]=>0100111
[2,4,1,6,3,8,7,5]=>[4,2,6,1,7,3,8,5]=>[2,8,7,1,4,3,6,5]=>0010111
[2,1,4,6,3,8,7,5]=>[2,1,6,4,7,3,8,5]=>[2,1,4,8,7,3,6,5]=>1000111
[2,1,4,6,8,3,7,5]=>[2,1,8,4,7,6,3,5]=>[2,1,4,6,7,3,8,5]=>1000011
[2,4,1,6,8,3,7,5]=>[4,2,8,1,7,6,3,5]=>[2,6,7,1,4,3,8,5]=>0010011
[2,4,6,1,8,3,7,5]=>[6,2,8,4,7,1,3,5]=>[2,4,7,1,8,3,6,5]=>0000111
[2,4,6,8,1,3,7,5]=>[8,2,1,4,7,6,3,5]=>[2,4,6,7,1,3,8,5]=>0000011
[2,4,6,8,3,1,7,5]=>[3,2,8,4,7,6,1,5]=>[2,4,6,7,3,1,8,5]=>0100011
[4,6,2,8,5,7,1,3]=>[7,6,1,4,8,2,5,3]=>[4,8,1,6,5,7,2,3]=>0000111
[6,2,4,8,7,1,3,5]=>[7,6,1,2,3,4,8,5]=>[6,1,8,7,2,3,4,5]=>0000111
[6,4,2,8,7,5,3,1]=>[3,5,4,7,6,2,8,1]=>[6,4,2,8,7,5,3,1]=>0111111
[2,6,4,8,1,7,5,3]=>[8,2,5,7,6,3,1,4]=>[2,6,3,7,5,1,8,4]=>0001111
[2,6,4,1,8,7,5,3]=>[4,2,6,5,7,3,8,1]=>[2,8,7,5,3,6,4,1]=>0011111
[2,6,1,4,8,7,3,5]=>[6,2,7,1,3,4,8,5]=>[2,8,7,1,6,3,4,5]=>0000111
[6,4,2,8,7,5,1,3]=>[5,4,2,7,6,1,8,3]=>[6,4,2,8,7,5,1,3]=>0011111
[1,6,4,7,3,8,2,5]=>[1,8,7,6,2,4,3,5]=>[1,6,2,7,4,8,3,5]=>0000111
[1,3,7,4,5,8,2,6]=>[1,8,3,7,4,2,5,6]=>[1,3,7,4,8,2,5,6]=>0000011
[5,2,4,7,3,6,8,1]=>[8,5,7,2,4,3,6,1]=>[7,2,4,5,3,6,8,1]=>0001011
[1,7,6,3,4,8,2,5]=>[1,8,6,3,2,7,4,5]=>[1,7,6,3,8,2,4,5]=>0000111
[7,1,6,3,8,2,4,5]=>[7,8,6,2,4,1,3,5]=>[6,2,4,8,1,7,3,5]=>0000111
[1,2,7,4,8,3,5,6]=>[1,2,8,7,3,5,4,6]=>[1,2,7,3,5,8,4,6]=>0000011
[6,1,7,3,4,8,2,5]=>[6,8,7,3,2,1,4,5]=>[7,3,8,2,6,1,4,5]=>0000111
[2,1,7,4,5,8,3,6]=>[2,1,8,7,4,3,5,6]=>[2,1,7,4,8,3,5,6]=>1000011
[2,8,6,3,7,1,4,5]=>[7,2,6,1,4,8,3,5]=>[2,8,6,1,4,7,3,5]=>0000111
[5,8,2,1,7,3,4,6]=>[2,8,7,3,5,4,1,6]=>[5,7,3,4,8,2,1,6]=>1000011
[6,7,1,3,8,2,4,5]=>[7,8,1,2,4,6,3,5]=>[6,8,1,4,7,2,3,5]=>0000011
[5,1,2,4,8,3,6,7]=>[5,1,8,2,4,3,6,7]=>[8,1,2,4,5,3,6,7]=>0001001
[2,6,1,4,5,8,3,7]=>[6,2,8,1,4,5,3,7]=>[2,8,1,4,5,6,3,7]=>0000101
[1,6,2,4,8,3,5,7]=>[1,6,8,2,3,4,5,7]=>[1,8,2,6,3,4,5,7]=>0000101
[1,5,3,2,8,4,6,7]=>[1,3,5,8,2,4,6,7]=>[1,8,3,2,5,4,6,7]=>0101001
[2,5,3,4,1,8,6,7]=>[4,2,5,3,1,8,6,7]=>[2,5,3,4,1,8,6,7]=>0011001
[4,3,5,2,1,8,6,7]=>[2,5,4,3,1,8,6,7]=>[4,3,5,2,1,8,6,7]=>1011001
[2,6,4,8,7,1,3,5]=>[7,2,1,6,3,4,8,5]=>[2,6,1,3,8,7,4,5]=>0000111
[1,6,4,8,7,2,3,5]=>[1,7,2,6,3,4,8,5]=>[1,6,2,3,8,7,4,5]=>0000111
[2,7,8,3,6,1,4,5]=>[6,2,8,1,4,3,7,5]=>[2,7,8,1,4,6,3,5]=>0000101
[4,3,2,8,7,1,5,6]=>[7,3,4,2,1,5,8,6]=>[4,3,2,8,7,1,5,6]=>0110011
[5,2,4,8,7,1,3,6]=>[7,5,1,2,4,3,8,6]=>[5,1,4,8,7,2,3,6]=>0001011
[6,2,8,3,7,1,4,5]=>[7,6,8,1,4,2,3,5]=>[8,1,4,6,2,7,3,5]=>0000111
[5,1,4,8,7,2,3,6]=>[5,7,2,1,4,3,8,6]=>[8,7,2,4,5,1,3,6]=>0001011
[4,8,2,5,1,3,7,6]=>[5,8,1,4,2,7,3,6]=>[4,7,1,5,2,3,8,6]=>0001011
[3,8,2,1,5,4,7,6]=>[2,8,3,5,1,7,4,6]=>[3,5,2,1,7,4,8,6]=>1001011
[8,3,2,1,5,4,6,7]=>[2,3,8,5,1,4,6,7]=>[5,3,2,1,8,4,6,7]=>1101001
[8,3,2,1,4,6,5,7]=>[2,3,8,1,6,4,5,7]=>[6,3,2,1,4,8,5,7]=>1100101
[3,8,2,1,4,5,7,6]=>[2,8,3,1,4,7,5,6]=>[3,7,2,1,4,5,8,6]=>1000011
[3,7,2,1,4,5,8,6]=>[2,7,3,1,4,8,5,6]=>[3,8,2,1,4,5,7,6]=>1000011
[3,2,8,1,4,6,7,5]=>[8,3,2,1,7,4,6,5]=>[3,2,7,1,4,6,8,5]=>0100011
[3,8,2,1,4,7,5,6]=>[2,8,3,1,7,5,4,6]=>[3,7,5,8,2,1,4,6]=>1000011
[3,8,2,1,5,7,4,6]=>[2,8,3,7,1,4,5,6]=>[3,7,2,1,8,4,5,6]=>1000011
[4,2,7,6,1,8,3,5]=>[6,4,7,2,1,8,3,5]=>[8,2,4,1,7,6,3,5]=>0010111
[4,3,7,6,8,1,2,5]=>[8,1,4,3,2,7,6,5]=>[4,3,7,6,8,1,2,5]=>0010011
[3,2,1,8,7,5,6,4]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,5,6,4]=>1100111
[3,2,8,1,7,4,6,5]=>[8,3,2,7,6,4,1,5]=>[3,2,6,4,7,1,8,5]=>0100111
[3,2,8,1,6,4,7,5]=>[8,3,2,6,7,1,4,5]=>[3,2,7,1,6,4,8,5]=>0100111
[3,2,7,1,6,4,8,5]=>[7,3,2,6,8,1,4,5]=>[3,2,8,1,6,4,7,5]=>0100111
[4,2,8,6,1,3,7,5]=>[6,4,1,2,8,7,5,3]=>[4,1,7,5,8,6,2,3]=>0010111
[4,2,8,7,1,3,6,5]=>[7,4,1,2,6,3,8,5]=>[4,1,6,2,3,8,7,5]=>0010111
[5,7,8,3,4,1,2,6]=>[4,1,8,3,5,2,7,6]=>[5,7,8,3,4,1,2,6]=>0010001
[4,2,7,8,1,3,6,5]=>[8,4,1,2,6,3,7,5]=>[4,1,6,2,3,7,8,5]=>0010101
[4,2,6,8,1,3,7,5]=>[8,4,1,2,7,6,3,5]=>[4,1,6,7,2,3,8,5]=>0010011
[4,2,6,7,1,3,8,5]=>[7,4,1,2,8,6,3,5]=>[4,1,6,8,2,3,7,5]=>0010011
[3,2,6,1,8,4,7,5]=>[6,3,2,8,7,1,4,5]=>[3,2,7,1,8,4,6,5]=>0100111
[4,7,3,8,5,1,2,6]=>[5,1,8,4,7,3,2,6]=>[4,7,3,8,5,1,2,6]=>0001011
[3,2,7,1,8,6,4,5]=>[7,3,2,6,4,8,1,5]=>[3,2,8,6,4,7,1,5]=>0100111
[3,2,1,6,8,5,7,4]=>[2,3,1,7,8,6,5,4]=>[3,2,1,6,8,5,7,4]=>1100011
[4,2,6,8,1,7,3,5]=>[8,4,7,2,3,6,1,5]=>[6,7,2,4,3,8,1,5]=>0010011
[3,2,6,1,7,8,4,5]=>[6,3,2,8,4,1,7,5]=>[3,2,7,8,4,6,1,5]=>0100101
[3,4,6,8,7,5,1,2]=>[5,1,3,4,7,6,8,2]=>[3,4,6,8,7,5,1,2]=>0001011
[5,3,6,4,8,7,1,2]=>[7,1,5,6,3,4,8,2]=>[6,3,5,4,8,7,1,2]=>0001111
[3,1,8,5,4,2,6,7]=>[3,4,1,5,8,2,6,7]=>[8,5,4,1,3,2,6,7]=>0111001
[1,2,7,5,4,8,6,3]=>[1,2,6,5,8,7,3,4]=>[1,2,7,5,3,8,6,4]=>0001111
[6,3,7,5,4,8,1,2]=>[8,1,6,5,7,3,4,2]=>[7,5,3,6,4,8,1,2]=>0001111
[7,3,8,5,4,6,1,2]=>[6,1,7,5,8,4,3,2]=>[8,5,4,7,3,6,1,2]=>0001111
[3,6,8,5,4,7,1,2]=>[7,1,3,5,8,6,4,2]=>[3,6,8,5,4,7,1,2]=>0001011
[6,8,3,5,4,7,1,2]=>[7,1,8,5,3,6,4,2]=>[5,3,6,8,4,7,1,2]=>0001011
[1,6,2,5,4,8,7,3]=>[1,6,7,5,2,4,8,3]=>[1,5,2,8,7,4,6,3]=>0001111
[7,1,2,5,8,3,6,4]=>[7,1,8,6,2,3,5,4]=>[6,1,2,8,3,5,7,4]=>0000111
[7,8,1,2,4,6,5,3]=>[8,1,5,2,6,4,7,3]=>[6,5,1,2,4,7,8,3]=>0001101
[2,3,8,5,4,1,6,7]=>[4,2,3,5,8,1,6,7]=>[2,3,8,5,4,1,6,7]=>0011001
[5,8,1,6,4,3,2,7]=>[8,3,4,6,5,1,2,7]=>[5,6,4,3,1,8,2,7]=>0110101
[1,5,8,6,4,3,2,7]=>[1,3,4,6,5,8,2,7]=>[1,5,8,6,4,3,2,7]=>0110101
[2,6,1,5,7,3,8,4]=>[6,2,7,8,1,5,3,4]=>[2,8,1,5,7,3,6,4]=>0000111
[7,1,8,6,4,3,2,5]=>[7,3,4,6,2,8,1,5]=>[8,6,4,3,2,7,1,5]=>0110111
[2,1,7,5,6,3,8,4]=>[2,1,6,8,7,5,3,4]=>[2,1,7,5,8,3,6,4]=>1000111
[3,1,6,7,5,8,2,4]=>[3,8,1,2,7,6,5,4]=>[6,7,5,8,1,3,2,4]=>0100011
[7,8,1,6,5,3,2,4]=>[8,3,5,2,6,1,7,4]=>[6,5,3,2,7,8,1,4]=>0101101
[7,2,1,5,4,6,8,3]=>[2,7,8,5,1,4,6,3]=>[5,2,1,8,4,6,7,3]=>1001011
[1,2,8,5,6,3,7,4]=>[1,2,6,7,8,5,3,4]=>[1,2,8,5,7,3,6,4]=>0000111
[6,1,2,5,7,3,8,4]=>[6,1,7,8,2,5,3,4]=>[8,1,2,5,7,3,6,4]=>0000111
[4,2,1,5,6,3,7,8]=>[2,4,6,1,5,3,7,8]=>[5,6,2,1,4,3,7,8]=>1010100
[5,1,6,3,7,8,2,4]=>[5,8,6,2,1,3,7,4]=>[6,2,7,8,1,5,3,4]=>0001101
[1,3,6,8,5,7,2,4]=>[1,7,3,2,8,6,5,4]=>[1,3,6,8,5,7,2,4]=>0000011
[2,4,6,3,7,1,8,5]=>[7,2,6,4,8,3,1,5]=>[2,4,8,3,6,1,7,5]=>0000111
[5,4,6,1,3,7,2,8]=>[6,7,1,5,4,3,2,8]=>[5,4,7,1,3,6,2,8]=>0001110
[4,1,7,5,2,3,8,6]=>[4,5,2,1,7,8,3,6]=>[8,5,2,4,1,3,7,6]=>0011011
[1,2,4,5,8,3,7,6]=>[1,2,8,4,5,7,3,6]=>[1,2,4,5,7,3,8,6]=>0000011
[2,8,3,5,4,1,7,6]=>[4,2,5,8,1,7,3,6]=>[2,7,1,5,4,3,8,6]=>0011011
[7,8,2,3,4,1,6,5]=>[4,8,2,3,6,1,7,5]=>[6,2,3,4,1,7,8,5]=>0010101
[1,8,5,7,4,3,2,6]=>[1,3,4,7,8,2,5,6]=>[1,8,4,3,2,7,5,6]=>0110011
[5,1,8,7,4,3,2,6]=>[5,3,4,7,1,2,8,6]=>[8,7,4,3,1,5,2,6]=>0111011
[7,5,8,1,4,3,2,6]=>[8,3,4,1,7,2,5,6]=>[4,3,1,7,2,8,5,6]=>0110011
[5,8,7,1,4,3,2,6]=>[7,3,4,1,5,2,8,6]=>[4,3,1,5,8,7,2,6]=>0110011
[1,5,7,8,4,3,2,6]=>[1,3,4,8,5,2,7,6]=>[1,5,7,8,4,3,2,6]=>0110001
[2,4,7,5,1,3,8,6]=>[5,2,1,4,7,8,3,6]=>[2,4,8,5,1,3,7,6]=>0001011
[7,8,4,6,1,3,2,5]=>[6,3,1,8,2,4,7,5]=>[3,1,7,8,2,6,4,5]=>0100101
[7,8,5,4,1,3,2,6]=>[4,3,1,5,8,2,7,6]=>[3,1,7,8,5,4,2,6]=>0111001
[1,6,5,8,4,3,2,7]=>[1,3,4,8,6,5,2,7]=>[1,6,5,8,4,3,2,7]=>0110101
[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8]=>00000001
[1,2,3,4,5,8,6,9,7]=>[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,9,6,8,7]=>00000011
[9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,7]=>[9,8,1,2,3,4,5,6,7]=>00000011
[7,8,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,7,8,6]=>[7,8,9,1,2,3,4,5,6]=>00000001
[9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,6]=>[9,8,7,1,2,3,4,5,6]=>00000111
[6,7,8,9,1,2,3,4,5]=>[9,1,2,3,4,6,7,8,5]=>[6,7,8,9,1,2,3,4,5]=>00000001
[9,6,7,8,1,2,3,4,5]=>[8,1,2,3,4,9,6,7,5]=>[9,6,7,8,1,2,3,4,5]=>00000011
[8,9,6,7,1,2,3,4,5]=>[7,1,2,3,4,9,6,8,5]=>[8,9,6,7,1,2,3,4,5]=>00000101
[9,8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,9,5]=>[9,8,6,7,1,2,3,4,5]=>00000111
[9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,5]=>[9,8,7,6,1,2,3,4,5]=>00001111
[9,5,6,7,8,1,2,3,4]=>[8,1,2,3,9,5,6,7,4]=>[9,5,6,7,8,1,2,3,4]=>00000011
[8,9,5,6,7,1,2,3,4]=>[7,1,2,3,9,5,6,8,4]=>[8,9,5,6,7,1,2,3,4]=>00000101
[9,8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,9,4]=>[9,8,5,6,7,1,2,3,4]=>00000111
[9,7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,9,7,4]=>[9,7,8,5,6,1,2,3,4]=>00001011
[9,8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,9,4]=>[9,8,7,5,6,1,2,3,4]=>00001111
[9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,4]=>[9,8,7,6,5,1,2,3,4]=>00011111
[7,8,9,4,5,6,1,2,3]=>[6,1,2,9,4,5,7,8,3]=>[7,8,9,4,5,6,1,2,3]=>00001001
[9,7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,9,7,3]=>[9,7,8,4,5,6,1,2,3]=>00001011
[9,8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,9,3]=>[9,8,7,4,5,6,1,2,3]=>00001111
[8,9,6,7,4,5,1,2,3]=>[5,1,2,7,4,9,6,8,3]=>[8,9,6,7,4,5,1,2,3]=>00010101
[9,8,6,7,4,5,1,2,3]=>[5,1,2,7,4,8,6,9,3]=>[9,8,6,7,4,5,1,2,3]=>00010111
[9,8,7,6,4,5,1,2,3]=>[5,1,2,6,4,7,8,9,3]=>[9,8,7,6,4,5,1,2,3]=>00011111
[9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,3]=>[9,8,7,6,5,4,1,2,3]=>00111111
[9,7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,9,7,2]=>[9,7,8,5,6,3,4,1,2]=>00101011
[9,8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,9,2]=>[9,8,7,5,6,3,4,1,2]=>00101111
[9,8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,9,2]=>[9,8,7,6,5,3,4,1,2]=>00111111
[9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,2]=>[9,8,7,6,5,4,3,1,2]=>01111111
[9,10,1,2,3,4,5,6,7,8]=>[10,1,2,3,4,5,6,7,9,8]=>[9,10,1,2,3,4,5,6,7,8]=>000000001
[8,9,10,1,2,3,4,5,6,7]=>[10,1,2,3,4,5,6,8,9,7]=>[8,9,10,1,2,3,4,5,6,7]=>000000001
[10,8,9,1,2,3,4,5,6,7]=>[9,1,2,3,4,5,6,10,8,7]=>[10,8,9,1,2,3,4,5,6,7]=>000000011
[10,9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,10,7]=>[10,9,8,1,2,3,4,5,6,7]=>000000111
[7,8,9,10,1,2,3,4,5,6]=>[10,1,2,3,4,5,7,8,9,6]=>[7,8,9,10,1,2,3,4,5,6]=>000000001
[10,7,8,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,10,7,8,6]=>[10,7,8,9,1,2,3,4,5,6]=>000000011
[9,10,7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,10,7,9,6]=>[9,10,7,8,1,2,3,4,5,6]=>000000101
[10,9,7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,9,7,10,6]=>[10,9,7,8,1,2,3,4,5,6]=>000000111
[10,9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,10,6]=>[10,9,8,7,1,2,3,4,5,6]=>000001111
[10,6,7,8,9,1,2,3,4,5]=>[9,1,2,3,4,10,6,7,8,5]=>[10,6,7,8,9,1,2,3,4,5]=>000000011
[9,10,6,7,8,1,2,3,4,5]=>[8,1,2,3,4,10,6,7,9,5]=>[9,10,6,7,8,1,2,3,4,5]=>000000101
[10,9,6,7,8,1,2,3,4,5]=>[8,1,2,3,4,9,6,7,10,5]=>[10,9,6,7,8,1,2,3,4,5]=>000000111
[10,8,9,6,7,1,2,3,4,5]=>[7,1,2,3,4,9,6,10,8,5]=>[10,8,9,6,7,1,2,3,4,5]=>000001011
[10,9,8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,9,10,5]=>[10,9,8,6,7,1,2,3,4,5]=>000001111
[10,9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,10,5]=>[10,9,8,7,6,1,2,3,4,5]=>000011111
[9,10,5,6,7,8,1,2,3,4]=>[8,1,2,3,10,5,6,7,9,4]=>[9,10,5,6,7,8,1,2,3,4]=>000000101
[10,9,5,6,7,8,1,2,3,4]=>[8,1,2,3,9,5,6,7,10,4]=>[10,9,5,6,7,8,1,2,3,4]=>000000111
[8,9,10,5,6,7,1,2,3,4]=>[7,1,2,3,10,5,6,8,9,4]=>[8,9,10,5,6,7,1,2,3,4]=>000001001
[10,9,8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,9,10,4]=>[10,9,8,5,6,7,1,2,3,4]=>000001111
[9,10,7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,10,7,9,4]=>[9,10,7,8,5,6,1,2,3,4]=>000010101
[10,9,7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,9,7,10,4]=>[10,9,7,8,5,6,1,2,3,4]=>000010111
[10,9,8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,9,10,4]=>[10,9,8,7,5,6,1,2,3,4]=>000011111
[10,9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,10,4]=>[10,9,8,7,6,5,1,2,3,4]=>000111111
[10,7,8,9,4,5,6,1,2,3]=>[6,1,2,9,4,5,10,7,8,3]=>[10,7,8,9,4,5,6,1,2,3]=>000010011
[9,10,7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,10,7,9,3]=>[9,10,7,8,4,5,6,1,2,3]=>000010101
[10,9,7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,9,7,10,3]=>[10,9,7,8,4,5,6,1,2,3]=>000010111
[10,9,8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,9,10,3]=>[10,9,8,7,4,5,6,1,2,3]=>000011111
[10,8,9,6,7,4,5,1,2,3]=>[5,1,2,7,4,9,6,10,8,3]=>[10,8,9,6,7,4,5,1,2,3]=>000101011
[10,9,8,6,7,4,5,1,2,3]=>[5,1,2,7,4,8,6,9,10,3]=>[10,9,8,6,7,4,5,1,2,3]=>000101111
[10,9,8,7,6,4,5,1,2,3]=>[5,1,2,6,4,7,8,9,10,3]=>[10,9,8,7,6,4,5,1,2,3]=>000111111
[10,9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,10,3]=>[10,9,8,7,6,5,4,1,2,3]=>001111111
[9,10,7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,10,7,9,2]=>[9,10,7,8,5,6,3,4,1,2]=>001010101
[10,9,7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,9,7,10,2]=>[10,9,7,8,5,6,3,4,1,2]=>001010111
[10,9,8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,9,10,2]=>[10,9,8,7,5,6,3,4,1,2]=>001011111
[10,9,8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,9,10,2]=>[10,9,8,7,6,5,3,4,1,2]=>001111111
[10,9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,10,2]=>[10,9,8,7,6,5,4,3,1,2]=>011111111
[3,2,7,5,4,1,6,8]=>[4,3,2,5,7,1,6,8]=>[3,2,7,5,4,1,6,8]=>0111010
[4,2,8,5,1,3,7,6]=>[5,4,1,2,8,7,3,6]=>[4,1,7,5,2,3,8,6]=>0011011
[4,3,6,8,1,7,2,5]=>[8,7,4,3,2,6,1,5]=>[4,3,6,7,2,8,1,5]=>0010011
[6,2,1,5,8,3,7,4]=>[2,6,8,7,1,5,3,4]=>[7,2,1,5,8,3,6,4]=>1000111
[1,4,6,3,5,8,7,2]=>[1,7,6,4,3,5,8,2]=>[1,4,6,3,5,8,7,2]=>0000111
[5,4,6,2,7,8,1,3]=>[8,6,1,5,4,2,7,3]=>[5,4,6,1,7,8,2,3]=>0001101
[2,5,4,1,6,7,3,8]=>[4,2,5,7,3,6,1,8]=>[2,6,7,3,5,4,1,8]=>0011010
[5,6,3,2,7,1,8,4]=>[7,3,6,8,5,2,1,4]=>[5,8,3,2,6,1,7,4]=>0100111
[5,4,6,2,8,1,7,3]=>[8,6,7,5,4,2,1,3]=>[5,4,7,2,6,1,8,3]=>0001111
[2,4,1,7,8,5,3,6]=>[4,2,5,1,8,3,7,6]=>[2,7,8,5,1,4,3,6]=>0011001
[2,5,4,1,6,3,8,7]=>[4,2,5,6,3,1,8,7]=>[2,6,3,5,4,1,8,7]=>0011101
[5,6,3,2,1,8,4,7]=>[2,3,6,8,5,1,4,7]=>[5,8,3,2,1,6,4,7]=>1100101
[3,5,2,1,6,4,7,8]=>[2,5,3,6,1,4,7,8]=>[3,6,2,1,5,4,7,8]=>1001100
[6,8,4,3,2,1,5,7]=>[2,3,4,8,1,6,5,7]=>[6,8,4,3,2,1,5,7]=>1110001
[5,3,8,2,1,6,4,7]=>[2,8,5,6,3,1,4,7]=>[6,3,5,2,1,8,4,7]=>1001101
[3,7,5,8,2,1,4,6]=>[2,8,3,1,7,4,5,6]=>[3,7,2,1,4,8,5,6]=>1000011
[8,6,4,3,2,1,7,5]=>[2,3,4,6,8,7,5,1]=>[7,5,8,6,4,3,2,1]=>1110111
[7,6,4,3,2,1,8,5]=>[2,3,4,6,7,8,5,1]=>[8,5,7,6,4,3,2,1]=>1110111
[7,8,4,3,2,1,6,5]=>[2,3,4,8,6,1,7,5]=>[6,4,3,2,1,7,8,5]=>1110101
[7,5,8,3,2,6,1,4]=>[6,3,8,1,7,2,5,4]=>[7,3,1,8,5,6,2,4]=>0100111
[5,7,3,2,1,6,8,4]=>[2,3,7,8,5,1,6,4]=>[5,8,3,2,1,6,7,4]=>1100011
[6,3,7,2,5,1,8,4]=>[5,7,6,8,2,3,1,4]=>[8,2,6,3,7,1,5,4]=>0001111
[6,2,5,7,8,4,1,3]=>[4,8,2,6,1,5,7,3]=>[6,2,5,7,8,4,1,3]=>0010101
[2,1,5,7,8,6,3,4]=>[2,1,6,3,5,8,7,4]=>[2,1,5,7,8,6,3,4]=>1000101
[3,6,7,2,8,1,4,5]=>[8,7,3,1,4,6,2,5]=>[3,6,7,1,4,8,2,5]=>0000011
[6,3,7,2,8,1,4,5]=>[8,7,6,1,4,3,2,5]=>[6,1,4,7,3,8,2,5]=>0000111
[2,5,8,4,1,3,7,6]=>[4,2,1,8,5,7,3,6]=>[2,5,7,4,1,3,8,6]=>0010011
[2,4,1,7,8,3,6,5]=>[4,2,8,1,6,3,7,5]=>[2,6,1,4,3,7,8,5]=>0010101
[3,7,2,8,6,1,4,5]=>[6,8,3,2,4,7,1,5]=>[3,7,2,4,8,6,1,5]=>0000111
[5,3,8,2,1,4,7,6]=>[2,8,5,1,3,7,4,6]=>[5,2,1,7,3,4,8,6]=>1001011
[8,4,7,3,2,1,5,6]=>[2,3,7,8,1,5,4,6]=>[8,3,2,1,5,7,4,6]=>1100011
[7,3,2,8,6,1,4,5]=>[6,3,8,2,4,7,1,5]=>[7,3,2,4,8,6,1,5]=>0100111
[7,8,6,5,4,3,2,1,9]=>[2,3,4,5,6,8,7,1,9]=>[7,8,6,5,4,3,2,1,9]=>11111010
[1,8,9,7,6,5,4,3,2]=>[1,3,4,5,6,7,9,8,2]=>[1,8,9,7,6,5,4,3,2]=>01111101
[8,9,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,9,8,1,10]=>[8,9,7,6,5,4,3,2,1,10]=>111111010
[6,8,7,5,4,3,2,1,9]=>[2,3,4,5,7,6,8,1,9]=>[6,8,7,5,4,3,2,1,9]=>11110110
[1,7,9,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,9,2]=>[1,7,9,8,6,5,4,3,2]=>01111011
[1,9,10,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,10,9,2]=>[1,9,10,8,7,6,5,4,3,2]=>011111101
[7,8,3,5,4,6,1,2]=>[6,1,8,5,3,4,7,2]=>[5,3,7,8,4,6,1,2]=>0001101
[8,6,3,7,5,2,4,1]=>[4,5,7,3,6,8,2,1]=>[8,6,3,7,5,2,4,1]=>0011111
[5,4,1,6,2,3,8,7]=>[4,5,1,6,2,3,8,7]=>[6,1,5,4,2,3,8,7]=>0011101
[5,7,1,6,2,8,4,3]=>[7,6,4,8,5,1,2,3]=>[5,8,4,1,6,2,7,3]=>0010111
[2,3,6,5,1,4,8,7]=>[5,2,3,1,6,4,8,7]=>[2,3,6,5,1,4,8,7]=>0001101
[2,3,6,4,1,5,8,7]=>[4,2,3,6,1,5,8,7]=>[2,3,6,4,1,5,8,7]=>0010101
[2,3,6,1,5,4,8,7]=>[6,2,3,5,1,4,8,7]=>[2,3,5,1,6,4,8,7]=>0001101
[7,3,5,1,8,4,2,6]=>[5,4,8,7,2,3,1,6]=>[7,2,8,4,3,5,1,6]=>0011011
[2,7,6,4,1,8,5,3]=>[4,2,6,5,7,8,1,3]=>[2,8,5,1,7,6,4,3]=>0011111
[2,1,7,6,3,8,5,4]=>[2,1,6,5,7,8,4,3]=>[2,1,8,5,4,7,6,3]=>1001111
[2,1,7,6,3,8,4,5]=>[2,1,6,7,3,8,4,5]=>[2,1,8,3,7,6,4,5]=>1000111
[5,7,3,6,2,8,4,1]=>[4,8,6,7,5,1,3,2]=>[5,7,1,6,3,8,4,2]=>0010111
[6,3,5,1,8,2,4,7]=>[5,8,6,2,3,1,4,7]=>[6,2,8,3,5,1,4,7]=>0001101
[2,3,4,8,7,6,1,5]=>[6,2,3,4,1,7,8,5]=>[2,3,4,8,7,6,1,5]=>0000111
[2,3,4,8,5,7,1,6]=>[7,2,3,4,8,1,5,6]=>[2,3,4,8,1,7,5,6]=>0000011
[7,3,5,4,8,1,2,6]=>[8,1,7,5,3,2,4,6]=>[5,3,7,1,2,8,4,6]=>0001011
[2,1,4,5,8,7,3,6]=>[2,1,7,4,5,3,8,6]=>[2,1,4,5,8,7,3,6]=>1000011
[7,3,5,4,8,1,6,2]=>[8,6,7,5,3,1,4,2]=>[5,3,7,1,6,4,8,2]=>0001111
[2,3,4,8,7,5,6,1]=>[6,2,3,4,7,5,8,1]=>[2,3,4,8,7,5,6,1]=>0000111
[2,3,4,8,7,5,1,6]=>[5,2,3,4,7,1,8,6]=>[2,3,4,8,7,5,1,6]=>0001011
[2,7,6,5,4,8,1,3]=>[8,2,1,5,6,7,4,3]=>[2,7,6,5,4,8,1,3]=>0001111
[5,7,1,6,3,8,2,4]=>[7,8,6,2,5,1,3,4]=>[5,6,2,8,1,7,3,4]=>0000111
[7,4,1,5,8,2,3,6]=>[4,7,1,8,2,3,5,6]=>[8,1,7,4,2,3,5,6]=>0010011
[5,7,3,6,1,8,4,2]=>[6,4,8,7,5,2,1,3]=>[5,7,2,8,4,1,6,3]=>0010111
[2,1,4,5,8,6,3,7]=>[2,1,6,4,5,8,3,7]=>[2,1,4,5,8,6,3,7]=>1000101
[2,3,4,8,5,6,1,7]=>[6,2,3,4,8,5,1,7]=>[2,3,4,8,5,6,1,7]=>0000101
[2,3,4,8,7,1,6,5]=>[7,2,3,4,6,1,8,5]=>[2,3,4,6,1,8,7,5]=>0000111
[2,3,4,8,1,7,6,5]=>[8,2,3,4,6,7,1,5]=>[2,3,4,7,6,1,8,5]=>0000111
[2,3,4,8,1,6,7,5]=>[8,2,3,4,7,1,6,5]=>[2,3,4,7,1,6,8,5]=>0000011
[2,3,4,8,5,1,7,6]=>[5,2,3,4,8,7,1,6]=>[2,3,4,7,5,1,8,6]=>0001011
[6,3,5,4,8,2,7,1]=>[7,8,6,5,3,4,2,1]=>[5,3,6,4,8,2,7,1]=>0001111
[2,1,4,5,8,3,7,6]=>[2,1,8,4,5,7,3,6]=>[2,1,4,5,7,3,8,6]=>1000011
[7,4,3,5,8,2,6,1]=>[6,8,4,7,3,2,5,1]=>[7,4,3,8,2,5,6,1]=>0010111
[6,3,5,4,8,2,1,7]=>[2,8,6,5,3,4,1,7]=>[5,3,6,4,8,2,1,7]=>1001101
[2,3,4,8,5,1,6,7]=>[5,2,3,4,8,1,6,7]=>[2,3,4,8,5,1,6,7]=>0001001
[2,3,4,8,1,6,5,7]=>[8,2,3,4,6,1,5,7]=>[2,3,4,6,1,8,5,7]=>0000101
[2,3,4,8,1,5,7,6]=>[8,2,3,4,1,7,5,6]=>[2,3,4,7,1,5,8,6]=>0000011
[7,8,2,6,1,5,3,4]=>[6,8,5,3,1,2,7,4]=>[5,3,7,8,1,6,2,4]=>0001101
[7,8,1,6,2,5,3,4]=>[8,6,5,3,2,1,7,4]=>[5,3,6,2,7,8,1,4]=>0001101
[1,8,6,7,2,5,3,4]=>[1,7,5,3,2,8,6,4]=>[1,5,3,8,6,7,2,4]=>0001011
[5,8,1,7,2,6,3,4]=>[8,7,6,3,5,2,1,4]=>[5,6,3,7,2,8,1,4]=>0000111
[2,8,5,7,1,6,3,4]=>[7,2,6,3,8,1,5,4]=>[2,8,3,6,5,7,1,4]=>0000111
[2,8,1,7,5,6,3,4]=>[8,2,6,3,7,5,1,4]=>[2,7,5,6,3,8,1,4]=>0000111
[1,8,2,7,5,6,3,4]=>[1,8,6,3,7,5,2,4]=>[1,7,5,6,3,8,2,4]=>0000111
[1,8,2,7,4,6,3,5]=>[1,8,6,7,3,4,2,5]=>[1,7,3,6,4,8,2,5]=>0000111
[4,8,1,7,2,6,3,5]=>[8,7,6,4,3,2,1,5]=>[4,6,3,7,2,8,1,5]=>0000111
[1,8,4,7,2,6,3,5]=>[1,7,6,8,3,2,4,5]=>[1,8,3,6,2,7,4,5]=>0000111
[4,8,1,7,5,6,2,3]=>[8,6,2,4,7,5,1,3]=>[4,7,5,6,2,8,1,3]=>0000111
[1,8,4,7,5,6,2,3]=>[1,6,2,8,7,5,4,3]=>[1,7,5,8,4,6,2,3]=>0000111
[1,8,3,7,5,6,2,4]=>[1,6,8,2,7,5,3,4]=>[1,7,5,8,2,6,3,4]=>0000111
[3,8,1,7,4,6,2,5]=>[8,6,3,7,2,4,1,5]=>[3,7,2,6,4,8,1,5]=>0000111
[1,8,3,7,2,6,4,5]=>[1,7,8,6,4,2,3,5]=>[1,6,4,8,2,7,3,5]=>0000111
[3,8,1,7,2,6,4,5]=>[8,7,3,6,4,2,1,5]=>[3,6,4,7,2,8,1,5]=>0000111
[3,8,2,7,4,6,1,5]=>[6,8,3,7,1,4,2,5]=>[3,7,1,8,4,6,2,5]=>0000111
[3,8,2,7,5,6,1,4]=>[6,8,3,1,7,5,2,4]=>[3,7,5,8,1,6,2,4]=>0000111
[4,8,3,7,5,6,1,2]=>[6,1,8,4,7,5,3,2]=>[4,7,5,8,3,6,1,2]=>0000111
[3,8,4,7,5,6,1,2]=>[6,1,3,8,7,5,4,2]=>[3,7,5,8,4,6,1,2]=>0000111
[2,8,3,7,5,6,1,4]=>[6,2,8,1,7,5,3,4]=>[2,7,5,8,1,6,3,4]=>0000111
[2,8,3,7,4,6,1,5]=>[6,2,8,7,1,4,3,5]=>[2,7,1,8,4,6,3,5]=>0000111
[2,8,3,7,1,6,4,5]=>[7,2,8,6,4,1,3,5]=>[2,6,4,8,1,7,3,5]=>0000111
[7,1,8,4,5,2,6,3]=>[7,5,6,8,4,2,1,3]=>[8,4,6,2,5,1,7,3]=>0001111
[6,8,1,7,4,2,5,3]=>[8,4,7,5,3,6,1,2]=>[5,3,6,7,4,1,8,2]=>0011011
[1,6,7,4,2,8,5,3]=>[1,4,7,5,8,6,3,2]=>[1,6,8,5,3,7,4,2]=>0011011
[1,6,7,3,8,5,2,4]=>[1,5,8,3,7,6,2,4]=>[1,6,7,3,8,5,2,4]=>0001011
[7,1,8,3,5,6,2,4]=>[7,6,8,2,3,5,1,4]=>[8,2,5,6,3,7,1,4]=>0000111
[7,3,8,6,2,5,1,4]=>[5,6,8,1,3,7,2,4]=>[7,1,8,6,3,5,2,4]=>0001111
[7,3,1,8,4,2,5,6]=>[3,7,4,8,1,5,2,6]=>[8,4,1,5,7,3,2,6]=>0110011
[7,2,8,4,1,5,3,6]=>[4,8,7,5,2,1,3,6]=>[5,2,7,1,8,4,3,6]=>0011011
[7,2,8,3,5,1,6,4]=>[5,7,8,6,3,1,2,4]=>[6,3,8,1,7,2,5,4]=>0001111
[7,2,8,3,4,6,1,5]=>[6,7,8,3,1,4,2,5]=>[8,3,7,1,4,6,2,5]=>0000111
[1,5,7,8,2,6,3,4]=>[1,8,6,3,5,2,7,4]=>[1,5,6,3,7,8,2,4]=>0000101
[6,2,3,8,5,7,4,1]=>[4,7,1,6,8,3,5,2]=>[8,1,3,6,5,7,4,2]=>0010111
[6,3,1,4,8,5,2,7]=>[3,6,5,2,8,4,1,7]=>[8,5,2,4,6,3,1,7]=>0101101
[3,1,5,4,7,8,2,6]=>[3,8,1,5,4,2,7,6]=>[5,4,7,8,1,3,2,6]=>0101001
[5,3,1,4,8,2,6,7]=>[3,5,8,2,4,1,6,7]=>[8,2,4,5,3,1,6,7]=>0101001
[5,2,3,8,4,6,7,1]=>[7,5,2,8,3,4,6,1]=>[8,2,3,5,4,6,7,1]=>0001011
[5,4,3,8,1,2,7,6]=>[8,1,4,5,3,7,2,6]=>[5,4,3,7,1,2,8,6]=>0011011
[6,4,2,8,1,3,7,5]=>[8,4,1,6,7,2,3,5]=>[7,4,1,6,2,3,8,5]=>0010111
[6,3,8,2,5,1,7,4]=>[5,8,6,7,2,3,1,4]=>[7,2,6,3,8,1,5,4]=>0001111
[6,3,8,1,4,7,2,5]=>[8,7,6,1,2,3,4,5]=>[6,1,7,2,8,3,4,5]=>0000111
[5,8,1,3,6,2,7,4]=>[8,6,1,7,5,3,2,4]=>[5,7,1,3,6,2,8,4]=>0000111
[6,5,1,2,8,7,3,4]=>[5,1,6,2,7,3,8,4]=>[8,7,1,2,6,5,3,4]=>0001111
[6,5,3,1,4,2,8,7]=>[3,5,4,2,6,1,8,7]=>[4,2,6,5,3,1,8,7]=>0111101
[5,2,6,4,1,7,3,8]=>[4,6,5,7,3,2,1,8]=>[7,3,5,2,6,4,1,8]=>0011110
[3,5,6,1,2,8,7,4]=>[6,1,3,7,5,2,8,4]=>[3,5,8,7,1,2,6,4]=>0000111
[3,5,7,1,8,6,2,4]=>[7,6,3,2,5,8,1,4]=>[3,5,8,6,2,7,1,4]=>0000111
[3,4,7,2,8,6,1,5]=>[6,8,3,4,2,7,1,5]=>[3,4,7,2,8,6,1,5]=>0000111
[3,4,5,8,2,7,1,6]=>[7,8,3,4,5,1,2,6]=>[3,4,5,8,1,7,2,6]=>0000011
[3,5,2,6,8,1,7,4]=>[8,5,3,7,2,6,1,4]=>[3,6,7,2,5,1,8,4]=>0001011
[5,3,6,8,4,7,2,1]=>[2,7,5,8,3,6,4,1]=>[6,8,3,5,4,7,2,1]=>1001011
[3,7,2,5,4,8,6,1]=>[6,8,3,5,1,7,4,2]=>[3,5,1,7,4,8,6,2]=>0001111
[4,7,2,5,8,3,6,1]=>[6,7,8,4,2,3,5,1]=>[4,8,2,7,3,5,6,1]=>0000111
[5,2,6,8,4,3,7,1]=>[7,5,4,8,2,6,3,1]=>[6,8,4,2,5,3,7,1]=>0011011
[5,1,6,8,4,3,2,7]=>[5,3,4,8,1,6,2,7]=>[6,8,4,3,1,5,2,7]=>0111001
[8,5,4,7,6,3,2,1]=>[2,3,6,5,7,8,1,4]=>[8,5,3,2,1,7,6,4]=>1101111
[5,7,1,8,4,3,2,6]=>[7,3,4,8,5,2,1,6]=>[5,8,4,3,2,7,1,6]=>0110011
[2,7,1,5,4,3,8,6]=>[7,2,4,5,1,8,3,6]=>[2,5,4,1,8,3,7,6]=>0011011
[8,5,6,7,1,3,2,4]=>[7,3,1,2,8,5,6,4]=>[3,1,8,5,6,7,2,4]=>0100011
[8,3,6,1,4,7,2,5]=>[6,7,8,1,2,3,4,5]=>[8,1,7,2,6,3,4,5]=>0000111
[2,7,6,1,4,3,8,5]=>[6,2,4,1,7,8,5,3]=>[2,4,1,8,5,7,6,3]=>0010111
[5,7,6,8,2,3,4,1]=>[4,8,2,3,5,7,6,1]=>[5,7,6,8,2,3,4,1]=>0010011
[5,7,2,8,4,3,6,1]=>[6,7,4,8,5,3,2,1]=>[5,8,4,3,7,2,6,1]=>0010111
[6,7,8,2,4,3,5,1]=>[5,8,4,2,3,6,7,1]=>[4,2,6,7,8,3,5,1]=>0011001
[3,7,6,2,4,8,5,1]=>[5,8,3,1,6,7,4,2]=>[3,7,6,1,4,8,5,2]=>0001111
[5,7,3,8,4,6,2,1]=>[2,6,7,8,5,4,3,1]=>[5,8,4,7,3,6,2,1]=>1000111
[4,7,3,5,8,6,2,1]=>[2,6,8,4,1,7,5,3]=>[4,7,2,1,5,8,6,3]=>1000111
[8,7,2,1,4,3,6,5]=>[2,7,4,1,6,3,8,5]=>[4,2,1,6,3,8,7,5]=>1010111
[8,7,6,3,2,5,4,1]=>[4,3,5,6,1,7,8,2]=>[8,7,6,3,1,5,4,2]=>0111111
[8,7,3,5,1,6,2,4]=>[5,6,7,2,3,1,8,4]=>[8,7,2,6,3,5,1,4]=>0001111
[8,7,2,5,1,3,6,4]=>[5,7,1,6,2,3,8,4]=>[6,1,8,7,2,3,5,4]=>0001111
[8,2,6,5,1,3,7,4]=>[5,6,2,8,7,4,3,1]=>[7,4,8,2,3,6,5,1]=>0001111
[8,4,6,5,7,1,2,3]=>[7,1,2,8,6,4,5,3]=>[6,4,8,5,7,1,2,3]=>0000111
[5,7,6,8,4,1,2,3]=>[4,1,2,8,5,7,6,3]=>[5,7,6,8,4,1,2,3]=>0010011
[4,7,6,5,8,1,2,3]=>[8,1,2,4,6,7,5,3]=>[4,7,6,5,8,1,2,3]=>0000111
[3,7,6,5,1,8,2,4]=>[5,6,3,2,7,8,1,4]=>[3,8,2,7,6,5,1,4]=>0001111
[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>00000010
[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>00000001
[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>000000010
[7,8,1,2,3,4,5,6,9]=>[8,1,2,3,4,5,7,6,9]=>[7,8,1,2,3,4,5,6,9]=>00000010
[1,8,9,2,3,4,5,6,7]=>[1,9,2,3,4,5,6,8,7]=>[1,8,9,2,3,4,5,6,7]=>00000001
[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]=>000000001
[10,1,2,3,4,5,6,7,8,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>0000000010
[8,9,1,2,3,4,5,6,7,10]=>[9,1,2,3,4,5,6,8,7,10]=>[8,9,1,2,3,4,5,6,7,10]=>000000010
[6,8,1,2,3,4,5,7,9]=>[8,1,2,3,4,6,5,7,9]=>[6,8,1,2,3,4,5,7,9]=>00000010
[1,7,9,2,3,4,5,6,8]=>[1,9,2,3,4,5,7,6,8]=>[1,7,9,2,3,4,5,6,8]=>00000001
[1,9,10,2,3,4,5,6,7,8]=>[1,10,2,3,4,5,6,7,9,8]=>[1,9,10,2,3,4,5,6,7,8]=>000000001
[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,2,3,4,5,6,7,8,9,10]=>0000000001
[5,6,4,3,8,7,1,2]=>[7,1,4,6,5,3,8,2]=>[5,6,4,3,8,7,1,2]=>0010111
[3,4,7,2,8,1,6,5]=>[8,7,3,4,6,1,2,5]=>[3,4,6,1,7,2,8,5]=>0000111
[7,3,8,4,5,6,1,2]=>[6,1,7,8,4,5,3,2]=>[8,4,5,7,3,6,1,2]=>0000111
[4,6,8,5,3,7,1,2]=>[7,1,5,4,8,6,3,2]=>[4,6,8,5,3,7,1,2]=>0001011
[6,8,5,3,4,7,1,2]=>[7,1,5,3,8,6,4,2]=>[6,8,5,3,4,7,1,2]=>0001011
[1,6,5,4,2,8,7,3]=>[1,4,5,6,7,2,8,3]=>[1,8,7,2,6,5,4,3]=>0011111
[1,8,5,2,7,3,6,4]=>[1,5,8,7,6,4,3,2]=>[1,6,4,7,3,8,5,2]=>0001111
[4,2,7,5,1,8,6,3]=>[5,4,7,2,6,8,3,1]=>[8,6,2,4,3,7,5,1]=>0011111
[7,8,1,4,2,6,5,3]=>[8,4,5,1,6,2,7,3]=>[6,5,1,4,2,7,8,3]=>0011101
[6,5,1,3,4,2,8,7]=>[5,4,1,3,6,2,8,7]=>[4,1,3,6,5,2,8,7]=>0011101
[7,4,5,3,2,8,1,6]=>[8,3,5,7,4,1,2,6]=>[7,4,5,3,1,8,2,6]=>0101011
[2,5,8,6,4,1,3,7]=>[4,2,1,6,5,8,3,7]=>[2,5,8,6,4,1,3,7]=>0010101
[1,4,6,2,5,8,3,7]=>[1,6,8,4,2,5,3,7]=>[1,4,8,2,5,6,3,7]=>0000101
[3,6,2,5,8,1,7,4]=>[8,6,3,7,2,5,1,4]=>[3,7,2,5,6,1,8,4]=>0000111
[1,6,8,7,4,2,3,5]=>[1,4,2,7,3,6,8,5]=>[1,6,8,7,4,2,3,5]=>0010011
[7,2,1,4,5,6,8,3]=>[2,7,8,1,4,5,6,3]=>[8,2,1,4,5,6,7,3]=>1000011
[1,2,8,3,6,5,7,4]=>[1,2,8,7,6,3,5,4]=>[1,2,6,3,7,5,8,4]=>0000111
[6,1,3,2,7,5,8,4]=>[6,3,1,8,7,2,5,4]=>[3,1,7,2,8,5,6,4]=>0100111
[1,6,3,8,5,7,2,4]=>[1,7,6,2,8,3,5,4]=>[1,8,2,6,5,7,3,4]=>0000111
[2,6,4,1,7,5,8,3]=>[4,2,6,8,7,3,5,1]=>[2,7,3,8,5,6,4,1]=>0010111
[7,6,5,8,1,4,2,3]=>[8,4,2,1,6,7,5,3]=>[4,2,7,6,5,8,1,3]=>0010111
[5,8,6,7,3,2,1,4]=>[2,3,7,1,5,8,6,4]=>[5,8,6,7,3,2,1,4]=>1100011
[1,6,4,3,7,2,8,5]=>[1,7,4,6,8,3,2,5]=>[1,8,4,3,6,2,7,5]=>0010111
[1,8,3,5,4,2,7,6]=>[1,4,5,8,2,7,3,6]=>[1,7,2,5,4,3,8,6]=>0011011
[4,1,6,3,8,2,7,5]=>[4,8,6,1,7,3,2,5]=>[7,1,6,3,4,2,8,5]=>0010111
[3,2,6,4,7,8,1,5]=>[8,3,2,6,1,4,7,5]=>[3,2,6,1,7,8,4,5]=>0100101
[7,2,5,8,3,4,1,6]=>[4,7,8,3,2,1,5,6]=>[8,3,7,2,4,1,5,6]=>0010011
[6,5,3,8,2,1,7,4]=>[2,8,5,6,7,4,1,3]=>[7,4,6,5,2,1,8,3]=>1001111
[7,5,8,4,1,2,3,6]=>[4,1,2,8,7,3,5,6]=>[7,4,1,2,3,8,5,6]=>0010011
[3,5,7,8,4,1,2,6]=>[4,1,3,8,5,2,7,6]=>[3,5,7,8,4,1,2,6]=>0010001
[1,4,7,5,3,8,2,6]=>[1,8,5,4,7,2,3,6]=>[1,4,7,5,2,8,3,6]=>0001011
[2,4,6,7,3,1,8,5]=>[3,2,7,4,8,6,1,5]=>[2,4,6,8,3,1,7,5]=>0100011
[7,8,4,6,3,1,2,5]=>[3,1,6,8,2,4,7,5]=>[7,8,3,1,2,6,4,5]=>0100101
[2,6,4,5,3,8,1,7]=>[8,2,5,6,4,3,1,7]=>[2,6,4,5,3,8,1,7]=>0001101
[3,6,5,8,4,2,1,7]=>[2,4,3,8,6,5,1,7]=>[3,6,5,8,4,2,1,7]=>1010101
[5,6,8,4,2,3,1,7]=>[3,4,2,8,5,6,1,7]=>[5,6,8,4,2,3,1,7]=>0110001
[6,8,5,4,3,1,2,7]=>[3,1,4,5,8,6,2,7]=>[6,8,5,4,3,1,2,7]=>0111001
[6,1,4,2,8,5,7,3]=>[6,4,7,1,8,2,5,3]=>[8,1,4,2,7,5,6,3]=>0010111
[4,8,6,5,3,2,7,1]=>[7,3,5,4,6,8,2,1]=>[4,8,6,5,3,2,7,1]=>0101111
[8,6,5,1,2,4,7,3]=>[5,1,6,2,8,7,4,3]=>[7,1,2,4,8,6,5,3]=>0001111
[1,7,5,8,2,6,4,3]=>[1,8,4,6,7,2,5,3]=>[1,7,4,2,6,5,8,3]=>0010111
[1,3,8,5,7,6,2,4]=>[1,6,3,2,7,8,4,5]=>[1,3,8,2,4,7,6,5]=>0000111
[6,3,8,5,7,1,2,4]=>[7,1,6,2,8,3,5,4]=>[8,1,2,6,5,7,3,4]=>0000111
[6,8,5,2,1,4,7,3]=>[2,5,8,3,7,6,4,1]=>[6,7,3,4,8,5,2,1]=>1001011
[2,8,1,5,6,3,7,4]=>[8,2,6,7,1,5,3,4]=>[2,7,1,5,6,3,8,4]=>0000111
[8,1,2,5,6,3,7,4]=>[8,1,6,7,2,5,3,4]=>[7,1,2,5,6,3,8,4]=>0000111
[1,8,2,5,7,6,3,4]=>[1,8,6,3,2,7,5,4]=>[1,7,6,3,5,8,2,4]=>0000111
[2,5,8,6,1,7,3,4]=>[6,2,8,1,5,7,3,4]=>[2,5,7,1,8,6,3,4]=>0000111
[8,6,1,5,7,2,3,4]=>[6,8,1,3,2,7,5,4]=>[7,1,3,5,8,6,2,4]=>0000111
[3,8,6,5,7,1,2,4]=>[7,1,3,2,6,8,5,4]=>[3,8,6,5,7,1,2,4]=>0000111
[7,6,5,8,1,2,4,3]=>[8,1,4,2,6,7,5,3]=>[4,1,2,7,6,5,8,3]=>0010111
[5,1,3,7,8,6,2,4]=>[5,6,1,2,3,8,7,4]=>[7,8,6,1,5,2,3,4]=>0001101
[7,2,5,8,1,6,4,3]=>[8,7,4,6,2,1,5,3]=>[6,4,2,7,1,5,8,3]=>0010111
[3,2,8,5,7,6,1,4]=>[6,3,2,1,7,8,4,5]=>[3,2,8,1,4,7,6,5]=>0100111
[1,2,8,6,5,7,3,4]=>[1,2,7,3,6,8,5,4]=>[1,2,8,6,5,7,3,4]=>0000111
[4,2,1,3,6,7,8,5]=>[2,4,1,3,8,6,7,5]=>[4,2,1,3,6,7,8,5]=>1010001
[7,2,6,5,4,1,8,3]=>[4,5,6,7,8,1,3,2]=>[8,1,7,3,6,5,4,2]=>0011111
[7,5,6,2,4,1,8,3]=>[4,6,8,2,7,5,1,3]=>[7,5,8,2,6,1,4,3]=>0010111
[8,5,2,6,3,7,1,4]=>[7,5,8,1,6,3,2,4]=>[6,1,8,5,3,7,2,4]=>0001111
[4,3,1,2,6,7,8,5]=>[3,1,4,2,8,6,7,5]=>[4,3,1,2,6,7,8,5]=>0110001
[8,1,6,5,7,3,2,4]=>[8,3,7,2,6,1,5,4]=>[6,3,2,7,5,8,1,4]=>0100111
[5,8,1,6,3,7,2,4]=>[8,7,6,2,5,1,3,4]=>[5,6,2,7,1,8,3,4]=>0000111
[1,8,5,6,3,7,2,4]=>[1,7,6,2,8,5,3,4]=>[1,8,5,6,2,7,3,4]=>0000111
[1,7,6,5,4,2,8,3]=>[1,4,5,6,7,8,3,2]=>[1,8,3,7,6,5,4,2]=>0011111
[7,1,4,2,6,5,8,3]=>[7,4,8,1,6,2,5,3]=>[6,1,4,2,8,5,7,3]=>0010111
[2,7,4,1,5,6,8,3]=>[4,2,7,8,3,5,6,1]=>[2,8,3,5,6,7,4,1]=>0010011
[5,7,6,4,1,2,8,3]=>[4,1,6,7,5,8,2,3]=>[5,8,1,2,7,6,4,3]=>0010111
[1,7,6,4,5,2,8,3]=>[1,5,8,6,4,7,2,3]=>[1,7,6,4,8,2,5,3]=>0001111
[7,8,5,4,1,6,2,3]=>[4,5,2,8,6,1,7,3]=>[6,2,7,8,5,4,1,3]=>0011101
[7,5,6,4,2,1,8,3]=>[2,4,6,8,7,5,3,1]=>[7,5,8,3,6,4,2,1]=>1010111
[7,4,6,2,5,1,8,3]=>[5,6,8,7,2,4,1,3]=>[7,2,8,4,6,1,5,3]=>0001111
[6,1,4,3,5,7,8,2]=>[6,8,4,1,3,5,7,2]=>[4,1,7,8,3,5,6,2]=>0010101
[6,1,3,4,5,7,8,2]=>[6,8,1,3,4,5,7,2]=>[7,8,1,3,4,5,6,2]=>0000101
[7,2,6,4,5,1,8,3]=>[5,7,8,6,4,2,1,3]=>[6,4,8,2,7,1,5,3]=>0001111
[8,2,3,6,5,7,1,4]=>[7,8,2,1,6,3,5,4]=>[6,2,8,5,7,1,3,4]=>0000111
[3,4,7,2,5,1,6,8]=>[5,7,3,4,2,1,6,8]=>[3,4,7,2,5,1,6,8]=>0001010
[1,4,7,2,5,8,3,6]=>[1,7,8,4,2,3,5,6]=>[1,4,8,2,7,3,5,6]=>0000011
[3,6,2,4,7,1,5,8]=>[7,6,3,2,1,4,5,8]=>[3,6,2,7,1,4,5,8]=>0000110
[4,3,6,7,5,8,1,2]=>[8,1,4,3,7,6,5,2]=>[4,3,6,7,5,8,1,2]=>0010011
[7,3,8,6,4,5,1,2]=>[5,1,7,6,4,8,3,2]=>[8,6,4,7,3,5,1,2]=>0001111
[3,2,7,6,5,1,4,8]=>[5,3,2,1,6,7,4,8]=>[3,2,7,6,5,1,4,8]=>0101110
[2,3,8,6,4,1,5,7]=>[4,2,3,6,1,8,5,7]=>[2,3,8,6,4,1,5,7]=>0010101
[4,3,6,2,5,1,8,7]=>[5,6,4,3,2,1,8,7]=>[4,3,6,2,5,1,8,7]=>0011101
[7,8,3,2,5,1,4,6]=>[5,3,8,1,2,4,7,6]=>[7,8,3,1,5,2,4,6]=>0101001
[2,1,8,6,4,7,3,5]=>[2,1,7,6,3,8,4,5]=>[2,1,8,6,3,7,4,5]=>1000111
[1,8,3,6,7,4,5,2]=>[1,5,8,7,4,3,6,2]=>[1,7,4,6,8,3,5,2]=>0001011
[7,1,5,8,3,6,2,4]=>[7,6,8,2,1,3,5,4]=>[8,2,6,1,5,7,3,4]=>0000111
[6,8,5,1,3,4,2,7]=>[5,4,1,3,8,6,2,7]=>[4,1,3,6,8,5,2,7]=>0011001
[4,2,8,3,1,7,5,6]=>[3,8,4,1,7,5,2,6]=>[4,1,7,5,8,3,2,6]=>0110011
[1,3,7,4,8,2,5,6]=>[1,8,3,7,2,5,4,6]=>[1,3,7,2,5,8,4,6]=>0000011
[2,4,7,3,6,1,8,5]=>[6,2,7,4,8,3,1,5]=>[2,4,8,3,7,1,6,5]=>0000111
[5,8,7,6,3,1,2,4]=>[3,1,6,2,5,7,8,4]=>[5,8,7,6,3,1,2,4]=>0100111
[7,5,6,8,1,4,3,2]=>[8,3,4,1,7,5,6,2]=>[4,3,1,7,5,6,8,2]=>0110011
[1,2,7,8,5,4,3,6]=>[1,2,4,5,8,3,7,6]=>[1,2,7,8,5,4,3,6]=>0011001
[6,3,1,2,8,4,5,7]=>[3,1,6,8,4,2,5,7]=>[8,4,6,3,1,2,5,7]=>0100101
[4,2,1,3,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>1010101
[2,8,1,4,5,6,3,7]=>[8,2,6,1,4,5,3,7]=>[2,6,1,4,5,8,3,7]=>0000101
[7,2,1,5,4,6,3,8]=>[2,7,6,5,1,4,3,8]=>[5,2,1,6,4,7,3,8]=>1001110
[7,8,2,1,4,5,3,6]=>[2,8,5,1,4,3,7,6]=>[5,2,1,4,7,8,3,6]=>1001001
[3,4,6,1,5,8,7,2]=>[6,7,3,4,1,5,8,2]=>[3,4,8,7,1,5,6,2]=>0000111
[5,8,1,6,3,4,7,2]=>[8,7,6,3,5,1,4,2]=>[5,6,3,7,1,4,8,2]=>0000111
[5,6,1,7,4,8,2,3]=>[6,8,2,7,5,1,4,3]=>[5,7,2,8,4,6,1,3]=>0000111
[3,6,1,5,7,4,2,8]=>[6,4,3,7,1,5,2,8]=>[3,7,4,1,5,6,2,8]=>0010110
[6,1,7,8,5,3,4,2]=>[6,4,5,3,8,1,7,2]=>[7,8,5,3,4,1,6,2]=>0011101
[2,6,5,7,3,4,8,1]=>[8,2,7,3,6,5,4,1]=>[2,6,5,7,3,4,8,1]=>0000111
[1,6,4,7,5,8,2,3]=>[1,8,2,6,7,4,5,3]=>[1,7,4,6,5,8,2,3]=>0000111
[1,3,7,4,6,8,2,5]=>[1,8,3,7,2,4,6,5]=>[1,3,7,2,6,8,4,5]=>0000011
[4,7,5,6,3,2,8,1]=>[8,3,6,4,7,5,2,1]=>[4,7,5,6,3,2,8,1]=>0100111
[1,7,6,5,4,8,2,3]=>[1,8,2,5,6,7,4,3]=>[1,7,6,5,4,8,2,3]=>0001111
[8,1,6,5,7,2,4,3]=>[8,7,4,2,6,1,5,3]=>[4,2,6,1,7,5,8,3]=>0010111
[1,2,7,6,8,3,4,5]=>[1,2,8,3,4,7,6,5]=>[1,2,7,6,8,3,4,5]=>0000011
[6,1,7,5,3,8,2,4]=>[6,8,5,2,7,1,3,4]=>[7,5,2,8,1,6,3,4]=>0001111
[2,1,7,5,6,8,3,4]=>[2,1,8,3,7,5,6,4]=>[2,1,7,5,6,8,3,4]=>1000011
[5,4,1,7,6,8,2,3]=>[4,5,1,8,2,7,6,3]=>[7,6,8,1,5,4,2,3]=>0011011
[4,8,5,6,2,7,3,1]=>[3,7,6,4,8,5,1,2]=>[4,8,5,6,1,7,3,2]=>0100111
[3,8,6,4,2,7,5,1]=>[5,4,3,7,6,8,1,2]=>[3,8,6,4,1,7,5,2]=>0011111
[7,8,5,2,4,6,3,1]=>[3,6,5,1,8,4,7,2]=>[7,8,5,1,4,6,3,2]=>0101101
[7,8,1,6,2,4,5,3]=>[8,6,5,2,4,1,7,3]=>[5,2,4,6,1,7,8,3]=>0001101
[5,4,7,1,8,3,2,6]=>[7,3,8,5,4,2,1,6]=>[5,4,8,3,2,7,1,6]=>0101011
[6,7,1,4,8,3,2,5]=>[7,3,8,1,2,6,4,5]=>[6,8,3,1,7,2,4,5]=>0100011
[2,7,1,8,4,5,3,6]=>[7,2,5,8,4,3,1,6]=>[2,8,4,5,3,7,1,6]=>0001011
[6,5,1,4,3,8,2,7]=>[5,6,4,2,8,3,1,7]=>[4,2,8,3,6,5,1,7]=>0011101
[1,6,2,5,8,3,4,7]=>[1,6,8,3,2,5,4,7]=>[1,8,3,5,6,2,4,7]=>0000101
[8,5,1,3,7,2,6,4]=>[5,8,2,7,6,4,3,1]=>[6,4,7,2,3,8,5,1]=>0001111
[8,4,2,1,7,3,6,5]=>[2,4,8,7,6,1,3,5]=>[6,2,1,7,4,3,8,5]=>1010111
[7,4,2,1,8,5,3,6]=>[2,4,7,5,8,1,3,6]=>[8,5,2,1,7,4,3,6]=>1011011
[6,4,3,1,5,8,2,7]=>[3,4,6,8,1,5,2,7]=>[8,1,5,6,4,3,2,7]=>0110101
[3,7,6,8,4,5,2,1]=>[2,5,3,8,4,7,6,1]=>[3,7,6,8,4,5,2,1]=>1001011
[2,7,6,8,5,3,4,1]=>[4,2,5,3,8,7,6,1]=>[2,7,6,8,5,3,4,1]=>0011011
[1,7,6,8,5,4,2,3]=>[1,4,2,5,8,7,6,3]=>[1,7,6,8,5,4,2,3]=>0011011
[1,4,8,6,7,5,2,3]=>[1,5,2,4,7,8,6,3]=>[1,4,8,6,7,5,2,3]=>0001011
[2,4,8,6,7,3,5,1]=>[5,2,7,4,3,8,6,1]=>[2,4,8,6,7,3,5,1]=>0001011
[7,3,8,5,4,6,2,1]=>[2,6,7,5,8,4,3,1]=>[8,5,4,7,3,6,2,1]=>1001111
[3,4,8,5,6,7,2,1]=>[2,7,3,4,8,5,6,1]=>[3,4,8,5,6,7,2,1]=>1000011
[6,3,5,8,4,7,2,1]=>[2,7,6,8,3,5,4,1]=>[8,3,5,6,4,7,2,1]=>1000111
[5,4,3,8,6,7,2,1]=>[2,7,4,5,3,8,6,1]=>[5,4,3,8,6,7,2,1]=>1011011
[5,4,2,8,7,3,6,1]=>[6,4,5,7,3,2,8,1]=>[8,7,3,5,4,2,6,1]=>0011111
[6,2,5,8,7,3,4,1]=>[4,6,7,3,2,5,8,1]=>[8,7,3,5,6,2,4,1]=>0010111
[1,3,8,7,5,6,2,4]=>[1,6,3,2,7,5,8,4]=>[1,3,8,7,5,6,2,4]=>0000111
[2,1,8,7,4,6,3,5]=>[2,1,6,7,3,4,8,5]=>[2,1,8,7,3,6,4,5]=>1000111
[3,1,8,5,7,6,2,4]=>[3,6,1,2,7,8,4,5]=>[8,1,3,2,4,7,6,5]=>0100111
[6,1,5,8,7,4,2,3]=>[6,4,2,7,1,5,8,3]=>[8,7,4,2,5,6,1,3]=>0010111
[5,4,1,8,7,6,2,3]=>[4,5,1,6,2,7,8,3]=>[8,7,6,1,5,4,2,3]=>0011111
[5,8,6,7,4,3,2,1]=>[2,3,4,7,5,8,6,1]=>[5,8,6,7,4,3,2,1]=>1110011
[4,8,7,5,6,3,2,1]=>[2,3,6,4,7,5,8,1]=>[4,8,7,5,6,3,2,1]=>1100111
[4,2,1,6,3,5,8,7]=>[2,4,6,1,3,5,8,7]=>[6,2,1,4,3,5,8,7]=>1010101
[6,2,1,4,3,5,8,7]=>[2,6,4,1,3,5,8,7]=>[4,2,1,6,3,5,8,7]=>1010101
[6,2,1,4,3,8,5,7]=>[2,6,4,1,8,3,5,7]=>[4,2,1,8,3,6,5,7]=>1010101
[8,2,1,4,3,6,5,7]=>[2,8,4,1,6,3,5,7]=>[4,2,1,6,3,8,5,7]=>1010101
[6,2,4,1,3,8,5,7]=>[4,6,1,2,8,3,5,7]=>[8,1,4,2,3,6,5,7]=>0010101
[6,2,4,1,3,5,8,7]=>[4,6,1,2,3,5,8,7]=>[6,1,4,2,3,5,8,7]=>0010101
[2,1,6,4,3,5,8,7]=>[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]=>1010101
[2,6,1,4,3,5,8,7]=>[6,2,4,1,3,5,8,7]=>[2,4,1,6,3,5,8,7]=>0010101
[2,6,4,1,3,5,8,7]=>[4,2,1,6,3,5,8,7]=>[2,6,4,1,3,5,8,7]=>0010101
[4,6,2,1,3,5,8,7]=>[2,6,1,4,3,5,8,7]=>[4,6,2,1,3,5,8,7]=>1000101
[6,4,2,1,3,5,8,7]=>[2,4,1,6,3,5,8,7]=>[6,4,2,1,3,5,8,7]=>1010101
[8,4,2,1,3,6,5,7]=>[2,4,1,8,6,3,5,7]=>[6,4,2,1,3,8,5,7]=>1010101
[8,4,2,1,6,3,5,7]=>[2,4,8,6,1,3,5,7]=>[6,2,1,8,4,3,5,7]=>1010101
[6,4,2,1,8,3,5,7]=>[2,4,6,8,1,3,5,7]=>[8,2,1,6,4,3,5,7]=>1010101
[2,6,1,4,3,8,5,7]=>[6,2,4,1,8,3,5,7]=>[2,4,1,8,3,6,5,7]=>0010101
[2,1,6,4,3,8,5,7]=>[2,1,4,6,8,3,5,7]=>[2,1,8,4,3,6,5,7]=>1010101
[2,1,8,4,3,6,5,7]=>[2,1,4,8,6,3,5,7]=>[2,1,6,4,3,8,5,7]=>1010101
[2,8,1,4,3,6,5,7]=>[8,2,4,1,6,3,5,7]=>[2,4,1,6,3,8,5,7]=>0010101
[2,8,4,1,3,6,5,7]=>[4,2,1,8,6,3,5,7]=>[2,6,4,1,3,8,5,7]=>0010101
[4,8,2,1,3,6,5,7]=>[2,8,1,4,6,3,5,7]=>[4,6,2,1,3,8,5,7]=>1000101
[6,8,2,1,4,3,5,7]=>[2,8,4,1,3,6,5,7]=>[4,2,1,6,8,3,5,7]=>1010001
[8,6,2,1,4,3,5,7]=>[2,6,4,1,3,8,5,7]=>[4,2,1,8,6,3,5,7]=>1010101
[2,1,8,4,6,3,5,7]=>[2,1,6,8,3,4,5,7]=>[2,1,8,3,6,4,5,7]=>1000101
[2,6,1,4,8,3,5,7]=>[6,2,8,1,3,4,5,7]=>[2,8,1,6,3,4,5,7]=>0000101
[2,6,4,1,8,3,5,7]=>[4,2,6,8,1,3,5,7]=>[2,8,1,6,4,3,5,7]=>0010101
[2,6,4,8,1,3,5,7]=>[8,2,1,6,3,4,5,7]=>[2,6,1,3,8,4,5,7]=>0000101
[4,2,6,1,3,8,5,7]=>[6,4,1,2,8,3,5,7]=>[4,1,8,2,3,6,5,7]=>0010101
[8,2,4,1,6,3,5,7]=>[4,8,6,2,3,1,5,7]=>[6,2,8,3,4,1,5,7]=>0010101
[6,2,1,4,8,3,5,7]=>[2,6,8,1,3,4,5,7]=>[8,2,1,6,3,4,5,7]=>1000101
[4,2,1,6,8,3,5,7]=>[2,4,8,1,3,6,5,7]=>[6,8,2,1,4,3,5,7]=>1010001
[4,2,1,6,3,8,5,7]=>[2,4,6,1,8,3,5,7]=>[8,2,1,4,3,6,5,7]=>1010101
[4,2,1,3,6,8,5,7]=>[2,4,1,3,8,6,5,7]=>[4,2,1,3,6,8,5,7]=>1010001
[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]=>1010101
[2,4,1,3,8,6,5,7]=>[4,2,1,3,6,8,5,7]=>[2,4,1,3,8,6,5,7]=>0010101
[4,2,1,3,8,6,5,7]=>[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]=>1010101
[4,2,1,8,3,6,5,7]=>[2,4,8,1,6,3,5,7]=>[6,2,1,4,3,8,5,7]=>1010101
[4,2,1,8,6,3,5,7]=>[2,4,6,1,3,8,5,7]=>[8,6,2,1,4,3,5,7]=>1010101
[6,2,1,8,4,3,5,7]=>[2,6,4,8,3,1,5,7]=>[8,4,3,6,2,1,5,7]=>1010101
[8,2,1,6,4,3,5,7]=>[2,8,4,6,3,1,5,7]=>[6,4,3,8,2,1,5,7]=>1010101
[8,2,6,1,4,3,5,7]=>[6,8,4,1,3,2,5,7]=>[4,1,8,3,6,2,5,7]=>0010101
[4,2,8,1,6,3,5,7]=>[8,4,6,2,3,1,5,7]=>[6,2,4,3,8,1,5,7]=>0010101
[4,2,8,1,3,6,5,7]=>[8,4,1,2,6,3,5,7]=>[4,1,6,2,3,8,5,7]=>0010101
