Identifier
Mp00236:
Permutations
—Clarke-Steingrimsson-Zeng inverse⟶
Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Images
=>
[1]=>[1]=>=>
[1,2]=>[1,2]=>0=>1
[2,1]=>[2,1]=>1=>0
[1,2,3]=>[1,2,3]=>00=>11
[1,3,2]=>[1,3,2]=>01=>10
[2,1,3]=>[2,1,3]=>10=>01
[2,3,1]=>[3,2,1]=>11=>00
[3,1,2]=>[3,1,2]=>10=>01
[3,2,1]=>[2,3,1]=>10=>01
[1,2,3,4]=>[1,2,3,4]=>000=>111
[1,2,4,3]=>[1,2,4,3]=>001=>110
[1,3,2,4]=>[1,3,2,4]=>010=>101
[1,3,4,2]=>[1,4,3,2]=>011=>100
[1,4,2,3]=>[1,4,2,3]=>010=>101
[1,4,3,2]=>[1,3,4,2]=>010=>101
[2,1,3,4]=>[2,1,3,4]=>100=>011
[2,1,4,3]=>[2,1,4,3]=>101=>010
[2,3,1,4]=>[3,2,1,4]=>110=>001
[2,3,4,1]=>[4,3,2,1]=>111=>000
[2,4,1,3]=>[4,2,1,3]=>110=>001
[2,4,3,1]=>[3,4,2,1]=>110=>001
[3,1,2,4]=>[3,1,2,4]=>100=>011
[3,1,4,2]=>[4,3,1,2]=>101=>010
[3,2,1,4]=>[2,3,1,4]=>100=>011
[3,2,4,1]=>[2,4,3,1]=>101=>010
[3,4,1,2]=>[4,1,3,2]=>110=>001
[3,4,2,1]=>[4,2,3,1]=>110=>001
[4,1,2,3]=>[4,1,2,3]=>100=>011
[4,1,3,2]=>[3,4,1,2]=>100=>011
[4,2,1,3]=>[2,4,1,3]=>100=>011
[4,2,3,1]=>[2,3,4,1]=>100=>011
[4,3,1,2]=>[3,1,4,2]=>110=>001
[4,3,2,1]=>[3,2,4,1]=>110=>001
[1,2,3,4,5]=>[1,2,3,4,5]=>0000=>1111
[1,2,3,5,4]=>[1,2,3,5,4]=>0001=>1110
[1,2,4,3,5]=>[1,2,4,3,5]=>0010=>1101
[1,2,4,5,3]=>[1,2,5,4,3]=>0011=>1100
[1,2,5,3,4]=>[1,2,5,3,4]=>0010=>1101
[1,2,5,4,3]=>[1,2,4,5,3]=>0010=>1101
[1,3,2,4,5]=>[1,3,2,4,5]=>0100=>1011
[1,3,2,5,4]=>[1,3,2,5,4]=>0101=>1010
[1,3,4,2,5]=>[1,4,3,2,5]=>0110=>1001
[1,3,4,5,2]=>[1,5,4,3,2]=>0111=>1000
[1,3,5,2,4]=>[1,5,3,2,4]=>0110=>1001
[1,3,5,4,2]=>[1,4,5,3,2]=>0110=>1001
[1,4,2,3,5]=>[1,4,2,3,5]=>0100=>1011
[1,4,2,5,3]=>[1,5,4,2,3]=>0101=>1010
[1,4,3,2,5]=>[1,3,4,2,5]=>0100=>1011
[1,4,3,5,2]=>[1,3,5,4,2]=>0101=>1010
[1,4,5,2,3]=>[1,5,2,4,3]=>0110=>1001
[1,4,5,3,2]=>[1,5,3,4,2]=>0110=>1001
[1,5,2,3,4]=>[1,5,2,3,4]=>0100=>1011
[1,5,2,4,3]=>[1,4,5,2,3]=>0100=>1011
[1,5,3,2,4]=>[1,3,5,2,4]=>0100=>1011
[1,5,3,4,2]=>[1,3,4,5,2]=>0100=>1011
[1,5,4,2,3]=>[1,4,2,5,3]=>0110=>1001
[1,5,4,3,2]=>[1,4,3,5,2]=>0110=>1001
[2,1,3,4,5]=>[2,1,3,4,5]=>1000=>0111
[2,1,3,5,4]=>[2,1,3,5,4]=>1001=>0110
[2,1,4,3,5]=>[2,1,4,3,5]=>1010=>0101
[2,1,4,5,3]=>[2,1,5,4,3]=>1011=>0100
[2,1,5,3,4]=>[2,1,5,3,4]=>1010=>0101
[2,1,5,4,3]=>[2,1,4,5,3]=>1010=>0101
[2,3,1,4,5]=>[3,2,1,4,5]=>1100=>0011
[2,3,1,5,4]=>[3,2,1,5,4]=>1101=>0010
[2,3,4,1,5]=>[4,3,2,1,5]=>1110=>0001
[2,3,4,5,1]=>[5,4,3,2,1]=>1111=>0000
[2,3,5,1,4]=>[5,3,2,1,4]=>1110=>0001
[2,3,5,4,1]=>[4,5,3,2,1]=>1110=>0001
[2,4,1,3,5]=>[4,2,1,3,5]=>1100=>0011
[2,4,1,5,3]=>[5,4,2,1,3]=>1101=>0010
[2,4,3,1,5]=>[3,4,2,1,5]=>1100=>0011
[2,4,3,5,1]=>[3,5,4,2,1]=>1101=>0010
[2,4,5,1,3]=>[5,2,1,4,3]=>1110=>0001
[2,4,5,3,1]=>[5,3,4,2,1]=>1110=>0001
[2,5,1,3,4]=>[5,2,1,3,4]=>1100=>0011
[2,5,1,4,3]=>[4,5,2,1,3]=>1100=>0011
[2,5,3,1,4]=>[3,5,2,1,4]=>1100=>0011
[2,5,3,4,1]=>[3,4,5,2,1]=>1100=>0011
[2,5,4,1,3]=>[4,2,1,5,3]=>1110=>0001
[2,5,4,3,1]=>[4,3,5,2,1]=>1110=>0001
[3,1,2,4,5]=>[3,1,2,4,5]=>1000=>0111
[3,1,2,5,4]=>[3,1,2,5,4]=>1001=>0110
[3,1,4,2,5]=>[4,3,1,2,5]=>1010=>0101
[3,1,4,5,2]=>[5,4,3,1,2]=>1011=>0100
[3,1,5,2,4]=>[5,3,1,2,4]=>1010=>0101
[3,1,5,4,2]=>[4,5,3,1,2]=>1010=>0101
[3,2,1,4,5]=>[2,3,1,4,5]=>1000=>0111
[3,2,1,5,4]=>[2,3,1,5,4]=>1001=>0110
[3,2,4,1,5]=>[2,4,3,1,5]=>1010=>0101
[3,2,4,5,1]=>[2,5,4,3,1]=>1011=>0100
[3,2,5,1,4]=>[2,5,3,1,4]=>1010=>0101
[3,2,5,4,1]=>[2,4,5,3,1]=>1010=>0101
[3,4,1,2,5]=>[4,1,3,2,5]=>1100=>0011
[3,4,1,5,2]=>[5,4,1,3,2]=>1101=>0010
[3,4,2,1,5]=>[4,2,3,1,5]=>1100=>0011
[3,4,2,5,1]=>[5,4,2,3,1]=>1101=>0010
[3,4,5,1,2]=>[5,1,4,3,2]=>1110=>0001
[3,4,5,2,1]=>[5,2,4,3,1]=>1110=>0001
[3,5,1,2,4]=>[5,1,3,2,4]=>1100=>0011
[3,5,1,4,2]=>[4,5,1,3,2]=>1100=>0011
[3,5,2,1,4]=>[5,2,3,1,4]=>1100=>0011
[3,5,2,4,1]=>[4,5,2,3,1]=>1100=>0011
[3,5,4,1,2]=>[4,1,5,3,2]=>1110=>0001
[3,5,4,2,1]=>[4,2,5,3,1]=>1110=>0001
[4,1,2,3,5]=>[4,1,2,3,5]=>1000=>0111
[4,1,2,5,3]=>[5,4,1,2,3]=>1001=>0110
[4,1,3,2,5]=>[3,4,1,2,5]=>1000=>0111
[4,1,3,5,2]=>[3,5,4,1,2]=>1001=>0110
[4,1,5,2,3]=>[5,1,2,4,3]=>1010=>0101
[4,1,5,3,2]=>[5,3,4,1,2]=>1010=>0101
[4,2,1,3,5]=>[2,4,1,3,5]=>1000=>0111
[4,2,1,5,3]=>[2,5,4,1,3]=>1001=>0110
[4,2,3,1,5]=>[2,3,4,1,5]=>1000=>0111
[4,2,3,5,1]=>[2,3,5,4,1]=>1001=>0110
[4,2,5,1,3]=>[2,5,1,4,3]=>1010=>0101
[4,2,5,3,1]=>[2,5,3,4,1]=>1010=>0101
[4,3,1,2,5]=>[3,1,4,2,5]=>1100=>0011
[4,3,1,5,2]=>[3,1,5,4,2]=>1101=>0010
[4,3,2,1,5]=>[3,2,4,1,5]=>1100=>0011
[4,3,2,5,1]=>[3,2,5,4,1]=>1101=>0010
[4,3,5,1,2]=>[5,3,1,4,2]=>1110=>0001
[4,3,5,2,1]=>[5,3,2,4,1]=>1110=>0001
[4,5,1,2,3]=>[5,1,4,2,3]=>1100=>0011
[4,5,1,3,2]=>[5,1,3,4,2]=>1100=>0011
[4,5,2,1,3]=>[5,2,4,1,3]=>1100=>0011
[4,5,2,3,1]=>[5,2,3,4,1]=>1100=>0011
[4,5,3,1,2]=>[3,5,1,4,2]=>1100=>0011
[4,5,3,2,1]=>[3,5,2,4,1]=>1100=>0011
[5,1,2,3,4]=>[5,1,2,3,4]=>1000=>0111
[5,1,2,4,3]=>[4,5,1,2,3]=>1000=>0111
[5,1,3,2,4]=>[3,5,1,2,4]=>1000=>0111
[5,1,3,4,2]=>[3,4,5,1,2]=>1000=>0111
[5,1,4,2,3]=>[4,1,2,5,3]=>1010=>0101
[5,1,4,3,2]=>[4,3,5,1,2]=>1010=>0101
[5,2,1,3,4]=>[2,5,1,3,4]=>1000=>0111
[5,2,1,4,3]=>[2,4,5,1,3]=>1000=>0111
[5,2,3,1,4]=>[2,3,5,1,4]=>1000=>0111
[5,2,3,4,1]=>[2,3,4,5,1]=>1000=>0111
[5,2,4,1,3]=>[2,4,1,5,3]=>1010=>0101
[5,2,4,3,1]=>[2,4,3,5,1]=>1010=>0101
[5,3,1,2,4]=>[3,1,5,2,4]=>1100=>0011
[5,3,1,4,2]=>[3,1,4,5,2]=>1100=>0011
[5,3,2,1,4]=>[3,2,5,1,4]=>1100=>0011
[5,3,2,4,1]=>[3,2,4,5,1]=>1100=>0011
[5,3,4,1,2]=>[4,3,1,5,2]=>1110=>0001
[5,3,4,2,1]=>[4,3,2,5,1]=>1110=>0001
[5,4,1,2,3]=>[4,1,5,2,3]=>1100=>0011
[5,4,1,3,2]=>[4,1,3,5,2]=>1100=>0011
[5,4,2,1,3]=>[4,2,5,1,3]=>1100=>0011
[5,4,2,3,1]=>[4,2,3,5,1]=>1100=>0011
[5,4,3,1,2]=>[3,4,1,5,2]=>1100=>0011
[5,4,3,2,1]=>[3,4,2,5,1]=>1100=>0011
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000=>11111
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>00001=>11110
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>00010=>11101
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>00011=>11100
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>00010=>11101
[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>00010=>11101
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>00100=>11011
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>00101=>11010
[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>00110=>11001
[1,2,4,5,6,3]=>[1,2,6,5,4,3]=>00111=>11000
[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>00110=>11001
[1,2,4,6,5,3]=>[1,2,5,6,4,3]=>00110=>11001
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>00100=>11011
[1,2,5,3,6,4]=>[1,2,6,5,3,4]=>00101=>11010
[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>00100=>11011
[1,2,5,4,6,3]=>[1,2,4,6,5,3]=>00101=>11010
[1,2,5,6,3,4]=>[1,2,6,3,5,4]=>00110=>11001
[1,2,5,6,4,3]=>[1,2,6,4,5,3]=>00110=>11001
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>00100=>11011
[1,2,6,3,5,4]=>[1,2,5,6,3,4]=>00100=>11011
[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>00100=>11011
[1,2,6,4,5,3]=>[1,2,4,5,6,3]=>00100=>11011
[1,2,6,5,3,4]=>[1,2,5,3,6,4]=>00110=>11001
[1,2,6,5,4,3]=>[1,2,5,4,6,3]=>00110=>11001
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>01000=>10111
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>01001=>10110
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>01010=>10101
[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>01011=>10100
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>01010=>10101
[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>01010=>10101
[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>01100=>10011
[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>01101=>10010
[1,3,4,5,2,6]=>[1,5,4,3,2,6]=>01110=>10001
[1,3,4,5,6,2]=>[1,6,5,4,3,2]=>01111=>10000
[1,3,4,6,2,5]=>[1,6,4,3,2,5]=>01110=>10001
[1,3,4,6,5,2]=>[1,5,6,4,3,2]=>01110=>10001
[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>01100=>10011
[1,3,5,2,6,4]=>[1,6,5,3,2,4]=>01101=>10010
[1,3,5,4,2,6]=>[1,4,5,3,2,6]=>01100=>10011
[1,3,5,4,6,2]=>[1,4,6,5,3,2]=>01101=>10010
[1,3,5,6,2,4]=>[1,6,3,2,5,4]=>01110=>10001
[1,3,5,6,4,2]=>[1,6,4,5,3,2]=>01110=>10001
[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>01100=>10011
[1,3,6,2,5,4]=>[1,5,6,3,2,4]=>01100=>10011
[1,3,6,4,2,5]=>[1,4,6,3,2,5]=>01100=>10011
[1,3,6,4,5,2]=>[1,4,5,6,3,2]=>01100=>10011
[1,3,6,5,2,4]=>[1,5,3,2,6,4]=>01110=>10001
[1,3,6,5,4,2]=>[1,5,4,6,3,2]=>01110=>10001
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>01000=>10111
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>01001=>10110
[1,4,2,5,3,6]=>[1,5,4,2,3,6]=>01010=>10101
[1,4,2,5,6,3]=>[1,6,5,4,2,3]=>01011=>10100
[1,4,2,6,3,5]=>[1,6,4,2,3,5]=>01010=>10101
[1,4,2,6,5,3]=>[1,5,6,4,2,3]=>01010=>10101
[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>01000=>10111
[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>01001=>10110
[1,4,3,5,2,6]=>[1,3,5,4,2,6]=>01010=>10101
[1,4,3,5,6,2]=>[1,3,6,5,4,2]=>01011=>10100
[1,4,3,6,2,5]=>[1,3,6,4,2,5]=>01010=>10101
[1,4,3,6,5,2]=>[1,3,5,6,4,2]=>01010=>10101
[1,4,5,2,3,6]=>[1,5,2,4,3,6]=>01100=>10011
[1,4,5,2,6,3]=>[1,6,5,2,4,3]=>01101=>10010
[1,4,5,3,2,6]=>[1,5,3,4,2,6]=>01100=>10011
[1,4,5,3,6,2]=>[1,6,5,3,4,2]=>01101=>10010
[1,4,5,6,2,3]=>[1,6,2,5,4,3]=>01110=>10001
[1,4,5,6,3,2]=>[1,6,3,5,4,2]=>01110=>10001
[1,4,6,2,3,5]=>[1,6,2,4,3,5]=>01100=>10011
[1,4,6,2,5,3]=>[1,5,6,2,4,3]=>01100=>10011
[1,4,6,3,2,5]=>[1,6,3,4,2,5]=>01100=>10011
[1,4,6,3,5,2]=>[1,5,6,3,4,2]=>01100=>10011
[1,4,6,5,2,3]=>[1,5,2,6,4,3]=>01110=>10001
[1,4,6,5,3,2]=>[1,5,3,6,4,2]=>01110=>10001
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>01000=>10111
[1,5,2,3,6,4]=>[1,6,5,2,3,4]=>01001=>10110
[1,5,2,4,3,6]=>[1,4,5,2,3,6]=>01000=>10111
[1,5,2,4,6,3]=>[1,4,6,5,2,3]=>01001=>10110
[1,5,2,6,3,4]=>[1,6,2,3,5,4]=>01010=>10101
[1,5,2,6,4,3]=>[1,6,4,5,2,3]=>01010=>10101
[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>01000=>10111
[1,5,3,2,6,4]=>[1,3,6,5,2,4]=>01001=>10110
[1,5,3,4,2,6]=>[1,3,4,5,2,6]=>01000=>10111
[1,5,3,4,6,2]=>[1,3,4,6,5,2]=>01001=>10110
[1,5,3,6,2,4]=>[1,3,6,2,5,4]=>01010=>10101
[1,5,3,6,4,2]=>[1,3,6,4,5,2]=>01010=>10101
[1,5,4,2,3,6]=>[1,4,2,5,3,6]=>01100=>10011
[1,5,4,2,6,3]=>[1,4,2,6,5,3]=>01101=>10010
[1,5,4,3,2,6]=>[1,4,3,5,2,6]=>01100=>10011
[1,5,4,3,6,2]=>[1,4,3,6,5,2]=>01101=>10010
[1,5,4,6,2,3]=>[1,6,4,2,5,3]=>01110=>10001
[1,5,4,6,3,2]=>[1,6,4,3,5,2]=>01110=>10001
[1,5,6,2,3,4]=>[1,6,2,5,3,4]=>01100=>10011
[1,5,6,2,4,3]=>[1,6,2,4,5,3]=>01100=>10011
[1,5,6,3,2,4]=>[1,6,3,5,2,4]=>01100=>10011
[1,5,6,3,4,2]=>[1,6,3,4,5,2]=>01100=>10011
[1,5,6,4,2,3]=>[1,4,6,2,5,3]=>01100=>10011
[1,5,6,4,3,2]=>[1,4,6,3,5,2]=>01100=>10011
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>01000=>10111
[1,6,2,3,5,4]=>[1,5,6,2,3,4]=>01000=>10111
[1,6,2,4,3,5]=>[1,4,6,2,3,5]=>01000=>10111
[1,6,2,4,5,3]=>[1,4,5,6,2,3]=>01000=>10111
[1,6,2,5,3,4]=>[1,5,2,3,6,4]=>01010=>10101
[1,6,2,5,4,3]=>[1,5,4,6,2,3]=>01010=>10101
[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>01000=>10111
[1,6,3,2,5,4]=>[1,3,5,6,2,4]=>01000=>10111
[1,6,3,4,2,5]=>[1,3,4,6,2,5]=>01000=>10111
[1,6,3,4,5,2]=>[1,3,4,5,6,2]=>01000=>10111
[1,6,3,5,2,4]=>[1,3,5,2,6,4]=>01010=>10101
[1,6,3,5,4,2]=>[1,3,5,4,6,2]=>01010=>10101
[1,6,4,2,3,5]=>[1,4,2,6,3,5]=>01100=>10011
[1,6,4,2,5,3]=>[1,4,2,5,6,3]=>01100=>10011
[1,6,4,3,2,5]=>[1,4,3,6,2,5]=>01100=>10011
[1,6,4,3,5,2]=>[1,4,3,5,6,2]=>01100=>10011
[1,6,4,5,2,3]=>[1,5,4,2,6,3]=>01110=>10001
[1,6,4,5,3,2]=>[1,5,4,3,6,2]=>01110=>10001
[1,6,5,2,3,4]=>[1,5,2,6,3,4]=>01100=>10011
[1,6,5,2,4,3]=>[1,5,2,4,6,3]=>01100=>10011
[1,6,5,3,2,4]=>[1,5,3,6,2,4]=>01100=>10011
[1,6,5,3,4,2]=>[1,5,3,4,6,2]=>01100=>10011
[1,6,5,4,2,3]=>[1,4,5,2,6,3]=>01100=>10011
[1,6,5,4,3,2]=>[1,4,5,3,6,2]=>01100=>10011
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000=>01111
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>10001=>01110
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>10010=>01101
[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>10011=>01100
[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>10010=>01101
[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>10010=>01101
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>10100=>01011
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>10101=>01010
[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>10110=>01001
[2,1,4,5,6,3]=>[2,1,6,5,4,3]=>10111=>01000
[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>10110=>01001
[2,1,4,6,5,3]=>[2,1,5,6,4,3]=>10110=>01001
[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>10100=>01011
[2,1,5,3,6,4]=>[2,1,6,5,3,4]=>10101=>01010
[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>10100=>01011
[2,1,5,4,6,3]=>[2,1,4,6,5,3]=>10101=>01010
[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>10110=>01001
[2,1,5,6,4,3]=>[2,1,6,4,5,3]=>10110=>01001
[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>10100=>01011
[2,1,6,3,5,4]=>[2,1,5,6,3,4]=>10100=>01011
[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>10100=>01011
[2,1,6,4,5,3]=>[2,1,4,5,6,3]=>10100=>01011
[2,1,6,5,3,4]=>[2,1,5,3,6,4]=>10110=>01001
[2,1,6,5,4,3]=>[2,1,5,4,6,3]=>10110=>01001
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>11000=>00111
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>11001=>00110
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>11010=>00101
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>11011=>00100
[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>11010=>00101
[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>11010=>00101
[2,3,4,1,5,6]=>[4,3,2,1,5,6]=>11100=>00011
[2,3,4,1,6,5]=>[4,3,2,1,6,5]=>11101=>00010
[2,3,4,5,1,6]=>[5,4,3,2,1,6]=>11110=>00001
[2,3,4,5,6,1]=>[6,5,4,3,2,1]=>11111=>00000
[2,3,4,6,1,5]=>[6,4,3,2,1,5]=>11110=>00001
[2,3,4,6,5,1]=>[5,6,4,3,2,1]=>11110=>00001
[2,3,5,1,4,6]=>[5,3,2,1,4,6]=>11100=>00011
[2,3,5,1,6,4]=>[6,5,3,2,1,4]=>11101=>00010
[2,3,5,4,1,6]=>[4,5,3,2,1,6]=>11100=>00011
[2,3,5,4,6,1]=>[4,6,5,3,2,1]=>11101=>00010
[2,3,5,6,1,4]=>[6,3,2,1,5,4]=>11110=>00001
[2,3,5,6,4,1]=>[6,4,5,3,2,1]=>11110=>00001
[2,3,6,1,4,5]=>[6,3,2,1,4,5]=>11100=>00011
[2,3,6,1,5,4]=>[5,6,3,2,1,4]=>11100=>00011
[2,3,6,4,1,5]=>[4,6,3,2,1,5]=>11100=>00011
[2,3,6,4,5,1]=>[4,5,6,3,2,1]=>11100=>00011
[2,3,6,5,1,4]=>[5,3,2,1,6,4]=>11110=>00001
[2,3,6,5,4,1]=>[5,4,6,3,2,1]=>11110=>00001
[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>11000=>00111
[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>11001=>00110
[2,4,1,5,3,6]=>[5,4,2,1,3,6]=>11010=>00101
[2,4,1,5,6,3]=>[6,5,4,2,1,3]=>11011=>00100
[2,4,1,6,3,5]=>[6,4,2,1,3,5]=>11010=>00101
[2,4,1,6,5,3]=>[5,6,4,2,1,3]=>11010=>00101
[2,4,3,1,5,6]=>[3,4,2,1,5,6]=>11000=>00111
[2,4,3,1,6,5]=>[3,4,2,1,6,5]=>11001=>00110
[2,4,3,5,1,6]=>[3,5,4,2,1,6]=>11010=>00101
[2,4,3,5,6,1]=>[3,6,5,4,2,1]=>11011=>00100
[2,4,3,6,1,5]=>[3,6,4,2,1,5]=>11010=>00101
[2,4,3,6,5,1]=>[3,5,6,4,2,1]=>11010=>00101
[2,4,5,1,3,6]=>[5,2,1,4,3,6]=>11100=>00011
[2,4,5,1,6,3]=>[6,5,2,1,4,3]=>11101=>00010
[2,4,5,3,1,6]=>[5,3,4,2,1,6]=>11100=>00011
[2,4,5,3,6,1]=>[6,5,3,4,2,1]=>11101=>00010
[2,4,5,6,1,3]=>[6,2,1,5,4,3]=>11110=>00001
[2,4,5,6,3,1]=>[6,3,5,4,2,1]=>11110=>00001
[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>11100=>00011
[2,4,6,1,5,3]=>[5,6,2,1,4,3]=>11100=>00011
[2,4,6,3,1,5]=>[6,3,4,2,1,5]=>11100=>00011
[2,4,6,3,5,1]=>[5,6,3,4,2,1]=>11100=>00011
[2,4,6,5,1,3]=>[5,2,1,6,4,3]=>11110=>00001
[2,4,6,5,3,1]=>[5,3,6,4,2,1]=>11110=>00001
[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>11000=>00111
[2,5,1,3,6,4]=>[6,5,2,1,3,4]=>11001=>00110
[2,5,1,4,3,6]=>[4,5,2,1,3,6]=>11000=>00111
[2,5,1,4,6,3]=>[4,6,5,2,1,3]=>11001=>00110
[2,5,1,6,3,4]=>[6,2,1,3,5,4]=>11010=>00101
[2,5,1,6,4,3]=>[6,4,5,2,1,3]=>11010=>00101
[2,5,3,1,4,6]=>[3,5,2,1,4,6]=>11000=>00111
[2,5,3,1,6,4]=>[3,6,5,2,1,4]=>11001=>00110
[2,5,3,4,1,6]=>[3,4,5,2,1,6]=>11000=>00111
[2,5,3,4,6,1]=>[3,4,6,5,2,1]=>11001=>00110
[2,5,3,6,1,4]=>[3,6,2,1,5,4]=>11010=>00101
[2,5,3,6,4,1]=>[3,6,4,5,2,1]=>11010=>00101
[2,5,4,1,3,6]=>[4,2,1,5,3,6]=>11100=>00011
[2,5,4,1,6,3]=>[4,2,1,6,5,3]=>11101=>00010
[2,5,4,3,1,6]=>[4,3,5,2,1,6]=>11100=>00011
[2,5,4,3,6,1]=>[4,3,6,5,2,1]=>11101=>00010
[2,5,4,6,1,3]=>[6,4,2,1,5,3]=>11110=>00001
[2,5,4,6,3,1]=>[6,4,3,5,2,1]=>11110=>00001
[2,5,6,1,3,4]=>[6,2,1,5,3,4]=>11100=>00011
[2,5,6,1,4,3]=>[6,2,1,4,5,3]=>11100=>00011
[2,5,6,3,1,4]=>[6,3,5,2,1,4]=>11100=>00011
[2,5,6,3,4,1]=>[6,3,4,5,2,1]=>11100=>00011
[2,5,6,4,1,3]=>[4,6,2,1,5,3]=>11100=>00011
[2,5,6,4,3,1]=>[4,6,3,5,2,1]=>11100=>00011
[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>11000=>00111
[2,6,1,3,5,4]=>[5,6,2,1,3,4]=>11000=>00111
[2,6,1,4,3,5]=>[4,6,2,1,3,5]=>11000=>00111
[2,6,1,4,5,3]=>[4,5,6,2,1,3]=>11000=>00111
[2,6,1,5,3,4]=>[5,2,1,3,6,4]=>11010=>00101
[2,6,1,5,4,3]=>[5,4,6,2,1,3]=>11010=>00101
[2,6,3,1,4,5]=>[3,6,2,1,4,5]=>11000=>00111
[2,6,3,1,5,4]=>[3,5,6,2,1,4]=>11000=>00111
[2,6,3,4,1,5]=>[3,4,6,2,1,5]=>11000=>00111
[2,6,3,4,5,1]=>[3,4,5,6,2,1]=>11000=>00111
[2,6,3,5,1,4]=>[3,5,2,1,6,4]=>11010=>00101
[2,6,3,5,4,1]=>[3,5,4,6,2,1]=>11010=>00101
[2,6,4,1,3,5]=>[4,2,1,6,3,5]=>11100=>00011
[2,6,4,1,5,3]=>[4,2,1,5,6,3]=>11100=>00011
[2,6,4,3,1,5]=>[4,3,6,2,1,5]=>11100=>00011
[2,6,4,3,5,1]=>[4,3,5,6,2,1]=>11100=>00011
[2,6,4,5,1,3]=>[5,4,2,1,6,3]=>11110=>00001
[2,6,4,5,3,1]=>[5,4,3,6,2,1]=>11110=>00001
[2,6,5,1,3,4]=>[5,2,1,6,3,4]=>11100=>00011
[2,6,5,1,4,3]=>[5,2,1,4,6,3]=>11100=>00011
[2,6,5,3,1,4]=>[5,3,6,2,1,4]=>11100=>00011
[2,6,5,3,4,1]=>[5,3,4,6,2,1]=>11100=>00011
[2,6,5,4,1,3]=>[4,5,2,1,6,3]=>11100=>00011
[2,6,5,4,3,1]=>[4,5,3,6,2,1]=>11100=>00011
[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>10000=>01111
[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>10001=>01110
[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>10010=>01101
[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>10011=>01100
[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>10010=>01101
[3,1,2,6,5,4]=>[3,1,2,5,6,4]=>10010=>01101
[3,1,4,2,5,6]=>[4,3,1,2,5,6]=>10100=>01011
[3,1,4,2,6,5]=>[4,3,1,2,6,5]=>10101=>01010
[3,1,4,5,2,6]=>[5,4,3,1,2,6]=>10110=>01001
[3,1,4,5,6,2]=>[6,5,4,3,1,2]=>10111=>01000
[3,1,4,6,2,5]=>[6,4,3,1,2,5]=>10110=>01001
[3,1,4,6,5,2]=>[5,6,4,3,1,2]=>10110=>01001
[3,1,5,2,4,6]=>[5,3,1,2,4,6]=>10100=>01011
[3,1,5,2,6,4]=>[6,5,3,1,2,4]=>10101=>01010
[3,1,5,4,2,6]=>[4,5,3,1,2,6]=>10100=>01011
[3,1,5,4,6,2]=>[4,6,5,3,1,2]=>10101=>01010
[3,1,5,6,2,4]=>[6,3,1,2,5,4]=>10110=>01001
[3,1,5,6,4,2]=>[6,4,5,3,1,2]=>10110=>01001
[3,1,6,2,4,5]=>[6,3,1,2,4,5]=>10100=>01011
[3,1,6,2,5,4]=>[5,6,3,1,2,4]=>10100=>01011
[3,1,6,4,2,5]=>[4,6,3,1,2,5]=>10100=>01011
[3,1,6,4,5,2]=>[4,5,6,3,1,2]=>10100=>01011
[3,1,6,5,2,4]=>[5,3,1,2,6,4]=>10110=>01001
[3,1,6,5,4,2]=>[5,4,6,3,1,2]=>10110=>01001
[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>10000=>01111
[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>10001=>01110
[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>10010=>01101
[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>10011=>01100
[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>10010=>01101
[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>10010=>01101
[3,2,4,1,5,6]=>[2,4,3,1,5,6]=>10100=>01011
[3,2,4,1,6,5]=>[2,4,3,1,6,5]=>10101=>01010
[3,2,4,5,1,6]=>[2,5,4,3,1,6]=>10110=>01001
[3,2,4,5,6,1]=>[2,6,5,4,3,1]=>10111=>01000
[3,2,4,6,1,5]=>[2,6,4,3,1,5]=>10110=>01001
[3,2,4,6,5,1]=>[2,5,6,4,3,1]=>10110=>01001
[3,2,5,1,4,6]=>[2,5,3,1,4,6]=>10100=>01011
[3,2,5,1,6,4]=>[2,6,5,3,1,4]=>10101=>01010
[3,2,5,4,1,6]=>[2,4,5,3,1,6]=>10100=>01011
[3,2,5,4,6,1]=>[2,4,6,5,3,1]=>10101=>01010
[3,2,5,6,1,4]=>[2,6,3,1,5,4]=>10110=>01001
[3,2,5,6,4,1]=>[2,6,4,5,3,1]=>10110=>01001
[3,2,6,1,4,5]=>[2,6,3,1,4,5]=>10100=>01011
[3,2,6,1,5,4]=>[2,5,6,3,1,4]=>10100=>01011
[3,2,6,4,1,5]=>[2,4,6,3,1,5]=>10100=>01011
[3,2,6,4,5,1]=>[2,4,5,6,3,1]=>10100=>01011
[3,2,6,5,1,4]=>[2,5,3,1,6,4]=>10110=>01001
[3,2,6,5,4,1]=>[2,5,4,6,3,1]=>10110=>01001
[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>11000=>00111
[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>11001=>00110
[3,4,1,5,2,6]=>[5,4,1,3,2,6]=>11010=>00101
[3,4,1,5,6,2]=>[6,5,4,1,3,2]=>11011=>00100
[3,4,1,6,2,5]=>[6,4,1,3,2,5]=>11010=>00101
[3,4,1,6,5,2]=>[5,6,4,1,3,2]=>11010=>00101
[3,4,2,1,5,6]=>[4,2,3,1,5,6]=>11000=>00111
[3,4,2,1,6,5]=>[4,2,3,1,6,5]=>11001=>00110
[3,4,2,5,1,6]=>[5,4,2,3,1,6]=>11010=>00101
[3,4,2,5,6,1]=>[6,5,4,2,3,1]=>11011=>00100
[3,4,2,6,1,5]=>[6,4,2,3,1,5]=>11010=>00101
[3,4,2,6,5,1]=>[5,6,4,2,3,1]=>11010=>00101
[3,4,5,1,2,6]=>[5,1,4,3,2,6]=>11100=>00011
[3,4,5,1,6,2]=>[6,5,1,4,3,2]=>11101=>00010
[3,4,5,2,1,6]=>[5,2,4,3,1,6]=>11100=>00011
[3,4,5,2,6,1]=>[6,5,2,4,3,1]=>11101=>00010
[3,4,5,6,1,2]=>[6,1,5,4,3,2]=>11110=>00001
[3,4,5,6,2,1]=>[6,2,5,4,3,1]=>11110=>00001
[3,4,6,1,2,5]=>[6,1,4,3,2,5]=>11100=>00011
[3,4,6,1,5,2]=>[5,6,1,4,3,2]=>11100=>00011
[3,4,6,2,1,5]=>[6,2,4,3,1,5]=>11100=>00011
[3,4,6,2,5,1]=>[5,6,2,4,3,1]=>11100=>00011
[3,4,6,5,1,2]=>[5,1,6,4,3,2]=>11110=>00001
[3,4,6,5,2,1]=>[5,2,6,4,3,1]=>11110=>00001
[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>11000=>00111
[3,5,1,2,6,4]=>[6,5,1,3,2,4]=>11001=>00110
[3,5,1,4,2,6]=>[4,5,1,3,2,6]=>11000=>00111
[3,5,1,4,6,2]=>[4,6,5,1,3,2]=>11001=>00110
[3,5,1,6,2,4]=>[6,1,3,2,5,4]=>11010=>00101
[3,5,1,6,4,2]=>[6,4,5,1,3,2]=>11010=>00101
[3,5,2,1,4,6]=>[5,2,3,1,4,6]=>11000=>00111
[3,5,2,1,6,4]=>[6,5,2,3,1,4]=>11001=>00110
[3,5,2,4,1,6]=>[4,5,2,3,1,6]=>11000=>00111
[3,5,2,4,6,1]=>[4,6,5,2,3,1]=>11001=>00110
[3,5,2,6,1,4]=>[6,2,3,1,5,4]=>11010=>00101
[3,5,2,6,4,1]=>[6,4,5,2,3,1]=>11010=>00101
[3,5,4,1,2,6]=>[4,1,5,3,2,6]=>11100=>00011
[3,5,4,1,6,2]=>[4,1,6,5,3,2]=>11101=>00010
[3,5,4,2,1,6]=>[4,2,5,3,1,6]=>11100=>00011
[3,5,4,2,6,1]=>[4,2,6,5,3,1]=>11101=>00010
[3,5,4,6,1,2]=>[6,4,1,5,3,2]=>11110=>00001
[3,5,4,6,2,1]=>[6,4,2,5,3,1]=>11110=>00001
[3,5,6,1,2,4]=>[6,1,5,3,2,4]=>11100=>00011
[3,5,6,1,4,2]=>[6,1,4,5,3,2]=>11100=>00011
[3,5,6,2,1,4]=>[6,2,5,3,1,4]=>11100=>00011
[3,5,6,2,4,1]=>[6,2,4,5,3,1]=>11100=>00011
[3,5,6,4,1,2]=>[4,6,1,5,3,2]=>11100=>00011
[3,5,6,4,2,1]=>[4,6,2,5,3,1]=>11100=>00011
[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>11000=>00111
[3,6,1,2,5,4]=>[5,6,1,3,2,4]=>11000=>00111
[3,6,1,4,2,5]=>[4,6,1,3,2,5]=>11000=>00111
[3,6,1,4,5,2]=>[4,5,6,1,3,2]=>11000=>00111
[3,6,1,5,2,4]=>[5,1,3,2,6,4]=>11010=>00101
[3,6,1,5,4,2]=>[5,4,6,1,3,2]=>11010=>00101
[3,6,2,1,4,5]=>[6,2,3,1,4,5]=>11000=>00111
[3,6,2,1,5,4]=>[5,6,2,3,1,4]=>11000=>00111
[3,6,2,4,1,5]=>[4,6,2,3,1,5]=>11000=>00111
[3,6,2,4,5,1]=>[4,5,6,2,3,1]=>11000=>00111
[3,6,2,5,1,4]=>[5,2,3,1,6,4]=>11010=>00101
[3,6,2,5,4,1]=>[5,4,6,2,3,1]=>11010=>00101
[3,6,4,1,2,5]=>[4,1,6,3,2,5]=>11100=>00011
[3,6,4,1,5,2]=>[4,1,5,6,3,2]=>11100=>00011
[3,6,4,2,1,5]=>[4,2,6,3,1,5]=>11100=>00011
[3,6,4,2,5,1]=>[4,2,5,6,3,1]=>11100=>00011
[3,6,4,5,1,2]=>[5,4,1,6,3,2]=>11110=>00001
[3,6,4,5,2,1]=>[5,4,2,6,3,1]=>11110=>00001
[3,6,5,1,2,4]=>[5,1,6,3,2,4]=>11100=>00011
[3,6,5,1,4,2]=>[5,1,4,6,3,2]=>11100=>00011
[3,6,5,2,1,4]=>[5,2,6,3,1,4]=>11100=>00011
[3,6,5,2,4,1]=>[5,2,4,6,3,1]=>11100=>00011
[3,6,5,4,1,2]=>[4,5,1,6,3,2]=>11100=>00011
[3,6,5,4,2,1]=>[4,5,2,6,3,1]=>11100=>00011
[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>10000=>01111
[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>10001=>01110
[4,1,2,5,3,6]=>[5,4,1,2,3,6]=>10010=>01101
[4,1,2,5,6,3]=>[6,5,4,1,2,3]=>10011=>01100
[4,1,2,6,3,5]=>[6,4,1,2,3,5]=>10010=>01101
[4,1,2,6,5,3]=>[5,6,4,1,2,3]=>10010=>01101
[4,1,3,2,5,6]=>[3,4,1,2,5,6]=>10000=>01111
[4,1,3,2,6,5]=>[3,4,1,2,6,5]=>10001=>01110
[4,1,3,5,2,6]=>[3,5,4,1,2,6]=>10010=>01101
[4,1,3,5,6,2]=>[3,6,5,4,1,2]=>10011=>01100
[4,1,3,6,2,5]=>[3,6,4,1,2,5]=>10010=>01101
[4,1,3,6,5,2]=>[3,5,6,4,1,2]=>10010=>01101
[4,1,5,2,3,6]=>[5,1,2,4,3,6]=>10100=>01011
[4,1,5,2,6,3]=>[6,5,1,2,4,3]=>10101=>01010
[4,1,5,3,2,6]=>[5,3,4,1,2,6]=>10100=>01011
[4,1,5,3,6,2]=>[6,5,3,4,1,2]=>10101=>01010
[4,1,5,6,2,3]=>[6,1,2,5,4,3]=>10110=>01001
[4,1,5,6,3,2]=>[6,3,5,4,1,2]=>10110=>01001
[4,1,6,2,3,5]=>[6,1,2,4,3,5]=>10100=>01011
[4,1,6,2,5,3]=>[5,6,1,2,4,3]=>10100=>01011
[4,1,6,3,2,5]=>[6,3,4,1,2,5]=>10100=>01011
[4,1,6,3,5,2]=>[5,6,3,4,1,2]=>10100=>01011
[4,1,6,5,2,3]=>[5,1,2,6,4,3]=>10110=>01001
[4,1,6,5,3,2]=>[5,3,6,4,1,2]=>10110=>01001
[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>10000=>01111
[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>10001=>01110
[4,2,1,5,3,6]=>[2,5,4,1,3,6]=>10010=>01101
[4,2,1,5,6,3]=>[2,6,5,4,1,3]=>10011=>01100
[4,2,1,6,3,5]=>[2,6,4,1,3,5]=>10010=>01101
[4,2,1,6,5,3]=>[2,5,6,4,1,3]=>10010=>01101
[4,2,3,1,5,6]=>[2,3,4,1,5,6]=>10000=>01111
[4,2,3,1,6,5]=>[2,3,4,1,6,5]=>10001=>01110
[4,2,3,5,1,6]=>[2,3,5,4,1,6]=>10010=>01101
[4,2,3,5,6,1]=>[2,3,6,5,4,1]=>10011=>01100
[4,2,3,6,1,5]=>[2,3,6,4,1,5]=>10010=>01101
[4,2,3,6,5,1]=>[2,3,5,6,4,1]=>10010=>01101
[4,2,5,1,3,6]=>[2,5,1,4,3,6]=>10100=>01011
[4,2,5,1,6,3]=>[2,6,5,1,4,3]=>10101=>01010
[4,2,5,3,1,6]=>[2,5,3,4,1,6]=>10100=>01011
[4,2,5,3,6,1]=>[2,6,5,3,4,1]=>10101=>01010
[4,2,5,6,1,3]=>[2,6,1,5,4,3]=>10110=>01001
[4,2,5,6,3,1]=>[2,6,3,5,4,1]=>10110=>01001
[4,2,6,1,3,5]=>[2,6,1,4,3,5]=>10100=>01011
[4,2,6,1,5,3]=>[2,5,6,1,4,3]=>10100=>01011
[4,2,6,3,1,5]=>[2,6,3,4,1,5]=>10100=>01011
[4,2,6,3,5,1]=>[2,5,6,3,4,1]=>10100=>01011
[4,2,6,5,1,3]=>[2,5,1,6,4,3]=>10110=>01001
[4,2,6,5,3,1]=>[2,5,3,6,4,1]=>10110=>01001
[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>11000=>00111
[4,3,1,2,6,5]=>[3,1,4,2,6,5]=>11001=>00110
[4,3,1,5,2,6]=>[3,1,5,4,2,6]=>11010=>00101
[4,3,1,5,6,2]=>[3,1,6,5,4,2]=>11011=>00100
[4,3,1,6,2,5]=>[3,1,6,4,2,5]=>11010=>00101
[4,3,1,6,5,2]=>[3,1,5,6,4,2]=>11010=>00101
[4,3,2,1,5,6]=>[3,2,4,1,5,6]=>11000=>00111
[4,3,2,1,6,5]=>[3,2,4,1,6,5]=>11001=>00110
[4,3,2,5,1,6]=>[3,2,5,4,1,6]=>11010=>00101
[4,3,2,5,6,1]=>[3,2,6,5,4,1]=>11011=>00100
[4,3,2,6,1,5]=>[3,2,6,4,1,5]=>11010=>00101
[4,3,2,6,5,1]=>[3,2,5,6,4,1]=>11010=>00101
[4,3,5,1,2,6]=>[5,3,1,4,2,6]=>11100=>00011
[4,3,5,1,6,2]=>[6,5,3,1,4,2]=>11101=>00010
[4,3,5,2,1,6]=>[5,3,2,4,1,6]=>11100=>00011
[4,3,5,2,6,1]=>[6,5,3,2,4,1]=>11101=>00010
[4,3,5,6,1,2]=>[6,3,1,5,4,2]=>11110=>00001
[4,3,5,6,2,1]=>[6,3,2,5,4,1]=>11110=>00001
[4,3,6,1,2,5]=>[6,3,1,4,2,5]=>11100=>00011
[4,3,6,1,5,2]=>[5,6,3,1,4,2]=>11100=>00011
[4,3,6,2,1,5]=>[6,3,2,4,1,5]=>11100=>00011
[4,3,6,2,5,1]=>[5,6,3,2,4,1]=>11100=>00011
[4,3,6,5,1,2]=>[5,3,1,6,4,2]=>11110=>00001
[4,3,6,5,2,1]=>[5,3,2,6,4,1]=>11110=>00001
[4,5,1,2,3,6]=>[5,1,4,2,3,6]=>11000=>00111
[4,5,1,2,6,3]=>[6,5,1,4,2,3]=>11001=>00110
[4,5,1,3,2,6]=>[5,1,3,4,2,6]=>11000=>00111
[4,5,1,3,6,2]=>[6,5,1,3,4,2]=>11001=>00110
[4,5,1,6,2,3]=>[6,1,5,4,2,3]=>11010=>00101
[4,5,1,6,3,2]=>[6,1,3,5,4,2]=>11010=>00101
[4,5,2,1,3,6]=>[5,2,4,1,3,6]=>11000=>00111
[4,5,2,1,6,3]=>[6,5,2,4,1,3]=>11001=>00110
[4,5,2,3,1,6]=>[5,2,3,4,1,6]=>11000=>00111
[4,5,2,3,6,1]=>[6,5,2,3,4,1]=>11001=>00110
[4,5,2,6,1,3]=>[6,2,5,4,1,3]=>11010=>00101
[4,5,2,6,3,1]=>[6,2,3,5,4,1]=>11010=>00101
[4,5,3,1,2,6]=>[3,5,1,4,2,6]=>11000=>00111
[4,5,3,1,6,2]=>[3,6,5,1,4,2]=>11001=>00110
[4,5,3,2,1,6]=>[3,5,2,4,1,6]=>11000=>00111
[4,5,3,2,6,1]=>[3,6,5,2,4,1]=>11001=>00110
[4,5,3,6,1,2]=>[3,6,1,5,4,2]=>11010=>00101
[4,5,3,6,2,1]=>[3,6,2,5,4,1]=>11010=>00101
[4,5,6,1,2,3]=>[6,1,5,2,4,3]=>11100=>00011
[4,5,6,1,3,2]=>[6,1,5,3,4,2]=>11100=>00011
[4,5,6,2,1,3]=>[6,2,5,1,4,3]=>11100=>00011
[4,5,6,2,3,1]=>[6,2,5,3,4,1]=>11100=>00011
[4,5,6,3,1,2]=>[6,3,5,1,4,2]=>11100=>00011
[4,5,6,3,2,1]=>[6,3,5,2,4,1]=>11100=>00011
[4,6,1,2,3,5]=>[6,1,4,2,3,5]=>11000=>00111
[4,6,1,2,5,3]=>[5,6,1,4,2,3]=>11000=>00111
[4,6,1,3,2,5]=>[6,1,3,4,2,5]=>11000=>00111
[4,6,1,3,5,2]=>[5,6,1,3,4,2]=>11000=>00111
[4,6,1,5,2,3]=>[5,1,6,4,2,3]=>11010=>00101
[4,6,1,5,3,2]=>[5,1,3,6,4,2]=>11010=>00101
[4,6,2,1,3,5]=>[6,2,4,1,3,5]=>11000=>00111
[4,6,2,1,5,3]=>[5,6,2,4,1,3]=>11000=>00111
[4,6,2,3,1,5]=>[6,2,3,4,1,5]=>11000=>00111
[4,6,2,3,5,1]=>[5,6,2,3,4,1]=>11000=>00111
[4,6,2,5,1,3]=>[5,2,6,4,1,3]=>11010=>00101
[4,6,2,5,3,1]=>[5,2,3,6,4,1]=>11010=>00101
[4,6,3,1,2,5]=>[3,6,1,4,2,5]=>11000=>00111
[4,6,3,1,5,2]=>[3,5,6,1,4,2]=>11000=>00111
[4,6,3,2,1,5]=>[3,6,2,4,1,5]=>11000=>00111
[4,6,3,2,5,1]=>[3,5,6,2,4,1]=>11000=>00111
[4,6,3,5,1,2]=>[3,5,1,6,4,2]=>11010=>00101
[4,6,3,5,2,1]=>[3,5,2,6,4,1]=>11010=>00101
[4,6,5,1,2,3]=>[5,1,6,2,4,3]=>11100=>00011
[4,6,5,1,3,2]=>[5,1,6,3,4,2]=>11100=>00011
[4,6,5,2,1,3]=>[5,2,6,1,4,3]=>11100=>00011
[4,6,5,2,3,1]=>[5,2,6,3,4,1]=>11100=>00011
[4,6,5,3,1,2]=>[5,3,6,1,4,2]=>11100=>00011
[4,6,5,3,2,1]=>[5,3,6,2,4,1]=>11100=>00011
[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>10000=>01111
[5,1,2,3,6,4]=>[6,5,1,2,3,4]=>10001=>01110
[5,1,2,4,3,6]=>[4,5,1,2,3,6]=>10000=>01111
[5,1,2,4,6,3]=>[4,6,5,1,2,3]=>10001=>01110
[5,1,2,6,3,4]=>[6,1,2,3,5,4]=>10010=>01101
[5,1,2,6,4,3]=>[6,4,5,1,2,3]=>10010=>01101
[5,1,3,2,4,6]=>[3,5,1,2,4,6]=>10000=>01111
[5,1,3,2,6,4]=>[3,6,5,1,2,4]=>10001=>01110
[5,1,3,4,2,6]=>[3,4,5,1,2,6]=>10000=>01111
[5,1,3,4,6,2]=>[3,4,6,5,1,2]=>10001=>01110
[5,1,3,6,2,4]=>[3,6,1,2,5,4]=>10010=>01101
[5,1,3,6,4,2]=>[3,6,4,5,1,2]=>10010=>01101
[5,1,4,2,3,6]=>[4,1,2,5,3,6]=>10100=>01011
[5,1,4,2,6,3]=>[4,1,2,6,5,3]=>10101=>01010
[5,1,4,3,2,6]=>[4,3,5,1,2,6]=>10100=>01011
[5,1,4,3,6,2]=>[4,3,6,5,1,2]=>10101=>01010
[5,1,4,6,2,3]=>[6,4,1,2,5,3]=>10110=>01001
[5,1,4,6,3,2]=>[6,4,3,5,1,2]=>10110=>01001
[5,1,6,2,3,4]=>[6,1,2,5,3,4]=>10100=>01011
[5,1,6,2,4,3]=>[6,1,2,4,5,3]=>10100=>01011
[5,1,6,3,2,4]=>[6,3,5,1,2,4]=>10100=>01011
[5,1,6,3,4,2]=>[6,3,4,5,1,2]=>10100=>01011
[5,1,6,4,2,3]=>[4,6,1,2,5,3]=>10100=>01011
[5,1,6,4,3,2]=>[4,6,3,5,1,2]=>10100=>01011
[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>10000=>01111
[5,2,1,3,6,4]=>[2,6,5,1,3,4]=>10001=>01110
[5,2,1,4,3,6]=>[2,4,5,1,3,6]=>10000=>01111
[5,2,1,4,6,3]=>[2,4,6,5,1,3]=>10001=>01110
[5,2,1,6,3,4]=>[2,6,1,3,5,4]=>10010=>01101
[5,2,1,6,4,3]=>[2,6,4,5,1,3]=>10010=>01101
[5,2,3,1,4,6]=>[2,3,5,1,4,6]=>10000=>01111
[5,2,3,1,6,4]=>[2,3,6,5,1,4]=>10001=>01110
[5,2,3,4,1,6]=>[2,3,4,5,1,6]=>10000=>01111
[5,2,3,4,6,1]=>[2,3,4,6,5,1]=>10001=>01110
[5,2,3,6,1,4]=>[2,3,6,1,5,4]=>10010=>01101
[5,2,3,6,4,1]=>[2,3,6,4,5,1]=>10010=>01101
[5,2,4,1,3,6]=>[2,4,1,5,3,6]=>10100=>01011
[5,2,4,1,6,3]=>[2,4,1,6,5,3]=>10101=>01010
[5,2,4,3,1,6]=>[2,4,3,5,1,6]=>10100=>01011
[5,2,4,3,6,1]=>[2,4,3,6,5,1]=>10101=>01010
[5,2,4,6,1,3]=>[2,6,4,1,5,3]=>10110=>01001
[5,2,4,6,3,1]=>[2,6,4,3,5,1]=>10110=>01001
[5,2,6,1,3,4]=>[2,6,1,5,3,4]=>10100=>01011
[5,2,6,1,4,3]=>[2,6,1,4,5,3]=>10100=>01011
[5,2,6,3,1,4]=>[2,6,3,5,1,4]=>10100=>01011
[5,2,6,3,4,1]=>[2,6,3,4,5,1]=>10100=>01011
[5,2,6,4,1,3]=>[2,4,6,1,5,3]=>10100=>01011
[5,2,6,4,3,1]=>[2,4,6,3,5,1]=>10100=>01011
[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>11000=>00111
[5,3,1,2,6,4]=>[3,1,6,5,2,4]=>11001=>00110
[5,3,1,4,2,6]=>[3,1,4,5,2,6]=>11000=>00111
[5,3,1,4,6,2]=>[3,1,4,6,5,2]=>11001=>00110
[5,3,1,6,2,4]=>[3,1,6,2,5,4]=>11010=>00101
[5,3,1,6,4,2]=>[3,1,6,4,5,2]=>11010=>00101
[5,3,2,1,4,6]=>[3,2,5,1,4,6]=>11000=>00111
[5,3,2,1,6,4]=>[3,2,6,5,1,4]=>11001=>00110
[5,3,2,4,1,6]=>[3,2,4,5,1,6]=>11000=>00111
[5,3,2,4,6,1]=>[3,2,4,6,5,1]=>11001=>00110
[5,3,2,6,1,4]=>[3,2,6,1,5,4]=>11010=>00101
[5,3,2,6,4,1]=>[3,2,6,4,5,1]=>11010=>00101
[5,3,4,1,2,6]=>[4,3,1,5,2,6]=>11100=>00011
[5,3,4,1,6,2]=>[4,3,1,6,5,2]=>11101=>00010
[5,3,4,2,1,6]=>[4,3,2,5,1,6]=>11100=>00011
[5,3,4,2,6,1]=>[4,3,2,6,5,1]=>11101=>00010
[5,3,4,6,1,2]=>[6,4,3,1,5,2]=>11110=>00001
[5,3,4,6,2,1]=>[6,4,3,2,5,1]=>11110=>00001
[5,3,6,1,2,4]=>[6,3,1,5,2,4]=>11100=>00011
[5,3,6,1,4,2]=>[6,3,1,4,5,2]=>11100=>00011
[5,3,6,2,1,4]=>[6,3,2,5,1,4]=>11100=>00011
[5,3,6,2,4,1]=>[6,3,2,4,5,1]=>11100=>00011
[5,3,6,4,1,2]=>[4,6,3,1,5,2]=>11100=>00011
[5,3,6,4,2,1]=>[4,6,3,2,5,1]=>11100=>00011
[5,4,1,2,3,6]=>[4,1,5,2,3,6]=>11000=>00111
[5,4,1,2,6,3]=>[4,1,6,5,2,3]=>11001=>00110
[5,4,1,3,2,6]=>[4,1,3,5,2,6]=>11000=>00111
[5,4,1,3,6,2]=>[4,1,3,6,5,2]=>11001=>00110
[5,4,1,6,2,3]=>[6,4,1,5,2,3]=>11010=>00101
[5,4,1,6,3,2]=>[6,4,1,3,5,2]=>11010=>00101
[5,4,2,1,3,6]=>[4,2,5,1,3,6]=>11000=>00111
[5,4,2,1,6,3]=>[4,2,6,5,1,3]=>11001=>00110
[5,4,2,3,1,6]=>[4,2,3,5,1,6]=>11000=>00111
[5,4,2,3,6,1]=>[4,2,3,6,5,1]=>11001=>00110
[5,4,2,6,1,3]=>[6,4,2,5,1,3]=>11010=>00101
[5,4,2,6,3,1]=>[6,4,2,3,5,1]=>11010=>00101
[5,4,3,1,2,6]=>[3,4,1,5,2,6]=>11000=>00111
[5,4,3,1,6,2]=>[3,4,1,6,5,2]=>11001=>00110
[5,4,3,2,1,6]=>[3,4,2,5,1,6]=>11000=>00111
[5,4,3,2,6,1]=>[3,4,2,6,5,1]=>11001=>00110
[5,4,3,6,1,2]=>[3,6,4,1,5,2]=>11010=>00101
[5,4,3,6,2,1]=>[3,6,4,2,5,1]=>11010=>00101
[5,4,6,1,2,3]=>[6,1,4,2,5,3]=>11100=>00011
[5,4,6,1,3,2]=>[6,1,4,3,5,2]=>11100=>00011
[5,4,6,2,1,3]=>[6,2,4,1,5,3]=>11100=>00011
[5,4,6,2,3,1]=>[6,2,4,3,5,1]=>11100=>00011
[5,4,6,3,1,2]=>[6,3,4,1,5,2]=>11100=>00011
[5,4,6,3,2,1]=>[6,3,4,2,5,1]=>11100=>00011
[5,6,1,2,3,4]=>[6,1,5,2,3,4]=>11000=>00111
[5,6,1,2,4,3]=>[6,1,4,5,2,3]=>11000=>00111
[5,6,1,3,2,4]=>[6,1,3,5,2,4]=>11000=>00111
[5,6,1,3,4,2]=>[6,1,3,4,5,2]=>11000=>00111
[5,6,1,4,2,3]=>[4,6,1,5,2,3]=>11000=>00111
[5,6,1,4,3,2]=>[4,6,1,3,5,2]=>11000=>00111
[5,6,2,1,3,4]=>[6,2,5,1,3,4]=>11000=>00111
[5,6,2,1,4,3]=>[6,2,4,5,1,3]=>11000=>00111
[5,6,2,3,1,4]=>[6,2,3,5,1,4]=>11000=>00111
[5,6,2,3,4,1]=>[6,2,3,4,5,1]=>11000=>00111
[5,6,2,4,1,3]=>[4,6,2,5,1,3]=>11000=>00111
[5,6,2,4,3,1]=>[4,6,2,3,5,1]=>11000=>00111
[5,6,3,1,2,4]=>[3,6,1,5,2,4]=>11000=>00111
[5,6,3,1,4,2]=>[3,6,1,4,5,2]=>11000=>00111
[5,6,3,2,1,4]=>[3,6,2,5,1,4]=>11000=>00111
[5,6,3,2,4,1]=>[3,6,2,4,5,1]=>11000=>00111
[5,6,3,4,1,2]=>[3,4,6,1,5,2]=>11000=>00111
[5,6,3,4,2,1]=>[3,4,6,2,5,1]=>11000=>00111
[5,6,4,1,2,3]=>[4,1,6,2,5,3]=>11100=>00011
[5,6,4,1,3,2]=>[4,1,6,3,5,2]=>11100=>00011
[5,6,4,2,1,3]=>[4,2,6,1,5,3]=>11100=>00011
[5,6,4,2,3,1]=>[4,2,6,3,5,1]=>11100=>00011
[5,6,4,3,1,2]=>[4,3,6,1,5,2]=>11100=>00011
[5,6,4,3,2,1]=>[4,3,6,2,5,1]=>11100=>00011
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>10000=>01111
[6,1,2,3,5,4]=>[5,6,1,2,3,4]=>10000=>01111
[6,1,2,4,3,5]=>[4,6,1,2,3,5]=>10000=>01111
[6,1,2,4,5,3]=>[4,5,6,1,2,3]=>10000=>01111
[6,1,2,5,3,4]=>[5,1,2,3,6,4]=>10010=>01101
[6,1,2,5,4,3]=>[5,4,6,1,2,3]=>10010=>01101
[6,1,3,2,4,5]=>[3,6,1,2,4,5]=>10000=>01111
[6,1,3,2,5,4]=>[3,5,6,1,2,4]=>10000=>01111
[6,1,3,4,2,5]=>[3,4,6,1,2,5]=>10000=>01111
[6,1,3,4,5,2]=>[3,4,5,6,1,2]=>10000=>01111
[6,1,3,5,2,4]=>[3,5,1,2,6,4]=>10010=>01101
[6,1,3,5,4,2]=>[3,5,4,6,1,2]=>10010=>01101
[6,1,4,2,3,5]=>[4,1,2,6,3,5]=>10100=>01011
[6,1,4,2,5,3]=>[4,1,2,5,6,3]=>10100=>01011
[6,1,4,3,2,5]=>[4,3,6,1,2,5]=>10100=>01011
[6,1,4,3,5,2]=>[4,3,5,6,1,2]=>10100=>01011
[6,1,4,5,2,3]=>[5,4,1,2,6,3]=>10110=>01001
[6,1,4,5,3,2]=>[5,4,3,6,1,2]=>10110=>01001
[6,1,5,2,3,4]=>[5,1,2,6,3,4]=>10100=>01011
[6,1,5,2,4,3]=>[5,1,2,4,6,3]=>10100=>01011
[6,1,5,3,2,4]=>[5,3,6,1,2,4]=>10100=>01011
[6,1,5,3,4,2]=>[5,3,4,6,1,2]=>10100=>01011
[6,1,5,4,2,3]=>[4,5,1,2,6,3]=>10100=>01011
[6,1,5,4,3,2]=>[4,5,3,6,1,2]=>10100=>01011
[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>10000=>01111
[6,2,1,3,5,4]=>[2,5,6,1,3,4]=>10000=>01111
[6,2,1,4,3,5]=>[2,4,6,1,3,5]=>10000=>01111
[6,2,1,4,5,3]=>[2,4,5,6,1,3]=>10000=>01111
[6,2,1,5,3,4]=>[2,5,1,3,6,4]=>10010=>01101
[6,2,1,5,4,3]=>[2,5,4,6,1,3]=>10010=>01101
[6,2,3,1,4,5]=>[2,3,6,1,4,5]=>10000=>01111
[6,2,3,1,5,4]=>[2,3,5,6,1,4]=>10000=>01111
[6,2,3,4,1,5]=>[2,3,4,6,1,5]=>10000=>01111
[6,2,3,4,5,1]=>[2,3,4,5,6,1]=>10000=>01111
[6,2,3,5,1,4]=>[2,3,5,1,6,4]=>10010=>01101
[6,2,3,5,4,1]=>[2,3,5,4,6,1]=>10010=>01101
[6,2,4,1,3,5]=>[2,4,1,6,3,5]=>10100=>01011
[6,2,4,1,5,3]=>[2,4,1,5,6,3]=>10100=>01011
[6,2,4,3,1,5]=>[2,4,3,6,1,5]=>10100=>01011
[6,2,4,3,5,1]=>[2,4,3,5,6,1]=>10100=>01011
[6,2,4,5,1,3]=>[2,5,4,1,6,3]=>10110=>01001
[6,2,4,5,3,1]=>[2,5,4,3,6,1]=>10110=>01001
[6,2,5,1,3,4]=>[2,5,1,6,3,4]=>10100=>01011
[6,2,5,1,4,3]=>[2,5,1,4,6,3]=>10100=>01011
[6,2,5,3,1,4]=>[2,5,3,6,1,4]=>10100=>01011
[6,2,5,3,4,1]=>[2,5,3,4,6,1]=>10100=>01011
[6,2,5,4,1,3]=>[2,4,5,1,6,3]=>10100=>01011
[6,2,5,4,3,1]=>[2,4,5,3,6,1]=>10100=>01011
[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>11000=>00111
[6,3,1,2,5,4]=>[3,1,5,6,2,4]=>11000=>00111
[6,3,1,4,2,5]=>[3,1,4,6,2,5]=>11000=>00111
[6,3,1,4,5,2]=>[3,1,4,5,6,2]=>11000=>00111
[6,3,1,5,2,4]=>[3,1,5,2,6,4]=>11010=>00101
[6,3,1,5,4,2]=>[3,1,5,4,6,2]=>11010=>00101
[6,3,2,1,4,5]=>[3,2,6,1,4,5]=>11000=>00111
[6,3,2,1,5,4]=>[3,2,5,6,1,4]=>11000=>00111
[6,3,2,4,1,5]=>[3,2,4,6,1,5]=>11000=>00111
[6,3,2,4,5,1]=>[3,2,4,5,6,1]=>11000=>00111
[6,3,2,5,1,4]=>[3,2,5,1,6,4]=>11010=>00101
[6,3,2,5,4,1]=>[3,2,5,4,6,1]=>11010=>00101
[6,3,4,1,2,5]=>[4,3,1,6,2,5]=>11100=>00011
[6,3,4,1,5,2]=>[4,3,1,5,6,2]=>11100=>00011
[6,3,4,2,1,5]=>[4,3,2,6,1,5]=>11100=>00011
[6,3,4,2,5,1]=>[4,3,2,5,6,1]=>11100=>00011
[6,3,4,5,1,2]=>[5,4,3,1,6,2]=>11110=>00001
[6,3,4,5,2,1]=>[5,4,3,2,6,1]=>11110=>00001
[6,3,5,1,2,4]=>[5,3,1,6,2,4]=>11100=>00011
[6,3,5,1,4,2]=>[5,3,1,4,6,2]=>11100=>00011
[6,3,5,2,1,4]=>[5,3,2,6,1,4]=>11100=>00011
[6,3,5,2,4,1]=>[5,3,2,4,6,1]=>11100=>00011
[6,3,5,4,1,2]=>[4,5,3,1,6,2]=>11100=>00011
[6,3,5,4,2,1]=>[4,5,3,2,6,1]=>11100=>00011
[6,4,1,2,3,5]=>[4,1,6,2,3,5]=>11000=>00111
[6,4,1,2,5,3]=>[4,1,5,6,2,3]=>11000=>00111
[6,4,1,3,2,5]=>[4,1,3,6,2,5]=>11000=>00111
[6,4,1,3,5,2]=>[4,1,3,5,6,2]=>11000=>00111
[6,4,1,5,2,3]=>[5,4,1,6,2,3]=>11010=>00101
[6,4,1,5,3,2]=>[5,4,1,3,6,2]=>11010=>00101
[6,4,2,1,3,5]=>[4,2,6,1,3,5]=>11000=>00111
[6,4,2,1,5,3]=>[4,2,5,6,1,3]=>11000=>00111
[6,4,2,3,1,5]=>[4,2,3,6,1,5]=>11000=>00111
[6,4,2,3,5,1]=>[4,2,3,5,6,1]=>11000=>00111
[6,4,2,5,1,3]=>[5,4,2,6,1,3]=>11010=>00101
[6,4,2,5,3,1]=>[5,4,2,3,6,1]=>11010=>00101
[6,4,3,1,2,5]=>[3,4,1,6,2,5]=>11000=>00111
[6,4,3,1,5,2]=>[3,4,1,5,6,2]=>11000=>00111
[6,4,3,2,1,5]=>[3,4,2,6,1,5]=>11000=>00111
[6,4,3,2,5,1]=>[3,4,2,5,6,1]=>11000=>00111
[6,4,3,5,1,2]=>[3,5,4,1,6,2]=>11010=>00101
[6,4,3,5,2,1]=>[3,5,4,2,6,1]=>11010=>00101
[6,4,5,1,2,3]=>[5,1,4,2,6,3]=>11100=>00011
[6,4,5,1,3,2]=>[5,1,4,3,6,2]=>11100=>00011
[6,4,5,2,1,3]=>[5,2,4,1,6,3]=>11100=>00011
[6,4,5,2,3,1]=>[5,2,4,3,6,1]=>11100=>00011
[6,4,5,3,1,2]=>[5,3,4,1,6,2]=>11100=>00011
[6,4,5,3,2,1]=>[5,3,4,2,6,1]=>11100=>00011
[6,5,1,2,3,4]=>[5,1,6,2,3,4]=>11000=>00111
[6,5,1,2,4,3]=>[5,1,4,6,2,3]=>11000=>00111
[6,5,1,3,2,4]=>[5,1,3,6,2,4]=>11000=>00111
[6,5,1,3,4,2]=>[5,1,3,4,6,2]=>11000=>00111
[6,5,1,4,2,3]=>[4,5,1,6,2,3]=>11000=>00111
[6,5,1,4,3,2]=>[4,5,1,3,6,2]=>11000=>00111
[6,5,2,1,3,4]=>[5,2,6,1,3,4]=>11000=>00111
[6,5,2,1,4,3]=>[5,2,4,6,1,3]=>11000=>00111
[6,5,2,3,1,4]=>[5,2,3,6,1,4]=>11000=>00111
[6,5,2,3,4,1]=>[5,2,3,4,6,1]=>11000=>00111
[6,5,2,4,1,3]=>[4,5,2,6,1,3]=>11000=>00111
[6,5,2,4,3,1]=>[4,5,2,3,6,1]=>11000=>00111
[6,5,3,1,2,4]=>[3,5,1,6,2,4]=>11000=>00111
[6,5,3,1,4,2]=>[3,5,1,4,6,2]=>11000=>00111
[6,5,3,2,1,4]=>[3,5,2,6,1,4]=>11000=>00111
[6,5,3,2,4,1]=>[3,5,2,4,6,1]=>11000=>00111
[6,5,3,4,1,2]=>[3,4,5,1,6,2]=>11000=>00111
[6,5,3,4,2,1]=>[3,4,5,2,6,1]=>11000=>00111
[6,5,4,1,2,3]=>[4,1,5,2,6,3]=>11100=>00011
[6,5,4,1,3,2]=>[4,1,5,3,6,2]=>11100=>00011
[6,5,4,2,1,3]=>[4,2,5,1,6,3]=>11100=>00011
[6,5,4,2,3,1]=>[4,2,5,3,6,1]=>11100=>00011
[6,5,4,3,1,2]=>[4,3,5,1,6,2]=>11100=>00011
[6,5,4,3,2,1]=>[4,3,5,2,6,1]=>11100=>00011
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000=>111111
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>000001=>111110
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>000010=>111101
[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>000011=>111100
[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>000010=>111101
[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>000010=>111101
[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>000100=>111011
[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>000101=>111010
[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>000110=>111001
[1,2,3,5,6,7,4]=>[1,2,3,7,6,5,4]=>000111=>111000
[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>000110=>111001
[1,2,3,5,7,6,4]=>[1,2,3,6,7,5,4]=>000110=>111001
[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>000100=>111011
[1,2,3,6,4,7,5]=>[1,2,3,7,6,4,5]=>000101=>111010
[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>000100=>111011
[1,2,3,6,5,7,4]=>[1,2,3,5,7,6,4]=>000101=>111010
[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]=>000110=>111001
[1,2,3,6,7,5,4]=>[1,2,3,7,5,6,4]=>000110=>111001
[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>000100=>111011
[1,2,3,7,4,6,5]=>[1,2,3,6,7,4,5]=>000100=>111011
[1,2,3,7,5,4,6]=>[1,2,3,5,7,4,6]=>000100=>111011
[1,2,3,7,5,6,4]=>[1,2,3,5,6,7,4]=>000100=>111011
[1,2,3,7,6,4,5]=>[1,2,3,6,4,7,5]=>000110=>111001
[1,2,3,7,6,5,4]=>[1,2,3,6,5,7,4]=>000110=>111001
[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000=>110111
[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>001001=>110110
[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>001010=>110101
[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>001011=>110100
[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>001010=>110101
[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>001010=>110101
[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>001100=>110011
[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>001101=>110010
[1,2,4,5,6,3,7]=>[1,2,6,5,4,3,7]=>001110=>110001
[1,2,4,5,6,7,3]=>[1,2,7,6,5,4,3]=>001111=>110000
[1,2,4,5,7,3,6]=>[1,2,7,5,4,3,6]=>001110=>110001
[1,2,4,5,7,6,3]=>[1,2,6,7,5,4,3]=>001110=>110001
[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>001100=>110011
[1,2,4,6,3,7,5]=>[1,2,7,6,4,3,5]=>001101=>110010
[1,2,4,6,5,3,7]=>[1,2,5,6,4,3,7]=>001100=>110011
[1,2,4,6,5,7,3]=>[1,2,5,7,6,4,3]=>001101=>110010
[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]=>001110=>110001
[1,2,4,6,7,5,3]=>[1,2,7,5,6,4,3]=>001110=>110001
[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>001100=>110011
[1,2,4,7,3,6,5]=>[1,2,6,7,4,3,5]=>001100=>110011
[1,2,4,7,5,3,6]=>[1,2,5,7,4,3,6]=>001100=>110011
[1,2,4,7,5,6,3]=>[1,2,5,6,7,4,3]=>001100=>110011
[1,2,4,7,6,3,5]=>[1,2,6,4,3,7,5]=>001110=>110001
[1,2,4,7,6,5,3]=>[1,2,6,5,7,4,3]=>001110=>110001
[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>001000=>110111
[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>001001=>110110
[1,2,5,3,6,4,7]=>[1,2,6,5,3,4,7]=>001010=>110101
[1,2,5,3,6,7,4]=>[1,2,7,6,5,3,4]=>001011=>110100
[1,2,5,3,7,4,6]=>[1,2,7,5,3,4,6]=>001010=>110101
[1,2,5,3,7,6,4]=>[1,2,6,7,5,3,4]=>001010=>110101
[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>001000=>110111
[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>001001=>110110
[1,2,5,4,6,3,7]=>[1,2,4,6,5,3,7]=>001010=>110101
[1,2,5,4,6,7,3]=>[1,2,4,7,6,5,3]=>001011=>110100
[1,2,5,4,7,3,6]=>[1,2,4,7,5,3,6]=>001010=>110101
[1,2,5,4,7,6,3]=>[1,2,4,6,7,5,3]=>001010=>110101
[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]=>001100=>110011
[1,2,5,6,3,7,4]=>[1,2,7,6,3,5,4]=>001101=>110010
[1,2,5,6,4,3,7]=>[1,2,6,4,5,3,7]=>001100=>110011
[1,2,5,6,4,7,3]=>[1,2,7,6,4,5,3]=>001101=>110010
[1,2,5,6,7,3,4]=>[1,2,7,3,6,5,4]=>001110=>110001
[1,2,5,6,7,4,3]=>[1,2,7,4,6,5,3]=>001110=>110001
[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]=>001100=>110011
[1,2,5,7,3,6,4]=>[1,2,6,7,3,5,4]=>001100=>110011
[1,2,5,7,4,3,6]=>[1,2,7,4,5,3,6]=>001100=>110011
[1,2,5,7,4,6,3]=>[1,2,6,7,4,5,3]=>001100=>110011
[1,2,5,7,6,3,4]=>[1,2,6,3,7,5,4]=>001110=>110001
[1,2,5,7,6,4,3]=>[1,2,6,4,7,5,3]=>001110=>110001
[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>001000=>110111
[1,2,6,3,4,7,5]=>[1,2,7,6,3,4,5]=>001001=>110110
[1,2,6,3,5,4,7]=>[1,2,5,6,3,4,7]=>001000=>110111
[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>001001=>110110
[1,2,6,3,7,4,5]=>[1,2,7,3,4,6,5]=>001010=>110101
[1,2,6,3,7,5,4]=>[1,2,7,5,6,3,4]=>001010=>110101
[1,2,6,4,3,5,7]=>[1,2,4,6,3,5,7]=>001000=>110111
[1,2,6,4,3,7,5]=>[1,2,4,7,6,3,5]=>001001=>110110
[1,2,6,4,5,3,7]=>[1,2,4,5,6,3,7]=>001000=>110111
[1,2,6,4,5,7,3]=>[1,2,4,5,7,6,3]=>001001=>110110
[1,2,6,4,7,3,5]=>[1,2,4,7,3,6,5]=>001010=>110101
[1,2,6,4,7,5,3]=>[1,2,4,7,5,6,3]=>001010=>110101
[1,2,6,5,3,4,7]=>[1,2,5,3,6,4,7]=>001100=>110011
[1,2,6,5,3,7,4]=>[1,2,5,3,7,6,4]=>001101=>110010
[1,2,6,5,4,3,7]=>[1,2,5,4,6,3,7]=>001100=>110011
[1,2,6,5,4,7,3]=>[1,2,5,4,7,6,3]=>001101=>110010
[1,2,6,5,7,3,4]=>[1,2,7,5,3,6,4]=>001110=>110001
[1,2,6,5,7,4,3]=>[1,2,7,5,4,6,3]=>001110=>110001
[1,2,6,7,3,4,5]=>[1,2,7,3,6,4,5]=>001100=>110011
[1,2,6,7,3,5,4]=>[1,2,7,3,5,6,4]=>001100=>110011
[1,2,6,7,4,3,5]=>[1,2,7,4,6,3,5]=>001100=>110011
[1,2,6,7,4,5,3]=>[1,2,7,4,5,6,3]=>001100=>110011
[1,2,6,7,5,3,4]=>[1,2,5,7,3,6,4]=>001100=>110011
[1,2,6,7,5,4,3]=>[1,2,5,7,4,6,3]=>001100=>110011
[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>001000=>110111
[1,2,7,3,4,6,5]=>[1,2,6,7,3,4,5]=>001000=>110111
[1,2,7,3,5,4,6]=>[1,2,5,7,3,4,6]=>001000=>110111
[1,2,7,3,5,6,4]=>[1,2,5,6,7,3,4]=>001000=>110111
[1,2,7,3,6,4,5]=>[1,2,6,3,4,7,5]=>001010=>110101
[1,2,7,3,6,5,4]=>[1,2,6,5,7,3,4]=>001010=>110101
[1,2,7,4,3,5,6]=>[1,2,4,7,3,5,6]=>001000=>110111
[1,2,7,4,3,6,5]=>[1,2,4,6,7,3,5]=>001000=>110111
[1,2,7,4,5,3,6]=>[1,2,4,5,7,3,6]=>001000=>110111
[1,2,7,4,5,6,3]=>[1,2,4,5,6,7,3]=>001000=>110111
[1,2,7,4,6,3,5]=>[1,2,4,6,3,7,5]=>001010=>110101
[1,2,7,4,6,5,3]=>[1,2,4,6,5,7,3]=>001010=>110101
[1,2,7,5,3,4,6]=>[1,2,5,3,7,4,6]=>001100=>110011
[1,2,7,5,3,6,4]=>[1,2,5,3,6,7,4]=>001100=>110011
[1,2,7,5,4,3,6]=>[1,2,5,4,7,3,6]=>001100=>110011
[1,2,7,5,4,6,3]=>[1,2,5,4,6,7,3]=>001100=>110011
[1,2,7,5,6,3,4]=>[1,2,6,5,3,7,4]=>001110=>110001
[1,2,7,5,6,4,3]=>[1,2,6,5,4,7,3]=>001110=>110001
[1,2,7,6,3,4,5]=>[1,2,6,3,7,4,5]=>001100=>110011
[1,2,7,6,3,5,4]=>[1,2,6,3,5,7,4]=>001100=>110011
[1,2,7,6,4,3,5]=>[1,2,6,4,7,3,5]=>001100=>110011
[1,2,7,6,4,5,3]=>[1,2,6,4,5,7,3]=>001100=>110011
[1,2,7,6,5,3,4]=>[1,2,5,6,3,7,4]=>001100=>110011
[1,2,7,6,5,4,3]=>[1,2,5,6,4,7,3]=>001100=>110011
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000=>101111
[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>010001=>101110
[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>010010=>101101
[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>010011=>101100
[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>010010=>101101
[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>010010=>101101
[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>010100=>101011
[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>010101=>101010
[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>010110=>101001
[1,3,2,5,6,7,4]=>[1,3,2,7,6,5,4]=>010111=>101000
[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>010110=>101001
[1,3,2,5,7,6,4]=>[1,3,2,6,7,5,4]=>010110=>101001
[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>010100=>101011
[1,3,2,6,4,7,5]=>[1,3,2,7,6,4,5]=>010101=>101010
[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>010100=>101011
[1,3,2,6,5,7,4]=>[1,3,2,5,7,6,4]=>010101=>101010
[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]=>010110=>101001
[1,3,2,6,7,5,4]=>[1,3,2,7,5,6,4]=>010110=>101001
[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>010100=>101011
[1,3,2,7,4,6,5]=>[1,3,2,6,7,4,5]=>010100=>101011
[1,3,2,7,5,4,6]=>[1,3,2,5,7,4,6]=>010100=>101011
[1,3,2,7,5,6,4]=>[1,3,2,5,6,7,4]=>010100=>101011
[1,3,2,7,6,4,5]=>[1,3,2,6,4,7,5]=>010110=>101001
[1,3,2,7,6,5,4]=>[1,3,2,6,5,7,4]=>010110=>101001
[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>011000=>100111
[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>011001=>100110
[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>011010=>100101
[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>011011=>100100
[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>011010=>100101
[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>011010=>100101
[1,3,4,5,2,6,7]=>[1,5,4,3,2,6,7]=>011100=>100011
[1,3,4,5,2,7,6]=>[1,5,4,3,2,7,6]=>011101=>100010
[1,3,4,5,6,2,7]=>[1,6,5,4,3,2,7]=>011110=>100001
[1,3,4,5,6,7,2]=>[1,7,6,5,4,3,2]=>011111=>100000
[1,3,4,5,7,2,6]=>[1,7,5,4,3,2,6]=>011110=>100001
[1,3,4,5,7,6,2]=>[1,6,7,5,4,3,2]=>011110=>100001
[1,3,4,6,2,5,7]=>[1,6,4,3,2,5,7]=>011100=>100011
[1,3,4,6,2,7,5]=>[1,7,6,4,3,2,5]=>011101=>100010
[1,3,4,6,5,2,7]=>[1,5,6,4,3,2,7]=>011100=>100011
[1,3,4,6,5,7,2]=>[1,5,7,6,4,3,2]=>011101=>100010
[1,3,4,6,7,2,5]=>[1,7,4,3,2,6,5]=>011110=>100001
[1,3,4,6,7,5,2]=>[1,7,5,6,4,3,2]=>011110=>100001
[1,3,4,7,2,5,6]=>[1,7,4,3,2,5,6]=>011100=>100011
[1,3,4,7,2,6,5]=>[1,6,7,4,3,2,5]=>011100=>100011
[1,3,4,7,5,2,6]=>[1,5,7,4,3,2,6]=>011100=>100011
[1,3,4,7,5,6,2]=>[1,5,6,7,4,3,2]=>011100=>100011
[1,3,4,7,6,2,5]=>[1,6,4,3,2,7,5]=>011110=>100001
[1,3,4,7,6,5,2]=>[1,6,5,7,4,3,2]=>011110=>100001
[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>011000=>100111
[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>011001=>100110
[1,3,5,2,6,4,7]=>[1,6,5,3,2,4,7]=>011010=>100101
[1,3,5,2,6,7,4]=>[1,7,6,5,3,2,4]=>011011=>100100
[1,3,5,2,7,4,6]=>[1,7,5,3,2,4,6]=>011010=>100101
[1,3,5,2,7,6,4]=>[1,6,7,5,3,2,4]=>011010=>100101
[1,3,5,4,2,6,7]=>[1,4,5,3,2,6,7]=>011000=>100111
[1,3,5,4,2,7,6]=>[1,4,5,3,2,7,6]=>011001=>100110
[1,3,5,4,6,2,7]=>[1,4,6,5,3,2,7]=>011010=>100101
[1,3,5,4,6,7,2]=>[1,4,7,6,5,3,2]=>011011=>100100
[1,3,5,4,7,2,6]=>[1,4,7,5,3,2,6]=>011010=>100101
[1,3,5,4,7,6,2]=>[1,4,6,7,5,3,2]=>011010=>100101
[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]=>011100=>100011
[1,3,5,6,2,7,4]=>[1,7,6,3,2,5,4]=>011101=>100010
[1,3,5,6,4,2,7]=>[1,6,4,5,3,2,7]=>011100=>100011
[1,3,5,6,4,7,2]=>[1,7,6,4,5,3,2]=>011101=>100010
[1,3,5,6,7,2,4]=>[1,7,3,2,6,5,4]=>011110=>100001
[1,3,5,6,7,4,2]=>[1,7,4,6,5,3,2]=>011110=>100001
[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]=>011100=>100011
[1,3,5,7,2,6,4]=>[1,6,7,3,2,5,4]=>011100=>100011
[1,3,5,7,4,2,6]=>[1,7,4,5,3,2,6]=>011100=>100011
[1,3,5,7,4,6,2]=>[1,6,7,4,5,3,2]=>011100=>100011
[1,3,5,7,6,2,4]=>[1,6,3,2,7,5,4]=>011110=>100001
[1,3,5,7,6,4,2]=>[1,6,4,7,5,3,2]=>011110=>100001
[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>011000=>100111
[1,3,6,2,4,7,5]=>[1,7,6,3,2,4,5]=>011001=>100110
[1,3,6,2,5,4,7]=>[1,5,6,3,2,4,7]=>011000=>100111
[1,3,6,2,5,7,4]=>[1,5,7,6,3,2,4]=>011001=>100110
[1,3,6,2,7,4,5]=>[1,7,3,2,4,6,5]=>011010=>100101
[1,3,6,2,7,5,4]=>[1,7,5,6,3,2,4]=>011010=>100101
[1,3,6,4,2,5,7]=>[1,4,6,3,2,5,7]=>011000=>100111
[1,3,6,4,2,7,5]=>[1,4,7,6,3,2,5]=>011001=>100110
[1,3,6,4,5,2,7]=>[1,4,5,6,3,2,7]=>011000=>100111
[1,3,6,4,5,7,2]=>[1,4,5,7,6,3,2]=>011001=>100110
[1,3,6,4,7,2,5]=>[1,4,7,3,2,6,5]=>011010=>100101
[1,3,6,4,7,5,2]=>[1,4,7,5,6,3,2]=>011010=>100101
[1,3,6,5,2,4,7]=>[1,5,3,2,6,4,7]=>011100=>100011
[1,3,6,5,2,7,4]=>[1,5,3,2,7,6,4]=>011101=>100010
[1,3,6,5,4,2,7]=>[1,5,4,6,3,2,7]=>011100=>100011
[1,3,6,5,4,7,2]=>[1,5,4,7,6,3,2]=>011101=>100010
[1,3,6,5,7,2,4]=>[1,7,5,3,2,6,4]=>011110=>100001
[1,3,6,5,7,4,2]=>[1,7,5,4,6,3,2]=>011110=>100001
[1,3,6,7,2,4,5]=>[1,7,3,2,6,4,5]=>011100=>100011
[1,3,6,7,2,5,4]=>[1,7,3,2,5,6,4]=>011100=>100011
[1,3,6,7,4,2,5]=>[1,7,4,6,3,2,5]=>011100=>100011
[1,3,6,7,4,5,2]=>[1,7,4,5,6,3,2]=>011100=>100011
[1,3,6,7,5,2,4]=>[1,5,7,3,2,6,4]=>011100=>100011
[1,3,6,7,5,4,2]=>[1,5,7,4,6,3,2]=>011100=>100011
[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>011000=>100111
[1,3,7,2,4,6,5]=>[1,6,7,3,2,4,5]=>011000=>100111
[1,3,7,2,5,4,6]=>[1,5,7,3,2,4,6]=>011000=>100111
[1,3,7,2,5,6,4]=>[1,5,6,7,3,2,4]=>011000=>100111
[1,3,7,2,6,4,5]=>[1,6,3,2,4,7,5]=>011010=>100101
[1,3,7,2,6,5,4]=>[1,6,5,7,3,2,4]=>011010=>100101
[1,3,7,4,2,5,6]=>[1,4,7,3,2,5,6]=>011000=>100111
[1,3,7,4,2,6,5]=>[1,4,6,7,3,2,5]=>011000=>100111
[1,3,7,4,5,2,6]=>[1,4,5,7,3,2,6]=>011000=>100111
[1,3,7,4,5,6,2]=>[1,4,5,6,7,3,2]=>011000=>100111
[1,3,7,4,6,2,5]=>[1,4,6,3,2,7,5]=>011010=>100101
[1,3,7,4,6,5,2]=>[1,4,6,5,7,3,2]=>011010=>100101
[1,3,7,5,2,4,6]=>[1,5,3,2,7,4,6]=>011100=>100011
[1,3,7,5,2,6,4]=>[1,5,3,2,6,7,4]=>011100=>100011
[1,3,7,5,4,2,6]=>[1,5,4,7,3,2,6]=>011100=>100011
[1,3,7,5,4,6,2]=>[1,5,4,6,7,3,2]=>011100=>100011
[1,3,7,5,6,2,4]=>[1,6,5,3,2,7,4]=>011110=>100001
[1,3,7,5,6,4,2]=>[1,6,5,4,7,3,2]=>011110=>100001
[1,3,7,6,2,4,5]=>[1,6,3,2,7,4,5]=>011100=>100011
[1,3,7,6,2,5,4]=>[1,6,3,2,5,7,4]=>011100=>100011
[1,3,7,6,4,2,5]=>[1,6,4,7,3,2,5]=>011100=>100011
[1,3,7,6,4,5,2]=>[1,6,4,5,7,3,2]=>011100=>100011
[1,3,7,6,5,2,4]=>[1,5,6,3,2,7,4]=>011100=>100011
[1,3,7,6,5,4,2]=>[1,5,6,4,7,3,2]=>011100=>100011
[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>010000=>101111
[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>010001=>101110
[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>010010=>101101
[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>010011=>101100
[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>010010=>101101
[1,4,2,3,7,6,5]=>[1,4,2,3,6,7,5]=>010010=>101101
[1,4,2,5,3,6,7]=>[1,5,4,2,3,6,7]=>010100=>101011
[1,4,2,5,3,7,6]=>[1,5,4,2,3,7,6]=>010101=>101010
[1,4,2,5,6,3,7]=>[1,6,5,4,2,3,7]=>010110=>101001
[1,4,2,5,6,7,3]=>[1,7,6,5,4,2,3]=>010111=>101000
[1,4,2,5,7,3,6]=>[1,7,5,4,2,3,6]=>010110=>101001
[1,4,2,5,7,6,3]=>[1,6,7,5,4,2,3]=>010110=>101001
[1,4,2,6,3,5,7]=>[1,6,4,2,3,5,7]=>010100=>101011
[1,4,2,6,3,7,5]=>[1,7,6,4,2,3,5]=>010101=>101010
[1,4,2,6,5,3,7]=>[1,5,6,4,2,3,7]=>010100=>101011
[1,4,2,6,5,7,3]=>[1,5,7,6,4,2,3]=>010101=>101010
[1,4,2,6,7,3,5]=>[1,7,4,2,3,6,5]=>010110=>101001
[1,4,2,6,7,5,3]=>[1,7,5,6,4,2,3]=>010110=>101001
[1,4,2,7,3,5,6]=>[1,7,4,2,3,5,6]=>010100=>101011
[1,4,2,7,3,6,5]=>[1,6,7,4,2,3,5]=>010100=>101011
[1,4,2,7,5,3,6]=>[1,5,7,4,2,3,6]=>010100=>101011
[1,4,2,7,5,6,3]=>[1,5,6,7,4,2,3]=>010100=>101011
[1,4,2,7,6,3,5]=>[1,6,4,2,3,7,5]=>010110=>101001
[1,4,2,7,6,5,3]=>[1,6,5,7,4,2,3]=>010110=>101001
[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>010000=>101111
[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>010001=>101110
[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>010010=>101101
[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>010011=>101100
[1,4,3,2,7,5,6]=>[1,3,4,2,7,5,6]=>010010=>101101
[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>010010=>101101
[1,4,3,5,2,6,7]=>[1,3,5,4,2,6,7]=>010100=>101011
[1,4,3,5,2,7,6]=>[1,3,5,4,2,7,6]=>010101=>101010
[1,4,3,5,6,2,7]=>[1,3,6,5,4,2,7]=>010110=>101001
[1,4,3,5,6,7,2]=>[1,3,7,6,5,4,2]=>010111=>101000
[1,4,3,5,7,2,6]=>[1,3,7,5,4,2,6]=>010110=>101001
[1,4,3,5,7,6,2]=>[1,3,6,7,5,4,2]=>010110=>101001
[1,4,3,6,2,5,7]=>[1,3,6,4,2,5,7]=>010100=>101011
[1,4,3,6,2,7,5]=>[1,3,7,6,4,2,5]=>010101=>101010
[1,4,3,6,5,2,7]=>[1,3,5,6,4,2,7]=>010100=>101011
[1,4,3,6,5,7,2]=>[1,3,5,7,6,4,2]=>010101=>101010
[1,4,3,6,7,2,5]=>[1,3,7,4,2,6,5]=>010110=>101001
[1,4,3,6,7,5,2]=>[1,3,7,5,6,4,2]=>010110=>101001
[1,4,3,7,2,5,6]=>[1,3,7,4,2,5,6]=>010100=>101011
[1,4,3,7,2,6,5]=>[1,3,6,7,4,2,5]=>010100=>101011
[1,4,3,7,5,2,6]=>[1,3,5,7,4,2,6]=>010100=>101011
[1,4,3,7,5,6,2]=>[1,3,5,6,7,4,2]=>010100=>101011
[1,4,3,7,6,2,5]=>[1,3,6,4,2,7,5]=>010110=>101001
[1,4,3,7,6,5,2]=>[1,3,6,5,7,4,2]=>010110=>101001
[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]=>011000=>100111
[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]=>011001=>100110
[1,4,5,2,6,3,7]=>[1,6,5,2,4,3,7]=>011010=>100101
[1,4,5,2,6,7,3]=>[1,7,6,5,2,4,3]=>011011=>100100
[1,4,5,2,7,3,6]=>[1,7,5,2,4,3,6]=>011010=>100101
[1,4,5,2,7,6,3]=>[1,6,7,5,2,4,3]=>011010=>100101
[1,4,5,3,2,6,7]=>[1,5,3,4,2,6,7]=>011000=>100111
[1,4,5,3,2,7,6]=>[1,5,3,4,2,7,6]=>011001=>100110