[2,4,8,1,3,6,5,7]=>[8,2,1,4,6,3,5,7]=>[2,4,6,1,3,8,5,7]=>0000101
[2,4,1,8,3,6,5,7]=>[4,2,8,1,6,3,5,7]=>[2,6,1,4,3,8,5,7]=>0010101
[2,1,4,8,3,6,5,7]=>[2,1,8,4,6,3,5,7]=>[2,1,4,6,3,8,5,7]=>1000101
[2,1,4,8,6,3,5,7]=>[2,1,6,4,3,8,5,7]=>[2,1,4,8,6,3,5,7]=>1000101
[2,4,8,6,1,3,5,7]=>[6,2,1,4,3,8,5,7]=>[2,4,8,6,1,3,5,7]=>0000101
[4,2,8,6,1,3,5,7]=>[6,4,1,2,3,8,5,7]=>[4,1,8,6,2,3,5,7]=>0010101
[6,2,8,4,1,3,5,7]=>[4,8,2,6,3,1,5,7]=>[6,2,3,8,4,1,5,7]=>0010101
[8,2,6,4,1,3,5,7]=>[4,6,2,8,3,1,5,7]=>[8,2,3,6,4,1,5,7]=>0010101
[8,4,6,2,1,3,5,7]=>[2,6,1,8,3,4,5,7]=>[8,2,1,3,6,4,5,7]=>1000101
[6,4,8,2,1,3,5,7]=>[2,8,1,6,3,4,5,7]=>[6,2,1,3,8,4,5,7]=>1000101
[4,6,8,2,1,3,5,7]=>[2,8,1,4,3,6,5,7]=>[4,6,8,2,1,3,5,7]=>1000001
[2,6,8,4,1,3,5,7]=>[4,2,1,8,3,6,5,7]=>[2,6,8,4,1,3,5,7]=>0010001
[2,6,8,1,4,3,5,7]=>[8,2,4,1,3,6,5,7]=>[2,4,1,6,8,3,5,7]=>0010001
[2,6,1,8,4,3,5,7]=>[6,2,4,8,3,1,5,7]=>[2,8,4,3,6,1,5,7]=>0010101
[2,1,6,8,4,3,5,7]=>[2,1,4,8,3,6,5,7]=>[2,1,6,8,4,3,5,7]=>1010001
[2,1,8,6,4,3,5,7]=>[2,1,4,6,3,8,5,7]=>[2,1,8,6,4,3,5,7]=>1010101
[2,8,6,4,1,3,5,7]=>[4,2,1,6,3,8,5,7]=>[2,8,6,4,1,3,5,7]=>0010101
[4,8,6,2,1,3,5,7]=>[2,6,1,4,3,8,5,7]=>[4,8,6,2,1,3,5,7]=>1000101
[6,8,4,2,1,3,5,7]=>[2,4,1,8,3,6,5,7]=>[6,8,4,2,1,3,5,7]=>1010001
[3,2,6,1,5,4,8,7]=>[6,3,2,5,1,4,8,7]=>[3,2,5,1,6,4,8,7]=>0101101
[5,2,4,3,8,1,7,6]=>[8,5,4,2,3,7,1,6]=>[4,2,5,3,7,1,8,6]=>0011011
[6,2,4,1,5,3,8,7]=>[4,6,5,2,1,3,8,7]=>[5,2,6,1,4,3,8,7]=>0011101
[4,3,6,1,5,2,8,7]=>[6,5,4,3,1,2,8,7]=>[4,3,5,1,6,2,8,7]=>0011101
[4,3,5,2,8,1,7,6]=>[8,5,4,3,2,7,1,6]=>[4,3,5,2,7,1,8,6]=>0011011
[4,3,7,2,6,5,8,1]=>[8,7,4,3,6,2,5,1]=>[4,3,6,2,7,5,8,1]=>0010111
[4,3,8,1,7,2,6,5]=>[8,7,4,3,6,2,1,5]=>[4,3,6,2,7,1,8,5]=>0010111
[4,3,8,1,5,2,7,6]=>[8,5,4,3,1,7,2,6]=>[4,3,5,1,7,2,8,6]=>0011011
[5,4,8,1,3,2,7,6]=>[8,3,1,5,4,7,2,6]=>[3,1,5,4,7,2,8,6]=>0101011
[2,1,5,4,8,3,7,6]=>[2,1,8,5,4,7,3,6]=>[2,1,5,4,7,3,8,6]=>1001011
[4,3,7,6,8,1,5,2]=>[8,5,4,3,1,7,6,2]=>[4,3,5,1,7,6,8,2]=>0011011
[4,3,7,1,8,5,6,2]=>[7,6,4,3,8,5,1,2]=>[4,3,8,5,6,1,7,2]=>0010111
[4,3,6,5,8,1,7,2]=>[8,7,4,3,6,5,1,2]=>[4,3,6,5,7,1,8,2]=>0010111
[6,3,5,4,7,2,8,1]=>[8,7,6,5,3,4,2,1]=>[5,3,6,4,7,2,8,1]=>0001111
[6,3,5,4,8,1,7,2]=>[8,7,6,5,3,4,1,2]=>[5,3,6,4,7,1,8,2]=>0001111
[7,4,6,5,8,1,3,2]=>[8,3,1,7,6,4,5,2]=>[3,1,6,4,7,5,8,2]=>0100111
[2,1,8,4,6,3,7,5]=>[2,1,6,8,7,4,3,5]=>[2,1,7,4,8,3,6,5]=>1000111
[8,4,6,1,3,2,7,5]=>[6,3,1,8,7,4,2,5]=>[3,1,7,4,8,2,6,5]=>0100111
[8,1,6,3,4,2,7,5]=>[8,4,6,3,7,1,2,5]=>[7,3,4,1,6,2,8,5]=>0010111
[8,1,6,3,7,2,5,4]=>[8,7,6,5,2,1,3,4]=>[5,2,6,1,7,3,8,4]=>0001111
[8,3,5,1,7,2,6,4]=>[5,7,8,6,3,2,1,4]=>[6,3,8,2,7,1,5,4]=>0001111
[8,3,5,2,6,1,7,4]=>[6,5,8,7,3,2,1,4]=>[7,3,8,2,5,1,6,4]=>0001111
[7,3,5,2,6,4,8,1]=>[8,5,7,6,3,2,4,1]=>[6,3,7,2,5,4,8,1]=>0001111
[8,2,6,3,5,1,7,4]=>[5,8,6,7,3,2,1,4]=>[7,3,6,2,8,1,5,4]=>0001111
[8,2,7,1,5,3,6,4]=>[7,8,5,6,1,3,2,4]=>[6,1,5,3,8,2,7,4]=>0001111
[8,2,4,1,5,3,7,6]=>[4,8,5,2,1,7,3,6]=>[5,2,7,1,4,3,8,6]=>0011011
[8,2,4,1,7,3,6,5]=>[4,8,7,2,6,3,1,5]=>[6,2,7,3,4,1,8,5]=>0010111
[8,2,4,3,6,1,7,5]=>[6,8,4,2,7,3,1,5]=>[4,2,7,3,8,1,6,5]=>0010111
[3,2,8,4,6,1,7,5]=>[6,3,2,8,7,4,1,5]=>[3,2,7,4,8,1,6,5]=>0100111
[3,2,8,1,5,4,7,6]=>[8,3,2,5,1,7,4,6]=>[3,2,5,1,7,4,8,6]=>0101011
[3,2,7,6,8,1,5,4]=>[8,3,2,5,1,7,6,4]=>[3,2,5,1,7,6,8,4]=>0101011
[3,2,7,1,8,5,6,4]=>[7,3,2,6,8,5,1,4]=>[3,2,8,5,6,1,7,4]=>0100111
[3,2,6,5,8,1,7,4]=>[8,3,2,7,6,5,1,4]=>[3,2,6,5,7,1,8,4]=>0100111
[6,5,7,2,4,3,8,1]=>[8,7,4,2,6,5,3,1]=>[4,2,6,5,7,3,8,1]=>0010111
[7,2,4,1,8,5,6,3]=>[4,7,6,2,8,5,1,3]=>[8,5,6,2,7,1,4,3]=>0010111
[7,6,8,1,5,2,4,3]=>[8,5,4,2,1,7,6,3]=>[4,2,5,1,7,6,8,3]=>0011011
[7,1,3,2,8,5,6,4]=>[7,3,1,6,8,5,2,4]=>[3,1,8,5,6,2,7,4]=>0100111
[7,2,8,1,5,4,6,3]=>[8,7,6,5,1,4,2,3]=>[5,1,6,4,7,2,8,3]=>0001111
[5,4,7,2,6,3,8,1]=>[8,7,6,5,4,2,3,1]=>[5,4,6,2,7,3,8,1]=>0001111
[5,4,8,2,6,1,7,3]=>[6,8,7,5,4,2,1,3]=>[5,4,7,2,8,1,6,3]=>0001111
[6,5,8,1,7,2,4,3]=>[8,7,4,2,6,5,1,3]=>[4,2,6,5,7,1,8,3]=>0010111
[2,1,6,5,8,3,7,4]=>[2,1,8,7,6,5,3,4]=>[2,1,6,5,7,3,8,4]=>1000111
[6,5,7,4,8,1,3,2]=>[8,3,1,7,6,5,4,2]=>[3,1,6,5,7,4,8,2]=>0100111
[6,5,7,1,8,3,4,2]=>[7,4,8,3,6,5,1,2]=>[6,5,8,3,4,1,7,2]=>0010111
[6,1,7,4,8,3,5,2]=>[6,5,8,7,3,1,4,2]=>[7,3,8,1,5,4,6,2]=>0001111
[5,4,7,1,8,3,6,2]=>[7,6,8,5,4,3,1,2]=>[5,4,8,3,6,1,7,2]=>0001111
[5,4,6,3,8,1,7,2]=>[8,7,6,5,4,3,1,2]=>[5,4,6,3,7,1,8,2]=>0001111
[2,1,4,3,6,5,8,7,11,12,10,9]=>[2,1,4,3,6,5,8,7,10,12,11,9]=>[2,1,4,3,6,5,8,7,11,12,10,9]=>10101010101
[2,1,4,3,6,5,9,10,8,7,12,11]=>[2,1,4,3,6,5,8,10,9,7,12,11]=>[2,1,4,3,6,5,9,10,8,7,12,11]=>10101010101
[2,1,4,3,6,5,10,11,12,9,8,7]=>[2,1,4,3,6,5,8,9,12,10,11,7]=>[2,1,4,3,6,5,10,11,12,9,8,7]=>10101011001
[2,1,4,3,7,8,6,5,10,9,12,11]=>[2,1,4,3,6,8,7,5,10,9,12,11]=>[2,1,4,3,7,8,6,5,10,9,12,11]=>10101010101
[2,1,4,3,7,8,6,5,11,12,10,9]=>[2,1,4,3,6,8,7,5,10,12,11,9]=>[2,1,4,3,7,8,6,5,11,12,10,9]=>10101010101
[2,1,4,3,7,10,6,11,12,9,8,5]=>[2,1,4,3,8,9,7,12,10,6,11,5]=>[2,1,4,3,7,10,6,11,12,9,8,5]=>10100011101
[2,1,4,3,8,9,10,7,6,5,12,11]=>[2,1,4,3,6,7,10,8,9,5,12,11]=>[2,1,4,3,8,9,10,7,6,5,12,11]=>10101100101
[2,1,4,3,9,10,11,12,8,7,6,5]=>[2,1,4,3,6,7,8,12,9,10,11,5]=>[2,1,4,3,9,10,11,12,8,7,6,5]=>10101110001
[2,1,5,6,4,3,8,7,10,9,12,11]=>[2,1,4,6,5,3,8,7,10,9,12,11]=>[2,1,5,6,4,3,8,7,10,9,12,11]=>10101010101
[2,1,5,6,4,3,8,7,11,12,10,9]=>[2,1,4,6,5,3,8,7,10,12,11,9]=>[2,1,5,6,4,3,8,7,11,12,10,9]=>10101010101
[2,1,5,6,4,3,9,10,8,7,12,11]=>[2,1,4,6,5,3,8,10,9,7,12,11]=>[2,1,5,6,4,3,9,10,8,7,12,11]=>10101010101
[2,1,5,6,4,3,10,11,12,9,8,7]=>[2,1,4,6,5,3,8,9,12,10,11,7]=>[2,1,5,6,4,3,10,11,12,9,8,7]=>10101011001
[2,1,5,8,4,9,10,7,6,3,12,11]=>[2,1,6,7,5,10,8,4,9,3,12,11]=>[2,1,5,8,4,9,10,7,6,3,12,11]=>10001110101
[2,1,6,7,8,5,4,3,10,9,12,11]=>[2,1,4,5,8,6,7,3,10,9,12,11]=>[2,1,6,7,8,5,4,3,10,9,12,11]=>10110010101
[2,1,6,7,8,5,4,3,11,12,10,9]=>[2,1,4,5,8,6,7,3,10,12,11,9]=>[2,1,6,7,8,5,4,3,11,12,10,9]=>10110010101
[2,1,6,7,10,5,4,11,12,9,8,3]=>[2,1,8,5,9,6,7,12,10,4,11,3]=>[2,1,6,7,10,5,4,11,12,9,8,3]=>10010011101
[2,1,6,9,10,5,11,12,8,7,4,3]=>[2,1,4,7,8,6,12,10,9,5,11,3]=>[2,1,6,9,10,5,11,12,8,7,4,3]=>10100110101
[2,1,7,8,9,10,6,5,4,3,12,11]=>[2,1,4,5,6,10,7,8,9,3,12,11]=>[2,1,7,8,9,10,6,5,4,3,12,11]=>10111000101
[2,1,8,9,10,11,12,7,6,5,4,3]=>[2,1,4,5,6,7,12,8,9,10,11,3]=>[2,1,8,9,10,11,12,7,6,5,4,3]=>10111100001
[3,4,2,1,6,5,8,7,10,9,12,11]=>[2,4,3,1,6,5,8,7,10,9,12,11]=>[3,4,2,1,6,5,8,7,10,9,12,11]=>10101010101
[3,4,2,1,6,5,8,7,11,12,10,9]=>[2,4,3,1,6,5,8,7,10,12,11,9]=>[3,4,2,1,6,5,8,7,11,12,10,9]=>10101010101
[3,4,2,1,6,5,9,10,8,7,12,11]=>[2,4,3,1,6,5,8,10,9,7,12,11]=>[3,4,2,1,6,5,9,10,8,7,12,11]=>10101010101
[3,4,2,1,6,5,10,11,12,9,8,7]=>[2,4,3,1,6,5,8,9,12,10,11,7]=>[3,4,2,1,6,5,10,11,12,9,8,7]=>10101011001
[3,4,2,1,7,8,6,5,10,9,12,11]=>[2,4,3,1,6,8,7,5,10,9,12,11]=>[3,4,2,1,7,8,6,5,10,9,12,11]=>10101010101
[3,4,2,1,7,8,6,5,11,12,10,9]=>[2,4,3,1,6,8,7,5,10,12,11,9]=>[3,4,2,1,7,8,6,5,11,12,10,9]=>10101010101
[3,4,2,1,7,10,6,11,12,9,8,5]=>[2,4,3,1,8,9,7,12,10,6,11,5]=>[3,4,2,1,7,10,6,11,12,9,8,5]=>10100011101
[3,4,2,1,8,9,10,7,6,5,12,11]=>[2,4,3,1,6,7,10,8,9,5,12,11]=>[3,4,2,1,8,9,10,7,6,5,12,11]=>10101100101
[3,4,2,1,9,10,11,12,8,7,6,5]=>[2,4,3,1,6,7,8,12,9,10,11,5]=>[3,4,2,1,9,10,11,12,8,7,6,5]=>10101110001
[3,6,2,7,8,5,4,1,10,9,12,11]=>[4,5,3,8,6,2,7,1,10,9,12,11]=>[3,6,2,7,8,5,4,1,10,9,12,11]=>00111010101
[3,6,2,7,8,5,4,1,11,12,10,9]=>[4,5,3,8,6,2,7,1,10,12,11,9]=>[3,6,2,7,8,5,4,1,11,12,10,9]=>00111010101
[3,8,2,9,10,11,12,7,6,5,4,1]=>[4,5,3,6,7,12,8,2,9,10,11,1]=>[3,8,2,9,10,11,12,7,6,5,4,1]=>00111110001
[4,5,6,3,2,1,8,7,10,9,12,11]=>[2,3,6,4,5,1,8,7,10,9,12,11]=>[4,5,6,3,2,1,8,7,10,9,12,11]=>11001010101
[4,5,6,3,2,1,8,7,11,12,10,9]=>[2,3,6,4,5,1,8,7,10,12,11,9]=>[4,5,6,3,2,1,8,7,11,12,10,9]=>11001010101
[4,5,6,3,2,1,9,10,8,7,12,11]=>[2,3,6,4,5,1,8,10,9,7,12,11]=>[4,5,6,3,2,1,9,10,8,7,12,11]=>11001010101
[4,5,6,3,2,1,10,11,12,9,8,7]=>[2,3,6,4,5,1,8,9,12,10,11,7]=>[4,5,6,3,2,1,10,11,12,9,8,7]=>11001011001
[4,5,8,3,2,9,10,7,6,1,12,11]=>[6,3,7,4,5,10,8,2,9,1,12,11]=>[4,5,8,3,2,9,10,7,6,1,12,11]=>01001110101
[4,7,8,3,9,10,6,5,2,1,12,11]=>[2,5,6,4,10,8,7,3,9,1,12,11]=>[4,7,8,3,9,10,6,5,2,1,12,11]=>10011010101
[5,6,7,8,4,3,2,1,10,9,12,11]=>[2,3,4,8,5,6,7,1,10,9,12,11]=>[5,6,7,8,4,3,2,1,10,9,12,11]=>11100010101
[5,6,7,8,4,3,2,1,11,12,10,9]=>[2,3,4,8,5,6,7,1,10,12,11,9]=>[5,6,7,8,4,3,2,1,11,12,10,9]=>11100010101
[5,6,7,10,4,3,2,11,12,9,8,1]=>[8,3,4,9,5,6,7,12,10,2,11,1]=>[5,6,7,10,4,3,2,11,12,9,8,1]=>01100011101
[5,6,9,10,4,3,11,12,8,7,2,1]=>[2,7,4,8,5,6,12,10,9,3,11,1]=>[5,6,9,10,4,3,11,12,8,7,2,1]=>10100110101
[5,8,9,10,4,11,12,7,6,3,2,1]=>[2,3,6,7,5,12,10,8,9,4,11,1]=>[5,8,9,10,4,11,12,7,6,3,2,1]=>11001100101
[6,7,8,9,10,5,4,3,2,1,12,11]=>[2,3,4,5,10,6,7,8,9,1,12,11]=>[6,7,8,9,10,5,4,3,2,1,12,11]=>11110000101
[7,8,9,10,11,12,6,5,4,3,2,1]=>[2,3,4,5,6,12,7,8,9,10,11,1]=>[7,8,9,10,11,12,6,5,4,3,2,1]=>11111000001
[2,5,3,4,7,1,8,6]=>[7,2,5,3,4,8,1,6]=>[2,5,3,4,8,1,7,6]=>0001011
[2,4,8,3,5,7,6,1]=>[6,2,7,4,1,8,5,3]=>[2,4,8,1,5,7,6,3]=>0000111
[4,2,5,3,1,8,6,7]=>[3,5,4,1,2,8,6,7]=>[4,1,5,3,2,8,6,7]=>0111001
[4,2,1,8,5,3,6,7]=>[2,4,5,1,8,3,6,7]=>[8,5,2,1,4,3,6,7]=>1011001
[1,5,8,4,3,2,6,7]=>[1,3,4,8,5,2,6,7]=>[1,5,8,4,3,2,6,7]=>0110001
[1,8,5,4,3,2,6,7]=>[1,3,4,5,8,2,6,7]=>[1,8,5,4,3,2,6,7]=>0111001
[1,7,4,3,8,5,2,6]=>[1,5,4,8,7,3,2,6]=>[1,7,4,3,8,5,2,6]=>0011011
[1,5,7,3,8,4,2,6]=>[1,4,8,7,5,3,2,6]=>[1,5,7,3,8,4,2,6]=>0010011
[4,8,1,5,7,3,6,2]=>[8,6,7,4,1,3,5,2]=>[4,7,1,6,3,5,8,2]=>0000111
[8,1,5,3,7,4,6,2]=>[8,6,5,7,1,4,3,2]=>[7,1,5,4,6,3,8,2]=>0001111
[3,8,4,7,6,5,2,1]=>[2,5,3,6,7,8,4,1]=>[3,8,4,7,6,5,2,1]=>1001111
[1,6,8,5,3,7,4,2]=>[1,4,7,5,8,6,2,3]=>[1,6,8,5,2,7,4,3]=>0011011
[6,8,1,7,4,3,5,2]=>[8,5,4,7,3,6,1,2]=>[6,7,4,3,5,1,8,2]=>0011011
[6,4,8,1,7,3,5,2]=>[8,5,7,6,3,4,1,2]=>[6,3,7,4,5,1,8,2]=>0001111
[6,4,8,7,1,5,2,3]=>[7,5,2,6,1,4,8,3]=>[6,2,5,4,8,7,1,3]=>0001111
[7,6,4,1,3,8,2,5]=>[4,6,1,7,2,8,3,5]=>[8,1,7,6,4,2,3,5]=>0010111
[4,2,1,7,8,5,3,6]=>[2,4,5,1,8,3,7,6]=>[7,8,5,2,1,4,3,6]=>1011001
[2,6,8,4,3,7,5,1]=>[5,2,4,7,8,6,1,3]=>[2,6,8,4,1,7,5,3]=>0011011
[7,2,6,3,4,1,8,5]=>[4,7,6,3,8,2,1,5]=>[8,3,6,2,4,1,7,5]=>0010111
[2,6,7,3,1,4,8,5]=>[3,2,7,1,8,6,4,5]=>[2,6,8,3,1,4,7,5]=>0100011
[2,7,1,8,3,5,4,6]=>[7,2,8,5,3,4,1,6]=>[2,5,3,8,4,7,1,6]=>0001011
[2,1,7,3,5,8,4,6]=>[2,1,7,8,3,4,5,6]=>[2,1,8,3,7,4,5,6]=>1000011
[8,7,1,3,6,2,4,5]=>[7,6,1,2,4,3,8,5]=>[6,1,4,8,7,2,3,5]=>0000111
[8,2,1,7,3,5,6,4]=>[2,8,7,6,3,5,1,4]=>[6,3,5,7,2,1,8,4]=>1000111
[1,2,8,7,4,5,6,3]=>[1,2,6,7,4,5,8,3]=>[1,2,8,7,4,5,6,3]=>0000111
[8,6,1,2,7,5,3,4]=>[6,1,5,2,8,7,3,4]=>[7,5,1,2,8,6,3,4]=>0001111
[8,1,6,2,7,4,5,3]=>[8,6,5,7,4,1,2,3]=>[7,4,5,1,6,2,8,3]=>0001111
[1,8,5,2,6,7,4,3]=>[1,5,4,8,7,3,6,2]=>[1,7,4,3,6,8,5,2]=>0011011
[5,2,1,8,6,7,4,3]=>[2,5,4,7,1,8,6,3]=>[8,6,7,4,2,1,5,3]=>1011011
[2,8,5,7,6,4,3,1]=>[3,2,4,6,7,8,1,5]=>[2,8,4,3,1,7,6,5]=>0110111
[1,7,8,5,2,6,4,3]=>[1,5,4,8,6,3,7,2]=>[1,6,4,3,7,8,5,2]=>0011101
[7,3,8,6,1,5,2,4]=>[6,5,8,2,3,7,1,4]=>[7,2,5,3,8,6,1,4]=>0001111
[8,7,1,6,4,5,3,2]=>[7,3,5,6,4,1,8,2]=>[6,4,5,3,1,8,7,2]=>0101111
[8,1,7,5,6,4,3,2]=>[8,3,4,6,7,5,1,2]=>[7,5,6,4,3,1,8,2]=>0110111
[1,8,6,7,5,4,3,2]=>[1,3,4,5,7,8,6,2]=>[1,8,6,7,5,4,3,2]=>0111011
[6,3,5,2,1,4,8,7]=>[2,5,6,1,3,4,8,7]=>[6,2,1,5,3,4,8,7]=>1001101
[6,3,5,7,2,8,4,1]=>[4,8,7,6,1,5,3,2]=>[6,1,5,7,3,8,4,2]=>0010111
[4,5,3,6,1,2,8,7]=>[6,1,5,4,3,2,8,7]=>[4,5,3,6,1,2,8,7]=>0001101
[3,5,1,4,6,2,8,7]=>[5,6,3,1,4,2,8,7]=>[3,6,1,4,5,2,8,7]=>0001101
[5,7,4,6,3,8,2,1]=>[2,8,6,7,5,4,3,1]=>[5,7,4,6,3,8,2,1]=>1000111
[8,1,4,7,3,6,2,5]=>[8,6,7,1,2,3,4,5]=>[7,1,6,2,8,3,4,5]=>0000111
[8,5,1,4,7,3,2,6]=>[5,3,8,2,7,1,4,6]=>[7,3,2,8,5,1,4,6]=>0101011
[2,1,8,5,7,4,3,6]=>[2,1,4,7,8,3,5,6]=>[2,1,8,4,3,7,5,6]=>1010011
[6,5,1,4,7,8,3,2]=>[5,3,6,2,8,4,7,1]=>[7,8,3,2,4,6,5,1]=>0101101
[5,1,4,6,8,3,7,2]=>[5,7,8,1,4,6,3,2]=>[6,8,1,4,7,3,5,2]=>0001011
[4,7,1,3,5,8,6,2]=>[7,6,1,4,3,8,5,2]=>[4,8,6,1,3,5,7,2]=>0000111
[4,8,3,7,1,2,6,5]=>[7,1,8,4,6,2,3,5]=>[4,6,1,2,8,3,7,5]=>0000111
[3,8,6,4,1,7,2,5]=>[4,6,3,8,2,7,1,5]=>[3,7,2,8,6,4,1,5]=>0010111
[2,8,7,5,4,1,3,6]=>[4,2,1,5,7,3,8,6]=>[2,8,7,5,4,1,3,6]=>0011011
[3,8,6,7,4,2,1,5]=>[2,4,3,7,1,8,6,5]=>[3,8,6,7,4,2,1,5]=>1010011
[5,7,6,8,4,2,3,1]=>[3,4,2,8,5,7,6,1]=>[5,7,6,8,4,2,3,1]=>0110011
[5,3,7,6,2,1,8,4]=>[2,6,5,7,3,8,4,1]=>[8,3,5,4,7,6,2,1]=>1001111
[5,3,6,2,8,7,1,4]=>[7,6,5,1,3,2,8,4]=>[5,1,6,3,8,7,2,4]=>0001111
[5,7,8,6,4,2,1,3]=>[2,4,1,6,5,8,7,3]=>[5,7,8,6,4,2,1,3]=>1010101
[2,6,7,5,4,8,1,3]=>[8,2,1,5,7,6,4,3]=>[2,6,7,5,4,8,1,3]=>0001011
[6,1,7,4,5,8,2,3]=>[6,8,2,7,4,1,5,3]=>[7,4,8,2,5,6,1,3]=>0000111
[6,7,3,5,1,8,2,4]=>[5,8,7,2,3,6,1,4]=>[6,7,2,8,3,5,1,4]=>0001011
[2,1,6,7,5,8,3,4]=>[2,1,8,3,7,6,5,4]=>[2,1,6,7,5,8,3,4]=>1000011
[2,1,5,7,3,6,8,4]=>[2,1,7,8,5,3,6,4]=>[2,1,5,8,3,6,7,4]=>1000011
[4,1,7,2,5,6,8,3]=>[4,7,8,1,2,5,6,3]=>[8,1,5,6,7,2,4,3]=>0010011
[2,4,7,1,6,5,8,3]=>[7,2,8,4,6,1,5,3]=>[2,4,6,1,8,5,7,3]=>0000111
[3,4,6,2,7,8,5,1]=>[5,8,3,4,6,1,7,2]=>[3,4,6,1,7,8,5,2]=>0001101
[4,6,1,2,5,8,7,3]=>[6,1,7,4,2,5,8,3]=>[4,8,7,1,2,5,6,3]=>0000111
[5,6,1,4,8,2,7,3]=>[6,8,7,1,5,4,2,3]=>[5,7,1,4,8,2,6,3]=>0000111
[3,5,6,4,7,1,8,2]=>[7,8,3,6,5,4,1,2]=>[3,5,6,4,8,1,7,2]=>0000111
[3,4,6,1,5,7,8,2]=>[6,8,3,4,1,5,7,2]=>[3,4,7,8,1,5,6,2]=>0000101
[3,4,1,5,7,6,8,2]=>[4,8,3,1,5,7,6,2]=>[3,5,7,6,8,1,4,2]=>0010011
[3,8,2,7,1,6,5,4]=>[7,8,3,5,6,1,2,4]=>[3,6,5,1,8,2,7,4]=>0001111
[3,8,2,7,6,1,5,4]=>[6,7,3,5,2,8,1,4]=>[3,5,2,8,1,7,6,4]=>0001111
[3,8,2,7,6,5,4,1]=>[4,5,3,6,7,8,1,2]=>[3,8,1,7,6,5,4,2]=>0011111
[4,8,7,2,6,5,3,1]=>[3,5,6,4,7,2,8,1]=>[4,8,7,2,6,5,3,1]=>0101111
[4,8,7,2,6,5,1,3]=>[5,6,2,4,7,1,8,3]=>[4,8,7,2,6,5,1,3]=>0001111
[4,8,7,2,6,1,5,3]=>[6,7,5,4,1,2,8,3]=>[4,5,1,8,7,2,6,3]=>0001111
[4,8,7,2,1,6,5,3]=>[2,7,5,4,6,1,8,3]=>[4,6,5,2,1,8,7,3]=>1001111
[4,8,7,3,1,6,5,2]=>[3,7,5,4,6,2,8,1]=>[4,6,5,2,8,7,3,1]=>0101111
[4,8,7,3,2,1,6,5]=>[2,3,7,4,6,1,8,5]=>[4,6,3,2,1,8,7,5]=>1100111
[4,8,7,3,2,6,1,5]=>[6,3,7,4,1,2,8,5]=>[4,8,7,3,1,6,2,5]=>0100111
[4,8,7,3,2,6,5,1]=>[5,3,6,4,7,1,8,2]=>[4,8,7,3,1,6,5,2]=>0101111
[4,8,7,3,6,2,5,1]=>[5,6,7,4,2,3,8,1]=>[4,8,7,2,6,3,5,1]=>0001111
[4,8,7,3,6,2,1,5]=>[2,6,7,4,1,3,8,5]=>[4,8,7,2,1,6,3,5]=>1000111
[4,8,7,3,6,5,1,2]=>[5,1,6,4,7,2,8,3]=>[4,8,7,1,2,6,5,3]=>0001111
[4,8,7,3,6,5,2,1]=>[2,5,6,4,7,1,8,3]=>[4,8,7,2,1,6,5,3]=>1001111
[5,8,7,6,3,4,2,1]=>[2,4,6,3,5,7,8,1]=>[5,8,7,6,3,4,2,1]=>1010111
[5,8,7,6,3,2,4,1]=>[4,3,6,2,5,7,8,1]=>[5,8,7,6,3,2,4,1]=>0110111
[5,8,7,6,2,4,3,1]=>[3,4,6,1,5,7,8,2]=>[5,8,7,6,1,4,3,2]=>0110111
[5,8,7,6,2,1,4,3]=>[2,6,4,1,5,7,8,3]=>[4,2,1,5,8,7,6,3]=>1010111
[5,8,7,6,4,2,3,1]=>[3,4,2,6,5,7,8,1]=>[5,8,7,6,4,2,3,1]=>0110111
[5,8,7,6,4,2,1,3]=>[2,4,1,6,5,7,8,3]=>[5,8,7,6,4,2,1,3]=>1010111
[5,8,7,6,4,3,1,2]=>[3,1,4,6,5,7,8,2]=>[5,8,7,6,4,3,1,2]=>0110111
[7,3,5,2,6,4,1,8]=>[4,6,5,7,1,3,2,8]=>[7,1,5,3,6,4,2,8]=>0011110
[6,3,5,2,7,4,8,1]=>[8,5,6,7,3,2,4,1]=>[7,3,6,2,5,4,8,1]=>0001111
[7,3,5,1,6,4,2,8]=>[5,4,6,7,2,1,3,8]=>[7,2,6,4,1,5,3,8]=>0011110
[1,4,5,7,3,2,8,6]=>[1,3,7,4,5,8,2,6]=>[1,4,5,8,3,2,7,6]=>0100011
[1,4,6,7,3,8,2,5]=>[1,8,7,4,2,6,3,5]=>[1,4,6,7,2,8,3,5]=>0000011
[6,3,5,1,7,4,8,2]=>[5,8,6,7,3,1,4,2]=>[7,3,6,1,8,4,5,2]=>0001111
[6,2,1,5,7,4,8,3]=>[2,6,8,7,1,5,4,3]=>[7,2,1,5,8,4,6,3]=>1000111
[1,4,6,7,3,8,5,2]=>[1,5,8,4,7,6,2,3]=>[1,4,6,7,2,8,5,3]=>0001011
[2,5,6,7,8,3,1,4]=>[3,2,8,1,5,6,7,4]=>[2,5,6,7,8,3,1,4]=>0100001
[3,2,1,6,7,8,4,5]=>[2,3,1,8,4,6,7,5]=>[3,2,1,6,7,8,4,5]=>1100001
[5,2,1,6,7,8,4,3]=>[2,5,4,8,1,6,7,3]=>[6,7,8,4,2,1,5,3]=>1011001
[5,3,6,1,7,8,4,2]=>[6,4,8,5,2,1,7,3]=>[5,2,7,8,4,1,6,3]=>0011101
[5,4,6,7,1,8,3,2]=>[7,3,8,5,4,6,1,2]=>[5,4,6,8,3,1,7,2]=>0101011
[1,5,6,7,8,3,2,4]=>[1,3,8,2,5,6,7,4]=>[1,5,6,7,8,3,2,4]=>0100001
[5,4,6,7,2,8,3,1]=>[3,8,7,5,4,6,1,2]=>[5,4,6,7,1,8,3,2]=>0101011
[5,3,6,2,7,8,4,1]=>[4,8,6,5,1,3,7,2]=>[5,1,6,3,7,8,4,2]=>0011101
[5,3,6,2,7,8,1,4]=>[8,6,5,1,3,2,7,4]=>[5,1,6,3,7,8,2,4]=>0001101
[6,3,4,2,1,7,8,5]=>[2,4,6,3,8,1,7,5]=>[7,8,3,4,2,1,6,5]=>1010101
[5,3,4,1,2,7,8,6]=>[4,1,5,3,2,8,7,6]=>[5,3,4,1,2,7,8,6]=>0011001
[4,3,6,2,7,8,5,1]=>[5,8,4,3,6,1,7,2]=>[4,3,6,1,7,8,5,2]=>0011101
[3,4,5,7,2,1,8,6]=>[2,7,3,4,5,8,1,6]=>[3,4,5,8,2,1,7,6]=>1000011
[4,2,1,6,7,8,3,5]=>[2,4,8,1,3,6,7,5]=>[6,7,8,2,1,4,3,5]=>1010001
[4,3,6,1,7,8,2,5]=>[6,8,4,3,2,1,7,5]=>[4,3,7,8,2,6,1,5]=>0010101
[1,5,6,7,8,2,4,3]=>[1,8,4,2,5,6,7,3]=>[1,4,2,5,6,7,8,3]=>0010001
[3,4,6,7,1,8,5,2]=>[7,5,3,4,8,6,1,2]=>[3,4,6,8,5,1,7,2]=>0001011
[4,3,6,1,7,8,5,2]=>[6,5,4,3,8,1,7,2]=>[4,3,7,8,5,1,6,2]=>0011101
[2,3,6,1,7,8,5,4]=>[6,2,3,5,8,1,7,4]=>[2,3,7,8,5,1,6,4]=>0001101
[2,4,6,7,1,8,5,3]=>[7,2,5,4,8,6,1,3]=>[2,4,6,8,5,1,7,3]=>0001011
[2,5,6,7,8,1,4,3]=>[8,2,4,1,5,6,7,3]=>[2,4,1,5,6,7,8,3]=>0010001
[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>10101010
[2,4,1,3,6,5,8,7,9]=>[4,2,1,3,6,5,8,7,9]=>[2,4,1,3,6,5,8,7,9]=>00101010
[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]=>01010101
[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>01010101
[2,4,1,3,6,5,8,7,10,9]=>[4,2,1,3,6,5,8,7,10,9]=>[2,4,1,3,6,5,8,7,10,9]=>001010101
[2,4,6,1,3,5,8,7,9]=>[6,2,1,4,3,5,8,7,9]=>[2,4,6,1,3,5,8,7,9]=>00001010
[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]=>010101010
[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>010101010
[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>00000100
[1,4,3,6,2,5,7,8]=>[1,6,4,3,2,5,7,8]=>[1,4,3,6,2,5,7,8]=>0010100
[1,4,3,7,2,5,6,8]=>[1,7,4,3,2,5,6,8]=>[1,4,3,7,2,5,6,8]=>0010010
[1,4,3,7,6,8,2,5]=>[1,8,4,3,2,7,6,5]=>[1,4,3,7,6,8,2,5]=>0010011
[1,4,3,7,2,6,5,8]=>[1,7,4,3,6,2,5,8]=>[1,4,3,6,2,7,5,8]=>0010110
[1,5,3,7,4,8,2,6]=>[1,8,5,7,3,2,4,6]=>[1,7,3,5,2,8,4,6]=>0001011
[1,3,2,6,5,8,4,7]=>[1,3,2,8,6,5,4,7]=>[1,3,2,6,5,8,4,7]=>0100101
[1,5,4,8,2,6,3,7]=>[1,8,6,5,4,2,3,7]=>[1,5,4,6,2,8,3,7]=>0001101
[1,5,4,8,3,7,2,6]=>[1,7,8,5,4,2,3,6]=>[1,5,4,8,2,7,3,6]=>0001011
[1,2,3,6,5,8,4,7]=>[1,2,3,8,6,5,4,7]=>[1,2,3,6,5,8,4,7]=>0000101
[6,8,2,4,5,7,1,3]=>[7,8,1,2,4,6,5,3]=>[6,8,1,4,5,7,2,3]=>0000011
[3,7,8,4,5,2,6,1]=>[6,5,3,8,4,2,7,1]=>[3,7,8,4,5,2,6,1]=>0001101
[7,8,1,4,5,3,6,2]=>[8,6,5,1,4,3,7,2]=>[5,1,4,6,3,7,8,2]=>0001101
[4,8,3,6,1,5,7,2]=>[6,7,8,4,1,3,5,2]=>[4,8,1,7,3,5,6,2]=>0000111
[5,8,3,1,6,4,7,2]=>[3,8,7,6,5,2,4,1]=>[5,6,2,7,4,8,3,1]=>0100111
[5,8,1,4,7,6,3,2]=>[8,3,6,1,5,7,4,2]=>[5,7,6,3,1,4,8,2]=>0100111
[7,5,1,8,6,2,4,3]=>[5,7,4,1,6,8,2,3]=>[4,1,8,6,2,7,5,3]=>0011111
[7,1,8,4,2,6,3,5]=>[7,4,8,6,2,3,1,5]=>[6,2,8,4,3,7,1,5]=>0010111
[6,1,3,8,5,2,4,7]=>[6,5,1,2,8,3,4,7]=>[8,5,1,6,2,3,4,7]=>0001101
[7,3,1,8,4,2,6,5]=>[3,7,4,8,6,1,2,5]=>[6,4,1,8,3,2,7,5]=>0110111
[7,2,8,3,6,1,5,4]=>[6,7,8,5,1,3,2,4]=>[5,1,8,3,7,2,6,4]=>0001111
[1,5,2,3,8,4,7,6]=>[1,5,2,8,3,7,4,6]=>[1,7,2,3,5,4,8,6]=>0001011
[3,1,6,4,2,8,5,7]=>[3,4,1,6,8,2,5,7]=>[8,4,1,3,2,6,5,7]=>0110101
[2,6,3,8,5,1,4,7]=>[5,2,8,3,6,1,4,7]=>[2,6,3,8,5,1,4,7]=>0001101
[1,2,5,3,8,4,7,6]=>[1,2,5,8,3,7,4,6]=>[1,2,7,3,5,4,8,6]=>0001011
[2,4,8,3,7,1,6,5]=>[7,2,8,4,6,1,3,5]=>[2,4,6,1,8,3,7,5]=>0000111
[2,4,8,3,7,6,1,5]=>[6,2,7,4,3,8,1,5]=>[2,4,8,3,7,6,1,5]=>0000111
[2,5,4,1,3,8,7,6]=>[4,2,1,5,3,7,8,6]=>[2,5,4,1,3,8,7,6]=>0011011
[3,1,5,4,8,2,7,6]=>[3,8,1,5,4,7,2,6]=>[5,4,7,1,3,2,8,6]=>0101011
[4,8,2,3,7,6,1,5]=>[6,7,1,4,2,8,3,5]=>[4,8,1,7,6,2,3,5]=>0000111
[4,8,2,3,7,1,6,5]=>[7,8,2,4,6,1,3,5]=>[4,6,2,8,1,3,7,5]=>0000111
[4,8,1,2,3,7,6,5]=>[8,1,2,4,6,7,3,5]=>[4,7,6,1,2,3,8,5]=>0000111
[1,4,8,2,3,7,6,5]=>[1,8,2,4,6,7,3,5]=>[1,4,7,6,2,3,8,5]=>0000111
[1,4,8,3,7,2,6,5]=>[1,7,8,4,6,2,3,5]=>[1,4,6,2,8,3,7,5]=>0000111
[6,3,8,1,5,2,4,7]=>[8,5,6,2,1,3,4,7]=>[6,2,5,1,8,3,4,7]=>0001101
[5,3,8,1,2,4,7,6]=>[8,1,5,2,3,7,4,6]=>[5,1,2,7,3,4,8,6]=>0001011
[5,1,3,8,2,4,7,6]=>[5,8,1,2,3,7,4,6]=>[7,1,5,2,3,4,8,6]=>0001011
[1,5,3,8,2,4,7,6]=>[1,8,5,2,3,7,4,6]=>[1,5,2,7,3,4,8,6]=>0001011
[6,5,1,2,8,7,4,3]=>[5,1,4,6,7,3,8,2]=>[8,7,4,3,6,5,1,2]=>0011111
[5,1,6,2,8,7,4,3]=>[5,6,4,7,1,2,8,3]=>[8,7,4,1,6,2,5,3]=>0011111
[3,6,2,8,7,5,1,4]=>[5,7,3,2,6,1,8,4]=>[3,6,2,8,7,5,1,4]=>0001111
[4,2,6,1,8,7,3,5]=>[6,4,7,2,3,1,8,5]=>[8,7,2,4,3,6,1,5]=>0010111
[3,5,2,8,7,1,4,6]=>[7,5,3,1,2,4,8,6]=>[3,5,1,8,7,2,4,6]=>0001011
[3,4,8,7,1,2,6,5]=>[7,1,3,4,6,2,8,5]=>[3,4,6,1,2,8,7,5]=>0000111
[3,4,8,1,2,7,6,5]=>[8,1,3,4,6,7,2,5]=>[3,4,7,6,1,2,8,5]=>0000111
[3,4,8,2,7,1,6,5]=>[7,8,3,4,6,1,2,5]=>[3,4,6,1,8,2,7,5]=>0000111
[3,4,8,2,7,6,1,5]=>[6,7,3,4,2,8,1,5]=>[3,4,8,2,7,6,1,5]=>0000111
[4,3,1,2,5,8,7,6]=>[3,1,4,2,5,7,8,6]=>[4,3,1,2,5,8,7,6]=>0110011
[6,4,1,2,7,3,5,8]=>[4,1,6,7,2,3,5,8]=>[7,1,2,6,4,3,5,8]=>0010110
[6,3,1,5,4,2,7,8]=>[3,6,4,5,2,1,7,8]=>[5,4,2,6,3,1,7,8]=>0111100
[7,8,1,5,4,2,6,3]=>[8,4,5,6,1,3,7,2]=>[6,1,5,4,3,7,8,2]=>0011101
[7,8,3,5,4,1,6,2]=>[4,5,6,8,1,2,7,3]=>[7,8,1,6,2,5,4,3]=>0011101
[5,3,6,1,4,7,8,2]=>[6,8,5,1,3,4,7,2]=>[5,1,7,8,3,4,6,2]=>0001101
[5,3,6,2,4,7,1,8]=>[7,6,5,2,3,4,1,8]=>[5,2,6,3,4,7,1,8]=>0001110
[6,4,2,1,7,3,8,5]=>[2,4,6,7,8,3,1,5]=>[8,3,7,4,2,1,6,5]=>1010111
[4,2,7,1,8,3,6,5]=>[7,4,8,2,6,3,1,5]=>[6,2,4,3,8,1,7,5]=>0010111
[3,2,6,7,4,8,1,5]=>[8,3,2,7,1,6,4,5]=>[3,2,6,7,1,8,4,5]=>0100011
[3,1,6,7,4,8,5,2]=>[3,5,1,8,7,6,2,4]=>[6,7,1,3,2,8,5,4]=>0101011
[1,7,6,5,3,8,4,2]=>[1,4,8,5,6,7,2,3]=>[1,7,6,5,2,8,4,3]=>0011111
[2,7,6,5,3,8,1,4]=>[8,2,5,1,6,7,3,4]=>[2,7,6,5,1,8,3,4]=>0001111
[2,7,6,5,3,1,4,8]=>[3,2,5,1,6,7,4,8]=>[2,7,6,5,3,1,4,8]=>0101110
[4,7,6,5,2,1,3,8]=>[2,5,1,4,6,7,3,8]=>[4,7,6,5,2,1,3,8]=>1001110
[4,7,6,5,1,8,3,2]=>[5,3,6,4,7,8,1,2]=>[4,8,3,1,7,6,5,2]=>0101111
[1,7,6,5,2,8,3,4]=>[1,5,6,3,7,8,2,4]=>[1,8,3,7,6,5,2,4]=>0001111
[1,7,6,5,3,2,8,4]=>[1,3,5,6,7,8,2,4]=>[1,8,3,2,7,6,5,4]=>0101111
[4,7,6,5,1,2,8,3]=>[5,1,6,4,7,8,2,3]=>[4,8,1,2,7,6,5,3]=>0001111
[4,7,6,5,3,1,8,2]=>[3,5,6,4,7,8,2,1]=>[4,8,2,7,6,5,3,1]=>0101111
[5,2,6,3,4,1,7,8]=>[4,5,6,3,2,1,7,8]=>[6,3,5,2,4,1,7,8]=>0011100
[1,2,6,3,4,8,7,5]=>[1,2,6,3,7,4,8,5]=>[1,2,8,7,3,4,6,5]=>0000111
[6,1,4,2,8,3,5,7]=>[6,4,8,1,3,2,5,7]=>[8,1,4,3,6,2,5,7]=>0010101
[4,1,8,2,6,3,5,7]=>[4,8,6,1,3,2,5,7]=>[6,1,8,3,4,2,5,7]=>0010101
[1,2,6,7,4,8,5,3]=>[1,2,5,8,7,6,3,4]=>[1,2,6,7,3,8,5,4]=>0001011
[3,2,8,5,4,6,1,7]=>[6,3,2,5,8,4,1,7]=>[3,2,8,5,4,6,1,7]=>0101101
[4,7,6,3,5,8,1,2]=>[8,1,6,4,3,7,5,2]=>[4,7,6,3,5,8,1,2]=>0000111
[4,7,1,2,5,3,8,6]=>[7,1,5,4,2,8,3,6]=>[4,5,1,2,8,3,7,6]=>0001011
[3,7,6,5,1,4,8,2]=>[5,6,3,1,7,8,4,2]=>[3,8,1,4,7,6,5,2]=>0001111
[1,7,6,5,8,2,4,3]=>[1,8,4,2,6,7,5,3]=>[1,4,2,7,6,5,8,3]=>0010111
[3,1,6,8,4,2,5,7]=>[3,4,1,8,2,6,5,7]=>[6,8,4,1,3,2,5,7]=>0110001
[6,3,2,1,7,4,8,5]=>[2,3,6,7,8,1,4,5]=>[8,3,2,1,7,4,6,5]=>1100111
[4,2,1,7,3,5,8,6]=>[2,4,7,1,3,8,5,6]=>[8,2,1,4,3,5,7,6]=>1010011
[8,4,1,5,2,7,6,3]=>[4,8,5,6,2,7,3,1]=>[7,6,2,5,3,8,4,1]=>0011111
[8,2,5,1,3,7,6,4]=>[5,8,1,6,2,7,3,4]=>[7,6,1,8,2,3,5,4]=>0001111
[2,7,5,4,1,3,8,6]=>[4,2,1,5,7,8,3,6]=>[2,8,5,4,1,3,7,6]=>0011011
[7,5,4,3,2,1,8,6]=>[2,3,4,5,7,8,1,6]=>[8,5,4,3,2,1,7,6]=>1111011
[8,5,3,2,1,7,6,4]=>[2,3,5,8,6,7,4,1]=>[7,6,4,8,5,3,2,1]=>1101111
[1,7,6,2,4,8,3,5]=>[1,6,7,3,2,8,4,5]=>[1,8,3,7,6,2,4,5]=>0000111
[2,7,3,6,4,8,1,5]=>[8,2,7,6,1,3,4,5]=>[2,6,1,7,3,8,4,5]=>0000111
[6,2,7,5,3,8,1,4]=>[8,6,5,1,7,2,3,4]=>[7,5,1,6,2,8,3,4]=>0001111
[5,8,1,6,2,7,4,3]=>[8,6,4,7,5,1,2,3]=>[5,7,4,1,6,2,8,3]=>0010111
[5,8,3,2,7,1,6,4]=>[7,3,8,6,5,1,2,4]=>[5,6,3,1,8,2,7,4]=>0100111
[8,7,2,6,1,5,4,3]=>[6,7,4,5,1,2,8,3]=>[5,4,1,8,7,2,6,3]=>0011111
[1,8,5,7,4,3,6,2]=>[1,6,4,7,8,3,5,2]=>[1,8,4,3,7,5,6,2]=>0010111
[3,8,6,1,7,2,5,4]=>[6,8,3,5,1,7,2,4]=>[3,5,1,7,2,8,6,4]=>0001111
[3,7,2,6,8,4,1,5]=>[4,8,3,7,2,1,6,5]=>[3,7,2,6,8,4,1,5]=>0010011
[2,6,5,8,4,1,3,7]=>[4,2,1,8,6,5,3,7]=>[2,6,5,8,4,1,3,7]=>0010101
[8,2,4,7,1,3,6,5]=>[7,8,1,2,6,3,4,5]=>[6,1,8,2,3,4,7,5]=>0000111
[6,2,5,8,1,4,3,7]=>[8,6,4,1,2,5,3,7]=>[4,1,6,2,5,8,3,7]=>0010101
[4,3,6,8,2,1,5,7]=>[2,8,4,3,1,6,5,7]=>[4,3,6,8,2,1,5,7]=>1010001
[6,3,5,1,8,4,2,7]=>[5,4,8,6,2,1,3,7]=>[6,2,8,4,1,5,3,7]=>0011101
[6,4,2,5,8,3,1,7]=>[3,8,4,6,1,5,2,7]=>[6,4,1,5,8,3,2,7]=>0110101
[6,5,2,1,7,8,3,4]=>[2,5,6,1,8,3,7,4]=>[7,8,2,1,6,5,3,4]=>1001101
[4,7,2,5,8,6,3,1]=>[3,6,8,4,2,7,5,1]=>[4,7,2,5,8,6,3,1]=>0100111
[6,3,1,8,4,7,5,2]=>[3,6,5,7,8,2,1,4]=>[8,2,7,5,3,1,6,4]=>0101111
[6,5,3,8,7,4,1,2]=>[4,1,7,5,6,2,8,3]=>[6,5,1,2,8,7,4,3]=>0011111
[8,5,3,7,6,4,2,1]=>[2,4,6,5,7,8,3,1]=>[8,5,3,7,6,4,2,1]=>1011111
[5,2,8,1,7,3,6,4]=>[8,5,7,6,2,3,1,4]=>[6,2,7,3,5,1,8,4]=>0001111
[6,4,7,8,1,5,3,2]=>[8,3,5,6,1,4,7,2]=>[6,3,1,5,4,7,8,2]=>0101101
[8,3,7,6,1,5,4,2]=>[6,4,5,7,2,8,1,3]=>[8,2,5,4,1,7,6,3]=>0011111
[2,4,8,7,6,1,3,5]=>[6,2,1,4,3,7,8,5]=>[2,4,8,7,6,1,3,5]=>0000111
[3,5,8,7,2,6,1,4]=>[6,7,3,1,5,2,8,4]=>[3,5,8,7,1,6,2,4]=>0000111
[7,5,8,6,4,3,2,1]=>[2,3,4,6,8,7,1,5]=>[7,4,3,2,1,8,6,5]=>1110111
[4,8,7,6,2,5,3,1]=>[3,5,6,4,1,7,8,2]=>[4,8,7,6,1,5,3,2]=>0101111
[3,8,7,6,5,1,4,2]=>[5,4,3,1,6,7,8,2]=>[3,4,1,8,7,6,5,2]=>0011111
[2,8,7,6,5,4,1,3]=>[4,2,1,5,6,7,8,3]=>[2,8,7,6,5,4,1,3]=>0011111
[3,4,1,2,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>00100000
[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000
[4,5,6,1,2,3,7,8,9]=>[6,1,2,4,5,3,7,8,9]=>[4,5,6,1,2,3,7,8,9]=>00001000
[4,3,2,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000
[5,6,7,8,1,2,3,4,9]=>[8,1,2,3,5,6,7,4,9]=>[5,6,7,8,1,2,3,4,9]=>00000010
[5,6,3,4,1,2,7,8,9]=>[4,1,6,3,5,2,7,8,9]=>[5,6,3,4,1,2,7,8,9]=>00101000
[5,4,3,2,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000
[6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>11111000
[7,4,8,2,5,9,1,3,6]=>[9,8,1,7,2,3,4,5,6]=>[7,1,8,2,3,9,4,5,6]=>00000111
[7,8,5,6,3,4,1,2,9]=>[4,1,6,3,8,5,7,2,9]=>[7,8,5,6,3,4,1,2,9]=>00101010
[7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>11111100
[3,4,1,2,5,6,7,8,9,10]=>[4,1,3,2,5,6,7,8,9,10]=>[3,4,1,2,5,6,7,8,9,10]=>001000000
[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000
[4,5,6,1,2,3,7,8,9,10]=>[6,1,2,4,5,3,7,8,9,10]=>[4,5,6,1,2,3,7,8,9,10]=>000010000
[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>111000000
[5,6,7,8,1,2,3,4,9,10]=>[8,1,2,3,5,6,7,4,9,10]=>[5,6,7,8,1,2,3,4,9,10]=>000000100
[5,6,3,4,1,2,7,8,9,10]=>[4,1,6,3,5,2,7,8,9,10]=>[5,6,3,4,1,2,7,8,9,10]=>001010000
[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>111100000
[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>111110000
[7,8,9,4,5,6,1,2,3,10]=>[6,1,2,9,4,5,7,8,3,10]=>[7,8,9,4,5,6,1,2,3,10]=>000010010
[7,8,5,6,3,4,1,2,9,10]=>[4,1,6,3,8,5,7,2,9,10]=>[7,8,5,6,3,4,1,2,9,10]=>001010100
[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>111111000
[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>111111100
[3,6,5,1,2,4,8,7]=>[5,1,3,2,6,4,8,7]=>[3,6,5,1,2,4,8,7]=>0001101
[5,1,7,8,4,3,2,6]=>[5,3,4,8,1,2,7,6]=>[7,8,4,3,1,5,2,6]=>0111001
[5,1,2,4,6,3,8,7]=>[5,1,6,2,4,3,8,7]=>[6,1,2,4,5,3,8,7]=>0001101
[4,1,2,6,5,3,8,7]=>[4,1,5,2,6,3,8,7]=>[6,5,1,2,4,3,8,7]=>0011101
[4,1,5,7,8,3,2,6]=>[4,3,8,1,5,2,7,6]=>[5,7,8,3,1,4,2,6]=>0110001
[4,1,5,8,7,3,2,6]=>[4,3,7,1,5,2,8,6]=>[5,8,7,3,1,4,2,6]=>0110011
[4,7,1,8,3,6,2,5]=>[7,6,8,4,2,3,1,5]=>[4,8,2,6,3,7,1,5]=>0000111
[4,1,7,8,5,2,3,6]=>[4,5,2,1,8,3,7,6]=>[7,8,5,2,4,1,3,6]=>0011001
[2,1,5,8,7,3,4,6]=>[2,1,7,3,5,4,8,6]=>[2,1,5,8,7,3,4,6]=>1000011
[4,7,1,6,3,2,8,5]=>[7,3,6,4,8,1,2,5]=>[4,8,3,1,6,2,7,5]=>0100111
[6,1,2,3,7,5,8,4]=>[6,1,2,8,7,3,5,4]=>[7,1,2,3,8,5,6,4]=>0000111
[7,1,2,3,5,8,6,4]=>[7,1,2,6,3,8,5,4]=>[8,6,1,2,3,5,7,4]=>0000111
[6,8,1,4,3,7,2,5]=>[8,7,4,1,2,6,3,5]=>[4,1,6,7,2,8,3,5]=>0010011
[8,7,3,2,4,1,6,5]=>[4,3,7,2,6,1,8,5]=>[6,3,2,4,1,8,7,5]=>0110111
[2,1,7,3,4,8,6,5]=>[2,1,7,3,6,8,4,5]=>[2,1,8,6,3,4,7,5]=>1000111
[7,1,2,3,6,8,5,4]=>[7,1,2,5,8,3,6,4]=>[8,5,1,2,3,6,7,4]=>0001011
[8,1,2,3,7,5,6,4]=>[8,1,2,6,7,5,3,4]=>[7,5,6,1,2,3,8,4]=>0000111
[8,1,2,3,6,5,7,4]=>[8,1,2,7,6,3,5,4]=>[6,1,2,3,7,5,8,4]=>0000111
[7,1,8,5,4,3,2,6]=>[7,3,4,5,8,2,1,6]=>[8,5,4,3,2,7,1,6]=>0111011
[6,7,2,8,3,4,1,5]=>[4,7,8,3,1,6,2,5]=>[6,8,3,7,1,4,2,5]=>0010011
[3,8,7,1,4,2,6,5]=>[7,4,3,1,6,2,8,5]=>[3,4,1,6,2,8,7,5]=>0010111
[3,6,8,1,4,2,7,5]=>[8,4,3,1,7,6,2,5]=>[3,4,1,6,7,2,8,5]=>0010011
[3,5,7,8,2,4,1,6]=>[4,8,3,2,5,1,7,6]=>[3,5,7,8,2,4,1,6]=>0010001
[7,6,2,8,3,1,4,5]=>[3,8,6,2,4,7,1,5]=>[7,6,2,4,8,3,1,5]=>0100111
[8,6,2,7,3,1,4,5]=>[3,7,6,2,4,8,1,5]=>[8,6,2,4,7,3,1,5]=>0100111
[8,1,7,5,4,3,2,6]=>[8,3,4,5,7,2,1,6]=>[7,5,4,3,2,8,1,6]=>0111011
[5,8,3,7,1,4,2,6]=>[7,4,8,1,5,2,3,6]=>[5,8,1,4,2,7,3,6]=>0010011
[2,1,7,3,4,6,8,5]=>[2,1,7,3,8,4,6,5]=>[2,1,8,3,4,6,7,5]=>1000011
[6,7,3,2,4,1,8,5]=>[4,3,7,2,8,6,1,5]=>[6,8,3,2,4,1,7,5]=>0110011
[8,7,2,4,3,6,1,5]=>[6,7,4,2,1,3,8,5]=>[4,2,8,7,1,6,3,5]=>0010111
[7,1,2,3,5,6,8,4]=>[7,1,2,8,3,5,6,4]=>[8,1,2,3,5,6,7,4]=>0000011
[6,1,2,3,8,7,4,5]=>[6,1,2,7,4,3,8,5]=>[8,7,4,6,1,2,3,5]=>0000111
[5,1,2,3,8,7,6,4]=>[5,1,2,6,3,7,8,4]=>[8,7,6,1,2,3,5,4]=>0001111
[8,6,2,4,3,1,7,5]=>[3,4,6,1,8,7,5,2]=>[7,5,8,6,1,4,3,2]=>0110111
[7,6,3,2,4,8,1,5]=>[8,3,6,2,1,7,4,5]=>[7,6,3,2,8,1,4,5]=>0100111
[2,1,6,3,4,8,7,5]=>[2,1,6,3,7,4,8,5]=>[2,1,8,7,3,4,6,5]=>1000111
[7,6,2,4,3,1,8,5]=>[3,4,6,1,7,8,5,2]=>[8,5,7,6,1,4,3,2]=>0110111
[6,1,2,3,5,7,8,4]=>[6,1,2,8,3,5,7,4]=>[7,8,1,2,3,5,6,4]=>0000101
[1,4,8,2,7,3,5,6]=>[1,8,7,4,3,5,2,6]=>[1,4,7,3,5,8,2,6]=>0000011
[1,2,8,5,4,7,3,6]=>[1,2,7,5,8,3,4,6]=>[1,2,8,5,3,7,4,6]=>0001011
[1,3,6,8,4,7,5,2]=>[1,5,3,7,8,6,2,4]=>[1,3,6,8,2,7,5,4]=>0001011
[7,4,6,1,5,2,3,8]=>[6,5,2,7,1,4,3,8]=>[7,2,5,4,6,1,3,8]=>0001110
[6,8,1,4,7,2,3,5]=>[8,7,2,1,3,6,4,5]=>[6,7,2,8,1,3,4,5]=>0000011
[1,6,4,2,8,3,5,7]=>[1,4,6,8,2,3,5,7]=>[1,8,2,6,4,3,5,7]=>0010101
[1,6,3,8,5,4,2,7]=>[1,4,5,8,6,3,2,7]=>[1,6,3,8,5,4,2,7]=>0011101
[6,8,1,2,7,3,5,4]=>[8,1,7,5,3,6,2,4]=>[5,3,6,7,1,2,8,4]=>0001011
[1,6,2,3,8,5,4,7]=>[1,6,2,5,8,3,4,7]=>[1,8,5,2,3,6,4,7]=>0001101
[6,2,8,1,7,3,5,4]=>[8,6,7,5,3,2,1,4]=>[5,3,7,2,6,1,8,4]=>0001111
[2,5,1,8,7,6,3,4]=>[5,2,6,3,1,7,8,4]=>[2,8,7,6,3,5,1,4]=>0001111
[1,2,5,3,8,7,4,6]=>[1,2,5,7,3,4,8,6]=>[1,2,8,7,3,5,4,6]=>0001011
[2,4,8,7,6,5,1,3]=>[5,2,1,4,6,7,8,3]=>[2,4,8,7,6,5,1,3]=>0001111
[2,5,8,4,1,7,6,3]=>[4,2,8,6,5,7,3,1]=>[2,5,7,6,3,8,4,1]=>0010111
[4,2,8,7,6,5,3,1]=>[3,5,4,1,6,7,8,2]=>[4,1,8,7,6,5,3,2]=>0111111
[4,1,8,7,6,5,3,2]=>[4,3,5,1,6,7,8,2]=>[8,7,6,5,3,1,4,2]=>0111111
[5,8,3,7,6,1,4,2]=>[6,4,7,3,5,8,1,2]=>[5,8,3,4,1,7,6,2]=>0010111
[5,1,3,8,7,6,2,4]=>[5,6,1,2,3,7,8,4]=>[8,7,6,1,5,2,3,4]=>0001111
[1,5,3,8,7,6,2,4]=>[1,6,5,2,3,7,8,4]=>[1,5,2,8,7,6,3,4]=>0001111
[1,5,8,4,7,2,6,3]=>[1,7,6,8,5,2,4,3]=>[1,5,8,2,6,4,7,3]=>0000111
[5,1,8,4,7,2,6,3]=>[5,7,6,8,1,2,4,3]=>[8,1,6,2,7,4,5,3]=>0001111
[6,8,5,1,2,4,7,3]=>[5,1,8,3,7,6,4,2]=>[6,7,3,4,8,5,1,2]=>0001011
[5,6,3,1,2,4,8,7]=>[3,1,6,2,5,4,8,7]=>[5,6,3,1,2,4,8,7]=>0100101
[5,6,1,2,4,3,8,7]=>[6,1,4,2,5,3,8,7]=>[4,1,2,5,6,3,8,7]=>0010101
[4,5,8,1,7,2,3,6]=>[8,7,2,4,5,3,1,6]=>[4,5,7,2,3,8,1,6]=>0000011
[4,5,8,1,7,2,6,3]=>[8,7,6,4,5,2,1,3]=>[4,5,6,2,7,1,8,3]=>0000111
[1,3,2,5,8,7,4,6]=>[1,3,2,7,5,4,8,6]=>[1,3,2,5,8,7,4,6]=>0100011
[3,5,1,8,7,4,6,2]=>[5,6,3,7,1,4,8,2]=>[3,8,7,1,6,4,5,2]=>0001111
[3,5,1,8,7,2,6,4]=>[5,7,3,6,1,2,8,4]=>[3,6,1,8,7,2,5,4]=>0001111
[3,2,5,8,7,1,6,4]=>[7,3,2,6,5,1,8,4]=>[3,2,5,6,1,8,7,4]=>0100111
[3,1,4,8,7,6,2,5]=>[3,6,1,4,2,7,8,5]=>[4,8,7,6,1,3,2,5]=>0100111
[3,4,8,7,6,5,1,2]=>[5,1,3,4,6,7,8,2]=>[3,4,8,7,6,5,1,2]=>0001111
[3,2,5,8,7,4,6,1]=>[6,3,2,7,5,4,8,1]=>[3,2,5,8,7,4,6,1]=>0100111
[2,1,3,5,8,7,4,6]=>[2,1,3,7,5,4,8,6]=>[2,1,3,5,8,7,4,6]=>1000011
[6,8,1,3,7,5,2,4]=>[8,5,1,2,7,6,3,4]=>[6,7,5,1,8,2,3,4]=>0001011
[1,3,7,8,2,6,5,4]=>[1,8,3,5,6,2,7,4]=>[1,3,6,5,2,7,8,4]=>0001101
[2,7,8,1,3,6,5,4]=>[8,2,1,5,6,3,7,4]=>[2,6,5,1,3,7,8,4]=>0001101
[8,1,2,6,7,3,5,4]=>[8,1,7,5,3,2,6,4]=>[5,3,7,1,2,6,8,4]=>0001011
[8,1,2,6,7,5,3,4]=>[8,1,5,3,7,2,6,4]=>[7,5,3,6,8,1,2,4]=>0001011
[8,2,5,7,1,3,6,4]=>[7,8,1,6,2,3,5,4]=>[6,1,8,2,3,5,7,4]=>0000111
[2,6,8,3,7,1,5,4]=>[7,2,8,5,1,6,3,4]=>[2,5,1,6,8,3,7,4]=>0001011
[6,8,3,4,1,7,5,2]=>[4,5,7,2,8,6,1,3]=>[6,8,2,7,5,1,4,3]=>0011011
[6,8,3,7,4,1,5,2]=>[4,7,5,8,2,6,1,3]=>[6,8,2,5,1,7,4,3]=>0011011
[2,6,8,3,7,5,1,4]=>[5,2,7,3,8,6,1,4]=>[2,6,8,3,7,5,1,4]=>0001011
[2,8,1,6,7,5,3,4]=>[8,2,5,3,7,1,6,4]=>[2,7,5,3,6,8,1,4]=>0001011
[8,4,7,2,3,6,1,5]=>[6,7,2,8,1,3,4,5]=>[8,2,7,1,3,6,4,5]=>0000111
[8,5,7,4,2,6,1,3]=>[6,4,1,7,8,2,5,3]=>[8,4,1,7,5,6,2,3]=>0010111
[8,2,3,5,7,1,6,4]=>[7,8,2,6,3,1,5,4]=>[6,2,3,8,1,5,7,4]=>0000111
[8,2,4,7,3,6,1,5]=>[6,8,7,2,1,3,4,5]=>[7,2,8,1,6,3,4,5]=>0000111
[1,6,8,3,7,2,5,4]=>[1,7,8,5,2,6,3,4]=>[1,5,2,6,8,3,7,4]=>0001011
[5,8,7,1,3,6,2,4]=>[7,6,1,2,5,3,8,4]=>[5,6,1,8,7,2,3,4]=>0000111
[1,6,5,8,2,7,4,3]=>[1,8,4,7,6,5,2,3]=>[1,6,5,7,4,2,8,3]=>0010111
[8,5,6,3,1,7,4,2]=>[3,6,4,7,8,5,2,1]=>[8,5,7,4,2,6,3,1]=>0110111
[5,6,2,8,1,7,4,3]=>[8,6,4,7,5,2,1,3]=>[5,7,4,2,6,1,8,3]=>0010111
[5,8,7,3,6,1,2,4]=>[6,1,7,2,5,3,8,4]=>[5,8,7,1,2,6,3,4]=>0000111
[8,3,5,7,1,6,2,4]=>[7,6,8,2,3,1,5,4]=>[8,2,6,3,5,7,1,4]=>0000111
[1,6,8,3,7,5,2,4]=>[1,5,7,3,8,6,2,4]=>[1,6,8,3,7,5,2,4]=>0001011
[8,4,5,7,3,1,6,2]=>[3,7,6,8,4,2,5,1]=>[8,4,6,2,5,7,3,1]=>0100111
[8,3,4,7,2,6,1,5]=>[6,7,8,3,1,2,4,5]=>[8,3,7,1,6,2,4,5]=>0000111
[8,7,1,3,4,6,2,5]=>[7,6,1,3,2,4,8,5]=>[6,1,3,8,7,2,4,5]=>0000111
[8,3,7,2,4,6,1,5]=>[6,7,8,2,1,4,3,5]=>[8,2,7,1,4,6,3,5]=>0000111
[2,8,4,5,7,1,6,3]=>[7,2,6,8,4,1,5,3]=>[2,8,4,6,1,5,7,3]=>0000111
[8,7,4,5,2,6,1,3]=>[6,5,1,7,4,2,8,3]=>[8,7,4,5,1,6,2,3]=>0001111
[8,7,2,3,6,1,4,5]=>[6,7,2,1,4,3,8,5]=>[8,7,2,4,6,1,3,5]=>0000111
[1,3,2,8,5,4,7,6]=>[1,3,2,5,8,7,4,6]=>[1,3,2,7,5,4,8,6]=>0101011
[7,2,8,4,3,1,6,5]=>[3,4,8,7,6,1,2,5]=>[6,1,7,4,3,2,8,5]=>0110111
[5,3,4,1,8,2,7,6]=>[4,8,5,3,1,7,2,6]=>[5,3,7,1,4,2,8,6]=>0011011
[8,1,5,4,3,2,7,6]=>[8,3,4,5,1,7,2,6]=>[5,4,3,1,7,2,8,6]=>0111011
[4,5,3,2,8,7,1,6]=>[7,3,5,4,2,1,8,6]=>[4,5,3,2,8,7,1,6]=>0101011
[6,4,3,2,8,7,5,1]=>[5,3,4,7,6,1,8,2]=>[6,4,3,1,8,7,5,2]=>0111111
[4,1,6,3,2,7,8,5]=>[4,3,6,1,8,2,7,5]=>[7,8,3,1,4,2,6,5]=>0110101
[4,1,7,3,2,6,5,8]=>[4,3,7,1,6,2,5,8]=>[6,3,1,4,2,7,5,8]=>0110110
[6,7,3,2,5,4,1,8]=>[4,3,5,7,1,6,2,8]=>[6,7,3,1,5,4,2,8]=>0111010
[7,6,3,2,1,5,4,8]=>[2,3,6,5,1,7,4,8]=>[5,3,2,1,7,6,4,8]=>1101110
[4,7,5,6,2,3,8,1]=>[8,6,2,4,7,5,3,1]=>[4,7,5,6,2,3,8,1]=>0000111
[4,6,5,7,2,8,1,3]=>[8,7,1,4,6,5,2,3]=>[4,6,5,7,1,8,2,3]=>0000111
[5,6,4,7,2,8,3,1]=>[3,8,7,6,5,4,1,2]=>[5,6,4,7,1,8,3,2]=>0100111
[6,5,4,1,7,2,8,3]=>[4,5,6,7,8,3,1,2]=>[8,3,7,1,6,5,4,2]=>0011111
[2,1,4,6,8,7,3,5]=>[2,1,7,4,3,6,8,5]=>[2,1,4,6,8,7,3,5]=>1000011
[3,4,6,8,7,1,2,5]=>[7,1,3,4,2,6,8,5]=>[3,4,6,8,7,1,2,5]=>0000011
[4,3,1,6,8,7,2,5]=>[3,4,7,2,1,6,8,5]=>[6,8,7,2,4,3,1,5]=>0110011
[5,3,6,8,7,2,4,1]=>[4,7,5,2,3,6,8,1]=>[5,2,6,8,7,3,4,1]=>0011011
[7,3,5,8,6,2,1,4]=>[2,6,8,3,1,7,5,4]=>[7,3,5,8,6,2,1,4]=>1000111
[7,2,8,5,6,3,1,4]=>[3,6,7,2,8,5,1,4]=>[8,5,7,2,6,3,1,4]=>0100111
[6,2,8,5,1,7,3,4]=>[5,8,6,1,7,3,2,4]=>[7,1,6,3,8,5,2,4]=>0001111
[4,2,1,8,6,7,3,5]=>[2,4,7,1,3,8,6,5]=>[8,6,7,2,1,4,3,5]=>1010011
[1,3,2,8,6,7,4,5]=>[1,3,2,7,4,8,6,5]=>[1,3,2,8,6,7,4,5]=>0100011
[2,3,8,6,7,1,4,5]=>[7,2,3,1,4,8,6,5]=>[2,3,8,6,7,1,4,5]=>0000011
[5,2,8,7,6,4,1,3]=>[4,6,2,5,1,7,8,3]=>[5,2,8,7,6,4,1,3]=>0011111
[7,2,1,8,6,5,4,3]=>[2,7,4,5,6,8,1,3]=>[8,6,5,4,2,1,7,3]=>1011111
[7,3,6,1,8,5,4,2]=>[6,4,5,8,7,3,1,2]=>[7,3,8,5,4,1,6,2]=>0011111
[8,1,5,7,6,2,4,3]=>[8,6,4,2,1,7,5,3]=>[4,2,7,6,1,5,8,3]=>0010111
[4,5,7,6,8,3,1,2]=>[3,1,8,4,5,7,6,2]=>[4,5,7,6,8,3,1,2]=>0100011
[7,4,6,5,1,8,3,2]=>[5,3,6,8,7,1,2,4]=>[7,3,1,8,2,6,5,4]=>0101111
[7,5,6,4,3,1,8,2]=>[3,4,6,8,7,5,1,2]=>[7,5,8,1,6,4,3,2]=>0110111
[6,5,1,7,4,3,8,2]=>[5,6,4,8,7,2,1,3]=>[7,4,2,8,1,6,5,3]=>0011111
[4,6,7,5,3,8,1,2]=>[8,1,5,4,7,6,3,2]=>[4,6,7,5,3,8,1,2]=>0001011
[3,6,7,5,1,4,8,2]=>[5,7,3,2,8,6,4,1]=>[3,6,8,2,4,7,5,1]=>0001011
[8,1,6,7,5,4,2,3]=>[8,4,2,5,7,1,6,3]=>[7,5,4,2,6,8,1,3]=>0011011
[8,1,7,6,5,4,3,2]=>[8,3,4,5,6,7,1,2]=>[7,6,5,4,3,1,8,2]=>0111111
[8,6,4,1,5,2,7,3]=>[4,6,5,8,1,7,3,2]=>[7,1,5,3,8,6,4,2]=>0011111
[8,6,3,1,7,2,4,5]=>[3,6,8,2,4,7,1,5]=>[7,2,4,8,6,3,1,5]=>0100111
[5,3,1,7,2,4,6,8]=>[3,5,7,1,2,4,6,8]=>[7,1,5,3,2,4,6,8]=>0101010
[8,7,1,2,4,5,3,6]=>[7,1,5,2,4,3,8,6]=>[5,1,2,4,8,7,3,6]=>0001011
[8,5,1,2,6,7,3,4]=>[5,1,8,2,7,3,6,4]=>[7,1,2,6,8,5,3,4]=>0001011
[8,6,1,2,5,7,3,4]=>[6,1,8,2,3,7,5,4]=>[7,1,2,5,8,6,3,4]=>0000111
[8,6,1,2,7,4,3,5]=>[6,1,4,8,2,7,3,5]=>[7,4,1,2,8,6,3,5]=>0010111
[8,7,1,2,5,4,3,6]=>[7,1,4,5,2,3,8,6]=>[5,4,1,2,8,7,3,6]=>0011011
[5,1,4,2,7,3,6,8]=>[5,4,7,1,2,3,6,8]=>[7,1,4,2,5,3,6,8]=>0011010
[7,1,5,8,2,6,3,4]=>[7,8,6,3,1,2,5,4]=>[6,3,8,1,5,7,2,4]=>0000111
[5,7,8,1,2,4,6,3]=>[8,1,6,2,5,4,7,3]=>[5,6,1,2,4,7,8,3]=>0000101