[1,4,5,3,6,2,7]=>[1,6,5,3,4,2,7]=>011010=>100101
[1,4,5,3,6,7,2]=>[1,7,6,5,3,4,2]=>011011=>100100
[1,4,5,3,7,2,6]=>[1,7,5,3,4,2,6]=>011010=>100101
[1,4,5,3,7,6,2]=>[1,6,7,5,3,4,2]=>011010=>100101
[1,4,5,6,2,3,7]=>[1,6,2,5,4,3,7]=>011100=>100011
[1,4,5,6,2,7,3]=>[1,7,6,2,5,4,3]=>011101=>100010
[1,4,5,6,3,2,7]=>[1,6,3,5,4,2,7]=>011100=>100011
[1,4,5,6,3,7,2]=>[1,7,6,3,5,4,2]=>011101=>100010
[1,4,5,6,7,2,3]=>[1,7,2,6,5,4,3]=>011110=>100001
[1,4,5,6,7,3,2]=>[1,7,3,6,5,4,2]=>011110=>100001
[1,4,5,7,2,3,6]=>[1,7,2,5,4,3,6]=>011100=>100011
[1,4,5,7,2,6,3]=>[1,6,7,2,5,4,3]=>011100=>100011
[1,4,5,7,3,2,6]=>[1,7,3,5,4,2,6]=>011100=>100011
[1,4,5,7,3,6,2]=>[1,6,7,3,5,4,2]=>011100=>100011
[1,4,5,7,6,2,3]=>[1,6,2,7,5,4,3]=>011110=>100001
[1,4,5,7,6,3,2]=>[1,6,3,7,5,4,2]=>011110=>100001
[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]=>011000=>100111
[1,4,6,2,3,7,5]=>[1,7,6,2,4,3,5]=>011001=>100110
[1,4,6,2,5,3,7]=>[1,5,6,2,4,3,7]=>011000=>100111
[1,4,6,2,5,7,3]=>[1,5,7,6,2,4,3]=>011001=>100110
[1,4,6,2,7,3,5]=>[1,7,2,4,3,6,5]=>011010=>100101
[1,4,6,2,7,5,3]=>[1,7,5,6,2,4,3]=>011010=>100101
[1,4,6,3,2,5,7]=>[1,6,3,4,2,5,7]=>011000=>100111
[1,4,6,3,2,7,5]=>[1,7,6,3,4,2,5]=>011001=>100110
[1,4,6,3,5,2,7]=>[1,5,6,3,4,2,7]=>011000=>100111
[1,4,6,3,5,7,2]=>[1,5,7,6,3,4,2]=>011001=>100110
[1,4,6,3,7,2,5]=>[1,7,3,4,2,6,5]=>011010=>100101
[1,4,6,3,7,5,2]=>[1,7,5,6,3,4,2]=>011010=>100101
[1,4,6,5,2,3,7]=>[1,5,2,6,4,3,7]=>011100=>100011
[1,4,6,5,2,7,3]=>[1,5,2,7,6,4,3]=>011101=>100010
[1,4,6,5,3,2,7]=>[1,5,3,6,4,2,7]=>011100=>100011
[1,4,6,5,3,7,2]=>[1,5,3,7,6,4,2]=>011101=>100010
[1,4,6,5,7,2,3]=>[1,7,5,2,6,4,3]=>011110=>100001
[1,4,6,5,7,3,2]=>[1,7,5,3,6,4,2]=>011110=>100001
[1,4,6,7,2,3,5]=>[1,7,2,6,4,3,5]=>011100=>100011
[1,4,6,7,2,5,3]=>[1,7,2,5,6,4,3]=>011100=>100011
[1,4,6,7,3,2,5]=>[1,7,3,6,4,2,5]=>011100=>100011
[1,4,6,7,3,5,2]=>[1,7,3,5,6,4,2]=>011100=>100011
[1,4,6,7,5,2,3]=>[1,5,7,2,6,4,3]=>011100=>100011
[1,4,6,7,5,3,2]=>[1,5,7,3,6,4,2]=>011100=>100011
[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]=>011000=>100111
[1,4,7,2,3,6,5]=>[1,6,7,2,4,3,5]=>011000=>100111
[1,4,7,2,5,3,6]=>[1,5,7,2,4,3,6]=>011000=>100111
[1,4,7,2,5,6,3]=>[1,5,6,7,2,4,3]=>011000=>100111
[1,4,7,2,6,3,5]=>[1,6,2,4,3,7,5]=>011010=>100101
[1,4,7,2,6,5,3]=>[1,6,5,7,2,4,3]=>011010=>100101
[1,4,7,3,2,5,6]=>[1,7,3,4,2,5,6]=>011000=>100111
[1,4,7,3,2,6,5]=>[1,6,7,3,4,2,5]=>011000=>100111
[1,4,7,3,5,2,6]=>[1,5,7,3,4,2,6]=>011000=>100111
[1,4,7,3,5,6,2]=>[1,5,6,7,3,4,2]=>011000=>100111
[1,4,7,3,6,2,5]=>[1,6,3,4,2,7,5]=>011010=>100101
[1,4,7,3,6,5,2]=>[1,6,5,7,3,4,2]=>011010=>100101
[1,4,7,5,2,3,6]=>[1,5,2,7,4,3,6]=>011100=>100011
[1,4,7,5,2,6,3]=>[1,5,2,6,7,4,3]=>011100=>100011
[1,4,7,5,3,2,6]=>[1,5,3,7,4,2,6]=>011100=>100011
[1,4,7,5,3,6,2]=>[1,5,3,6,7,4,2]=>011100=>100011
[1,4,7,5,6,2,3]=>[1,6,5,2,7,4,3]=>011110=>100001
[1,4,7,5,6,3,2]=>[1,6,5,3,7,4,2]=>011110=>100001
[1,4,7,6,2,3,5]=>[1,6,2,7,4,3,5]=>011100=>100011
[1,4,7,6,2,5,3]=>[1,6,2,5,7,4,3]=>011100=>100011
[1,4,7,6,3,2,5]=>[1,6,3,7,4,2,5]=>011100=>100011
[1,4,7,6,3,5,2]=>[1,6,3,5,7,4,2]=>011100=>100011
[1,4,7,6,5,2,3]=>[1,5,6,2,7,4,3]=>011100=>100011
[1,4,7,6,5,3,2]=>[1,5,6,3,7,4,2]=>011100=>100011
[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>010000=>101111
[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>010001=>101110
[1,5,2,3,6,4,7]=>[1,6,5,2,3,4,7]=>010010=>101101
[1,5,2,3,6,7,4]=>[1,7,6,5,2,3,4]=>010011=>101100
[1,5,2,3,7,4,6]=>[1,7,5,2,3,4,6]=>010010=>101101
[1,5,2,3,7,6,4]=>[1,6,7,5,2,3,4]=>010010=>101101
[1,5,2,4,3,6,7]=>[1,4,5,2,3,6,7]=>010000=>101111
[1,5,2,4,3,7,6]=>[1,4,5,2,3,7,6]=>010001=>101110
[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>010010=>101101
[1,5,2,4,6,7,3]=>[1,4,7,6,5,2,3]=>010011=>101100
[1,5,2,4,7,3,6]=>[1,4,7,5,2,3,6]=>010010=>101101
[1,5,2,4,7,6,3]=>[1,4,6,7,5,2,3]=>010010=>101101
[1,5,2,6,3,4,7]=>[1,6,2,3,5,4,7]=>010100=>101011
[1,5,2,6,3,7,4]=>[1,7,6,2,3,5,4]=>010101=>101010
[1,5,2,6,4,3,7]=>[1,6,4,5,2,3,7]=>010100=>101011
[1,5,2,6,4,7,3]=>[1,7,6,4,5,2,3]=>010101=>101010
[1,5,2,6,7,3,4]=>[1,7,2,3,6,5,4]=>010110=>101001
[1,5,2,6,7,4,3]=>[1,7,4,6,5,2,3]=>010110=>101001
[1,5,2,7,3,4,6]=>[1,7,2,3,5,4,6]=>010100=>101011
[1,5,2,7,3,6,4]=>[1,6,7,2,3,5,4]=>010100=>101011
[1,5,2,7,4,3,6]=>[1,7,4,5,2,3,6]=>010100=>101011
[1,5,2,7,4,6,3]=>[1,6,7,4,5,2,3]=>010100=>101011
[1,5,2,7,6,3,4]=>[1,6,2,3,7,5,4]=>010110=>101001
[1,5,2,7,6,4,3]=>[1,6,4,7,5,2,3]=>010110=>101001
[1,5,3,2,4,6,7]=>[1,3,5,2,4,6,7]=>010000=>101111
[1,5,3,2,4,7,6]=>[1,3,5,2,4,7,6]=>010001=>101110
[1,5,3,2,6,4,7]=>[1,3,6,5,2,4,7]=>010010=>101101
[1,5,3,2,6,7,4]=>[1,3,7,6,5,2,4]=>010011=>101100
[1,5,3,2,7,4,6]=>[1,3,7,5,2,4,6]=>010010=>101101
[1,5,3,2,7,6,4]=>[1,3,6,7,5,2,4]=>010010=>101101
[1,5,3,4,2,6,7]=>[1,3,4,5,2,6,7]=>010000=>101111
[1,5,3,4,2,7,6]=>[1,3,4,5,2,7,6]=>010001=>101110
[1,5,3,4,6,2,7]=>[1,3,4,6,5,2,7]=>010010=>101101
[1,5,3,4,6,7,2]=>[1,3,4,7,6,5,2]=>010011=>101100
[1,5,3,4,7,2,6]=>[1,3,4,7,5,2,6]=>010010=>101101
[1,5,3,4,7,6,2]=>[1,3,4,6,7,5,2]=>010010=>101101
[1,5,3,6,2,4,7]=>[1,3,6,2,5,4,7]=>010100=>101011
[1,5,3,6,2,7,4]=>[1,3,7,6,2,5,4]=>010101=>101010
[1,5,3,6,4,2,7]=>[1,3,6,4,5,2,7]=>010100=>101011
[1,5,3,6,4,7,2]=>[1,3,7,6,4,5,2]=>010101=>101010
[1,5,3,6,7,2,4]=>[1,3,7,2,6,5,4]=>010110=>101001
[1,5,3,6,7,4,2]=>[1,3,7,4,6,5,2]=>010110=>101001
[1,5,3,7,2,4,6]=>[1,3,7,2,5,4,6]=>010100=>101011
[1,5,3,7,2,6,4]=>[1,3,6,7,2,5,4]=>010100=>101011
[1,5,3,7,4,2,6]=>[1,3,7,4,5,2,6]=>010100=>101011
[1,5,3,7,4,6,2]=>[1,3,6,7,4,5,2]=>010100=>101011
[1,5,3,7,6,2,4]=>[1,3,6,2,7,5,4]=>010110=>101001
[1,5,3,7,6,4,2]=>[1,3,6,4,7,5,2]=>010110=>101001
[1,5,4,2,3,6,7]=>[1,4,2,5,3,6,7]=>011000=>100111
[1,5,4,2,3,7,6]=>[1,4,2,5,3,7,6]=>011001=>100110
[1,5,4,2,6,3,7]=>[1,4,2,6,5,3,7]=>011010=>100101
[1,5,4,2,6,7,3]=>[1,4,2,7,6,5,3]=>011011=>100100
[1,5,4,2,7,3,6]=>[1,4,2,7,5,3,6]=>011010=>100101
[1,5,4,2,7,6,3]=>[1,4,2,6,7,5,3]=>011010=>100101
[1,5,4,3,2,6,7]=>[1,4,3,5,2,6,7]=>011000=>100111
[1,5,4,3,2,7,6]=>[1,4,3,5,2,7,6]=>011001=>100110
[1,5,4,3,6,2,7]=>[1,4,3,6,5,2,7]=>011010=>100101
[1,5,4,3,6,7,2]=>[1,4,3,7,6,5,2]=>011011=>100100
[1,5,4,3,7,2,6]=>[1,4,3,7,5,2,6]=>011010=>100101
[1,5,4,3,7,6,2]=>[1,4,3,6,7,5,2]=>011010=>100101
[1,5,4,6,2,3,7]=>[1,6,4,2,5,3,7]=>011100=>100011
[1,5,4,6,2,7,3]=>[1,7,6,4,2,5,3]=>011101=>100010
[1,5,4,6,3,2,7]=>[1,6,4,3,5,2,7]=>011100=>100011
[1,5,4,6,3,7,2]=>[1,7,6,4,3,5,2]=>011101=>100010
[1,5,4,6,7,2,3]=>[1,7,4,2,6,5,3]=>011110=>100001
[1,5,4,6,7,3,2]=>[1,7,4,3,6,5,2]=>011110=>100001
[1,5,4,7,2,3,6]=>[1,7,4,2,5,3,6]=>011100=>100011
[1,5,4,7,2,6,3]=>[1,6,7,4,2,5,3]=>011100=>100011
[1,5,4,7,3,2,6]=>[1,7,4,3,5,2,6]=>011100=>100011
[1,5,4,7,3,6,2]=>[1,6,7,4,3,5,2]=>011100=>100011
[1,5,4,7,6,2,3]=>[1,6,4,2,7,5,3]=>011110=>100001
[1,5,4,7,6,3,2]=>[1,6,4,3,7,5,2]=>011110=>100001
[1,5,6,2,3,4,7]=>[1,6,2,5,3,4,7]=>011000=>100111
[1,5,6,2,3,7,4]=>[1,7,6,2,5,3,4]=>011001=>100110
[1,5,6,2,4,3,7]=>[1,6,2,4,5,3,7]=>011000=>100111
[1,5,6,2,4,7,3]=>[1,7,6,2,4,5,3]=>011001=>100110
[1,5,6,2,7,3,4]=>[1,7,2,6,5,3,4]=>011010=>100101
[1,5,6,2,7,4,3]=>[1,7,2,4,6,5,3]=>011010=>100101
[1,5,6,3,2,4,7]=>[1,6,3,5,2,4,7]=>011000=>100111
[1,5,6,3,2,7,4]=>[1,7,6,3,5,2,4]=>011001=>100110
[1,5,6,3,4,2,7]=>[1,6,3,4,5,2,7]=>011000=>100111
[1,5,6,3,4,7,2]=>[1,7,6,3,4,5,2]=>011001=>100110
[1,5,6,3,7,2,4]=>[1,7,3,6,5,2,4]=>011010=>100101
[1,5,6,3,7,4,2]=>[1,7,3,4,6,5,2]=>011010=>100101
[1,5,6,4,2,3,7]=>[1,4,6,2,5,3,7]=>011000=>100111
[1,5,6,4,2,7,3]=>[1,4,7,6,2,5,3]=>011001=>100110
[1,5,6,4,3,2,7]=>[1,4,6,3,5,2,7]=>011000=>100111
[1,5,6,4,3,7,2]=>[1,4,7,6,3,5,2]=>011001=>100110
[1,5,6,4,7,2,3]=>[1,4,7,2,6,5,3]=>011010=>100101
[1,5,6,4,7,3,2]=>[1,4,7,3,6,5,2]=>011010=>100101
[1,5,6,7,2,3,4]=>[1,7,2,6,3,5,4]=>011100=>100011
[1,5,6,7,2,4,3]=>[1,7,2,6,4,5,3]=>011100=>100011
[1,5,6,7,3,2,4]=>[1,7,3,6,2,5,4]=>011100=>100011
[1,5,6,7,3,4,2]=>[1,7,3,6,4,5,2]=>011100=>100011
[1,5,6,7,4,2,3]=>[1,7,4,6,2,5,3]=>011100=>100011
[1,5,6,7,4,3,2]=>[1,7,4,6,3,5,2]=>011100=>100011
[1,5,7,2,3,4,6]=>[1,7,2,5,3,4,6]=>011000=>100111
[1,5,7,2,3,6,4]=>[1,6,7,2,5,3,4]=>011000=>100111
[1,5,7,2,4,3,6]=>[1,7,2,4,5,3,6]=>011000=>100111
[1,5,7,2,4,6,3]=>[1,6,7,2,4,5,3]=>011000=>100111
[1,5,7,2,6,3,4]=>[1,6,2,7,5,3,4]=>011010=>100101
[1,5,7,2,6,4,3]=>[1,6,2,4,7,5,3]=>011010=>100101
[1,5,7,3,2,4,6]=>[1,7,3,5,2,4,6]=>011000=>100111
[1,5,7,3,2,6,4]=>[1,6,7,3,5,2,4]=>011000=>100111
[1,5,7,3,4,2,6]=>[1,7,3,4,5,2,6]=>011000=>100111
[1,5,7,3,4,6,2]=>[1,6,7,3,4,5,2]=>011000=>100111
[1,5,7,3,6,2,4]=>[1,6,3,7,5,2,4]=>011010=>100101
[1,5,7,3,6,4,2]=>[1,6,3,4,7,5,2]=>011010=>100101
[1,5,7,4,2,3,6]=>[1,4,7,2,5,3,6]=>011000=>100111
[1,5,7,4,2,6,3]=>[1,4,6,7,2,5,3]=>011000=>100111
[1,5,7,4,3,2,6]=>[1,4,7,3,5,2,6]=>011000=>100111
[1,5,7,4,3,6,2]=>[1,4,6,7,3,5,2]=>011000=>100111
[1,5,7,4,6,2,3]=>[1,4,6,2,7,5,3]=>011010=>100101
[1,5,7,4,6,3,2]=>[1,4,6,3,7,5,2]=>011010=>100101
[1,5,7,6,2,3,4]=>[1,6,2,7,3,5,4]=>011100=>100011
[1,5,7,6,2,4,3]=>[1,6,2,7,4,5,3]=>011100=>100011
[1,5,7,6,3,2,4]=>[1,6,3,7,2,5,4]=>011100=>100011
[1,5,7,6,3,4,2]=>[1,6,3,7,4,5,2]=>011100=>100011
[1,5,7,6,4,2,3]=>[1,6,4,7,2,5,3]=>011100=>100011
[1,5,7,6,4,3,2]=>[1,6,4,7,3,5,2]=>011100=>100011
[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>010000=>101111
[1,6,2,3,4,7,5]=>[1,7,6,2,3,4,5]=>010001=>101110
[1,6,2,3,5,4,7]=>[1,5,6,2,3,4,7]=>010000=>101111
[1,6,2,3,5,7,4]=>[1,5,7,6,2,3,4]=>010001=>101110
[1,6,2,3,7,4,5]=>[1,7,2,3,4,6,5]=>010010=>101101
[1,6,2,3,7,5,4]=>[1,7,5,6,2,3,4]=>010010=>101101
[1,6,2,4,3,5,7]=>[1,4,6,2,3,5,7]=>010000=>101111
[1,6,2,4,3,7,5]=>[1,4,7,6,2,3,5]=>010001=>101110
[1,6,2,4,5,3,7]=>[1,4,5,6,2,3,7]=>010000=>101111
[1,6,2,4,5,7,3]=>[1,4,5,7,6,2,3]=>010001=>101110
[1,6,2,4,7,3,5]=>[1,4,7,2,3,6,5]=>010010=>101101
[1,6,2,4,7,5,3]=>[1,4,7,5,6,2,3]=>010010=>101101
[1,6,2,5,3,4,7]=>[1,5,2,3,6,4,7]=>010100=>101011
[1,6,2,5,3,7,4]=>[1,5,2,3,7,6,4]=>010101=>101010
[1,6,2,5,4,3,7]=>[1,5,4,6,2,3,7]=>010100=>101011
[1,6,2,5,4,7,3]=>[1,5,4,7,6,2,3]=>010101=>101010
[1,6,2,5,7,3,4]=>[1,7,5,2,3,6,4]=>010110=>101001
[1,6,2,5,7,4,3]=>[1,7,5,4,6,2,3]=>010110=>101001
[1,6,2,7,3,4,5]=>[1,7,2,3,6,4,5]=>010100=>101011
[1,6,2,7,3,5,4]=>[1,7,2,3,5,6,4]=>010100=>101011
[1,6,2,7,4,3,5]=>[1,7,4,6,2,3,5]=>010100=>101011
[1,6,2,7,4,5,3]=>[1,7,4,5,6,2,3]=>010100=>101011
[1,6,2,7,5,3,4]=>[1,5,7,2,3,6,4]=>010100=>101011
[1,6,2,7,5,4,3]=>[1,5,7,4,6,2,3]=>010100=>101011
[1,6,3,2,4,5,7]=>[1,3,6,2,4,5,7]=>010000=>101111
[1,6,3,2,4,7,5]=>[1,3,7,6,2,4,5]=>010001=>101110
[1,6,3,2,5,4,7]=>[1,3,5,6,2,4,7]=>010000=>101111
[1,6,3,2,5,7,4]=>[1,3,5,7,6,2,4]=>010001=>101110
[1,6,3,2,7,4,5]=>[1,3,7,2,4,6,5]=>010010=>101101
[1,6,3,2,7,5,4]=>[1,3,7,5,6,2,4]=>010010=>101101
[1,6,3,4,2,5,7]=>[1,3,4,6,2,5,7]=>010000=>101111
[1,6,3,4,2,7,5]=>[1,3,4,7,6,2,5]=>010001=>101110
[1,6,3,4,5,2,7]=>[1,3,4,5,6,2,7]=>010000=>101111
[1,6,3,4,5,7,2]=>[1,3,4,5,7,6,2]=>010001=>101110
[1,6,3,4,7,2,5]=>[1,3,4,7,2,6,5]=>010010=>101101
[1,6,3,4,7,5,2]=>[1,3,4,7,5,6,2]=>010010=>101101
[1,6,3,5,2,4,7]=>[1,3,5,2,6,4,7]=>010100=>101011
[1,6,3,5,2,7,4]=>[1,3,5,2,7,6,4]=>010101=>101010
[1,6,3,5,4,2,7]=>[1,3,5,4,6,2,7]=>010100=>101011
[1,6,3,5,4,7,2]=>[1,3,5,4,7,6,2]=>010101=>101010
[1,6,3,5,7,2,4]=>[1,3,7,5,2,6,4]=>010110=>101001
[1,6,3,5,7,4,2]=>[1,3,7,5,4,6,2]=>010110=>101001
[1,6,3,7,2,4,5]=>[1,3,7,2,6,4,5]=>010100=>101011
[1,6,3,7,2,5,4]=>[1,3,7,2,5,6,4]=>010100=>101011
[1,6,3,7,4,2,5]=>[1,3,7,4,6,2,5]=>010100=>101011
[1,6,3,7,4,5,2]=>[1,3,7,4,5,6,2]=>010100=>101011
[1,6,3,7,5,2,4]=>[1,3,5,7,2,6,4]=>010100=>101011
[1,6,3,7,5,4,2]=>[1,3,5,7,4,6,2]=>010100=>101011
[1,6,4,2,3,5,7]=>[1,4,2,6,3,5,7]=>011000=>100111
[1,6,4,2,3,7,5]=>[1,4,2,7,6,3,5]=>011001=>100110
[1,6,4,2,5,3,7]=>[1,4,2,5,6,3,7]=>011000=>100111
[1,6,4,2,5,7,3]=>[1,4,2,5,7,6,3]=>011001=>100110
[1,6,4,2,7,3,5]=>[1,4,2,7,3,6,5]=>011010=>100101
[1,6,4,2,7,5,3]=>[1,4,2,7,5,6,3]=>011010=>100101
[1,6,4,3,2,5,7]=>[1,4,3,6,2,5,7]=>011000=>100111
[1,6,4,3,2,7,5]=>[1,4,3,7,6,2,5]=>011001=>100110
[1,6,4,3,5,2,7]=>[1,4,3,5,6,2,7]=>011000=>100111
[1,6,4,3,5,7,2]=>[1,4,3,5,7,6,2]=>011001=>100110
[1,6,4,3,7,2,5]=>[1,4,3,7,2,6,5]=>011010=>100101
[1,6,4,3,7,5,2]=>[1,4,3,7,5,6,2]=>011010=>100101
[1,6,4,5,2,3,7]=>[1,5,4,2,6,3,7]=>011100=>100011
[1,6,4,5,2,7,3]=>[1,5,4,2,7,6,3]=>011101=>100010
[1,6,4,5,3,2,7]=>[1,5,4,3,6,2,7]=>011100=>100011
[1,6,4,5,3,7,2]=>[1,5,4,3,7,6,2]=>011101=>100010
[1,6,4,5,7,2,3]=>[1,7,5,4,2,6,3]=>011110=>100001
[1,6,4,5,7,3,2]=>[1,7,5,4,3,6,2]=>011110=>100001
[1,6,4,7,2,3,5]=>[1,7,4,2,6,3,5]=>011100=>100011
[1,6,4,7,2,5,3]=>[1,7,4,2,5,6,3]=>011100=>100011
[1,6,4,7,3,2,5]=>[1,7,4,3,6,2,5]=>011100=>100011
[1,6,4,7,3,5,2]=>[1,7,4,3,5,6,2]=>011100=>100011
[1,6,4,7,5,2,3]=>[1,5,7,4,2,6,3]=>011100=>100011
[1,6,4,7,5,3,2]=>[1,5,7,4,3,6,2]=>011100=>100011
[1,6,5,2,3,4,7]=>[1,5,2,6,3,4,7]=>011000=>100111
[1,6,5,2,3,7,4]=>[1,5,2,7,6,3,4]=>011001=>100110
[1,6,5,2,4,3,7]=>[1,5,2,4,6,3,7]=>011000=>100111
[1,6,5,2,4,7,3]=>[1,5,2,4,7,6,3]=>011001=>100110
[1,6,5,2,7,3,4]=>[1,7,5,2,6,3,4]=>011010=>100101
[1,6,5,2,7,4,3]=>[1,7,5,2,4,6,3]=>011010=>100101
[1,6,5,3,2,4,7]=>[1,5,3,6,2,4,7]=>011000=>100111
[1,6,5,3,2,7,4]=>[1,5,3,7,6,2,4]=>011001=>100110
[1,6,5,3,4,2,7]=>[1,5,3,4,6,2,7]=>011000=>100111
[1,6,5,3,4,7,2]=>[1,5,3,4,7,6,2]=>011001=>100110
[1,6,5,3,7,2,4]=>[1,7,5,3,6,2,4]=>011010=>100101
[1,6,5,3,7,4,2]=>[1,7,5,3,4,6,2]=>011010=>100101
[1,6,5,4,2,3,7]=>[1,4,5,2,6,3,7]=>011000=>100111
[1,6,5,4,2,7,3]=>[1,4,5,2,7,6,3]=>011001=>100110
[1,6,5,4,3,2,7]=>[1,4,5,3,6,2,7]=>011000=>100111
[1,6,5,4,3,7,2]=>[1,4,5,3,7,6,2]=>011001=>100110
[1,6,5,4,7,2,3]=>[1,4,7,5,2,6,3]=>011010=>100101
[1,6,5,4,7,3,2]=>[1,4,7,5,3,6,2]=>011010=>100101
[1,6,5,7,2,3,4]=>[1,7,2,5,3,6,4]=>011100=>100011
[1,6,5,7,2,4,3]=>[1,7,2,5,4,6,3]=>011100=>100011
[1,6,5,7,3,2,4]=>[1,7,3,5,2,6,4]=>011100=>100011
[1,6,5,7,3,4,2]=>[1,7,3,5,4,6,2]=>011100=>100011
[1,6,5,7,4,2,3]=>[1,7,4,5,2,6,3]=>011100=>100011
[1,6,5,7,4,3,2]=>[1,7,4,5,3,6,2]=>011100=>100011
[1,6,7,2,3,4,5]=>[1,7,2,6,3,4,5]=>011000=>100111
[1,6,7,2,3,5,4]=>[1,7,2,5,6,3,4]=>011000=>100111
[1,6,7,2,4,3,5]=>[1,7,2,4,6,3,5]=>011000=>100111
[1,6,7,2,4,5,3]=>[1,7,2,4,5,6,3]=>011000=>100111
[1,6,7,2,5,3,4]=>[1,5,7,2,6,3,4]=>011000=>100111
[1,6,7,2,5,4,3]=>[1,5,7,2,4,6,3]=>011000=>100111
[1,6,7,3,2,4,5]=>[1,7,3,6,2,4,5]=>011000=>100111
[1,6,7,3,2,5,4]=>[1,7,3,5,6,2,4]=>011000=>100111
[1,6,7,3,4,2,5]=>[1,7,3,4,6,2,5]=>011000=>100111
[1,6,7,3,4,5,2]=>[1,7,3,4,5,6,2]=>011000=>100111
[1,6,7,3,5,2,4]=>[1,5,7,3,6,2,4]=>011000=>100111
[1,6,7,3,5,4,2]=>[1,5,7,3,4,6,2]=>011000=>100111
[1,6,7,4,2,3,5]=>[1,4,7,2,6,3,5]=>011000=>100111
[1,6,7,4,2,5,3]=>[1,4,7,2,5,6,3]=>011000=>100111
[1,6,7,4,3,2,5]=>[1,4,7,3,6,2,5]=>011000=>100111
[1,6,7,4,3,5,2]=>[1,4,7,3,5,6,2]=>011000=>100111
[1,6,7,4,5,2,3]=>[1,4,5,7,2,6,3]=>011000=>100111
[1,6,7,4,5,3,2]=>[1,4,5,7,3,6,2]=>011000=>100111
[1,6,7,5,2,3,4]=>[1,5,2,7,3,6,4]=>011100=>100011
[1,6,7,5,2,4,3]=>[1,5,2,7,4,6,3]=>011100=>100011
[1,6,7,5,3,2,4]=>[1,5,3,7,2,6,4]=>011100=>100011
[1,6,7,5,3,4,2]=>[1,5,3,7,4,6,2]=>011100=>100011
[1,6,7,5,4,2,3]=>[1,5,4,7,2,6,3]=>011100=>100011
[1,6,7,5,4,3,2]=>[1,5,4,7,3,6,2]=>011100=>100011
[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>010000=>101111
[1,7,2,3,4,6,5]=>[1,6,7,2,3,4,5]=>010000=>101111
[1,7,2,3,5,4,6]=>[1,5,7,2,3,4,6]=>010000=>101111
[1,7,2,3,5,6,4]=>[1,5,6,7,2,3,4]=>010000=>101111
[1,7,2,3,6,4,5]=>[1,6,2,3,4,7,5]=>010010=>101101
[1,7,2,3,6,5,4]=>[1,6,5,7,2,3,4]=>010010=>101101
[1,7,2,4,3,5,6]=>[1,4,7,2,3,5,6]=>010000=>101111
[1,7,2,4,3,6,5]=>[1,4,6,7,2,3,5]=>010000=>101111
[1,7,2,4,5,3,6]=>[1,4,5,7,2,3,6]=>010000=>101111
[1,7,2,4,5,6,3]=>[1,4,5,6,7,2,3]=>010000=>101111
[1,7,2,4,6,3,5]=>[1,4,6,2,3,7,5]=>010010=>101101
[1,7,2,4,6,5,3]=>[1,4,6,5,7,2,3]=>010010=>101101
[1,7,2,5,3,4,6]=>[1,5,2,3,7,4,6]=>010100=>101011
[1,7,2,5,3,6,4]=>[1,5,2,3,6,7,4]=>010100=>101011
[1,7,2,5,4,3,6]=>[1,5,4,7,2,3,6]=>010100=>101011
[1,7,2,5,4,6,3]=>[1,5,4,6,7,2,3]=>010100=>101011
[1,7,2,5,6,3,4]=>[1,6,5,2,3,7,4]=>010110=>101001
[1,7,2,5,6,4,3]=>[1,6,5,4,7,2,3]=>010110=>101001
[1,7,2,6,3,4,5]=>[1,6,2,3,7,4,5]=>010100=>101011
[1,7,2,6,3,5,4]=>[1,6,2,3,5,7,4]=>010100=>101011
[1,7,2,6,4,3,5]=>[1,6,4,7,2,3,5]=>010100=>101011
[1,7,2,6,4,5,3]=>[1,6,4,5,7,2,3]=>010100=>101011
[1,7,2,6,5,3,4]=>[1,5,6,2,3,7,4]=>010100=>101011
[1,7,2,6,5,4,3]=>[1,5,6,4,7,2,3]=>010100=>101011
[1,7,3,2,4,5,6]=>[1,3,7,2,4,5,6]=>010000=>101111
[1,7,3,2,4,6,5]=>[1,3,6,7,2,4,5]=>010000=>101111
[1,7,3,2,5,4,6]=>[1,3,5,7,2,4,6]=>010000=>101111
[1,7,3,2,5,6,4]=>[1,3,5,6,7,2,4]=>010000=>101111
[1,7,3,2,6,4,5]=>[1,3,6,2,4,7,5]=>010010=>101101
[1,7,3,2,6,5,4]=>[1,3,6,5,7,2,4]=>010010=>101101
[1,7,3,4,2,5,6]=>[1,3,4,7,2,5,6]=>010000=>101111
[1,7,3,4,2,6,5]=>[1,3,4,6,7,2,5]=>010000=>101111
[1,7,3,4,5,2,6]=>[1,3,4,5,7,2,6]=>010000=>101111
[1,7,3,4,5,6,2]=>[1,3,4,5,6,7,2]=>010000=>101111
[1,7,3,4,6,2,5]=>[1,3,4,6,2,7,5]=>010010=>101101
[1,7,3,4,6,5,2]=>[1,3,4,6,5,7,2]=>010010=>101101
[1,7,3,5,2,4,6]=>[1,3,5,2,7,4,6]=>010100=>101011
[1,7,3,5,2,6,4]=>[1,3,5,2,6,7,4]=>010100=>101011
[1,7,3,5,4,2,6]=>[1,3,5,4,7,2,6]=>010100=>101011
[1,7,3,5,4,6,2]=>[1,3,5,4,6,7,2]=>010100=>101011
[1,7,3,5,6,2,4]=>[1,3,6,5,2,7,4]=>010110=>101001
[1,7,3,5,6,4,2]=>[1,3,6,5,4,7,2]=>010110=>101001
[1,7,3,6,2,4,5]=>[1,3,6,2,7,4,5]=>010100=>101011
[1,7,3,6,2,5,4]=>[1,3,6,2,5,7,4]=>010100=>101011
[1,7,3,6,4,2,5]=>[1,3,6,4,7,2,5]=>010100=>101011
[1,7,3,6,4,5,2]=>[1,3,6,4,5,7,2]=>010100=>101011
[1,7,3,6,5,2,4]=>[1,3,5,6,2,7,4]=>010100=>101011
[1,7,3,6,5,4,2]=>[1,3,5,6,4,7,2]=>010100=>101011
[1,7,4,2,3,5,6]=>[1,4,2,7,3,5,6]=>011000=>100111
[1,7,4,2,3,6,5]=>[1,4,2,6,7,3,5]=>011000=>100111
[1,7,4,2,5,3,6]=>[1,4,2,5,7,3,6]=>011000=>100111
[1,7,4,2,5,6,3]=>[1,4,2,5,6,7,3]=>011000=>100111
[1,7,4,2,6,3,5]=>[1,4,2,6,3,7,5]=>011010=>100101
[1,7,4,2,6,5,3]=>[1,4,2,6,5,7,3]=>011010=>100101
[1,7,4,3,2,5,6]=>[1,4,3,7,2,5,6]=>011000=>100111
[1,7,4,3,2,6,5]=>[1,4,3,6,7,2,5]=>011000=>100111
[1,7,4,3,5,2,6]=>[1,4,3,5,7,2,6]=>011000=>100111
[1,7,4,3,5,6,2]=>[1,4,3,5,6,7,2]=>011000=>100111
[1,7,4,3,6,2,5]=>[1,4,3,6,2,7,5]=>011010=>100101
[1,7,4,3,6,5,2]=>[1,4,3,6,5,7,2]=>011010=>100101
[1,7,4,5,2,3,6]=>[1,5,4,2,7,3,6]=>011100=>100011
[1,7,4,5,2,6,3]=>[1,5,4,2,6,7,3]=>011100=>100011
[1,7,4,5,3,2,6]=>[1,5,4,3,7,2,6]=>011100=>100011
[1,7,4,5,3,6,2]=>[1,5,4,3,6,7,2]=>011100=>100011
[1,7,4,5,6,2,3]=>[1,6,5,4,2,7,3]=>011110=>100001
[1,7,4,5,6,3,2]=>[1,6,5,4,3,7,2]=>011110=>100001
[1,7,4,6,2,3,5]=>[1,6,4,2,7,3,5]=>011100=>100011
[1,7,4,6,2,5,3]=>[1,6,4,2,5,7,3]=>011100=>100011
[1,7,4,6,3,2,5]=>[1,6,4,3,7,2,5]=>011100=>100011
[1,7,4,6,3,5,2]=>[1,6,4,3,5,7,2]=>011100=>100011
[1,7,4,6,5,2,3]=>[1,5,6,4,2,7,3]=>011100=>100011
[1,7,4,6,5,3,2]=>[1,5,6,4,3,7,2]=>011100=>100011
[1,7,5,2,3,4,6]=>[1,5,2,7,3,4,6]=>011000=>100111
[1,7,5,2,3,6,4]=>[1,5,2,6,7,3,4]=>011000=>100111
[1,7,5,2,4,3,6]=>[1,5,2,4,7,3,6]=>011000=>100111
[1,7,5,2,4,6,3]=>[1,5,2,4,6,7,3]=>011000=>100111
[1,7,5,2,6,3,4]=>[1,6,5,2,7,3,4]=>011010=>100101
[1,7,5,2,6,4,3]=>[1,6,5,2,4,7,3]=>011010=>100101
[1,7,5,3,2,4,6]=>[1,5,3,7,2,4,6]=>011000=>100111
[1,7,5,3,2,6,4]=>[1,5,3,6,7,2,4]=>011000=>100111
[1,7,5,3,4,2,6]=>[1,5,3,4,7,2,6]=>011000=>100111
[1,7,5,3,4,6,2]=>[1,5,3,4,6,7,2]=>011000=>100111
[1,7,5,3,6,2,4]=>[1,6,5,3,7,2,4]=>011010=>100101
[1,7,5,3,6,4,2]=>[1,6,5,3,4,7,2]=>011010=>100101
[1,7,5,4,2,3,6]=>[1,4,5,2,7,3,6]=>011000=>100111
[1,7,5,4,2,6,3]=>[1,4,5,2,6,7,3]=>011000=>100111
[1,7,5,4,3,2,6]=>[1,4,5,3,7,2,6]=>011000=>100111
[1,7,5,4,3,6,2]=>[1,4,5,3,6,7,2]=>011000=>100111
[1,7,5,4,6,2,3]=>[1,4,6,5,2,7,3]=>011010=>100101
[1,7,5,4,6,3,2]=>[1,4,6,5,3,7,2]=>011010=>100101
[1,7,5,6,2,3,4]=>[1,6,2,5,3,7,4]=>011100=>100011
[1,7,5,6,2,4,3]=>[1,6,2,5,4,7,3]=>011100=>100011
[1,7,5,6,3,2,4]=>[1,6,3,5,2,7,4]=>011100=>100011
[1,7,5,6,3,4,2]=>[1,6,3,5,4,7,2]=>011100=>100011
[1,7,5,6,4,2,3]=>[1,6,4,5,2,7,3]=>011100=>100011
[1,7,5,6,4,3,2]=>[1,6,4,5,3,7,2]=>011100=>100011
[1,7,6,2,3,4,5]=>[1,6,2,7,3,4,5]=>011000=>100111
[1,7,6,2,3,5,4]=>[1,6,2,5,7,3,4]=>011000=>100111
[1,7,6,2,4,3,5]=>[1,6,2,4,7,3,5]=>011000=>100111
[1,7,6,2,4,5,3]=>[1,6,2,4,5,7,3]=>011000=>100111
[1,7,6,2,5,3,4]=>[1,5,6,2,7,3,4]=>011000=>100111
[1,7,6,2,5,4,3]=>[1,5,6,2,4,7,3]=>011000=>100111
[1,7,6,3,2,4,5]=>[1,6,3,7,2,4,5]=>011000=>100111
[1,7,6,3,2,5,4]=>[1,6,3,5,7,2,4]=>011000=>100111
[1,7,6,3,4,2,5]=>[1,6,3,4,7,2,5]=>011000=>100111
[1,7,6,3,4,5,2]=>[1,6,3,4,5,7,2]=>011000=>100111
[1,7,6,3,5,2,4]=>[1,5,6,3,7,2,4]=>011000=>100111
[1,7,6,3,5,4,2]=>[1,5,6,3,4,7,2]=>011000=>100111
[1,7,6,4,2,3,5]=>[1,4,6,2,7,3,5]=>011000=>100111
[1,7,6,4,2,5,3]=>[1,4,6,2,5,7,3]=>011000=>100111
[1,7,6,4,3,2,5]=>[1,4,6,3,7,2,5]=>011000=>100111
[1,7,6,4,3,5,2]=>[1,4,6,3,5,7,2]=>011000=>100111
[1,7,6,4,5,2,3]=>[1,4,5,6,2,7,3]=>011000=>100111
[1,7,6,4,5,3,2]=>[1,4,5,6,3,7,2]=>011000=>100111
[1,7,6,5,2,3,4]=>[1,5,2,6,3,7,4]=>011100=>100011
[1,7,6,5,2,4,3]=>[1,5,2,6,4,7,3]=>011100=>100011
[1,7,6,5,3,2,4]=>[1,5,3,6,2,7,4]=>011100=>100011
[1,7,6,5,3,4,2]=>[1,5,3,6,4,7,2]=>011100=>100011
[1,7,6,5,4,2,3]=>[1,5,4,6,2,7,3]=>011100=>100011
[1,7,6,5,4,3,2]=>[1,5,4,6,3,7,2]=>011100=>100011
[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000=>011111
[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>100001=>011110
[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>100010=>011101
[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>100011=>011100
[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>100010=>011101
[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>100010=>011101
[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>100100=>011011
[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>100101=>011010
[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>100110=>011001
[2,1,3,5,6,7,4]=>[2,1,3,7,6,5,4]=>100111=>011000
[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>100110=>011001
[2,1,3,5,7,6,4]=>[2,1,3,6,7,5,4]=>100110=>011001
[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>100100=>011011
[2,1,3,6,4,7,5]=>[2,1,3,7,6,4,5]=>100101=>011010
[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>100100=>011011
[2,1,3,6,5,7,4]=>[2,1,3,5,7,6,4]=>100101=>011010
[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]=>100110=>011001
[2,1,3,6,7,5,4]=>[2,1,3,7,5,6,4]=>100110=>011001
[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>100100=>011011
[2,1,3,7,4,6,5]=>[2,1,3,6,7,4,5]=>100100=>011011
[2,1,3,7,5,4,6]=>[2,1,3,5,7,4,6]=>100100=>011011
[2,1,3,7,5,6,4]=>[2,1,3,5,6,7,4]=>100100=>011011
[2,1,3,7,6,4,5]=>[2,1,3,6,4,7,5]=>100110=>011001
[2,1,3,7,6,5,4]=>[2,1,3,6,5,7,4]=>100110=>011001
[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>101000=>010111
[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>101001=>010110
[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>101010=>010101
[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>101011=>010100
[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>101010=>010101
[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>101010=>010101
[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>101100=>010011
[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>101101=>010010
[2,1,4,5,6,3,7]=>[2,1,6,5,4,3,7]=>101110=>010001
[2,1,4,5,6,7,3]=>[2,1,7,6,5,4,3]=>101111=>010000
[2,1,4,5,7,3,6]=>[2,1,7,5,4,3,6]=>101110=>010001
[2,1,4,5,7,6,3]=>[2,1,6,7,5,4,3]=>101110=>010001
[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>101100=>010011
[2,1,4,6,3,7,5]=>[2,1,7,6,4,3,5]=>101101=>010010
[2,1,4,6,5,3,7]=>[2,1,5,6,4,3,7]=>101100=>010011
[2,1,4,6,5,7,3]=>[2,1,5,7,6,4,3]=>101101=>010010
[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]=>101110=>010001
[2,1,4,6,7,5,3]=>[2,1,7,5,6,4,3]=>101110=>010001
[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>101100=>010011
[2,1,4,7,3,6,5]=>[2,1,6,7,4,3,5]=>101100=>010011
[2,1,4,7,5,3,6]=>[2,1,5,7,4,3,6]=>101100=>010011
[2,1,4,7,5,6,3]=>[2,1,5,6,7,4,3]=>101100=>010011
[2,1,4,7,6,3,5]=>[2,1,6,4,3,7,5]=>101110=>010001
[2,1,4,7,6,5,3]=>[2,1,6,5,7,4,3]=>101110=>010001
[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>101000=>010111
[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>101001=>010110
[2,1,5,3,6,4,7]=>[2,1,6,5,3,4,7]=>101010=>010101
[2,1,5,3,6,7,4]=>[2,1,7,6,5,3,4]=>101011=>010100
[2,1,5,3,7,4,6]=>[2,1,7,5,3,4,6]=>101010=>010101
[2,1,5,3,7,6,4]=>[2,1,6,7,5,3,4]=>101010=>010101
[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>101000=>010111
[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>101001=>010110
[2,1,5,4,6,3,7]=>[2,1,4,6,5,3,7]=>101010=>010101
[2,1,5,4,6,7,3]=>[2,1,4,7,6,5,3]=>101011=>010100
[2,1,5,4,7,3,6]=>[2,1,4,7,5,3,6]=>101010=>010101
[2,1,5,4,7,6,3]=>[2,1,4,6,7,5,3]=>101010=>010101
[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]=>101100=>010011
[2,1,5,6,3,7,4]=>[2,1,7,6,3,5,4]=>101101=>010010
[2,1,5,6,4,3,7]=>[2,1,6,4,5,3,7]=>101100=>010011
[2,1,5,6,4,7,3]=>[2,1,7,6,4,5,3]=>101101=>010010
[2,1,5,6,7,3,4]=>[2,1,7,3,6,5,4]=>101110=>010001
[2,1,5,6,7,4,3]=>[2,1,7,4,6,5,3]=>101110=>010001
[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]=>101100=>010011
[2,1,5,7,3,6,4]=>[2,1,6,7,3,5,4]=>101100=>010011
[2,1,5,7,4,3,6]=>[2,1,7,4,5,3,6]=>101100=>010011
[2,1,5,7,4,6,3]=>[2,1,6,7,4,5,3]=>101100=>010011
[2,1,5,7,6,3,4]=>[2,1,6,3,7,5,4]=>101110=>010001
[2,1,5,7,6,4,3]=>[2,1,6,4,7,5,3]=>101110=>010001
[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>101000=>010111
[2,1,6,3,4,7,5]=>[2,1,7,6,3,4,5]=>101001=>010110
[2,1,6,3,5,4,7]=>[2,1,5,6,3,4,7]=>101000=>010111
[2,1,6,3,5,7,4]=>[2,1,5,7,6,3,4]=>101001=>010110
[2,1,6,3,7,4,5]=>[2,1,7,3,4,6,5]=>101010=>010101
[2,1,6,3,7,5,4]=>[2,1,7,5,6,3,4]=>101010=>010101
[2,1,6,4,3,5,7]=>[2,1,4,6,3,5,7]=>101000=>010111
[2,1,6,4,3,7,5]=>[2,1,4,7,6,3,5]=>101001=>010110
[2,1,6,4,5,3,7]=>[2,1,4,5,6,3,7]=>101000=>010111
[2,1,6,4,5,7,3]=>[2,1,4,5,7,6,3]=>101001=>010110
[2,1,6,4,7,3,5]=>[2,1,4,7,3,6,5]=>101010=>010101
[2,1,6,4,7,5,3]=>[2,1,4,7,5,6,3]=>101010=>010101
[2,1,6,5,3,4,7]=>[2,1,5,3,6,4,7]=>101100=>010011
[2,1,6,5,3,7,4]=>[2,1,5,3,7,6,4]=>101101=>010010
[2,1,6,5,4,3,7]=>[2,1,5,4,6,3,7]=>101100=>010011
[2,1,6,5,4,7,3]=>[2,1,5,4,7,6,3]=>101101=>010010
[2,1,6,5,7,3,4]=>[2,1,7,5,3,6,4]=>101110=>010001
[2,1,6,5,7,4,3]=>[2,1,7,5,4,6,3]=>101110=>010001
[2,1,6,7,3,4,5]=>[2,1,7,3,6,4,5]=>101100=>010011
[2,1,6,7,3,5,4]=>[2,1,7,3,5,6,4]=>101100=>010011
[2,1,6,7,4,3,5]=>[2,1,7,4,6,3,5]=>101100=>010011
[2,1,6,7,4,5,3]=>[2,1,7,4,5,6,3]=>101100=>010011
[2,1,6,7,5,3,4]=>[2,1,5,7,3,6,4]=>101100=>010011
[2,1,6,7,5,4,3]=>[2,1,5,7,4,6,3]=>101100=>010011
[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>101000=>010111
[2,1,7,3,4,6,5]=>[2,1,6,7,3,4,5]=>101000=>010111
[2,1,7,3,5,4,6]=>[2,1,5,7,3,4,6]=>101000=>010111
[2,1,7,3,5,6,4]=>[2,1,5,6,7,3,4]=>101000=>010111
[2,1,7,3,6,4,5]=>[2,1,6,3,4,7,5]=>101010=>010101
[2,1,7,3,6,5,4]=>[2,1,6,5,7,3,4]=>101010=>010101
[2,1,7,4,3,5,6]=>[2,1,4,7,3,5,6]=>101000=>010111
[2,1,7,4,3,6,5]=>[2,1,4,6,7,3,5]=>101000=>010111
[2,1,7,4,5,3,6]=>[2,1,4,5,7,3,6]=>101000=>010111
[2,1,7,4,5,6,3]=>[2,1,4,5,6,7,3]=>101000=>010111
[2,1,7,4,6,3,5]=>[2,1,4,6,3,7,5]=>101010=>010101
[2,1,7,4,6,5,3]=>[2,1,4,6,5,7,3]=>101010=>010101
[2,1,7,5,3,4,6]=>[2,1,5,3,7,4,6]=>101100=>010011
[2,1,7,5,3,6,4]=>[2,1,5,3,6,7,4]=>101100=>010011
[2,1,7,5,4,3,6]=>[2,1,5,4,7,3,6]=>101100=>010011
[2,1,7,5,4,6,3]=>[2,1,5,4,6,7,3]=>101100=>010011
[2,1,7,5,6,3,4]=>[2,1,6,5,3,7,4]=>101110=>010001
[2,1,7,5,6,4,3]=>[2,1,6,5,4,7,3]=>101110=>010001
[2,1,7,6,3,4,5]=>[2,1,6,3,7,4,5]=>101100=>010011
[2,1,7,6,3,5,4]=>[2,1,6,3,5,7,4]=>101100=>010011
[2,1,7,6,4,3,5]=>[2,1,6,4,7,3,5]=>101100=>010011
[2,1,7,6,4,5,3]=>[2,1,6,4,5,7,3]=>101100=>010011
[2,1,7,6,5,3,4]=>[2,1,5,6,3,7,4]=>101100=>010011
[2,1,7,6,5,4,3]=>[2,1,5,6,4,7,3]=>101100=>010011
[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000=>001111
[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>110001=>001110
[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>110010=>001101
[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>110011=>001100
[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>110010=>001101
[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>110010=>001101
[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>110100=>001011
[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>110101=>001010
[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>110110=>001001
[2,3,1,5,6,7,4]=>[3,2,1,7,6,5,4]=>110111=>001000
[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>110110=>001001
[2,3,1,5,7,6,4]=>[3,2,1,6,7,5,4]=>110110=>001001
[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>110100=>001011
[2,3,1,6,4,7,5]=>[3,2,1,7,6,4,5]=>110101=>001010
[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>110100=>001011
[2,3,1,6,5,7,4]=>[3,2,1,5,7,6,4]=>110101=>001010
[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]=>110110=>001001
[2,3,1,6,7,5,4]=>[3,2,1,7,5,6,4]=>110110=>001001
[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>110100=>001011
[2,3,1,7,4,6,5]=>[3,2,1,6,7,4,5]=>110100=>001011
[2,3,1,7,5,4,6]=>[3,2,1,5,7,4,6]=>110100=>001011
[2,3,1,7,5,6,4]=>[3,2,1,5,6,7,4]=>110100=>001011
[2,3,1,7,6,4,5]=>[3,2,1,6,4,7,5]=>110110=>001001
[2,3,1,7,6,5,4]=>[3,2,1,6,5,7,4]=>110110=>001001
[2,3,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000=>000111
[2,3,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>111001=>000110
[2,3,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>111010=>000101
[2,3,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>111011=>000100
[2,3,4,1,7,5,6]=>[4,3,2,1,7,5,6]=>111010=>000101
[2,3,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>111010=>000101
[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]=>111100=>000011
[2,3,4,5,1,7,6]=>[5,4,3,2,1,7,6]=>111101=>000010
[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]=>111110=>000001
[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]=>111111=>000000
[2,3,4,5,7,1,6]=>[7,5,4,3,2,1,6]=>111110=>000001
[2,3,4,5,7,6,1]=>[6,7,5,4,3,2,1]=>111110=>000001
[2,3,4,6,1,5,7]=>[6,4,3,2,1,5,7]=>111100=>000011
[2,3,4,6,1,7,5]=>[7,6,4,3,2,1,5]=>111101=>000010
[2,3,4,6,5,1,7]=>[5,6,4,3,2,1,7]=>111100=>000011
[2,3,4,6,5,7,1]=>[5,7,6,4,3,2,1]=>111101=>000010
[2,3,4,6,7,1,5]=>[7,4,3,2,1,6,5]=>111110=>000001
[2,3,4,6,7,5,1]=>[7,5,6,4,3,2,1]=>111110=>000001
[2,3,4,7,1,5,6]=>[7,4,3,2,1,5,6]=>111100=>000011
[2,3,4,7,1,6,5]=>[6,7,4,3,2,1,5]=>111100=>000011
[2,3,4,7,5,1,6]=>[5,7,4,3,2,1,6]=>111100=>000011
[2,3,4,7,5,6,1]=>[5,6,7,4,3,2,1]=>111100=>000011
[2,3,4,7,6,1,5]=>[6,4,3,2,1,7,5]=>111110=>000001
[2,3,4,7,6,5,1]=>[6,5,7,4,3,2,1]=>111110=>000001
[2,3,5,1,4,6,7]=>[5,3,2,1,4,6,7]=>111000=>000111
[2,3,5,1,4,7,6]=>[5,3,2,1,4,7,6]=>111001=>000110
[2,3,5,1,6,4,7]=>[6,5,3,2,1,4,7]=>111010=>000101
[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>111011=>000100
[2,3,5,1,7,4,6]=>[7,5,3,2,1,4,6]=>111010=>000101
[2,3,5,1,7,6,4]=>[6,7,5,3,2,1,4]=>111010=>000101
[2,3,5,4,1,6,7]=>[4,5,3,2,1,6,7]=>111000=>000111
[2,3,5,4,1,7,6]=>[4,5,3,2,1,7,6]=>111001=>000110
[2,3,5,4,6,1,7]=>[4,6,5,3,2,1,7]=>111010=>000101
[2,3,5,4,6,7,1]=>[4,7,6,5,3,2,1]=>111011=>000100
[2,3,5,4,7,1,6]=>[4,7,5,3,2,1,6]=>111010=>000101
[2,3,5,4,7,6,1]=>[4,6,7,5,3,2,1]=>111010=>000101
[2,3,5,6,1,4,7]=>[6,3,2,1,5,4,7]=>111100=>000011
[2,3,5,6,1,7,4]=>[7,6,3,2,1,5,4]=>111101=>000010
[2,3,5,6,4,1,7]=>[6,4,5,3,2,1,7]=>111100=>000011
[2,3,5,6,4,7,1]=>[7,6,4,5,3,2,1]=>111101=>000010
[2,3,5,6,7,1,4]=>[7,3,2,1,6,5,4]=>111110=>000001
[2,3,5,6,7,4,1]=>[7,4,6,5,3,2,1]=>111110=>000001
[2,3,5,7,1,4,6]=>[7,3,2,1,5,4,6]=>111100=>000011
[2,3,5,7,1,6,4]=>[6,7,3,2,1,5,4]=>111100=>000011
[2,3,5,7,4,1,6]=>[7,4,5,3,2,1,6]=>111100=>000011
[2,3,5,7,4,6,1]=>[6,7,4,5,3,2,1]=>111100=>000011
[2,3,5,7,6,1,4]=>[6,3,2,1,7,5,4]=>111110=>000001
[2,3,5,7,6,4,1]=>[6,4,7,5,3,2,1]=>111110=>000001
[2,3,6,1,4,5,7]=>[6,3,2,1,4,5,7]=>111000=>000111
[2,3,6,1,4,7,5]=>[7,6,3,2,1,4,5]=>111001=>000110
[2,3,6,1,5,4,7]=>[5,6,3,2,1,4,7]=>111000=>000111
[2,3,6,1,5,7,4]=>[5,7,6,3,2,1,4]=>111001=>000110
[2,3,6,1,7,4,5]=>[7,3,2,1,4,6,5]=>111010=>000101
[2,3,6,1,7,5,4]=>[7,5,6,3,2,1,4]=>111010=>000101
[2,3,6,4,1,5,7]=>[4,6,3,2,1,5,7]=>111000=>000111
[2,3,6,4,1,7,5]=>[4,7,6,3,2,1,5]=>111001=>000110
[2,3,6,4,5,1,7]=>[4,5,6,3,2,1,7]=>111000=>000111
[2,3,6,4,5,7,1]=>[4,5,7,6,3,2,1]=>111001=>000110
[2,3,6,4,7,1,5]=>[4,7,3,2,1,6,5]=>111010=>000101
[2,3,6,4,7,5,1]=>[4,7,5,6,3,2,1]=>111010=>000101
[2,3,6,5,1,4,7]=>[5,3,2,1,6,4,7]=>111100=>000011
[2,3,6,5,1,7,4]=>[5,3,2,1,7,6,4]=>111101=>000010
[2,3,6,5,4,1,7]=>[5,4,6,3,2,1,7]=>111100=>000011
[2,3,6,5,4,7,1]=>[5,4,7,6,3,2,1]=>111101=>000010
[2,3,6,5,7,1,4]=>[7,5,3,2,1,6,4]=>111110=>000001
[2,3,6,5,7,4,1]=>[7,5,4,6,3,2,1]=>111110=>000001
[2,3,6,7,1,4,5]=>[7,3,2,1,6,4,5]=>111100=>000011
[2,3,6,7,1,5,4]=>[7,3,2,1,5,6,4]=>111100=>000011
[2,3,6,7,4,1,5]=>[7,4,6,3,2,1,5]=>111100=>000011
[2,3,6,7,4,5,1]=>[7,4,5,6,3,2,1]=>111100=>000011
[2,3,6,7,5,1,4]=>[5,7,3,2,1,6,4]=>111100=>000011
[2,3,6,7,5,4,1]=>[5,7,4,6,3,2,1]=>111100=>000011
[2,3,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>111000=>000111
[2,3,7,1,4,6,5]=>[6,7,3,2,1,4,5]=>111000=>000111
[2,3,7,1,5,4,6]=>[5,7,3,2,1,4,6]=>111000=>000111
[2,3,7,1,5,6,4]=>[5,6,7,3,2,1,4]=>111000=>000111
[2,3,7,1,6,4,5]=>[6,3,2,1,4,7,5]=>111010=>000101
[2,3,7,1,6,5,4]=>[6,5,7,3,2,1,4]=>111010=>000101
[2,3,7,4,1,5,6]=>[4,7,3,2,1,5,6]=>111000=>000111
[2,3,7,4,1,6,5]=>[4,6,7,3,2,1,5]=>111000=>000111
[2,3,7,4,5,1,6]=>[4,5,7,3,2,1,6]=>111000=>000111
[2,3,7,4,5,6,1]=>[4,5,6,7,3,2,1]=>111000=>000111
[2,3,7,4,6,1,5]=>[4,6,3,2,1,7,5]=>111010=>000101
[2,3,7,4,6,5,1]=>[4,6,5,7,3,2,1]=>111010=>000101
[2,3,7,5,1,4,6]=>[5,3,2,1,7,4,6]=>111100=>000011
[2,3,7,5,1,6,4]=>[5,3,2,1,6,7,4]=>111100=>000011
[2,3,7,5,4,1,6]=>[5,4,7,3,2,1,6]=>111100=>000011
[2,3,7,5,4,6,1]=>[5,4,6,7,3,2,1]=>111100=>000011
[2,3,7,5,6,1,4]=>[6,5,3,2,1,7,4]=>111110=>000001
[2,3,7,5,6,4,1]=>[6,5,4,7,3,2,1]=>111110=>000001
[2,3,7,6,1,4,5]=>[6,3,2,1,7,4,5]=>111100=>000011
[2,3,7,6,1,5,4]=>[6,3,2,1,5,7,4]=>111100=>000011
[2,3,7,6,4,1,5]=>[6,4,7,3,2,1,5]=>111100=>000011
[2,3,7,6,4,5,1]=>[6,4,5,7,3,2,1]=>111100=>000011
[2,3,7,6,5,1,4]=>[5,6,3,2,1,7,4]=>111100=>000011
[2,3,7,6,5,4,1]=>[5,6,4,7,3,2,1]=>111100=>000011
[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>110000=>001111
[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>110001=>001110
[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>110010=>001101
[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>110011=>001100
[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>110010=>001101
[2,4,1,3,7,6,5]=>[4,2,1,3,6,7,5]=>110010=>001101
[2,4,1,5,3,6,7]=>[5,4,2,1,3,6,7]=>110100=>001011
[2,4,1,5,3,7,6]=>[5,4,2,1,3,7,6]=>110101=>001010
[2,4,1,5,6,3,7]=>[6,5,4,2,1,3,7]=>110110=>001001
[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>110111=>001000
[2,4,1,5,7,3,6]=>[7,5,4,2,1,3,6]=>110110=>001001
[2,4,1,5,7,6,3]=>[6,7,5,4,2,1,3]=>110110=>001001
[2,4,1,6,3,5,7]=>[6,4,2,1,3,5,7]=>110100=>001011
[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>110101=>001010
[2,4,1,6,5,3,7]=>[5,6,4,2,1,3,7]=>110100=>001011
[2,4,1,6,5,7,3]=>[5,7,6,4,2,1,3]=>110101=>001010
[2,4,1,6,7,3,5]=>[7,4,2,1,3,6,5]=>110110=>001001
[2,4,1,6,7,5,3]=>[7,5,6,4,2,1,3]=>110110=>001001
[2,4,1,7,3,5,6]=>[7,4,2,1,3,5,6]=>110100=>001011
[2,4,1,7,3,6,5]=>[6,7,4,2,1,3,5]=>110100=>001011
[2,4,1,7,5,3,6]=>[5,7,4,2,1,3,6]=>110100=>001011
[2,4,1,7,5,6,3]=>[5,6,7,4,2,1,3]=>110100=>001011
[2,4,1,7,6,3,5]=>[6,4,2,1,3,7,5]=>110110=>001001
[2,4,1,7,6,5,3]=>[6,5,7,4,2,1,3]=>110110=>001001
[2,4,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>110000=>001111
[2,4,3,1,5,7,6]=>[3,4,2,1,5,7,6]=>110001=>001110
[2,4,3,1,6,5,7]=>[3,4,2,1,6,5,7]=>110010=>001101
[2,4,3,1,6,7,5]=>[3,4,2,1,7,6,5]=>110011=>001100
[2,4,3,1,7,5,6]=>[3,4,2,1,7,5,6]=>110010=>001101
[2,4,3,1,7,6,5]=>[3,4,2,1,6,7,5]=>110010=>001101
[2,4,3,5,1,6,7]=>[3,5,4,2,1,6,7]=>110100=>001011
[2,4,3,5,1,7,6]=>[3,5,4,2,1,7,6]=>110101=>001010
[2,4,3,5,6,1,7]=>[3,6,5,4,2,1,7]=>110110=>001001
[2,4,3,5,6,7,1]=>[3,7,6,5,4,2,1]=>110111=>001000
[2,4,3,5,7,1,6]=>[3,7,5,4,2,1,6]=>110110=>001001
[2,4,3,5,7,6,1]=>[3,6,7,5,4,2,1]=>110110=>001001
[2,4,3,6,1,5,7]=>[3,6,4,2,1,5,7]=>110100=>001011
[2,4,3,6,1,7,5]=>[3,7,6,4,2,1,5]=>110101=>001010
[2,4,3,6,5,1,7]=>[3,5,6,4,2,1,7]=>110100=>001011
[2,4,3,6,5,7,1]=>[3,5,7,6,4,2,1]=>110101=>001010
[2,4,3,6,7,1,5]=>[3,7,4,2,1,6,5]=>110110=>001001
[2,4,3,6,7,5,1]=>[3,7,5,6,4,2,1]=>110110=>001001
[2,4,3,7,1,5,6]=>[3,7,4,2,1,5,6]=>110100=>001011
[2,4,3,7,1,6,5]=>[3,6,7,4,2,1,5]=>110100=>001011
[2,4,3,7,5,1,6]=>[3,5,7,4,2,1,6]=>110100=>001011
[2,4,3,7,5,6,1]=>[3,5,6,7,4,2,1]=>110100=>001011
[2,4,3,7,6,1,5]=>[3,6,4,2,1,7,5]=>110110=>001001
[2,4,3,7,6,5,1]=>[3,6,5,7,4,2,1]=>110110=>001001
[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]=>111000=>000111
[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]=>111001=>000110
[2,4,5,1,6,3,7]=>[6,5,2,1,4,3,7]=>111010=>000101
[2,4,5,1,6,7,3]=>[7,6,5,2,1,4,3]=>111011=>000100
[2,4,5,1,7,3,6]=>[7,5,2,1,4,3,6]=>111010=>000101
[2,4,5,1,7,6,3]=>[6,7,5,2,1,4,3]=>111010=>000101
[2,4,5,3,1,6,7]=>[5,3,4,2,1,6,7]=>111000=>000111
[2,4,5,3,1,7,6]=>[5,3,4,2,1,7,6]=>111001=>000110
[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]=>111010=>000101
[2,4,5,3,6,7,1]=>[7,6,5,3,4,2,1]=>111011=>000100
[2,4,5,3,7,1,6]=>[7,5,3,4,2,1,6]=>111010=>000101
[2,4,5,3,7,6,1]=>[6,7,5,3,4,2,1]=>111010=>000101
[2,4,5,6,1,3,7]=>[6,2,1,5,4,3,7]=>111100=>000011
[2,4,5,6,1,7,3]=>[7,6,2,1,5,4,3]=>111101=>000010
[2,4,5,6,3,1,7]=>[6,3,5,4,2,1,7]=>111100=>000011
[2,4,5,6,3,7,1]=>[7,6,3,5,4,2,1]=>111101=>000010
[2,4,5,6,7,1,3]=>[7,2,1,6,5,4,3]=>111110=>000001
[2,4,5,6,7,3,1]=>[7,3,6,5,4,2,1]=>111110=>000001
[2,4,5,7,1,3,6]=>[7,2,1,5,4,3,6]=>111100=>000011
[2,4,5,7,1,6,3]=>[6,7,2,1,5,4,3]=>111100=>000011
[2,4,5,7,3,1,6]=>[7,3,5,4,2,1,6]=>111100=>000011
[2,4,5,7,3,6,1]=>[6,7,3,5,4,2,1]=>111100=>000011
[2,4,5,7,6,1,3]=>[6,2,1,7,5,4,3]=>111110=>000001
[2,4,5,7,6,3,1]=>[6,3,7,5,4,2,1]=>111110=>000001
[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>111000=>000111
[2,4,6,1,3,7,5]=>[7,6,2,1,4,3,5]=>111001=>000110
[2,4,6,1,5,3,7]=>[5,6,2,1,4,3,7]=>111000=>000111
[2,4,6,1,5,7,3]=>[5,7,6,2,1,4,3]=>111001=>000110
[2,4,6,1,7,3,5]=>[7,2,1,4,3,6,5]=>111010=>000101
[2,4,6,1,7,5,3]=>[7,5,6,2,1,4,3]=>111010=>000101
[2,4,6,3,1,5,7]=>[6,3,4,2,1,5,7]=>111000=>000111
[2,4,6,3,1,7,5]=>[7,6,3,4,2,1,5]=>111001=>000110
[2,4,6,3,5,1,7]=>[5,6,3,4,2,1,7]=>111000=>000111
[2,4,6,3,5,7,1]=>[5,7,6,3,4,2,1]=>111001=>000110
[2,4,6,3,7,1,5]=>[7,3,4,2,1,6,5]=>111010=>000101
[2,4,6,3,7,5,1]=>[7,5,6,3,4,2,1]=>111010=>000101
[2,4,6,5,1,3,7]=>[5,2,1,6,4,3,7]=>111100=>000011
[2,4,6,5,1,7,3]=>[5,2,1,7,6,4,3]=>111101=>000010
[2,4,6,5,3,1,7]=>[5,3,6,4,2,1,7]=>111100=>000011
[2,4,6,5,3,7,1]=>[5,3,7,6,4,2,1]=>111101=>000010
[2,4,6,5,7,1,3]=>[7,5,2,1,6,4,3]=>111110=>000001
[2,4,6,5,7,3,1]=>[7,5,3,6,4,2,1]=>111110=>000001
[2,4,6,7,1,3,5]=>[7,2,1,6,4,3,5]=>111100=>000011
[2,4,6,7,1,5,3]=>[7,2,1,5,6,4,3]=>111100=>000011
[2,4,6,7,3,1,5]=>[7,3,6,4,2,1,5]=>111100=>000011
[2,4,6,7,3,5,1]=>[7,3,5,6,4,2,1]=>111100=>000011
[2,4,6,7,5,1,3]=>[5,7,2,1,6,4,3]=>111100=>000011
[2,4,6,7,5,3,1]=>[5,7,3,6,4,2,1]=>111100=>000011
[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>111000=>000111
[2,4,7,1,3,6,5]=>[6,7,2,1,4,3,5]=>111000=>000111
[2,4,7,1,5,3,6]=>[5,7,2,1,4,3,6]=>111000=>000111
[2,4,7,1,5,6,3]=>[5,6,7,2,1,4,3]=>111000=>000111
[2,4,7,1,6,3,5]=>[6,2,1,4,3,7,5]=>111010=>000101
[2,4,7,1,6,5,3]=>[6,5,7,2,1,4,3]=>111010=>000101
[2,4,7,3,1,5,6]=>[7,3,4,2,1,5,6]=>111000=>000111
[2,4,7,3,1,6,5]=>[6,7,3,4,2,1,5]=>111000=>000111
[2,4,7,3,5,1,6]=>[5,7,3,4,2,1,6]=>111000=>000111
[2,4,7,3,5,6,1]=>[5,6,7,3,4,2,1]=>111000=>000111
[2,4,7,3,6,1,5]=>[6,3,4,2,1,7,5]=>111010=>000101
[2,4,7,3,6,5,1]=>[6,5,7,3,4,2,1]=>111010=>000101
[2,4,7,5,1,3,6]=>[5,2,1,7,4,3,6]=>111100=>000011
[2,4,7,5,1,6,3]=>[5,2,1,6,7,4,3]=>111100=>000011
[2,4,7,5,3,1,6]=>[5,3,7,4,2,1,6]=>111100=>000011
[2,4,7,5,3,6,1]=>[5,3,6,7,4,2,1]=>111100=>000011
[2,4,7,5,6,1,3]=>[6,5,2,1,7,4,3]=>111110=>000001
[2,4,7,5,6,3,1]=>[6,5,3,7,4,2,1]=>111110=>000001
[2,4,7,6,1,3,5]=>[6,2,1,7,4,3,5]=>111100=>000011
[2,4,7,6,1,5,3]=>[6,2,1,5,7,4,3]=>111100=>000011
[2,4,7,6,3,1,5]=>[6,3,7,4,2,1,5]=>111100=>000011
[2,4,7,6,3,5,1]=>[6,3,5,7,4,2,1]=>111100=>000011
[2,4,7,6,5,1,3]=>[5,6,2,1,7,4,3]=>111100=>000011
[2,4,7,6,5,3,1]=>[5,6,3,7,4,2,1]=>111100=>000011
[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>110000=>001111
[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>110001=>001110
[2,5,1,3,6,4,7]=>[6,5,2,1,3,4,7]=>110010=>001101
[2,5,1,3,6,7,4]=>[7,6,5,2,1,3,4]=>110011=>001100
[2,5,1,3,7,4,6]=>[7,5,2,1,3,4,6]=>110010=>001101
[2,5,1,3,7,6,4]=>[6,7,5,2,1,3,4]=>110010=>001101
[2,5,1,4,3,6,7]=>[4,5,2,1,3,6,7]=>110000=>001111
[2,5,1,4,3,7,6]=>[4,5,2,1,3,7,6]=>110001=>001110
[2,5,1,4,6,3,7]=>[4,6,5,2,1,3,7]=>110010=>001101
[2,5,1,4,6,7,3]=>[4,7,6,5,2,1,3]=>110011=>001100
[2,5,1,4,7,3,6]=>[4,7,5,2,1,3,6]=>110010=>001101
[2,5,1,4,7,6,3]=>[4,6,7,5,2,1,3]=>110010=>001101
[2,5,1,6,3,4,7]=>[6,2,1,3,5,4,7]=>110100=>001011
[2,5,1,6,3,7,4]=>[7,6,2,1,3,5,4]=>110101=>001010
[2,5,1,6,4,3,7]=>[6,4,5,2,1,3,7]=>110100=>001011
[2,5,1,6,4,7,3]=>[7,6,4,5,2,1,3]=>110101=>001010
[2,5,1,6,7,3,4]=>[7,2,1,3,6,5,4]=>110110=>001001
[2,5,1,6,7,4,3]=>[7,4,6,5,2,1,3]=>110110=>001001
[2,5,1,7,3,4,6]=>[7,2,1,3,5,4,6]=>110100=>001011
[2,5,1,7,3,6,4]=>[6,7,2,1,3,5,4]=>110100=>001011
[2,5,1,7,4,3,6]=>[7,4,5,2,1,3,6]=>110100=>001011
[2,5,1,7,4,6,3]=>[6,7,4,5,2,1,3]=>110100=>001011
[2,5,1,7,6,3,4]=>[6,2,1,3,7,5,4]=>110110=>001001
[2,5,1,7,6,4,3]=>[6,4,7,5,2,1,3]=>110110=>001001
[2,5,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>110000=>001111
[2,5,3,1,4,7,6]=>[3,5,2,1,4,7,6]=>110001=>001110
[2,5,3,1,6,4,7]=>[3,6,5,2,1,4,7]=>110010=>001101
[2,5,3,1,6,7,4]=>[3,7,6,5,2,1,4]=>110011=>001100
[2,5,3,1,7,4,6]=>[3,7,5,2,1,4,6]=>110010=>001101
[2,5,3,1,7,6,4]=>[3,6,7,5,2,1,4]=>110010=>001101
[2,5,3,4,1,6,7]=>[3,4,5,2,1,6,7]=>110000=>001111
[2,5,3,4,1,7,6]=>[3,4,5,2,1,7,6]=>110001=>001110
[2,5,3,4,6,1,7]=>[3,4,6,5,2,1,7]=>110010=>001101
[2,5,3,4,6,7,1]=>[3,4,7,6,5,2,1]=>110011=>001100
[2,5,3,4,7,1,6]=>[3,4,7,5,2,1,6]=>110010=>001101
[2,5,3,4,7,6,1]=>[3,4,6,7,5,2,1]=>110010=>001101
[2,5,3,6,1,4,7]=>[3,6,2,1,5,4,7]=>110100=>001011
[2,5,3,6,1,7,4]=>[3,7,6,2,1,5,4]=>110101=>001010
[2,5,3,6,4,1,7]=>[3,6,4,5,2,1,7]=>110100=>001011
[2,5,3,6,4,7,1]=>[3,7,6,4,5,2,1]=>110101=>001010
[2,5,3,6,7,1,4]=>[3,7,2,1,6,5,4]=>110110=>001001
[2,5,3,6,7,4,1]=>[3,7,4,6,5,2,1]=>110110=>001001
[2,5,3,7,1,4,6]=>[3,7,2,1,5,4,6]=>110100=>001011
[2,5,3,7,1,6,4]=>[3,6,7,2,1,5,4]=>110100=>001011
[2,5,3,7,4,1,6]=>[3,7,4,5,2,1,6]=>110100=>001011
[2,5,3,7,4,6,1]=>[3,6,7,4,5,2,1]=>110100=>001011
[2,5,3,7,6,1,4]=>[3,6,2,1,7,5,4]=>110110=>001001
[2,5,3,7,6,4,1]=>[3,6,4,7,5,2,1]=>110110=>001001
[2,5,4,1,3,6,7]=>[4,2,1,5,3,6,7]=>111000=>000111
[2,5,4,1,3,7,6]=>[4,2,1,5,3,7,6]=>111001=>000110
[2,5,4,1,6,3,7]=>[4,2,1,6,5,3,7]=>111010=>000101
[2,5,4,1,6,7,3]=>[4,2,1,7,6,5,3]=>111011=>000100
[2,5,4,1,7,3,6]=>[4,2,1,7,5,3,6]=>111010=>000101
[2,5,4,1,7,6,3]=>[4,2,1,6,7,5,3]=>111010=>000101
[2,5,4,3,1,6,7]=>[4,3,5,2,1,6,7]=>111000=>000111
[2,5,4,3,1,7,6]=>[4,3,5,2,1,7,6]=>111001=>000110
[2,5,4,3,6,1,7]=>[4,3,6,5,2,1,7]=>111010=>000101
[2,5,4,3,6,7,1]=>[4,3,7,6,5,2,1]=>111011=>000100
[2,5,4,3,7,1,6]=>[4,3,7,5,2,1,6]=>111010=>000101
[2,5,4,3,7,6,1]=>[4,3,6,7,5,2,1]=>111010=>000101
[2,5,4,6,1,3,7]=>[6,4,2,1,5,3,7]=>111100=>000011
[2,5,4,6,1,7,3]=>[7,6,4,2,1,5,3]=>111101=>000010
[2,5,4,6,3,1,7]=>[6,4,3,5,2,1,7]=>111100=>000011
[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]=>111101=>000010
[2,5,4,6,7,1,3]=>[7,4,2,1,6,5,3]=>111110=>000001
[2,5,4,6,7,3,1]=>[7,4,3,6,5,2,1]=>111110=>000001
[2,5,4,7,1,3,6]=>[7,4,2,1,5,3,6]=>111100=>000011
[2,5,4,7,1,6,3]=>[6,7,4,2,1,5,3]=>111100=>000011
[2,5,4,7,3,1,6]=>[7,4,3,5,2,1,6]=>111100=>000011
[2,5,4,7,3,6,1]=>[6,7,4,3,5,2,1]=>111100=>000011
[2,5,4,7,6,1,3]=>[6,4,2,1,7,5,3]=>111110=>000001
[2,5,4,7,6,3,1]=>[6,4,3,7,5,2,1]=>111110=>000001
[2,5,6,1,3,4,7]=>[6,2,1,5,3,4,7]=>111000=>000111
[2,5,6,1,3,7,4]=>[7,6,2,1,5,3,4]=>111001=>000110
[2,5,6,1,4,3,7]=>[6,2,1,4,5,3,7]=>111000=>000111
[2,5,6,1,4,7,3]=>[7,6,2,1,4,5,3]=>111001=>000110
[2,5,6,1,7,3,4]=>[7,2,1,6,5,3,4]=>111010=>000101
[2,5,6,1,7,4,3]=>[7,2,1,4,6,5,3]=>111010=>000101
[2,5,6,3,1,4,7]=>[6,3,5,2,1,4,7]=>111000=>000111
[2,5,6,3,1,7,4]=>[7,6,3,5,2,1,4]=>111001=>000110
[2,5,6,3,4,1,7]=>[6,3,4,5,2,1,7]=>111000=>000111
[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]=>111001=>000110
[2,5,6,3,7,1,4]=>[7,3,6,5,2,1,4]=>111010=>000101
[2,5,6,3,7,4,1]=>[7,3,4,6,5,2,1]=>111010=>000101
[2,5,6,4,1,3,7]=>[4,6,2,1,5,3,7]=>111000=>000111
[2,5,6,4,1,7,3]=>[4,7,6,2,1,5,3]=>111001=>000110
[2,5,6,4,3,1,7]=>[4,6,3,5,2,1,7]=>111000=>000111
[2,5,6,4,3,7,1]=>[4,7,6,3,5,2,1]=>111001=>000110
[2,5,6,4,7,1,3]=>[4,7,2,1,6,5,3]=>111010=>000101
[2,5,6,4,7,3,1]=>[4,7,3,6,5,2,1]=>111010=>000101
[2,5,6,7,1,3,4]=>[7,2,1,6,3,5,4]=>111100=>000011
[2,5,6,7,1,4,3]=>[7,2,1,6,4,5,3]=>111100=>000011
[2,5,6,7,3,1,4]=>[7,3,6,2,1,5,4]=>111100=>000011
[2,5,6,7,3,4,1]=>[7,3,6,4,5,2,1]=>111100=>000011
[2,5,6,7,4,1,3]=>[7,4,6,2,1,5,3]=>111100=>000011
[2,5,6,7,4,3,1]=>[7,4,6,3,5,2,1]=>111100=>000011
[2,5,7,1,3,4,6]=>[7,2,1,5,3,4,6]=>111000=>000111
[2,5,7,1,3,6,4]=>[6,7,2,1,5,3,4]=>111000=>000111
[2,5,7,1,4,3,6]=>[7,2,1,4,5,3,6]=>111000=>000111
[2,5,7,1,4,6,3]=>[6,7,2,1,4,5,3]=>111000=>000111
[2,5,7,1,6,3,4]=>[6,2,1,7,5,3,4]=>111010=>000101
[2,5,7,1,6,4,3]=>[6,2,1,4,7,5,3]=>111010=>000101
[2,5,7,3,1,4,6]=>[7,3,5,2,1,4,6]=>111000=>000111
[2,5,7,3,1,6,4]=>[6,7,3,5,2,1,4]=>111000=>000111
[2,5,7,3,4,1,6]=>[7,3,4,5,2,1,6]=>111000=>000111
[2,5,7,3,4,6,1]=>[6,7,3,4,5,2,1]=>111000=>000111
[2,5,7,3,6,1,4]=>[6,3,7,5,2,1,4]=>111010=>000101
[2,5,7,3,6,4,1]=>[6,3,4,7,5,2,1]=>111010=>000101
[2,5,7,4,1,3,6]=>[4,7,2,1,5,3,6]=>111000=>000111
[2,5,7,4,1,6,3]=>[4,6,7,2,1,5,3]=>111000=>000111
[2,5,7,4,3,1,6]=>[4,7,3,5,2,1,6]=>111000=>000111
[2,5,7,4,3,6,1]=>[4,6,7,3,5,2,1]=>111000=>000111
[2,5,7,4,6,1,3]=>[4,6,2,1,7,5,3]=>111010=>000101
[2,5,7,4,6,3,1]=>[4,6,3,7,5,2,1]=>111010=>000101
[2,5,7,6,1,3,4]=>[6,2,1,7,3,5,4]=>111100=>000011
[2,5,7,6,1,4,3]=>[6,2,1,7,4,5,3]=>111100=>000011
[2,5,7,6,3,1,4]=>[6,3,7,2,1,5,4]=>111100=>000011
[2,5,7,6,3,4,1]=>[6,3,7,4,5,2,1]=>111100=>000011
[2,5,7,6,4,1,3]=>[6,4,7,2,1,5,3]=>111100=>000011
[2,5,7,6,4,3,1]=>[6,4,7,3,5,2,1]=>111100=>000011
[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>110000=>001111
[2,6,1,3,4,7,5]=>[7,6,2,1,3,4,5]=>110001=>001110
[2,6,1,3,5,4,7]=>[5,6,2,1,3,4,7]=>110000=>001111
[2,6,1,3,5,7,4]=>[5,7,6,2,1,3,4]=>110001=>001110
[2,6,1,3,7,4,5]=>[7,2,1,3,4,6,5]=>110010=>001101
[2,6,1,3,7,5,4]=>[7,5,6,2,1,3,4]=>110010=>001101
[2,6,1,4,3,5,7]=>[4,6,2,1,3,5,7]=>110000=>001111
[2,6,1,4,3,7,5]=>[4,7,6,2,1,3,5]=>110001=>001110
[2,6,1,4,5,3,7]=>[4,5,6,2,1,3,7]=>110000=>001111
[2,6,1,4,5,7,3]=>[4,5,7,6,2,1,3]=>110001=>001110
[2,6,1,4,7,3,5]=>[4,7,2,1,3,6,5]=>110010=>001101
[2,6,1,4,7,5,3]=>[4,7,5,6,2,1,3]=>110010=>001101
[2,6,1,5,3,4,7]=>[5,2,1,3,6,4,7]=>110100=>001011
[2,6,1,5,3,7,4]=>[5,2,1,3,7,6,4]=>110101=>001010
[2,6,1,5,4,3,7]=>[5,4,6,2,1,3,7]=>110100=>001011
[2,6,1,5,4,7,3]=>[5,4,7,6,2,1,3]=>110101=>001010
[2,6,1,5,7,3,4]=>[7,5,2,1,3,6,4]=>110110=>001001
[2,6,1,5,7,4,3]=>[7,5,4,6,2,1,3]=>110110=>001001
[2,6,1,7,3,4,5]=>[7,2,1,3,6,4,5]=>110100=>001011
[2,6,1,7,3,5,4]=>[7,2,1,3,5,6,4]=>110100=>001011
[2,6,1,7,4,3,5]=>[7,4,6,2,1,3,5]=>110100=>001011
[2,6,1,7,4,5,3]=>[7,4,5,6,2,1,3]=>110100=>001011
[2,6,1,7,5,3,4]=>[5,7,2,1,3,6,4]=>110100=>001011
[2,6,1,7,5,4,3]=>[5,7,4,6,2,1,3]=>110100=>001011
[2,6,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>110000=>001111
[2,6,3,1,4,7,5]=>[3,7,6,2,1,4,5]=>110001=>001110
[2,6,3,1,5,4,7]=>[3,5,6,2,1,4,7]=>110000=>001111
[2,6,3,1,5,7,4]=>[3,5,7,6,2,1,4]=>110001=>001110
[2,6,3,1,7,4,5]=>[3,7,2,1,4,6,5]=>110010=>001101
[2,6,3,1,7,5,4]=>[3,7,5,6,2,1,4]=>110010=>001101
[2,6,3,4,1,5,7]=>[3,4,6,2,1,5,7]=>110000=>001111
[2,6,3,4,1,7,5]=>[3,4,7,6,2,1,5]=>110001=>001110
[2,6,3,4,5,1,7]=>[3,4,5,6,2,1,7]=>110000=>001111
[2,6,3,4,5,7,1]=>[3,4,5,7,6,2,1]=>110001=>001110
[2,6,3,4,7,1,5]=>[3,4,7,2,1,6,5]=>110010=>001101
[2,6,3,4,7,5,1]=>[3,4,7,5,6,2,1]=>110010=>001101
[2,6,3,5,1,4,7]=>[3,5,2,1,6,4,7]=>110100=>001011
[2,6,3,5,1,7,4]=>[3,5,2,1,7,6,4]=>110101=>001010
[2,6,3,5,4,1,7]=>[3,5,4,6,2,1,7]=>110100=>001011
[2,6,3,5,4,7,1]=>[3,5,4,7,6,2,1]=>110101=>001010
[2,6,3,5,7,1,4]=>[3,7,5,2,1,6,4]=>110110=>001001
[2,6,3,5,7,4,1]=>[3,7,5,4,6,2,1]=>110110=>001001
[2,6,3,7,1,4,5]=>[3,7,2,1,6,4,5]=>110100=>001011
[2,6,3,7,1,5,4]=>[3,7,2,1,5,6,4]=>110100=>001011
[2,6,3,7,4,1,5]=>[3,7,4,6,2,1,5]=>110100=>001011
[2,6,3,7,4,5,1]=>[3,7,4,5,6,2,1]=>110100=>001011
[2,6,3,7,5,1,4]=>[3,5,7,2,1,6,4]=>110100=>001011
[2,6,3,7,5,4,1]=>[3,5,7,4,6,2,1]=>110100=>001011
[2,6,4,1,3,5,7]=>[4,2,1,6,3,5,7]=>111000=>000111
[2,6,4,1,3,7,5]=>[4,2,1,7,6,3,5]=>111001=>000110
[2,6,4,1,5,3,7]=>[4,2,1,5,6,3,7]=>111000=>000111
[2,6,4,1,5,7,3]=>[4,2,1,5,7,6,3]=>111001=>000110
[2,6,4,1,7,3,5]=>[4,2,1,7,3,6,5]=>111010=>000101
[2,6,4,1,7,5,3]=>[4,2,1,7,5,6,3]=>111010=>000101
[2,6,4,3,1,5,7]=>[4,3,6,2,1,5,7]=>111000=>000111
[2,6,4,3,1,7,5]=>[4,3,7,6,2,1,5]=>111001=>000110
[2,6,4,3,5,1,7]=>[4,3,5,6,2,1,7]=>111000=>000111
[2,6,4,3,5,7,1]=>[4,3,5,7,6,2,1]=>111001=>000110
[2,6,4,3,7,1,5]=>[4,3,7,2,1,6,5]=>111010=>000101
[2,6,4,3,7,5,1]=>[4,3,7,5,6,2,1]=>111010=>000101
[2,6,4,5,1,3,7]=>[5,4,2,1,6,3,7]=>111100=>000011
[2,6,4,5,1,7,3]=>[5,4,2,1,7,6,3]=>111101=>000010
[2,6,4,5,3,1,7]=>[5,4,3,6,2,1,7]=>111100=>000011
[2,6,4,5,3,7,1]=>[5,4,3,7,6,2,1]=>111101=>000010
[2,6,4,5,7,1,3]=>[7,5,4,2,1,6,3]=>111110=>000001
[2,6,4,5,7,3,1]=>[7,5,4,3,6,2,1]=>111110=>000001
[2,6,4,7,1,3,5]=>[7,4,2,1,6,3,5]=>111100=>000011
[2,6,4,7,1,5,3]=>[7,4,2,1,5,6,3]=>111100=>000011
[2,6,4,7,3,1,5]=>[7,4,3,6,2,1,5]=>111100=>000011
[2,6,4,7,3,5,1]=>[7,4,3,5,6,2,1]=>111100=>000011
[2,6,4,7,5,1,3]=>[5,7,4,2,1,6,3]=>111100=>000011
[2,6,4,7,5,3,1]=>[5,7,4,3,6,2,1]=>111100=>000011
[2,6,5,1,3,4,7]=>[5,2,1,6,3,4,7]=>111000=>000111
[2,6,5,1,3,7,4]=>[5,2,1,7,6,3,4]=>111001=>000110
[2,6,5,1,4,3,7]=>[5,2,1,4,6,3,7]=>111000=>000111
[2,6,5,1,4,7,3]=>[5,2,1,4,7,6,3]=>111001=>000110
[2,6,5,1,7,3,4]=>[7,5,2,1,6,3,4]=>111010=>000101
[2,6,5,1,7,4,3]=>[7,5,2,1,4,6,3]=>111010=>000101
[2,6,5,3,1,4,7]=>[5,3,6,2,1,4,7]=>111000=>000111
[2,6,5,3,1,7,4]=>[5,3,7,6,2,1,4]=>111001=>000110
[2,6,5,3,4,1,7]=>[5,3,4,6,2,1,7]=>111000=>000111
[2,6,5,3,4,7,1]=>[5,3,4,7,6,2,1]=>111001=>000110
[2,6,5,3,7,1,4]=>[7,5,3,6,2,1,4]=>111010=>000101
[2,6,5,3,7,4,1]=>[7,5,3,4,6,2,1]=>111010=>000101
[2,6,5,4,1,3,7]=>[4,5,2,1,6,3,7]=>111000=>000111
[2,6,5,4,1,7,3]=>[4,5,2,1,7,6,3]=>111001=>000110
[2,6,5,4,3,1,7]=>[4,5,3,6,2,1,7]=>111000=>000111
[2,6,5,4,3,7,1]=>[4,5,3,7,6,2,1]=>111001=>000110
[2,6,5,4,7,1,3]=>[4,7,5,2,1,6,3]=>111010=>000101
[2,6,5,4,7,3,1]=>[4,7,5,3,6,2,1]=>111010=>000101
[2,6,5,7,1,3,4]=>[7,2,1,5,3,6,4]=>111100=>000011
[2,6,5,7,1,4,3]=>[7,2,1,5,4,6,3]=>111100=>000011
[2,6,5,7,3,1,4]=>[7,3,5,2,1,6,4]=>111100=>000011
[2,6,5,7,3,4,1]=>[7,3,5,4,6,2,1]=>111100=>000011
[2,6,5,7,4,1,3]=>[7,4,5,2,1,6,3]=>111100=>000011
[2,6,5,7,4,3,1]=>[7,4,5,3,6,2,1]=>111100=>000011
[2,6,7,1,3,4,5]=>[7,2,1,6,3,4,5]=>111000=>000111
[2,6,7,1,3,5,4]=>[7,2,1,5,6,3,4]=>111000=>000111
[2,6,7,1,4,3,5]=>[7,2,1,4,6,3,5]=>111000=>000111
[2,6,7,1,4,5,3]=>[7,2,1,4,5,6,3]=>111000=>000111
[2,6,7,1,5,3,4]=>[5,7,2,1,6,3,4]=>111000=>000111
[2,6,7,1,5,4,3]=>[5,7,2,1,4,6,3]=>111000=>000111
[2,6,7,3,1,4,5]=>[7,3,6,2,1,4,5]=>111000=>000111
[2,6,7,3,1,5,4]=>[7,3,5,6,2,1,4]=>111000=>000111
[2,6,7,3,4,1,5]=>[7,3,4,6,2,1,5]=>111000=>000111
[2,6,7,3,4,5,1]=>[7,3,4,5,6,2,1]=>111000=>000111
[2,6,7,3,5,1,4]=>[5,7,3,6,2,1,4]=>111000=>000111
[2,6,7,3,5,4,1]=>[5,7,3,4,6,2,1]=>111000=>000111
[2,6,7,4,1,3,5]=>[4,7,2,1,6,3,5]=>111000=>000111
[2,6,7,4,1,5,3]=>[4,7,2,1,5,6,3]=>111000=>000111
[2,6,7,4,3,1,5]=>[4,7,3,6,2,1,5]=>111000=>000111
[2,6,7,4,3,5,1]=>[4,7,3,5,6,2,1]=>111000=>000111
[2,6,7,4,5,1,3]=>[4,5,7,2,1,6,3]=>111000=>000111
[2,6,7,4,5,3,1]=>[4,5,7,3,6,2,1]=>111000=>000111
[2,6,7,5,1,3,4]=>[5,2,1,7,3,6,4]=>111100=>000011
[2,6,7,5,1,4,3]=>[5,2,1,7,4,6,3]=>111100=>000011
[2,6,7,5,3,1,4]=>[5,3,7,2,1,6,4]=>111100=>000011
[2,6,7,5,3,4,1]=>[5,3,7,4,6,2,1]=>111100=>000011
[2,6,7,5,4,1,3]=>[5,4,7,2,1,6,3]=>111100=>000011
[2,6,7,5,4,3,1]=>[5,4,7,3,6,2,1]=>111100=>000011
[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>110000=>001111
[2,7,1,3,4,6,5]=>[6,7,2,1,3,4,5]=>110000=>001111
[2,7,1,3,5,4,6]=>[5,7,2,1,3,4,6]=>110000=>001111
[2,7,1,3,5,6,4]=>[5,6,7,2,1,3,4]=>110000=>001111
[2,7,1,3,6,4,5]=>[6,2,1,3,4,7,5]=>110010=>001101
[2,7,1,3,6,5,4]=>[6,5,7,2,1,3,4]=>110010=>001101
[2,7,1,4,3,5,6]=>[4,7,2,1,3,5,6]=>110000=>001111
[2,7,1,4,3,6,5]=>[4,6,7,2,1,3,5]=>110000=>001111
[2,7,1,4,5,3,6]=>[4,5,7,2,1,3,6]=>110000=>001111
[2,7,1,4,5,6,3]=>[4,5,6,7,2,1,3]=>110000=>001111
[2,7,1,4,6,3,5]=>[4,6,2,1,3,7,5]=>110010=>001101
[2,7,1,4,6,5,3]=>[4,6,5,7,2,1,3]=>110010=>001101
[2,7,1,5,3,4,6]=>[5,2,1,3,7,4,6]=>110100=>001011
[2,7,1,5,3,6,4]=>[5,2,1,3,6,7,4]=>110100=>001011
[2,7,1,5,4,3,6]=>[5,4,7,2,1,3,6]=>110100=>001011
[2,7,1,5,4,6,3]=>[5,4,6,7,2,1,3]=>110100=>001011
[2,7,1,5,6,3,4]=>[6,5,2,1,3,7,4]=>110110=>001001
[2,7,1,5,6,4,3]=>[6,5,4,7,2,1,3]=>110110=>001001
[2,7,1,6,3,4,5]=>[6,2,1,3,7,4,5]=>110100=>001011
[2,7,1,6,3,5,4]=>[6,2,1,3,5,7,4]=>110100=>001011
[2,7,1,6,4,3,5]=>[6,4,7,2,1,3,5]=>110100=>001011
[2,7,1,6,4,5,3]=>[6,4,5,7,2,1,3]=>110100=>001011
[2,7,1,6,5,3,4]=>[5,6,2,1,3,7,4]=>110100=>001011
[2,7,1,6,5,4,3]=>[5,6,4,7,2,1,3]=>110100=>001011
[2,7,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>110000=>001111
[2,7,3,1,4,6,5]=>[3,6,7,2,1,4,5]=>110000=>001111
[2,7,3,1,5,4,6]=>[3,5,7,2,1,4,6]=>110000=>001111
[2,7,3,1,5,6,4]=>[3,5,6,7,2,1,4]=>110000=>001111
[2,7,3,1,6,4,5]=>[3,6,2,1,4,7,5]=>110010=>001101
[2,7,3,1,6,5,4]=>[3,6,5,7,2,1,4]=>110010=>001101
[2,7,3,4,1,5,6]=>[3,4,7,2,1,5,6]=>110000=>001111
[2,7,3,4,1,6,5]=>[3,4,6,7,2,1,5]=>110000=>001111
[2,7,3,4,5,1,6]=>[3,4,5,7,2,1,6]=>110000=>001111
[2,7,3,4,5,6,1]=>[3,4,5,6,7,2,1]=>110000=>001111
[2,7,3,4,6,1,5]=>[3,4,6,2,1,7,5]=>110010=>001101
[2,7,3,4,6,5,1]=>[3,4,6,5,7,2,1]=>110010=>001101
[2,7,3,5,1,4,6]=>[3,5,2,1,7,4,6]=>110100=>001011
[2,7,3,5,1,6,4]=>[3,5,2,1,6,7,4]=>110100=>001011
[2,7,3,5,4,1,6]=>[3,5,4,7,2,1,6]=>110100=>001011
[2,7,3,5,4,6,1]=>[3,5,4,6,7,2,1]=>110100=>001011
[2,7,3,5,6,1,4]=>[3,6,5,2,1,7,4]=>110110=>001001
[2,7,3,5,6,4,1]=>[3,6,5,4,7,2,1]=>110110=>001001
[2,7,3,6,1,4,5]=>[3,6,2,1,7,4,5]=>110100=>001011
[2,7,3,6,1,5,4]=>[3,6,2,1,5,7,4]=>110100=>001011
[2,7,3,6,4,1,5]=>[3,6,4,7,2,1,5]=>110100=>001011
[2,7,3,6,4,5,1]=>[3,6,4,5,7,2,1]=>110100=>001011
[2,7,3,6,5,1,4]=>[3,5,6,2,1,7,4]=>110100=>001011
[2,7,3,6,5,4,1]=>[3,5,6,4,7,2,1]=>110100=>001011
[2,7,4,1,3,5,6]=>[4,2,1,7,3,5,6]=>111000=>000111
[2,7,4,1,3,6,5]=>[4,2,1,6,7,3,5]=>111000=>000111
[2,7,4,1,5,3,6]=>[4,2,1,5,7,3,6]=>111000=>000111
[2,7,4,1,5,6,3]=>[4,2,1,5,6,7,3]=>111000=>000111