[1,4,2,3,8,7,5,6]=>[1,4,2,3,7,5,8,6]=>[1,4,2,3,8,7,5,6]=>0010011
[6,1,2,4,8,7,5,3]=>[6,1,5,2,7,4,8,3]=>[8,7,5,1,2,4,6,3]=>0001111
[3,1,8,4,6,7,5,2]=>[3,5,1,7,8,2,6,4]=>[8,1,3,2,6,7,5,4]=>0101011
[7,1,2,4,6,8,5,3]=>[7,1,5,2,8,4,6,3]=>[8,5,1,2,4,6,7,3]=>0001011
[7,1,2,6,8,5,3,4]=>[7,1,5,3,8,2,6,4]=>[8,5,3,6,7,1,2,4]=>0001011
[6,1,2,7,8,5,3,4]=>[6,1,5,3,8,2,7,4]=>[7,8,5,3,6,1,2,4]=>0001101
[5,7,1,3,8,4,6,2]=>[7,6,1,8,5,4,3,2]=>[5,8,4,6,1,3,7,2]=>0000111
[5,7,1,8,4,2,6,3]=>[7,4,8,6,5,3,1,2]=>[5,6,3,8,4,1,7,2]=>0010111
[4,7,3,1,5,8,6,2]=>[3,7,6,4,2,8,5,1]=>[4,8,6,2,5,7,3,1]=>0100111
[8,3,7,1,2,6,4,5]=>[7,1,8,6,4,2,3,5]=>[6,4,8,1,2,7,3,5]=>0000111
[3,1,2,8,4,7,5,6]=>[3,1,2,8,7,5,4,6]=>[3,1,2,7,5,8,4,6]=>0100011
[1,4,2,3,8,5,7,6]=>[1,4,2,3,8,7,5,6]=>[1,4,2,3,7,5,8,6]=>0010011
[5,8,1,7,2,4,6,3]=>[8,7,6,2,5,4,1,3]=>[5,6,2,4,7,1,8,3]=>0000111
[3,1,8,6,4,7,5,2]=>[3,5,1,7,6,8,2,4]=>[8,6,1,3,2,7,5,4]=>0101111
[8,1,2,6,7,4,5,3]=>[8,1,5,7,4,2,6,3]=>[7,4,5,1,2,6,8,3]=>0001011
[6,1,2,8,7,3,5,4]=>[6,1,7,5,3,2,8,4]=>[5,3,8,7,1,2,6,4]=>0001111
[1,2,3,5,8,4,7,6]=>[1,2,3,8,5,7,4,6]=>[1,2,3,5,7,4,8,6]=>0000011
[1,2,3,5,8,6,4,7]=>[1,2,3,6,5,8,4,7]=>[1,2,3,5,8,6,4,7]=>0000101
[3,1,7,8,4,6,5,2]=>[3,5,1,6,8,2,7,4]=>[7,8,1,3,2,6,5,4]=>0101101
[3,1,8,7,6,4,5,2]=>[3,5,1,6,4,7,8,2]=>[8,7,6,4,5,1,3,2]=>0101111
[8,1,2,7,4,6,5,3]=>[8,1,5,6,7,3,2,4]=>[7,3,6,5,1,2,8,4]=>0001111
[1,2,3,5,8,7,4,6]=>[1,2,3,7,5,4,8,6]=>[1,2,3,5,8,7,4,6]=>0000011
[1,2,3,6,8,5,4,7]=>[1,2,3,5,8,6,4,7]=>[1,2,3,6,8,5,4,7]=>0001001
[7,8,5,3,6,1,2,4]=>[6,1,5,2,8,3,7,4]=>[7,8,5,1,2,6,3,4]=>0001101
[7,8,5,3,1,4,2,6]=>[3,5,4,2,8,1,7,6]=>[4,2,7,8,5,3,1,6]=>0111001
[7,8,5,3,1,6,4,2]=>[3,5,4,8,6,1,7,2]=>[6,4,1,7,8,5,3,2]=>0111101
[7,8,5,3,4,1,6,2]=>[4,6,5,3,8,1,7,2]=>[7,8,5,3,6,1,4,2]=>0011101
[7,8,5,3,1,2,6,4]=>[3,1,5,8,6,4,7,2]=>[6,4,7,8,5,3,1,2]=>0101101
[7,5,8,3,4,1,6,2]=>[4,6,8,3,7,1,5,2]=>[7,3,8,5,6,1,4,2]=>0010111
[7,5,6,3,4,1,8,2]=>[4,8,6,3,7,5,1,2]=>[7,5,6,3,8,1,4,2]=>0010111
[7,5,6,3,1,2,8,4]=>[3,1,6,8,7,5,2,4]=>[7,5,8,3,1,2,6,4]=>0100111
[7,5,3,6,1,2,8,4]=>[6,1,5,7,8,4,2,3]=>[8,4,7,5,1,2,6,3]=>0001111
[7,5,3,1,4,2,8,6]=>[3,5,4,2,7,8,1,6]=>[4,2,8,5,3,1,7,6]=>0111011
[7,5,3,1,6,2,8,4]=>[3,5,7,6,8,1,4,2]=>[8,1,6,4,7,5,3,2]=>0101111
[7,5,3,1,6,4,8,2]=>[3,5,7,8,6,1,2,4]=>[6,1,8,3,2,7,5,4]=>0101111
[7,5,3,6,1,4,8,2]=>[6,8,5,1,7,3,4,2]=>[7,5,1,8,3,4,6,2]=>0001111
[7,5,3,6,4,1,8,2]=>[4,6,8,5,7,1,2,3]=>[7,5,1,8,2,6,4,3]=>0011111
[7,5,3,6,4,8,1,2]=>[8,1,5,7,6,4,3,2]=>[6,4,7,5,3,8,1,2]=>0001111
[7,5,3,1,8,2,6,4]=>[3,5,7,8,6,4,1,2]=>[6,4,8,1,7,5,3,2]=>0101111
[7,5,3,1,8,2,4,6]=>[3,5,7,2,8,4,1,6]=>[8,2,4,7,5,3,1,6]=>0101011
[7,5,3,1,6,2,4,8]=>[3,5,7,2,6,1,4,8]=>[6,2,7,5,3,1,4,8]=>0101110
[7,5,3,1,6,4,2,8]=>[3,5,4,7,6,1,2,8]=>[6,4,1,7,5,3,2,8]=>0111110
[7,5,3,1,8,6,2,4]=>[3,5,7,2,6,8,1,4]=>[8,6,2,7,5,3,1,4]=>0101111
[7,5,3,8,6,1,4,2]=>[6,4,5,3,8,7,1,2]=>[7,5,3,4,1,8,6,2]=>0011111
[7,5,3,8,6,4,1,2]=>[4,1,6,5,8,7,3,2]=>[7,5,3,8,6,4,1,2]=>0011111
[7,5,8,3,6,1,4,2]=>[6,4,8,1,7,3,5,2]=>[7,1,4,3,8,5,6,2]=>0010111
[7,5,8,3,1,6,2,4]=>[3,8,6,1,7,2,5,4]=>[7,1,6,5,8,3,2,4]=>0100111
[7,5,3,8,4,1,2,6]=>[4,1,8,5,7,3,2,6]=>[7,5,3,8,4,1,2,6]=>0011011
[7,5,8,6,3,1,2,4]=>[3,1,6,2,8,7,4,5]=>[7,3,1,2,4,8,6,5]=>0100111
[7,5,3,4,1,6,2,8]=>[4,6,5,3,7,1,2,8]=>[7,5,3,6,1,4,2,8]=>0011110
[7,5,6,3,1,8,2,4]=>[3,6,8,1,7,5,2,4]=>[7,5,8,1,6,3,2,4]=>0100111
[7,5,6,3,1,8,4,2]=>[3,6,4,8,7,5,2,1]=>[7,5,8,4,2,6,3,1]=>0110111
[7,5,6,3,8,1,4,2]=>[8,4,6,1,7,5,3,2]=>[7,5,6,1,4,3,8,2]=>0010111
[7,5,6,3,8,4,1,2]=>[4,1,8,6,7,5,2,3]=>[7,5,6,1,2,8,4,3]=>0010111
[7,5,3,6,8,4,1,2]=>[4,1,8,5,7,2,6,3]=>[7,5,1,2,6,8,4,3]=>0011011
[7,5,3,6,1,8,4,2]=>[6,4,8,5,7,2,1,3]=>[7,5,2,8,4,1,6,3]=>0011111
[7,5,3,1,2,8,6,4]=>[3,1,5,7,6,8,4,2]=>[8,6,4,7,5,3,1,2]=>0101111
[7,5,3,4,1,8,6,2]=>[4,6,5,2,8,7,1,3]=>[7,5,2,8,6,1,4,3]=>0011111
[7,5,3,4,8,6,1,2]=>[6,1,5,2,8,7,4,3]=>[7,5,1,2,4,8,6,3]=>0001111
[7,5,3,1,2,6,8,4]=>[3,1,5,7,8,4,6,2]=>[8,4,6,7,5,3,1,2]=>0101011
[7,5,3,1,2,4,8,6]=>[3,1,5,2,7,8,4,6]=>[8,5,3,1,2,4,7,6]=>0101011
[3,6,2,5,4,1,8,7]=>[4,5,3,6,1,2,8,7]=>[3,6,1,5,4,2,8,7]=>0011101
[5,4,7,3,2,8,6,1]=>[6,3,8,5,4,7,1,2]=>[5,4,7,3,1,8,6,2]=>0101111
[5,4,8,3,2,7,6,1]=>[6,3,7,5,4,8,1,2]=>[5,4,8,3,1,7,6,2]=>0101111
[6,4,5,3,2,1,8,7]=>[2,3,5,6,4,1,8,7]=>[6,4,5,3,2,1,8,7]=>1101101
[4,5,8,3,2,7,6,1]=>[6,3,7,4,5,8,1,2]=>[4,5,8,3,1,7,6,2]=>0100111
[5,8,4,3,2,7,6,1]=>[6,3,4,7,5,8,1,2]=>[5,8,4,3,1,7,6,2]=>0110111
[5,3,2,8,4,7,6,1]=>[6,3,5,7,2,8,1,4]=>[8,3,2,5,1,7,6,4]=>0101111
[2,1,5,8,4,7,6,3]=>[2,1,6,7,5,8,3,4]=>[2,1,5,8,3,7,6,4]=>1000111
[5,3,2,7,4,8,6,1]=>[6,3,5,8,2,7,1,4]=>[7,3,2,5,1,8,6,4]=>0101111
[4,7,5,3,2,8,6,1]=>[6,3,5,4,8,7,1,2]=>[4,7,5,3,1,8,6,2]=>0101111
[4,6,8,3,7,5,2,1]=>[2,5,7,4,8,6,1,3]=>[4,6,8,2,1,7,5,3]=>1001011
[7,3,2,6,8,5,4,1]=>[4,3,5,8,7,2,6,1]=>[7,3,2,6,8,5,4,1]=>0111011
[2,1,8,6,7,5,4,3]=>[2,1,4,5,7,8,6,3]=>[2,1,8,6,7,5,4,3]=>1011011
[8,3,2,6,7,5,4,1]=>[4,3,5,7,8,2,6,1]=>[8,3,2,6,7,5,4,1]=>0111011
[8,6,4,3,7,5,2,1]=>[2,5,4,7,6,8,1,3]=>[8,6,4,2,1,7,5,3]=>1011111
[8,5,7,6,4,3,2,1]=>[2,3,4,6,7,8,1,5]=>[8,4,3,2,1,7,6,5]=>1110111
[8,4,7,3,6,5,2,1]=>[2,5,6,7,8,4,1,3]=>[8,4,7,2,1,6,5,3]=>1001111
[7,4,6,3,8,5,2,1]=>[2,5,8,6,7,1,4,3]=>[7,2,1,6,4,8,5,3]=>1001111
[3,7,2,6,8,5,4,1]=>[4,5,3,8,7,2,6,1]=>[3,7,2,6,8,5,4,1]=>0011011
[3,8,2,6,7,5,4,1]=>[4,5,3,7,8,2,6,1]=>[3,8,2,6,7,5,4,1]=>0011011
[3,7,2,8,6,5,4,1]=>[4,5,3,6,8,7,1,2]=>[3,7,1,8,6,5,4,2]=>0011111
[3,6,2,8,7,5,4,1]=>[4,5,3,7,6,2,8,1]=>[3,6,2,8,7,5,4,1]=>0011111
[6,4,8,3,7,5,2,1]=>[2,5,7,8,6,1,4,3]=>[6,2,1,8,4,7,5,3]=>1001111
[7,5,4,3,2,8,6,1]=>[6,3,4,5,8,7,1,2]=>[7,5,4,3,1,8,6,2]=>0111111
[7,3,2,5,4,8,6,1]=>[6,3,8,5,1,7,4,2]=>[5,3,1,7,4,8,6,2]=>0101111
[2,1,7,5,4,8,6,3]=>[2,1,6,5,8,7,3,4]=>[2,1,7,5,3,8,6,4]=>1001111
[7,3,2,8,6,5,4,1]=>[4,3,5,6,8,7,1,2]=>[7,3,1,8,6,5,4,2]=>0111111
[7,8,4,3,6,5,2,1]=>[2,5,4,6,8,1,7,3]=>[7,8,4,2,1,6,5,3]=>1011101
[6,8,5,7,4,3,2,1]=>[2,3,4,7,8,6,5,1]=>[6,8,5,7,4,3,2,1]=>1110011
[6,8,4,3,7,5,2,1]=>[2,5,4,7,8,6,1,3]=>[6,8,4,2,1,7,5,3]=>1011011
[6,7,4,3,8,5,2,1]=>[2,5,4,8,7,6,1,3]=>[6,7,4,2,1,8,5,3]=>1011011
[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>01000000
[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>00100000
[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>00010000
[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>00001000
[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>010000000
[2,4,3,1,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>01100000
[2,3,4,5,6,7,9,8,1]=>[8,2,3,4,5,6,7,9,1]=>[2,3,4,5,6,7,9,8,1]=>00000011
[4,6,8,3,5,7,1,2]=>[7,1,8,4,3,6,5,2]=>[4,6,8,3,5,7,1,2]=>0000011
[6,8,1,2,4,5,7,3]=>[8,1,7,2,4,6,5,3]=>[6,7,1,2,4,5,8,3]=>0000011
[4,2,5,7,3,6,1,8]=>[6,4,7,2,5,3,1,8]=>[5,7,2,4,3,6,1,8]=>0010110
[2,1,6,8,4,7,3,5]=>[2,1,7,8,3,6,4,5]=>[2,1,6,8,3,7,4,5]=>1000011
[1,2,5,8,3,6,7,4]=>[1,2,8,7,5,3,6,4]=>[1,2,5,7,3,6,8,4]=>0000011
[5,3,6,8,4,7,1,2]=>[7,1,5,8,3,6,4,2]=>[6,8,3,5,4,7,1,2]=>0001011
[5,4,8,3,2,1,6,7]=>[2,3,8,5,4,1,6,7]=>[5,4,8,3,2,1,6,7]=>1101001
[5,4,3,7,2,6,1,8]=>[6,7,4,5,3,2,1,8]=>[5,4,3,7,2,6,1,8]=>0011110
[4,1,7,3,2,5,8,6]=>[4,3,7,1,2,8,5,6]=>[8,3,1,4,2,5,7,6]=>0110011
[7,5,1,4,8,2,6,3]=>[5,7,8,2,6,3,4,1]=>[6,2,8,3,4,7,5,1]=>0001111
[5,8,4,7,6,3,1,2]=>[3,1,6,7,5,8,2,4]=>[5,8,3,1,2,7,6,4]=>0100111
[4,8,3,1,7,2,6,5]=>[3,8,7,4,6,1,2,5]=>[4,6,1,7,3,2,8,5]=>0100111
[1,8,4,3,5,2,7,6]=>[1,5,4,8,3,7,2,6]=>[1,7,4,3,5,2,8,6]=>0011011
[4,6,3,1,5,2,8,7]=>[3,6,5,4,2,1,8,7]=>[4,5,2,6,3,1,8,7]=>0101101
[6,4,8,7,5,3,1,2]=>[3,1,5,7,6,2,8,4]=>[6,3,1,2,8,7,5,4]=>0101111
[1,7,6,2,8,4,5,3]=>[1,6,5,7,2,8,4,3]=>[1,8,2,5,4,7,6,3]=>0001111
[1,5,3,2,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>[1,8,3,2,5,4,7,6]=>0101011
[6,3,2,1,8,5,4,7]=>[2,3,6,5,8,1,4,7]=>[8,5,3,2,1,6,4,7]=>1101101
[1,6,7,2,8,4,5,3]=>[1,7,5,8,4,6,2,3]=>[1,6,8,4,5,2,7,3]=>0001011
[2,4,1,7,8,6,3,5]=>[4,2,6,1,3,8,7,5]=>[2,7,8,6,1,4,3,5]=>0010101
[4,2,1,7,3,8,5,6]=>[2,4,7,1,8,5,3,6]=>[8,5,7,2,1,4,3,6]=>1010011
[6,2,8,4,3,1,5,7]=>[3,4,8,6,1,2,5,7]=>[6,1,8,4,3,2,5,7]=>0110101
[7,8,3,2,5,6,1,4]=>[6,3,8,1,2,5,7,4]=>[7,8,3,1,5,6,2,4]=>0100101
[8,7,6,1,2,4,5,3]=>[6,1,5,2,4,7,8,3]=>[5,1,2,4,8,7,6,3]=>0001111
[8,3,7,6,2,1,4,5]=>[2,6,7,3,4,8,1,5]=>[8,3,4,7,6,2,1,5]=>1000111
[3,2,8,7,5,1,4,6]=>[5,3,2,1,7,4,8,6]=>[3,2,8,7,5,1,4,6]=>0101011
[8,3,6,5,2,1,4,7]=>[2,5,6,3,8,1,4,7]=>[8,3,6,5,2,1,4,7]=>1001101
[8,2,4,1,6,5,3,7]=>[4,8,5,2,6,1,3,7]=>[6,5,2,8,1,4,3,7]=>0011101
[8,7,1,5,6,2,4,3]=>[7,6,4,2,1,5,8,3]=>[4,2,6,1,5,8,7,3]=>0010111
[6,8,3,7,5,4,1,2]=>[4,1,5,7,8,6,3,2]=>[6,8,3,7,5,4,1,2]=>0011011
[2,8,1,7,5,4,3,6]=>[8,2,4,5,7,3,1,6]=>[2,7,5,4,3,8,1,6]=>0011011
[2,1,8,6,5,4,3,7]=>[2,1,4,5,6,8,3,7]=>[2,1,8,6,5,4,3,7]=>1011101
[1,7,2,8,3,6,5,4]=>[1,7,8,5,6,3,2,4]=>[1,6,5,3,8,2,7,4]=>0001111
[1,7,8,6,5,2,4,3]=>[1,5,4,2,6,8,7,3]=>[1,4,2,7,8,6,5,3]=>0011101
[7,3,8,6,5,4,1,2]=>[4,1,5,6,8,7,2,3]=>[7,1,2,8,6,5,4,3]=>0011111
[8,1,7,3,2,6,5,4]=>[8,3,7,5,6,2,1,4]=>[6,5,3,2,7,1,8,4]=>0101111
[8,6,3,2,1,7,4,5]=>[2,3,6,8,1,7,4,5]=>[7,3,2,1,8,6,4,5]=>1100111
[8,6,5,4,1,7,2,3]=>[4,5,1,6,8,7,2,3]=>[7,1,8,6,5,4,2,3]=>0011111
[8,6,5,1,7,3,2,4]=>[5,3,6,2,8,7,1,4]=>[7,3,2,8,6,5,1,4]=>0101111
[8,6,1,7,4,3,2,5]=>[6,3,4,8,1,7,2,5]=>[7,4,3,1,8,6,2,5]=>0110111
[4,6,3,2,7,5,1,8]=>[5,3,7,4,6,1,2,8]=>[4,6,3,1,7,5,2,8]=>0101110
[5,7,4,1,8,2,6,3]=>[4,7,8,6,5,3,2,1]=>[5,6,3,8,2,7,4,1]=>0010111
[1,8,7,2,5,4,6,3]=>[1,7,6,5,2,4,8,3]=>[1,5,2,6,4,8,7,3]=>0001111
[1,3,5,6,8,4,2,7]=>[1,4,3,8,5,6,2,7]=>[1,3,5,6,8,4,2,7]=>0010001
[3,5,4,8,7,1,2,6]=>[7,1,3,5,4,2,8,6]=>[3,5,4,8,7,1,2,6]=>0001011
[1,6,2,4,8,7,5,3]=>[1,6,5,2,7,4,8,3]=>[1,8,7,5,2,4,6,3]=>0001111
[7,3,6,8,5,1,2,4]=>[5,1,8,3,7,2,6,4]=>[7,3,6,8,5,1,2,4]=>0001011
[3,6,5,2,8,1,4,7]=>[8,5,3,1,6,2,4,7]=>[3,6,5,1,8,2,4,7]=>0001101
[3,6,5,7,2,4,1,8]=>[4,7,3,2,6,5,1,8]=>[3,6,5,7,2,4,1,8]=>0010110
[4,2,6,3,8,1,5,7]=>[8,4,6,2,1,3,5,7]=>[6,2,4,1,8,3,5,7]=>0010101
[7,3,8,2,1,6,4,5]=>[2,8,7,6,4,1,3,5]=>[6,4,7,2,1,8,3,5]=>1000111
[8,7,6,4,3,1,5,2]=>[3,4,6,5,1,7,8,2]=>[5,1,8,7,6,4,3,2]=>0111111
[3,6,8,2,1,5,4,7]=>[2,8,3,5,1,6,4,7]=>[3,5,2,1,6,8,4,7]=>1001001
[2,4,8,1,6,5,3,7]=>[8,2,5,4,6,1,3,7]=>[2,4,6,5,1,8,3,7]=>0001101
[4,2,8,1,5,7,3,6]=>[8,4,7,2,1,3,5,6]=>[7,2,4,1,8,3,5,6]=>0010011
[8,5,7,6,1,4,2,3]=>[6,4,2,1,7,8,3,5]=>[4,2,8,1,3,7,6,5]=>0010111
[8,6,1,7,3,5,4,2]=>[6,4,5,8,1,7,2,3]=>[7,1,5,4,2,8,6,3]=>0011111
[2,8,5,4,7,1,3,6]=>[7,2,1,5,8,3,4,6]=>[2,8,5,1,3,7,4,6]=>0001011
[2,1,5,8,6,4,3,7]=>[2,1,4,6,5,8,3,7]=>[2,1,5,8,6,4,3,7]=>1010101
[1,2,5,7,8,4,3,6]=>[1,2,4,8,5,3,7,6]=>[1,2,5,7,8,4,3,6]=>0010001
[1,2,7,4,8,6,3,5]=>[1,2,6,8,4,7,3,5]=>[1,2,7,4,8,6,3,5]=>0000111
[1,2,7,8,3,6,5,4]=>[1,2,8,5,6,3,7,4]=>[1,2,6,5,3,7,8,4]=>0001101
[1,8,7,4,6,3,2,5]=>[1,3,6,7,2,4,8,5]=>[1,8,7,3,2,6,4,5]=>0100111
[8,6,2,4,7,3,5,1]=>[5,6,8,3,2,7,4,1]=>[7,3,8,6,2,4,5,1]=>0001111
[7,1,6,4,5,2,3,8]=>[7,5,2,6,4,1,3,8]=>[6,4,5,2,7,1,3,8]=>0001110
[7,1,4,6,5,8,3,2]=>[7,3,8,1,6,4,5,2]=>[6,3,1,4,8,5,7,2]=>0100111
[7,1,3,4,2,6,8,5]=>[7,4,1,3,8,2,6,5]=>[4,1,3,8,2,6,7,5]=>0010011
[7,1,5,4,6,2,8,3]=>[7,6,8,5,1,4,2,3]=>[5,1,8,4,6,2,7,3]=>0001111
[3,6,2,4,7,8,1,5]=>[8,6,3,2,1,4,7,5]=>[3,6,2,7,8,1,4,5]=>0000101
[6,5,7,8,2,4,1,3]=>[4,8,1,2,6,5,7,3]=>[6,5,7,8,1,4,2,3]=>0010101
[6,3,4,2,8,5,1,7]=>[5,4,8,1,6,2,3,7]=>[6,1,4,2,8,5,3,7]=>0011101
[3,4,7,2,5,8,1,6]=>[8,7,3,4,2,1,5,6]=>[3,4,7,2,8,1,5,6]=>0000011
[3,6,4,1,7,2,5,8]=>[4,6,3,7,1,2,5,8]=>[3,7,1,6,4,2,5,8]=>0010110
[2,8,3,1,5,6,4,7]=>[3,2,8,6,1,5,4,7]=>[2,6,3,1,5,8,4,7]=>0100101
[2,8,6,1,5,3,7,4]=>[6,2,5,8,4,7,3,1]=>[2,7,4,5,3,8,6,1]=>0001111
[7,6,5,1,3,8,2,4]=>[5,6,1,2,7,8,3,4]=>[8,1,7,6,5,2,3,4]=>0001111
[7,2,6,4,1,3,8,5]=>[4,6,2,7,8,1,3,5]=>[8,2,7,4,1,3,6,5]=>0010111
[6,7,5,2,1,3,8,4]=>[2,5,1,7,8,6,4,3]=>[6,8,4,7,5,2,1,3]=>1001011
[2,6,4,3,1,5,7,8]=>[3,2,4,6,1,5,7,8]=>[2,6,4,3,1,5,7,8]=>0110100
[7,3,8,4,1,5,2,6]=>[4,8,5,7,2,3,1,6]=>[7,2,5,3,8,4,1,6]=>0011011
[4,2,8,3,6,1,5,7]=>[6,4,8,2,1,3,5,7]=>[8,2,4,1,6,3,5,7]=>0010101
[6,8,5,7,2,1,3,4]=>[2,7,1,3,8,6,5,4]=>[6,8,5,7,2,1,3,4]=>1000011
[4,8,5,2,7,1,3,6]=>[7,5,1,4,8,3,2,6]=>[4,8,5,1,3,7,2,6]=>0001011
[6,8,5,3,1,4,2,7]=>[3,5,4,2,8,6,1,7]=>[4,2,6,8,5,3,1,7]=>0111001
[3,6,5,4,2,8,1,7]=>[8,4,3,5,6,2,1,7]=>[3,6,5,4,2,8,1,7]=>0011101
[1,6,4,8,2,5,3,7]=>[1,8,5,6,2,4,3,7]=>[1,6,2,5,4,8,3,7]=>0001101
[1,6,5,8,2,4,3,7]=>[1,8,4,2,6,5,3,7]=>[1,4,2,6,5,8,3,7]=>0010101
[1,6,2,4,3,7,8,5]=>[1,6,4,2,8,3,7,5]=>[1,4,2,7,8,3,6,5]=>0010101
[1,5,6,2,4,7,8,3]=>[1,6,8,2,5,4,7,3]=>[1,5,7,8,2,4,6,3]=>0000101
[1,5,8,2,4,7,3,6]=>[1,8,7,2,5,3,4,6]=>[1,5,7,2,8,3,4,6]=>0000011
[1,5,7,2,4,8,3,6]=>[1,7,8,2,5,3,4,6]=>[1,5,8,2,7,3,4,6]=>0000011
[1,6,5,7,2,4,3,8]=>[1,7,4,2,6,5,3,8]=>[1,4,2,6,5,7,3,8]=>0010110
[1,6,7,2,4,3,8,5]=>[1,7,4,2,8,6,3,5]=>[1,4,2,6,8,3,7,5]=>0010011
[1,5,8,2,4,6,7,3]=>[1,8,7,2,5,4,6,3]=>[1,5,7,2,4,6,8,3]=>0000011
[1,5,7,8,3,2,4,6]=>[1,3,8,2,5,4,7,6]=>[1,5,7,8,3,2,4,6]=>0100001
[1,5,8,3,2,4,6,7]=>[1,3,8,2,5,4,6,7]=>[1,5,8,3,2,4,6,7]=>0100001
[1,7,6,2,8,3,4,5]=>[1,6,7,2,4,8,3,5]=>[1,8,2,4,7,6,3,5]=>0000111
[1,6,2,4,3,8,7,5]=>[1,6,4,2,7,3,8,5]=>[1,4,2,8,7,3,6,5]=>0010111
[1,5,8,7,3,2,4,6]=>[1,3,7,2,5,4,8,6]=>[1,5,8,7,3,2,4,6]=>0100011
[1,4,2,3,5,8,7,6]=>[1,4,2,3,5,7,8,6]=>[1,4,2,3,5,8,7,6]=>0010011
[1,5,2,3,4,8,7,6]=>[1,5,2,3,4,7,8,6]=>[1,5,2,3,4,8,7,6]=>0001011
[1,7,6,5,2,8,4,3]=>[1,5,4,6,7,8,2,3]=>[1,8,4,2,7,6,5,3]=>0011111
[1,6,7,5,2,3,8,4]=>[1,5,2,7,8,6,4,3]=>[1,6,8,4,7,5,2,3]=>0001011
[1,5,8,3,2,4,7,6]=>[1,3,8,2,5,7,4,6]=>[1,5,7,3,2,4,8,6]=>0100011
[1,6,5,2,3,7,8,4]=>[1,5,2,6,8,4,7,3]=>[1,7,8,4,6,5,2,3]=>0001101
[1,6,8,4,2,3,7,5]=>[1,4,2,8,7,6,3,5]=>[1,6,7,4,2,3,8,5]=>0010011
[1,7,4,6,2,8,3,5]=>[1,6,8,7,3,4,2,5]=>[1,7,3,8,4,6,2,5]=>0000111
[1,6,4,2,3,7,8,5]=>[1,4,2,6,8,3,7,5]=>[1,7,8,4,2,3,6,5]=>0010101
[1,5,7,3,2,4,8,6]=>[1,3,7,2,5,8,4,6]=>[1,5,8,3,2,4,7,6]=>0100011
[1,7,4,2,8,5,3,6]=>[1,4,7,5,8,2,3,6]=>[1,8,5,2,7,4,3,6]=>0011011
[1,6,7,4,2,3,8,5]=>[1,4,2,7,8,6,3,5]=>[1,6,8,4,2,3,7,5]=>0010011
[1,6,4,2,3,8,5,7]=>[1,4,2,6,8,3,5,7]=>[1,8,4,2,3,6,5,7]=>0010101
[7,3,5,6,1,4,8,2]=>[6,8,7,1,3,5,4,2]=>[7,1,5,8,3,4,6,2]=>0000111
[3,7,5,6,1,4,8,2]=>[6,8,3,1,7,5,4,2]=>[3,7,5,8,1,4,6,2]=>0000111
[8,2,4,1,6,7,5,3]=>[4,8,5,2,7,1,6,3]=>[7,5,2,6,8,1,4,3]=>0011011
[3,6,1,4,2,8,5,7]=>[6,4,3,1,8,2,5,7]=>[3,4,1,8,2,6,5,7]=>0010101
[1,6,7,4,3,5,8,2]=>[1,8,4,7,3,6,5,2]=>[1,6,7,4,3,5,8,2]=>0010011
[6,7,1,4,3,5,8,2]=>[7,8,4,1,3,6,5,2]=>[4,1,6,8,3,5,7,2]=>0010011
[7,6,1,4,3,5,8,2]=>[6,7,4,2,3,8,5,1]=>[4,2,8,3,5,7,6,1]=>0010111
[4,7,1,6,3,5,8,2]=>[7,8,6,4,3,1,5,2]=>[4,6,3,8,1,5,7,2]=>0000111
[3,1,4,7,6,5,8,2]=>[3,8,1,4,6,7,5,2]=>[4,7,6,5,8,1,3,2]=>0100111
[6,1,7,4,3,5,8,2]=>[6,8,4,7,3,1,5,2]=>[7,4,3,8,1,5,6,2]=>0010111
[1,7,6,4,3,5,8,2]=>[1,8,4,6,3,7,5,2]=>[1,7,6,4,3,5,8,2]=>0010111
[8,1,6,4,2,7,5,3]=>[8,4,6,5,7,1,3,2]=>[7,5,1,6,4,3,8,2]=>0011111
[8,4,1,3,7,2,5,6]=>[4,8,2,7,1,5,3,6]=>[7,2,5,8,4,1,3,6]=>0010011
[4,7,1,3,8,2,5,6]=>[7,8,1,4,2,5,3,6]=>[4,8,1,5,7,2,3,6]=>0000011
[1,3,6,4,2,8,5,7]=>[1,4,3,6,8,2,5,7]=>[1,3,8,4,2,6,5,7]=>0010101
[4,7,3,1,2,8,5,6]=>[3,1,7,4,8,5,2,6]=>[4,8,5,7,3,1,2,6]=>0100011
[6,8,1,4,2,7,5,3]=>[8,4,5,1,7,6,2,3]=>[6,7,5,1,4,2,8,3]=>0011011
[4,8,1,3,7,2,5,6]=>[8,7,1,4,2,5,3,6]=>[4,7,1,5,8,2,3,6]=>0000011
[1,8,4,3,7,2,5,6]=>[1,7,4,8,2,5,3,6]=>[1,8,4,2,5,7,3,6]=>0010011
[3,7,8,4,6,2,1,5]=>[2,6,3,8,1,4,7,5]=>[3,7,8,2,1,6,4,5]=>1000101
[3,7,4,6,8,2,1,5]=>[2,8,3,7,1,4,6,5]=>[3,7,2,1,6,8,4,5]=>1000011
[2,4,3,7,8,6,1,5]=>[6,2,4,3,1,8,7,5]=>[2,4,3,7,8,6,1,5]=>0010101
[1,4,7,3,8,2,5,6]=>[1,8,7,4,2,5,3,6]=>[1,4,7,2,5,8,3,6]=>0000011
[5,7,6,8,3,2,1,4]=>[2,3,8,1,5,7,6,4]=>[5,7,6,8,3,2,1,4]=>1100011
[2,5,3,4,8,6,1,7]=>[6,2,5,3,4,8,1,7]=>[2,5,3,4,8,6,1,7]=>0001101
[6,1,4,3,8,2,5,7]=>[6,8,4,1,2,3,5,7]=>[4,1,8,2,6,3,5,7]=>0010101
[8,1,4,3,7,2,5,6]=>[8,7,4,1,2,5,3,6]=>[4,1,7,2,5,8,3,6]=>0010011
[8,2,3,4,7,6,1,5]=>[6,7,1,3,2,8,4,5]=>[8,1,3,7,6,2,4,5]=>0000111
[4,2,3,7,8,6,1,5]=>[6,4,2,3,1,8,7,5]=>[4,2,3,7,8,6,1,5]=>0010101
[5,2,3,4,8,6,1,7]=>[6,5,2,3,4,8,1,7]=>[5,2,3,4,8,6,1,7]=>0001101
[5,7,2,6,3,8,1,4]=>[8,7,6,1,5,2,3,4]=>[5,6,1,7,2,8,3,4]=>0000111
[5,7,2,6,8,4,1,3]=>[4,8,2,7,5,1,6,3]=>[5,7,2,6,8,4,1,3]=>0010011
[7,2,5,6,8,4,1,3]=>[4,8,2,7,1,5,6,3]=>[7,2,5,6,8,4,1,3]=>0010011
[4,2,3,8,5,6,1,7]=>[6,4,2,3,8,5,1,7]=>[4,2,3,8,5,6,1,7]=>0010101
[5,2,3,8,7,6,1,4]=>[6,5,2,1,3,7,8,4]=>[5,2,8,7,6,1,3,4]=>0001111
[8,2,3,7,5,6,1,4]=>[6,8,2,1,7,5,3,4]=>[7,5,8,2,6,1,3,4]=>0000111
[6,1,8,3,7,2,5,4]=>[6,7,8,5,2,1,3,4]=>[5,2,8,1,7,3,6,4]=>0001111
[3,7,4,8,5,2,1,6]=>[2,5,3,8,7,4,1,6]=>[3,7,4,8,5,2,1,6]=>1001011
[2,4,3,8,5,6,1,7]=>[6,2,4,3,8,5,1,7]=>[2,4,3,8,5,6,1,7]=>0010101
[6,5,8,7,3,2,1,4]=>[2,3,7,1,6,5,8,4]=>[6,5,8,7,3,2,1,4]=>1100111
[8,5,7,6,3,2,1,4]=>[2,3,6,1,7,8,4,5]=>[8,3,2,1,4,7,6,5]=>1100111
[2,5,3,8,7,6,1,4]=>[6,2,5,1,3,7,8,4]=>[2,5,1,8,7,6,3,4]=>0001111
[3,7,5,8,6,2,1,4]=>[2,6,3,1,8,7,4,5]=>[3,7,2,1,4,8,6,5]=>1000111
[6,8,7,5,3,2,1,4]=>[2,3,5,1,7,6,8,4]=>[6,8,7,5,3,2,1,4]=>1101011
[3,7,6,8,4,5,1,2]=>[5,1,3,8,4,7,6,2]=>[3,7,6,8,4,5,1,2]=>0001011
[1,5,4,7,6,8,2,3]=>[1,8,2,5,4,7,6,3]=>[1,5,4,7,6,8,2,3]=>0001011
[1,7,4,6,5,8,2,3]=>[1,8,2,7,6,4,5,3]=>[1,6,4,7,5,8,2,3]=>0000111
[3,7,4,6,5,8,1,2]=>[8,1,3,7,6,4,5,2]=>[3,6,4,7,5,8,1,2]=>0000111
[3,8,4,6,5,7,1,2]=>[7,1,3,8,6,4,5,2]=>[3,6,4,8,5,7,1,2]=>0000111
[3,6,4,7,5,8,1,2]=>[8,1,3,6,7,4,5,2]=>[3,7,4,6,5,8,1,2]=>0000111
[1,6,2,7,5,8,3,4]=>[1,6,8,3,7,2,5,4]=>[1,7,3,8,5,6,2,4]=>0000111
[1,8,4,6,5,7,2,3]=>[1,7,2,8,6,4,5,3]=>[1,6,4,8,5,7,2,3]=>0000111
[7,8,1,5,2,4,3,6]=>[8,5,4,2,1,3,7,6]=>[4,2,5,1,7,8,3,6]=>0011001
[1,8,2,6,5,7,3,4]=>[1,8,7,3,6,2,5,4]=>[1,6,3,7,5,8,2,4]=>0000111
[1,7,2,8,5,6,3,4]=>[1,7,6,3,8,5,2,4]=>[1,8,5,6,3,7,2,4]=>0000111
[1,7,2,6,5,8,3,4]=>[1,7,8,3,6,2,5,4]=>[1,6,3,8,5,7,2,4]=>0000111
[7,8,5,6,1,3,2,4]=>[6,3,1,2,8,5,7,4]=>[3,1,7,8,5,6,2,4]=>0100101
[5,8,6,7,1,3,2,4]=>[7,3,1,2,5,8,6,4]=>[3,1,5,8,6,7,2,4]=>0100011
[1,7,6,8,2,4,3,5]=>[1,8,4,2,3,7,6,5]=>[1,4,2,7,6,8,3,5]=>0010011
[7,8,1,6,2,4,3,5]=>[8,6,4,2,3,1,7,5]=>[4,2,6,3,7,8,1,5]=>0010101
[7,8,1,4,2,6,3,5]=>[8,4,6,1,3,2,7,5]=>[6,1,4,3,7,8,2,5]=>0010101
[7,8,2,1,4,3,6,5]=>[2,8,4,1,6,3,7,5]=>[4,2,1,6,3,7,8,5]=>1010101
[7,8,1,2,4,3,5,6]=>[8,1,4,2,3,5,7,6]=>[4,1,2,7,8,3,5,6]=>0010001
[4,3,6,5,8,7,1,2]=>[7,1,4,3,6,5,8,2]=>[4,3,6,5,8,7,1,2]=>0010111
[3,4,5,6,7,1,8,9,2]=>[7,9,3,4,5,6,1,8,2]=>[3,4,5,6,8,9,1,7,2]=>00000101
[3,4,5,6,7,8,1,9,2]=>[8,9,3,4,5,6,7,1,2]=>[3,4,5,6,7,9,1,8,2]=>00000011
[3,4,5,6,7,8,1,9,10,2]=>[8,10,3,4,5,6,7,1,9,2]=>[3,4,5,6,7,9,10,1,8,2]=>000000101
[3,4,5,6,7,8,9,1,10,2]=>[9,10,3,4,5,6,7,8,1,2]=>[3,4,5,6,7,8,10,1,9,2]=>000000011
[1,6,2,3,8,7,4,5]=>[1,6,2,7,4,3,8,5]=>[1,8,7,4,6,2,3,5]=>0000111
[1,4,7,6,2,5,8,3]=>[1,6,7,4,3,8,5,2]=>[1,4,8,3,5,7,6,2]=>0000111
[1,3,7,5,2,6,8,4]=>[1,5,3,7,8,4,6,2]=>[1,3,8,4,6,7,5,2]=>0001011
[1,2,6,4,3,7,8,5]=>[1,2,4,6,8,3,7,5]=>[1,2,7,8,4,3,6,5]=>0010101
[1,4,7,3,2,5,8,6]=>[1,3,7,4,2,8,5,6]=>[1,4,8,3,2,5,7,6]=>0100011
[1,4,3,2,5,8,6,7]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,8,6,7]=>0110001
[1,5,3,2,4,8,6,7]=>[1,3,5,2,4,8,6,7]=>[1,5,3,2,4,8,6,7]=>0101001
[1,7,5,3,2,8,6,4]=>[1,3,5,7,6,8,4,2]=>[1,8,6,4,7,5,3,2]=>0101111
[1,5,3,2,4,8,7,6]=>[1,3,5,2,4,7,8,6]=>[1,5,3,2,4,8,7,6]=>0101011
[7,6,5,4,3,1,8,2]=>[3,4,5,6,7,8,1,2]=>[8,1,7,6,5,4,3,2]=>0111111
[6,8,5,4,3,2,1,7]=>[2,3,4,5,8,6,1,7]=>[6,8,5,4,3,2,1,7]=>1111001
[8,7,6,5,4,3,1,9,2]=>[3,4,5,6,7,8,9,2,1]=>[9,2,8,7,6,5,4,3,1]=>01111111
[9,8,7,6,5,4,3,1,10,2]=>[3,4,5,6,7,8,9,10,1,2]=>[10,1,9,8,7,6,5,4,3,2]=>011111111
[7,6,1,4,3,8,5,2]=>[6,5,4,2,7,8,3,1]=>[4,2,8,5,3,7,6,1]=>0011111
[6,8,5,1,3,2,7,4]=>[5,3,1,8,7,6,4,2]=>[3,1,6,7,4,8,5,2]=>0101011
[7,6,5,1,3,8,4,2]=>[5,4,1,6,7,8,3,2]=>[8,4,1,3,7,6,5,2]=>0011111
[1,6,3,4,8,7,5,2]=>[1,5,7,2,6,4,8,3]=>[1,6,2,4,8,7,5,3]=>0001111
[6,8,5,4,1,2,7,3]=>[4,1,5,8,7,6,2,3]=>[6,7,1,2,8,5,4,3]=>0011011
[6,8,2,4,3,7,1,5]=>[7,8,4,2,1,6,3,5]=>[4,2,6,8,1,7,3,5]=>0010011
[1,8,3,4,7,2,6,5]=>[1,7,8,3,6,2,4,5]=>[1,6,3,8,2,4,7,5]=>0000111
[7,5,8,4,3,2,1,6]=>[2,3,4,8,7,1,5,6]=>[7,4,3,2,1,8,5,6]=>1110011
[5,1,8,6,7,4,3,2]=>[5,3,4,7,1,8,6,2]=>[8,6,7,4,3,1,5,2]=>0111011
[8,4,7,5,2,6,1,3]=>[6,5,1,7,8,4,2,3]=>[8,4,7,5,1,6,2,3]=>0001111
[6,4,5,8,1,2,7,3]=>[8,1,7,6,4,5,2,3]=>[6,4,5,7,1,2,8,3]=>0000111
[2,7,5,1,8,4,3,6]=>[5,2,4,7,8,1,3,6]=>[2,8,4,1,7,5,3,6]=>0011011
[2,8,6,7,4,3,5,1]=>[5,2,4,7,3,8,6,1]=>[2,8,6,7,4,3,5,1]=>0011011
[3,6,5,2,4,1,8,7]=>[4,5,3,2,6,1,8,7]=>[3,6,5,2,4,1,8,7]=>0011101
[6,1,4,5,3,2,8,7]=>[6,3,5,1,4,2,8,7]=>[5,3,1,4,6,2,8,7]=>0101101
[3,8,7,1,4,6,5,2]=>[7,5,3,1,6,4,8,2]=>[3,6,5,1,4,8,7,2]=>0001111
[4,3,7,6,8,2,5,1]=>[5,8,4,3,2,7,6,1]=>[4,3,7,6,8,2,5,1]=>0011011
[3,2,6,8,5,7,1,4]=>[7,3,2,1,8,6,5,4]=>[3,2,6,8,5,7,1,4]=>0100011
[6,3,7,2,4,8,5,1]=>[5,8,7,3,6,1,4,2]=>[6,3,7,1,4,8,5,2]=>0001111
[2,5,3,7,4,1,8,6]=>[4,2,7,5,1,8,3,6]=>[2,5,1,8,4,3,7,6]=>0011011
[3,6,4,7,5,1,8,2]=>[5,7,3,8,6,1,2,4]=>[3,6,1,8,2,7,5,4]=>0001111
[8,4,7,6,2,3,1,5]=>[3,6,2,7,4,8,1,5]=>[8,4,7,6,2,3,1,5]=>0100111
[4,2,8,7,3,5,6,1]=>[6,4,7,2,3,5,8,1]=>[8,7,2,4,3,5,6,1]=>0010111
[7,4,3,8,2,5,6,1]=>[6,8,4,7,2,5,3,1]=>[7,4,2,5,8,3,6,1]=>0010111
[2,5,8,7,3,6,1,4]=>[6,2,7,1,5,3,8,4]=>[2,5,8,7,1,6,3,4]=>0000111
[2,1,5,8,7,4,6,3]=>[2,1,6,7,5,4,8,3]=>[2,1,5,8,7,4,6,3]=>1000111
[7,4,3,2,8,5,6,1]=>[6,3,4,7,8,5,2,1]=>[8,5,7,4,3,2,6,1]=>0110111
[4,2,7,1,8,5,6,3]=>[7,4,6,2,8,5,1,3]=>[8,5,6,2,4,1,7,3]=>0010111
[4,1,7,2,8,5,6,3]=>[4,7,6,1,8,5,2,3]=>[8,5,6,1,7,2,4,3]=>0010111
[2,4,8,7,3,5,6,1]=>[6,2,7,4,3,5,8,1]=>[2,4,8,7,3,5,6,1]=>0000111
[3,4,7,2,8,5,6,1]=>[6,7,3,4,8,5,2,1]=>[3,4,8,5,7,2,6,1]=>0000111
[6,1,8,5,2,7,4,3]=>[6,5,4,8,7,1,3,2]=>[7,4,1,8,5,3,6,2]=>0011111
[2,1,7,4,5,8,6,3]=>[2,1,6,8,3,7,5,4]=>[2,1,7,3,5,8,6,4]=>1000111
[2,1,8,3,6,7,5,4]=>[2,1,8,5,7,3,6,4]=>[2,1,7,5,3,6,8,4]=>1001011
[8,2,1,6,4,7,5,3]=>[2,8,5,7,6,1,3,4]=>[6,2,1,7,5,3,8,4]=>1001111
[2,6,3,5,8,7,1,4]=>[7,2,6,1,3,5,8,4]=>[2,6,1,5,8,7,3,4]=>0000111
[7,6,2,1,5,8,4,3]=>[2,6,4,7,3,8,5,1]=>[8,4,3,5,7,6,2,1]=>1010111
[3,6,8,7,5,2,1,4]=>[2,5,3,1,7,6,8,4]=>[3,6,8,7,5,2,1,4]=>1001011
[7,4,8,6,5,2,3,1]=>[3,5,2,6,8,7,4,1]=>[7,4,8,6,5,2,3,1]=>0101111
[8,1,6,4,7,3,2,5]=>[8,3,7,6,2,1,4,5]=>[6,3,2,7,1,8,4,5]=>0100111
[7,6,4,1,2,3,8,5]=>[4,1,2,6,7,8,5,3]=>[8,5,7,6,4,1,2,3]=>0010111
[7,3,5,8,4,2,1,6]=>[2,4,8,7,1,3,5,6]=>[7,2,1,8,4,3,5,6]=>1010011
[3,2,5,8,4,1,7,6]=>[4,3,2,8,5,7,1,6]=>[3,2,5,7,4,1,8,6]=>0110011
[7,2,8,4,3,5,6,1]=>[6,7,4,8,3,5,2,1]=>[8,4,3,5,7,2,6,1]=>0010111
[8,7,3,4,1,5,6,2]=>[4,6,7,3,1,5,8,2]=>[8,7,3,5,6,1,4,2]=>0010111
[4,8,2,7,3,5,6,1]=>[6,8,7,4,3,5,2,1]=>[4,7,3,5,8,2,6,1]=>0000111
[3,1,8,7,2,5,6,4]=>[3,7,1,6,2,5,8,4]=>[6,1,3,2,5,8,7,4]=>0100111
[6,4,8,7,1,3,2,5]=>[7,3,1,6,2,4,8,5]=>[3,1,6,2,8,7,4,5]=>0100111
[2,8,4,6,7,3,1,5]=>[3,2,7,8,1,4,6,5]=>[2,8,3,1,6,7,4,5]=>0100011
[6,8,4,2,1,3,7,5]=>[2,4,1,8,7,6,3,5]=>[6,7,4,2,1,3,8,5]=>1010011
[6,8,5,2,7,4,3,1]=>[3,4,7,5,8,6,2,1]=>[6,8,5,2,7,4,3,1]=>0111011
[4,3,8,6,2,5,1,7]=>[5,6,4,3,2,8,1,7]=>[4,3,8,6,2,5,1,7]=>0011101
[8,3,6,1,4,5,2,7]=>[6,5,8,1,4,3,2,7]=>[8,1,4,5,3,6,2,7]=>0001101
[5,8,4,3,7,6,1,2]=>[6,1,4,7,5,8,2,3]=>[5,8,4,1,2,7,6,3]=>0010111
[7,1,5,3,4,8,2,6]=>[7,8,5,3,1,2,4,6]=>[5,3,8,1,7,2,4,6]=>0001011
[6,5,8,4,3,1,7,2]=>[3,4,8,7,6,5,1,2]=>[6,5,7,1,8,4,3,2]=>0110111
[4,6,5,2,8,1,7,3]=>[8,5,6,4,7,3,1,2]=>[4,7,3,6,5,1,8,2]=>0001111
[2,8,3,1,5,6,7,4]=>[3,2,8,7,1,5,6,4]=>[2,7,3,1,5,6,8,4]=>0100011
[8,2,3,1,5,6,7,4]=>[3,8,2,7,1,5,6,4]=>[7,2,3,1,5,6,8,4]=>0100011
[1,4,8,2,3,6,7,5]=>[1,8,2,4,7,3,6,5]=>[1,4,7,2,3,6,8,5]=>0000011
[3,1,2,7,8,6,4,5]=>[3,1,2,6,4,8,7,5]=>[3,1,2,7,8,6,4,5]=>0100101
[7,5,1,8,2,4,3,6]=>[5,7,4,1,8,3,2,6]=>[4,1,8,3,7,5,2,6]=>0011011
[5,4,8,2,3,6,7,1]=>[7,8,2,5,4,3,6,1]=>[5,4,8,2,3,6,7,1]=>0001011
[2,4,3,7,1,8,5,6]=>[7,2,4,3,8,5,1,6]=>[2,4,3,8,5,7,1,6]=>0010011
[2,7,1,4,3,8,5,6]=>[7,2,4,1,8,5,3,6]=>[2,4,1,8,5,7,3,6]=>0010011
[6,8,5,1,7,2,3,4]=>[5,8,1,3,7,6,2,4]=>[6,7,1,3,8,5,2,4]=>0001011
[7,3,6,5,8,2,1,4]=>[2,8,7,1,6,3,5,4]=>[6,2,1,7,5,8,3,4]=>1000111
[4,5,8,7,3,6,1,2]=>[6,1,7,4,5,3,8,2]=>[4,5,8,7,3,6,1,2]=>0000111
[3,5,2,8,6,1,7,4]=>[6,5,3,8,2,7,4,1]=>[3,7,2,5,4,8,6,1]=>0001111
[8,6,5,4,1,2,7,3]=>[4,1,5,6,8,7,3,2]=>[7,3,8,6,5,4,1,2]=>0011111
[2,6,1,8,3,7,5,4]=>[6,2,8,5,7,1,3,4]=>[2,7,5,1,8,3,6,4]=>0001111
[6,1,5,3,8,7,2,4]=>[6,7,5,2,1,3,8,4]=>[5,2,8,7,1,6,3,4]=>0001111
[2,8,6,3,7,1,5,4]=>[7,2,6,5,1,8,3,4]=>[2,5,1,8,6,3,7,4]=>0001111
[7,6,1,5,8,2,3,4]=>[6,7,1,3,2,8,5,4]=>[8,1,3,5,7,6,2,4]=>0000111
[3,6,8,5,1,2,7,4]=>[5,1,3,8,7,6,4,2]=>[3,6,7,4,8,5,1,2]=>0001011
[4,8,2,5,1,6,7,3]=>[5,8,7,4,2,1,6,3]=>[4,7,2,6,8,1,5,3]=>0001011
[4,2,1,8,5,6,7,3]=>[2,4,7,1,8,5,6,3]=>[8,5,6,7,2,1,4,3]=>1010011
[2,8,4,5,1,6,7,3]=>[5,2,7,8,4,1,6,3]=>[2,8,4,6,7,1,5,3]=>0001011
[5,4,8,3,7,6,1,2]=>[6,1,7,5,4,8,2,3]=>[5,4,8,1,2,7,6,3]=>0001111
[3,1,5,8,6,2,7,4]=>[3,6,1,8,5,7,4,2]=>[5,7,4,8,6,1,3,2]=>0100111
[6,3,4,8,5,1,7,2]=>[5,8,7,1,6,4,2,3]=>[6,1,4,7,2,8,5,3]=>0001111
[7,6,1,2,8,3,5,4]=>[6,1,7,5,2,8,3,4]=>[5,1,2,8,3,7,6,4]=>0001111
[6,5,4,8,1,2,7,3]=>[8,1,7,5,6,4,2,3]=>[6,5,4,7,1,2,8,3]=>0001111
[7,5,1,6,8,2,4,3]=>[5,7,4,1,8,2,6,3]=>[4,1,8,2,6,7,5,3]=>0011011
[6,5,4,1,8,2,7,3]=>[4,5,6,8,7,3,1,2]=>[7,3,8,1,6,5,4,2]=>0011111
[6,5,4,7,1,2,8,3]=>[7,1,8,5,6,4,2,3]=>[6,5,4,8,1,2,7,3]=>0001111
[6,5,3,1,8,4,2,7]=>[3,5,4,6,8,1,2,7]=>[8,4,1,6,5,3,2,7]=>0111101
[8,1,6,4,7,3,5,2]=>[8,5,7,6,3,1,4,2]=>[6,3,7,1,5,4,8,2]=>0001111
[6,5,3,7,1,4,8,2]=>[7,8,5,1,6,3,4,2]=>[6,5,1,8,3,4,7,2]=>0001111
[6,4,3,1,5,8,7,2]=>[3,4,6,7,1,5,8,2]=>[8,7,1,5,6,4,3,2]=>0110111
[7,4,1,5,3,8,2,6]=>[4,7,8,5,2,3,1,6]=>[5,2,8,3,7,4,1,6]=>0011011
[7,4,1,5,3,2,6,8]=>[4,3,7,5,2,1,6,8]=>[5,3,2,7,4,1,6,8]=>0111010
[8,1,7,2,5,4,3,6]=>[8,7,4,5,2,3,1,6]=>[5,4,2,7,3,8,1,6]=>0011011
[8,1,7,2,5,4,6,3]=>[8,7,6,5,2,4,1,3]=>[5,2,6,4,7,1,8,3]=>0001111
[7,6,1,2,5,4,8,3]=>[6,1,7,5,3,8,4,2]=>[5,3,8,4,7,6,1,2]=>0001111
[6,4,3,1,5,2,8,7]=>[3,4,6,5,1,2,8,7]=>[5,1,6,4,3,2,8,7]=>0111101
[8,1,5,4,3,6,7,2]=>[8,7,4,5,1,3,6,2]=>[5,4,1,7,3,6,8,2]=>0011011
[6,4,3,1,5,7,8,2]=>[3,4,6,8,1,5,7,2]=>[7,8,1,5,6,4,3,2]=>0110101
[6,7,4,5,1,8,2,3]=>[5,8,2,7,4,6,1,3]=>[6,7,4,8,2,5,1,3]=>0001011
[4,7,5,6,2,3,1,8]=>[3,6,2,4,7,5,1,8]=>[4,7,5,6,2,3,1,8]=>0100110
[4,7,5,6,1,8,2,3]=>[6,8,2,4,7,5,1,3]=>[4,7,5,8,2,6,1,3]=>0000111
[4,7,5,6,3,8,1,2]=>[8,1,6,4,7,5,3,2]=>[4,7,5,6,3,8,1,2]=>0000111
[3,7,5,8,4,6,1,2]=>[6,1,3,8,7,4,5,2]=>[3,7,4,8,5,6,1,2]=>0000111
[4,5,3,8,6,7,1,2]=>[7,1,5,4,3,8,6,2]=>[4,5,3,8,6,7,1,2]=>0001011
[4,8,3,6,5,7,1,2]=>[7,1,8,4,6,3,5,2]=>[4,6,3,8,5,7,1,2]=>0000111
[5,6,4,7,1,8,2,3]=>[7,8,2,6,5,4,1,3]=>[5,6,4,8,2,7,1,3]=>0000111
[5,6,1,7,3,8,2,4]=>[6,8,7,2,5,1,3,4]=>[5,7,2,8,1,6,3,4]=>0000111
[5,6,1,8,2,7,3,4]=>[6,8,7,3,5,1,2,4]=>[5,7,3,8,1,6,2,4]=>0000111
[4,8,1,6,5,7,2,3]=>[8,7,2,4,6,1,5,3]=>[4,6,2,7,5,8,1,3]=>0000111
[4,5,1,8,6,7,2,3]=>[5,7,2,4,1,8,6,3]=>[4,8,6,7,2,5,1,3]=>0001011
[7,8,4,5,1,6,2,3]=>[5,6,2,8,4,1,7,3]=>[7,8,4,6,2,5,1,3]=>0001101
[5,6,2,8,1,4,3,7]=>[8,6,4,1,5,2,3,7]=>[4,1,5,6,2,8,3,7]=>0010101
[5,6,3,4,1,8,2,7]=>[4,8,6,3,5,1,2,7]=>[5,6,3,8,1,4,2,7]=>0010101
[3,6,4,5,2,7,1,8]=>[7,5,3,6,4,2,1,8]=>[3,6,4,5,2,7,1,8]=>0001110
[3,6,4,5,1,8,2,7]=>[5,8,3,6,4,1,2,7]=>[3,6,4,8,1,5,2,7]=>0001101
[2,8,3,6,1,5,4,7]=>[6,2,8,5,1,3,4,7]=>[2,5,1,8,3,6,4,7]=>0001101
[1,5,3,8,6,7,2,4]=>[1,7,5,2,3,8,6,4]=>[1,5,2,8,6,7,3,4]=>0001011
[1,8,3,6,2,7,4,5]=>[1,6,8,7,4,3,2,5]=>[1,7,4,8,3,6,2,5]=>0000111
[1,7,3,6,4,8,2,5]=>[1,8,7,6,2,3,4,5]=>[1,6,2,7,3,8,4,5]=>0000111
[1,7,2,8,4,6,3,5]=>[1,7,6,8,3,4,2,5]=>[1,8,3,6,4,7,2,5]=>0000111
[2,7,5,6,3,4,1,8]=>[4,2,6,3,7,5,1,8]=>[2,7,5,6,3,4,1,8]=>0010110
[6,7,5,8,1,4,2,3]=>[8,4,2,1,7,6,5,3]=>[4,2,6,7,5,8,1,3]=>0010011
[5,8,6,7,2,3,1,4]=>[3,7,2,1,5,8,6,4]=>[5,8,6,7,2,3,1,4]=>0100011
[6,7,2,3,1,8,4,5]=>[3,7,2,8,4,6,1,5]=>[6,8,4,7,2,3,1,5]=>0100011
[3,4,1,7,5,8,2,6]=>[4,8,3,1,7,2,5,6]=>[3,7,1,4,2,8,5,6]=>0010011
[2,7,5,8,1,4,3,6]=>[8,2,4,1,7,3,5,6]=>[2,4,1,7,3,8,5,6]=>0010011
[2,3,1,7,5,8,4,6]=>[3,2,1,8,7,4,5,6]=>[2,3,1,7,4,8,5,6]=>0100011
[2,3,1,8,4,7,5,6]=>[3,2,1,8,7,5,4,6]=>[2,3,1,7,5,8,4,6]=>0100011
[2,8,1,4,3,7,5,6]=>[8,2,4,1,7,5,3,6]=>[2,4,1,7,5,8,3,6]=>0010011
[3,7,2,5,4,6,1,8]=>[6,7,3,5,2,4,1,8]=>[3,5,2,7,4,6,1,8]=>0001110
[4,5,1,8,2,7,3,6]=>[5,8,7,4,1,3,2,6]=>[4,7,1,8,3,5,2,6]=>0001011
[3,4,2,5,1,8,6,7]=>[5,4,3,2,1,8,6,7]=>[3,4,2,5,1,8,6,7]=>0011001
[3,8,2,5,1,6,4,7]=>[5,8,3,6,2,1,4,7]=>[3,6,2,8,1,5,4,7]=>0001101
[4,5,2,8,1,6,3,7]=>[8,5,6,4,2,1,3,7]=>[4,6,2,5,1,8,3,7]=>0001101
[8,6,7,1,4,2,5,3]=>[7,4,5,1,2,8,6,3]=>[5,1,4,2,8,6,7,3]=>0011011
[8,6,3,7,5,1,2,4]=>[5,1,7,3,6,8,2,4]=>[8,6,3,7,5,1,2,4]=>0001111
[7,6,1,8,3,5,2,4]=>[6,5,7,2,1,8,3,4]=>[8,2,5,1,7,6,3,4]=>0001111
[7,6,1,3,8,5,2,4]=>[6,5,2,1,7,8,3,4]=>[8,5,2,7,6,1,3,4]=>0001111
[7,6,8,2,4,5,1,3]=>[5,8,1,2,4,7,6,3]=>[7,6,8,1,4,5,2,3]=>0001011
[7,6,2,3,8,5,1,4]=>[5,8,1,2,6,7,3,4]=>[7,6,1,8,5,2,3,4]=>0001111
[8,7,1,5,2,6,3,4]=>[7,5,6,3,1,2,8,4]=>[6,3,5,1,8,7,2,4]=>0001111
[8,5,2,3,1,7,6,4]=>[3,5,2,8,6,7,4,1]=>[7,6,4,8,5,2,3,1]=>0101111
[8,6,2,7,3,1,5,4]=>[3,7,6,5,2,8,1,4]=>[5,2,8,6,3,1,7,4]=>0101111
[6,8,7,3,4,1,5,2]=>[4,5,7,3,1,6,8,2]=>[6,8,7,3,5,1,4,2]=>0011011
[8,7,2,5,1,6,3,4]=>[5,7,6,3,2,1,8,4]=>[6,3,8,7,2,5,1,4]=>0001111
[8,7,2,1,4,6,3,5]=>[2,7,6,1,3,4,8,5]=>[6,2,1,8,7,3,4,5]=>1000111
[8,4,2,1,7,6,3,5]=>[2,4,8,6,1,7,3,5]=>[7,6,2,1,8,4,3,5]=>1010111
[8,5,2,7,1,6,3,4]=>[7,5,8,2,6,1,3,4]=>[6,2,8,5,1,7,3,4]=>0001111
[8,5,7,2,1,4,3,6]=>[2,7,4,1,8,3,5,6]=>[4,2,1,8,3,7,5,6]=>1010011
[5,8,7,3,1,4,2,6]=>[3,7,4,2,5,1,8,6]=>[4,2,5,8,7,3,1,6]=>0110011
[8,5,2,7,1,3,6,4]=>[7,5,1,8,6,3,4,2]=>[6,1,3,8,5,4,7,2]=>0001111
[8,4,2,1,3,7,6,5]=>[2,4,1,8,6,7,3,5]=>[7,6,4,2,1,3,8,5]=>1010111
[8,7,4,1,2,3,6,5]=>[4,1,2,7,6,3,8,5]=>[6,4,1,2,3,8,7,5]=>0010111
[8,7,4,1,2,6,3,5]=>[4,1,7,6,2,3,8,5]=>[6,1,2,8,7,4,3,5]=>0010111
[8,4,3,1,2,7,6,5]=>[3,1,4,8,6,7,2,5]=>[7,6,4,3,1,2,8,5]=>0110111
[8,6,1,3,7,2,5,4]=>[6,8,2,5,1,7,3,4]=>[5,2,7,1,3,8,6,4]=>0001111
[8,5,1,3,2,7,6,4]=>[5,3,1,8,6,7,4,2]=>[3,1,7,6,4,8,5,2]=>0101111
[8,1,6,4,7,2,5,3]=>[8,7,5,6,2,1,4,3]=>[6,2,5,1,7,4,8,3]=>0001111
[5,2,8,6,4,1,3,7]=>[4,6,2,5,1,8,3,7]=>[5,2,8,6,4,1,3,7]=>0011101
[8,4,7,5,1,6,2,3]=>[5,7,1,6,8,2,3,4]=>[8,1,6,2,3,7,5,4]=>0001111
[8,4,7,5,1,2,3,6]=>[5,1,2,7,8,4,3,6]=>[8,4,7,5,1,2,3,6]=>0001011
[8,3,2,6,5,1,4,7]=>[5,3,6,2,8,1,4,7]=>[8,3,2,6,5,1,4,7]=>0101101
[4,8,6,3,5,1,2,7]=>[5,1,6,4,3,8,2,7]=>[4,8,6,3,5,1,2,7]=>0001101
[4,8,7,3,1,5,2,6]=>[3,7,5,4,2,1,8,6]=>[4,5,2,8,7,3,1,6]=>0101011
[8,4,7,2,1,5,3,6]=>[2,7,5,8,1,3,4,6]=>[8,2,1,5,3,7,4,6]=>1001011
[8,3,2,7,1,5,4,6]=>[7,3,8,5,1,4,2,6]=>[5,3,1,8,4,7,2,6]=>0101011
[8,7,3,1,2,4,6,5]=>[3,1,7,2,6,4,8,5]=>[6,3,1,2,4,8,7,5]=>0100111
[8,3,2,1,7,4,6,5]=>[2,3,8,7,6,4,1,5]=>[6,4,7,3,2,1,8,5]=>1100111
[8,4,7,2,1,5,6,3]=>[2,7,6,8,1,5,4,3]=>[8,2,1,5,6,4,7,3]=>1000111
[3,8,7,4,1,2,5,6]=>[4,1,3,7,2,5,8,6]=>[3,8,7,4,1,2,5,6]=>0010011
[8,7,2,1,6,3,4,5]=>[2,7,6,3,4,1,8,5]=>[6,3,4,8,7,2,1,5]=>1000111
[8,7,2,1,3,4,6,5]=>[2,7,1,3,6,4,8,5]=>[6,2,1,3,4,8,7,5]=>1000111
[3,6,5,4,1,2,8,7]=>[4,1,3,5,6,2,8,7]=>[3,6,5,4,1,2,8,7]=>0011101
[4,7,5,8,6,2,1,3]=>[2,6,1,4,8,7,3,5]=>[4,7,2,1,3,8,6,5]=>1000111
[2,5,7,8,6,3,4,1]=>[4,2,6,3,5,8,7,1]=>[2,5,7,8,6,3,4,1]=>0010101
[4,8,5,7,6,3,1,2]=>[3,1,6,4,7,8,2,5]=>[4,8,3,1,2,7,6,5]=>0100111
[4,6,3,2,1,5,8,7]=>[2,3,6,4,1,5,8,7]=>[4,6,3,2,1,5,8,7]=>1100101
[5,8,1,3,7,6,4,2]=>[8,4,1,6,5,7,3,2]=>[5,7,6,4,1,3,8,2]=>0010111
[3,7,4,2,8,1,5,6]=>[8,4,3,7,1,5,2,6]=>[3,7,4,1,5,8,2,6]=>0010011
[4,2,6,8,5,7,3,1]=>[3,7,4,1,8,6,5,2]=>[4,1,6,8,5,7,3,2]=>0110011
[2,1,5,8,7,6,3,4]=>[2,1,6,3,5,7,8,4]=>[2,1,5,8,7,6,3,4]=>1000111
[2,1,4,7,6,3,8,5]=>[2,1,6,4,7,8,5,3]=>[2,1,4,8,5,7,6,3]=>1000111
[6,4,7,8,5,3,2,1]=>[2,3,5,8,6,1,7,4]=>[6,3,2,1,7,8,5,4]=>1101101
[6,3,7,1,5,2,8,4]=>[7,5,6,8,1,3,2,4]=>[8,1,6,3,5,2,7,4]=>0001111
[8,4,6,1,3,2,5,7]=>[6,3,1,8,2,4,5,7]=>[3,1,8,2,6,4,5,7]=>0100101
[7,4,3,8,2,1,5,6]=>[2,8,4,7,1,5,3,6]=>[7,4,2,1,5,8,3,6]=>1010011
[2,4,8,5,7,1,3,6]=>[7,2,1,4,8,3,5,6]=>[2,4,8,1,3,7,5,6]=>0000011
[7,8,2,5,6,1,4,3]=>[6,8,4,1,2,5,7,3]=>[4,1,7,8,2,5,6,3]=>0010101
[2,4,3,8,7,5,6,1]=>[6,2,4,3,7,5,8,1]=>[2,4,3,8,7,5,6,1]=>0010111
[2,6,7,3,5,1,8,4]=>[5,2,7,8,3,6,1,4]=>[2,6,8,3,7,1,5,4]=>0001011
[8,5,7,1,6,3,2,4]=>[7,3,6,2,8,1,5,4]=>[8,3,2,6,5,7,1,4]=>0100111
[6,5,7,2,8,4,3,1]=>[3,4,8,7,6,5,2,1]=>[6,5,7,2,8,4,3,1]=>0110111
[3,4,8,6,5,2,1,7]=>[2,5,3,4,6,8,1,7]=>[3,4,8,6,5,2,1,7]=>1001101
[6,5,8,2,1,7,3,4]=>[2,8,7,3,6,5,1,4]=>[6,5,7,3,8,2,1,4]=>1000111
[2,1,6,5,8,4,7,3]=>[2,1,7,8,6,5,4,3]=>[2,1,6,5,8,4,7,3]=>1000111
[2,1,6,8,5,4,3,7]=>[2,1,4,5,8,6,3,7]=>[2,1,6,8,5,4,3,7]=>1011001
[6,2,8,4,3,5,1,7]=>[5,6,4,8,3,2,1,7]=>[8,4,3,6,2,5,1,7]=>0011101
[4,8,2,7,6,1,3,5]=>[6,7,2,4,3,8,1,5]=>[4,8,2,3,7,6,1,5]=>0000111
[7,4,8,6,3,2,5,1]=>[5,3,6,8,4,7,2,1]=>[7,4,8,6,3,2,5,1]=>0101111
[5,8,4,2,3,6,1,7]=>[6,4,2,8,5,3,1,7]=>[5,8,4,2,3,6,1,7]=>0010101
[5,8,2,4,3,1,6,7]=>[3,4,8,1,5,2,6,7]=>[5,8,1,4,3,2,6,7]=>0110001
[8,2,1,3,4,7,5,6]=>[2,8,1,3,7,5,4,6]=>[7,5,8,2,1,3,4,6]=>1000011
[1,2,7,3,5,4,8,6]=>[1,2,7,5,3,8,4,6]=>[1,2,5,3,8,4,7,6]=>0001011
[1,2,3,8,4,5,7,6]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,4,5,8,6]=>0000011
[1,7,2,3,5,4,8,6]=>[1,7,2,5,3,8,4,6]=>[1,5,2,3,8,4,7,6]=>0001011
[1,3,8,2,4,5,7,6]=>[1,8,3,2,4,7,5,6]=>[1,3,7,2,4,5,8,6]=>0000011
[1,2,3,8,4,6,7,5]=>[1,2,3,8,7,4,6,5]=>[1,2,3,7,4,6,8,5]=>0000011
[1,8,2,3,5,4,6,7]=>[1,8,2,5,3,4,6,7]=>[1,5,2,3,8,4,6,7]=>0001001
[1,6,7,8,2,3,5,4]=>[1,8,2,5,3,6,7,4]=>[1,5,2,3,6,7,8,4]=>0001001
[1,8,2,3,6,4,5,7]=>[1,8,2,6,4,3,5,7]=>[1,6,4,8,2,3,5,7]=>0000101
[1,2,8,3,5,4,6,7]=>[1,2,8,5,3,4,6,7]=>[1,2,5,3,8,4,6,7]=>0001001
[1,2,7,8,3,6,4,5]=>[1,2,8,6,4,3,7,5]=>[1,2,6,4,7,8,3,5]=>0000101
[1,3,2,8,4,6,7,5]=>[1,3,2,8,7,4,6,5]=>[1,3,2,7,4,6,8,5]=>0100011
[6,7,4,5,1,2,8,3]=>[5,1,8,7,4,6,2,3]=>[6,7,4,8,1,2,5,3]=>0001011
[7,4,6,5,1,2,3,8]=>[5,1,2,6,7,3,4,8]=>[7,1,2,3,6,5,4,8]=>0001110
[6,7,5,4,1,2,8,3]=>[4,1,5,7,8,6,2,3]=>[6,8,1,2,7,5,4,3]=>0011011
[5,8,6,4,1,7,2,3]=>[4,6,2,8,5,7,1,3]=>[5,7,2,8,6,4,1,3]=>0010111
[5,7,6,4,1,8,2,3]=>[4,6,2,7,5,8,1,3]=>[5,8,2,7,6,4,1,3]=>0010111
[6,5,7,4,1,2,8,3]=>[4,1,7,8,6,5,3,2]=>[6,5,8,3,7,4,1,2]=>0010111
[6,4,8,5,1,2,7,3]=>[5,1,8,7,6,2,3,4]=>[6,1,2,7,3,8,5,4]=>0001111
[6,5,8,4,1,2,7,3]=>[4,1,8,7,6,5,3,2]=>[6,5,7,3,8,4,1,2]=>0010111
[5,6,8,4,1,7,2,3]=>[4,8,1,7,5,6,2,3]=>[5,6,7,1,8,4,2,3]=>0010011
[4,6,8,5,7,1,2,3]=>[7,1,2,4,8,6,5,3]=>[4,6,8,5,7,1,2,3]=>0000011
[4,5,8,6,7,1,2,3]=>[7,1,2,4,5,8,6,3]=>[4,5,8,6,7,1,2,3]=>0000011
[5,3,8,1,6,7,2,4]=>[8,7,5,2,3,1,6,4]=>[5,2,7,3,6,8,1,4]=>0001011
[5,2,1,8,6,7,3,4]=>[2,5,7,3,1,8,6,4]=>[8,6,7,3,5,2,1,4]=>1001011
[5,2,1,7,6,8,3,4]=>[2,5,8,3,1,7,6,4]=>[7,6,8,3,5,2,1,4]=>1001011
[4,6,7,5,8,1,2,3]=>[8,1,2,4,7,6,5,3]=>[4,6,7,5,8,1,2,3]=>0000011
[4,8,6,5,7,1,2,3]=>[7,1,2,4,6,8,5,3]=>[4,8,6,5,7,1,2,3]=>0000111
[4,8,5,6,7,1,2,3]=>[7,1,2,4,8,5,6,3]=>[4,8,5,6,7,1,2,3]=>0000011
[4,7,5,6,8,1,2,3]=>[8,1,2,4,7,5,6,3]=>[4,7,5,6,8,1,2,3]=>0000011
[4,6,5,7,8,1,2,3]=>[8,1,2,4,6,5,7,3]=>[4,6,5,7,8,1,2,3]=>0000101
[5,7,4,6,1,8,2,3]=>[6,8,2,7,5,4,1,3]=>[5,7,4,8,2,6,1,3]=>0000111
[5,8,4,6,1,7,2,3]=>[6,7,2,8,5,4,1,3]=>[5,8,4,7,2,6,1,3]=>0000111
[5,7,4,8,1,6,2,3]=>[8,6,2,7,5,1,4,3]=>[5,7,2,6,4,8,1,3]=>0000111
[5,4,6,8,1,7,2,3]=>[8,7,2,5,4,6,1,3]=>[5,4,6,7,2,8,1,3]=>0001011
[4,5,6,8,7,1,2,3]=>[7,1,2,4,5,6,8,3]=>[4,5,6,8,7,1,2,3]=>0000011
[4,8,5,7,6,1,2,3]=>[6,1,2,4,7,8,3,5]=>[4,8,1,2,3,7,6,5]=>0000111
[4,8,6,7,5,1,2,3]=>[5,1,2,4,7,8,6,3]=>[4,8,6,7,5,1,2,3]=>0001011
[4,7,6,8,5,1,2,3]=>[5,1,2,4,8,7,6,3]=>[4,7,6,8,5,1,2,3]=>0001011
[4,6,7,8,5,1,2,3]=>[5,1,2,4,8,6,7,3]=>[4,6,7,8,5,1,2,3]=>0001001
[5,4,7,8,1,6,2,3]=>[8,6,2,5,4,1,7,3]=>[5,4,6,2,7,8,1,3]=>0001101
[5,3,7,1,8,6,2,4]=>[7,6,5,2,3,8,1,4]=>[5,2,8,6,3,7,1,4]=>0001111
[4,6,8,7,5,1,2,3]=>[5,1,2,4,7,6,8,3]=>[4,6,8,7,5,1,2,3]=>0001011
[4,8,7,6,5,1,2,3]=>[5,1,2,4,6,7,8,3]=>[4,8,7,6,5,1,2,3]=>0001111
[2,5,4,7,3,6,1,8]=>[6,2,7,5,4,3,1,8]=>[2,5,4,7,3,6,1,8]=>0001110
[2,4,6,3,7,5,1,8]=>[5,2,7,4,6,1,3,8]=>[2,4,6,1,7,5,3,8]=>0001110
[4,2,7,3,6,5,1,8]=>[5,4,6,2,7,1,3,8]=>[7,2,4,1,6,5,3,8]=>0011110
[4,2,6,3,1,5,8,7]=>[3,6,4,1,2,5,8,7]=>[4,1,6,3,2,5,8,7]=>0110101
[4,2,7,6,3,5,1,8]=>[5,4,6,2,3,7,1,8]=>[7,6,2,4,3,5,1,8]=>0011110
[2,6,3,7,5,4,1,8]=>[4,2,5,7,6,3,1,8]=>[2,6,3,7,5,4,1,8]=>0011110
[1,7,5,2,3,8,4,6]=>[1,5,2,7,8,3,4,6]=>[1,8,2,3,7,5,4,6]=>0001011
[2,3,1,8,6,5,4,7]=>[3,2,1,5,6,8,4,7]=>[2,3,1,8,6,5,4,7]=>0101101
[2,5,3,1,8,6,4,7]=>[3,2,5,6,1,8,4,7]=>[2,8,6,3,1,5,4,7]=>0101101
[8,3,2,6,4,1,5,7]=>[4,3,6,8,2,1,5,7]=>[8,3,2,6,4,1,5,7]=>0110101