[2,7,4,1,6,3,5]=>[4,2,1,6,3,7,5]=>111010=>000101
[2,7,4,1,6,5,3]=>[4,2,1,6,5,7,3]=>111010=>000101
[2,7,4,3,1,5,6]=>[4,3,7,2,1,5,6]=>111000=>000111
[2,7,4,3,1,6,5]=>[4,3,6,7,2,1,5]=>111000=>000111
[2,7,4,3,5,1,6]=>[4,3,5,7,2,1,6]=>111000=>000111
[2,7,4,3,5,6,1]=>[4,3,5,6,7,2,1]=>111000=>000111
[2,7,4,3,6,1,5]=>[4,3,6,2,1,7,5]=>111010=>000101
[2,7,4,3,6,5,1]=>[4,3,6,5,7,2,1]=>111010=>000101
[2,7,4,5,1,3,6]=>[5,4,2,1,7,3,6]=>111100=>000011
[2,7,4,5,1,6,3]=>[5,4,2,1,6,7,3]=>111100=>000011
[2,7,4,5,3,1,6]=>[5,4,3,7,2,1,6]=>111100=>000011
[2,7,4,5,3,6,1]=>[5,4,3,6,7,2,1]=>111100=>000011
[2,7,4,5,6,1,3]=>[6,5,4,2,1,7,3]=>111110=>000001
[2,7,4,5,6,3,1]=>[6,5,4,3,7,2,1]=>111110=>000001
[2,7,4,6,1,3,5]=>[6,4,2,1,7,3,5]=>111100=>000011
[2,7,4,6,1,5,3]=>[6,4,2,1,5,7,3]=>111100=>000011
[2,7,4,6,3,1,5]=>[6,4,3,7,2,1,5]=>111100=>000011
[2,7,4,6,3,5,1]=>[6,4,3,5,7,2,1]=>111100=>000011
[2,7,4,6,5,1,3]=>[5,6,4,2,1,7,3]=>111100=>000011
[2,7,4,6,5,3,1]=>[5,6,4,3,7,2,1]=>111100=>000011
[2,7,5,1,3,4,6]=>[5,2,1,7,3,4,6]=>111000=>000111
[2,7,5,1,3,6,4]=>[5,2,1,6,7,3,4]=>111000=>000111
[2,7,5,1,4,3,6]=>[5,2,1,4,7,3,6]=>111000=>000111
[2,7,5,1,4,6,3]=>[5,2,1,4,6,7,3]=>111000=>000111
[2,7,5,1,6,3,4]=>[6,5,2,1,7,3,4]=>111010=>000101
[2,7,5,1,6,4,3]=>[6,5,2,1,4,7,3]=>111010=>000101
[2,7,5,3,1,4,6]=>[5,3,7,2,1,4,6]=>111000=>000111
[2,7,5,3,1,6,4]=>[5,3,6,7,2,1,4]=>111000=>000111
[2,7,5,3,4,1,6]=>[5,3,4,7,2,1,6]=>111000=>000111
[2,7,5,3,4,6,1]=>[5,3,4,6,7,2,1]=>111000=>000111
[2,7,5,3,6,1,4]=>[6,5,3,7,2,1,4]=>111010=>000101
[2,7,5,3,6,4,1]=>[6,5,3,4,7,2,1]=>111010=>000101
[2,7,5,4,1,3,6]=>[4,5,2,1,7,3,6]=>111000=>000111
[2,7,5,4,1,6,3]=>[4,5,2,1,6,7,3]=>111000=>000111
[2,7,5,4,3,1,6]=>[4,5,3,7,2,1,6]=>111000=>000111
[2,7,5,4,3,6,1]=>[4,5,3,6,7,2,1]=>111000=>000111
[2,7,5,4,6,1,3]=>[4,6,5,2,1,7,3]=>111010=>000101
[2,7,5,4,6,3,1]=>[4,6,5,3,7,2,1]=>111010=>000101
[2,7,5,6,1,3,4]=>[6,2,1,5,3,7,4]=>111100=>000011
[2,7,5,6,1,4,3]=>[6,2,1,5,4,7,3]=>111100=>000011
[2,7,5,6,3,1,4]=>[6,3,5,2,1,7,4]=>111100=>000011
[2,7,5,6,3,4,1]=>[6,3,5,4,7,2,1]=>111100=>000011
[2,7,5,6,4,1,3]=>[6,4,5,2,1,7,3]=>111100=>000011
[2,7,5,6,4,3,1]=>[6,4,5,3,7,2,1]=>111100=>000011
[2,7,6,1,3,4,5]=>[6,2,1,7,3,4,5]=>111000=>000111
[2,7,6,1,3,5,4]=>[6,2,1,5,7,3,4]=>111000=>000111
[2,7,6,1,4,3,5]=>[6,2,1,4,7,3,5]=>111000=>000111
[2,7,6,1,4,5,3]=>[6,2,1,4,5,7,3]=>111000=>000111
[2,7,6,1,5,3,4]=>[5,6,2,1,7,3,4]=>111000=>000111
[2,7,6,1,5,4,3]=>[5,6,2,1,4,7,3]=>111000=>000111
[2,7,6,3,1,4,5]=>[6,3,7,2,1,4,5]=>111000=>000111
[2,7,6,3,1,5,4]=>[6,3,5,7,2,1,4]=>111000=>000111
[2,7,6,3,4,1,5]=>[6,3,4,7,2,1,5]=>111000=>000111
[2,7,6,3,4,5,1]=>[6,3,4,5,7,2,1]=>111000=>000111
[2,7,6,3,5,1,4]=>[5,6,3,7,2,1,4]=>111000=>000111
[2,7,6,3,5,4,1]=>[5,6,3,4,7,2,1]=>111000=>000111
[2,7,6,4,1,3,5]=>[4,6,2,1,7,3,5]=>111000=>000111
[2,7,6,4,1,5,3]=>[4,6,2,1,5,7,3]=>111000=>000111
[2,7,6,4,3,1,5]=>[4,6,3,7,2,1,5]=>111000=>000111
[2,7,6,4,3,5,1]=>[4,6,3,5,7,2,1]=>111000=>000111
[2,7,6,4,5,1,3]=>[4,5,6,2,1,7,3]=>111000=>000111
[2,7,6,4,5,3,1]=>[4,5,6,3,7,2,1]=>111000=>000111
[2,7,6,5,1,3,4]=>[5,2,1,6,3,7,4]=>111100=>000011
[2,7,6,5,1,4,3]=>[5,2,1,6,4,7,3]=>111100=>000011
[2,7,6,5,3,1,4]=>[5,3,6,2,1,7,4]=>111100=>000011
[2,7,6,5,3,4,1]=>[5,3,6,4,7,2,1]=>111100=>000011
[2,7,6,5,4,1,3]=>[5,4,6,2,1,7,3]=>111100=>000011
[2,7,6,5,4,3,1]=>[5,4,6,3,7,2,1]=>111100=>000011
[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>100000=>011111
[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>100001=>011110
[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>100010=>011101
[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>100011=>011100
[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>100010=>011101
[3,1,2,4,7,6,5]=>[3,1,2,4,6,7,5]=>100010=>011101
[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>100100=>011011
[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>100101=>011010
[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>100110=>011001
[3,1,2,5,6,7,4]=>[3,1,2,7,6,5,4]=>100111=>011000
[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>100110=>011001
[3,1,2,5,7,6,4]=>[3,1,2,6,7,5,4]=>100110=>011001
[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>100100=>011011
[3,1,2,6,4,7,5]=>[3,1,2,7,6,4,5]=>100101=>011010
[3,1,2,6,5,4,7]=>[3,1,2,5,6,4,7]=>100100=>011011
[3,1,2,6,5,7,4]=>[3,1,2,5,7,6,4]=>100101=>011010
[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]=>100110=>011001
[3,1,2,6,7,5,4]=>[3,1,2,7,5,6,4]=>100110=>011001
[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>100100=>011011
[3,1,2,7,4,6,5]=>[3,1,2,6,7,4,5]=>100100=>011011
[3,1,2,7,5,4,6]=>[3,1,2,5,7,4,6]=>100100=>011011
[3,1,2,7,5,6,4]=>[3,1,2,5,6,7,4]=>100100=>011011
[3,1,2,7,6,4,5]=>[3,1,2,6,4,7,5]=>100110=>011001
[3,1,2,7,6,5,4]=>[3,1,2,6,5,7,4]=>100110=>011001
[3,1,4,2,5,6,7]=>[4,3,1,2,5,6,7]=>101000=>010111
[3,1,4,2,5,7,6]=>[4,3,1,2,5,7,6]=>101001=>010110
[3,1,4,2,6,5,7]=>[4,3,1,2,6,5,7]=>101010=>010101
[3,1,4,2,6,7,5]=>[4,3,1,2,7,6,5]=>101011=>010100
[3,1,4,2,7,5,6]=>[4,3,1,2,7,5,6]=>101010=>010101
[3,1,4,2,7,6,5]=>[4,3,1,2,6,7,5]=>101010=>010101
[3,1,4,5,2,6,7]=>[5,4,3,1,2,6,7]=>101100=>010011
[3,1,4,5,2,7,6]=>[5,4,3,1,2,7,6]=>101101=>010010
[3,1,4,5,6,2,7]=>[6,5,4,3,1,2,7]=>101110=>010001
[3,1,4,5,6,7,2]=>[7,6,5,4,3,1,2]=>101111=>010000
[3,1,4,5,7,2,6]=>[7,5,4,3,1,2,6]=>101110=>010001
[3,1,4,5,7,6,2]=>[6,7,5,4,3,1,2]=>101110=>010001
[3,1,4,6,2,5,7]=>[6,4,3,1,2,5,7]=>101100=>010011
[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>101101=>010010
[3,1,4,6,5,2,7]=>[5,6,4,3,1,2,7]=>101100=>010011
[3,1,4,6,5,7,2]=>[5,7,6,4,3,1,2]=>101101=>010010
[3,1,4,6,7,2,5]=>[7,4,3,1,2,6,5]=>101110=>010001
[3,1,4,6,7,5,2]=>[7,5,6,4,3,1,2]=>101110=>010001
[3,1,4,7,2,5,6]=>[7,4,3,1,2,5,6]=>101100=>010011
[3,1,4,7,2,6,5]=>[6,7,4,3,1,2,5]=>101100=>010011
[3,1,4,7,5,2,6]=>[5,7,4,3,1,2,6]=>101100=>010011
[3,1,4,7,5,6,2]=>[5,6,7,4,3,1,2]=>101100=>010011
[3,1,4,7,6,2,5]=>[6,4,3,1,2,7,5]=>101110=>010001
[3,1,4,7,6,5,2]=>[6,5,7,4,3,1,2]=>101110=>010001
[3,1,5,2,4,6,7]=>[5,3,1,2,4,6,7]=>101000=>010111
[3,1,5,2,4,7,6]=>[5,3,1,2,4,7,6]=>101001=>010110
[3,1,5,2,6,4,7]=>[6,5,3,1,2,4,7]=>101010=>010101
[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>101011=>010100
[3,1,5,2,7,4,6]=>[7,5,3,1,2,4,6]=>101010=>010101
[3,1,5,2,7,6,4]=>[6,7,5,3,1,2,4]=>101010=>010101
[3,1,5,4,2,6,7]=>[4,5,3,1,2,6,7]=>101000=>010111
[3,1,5,4,2,7,6]=>[4,5,3,1,2,7,6]=>101001=>010110
[3,1,5,4,6,2,7]=>[4,6,5,3,1,2,7]=>101010=>010101
[3,1,5,4,6,7,2]=>[4,7,6,5,3,1,2]=>101011=>010100
[3,1,5,4,7,2,6]=>[4,7,5,3,1,2,6]=>101010=>010101
[3,1,5,4,7,6,2]=>[4,6,7,5,3,1,2]=>101010=>010101
[3,1,5,6,2,4,7]=>[6,3,1,2,5,4,7]=>101100=>010011
[3,1,5,6,2,7,4]=>[7,6,3,1,2,5,4]=>101101=>010010
[3,1,5,6,4,2,7]=>[6,4,5,3,1,2,7]=>101100=>010011
[3,1,5,6,4,7,2]=>[7,6,4,5,3,1,2]=>101101=>010010
[3,1,5,6,7,2,4]=>[7,3,1,2,6,5,4]=>101110=>010001
[3,1,5,6,7,4,2]=>[7,4,6,5,3,1,2]=>101110=>010001
[3,1,5,7,2,4,6]=>[7,3,1,2,5,4,6]=>101100=>010011
[3,1,5,7,2,6,4]=>[6,7,3,1,2,5,4]=>101100=>010011
[3,1,5,7,4,2,6]=>[7,4,5,3,1,2,6]=>101100=>010011
[3,1,5,7,4,6,2]=>[6,7,4,5,3,1,2]=>101100=>010011
[3,1,5,7,6,2,4]=>[6,3,1,2,7,5,4]=>101110=>010001
[3,1,5,7,6,4,2]=>[6,4,7,5,3,1,2]=>101110=>010001
[3,1,6,2,4,5,7]=>[6,3,1,2,4,5,7]=>101000=>010111
[3,1,6,2,4,7,5]=>[7,6,3,1,2,4,5]=>101001=>010110
[3,1,6,2,5,4,7]=>[5,6,3,1,2,4,7]=>101000=>010111
[3,1,6,2,5,7,4]=>[5,7,6,3,1,2,4]=>101001=>010110
[3,1,6,2,7,4,5]=>[7,3,1,2,4,6,5]=>101010=>010101
[3,1,6,2,7,5,4]=>[7,5,6,3,1,2,4]=>101010=>010101
[3,1,6,4,2,5,7]=>[4,6,3,1,2,5,7]=>101000=>010111
[3,1,6,4,2,7,5]=>[4,7,6,3,1,2,5]=>101001=>010110
[3,1,6,4,5,2,7]=>[4,5,6,3,1,2,7]=>101000=>010111
[3,1,6,4,5,7,2]=>[4,5,7,6,3,1,2]=>101001=>010110
[3,1,6,4,7,2,5]=>[4,7,3,1,2,6,5]=>101010=>010101
[3,1,6,4,7,5,2]=>[4,7,5,6,3,1,2]=>101010=>010101
[3,1,6,5,2,4,7]=>[5,3,1,2,6,4,7]=>101100=>010011
[3,1,6,5,2,7,4]=>[5,3,1,2,7,6,4]=>101101=>010010
[3,1,6,5,4,2,7]=>[5,4,6,3,1,2,7]=>101100=>010011
[3,1,6,5,4,7,2]=>[5,4,7,6,3,1,2]=>101101=>010010
[3,1,6,5,7,2,4]=>[7,5,3,1,2,6,4]=>101110=>010001
[3,1,6,5,7,4,2]=>[7,5,4,6,3,1,2]=>101110=>010001
[3,1,6,7,2,4,5]=>[7,3,1,2,6,4,5]=>101100=>010011
[3,1,6,7,2,5,4]=>[7,3,1,2,5,6,4]=>101100=>010011
[3,1,6,7,4,2,5]=>[7,4,6,3,1,2,5]=>101100=>010011
[3,1,6,7,4,5,2]=>[7,4,5,6,3,1,2]=>101100=>010011
[3,1,6,7,5,2,4]=>[5,7,3,1,2,6,4]=>101100=>010011
[3,1,6,7,5,4,2]=>[5,7,4,6,3,1,2]=>101100=>010011
[3,1,7,2,4,5,6]=>[7,3,1,2,4,5,6]=>101000=>010111
[3,1,7,2,4,6,5]=>[6,7,3,1,2,4,5]=>101000=>010111
[3,1,7,2,5,4,6]=>[5,7,3,1,2,4,6]=>101000=>010111
[3,1,7,2,5,6,4]=>[5,6,7,3,1,2,4]=>101000=>010111
[3,1,7,2,6,4,5]=>[6,3,1,2,4,7,5]=>101010=>010101
[3,1,7,2,6,5,4]=>[6,5,7,3,1,2,4]=>101010=>010101
[3,1,7,4,2,5,6]=>[4,7,3,1,2,5,6]=>101000=>010111
[3,1,7,4,2,6,5]=>[4,6,7,3,1,2,5]=>101000=>010111
[3,1,7,4,5,2,6]=>[4,5,7,3,1,2,6]=>101000=>010111
[3,1,7,4,5,6,2]=>[4,5,6,7,3,1,2]=>101000=>010111
[3,1,7,4,6,2,5]=>[4,6,3,1,2,7,5]=>101010=>010101
[3,1,7,4,6,5,2]=>[4,6,5,7,3,1,2]=>101010=>010101
[3,1,7,5,2,4,6]=>[5,3,1,2,7,4,6]=>101100=>010011
[3,1,7,5,2,6,4]=>[5,3,1,2,6,7,4]=>101100=>010011
[3,1,7,5,4,2,6]=>[5,4,7,3,1,2,6]=>101100=>010011
[3,1,7,5,4,6,2]=>[5,4,6,7,3,1,2]=>101100=>010011
[3,1,7,5,6,2,4]=>[6,5,3,1,2,7,4]=>101110=>010001
[3,1,7,5,6,4,2]=>[6,5,4,7,3,1,2]=>101110=>010001
[3,1,7,6,2,4,5]=>[6,3,1,2,7,4,5]=>101100=>010011
[3,1,7,6,2,5,4]=>[6,3,1,2,5,7,4]=>101100=>010011
[3,1,7,6,4,2,5]=>[6,4,7,3,1,2,5]=>101100=>010011
[3,1,7,6,4,5,2]=>[6,4,5,7,3,1,2]=>101100=>010011
[3,1,7,6,5,2,4]=>[5,6,3,1,2,7,4]=>101100=>010011
[3,1,7,6,5,4,2]=>[5,6,4,7,3,1,2]=>101100=>010011
[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>100000=>011111
[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>100001=>011110
[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>100010=>011101
[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>100011=>011100
[3,2,1,4,7,5,6]=>[2,3,1,4,7,5,6]=>100010=>011101
[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>100010=>011101
[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>100100=>011011
[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>100101=>011010
[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>100110=>011001
[3,2,1,5,6,7,4]=>[2,3,1,7,6,5,4]=>100111=>011000
[3,2,1,5,7,4,6]=>[2,3,1,7,5,4,6]=>100110=>011001
[3,2,1,5,7,6,4]=>[2,3,1,6,7,5,4]=>100110=>011001
[3,2,1,6,4,5,7]=>[2,3,1,6,4,5,7]=>100100=>011011
[3,2,1,6,4,7,5]=>[2,3,1,7,6,4,5]=>100101=>011010
[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>100100=>011011
[3,2,1,6,5,7,4]=>[2,3,1,5,7,6,4]=>100101=>011010
[3,2,1,6,7,4,5]=>[2,3,1,7,4,6,5]=>100110=>011001
[3,2,1,6,7,5,4]=>[2,3,1,7,5,6,4]=>100110=>011001
[3,2,1,7,4,5,6]=>[2,3,1,7,4,5,6]=>100100=>011011
[3,2,1,7,4,6,5]=>[2,3,1,6,7,4,5]=>100100=>011011
[3,2,1,7,5,4,6]=>[2,3,1,5,7,4,6]=>100100=>011011
[3,2,1,7,5,6,4]=>[2,3,1,5,6,7,4]=>100100=>011011
[3,2,1,7,6,4,5]=>[2,3,1,6,4,7,5]=>100110=>011001
[3,2,1,7,6,5,4]=>[2,3,1,6,5,7,4]=>100110=>011001
[3,2,4,1,5,6,7]=>[2,4,3,1,5,6,7]=>101000=>010111
[3,2,4,1,5,7,6]=>[2,4,3,1,5,7,6]=>101001=>010110
[3,2,4,1,6,5,7]=>[2,4,3,1,6,5,7]=>101010=>010101
[3,2,4,1,6,7,5]=>[2,4,3,1,7,6,5]=>101011=>010100
[3,2,4,1,7,5,6]=>[2,4,3,1,7,5,6]=>101010=>010101
[3,2,4,1,7,6,5]=>[2,4,3,1,6,7,5]=>101010=>010101
[3,2,4,5,1,6,7]=>[2,5,4,3,1,6,7]=>101100=>010011
[3,2,4,5,1,7,6]=>[2,5,4,3,1,7,6]=>101101=>010010
[3,2,4,5,6,1,7]=>[2,6,5,4,3,1,7]=>101110=>010001
[3,2,4,5,6,7,1]=>[2,7,6,5,4,3,1]=>101111=>010000
[3,2,4,5,7,1,6]=>[2,7,5,4,3,1,6]=>101110=>010001
[3,2,4,5,7,6,1]=>[2,6,7,5,4,3,1]=>101110=>010001
[3,2,4,6,1,5,7]=>[2,6,4,3,1,5,7]=>101100=>010011
[3,2,4,6,1,7,5]=>[2,7,6,4,3,1,5]=>101101=>010010
[3,2,4,6,5,1,7]=>[2,5,6,4,3,1,7]=>101100=>010011
[3,2,4,6,5,7,1]=>[2,5,7,6,4,3,1]=>101101=>010010
[3,2,4,6,7,1,5]=>[2,7,4,3,1,6,5]=>101110=>010001
[3,2,4,6,7,5,1]=>[2,7,5,6,4,3,1]=>101110=>010001
[3,2,4,7,1,5,6]=>[2,7,4,3,1,5,6]=>101100=>010011
[3,2,4,7,1,6,5]=>[2,6,7,4,3,1,5]=>101100=>010011
[3,2,4,7,5,1,6]=>[2,5,7,4,3,1,6]=>101100=>010011
[3,2,4,7,5,6,1]=>[2,5,6,7,4,3,1]=>101100=>010011
[3,2,4,7,6,1,5]=>[2,6,4,3,1,7,5]=>101110=>010001
[3,2,4,7,6,5,1]=>[2,6,5,7,4,3,1]=>101110=>010001
[3,2,5,1,4,6,7]=>[2,5,3,1,4,6,7]=>101000=>010111
[3,2,5,1,4,7,6]=>[2,5,3,1,4,7,6]=>101001=>010110
[3,2,5,1,6,4,7]=>[2,6,5,3,1,4,7]=>101010=>010101
[3,2,5,1,6,7,4]=>[2,7,6,5,3,1,4]=>101011=>010100
[3,2,5,1,7,4,6]=>[2,7,5,3,1,4,6]=>101010=>010101
[3,2,5,1,7,6,4]=>[2,6,7,5,3,1,4]=>101010=>010101
[3,2,5,4,1,6,7]=>[2,4,5,3,1,6,7]=>101000=>010111
[3,2,5,4,1,7,6]=>[2,4,5,3,1,7,6]=>101001=>010110
[3,2,5,4,6,1,7]=>[2,4,6,5,3,1,7]=>101010=>010101
[3,2,5,4,6,7,1]=>[2,4,7,6,5,3,1]=>101011=>010100
[3,2,5,4,7,1,6]=>[2,4,7,5,3,1,6]=>101010=>010101
[3,2,5,4,7,6,1]=>[2,4,6,7,5,3,1]=>101010=>010101
[3,2,5,6,1,4,7]=>[2,6,3,1,5,4,7]=>101100=>010011
[3,2,5,6,1,7,4]=>[2,7,6,3,1,5,4]=>101101=>010010
[3,2,5,6,4,1,7]=>[2,6,4,5,3,1,7]=>101100=>010011
[3,2,5,6,4,7,1]=>[2,7,6,4,5,3,1]=>101101=>010010
[3,2,5,6,7,1,4]=>[2,7,3,1,6,5,4]=>101110=>010001
[3,2,5,6,7,4,1]=>[2,7,4,6,5,3,1]=>101110=>010001
[3,2,5,7,1,4,6]=>[2,7,3,1,5,4,6]=>101100=>010011
[3,2,5,7,1,6,4]=>[2,6,7,3,1,5,4]=>101100=>010011
[3,2,5,7,4,1,6]=>[2,7,4,5,3,1,6]=>101100=>010011
[3,2,5,7,4,6,1]=>[2,6,7,4,5,3,1]=>101100=>010011
[3,2,5,7,6,1,4]=>[2,6,3,1,7,5,4]=>101110=>010001
[3,2,5,7,6,4,1]=>[2,6,4,7,5,3,1]=>101110=>010001
[3,2,6,1,4,5,7]=>[2,6,3,1,4,5,7]=>101000=>010111
[3,2,6,1,4,7,5]=>[2,7,6,3,1,4,5]=>101001=>010110
[3,2,6,1,5,4,7]=>[2,5,6,3,1,4,7]=>101000=>010111
[3,2,6,1,5,7,4]=>[2,5,7,6,3,1,4]=>101001=>010110
[3,2,6,1,7,4,5]=>[2,7,3,1,4,6,5]=>101010=>010101
[3,2,6,1,7,5,4]=>[2,7,5,6,3,1,4]=>101010=>010101
[3,2,6,4,1,5,7]=>[2,4,6,3,1,5,7]=>101000=>010111
[3,2,6,4,1,7,5]=>[2,4,7,6,3,1,5]=>101001=>010110
[3,2,6,4,5,1,7]=>[2,4,5,6,3,1,7]=>101000=>010111
[3,2,6,4,5,7,1]=>[2,4,5,7,6,3,1]=>101001=>010110
[3,2,6,4,7,1,5]=>[2,4,7,3,1,6,5]=>101010=>010101
[3,2,6,4,7,5,1]=>[2,4,7,5,6,3,1]=>101010=>010101
[3,2,6,5,1,4,7]=>[2,5,3,1,6,4,7]=>101100=>010011
[3,2,6,5,1,7,4]=>[2,5,3,1,7,6,4]=>101101=>010010
[3,2,6,5,4,1,7]=>[2,5,4,6,3,1,7]=>101100=>010011
[3,2,6,5,4,7,1]=>[2,5,4,7,6,3,1]=>101101=>010010
[3,2,6,5,7,1,4]=>[2,7,5,3,1,6,4]=>101110=>010001
[3,2,6,5,7,4,1]=>[2,7,5,4,6,3,1]=>101110=>010001
[3,2,6,7,1,4,5]=>[2,7,3,1,6,4,5]=>101100=>010011
[3,2,6,7,1,5,4]=>[2,7,3,1,5,6,4]=>101100=>010011
[3,2,6,7,4,1,5]=>[2,7,4,6,3,1,5]=>101100=>010011
[3,2,6,7,4,5,1]=>[2,7,4,5,6,3,1]=>101100=>010011
[3,2,6,7,5,1,4]=>[2,5,7,3,1,6,4]=>101100=>010011
[3,2,6,7,5,4,1]=>[2,5,7,4,6,3,1]=>101100=>010011
[3,2,7,1,4,5,6]=>[2,7,3,1,4,5,6]=>101000=>010111
[3,2,7,1,4,6,5]=>[2,6,7,3,1,4,5]=>101000=>010111
[3,2,7,1,5,4,6]=>[2,5,7,3,1,4,6]=>101000=>010111
[3,2,7,1,5,6,4]=>[2,5,6,7,3,1,4]=>101000=>010111
[3,2,7,1,6,4,5]=>[2,6,3,1,4,7,5]=>101010=>010101
[3,2,7,1,6,5,4]=>[2,6,5,7,3,1,4]=>101010=>010101
[3,2,7,4,1,5,6]=>[2,4,7,3,1,5,6]=>101000=>010111
[3,2,7,4,1,6,5]=>[2,4,6,7,3,1,5]=>101000=>010111
[3,2,7,4,5,1,6]=>[2,4,5,7,3,1,6]=>101000=>010111
[3,2,7,4,5,6,1]=>[2,4,5,6,7,3,1]=>101000=>010111
[3,2,7,4,6,1,5]=>[2,4,6,3,1,7,5]=>101010=>010101
[3,2,7,4,6,5,1]=>[2,4,6,5,7,3,1]=>101010=>010101
[3,2,7,5,1,4,6]=>[2,5,3,1,7,4,6]=>101100=>010011
[3,2,7,5,1,6,4]=>[2,5,3,1,6,7,4]=>101100=>010011
[3,2,7,5,4,1,6]=>[2,5,4,7,3,1,6]=>101100=>010011
[3,2,7,5,4,6,1]=>[2,5,4,6,7,3,1]=>101100=>010011
[3,2,7,5,6,1,4]=>[2,6,5,3,1,7,4]=>101110=>010001
[3,2,7,5,6,4,1]=>[2,6,5,4,7,3,1]=>101110=>010001
[3,2,7,6,1,4,5]=>[2,6,3,1,7,4,5]=>101100=>010011
[3,2,7,6,1,5,4]=>[2,6,3,1,5,7,4]=>101100=>010011
[3,2,7,6,4,1,5]=>[2,6,4,7,3,1,5]=>101100=>010011
[3,2,7,6,4,5,1]=>[2,6,4,5,7,3,1]=>101100=>010011
[3,2,7,6,5,1,4]=>[2,5,6,3,1,7,4]=>101100=>010011
[3,2,7,6,5,4,1]=>[2,5,6,4,7,3,1]=>101100=>010011
[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>110000=>001111
[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]=>110001=>001110
[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]=>110010=>001101
[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]=>110011=>001100
[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]=>110010=>001101
[3,4,1,2,7,6,5]=>[4,1,3,2,6,7,5]=>110010=>001101
[3,4,1,5,2,6,7]=>[5,4,1,3,2,6,7]=>110100=>001011
[3,4,1,5,2,7,6]=>[5,4,1,3,2,7,6]=>110101=>001010
[3,4,1,5,6,2,7]=>[6,5,4,1,3,2,7]=>110110=>001001
[3,4,1,5,6,7,2]=>[7,6,5,4,1,3,2]=>110111=>001000
[3,4,1,5,7,2,6]=>[7,5,4,1,3,2,6]=>110110=>001001
[3,4,1,5,7,6,2]=>[6,7,5,4,1,3,2]=>110110=>001001
[3,4,1,6,2,5,7]=>[6,4,1,3,2,5,7]=>110100=>001011
[3,4,1,6,2,7,5]=>[7,6,4,1,3,2,5]=>110101=>001010
[3,4,1,6,5,2,7]=>[5,6,4,1,3,2,7]=>110100=>001011
[3,4,1,6,5,7,2]=>[5,7,6,4,1,3,2]=>110101=>001010
[3,4,1,6,7,2,5]=>[7,4,1,3,2,6,5]=>110110=>001001
[3,4,1,6,7,5,2]=>[7,5,6,4,1,3,2]=>110110=>001001
[3,4,1,7,2,5,6]=>[7,4,1,3,2,5,6]=>110100=>001011
[3,4,1,7,2,6,5]=>[6,7,4,1,3,2,5]=>110100=>001011
[3,4,1,7,5,2,6]=>[5,7,4,1,3,2,6]=>110100=>001011
[3,4,1,7,5,6,2]=>[5,6,7,4,1,3,2]=>110100=>001011
[3,4,1,7,6,2,5]=>[6,4,1,3,2,7,5]=>110110=>001001
[3,4,1,7,6,5,2]=>[6,5,7,4,1,3,2]=>110110=>001001
[3,4,2,1,5,6,7]=>[4,2,3,1,5,6,7]=>110000=>001111
[3,4,2,1,5,7,6]=>[4,2,3,1,5,7,6]=>110001=>001110
[3,4,2,1,6,5,7]=>[4,2,3,1,6,5,7]=>110010=>001101
[3,4,2,1,6,7,5]=>[4,2,3,1,7,6,5]=>110011=>001100
[3,4,2,1,7,5,6]=>[4,2,3,1,7,5,6]=>110010=>001101
[3,4,2,1,7,6,5]=>[4,2,3,1,6,7,5]=>110010=>001101
[3,4,2,5,1,6,7]=>[5,4,2,3,1,6,7]=>110100=>001011
[3,4,2,5,1,7,6]=>[5,4,2,3,1,7,6]=>110101=>001010
[3,4,2,5,6,1,7]=>[6,5,4,2,3,1,7]=>110110=>001001
[3,4,2,5,6,7,1]=>[7,6,5,4,2,3,1]=>110111=>001000
[3,4,2,5,7,1,6]=>[7,5,4,2,3,1,6]=>110110=>001001
[3,4,2,5,7,6,1]=>[6,7,5,4,2,3,1]=>110110=>001001
[3,4,2,6,1,5,7]=>[6,4,2,3,1,5,7]=>110100=>001011
[3,4,2,6,1,7,5]=>[7,6,4,2,3,1,5]=>110101=>001010
[3,4,2,6,5,1,7]=>[5,6,4,2,3,1,7]=>110100=>001011
[3,4,2,6,5,7,1]=>[5,7,6,4,2,3,1]=>110101=>001010
[3,4,2,6,7,1,5]=>[7,4,2,3,1,6,5]=>110110=>001001
[3,4,2,6,7,5,1]=>[7,5,6,4,2,3,1]=>110110=>001001
[3,4,2,7,1,5,6]=>[7,4,2,3,1,5,6]=>110100=>001011
[3,4,2,7,1,6,5]=>[6,7,4,2,3,1,5]=>110100=>001011
[3,4,2,7,5,1,6]=>[5,7,4,2,3,1,6]=>110100=>001011
[3,4,2,7,5,6,1]=>[5,6,7,4,2,3,1]=>110100=>001011
[3,4,2,7,6,1,5]=>[6,4,2,3,1,7,5]=>110110=>001001
[3,4,2,7,6,5,1]=>[6,5,7,4,2,3,1]=>110110=>001001
[3,4,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>111000=>000111
[3,4,5,1,2,7,6]=>[5,1,4,3,2,7,6]=>111001=>000110
[3,4,5,1,6,2,7]=>[6,5,1,4,3,2,7]=>111010=>000101
[3,4,5,1,6,7,2]=>[7,6,5,1,4,3,2]=>111011=>000100
[3,4,5,1,7,2,6]=>[7,5,1,4,3,2,6]=>111010=>000101
[3,4,5,1,7,6,2]=>[6,7,5,1,4,3,2]=>111010=>000101
[3,4,5,2,1,6,7]=>[5,2,4,3,1,6,7]=>111000=>000111
[3,4,5,2,1,7,6]=>[5,2,4,3,1,7,6]=>111001=>000110
[3,4,5,2,6,1,7]=>[6,5,2,4,3,1,7]=>111010=>000101
[3,4,5,2,6,7,1]=>[7,6,5,2,4,3,1]=>111011=>000100
[3,4,5,2,7,1,6]=>[7,5,2,4,3,1,6]=>111010=>000101
[3,4,5,2,7,6,1]=>[6,7,5,2,4,3,1]=>111010=>000101
[3,4,5,6,1,2,7]=>[6,1,5,4,3,2,7]=>111100=>000011
[3,4,5,6,1,7,2]=>[7,6,1,5,4,3,2]=>111101=>000010
[3,4,5,6,2,1,7]=>[6,2,5,4,3,1,7]=>111100=>000011
[3,4,5,6,2,7,1]=>[7,6,2,5,4,3,1]=>111101=>000010
[3,4,5,6,7,1,2]=>[7,1,6,5,4,3,2]=>111110=>000001
[3,4,5,6,7,2,1]=>[7,2,6,5,4,3,1]=>111110=>000001
[3,4,5,7,1,2,6]=>[7,1,5,4,3,2,6]=>111100=>000011
[3,4,5,7,1,6,2]=>[6,7,1,5,4,3,2]=>111100=>000011
[3,4,5,7,2,1,6]=>[7,2,5,4,3,1,6]=>111100=>000011
[3,4,5,7,2,6,1]=>[6,7,2,5,4,3,1]=>111100=>000011
[3,4,5,7,6,1,2]=>[6,1,7,5,4,3,2]=>111110=>000001
[3,4,5,7,6,2,1]=>[6,2,7,5,4,3,1]=>111110=>000001
[3,4,6,1,2,5,7]=>[6,1,4,3,2,5,7]=>111000=>000111
[3,4,6,1,2,7,5]=>[7,6,1,4,3,2,5]=>111001=>000110
[3,4,6,1,5,2,7]=>[5,6,1,4,3,2,7]=>111000=>000111
[3,4,6,1,5,7,2]=>[5,7,6,1,4,3,2]=>111001=>000110
[3,4,6,1,7,2,5]=>[7,1,4,3,2,6,5]=>111010=>000101
[3,4,6,1,7,5,2]=>[7,5,6,1,4,3,2]=>111010=>000101
[3,4,6,2,1,5,7]=>[6,2,4,3,1,5,7]=>111000=>000111
[3,4,6,2,1,7,5]=>[7,6,2,4,3,1,5]=>111001=>000110
[3,4,6,2,5,1,7]=>[5,6,2,4,3,1,7]=>111000=>000111
[3,4,6,2,5,7,1]=>[5,7,6,2,4,3,1]=>111001=>000110
[3,4,6,2,7,1,5]=>[7,2,4,3,1,6,5]=>111010=>000101
[3,4,6,2,7,5,1]=>[7,5,6,2,4,3,1]=>111010=>000101
[3,4,6,5,1,2,7]=>[5,1,6,4,3,2,7]=>111100=>000011
[3,4,6,5,1,7,2]=>[5,1,7,6,4,3,2]=>111101=>000010
[3,4,6,5,2,1,7]=>[5,2,6,4,3,1,7]=>111100=>000011
[3,4,6,5,2,7,1]=>[5,2,7,6,4,3,1]=>111101=>000010
[3,4,6,5,7,1,2]=>[7,5,1,6,4,3,2]=>111110=>000001
[3,4,6,5,7,2,1]=>[7,5,2,6,4,3,1]=>111110=>000001
[3,4,6,7,1,2,5]=>[7,1,6,4,3,2,5]=>111100=>000011
[3,4,6,7,1,5,2]=>[7,1,5,6,4,3,2]=>111100=>000011
[3,4,6,7,2,1,5]=>[7,2,6,4,3,1,5]=>111100=>000011
[3,4,6,7,2,5,1]=>[7,2,5,6,4,3,1]=>111100=>000011
[3,4,6,7,5,1,2]=>[5,7,1,6,4,3,2]=>111100=>000011
[3,4,6,7,5,2,1]=>[5,7,2,6,4,3,1]=>111100=>000011
[3,4,7,1,2,5,6]=>[7,1,4,3,2,5,6]=>111000=>000111
[3,4,7,1,2,6,5]=>[6,7,1,4,3,2,5]=>111000=>000111
[3,4,7,1,5,2,6]=>[5,7,1,4,3,2,6]=>111000=>000111
[3,4,7,1,5,6,2]=>[5,6,7,1,4,3,2]=>111000=>000111
[3,4,7,1,6,2,5]=>[6,1,4,3,2,7,5]=>111010=>000101
[3,4,7,1,6,5,2]=>[6,5,7,1,4,3,2]=>111010=>000101
[3,4,7,2,1,5,6]=>[7,2,4,3,1,5,6]=>111000=>000111
[3,4,7,2,1,6,5]=>[6,7,2,4,3,1,5]=>111000=>000111
[3,4,7,2,5,1,6]=>[5,7,2,4,3,1,6]=>111000=>000111
[3,4,7,2,5,6,1]=>[5,6,7,2,4,3,1]=>111000=>000111
[3,4,7,2,6,1,5]=>[6,2,4,3,1,7,5]=>111010=>000101
[3,4,7,2,6,5,1]=>[6,5,7,2,4,3,1]=>111010=>000101
[3,4,7,5,1,2,6]=>[5,1,7,4,3,2,6]=>111100=>000011
[3,4,7,5,1,6,2]=>[5,1,6,7,4,3,2]=>111100=>000011
[3,4,7,5,2,1,6]=>[5,2,7,4,3,1,6]=>111100=>000011
[3,4,7,5,2,6,1]=>[5,2,6,7,4,3,1]=>111100=>000011
[3,4,7,5,6,1,2]=>[6,5,1,7,4,3,2]=>111110=>000001
[3,4,7,5,6,2,1]=>[6,5,2,7,4,3,1]=>111110=>000001
[3,4,7,6,1,2,5]=>[6,1,7,4,3,2,5]=>111100=>000011
[3,4,7,6,1,5,2]=>[6,1,5,7,4,3,2]=>111100=>000011
[3,4,7,6,2,1,5]=>[6,2,7,4,3,1,5]=>111100=>000011
[3,4,7,6,2,5,1]=>[6,2,5,7,4,3,1]=>111100=>000011
[3,4,7,6,5,1,2]=>[5,6,1,7,4,3,2]=>111100=>000011
[3,4,7,6,5,2,1]=>[5,6,2,7,4,3,1]=>111100=>000011
[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>110000=>001111
[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]=>110001=>001110
[3,5,1,2,6,4,7]=>[6,5,1,3,2,4,7]=>110010=>001101
[3,5,1,2,6,7,4]=>[7,6,5,1,3,2,4]=>110011=>001100
[3,5,1,2,7,4,6]=>[7,5,1,3,2,4,6]=>110010=>001101
[3,5,1,2,7,6,4]=>[6,7,5,1,3,2,4]=>110010=>001101
[3,5,1,4,2,6,7]=>[4,5,1,3,2,6,7]=>110000=>001111
[3,5,1,4,2,7,6]=>[4,5,1,3,2,7,6]=>110001=>001110
[3,5,1,4,6,2,7]=>[4,6,5,1,3,2,7]=>110010=>001101
[3,5,1,4,6,7,2]=>[4,7,6,5,1,3,2]=>110011=>001100
[3,5,1,4,7,2,6]=>[4,7,5,1,3,2,6]=>110010=>001101
[3,5,1,4,7,6,2]=>[4,6,7,5,1,3,2]=>110010=>001101
[3,5,1,6,2,4,7]=>[6,1,3,2,5,4,7]=>110100=>001011
[3,5,1,6,2,7,4]=>[7,6,1,3,2,5,4]=>110101=>001010
[3,5,1,6,4,2,7]=>[6,4,5,1,3,2,7]=>110100=>001011
[3,5,1,6,4,7,2]=>[7,6,4,5,1,3,2]=>110101=>001010
[3,5,1,6,7,2,4]=>[7,1,3,2,6,5,4]=>110110=>001001
[3,5,1,6,7,4,2]=>[7,4,6,5,1,3,2]=>110110=>001001
[3,5,1,7,2,4,6]=>[7,1,3,2,5,4,6]=>110100=>001011
[3,5,1,7,2,6,4]=>[6,7,1,3,2,5,4]=>110100=>001011
[3,5,1,7,4,2,6]=>[7,4,5,1,3,2,6]=>110100=>001011
[3,5,1,7,4,6,2]=>[6,7,4,5,1,3,2]=>110100=>001011
[3,5,1,7,6,2,4]=>[6,1,3,2,7,5,4]=>110110=>001001
[3,5,1,7,6,4,2]=>[6,4,7,5,1,3,2]=>110110=>001001
[3,5,2,1,4,6,7]=>[5,2,3,1,4,6,7]=>110000=>001111
[3,5,2,1,4,7,6]=>[5,2,3,1,4,7,6]=>110001=>001110
[3,5,2,1,6,4,7]=>[6,5,2,3,1,4,7]=>110010=>001101
[3,5,2,1,6,7,4]=>[7,6,5,2,3,1,4]=>110011=>001100
[3,5,2,1,7,4,6]=>[7,5,2,3,1,4,6]=>110010=>001101
[3,5,2,1,7,6,4]=>[6,7,5,2,3,1,4]=>110010=>001101
[3,5,2,4,1,6,7]=>[4,5,2,3,1,6,7]=>110000=>001111
[3,5,2,4,1,7,6]=>[4,5,2,3,1,7,6]=>110001=>001110
[3,5,2,4,6,1,7]=>[4,6,5,2,3,1,7]=>110010=>001101
[3,5,2,4,6,7,1]=>[4,7,6,5,2,3,1]=>110011=>001100
[3,5,2,4,7,1,6]=>[4,7,5,2,3,1,6]=>110010=>001101
[3,5,2,4,7,6,1]=>[4,6,7,5,2,3,1]=>110010=>001101
[3,5,2,6,1,4,7]=>[6,2,3,1,5,4,7]=>110100=>001011
[3,5,2,6,1,7,4]=>[7,6,2,3,1,5,4]=>110101=>001010
[3,5,2,6,4,1,7]=>[6,4,5,2,3,1,7]=>110100=>001011
[3,5,2,6,4,7,1]=>[7,6,4,5,2,3,1]=>110101=>001010
[3,5,2,6,7,1,4]=>[7,2,3,1,6,5,4]=>110110=>001001
[3,5,2,6,7,4,1]=>[7,4,6,5,2,3,1]=>110110=>001001
[3,5,2,7,1,4,6]=>[7,2,3,1,5,4,6]=>110100=>001011
[3,5,2,7,1,6,4]=>[6,7,2,3,1,5,4]=>110100=>001011
[3,5,2,7,4,1,6]=>[7,4,5,2,3,1,6]=>110100=>001011
[3,5,2,7,4,6,1]=>[6,7,4,5,2,3,1]=>110100=>001011
[3,5,2,7,6,1,4]=>[6,2,3,1,7,5,4]=>110110=>001001
[3,5,2,7,6,4,1]=>[6,4,7,5,2,3,1]=>110110=>001001
[3,5,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>111000=>000111
[3,5,4,1,2,7,6]=>[4,1,5,3,2,7,6]=>111001=>000110
[3,5,4,1,6,2,7]=>[4,1,6,5,3,2,7]=>111010=>000101
[3,5,4,1,6,7,2]=>[4,1,7,6,5,3,2]=>111011=>000100
[3,5,4,1,7,2,6]=>[4,1,7,5,3,2,6]=>111010=>000101
[3,5,4,1,7,6,2]=>[4,1,6,7,5,3,2]=>111010=>000101
[3,5,4,2,1,6,7]=>[4,2,5,3,1,6,7]=>111000=>000111
[3,5,4,2,1,7,6]=>[4,2,5,3,1,7,6]=>111001=>000110
[3,5,4,2,6,1,7]=>[4,2,6,5,3,1,7]=>111010=>000101
[3,5,4,2,6,7,1]=>[4,2,7,6,5,3,1]=>111011=>000100
[3,5,4,2,7,1,6]=>[4,2,7,5,3,1,6]=>111010=>000101
[3,5,4,2,7,6,1]=>[4,2,6,7,5,3,1]=>111010=>000101
[3,5,4,6,1,2,7]=>[6,4,1,5,3,2,7]=>111100=>000011
[3,5,4,6,1,7,2]=>[7,6,4,1,5,3,2]=>111101=>000010
[3,5,4,6,2,1,7]=>[6,4,2,5,3,1,7]=>111100=>000011
[3,5,4,6,2,7,1]=>[7,6,4,2,5,3,1]=>111101=>000010
[3,5,4,6,7,1,2]=>[7,4,1,6,5,3,2]=>111110=>000001
[3,5,4,6,7,2,1]=>[7,4,2,6,5,3,1]=>111110=>000001
[3,5,4,7,1,2,6]=>[7,4,1,5,3,2,6]=>111100=>000011
[3,5,4,7,1,6,2]=>[6,7,4,1,5,3,2]=>111100=>000011
[3,5,4,7,2,1,6]=>[7,4,2,5,3,1,6]=>111100=>000011
[3,5,4,7,2,6,1]=>[6,7,4,2,5,3,1]=>111100=>000011
[3,5,4,7,6,1,2]=>[6,4,1,7,5,3,2]=>111110=>000001
[3,5,4,7,6,2,1]=>[6,4,2,7,5,3,1]=>111110=>000001
[3,5,6,1,2,4,7]=>[6,1,5,3,2,4,7]=>111000=>000111
[3,5,6,1,2,7,4]=>[7,6,1,5,3,2,4]=>111001=>000110
[3,5,6,1,4,2,7]=>[6,1,4,5,3,2,7]=>111000=>000111
[3,5,6,1,4,7,2]=>[7,6,1,4,5,3,2]=>111001=>000110
[3,5,6,1,7,2,4]=>[7,1,6,5,3,2,4]=>111010=>000101
[3,5,6,1,7,4,2]=>[7,1,4,6,5,3,2]=>111010=>000101
[3,5,6,2,1,4,7]=>[6,2,5,3,1,4,7]=>111000=>000111
[3,5,6,2,1,7,4]=>[7,6,2,5,3,1,4]=>111001=>000110
[3,5,6,2,4,1,7]=>[6,2,4,5,3,1,7]=>111000=>000111
[3,5,6,2,4,7,1]=>[7,6,2,4,5,3,1]=>111001=>000110
[3,5,6,2,7,1,4]=>[7,2,6,5,3,1,4]=>111010=>000101
[3,5,6,2,7,4,1]=>[7,2,4,6,5,3,1]=>111010=>000101
[3,5,6,4,1,2,7]=>[4,6,1,5,3,2,7]=>111000=>000111
[3,5,6,4,1,7,2]=>[4,7,6,1,5,3,2]=>111001=>000110
[3,5,6,4,2,1,7]=>[4,6,2,5,3,1,7]=>111000=>000111
[3,5,6,4,2,7,1]=>[4,7,6,2,5,3,1]=>111001=>000110
[3,5,6,4,7,1,2]=>[4,7,1,6,5,3,2]=>111010=>000101
[3,5,6,4,7,2,1]=>[4,7,2,6,5,3,1]=>111010=>000101
[3,5,6,7,1,2,4]=>[7,1,6,3,2,5,4]=>111100=>000011
[3,5,6,7,1,4,2]=>[7,1,6,4,5,3,2]=>111100=>000011
[3,5,6,7,2,1,4]=>[7,2,6,3,1,5,4]=>111100=>000011
[3,5,6,7,2,4,1]=>[7,2,6,4,5,3,1]=>111100=>000011
[3,5,6,7,4,1,2]=>[7,4,6,1,5,3,2]=>111100=>000011
[3,5,6,7,4,2,1]=>[7,4,6,2,5,3,1]=>111100=>000011
[3,5,7,1,2,4,6]=>[7,1,5,3,2,4,6]=>111000=>000111
[3,5,7,1,2,6,4]=>[6,7,1,5,3,2,4]=>111000=>000111
[3,5,7,1,4,2,6]=>[7,1,4,5,3,2,6]=>111000=>000111
[3,5,7,1,4,6,2]=>[6,7,1,4,5,3,2]=>111000=>000111
[3,5,7,1,6,2,4]=>[6,1,7,5,3,2,4]=>111010=>000101
[3,5,7,1,6,4,2]=>[6,1,4,7,5,3,2]=>111010=>000101
[3,5,7,2,1,4,6]=>[7,2,5,3,1,4,6]=>111000=>000111
[3,5,7,2,1,6,4]=>[6,7,2,5,3,1,4]=>111000=>000111
[3,5,7,2,4,1,6]=>[7,2,4,5,3,1,6]=>111000=>000111
[3,5,7,2,4,6,1]=>[6,7,2,4,5,3,1]=>111000=>000111
[3,5,7,2,6,1,4]=>[6,2,7,5,3,1,4]=>111010=>000101
[3,5,7,2,6,4,1]=>[6,2,4,7,5,3,1]=>111010=>000101
[3,5,7,4,1,2,6]=>[4,7,1,5,3,2,6]=>111000=>000111
[3,5,7,4,1,6,2]=>[4,6,7,1,5,3,2]=>111000=>000111
[3,5,7,4,2,1,6]=>[4,7,2,5,3,1,6]=>111000=>000111
[3,5,7,4,2,6,1]=>[4,6,7,2,5,3,1]=>111000=>000111
[3,5,7,4,6,1,2]=>[4,6,1,7,5,3,2]=>111010=>000101
[3,5,7,4,6,2,1]=>[4,6,2,7,5,3,1]=>111010=>000101
[3,5,7,6,1,2,4]=>[6,1,7,3,2,5,4]=>111100=>000011
[3,5,7,6,1,4,2]=>[6,1,7,4,5,3,2]=>111100=>000011
[3,5,7,6,2,1,4]=>[6,2,7,3,1,5,4]=>111100=>000011
[3,5,7,6,2,4,1]=>[6,2,7,4,5,3,1]=>111100=>000011
[3,5,7,6,4,1,2]=>[6,4,7,1,5,3,2]=>111100=>000011
[3,5,7,6,4,2,1]=>[6,4,7,2,5,3,1]=>111100=>000011
[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>110000=>001111
[3,6,1,2,4,7,5]=>[7,6,1,3,2,4,5]=>110001=>001110
[3,6,1,2,5,4,7]=>[5,6,1,3,2,4,7]=>110000=>001111
[3,6,1,2,5,7,4]=>[5,7,6,1,3,2,4]=>110001=>001110
[3,6,1,2,7,4,5]=>[7,1,3,2,4,6,5]=>110010=>001101
[3,6,1,2,7,5,4]=>[7,5,6,1,3,2,4]=>110010=>001101
[3,6,1,4,2,5,7]=>[4,6,1,3,2,5,7]=>110000=>001111
[3,6,1,4,2,7,5]=>[4,7,6,1,3,2,5]=>110001=>001110
[3,6,1,4,5,2,7]=>[4,5,6,1,3,2,7]=>110000=>001111
[3,6,1,4,5,7,2]=>[4,5,7,6,1,3,2]=>110001=>001110
[3,6,1,4,7,2,5]=>[4,7,1,3,2,6,5]=>110010=>001101
[3,6,1,4,7,5,2]=>[4,7,5,6,1,3,2]=>110010=>001101
[3,6,1,5,2,4,7]=>[5,1,3,2,6,4,7]=>110100=>001011
[3,6,1,5,2,7,4]=>[5,1,3,2,7,6,4]=>110101=>001010
[3,6,1,5,4,2,7]=>[5,4,6,1,3,2,7]=>110100=>001011
[3,6,1,5,4,7,2]=>[5,4,7,6,1,3,2]=>110101=>001010
[3,6,1,5,7,2,4]=>[7,5,1,3,2,6,4]=>110110=>001001
[3,6,1,5,7,4,2]=>[7,5,4,6,1,3,2]=>110110=>001001
[3,6,1,7,2,4,5]=>[7,1,3,2,6,4,5]=>110100=>001011
[3,6,1,7,2,5,4]=>[7,1,3,2,5,6,4]=>110100=>001011
[3,6,1,7,4,2,5]=>[7,4,6,1,3,2,5]=>110100=>001011
[3,6,1,7,4,5,2]=>[7,4,5,6,1,3,2]=>110100=>001011
[3,6,1,7,5,2,4]=>[5,7,1,3,2,6,4]=>110100=>001011
[3,6,1,7,5,4,2]=>[5,7,4,6,1,3,2]=>110100=>001011
[3,6,2,1,4,5,7]=>[6,2,3,1,4,5,7]=>110000=>001111
[3,6,2,1,4,7,5]=>[7,6,2,3,1,4,5]=>110001=>001110
[3,6,2,1,5,4,7]=>[5,6,2,3,1,4,7]=>110000=>001111
[3,6,2,1,5,7,4]=>[5,7,6,2,3,1,4]=>110001=>001110
[3,6,2,1,7,4,5]=>[7,2,3,1,4,6,5]=>110010=>001101
[3,6,2,1,7,5,4]=>[7,5,6,2,3,1,4]=>110010=>001101
[3,6,2,4,1,5,7]=>[4,6,2,3,1,5,7]=>110000=>001111
[3,6,2,4,1,7,5]=>[4,7,6,2,3,1,5]=>110001=>001110
[3,6,2,4,5,1,7]=>[4,5,6,2,3,1,7]=>110000=>001111
[3,6,2,4,5,7,1]=>[4,5,7,6,2,3,1]=>110001=>001110
[3,6,2,4,7,1,5]=>[4,7,2,3,1,6,5]=>110010=>001101
[3,6,2,4,7,5,1]=>[4,7,5,6,2,3,1]=>110010=>001101
[3,6,2,5,1,4,7]=>[5,2,3,1,6,4,7]=>110100=>001011
[3,6,2,5,1,7,4]=>[5,2,3,1,7,6,4]=>110101=>001010
[3,6,2,5,4,1,7]=>[5,4,6,2,3,1,7]=>110100=>001011
[3,6,2,5,4,7,1]=>[5,4,7,6,2,3,1]=>110101=>001010
[3,6,2,5,7,1,4]=>[7,5,2,3,1,6,4]=>110110=>001001
[3,6,2,5,7,4,1]=>[7,5,4,6,2,3,1]=>110110=>001001
[3,6,2,7,1,4,5]=>[7,2,3,1,6,4,5]=>110100=>001011
[3,6,2,7,1,5,4]=>[7,2,3,1,5,6,4]=>110100=>001011
[3,6,2,7,4,1,5]=>[7,4,6,2,3,1,5]=>110100=>001011
[3,6,2,7,4,5,1]=>[7,4,5,6,2,3,1]=>110100=>001011
[3,6,2,7,5,1,4]=>[5,7,2,3,1,6,4]=>110100=>001011
[3,6,2,7,5,4,1]=>[5,7,4,6,2,3,1]=>110100=>001011
[3,6,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>111000=>000111
[3,6,4,1,2,7,5]=>[4,1,7,6,3,2,5]=>111001=>000110
[3,6,4,1,5,2,7]=>[4,1,5,6,3,2,7]=>111000=>000111
[3,6,4,1,5,7,2]=>[4,1,5,7,6,3,2]=>111001=>000110
[3,6,4,1,7,2,5]=>[4,1,7,3,2,6,5]=>111010=>000101
[3,6,4,1,7,5,2]=>[4,1,7,5,6,3,2]=>111010=>000101
[3,6,4,2,1,5,7]=>[4,2,6,3,1,5,7]=>111000=>000111
[3,6,4,2,1,7,5]=>[4,2,7,6,3,1,5]=>111001=>000110
[3,6,4,2,5,1,7]=>[4,2,5,6,3,1,7]=>111000=>000111
[3,6,4,2,5,7,1]=>[4,2,5,7,6,3,1]=>111001=>000110
[3,6,4,2,7,1,5]=>[4,2,7,3,1,6,5]=>111010=>000101
[3,6,4,2,7,5,1]=>[4,2,7,5,6,3,1]=>111010=>000101
[3,6,4,5,1,2,7]=>[5,4,1,6,3,2,7]=>111100=>000011
[3,6,4,5,1,7,2]=>[5,4,1,7,6,3,2]=>111101=>000010
[3,6,4,5,2,1,7]=>[5,4,2,6,3,1,7]=>111100=>000011
[3,6,4,5,2,7,1]=>[5,4,2,7,6,3,1]=>111101=>000010
[3,6,4,5,7,1,2]=>[7,5,4,1,6,3,2]=>111110=>000001
[3,6,4,5,7,2,1]=>[7,5,4,2,6,3,1]=>111110=>000001
[3,6,4,7,1,2,5]=>[7,4,1,6,3,2,5]=>111100=>000011
[3,6,4,7,1,5,2]=>[7,4,1,5,6,3,2]=>111100=>000011
[3,6,4,7,2,1,5]=>[7,4,2,6,3,1,5]=>111100=>000011
[3,6,4,7,2,5,1]=>[7,4,2,5,6,3,1]=>111100=>000011
[3,6,4,7,5,1,2]=>[5,7,4,1,6,3,2]=>111100=>000011
[3,6,4,7,5,2,1]=>[5,7,4,2,6,3,1]=>111100=>000011
[3,6,5,1,2,4,7]=>[5,1,6,3,2,4,7]=>111000=>000111
[3,6,5,1,2,7,4]=>[5,1,7,6,3,2,4]=>111001=>000110
[3,6,5,1,4,2,7]=>[5,1,4,6,3,2,7]=>111000=>000111
[3,6,5,1,4,7,2]=>[5,1,4,7,6,3,2]=>111001=>000110
[3,6,5,1,7,2,4]=>[7,5,1,6,3,2,4]=>111010=>000101
[3,6,5,1,7,4,2]=>[7,5,1,4,6,3,2]=>111010=>000101
[3,6,5,2,1,4,7]=>[5,2,6,3,1,4,7]=>111000=>000111
[3,6,5,2,1,7,4]=>[5,2,7,6,3,1,4]=>111001=>000110
[3,6,5,2,4,1,7]=>[5,2,4,6,3,1,7]=>111000=>000111
[3,6,5,2,4,7,1]=>[5,2,4,7,6,3,1]=>111001=>000110
[3,6,5,2,7,1,4]=>[7,5,2,6,3,1,4]=>111010=>000101
[3,6,5,2,7,4,1]=>[7,5,2,4,6,3,1]=>111010=>000101
[3,6,5,4,1,2,7]=>[4,5,1,6,3,2,7]=>111000=>000111
[3,6,5,4,1,7,2]=>[4,5,1,7,6,3,2]=>111001=>000110
[3,6,5,4,2,1,7]=>[4,5,2,6,3,1,7]=>111000=>000111
[3,6,5,4,2,7,1]=>[4,5,2,7,6,3,1]=>111001=>000110
[3,6,5,4,7,1,2]=>[4,7,5,1,6,3,2]=>111010=>000101
[3,6,5,4,7,2,1]=>[4,7,5,2,6,3,1]=>111010=>000101
[3,6,5,7,1,2,4]=>[7,1,5,3,2,6,4]=>111100=>000011
[3,6,5,7,1,4,2]=>[7,1,5,4,6,3,2]=>111100=>000011
[3,6,5,7,2,1,4]=>[7,2,5,3,1,6,4]=>111100=>000011
[3,6,5,7,2,4,1]=>[7,2,5,4,6,3,1]=>111100=>000011
[3,6,5,7,4,1,2]=>[7,4,5,1,6,3,2]=>111100=>000011
[3,6,5,7,4,2,1]=>[7,4,5,2,6,3,1]=>111100=>000011
[3,6,7,1,2,4,5]=>[7,1,6,3,2,4,5]=>111000=>000111
[3,6,7,1,2,5,4]=>[7,1,5,6,3,2,4]=>111000=>000111
[3,6,7,1,4,2,5]=>[7,1,4,6,3,2,5]=>111000=>000111
[3,6,7,1,4,5,2]=>[7,1,4,5,6,3,2]=>111000=>000111
[3,6,7,1,5,2,4]=>[5,7,1,6,3,2,4]=>111000=>000111
[3,6,7,1,5,4,2]=>[5,7,1,4,6,3,2]=>111000=>000111
[3,6,7,2,1,4,5]=>[7,2,6,3,1,4,5]=>111000=>000111
[3,6,7,2,1,5,4]=>[7,2,5,6,3,1,4]=>111000=>000111
[3,6,7,2,4,1,5]=>[7,2,4,6,3,1,5]=>111000=>000111
[3,6,7,2,4,5,1]=>[7,2,4,5,6,3,1]=>111000=>000111
[3,6,7,2,5,1,4]=>[5,7,2,6,3,1,4]=>111000=>000111
[3,6,7,2,5,4,1]=>[5,7,2,4,6,3,1]=>111000=>000111
[3,6,7,4,1,2,5]=>[4,7,1,6,3,2,5]=>111000=>000111
[3,6,7,4,1,5,2]=>[4,7,1,5,6,3,2]=>111000=>000111
[3,6,7,4,2,1,5]=>[4,7,2,6,3,1,5]=>111000=>000111
[3,6,7,4,2,5,1]=>[4,7,2,5,6,3,1]=>111000=>000111
[3,6,7,4,5,1,2]=>[4,5,7,1,6,3,2]=>111000=>000111
[3,6,7,4,5,2,1]=>[4,5,7,2,6,3,1]=>111000=>000111
[3,6,7,5,1,2,4]=>[5,1,7,3,2,6,4]=>111100=>000011
[3,6,7,5,1,4,2]=>[5,1,7,4,6,3,2]=>111100=>000011
[3,6,7,5,2,1,4]=>[5,2,7,3,1,6,4]=>111100=>000011
[3,6,7,5,2,4,1]=>[5,2,7,4,6,3,1]=>111100=>000011
[3,6,7,5,4,1,2]=>[5,4,7,1,6,3,2]=>111100=>000011
[3,6,7,5,4,2,1]=>[5,4,7,2,6,3,1]=>111100=>000011
[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>110000=>001111
[3,7,1,2,4,6,5]=>[6,7,1,3,2,4,5]=>110000=>001111
[3,7,1,2,5,4,6]=>[5,7,1,3,2,4,6]=>110000=>001111
[3,7,1,2,5,6,4]=>[5,6,7,1,3,2,4]=>110000=>001111
[3,7,1,2,6,4,5]=>[6,1,3,2,4,7,5]=>110010=>001101
[3,7,1,2,6,5,4]=>[6,5,7,1,3,2,4]=>110010=>001101
[3,7,1,4,2,5,6]=>[4,7,1,3,2,5,6]=>110000=>001111
[3,7,1,4,2,6,5]=>[4,6,7,1,3,2,5]=>110000=>001111
[3,7,1,4,5,2,6]=>[4,5,7,1,3,2,6]=>110000=>001111
[3,7,1,4,5,6,2]=>[4,5,6,7,1,3,2]=>110000=>001111
[3,7,1,4,6,2,5]=>[4,6,1,3,2,7,5]=>110010=>001101
[3,7,1,4,6,5,2]=>[4,6,5,7,1,3,2]=>110010=>001101
[3,7,1,5,2,4,6]=>[5,1,3,2,7,4,6]=>110100=>001011
[3,7,1,5,2,6,4]=>[5,1,3,2,6,7,4]=>110100=>001011
[3,7,1,5,4,2,6]=>[5,4,7,1,3,2,6]=>110100=>001011
[3,7,1,5,4,6,2]=>[5,4,6,7,1,3,2]=>110100=>001011
[3,7,1,5,6,2,4]=>[6,5,1,3,2,7,4]=>110110=>001001
[3,7,1,5,6,4,2]=>[6,5,4,7,1,3,2]=>110110=>001001
[3,7,1,6,2,4,5]=>[6,1,3,2,7,4,5]=>110100=>001011
[3,7,1,6,2,5,4]=>[6,1,3,2,5,7,4]=>110100=>001011
[3,7,1,6,4,2,5]=>[6,4,7,1,3,2,5]=>110100=>001011
[3,7,1,6,4,5,2]=>[6,4,5,7,1,3,2]=>110100=>001011
[3,7,1,6,5,2,4]=>[5,6,1,3,2,7,4]=>110100=>001011
[3,7,1,6,5,4,2]=>[5,6,4,7,1,3,2]=>110100=>001011
[3,7,2,1,4,5,6]=>[7,2,3,1,4,5,6]=>110000=>001111
[3,7,2,1,4,6,5]=>[6,7,2,3,1,4,5]=>110000=>001111
[3,7,2,1,5,4,6]=>[5,7,2,3,1,4,6]=>110000=>001111
[3,7,2,1,5,6,4]=>[5,6,7,2,3,1,4]=>110000=>001111
[3,7,2,1,6,4,5]=>[6,2,3,1,4,7,5]=>110010=>001101
[3,7,2,1,6,5,4]=>[6,5,7,2,3,1,4]=>110010=>001101
[3,7,2,4,1,5,6]=>[4,7,2,3,1,5,6]=>110000=>001111
[3,7,2,4,1,6,5]=>[4,6,7,2,3,1,5]=>110000=>001111
[3,7,2,4,5,1,6]=>[4,5,7,2,3,1,6]=>110000=>001111
[3,7,2,4,5,6,1]=>[4,5,6,7,2,3,1]=>110000=>001111
[3,7,2,4,6,1,5]=>[4,6,2,3,1,7,5]=>110010=>001101
[3,7,2,4,6,5,1]=>[4,6,5,7,2,3,1]=>110010=>001101
[3,7,2,5,1,4,6]=>[5,2,3,1,7,4,6]=>110100=>001011
[3,7,2,5,1,6,4]=>[5,2,3,1,6,7,4]=>110100=>001011
[3,7,2,5,4,1,6]=>[5,4,7,2,3,1,6]=>110100=>001011
[3,7,2,5,4,6,1]=>[5,4,6,7,2,3,1]=>110100=>001011
[3,7,2,5,6,1,4]=>[6,5,2,3,1,7,4]=>110110=>001001
[3,7,2,5,6,4,1]=>[6,5,4,7,2,3,1]=>110110=>001001
[3,7,2,6,1,4,5]=>[6,2,3,1,7,4,5]=>110100=>001011
[3,7,2,6,1,5,4]=>[6,2,3,1,5,7,4]=>110100=>001011
[3,7,2,6,4,1,5]=>[6,4,7,2,3,1,5]=>110100=>001011
[3,7,2,6,4,5,1]=>[6,4,5,7,2,3,1]=>110100=>001011
[3,7,2,6,5,1,4]=>[5,6,2,3,1,7,4]=>110100=>001011
[3,7,2,6,5,4,1]=>[5,6,4,7,2,3,1]=>110100=>001011
[3,7,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>111000=>000111
[3,7,4,1,2,6,5]=>[4,1,6,7,3,2,5]=>111000=>000111
[3,7,4,1,5,2,6]=>[4,1,5,7,3,2,6]=>111000=>000111
[3,7,4,1,5,6,2]=>[4,1,5,6,7,3,2]=>111000=>000111
[3,7,4,1,6,2,5]=>[4,1,6,3,2,7,5]=>111010=>000101
[3,7,4,1,6,5,2]=>[4,1,6,5,7,3,2]=>111010=>000101
[3,7,4,2,1,5,6]=>[4,2,7,3,1,5,6]=>111000=>000111
[3,7,4,2,1,6,5]=>[4,2,6,7,3,1,5]=>111000=>000111
[3,7,4,2,5,1,6]=>[4,2,5,7,3,1,6]=>111000=>000111
[3,7,4,2,5,6,1]=>[4,2,5,6,7,3,1]=>111000=>000111
[3,7,4,2,6,1,5]=>[4,2,6,3,1,7,5]=>111010=>000101
[3,7,4,2,6,5,1]=>[4,2,6,5,7,3,1]=>111010=>000101
[3,7,4,5,1,2,6]=>[5,4,1,7,3,2,6]=>111100=>000011
[3,7,4,5,1,6,2]=>[5,4,1,6,7,3,2]=>111100=>000011
[3,7,4,5,2,1,6]=>[5,4,2,7,3,1,6]=>111100=>000011
[3,7,4,5,2,6,1]=>[5,4,2,6,7,3,1]=>111100=>000011
[3,7,4,5,6,1,2]=>[6,5,4,1,7,3,2]=>111110=>000001
[3,7,4,5,6,2,1]=>[6,5,4,2,7,3,1]=>111110=>000001
[3,7,4,6,1,2,5]=>[6,4,1,7,3,2,5]=>111100=>000011
[3,7,4,6,1,5,2]=>[6,4,1,5,7,3,2]=>111100=>000011
[3,7,4,6,2,1,5]=>[6,4,2,7,3,1,5]=>111100=>000011
[3,7,4,6,2,5,1]=>[6,4,2,5,7,3,1]=>111100=>000011
[3,7,4,6,5,1,2]=>[5,6,4,1,7,3,2]=>111100=>000011
[3,7,4,6,5,2,1]=>[5,6,4,2,7,3,1]=>111100=>000011
[3,7,5,1,2,4,6]=>[5,1,7,3,2,4,6]=>111000=>000111
[3,7,5,1,2,6,4]=>[5,1,6,7,3,2,4]=>111000=>000111
[3,7,5,1,4,2,6]=>[5,1,4,7,3,2,6]=>111000=>000111
[3,7,5,1,4,6,2]=>[5,1,4,6,7,3,2]=>111000=>000111
[3,7,5,1,6,2,4]=>[6,5,1,7,3,2,4]=>111010=>000101
[3,7,5,1,6,4,2]=>[6,5,1,4,7,3,2]=>111010=>000101
[3,7,5,2,1,4,6]=>[5,2,7,3,1,4,6]=>111000=>000111
[3,7,5,2,1,6,4]=>[5,2,6,7,3,1,4]=>111000=>000111
[3,7,5,2,4,1,6]=>[5,2,4,7,3,1,6]=>111000=>000111
[3,7,5,2,4,6,1]=>[5,2,4,6,7,3,1]=>111000=>000111
[3,7,5,2,6,1,4]=>[6,5,2,7,3,1,4]=>111010=>000101
[3,7,5,2,6,4,1]=>[6,5,2,4,7,3,1]=>111010=>000101
[3,7,5,4,1,2,6]=>[4,5,1,7,3,2,6]=>111000=>000111
[3,7,5,4,1,6,2]=>[4,5,1,6,7,3,2]=>111000=>000111
[3,7,5,4,2,1,6]=>[4,5,2,7,3,1,6]=>111000=>000111
[3,7,5,4,2,6,1]=>[4,5,2,6,7,3,1]=>111000=>000111
[3,7,5,4,6,1,2]=>[4,6,5,1,7,3,2]=>111010=>000101
[3,7,5,4,6,2,1]=>[4,6,5,2,7,3,1]=>111010=>000101
[3,7,5,6,1,2,4]=>[6,1,5,3,2,7,4]=>111100=>000011
[3,7,5,6,1,4,2]=>[6,1,5,4,7,3,2]=>111100=>000011
[3,7,5,6,2,1,4]=>[6,2,5,3,1,7,4]=>111100=>000011
[3,7,5,6,2,4,1]=>[6,2,5,4,7,3,1]=>111100=>000011
[3,7,5,6,4,1,2]=>[6,4,5,1,7,3,2]=>111100=>000011
[3,7,5,6,4,2,1]=>[6,4,5,2,7,3,1]=>111100=>000011
[3,7,6,1,2,4,5]=>[6,1,7,3,2,4,5]=>111000=>000111
[3,7,6,1,2,5,4]=>[6,1,5,7,3,2,4]=>111000=>000111
[3,7,6,1,4,2,5]=>[6,1,4,7,3,2,5]=>111000=>000111
[3,7,6,1,4,5,2]=>[6,1,4,5,7,3,2]=>111000=>000111
[3,7,6,1,5,2,4]=>[5,6,1,7,3,2,4]=>111000=>000111
[3,7,6,1,5,4,2]=>[5,6,1,4,7,3,2]=>111000=>000111
[3,7,6,2,1,4,5]=>[6,2,7,3,1,4,5]=>111000=>000111
[3,7,6,2,1,5,4]=>[6,2,5,7,3,1,4]=>111000=>000111
[3,7,6,2,4,1,5]=>[6,2,4,7,3,1,5]=>111000=>000111
[3,7,6,2,4,5,1]=>[6,2,4,5,7,3,1]=>111000=>000111
[3,7,6,2,5,1,4]=>[5,6,2,7,3,1,4]=>111000=>000111
[3,7,6,2,5,4,1]=>[5,6,2,4,7,3,1]=>111000=>000111
[3,7,6,4,1,2,5]=>[4,6,1,7,3,2,5]=>111000=>000111
[3,7,6,4,1,5,2]=>[4,6,1,5,7,3,2]=>111000=>000111
[3,7,6,4,2,1,5]=>[4,6,2,7,3,1,5]=>111000=>000111
[3,7,6,4,2,5,1]=>[4,6,2,5,7,3,1]=>111000=>000111
[3,7,6,4,5,1,2]=>[4,5,6,1,7,3,2]=>111000=>000111
[3,7,6,4,5,2,1]=>[4,5,6,2,7,3,1]=>111000=>000111
[3,7,6,5,1,2,4]=>[5,1,6,3,2,7,4]=>111100=>000011
[3,7,6,5,1,4,2]=>[5,1,6,4,7,3,2]=>111100=>000011
[3,7,6,5,2,1,4]=>[5,2,6,3,1,7,4]=>111100=>000011
[3,7,6,5,2,4,1]=>[5,2,6,4,7,3,1]=>111100=>000011
[3,7,6,5,4,1,2]=>[5,4,6,1,7,3,2]=>111100=>000011
[3,7,6,5,4,2,1]=>[5,4,6,2,7,3,1]=>111100=>000011
[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>100000=>011111
[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>100001=>011110
[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>100010=>011101
[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>100011=>011100
[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>100010=>011101
[4,1,2,3,7,6,5]=>[4,1,2,3,6,7,5]=>100010=>011101
[4,1,2,5,3,6,7]=>[5,4,1,2,3,6,7]=>100100=>011011
[4,1,2,5,3,7,6]=>[5,4,1,2,3,7,6]=>100101=>011010
[4,1,2,5,6,3,7]=>[6,5,4,1,2,3,7]=>100110=>011001
[4,1,2,5,6,7,3]=>[7,6,5,4,1,2,3]=>100111=>011000
[4,1,2,5,7,3,6]=>[7,5,4,1,2,3,6]=>100110=>011001
[4,1,2,5,7,6,3]=>[6,7,5,4,1,2,3]=>100110=>011001
[4,1,2,6,3,5,7]=>[6,4,1,2,3,5,7]=>100100=>011011
[4,1,2,6,3,7,5]=>[7,6,4,1,2,3,5]=>100101=>011010
[4,1,2,6,5,3,7]=>[5,6,4,1,2,3,7]=>100100=>011011
[4,1,2,6,5,7,3]=>[5,7,6,4,1,2,3]=>100101=>011010
[4,1,2,6,7,3,5]=>[7,4,1,2,3,6,5]=>100110=>011001
[4,1,2,6,7,5,3]=>[7,5,6,4,1,2,3]=>100110=>011001
[4,1,2,7,3,5,6]=>[7,4,1,2,3,5,6]=>100100=>011011
[4,1,2,7,3,6,5]=>[6,7,4,1,2,3,5]=>100100=>011011
[4,1,2,7,5,3,6]=>[5,7,4,1,2,3,6]=>100100=>011011
[4,1,2,7,5,6,3]=>[5,6,7,4,1,2,3]=>100100=>011011
[4,1,2,7,6,3,5]=>[6,4,1,2,3,7,5]=>100110=>011001
[4,1,2,7,6,5,3]=>[6,5,7,4,1,2,3]=>100110=>011001
[4,1,3,2,5,6,7]=>[3,4,1,2,5,6,7]=>100000=>011111
[4,1,3,2,5,7,6]=>[3,4,1,2,5,7,6]=>100001=>011110
[4,1,3,2,6,5,7]=>[3,4,1,2,6,5,7]=>100010=>011101
[4,1,3,2,6,7,5]=>[3,4,1,2,7,6,5]=>100011=>011100
[4,1,3,2,7,5,6]=>[3,4,1,2,7,5,6]=>100010=>011101
[4,1,3,2,7,6,5]=>[3,4,1,2,6,7,5]=>100010=>011101
[4,1,3,5,2,6,7]=>[3,5,4,1,2,6,7]=>100100=>011011
[4,1,3,5,2,7,6]=>[3,5,4,1,2,7,6]=>100101=>011010
[4,1,3,5,6,2,7]=>[3,6,5,4,1,2,7]=>100110=>011001
[4,1,3,5,6,7,2]=>[3,7,6,5,4,1,2]=>100111=>011000
[4,1,3,5,7,2,6]=>[3,7,5,4,1,2,6]=>100110=>011001
[4,1,3,5,7,6,2]=>[3,6,7,5,4,1,2]=>100110=>011001
[4,1,3,6,2,5,7]=>[3,6,4,1,2,5,7]=>100100=>011011
[4,1,3,6,2,7,5]=>[3,7,6,4,1,2,5]=>100101=>011010
[4,1,3,6,5,2,7]=>[3,5,6,4,1,2,7]=>100100=>011011
[4,1,3,6,5,7,2]=>[3,5,7,6,4,1,2]=>100101=>011010
[4,1,3,6,7,2,5]=>[3,7,4,1,2,6,5]=>100110=>011001
[4,1,3,6,7,5,2]=>[3,7,5,6,4,1,2]=>100110=>011001
[4,1,3,7,2,5,6]=>[3,7,4,1,2,5,6]=>100100=>011011
[4,1,3,7,2,6,5]=>[3,6,7,4,1,2,5]=>100100=>011011
[4,1,3,7,5,2,6]=>[3,5,7,4,1,2,6]=>100100=>011011
[4,1,3,7,5,6,2]=>[3,5,6,7,4,1,2]=>100100=>011011
[4,1,3,7,6,2,5]=>[3,6,4,1,2,7,5]=>100110=>011001
[4,1,3,7,6,5,2]=>[3,6,5,7,4,1,2]=>100110=>011001
[4,1,5,2,3,6,7]=>[5,1,2,4,3,6,7]=>101000=>010111
[4,1,5,2,3,7,6]=>[5,1,2,4,3,7,6]=>101001=>010110
[4,1,5,2,6,3,7]=>[6,5,1,2,4,3,7]=>101010=>010101
[4,1,5,2,6,7,3]=>[7,6,5,1,2,4,3]=>101011=>010100
[4,1,5,2,7,3,6]=>[7,5,1,2,4,3,6]=>101010=>010101
[4,1,5,2,7,6,3]=>[6,7,5,1,2,4,3]=>101010=>010101
[4,1,5,3,2,6,7]=>[5,3,4,1,2,6,7]=>101000=>010111
[4,1,5,3,2,7,6]=>[5,3,4,1,2,7,6]=>101001=>010110
[4,1,5,3,6,2,7]=>[6,5,3,4,1,2,7]=>101010=>010101
[4,1,5,3,6,7,2]=>[7,6,5,3,4,1,2]=>101011=>010100
[4,1,5,3,7,2,6]=>[7,5,3,4,1,2,6]=>101010=>010101
[4,1,5,3,7,6,2]=>[6,7,5,3,4,1,2]=>101010=>010101
[4,1,5,6,2,3,7]=>[6,1,2,5,4,3,7]=>101100=>010011
[4,1,5,6,2,7,3]=>[7,6,1,2,5,4,3]=>101101=>010010
[4,1,5,6,3,2,7]=>[6,3,5,4,1,2,7]=>101100=>010011
[4,1,5,6,3,7,2]=>[7,6,3,5,4,1,2]=>101101=>010010
[4,1,5,6,7,2,3]=>[7,1,2,6,5,4,3]=>101110=>010001
[4,1,5,6,7,3,2]=>[7,3,6,5,4,1,2]=>101110=>010001
[4,1,5,7,2,3,6]=>[7,1,2,5,4,3,6]=>101100=>010011
[4,1,5,7,2,6,3]=>[6,7,1,2,5,4,3]=>101100=>010011
[4,1,5,7,3,2,6]=>[7,3,5,4,1,2,6]=>101100=>010011
[4,1,5,7,3,6,2]=>[6,7,3,5,4,1,2]=>101100=>010011
[4,1,5,7,6,2,3]=>[6,1,2,7,5,4,3]=>101110=>010001
[4,1,5,7,6,3,2]=>[6,3,7,5,4,1,2]=>101110=>010001
[4,1,6,2,3,5,7]=>[6,1,2,4,3,5,7]=>101000=>010111
[4,1,6,2,3,7,5]=>[7,6,1,2,4,3,5]=>101001=>010110
[4,1,6,2,5,3,7]=>[5,6,1,2,4,3,7]=>101000=>010111
[4,1,6,2,5,7,3]=>[5,7,6,1,2,4,3]=>101001=>010110
[4,1,6,2,7,3,5]=>[7,1,2,4,3,6,5]=>101010=>010101
[4,1,6,2,7,5,3]=>[7,5,6,1,2,4,3]=>101010=>010101
[4,1,6,3,2,5,7]=>[6,3,4,1,2,5,7]=>101000=>010111
[4,1,6,3,2,7,5]=>[7,6,3,4,1,2,5]=>101001=>010110
[4,1,6,3,5,2,7]=>[5,6,3,4,1,2,7]=>101000=>010111
[4,1,6,3,5,7,2]=>[5,7,6,3,4,1,2]=>101001=>010110
[4,1,6,3,7,2,5]=>[7,3,4,1,2,6,5]=>101010=>010101
[4,1,6,3,7,5,2]=>[7,5,6,3,4,1,2]=>101010=>010101
[4,1,6,5,2,3,7]=>[5,1,2,6,4,3,7]=>101100=>010011
[4,1,6,5,2,7,3]=>[5,1,2,7,6,4,3]=>101101=>010010
[4,1,6,5,3,2,7]=>[5,3,6,4,1,2,7]=>101100=>010011
[4,1,6,5,3,7,2]=>[5,3,7,6,4,1,2]=>101101=>010010
[4,1,6,5,7,2,3]=>[7,5,1,2,6,4,3]=>101110=>010001
[4,1,6,5,7,3,2]=>[7,5,3,6,4,1,2]=>101110=>010001
[4,1,6,7,2,3,5]=>[7,1,2,6,4,3,5]=>101100=>010011
[4,1,6,7,2,5,3]=>[7,1,2,5,6,4,3]=>101100=>010011
[4,1,6,7,3,2,5]=>[7,3,6,4,1,2,5]=>101100=>010011
[4,1,6,7,3,5,2]=>[7,3,5,6,4,1,2]=>101100=>010011
[4,1,6,7,5,2,3]=>[5,7,1,2,6,4,3]=>101100=>010011
[4,1,6,7,5,3,2]=>[5,7,3,6,4,1,2]=>101100=>010011
[4,1,7,2,3,5,6]=>[7,1,2,4,3,5,6]=>101000=>010111
[4,1,7,2,3,6,5]=>[6,7,1,2,4,3,5]=>101000=>010111
[4,1,7,2,5,3,6]=>[5,7,1,2,4,3,6]=>101000=>010111
[4,1,7,2,5,6,3]=>[5,6,7,1,2,4,3]=>101000=>010111
[4,1,7,2,6,3,5]=>[6,1,2,4,3,7,5]=>101010=>010101
[4,1,7,2,6,5,3]=>[6,5,7,1,2,4,3]=>101010=>010101
[4,1,7,3,2,5,6]=>[7,3,4,1,2,5,6]=>101000=>010111
[4,1,7,3,2,6,5]=>[6,7,3,4,1,2,5]=>101000=>010111
[4,1,7,3,5,2,6]=>[5,7,3,4,1,2,6]=>101000=>010111
[4,1,7,3,5,6,2]=>[5,6,7,3,4,1,2]=>101000=>010111
[4,1,7,3,6,2,5]=>[6,3,4,1,2,7,5]=>101010=>010101
[4,1,7,3,6,5,2]=>[6,5,7,3,4,1,2]=>101010=>010101
[4,1,7,5,2,3,6]=>[5,1,2,7,4,3,6]=>101100=>010011
[4,1,7,5,2,6,3]=>[5,1,2,6,7,4,3]=>101100=>010011
[4,1,7,5,3,2,6]=>[5,3,7,4,1,2,6]=>101100=>010011
[4,1,7,5,3,6,2]=>[5,3,6,7,4,1,2]=>101100=>010011
[4,1,7,5,6,2,3]=>[6,5,1,2,7,4,3]=>101110=>010001
[4,1,7,5,6,3,2]=>[6,5,3,7,4,1,2]=>101110=>010001
[4,1,7,6,2,3,5]=>[6,1,2,7,4,3,5]=>101100=>010011
[4,1,7,6,2,5,3]=>[6,1,2,5,7,4,3]=>101100=>010011
[4,1,7,6,3,2,5]=>[6,3,7,4,1,2,5]=>101100=>010011
[4,1,7,6,3,5,2]=>[6,3,5,7,4,1,2]=>101100=>010011
[4,1,7,6,5,2,3]=>[5,6,1,2,7,4,3]=>101100=>010011
[4,1,7,6,5,3,2]=>[5,6,3,7,4,1,2]=>101100=>010011
[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>100000=>011111
[4,2,1,3,5,7,6]=>[2,4,1,3,5,7,6]=>100001=>011110
[4,2,1,3,6,5,7]=>[2,4,1,3,6,5,7]=>100010=>011101
[4,2,1,3,6,7,5]=>[2,4,1,3,7,6,5]=>100011=>011100
[4,2,1,3,7,5,6]=>[2,4,1,3,7,5,6]=>100010=>011101
[4,2,1,3,7,6,5]=>[2,4,1,3,6,7,5]=>100010=>011101
[4,2,1,5,3,6,7]=>[2,5,4,1,3,6,7]=>100100=>011011
[4,2,1,5,3,7,6]=>[2,5,4,1,3,7,6]=>100101=>011010
[4,2,1,5,6,3,7]=>[2,6,5,4,1,3,7]=>100110=>011001
[4,2,1,5,6,7,3]=>[2,7,6,5,4,1,3]=>100111=>011000
[4,2,1,5,7,3,6]=>[2,7,5,4,1,3,6]=>100110=>011001
[4,2,1,5,7,6,3]=>[2,6,7,5,4,1,3]=>100110=>011001
[4,2,1,6,3,5,7]=>[2,6,4,1,3,5,7]=>100100=>011011
[4,2,1,6,3,7,5]=>[2,7,6,4,1,3,5]=>100101=>011010
[4,2,1,6,5,3,7]=>[2,5,6,4,1,3,7]=>100100=>011011
[4,2,1,6,5,7,3]=>[2,5,7,6,4,1,3]=>100101=>011010
[4,2,1,6,7,3,5]=>[2,7,4,1,3,6,5]=>100110=>011001
[4,2,1,6,7,5,3]=>[2,7,5,6,4,1,3]=>100110=>011001
[4,2,1,7,3,5,6]=>[2,7,4,1,3,5,6]=>100100=>011011
[4,2,1,7,3,6,5]=>[2,6,7,4,1,3,5]=>100100=>011011
[4,2,1,7,5,3,6]=>[2,5,7,4,1,3,6]=>100100=>011011
[4,2,1,7,5,6,3]=>[2,5,6,7,4,1,3]=>100100=>011011
[4,2,1,7,6,3,5]=>[2,6,4,1,3,7,5]=>100110=>011001
[4,2,1,7,6,5,3]=>[2,6,5,7,4,1,3]=>100110=>011001
[4,2,3,1,5,6,7]=>[2,3,4,1,5,6,7]=>100000=>011111
[4,2,3,1,5,7,6]=>[2,3,4,1,5,7,6]=>100001=>011110
[4,2,3,1,6,5,7]=>[2,3,4,1,6,5,7]=>100010=>011101
[4,2,3,1,6,7,5]=>[2,3,4,1,7,6,5]=>100011=>011100
[4,2,3,1,7,5,6]=>[2,3,4,1,7,5,6]=>100010=>011101
[4,2,3,1,7,6,5]=>[2,3,4,1,6,7,5]=>100010=>011101
[4,2,3,5,1,6,7]=>[2,3,5,4,1,6,7]=>100100=>011011
[4,2,3,5,1,7,6]=>[2,3,5,4,1,7,6]=>100101=>011010
[4,2,3,5,6,1,7]=>[2,3,6,5,4,1,7]=>100110=>011001
[4,2,3,5,6,7,1]=>[2,3,7,6,5,4,1]=>100111=>011000
[4,2,3,5,7,1,6]=>[2,3,7,5,4,1,6]=>100110=>011001
[4,2,3,5,7,6,1]=>[2,3,6,7,5,4,1]=>100110=>011001
[4,2,3,6,1,5,7]=>[2,3,6,4,1,5,7]=>100100=>011011
[4,2,3,6,1,7,5]=>[2,3,7,6,4,1,5]=>100101=>011010
[4,2,3,6,5,1,7]=>[2,3,5,6,4,1,7]=>100100=>011011
[4,2,3,6,5,7,1]=>[2,3,5,7,6,4,1]=>100101=>011010
[4,2,3,6,7,1,5]=>[2,3,7,4,1,6,5]=>100110=>011001
[4,2,3,6,7,5,1]=>[2,3,7,5,6,4,1]=>100110=>011001
[4,2,3,7,1,5,6]=>[2,3,7,4,1,5,6]=>100100=>011011
[4,2,3,7,1,6,5]=>[2,3,6,7,4,1,5]=>100100=>011011
[4,2,3,7,5,1,6]=>[2,3,5,7,4,1,6]=>100100=>011011
[4,2,3,7,5,6,1]=>[2,3,5,6,7,4,1]=>100100=>011011
[4,2,3,7,6,1,5]=>[2,3,6,4,1,7,5]=>100110=>011001
[4,2,3,7,6,5,1]=>[2,3,6,5,7,4,1]=>100110=>011001
[4,2,5,1,3,6,7]=>[2,5,1,4,3,6,7]=>101000=>010111
[4,2,5,1,3,7,6]=>[2,5,1,4,3,7,6]=>101001=>010110
[4,2,5,1,6,3,7]=>[2,6,5,1,4,3,7]=>101010=>010101
[4,2,5,1,6,7,3]=>[2,7,6,5,1,4,3]=>101011=>010100
[4,2,5,1,7,3,6]=>[2,7,5,1,4,3,6]=>101010=>010101
[4,2,5,1,7,6,3]=>[2,6,7,5,1,4,3]=>101010=>010101
[4,2,5,3,1,6,7]=>[2,5,3,4,1,6,7]=>101000=>010111
[4,2,5,3,1,7,6]=>[2,5,3,4,1,7,6]=>101001=>010110
[4,2,5,3,6,1,7]=>[2,6,5,3,4,1,7]=>101010=>010101
[4,2,5,3,6,7,1]=>[2,7,6,5,3,4,1]=>101011=>010100
[4,2,5,3,7,1,6]=>[2,7,5,3,4,1,6]=>101010=>010101
[4,2,5,3,7,6,1]=>[2,6,7,5,3,4,1]=>101010=>010101
[4,2,5,6,1,3,7]=>[2,6,1,5,4,3,7]=>101100=>010011
[4,2,5,6,1,7,3]=>[2,7,6,1,5,4,3]=>101101=>010010
[4,2,5,6,3,1,7]=>[2,6,3,5,4,1,7]=>101100=>010011
[4,2,5,6,3,7,1]=>[2,7,6,3,5,4,1]=>101101=>010010
[4,2,5,6,7,1,3]=>[2,7,1,6,5,4,3]=>101110=>010001
[4,2,5,6,7,3,1]=>[2,7,3,6,5,4,1]=>101110=>010001
[4,2,5,7,1,3,6]=>[2,7,1,5,4,3,6]=>101100=>010011
[4,2,5,7,1,6,3]=>[2,6,7,1,5,4,3]=>101100=>010011
[4,2,5,7,3,1,6]=>[2,7,3,5,4,1,6]=>101100=>010011
[4,2,5,7,3,6,1]=>[2,6,7,3,5,4,1]=>101100=>010011
[4,2,5,7,6,1,3]=>[2,6,1,7,5,4,3]=>101110=>010001
[4,2,5,7,6,3,1]=>[2,6,3,7,5,4,1]=>101110=>010001
[4,2,6,1,3,5,7]=>[2,6,1,4,3,5,7]=>101000=>010111
[4,2,6,1,3,7,5]=>[2,7,6,1,4,3,5]=>101001=>010110
[4,2,6,1,5,3,7]=>[2,5,6,1,4,3,7]=>101000=>010111
[4,2,6,1,5,7,3]=>[2,5,7,6,1,4,3]=>101001=>010110
[4,2,6,1,7,3,5]=>[2,7,1,4,3,6,5]=>101010=>010101
[4,2,6,1,7,5,3]=>[2,7,5,6,1,4,3]=>101010=>010101
[4,2,6,3,1,5,7]=>[2,6,3,4,1,5,7]=>101000=>010111
[4,2,6,3,1,7,5]=>[2,7,6,3,4,1,5]=>101001=>010110
[4,2,6,3,5,1,7]=>[2,5,6,3,4,1,7]=>101000=>010111
[4,2,6,3,5,7,1]=>[2,5,7,6,3,4,1]=>101001=>010110
[4,2,6,3,7,1,5]=>[2,7,3,4,1,6,5]=>101010=>010101
[4,2,6,3,7,5,1]=>[2,7,5,6,3,4,1]=>101010=>010101
[4,2,6,5,1,3,7]=>[2,5,1,6,4,3,7]=>101100=>010011
[4,2,6,5,1,7,3]=>[2,5,1,7,6,4,3]=>101101=>010010
[4,2,6,5,3,1,7]=>[2,5,3,6,4,1,7]=>101100=>010011
[4,2,6,5,3,7,1]=>[2,5,3,7,6,4,1]=>101101=>010010
[4,2,6,5,7,1,3]=>[2,7,5,1,6,4,3]=>101110=>010001
[4,2,6,5,7,3,1]=>[2,7,5,3,6,4,1]=>101110=>010001
[4,2,6,7,1,3,5]=>[2,7,1,6,4,3,5]=>101100=>010011
[4,2,6,7,1,5,3]=>[2,7,1,5,6,4,3]=>101100=>010011
[4,2,6,7,3,1,5]=>[2,7,3,6,4,1,5]=>101100=>010011
[4,2,6,7,3,5,1]=>[2,7,3,5,6,4,1]=>101100=>010011
[4,2,6,7,5,1,3]=>[2,5,7,1,6,4,3]=>101100=>010011
[4,2,6,7,5,3,1]=>[2,5,7,3,6,4,1]=>101100=>010011
[4,2,7,1,3,5,6]=>[2,7,1,4,3,5,6]=>101000=>010111
[4,2,7,1,3,6,5]=>[2,6,7,1,4,3,5]=>101000=>010111
[4,2,7,1,5,3,6]=>[2,5,7,1,4,3,6]=>101000=>010111
[4,2,7,1,5,6,3]=>[2,5,6,7,1,4,3]=>101000=>010111
[4,2,7,1,6,3,5]=>[2,6,1,4,3,7,5]=>101010=>010101
[4,2,7,1,6,5,3]=>[2,6,5,7,1,4,3]=>101010=>010101
[4,2,7,3,1,5,6]=>[2,7,3,4,1,5,6]=>101000=>010111
[4,2,7,3,1,6,5]=>[2,6,7,3,4,1,5]=>101000=>010111
[4,2,7,3,5,1,6]=>[2,5,7,3,4,1,6]=>101000=>010111
[4,2,7,3,5,6,1]=>[2,5,6,7,3,4,1]=>101000=>010111
[4,2,7,3,6,1,5]=>[2,6,3,4,1,7,5]=>101010=>010101
[4,2,7,3,6,5,1]=>[2,6,5,7,3,4,1]=>101010=>010101
[4,2,7,5,1,3,6]=>[2,5,1,7,4,3,6]=>101100=>010011
[4,2,7,5,1,6,3]=>[2,5,1,6,7,4,3]=>101100=>010011
[4,2,7,5,3,1,6]=>[2,5,3,7,4,1,6]=>101100=>010011
[4,2,7,5,3,6,1]=>[2,5,3,6,7,4,1]=>101100=>010011
[4,2,7,5,6,1,3]=>[2,6,5,1,7,4,3]=>101110=>010001
[4,2,7,5,6,3,1]=>[2,6,5,3,7,4,1]=>101110=>010001
[4,2,7,6,1,3,5]=>[2,6,1,7,4,3,5]=>101100=>010011
[4,2,7,6,1,5,3]=>[2,6,1,5,7,4,3]=>101100=>010011
[4,2,7,6,3,1,5]=>[2,6,3,7,4,1,5]=>101100=>010011
[4,2,7,6,3,5,1]=>[2,6,3,5,7,4,1]=>101100=>010011
[4,2,7,6,5,1,3]=>[2,5,6,1,7,4,3]=>101100=>010011
[4,2,7,6,5,3,1]=>[2,5,6,3,7,4,1]=>101100=>010011
[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>110000=>001111
[4,3,1,2,5,7,6]=>[3,1,4,2,5,7,6]=>110001=>001110
[4,3,1,2,6,5,7]=>[3,1,4,2,6,5,7]=>110010=>001101
[4,3,1,2,6,7,5]=>[3,1,4,2,7,6,5]=>110011=>001100
[4,3,1,2,7,5,6]=>[3,1,4,2,7,5,6]=>110010=>001101
[4,3,1,2,7,6,5]=>[3,1,4,2,6,7,5]=>110010=>001101
[4,3,1,5,2,6,7]=>[3,1,5,4,2,6,7]=>110100=>001011
[4,3,1,5,2,7,6]=>[3,1,5,4,2,7,6]=>110101=>001010
[4,3,1,5,6,2,7]=>[3,1,6,5,4,2,7]=>110110=>001001
[4,3,1,5,6,7,2]=>[3,1,7,6,5,4,2]=>110111=>001000
[4,3,1,5,7,2,6]=>[3,1,7,5,4,2,6]=>110110=>001001
[4,3,1,5,7,6,2]=>[3,1,6,7,5,4,2]=>110110=>001001
[4,3,1,6,2,5,7]=>[3,1,6,4,2,5,7]=>110100=>001011
[4,3,1,6,2,7,5]=>[3,1,7,6,4,2,5]=>110101=>001010
[4,3,1,6,5,2,7]=>[3,1,5,6,4,2,7]=>110100=>001011
[4,3,1,6,5,7,2]=>[3,1,5,7,6,4,2]=>110101=>001010
[4,3,1,6,7,2,5]=>[3,1,7,4,2,6,5]=>110110=>001001
[4,3,1,6,7,5,2]=>[3,1,7,5,6,4,2]=>110110=>001001
[4,3,1,7,2,5,6]=>[3,1,7,4,2,5,6]=>110100=>001011
[4,3,1,7,2,6,5]=>[3,1,6,7,4,2,5]=>110100=>001011
[4,3,1,7,5,2,6]=>[3,1,5,7,4,2,6]=>110100=>001011
[4,3,1,7,5,6,2]=>[3,1,5,6,7,4,2]=>110100=>001011
[4,3,1,7,6,2,5]=>[3,1,6,4,2,7,5]=>110110=>001001
[4,3,1,7,6,5,2]=>[3,1,6,5,7,4,2]=>110110=>001001
[4,3,2,1,5,6,7]=>[3,2,4,1,5,6,7]=>110000=>001111
[4,3,2,1,5,7,6]=>[3,2,4,1,5,7,6]=>110001=>001110
[4,3,2,1,6,5,7]=>[3,2,4,1,6,5,7]=>110010=>001101
[4,3,2,1,6,7,5]=>[3,2,4,1,7,6,5]=>110011=>001100
[4,3,2,1,7,5,6]=>[3,2,4,1,7,5,6]=>110010=>001101
[4,3,2,1,7,6,5]=>[3,2,4,1,6,7,5]=>110010=>001101
[4,3,2,5,1,6,7]=>[3,2,5,4,1,6,7]=>110100=>001011
[4,3,2,5,1,7,6]=>[3,2,5,4,1,7,6]=>110101=>001010
[4,3,2,5,6,1,7]=>[3,2,6,5,4,1,7]=>110110=>001001
[4,3,2,5,6,7,1]=>[3,2,7,6,5,4,1]=>110111=>001000
[4,3,2,5,7,1,6]=>[3,2,7,5,4,1,6]=>110110=>001001
[4,3,2,5,7,6,1]=>[3,2,6,7,5,4,1]=>110110=>001001
[4,3,2,6,1,5,7]=>[3,2,6,4,1,5,7]=>110100=>001011
[4,3,2,6,1,7,5]=>[3,2,7,6,4,1,5]=>110101=>001010
[4,3,2,6,5,1,7]=>[3,2,5,6,4,1,7]=>110100=>001011
[4,3,2,6,5,7,1]=>[3,2,5,7,6,4,1]=>110101=>001010
[4,3,2,6,7,1,5]=>[3,2,7,4,1,6,5]=>110110=>001001
[4,3,2,6,7,5,1]=>[3,2,7,5,6,4,1]=>110110=>001001
[4,3,2,7,1,5,6]=>[3,2,7,4,1,5,6]=>110100=>001011
[4,3,2,7,1,6,5]=>[3,2,6,7,4,1,5]=>110100=>001011
[4,3,2,7,5,1,6]=>[3,2,5,7,4,1,6]=>110100=>001011
[4,3,2,7,5,6,1]=>[3,2,5,6,7,4,1]=>110100=>001011
[4,3,2,7,6,1,5]=>[3,2,6,4,1,7,5]=>110110=>001001
[4,3,2,7,6,5,1]=>[3,2,6,5,7,4,1]=>110110=>001001
[4,3,5,1,2,6,7]=>[5,3,1,4,2,6,7]=>111000=>000111
[4,3,5,1,2,7,6]=>[5,3,1,4,2,7,6]=>111001=>000110
[4,3,5,1,6,2,7]=>[6,5,3,1,4,2,7]=>111010=>000101
[4,3,5,1,6,7,2]=>[7,6,5,3,1,4,2]=>111011=>000100
[4,3,5,1,7,2,6]=>[7,5,3,1,4,2,6]=>111010=>000101
[4,3,5,1,7,6,2]=>[6,7,5,3,1,4,2]=>111010=>000101
[4,3,5,2,1,6,7]=>[5,3,2,4,1,6,7]=>111000=>000111
[4,3,5,2,1,7,6]=>[5,3,2,4,1,7,6]=>111001=>000110
[4,3,5,2,6,1,7]=>[6,5,3,2,4,1,7]=>111010=>000101
[4,3,5,2,6,7,1]=>[7,6,5,3,2,4,1]=>111011=>000100
[4,3,5,2,7,1,6]=>[7,5,3,2,4,1,6]=>111010=>000101
[4,3,5,2,7,6,1]=>[6,7,5,3,2,4,1]=>111010=>000101
[4,3,5,6,1,2,7]=>[6,3,1,5,4,2,7]=>111100=>000011
[4,3,5,6,1,7,2]=>[7,6,3,1,5,4,2]=>111101=>000010
[4,3,5,6,2,1,7]=>[6,3,2,5,4,1,7]=>111100=>000011
[4,3,5,6,2,7,1]=>[7,6,3,2,5,4,1]=>111101=>000010
[4,3,5,6,7,1,2]=>[7,3,1,6,5,4,2]=>111110=>000001
[4,3,5,6,7,2,1]=>[7,3,2,6,5,4,1]=>111110=>000001
[4,3,5,7,1,2,6]=>[7,3,1,5,4,2,6]=>111100=>000011