[3,6,8,2,1,4,5,7]=>[2,8,3,1,4,6,5,7]=>[3,6,8,2,1,4,5,7]=>1000001
[1,5,2,8,3,4,7,6]=>[1,5,8,3,2,7,4,6]=>[1,7,3,5,2,4,8,6]=>0001011
[1,2,6,3,8,7,4,5]=>[1,2,6,7,4,3,8,5]=>[1,2,8,7,4,6,3,5]=>0000111
[1,2,3,8,6,4,7,5]=>[1,2,3,6,8,7,5,4]=>[1,2,3,7,5,8,6,4]=>0000111
[1,2,3,7,4,8,6,5]=>[1,2,3,7,6,8,4,5]=>[1,2,3,8,6,4,7,5]=>0000111
[1,2,7,6,3,8,4,5]=>[1,2,6,7,3,8,4,5]=>[1,2,8,3,7,6,4,5]=>0000111
[1,2,3,6,4,8,7,5]=>[1,2,3,6,7,4,8,5]=>[1,2,3,8,7,4,6,5]=>0000111
[1,2,3,7,6,4,8,5]=>[1,2,3,6,7,8,5,4]=>[1,2,3,8,5,7,6,4]=>0000111
[2,1,3,8,5,4,7,6]=>[2,1,3,5,8,7,4,6]=>[2,1,3,7,5,4,8,6]=>1001011
[7,1,8,4,2,3,5,6]=>[7,4,2,8,3,5,1,6]=>[8,4,2,3,5,7,1,6]=>0010011
[2,1,8,4,3,5,7,6]=>[2,1,4,8,3,7,5,6]=>[2,1,7,4,3,5,8,6]=>1010011
[3,5,8,2,4,1,6,7]=>[4,8,3,2,5,1,6,7]=>[3,5,8,2,4,1,6,7]=>0010001
[2,5,4,8,3,1,6,7]=>[3,2,8,5,4,1,6,7]=>[2,5,4,8,3,1,6,7]=>0101001
[4,2,1,8,3,5,7,6]=>[2,4,8,1,3,7,5,6]=>[7,2,1,4,3,5,8,6]=>1010011
[1,8,7,4,2,3,5,6]=>[1,4,2,7,3,5,8,6]=>[1,8,7,4,2,3,5,6]=>0010011
[1,2,7,3,6,4,8,5]=>[1,2,7,6,8,3,4,5]=>[1,2,8,3,6,4,7,5]=>0000111
[1,2,8,6,3,7,4,5]=>[1,2,6,8,3,7,4,5]=>[1,2,7,3,8,6,4,5]=>0000111
[1,2,3,8,4,7,6,5]=>[1,2,3,8,6,7,4,5]=>[1,2,3,7,6,4,8,5]=>0000111
[1,2,7,3,4,8,6,5]=>[1,2,7,3,6,8,4,5]=>[1,2,8,6,3,4,7,5]=>0000111
[1,2,6,3,8,4,7,5]=>[1,2,6,8,7,3,4,5]=>[1,2,7,3,8,4,6,5]=>0000111
[1,5,2,3,8,7,4,6]=>[1,5,2,7,3,4,8,6]=>[1,8,7,2,3,5,4,6]=>0001011
[8,3,2,1,7,4,5,6]=>[2,3,8,7,4,5,1,6]=>[7,4,5,8,3,2,1,6]=>1100011
[1,2,8,6,3,4,7,5]=>[1,2,6,3,8,7,5,4]=>[1,2,7,5,8,6,3,4]=>0000111
[1,2,7,3,8,4,6,5]=>[1,2,7,8,6,4,3,5]=>[1,2,6,4,8,3,7,5]=>0000111
[1,2,3,8,7,4,6,5]=>[1,2,3,7,6,4,8,5]=>[1,2,3,6,4,8,7,5]=>0000111
[1,2,3,8,7,6,4,5]=>[1,2,3,6,4,7,8,5]=>[1,2,3,8,7,6,4,5]=>0000111
[2,6,5,7,1,4,3,8]=>[7,2,4,1,6,5,3,8]=>[2,4,1,6,5,7,3,8]=>0010110
[3,8,5,7,2,6,4,1]=>[4,6,3,7,8,1,5,2]=>[3,8,1,7,5,6,4,2]=>0010111
[3,4,8,6,1,2,5,7]=>[6,1,3,4,2,8,5,7]=>[3,4,8,6,1,2,5,7]=>0000101
[2,4,3,8,1,6,5,7]=>[8,2,4,3,6,1,5,7]=>[2,4,3,6,1,8,5,7]=>0010101
[2,4,8,1,3,5,7,6]=>[8,2,1,4,3,7,5,6]=>[2,4,7,1,3,5,8,6]=>0000011
[3,5,7,6,2,4,8,1]=>[8,6,3,2,5,7,4,1]=>[3,5,7,6,2,4,8,1]=>0000111
[4,8,6,7,1,2,3,5]=>[7,1,2,4,3,8,6,5]=>[4,8,6,7,1,2,3,5]=>0000011
[3,2,8,5,6,1,7,4]=>[6,3,2,7,8,5,1,4]=>[3,2,8,5,7,1,6,4]=>0100111
[4,8,6,7,2,1,3,5]=>[2,7,1,4,3,8,6,5]=>[4,8,6,7,2,1,3,5]=>1000011
[4,8,6,7,3,5,2,1]=>[2,5,7,4,3,8,6,1]=>[4,8,6,7,3,5,2,1]=>1001011
[5,8,6,7,3,4,2,1]=>[2,4,7,3,5,8,6,1]=>[5,8,6,7,3,4,2,1]=>1010011
[5,8,6,7,2,1,4,3]=>[2,7,4,1,5,8,6,3]=>[4,2,1,5,8,6,7,3]=>1010011
[4,8,6,7,2,1,5,3]=>[2,7,5,4,1,8,6,3]=>[4,5,2,1,8,6,7,3]=>1001011
[4,3,1,7,5,2,8,6]=>[3,4,5,2,7,8,1,6]=>[8,5,2,4,3,1,7,6]=>0111011
[4,3,2,8,5,1,7,6]=>[5,3,4,2,8,7,1,6]=>[4,3,2,7,5,1,8,6]=>0111011
[4,3,8,5,1,6,7,2]=>[5,8,4,3,7,2,6,1]=>[4,3,7,2,6,8,5,1]=>0011011
[4,8,6,7,1,5,3,2]=>[7,3,5,4,1,8,6,2]=>[4,5,3,1,8,6,7,2]=>0101011
[5,8,6,7,1,4,3,2]=>[7,3,4,1,5,8,6,2]=>[4,3,1,5,8,6,7,2]=>0110011
[5,8,6,7,2,4,3,1]=>[3,4,7,1,5,8,6,2]=>[5,8,6,7,1,4,3,2]=>0110011
[4,2,3,8,5,1,6,7]=>[5,4,2,3,8,1,6,7]=>[4,2,3,8,5,1,6,7]=>0011001
[3,2,5,7,6,1,4,8]=>[6,3,2,1,5,7,4,8]=>[3,2,5,7,6,1,4,8]=>0100110
[4,8,6,7,1,3,2,5]=>[7,3,1,4,2,8,6,5]=>[3,1,4,8,6,7,2,5]=>0100011
[4,8,6,7,1,2,5,3]=>[7,1,5,4,2,8,6,3]=>[4,5,1,2,8,6,7,3]=>0001011
[4,3,8,5,2,6,7,1]=>[7,5,4,3,8,2,6,1]=>[4,3,8,5,2,6,7,1]=>0011011
[4,3,8,5,1,2,6,7]=>[5,1,4,3,8,2,6,7]=>[4,3,8,5,1,2,6,7]=>0011001
[4,2,6,7,5,1,3,8]=>[5,4,1,2,7,6,3,8]=>[4,1,6,7,5,2,3,8]=>0011010
[3,8,5,7,1,4,2,6]=>[7,4,3,1,8,2,5,6]=>[3,4,1,8,2,7,5,6]=>0010011
[3,8,4,7,1,5,2,6]=>[7,5,3,8,1,2,4,6]=>[3,8,1,5,2,7,4,6]=>0001011
[3,8,4,7,2,5,1,6]=>[5,7,3,8,2,1,4,6]=>[3,8,2,7,1,5,4,6]=>0001011
[4,8,6,7,3,2,5,1]=>[5,3,7,4,2,8,6,1]=>[4,8,6,7,3,2,5,1]=>0101011
[4,8,6,7,3,1,2,5]=>[3,1,7,4,2,8,6,5]=>[4,8,6,7,3,1,2,5]=>0100011
[3,4,1,7,5,6,2,8]=>[4,6,3,1,7,5,2,8]=>[3,7,5,6,1,4,2,8]=>0010110
[4,8,6,7,2,3,1,5]=>[3,7,2,4,1,8,6,5]=>[4,8,6,7,2,3,1,5]=>0100011
[5,8,6,7,3,2,4,1]=>[4,3,7,2,5,8,6,1]=>[5,8,6,7,3,2,4,1]=>0110011
[5,8,6,7,4,2,3,1]=>[3,4,2,7,5,8,6,1]=>[5,8,6,7,4,2,3,1]=>0110011
[5,8,6,7,4,1,3,2]=>[4,3,1,7,5,8,6,2]=>[3,1,5,8,6,7,4,2]=>0110011
[4,2,8,5,3,1,7,6]=>[3,5,4,1,8,7,2,6]=>[4,1,7,5,3,2,8,6]=>0111011
[4,8,6,7,3,2,1,5]=>[2,3,7,4,1,8,6,5]=>[4,8,6,7,3,2,1,5]=>1100011
[5,8,6,7,4,2,1,3]=>[2,4,1,7,5,8,6,3]=>[5,8,6,7,4,2,1,3]=>1010011
[3,8,7,6,1,4,2,5]=>[6,4,3,1,2,7,8,5]=>[3,4,1,8,7,6,2,5]=>0010111
[5,1,8,3,6,7,2,4]=>[5,7,8,2,1,3,6,4]=>[8,2,6,7,1,5,3,4]=>0001011
[1,4,7,8,5,6,2,3]=>[1,6,2,4,8,5,7,3]=>[1,4,7,8,5,6,2,3]=>0000101
[3,4,7,1,5,8,6,2]=>[7,6,3,4,1,8,5,2]=>[3,4,8,6,1,5,7,2]=>0000111
[3,6,1,4,7,8,5,2]=>[6,5,3,1,8,4,7,2]=>[3,7,8,5,1,4,6,2]=>0001101
[1,6,8,4,7,5,2,3]=>[1,5,2,7,8,6,3,4]=>[1,6,8,2,3,7,5,4]=>0001011
[6,8,1,3,5,7,2,4]=>[8,7,1,2,3,6,5,4]=>[6,7,1,5,8,2,3,4]=>0000011
[7,6,1,4,3,8,2,5]=>[6,7,4,2,1,8,3,5]=>[4,2,8,1,7,6,3,5]=>0010111
[4,1,3,7,5,8,2,6]=>[4,8,1,3,7,2,5,6]=>[7,1,3,4,2,8,5,6]=>0010011
[3,1,7,6,5,8,4,2]=>[3,4,1,8,6,7,5,2]=>[7,6,5,8,4,1,3,2]=>0110111
[8,4,2,6,7,5,3,1]=>[3,5,4,7,8,2,6,1]=>[8,4,2,6,7,5,3,1]=>0111011
[1,3,8,6,2,7,5,4]=>[1,6,3,5,8,7,4,2]=>[1,3,7,5,4,8,6,2]=>0001111
[6,1,3,2,7,8,4,5]=>[6,3,1,8,4,2,7,5]=>[3,1,7,8,4,6,2,5]=>0100101
[5,7,8,6,2,1,4,3]=>[2,6,4,1,5,8,7,3]=>[4,2,1,5,7,8,6,3]=>1010101
[3,7,2,4,5,1,6,8]=>[5,7,3,2,4,1,6,8]=>[3,7,2,4,5,1,6,8]=>0001010
[1,8,6,4,5,2,3,7]=>[1,5,2,6,4,8,3,7]=>[1,8,6,4,5,2,3,7]=>0001101
[2,8,4,6,5,1,3,7]=>[5,2,1,6,8,3,4,7]=>[2,8,1,3,6,5,4,7]=>0001101
[7,5,8,6,1,2,4,3]=>[6,1,4,2,8,7,3,5]=>[4,1,2,7,3,8,6,5]=>0010111
[6,4,1,2,7,5,8,3]=>[4,1,6,8,7,3,5,2]=>[7,3,8,5,6,4,1,2]=>0010111
[4,3,7,8,5,1,6,2]=>[5,8,4,3,6,2,7,1]=>[4,3,6,2,7,8,5,1]=>0011101
[5,4,8,2,7,6,1,3]=>[6,7,2,5,4,8,1,3]=>[5,4,8,2,7,6,1,3]=>0001111
[1,2,7,3,6,5,8,4]=>[1,2,7,8,6,3,5,4]=>[1,2,6,3,8,5,7,4]=>0000111
[2,8,7,6,3,4,1,5]=>[4,2,6,3,1,7,8,5]=>[2,8,7,6,3,4,1,5]=>0010111
[5,8,2,6,3,4,1,7]=>[4,8,6,3,5,2,1,7]=>[5,6,3,8,2,4,1,7]=>0010101
[8,2,7,5,4,3,6,1]=>[6,8,4,5,7,3,2,1]=>[7,5,4,3,8,2,6,1]=>0011111
[6,3,8,1,4,7,5,2]=>[8,5,7,1,6,2,4,3]=>[6,1,7,5,2,4,8,3]=>0001111
[3,8,4,5,6,1,2,7]=>[6,1,3,8,4,5,2,7]=>[3,8,4,5,6,1,2,7]=>0000101
[1,4,3,5,7,8,2,6]=>[1,8,4,3,5,2,7,6]=>[1,4,3,5,7,8,2,6]=>0010001
[3,6,7,2,4,8,1,5]=>[8,7,3,2,1,6,4,5]=>[3,6,7,2,8,1,4,5]=>0000011
[1,5,2,7,4,3,8,6]=>[1,5,4,7,2,8,3,6]=>[1,8,4,2,5,3,7,6]=>0011011
[1,8,6,5,4,3,2,7]=>[1,3,4,5,6,8,2,7]=>[1,8,6,5,4,3,2,7]=>0111101
[6,1,5,2,8,4,7,3]=>[6,5,7,8,1,2,4,3]=>[8,1,7,2,5,4,6,3]=>0001111
[4,6,1,8,5,7,2,3]=>[6,7,2,4,8,1,5,3]=>[4,8,2,7,5,6,1,3]=>0000111
[4,7,1,2,8,5,6,3]=>[7,1,6,4,8,5,2,3]=>[4,8,5,6,1,2,7,3]=>0000111
[1,7,3,5,8,6,2,4]=>[1,6,8,3,2,7,5,4]=>[1,7,3,5,8,6,2,4]=>0000111
[7,3,5,8,6,1,2,4]=>[6,1,8,3,2,7,5,4]=>[7,3,5,8,6,1,2,4]=>0000111
[3,6,8,1,5,7,2,4]=>[8,7,3,2,1,6,5,4]=>[3,6,7,2,5,8,1,4]=>0000011
[3,4,6,5,8,1,7,2]=>[8,7,3,4,6,5,1,2]=>[3,4,6,5,7,1,8,2]=>0000111
[1,7,6,8,2,3,5,4]=>[1,8,2,5,3,7,6,4]=>[1,5,2,3,7,6,8,4]=>0001011
[7,6,8,1,2,3,5,4]=>[8,1,2,5,3,7,6,4]=>[5,1,2,3,7,6,8,4]=>0001011
[4,7,5,8,3,1,6,2]=>[3,8,6,4,7,2,5,1]=>[4,7,2,6,5,8,3,1]=>0100111
[7,6,8,2,1,3,5,4]=>[2,8,1,5,3,7,6,4]=>[5,2,1,3,7,6,8,4]=>1001011
[1,2,7,6,8,3,5,4]=>[1,2,8,5,3,7,6,4]=>[1,2,5,3,7,6,8,4]=>0001011
[6,7,4,3,1,8,5,2]=>[3,4,7,5,8,6,1,2]=>[6,8,5,1,7,4,3,2]=>0111011
[2,7,4,1,6,8,5,3]=>[4,2,7,5,8,3,6,1]=>[2,8,5,3,6,7,4,1]=>0011011
[2,3,7,6,8,1,5,4]=>[8,2,3,5,1,7,6,4]=>[2,3,5,1,7,6,8,4]=>0001011
[7,4,2,6,8,5,1,3]=>[5,4,2,8,7,1,6,3]=>[7,4,2,6,8,5,1,3]=>0011011
[7,3,2,5,8,6,1,4]=>[6,3,8,2,1,7,5,4]=>[7,3,2,5,8,6,1,4]=>0100111
[3,1,7,6,8,2,5,4]=>[3,8,1,5,2,7,6,4]=>[5,1,3,2,7,6,8,4]=>0101011
[3,7,6,8,1,2,5,4]=>[8,1,3,5,2,7,6,4]=>[3,5,1,2,7,6,8,4]=>0001011
[1,7,4,2,6,8,5,3]=>[1,4,7,5,8,3,6,2]=>[1,8,5,3,6,7,4,2]=>0011011
[7,1,6,8,5,4,2,3]=>[7,4,2,5,8,1,6,3]=>[8,5,4,2,6,7,1,3]=>0011011
[1,7,6,8,3,2,5,4]=>[1,3,8,5,2,7,6,4]=>[1,5,3,2,7,6,8,4]=>0101011
[7,6,8,3,1,2,5,4]=>[3,1,8,5,2,7,6,4]=>[5,3,1,2,7,6,8,4]=>0101011
[7,1,5,8,6,3,2,4]=>[7,3,6,2,1,8,5,4]=>[8,6,3,2,5,7,1,4]=>0100111
[7,2,5,8,6,3,1,4]=>[3,6,8,1,2,7,5,4]=>[7,1,5,8,6,3,2,4]=>0100111
[3,6,7,1,8,5,4,2]=>[7,4,3,5,8,6,1,2]=>[3,6,8,5,4,1,7,2]=>0011011
[7,2,6,8,5,4,1,3]=>[4,5,1,8,7,2,6,3]=>[7,1,6,8,5,4,2,3]=>0011011
[7,6,8,2,3,1,5,4]=>[3,8,2,5,1,7,6,4]=>[5,2,3,1,7,6,8,4]=>0101011
[6,7,3,1,8,5,4,2]=>[3,7,4,5,8,6,2,1]=>[6,8,5,4,2,7,3,1]=>0111011
[6,7,1,8,5,4,3,2]=>[7,3,4,5,8,6,1,2]=>[6,8,5,4,3,1,7,2]=>0111011
[7,2,1,6,8,5,4,3]=>[2,7,4,5,8,1,6,3]=>[8,5,4,2,1,6,7,3]=>1011011
[5,6,4,8,1,2,7,3]=>[8,1,7,6,5,4,2,3]=>[5,6,4,7,1,2,8,3]=>0000111
[8,1,5,6,7,2,4,3]=>[8,7,4,2,1,5,6,3]=>[4,2,7,1,5,6,8,3]=>0010011
[6,4,5,1,8,2,7,3]=>[5,8,7,6,4,1,2,3]=>[6,4,7,1,8,2,5,3]=>0001111
[8,1,4,6,7,3,2,5]=>[8,3,7,1,2,4,6,5]=>[7,3,1,6,8,2,4,5]=>0100011
[4,2,6,7,3,1,8,5]=>[3,7,4,1,8,6,2,5]=>[4,1,6,8,3,2,7,5]=>0110011
[6,2,4,1,5,8,7,3]=>[4,6,7,2,1,5,8,3]=>[8,7,2,5,6,1,4,3]=>0010111
[8,1,4,5,3,7,2,6]=>[8,7,5,1,4,2,3,6]=>[5,1,4,7,2,8,3,6]=>0001011
[5,3,4,2,1,8,6,7]=>[2,4,5,3,1,8,6,7]=>[5,3,4,2,1,8,6,7]=>1011001
[4,3,5,2,7,1,6,8]=>[7,5,4,3,2,1,6,8]=>[4,3,5,2,7,1,6,8]=>0011010
[8,1,7,2,4,5,6,3]=>[8,7,6,2,4,5,1,3]=>[6,2,4,5,7,1,8,3]=>0000111
[7,6,1,2,4,5,8,3]=>[6,1,7,3,4,8,5,2]=>[8,3,4,5,7,6,1,2]=>0000111
[7,5,1,3,2,6,8,4]=>[5,3,1,7,8,4,6,2]=>[3,1,8,4,6,7,5,2]=>0101011
[8,1,6,3,2,5,7,4]=>[8,3,6,7,2,1,5,4]=>[7,3,2,6,1,5,8,4]=>0100111
[7,4,1,3,5,2,8,6]=>[4,7,2,5,3,8,1,6]=>[5,2,3,8,4,1,7,6]=>0011011
[7,3,1,4,5,6,2,8]=>[3,7,6,2,4,5,1,8]=>[6,2,4,5,7,3,1,8]=>0100110
[8,1,4,3,5,6,2,7]=>[8,6,4,1,3,5,2,7]=>[4,1,6,3,5,8,2,7]=>0010101
[6,2,3,1,5,7,8,4]=>[3,6,2,8,1,5,7,4]=>[7,8,2,3,1,5,6,4]=>0100101
[6,2,3,4,8,7,1,5]=>[7,6,2,3,1,4,8,5]=>[6,2,3,8,7,1,4,5]=>0000111
[7,8,3,4,6,2,1,5]=>[2,6,8,3,1,4,7,5]=>[7,8,3,6,2,1,4,5]=>1000101
[7,8,3,6,4,2,1,5]=>[2,4,6,8,3,1,7,5]=>[7,8,3,6,4,2,1,5]=>1010101
[6,2,3,8,7,5,1,4]=>[5,7,1,2,6,3,8,4]=>[6,1,8,7,5,2,3,4]=>0001111
[6,2,3,7,8,5,1,4]=>[5,8,1,2,6,3,7,4]=>[6,1,7,8,5,2,3,4]=>0001101
[5,2,6,3,8,1,7,4]=>[8,5,6,7,2,3,1,4]=>[7,2,6,3,5,1,8,4]=>0001111
[6,2,4,1,7,3,5,8]=>[4,6,7,2,3,1,5,8]=>[7,2,6,3,4,1,5,8]=>0010110
[5,8,2,3,6,1,7,4]=>[6,8,2,7,5,3,1,4]=>[5,7,2,3,8,1,6,4]=>0000111
[4,6,8,5,3,2,1,7]=>[2,3,5,4,8,6,1,7]=>[4,6,8,5,3,2,1,7]=>1101001
[5,6,8,4,3,7,1,2]=>[7,1,4,8,5,6,3,2]=>[5,6,8,4,3,7,1,2]=>0010011
[5,6,1,4,2,3,8,7]=>[6,4,2,1,5,3,8,7]=>[4,2,5,6,1,3,8,7]=>0010101
[4,7,5,6,3,2,1,8]=>[2,3,6,4,7,5,1,8]=>[4,7,5,6,3,2,1,8]=>1100110
[5,1,4,3,8,2,7,6]=>[5,8,4,1,3,7,2,6]=>[4,1,7,3,5,2,8,6]=>0011011
[5,6,2,4,1,8,7,3]=>[4,6,7,2,5,1,8,3]=>[5,8,7,2,6,1,4,3]=>0010111
[6,1,4,2,8,7,5,3]=>[6,4,5,1,7,2,8,3]=>[8,7,5,1,4,2,6,3]=>0011111
[6,1,4,2,7,8,5,3]=>[6,4,5,1,8,2,7,3]=>[7,8,5,1,4,2,6,3]=>0011101
[5,8,2,4,1,7,6,3]=>[4,8,6,2,5,7,1,3]=>[5,7,6,2,8,1,4,3]=>0010111
[5,2,7,4,1,6,8,3]=>[4,7,5,8,3,2,6,1]=>[8,3,5,2,6,7,4,1]=>0011011
[5,4,1,3,7,2,6,8]=>[4,5,2,7,3,1,6,8]=>[7,2,3,5,4,1,6,8]=>0011010
[5,8,6,4,3,7,1,2]=>[7,1,4,6,5,8,3,2]=>[5,8,6,4,3,7,1,2]=>0010111
[5,1,6,3,4,2,7,8]=>[5,4,6,3,1,2,7,8]=>[6,3,4,1,5,2,7,8]=>0011100
[5,4,8,7,3,2,1,6]=>[2,3,7,5,4,1,8,6]=>[5,4,8,7,3,2,1,6]=>1101011
[4,6,8,7,3,2,1,5]=>[2,3,7,4,1,6,8,5]=>[4,6,8,7,3,2,1,5]=>1100011
[4,6,7,8,3,2,1,5]=>[2,3,8,4,1,6,7,5]=>[4,6,7,8,3,2,1,5]=>1100001
[4,7,6,8,3,2,1,5]=>[2,3,8,4,1,7,6,5]=>[4,7,6,8,3,2,1,5]=>1100011
[5,8,1,3,4,2,6,7]=>[8,4,1,3,5,2,6,7]=>[4,1,3,5,8,2,6,7]=>0010001
[4,8,7,5,3,2,1,6]=>[2,3,5,4,7,1,8,6]=>[4,8,7,5,3,2,1,6]=>1101011
[4,7,8,6,3,2,1,5]=>[2,3,6,4,1,8,7,5]=>[4,7,8,6,3,2,1,5]=>1100101
[4,8,7,6,3,2,1,5]=>[2,3,6,4,1,7,8,5]=>[4,8,7,6,3,2,1,5]=>1100111
[4,8,2,3,6,7,5,1]=>[5,7,1,4,8,3,6,2]=>[4,8,1,3,6,7,5,2]=>0001011
[4,3,8,1,6,2,5,7]=>[8,6,4,3,2,1,5,7]=>[4,3,6,2,8,1,5,7]=>0010101
[4,3,8,7,2,5,1,6]=>[5,7,4,3,2,1,8,6]=>[4,3,8,7,2,5,1,6]=>0011011
[5,8,4,3,7,1,6,2]=>[7,6,4,8,5,1,3,2]=>[5,8,4,1,6,3,7,2]=>0010111
[5,8,1,4,7,2,6,3]=>[8,7,6,1,5,2,4,3]=>[5,6,1,7,2,4,8,3]=>0000111
[5,8,1,7,4,2,3,6]=>[8,4,2,7,5,3,1,6]=>[5,7,4,2,3,8,1,6]=>0010011
[4,3,8,2,7,5,6,1]=>[6,8,4,3,7,5,2,1]=>[4,3,7,5,8,2,6,1]=>0010111
[1,4,8,3,7,5,6,2]=>[1,6,8,4,7,5,3,2]=>[1,4,7,5,8,3,6,2]=>0000111
[3,4,8,1,6,2,5,7]=>[8,6,3,4,2,1,5,7]=>[3,4,6,2,8,1,5,7]=>0000101
[3,4,8,7,2,5,1,6]=>[5,7,3,4,2,1,8,6]=>[3,4,8,7,2,5,1,6]=>0001011
[3,4,8,2,7,5,6,1]=>[6,8,3,4,7,5,2,1]=>[3,4,7,5,8,2,6,1]=>0000111
[1,2,4,8,3,6,5,7]=>[1,2,8,4,6,3,5,7]=>[1,2,4,6,3,8,5,7]=>0000101
[1,2,4,3,8,6,5,7]=>[1,2,4,3,6,8,5,7]=>[1,2,4,3,8,6,5,7]=>0010101
[3,4,2,1,8,6,5,7]=>[2,4,3,1,6,8,5,7]=>[3,4,2,1,8,6,5,7]=>1010101
[3,6,7,8,4,1,2,5]=>[4,1,3,8,2,6,7,5]=>[3,6,7,8,4,1,2,5]=>0010001
[4,1,7,8,5,3,2,6]=>[4,3,5,1,8,2,7,6]=>[7,8,5,3,1,4,2,6]=>0111001
[4,2,3,1,8,6,5,7]=>[3,4,2,1,6,8,5,7]=>[4,2,3,1,8,6,5,7]=>0110101
[3,7,8,6,2,4,1,5]=>[4,6,3,2,1,8,7,5]=>[3,7,8,6,2,4,1,5]=>0010101
[4,2,3,8,1,6,5,7]=>[8,4,2,3,6,1,5,7]=>[4,2,3,6,1,8,5,7]=>0010101
[1,4,7,8,5,3,2,6]=>[1,3,5,4,8,2,7,6]=>[1,4,7,8,5,3,2,6]=>0101001
[2,6,8,4,7,3,1,5]=>[3,2,7,8,1,6,4,5]=>[2,6,8,3,1,7,4,5]=>0100011
[2,4,8,6,3,1,5,7]=>[3,2,6,4,1,8,5,7]=>[2,4,8,6,3,1,5,7]=>0100101
[7,3,6,8,4,2,1,5]=>[2,4,8,7,3,1,6,5]=>[7,3,6,8,4,2,1,5]=>1010011
[7,6,2,8,3,5,4,1]=>[4,5,6,7,3,8,1,2]=>[8,3,7,6,1,5,4,2]=>0011111
[1,7,3,8,4,6,5,2]=>[1,5,6,7,8,2,4,3]=>[1,8,2,7,4,6,5,3]=>0001111
[2,4,8,3,6,1,5,7]=>[6,2,8,4,1,3,5,7]=>[2,4,8,1,6,3,5,7]=>0000101
[7,4,1,8,5,2,6,3]=>[4,7,5,8,6,1,2,3]=>[6,1,8,5,2,7,4,3]=>0011111
[2,4,3,1,8,6,5,7]=>[3,2,4,1,6,8,5,7]=>[2,4,3,1,8,6,5,7]=>0110101
[1,3,2,4,8,6,5,7]=>[1,3,2,4,6,8,5,7]=>[1,3,2,4,8,6,5,7]=>0100101
[3,1,2,4,8,6,5,7]=>[3,1,2,4,6,8,5,7]=>[3,1,2,4,8,6,5,7]=>0100101
[3,1,4,2,8,6,5,7]=>[3,4,1,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]=>0110101
[3,1,4,8,2,6,5,7]=>[3,8,1,4,6,2,5,7]=>[4,6,1,3,2,8,5,7]=>0100101
[6,7,2,8,3,5,4,1]=>[4,5,7,8,1,6,3,2]=>[6,8,1,7,3,5,4,2]=>0011011
[2,3,1,4,8,6,5,7]=>[3,2,1,4,6,8,5,7]=>[2,3,1,4,8,6,5,7]=>0100101
[1,2,3,4,8,6,5,7]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,8,6,5,7]=>0000101
[4,8,3,6,2,1,5,7]=>[2,6,8,4,1,3,5,7]=>[4,8,2,1,6,3,5,7]=>1000101
[2,8,4,5,7,3,6,1]=>[6,2,7,8,4,3,5,1]=>[2,8,4,7,3,5,6,1]=>0000111
[4,8,1,2,5,6,3,7]=>[8,1,6,4,2,5,3,7]=>[4,6,1,2,5,8,3,7]=>0000101
[8,1,3,5,2,6,4,7]=>[8,5,1,6,3,2,4,7]=>[6,1,3,5,2,8,4,7]=>0001101
[4,6,8,3,7,2,5,1]=>[5,7,8,4,2,6,3,1]=>[4,6,8,2,7,3,5,1]=>0001011
[4,7,8,5,3,1,2,6]=>[3,1,5,4,8,2,7,6]=>[4,7,8,5,3,1,2,6]=>0101001
[1,3,8,6,4,7,5,2]=>[1,5,3,7,6,8,2,4]=>[1,3,8,6,2,7,5,4]=>0001111
[8,6,2,7,4,1,5,3]=>[4,7,6,5,2,8,3,1]=>[5,2,8,6,3,7,4,1]=>0011111
[7,6,1,3,4,2,8,5]=>[6,4,1,3,7,8,5,2]=>[4,1,3,8,5,7,6,2]=>0010111
[1,5,7,3,2,6,8,4]=>[1,3,7,8,5,2,6,4]=>[1,5,8,3,2,6,7,4]=>0100011
[1,6,7,3,2,5,8,4]=>[1,3,7,8,2,6,5,4]=>[1,6,8,3,2,5,7,4]=>0100011
[3,2,6,8,5,7,4,1]=>[4,3,2,7,8,6,5,1]=>[3,2,6,8,5,7,4,1]=>0110011
[7,5,2,3,1,6,8,4]=>[3,5,2,7,8,4,6,1]=>[8,4,6,7,5,2,3,1]=>0101011
[3,1,7,5,2,8,4,6]=>[3,5,1,7,8,2,4,6]=>[8,1,3,2,7,5,4,6]=>0101011
[6,4,8,7,2,3,5,1]=>[5,7,2,6,3,4,8,1]=>[6,2,3,8,7,4,5,1]=>0001111
[3,2,6,8,7,4,5,1]=>[5,3,2,7,4,6,8,1]=>[3,2,6,8,7,4,5,1]=>0101011
[6,3,2,1,7,8,4,5]=>[2,3,6,8,4,1,7,5]=>[7,8,4,6,3,2,1,5]=>1100101
[3,7,1,8,4,2,5,6]=>[7,4,3,8,2,5,1,6]=>[3,8,4,2,5,7,1,6]=>0010011
[4,2,1,3,7,5,8,6]=>[2,4,1,3,7,8,5,6]=>[4,2,1,3,8,5,7,6]=>1010011
[8,1,3,7,4,2,6,5]=>[8,4,1,7,6,2,3,5]=>[6,4,1,7,2,3,8,5]=>0010111
[7,3,2,8,1,6,5,4]=>[8,3,7,5,6,1,2,4]=>[6,5,3,1,7,2,8,4]=>0101111
[3,8,7,2,6,5,4,1]=>[4,5,3,6,7,2,8,1]=>[3,8,7,2,6,5,4,1]=>0011111
[5,8,1,6,7,2,4,3]=>[8,7,4,2,5,1,6,3]=>[4,2,5,7,1,6,8,3]=>0010011
[6,2,8,1,5,7,4,3]=>[8,6,4,7,1,2,5,3]=>[7,4,1,6,2,5,8,3]=>0010111
[5,7,8,2,6,1,4,3]=>[6,8,4,1,5,2,7,3]=>[4,1,5,7,8,2,6,3]=>0010101
[8,7,2,5,6,4,3,1]=>[3,4,6,7,2,5,8,1]=>[8,7,2,5,6,4,3,1]=>0110111
[1,2,7,8,5,6,4,3]=>[1,2,4,6,8,5,7,3]=>[1,2,7,8,5,6,4,3]=>0010101
[7,4,8,1,6,2,5,3]=>[8,6,5,7,2,1,4,3]=>[7,2,5,1,6,4,8,3]=>0001111
[3,7,1,8,2,6,5,4]=>[7,8,3,5,6,2,1,4]=>[3,6,5,2,8,1,7,4]=>0001111
[8,2,1,7,6,5,4,3]=>[2,8,4,5,6,7,1,3]=>[7,6,5,4,2,1,8,3]=>1011111
[8,6,7,5,1,4,3,2]=>[5,3,4,1,7,8,6,2]=>[4,3,1,8,6,7,5,2]=>0111011
[5,8,4,3,2,1,6,7]=>[2,3,4,8,5,1,6,7]=>[5,8,4,3,2,1,6,7]=>1110001
[5,4,7,3,2,1,6,8]=>[2,3,7,5,4,1,6,8]=>[5,4,7,3,2,1,6,8]=>1101010
[5,8,3,6,2,1,4,7]=>[2,6,8,1,5,3,4,7]=>[5,8,2,1,6,3,4,7]=>1000101
[5,3,7,6,2,1,4,8]=>[2,6,5,1,3,7,4,8]=>[5,2,1,7,6,3,4,8]=>1001110
[3,8,7,6,2,1,4,5]=>[2,6,3,1,4,7,8,5]=>[3,8,7,6,2,1,4,5]=>1000111
[4,8,7,2,5,1,3,6]=>[5,7,1,4,2,3,8,6]=>[4,8,7,1,5,2,3,6]=>0001011
[4,3,7,2,5,1,8,6]=>[5,7,4,3,2,8,1,6]=>[4,3,8,2,5,1,7,6]=>0011011
[6,4,2,7,5,1,3,8]=>[5,4,2,7,6,1,3,8]=>[6,4,2,7,5,1,3,8]=>0011110
[6,3,2,7,5,1,4,8]=>[5,3,7,2,6,1,4,8]=>[6,3,2,7,5,1,4,8]=>0101110
[5,3,2,6,7,1,4,8]=>[7,3,5,1,2,6,4,8]=>[5,3,1,6,7,2,4,8]=>0101010
[3,8,2,6,5,1,4,7]=>[5,6,3,2,8,1,4,7]=>[3,8,2,6,5,1,4,7]=>0001101
[6,2,7,8,5,1,3,4]=>[5,8,2,3,6,1,7,4]=>[6,2,3,7,8,5,1,4]=>0001101
[2,8,7,6,5,1,3,4]=>[5,2,1,3,6,7,8,4]=>[2,8,7,6,5,1,3,4]=>0001111
[6,5,4,3,1,7,8,2]=>[3,4,5,6,8,2,7,1]=>[7,8,2,6,5,4,3,1]=>0111101
[6,4,7,3,1,5,8,2]=>[3,7,8,6,2,4,5,1]=>[6,2,8,4,5,7,3,1]=>0100111
[5,4,7,3,1,8,6,2]=>[3,7,6,5,4,8,2,1]=>[5,4,8,6,2,7,3,1]=>0101111
[6,4,3,7,1,5,8,2]=>[7,8,4,6,1,3,5,2]=>[6,4,1,8,3,5,7,2]=>0010111
[6,3,7,8,1,4,5,2]=>[8,5,6,1,4,3,7,2]=>[6,1,4,5,3,7,8,2]=>0001101
[5,3,7,6,1,4,8,2]=>[6,7,5,2,3,8,4,1]=>[5,2,8,3,4,7,6,1]=>0001111
[6,5,4,2,1,7,3,8]=>[2,4,5,6,7,1,3,8]=>[7,2,1,6,5,4,3,8]=>1011110
[4,8,7,2,1,5,3,6]=>[2,7,5,4,1,3,8,6]=>[4,5,2,1,8,7,3,6]=>1001011
[3,8,7,2,1,4,5,6]=>[2,7,3,1,4,5,8,6]=>[3,8,7,2,1,4,5,6]=>1000011
[6,5,2,7,1,4,3,8]=>[7,5,4,1,6,2,3,8]=>[4,1,6,5,2,7,3,8]=>0011110
[5,4,2,6,1,8,3,7]=>[6,4,5,8,3,1,2,7]=>[8,3,5,4,1,6,2,7]=>0011101
[4,3,2,6,1,5,8,7]=>[6,3,4,2,1,5,8,7]=>[4,3,2,6,1,5,8,7]=>0110101
[6,2,7,8,1,4,3,5]=>[8,6,4,1,3,2,7,5]=>[4,1,6,3,7,8,2,5]=>0010101
[3,2,7,6,1,4,5,8]=>[6,3,2,1,4,7,5,8]=>[3,2,7,6,1,4,5,8]=>0100110
[6,5,4,1,8,7,3,2]=>[4,3,5,6,7,1,8,2]=>[8,7,3,1,6,5,4,2]=>0111111
[5,8,4,1,6,7,3,2]=>[4,3,8,7,5,2,6,1]=>[5,7,3,2,6,8,4,1]=>0110011
[5,8,2,1,6,4,3,7]=>[2,8,4,6,5,1,3,7]=>[5,6,4,2,1,8,3,7]=>1010101
[6,3,2,1,5,4,8,7]=>[2,3,6,5,1,4,8,7]=>[5,3,2,1,6,4,8,7]=>1101101
[5,3,2,1,6,4,8,7]=>[2,3,5,6,1,4,8,7]=>[6,3,2,1,5,4,8,7]=>1101101
[6,2,7,1,5,4,3,8]=>[7,6,4,5,1,2,3,8]=>[5,4,1,6,2,7,3,8]=>0011110
[5,2,7,1,6,4,3,8]=>[7,5,4,6,2,1,3,8]=>[6,4,2,5,1,7,3,8]=>0011110
[3,2,7,1,5,4,6,8]=>[7,3,2,5,1,4,6,8]=>[3,2,5,1,7,4,6,8]=>0101010
[6,5,1,7,8,4,3,2]=>[5,3,4,6,8,2,7,1]=>[7,8,4,3,2,6,5,1]=>0111101
[6,3,1,7,5,4,8,2]=>[3,6,8,5,7,2,4,1]=>[7,5,2,8,4,6,3,1]=>0101111
[5,3,1,6,7,4,8,2]=>[3,5,8,7,2,6,4,1]=>[6,7,2,8,4,5,3,1]=>0101011
[2,8,1,6,5,4,3,7]=>[8,2,4,5,6,1,3,7]=>[2,6,5,4,1,8,3,7]=>0011101
[6,1,7,8,5,4,3,2]=>[6,3,4,5,8,1,7,2]=>[7,8,5,4,3,1,6,2]=>0111101
[4,1,7,6,5,8,3,2]=>[4,3,8,1,6,7,5,2]=>[7,6,5,8,3,1,4,2]=>0110111
[3,1,7,6,5,4,8,2]=>[3,8,1,5,6,7,4,2]=>[7,6,5,4,8,1,3,2]=>0101111
[4,5,8,1,2,6,3,7]=>[8,1,6,4,5,2,3,7]=>[4,5,6,1,2,8,3,7]=>0000101
[1,7,3,5,6,2,4,8]=>[1,6,7,2,3,5,4,8]=>[1,7,2,5,6,3,4,8]=>0000110
[8,1,3,5,7,2,4,6]=>[8,7,1,2,3,4,5,6]=>[7,1,8,2,3,4,5,6]=>0000011
[3,6,8,1,7,2,4,5]=>[8,7,3,2,4,6,1,5]=>[3,6,7,2,4,8,1,5]=>0000011
[3,4,5,6,8,1,7,2]=>[8,7,3,4,5,6,1,2]=>[3,4,5,6,7,1,8,2]=>0000011
[4,5,8,2,6,7,1,3]=>[7,8,1,4,5,2,6,3]=>[4,5,8,1,6,7,2,3]=>0000011
[1,7,2,3,5,4,6,8]=>[1,7,2,5,3,4,6,8]=>[1,5,2,3,7,4,6,8]=>0001010
[8,1,2,3,5,4,6,7]=>[8,1,2,5,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>0001001
[2,7,8,3,5,6,1,4]=>[6,2,8,1,3,5,7,4]=>[2,7,8,1,5,6,3,4]=>0000101
[2,4,5,7,8,1,6,3]=>[8,2,6,4,5,1,7,3]=>[2,4,5,6,1,7,8,3]=>0000101
[4,5,8,7,2,1,6,3]=>[2,7,6,4,5,1,8,3]=>[4,5,6,2,1,8,7,3]=>1000111
[8,7,3,5,6,2,1,4]=>[2,6,7,1,3,5,8,4]=>[8,7,2,1,5,6,3,4]=>1000111
[8,7,2,1,3,5,4,6]=>[2,7,1,5,3,4,8,6]=>[5,2,1,3,8,7,4,6]=>1001011
[3,6,8,7,2,1,5,4]=>[2,7,3,5,1,6,8,4]=>[3,5,2,1,6,8,7,4]=>1001011
[8,6,4,1,7,5,3,2]=>[4,3,6,5,8,7,1,2]=>[7,5,3,1,8,6,4,2]=>0111111
[2,3,6,7,8,1,5,4]=>[8,2,3,5,1,6,7,4]=>[2,3,5,1,6,7,8,4]=>0001001
[3,6,8,1,2,5,4,7]=>[8,1,3,5,2,6,4,7]=>[3,5,1,2,6,8,4,7]=>0001001
[1,3,6,7,2,5,4,8]=>[1,7,3,5,2,6,4,8]=>[1,3,5,2,6,7,4,8]=>0001010
[7,4,1,8,5,2,3,6]=>[4,7,1,5,8,3,2,6]=>[8,5,1,3,7,4,2,6]=>0011011
[7,1,4,2,8,3,6,5]=>[7,4,8,1,6,3,2,5]=>[6,1,4,3,8,2,7,5]=>0010111
[8,1,7,5,4,2,3,6]=>[8,4,2,5,7,3,1,6]=>[7,5,4,2,3,8,1,6]=>0011011
[1,7,6,3,2,5,4,8]=>[1,3,6,5,2,7,4,8]=>[1,5,3,2,7,6,4,8]=>0101110
[8,6,3,1,2,5,4,7]=>[3,1,6,5,2,8,4,7]=>[5,3,1,2,8,6,4,7]=>0101101
[8,1,7,6,3,2,4,5]=>[8,3,6,2,4,7,1,5]=>[7,6,3,2,4,8,1,5]=>0100111
[2,7,8,6,3,1,5,4]=>[3,2,6,5,1,8,7,4]=>[2,5,3,1,7,8,6,4]=>0101101
[7,3,1,8,6,5,4,2]=>[3,7,4,5,6,8,2,1]=>[8,6,5,4,2,7,3,1]=>0111111
[8,7,6,3,2,1,5,4]=>[2,3,6,5,1,7,8,4]=>[5,3,2,1,8,7,6,4]=>1101111
[2,1,8,6,3,7,4,5]=>[2,1,6,8,3,7,4,5]=>[2,1,7,3,8,6,4,5]=>1000111
[2,1,7,5,4,3,8,6]=>[2,1,4,5,7,8,3,6]=>[2,1,8,5,4,3,7,6]=>1011011
[2,1,7,8,3,6,5,4]=>[2,1,8,5,6,3,7,4]=>[2,1,6,5,3,7,8,4]=>1001101
[2,1,8,5,7,6,3,4]=>[2,1,6,3,7,8,4,5]=>[2,1,8,3,4,7,6,5]=>1000111
[2,1,4,8,5,7,3,6]=>[2,1,7,4,8,3,5,6]=>[2,1,4,8,3,7,5,6]=>1000011
[7,5,1,4,6,8,3,2]=>[5,3,7,2,8,4,6,1]=>[8,3,2,4,6,7,5,1]=>0101011
[6,4,1,5,2,3,8,7]=>[4,6,1,5,2,3,8,7]=>[5,1,6,4,2,3,8,7]=>0011101
[5,3,7,4,6,8,1,2]=>[8,1,5,7,3,4,6,2]=>[7,3,5,4,6,8,1,2]=>0001011
[5,8,3,7,6,2,1,4]=>[2,6,7,3,5,8,1,4]=>[5,8,3,7,6,2,1,4]=>1000111
[5,2,4,8,6,3,1,7]=>[3,6,5,1,4,8,2,7]=>[5,1,4,8,6,3,2,7]=>0101101
[4,2,6,3,8,5,1,7]=>[5,4,8,2,6,1,3,7]=>[6,2,4,1,8,5,3,7]=>0011101
[3,8,2,4,7,5,1,6]=>[5,7,3,1,8,2,4,6]=>[3,8,1,7,5,2,4,6]=>0001011
[6,3,8,1,5,7,4,2]=>[8,4,7,6,1,2,5,3]=>[6,1,7,4,2,5,8,3]=>0010111
[8,3,2,4,1,7,5,6]=>[4,3,8,2,7,5,1,6]=>[7,5,8,3,2,4,1,6]=>0110011
[6,2,3,1,4,5,8,7]=>[3,6,2,1,4,5,8,7]=>[6,2,3,1,4,5,8,7]=>0100101
[5,6,1,4,3,2,8,7]=>[6,3,4,1,5,2,8,7]=>[4,3,1,5,6,2,8,7]=>0110101
[8,7,5,1,3,4,2,6]=>[5,4,1,3,7,2,8,6]=>[4,1,3,8,7,5,2,6]=>0011011
[5,8,1,6,3,7,4,2]=>[8,4,7,6,5,1,2,3]=>[5,6,1,7,4,2,8,3]=>0010111
[7,5,4,8,2,1,3,6]=>[2,8,1,5,7,3,4,6]=>[7,5,2,1,3,8,4,6]=>1001011
[8,3,6,4,5,1,2,7]=>[5,1,8,6,4,3,2,7]=>[6,4,8,3,5,1,2,7]=>0001101
[6,3,5,4,1,2,8,7]=>[4,1,5,6,2,3,8,7]=>[6,1,2,5,4,3,8,7]=>0011101
[2,6,3,5,1,4,8,7]=>[5,2,6,1,3,4,8,7]=>[2,6,1,5,3,4,8,7]=>0001101
[8,7,3,6,5,1,4,2]=>[5,4,6,3,7,1,8,2]=>[8,7,3,4,1,6,5,2]=>0011111
[2,8,3,4,6,1,5,7]=>[6,2,8,3,1,4,5,7]=>[2,8,3,6,1,4,5,7]=>0000101
[3,4,7,2,8,1,5,6]=>[8,7,3,4,1,5,2,6]=>[3,4,7,1,5,8,2,6]=>0000011
[4,2,3,5,8,1,6,7]=>[8,4,2,3,5,1,6,7]=>[4,2,3,5,8,1,6,7]=>0010001
[3,2,8,4,7,1,6,5]=>[7,3,2,8,6,1,4,5]=>[3,2,6,1,8,4,7,5]=>0100111
[3,8,4,7,1,6,5,2]=>[7,5,3,6,8,1,2,4]=>[3,8,1,6,5,2,7,4]=>0001111
[3,2,4,5,6,8,1,7]=>[8,3,2,4,5,6,1,7]=>[3,2,4,5,6,8,1,7]=>0100001
[1,3,5,7,8,6,2,4]=>[1,6,3,2,5,8,7,4]=>[1,3,5,7,8,6,2,4]=>0000101
[3,5,7,8,6,1,2,4]=>[6,1,3,2,5,8,7,4]=>[3,5,7,8,6,1,2,4]=>0000101
[3,5,1,6,8,2,7,4]=>[5,8,3,7,1,6,2,4]=>[3,6,7,1,8,2,5,4]=>0001011
[3,1,5,6,8,2,7,4]=>[3,8,1,7,5,6,2,4]=>[5,6,7,1,3,2,8,4]=>0100011
[2,3,5,6,8,1,7,4]=>[8,2,3,7,5,6,1,4]=>[2,3,5,6,7,1,8,4]=>0000011
[5,1,6,3,8,4,7,2]=>[5,7,6,8,1,3,4,2]=>[8,1,6,3,7,4,5,2]=>0001111
[5,1,2,6,8,3,7,4]=>[5,1,8,7,2,6,3,4]=>[6,7,1,2,8,3,5,4]=>0001011
[2,6,7,5,1,8,3,4]=>[5,2,7,1,8,6,3,4]=>[2,6,8,1,7,5,3,4]=>0001011
[5,7,2,8,6,1,3,4]=>[6,8,2,3,5,7,1,4]=>[5,7,2,3,8,6,1,4]=>0000111
[3,5,7,8,6,2,1,4]=>[2,6,3,1,5,8,7,4]=>[3,5,7,8,6,2,1,4]=>1000101
[1,2,6,7,5,8,3,4]=>[1,2,8,3,7,6,5,4]=>[1,2,6,7,5,8,3,4]=>0000011
[6,2,7,5,4,1,8,3]=>[4,5,7,6,8,1,3,2]=>[8,1,6,3,7,5,4,2]=>0011111
[6,7,5,2,4,1,8,3]=>[4,5,7,3,8,6,1,2]=>[6,8,3,7,5,1,4,2]=>0011011
[6,7,2,5,3,8,1,4]=>[8,7,5,1,2,6,3,4]=>[5,1,6,7,2,8,3,4]=>0001011
[6,7,4,5,2,1,8,3]=>[2,5,8,7,4,6,1,3]=>[6,7,4,8,2,1,5,3]=>1001011
[2,5,7,8,6,3,1,4]=>[3,2,6,1,5,8,7,4]=>[2,5,7,8,6,3,1,4]=>0100101
[6,3,7,5,1,8,2,4]=>[5,7,8,3,6,1,2,4]=>[6,3,8,1,7,5,2,4]=>0001111
[5,7,8,6,4,1,2,3]=>[4,1,2,6,5,8,7,3]=>[5,7,8,6,4,1,2,3]=>0010101
[2,4,7,1,5,6,8,3]=>[7,2,8,4,1,5,6,3]=>[2,4,8,1,5,6,7,3]=>0000011
[1,6,7,4,5,2,8,3]=>[1,5,8,7,4,6,2,3]=>[1,6,7,4,8,2,5,3]=>0001011
[1,6,3,7,5,8,2,4]=>[1,8,6,2,7,3,5,4]=>[1,7,2,6,5,8,3,4]=>0000111
[2,5,3,7,8,6,1,4]=>[6,2,5,1,3,8,7,4]=>[2,5,1,7,8,6,3,4]=>0001101
[6,7,4,2,5,1,8,3]=>[5,4,7,8,3,6,1,2]=>[6,8,3,7,4,1,5,2]=>0011011
[6,2,7,4,5,1,8,3]=>[5,6,8,7,4,2,1,3]=>[7,4,8,2,6,1,5,3]=>0001111
[6,2,3,7,5,8,1,4]=>[8,6,2,1,7,3,5,4]=>[7,2,6,5,8,1,3,4]=>0000111
[4,5,1,6,3,2,8,7]=>[5,3,6,4,1,2,8,7]=>[4,6,3,1,5,2,8,7]=>0101101
[7,5,1,6,3,8,2,4]=>[5,7,8,3,6,2,1,4]=>[6,3,8,2,7,5,1,4]=>0001111
[7,3,5,1,8,2,6,4]=>[5,8,7,6,3,2,1,4]=>[6,3,7,2,8,1,5,4]=>0001111
[3,7,5,1,8,6,2,4]=>[5,7,3,1,6,8,2,4]=>[3,8,6,1,7,5,2,4]=>0001111
[2,1,6,7,3,8,5,4]=>[2,1,7,5,8,6,3,4]=>[2,1,6,8,5,3,7,4]=>1001011
[3,6,5,1,8,4,7,2]=>[5,6,3,7,8,2,1,4]=>[3,8,2,7,1,6,5,4]=>0001111
[3,7,5,4,8,1,2,6]=>[8,1,3,5,7,2,4,6]=>[3,7,5,1,2,8,4,6]=>0001011
[4,6,1,5,8,2,7,3]=>[6,8,7,4,1,5,2,3]=>[4,7,1,5,8,2,6,3]=>0000111
[7,5,1,6,2,8,3,4]=>[5,7,6,1,8,2,3,4]=>[8,1,6,2,7,5,3,4]=>0001111
[4,7,1,5,8,3,6,2]=>[7,6,8,4,1,3,5,2]=>[4,8,1,6,3,5,7,2]=>0000111
[2,3,4,7,8,1,6,5]=>[8,2,3,4,6,1,7,5]=>[2,3,4,6,1,7,8,5]=>0000101
[6,8,5,4,3,2,7,1]=>[7,3,4,5,8,6,2,1]=>[6,8,5,4,3,2,7,1]=>0111011
[10,11,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,11,10,1]=>[10,11,9,8,7,6,5,4,3,2,1]=>1111111101
[5,8,4,3,2,1,7,6]=>[2,3,4,8,5,7,1,6]=>[5,7,4,3,2,1,8,6]=>1110011
[6,5,4,3,1,8,7,2]=>[3,4,5,6,7,2,8,1]=>[8,7,2,6,5,4,3,1]=>0111111
[8,7,5,4,3,1,6,2]=>[3,4,5,7,6,2,8,1]=>[6,2,8,7,5,4,3,1]=>0111111
[11,10,9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,10,11,2]=>[11,10,9,8,7,6,5,4,3,1,2]=>0111111111
[2,4,5,7,3,8,6,1]=>[6,2,8,4,5,7,1,3]=>[2,4,5,7,1,8,6,3]=>0000111
[2,5,6,1,8,4,3,7]=>[6,2,4,8,5,1,3,7]=>[2,5,8,4,1,6,3,7]=>0010101
[6,4,7,3,2,8,5,1]=>[5,3,8,7,6,1,4,2]=>[6,3,1,7,4,8,5,2]=>0101111
[6,1,4,7,3,2,8,5]=>[6,3,7,1,8,4,2,5]=>[8,3,1,4,7,2,6,5]=>0100111
[5,1,7,3,8,4,2,6]=>[5,4,8,7,1,3,2,6]=>[7,1,8,4,3,5,2,6]=>0011011
[2,5,1,7,4,3,8,6]=>[5,2,4,7,1,8,3,6]=>[2,8,4,1,5,3,7,6]=>0011011
[5,3,7,1,4,8,6,2]=>[7,6,5,1,3,8,4,2]=>[5,1,8,6,3,4,7,2]=>0001111
[6,4,3,1,7,8,5,2]=>[3,4,6,5,8,1,7,2]=>[7,8,5,1,6,4,3,2]=>0111101
[6,4,1,7,3,8,5,2]=>[4,6,5,8,7,2,3,1]=>[7,2,8,5,3,6,4,1]=>0011111
[5,1,6,3,7,8,4,2]=>[5,4,8,6,1,2,7,3]=>[6,1,7,8,4,2,5,3]=>0011101
[5,6,1,3,7,8,4,2]=>[6,4,1,8,5,3,7,2]=>[5,7,8,4,1,3,6,2]=>0010101
[1,6,3,7,4,8,5,2]=>[1,5,8,6,7,4,2,3]=>[1,7,4,6,2,8,5,3]=>0001111
[6,7,2,4,1,8,5,3]=>[4,7,5,2,8,6,1,3]=>[6,8,5,2,7,1,4,3]=>0011011
[5,6,3,1,2,7,8,4]=>[3,1,6,8,5,2,7,4]=>[5,7,8,3,1,2,6,4]=>0100101
[5,6,3,2,1,7,8,4]=>[2,3,6,8,5,1,7,4]=>[5,7,8,3,2,1,6,4]=>1100101
[2,5,6,3,7,8,4,1]=>[4,2,8,6,5,1,7,3]=>[2,5,6,1,7,8,4,3]=>0010101
[2,5,6,3,1,7,8,4]=>[3,2,6,8,5,1,7,4]=>[2,5,7,8,3,1,6,4]=>0100101
[6,3,7,2,8,4,5,1]=>[5,7,6,8,4,3,2,1]=>[8,4,6,3,7,2,5,1]=>0001111
[6,3,7,2,8,4,1,5]=>[4,8,7,6,2,1,3,5]=>[6,2,7,1,8,4,3,5]=>0010111
[7,3,8,4,2,1,5,6]=>[2,4,8,7,3,5,1,6]=>[7,3,5,8,4,2,1,6]=>1010011
[7,3,8,4,6,2,1,5]=>[2,6,7,8,1,4,3,5]=>[8,2,1,7,4,6,3,5]=>1000111
[5,7,3,8,2,1,6,4]=>[2,8,7,6,5,1,3,4]=>[5,6,2,1,7,3,8,4]=>1000111
[5,1,6,7,8,2,4,3]=>[5,8,4,2,1,6,7,3]=>[4,2,6,7,8,1,5,3]=>0011001
[6,3,7,1,8,5,2,4]=>[7,5,8,3,6,2,1,4]=>[6,3,8,5,2,7,1,4]=>0001111
[6,2,7,1,8,5,4,3]=>[7,6,4,5,8,2,1,3]=>[8,5,4,2,6,1,7,3]=>0011111
[4,1,3,6,8,2,5,7]=>[4,8,1,3,2,6,5,7]=>[6,8,1,3,4,2,5,7]=>0010001
[4,2,3,6,8,1,5,7]=>[8,4,2,3,1,6,5,7]=>[4,2,3,6,8,1,5,7]=>0010001
[4,5,2,1,3,8,7,6]=>[2,5,1,4,3,7,8,6]=>[4,5,2,1,3,8,7,6]=>1001011
[3,2,6,4,5,8,1,7]=>[8,3,2,6,4,5,1,7]=>[3,2,6,4,5,8,1,7]=>0100101
[2,4,6,5,8,1,3,7]=>[8,2,1,4,6,5,3,7]=>[2,4,6,5,8,1,3,7]=>0000101
[1,6,3,4,5,8,2,7]=>[1,8,6,3,4,5,2,7]=>[1,6,3,4,5,8,2,7]=>0000101
[2,8,4,1,7,6,3,5]=>[4,2,8,6,1,7,3,5]=>[2,7,6,1,8,4,3,5]=>0010111
[1,5,3,2,8,7,4,6]=>[1,3,5,7,2,4,8,6]=>[1,8,7,3,2,5,4,6]=>0101011
[1,7,6,4,5,8,3,2]=>[1,3,8,6,4,7,5,2]=>[1,7,6,4,5,8,3,2]=>0100111
[4,1,3,5,6,8,7,2]=>[4,7,1,3,5,6,8,2]=>[5,6,8,7,1,3,4,2]=>0010011
[2,4,8,6,7,1,3,5]=>[7,2,1,4,3,8,6,5]=>[2,4,8,6,7,1,3,5]=>0000011
[3,7,4,8,2,1,6,5]=>[2,8,3,7,6,1,4,5]=>[3,6,2,1,7,4,8,5]=>1000111
[2,3,5,8,6,7,1,4]=>[7,2,3,1,5,8,6,4]=>[2,3,5,8,6,7,1,4]=>0000011
[2,1,8,5,6,7,3,4]=>[2,1,7,3,8,5,6,4]=>[2,1,8,5,6,7,3,4]=>1000011
[3,2,6,4,8,1,7,5]=>[8,3,2,6,7,4,1,5]=>[3,2,7,4,6,1,8,5]=>0100111
[8,2,1,6,7,3,4,5]=>[2,8,7,3,4,1,6,5]=>[7,3,4,6,8,2,1,5]=>1000011
[2,7,8,5,4,1,3,6]=>[4,2,1,5,8,3,7,6]=>[2,7,8,5,4,1,3,6]=>0011001
[4,7,5,3,1,2,8,6]=>[3,1,5,4,7,8,2,6]=>[4,8,5,3,1,2,7,6]=>0101011
[3,5,2,7,4,1,8,6]=>[4,7,3,5,1,8,2,6]=>[3,5,1,8,4,2,7,6]=>0011011
[8,4,2,3,7,1,5,6]=>[7,4,2,8,1,5,3,6]=>[8,4,2,5,7,1,3,6]=>0010011
[8,2,4,6,7,1,3,5]=>[7,8,1,2,3,4,6,5]=>[8,1,6,7,2,3,4,5]=>0000011
[3,5,2,7,6,1,8,4]=>[6,5,3,7,2,8,4,1]=>[3,8,2,5,4,7,6,1]=>0001111
[1,6,3,2,5,8,7,4]=>[1,3,6,7,2,5,8,4]=>[1,8,7,3,2,5,6,4]=>0100111
[5,8,3,2,1,6,7,4]=>[2,3,8,7,5,1,6,4]=>[5,7,3,2,1,6,8,4]=>1100011
[4,2,5,6,8,7,1,3]=>[7,4,1,2,5,6,8,3]=>[4,1,5,6,8,7,2,3]=>0010011
[1,8,4,2,5,6,7,3]=>[1,4,8,7,3,5,6,2]=>[1,7,3,5,6,8,4,2]=>0010011
[4,2,8,5,6,7,1,3]=>[7,4,1,2,8,5,6,3]=>[4,1,8,5,6,7,2,3]=>0010011
[8,1,3,6,5,2,4,7]=>[8,5,1,2,6,3,4,7]=>[6,5,1,8,2,3,4,7]=>0001101
[8,1,4,3,6,5,2,7]=>[8,5,4,1,6,3,2,7]=>[4,1,6,5,3,8,2,7]=>0011101
[8,3,2,4,6,5,1,7]=>[5,3,6,1,8,4,2,7]=>[8,3,1,4,6,5,2,7]=>0101101
[8,4,2,1,6,5,3,7]=>[2,4,8,5,6,3,1,7]=>[6,5,3,8,4,2,1,7]=>1011101
[8,4,1,2,6,5,3,7]=>[4,1,8,5,6,3,2,7]=>[6,5,3,8,4,1,2,7]=>0011101
[1,3,4,8,5,7,2,6]=>[1,7,3,4,8,2,5,6]=>[1,3,4,8,2,7,5,6]=>0000011
[1,3,5,2,4,8,7,6]=>[1,5,3,2,4,7,8,6]=>[1,3,5,2,4,8,7,6]=>0001011
[4,7,1,6,5,8,3,2]=>[7,3,8,4,6,1,5,2]=>[4,6,3,1,8,5,7,2]=>0100111
[4,3,1,5,8,6,7,2]=>[3,4,7,2,5,8,6,1]=>[5,8,6,7,2,4,3,1]=>0110011
[4,1,3,5,8,6,7,2]=>[4,7,1,3,5,8,6,2]=>[5,8,6,7,1,3,4,2]=>0010011
[5,4,2,1,6,8,7,3]=>[2,4,5,7,3,6,8,1]=>[6,8,7,3,5,4,2,1]=>1011011
[6,8,4,3,2,7,1,5]=>[7,3,4,8,1,6,2,5]=>[6,8,4,3,1,7,2,5]=>0110011
[2,4,7,3,8,1,6,5]=>[8,2,7,4,6,1,3,5]=>[2,4,6,1,7,3,8,5]=>0000111
[3,5,1,7,8,4,2,6]=>[5,4,3,8,1,2,7,6]=>[3,7,8,4,1,5,2,6]=>0011001
[2,7,4,5,8,3,1,6]=>[3,2,8,7,4,1,5,6]=>[2,7,4,8,3,1,5,6]=>0100011
[1,8,4,3,7,2,6,5]=>[1,7,4,8,6,2,3,5]=>[1,6,4,2,8,3,7,5]=>0010111
[5,4,7,8,3,6,2,1]=>[2,6,8,5,4,3,7,1]=>[5,4,7,8,3,6,2,1]=>1001101
[6,3,8,7,4,1,2,5]=>[4,1,7,6,3,2,8,5]=>[6,3,8,7,4,1,2,5]=>0010111
[3,5,7,2,4,8,1,6]=>[8,7,3,2,5,1,4,6]=>[3,5,7,2,8,1,4,6]=>0000011
[8,4,7,2,1,3,5,6]=>[2,7,1,8,3,5,4,6]=>[8,2,1,3,5,7,4,6]=>1000011
[8,6,4,2,1,3,7,5]=>[2,4,1,6,8,7,5,3]=>[7,5,8,6,4,2,1,3]=>1010111
[8,6,4,1,3,2,7,5]=>[4,3,1,6,8,7,5,2]=>[3,1,7,5,8,6,4,2]=>0110111
[3,5,7,2,6,1,8,4]=>[6,7,3,8,5,2,1,4]=>[3,5,8,2,7,1,6,4]=>0000111
[6,1,3,8,5,7,2,4]=>[6,7,1,2,8,3,5,4]=>[8,1,7,5,6,2,3,4]=>0000111
[5,8,3,2,6,7,1,4]=>[7,3,8,1,5,2,6,4]=>[5,8,3,1,6,7,2,4]=>0100011
[4,8,5,3,6,2,7,1]=>[7,6,5,4,8,3,2,1]=>[4,8,5,3,6,2,7,1]=>0001111
[2,1,7,6,4,5,8,3]=>[2,1,8,6,4,7,5,3]=>[2,1,7,6,4,5,8,3]=>1000111
[1,7,2,4,6,5,8,3]=>[1,7,8,2,6,4,5,3]=>[1,6,2,4,8,5,7,3]=>0000111
[3,5,1,7,6,8,2,4]=>[5,8,3,2,1,7,6,4]=>[3,7,6,8,2,5,1,4]=>0001011
[5,8,2,6,1,3,7,4]=>[6,8,1,7,5,2,3,4]=>[5,7,1,8,2,3,6,4]=>0000111
[6,3,5,8,7,2,1,4]=>[2,7,6,1,3,5,8,4]=>[6,2,1,5,8,7,3,4]=>1000111
[2,5,7,8,4,1,6,3]=>[4,2,8,6,5,3,7,1]=>[2,5,6,3,7,8,4,1]=>0010101
[3,4,5,1,6,8,7,2]=>[5,7,3,4,1,6,8,2]=>[3,4,6,8,7,1,5,2]=>0001011
[2,7,1,8,5,4,6,3]=>[7,2,6,5,8,4,1,3]=>[2,8,5,4,6,1,7,3]=>0001111
[5,8,6,2,1,3,7,4]=>[2,6,1,8,5,7,4,3]=>[5,7,4,8,6,2,1,3]=>1000111
[3,4,5,1,8,6,7,2]=>[5,7,3,4,1,8,6,2]=>[3,4,8,6,7,1,5,2]=>0001011
[3,8,1,4,5,6,7,2]=>[8,7,3,1,4,5,6,2]=>[3,7,1,4,5,6,8,2]=>0000011
[3,4,5,7,1,8,6,2]=>[7,6,3,4,5,8,1,2]=>[3,4,5,8,6,1,7,2]=>0000111
[3,4,6,2,8,5,1,7]=>[5,8,3,4,6,1,2,7]=>[3,4,6,1,8,5,2,7]=>0001101
[3,4,8,2,1,5,6,7]=>[2,8,3,4,1,5,6,7]=>[3,4,8,2,1,5,6,7]=>1000001
[3,5,2,6,7,8,1,4]=>[8,5,3,1,2,6,7,4]=>[3,5,1,6,7,8,2,4]=>0001001
[3,5,6,8,4,1,2,7]=>[4,1,3,8,5,6,2,7]=>[3,5,6,8,4,1,2,7]=>0010001
[3,5,7,2,4,8,6,1]=>[6,8,3,1,5,7,4,2]=>[3,5,7,1,4,8,6,2]=>0000111
[3,5,7,2,8,4,6,1]=>[6,7,3,8,5,4,2,1]=>[3,5,8,4,7,2,6,1]=>0000111
[3,5,7,8,4,1,6,2]=>[4,8,3,6,5,2,7,1]=>[3,5,6,2,7,8,4,1]=>0010101
[3,6,2,1,7,8,5,4]=>[2,6,3,5,8,1,7,4]=>[3,7,8,5,2,1,6,4]=>1001101
[3,6,7,2,4,8,5,1]=>[5,8,3,1,7,6,4,2]=>[3,6,7,1,4,8,5,2]=>0001011
[3,6,7,8,4,5,1,2]=>[5,1,3,8,4,6,7,2]=>[3,6,7,8,4,5,1,2]=>0001001
[3,6,8,2,4,5,1,7]=>[5,8,3,2,4,6,1,7]=>[3,6,8,2,4,5,1,7]=>0001001
[3,7,2,8,4,5,6,1]=>[6,7,3,8,4,5,2,1]=>[3,8,4,5,7,2,6,1]=>0000111
[3,8,2,1,4,5,6,7]=>[2,8,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]=>1000001
[4,1,5,6,7,8,3,2]=>[4,3,8,1,5,6,7,2]=>[5,6,7,8,3,1,4,2]=>0110001
[4,1,6,3,7,8,5,2]=>[4,5,8,1,6,2,7,3]=>[6,1,7,8,5,2,4,3]=>0011101
[4,1,6,3,8,5,2,7]=>[4,5,8,1,6,2,3,7]=>[6,1,8,5,2,4,3,7]=>0011101
[4,1,6,7,3,8,5,2]=>[4,5,8,1,7,6,2,3]=>[6,7,1,8,5,2,4,3]=>0011011
[4,1,6,7,8,5,2,3]=>[4,5,2,1,8,6,7,3]=>[6,7,8,5,2,4,1,3]=>0011001
[4,1,7,3,2,8,6,5]=>[4,3,7,1,6,8,2,5]=>[8,6,3,1,4,2,7,5]=>0110111
[4,1,7,8,3,5,6,2]=>[4,6,8,1,3,5,7,2]=>[7,8,1,5,6,3,4,2]=>0010101
[4,5,2,6,8,1,3,7]=>[8,5,1,4,2,6,3,7]=>[4,5,1,6,8,2,3,7]=>0001001
[4,5,6,3,8,1,2,7]=>[8,1,6,4,5,3,2,7]=>[4,5,6,3,8,1,2,7]=>0000101
[4,5,6,8,3,1,2,7]=>[3,1,8,4,5,6,2,7]=>[4,5,6,8,3,1,2,7]=>0100001
[4,5,7,3,8,1,6,2]=>[8,6,7,4,5,1,3,2]=>[4,5,7,1,6,3,8,2]=>0000111
[4,6,2,3,7,8,5,1]=>[5,8,1,4,6,3,7,2]=>[4,6,1,3,7,8,5,2]=>0001101
[4,6,2,3,8,5,1,7]=>[5,8,1,4,6,3,2,7]=>[4,6,1,3,8,5,2,7]=>0001101
[4,6,7,3,2,8,5,1]=>[5,3,8,4,7,6,1,2]=>[4,6,7,3,1,8,5,2]=>0101011
[4,7,2,3,1,8,6,5]=>[3,7,2,4,6,8,1,5]=>[4,8,6,2,3,1,7,5]=>0100111
[4,7,2,8,3,5,6,1]=>[6,7,8,4,3,5,2,1]=>[4,8,3,5,7,2,6,1]=>0000111
[4,7,8,3,2,5,6,1]=>[6,3,8,4,2,5,7,1]=>[4,7,8,3,2,5,6,1]=>0100101
[5,1,2,6,8,4,3,7]=>[5,1,4,8,2,6,3,7]=>[6,8,4,1,2,5,3,7]=>0011001
[5,1,6,7,4,8,2,3]=>[5,8,2,7,1,6,4,3]=>[6,7,2,8,4,5,1,3]=>0001011
[5,6,2,7,8,4,1,3]=>[4,8,2,6,5,1,7,3]=>[5,6,2,7,8,4,1,3]=>0010101
[5,6,8,3,4,2,1,7]=>[2,4,8,3,5,6,1,7]=>[5,6,8,3,4,2,1,7]=>1010001
[5,7,8,3,4,2,6,1]=>[6,4,8,3,5,2,7,1]=>[5,7,8,3,4,2,6,1]=>0010101
[5,8,2,3,4,1,6,7]=>[4,8,2,3,5,1,6,7]=>[5,8,2,3,4,1,6,7]=>0010001
[6,1,7,3,4,8,5,2]=>[6,5,8,2,7,1,4,3]=>[7,2,8,5,1,4,6,3]=>0001111
[6,7,2,8,4,5,3,1]=>[3,5,7,8,4,6,1,2]=>[6,8,4,7,1,5,3,2]=>0101011
[6,8,2,3,4,5,1,7]=>[5,8,2,3,4,6,1,7]=>[6,8,2,3,4,5,1,7]=>0001001
[7,1,2,3,4,8,6,5]=>[7,1,2,3,6,8,4,5]=>[8,6,1,2,3,4,7,5]=>0000111
[5,8,1,2,4,3,7,6]=>[8,1,4,2,5,7,3,6]=>[4,1,2,5,7,3,8,6]=>0010011
[1,3,5,7,2,6,4,8]=>[1,7,3,6,5,2,4,8]=>[1,3,5,6,2,7,4,8]=>0000110
[2,6,1,3,8,4,7,5]=>[6,2,1,8,7,3,4,5]=>[2,7,1,3,8,4,6,5]=>0000111
[1,7,5,2,3,4,6,8]=>[1,5,2,3,7,4,6,8]=>[1,7,5,2,3,4,6,8]=>0001010
[2,7,5,1,3,8,4,6]=>[5,2,1,7,8,3,4,6]=>[2,8,1,3,7,5,4,6]=>0001011
[8,2,5,1,3,7,4,6]=>[5,8,1,7,2,4,3,6]=>[7,1,8,4,5,2,3,6]=>0001011
[8,2,7,5,3,1,6,4]=>[3,5,7,8,6,1,4,2]=>[6,1,8,4,7,5,3,2]=>0101111
[7,1,8,6,3,2,4,5]=>[7,3,6,2,4,8,1,5]=>[8,6,3,2,4,7,1,5]=>0100111
[6,8,1,5,3,2,4,7]=>[8,3,5,2,1,6,4,7]=>[5,3,2,6,8,1,4,7]=>0101001
[1,6,7,5,3,2,4,8]=>[1,3,5,2,7,6,4,8]=>[1,6,7,5,3,2,4,8]=>0101010
[6,5,1,2,4,8,3,7]=>[5,1,6,3,8,4,2,7]=>[8,3,4,6,5,1,2,7]=>0001101
[7,8,1,6,4,2,3,5]=>[8,4,2,6,3,1,7,5]=>[6,4,2,3,7,8,1,5]=>0010101
[8,4,1,2,5,6,3,7]=>[4,1,8,6,3,5,2,7]=>[6,3,5,8,4,1,2,7]=>0010101
[1,7,3,6,5,2,4,8]=>[1,5,6,3,7,2,4,8]=>[1,7,3,6,5,2,4,8]=>0001110
[7,8,4,2,5,6,1,3]=>[6,4,1,8,2,5,7,3]=>[7,8,4,1,5,6,2,3]=>0010101
[8,2,7,4,5,6,1,3]=>[6,8,1,7,4,5,2,3]=>[7,4,5,8,1,6,2,3]=>0000111
[7,9,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,9,1]=>[7,9,8,6,5,4,3,2,1]=>11111011
[6,9,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,9,1]=>[6,9,8,7,5,4,3,2,1]=>11110111
[5,9,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,9,1]=>[5,9,8,7,6,4,3,2,1]=>11101111
[3,9,8,7,6,5,4,2,1]=>[2,4,3,5,6,7,8,9,1]=>[3,9,8,7,6,5,4,2,1]=>10111111
[2,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,1]=>[2,9,8,7,6,5,4,3,1]=>01111111
[6,10,9,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,9,10,1]=>[6,10,9,8,7,5,4,3,2,1]=>111101111
[5,10,9,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,9,10,1]=>[5,10,9,8,7,6,4,3,2,1]=>111011111
[1,8,7,6,5,3,2,4]=>[1,3,5,2,6,7,8,4]=>[1,8,7,6,5,3,2,4]=>0101111
[1,8,7,6,5,2,3,4]=>[1,5,2,3,6,7,8,4]=>[1,8,7,6,5,2,3,4]=>0001111
[1,9,8,7,6,5,4,2,3]=>[1,4,2,5,6,7,8,9,3]=>[1,9,8,7,6,5,4,2,3]=>00111111
[2,10,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,9,8,7,6,5,4,3,1]=>011111111
[7,2,8,6,5,4,1,3]=>[4,5,2,6,8,7,1,3]=>[7,2,8,6,5,4,1,3]=>0011111
[8,4,7,2,5,6,3,1]=>[3,6,7,8,1,5,4,2]=>[8,1,5,7,4,6,3,2]=>0100111
[5,8,6,4,1,3,7,2]=>[4,6,1,8,5,7,3,2]=>[5,7,1,3,8,6,4,2]=>0010111
[4,8,6,1,5,3,7,2]=>[6,8,5,4,2,7,3,1]=>[4,5,2,7,3,8,6,1]=>0001111
[3,6,1,8,5,2,7,4]=>[6,5,3,8,7,1,4,2]=>[3,7,1,8,5,4,6,2]=>0001111
[7,2,5,8,3,6,1,4]=>[6,7,8,1,2,3,5,4]=>[8,1,7,2,5,6,3,4]=>0000111
[1,7,5,6,3,4,2,8]=>[1,4,6,3,7,5,2,8]=>[1,7,5,6,3,4,2,8]=>0010110