[4,3,5,7,1,6,2]=>[6,7,3,1,5,4,2]=>111100=>000011
[4,3,5,7,2,1,6]=>[7,3,2,5,4,1,6]=>111100=>000011
[4,3,5,7,2,6,1]=>[6,7,3,2,5,4,1]=>111100=>000011
[4,3,5,7,6,1,2]=>[6,3,1,7,5,4,2]=>111110=>000001
[4,3,5,7,6,2,1]=>[6,3,2,7,5,4,1]=>111110=>000001
[4,3,6,1,2,5,7]=>[6,3,1,4,2,5,7]=>111000=>000111
[4,3,6,1,2,7,5]=>[7,6,3,1,4,2,5]=>111001=>000110
[4,3,6,1,5,2,7]=>[5,6,3,1,4,2,7]=>111000=>000111
[4,3,6,1,5,7,2]=>[5,7,6,3,1,4,2]=>111001=>000110
[4,3,6,1,7,2,5]=>[7,3,1,4,2,6,5]=>111010=>000101
[4,3,6,1,7,5,2]=>[7,5,6,3,1,4,2]=>111010=>000101
[4,3,6,2,1,5,7]=>[6,3,2,4,1,5,7]=>111000=>000111
[4,3,6,2,1,7,5]=>[7,6,3,2,4,1,5]=>111001=>000110
[4,3,6,2,5,1,7]=>[5,6,3,2,4,1,7]=>111000=>000111
[4,3,6,2,5,7,1]=>[5,7,6,3,2,4,1]=>111001=>000110
[4,3,6,2,7,1,5]=>[7,3,2,4,1,6,5]=>111010=>000101
[4,3,6,2,7,5,1]=>[7,5,6,3,2,4,1]=>111010=>000101
[4,3,6,5,1,2,7]=>[5,3,1,6,4,2,7]=>111100=>000011
[4,3,6,5,1,7,2]=>[5,3,1,7,6,4,2]=>111101=>000010
[4,3,6,5,2,1,7]=>[5,3,2,6,4,1,7]=>111100=>000011
[4,3,6,5,2,7,1]=>[5,3,2,7,6,4,1]=>111101=>000010
[4,3,6,5,7,1,2]=>[7,5,3,1,6,4,2]=>111110=>000001
[4,3,6,5,7,2,1]=>[7,5,3,2,6,4,1]=>111110=>000001
[4,3,6,7,1,2,5]=>[7,3,1,6,4,2,5]=>111100=>000011
[4,3,6,7,1,5,2]=>[7,3,1,5,6,4,2]=>111100=>000011
[4,3,6,7,2,1,5]=>[7,3,2,6,4,1,5]=>111100=>000011
[4,3,6,7,2,5,1]=>[7,3,2,5,6,4,1]=>111100=>000011
[4,3,6,7,5,1,2]=>[5,7,3,1,6,4,2]=>111100=>000011
[4,3,6,7,5,2,1]=>[5,7,3,2,6,4,1]=>111100=>000011
[4,3,7,1,2,5,6]=>[7,3,1,4,2,5,6]=>111000=>000111
[4,3,7,1,2,6,5]=>[6,7,3,1,4,2,5]=>111000=>000111
[4,3,7,1,5,2,6]=>[5,7,3,1,4,2,6]=>111000=>000111
[4,3,7,1,5,6,2]=>[5,6,7,3,1,4,2]=>111000=>000111
[4,3,7,1,6,2,5]=>[6,3,1,4,2,7,5]=>111010=>000101
[4,3,7,1,6,5,2]=>[6,5,7,3,1,4,2]=>111010=>000101
[4,3,7,2,1,5,6]=>[7,3,2,4,1,5,6]=>111000=>000111
[4,3,7,2,1,6,5]=>[6,7,3,2,4,1,5]=>111000=>000111
[4,3,7,2,5,1,6]=>[5,7,3,2,4,1,6]=>111000=>000111
[4,3,7,2,5,6,1]=>[5,6,7,3,2,4,1]=>111000=>000111
[4,3,7,2,6,1,5]=>[6,3,2,4,1,7,5]=>111010=>000101
[4,3,7,2,6,5,1]=>[6,5,7,3,2,4,1]=>111010=>000101
[4,3,7,5,1,2,6]=>[5,3,1,7,4,2,6]=>111100=>000011
[4,3,7,5,1,6,2]=>[5,3,1,6,7,4,2]=>111100=>000011
[4,3,7,5,2,1,6]=>[5,3,2,7,4,1,6]=>111100=>000011
[4,3,7,5,2,6,1]=>[5,3,2,6,7,4,1]=>111100=>000011
[4,3,7,5,6,1,2]=>[6,5,3,1,7,4,2]=>111110=>000001
[4,3,7,5,6,2,1]=>[6,5,3,2,7,4,1]=>111110=>000001
[4,3,7,6,1,2,5]=>[6,3,1,7,4,2,5]=>111100=>000011
[4,3,7,6,1,5,2]=>[6,3,1,5,7,4,2]=>111100=>000011
[4,3,7,6,2,1,5]=>[6,3,2,7,4,1,5]=>111100=>000011
[4,3,7,6,2,5,1]=>[6,3,2,5,7,4,1]=>111100=>000011
[4,3,7,6,5,1,2]=>[5,6,3,1,7,4,2]=>111100=>000011
[4,3,7,6,5,2,1]=>[5,6,3,2,7,4,1]=>111100=>000011
[4,5,1,2,3,6,7]=>[5,1,4,2,3,6,7]=>110000=>001111
[4,5,1,2,3,7,6]=>[5,1,4,2,3,7,6]=>110001=>001110
[4,5,1,2,6,3,7]=>[6,5,1,4,2,3,7]=>110010=>001101
[4,5,1,2,6,7,3]=>[7,6,5,1,4,2,3]=>110011=>001100
[4,5,1,2,7,3,6]=>[7,5,1,4,2,3,6]=>110010=>001101
[4,5,1,2,7,6,3]=>[6,7,5,1,4,2,3]=>110010=>001101
[4,5,1,3,2,6,7]=>[5,1,3,4,2,6,7]=>110000=>001111
[4,5,1,3,2,7,6]=>[5,1,3,4,2,7,6]=>110001=>001110
[4,5,1,3,6,2,7]=>[6,5,1,3,4,2,7]=>110010=>001101
[4,5,1,3,6,7,2]=>[7,6,5,1,3,4,2]=>110011=>001100
[4,5,1,3,7,2,6]=>[7,5,1,3,4,2,6]=>110010=>001101
[4,5,1,3,7,6,2]=>[6,7,5,1,3,4,2]=>110010=>001101
[4,5,1,6,2,3,7]=>[6,1,5,4,2,3,7]=>110100=>001011
[4,5,1,6,2,7,3]=>[7,6,1,5,4,2,3]=>110101=>001010
[4,5,1,6,3,2,7]=>[6,1,3,5,4,2,7]=>110100=>001011
[4,5,1,6,3,7,2]=>[7,6,1,3,5,4,2]=>110101=>001010
[4,5,1,6,7,2,3]=>[7,1,6,5,4,2,3]=>110110=>001001
[4,5,1,6,7,3,2]=>[7,1,3,6,5,4,2]=>110110=>001001
[4,5,1,7,2,3,6]=>[7,1,5,4,2,3,6]=>110100=>001011
[4,5,1,7,2,6,3]=>[6,7,1,5,4,2,3]=>110100=>001011
[4,5,1,7,3,2,6]=>[7,1,3,5,4,2,6]=>110100=>001011
[4,5,1,7,3,6,2]=>[6,7,1,3,5,4,2]=>110100=>001011
[4,5,1,7,6,2,3]=>[6,1,7,5,4,2,3]=>110110=>001001
[4,5,1,7,6,3,2]=>[6,1,3,7,5,4,2]=>110110=>001001
[4,5,2,1,3,6,7]=>[5,2,4,1,3,6,7]=>110000=>001111
[4,5,2,1,3,7,6]=>[5,2,4,1,3,7,6]=>110001=>001110
[4,5,2,1,6,3,7]=>[6,5,2,4,1,3,7]=>110010=>001101
[4,5,2,1,6,7,3]=>[7,6,5,2,4,1,3]=>110011=>001100
[4,5,2,1,7,3,6]=>[7,5,2,4,1,3,6]=>110010=>001101
[4,5,2,1,7,6,3]=>[6,7,5,2,4,1,3]=>110010=>001101
[4,5,2,3,1,6,7]=>[5,2,3,4,1,6,7]=>110000=>001111
[4,5,2,3,1,7,6]=>[5,2,3,4,1,7,6]=>110001=>001110
[4,5,2,3,6,1,7]=>[6,5,2,3,4,1,7]=>110010=>001101
[4,5,2,3,6,7,1]=>[7,6,5,2,3,4,1]=>110011=>001100
[4,5,2,3,7,1,6]=>[7,5,2,3,4,1,6]=>110010=>001101
[4,5,2,3,7,6,1]=>[6,7,5,2,3,4,1]=>110010=>001101
[4,5,2,6,1,3,7]=>[6,2,5,4,1,3,7]=>110100=>001011
[4,5,2,6,1,7,3]=>[7,6,2,5,4,1,3]=>110101=>001010
[4,5,2,6,3,1,7]=>[6,2,3,5,4,1,7]=>110100=>001011
[4,5,2,6,3,7,1]=>[7,6,2,3,5,4,1]=>110101=>001010
[4,5,2,6,7,1,3]=>[7,2,6,5,4,1,3]=>110110=>001001
[4,5,2,6,7,3,1]=>[7,2,3,6,5,4,1]=>110110=>001001
[4,5,2,7,1,3,6]=>[7,2,5,4,1,3,6]=>110100=>001011
[4,5,2,7,1,6,3]=>[6,7,2,5,4,1,3]=>110100=>001011
[4,5,2,7,3,1,6]=>[7,2,3,5,4,1,6]=>110100=>001011
[4,5,2,7,3,6,1]=>[6,7,2,3,5,4,1]=>110100=>001011
[4,5,2,7,6,1,3]=>[6,2,7,5,4,1,3]=>110110=>001001
[4,5,2,7,6,3,1]=>[6,2,3,7,5,4,1]=>110110=>001001
[4,5,3,1,2,6,7]=>[3,5,1,4,2,6,7]=>110000=>001111
[4,5,3,1,2,7,6]=>[3,5,1,4,2,7,6]=>110001=>001110
[4,5,3,1,6,2,7]=>[3,6,5,1,4,2,7]=>110010=>001101
[4,5,3,1,6,7,2]=>[3,7,6,5,1,4,2]=>110011=>001100
[4,5,3,1,7,2,6]=>[3,7,5,1,4,2,6]=>110010=>001101
[4,5,3,1,7,6,2]=>[3,6,7,5,1,4,2]=>110010=>001101
[4,5,3,2,1,6,7]=>[3,5,2,4,1,6,7]=>110000=>001111
[4,5,3,2,1,7,6]=>[3,5,2,4,1,7,6]=>110001=>001110
[4,5,3,2,6,1,7]=>[3,6,5,2,4,1,7]=>110010=>001101
[4,5,3,2,6,7,1]=>[3,7,6,5,2,4,1]=>110011=>001100
[4,5,3,2,7,1,6]=>[3,7,5,2,4,1,6]=>110010=>001101
[4,5,3,2,7,6,1]=>[3,6,7,5,2,4,1]=>110010=>001101
[4,5,3,6,1,2,7]=>[3,6,1,5,4,2,7]=>110100=>001011
[4,5,3,6,1,7,2]=>[3,7,6,1,5,4,2]=>110101=>001010
[4,5,3,6,2,1,7]=>[3,6,2,5,4,1,7]=>110100=>001011
[4,5,3,6,2,7,1]=>[3,7,6,2,5,4,1]=>110101=>001010
[4,5,3,6,7,1,2]=>[3,7,1,6,5,4,2]=>110110=>001001
[4,5,3,6,7,2,1]=>[3,7,2,6,5,4,1]=>110110=>001001
[4,5,3,7,1,2,6]=>[3,7,1,5,4,2,6]=>110100=>001011
[4,5,3,7,1,6,2]=>[3,6,7,1,5,4,2]=>110100=>001011
[4,5,3,7,2,1,6]=>[3,7,2,5,4,1,6]=>110100=>001011
[4,5,3,7,2,6,1]=>[3,6,7,2,5,4,1]=>110100=>001011
[4,5,3,7,6,1,2]=>[3,6,1,7,5,4,2]=>110110=>001001
[4,5,3,7,6,2,1]=>[3,6,2,7,5,4,1]=>110110=>001001
[4,5,6,1,2,3,7]=>[6,1,5,2,4,3,7]=>111000=>000111
[4,5,6,1,2,7,3]=>[7,6,1,5,2,4,3]=>111001=>000110
[4,5,6,1,3,2,7]=>[6,1,5,3,4,2,7]=>111000=>000111
[4,5,6,1,3,7,2]=>[7,6,1,5,3,4,2]=>111001=>000110
[4,5,6,1,7,2,3]=>[7,1,6,5,2,4,3]=>111010=>000101
[4,5,6,1,7,3,2]=>[7,1,6,5,3,4,2]=>111010=>000101
[4,5,6,2,1,3,7]=>[6,2,5,1,4,3,7]=>111000=>000111
[4,5,6,2,1,7,3]=>[7,6,2,5,1,4,3]=>111001=>000110
[4,5,6,2,3,1,7]=>[6,2,5,3,4,1,7]=>111000=>000111
[4,5,6,2,3,7,1]=>[7,6,2,5,3,4,1]=>111001=>000110
[4,5,6,2,7,1,3]=>[7,2,6,5,1,4,3]=>111010=>000101
[4,5,6,2,7,3,1]=>[7,2,6,5,3,4,1]=>111010=>000101
[4,5,6,3,1,2,7]=>[6,3,5,1,4,2,7]=>111000=>000111
[4,5,6,3,1,7,2]=>[7,6,3,5,1,4,2]=>111001=>000110
[4,5,6,3,2,1,7]=>[6,3,5,2,4,1,7]=>111000=>000111
[4,5,6,3,2,7,1]=>[7,6,3,5,2,4,1]=>111001=>000110
[4,5,6,3,7,1,2]=>[7,3,6,5,1,4,2]=>111010=>000101
[4,5,6,3,7,2,1]=>[7,3,6,5,2,4,1]=>111010=>000101
[4,5,6,7,1,2,3]=>[7,1,6,2,5,4,3]=>111100=>000011
[4,5,6,7,1,3,2]=>[7,1,6,3,5,4,2]=>111100=>000011
[4,5,6,7,2,1,3]=>[7,2,6,1,5,4,3]=>111100=>000011
[4,5,6,7,2,3,1]=>[7,2,6,3,5,4,1]=>111100=>000011
[4,5,6,7,3,1,2]=>[7,3,6,1,5,4,2]=>111100=>000011
[4,5,6,7,3,2,1]=>[7,3,6,2,5,4,1]=>111100=>000011
[4,5,7,1,2,3,6]=>[7,1,5,2,4,3,6]=>111000=>000111
[4,5,7,1,2,6,3]=>[6,7,1,5,2,4,3]=>111000=>000111
[4,5,7,1,3,2,6]=>[7,1,5,3,4,2,6]=>111000=>000111
[4,5,7,1,3,6,2]=>[6,7,1,5,3,4,2]=>111000=>000111
[4,5,7,1,6,2,3]=>[6,1,7,5,2,4,3]=>111010=>000101
[4,5,7,1,6,3,2]=>[6,1,7,5,3,4,2]=>111010=>000101
[4,5,7,2,1,3,6]=>[7,2,5,1,4,3,6]=>111000=>000111
[4,5,7,2,1,6,3]=>[6,7,2,5,1,4,3]=>111000=>000111
[4,5,7,2,3,1,6]=>[7,2,5,3,4,1,6]=>111000=>000111
[4,5,7,2,3,6,1]=>[6,7,2,5,3,4,1]=>111000=>000111
[4,5,7,2,6,1,3]=>[6,2,7,5,1,4,3]=>111010=>000101
[4,5,7,2,6,3,1]=>[6,2,7,5,3,4,1]=>111010=>000101
[4,5,7,3,1,2,6]=>[7,3,5,1,4,2,6]=>111000=>000111
[4,5,7,3,1,6,2]=>[6,7,3,5,1,4,2]=>111000=>000111
[4,5,7,3,2,1,6]=>[7,3,5,2,4,1,6]=>111000=>000111
[4,5,7,3,2,6,1]=>[6,7,3,5,2,4,1]=>111000=>000111
[4,5,7,3,6,1,2]=>[6,3,7,5,1,4,2]=>111010=>000101
[4,5,7,3,6,2,1]=>[6,3,7,5,2,4,1]=>111010=>000101
[4,5,7,6,1,2,3]=>[6,1,7,2,5,4,3]=>111100=>000011
[4,5,7,6,1,3,2]=>[6,1,7,3,5,4,2]=>111100=>000011
[4,5,7,6,2,1,3]=>[6,2,7,1,5,4,3]=>111100=>000011
[4,5,7,6,2,3,1]=>[6,2,7,3,5,4,1]=>111100=>000011
[4,5,7,6,3,1,2]=>[6,3,7,1,5,4,2]=>111100=>000011
[4,5,7,6,3,2,1]=>[6,3,7,2,5,4,1]=>111100=>000011
[4,6,1,2,3,5,7]=>[6,1,4,2,3,5,7]=>110000=>001111
[4,6,1,2,3,7,5]=>[7,6,1,4,2,3,5]=>110001=>001110
[4,6,1,2,5,3,7]=>[5,6,1,4,2,3,7]=>110000=>001111
[4,6,1,2,5,7,3]=>[5,7,6,1,4,2,3]=>110001=>001110
[4,6,1,2,7,3,5]=>[7,1,4,2,3,6,5]=>110010=>001101
[4,6,1,2,7,5,3]=>[7,5,6,1,4,2,3]=>110010=>001101
[4,6,1,3,2,5,7]=>[6,1,3,4,2,5,7]=>110000=>001111
[4,6,1,3,2,7,5]=>[7,6,1,3,4,2,5]=>110001=>001110
[4,6,1,3,5,2,7]=>[5,6,1,3,4,2,7]=>110000=>001111
[4,6,1,3,5,7,2]=>[5,7,6,1,3,4,2]=>110001=>001110
[4,6,1,3,7,2,5]=>[7,1,3,4,2,6,5]=>110010=>001101
[4,6,1,3,7,5,2]=>[7,5,6,1,3,4,2]=>110010=>001101
[4,6,1,5,2,3,7]=>[5,1,6,4,2,3,7]=>110100=>001011
[4,6,1,5,2,7,3]=>[5,1,7,6,4,2,3]=>110101=>001010
[4,6,1,5,3,2,7]=>[5,1,3,6,4,2,7]=>110100=>001011
[4,6,1,5,3,7,2]=>[5,1,3,7,6,4,2]=>110101=>001010
[4,6,1,5,7,2,3]=>[7,5,1,6,4,2,3]=>110110=>001001
[4,6,1,5,7,3,2]=>[7,5,1,3,6,4,2]=>110110=>001001
[4,6,1,7,2,3,5]=>[7,1,6,4,2,3,5]=>110100=>001011
[4,6,1,7,2,5,3]=>[7,1,5,6,4,2,3]=>110100=>001011
[4,6,1,7,3,2,5]=>[7,1,3,6,4,2,5]=>110100=>001011
[4,6,1,7,3,5,2]=>[7,1,3,5,6,4,2]=>110100=>001011
[4,6,1,7,5,2,3]=>[5,7,1,6,4,2,3]=>110100=>001011
[4,6,1,7,5,3,2]=>[5,7,1,3,6,4,2]=>110100=>001011
[4,6,2,1,3,5,7]=>[6,2,4,1,3,5,7]=>110000=>001111
[4,6,2,1,3,7,5]=>[7,6,2,4,1,3,5]=>110001=>001110
[4,6,2,1,5,3,7]=>[5,6,2,4,1,3,7]=>110000=>001111
[4,6,2,1,5,7,3]=>[5,7,6,2,4,1,3]=>110001=>001110
[4,6,2,1,7,3,5]=>[7,2,4,1,3,6,5]=>110010=>001101
[4,6,2,1,7,5,3]=>[7,5,6,2,4,1,3]=>110010=>001101
[4,6,2,3,1,5,7]=>[6,2,3,4,1,5,7]=>110000=>001111
[4,6,2,3,1,7,5]=>[7,6,2,3,4,1,5]=>110001=>001110
[4,6,2,3,5,1,7]=>[5,6,2,3,4,1,7]=>110000=>001111
[4,6,2,3,5,7,1]=>[5,7,6,2,3,4,1]=>110001=>001110
[4,6,2,3,7,1,5]=>[7,2,3,4,1,6,5]=>110010=>001101
[4,6,2,3,7,5,1]=>[7,5,6,2,3,4,1]=>110010=>001101
[4,6,2,5,1,3,7]=>[5,2,6,4,1,3,7]=>110100=>001011
[4,6,2,5,1,7,3]=>[5,2,7,6,4,1,3]=>110101=>001010
[4,6,2,5,3,1,7]=>[5,2,3,6,4,1,7]=>110100=>001011
[4,6,2,5,3,7,1]=>[5,2,3,7,6,4,1]=>110101=>001010
[4,6,2,5,7,1,3]=>[7,5,2,6,4,1,3]=>110110=>001001
[4,6,2,5,7,3,1]=>[7,5,2,3,6,4,1]=>110110=>001001
[4,6,2,7,1,3,5]=>[7,2,6,4,1,3,5]=>110100=>001011
[4,6,2,7,1,5,3]=>[7,2,5,6,4,1,3]=>110100=>001011
[4,6,2,7,3,1,5]=>[7,2,3,6,4,1,5]=>110100=>001011
[4,6,2,7,3,5,1]=>[7,2,3,5,6,4,1]=>110100=>001011
[4,6,2,7,5,1,3]=>[5,7,2,6,4,1,3]=>110100=>001011
[4,6,2,7,5,3,1]=>[5,7,2,3,6,4,1]=>110100=>001011
[4,6,3,1,2,5,7]=>[3,6,1,4,2,5,7]=>110000=>001111
[4,6,3,1,2,7,5]=>[3,7,6,1,4,2,5]=>110001=>001110
[4,6,3,1,5,2,7]=>[3,5,6,1,4,2,7]=>110000=>001111
[4,6,3,1,5,7,2]=>[3,5,7,6,1,4,2]=>110001=>001110
[4,6,3,1,7,2,5]=>[3,7,1,4,2,6,5]=>110010=>001101
[4,6,3,1,7,5,2]=>[3,7,5,6,1,4,2]=>110010=>001101
[4,6,3,2,1,5,7]=>[3,6,2,4,1,5,7]=>110000=>001111
[4,6,3,2,1,7,5]=>[3,7,6,2,4,1,5]=>110001=>001110
[4,6,3,2,5,1,7]=>[3,5,6,2,4,1,7]=>110000=>001111
[4,6,3,2,5,7,1]=>[3,5,7,6,2,4,1]=>110001=>001110
[4,6,3,2,7,1,5]=>[3,7,2,4,1,6,5]=>110010=>001101
[4,6,3,2,7,5,1]=>[3,7,5,6,2,4,1]=>110010=>001101
[4,6,3,5,1,2,7]=>[3,5,1,6,4,2,7]=>110100=>001011
[4,6,3,5,1,7,2]=>[3,5,1,7,6,4,2]=>110101=>001010
[4,6,3,5,2,1,7]=>[3,5,2,6,4,1,7]=>110100=>001011
[4,6,3,5,2,7,1]=>[3,5,2,7,6,4,1]=>110101=>001010
[4,6,3,5,7,1,2]=>[3,7,5,1,6,4,2]=>110110=>001001
[4,6,3,5,7,2,1]=>[3,7,5,2,6,4,1]=>110110=>001001
[4,6,3,7,1,2,5]=>[3,7,1,6,4,2,5]=>110100=>001011
[4,6,3,7,1,5,2]=>[3,7,1,5,6,4,2]=>110100=>001011
[4,6,3,7,2,1,5]=>[3,7,2,6,4,1,5]=>110100=>001011
[4,6,3,7,2,5,1]=>[3,7,2,5,6,4,1]=>110100=>001011
[4,6,3,7,5,1,2]=>[3,5,7,1,6,4,2]=>110100=>001011
[4,6,3,7,5,2,1]=>[3,5,7,2,6,4,1]=>110100=>001011
[4,6,5,1,2,3,7]=>[5,1,6,2,4,3,7]=>111000=>000111
[4,6,5,1,2,7,3]=>[5,1,7,6,2,4,3]=>111001=>000110
[4,6,5,1,3,2,7]=>[5,1,6,3,4,2,7]=>111000=>000111
[4,6,5,1,3,7,2]=>[5,1,7,6,3,4,2]=>111001=>000110
[4,6,5,1,7,2,3]=>[7,5,1,6,2,4,3]=>111010=>000101
[4,6,5,1,7,3,2]=>[7,5,1,6,3,4,2]=>111010=>000101
[4,6,5,2,1,3,7]=>[5,2,6,1,4,3,7]=>111000=>000111
[4,6,5,2,1,7,3]=>[5,2,7,6,1,4,3]=>111001=>000110
[4,6,5,2,3,1,7]=>[5,2,6,3,4,1,7]=>111000=>000111
[4,6,5,2,3,7,1]=>[5,2,7,6,3,4,1]=>111001=>000110
[4,6,5,2,7,1,3]=>[7,5,2,6,1,4,3]=>111010=>000101
[4,6,5,2,7,3,1]=>[7,5,2,6,3,4,1]=>111010=>000101
[4,6,5,3,1,2,7]=>[5,3,6,1,4,2,7]=>111000=>000111
[4,6,5,3,1,7,2]=>[5,3,7,6,1,4,2]=>111001=>000110
[4,6,5,3,2,1,7]=>[5,3,6,2,4,1,7]=>111000=>000111
[4,6,5,3,2,7,1]=>[5,3,7,6,2,4,1]=>111001=>000110
[4,6,5,3,7,1,2]=>[7,5,3,6,1,4,2]=>111010=>000101
[4,6,5,3,7,2,1]=>[7,5,3,6,2,4,1]=>111010=>000101
[4,6,5,7,1,2,3]=>[7,1,5,2,6,4,3]=>111100=>000011
[4,6,5,7,1,3,2]=>[7,1,5,3,6,4,2]=>111100=>000011
[4,6,5,7,2,1,3]=>[7,2,5,1,6,4,3]=>111100=>000011
[4,6,5,7,2,3,1]=>[7,2,5,3,6,4,1]=>111100=>000011
[4,6,5,7,3,1,2]=>[7,3,5,1,6,4,2]=>111100=>000011
[4,6,5,7,3,2,1]=>[7,3,5,2,6,4,1]=>111100=>000011
[4,6,7,1,2,3,5]=>[7,1,6,2,4,3,5]=>111000=>000111
[4,6,7,1,2,5,3]=>[7,1,5,6,2,4,3]=>111000=>000111
[4,6,7,1,3,2,5]=>[7,1,6,3,4,2,5]=>111000=>000111
[4,6,7,1,3,5,2]=>[7,1,5,6,3,4,2]=>111000=>000111
[4,6,7,1,5,2,3]=>[5,7,1,6,2,4,3]=>111000=>000111
[4,6,7,1,5,3,2]=>[5,7,1,6,3,4,2]=>111000=>000111
[4,6,7,2,1,3,5]=>[7,2,6,1,4,3,5]=>111000=>000111
[4,6,7,2,1,5,3]=>[7,2,5,6,1,4,3]=>111000=>000111
[4,6,7,2,3,1,5]=>[7,2,6,3,4,1,5]=>111000=>000111
[4,6,7,2,3,5,1]=>[7,2,5,6,3,4,1]=>111000=>000111
[4,6,7,2,5,1,3]=>[5,7,2,6,1,4,3]=>111000=>000111
[4,6,7,2,5,3,1]=>[5,7,2,6,3,4,1]=>111000=>000111
[4,6,7,3,1,2,5]=>[7,3,6,1,4,2,5]=>111000=>000111
[4,6,7,3,1,5,2]=>[7,3,5,6,1,4,2]=>111000=>000111
[4,6,7,3,2,1,5]=>[7,3,6,2,4,1,5]=>111000=>000111
[4,6,7,3,2,5,1]=>[7,3,5,6,2,4,1]=>111000=>000111
[4,6,7,3,5,1,2]=>[5,7,3,6,1,4,2]=>111000=>000111
[4,6,7,3,5,2,1]=>[5,7,3,6,2,4,1]=>111000=>000111
[4,6,7,5,1,2,3]=>[5,1,7,2,6,4,3]=>111100=>000011
[4,6,7,5,1,3,2]=>[5,1,7,3,6,4,2]=>111100=>000011
[4,6,7,5,2,1,3]=>[5,2,7,1,6,4,3]=>111100=>000011
[4,6,7,5,2,3,1]=>[5,2,7,3,6,4,1]=>111100=>000011
[4,6,7,5,3,1,2]=>[5,3,7,1,6,4,2]=>111100=>000011
[4,6,7,5,3,2,1]=>[5,3,7,2,6,4,1]=>111100=>000011
[4,7,1,2,3,5,6]=>[7,1,4,2,3,5,6]=>110000=>001111
[4,7,1,2,3,6,5]=>[6,7,1,4,2,3,5]=>110000=>001111
[4,7,1,2,5,3,6]=>[5,7,1,4,2,3,6]=>110000=>001111
[4,7,1,2,5,6,3]=>[5,6,7,1,4,2,3]=>110000=>001111
[4,7,1,2,6,3,5]=>[6,1,4,2,3,7,5]=>110010=>001101
[4,7,1,2,6,5,3]=>[6,5,7,1,4,2,3]=>110010=>001101
[4,7,1,3,2,5,6]=>[7,1,3,4,2,5,6]=>110000=>001111
[4,7,1,3,2,6,5]=>[6,7,1,3,4,2,5]=>110000=>001111
[4,7,1,3,5,2,6]=>[5,7,1,3,4,2,6]=>110000=>001111
[4,7,1,3,5,6,2]=>[5,6,7,1,3,4,2]=>110000=>001111
[4,7,1,3,6,2,5]=>[6,1,3,4,2,7,5]=>110010=>001101
[4,7,1,3,6,5,2]=>[6,5,7,1,3,4,2]=>110010=>001101
[4,7,1,5,2,3,6]=>[5,1,7,4,2,3,6]=>110100=>001011
[4,7,1,5,2,6,3]=>[5,1,6,7,4,2,3]=>110100=>001011
[4,7,1,5,3,2,6]=>[5,1,3,7,4,2,6]=>110100=>001011
[4,7,1,5,3,6,2]=>[5,1,3,6,7,4,2]=>110100=>001011
[4,7,1,5,6,2,3]=>[6,5,1,7,4,2,3]=>110110=>001001
[4,7,1,5,6,3,2]=>[6,5,1,3,7,4,2]=>110110=>001001
[4,7,1,6,2,3,5]=>[6,1,7,4,2,3,5]=>110100=>001011
[4,7,1,6,2,5,3]=>[6,1,5,7,4,2,3]=>110100=>001011
[4,7,1,6,3,2,5]=>[6,1,3,7,4,2,5]=>110100=>001011
[4,7,1,6,3,5,2]=>[6,1,3,5,7,4,2]=>110100=>001011
[4,7,1,6,5,2,3]=>[5,6,1,7,4,2,3]=>110100=>001011
[4,7,1,6,5,3,2]=>[5,6,1,3,7,4,2]=>110100=>001011
[4,7,2,1,3,5,6]=>[7,2,4,1,3,5,6]=>110000=>001111
[4,7,2,1,3,6,5]=>[6,7,2,4,1,3,5]=>110000=>001111
[4,7,2,1,5,3,6]=>[5,7,2,4,1,3,6]=>110000=>001111
[4,7,2,1,5,6,3]=>[5,6,7,2,4,1,3]=>110000=>001111
[4,7,2,1,6,3,5]=>[6,2,4,1,3,7,5]=>110010=>001101
[4,7,2,1,6,5,3]=>[6,5,7,2,4,1,3]=>110010=>001101
[4,7,2,3,1,5,6]=>[7,2,3,4,1,5,6]=>110000=>001111
[4,7,2,3,1,6,5]=>[6,7,2,3,4,1,5]=>110000=>001111
[4,7,2,3,5,1,6]=>[5,7,2,3,4,1,6]=>110000=>001111
[4,7,2,3,5,6,1]=>[5,6,7,2,3,4,1]=>110000=>001111
[4,7,2,3,6,1,5]=>[6,2,3,4,1,7,5]=>110010=>001101
[4,7,2,3,6,5,1]=>[6,5,7,2,3,4,1]=>110010=>001101
[4,7,2,5,1,3,6]=>[5,2,7,4,1,3,6]=>110100=>001011
[4,7,2,5,1,6,3]=>[5,2,6,7,4,1,3]=>110100=>001011
[4,7,2,5,3,1,6]=>[5,2,3,7,4,1,6]=>110100=>001011
[4,7,2,5,3,6,1]=>[5,2,3,6,7,4,1]=>110100=>001011
[4,7,2,5,6,1,3]=>[6,5,2,7,4,1,3]=>110110=>001001
[4,7,2,5,6,3,1]=>[6,5,2,3,7,4,1]=>110110=>001001
[4,7,2,6,1,3,5]=>[6,2,7,4,1,3,5]=>110100=>001011
[4,7,2,6,1,5,3]=>[6,2,5,7,4,1,3]=>110100=>001011
[4,7,2,6,3,1,5]=>[6,2,3,7,4,1,5]=>110100=>001011
[4,7,2,6,3,5,1]=>[6,2,3,5,7,4,1]=>110100=>001011
[4,7,2,6,5,1,3]=>[5,6,2,7,4,1,3]=>110100=>001011
[4,7,2,6,5,3,1]=>[5,6,2,3,7,4,1]=>110100=>001011
[4,7,3,1,2,5,6]=>[3,7,1,4,2,5,6]=>110000=>001111
[4,7,3,1,2,6,5]=>[3,6,7,1,4,2,5]=>110000=>001111
[4,7,3,1,5,2,6]=>[3,5,7,1,4,2,6]=>110000=>001111
[4,7,3,1,5,6,2]=>[3,5,6,7,1,4,2]=>110000=>001111
[4,7,3,1,6,2,5]=>[3,6,1,4,2,7,5]=>110010=>001101
[4,7,3,1,6,5,2]=>[3,6,5,7,1,4,2]=>110010=>001101
[4,7,3,2,1,5,6]=>[3,7,2,4,1,5,6]=>110000=>001111
[4,7,3,2,1,6,5]=>[3,6,7,2,4,1,5]=>110000=>001111
[4,7,3,2,5,1,6]=>[3,5,7,2,4,1,6]=>110000=>001111
[4,7,3,2,5,6,1]=>[3,5,6,7,2,4,1]=>110000=>001111
[4,7,3,2,6,1,5]=>[3,6,2,4,1,7,5]=>110010=>001101
[4,7,3,2,6,5,1]=>[3,6,5,7,2,4,1]=>110010=>001101
[4,7,3,5,1,2,6]=>[3,5,1,7,4,2,6]=>110100=>001011
[4,7,3,5,1,6,2]=>[3,5,1,6,7,4,2]=>110100=>001011
[4,7,3,5,2,1,6]=>[3,5,2,7,4,1,6]=>110100=>001011
[4,7,3,5,2,6,1]=>[3,5,2,6,7,4,1]=>110100=>001011
[4,7,3,5,6,1,2]=>[3,6,5,1,7,4,2]=>110110=>001001
[4,7,3,5,6,2,1]=>[3,6,5,2,7,4,1]=>110110=>001001
[4,7,3,6,1,2,5]=>[3,6,1,7,4,2,5]=>110100=>001011
[4,7,3,6,1,5,2]=>[3,6,1,5,7,4,2]=>110100=>001011
[4,7,3,6,2,1,5]=>[3,6,2,7,4,1,5]=>110100=>001011
[4,7,3,6,2,5,1]=>[3,6,2,5,7,4,1]=>110100=>001011
[4,7,3,6,5,1,2]=>[3,5,6,1,7,4,2]=>110100=>001011
[4,7,3,6,5,2,1]=>[3,5,6,2,7,4,1]=>110100=>001011
[4,7,5,1,2,3,6]=>[5,1,7,2,4,3,6]=>111000=>000111
[4,7,5,1,2,6,3]=>[5,1,6,7,2,4,3]=>111000=>000111
[4,7,5,1,3,2,6]=>[5,1,7,3,4,2,6]=>111000=>000111
[4,7,5,1,3,6,2]=>[5,1,6,7,3,4,2]=>111000=>000111
[4,7,5,1,6,2,3]=>[6,5,1,7,2,4,3]=>111010=>000101
[4,7,5,1,6,3,2]=>[6,5,1,7,3,4,2]=>111010=>000101
[4,7,5,2,1,3,6]=>[5,2,7,1,4,3,6]=>111000=>000111
[4,7,5,2,1,6,3]=>[5,2,6,7,1,4,3]=>111000=>000111
[4,7,5,2,3,1,6]=>[5,2,7,3,4,1,6]=>111000=>000111
[4,7,5,2,3,6,1]=>[5,2,6,7,3,4,1]=>111000=>000111
[4,7,5,2,6,1,3]=>[6,5,2,7,1,4,3]=>111010=>000101
[4,7,5,2,6,3,1]=>[6,5,2,7,3,4,1]=>111010=>000101
[4,7,5,3,1,2,6]=>[5,3,7,1,4,2,6]=>111000=>000111
[4,7,5,3,1,6,2]=>[5,3,6,7,1,4,2]=>111000=>000111
[4,7,5,3,2,1,6]=>[5,3,7,2,4,1,6]=>111000=>000111
[4,7,5,3,2,6,1]=>[5,3,6,7,2,4,1]=>111000=>000111
[4,7,5,3,6,1,2]=>[6,5,3,7,1,4,2]=>111010=>000101
[4,7,5,3,6,2,1]=>[6,5,3,7,2,4,1]=>111010=>000101
[4,7,5,6,1,2,3]=>[6,1,5,2,7,4,3]=>111100=>000011
[4,7,5,6,1,3,2]=>[6,1,5,3,7,4,2]=>111100=>000011
[4,7,5,6,2,1,3]=>[6,2,5,1,7,4,3]=>111100=>000011
[4,7,5,6,2,3,1]=>[6,2,5,3,7,4,1]=>111100=>000011
[4,7,5,6,3,1,2]=>[6,3,5,1,7,4,2]=>111100=>000011
[4,7,5,6,3,2,1]=>[6,3,5,2,7,4,1]=>111100=>000011
[4,7,6,1,2,3,5]=>[6,1,7,2,4,3,5]=>111000=>000111
[4,7,6,1,2,5,3]=>[6,1,5,7,2,4,3]=>111000=>000111
[4,7,6,1,3,2,5]=>[6,1,7,3,4,2,5]=>111000=>000111
[4,7,6,1,3,5,2]=>[6,1,5,7,3,4,2]=>111000=>000111
[4,7,6,1,5,2,3]=>[5,6,1,7,2,4,3]=>111000=>000111
[4,7,6,1,5,3,2]=>[5,6,1,7,3,4,2]=>111000=>000111
[4,7,6,2,1,3,5]=>[6,2,7,1,4,3,5]=>111000=>000111
[4,7,6,2,1,5,3]=>[6,2,5,7,1,4,3]=>111000=>000111
[4,7,6,2,3,1,5]=>[6,2,7,3,4,1,5]=>111000=>000111
[4,7,6,2,3,5,1]=>[6,2,5,7,3,4,1]=>111000=>000111
[4,7,6,2,5,1,3]=>[5,6,2,7,1,4,3]=>111000=>000111
[4,7,6,2,5,3,1]=>[5,6,2,7,3,4,1]=>111000=>000111
[4,7,6,3,1,2,5]=>[6,3,7,1,4,2,5]=>111000=>000111
[4,7,6,3,1,5,2]=>[6,3,5,7,1,4,2]=>111000=>000111
[4,7,6,3,2,1,5]=>[6,3,7,2,4,1,5]=>111000=>000111
[4,7,6,3,2,5,1]=>[6,3,5,7,2,4,1]=>111000=>000111
[4,7,6,3,5,1,2]=>[5,6,3,7,1,4,2]=>111000=>000111
[4,7,6,3,5,2,1]=>[5,6,3,7,2,4,1]=>111000=>000111
[4,7,6,5,1,2,3]=>[5,1,6,2,7,4,3]=>111100=>000011
[4,7,6,5,1,3,2]=>[5,1,6,3,7,4,2]=>111100=>000011
[4,7,6,5,2,1,3]=>[5,2,6,1,7,4,3]=>111100=>000011
[4,7,6,5,2,3,1]=>[5,2,6,3,7,4,1]=>111100=>000011
[4,7,6,5,3,1,2]=>[5,3,6,1,7,4,2]=>111100=>000011
[4,7,6,5,3,2,1]=>[5,3,6,2,7,4,1]=>111100=>000011
[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>100000=>011111
[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>100001=>011110
[5,1,2,3,6,4,7]=>[6,5,1,2,3,4,7]=>100010=>011101
[5,1,2,3,6,7,4]=>[7,6,5,1,2,3,4]=>100011=>011100
[5,1,2,3,7,4,6]=>[7,5,1,2,3,4,6]=>100010=>011101
[5,1,2,3,7,6,4]=>[6,7,5,1,2,3,4]=>100010=>011101
[5,1,2,4,3,6,7]=>[4,5,1,2,3,6,7]=>100000=>011111
[5,1,2,4,3,7,6]=>[4,5,1,2,3,7,6]=>100001=>011110
[5,1,2,4,6,3,7]=>[4,6,5,1,2,3,7]=>100010=>011101
[5,1,2,4,6,7,3]=>[4,7,6,5,1,2,3]=>100011=>011100
[5,1,2,4,7,3,6]=>[4,7,5,1,2,3,6]=>100010=>011101
[5,1,2,4,7,6,3]=>[4,6,7,5,1,2,3]=>100010=>011101
[5,1,2,6,3,4,7]=>[6,1,2,3,5,4,7]=>100100=>011011
[5,1,2,6,3,7,4]=>[7,6,1,2,3,5,4]=>100101=>011010
[5,1,2,6,4,3,7]=>[6,4,5,1,2,3,7]=>100100=>011011
[5,1,2,6,4,7,3]=>[7,6,4,5,1,2,3]=>100101=>011010
[5,1,2,6,7,3,4]=>[7,1,2,3,6,5,4]=>100110=>011001
[5,1,2,6,7,4,3]=>[7,4,6,5,1,2,3]=>100110=>011001
[5,1,2,7,3,4,6]=>[7,1,2,3,5,4,6]=>100100=>011011
[5,1,2,7,3,6,4]=>[6,7,1,2,3,5,4]=>100100=>011011
[5,1,2,7,4,3,6]=>[7,4,5,1,2,3,6]=>100100=>011011
[5,1,2,7,4,6,3]=>[6,7,4,5,1,2,3]=>100100=>011011
[5,1,2,7,6,3,4]=>[6,1,2,3,7,5,4]=>100110=>011001
[5,1,2,7,6,4,3]=>[6,4,7,5,1,2,3]=>100110=>011001
[5,1,3,2,4,6,7]=>[3,5,1,2,4,6,7]=>100000=>011111
[5,1,3,2,4,7,6]=>[3,5,1,2,4,7,6]=>100001=>011110
[5,1,3,2,6,4,7]=>[3,6,5,1,2,4,7]=>100010=>011101
[5,1,3,2,6,7,4]=>[3,7,6,5,1,2,4]=>100011=>011100
[5,1,3,2,7,4,6]=>[3,7,5,1,2,4,6]=>100010=>011101
[5,1,3,2,7,6,4]=>[3,6,7,5,1,2,4]=>100010=>011101
[5,1,3,4,2,6,7]=>[3,4,5,1,2,6,7]=>100000=>011111
[5,1,3,4,2,7,6]=>[3,4,5,1,2,7,6]=>100001=>011110
[5,1,3,4,6,2,7]=>[3,4,6,5,1,2,7]=>100010=>011101
[5,1,3,4,6,7,2]=>[3,4,7,6,5,1,2]=>100011=>011100
[5,1,3,4,7,2,6]=>[3,4,7,5,1,2,6]=>100010=>011101
[5,1,3,4,7,6,2]=>[3,4,6,7,5,1,2]=>100010=>011101
[5,1,3,6,2,4,7]=>[3,6,1,2,5,4,7]=>100100=>011011
[5,1,3,6,2,7,4]=>[3,7,6,1,2,5,4]=>100101=>011010
[5,1,3,6,4,2,7]=>[3,6,4,5,1,2,7]=>100100=>011011
[5,1,3,6,4,7,2]=>[3,7,6,4,5,1,2]=>100101=>011010
[5,1,3,6,7,2,4]=>[3,7,1,2,6,5,4]=>100110=>011001
[5,1,3,6,7,4,2]=>[3,7,4,6,5,1,2]=>100110=>011001
[5,1,3,7,2,4,6]=>[3,7,1,2,5,4,6]=>100100=>011011
[5,1,3,7,2,6,4]=>[3,6,7,1,2,5,4]=>100100=>011011
[5,1,3,7,4,2,6]=>[3,7,4,5,1,2,6]=>100100=>011011
[5,1,3,7,4,6,2]=>[3,6,7,4,5,1,2]=>100100=>011011
[5,1,3,7,6,2,4]=>[3,6,1,2,7,5,4]=>100110=>011001
[5,1,3,7,6,4,2]=>[3,6,4,7,5,1,2]=>100110=>011001
[5,1,4,2,3,6,7]=>[4,1,2,5,3,6,7]=>101000=>010111
[5,1,4,2,3,7,6]=>[4,1,2,5,3,7,6]=>101001=>010110
[5,1,4,2,6,3,7]=>[4,1,2,6,5,3,7]=>101010=>010101
[5,1,4,2,6,7,3]=>[4,1,2,7,6,5,3]=>101011=>010100
[5,1,4,2,7,3,6]=>[4,1,2,7,5,3,6]=>101010=>010101
[5,1,4,2,7,6,3]=>[4,1,2,6,7,5,3]=>101010=>010101
[5,1,4,3,2,6,7]=>[4,3,5,1,2,6,7]=>101000=>010111
[5,1,4,3,2,7,6]=>[4,3,5,1,2,7,6]=>101001=>010110
[5,1,4,3,6,2,7]=>[4,3,6,5,1,2,7]=>101010=>010101
[5,1,4,3,6,7,2]=>[4,3,7,6,5,1,2]=>101011=>010100
[5,1,4,3,7,2,6]=>[4,3,7,5,1,2,6]=>101010=>010101
[5,1,4,3,7,6,2]=>[4,3,6,7,5,1,2]=>101010=>010101
[5,1,4,6,2,3,7]=>[6,4,1,2,5,3,7]=>101100=>010011
[5,1,4,6,2,7,3]=>[7,6,4,1,2,5,3]=>101101=>010010
[5,1,4,6,3,2,7]=>[6,4,3,5,1,2,7]=>101100=>010011
[5,1,4,6,3,7,2]=>[7,6,4,3,5,1,2]=>101101=>010010
[5,1,4,6,7,2,3]=>[7,4,1,2,6,5,3]=>101110=>010001
[5,1,4,6,7,3,2]=>[7,4,3,6,5,1,2]=>101110=>010001
[5,1,4,7,2,3,6]=>[7,4,1,2,5,3,6]=>101100=>010011
[5,1,4,7,2,6,3]=>[6,7,4,1,2,5,3]=>101100=>010011
[5,1,4,7,3,2,6]=>[7,4,3,5,1,2,6]=>101100=>010011
[5,1,4,7,3,6,2]=>[6,7,4,3,5,1,2]=>101100=>010011
[5,1,4,7,6,2,3]=>[6,4,1,2,7,5,3]=>101110=>010001
[5,1,4,7,6,3,2]=>[6,4,3,7,5,1,2]=>101110=>010001
[5,1,6,2,3,4,7]=>[6,1,2,5,3,4,7]=>101000=>010111
[5,1,6,2,3,7,4]=>[7,6,1,2,5,3,4]=>101001=>010110
[5,1,6,2,4,3,7]=>[6,1,2,4,5,3,7]=>101000=>010111
[5,1,6,2,4,7,3]=>[7,6,1,2,4,5,3]=>101001=>010110
[5,1,6,2,7,3,4]=>[7,1,2,6,5,3,4]=>101010=>010101
[5,1,6,2,7,4,3]=>[7,1,2,4,6,5,3]=>101010=>010101
[5,1,6,3,2,4,7]=>[6,3,5,1,2,4,7]=>101000=>010111
[5,1,6,3,2,7,4]=>[7,6,3,5,1,2,4]=>101001=>010110
[5,1,6,3,4,2,7]=>[6,3,4,5,1,2,7]=>101000=>010111
[5,1,6,3,4,7,2]=>[7,6,3,4,5,1,2]=>101001=>010110
[5,1,6,3,7,2,4]=>[7,3,6,5,1,2,4]=>101010=>010101
[5,1,6,3,7,4,2]=>[7,3,4,6,5,1,2]=>101010=>010101
[5,1,6,4,2,3,7]=>[4,6,1,2,5,3,7]=>101000=>010111
[5,1,6,4,2,7,3]=>[4,7,6,1,2,5,3]=>101001=>010110
[5,1,6,4,3,2,7]=>[4,6,3,5,1,2,7]=>101000=>010111
[5,1,6,4,3,7,2]=>[4,7,6,3,5,1,2]=>101001=>010110
[5,1,6,4,7,2,3]=>[4,7,1,2,6,5,3]=>101010=>010101
[5,1,6,4,7,3,2]=>[4,7,3,6,5,1,2]=>101010=>010101
[5,1,6,7,2,3,4]=>[7,1,2,6,3,5,4]=>101100=>010011
[5,1,6,7,2,4,3]=>[7,1,2,6,4,5,3]=>101100=>010011
[5,1,6,7,3,2,4]=>[7,3,6,1,2,5,4]=>101100=>010011
[5,1,6,7,3,4,2]=>[7,3,6,4,5,1,2]=>101100=>010011
[5,1,6,7,4,2,3]=>[7,4,6,1,2,5,3]=>101100=>010011
[5,1,6,7,4,3,2]=>[7,4,6,3,5,1,2]=>101100=>010011
[5,1,7,2,3,4,6]=>[7,1,2,5,3,4,6]=>101000=>010111
[5,1,7,2,3,6,4]=>[6,7,1,2,5,3,4]=>101000=>010111
[5,1,7,2,4,3,6]=>[7,1,2,4,5,3,6]=>101000=>010111
[5,1,7,2,4,6,3]=>[6,7,1,2,4,5,3]=>101000=>010111
[5,1,7,2,6,3,4]=>[6,1,2,7,5,3,4]=>101010=>010101
[5,1,7,2,6,4,3]=>[6,1,2,4,7,5,3]=>101010=>010101
[5,1,7,3,2,4,6]=>[7,3,5,1,2,4,6]=>101000=>010111
[5,1,7,3,2,6,4]=>[6,7,3,5,1,2,4]=>101000=>010111
[5,1,7,3,4,2,6]=>[7,3,4,5,1,2,6]=>101000=>010111
[5,1,7,3,4,6,2]=>[6,7,3,4,5,1,2]=>101000=>010111
[5,1,7,3,6,2,4]=>[6,3,7,5,1,2,4]=>101010=>010101
[5,1,7,3,6,4,2]=>[6,3,4,7,5,1,2]=>101010=>010101
[5,1,7,4,2,3,6]=>[4,7,1,2,5,3,6]=>101000=>010111
[5,1,7,4,2,6,3]=>[4,6,7,1,2,5,3]=>101000=>010111
[5,1,7,4,3,2,6]=>[4,7,3,5,1,2,6]=>101000=>010111
[5,1,7,4,3,6,2]=>[4,6,7,3,5,1,2]=>101000=>010111
[5,1,7,4,6,2,3]=>[4,6,1,2,7,5,3]=>101010=>010101
[5,1,7,4,6,3,2]=>[4,6,3,7,5,1,2]=>101010=>010101
[5,1,7,6,2,3,4]=>[6,1,2,7,3,5,4]=>101100=>010011
[5,1,7,6,2,4,3]=>[6,1,2,7,4,5,3]=>101100=>010011
[5,1,7,6,3,2,4]=>[6,3,7,1,2,5,4]=>101100=>010011
[5,1,7,6,3,4,2]=>[6,3,7,4,5,1,2]=>101100=>010011
[5,1,7,6,4,2,3]=>[6,4,7,1,2,5,3]=>101100=>010011
[5,1,7,6,4,3,2]=>[6,4,7,3,5,1,2]=>101100=>010011
[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>100000=>011111
[5,2,1,3,4,7,6]=>[2,5,1,3,4,7,6]=>100001=>011110
[5,2,1,3,6,4,7]=>[2,6,5,1,3,4,7]=>100010=>011101
[5,2,1,3,6,7,4]=>[2,7,6,5,1,3,4]=>100011=>011100
[5,2,1,3,7,4,6]=>[2,7,5,1,3,4,6]=>100010=>011101
[5,2,1,3,7,6,4]=>[2,6,7,5,1,3,4]=>100010=>011101
[5,2,1,4,3,6,7]=>[2,4,5,1,3,6,7]=>100000=>011111
[5,2,1,4,3,7,6]=>[2,4,5,1,3,7,6]=>100001=>011110
[5,2,1,4,6,3,7]=>[2,4,6,5,1,3,7]=>100010=>011101
[5,2,1,4,6,7,3]=>[2,4,7,6,5,1,3]=>100011=>011100
[5,2,1,4,7,3,6]=>[2,4,7,5,1,3,6]=>100010=>011101
[5,2,1,4,7,6,3]=>[2,4,6,7,5,1,3]=>100010=>011101
[5,2,1,6,3,4,7]=>[2,6,1,3,5,4,7]=>100100=>011011
[5,2,1,6,3,7,4]=>[2,7,6,1,3,5,4]=>100101=>011010
[5,2,1,6,4,3,7]=>[2,6,4,5,1,3,7]=>100100=>011011
[5,2,1,6,4,7,3]=>[2,7,6,4,5,1,3]=>100101=>011010
[5,2,1,6,7,3,4]=>[2,7,1,3,6,5,4]=>100110=>011001
[5,2,1,6,7,4,3]=>[2,7,4,6,5,1,3]=>100110=>011001
[5,2,1,7,3,4,6]=>[2,7,1,3,5,4,6]=>100100=>011011
[5,2,1,7,3,6,4]=>[2,6,7,1,3,5,4]=>100100=>011011
[5,2,1,7,4,3,6]=>[2,7,4,5,1,3,6]=>100100=>011011
[5,2,1,7,4,6,3]=>[2,6,7,4,5,1,3]=>100100=>011011
[5,2,1,7,6,3,4]=>[2,6,1,3,7,5,4]=>100110=>011001
[5,2,1,7,6,4,3]=>[2,6,4,7,5,1,3]=>100110=>011001
[5,2,3,1,4,6,7]=>[2,3,5,1,4,6,7]=>100000=>011111
[5,2,3,1,4,7,6]=>[2,3,5,1,4,7,6]=>100001=>011110
[5,2,3,1,6,4,7]=>[2,3,6,5,1,4,7]=>100010=>011101
[5,2,3,1,6,7,4]=>[2,3,7,6,5,1,4]=>100011=>011100
[5,2,3,1,7,4,6]=>[2,3,7,5,1,4,6]=>100010=>011101
[5,2,3,1,7,6,4]=>[2,3,6,7,5,1,4]=>100010=>011101
[5,2,3,4,1,6,7]=>[2,3,4,5,1,6,7]=>100000=>011111
[5,2,3,4,1,7,6]=>[2,3,4,5,1,7,6]=>100001=>011110
[5,2,3,4,6,1,7]=>[2,3,4,6,5,1,7]=>100010=>011101
[5,2,3,4,6,7,1]=>[2,3,4,7,6,5,1]=>100011=>011100
[5,2,3,4,7,1,6]=>[2,3,4,7,5,1,6]=>100010=>011101
[5,2,3,4,7,6,1]=>[2,3,4,6,7,5,1]=>100010=>011101
[5,2,3,6,1,4,7]=>[2,3,6,1,5,4,7]=>100100=>011011
[5,2,3,6,1,7,4]=>[2,3,7,6,1,5,4]=>100101=>011010
[5,2,3,6,4,1,7]=>[2,3,6,4,5,1,7]=>100100=>011011
[5,2,3,6,4,7,1]=>[2,3,7,6,4,5,1]=>100101=>011010
[5,2,3,6,7,1,4]=>[2,3,7,1,6,5,4]=>100110=>011001
[5,2,3,6,7,4,1]=>[2,3,7,4,6,5,1]=>100110=>011001
[5,2,3,7,1,4,6]=>[2,3,7,1,5,4,6]=>100100=>011011
[5,2,3,7,1,6,4]=>[2,3,6,7,1,5,4]=>100100=>011011
[5,2,3,7,4,1,6]=>[2,3,7,4,5,1,6]=>100100=>011011
[5,2,3,7,4,6,1]=>[2,3,6,7,4,5,1]=>100100=>011011
[5,2,3,7,6,1,4]=>[2,3,6,1,7,5,4]=>100110=>011001
[5,2,3,7,6,4,1]=>[2,3,6,4,7,5,1]=>100110=>011001
[5,2,4,1,3,6,7]=>[2,4,1,5,3,6,7]=>101000=>010111
[5,2,4,1,3,7,6]=>[2,4,1,5,3,7,6]=>101001=>010110
[5,2,4,1,6,3,7]=>[2,4,1,6,5,3,7]=>101010=>010101
[5,2,4,1,6,7,3]=>[2,4,1,7,6,5,3]=>101011=>010100
[5,2,4,1,7,3,6]=>[2,4,1,7,5,3,6]=>101010=>010101
[5,2,4,1,7,6,3]=>[2,4,1,6,7,5,3]=>101010=>010101
[5,2,4,3,1,6,7]=>[2,4,3,5,1,6,7]=>101000=>010111
[5,2,4,3,1,7,6]=>[2,4,3,5,1,7,6]=>101001=>010110
[5,2,4,3,6,1,7]=>[2,4,3,6,5,1,7]=>101010=>010101
[5,2,4,3,6,7,1]=>[2,4,3,7,6,5,1]=>101011=>010100
[5,2,4,3,7,1,6]=>[2,4,3,7,5,1,6]=>101010=>010101
[5,2,4,3,7,6,1]=>[2,4,3,6,7,5,1]=>101010=>010101
[5,2,4,6,1,3,7]=>[2,6,4,1,5,3,7]=>101100=>010011
[5,2,4,6,1,7,3]=>[2,7,6,4,1,5,3]=>101101=>010010
[5,2,4,6,3,1,7]=>[2,6,4,3,5,1,7]=>101100=>010011
[5,2,4,6,3,7,1]=>[2,7,6,4,3,5,1]=>101101=>010010
[5,2,4,6,7,1,3]=>[2,7,4,1,6,5,3]=>101110=>010001
[5,2,4,6,7,3,1]=>[2,7,4,3,6,5,1]=>101110=>010001
[5,2,4,7,1,3,6]=>[2,7,4,1,5,3,6]=>101100=>010011
[5,2,4,7,1,6,3]=>[2,6,7,4,1,5,3]=>101100=>010011
[5,2,4,7,3,1,6]=>[2,7,4,3,5,1,6]=>101100=>010011
[5,2,4,7,3,6,1]=>[2,6,7,4,3,5,1]=>101100=>010011
[5,2,4,7,6,1,3]=>[2,6,4,1,7,5,3]=>101110=>010001
[5,2,4,7,6,3,1]=>[2,6,4,3,7,5,1]=>101110=>010001
[5,2,6,1,3,4,7]=>[2,6,1,5,3,4,7]=>101000=>010111
[5,2,6,1,3,7,4]=>[2,7,6,1,5,3,4]=>101001=>010110
[5,2,6,1,4,3,7]=>[2,6,1,4,5,3,7]=>101000=>010111
[5,2,6,1,4,7,3]=>[2,7,6,1,4,5,3]=>101001=>010110
[5,2,6,1,7,3,4]=>[2,7,1,6,5,3,4]=>101010=>010101
[5,2,6,1,7,4,3]=>[2,7,1,4,6,5,3]=>101010=>010101
[5,2,6,3,1,4,7]=>[2,6,3,5,1,4,7]=>101000=>010111
[5,2,6,3,1,7,4]=>[2,7,6,3,5,1,4]=>101001=>010110
[5,2,6,3,4,1,7]=>[2,6,3,4,5,1,7]=>101000=>010111
[5,2,6,3,4,7,1]=>[2,7,6,3,4,5,1]=>101001=>010110
[5,2,6,3,7,1,4]=>[2,7,3,6,5,1,4]=>101010=>010101
[5,2,6,3,7,4,1]=>[2,7,3,4,6,5,1]=>101010=>010101
[5,2,6,4,1,3,7]=>[2,4,6,1,5,3,7]=>101000=>010111
[5,2,6,4,1,7,3]=>[2,4,7,6,1,5,3]=>101001=>010110
[5,2,6,4,3,1,7]=>[2,4,6,3,5,1,7]=>101000=>010111
[5,2,6,4,3,7,1]=>[2,4,7,6,3,5,1]=>101001=>010110
[5,2,6,4,7,1,3]=>[2,4,7,1,6,5,3]=>101010=>010101
[5,2,6,4,7,3,1]=>[2,4,7,3,6,5,1]=>101010=>010101
[5,2,6,7,1,3,4]=>[2,7,1,6,3,5,4]=>101100=>010011
[5,2,6,7,1,4,3]=>[2,7,1,6,4,5,3]=>101100=>010011
[5,2,6,7,3,1,4]=>[2,7,3,6,1,5,4]=>101100=>010011
[5,2,6,7,3,4,1]=>[2,7,3,6,4,5,1]=>101100=>010011
[5,2,6,7,4,1,3]=>[2,7,4,6,1,5,3]=>101100=>010011
[5,2,6,7,4,3,1]=>[2,7,4,6,3,5,1]=>101100=>010011
[5,2,7,1,3,4,6]=>[2,7,1,5,3,4,6]=>101000=>010111
[5,2,7,1,3,6,4]=>[2,6,7,1,5,3,4]=>101000=>010111
[5,2,7,1,4,3,6]=>[2,7,1,4,5,3,6]=>101000=>010111
[5,2,7,1,4,6,3]=>[2,6,7,1,4,5,3]=>101000=>010111
[5,2,7,1,6,3,4]=>[2,6,1,7,5,3,4]=>101010=>010101
[5,2,7,1,6,4,3]=>[2,6,1,4,7,5,3]=>101010=>010101
[5,2,7,3,1,4,6]=>[2,7,3,5,1,4,6]=>101000=>010111
[5,2,7,3,1,6,4]=>[2,6,7,3,5,1,4]=>101000=>010111
[5,2,7,3,4,1,6]=>[2,7,3,4,5,1,6]=>101000=>010111
[5,2,7,3,4,6,1]=>[2,6,7,3,4,5,1]=>101000=>010111
[5,2,7,3,6,1,4]=>[2,6,3,7,5,1,4]=>101010=>010101
[5,2,7,3,6,4,1]=>[2,6,3,4,7,5,1]=>101010=>010101
[5,2,7,4,1,3,6]=>[2,4,7,1,5,3,6]=>101000=>010111
[5,2,7,4,1,6,3]=>[2,4,6,7,1,5,3]=>101000=>010111
[5,2,7,4,3,1,6]=>[2,4,7,3,5,1,6]=>101000=>010111
[5,2,7,4,3,6,1]=>[2,4,6,7,3,5,1]=>101000=>010111
[5,2,7,4,6,1,3]=>[2,4,6,1,7,5,3]=>101010=>010101
[5,2,7,4,6,3,1]=>[2,4,6,3,7,5,1]=>101010=>010101
[5,2,7,6,1,3,4]=>[2,6,1,7,3,5,4]=>101100=>010011
[5,2,7,6,1,4,3]=>[2,6,1,7,4,5,3]=>101100=>010011
[5,2,7,6,3,1,4]=>[2,6,3,7,1,5,4]=>101100=>010011
[5,2,7,6,3,4,1]=>[2,6,3,7,4,5,1]=>101100=>010011
[5,2,7,6,4,1,3]=>[2,6,4,7,1,5,3]=>101100=>010011
[5,2,7,6,4,3,1]=>[2,6,4,7,3,5,1]=>101100=>010011
[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>110000=>001111
[5,3,1,2,4,7,6]=>[3,1,5,2,4,7,6]=>110001=>001110
[5,3,1,2,6,4,7]=>[3,1,6,5,2,4,7]=>110010=>001101
[5,3,1,2,6,7,4]=>[3,1,7,6,5,2,4]=>110011=>001100
[5,3,1,2,7,4,6]=>[3,1,7,5,2,4,6]=>110010=>001101
[5,3,1,2,7,6,4]=>[3,1,6,7,5,2,4]=>110010=>001101
[5,3,1,4,2,6,7]=>[3,1,4,5,2,6,7]=>110000=>001111
[5,3,1,4,2,7,6]=>[3,1,4,5,2,7,6]=>110001=>001110
[5,3,1,4,6,2,7]=>[3,1,4,6,5,2,7]=>110010=>001101
[5,3,1,4,6,7,2]=>[3,1,4,7,6,5,2]=>110011=>001100
[5,3,1,4,7,2,6]=>[3,1,4,7,5,2,6]=>110010=>001101
[5,3,1,4,7,6,2]=>[3,1,4,6,7,5,2]=>110010=>001101
[5,3,1,6,2,4,7]=>[3,1,6,2,5,4,7]=>110100=>001011
[5,3,1,6,2,7,4]=>[3,1,7,6,2,5,4]=>110101=>001010
[5,3,1,6,4,2,7]=>[3,1,6,4,5,2,7]=>110100=>001011
[5,3,1,6,4,7,2]=>[3,1,7,6,4,5,2]=>110101=>001010
[5,3,1,6,7,2,4]=>[3,1,7,2,6,5,4]=>110110=>001001
[5,3,1,6,7,4,2]=>[3,1,7,4,6,5,2]=>110110=>001001
[5,3,1,7,2,4,6]=>[3,1,7,2,5,4,6]=>110100=>001011
[5,3,1,7,2,6,4]=>[3,1,6,7,2,5,4]=>110100=>001011
[5,3,1,7,4,2,6]=>[3,1,7,4,5,2,6]=>110100=>001011
[5,3,1,7,4,6,2]=>[3,1,6,7,4,5,2]=>110100=>001011
[5,3,1,7,6,2,4]=>[3,1,6,2,7,5,4]=>110110=>001001
[5,3,1,7,6,4,2]=>[3,1,6,4,7,5,2]=>110110=>001001
[5,3,2,1,4,6,7]=>[3,2,5,1,4,6,7]=>110000=>001111
[5,3,2,1,4,7,6]=>[3,2,5,1,4,7,6]=>110001=>001110
[5,3,2,1,6,4,7]=>[3,2,6,5,1,4,7]=>110010=>001101
[5,3,2,1,6,7,4]=>[3,2,7,6,5,1,4]=>110011=>001100
[5,3,2,1,7,4,6]=>[3,2,7,5,1,4,6]=>110010=>001101
[5,3,2,1,7,6,4]=>[3,2,6,7,5,1,4]=>110010=>001101
[5,3,2,4,1,6,7]=>[3,2,4,5,1,6,7]=>110000=>001111
[5,3,2,4,1,7,6]=>[3,2,4,5,1,7,6]=>110001=>001110
[5,3,2,4,6,1,7]=>[3,2,4,6,5,1,7]=>110010=>001101
[5,3,2,4,6,7,1]=>[3,2,4,7,6,5,1]=>110011=>001100
[5,3,2,4,7,1,6]=>[3,2,4,7,5,1,6]=>110010=>001101
[5,3,2,4,7,6,1]=>[3,2,4,6,7,5,1]=>110010=>001101
[5,3,2,6,1,4,7]=>[3,2,6,1,5,4,7]=>110100=>001011
[5,3,2,6,1,7,4]=>[3,2,7,6,1,5,4]=>110101=>001010
[5,3,2,6,4,1,7]=>[3,2,6,4,5,1,7]=>110100=>001011
[5,3,2,6,4,7,1]=>[3,2,7,6,4,5,1]=>110101=>001010
[5,3,2,6,7,1,4]=>[3,2,7,1,6,5,4]=>110110=>001001
[5,3,2,6,7,4,1]=>[3,2,7,4,6,5,1]=>110110=>001001
[5,3,2,7,1,4,6]=>[3,2,7,1,5,4,6]=>110100=>001011
[5,3,2,7,1,6,4]=>[3,2,6,7,1,5,4]=>110100=>001011
[5,3,2,7,4,1,6]=>[3,2,7,4,5,1,6]=>110100=>001011
[5,3,2,7,4,6,1]=>[3,2,6,7,4,5,1]=>110100=>001011
[5,3,2,7,6,1,4]=>[3,2,6,1,7,5,4]=>110110=>001001
[5,3,2,7,6,4,1]=>[3,2,6,4,7,5,1]=>110110=>001001
[5,3,4,1,2,6,7]=>[4,3,1,5,2,6,7]=>111000=>000111
[5,3,4,1,2,7,6]=>[4,3,1,5,2,7,6]=>111001=>000110
[5,3,4,1,6,2,7]=>[4,3,1,6,5,2,7]=>111010=>000101
[5,3,4,1,6,7,2]=>[4,3,1,7,6,5,2]=>111011=>000100
[5,3,4,1,7,2,6]=>[4,3,1,7,5,2,6]=>111010=>000101
[5,3,4,1,7,6,2]=>[4,3,1,6,7,5,2]=>111010=>000101
[5,3,4,2,1,6,7]=>[4,3,2,5,1,6,7]=>111000=>000111
[5,3,4,2,1,7,6]=>[4,3,2,5,1,7,6]=>111001=>000110
[5,3,4,2,6,1,7]=>[4,3,2,6,5,1,7]=>111010=>000101
[5,3,4,2,6,7,1]=>[4,3,2,7,6,5,1]=>111011=>000100
[5,3,4,2,7,1,6]=>[4,3,2,7,5,1,6]=>111010=>000101
[5,3,4,2,7,6,1]=>[4,3,2,6,7,5,1]=>111010=>000101
[5,3,4,6,1,2,7]=>[6,4,3,1,5,2,7]=>111100=>000011
[5,3,4,6,1,7,2]=>[7,6,4,3,1,5,2]=>111101=>000010
[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]=>111100=>000011
[5,3,4,6,2,7,1]=>[7,6,4,3,2,5,1]=>111101=>000010
[5,3,4,6,7,1,2]=>[7,4,3,1,6,5,2]=>111110=>000001
[5,3,4,6,7,2,1]=>[7,4,3,2,6,5,1]=>111110=>000001
[5,3,4,7,1,2,6]=>[7,4,3,1,5,2,6]=>111100=>000011
[5,3,4,7,1,6,2]=>[6,7,4,3,1,5,2]=>111100=>000011
[5,3,4,7,2,1,6]=>[7,4,3,2,5,1,6]=>111100=>000011
[5,3,4,7,2,6,1]=>[6,7,4,3,2,5,1]=>111100=>000011
[5,3,4,7,6,1,2]=>[6,4,3,1,7,5,2]=>111110=>000001
[5,3,4,7,6,2,1]=>[6,4,3,2,7,5,1]=>111110=>000001
[5,3,6,1,2,4,7]=>[6,3,1,5,2,4,7]=>111000=>000111
[5,3,6,1,2,7,4]=>[7,6,3,1,5,2,4]=>111001=>000110
[5,3,6,1,4,2,7]=>[6,3,1,4,5,2,7]=>111000=>000111
[5,3,6,1,4,7,2]=>[7,6,3,1,4,5,2]=>111001=>000110
[5,3,6,1,7,2,4]=>[7,3,1,6,5,2,4]=>111010=>000101
[5,3,6,1,7,4,2]=>[7,3,1,4,6,5,2]=>111010=>000101
[5,3,6,2,1,4,7]=>[6,3,2,5,1,4,7]=>111000=>000111
[5,3,6,2,1,7,4]=>[7,6,3,2,5,1,4]=>111001=>000110
[5,3,6,2,4,1,7]=>[6,3,2,4,5,1,7]=>111000=>000111
[5,3,6,2,4,7,1]=>[7,6,3,2,4,5,1]=>111001=>000110
[5,3,6,2,7,1,4]=>[7,3,2,6,5,1,4]=>111010=>000101
[5,3,6,2,7,4,1]=>[7,3,2,4,6,5,1]=>111010=>000101
[5,3,6,4,1,2,7]=>[4,6,3,1,5,2,7]=>111000=>000111
[5,3,6,4,1,7,2]=>[4,7,6,3,1,5,2]=>111001=>000110
[5,3,6,4,2,1,7]=>[4,6,3,2,5,1,7]=>111000=>000111
[5,3,6,4,2,7,1]=>[4,7,6,3,2,5,1]=>111001=>000110
[5,3,6,4,7,1,2]=>[4,7,3,1,6,5,2]=>111010=>000101
[5,3,6,4,7,2,1]=>[4,7,3,2,6,5,1]=>111010=>000101
[5,3,6,7,1,2,4]=>[7,3,1,6,2,5,4]=>111100=>000011
[5,3,6,7,1,4,2]=>[7,3,1,6,4,5,2]=>111100=>000011
[5,3,6,7,2,1,4]=>[7,3,2,6,1,5,4]=>111100=>000011
[5,3,6,7,2,4,1]=>[7,3,2,6,4,5,1]=>111100=>000011
[5,3,6,7,4,1,2]=>[7,4,6,3,1,5,2]=>111100=>000011
[5,3,6,7,4,2,1]=>[7,4,6,3,2,5,1]=>111100=>000011
[5,3,7,1,2,4,6]=>[7,3,1,5,2,4,6]=>111000=>000111
[5,3,7,1,2,6,4]=>[6,7,3,1,5,2,4]=>111000=>000111
[5,3,7,1,4,2,6]=>[7,3,1,4,5,2,6]=>111000=>000111
[5,3,7,1,4,6,2]=>[6,7,3,1,4,5,2]=>111000=>000111
[5,3,7,1,6,2,4]=>[6,3,1,7,5,2,4]=>111010=>000101
[5,3,7,1,6,4,2]=>[6,3,1,4,7,5,2]=>111010=>000101
[5,3,7,2,1,4,6]=>[7,3,2,5,1,4,6]=>111000=>000111
[5,3,7,2,1,6,4]=>[6,7,3,2,5,1,4]=>111000=>000111
[5,3,7,2,4,1,6]=>[7,3,2,4,5,1,6]=>111000=>000111
[5,3,7,2,4,6,1]=>[6,7,3,2,4,5,1]=>111000=>000111
[5,3,7,2,6,1,4]=>[6,3,2,7,5,1,4]=>111010=>000101
[5,3,7,2,6,4,1]=>[6,3,2,4,7,5,1]=>111010=>000101
[5,3,7,4,1,2,6]=>[4,7,3,1,5,2,6]=>111000=>000111
[5,3,7,4,1,6,2]=>[4,6,7,3,1,5,2]=>111000=>000111
[5,3,7,4,2,1,6]=>[4,7,3,2,5,1,6]=>111000=>000111
[5,3,7,4,2,6,1]=>[4,6,7,3,2,5,1]=>111000=>000111
[5,3,7,4,6,1,2]=>[4,6,3,1,7,5,2]=>111010=>000101
[5,3,7,4,6,2,1]=>[4,6,3,2,7,5,1]=>111010=>000101
[5,3,7,6,1,2,4]=>[6,3,1,7,2,5,4]=>111100=>000011
[5,3,7,6,1,4,2]=>[6,3,1,7,4,5,2]=>111100=>000011
[5,3,7,6,2,1,4]=>[6,3,2,7,1,5,4]=>111100=>000011
[5,3,7,6,2,4,1]=>[6,3,2,7,4,5,1]=>111100=>000011
[5,3,7,6,4,1,2]=>[6,4,7,3,1,5,2]=>111100=>000011
[5,3,7,6,4,2,1]=>[6,4,7,3,2,5,1]=>111100=>000011
[5,4,1,2,3,6,7]=>[4,1,5,2,3,6,7]=>110000=>001111
[5,4,1,2,3,7,6]=>[4,1,5,2,3,7,6]=>110001=>001110
[5,4,1,2,6,3,7]=>[4,1,6,5,2,3,7]=>110010=>001101
[5,4,1,2,6,7,3]=>[4,1,7,6,5,2,3]=>110011=>001100
[5,4,1,2,7,3,6]=>[4,1,7,5,2,3,6]=>110010=>001101
[5,4,1,2,7,6,3]=>[4,1,6,7,5,2,3]=>110010=>001101
[5,4,1,3,2,6,7]=>[4,1,3,5,2,6,7]=>110000=>001111
[5,4,1,3,2,7,6]=>[4,1,3,5,2,7,6]=>110001=>001110
[5,4,1,3,6,2,7]=>[4,1,3,6,5,2,7]=>110010=>001101
[5,4,1,3,6,7,2]=>[4,1,3,7,6,5,2]=>110011=>001100
[5,4,1,3,7,2,6]=>[4,1,3,7,5,2,6]=>110010=>001101
[5,4,1,3,7,6,2]=>[4,1,3,6,7,5,2]=>110010=>001101
[5,4,1,6,2,3,7]=>[6,4,1,5,2,3,7]=>110100=>001011
[5,4,1,6,2,7,3]=>[7,6,4,1,5,2,3]=>110101=>001010
[5,4,1,6,3,2,7]=>[6,4,1,3,5,2,7]=>110100=>001011
[5,4,1,6,3,7,2]=>[7,6,4,1,3,5,2]=>110101=>001010
[5,4,1,6,7,2,3]=>[7,4,1,6,5,2,3]=>110110=>001001
[5,4,1,6,7,3,2]=>[7,4,1,3,6,5,2]=>110110=>001001
[5,4,1,7,2,3,6]=>[7,4,1,5,2,3,6]=>110100=>001011
[5,4,1,7,2,6,3]=>[6,7,4,1,5,2,3]=>110100=>001011
[5,4,1,7,3,2,6]=>[7,4,1,3,5,2,6]=>110100=>001011
[5,4,1,7,3,6,2]=>[6,7,4,1,3,5,2]=>110100=>001011
[5,4,1,7,6,2,3]=>[6,4,1,7,5,2,3]=>110110=>001001
[5,4,1,7,6,3,2]=>[6,4,1,3,7,5,2]=>110110=>001001
[5,4,2,1,3,6,7]=>[4,2,5,1,3,6,7]=>110000=>001111
[5,4,2,1,3,7,6]=>[4,2,5,1,3,7,6]=>110001=>001110
[5,4,2,1,6,3,7]=>[4,2,6,5,1,3,7]=>110010=>001101
[5,4,2,1,6,7,3]=>[4,2,7,6,5,1,3]=>110011=>001100
[5,4,2,1,7,3,6]=>[4,2,7,5,1,3,6]=>110010=>001101
[5,4,2,1,7,6,3]=>[4,2,6,7,5,1,3]=>110010=>001101
[5,4,2,3,1,6,7]=>[4,2,3,5,1,6,7]=>110000=>001111
[5,4,2,3,1,7,6]=>[4,2,3,5,1,7,6]=>110001=>001110
[5,4,2,3,6,1,7]=>[4,2,3,6,5,1,7]=>110010=>001101
[5,4,2,3,6,7,1]=>[4,2,3,7,6,5,1]=>110011=>001100
[5,4,2,3,7,1,6]=>[4,2,3,7,5,1,6]=>110010=>001101
[5,4,2,3,7,6,1]=>[4,2,3,6,7,5,1]=>110010=>001101
[5,4,2,6,1,3,7]=>[6,4,2,5,1,3,7]=>110100=>001011
[5,4,2,6,1,7,3]=>[7,6,4,2,5,1,3]=>110101=>001010
[5,4,2,6,3,1,7]=>[6,4,2,3,5,1,7]=>110100=>001011
[5,4,2,6,3,7,1]=>[7,6,4,2,3,5,1]=>110101=>001010
[5,4,2,6,7,1,3]=>[7,4,2,6,5,1,3]=>110110=>001001
[5,4,2,6,7,3,1]=>[7,4,2,3,6,5,1]=>110110=>001001
[5,4,2,7,1,3,6]=>[7,4,2,5,1,3,6]=>110100=>001011
[5,4,2,7,1,6,3]=>[6,7,4,2,5,1,3]=>110100=>001011
[5,4,2,7,3,1,6]=>[7,4,2,3,5,1,6]=>110100=>001011
[5,4,2,7,3,6,1]=>[6,7,4,2,3,5,1]=>110100=>001011
[5,4,2,7,6,1,3]=>[6,4,2,7,5,1,3]=>110110=>001001
[5,4,2,7,6,3,1]=>[6,4,2,3,7,5,1]=>110110=>001001
[5,4,3,1,2,6,7]=>[3,4,1,5,2,6,7]=>110000=>001111
[5,4,3,1,2,7,6]=>[3,4,1,5,2,7,6]=>110001=>001110
[5,4,3,1,6,2,7]=>[3,4,1,6,5,2,7]=>110010=>001101
[5,4,3,1,6,7,2]=>[3,4,1,7,6,5,2]=>110011=>001100
[5,4,3,1,7,2,6]=>[3,4,1,7,5,2,6]=>110010=>001101
[5,4,3,1,7,6,2]=>[3,4,1,6,7,5,2]=>110010=>001101
[5,4,3,2,1,6,7]=>[3,4,2,5,1,6,7]=>110000=>001111
[5,4,3,2,1,7,6]=>[3,4,2,5,1,7,6]=>110001=>001110
[5,4,3,2,6,1,7]=>[3,4,2,6,5,1,7]=>110010=>001101
[5,4,3,2,6,7,1]=>[3,4,2,7,6,5,1]=>110011=>001100
[5,4,3,2,7,1,6]=>[3,4,2,7,5,1,6]=>110010=>001101
[5,4,3,2,7,6,1]=>[3,4,2,6,7,5,1]=>110010=>001101
[5,4,3,6,1,2,7]=>[3,6,4,1,5,2,7]=>110100=>001011
[5,4,3,6,1,7,2]=>[3,7,6,4,1,5,2]=>110101=>001010
[5,4,3,6,2,1,7]=>[3,6,4,2,5,1,7]=>110100=>001011
[5,4,3,6,2,7,1]=>[3,7,6,4,2,5,1]=>110101=>001010
[5,4,3,6,7,1,2]=>[3,7,4,1,6,5,2]=>110110=>001001
[5,4,3,6,7,2,1]=>[3,7,4,2,6,5,1]=>110110=>001001
[5,4,3,7,1,2,6]=>[3,7,4,1,5,2,6]=>110100=>001011
[5,4,3,7,1,6,2]=>[3,6,7,4,1,5,2]=>110100=>001011
[5,4,3,7,2,1,6]=>[3,7,4,2,5,1,6]=>110100=>001011
[5,4,3,7,2,6,1]=>[3,6,7,4,2,5,1]=>110100=>001011
[5,4,3,7,6,1,2]=>[3,6,4,1,7,5,2]=>110110=>001001
[5,4,3,7,6,2,1]=>[3,6,4,2,7,5,1]=>110110=>001001
[5,4,6,1,2,3,7]=>[6,1,4,2,5,3,7]=>111000=>000111
[5,4,6,1,2,7,3]=>[7,6,1,4,2,5,3]=>111001=>000110
[5,4,6,1,3,2,7]=>[6,1,4,3,5,2,7]=>111000=>000111
[5,4,6,1,3,7,2]=>[7,6,1,4,3,5,2]=>111001=>000110
[5,4,6,1,7,2,3]=>[7,1,4,2,6,5,3]=>111010=>000101
[5,4,6,1,7,3,2]=>[7,1,4,3,6,5,2]=>111010=>000101
[5,4,6,2,1,3,7]=>[6,2,4,1,5,3,7]=>111000=>000111
[5,4,6,2,1,7,3]=>[7,6,2,4,1,5,3]=>111001=>000110
[5,4,6,2,3,1,7]=>[6,2,4,3,5,1,7]=>111000=>000111
[5,4,6,2,3,7,1]=>[7,6,2,4,3,5,1]=>111001=>000110
[5,4,6,2,7,1,3]=>[7,2,4,1,6,5,3]=>111010=>000101
[5,4,6,2,7,3,1]=>[7,2,4,3,6,5,1]=>111010=>000101
[5,4,6,3,1,2,7]=>[6,3,4,1,5,2,7]=>111000=>000111
[5,4,6,3,1,7,2]=>[7,6,3,4,1,5,2]=>111001=>000110
[5,4,6,3,2,1,7]=>[6,3,4,2,5,1,7]=>111000=>000111
[5,4,6,3,2,7,1]=>[7,6,3,4,2,5,1]=>111001=>000110
[5,4,6,3,7,1,2]=>[7,3,4,1,6,5,2]=>111010=>000101
[5,4,6,3,7,2,1]=>[7,3,4,2,6,5,1]=>111010=>000101
[5,4,6,7,1,2,3]=>[7,1,6,4,2,5,3]=>111100=>000011
[5,4,6,7,1,3,2]=>[7,1,6,4,3,5,2]=>111100=>000011
[5,4,6,7,2,1,3]=>[7,2,6,4,1,5,3]=>111100=>000011
[5,4,6,7,2,3,1]=>[7,2,6,4,3,5,1]=>111100=>000011
[5,4,6,7,3,1,2]=>[7,3,6,4,1,5,2]=>111100=>000011
[5,4,6,7,3,2,1]=>[7,3,6,4,2,5,1]=>111100=>000011
[5,4,7,1,2,3,6]=>[7,1,4,2,5,3,6]=>111000=>000111
[5,4,7,1,2,6,3]=>[6,7,1,4,2,5,3]=>111000=>000111
[5,4,7,1,3,2,6]=>[7,1,4,3,5,2,6]=>111000=>000111
[5,4,7,1,3,6,2]=>[6,7,1,4,3,5,2]=>111000=>000111
[5,4,7,1,6,2,3]=>[6,1,4,2,7,5,3]=>111010=>000101
[5,4,7,1,6,3,2]=>[6,1,4,3,7,5,2]=>111010=>000101
[5,4,7,2,1,3,6]=>[7,2,4,1,5,3,6]=>111000=>000111
[5,4,7,2,1,6,3]=>[6,7,2,4,1,5,3]=>111000=>000111
[5,4,7,2,3,1,6]=>[7,2,4,3,5,1,6]=>111000=>000111
[5,4,7,2,3,6,1]=>[6,7,2,4,3,5,1]=>111000=>000111
[5,4,7,2,6,1,3]=>[6,2,4,1,7,5,3]=>111010=>000101
[5,4,7,2,6,3,1]=>[6,2,4,3,7,5,1]=>111010=>000101
[5,4,7,3,1,2,6]=>[7,3,4,1,5,2,6]=>111000=>000111
[5,4,7,3,1,6,2]=>[6,7,3,4,1,5,2]=>111000=>000111
[5,4,7,3,2,1,6]=>[7,3,4,2,5,1,6]=>111000=>000111
[5,4,7,3,2,6,1]=>[6,7,3,4,2,5,1]=>111000=>000111
[5,4,7,3,6,1,2]=>[6,3,4,1,7,5,2]=>111010=>000101
[5,4,7,3,6,2,1]=>[6,3,4,2,7,5,1]=>111010=>000101
[5,4,7,6,1,2,3]=>[6,1,7,4,2,5,3]=>111100=>000011
[5,4,7,6,1,3,2]=>[6,1,7,4,3,5,2]=>111100=>000011
[5,4,7,6,2,1,3]=>[6,2,7,4,1,5,3]=>111100=>000011
[5,4,7,6,2,3,1]=>[6,2,7,4,3,5,1]=>111100=>000011
[5,4,7,6,3,1,2]=>[6,3,7,4,1,5,2]=>111100=>000011
[5,4,7,6,3,2,1]=>[6,3,7,4,2,5,1]=>111100=>000011
[5,6,1,2,3,4,7]=>[6,1,5,2,3,4,7]=>110000=>001111
[5,6,1,2,3,7,4]=>[7,6,1,5,2,3,4]=>110001=>001110
[5,6,1,2,4,3,7]=>[6,1,4,5,2,3,7]=>110000=>001111
[5,6,1,2,4,7,3]=>[7,6,1,4,5,2,3]=>110001=>001110
[5,6,1,2,7,3,4]=>[7,1,6,5,2,3,4]=>110010=>001101
[5,6,1,2,7,4,3]=>[7,1,4,6,5,2,3]=>110010=>001101
[5,6,1,3,2,4,7]=>[6,1,3,5,2,4,7]=>110000=>001111
[5,6,1,3,2,7,4]=>[7,6,1,3,5,2,4]=>110001=>001110
[5,6,1,3,4,2,7]=>[6,1,3,4,5,2,7]=>110000=>001111
[5,6,1,3,4,7,2]=>[7,6,1,3,4,5,2]=>110001=>001110
[5,6,1,3,7,2,4]=>[7,1,3,6,5,2,4]=>110010=>001101
[5,6,1,3,7,4,2]=>[7,1,3,4,6,5,2]=>110010=>001101
[5,6,1,4,2,3,7]=>[4,6,1,5,2,3,7]=>110000=>001111
[5,6,1,4,2,7,3]=>[4,7,6,1,5,2,3]=>110001=>001110
[5,6,1,4,3,2,7]=>[4,6,1,3,5,2,7]=>110000=>001111
[5,6,1,4,3,7,2]=>[4,7,6,1,3,5,2]=>110001=>001110
[5,6,1,4,7,2,3]=>[4,7,1,6,5,2,3]=>110010=>001101
[5,6,1,4,7,3,2]=>[4,7,1,3,6,5,2]=>110010=>001101
[5,6,1,7,2,3,4]=>[7,1,6,2,3,5,4]=>110100=>001011
[5,6,1,7,2,4,3]=>[7,1,6,4,5,2,3]=>110100=>001011
[5,6,1,7,3,2,4]=>[7,1,3,6,2,5,4]=>110100=>001011
[5,6,1,7,3,4,2]=>[7,1,3,6,4,5,2]=>110100=>001011
[5,6,1,7,4,2,3]=>[7,4,6,1,5,2,3]=>110100=>001011
[5,6,1,7,4,3,2]=>[7,4,6,1,3,5,2]=>110100=>001011
[5,6,2,1,3,4,7]=>[6,2,5,1,3,4,7]=>110000=>001111
[5,6,2,1,3,7,4]=>[7,6,2,5,1,3,4]=>110001=>001110
[5,6,2,1,4,3,7]=>[6,2,4,5,1,3,7]=>110000=>001111
[5,6,2,1,4,7,3]=>[7,6,2,4,5,1,3]=>110001=>001110
[5,6,2,1,7,3,4]=>[7,2,6,5,1,3,4]=>110010=>001101
[5,6,2,1,7,4,3]=>[7,2,4,6,5,1,3]=>110010=>001101
[5,6,2,3,1,4,7]=>[6,2,3,5,1,4,7]=>110000=>001111
[5,6,2,3,1,7,4]=>[7,6,2,3,5,1,4]=>110001=>001110
[5,6,2,3,4,1,7]=>[6,2,3,4,5,1,7]=>110000=>001111
[5,6,2,3,4,7,1]=>[7,6,2,3,4,5,1]=>110001=>001110
[5,6,2,3,7,1,4]=>[7,2,3,6,5,1,4]=>110010=>001101
[5,6,2,3,7,4,1]=>[7,2,3,4,6,5,1]=>110010=>001101
[5,6,2,4,1,3,7]=>[4,6,2,5,1,3,7]=>110000=>001111
[5,6,2,4,1,7,3]=>[4,7,6,2,5,1,3]=>110001=>001110
[5,6,2,4,3,1,7]=>[4,6,2,3,5,1,7]=>110000=>001111
[5,6,2,4,3,7,1]=>[4,7,6,2,3,5,1]=>110001=>001110
[5,6,2,4,7,1,3]=>[4,7,2,6,5,1,3]=>110010=>001101
[5,6,2,4,7,3,1]=>[4,7,2,3,6,5,1]=>110010=>001101
[5,6,2,7,1,3,4]=>[7,2,6,1,3,5,4]=>110100=>001011
[5,6,2,7,1,4,3]=>[7,2,6,4,5,1,3]=>110100=>001011
[5,6,2,7,3,1,4]=>[7,2,3,6,1,5,4]=>110100=>001011
[5,6,2,7,3,4,1]=>[7,2,3,6,4,5,1]=>110100=>001011
[5,6,2,7,4,1,3]=>[7,4,6,2,5,1,3]=>110100=>001011
[5,6,2,7,4,3,1]=>[7,4,6,2,3,5,1]=>110100=>001011
[5,6,3,1,2,4,7]=>[3,6,1,5,2,4,7]=>110000=>001111
[5,6,3,1,2,7,4]=>[3,7,6,1,5,2,4]=>110001=>001110
[5,6,3,1,4,2,7]=>[3,6,1,4,5,2,7]=>110000=>001111
[5,6,3,1,4,7,2]=>[3,7,6,1,4,5,2]=>110001=>001110
[5,6,3,1,7,2,4]=>[3,7,1,6,5,2,4]=>110010=>001101
[5,6,3,1,7,4,2]=>[3,7,1,4,6,5,2]=>110010=>001101
[5,6,3,2,1,4,7]=>[3,6,2,5,1,4,7]=>110000=>001111
[5,6,3,2,1,7,4]=>[3,7,6,2,5,1,4]=>110001=>001110
[5,6,3,2,4,1,7]=>[3,6,2,4,5,1,7]=>110000=>001111
[5,6,3,2,4,7,1]=>[3,7,6,2,4,5,1]=>110001=>001110
[5,6,3,2,7,1,4]=>[3,7,2,6,5,1,4]=>110010=>001101
[5,6,3,2,7,4,1]=>[3,7,2,4,6,5,1]=>110010=>001101
[5,6,3,4,1,2,7]=>[3,4,6,1,5,2,7]=>110000=>001111
[5,6,3,4,1,7,2]=>[3,4,7,6,1,5,2]=>110001=>001110
[5,6,3,4,2,1,7]=>[3,4,6,2,5,1,7]=>110000=>001111
[5,6,3,4,2,7,1]=>[3,4,7,6,2,5,1]=>110001=>001110
[5,6,3,4,7,1,2]=>[3,4,7,1,6,5,2]=>110010=>001101
[5,6,3,4,7,2,1]=>[3,4,7,2,6,5,1]=>110010=>001101
[5,6,3,7,1,2,4]=>[3,7,1,6,2,5,4]=>110100=>001011
[5,6,3,7,1,4,2]=>[3,7,1,6,4,5,2]=>110100=>001011
[5,6,3,7,2,1,4]=>[3,7,2,6,1,5,4]=>110100=>001011
[5,6,3,7,2,4,1]=>[3,7,2,6,4,5,1]=>110100=>001011
[5,6,3,7,4,1,2]=>[3,7,4,6,1,5,2]=>110100=>001011
[5,6,3,7,4,2,1]=>[3,7,4,6,2,5,1]=>110100=>001011
[5,6,4,1,2,3,7]=>[4,1,6,2,5,3,7]=>111000=>000111
[5,6,4,1,2,7,3]=>[4,1,7,6,2,5,3]=>111001=>000110
[5,6,4,1,3,2,7]=>[4,1,6,3,5,2,7]=>111000=>000111
[5,6,4,1,3,7,2]=>[4,1,7,6,3,5,2]=>111001=>000110
[5,6,4,1,7,2,3]=>[4,1,7,2,6,5,3]=>111010=>000101
[5,6,4,1,7,3,2]=>[4,1,7,3,6,5,2]=>111010=>000101
[5,6,4,2,1,3,7]=>[4,2,6,1,5,3,7]=>111000=>000111
[5,6,4,2,1,7,3]=>[4,2,7,6,1,5,3]=>111001=>000110
[5,6,4,2,3,1,7]=>[4,2,6,3,5,1,7]=>111000=>000111
[5,6,4,2,3,7,1]=>[4,2,7,6,3,5,1]=>111001=>000110
[5,6,4,2,7,1,3]=>[4,2,7,1,6,5,3]=>111010=>000101
[5,6,4,2,7,3,1]=>[4,2,7,3,6,5,1]=>111010=>000101
[5,6,4,3,1,2,7]=>[4,3,6,1,5,2,7]=>111000=>000111
[5,6,4,3,1,7,2]=>[4,3,7,6,1,5,2]=>111001=>000110
[5,6,4,3,2,1,7]=>[4,3,6,2,5,1,7]=>111000=>000111
[5,6,4,3,2,7,1]=>[4,3,7,6,2,5,1]=>111001=>000110
[5,6,4,3,7,1,2]=>[4,3,7,1,6,5,2]=>111010=>000101
[5,6,4,3,7,2,1]=>[4,3,7,2,6,5,1]=>111010=>000101
[5,6,4,7,1,2,3]=>[7,4,1,6,2,5,3]=>111100=>000011
[5,6,4,7,1,3,2]=>[7,4,1,6,3,5,2]=>111100=>000011
[5,6,4,7,2,1,3]=>[7,4,2,6,1,5,3]=>111100=>000011
[5,6,4,7,2,3,1]=>[7,4,2,6,3,5,1]=>111100=>000011
[5,6,4,7,3,1,2]=>[7,4,3,6,1,5,2]=>111100=>000011
[5,6,4,7,3,2,1]=>[7,4,3,6,2,5,1]=>111100=>000011
[5,6,7,1,2,3,4]=>[7,1,6,2,5,3,4]=>111000=>000111
[5,6,7,1,2,4,3]=>[7,1,6,2,4,5,3]=>111000=>000111
[5,6,7,1,3,2,4]=>[7,1,6,3,5,2,4]=>111000=>000111
[5,6,7,1,3,4,2]=>[7,1,6,3,4,5,2]=>111000=>000111
[5,6,7,1,4,2,3]=>[7,1,4,6,2,5,3]=>111000=>000111
[5,6,7,1,4,3,2]=>[7,1,4,6,3,5,2]=>111000=>000111
[5,6,7,2,1,3,4]=>[7,2,6,1,5,3,4]=>111000=>000111
[5,6,7,2,1,4,3]=>[7,2,6,1,4,5,3]=>111000=>000111
[5,6,7,2,3,1,4]=>[7,2,6,3,5,1,4]=>111000=>000111
[5,6,7,2,3,4,1]=>[7,2,6,3,4,5,1]=>111000=>000111
[5,6,7,2,4,1,3]=>[7,2,4,6,1,5,3]=>111000=>000111
[5,6,7,2,4,3,1]=>[7,2,4,6,3,5,1]=>111000=>000111
[5,6,7,3,1,2,4]=>[7,3,6,1,5,2,4]=>111000=>000111
[5,6,7,3,1,4,2]=>[7,3,6,1,4,5,2]=>111000=>000111
[5,6,7,3,2,1,4]=>[7,3,6,2,5,1,4]=>111000=>000111
[5,6,7,3,2,4,1]=>[7,3,6,2,4,5,1]=>111000=>000111
[5,6,7,3,4,1,2]=>[7,3,4,6,1,5,2]=>111000=>000111
[5,6,7,3,4,2,1]=>[7,3,4,6,2,5,1]=>111000=>000111
[5,6,7,4,1,2,3]=>[4,7,1,6,2,5,3]=>111000=>000111
[5,6,7,4,1,3,2]=>[4,7,1,6,3,5,2]=>111000=>000111
[5,6,7,4,2,1,3]=>[4,7,2,6,1,5,3]=>111000=>000111
[5,6,7,4,2,3,1]=>[4,7,2,6,3,5,1]=>111000=>000111
[5,6,7,4,3,1,2]=>[4,7,3,6,1,5,2]=>111000=>000111
[5,6,7,4,3,2,1]=>[4,7,3,6,2,5,1]=>111000=>000111
[5,7,1,2,3,4,6]=>[7,1,5,2,3,4,6]=>110000=>001111
[5,7,1,2,3,6,4]=>[6,7,1,5,2,3,4]=>110000=>001111
[5,7,1,2,4,3,6]=>[7,1,4,5,2,3,6]=>110000=>001111
[5,7,1,2,4,6,3]=>[6,7,1,4,5,2,3]=>110000=>001111
[5,7,1,2,6,3,4]=>[6,1,7,5,2,3,4]=>110010=>001101
[5,7,1,2,6,4,3]=>[6,1,4,7,5,2,3]=>110010=>001101
[5,7,1,3,2,4,6]=>[7,1,3,5,2,4,6]=>110000=>001111
[5,7,1,3,2,6,4]=>[6,7,1,3,5,2,4]=>110000=>001111
[5,7,1,3,4,2,6]=>[7,1,3,4,5,2,6]=>110000=>001111
[5,7,1,3,4,6,2]=>[6,7,1,3,4,5,2]=>110000=>001111
[5,7,1,3,6,2,4]=>[6,1,3,7,5,2,4]=>110010=>001101
[5,7,1,3,6,4,2]=>[6,1,3,4,7,5,2]=>110010=>001101
[5,7,1,4,2,3,6]=>[4,7,1,5,2,3,6]=>110000=>001111
[5,7,1,4,2,6,3]=>[4,6,7,1,5,2,3]=>110000=>001111
[5,7,1,4,3,2,6]=>[4,7,1,3,5,2,6]=>110000=>001111
[5,7,1,4,3,6,2]=>[4,6,7,1,3,5,2]=>110000=>001111
[5,7,1,4,6,2,3]=>[4,6,1,7,5,2,3]=>110010=>001101
[5,7,1,4,6,3,2]=>[4,6,1,3,7,5,2]=>110010=>001101
[5,7,1,6,2,3,4]=>[6,1,7,2,3,5,4]=>110100=>001011
[5,7,1,6,2,4,3]=>[6,1,7,4,5,2,3]=>110100=>001011
[5,7,1,6,3,2,4]=>[6,1,3,7,2,5,4]=>110100=>001011
[5,7,1,6,3,4,2]=>[6,1,3,7,4,5,2]=>110100=>001011
[5,7,1,6,4,2,3]=>[6,4,7,1,5,2,3]=>110100=>001011
[5,7,1,6,4,3,2]=>[6,4,7,1,3,5,2]=>110100=>001011
[5,7,2,1,3,4,6]=>[7,2,5,1,3,4,6]=>110000=>001111
[5,7,2,1,3,6,4]=>[6,7,2,5,1,3,4]=>110000=>001111
[5,7,2,1,4,3,6]=>[7,2,4,5,1,3,6]=>110000=>001111
[5,7,2,1,4,6,3]=>[6,7,2,4,5,1,3]=>110000=>001111
[5,7,2,1,6,3,4]=>[6,2,7,5,1,3,4]=>110010=>001101
[5,7,2,1,6,4,3]=>[6,2,4,7,5,1,3]=>110010=>001101
[5,7,2,3,1,4,6]=>[7,2,3,5,1,4,6]=>110000=>001111
[5,7,2,3,1,6,4]=>[6,7,2,3,5,1,4]=>110000=>001111
[5,7,2,3,4,1,6]=>[7,2,3,4,5,1,6]=>110000=>001111
[5,7,2,3,4,6,1]=>[6,7,2,3,4,5,1]=>110000=>001111
[5,7,2,3,6,1,4]=>[6,2,3,7,5,1,4]=>110010=>001101
[5,7,2,3,6,4,1]=>[6,2,3,4,7,5,1]=>110010=>001101
[5,7,2,4,1,3,6]=>[4,7,2,5,1,3,6]=>110000=>001111
[5,7,2,4,1,6,3]=>[4,6,7,2,5,1,3]=>110000=>001111
[5,7,2,4,3,1,6]=>[4,7,2,3,5,1,6]=>110000=>001111
[5,7,2,4,3,6,1]=>[4,6,7,2,3,5,1]=>110000=>001111
[5,7,2,4,6,1,3]=>[4,6,2,7,5,1,3]=>110010=>001101
[5,7,2,4,6,3,1]=>[4,6,2,3,7,5,1]=>110010=>001101
[5,7,2,6,1,3,4]=>[6,2,7,1,3,5,4]=>110100=>001011
[5,7,2,6,1,4,3]=>[6,2,7,4,5,1,3]=>110100=>001011
[5,7,2,6,3,1,4]=>[6,2,3,7,1,5,4]=>110100=>001011
[5,7,2,6,3,4,1]=>[6,2,3,7,4,5,1]=>110100=>001011
[5,7,2,6,4,1,3]=>[6,4,7,2,5,1,3]=>110100=>001011
[5,7,2,6,4,3,1]=>[6,4,7,2,3,5,1]=>110100=>001011
[5,7,3,1,2,4,6]=>[3,7,1,5,2,4,6]=>110000=>001111
[5,7,3,1,2,6,4]=>[3,6,7,1,5,2,4]=>110000=>001111
[5,7,3,1,4,2,6]=>[3,7,1,4,5,2,6]=>110000=>001111
[5,7,3,1,4,6,2]=>[3,6,7,1,4,5,2]=>110000=>001111
[5,7,3,1,6,2,4]=>[3,6,1,7,5,2,4]=>110010=>001101
[5,7,3,1,6,4,2]=>[3,6,1,4,7,5,2]=>110010=>001101
[5,7,3,2,1,4,6]=>[3,7,2,5,1,4,6]=>110000=>001111
[5,7,3,2,1,6,4]=>[3,6,7,2,5,1,4]=>110000=>001111
[5,7,3,2,4,1,6]=>[3,7,2,4,5,1,6]=>110000=>001111
[5,7,3,2,4,6,1]=>[3,6,7,2,4,5,1]=>110000=>001111
[5,7,3,2,6,1,4]=>[3,6,2,7,5,1,4]=>110010=>001101
[5,7,3,2,6,4,1]=>[3,6,2,4,7,5,1]=>110010=>001101
[5,7,3,4,1,2,6]=>[3,4,7,1,5,2,6]=>110000=>001111
[5,7,3,4,1,6,2]=>[3,4,6,7,1,5,2]=>110000=>001111
[5,7,3,4,2,1,6]=>[3,4,7,2,5,1,6]=>110000=>001111
[5,7,3,4,2,6,1]=>[3,4,6,7,2,5,1]=>110000=>001111
[5,7,3,4,6,1,2]=>[3,4,6,1,7,5,2]=>110010=>001101
[5,7,3,4,6,2,1]=>[3,4,6,2,7,5,1]=>110010=>001101
[5,7,3,6,1,2,4]=>[3,6,1,7,2,5,4]=>110100=>001011
[5,7,3,6,1,4,2]=>[3,6,1,7,4,5,2]=>110100=>001011
[5,7,3,6,2,1,4]=>[3,6,2,7,1,5,4]=>110100=>001011
[5,7,3,6,2,4,1]=>[3,6,2,7,4,5,1]=>110100=>001011
[5,7,3,6,4,1,2]=>[3,6,4,7,1,5,2]=>110100=>001011
[5,7,3,6,4,2,1]=>[3,6,4,7,2,5,1]=>110100=>001011
[5,7,4,1,2,3,6]=>[4,1,7,2,5,3,6]=>111000=>000111
[5,7,4,1,2,6,3]=>[4,1,6,7,2,5,3]=>111000=>000111
[5,7,4,1,3,2,6]=>[4,1,7,3,5,2,6]=>111000=>000111
[5,7,4,1,3,6,2]=>[4,1,6,7,3,5,2]=>111000=>000111
[5,7,4,1,6,2,3]=>[4,1,6,2,7,5,3]=>111010=>000101
[5,7,4,1,6,3,2]=>[4,1,6,3,7,5,2]=>111010=>000101
[5,7,4,2,1,3,6]=>[4,2,7,1,5,3,6]=>111000=>000111
[5,7,4,2,1,6,3]=>[4,2,6,7,1,5,3]=>111000=>000111
[5,7,4,2,3,1,6]=>[4,2,7,3,5,1,6]=>111000=>000111
[5,7,4,2,3,6,1]=>[4,2,6,7,3,5,1]=>111000=>000111
[5,7,4,2,6,1,3]=>[4,2,6,1,7,5,3]=>111010=>000101
[5,7,4,2,6,3,1]=>[4,2,6,3,7,5,1]=>111010=>000101
[5,7,4,3,1,2,6]=>[4,3,7,1,5,2,6]=>111000=>000111
[5,7,4,3,1,6,2]=>[4,3,6,7,1,5,2]=>111000=>000111
[5,7,4,3,2,1,6]=>[4,3,7,2,5,1,6]=>111000=>000111
[5,7,4,3,2,6,1]=>[4,3,6,7,2,5,1]=>111000=>000111
[5,7,4,3,6,1,2]=>[4,3,6,1,7,5,2]=>111010=>000101
[5,7,4,3,6,2,1]=>[4,3,6,2,7,5,1]=>111010=>000101
[5,7,4,6,1,2,3]=>[6,4,1,7,2,5,3]=>111100=>000011
[5,7,4,6,1,3,2]=>[6,4,1,7,3,5,2]=>111100=>000011
[5,7,4,6,2,1,3]=>[6,4,2,7,1,5,3]=>111100=>000011
[5,7,4,6,2,3,1]=>[6,4,2,7,3,5,1]=>111100=>000011
[5,7,4,6,3,1,2]=>[6,4,3,7,1,5,2]=>111100=>000011
[5,7,4,6,3,2,1]=>[6,4,3,7,2,5,1]=>111100=>000011
[5,7,6,1,2,3,4]=>[6,1,7,2,5,3,4]=>111000=>000111
[5,7,6,1,2,4,3]=>[6,1,7,2,4,5,3]=>111000=>000111
[5,7,6,1,3,2,4]=>[6,1,7,3,5,2,4]=>111000=>000111
[5,7,6,1,3,4,2]=>[6,1,7,3,4,5,2]=>111000=>000111
[5,7,6,1,4,2,3]=>[6,1,4,7,2,5,3]=>111000=>000111
[5,7,6,1,4,3,2]=>[6,1,4,7,3,5,2]=>111000=>000111
[5,7,6,2,1,3,4]=>[6,2,7,1,5,3,4]=>111000=>000111
[5,7,6,2,1,4,3]=>[6,2,7,1,4,5,3]=>111000=>000111
[5,7,6,2,3,1,4]=>[6,2,7,3,5,1,4]=>111000=>000111
[5,7,6,2,3,4,1]=>[6,2,7,3,4,5,1]=>111000=>000111
[5,7,6,2,4,1,3]=>[6,2,4,7,1,5,3]=>111000=>000111
[5,7,6,2,4,3,1]=>[6,2,4,7,3,5,1]=>111000=>000111
[5,7,6,3,1,2,4]=>[6,3,7,1,5,2,4]=>111000=>000111
[5,7,6,3,1,4,2]=>[6,3,7,1,4,5,2]=>111000=>000111
[5,7,6,3,2,1,4]=>[6,3,7,2,5,1,4]=>111000=>000111
[5,7,6,3,2,4,1]=>[6,3,7,2,4,5,1]=>111000=>000111
[5,7,6,3,4,1,2]=>[6,3,4,7,1,5,2]=>111000=>000111
[5,7,6,3,4,2,1]=>[6,3,4,7,2,5,1]=>111000=>000111
[5,7,6,4,1,2,3]=>[4,6,1,7,2,5,3]=>111000=>000111
[5,7,6,4,1,3,2]=>[4,6,1,7,3,5,2]=>111000=>000111
[5,7,6,4,2,1,3]=>[4,6,2,7,1,5,3]=>111000=>000111
[5,7,6,4,2,3,1]=>[4,6,2,7,3,5,1]=>111000=>000111
[5,7,6,4,3,1,2]=>[4,6,3,7,1,5,2]=>111000=>000111
[5,7,6,4,3,2,1]=>[4,6,3,7,2,5,1]=>111000=>000111
[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>100000=>011111
[6,1,2,3,4,7,5]=>[7,6,1,2,3,4,5]=>100001=>011110
[6,1,2,3,5,4,7]=>[5,6,1,2,3,4,7]=>100000=>011111
[6,1,2,3,5,7,4]=>[5,7,6,1,2,3,4]=>100001=>011110
[6,1,2,3,7,4,5]=>[7,1,2,3,4,6,5]=>100010=>011101
[6,1,2,3,7,5,4]=>[7,5,6,1,2,3,4]=>100010=>011101
[6,1,2,4,3,5,7]=>[4,6,1,2,3,5,7]=>100000=>011111
[6,1,2,4,3,7,5]=>[4,7,6,1,2,3,5]=>100001=>011110
[6,1,2,4,5,3,7]=>[4,5,6,1,2,3,7]=>100000=>011111
[6,1,2,4,5,7,3]=>[4,5,7,6,1,2,3]=>100001=>011110
[6,1,2,4,7,3,5]=>[4,7,1,2,3,6,5]=>100010=>011101
[6,1,2,4,7,5,3]=>[4,7,5,6,1,2,3]=>100010=>011101
[6,1,2,5,3,4,7]=>[5,1,2,3,6,4,7]=>100100=>011011
[6,1,2,5,3,7,4]=>[5,1,2,3,7,6,4]=>100101=>011010
[6,1,2,5,4,3,7]=>[5,4,6,1,2,3,7]=>100100=>011011
[6,1,2,5,4,7,3]=>[5,4,7,6,1,2,3]=>100101=>011010
[6,1,2,5,7,3,4]=>[7,5,1,2,3,6,4]=>100110=>011001
[6,1,2,5,7,4,3]=>[7,5,4,6,1,2,3]=>100110=>011001
[6,1,2,7,3,4,5]=>[7,1,2,3,6,4,5]=>100100=>011011
[6,1,2,7,3,5,4]=>[7,1,2,3,5,6,4]=>100100=>011011
[6,1,2,7,4,3,5]=>[7,4,6,1,2,3,5]=>100100=>011011
[6,1,2,7,4,5,3]=>[7,4,5,6,1,2,3]=>100100=>011011
[6,1,2,7,5,3,4]=>[5,7,1,2,3,6,4]=>100100=>011011
[6,1,2,7,5,4,3]=>[5,7,4,6,1,2,3]=>100100=>011011
[6,1,3,2,4,5,7]=>[3,6,1,2,4,5,7]=>100000=>011111
[6,1,3,2,4,7,5]=>[3,7,6,1,2,4,5]=>100001=>011110
[6,1,3,2,5,4,7]=>[3,5,6,1,2,4,7]=>100000=>011111
[6,1,3,2,5,7,4]=>[3,5,7,6,1,2,4]=>100001=>011110
[6,1,3,2,7,4,5]=>[3,7,1,2,4,6,5]=>100010=>011101
[6,1,3,2,7,5,4]=>[3,7,5,6,1,2,4]=>100010=>011101
[6,1,3,4,2,5,7]=>[3,4,6,1,2,5,7]=>100000=>011111
[6,1,3,4,2,7,5]=>[3,4,7,6,1,2,5]=>100001=>011110
[6,1,3,4,5,2,7]=>[3,4,5,6,1,2,7]=>100000=>011111
[6,1,3,4,5,7,2]=>[3,4,5,7,6,1,2]=>100001=>011110
[6,1,3,4,7,2,5]=>[3,4,7,1,2,6,5]=>100010=>011101
[6,1,3,4,7,5,2]=>[3,4,7,5,6,1,2]=>100010=>011101
[6,1,3,5,2,4,7]=>[3,5,1,2,6,4,7]=>100100=>011011
[6,1,3,5,2,7,4]=>[3,5,1,2,7,6,4]=>100101=>011010
[6,1,3,5,4,2,7]=>[3,5,4,6,1,2,7]=>100100=>011011
[6,1,3,5,4,7,2]=>[3,5,4,7,6,1,2]=>100101=>011010
[6,1,3,5,7,2,4]=>[3,7,5,1,2,6,4]=>100110=>011001
[6,1,3,5,7,4,2]=>[3,7,5,4,6,1,2]=>100110=>011001
[6,1,3,7,2,4,5]=>[3,7,1,2,6,4,5]=>100100=>011011
[6,1,3,7,2,5,4]=>[3,7,1,2,5,6,4]=>100100=>011011
[6,1,3,7,4,2,5]=>[3,7,4,6,1,2,5]=>100100=>011011
[6,1,3,7,4,5,2]=>[3,7,4,5,6,1,2]=>100100=>011011
[6,1,3,7,5,2,4]=>[3,5,7,1,2,6,4]=>100100=>011011
[6,1,3,7,5,4,2]=>[3,5,7,4,6,1,2]=>100100=>011011
[6,1,4,2,3,5,7]=>[4,1,2,6,3,5,7]=>101000=>010111
[6,1,4,2,3,7,5]=>[4,1,2,7,6,3,5]=>101001=>010110
[6,1,4,2,5,3,7]=>[4,1,2,5,6,3,7]=>101000=>010111
[6,1,4,2,5,7,3]=>[4,1,2,5,7,6,3]=>101001=>010110
[6,1,4,2,7,3,5]=>[4,1,2,7,3,6,5]=>101010=>010101
[6,1,4,2,7,5,3]=>[4,1,2,7,5,6,3]=>101010=>010101
[6,1,4,3,2,5,7]=>[4,3,6,1,2,5,7]=>101000=>010111
[6,1,4,3,2,7,5]=>[4,3,7,6,1,2,5]=>101001=>010110
[6,1,4,3,5,2,7]=>[4,3,5,6,1,2,7]=>101000=>010111
[6,1,4,3,5,7,2]=>[4,3,5,7,6,1,2]=>101001=>010110
[6,1,4,3,7,2,5]=>[4,3,7,1,2,6,5]=>101010=>010101
[6,1,4,3,7,5,2]=>[4,3,7,5,6,1,2]=>101010=>010101
[6,1,4,5,2,3,7]=>[5,4,1,2,6,3,7]=>101100=>010011
[6,1,4,5,2,7,3]=>[5,4,1,2,7,6,3]=>101101=>010010
[6,1,4,5,3,2,7]=>[5,4,3,6,1,2,7]=>101100=>010011
[6,1,4,5,3,7,2]=>[5,4,3,7,6,1,2]=>101101=>010010
[6,1,4,5,7,2,3]=>[7,5,4,1,2,6,3]=>101110=>010001
[6,1,4,5,7,3,2]=>[7,5,4,3,6,1,2]=>101110=>010001
[6,1,4,7,2,3,5]=>[7,4,1,2,6,3,5]=>101100=>010011
[6,1,4,7,2,5,3]=>[7,4,1,2,5,6,3]=>101100=>010011
[6,1,4,7,3,2,5]=>[7,4,3,6,1,2,5]=>101100=>010011
[6,1,4,7,3,5,2]=>[7,4,3,5,6,1,2]=>101100=>010011
[6,1,4,7,5,2,3]=>[5,7,4,1,2,6,3]=>101100=>010011
[6,1,4,7,5,3,2]=>[5,7,4,3,6,1,2]=>101100=>010011
[6,1,5,2,3,4,7]=>[5,1,2,6,3,4,7]=>101000=>010111
[6,1,5,2,3,7,4]=>[5,1,2,7,6,3,4]=>101001=>010110
[6,1,5,2,4,3,7]=>[5,1,2,4,6,3,7]=>101000=>010111
[6,1,5,2,4,7,3]=>[5,1,2,4,7,6,3]=>101001=>010110
[6,1,5,2,7,3,4]=>[7,5,1,2,6,3,4]=>101010=>010101
[6,1,5,2,7,4,3]=>[7,5,1,2,4,6,3]=>101010=>010101
[6,1,5,3,2,4,7]=>[5,3,6,1,2,4,7]=>101000=>010111
[6,1,5,3,2,7,4]=>[5,3,7,6,1,2,4]=>101001=>010110
[6,1,5,3,4,2,7]=>[5,3,4,6,1,2,7]=>101000=>010111
[6,1,5,3,4,7,2]=>[5,3,4,7,6,1,2]=>101001=>010110
[6,1,5,3,7,2,4]=>[7,5,3,6,1,2,4]=>101010=>010101
[6,1,5,3,7,4,2]=>[7,5,3,4,6,1,2]=>101010=>010101
[6,1,5,4,2,3,7]=>[4,5,1,2,6,3,7]=>101000=>010111
[6,1,5,4,2,7,3]=>[4,5,1,2,7,6,3]=>101001=>010110
[6,1,5,4,3,2,7]=>[4,5,3,6,1,2,7]=>101000=>010111
[6,1,5,4,3,7,2]=>[4,5,3,7,6,1,2]=>101001=>010110
[6,1,5,4,7,2,3]=>[4,7,5,1,2,6,3]=>101010=>010101
[6,1,5,4,7,3,2]=>[4,7,5,3,6,1,2]=>101010=>010101
[6,1,5,7,2,3,4]=>[7,1,2,5,3,6,4]=>101100=>010011
[6,1,5,7,2,4,3]=>[7,1,2,5,4,6,3]=>101100=>010011
[6,1,5,7,3,2,4]=>[7,3,5,1,2,6,4]=>101100=>010011
[6,1,5,7,3,4,2]=>[7,3,5,4,6,1,2]=>101100=>010011
[6,1,5,7,4,2,3]=>[7,4,5,1,2,6,3]=>101100=>010011
[6,1,5,7,4,3,2]=>[7,4,5,3,6,1,2]=>101100=>010011
[6,1,7,2,3,4,5]=>[7,1,2,6,3,4,5]=>101000=>010111
[6,1,7,2,3,5,4]=>[7,1,2,5,6,3,4]=>101000=>010111
[6,1,7,2,4,3,5]=>[7,1,2,4,6,3,5]=>101000=>010111
[6,1,7,2,4,5,3]=>[7,1,2,4,5,6,3]=>101000=>010111
[6,1,7,2,5,3,4]=>[5,7,1,2,6,3,4]=>101000=>010111
[6,1,7,2,5,4,3]=>[5,7,1,2,4,6,3]=>101000=>010111
[6,1,7,3,2,4,5]=>[7,3,6,1,2,4,5]=>101000=>010111
[6,1,7,3,2,5,4]=>[7,3,5,6,1,2,4]=>101000=>010111
[6,1,7,3,4,2,5]=>[7,3,4,6,1,2,5]=>101000=>010111
[6,1,7,3,4,5,2]=>[7,3,4,5,6,1,2]=>101000=>010111
[6,1,7,3,5,2,4]=>[5,7,3,6,1,2,4]=>101000=>010111
[6,1,7,3,5,4,2]=>[5,7,3,4,6,1,2]=>101000=>010111
[6,1,7,4,2,3,5]=>[4,7,1,2,6,3,5]=>101000=>010111
[6,1,7,4,2,5,3]=>[4,7,1,2,5,6,3]=>101000=>010111
[6,1,7,4,3,2,5]=>[4,7,3,6,1,2,5]=>101000=>010111
[6,1,7,4,3,5,2]=>[4,7,3,5,6,1,2]=>101000=>010111
[6,1,7,4,5,2,3]=>[4,5,7,1,2,6,3]=>101000=>010111
[6,1,7,4,5,3,2]=>[4,5,7,3,6,1,2]=>101000=>010111
[6,1,7,5,2,3,4]=>[5,1,2,7,3,6,4]=>101100=>010011
[6,1,7,5,2,4,3]=>[5,1,2,7,4,6,3]=>101100=>010011
[6,1,7,5,3,2,4]=>[5,3,7,1,2,6,4]=>101100=>010011
[6,1,7,5,3,4,2]=>[5,3,7,4,6,1,2]=>101100=>010011
[6,1,7,5,4,2,3]=>[5,4,7,1,2,6,3]=>101100=>010011
[6,1,7,5,4,3,2]=>[5,4,7,3,6,1,2]=>101100=>010011
[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>100000=>011111
[6,2,1,3,4,7,5]=>[2,7,6,1,3,4,5]=>100001=>011110
[6,2,1,3,5,4,7]=>[2,5,6,1,3,4,7]=>100000=>011111
[6,2,1,3,5,7,4]=>[2,5,7,6,1,3,4]=>100001=>011110
[6,2,1,3,7,4,5]=>[2,7,1,3,4,6,5]=>100010=>011101
[6,2,1,3,7,5,4]=>[2,7,5,6,1,3,4]=>100010=>011101
[6,2,1,4,3,5,7]=>[2,4,6,1,3,5,7]=>100000=>011111
[6,2,1,4,3,7,5]=>[2,4,7,6,1,3,5]=>100001=>011110
[6,2,1,4,5,3,7]=>[2,4,5,6,1,3,7]=>100000=>011111
[6,2,1,4,5,7,3]=>[2,4,5,7,6,1,3]=>100001=>011110
[6,2,1,4,7,3,5]=>[2,4,7,1,3,6,5]=>100010=>011101
[6,2,1,4,7,5,3]=>[2,4,7,5,6,1,3]=>100010=>011101
[6,2,1,5,3,4,7]=>[2,5,1,3,6,4,7]=>100100=>011011
[6,2,1,5,3,7,4]=>[2,5,1,3,7,6,4]=>100101=>011010
[6,2,1,5,4,3,7]=>[2,5,4,6,1,3,7]=>100100=>011011
[6,2,1,5,4,7,3]=>[2,5,4,7,6,1,3]=>100101=>011010
[6,2,1,5,7,3,4]=>[2,7,5,1,3,6,4]=>100110=>011001
[6,2,1,5,7,4,3]=>[2,7,5,4,6,1,3]=>100110=>011001
[6,2,1,7,3,4,5]=>[2,7,1,3,6,4,5]=>100100=>011011
[6,2,1,7,3,5,4]=>[2,7,1,3,5,6,4]=>100100=>011011
[6,2,1,7,4,3,5]=>[2,7,4,6,1,3,5]=>100100=>011011
[6,2,1,7,4,5,3]=>[2,7,4,5,6,1,3]=>100100=>011011
[6,2,1,7,5,3,4]=>[2,5,7,1,3,6,4]=>100100=>011011
[6,2,1,7,5,4,3]=>[2,5,7,4,6,1,3]=>100100=>011011
[6,2,3,1,4,5,7]=>[2,3,6,1,4,5,7]=>100000=>011111
[6,2,3,1,4,7,5]=>[2,3,7,6,1,4,5]=>100001=>011110
[6,2,3,1,5,4,7]=>[2,3,5,6,1,4,7]=>100000=>011111
[6,2,3,1,5,7,4]=>[2,3,5,7,6,1,4]=>100001=>011110
[6,2,3,1,7,4,5]=>[2,3,7,1,4,6,5]=>100010=>011101
[6,2,3,1,7,5,4]=>[2,3,7,5,6,1,4]=>100010=>011101
[6,2,3,4,1,5,7]=>[2,3,4,6,1,5,7]=>100000=>011111
[6,2,3,4,1,7,5]=>[2,3,4,7,6,1,5]=>100001=>011110
[6,2,3,4,5,1,7]=>[2,3,4,5,6,1,7]=>100000=>011111
[6,2,3,4,5,7,1]=>[2,3,4,5,7,6,1]=>100001=>011110
[6,2,3,4,7,1,5]=>[2,3,4,7,1,6,5]=>100010=>011101
[6,2,3,4,7,5,1]=>[2,3,4,7,5,6,1]=>100010=>011101
[6,2,3,5,1,4,7]=>[2,3,5,1,6,4,7]=>100100=>011011
[6,2,3,5,1,7,4]=>[2,3,5,1,7,6,4]=>100101=>011010
[6,2,3,5,4,1,7]=>[2,3,5,4,6,1,7]=>100100=>011011
[6,2,3,5,4,7,1]=>[2,3,5,4,7,6,1]=>100101=>011010
[6,2,3,5,7,1,4]=>[2,3,7,5,1,6,4]=>100110=>011001
[6,2,3,5,7,4,1]=>[2,3,7,5,4,6,1]=>100110=>011001
[6,2,3,7,1,4,5]=>[2,3,7,1,6,4,5]=>100100=>011011
[6,2,3,7,1,5,4]=>[2,3,7,1,5,6,4]=>100100=>011011
[6,2,3,7,4,1,5]=>[2,3,7,4,6,1,5]=>100100=>011011
[6,2,3,7,4,5,1]=>[2,3,7,4,5,6,1]=>100100=>011011
[6,2,3,7,5,1,4]=>[2,3,5,7,1,6,4]=>100100=>011011
[6,2,3,7,5,4,1]=>[2,3,5,7,4,6,1]=>100100=>011011
[6,2,4,1,3,5,7]=>[2,4,1,6,3,5,7]=>101000=>010111
[6,2,4,1,3,7,5]=>[2,4,1,7,6,3,5]=>101001=>010110
[6,2,4,1,5,3,7]=>[2,4,1,5,6,3,7]=>101000=>010111
[6,2,4,1,5,7,3]=>[2,4,1,5,7,6,3]=>101001=>010110
[6,2,4,1,7,3,5]=>[2,4,1,7,3,6,5]=>101010=>010101
[6,2,4,1,7,5,3]=>[2,4,1,7,5,6,3]=>101010=>010101
[6,2,4,3,1,5,7]=>[2,4,3,6,1,5,7]=>101000=>010111
[6,2,4,3,1,7,5]=>[2,4,3,7,6,1,5]=>101001=>010110
[6,2,4,3,5,1,7]=>[2,4,3,5,6,1,7]=>101000=>010111
[6,2,4,3,5,7,1]=>[2,4,3,5,7,6,1]=>101001=>010110
[6,2,4,3,7,1,5]=>[2,4,3,7,1,6,5]=>101010=>010101
[6,2,4,3,7,5,1]=>[2,4,3,7,5,6,1]=>101010=>010101
[6,2,4,5,1,3,7]=>[2,5,4,1,6,3,7]=>101100=>010011
[6,2,4,5,1,7,3]=>[2,5,4,1,7,6,3]=>101101=>010010
[6,2,4,5,3,1,7]=>[2,5,4,3,6,1,7]=>101100=>010011
[6,2,4,5,3,7,1]=>[2,5,4,3,7,6,1]=>101101=>010010
[6,2,4,5,7,1,3]=>[2,7,5,4,1,6,3]=>101110=>010001
[6,2,4,5,7,3,1]=>[2,7,5,4,3,6,1]=>101110=>010001
[6,2,4,7,1,3,5]=>[2,7,4,1,6,3,5]=>101100=>010011
[6,2,4,7,1,5,3]=>[2,7,4,1,5,6,3]=>101100=>010011
[6,2,4,7,3,1,5]=>[2,7,4,3,6,1,5]=>101100=>010011
[6,2,4,7,3,5,1]=>[2,7,4,3,5,6,1]=>101100=>010011
[6,2,4,7,5,1,3]=>[2,5,7,4,1,6,3]=>101100=>010011
[6,2,4,7,5,3,1]=>[2,5,7,4,3,6,1]=>101100=>010011
[6,2,5,1,3,4,7]=>[2,5,1,6,3,4,7]=>101000=>010111
[6,2,5,1,3,7,4]=>[2,5,1,7,6,3,4]=>101001=>010110
[6,2,5,1,4,3,7]=>[2,5,1,4,6,3,7]=>101000=>010111
[6,2,5,1,4,7,3]=>[2,5,1,4,7,6,3]=>101001=>010110
[6,2,5,1,7,3,4]=>[2,7,5,1,6,3,4]=>101010=>010101
[6,2,5,1,7,4,3]=>[2,7,5,1,4,6,3]=>101010=>010101
[6,2,5,3,1,4,7]=>[2,5,3,6,1,4,7]=>101000=>010111
[6,2,5,3,1,7,4]=>[2,5,3,7,6,1,4]=>101001=>010110
[6,2,5,3,4,1,7]=>[2,5,3,4,6,1,7]=>101000=>010111
[6,2,5,3,4,7,1]=>[2,5,3,4,7,6,1]=>101001=>010110
[6,2,5,3,7,1,4]=>[2,7,5,3,6,1,4]=>101010=>010101
[6,2,5,3,7,4,1]=>[2,7,5,3,4,6,1]=>101010=>010101
[6,2,5,4,1,3,7]=>[2,4,5,1,6,3,7]=>101000=>010111
[6,2,5,4,1,7,3]=>[2,4,5,1,7,6,3]=>101001=>010110
[6,2,5,4,3,1,7]=>[2,4,5,3,6,1,7]=>101000=>010111
[6,2,5,4,3,7,1]=>[2,4,5,3,7,6,1]=>101001=>010110
[6,2,5,4,7,1,3]=>[2,4,7,5,1,6,3]=>101010=>010101
[6,2,5,4,7,3,1]=>[2,4,7,5,3,6,1]=>101010=>010101
[6,2,5,7,1,3,4]=>[2,7,1,5,3,6,4]=>101100=>010011
[6,2,5,7,1,4,3]=>[2,7,1,5,4,6,3]=>101100=>010011
[6,2,5,7,3,1,4]=>[2,7,3,5,1,6,4]=>101100=>010011
[6,2,5,7,3,4,1]=>[2,7,3,5,4,6,1]=>101100=>010011
[6,2,5,7,4,1,3]=>[2,7,4,5,1,6,3]=>101100=>010011
[6,2,5,7,4,3,1]=>[2,7,4,5,3,6,1]=>101100=>010011
[6,2,7,1,3,4,5]=>[2,7,1,6,3,4,5]=>101000=>010111
[6,2,7,1,3,5,4]=>[2,7,1,5,6,3,4]=>101000=>010111
[6,2,7,1,4,3,5]=>[2,7,1,4,6,3,5]=>101000=>010111
[6,2,7,1,4,5,3]=>[2,7,1,4,5,6,3]=>101000=>010111
[6,2,7,1,5,3,4]=>[2,5,7,1,6,3,4]=>101000=>010111
[6,2,7,1,5,4,3]=>[2,5,7,1,4,6,3]=>101000=>010111
[6,2,7,3,1,4,5]=>[2,7,3,6,1,4,5]=>101000=>010111
[6,2,7,3,1,5,4]=>[2,7,3,5,6,1,4]=>101000=>010111
[6,2,7,3,4,1,5]=>[2,7,3,4,6,1,5]=>101000=>010111
[6,2,7,3,4,5,1]=>[2,7,3,4,5,6,1]=>101000=>010111
[6,2,7,3,5,1,4]=>[2,5,7,3,6,1,4]=>101000=>010111
[6,2,7,3,5,4,1]=>[2,5,7,3,4,6,1]=>101000=>010111
[6,2,7,4,1,3,5]=>[2,4,7,1,6,3,5]=>101000=>010111
[6,2,7,4,1,5,3]=>[2,4,7,1,5,6,3]=>101000=>010111
[6,2,7,4,3,1,5]=>[2,4,7,3,6,1,5]=>101000=>010111
[6,2,7,4,3,5,1]=>[2,4,7,3,5,6,1]=>101000=>010111
[6,2,7,4,5,1,3]=>[2,4,5,7,1,6,3]=>101000=>010111
[6,2,7,4,5,3,1]=>[2,4,5,7,3,6,1]=>101000=>010111
[6,2,7,5,1,3,4]=>[2,5,1,7,3,6,4]=>101100=>010011
[6,2,7,5,1,4,3]=>[2,5,1,7,4,6,3]=>101100=>010011
[6,2,7,5,3,1,4]=>[2,5,3,7,1,6,4]=>101100=>010011
[6,2,7,5,3,4,1]=>[2,5,3,7,4,6,1]=>101100=>010011
[6,2,7,5,4,1,3]=>[2,5,4,7,1,6,3]=>101100=>010011
[6,2,7,5,4,3,1]=>[2,5,4,7,3,6,1]=>101100=>010011
[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>110000=>001111
[6,3,1,2,4,7,5]=>[3,1,7,6,2,4,5]=>110001=>001110
[6,3,1,2,5,4,7]=>[3,1,5,6,2,4,7]=>110000=>001111
[6,3,1,2,5,7,4]=>[3,1,5,7,6,2,4]=>110001=>001110
[6,3,1,2,7,4,5]=>[3,1,7,2,4,6,5]=>110010=>001101
[6,3,1,2,7,5,4]=>[3,1,7,5,6,2,4]=>110010=>001101
[6,3,1,4,2,5,7]=>[3,1,4,6,2,5,7]=>110000=>001111
[6,3,1,4,2,7,5]=>[3,1,4,7,6,2,5]=>110001=>001110
[6,3,1,4,5,2,7]=>[3,1,4,5,6,2,7]=>110000=>001111
[6,3,1,4,5,7,2]=>[3,1,4,5,7,6,2]=>110001=>001110
[6,3,1,4,7,2,5]=>[3,1,4,7,2,6,5]=>110010=>001101
[6,3,1,4,7,5,2]=>[3,1,4,7,5,6,2]=>110010=>001101
[6,3,1,5,2,4,7]=>[3,1,5,2,6,4,7]=>110100=>001011
[6,3,1,5,2,7,4]=>[3,1,5,2,7,6,4]=>110101=>001010
[6,3,1,5,4,2,7]=>[3,1,5,4,6,2,7]=>110100=>001011
[6,3,1,5,4,7,2]=>[3,1,5,4,7,6,2]=>110101=>001010
[6,3,1,5,7,2,4]=>[3,1,7,5,2,6,4]=>110110=>001001
[6,3,1,5,7,4,2]=>[3,1,7,5,4,6,2]=>110110=>001001
[6,3,1,7,2,4,5]=>[3,1,7,2,6,4,5]=>110100=>001011
[6,3,1,7,2,5,4]=>[3,1,7,2,5,6,4]=>110100=>001011
[6,3,1,7,4,2,5]=>[3,1,7,4,6,2,5]=>110100=>001011
[6,3,1,7,4,5,2]=>[3,1,7,4,5,6,2]=>110100=>001011
[6,3,1,7,5,2,4]=>[3,1,5,7,2,6,4]=>110100=>001011
[6,3,1,7,5,4,2]=>[3,1,5,7,4,6,2]=>110100=>001011
[6,3,2,1,4,5,7]=>[3,2,6,1,4,5,7]=>110000=>001111
[6,3,2,1,4,7,5]=>[3,2,7,6,1,4,5]=>110001=>001110
[6,3,2,1,5,4,7]=>[3,2,5,6,1,4,7]=>110000=>001111
[6,3,2,1,5,7,4]=>[3,2,5,7,6,1,4]=>110001=>001110
[6,3,2,1,7,4,5]=>[3,2,7,1,4,6,5]=>110010=>001101
[6,3,2,1,7,5,4]=>[3,2,7,5,6,1,4]=>110010=>001101
[6,3,2,4,1,5,7]=>[3,2,4,6,1,5,7]=>110000=>001111
[6,3,2,4,1,7,5]=>[3,2,4,7,6,1,5]=>110001=>001110
[6,3,2,4,5,1,7]=>[3,2,4,5,6,1,7]=>110000=>001111
[6,3,2,4,5,7,1]=>[3,2,4,5,7,6,1]=>110001=>001110
[6,3,2,4,7,1,5]=>[3,2,4,7,1,6,5]=>110010=>001101
[6,3,2,4,7,5,1]=>[3,2,4,7,5,6,1]=>110010=>001101
[6,3,2,5,1,4,7]=>[3,2,5,1,6,4,7]=>110100=>001011
[6,3,2,5,1,7,4]=>[3,2,5,1,7,6,4]=>110101=>001010
[6,3,2,5,4,1,7]=>[3,2,5,4,6,1,7]=>110100=>001011
[6,3,2,5,4,7,1]=>[3,2,5,4,7,6,1]=>110101=>001010
[6,3,2,5,7,1,4]=>[3,2,7,5,1,6,4]=>110110=>001001
[6,3,2,5,7,4,1]=>[3,2,7,5,4,6,1]=>110110=>001001
[6,3,2,7,1,4,5]=>[3,2,7,1,6,4,5]=>110100=>001011
[6,3,2,7,1,5,4]=>[3,2,7,1,5,6,4]=>110100=>001011
[6,3,2,7,4,1,5]=>[3,2,7,4,6,1,5]=>110100=>001011
[6,3,2,7,4,5,1]=>[3,2,7,4,5,6,1]=>110100=>001011
[6,3,2,7,5,1,4]=>[3,2,5,7,1,6,4]=>110100=>001011
[6,3,2,7,5,4,1]=>[3,2,5,7,4,6,1]=>110100=>001011
[6,3,4,1,2,5,7]=>[4,3,1,6,2,5,7]=>111000=>000111
[6,3,4,1,2,7,5]=>[4,3,1,7,6,2,5]=>111001=>000110
[6,3,4,1,5,2,7]=>[4,3,1,5,6,2,7]=>111000=>000111
[6,3,4,1,5,7,2]=>[4,3,1,5,7,6,2]=>111001=>000110
[6,3,4,1,7,2,5]=>[4,3,1,7,2,6,5]=>111010=>000101
[6,3,4,1,7,5,2]=>[4,3,1,7,5,6,2]=>111010=>000101
[6,3,4,2,1,5,7]=>[4,3,2,6,1,5,7]=>111000=>000111
[6,3,4,2,1,7,5]=>[4,3,2,7,6,1,5]=>111001=>000110
[6,3,4,2,5,1,7]=>[4,3,2,5,6,1,7]=>111000=>000111
[6,3,4,2,5,7,1]=>[4,3,2,5,7,6,1]=>111001=>000110
[6,3,4,2,7,1,5]=>[4,3,2,7,1,6,5]=>111010=>000101
[6,3,4,2,7,5,1]=>[4,3,2,7,5,6,1]=>111010=>000101
[6,3,4,5,1,2,7]=>[5,4,3,1,6,2,7]=>111100=>000011
[6,3,4,5,1,7,2]=>[5,4,3,1,7,6,2]=>111101=>000010
[6,3,4,5,2,1,7]=>[5,4,3,2,6,1,7]=>111100=>000011
[6,3,4,5,2,7,1]=>[5,4,3,2,7,6,1]=>111101=>000010
[6,3,4,5,7,1,2]=>[7,5,4,3,1,6,2]=>111110=>000001
[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]=>111110=>000001
[6,3,4,7,1,2,5]=>[7,4,3,1,6,2,5]=>111100=>000011
[6,3,4,7,1,5,2]=>[7,4,3,1,5,6,2]=>111100=>000011
[6,3,4,7,2,1,5]=>[7,4,3,2,6,1,5]=>111100=>000011
[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]=>111100=>000011
[6,3,4,7,5,1,2]=>[5,7,4,3,1,6,2]=>111100=>000011
[6,3,4,7,5,2,1]=>[5,7,4,3,2,6,1]=>111100=>000011
[6,3,5,1,2,4,7]=>[5,3,1,6,2,4,7]=>111000=>000111
[6,3,5,1,2,7,4]=>[5,3,1,7,6,2,4]=>111001=>000110
[6,3,5,1,4,2,7]=>[5,3,1,4,6,2,7]=>111000=>000111
[6,3,5,1,4,7,2]=>[5,3,1,4,7,6,2]=>111001=>000110
[6,3,5,1,7,2,4]=>[7,5,3,1,6,2,4]=>111010=>000101
[6,3,5,1,7,4,2]=>[7,5,3,1,4,6,2]=>111010=>000101
[6,3,5,2,1,4,7]=>[5,3,2,6,1,4,7]=>111000=>000111
[6,3,5,2,1,7,4]=>[5,3,2,7,6,1,4]=>111001=>000110
[6,3,5,2,4,1,7]=>[5,3,2,4,6,1,7]=>111000=>000111
[6,3,5,2,4,7,1]=>[5,3,2,4,7,6,1]=>111001=>000110
[6,3,5,2,7,1,4]=>[7,5,3,2,6,1,4]=>111010=>000101
[6,3,5,2,7,4,1]=>[7,5,3,2,4,6,1]=>111010=>000101
[6,3,5,4,1,2,7]=>[4,5,3,1,6,2,7]=>111000=>000111
[6,3,5,4,1,7,2]=>[4,5,3,1,7,6,2]=>111001=>000110
[6,3,5,4,2,1,7]=>[4,5,3,2,6,1,7]=>111000=>000111
[6,3,5,4,2,7,1]=>[4,5,3,2,7,6,1]=>111001=>000110
[6,3,5,4,7,1,2]=>[4,7,5,3,1,6,2]=>111010=>000101
[6,3,5,4,7,2,1]=>[4,7,5,3,2,6,1]=>111010=>000101
[6,3,5,7,1,2,4]=>[7,3,1,5,2,6,4]=>111100=>000011
[6,3,5,7,1,4,2]=>[7,3,1,5,4,6,2]=>111100=>000011
[6,3,5,7,2,1,4]=>[7,3,2,5,1,6,4]=>111100=>000011
[6,3,5,7,2,4,1]=>[7,3,2,5,4,6,1]=>111100=>000011
[6,3,5,7,4,1,2]=>[7,4,5,3,1,6,2]=>111100=>000011
[6,3,5,7,4,2,1]=>[7,4,5,3,2,6,1]=>111100=>000011
[6,3,7,1,2,4,5]=>[7,3,1,6,2,4,5]=>111000=>000111
[6,3,7,1,2,5,4]=>[7,3,1,5,6,2,4]=>111000=>000111
[6,3,7,1,4,2,5]=>[7,3,1,4,6,2,5]=>111000=>000111
[6,3,7,1,4,5,2]=>[7,3,1,4,5,6,2]=>111000=>000111
[6,3,7,1,5,2,4]=>[5,7,3,1,6,2,4]=>111000=>000111
[6,3,7,1,5,4,2]=>[5,7,3,1,4,6,2]=>111000=>000111
[6,3,7,2,1,4,5]=>[7,3,2,6,1,4,5]=>111000=>000111
[6,3,7,2,1,5,4]=>[7,3,2,5,6,1,4]=>111000=>000111
[6,3,7,2,4,1,5]=>[7,3,2,4,6,1,5]=>111000=>000111
[6,3,7,2,4,5,1]=>[7,3,2,4,5,6,1]=>111000=>000111
[6,3,7,2,5,1,4]=>[5,7,3,2,6,1,4]=>111000=>000111
[6,3,7,2,5,4,1]=>[5,7,3,2,4,6,1]=>111000=>000111
[6,3,7,4,1,2,5]=>[4,7,3,1,6,2,5]=>111000=>000111
[6,3,7,4,1,5,2]=>[4,7,3,1,5,6,2]=>111000=>000111
[6,3,7,4,2,1,5]=>[4,7,3,2,6,1,5]=>111000=>000111
[6,3,7,4,2,5,1]=>[4,7,3,2,5,6,1]=>111000=>000111
[6,3,7,4,5,1,2]=>[4,5,7,3,1,6,2]=>111000=>000111
[6,3,7,4,5,2,1]=>[4,5,7,3,2,6,1]=>111000=>000111
[6,3,7,5,1,2,4]=>[5,3,1,7,2,6,4]=>111100=>000011
[6,3,7,5,1,4,2]=>[5,3,1,7,4,6,2]=>111100=>000011
[6,3,7,5,2,1,4]=>[5,3,2,7,1,6,4]=>111100=>000011
[6,3,7,5,2,4,1]=>[5,3,2,7,4,6,1]=>111100=>000011
[6,3,7,5,4,1,2]=>[5,4,7,3,1,6,2]=>111100=>000011
[6,3,7,5,4,2,1]=>[5,4,7,3,2,6,1]=>111100=>000011
[6,4,1,2,3,5,7]=>[4,1,6,2,3,5,7]=>110000=>001111
[6,4,1,2,3,7,5]=>[4,1,7,6,2,3,5]=>110001=>001110
[6,4,1,2,5,3,7]=>[4,1,5,6,2,3,7]=>110000=>001111
[6,4,1,2,5,7,3]=>[4,1,5,7,6,2,3]=>110001=>001110
[6,4,1,2,7,3,5]=>[4,1,7,2,3,6,5]=>110010=>001101
[6,4,1,2,7,5,3]=>[4,1,7,5,6,2,3]=>110010=>001101
[6,4,1,3,2,5,7]=>[4,1,3,6,2,5,7]=>110000=>001111
[6,4,1,3,2,7,5]=>[4,1,3,7,6,2,5]=>110001=>001110
[6,4,1,3,5,2,7]=>[4,1,3,5,6,2,7]=>110000=>001111
[6,4,1,3,5,7,2]=>[4,1,3,5,7,6,2]=>110001=>001110
[6,4,1,3,7,2,5]=>[4,1,3,7,2,6,5]=>110010=>001101
[6,4,1,3,7,5,2]=>[4,1,3,7,5,6,2]=>110010=>001101
[6,4,1,5,2,3,7]=>[5,4,1,6,2,3,7]=>110100=>001011
[6,4,1,5,2,7,3]=>[5,4,1,7,6,2,3]=>110101=>001010
[6,4,1,5,3,2,7]=>[5,4,1,3,6,2,7]=>110100=>001011
[6,4,1,5,3,7,2]=>[5,4,1,3,7,6,2]=>110101=>001010
[6,4,1,5,7,2,3]=>[7,5,4,1,6,2,3]=>110110=>001001
[6,4,1,5,7,3,2]=>[7,5,4,1,3,6,2]=>110110=>001001
[6,4,1,7,2,3,5]=>[7,4,1,6,2,3,5]=>110100=>001011
[6,4,1,7,2,5,3]=>[7,4,1,5,6,2,3]=>110100=>001011
[6,4,1,7,3,2,5]=>[7,4,1,3,6,2,5]=>110100=>001011
[6,4,1,7,3,5,2]=>[7,4,1,3,5,6,2]=>110100=>001011
[6,4,1,7,5,2,3]=>[5,7,4,1,6,2,3]=>110100=>001011
[6,4,1,7,5,3,2]=>[5,7,4,1,3,6,2]=>110100=>001011
[6,4,2,1,3,5,7]=>[4,2,6,1,3,5,7]=>110000=>001111
[6,4,2,1,3,7,5]=>[4,2,7,6,1,3,5]=>110001=>001110
[6,4,2,1,5,3,7]=>[4,2,5,6,1,3,7]=>110000=>001111
[6,4,2,1,5,7,3]=>[4,2,5,7,6,1,3]=>110001=>001110
[6,4,2,1,7,3,5]=>[4,2,7,1,3,6,5]=>110010=>001101
[6,4,2,1,7,5,3]=>[4,2,7,5,6,1,3]=>110010=>001101
[6,4,2,3,1,5,7]=>[4,2,3,6,1,5,7]=>110000=>001111
[6,4,2,3,1,7,5]=>[4,2,3,7,6,1,5]=>110001=>001110
[6,4,2,3,5,1,7]=>[4,2,3,5,6,1,7]=>110000=>001111
[6,4,2,3,5,7,1]=>[4,2,3,5,7,6,1]=>110001=>001110
[6,4,2,3,7,1,5]=>[4,2,3,7,1,6,5]=>110010=>001101
[6,4,2,3,7,5,1]=>[4,2,3,7,5,6,1]=>110010=>001101
[6,4,2,5,1,3,7]=>[5,4,2,6,1,3,7]=>110100=>001011
[6,4,2,5,1,7,3]=>[5,4,2,7,6,1,3]=>110101=>001010
[6,4,2,5,3,1,7]=>[5,4,2,3,6,1,7]=>110100=>001011
[6,4,2,5,3,7,1]=>[5,4,2,3,7,6,1]=>110101=>001010
[6,4,2,5,7,1,3]=>[7,5,4,2,6,1,3]=>110110=>001001
[6,4,2,5,7,3,1]=>[7,5,4,2,3,6,1]=>110110=>001001
[6,4,2,7,1,3,5]=>[7,4,2,6,1,3,5]=>110100=>001011
[6,4,2,7,1,5,3]=>[7,4,2,5,6,1,3]=>110100=>001011
[6,4,2,7,3,1,5]=>[7,4,2,3,6,1,5]=>110100=>001011
[6,4,2,7,3,5,1]=>[7,4,2,3,5,6,1]=>110100=>001011
[6,4,2,7,5,1,3]=>[5,7,4,2,6,1,3]=>110100=>001011
[6,4,2,7,5,3,1]=>[5,7,4,2,3,6,1]=>110100=>001011
[6,4,3,1,2,5,7]=>[3,4,1,6,2,5,7]=>110000=>001111
[6,4,3,1,2,7,5]=>[3,4,1,7,6,2,5]=>110001=>001110
[6,4,3,1,5,2,7]=>[3,4,1,5,6,2,7]=>110000=>001111
[6,4,3,1,5,7,2]=>[3,4,1,5,7,6,2]=>110001=>001110
[6,4,3,1,7,2,5]=>[3,4,1,7,2,6,5]=>110010=>001101
[6,4,3,1,7,5,2]=>[3,4,1,7,5,6,2]=>110010=>001101
[6,4,3,2,1,5,7]=>[3,4,2,6,1,5,7]=>110000=>001111
[6,4,3,2,1,7,5]=>[3,4,2,7,6,1,5]=>110001=>001110
[6,4,3,2,5,1,7]=>[3,4,2,5,6,1,7]=>110000=>001111
[6,4,3,2,5,7,1]=>[3,4,2,5,7,6,1]=>110001=>001110
[6,4,3,2,7,1,5]=>[3,4,2,7,1,6,5]=>110010=>001101
[6,4,3,2,7,5,1]=>[3,4,2,7,5,6,1]=>110010=>001101
[6,4,3,5,1,2,7]=>[3,5,4,1,6,2,7]=>110100=>001011
[6,4,3,5,1,7,2]=>[3,5,4,1,7,6,2]=>110101=>001010
[6,4,3,5,2,1,7]=>[3,5,4,2,6,1,7]=>110100=>001011
[6,4,3,5,2,7,1]=>[3,5,4,2,7,6,1]=>110101=>001010
[6,4,3,5,7,1,2]=>[3,7,5,4,1,6,2]=>110110=>001001
[6,4,3,5,7,2,1]=>[3,7,5,4,2,6,1]=>110110=>001001
[6,4,3,7,1,2,5]=>[3,7,4,1,6,2,5]=>110100=>001011
[6,4,3,7,1,5,2]=>[3,7,4,1,5,6,2]=>110100=>001011
[6,4,3,7,2,1,5]=>[3,7,4,2,6,1,5]=>110100=>001011
[6,4,3,7,2,5,1]=>[3,7,4,2,5,6,1]=>110100=>001011
[6,4,3,7,5,1,2]=>[3,5,7,4,1,6,2]=>110100=>001011
[6,4,3,7,5,2,1]=>[3,5,7,4,2,6,1]=>110100=>001011
[6,4,5,1,2,3,7]=>[5,1,4,2,6,3,7]=>111000=>000111
[6,4,5,1,2,7,3]=>[5,1,4,2,7,6,3]=>111001=>000110
[6,4,5,1,3,2,7]=>[5,1,4,3,6,2,7]=>111000=>000111
[6,4,5,1,3,7,2]=>[5,1,4,3,7,6,2]=>111001=>000110
[6,4,5,1,7,2,3]=>[7,5,1,4,2,6,3]=>111010=>000101
[6,4,5,1,7,3,2]=>[7,5,1,4,3,6,2]=>111010=>000101
[6,4,5,2,1,3,7]=>[5,2,4,1,6,3,7]=>111000=>000111
[6,4,5,2,1,7,3]=>[5,2,4,1,7,6,3]=>111001=>000110
[6,4,5,2,3,1,7]=>[5,2,4,3,6,1,7]=>111000=>000111
[6,4,5,2,3,7,1]=>[5,2,4,3,7,6,1]=>111001=>000110
[6,4,5,2,7,1,3]=>[7,5,2,4,1,6,3]=>111010=>000101
[6,4,5,2,7,3,1]=>[7,5,2,4,3,6,1]=>111010=>000101
[6,4,5,3,1,2,7]=>[5,3,4,1,6,2,7]=>111000=>000111
[6,4,5,3,1,7,2]=>[5,3,4,1,7,6,2]=>111001=>000110
[6,4,5,3,2,1,7]=>[5,3,4,2,6,1,7]=>111000=>000111
[6,4,5,3,2,7,1]=>[5,3,4,2,7,6,1]=>111001=>000110
[6,4,5,3,7,1,2]=>[7,5,3,4,1,6,2]=>111010=>000101
[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]=>111010=>000101
[6,4,5,7,1,2,3]=>[7,1,5,4,2,6,3]=>111100=>000011
[6,4,5,7,1,3,2]=>[7,1,5,4,3,6,2]=>111100=>000011
[6,4,5,7,2,1,3]=>[7,2,5,4,1,6,3]=>111100=>000011
[6,4,5,7,2,3,1]=>[7,2,5,4,3,6,1]=>111100=>000011
[6,4,5,7,3,1,2]=>[7,3,5,4,1,6,2]=>111100=>000011
[6,4,5,7,3,2,1]=>[7,3,5,4,2,6,1]=>111100=>000011
[6,4,7,1,2,3,5]=>[7,1,4,2,6,3,5]=>111000=>000111
[6,4,7,1,2,5,3]=>[7,1,4,2,5,6,3]=>111000=>000111
[6,4,7,1,3,2,5]=>[7,1,4,3,6,2,5]=>111000=>000111
[6,4,7,1,3,5,2]=>[7,1,4,3,5,6,2]=>111000=>000111
[6,4,7,1,5,2,3]=>[5,7,1,4,2,6,3]=>111000=>000111
[6,4,7,1,5,3,2]=>[5,7,1,4,3,6,2]=>111000=>000111
[6,4,7,2,1,3,5]=>[7,2,4,1,6,3,5]=>111000=>000111
[6,4,7,2,1,5,3]=>[7,2,4,1,5,6,3]=>111000=>000111
[6,4,7,2,3,1,5]=>[7,2,4,3,6,1,5]=>111000=>000111
[6,4,7,2,3,5,1]=>[7,2,4,3,5,6,1]=>111000=>000111
[6,4,7,2,5,1,3]=>[5,7,2,4,1,6,3]=>111000=>000111
[6,4,7,2,5,3,1]=>[5,7,2,4,3,6,1]=>111000=>000111
[6,4,7,3,1,2,5]=>[7,3,4,1,6,2,5]=>111000=>000111
[6,4,7,3,1,5,2]=>[7,3,4,1,5,6,2]=>111000=>000111
[6,4,7,3,2,1,5]=>[7,3,4,2,6,1,5]=>111000=>000111
[6,4,7,3,2,5,1]=>[7,3,4,2,5,6,1]=>111000=>000111
[6,4,7,3,5,1,2]=>[5,7,3,4,1,6,2]=>111000=>000111
[6,4,7,3,5,2,1]=>[5,7,3,4,2,6,1]=>111000=>000111
[6,4,7,5,1,2,3]=>[5,1,7,4,2,6,3]=>111100=>000011
[6,4,7,5,1,3,2]=>[5,1,7,4,3,6,2]=>111100=>000011
[6,4,7,5,2,1,3]=>[5,2,7,4,1,6,3]=>111100=>000011
[6,4,7,5,2,3,1]=>[5,2,7,4,3,6,1]=>111100=>000011
[6,4,7,5,3,1,2]=>[5,3,7,4,1,6,2]=>111100=>000011
[6,4,7,5,3,2,1]=>[5,3,7,4,2,6,1]=>111100=>000011
[6,5,1,2,3,4,7]=>[5,1,6,2,3,4,7]=>110000=>001111
[6,5,1,2,3,7,4]=>[5,1,7,6,2,3,4]=>110001=>001110
[6,5,1,2,4,3,7]=>[5,1,4,6,2,3,7]=>110000=>001111
[6,5,1,2,4,7,3]=>[5,1,4,7,6,2,3]=>110001=>001110
[6,5,1,2,7,3,4]=>[7,5,1,6,2,3,4]=>110010=>001101
[6,5,1,2,7,4,3]=>[7,5,1,4,6,2,3]=>110010=>001101
[6,5,1,3,2,4,7]=>[5,1,3,6,2,4,7]=>110000=>001111
[6,5,1,3,2,7,4]=>[5,1,3,7,6,2,4]=>110001=>001110
[6,5,1,3,4,2,7]=>[5,1,3,4,6,2,7]=>110000=>001111
[6,5,1,3,4,7,2]=>[5,1,3,4,7,6,2]=>110001=>001110
[6,5,1,3,7,2,4]=>[7,5,1,3,6,2,4]=>110010=>001101
[6,5,1,3,7,4,2]=>[7,5,1,3,4,6,2]=>110010=>001101
[6,5,1,4,2,3,7]=>[4,5,1,6,2,3,7]=>110000=>001111
[6,5,1,4,2,7,3]=>[4,5,1,7,6,2,3]=>110001=>001110
[6,5,1,4,3,2,7]=>[4,5,1,3,6,2,7]=>110000=>001111
[6,5,1,4,3,7,2]=>[4,5,1,3,7,6,2]=>110001=>001110
[6,5,1,4,7,2,3]=>[4,7,5,1,6,2,3]=>110010=>001101
[6,5,1,4,7,3,2]=>[4,7,5,1,3,6,2]=>110010=>001101
[6,5,1,7,2,3,4]=>[7,1,5,2,3,6,4]=>110100=>001011
[6,5,1,7,2,4,3]=>[7,1,5,4,6,2,3]=>110100=>001011
[6,5,1,7,3,2,4]=>[7,1,3,5,2,6,4]=>110100=>001011
[6,5,1,7,3,4,2]=>[7,1,3,5,4,6,2]=>110100=>001011
[6,5,1,7,4,2,3]=>[7,4,5,1,6,2,3]=>110100=>001011
[6,5,1,7,4,3,2]=>[7,4,5,1,3,6,2]=>110100=>001011
[6,5,2,1,3,4,7]=>[5,2,6,1,3,4,7]=>110000=>001111
[6,5,2,1,3,7,4]=>[5,2,7,6,1,3,4]=>110001=>001110
[6,5,2,1,4,3,7]=>[5,2,4,6,1,3,7]=>110000=>001111
[6,5,2,1,4,7,3]=>[5,2,4,7,6,1,3]=>110001=>001110
[6,5,2,1,7,3,4]=>[7,5,2,6,1,3,4]=>110010=>001101
[6,5,2,1,7,4,3]=>[7,5,2,4,6,1,3]=>110010=>001101
[6,5,2,3,1,4,7]=>[5,2,3,6,1,4,7]=>110000=>001111
[6,5,2,3,1,7,4]=>[5,2,3,7,6,1,4]=>110001=>001110
[6,5,2,3,4,1,7]=>[5,2,3,4,6,1,7]=>110000=>001111
[6,5,2,3,4,7,1]=>[5,2,3,4,7,6,1]=>110001=>001110
[6,5,2,3,7,1,4]=>[7,5,2,3,6,1,4]=>110010=>001101
[6,5,2,3,7,4,1]=>[7,5,2,3,4,6,1]=>110010=>001101
[6,5,2,4,1,3,7]=>[4,5,2,6,1,3,7]=>110000=>001111
[6,5,2,4,1,7,3]=>[4,5,2,7,6,1,3]=>110001=>001110
[6,5,2,4,3,1,7]=>[4,5,2,3,6,1,7]=>110000=>001111
[6,5,2,4,3,7,1]=>[4,5,2,3,7,6,1]=>110001=>001110
[6,5,2,4,7,1,3]=>[4,7,5,2,6,1,3]=>110010=>001101
[6,5,2,4,7,3,1]=>[4,7,5,2,3,6,1]=>110010=>001101
[6,5,2,7,1,3,4]=>[7,2,5,1,3,6,4]=>110100=>001011
[6,5,2,7,1,4,3]=>[7,2,5,4,6,1,3]=>110100=>001011
[6,5,2,7,3,1,4]=>[7,2,3,5,1,6,4]=>110100=>001011
[6,5,2,7,3,4,1]=>[7,2,3,5,4,6,1]=>110100=>001011
[6,5,2,7,4,1,3]=>[7,4,5,2,6,1,3]=>110100=>001011
[6,5,2,7,4,3,1]=>[7,4,5,2,3,6,1]=>110100=>001011
[6,5,3,1,2,4,7]=>[3,5,1,6,2,4,7]=>110000=>001111
[6,5,3,1,2,7,4]=>[3,5,1,7,6,2,4]=>110001=>001110
[6,5,3,1,4,2,7]=>[3,5,1,4,6,2,7]=>110000=>001111
[6,5,3,1,4,7,2]=>[3,5,1,4,7,6,2]=>110001=>001110
[6,5,3,1,7,2,4]=>[3,7,5,1,6,2,4]=>110010=>001101
[6,5,3,1,7,4,2]=>[3,7,5,1,4,6,2]=>110010=>001101
[6,5,3,2,1,4,7]=>[3,5,2,6,1,4,7]=>110000=>001111
[6,5,3,2,1,7,4]=>[3,5,2,7,6,1,4]=>110001=>001110
[6,5,3,2,4,1,7]=>[3,5,2,4,6,1,7]=>110000=>001111
[6,5,3,2,4,7,1]=>[3,5,2,4,7,6,1]=>110001=>001110
[6,5,3,2,7,1,4]=>[3,7,5,2,6,1,4]=>110010=>001101
[6,5,3,2,7,4,1]=>[3,7,5,2,4,6,1]=>110010=>001101
[6,5,3,4,1,2,7]=>[3,4,5,1,6,2,7]=>110000=>001111
[6,5,3,4,1,7,2]=>[3,4,5,1,7,6,2]=>110001=>001110
[6,5,3,4,2,1,7]=>[3,4,5,2,6,1,7]=>110000=>001111
[6,5,3,4,2,7,1]=>[3,4,5,2,7,6,1]=>110001=>001110
[6,5,3,4,7,1,2]=>[3,4,7,5,1,6,2]=>110010=>001101
[6,5,3,4,7,2,1]=>[3,4,7,5,2,6,1]=>110010=>001101
[6,5,3,7,1,2,4]=>[3,7,1,5,2,6,4]=>110100=>001011
[6,5,3,7,1,4,2]=>[3,7,1,5,4,6,2]=>110100=>001011
[6,5,3,7,2,1,4]=>[3,7,2,5,1,6,4]=>110100=>001011
[6,5,3,7,2,4,1]=>[3,7,2,5,4,6,1]=>110100=>001011
[6,5,3,7,4,1,2]=>[3,7,4,5,1,6,2]=>110100=>001011
[6,5,3,7,4,2,1]=>[3,7,4,5,2,6,1]=>110100=>001011
[6,5,4,1,2,3,7]=>[4,1,5,2,6,3,7]=>111000=>000111
[6,5,4,1,2,7,3]=>[4,1,5,2,7,6,3]=>111001=>000110
[6,5,4,1,3,2,7]=>[4,1,5,3,6,2,7]=>111000=>000111
[6,5,4,1,3,7,2]=>[4,1,5,3,7,6,2]=>111001=>000110
[6,5,4,1,7,2,3]=>[4,1,7,5,2,6,3]=>111010=>000101
[6,5,4,1,7,3,2]=>[4,1,7,5,3,6,2]=>111010=>000101
[6,5,4,2,1,3,7]=>[4,2,5,1,6,3,7]=>111000=>000111
[6,5,4,2,1,7,3]=>[4,2,5,1,7,6,3]=>111001=>000110
[6,5,4,2,3,1,7]=>[4,2,5,3,6,1,7]=>111000=>000111
[6,5,4,2,3,7,1]=>[4,2,5,3,7,6,1]=>111001=>000110
[6,5,4,2,7,1,3]=>[4,2,7,5,1,6,3]=>111010=>000101
[6,5,4,2,7,3,1]=>[4,2,7,5,3,6,1]=>111010=>000101
[6,5,4,3,1,2,7]=>[4,3,5,1,6,2,7]=>111000=>000111
[6,5,4,3,1,7,2]=>[4,3,5,1,7,6,2]=>111001=>000110
[6,5,4,3,2,1,7]=>[4,3,5,2,6,1,7]=>111000=>000111
[6,5,4,3,2,7,1]=>[4,3,5,2,7,6,1]=>111001=>000110
[6,5,4,3,7,1,2]=>[4,3,7,5,1,6,2]=>111010=>000101
[6,5,4,3,7,2,1]=>[4,3,7,5,2,6,1]=>111010=>000101
[6,5,4,7,1,2,3]=>[7,4,1,5,2,6,3]=>111100=>000011
[6,5,4,7,1,3,2]=>[7,4,1,5,3,6,2]=>111100=>000011
[6,5,4,7,2,1,3]=>[7,4,2,5,1,6,3]=>111100=>000011
[6,5,4,7,2,3,1]=>[7,4,2,5,3,6,1]=>111100=>000011
[6,5,4,7,3,1,2]=>[7,4,3,5,1,6,2]=>111100=>000011
[6,5,4,7,3,2,1]=>[7,4,3,5,2,6,1]=>111100=>000011
[6,5,7,1,2,3,4]=>[7,1,5,2,6,3,4]=>111000=>000111
[6,5,7,1,2,4,3]=>[7,1,5,2,4,6,3]=>111000=>000111
[6,5,7,1,3,2,4]=>[7,1,5,3,6,2,4]=>111000=>000111
[6,5,7,1,3,4,2]=>[7,1,5,3,4,6,2]=>111000=>000111
[6,5,7,1,4,2,3]=>[7,1,4,5,2,6,3]=>111000=>000111
[6,5,7,1,4,3,2]=>[7,1,4,5,3,6,2]=>111000=>000111
[6,5,7,2,1,3,4]=>[7,2,5,1,6,3,4]=>111000=>000111
[6,5,7,2,1,4,3]=>[7,2,5,1,4,6,3]=>111000=>000111
[6,5,7,2,3,1,4]=>[7,2,5,3,6,1,4]=>111000=>000111
[6,5,7,2,3,4,1]=>[7,2,5,3,4,6,1]=>111000=>000111
[6,5,7,2,4,1,3]=>[7,2,4,5,1,6,3]=>111000=>000111
[6,5,7,2,4,3,1]=>[7,2,4,5,3,6,1]=>111000=>000111
[6,5,7,3,1,2,4]=>[7,3,5,1,6,2,4]=>111000=>000111
[6,5,7,3,1,4,2]=>[7,3,5,1,4,6,2]=>111000=>000111
[6,5,7,3,2,1,4]=>[7,3,5,2,6,1,4]=>111000=>000111
[6,5,7,3,2,4,1]=>[7,3,5,2,4,6,1]=>111000=>000111
[6,5,7,3,4,1,2]=>[7,3,4,5,1,6,2]=>111000=>000111
[6,5,7,3,4,2,1]=>[7,3,4,5,2,6,1]=>111000=>000111
[6,5,7,4,1,2,3]=>[4,7,1,5,2,6,3]=>111000=>000111
[6,5,7,4,1,3,2]=>[4,7,1,5,3,6,2]=>111000=>000111
[6,5,7,4,2,1,3]=>[4,7,2,5,1,6,3]=>111000=>000111
[6,5,7,4,2,3,1]=>[4,7,2,5,3,6,1]=>111000=>000111
[6,5,7,4,3,1,2]=>[4,7,3,5,1,6,2]=>111000=>000111
[6,5,7,4,3,2,1]=>[4,7,3,5,2,6,1]=>111000=>000111
[6,7,1,2,3,4,5]=>[7,1,6,2,3,4,5]=>110000=>001111
[6,7,1,2,3,5,4]=>[7,1,5,6,2,3,4]=>110000=>001111
[6,7,1,2,4,3,5]=>[7,1,4,6,2,3,5]=>110000=>001111
[6,7,1,2,4,5,3]=>[7,1,4,5,6,2,3]=>110000=>001111
[6,7,1,2,5,3,4]=>[5,7,1,6,2,3,4]=>110000=>001111
[6,7,1,2,5,4,3]=>[5,7,1,4,6,2,3]=>110000=>001111
[6,7,1,3,2,4,5]=>[7,1,3,6,2,4,5]=>110000=>001111
[6,7,1,3,2,5,4]=>[7,1,3,5,6,2,4]=>110000=>001111
[6,7,1,3,4,2,5]=>[7,1,3,4,6,2,5]=>110000=>001111
[6,7,1,3,4,5,2]=>[7,1,3,4,5,6,2]=>110000=>001111
[6,7,1,3,5,2,4]=>[5,7,1,3,6,2,4]=>110000=>001111
[6,7,1,3,5,4,2]=>[5,7,1,3,4,6,2]=>110000=>001111
[6,7,1,4,2,3,5]=>[4,7,1,6,2,3,5]=>110000=>001111
[6,7,1,4,2,5,3]=>[4,7,1,5,6,2,3]=>110000=>001111
[6,7,1,4,3,2,5]=>[4,7,1,3,6,2,5]=>110000=>001111
[6,7,1,4,3,5,2]=>[4,7,1,3,5,6,2]=>110000=>001111
[6,7,1,4,5,2,3]=>[4,5,7,1,6,2,3]=>110000=>001111
[6,7,1,4,5,3,2]=>[4,5,7,1,3,6,2]=>110000=>001111
[6,7,1,5,2,3,4]=>[5,1,7,2,3,6,4]=>110100=>001011
[6,7,1,5,2,4,3]=>[5,1,7,4,6,2,3]=>110100=>001011
[6,7,1,5,3,2,4]=>[5,1,3,7,2,6,4]=>110100=>001011
[6,7,1,5,3,4,2]=>[5,1,3,7,4,6,2]=>110100=>001011
[6,7,1,5,4,2,3]=>[5,4,7,1,6,2,3]=>110100=>001011
[6,7,1,5,4,3,2]=>[5,4,7,1,3,6,2]=>110100=>001011
[6,7,2,1,3,4,5]=>[7,2,6,1,3,4,5]=>110000=>001111
[6,7,2,1,3,5,4]=>[7,2,5,6,1,3,4]=>110000=>001111
[6,7,2,1,4,3,5]=>[7,2,4,6,1,3,5]=>110000=>001111
[6,7,2,1,4,5,3]=>[7,2,4,5,6,1,3]=>110000=>001111
[6,7,2,1,5,3,4]=>[5,7,2,6,1,3,4]=>110000=>001111
[6,7,2,1,5,4,3]=>[5,7,2,4,6,1,3]=>110000=>001111
[6,7,2,3,1,4,5]=>[7,2,3,6,1,4,5]=>110000=>001111
[6,7,2,3,1,5,4]=>[7,2,3,5,6,1,4]=>110000=>001111
[6,7,2,3,4,1,5]=>[7,2,3,4,6,1,5]=>110000=>001111
[6,7,2,3,4,5,1]=>[7,2,3,4,5,6,1]=>110000=>001111
[6,7,2,3,5,1,4]=>[5,7,2,3,6,1,4]=>110000=>001111
[6,7,2,3,5,4,1]=>[5,7,2,3,4,6,1]=>110000=>001111
[6,7,2,4,1,3,5]=>[4,7,2,6,1,3,5]=>110000=>001111
[6,7,2,4,1,5,3]=>[4,7,2,5,6,1,3]=>110000=>001111
[6,7,2,4,3,1,5]=>[4,7,2,3,6,1,5]=>110000=>001111
[6,7,2,4,3,5,1]=>[4,7,2,3,5,6,1]=>110000=>001111
[6,7,2,4,5,1,3]=>[4,5,7,2,6,1,3]=>110000=>001111
[6,7,2,4,5,3,1]=>[4,5,7,2,3,6,1]=>110000=>001111
[6,7,2,5,1,3,4]=>[5,2,7,1,3,6,4]=>110100=>001011
[6,7,2,5,1,4,3]=>[5,2,7,4,6,1,3]=>110100=>001011
[6,7,2,5,3,1,4]=>[5,2,3,7,1,6,4]=>110100=>001011
[6,7,2,5,3,4,1]=>[5,2,3,7,4,6,1]=>110100=>001011
[6,7,2,5,4,1,3]=>[5,4,7,2,6,1,3]=>110100=>001011
[6,7,2,5,4,3,1]=>[5,4,7,2,3,6,1]=>110100=>001011
[6,7,3,1,2,4,5]=>[3,7,1,6,2,4,5]=>110000=>001111
[6,7,3,1,2,5,4]=>[3,7,1,5,6,2,4]=>110000=>001111
[6,7,3,1,4,2,5]=>[3,7,1,4,6,2,5]=>110000=>001111
[6,7,3,1,4,5,2]=>[3,7,1,4,5,6,2]=>110000=>001111
[6,7,3,1,5,2,4]=>[3,5,7,1,6,2,4]=>110000=>001111
[6,7,3,1,5,4,2]=>[3,5,7,1,4,6,2]=>110000=>001111
[6,7,3,2,1,4,5]=>[3,7,2,6,1,4,5]=>110000=>001111
[6,7,3,2,1,5,4]=>[3,7,2,5,6,1,4]=>110000=>001111
[6,7,3,2,4,1,5]=>[3,7,2,4,6,1,5]=>110000=>001111
[6,7,3,2,4,5,1]=>[3,7,2,4,5,6,1]=>110000=>001111
[6,7,3,2,5,1,4]=>[3,5,7,2,6,1,4]=>110000=>001111
[6,7,3,2,5,4,1]=>[3,5,7,2,4,6,1]=>110000=>001111
[6,7,3,4,1,2,5]=>[3,4,7,1,6,2,5]=>110000=>001111
[6,7,3,4,1,5,2]=>[3,4,7,1,5,6,2]=>110000=>001111
[6,7,3,4,2,1,5]=>[3,4,7,2,6,1,5]=>110000=>001111
[6,7,3,4,2,5,1]=>[3,4,7,2,5,6,1]=>110000=>001111
[6,7,3,4,5,1,2]=>[3,4,5,7,1,6,2]=>110000=>001111
[6,7,3,4,5,2,1]=>[3,4,5,7,2,6,1]=>110000=>001111
[6,7,3,5,1,2,4]=>[3,5,1,7,2,6,4]=>110100=>001011
[6,7,3,5,1,4,2]=>[3,5,1,7,4,6,2]=>110100=>001011
[6,7,3,5,2,1,4]=>[3,5,2,7,1,6,4]=>110100=>001011
[6,7,3,5,2,4,1]=>[3,5,2,7,4,6,1]=>110100=>001011
[6,7,3,5,4,1,2]=>[3,5,4,7,1,6,2]=>110100=>001011
[6,7,3,5,4,2,1]=>[3,5,4,7,2,6,1]=>110100=>001011
[6,7,4,1,2,3,5]=>[4,1,7,2,6,3,5]=>111000=>000111
[6,7,4,1,2,5,3]=>[4,1,7,2,5,6,3]=>111000=>000111
[6,7,4,1,3,2,5]=>[4,1,7,3,6,2,5]=>111000=>000111
[6,7,4,1,3,5,2]=>[4,1,7,3,5,6,2]=>111000=>000111
[6,7,4,1,5,2,3]=>[4,1,5,7,2,6,3]=>111000=>000111
[6,7,4,1,5,3,2]=>[4,1,5,7,3,6,2]=>111000=>000111
[6,7,4,2,1,3,5]=>[4,2,7,1,6,3,5]=>111000=>000111
[6,7,4,2,1,5,3]=>[4,2,7,1,5,6,3]=>111000=>000111
[6,7,4,2,3,1,5]=>[4,2,7,3,6,1,5]=>111000=>000111
[6,7,4,2,3,5,1]=>[4,2,7,3,5,6,1]=>111000=>000111
[6,7,4,2,5,1,3]=>[4,2,5,7,1,6,3]=>111000=>000111
[6,7,4,2,5,3,1]=>[4,2,5,7,3,6,1]=>111000=>000111
[6,7,4,3,1,2,5]=>[4,3,7,1,6,2,5]=>111000=>000111
[6,7,4,3,1,5,2]=>[4,3,7,1,5,6,2]=>111000=>000111
[6,7,4,3,2,1,5]=>[4,3,7,2,6,1,5]=>111000=>000111
[6,7,4,3,2,5,1]=>[4,3,7,2,5,6,1]=>111000=>000111
[6,7,4,3,5,1,2]=>[4,3,5,7,1,6,2]=>111000=>000111
[6,7,4,3,5,2,1]=>[4,3,5,7,2,6,1]=>111000=>000111
[6,7,4,5,1,2,3]=>[5,4,1,7,2,6,3]=>111100=>000011
[6,7,4,5,1,3,2]=>[5,4,1,7,3,6,2]=>111100=>000011
[6,7,4,5,2,1,3]=>[5,4,2,7,1,6,3]=>111100=>000011
[6,7,4,5,2,3,1]=>[5,4,2,7,3,6,1]=>111100=>000011
[6,7,4,5,3,1,2]=>[5,4,3,7,1,6,2]=>111100=>000011
[6,7,4,5,3,2,1]=>[5,4,3,7,2,6,1]=>111100=>000011
[6,7,5,1,2,3,4]=>[5,1,7,2,6,3,4]=>111000=>000111
[6,7,5,1,2,4,3]=>[5,1,7,2,4,6,3]=>111000=>000111
[6,7,5,1,3,2,4]=>[5,1,7,3,6,2,4]=>111000=>000111
[6,7,5,1,3,4,2]=>[5,1,7,3,4,6,2]=>111000=>000111
[6,7,5,1,4,2,3]=>[5,1,4,7,2,6,3]=>111000=>000111
[6,7,5,1,4,3,2]=>[5,1,4,7,3,6,2]=>111000=>000111
[6,7,5,2,1,3,4]=>[5,2,7,1,6,3,4]=>111000=>000111
[6,7,5,2,1,4,3]=>[5,2,7,1,4,6,3]=>111000=>000111
[6,7,5,2,3,1,4]=>[5,2,7,3,6,1,4]=>111000=>000111
[6,7,5,2,3,4,1]=>[5,2,7,3,4,6,1]=>111000=>000111
[6,7,5,2,4,1,3]=>[5,2,4,7,1,6,3]=>111000=>000111
[6,7,5,2,4,3,1]=>[5,2,4,7,3,6,1]=>111000=>000111
[6,7,5,3,1,2,4]=>[5,3,7,1,6,2,4]=>111000=>000111
[6,7,5,3,1,4,2]=>[5,3,7,1,4,6,2]=>111000=>000111
[6,7,5,3,2,1,4]=>[5,3,7,2,6,1,4]=>111000=>000111
[6,7,5,3,2,4,1]=>[5,3,7,2,4,6,1]=>111000=>000111
[6,7,5,3,4,1,2]=>[5,3,4,7,1,6,2]=>111000=>000111
[6,7,5,3,4,2,1]=>[5,3,4,7,2,6,1]=>111000=>000111
[6,7,5,4,1,2,3]=>[4,5,1,7,2,6,3]=>111000=>000111
[6,7,5,4,1,3,2]=>[4,5,1,7,3,6,2]=>111000=>000111
[6,7,5,4,2,1,3]=>[4,5,2,7,1,6,3]=>111000=>000111
[6,7,5,4,2,3,1]=>[4,5,2,7,3,6,1]=>111000=>000111
[6,7,5,4,3,1,2]=>[4,5,3,7,1,6,2]=>111000=>000111
[6,7,5,4,3,2,1]=>[4,5,3,7,2,6,1]=>111000=>000111
[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>100000=>011111
[7,1,2,3,4,6,5]=>[6,7,1,2,3,4,5]=>100000=>011111
[7,1,2,3,5,4,6]=>[5,7,1,2,3,4,6]=>100000=>011111
[7,1,2,3,5,6,4]=>[5,6,7,1,2,3,4]=>100000=>011111
[7,1,2,3,6,4,5]=>[6,1,2,3,4,7,5]=>100010=>011101
[7,1,2,3,6,5,4]=>[6,5,7,1,2,3,4]=>100010=>011101
[7,1,2,4,3,5,6]=>[4,7,1,2,3,5,6]=>100000=>011111
[7,1,2,4,3,6,5]=>[4,6,7,1,2,3,5]=>100000=>011111
[7,1,2,4,5,3,6]=>[4,5,7,1,2,3,6]=>100000=>011111
[7,1,2,4,5,6,3]=>[4,5,6,7,1,2,3]=>100000=>011111
[7,1,2,4,6,3,5]=>[4,6,1,2,3,7,5]=>100010=>011101
[7,1,2,4,6,5,3]=>[4,6,5,7,1,2,3]=>100010=>011101
[7,1,2,5,3,4,6]=>[5,1,2,3,7,4,6]=>100100=>011011
[7,1,2,5,3,6,4]=>[5,1,2,3,6,7,4]=>100100=>011011
[7,1,2,5,4,3,6]=>[5,4,7,1,2,3,6]=>100100=>011011
[7,1,2,5,4,6,3]=>[5,4,6,7,1,2,3]=>100100=>011011
[7,1,2,5,6,3,4]=>[6,5,1,2,3,7,4]=>100110=>011001
[7,1,2,5,6,4,3]=>[6,5,4,7,1,2,3]=>100110=>011001
[7,1,2,6,3,4,5]=>[6,1,2,3,7,4,5]=>100100=>011011
[7,1,2,6,3,5,4]=>[6,1,2,3,5,7,4]=>100100=>011011
[7,1,2,6,4,3,5]=>[6,4,7,1,2,3,5]=>100100=>011011
[7,1,2,6,4,5,3]=>[6,4,5,7,1,2,3]=>100100=>011011
[7,1,2,6,5,3,4]=>[5,6,1,2,3,7,4]=>100100=>011011
[7,1,2,6,5,4,3]=>[5,6,4,7,1,2,3]=>100100=>011011
[7,1,3,2,4,5,6]=>[3,7,1,2,4,5,6]=>100000=>011111
[7,1,3,2,4,6,5]=>[3,6,7,1,2,4,5]=>100000=>011111
[7,1,3,2,5,4,6]=>[3,5,7,1,2,4,6]=>100000=>011111
[7,1,3,2,5,6,4]=>[3,5,6,7,1,2,4]=>100000=>011111
[7,1,3,2,6,4,5]=>[3,6,1,2,4,7,5]=>100010=>011101
[7,1,3,2,6,5,4]=>[3,6,5,7,1,2,4]=>100010=>011101
[7,1,3,4,2,5,6]=>[3,4,7,1,2,5,6]=>100000=>011111
[7,1,3,4,2,6,5]=>[3,4,6,7,1,2,5]=>100000=>011111
[7,1,3,4,5,2,6]=>[3,4,5,7,1,2,6]=>100000=>011111
[7,1,3,4,5,6,2]=>[3,4,5,6,7,1,2]=>100000=>011111
[7,1,3,4,6,2,5]=>[3,4,6,1,2,7,5]=>100010=>011101
[7,1,3,4,6,5,2]=>[3,4,6,5,7,1,2]=>100010=>011101
[7,1,3,5,2,4,6]=>[3,5,1,2,7,4,6]=>100100=>011011
[7,1,3,5,2,6,4]=>[3,5,1,2,6,7,4]=>100100=>011011
[7,1,3,5,4,2,6]=>[3,5,4,7,1,2,6]=>100100=>011011
[7,1,3,5,4,6,2]=>[3,5,4,6,7,1,2]=>100100=>011011
[7,1,3,5,6,2,4]=>[3,6,5,1,2,7,4]=>100110=>011001
[7,1,3,5,6,4,2]=>[3,6,5,4,7,1,2]=>100110=>011001
[7,1,3,6,2,4,5]=>[3,6,1,2,7,4,5]=>100100=>011011
[7,1,3,6,2,5,4]=>[3,6,1,2,5,7,4]=>100100=>011011
[7,1,3,6,4,2,5]=>[3,6,4,7,1,2,5]=>100100=>011011
[7,1,3,6,4,5,2]=>[3,6,4,5,7,1,2]=>100100=>011011
[7,1,3,6,5,2,4]=>[3,5,6,1,2,7,4]=>100100=>011011
[7,1,3,6,5,4,2]=>[3,5,6,4,7,1,2]=>100100=>011011
[7,1,4,2,3,5,6]=>[4,1,2,7,3,5,6]=>101000=>010111
[7,1,4,2,3,6,5]=>[4,1,2,6,7,3,5]=>101000=>010111
[7,1,4,2,5,3,6]=>[4,1,2,5,7,3,6]=>101000=>010111
[7,1,4,2,5,6,3]=>[4,1,2,5,6,7,3]=>101000=>010111
[7,1,4,2,6,3,5]=>[4,1,2,6,3,7,5]=>101010=>010101
[7,1,4,2,6,5,3]=>[4,1,2,6,5,7,3]=>101010=>010101
[7,1,4,3,2,5,6]=>[4,3,7,1,2,5,6]=>101000=>010111
[7,1,4,3,2,6,5]=>[4,3,6,7,1,2,5]=>101000=>010111
[7,1,4,3,5,2,6]=>[4,3,5,7,1,2,6]=>101000=>010111
[7,1,4,3,5,6,2]=>[4,3,5,6,7,1,2]=>101000=>010111
[7,1,4,3,6,2,5]=>[4,3,6,1,2,7,5]=>101010=>010101
[7,1,4,3,6,5,2]=>[4,3,6,5,7,1,2]=>101010=>010101
[7,1,4,5,2,3,6]=>[5,4,1,2,7,3,6]=>101100=>010011
[7,1,4,5,2,6,3]=>[5,4,1,2,6,7,3]=>101100=>010011
[7,1,4,5,3,2,6]=>[5,4,3,7,1,2,6]=>101100=>010011
[7,1,4,5,3,6,2]=>[5,4,3,6,7,1,2]=>101100=>010011
[7,1,4,5,6,2,3]=>[6,5,4,1,2,7,3]=>101110=>010001
[7,1,4,5,6,3,2]=>[6,5,4,3,7,1,2]=>101110=>010001
[7,1,4,6,2,3,5]=>[6,4,1,2,7,3,5]=>101100=>010011
[7,1,4,6,2,5,3]=>[6,4,1,2,5,7,3]=>101100=>010011
[7,1,4,6,3,2,5]=>[6,4,3,7,1,2,5]=>101100=>010011
[7,1,4,6,3,5,2]=>[6,4,3,5,7,1,2]=>101100=>010011
[7,1,4,6,5,2,3]=>[5,6,4,1,2,7,3]=>101100=>010011
[7,1,4,6,5,3,2]=>[5,6,4,3,7,1,2]=>101100=>010011
[7,1,5,2,3,4,6]=>[5,1,2,7,3,4,6]=>101000=>010111
[7,1,5,2,3,6,4]=>[5,1,2,6,7,3,4]=>101000=>010111
[7,1,5,2,4,3,6]=>[5,1,2,4,7,3,6]=>101000=>010111
[7,1,5,2,4,6,3]=>[5,1,2,4,6,7,3]=>101000=>010111
[7,1,5,2,6,3,4]=>[6,5,1,2,7,3,4]=>101010=>010101
[7,1,5,2,6,4,3]=>[6,5,1,2,4,7,3]=>101010=>010101
[7,1,5,3,2,4,6]=>[5,3,7,1,2,4,6]=>101000=>010111
[7,1,5,3,2,6,4]=>[5,3,6,7,1,2,4]=>101000=>010111
[7,1,5,3,4,2,6]=>[5,3,4,7,1,2,6]=>101000=>010111
[7,1,5,3,4,6,2]=>[5,3,4,6,7,1,2]=>101000=>010111
[7,1,5,3,6,2,4]=>[6,5,3,7,1,2,4]=>101010=>010101
[7,1,5,3,6,4,2]=>[6,5,3,4,7,1,2]=>101010=>010101
[7,1,5,4,2,3,6]=>[4,5,1,2,7,3,6]=>101000=>010111
[7,1,5,4,2,6,3]=>[4,5,1,2,6,7,3]=>101000=>010111
[7,1,5,4,3,2,6]=>[4,5,3,7,1,2,6]=>101000=>010111
[7,1,5,4,3,6,2]=>[4,5,3,6,7,1,2]=>101000=>010111
[7,1,5,4,6,2,3]=>[4,6,5,1,2,7,3]=>101010=>010101
[7,1,5,4,6,3,2]=>[4,6,5,3,7,1,2]=>101010=>010101
[7,1,5,6,2,3,4]=>[6,1,2,5,3,7,4]=>101100=>010011
[7,1,5,6,2,4,3]=>[6,1,2,5,4,7,3]=>101100=>010011
[7,1,5,6,3,2,4]=>[6,3,5,1,2,7,4]=>101100=>010011
[7,1,5,6,3,4,2]=>[6,3,5,4,7,1,2]=>101100=>010011
[7,1,5,6,4,2,3]=>[6,4,5,1,2,7,3]=>101100=>010011
[7,1,5,6,4,3,2]=>[6,4,5,3,7,1,2]=>101100=>010011
[7,1,6,2,3,4,5]=>[6,1,2,7,3,4,5]=>101000=>010111
[7,1,6,2,3,5,4]=>[6,1,2,5,7,3,4]=>101000=>010111
[7,1,6,2,4,3,5]=>[6,1,2,4,7,3,5]=>101000=>010111
[7,1,6,2,4,5,3]=>[6,1,2,4,5,7,3]=>101000=>010111
[7,1,6,2,5,3,4]=>[5,6,1,2,7,3,4]=>101000=>010111
[7,1,6,2,5,4,3]=>[5,6,1,2,4,7,3]=>101000=>010111
[7,1,6,3,2,4,5]=>[6,3,7,1,2,4,5]=>101000=>010111
[7,1,6,3,2,5,4]=>[6,3,5,7,1,2,4]=>101000=>010111
[7,1,6,3,4,2,5]=>[6,3,4,7,1,2,5]=>101000=>010111
[7,1,6,3,4,5,2]=>[6,3,4,5,7,1,2]=>101000=>010111
[7,1,6,3,5,2,4]=>[5,6,3,7,1,2,4]=>101000=>010111
[7,1,6,3,5,4,2]=>[5,6,3,4,7,1,2]=>101000=>010111
[7,1,6,4,2,3,5]=>[4,6,1,2,7,3,5]=>101000=>010111
[7,1,6,4,2,5,3]=>[4,6,1,2,5,7,3]=>101000=>010111
[7,1,6,4,3,2,5]=>[4,6,3,7,1,2,5]=>101000=>010111
[7,1,6,4,3,5,2]=>[4,6,3,5,7,1,2]=>101000=>010111
[7,1,6,4,5,2,3]=>[4,5,6,1,2,7,3]=>101000=>010111
[7,1,6,4,5,3,2]=>[4,5,6,3,7,1,2]=>101000=>010111
[7,1,6,5,2,3,4]=>[5,1,2,6,3,7,4]=>101100=>010011
[7,1,6,5,2,4,3]=>[5,1,2,6,4,7,3]=>101100=>010011
[7,1,6,5,3,2,4]=>[5,3,6,1,2,7,4]=>101100=>010011
[7,1,6,5,3,4,2]=>[5,3,6,4,7,1,2]=>101100=>010011
[7,1,6,5,4,2,3]=>[5,4,6,1,2,7,3]=>101100=>010011
[7,1,6,5,4,3,2]=>[5,4,6,3,7,1,2]=>101100=>010011
[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>100000=>011111
[7,2,1,3,4,6,5]=>[2,6,7,1,3,4,5]=>100000=>011111
[7,2,1,3,5,4,6]=>[2,5,7,1,3,4,6]=>100000=>011111
[7,2,1,3,5,6,4]=>[2,5,6,7,1,3,4]=>100000=>011111
[7,2,1,3,6,4,5]=>[2,6,1,3,4,7,5]=>100010=>011101
[7,2,1,3,6,5,4]=>[2,6,5,7,1,3,4]=>100010=>011101
[7,2,1,4,3,5,6]=>[2,4,7,1,3,5,6]=>100000=>011111
[7,2,1,4,3,6,5]=>[2,4,6,7,1,3,5]=>100000=>011111
[7,2,1,4,5,3,6]=>[2,4,5,7,1,3,6]=>100000=>011111
[7,2,1,4,5,6,3]=>[2,4,5,6,7,1,3]=>100000=>011111
[7,2,1,4,6,3,5]=>[2,4,6,1,3,7,5]=>100010=>011101
[7,2,1,4,6,5,3]=>[2,4,6,5,7,1,3]=>100010=>011101
[7,2,1,5,3,4,6]=>[2,5,1,3,7,4,6]=>100100=>011011
[7,2,1,5,3,6,4]=>[2,5,1,3,6,7,4]=>100100=>011011
[7,2,1,5,4,3,6]=>[2,5,4,7,1,3,6]=>100100=>011011
[7,2,1,5,4,6,3]=>[2,5,4,6,7,1,3]=>100100=>011011
[7,2,1,5,6,3,4]=>[2,6,5,1,3,7,4]=>100110=>011001
[7,2,1,5,6,4,3]=>[2,6,5,4,7,1,3]=>100110=>011001
[7,2,1,6,3,4,5]=>[2,6,1,3,7,4,5]=>100100=>011011
[7,2,1,6,3,5,4]=>[2,6,1,3,5,7,4]=>100100=>011011
[7,2,1,6,4,3,5]=>[2,6,4,7,1,3,5]=>100100=>011011
[7,2,1,6,4,5,3]=>[2,6,4,5,7,1,3]=>100100=>011011
[7,2,1,6,5,3,4]=>[2,5,6,1,3,7,4]=>100100=>011011
[7,2,1,6,5,4,3]=>[2,5,6,4,7,1,3]=>100100=>011011
[7,2,3,1,4,5,6]=>[2,3,7,1,4,5,6]=>100000=>011111
[7,2,3,1,4,6,5]=>[2,3,6,7,1,4,5]=>100000=>011111
[7,2,3,1,5,4,6]=>[2,3,5,7,1,4,6]=>100000=>011111
[7,2,3,1,5,6,4]=>[2,3,5,6,7,1,4]=>100000=>011111
[7,2,3,1,6,4,5]=>[2,3,6,1,4,7,5]=>100010=>011101
[7,2,3,1,6,5,4]=>[2,3,6,5,7,1,4]=>100010=>011101
[7,2,3,4,1,5,6]=>[2,3,4,7,1,5,6]=>100000=>011111
[7,2,3,4,1,6,5]=>[2,3,4,6,7,1,5]=>100000=>011111
[7,2,3,4,5,1,6]=>[2,3,4,5,7,1,6]=>100000=>011111
[7,2,3,4,5,6,1]=>[2,3,4,5,6,7,1]=>100000=>011111
[7,2,3,4,6,1,5]=>[2,3,4,6,1,7,5]=>100010=>011101
[7,2,3,4,6,5,1]=>[2,3,4,6,5,7,1]=>100010=>011101
[7,2,3,5,1,4,6]=>[2,3,5,1,7,4,6]=>100100=>011011
[7,2,3,5,1,6,4]=>[2,3,5,1,6,7,4]=>100100=>011011
[7,2,3,5,4,1,6]=>[2,3,5,4,7,1,6]=>100100=>011011
[7,2,3,5,4,6,1]=>[2,3,5,4,6,7,1]=>100100=>011011
[7,2,3,5,6,1,4]=>[2,3,6,5,1,7,4]=>100110=>011001
[7,2,3,5,6,4,1]=>[2,3,6,5,4,7,1]=>100110=>011001
[7,2,3,6,1,4,5]=>[2,3,6,1,7,4,5]=>100100=>011011
[7,2,3,6,1,5,4]=>[2,3,6,1,5,7,4]=>100100=>011011
[7,2,3,6,4,1,5]=>[2,3,6,4,7,1,5]=>100100=>011011
[7,2,3,6,4,5,1]=>[2,3,6,4,5,7,1]=>100100=>011011
[7,2,3,6,5,1,4]=>[2,3,5,6,1,7,4]=>100100=>011011
[7,2,3,6,5,4,1]=>[2,3,5,6,4,7,1]=>100100=>011011
[7,2,4,1,3,5,6]=>[2,4,1,7,3,5,6]=>101000=>010111
[7,2,4,1,3,6,5]=>[2,4,1,6,7,3,5]=>101000=>010111
[7,2,4,1,5,3,6]=>[2,4,1,5,7,3,6]=>101000=>010111
[7,2,4,1,5,6,3]=>[2,4,1,5,6,7,3]=>101000=>010111
[7,2,4,1,6,3,5]=>[2,4,1,6,3,7,5]=>101010=>010101
[7,2,4,1,6,5,3]=>[2,4,1,6,5,7,3]=>101010=>010101
[7,2,4,3,1,5,6]=>[2,4,3,7,1,5,6]=>101000=>010111
[7,2,4,3,1,6,5]=>[2,4,3,6,7,1,5]=>101000=>010111
[7,2,4,3,5,1,6]=>[2,4,3,5,7,1,6]=>101000=>010111
[7,2,4,3,5,6,1]=>[2,4,3,5,6,7,1]=>101000=>010111
[7,2,4,3,6,1,5]=>[2,4,3,6,1,7,5]=>101010=>010101
[7,2,4,3,6,5,1]=>[2,4,3,6,5,7,1]=>101010=>010101
[7,2,4,5,1,3,6]=>[2,5,4,1,7,3,6]=>101100=>010011
[7,2,4,5,1,6,3]=>[2,5,4,1,6,7,3]=>101100=>010011
[7,2,4,5,3,1,6]=>[2,5,4,3,7,1,6]=>101100=>010011
[7,2,4,5,3,6,1]=>[2,5,4,3,6,7,1]=>101100=>010011
[7,2,4,5,6,1,3]=>[2,6,5,4,1,7,3]=>101110=>010001
[7,2,4,5,6,3,1]=>[2,6,5,4,3,7,1]=>101110=>010001
[7,2,4,6,1,3,5]=>[2,6,4,1,7,3,5]=>101100=>010011
[7,2,4,6,1,5,3]=>[2,6,4,1,5,7,3]=>101100=>010011
[7,2,4,6,3,1,5]=>[2,6,4,3,7,1,5]=>101100=>010011
[7,2,4,6,3,5,1]=>[2,6,4,3,5,7,1]=>101100=>010011
[7,2,4,6,5,1,3]=>[2,5,6,4,1,7,3]=>101100=>010011
[7,2,4,6,5,3,1]=>[2,5,6,4,3,7,1]=>101100=>010011
[7,2,5,1,3,4,6]=>[2,5,1,7,3,4,6]=>101000=>010111
[7,2,5,1,3,6,4]=>[2,5,1,6,7,3,4]=>101000=>010111
[7,2,5,1,4,3,6]=>[2,5,1,4,7,3,6]=>101000=>010111
[7,2,5,1,4,6,3]=>[2,5,1,4,6,7,3]=>101000=>010111
[7,2,5,1,6,3,4]=>[2,6,5,1,7,3,4]=>101010=>010101
[7,2,5,1,6,4,3]=>[2,6,5,1,4,7,3]=>101010=>010101
[7,2,5,3,1,4,6]=>[2,5,3,7,1,4,6]=>101000=>010111
[7,2,5,3,1,6,4]=>[2,5,3,6,7,1,4]=>101000=>010111
[7,2,5,3,4,1,6]=>[2,5,3,4,7,1,6]=>101000=>010111
[7,2,5,3,4,6,1]=>[2,5,3,4,6,7,1]=>101000=>010111
[7,2,5,3,6,1,4]=>[2,6,5,3,7,1,4]=>101010=>010101
[7,2,5,3,6,4,1]=>[2,6,5,3,4,7,1]=>101010=>010101
[7,2,5,4,1,3,6]=>[2,4,5,1,7,3,6]=>101000=>010111
[7,2,5,4,1,6,3]=>[2,4,5,1,6,7,3]=>101000=>010111
[7,2,5,4,3,1,6]=>[2,4,5,3,7,1,6]=>101000=>010111
[7,2,5,4,3,6,1]=>[2,4,5,3,6,7,1]=>101000=>010111
[7,2,5,4,6,1,3]=>[2,4,6,5,1,7,3]=>101010=>010101
[7,2,5,4,6,3,1]=>[2,4,6,5,3,7,1]=>101010=>010101
[7,2,5,6,1,3,4]=>[2,6,1,5,3,7,4]=>101100=>010011
[7,2,5,6,1,4,3]=>[2,6,1,5,4,7,3]=>101100=>010011
[7,2,5,6,3,1,4]=>[2,6,3,5,1,7,4]=>101100=>010011
[7,2,5,6,3,4,1]=>[2,6,3,5,4,7,1]=>101100=>010011
[7,2,5,6,4,1,3]=>[2,6,4,5,1,7,3]=>101100=>010011
[7,2,5,6,4,3,1]=>[2,6,4,5,3,7,1]=>101100=>010011
[7,2,6,1,3,4,5]=>[2,6,1,7,3,4,5]=>101000=>010111
[7,2,6,1,3,5,4]=>[2,6,1,5,7,3,4]=>101000=>010111
[7,2,6,1,4,3,5]=>[2,6,1,4,7,3,5]=>101000=>010111
[7,2,6,1,4,5,3]=>[2,6,1,4,5,7,3]=>101000=>010111
[7,2,6,1,5,3,4]=>[2,5,6,1,7,3,4]=>101000=>010111
[7,2,6,1,5,4,3]=>[2,5,6,1,4,7,3]=>101000=>010111
[7,2,6,3,1,4,5]=>[2,6,3,7,1,4,5]=>101000=>010111
[7,2,6,3,1,5,4]=>[2,6,3,5,7,1,4]=>101000=>010111
[7,2,6,3,4,1,5]=>[2,6,3,4,7,1,5]=>101000=>010111
[7,2,6,3,4,5,1]=>[2,6,3,4,5,7,1]=>101000=>010111
[7,2,6,3,5,1,4]=>[2,5,6,3,7,1,4]=>101000=>010111
[7,2,6,3,5,4,1]=>[2,5,6,3,4,7,1]=>101000=>010111
[7,2,6,4,1,3,5]=>[2,4,6,1,7,3,5]=>101000=>010111
[7,2,6,4,1,5,3]=>[2,4,6,1,5,7,3]=>101000=>010111
[7,2,6,4,3,1,5]=>[2,4,6,3,7,1,5]=>101000=>010111
[7,2,6,4,3,5,1]=>[2,4,6,3,5,7,1]=>101000=>010111
[7,2,6,4,5,1,3]=>[2,4,5,6,1,7,3]=>101000=>010111
[7,2,6,4,5,3,1]=>[2,4,5,6,3,7,1]=>101000=>010111
[7,2,6,5,1,3,4]=>[2,5,1,6,3,7,4]=>101100=>010011
[7,2,6,5,1,4,3]=>[2,5,1,6,4,7,3]=>101100=>010011
[7,2,6,5,3,1,4]=>[2,5,3,6,1,7,4]=>101100=>010011
[7,2,6,5,3,4,1]=>[2,5,3,6,4,7,1]=>101100=>010011
[7,2,6,5,4,1,3]=>[2,5,4,6,1,7,3]=>101100=>010011
[7,2,6,5,4,3,1]=>[2,5,4,6,3,7,1]=>101100=>010011
[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>110000=>001111
[7,3,1,2,4,6,5]=>[3,1,6,7,2,4,5]=>110000=>001111
[7,3,1,2,5,4,6]=>[3,1,5,7,2,4,6]=>110000=>001111
[7,3,1,2,5,6,4]=>[3,1,5,6,7,2,4]=>110000=>001111
[7,3,1,2,6,4,5]=>[3,1,6,2,4,7,5]=>110010=>001101
[7,3,1,2,6,5,4]=>[3,1,6,5,7,2,4]=>110010=>001101
[7,3,1,4,2,5,6]=>[3,1,4,7,2,5,6]=>110000=>001111
[7,3,1,4,2,6,5]=>[3,1,4,6,7,2,5]=>110000=>001111
[7,3,1,4,5,2,6]=>[3,1,4,5,7,2,6]=>110000=>001111
[7,3,1,4,5,6,2]=>[3,1,4,5,6,7,2]=>110000=>001111
[7,3,1,4,6,2,5]=>[3,1,4,6,2,7,5]=>110010=>001101
[7,3,1,4,6,5,2]=>[3,1,4,6,5,7,2]=>110010=>001101
[7,3,1,5,2,4,6]=>[3,1,5,2,7,4,6]=>110100=>001011
[7,3,1,5,2,6,4]=>[3,1,5,2,6,7,4]=>110100=>001011
[7,3,1,5,4,2,6]=>[3,1,5,4,7,2,6]=>110100=>001011
[7,3,1,5,4,6,2]=>[3,1,5,4,6,7,2]=>110100=>001011
[7,3,1,5,6,2,4]=>[3,1,6,5,2,7,4]=>110110=>001001
[7,3,1,5,6,4,2]=>[3,1,6,5,4,7,2]=>110110=>001001
[7,3,1,6,2,4,5]=>[3,1,6,2,7,4,5]=>110100=>001011
[7,3,1,6,2,5,4]=>[3,1,6,2,5,7,4]=>110100=>001011
[7,3,1,6,4,2,5]=>[3,1,6,4,7,2,5]=>110100=>001011
[7,3,1,6,4,5,2]=>[3,1,6,4,5,7,2]=>110100=>001011
[7,3,1,6,5,2,4]=>[3,1,5,6,2,7,4]=>110100=>001011
[7,3,1,6,5,4,2]=>[3,1,5,6,4,7,2]=>110100=>001011
[7,3,2,1,4,5,6]=>[3,2,7,1,4,5,6]=>110000=>001111
[7,3,2,1,4,6,5]=>[3,2,6,7,1,4,5]=>110000=>001111
[7,3,2,1,5,4,6]=>[3,2,5,7,1,4,6]=>110000=>001111
[7,3,2,1,5,6,4]=>[3,2,5,6,7,1,4]=>110000=>001111
[7,3,2,1,6,4,5]=>[3,2,6,1,4,7,5]=>110010=>001101
[7,3,2,1,6,5,4]=>[3,2,6,5,7,1,4]=>110010=>001101
[7,3,2,4,1,5,6]=>[3,2,4,7,1,5,6]=>110000=>001111
[7,3,2,4,1,6,5]=>[3,2,4,6,7,1,5]=>110000=>001111
[7,3,2,4,5,1,6]=>[3,2,4,5,7,1,6]=>110000=>001111
[7,3,2,4,5,6,1]=>[3,2,4,5,6,7,1]=>110000=>001111
[7,3,2,4,6,1,5]=>[3,2,4,6,1,7,5]=>110010=>001101
[7,3,2,4,6,5,1]=>[3,2,4,6,5,7,1]=>110010=>001101
[7,3,2,5,1,4,6]=>[3,2,5,1,7,4,6]=>110100=>001011
[7,3,2,5,1,6,4]=>[3,2,5,1,6,7,4]=>110100=>001011
[7,3,2,5,4,1,6]=>[3,2,5,4,7,1,6]=>110100=>001011
[7,3,2,5,4,6,1]=>[3,2,5,4,6,7,1]=>110100=>001011
[7,3,2,5,6,1,4]=>[3,2,6,5,1,7,4]=>110110=>001001
[7,3,2,5,6,4,1]=>[3,2,6,5,4,7,1]=>110110=>001001
[7,3,2,6,1,4,5]=>[3,2,6,1,7,4,5]=>110100=>001011
[7,3,2,6,1,5,4]=>[3,2,6,1,5,7,4]=>110100=>001011
[7,3,2,6,4,1,5]=>[3,2,6,4,7,1,5]=>110100=>001011
[7,3,2,6,4,5,1]=>[3,2,6,4,5,7,1]=>110100=>001011
[7,3,2,6,5,1,4]=>[3,2,5,6,1,7,4]=>110100=>001011
[7,3,2,6,5,4,1]=>[3,2,5,6,4,7,1]=>110100=>001011
[7,3,4,1,2,5,6]=>[4,3,1,7,2,5,6]=>111000=>000111
[7,3,4,1,2,6,5]=>[4,3,1,6,7,2,5]=>111000=>000111
[7,3,4,1,5,2,6]=>[4,3,1,5,7,2,6]=>111000=>000111
[7,3,4,1,5,6,2]=>[4,3,1,5,6,7,2]=>111000=>000111
[7,3,4,1,6,2,5]=>[4,3,1,6,2,7,5]=>111010=>000101
[7,3,4,1,6,5,2]=>[4,3,1,6,5,7,2]=>111010=>000101
[7,3,4,2,1,5,6]=>[4,3,2,7,1,5,6]=>111000=>000111
[7,3,4,2,1,6,5]=>[4,3,2,6,7,1,5]=>111000=>000111
[7,3,4,2,5,1,6]=>[4,3,2,5,7,1,6]=>111000=>000111
[7,3,4,2,5,6,1]=>[4,3,2,5,6,7,1]=>111000=>000111
[7,3,4,2,6,1,5]=>[4,3,2,6,1,7,5]=>111010=>000101
[7,3,4,2,6,5,1]=>[4,3,2,6,5,7,1]=>111010=>000101
[7,3,4,5,1,2,6]=>[5,4,3,1,7,2,6]=>111100=>000011
[7,3,4,5,1,6,2]=>[5,4,3,1,6,7,2]=>111100=>000011
[7,3,4,5,2,1,6]=>[5,4,3,2,7,1,6]=>111100=>000011
[7,3,4,5,2,6,1]=>[5,4,3,2,6,7,1]=>111100=>000011
[7,3,4,5,6,1,2]=>[6,5,4,3,1,7,2]=>111110=>000001
[7,3,4,5,6,2,1]=>[6,5,4,3,2,7,1]=>111110=>000001
[7,3,4,6,1,2,5]=>[6,4,3,1,7,2,5]=>111100=>000011
[7,3,4,6,1,5,2]=>[6,4,3,1,5,7,2]=>111100=>000011
[7,3,4,6,2,1,5]=>[6,4,3,2,7,1,5]=>111100=>000011
[7,3,4,6,2,5,1]=>[6,4,3,2,5,7,1]=>111100=>000011
[7,3,4,6,5,1,2]=>[5,6,4,3,1,7,2]=>111100=>000011
[7,3,4,6,5,2,1]=>[5,6,4,3,2,7,1]=>111100=>000011
[7,3,5,1,2,4,6]=>[5,3,1,7,2,4,6]=>111000=>000111
[7,3,5,1,2,6,4]=>[5,3,1,6,7,2,4]=>111000=>000111
[7,3,5,1,4,2,6]=>[5,3,1,4,7,2,6]=>111000=>000111
[7,3,5,1,4,6,2]=>[5,3,1,4,6,7,2]=>111000=>000111
[7,3,5,1,6,2,4]=>[6,5,3,1,7,2,4]=>111010=>000101
[7,3,5,1,6,4,2]=>[6,5,3,1,4,7,2]=>111010=>000101
[7,3,5,2,1,4,6]=>[5,3,2,7,1,4,6]=>111000=>000111
[7,3,5,2,1,6,4]=>[5,3,2,6,7,1,4]=>111000=>000111
[7,3,5,2,4,1,6]=>[5,3,2,4,7,1,6]=>111000=>000111
[7,3,5,2,4,6,1]=>[5,3,2,4,6,7,1]=>111000=>000111
[7,3,5,2,6,1,4]=>[6,5,3,2,7,1,4]=>111010=>000101
[7,3,5,2,6,4,1]=>[6,5,3,2,4,7,1]=>111010=>000101
[7,3,5,4,1,2,6]=>[4,5,3,1,7,2,6]=>111000=>000111
[7,3,5,4,1,6,2]=>[4,5,3,1,6,7,2]=>111000=>000111
[7,3,5,4,2,1,6]=>[4,5,3,2,7,1,6]=>111000=>000111
[7,3,5,4,2,6,1]=>[4,5,3,2,6,7,1]=>111000=>000111
[7,3,5,4,6,1,2]=>[4,6,5,3,1,7,2]=>111010=>000101
[7,3,5,4,6,2,1]=>[4,6,5,3,2,7,1]=>111010=>000101
[7,3,5,6,1,2,4]=>[6,3,1,5,2,7,4]=>111100=>000011
[7,3,5,6,1,4,2]=>[6,3,1,5,4,7,2]=>111100=>000011
[7,3,5,6,2,1,4]=>[6,3,2,5,1,7,4]=>111100=>000011
[7,3,5,6,2,4,1]=>[6,3,2,5,4,7,1]=>111100=>000011
[7,3,5,6,4,1,2]=>[6,4,5,3,1,7,2]=>111100=>000011
[7,3,5,6,4,2,1]=>[6,4,5,3,2,7,1]=>111100=>000011
[7,3,6,1,2,4,5]=>[6,3,1,7,2,4,5]=>111000=>000111
[7,3,6,1,2,5,4]=>[6,3,1,5,7,2,4]=>111000=>000111
[7,3,6,1,4,2,5]=>[6,3,1,4,7,2,5]=>111000=>000111
[7,3,6,1,4,5,2]=>[6,3,1,4,5,7,2]=>111000=>000111
[7,3,6,1,5,2,4]=>[5,6,3,1,7,2,4]=>111000=>000111
[7,3,6,1,5,4,2]=>[5,6,3,1,4,7,2]=>111000=>000111
[7,3,6,2,1,4,5]=>[6,3,2,7,1,4,5]=>111000=>000111
[7,3,6,2,1,5,4]=>[6,3,2,5,7,1,4]=>111000=>000111
[7,3,6,2,4,1,5]=>[6,3,2,4,7,1,5]=>111000=>000111
[7,3,6,2,4,5,1]=>[6,3,2,4,5,7,1]=>111000=>000111
[7,3,6,2,5,1,4]=>[5,6,3,2,7,1,4]=>111000=>000111
[7,3,6,2,5,4,1]=>[5,6,3,2,4,7,1]=>111000=>000111
[7,3,6,4,1,2,5]=>[4,6,3,1,7,2,5]=>111000=>000111
[7,3,6,4,1,5,2]=>[4,6,3,1,5,7,2]=>111000=>000111
[7,3,6,4,2,1,5]=>[4,6,3,2,7,1,5]=>111000=>000111
[7,3,6,4,2,5,1]=>[4,6,3,2,5,7,1]=>111000=>000111
[7,3,6,4,5,1,2]=>[4,5,6,3,1,7,2]=>111000=>000111
[7,3,6,4,5,2,1]=>[4,5,6,3,2,7,1]=>111000=>000111
[7,3,6,5,1,2,4]=>[5,3,1,6,2,7,4]=>111100=>000011
[7,3,6,5,1,4,2]=>[5,3,1,6,4,7,2]=>111100=>000011
[7,3,6,5,2,1,4]=>[5,3,2,6,1,7,4]=>111100=>000011
[7,3,6,5,2,4,1]=>[5,3,2,6,4,7,1]=>111100=>000011
[7,3,6,5,4,1,2]=>[5,4,6,3,1,7,2]=>111100=>000011
[7,3,6,5,4,2,1]=>[5,4,6,3,2,7,1]=>111100=>000011
[7,4,1,2,3,5,6]=>[4,1,7,2,3,5,6]=>110000=>001111
[7,4,1,2,3,6,5]=>[4,1,6,7,2,3,5]=>110000=>001111
[7,4,1,2,5,3,6]=>[4,1,5,7,2,3,6]=>110000=>001111
[7,4,1,2,5,6,3]=>[4,1,5,6,7,2,3]=>110000=>001111
[7,4,1,2,6,3,5]=>[4,1,6,2,3,7,5]=>110010=>001101
[7,4,1,2,6,5,3]=>[4,1,6,5,7,2,3]=>110010=>001101
[7,4,1,3,2,5,6]=>[4,1,3,7,2,5,6]=>110000=>001111
[7,4,1,3,2,6,5]=>[4,1,3,6,7,2,5]=>110000=>001111
[7,4,1,3,5,2,6]=>[4,1,3,5,7,2,6]=>110000=>001111