[1,5,7,4,2,6,3,8]=>[1,4,7,6,5,3,2,8]=>[1,5,6,3,7,4,2,8]=>0010110
[6,8,3,4,5,1,7,2]=>[5,7,8,3,4,6,1,2]=>[6,8,3,4,7,1,5,2]=>0001011
[1,6,3,2,5,8,4,7]=>[1,3,6,8,2,5,4,7]=>[1,8,3,2,5,6,4,7]=>0100101
[8,3,2,1,5,4,7,6]=>[2,3,8,5,1,7,4,6]=>[5,3,2,1,7,4,8,6]=>1101011
[6,2,5,4,8,1,3,7]=>[8,6,1,5,2,4,3,7]=>[5,1,6,4,8,2,3,7]=>0001101
[8,3,4,1,5,2,7,6]=>[4,5,8,3,1,7,2,6]=>[7,3,5,1,4,2,8,6]=>0011011
[7,3,8,4,5,2,1,6]=>[2,5,7,8,4,1,3,6]=>[8,4,7,2,1,5,3,6]=>1001011
[8,7,2,1,5,3,4,6]=>[2,7,5,3,1,4,8,6]=>[5,3,8,7,2,1,4,6]=>1001011
[5,4,6,8,1,2,7,3]=>[8,1,7,5,4,6,2,3]=>[5,4,6,7,1,2,8,3]=>0001011
[6,8,4,1,3,5,7,2]=>[4,8,2,7,3,6,5,1]=>[6,7,2,3,5,8,4,1]=>0010011
[3,4,7,8,6,2,5,1]=>[5,6,3,4,2,8,7,1]=>[3,4,7,8,6,2,5,1]=>0001101
[4,1,3,5,7,8,6,2]=>[4,6,1,3,5,8,7,2]=>[5,7,8,6,1,3,4,2]=>0010101
[6,5,1,8,4,7,3,2]=>[5,3,6,7,8,2,1,4]=>[8,3,2,7,1,6,5,4]=>0101111
[8,2,7,4,6,1,3,5]=>[6,8,1,7,3,4,2,5]=>[7,1,3,8,4,6,2,5]=>0000111
[4,7,3,2,8,1,6,5]=>[8,3,7,4,6,1,2,5]=>[4,6,3,1,7,2,8,5]=>0100111
[6,3,1,4,7,2,8,5]=>[3,6,7,2,8,4,1,5]=>[8,2,4,7,3,1,6,5]=>0100111
[2,4,7,3,8,5,6,1]=>[6,2,7,4,8,5,3,1]=>[2,4,8,5,7,3,6,1]=>0000111
[2,8,6,1,5,7,3,4]=>[6,2,8,1,3,7,5,4]=>[2,7,1,5,8,6,3,4]=>0000111
[7,8,2,5,4,3,1,6]=>[3,4,5,8,2,1,7,6]=>[7,8,2,5,4,3,1,6]=>0111001
[8,5,3,7,4,2,6,1]=>[6,4,7,5,8,3,2,1]=>[8,5,3,7,4,2,6,1]=>0011111
[5,7,3,2,4,1,8,6]=>[4,3,7,2,5,8,1,6]=>[5,8,3,2,4,1,7,6]=>0110011
[3,8,1,5,6,2,7,4]=>[8,6,3,7,1,5,2,4]=>[3,7,1,5,6,2,8,4]=>0000111
[8,2,5,6,1,7,4,3]=>[6,8,4,7,2,5,1,3]=>[7,4,2,5,8,1,6,3]=>0010111
[6,5,4,8,7,2,1,3]=>[2,7,1,5,6,4,8,3]=>[6,5,4,8,7,2,1,3]=>1001111
[1,8,5,3,6,2,7,4]=>[1,6,5,8,7,4,2,3]=>[1,7,4,8,5,2,6,3]=>0001111
[3,6,2,1,7,5,8,4]=>[2,6,3,8,7,1,5,4]=>[3,7,2,1,8,5,6,4]=>1000111
[6,8,1,4,2,7,3,5]=>[8,4,7,1,3,6,2,5]=>[6,7,1,4,3,8,2,5]=>0010011
[1,8,2,4,5,6,7,3]=>[1,8,7,2,4,5,6,3]=>[1,7,2,4,5,6,8,3]=>0000011
[1,4,7,3,5,6,8,2]=>[1,8,7,4,3,5,6,2]=>[1,4,7,3,5,6,8,2]=>0000011
[1,3,2,7,5,8,6,4]=>[1,3,2,6,8,7,4,5]=>[1,3,2,7,4,8,6,5]=>0100111
[1,4,2,5,8,3,7,6]=>[1,4,8,2,5,7,3,6]=>[1,5,7,2,4,3,8,6]=>0010011
[5,1,2,6,8,4,7,3]=>[5,1,7,8,2,6,4,3]=>[6,8,1,2,7,4,5,3]=>0001011
[3,1,2,6,5,8,4,7]=>[3,1,2,8,6,5,4,7]=>[3,1,2,6,5,8,4,7]=>0100101
[1,5,2,4,8,7,6,3]=>[1,5,6,2,4,7,8,3]=>[1,8,7,6,2,4,5,3]=>0001111
[1,2,7,4,8,6,5,3]=>[1,2,5,6,8,7,4,3]=>[1,2,7,4,8,6,5,3]=>0001111
[1,3,2,7,5,8,4,6]=>[1,3,2,8,7,4,5,6]=>[1,3,2,7,4,8,5,6]=>0100011
[2,3,1,7,5,4,8,6]=>[3,2,1,5,7,8,4,6]=>[2,3,1,8,5,4,7,6]=>0101011
[1,4,2,5,8,7,3,6]=>[1,4,7,2,5,3,8,6]=>[1,5,8,7,2,4,3,6]=>0010011
[1,5,2,4,8,7,3,6]=>[1,5,7,2,4,3,8,6]=>[1,8,7,2,4,5,3,6]=>0001011
[1,2,6,4,8,7,3,5]=>[1,2,7,6,3,4,8,5]=>[1,2,6,3,8,7,4,5]=>0000111
[1,2,7,8,5,6,3,4]=>[1,2,6,3,8,5,7,4]=>[1,2,7,8,5,6,3,4]=>0000101
[1,2,6,8,5,7,3,4]=>[1,2,7,3,8,6,5,4]=>[1,2,6,8,5,7,3,4]=>0000011
[1,5,6,8,2,7,3,4]=>[1,8,7,3,5,6,2,4]=>[1,5,6,7,3,8,2,4]=>0000011
[1,4,7,2,8,6,3,5]=>[1,7,6,4,3,8,2,5]=>[1,4,8,6,3,7,2,5]=>0000111
[1,6,7,8,2,5,3,4]=>[1,8,5,3,2,6,7,4]=>[1,5,3,6,7,8,2,4]=>0001001
[1,5,7,8,2,3,6,4]=>[1,8,2,6,5,3,7,4]=>[1,5,6,2,3,7,8,4]=>0000101
[1,5,2,7,8,4,6,3]=>[1,5,6,8,2,4,7,3]=>[1,7,8,2,6,4,5,3]=>0001101
[1,4,7,2,8,3,6,5]=>[1,7,8,4,6,3,2,5]=>[1,4,6,3,8,2,7,5]=>0000111
[1,3,6,2,4,8,7,5]=>[1,6,3,2,7,4,8,5]=>[1,3,8,7,2,4,6,5]=>0000111
[1,6,7,3,4,8,5,2]=>[1,5,8,2,7,6,4,3]=>[1,6,7,2,4,8,5,3]=>0001011
[2,8,4,1,5,3,7,6]=>[4,2,8,5,3,7,1,6]=>[2,5,3,7,4,1,8,6]=>0011011
[3,8,4,1,5,7,2,6]=>[4,8,3,7,2,1,5,6]=>[3,7,2,8,4,1,5,6]=>0010011
[1,3,6,4,2,8,7,5]=>[1,4,3,6,7,2,8,5]=>[1,3,8,7,4,2,6,5]=>0010111
[1,2,8,4,7,3,6,5]=>[1,2,7,8,6,3,4,5]=>[1,2,6,3,8,4,7,5]=>0000111
[1,2,7,4,8,3,6,5]=>[1,2,8,7,6,3,4,5]=>[1,2,6,3,7,4,8,5]=>0000111
[1,8,4,5,7,2,3,6]=>[1,7,2,8,4,3,5,6]=>[1,8,4,7,2,3,5,6]=>0000011
[2,8,3,5,1,4,7,6]=>[5,2,8,1,3,7,4,6]=>[2,7,1,5,3,4,8,6]=>0001011
[1,3,8,6,2,7,4,5]=>[1,6,3,8,2,7,4,5]=>[1,3,7,2,8,6,4,5]=>0000111
[1,4,8,6,7,2,3,5]=>[1,7,2,4,3,8,6,5]=>[1,4,8,6,7,2,3,5]=>0000011
[1,5,6,8,7,2,3,4]=>[1,7,2,3,5,6,8,4]=>[1,5,6,8,7,2,3,4]=>0000011
[1,2,6,8,5,3,7,4]=>[1,2,5,8,7,6,4,3]=>[1,2,6,7,4,8,5,3]=>0001011
[1,2,5,8,7,3,6,4]=>[1,2,7,6,5,3,8,4]=>[1,2,5,6,3,8,7,4]=>0000111
[1,2,7,8,6,3,5,4]=>[1,2,6,5,3,8,7,4]=>[1,2,5,3,7,8,6,4]=>0001101
[1,5,7,8,6,2,3,4]=>[1,6,2,3,5,8,7,4]=>[1,5,7,8,6,2,3,4]=>0000101
[1,4,7,6,8,2,3,5]=>[1,8,2,4,3,7,6,5]=>[1,4,7,6,8,2,3,5]=>0000011
[1,3,7,6,2,8,4,5]=>[1,6,3,7,2,8,4,5]=>[1,3,8,2,7,6,4,5]=>0000111
[2,3,8,7,4,1,6,5]=>[4,2,3,7,6,1,8,5]=>[2,3,6,4,1,8,7,5]=>0010111
[1,2,8,4,7,6,3,5]=>[1,2,6,7,4,8,3,5]=>[1,2,8,4,7,6,3,5]=>0000111
[1,2,6,8,7,5,3,4]=>[1,2,5,3,7,6,8,4]=>[1,2,6,8,7,5,3,4]=>0001011
[1,2,7,8,6,5,3,4]=>[1,2,5,3,6,8,7,4]=>[1,2,7,8,6,5,3,4]=>0001101
[5,2,4,7,6,3,8,1]=>[8,5,6,2,4,7,3,1]=>[7,6,2,4,5,3,8,1]=>0001111
[5,6,2,1,4,8,7,3]=>[2,6,7,1,5,4,8,3]=>[5,8,7,2,1,4,6,3]=>1000111
[2,3,7,6,4,5,8,1]=>[8,2,3,6,4,7,5,1]=>[2,3,7,6,4,5,8,1]=>0000111
[2,6,1,7,5,8,3,4]=>[6,2,8,3,7,1,5,4]=>[2,7,3,8,5,6,1,4]=>0000111
[5,1,2,7,8,4,3,6]=>[5,1,4,8,2,3,7,6]=>[7,8,4,1,2,5,3,6]=>0011001
[2,6,1,5,4,8,7,3]=>[6,2,7,5,1,4,8,3]=>[2,5,1,8,7,4,6,3]=>0001111
[2,6,1,4,7,8,5,3]=>[6,2,5,1,8,4,7,3]=>[2,7,8,5,1,4,6,3]=>0001101
[5,1,2,4,8,7,3,6]=>[5,1,7,2,4,3,8,6]=>[8,7,1,2,4,5,3,6]=>0001011
[5,1,2,4,8,7,6,3]=>[5,1,6,2,4,7,8,3]=>[8,7,6,1,2,4,5,3]=>0001111
[1,2,3,8,5,4,7,6]=>[1,2,3,5,8,7,4,6]=>[1,2,3,7,5,4,8,6]=>0001011
[1,2,3,8,5,6,4,7]=>[1,2,3,6,8,5,4,7]=>[1,2,3,8,5,6,4,7]=>0000101
[1,2,3,8,6,4,5,7]=>[1,2,3,6,4,8,5,7]=>[1,2,3,8,6,4,5,7]=>0000101
[1,2,3,8,6,5,4,7]=>[1,2,3,5,6,8,4,7]=>[1,2,3,8,6,5,4,7]=>0001101
[1,2,3,8,5,4,6,7]=>[1,2,3,5,8,4,6,7]=>[1,2,3,8,5,4,6,7]=>0001001
[2,5,4,3,1,8,6,7]=>[3,2,4,5,1,8,6,7]=>[2,5,4,3,1,8,6,7]=>0111001
[3,6,4,5,1,8,7,2]=>[5,7,3,6,4,1,8,2]=>[3,6,4,8,7,1,5,2]=>0001111
[3,6,5,4,1,8,7,2]=>[4,5,3,6,7,1,8,2]=>[3,8,7,1,6,5,4,2]=>0011111
[5,2,6,1,7,8,4,3]=>[6,5,4,8,2,1,7,3]=>[7,8,4,2,5,1,6,3]=>0011101
[5,1,6,2,8,7,3,4]=>[5,6,7,3,1,2,8,4]=>[8,7,3,6,1,5,2,4]=>0001111
[2,1,3,7,8,6,4,5]=>[2,1,3,6,4,8,7,5]=>[2,1,3,7,8,6,4,5]=>1000101
[2,1,3,7,8,5,6,4]=>[2,1,3,6,8,5,7,4]=>[2,1,3,7,8,5,6,4]=>1000101
[4,3,1,2,8,6,7,5]=>[3,1,4,2,7,8,6,5]=>[4,3,1,2,8,6,7,5]=>0110011
[5,1,4,2,8,6,7,3]=>[5,4,7,1,2,8,6,3]=>[8,6,7,1,4,2,5,3]=>0011011
[2,1,3,6,8,5,7,4]=>[2,1,3,7,8,6,5,4]=>[2,1,3,6,8,5,7,4]=>1000011
[1,2,3,8,6,7,4,5]=>[1,2,3,7,4,8,6,5]=>[1,2,3,8,6,7,4,5]=>0000011
[1,2,3,8,7,5,4,6]=>[1,2,3,5,7,4,8,6]=>[1,2,3,8,7,5,4,6]=>0001011
[1,2,3,8,7,4,5,6]=>[1,2,3,7,4,5,8,6]=>[1,2,3,8,7,4,5,6]=>0000011
[1,2,3,8,5,7,4,6]=>[1,2,3,7,8,4,5,6]=>[1,2,3,8,4,7,5,6]=>0000011
[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,6,7,8]=>00000001
[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,5,6,7,8]=>00000001
[1,2,3,9,4,5,6,7,8]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,9,4,5,6,7,8]=>00000001
[1,2,9,3,4,5,6,7,8]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,3,4,5,6,7,8]=>00000001
[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,8,9]=>000000001
[1,2,3,4,5,9,7,6,8]=>[1,2,3,4,5,7,9,6,8]=>[1,2,3,4,5,9,7,6,8]=>00000101
[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,7,8,9]=>000000001
[1,2,3,4,9,6,5,7,8]=>[1,2,3,4,6,9,5,7,8]=>[1,2,3,4,9,6,5,7,8]=>00001001
[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,10,6,7,8,9]=>000000001
[1,2,8,4,5,3,6,7]=>[1,2,5,8,4,3,6,7]=>[1,2,8,4,5,3,6,7]=>0001001
[1,2,3,9,5,4,6,7,8]=>[1,2,3,5,9,4,6,7,8]=>[1,2,3,9,5,4,6,7,8]=>00010001
[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,10,5,6,7,8,9]=>000000001
[1,8,3,4,2,5,6,7]=>[1,4,8,3,2,5,6,7]=>[1,8,3,4,2,5,6,7]=>0010001
[1,2,9,4,3,5,6,7,8]=>[1,2,4,9,3,5,6,7,8]=>[1,2,9,4,3,5,6,7,8]=>00100001
[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,10,4,5,6,7,8,9]=>000000001
[1,8,4,3,2,5,6,7]=>[1,3,4,8,2,5,6,7]=>[1,8,4,3,2,5,6,7]=>0110001
[1,9,3,2,4,5,6,7,8]=>[1,3,9,2,4,5,6,7,8]=>[1,9,3,2,4,5,6,7,8]=>01000001
[1,2,10,3,4,5,6,7,8,9]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,10,3,4,5,6,7,8,9]=>000000001
[8,4,7,6,5,3,2,1]=>[2,3,5,6,7,8,4,1]=>[8,4,7,6,5,3,2,1]=>1101111
[8,5,7,3,6,4,2,1]=>[2,4,6,7,8,1,5,3]=>[8,2,1,7,5,6,4,3]=>1010111
[8,2,7,3,6,5,4,1]=>[4,5,6,8,7,2,1,3]=>[7,2,8,1,6,5,4,3]=>0011111
[8,3,7,2,6,5,4,1]=>[4,5,6,7,8,1,2,3]=>[8,1,7,2,6,5,4,3]=>0011111
[8,5,7,2,6,4,3,1]=>[3,4,6,7,8,2,5,1]=>[8,2,7,5,6,4,3,1]=>0110111
[8,6,7,2,5,4,3,1]=>[3,4,5,7,2,8,6,1]=>[8,6,7,2,5,4,3,1]=>0111011
[8,7,6,2,5,4,3,1]=>[3,4,5,6,2,7,8,1]=>[8,7,6,2,5,4,3,1]=>0111111
[8,2,7,1,6,5,4,3]=>[7,8,4,5,6,1,2,3]=>[6,5,4,1,8,2,7,3]=>0011111
[8,3,7,6,5,2,4,1]=>[4,5,6,2,7,8,3,1]=>[8,2,7,6,5,3,4,1]=>0011111
[8,4,7,6,5,2,3,1]=>[3,5,2,6,7,8,4,1]=>[8,4,7,6,5,2,3,1]=>0101111
[8,6,7,5,4,1,3,2]=>[4,3,1,5,7,8,6,2]=>[3,1,8,6,7,5,4,2]=>0111011
[8,5,7,6,4,1,3,2]=>[4,3,1,6,7,8,2,5]=>[3,1,8,4,2,7,6,5]=>0110111
[8,3,7,6,5,1,4,2]=>[5,4,6,1,7,8,3,2]=>[8,1,4,3,7,6,5,2]=>0011111
[8,7,6,2,5,1,4,3]=>[5,6,4,1,2,7,8,3]=>[4,1,8,7,6,2,5,3]=>0011111
[8,7,6,1,5,2,4,3]=>[6,5,4,2,1,7,8,3]=>[4,2,5,1,8,7,6,3]=>0011111
[6,8,1,4,2,5,3,7]=>[8,4,5,1,2,6,3,7]=>[5,1,4,2,6,8,3,7]=>0011001
[7,8,3,6,1,4,2,5]=>[6,4,8,1,2,3,7,5]=>[7,8,1,4,2,6,3,5]=>0010101
[5,8,1,4,3,7,2,6]=>[8,7,4,1,5,2,3,6]=>[4,1,5,7,2,8,3,6]=>0010011
[2,5,3,7,6,8,1,4]=>[8,2,5,1,3,7,6,4]=>[2,5,1,7,6,8,3,4]=>0001011
[2,6,5,8,1,4,3,7]=>[8,2,4,1,6,5,3,7]=>[2,4,1,6,5,8,3,7]=>0010101
[2,6,4,7,5,8,1,3]=>[8,2,1,6,7,4,5,3]=>[2,7,4,6,5,8,1,3]=>0000111
[5,8,2,6,4,7,1,3]=>[7,8,1,6,5,2,4,3]=>[5,6,1,8,4,7,2,3]=>0000111
[4,8,1,5,3,7,2,6]=>[8,7,5,4,1,2,3,6]=>[4,5,1,7,2,8,3,6]=>0001011
[4,8,3,7,1,5,2,6]=>[7,5,8,4,1,2,3,6]=>[4,8,1,5,2,7,3,6]=>0001011
[5,8,1,3,2,6,4,7]=>[8,3,1,6,5,2,4,7]=>[3,1,5,6,2,8,4,7]=>0100101
[6,8,5,7,1,3,2,4]=>[7,3,1,2,8,6,5,4]=>[3,1,6,8,5,7,2,4]=>0100011
[4,7,5,8,1,3,2,6]=>[8,3,1,4,7,2,5,6]=>[3,1,4,7,2,8,5,6]=>0100011
[3,7,6,8,1,4,2,5]=>[8,4,3,1,2,7,6,5]=>[3,4,1,7,6,8,2,5]=>0010011
[3,7,6,8,2,5,1,4]=>[5,8,3,1,2,7,6,4]=>[3,7,6,8,1,5,2,4]=>0001011
[4,7,5,8,3,6,1,2]=>[6,1,8,4,7,3,5,2]=>[4,7,3,8,5,6,1,2]=>0000111
[4,7,5,8,2,6,1,3]=>[6,8,1,4,7,2,5,3]=>[4,7,1,8,5,6,2,3]=>0000111
[3,7,5,8,2,6,1,4]=>[6,8,3,1,7,2,5,4]=>[3,7,1,8,5,6,2,4]=>0000111
[3,7,4,8,1,5,2,6]=>[8,5,3,7,1,2,4,6]=>[3,7,1,5,2,8,4,6]=>0001011
[3,7,2,6,5,8,1,4]=>[8,7,3,1,6,2,5,4]=>[3,6,1,7,5,8,2,4]=>0000111
[4,7,3,6,5,8,1,2]=>[8,1,7,4,6,3,5,2]=>[4,6,3,7,5,8,1,2]=>0000111
[3,6,5,8,4,7,1,2]=>[7,1,3,8,6,5,4,2]=>[3,6,5,8,4,7,1,2]=>0000111
[2,6,5,8,4,7,1,3]=>[7,2,1,8,6,5,4,3]=>[2,6,5,8,4,7,1,3]=>0000111
[2,6,5,8,3,7,1,4]=>[7,2,8,1,6,5,3,4]=>[2,6,5,8,1,7,3,4]=>0000111
[6,8,4,3,7,2,1,5]=>[2,7,4,8,1,6,3,5]=>[6,8,4,2,1,7,3,5]=>1010011
[6,7,4,3,5,1,8,2]=>[5,8,4,7,3,6,1,2]=>[6,7,4,3,8,1,5,2]=>0011011
[6,7,3,5,4,8,2,1]=>[2,8,7,5,3,6,4,1]=>[5,3,6,7,4,8,2,1]=>1001011
[6,8,3,7,5,2,4,1]=>[4,5,7,3,8,6,2,1]=>[6,8,3,7,5,2,4,1]=>0011011
[7,6,8,3,5,2,4,1]=>[4,5,8,2,3,7,6,1]=>[7,6,8,2,5,3,4,1]=>0011011
[7,6,4,2,5,1,8,3]=>[5,4,6,7,2,8,1,3]=>[8,2,7,6,4,1,5,3]=>0011111
[7,6,3,8,2,4,1,5]=>[4,8,6,2,1,7,3,5]=>[7,6,2,8,1,4,3,5]=>0010111
[6,8,3,7,4,5,2,1]=>[2,5,8,7,4,6,3,1]=>[6,7,4,8,3,5,2,1]=>1001011
[6,7,3,5,8,4,2,1]=>[2,4,8,7,1,6,5,3]=>[6,7,2,1,5,8,4,3]=>1010011
[5,7,8,3,6,2,1,4]=>[2,6,8,1,5,3,7,4]=>[5,7,8,2,1,6,3,4]=>1000101
[6,3,4,8,7,2,5,1]=>[5,7,6,3,2,4,8,1]=>[6,3,8,7,2,4,5,1]=>0001111
[5,7,3,6,8,2,1,4]=>[2,8,7,1,5,3,6,4]=>[5,7,2,1,6,8,3,4]=>1000011
[4,6,8,3,5,7,2,1]=>[2,7,8,4,3,6,5,1]=>[4,6,8,3,5,7,2,1]=>1000011
[4,7,3,5,8,2,6,1]=>[6,8,7,4,3,2,5,1]=>[4,7,3,8,2,5,6,1]=>0000111
[5,3,4,7,8,2,1,6]=>[2,8,5,3,4,1,7,6]=>[5,3,4,7,8,2,1,6]=>1001001
[5,3,8,2,4,1,6,7]=>[4,8,5,2,3,1,6,7]=>[5,2,8,3,4,1,6,7]=>0011001
[5,3,4,8,2,6,1,7]=>[6,8,5,3,4,2,1,7]=>[5,3,4,8,2,6,1,7]=>0001101
[4,8,3,6,2,5,7,1]=>[7,6,8,4,2,3,5,1]=>[4,8,2,6,3,5,7,1]=>0000111
[4,8,3,5,7,2,6,1]=>[6,7,8,4,3,2,5,1]=>[4,8,3,7,2,5,6,1]=>0000111
[4,8,3,5,6,7,2,1]=>[2,7,8,4,3,5,6,1]=>[4,8,3,5,6,7,2,1]=>1000011
[4,7,8,3,5,6,2,1]=>[2,6,8,4,3,5,7,1]=>[4,7,8,3,5,6,2,1]=>1000101
[5,2,8,4,1,7,3,6]=>[4,8,5,7,3,1,2,6]=>[7,3,5,1,8,4,2,6]=>0011011
[6,4,3,5,8,2,1,7]=>[2,8,4,6,3,5,1,7]=>[6,4,3,5,8,2,1,7]=>1010101
[5,7,3,4,8,2,1,6]=>[2,8,7,3,5,1,4,6]=>[5,7,3,8,2,1,4,6]=>1000011
[5,8,4,2,3,1,6,7]=>[3,4,2,8,5,1,6,7]=>[5,8,4,2,3,1,6,7]=>0110001
[6,4,5,3,8,2,1,7]=>[2,8,5,6,4,3,1,7]=>[6,4,5,3,8,2,1,7]=>1001101
[6,4,8,5,3,7,2,1]=>[2,7,5,8,6,3,4,1]=>[6,3,8,5,4,7,2,1]=>1001111
[6,4,5,3,7,1,8,2]=>[7,8,5,6,4,3,1,2]=>[6,4,5,3,8,1,7,2]=>0001111
[5,6,3,7,1,8,2,4]=>[7,8,6,2,5,3,1,4]=>[5,6,2,8,3,7,1,4]=>0000111
[5,6,3,4,8,2,1,7]=>[2,8,6,3,5,4,1,7]=>[5,6,3,4,8,2,1,7]=>1000101
[6,4,3,5,7,1,8,2]=>[7,8,4,6,3,5,1,2]=>[6,4,3,5,8,1,7,2]=>0010111
[5,3,4,7,2,6,1,8]=>[6,7,5,3,4,2,1,8]=>[5,3,4,7,2,6,1,8]=>0001110
[4,7,3,6,2,5,8,1]=>[8,6,7,4,2,3,5,1]=>[4,7,2,6,3,5,8,1]=>0000111
[4,5,8,3,6,7,2,1]=>[2,7,8,4,5,3,6,1]=>[4,5,8,3,6,7,2,1]=>1000011
[5,3,4,6,8,2,1,7]=>[2,8,5,3,4,6,1,7]=>[5,3,4,6,8,2,1,7]=>1001001
[5,3,6,7,1,8,2,4]=>[7,8,5,2,3,6,1,4]=>[5,2,6,8,3,7,1,4]=>0001011
[4,6,3,5,7,8,2,1]=>[2,8,6,4,3,5,7,1]=>[4,6,3,5,7,8,2,1]=>1000101
[4,5,6,8,3,7,2,1]=>[2,7,8,4,5,6,3,1]=>[4,5,6,8,3,7,2,1]=>1000011
[3,2,6,5,1,8,7,4]=>[5,3,2,6,7,4,8,1]=>[3,2,8,7,4,6,5,1]=>0101111
[3,5,6,7,2,8,4,1]=>[4,8,3,7,5,6,1,2]=>[3,5,6,7,1,8,4,2]=>0010011
[7,6,9,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,9,1]=>[7,6,9,8,5,4,3,2,1]=>11110111
[6,7,8,9,5,4,3,2,1]=>[2,3,4,5,9,6,7,8,1]=>[6,7,8,9,5,4,3,2,1]=>11110001
[5,6,7,8,9,4,3,2,1]=>[2,3,4,9,5,6,7,8,1]=>[5,6,7,8,9,4,3,2,1]=>11100001
[4,5,6,7,8,9,3,2,1]=>[2,3,9,4,5,6,7,8,1]=>[4,5,6,7,8,9,3,2,1]=>11000001
[3,4,5,6,7,8,9,2,1]=>[2,9,3,4,5,6,7,8,1]=>[3,4,5,6,7,8,9,2,1]=>10000001
[8,9,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,8,9,1]=>[8,9,10,7,6,5,4,3,2,1]=>111111001
[7,8,9,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,7,8,9,1]=>[7,8,9,10,6,5,4,3,2,1]=>111110001
[5,4,3,2,1,10,9,8,7,6]=>[2,3,4,5,1,7,8,9,10,6]=>[5,4,3,2,1,10,9,8,7,6]=>111101111
[5,6,7,8,9,10,4,3,2,1]=>[2,3,4,10,5,6,7,8,9,1]=>[5,6,7,8,9,10,4,3,2,1]=>111000001
[4,5,6,7,8,9,10,3,2,1]=>[2,3,10,4,5,6,7,8,9,1]=>[4,5,6,7,8,9,10,3,2,1]=>110000001
[3,4,5,6,7,8,9,10,2,1]=>[2,10,3,4,5,6,7,8,9,1]=>[3,4,5,6,7,8,9,10,2,1]=>100000001
[1,3,8,2,4,6,5,7]=>[1,8,3,2,6,4,5,7]=>[1,3,6,2,4,8,5,7]=>0000101
[1,8,2,3,6,4,7,5]=>[1,8,2,6,7,3,4,5]=>[1,7,2,3,6,4,8,5]=>0000111
[1,3,5,2,8,4,7,6]=>[1,5,3,8,2,7,4,6]=>[1,3,7,2,5,4,8,6]=>0001011
[1,2,7,3,5,4,6,8]=>[1,2,7,5,3,4,6,8]=>[1,2,5,3,7,4,6,8]=>0001010
[1,5,8,2,3,7,4,6]=>[1,8,2,7,5,4,3,6]=>[1,5,7,4,8,2,3,6]=>0000011
[1,6,8,2,3,5,4,7]=>[1,8,2,5,3,6,4,7]=>[1,5,2,3,6,8,4,7]=>0001001
[5,3,6,1,2,4,8,7]=>[6,1,5,2,3,4,8,7]=>[5,1,2,6,3,4,8,7]=>0001101
[7,1,5,8,4,2,3,6]=>[7,4,2,8,1,3,5,6]=>[8,4,2,7,1,3,5,6]=>0010011
[8,1,5,7,4,2,3,6]=>[8,4,2,7,1,3,5,6]=>[7,4,2,8,1,3,5,6]=>0010011
[7,1,4,5,8,2,3,6]=>[7,8,2,1,4,3,5,6]=>[8,2,4,7,1,3,5,6]=>0000011
[8,4,1,7,2,6,3,5]=>[4,8,7,6,1,3,2,5]=>[6,1,7,3,8,4,2,5]=>0010111
[8,1,5,4,7,2,3,6]=>[8,7,2,5,1,3,4,6]=>[5,2,7,1,3,8,4,6]=>0001011
[2,1,7,5,8,3,4,6]=>[2,1,8,3,7,4,5,6]=>[2,1,7,3,4,8,5,6]=>1000011
[7,1,5,4,8,2,3,6]=>[7,8,2,5,1,3,4,6]=>[5,2,8,1,3,7,4,6]=>0001011
[7,1,4,8,5,2,3,6]=>[7,5,2,1,8,3,4,6]=>[8,5,2,7,1,3,4,6]=>0001011
[6,4,1,7,2,3,8,5]=>[4,6,1,7,8,2,3,5]=>[8,1,7,4,2,3,6,5]=>0010111
[7,8,3,1,2,4,6,5]=>[3,1,8,2,6,4,7,5]=>[6,3,1,2,4,7,8,5]=>0100101
[7,6,1,8,4,2,3,5]=>[6,4,1,7,3,8,2,5]=>[8,4,1,3,7,6,2,5]=>0010111
[7,3,8,1,2,4,6,5]=>[8,1,7,2,6,4,3,5]=>[6,1,2,4,7,3,8,5]=>0000111
[8,3,7,1,2,4,6,5]=>[7,1,8,2,6,4,3,5]=>[6,1,2,4,8,3,7,5]=>0000111
[8,3,7,5,1,2,4,6]=>[5,1,7,3,8,4,2,6]=>[8,3,4,7,5,1,2,6]=>0001011
[7,3,6,1,2,4,8,5]=>[6,1,7,2,8,3,4,5]=>[8,1,2,7,3,4,6,5]=>0000111
[7,1,8,5,4,2,3,6]=>[7,4,2,5,8,3,1,6]=>[8,5,4,2,3,7,1,6]=>0011011
[7,1,8,4,5,2,3,6]=>[7,5,2,8,4,3,1,6]=>[8,4,5,2,3,7,1,6]=>0001011
[2,1,7,8,5,3,4,6]=>[2,1,5,3,8,4,7,6]=>[2,1,7,8,5,3,4,6]=>1001001
[6,1,2,3,8,7,5,4]=>[6,1,2,5,7,3,8,4]=>[8,7,5,1,2,3,6,4]=>0001111
[6,8,1,4,2,3,7,5]=>[8,4,2,1,7,6,3,5]=>[4,2,6,7,1,3,8,5]=>0010011
[6,7,1,4,2,3,8,5]=>[7,4,2,1,8,6,3,5]=>[4,2,6,8,1,3,7,5]=>0010011
[4,3,6,8,5,7,1,2]=>[7,1,4,3,8,6,5,2]=>[4,3,6,8,5,7,1,2]=>0010011
[7,2,1,5,8,3,4,6]=>[2,7,8,3,1,4,5,6]=>[8,3,7,2,1,4,5,6]=>1000011
[3,5,6,1,8,4,2,7]=>[6,4,3,8,5,1,2,7]=>[3,5,8,4,1,6,2,7]=>0010101
[5,7,1,6,8,4,3,2]=>[7,3,4,8,5,1,6,2]=>[5,8,4,3,1,6,7,2]=>0110011
[4,8,1,2,5,7,3,6]=>[8,1,7,4,2,3,5,6]=>[4,7,1,2,8,3,5,6]=>0000011
[8,3,6,4,7,2,5,1]=>[5,7,8,6,2,3,4,1]=>[6,2,8,3,7,4,5,1]=>0001111
[3,7,1,6,5,4,8,2]=>[7,8,3,5,6,1,4,2]=>[3,6,5,1,8,4,7,2]=>0001111
[2,7,3,1,5,8,4,6]=>[3,2,7,8,1,4,5,6]=>[2,8,3,1,7,4,5,6]=>0100011
[8,2,6,7,5,4,3,1]=>[3,4,5,7,8,1,6,2]=>[8,1,6,7,5,4,3,2]=>0111011
[3,8,7,1,6,4,5,2]=>[7,5,3,6,4,1,8,2]=>[3,6,4,5,1,8,7,2]=>0001111
[3,6,8,2,7,4,1,5]=>[4,7,3,8,2,6,1,5]=>[3,6,8,2,7,4,1,5]=>0010011
[1,5,2,8,7,4,6,3]=>[1,5,6,7,2,4,8,3]=>[1,8,7,2,6,4,5,3]=>0001111
[4,1,3,7,5,6,8,2]=>[4,8,1,3,7,5,6,2]=>[7,5,6,8,1,3,4,2]=>0010011
[4,1,7,3,8,5,2,6]=>[4,5,8,1,7,3,2,6]=>[7,1,8,5,3,4,2,6]=>0011011
[3,6,1,4,5,8,2,7]=>[6,8,3,1,4,5,2,7]=>[3,8,1,4,5,6,2,7]=>0000101
[1,6,7,4,5,3,8,2]=>[1,8,5,7,4,6,3,2]=>[1,6,7,4,5,3,8,2]=>0001011
[6,1,7,3,5,4,8,2]=>[6,8,7,5,3,1,4,2]=>[5,3,7,1,8,4,6,2]=>0001111
[5,6,8,7,2,4,1,3]=>[4,7,1,2,5,6,8,3]=>[5,6,8,7,1,4,2,3]=>0010011
[6,8,5,7,1,2,4,3]=>[7,1,4,2,8,6,5,3]=>[4,1,2,6,8,5,7,3]=>0010011
[2,8,4,1,7,5,6,3]=>[4,2,8,6,7,5,3,1]=>[2,7,5,6,3,8,4,1]=>0010111
[8,2,4,3,7,5,6,1]=>[6,8,4,2,7,5,3,1]=>[4,2,7,5,8,3,6,1]=>0010111
[7,2,8,4,1,6,3,5]=>[4,8,7,6,1,2,3,5]=>[6,1,7,2,8,4,3,5]=>0010111
[4,1,6,8,5,3,7,2]=>[4,7,5,1,8,6,3,2]=>[6,8,5,1,7,3,4,2]=>0011011
[1,7,3,2,4,8,5,6]=>[1,3,7,2,8,5,4,6]=>[1,8,5,7,3,2,4,6]=>0100011
[7,1,6,5,3,4,8,2]=>[7,8,5,3,6,1,4,2]=>[6,5,3,8,1,4,7,2]=>0001111
[6,3,4,2,8,7,5,1]=>[5,4,7,1,6,2,8,3]=>[6,1,4,2,8,7,5,3]=>0011111
[4,3,8,7,5,2,6,1]=>[6,5,4,3,7,2,8,1]=>[4,3,8,7,5,2,6,1]=>0011111
[6,8,7,4,2,3,5,1]=>[5,4,2,7,3,6,8,1]=>[6,8,7,4,2,3,5,1]=>0011011
[3,6,4,5,2,8,7,1]=>[7,5,3,6,4,2,8,1]=>[3,6,4,5,2,8,7,1]=>0001111
[8,6,1,3,5,4,2,7]=>[6,4,1,5,3,8,2,7]=>[5,4,1,3,8,6,2,7]=>0011101
[5,3,8,6,1,2,4,7]=>[6,1,5,2,3,8,4,7]=>[5,1,2,8,6,3,4,7]=>0001101
[2,5,6,3,4,8,7,1]=>[7,2,6,3,5,4,8,1]=>[2,5,6,3,4,8,7,1]=>0000111
[4,8,7,3,5,2,6,1]=>[6,5,7,4,3,2,8,1]=>[4,8,7,3,5,2,6,1]=>0001111
[3,8,7,2,6,4,5,1]=>[5,7,3,6,4,2,8,1]=>[3,6,4,8,7,2,5,1]=>0001111
[6,3,5,4,8,7,2,1]=>[2,7,6,5,3,4,8,1]=>[5,3,6,4,8,7,2,1]=>1001111
[4,3,8,6,1,5,2,7]=>[6,5,4,3,1,8,2,7]=>[4,3,5,1,8,6,2,7]=>0011101
[4,7,6,2,5,3,8,1]=>[8,6,5,4,2,7,3,1]=>[4,5,2,7,6,3,8,1]=>0001111
[7,5,2,6,8,1,4,3]=>[8,5,4,1,7,2,6,3]=>[4,1,7,5,2,6,8,3]=>0011011
[1,8,5,3,6,2,4,7]=>[1,6,5,2,8,3,4,7]=>[1,8,5,2,6,3,4,7]=>0001101
[5,1,7,2,4,3,8,6]=>[5,7,4,2,1,8,3,6]=>[4,2,8,1,5,3,7,6]=>0011011
[1,5,3,4,8,6,2,7]=>[1,6,5,3,4,8,2,7]=>[1,5,3,4,8,6,2,7]=>0001101
[5,4,1,3,8,6,2,7]=>[4,5,2,6,3,8,1,7]=>[8,6,2,3,5,4,1,7]=>0011101
[5,1,8,6,3,4,2,7]=>[5,4,6,3,1,8,2,7]=>[8,6,3,4,1,5,2,7]=>0011101
[8,2,3,7,6,4,5,1]=>[5,8,2,6,4,7,3,1]=>[7,6,4,8,2,3,5,1]=>0001111
[5,8,2,4,7,6,3,1]=>[3,6,7,2,5,8,4,1]=>[5,8,2,4,7,6,3,1]=>0100111
[6,8,2,5,3,4,7,1]=>[7,8,5,3,2,6,4,1]=>[5,3,6,8,2,4,7,1]=>0001011
[1,6,7,4,8,2,3,5]=>[1,8,2,7,3,6,4,5]=>[1,6,7,2,3,8,4,5]=>0000011
[8,2,1,3,5,6,7,4]=>[2,8,1,7,3,5,6,4]=>[7,2,1,3,5,6,8,4]=>1000011
[4,1,3,8,2,6,7,5]=>[4,8,1,3,7,2,6,5]=>[7,1,3,4,2,6,8,5]=>0010011
[3,1,7,2,8,5,4,6]=>[3,7,1,5,8,4,2,6]=>[8,5,4,7,1,3,2,6]=>0101011
[3,6,1,4,7,2,8,5]=>[6,7,3,1,8,4,2,5]=>[3,8,1,4,7,2,6,5]=>0000111
[1,5,8,4,7,2,3,6]=>[1,7,2,8,5,3,4,6]=>[1,5,8,2,3,7,4,6]=>0000011
[7,1,3,6,2,8,4,5]=>[7,6,1,8,4,3,2,5]=>[8,4,6,1,3,7,2,5]=>0000111
[1,8,5,7,3,2,4,6]=>[1,3,7,2,8,4,5,6]=>[1,8,3,2,4,7,5,6]=>0100011
[2,1,8,5,4,3,6,7]=>[2,1,4,5,8,3,6,7]=>[2,1,8,5,4,3,6,7]=>1011001
[7,4,8,6,2,3,1,5]=>[3,6,2,8,4,7,1,5]=>[7,4,8,6,2,3,1,5]=>0100111
[7,1,3,2,8,5,4,6]=>[7,3,1,5,8,4,2,6]=>[3,1,8,5,4,7,2,6]=>0101011
[2,8,5,4,1,3,6,7]=>[4,2,1,5,8,3,6,7]=>[2,8,5,4,1,3,6,7]=>0011001
[5,1,7,4,2,3,8,6]=>[5,4,2,7,1,8,3,6]=>[8,4,2,5,1,3,7,6]=>0011011
[1,3,4,8,6,5,2,7]=>[1,5,3,4,6,8,2,7]=>[1,3,4,8,6,5,2,7]=>0001101
[8,4,7,5,2,3,6,1]=>[6,5,2,7,8,4,3,1]=>[8,4,7,5,2,3,6,1]=>0001111
[5,7,4,3,6,2,8,1]=>[8,6,4,7,5,3,2,1]=>[5,7,4,3,6,2,8,1]=>0010111
[7,6,2,4,5,8,3,1]=>[3,8,6,1,4,7,5,2]=>[7,6,1,4,5,8,3,2]=>0100111
[7,6,3,8,4,2,5,1]=>[5,4,8,6,3,7,2,1]=>[7,6,3,8,4,2,5,1]=>0011111
[2,6,3,8,4,7,5,1]=>[5,2,7,6,8,4,1,3]=>[2,8,4,6,1,7,5,3]=>0001111
[7,2,3,6,5,8,4,1]=>[4,8,1,7,6,3,5,2]=>[6,1,3,7,5,8,4,2]=>0010111
[2,8,3,6,4,5,7,1]=>[7,2,8,6,4,3,5,1]=>[2,6,4,8,3,5,7,1]=>0000111
[2,1,5,6,8,3,7,4]=>[2,1,8,7,5,6,3,4]=>[2,1,5,6,7,3,8,4]=>1000011
[5,8,1,2,6,4,7,3]=>[8,1,7,6,5,2,4,3]=>[5,6,1,2,7,4,8,3]=>0000111
[1,6,8,3,2,7,4,5]=>[1,3,8,7,4,6,2,5]=>[1,6,7,4,8,3,2,5]=>0100011
[6,5,7,2,8,4,1,3]=>[4,8,2,7,6,5,1,3]=>[6,5,7,2,8,4,1,3]=>0010111
[7,5,1,2,8,4,6,3]=>[5,1,7,6,8,2,3,4]=>[8,1,2,6,3,7,5,4]=>0001111
[5,4,8,3,6,2,7,1]=>[7,6,8,5,4,3,2,1]=>[5,4,8,3,6,2,7,1]=>0001111
[5,8,2,7,4,3,6,1]=>[6,8,4,7,5,3,2,1]=>[5,7,4,3,8,2,6,1]=>0010111
[5,7,3,6,4,8,2,1]=>[2,8,7,6,5,3,4,1]=>[5,6,3,7,4,8,2,1]=>1000111
[1,4,6,3,5,7,8,2]=>[1,8,6,4,3,5,7,2]=>[1,4,6,3,5,7,8,2]=>0000101
[3,5,1,6,4,7,8,2]=>[5,8,3,6,1,4,7,2]=>[3,6,1,7,8,4,5,2]=>0001101
[2,4,6,3,1,7,8,5]=>[3,2,6,4,8,1,7,5]=>[2,4,7,8,3,1,6,5]=>0100101
[1,3,6,5,2,7,8,4]=>[1,5,3,6,8,4,7,2]=>[1,3,7,8,4,6,5,2]=>0001101
[1,2,6,4,3,8,5,7]=>[1,2,4,6,8,3,5,7]=>[1,2,8,4,3,6,5,7]=>0010101
[1,2,7,4,6,8,3,5]=>[1,2,8,7,3,4,6,5]=>[1,2,7,3,6,8,4,5]=>0000011
[1,2,7,6,4,8,5,3]=>[1,2,5,8,6,7,3,4]=>[1,2,7,6,3,8,5,4]=>0001111
[3,1,5,4,8,7,6,2]=>[3,6,1,5,4,7,8,2]=>[5,4,8,7,6,1,3,2]=>0101111
[1,2,5,8,4,7,3,6]=>[1,2,7,8,5,3,4,6]=>[1,2,5,8,3,7,4,6]=>0000011
[1,2,6,8,5,4,7,3]=>[1,2,7,5,8,6,4,3]=>[1,2,6,8,5,4,7,3]=>0001011
[1,3,6,8,5,2,7,4]=>[1,5,3,8,7,6,4,2]=>[1,3,6,7,4,8,5,2]=>0001011
[2,4,7,6,8,3,1,5]=>[3,2,8,4,1,7,6,5]=>[2,4,7,6,8,3,1,5]=>0100011
[1,3,6,8,5,2,4,7]=>[1,5,3,2,8,6,4,7]=>[1,3,6,8,5,2,4,7]=>0001001
[1,2,6,8,5,4,3,7]=>[1,2,4,5,8,6,3,7]=>[1,2,6,8,5,4,3,7]=>0011001
[1,2,5,8,4,3,7,6]=>[1,2,4,8,5,7,3,6]=>[1,2,5,7,4,3,8,6]=>0010011
[1,3,5,8,2,4,7,6]=>[1,8,3,2,5,7,4,6]=>[1,3,5,7,2,4,8,6]=>0000011
[1,3,6,8,2,5,4,7]=>[1,8,3,5,2,6,4,7]=>[1,3,5,2,6,8,4,7]=>0001001
[1,4,6,8,3,2,5,7]=>[1,3,8,4,2,6,5,7]=>[1,4,6,8,3,2,5,7]=>0100001
[4,6,1,7,5,8,2,3]=>[6,8,2,4,7,1,5,3]=>[4,7,2,8,5,6,1,3]=>0000111
[2,3,6,7,5,8,1,4]=>[8,2,3,1,7,6,5,4]=>[2,3,6,7,5,8,1,4]=>0000011
[1,3,7,5,6,8,2,4]=>[1,8,3,2,7,5,6,4]=>[1,3,7,5,6,8,2,4]=>0000011
[3,4,6,2,8,1,7,5]=>[8,6,3,4,7,2,1,5]=>[3,4,7,2,6,1,8,5]=>0000111
[3,5,4,6,8,1,2,7]=>[8,1,3,5,4,6,2,7]=>[3,5,4,6,8,1,2,7]=>0001001
[1,2,4,7,5,8,3,6]=>[1,2,8,4,7,3,5,6]=>[1,2,4,7,3,8,5,6]=>0000011
[3,6,4,7,1,8,5,2]=>[7,5,3,8,6,2,1,4]=>[3,6,2,8,5,1,7,4]=>0001111
[1,2,6,7,3,8,5,4]=>[1,2,7,5,8,6,3,4]=>[1,2,6,8,5,3,7,4]=>0001011
[1,2,5,7,3,8,6,4]=>[1,2,7,6,5,8,3,4]=>[1,2,5,8,6,3,7,4]=>0000111
[3,1,5,7,6,8,4,2]=>[3,4,1,8,5,7,6,2]=>[5,7,6,8,4,1,3,2]=>0110011
[4,2,6,1,8,7,5,3]=>[6,4,5,2,7,1,8,3]=>[8,7,5,2,4,1,6,3]=>0011111
[1,2,7,4,6,8,5,3]=>[1,2,5,8,7,3,6,4]=>[1,2,7,3,6,8,5,4]=>0001011
[3,1,6,7,5,8,4,2]=>[3,4,1,8,7,6,5,2]=>[6,7,5,8,4,1,3,2]=>0110011
[4,6,2,7,5,8,3,1]=>[3,8,6,4,7,1,5,2]=>[4,7,1,6,5,8,3,2]=>0100111
[3,5,7,4,8,2,6,1]=>[6,8,3,7,5,2,4,1]=>[3,5,7,2,8,4,6,1]=>0000111
[2,4,7,6,8,3,5,1]=>[5,2,8,4,3,7,6,1]=>[2,4,7,6,8,3,5,1]=>0001011
[1,4,6,8,3,5,7,2]=>[1,7,8,4,3,6,5,2]=>[1,4,6,8,3,5,7,2]=>0000011
[1,3,6,8,2,5,7,4]=>[1,8,3,7,2,6,5,4]=>[1,3,6,7,2,5,8,4]=>0000011
[1,2,5,8,4,7,6,3]=>[1,2,6,7,5,8,3,4]=>[1,2,5,8,3,7,6,4]=>0000111
[1,2,4,8,7,3,6,5]=>[1,2,7,4,6,3,8,5]=>[1,2,4,6,3,8,7,5]=>0000111
[1,3,5,8,7,2,4,6]=>[1,7,3,2,5,4,8,6]=>[1,3,5,8,7,2,4,6]=>0000011
[5,7,1,2,8,6,4,3]=>[7,1,4,6,5,8,2,3]=>[5,8,6,4,1,2,7,3]=>0010111
[1,2,6,8,5,7,4,3]=>[1,2,4,7,8,6,5,3]=>[1,2,6,8,5,7,4,3]=>0010011
[1,2,4,8,7,6,3,5]=>[1,2,6,4,3,7,8,5]=>[1,2,4,8,7,6,3,5]=>0000111
[6,4,5,7,2,8,1,3]=>[8,7,1,6,4,5,2,3]=>[6,4,5,7,1,8,2,3]=>0000111
[3,7,4,5,6,8,1,2]=>[8,1,3,7,4,5,6,2]=>[3,7,4,5,6,8,1,2]=>0000011
[5,3,1,2,8,4,7,6]=>[3,1,5,8,2,7,4,6]=>[7,3,1,2,5,4,8,6]=>0101011
[6,5,2,3,7,1,4,8]=>[7,5,2,1,6,3,4,8]=>[6,5,2,7,1,3,4,8]=>0001110
[5,2,1,7,3,4,6,8]=>[2,5,7,3,1,4,6,8]=>[7,3,5,2,1,4,6,8]=>1001010
[5,2,1,8,3,4,6,7]=>[2,5,8,3,1,4,6,7]=>[8,3,5,2,1,4,6,7]=>1001001
[6,4,1,3,8,5,7,2]=>[4,6,2,7,8,3,5,1]=>[8,2,3,7,5,6,4,1]=>0010111
[6,2,3,1,8,4,7,5]=>[3,6,2,8,7,1,4,5]=>[7,2,3,1,8,4,6,5]=>0100111
[8,3,5,2,7,1,4,6]=>[7,5,8,1,3,4,2,6]=>[8,1,5,3,4,7,2,6]=>0001011
[8,2,1,7,3,4,5,6]=>[2,8,7,3,4,5,1,6]=>[7,3,4,5,8,2,1,6]=>1000011
[8,6,3,7,2,4,5,1]=>[5,7,6,2,4,8,3,1]=>[8,6,2,4,7,3,5,1]=>0001111
[8,2,7,3,4,5,6,1]=>[6,8,7,3,4,5,2,1]=>[7,3,4,5,8,2,6,1]=>0000111
[8,1,6,2,3,4,5,7]=>[8,6,2,3,4,1,5,7]=>[6,2,3,4,8,1,5,7]=>0000101
[8,1,7,3,4,5,6,2]=>[8,6,7,3,4,5,1,2]=>[7,3,4,5,6,1,8,2]=>0000111
[7,2,1,8,3,4,5,6]=>[2,7,8,3,4,5,1,6]=>[8,3,4,5,7,2,1,6]=>1000011
[7,3,8,2,4,5,6,1]=>[6,8,7,2,4,5,3,1]=>[7,2,4,5,8,3,6,1]=>0000111
[1,7,8,3,4,5,6,2]=>[1,6,8,3,4,5,7,2]=>[1,7,8,3,4,5,6,2]=>0000101
[1,4,5,8,3,6,7,2]=>[1,7,8,4,5,3,6,2]=>[1,4,5,8,3,6,7,2]=>0000011
[6,2,7,1,8,4,5,3]=>[7,6,5,8,4,2,1,3]=>[8,4,5,2,6,1,7,3]=>0001111
[5,3,4,6,8,2,7,1]=>[7,8,5,3,4,6,2,1]=>[5,3,4,6,8,2,7,1]=>0001011
[4,6,3,8,7,1,2,5]=>[7,1,6,4,2,3,8,5]=>[4,6,1,2,8,7,3,5]=>0000111
[6,4,5,8,7,1,2,3]=>[7,1,2,6,4,5,8,3]=>[6,4,5,8,7,1,2,3]=>0000111
[5,3,4,8,7,1,2,6]=>[7,1,5,3,4,2,8,6]=>[5,3,4,8,7,1,2,6]=>0001011
[3,2,8,7,1,4,6,5]=>[7,3,2,1,6,4,8,5]=>[3,2,6,1,4,8,7,5]=>0100111
[4,7,8,2,6,1,3,5]=>[6,8,1,4,3,2,7,5]=>[4,7,8,1,3,6,2,5]=>0000101
[6,2,8,7,1,4,5,3]=>[7,6,5,1,4,2,8,3]=>[5,1,4,6,2,8,7,3]=>0001111
[1,7,6,2,3,4,5,8]=>[1,6,2,3,4,7,5,8]=>[1,7,6,2,3,4,5,8]=>0000110
[1,8,6,2,3,4,5,7]=>[1,6,2,3,4,8,5,7]=>[1,8,6,2,3,4,5,7]=>0000101
[2,8,7,3,4,5,6,1]=>[6,2,7,3,4,5,8,1]=>[2,8,7,3,4,5,6,1]=>0000111
[3,8,7,2,4,5,6,1]=>[6,7,3,2,4,5,8,1]=>[3,8,7,2,4,5,6,1]=>0000111
[3,6,2,4,7,1,8,5]=>[7,6,3,2,8,4,1,5]=>[3,8,2,4,6,1,7,5]=>0000111
[3,4,7,2,5,1,8,6]=>[5,7,3,4,2,8,1,6]=>[3,4,8,2,5,1,7,6]=>0001011
[4,1,8,5,3,2,7,6]=>[4,3,5,1,8,7,2,6]=>[7,5,3,1,4,2,8,6]=>0111011
[1,2,8,3,7,5,4,6]=>[1,2,8,5,7,4,3,6]=>[1,2,7,5,4,8,3,6]=>0001011
[4,3,8,1,2,6,7,5]=>[8,1,4,3,7,2,6,5]=>[4,3,7,1,2,6,8,5]=>0010011
[1,2,3,4,5,10,9,8,7,6]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,9,8,7,6]=>000001111
[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>01000000
[3,5,1,2,4,8,7,6]=>[5,1,3,2,4,7,8,6]=>[3,5,1,2,4,8,7,6]=>0001011
[5,2,8,4,7,3,1,6]=>[3,7,5,8,1,2,4,6]=>[8,1,5,3,2,7,4,6]=>0101011
[4,3,5,1,2,8,7,6]=>[5,1,4,3,2,7,8,6]=>[4,3,5,1,2,8,7,6]=>0011011
[3,1,4,6,2,8,7,5]=>[3,6,1,4,7,2,8,5]=>[4,8,7,1,3,2,6,5]=>0100111
[1,4,6,5,2,8,7,3]=>[1,5,6,4,7,3,8,2]=>[1,4,8,7,3,6,5,2]=>0001111
[8,1,4,7,2,3,6,5]=>[8,7,2,1,6,3,4,5]=>[6,2,7,1,3,4,8,5]=>0000111
[6,1,4,8,7,3,2,5]=>[6,3,7,1,2,4,8,5]=>[8,7,3,1,6,2,4,5]=>0100111
[5,4,8,1,6,3,2,7]=>[8,3,6,5,4,1,2,7]=>[5,4,6,3,1,8,2,7]=>0101101
[1,4,8,6,3,7,2,5]=>[1,7,6,4,2,8,3,5]=>[1,4,8,6,2,7,3,5]=>0000111
[4,6,3,7,5,8,1,2]=>[8,1,6,4,7,3,5,2]=>[4,7,3,6,5,8,1,2]=>0000111
[4,1,3,5,8,6,2,7]=>[4,6,1,3,5,8,2,7]=>[5,8,6,1,3,4,2,7]=>0010101
[5,7,4,3,8,1,2,6]=>[8,1,4,7,5,2,3,6]=>[5,7,4,1,2,8,3,6]=>0010011
[1,4,8,3,7,6,5,2]=>[1,5,6,4,7,8,3,2]=>[1,4,8,3,7,6,5,2]=>0001111
[4,3,8,2,1,6,5,7]=>[2,8,4,3,6,1,5,7]=>[4,3,6,2,1,8,5,7]=>1010101
[3,8,4,2,7,1,5,6]=>[7,4,3,8,1,5,2,6]=>[3,8,4,1,5,7,2,6]=>0010011
[1,8,2,7,6,5,4,3]=>[1,8,4,5,6,7,2,3]=>[1,7,6,5,4,2,8,3]=>0011111
[3,8,1,6,7,5,4,2]=>[8,4,3,5,7,1,6,2]=>[3,7,5,4,1,6,8,2]=>0011011
[3,7,2,6,8,5,1,4]=>[5,8,3,2,7,1,6,4]=>[3,7,2,6,8,5,1,4]=>0001011
[7,2,3,8,5,6,1,4]=>[6,7,2,1,8,5,3,4]=>[8,5,7,2,6,1,3,4]=>0000111
[8,2,4,3,6,1,5,7]=>[6,8,4,2,1,3,5,7]=>[4,2,8,1,6,3,5,7]=>0010101
[6,8,7,1,4,2,5,3]=>[7,4,5,1,2,6,8,3]=>[5,1,4,2,6,8,7,3]=>0011011
[3,8,5,6,7,2,1,4]=>[2,7,3,1,8,5,6,4]=>[3,8,5,6,7,2,1,4]=>1000011
[8,1,7,6,2,4,3,5]=>[8,6,4,2,3,7,1,5]=>[4,2,7,6,3,8,1,5]=>0010111
[8,3,6,1,7,2,4,5]=>[6,7,8,2,4,3,1,5]=>[8,2,4,7,3,6,1,5]=>0000111
[1,8,6,5,7,3,4,2]=>[1,4,7,3,6,8,5,2]=>[1,8,6,5,7,3,4,2]=>0010111
[7,4,1,6,5,8,3,2]=>[4,3,7,8,6,2,5,1]=>[6,3,2,8,5,7,4,1]=>0110111
[4,1,5,8,7,6,3,2]=>[4,3,6,1,5,7,8,2]=>[5,8,7,6,3,1,4,2]=>0110111
[1,2,5,8,6,7,3,4]=>[1,2,7,3,5,8,6,4]=>[1,2,5,8,6,7,3,4]=>0000011
[4,2,1,5,8,7,3,6]=>[2,4,7,1,5,3,8,6]=>[5,8,7,2,1,4,3,6]=>1010011
[1,5,3,6,8,7,4,2]=>[1,4,7,5,2,6,8,3]=>[1,5,2,6,8,7,4,3]=>0011011
[1,4,5,6,8,7,2,3]=>[1,7,2,4,5,6,8,3]=>[1,4,5,6,8,7,2,3]=>0000011
[1,4,6,3,7,2,8,5]=>[1,7,6,4,8,3,2,5]=>[1,4,8,3,6,2,7,5]=>0000111
[1,7,3,6,5,2,8,4]=>[1,5,6,7,8,4,3,2]=>[1,8,4,7,3,6,5,2]=>0001111
[7,6,2,5,4,3,1,8]=>[3,4,5,6,2,7,1,8]=>[7,6,2,5,4,3,1,8]=>0111110
[6,2,3,7,5,4,1,8]=>[4,5,2,7,6,3,1,8]=>[6,2,3,7,5,4,1,8]=>0011110
[8,7,2,5,1,6,4,3]=>[5,7,4,6,2,1,8,3]=>[6,4,2,8,7,1,5,3]=>0011111
[7,8,2,5,4,1,6,3]=>[4,5,8,6,3,2,7,1]=>[6,3,7,8,2,5,4,1]=>0011101
[8,1,3,6,2,7,5,4]=>[8,6,1,5,7,3,2,4]=>[7,5,1,3,6,2,8,4]=>0001111
[1,2,4,7,3,8,6,5]=>[1,2,7,4,6,8,3,5]=>[1,2,4,8,6,3,7,5]=>0000111
[3,1,8,6,2,7,5,4]=>[3,6,1,5,8,7,4,2]=>[7,5,4,8,6,1,3,2]=>0101111
[5,6,1,8,2,7,4,3]=>[6,8,4,7,5,1,2,3]=>[5,7,4,1,8,2,6,3]=>0010111
[4,2,7,8,1,6,5,3]=>[8,4,5,2,6,1,7,3]=>[6,5,2,4,1,7,8,3]=>0011101
[7,2,8,1,6,5,4,3]=>[8,7,4,5,6,1,2,3]=>[6,5,4,1,7,2,8,3]=>0011111
[3,8,7,1,6,5,4,2]=>[7,4,3,5,6,1,8,2]=>[3,6,5,4,1,8,7,2]=>0011111
[4,8,7,5,1,6,3,2]=>[5,3,7,4,6,2,8,1]=>[4,6,3,2,8,7,5,1]=>0101111
[6,7,8,5,1,4,3,2]=>[5,3,4,1,8,6,7,2]=>[4,3,1,6,7,8,5,2]=>0111001
[5,6,3,8,4,1,7,2]=>[4,8,7,6,5,1,2,3]=>[5,6,1,7,2,8,4,3]=>0010111
[8,3,7,5,1,6,4,2]=>[5,4,7,6,8,3,1,2]=>[8,3,6,4,1,7,5,2]=>0011111
[8,4,6,7,1,5,3,2]=>[7,3,5,8,1,4,6,2]=>[8,3,1,5,4,6,7,2]=>0101011
[3,4,6,5,1,2,8,7]=>[5,1,3,4,6,2,8,7]=>[3,4,6,5,1,2,8,7]=>0001101
[1,4,6,2,3,8,7,5]=>[1,6,2,4,7,3,8,5]=>[1,4,8,7,2,3,6,5]=>0000111
[7,2,1,6,3,8,5,4]=>[2,7,6,5,8,1,3,4]=>[8,5,2,1,6,3,7,4]=>1001111
[5,6,7,1,2,8,4,3]=>[7,1,4,8,5,6,2,3]=>[5,6,8,4,1,2,7,3]=>0010011
[4,7,5,1,2,8,6,3]=>[5,1,7,4,6,8,3,2]=>[4,8,6,3,7,5,1,2]=>0001111
[3,7,1,6,2,8,5,4]=>[7,6,3,5,8,1,2,4]=>[3,8,5,1,6,2,7,4]=>0001111
[7,8,1,2,6,5,4,3]=>[8,1,4,5,6,2,7,3]=>[6,5,4,1,2,7,8,3]=>0011101
[4,8,5,1,2,7,6,3]=>[5,1,8,4,6,7,3,2]=>[4,7,6,3,8,5,1,2]=>0001111
[4,1,5,3,8,2,7,6]=>[4,8,5,1,3,7,2,6]=>[5,1,7,3,4,2,8,6]=>0011011
[2,6,3,4,7,5,1,8]=>[5,2,7,1,6,4,3,8]=>[2,6,1,4,7,5,3,8]=>0001110
[2,7,4,3,5,8,1,6]=>[8,2,4,7,3,1,5,6]=>[2,7,4,3,8,1,5,6]=>0010011
[5,4,3,1,8,2,7,6]=>[3,4,5,8,1,7,2,6]=>[7,1,5,4,3,2,8,6]=>0111011
[5,4,1,8,3,2,6,7]=>[4,3,5,8,2,1,6,7]=>[8,3,2,5,4,1,6,7]=>0111001
[7,4,2,1,8,3,6,5]=>[2,4,7,8,6,1,3,5]=>[6,2,1,8,4,3,7,5]=>1010111
[6,5,3,4,8,2,7,1]=>[7,8,5,3,6,4,2,1]=>[6,5,3,4,8,2,7,1]=>0001111
[6,1,5,3,8,2,7,4]=>[6,8,5,7,1,3,2,4]=>[7,1,5,3,8,2,6,4]=>0001111
[4,6,3,1,8,2,7,5]=>[3,6,8,4,7,2,1,5]=>[4,7,2,8,3,1,6,5]=>0100111
[5,8,4,2,7,3,1,6]=>[3,7,4,8,5,2,1,6]=>[5,8,4,2,7,3,1,6]=>0110011
[8,2,6,4,7,3,1,5]=>[3,7,8,6,2,1,4,5]=>[6,2,8,3,1,7,4,5]=>0100111
[8,6,1,7,4,5,2,3]=>[6,5,2,8,1,7,4,3]=>[7,2,5,4,8,6,1,3]=>0001111
[8,1,3,7,2,6,5,4]=>[8,7,1,5,6,2,3,4]=>[6,5,1,7,2,3,8,4]=>0001111
[1,7,6,8,3,2,4,5]=>[1,3,8,2,4,7,6,5]=>[1,7,6,8,3,2,4,5]=>0100011
[1,2,7,3,4,6,5,8]=>[1,2,7,3,6,4,5,8]=>[1,2,6,3,4,7,5,8]=>0000110
[1,7,8,4,3,5,6,2]=>[1,6,4,8,3,5,7,2]=>[1,7,8,4,3,5,6,2]=>0010101
[2,6,1,7,3,5,4,8]=>[6,2,7,5,3,1,4,8]=>[2,5,3,7,1,6,4,8]=>0001110
[5,4,8,2,7,3,1,6]=>[3,7,8,5,4,2,1,6]=>[5,4,8,2,7,3,1,6]=>0101011
[4,6,8,2,7,3,1,5]=>[3,7,8,4,2,6,1,5]=>[4,6,8,2,7,3,1,5]=>0100011
[2,6,8,7,3,4,1,5]=>[4,2,7,3,1,6,8,5]=>[2,6,8,7,3,4,1,5]=>0010011
[6,8,1,7,2,5,4,3]=>[8,7,4,5,2,6,1,3]=>[5,4,2,6,7,1,8,3]=>0011011
[3,8,7,4,5,6,1,2]=>[6,1,3,7,4,5,8,2]=>[3,8,7,4,5,6,1,2]=>0000111
[2,7,6,3,5,4,1,8]=>[4,2,5,6,1,7,3,8]=>[2,7,6,1,5,4,3,8]=>0011110
[1,8,6,5,3,2,4,7]=>[1,3,5,2,6,8,4,7]=>[1,8,6,5,3,2,4,7]=>0101101
[3,8,7,4,6,2,5,1]=>[5,6,3,7,2,4,8,1]=>[3,8,7,2,6,4,5,1]=>0001111
[5,8,3,7,6,2,4,1]=>[4,6,7,3,5,8,2,1]=>[5,8,3,7,6,2,4,1]=>0010111
[8,7,2,5,4,3,1,6]=>[3,4,5,7,2,1,8,6]=>[8,7,2,5,4,3,1,6]=>0111011
[6,8,3,2,5,4,7,1]=>[7,3,8,5,2,6,4,1]=>[5,3,2,6,8,4,7,1]=>0101011
[6,8,4,5,2,3,7,1]=>[7,5,2,8,4,6,3,1]=>[6,8,4,5,2,3,7,1]=>0001011
[1,5,7,8,4,3,6,2]=>[1,6,4,8,5,3,7,2]=>[1,5,7,8,4,3,6,2]=>0010101
[6,3,8,1,5,4,7,2]=>[8,7,6,5,1,3,4,2]=>[5,1,6,3,7,4,8,2]=>0001111
[6,2,1,8,5,4,7,3]=>[2,6,7,5,8,1,4,3]=>[8,5,2,1,7,4,6,3]=>1001111
[2,4,7,5,8,1,6,3]=>[8,2,6,4,7,1,5,3]=>[2,4,7,1,6,5,8,3]=>0000111
[5,2,1,8,7,6,4,3]=>[2,5,4,6,1,7,8,3]=>[8,7,6,4,2,1,5,3]=>1011111
[4,8,6,7,5,3,1,2]=>[3,1,5,4,7,8,6,2]=>[4,8,6,7,5,3,1,2]=>0101011
[4,8,7,5,6,2,3,1]=>[3,6,2,4,7,5,8,1]=>[4,8,7,5,6,2,3,1]=>0100111
[6,5,4,8,2,1,7,3]=>[2,8,7,5,6,4,1,3]=>[6,5,4,7,2,1,8,3]=>1001111
[1,5,7,3,2,8,6,4]=>[1,3,7,6,5,8,2,4]=>[1,5,8,6,3,2,7,4]=>0100111
[5,2,1,4,3,6,7,8]=>[2,5,4,1,3,6,7,8]=>[4,2,1,5,3,6,7,8]=>1011000
[3,5,7,4,2,6,1,8]=>[6,4,3,7,5,2,1,8]=>[3,5,7,4,2,6,1,8]=>0010110
[3,6,4,5,1,2,7,8]=>[5,1,3,6,4,2,7,8]=>[3,6,4,5,1,2,7,8]=>0001100
[4,2,1,5,6,8,7,3]=>[2,4,7,1,5,6,8,3]=>[5,6,8,7,2,1,4,3]=>1010011
[2,1,4,3,6,5,10,9,7,8]=>[2,1,4,3,6,5,9,7,10,8]=>[2,1,4,3,6,5,10,9,7,8]=>101010011
[2,1,4,3,8,7,5,6,10,9]=>[2,1,4,3,7,5,8,6,10,9]=>[2,1,4,3,8,7,5,6,10,9]=>101001101
[2,1,6,5,3,4,8,7,10,9]=>[2,1,5,3,6,4,8,7,10,9]=>[2,1,6,5,3,4,8,7,10,9]=>100110101
[2,1,6,5,3,4,10,9,7,8]=>[2,1,5,3,6,4,9,7,10,8]=>[2,1,6,5,3,4,10,9,7,8]=>100110011
[4,3,1,2,6,5,8,7,10,9]=>[3,1,4,2,6,5,8,7,10,9]=>[4,3,1,2,6,5,8,7,10,9]=>011010101
[4,3,1,2,6,5,10,9,7,8]=>[3,1,4,2,6,5,9,7,10,8]=>[4,3,1,2,6,5,10,9,7,8]=>011010011
[4,3,1,2,8,7,5,6,10,9]=>[3,1,4,2,7,5,8,6,10,9]=>[4,3,1,2,8,7,5,6,10,9]=>011001101
[2,1,4,3,6,5,8,7,12,11,9,10]=>[2,1,4,3,6,5,8,7,11,9,12,10]=>[2,1,4,3,6,5,8,7,12,11,9,10]=>10101010011
[2,1,4,3,6,5,10,9,7,8,12,11]=>[2,1,4,3,6,5,9,7,10,8,12,11]=>[2,1,4,3,6,5,10,9,7,8,12,11]=>10101001101
[2,1,4,3,8,7,5,6,10,9,12,11]=>[2,1,4,3,7,5,8,6,10,9,12,11]=>[2,1,4,3,8,7,5,6,10,9,12,11]=>10100110101
[2,1,4,3,8,7,5,6,12,11,9,10]=>[2,1,4,3,7,5,8,6,11,9,12,10]=>[2,1,4,3,8,7,5,6,12,11,9,10]=>10100110011
[2,1,6,5,3,4,8,7,10,9,12,11]=>[2,1,5,3,6,4,8,7,10,9,12,11]=>[2,1,6,5,3,4,8,7,10,9,12,11]=>10011010101
[2,1,6,5,3,4,8,7,12,11,9,10]=>[2,1,5,3,6,4,8,7,11,9,12,10]=>[2,1,6,5,3,4,8,7,12,11,9,10]=>10011010011
[2,1,6,5,3,4,10,9,7,8,12,11]=>[2,1,5,3,6,4,9,7,10,8,12,11]=>[2,1,6,5,3,4,10,9,7,8,12,11]=>10011001101
[4,3,1,2,6,5,8,7,10,9,12,11]=>[3,1,4,2,6,5,8,7,10,9,12,11]=>[4,3,1,2,6,5,8,7,10,9,12,11]=>01101010101
[4,3,1,2,6,5,8,7,12,11,9,10]=>[3,1,4,2,6,5,8,7,11,9,12,10]=>[4,3,1,2,6,5,8,7,12,11,9,10]=>01101010011
[4,3,1,2,6,5,10,9,7,8,12,11]=>[3,1,4,2,6,5,9,7,10,8,12,11]=>[4,3,1,2,6,5,10,9,7,8,12,11]=>01101001101
[4,3,1,2,8,7,5,6,10,9,12,11]=>[3,1,4,2,7,5,8,6,10,9,12,11]=>[4,3,1,2,8,7,5,6,10,9,12,11]=>01100110101
[4,3,1,2,8,7,5,6,12,11,9,10]=>[3,1,4,2,7,5,8,6,11,9,12,10]=>[4,3,1,2,8,7,5,6,12,11,9,10]=>01100110011
[7,6,5,4,3,2,9,1,8]=>[9,3,4,5,6,7,2,1,8]=>[7,6,5,4,3,2,9,1,8]=>01111101
[2,4,6,8,1,3,5,7,9]=>[8,2,1,4,3,6,5,7,9]=>[2,4,6,8,1,3,5,7,9]=>00000010
[8,7,6,5,4,3,2,10,1,9]=>[10,3,4,5,6,7,8,2,1,9]=>[8,7,6,5,4,3,2,10,1,9]=>011111101
[2,1,7,3,8,4,6,5]=>[2,1,7,8,6,4,3,5]=>[2,1,6,4,8,3,7,5]=>1000111
[4,1,8,2,7,3,6,5]=>[4,8,7,1,6,3,2,5]=>[6,1,7,3,4,2,8,5]=>0010111
[4,1,7,2,8,3,6,5]=>[4,7,8,1,6,3,2,5]=>[6,1,8,3,4,2,7,5]=>0010111
[7,1,3,2,8,4,6,5]=>[7,3,1,8,6,4,2,5]=>[3,1,6,4,8,2,7,5]=>0100111
[7,1,8,2,4,3,6,5]=>[7,8,4,2,6,3,1,5]=>[4,2,6,3,8,1,7,5]=>0010111
[8,1,7,2,5,3,6,4]=>[8,7,5,6,2,3,1,4]=>[6,2,5,3,7,1,8,4]=>0001111
[5,1,7,2,8,3,6,4]=>[5,7,8,6,1,3,2,4]=>[6,1,8,3,7,2,5,4]=>0001111
[5,1,8,2,7,3,6,4]=>[5,8,7,6,1,3,2,4]=>[6,1,7,3,8,2,5,4]=>0001111
[5,1,8,2,4,3,7,6]=>[5,8,4,2,1,7,3,6]=>[4,2,7,1,5,3,8,6]=>0011011
[8,1,6,2,4,3,7,5]=>[8,6,4,2,7,1,3,5]=>[4,2,7,1,6,3,8,5]=>0010111
[6,1,8,2,4,3,7,5]=>[6,8,4,2,7,1,3,5]=>[4,2,7,1,8,3,6,5]=>0010111
[8,1,6,2,5,3,7,4]=>[8,6,5,7,2,1,3,4]=>[7,2,5,1,6,3,8,4]=>0001111
[8,1,6,2,7,3,5,4]=>[8,6,7,5,3,1,2,4]=>[5,3,7,1,6,2,8,4]=>0001111
[6,1,7,2,4,3,8,5]=>[6,7,4,2,8,1,3,5]=>[4,2,8,1,7,3,6,5]=>0010111
[5,1,6,2,4,3,8,7]=>[5,6,4,2,1,3,8,7]=>[4,2,6,1,5,3,8,7]=>0011101
[7,1,5,2,4,3,8,6]=>[7,5,4,2,1,8,3,6]=>[4,2,5,1,8,3,7,6]=>0011011
[7,1,6,2,5,3,8,4]=>[7,6,5,8,2,1,3,4]=>[8,2,5,1,6,3,7,4]=>0001111
[7,1,8,2,6,3,5,4]=>[7,8,6,5,3,2,1,4]=>[5,3,6,2,8,1,7,4]=>0001111
[1,8,6,4,7,2,3,5]=>[1,7,2,6,3,8,4,5]=>[1,8,6,2,3,7,4,5]=>0000111
[1,8,4,2,6,3,5,7]=>[1,4,8,6,2,3,5,7]=>[1,6,2,8,4,3,5,7]=>0010101
[5,1,7,4,3,6,2,8]=>[5,6,4,7,1,3,2,8]=>[7,4,1,6,3,5,2,8]=>0011110
[1,8,5,4,3,6,2,7]=>[1,6,4,5,8,3,2,7]=>[1,8,5,4,3,6,2,7]=>0011101
[1,8,5,4,2,6,7,3]=>[1,4,5,8,7,2,6,3]=>[1,7,2,6,8,5,4,3]=>0011011
[7,4,8,2,1,3,5,6]=>[2,8,1,7,3,5,4,6]=>[7,2,1,3,5,8,4,6]=>1000011
[6,5,4,3,7,1,8,2]=>[7,8,4,5,6,3,1,2]=>[6,5,4,3,8,1,7,2]=>0011111
[6,5,1,7,3,8,2,4]=>[5,6,8,3,7,2,1,4]=>[7,3,8,2,6,5,1,4]=>0001111
[7,6,3,8,5,4,1,2]=>[4,1,5,8,6,7,3,2]=>[7,6,3,8,5,4,1,2]=>0011111
[6,5,8,3,1,7,4,2]=>[3,8,4,7,6,5,2,1]=>[6,5,7,4,2,8,3,1]=>0110111
[5,4,8,2,1,7,3,6]=>[2,8,7,5,4,3,1,6]=>[5,4,7,3,8,2,1,6]=>1001011
[5,4,3,7,1,6,2,8]=>[7,6,4,5,3,1,2,8]=>[5,4,3,6,1,7,2,8]=>0011110
[6,4,2,8,5,1,3,7]=>[5,4,2,8,6,1,3,7]=>[6,4,2,8,5,1,3,7]=>0011101
[7,6,4,8,5,1,2,3]=>[5,1,2,8,6,7,3,4]=>[7,6,1,2,3,8,5,4]=>0001111
[7,2,8,6,1,5,3,4]=>[6,8,5,3,2,7,1,4]=>[5,3,7,2,8,6,1,4]=>0001111
[2,1,7,8,3,6,4,5]=>[2,1,8,6,4,3,7,5]=>[2,1,6,4,7,8,3,5]=>1000101
[6,4,1,7,8,2,3,5]=>[4,6,1,8,3,2,7,5]=>[7,8,1,3,6,4,2,5]=>0010101
[4,3,1,5,2,7,6,8]=>[3,4,5,2,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>0111010
[6,3,1,7,8,5,2,4]=>[3,6,5,1,8,2,7,4]=>[7,8,5,1,6,3,2,4]=>0101101
[5,4,1,7,8,2,6,3]=>[4,5,8,6,2,3,7,1]=>[6,2,7,8,3,5,4,1]=>0011101
[6,5,4,1,7,8,3,2]=>[4,3,5,6,8,1,7,2]=>[7,8,3,1,6,5,4,2]=>0111101
[6,5,4,2,7,8,3,1]=>[3,8,4,5,6,1,7,2]=>[6,5,4,1,7,8,3,2]=>0111101
[5,4,2,6,3,8,7,1]=>[7,4,5,6,3,2,8,1]=>[6,3,5,4,2,8,7,1]=>0011111
[4,3,1,5,2,6,8,7]=>[3,4,5,2,1,6,8,7]=>[5,2,4,3,1,6,8,7]=>0111001
[5,4,2,1,6,7,8,3]=>[2,4,5,8,3,6,7,1]=>[6,7,8,3,5,4,2,1]=>1011001
[5,4,3,1,6,7,8,2]=>[3,4,5,8,1,6,7,2]=>[6,7,8,1,5,4,3,2]=>0111001
[3,6,7,1,2,5,8,4]=>[7,1,3,8,2,6,5,4]=>[3,6,8,1,2,5,7,4]=>0000011
[7,8,1,3,2,4,6,5]=>[8,3,1,2,6,4,7,5]=>[3,1,6,2,4,7,8,5]=>0100101
[5,2,3,7,1,8,6,4]=>[7,5,2,6,3,8,1,4]=>[8,6,2,3,5,1,7,4]=>0001111
[2,6,7,3,1,8,4,5]=>[3,2,7,8,4,6,1,5]=>[2,6,8,4,7,3,1,5]=>0100011
[4,3,1,2,7,8,6,5]=>[3,1,4,2,6,8,7,5]=>[4,3,1,2,7,8,6,5]=>0110101
[5,3,4,7,8,6,1,2]=>[6,1,5,3,4,8,7,2]=>[5,3,4,7,8,6,1,2]=>0001101
[1,6,7,3,2,4,8,5]=>[1,3,7,2,8,6,4,5]=>[1,6,8,3,2,4,7,5]=>0100011
[1,5,3,6,2,7,8,4]=>[1,6,5,8,3,2,7,4]=>[1,7,8,3,5,2,6,4]=>0001101
[5,2,4,7,8,1,6,3]=>[8,5,6,2,4,1,7,3]=>[6,2,4,5,1,7,8,3]=>0001101
[4,2,5,7,6,1,8,3]=>[6,4,7,2,5,8,3,1]=>[5,8,2,4,3,7,6,1]=>0010111
[4,5,2,8,6,1,7,3]=>[6,5,8,4,2,7,3,1]=>[4,7,2,5,3,8,6,1]=>0001111
[6,1,8,3,2,4,7,5]=>[6,3,8,2,7,1,4,5]=>[7,3,2,8,1,4,6,5]=>0100111
[4,3,5,7,6,8,1,2]=>[8,1,4,3,5,7,6,2]=>[4,3,5,7,6,8,1,2]=>0010011
[7,6,5,4,2,1,8,3]=>[2,4,5,6,7,8,3,1]=>[8,3,7,6,5,4,2,1]=>1011111
[8,7,6,5,4,2,1,9,3]=>[2,4,5,6,7,8,9,1,3]=>[9,2,1,8,7,6,5,4,3]=>10111111
[8,7,6,4,3,2,1,9,5]=>[2,3,4,6,7,8,9,1,5]=>[9,4,3,2,1,8,7,6,5]=>11101111
[8,5,4,3,2,1,7,6]=>[2,3,4,5,8,7,1,6]=>[7,5,4,3,2,1,8,6]=>1111011
[8,6,5,4,3,2,1,9,7]=>[2,3,4,5,6,8,9,1,7]=>[9,6,5,4,3,2,1,8,7]=>11111011
[7,6,5,4,3,2,1,9,8]=>[2,3,4,5,6,7,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>11111101
[7,6,5,4,1,8,3,2]=>[4,3,5,6,7,8,2,1]=>[8,3,2,7,6,5,4,1]=>0111111
[9,8,7,6,5,4,2,1,10,3]=>[2,4,5,6,7,8,9,10,3,1]=>[10,3,9,8,7,6,5,4,2,1]=>101111111
[7,6,5,2,8,1,4,3]=>[8,5,4,1,6,7,2,3]=>[4,1,7,6,5,2,8,3]=>0011111
[7,6,5,8,4,1,3,2]=>[4,3,1,8,6,7,5,2]=>[3,1,7,6,5,8,4,2]=>0110111
[7,8,6,3,2,1,5,4]=>[2,3,6,5,1,8,7,4]=>[5,3,2,1,7,8,6,4]=>1101101
[8,7,4,3,2,1,6,5]=>[2,3,4,7,6,1,8,5]=>[6,4,3,2,1,8,7,5]=>1110111
[9,6,5,4,3,2,1,8,7]=>[2,3,4,5,6,9,8,1,7]=>[8,6,5,4,3,2,1,9,7]=>11111011
[9,7,6,5,4,3,2,1,10,8]=>[2,3,4,5,6,7,9,10,1,8]=>[10,7,6,5,4,3,2,1,9,8]=>111111011
[4,6,7,2,5,1,3,8]=>[5,7,1,4,2,6,3,8]=>[4,6,7,1,5,2,3,8]=>0001010
[7,8,1,3,2,4,5,6]=>[8,3,1,2,4,5,7,6]=>[3,1,7,8,2,4,5,6]=>0100001
[7,8,4,1,5,2,3,6]=>[4,8,1,5,2,3,7,6]=>[5,1,7,8,4,2,3,6]=>0011001
[2,6,7,3,1,4,5,8]=>[3,2,7,1,4,6,5,8]=>[2,6,7,3,1,4,5,8]=>0100010
[4,6,7,3,5,8,1,2]=>[8,1,7,4,3,6,5,2]=>[4,6,7,3,5,8,1,2]=>0000011
[3,2,5,6,1,4,7,8]=>[6,3,2,1,5,4,7,8]=>[3,2,5,6,1,4,7,8]=>0100100
[1,5,4,6,7,2,3,8]=>[1,7,2,5,4,6,3,8]=>[1,5,4,6,7,2,3,8]=>0001010
[1,6,7,3,2,4,5,8]=>[1,3,7,2,4,6,5,8]=>[1,6,7,3,2,4,5,8]=>0100010
[5,1,3,6,2,4,7,8]=>[5,6,1,2,3,4,7,8]=>[6,1,5,2,3,4,7,8]=>0001100
[2,5,4,6,7,1,3,8]=>[7,2,1,5,4,6,3,8]=>[2,5,4,6,7,1,3,8]=>0001010
[4,2,5,6,7,1,3,8]=>[7,4,1,2,5,6,3,8]=>[4,1,5,6,7,2,3,8]=>0010010
[4,5,2,6,7,1,3,8]=>[7,5,1,4,2,6,3,8]=>[4,5,1,6,7,2,3,8]=>0001010
[6,1,7,4,5,2,3,8]=>[6,5,2,7,4,1,3,8]=>[7,4,5,2,6,1,3,8]=>0001110
[7,3,2,5,4,1,6,8]=>[4,3,5,7,1,2,6,8]=>[7,3,1,5,4,2,6,8]=>0111010
[1,3,6,7,5,2,8,4]=>[1,5,3,7,8,6,4,2]=>[1,3,6,8,4,7,5,2]=>0001011
[7,3,4,1,5,6,2,8]=>[4,6,7,3,1,5,2,8]=>[7,3,5,6,1,4,2,8]=>0010110
[7,3,2,5,1,6,4,8]=>[5,3,7,6,2,1,4,8]=>[6,3,2,7,1,5,4,8]=>0101110
[1,3,6,7,2,5,8,4]=>[1,7,3,8,2,6,5,4]=>[1,3,6,8,2,5,7,4]=>0000011
[1,7,4,6,2,8,5,3]=>[1,6,5,8,7,3,2,4]=>[1,7,3,8,5,2,6,4]=>0001111
[5,6,1,4,7,3,8,2]=>[6,8,7,1,5,4,3,2]=>[5,7,1,4,8,3,6,2]=>0000111
[5,3,2,1,7,4,8,6]=>[2,3,5,7,1,8,4,6]=>[8,3,2,1,5,4,7,6]=>1101011
[1,3,4,5,8,7,2,6]=>[1,7,3,4,5,2,8,6]=>[1,3,4,5,8,7,2,6]=>0000011
[6,3,4,5,8,1,7,2]=>[8,7,6,3,4,5,1,2]=>[6,3,4,5,7,1,8,2]=>0000111
[2,4,5,1,6,8,7,3]=>[5,2,7,4,1,6,8,3]=>[2,4,6,8,7,1,5,3]=>0001011
[3,1,2,5,6,8,7,4]=>[3,1,2,7,5,6,8,4]=>[3,1,2,5,6,8,7,4]=>0100011
[4,3,2,5,6,8,1,7]=>[8,3,4,2,5,6,1,7]=>[4,3,2,5,6,8,1,7]=>0110001
[3,7,5,4,6,8,1,2]=>[8,1,3,5,7,4,6,2]=>[3,7,5,4,6,8,1,2]=>0001011
[3,1,4,6,5,8,2,7]=>[3,8,1,4,6,5,2,7]=>[4,6,5,8,1,3,2,7]=>0100101
[2,3,4,5,8,6,1,7]=>[6,2,3,4,5,8,1,7]=>[2,3,4,5,8,6,1,7]=>0000101
[2,3,4,5,8,1,7,6]=>[8,2,3,4,5,7,1,6]=>[2,3,4,5,7,1,8,6]=>0000011
[5,6,1,4,7,2,8,3]=>[6,7,8,1,5,4,2,3]=>[5,8,1,4,7,2,6,3]=>0000111
[4,3,1,7,6,5,8,2]=>[3,4,8,2,6,7,5,1]=>[7,6,5,8,2,4,3,1]=>0110111
[1,4,5,2,6,8,7,3]=>[1,5,7,4,2,6,8,3]=>[1,4,6,8,7,2,5,3]=>0001011
[3,7,5,2,6,8,1,4]=>[8,5,3,1,7,2,6,4]=>[3,7,5,1,6,8,2,4]=>0001011
[5,3,2,1,4,7,8,6]=>[2,3,5,1,4,8,7,6]=>[5,3,2,1,4,7,8,6]=>1101001
[5,3,1,4,2,7,8,6]=>[3,5,4,2,1,8,7,6]=>[4,2,5,3,1,7,8,6]=>0111001
[5,3,1,2,4,7,8,6]=>[3,1,5,2,4,8,7,6]=>[5,3,1,2,4,7,8,6]=>0101001
[7,1,5,2,6,8,3,4]=>[7,5,8,3,1,2,6,4]=>[8,3,5,1,6,7,2,4]=>0001011
[2,7,4,6,1,8,5,3]=>[6,2,5,8,7,3,1,4]=>[2,7,3,8,5,1,6,4]=>0001111
[2,3,6,7,1,5,8,4]=>[7,2,3,8,1,6,5,4]=>[2,3,6,8,1,5,7,4]=>0000011
[7,3,4,5,8,1,6,2]=>[8,6,7,3,4,1,5,2]=>[7,3,4,6,1,5,8,2]=>0000111
[1,3,4,5,8,6,2,7]=>[1,6,3,4,5,8,2,7]=>[1,3,4,5,8,6,2,7]=>0000101
[1,3,4,5,8,2,7,6]=>[1,8,3,4,5,7,2,6]=>[1,3,4,5,7,2,8,6]=>0000011
[6,3,4,5,8,2,7,1]=>[7,8,6,3,4,5,2,1]=>[6,3,4,5,8,2,7,1]=>0000111
[7,3,4,5,8,6,2,1]=>[2,6,8,1,4,7,5,3]=>[7,2,1,4,5,8,6,3]=>1000111
[7,3,2,5,6,8,4,1]=>[4,3,8,7,1,5,6,2]=>[7,3,1,5,6,8,4,2]=>0110011
[5,7,4,6,1,8,3,2]=>[6,3,8,7,5,4,1,2]=>[5,7,4,8,3,1,6,2]=>0100111
[6,3,4,5,8,1,2,7]=>[8,1,6,3,4,5,2,7]=>[6,3,4,5,8,1,2,7]=>0000101
[7,3,4,5,8,2,1,6]=>[2,8,7,3,4,1,5,6]=>[7,3,4,8,2,1,5,6]=>1000011
[4,7,6,1,8,2,5,3]=>[6,7,5,4,1,8,2,3]=>[4,5,1,8,2,7,6,3]=>0001111
[8,6,4,2,7,5,3,1]=>[3,5,4,7,6,8,2,1]=>[8,6,4,2,7,5,3,1]=>0111111
[8,4,7,3,6,5,1,2]=>[5,1,6,7,8,4,2,3]=>[8,4,7,1,2,6,5,3]=>0001111
[6,4,7,1,8,3,2,5]=>[7,3,8,6,2,4,1,5]=>[6,3,2,8,4,7,1,5]=>0100111
[7,4,8,3,6,1,5,2]=>[6,5,8,7,1,3,4,2]=>[7,1,8,3,5,4,6,2]=>0001111
[7,8,4,3,6,2,5,1]=>[5,6,4,8,2,3,7,1]=>[7,8,4,2,6,3,5,1]=>0011101
[2,1,8,6,3,5,4,7]=>[2,1,6,5,3,8,4,7]=>[2,1,5,3,8,6,4,7]=>1001101
[2,1,7,3,5,8,6,4]=>[2,1,7,6,3,8,5,4]=>[2,1,8,6,3,5,7,4]=>1000111
[2,1,8,6,3,5,7,4]=>[2,1,6,8,4,7,5,3]=>[2,1,7,4,5,8,6,3]=>1000111
[2,7,3,1,4,8,5,6]=>[3,2,7,1,8,5,4,6]=>[2,8,5,7,3,1,4,6]=>0100011
[3,2,1,6,4,5,7,8]=>[2,3,1,6,4,5,7,8]=>[3,2,1,6,4,5,7,8]=>1100100
[3,2,1,5,7,8,4,6]=>[2,3,1,8,5,4,7,6]=>[3,2,1,5,7,8,4,6]=>1100001
[2,7,3,1,5,6,8,4]=>[3,2,7,8,1,5,6,4]=>[2,8,3,1,5,6,7,4]=>0100011
[2,1,6,8,3,7,4,5]=>[2,1,8,7,4,6,3,5]=>[2,1,6,7,4,8,3,5]=>1000011
[2,1,8,3,5,7,4,6]=>[2,1,8,7,3,4,5,6]=>[2,1,7,3,8,4,5,6]=>1000011
[3,2,1,5,6,8,4,7]=>[2,3,1,8,5,6,4,7]=>[3,2,1,5,6,8,4,7]=>1100001
[8,2,1,7,3,5,4,6]=>[2,8,7,5,3,4,1,6]=>[5,3,7,4,8,2,1,6]=>1001011
[8,2,4,1,7,5,3,6]=>[4,8,5,2,7,3,1,6]=>[7,5,2,8,3,4,1,6]=>0011011
[5,8,6,3,1,7,4,2]=>[3,6,4,8,5,7,1,2]=>[5,7,4,1,8,6,3,2]=>0110111
[6,2,1,7,8,3,5,4]=>[2,6,8,5,3,1,7,4]=>[5,3,7,8,2,1,6,4]=>1001101
[2,7,1,8,3,5,6,4]=>[7,2,8,6,3,5,1,4]=>[2,6,3,5,8,1,7,4]=>0000111
[2,1,8,3,6,4,5,7]=>[2,1,8,6,4,3,5,7]=>[2,1,6,4,8,3,5,7]=>1000101
[3,2,1,6,8,4,5,7]=>[2,3,1,8,4,6,5,7]=>[3,2,1,6,8,4,5,7]=>1100001
[2,1,8,3,7,4,5,6]=>[2,1,8,7,4,5,3,6]=>[2,1,7,4,5,8,3,6]=>1000011
[2,1,8,3,6,7,4,5]=>[2,1,8,7,4,3,6,5]=>[2,1,7,4,6,8,3,5]=>1000011
[3,2,1,8,4,5,6,7]=>[2,3,1,8,4,5,6,7]=>[3,2,1,8,4,5,6,7]=>1100001
[3,8,1,5,7,2,4,6]=>[8,7,3,2,1,4,5,6]=>[3,7,2,8,1,4,5,6]=>0000011
[1,2,6,8,4,7,3,5]=>[1,2,7,8,3,6,4,5]=>[1,2,6,8,3,7,4,5]=>0000011
[6,1,5,8,2,4,7,3]=>[6,8,7,2,1,5,4,3]=>[7,2,5,8,1,4,6,3]=>0000111
[4,1,2,7,8,3,6,5]=>[4,1,8,2,6,3,7,5]=>[6,1,2,4,3,7,8,5]=>0010101
[3,5,7,4,8,6,1,2]=>[6,1,3,8,5,7,2,4]=>[3,5,7,1,2,8,6,4]=>0000111
[5,3,8,4,7,6,1,2]=>[6,1,5,7,3,8,2,4]=>[8,3,5,1,2,7,6,4]=>0001111
[5,8,1,2,3,7,6,4]=>[8,1,2,6,5,7,3,4]=>[5,7,6,1,2,3,8,4]=>0000111
[6,1,2,8,7,4,5,3]=>[6,1,5,7,4,2,8,3]=>[8,7,4,5,1,2,6,3]=>0001111
[7,1,6,2,8,4,5,3]=>[7,6,5,8,4,1,2,3]=>[8,4,5,1,6,2,7,3]=>0001111
[1,2,6,3,8,5,4,7]=>[1,2,6,5,8,3,4,7]=>[1,2,8,5,3,6,4,7]=>0001101
[1,2,7,3,8,5,4,6]=>[1,2,7,5,8,4,3,6]=>[1,2,8,5,4,7,3,6]=>0001011
[1,6,2,8,4,3,5,7]=>[1,6,4,8,3,2,5,7]=>[1,8,4,3,6,2,5,7]=>0010101
[1,6,4,2,7,3,5,8]=>[1,4,6,7,2,3,5,8]=>[1,7,2,6,4,3,5,8]=>0010110
[1,8,6,3,2,4,5,7]=>[1,3,6,2,4,8,5,7]=>[1,8,6,3,2,4,5,7]=>0100101
[3,1,7,8,6,2,4,5]=>[3,6,1,2,4,8,7,5]=>[7,8,6,1,3,2,4,5]=>0100101
[1,8,7,3,5,6,2,4]=>[1,6,7,2,3,5,8,4]=>[1,8,7,2,5,6,3,4]=>0000111
[1,8,3,2,6,4,5,7]=>[1,3,8,6,4,2,5,7]=>[1,6,4,8,3,2,5,7]=>0100101
[1,7,6,3,2,4,5,8]=>[1,3,6,2,4,7,5,8]=>[1,7,6,3,2,4,5,8]=>0100110
[1,2,8,4,3,7,5,6]=>[1,2,4,8,7,5,3,6]=>[1,2,7,5,8,4,3,6]=>0010011
[8,5,1,7,2,4,6,3]=>[5,8,7,3,6,4,2,1]=>[6,3,4,7,2,8,5,1]=>0001111
[1,2,7,5,3,6,4,8]=>[1,2,5,7,6,4,3,8]=>[1,2,6,4,7,5,3,8]=>0001110
[1,2,3,7,5,4,8,6]=>[1,2,3,5,7,8,4,6]=>[1,2,3,8,5,4,7,6]=>0001011
[1,8,2,7,6,4,5,3]=>[1,8,5,6,4,7,2,3]=>[1,7,6,4,5,2,8,3]=>0001111
[2,8,7,6,5,1,4,3]=>[5,2,4,1,6,7,8,3]=>[2,4,1,8,7,6,5,3]=>0011111
[7,1,6,3,2,5,4,8]=>[7,3,6,5,2,1,4,8]=>[5,3,2,6,1,7,4,8]=>0101110
[1,8,4,3,6,5,2,7]=>[1,5,4,6,8,2,3,7]=>[1,8,4,2,6,5,3,7]=>0011101
[7,3,1,2,4,6,5,8]=>[3,1,7,2,6,4,5,8]=>[6,3,1,2,4,7,5,8]=>0100110
[1,8,6,3,4,5,2,7]=>[1,5,6,3,4,8,2,7]=>[1,8,6,3,4,5,2,7]=>0001101
[3,6,2,1,4,8,5,7]=>[2,6,3,1,8,4,5,7]=>[3,8,2,1,4,6,5,7]=>1000101
[3,1,7,2,4,6,8,5]=>[3,7,1,2,8,4,6,5]=>[8,1,3,2,4,6,7,5]=>0100011
[3,4,7,1,5,2,8,6]=>[7,5,3,4,1,8,2,6]=>[3,4,5,1,8,2,7,6]=>0001011
[3,6,7,4,1,5,8,2]=>[4,7,3,8,2,6,5,1]=>[3,6,8,2,5,7,4,1]=>0010011
[3,1,2,8,6,5,4,7]=>[3,1,2,5,6,8,4,7]=>[3,1,2,8,6,5,4,7]=>0101101
[5,4,8,6,1,2,3,7]=>[6,1,2,5,4,8,3,7]=>[5,4,8,6,1,2,3,7]=>0001101
[6,5,8,2,3,7,1,4]=>[7,8,2,1,6,5,3,4]=>[6,5,8,2,7,1,3,4]=>0000111
[2,4,8,1,6,3,7,5]=>[8,2,6,4,7,1,3,5]=>[2,4,7,1,6,3,8,5]=>0000111
[5,3,2,6,4,8,1,7]=>[8,3,5,6,2,4,1,7]=>[6,3,2,5,4,8,1,7]=>0101101
[4,1,6,3,5,8,2,7]=>[4,8,6,1,3,5,2,7]=>[6,1,5,8,3,4,2,7]=>0010101
[1,8,4,5,2,6,7,3]=>[1,5,7,8,4,2,6,3]=>[1,8,4,6,7,2,5,3]=>0001011
[4,1,2,7,6,5,8,3]=>[4,1,8,2,6,7,5,3]=>[7,6,5,8,1,2,4,3]=>0010111
[5,6,7,3,2,8,1,4]=>[8,3,7,1,5,6,2,4]=>[5,6,7,3,1,8,2,4]=>0100011
[5,3,2,1,4,8,6,7]=>[2,3,5,1,4,8,6,7]=>[5,3,2,1,4,8,6,7]=>1101001
[3,6,7,8,1,4,5,2]=>[8,5,3,1,4,6,7,2]=>[3,5,1,4,6,7,8,2]=>0001001
[7,3,2,6,8,5,1,4]=>[5,3,8,2,7,1,6,4]=>[7,3,2,6,8,5,1,4]=>0101011
[1,8,4,2,3,5,7,6]=>[1,4,2,8,3,7,5,6]=>[1,7,4,2,3,5,8,6]=>0010011
[6,4,2,8,3,5,1,7]=>[5,4,6,8,2,3,1,7]=>[8,2,6,4,3,5,1,7]=>0011101
[6,3,4,8,2,5,7,1]=>[7,8,6,3,2,4,5,1]=>[6,3,8,2,4,5,7,1]=>0000111
[8,4,6,2,7,5,3,1]=>[3,5,7,6,8,2,4,1]=>[8,2,6,4,7,5,3,1]=>0101111
[8,5,6,7,2,4,3,1]=>[3,4,7,1,8,5,6,2]=>[8,5,6,7,1,4,3,2]=>0110011
[6,5,7,8,4,1,3,2]=>[4,3,1,8,6,5,7,2]=>[3,1,6,5,7,8,4,2]=>0110101
[7,5,6,8,2,4,1,3]=>[4,8,1,2,7,5,6,3]=>[7,5,6,8,1,4,2,3]=>0010011
[3,5,6,8,2,4,1,7]=>[4,8,3,2,5,6,1,7]=>[3,5,6,8,2,4,1,7]=>0010001
[3,5,6,8,4,2,1,7]=>[2,4,3,8,5,6,1,7]=>[3,5,6,8,4,2,1,7]=>1010001
[3,6,7,8,1,4,2,5]=>[8,4,3,1,2,6,7,5]=>[3,4,1,6,7,8,2,5]=>0010001
[3,5,7,8,2,1,4,6]=>[2,8,3,1,5,4,7,6]=>[3,5,7,8,2,1,4,6]=>1000001
[2,6,7,8,1,4,3,5]=>[8,2,4,1,3,6,7,5]=>[2,4,1,6,7,8,3,5]=>0010001
[2,5,7,8,3,1,4,6]=>[3,2,8,1,5,4,7,6]=>[2,5,7,8,3,1,4,6]=>0100001
[6,4,7,3,8,1,5,2]=>[8,5,7,6,1,4,3,2]=>[6,1,7,4,5,3,8,2]=>0001111
[7,4,6,3,8,2,1,5]=>[2,8,6,7,1,4,3,5]=>[7,2,1,6,4,8,3,5]=>1000111
[6,4,5,2,3,8,1,7]=>[8,5,2,6,4,3,1,7]=>[6,4,5,2,3,8,1,7]=>0001101
[5,4,6,3,8,2,1,7]=>[2,8,6,5,4,3,1,7]=>[5,4,6,3,8,2,1,7]=>1001101
[2,5,7,8,3,1,6,4]=>[3,2,8,6,5,1,7,4]=>[2,5,6,3,1,7,8,4]=>0100101
[4,5,7,8,3,1,2,6]=>[3,1,8,4,5,2,7,6]=>[4,5,7,8,3,1,2,6]=>0100001
[4,6,7,8,1,5,2,3]=>[8,5,2,4,1,6,7,3]=>[4,5,2,6,7,8,1,3]=>0001001
[4,5,7,8,2,1,6,3]=>[2,8,6,4,5,1,7,3]=>[4,5,6,2,1,7,8,3]=>1000101
[5,4,7,2,8,1,6,3]=>[8,7,6,5,4,1,2,3]=>[5,4,6,1,7,2,8,3]=>0001111
[4,3,2,7,8,1,6,5]=>[8,3,4,2,6,1,7,5]=>[4,3,2,6,1,7,8,5]=>0110101
[3,6,7,8,1,5,2,4]=>[8,5,3,2,1,6,7,4]=>[3,5,2,6,7,8,1,4]=>0001001
[2,6,7,8,1,5,4,3]=>[8,2,4,5,1,6,7,3]=>[2,5,4,1,6,7,8,3]=>0011001
[3,2,6,7,5,1,4,8]=>[5,3,2,1,7,6,4,8]=>[3,2,6,7,5,1,4,8]=>0101010
[2,7,1,3,5,4,8,6]=>[7,2,1,5,3,8,4,6]=>[2,5,1,3,8,4,7,6]=>0001011
[4,7,2,1,5,8,6,3]=>[2,7,6,4,1,8,5,3]=>[4,8,6,2,1,5,7,3]=>1000111
[3,1,4,8,2,6,7,5]=>[3,8,1,4,7,2,6,5]=>[4,7,1,3,2,6,8,5]=>0100011
[4,8,6,2,1,5,7,3]=>[2,6,8,4,3,7,5,1]=>[4,7,3,5,8,6,2,1]=>1000111
[4,8,3,6,5,1,7,2]=>[5,6,7,4,8,1,2,3]=>[4,8,1,7,2,6,5,3]=>0001111
[6,4,7,3,5,1,8,2]=>[5,8,7,6,3,4,1,2]=>[6,3,7,4,8,1,5,2]=>0001111
[6,4,7,5,1,8,2,3]=>[5,7,1,8,6,3,2,4]=>[6,1,3,8,2,7,5,4]=>0001111
[3,6,1,7,5,8,2,4]=>[6,8,3,2,7,1,5,4]=>[3,7,2,8,5,6,1,4]=>0000111
[4,7,3,5,6,1,8,2]=>[6,8,7,4,3,5,1,2]=>[4,7,3,5,8,1,6,2]=>0000111
[4,6,8,2,1,5,7,3]=>[2,8,7,4,1,6,5,3]=>[4,6,7,2,1,5,8,3]=>1000011
[1,8,2,3,5,7,4,6]=>[1,8,2,7,3,4,5,6]=>[1,7,2,3,8,4,5,6]=>0000011
[2,7,3,6,1,4,5,8]=>[6,2,7,1,4,3,5,8]=>[2,7,1,4,6,3,5,8]=>0000110
[4,6,2,8,1,5,3,7]=>[8,6,5,4,1,2,3,7]=>[4,5,1,6,2,8,3,7]=>0001101
[8,5,1,2,6,3,4,7]=>[5,1,8,2,6,3,4,7]=>[6,1,2,8,5,3,4,7]=>0001101
[1,6,2,7,4,8,3,5]=>[1,6,8,7,3,2,4,5]=>[1,7,3,8,2,6,4,5]=>0000111
[6,2,1,7,8,5,3,4]=>[2,6,5,3,8,1,7,4]=>[7,8,5,3,6,2,1,4]=>1001101
[6,7,3,8,4,1,5,2]=>[4,8,5,7,2,6,1,3]=>[6,7,2,5,1,8,4,3]=>0011011
[8,2,4,5,1,6,7,3]=>[5,8,7,2,4,1,6,3]=>[7,2,4,6,8,1,5,3]=>0001011
[4,5,8,3,6,7,1,2]=>[7,1,8,4,5,3,6,2]=>[4,5,8,3,6,7,1,2]=>0000011
[4,2,8,3,7,1,6,5]=>[7,4,8,2,6,1,3,5]=>[6,2,4,1,8,3,7,5]=>0010111
[7,6,3,8,4,5,1,2]=>[5,1,6,7,3,8,4,2]=>[8,3,7,6,4,5,1,2]=>0001111
[7,2,3,8,5,1,4,6]=>[5,8,1,2,7,4,3,6]=>[7,1,4,8,5,2,3,6]=>0001011
[7,2,3,8,5,1,6,4]=>[5,8,1,7,6,2,4,3]=>[6,1,7,4,8,5,2,3]=>0001111
[7,2,3,8,4,1,5,6]=>[4,8,1,7,2,5,3,6]=>[7,1,5,8,4,2,3,6]=>0010011
[7,2,3,5,8,1,4,6]=>[8,7,2,1,3,4,5,6]=>[7,2,8,1,3,4,5,6]=>0000011
[7,8,2,3,6,1,4,5]=>[6,8,2,1,4,3,7,5]=>[7,8,2,4,6,1,3,5]=>0000101
[2,6,4,8,1,3,7,5]=>[8,2,1,6,7,4,3,5]=>[2,7,4,6,1,3,8,5]=>0000111
[7,6,5,1,2,3,8,4]=>[5,1,2,6,7,8,3,4]=>[8,1,2,3,7,6,5,4]=>0001111
[3,5,6,4,1,2,7,8]=>[4,1,3,6,5,2,7,8]=>[3,5,6,4,1,2,7,8]=>0010100
[3,5,6,4,1,2,8,7]=>[4,1,3,6,5,2,8,7]=>[3,5,6,4,1,2,8,7]=>0010101
[7,6,5,1,4,2,3,8]=>[5,4,2,1,6,7,3,8]=>[4,2,7,6,5,1,3,8]=>0011110
[7,6,5,1,2,4,8,3]=>[5,1,6,2,7,8,4,3]=>[8,1,2,4,7,6,5,3]=>0001111
[7,6,5,1,3,4,2,8]=>[5,4,1,3,6,7,2,8]=>[4,1,3,7,6,5,2,8]=>0011110
[2,6,4,3,1,5,8,7]=>[3,2,4,6,1,5,8,7]=>[2,6,4,3,1,5,8,7]=>0110101
[2,6,4,3,1,8,5,7]=>[3,2,4,6,8,1,5,7]=>[2,8,4,3,1,6,5,7]=>0110101
[3,5,8,4,1,2,6,7]=>[4,1,3,8,5,2,6,7]=>[3,5,8,4,1,2,6,7]=>0010001
[3,5,8,4,1,6,2,7]=>[4,8,3,6,5,2,1,7]=>[3,5,6,2,8,4,1,7]=>0010101
[2,5,8,4,1,7,3,6]=>[4,2,8,7,5,1,3,6]=>[2,5,7,1,8,4,3,6]=>0010011
[3,6,4,2,1,7,8,5]=>[2,4,3,6,8,1,7,5]=>[3,7,8,4,2,1,6,5]=>1010101
[3,5,6,4,1,8,7,2]=>[4,6,3,7,5,2,8,1]=>[3,5,8,7,2,6,4,1]=>0010111
[2,6,4,5,1,3,7,8]=>[5,2,1,6,4,3,7,8]=>[2,6,4,5,1,3,7,8]=>0001100
[7,6,5,1,2,8,4,3]=>[5,1,4,6,7,8,2,3]=>[8,4,1,2,7,6,5,3]=>0011111
[7,6,5,1,8,2,4,3]=>[5,6,4,2,7,8,1,3]=>[4,2,8,1,7,6,5,3]=>0011111
[7,6,5,1,8,3,2,4]=>[5,3,6,2,7,8,1,4]=>[8,3,2,7,6,5,1,4]=>0101111
[7,6,5,1,4,8,2,3]=>[5,6,2,1,7,8,4,3]=>[8,2,4,7,6,5,1,3]=>0001111
[7,8,5,4,1,6,3,2]=>[4,3,5,8,6,1,7,2]=>[6,3,1,7,8,5,4,2]=>0111101
[3,6,4,5,1,7,8,2]=>[5,8,3,6,4,1,7,2]=>[3,6,4,7,8,1,5,2]=>0001101
[7,6,5,1,8,4,2,3]=>[5,4,2,6,7,8,1,3]=>[8,4,2,7,6,5,1,3]=>0011111
[2,6,5,3,1,4,8,7]=>[3,2,5,1,6,4,8,7]=>[2,6,5,3,1,4,8,7]=>0101101
[3,6,1,4,2,5,8,7]=>[6,4,3,1,2,5,8,7]=>[3,4,1,6,2,5,8,7]=>0010101
[8,7,1,6,5,2,4,3]=>[7,5,4,2,6,1,8,3]=>[4,2,6,5,1,8,7,3]=>0011111
[6,1,3,4,2,8,7,5]=>[6,4,1,3,7,2,8,5]=>[4,1,3,8,7,2,6,5]=>0010111
[2,4,5,6,1,8,7,3]=>[6,2,7,4,5,1,8,3]=>[2,4,5,8,7,1,6,3]=>0000111
[8,4,1,6,5,7,3,2]=>[4,3,8,7,6,2,5,1]=>[6,3,2,7,5,8,4,1]=>0110111
[2,8,3,4,7,5,1,6]=>[5,2,7,1,8,3,4,6]=>[2,8,1,7,5,3,4,6]=>0001011
[6,8,2,7,4,3,5,1]=>[5,8,4,7,3,6,2,1]=>[6,7,4,3,8,2,5,1]=>0011011
[4,7,8,5,1,6,3,2]=>[5,3,8,4,6,2,7,1]=>[4,6,3,2,7,8,5,1]=>0101101
[8,2,6,4,7,3,5,1]=>[5,8,7,6,3,2,4,1]=>[6,3,7,2,8,4,5,1]=>0001111
[4,8,6,1,7,3,2,5]=>[6,3,8,4,1,7,2,5]=>[4,7,3,1,8,6,2,5]=>0100111
[6,8,7,1,3,2,4,5]=>[7,3,1,2,4,6,8,5]=>[3,1,6,8,7,2,4,5]=>0100011
[2,5,1,8,7,4,6,3]=>[5,2,6,7,1,4,8,3]=>[2,8,7,1,6,4,5,3]=>0001111
[3,7,1,8,4,5,6,2]=>[7,6,3,8,4,5,1,2]=>[3,8,4,5,6,1,7,2]=>0000111
[8,6,4,3,1,7,2,5]=>[3,4,6,8,1,7,2,5]=>[7,1,8,6,4,3,2,5]=>0110111
[4,6,7,2,5,8,3,1]=>[3,8,7,4,1,6,5,2]=>[4,6,7,1,5,8,3,2]=>0100011
[6,2,1,3,4,8,7,5]=>[2,6,1,3,7,4,8,5]=>[8,7,2,1,3,4,6,5]=>1000111
[4,7,6,2,8,1,5,3]=>[8,6,5,4,1,7,2,3]=>[4,5,1,7,6,2,8,3]=>0001111
[6,4,5,1,7,8,3,2]=>[5,3,8,6,4,1,7,2]=>[6,4,7,8,3,1,5,2]=>0101101
[4,2,3,1,7,8,6,5]=>[3,4,2,1,6,8,7,5]=>[4,2,3,1,7,8,6,5]=>0110101
[3,4,2,1,8,6,7,5]=>[2,4,3,1,7,8,6,5]=>[3,4,2,1,8,6,7,5]=>1010011
[3,6,8,1,5,2,4,7]=>[8,5,3,2,1,6,4,7]=>[3,5,2,6,8,1,4,7]=>0001001
[3,2,8,7,4,5,1,6]=>[5,3,2,7,4,1,8,6]=>[3,2,8,7,4,5,1,6]=>0101011
[2,1,4,8,7,5,3,6]=>[2,1,5,4,7,3,8,6]=>[2,1,4,8,7,5,3,6]=>1001011
[2,1,6,8,3,7,5,4]=>[2,1,8,5,7,6,3,4]=>[2,1,6,7,5,3,8,4]=>1001011
[6,2,8,1,7,5,4,3]=>[8,6,4,5,7,2,1,3]=>[7,5,4,2,6,1,8,3]=>0011111
[2,6,5,4,8,1,3,7]=>[8,2,1,5,6,4,3,7]=>[2,6,5,4,8,1,3,7]=>0001101
[7,4,8,6,2,1,3,5]=>[2,6,1,8,4,7,3,5]=>[7,4,8,6,2,1,3,5]=>1000111
[4,6,2,8,3,7,5,1]=>[5,7,6,4,8,3,1,2]=>[4,8,3,6,1,7,5,2]=>0001111
[2,8,5,3,6,7,1,4]=>[7,2,5,1,8,3,6,4]=>[2,8,5,1,6,7,3,4]=>0001011
[7,8,5,6,4,1,3,2]=>[4,3,1,6,8,5,7,2]=>[3,1,7,8,5,6,4,2]=>0110101
[5,8,4,1,6,3,7,2]=>[4,8,7,6,5,2,1,3]=>[5,6,2,7,1,8,4,3]=>0010111
[7,6,8,3,5,1,4,2]=>[5,4,8,1,3,7,6,2]=>[7,6,8,1,4,3,5,2]=>0011011
[7,8,6,3,5,1,4,2]=>[5,4,6,1,3,8,7,2]=>[7,8,6,1,4,3,5,2]=>0011101
[3,4,7,5,6,2,1,8]=>[2,6,3,4,7,5,1,8]=>[3,4,7,5,6,2,1,8]=>1000110
[7,8,3,5,6,1,4,2]=>[6,4,8,1,3,5,7,2]=>[7,8,1,4,3,5,6,2]=>0010101
[4,1,8,5,6,3,2,7]=>[4,3,6,1,8,5,2,7]=>[8,5,6,3,1,4,2,7]=>0110101
[1,8,2,5,6,4,3,7]=>[1,8,4,6,2,5,3,7]=>[1,6,4,2,5,8,3,7]=>0010101
[6,1,8,5,3,7,4,2]=>[6,4,7,5,8,1,2,3]=>[8,5,1,7,4,2,6,3]=>0011111
[3,8,1,5,2,7,6,4]=>[8,5,3,6,1,7,2,4]=>[3,7,6,1,5,2,8,4]=>0001111
[1,5,2,4,6,7,8,3]=>[1,5,8,2,4,6,7,3]=>[1,6,7,8,2,4,5,3]=>0001001
[4,1,5,3,6,7,8,2]=>[4,8,5,1,3,6,7,2]=>[5,1,6,7,8,3,4,2]=>0011001
[8,1,6,5,3,7,2,4]=>[8,7,5,2,6,1,3,4]=>[6,5,2,7,1,8,3,4]=>0001111
[3,2,6,4,1,7,8,5]=>[4,3,2,6,8,1,7,5]=>[3,2,7,8,4,1,6,5]=>0110101
[7,6,4,3,1,2,8,5]=>[3,1,4,6,7,8,5,2]=>[8,5,7,6,4,3,1,2]=>0110111
[8,6,3,5,1,7,2,4]=>[5,7,6,2,3,8,1,4]=>[8,6,2,7,3,5,1,4]=>0001111
[1,5,3,2,6,7,8,4]=>[1,3,5,8,2,6,7,4]=>[1,6,7,8,3,2,5,4]=>0101001
[3,2,5,6,1,7,8,4]=>[6,3,2,8,5,1,7,4]=>[3,2,5,7,8,1,6,4]=>0100101
[3,2,8,7,6,1,4,5]=>[6,3,2,1,4,7,8,5]=>[3,2,8,7,6,1,4,5]=>0100111
[3,8,7,5,6,1,2,4]=>[6,1,3,2,7,5,8,4]=>[3,8,7,5,6,1,2,4]=>0000111
[8,2,7,5,6,1,3,4]=>[6,8,1,3,7,5,2,4]=>[7,5,8,1,3,6,2,4]=>0000111
[4,8,6,5,1,7,3,2]=>[5,3,6,4,8,7,1,2]=>[4,7,3,1,8,6,5,2]=>0101111
[1,7,4,6,2,3,8,5]=>[1,6,2,7,8,4,3,5]=>[1,8,4,7,2,3,6,5]=>0000111
[7,6,4,2,1,5,8,3]=>[2,4,6,7,1,8,5,3]=>[8,2,1,5,7,6,4,3]=>1010111
[5,7,4,6,1,3,8,2]=>[6,8,1,7,5,4,3,2]=>[5,7,4,8,1,3,6,2]=>0000111
[5,2,4,3,7,1,8,6]=>[7,5,4,2,3,8,1,6]=>[4,2,5,3,8,1,7,6]=>0011011
[3,5,4,2,7,1,8,6]=>[7,4,3,5,2,8,1,6]=>[3,5,4,2,8,1,7,6]=>0011011
[7,5,4,1,2,6,8,3]=>[4,1,5,7,8,2,6,3]=>[8,1,2,6,7,5,4,3]=>0011011
[1,7,4,2,3,6,8,5]=>[1,4,2,7,8,3,6,5]=>[1,8,4,2,3,6,7,5]=>0010011
[1,8,2,5,3,7,6,4]=>[1,8,5,6,2,7,3,4]=>[1,7,6,2,5,3,8,4]=>0001111
[6,8,1,5,4,7,3,2]=>[8,3,7,5,1,6,4,2]=>[5,3,1,6,7,4,8,2]=>0101011
[8,2,1,5,6,4,3,7]=>[2,8,4,6,1,5,3,7]=>[6,4,2,1,5,8,3,7]=>1010101
[3,2,8,1,6,5,4,7]=>[8,3,2,5,6,1,4,7]=>[3,2,6,5,1,8,4,7]=>0101101
[3,2,6,1,5,7,8,4]=>[6,3,2,8,1,5,7,4]=>[3,2,7,8,1,5,6,4]=>0100101
[8,6,1,5,4,7,2,3]=>[6,8,1,5,2,7,4,3]=>[5,1,7,4,8,6,2,3]=>0001111
[3,5,1,4,6,7,8,2]=>[5,8,3,1,4,6,7,2]=>[3,6,7,8,1,4,5,2]=>0001001
[5,2,1,4,6,7,8,3]=>[2,5,8,1,4,6,7,3]=>[6,7,8,2,1,4,5,3]=>1001001
[8,4,1,5,3,7,2,6]=>[4,8,7,5,2,3,1,6]=>[5,2,7,3,8,4,1,6]=>0011011
[7,5,4,1,3,2,8,6]=>[4,3,1,5,7,8,2,6]=>[3,1,8,5,4,2,7,6]=>0111011
[3,2,5,1,4,7,8,6]=>[5,3,2,1,4,8,7,6]=>[3,2,5,1,4,7,8,6]=>0101001
[7,1,4,3,5,2,8,6]=>[7,5,4,1,3,8,2,6]=>[4,1,5,3,8,2,7,6]=>0011011
[3,1,8,2,5,7,4,6]=>[3,8,1,7,2,4,5,6]=>[7,1,3,2,8,4,5,6]=>0100011
[2,8,1,6,4,3,7,5]=>[8,2,4,6,7,1,3,5]=>[2,7,4,1,6,3,8,5]=>0010111
[2,7,1,6,4,8,3,5]=>[7,2,8,6,3,1,4,5]=>[2,6,3,8,1,7,4,5]=>0000111
[8,3,2,7,1,6,5,4]=>[7,3,8,5,6,1,2,4]=>[6,5,3,1,8,2,7,4]=>0101111
[4,1,8,7,3,2,6,5]=>[4,3,7,1,6,2,8,5]=>[6,3,1,4,2,8,7,5]=>0110111
[4,1,7,2,8,6,5,3]=>[4,7,5,1,6,8,2,3]=>[8,6,5,1,7,2,4,3]=>0011111
[3,7,5,1,4,6,8,2]=>[5,7,3,2,8,4,6,1]=>[3,8,2,4,6,7,5,1]=>0001011
[3,6,8,5,1,4,7,2]=>[5,8,3,2,7,6,4,1]=>[3,6,7,2,4,8,5,1]=>0001011
[7,3,5,8,2,1,4,6]=>[2,8,7,1,3,4,5,6]=>[7,2,1,8,3,4,5,6]=>1000011
[7,4,2,8,1,6,5,3]=>[8,4,7,5,6,1,3,2]=>[6,5,1,7,4,3,8,2]=>0011111
[8,7,5,3,2,1,6,4]=>[2,3,5,7,6,4,8,1]=>[6,4,8,7,5,3,2,1]=>1101111
[7,5,2,6,3,1,4,8]=>[3,6,5,2,7,1,4,8]=>[7,5,2,6,3,1,4,8]=>0101110
[7,4,6,2,1,8,3,5]=>[2,6,8,7,3,4,1,5]=>[7,3,8,4,6,2,1,5]=>1000111
[6,8,4,5,2,1,7,3]=>[2,5,7,8,4,6,1,3]=>[6,8,4,7,2,1,5,3]=>1001011
[4,6,8,5,1,7,3,2]=>[5,3,8,4,7,6,2,1]=>[4,6,7,3,2,8,5,1]=>0101011
[5,1,7,6,4,2,8,3]=>[5,4,6,7,1,8,2,3]=>[8,1,7,6,4,2,5,3]=>0011111
[8,5,2,1,7,6,4,3]=>[2,5,4,8,6,7,3,1]=>[7,6,4,3,8,5,2,1]=>1011111
[3,6,1,7,4,8,2,5]=>[6,8,3,7,2,1,4,5]=>[3,7,2,8,1,6,4,5]=>0000111
[8,4,2,5,7,3,1,6]=>[3,7,4,8,1,2,5,6]=>[8,4,1,7,3,2,5,6]=>0110011
[3,4,6,8,5,7,1,2]=>[7,1,3,4,8,6,5,2]=>[3,4,6,8,5,7,1,2]=>0000011
[5,4,8,2,7,3,6,1]=>[6,8,7,5,4,3,2,1]=>[5,4,7,3,8,2,6,1]=>0001111
[6,4,3,8,7,1,2,5]=>[7,1,4,6,2,3,8,5]=>[6,4,1,2,8,7,3,5]=>0010111
[6,3,7,2,4,8,1,5]=>[8,7,6,2,1,3,4,5]=>[6,2,7,1,8,3,4,5]=>0000111
[5,6,8,4,2,7,3,1]=>[3,7,4,8,5,6,1,2]=>[5,6,8,4,1,7,3,2]=>0110011
[6,5,2,7,1,3,8,4]=>[7,5,1,6,8,4,3,2]=>[8,4,6,5,1,3,7,2]=>0001111
[8,6,5,4,2,1,7,3]=>[2,4,5,6,8,7,3,1]=>[7,3,8,6,5,4,2,1]=>1011111
[6,4,7,3,1,8,2,5]=>[3,7,8,6,1,4,2,5]=>[6,1,8,4,7,3,2,5]=>0100111
[7,5,8,4,6,3,2,1]=>[2,3,6,8,7,4,5,1]=>[7,4,8,5,6,3,2,1]=>1100111
[7,6,5,3,8,2,4,1]=>[4,8,5,2,6,7,3,1]=>[7,6,5,2,8,3,4,1]=>0011111
[6,5,4,3,2,1,9,8,7]=>[2,3,4,5,6,1,8,9,7]=>[6,5,4,3,2,1,9,8,7]=>11111011
[6,5,4,3,2,1,8,7,9]=>[2,3,4,5,6,1,8,7,9]=>[6,5,4,3,2,1,8,7,9]=>11111010
[5,4,3,2,1,9,8,7,6]=>[2,3,4,5,1,7,8,9,6]=>[5,4,3,2,1,9,8,7,6]=>11110111
[5,4,3,2,1,7,6,9,8]=>[2,3,4,5,1,7,6,9,8]=>[5,4,3,2,1,7,6,9,8]=>11110101
[5,4,3,2,1,7,6,8,9]=>[2,3,4,5,1,7,6,8,9]=>[5,4,3,2,1,7,6,8,9]=>11110100
[4,3,2,1,6,5,8,7,9]=>[2,3,4,1,6,5,8,7,9]=>[4,3,2,1,6,5,8,7,9]=>11101010
[4,3,2,1,6,5,7,8,9]=>[2,3,4,1,6,5,7,8,9]=>[4,3,2,1,6,5,7,8,9]=>11101000
[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>11010101
[3,2,1,5,4,6,7,8,9]=>[2,3,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>11010000
[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>10101000
[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>10100000
[7,6,5,4,3,2,1,10,9,8]=>[2,3,4,5,6,7,1,9,10,8]=>[7,6,5,4,3,2,1,10,9,8]=>111111011
[7,6,5,4,3,2,1,9,8,10]=>[2,3,4,5,6,7,1,9,8,10]=>[7,6,5,4,3,2,1,9,8,10]=>111111010
[5,4,3,2,1,7,6,9,8,10]=>[2,3,4,5,1,7,6,9,8,10]=>[5,4,3,2,1,7,6,9,8,10]=>111101010
[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>110101010
[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>101010100
[2,1,4,3,6,5,7,8,9,10]=>[2,1,4,3,6,5,7,8,9,10]=>[2,1,4,3,6,5,7,8,9,10]=>101010000
[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>101000000
[7,6,3,8,5,1,4,2]=>[5,4,8,3,6,7,1,2]=>[7,6,3,4,1,8,5,2]=>0011111
[6,4,8,1,3,2,5,7]=>[8,3,1,6,2,4,5,7]=>[3,1,6,2,8,4,5,7]=>0100101
[7,4,8,6,3,1,5,2]=>[3,6,5,8,4,7,2,1]=>[7,4,5,2,8,6,3,1]=>0101111
[3,2,7,8,5,1,6,4]=>[5,3,2,8,6,4,7,1]=>[3,2,6,4,7,8,5,1]=>0101101
[3,2,8,1,5,4,6,7]=>[8,3,2,5,1,4,6,7]=>[3,2,5,1,8,4,6,7]=>0101001
[6,1,4,8,5,3,7,2]=>[6,7,5,1,8,4,3,2]=>[8,5,1,4,7,3,6,2]=>0001111
[1,4,8,5,2,6,7,3]=>[1,5,8,4,7,3,6,2]=>[1,4,7,3,6,8,5,2]=>0001011
[6,1,8,4,3,7,2,5]=>[6,7,4,8,2,1,3,5]=>[8,4,2,7,1,6,3,5]=>0010111
[4,1,5,3,6,8,2,7]=>[4,8,5,1,3,6,2,7]=>[5,1,6,8,3,4,2,7]=>0011001
[7,1,4,6,3,8,5,2]=>[7,5,8,1,6,4,2,3]=>[6,1,4,8,5,2,7,3]=>0001111
[7,6,4,3,1,8,2,5]=>[3,4,6,7,1,8,2,5]=>[8,1,7,6,4,3,2,5]=>0110111
[1,5,3,2,8,6,4,7]=>[1,3,5,6,2,8,4,7]=>[1,8,6,3,2,5,4,7]=>0101101
[5,4,2,1,7,8,6,3]=>[2,4,5,6,3,8,7,1]=>[7,8,6,3,5,4,2,1]=>1011101
[8,6,2,7,1,4,5,3]=>[7,6,5,1,4,8,2,3]=>[5,1,4,8,6,2,7,3]=>0001111
[1,7,3,6,2,8,5,4]=>[1,6,7,5,8,3,2,4]=>[1,8,5,3,7,2,6,4]=>0001111
[8,6,3,7,4,1,2,5]=>[4,1,7,6,3,8,2,5]=>[8,6,3,7,4,1,2,5]=>0010111
[5,8,3,1,2,4,7,6]=>[3,1,8,2,5,7,4,6]=>[5,7,3,1,2,4,8,6]=>0100011
[8,1,3,2,4,5,6,7]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>0100001
[8,4,1,7,2,3,6,5]=>[4,8,1,7,6,3,2,5]=>[6,1,3,7,4,2,8,5]=>0010111
[8,2,1,6,5,4,7,3]=>[2,8,7,5,6,1,4,3]=>[6,5,2,1,7,4,8,3]=>1001111
[3,2,8,1,6,5,7,4]=>[8,3,2,7,6,1,5,4]=>[3,2,6,1,7,5,8,4]=>0100111
[8,6,1,5,4,7,3,2]=>[6,3,8,5,2,7,4,1]=>[5,3,2,7,4,8,6,1]=>0101111
[5,8,2,3,1,4,6,7]=>[3,8,2,1,5,4,6,7]=>[5,8,2,3,1,4,6,7]=>0100001
[4,2,1,3,5,8,7,6]=>[2,4,1,3,5,7,8,6]=>[4,2,1,3,5,8,7,6]=>1010011
[5,4,1,3,6,2,8,7]=>[4,5,2,6,3,1,8,7]=>[6,2,3,5,4,1,8,7]=>0011101
[3,2,5,1,4,6,8,7]=>[5,3,2,1,4,6,8,7]=>[3,2,5,1,4,6,8,7]=>0101001
[5,1,3,4,6,2,7,8]=>[5,6,1,3,4,2,7,8]=>[6,1,3,4,5,2,7,8]=>0001100
[3,1,2,5,4,7,6,9,8]=>[3,1,2,5,4,7,6,9,8]=>[3,1,2,5,4,7,6,9,8]=>01010101
[3,1,4,2,6,5,8,7,10,9]=>[3,4,1,2,6,5,8,7,10,9]=>[4,1,3,2,6,5,8,7,10,9]=>011010101
[3,1,5,2,7,4,9,6,10,8]=>[3,5,1,7,2,9,4,10,6,8]=>[10,1,3,2,5,4,7,6,9,8]=>010101011
[3,1,2,5,7,4,6,9,8]=>[3,1,2,7,5,4,6,9,8]=>[3,1,2,5,7,4,6,9,8]=>01000101
[1,3,5,2,4,7,6,9,8]=>[1,5,3,2,4,7,6,9,8]=>[1,3,5,2,4,7,6,9,8]=>00010101
[3,1,2,5,4,7,6,9,8,10]=>[3,1,2,5,4,7,6,9,8,10]=>[3,1,2,5,4,7,6,9,8,10]=>010101010
[6,8,2,4,5,1,3,7]=>[5,8,1,2,4,6,3,7]=>[6,8,1,4,5,2,3,7]=>0001001
[5,8,1,2,4,7,3,6]=>[8,1,7,2,5,3,4,6]=>[5,7,1,2,8,3,4,6]=>0000011
[7,5,1,8,2,3,6,4]=>[5,7,1,8,6,4,2,3]=>[6,4,8,1,7,5,2,3]=>0001111
[5,1,8,4,6,3,7,2]=>[5,7,6,8,1,4,3,2]=>[8,1,6,4,7,3,5,2]=>0001111
[4,5,7,3,2,6,8,1]=>[8,3,7,4,5,2,6,1]=>[4,5,7,3,2,6,8,1]=>0100011
[4,5,7,2,3,6,8,1]=>[8,7,2,4,5,3,6,1]=>[4,5,7,2,3,6,8,1]=>0000011
[4,5,2,7,1,6,8,3]=>[7,5,8,4,2,1,6,3]=>[4,8,2,5,1,6,7,3]=>0001011
[5,6,3,1,7,4,2,8]=>[3,6,4,7,5,2,1,8]=>[5,7,4,2,6,3,1,8]=>0110110
[7,3,4,1,8,5,2,6]=>[4,5,8,2,7,3,1,6]=>[7,2,8,5,3,4,1,6]=>0011011
[6,4,2,8,7,1,5,3]=>[7,4,6,5,1,3,8,2]=>[5,1,6,4,3,8,7,2]=>0011111
[7,2,4,8,1,5,3,6]=>[8,7,5,2,1,3,4,6]=>[5,2,7,1,8,3,4,6]=>0001011
[1,5,3,7,8,2,4,6]=>[1,8,5,2,3,4,7,6]=>[1,5,2,7,8,3,4,6]=>0001001
[3,2,6,7,1,8,4,5]=>[7,3,2,8,4,6,1,5]=>[3,2,6,8,4,7,1,5]=>0100011
[5,3,1,6,7,8,4,2]=>[3,5,4,8,2,6,7,1]=>[6,7,8,4,2,5,3,1]=>0111001
[2,1,3,4,8,7,5,6]=>[2,1,3,4,7,5,8,6]=>[2,1,3,4,8,7,5,6]=>1000011
[4,5,6,7,8,9,2,3,1]=>[3,9,2,4,5,6,7,8,1]=>[4,5,6,7,8,9,2,3,1]=>01000001
[5,6,7,8,9,3,4,2,1]=>[2,4,9,3,5,6,7,8,1]=>[5,6,7,8,9,3,4,2,1]=>10100001
[6,7,8,9,4,5,3,2,1]=>[2,3,5,9,4,6,7,8,1]=>[6,7,8,9,4,5,3,2,1]=>11010001
[7,8,9,5,6,4,3,2,1]=>[2,3,4,6,9,5,7,8,1]=>[7,8,9,5,6,4,3,2,1]=>11101001
[8,9,6,7,5,4,3,2,1]=>[2,3,4,5,7,9,6,8,1]=>[8,9,6,7,5,4,3,2,1]=>11110101
[6,3,8,7,5,4,1,2]=>[4,1,5,7,6,3,8,2]=>[6,3,8,7,5,4,1,2]=>0011111
[2,8,7,6,1,5,4,3]=>[6,2,4,5,1,7,8,3]=>[2,5,4,1,8,7,6,3]=>0011111
[5,2,8,7,6,1,4,3]=>[6,5,4,1,2,7,8,3]=>[4,1,5,2,8,7,6,3]=>0011111
[6,2,8,7,5,1,4,3]=>[5,7,4,2,6,1,8,3]=>[4,2,6,1,8,7,5,3]=>0011111
[6,1,8,7,5,4,3,2]=>[6,3,4,5,7,1,8,2]=>[8,7,5,4,3,1,6,2]=>0111111
[3,1,8,7,6,5,4,2]=>[3,4,1,5,6,7,8,2]=>[8,7,6,5,4,1,3,2]=>0111111
[7,8,2,6,1,5,4,3]=>[6,8,4,5,1,2,7,3]=>[5,4,1,7,8,2,6,3]=>0011101
[6,5,8,7,1,4,3,2]=>[7,3,4,1,6,5,8,2]=>[4,3,1,6,5,8,7,2]=>0110111
[4,8,1,7,6,5,3,2]=>[8,3,5,4,6,7,1,2]=>[4,7,6,5,3,1,8,2]=>0101111
[5,4,1,8,7,6,3,2]=>[4,3,5,6,2,7,8,1]=>[8,7,6,3,2,5,4,1]=>0111111
[6,4,8,1,7,5,3,2]=>[8,3,5,7,6,2,1,4]=>[6,3,2,7,5,1,8,4]=>0101111
[5,3,1,8,7,6,4,2]=>[3,5,4,6,2,7,8,1]=>[8,7,6,4,2,5,3,1]=>0111111
[7,8,2,1,6,5,4,3]=>[2,8,4,5,6,1,7,3]=>[6,5,4,2,1,7,8,3]=>1011101
[6,5,3,1,8,7,4,2]=>[3,5,4,6,7,1,8,2]=>[8,7,4,1,6,5,3,2]=>0111111
[6,4,3,1,8,7,5,2]=>[3,4,6,5,7,1,8,2]=>[8,7,5,1,6,4,3,2]=>0111111
[5,4,3,1,8,7,6,2]=>[3,4,5,6,1,7,8,2]=>[8,7,6,1,5,4,3,2]=>0111111
[7,5,2,1,8,6,4,3]=>[2,5,4,7,6,8,3,1]=>[8,6,4,3,7,5,2,1]=>1011111
[5,4,2,1,8,7,6,3]=>[2,4,5,6,3,7,8,1]=>[8,7,6,3,5,4,2,1]=>1011111
[7,3,2,1,8,6,5,4]=>[2,3,7,5,6,8,1,4]=>[8,6,5,3,2,1,7,4]=>1101111
[6,3,2,1,8,7,5,4]=>[2,3,6,5,7,1,8,4]=>[8,7,5,3,2,1,6,4]=>1101111
[6,1,4,2,3,5,8,7]=>[6,4,2,1,3,5,8,7]=>[4,2,6,1,3,5,8,7]=>0010101
[8,6,1,4,2,3,5,7]=>[6,4,2,1,3,8,5,7]=>[4,2,8,6,1,3,5,7]=>0010101
[6,8,1,4,2,3,5,7]=>[8,4,2,1,3,6,5,7]=>[4,2,6,8,1,3,5,7]=>0010001
[8,1,4,2,3,6,5,7]=>[8,4,2,1,6,3,5,7]=>[4,2,6,1,3,8,5,7]=>0010101
[4,1,8,2,3,6,5,7]=>[4,8,2,1,6,3,5,7]=>[6,2,4,1,3,8,5,7]=>0010101
[8,2,3,6,1,4,5,7]=>[6,8,2,1,4,3,5,7]=>[8,2,4,6,1,3,5,7]=>0000101
[6,2,3,8,1,4,5,7]=>[8,6,2,1,4,3,5,7]=>[6,2,4,8,1,3,5,7]=>0000101
[4,6,2,3,8,1,5,7]=>[8,6,2,4,1,3,5,7]=>[4,6,2,8,1,3,5,7]=>0000101
[4,8,2,3,6,1,5,7]=>[6,8,2,4,1,3,5,7]=>[4,8,2,6,1,3,5,7]=>0000101
[8,2,3,6,4,1,5,7]=>[4,6,1,8,2,3,5,7]=>[8,1,6,4,2,3,5,7]=>0010101
[8,4,3,6,2,1,5,7]=>[2,6,4,8,1,3,5,7]=>[8,4,2,1,6,3,5,7]=>1010101
[6,2,3,8,4,1,5,7]=>[4,8,1,6,2,3,5,7]=>[6,1,8,4,2,3,5,7]=>0010101
[8,4,2,3,6,1,5,7]=>[6,4,2,8,1,3,5,7]=>[8,4,2,6,1,3,5,7]=>0010101
[6,4,2,3,8,1,5,7]=>[8,4,2,6,1,3,5,7]=>[6,4,2,8,1,3,5,7]=>0010101
[2,6,4,3,8,1,5,7]=>[8,2,4,6,1,3,5,7]=>[2,6,4,1,8,3,5,7]=>0010101
[2,8,4,3,6,1,5,7]=>[6,2,4,8,1,3,5,7]=>[2,8,4,1,6,3,5,7]=>0010101
[2,6,3,8,4,1,5,7]=>[4,2,8,6,3,1,5,7]=>[2,6,3,8,4,1,5,7]=>0010101
[6,3,8,4,2,1,5,7]=>[2,4,8,6,3,1,5,7]=>[6,3,8,4,2,1,5,7]=>1010101
[2,6,3,8,1,4,5,7]=>[8,2,6,1,4,3,5,7]=>[2,6,1,4,8,3,5,7]=>0000101
[2,8,3,6,1,4,5,7]=>[6,2,8,1,4,3,5,7]=>[2,8,1,4,6,3,5,7]=>0000101
[8,3,6,4,2,1,5,7]=>[2,4,6,8,3,1,5,7]=>[8,3,6,4,2,1,5,7]=>1010101
[2,8,3,6,4,1,5,7]=>[4,2,6,8,3,1,5,7]=>[2,8,3,6,4,1,5,7]=>0010101
[8,3,6,2,4,1,5,7]=>[4,6,8,2,1,3,5,7]=>[8,2,6,1,4,3,5,7]=>0010101
[8,3,6,2,1,4,5,7]=>[2,6,8,1,4,3,5,7]=>[8,2,1,4,6,3,5,7]=>1000101
[6,2,1,3,8,4,5,7]=>[2,6,1,8,4,3,5,7]=>[8,4,6,2,1,3,5,7]=>1000101
[8,2,1,3,6,4,5,7]=>[2,8,1,6,4,3,5,7]=>[6,4,8,2,1,3,5,7]=>1000101
[6,3,8,2,4,1,5,7]=>[4,8,6,2,1,3,5,7]=>[6,2,8,1,4,3,5,7]=>0010101
[6,2,4,3,8,1,5,7]=>[8,6,4,2,1,3,5,7]=>[4,2,6,1,8,3,5,7]=>0010101
[1,6,4,2,7,5,8,3]=>[1,4,6,8,7,3,5,2]=>[1,7,3,8,5,6,4,2]=>0010111
[3,6,4,2,7,1,5,8]=>[7,4,3,6,1,2,5,8]=>[3,6,4,1,7,2,5,8]=>0010110
[6,4,8,5,3,7,1,2]=>[7,1,5,8,6,3,4,2]=>[6,3,8,5,4,7,1,2]=>0001111
[7,1,5,3,6,2,8,4]=>[7,6,5,8,1,3,2,4]=>[8,1,5,3,6,2,7,4]=>0001111
[7,8,1,4,2,5,6,3]=>[8,4,6,1,2,5,7,3]=>[6,1,4,2,5,7,8,3]=>0010101
[6,1,3,5,8,2,7,4]=>[6,8,1,7,3,5,2,4]=>[7,1,3,5,8,2,6,4]=>0000111
[6,1,8,7,4,2,3,5]=>[6,4,2,7,3,1,8,5]=>[8,7,4,2,3,6,1,5]=>0010111
[1,2,8,5,7,3,6,4]=>[1,2,7,6,8,3,5,4]=>[1,2,8,3,6,5,7,4]=>0000111
[1,3,6,8,7,5,2,4]=>[1,5,3,2,7,6,8,4]=>[1,3,6,8,7,5,2,4]=>0001011
[1,8,2,5,4,7,6,3]=>[1,8,6,5,2,7,4,3]=>[1,5,2,7,6,4,8,3]=>0001111
[1,2,7,3,5,8,6,4]=>[1,2,7,6,3,8,5,4]=>[1,2,8,6,3,5,7,4]=>0000111
[4,6,2,1,7,5,3,8]=>[2,6,5,4,7,1,3,8]=>[4,7,5,2,1,6,3,8]=>1001110
[1,6,3,7,8,5,2,4]=>[1,5,8,3,6,2,7,4]=>[1,6,3,7,8,5,2,4]=>0001101
[4,6,2,3,7,8,1,5]=>[8,6,2,4,1,3,7,5]=>[4,6,2,7,8,1,3,5]=>0000101
[4,2,1,3,5,7,8,6]=>[2,4,1,3,5,8,7,6]=>[4,2,1,3,5,7,8,6]=>1010001
[3,8,2,5,4,1,7,6]=>[4,5,3,8,1,7,2,6]=>[3,7,1,5,4,2,8,6]=>0011011
[4,2,6,3,8,7,1,5]=>[7,4,6,2,1,3,8,5]=>[6,2,4,1,8,7,3,5]=>0010111
[5,8,2,7,4,3,1,6]=>[3,4,7,8,5,1,2,6]=>[5,8,1,7,4,3,2,6]=>0110011
[4,3,8,5,1,7,2,6]=>[5,8,4,3,7,1,2,6]=>[4,3,7,1,8,5,2,6]=>0011011
[6,4,3,5,2,8,1,7]=>[8,5,4,6,3,2,1,7]=>[6,4,3,5,2,8,1,7]=>0011101
[6,5,3,8,4,2,1,7]=>[2,4,8,5,6,1,3,7]=>[6,5,2,1,8,4,3,7]=>1011101
[6,1,7,2,8,3,9,4,10,5]=>[6,7,8,9,10,1,2,3,4,5]=>[10,1,9,2,8,3,7,4,6,5]=>000011111
[8,2,5,7,3,6,4,1]=>[4,6,8,7,3,1,5,2]=>[7,3,8,1,5,6,4,2]=>0010111
[1,8,6,7,5,3,4,2]=>[1,4,5,3,7,8,6,2]=>[1,8,6,7,5,3,4,2]=>0011011
[2,7,6,1,3,5,4,8]=>[6,2,1,5,3,7,4,8]=>[2,5,1,3,7,6,4,8]=>0001110
[2,4,1,3,8,5,7,6]=>[4,2,1,3,8,7,5,6]=>[2,4,1,3,7,5,8,6]=>0010011
[2,4,1,3,5,8,7,6]=>[4,2,1,3,5,7,8,6]=>[2,4,1,3,5,8,7,6]=>0010011
[2,6,1,3,5,8,7,4]=>[6,2,1,7,3,5,8,4]=>[2,8,7,1,3,5,6,4]=>0000111
[4,6,1,3,5,8,7,2]=>[6,7,1,4,3,5,8,2]=>[4,8,7,1,3,5,6,2]=>0000111
[6,2,1,3,5,8,7,4]=>[2,6,1,7,3,5,8,4]=>[8,7,2,1,3,5,6,4]=>1000111
[4,2,1,3,6,5,7,8]=>[2,4,1,3,6,5,7,8]=>[4,2,1,3,6,5,7,8]=>1010100
[4,2,1,6,3,5,7,8]=>[2,4,6,1,3,5,7,8]=>[6,2,1,4,3,5,7,8]=>1010100
[1,6,4,3,8,5,7,2]=>[1,7,4,6,8,3,5,2]=>[1,8,4,3,6,5,7,2]=>0010111
[8,1,4,3,6,5,7,2]=>[8,7,4,1,6,3,5,2]=>[4,1,6,3,7,5,8,2]=>0010111
[8,2,1,4,3,5,7,6]=>[2,8,4,1,3,7,5,6]=>[4,2,1,7,3,5,8,6]=>1010011
[6,2,1,4,3,5,7,8]=>[2,6,4,1,3,5,7,8]=>[4,2,1,6,3,5,7,8]=>1010100
[8,2,4,1,3,5,7,6]=>[4,8,1,2,3,7,5,6]=>[7,1,4,2,3,5,8,6]=>0010011
[8,4,6,1,3,5,7,2]=>[6,7,1,8,3,4,5,2]=>[8,1,3,7,4,5,6,2]=>0000111
[8,1,4,6,3,5,7,2]=>[8,7,6,1,3,4,5,2]=>[6,1,7,3,4,5,8,2]=>0000111
[1,8,4,6,3,5,7,2]=>[1,7,6,8,3,4,5,2]=>[1,8,3,6,4,5,7,2]=>0000111
[1,6,4,8,3,5,7,2]=>[1,7,8,6,3,4,5,2]=>[1,6,3,8,4,5,7,2]=>0000111
[6,4,1,8,3,5,7,2]=>[4,6,7,8,1,2,5,3]=>[8,1,7,2,5,6,4,3]=>0010111
[4,2,8,1,3,5,7,6]=>[8,4,1,2,3,7,5,6]=>[4,1,7,2,3,5,8,6]=>0010011
[4,6,8,1,3,5,7,2]=>[8,7,1,4,3,6,5,2]=>[4,6,7,1,3,5,8,2]=>0000011
[4,6,1,3,8,5,7,2]=>[6,7,1,4,8,3,5,2]=>[4,8,1,3,7,5,6,2]=>0000111
[2,1,8,3,6,5,7,4]=>[2,1,8,7,6,3,5,4]=>[2,1,6,3,7,5,8,4]=>1000111
[2,1,6,4,3,5,7,8]=>[2,1,4,6,3,5,7,8]=>[2,1,6,4,3,5,7,8]=>1010100
[2,6,1,4,3,5,7,8]=>[6,2,4,1,3,5,7,8]=>[2,4,1,6,3,5,7,8]=>0010100
[2,8,1,4,3,5,7,6]=>[8,2,4,1,3,7,5,6]=>[2,4,1,7,3,5,8,6]=>0010011
[1,4,8,6,3,5,7,2]=>[1,7,6,4,3,8,5,2]=>[1,4,8,6,3,5,7,2]=>0000111
[2,8,4,1,3,5,7,6]=>[4,2,1,8,3,7,5,6]=>[2,7,4,1,3,5,8,6]=>0010011
[2,6,4,1,3,5,7,8]=>[4,2,1,6,3,5,7,8]=>[2,6,4,1,3,5,7,8]=>0010100
[4,6,2,1,3,5,7,8]=>[2,6,1,4,3,5,7,8]=>[4,6,2,1,3,5,7,8]=>1000100
[6,1,8,4,3,5,7,2]=>[6,7,4,8,3,1,5,2]=>[8,4,3,7,1,5,6,2]=>0010111
[1,8,6,4,3,5,7,2]=>[1,7,4,6,3,8,5,2]=>[1,8,6,4,3,5,7,2]=>0010111
[8,6,1,4,3,5,7,2]=>[6,8,4,2,3,7,5,1]=>[4,2,7,3,5,8,6,1]=>0010111
[8,6,4,1,3,5,7,2]=>[4,6,1,8,3,7,5,2]=>[7,1,3,5,8,6,4,2]=>0010111
[8,6,2,1,3,5,7,4]=>[2,6,1,8,4,7,5,3]=>[7,4,5,8,6,2,1,3]=>1000111
[5,8,1,4,6,3,7,2]=>[8,7,6,1,5,4,3,2]=>[5,6,1,4,7,3,8,2]=>0000111
[3,6,7,4,5,8,2,1]=>[2,8,3,7,4,6,5,1]=>[3,6,7,4,5,8,2,1]=>1000011
[5,6,4,1,8,7,3,2]=>[4,3,6,7,5,2,8,1]=>[5,8,7,3,2,6,4,1]=>0110111
[3,6,8,4,5,7,2,1]=>[2,7,3,8,4,6,5,1]=>[3,6,8,4,5,7,2,1]=>1000011
[3,7,8,4,5,6,2,1]=>[2,6,3,8,4,5,7,1]=>[3,7,8,4,5,6,2,1]=>1000101
[6,8,1,4,5,3,7,2]=>[8,7,5,1,4,6,3,2]=>[5,1,4,6,7,3,8,2]=>0001011
[3,8,1,5,4,6,7,2]=>[8,7,3,5,1,4,6,2]=>[3,5,1,7,4,6,8,2]=>0001011
[3,7,1,5,4,6,8,2]=>[7,8,3,5,1,4,6,2]=>[3,5,1,8,4,6,7,2]=>0001011
[6,7,1,4,5,3,8,2]=>[7,8,5,1,4,6,3,2]=>[5,1,4,6,8,3,7,2]=>0001011
[5,6,4,2,7,3,8,1]=>[8,4,6,7,5,3,2,1]=>[5,7,3,6,4,2,8,1]=>0010111
[5,4,7,2,8,3,6,1]=>[6,7,8,5,4,3,2,1]=>[5,4,8,3,7,2,6,1]=>0001111
[5,8,1,4,6,3,2,7]=>[8,3,6,1,5,4,2,7]=>[5,6,3,1,4,8,2,7]=>0100101
[3,8,1,5,4,6,2,7]=>[8,6,3,5,1,4,2,7]=>[3,5,1,6,4,8,2,7]=>0001101
[3,6,1,5,4,2,7,8]=>[6,4,3,5,1,2,7,8]=>[3,5,4,1,6,2,7,8]=>0011100
[3,6,1,5,4,7,8,2]=>[6,8,3,5,1,4,7,2]=>[3,5,1,7,8,4,6,2]=>0001101
[3,4,1,2,6,8,7,5]=>[4,1,3,2,7,6,8,5]=>[3,4,1,2,6,8,7,5]=>0010011
[6,8,3,1,4,7,2,5]=>[3,8,7,2,1,6,4,5]=>[6,7,2,8,3,1,4,5]=>0100011
[6,4,7,2,8,5,1,3]=>[5,8,2,7,6,1,4,3]=>[6,2,7,4,8,5,1,3]=>0001111
[5,8,1,4,7,3,2,6]=>[8,3,7,1,5,2,4,6]=>[5,7,3,1,8,2,4,6]=>0100011
[7,8,1,4,5,3,2,6]=>[8,3,5,1,4,2,7,6]=>[5,3,1,4,7,8,2,6]=>0101001
[3,8,1,5,4,7,2,6]=>[8,7,3,5,1,2,4,6]=>[3,5,1,7,2,8,4,6]=>0001011
[3,6,1,5,4,8,7,2]=>[6,7,3,5,1,4,8,2]=>[3,5,1,8,7,4,6,2]=>0001111
[3,6,1,5,4,7,2,8]=>[6,7,3,5,1,4,2,8]=>[3,5,1,7,4,6,2,8]=>0001110
[7,8,4,2,6,5,1,3]=>[5,4,2,6,8,1,7,3]=>[7,8,4,2,6,5,1,3]=>0011101
[6,8,4,2,7,5,3,1]=>[3,5,4,7,8,6,2,1]=>[6,8,4,2,7,5,3,1]=>0111011
[6,4,7,2,8,5,3,1]=>[3,5,8,7,6,2,4,1]=>[6,2,7,4,8,5,3,1]=>0101111
[3,4,1,2,8,5,7,6]=>[4,1,3,2,8,7,5,6]=>[3,4,1,2,7,5,8,6]=>0010011