[7,4,1,3,5,6,2]=>[4,1,3,5,6,7,2]=>110000=>001111
[7,4,1,3,6,2,5]=>[4,1,3,6,2,7,5]=>110010=>001101
[7,4,1,3,6,5,2]=>[4,1,3,6,5,7,2]=>110010=>001101
[7,4,1,5,2,3,6]=>[5,4,1,7,2,3,6]=>110100=>001011
[7,4,1,5,2,6,3]=>[5,4,1,6,7,2,3]=>110100=>001011
[7,4,1,5,3,2,6]=>[5,4,1,3,7,2,6]=>110100=>001011
[7,4,1,5,3,6,2]=>[5,4,1,3,6,7,2]=>110100=>001011
[7,4,1,5,6,2,3]=>[6,5,4,1,7,2,3]=>110110=>001001
[7,4,1,5,6,3,2]=>[6,5,4,1,3,7,2]=>110110=>001001
[7,4,1,6,2,3,5]=>[6,4,1,7,2,3,5]=>110100=>001011
[7,4,1,6,2,5,3]=>[6,4,1,5,7,2,3]=>110100=>001011
[7,4,1,6,3,2,5]=>[6,4,1,3,7,2,5]=>110100=>001011
[7,4,1,6,3,5,2]=>[6,4,1,3,5,7,2]=>110100=>001011
[7,4,1,6,5,2,3]=>[5,6,4,1,7,2,3]=>110100=>001011
[7,4,1,6,5,3,2]=>[5,6,4,1,3,7,2]=>110100=>001011
[7,4,2,1,3,5,6]=>[4,2,7,1,3,5,6]=>110000=>001111
[7,4,2,1,3,6,5]=>[4,2,6,7,1,3,5]=>110000=>001111
[7,4,2,1,5,3,6]=>[4,2,5,7,1,3,6]=>110000=>001111
[7,4,2,1,5,6,3]=>[4,2,5,6,7,1,3]=>110000=>001111
[7,4,2,1,6,3,5]=>[4,2,6,1,3,7,5]=>110010=>001101
[7,4,2,1,6,5,3]=>[4,2,6,5,7,1,3]=>110010=>001101
[7,4,2,3,1,5,6]=>[4,2,3,7,1,5,6]=>110000=>001111
[7,4,2,3,1,6,5]=>[4,2,3,6,7,1,5]=>110000=>001111
[7,4,2,3,5,1,6]=>[4,2,3,5,7,1,6]=>110000=>001111
[7,4,2,3,5,6,1]=>[4,2,3,5,6,7,1]=>110000=>001111
[7,4,2,3,6,1,5]=>[4,2,3,6,1,7,5]=>110010=>001101
[7,4,2,3,6,5,1]=>[4,2,3,6,5,7,1]=>110010=>001101
[7,4,2,5,1,3,6]=>[5,4,2,7,1,3,6]=>110100=>001011
[7,4,2,5,1,6,3]=>[5,4,2,6,7,1,3]=>110100=>001011
[7,4,2,5,3,1,6]=>[5,4,2,3,7,1,6]=>110100=>001011
[7,4,2,5,3,6,1]=>[5,4,2,3,6,7,1]=>110100=>001011
[7,4,2,5,6,1,3]=>[6,5,4,2,7,1,3]=>110110=>001001
[7,4,2,5,6,3,1]=>[6,5,4,2,3,7,1]=>110110=>001001
[7,4,2,6,1,3,5]=>[6,4,2,7,1,3,5]=>110100=>001011
[7,4,2,6,1,5,3]=>[6,4,2,5,7,1,3]=>110100=>001011
[7,4,2,6,3,1,5]=>[6,4,2,3,7,1,5]=>110100=>001011
[7,4,2,6,3,5,1]=>[6,4,2,3,5,7,1]=>110100=>001011
[7,4,2,6,5,1,3]=>[5,6,4,2,7,1,3]=>110100=>001011
[7,4,2,6,5,3,1]=>[5,6,4,2,3,7,1]=>110100=>001011
[7,4,3,1,2,5,6]=>[3,4,1,7,2,5,6]=>110000=>001111
[7,4,3,1,2,6,5]=>[3,4,1,6,7,2,5]=>110000=>001111
[7,4,3,1,5,2,6]=>[3,4,1,5,7,2,6]=>110000=>001111
[7,4,3,1,5,6,2]=>[3,4,1,5,6,7,2]=>110000=>001111
[7,4,3,1,6,2,5]=>[3,4,1,6,2,7,5]=>110010=>001101
[7,4,3,1,6,5,2]=>[3,4,1,6,5,7,2]=>110010=>001101
[7,4,3,2,1,5,6]=>[3,4,2,7,1,5,6]=>110000=>001111
[7,4,3,2,1,6,5]=>[3,4,2,6,7,1,5]=>110000=>001111
[7,4,3,2,5,1,6]=>[3,4,2,5,7,1,6]=>110000=>001111
[7,4,3,2,5,6,1]=>[3,4,2,5,6,7,1]=>110000=>001111
[7,4,3,2,6,1,5]=>[3,4,2,6,1,7,5]=>110010=>001101
[7,4,3,2,6,5,1]=>[3,4,2,6,5,7,1]=>110010=>001101
[7,4,3,5,1,2,6]=>[3,5,4,1,7,2,6]=>110100=>001011
[7,4,3,5,1,6,2]=>[3,5,4,1,6,7,2]=>110100=>001011
[7,4,3,5,2,1,6]=>[3,5,4,2,7,1,6]=>110100=>001011
[7,4,3,5,2,6,1]=>[3,5,4,2,6,7,1]=>110100=>001011
[7,4,3,5,6,1,2]=>[3,6,5,4,1,7,2]=>110110=>001001
[7,4,3,5,6,2,1]=>[3,6,5,4,2,7,1]=>110110=>001001
[7,4,3,6,1,2,5]=>[3,6,4,1,7,2,5]=>110100=>001011
[7,4,3,6,1,5,2]=>[3,6,4,1,5,7,2]=>110100=>001011
[7,4,3,6,2,1,5]=>[3,6,4,2,7,1,5]=>110100=>001011
[7,4,3,6,2,5,1]=>[3,6,4,2,5,7,1]=>110100=>001011
[7,4,3,6,5,1,2]=>[3,5,6,4,1,7,2]=>110100=>001011
[7,4,3,6,5,2,1]=>[3,5,6,4,2,7,1]=>110100=>001011
[7,4,5,1,2,3,6]=>[5,1,4,2,7,3,6]=>111000=>000111
[7,4,5,1,2,6,3]=>[5,1,4,2,6,7,3]=>111000=>000111
[7,4,5,1,3,2,6]=>[5,1,4,3,7,2,6]=>111000=>000111
[7,4,5,1,3,6,2]=>[5,1,4,3,6,7,2]=>111000=>000111
[7,4,5,1,6,2,3]=>[6,5,1,4,2,7,3]=>111010=>000101
[7,4,5,1,6,3,2]=>[6,5,1,4,3,7,2]=>111010=>000101
[7,4,5,2,1,3,6]=>[5,2,4,1,7,3,6]=>111000=>000111
[7,4,5,2,1,6,3]=>[5,2,4,1,6,7,3]=>111000=>000111
[7,4,5,2,3,1,6]=>[5,2,4,3,7,1,6]=>111000=>000111
[7,4,5,2,3,6,1]=>[5,2,4,3,6,7,1]=>111000=>000111
[7,4,5,2,6,1,3]=>[6,5,2,4,1,7,3]=>111010=>000101
[7,4,5,2,6,3,1]=>[6,5,2,4,3,7,1]=>111010=>000101
[7,4,5,3,1,2,6]=>[5,3,4,1,7,2,6]=>111000=>000111
[7,4,5,3,1,6,2]=>[5,3,4,1,6,7,2]=>111000=>000111
[7,4,5,3,2,1,6]=>[5,3,4,2,7,1,6]=>111000=>000111
[7,4,5,3,2,6,1]=>[5,3,4,2,6,7,1]=>111000=>000111
[7,4,5,3,6,1,2]=>[6,5,3,4,1,7,2]=>111010=>000101
[7,4,5,3,6,2,1]=>[6,5,3,4,2,7,1]=>111010=>000101
[7,4,5,6,1,2,3]=>[6,1,5,4,2,7,3]=>111100=>000011
[7,4,5,6,1,3,2]=>[6,1,5,4,3,7,2]=>111100=>000011
[7,4,5,6,2,1,3]=>[6,2,5,4,1,7,3]=>111100=>000011
[7,4,5,6,2,3,1]=>[6,2,5,4,3,7,1]=>111100=>000011
[7,4,5,6,3,1,2]=>[6,3,5,4,1,7,2]=>111100=>000011
[7,4,5,6,3,2,1]=>[6,3,5,4,2,7,1]=>111100=>000011
[7,4,6,1,2,3,5]=>[6,1,4,2,7,3,5]=>111000=>000111
[7,4,6,1,2,5,3]=>[6,1,4,2,5,7,3]=>111000=>000111
[7,4,6,1,3,2,5]=>[6,1,4,3,7,2,5]=>111000=>000111
[7,4,6,1,3,5,2]=>[6,1,4,3,5,7,2]=>111000=>000111
[7,4,6,1,5,2,3]=>[5,6,1,4,2,7,3]=>111000=>000111
[7,4,6,1,5,3,2]=>[5,6,1,4,3,7,2]=>111000=>000111
[7,4,6,2,1,3,5]=>[6,2,4,1,7,3,5]=>111000=>000111
[7,4,6,2,1,5,3]=>[6,2,4,1,5,7,3]=>111000=>000111
[7,4,6,2,3,1,5]=>[6,2,4,3,7,1,5]=>111000=>000111
[7,4,6,2,3,5,1]=>[6,2,4,3,5,7,1]=>111000=>000111
[7,4,6,2,5,1,3]=>[5,6,2,4,1,7,3]=>111000=>000111
[7,4,6,2,5,3,1]=>[5,6,2,4,3,7,1]=>111000=>000111
[7,4,6,3,1,2,5]=>[6,3,4,1,7,2,5]=>111000=>000111
[7,4,6,3,1,5,2]=>[6,3,4,1,5,7,2]=>111000=>000111
[7,4,6,3,2,1,5]=>[6,3,4,2,7,1,5]=>111000=>000111
[7,4,6,3,2,5,1]=>[6,3,4,2,5,7,1]=>111000=>000111
[7,4,6,3,5,1,2]=>[5,6,3,4,1,7,2]=>111000=>000111
[7,4,6,3,5,2,1]=>[5,6,3,4,2,7,1]=>111000=>000111
[7,4,6,5,1,2,3]=>[5,1,6,4,2,7,3]=>111100=>000011
[7,4,6,5,1,3,2]=>[5,1,6,4,3,7,2]=>111100=>000011
[7,4,6,5,2,1,3]=>[5,2,6,4,1,7,3]=>111100=>000011
[7,4,6,5,2,3,1]=>[5,2,6,4,3,7,1]=>111100=>000011
[7,4,6,5,3,1,2]=>[5,3,6,4,1,7,2]=>111100=>000011
[7,4,6,5,3,2,1]=>[5,3,6,4,2,7,1]=>111100=>000011
[7,5,1,2,3,4,6]=>[5,1,7,2,3,4,6]=>110000=>001111
[7,5,1,2,3,6,4]=>[5,1,6,7,2,3,4]=>110000=>001111
[7,5,1,2,4,3,6]=>[5,1,4,7,2,3,6]=>110000=>001111
[7,5,1,2,4,6,3]=>[5,1,4,6,7,2,3]=>110000=>001111
[7,5,1,2,6,3,4]=>[6,5,1,7,2,3,4]=>110010=>001101
[7,5,1,2,6,4,3]=>[6,5,1,4,7,2,3]=>110010=>001101
[7,5,1,3,2,4,6]=>[5,1,3,7,2,4,6]=>110000=>001111
[7,5,1,3,2,6,4]=>[5,1,3,6,7,2,4]=>110000=>001111
[7,5,1,3,4,2,6]=>[5,1,3,4,7,2,6]=>110000=>001111
[7,5,1,3,4,6,2]=>[5,1,3,4,6,7,2]=>110000=>001111
[7,5,1,3,6,2,4]=>[6,5,1,3,7,2,4]=>110010=>001101
[7,5,1,3,6,4,2]=>[6,5,1,3,4,7,2]=>110010=>001101
[7,5,1,4,2,3,6]=>[4,5,1,7,2,3,6]=>110000=>001111
[7,5,1,4,2,6,3]=>[4,5,1,6,7,2,3]=>110000=>001111
[7,5,1,4,3,2,6]=>[4,5,1,3,7,2,6]=>110000=>001111
[7,5,1,4,3,6,2]=>[4,5,1,3,6,7,2]=>110000=>001111
[7,5,1,4,6,2,3]=>[4,6,5,1,7,2,3]=>110010=>001101
[7,5,1,4,6,3,2]=>[4,6,5,1,3,7,2]=>110010=>001101
[7,5,1,6,2,3,4]=>[6,1,5,2,3,7,4]=>110100=>001011
[7,5,1,6,2,4,3]=>[6,1,5,4,7,2,3]=>110100=>001011
[7,5,1,6,3,2,4]=>[6,1,3,5,2,7,4]=>110100=>001011
[7,5,1,6,3,4,2]=>[6,1,3,5,4,7,2]=>110100=>001011
[7,5,1,6,4,2,3]=>[6,4,5,1,7,2,3]=>110100=>001011
[7,5,1,6,4,3,2]=>[6,4,5,1,3,7,2]=>110100=>001011
[7,5,2,1,3,4,6]=>[5,2,7,1,3,4,6]=>110000=>001111
[7,5,2,1,3,6,4]=>[5,2,6,7,1,3,4]=>110000=>001111
[7,5,2,1,4,3,6]=>[5,2,4,7,1,3,6]=>110000=>001111
[7,5,2,1,4,6,3]=>[5,2,4,6,7,1,3]=>110000=>001111
[7,5,2,1,6,3,4]=>[6,5,2,7,1,3,4]=>110010=>001101
[7,5,2,1,6,4,3]=>[6,5,2,4,7,1,3]=>110010=>001101
[7,5,2,3,1,4,6]=>[5,2,3,7,1,4,6]=>110000=>001111
[7,5,2,3,1,6,4]=>[5,2,3,6,7,1,4]=>110000=>001111
[7,5,2,3,4,1,6]=>[5,2,3,4,7,1,6]=>110000=>001111
[7,5,2,3,4,6,1]=>[5,2,3,4,6,7,1]=>110000=>001111
[7,5,2,3,6,1,4]=>[6,5,2,3,7,1,4]=>110010=>001101
[7,5,2,3,6,4,1]=>[6,5,2,3,4,7,1]=>110010=>001101
[7,5,2,4,1,3,6]=>[4,5,2,7,1,3,6]=>110000=>001111
[7,5,2,4,1,6,3]=>[4,5,2,6,7,1,3]=>110000=>001111
[7,5,2,4,3,1,6]=>[4,5,2,3,7,1,6]=>110000=>001111
[7,5,2,4,3,6,1]=>[4,5,2,3,6,7,1]=>110000=>001111
[7,5,2,4,6,1,3]=>[4,6,5,2,7,1,3]=>110010=>001101
[7,5,2,4,6,3,1]=>[4,6,5,2,3,7,1]=>110010=>001101
[7,5,2,6,1,3,4]=>[6,2,5,1,3,7,4]=>110100=>001011
[7,5,2,6,1,4,3]=>[6,2,5,4,7,1,3]=>110100=>001011
[7,5,2,6,3,1,4]=>[6,2,3,5,1,7,4]=>110100=>001011
[7,5,2,6,3,4,1]=>[6,2,3,5,4,7,1]=>110100=>001011
[7,5,2,6,4,1,3]=>[6,4,5,2,7,1,3]=>110100=>001011
[7,5,2,6,4,3,1]=>[6,4,5,2,3,7,1]=>110100=>001011
[7,5,3,1,2,4,6]=>[3,5,1,7,2,4,6]=>110000=>001111
[7,5,3,1,2,6,4]=>[3,5,1,6,7,2,4]=>110000=>001111
[7,5,3,1,4,2,6]=>[3,5,1,4,7,2,6]=>110000=>001111
[7,5,3,1,4,6,2]=>[3,5,1,4,6,7,2]=>110000=>001111
[7,5,3,1,6,2,4]=>[3,6,5,1,7,2,4]=>110010=>001101
[7,5,3,1,6,4,2]=>[3,6,5,1,4,7,2]=>110010=>001101
[7,5,3,2,1,4,6]=>[3,5,2,7,1,4,6]=>110000=>001111
[7,5,3,2,1,6,4]=>[3,5,2,6,7,1,4]=>110000=>001111
[7,5,3,2,4,1,6]=>[3,5,2,4,7,1,6]=>110000=>001111
[7,5,3,2,4,6,1]=>[3,5,2,4,6,7,1]=>110000=>001111
[7,5,3,2,6,1,4]=>[3,6,5,2,7,1,4]=>110010=>001101
[7,5,3,2,6,4,1]=>[3,6,5,2,4,7,1]=>110010=>001101
[7,5,3,4,1,2,6]=>[3,4,5,1,7,2,6]=>110000=>001111
[7,5,3,4,1,6,2]=>[3,4,5,1,6,7,2]=>110000=>001111
[7,5,3,4,2,1,6]=>[3,4,5,2,7,1,6]=>110000=>001111
[7,5,3,4,2,6,1]=>[3,4,5,2,6,7,1]=>110000=>001111
[7,5,3,4,6,1,2]=>[3,4,6,5,1,7,2]=>110010=>001101
[7,5,3,4,6,2,1]=>[3,4,6,5,2,7,1]=>110010=>001101
[7,5,3,6,1,2,4]=>[3,6,1,5,2,7,4]=>110100=>001011
[7,5,3,6,1,4,2]=>[3,6,1,5,4,7,2]=>110100=>001011
[7,5,3,6,2,1,4]=>[3,6,2,5,1,7,4]=>110100=>001011
[7,5,3,6,2,4,1]=>[3,6,2,5,4,7,1]=>110100=>001011
[7,5,3,6,4,1,2]=>[3,6,4,5,1,7,2]=>110100=>001011
[7,5,3,6,4,2,1]=>[3,6,4,5,2,7,1]=>110100=>001011
[7,5,4,1,2,3,6]=>[4,1,5,2,7,3,6]=>111000=>000111
[7,5,4,1,2,6,3]=>[4,1,5,2,6,7,3]=>111000=>000111
[7,5,4,1,3,2,6]=>[4,1,5,3,7,2,6]=>111000=>000111
[7,5,4,1,3,6,2]=>[4,1,5,3,6,7,2]=>111000=>000111
[7,5,4,1,6,2,3]=>[4,1,6,5,2,7,3]=>111010=>000101
[7,5,4,1,6,3,2]=>[4,1,6,5,3,7,2]=>111010=>000101
[7,5,4,2,1,3,6]=>[4,2,5,1,7,3,6]=>111000=>000111
[7,5,4,2,1,6,3]=>[4,2,5,1,6,7,3]=>111000=>000111
[7,5,4,2,3,1,6]=>[4,2,5,3,7,1,6]=>111000=>000111
[7,5,4,2,3,6,1]=>[4,2,5,3,6,7,1]=>111000=>000111
[7,5,4,2,6,1,3]=>[4,2,6,5,1,7,3]=>111010=>000101
[7,5,4,2,6,3,1]=>[4,2,6,5,3,7,1]=>111010=>000101
[7,5,4,3,1,2,6]=>[4,3,5,1,7,2,6]=>111000=>000111
[7,5,4,3,1,6,2]=>[4,3,5,1,6,7,2]=>111000=>000111
[7,5,4,3,2,1,6]=>[4,3,5,2,7,1,6]=>111000=>000111
[7,5,4,3,2,6,1]=>[4,3,5,2,6,7,1]=>111000=>000111
[7,5,4,3,6,1,2]=>[4,3,6,5,1,7,2]=>111010=>000101
[7,5,4,3,6,2,1]=>[4,3,6,5,2,7,1]=>111010=>000101
[7,5,4,6,1,2,3]=>[6,4,1,5,2,7,3]=>111100=>000011
[7,5,4,6,1,3,2]=>[6,4,1,5,3,7,2]=>111100=>000011
[7,5,4,6,2,1,3]=>[6,4,2,5,1,7,3]=>111100=>000011
[7,5,4,6,2,3,1]=>[6,4,2,5,3,7,1]=>111100=>000011
[7,5,4,6,3,1,2]=>[6,4,3,5,1,7,2]=>111100=>000011
[7,5,4,6,3,2,1]=>[6,4,3,5,2,7,1]=>111100=>000011
[7,5,6,1,2,3,4]=>[6,1,5,2,7,3,4]=>111000=>000111
[7,5,6,1,2,4,3]=>[6,1,5,2,4,7,3]=>111000=>000111
[7,5,6,1,3,2,4]=>[6,1,5,3,7,2,4]=>111000=>000111
[7,5,6,1,3,4,2]=>[6,1,5,3,4,7,2]=>111000=>000111
[7,5,6,1,4,2,3]=>[6,1,4,5,2,7,3]=>111000=>000111
[7,5,6,1,4,3,2]=>[6,1,4,5,3,7,2]=>111000=>000111
[7,5,6,2,1,3,4]=>[6,2,5,1,7,3,4]=>111000=>000111
[7,5,6,2,1,4,3]=>[6,2,5,1,4,7,3]=>111000=>000111
[7,5,6,2,3,1,4]=>[6,2,5,3,7,1,4]=>111000=>000111
[7,5,6,2,3,4,1]=>[6,2,5,3,4,7,1]=>111000=>000111
[7,5,6,2,4,1,3]=>[6,2,4,5,1,7,3]=>111000=>000111
[7,5,6,2,4,3,1]=>[6,2,4,5,3,7,1]=>111000=>000111
[7,5,6,3,1,2,4]=>[6,3,5,1,7,2,4]=>111000=>000111
[7,5,6,3,1,4,2]=>[6,3,5,1,4,7,2]=>111000=>000111
[7,5,6,3,2,1,4]=>[6,3,5,2,7,1,4]=>111000=>000111
[7,5,6,3,2,4,1]=>[6,3,5,2,4,7,1]=>111000=>000111
[7,5,6,3,4,1,2]=>[6,3,4,5,1,7,2]=>111000=>000111
[7,5,6,3,4,2,1]=>[6,3,4,5,2,7,1]=>111000=>000111
[7,5,6,4,1,2,3]=>[4,6,1,5,2,7,3]=>111000=>000111
[7,5,6,4,1,3,2]=>[4,6,1,5,3,7,2]=>111000=>000111
[7,5,6,4,2,1,3]=>[4,6,2,5,1,7,3]=>111000=>000111
[7,5,6,4,2,3,1]=>[4,6,2,5,3,7,1]=>111000=>000111
[7,5,6,4,3,1,2]=>[4,6,3,5,1,7,2]=>111000=>000111
[7,5,6,4,3,2,1]=>[4,6,3,5,2,7,1]=>111000=>000111
[7,6,1,2,3,4,5]=>[6,1,7,2,3,4,5]=>110000=>001111
[7,6,1,2,3,5,4]=>[6,1,5,7,2,3,4]=>110000=>001111
[7,6,1,2,4,3,5]=>[6,1,4,7,2,3,5]=>110000=>001111
[7,6,1,2,4,5,3]=>[6,1,4,5,7,2,3]=>110000=>001111
[7,6,1,2,5,3,4]=>[5,6,1,7,2,3,4]=>110000=>001111
[7,6,1,2,5,4,3]=>[5,6,1,4,7,2,3]=>110000=>001111
[7,6,1,3,2,4,5]=>[6,1,3,7,2,4,5]=>110000=>001111
[7,6,1,3,2,5,4]=>[6,1,3,5,7,2,4]=>110000=>001111
[7,6,1,3,4,2,5]=>[6,1,3,4,7,2,5]=>110000=>001111
[7,6,1,3,4,5,2]=>[6,1,3,4,5,7,2]=>110000=>001111
[7,6,1,3,5,2,4]=>[5,6,1,3,7,2,4]=>110000=>001111
[7,6,1,3,5,4,2]=>[5,6,1,3,4,7,2]=>110000=>001111
[7,6,1,4,2,3,5]=>[4,6,1,7,2,3,5]=>110000=>001111
[7,6,1,4,2,5,3]=>[4,6,1,5,7,2,3]=>110000=>001111
[7,6,1,4,3,2,5]=>[4,6,1,3,7,2,5]=>110000=>001111
[7,6,1,4,3,5,2]=>[4,6,1,3,5,7,2]=>110000=>001111
[7,6,1,4,5,2,3]=>[4,5,6,1,7,2,3]=>110000=>001111
[7,6,1,4,5,3,2]=>[4,5,6,1,3,7,2]=>110000=>001111
[7,6,1,5,2,3,4]=>[5,1,6,2,3,7,4]=>110100=>001011
[7,6,1,5,2,4,3]=>[5,1,6,4,7,2,3]=>110100=>001011
[7,6,1,5,3,2,4]=>[5,1,3,6,2,7,4]=>110100=>001011
[7,6,1,5,3,4,2]=>[5,1,3,6,4,7,2]=>110100=>001011
[7,6,1,5,4,2,3]=>[5,4,6,1,7,2,3]=>110100=>001011
[7,6,1,5,4,3,2]=>[5,4,6,1,3,7,2]=>110100=>001011
[7,6,2,1,3,4,5]=>[6,2,7,1,3,4,5]=>110000=>001111
[7,6,2,1,3,5,4]=>[6,2,5,7,1,3,4]=>110000=>001111
[7,6,2,1,4,3,5]=>[6,2,4,7,1,3,5]=>110000=>001111
[7,6,2,1,4,5,3]=>[6,2,4,5,7,1,3]=>110000=>001111
[7,6,2,1,5,3,4]=>[5,6,2,7,1,3,4]=>110000=>001111
[7,6,2,1,5,4,3]=>[5,6,2,4,7,1,3]=>110000=>001111
[7,6,2,3,1,4,5]=>[6,2,3,7,1,4,5]=>110000=>001111
[7,6,2,3,1,5,4]=>[6,2,3,5,7,1,4]=>110000=>001111
[7,6,2,3,4,1,5]=>[6,2,3,4,7,1,5]=>110000=>001111
[7,6,2,3,4,5,1]=>[6,2,3,4,5,7,1]=>110000=>001111
[7,6,2,3,5,1,4]=>[5,6,2,3,7,1,4]=>110000=>001111
[7,6,2,3,5,4,1]=>[5,6,2,3,4,7,1]=>110000=>001111
[7,6,2,4,1,3,5]=>[4,6,2,7,1,3,5]=>110000=>001111
[7,6,2,4,1,5,3]=>[4,6,2,5,7,1,3]=>110000=>001111
[7,6,2,4,3,1,5]=>[4,6,2,3,7,1,5]=>110000=>001111
[7,6,2,4,3,5,1]=>[4,6,2,3,5,7,1]=>110000=>001111
[7,6,2,4,5,1,3]=>[4,5,6,2,7,1,3]=>110000=>001111
[7,6,2,4,5,3,1]=>[4,5,6,2,3,7,1]=>110000=>001111
[7,6,2,5,1,3,4]=>[5,2,6,1,3,7,4]=>110100=>001011
[7,6,2,5,1,4,3]=>[5,2,6,4,7,1,3]=>110100=>001011
[7,6,2,5,3,1,4]=>[5,2,3,6,1,7,4]=>110100=>001011
[7,6,2,5,3,4,1]=>[5,2,3,6,4,7,1]=>110100=>001011
[7,6,2,5,4,1,3]=>[5,4,6,2,7,1,3]=>110100=>001011
[7,6,2,5,4,3,1]=>[5,4,6,2,3,7,1]=>110100=>001011
[7,6,3,1,2,4,5]=>[3,6,1,7,2,4,5]=>110000=>001111
[7,6,3,1,2,5,4]=>[3,6,1,5,7,2,4]=>110000=>001111
[7,6,3,1,4,2,5]=>[3,6,1,4,7,2,5]=>110000=>001111
[7,6,3,1,4,5,2]=>[3,6,1,4,5,7,2]=>110000=>001111
[7,6,3,1,5,2,4]=>[3,5,6,1,7,2,4]=>110000=>001111
[7,6,3,1,5,4,2]=>[3,5,6,1,4,7,2]=>110000=>001111
[7,6,3,2,1,4,5]=>[3,6,2,7,1,4,5]=>110000=>001111
[7,6,3,2,1,5,4]=>[3,6,2,5,7,1,4]=>110000=>001111
[7,6,3,2,4,1,5]=>[3,6,2,4,7,1,5]=>110000=>001111
[7,6,3,2,4,5,1]=>[3,6,2,4,5,7,1]=>110000=>001111
[7,6,3,2,5,1,4]=>[3,5,6,2,7,1,4]=>110000=>001111
[7,6,3,2,5,4,1]=>[3,5,6,2,4,7,1]=>110000=>001111
[7,6,3,4,1,2,5]=>[3,4,6,1,7,2,5]=>110000=>001111
[7,6,3,4,1,5,2]=>[3,4,6,1,5,7,2]=>110000=>001111
[7,6,3,4,2,1,5]=>[3,4,6,2,7,1,5]=>110000=>001111
[7,6,3,4,2,5,1]=>[3,4,6,2,5,7,1]=>110000=>001111
[7,6,3,4,5,1,2]=>[3,4,5,6,1,7,2]=>110000=>001111
[7,6,3,4,5,2,1]=>[3,4,5,6,2,7,1]=>110000=>001111
[7,6,3,5,1,2,4]=>[3,5,1,6,2,7,4]=>110100=>001011
[7,6,3,5,1,4,2]=>[3,5,1,6,4,7,2]=>110100=>001011
[7,6,3,5,2,1,4]=>[3,5,2,6,1,7,4]=>110100=>001011
[7,6,3,5,2,4,1]=>[3,5,2,6,4,7,1]=>110100=>001011
[7,6,3,5,4,1,2]=>[3,5,4,6,1,7,2]=>110100=>001011
[7,6,3,5,4,2,1]=>[3,5,4,6,2,7,1]=>110100=>001011
[7,6,4,1,2,3,5]=>[4,1,6,2,7,3,5]=>111000=>000111
[7,6,4,1,2,5,3]=>[4,1,6,2,5,7,3]=>111000=>000111
[7,6,4,1,3,2,5]=>[4,1,6,3,7,2,5]=>111000=>000111
[7,6,4,1,3,5,2]=>[4,1,6,3,5,7,2]=>111000=>000111
[7,6,4,1,5,2,3]=>[4,1,5,6,2,7,3]=>111000=>000111
[7,6,4,1,5,3,2]=>[4,1,5,6,3,7,2]=>111000=>000111
[7,6,4,2,1,3,5]=>[4,2,6,1,7,3,5]=>111000=>000111
[7,6,4,2,1,5,3]=>[4,2,6,1,5,7,3]=>111000=>000111
[7,6,4,2,3,1,5]=>[4,2,6,3,7,1,5]=>111000=>000111
[7,6,4,2,3,5,1]=>[4,2,6,3,5,7,1]=>111000=>000111
[7,6,4,2,5,1,3]=>[4,2,5,6,1,7,3]=>111000=>000111
[7,6,4,2,5,3,1]=>[4,2,5,6,3,7,1]=>111000=>000111
[7,6,4,3,1,2,5]=>[4,3,6,1,7,2,5]=>111000=>000111
[7,6,4,3,1,5,2]=>[4,3,6,1,5,7,2]=>111000=>000111
[7,6,4,3,2,1,5]=>[4,3,6,2,7,1,5]=>111000=>000111
[7,6,4,3,2,5,1]=>[4,3,6,2,5,7,1]=>111000=>000111
[7,6,4,3,5,1,2]=>[4,3,5,6,1,7,2]=>111000=>000111
[7,6,4,3,5,2,1]=>[4,3,5,6,2,7,1]=>111000=>000111
[7,6,4,5,1,2,3]=>[5,4,1,6,2,7,3]=>111100=>000011
[7,6,4,5,1,3,2]=>[5,4,1,6,3,7,2]=>111100=>000011
[7,6,4,5,2,1,3]=>[5,4,2,6,1,7,3]=>111100=>000011
[7,6,4,5,2,3,1]=>[5,4,2,6,3,7,1]=>111100=>000011
[7,6,4,5,3,1,2]=>[5,4,3,6,1,7,2]=>111100=>000011
[7,6,4,5,3,2,1]=>[5,4,3,6,2,7,1]=>111100=>000011
[7,6,5,1,2,3,4]=>[5,1,6,2,7,3,4]=>111000=>000111
[7,6,5,1,2,4,3]=>[5,1,6,2,4,7,3]=>111000=>000111
[7,6,5,1,3,2,4]=>[5,1,6,3,7,2,4]=>111000=>000111
[7,6,5,1,3,4,2]=>[5,1,6,3,4,7,2]=>111000=>000111
[7,6,5,1,4,2,3]=>[5,1,4,6,2,7,3]=>111000=>000111
[7,6,5,1,4,3,2]=>[5,1,4,6,3,7,2]=>111000=>000111
[7,6,5,2,1,3,4]=>[5,2,6,1,7,3,4]=>111000=>000111
[7,6,5,2,1,4,3]=>[5,2,6,1,4,7,3]=>111000=>000111
[7,6,5,2,3,1,4]=>[5,2,6,3,7,1,4]=>111000=>000111
[7,6,5,2,3,4,1]=>[5,2,6,3,4,7,1]=>111000=>000111
[7,6,5,2,4,1,3]=>[5,2,4,6,1,7,3]=>111000=>000111
[7,6,5,2,4,3,1]=>[5,2,4,6,3,7,1]=>111000=>000111
[7,6,5,3,1,2,4]=>[5,3,6,1,7,2,4]=>111000=>000111
[7,6,5,3,1,4,2]=>[5,3,6,1,4,7,2]=>111000=>000111
[7,6,5,3,2,1,4]=>[5,3,6,2,7,1,4]=>111000=>000111
[7,6,5,3,2,4,1]=>[5,3,6,2,4,7,1]=>111000=>000111
[7,6,5,3,4,1,2]=>[5,3,4,6,1,7,2]=>111000=>000111
[7,6,5,3,4,2,1]=>[5,3,4,6,2,7,1]=>111000=>000111
[7,6,5,4,1,2,3]=>[4,5,1,6,2,7,3]=>111000=>000111
[7,6,5,4,1,3,2]=>[4,5,1,6,3,7,2]=>111000=>000111
[7,6,5,4,2,1,3]=>[4,5,2,6,1,7,3]=>111000=>000111
[7,6,5,4,2,3,1]=>[4,5,2,6,3,7,1]=>111000=>000111
[7,6,5,4,3,1,2]=>[4,5,3,6,1,7,2]=>111000=>000111
[7,6,5,4,3,2,1]=>[4,5,3,6,2,7,1]=>111000=>000111
[8,7,6,5,4,3,2,1]=>[5,4,6,3,7,2,8,1]=>1111000=>0000111
[7,8,6,5,4,3,2,1]=>[5,4,6,3,8,2,7,1]=>1111000=>0000111
[8,6,7,5,4,3,2,1]=>[5,4,7,3,6,2,8,1]=>1111000=>0000111
[7,6,8,5,4,3,2,1]=>[5,4,8,3,6,2,7,1]=>1111000=>0000111
[6,7,8,5,4,3,2,1]=>[5,4,8,3,7,2,6,1]=>1111000=>0000111
[8,7,5,6,4,3,2,1]=>[6,4,5,3,7,2,8,1]=>1111000=>0000111
[7,8,5,6,4,3,2,1]=>[6,4,5,3,8,2,7,1]=>1111000=>0000111
[8,6,5,7,4,3,2,1]=>[7,4,5,3,6,2,8,1]=>1111000=>0000111
[8,5,6,7,4,3,2,1]=>[7,4,6,3,5,2,8,1]=>1111000=>0000111
[7,6,5,8,4,3,2,1]=>[8,4,5,3,6,2,7,1]=>1111000=>0000111
[6,7,5,8,4,3,2,1]=>[8,4,5,3,7,2,6,1]=>1111000=>0000111
[7,5,6,8,4,3,2,1]=>[8,4,6,3,5,2,7,1]=>1111000=>0000111
[6,5,7,8,4,3,2,1]=>[8,4,7,3,5,2,6,1]=>1111000=>0000111
[5,6,7,8,4,3,2,1]=>[8,4,7,3,6,2,5,1]=>1111000=>0000111
[8,7,6,4,5,3,2,1]=>[4,5,6,3,7,2,8,1]=>1110000=>0001111
[7,8,6,4,5,3,2,1]=>[4,5,6,3,8,2,7,1]=>1110000=>0001111
[8,6,7,4,5,3,2,1]=>[4,5,7,3,6,2,8,1]=>1110000=>0001111
[6,7,8,4,5,3,2,1]=>[4,5,8,3,7,2,6,1]=>1110000=>0001111
[8,7,5,4,6,3,2,1]=>[4,6,5,3,7,2,8,1]=>1110100=>0001011
[8,7,4,5,6,3,2,1]=>[6,5,4,3,7,2,8,1]=>1111100=>0000011
[8,6,4,5,7,3,2,1]=>[7,5,4,3,6,2,8,1]=>1111100=>0000011
[8,5,4,6,7,3,2,1]=>[7,4,3,6,5,2,8,1]=>1111100=>0000011
[8,4,5,6,7,3,2,1]=>[7,3,6,5,4,2,8,1]=>1111100=>0000011
[7,6,5,4,8,3,2,1]=>[4,8,5,3,6,2,7,1]=>1110100=>0001011
[7,5,6,4,8,3,2,1]=>[4,8,3,6,5,2,7,1]=>1110100=>0001011
[7,6,4,5,8,3,2,1]=>[8,5,4,3,6,2,7,1]=>1111100=>0000011
[6,7,4,5,8,3,2,1]=>[8,5,4,3,7,2,6,1]=>1111100=>0000011
[7,4,5,6,8,3,2,1]=>[8,3,6,5,4,2,7,1]=>1111100=>0000011
[6,5,4,7,8,3,2,1]=>[8,4,3,7,5,2,6,1]=>1111100=>0000011
[6,4,5,7,8,3,2,1]=>[8,3,7,5,4,2,6,1]=>1111100=>0000011
[5,4,6,7,8,3,2,1]=>[8,3,7,4,2,6,5,1]=>1111100=>0000011
[4,5,6,7,8,3,2,1]=>[8,3,7,2,6,5,4,1]=>1111100=>0000011
[8,7,6,5,3,4,2,1]=>[5,3,6,4,7,2,8,1]=>1111000=>0000111
[7,8,6,5,3,4,2,1]=>[5,3,6,4,8,2,7,1]=>1111000=>0000111
[8,6,7,5,3,4,2,1]=>[5,3,7,4,6,2,8,1]=>1111000=>0000111
[7,6,8,5,3,4,2,1]=>[5,3,8,4,6,2,7,1]=>1111000=>0000111
[8,7,5,6,3,4,2,1]=>[6,3,5,4,7,2,8,1]=>1111000=>0000111
[7,8,5,6,3,4,2,1]=>[6,3,5,4,8,2,7,1]=>1111000=>0000111
[6,5,7,8,3,4,2,1]=>[8,3,7,4,5,2,6,1]=>1111000=>0000111
[5,6,7,8,3,4,2,1]=>[8,3,7,4,6,2,5,1]=>1111000=>0000111
[8,7,6,4,3,5,2,1]=>[4,6,3,5,7,2,8,1]=>1110000=>0001111
[7,8,6,4,3,5,2,1]=>[4,6,3,5,8,2,7,1]=>1110000=>0001111
[8,6,7,4,3,5,2,1]=>[4,7,3,5,6,2,8,1]=>1110000=>0001111
[6,7,8,4,3,5,2,1]=>[4,8,3,5,7,2,6,1]=>1110000=>0001111
[8,7,6,3,4,5,2,1]=>[6,3,4,5,7,2,8,1]=>1110000=>0001111
[7,8,6,3,4,5,2,1]=>[6,3,4,5,8,2,7,1]=>1110000=>0001111
[8,6,7,3,4,5,2,1]=>[7,3,4,5,6,2,8,1]=>1110000=>0001111
[7,6,8,3,4,5,2,1]=>[8,3,4,5,6,2,7,1]=>1110000=>0001111
[8,7,5,4,3,6,2,1]=>[4,5,3,6,7,2,8,1]=>1110000=>0001111
[7,8,5,4,3,6,2,1]=>[4,5,3,6,8,2,7,1]=>1110000=>0001111
[8,7,4,5,3,6,2,1]=>[5,4,3,6,7,2,8,1]=>1111000=>0000111
[7,8,5,3,4,6,2,1]=>[5,3,4,6,8,2,7,1]=>1110000=>0001111
[8,7,4,3,5,6,2,1]=>[4,3,5,6,7,2,8,1]=>1110000=>0001111
[8,7,3,4,5,6,2,1]=>[3,4,5,6,7,2,8,1]=>1100000=>0011111
[7,8,3,4,5,6,2,1]=>[3,4,5,6,8,2,7,1]=>1100000=>0011111
[8,6,5,4,3,7,2,1]=>[4,5,3,7,6,2,8,1]=>1110010=>0001101
[8,6,4,5,3,7,2,1]=>[5,4,3,7,6,2,8,1]=>1111010=>0000101
[8,5,4,6,3,7,2,1]=>[7,6,4,3,5,2,8,1]=>1111010=>0000101
[8,5,4,3,6,7,2,1]=>[4,3,7,6,5,2,8,1]=>1110110=>0001001
[8,5,3,4,6,7,2,1]=>[3,4,7,6,5,2,8,1]=>1100110=>0011001
[8,3,4,5,6,7,2,1]=>[7,6,5,4,3,2,8,1]=>1111110=>0000001
[7,6,5,4,3,8,2,1]=>[4,5,3,8,6,2,7,1]=>1110010=>0001101
[6,7,5,4,3,8,2,1]=>[4,5,3,8,2,7,6,1]=>1110010=>0001101
[5,6,7,4,3,8,2,1]=>[4,8,3,7,6,2,5,1]=>1110010=>0001101
[7,6,4,5,3,8,2,1]=>[5,4,3,8,6,2,7,1]=>1111010=>0000101
[7,5,4,6,3,8,2,1]=>[8,6,4,3,5,2,7,1]=>1111010=>0000101
[7,4,5,6,3,8,2,1]=>[8,6,3,5,4,2,7,1]=>1111010=>0000101
[6,5,4,7,3,8,2,1]=>[8,4,3,5,2,7,6,1]=>1111010=>0000101
[6,4,5,7,3,8,2,1]=>[8,3,5,4,2,7,6,1]=>1111010=>0000101
[4,5,6,7,3,8,2,1]=>[8,3,7,6,2,5,4,1]=>1111010=>0000101
[7,6,5,3,4,8,2,1]=>[5,3,4,8,6,2,7,1]=>1110010=>0001101
[7,6,3,4,5,8,2,1]=>[3,4,5,8,6,2,7,1]=>1100010=>0011101
[7,5,4,3,6,8,2,1]=>[4,3,8,6,5,2,7,1]=>1110110=>0001001
[7,5,3,4,6,8,2,1]=>[3,4,8,6,5,2,7,1]=>1100110=>0011001
[7,3,4,5,6,8,2,1]=>[8,6,5,4,3,2,7,1]=>1111110=>0000001
[4,5,6,3,7,8,2,1]=>[8,3,7,6,5,2,4,1]=>1110110=>0001001
[6,3,4,5,7,8,2,1]=>[8,5,4,3,2,7,6,1]=>1111110=>0000001
[5,4,3,6,7,8,2,1]=>[3,8,4,2,7,6,5,1]=>1101110=>0010001
[5,3,4,6,7,8,2,1]=>[8,4,3,2,7,6,5,1]=>1111110=>0000001
[4,3,5,6,7,8,2,1]=>[8,3,2,7,6,5,4,1]=>1111110=>0000001
[3,4,5,6,7,8,2,1]=>[8,2,7,6,5,4,3,1]=>1111110=>0000001
[8,7,6,5,4,2,3,1]=>[5,4,6,2,7,3,8,1]=>1111000=>0000111
[7,8,6,5,4,2,3,1]=>[5,4,6,2,8,3,7,1]=>1111000=>0000111
[8,6,7,5,4,2,3,1]=>[5,4,7,2,6,3,8,1]=>1111000=>0000111
[7,6,8,5,4,2,3,1]=>[5,4,8,2,6,3,7,1]=>1111000=>0000111
[8,7,5,6,4,2,3,1]=>[6,4,5,2,7,3,8,1]=>1111000=>0000111
[7,6,5,8,4,2,3,1]=>[8,4,5,2,6,3,7,1]=>1111000=>0000111
[7,5,6,8,4,2,3,1]=>[8,4,6,2,5,3,7,1]=>1111000=>0000111
[5,6,7,8,4,2,3,1]=>[8,4,7,2,6,3,5,1]=>1111000=>0000111
[8,7,6,4,5,2,3,1]=>[4,5,6,2,7,3,8,1]=>1110000=>0001111
[8,6,7,4,5,2,3,1]=>[4,5,7,2,6,3,8,1]=>1110000=>0001111
[8,7,5,4,6,2,3,1]=>[4,6,5,2,7,3,8,1]=>1110100=>0001011
[7,8,4,5,6,2,3,1]=>[6,5,4,2,8,3,7,1]=>1111100=>0000011
[8,6,5,4,7,2,3,1]=>[4,7,5,2,6,3,8,1]=>1110100=>0001011
[8,6,4,5,7,2,3,1]=>[7,5,4,2,6,3,8,1]=>1111100=>0000011
[8,4,5,6,7,2,3,1]=>[7,2,6,5,4,3,8,1]=>1111100=>0000011
[7,5,6,4,8,2,3,1]=>[4,8,2,6,5,3,7,1]=>1110100=>0001011
[6,5,7,4,8,2,3,1]=>[4,8,2,7,5,3,6,1]=>1110100=>0001011
[7,6,4,5,8,2,3,1]=>[8,5,4,2,6,3,7,1]=>1111100=>0000011
[6,7,4,5,8,2,3,1]=>[8,5,4,2,7,3,6,1]=>1111100=>0000011
[4,5,6,7,8,2,3,1]=>[8,2,7,3,6,5,4,1]=>1111100=>0000011
[8,7,6,5,3,2,4,1]=>[5,3,6,2,7,4,8,1]=>1111000=>0000111
[7,8,6,5,3,2,4,1]=>[5,3,6,2,8,4,7,1]=>1111000=>0000111
[8,6,7,5,3,2,4,1]=>[5,3,7,2,6,4,8,1]=>1111000=>0000111
[7,6,8,5,3,2,4,1]=>[5,3,8,2,6,4,7,1]=>1111000=>0000111
[8,7,5,6,3,2,4,1]=>[6,3,5,2,7,4,8,1]=>1111000=>0000111
[8,6,5,7,3,2,4,1]=>[7,3,5,2,6,4,8,1]=>1111000=>0000111
[8,5,6,7,3,2,4,1]=>[7,3,6,2,5,4,8,1]=>1111000=>0000111
[6,7,5,8,3,2,4,1]=>[8,3,5,2,7,4,6,1]=>1111000=>0000111
[5,6,7,8,3,2,4,1]=>[8,3,7,2,6,4,5,1]=>1111000=>0000111
[8,7,6,5,2,3,4,1]=>[5,2,6,3,7,4,8,1]=>1111000=>0000111
[8,6,7,5,2,3,4,1]=>[5,2,7,3,6,4,8,1]=>1111000=>0000111
[6,7,8,5,2,3,4,1]=>[5,2,8,3,7,4,6,1]=>1111000=>0000111
[8,7,5,6,2,3,4,1]=>[6,2,5,3,7,4,8,1]=>1111000=>0000111
[7,8,5,6,2,3,4,1]=>[6,2,5,3,8,4,7,1]=>1111000=>0000111
[8,5,6,7,2,3,4,1]=>[7,2,6,3,5,4,8,1]=>1111000=>0000111
[5,6,7,8,2,3,4,1]=>[8,2,7,3,6,4,5,1]=>1111000=>0000111
[8,7,6,4,3,2,5,1]=>[4,6,3,7,2,5,8,1]=>1110000=>0001111
[8,6,7,4,3,2,5,1]=>[4,7,3,6,2,5,8,1]=>1110000=>0001111
[7,6,8,4,3,2,5,1]=>[4,8,3,6,2,5,7,1]=>1110000=>0001111
[6,7,8,4,3,2,5,1]=>[4,8,3,7,2,5,6,1]=>1110000=>0001111
[7,8,6,3,4,2,5,1]=>[6,3,4,8,2,5,7,1]=>1110000=>0001111
[6,7,8,3,4,2,5,1]=>[8,3,4,7,2,5,6,1]=>1110000=>0001111
[8,7,6,4,2,3,5,1]=>[4,6,2,7,3,5,8,1]=>1110000=>0001111
[8,6,7,4,2,3,5,1]=>[4,7,2,6,3,5,8,1]=>1110000=>0001111
[7,6,8,4,2,3,5,1]=>[4,8,2,6,3,5,7,1]=>1110000=>0001111
[6,7,8,4,2,3,5,1]=>[4,8,2,7,3,5,6,1]=>1110000=>0001111
[8,7,6,3,2,4,5,1]=>[6,3,7,2,4,5,8,1]=>1110000=>0001111
[7,8,6,3,2,4,5,1]=>[6,3,8,2,4,5,7,1]=>1110000=>0001111
[8,6,7,3,2,4,5,1]=>[7,3,6,2,4,5,8,1]=>1110000=>0001111
[6,7,8,3,2,4,5,1]=>[8,3,7,2,4,5,6,1]=>1110000=>0001111
[8,7,6,2,3,4,5,1]=>[6,2,7,3,4,5,8,1]=>1110000=>0001111
[8,6,7,2,3,4,5,1]=>[7,2,6,3,4,5,8,1]=>1110000=>0001111
[7,6,8,2,3,4,5,1]=>[8,2,6,3,4,5,7,1]=>1110000=>0001111
[6,7,8,2,3,4,5,1]=>[8,2,7,3,4,5,6,1]=>1110000=>0001111
[7,8,5,3,4,2,6,1]=>[5,3,4,8,2,6,7,1]=>1110000=>0001111
[8,7,4,3,5,2,6,1]=>[4,3,5,7,2,6,8,1]=>1110000=>0001111
[8,7,5,3,2,4,6,1]=>[5,3,7,2,4,6,8,1]=>1110000=>0001111
[8,7,4,3,2,5,6,1]=>[4,3,7,2,5,6,8,1]=>1110000=>0001111
[7,8,4,3,2,5,6,1]=>[4,3,8,2,5,6,7,1]=>1110000=>0001111
[7,8,3,4,2,5,6,1]=>[3,4,8,2,5,6,7,1]=>1100000=>0011111
[7,8,3,2,4,5,6,1]=>[3,8,2,4,5,6,7,1]=>1100000=>0011111
[8,7,2,3,4,5,6,1]=>[7,2,3,4,5,6,8,1]=>1100000=>0011111
[7,8,2,3,4,5,6,1]=>[8,2,3,4,5,6,7,1]=>1100000=>0011111
[8,5,6,4,3,2,7,1]=>[4,6,3,5,2,7,8,1]=>1110000=>0001111
[8,6,4,5,3,2,7,1]=>[5,4,3,6,2,7,8,1]=>1111000=>0000111
[8,5,6,3,4,2,7,1]=>[6,3,4,5,2,7,8,1]=>1110000=>0001111
[8,6,4,3,5,2,7,1]=>[4,3,5,6,2,7,8,1]=>1110000=>0001111
[8,6,3,4,5,2,7,1]=>[3,4,5,6,2,7,8,1]=>1100000=>0011111
[8,4,5,3,6,2,7,1]=>[6,5,3,4,2,7,8,1]=>1110100=>0001011
[8,4,3,5,6,2,7,1]=>[3,6,5,4,2,7,8,1]=>1101100=>0010011
[8,3,4,5,6,2,7,1]=>[6,5,4,3,2,7,8,1]=>1111100=>0000011
[8,6,5,4,2,3,7,1]=>[4,5,2,6,3,7,8,1]=>1110000=>0001111
[8,6,4,5,2,3,7,1]=>[5,4,2,6,3,7,8,1]=>1111000=>0000111
[8,6,5,3,2,4,7,1]=>[5,3,6,2,4,7,8,1]=>1110000=>0001111
[8,6,4,3,2,5,7,1]=>[4,3,6,2,5,7,8,1]=>1110000=>0001111
[8,6,4,2,3,5,7,1]=>[4,2,6,3,5,7,8,1]=>1110000=>0001111
[8,6,2,3,4,5,7,1]=>[6,2,3,4,5,7,8,1]=>1100000=>0011111
[8,5,4,3,2,6,7,1]=>[4,3,5,2,6,7,8,1]=>1110000=>0001111
[8,4,5,3,2,6,7,1]=>[5,3,4,2,6,7,8,1]=>1110000=>0001111
[8,5,3,4,2,6,7,1]=>[3,4,5,2,6,7,8,1]=>1100000=>0011111
[8,3,4,5,2,6,7,1]=>[5,4,3,2,6,7,8,1]=>1111000=>0000111
[8,5,4,2,3,6,7,1]=>[4,2,5,3,6,7,8,1]=>1110000=>0001111
[8,4,3,2,5,6,7,1]=>[3,4,2,5,6,7,8,1]=>1100000=>0011111
[8,3,4,2,5,6,7,1]=>[4,3,2,5,6,7,8,1]=>1110000=>0001111
[8,4,2,3,5,6,7,1]=>[4,2,3,5,6,7,8,1]=>1100000=>0011111
[8,3,2,4,5,6,7,1]=>[3,2,4,5,6,7,8,1]=>1100000=>0011111
[8,2,3,4,5,6,7,1]=>[2,3,4,5,6,7,8,1]=>1000000=>0111111
[7,6,5,4,3,2,8,1]=>[4,5,3,6,2,8,7,1]=>1110001=>0001110
[6,7,5,4,3,2,8,1]=>[4,5,3,8,7,2,6,1]=>1110001=>0001110
[7,5,6,4,3,2,8,1]=>[4,6,3,5,2,8,7,1]=>1110001=>0001110
[6,5,7,4,3,2,8,1]=>[4,8,7,3,5,2,6,1]=>1110001=>0001110
[5,6,7,4,3,2,8,1]=>[4,8,7,3,6,2,5,1]=>1110001=>0001110
[7,6,4,5,3,2,8,1]=>[5,4,3,6,2,8,7,1]=>1111001=>0000110
[7,4,5,6,3,2,8,1]=>[6,3,5,4,2,8,7,1]=>1111001=>0000110
[6,5,4,7,3,2,8,1]=>[8,7,4,3,5,2,6,1]=>1111001=>0000110
[6,4,5,7,3,2,8,1]=>[8,7,3,5,4,2,6,1]=>1111001=>0000110
[4,5,6,7,3,2,8,1]=>[8,7,3,6,2,5,4,1]=>1111001=>0000110
[7,5,6,3,4,2,8,1]=>[6,3,4,5,2,8,7,1]=>1110001=>0001110
[5,6,7,3,4,2,8,1]=>[8,7,3,4,6,2,5,1]=>1110001=>0001110
[7,6,3,4,5,2,8,1]=>[3,4,5,6,2,8,7,1]=>1100001=>0011110
[7,5,4,3,6,2,8,1]=>[4,3,6,5,2,8,7,1]=>1110101=>0001010
[7,3,4,5,6,2,8,1]=>[6,5,4,3,2,8,7,1]=>1111101=>0000010
[6,5,4,3,7,2,8,1]=>[4,3,8,7,5,2,6,1]=>1110101=>0001010
[6,4,5,3,7,2,8,1]=>[8,7,5,3,4,2,6,1]=>1110101=>0001010
[5,4,6,3,7,2,8,1]=>[8,7,3,4,2,6,5,1]=>1110101=>0001010
[4,5,6,3,7,2,8,1]=>[8,7,3,6,5,2,4,1]=>1110101=>0001010
[6,5,3,4,7,2,8,1]=>[3,4,8,7,5,2,6,1]=>1100101=>0011010
[6,4,3,5,7,2,8,1]=>[3,8,7,5,4,2,6,1]=>1101101=>0010010
[6,3,4,5,7,2,8,1]=>[8,7,5,4,3,2,6,1]=>1111101=>0000010
[5,4,3,6,7,2,8,1]=>[3,8,7,4,2,6,5,1]=>1101101=>0010010
[4,5,3,6,7,2,8,1]=>[3,8,7,2,6,5,4,1]=>1101101=>0010010
[3,4,5,6,7,2,8,1]=>[8,7,2,6,5,4,3,1]=>1111101=>0000010
[7,5,6,4,2,3,8,1]=>[4,6,2,5,3,8,7,1]=>1110001=>0001110
[5,6,7,4,2,3,8,1]=>[4,8,7,2,6,3,5,1]=>1110001=>0001110
[7,6,4,5,2,3,8,1]=>[5,4,2,6,3,8,7,1]=>1111001=>0000110
[6,7,4,5,2,3,8,1]=>[5,4,2,8,7,3,6,1]=>1111001=>0000110
[7,5,4,6,2,3,8,1]=>[6,4,2,5,3,8,7,1]=>1111001=>0000110
[6,5,4,7,2,3,8,1]=>[8,7,4,2,5,3,6,1]=>1111001=>0000110
[5,6,4,7,2,3,8,1]=>[8,7,4,2,6,3,5,1]=>1111001=>0000110
[6,4,5,7,2,3,8,1]=>[8,7,2,5,4,3,6,1]=>1111001=>0000110
[4,5,6,7,2,3,8,1]=>[8,7,2,6,3,5,4,1]=>1111001=>0000110
[7,6,5,3,2,4,8,1]=>[5,3,6,2,4,8,7,1]=>1110001=>0001110
[6,7,5,3,2,4,8,1]=>[5,3,8,7,2,4,6,1]=>1110001=>0001110
[6,5,7,3,2,4,8,1]=>[8,7,3,5,2,4,6,1]=>1110001=>0001110
[7,5,6,2,3,4,8,1]=>[6,2,5,3,4,8,7,1]=>1110001=>0001110
[6,7,4,3,2,5,8,1]=>[4,3,8,7,2,5,6,1]=>1110001=>0001110
[7,6,4,2,3,5,8,1]=>[4,2,6,3,5,8,7,1]=>1110001=>0001110
[7,6,3,2,4,5,8,1]=>[3,6,2,4,5,8,7,1]=>1100001=>0011110
[6,7,3,2,4,5,8,1]=>[3,8,7,2,4,5,6,1]=>1100001=>0011110
[7,6,2,3,4,5,8,1]=>[6,2,3,4,5,8,7,1]=>1100001=>0011110
[6,7,2,3,4,5,8,1]=>[8,7,2,3,4,5,6,1]=>1100001=>0011110
[7,4,3,2,5,6,8,1]=>[3,4,2,5,6,8,7,1]=>1100001=>0011110
[7,4,2,3,5,6,8,1]=>[4,2,3,5,6,8,7,1]=>1100001=>0011110
[7,3,2,4,5,6,8,1]=>[3,2,4,5,6,8,7,1]=>1100001=>0011110
[7,2,3,4,5,6,8,1]=>[2,3,4,5,6,8,7,1]=>1000001=>0111110
[6,5,4,3,2,7,8,1]=>[4,3,5,2,8,7,6,1]=>1110011=>0001100
[5,4,6,3,2,7,8,1]=>[8,7,6,3,4,2,5,1]=>1110011=>0001100
[4,5,6,3,2,7,8,1]=>[8,7,6,3,5,2,4,1]=>1110011=>0001100
[6,3,4,5,2,7,8,1]=>[5,4,3,2,8,7,6,1]=>1111011=>0000100
[4,3,5,6,2,7,8,1]=>[8,7,6,3,2,5,4,1]=>1111011=>0000100
[3,4,5,6,2,7,8,1]=>[8,7,6,2,5,4,3,1]=>1111011=>0000100
[6,5,4,2,3,7,8,1]=>[4,2,5,3,8,7,6,1]=>1110011=>0001100
[5,6,4,2,3,7,8,1]=>[4,2,8,7,6,3,5,1]=>1110011=>0001100
[6,4,5,2,3,7,8,1]=>[5,2,4,3,8,7,6,1]=>1110011=>0001100
[4,5,6,2,3,7,8,1]=>[8,7,6,2,5,3,4,1]=>1110011=>0001100
[6,5,3,2,4,7,8,1]=>[3,5,2,4,8,7,6,1]=>1100011=>0011100
[6,5,2,3,4,7,8,1]=>[5,2,3,4,8,7,6,1]=>1100011=>0011100
[5,6,2,3,4,7,8,1]=>[8,7,6,2,3,4,5,1]=>1100011=>0011100
[6,2,3,4,5,7,8,1]=>[2,3,4,5,8,7,6,1]=>1000011=>0111100
[5,4,3,2,6,7,8,1]=>[3,4,2,8,7,6,5,1]=>1100111=>0011000
[4,5,3,2,6,7,8,1]=>[3,8,7,6,5,2,4,1]=>1100111=>0011000
[5,3,4,2,6,7,8,1]=>[4,3,2,8,7,6,5,1]=>1110111=>0001000
[4,3,5,2,6,7,8,1]=>[8,7,6,5,3,2,4,1]=>1110111=>0001000
[3,4,5,2,6,7,8,1]=>[8,7,6,5,2,4,3,1]=>1110111=>0001000
[5,4,2,3,6,7,8,1]=>[4,2,3,8,7,6,5,1]=>1100111=>0011000
[4,5,2,3,6,7,8,1]=>[8,7,6,5,2,3,4,1]=>1100111=>0011000
[5,3,2,4,6,7,8,1]=>[3,2,4,8,7,6,5,1]=>1100111=>0011000
[5,2,3,4,6,7,8,1]=>[2,3,4,8,7,6,5,1]=>1000111=>0111000
[4,3,2,5,6,7,8,1]=>[3,2,8,7,6,5,4,1]=>1101111=>0010000
[3,4,2,5,6,7,8,1]=>[8,7,6,5,4,2,3,1]=>1101111=>0010000
[4,2,3,5,6,7,8,1]=>[2,3,8,7,6,5,4,1]=>1001111=>0110000
[3,2,4,5,6,7,8,1]=>[2,8,7,6,5,4,3,1]=>1011111=>0100000
[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]=>1111111=>0000000
[8,7,6,5,4,3,1,2]=>[5,4,6,3,7,1,8,2]=>1111000=>0000111
[7,8,6,5,4,3,1,2]=>[5,4,6,3,8,1,7,2]=>1111000=>0000111
[8,6,7,5,4,3,1,2]=>[5,4,7,3,6,1,8,2]=>1111000=>0000111
[7,6,8,5,4,3,1,2]=>[5,4,8,3,6,1,7,2]=>1111000=>0000111
[6,7,8,5,4,3,1,2]=>[5,4,8,3,7,1,6,2]=>1111000=>0000111
[8,7,5,6,4,3,1,2]=>[6,4,5,3,7,1,8,2]=>1111000=>0000111
[7,8,5,6,4,3,1,2]=>[6,4,5,3,8,1,7,2]=>1111000=>0000111
[7,6,5,8,4,3,1,2]=>[8,4,5,3,6,1,7,2]=>1111000=>0000111
[7,5,6,8,4,3,1,2]=>[8,4,6,3,5,1,7,2]=>1111000=>0000111
[6,5,7,8,4,3,1,2]=>[8,4,7,3,5,1,6,2]=>1111000=>0000111
[5,6,7,8,4,3,1,2]=>[8,4,7,3,6,1,5,2]=>1111000=>0000111
[8,7,6,4,5,3,1,2]=>[4,5,6,3,7,1,8,2]=>1110000=>0001111
[7,8,6,4,5,3,1,2]=>[4,5,6,3,8,1,7,2]=>1110000=>0001111
[8,7,5,4,6,3,1,2]=>[4,6,5,3,7,1,8,2]=>1110100=>0001011
[7,8,4,5,6,3,1,2]=>[6,5,4,3,8,1,7,2]=>1111100=>0000011
[8,5,6,4,7,3,1,2]=>[4,7,3,6,5,1,8,2]=>1110100=>0001011
[8,6,4,5,7,3,1,2]=>[7,5,4,3,6,1,8,2]=>1111100=>0000011
[7,6,5,4,8,3,1,2]=>[4,8,5,3,6,1,7,2]=>1110100=>0001011
[7,5,6,4,8,3,1,2]=>[4,8,3,6,5,1,7,2]=>1110100=>0001011
[6,5,7,4,8,3,1,2]=>[4,8,3,7,5,1,6,2]=>1110100=>0001011
[6,5,4,7,8,3,1,2]=>[8,4,3,7,5,1,6,2]=>1111100=>0000011
[5,6,4,7,8,3,1,2]=>[8,4,3,7,1,6,5,2]=>1111100=>0000011
[5,4,6,7,8,3,1,2]=>[8,3,7,4,1,6,5,2]=>1111100=>0000011
[4,5,6,7,8,3,1,2]=>[8,3,7,1,6,5,4,2]=>1111100=>0000011
[8,7,6,5,3,4,1,2]=>[5,3,6,4,7,1,8,2]=>1111000=>0000111
[7,6,8,5,3,4,1,2]=>[5,3,8,4,6,1,7,2]=>1111000=>0000111
[6,7,8,5,3,4,1,2]=>[5,3,8,4,7,1,6,2]=>1111000=>0000111
[8,7,5,6,3,4,1,2]=>[6,3,5,4,7,1,8,2]=>1111000=>0000111
[7,8,5,6,3,4,1,2]=>[6,3,5,4,8,1,7,2]=>1111000=>0000111
[6,7,5,8,3,4,1,2]=>[8,3,5,4,7,1,6,2]=>1111000=>0000111
[7,5,6,8,3,4,1,2]=>[8,3,6,4,5,1,7,2]=>1111000=>0000111
[6,5,7,8,3,4,1,2]=>[8,3,7,4,5,1,6,2]=>1111000=>0000111
[5,6,7,8,3,4,1,2]=>[8,3,7,4,6,1,5,2]=>1111000=>0000111
[6,7,8,4,3,5,1,2]=>[4,8,3,5,7,1,6,2]=>1110000=>0001111
[8,7,6,3,4,5,1,2]=>[6,3,4,5,7,1,8,2]=>1110000=>0001111
[7,8,6,3,4,5,1,2]=>[6,3,4,5,8,1,7,2]=>1110000=>0001111
[8,6,7,3,4,5,1,2]=>[7,3,4,5,6,1,8,2]=>1110000=>0001111
[6,7,8,3,4,5,1,2]=>[8,3,4,5,7,1,6,2]=>1110000=>0001111
[7,8,5,4,3,6,1,2]=>[4,5,3,6,8,1,7,2]=>1110000=>0001111
[8,7,4,5,3,6,1,2]=>[5,4,3,6,7,1,8,2]=>1111000=>0000111
[7,8,4,5,3,6,1,2]=>[5,4,3,6,8,1,7,2]=>1111000=>0000111
[8,7,4,3,5,6,1,2]=>[4,3,5,6,7,1,8,2]=>1110000=>0001111
[7,8,4,3,5,6,1,2]=>[4,3,5,6,8,1,7,2]=>1110000=>0001111
[8,7,3,4,5,6,1,2]=>[3,4,5,6,7,1,8,2]=>1100000=>0011111
[7,8,3,4,5,6,1,2]=>[3,4,5,6,8,1,7,2]=>1100000=>0011111
[8,6,5,4,3,7,1,2]=>[4,5,3,7,6,1,8,2]=>1110010=>0001101
[8,5,4,3,6,7,1,2]=>[4,3,7,6,5,1,8,2]=>1110110=>0001001
[8,3,4,5,6,7,1,2]=>[7,6,5,4,3,1,8,2]=>1111110=>0000001
[7,6,5,4,3,8,1,2]=>[4,5,3,8,6,1,7,2]=>1110010=>0001101
[5,6,7,4,3,8,1,2]=>[4,8,3,7,6,1,5,2]=>1110010=>0001101
[6,7,4,5,3,8,1,2]=>[5,4,3,8,1,7,6,2]=>1111010=>0000101
[5,6,4,7,3,8,1,2]=>[8,4,3,7,6,1,5,2]=>1111010=>0000101
[4,5,6,7,3,8,1,2]=>[8,3,7,6,1,5,4,2]=>1111010=>0000101
[7,5,6,3,4,8,1,2]=>[8,6,3,4,5,1,7,2]=>1110010=>0001101
[5,6,7,3,4,8,1,2]=>[8,3,4,7,6,1,5,2]=>1110010=>0001101
[7,6,4,3,5,8,1,2]=>[4,3,5,8,6,1,7,2]=>1110010=>0001101
[7,6,3,4,5,8,1,2]=>[3,4,5,8,6,1,7,2]=>1100010=>0011101
[7,5,3,4,6,8,1,2]=>[3,4,8,6,5,1,7,2]=>1100110=>0011001
[7,3,4,5,6,8,1,2]=>[8,6,5,4,3,1,7,2]=>1111110=>0000001
[6,5,4,3,7,8,1,2]=>[4,3,8,5,1,7,6,2]=>1110110=>0001001
[5,6,4,3,7,8,1,2]=>[4,3,8,1,7,6,5,2]=>1110110=>0001001
[4,5,6,3,7,8,1,2]=>[8,3,7,6,5,1,4,2]=>1110110=>0001001
[6,4,3,5,7,8,1,2]=>[3,8,5,4,1,7,6,2]=>1101110=>0010001
[6,3,4,5,7,8,1,2]=>[8,5,4,3,1,7,6,2]=>1111110=>0000001
[5,4,3,6,7,8,1,2]=>[3,8,4,1,7,6,5,2]=>1101110=>0010001
[4,5,3,6,7,8,1,2]=>[3,8,1,7,6,5,4,2]=>1101110=>0010001
[5,3,4,6,7,8,1,2]=>[8,4,3,1,7,6,5,2]=>1111110=>0000001
[4,3,5,6,7,8,1,2]=>[8,3,1,7,6,5,4,2]=>1111110=>0000001
[3,4,5,6,7,8,1,2]=>[8,1,7,6,5,4,3,2]=>1111110=>0000001
[8,7,6,5,4,2,1,3]=>[5,4,6,2,7,1,8,3]=>1111000=>0000111
[7,8,6,5,4,2,1,3]=>[5,4,6,2,8,1,7,3]=>1111000=>0000111
[8,6,7,5,4,2,1,3]=>[5,4,7,2,6,1,8,3]=>1111000=>0000111
[7,6,8,5,4,2,1,3]=>[5,4,8,2,6,1,7,3]=>1111000=>0000111
[6,7,8,5,4,2,1,3]=>[5,4,8,2,7,1,6,3]=>1111000=>0000111
[8,7,5,6,4,2,1,3]=>[6,4,5,2,7,1,8,3]=>1111000=>0000111
[8,6,5,7,4,2,1,3]=>[7,4,5,2,6,1,8,3]=>1111000=>0000111
[7,6,5,8,4,2,1,3]=>[8,4,5,2,6,1,7,3]=>1111000=>0000111
[7,5,6,8,4,2,1,3]=>[8,4,6,2,5,1,7,3]=>1111000=>0000111
[6,5,7,8,4,2,1,3]=>[8,4,7,2,5,1,6,3]=>1111000=>0000111
[5,6,7,8,4,2,1,3]=>[8,4,7,2,6,1,5,3]=>1111000=>0000111
[8,7,6,4,5,2,1,3]=>[4,5,6,2,7,1,8,3]=>1110000=>0001111
[8,6,4,5,7,2,1,3]=>[7,5,4,2,6,1,8,3]=>1111100=>0000011
[8,4,5,6,7,2,1,3]=>[7,2,6,5,4,1,8,3]=>1111100=>0000011
[7,6,5,4,8,2,1,3]=>[4,8,5,2,6,1,7,3]=>1110100=>0001011
[6,7,5,4,8,2,1,3]=>[4,8,5,2,7,1,6,3]=>1110100=>0001011
[7,5,6,4,8,2,1,3]=>[4,8,2,6,5,1,7,3]=>1110100=>0001011
[6,5,7,4,8,2,1,3]=>[4,8,2,7,5,1,6,3]=>1110100=>0001011
[5,6,7,4,8,2,1,3]=>[4,8,2,7,1,6,5,3]=>1110100=>0001011
[7,6,4,5,8,2,1,3]=>[8,5,4,2,6,1,7,3]=>1111100=>0000011
[5,4,6,7,8,2,1,3]=>[8,2,7,4,1,6,5,3]=>1111100=>0000011
[4,5,6,7,8,2,1,3]=>[8,2,7,1,6,5,4,3]=>1111100=>0000011
[8,7,6,5,4,1,2,3]=>[5,4,6,1,7,2,8,3]=>1111000=>0000111
[7,6,8,5,4,1,2,3]=>[5,4,8,1,6,2,7,3]=>1111000=>0000111
[6,7,8,5,4,1,2,3]=>[5,4,8,1,7,2,6,3]=>1111000=>0000111
[7,8,5,6,4,1,2,3]=>[6,4,5,1,8,2,7,3]=>1111000=>0000111
[8,6,5,7,4,1,2,3]=>[7,4,5,1,6,2,8,3]=>1111000=>0000111
[7,6,5,8,4,1,2,3]=>[8,4,5,1,6,2,7,3]=>1111000=>0000111
[6,7,5,8,4,1,2,3]=>[8,4,5,1,7,2,6,3]=>1111000=>0000111
[6,5,7,8,4,1,2,3]=>[8,4,7,1,5,2,6,3]=>1111000=>0000111
[5,6,7,8,4,1,2,3]=>[8,4,7,1,6,2,5,3]=>1111000=>0000111
[8,7,6,4,5,1,2,3]=>[4,5,6,1,7,2,8,3]=>1110000=>0001111
[6,7,8,4,5,1,2,3]=>[4,5,8,1,7,2,6,3]=>1110000=>0001111
[8,7,4,5,6,1,2,3]=>[6,5,4,1,7,2,8,3]=>1111100=>0000011
[7,8,4,5,6,1,2,3]=>[6,5,4,1,8,2,7,3]=>1111100=>0000011
[8,6,5,4,7,1,2,3]=>[4,7,5,1,6,2,8,3]=>1110100=>0001011
[8,5,6,4,7,1,2,3]=>[4,7,1,6,5,2,8,3]=>1110100=>0001011
[8,6,4,5,7,1,2,3]=>[7,5,4,1,6,2,8,3]=>1111100=>0000011
[8,5,4,6,7,1,2,3]=>[7,4,1,6,5,2,8,3]=>1111100=>0000011
[8,4,5,6,7,1,2,3]=>[7,1,6,5,4,2,8,3]=>1111100=>0000011
[6,7,5,4,8,1,2,3]=>[4,8,5,1,7,2,6,3]=>1110100=>0001011
[7,5,6,4,8,1,2,3]=>[4,8,1,6,5,2,7,3]=>1110100=>0001011
[6,5,7,4,8,1,2,3]=>[4,8,1,7,5,2,6,3]=>1110100=>0001011
[5,6,7,4,8,1,2,3]=>[4,8,1,7,2,6,5,3]=>1110100=>0001011
[7,6,4,5,8,1,2,3]=>[8,5,4,1,6,2,7,3]=>1111100=>0000011
[6,7,4,5,8,1,2,3]=>[8,5,4,1,7,2,6,3]=>1111100=>0000011
[7,5,4,6,8,1,2,3]=>[8,4,1,6,5,2,7,3]=>1111100=>0000011
[6,5,4,7,8,1,2,3]=>[8,4,1,7,5,2,6,3]=>1111100=>0000011
[5,6,4,7,8,1,2,3]=>[8,4,1,7,2,6,5,3]=>1111100=>0000011
[6,4,5,7,8,1,2,3]=>[8,1,7,5,4,2,6,3]=>1111100=>0000011
[5,4,6,7,8,1,2,3]=>[8,1,7,4,2,6,5,3]=>1111100=>0000011
[4,5,6,7,8,1,2,3]=>[8,1,7,2,6,5,4,3]=>1111100=>0000011
[8,7,6,5,3,2,1,4]=>[5,3,6,2,7,1,8,4]=>1111000=>0000111
[7,8,6,5,3,2,1,4]=>[5,3,6,2,8,1,7,4]=>1111000=>0000111
[8,6,7,5,3,2,1,4]=>[5,3,7,2,6,1,8,4]=>1111000=>0000111
[7,6,8,5,3,2,1,4]=>[5,3,8,2,6,1,7,4]=>1111000=>0000111
[6,7,8,5,3,2,1,4]=>[5,3,8,2,7,1,6,4]=>1111000=>0000111
[8,7,5,6,3,2,1,4]=>[6,3,5,2,7,1,8,4]=>1111000=>0000111
[7,8,5,6,3,2,1,4]=>[6,3,5,2,8,1,7,4]=>1111000=>0000111
[8,6,5,7,3,2,1,4]=>[7,3,5,2,6,1,8,4]=>1111000=>0000111
[8,5,6,7,3,2,1,4]=>[7,3,6,2,5,1,8,4]=>1111000=>0000111
[7,6,5,8,3,2,1,4]=>[8,3,5,2,6,1,7,4]=>1111000=>0000111
[6,7,5,8,3,2,1,4]=>[8,3,5,2,7,1,6,4]=>1111000=>0000111
[6,5,7,8,3,2,1,4]=>[8,3,7,2,5,1,6,4]=>1111000=>0000111
[5,6,7,8,3,2,1,4]=>[8,3,7,2,6,1,5,4]=>1111000=>0000111
[8,7,6,5,2,3,1,4]=>[5,2,6,3,7,1,8,4]=>1111000=>0000111
[7,8,6,5,2,3,1,4]=>[5,2,6,3,8,1,7,4]=>1111000=>0000111
[6,7,8,5,2,3,1,4]=>[5,2,8,3,7,1,6,4]=>1111000=>0000111
[8,7,5,6,2,3,1,4]=>[6,2,5,3,7,1,8,4]=>1111000=>0000111
[8,5,6,7,2,3,1,4]=>[7,2,6,3,5,1,8,4]=>1111000=>0000111
[6,7,5,8,2,3,1,4]=>[8,2,5,3,7,1,6,4]=>1111000=>0000111
[7,5,6,8,2,3,1,4]=>[8,2,6,3,5,1,7,4]=>1111000=>0000111
[5,6,7,8,2,3,1,4]=>[8,2,7,3,6,1,5,4]=>1111000=>0000111
[8,7,6,5,3,1,2,4]=>[5,3,6,1,7,2,8,4]=>1111000=>0000111
[7,8,6,5,3,1,2,4]=>[5,3,6,1,8,2,7,4]=>1111000=>0000111
[8,6,7,5,3,1,2,4]=>[5,3,7,1,6,2,8,4]=>1111000=>0000111
[8,7,5,6,3,1,2,4]=>[6,3,5,1,7,2,8,4]=>1111000=>0000111
[7,8,5,6,3,1,2,4]=>[6,3,5,1,8,2,7,4]=>1111000=>0000111
[8,6,5,7,3,1,2,4]=>[7,3,5,1,6,2,8,4]=>1111000=>0000111
[6,7,5,8,3,1,2,4]=>[8,3,5,1,7,2,6,4]=>1111000=>0000111
[6,5,7,8,3,1,2,4]=>[8,3,7,1,5,2,6,4]=>1111000=>0000111
[5,6,7,8,3,1,2,4]=>[8,3,7,1,6,2,5,4]=>1111000=>0000111
[8,7,6,5,2,1,3,4]=>[5,2,6,1,7,3,8,4]=>1111000=>0000111
[7,8,6,5,2,1,3,4]=>[5,2,6,1,8,3,7,4]=>1111000=>0000111
[7,6,8,5,2,1,3,4]=>[5,2,8,1,6,3,7,4]=>1111000=>0000111
[6,7,8,5,2,1,3,4]=>[5,2,8,1,7,3,6,4]=>1111000=>0000111
[8,7,5,6,2,1,3,4]=>[6,2,5,1,7,3,8,4]=>1111000=>0000111
[7,8,5,6,2,1,3,4]=>[6,2,5,1,8,3,7,4]=>1111000=>0000111
[8,6,5,7,2,1,3,4]=>[7,2,5,1,6,3,8,4]=>1111000=>0000111
[8,5,6,7,2,1,3,4]=>[7,2,6,1,5,3,8,4]=>1111000=>0000111
[7,6,5,8,2,1,3,4]=>[8,2,5,1,6,3,7,4]=>1111000=>0000111
[7,5,6,8,2,1,3,4]=>[8,2,6,1,5,3,7,4]=>1111000=>0000111
[6,5,7,8,2,1,3,4]=>[8,2,7,1,5,3,6,4]=>1111000=>0000111
[5,6,7,8,2,1,3,4]=>[8,2,7,1,6,3,5,4]=>1111000=>0000111
[8,7,6,5,1,2,3,4]=>[5,1,6,2,7,3,8,4]=>1111000=>0000111
[7,8,6,5,1,2,3,4]=>[5,1,6,2,8,3,7,4]=>1111000=>0000111
[8,6,7,5,1,2,3,4]=>[5,1,7,2,6,3,8,4]=>1111000=>0000111
[7,6,8,5,1,2,3,4]=>[5,1,8,2,6,3,7,4]=>1111000=>0000111
[8,7,5,6,1,2,3,4]=>[6,1,5,2,7,3,8,4]=>1111000=>0000111
[7,8,5,6,1,2,3,4]=>[6,1,5,2,8,3,7,4]=>1111000=>0000111
[8,6,5,7,1,2,3,4]=>[7,1,5,2,6,3,8,4]=>1111000=>0000111
[7,6,5,8,1,2,3,4]=>[8,1,5,2,6,3,7,4]=>1111000=>0000111
[6,7,5,8,1,2,3,4]=>[8,1,5,2,7,3,6,4]=>1111000=>0000111
[7,5,6,8,1,2,3,4]=>[8,1,6,2,5,3,7,4]=>1111000=>0000111
[5,6,7,8,1,2,3,4]=>[8,1,7,2,6,3,5,4]=>1111000=>0000111
[8,7,6,4,3,2,1,5]=>[4,6,3,7,2,8,1,5]=>1110000=>0001111
[7,8,6,4,3,2,1,5]=>[4,6,3,8,2,7,1,5]=>1110000=>0001111
[8,6,7,4,3,2,1,5]=>[4,7,3,6,2,8,1,5]=>1110000=>0001111
[7,6,8,4,3,2,1,5]=>[4,8,3,6,2,7,1,5]=>1110000=>0001111
[6,7,8,4,3,2,1,5]=>[4,8,3,7,2,6,1,5]=>1110000=>0001111
[6,7,8,3,4,2,1,5]=>[8,3,4,7,2,6,1,5]=>1110000=>0001111
[8,7,6,4,2,3,1,5]=>[4,6,2,7,3,8,1,5]=>1110000=>0001111
[8,6,7,4,2,3,1,5]=>[4,7,2,6,3,8,1,5]=>1110000=>0001111
[7,6,8,4,2,3,1,5]=>[4,8,2,6,3,7,1,5]=>1110000=>0001111
[6,7,8,4,2,3,1,5]=>[4,8,2,7,3,6,1,5]=>1110000=>0001111
[8,7,6,3,2,4,1,5]=>[6,3,7,2,4,8,1,5]=>1110000=>0001111
[8,6,7,3,2,4,1,5]=>[7,3,6,2,4,8,1,5]=>1110000=>0001111
[6,7,8,3,2,4,1,5]=>[8,3,7,2,4,6,1,5]=>1110000=>0001111
[7,6,8,2,3,4,1,5]=>[8,2,6,3,4,7,1,5]=>1110000=>0001111
[6,7,8,2,3,4,1,5]=>[8,2,7,3,4,6,1,5]=>1110000=>0001111
[8,7,6,4,3,1,2,5]=>[4,6,3,7,1,8,2,5]=>1110000=>0001111
[6,7,8,4,3,1,2,5]=>[4,8,3,7,1,6,2,5]=>1110000=>0001111
[8,7,6,3,4,1,2,5]=>[6,3,4,7,1,8,2,5]=>1110000=>0001111
[7,8,6,3,4,1,2,5]=>[6,3,4,8,1,7,2,5]=>1110000=>0001111
[6,7,8,3,4,1,2,5]=>[8,3,4,7,1,6,2,5]=>1110000=>0001111
[8,7,6,4,2,1,3,5]=>[4,6,2,7,1,8,3,5]=>1110000=>0001111
[8,6,7,4,2,1,3,5]=>[4,7,2,6,1,8,3,5]=>1110000=>0001111
[6,7,8,4,2,1,3,5]=>[4,8,2,7,1,6,3,5]=>1110000=>0001111
[8,7,6,4,1,2,3,5]=>[4,6,1,7,2,8,3,5]=>1110000=>0001111
[7,6,8,4,1,2,3,5]=>[4,8,1,6,2,7,3,5]=>1110000=>0001111
[6,7,8,4,1,2,3,5]=>[4,8,1,7,2,6,3,5]=>1110000=>0001111
[8,7,6,3,2,1,4,5]=>[6,3,7,2,8,1,4,5]=>1110000=>0001111
[7,8,6,3,2,1,4,5]=>[6,3,8,2,7,1,4,5]=>1110000=>0001111
[6,7,8,3,2,1,4,5]=>[8,3,7,2,6,1,4,5]=>1110000=>0001111
[8,7,6,2,3,1,4,5]=>[6,2,7,3,8,1,4,5]=>1110000=>0001111
[7,8,6,2,3,1,4,5]=>[6,2,8,3,7,1,4,5]=>1110000=>0001111
[7,6,8,2,3,1,4,5]=>[8,2,6,3,7,1,4,5]=>1110000=>0001111
[6,7,8,2,3,1,4,5]=>[8,2,7,3,6,1,4,5]=>1110000=>0001111
[8,7,6,3,1,2,4,5]=>[6,3,7,1,8,2,4,5]=>1110000=>0001111
[7,8,6,3,1,2,4,5]=>[6,3,8,1,7,2,4,5]=>1110000=>0001111
[8,6,7,3,1,2,4,5]=>[7,3,6,1,8,2,4,5]=>1110000=>0001111
[7,6,8,3,1,2,4,5]=>[8,3,6,1,7,2,4,5]=>1110000=>0001111
[6,7,8,3,1,2,4,5]=>[8,3,7,1,6,2,4,5]=>1110000=>0001111
[8,7,6,2,1,3,4,5]=>[6,2,7,1,8,3,4,5]=>1110000=>0001111
[8,6,7,2,1,3,4,5]=>[7,2,6,1,8,3,4,5]=>1110000=>0001111
[6,7,8,2,1,3,4,5]=>[8,2,7,1,6,3,4,5]=>1110000=>0001111
[8,7,6,1,2,3,4,5]=>[6,1,7,2,8,3,4,5]=>1110000=>0001111
[7,8,6,1,2,3,4,5]=>[6,1,8,2,7,3,4,5]=>1110000=>0001111
[8,6,7,1,2,3,4,5]=>[7,1,6,2,8,3,4,5]=>1110000=>0001111
[6,7,8,1,2,3,4,5]=>[8,1,7,2,6,3,4,5]=>1110000=>0001111
[8,7,5,4,3,2,1,6]=>[4,5,3,7,2,8,1,6]=>1110000=>0001111
[7,8,5,4,3,2,1,6]=>[4,5,3,8,2,7,1,6]=>1110000=>0001111
[8,7,4,5,3,2,1,6]=>[5,4,3,7,2,8,1,6]=>1111000=>0000111
[7,8,4,5,3,2,1,6]=>[5,4,3,8,2,7,1,6]=>1111000=>0000111
[8,7,5,3,4,2,1,6]=>[5,3,4,7,2,8,1,6]=>1110000=>0001111
[8,7,4,3,5,2,1,6]=>[4,3,5,7,2,8,1,6]=>1110000=>0001111
[7,8,3,4,5,2,1,6]=>[3,4,5,8,2,7,1,6]=>1100000=>0011111
[8,7,4,5,2,3,1,6]=>[5,4,2,7,3,8,1,6]=>1111000=>0000111
[8,7,5,3,2,4,1,6]=>[5,3,7,2,4,8,1,6]=>1110000=>0001111
[8,7,4,3,2,5,1,6]=>[4,3,7,2,5,8,1,6]=>1110000=>0001111
[7,8,4,3,2,5,1,6]=>[4,3,8,2,5,7,1,6]=>1110000=>0001111
[8,7,3,4,2,5,1,6]=>[3,4,7,2,5,8,1,6]=>1100000=>0011111
[8,7,2,3,4,5,1,6]=>[7,2,3,4,5,8,1,6]=>1100000=>0011111
[7,8,2,3,4,5,1,6]=>[8,2,3,4,5,7,1,6]=>1100000=>0011111
[8,7,5,4,3,1,2,6]=>[4,5,3,7,1,8,2,6]=>1110000=>0001111
[7,8,5,4,3,1,2,6]=>[4,5,3,8,1,7,2,6]=>1110000=>0001111
[7,8,5,3,4,1,2,6]=>[5,3,4,8,1,7,2,6]=>1110000=>0001111
[8,7,3,4,5,1,2,6]=>[3,4,5,7,1,8,2,6]=>1100000=>0011111
[7,8,3,4,5,1,2,6]=>[3,4,5,8,1,7,2,6]=>1100000=>0011111
[8,7,5,4,1,2,3,6]=>[4,5,1,7,2,8,3,6]=>1110000=>0001111
[7,8,5,4,1,2,3,6]=>[4,5,1,8,2,7,3,6]=>1110000=>0001111
[8,7,5,3,2,1,4,6]=>[5,3,7,2,8,1,4,6]=>1110000=>0001111
[7,8,5,3,2,1,4,6]=>[5,3,8,2,7,1,4,6]=>1110000=>0001111
[8,7,5,3,1,2,4,6]=>[5,3,7,1,8,2,4,6]=>1110000=>0001111
[7,8,5,3,1,2,4,6]=>[5,3,8,1,7,2,4,6]=>1110000=>0001111
[8,7,5,2,1,3,4,6]=>[5,2,7,1,8,3,4,6]=>1110000=>0001111
[7,8,5,2,1,3,4,6]=>[5,2,8,1,7,3,4,6]=>1110000=>0001111
[8,7,5,1,2,3,4,6]=>[5,1,7,2,8,3,4,6]=>1110000=>0001111
[7,8,5,1,2,3,4,6]=>[5,1,8,2,7,3,4,6]=>1110000=>0001111
[8,7,4,3,2,1,5,6]=>[4,3,7,2,8,1,5,6]=>1110000=>0001111
[7,8,4,3,2,1,5,6]=>[4,3,8,2,7,1,5,6]=>1110000=>0001111
[8,7,3,4,2,1,5,6]=>[3,4,7,2,8,1,5,6]=>1100000=>0011111
[7,8,3,4,2,1,5,6]=>[3,4,8,2,7,1,5,6]=>1100000=>0011111
[7,8,4,2,3,1,5,6]=>[4,2,8,3,7,1,5,6]=>1110000=>0001111
[8,7,3,2,4,1,5,6]=>[3,7,2,4,8,1,5,6]=>1100000=>0011111
[7,8,3,2,4,1,5,6]=>[3,8,2,4,7,1,5,6]=>1100000=>0011111
[8,7,2,3,4,1,5,6]=>[7,2,3,4,8,1,5,6]=>1100000=>0011111
[7,8,2,3,4,1,5,6]=>[8,2,3,4,7,1,5,6]=>1100000=>0011111
[7,8,4,3,1,2,5,6]=>[4,3,8,1,7,2,5,6]=>1110000=>0001111
[8,7,3,4,1,2,5,6]=>[3,4,7,1,8,2,5,6]=>1100000=>0011111
[7,8,3,4,1,2,5,6]=>[3,4,8,1,7,2,5,6]=>1100000=>0011111
[8,7,4,2,1,3,5,6]=>[4,2,7,1,8,3,5,6]=>1110000=>0001111
[7,8,4,2,1,3,5,6]=>[4,2,8,1,7,3,5,6]=>1110000=>0001111
[8,7,4,1,2,3,5,6]=>[4,1,7,2,8,3,5,6]=>1110000=>0001111
[7,8,4,1,2,3,5,6]=>[4,1,8,2,7,3,5,6]=>1110000=>0001111
[8,7,3,2,1,4,5,6]=>[3,7,2,8,1,4,5,6]=>1100000=>0011111
[7,8,3,2,1,4,5,6]=>[3,8,2,7,1,4,5,6]=>1100000=>0011111
[7,8,2,3,1,4,5,6]=>[8,2,3,7,1,4,5,6]=>1100000=>0011111
[7,8,3,1,2,4,5,6]=>[3,8,1,7,2,4,5,6]=>1100000=>0011111
[8,7,2,1,3,4,5,6]=>[7,2,8,1,3,4,5,6]=>1100000=>0011111
[8,7,1,2,3,4,5,6]=>[7,1,8,2,3,4,5,6]=>1100000=>0011111
[7,8,1,2,3,4,5,6]=>[8,1,7,2,3,4,5,6]=>1100000=>0011111
[8,6,5,4,3,2,1,7]=>[4,5,3,6,2,8,1,7]=>1110000=>0001111
[8,5,6,4,3,2,1,7]=>[4,6,3,5,2,8,1,7]=>1110000=>0001111
[8,5,4,6,3,2,1,7]=>[6,4,3,5,2,8,1,7]=>1111000=>0000111
[8,4,5,6,3,2,1,7]=>[6,3,5,4,2,8,1,7]=>1111000=>0000111
[8,6,5,3,4,2,1,7]=>[5,3,4,6,2,8,1,7]=>1110000=>0001111
[8,6,4,3,5,2,1,7]=>[4,3,5,6,2,8,1,7]=>1110000=>0001111
[8,4,5,3,6,2,1,7]=>[6,5,3,4,2,8,1,7]=>1110100=>0001011
[8,4,3,5,6,2,1,7]=>[3,6,5,4,2,8,1,7]=>1101100=>0010011
[8,3,4,5,6,2,1,7]=>[6,5,4,3,2,8,1,7]=>1111100=>0000011
[8,6,5,4,2,3,1,7]=>[4,5,2,6,3,8,1,7]=>1110000=>0001111
[8,5,6,4,2,3,1,7]=>[4,6,2,5,3,8,1,7]=>1110000=>0001111
[8,6,5,3,2,4,1,7]=>[5,3,6,2,4,8,1,7]=>1110000=>0001111
[8,5,6,2,3,4,1,7]=>[6,2,5,3,4,8,1,7]=>1110000=>0001111
[8,6,4,3,2,5,1,7]=>[4,3,6,2,5,8,1,7]=>1110000=>0001111
[8,6,4,2,3,5,1,7]=>[4,2,6,3,5,8,1,7]=>1110000=>0001111
[8,5,4,3,2,6,1,7]=>[4,3,5,2,6,8,1,7]=>1110000=>0001111
[8,4,3,5,2,6,1,7]=>[3,5,4,2,6,8,1,7]=>1101000=>0010111
[8,4,5,2,3,6,1,7]=>[5,2,4,3,6,8,1,7]=>1110000=>0001111
[8,5,3,2,4,6,1,7]=>[3,5,2,4,6,8,1,7]=>1100000=>0011111
[8,5,2,3,4,6,1,7]=>[5,2,3,4,6,8,1,7]=>1100000=>0011111
[8,3,4,2,5,6,1,7]=>[4,3,2,5,6,8,1,7]=>1110000=>0001111
[8,3,2,4,5,6,1,7]=>[3,2,4,5,6,8,1,7]=>1100000=>0011111
[8,2,3,4,5,6,1,7]=>[2,3,4,5,6,8,1,7]=>1000000=>0111111
[8,6,5,4,3,1,2,7]=>[4,5,3,6,1,8,2,7]=>1110000=>0001111
[8,5,6,3,4,1,2,7]=>[6,3,4,5,1,8,2,7]=>1110000=>0001111
[8,6,3,4,5,1,2,7]=>[3,4,5,6,1,8,2,7]=>1100000=>0011111
[8,5,4,3,6,1,2,7]=>[4,3,6,5,1,8,2,7]=>1110100=>0001011
[8,4,5,3,6,1,2,7]=>[6,5,3,4,1,8,2,7]=>1110100=>0001011
[8,5,3,4,6,1,2,7]=>[3,4,6,5,1,8,2,7]=>1100100=>0011011
[8,3,4,5,6,1,2,7]=>[6,5,4,3,1,8,2,7]=>1111100=>0000011
[8,6,5,4,2,1,3,7]=>[4,5,2,6,1,8,3,7]=>1110000=>0001111
[8,5,6,4,2,1,3,7]=>[4,6,2,5,1,8,3,7]=>1110000=>0001111
[8,6,4,5,2,1,3,7]=>[5,4,2,6,1,8,3,7]=>1111000=>0000111
[8,4,5,6,2,1,3,7]=>[6,2,5,4,1,8,3,7]=>1111000=>0000111
[8,6,5,4,1,2,3,7]=>[4,5,1,6,2,8,3,7]=>1110000=>0001111
[8,6,4,5,1,2,3,7]=>[5,4,1,6,2,8,3,7]=>1111000=>0000111
[8,6,5,3,2,1,4,7]=>[5,3,6,2,8,1,4,7]=>1110000=>0001111
[8,5,6,3,2,1,4,7]=>[6,3,5,2,8,1,4,7]=>1110000=>0001111
[8,6,5,2,3,1,4,7]=>[5,2,6,3,8,1,4,7]=>1110000=>0001111
[8,5,6,3,1,2,4,7]=>[6,3,5,1,8,2,4,7]=>1110000=>0001111
[8,6,5,2,1,3,4,7]=>[5,2,6,1,8,3,4,7]=>1110000=>0001111
[8,5,6,2,1,3,4,7]=>[6,2,5,1,8,3,4,7]=>1110000=>0001111
[8,6,5,1,2,3,4,7]=>[5,1,6,2,8,3,4,7]=>1110000=>0001111
[8,5,6,1,2,3,4,7]=>[6,1,5,2,8,3,4,7]=>1110000=>0001111
[8,6,4,3,2,1,5,7]=>[4,3,6,2,8,1,5,7]=>1110000=>0001111
[8,6,3,4,2,1,5,7]=>[3,4,6,2,8,1,5,7]=>1100000=>0011111
[8,6,4,2,3,1,5,7]=>[4,2,6,3,8,1,5,7]=>1110000=>0001111
[8,6,3,2,4,1,5,7]=>[3,6,2,4,8,1,5,7]=>1100000=>0011111
[8,6,2,3,4,1,5,7]=>[6,2,3,4,8,1,5,7]=>1100000=>0011111
[8,6,4,2,1,3,5,7]=>[4,2,6,1,8,3,5,7]=>1110000=>0001111
[8,6,4,1,2,3,5,7]=>[4,1,6,2,8,3,5,7]=>1110000=>0001111
[8,6,1,2,3,4,5,7]=>[6,1,8,2,3,4,5,7]=>1100000=>0011111
[8,5,4,3,2,1,6,7]=>[4,3,5,2,8,1,6,7]=>1110000=>0001111
[8,4,3,5,2,1,6,7]=>[3,5,4,2,8,1,6,7]=>1101000=>0010111
[8,3,4,5,2,1,6,7]=>[5,4,3,2,8,1,6,7]=>1111000=>0000111
[8,4,5,2,3,1,6,7]=>[5,2,4,3,8,1,6,7]=>1110000=>0001111
[8,5,2,3,4,1,6,7]=>[5,2,3,4,8,1,6,7]=>1100000=>0011111
[8,4,2,3,5,1,6,7]=>[4,2,3,5,8,1,6,7]=>1100000=>0011111
[8,2,3,4,5,1,6,7]=>[2,3,4,5,8,1,6,7]=>1000000=>0111111
[8,5,4,2,1,3,6,7]=>[4,2,5,1,8,3,6,7]=>1110000=>0001111
[8,5,4,1,2,3,6,7]=>[4,1,5,2,8,3,6,7]=>1110000=>0001111
[8,4,5,1,2,3,6,7]=>[5,1,4,2,8,3,6,7]=>1110000=>0001111
[8,5,3,1,2,4,6,7]=>[3,5,1,8,2,4,6,7]=>1100000=>0011111
[8,5,2,1,3,4,6,7]=>[5,2,8,1,3,4,6,7]=>1100000=>0011111
[8,5,1,2,3,4,6,7]=>[5,1,8,2,3,4,6,7]=>1100000=>0011111
[8,4,3,2,1,5,6,7]=>[3,4,2,8,1,5,6,7]=>1100000=>0011111
[8,3,4,2,1,5,6,7]=>[4,3,2,8,1,5,6,7]=>1110000=>0001111
[8,4,2,3,1,5,6,7]=>[4,2,3,8,1,5,6,7]=>1100000=>0011111
[8,2,3,4,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>1000000=>0111111
[8,3,4,1,2,5,6,7]=>[4,3,1,8,2,5,6,7]=>1110000=>0001111
[8,4,2,1,3,5,6,7]=>[4,2,8,1,3,5,6,7]=>1100000=>0011111
[8,4,1,2,3,5,6,7]=>[4,1,8,2,3,5,6,7]=>1100000=>0011111
[8,3,2,1,4,5,6,7]=>[3,2,8,1,4,5,6,7]=>1100000=>0011111
[8,2,3,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>1000000=>0111111
[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>1100000=>0011111
[8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,7]=>1000000=>0111111
[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>1000000=>0111111
[7,6,5,4,3,2,1,8]=>[4,5,3,6,2,7,1,8]=>1110000=>0001111
[6,7,5,4,3,2,1,8]=>[4,5,3,7,2,6,1,8]=>1110000=>0001111
[7,5,6,4,3,2,1,8]=>[4,6,3,5,2,7,1,8]=>1110000=>0001111
[6,5,7,4,3,2,1,8]=>[4,7,3,5,2,6,1,8]=>1110000=>0001111
[5,6,7,4,3,2,1,8]=>[4,7,3,6,2,5,1,8]=>1110000=>0001111
[7,6,4,5,3,2,1,8]=>[5,4,3,6,2,7,1,8]=>1111000=>0000111
[6,7,4,5,3,2,1,8]=>[5,4,3,7,2,6,1,8]=>1111000=>0000111
[7,4,5,6,3,2,1,8]=>[6,3,5,4,2,7,1,8]=>1111000=>0000111
[6,5,4,7,3,2,1,8]=>[7,4,3,5,2,6,1,8]=>1111000=>0000111
[4,5,6,7,3,2,1,8]=>[7,3,6,2,5,4,1,8]=>1111000=>0000111
[7,6,5,3,4,2,1,8]=>[5,3,4,6,2,7,1,8]=>1110000=>0001111
[6,7,5,3,4,2,1,8]=>[5,3,4,7,2,6,1,8]=>1110000=>0001111
[7,5,6,3,4,2,1,8]=>[6,3,4,5,2,7,1,8]=>1110000=>0001111
[7,6,4,3,5,2,1,8]=>[4,3,5,6,2,7,1,8]=>1110000=>0001111
[6,7,4,3,5,2,1,8]=>[4,3,5,7,2,6,1,8]=>1110000=>0001111
[7,6,3,4,5,2,1,8]=>[3,4,5,6,2,7,1,8]=>1100000=>0011111
[7,3,4,5,6,2,1,8]=>[6,5,4,3,2,7,1,8]=>1111100=>0000011
[6,5,4,3,7,2,1,8]=>[4,3,7,5,2,6,1,8]=>1110100=>0001011
[5,6,4,3,7,2,1,8]=>[4,3,7,2,6,5,1,8]=>1110100=>0001011
[5,4,6,3,7,2,1,8]=>[7,3,4,2,6,5,1,8]=>1110100=>0001011
[3,4,5,6,7,2,1,8]=>[7,2,6,5,4,3,1,8]=>1111100=>0000011
[7,6,5,4,2,3,1,8]=>[4,5,2,6,3,7,1,8]=>1110000=>0001111
[6,7,5,4,2,3,1,8]=>[4,5,2,7,3,6,1,8]=>1110000=>0001111
[5,6,7,4,2,3,1,8]=>[4,7,2,6,3,5,1,8]=>1110000=>0001111
[7,6,4,5,2,3,1,8]=>[5,4,2,6,3,7,1,8]=>1111000=>0000111
[6,7,4,5,2,3,1,8]=>[5,4,2,7,3,6,1,8]=>1111000=>0000111
[7,5,4,6,2,3,1,8]=>[6,4,2,5,3,7,1,8]=>1111000=>0000111
[7,4,5,6,2,3,1,8]=>[6,2,5,4,3,7,1,8]=>1111000=>0000111
[6,5,4,7,2,3,1,8]=>[7,4,2,5,3,6,1,8]=>1111000=>0000111
[5,6,4,7,2,3,1,8]=>[7,4,2,6,3,5,1,8]=>1111000=>0000111
[7,6,5,3,2,4,1,8]=>[5,3,6,2,4,7,1,8]=>1110000=>0001111
[6,5,7,3,2,4,1,8]=>[7,3,5,2,4,6,1,8]=>1110000=>0001111
[7,6,5,2,3,4,1,8]=>[5,2,6,3,4,7,1,8]=>1110000=>0001111
[6,5,7,2,3,4,1,8]=>[7,2,5,3,4,6,1,8]=>1110000=>0001111
[5,6,7,2,3,4,1,8]=>[7,2,6,3,4,5,1,8]=>1110000=>0001111
[7,6,4,3,2,5,1,8]=>[4,3,6,2,5,7,1,8]=>1110000=>0001111
[6,7,4,3,2,5,1,8]=>[4,3,7,2,5,6,1,8]=>1110000=>0001111
[7,6,4,2,3,5,1,8]=>[4,2,6,3,5,7,1,8]=>1110000=>0001111
[7,6,3,2,4,5,1,8]=>[3,6,2,4,5,7,1,8]=>1100000=>0011111
[6,7,3,2,4,5,1,8]=>[3,7,2,4,5,6,1,8]=>1100000=>0011111
[7,6,2,3,4,5,1,8]=>[6,2,3,4,5,7,1,8]=>1100000=>0011111
[6,7,2,3,4,5,1,8]=>[7,2,3,4,5,6,1,8]=>1100000=>0011111
[7,5,3,4,2,6,1,8]=>[3,4,5,2,6,7,1,8]=>1100000=>0011111
[7,4,3,5,2,6,1,8]=>[3,5,4,2,6,7,1,8]=>1101000=>0010111
[7,4,5,2,3,6,1,8]=>[5,2,4,3,6,7,1,8]=>1110000=>0001111
[7,4,2,3,5,6,1,8]=>[4,2,3,5,6,7,1,8]=>1100000=>0011111
[7,2,3,4,5,6,1,8]=>[2,3,4,5,6,7,1,8]=>1000000=>0111111
[6,5,4,3,2,7,1,8]=>[4,3,5,2,7,6,1,8]=>1110010=>0001101
[6,3,4,5,2,7,1,8]=>[5,4,3,2,7,6,1,8]=>1111010=>0000101
[4,5,3,6,2,7,1,8]=>[3,7,6,2,5,4,1,8]=>1101010=>0010101
[5,3,4,6,2,7,1,8]=>[7,6,4,3,2,5,1,8]=>1111010=>0000101
[4,3,5,6,2,7,1,8]=>[7,6,3,2,5,4,1,8]=>1111010=>0000101
[3,4,5,6,2,7,1,8]=>[7,6,2,5,4,3,1,8]=>1111010=>0000101
[5,4,6,2,3,7,1,8]=>[7,6,2,4,3,5,1,8]=>1110010=>0001101
[6,5,3,2,4,7,1,8]=>[3,5,2,4,7,6,1,8]=>1100010=>0011101
[6,4,2,3,5,7,1,8]=>[4,2,3,5,7,6,1,8]=>1100010=>0011101
[6,2,3,4,5,7,1,8]=>[2,3,4,5,7,6,1,8]=>1000010=>0111101
[5,4,3,2,6,7,1,8]=>[3,4,2,7,6,5,1,8]=>1100110=>0011001
[4,5,2,3,6,7,1,8]=>[7,6,5,2,3,4,1,8]=>1100110=>0011001
[5,2,3,4,6,7,1,8]=>[2,3,4,7,6,5,1,8]=>1000110=>0111001
[4,3,2,5,6,7,1,8]=>[3,2,7,6,5,4,1,8]=>1101110=>0010001
[3,4,2,5,6,7,1,8]=>[7,6,5,4,2,3,1,8]=>1101110=>0010001
[4,2,3,5,6,7,1,8]=>[2,3,7,6,5,4,1,8]=>1001110=>0110001
[3,2,4,5,6,7,1,8]=>[2,7,6,5,4,3,1,8]=>1011110=>0100001
[2,3,4,5,6,7,1,8]=>[7,6,5,4,3,2,1,8]=>1111110=>0000001
[7,6,5,4,3,1,2,8]=>[4,5,3,6,1,7,2,8]=>1110000=>0001111
[6,7,5,4,3,1,2,8]=>[4,5,3,7,1,6,2,8]=>1110000=>0001111
[7,5,6,4,3,1,2,8]=>[4,6,3,5,1,7,2,8]=>1110000=>0001111
[7,6,4,5,3,1,2,8]=>[5,4,3,6,1,7,2,8]=>1111000=>0000111
[4,5,6,7,3,1,2,8]=>[7,3,6,1,5,4,2,8]=>1111000=>0000111
[6,5,4,3,7,1,2,8]=>[4,3,7,5,1,6,2,8]=>1110100=>0001011
[6,4,5,3,7,1,2,8]=>[7,5,3,4,1,6,2,8]=>1110100=>0001011
[4,3,5,6,7,1,2,8]=>[7,3,1,6,5,4,2,8]=>1111100=>0000011
[3,4,5,6,7,1,2,8]=>[7,1,6,5,4,3,2,8]=>1111100=>0000011
[7,6,5,4,2,1,3,8]=>[4,5,2,6,1,7,3,8]=>1110000=>0001111
[7,5,4,6,2,1,3,8]=>[6,4,2,5,1,7,3,8]=>1111000=>0000111
[5,4,6,7,2,1,3,8]=>[7,2,6,4,1,5,3,8]=>1111000=>0000111
[4,5,6,7,2,1,3,8]=>[7,2,6,1,5,4,3,8]=>1111000=>0000111
[7,6,5,4,1,2,3,8]=>[4,5,1,6,2,7,3,8]=>1110000=>0001111
[7,5,6,4,1,2,3,8]=>[4,6,1,5,2,7,3,8]=>1110000=>0001111
[5,6,7,4,1,2,3,8]=>[4,7,1,6,2,5,3,8]=>1110000=>0001111
[7,6,4,5,1,2,3,8]=>[5,4,1,6,2,7,3,8]=>1111000=>0000111
[7,5,4,6,1,2,3,8]=>[6,4,1,5,2,7,3,8]=>1111000=>0000111
[7,4,5,6,1,2,3,8]=>[6,1,5,4,2,7,3,8]=>1111000=>0000111
[5,6,4,7,1,2,3,8]=>[7,4,1,6,2,5,3,8]=>1111000=>0000111
[5,4,6,7,1,2,3,8]=>[7,1,6,4,2,5,3,8]=>1111000=>0000111
[4,5,6,7,1,2,3,8]=>[7,1,6,2,5,4,3,8]=>1111000=>0000111
[7,6,5,3,2,1,4,8]=>[5,3,6,2,7,1,4,8]=>1110000=>0001111
[5,6,7,2,3,1,4,8]=>[7,2,6,3,5,1,4,8]=>1110000=>0001111
[7,5,6,3,1,2,4,8]=>[6,3,5,1,7,2,4,8]=>1110000=>0001111
[5,6,7,3,1,2,4,8]=>[7,3,6,1,5,2,4,8]=>1110000=>0001111
[7,6,5,2,1,3,4,8]=>[5,2,6,1,7,3,4,8]=>1110000=>0001111
[6,7,5,2,1,3,4,8]=>[5,2,7,1,6,3,4,8]=>1110000=>0001111
[7,5,6,2,1,3,4,8]=>[6,2,5,1,7,3,4,8]=>1110000=>0001111
[5,6,7,2,1,3,4,8]=>[7,2,6,1,5,3,4,8]=>1110000=>0001111
[7,6,5,1,2,3,4,8]=>[5,1,6,2,7,3,4,8]=>1110000=>0001111
[6,7,5,1,2,3,4,8]=>[5,1,7,2,6,3,4,8]=>1110000=>0001111
[5,6,7,1,2,3,4,8]=>[7,1,6,2,5,3,4,8]=>1110000=>0001111
[6,7,4,3,2,1,5,8]=>[4,3,7,2,6,1,5,8]=>1110000=>0001111
[7,6,3,4,2,1,5,8]=>[3,4,6,2,7,1,5,8]=>1100000=>0011111
[7,6,4,2,3,1,5,8]=>[4,2,6,3,7,1,5,8]=>1110000=>0001111
[7,6,3,2,4,1,5,8]=>[3,6,2,4,7,1,5,8]=>1100000=>0011111
[7,6,4,3,1,2,5,8]=>[4,3,6,1,7,2,5,8]=>1110000=>0001111
[6,7,3,4,1,2,5,8]=>[3,4,7,1,6,2,5,8]=>1100000=>0011111
[7,6,4,2,1,3,5,8]=>[4,2,6,1,7,3,5,8]=>1110000=>0001111
[7,6,3,2,1,4,5,8]=>[3,6,2,7,1,4,5,8]=>1100000=>0011111
[6,7,3,2,1,4,5,8]=>[3,7,2,6,1,4,5,8]=>1100000=>0011111
[7,6,2,3,1,4,5,8]=>[6,2,3,7,1,4,5,8]=>1100000=>0011111
[7,6,1,2,3,4,5,8]=>[6,1,7,2,3,4,5,8]=>1100000=>0011111
[6,7,1,2,3,4,5,8]=>[7,1,6,2,3,4,5,8]=>1100000=>0011111
[7,5,4,3,2,1,6,8]=>[4,3,5,2,7,1,6,8]=>1110000=>0001111
[7,4,5,3,2,1,6,8]=>[5,3,4,2,7,1,6,8]=>1110000=>0001111
[7,4,3,5,2,1,6,8]=>[3,5,4,2,7,1,6,8]=>1101000=>0010111
[7,3,4,5,2,1,6,8]=>[5,4,3,2,7,1,6,8]=>1111000=>0000111
[7,5,4,2,3,1,6,8]=>[4,2,5,3,7,1,6,8]=>1110000=>0001111
[7,5,3,2,4,1,6,8]=>[3,5,2,4,7,1,6,8]=>1100000=>0011111
[7,5,2,3,4,1,6,8]=>[5,2,3,4,7,1,6,8]=>1100000=>0011111
[7,2,3,4,5,1,6,8]=>[2,3,4,5,7,1,6,8]=>1000000=>0111111
[7,5,3,4,1,2,6,8]=>[3,4,5,1,7,2,6,8]=>1100000=>0011111
[7,4,5,1,2,3,6,8]=>[5,1,4,2,7,3,6,8]=>1110000=>0001111
[7,5,3,2,1,4,6,8]=>[3,5,2,7,1,4,6,8]=>1100000=>0011111
[7,5,3,1,2,4,6,8]=>[3,5,1,7,2,4,6,8]=>1100000=>0011111
[7,5,1,2,3,4,6,8]=>[5,1,7,2,3,4,6,8]=>1100000=>0011111
[7,4,3,2,1,5,6,8]=>[3,4,2,7,1,5,6,8]=>1100000=>0011111
[7,2,3,4,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>1000000=>0111111
[7,4,1,2,3,5,6,8]=>[4,1,7,2,3,5,6,8]=>1100000=>0011111
[7,2,3,1,4,5,6,8]=>[2,3,7,1,4,5,6,8]=>1000000=>0111111
[7,3,1,2,4,5,6,8]=>[3,1,7,2,4,5,6,8]=>1100000=>0011111
[7,2,1,3,4,5,6,8]=>[2,7,1,3,4,5,6,8]=>1000000=>0111111
[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>1000000=>0111111
[6,5,4,3,2,1,7,8]=>[4,3,5,2,6,1,7,8]=>1110000=>0001111
[5,6,4,3,2,1,7,8]=>[4,3,6,2,5,1,7,8]=>1110000=>0001111
[4,5,6,3,2,1,7,8]=>[6,3,5,2,4,1,7,8]=>1110000=>0001111
[6,5,3,4,2,1,7,8]=>[3,4,5,2,6,1,7,8]=>1100000=>0011111
[5,6,3,4,2,1,7,8]=>[3,4,6,2,5,1,7,8]=>1100000=>0011111
[6,3,4,5,2,1,7,8]=>[5,4,3,2,6,1,7,8]=>1111000=>0000111
[5,4,3,6,2,1,7,8]=>[3,6,4,2,5,1,7,8]=>1101000=>0010111
[3,4,5,6,2,1,7,8]=>[6,2,5,4,3,1,7,8]=>1111000=>0000111
[6,5,2,3,4,1,7,8]=>[5,2,3,4,6,1,7,8]=>1100000=>0011111
[5,6,2,3,4,1,7,8]=>[6,2,3,4,5,1,7,8]=>1100000=>0011111
[6,4,3,2,5,1,7,8]=>[3,4,2,5,6,1,7,8]=>1100000=>0011111
[6,2,3,4,5,1,7,8]=>[2,3,4,5,6,1,7,8]=>1000000=>0111111
[4,5,3,2,6,1,7,8]=>[3,6,5,2,4,1,7,8]=>1100100=>0011011
[5,2,3,4,6,1,7,8]=>[2,3,4,6,5,1,7,8]=>1000100=>0111011
[4,2,3,5,6,1,7,8]=>[2,3,6,5,4,1,7,8]=>1001100=>0110011
[2,3,4,5,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100=>0000011
[6,5,4,3,1,2,7,8]=>[4,3,5,1,6,2,7,8]=>1110000=>0001111
[5,6,4,3,1,2,7,8]=>[4,3,6,1,5,2,7,8]=>1110000=>0001111
[6,4,5,3,1,2,7,8]=>[5,3,4,1,6,2,7,8]=>1110000=>0001111
[5,4,6,3,1,2,7,8]=>[6,3,4,1,5,2,7,8]=>1110000=>0001111
[5,6,3,4,1,2,7,8]=>[3,4,6,1,5,2,7,8]=>1100000=>0011111
[6,4,3,5,1,2,7,8]=>[3,5,4,1,6,2,7,8]=>1101000=>0010111
[5,4,3,6,1,2,7,8]=>[3,6,4,1,5,2,7,8]=>1101000=>0010111
[4,3,5,6,1,2,7,8]=>[6,3,1,5,4,2,7,8]=>1111000=>0000111
[6,5,4,2,1,3,7,8]=>[4,2,5,1,6,3,7,8]=>1110000=>0001111
[5,6,4,2,1,3,7,8]=>[4,2,6,1,5,3,7,8]=>1110000=>0001111
[5,4,6,2,1,3,7,8]=>[6,2,4,1,5,3,7,8]=>1110000=>0001111
[6,5,4,1,2,3,7,8]=>[4,1,5,2,6,3,7,8]=>1110000=>0001111
[6,5,3,2,1,4,7,8]=>[3,5,2,6,1,4,7,8]=>1100000=>0011111
[5,6,3,2,1,4,7,8]=>[3,6,2,5,1,4,7,8]=>1100000=>0011111
[6,5,1,2,3,4,7,8]=>[5,1,6,2,3,4,7,8]=>1100000=>0011111
[5,6,1,2,3,4,7,8]=>[6,1,5,2,3,4,7,8]=>1100000=>0011111
[6,3,4,2,1,5,7,8]=>[4,3,2,6,1,5,7,8]=>1110000=>0001111
[6,4,2,1,3,5,7,8]=>[4,2,6,1,3,5,7,8]=>1100000=>0011111
[6,4,1,2,3,5,7,8]=>[4,1,6,2,3,5,7,8]=>1100000=>0011111
[6,3,2,1,4,5,7,8]=>[3,2,6,1,4,5,7,8]=>1100000=>0011111
[6,2,3,1,4,5,7,8]=>[2,3,6,1,4,5,7,8]=>1000000=>0111111
[6,3,1,2,4,5,7,8]=>[3,1,6,2,4,5,7,8]=>1100000=>0011111
[6,2,1,3,4,5,7,8]=>[2,6,1,3,4,5,7,8]=>1000000=>0111111
[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>1000000=>0111111
[5,4,3,2,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>1100000=>0011111
[4,5,3,2,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>1100000=>0011111
[5,3,4,2,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>1110000=>0001111
[4,3,5,2,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>1110000=>0001111
[3,4,5,2,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>1110000=>0001111
[5,4,2,3,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>1100000=>0011111
[4,5,2,3,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>1100000=>0011111
[5,3,2,4,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>1100000=>0011111
[5,2,3,4,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>1000000=>0111111
[4,3,2,5,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>1101000=>0010111
[3,4,2,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>1101000=>0010111
[4,2,3,5,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>1001000=>0110111
[3,2,4,5,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>1011000=>0100111
[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000=>0000111
[5,4,3,1,2,6,7,8]=>[3,4,1,5,2,6,7,8]=>1100000=>0011111
[4,3,5,1,2,6,7,8]=>[5,3,1,4,2,6,7,8]=>1110000=>0001111
[3,4,5,1,2,6,7,8]=>[5,1,4,3,2,6,7,8]=>1110000=>0001111
[5,4,2,1,3,6,7,8]=>[4,2,5,1,3,6,7,8]=>1100000=>0011111
[4,5,2,1,3,6,7,8]=>[5,2,4,1,3,6,7,8]=>1100000=>0011111
[5,4,1,2,3,6,7,8]=>[4,1,5,2,3,6,7,8]=>1100000=>0011111
[4,5,1,2,3,6,7,8]=>[5,1,4,2,3,6,7,8]=>1100000=>0011111
[5,3,2,1,4,6,7,8]=>[3,2,5,1,4,6,7,8]=>1100000=>0011111
[5,2,3,1,4,6,7,8]=>[2,3,5,1,4,6,7,8]=>1000000=>0111111
[5,3,1,2,4,6,7,8]=>[3,1,5,2,4,6,7,8]=>1100000=>0011111
[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>1000000=>0111111
[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>1000000=>0111111
[4,3,2,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>1100000=>0011111
[3,4,2,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>1100000=>0011111
[4,2,3,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>1000000=>0111111
[3,2,4,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>1010000=>0101111
[2,3,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000=>0001111
[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>1100000=>0011111
[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>1100000=>0011111
[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>1000000=>0111111
[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>1000000=>0111111
[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>1000000=>0111111
[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000=>0011111
[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>1000000=>0111111
[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000=>0111111
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000=>1111111
[6,8,7,5,4,3,2,1]=>[5,4,7,3,8,2,6,1]=>1111000=>0000111
[5,8,7,6,4,3,2,1]=>[6,4,7,3,8,2,5,1]=>1111000=>0000111
[5,7,8,6,4,3,2,1]=>[6,4,8,3,7,2,5,1]=>1111000=>0000111
[6,5,8,7,4,3,2,1]=>[7,4,8,3,5,2,6,1]=>1111000=>0000111
[5,6,8,7,4,3,2,1]=>[7,4,8,3,6,2,5,1]=>1111000=>0000111
[5,7,6,8,4,3,2,1]=>[8,4,6,3,7,2,5,1]=>1111000=>0000111
[4,8,7,6,5,3,2,1]=>[5,6,3,7,2,8,4,1]=>1111000=>0000111
[4,7,8,6,5,3,2,1]=>[5,6,3,8,2,7,4,1]=>1111000=>0000111
[4,6,8,7,5,3,2,1]=>[5,7,3,8,2,6,4,1]=>1111000=>0000111
[4,6,7,8,5,3,2,1]=>[5,8,3,7,2,6,4,1]=>1111000=>0000111
[5,4,7,8,6,3,2,1]=>[6,3,8,4,2,7,5,1]=>1111100=>0000011
[4,5,8,7,6,3,2,1]=>[6,3,7,2,8,5,4,1]=>1111100=>0000011
[6,5,4,8,7,3,2,1]=>[7,4,3,8,5,2,6,1]=>1111100=>0000011
[5,6,4,8,7,3,2,1]=>[7,4,3,8,2,6,5,1]=>1111100=>0000011
[4,5,6,8,7,3,2,1]=>[7,3,8,2,6,5,4,1]=>1111100=>0000011
[4,7,6,5,8,3,2,1]=>[8,5,3,6,2,7,4,1]=>1111100=>0000011
[4,6,7,5,8,3,2,1]=>[8,5,3,7,2,6,4,1]=>1111100=>0000011
[4,5,7,6,8,3,2,1]=>[8,3,6,2,7,5,4,1]=>1111100=>0000011
[4,6,5,7,8,3,2,1]=>[8,3,7,5,2,6,4,1]=>1111100=>0000011
[3,8,7,6,5,4,2,1]=>[5,6,4,7,2,8,3,1]=>1111000=>0000111
[3,7,8,6,5,4,2,1]=>[5,6,4,8,2,7,3,1]=>1111000=>0000111
[3,6,8,7,5,4,2,1]=>[5,7,4,8,2,6,3,1]=>1111000=>0000111
[3,5,8,7,6,4,2,1]=>[6,4,7,2,8,5,3,1]=>1111100=>0000011
[3,5,7,8,6,4,2,1]=>[6,4,8,2,7,5,3,1]=>1111100=>0000011
[3,5,6,8,7,4,2,1]=>[7,4,8,2,6,5,3,1]=>1111100=>0000011
[3,6,7,5,8,4,2,1]=>[8,5,4,7,2,6,3,1]=>1111100=>0000011
[3,5,7,6,8,4,2,1]=>[8,4,6,2,7,5,3,1]=>1111100=>0000011
[3,5,6,7,8,4,2,1]=>[8,4,7,2,6,5,3,1]=>1111100=>0000011
[3,4,8,7,6,5,2,1]=>[6,5,7,2,8,4,3,1]=>1111100=>0000011
[3,4,6,7,8,5,2,1]=>[8,5,7,2,6,4,3,1]=>1111100=>0000011
[5,4,3,8,7,6,2,1]=>[3,6,7,4,2,8,5,1]=>1101100=>0010011
[5,4,3,7,8,6,2,1]=>[3,6,8,4,2,7,5,1]=>1101100=>0010011
[3,5,4,7,8,6,2,1]=>[6,8,4,2,7,5,3,1]=>1111100=>0000011
[4,3,5,7,8,6,2,1]=>[6,8,3,2,7,5,4,1]=>1111100=>0000011
[3,4,5,7,8,6,2,1]=>[6,8,2,7,5,4,3,1]=>1111100=>0000011
[5,6,4,3,8,7,2,1]=>[4,3,7,2,8,6,5,1]=>1110110=>0001001
[3,6,5,4,8,7,2,1]=>[4,7,5,2,8,6,3,1]=>1110110=>0001001
[4,3,6,5,8,7,2,1]=>[7,5,3,2,8,6,4,1]=>1111110=>0000001
[5,4,3,6,8,7,2,1]=>[3,7,4,2,8,6,5,1]=>1101110=>0010001
[4,5,3,6,8,7,2,1]=>[3,7,2,8,6,5,4,1]=>1101110=>0010001
[4,3,5,6,8,7,2,1]=>[7,3,2,8,6,5,4,1]=>1111110=>0000001
[3,4,5,6,8,7,2,1]=>[7,2,8,6,5,4,3,1]=>1111110=>0000001
[4,7,6,5,3,8,2,1]=>[5,3,8,6,2,7,4,1]=>1111010=>0000101
[5,4,7,6,3,8,2,1]=>[8,6,3,7,4,2,5,1]=>1111010=>0000101
[3,7,6,5,4,8,2,1]=>[5,4,8,6,2,7,3,1]=>1111010=>0000101
[3,5,7,6,4,8,2,1]=>[8,6,4,7,2,5,3,1]=>1111010=>0000101
[3,5,6,7,4,8,2,1]=>[8,4,7,6,2,5,3,1]=>1111010=>0000101
[3,4,6,7,5,8,2,1]=>[5,8,2,7,6,4,3,1]=>1111010=>0000101
[4,5,3,7,6,8,2,1]=>[3,8,6,2,7,5,4,1]=>1101110=>0010001
[3,5,4,7,6,8,2,1]=>[8,6,4,2,7,5,3,1]=>1111110=>0000001
[4,3,5,7,6,8,2,1]=>[8,6,3,2,7,5,4,1]=>1111110=>0000001
[3,4,5,7,6,8,2,1]=>[8,6,2,7,5,4,3,1]=>1111110=>0000001
[3,6,5,4,7,8,2,1]=>[4,8,5,2,7,6,3,1]=>1110110=>0001001
[3,5,6,4,7,8,2,1]=>[4,8,2,7,6,5,3,1]=>1110110=>0001001
[4,3,6,5,7,8,2,1]=>[8,5,3,2,7,6,4,1]=>1111110=>0000001
[3,5,4,6,7,8,2,1]=>[8,4,2,7,6,5,3,1]=>1111110=>0000001
[2,7,8,6,5,4,3,1]=>[5,6,4,8,3,7,2,1]=>1111000=>0000111
[2,6,8,7,5,4,3,1]=>[5,7,4,8,3,6,2,1]=>1111000=>0000111
[2,6,7,8,5,4,3,1]=>[5,8,4,7,3,6,2,1]=>1111000=>0000111
[2,5,8,7,6,4,3,1]=>[6,4,7,3,8,5,2,1]=>1111100=>0000011
[2,6,7,5,8,4,3,1]=>[8,5,4,7,3,6,2,1]=>1111100=>0000011
[2,5,6,7,8,4,3,1]=>[8,4,7,3,6,5,2,1]=>1111100=>0000011
[2,4,8,7,6,5,3,1]=>[6,5,7,3,8,4,2,1]=>1111100=>0000011
[2,4,7,8,6,5,3,1]=>[6,5,8,3,7,4,2,1]=>1111100=>0000011
[2,4,6,8,7,5,3,1]=>[7,5,8,3,6,4,2,1]=>1111100=>0000011
[2,4,6,7,8,5,3,1]=>[8,5,7,3,6,4,2,1]=>1111100=>0000011
[2,5,4,8,7,6,3,1]=>[6,7,4,3,8,5,2,1]=>1111100=>0000011
[2,5,4,7,8,6,3,1]=>[6,8,4,3,7,5,2,1]=>1111100=>0000011
[2,5,6,4,8,7,3,1]=>[4,7,3,8,6,5,2,1]=>1110110=>0001001
[2,4,6,5,8,7,3,1]=>[7,5,3,8,6,4,2,1]=>1111110=>0000001
[2,4,5,6,8,7,3,1]=>[7,3,8,6,5,4,2,1]=>1111110=>0000001
[2,7,6,5,4,8,3,1]=>[5,4,8,6,3,7,2,1]=>1111010=>0000101
[2,5,6,7,4,8,3,1]=>[8,4,7,6,3,5,2,1]=>1111010=>0000101
[2,4,6,7,5,8,3,1]=>[5,8,3,7,6,4,2,1]=>1111010=>0000101
[2,5,4,7,6,8,3,1]=>[8,6,4,3,7,5,2,1]=>1111110=>0000001
[2,5,6,4,7,8,3,1]=>[4,8,3,7,6,5,2,1]=>1110110=>0001001
[2,4,6,5,7,8,3,1]=>[8,5,3,7,6,4,2,1]=>1111110=>0000001
[2,5,4,6,7,8,3,1]=>[8,4,3,7,6,5,2,1]=>1111110=>0000001
[2,4,5,6,7,8,3,1]=>[8,3,7,6,5,4,2,1]=>1111110=>0000001
[3,2,6,8,7,5,4,1]=>[2,7,5,8,4,6,3,1]=>1011100=>0100011
[3,2,5,7,8,6,4,1]=>[2,6,8,4,7,5,3,1]=>1011100=>0100011
[3,2,6,5,8,7,4,1]=>[2,7,5,4,8,6,3,1]=>1011110=>0100001
[3,2,6,7,5,8,4,1]=>[2,5,8,4,7,6,3,1]=>1011010=>0100101
[3,2,5,7,6,8,4,1]=>[2,8,6,4,7,5,3,1]=>1011110=>0100001
[3,2,5,6,7,8,4,1]=>[2,8,4,7,6,5,3,1]=>1011110=>0100001
[2,3,8,7,6,5,4,1]=>[6,5,7,4,8,3,2,1]=>1111100=>0000011
[2,3,6,7,8,5,4,1]=>[8,5,7,4,6,3,2,1]=>1111100=>0000011
[2,3,5,8,7,6,4,1]=>[6,7,4,8,5,3,2,1]=>1111100=>0000011
[2,3,5,7,8,6,4,1]=>[6,8,4,7,5,3,2,1]=>1111100=>0000011
[2,3,6,5,8,7,4,1]=>[7,5,4,8,6,3,2,1]=>1111110=>0000001
[2,3,5,6,8,7,4,1]=>[7,4,8,6,5,3,2,1]=>1111110=>0000001
[2,3,7,6,5,8,4,1]=>[5,8,6,4,7,3,2,1]=>1111010=>0000101
[2,3,5,7,6,8,4,1]=>[8,6,4,7,5,3,2,1]=>1111110=>0000001
[2,3,5,6,7,8,4,1]=>[8,4,7,6,5,3,2,1]=>1111110=>0000001
[4,3,2,7,8,6,5,1]=>[3,2,6,8,5,7,4,1]=>1101100=>0010011
[4,3,2,6,8,7,5,1]=>[3,2,7,5,8,6,4,1]=>1101110=>0010001
[3,4,2,8,7,6,5,1]=>[6,7,5,8,4,2,3,1]=>1101100=>0010011
[3,4,2,7,8,6,5,1]=>[6,8,5,7,4,2,3,1]=>1101100=>0010011
[2,4,3,8,7,6,5,1]=>[3,6,7,5,8,4,2,1]=>1101100=>0010011
[2,4,3,6,7,8,5,1]=>[3,8,5,7,6,4,2,1]=>1101110=>0010001
[3,2,4,8,7,6,5,1]=>[2,6,7,5,8,4,3,1]=>1011100=>0100011
[3,2,4,7,8,6,5,1]=>[2,6,8,5,7,4,3,1]=>1011100=>0100011
[2,3,4,8,7,6,5,1]=>[6,7,5,8,4,3,2,1]=>1111100=>0000011
[2,3,4,7,8,6,5,1]=>[6,8,5,7,4,3,2,1]=>1111100=>0000011
[2,3,4,6,8,7,5,1]=>[7,5,8,6,4,3,2,1]=>1111110=>0000001
[2,3,4,7,6,8,5,1]=>[8,6,5,7,4,3,2,1]=>1111110=>0000001
[2,3,4,6,7,8,5,1]=>[8,5,7,6,4,3,2,1]=>1111110=>0000001
[5,4,3,2,7,8,6,1]=>[3,4,2,8,6,7,5,1]=>1100110=>0011001
[4,5,3,2,8,7,6,1]=>[3,7,6,8,5,2,4,1]=>1100110=>0011001
[3,5,4,2,7,8,6,1]=>[4,2,8,6,7,5,3,1]=>1110110=>0001001
[4,3,5,2,8,7,6,1]=>[7,6,8,5,3,2,4,1]=>1110110=>0001001
[3,4,5,2,7,8,6,1]=>[8,6,7,5,2,4,3,1]=>1110110=>0001001
[2,4,5,3,8,7,6,1]=>[7,6,8,5,3,4,2,1]=>1110110=>0001001
[2,4,5,3,7,8,6,1]=>[8,6,7,5,3,4,2,1]=>1110110=>0001001
[3,2,5,4,7,8,6,1]=>[2,4,8,6,7,5,3,1]=>1010110=>0101001
[2,3,5,4,8,7,6,1]=>[4,7,6,8,5,3,2,1]=>1110110=>0001001
[2,3,5,4,7,8,6,1]=>[4,8,6,7,5,3,2,1]=>1110110=>0001001
[3,4,2,5,8,7,6,1]=>[7,6,8,5,4,2,3,1]=>1101110=>0010001
[3,4,2,5,7,8,6,1]=>[8,6,7,5,4,2,3,1]=>1101110=>0010001
[2,4,3,5,8,7,6,1]=>[3,7,6,8,5,4,2,1]=>1101110=>0010001
[3,2,4,5,7,8,6,1]=>[2,8,6,7,5,4,3,1]=>1011110=>0100001
[2,3,4,5,8,7,6,1]=>[7,6,8,5,4,3,2,1]=>1111110=>0000001
[2,3,4,5,7,8,6,1]=>[8,6,7,5,4,3,2,1]=>1111110=>0000001
[4,6,5,3,2,8,7,1]=>[5,3,7,8,6,2,4,1]=>1110010=>0001101
[5,4,6,3,2,8,7,1]=>[7,8,6,3,4,2,5,1]=>1110010=>0001101
[3,6,5,4,2,8,7,1]=>[4,5,2,7,8,6,3,1]=>1110010=>0001101
[4,3,6,5,2,8,7,1]=>[5,3,2,7,8,6,4,1]=>1111010=>0000101
[5,4,3,6,2,8,7,1]=>[3,7,8,6,4,2,5,1]=>1101010=>0010101
[3,5,4,6,2,8,7,1]=>[7,8,6,4,2,5,3,1]=>1111010=>0000101
[2,6,5,4,3,8,7,1]=>[4,5,3,7,8,6,2,1]=>1110010=>0001101
[2,4,5,6,3,8,7,1]=>[7,8,6,3,5,4,2,1]=>1111010=>0000101
[3,2,6,5,4,8,7,1]=>[2,5,4,7,8,6,3,1]=>1011010=>0100101
[2,3,5,6,4,8,7,1]=>[7,8,6,4,5,3,2,1]=>1111010=>0000101
[4,3,2,6,5,8,7,1]=>[3,2,5,7,8,6,4,1]=>1101010=>0010101
[3,4,2,6,5,8,7,1]=>[5,7,8,6,4,2,3,1]=>1101010=>0010101
[2,4,3,6,5,8,7,1]=>[3,5,7,8,6,4,2,1]=>1101010=>0010101
[2,3,4,6,5,8,7,1]=>[5,7,8,6,4,3,2,1]=>1111010=>0000101
[5,4,3,2,6,8,7,1]=>[3,4,2,7,8,6,5,1]=>1100110=>0011001
[4,5,3,2,6,8,7,1]=>[3,7,8,6,5,2,4,1]=>1100110=>0011001
[2,5,4,3,6,8,7,1]=>[4,3,7,8,6,5,2,1]=>1110110=>0001001
[2,4,5,3,6,8,7,1]=>[7,8,6,5,3,4,2,1]=>1110110=>0001001
[3,2,5,4,6,8,7,1]=>[2,4,7,8,6,5,3,1]=>1010110=>0101001
[3,4,2,5,6,8,7,1]=>[7,8,6,5,4,2,3,1]=>1101110=>0010001
[2,4,3,5,6,8,7,1]=>[3,7,8,6,5,4,2,1]=>1101110=>0010001
[3,2,4,5,6,8,7,1]=>[2,7,8,6,5,4,3,1]=>1011110=>0100001
[2,3,4,5,6,8,7,1]=>[7,8,6,5,4,3,2,1]=>1111110=>0000001
[5,7,6,4,3,2,8,1]=>[4,6,3,8,7,2,5,1]=>1110001=>0001110
[4,7,6,5,3,2,8,1]=>[5,3,6,2,8,7,4,1]=>1111001=>0000110
[4,6,7,5,3,2,8,1]=>[5,3,8,7,2,6,4,1]=>1111001=>0000110
[3,5,7,6,4,2,8,1]=>[6,4,8,7,2,5,3,1]=>1111001=>0000110
[3,5,6,7,4,2,8,1]=>[8,7,4,6,2,5,3,1]=>1111001=>0000110
[4,3,6,7,5,2,8,1]=>[5,8,7,3,2,6,4,1]=>1111001=>0000110
[3,4,7,6,5,2,8,1]=>[5,6,2,8,7,4,3,1]=>1111001=>0000110
[3,4,6,7,5,2,8,1]=>[5,8,7,2,6,4,3,1]=>1111001=>0000110
[5,4,3,7,6,2,8,1]=>[3,6,4,2,8,7,5,1]=>1101101=>0010010
[4,5,3,7,6,2,8,1]=>[3,6,2,8,7,5,4,1]=>1101101=>0010010
[3,5,4,7,6,2,8,1]=>[6,4,2,8,7,5,3,1]=>1111101=>0000010
[3,4,5,7,6,2,8,1]=>[6,2,8,7,5,4,3,1]=>1111101=>0000010
[4,6,5,3,7,2,8,1]=>[8,7,5,3,6,2,4,1]=>1110101=>0001010
[3,6,5,4,7,2,8,1]=>[4,8,7,5,2,6,3,1]=>1110101=>0001010
[3,5,6,4,7,2,8,1]=>[4,8,7,2,6,5,3,1]=>1110101=>0001010
[4,3,6,5,7,2,8,1]=>[8,7,5,3,2,6,4,1]=>1111101=>0000010
[3,4,6,5,7,2,8,1]=>[8,7,5,2,6,4,3,1]=>1111101=>0000010
[3,5,4,6,7,2,8,1]=>[8,7,4,2,6,5,3,1]=>1111101=>0000010
[2,6,5,7,4,3,8,1]=>[8,7,4,5,3,6,2,1]=>1111001=>0000110
[2,5,6,7,4,3,8,1]=>[8,7,4,6,3,5,2,1]=>1111001=>0000110
[2,4,6,7,5,3,8,1]=>[5,8,7,3,6,4,2,1]=>1111001=>0000110
[2,4,6,5,7,3,8,1]=>[8,7,5,3,6,4,2,1]=>1111101=>0000010
[2,5,4,6,7,3,8,1]=>[8,7,4,3,6,5,2,1]=>1111101=>0000010
[2,4,5,6,7,3,8,1]=>[8,7,3,6,5,4,2,1]=>1111101=>0000010
[3,2,7,6,5,4,8,1]=>[2,5,6,4,8,7,3,1]=>1011001=>0100110
[3,2,6,7,5,4,8,1]=>[2,5,8,7,4,6,3,1]=>1011001=>0100110
[3,2,5,7,6,4,8,1]=>[2,6,4,8,7,5,3,1]=>1011101=>0100010
[3,2,6,5,7,4,8,1]=>[2,8,7,5,4,6,3,1]=>1011101=>0100010
[3,2,5,6,7,4,8,1]=>[2,8,7,4,6,5,3,1]=>1011101=>0100010
[2,3,7,6,5,4,8,1]=>[5,6,4,8,7,3,2,1]=>1111001=>0000110
[2,3,5,7,6,4,8,1]=>[6,4,8,7,5,3,2,1]=>1111101=>0000010
[2,3,5,6,7,4,8,1]=>[8,7,4,6,5,3,2,1]=>1111101=>0000010
[4,3,2,7,6,5,8,1]=>[3,2,6,5,8,7,4,1]=>1101101=>0010010
[4,3,2,6,7,5,8,1]=>[3,2,8,7,5,6,4,1]=>1101101=>0010010
[3,4,2,7,6,5,8,1]=>[6,5,8,7,4,2,3,1]=>1101101=>0010010
[3,4,2,6,7,5,8,1]=>[8,7,5,6,4,2,3,1]=>1101101=>0010010
[2,4,3,6,7,5,8,1]=>[3,8,7,5,6,4,2,1]=>1101101=>0010010
[2,3,4,7,6,5,8,1]=>[6,5,8,7,4,3,2,1]=>1111101=>0000010
[2,3,4,6,7,5,8,1]=>[8,7,5,6,4,3,2,1]=>1111101=>0000010
[3,5,4,2,7,6,8,1]=>[4,2,6,8,7,5,3,1]=>1110101=>0001010
[4,3,5,2,7,6,8,1]=>[6,8,7,5,3,2,4,1]=>1110101=>0001010
[3,4,5,2,7,6,8,1]=>[6,8,7,5,2,4,3,1]=>1110101=>0001010
[3,2,5,4,7,6,8,1]=>[2,4,6,8,7,5,3,1]=>1010101=>0101010
[2,3,5,4,7,6,8,1]=>[4,6,8,7,5,3,2,1]=>1110101=>0001010
[4,3,2,5,7,6,8,1]=>[3,2,6,8,7,5,4,1]=>1101101=>0010010
[3,4,2,5,7,6,8,1]=>[6,8,7,5,4,2,3,1]=>1101101=>0010010
[2,4,3,5,7,6,8,1]=>[3,6,8,7,5,4,2,1]=>1101101=>0010010
[3,2,4,5,7,6,8,1]=>[2,6,8,7,5,4,3,1]=>1011101=>0100010
[2,3,4,5,7,6,8,1]=>[6,8,7,5,4,3,2,1]=>1111101=>0000010
[3,5,6,4,2,7,8,1]=>[4,8,7,6,2,5,3,1]=>1110011=>0001100
[3,4,6,5,2,7,8,1]=>[5,2,8,7,6,4,3,1]=>1111011=>0000100
[3,5,4,6,2,7,8,1]=>[8,7,6,4,2,5,3,1]=>1111011=>0000100
[2,5,6,4,3,7,8,1]=>[4,8,7,6,3,5,2,1]=>1110011=>0001100
[2,4,6,5,3,7,8,1]=>[5,3,8,7,6,4,2,1]=>1111011=>0000100
[2,5,4,6,3,7,8,1]=>[8,7,6,4,3,5,2,1]=>1111011=>0000100
[2,4,5,6,3,7,8,1]=>[8,7,6,3,5,4,2,1]=>1111011=>0000100
[3,2,5,6,4,7,8,1]=>[2,8,7,6,4,5,3,1]=>1011011=>0100100
[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]=>1111011=>0000100
[3,4,2,6,5,7,8,1]=>[5,8,7,6,4,2,3,1]=>1101011=>0010100
[2,4,3,6,5,7,8,1]=>[3,5,8,7,6,4,2,1]=>1101011=>0010100
[2,3,4,6,5,7,8,1]=>[5,8,7,6,4,3,2,1]=>1111011=>0000100
[3,5,4,2,6,7,8,1]=>[4,2,8,7,6,5,3,1]=>1110111=>0001000
[2,5,4,3,6,7,8,1]=>[4,3,8,7,6,5,2,1]=>1110111=>0001000
[2,4,5,3,6,7,8,1]=>[8,7,6,5,3,4,2,1]=>1110111=>0001000
[3,2,5,4,6,7,8,1]=>[2,4,8,7,6,5,3,1]=>1010111=>0101000
[2,3,5,4,6,7,8,1]=>[4,8,7,6,5,3,2,1]=>1110111=>0001000
[2,4,3,5,6,7,8,1]=>[3,8,7,6,5,4,2,1]=>1101111=>0010000
[1,8,7,6,5,4,3,2]=>[1,5,6,4,7,3,8,2]=>0111000=>1000111
[1,7,8,6,5,4,3,2]=>[1,5,6,4,8,3,7,2]=>0111000=>1000111
[1,6,8,7,5,4,3,2]=>[1,5,7,4,8,3,6,2]=>0111000=>1000111
[1,7,6,8,5,4,3,2]=>[1,5,8,4,6,3,7,2]=>0111000=>1000111
[1,6,7,8,5,4,3,2]=>[1,5,8,4,7,3,6,2]=>0111000=>1000111
[1,5,8,7,6,4,3,2]=>[1,6,4,7,3,8,5,2]=>0111100=>1000011
[1,7,6,5,8,4,3,2]=>[1,8,5,4,6,3,7,2]=>0111100=>1000011
[1,5,7,6,8,4,3,2]=>[1,8,4,6,3,7,5,2]=>0111100=>1000011
[1,5,6,7,8,4,3,2]=>[1,8,4,7,3,6,5,2]=>0111100=>1000011
[1,4,8,7,6,5,3,2]=>[1,6,5,7,3,8,4,2]=>0111100=>1000011
[1,4,7,8,6,5,3,2]=>[1,6,5,8,3,7,4,2]=>0111100=>1000011
[1,4,6,8,7,5,3,2]=>[1,7,5,8,3,6,4,2]=>0111100=>1000011
[1,4,6,7,8,5,3,2]=>[1,8,5,7,3,6,4,2]=>0111100=>1000011
[1,5,4,7,8,6,3,2]=>[1,6,8,4,3,7,5,2]=>0111100=>1000011
[1,4,5,8,7,6,3,2]=>[1,6,7,3,8,5,4,2]=>0111100=>1000011
[1,4,6,5,8,7,3,2]=>[1,7,5,3,8,6,4,2]=>0111110=>1000001
[1,7,6,5,4,8,3,2]=>[1,5,4,8,6,3,7,2]=>0111010=>1000101
[1,4,7,6,5,8,3,2]=>[1,5,8,6,3,7,4,2]=>0111010=>1000101
[1,4,6,7,5,8,3,2]=>[1,5,8,3,7,6,4,2]=>0111010=>1000101
[1,5,6,4,7,8,3,2]=>[1,4,8,3,7,6,5,2]=>0110110=>1001001
[1,4,5,6,7,8,3,2]=>[1,8,3,7,6,5,4,2]=>0111110=>1000001
[1,3,6,8,7,5,4,2]=>[1,7,5,8,4,6,3,2]=>0111100=>1000011
[1,3,6,7,8,5,4,2]=>[1,8,5,7,4,6,3,2]=>0111100=>1000011
[1,3,5,8,7,6,4,2]=>[1,6,7,4,8,5,3,2]=>0111100=>1000011
[1,3,5,7,8,6,4,2]=>[1,6,8,4,7,5,3,2]=>0111100=>1000011
[1,3,5,6,8,7,4,2]=>[1,7,4,8,6,5,3,2]=>0111110=>1000001
[1,3,6,7,5,8,4,2]=>[1,5,8,4,7,6,3,2]=>0111010=>1000101
[1,3,5,7,6,8,4,2]=>[1,8,6,4,7,5,3,2]=>0111110=>1000001
[1,3,6,5,7,8,4,2]=>[1,8,5,4,7,6,3,2]=>0111110=>1000001
[1,3,5,6,7,8,4,2]=>[1,8,4,7,6,5,3,2]=>0111110=>1000001
[1,4,3,6,8,7,5,2]=>[1,3,7,5,8,6,4,2]=>0101110=>1010001
[1,4,3,7,6,8,5,2]=>[1,3,8,6,5,7,4,2]=>0101110=>1010001
[1,4,3,6,7,8,5,2]=>[1,3,8,5,7,6,4,2]=>0101110=>1010001
[1,3,4,8,7,6,5,2]=>[1,6,7,5,8,4,3,2]=>0111100=>1000011
[1,3,4,6,7,8,5,2]=>[1,8,5,7,6,4,3,2]=>0111110=>1000001
[1,5,4,3,8,7,6,2]=>[1,4,3,7,6,8,5,2]=>0110110=>1001001
[1,4,5,3,7,8,6,2]=>[1,8,6,7,5,3,4,2]=>0110110=>1001001
[1,3,5,4,7,8,6,2]=>[1,4,8,6,7,5,3,2]=>0110110=>1001001
[1,3,4,5,8,7,6,2]=>[1,7,6,8,5,4,3,2]=>0111110=>1000001
[1,3,4,5,7,8,6,2]=>[1,8,6,7,5,4,3,2]=>0111110=>1000001
[1,5,6,4,3,8,7,2]=>[1,4,7,8,6,3,5,2]=>0110010=>1001101
[1,4,6,5,3,8,7,2]=>[1,5,3,7,8,6,4,2]=>0111010=>1000101
[1,4,5,6,3,8,7,2]=>[1,7,8,6,3,5,4,2]=>0111010=>1000101
[1,3,6,5,4,8,7,2]=>[1,5,4,7,8,6,3,2]=>0111010=>1000101
[1,4,3,6,5,8,7,2]=>[1,3,5,7,8,6,4,2]=>0101010=>1010101
[1,5,4,3,6,8,7,2]=>[1,4,3,7,8,6,5,2]=>0110110=>1001001
[1,4,5,3,6,8,7,2]=>[1,7,8,6,5,3,4,2]=>0110110=>1001001
[1,3,4,5,6,8,7,2]=>[1,7,8,6,5,4,3,2]=>0111110=>1000001
[1,6,7,5,4,3,8,2]=>[1,5,4,8,7,3,6,2]=>0111001=>1000110
[1,6,5,7,4,3,8,2]=>[1,8,7,4,5,3,6,2]=>0111001=>1000110
[1,5,6,7,4,3,8,2]=>[1,8,7,4,6,3,5,2]=>0111001=>1000110
[1,5,6,4,7,3,8,2]=>[1,4,8,7,3,6,5,2]=>0110101=>1001010
[1,4,6,5,7,3,8,2]=>[1,8,7,5,3,6,4,2]=>0111101=>1000010
[1,5,4,6,7,3,8,2]=>[1,8,7,4,3,6,5,2]=>0111101=>1000010
[1,4,5,6,7,3,8,2]=>[1,8,7,3,6,5,4,2]=>0111101=>1000010
[1,3,5,7,6,4,8,2]=>[1,6,4,8,7,5,3,2]=>0111101=>1000010
[1,3,6,5,7,4,8,2]=>[1,8,7,5,4,6,3,2]=>0111101=>1000010
[1,3,5,6,7,4,8,2]=>[1,8,7,4,6,5,3,2]=>0111101=>1000010
[1,4,3,6,7,5,8,2]=>[1,3,8,7,5,6,4,2]=>0101101=>1010010
[1,3,4,7,6,5,8,2]=>[1,6,5,8,7,4,3,2]=>0111101=>1000010
[1,3,4,6,7,5,8,2]=>[1,8,7,5,6,4,3,2]=>0111101=>1000010
[1,3,5,4,7,6,8,2]=>[1,4,6,8,7,5,3,2]=>0110101=>1001010
[1,3,4,5,7,6,8,2]=>[1,6,8,7,5,4,3,2]=>0111101=>1000010
[1,6,5,4,3,7,8,2]=>[1,4,5,3,8,7,6,2]=>0110011=>1001100
[1,5,4,6,3,7,8,2]=>[1,8,7,6,4,3,5,2]=>0111011=>1000100
[1,3,5,6,4,7,8,2]=>[1,8,7,6,4,5,3,2]=>0111011=>1000100
[1,4,3,6,5,7,8,2]=>[1,3,5,8,7,6,4,2]=>0101011=>1010100
[1,3,4,6,5,7,8,2]=>[1,5,8,7,6,4,3,2]=>0111011=>1000100
[1,5,4,3,6,7,8,2]=>[1,4,3,8,7,6,5,2]=>0110111=>1001000
[1,4,5,3,6,7,8,2]=>[1,8,7,6,5,3,4,2]=>0110111=>1001000
[1,3,5,4,6,7,8,2]=>[1,4,8,7,6,5,3,2]=>0110111=>1001000
[1,4,3,5,6,7,8,2]=>[1,3,8,7,6,5,4,2]=>0101111=>1010000
[1,3,4,5,6,7,8,2]=>[1,8,7,6,5,4,3,2]=>0111111=>1000000
[2,1,8,7,6,5,4,3]=>[2,1,6,5,7,4,8,3]=>1011100=>0100011
[2,1,7,8,6,5,4,3]=>[2,1,6,5,8,4,7,3]=>1011100=>0100011
[2,1,6,8,7,5,4,3]=>[2,1,7,5,8,4,6,3]=>1011100=>0100011
[2,1,6,7,8,5,4,3]=>[2,1,8,5,7,4,6,3]=>1011100=>0100011
[2,1,5,8,7,6,4,3]=>[2,1,6,7,4,8,5,3]=>1011100=>0100011
[2,1,5,7,8,6,4,3]=>[2,1,6,8,4,7,5,3]=>1011100=>0100011
[2,1,6,5,8,7,4,3]=>[2,1,7,5,4,8,6,3]=>1011110=>0100001
[2,1,7,6,5,8,4,3]=>[2,1,5,8,6,4,7,3]=>1011010=>0100101
[2,1,6,7,5,8,4,3]=>[2,1,5,8,4,7,6,3]=>1011010=>0100101
[2,1,5,7,6,8,4,3]=>[2,1,8,6,4,7,5,3]=>1011110=>0100001
[2,1,6,5,7,8,4,3]=>[2,1,8,5,4,7,6,3]=>1011110=>0100001
[2,1,5,6,7,8,4,3]=>[2,1,8,4,7,6,5,3]=>1011110=>0100001
[2,1,4,8,7,6,5,3]=>[2,1,6,7,5,8,4,3]=>1011100=>0100011
[2,1,4,7,8,6,5,3]=>[2,1,6,8,5,7,4,3]=>1011100=>0100011
[2,1,4,6,8,7,5,3]=>[2,1,7,5,8,6,4,3]=>1011110=>0100001
[2,1,4,7,6,8,5,3]=>[2,1,8,6,5,7,4,3]=>1011110=>0100001
[2,1,4,6,7,8,5,3]=>[2,1,8,5,7,6,4,3]=>1011110=>0100001
[2,1,5,4,8,7,6,3]=>[2,1,4,7,6,8,5,3]=>1010110=>0101001
[2,1,5,4,7,8,6,3]=>[2,1,4,8,6,7,5,3]=>1010110=>0101001
[2,1,4,5,8,7,6,3]=>[2,1,7,6,8,5,4,3]=>1011110=>0100001
[2,1,4,5,7,8,6,3]=>[2,1,8,6,7,5,4,3]=>1011110=>0100001
[2,1,6,5,4,8,7,3]=>[2,1,5,4,7,8,6,3]=>1011010=>0100101
[2,1,5,6,4,8,7,3]=>[2,1,7,8,6,4,5,3]=>1011010=>0100101
[2,1,4,6,5,8,7,3]=>[2,1,5,7,8,6,4,3]=>1011010=>0100101
[2,1,5,4,6,8,7,3]=>[2,1,4,7,8,6,5,3]=>1010110=>0101001
[2,1,4,5,6,8,7,3]=>[2,1,7,8,6,5,4,3]=>1011110=>0100001
[2,1,7,6,5,4,8,3]=>[2,1,5,6,4,8,7,3]=>1011001=>0100110
[2,1,6,7,5,4,8,3]=>[2,1,5,8,7,4,6,3]=>1011001=>0100110
[2,1,5,7,6,4,8,3]=>[2,1,6,4,8,7,5,3]=>1011101=>0100010
[2,1,6,5,7,4,8,3]=>[2,1,8,7,5,4,6,3]=>1011101=>0100010
[2,1,5,6,7,4,8,3]=>[2,1,8,7,4,6,5,3]=>1011101=>0100010
[2,1,4,7,6,5,8,3]=>[2,1,6,5,8,7,4,3]=>1011101=>0100010
[2,1,4,6,7,5,8,3]=>[2,1,8,7,5,6,4,3]=>1011101=>0100010
[2,1,5,4,7,6,8,3]=>[2,1,4,6,8,7,5,3]=>1010101=>0101010
[2,1,5,6,4,7,8,3]=>[2,1,8,7,6,4,5,3]=>1011011=>0100100
[2,1,5,4,6,7,8,3]=>[2,1,4,8,7,6,5,3]=>1010111=>0101000
[2,1,4,5,6,7,8,3]=>[2,1,8,7,6,5,4,3]=>1011111=>0100000
[1,2,7,6,8,5,4,3]=>[1,2,8,5,6,4,7,3]=>0011100=>1100011
[1,2,6,7,8,5,4,3]=>[1,2,8,5,7,4,6,3]=>0011100=>1100011
[1,2,5,8,7,6,4,3]=>[1,2,6,7,4,8,5,3]=>0011100=>1100011
[1,2,6,5,8,7,4,3]=>[1,2,7,5,4,8,6,3]=>0011110=>1100001
[1,2,5,6,8,7,4,3]=>[1,2,7,4,8,6,5,3]=>0011110=>1100001
[1,2,5,7,6,8,4,3]=>[1,2,8,6,4,7,5,3]=>0011110=>1100001
[1,2,6,5,7,8,4,3]=>[1,2,8,5,4,7,6,3]=>0011110=>1100001
[1,2,5,6,7,8,4,3]=>[1,2,8,4,7,6,5,3]=>0011110=>1100001
[1,2,4,7,8,6,5,3]=>[1,2,6,8,5,7,4,3]=>0011100=>1100011
[1,2,4,6,8,7,5,3]=>[1,2,7,5,8,6,4,3]=>0011110=>1100001
[1,2,4,7,6,8,5,3]=>[1,2,8,6,5,7,4,3]=>0011110=>1100001
[1,2,5,4,8,7,6,3]=>[1,2,4,7,6,8,5,3]=>0010110=>1101001
[1,2,4,5,8,7,6,3]=>[1,2,7,6,8,5,4,3]=>0011110=>1100001
[1,2,4,5,7,8,6,3]=>[1,2,8,6,7,5,4,3]=>0011110=>1100001
[1,2,6,5,4,8,7,3]=>[1,2,5,4,7,8,6,3]=>0011010=>1100101
[1,2,5,4,6,8,7,3]=>[1,2,4,7,8,6,5,3]=>0010110=>1101001
[1,2,4,5,6,8,7,3]=>[1,2,7,8,6,5,4,3]=>0011110=>1100001
[1,2,5,7,6,4,8,3]=>[1,2,6,4,8,7,5,3]=>0011101=>1100010
[1,2,5,6,7,4,8,3]=>[1,2,8,7,4,6,5,3]=>0011101=>1100010
[1,2,4,7,6,5,8,3]=>[1,2,6,5,8,7,4,3]=>0011101=>1100010
[1,2,5,4,7,6,8,3]=>[1,2,4,6,8,7,5,3]=>0010101=>1101010
[1,2,6,5,4,7,8,3]=>[1,2,5,4,8,7,6,3]=>0011011=>1100100
[1,2,4,6,5,7,8,3]=>[1,2,5,8,7,6,4,3]=>0011011=>1100100
[1,2,5,4,6,7,8,3]=>[1,2,4,8,7,6,5,3]=>0010111=>1101000
[1,2,4,5,6,7,8,3]=>[1,2,8,7,6,5,4,3]=>0011111=>1100000
[3,2,1,8,7,6,5,4]=>[2,3,1,6,7,5,8,4]=>1001100=>0110011
[3,2,1,7,8,6,5,4]=>[2,3,1,6,8,5,7,4]=>1001100=>0110011
[3,2,1,6,8,7,5,4]=>[2,3,1,7,5,8,6,4]=>1001110=>0110001
[3,2,1,5,8,7,6,4]=>[2,3,1,7,6,8,5,4]=>1001110=>0110001
[3,2,1,5,7,8,6,4]=>[2,3,1,8,6,7,5,4]=>1001110=>0110001
[3,2,1,5,6,8,7,4]=>[2,3,1,7,8,6,5,4]=>1001110=>0110001
[3,2,1,7,6,5,8,4]=>[2,3,1,6,5,8,7,4]=>1001101=>0110010
[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,5,6,4]=>1001101=>0110010
[3,2,1,5,7,6,8,4]=>[2,3,1,6,8,7,5,4]=>1001101=>0110010
[3,2,1,5,6,7,8,4]=>[2,3,1,8,7,6,5,4]=>1001111=>0110000
[2,3,1,8,7,6,5,4]=>[3,2,1,6,7,5,8,4]=>1101100=>0010011
[2,3,1,7,8,6,5,4]=>[3,2,1,6,8,5,7,4]=>1101100=>0010011
[2,3,1,6,8,7,5,4]=>[3,2,1,7,5,8,6,4]=>1101110=>0010001
[2,3,1,7,6,8,5,4]=>[3,2,1,8,6,5,7,4]=>1101110=>0010001
[2,3,1,6,7,8,5,4]=>[3,2,1,8,5,7,6,4]=>1101110=>0010001
[2,3,1,5,7,8,6,4]=>[3,2,1,8,6,7,5,4]=>1101110=>0010001
[2,3,1,6,5,8,7,4]=>[3,2,1,5,7,8,6,4]=>1101010=>0010101
[2,3,1,7,6,5,8,4]=>[3,2,1,6,5,8,7,4]=>1101101=>0010010
[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,5,6,4]=>1101101=>0010010
[2,3,1,5,7,6,8,4]=>[3,2,1,6,8,7,5,4]=>1101101=>0010010
[2,3,1,5,6,7,8,4]=>[3,2,1,8,7,6,5,4]=>1101111=>0010000
[1,3,2,8,7,6,5,4]=>[1,3,2,6,7,5,8,4]=>0101100=>1010011
[1,3,2,6,8,7,5,4]=>[1,3,2,7,5,8,6,4]=>0101110=>1010001
[1,3,2,7,6,8,5,4]=>[1,3,2,8,6,5,7,4]=>0101110=>1010001
[1,3,2,6,7,8,5,4]=>[1,3,2,8,5,7,6,4]=>0101110=>1010001
[1,3,2,5,8,7,6,4]=>[1,3,2,7,6,8,5,4]=>0101110=>1010001
[1,3,2,5,7,8,6,4]=>[1,3,2,8,6,7,5,4]=>0101110=>1010001
[1,3,2,6,5,8,7,4]=>[1,3,2,5,7,8,6,4]=>0101010=>1010101
[1,3,2,7,6,5,8,4]=>[1,3,2,6,5,8,7,4]=>0101101=>1010010
[1,3,2,5,7,6,8,4]=>[1,3,2,6,8,7,5,4]=>0101101=>1010010
[1,3,2,6,5,7,8,4]=>[1,3,2,5,8,7,6,4]=>0101011=>1010100
[1,3,2,5,6,7,8,4]=>[1,3,2,8,7,6,5,4]=>0101111=>1010000
[2,1,3,7,8,6,5,4]=>[2,1,3,6,8,5,7,4]=>1001100=>0110011
[2,1,3,6,7,8,5,4]=>[2,1,3,8,5,7,6,4]=>1001110=>0110001
[2,1,3,5,7,6,8,4]=>[2,1,3,6,8,7,5,4]=>1001101=>0110010
[2,1,3,5,6,7,8,4]=>[2,1,3,8,7,6,5,4]=>1001111=>0110000
[1,2,3,8,7,6,5,4]=>[1,2,3,6,7,5,8,4]=>0001100=>1110011
[1,2,3,7,8,6,5,4]=>[1,2,3,6,8,5,7,4]=>0001100=>1110011
[1,2,3,6,8,7,5,4]=>[1,2,3,7,5,8,6,4]=>0001110=>1110001
[1,2,3,7,6,8,5,4]=>[1,2,3,8,6,5,7,4]=>0001110=>1110001
[1,2,3,6,7,8,5,4]=>[1,2,3,8,5,7,6,4]=>0001110=>1110001
[1,2,3,5,8,7,6,4]=>[1,2,3,7,6,8,5,4]=>0001110=>1110001
[1,2,3,5,7,8,6,4]=>[1,2,3,8,6,7,5,4]=>0001110=>1110001
[1,2,3,6,5,8,7,4]=>[1,2,3,5,7,8,6,4]=>0001010=>1110101
[1,2,3,5,6,8,7,4]=>[1,2,3,7,8,6,5,4]=>0001110=>1110001
[1,2,3,7,6,5,8,4]=>[1,2,3,6,5,8,7,4]=>0001101=>1110010
[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,5,6,4]=>0001101=>1110010
[1,2,3,5,7,6,8,4]=>[1,2,3,6,8,7,5,4]=>0001101=>1110010
[1,2,3,6,5,7,8,4]=>[1,2,3,5,8,7,6,4]=>0001011=>1110100
[1,2,3,5,6,7,8,4]=>[1,2,3,8,7,6,5,4]=>0001111=>1110000
[4,3,2,1,8,7,6,5]=>[3,2,4,1,7,6,8,5]=>1100110=>0011001
[4,3,2,1,7,8,6,5]=>[3,2,4,1,8,6,7,5]=>1100110=>0011001
[4,3,2,1,6,8,7,5]=>[3,2,4,1,7,8,6,5]=>1100110=>0011001
[4,3,2,1,7,6,8,5]=>[3,2,4,1,6,8,7,5]=>1100101=>0011010
[4,3,2,1,6,7,8,5]=>[3,2,4,1,8,7,6,5]=>1100111=>0011000
[3,4,2,1,8,7,6,5]=>[4,2,3,1,7,6,8,5]=>1100110=>0011001
[3,4,2,1,7,8,6,5]=>[4,2,3,1,8,6,7,5]=>1100110=>0011001
[3,4,2,1,6,8,7,5]=>[4,2,3,1,7,8,6,5]=>1100110=>0011001
[3,4,2,1,7,6,8,5]=>[4,2,3,1,6,8,7,5]=>1100101=>0011010
[3,4,2,1,6,7,8,5]=>[4,2,3,1,8,7,6,5]=>1100111=>0011000
[2,4,3,1,8,7,6,5]=>[3,4,2,1,7,6,8,5]=>1100110=>0011001
[2,4,3,1,7,8,6,5]=>[3,4,2,1,8,6,7,5]=>1100110=>0011001
[2,4,3,1,6,8,7,5]=>[3,4,2,1,7,8,6,5]=>1100110=>0011001
[2,4,3,1,7,6,8,5]=>[3,4,2,1,6,8,7,5]=>1100101=>0011010
[2,4,3,1,6,7,8,5]=>[3,4,2,1,8,7,6,5]=>1100111=>0011000
[3,2,4,1,8,7,6,5]=>[2,4,3,1,7,6,8,5]=>1010110=>0101001
[3,2,4,1,7,8,6,5]=>[2,4,3,1,8,6,7,5]=>1010110=>0101001
[3,2,4,1,6,8,7,5]=>[2,4,3,1,7,8,6,5]=>1010110=>0101001
[3,2,4,1,7,6,8,5]=>[2,4,3,1,6,8,7,5]=>1010101=>0101010
[3,2,4,1,6,7,8,5]=>[2,4,3,1,8,7,6,5]=>1010111=>0101000
[2,3,4,1,8,7,6,5]=>[4,3,2,1,7,6,8,5]=>1110110=>0001001
[2,3,4,1,7,8,6,5]=>[4,3,2,1,8,6,7,5]=>1110110=>0001001
[2,3,4,1,6,8,7,5]=>[4,3,2,1,7,8,6,5]=>1110110=>0001001
[2,3,4,1,7,6,8,5]=>[4,3,2,1,6,8,7,5]=>1110101=>0001010
[2,3,4,1,6,7,8,5]=>[4,3,2,1,8,7,6,5]=>1110111=>0001000
[1,4,3,2,8,7,6,5]=>[1,3,4,2,7,6,8,5]=>0100110=>1011001
[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,8,6,5]=>0100110=>1011001
[1,4,3,2,7,6,8,5]=>[1,3,4,2,6,8,7,5]=>0100101=>1011010
[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,7,6,5]=>0100111=>1011000
[1,3,4,2,8,7,6,5]=>[1,4,3,2,7,6,8,5]=>0110110=>1001001
[1,3,4,2,7,8,6,5]=>[1,4,3,2,8,6,7,5]=>0110110=>1001001
[1,3,4,2,7,6,8,5]=>[1,4,3,2,6,8,7,5]=>0110101=>1001010
[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,7,6,5]=>0110111=>1001000
[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,6,8,5]=>1010110=>0101001
[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,6,7,5]=>1010110=>0101001
[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,8,6,5]=>1010110=>0101001
[2,1,4,3,7,6,8,5]=>[2,1,4,3,6,8,7,5]=>1010101=>0101010
[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,7,6,5]=>1010111=>0101000
[1,2,4,3,8,7,6,5]=>[1,2,4,3,7,6,8,5]=>0010110=>1101001
[1,2,4,3,7,8,6,5]=>[1,2,4,3,8,6,7,5]=>0010110=>1101001
[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,8,6,5]=>0010110=>1101001
[1,2,4,3,7,6,8,5]=>[1,2,4,3,6,8,7,5]=>0010101=>1101010
[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,7,6,5]=>0010111=>1101000
[3,2,1,4,8,7,6,5]=>[2,3,1,4,7,6,8,5]=>1000110=>0111001
[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,8,6,5]=>1000110=>0111001
[3,2,1,4,6,7,8,5]=>[2,3,1,4,8,7,6,5]=>1000111=>0111000
[2,3,1,4,8,7,6,5]=>[3,2,1,4,7,6,8,5]=>1100110=>0011001
[2,3,1,4,7,8,6,5]=>[3,2,1,4,8,6,7,5]=>1100110=>0011001
[2,3,1,4,7,6,8,5]=>[3,2,1,4,6,8,7,5]=>1100101=>0011010
[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,7,6,5]=>1100111=>0011000
[1,3,2,4,8,7,6,5]=>[1,3,2,4,7,6,8,5]=>0100110=>1011001
[1,3,2,4,7,6,8,5]=>[1,3,2,4,6,8,7,5]=>0100101=>1011010
[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,7,6,5]=>0100111=>1011000
[2,1,3,4,8,7,6,5]=>[2,1,3,4,7,6,8,5]=>1000110=>0111001
[2,1,3,4,7,8,6,5]=>[2,1,3,4,8,6,7,5]=>1000110=>0111001
[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,7,6,5]=>1000111=>0111000
[1,2,3,4,8,7,6,5]=>[1,2,3,4,7,6,8,5]=>0000110=>1111001
[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,6,7,5]=>0000110=>1111001
[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,8,6,5]=>0000110=>1111001
[1,2,3,4,7,6,8,5]=>[1,2,3,4,6,8,7,5]=>0000101=>1111010
[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,7,6,5]=>0000111=>1111000
[5,4,3,2,1,8,7,6]=>[3,4,2,5,1,7,8,6]=>1100010=>0011101
[5,4,3,2,1,7,8,6]=>[3,4,2,5,1,8,7,6]=>1100011=>0011100
[4,5,3,2,1,8,7,6]=>[3,5,2,4,1,7,8,6]=>1100010=>0011101
[3,5,4,2,1,8,7,6]=>[4,2,5,3,1,7,8,6]=>1110010=>0001101
[3,5,4,2,1,7,8,6]=>[4,2,5,3,1,8,7,6]=>1110011=>0001100
[3,4,5,2,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>1110011=>0001100
[2,5,4,3,1,7,8,6]=>[4,3,5,2,1,8,7,6]=>1110011=>0001100
[2,4,5,3,1,8,7,6]=>[5,3,4,2,1,7,8,6]=>1110010=>0001101
[2,4,5,3,1,7,8,6]=>[5,3,4,2,1,8,7,6]=>1110011=>0001100
[3,2,5,4,1,8,7,6]=>[2,4,5,3,1,7,8,6]=>1010010=>0101101
[3,2,5,4,1,7,8,6]=>[2,4,5,3,1,8,7,6]=>1010011=>0101100
[4,3,2,5,1,8,7,6]=>[3,2,5,4,1,7,8,6]=>1101010=>0010101
[4,3,2,5,1,7,8,6]=>[3,2,5,4,1,8,7,6]=>1101011=>0010100
[3,4,2,5,1,8,7,6]=>[5,4,2,3,1,7,8,6]=>1101010=>0010101
[3,4,2,5,1,7,8,6]=>[5,4,2,3,1,8,7,6]=>1101011=>0010100
[2,4,3,5,1,8,7,6]=>[3,5,4,2,1,7,8,6]=>1101010=>0010101
[2,4,3,5,1,7,8,6]=>[3,5,4,2,1,8,7,6]=>1101011=>0010100
[3,2,4,5,1,8,7,6]=>[2,5,4,3,1,7,8,6]=>1011010=>0100101
[2,3,4,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]=>1111010=>0000101
[2,3,4,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>1111011=>0000100
[1,5,4,3,2,8,7,6]=>[1,4,3,5,2,7,8,6]=>0110010=>1001101
[1,5,4,3,2,7,8,6]=>[1,4,3,5,2,8,7,6]=>0110011=>1001100
[1,4,5,3,2,8,7,6]=>[1,5,3,4,2,7,8,6]=>0110010=>1001101
[1,4,5,3,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>0110011=>1001100
[1,3,5,4,2,7,8,6]=>[1,4,5,3,2,8,7,6]=>0110011=>1001100
[1,4,3,5,2,8,7,6]=>[1,3,5,4,2,7,8,6]=>0101010=>1010101
[1,3,4,5,2,8,7,6]=>[1,5,4,3,2,7,8,6]=>0111010=>1000101
[1,3,4,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>0111011=>1000100
[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]=>0010010=>1101101
[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,7,6]=>0010011=>1101100
[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,7,8,6]=>0011010=>1100101
[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>0011011=>1100100
[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>0101010=>1010101
[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>0101011=>1010100
[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]=>1001010=>0110101
[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>1001011=>0110100
[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>0001010=>1110101
[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>0001011=>1110100
[4,3,2,1,5,8,7,6]=>[3,2,4,1,5,7,8,6]=>1100010=>0011101
[4,3,2,1,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>1100011=>0011100
[3,4,2,1,5,8,7,6]=>[4,2,3,1,5,7,8,6]=>1100010=>0011101
[3,2,4,1,5,7,8,6]=>[2,4,3,1,5,8,7,6]=>1010011=>0101100
[2,3,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>1110010=>0001101
[2,3,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>1110011=>0001100
[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>0100010=>1011101
[1,4,3,2,5,7,8,6]=>[1,3,4,2,5,8,7,6]=>0100011=>1011100
[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,7,8,6]=>0110010=>1001101
[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>0110011=>1001100
[2,1,4,3,5,8,7,6]=>[2,1,4,3,5,7,8,6]=>1010010=>0101101
[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>1010011=>0101100
[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,7,8,6]=>0010010=>1101101
[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>0010011=>1101100
[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>1000010=>0111101
[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>1100011=>0011100
[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]=>0100010=>1011101
[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>0100011=>1011100
[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]=>1000010=>0111101
[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>1000011=>0111100
[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>0000010=>1111101
[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>0000011=>1111100
[6,5,4,3,2,1,8,7]=>[4,3,5,2,6,1,8,7]=>1110001=>0001110
[5,6,4,3,2,1,8,7]=>[4,3,6,2,5,1,8,7]=>1110001=>0001110
[4,6,5,3,2,1,8,7]=>[5,3,6,2,4,1,8,7]=>1110001=>0001110
[4,5,6,3,2,1,8,7]=>[6,3,5,2,4,1,8,7]=>1110001=>0001110
[3,6,5,4,2,1,8,7]=>[4,5,2,6,3,1,8,7]=>1110001=>0001110
[3,5,6,4,2,1,8,7]=>[4,6,2,5,3,1,8,7]=>1110001=>0001110
[4,3,6,5,2,1,8,7]=>[5,3,2,6,4,1,8,7]=>1111001=>0000110
[4,5,3,6,2,1,8,7]=>[3,6,2,5,4,1,8,7]=>1101001=>0010110
[3,4,5,6,2,1,8,7]=>[6,2,5,4,3,1,8,7]=>1111001=>0000110
[2,6,5,4,3,1,8,7]=>[4,5,3,6,2,1,8,7]=>1110001=>0001110
[2,5,6,4,3,1,8,7]=>[4,6,3,5,2,1,8,7]=>1110001=>0001110
[3,2,5,6,4,1,8,7]=>[2,6,4,5,3,1,8,7]=>1011001=>0100110
[2,3,6,5,4,1,8,7]=>[5,4,6,3,2,1,8,7]=>1111001=>0000110
[2,3,5,6,4,1,8,7]=>[6,4,5,3,2,1,8,7]=>1111001=>0000110
[4,3,2,6,5,1,8,7]=>[3,2,5,6,4,1,8,7]=>1101001=>0010110
[3,4,2,6,5,1,8,7]=>[5,6,4,2,3,1,8,7]=>1101001=>0010110
[2,4,3,6,5,1,8,7]=>[3,5,6,4,2,1,8,7]=>1101001=>0010110
[5,4,3,2,6,1,8,7]=>[3,4,2,6,5,1,8,7]=>1100101=>0011010
[4,5,3,2,6,1,8,7]=>[3,6,5,2,4,1,8,7]=>1100101=>0011010
[3,5,4,2,6,1,8,7]=>[4,2,6,5,3,1,8,7]=>1110101=>0001010
[4,3,5,2,6,1,8,7]=>[6,5,3,2,4,1,8,7]=>1110101=>0001010
[2,5,4,3,6,1,8,7]=>[4,3,6,5,2,1,8,7]=>1110101=>0001010
[2,4,5,3,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>1110101=>0001010
[3,2,5,4,6,1,8,7]=>[2,4,6,5,3,1,8,7]=>1010101=>0101010
[4,3,2,5,6,1,8,7]=>[3,2,6,5,4,1,8,7]=>1101101=>0010010
[3,4,2,5,6,1,8,7]=>[6,5,4,2,3,1,8,7]=>1101101=>0010010
[2,4,3,5,6,1,8,7]=>[3,6,5,4,2,1,8,7]=>1101101=>0010010
[2,3,4,5,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>1111101=>0000010
[1,3,6,5,4,2,8,7]=>[1,5,4,6,3,2,8,7]=>0111001=>1000110
[1,3,4,5,6,2,8,7]=>[1,6,5,4,3,2,8,7]=>0111101=>1000010
[2,1,6,5,4,3,8,7]=>[2,1,5,4,6,3,8,7]=>1011001=>0100110
[2,1,5,6,4,3,8,7]=>[2,1,6,4,5,3,8,7]=>1011001=>0100110
[2,1,4,6,5,3,8,7]=>[2,1,5,6,4,3,8,7]=>1011001=>0100110
[2,1,5,4,6,3,8,7]=>[2,1,4,6,5,3,8,7]=>1010101=>0101010
[2,1,4,5,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>1011101=>0100010
[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]=>0101001=>1010110
[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>0101101=>1010010
[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]=>1001001=>0110110
[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>1001101=>0110010
[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>0001001=>1110110
[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>0001101=>1110010
[4,3,2,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>1100101=>0011010
[3,4,2,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>1100101=>0011010
[2,4,3,1,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>1100101=>0011010
[3,2,4,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>1010101=>0101010
[2,3,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>1110101=>0001010
[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>0101010
[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>0010101=>1101010
[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>0100101=>1011010
[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>1000101=>0111010
[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>0000101=>1111010
[4,3,5,2,1,6,8,7]=>[5,3,2,4,1,6,8,7]=>1110001=>0001110
[3,4,5,2,1,6,8,7]=>[5,2,4,3,1,6,8,7]=>1110001=>0001110
[2,5,4,3,1,6,8,7]=>[4,3,5,2,1,6,8,7]=>1110001=>0001110
[2,4,5,3,1,6,8,7]=>[5,3,4,2,1,6,8,7]=>1110001=>0001110
[3,2,5,4,1,6,8,7]=>[2,4,5,3,1,6,8,7]=>1010001=>0101110
[2,3,5,4,1,6,8,7]=>[4,5,3,2,1,6,8,7]=>1110001=>0001110
[2,4,3,5,1,6,8,7]=>[3,5,4,2,1,6,8,7]=>1101001=>0010110
[2,3,4,5,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>1111001=>0000110
[1,3,5,4,2,6,8,7]=>[1,4,5,3,2,6,8,7]=>0110001=>1001110
[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>1010001=>0101110
[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>1011001=>0100110
[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>1001001=>0110110
[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>0001001=>1110110
[4,3,2,1,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>1100001=>0011110
[2,3,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>1110001=>0001110
[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>0100001=>1011110
[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>0110001=>1001110
[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>1010001=>0101110
[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>0010001=>1101110
[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]=>1000001=>0111110
[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>1100001=>0011110
[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>0100001=>1011110
[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>1000001=>0111110
[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>0000001=>1111110
[5,7,6,4,3,2,1,8]=>[4,6,3,7,2,5,1,8]=>1110000=>0001111
[4,7,6,5,3,2,1,8]=>[5,3,6,2,7,4,1,8]=>1111000=>0000111
[4,6,7,5,3,2,1,8]=>[5,3,7,2,6,4,1,8]=>1111000=>0000111
[4,5,7,6,3,2,1,8]=>[6,3,7,2,5,4,1,8]=>1111000=>0000111
[4,6,5,7,3,2,1,8]=>[7,3,5,2,6,4,1,8]=>1111000=>0000111
[3,5,7,6,4,2,1,8]=>[6,4,7,2,5,3,1,8]=>1111000=>0000111
[3,5,6,7,4,2,1,8]=>[7,4,6,2,5,3,1,8]=>1111000=>0000111
[4,3,7,6,5,2,1,8]=>[5,6,3,2,7,4,1,8]=>1111000=>0000111
[3,4,7,6,5,2,1,8]=>[5,6,2,7,4,3,1,8]=>1111000=>0000111
[4,5,3,7,6,2,1,8]=>[3,6,2,7,5,4,1,8]=>1101100=>0010011
[3,5,4,7,6,2,1,8]=>[6,4,2,7,5,3,1,8]=>1111100=>0000011
[4,3,5,7,6,2,1,8]=>[6,3,2,7,5,4,1,8]=>1111100=>0000011
[3,6,5,4,7,2,1,8]=>[4,7,5,2,6,3,1,8]=>1110100=>0001011
[3,5,6,4,7,2,1,8]=>[4,7,2,6,5,3,1,8]=>1110100=>0001011
[2,7,6,5,4,3,1,8]=>[5,4,6,3,7,2,1,8]=>1111000=>0000111
[2,6,7,5,4,3,1,8]=>[5,4,7,3,6,2,1,8]=>1111000=>0000111
[2,5,7,6,4,3,1,8]=>[6,4,7,3,5,2,1,8]=>1111000=>0000111
[2,5,6,7,4,3,1,8]=>[7,4,6,3,5,2,1,8]=>1111000=>0000111
[2,4,6,7,5,3,1,8]=>[5,7,3,6,4,2,1,8]=>1111000=>0000111
[2,5,4,7,6,3,1,8]=>[6,4,3,7,5,2,1,8]=>1111100=>0000011
[2,5,6,4,7,3,1,8]=>[4,7,3,6,5,2,1,8]=>1110100=>0001011
[2,4,5,6,7,3,1,8]=>[7,3,6,5,4,2,1,8]=>1111100=>0000011
[3,2,7,6,5,4,1,8]=>[2,5,6,4,7,3,1,8]=>1011000=>0100111
[3,2,5,7,6,4,1,8]=>[2,6,4,7,5,3,1,8]=>1011100=>0100011
[3,2,5,6,7,4,1,8]=>[2,7,4,6,5,3,1,8]=>1011100=>0100011
[2,3,7,6,5,4,1,8]=>[5,6,4,7,3,2,1,8]=>1111000=>0000111
[2,3,6,7,5,4,1,8]=>[5,7,4,6,3,2,1,8]=>1111000=>0000111
[2,3,5,7,6,4,1,8]=>[6,4,7,5,3,2,1,8]=>1111100=>0000011
[2,3,6,5,7,4,1,8]=>[7,5,4,6,3,2,1,8]=>1111100=>0000011
[4,3,2,6,7,5,1,8]=>[3,2,7,5,6,4,1,8]=>1101100=>0010011
[3,4,2,6,7,5,1,8]=>[7,5,6,4,2,3,1,8]=>1101100=>0010011
[2,3,4,7,6,5,1,8]=>[6,5,7,4,3,2,1,8]=>1111100=>0000011
[2,3,4,6,7,5,1,8]=>[7,5,6,4,3,2,1,8]=>1111100=>0000011
[4,5,3,2,7,6,1,8]=>[3,6,7,5,2,4,1,8]=>1100100=>0011011
[3,5,4,2,7,6,1,8]=>[4,2,6,7,5,3,1,8]=>1110100=>0001011
[3,2,5,4,7,6,1,8]=>[2,4,6,7,5,3,1,8]=>1010100=>0101011
[4,3,2,5,7,6,1,8]=>[3,2,6,7,5,4,1,8]=>1101100=>0010011
[3,4,2,5,7,6,1,8]=>[6,7,5,4,2,3,1,8]=>1101100=>0010011
[2,3,4,5,7,6,1,8]=>[6,7,5,4,3,2,1,8]=>1111100=>0000011
[3,6,5,4,2,7,1,8]=>[4,5,2,7,6,3,1,8]=>1110010=>0001101
[3,5,4,6,2,7,1,8]=>[7,6,4,2,5,3,1,8]=>1111010=>0000101
[2,5,4,6,3,7,1,8]=>[7,6,4,3,5,2,1,8]=>1111010=>0000101
[2,4,5,6,3,7,1,8]=>[7,6,3,5,4,2,1,8]=>1111010=>0000101
[3,2,6,5,4,7,1,8]=>[2,5,4,7,6,3,1,8]=>1011010=>0100101
[2,3,5,6,4,7,1,8]=>[7,6,4,5,3,2,1,8]=>1111010=>0000101
[4,3,2,6,5,7,1,8]=>[3,2,5,7,6,4,1,8]=>1101010=>0010101
[3,4,2,6,5,7,1,8]=>[5,7,6,4,2,3,1,8]=>1101010=>0010101
[2,4,3,6,5,7,1,8]=>[3,5,7,6,4,2,1,8]=>1101010=>0010101
[2,3,4,6,5,7,1,8]=>[5,7,6,4,3,2,1,8]=>1111010=>0000101
[3,5,4,2,6,7,1,8]=>[4,2,7,6,5,3,1,8]=>1110110=>0001001
[2,5,4,3,6,7,1,8]=>[4,3,7,6,5,2,1,8]=>1110110=>0001001
[2,4,5,3,6,7,1,8]=>[7,6,5,3,4,2,1,8]=>1110110=>0001001
[2,3,5,4,6,7,1,8]=>[4,7,6,5,3,2,1,8]=>1110110=>0001001
[1,7,6,5,4,3,2,8]=>[1,5,4,6,3,7,2,8]=>0111000=>1000111
[1,6,7,5,4,3,2,8]=>[1,5,4,7,3,6,2,8]=>0111000=>1000111
[1,5,6,7,4,3,2,8]=>[1,7,4,6,3,5,2,8]=>0111000=>1000111
[1,4,7,6,5,3,2,8]=>[1,5,6,3,7,4,2,8]=>0111000=>1000111
[1,4,6,7,5,3,2,8]=>[1,5,7,3,6,4,2,8]=>0111000=>1000111
[1,5,4,7,6,3,2,8]=>[1,6,4,3,7,5,2,8]=>0111100=>1000011
[1,5,6,4,7,3,2,8]=>[1,4,7,3,6,5,2,8]=>0110100=>1001011
[1,4,5,6,7,3,2,8]=>[1,7,3,6,5,4,2,8]=>0111100=>1000011
[1,3,7,6,5,4,2,8]=>[1,5,6,4,7,3,2,8]=>0111000=>1000111
[1,3,6,7,5,4,2,8]=>[1,5,7,4,6,3,2,8]=>0111000=>1000111
[1,3,5,7,6,4,2,8]=>[1,6,4,7,5,3,2,8]=>0111100=>1000011
[1,3,5,6,7,4,2,8]=>[1,7,4,6,5,3,2,8]=>0111100=>1000011
[1,3,4,6,7,5,2,8]=>[1,7,5,6,4,3,2,8]=>0111100=>1000011
[1,3,5,4,7,6,2,8]=>[1,4,6,7,5,3,2,8]=>0110100=>1001011
[1,4,3,5,7,6,2,8]=>[1,3,6,7,5,4,2,8]=>0101100=>1010011
[1,3,4,5,7,6,2,8]=>[1,6,7,5,4,3,2,8]=>0111100=>1000011
[1,4,5,6,3,7,2,8]=>[1,7,6,3,5,4,2,8]=>0111010=>1000101
[1,3,6,5,4,7,2,8]=>[1,5,4,7,6,3,2,8]=>0111010=>1000101
[1,3,5,6,4,7,2,8]=>[1,7,6,4,5,3,2,8]=>0111010=>1000101
[1,4,3,6,5,7,2,8]=>[1,3,5,7,6,4,2,8]=>0101010=>1010101
[1,3,5,4,6,7,2,8]=>[1,4,7,6,5,3,2,8]=>0110110=>1001001
[1,4,3,5,6,7,2,8]=>[1,3,7,6,5,4,2,8]=>0101110=>1010001
[1,3,4,5,6,7,2,8]=>[1,7,6,5,4,3,2,8]=>0111110=>1000001
[2,1,4,5,6,7,3,8]=>[2,1,7,6,5,4,3,8]=>1011110=>0100001
[1,2,7,6,5,4,3,8]=>[1,2,5,6,4,7,3,8]=>0011000=>1100111
[1,2,5,7,6,4,3,8]=>[1,2,6,4,7,5,3,8]=>0011100=>1100011
[1,2,4,6,5,7,3,8]=>[1,2,5,7,6,4,3,8]=>0011010=>1100101
[1,2,4,5,6,7,3,8]=>[1,2,7,6,5,4,3,8]=>0011110=>1100001
[3,2,1,7,6,5,4,8]=>[2,3,1,6,5,7,4,8]=>1001100=>0110011
[3,2,1,6,7,5,4,8]=>[2,3,1,7,5,6,4,8]=>1001100=>0110011
[3,2,1,5,7,6,4,8]=>[2,3,1,6,7,5,4,8]=>1001100=>0110011
[2,3,1,6,7,5,4,8]=>[3,2,1,7,5,6,4,8]=>1101100=>0010011
[2,3,1,6,5,7,4,8]=>[3,2,1,5,7,6,4,8]=>1101010=>0010101
[2,3,1,5,6,7,4,8]=>[3,2,1,7,6,5,4,8]=>1101110=>0010001
[1,3,2,7,6,5,4,8]=>[1,3,2,6,5,7,4,8]=>0101100=>1010011
[1,3,2,5,7,6,4,8]=>[1,3,2,6,7,5,4,8]=>0101100=>1010011
[1,3,2,6,5,7,4,8]=>[1,3,2,5,7,6,4,8]=>0101010=>1010101
[1,3,2,5,6,7,4,8]=>[1,3,2,7,6,5,4,8]=>0101110=>1010001
[1,2,3,7,6,5,4,8]=>[1,2,3,6,5,7,4,8]=>0001100=>1110011
[1,2,3,6,7,5,4,8]=>[1,2,3,7,5,6,4,8]=>0001100=>1110011
[1,2,3,5,7,6,4,8]=>[1,2,3,6,7,5,4,8]=>0001100=>1110011
[1,2,3,6,5,7,4,8]=>[1,2,3,5,7,6,4,8]=>0001010=>1110101
[1,2,3,5,6,7,4,8]=>[1,2,3,7,6,5,4,8]=>0001110=>1110001
[4,3,2,1,7,6,5,8]=>[3,2,4,1,6,7,5,8]=>1100100=>0011011
[4,3,2,1,6,7,5,8]=>[3,2,4,1,7,6,5,8]=>1100110=>0011001
[2,3,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>1110100=>0001011
[2,3,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>1110110=>0001001
[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>0100100=>1011011
[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>0110110=>1001001
[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>1000100=>0111011
[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>1100110=>0011001
[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>0100110=>1011001
[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>0000100=>1111011
[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>0000110=>1111001
[5,4,3,2,1,7,6,8]=>[3,4,2,5,1,7,6,8]=>1100010=>0011101
[4,5,3,2,1,7,6,8]=>[3,5,2,4,1,7,6,8]=>1100010=>0011101
[3,5,4,2,1,7,6,8]=>[4,2,5,3,1,7,6,8]=>1110010=>0001101
[3,4,5,2,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>1110010=>0001101
[3,2,5,4,1,7,6,8]=>[2,4,5,3,1,7,6,8]=>1010010=>0101101
[2,3,5,4,1,7,6,8]=>[4,5,3,2,1,7,6,8]=>1110010=>0001101
[2,4,3,5,1,7,6,8]=>[3,5,4,2,1,7,6,8]=>1101010=>0010101
[2,3,4,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>1111010=>0000101
[1,5,4,3,2,7,6,8]=>[1,4,3,5,2,7,6,8]=>0110010=>1001101
[1,3,5,4,2,7,6,8]=>[1,4,5,3,2,7,6,8]=>0110010=>1001101
[1,4,3,5,2,7,6,8]=>[1,3,5,4,2,7,6,8]=>0101010=>1010101
[1,3,4,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>0111010=>1000101
[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>1001010=>0110101
[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>1101010=>0010101
[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>0101010=>1010101
[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>0001010=>1110101
[4,3,2,1,5,7,6,8]=>[3,2,4,1,5,7,6,8]=>1100010=>0011101
[2,3,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>1110010=>0001101
[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>0100010=>1011101
[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>0110010=>1001101
[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>0010010=>1101101
[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]=>1000010=>0111101
[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>1100010=>0011101
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>0100010=>1011101
[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>1000010=>0111101
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>0000010=>1111101
[3,6,5,4,2,1,7,8]=>[4,5,2,6,3,1,7,8]=>1110000=>0001111
[4,3,6,5,2,1,7,8]=>[5,3,2,6,4,1,7,8]=>1111000=>0000111
[2,4,6,5,3,1,7,8]=>[5,3,6,4,2,1,7,8]=>1111000=>0000111
[2,3,6,5,4,1,7,8]=>[5,4,6,3,2,1,7,8]=>1111000=>0000111
[2,3,4,6,5,1,7,8]=>[5,6,4,3,2,1,7,8]=>1111000=>0000111
[3,5,4,2,6,1,7,8]=>[4,2,6,5,3,1,7,8]=>1110100=>0001011
[1,6,5,4,3,2,7,8]=>[1,4,5,3,6,2,7,8]=>0110000=>1001111
[1,4,6,5,3,2,7,8]=>[1,5,3,6,4,2,7,8]=>0111000=>1000111
[1,5,4,6,3,2,7,8]=>[1,6,4,3,5,2,7,8]=>0111000=>1000111
[1,4,5,6,3,2,7,8]=>[1,6,3,5,4,2,7,8]=>0111000=>1000111
[1,3,5,6,4,2,7,8]=>[1,6,4,5,3,2,7,8]=>0111000=>1000111
[1,4,3,6,5,2,7,8]=>[1,3,5,6,4,2,7,8]=>0101000=>1010111
[1,5,4,3,6,2,7,8]=>[1,4,3,6,5,2,7,8]=>0110100=>1001011
[1,3,5,4,6,2,7,8]=>[1,4,6,5,3,2,7,8]=>0110100=>1001011
[1,3,4,5,6,2,7,8]=>[1,6,5,4,3,2,7,8]=>0111100=>1000011
[2,1,4,6,5,3,7,8]=>[2,1,5,6,4,3,7,8]=>1011000=>0100111
[1,2,5,6,4,3,7,8]=>[1,2,6,4,5,3,7,8]=>0011000=>1100111
[1,2,4,6,5,3,7,8]=>[1,2,5,6,4,3,7,8]=>0011000=>1100111
[1,2,4,5,6,3,7,8]=>[1,2,6,5,4,3,7,8]=>0011100=>1100011
[3,2,1,6,5,4,7,8]=>[2,3,1,5,6,4,7,8]=>1001000=>0110111
[3,2,1,5,6,4,7,8]=>[2,3,1,6,5,4,7,8]=>1001100=>0110011
[2,3,1,6,5,4,7,8]=>[3,2,1,5,6,4,7,8]=>1101000=>0010111
[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>1101100=>0010011
[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]=>0101000=>1010111
[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>0101100=>1010011
[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>0001000=>1110111
[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>0001100=>1110011
[4,3,2,1,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>1100100=>0011011
[3,2,4,1,6,5,7,8]=>[2,4,3,1,6,5,7,8]=>1010100=>0101011
[2,3,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>1110100=>0001011
[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>1010100=>0101011
[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>0010100=>1101011
[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>0100100=>1011011
[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>1000100=>0111011
[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>0000100=>1111011
[3,5,4,2,1,6,7,8]=>[4,2,5,3,1,6,7,8]=>1110000=>0001111
[2,5,4,3,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>1110000=>0001111
[2,4,5,3,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>1110000=>0001111
[3,2,5,4,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>1010000=>0101111
[2,3,5,4,1,6,7,8]=>[4,5,3,2,1,6,7,8]=>1110000=>0001111
[2,4,3,5,1,6,7,8]=>[3,5,4,2,1,6,7,8]=>1101000=>0010111
[1,4,5,3,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>0110000=>1001111
[1,3,5,4,2,6,7,8]=>[1,4,5,3,2,6,7,8]=>0110000=>1001111
[1,4,3,5,2,6,7,8]=>[1,3,5,4,2,6,7,8]=>0101000=>1010111
[1,3,4,5,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>0111000=>1000111
[2,1,5,4,3,6,7,8]=>[2,1,4,5,3,6,7,8]=>1010000=>0101111
[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>1011000=>0100111
[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>0011000=>1100111
[3,2,1,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>1001000=>0110111
[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>1101000=>0010111
[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>0101000=>1010111
[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>1001000=>0110111
[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000=>1110111
[2,4,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>1100000=>0011111
[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>0100000=>1011111
[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000=>1001111
[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>1010000=>0101111
[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000=>1101111
[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000=>1011111
[1,2,3,4,8,6,7,5]=>[1,2,3,4,6,7,8,5]=>0000100=>1111011
[1,2,3,5,8,6,7,4]=>[1,2,3,6,7,8,5,4]=>0001100=>1110011
[1,2,3,7,5,6,4,8]=>[1,2,3,5,6,7,4,8]=>0001000=>1110111
[1,2,3,7,5,6,8,4]=>[1,2,3,5,6,8,7,4]=>0001001=>1110110
[1,2,3,8,5,6,7,4]=>[1,2,3,5,6,7,8,4]=>0001000=>1110111
[1,2,3,8,5,7,6,4]=>[1,2,3,5,7,6,8,4]=>0001010=>1110101
[1,2,3,8,6,5,7,4]=>[1,2,3,6,5,7,8,4]=>0001100=>1110011
[1,2,3,8,6,7,5,4]=>[1,2,3,7,6,5,8,4]=>0001110=>1110001
[1,2,4,3,8,6,7,5]=>[1,2,4,3,6,7,8,5]=>0010100=>1101011
[1,2,4,5,8,6,7,3]=>[1,2,6,7,8,5,4,3]=>0011100=>1100011
[1,2,4,7,5,6,8,3]=>[1,2,5,6,8,7,4,3]=>0011001=>1100110
[1,2,4,8,5,6,7,3]=>[1,2,5,6,7,8,4,3]=>0011000=>1100111
[1,2,4,8,6,5,7,3]=>[1,2,6,5,7,8,4,3]=>0011100=>1100011
[1,2,5,4,8,6,7,3]=>[1,2,4,6,7,8,5,3]=>0010100=>1101011
[1,2,6,4,5,3,7,8]=>[1,2,4,5,6,3,7,8]=>0010000=>1101111
[1,2,6,4,5,7,8,3]=>[1,2,4,5,8,7,6,3]=>0010011=>1101100
[1,2,6,4,5,8,7,3]=>[1,2,4,5,7,8,6,3]=>0010010=>1101101
[1,2,7,4,5,6,8,3]=>[1,2,4,5,6,8,7,3]=>0010001=>1101110
[1,2,8,4,5,6,7,3]=>[1,2,4,5,6,7,8,3]=>0010000=>1101111