[3,4,1,2,5,8,7,6]=>[4,1,3,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>0010011
[9,8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,9,3]=>[9,8,7,6,5,4,2,1,3]=>10111111
[9,8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,9,4]=>[9,8,7,6,5,3,2,1,4]=>11011111
[8,7,6,3,5,2,1,4]=>[2,5,6,1,3,7,8,4]=>[8,7,6,2,1,5,3,4]=>1001111
[9,8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,9,5]=>[9,8,7,6,4,3,2,1,5]=>11101111
[8,7,4,6,3,2,1,5]=>[2,3,6,7,1,4,8,5]=>[8,7,3,2,1,6,4,5]=>1100111
[9,8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,9,6]=>[9,8,7,5,4,3,2,1,6]=>11110111
[8,5,7,4,3,2,1,6]=>[2,3,4,7,8,1,5,6]=>[8,4,3,2,1,7,5,6]=>1110011
[9,8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,9,7]=>[9,8,6,5,4,3,2,1,7]=>11111011
[9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,8]=>[9,7,6,5,4,3,2,1,8]=>11111101
[9,8,7,6,5,4,1,3,2]=>[4,3,1,5,6,7,8,9,2]=>[3,1,9,8,7,6,5,4,2]=>01111111
[10,9,8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,9,10,3]=>[10,9,8,7,6,5,4,2,1,3]=>101111111
[10,9,8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,9,10,4]=>[10,9,8,7,6,5,3,2,1,4]=>110111111
[10,9,8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,9,10,5]=>[10,9,8,7,6,4,3,2,1,5]=>111011111
[10,9,8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,9,10,6]=>[10,9,8,7,5,4,3,2,1,6]=>111101111
[10,9,8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,9,10,7]=>[10,9,8,6,5,4,3,2,1,7]=>111110111
[6,5,8,4,3,2,1,7]=>[2,3,4,8,6,5,1,7]=>[6,5,8,4,3,2,1,7]=>1110101
[8,4,7,6,3,2,1,5]=>[2,3,6,7,4,8,1,5]=>[8,4,7,6,3,2,1,5]=>1100111
[10,9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,10,8]=>[10,9,7,6,5,4,3,2,1,8]=>111111011
[5,8,7,4,3,2,1,6]=>[2,3,4,7,5,1,8,6]=>[5,8,7,4,3,2,1,6]=>1110011
[10,8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,10,1,9]=>[10,8,7,6,5,4,3,2,1,9]=>111111101
[5,8,6,2,3,4,7,1]=>[7,6,2,3,5,8,4,1]=>[5,8,6,2,3,4,7,1]=>0000111
[4,5,2,7,3,1,8,6]=>[3,7,5,4,1,8,2,6]=>[4,5,1,8,3,2,7,6]=>0101011
[4,3,7,8,6,5,1,2]=>[5,1,4,3,6,8,7,2]=>[4,3,7,8,6,5,1,2]=>0011101
[2,1,8,7,4,5,3,6]=>[2,1,5,7,4,3,8,6]=>[2,1,8,7,4,5,3,6]=>1001011
[6,5,2,8,1,7,3,4]=>[8,5,6,2,7,3,1,4]=>[7,2,6,5,3,8,1,4]=>0001111
[8,5,4,3,7,2,6,1]=>[6,7,4,5,8,2,3,1]=>[8,5,4,2,7,3,6,1]=>0011111
[8,3,7,4,2,6,5,1]=>[5,4,6,7,8,2,1,3]=>[8,2,7,4,1,6,5,3]=>0011111
[2,8,3,4,1,7,5,6]=>[4,2,8,3,7,5,1,6]=>[2,7,5,8,3,4,1,6]=>0010011
[2,8,5,3,1,7,6,4]=>[3,2,5,8,6,7,4,1]=>[2,7,6,4,8,5,3,1]=>0101111
[3,8,7,5,1,6,4,2]=>[5,4,3,7,6,2,8,1]=>[3,6,4,2,8,7,5,1]=>0011111
[4,8,7,6,1,5,3,2]=>[6,3,5,4,1,7,8,2]=>[4,5,3,1,8,7,6,2]=>0101111
[7,4,8,6,2,1,5,3]=>[2,6,5,8,4,7,1,3]=>[7,4,5,2,1,8,6,3]=>1001111
[7,5,4,3,8,2,1,6]=>[2,8,4,5,7,1,3,6]=>[7,5,4,2,1,8,3,6]=>1011011
[3,7,8,4,1,2,6,5]=>[4,1,3,8,6,2,7,5]=>[3,6,4,1,2,7,8,5]=>0010101
[4,7,8,6,1,2,5,3]=>[6,1,5,4,2,8,7,3]=>[4,5,1,2,7,8,6,3]=>0001101
[6,4,7,8,3,1,2,5]=>[3,1,8,6,2,4,7,5]=>[6,3,1,2,7,8,4,5]=>0100101
[7,6,4,8,3,2,1,5]=>[2,3,8,6,1,7,4,5]=>[7,6,3,2,1,8,4,5]=>1100111
[7,5,8,6,2,1,4,3]=>[2,6,4,1,8,7,3,5]=>[4,2,1,7,3,8,6,5]=>1010111
[6,3,2,4,8,1,5,7]=>[8,3,6,2,1,4,5,7]=>[6,3,2,8,1,4,5,7]=>0100101
[8,3,4,7,2,5,6,1]=>[6,7,8,3,2,5,4,1]=>[8,3,5,7,2,4,6,1]=>0000111
[2,4,8,6,1,5,7,3]=>[6,2,8,4,3,7,5,1]=>[2,4,7,3,5,8,6,1]=>0000111
[2,5,8,6,1,4,7,3]=>[6,2,8,3,5,7,4,1]=>[2,5,7,3,4,8,6,1]=>0000111
[8,3,5,7,2,4,6,1]=>[6,7,8,2,3,4,5,1]=>[8,2,7,3,4,5,6,1]=>0000111
[8,4,6,7,2,3,5,1]=>[5,7,2,8,3,4,6,1]=>[8,2,3,6,7,4,5,1]=>0001011
[2,6,8,5,1,3,7,4]=>[5,2,1,8,7,6,4,3]=>[2,6,7,4,8,5,1,3]=>0001011
[2,6,8,4,1,3,7,5]=>[4,2,1,8,7,6,3,5]=>[2,6,7,4,1,3,8,5]=>0010011
[2,5,8,3,1,4,7,6]=>[3,2,8,1,5,7,4,6]=>[2,5,7,3,1,4,8,6]=>0100011
[2,3,5,4,1,8,6,7]=>[4,2,3,5,1,8,6,7]=>[2,3,5,4,1,8,6,7]=>0011001
[2,3,6,4,8,1,5,7]=>[8,2,3,6,1,4,5,7]=>[2,3,6,1,8,4,5,7]=>0000101
[1,8,4,6,3,5,2,7]=>[1,5,6,8,3,4,2,7]=>[1,8,3,6,4,5,2,7]=>0001101
[5,4,8,6,2,1,3,7]=>[2,6,1,5,4,8,3,7]=>[5,4,8,6,2,1,3,7]=>1001101
[2,5,6,1,4,7,8,3]=>[6,2,8,1,5,4,7,3]=>[2,5,7,8,1,4,6,3]=>0000101
[2,5,6,1,4,7,3,8]=>[6,2,7,1,5,4,3,8]=>[2,5,7,1,4,6,3,8]=>0000110
[1,8,7,6,3,2,5,4]=>[1,3,6,5,2,7,8,4]=>[1,5,3,2,8,7,6,4]=>0101111
[1,8,7,6,3,2,4,5]=>[1,3,6,2,4,7,8,5]=>[1,8,7,6,3,2,4,5]=>0100111
[6,3,5,1,7,2,4,8]=>[5,7,6,2,3,1,4,8]=>[6,2,7,3,5,1,4,8]=>0001110
[1,8,4,5,2,7,3,6]=>[1,5,7,8,4,3,2,6]=>[1,8,4,7,3,5,2,6]=>0001011
[1,8,4,5,2,7,6,3]=>[1,5,6,7,3,8,2,4]=>[1,8,3,7,6,2,5,4]=>0001111
[2,7,6,4,8,5,1,3]=>[5,2,1,8,6,7,3,4]=>[2,7,6,1,3,8,5,4]=>0001111
[3,7,1,6,8,5,2,4]=>[7,5,3,2,8,1,6,4]=>[3,8,5,2,6,7,1,4]=>0001011
[2,3,1,8,6,4,7,5]=>[3,2,1,6,8,7,5,4]=>[2,3,1,7,5,8,6,4]=>0100111
[1,8,4,3,6,2,5,7]=>[1,6,4,8,2,3,5,7]=>[1,8,4,2,6,3,5,7]=>0010101
[2,3,1,8,6,4,5,7]=>[3,2,1,6,4,8,5,7]=>[2,3,1,8,6,4,5,7]=>0100101
[1,8,4,5,2,6,3,7]=>[1,5,6,8,4,2,3,7]=>[1,8,4,6,2,5,3,7]=>0001101
[2,3,4,7,5,1,8,6]=>[5,2,3,4,7,8,1,6]=>[2,3,4,8,5,1,7,6]=>0001011
[2,3,4,7,5,1,6,8]=>[5,2,3,4,7,1,6,8]=>[2,3,4,7,5,1,6,8]=>0001010
[2,3,4,7,1,6,8,5]=>[7,2,3,4,8,1,6,5]=>[2,3,4,8,1,6,7,5]=>0000011
[2,3,4,6,1,8,7,5]=>[6,2,3,4,7,1,8,5]=>[2,3,4,8,7,1,6,5]=>0000111
[6,3,5,8,4,2,7,1]=>[7,4,8,6,2,5,3,1]=>[6,2,5,8,4,3,7,1]=>0010111
[7,4,8,5,3,2,1,6]=>[2,3,5,8,7,4,1,6]=>[7,4,8,5,3,2,1,6]=>1101011
[1,8,4,5,2,3,6,7]=>[1,5,2,8,4,3,6,7]=>[1,8,4,5,2,3,6,7]=>0001001
[5,2,4,6,8,3,7,1]=>[7,5,8,2,4,6,3,1]=>[6,8,2,4,5,3,7,1]=>0001011
[1,5,7,4,6,3,2,8]=>[1,3,6,7,5,4,2,8]=>[1,5,7,4,6,3,2,8]=>0100110
[6,8,3,4,5,7,2,1]=>[2,7,8,3,4,6,5,1]=>[6,8,3,4,5,7,2,1]=>1000011
[2,5,7,4,6,3,8,1]=>[8,2,6,7,5,4,3,1]=>[2,5,7,4,6,3,8,1]=>0000111
[5,1,4,6,8,3,2,7]=>[5,3,8,1,4,6,2,7]=>[6,8,3,1,4,5,2,7]=>0101001
[8,1,6,2,4,3,5,7]=>[8,6,4,2,3,1,5,7]=>[4,2,6,3,8,1,5,7]=>0010101
[8,7,1,2,4,3,5,6]=>[7,1,4,2,3,5,8,6]=>[4,1,2,8,7,3,5,6]=>0010011
[1,7,6,2,4,3,5,8]=>[1,6,4,2,3,7,5,8]=>[1,4,2,7,6,3,5,8]=>0010110
[8,7,3,2,4,6,5,1]=>[5,3,6,1,7,4,8,2]=>[8,7,3,1,4,6,5,2]=>0101111
[8,2,6,3,4,5,7,1]=>[7,8,6,3,4,2,5,1]=>[6,3,4,8,2,5,7,1]=>0000111
[1,7,6,3,4,5,2,8]=>[1,5,6,3,4,7,2,8]=>[1,7,6,3,4,5,2,8]=>0001110
[1,7,2,5,4,3,6,8]=>[1,7,4,5,2,3,6,8]=>[1,5,4,2,7,3,6,8]=>0011010
[6,8,3,2,4,7,5,1]=>[5,3,7,1,8,6,4,2]=>[6,8,3,1,4,7,5,2]=>0101011
[8,1,6,3,4,5,2,7]=>[8,5,6,3,4,1,2,7]=>[6,3,4,5,1,8,2,7]=>0001101
[8,1,2,5,4,3,6,7]=>[8,1,4,5,2,3,6,7]=>[5,4,1,2,8,3,6,7]=>0011001
[3,4,8,7,5,2,6,1]=>[6,5,3,4,7,2,8,1]=>[3,4,8,7,5,2,6,1]=>0001111
[3,2,8,6,1,5,4,7]=>[6,3,2,5,1,8,4,7]=>[3,2,5,1,8,6,4,7]=>0101101
[8,6,1,2,4,3,5,7]=>[6,1,4,2,3,8,5,7]=>[4,1,2,8,6,3,5,7]=>0010101
[3,5,2,8,6,1,4,7]=>[6,5,3,1,2,8,4,7]=>[3,5,1,8,6,2,4,7]=>0001101
[3,7,2,5,1,4,8,6]=>[5,7,3,1,2,8,4,6]=>[3,8,1,5,2,4,7,6]=>0001011
[5,1,8,6,2,3,4,7]=>[5,6,2,3,1,8,4,7]=>[8,6,2,3,5,1,4,7]=>0001101
[2,5,4,1,8,6,3,7]=>[4,2,5,6,3,8,1,7]=>[2,8,6,3,5,4,1,7]=>0011101
[3,7,6,1,8,2,5,4]=>[6,7,3,5,1,8,2,4]=>[3,5,1,8,2,7,6,4]=>0001111
[7,6,3,1,8,2,4,5]=>[3,6,7,2,4,8,1,5]=>[8,2,4,7,6,3,1,5]=>0100111
[8,1,3,6,4,7,2,5]=>[8,7,1,6,2,3,4,5]=>[6,1,7,2,3,8,4,5]=>0000111
[7,1,3,6,4,8,2,5]=>[7,8,1,6,2,3,4,5]=>[6,1,8,2,3,7,4,5]=>0000111
[7,5,4,1,3,8,2,6]=>[4,5,1,7,8,2,3,6]=>[8,1,7,5,4,2,3,6]=>0011011
[2,7,5,8,3,4,1,6]=>[4,2,8,3,7,1,5,6]=>[2,7,3,4,1,8,5,6]=>0010011
[7,2,3,6,1,4,8,5]=>[6,7,2,1,8,3,4,5]=>[8,2,7,1,3,4,6,5]=>0000111
[7,4,8,1,3,6,2,5]=>[8,6,1,7,2,3,4,5]=>[7,1,6,2,3,8,4,5]=>0000111
[8,1,2,3,5,7,4,6]=>[8,1,2,7,3,4,5,6]=>[7,1,2,3,8,4,5,6]=>0000011
[7,1,2,3,5,8,4,6]=>[7,1,2,8,3,4,5,6]=>[8,1,2,3,7,4,5,6]=>0000011
[8,6,1,4,7,3,2,5]=>[6,3,8,2,1,7,4,5]=>[7,3,2,8,6,1,4,5]=>0100111
[2,6,3,7,1,4,8,5]=>[7,2,6,1,8,3,4,5]=>[2,8,1,6,3,4,7,5]=>0000111
[2,6,3,8,1,4,7,5]=>[8,2,6,1,7,3,4,5]=>[2,7,1,6,3,4,8,5]=>0000111
[7,5,4,8,1,3,2,6]=>[8,3,1,5,7,2,4,6]=>[3,1,7,5,2,8,4,6]=>0101011
[8,5,4,7,1,3,2,6]=>[7,3,1,5,8,2,4,6]=>[3,1,8,5,2,7,4,6]=>0101011
[2,3,1,8,5,4,6,7]=>[3,2,1,5,8,4,6,7]=>[2,3,1,8,5,4,6,7]=>0101001
[3,5,2,6,7,1,8,4]=>[7,5,3,8,2,6,1,4]=>[3,6,8,2,5,1,7,4]=>0001011
[8,4,7,5,1,3,2,6]=>[5,3,1,7,8,4,2,6]=>[3,1,8,4,7,5,2,6]=>0101011
[6,1,2,8,3,4,7,5]=>[6,1,8,3,7,2,4,5]=>[7,3,8,1,2,4,6,5]=>0000111
[3,7,2,5,6,1,8,4]=>[6,7,3,8,2,5,1,4]=>[3,8,2,5,7,1,6,4]=>0000111
[6,8,4,2,5,1,7,3]=>[5,4,8,7,3,6,1,2]=>[6,7,3,8,4,1,5,2]=>0011011
[8,3,2,1,5,7,4,6]=>[2,3,8,7,1,4,5,6]=>[7,3,2,1,8,4,5,6]=>1100011
[2,8,3,6,4,7,1,5]=>[7,2,8,6,1,3,4,5]=>[2,6,1,8,3,7,4,5]=>0000111
[7,3,6,4,8,1,2,5]=>[8,1,7,6,2,3,4,5]=>[6,1,2,7,3,8,4,5]=>0000111
[8,3,6,4,7,1,2,5]=>[7,1,8,6,2,3,4,5]=>[6,1,2,8,3,7,4,5]=>0000111
[1,2,8,3,5,7,4,6]=>[1,2,8,7,3,4,5,6]=>[1,2,7,3,8,4,5,6]=>0000011
[1,8,3,2,5,7,4,6]=>[1,3,8,7,2,4,5,6]=>[1,7,3,2,8,4,5,6]=>0100011
[6,5,1,7,4,2,8,3]=>[5,4,6,7,8,3,2,1]=>[8,3,7,4,2,6,5,1]=>0011111
[7,3,6,4,8,2,1,5]=>[2,8,7,6,1,3,4,5]=>[6,2,1,7,3,8,4,5]=>1000111
[5,6,1,7,3,4,2,8]=>[6,4,7,3,5,1,2,8]=>[5,7,3,4,1,6,2,8]=>0010110
[8,3,7,1,6,5,2,4]=>[7,5,6,3,8,1,2,4]=>[8,3,6,5,1,7,2,4]=>0001111
[2,8,1,7,6,5,3,4]=>[8,2,5,3,6,7,1,4]=>[2,7,6,5,3,8,1,4]=>0001111
[6,4,2,8,5,1,7,3]=>[5,4,8,6,7,2,3,1]=>[7,2,6,4,3,8,5,1]=>0011111
[2,4,3,8,1,6,7,5]=>[8,2,4,3,7,1,6,5]=>[2,4,3,7,1,6,8,5]=>0010011
[4,2,3,7,8,5,1,6]=>[5,4,2,3,8,1,7,6]=>[4,2,3,7,8,5,1,6]=>0011001
[5,1,6,4,2,3,7,8]=>[5,4,2,6,1,3,7,8]=>[6,4,2,5,1,3,7,8]=>0011100
[6,4,7,8,1,5,2,3]=>[8,5,2,6,1,4,7,3]=>[6,2,5,4,7,8,1,3]=>0001101
[8,7,4,6,1,5,2,3]=>[6,5,2,7,1,4,8,3]=>[8,7,2,5,4,6,1,3]=>0001111
[8,6,5,7,1,4,2,3]=>[7,4,2,1,6,8,5,3]=>[4,2,8,6,5,7,1,3]=>0010111
[6,7,4,8,1,5,2,3]=>[8,5,2,7,1,6,4,3]=>[6,7,2,5,4,8,1,3]=>0001011
[8,4,7,6,1,5,2,3]=>[6,5,2,7,4,8,1,3]=>[8,4,5,2,7,6,1,3]=>0001111
[8,4,6,7,1,5,2,3]=>[7,5,2,8,1,4,6,3]=>[8,2,5,4,6,7,1,3]=>0001011
[5,1,6,8,4,2,3,7]=>[5,4,2,8,1,6,3,7]=>[6,8,4,2,5,1,3,7]=>0011001
[3,7,5,8,1,6,2,4]=>[8,6,3,2,7,1,5,4]=>[3,7,2,6,5,8,1,4]=>0000111
[2,4,7,1,5,8,6,3]=>[7,2,6,4,1,8,5,3]=>[2,4,8,6,1,5,7,3]=>0000111
[8,5,6,7,1,4,2,3]=>[7,4,2,1,8,5,6,3]=>[4,2,8,5,6,7,1,3]=>0010011
[8,6,7,5,1,4,2,3]=>[5,4,2,1,7,8,6,3]=>[4,2,8,6,7,5,1,3]=>0011011
[7,6,8,5,1,4,2,3]=>[5,4,2,1,8,7,6,3]=>[4,2,7,6,8,5,1,3]=>0011011
[2,4,6,7,1,5,8,3]=>[7,2,8,4,1,6,5,3]=>[2,4,6,8,1,5,7,3]=>0000011
[7,8,6,5,1,4,2,3]=>[5,4,2,1,6,8,7,3]=>[4,2,7,8,6,5,1,3]=>0011101
[3,1,7,5,4,2,8,6]=>[3,4,1,5,7,8,2,6]=>[8,5,4,1,3,2,7,6]=>0111011
[8,2,7,1,5,3,4,6]=>[7,8,5,3,1,4,2,6]=>[5,3,8,1,4,7,2,6]=>0001011
[6,3,7,1,5,4,2,8]=>[7,4,5,6,1,2,3,8]=>[6,1,5,4,2,7,3,8]=>0011110
[4,5,1,3,6,8,2,7]=>[5,8,1,4,3,6,2,7]=>[4,6,8,1,3,5,2,7]=>0001001
[3,6,2,1,5,8,4,7]=>[2,6,3,8,1,5,4,7]=>[3,8,2,1,5,6,4,7]=>1000101
[4,8,2,1,7,5,3,6]=>[2,8,5,4,7,3,1,6]=>[4,7,5,3,8,2,1,6]=>1001011
[4,7,1,2,6,3,8,5]=>[7,1,6,4,8,2,3,5]=>[4,8,1,2,6,3,7,5]=>0000111
[4,7,2,1,8,5,3,6]=>[2,7,5,4,8,3,1,6]=>[4,8,5,3,7,2,1,6]=>1001011
[2,7,4,1,6,5,3,8]=>[4,2,7,5,6,3,1,8]=>[2,6,5,3,7,4,1,8]=>0011110
[7,1,6,4,5,8,3,2]=>[7,3,8,6,4,1,5,2]=>[6,4,8,3,1,5,7,2]=>0100111
[2,6,4,1,7,5,3,8]=>[4,2,6,5,7,3,1,8]=>[2,7,5,3,6,4,1,8]=>0011110
[6,8,5,7,1,4,3,2]=>[7,3,4,1,8,6,5,2]=>[4,3,1,6,8,5,7,2]=>0110011
[8,6,5,7,1,4,3,2]=>[7,3,4,1,6,8,5,2]=>[4,3,1,8,6,5,7,2]=>0110111
[6,5,7,8,1,4,3,2]=>[8,3,4,1,6,5,7,2]=>[4,3,1,6,5,7,8,2]=>0110101
[4,2,8,1,6,5,3,7]=>[8,4,5,2,6,1,3,7]=>[6,5,2,4,1,8,3,7]=>0011101
[8,3,1,4,5,6,7,2]=>[3,8,7,2,4,5,6,1]=>[7,2,4,5,6,8,3,1]=>0100011
[5,3,1,4,8,6,7,2]=>[3,5,7,2,4,8,6,1]=>[8,6,7,2,4,5,3,1]=>0101011
[7,1,5,8,4,3,6,2]=>[7,6,4,8,1,3,5,2]=>[8,4,1,6,3,5,7,2]=>0010111
[5,8,1,6,4,3,7,2]=>[8,7,4,6,5,1,3,2]=>[5,6,4,1,7,3,8,2]=>0010111
[5,3,1,8,4,6,7,2]=>[3,5,7,8,2,4,6,1]=>[8,2,6,7,4,5,3,1]=>0101011
[8,2,6,1,4,5,3,7]=>[6,8,5,1,4,2,3,7]=>[5,1,4,8,2,6,3,7]=>0001101
[7,1,4,5,6,8,3,2]=>[7,3,8,1,4,5,6,2]=>[8,3,1,4,5,6,7,2]=>0100011
[8,5,6,7,1,4,3,2]=>[7,3,4,1,8,5,6,2]=>[4,3,1,8,5,6,7,2]=>0110011
[6,8,7,5,1,4,3,2]=>[5,3,4,1,7,6,8,2]=>[4,3,1,6,8,7,5,2]=>0111011
[3,5,1,7,4,6,8,2]=>[5,8,3,7,1,4,6,2]=>[3,7,1,6,8,4,5,2]=>0001011
[7,1,6,5,4,8,3,2]=>[7,3,8,5,6,1,4,2]=>[6,5,3,1,8,4,7,2]=>0101111
[5,7,6,8,1,4,3,2]=>[8,3,4,1,5,7,6,2]=>[4,3,1,5,7,6,8,2]=>0110011
[4,3,1,6,5,8,7,2]=>[3,4,7,2,6,5,8,1]=>[6,5,8,7,2,4,3,1]=>0110111
[5,3,1,2,4,8,7,6]=>[3,1,5,2,4,7,8,6]=>[5,3,1,2,4,8,7,6]=>0101011
[5,3,6,2,1,8,7,4]=>[2,6,5,7,3,1,8,4]=>[8,7,3,5,2,1,6,4]=>1001111
[5,3,7,2,8,4,1,6]=>[4,8,7,5,1,2,3,6]=>[5,1,7,2,8,4,3,6]=>0011011
[6,2,4,5,1,8,7,3]=>[5,6,7,2,4,1,8,3]=>[8,7,2,4,6,1,5,3]=>0001111
[1,6,4,5,2,8,7,3]=>[1,5,7,6,4,2,8,3]=>[1,6,4,8,7,2,5,3]=>0001111
[5,7,4,1,6,3,2,8]=>[4,3,7,6,5,2,1,8]=>[5,6,3,2,7,4,1,8]=>0110110
[4,8,3,5,6,7,1,2]=>[7,1,8,4,3,5,6,2]=>[4,8,3,5,6,7,1,2]=>0000011
[1,8,3,5,6,7,2,4]=>[1,7,8,2,3,5,6,4]=>[1,8,2,5,6,7,3,4]=>0000011
[4,8,1,5,6,7,2,3]=>[8,7,2,4,1,5,6,3]=>[4,7,2,5,6,8,1,3]=>0000011
[5,8,4,3,6,1,2,7]=>[6,1,4,8,5,3,2,7]=>[5,8,4,3,6,1,2,7]=>0010101
[5,3,8,4,1,7,2,6]=>[4,8,7,5,1,3,2,6]=>[5,1,7,3,8,4,2,6]=>0011011
[1,5,8,4,6,7,3,2]=>[1,3,7,8,5,4,6,2]=>[1,5,8,4,6,7,3,2]=>0100011
[1,4,8,3,6,7,5,2]=>[1,5,7,4,8,2,6,3]=>[1,4,8,2,6,7,5,3]=>0001011
[3,8,2,5,6,7,1,4]=>[7,8,3,1,2,5,6,4]=>[3,8,1,5,6,7,2,4]=>0000011
[7,8,4,3,6,2,1,5]=>[2,6,4,8,1,3,7,5]=>[7,8,4,2,1,6,3,5]=>1010101
[4,3,1,6,8,7,5,2]=>[3,4,5,2,7,6,8,1]=>[6,8,7,5,2,4,3,1]=>0111011
[6,3,5,8,2,7,1,4]=>[7,8,6,1,3,5,2,4]=>[6,1,5,8,3,7,2,4]=>0000111
[7,5,4,8,6,2,1,3]=>[2,6,1,5,8,7,3,4]=>[7,5,2,1,3,8,6,4]=>1001111
[7,3,6,1,8,2,4,5]=>[6,8,7,2,4,3,1,5]=>[7,2,4,8,3,6,1,5]=>0000111
[1,7,6,5,8,3,4,2]=>[1,4,8,3,6,7,5,2]=>[1,7,6,5,8,3,4,2]=>0010111
[1,8,5,3,6,7,4,2]=>[1,4,7,5,8,2,6,3]=>[1,8,5,2,6,7,4,3]=>0011011
[8,4,1,5,6,7,3,2]=>[4,3,8,7,2,5,6,1]=>[7,3,2,5,6,8,4,1]=>0110011
[8,4,2,5,6,7,1,3]=>[7,4,1,8,2,5,6,3]=>[8,4,1,5,6,7,2,3]=>0010011
[4,1,8,5,6,7,3,2]=>[4,3,7,1,8,5,6,2]=>[8,5,6,7,3,1,4,2]=>0110011
[1,2,8,5,6,7,3,4]=>[1,2,7,3,8,5,6,4]=>[1,2,8,5,6,7,3,4]=>0000011
[1,5,3,8,6,7,4,2]=>[1,4,7,5,2,8,6,3]=>[1,5,2,8,6,7,4,3]=>0011011
[1,4,5,8,6,7,3,2]=>[1,3,7,4,5,8,6,2]=>[1,4,5,8,6,7,3,2]=>0100011
[4,3,5,8,1,7,2,6]=>[8,7,4,3,5,2,1,6]=>[4,3,5,7,2,8,1,6]=>0010011
[3,5,4,8,6,1,2,7]=>[6,1,3,5,4,8,2,7]=>[3,5,4,8,6,1,2,7]=>0001101
[1,4,8,5,6,7,2,3]=>[1,7,2,4,8,5,6,3]=>[1,4,8,5,6,7,2,3]=>0000011
[2,7,1,5,6,3,4,8]=>[7,2,6,3,1,5,4,8]=>[2,6,3,5,7,1,4,8]=>0000110
[2,7,1,4,3,6,5,8]=>[7,2,4,1,6,3,5,8]=>[2,4,1,6,3,7,5,8]=>0010110
[4,3,7,2,5,6,8,1]=>[8,7,4,3,2,5,6,1]=>[4,3,7,2,5,6,8,1]=>0010011
[2,6,3,1,4,5,8,7]=>[3,2,6,1,4,5,8,7]=>[2,6,3,1,4,5,8,7]=>0100101
[3,7,1,4,2,6,8,5]=>[7,4,3,1,8,2,6,5]=>[3,4,1,8,2,6,7,5]=>0010011
[3,7,1,5,6,2,8,4]=>[7,6,3,8,1,5,2,4]=>[3,8,1,5,6,2,7,4]=>0000111
[8,4,2,6,3,7,1,5]=>[7,4,8,6,1,3,2,5]=>[6,1,8,4,3,7,2,5]=>0010111
[8,4,2,3,5,7,1,6]=>[7,4,2,8,3,1,5,6]=>[8,4,2,3,7,1,5,6]=>0010011
[5,3,4,6,2,8,1,7]=>[8,6,5,3,4,2,1,7]=>[5,3,4,6,2,8,1,7]=>0001101
[6,4,7,2,3,8,1,5]=>[8,7,2,6,1,4,3,5]=>[6,2,7,4,8,1,3,5]=>0000111
[6,5,7,2,8,3,1,4]=>[3,8,7,2,6,5,1,4]=>[6,5,7,2,8,3,1,4]=>0100111
[8,7,6,1,4,5,2,3]=>[6,5,2,1,4,7,8,3]=>[5,2,4,8,7,6,1,3]=>0001111
[8,7,6,1,3,2,5,4]=>[6,3,1,5,2,7,8,4]=>[3,1,5,2,8,7,6,4]=>0101111
[8,7,4,5,1,6,2,3]=>[5,6,2,7,4,1,8,3]=>[8,7,4,6,2,5,1,3]=>0001111
[8,5,6,4,1,7,2,3]=>[4,6,1,7,8,5,2,3]=>[8,5,7,1,6,4,2,3]=>0010111
[6,7,4,2,3,1,8,5]=>[3,4,2,7,8,6,1,5]=>[6,8,4,2,3,1,7,5]=>0110011
[6,7,5,3,1,2,8,4]=>[3,1,5,7,8,6,4,2]=>[6,8,4,7,5,3,1,2]=>0101011
[6,7,5,4,1,8,2,3]=>[4,5,2,7,8,6,1,3]=>[6,8,2,7,5,4,1,3]=>0011011
[10,4,1,2,3,5,6,7,8,9]=>[4,1,2,10,3,5,6,7,8,9]=>[10,4,1,2,3,5,6,7,8,9]=>001000001
[5,10,1,2,3,4,6,7,8,9]=>[10,1,2,3,5,4,6,7,8,9]=>[5,10,1,2,3,4,6,7,8,9]=>000000001
[2,11,1,3,4,5,6,7,8,9,10]=>[11,2,1,3,4,5,6,7,8,9,10]=>[2,11,1,3,4,5,6,7,8,9,10]=>0000000001
[2,3,10,1,4,5,6,7,8,9]=>[10,2,3,1,4,5,6,7,8,9]=>[2,3,10,1,4,5,6,7,8,9]=>000000001
[11,7,1,2,3,4,5,6,8,9,10]=>[7,1,2,3,4,5,11,6,8,9,10]=>[11,7,1,2,3,4,5,6,8,9,10]=>0000010001
[6,3,2,4,7,5,1,8]=>[5,3,7,1,6,4,2,8]=>[6,3,1,4,7,5,2,8]=>0101110
[4,2,1,6,3,7,8,5]=>[2,4,6,1,8,3,7,5]=>[7,8,2,1,4,3,6,5]=>1010101
[2,7,6,8,3,1,4,5]=>[3,2,8,1,4,7,6,5]=>[2,7,6,8,3,1,4,5]=>0100011
[7,4,3,5,8,6,2,1]=>[2,6,4,8,1,7,5,3]=>[7,4,2,1,5,8,6,3]=>1010111
[4,2,1,3,7,8,6,5]=>[2,4,1,3,6,8,7,5]=>[4,2,1,3,7,8,6,5]=>1010101
[5,8,1,7,4,3,6,2]=>[8,6,4,7,5,3,1,2]=>[5,7,4,3,6,1,8,2]=>0010111
[3,7,8,6,2,1,4,5]=>[2,6,3,1,4,8,7,5]=>[3,7,8,6,2,1,4,5]=>1000101
[4,2,1,3,6,8,7,5]=>[2,4,1,3,7,6,8,5]=>[4,2,1,3,6,8,7,5]=>1010011
[7,3,2,4,8,6,5,1]=>[5,3,6,2,8,7,4,1]=>[7,3,2,4,8,6,5,1]=>0101111
[4,2,1,6,3,8,7,5]=>[2,4,6,1,7,3,8,5]=>[8,7,2,1,4,3,6,5]=>1010111
[4,8,6,2,7,3,5,1]=>[5,6,8,4,2,7,3,1]=>[4,7,2,8,6,3,5,1]=>0001111
[7,3,4,2,6,8,1,5]=>[8,4,7,3,1,2,6,5]=>[7,3,4,1,6,8,2,5]=>0010011
[3,6,7,5,2,4,8,1]=>[8,5,3,2,7,6,4,1]=>[3,6,7,5,2,4,8,1]=>0001011
[3,6,7,5,2,4,1,8]=>[4,5,3,2,7,6,1,8]=>[3,6,7,5,2,4,1,8]=>0011010
[3,7,6,8,4,2,5,1]=>[5,4,3,8,2,7,6,1]=>[3,7,6,8,4,2,5,1]=>0011011
[5,8,1,7,4,2,6,3]=>[8,4,7,6,5,3,1,2]=>[5,6,3,7,4,1,8,2]=>0010111
[4,2,1,3,8,6,7,5]=>[2,4,1,3,7,8,6,5]=>[4,2,1,3,8,6,7,5]=>1010011
[4,2,1,8,3,7,6,5]=>[2,4,8,1,6,7,3,5]=>[7,6,2,1,4,3,8,5]=>1010111
[7,8,2,4,1,3,6,5]=>[4,8,1,2,6,3,7,5]=>[6,1,4,2,3,7,8,5]=>0010101
[2,6,1,5,4,7,8,3]=>[6,2,8,5,1,4,7,3]=>[2,5,1,7,8,4,6,3]=>0001101
[4,6,3,5,8,7,1,2]=>[7,1,6,4,3,5,8,2]=>[4,6,3,5,8,7,1,2]=>0000111
[2,3,6,8,4,1,5,7]=>[4,2,3,8,1,6,5,7]=>[2,3,6,8,4,1,5,7]=>0010001
[4,7,5,2,1,3,6,8]=>[2,5,1,4,7,3,6,8]=>[4,7,5,2,1,3,6,8]=>1001010
[3,5,6,2,4,1,7,8]=>[4,6,3,2,5,1,7,8]=>[3,5,6,2,4,1,7,8]=>0010100
[7,1,6,8,4,5,3,2]=>[7,3,5,8,4,1,6,2]=>[8,4,5,3,1,6,7,2]=>0101011
[5,7,4,6,8,1,3,2]=>[8,3,1,7,5,4,6,2]=>[3,1,5,7,4,6,8,2]=>0100011
[1,8,4,6,7,5,3,2]=>[1,3,5,7,8,2,6,4]=>[1,8,3,2,6,7,5,4]=>0101011
[4,5,8,6,1,7,3,2]=>[6,3,8,4,5,7,2,1]=>[4,5,7,3,2,8,6,1]=>0100111
[4,8,5,1,6,7,3,2]=>[5,3,8,4,7,2,6,1]=>[4,7,3,2,6,8,5,1]=>0101011
[8,1,4,5,6,7,3,2]=>[8,3,7,1,4,5,6,2]=>[7,3,1,4,5,6,8,2]=>0100011
[5,6,7,1,4,2,3,8]=>[7,4,2,1,5,6,3,8]=>[4,2,5,6,7,1,3,8]=>0010010
[8,3,1,4,6,2,5,7]=>[3,8,6,2,1,4,5,7]=>[6,2,8,3,1,4,5,7]=>0100101
[3,5,1,2,8,4,7,6]=>[5,1,3,8,2,7,4,6]=>[3,7,1,2,5,4,8,6]=>0001011
[2,3,5,8,6,1,7,4]=>[6,2,3,8,5,7,4,1]=>[2,3,5,7,4,8,6,1]=>0000111
[8,2,4,3,6,7,1,5]=>[7,8,4,2,1,3,6,5]=>[4,2,8,1,6,7,3,5]=>0010011
[3,2,8,5,7,1,6,4]=>[7,3,2,6,8,1,5,4]=>[3,2,8,1,6,5,7,4]=>0100111
[2,8,7,1,4,6,5,3]=>[7,2,5,1,6,4,8,3]=>[2,6,5,1,4,8,7,3]=>0001111
[2,7,3,6,5,8,1,4]=>[8,2,7,1,6,3,5,4]=>[2,6,1,7,5,8,3,4]=>0000111
[1,7,8,2,6,4,3,5]=>[1,8,4,6,3,2,7,5]=>[1,6,4,3,7,8,2,5]=>0010101
[1,7,3,8,2,6,4,5]=>[1,8,7,6,4,2,3,5]=>[1,6,4,7,2,8,3,5]=>0000111
[1,2,7,3,6,4,5,8]=>[1,2,7,6,4,3,5,8]=>[1,2,6,4,7,3,5,8]=>0000110
[7,1,5,8,3,2,4,6]=>[7,3,8,2,1,4,5,6]=>[8,3,2,7,1,4,5,6]=>0100011
[1,6,2,8,4,3,7,5]=>[1,6,4,8,7,2,3,5]=>[1,7,4,2,8,3,6,5]=>0010111
[1,3,8,7,2,4,6,5]=>[1,7,3,2,6,4,8,5]=>[1,3,6,2,4,8,7,5]=>0000111
[1,2,3,4,8,5,7,6]=>[1,2,3,4,8,7,5,6]=>[1,2,3,4,7,5,8,6]=>0000011
[2,4,7,5,6,8,3,1]=>[3,2,8,4,7,5,6,1]=>[2,4,7,5,6,8,3,1]=>0100011
[2,4,8,7,5,6,3,1]=>[3,2,6,4,7,5,8,1]=>[2,4,8,7,5,6,3,1]=>0100111
[2,8,5,7,3,6,4,1]=>[4,2,6,7,8,1,5,3]=>[2,8,1,7,5,6,4,3]=>0010111
[3,1,8,5,2,7,6,4]=>[3,5,1,8,6,7,4,2]=>[7,6,4,8,5,1,3,2]=>0101111
[8,3,5,7,1,6,4,2]=>[7,4,6,8,2,1,5,3]=>[8,2,6,4,1,5,7,3]=>0010111
[8,3,6,1,4,5,7,2]=>[6,7,8,1,4,3,5,2]=>[8,1,4,7,3,5,6,2]=>0000111
[2,5,7,3,4,8,6,1]=>[6,2,8,1,5,7,4,3]=>[2,5,7,1,4,8,6,3]=>0000111
[3,1,8,7,2,6,4,5]=>[3,7,1,6,4,2,8,5]=>[6,4,8,7,1,3,2,5]=>0100111
[4,8,1,7,2,3,6,5]=>[8,7,2,4,6,3,1,5]=>[4,6,2,3,7,1,8,5]=>0000111
[3,7,1,8,2,6,4,5]=>[7,8,3,6,4,2,1,5]=>[3,6,4,8,2,7,1,5]=>0000111
[7,3,8,5,1,6,4,2]=>[5,4,8,6,7,3,1,2]=>[7,3,6,4,1,8,5,2]=>0011111
[7,8,3,6,1,4,5,2]=>[6,5,8,1,4,3,7,2]=>[7,8,1,4,5,3,6,2]=>0001101
[7,4,8,1,2,3,6,5]=>[8,1,2,7,6,3,4,5]=>[6,1,2,3,7,4,8,5]=>0000111
[8,7,4,6,1,2,5,3]=>[6,1,5,7,2,4,8,3]=>[8,7,1,2,5,4,6,3]=>0001111
[4,8,6,1,2,3,7,5]=>[6,1,2,4,8,7,5,3]=>[4,7,5,8,6,1,2,3]=>0000111
[4,1,2,5,3,8,7,6]=>[4,1,5,2,3,7,8,6]=>[5,1,2,4,3,8,7,6]=>0011011
[3,1,4,8,7,5,2,6]=>[3,5,1,4,7,2,8,6]=>[4,8,7,5,1,3,2,6]=>0101011
[5,4,1,8,2,7,6,3]=>[4,5,8,6,2,7,3,1]=>[7,6,2,8,3,5,4,1]=>0011111
[6,4,8,1,2,5,3,7]=>[8,1,5,6,2,4,3,7]=>[6,1,2,5,4,8,3,7]=>0001101
[5,6,3,8,7,1,4,2]=>[7,4,6,1,5,3,8,2]=>[5,6,1,4,3,8,7,2]=>0010111
[5,4,1,6,8,2,7,3]=>[4,5,8,7,2,6,3,1]=>[6,7,2,8,3,5,4,1]=>0011011
[6,7,4,1,2,8,3,5]=>[4,1,7,8,2,6,3,5]=>[6,8,1,2,7,4,3,5]=>0010011
[8,6,5,1,2,3,7,4]=>[5,1,2,6,8,7,3,4]=>[7,1,2,3,8,6,5,4]=>0001111
[7,8,6,4,1,2,5,3]=>[4,1,6,5,3,8,7,2]=>[5,3,7,8,6,4,1,2]=>0011101
[1,4,6,3,7,2,5,8]=>[1,7,6,4,2,3,5,8]=>[1,4,6,2,7,3,5,8]=>0000110
[8,6,2,5,3,1,7,4]=>[3,5,6,8,4,7,2,1]=>[7,4,8,6,2,5,3,1]=>0101111
[8,2,3,4,5,1,7,6]=>[5,8,2,3,4,7,1,6]=>[7,2,3,4,5,1,8,6]=>0001011
[1,8,3,4,2,7,5,6]=>[1,4,8,3,7,5,2,6]=>[1,7,5,8,3,4,2,6]=>0010011
[8,7,2,3,1,6,5,4]=>[3,7,2,5,6,1,8,4]=>[6,5,2,3,1,8,7,4]=>0101111
[7,8,2,4,3,1,6,5]=>[3,4,8,1,6,2,7,5]=>[6,1,4,3,2,7,8,5]=>0110101
[5,1,4,3,7,2,6,8]=>[5,7,4,1,3,2,6,8]=>[4,1,7,3,5,2,6,8]=>0011010
[2,1,8,3,7,5,4,6]=>[2,1,8,5,7,4,3,6]=>[2,1,7,5,4,8,3,6]=>1001011
[4,5,2,8,1,6,7,3]=>[8,5,7,4,2,1,6,3]=>[4,7,2,5,1,6,8,3]=>0001011
[1,3,8,2,5,7,4,6]=>[1,8,3,7,2,4,5,6]=>[1,3,7,2,8,4,5,6]=>0000011
[1,4,8,6,2,7,3,5]=>[1,6,8,4,2,7,3,5]=>[1,4,7,2,8,6,3,5]=>0000111
[3,5,6,8,4,1,7,2]=>[4,8,3,7,5,6,2,1]=>[3,5,6,7,2,8,4,1]=>0010011
[8,2,3,1,4,5,7,6]=>[3,8,2,1,4,7,5,6]=>[7,2,3,1,4,5,8,6]=>0100011
[8,5,1,3,2,4,7,6]=>[5,3,1,2,8,7,4,6]=>[3,1,7,5,2,4,8,6]=>0101011
[7,5,1,3,2,6,4,8]=>[5,3,1,7,6,4,2,8]=>[3,1,6,4,7,5,2,8]=>0101110
[4,5,7,1,2,6,3,8]=>[7,1,6,4,5,2,3,8]=>[4,5,6,1,2,7,3,8]=>0000110
[3,7,4,1,2,6,5,8]=>[4,1,3,7,6,2,5,8]=>[3,6,4,1,2,7,5,8]=>0010110
[7,8,1,2,5,3,6,4]=>[8,1,5,6,2,3,7,4]=>[6,1,2,5,3,7,8,4]=>0001101
[3,8,4,1,2,5,7,6]=>[4,1,3,8,2,7,5,6]=>[3,7,4,1,2,5,8,6]=>0010011
[1,7,5,3,2,8,4,6]=>[1,3,5,7,8,2,4,6]=>[1,8,3,2,7,5,4,6]=>0101011
[1,3,4,8,2,5,7,6]=>[1,8,3,4,2,7,5,6]=>[1,3,4,7,2,5,8,6]=>0000011
[1,4,8,3,2,5,7,6]=>[1,3,8,4,2,7,5,6]=>[1,4,7,3,2,5,8,6]=>0100011
[1,2,4,8,3,5,7,6]=>[1,2,8,4,3,7,5,6]=>[1,2,4,7,3,5,8,6]=>0000011
[1,3,8,4,2,6,7,5]=>[1,4,3,8,7,2,6,5]=>[1,3,7,4,2,6,8,5]=>0010011
[1,4,8,2,3,5,7,6]=>[1,8,2,4,3,7,5,6]=>[1,4,7,2,3,5,8,6]=>0000011
[6,5,7,3,8,2,4,1]=>[4,8,7,2,6,5,3,1]=>[6,5,7,2,8,3,4,1]=>0010111
[6,7,5,2,1,8,4,3]=>[2,5,4,7,8,6,3,1]=>[6,8,4,3,7,5,2,1]=>1011011
[3,4,8,7,5,2,1,6]=>[2,5,3,4,7,1,8,6]=>[3,4,8,7,5,2,1,6]=>1001011
[1,7,5,2,8,4,6,3]=>[1,5,7,6,8,2,3,4]=>[1,8,2,6,3,7,5,4]=>0001111
[5,6,8,3,1,7,2,4]=>[3,8,7,1,5,6,2,4]=>[5,6,7,1,8,3,2,4]=>0100011
[3,4,7,1,8,6,2,5]=>[7,6,3,4,2,8,1,5]=>[3,4,8,6,2,7,1,5]=>0000111
[3,4,6,8,2,1,5,7]=>[2,8,3,4,1,6,5,7]=>[3,4,6,8,2,1,5,7]=>1000001
[3,8,2,5,6,1,4,7]=>[6,8,3,1,2,5,4,7]=>[3,8,1,5,6,2,4,7]=>0000101
[3,5,2,8,6,4,1,7]=>[4,6,3,5,1,8,2,7]=>[3,5,1,8,6,4,2,7]=>0011101
[4,2,5,7,3,8,6,1]=>[6,4,8,2,5,7,1,3]=>[5,7,2,4,1,8,6,3]=>0010111
[3,1,2,8,5,6,4,7]=>[3,1,2,6,8,5,4,7]=>[3,1,2,8,5,6,4,7]=>0100101
[5,2,6,8,4,1,3,7]=>[4,8,2,5,1,6,3,7]=>[5,2,6,8,4,1,3,7]=>0011001
[1,5,6,8,3,4,2,7]=>[1,4,8,3,5,6,2,7]=>[1,5,6,8,3,4,2,7]=>0010001
[4,5,8,1,6,3,2,7]=>[8,3,6,4,5,1,2,7]=>[4,5,6,3,1,8,2,7]=>0100101
[4,5,7,3,8,2,6,1]=>[6,8,7,4,5,2,3,1]=>[4,5,7,2,8,3,6,1]=>0000111
[7,1,3,5,4,8,2,6]=>[7,8,1,5,3,2,4,6]=>[5,1,3,8,2,7,4,6]=>0001011
[5,7,3,8,4,6,1,2]=>[6,1,7,8,5,4,3,2]=>[5,8,4,7,3,6,1,2]=>0000111
[4,6,3,7,8,5,2,1]=>[2,5,8,4,6,1,7,3]=>[4,6,2,1,7,8,5,3]=>1001101
[5,3,6,7,8,4,2,1]=>[2,4,8,5,1,6,7,3]=>[5,2,1,6,7,8,4,3]=>1011001
[1,5,3,6,7,8,4,2]=>[1,4,8,5,2,6,7,3]=>[1,5,2,6,7,8,4,3]=>0011001
[6,3,7,1,8,4,5,2]=>[7,5,6,8,4,3,1,2]=>[8,4,6,3,5,1,7,2]=>0001111
[6,7,2,4,8,1,5,3]=>[8,7,5,2,1,6,4,3]=>[5,2,6,7,1,4,8,3]=>0001011
[3,2,5,6,7,8,1,4]=>[8,3,2,1,5,6,7,4]=>[3,2,5,6,7,8,1,4]=>0100001
[6,2,7,1,3,4,8,5]=>[7,6,1,3,8,2,4,5]=>[8,1,3,6,2,4,7,5]=>0000111
[4,2,6,3,7,8,5,1]=>[5,4,8,2,6,1,7,3]=>[6,2,4,1,7,8,5,3]=>0011101
[3,6,2,7,4,1,8,5]=>[4,7,3,6,8,1,2,5]=>[3,8,1,6,4,2,7,5]=>0010111
[6,7,3,2,1,4,8,5]=>[2,3,7,1,8,6,4,5]=>[6,8,3,2,1,4,7,5]=>1100011
[7,3,4,8,6,2,1,5]=>[2,6,8,1,3,7,4,5]=>[7,2,1,8,6,3,4,5]=>1000111
[6,3,7,8,2,5,4,1]=>[4,5,8,6,3,1,7,2]=>[6,3,7,8,1,5,4,2]=>0011101
[2,6,7,4,8,5,3,1]=>[3,2,5,8,7,6,1,4]=>[2,6,7,3,1,8,5,4]=>0101011
[6,2,4,7,1,8,5,3]=>[7,6,5,2,8,4,1,3]=>[8,5,2,4,6,1,7,3]=>0001111
[4,6,2,7,1,8,5,3]=>[7,6,5,4,8,2,1,3]=>[4,8,5,2,6,1,7,3]=>0001111
[2,5,7,8,1,6,3,4]=>[8,2,6,3,5,1,7,4]=>[2,5,6,3,7,8,1,4]=>0000101
[6,3,7,1,8,2,5,4]=>[7,8,6,5,2,3,1,4]=>[5,2,6,3,8,1,7,4]=>0001111
[1,6,4,7,8,2,5,3]=>[1,8,5,6,2,4,7,3]=>[1,6,2,5,4,7,8,3]=>0001101
[2,5,6,1,7,8,4,3]=>[6,2,4,8,5,1,7,3]=>[2,5,7,8,4,1,6,3]=>0010101
[5,6,1,2,7,8,4,3]=>[6,1,4,8,5,2,7,3]=>[5,7,8,4,1,2,6,3]=>0010101
[6,7,2,8,5,4,1,3]=>[4,5,1,8,7,6,2,3]=>[6,7,1,8,5,4,2,3]=>0011011
[1,6,7,4,8,5,3,2]=>[1,3,5,8,7,6,2,4]=>[1,6,7,3,2,8,5,4]=>0101011
[1,8,2,4,6,3,5,7]=>[1,8,6,2,3,4,5,7]=>[1,6,2,8,3,4,5,7]=>0000101
[7,2,8,3,5,1,4,6]=>[5,7,8,1,3,4,2,6]=>[8,1,7,3,4,5,2,6]=>0001011
[1,3,7,4,6,2,5,8]=>[1,6,3,7,2,4,5,8]=>[1,3,7,2,6,4,5,8]=>0000110
[1,5,7,4,3,6,2,8]=>[1,6,4,7,5,3,2,8]=>[1,5,7,4,3,6,2,8]=>0010110
[1,8,4,5,3,6,2,7]=>[1,6,5,8,4,3,2,7]=>[1,8,4,5,3,6,2,7]=>0001101
[1,8,2,5,4,6,7,3]=>[1,8,7,5,2,4,6,3]=>[1,5,2,7,4,6,8,3]=>0001011
[3,6,2,7,1,4,5,8]=>[7,6,3,1,4,2,5,8]=>[3,6,1,4,7,2,5,8]=>0000110
[6,3,8,1,2,4,7,5]=>[8,1,6,2,7,3,4,5]=>[7,1,2,6,3,4,8,5]=>0000111
[1,3,7,4,6,2,8,5]=>[1,6,3,7,8,4,2,5]=>[1,3,8,4,7,2,6,5]=>0000111
[1,4,7,5,2,6,8,3]=>[1,5,7,4,8,3,6,2]=>[1,4,8,3,6,7,5,2]=>0001011
[2,5,4,7,1,6,8,3]=>[7,2,8,5,4,1,6,3]=>[2,5,4,8,1,6,7,3]=>0001011
[4,2,3,8,6,7,1,5]=>[7,4,2,3,1,8,6,5]=>[4,2,3,8,6,7,1,5]=>0010011
[6,2,5,4,8,3,7,1]=>[7,6,8,5,2,4,3,1]=>[5,2,8,4,6,3,7,1]=>0001111
[5,2,3,4,8,1,6,7]=>[8,5,2,3,4,1,6,7]=>[5,2,3,4,8,1,6,7]=>0001001
[3,5,2,4,7,1,6,8]=>[7,5,3,2,4,1,6,8]=>[3,5,2,4,7,1,6,8]=>0001010
[4,5,3,7,1,6,2,8]=>[7,6,5,4,3,1,2,8]=>[4,5,3,6,1,7,2,8]=>0001110
[6,2,4,8,5,1,3,7]=>[5,8,2,1,6,4,3,7]=>[6,2,4,8,5,1,3,7]=>0001101
[7,6,3,8,5,1,2,4]=>[5,1,8,3,6,7,2,4]=>[7,6,3,8,5,1,2,4]=>0001111
[1,4,3,7,8,2,5,6]=>[1,8,4,3,2,5,7,6]=>[1,4,3,7,8,2,5,6]=>0010001
[4,2,6,7,3,8,1,5]=>[8,4,7,2,1,6,3,5]=>[6,7,2,4,1,8,3,5]=>0010011
[1,5,7,4,2,8,6,3]=>[1,4,7,6,5,8,3,2]=>[1,5,8,6,3,7,4,2]=>0010111
[1,3,7,2,8,6,4,5]=>[1,7,3,6,4,8,2,5]=>[1,3,8,6,4,7,2,5]=>0000111
[1,4,3,7,8,6,2,5]=>[1,6,4,3,2,8,7,5]=>[1,4,3,7,8,6,2,5]=>0010101
[4,3,6,5,7,8,1,2]=>[8,1,4,3,6,5,7,2]=>[4,3,6,5,7,8,1,2]=>0010101
[4,2,6,7,3,8,5,1]=>[5,4,8,2,7,6,1,3]=>[6,7,2,4,1,8,5,3]=>0011011
[4,6,5,2,3,1,8,7]=>[3,5,2,4,6,1,8,7]=>[4,6,5,2,3,1,8,7]=>0101101
[6,4,2,5,3,1,8,7]=>[3,5,4,6,1,2,8,7]=>[6,4,1,5,3,2,8,7]=>0111101
[6,4,2,5,3,8,7,1]=>[7,4,6,5,3,2,8,1]=>[5,3,6,4,2,8,7,1]=>0011111
[6,4,2,5,8,7,3,1]=>[3,7,4,6,1,5,8,2]=>[6,4,1,5,8,7,3,2]=>0110111
[6,8,7,4,5,2,3,1]=>[3,5,2,7,4,6,8,1]=>[6,8,7,4,5,2,3,1]=>0101011
[4,8,6,7,5,2,3,1]=>[3,5,2,4,7,8,6,1]=>[4,8,6,7,5,2,3,1]=>0101011
[8,6,2,4,7,5,3,1]=>[3,5,7,2,6,8,4,1]=>[8,6,2,4,7,5,3,1]=>0101111
[6,8,2,4,7,5,3,1]=>[3,5,7,2,8,6,4,1]=>[6,8,2,4,7,5,3,1]=>0101011
[4,8,2,6,7,5,3,1]=>[3,5,7,4,8,2,6,1]=>[4,8,2,6,7,5,3,1]=>0101011
[2,8,4,6,7,5,3,1]=>[3,2,5,7,8,1,6,4]=>[2,8,3,1,6,7,5,4]=>0101011
[2,8,6,7,4,5,3,1]=>[3,2,5,7,4,8,6,1]=>[2,8,6,7,4,5,3,1]=>0101011
[2,6,4,5,8,7,3,1]=>[3,2,7,6,4,5,8,1]=>[2,6,4,5,8,7,3,1]=>0100111
[4,6,2,8,7,5,3,1]=>[3,5,7,4,6,2,8,1]=>[4,6,2,8,7,5,3,1]=>0101111
[8,2,4,6,7,5,3,1]=>[3,5,7,2,8,4,6,1]=>[8,2,4,6,7,5,3,1]=>0101011
[6,2,4,8,7,5,3,1]=>[3,5,7,2,6,4,8,1]=>[6,2,4,8,7,5,3,1]=>0101111
[8,6,7,2,4,5,3,1]=>[3,5,7,1,4,8,6,2]=>[8,6,7,1,4,5,3,2]=>0101011
[6,4,5,2,8,7,3,1]=>[3,7,5,6,4,1,8,2]=>[6,4,5,1,8,7,3,2]=>0101111
[4,2,3,6,8,7,5,1]=>[5,4,2,3,7,6,8,1]=>[4,2,3,6,8,7,5,1]=>0011011
[8,6,7,4,2,5,3,1]=>[3,5,4,7,1,8,6,2]=>[8,6,7,4,1,5,3,2]=>0111011
[8,4,6,7,2,5,3,1]=>[3,5,7,8,1,4,6,2]=>[8,1,6,7,4,5,3,2]=>0101011
[6,4,8,7,2,5,3,1]=>[3,5,7,6,1,4,8,2]=>[6,1,8,7,4,5,3,2]=>0101111
[6,2,8,7,4,5,3,1]=>[3,5,6,7,4,1,8,2]=>[8,7,4,6,1,5,3,2]=>0101111
[4,6,8,7,5,2,3,1]=>[3,5,2,4,7,6,8,1]=>[4,6,8,7,5,2,3,1]=>0101011
[2,1,6,8,7,4,5,3]=>[2,1,5,7,4,6,8,3]=>[2,1,6,8,7,4,5,3]=>1001011
[2,6,8,7,4,5,3,1]=>[3,2,5,7,4,6,8,1]=>[2,6,8,7,4,5,3,1]=>0101011
[2,4,8,6,7,5,3,1]=>[3,2,5,4,7,8,6,1]=>[2,4,8,6,7,5,3,1]=>0101011
[4,2,8,6,7,5,3,1]=>[3,5,4,1,7,8,6,2]=>[4,1,8,6,7,5,3,2]=>0111011
[6,2,8,4,7,5,3,1]=>[3,5,7,6,8,4,2,1]=>[8,4,6,2,7,5,3,1]=>0101111
[8,2,6,4,7,5,3,1]=>[3,5,7,8,6,4,2,1]=>[6,4,8,2,7,5,3,1]=>0101111
[6,4,8,2,7,5,3,1]=>[3,5,7,8,6,2,4,1]=>[6,2,8,4,7,5,3,1]=>0101111
[4,6,8,2,7,5,3,1]=>[3,5,7,4,8,6,2,1]=>[4,6,8,2,7,5,3,1]=>0101011
[2,1,6,8,4,7,5,3]=>[2,1,5,7,8,6,3,4]=>[2,1,6,8,3,7,5,4]=>1001011
[4,8,6,2,7,5,3,1]=>[3,5,7,4,6,8,2,1]=>[4,8,6,2,7,5,3,1]=>0101111
[9,4,8,3,7,2,6,1,5]=>[6,7,8,9,1,2,3,4,5]=>[9,1,8,2,7,3,6,4,5]=>00001111
[9,2,4,6,8,1,3,5,7]=>[8,9,1,2,3,4,5,6,7]=>[9,1,8,2,3,4,5,6,7]=>00000011
[9,6,8,1,2,3,4,5,7]=>[8,1,2,3,4,9,5,6,7]=>[9,1,2,3,4,5,8,6,7]=>00000011
[7,9,1,2,3,4,5,6,8]=>[9,1,2,3,4,5,7,6,8]=>[7,9,1,2,3,4,5,6,8]=>00000001
[10,3,6,9,2,5,8,1,4,7]=>[8,9,10,1,2,3,4,5,6,7]=>[10,1,9,2,8,3,4,5,6,7]=>000000111
[10,3,5,7,9,1,2,4,6,8]=>[9,1,10,2,3,4,5,6,7,8]=>[10,1,2,9,3,4,5,6,7,8]=>000000011
[10,7,9,1,2,3,4,5,6,8]=>[9,1,2,3,4,5,10,6,7,8]=>[10,1,2,3,4,5,6,9,7,8]=>000000011
[6,2,5,7,4,8,3,1]=>[3,8,6,7,1,5,4,2]=>[7,1,5,6,4,8,3,2]=>0100111
[6,7,3,2,5,8,4,1]=>[4,3,8,7,1,6,5,2]=>[6,7,3,1,5,8,4,2]=>0110011
[7,1,6,3,5,8,4,2]=>[7,4,8,6,2,1,5,3]=>[6,2,8,4,1,5,7,3]=>0010111
[7,3,1,2,5,8,6,4]=>[3,1,7,6,2,8,5,4]=>[8,6,3,1,2,5,7,4]=>0100111
[1,6,3,5,2,4,8,7]=>[1,5,6,2,3,4,8,7]=>[1,6,2,5,3,4,8,7]=>0001101
[3,4,8,2,7,5,1,6]=>[5,7,3,4,8,2,1,6]=>[3,4,8,2,7,5,1,6]=>0001011
[6,3,2,8,5,7,4,1]=>[4,3,7,6,8,1,5,2]=>[8,3,1,6,5,7,4,2]=>0110111
[3,8,4,7,2,5,6,1]=>[6,7,3,8,2,5,4,1]=>[3,8,2,5,7,4,6,1]=>0000111
[2,4,8,1,5,3,7,6]=>[8,2,5,4,1,7,3,6]=>[2,4,5,1,7,3,8,6]=>0001011
[1,8,4,6,7,3,5,2]=>[1,5,7,8,3,4,6,2]=>[1,8,3,6,7,4,5,2]=>0001011
[5,7,6,8,3,4,2,1]=>[2,4,8,3,5,7,6,1]=>[5,7,6,8,3,4,2,1]=>1010011
[5,2,3,7,4,8,6,1]=>[6,5,2,8,3,7,1,4]=>[7,2,3,5,1,8,6,4]=>0001111
[7,8,1,5,4,3,6,2]=>[8,6,4,5,1,3,7,2]=>[5,4,1,6,3,7,8,2]=>0011101
[2,7,8,5,4,6,1,3]=>[6,2,1,5,8,4,7,3]=>[2,7,8,5,4,6,1,3]=>0001101
[8,3,1,7,4,2,5,6]=>[3,8,4,7,1,5,2,6]=>[7,4,1,5,8,3,2,6]=>0110011
[8,1,3,7,6,2,4,5]=>[8,6,1,2,4,7,3,5]=>[7,6,1,4,8,2,3,5]=>0000111
[4,7,3,2,5,1,8,6]=>[5,3,7,4,2,8,1,6]=>[4,8,3,2,5,1,7,6]=>0101011
[3,2,4,7,5,8,6,1]=>[6,3,2,4,8,7,1,5]=>[3,2,4,7,1,8,6,5]=>0100111
[4,2,3,8,6,5,1,7]=>[5,4,2,3,6,8,1,7]=>[4,2,3,8,6,5,1,7]=>0011101
[3,2,8,1,4,6,5,7]=>[8,3,2,1,6,4,5,7]=>[3,2,6,1,4,8,5,7]=>0100101
[3,7,8,5,6,1,2,4]=>[6,1,3,2,8,5,7,4]=>[3,7,8,5,6,1,2,4]=>0000101
[3,6,1,8,4,7,2,5]=>[6,7,3,8,2,1,4,5]=>[3,8,2,7,1,6,4,5]=>0000111
[4,7,8,1,3,2,6,5]=>[8,3,1,4,6,2,7,5]=>[3,1,4,6,2,7,8,5]=>0100101
[4,7,8,3,1,2,6,5]=>[3,1,8,4,6,2,7,5]=>[4,6,3,1,2,7,8,5]=>0100101
[4,1,6,8,2,3,7,5]=>[4,8,2,1,7,6,3,5]=>[6,7,2,4,1,3,8,5]=>0010011
[4,5,1,2,8,3,7,6]=>[5,1,8,4,2,7,3,6]=>[4,7,1,2,5,3,8,6]=>0001011
[4,5,2,1,8,3,7,6]=>[2,5,8,4,1,7,3,6]=>[4,7,2,1,5,3,8,6]=>1001011
[3,2,6,8,4,7,1,5]=>[7,3,2,8,1,6,4,5]=>[3,2,6,8,1,7,4,5]=>0100011
[4,2,6,8,3,1,7,5]=>[3,8,4,1,7,6,2,5]=>[4,1,6,7,3,2,8,5]=>0110011
[4,2,5,1,8,3,7,6]=>[5,4,8,2,1,7,3,6]=>[7,2,4,1,5,3,8,6]=>0011011
[4,1,2,5,8,3,7,6]=>[4,1,8,2,5,7,3,6]=>[5,7,1,2,4,3,8,6]=>0010011
[5,1,2,4,3,8,7,6]=>[5,1,4,2,3,7,8,6]=>[4,1,2,5,3,8,7,6]=>0011011
[4,2,5,3,8,1,7,6]=>[8,4,5,2,3,7,1,6]=>[5,2,4,3,7,1,8,6]=>0011011
[3,2,5,4,8,7,1,6]=>[7,3,2,5,4,1,8,6]=>[3,2,5,4,8,7,1,6]=>0101011
[3,5,2,4,8,7,1,6]=>[7,5,3,2,4,1,8,6]=>[3,5,2,4,8,7,1,6]=>0001011
[5,4,2,1,3,8,7,6]=>[2,4,1,5,3,7,8,6]=>[5,4,2,1,3,8,7,6]=>1011011
[5,1,4,2,3,8,7,6]=>[5,4,2,1,3,7,8,6]=>[4,2,5,1,3,8,7,6]=>0011011
[5,4,3,1,2,8,7,6]=>[3,1,4,5,2,7,8,6]=>[5,4,3,1,2,8,7,6]=>0111011
[3,1,5,4,8,7,2,6]=>[3,7,1,5,4,2,8,6]=>[5,4,8,7,1,3,2,6]=>0101011
[3,5,4,1,8,7,2,6]=>[4,5,3,7,2,1,8,6]=>[3,8,7,2,5,4,1,6]=>0011011
[3,6,5,8,7,1,2,4]=>[7,1,3,2,6,5,8,4]=>[3,6,5,8,7,1,2,4]=>0000111
[3,4,1,5,8,7,2,6]=>[4,7,3,1,5,2,8,6]=>[3,5,8,7,1,4,2,6]=>0010011
[4,1,3,5,8,2,7,6]=>[4,8,1,3,5,7,2,6]=>[5,7,1,3,4,2,8,6]=>0010011
[4,3,6,8,2,1,7,5]=>[2,8,4,3,7,6,1,5]=>[4,3,6,7,2,1,8,5]=>1010011
[2,4,6,8,3,7,5,1]=>[5,2,7,4,8,6,1,3]=>[2,4,6,8,1,7,5,3]=>0001011
[5,3,1,4,2,8,7,6]=>[3,5,4,2,1,7,8,6]=>[4,2,5,3,1,8,7,6]=>0111011
[5,1,3,2,4,8,7,6]=>[5,3,1,2,4,7,8,6]=>[3,1,5,2,4,8,7,6]=>0101011
[3,4,2,5,8,7,1,6]=>[7,4,3,2,5,1,8,6]=>[3,4,2,5,8,7,1,6]=>0010011
[3,2,4,5,8,7,1,6]=>[7,3,2,4,5,1,8,6]=>[3,2,4,5,8,7,1,6]=>0100011
[5,1,2,3,4,8,7,6]=>[5,1,2,3,4,7,8,6]=>[5,1,2,3,4,8,7,6]=>0001011
[8,6,2,5,4,1,3,7]=>[4,5,2,6,1,8,3,7]=>[8,6,2,5,4,1,3,7]=>0011101
[8,1,2,3,4,6,5,7]=>[8,1,2,3,6,4,5,7]=>[6,1,2,3,4,8,5,7]=>0000101
[8,4,7,6,2,1,3,5]=>[2,6,1,7,4,8,3,5]=>[8,4,7,6,2,1,3,5]=>1000111
[5,3,8,4,7,2,6,1]=>[6,7,5,8,3,2,4,1]=>[8,3,5,2,7,4,6,1]=>0001111
[8,1,3,7,6,4,2,5]=>[8,4,1,6,2,7,3,5]=>[7,6,4,1,8,2,3,5]=>0010111
[5,3,1,7,8,6,2,4]=>[3,5,6,1,2,8,7,4]=>[7,8,6,1,5,3,2,4]=>0101101
[3,5,8,2,7,1,6,4]=>[7,8,3,6,5,1,2,4]=>[3,5,6,1,8,2,7,4]=>0000111
[6,2,8,5,3,1,7,4]=>[3,5,8,6,7,4,1,2]=>[7,4,6,1,8,5,3,2]=>0101111
[8,3,7,4,2,5,6,1]=>[6,4,7,8,3,5,2,1]=>[8,3,5,7,4,2,6,1]=>0010111
[4,8,5,7,2,1,3,6]=>[2,7,1,4,8,3,5,6]=>[4,8,2,1,3,7,5,6]=>1000011
[3,4,1,8,2,6,7,5]=>[4,8,3,1,7,2,6,5]=>[3,7,1,4,2,6,8,5]=>0010011
[6,8,3,4,1,5,7,2]=>[4,7,8,3,1,6,5,2]=>[6,8,3,5,7,1,4,2]=>0010011
[6,8,2,5,7,4,1,3]=>[4,7,2,8,1,6,5,3]=>[6,8,2,5,7,4,1,3]=>0010011
[2,5,7,6,3,1,8,4]=>[3,2,6,7,5,8,4,1]=>[2,5,8,4,7,6,3,1]=>0100111
[4,2,1,8,7,5,6,3]=>[2,4,6,1,7,5,8,3]=>[8,7,5,6,2,1,4,3]=>1010111
[1,3,7,5,8,6,4,2]=>[1,4,3,6,8,7,2,5]=>[1,3,7,4,2,8,6,5]=>0010111
[5,7,8,4,3,1,6,2]=>[3,4,8,6,5,1,7,2]=>[5,6,1,7,8,4,3,2]=>0110101
[2,7,4,5,8,3,6,1]=>[6,2,8,7,4,3,5,1]=>[2,7,4,8,3,5,6,1]=>0000111
[3,5,7,1,4,8,6,2]=>[7,6,3,1,5,8,4,2]=>[3,5,8,6,1,4,7,2]=>0000111
[5,7,4,8,3,6,2,1]=>[2,6,8,7,5,3,4,1]=>[5,7,3,8,4,6,2,1]=>1000111
[4,8,6,1,3,5,2,7]=>[6,5,1,4,3,8,2,7]=>[4,5,1,3,8,6,2,7]=>0001101
[3,6,4,8,2,5,7,1]=>[7,8,3,6,2,4,5,1]=>[3,6,2,8,4,5,7,1]=>0000111
[4,3,7,2,5,8,1,6]=>[8,7,4,3,2,1,5,6]=>[4,3,7,2,8,1,5,6]=>0010011
[2,6,4,3,8,5,1,7]=>[5,2,4,8,6,1,3,7]=>[2,6,4,1,8,5,3,7]=>0011101
[3,8,2,1,6,4,5,7]=>[2,8,3,6,4,1,5,7]=>[3,6,4,8,2,1,5,7]=>1000101
[8,2,1,3,4,5,7,6]=>[2,8,1,3,4,7,5,6]=>[7,2,1,3,4,5,8,6]=>1000011
[4,6,8,3,2,1,5,7]=>[2,3,8,4,1,6,5,7]=>[4,6,8,3,2,1,5,7]=>1100001
[7,3,8,2,5,4,1,6]=>[4,5,8,7,3,2,1,6]=>[7,3,8,2,5,4,1,6]=>0011011
[4,2,5,3,8,7,6,1]=>[6,4,5,2,3,7,8,1]=>[5,2,4,3,8,7,6,1]=>0011111
[4,8,2,6,5,3,1,7]=>[3,5,6,4,8,2,1,7]=>[4,8,2,6,5,3,1,7]=>0101101
[2,6,8,5,4,1,3,7]=>[4,2,1,5,8,6,3,7]=>[2,6,8,5,4,1,3,7]=>0011001
[3,1,8,6,5,4,2,7]=>[3,4,1,5,6,8,2,7]=>[8,6,5,4,1,3,2,7]=>0111101
[5,4,8,7,3,2,6,1]=>[6,3,7,5,4,2,8,1]=>[5,4,8,7,3,2,6,1]=>0101111
[4,7,3,6,2,1,8,5]=>[2,6,7,4,8,3,1,5]=>[4,8,3,7,2,1,6,5]=>1000111
[5,4,3,7,1,8,2,6]=>[7,8,4,5,3,2,1,6]=>[5,4,3,8,2,7,1,6]=>0011011
[7,3,8,5,1,4,2,6]=>[5,4,8,3,7,2,1,6]=>[7,3,4,2,8,5,1,6]=>0011011
[5,4,8,7,6,2,1,3]=>[2,6,1,5,4,7,8,3]=>[5,4,8,7,6,2,1,3]=>1001111
[1,5,4,8,3,7,6,2]=>[1,6,7,5,4,8,2,3]=>[1,5,4,8,2,7,6,3]=>0001111
[4,8,3,6,7,1,5,2]=>[7,5,8,4,1,3,6,2]=>[4,8,1,5,3,6,7,2]=>0001011
[8,7,5,3,6,4,2,1]=>[2,4,6,5,7,1,8,3]=>[8,7,5,2,1,6,4,3]=>1011111
[6,8,2,1,7,4,5,3]=>[2,8,5,7,4,6,1,3]=>[6,7,4,5,2,1,8,3]=>1001011
[3,1,2,7,5,6,8,4]=>[3,1,2,8,7,5,6,4]=>[3,1,2,7,5,6,8,4]=>0100011
[3,6,1,2,7,5,8,4]=>[6,1,3,8,7,2,5,4]=>[3,7,1,2,8,5,6,4]=>0000111
[4,7,2,6,3,8,1,5]=>[8,7,6,4,1,2,3,5]=>[4,6,1,7,2,8,3,5]=>0000111
[6,3,2,4,8,7,5,1]=>[5,3,7,1,6,4,8,2]=>[6,3,1,4,8,7,5,2]=>0101111
[3,7,2,4,6,1,8,5]=>[6,7,3,2,8,4,1,5]=>[3,8,2,4,7,1,6,5]=>0000111
[5,3,7,2,8,1,4,6]=>[8,7,5,1,3,4,2,6]=>[5,1,7,3,4,8,2,6]=>0001011
[6,3,2,8,7,5,1,4]=>[5,3,7,2,6,1,8,4]=>[6,3,2,8,7,5,1,4]=>0101111
[6,2,1,3,8,7,5,4]=>[2,6,1,5,7,3,8,4]=>[8,7,5,2,1,3,6,4]=>1001111
[3,6,1,8,7,5,2,4]=>[6,5,3,2,7,1,8,4]=>[3,8,7,5,2,6,1,4]=>0001111
[7,8,5,1,6,2,4,3]=>[5,8,4,1,6,2,7,3]=>[4,1,6,2,7,8,5,3]=>0011101
[11,9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,11,1,10]=>[11,9,8,7,6,5,4,3,2,1,10]=>1111111101
[10,7,6,5,4,3,2,1,9,8]=>[2,3,4,5,6,7,10,9,1,8]=>[9,7,6,5,4,3,2,1,10,8]=>111111011
[9,7,5,4,3,2,1,8,6]=>[2,3,4,5,7,9,8,6,1]=>[8,6,9,7,5,4,3,2,1]=>11110111
[8,5,4,3,7,2,1,6]=>[2,7,4,5,8,1,3,6]=>[8,5,4,2,1,7,3,6]=>1011011
[7,6,4,3,2,8,5,1]=>[5,3,4,8,6,7,1,2]=>[7,6,4,3,1,8,5,2]=>0111111
[10,9,8,7,6,5,4,3,2,11,1]=>[11,3,4,5,6,7,8,9,10,2,1]=>[10,9,8,7,6,5,4,3,2,11,1]=>0111111111
[7,3,1,4,8,2,5,6]=>[3,7,8,2,1,5,4,6]=>[8,2,5,7,3,1,4,6]=>0100011
[7,4,1,2,5,8,3,6]=>[4,1,7,8,3,2,5,6]=>[8,3,7,4,1,2,5,6]=>0010011
[5,7,2,4,6,8,1,3]=>[8,7,1,2,5,4,6,3]=>[5,7,1,4,6,8,2,3]=>0000011
[5,7,4,6,3,1,8,2]=>[3,6,8,7,5,4,2,1]=>[5,7,4,8,2,6,3,1]=>0100111
[7,5,1,4,3,2,8,6]=>[5,3,4,1,7,8,2,6]=>[4,3,1,8,5,2,7,6]=>0111011
[8,6,4,2,3,7,5,1]=>[5,4,1,7,6,8,3,2]=>[8,6,4,1,3,7,5,2]=>0011111
[5,4,6,8,3,1,2,7]=>[3,1,8,5,4,6,2,7]=>[5,4,6,8,3,1,2,7]=>0101001
[4,6,1,3,8,5,2,7]=>[6,5,1,4,8,3,2,7]=>[4,8,5,1,3,6,2,7]=>0001101
[1,3,8,4,5,7,2,6]=>[1,7,3,8,4,2,5,6]=>[1,3,8,4,7,2,5,6]=>0000011
[2,6,7,4,5,3,1,8]=>[3,2,5,7,4,6,1,8]=>[2,6,7,4,5,3,1,8]=>0101010
[1,3,7,4,2,8,5,6]=>[1,4,3,7,8,5,2,6]=>[1,3,8,5,7,4,2,6]=>0010011
[4,6,1,3,7,2,5,8]=>[6,7,1,4,2,3,5,8]=>[4,7,1,6,2,3,5,8]=>0000110
[7,5,8,6,2,1,3,4]=>[2,6,1,3,8,7,4,5]=>[7,2,1,3,4,8,6,5]=>1000111
[3,4,2,6,8,7,1,5]=>[7,4,3,2,1,6,8,5]=>[3,4,2,6,8,7,1,5]=>0010011
[8,4,2,3,6,5,7,1]=>[7,4,2,8,6,3,5,1]=>[6,4,2,3,8,5,7,1]=>0010111
[2,7,8,3,4,5,1,6]=>[5,2,8,3,4,1,7,6]=>[2,7,8,3,4,5,1,6]=>0001001
[7,5,6,8,2,1,4,3]=>[2,8,4,1,7,5,6,3]=>[4,2,1,7,5,6,8,3]=>1010011
[3,1,6,5,2,7,4,8]=>[3,5,1,6,7,4,2,8]=>[7,4,6,5,1,3,2,8]=>0101110
[3,4,6,2,8,5,7,1]=>[7,6,3,4,8,2,5,1]=>[3,4,8,2,6,5,7,1]=>0000111
[4,3,7,1,6,8,5,2]=>[7,5,4,3,8,1,6,2]=>[4,3,8,5,1,6,7,2]=>0011011
[3,2,4,8,6,7,1,5]=>[7,3,2,4,1,8,6,5]=>[3,2,4,8,6,7,1,5]=>0100011
[4,1,6,7,5,8,2,3]=>[4,8,2,1,7,6,5,3]=>[6,7,5,8,2,4,1,3]=>0010011
[4,3,7,1,6,8,2,5]=>[7,8,4,3,2,1,6,5]=>[4,3,8,2,6,7,1,5]=>0010011
[4,3,7,5,6,8,2,1]=>[2,8,4,3,7,5,6,1]=>[4,3,7,5,6,8,2,1]=>1010011
[4,1,7,3,6,5,2,8]=>[4,5,6,1,7,2,3,8]=>[7,1,6,5,2,4,3,8]=>0011110
[2,8,7,4,5,3,1,6]=>[3,2,5,7,4,1,8,6]=>[2,8,7,4,5,3,1,6]=>0101011
[3,8,1,4,2,6,5,7]=>[8,4,3,1,6,2,5,7]=>[3,4,1,6,2,8,5,7]=>0010101
[5,8,7,6,1,2,4,3]=>[6,1,4,2,5,7,8,3]=>[4,1,2,5,8,7,6,3]=>0010111
[4,1,7,2,6,8,5,3]=>[4,7,5,1,8,2,6,3]=>[8,5,1,6,7,2,4,3]=>0011011
[4,2,7,3,6,1,8,5]=>[6,4,7,2,8,3,1,5]=>[8,2,4,3,7,1,6,5]=>0010111
[4,2,7,3,6,5,8,1]=>[8,4,7,2,6,3,5,1]=>[6,2,4,3,7,5,8,1]=>0010111
[3,8,2,4,5,6,7,1]=>[7,8,3,2,4,5,6,1]=>[3,8,2,4,5,6,7,1]=>0000011
[2,8,6,5,3,7,1,4]=>[7,2,5,1,6,8,3,4]=>[2,8,6,5,1,7,3,4]=>0001111
[3,8,6,5,1,4,7,2]=>[5,6,3,1,8,7,4,2]=>[3,7,1,4,8,6,5,2]=>0001111
[3,8,2,5,4,6,7,1]=>[7,8,3,5,2,4,6,1]=>[3,5,2,8,4,6,7,1]=>0001011
[4,2,7,5,6,3,8,1]=>[8,4,6,2,7,5,3,1]=>[7,5,6,2,4,3,8,1]=>0010111
[4,2,7,5,6,1,8,3]=>[6,4,8,2,7,5,1,3]=>[7,5,8,2,4,1,6,3]=>0010111
[3,2,6,1,4,5,8,7]=>[6,3,2,1,4,5,8,7]=>[3,2,6,1,4,5,8,7]=>0100101
[2,8,7,3,4,5,1,6]=>[5,2,7,3,4,1,8,6]=>[2,8,7,3,4,5,1,6]=>0001011
[2,8,7,5,3,4,1,6]=>[4,2,5,3,7,1,8,6]=>[2,8,7,5,3,4,1,6]=>0011011
[4,1,7,5,6,3,2,8]=>[4,3,6,1,7,5,2,8]=>[7,5,6,3,1,4,2,8]=>0110110
[5,8,7,6,4,1,2,3]=>[4,1,2,6,5,7,8,3]=>[5,8,7,6,4,1,2,3]=>0010111
[5,4,2,3,7,6,8,1]=>[8,4,2,5,3,7,6,1]=>[5,4,2,3,7,6,8,1]=>0011011
[8,4,7,2,5,1,6,3]=>[5,7,6,8,2,1,4,3]=>[8,2,6,1,7,4,5,3]=>0001111
[5,1,7,2,4,6,8,3]=>[5,7,8,2,1,4,6,3]=>[8,2,6,7,1,4,5,3]=>0001011
[4,5,7,1,2,6,8,3]=>[7,1,8,4,5,2,6,3]=>[4,5,8,1,2,6,7,3]=>0000011
[5,4,1,7,3,6,8,2]=>[4,5,8,7,2,1,6,3]=>[7,2,6,8,1,5,4,3]=>0011011
[3,6,4,7,5,2,8,1]=>[8,5,3,7,6,2,4,1]=>[3,6,2,7,5,4,8,1]=>0001111
[5,7,6,4,3,1,8,2]=>[3,4,6,7,5,8,2,1]=>[5,8,2,7,6,4,3,1]=>0110111
[6,7,1,3,8,4,2,5]=>[7,4,1,8,2,6,3,5]=>[6,8,4,1,7,2,3,5]=>0010011
[3,2,8,6,7,1,4,5]=>[7,3,2,1,4,8,6,5]=>[3,2,8,6,7,1,4,5]=>0100011
[1,8,6,5,4,2,3,7]=>[1,4,2,5,6,8,3,7]=>[1,8,6,5,4,2,3,7]=>0011101
[1,8,7,2,3,5,4,6]=>[1,7,2,5,3,4,8,6]=>[1,5,2,3,8,7,4,6]=>0001011
[7,5,6,1,2,8,4,3]=>[6,1,4,8,7,5,2,3]=>[7,5,8,4,1,2,6,3]=>0010111
[5,1,4,3,6,8,7,2]=>[5,7,4,1,3,6,8,2]=>[4,1,6,8,7,3,5,2]=>0011011
[4,5,7,6,8,2,1,3]=>[2,8,1,4,5,7,6,3]=>[4,5,7,6,8,2,1,3]=>1000011
[5,7,6,8,4,2,1,3]=>[2,4,1,8,5,7,6,3]=>[5,7,6,8,4,2,1,3]=>1010011
[5,1,6,8,4,2,7,3]=>[5,4,8,7,1,6,3,2]=>[6,7,1,8,4,3,5,2]=>0011011
[7,6,8,3,2,5,4,1]=>[4,3,5,8,1,7,6,2]=>[7,6,8,3,1,5,4,2]=>0111011
[8,7,1,3,5,4,6,2]=>[7,6,1,5,3,4,8,2]=>[5,1,3,6,4,8,7,2]=>0001111
[7,6,8,3,1,4,5,2]=>[3,8,5,2,4,7,6,1]=>[5,2,4,7,6,8,3,1]=>0101011
[5,8,2,6,3,1,4,7]=>[3,6,8,2,5,1,4,7]=>[5,8,2,6,3,1,4,7]=>0100101
[6,8,2,3,7,4,1,5]=>[4,7,1,8,2,6,3,5]=>[6,8,1,7,4,2,3,5]=>0010011
[8,1,3,6,2,5,4,7]=>[8,6,1,5,2,3,4,7]=>[5,1,6,2,3,8,4,7]=>0001101
[2,7,1,6,3,5,4,8]=>[7,2,6,5,3,1,4,8]=>[2,5,3,6,1,7,4,8]=>0001110
[8,1,3,5,4,2,6,7]=>[8,4,1,5,3,2,6,7]=>[5,4,1,3,8,2,6,7]=>0011001
[8,1,5,6,2,3,7,4]=>[8,6,2,7,1,5,3,4]=>[7,2,5,6,1,3,8,4]=>0000111
[8,1,4,3,5,2,6,7]=>[8,5,4,1,3,2,6,7]=>[4,1,5,3,8,2,6,7]=>0011001
[7,3,1,6,2,5,4,8]=>[3,7,6,5,1,2,4,8]=>[5,1,6,3,2,7,4,8]=>0101110
[3,7,1,4,5,2,6,8]=>[7,5,3,1,4,2,6,8]=>[3,5,1,4,7,2,6,8]=>0001010
[3,5,2,4,1,6,7,8]=>[4,5,3,2,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>0011000
[6,2,4,1,5,3,7,8]=>[4,6,5,2,1,3,7,8]=>[5,2,6,1,4,3,7,8]=>0011100
[5,2,6,1,3,7,4,8]=>[6,5,1,7,2,3,4,8]=>[7,1,5,2,3,6,4,8]=>0001110
[4,7,1,5,3,2,6,8]=>[7,3,5,4,1,2,6,8]=>[4,5,3,1,7,2,6,8]=>0101010
[5,7,1,4,2,6,3,8]=>[7,4,6,1,5,2,3,8]=>[5,6,1,4,2,7,3,8]=>0010110
[5,7,1,6,2,3,8,4]=>[7,6,2,8,5,1,3,4]=>[5,8,2,6,1,3,7,4]=>0000111
[5,6,3,1,2,7,4,8]=>[3,1,6,7,5,2,4,8]=>[5,7,3,1,2,6,4,8]=>0100110
[5,3,6,1,2,7,4,8]=>[6,1,5,7,3,2,4,8]=>[7,3,5,1,2,6,4,8]=>0001110
[6,5,1,8,7,3,4,2]=>[5,4,6,1,7,3,8,2]=>[8,7,1,4,3,6,5,2]=>0011111
[6,8,5,2,3,4,1,7]=>[4,5,2,3,8,6,1,7]=>[6,8,5,2,3,4,1,7]=>0011001
[8,5,6,2,7,1,4,3]=>[7,6,4,1,8,5,2,3]=>[4,1,8,5,6,2,7,3]=>0010111
[5,7,6,4,1,3,8,2]=>[4,6,1,7,5,8,3,2]=>[5,8,1,3,7,6,4,2]=>0010111
[6,1,7,5,3,8,4,2]=>[6,4,8,5,7,1,2,3]=>[7,5,1,8,4,2,6,3]=>0011111
[8,6,7,5,3,1,4,2]=>[3,5,4,2,7,8,6,1]=>[4,2,8,6,7,5,3,1]=>0111011
[8,5,2,7,1,6,4,3]=>[7,5,4,8,6,1,3,2]=>[6,4,1,8,5,3,7,2]=>0011111
[3,4,6,1,7,8,5,2]=>[6,5,3,4,8,1,7,2]=>[3,4,7,8,5,1,6,2]=>0001101
[3,4,8,6,7,1,5,2]=>[7,5,3,4,1,8,6,2]=>[3,4,5,1,8,6,7,2]=>0001011
[5,8,1,7,2,6,4,3]=>[8,7,4,6,5,2,1,3]=>[5,6,4,2,7,1,8,3]=>0010111
[8,1,7,2,5,6,3,4]=>[8,7,6,3,2,5,1,4]=>[6,3,5,7,2,8,1,4]=>0000111
[4,8,1,5,2,6,7,3]=>[8,5,7,4,1,2,6,3]=>[4,7,1,5,2,6,8,3]=>0001011
[3,7,8,5,1,6,2,4]=>[5,8,3,1,6,2,7,4]=>[3,6,1,7,8,5,2,4]=>0001101
[6,5,2,7,8,1,4,3]=>[8,5,4,1,6,2,7,3]=>[4,1,6,5,2,7,8,3]=>0011101
[8,7,2,1,5,6,3,4]=>[2,7,6,3,1,5,8,4]=>[6,3,5,8,7,2,1,4]=>1000111
[7,5,6,2,1,8,4,3]=>[2,6,4,8,7,5,1,3]=>[7,5,8,4,2,1,6,3]=>1010111
[7,1,3,5,8,6,2,4]=>[7,6,1,2,3,8,5,4]=>[8,6,1,5,7,2,3,4]=>0000111
[5,1,3,4,6,8,7,2]=>[5,7,1,3,4,6,8,2]=>[6,8,7,1,3,4,5,2]=>0001011
[4,5,3,6,8,2,7,1]=>[7,8,5,4,3,6,2,1]=>[4,5,3,6,8,2,7,1]=>0001011
[5,6,3,4,8,1,7,2]=>[8,7,6,3,5,4,1,2]=>[5,6,3,4,7,1,8,2]=>0000111
[4,6,7,8,5,1,3,2]=>[5,3,1,4,8,6,7,2]=>[3,1,4,6,7,8,5,2]=>0101001
[4,6,8,1,5,3,7,2]=>[8,7,5,4,1,6,3,2]=>[4,5,1,6,7,3,8,2]=>0001011
[3,6,4,8,7,1,5,2]=>[7,5,3,6,1,4,8,2]=>[3,6,1,5,4,8,7,2]=>0001111
[6,5,8,1,3,4,7,2]=>[8,7,1,3,6,5,4,2]=>[6,5,7,1,3,4,8,2]=>0000111
[5,6,8,3,1,2,7,4]=>[3,1,8,7,5,6,2,4]=>[5,6,7,3,1,2,8,4]=>0100011
[6,1,8,3,5,2,7,4]=>[6,5,8,7,3,1,2,4]=>[7,3,8,1,5,2,6,4]=>0001111
[7,6,8,3,5,2,1,4]=>[2,5,8,1,3,7,6,4]=>[7,6,8,2,1,5,3,4]=>1001011
[8,6,1,3,5,2,7,4]=>[6,5,1,8,4,7,2,3]=>[7,4,5,1,8,6,2,3]=>0001111
[6,7,8,3,5,1,2,4]=>[5,1,8,2,3,6,7,4]=>[6,7,8,1,2,5,3,4]=>0001001
[7,8,2,3,5,6,1,4]=>[6,8,2,1,3,5,7,4]=>[7,8,2,5,6,1,3,4]=>0000101
[2,7,8,6,1,4,3,5]=>[6,2,4,1,3,8,7,5]=>[2,4,1,7,8,6,3,5]=>0010101
[2,6,5,4,1,3,8,7]=>[4,2,1,5,6,3,8,7]=>[2,6,5,4,1,3,8,7]=>0011101
[4,8,2,5,7,6,3,1]=>[3,6,7,4,2,8,5,1]=>[4,8,2,5,7,6,3,1]=>0100111
[2,6,5,3,4,1,8,7]=>[4,2,5,3,6,1,8,7]=>[2,6,5,3,4,1,8,7]=>0011101
[4,6,1,5,2,3,8,7]=>[6,5,2,4,1,3,8,7]=>[4,5,2,6,1,3,8,7]=>0001101
[6,2,3,5,1,4,8,7]=>[5,6,2,1,3,4,8,7]=>[6,2,5,1,3,4,8,7]=>0001101
[2,6,7,5,1,8,4,3]=>[5,2,4,7,8,6,3,1]=>[2,6,8,4,3,7,5,1]=>0011011
[8,6,1,2,5,3,4,7]=>[6,1,5,3,2,8,4,7]=>[5,3,8,6,1,2,4,7]=>0001101
[6,2,5,1,8,3,4,7]=>[5,6,8,3,2,1,4,7]=>[8,3,6,2,5,1,4,7]=>0001101
[7,6,5,2,8,3,4,1]=>[4,5,6,3,7,8,2,1]=>[8,3,7,6,5,2,4,1]=>0011111
[2,1,4,8,7,6,3,5]=>[2,1,6,4,3,7,8,5]=>[2,1,4,8,7,6,3,5]=>1000111
[8,1,3,5,7,4,6,2]=>[8,6,1,7,3,4,5,2]=>[7,1,3,6,4,5,8,2]=>0000111
[3,2,8,7,5,1,6,4]=>[5,3,2,7,6,4,8,1]=>[3,2,6,4,8,7,5,1]=>0101111
[4,8,5,1,6,7,2,3]=>[5,8,1,4,7,2,6,3]=>[4,7,1,6,8,5,2,3]=>0001011
[7,8,6,1,3,5,2,4]=>[6,5,1,2,3,8,7,4]=>[5,1,7,8,6,2,3,4]=>0001101
[5,6,7,2,8,1,3,4]=>[8,7,1,3,5,6,2,4]=>[5,6,7,1,3,8,2,4]=>0000011
[5,2,3,8,6,7,4,1]=>[4,7,1,5,3,8,6,2]=>[5,1,3,8,6,7,4,2]=>0011011
[6,2,1,5,3,8,7,4]=>[2,6,5,7,1,3,8,4]=>[8,7,2,1,5,3,6,4]=>1001111
[5,6,3,2,8,1,4,7]=>[8,3,6,1,5,2,4,7]=>[5,6,3,1,8,2,4,7]=>0100101
[8,7,6,2,5,3,1,4]=>[3,5,6,2,1,7,8,4]=>[8,7,6,2,5,3,1,4]=>0101111
[4,7,6,8,3,2,5,1]=>[5,3,8,4,2,7,6,1]=>[4,7,6,8,3,2,5,1]=>0101011
[7,6,2,8,5,1,4,3]=>[5,8,4,2,6,7,1,3]=>[4,2,7,6,1,8,5,3]=>0011111
[8,1,3,7,5,2,6,4]=>[8,5,1,7,6,4,3,2]=>[6,4,7,5,1,3,8,2]=>0001111
[3,4,8,7,5,1,6,2]=>[5,7,3,4,6,2,8,1]=>[3,4,6,2,8,7,5,1]=>0001111
[6,3,8,5,7,4,1,2]=>[4,1,7,6,8,2,5,3]=>[8,1,2,6,5,7,4,3]=>0010111
[2,1,4,8,7,5,6,3]=>[2,1,6,4,7,5,8,3]=>[2,1,4,8,7,5,6,3]=>1000111
[3,6,8,2,4,1,7,5]=>[4,8,3,2,7,6,1,5]=>[3,6,7,2,4,1,8,5]=>0010011
[4,5,8,2,6,7,3,1]=>[3,7,8,4,5,1,6,2]=>[4,5,8,1,6,7,3,2]=>0100011
[5,2,8,1,6,7,3,4]=>[8,5,7,3,2,1,6,4]=>[7,3,5,2,6,8,1,4]=>0001011
[3,4,8,7,2,1,5,6]=>[2,7,3,4,1,5,8,6]=>[3,4,8,7,2,1,5,6]=>1000011
[7,8,5,3,6,4,2,1]=>[2,4,6,5,8,1,7,3]=>[7,8,5,2,1,6,4,3]=>1011101
[2,8,5,7,4,1,3,6]=>[4,2,1,7,8,3,5,6]=>[2,8,4,1,3,7,5,6]=>0010011
[3,8,1,4,6,7,2,5]=>[8,7,3,1,2,4,6,5]=>[3,7,1,6,8,2,4,5]=>0000011
[6,2,7,3,8,4,1,5]=>[4,8,6,7,2,3,1,5]=>[7,2,6,3,8,4,1,5]=>0010111
[8,4,2,6,5,3,1,7]=>[3,5,4,6,8,2,1,7]=>[8,4,2,6,5,3,1,7]=>0111101
[7,4,2,5,3,1,6,8]=>[3,5,4,7,1,2,6,8]=>[7,4,1,5,3,2,6,8]=>0111010
[8,3,6,2,5,4,1,7]=>[4,5,6,8,3,1,2,7]=>[8,3,6,1,5,4,2,7]=>0011101
[5,8,3,6,4,2,1,7]=>[2,4,6,8,5,1,3,7]=>[5,8,2,1,6,4,3,7]=>1010101
[4,8,6,2,5,3,1,7]=>[3,5,6,4,1,8,2,7]=>[4,8,6,1,5,3,2,7]=>0101101
[1,6,4,3,2,8,7,5]=>[1,3,4,6,7,2,8,5]=>[1,8,7,4,3,2,6,5]=>0110111
[1,5,3,2,8,4,7,6]=>[1,3,5,8,2,7,4,6]=>[1,7,3,2,5,4,8,6]=>0101011
[6,1,2,7,3,8,5,4]=>[6,1,7,5,8,2,3,4]=>[8,5,1,2,7,3,6,4]=>0001111
[1,8,4,2,7,6,5,3]=>[1,4,8,5,6,7,3,2]=>[1,7,6,5,3,8,4,2]=>0011111
[2,1,6,8,5,4,7,3]=>[2,1,7,5,8,6,4,3]=>[2,1,6,8,5,4,7,3]=>1001011
[8,3,1,6,7,2,5,4]=>[3,8,7,5,1,2,6,4]=>[5,1,7,3,2,6,8,4]=>0101011
[4,7,6,1,2,5,3,8]=>[6,1,5,4,2,7,3,8]=>[4,5,1,2,7,6,3,8]=>0001110
[7,3,6,1,2,5,4,8]=>[6,1,7,5,2,3,4,8]=>[5,1,2,7,3,6,4,8]=>0001110
[5,4,7,1,3,2,6,8]=>[7,3,1,5,4,2,6,8]=>[3,1,5,4,7,2,6,8]=>0101010
[5,7,4,8,2,1,3,6]=>[2,8,1,7,5,3,4,6]=>[5,7,2,1,3,8,4,6]=>1000011
[7,4,6,2,1,5,3,8]=>[2,6,5,7,1,4,3,8]=>[7,2,1,5,4,6,3,8]=>1001110
[1,5,2,6,8,4,7,3]=>[1,5,7,8,2,6,4,3]=>[1,6,8,2,7,4,5,3]=>0001011
[5,7,2,3,8,1,4,6]=>[8,7,2,1,5,4,3,6]=>[5,7,2,4,8,1,3,6]=>0000011
[6,4,7,5,8,1,2,3]=>[8,1,2,6,7,4,5,3]=>[7,4,6,5,8,1,2,3]=>0000111
[7,4,8,5,1,6,3,2]=>[5,3,8,6,7,2,1,4]=>[7,3,2,6,1,8,5,4]=>0101111
[5,8,3,6,1,7,4,2]=>[6,4,7,8,5,2,1,3]=>[5,8,2,7,4,1,6,3]=>0010111
[8,6,4,2,1,7,5,3]=>[2,4,6,5,8,7,1,3]=>[7,5,2,1,8,6,4,3]=>1011111
[6,3,1,2,8,4,7,5]=>[3,1,6,8,7,2,4,5]=>[7,3,1,2,8,4,6,5]=>0100111
[6,8,4,1,2,7,5,3]=>[4,1,8,5,7,6,3,2]=>[6,7,5,3,8,4,1,2]=>0011011
[7,5,8,1,2,6,4,3]=>[8,1,4,6,7,2,5,3]=>[7,4,1,2,6,5,8,3]=>0010111
[1,3,8,7,6,2,5,4]=>[1,6,3,5,2,7,8,4]=>[1,3,5,2,8,7,6,4]=>0001111
[4,6,1,8,3,7,2,5]=>[6,7,8,4,2,1,3,5]=>[4,8,2,7,1,6,3,5]=>0000111
[8,6,1,7,5,4,3,2]=>[6,3,4,5,8,7,2,1]=>[7,5,4,3,2,8,6,1]=>0111111
[3,1,8,7,6,5,2,4]=>[3,5,1,2,6,7,8,4]=>[8,7,6,5,1,3,2,4]=>0101111
[1,6,4,5,2,3,7,8]=>[1,5,2,6,4,3,7,8]=>[1,6,4,5,2,3,7,8]=>0001100
[1,7,4,5,2,3,6,8]=>[1,5,2,7,4,3,6,8]=>[1,7,4,5,2,3,6,8]=>0001010
[1,7,3,5,2,4,6,8]=>[1,5,7,2,3,4,6,8]=>[1,7,2,5,3,4,6,8]=>0001010
[1,6,3,5,2,4,7,8]=>[1,5,6,2,3,4,7,8]=>[1,6,2,5,3,4,7,8]=>0001100
[1,7,3,4,2,5,6,8]=>[1,4,7,3,2,5,6,8]=>[1,7,3,4,2,5,6,8]=>0010010
[1,8,6,7,3,4,2,5]=>[1,4,7,3,2,8,6,5]=>[1,8,6,7,3,4,2,5]=>0010011
[1,8,5,7,3,4,2,6]=>[1,4,7,3,8,2,5,6]=>[1,8,3,4,2,7,5,6]=>0010011
[1,7,3,4,2,6,5,8]=>[1,4,7,3,6,2,5,8]=>[1,6,3,4,2,7,5,8]=>0010110
[1,5,2,8,4,7,3,6]=>[1,5,7,8,2,3,4,6]=>[1,8,2,7,3,5,4,6]=>0001011
[1,4,2,8,5,7,3,6]=>[1,4,7,2,8,3,5,6]=>[1,8,2,4,3,7,5,6]=>0010011
[1,7,3,5,2,6,4,8]=>[1,5,7,6,3,2,4,8]=>[1,6,3,7,2,5,4,8]=>0001110
[1,8,4,7,3,5,2,6]=>[1,5,7,8,3,2,4,6]=>[1,8,3,7,2,5,4,6]=>0001011
[1,7,3,6,2,4,5,8]=>[1,6,7,2,4,3,5,8]=>[1,7,2,4,6,3,5,8]=>0000110
[1,7,4,6,2,3,5,8]=>[1,6,2,7,3,4,5,8]=>[1,7,2,3,6,4,5,8]=>0000110
[1,8,5,6,2,3,4,7]=>[1,6,2,3,8,5,4,7]=>[1,8,5,6,2,3,4,7]=>0000101
[1,8,5,6,2,4,3,7]=>[1,6,4,2,8,5,3,7]=>[1,4,2,8,5,6,3,7]=>0010101
[1,3,2,8,5,6,4,7]=>[1,3,2,6,8,5,4,7]=>[1,3,2,8,5,6,4,7]=>0100101
[1,4,2,8,5,6,3,7]=>[1,4,6,2,8,5,3,7]=>[1,8,5,6,2,4,3,7]=>0010101
[9,1,2,3,5,4,6,7,8]=>[9,1,2,5,3,4,6,7,8]=>[5,1,2,3,9,4,6,7,8]=>00010001
[3,4,5,6,7,8,9,10,11,12,1,2]=>[12,1,3,4,5,6,7,8,9,10,11,2]=>[3,4,5,6,7,8,9,10,11,12,1,2]=>00000000001
[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>00000000000
[8,6,4,7,2,1,3,5]=>[2,7,1,6,3,8,4,5]=>[8,6,2,1,3,7,4,5]=>1000111
[1,6,4,7,2,8,3,5]=>[1,7,8,6,3,4,2,5]=>[1,6,3,8,4,7,2,5]=>0000111
[1,4,7,3,5,8,2,6]=>[1,8,7,4,3,2,5,6]=>[1,4,7,3,8,2,5,6]=>0000011
[5,4,8,2,3,6,1,7]=>[6,8,2,5,4,3,1,7]=>[5,4,8,2,3,6,1,7]=>0001101
[4,8,6,2,3,5,1,7]=>[5,6,2,4,3,8,1,7]=>[4,8,6,2,3,5,1,7]=>0001101
[1,7,6,4,8,2,3,5]=>[1,8,2,6,3,7,4,5]=>[1,7,6,2,3,8,4,5]=>0000111
[1,8,5,7,2,3,4,6]=>[1,7,2,3,8,4,5,6]=>[1,8,2,3,4,7,5,6]=>0000011
[6,1,5,8,2,3,4,7]=>[6,8,2,3,1,5,4,7]=>[8,2,3,5,6,1,4,7]=>0000101
[5,1,7,3,8,2,4,6]=>[5,8,7,2,1,4,3,6]=>[7,2,8,1,4,5,3,6]=>0001011
[6,1,5,7,8,2,3,4]=>[6,8,2,3,1,5,7,4]=>[7,8,2,3,5,6,1,4]=>0000101
[3,8,7,5,1,2,4,6]=>[5,1,3,2,7,4,8,6]=>[3,8,7,5,1,2,4,6]=>0001011
[1,6,5,8,2,3,4,7]=>[1,8,2,3,6,5,4,7]=>[1,6,5,8,2,3,4,7]=>0000101
[8,5,7,4,1,2,3,6]=>[4,1,2,7,8,3,5,6]=>[8,4,1,2,3,7,5,6]=>0010011
[1,5,7,4,8,2,3,6]=>[1,8,2,7,5,3,4,6]=>[1,5,7,2,3,8,4,6]=>0000011
[7,4,8,5,1,6,2,3]=>[5,8,1,6,7,2,3,4]=>[7,1,6,2,3,8,5,4]=>0001111
[8,6,4,1,2,7,3,5]=>[4,1,6,8,3,7,2,5]=>[7,3,8,6,4,1,2,5]=>0010111
[1,7,2,8,6,3,4,5]=>[1,7,6,3,4,8,2,5]=>[1,8,6,3,4,7,2,5]=>0000111
[5,4,1,8,2,3,6,7]=>[4,5,1,8,2,3,6,7]=>[8,1,5,4,2,3,6,7]=>0011001
[1,4,8,7,2,3,5,6]=>[1,7,2,4,3,5,8,6]=>[1,4,8,7,2,3,5,6]=>0000011
[1,5,8,7,2,3,4,6]=>[1,7,2,3,5,4,8,6]=>[1,5,8,7,2,3,4,6]=>0000011
[5,7,1,3,8,2,4,6]=>[7,8,1,2,5,4,3,6]=>[5,8,1,4,7,2,3,6]=>0000011
[6,1,8,2,7,3,4,5]=>[6,8,7,3,4,1,2,5]=>[7,3,4,8,1,6,2,5]=>0000111
[4,1,8,7,2,3,5,6]=>[4,7,2,1,3,5,8,6]=>[8,7,2,4,1,3,5,6]=>0010011
[5,1,8,7,2,3,4,6]=>[5,7,2,3,1,4,8,6]=>[8,7,2,3,5,1,4,6]=>0001011
[1,8,7,6,4,5,3,2]=>[1,3,5,6,4,7,8,2]=>[1,8,7,6,4,5,3,2]=>0101111
[1,8,7,3,6,5,4,2]=>[1,4,5,6,7,3,8,2]=>[1,8,7,3,6,5,4,2]=>0011111
[7,1,5,8,3,4,2,6]=>[7,4,8,3,1,2,5,6]=>[8,3,4,1,7,2,5,6]=>0010011
[2,4,1,7,5,8,3,6]=>[4,2,8,1,7,3,5,6]=>[2,7,1,4,3,8,5,6]=>0010011
[7,1,4,6,5,2,8,3]=>[7,5,6,1,8,4,3,2]=>[8,1,4,6,5,3,7,2]=>0001111
[7,1,4,6,5,3,2,8]=>[7,3,5,1,6,4,2,8]=>[6,5,3,1,4,7,2,8]=>0101110
[3,4,7,2,6,8,5,1]=>[5,8,3,4,7,1,6,2]=>[3,4,7,1,6,8,5,2]=>0001011
[3,4,7,1,6,8,2,5]=>[7,8,3,4,2,1,6,5]=>[3,4,8,2,6,7,1,5]=>0000011
[3,4,7,1,6,8,5,2]=>[7,5,3,4,8,1,6,2]=>[3,4,8,5,1,6,7,2]=>0001011
[3,4,1,7,8,6,2,5]=>[4,6,3,1,2,8,7,5]=>[3,7,8,6,1,4,2,5]=>0010101
[6,4,2,7,5,3,1,8]=>[3,5,4,7,6,2,1,8]=>[6,4,2,7,5,3,1,8]=>0111110
[3,4,7,2,6,8,1,5]=>[8,7,3,4,1,2,6,5]=>[3,4,7,1,6,8,2,5]=>0000011
[4,8,7,1,3,5,2,6]=>[7,5,1,4,3,2,8,6]=>[4,5,1,3,8,7,2,6]=>0001011
[3,4,7,1,6,2,5,8]=>[7,6,3,4,2,1,5,8]=>[3,4,6,2,7,1,5,8]=>0000110
[4,8,3,1,2,6,7,5]=>[3,1,8,4,7,2,6,5]=>[4,7,3,1,2,6,8,5]=>0100011
[6,8,5,1,3,7,2,4]=>[5,8,2,1,7,6,3,4]=>[6,7,2,8,5,1,3,4]=>0001011
[6,8,5,1,3,4,7,2]=>[5,8,2,3,7,6,4,1]=>[6,7,2,3,4,8,5,1]=>0001011
[5,8,3,4,2,6,7,1]=>[7,4,8,3,5,2,6,1]=>[5,8,3,4,2,6,7,1]=>0010011
[5,4,7,3,6,2,8,1]=>[8,6,7,5,4,3,2,1]=>[5,4,7,3,6,2,8,1]=>0001111
[5,4,7,2,6,1,8,3]=>[6,7,8,5,4,2,1,3]=>[5,4,8,2,7,1,6,3]=>0001111
[5,8,7,4,3,1,2,6]=>[3,1,4,7,5,2,8,6]=>[5,8,7,4,3,1,2,6]=>0110011
[5,4,7,3,6,2,1,8]=>[2,6,7,5,4,3,1,8]=>[5,4,7,3,6,2,1,8]=>1001110
[7,3,8,2,1,6,5,4]=>[2,8,7,5,6,1,3,4]=>[6,5,2,1,7,3,8,4]=>1001111
[6,5,2,8,4,3,1,7]=>[3,4,8,5,6,2,1,7]=>[6,5,2,8,4,3,1,7]=>0111101
[4,3,8,7,5,1,6,2]=>[5,7,4,3,6,2,8,1]=>[4,3,6,2,8,7,5,1]=>0011111
[3,2,5,8,6,1,4,7]=>[6,3,2,1,5,8,4,7]=>[3,2,5,8,6,1,4,7]=>0100101
[8,4,3,7,5,2,6,1]=>[6,5,4,7,8,3,2,1]=>[8,4,3,7,5,2,6,1]=>0011111
[4,3,7,8,5,1,2,6]=>[5,1,4,3,8,2,7,6]=>[4,3,7,8,5,1,2,6]=>0011001
[5,3,7,8,4,1,2,6]=>[4,1,8,5,2,3,7,6]=>[5,1,2,7,8,4,3,6]=>0011001
[6,2,4,8,3,1,5,7]=>[3,8,6,1,2,4,5,7]=>[6,1,8,3,2,4,5,7]=>0100101
[5,3,8,7,4,1,6,2]=>[4,7,6,5,1,2,8,3]=>[5,1,6,2,8,7,4,3]=>0011111
[5,3,2,8,6,4,1,7]=>[4,3,6,5,1,8,2,7]=>[5,3,1,8,6,4,2,7]=>0111101
[7,5,3,8,4,2,1,6]=>[2,4,8,5,7,3,1,6]=>[7,5,3,8,4,2,1,6]=>1011011
[8,7,5,3,6,2,4,1]=>[4,6,5,2,7,3,8,1]=>[8,7,5,2,6,3,4,1]=>0011111
[6,4,5,3,8,2,7,1]=>[7,8,5,6,4,3,2,1]=>[6,4,5,3,8,2,7,1]=>0001111
[7,5,6,3,8,2,4,1]=>[4,8,6,2,7,5,3,1]=>[7,5,6,2,8,3,4,1]=>0010111
[8,5,7,3,4,2,6,1]=>[6,4,7,3,8,2,5,1]=>[8,3,4,2,7,5,6,1]=>0010111
[7,5,8,4,3,2,6,1]=>[6,3,4,8,7,2,5,1]=>[7,4,3,2,8,5,6,1]=>0110111
[6,5,8,3,4,2,7,1]=>[7,4,8,3,6,5,2,1]=>[6,5,8,3,4,2,7,1]=>0010111
[7,5,8,3,4,2,6,1]=>[6,4,8,3,7,2,5,1]=>[7,3,4,2,8,5,6,1]=>0010111
[7,5,8,4,6,2,3,1]=>[3,6,2,8,7,4,5,1]=>[7,4,8,5,6,2,3,1]=>0100111
[7,4,8,3,5,2,6,1]=>[6,5,8,7,3,2,4,1]=>[7,3,8,2,5,4,6,1]=>0001111
[6,4,8,3,5,2,7,1]=>[7,5,8,6,3,4,2,1]=>[6,3,8,4,5,2,7,1]=>0001111
[6,5,8,4,7,2,3,1]=>[3,7,2,8,6,5,4,1]=>[6,5,8,4,7,2,3,1]=>0100111
[5,4,7,3,8,2,6,1]=>[6,8,7,5,4,2,3,1]=>[5,4,7,2,8,3,6,1]=>0001111
[5,4,6,3,8,2,7,1]=>[7,8,6,5,4,3,2,1]=>[5,4,6,3,8,2,7,1]=>0001111
[4,3,1,5,6,8,7,2]=>[3,4,7,2,5,6,8,1]=>[5,6,8,7,2,4,3,1]=>0110011
[4,2,1,5,8,6,3,7]=>[2,4,6,1,5,8,3,7]=>[5,8,6,2,1,4,3,7]=>1010101
[4,2,1,5,8,6,7,3]=>[2,4,7,1,5,8,6,3]=>[5,8,6,7,2,1,4,3]=>1010011
[5,3,7,1,4,8,2,6]=>[7,8,5,1,3,2,4,6]=>[5,1,8,3,7,2,4,6]=>0001011
[4,3,1,5,7,8,2,6]=>[3,4,8,2,5,1,7,6]=>[5,7,8,2,4,3,1,6]=>0110001
[3,2,1,8,5,7,4,6]=>[2,3,1,7,8,4,5,6]=>[3,2,1,8,4,7,5,6]=>1100011
[6,7,2,1,8,4,3,5]=>[2,7,4,8,3,6,1,5]=>[6,8,4,3,7,2,1,5]=>1010011
[3,2,1,8,5,6,4,7]=>[2,3,1,6,8,5,4,7]=>[3,2,1,8,5,6,4,7]=>1100101
[3,2,1,8,6,5,4,7]=>[2,3,1,5,6,8,4,7]=>[3,2,1,8,6,5,4,7]=>1101101
[5,2,6,1,8,7,4,3]=>[6,5,4,7,2,1,8,3]=>[8,7,4,2,5,1,6,3]=>0011111
[5,2,6,1,8,3,4,7]=>[6,5,8,3,2,1,4,7]=>[8,3,5,2,6,1,4,7]=>0001101
[6,7,3,1,5,8,2,4]=>[3,7,8,1,2,6,5,4]=>[6,8,1,5,7,3,2,4]=>0100011
[4,2,1,7,8,6,3,5]=>[2,4,6,1,3,8,7,5]=>[7,8,6,2,1,4,3,5]=>1010101
[3,2,1,8,6,4,7,5]=>[2,3,1,6,8,7,5,4]=>[3,2,1,7,5,8,6,4]=>1100111
[3,2,1,8,6,4,5,7]=>[2,3,1,6,4,8,5,7]=>[3,2,1,8,6,4,5,7]=>1100101
[3,2,1,8,4,6,5,7]=>[2,3,1,8,6,4,5,7]=>[3,2,1,6,4,8,5,7]=>1100101
[3,2,1,8,4,6,7,5]=>[2,3,1,8,7,4,6,5]=>[3,2,1,7,4,6,8,5]=>1100011
[3,2,1,8,4,7,6,5]=>[2,3,1,8,6,7,4,5]=>[3,2,1,7,6,4,8,5]=>1100111
[4,2,1,7,8,3,6,5]=>[2,4,8,1,6,3,7,5]=>[6,2,1,4,3,7,8,5]=>1010101
[5,2,7,1,8,3,6,4]=>[7,5,8,6,2,3,1,4]=>[6,2,8,3,5,1,7,4]=>0001111
[5,2,7,1,8,3,4,6]=>[7,5,8,3,2,4,1,6]=>[8,3,5,2,4,7,1,6]=>0001011
[4,2,1,7,8,3,5,6]=>[2,4,8,1,3,5,7,6]=>[7,8,2,1,4,3,5,6]=>1010001
[3,2,1,8,4,5,7,6]=>[2,3,1,8,4,7,5,6]=>[3,2,1,7,4,5,8,6]=>1100011
[7,4,8,6,2,5,3,1]=>[3,5,6,8,4,7,1,2]=>[7,4,8,6,1,5,3,2]=>0101111
[7,4,2,8,5,6,1,3]=>[6,4,1,7,8,5,2,3]=>[8,5,7,4,1,6,2,3]=>0010111
[7,3,8,4,5,6,2,1]=>[2,6,7,8,4,5,3,1]=>[8,4,5,7,3,6,2,1]=>1000111
[6,3,7,8,2,4,1,5]=>[4,8,6,2,1,3,7,5]=>[6,2,7,8,1,4,3,5]=>0010101
[6,3,8,2,4,7,5,1]=>[5,7,8,3,6,1,4,2]=>[6,3,8,1,4,7,5,2]=>0001111
[5,7,4,2,6,8,1,3]=>[8,4,1,7,5,2,6,3]=>[5,7,4,1,6,8,2,3]=>0010011
[6,5,3,1,4,2,7,8]=>[3,5,4,2,6,1,7,8]=>[4,2,6,5,3,1,7,8]=>0111100
[5,7,4,2,6,1,3,8]=>[6,4,1,7,5,2,3,8]=>[5,7,4,1,6,2,3,8]=>0010110
[5,6,4,2,3,8,1,7]=>[8,4,2,6,5,3,1,7]=>[5,6,4,2,3,8,1,7]=>0010101
[6,3,7,2,4,5,1,8]=>[5,7,6,2,4,3,1,8]=>[6,2,4,7,3,5,1,8]=>0001110
[6,3,7,2,5,8,4,1]=>[4,8,7,6,3,1,5,2]=>[6,3,7,1,5,8,4,2]=>0010111
[5,3,6,8,2,4,7,1]=>[7,8,5,2,3,6,4,1]=>[5,2,6,8,3,4,7,1]=>0001011
[3,6,4,2,1,5,8,7]=>[2,4,3,6,1,5,8,7]=>[3,6,4,2,1,5,8,7]=>1010101
[3,5,8,6,4,2,1,7]=>[2,4,3,6,5,8,1,7]=>[3,5,8,6,4,2,1,7]=>1010101
[5,8,6,3,4,2,1,7]=>[2,4,6,3,5,8,1,7]=>[5,8,6,3,4,2,1,7]=>1010101
[5,6,3,4,2,1,8,7]=>[2,4,6,3,5,1,8,7]=>[5,6,3,4,2,1,8,7]=>1010101
[6,3,4,2,1,5,8,7]=>[2,4,6,3,1,5,8,7]=>[6,3,4,2,1,5,8,7]=>1010101
[5,6,4,2,1,3,8,7]=>[2,4,1,6,5,3,8,7]=>[5,6,4,2,1,3,8,7]=>1010101
[5,8,6,4,2,1,3,7]=>[2,4,1,6,5,8,3,7]=>[5,8,6,4,2,1,3,7]=>1010101
[4,2,1,5,7,8,6,3]=>[2,4,6,1,5,8,7,3]=>[5,7,8,6,2,1,4,3]=>1010101
[2,1,8,5,6,4,3,7]=>[2,1,4,6,8,5,3,7]=>[2,1,8,5,6,4,3,7]=>1010101
[4,2,1,8,5,6,3,7]=>[2,4,6,1,8,5,3,7]=>[8,5,6,2,1,4,3,7]=>1010101
[8,4,2,1,5,6,3,7]=>[2,4,8,6,3,5,1,7]=>[6,3,5,8,4,2,1,7]=>1010101
[2,5,6,3,8,4,1,7]=>[4,2,8,6,5,1,3,7]=>[2,5,6,1,8,4,3,7]=>0010101
[6,3,4,2,1,8,5,7]=>[2,4,6,3,8,1,5,7]=>[8,3,4,2,1,6,5,7]=>1010101
[3,7,8,5,6,4,2,1]=>[2,4,3,6,8,5,7,1]=>[3,7,8,5,6,4,2,1]=>1010101
[3,8,5,6,4,2,1,7]=>[2,4,3,6,8,5,1,7]=>[3,8,5,6,4,2,1,7]=>1010101
[3,8,6,4,2,1,5,7]=>[2,4,3,6,1,8,5,7]=>[3,8,6,4,2,1,5,7]=>1010101
[3,7,8,6,4,2,1,5]=>[2,4,3,6,1,8,7,5]=>[3,7,8,6,4,2,1,5]=>1010101
[7,6,2,4,1,8,5,3]=>[4,6,5,3,7,8,1,2]=>[8,5,3,7,6,1,4,2]=>0011111
[7,6,2,3,8,5,4,1]=>[4,5,2,8,6,7,3,1]=>[7,6,2,3,8,5,4,1]=>0011111
[2,1,7,8,6,4,3,5]=>[2,1,4,6,3,8,7,5]=>[2,1,7,8,6,4,3,5]=>1010101
[6,4,2,1,3,7,8,5]=>[2,4,1,6,8,3,7,5]=>[7,8,4,2,1,3,6,5]=>1010101
[6,3,7,8,4,2,1,5]=>[2,4,8,6,3,1,7,5]=>[6,3,7,8,4,2,1,5]=>1010101
[7,8,4,2,1,6,3,5]=>[2,4,8,6,1,3,7,5]=>[6,2,1,7,8,4,3,5]=>1010101
[5,7,6,2,3,8,4,1]=>[4,8,1,6,5,7,3,2]=>[5,7,6,1,3,8,4,2]=>0010111
[2,6,1,8,4,3,7,5]=>[6,2,4,8,7,1,3,5]=>[2,7,4,1,8,3,6,5]=>0010111
[8,4,2,3,7,5,6,1]=>[6,4,2,8,7,5,3,1]=>[7,5,8,4,2,3,6,1]=>0010111
[8,5,7,6,2,1,4,3]=>[2,6,4,1,7,8,3,5]=>[4,2,1,8,3,7,6,5]=>1010111
[4,8,5,7,6,2,1,3]=>[2,6,1,4,7,8,3,5]=>[4,8,2,1,3,7,6,5]=>1000111
[4,7,6,2,1,3,8,5]=>[2,6,1,4,7,8,5,3]=>[4,8,5,7,6,2,1,3]=>1000111
[7,5,6,1,8,4,2,3]=>[6,4,2,8,7,5,1,3]=>[7,5,8,4,2,6,1,3]=>0010111
[2,7,5,8,4,3,6,1]=>[6,2,4,8,7,3,5,1]=>[2,7,4,3,8,5,6,1]=>0010111
[6,4,7,8,3,2,1,5]=>[2,3,8,6,1,4,7,5]=>[6,3,2,1,7,8,4,5]=>1100101
[6,4,3,7,5,2,1,8]=>[2,5,4,7,6,1,3,8]=>[6,4,2,1,7,5,3,8]=>1011110
[7,6,5,4,3,1,8,9,2]=>[3,4,5,6,7,9,1,8,2]=>[8,9,1,7,6,5,4,3,2]=>01111101
[6,3,2,7,5,4,1,8]=>[4,3,5,7,6,2,1,8]=>[6,3,2,7,5,4,1,8]=>0111110
[1,5,3,7,4,2,8,6]=>[1,4,7,5,2,8,3,6]=>[1,5,2,8,4,3,7,6]=>0011011
[1,6,7,3,4,2,8,5]=>[1,4,7,3,8,6,2,5]=>[1,6,8,3,4,2,7,5]=>0010011
[3,2,8,6,4,1,7,5]=>[4,3,2,6,8,7,5,1]=>[3,2,7,5,8,6,4,1]=>0110111
[3,2,1,7,5,4,8,6]=>[2,3,1,5,7,8,4,6]=>[3,2,1,8,5,4,7,6]=>1101011
[5,1,7,3,4,2,8,6]=>[5,4,7,3,1,8,2,6]=>[8,3,4,1,5,2,7,6]=>0011011
[5,1,8,3,2,6,7,4]=>[5,3,8,7,1,2,6,4]=>[7,3,1,6,8,2,5,4]=>0101011
[3,2,8,7,1,5,6,4]=>[7,3,2,6,1,5,8,4]=>[3,2,6,1,5,8,7,4]=>0100111
[8,6,7,1,3,4,5,2]=>[7,5,1,3,4,8,6,2]=>[5,1,3,4,8,6,7,2]=>0001011
[6,4,2,8,3,1,7,5]=>[3,8,4,6,7,1,2,5]=>[7,4,1,6,3,2,8,5]=>0110111
[7,4,2,1,3,6,8,5]=>[2,4,1,7,8,3,6,5]=>[8,4,2,1,3,6,7,5]=>1010011
[8,4,2,1,3,6,7,5]=>[2,4,1,8,7,3,6,5]=>[7,4,2,1,3,6,8,5]=>1010011
[1,5,3,2,4,7,8,6]=>[1,3,5,2,4,8,7,6]=>[1,5,3,2,4,7,8,6]=>0101001
[4,6,2,1,5,3,8,7]=>[2,6,5,4,1,3,8,7]=>[4,5,2,1,6,3,8,7]=>1001101
[4,7,2,1,3,6,8,5]=>[2,7,1,4,8,3,6,5]=>[4,8,2,1,3,6,7,5]=>1000011
[6,7,1,2,4,5,8,3]=>[7,1,8,2,4,6,5,3]=>[6,8,1,2,4,5,7,3]=>0000011
[8,6,1,2,4,5,7,3]=>[6,1,8,3,4,7,5,2]=>[7,3,4,5,8,6,1,2]=>0000111
[1,8,2,3,5,6,7,4]=>[1,8,2,7,3,5,6,4]=>[1,7,2,3,5,6,8,4]=>0000011
[4,1,3,2,5,7,8,6]=>[4,3,1,2,5,8,7,6]=>[3,1,4,2,5,7,8,6]=>0110001
[5,1,2,4,3,7,8,6]=>[5,1,4,2,3,8,7,6]=>[4,1,2,5,3,7,8,6]=>0011001
[1,4,7,6,3,2,5,8]=>[1,3,6,4,2,7,5,8]=>[1,4,7,6,3,2,5,8]=>0100110
[4,1,8,7,3,2,5,6]=>[4,3,7,1,2,5,8,6]=>[8,7,3,1,4,2,5,6]=>0110011
[3,4,2,7,1,6,8,5]=>[7,4,3,2,8,1,6,5]=>[3,4,2,8,1,6,7,5]=>0010011
[2,3,6,7,4,1,8,5]=>[4,2,3,7,8,6,1,5]=>[2,3,6,8,4,1,7,5]=>0010011
[2,6,3,4,7,8,1,5]=>[8,2,6,3,1,4,7,5]=>[2,6,3,7,8,1,4,5]=>0000101
[2,6,7,8,3,4,1,5]=>[4,2,8,3,1,6,7,5]=>[2,6,7,8,3,4,1,5]=>0010001
[3,7,8,2,6,4,1,5]=>[4,6,3,8,2,1,7,5]=>[3,7,8,2,6,4,1,5]=>0010101
[1,3,6,7,4,2,5,8]=>[1,4,3,7,2,6,5,8]=>[1,3,6,7,4,2,5,8]=>0010010
[4,2,8,6,3,1,7,5]=>[3,6,4,1,8,7,5,2]=>[4,1,7,5,8,6,3,2]=>0110111
[3,7,2,4,8,6,1,5]=>[6,8,3,1,2,7,4,5]=>[3,7,1,8,6,2,4,5]=>0000111
[3,2,7,4,8,1,6,5]=>[8,3,2,7,6,1,4,5]=>[3,2,6,1,7,4,8,5]=>0100111
[1,3,6,4,7,2,5,8]=>[1,7,3,6,2,4,5,8]=>[1,3,6,2,7,4,5,8]=>0000110
[3,2,4,7,1,8,6,5]=>[7,3,2,4,6,8,1,5]=>[3,2,4,8,6,1,7,5]=>0100111
[4,7,1,5,8,2,3,6]=>[7,8,2,4,1,3,5,6]=>[4,8,2,7,1,3,5,6]=>0000011
[3,7,6,4,8,2,1,5]=>[2,8,3,6,1,7,4,5]=>[3,7,6,2,1,8,4,5]=>1000111
[2,6,7,3,8,4,1,5]=>[4,2,8,7,3,6,1,5]=>[2,6,7,3,8,4,1,5]=>0010011
[7,4,8,5,6,3,2,1]=>[2,3,6,7,8,5,4,1]=>[8,5,7,4,6,3,2,1]=>1100111
[3,4,6,7,8,5,1,2]=>[5,1,3,4,8,6,7,2]=>[3,4,6,7,8,5,1,2]=>0001001
[3,1,7,5,4,2,6,8]=>[3,4,1,5,7,2,6,8]=>[7,5,4,1,3,2,6,8]=>0111010
[1,2,7,5,8,3,6,4]=>[1,2,8,6,7,3,5,4]=>[1,2,7,3,6,5,8,4]=>0000111
[1,3,6,7,8,5,2,4]=>[1,5,3,2,8,6,7,4]=>[1,3,6,7,8,5,2,4]=>0001001
[1,2,6,4,7,8,5,3]=>[1,2,5,8,6,3,7,4]=>[1,2,6,3,7,8,5,4]=>0001101
[4,1,6,3,7,8,2,5]=>[4,8,6,1,2,3,7,5]=>[6,1,7,8,2,4,3,5]=>0010101
[3,1,6,4,8,2,7,5]=>[3,8,1,6,7,4,2,5]=>[7,4,6,1,3,2,8,5]=>0100111
[7,5,1,8,4,3,2,6]=>[5,3,4,7,8,1,2,6]=>[8,4,3,1,7,5,2,6]=>0111011
[4,1,8,5,2,3,7,6]=>[4,5,2,1,8,7,3,6]=>[7,5,2,4,1,3,8,6]=>0011011
[6,5,8,1,4,3,2,7]=>[8,3,4,1,6,5,2,7]=>[4,3,1,6,5,8,2,7]=>0110101
[1,3,5,7,2,6,8,4]=>[1,7,3,8,5,2,6,4]=>[1,3,5,8,2,6,7,4]=>0000011
[1,3,5,7,6,2,4,8]=>[1,6,3,2,5,7,4,8]=>[1,3,5,7,6,2,4,8]=>0000110
[1,3,5,7,4,6,2,8]=>[1,6,3,7,5,4,2,8]=>[1,3,5,7,4,6,2,8]=>0000110
[1,3,5,4,7,2,6,8]=>[1,7,3,5,4,2,6,8]=>[1,3,5,4,7,2,6,8]=>0001010
[1,3,5,4,7,8,2,6]=>[1,8,3,5,4,2,7,6]=>[1,3,5,4,7,8,2,6]=>0001001
[1,3,5,4,7,2,8,6]=>[1,7,3,5,4,8,2,6]=>[1,3,5,4,8,2,7,6]=>0001011
[1,3,5,7,4,8,2,6]=>[1,8,3,7,5,2,4,6]=>[1,3,5,7,2,8,4,6]=>0000011
[1,3,5,7,4,8,6,2]=>[1,6,3,8,5,7,2,4]=>[1,3,5,7,2,8,6,4]=>0000111
[1,3,5,7,2,8,6,4]=>[1,7,3,6,5,8,2,4]=>[1,3,5,8,6,2,7,4]=>0000111
[1,3,5,7,8,2,6,4]=>[1,8,3,6,5,2,7,4]=>[1,3,5,6,2,7,8,4]=>0000101
[1,3,7,2,5,4,8,6]=>[1,7,3,5,2,8,4,6]=>[1,3,5,2,8,4,7,6]=>0001011
[1,4,7,2,3,8,6,5]=>[1,7,2,4,6,8,3,5]=>[1,4,8,6,2,3,7,5]=>0000111
[2,4,7,3,1,8,6,5]=>[3,2,7,4,6,8,1,5]=>[2,4,8,6,3,1,7,5]=>0100111
[1,4,6,3,8,2,7,5]=>[1,8,6,4,7,3,2,5]=>[1,4,7,3,6,2,8,5]=>0000111
[1,3,5,2,8,7,6,4]=>[1,5,3,6,2,7,8,4]=>[1,3,8,7,6,2,5,4]=>0001111
[1,4,7,3,8,2,6,5]=>[1,8,7,4,6,2,3,5]=>[1,4,6,2,7,3,8,5]=>0000111
[3,2,6,7,8,1,5,4]=>[8,3,2,5,1,6,7,4]=>[3,2,5,1,6,7,8,4]=>0101001
[3,5,2,7,8,4,1,6]=>[4,8,3,5,1,2,7,6]=>[3,5,1,7,8,4,2,6]=>0011001
[1,5,7,4,8,3,2,6]=>[1,3,8,7,5,2,4,6]=>[1,5,7,3,2,8,4,6]=>0100011
[5,3,6,4,7,8,2,1]=>[2,8,5,6,3,4,7,1]=>[6,3,5,4,7,8,2,1]=>1001101
[3,5,2,6,8,4,7,1]=>[7,5,3,8,2,6,4,1]=>[3,6,8,2,5,4,7,1]=>0001011
[2,5,4,6,8,7,1,3]=>[7,2,1,5,4,6,8,3]=>[2,5,4,6,8,7,1,3]=>0001011
[2,5,7,4,3,8,6,1]=>[6,2,4,8,5,7,1,3]=>[2,5,7,4,1,8,6,3]=>0010111
[1,5,7,2,4,8,6,3]=>[1,7,6,2,5,8,4,3]=>[1,5,8,6,2,4,7,3]=>0000111
[4,6,3,7,2,8,5,1]=>[5,8,7,4,6,1,3,2]=>[4,6,1,7,3,8,5,2]=>0001111
[4,3,6,7,8,2,5,1]=>[5,8,4,3,2,6,7,1]=>[4,3,6,7,8,2,5,1]=>0011001
[1,4,7,3,8,6,2,5]=>[1,6,8,4,3,7,2,5]=>[1,4,7,3,8,6,2,5]=>0000111
[2,5,4,7,8,6,1,3]=>[6,2,1,5,4,8,7,3]=>[2,5,4,7,8,6,1,3]=>0001101
[3,2,6,7,8,5,1,4]=>[5,3,2,1,8,6,7,4]=>[3,2,6,7,8,5,1,4]=>0101001
[1,3,7,2,8,6,5,4]=>[1,7,3,5,6,8,2,4]=>[1,3,8,6,5,2,7,4]=>0001111
[5,1,6,8,2,4,3,7]=>[5,8,4,2,1,6,3,7]=>[4,2,6,8,1,5,3,7]=>0011001
[8,5,3,7,2,4,1,6]=>[4,7,5,2,8,1,3,6]=>[8,5,2,7,1,4,3,6]=>0011011
[6,3,1,5,8,2,4,7]=>[3,6,8,1,2,5,4,7]=>[8,1,5,6,3,2,4,7]=>0100101
[6,5,3,4,2,8,1,7]=>[8,4,5,3,6,2,1,7]=>[6,5,3,4,2,8,1,7]=>0011101
[8,1,5,7,3,2,4,6]=>[8,3,7,2,1,4,5,6]=>[7,3,2,8,1,4,5,6]=>0100011
[4,6,7,8,2,3,1,5]=>[3,8,2,4,1,6,7,5]=>[4,6,7,8,2,3,1,5]=>0100001
[8,7,4,6,2,3,1,5]=>[3,6,2,7,1,4,8,5]=>[8,7,2,3,1,6,4,5]=>0100111
[5,6,8,7,2,3,1,4]=>[3,7,2,1,5,6,8,4]=>[5,6,8,7,2,3,1,4]=>0100011
[3,1,7,4,2,8,6,5]=>[3,4,1,7,6,8,2,5]=>[8,6,4,1,3,2,7,5]=>0110111
[7,6,4,8,2,3,1,5]=>[3,8,2,6,1,7,4,5]=>[7,6,2,3,1,8,4,5]=>0100111
[5,7,6,8,2,3,1,4]=>[3,8,2,1,5,7,6,4]=>[5,7,6,8,2,3,1,4]=>0100011
[8,6,4,7,2,3,1,5]=>[3,7,2,6,1,8,4,5]=>[8,6,2,3,1,7,4,5]=>0100111
[2,3,7,8,4,1,6,5]=>[4,2,3,8,6,1,7,5]=>[2,3,6,4,1,7,8,5]=>0010101
[3,7,4,8,2,5,1,6]=>[5,8,3,7,2,1,4,6]=>[3,7,2,8,1,5,4,6]=>0001011
[2,3,7,4,1,6,8,5]=>[4,2,3,7,8,1,6,5]=>[2,3,8,4,1,6,7,5]=>0010011
[4,7,8,6,2,3,1,5]=>[3,6,2,4,1,8,7,5]=>[4,7,8,6,2,3,1,5]=>0100101
[3,1,7,6,4,2,8,5]=>[3,4,1,6,7,8,5,2]=>[8,5,7,6,4,1,3,2]=>0110111
[4,8,7,6,2,3,1,5]=>[3,6,2,4,1,7,8,5]=>[4,8,7,6,2,3,1,5]=>0100111
[6,8,7,5,2,3,1,4]=>[3,5,2,1,7,6,8,4]=>[6,8,7,5,2,3,1,4]=>0101011
[4,3,6,1,5,8,7,2]=>[6,7,4,3,1,5,8,2]=>[4,3,8,7,1,5,6,2]=>0010111
[4,6,3,5,1,8,7,2]=>[5,7,6,4,3,1,8,2]=>[4,6,3,8,7,1,5,2]=>0001111
[2,6,5,3,1,8,7,4]=>[3,2,5,6,7,4,8,1]=>[2,8,7,4,6,5,3,1]=>0101111
[2,6,5,1,8,7,3,4]=>[5,2,6,1,7,3,8,4]=>[2,8,7,1,6,5,3,4]=>0001111
[2,6,5,8,1,3,7,4]=>[8,2,1,7,6,5,3,4]=>[2,6,5,7,1,3,8,4]=>0000111
[2,6,5,8,3,1,7,4]=>[3,2,8,7,6,5,1,4]=>[2,6,5,7,3,1,8,4]=>0100111
[2,6,5,3,8,1,7,4]=>[8,2,5,6,7,4,1,3]=>[2,7,4,6,5,1,8,3]=>0001111
[4,6,1,5,8,3,7,2]=>[6,7,8,4,1,5,3,2]=>[4,8,1,5,7,3,6,2]=>0000111
[4,1,6,5,8,7,3,2]=>[4,3,7,1,6,5,8,2]=>[6,5,8,7,3,1,4,2]=>0110111
[2,6,5,3,8,7,1,4]=>[7,2,5,1,6,3,8,4]=>[2,6,5,1,8,7,3,4]=>0001111
[6,4,8,3,7,1,5,2]=>[7,5,8,6,1,4,3,2]=>[6,1,8,4,5,3,7,2]=>0001111
[4,6,1,8,5,7,3,2]=>[6,3,7,4,8,1,5,2]=>[4,8,3,1,7,5,6,2]=>0100111
[4,1,6,8,5,7,3,2]=>[4,3,7,1,8,6,5,2]=>[6,8,5,7,3,1,4,2]=>0110011
[1,4,6,8,5,3,7,2]=>[1,7,5,4,8,6,3,2]=>[1,4,6,8,5,3,7,2]=>0001011
[2,6,8,5,1,7,3,4]=>[5,2,8,1,7,6,3,4]=>[2,6,7,1,8,5,3,4]=>0001011
[4,6,8,3,5,1,7,2]=>[5,7,8,4,3,6,1,2]=>[4,6,8,3,7,1,5,2]=>0001011
[4,6,8,3,1,5,7,2]=>[3,8,7,4,2,6,5,1]=>[4,6,7,2,5,8,3,1]=>0100011
[4,6,3,8,5,7,1,2]=>[7,1,6,4,8,3,5,2]=>[4,8,3,6,5,7,1,2]=>0000111
[4,3,6,1,8,5,7,2]=>[6,7,4,3,8,1,5,2]=>[4,3,8,1,7,5,6,2]=>0010111
[4,1,3,6,8,7,5,2]=>[4,5,1,3,7,6,8,2]=>[6,8,7,5,1,3,4,2]=>0011011
[4,3,6,1,8,7,5,2]=>[6,5,4,3,7,1,8,2]=>[4,3,8,7,5,1,6,2]=>0011111
[6,2,5,8,7,3,1,4]=>[3,7,6,2,1,5,8,4]=>[6,2,5,8,7,3,1,4]=>0100111
[4,6,3,8,1,7,5,2]=>[8,5,7,4,6,2,1,3]=>[4,6,2,7,5,1,8,3]=>0001111
[4,6,3,1,8,7,5,2]=>[3,6,5,4,7,2,8,1]=>[4,8,7,5,2,6,3,1]=>0101111
[4,1,6,8,3,7,5,2]=>[4,5,7,1,8,6,2,3]=>[6,8,1,7,5,2,4,3]=>0011011
[4,6,1,8,3,7,5,2]=>[6,5,7,4,8,1,2,3]=>[4,8,1,7,5,2,6,3]=>0001111
[6,4,1,8,7,5,3,2]=>[4,3,6,5,7,2,8,1]=>[8,7,5,3,2,6,4,1]=>0111111
[6,1,4,8,7,5,3,2]=>[6,3,5,1,7,4,8,2]=>[8,7,5,3,1,4,6,2]=>0101111
[1,6,4,8,7,3,5,2]=>[1,5,7,6,3,4,8,2]=>[1,6,3,8,7,4,5,2]=>0001111
[4,2,8,7,5,1,3,6]=>[5,4,1,2,7,3,8,6]=>[4,1,8,7,5,2,3,6]=>0011011
[2,3,4,5,6,8,9,7,1]=>[7,2,3,4,5,6,9,8,1]=>[2,3,4,5,6,8,9,7,1]=>00000101
[2,3,4,7,1,8,6,5]=>[7,2,3,4,6,8,1,5]=>[2,3,4,8,6,1,7,5]=>0000111
[2,3,4,5,7,8,9,6,1]=>[6,2,3,4,5,9,7,8,1]=>[2,3,4,5,7,8,9,6,1]=>00001001
[2,3,5,6,7,8,9,4,1]=>[4,2,3,9,5,6,7,8,1]=>[2,3,5,6,7,8,9,4,1]=>00100001
[2,4,5,6,7,8,9,3,1]=>[3,2,9,4,5,6,7,8,1]=>[2,4,5,6,7,8,9,3,1]=>01000001
[2,3,4,5,6,7,9,10,8,1]=>[8,2,3,4,5,6,7,10,9,1]=>[2,3,4,5,6,7,9,10,8,1]=>000000101
[2,3,4,5,6,8,9,10,7,1]=>[7,2,3,4,5,6,10,8,9,1]=>[2,3,4,5,6,8,9,10,7,1]=>000001001
[2,3,6,7,4,8,5,1]=>[5,2,3,8,7,6,1,4]=>[2,3,6,7,1,8,5,4]=>0001011
[2,5,6,3,7,8,1,4]=>[8,2,6,1,5,3,7,4]=>[2,5,6,1,7,8,3,4]=>0000101
[2,3,7,1,4,8,6,5]=>[7,2,3,1,6,8,4,5]=>[2,3,8,6,1,4,7,5]=>0000111
[2,3,4,6,7,8,9,10,5,1]=>[5,2,3,4,10,6,7,8,9,1]=>[2,3,4,6,7,8,9,10,5,1]=>000100001
[2,6,1,3,7,8,5,4]=>[6,2,1,5,8,3,7,4]=>[2,7,8,5,1,3,6,4]=>0001101
[2,3,5,6,7,8,9,10,4,1]=>[4,2,3,10,5,6,7,8,9,1]=>[2,3,5,6,7,8,9,10,4,1]=>001000001
[2,3,4,5,6,7,10,1,8,9]=>[10,2,3,4,5,6,7,1,8,9]=>[2,3,4,5,6,7,10,1,8,9]=>000000001
[2,5,6,7,4,8,1,3]=>[8,2,1,7,5,6,4,3]=>[2,5,6,7,4,8,1,3]=>0000011
[1,5,3,2,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>[1,6,3,2,5,4,7,8]=>0101100
[1,5,3,2,6,7,4,8]=>[1,3,5,7,2,6,4,8]=>[1,6,7,3,2,5,4,8]=>0101010
[1,3,2,7,5,4,8,6]=>[1,3,2,5,7,8,4,6]=>[1,3,2,8,5,4,7,6]=>0101011
[5,4,7,6,2,3,1,8]=>[3,6,2,5,4,7,1,8]=>[5,4,7,6,2,3,1,8]=>0101110
[1,6,2,8,5,3,4,7]=>[1,6,5,3,8,2,4,7]=>[1,8,5,3,6,2,4,7]=>0001101
[4,7,2,3,5,6,1,8]=>[6,7,2,4,3,5,1,8]=>[4,7,2,3,5,6,1,8]=>0000110
[4,6,2,3,5,7,1,8]=>[7,6,2,4,3,5,1,8]=>[4,6,2,3,5,7,1,8]=>0000110
[3,5,2,1,6,8,4,7]=>[2,5,3,8,1,6,4,7]=>[3,6,8,2,1,5,4,7]=>1001001
[1,5,2,6,8,4,3,7]=>[1,5,4,8,2,6,3,7]=>[1,6,8,4,2,5,3,7]=>0011001
[3,6,8,4,2,1,5,7]=>[2,4,3,8,1,6,5,7]=>[3,6,8,4,2,1,5,7]=>1010001
[1,5,8,2,7,4,3,6]=>[1,8,4,7,5,3,2,6]=>[1,5,7,4,3,8,2,6]=>0010011
[6,8,2,3,4,1,7,5]=>[4,8,2,3,7,6,1,5]=>[6,7,2,3,4,1,8,5]=>0010011
[2,3,1,8,4,5,7,6]=>[3,2,1,8,4,7,5,6]=>[2,3,1,7,4,5,8,6]=>0100011
[7,3,2,1,4,5,8,6]=>[2,3,7,1,4,8,5,6]=>[8,3,2,1,4,5,7,6]=>1100011
[7,8,1,4,3,5,2,6]=>[8,5,4,1,3,2,7,6]=>[4,1,5,3,7,8,2,6]=>0011001
[6,1,2,3,4,8,7,5]=>[6,1,2,3,7,4,8,5]=>[8,7,1,2,3,4,6,5]=>0000111
[2,8,1,3,5,4,7,6]=>[8,2,1,5,3,7,4,6]=>[2,5,1,3,7,4,8,6]=>0001011
[8,3,2,1,4,5,7,6]=>[2,3,8,1,4,7,5,6]=>[7,3,2,1,4,5,8,6]=>1100011
[3,8,2,1,5,6,4,7]=>[2,8,3,6,1,5,4,7]=>[3,6,2,1,5,8,4,7]=>1000101
[3,8,2,1,6,5,4,7]=>[2,8,3,5,6,1,4,7]=>[3,6,5,2,1,8,4,7]=>1001101
[1,7,8,3,5,4,2,6]=>[1,4,5,8,2,3,7,6]=>[1,7,8,2,5,4,3,6]=>0011001
[7,4,1,8,3,5,2,6]=>[4,7,5,8,1,3,2,6]=>[8,1,5,3,7,4,2,6]=>0011011
[8,4,1,7,3,5,2,6]=>[4,8,5,7,1,3,2,6]=>[7,1,5,3,8,4,2,6]=>0011011
[3,8,4,6,2,1,5,7]=>[2,6,3,8,1,4,5,7]=>[3,8,2,1,6,4,5,7]=>1000101
[4,3,2,5,1,8,6,7]=>[5,3,4,2,1,8,6,7]=>[4,3,2,5,1,8,6,7]=>0111001
[3,5,2,4,1,8,6,7]=>[4,5,3,2,1,8,6,7]=>[3,5,2,4,1,8,6,7]=>0011001
[2,4,7,8,1,5,3,6]=>[8,2,5,4,1,3,7,6]=>[2,4,5,1,7,8,3,6]=>0001001
[1,8,7,3,5,4,2,6]=>[1,4,5,7,2,3,8,6]=>[1,8,7,2,5,4,3,6]=>0011011
[5,1,8,2,7,4,3,6]=>[5,8,4,7,1,3,2,6]=>[7,4,1,8,3,5,2,6]=>0011011
[5,1,7,2,8,4,3,6]=>[5,7,4,8,1,3,2,6]=>[8,4,1,7,3,5,2,6]=>0011011
[6,1,2,8,5,3,4,7]=>[6,1,5,3,8,2,4,7]=>[8,5,3,6,1,2,4,7]=>0001101
[7,3,2,8,4,5,1,6]=>[5,3,7,8,4,1,2,6]=>[8,4,7,3,1,5,2,6]=>0101011
[7,1,8,3,5,4,2,6]=>[7,4,5,8,2,3,1,6]=>[8,2,5,4,3,7,1,6]=>0011011
[6,7,1,3,4,8,2,5]=>[7,8,1,3,2,6,4,5]=>[6,8,1,3,7,2,4,5]=>0000011
[6,8,1,3,4,7,2,5]=>[8,7,1,3,2,6,4,5]=>[6,7,1,3,8,2,4,5]=>0000011
[1,6,2,3,4,8,7,5]=>[1,6,2,3,7,4,8,5]=>[1,8,7,2,3,4,6,5]=>0000111
[7,6,2,3,4,1,8,5]=>[4,6,2,3,7,8,5,1]=>[8,5,7,6,2,3,4,1]=>0010111
[8,3,2,7,4,5,1,6]=>[5,3,8,7,4,1,2,6]=>[7,4,8,3,1,5,2,6]=>0101011
[7,6,2,3,4,8,1,5]=>[8,6,2,3,1,7,4,5]=>[7,6,2,3,8,1,4,5]=>0000111
[8,6,2,3,4,7,1,5]=>[7,6,2,3,1,8,4,5]=>[8,6,2,3,7,1,4,5]=>0000111
[6,3,4,8,7,5,1,2]=>[5,1,7,2,6,4,8,3]=>[6,1,2,4,8,7,5,3]=>0001111
[4,8,7,3,5,6,1,2]=>[6,1,7,4,3,5,8,2]=>[4,8,7,3,5,6,1,2]=>0000111
[4,8,7,5,3,6,1,2]=>[6,1,5,4,7,3,8,2]=>[4,8,7,5,3,6,1,2]=>0001111
[5,8,7,3,4,6,1,2]=>[6,1,7,3,5,4,8,2]=>[5,8,7,3,4,6,1,2]=>0000111
[5,3,7,2,6,1,8,4]=>[6,7,5,8,3,2,1,4]=>[8,3,5,2,7,1,6,4]=>0001111
[5,2,8,1,6,3,7,4]=>[8,5,6,7,2,1,3,4]=>[7,2,6,1,5,3,8,4]=>0001111
[7,8,4,1,2,6,5,3]=>[4,1,8,5,6,3,7,2]=>[6,5,3,7,8,4,1,2]=>0011101
[4,8,1,5,2,7,6,3]=>[8,5,6,4,1,7,2,3]=>[4,7,6,1,5,2,8,3]=>0001111
[5,8,1,2,4,7,6,3]=>[8,1,6,2,5,7,4,3]=>[5,7,6,1,2,4,8,3]=>0000111
[5,2,8,3,6,7,1,4]=>[7,5,8,1,2,3,6,4]=>[8,1,5,2,6,7,3,4]=>0001011
[2,8,7,6,4,1,3,5]=>[4,2,1,6,3,7,8,5]=>[2,8,7,6,4,1,3,5]=>0010111
[2,8,7,6,3,1,4,5]=>[3,2,6,1,4,7,8,5]=>[2,8,7,6,3,1,4,5]=>0100111
[1,8,7,6,2,4,3,5]=>[1,6,4,2,3,7,8,5]=>[1,4,2,8,7,6,3,5]=>0010111
[1,8,7,6,3,4,2,5]=>[1,4,6,3,2,7,8,5]=>[1,8,7,6,3,4,2,5]=>0010111
[3,1,7,2,6,5,8,4]=>[3,7,1,8,6,2,5,4]=>[6,1,3,2,8,5,7,4]=>0100111
[6,1,2,8,5,7,3,4]=>[6,1,7,3,8,2,5,4]=>[8,3,7,5,6,1,2,4]=>0000111
[6,2,1,8,5,7,3,4]=>[2,6,7,3,8,1,5,4]=>[8,3,7,5,6,2,1,4]=>1000111
[2,3,7,1,6,8,5,4]=>[7,2,3,5,8,1,6,4]=>[2,3,8,5,1,6,7,4]=>0001011
[1,3,7,2,6,8,5,4]=>[1,7,3,5,8,2,6,4]=>[1,3,8,5,2,6,7,4]=>0001011
[7,8,2,6,5,3,1,4]=>[3,5,6,1,8,2,7,4]=>[7,8,1,6,5,3,2,4]=>0101101
[3,2,6,7,5,8,1,4]=>[8,3,2,1,7,6,5,4]=>[3,2,6,7,5,8,1,4]=>0100011
[1,2,7,5,6,3,8,4]=>[1,2,6,8,7,5,3,4]=>[1,2,7,5,8,3,6,4]=>0000111
[4,8,7,6,2,1,3,5]=>[2,6,1,4,3,7,8,5]=>[4,8,7,6,2,1,3,5]=>1000111
[4,8,7,6,1,3,2,5]=>[6,3,1,4,2,7,8,5]=>[3,1,4,8,7,6,2,5]=>0100111
[7,8,3,6,5,1,2,4]=>[5,1,6,3,8,2,7,4]=>[7,8,3,6,5,1,2,4]=>0001101
[2,3,7,5,6,8,1,4]=>[8,2,3,1,7,5,6,4]=>[2,3,7,5,6,8,1,4]=>0000011
[5,1,4,6,8,2,3,7]=>[5,8,2,1,4,6,3,7]=>[6,8,2,4,5,1,3,7]=>0001001
[1,7,6,3,5,4,8,2]=>[1,8,6,5,3,7,4,2]=>[1,5,3,7,6,4,8,2]=>0001111
[3,4,6,1,5,7,2,8]=>[6,7,3,4,1,5,2,8]=>[3,4,7,1,5,6,2,8]=>0000110
[7,8,6,5,1,2,4,3]=>[5,1,4,2,6,8,7,3]=>[4,1,2,7,8,6,5,3]=>0011101
[6,8,5,2,4,1,7,3]=>[4,5,8,3,7,6,1,2]=>[6,7,3,8,5,1,4,2]=>0011011
[2,3,1,6,8,5,7,4]=>[3,2,1,7,8,6,5,4]=>[2,3,1,6,8,5,7,4]=>0100011
[7,3,2,5,1,4,8,6]=>[5,3,7,1,2,8,4,6]=>[8,3,1,5,2,4,7,6]=>0101011
[7,1,4,2,3,6,8,5]=>[7,4,2,1,8,3,6,5]=>[4,2,8,1,3,6,7,5]=>0010011
[1,5,8,3,4,6,7,2]=>[1,7,8,3,5,4,6,2]=>[1,5,8,3,4,6,7,2]=>0000011
[8,3,1,2,4,7,6,5]=>[3,1,8,2,6,7,4,5]=>[7,6,3,1,2,4,8,5]=>0100111
[2,3,8,1,6,5,4,7]=>[8,2,3,5,6,1,4,7]=>[2,3,6,5,1,8,4,7]=>0001101
[8,1,4,7,2,5,3,6]=>[8,7,5,1,2,3,4,6]=>[5,1,7,2,8,3,4,6]=>0001011
[3,5,2,4,1,7,8,6]=>[4,5,3,2,1,8,7,6]=>[3,5,2,4,1,7,8,6]=>0011001
[7,3,2,8,6,4,1,5]=>[4,3,6,8,1,7,2,5]=>[7,3,1,8,6,4,2,5]=>0110111
[7,3,5,2,6,1,8,4]=>[6,5,7,8,3,2,1,4]=>[8,3,7,2,5,1,6,4]=>0001111
[2,8,6,4,3,7,1,5]=>[7,2,4,6,1,8,3,5]=>[2,8,6,4,1,7,3,5]=>0010111
[8,3,2,6,4,7,1,5]=>[7,3