[1,2,8,4,6,7,5,3]=>[1,2,4,7,6,5,8,3]=>0010110=>1101001
[1,2,7,5,4,6,3,8]=>[1,2,5,4,6,7,3,8]=>0011000=>1100111
[1,2,7,5,4,6,8,3]=>[1,2,5,4,6,8,7,3]=>0011001=>1100110
[1,2,8,5,4,6,7,3]=>[1,2,5,4,6,7,8,3]=>0011000=>1100111
[1,2,8,5,4,7,6,3]=>[1,2,5,4,7,6,8,3]=>0011010=>1100101
[1,2,8,5,6,4,7,3]=>[1,2,6,5,4,7,8,3]=>0011100=>1100011
[1,2,8,5,6,7,4,3]=>[1,2,7,6,5,4,8,3]=>0011110=>1100001
[1,2,8,6,5,4,7,3]=>[1,2,5,6,4,7,8,3]=>0011000=>1100111
[1,2,8,6,5,7,4,3]=>[1,2,5,7,6,4,8,3]=>0011010=>1100101
[1,2,8,7,5,6,4,3]=>[1,2,5,6,7,4,8,3]=>0011000=>1100111
[1,3,2,4,8,6,7,5]=>[1,3,2,4,6,7,8,5]=>0100100=>1011011
[1,3,2,7,5,6,8,4]=>[1,3,2,5,6,8,7,4]=>0101001=>1010110
[1,3,2,8,5,7,6,4]=>[1,3,2,5,7,6,8,4]=>0101010=>1010101
[1,3,2,8,6,5,7,4]=>[1,3,2,6,5,7,8,4]=>0101100=>1010011
[1,3,2,8,6,7,5,4]=>[1,3,2,7,6,5,8,4]=>0101110=>1010001
[1,3,4,2,8,6,7,5]=>[1,4,3,2,6,7,8,5]=>0110100=>1001011
[1,3,4,5,8,6,7,2]=>[1,6,7,8,5,4,3,2]=>0111100=>1000011
[1,3,4,8,5,6,7,2]=>[1,5,6,7,8,4,3,2]=>0111000=>1000111
[1,3,4,8,6,5,7,2]=>[1,6,5,7,8,4,3,2]=>0111100=>1000011
[1,3,6,4,5,7,8,2]=>[1,4,5,8,7,6,3,2]=>0110011=>1001100
[1,3,6,4,5,8,7,2]=>[1,4,5,7,8,6,3,2]=>0110010=>1001101
[1,3,7,4,5,6,2,8]=>[1,4,5,6,7,3,2,8]=>0110000=>1001111
[1,3,8,4,5,6,7,2]=>[1,4,5,6,7,8,3,2]=>0110000=>1001111
[1,3,8,4,6,7,5,2]=>[1,4,7,6,5,8,3,2]=>0110110=>1001001
[1,3,8,5,4,6,7,2]=>[1,5,4,6,7,8,3,2]=>0111000=>1000111
[1,3,8,5,6,7,4,2]=>[1,7,6,5,4,8,3,2]=>0111110=>1000001
[1,4,3,2,8,6,7,5]=>[1,3,4,2,6,7,8,5]=>0100100=>1011011
[1,4,3,5,8,6,7,2]=>[1,3,6,7,8,5,4,2]=>0101100=>1010011
[1,4,3,8,5,6,7,2]=>[1,3,5,6,7,8,4,2]=>0101000=>1010111
[1,4,3,8,5,7,6,2]=>[1,3,5,7,6,8,4,2]=>0101010=>1010101
[1,4,3,8,6,5,7,2]=>[1,3,6,5,7,8,4,2]=>0101100=>1010011
[1,5,3,4,2,6,7,8]=>[1,3,4,5,2,6,7,8]=>0100000=>1011111
[1,5,3,4,2,7,8,6]=>[1,3,4,5,2,8,7,6]=>0100011=>1011100
[1,5,3,4,2,8,7,6]=>[1,3,4,5,2,7,8,6]=>0100010=>1011101
[1,5,3,4,6,7,8,2]=>[1,3,4,8,7,6,5,2]=>0100111=>1011000
[1,5,3,4,7,6,2,8]=>[1,3,4,6,7,5,2,8]=>0100100=>1011011
[1,5,3,4,8,6,7,2]=>[1,3,4,6,7,8,5,2]=>0100100=>1011011
[1,6,3,4,5,2,7,8]=>[1,3,4,5,6,2,7,8]=>0100000=>1011111
[1,6,3,4,5,8,7,2]=>[1,3,4,5,7,8,6,2]=>0100010=>1011101
[1,7,3,4,5,6,2,8]=>[1,3,4,5,6,7,2,8]=>0100000=>1011111
[1,7,3,4,5,6,8,2]=>[1,3,4,5,6,8,7,2]=>0100001=>1011110
[1,8,3,4,5,6,7,2]=>[1,3,4,5,6,7,8,2]=>0100000=>1011111
[1,8,3,4,6,7,5,2]=>[1,3,4,7,6,5,8,2]=>0100110=>1011001
[1,8,3,4,7,6,5,2]=>[1,3,4,6,7,5,8,2]=>0100100=>1011011
[1,6,3,5,4,2,7,8]=>[1,3,5,4,6,2,7,8]=>0101000=>1010111
[1,6,3,5,4,8,7,2]=>[1,3,5,4,7,8,6,2]=>0101010=>1010101
[1,7,3,5,4,6,2,8]=>[1,3,5,4,6,7,2,8]=>0101000=>1010111
[1,8,3,5,4,6,7,2]=>[1,3,5,4,6,7,8,2]=>0101000=>1010111
[1,8,3,5,4,7,6,2]=>[1,3,5,4,7,6,8,2]=>0101010=>1010101
[1,7,3,6,5,4,2,8]=>[1,3,5,6,4,7,2,8]=>0101000=>1010111
[1,8,3,6,5,4,7,2]=>[1,3,5,6,4,7,8,2]=>0101000=>1010111
[1,8,3,7,5,6,4,2]=>[1,3,5,6,7,4,8,2]=>0101000=>1010111
[1,8,3,7,6,5,4,2]=>[1,3,6,5,7,4,8,2]=>0101100=>1010011
[1,6,4,3,5,2,7,8]=>[1,4,3,5,6,2,7,8]=>0110000=>1001111
[1,6,4,3,5,8,7,2]=>[1,4,3,5,7,8,6,2]=>0110010=>1001101
[1,8,4,3,5,6,7,2]=>[1,4,3,5,6,7,8,2]=>0110000=>1001111
[1,7,4,3,6,5,8,2]=>[1,4,3,6,5,8,7,2]=>0110101=>1001010
[1,8,4,3,6,5,7,2]=>[1,4,3,6,5,7,8,2]=>0110100=>1001011
[1,6,4,5,3,2,7,8]=>[1,5,4,3,6,2,7,8]=>0111000=>1000111
[1,7,4,5,3,6,8,2]=>[1,5,4,3,6,8,7,2]=>0111001=>1000110
[1,8,4,5,3,6,7,2]=>[1,5,4,3,6,7,8,2]=>0111000=>1000111
[1,7,4,5,6,3,8,2]=>[1,6,5,4,3,8,7,2]=>0111101=>1000010
[1,8,4,5,6,3,7,2]=>[1,6,5,4,3,7,8,2]=>0111100=>1000011
[1,8,4,5,6,7,3,2]=>[1,7,6,5,4,3,8,2]=>0111110=>1000001
[1,8,4,7,6,5,3,2]=>[1,6,5,7,4,3,8,2]=>0111100=>1000011
[1,7,5,4,3,6,2,8]=>[1,4,5,3,6,7,2,8]=>0110000=>1001111
[1,7,5,4,3,6,8,2]=>[1,4,5,3,6,8,7,2]=>0110001=>1001110
[1,8,5,4,3,6,7,2]=>[1,4,5,3,6,7,8,2]=>0110000=>1001111
[1,8,5,4,7,6,3,2]=>[1,4,6,7,5,3,8,2]=>0110100=>1001011
[1,7,6,4,5,3,2,8]=>[1,4,5,6,3,7,2,8]=>0110000=>1001111
[1,8,7,4,5,6,3,2]=>[1,4,5,6,7,3,8,2]=>0110000=>1001111
[1,8,7,4,6,5,3,2]=>[1,4,6,5,7,3,8,2]=>0110100=>1001011
[1,8,6,5,4,3,7,2]=>[1,5,4,6,3,7,8,2]=>0111000=>1000111
[1,8,7,5,4,6,3,2]=>[1,5,4,6,7,3,8,2]=>0111000=>1000111
[2,1,3,4,8,6,7,5]=>[2,1,3,4,6,7,8,5]=>1000100=>0111011
[2,1,3,5,8,6,7,4]=>[2,1,3,6,7,8,5,4]=>1001100=>0110011
[2,1,3,8,5,6,7,4]=>[2,1,3,5,6,7,8,4]=>1001000=>0110111
[2,1,3,8,5,7,6,4]=>[2,1,3,5,7,6,8,4]=>1001010=>0110101
[2,1,4,3,8,6,7,5]=>[2,1,4,3,6,7,8,5]=>1010100=>0101011
[2,1,4,5,8,6,7,3]=>[2,1,6,7,8,5,4,3]=>1011100=>0100011
[2,1,4,8,5,6,7,3]=>[2,1,5,6,7,8,4,3]=>1011000=>0100111
[2,1,4,8,5,7,6,3]=>[2,1,5,7,6,8,4,3]=>1011010=>0100101
[2,1,4,8,6,5,7,3]=>[2,1,6,5,7,8,4,3]=>1011100=>0100011
[2,1,4,8,6,7,5,3]=>[2,1,7,6,5,8,4,3]=>1011110=>0100001
[2,1,5,4,8,6,7,3]=>[2,1,4,6,7,8,5,3]=>1010100=>0101011
[2,1,6,4,5,3,8,7]=>[2,1,4,5,6,3,8,7]=>1010001=>0101110
[2,1,6,4,5,7,8,3]=>[2,1,4,5,8,7,6,3]=>1010011=>0101100
[2,1,6,4,5,8,7,3]=>[2,1,4,5,7,8,6,3]=>1010010=>0101101
[2,1,8,4,5,6,7,3]=>[2,1,4,5,6,7,8,3]=>1010000=>0101111
[2,1,7,4,6,5,8,3]=>[2,1,4,6,5,8,7,3]=>1010101=>0101010
[2,1,8,4,6,7,5,3]=>[2,1,4,7,6,5,8,3]=>1010110=>0101001
[2,1,8,4,7,6,5,3]=>[2,1,4,6,7,5,8,3]=>1010100=>0101011
[2,1,7,5,4,6,8,3]=>[2,1,5,4,6,8,7,3]=>1011001=>0100110
[2,1,8,5,4,6,7,3]=>[2,1,5,4,6,7,8,3]=>1011000=>0100111
[2,1,8,5,4,7,6,3]=>[2,1,5,4,7,6,8,3]=>1011010=>0100101
[2,1,7,5,6,4,8,3]=>[2,1,6,5,4,8,7,3]=>1011101=>0100010
[2,1,8,5,6,7,4,3]=>[2,1,7,6,5,4,8,3]=>1011110=>0100001
[2,1,8,5,7,6,4,3]=>[2,1,6,7,5,4,8,3]=>1011100=>0100011
[2,1,8,6,5,4,7,3]=>[2,1,5,6,4,7,8,3]=>1011000=>0100111
[2,1,8,6,5,7,4,3]=>[2,1,5,7,6,4,8,3]=>1011010=>0100101
[2,1,8,7,5,6,4,3]=>[2,1,5,6,7,4,8,3]=>1011000=>0100111
[2,3,1,5,8,6,7,4]=>[3,2,1,6,7,8,5,4]=>1101100=>0010011
[2,3,1,7,5,6,4,8]=>[3,2,1,5,6,7,4,8]=>1101000=>0010111
[2,3,1,8,5,6,7,4]=>[3,2,1,5,6,7,8,4]=>1101000=>0010111
[2,3,1,8,6,7,5,4]=>[3,2,1,7,6,5,8,4]=>1101110=>0010001
[2,3,4,1,8,6,7,5]=>[4,3,2,1,6,7,8,5]=>1110100=>0001011
[2,3,4,5,8,6,7,1]=>[6,7,8,5,4,3,2,1]=>1111100=>0000011
[2,3,4,7,5,6,1,8]=>[5,6,7,4,3,2,1,8]=>1111000=>0000111
[2,3,4,7,5,6,8,1]=>[5,6,8,7,4,3,2,1]=>1111001=>0000110
[2,3,4,8,5,6,7,1]=>[5,6,7,8,4,3,2,1]=>1111000=>0000111
[2,3,4,8,5,7,6,1]=>[5,7,6,8,4,3,2,1]=>1111010=>0000101
[2,3,4,8,6,5,7,1]=>[6,5,7,8,4,3,2,1]=>1111100=>0000011
[2,3,4,8,6,7,5,1]=>[7,6,5,8,4,3,2,1]=>1111110=>0000001
[2,3,5,4,8,6,7,1]=>[4,6,7,8,5,3,2,1]=>1110100=>0001011
[2,3,6,4,5,1,7,8]=>[4,5,6,3,2,1,7,8]=>1110000=>0001111
[2,3,6,4,5,1,8,7]=>[4,5,6,3,2,1,8,7]=>1110001=>0001110
[2,3,6,4,5,7,8,1]=>[4,5,8,7,6,3,2,1]=>1110011=>0001100
[2,3,6,4,5,8,7,1]=>[4,5,7,8,6,3,2,1]=>1110010=>0001101
[2,3,7,4,5,6,8,1]=>[4,5,6,8,7,3,2,1]=>1110001=>0001110
[2,3,8,4,5,6,7,1]=>[4,5,6,7,8,3,2,1]=>1110000=>0001111
[2,3,7,4,6,5,8,1]=>[4,6,5,8,7,3,2,1]=>1110101=>0001010
[2,3,8,4,6,7,5,1]=>[4,7,6,5,8,3,2,1]=>1110110=>0001001
[2,3,7,5,4,6,1,8]=>[5,4,6,7,3,2,1,8]=>1111000=>0000111
[2,3,8,5,4,6,7,1]=>[5,4,6,7,8,3,2,1]=>1111000=>0000111
[2,3,7,5,6,4,1,8]=>[6,5,4,7,3,2,1,8]=>1111100=>0000011
[2,3,7,5,6,4,8,1]=>[6,5,4,8,7,3,2,1]=>1111101=>0000010
[2,3,8,5,6,4,7,1]=>[6,5,4,7,8,3,2,1]=>1111100=>0000011
[2,3,8,5,6,7,4,1]=>[7,6,5,4,8,3,2,1]=>1111110=>0000001
[2,3,8,5,7,6,4,1]=>[6,7,5,4,8,3,2,1]=>1111100=>0000011
[2,3,8,6,5,4,7,1]=>[5,6,4,7,8,3,2,1]=>1111000=>0000111
[2,4,3,1,8,6,7,5]=>[3,4,2,1,6,7,8,5]=>1100100=>0011011
[2,4,3,7,5,6,8,1]=>[3,5,6,8,7,4,2,1]=>1101001=>0010110
[2,4,3,8,5,6,7,1]=>[3,5,6,7,8,4,2,1]=>1101000=>0010111
[2,4,3,8,5,7,6,1]=>[3,5,7,6,8,4,2,1]=>1101010=>0010101
[2,4,3,8,6,7,5,1]=>[3,7,6,5,8,4,2,1]=>1101110=>0010001
[2,5,3,4,1,6,7,8]=>[3,4,5,2,1,6,7,8]=>1100000=>0011111
[2,5,3,4,1,8,7,6]=>[3,4,5,2,1,7,8,6]=>1100010=>0011101
[2,5,3,4,6,7,1,8]=>[3,4,7,6,5,2,1,8]=>1100110=>0011001
[2,5,3,4,6,7,8,1]=>[3,4,8,7,6,5,2,1]=>1100111=>0011000
[2,5,3,4,8,6,7,1]=>[3,4,6,7,8,5,2,1]=>1100100=>0011011
[2,6,3,4,5,1,7,8]=>[3,4,5,6,2,1,7,8]=>1100000=>0011111
[2,6,3,4,5,7,8,1]=>[3,4,5,8,7,6,2,1]=>1100011=>0011100
[2,6,3,4,5,8,7,1]=>[3,4,5,7,8,6,2,1]=>1100010=>0011101
[2,7,3,4,5,6,1,8]=>[3,4,5,6,7,2,1,8]=>1100000=>0011111
[2,8,3,4,5,6,7,1]=>[3,4,5,6,7,8,2,1]=>1100000=>0011111
[2,8,3,4,5,7,6,1]=>[3,4,5,7,6,8,2,1]=>1100010=>0011101
[2,6,3,5,4,8,7,1]=>[3,5,4,7,8,6,2,1]=>1101010=>0010101
[2,8,3,5,4,7,6,1]=>[3,5,4,7,6,8,2,1]=>1101010=>0010101
[2,7,3,5,6,4,8,1]=>[3,6,5,4,8,7,2,1]=>1101101=>0010010
[2,8,3,5,6,7,4,1]=>[3,7,6,5,4,8,2,1]=>1101110=>0010001
[2,7,3,6,5,4,1,8]=>[3,5,6,4,7,2,1,8]=>1101000=>0010111
[2,8,3,7,5,6,4,1]=>[3,5,6,7,4,8,2,1]=>1101000=>0010111
[2,5,4,3,8,6,7,1]=>[4,3,6,7,8,5,2,1]=>1110100=>0001011
[2,6,4,3,5,1,8,7]=>[4,3,5,6,2,1,8,7]=>1110001=>0001110
[2,6,4,3,5,8,7,1]=>[4,3,5,7,8,6,2,1]=>1110010=>0001101
[2,7,4,3,5,6,8,1]=>[4,3,5,6,8,7,2,1]=>1110001=>0001110
[2,8,4,3,5,6,7,1]=>[4,3,5,6,7,8,2,1]=>1110000=>0001111
[2,8,4,3,5,7,6,1]=>[4,3,5,7,6,8,2,1]=>1110010=>0001101
[2,7,4,3,6,5,8,1]=>[4,3,6,5,8,7,2,1]=>1110101=>0001010
[2,8,4,3,6,5,7,1]=>[4,3,6,5,7,8,2,1]=>1110100=>0001011
[2,8,4,3,6,7,5,1]=>[4,3,7,6,5,8,2,1]=>1110110=>0001001
[2,6,4,5,3,1,7,8]=>[5,4,3,6,2,1,7,8]=>1111000=>0000111
[2,6,4,5,3,1,8,7]=>[5,4,3,6,2,1,8,7]=>1111001=>0000110
[2,6,4,5,3,7,8,1]=>[5,4,3,8,7,6,2,1]=>1111011=>0000100
[2,6,4,5,3,8,7,1]=>[5,4,3,7,8,6,2,1]=>1111010=>0000101
[2,8,4,5,3,6,7,1]=>[5,4,3,6,7,8,2,1]=>1111000=>0000111
[2,7,4,5,6,3,1,8]=>[6,5,4,3,7,2,1,8]=>1111100=>0000011
[2,7,4,5,6,3,8,1]=>[6,5,4,3,8,7,2,1]=>1111101=>0000010
[2,8,4,5,6,3,7,1]=>[6,5,4,3,7,8,2,1]=>1111100=>0000011
[2,8,4,5,6,7,3,1]=>[7,6,5,4,3,8,2,1]=>1111110=>0000001
[2,7,4,6,5,3,1,8]=>[5,6,4,3,7,2,1,8]=>1111000=>0000111
[2,7,4,6,5,3,8,1]=>[5,6,4,3,8,7,2,1]=>1111001=>0000110
[2,8,4,7,6,5,3,1]=>[6,5,7,4,3,8,2,1]=>1111100=>0000011
[2,7,5,4,3,6,8,1]=>[4,5,3,6,8,7,2,1]=>1110001=>0001110
[2,8,5,4,3,7,6,1]=>[4,5,3,7,6,8,2,1]=>1110010=>0001101
[2,8,5,4,6,7,3,1]=>[4,7,6,5,3,8,2,1]=>1110110=>0001001
[2,7,6,4,5,3,8,1]=>[4,5,6,3,8,7,2,1]=>1110001=>0001110
[2,8,7,4,5,6,3,1]=>[4,5,6,7,3,8,2,1]=>1110000=>0001111
[2,8,7,5,4,6,3,1]=>[5,4,6,7,3,8,2,1]=>1111000=>0000111
[2,8,7,5,6,4,3,1]=>[6,5,4,7,3,8,2,1]=>1111100=>0000011
[3,2,1,4,8,6,7,5]=>[2,3,1,4,6,7,8,5]=>1000100=>0111011
[3,2,1,5,8,6,7,4]=>[2,3,1,6,7,8,5,4]=>1001100=>0110011
[3,2,1,7,5,6,4,8]=>[2,3,1,5,6,7,4,8]=>1001000=>0110111
[3,2,1,8,5,6,7,4]=>[2,3,1,5,6,7,8,4]=>1001000=>0110111
[3,2,1,8,5,7,6,4]=>[2,3,1,5,7,6,8,4]=>1001010=>0110101
[3,2,1,8,6,7,5,4]=>[2,3,1,7,6,5,8,4]=>1001110=>0110001
[3,2,4,1,8,6,7,5]=>[2,4,3,1,6,7,8,5]=>1010100=>0101011
[3,2,4,5,8,6,7,1]=>[2,6,7,8,5,4,3,1]=>1011100=>0100011
[3,2,4,8,5,6,7,1]=>[2,5,6,7,8,4,3,1]=>1011000=>0100111
[3,2,5,4,8,6,7,1]=>[2,4,6,7,8,5,3,1]=>1010100=>0101011
[3,2,6,4,5,1,7,8]=>[2,4,5,6,3,1,7,8]=>1010000=>0101111
[3,2,7,4,5,6,1,8]=>[2,4,5,6,7,3,1,8]=>1010000=>0101111
[3,2,8,4,5,6,7,1]=>[2,4,5,6,7,8,3,1]=>1010000=>0101111
[3,2,7,4,6,5,8,1]=>[2,4,6,5,8,7,3,1]=>1010101=>0101010
[3,2,8,4,6,5,7,1]=>[2,4,6,5,7,8,3,1]=>1010100=>0101011
[3,2,7,5,4,6,1,8]=>[2,5,4,6,7,3,1,8]=>1011000=>0100111
[3,2,8,5,4,6,7,1]=>[2,5,4,6,7,8,3,1]=>1011000=>0100111
[3,2,8,5,4,7,6,1]=>[2,5,4,7,6,8,3,1]=>1011010=>0100101
[3,2,7,5,6,4,8,1]=>[2,6,5,4,8,7,3,1]=>1011101=>0100010
[3,2,8,5,6,4,7,1]=>[2,6,5,4,7,8,3,1]=>1011100=>0100011
[3,2,8,5,7,6,4,1]=>[2,6,7,5,4,8,3,1]=>1011100=>0100011
[3,2,8,7,5,6,4,1]=>[2,5,6,7,4,8,3,1]=>1011000=>0100111
[4,2,3,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>1000010=>0111101
[4,2,3,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>1000011=>0111100
[4,2,3,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>1000010=>0111101
[4,2,3,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>1000100=>0111011
[4,2,3,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>1000101=>0111010
[4,2,3,1,6,7,8,5]=>[2,3,4,1,8,7,6,5]=>1000111=>0111000
[4,2,3,1,6,8,7,5]=>[2,3,4,1,7,8,6,5]=>1000110=>0111001
[4,2,3,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>1000100=>0111011
[4,2,3,1,7,6,8,5]=>[2,3,4,1,6,8,7,5]=>1000101=>0111010
[4,2,3,1,8,6,7,5]=>[2,3,4,1,6,7,8,5]=>1000100=>0111011
[4,2,3,1,8,7,6,5]=>[2,3,4,1,7,6,8,5]=>1000110=>0111001
[4,2,3,5,1,6,8,7]=>[2,3,5,4,1,6,8,7]=>1001001=>0110110
[4,2,3,5,1,7,8,6]=>[2,3,5,4,1,8,7,6]=>1001011=>0110100
[4,2,3,5,6,1,8,7]=>[2,3,6,5,4,1,8,7]=>1001101=>0110010
[4,2,3,5,7,6,1,8]=>[2,3,6,7,5,4,1,8]=>1001100=>0110011
[4,2,3,6,5,1,7,8]=>[2,3,5,6,4,1,7,8]=>1001000=>0110111
[4,2,3,6,5,1,8,7]=>[2,3,5,6,4,1,8,7]=>1001001=>0110110
[4,2,3,6,5,8,7,1]=>[2,3,5,7,8,6,4,1]=>1001010=>0110101
[4,2,3,7,5,6,1,8]=>[2,3,5,6,7,4,1,8]=>1001000=>0110111
[4,2,3,7,5,6,8,1]=>[2,3,5,6,8,7,4,1]=>1001001=>0110110
[4,2,3,8,5,6,7,1]=>[2,3,5,6,7,8,4,1]=>1001000=>0110111
[4,2,3,8,5,7,6,1]=>[2,3,5,7,6,8,4,1]=>1001010=>0110101
[4,2,3,7,6,5,8,1]=>[2,3,6,5,8,7,4,1]=>1001101=>0110010
[4,2,3,8,6,7,5,1]=>[2,3,7,6,5,8,4,1]=>1001110=>0110001
[5,2,3,4,1,6,8,7]=>[2,3,4,5,1,6,8,7]=>1000001=>0111110
[5,2,3,4,1,7,8,6]=>[2,3,4,5,1,8,7,6]=>1000011=>0111100
[5,2,3,4,1,8,7,6]=>[2,3,4,5,1,7,8,6]=>1000010=>0111101
[5,2,3,4,7,6,1,8]=>[2,3,4,6,7,5,1,8]=>1000100=>0111011
[5,2,3,4,8,6,7,1]=>[2,3,4,6,7,8,5,1]=>1000100=>0111011
[5,2,3,4,8,7,6,1]=>[2,3,4,7,6,8,5,1]=>1000110=>0111001
[6,2,3,4,5,1,8,7]=>[2,3,4,5,6,1,8,7]=>1000001=>0111110
[6,2,3,4,5,8,7,1]=>[2,3,4,5,7,8,6,1]=>1000010=>0111101
[8,2,3,4,5,7,6,1]=>[2,3,4,5,7,6,8,1]=>1000010=>0111101
[7,2,3,4,6,5,1,8]=>[2,3,4,6,5,7,1,8]=>1000100=>0111011
[8,2,3,4,7,6,5,1]=>[2,3,4,6,7,5,8,1]=>1000100=>0111011
[6,2,3,5,4,1,7,8]=>[2,3,5,4,6,1,7,8]=>1001000=>0110111
[6,2,3,5,4,7,8,1]=>[2,3,5,4,8,7,6,1]=>1001011=>0110100
[7,2,3,5,4,6,1,8]=>[2,3,5,4,6,7,1,8]=>1001000=>0110111
[8,2,3,5,4,6,7,1]=>[2,3,5,4,6,7,8,1]=>1001000=>0110111
[8,2,3,5,4,7,6,1]=>[2,3,5,4,7,6,8,1]=>1001010=>0110101
[8,2,3,5,6,7,4,1]=>[2,3,7,6,5,4,8,1]=>1001110=>0110001
[7,2,3,6,5,4,1,8]=>[2,3,5,6,4,7,1,8]=>1001000=>0110111
[8,2,3,6,5,4,7,1]=>[2,3,5,6,4,7,8,1]=>1001000=>0110111
[8,2,3,7,5,6,4,1]=>[2,3,5,6,7,4,8,1]=>1001000=>0110111
[5,2,4,3,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>1010000=>0101111
[5,2,4,3,1,6,8,7]=>[2,4,3,5,1,6,8,7]=>1010001=>0101110
[5,2,4,3,1,7,6,8]=>[2,4,3,5,1,7,6,8]=>1010010=>0101101
[5,2,4,3,1,8,7,6]=>[2,4,3,5,1,7,8,6]=>1010010=>0101101
[5,2,4,3,6,1,7,8]=>[2,4,3,6,5,1,7,8]=>1010100=>0101011
[5,2,4,3,6,1,8,7]=>[2,4,3,6,5,1,8,7]=>1010101=>0101010
[5,2,4,3,7,6,8,1]=>[2,4,3,6,8,7,5,1]=>1010101=>0101010
[6,2,4,3,5,1,8,7]=>[2,4,3,5,6,1,8,7]=>1010001=>0101110
[7,2,4,3,6,5,1,8]=>[2,4,3,6,5,7,1,8]=>1010100=>0101011
[7,2,4,3,6,5,8,1]=>[2,4,3,6,5,8,7,1]=>1010101=>0101010
[8,2,4,3,6,5,7,1]=>[2,4,3,6,5,7,8,1]=>1010100=>0101011
[8,2,4,3,6,7,5,1]=>[2,4,3,7,6,5,8,1]=>1010110=>0101001
[8,2,4,3,7,6,5,1]=>[2,4,3,6,7,5,8,1]=>1010100=>0101011
[6,2,4,5,3,1,8,7]=>[2,5,4,3,6,1,8,7]=>1011001=>0100110
[6,2,4,5,3,8,7,1]=>[2,5,4,3,7,8,6,1]=>1011010=>0100101
[7,2,4,5,3,6,1,8]=>[2,5,4,3,6,7,1,8]=>1011000=>0100111
[7,2,4,5,3,6,8,1]=>[2,5,4,3,6,8,7,1]=>1011001=>0100110
[8,2,4,5,3,7,6,1]=>[2,5,4,3,7,6,8,1]=>1011010=>0100101
[8,2,4,5,6,3,7,1]=>[2,6,5,4,3,7,8,1]=>1011100=>0100011
[8,2,4,5,6,7,3,1]=>[2,7,6,5,4,3,8,1]=>1011110=>0100001
[8,2,4,7,5,6,3,1]=>[2,5,6,7,4,3,8,1]=>1011000=>0100111
[8,2,4,7,6,5,3,1]=>[2,6,5,7,4,3,8,1]=>1011100=>0100011
[6,2,5,4,3,1,8,7]=>[2,4,5,3,6,1,8,7]=>1010001=>0101110
[6,2,5,4,3,7,8,1]=>[2,4,5,3,8,7,6,1]=>1010011=>0101100
[7,2,5,4,3,6,1,8]=>[2,4,5,3,6,7,1,8]=>1010000=>0101111
[8,2,5,4,3,6,7,1]=>[2,4,5,3,6,7,8,1]=>1010000=>0101111
[7,2,5,4,6,3,8,1]=>[2,4,6,5,3,8,7,1]=>1010101=>0101010
[8,2,5,4,7,6,3,1]=>[2,4,6,7,5,3,8,1]=>1010100=>0101011
[7,2,6,4,5,3,8,1]=>[2,4,5,6,3,8,7,1]=>1010001=>0101110
[8,2,6,4,5,3,7,1]=>[2,4,5,6,3,7,8,1]=>1010000=>0101111
[8,2,7,4,5,6,3,1]=>[2,4,5,6,7,3,8,1]=>1010000=>0101111
[8,2,7,4,6,5,3,1]=>[2,4,6,5,7,3,8,1]=>1010100=>0101011
[7,2,6,5,4,3,1,8]=>[2,5,4,6,3,7,1,8]=>1011000=>0100111
[8,2,6,5,4,3,7,1]=>[2,5,4,6,3,7,8,1]=>1011000=>0100111
[8,2,6,5,4,7,3,1]=>[2,5,4,7,6,3,8,1]=>1011010=>0100101
[8,2,7,5,4,6,3,1]=>[2,5,4,6,7,3,8,1]=>1011000=>0100111
[4,3,2,1,8,6,7,5]=>[3,2,4,1,6,7,8,5]=>1100100=>0011011
[4,3,2,8,5,6,7,1]=>[3,2,5,6,7,8,4,1]=>1101000=>0010111
[4,3,2,8,5,7,6,1]=>[3,2,5,7,6,8,4,1]=>1101010=>0010101
[5,3,2,4,7,6,1,8]=>[3,2,4,6,7,5,1,8]=>1100100=>0011011
[8,3,2,4,6,7,5,1]=>[3,2,4,7,6,5,8,1]=>1100110=>0011001
[6,3,2,5,4,1,8,7]=>[3,2,5,4,6,1,8,7]=>1101001=>0010110
[6,3,2,5,4,7,1,8]=>[3,2,5,4,7,6,1,8]=>1101010=>0010101
[6,3,2,5,4,8,7,1]=>[3,2,5,4,7,8,6,1]=>1101010=>0010101
[8,3,2,5,4,7,6,1]=>[3,2,5,4,7,6,8,1]=>1101010=>0010101
[7,3,2,5,6,4,8,1]=>[3,2,6,5,4,8,7,1]=>1101101=>0010010
[8,3,2,5,6,7,4,1]=>[3,2,7,6,5,4,8,1]=>1101110=>0010001
[8,3,2,5,7,6,4,1]=>[3,2,6,7,5,4,8,1]=>1101100=>0010011
[8,3,2,6,5,7,4,1]=>[3,2,5,7,6,4,8,1]=>1101010=>0010101
[8,3,2,7,5,6,4,1]=>[3,2,5,6,7,4,8,1]=>1101000=>0010111
[8,3,2,7,6,5,4,1]=>[3,2,6,5,7,4,8,1]=>1101100=>0010011
[5,3,4,2,1,7,8,6]=>[4,3,2,5,1,8,7,6]=>1110011=>0001100
[5,3,4,2,1,8,7,6]=>[4,3,2,5,1,7,8,6]=>1110010=>0001101
[5,3,4,2,6,1,8,7]=>[4,3,2,6,5,1,8,7]=>1110101=>0001010
[5,3,4,2,7,6,1,8]=>[4,3,2,6,7,5,1,8]=>1110100=>0001011
[5,3,4,2,7,6,8,1]=>[4,3,2,6,8,7,5,1]=>1110101=>0001010
[6,3,4,2,5,1,8,7]=>[4,3,2,5,6,1,8,7]=>1110001=>0001110
[7,3,4,2,6,5,1,8]=>[4,3,2,6,5,7,1,8]=>1110100=>0001011
[7,3,4,2,6,5,8,1]=>[4,3,2,6,5,8,7,1]=>1110101=>0001010
[8,3,4,2,6,5,7,1]=>[4,3,2,6,5,7,8,1]=>1110100=>0001011
[6,3,4,5,2,1,8,7]=>[5,4,3,2,6,1,8,7]=>1111001=>0000110
[6,3,4,5,2,8,7,1]=>[5,4,3,2,7,8,6,1]=>1111010=>0000101
[8,3,4,5,2,7,6,1]=>[5,4,3,2,7,6,8,1]=>1111010=>0000101
[8,3,4,5,7,6,2,1]=>[6,7,5,4,3,2,8,1]=>1111100=>0000011
[7,3,4,6,5,2,1,8]=>[5,6,4,3,2,7,1,8]=>1111000=>0000111
[8,3,4,7,6,5,2,1]=>[6,5,7,4,3,2,8,1]=>1111100=>0000011
[6,3,5,4,2,1,8,7]=>[4,5,3,2,6,1,8,7]=>1110001=>0001110
[6,3,5,4,2,7,1,8]=>[4,5,3,2,7,6,1,8]=>1110010=>0001101
[6,3,5,4,2,7,8,1]=>[4,5,3,2,8,7,6,1]=>1110011=>0001100
[8,3,5,4,2,6,7,1]=>[4,5,3,2,6,7,8,1]=>1110000=>0001111
[7,3,5,4,6,2,8,1]=>[4,6,5,3,2,8,7,1]=>1110101=>0001010
[8,3,5,4,6,7,2,1]=>[4,7,6,5,3,2,8,1]=>1110110=>0001001
[8,3,5,4,7,6,2,1]=>[4,6,7,5,3,2,8,1]=>1110100=>0001011
[7,3,6,4,5,2,8,1]=>[4,5,6,3,2,8,7,1]=>1110001=>0001110
[8,3,6,4,5,2,7,1]=>[4,5,6,3,2,7,8,1]=>1110000=>0001111
[8,3,7,4,5,6,2,1]=>[4,5,6,7,3,2,8,1]=>1110000=>0001111
[8,3,7,4,6,5,2,1]=>[4,6,5,7,3,2,8,1]=>1110100=>0001011
[7,3,6,5,4,2,1,8]=>[5,4,6,3,2,7,1,8]=>1111000=>0000111
[7,3,6,5,4,2,8,1]=>[5,4,6,3,2,8,7,1]=>1111001=>0000110
[8,3,6,5,4,2,7,1]=>[5,4,6,3,2,7,8,1]=>1111000=>0000111
[8,3,7,5,6,4,2,1]=>[6,5,4,7,3,2,8,1]=>1111100=>0000011
[6,4,3,2,5,1,8,7]=>[3,4,2,5,6,1,8,7]=>1100001=>0011110
[6,4,3,2,5,8,7,1]=>[3,4,2,5,7,8,6,1]=>1100010=>0011101
[8,4,3,2,5,7,6,1]=>[3,4,2,5,7,6,8,1]=>1100010=>0011101
[7,4,3,2,6,5,1,8]=>[3,4,2,6,5,7,1,8]=>1100100=>0011011
[7,4,3,2,6,5,8,1]=>[3,4,2,6,5,8,7,1]=>1100101=>0011010
[8,4,3,2,6,5,7,1]=>[3,4,2,6,5,7,8,1]=>1100100=>0011011
[8,4,3,2,6,7,5,1]=>[3,4,2,7,6,5,8,1]=>1100110=>0011001
[8,4,3,2,7,6,5,1]=>[3,4,2,6,7,5,8,1]=>1100100=>0011011
[6,4,3,5,2,1,8,7]=>[3,5,4,2,6,1,8,7]=>1101001=>0010110
[8,4,3,5,2,7,6,1]=>[3,5,4,2,7,6,8,1]=>1101010=>0010101
[7,4,3,6,5,2,8,1]=>[3,5,6,4,2,8,7,1]=>1101001=>0010110
[8,4,3,7,5,6,2,1]=>[3,5,6,7,4,2,8,1]=>1101000=>0010111
[6,5,3,4,2,1,8,7]=>[3,4,5,2,6,1,8,7]=>1100001=>0011110
[8,5,3,4,2,7,6,1]=>[3,4,5,2,7,6,8,1]=>1100010=>0011101
[8,5,3,4,7,6,2,1]=>[3,4,6,7,5,2,8,1]=>1100100=>0011011
[8,7,3,4,6,5,2,1]=>[3,4,6,5,7,2,8,1]=>1100100=>0011011
[7,6,3,5,4,2,1,8]=>[3,5,4,6,2,7,1,8]=>1101000=>0010111
[7,6,3,5,4,2,8,1]=>[3,5,4,6,2,8,7,1]=>1101001=>0010110
[8,6,3,5,4,2,7,1]=>[3,5,4,6,2,7,8,1]=>1101000=>0010111
[8,6,3,5,4,7,2,1]=>[3,5,4,7,6,2,8,1]=>1101010=>0010101
[8,7,3,5,4,6,2,1]=>[3,5,4,6,7,2,8,1]=>1101000=>0010111
[8,7,3,5,6,4,2,1]=>[3,6,5,4,7,2,8,1]=>1101100=>0010011
[8,7,3,6,5,4,2,1]=>[3,5,6,4,7,2,8,1]=>1101000=>0010111
[8,5,4,3,2,7,6,1]=>[4,3,5,2,7,6,8,1]=>1110010=>0001101
[8,5,4,3,7,6,2,1]=>[4,3,6,7,5,2,8,1]=>1110100=>0001011
[8,7,4,3,6,5,2,1]=>[4,3,6,5,7,2,8,1]=>1110100=>0001011
[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>1100101=>0011010
[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]=>1011001=>0100110
[2,4,1,6,3,5,8,7]=>[6,4,2,1,3,5,8,7]=>1101001=>0010110
[2,4,6,1,3,5,8,7]=>[6,2,1,4,3,5,8,7]=>1110001=>0001110
[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]=>1010110=>0101001
[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]=>1100110=>0011001
[2,1,4,6,3,8,5,7]=>[2,1,8,6,4,3,5,7]=>1011010=>0100101
[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>1101010=>0010101
[2,4,6,1,3,8,5,7]=>[8,6,2,1,4,3,5,7]=>1110010=>0001101
[2,1,4,6,8,3,5,7]=>[2,1,8,4,3,6,5,7]=>1011100=>0100011
[2,4,1,6,8,3,5,7]=>[8,4,2,1,3,6,5,7]=>1101100=>0010011
[2,4,6,1,8,3,5,7]=>[8,2,1,4,3,6,5,7]=>1110100=>0001011
[2,4,6,8,1,3,5,7]=>[8,2,1,6,4,3,5,7]=>1111000=>0000111
[2,4,1,3,6,5,7,8]=>[4,2,1,3,6,5,7,8]=>1100100=>0011011
[2,1,4,6,3,5,7,8]=>[2,1,6,4,3,5,7,8]=>1011000=>0100111
[2,4,1,6,3,5,7,8]=>[6,4,2,1,3,5,7,8]=>1101000=>0010111
[2,4,6,1,3,5,7,8]=>[6,2,1,4,3,5,7,8]=>1110000=>0001111
[2,4,1,6,3,7,5,8]=>[7,6,4,2,1,3,5,8]=>1101010=>0010101
[2,4,1,3,6,7,8,5]=>[4,2,1,3,8,7,6,5]=>1100111=>0011000
[2,1,4,6,3,7,8,5]=>[2,1,8,7,6,4,3,5]=>1011011=>0100100
[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>1101011=>0010100
[2,4,6,1,3,7,8,5]=>[8,7,6,2,1,4,3,5]=>1110011=>0001100
[2,1,4,6,7,3,8,5]=>[2,1,8,7,4,3,6,5]=>1011101=>0100010
[2,4,1,6,7,3,8,5]=>[8,7,4,2,1,3,6,5]=>1101101=>0010010
[2,4,6,1,7,3,8,5]=>[8,7,2,1,4,3,6,5]=>1110101=>0001010
[2,1,4,6,7,8,3,5]=>[2,1,8,4,3,7,6,5]=>1011110=>0100001
[2,4,1,6,7,8,3,5]=>[8,4,2,1,3,7,6,5]=>1101110=>0010001
[2,4,6,1,7,8,3,5]=>[8,2,1,4,3,7,6,5]=>1110110=>0001001
[2,4,6,7,1,8,3,5]=>[8,2,1,7,6,4,3,5]=>1111010=>0000101
[2,4,6,7,8,1,3,5]=>[8,2,1,7,4,3,6,5]=>1111100=>0000011
[2,1,4,3,7,5,8,6]=>[2,1,4,3,8,7,5,6]=>1010101=>0101010
[2,4,1,3,7,5,8,6]=>[4,2,1,3,8,7,5,6]=>1100101=>0011010
[2,1,4,7,3,5,8,6]=>[2,1,8,7,4,3,5,6]=>1011001=>0100110
[2,4,1,7,3,5,8,6]=>[8,7,4,2,1,3,5,6]=>1101001=>0010110
[2,4,7,1,3,5,8,6]=>[8,7,2,1,4,3,5,6]=>1110001=>0001110
[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>1010110=>0101001
[2,4,1,3,7,8,5,6]=>[4,2,1,3,8,5,7,6]=>1100110=>0011001
[2,4,1,7,3,8,5,6]=>[8,4,2,1,3,5,7,6]=>1101010=>0010101
[2,4,7,1,3,8,5,6]=>[8,2,1,4,3,5,7,6]=>1110010=>0001101
[2,1,4,7,8,3,5,6]=>[2,1,8,4,3,7,5,6]=>1011100=>0100011
[2,4,1,7,8,3,5,6]=>[8,4,2,1,3,7,5,6]=>1101100=>0010011
[2,4,7,1,8,3,5,6]=>[8,2,1,4,3,7,5,6]=>1110100=>0001011
[2,4,7,8,1,3,5,6]=>[8,2,1,7,4,3,5,6]=>1111000=>0000111
[2,4,5,1,3,7,6,8]=>[5,2,1,4,3,7,6,8]=>1110010=>0001101
[2,4,1,3,5,7,8,6]=>[4,2,1,3,5,8,7,6]=>1100011=>0011100
[2,4,1,5,3,7,8,6]=>[5,4,2,1,3,8,7,6]=>1101011=>0010100
[2,4,5,1,3,7,8,6]=>[5,2,1,4,3,8,7,6]=>1110011=>0001100
[2,1,4,5,7,3,8,6]=>[2,1,8,7,5,4,3,6]=>1011101=>0100010
[2,4,5,7,1,3,8,6]=>[8,7,2,1,5,4,3,6]=>1111001=>0000110
[2,1,4,5,7,8,3,6]=>[2,1,8,5,4,3,7,6]=>1011110=>0100001
[2,4,5,1,7,8,3,6]=>[8,5,2,1,4,3,7,6]=>1110110=>0001001
[2,4,5,7,1,8,3,6]=>[8,2,1,5,4,3,7,6]=>1111010=>0000101
[2,4,5,7,8,1,3,6]=>[8,2,1,7,5,4,3,6]=>1111100=>0000011
[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>1010100=>0101011
[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]=>1100100=>0011011
[2,4,1,8,3,5,6,7]=>[8,4,2,1,3,5,6,7]=>1101000=>0010111
[2,1,4,3,5,8,6,7]=>[2,1,4,3,5,8,6,7]=>1010010=>0101101
[2,1,4,5,8,3,6,7]=>[2,1,8,5,4,3,6,7]=>1011100=>0100011
[2,4,1,5,8,3,6,7]=>[8,5,4,2,1,3,6,7]=>1101100=>0010011
[2,4,5,1,8,3,6,7]=>[8,5,2,1,4,3,6,7]=>1110100=>0001011
[2,4,1,5,6,3,8,7]=>[6,5,4,2,1,3,8,7]=>1101101=>0010010
[2,4,5,1,6,3,8,7]=>[6,5,2,1,4,3,8,7]=>1110101=>0001010
[2,4,5,6,1,3,8,7]=>[6,2,1,5,4,3,8,7]=>1111001=>0000110
[2,1,4,5,6,8,3,7]=>[2,1,8,6,5,4,3,7]=>1011110=>0100001
[2,4,1,5,6,8,3,7]=>[8,6,5,4,2,1,3,7]=>1101110=>0010001
[2,4,5,1,6,8,3,7]=>[8,6,5,2,1,4,3,7]=>1110110=>0001001
[2,4,5,6,1,8,3,7]=>[8,6,2,1,5,4,3,7]=>1111010=>0000101
[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>1100000=>0011111
[2,4,1,5,3,6,7,8]=>[5,4,2,1,3,6,7,8]=>1101000=>0010111
[2,4,5,1,3,6,7,8]=>[5,2,1,4,3,6,7,8]=>1110000=>0001111
[2,4,1,5,6,3,7,8]=>[6,5,4,2,1,3,7,8]=>1101100=>0010011
[2,4,5,6,1,3,7,8]=>[6,2,1,5,4,3,7,8]=>1111000=>0000111
[2,4,1,5,6,7,3,8]=>[7,6,5,4,2,1,3,8]=>1101110=>0010001
[2,4,5,1,6,7,3,8]=>[7,6,5,2,1,4,3,8]=>1110110=>0001001
[2,4,5,6,1,7,3,8]=>[7,6,2,1,5,4,3,8]=>1111010=>0000101
[2,4,5,6,7,1,3,8]=>[7,2,1,6,5,4,3,8]=>1111100=>0000011
[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>1101111=>0010000
[2,4,5,1,6,7,8,3]=>[8,7,6,5,2,1,4,3]=>1110111=>0001000
[2,4,5,6,7,1,8,3]=>[8,7,2,1,6,5,4,3]=>1111101=>0000010
[2,4,5,6,7,8,1,3]=>[8,2,1,7,6,5,4,3]=>1111110=>0000001
[2,1,5,3,6,4,8,7]=>[2,1,6,5,3,4,8,7]=>1010101=>0101010
[2,5,1,3,6,4,8,7]=>[6,5,2,1,3,4,8,7]=>1100101=>0011010
[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>1011001=>0100110
[2,5,6,1,3,4,8,7]=>[6,2,1,5,3,4,8,7]=>1110001=>0001110
[2,5,1,3,6,8,4,7]=>[8,6,5,2,1,3,4,7]=>1100110=>0011001
[2,5,1,6,3,8,4,7]=>[8,6,2,1,3,5,4,7]=>1101010=>0010101
[2,5,6,1,3,8,4,7]=>[8,6,2,1,5,3,4,7]=>1110010=>0001101
[2,5,1,6,8,3,4,7]=>[8,2,1,3,6,5,4,7]=>1101100=>0010011
[2,1,5,3,6,7,4,8]=>[2,1,7,6,5,3,4,8]=>1010110=>0101001
[2,5,6,1,7,3,4,8]=>[7,2,1,6,5,3,4,8]=>1110100=>0001011
[2,1,5,3,6,7,8,4]=>[2,1,8,7,6,5,3,4]=>1010111=>0101000
[2,5,1,3,6,7,8,4]=>[8,7,6,5,2,1,3,4]=>1100111=>0011000
[2,1,5,6,3,7,8,4]=>[2,1,8,7,6,3,5,4]=>1011011=>0100100
[2,5,6,1,3,7,8,4]=>[8,7,6,2,1,5,3,4]=>1110011=>0001100
[2,1,5,6,7,3,8,4]=>[2,1,8,7,3,6,5,4]=>1011101=>0100010
[2,5,1,6,7,3,8,4]=>[8,7,2,1,3,6,5,4]=>1101101=>0010010
[2,1,5,6,7,8,3,4]=>[2,1,8,3,7,6,5,4]=>1011110=>0100001
[2,5,1,6,7,8,3,4]=>[8,2,1,3,7,6,5,4]=>1101110=>0010001
[2,5,6,1,7,8,3,4]=>[8,2,1,7,6,5,3,4]=>1110110=>0001001
[2,5,6,7,1,8,3,4]=>[8,2,1,7,6,3,5,4]=>1111010=>0000101
[2,1,5,3,7,4,8,6]=>[2,1,8,7,5,3,4,6]=>1010101=>0101010
[2,5,1,3,7,4,8,6]=>[8,7,5,2,1,3,4,6]=>1100101=>0011010
[2,1,5,7,3,4,8,6]=>[2,1,8,7,3,5,4,6]=>1011001=>0100110
[2,5,1,7,3,4,8,6]=>[8,7,2,1,3,5,4,6]=>1101001=>0010110
[2,5,7,1,3,4,8,6]=>[8,7,2,1,5,3,4,6]=>1110001=>0001110
[2,1,5,3,7,8,4,6]=>[2,1,8,5,3,4,7,6]=>1010110=>0101001
[2,1,5,7,3,8,4,6]=>[2,1,8,3,5,4,7,6]=>1011010=>0100101
[2,5,1,7,3,8,4,6]=>[8,2,1,3,5,4,7,6]=>1101010=>0010101
[2,1,5,7,8,3,4,6]=>[2,1,8,3,7,5,4,6]=>1011100=>0100011
[2,5,7,1,8,3,4,6]=>[8,2,1,7,5,3,4,6]=>1110100=>0001011
[2,5,7,8,1,3,4,6]=>[8,2,1,7,3,5,4,6]=>1111000=>0000111
[2,3,5,1,4,7,6,8]=>[5,3,2,1,4,7,6,8]=>1110010=>0001101
[2,3,5,7,1,4,6,8]=>[7,3,2,1,5,4,6,8]=>1111000=>0000111
[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>1110101=>0001010
[2,3,5,7,1,4,8,6]=>[8,7,3,2,1,5,4,6]=>1111001=>0000110
[2,3,1,5,7,8,4,6]=>[3,2,1,8,5,4,7,6]=>1101110=>0010001
[2,3,5,7,1,8,4,6]=>[8,3,2,1,5,4,7,6]=>1111010=>0000101
[2,1,5,3,8,4,6,7]=>[2,1,8,5,3,4,6,7]=>1010100=>0101011
[2,5,1,3,8,4,6,7]=>[8,5,2,1,3,4,6,7]=>1100100=>0011011
[2,3,5,1,4,8,6,7]=>[5,3,2,1,4,8,6,7]=>1110010=>0001101
[2,1,3,5,8,4,6,7]=>[2,1,3,8,5,4,6,7]=>1001100=>0110011
[2,3,5,1,8,4,6,7]=>[8,5,3,2,1,4,6,7]=>1110100=>0001011
[2,3,5,8,1,4,6,7]=>[8,3,2,1,5,4,6,7]=>1111000=>0000111
[2,1,5,3,4,6,8,7]=>[2,1,5,3,4,6,8,7]=>1010001=>0101110
[2,3,5,1,6,4,8,7]=>[6,5,3,2,1,4,8,7]=>1110101=>0001010
[2,3,5,6,1,4,8,7]=>[6,3,2,1,5,4,8,7]=>1111001=>0000110
[2,1,3,5,6,8,4,7]=>[2,1,3,8,6,5,4,7]=>1001110=>0110001
[2,3,1,5,6,8,4,7]=>[3,2,1,8,6,5,4,7]=>1101110=>0010001
[2,3,5,1,6,8,4,7]=>[8,6,5,3,2,1,4,7]=>1110110=>0001001
[2,3,5,6,1,8,4,7]=>[8,6,3,2,1,5,4,7]=>1111010=>0000101
[2,3,5,6,8,1,4,7]=>[8,3,2,1,6,5,4,7]=>1111100=>0000011
[2,1,5,3,4,6,7,8]=>[2,1,5,3,4,6,7,8]=>1010000=>0101111
[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>1100000=>0011111
[2,3,5,1,4,6,7,8]=>[5,3,2,1,4,6,7,8]=>1110000=>0001111
[2,3,5,1,6,4,7,8]=>[6,5,3,2,1,4,7,8]=>1110100=>0001011
[2,3,5,6,1,4,7,8]=>[6,3,2,1,5,4,7,8]=>1111000=>0000111
[2,3,5,6,1,7,4,8]=>[7,6,3,2,1,5,4,8]=>1111010=>0000101
[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>1110111=>0001000
[2,3,5,6,1,7,8,4]=>[8,7,6,3,2,1,5,4]=>1111011=>0000100
[2,3,5,6,7,1,8,4]=>[8,7,3,2,1,6,5,4]=>1111101=>0000010
[2,3,5,6,7,8,1,4]=>[8,3,2,1,7,6,5,4]=>1111110=>0000001
[2,1,6,3,7,4,8,5]=>[2,1,8,7,3,4,6,5]=>1010101=>0101010
[2,6,1,3,7,4,8,5]=>[8,7,2,1,3,4,6,5]=>1100101=>0011010
[2,1,6,7,3,4,8,5]=>[2,1,8,7,3,6,4,5]=>1011001=>0100110
[2,6,1,7,3,4,8,5]=>[8,7,2,1,3,6,4,5]=>1101001=>0010110
[2,6,7,1,3,4,8,5]=>[8,7,2,1,6,3,4,5]=>1110001=>0001110
[2,1,6,3,7,8,4,5]=>[2,1,8,3,4,7,6,5]=>1010110=>0101001
[2,1,6,7,3,8,4,5]=>[2,1,8,3,7,6,4,5]=>1011010=>0100101
[2,6,1,7,3,8,4,5]=>[8,2,1,3,7,6,4,5]=>1101010=>0010101
[2,6,7,1,3,8,4,5]=>[8,2,1,7,6,3,4,5]=>1110010=>0001101
[2,1,6,7,8,3,4,5]=>[2,1,8,3,7,4,6,5]=>1011100=>0100011
[2,6,1,7,8,3,4,5]=>[8,2,1,3,7,4,6,5]=>1101100=>0010011
[2,3,1,6,4,7,5,8]=>[3,2,1,7,6,4,5,8]=>1101010=>0010101
[2,3,6,1,4,7,5,8]=>[7,6,3,2,1,4,5,8]=>1110010=>0001101
[2,3,6,7,1,4,5,8]=>[7,3,2,1,6,4,5,8]=>1111000=>0000111
[2,1,6,3,4,7,8,5]=>[2,1,8,7,6,3,4,5]=>1010011=>0101100
[2,6,1,3,4,7,8,5]=>[8,7,6,2,1,3,4,5]=>1100011=>0011100
[2,3,6,1,4,7,8,5]=>[8,7,6,3,2,1,4,5]=>1110011=>0001100
[2,1,3,6,7,4,8,5]=>[2,1,3,8,7,4,6,5]=>1001101=>0110010
[2,3,6,7,1,4,8,5]=>[8,7,3,2,1,6,4,5]=>1111001=>0000110
[2,1,3,6,7,8,4,5]=>[2,1,3,8,4,7,6,5]=>1001110=>0110001
[2,3,1,6,7,8,4,5]=>[3,2,1,8,4,7,6,5]=>1101110=>0010001
[2,3,6,1,7,8,4,5]=>[8,3,2,1,4,7,6,5]=>1110110=>0001001
[2,3,6,7,1,8,4,5]=>[8,3,2,1,7,6,4,5]=>1111010=>0000101
[2,3,6,7,8,1,4,5]=>[8,3,2,1,7,4,6,5]=>1111100=>0000011
[2,6,1,3,8,4,5,7]=>[8,2,1,3,4,6,5,7]=>1100100=>0011011
[2,1,6,8,3,4,5,7]=>[2,1,8,3,6,4,5,7]=>1011000=>0100111
[2,6,1,8,3,4,5,7]=>[8,2,1,3,6,4,5,7]=>1101000=>0010111
[2,6,8,1,3,4,5,7]=>[8,2,1,6,3,4,5,7]=>1110000=>0001111
[2,1,3,6,4,8,5,7]=>[2,1,3,8,6,4,5,7]=>1001010=>0110101
[2,3,1,6,4,8,5,7]=>[3,2,1,8,6,4,5,7]=>1101010=>0010101
[2,3,6,1,4,8,5,7]=>[8,6,3,2,1,4,5,7]=>1110010=>0001101
[2,3,1,6,8,4,5,7]=>[3,2,1,8,4,6,5,7]=>1101100=>0010011
[2,3,6,1,8,4,5,7]=>[8,3,2,1,4,6,5,7]=>1110100=>0001011
[2,3,6,8,1,4,5,7]=>[8,3,2,1,6,4,5,7]=>1111000=>0000111
[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>1010001=>0101110
[2,1,3,6,4,5,8,7]=>[2,1,3,6,4,5,8,7]=>1001001=>0110110
[2,3,6,1,4,5,8,7]=>[6,3,2,1,4,5,8,7]=>1110001=>0001110
[2,3,4,1,6,8,5,7]=>[4,3,2,1,8,6,5,7]=>1110110=>0001001
[2,3,4,6,1,8,5,7]=>[8,6,4,3,2,1,5,7]=>1111010=>0000101
[2,3,4,6,8,1,5,7]=>[8,4,3,2,1,6,5,7]=>1111100=>0000011
[2,6,1,3,4,5,7,8]=>[6,2,1,3,4,5,7,8]=>1100000=>0011111
[2,1,3,6,4,5,7,8]=>[2,1,3,6,4,5,7,8]=>1001000=>0110111
[2,3,1,6,4,5,7,8]=>[3,2,1,6,4,5,7,8]=>1101000=>0010111
[2,3,6,1,4,5,7,8]=>[6,3,2,1,4,5,7,8]=>1110000=>0001111
[2,3,4,6,1,5,7,8]=>[6,4,3,2,1,5,7,8]=>1111000=>0000111
[2,3,4,6,1,7,5,8]=>[7,6,4,3,2,1,5,8]=>1111010=>0000101
[2,3,4,6,7,1,5,8]=>[7,4,3,2,1,6,5,8]=>1111100=>0000011
[2,3,4,6,1,7,8,5]=>[8,7,6,4,3,2,1,5]=>1111011=>0000100
[2,3,4,6,7,8,1,5]=>[8,4,3,2,1,7,6,5]=>1111110=>0000001
[2,1,7,3,8,4,5,6]=>[2,1,8,3,4,7,5,6]=>1010100=>0101011
[2,7,1,3,8,4,5,6]=>[8,2,1,3,4,7,5,6]=>1100100=>0011011
[2,1,7,8,3,4,5,6]=>[2,1,8,3,7,4,5,6]=>1011000=>0100111
[2,7,8,1,3,4,5,6]=>[8,2,1,7,3,4,5,6]=>1110000=>0001111
[2,7,1,3,4,8,5,6]=>[8,2,1,3,4,5,7,6]=>1100010=>0011101
[2,1,3,7,4,8,5,6]=>[2,1,3,8,4,5,7,6]=>1001010=>0110101
[2,3,1,7,4,8,5,6]=>[3,2,1,8,4,5,7,6]=>1101010=>0010101
[2,3,7,1,4,8,5,6]=>[8,3,2,1,4,5,7,6]=>1110010=>0001101
[2,1,3,7,8,4,5,6]=>[2,1,3,8,4,7,5,6]=>1001100=>0110011
[2,3,1,7,8,4,5,6]=>[3,2,1,8,4,7,5,6]=>1101100=>0010011
[2,3,7,8,1,4,5,6]=>[8,3,2,1,7,4,5,6]=>1111000=>0000111
[2,1,7,3,4,5,8,6]=>[2,1,8,7,3,4,5,6]=>1010001=>0101110
[2,7,1,3,4,5,8,6]=>[8,7,2,1,3,4,5,6]=>1100001=>0011110
[2,3,1,7,4,5,8,6]=>[3,2,1,8,7,4,5,6]=>1101001=>0010110
[2,3,7,1,4,5,8,6]=>[8,7,3,2,1,4,5,6]=>1110001=>0001110
[2,1,3,4,7,5,8,6]=>[2,1,3,4,8,7,5,6]=>1000101=>0111010
[2,3,4,1,7,5,8,6]=>[4,3,2,1,8,7,5,6]=>1110101=>0001010
[2,3,4,7,1,5,8,6]=>[8,7,4,3,2,1,5,6]=>1111001=>0000110
[2,1,3,4,7,8,5,6]=>[2,1,3,4,8,5,7,6]=>1000110=>0111001
[2,3,1,4,7,8,5,6]=>[3,2,1,4,8,5,7,6]=>1100110=>0011001
[2,3,4,1,7,8,5,6]=>[4,3,2,1,8,5,7,6]=>1110110=>0001001
[2,3,4,7,1,8,5,6]=>[8,4,3,2,1,5,7,6]=>1111010=>0000101
[2,3,4,7,8,1,5,6]=>[8,4,3,2,1,7,5,6]=>1111100=>0000011
[2,1,7,3,4,5,6,8]=>[2,1,7,3,4,5,6,8]=>1010000=>0101111
[2,7,1,3,4,5,6,8]=>[7,2,1,3,4,5,6,8]=>1100000=>0011111
[2,3,7,1,4,5,6,8]=>[7,3,2,1,4,5,6,8]=>1110000=>0001111
[2,1,3,4,7,5,6,8]=>[2,1,3,4,7,5,6,8]=>1000100=>0111011
[2,3,4,1,7,5,6,8]=>[4,3,2,1,7,5,6,8]=>1110100=>0001011
[2,3,4,7,1,5,6,8]=>[7,4,3,2,1,5,6,8]=>1111000=>0000111
[2,3,4,5,7,1,6,8]=>[7,5,4,3,2,1,6,8]=>1111100=>0000011
[2,3,4,5,7,1,8,6]=>[8,7,5,4,3,2,1,6]=>1111101=>0000010
[2,3,4,5,7,8,1,6]=>[8,5,4,3,2,1,7,6]=>1111110=>0000001
[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>1010000=>0101111
[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]=>1100000=>0011111
[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>1001000=>0110111
[2,3,1,8,4,5,6,7]=>[3,2,1,8,4,5,6,7]=>1101000=>0010111
[2,3,8,1,4,5,6,7]=>[8,3,2,1,4,5,6,7]=>1110000=>0001111
[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>1000100=>0111011
[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>1100100=>0011011
[2,3,4,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>1110100=>0001011
[2,3,4,8,1,5,6,7]=>[8,4,3,2,1,5,6,7]=>1111000=>0000111
[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,6,7]=>1000010=>0111101
[2,3,1,4,5,8,6,7]=>[3,2,1,4,5,8,6,7]=>1100010=>0011101
[2,3,4,1,5,8,6,7]=>[4,3,2,1,5,8,6,7]=>1110010=>0001101
[2,3,4,5,1,8,6,7]=>[5,4,3,2,1,8,6,7]=>1111010=>0000101
[2,3,4,5,8,1,6,7]=>[8,5,4,3,2,1,6,7]=>1111100=>0000011
[2,3,4,5,6,8,1,7]=>[8,6,5,4,3,2,1,7]=>1111110=>0000001
[3,1,4,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>1010101=>0101010
[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>1100101=>0011010
[3,1,4,6,2,5,8,7]=>[6,4,3,1,2,5,8,7]=>1011001=>0100110
[3,4,1,6,2,5,8,7]=>[6,4,1,3,2,5,8,7]=>1101001=>0010110
[3,1,4,2,6,8,5,7]=>[4,3,1,2,8,6,5,7]=>1010110=>0101001
[3,4,1,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]=>1100110=>0011001
[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>1011010=>0100101
[3,4,1,6,2,8,5,7]=>[8,6,4,1,3,2,5,7]=>1101010=>0010101
[3,1,4,6,8,2,5,7]=>[8,4,3,1,2,6,5,7]=>1011100=>0100011
[3,4,1,6,8,2,5,7]=>[8,4,1,3,2,6,5,7]=>1101100=>0010011
[3,1,4,2,6,5,7,8]=>[4,3,1,2,6,5,7,8]=>1010100=>0101011
[3,4,6,1,2,7,5,8]=>[7,6,1,4,3,2,5,8]=>1110010=>0001101
[3,4,1,6,7,2,5,8]=>[7,4,1,3,2,6,5,8]=>1101100=>0010011
[3,1,4,2,6,7,8,5]=>[4,3,1,2,8,7,6,5]=>1010111=>0101000
[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,7,6,5]=>1100111=>0011000
[3,1,4,6,2,7,8,5]=>[8,7,6,4,3,1,2,5]=>1011011=>0100100
[3,4,1,6,2,7,8,5]=>[8,7,6,4,1,3,2,5]=>1101011=>0010100
[3,4,6,1,2,7,8,5]=>[8,7,6,1,4,3,2,5]=>1110011=>0001100
[3,4,1,6,7,2,8,5]=>[8,7,4,1,3,2,6,5]=>1101101=>0010010
[3,4,6,1,7,2,8,5]=>[8,7,1,4,3,2,6,5]=>1110101=>0001010
[3,4,6,7,1,2,8,5]=>[8,7,1,6,4,3,2,5]=>1111001=>0000110
[3,1,4,6,7,8,2,5]=>[8,4,3,1,2,7,6,5]=>1011110=>0100001
[3,4,1,6,7,8,2,5]=>[8,4,1,3,2,7,6,5]=>1101110=>0010001
[3,4,6,1,7,8,2,5]=>[8,1,4,3,2,7,6,5]=>1110110=>0001001
[3,4,6,7,1,8,2,5]=>[8,1,7,6,4,3,2,5]=>1111010=>0000101
[3,4,6,7,8,1,2,5]=>[8,1,7,4,3,2,6,5]=>1111100=>0000011
[3,1,4,2,7,5,8,6]=>[4,3,1,2,8,7,5,6]=>1010101=>0101010
[3,4,1,2,7,5,8,6]=>[4,1,3,2,8,7,5,6]=>1100101=>0011010
[3,4,7,1,2,5,8,6]=>[8,7,1,4,3,2,5,6]=>1110001=>0001110
[3,1,4,2,7,8,5,6]=>[4,3,1,2,8,5,7,6]=>1010110=>0101001
[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>1100110=>0011001
[3,1,4,7,2,8,5,6]=>[8,4,3,1,2,5,7,6]=>1011010=>0100101
[3,4,7,1,8,2,5,6]=>[8,1,4,3,2,7,5,6]=>1110100=>0001011
[3,4,1,2,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>1100010=>0011101
[3,1,4,5,2,7,6,8]=>[5,4,3,1,2,7,6,8]=>1011010=>0100101
[3,4,1,5,7,2,6,8]=>[7,5,4,1,3,2,6,8]=>1101100=>0010011
[3,1,4,2,5,7,8,6]=>[4,3,1,2,5,8,7,6]=>1010011=>0101100
[3,1,4,5,2,7,8,6]=>[5,4,3,1,2,8,7,6]=>1011011=>0100100
[3,4,5,1,2,7,8,6]=>[5,1,4,3,2,8,7,6]=>1110011=>0001100
[3,1,4,5,7,2,8,6]=>[8,7,5,4,3,1,2,6]=>1011101=>0100010
[3,4,1,5,7,2,8,6]=>[8,7,5,4,1,3,2,6]=>1101101=>0010010
[3,4,1,5,7,8,2,6]=>[8,5,4,1,3,2,7,6]=>1101110=>0010001
[3,4,5,7,1,8,2,6]=>[8,1,5,4,3,2,7,6]=>1111010=>0000101
[3,4,5,7,8,1,2,6]=>[8,1,7,5,4,3,2,6]=>1111100=>0000011
[3,1,4,2,8,5,6,7]=>[4,3,1,2,8,5,6,7]=>1010100=>0101011
[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>1100100=>0011011
[3,4,1,8,2,5,6,7]=>[8,4,1,3,2,5,6,7]=>1101000=>0010111
[3,4,8,1,2,5,6,7]=>[8,1,4,3,2,5,6,7]=>1110000=>0001111
[3,4,1,5,2,8,6,7]=>[5,4,1,3,2,8,6,7]=>1101010=>0010101
[3,4,1,5,8,2,6,7]=>[8,5,4,1,3,2,6,7]=>1101100=>0010011
[3,4,5,8,1,2,6,7]=>[8,1,5,4,3,2,6,7]=>1111000=>0000111
[3,4,5,1,2,6,8,7]=>[5,1,4,3,2,6,8,7]=>1110001=>0001110
[3,1,4,5,6,2,8,7]=>[6,5,4,3,1,2,8,7]=>1011101=>0100010
[3,4,1,5,6,2,8,7]=>[6,5,4,1,3,2,8,7]=>1101101=>0010010
[3,4,5,1,6,2,8,7]=>[6,5,1,4,3,2,8,7]=>1110101=>0001010
[3,4,5,6,1,2,8,7]=>[6,1,5,4,3,2,8,7]=>1111001=>0000110
[3,1,4,5,6,8,2,7]=>[8,6,5,4,3,1,2,7]=>1011110=>0100001
[3,4,1,5,6,8,2,7]=>[8,6,5,4,1,3,2,7]=>1101110=>0010001
[3,4,5,6,1,8,2,7]=>[8,6,1,5,4,3,2,7]=>1111010=>0000101
[3,4,5,6,8,1,2,7]=>[8,1,6,5,4,3,2,7]=>1111100=>0000011
[3,1,4,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>1010000=>0101111
[3,1,4,5,2,6,7,8]=>[5,4,3,1,2,6,7,8]=>1011000=>0100111
[3,4,1,5,2,6,7,8]=>[5,4,1,3,2,6,7,8]=>1101000=>0010111
[3,1,4,5,6,2,7,8]=>[6,5,4,3,1,2,7,8]=>1011100=>0100011
[3,4,5,1,6,2,7,8]=>[6,5,1,4,3,2,7,8]=>1110100=>0001011
[3,1,4,5,6,7,2,8]=>[7,6,5,4,3,1,2,8]=>1011110=>0100001
[3,4,1,5,6,7,2,8]=>[7,6,5,4,1,3,2,8]=>1101110=>0010001
[3,4,5,1,6,7,2,8]=>[7,6,5,1,4,3,2,8]=>1110110=>0001001
[3,1,4,5,6,7,8,2]=>[8,7,6,5,4,3,1,2]=>1011111=>0100000
[3,4,1,5,6,7,8,2]=>[8,7,6,5,4,1,3,2]=>1101111=>0010000
[3,4,5,1,6,7,8,2]=>[8,7,6,5,1,4,3,2]=>1110111=>0001000
[3,4,5,6,1,7,8,2]=>[8,7,6,1,5,4,3,2]=>1111011=>0000100
[3,4,5,6,7,1,8,2]=>[8,7,1,6,5,4,3,2]=>1111101=>0000010
[3,1,5,2,6,4,8,7]=>[6,5,3,1,2,4,8,7]=>1010101=>0101010
[3,1,5,6,2,4,8,7]=>[6,3,1,2,5,4,8,7]=>1011001=>0100110
[3,5,1,6,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>1101001=>0010110
[3,5,1,2,6,8,4,7]=>[8,6,5,1,3,2,4,7]=>1100110=>0011001
[3,1,5,6,2,8,4,7]=>[8,6,3,1,2,5,4,7]=>1011010=>0100101
[3,5,6,1,2,8,4,7]=>[8,6,1,5,3,2,4,7]=>1110010=>0001101
[3,1,5,6,8,2,4,7]=>[8,3,1,2,6,5,4,7]=>1011100=>0100011
[3,5,1,6,8,2,4,7]=>[8,1,3,2,6,5,4,7]=>1101100=>0010011
[3,5,6,8,1,2,4,7]=>[8,1,6,3,2,5,4,7]=>1111000=>0000111
[3,5,1,2,6,7,4,8]=>[7,6,5,1,3,2,4,8]=>1100110=>0011001
[3,5,6,1,7,2,4,8]=>[7,1,6,5,3,2,4,8]=>1110100=>0001011
[3,5,6,7,1,2,4,8]=>[7,1,6,3,2,5,4,8]=>1111000=>0000111
[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>1010111=>0101000
[3,5,1,2,6,7,8,4]=>[8,7,6,5,1,3,2,4]=>1100111=>0011000
[3,5,1,6,2,7,8,4]=>[8,7,6,1,3,2,5,4]=>1101011=>0010100
[3,5,6,1,2,7,8,4]=>[8,7,6,1,5,3,2,4]=>1110011=>0001100
[3,5,6,1,7,2,8,4]=>[8,7,1,6,5,3,2,4]=>1110101=>0001010
[3,1,5,6,7,8,2,4]=>[8,3,1,2,7,6,5,4]=>1011110=>0100001
[3,5,1,6,7,8,2,4]=>[8,1,3,2,7,6,5,4]=>1101110=>0010001
[3,5,6,1,7,8,2,4]=>[8,1,7,6,5,3,2,4]=>1110110=>0001001
[3,5,6,7,8,1,2,4]=>[8,1,7,3,2,6,5,4]=>1111100=>0000011
[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>1010101=>0101010
[3,5,1,7,2,4,8,6]=>[8,7,1,3,2,5,4,6]=>1101001=>0010110
[3,1,5,2,7,8,4,6]=>[8,5,3,1,2,4,7,6]=>1010110=>0101001
[3,5,1,2,7,8,4,6]=>[8,5,1,3,2,4,7,6]=>1100110=>0011001
[3,1,5,7,2,8,4,6]=>[8,3,1,2,5,4,7,6]=>1011010=>0100101
[3,5,1,7,2,8,4,6]=>[8,1,3,2,5,4,7,6]=>1101010=>0010101
[3,5,7,1,2,8,4,6]=>[8,1,5,3,2,4,7,6]=>1110010=>0001101
[3,5,1,7,8,2,4,6]=>[8,1,3,2,7,5,4,6]=>1101100=>0010011
[3,5,7,8,1,2,4,6]=>[8,1,7,3,2,5,4,6]=>1111000=>0000111
[3,1,5,2,7,4,6,8]=>[7,5,3,1,2,4,6,8]=>1010100=>0101011
[3,5,1,2,7,4,6,8]=>[7,5,1,3,2,4,6,8]=>1100100=>0011011
[3,1,5,7,2,4,6,8]=>[7,3,1,2,5,4,6,8]=>1011000=>0100111
[3,5,1,7,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>1101000=>0010111
[3,5,7,1,2,4,6,8]=>[7,1,5,3,2,4,6,8]=>1110000=>0001111
[3,1,5,2,4,7,6,8]=>[5,3,1,2,4,7,6,8]=>1010010=>0101101
[3,5,1,2,4,7,6,8]=>[5,1,3,2,4,7,6,8]=>1100010=>0011101
[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>1001010=>0110101
[1,3,5,2,4,7,6,8]=>[1,5,3,2,4,7,6,8]=>0110010=>1001101
[3,1,2,5,7,4,6,8]=>[3,1,2,7,5,4,6,8]=>1001100=>0110011
[1,3,2,5,7,4,6,8]=>[1,3,2,7,5,4,6,8]=>0101100=>1010011
[1,3,5,2,7,4,6,8]=>[1,7,5,3,2,4,6,8]=>0110100=>1001011
[1,3,5,7,2,4,6,8]=>[1,7,3,2,5,4,6,8]=>0111000=>1000111
[3,1,5,2,4,7,8,6]=>[5,3,1,2,4,8,7,6]=>1010011=>0101100
[3,5,1,2,4,7,8,6]=>[5,1,3,2,4,8,7,6]=>1100011=>0011100
[1,3,5,2,4,7,8,6]=>[1,5,3,2,4,8,7,6]=>0110011=>1001100
[3,1,2,5,7,4,8,6]=>[3,1,2,8,7,5,4,6]=>1001101=>0110010
[1,3,2,5,7,4,8,6]=>[1,3,2,8,7,5,4,6]=>0101101=>1010010
[1,3,5,2,7,4,8,6]=>[1,8,7,5,3,2,4,6]=>0110101=>1001010
[1,3,5,7,2,4,8,6]=>[1,8,7,3,2,5,4,6]=>0111001=>1000110
[3,1,2,5,7,8,4,6]=>[3,1,2,8,5,4,7,6]=>1001110=>0110001
[1,3,2,5,7,8,4,6]=>[1,3,2,8,5,4,7,6]=>0101110=>1010001
[1,3,5,2,7,8,4,6]=>[1,8,5,3,2,4,7,6]=>0110110=>1001001
[1,3,5,7,2,8,4,6]=>[1,8,3,2,5,4,7,6]=>0111010=>1000101
[1,3,5,7,8,2,4,6]=>[1,8,3,2,7,5,4,6]=>0111100=>1000011
[3,1,5,2,8,4,6,7]=>[8,5,3,1,2,4,6,7]=>1010100=>0101011
[3,5,1,2,8,4,6,7]=>[8,5,1,3,2,4,6,7]=>1100100=>0011011
[3,1,5,8,2,4,6,7]=>[8,3,1,2,5,4,6,7]=>1011000=>0100111
[3,5,1,8,2,4,6,7]=>[8,1,3,2,5,4,6,7]=>1101000=>0010111
[3,1,5,2,4,8,6,7]=>[5,3,1,2,4,8,6,7]=>1010010=>0101101
[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>1100010=>0011101
[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>0101010=>1010101
[1,3,5,2,4,8,6,7]=>[1,5,3,2,4,8,6,7]=>0110010=>1001101
[1,3,2,5,8,4,6,7]=>[1,3,2,8,5,4,6,7]=>0101100=>1010011
[1,3,5,2,8,4,6,7]=>[1,8,5,3,2,4,6,7]=>0110100=>1001011
[1,3,5,8,2,4,6,7]=>[1,8,3,2,5,4,6,7]=>0111000=>1000111
[3,1,5,2,4,6,8,7]=>[5,3,1,2,4,6,8,7]=>1010001=>0101110
[3,5,1,2,4,6,8,7]=>[5,1,3,2,4,6,8,7]=>1100001=>0011110
[3,1,2,5,4,6,8,7]=>[3,1,2,5,4,6,8,7]=>1001001=>0110110
[1,3,5,2,4,6,8,7]=>[1,5,3,2,4,6,8,7]=>0110001=>1001110
[1,3,5,2,6,4,8,7]=>[1,6,5,3,2,4,8,7]=>0110101=>1001010
[3,1,2,5,6,8,4,7]=>[3,1,2,8,6,5,4,7]=>1001110=>0110001
[1,3,5,2,6,8,4,7]=>[1,8,6,5,3,2,4,7]=>0110110=>1001001
[1,3,5,6,2,8,4,7]=>[1,8,6,3,2,5,4,7]=>0111010=>1000101
[3,1,5,2,4,6,7,8]=>[5,3,1,2,4,6,7,8]=>1010000=>0101111
[3,5,1,2,4,6,7,8]=>[5,1,3,2,4,6,7,8]=>1100000=>0011111
[1,3,5,2,4,6,7,8]=>[1,5,3,2,4,6,7,8]=>0110000=>1001111
[1,3,5,2,6,4,7,8]=>[1,6,5,3,2,4,7,8]=>0110100=>1001011
[1,3,5,6,2,4,7,8]=>[1,6,3,2,5,4,7,8]=>0111000=>1000111
[1,3,5,2,6,7,4,8]=>[1,7,6,5,3,2,4,8]=>0110110=>1001001
[1,3,5,6,2,7,4,8]=>[1,7,6,3,2,5,4,8]=>0111010=>1000101
[3,1,2,5,6,7,8,4]=>[3,1,2,8,7,6,5,4]=>1001111=>0110000
[1,3,5,2,6,7,8,4]=>[1,8,7,6,5,3,2,4]=>0110111=>1001000
[1,3,5,6,2,7,8,4]=>[1,8,7,6,3,2,5,4]=>0111011=>1000100
[1,3,5,6,7,8,2,4]=>[1,8,3,2,7,6,5,4]=>0111110=>1000001
[3,1,6,2,7,4,8,5]=>[8,7,3,1,2,4,6,5]=>1010101=>0101010
[3,6,1,2,7,4,8,5]=>[8,7,1,3,2,4,6,5]=>1100101=>0011010
[3,6,1,7,2,4,8,5]=>[8,7,1,3,2,6,4,5]=>1101001=>0010110
[3,6,1,2,7,8,4,5]=>[8,1,3,2,4,7,6,5]=>1100110=>0011001
[3,1,6,7,2,8,4,5]=>[8,3,1,2,7,6,4,5]=>1011010=>0100101
[3,6,1,7,2,8,4,5]=>[8,1,3,2,7,6,4,5]=>1101010=>0010101
[3,6,7,1,2,8,4,5]=>[8,1,7,6,3,2,4,5]=>1110010=>0001101
[3,6,1,7,8,2,4,5]=>[8,1,3,2,7,4,6,5]=>1101100=>0010011
[3,6,7,8,1,2,4,5]=>[8,1,7,3,2,6,4,5]=>1111000=>0000111
[3,1,6,2,7,4,5,8]=>[7,3,1,2,4,6,5,8]=>1010100=>0101011
[3,1,2,6,4,7,5,8]=>[3,1,2,7,6,4,5,8]=>1001010=>0110101
[1,3,2,6,4,7,5,8]=>[1,3,2,7,6,4,5,8]=>0101010=>1010101
[1,3,6,2,4,7,5,8]=>[1,7,6,3,2,4,5,8]=>0110010=>1001101
[1,3,2,6,7,4,5,8]=>[1,3,2,7,4,6,5,8]=>0101100=>1010011
[1,3,6,2,7,4,5,8]=>[1,7,3,2,4,6,5,8]=>0110100=>1001011
[3,1,6,2,4,7,8,5]=>[8,7,6,3,1,2,4,5]=>1010011=>0101100
[3,6,1,2,4,7,8,5]=>[8,7,6,1,3,2,4,5]=>1100011=>0011100
[3,1,2,6,4,7,8,5]=>[3,1,2,8,7,6,4,5]=>1001011=>0110100
[1,3,2,6,4,7,8,5]=>[1,3,2,8,7,6,4,5]=>0101011=>1010100
[1,3,6,2,4,7,8,5]=>[1,8,7,6,3,2,4,5]=>0110011=>1001100
[3,1,2,6,7,4,8,5]=>[3,1,2,8,7,4,6,5]=>1001101=>0110010
[1,3,2,6,7,4,8,5]=>[1,3,2,8,7,4,6,5]=>0101101=>1010010
[1,3,6,2,7,4,8,5]=>[1,8,7,3,2,4,6,5]=>0110101=>1001010
[1,3,6,7,2,4,8,5]=>[1,8,7,3,2,6,4,5]=>0111001=>1000110
[3,1,6,2,8,4,5,7]=>[8,3,1,2,4,6,5,7]=>1010100=>0101011
[3,6,1,2,8,4,5,7]=>[8,1,3,2,4,6,5,7]=>1100100=>0011011
[3,1,6,8,2,4,5,7]=>[8,3,1,2,6,4,5,7]=>1011000=>0100111
[3,6,8,1,2,4,5,7]=>[8,1,6,3,2,4,5,7]=>1110000=>0001111
[3,6,1,2,4,8,5,7]=>[8,6,1,3,2,4,5,7]=>1100010=>0011101
[1,3,2,6,4,8,5,7]=>[1,3,2,8,6,4,5,7]=>0101010=>1010101
[1,3,6,2,4,8,5,7]=>[1,8,6,3,2,4,5,7]=>0110010=>1001101
[1,3,2,6,8,4,5,7]=>[1,3,2,8,4,6,5,7]=>0101100=>1010011
[3,1,6,2,4,5,8,7]=>[6,3,1,2,4,5,8,7]=>1010001=>0101110
[3,6,1,2,4,5,8,7]=>[6,1,3,2,4,5,8,7]=>1100001=>0011110
[3,1,2,6,4,5,8,7]=>[3,1,2,6,4,5,8,7]=>1001001=>0110110
[3,1,2,4,6,5,8,7]=>[3,1,2,4,6,5,8,7]=>1000101=>0111010
[3,1,2,4,6,8,5,7]=>[3,1,2,4,8,6,5,7]=>1000110=>0111001
[1,3,2,4,6,8,5,7]=>[1,3,2,4,8,6,5,7]=>0100110=>1011001
[3,1,6,2,4,5,7,8]=>[6,3,1,2,4,5,7,8]=>1010000=>0101111
[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>0101000=>1010111
[1,3,6,2,4,5,7,8]=>[1,6,3,2,4,5,7,8]=>0110000=>1001111
[1,3,4,6,2,5,7,8]=>[1,6,4,3,2,5,7,8]=>0111000=>1000111
[3,1,2,4,6,7,8,5]=>[3,1,2,4,8,7,6,5]=>1000111=>0111000
[1,3,4,6,7,2,8,5]=>[1,8,7,4,3,2,6,5]=>0111101=>1000010
[1,3,4,6,7,8,2,5]=>[1,8,4,3,2,7,6,5]=>0111110=>1000001
[3,1,7,2,8,4,5,6]=>[8,3,1,2,4,7,5,6]=>1010100=>0101011
[3,1,7,8,2,4,5,6]=>[8,3,1,2,7,4,5,6]=>1011000=>0100111
[3,7,8,1,2,4,5,6]=>[8,1,7,3,2,4,5,6]=>1110000=>0001111
[3,7,1,2,4,8,5,6]=>[8,1,3,2,4,5,7,6]=>1100010=>0011101
[3,1,2,7,4,8,5,6]=>[3,1,2,8,4,5,7,6]=>1001010=>0110101
[1,3,2,7,4,8,5,6]=>[1,3,2,8,4,5,7,6]=>0101010=>1010101
[1,3,7,2,4,8,5,6]=>[1,8,3,2,4,5,7,6]=>0110010=>1001101
[3,1,2,7,8,4,5,6]=>[3,1,2,8,4,7,5,6]=>1001100=>0110011
[1,3,7,2,8,4,5,6]=>[1,8,3,2,4,7,5,6]=>0110100=>1001011
[3,7,1,2,4,5,8,6]=>[8,7,1,3,2,4,5,6]=>1100001=>0011110
[1,3,7,2,4,5,8,6]=>[1,8,7,3,2,4,5,6]=>0110001=>1001110
[3,1,2,4,7,5,8,6]=>[3,1,2,4,8,7,5,6]=>1000101=>0111010
[1,3,4,7,2,5,8,6]=>[1,8,7,4,3,2,5,6]=>0111001=>1000110
[3,1,2,4,7,8,5,6]=>[3,1,2,4,8,5,7,6]=>1000110=>0111001
[1,3,2,4,7,8,5,6]=>[1,3,2,4,8,5,7,6]=>0100110=>1011001
[1,3,4,7,8,2,5,6]=>[1,8,4,3,2,7,5,6]=>0111100=>1000011
[3,1,7,2,4,5,6,8]=>[7,3,1,2,4,5,6,8]=>1010000=>0101111
[3,7,1,2,4,5,6,8]=>[7,1,3,2,4,5,6,8]=>1100000=>0011111
[3,1,2,7,4,5,6,8]=>[3,1,2,7,4,5,6,8]=>1001000=>0110111
[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>0101000=>1010111
[1,3,7,2,4,5,6,8]=>[1,7,3,2,4,5,6,8]=>0110000=>1001111
[3,1,2,4,7,5,6,8]=>[3,1,2,4,7,5,6,8]=>1000100=>0111011
[1,3,4,7,2,5,6,8]=>[1,7,4,3,2,5,6,8]=>0111000=>1000111
[3,1,2,4,5,7,6,8]=>[3,1,2,4,5,7,6,8]=>1000010=>0111101
[1,3,4,5,7,2,6,8]=>[1,7,5,4,3,2,6,8]=>0111100=>1000011
[1,3,4,5,7,2,8,6]=>[1,8,7,5,4,3,2,6]=>0111101=>1000010
[1,3,4,5,7,8,2,6]=>[1,8,5,4,3,2,7,6]=>0111110=>1000001
[3,1,8,2,4,5,6,7]=>[8,3,1,2,4,5,6,7]=>1010000=>0101111
[3,8,1,2,4,5,6,7]=>[8,1,3,2,4,5,6,7]=>1100000=>0011111
[3,1,2,8,4,5,6,7]=>[3,1,2,8,4,5,6,7]=>1001000=>0110111
[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>0101000=>1010111
[1,3,8,2,4,5,6,7]=>[1,8,3,2,4,5,6,7]=>0110000=>1001111
[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>1000100=>0111011
[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>0100100=>1011011
[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>0110100=>1001011
[1,3,4,8,2,5,6,7]=>[1,8,4,3,2,5,6,7]=>0111000=>1000111
[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>1000010=>0111101
[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>0100010=>1011101
[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,8,6,7]=>0110010=>1001101
[1,3,4,5,8,2,6,7]=>[1,8,5,4,3,2,6,7]=>0111100=>1000011
[3,1,2,4,5,6,8,7]=>[3,1,2,4,5,6,8,7]=>1000001=>0111110
[1,3,4,5,6,8,2,7]=>[1,8,6,5,4,3,2,7]=>0111110=>1000001
[4,1,5,2,6,3,8,7]=>[6,5,1,2,4,3,8,7]=>1010101=>0101010
[4,5,1,2,6,3,8,7]=>[6,5,1,4,2,3,8,7]=>1100101=>0011010
[4,1,5,6,2,3,8,7]=>[6,1,2,5,4,3,8,7]=>1011001=>0100110
[4,5,1,6,2,3,8,7]=>[6,1,5,4,2,3,8,7]=>1101001=>0010110
[4,5,6,1,2,3,8,7]=>[6,1,5,2,4,3,8,7]=>1110001=>0001110
[4,1,5,2,6,8,3,7]=>[8,6,5,1,2,4,3,7]=>1010110=>0101001
[4,1,5,6,2,8,3,7]=>[8,6,1,2,5,4,3,7]=>1011010=>0100101
[4,5,6,1,2,8,3,7]=>[8,6,1,5,2,4,3,7]=>1110010=>0001101
[4,1,5,6,8,2,3,7]=>[8,1,2,6,5,4,3,7]=>1011100=>0100011
[4,5,1,2,6,7,3,8]=>[7,6,5,1,4,2,3,8]=>1100110=>0011001
[4,5,6,1,2,7,3,8]=>[7,6,1,5,2,4,3,8]=>1110010=>0001101
[4,1,5,6,7,2,3,8]=>[7,1,2,6,5,4,3,8]=>1011100=>0100011
[4,5,1,6,7,2,3,8]=>[7,1,6,5,4,2,3,8]=>1101100=>0010011
[4,5,6,1,7,2,3,8]=>[7,1,6,5,2,4,3,8]=>1110100=>0001011
[4,1,5,2,6,7,8,3]=>[8,7,6,5,1,2,4,3]=>1010111=>0101000
[4,5,1,2,6,7,8,3]=>[8,7,6,5,1,4,2,3]=>1100111=>0011000
[4,5,1,6,2,7,8,3]=>[8,7,6,1,5,4,2,3]=>1101011=>0010100
[4,5,6,1,2,7,8,3]=>[8,7,6,1,5,2,4,3]=>1110011=>0001100
[4,1,5,6,7,2,8,3]=>[8,7,1,2,6,5,4,3]=>1011101=>0100010
[4,5,6,1,7,2,8,3]=>[8,7,1,6,5,2,4,3]=>1110101=>0001010
[4,5,6,7,1,2,8,3]=>[8,7,1,6,2,5,4,3]=>1111001=>0000110
[4,1,5,6,7,8,2,3]=>[8,1,2,7,6,5,4,3]=>1011110=>0100001
[4,5,1,6,7,8,2,3]=>[8,1,7,6,5,4,2,3]=>1101110=>0010001
[4,5,6,1,7,8,2,3]=>[8,1,7,6,5,2,4,3]=>1110110=>0001001
[4,5,6,7,1,8,2,3]=>[8,1,7,6,2,5,4,3]=>1111010=>0000101
[4,1,5,2,7,3,8,6]=>[8,7,5,1,2,4,3,6]=>1010101=>0101010
[4,5,1,2,7,3,8,6]=>[8,7,5,1,4,2,3,6]=>1100101=>0011010
[4,5,1,7,2,3,8,6]=>[8,7,1,5,4,2,3,6]=>1101001=>0010110
[4,1,5,2,7,8,3,6]=>[8,5,1,2,4,3,7,6]=>1010110=>0101001
[4,5,1,2,7,8,3,6]=>[8,5,1,4,2,3,7,6]=>1100110=>0011001
[4,5,7,1,2,8,3,6]=>[8,1,5,2,4,3,7,6]=>1110010=>0001101
[4,5,1,7,8,2,3,6]=>[8,1,7,5,4,2,3,6]=>1101100=>0010011
[4,5,7,8,1,2,3,6]=>[8,1,7,2,5,4,3,6]=>1111000=>0000111
[4,1,5,2,7,3,6,8]=>[7,5,1,2,4,3,6,8]=>1010100=>0101011
[4,5,1,2,7,3,6,8]=>[7,5,1,4,2,3,6,8]=>1100100=>0011011
[4,5,1,7,2,3,6,8]=>[7,1,5,4,2,3,6,8]=>1101000=>0010111
[4,1,5,2,3,7,6,8]=>[5,1,2,4,3,7,6,8]=>1010010=>0101101
[1,4,2,5,3,7,6,8]=>[1,5,4,2,3,7,6,8]=>0101010=>1010101
[1,4,5,2,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>0110010=>1001101
[1,4,5,7,2,3,6,8]=>[1,7,2,5,4,3,6,8]=>0111000=>1000111
[4,1,5,2,3,7,8,6]=>[5,1,2,4,3,8,7,6]=>1010011=>0101100
[4,1,2,5,3,7,8,6]=>[5,4,1,2,3,8,7,6]=>1001011=>0110100
[1,4,2,5,3,7,8,6]=>[1,5,4,2,3,8,7,6]=>0101011=>1010100
[1,4,5,2,3,7,8,6]=>[1,5,2,4,3,8,7,6]=>0110011=>1001100
[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>1001101=>0110010
[1,4,5,7,2,3,8,6]=>[1,8,7,2,5,4,3,6]=>0111001=>1000110
[4,1,2,5,7,8,3,6]=>[8,5,4,1,2,3,7,6]=>1001110=>0110001
[1,4,2,5,7,8,3,6]=>[1,8,5,4,2,3,7,6]=>0101110=>1010001
[1,4,5,7,8,2,3,6]=>[1,8,2,7,5,4,3,6]=>0111100=>1000011
[4,1,5,2,8,3,6,7]=>[8,5,1,2,4,3,6,7]=>1010100=>0101011
[4,5,1,2,8,3,6,7]=>[8,5,1,4,2,3,6,7]=>1100100=>0011011
[4,1,5,8,2,3,6,7]=>[8,1,2,5,4,3,6,7]=>1011000=>0100111
[4,5,1,8,2,3,6,7]=>[8,1,5,4,2,3,6,7]=>1101000=>0010111
[4,5,1,2,3,8,6,7]=>[5,1,4,2,3,8,6,7]=>1100010=>0011101
[4,1,2,5,3,8,6,7]=>[5,4,1,2,3,8,6,7]=>1001010=>0110101
[1,4,2,5,3,8,6,7]=>[1,5,4,2,3,8,6,7]=>0101010=>1010101
[1,4,5,2,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>0110010=>1001101
[4,1,2,5,8,3,6,7]=>[8,5,4,1,2,3,6,7]=>1001100=>0110011
[1,4,2,5,8,3,6,7]=>[1,8,5,4,2,3,6,7]=>0101100=>1010011
[1,4,2,5,3,6,8,7]=>[1,5,4,2,3,6,8,7]=>0101001=>1010110
[4,1,2,5,6,3,8,7]=>[6,5,4,1,2,3,8,7]=>1001101=>0110010
[4,1,2,5,6,8,3,7]=>[8,6,5,4,1,2,3,7]=>1001110=>0110001
[1,4,2,5,6,8,3,7]=>[1,8,6,5,4,2,3,7]=>0101110=>1010001
[4,1,5,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>1010000=>0101111
[4,1,2,5,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>1001000=>0110111
[1,4,2,5,3,6,7,8]=>[1,5,4,2,3,6,7,8]=>0101000=>1010111
[1,4,5,2,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>0110000=>1001111
[4,1,2,5,6,3,7,8]=>[6,5,4,1,2,3,7,8]=>1001100=>0110011
[4,1,2,5,6,7,3,8]=>[7,6,5,4,1,2,3,8]=>1001110=>0110001
[1,4,2,5,6,7,3,8]=>[1,7,6,5,4,2,3,8]=>0101110=>1010001
[1,4,5,2,6,7,3,8]=>[1,7,6,5,2,4,3,8]=>0110110=>1001001
[1,4,5,6,7,2,3,8]=>[1,7,2,6,5,4,3,8]=>0111100=>1000011
[4,1,2,5,6,7,8,3]=>[8,7,6,5,4,1,2,3]=>1001111=>0110000
[1,4,2,5,6,7,8,3]=>[1,8,7,6,5,4,2,3]=>0101111=>1010000
[1,4,5,2,6,7,8,3]=>[1,8,7,6,5,2,4,3]=>0110111=>1001000
[1,4,5,6,2,7,8,3]=>[1,8,7,6,2,5,4,3]=>0111011=>1000100
[1,4,5,6,7,2,8,3]=>[1,8,7,2,6,5,4,3]=>0111101=>1000010
[1,4,5,6,7,8,2,3]=>[1,8,2,7,6,5,4,3]=>0111110=>1000001
[4,1,6,2,7,3,8,5]=>[8,7,1,2,4,3,6,5]=>1010101=>0101010
[4,6,1,7,2,3,8,5]=>[8,7,1,6,4,2,3,5]=>1101001=>0010110
[4,6,1,2,7,8,3,5]=>[8,1,4,2,3,7,6,5]=>1100110=>0011001
[4,6,1,7,2,8,3,5]=>[8,1,7,6,4,2,3,5]=>1101010=>0010101
[4,6,7,1,2,8,3,5]=>[8,1,7,6,2,4,3,5]=>1110010=>0001101
[4,1,6,7,8,2,3,5]=>[8,1,2,7,4,3,6,5]=>1011100=>0100011
[4,6,1,7,8,2,3,5]=>[8,1,7,4,2,3,6,5]=>1101100=>0010011
[4,6,7,1,8,2,3,5]=>[8,1,7,2,4,3,6,5]=>1110100=>0001011
[4,6,7,8,1,2,3,5]=>[8,1,7,2,6,4,3,5]=>1111000=>0000111
[4,1,6,7,2,3,5,8]=>[7,1,2,6,4,3,5,8]=>1011000=>0100111
[4,6,1,7,2,3,5,8]=>[7,1,6,4,2,3,5,8]=>1101000=>0010111
[4,6,1,2,3,7,5,8]=>[7,6,1,4,2,3,5,8]=>1100010=>0011101
[1,4,2,6,3,7,5,8]=>[1,7,6,4,2,3,5,8]=>0101010=>1010101
[1,4,6,2,7,3,5,8]=>[1,7,2,4,3,6,5,8]=>0110100=>1001011
[1,4,6,7,2,3,5,8]=>[1,7,2,6,4,3,5,8]=>0111000=>1000111
[4,1,6,2,3,7,8,5]=>[8,7,6,1,2,4,3,5]=>1010011=>0101100
[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>1001011=>0110100
[1,4,6,2,3,7,8,5]=>[1,8,7,6,2,4,3,5]=>0110011=>1001100
[4,1,2,6,7,3,8,5]=>[8,7,4,1,2,3,6,5]=>1001101=>0110010
[1,4,2,6,7,8,3,5]=>[1,8,4,2,3,7,6,5]=>0101110=>1010001
[1,4,6,2,7,8,3,5]=>[1,8,2,4,3,7,6,5]=>0110110=>1001001
[1,4,6,7,2,8,3,5]=>[1,8,2,7,6,4,3,5]=>0111010=>1000101
[1,4,6,7,8,2,3,5]=>[1,8,2,7,4,3,6,5]=>0111100=>1000011
[4,1,6,2,8,3,5,7]=>[8,1,2,4,3,6,5,7]=>1010100=>0101011
[4,6,1,2,8,3,5,7]=>[8,1,4,2,3,6,5,7]=>1100100=>0011011
[4,6,1,8,2,3,5,7]=>[8,1,6,4,2,3,5,7]=>1101000=>0010111
[4,6,8,1,2,3,5,7]=>[8,1,6,2,4,3,5,7]=>1110000=>0001111
[4,1,6,2,3,8,5,7]=>[8,6,1,2,4,3,5,7]=>1010010=>0101101
[4,6,1,2,3,8,5,7]=>[8,6,1,4,2,3,5,7]=>1100010=>0011101
[1,4,2,6,3,8,5,7]=>[1,8,6,4,2,3,5,7]=>0101010=>1010101
[1,4,6,2,3,8,5,7]=>[1,8,6,2,4,3,5,7]=>0110010=>1001101
[1,4,2,6,8,3,5,7]=>[1,8,4,2,3,6,5,7]=>0101100=>1010011
[1,4,6,2,8,3,5,7]=>[1,8,2,4,3,6,5,7]=>0110100=>1001011
[1,4,6,8,2,3,5,7]=>[1,8,2,6,4,3,5,7]=>0111000=>1000111
[4,1,6,2,3,5,8,7]=>[6,1,2,4,3,5,8,7]=>1010001=>0101110
[4,6,1,2,3,5,8,7]=>[6,1,4,2,3,5,8,7]=>1100001=>0011110
[1,4,2,6,3,5,8,7]=>[1,6,4,2,3,5,8,7]=>0101001=>1010110
[1,4,6,2,3,5,8,7]=>[1,6,2,4,3,5,8,7]=>0110001=>1001110
[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>1000101=>0111010
[1,4,2,3,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>0100101=>1011010
[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]=>1000110=>0111001
[1,2,4,3,6,8,5,7]=>[1,2,4,3,8,6,5,7]=>0010110=>1101001
[1,2,4,6,3,8,5,7]=>[1,2,8,6,4,3,5,7]=>0011010=>1100101
[1,2,4,6,8,3,5,7]=>[1,2,8,4,3,6,5,7]=>0011100=>1100011
[4,1,6,2,3,5,7,8]=>[6,1,2,4,3,5,7,8]=>1010000=>0101111
[4,6,1,2,3,5,7,8]=>[6,1,4,2,3,5,7,8]=>1100000=>0011111
[4,1,2,6,3,5,7,8]=>[6,4,1,2,3,5,7,8]=>1001000=>0110111
[1,4,2,6,3,5,7,8]=>[1,6,4,2,3,5,7,8]=>0101000=>1010111
[1,4,6,2,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>0110000=>1001111
[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>1000100=>0111011
[1,4,2,3,6,5,7,8]=>[1,4,2,3,6,5,7,8]=>0100100=>1011011
[1,2,4,6,3,5,7,8]=>[1,2,6,4,3,5,7,8]=>0011000=>1100111
[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>1000110=>0111001
[1,2,4,6,3,7,5,8]=>[1,2,7,6,4,3,5,8]=>0011010=>1100101
[4,1,2,3,6,7,8,5]=>[4,1,2,3,8,7,6,5]=>1000111=>0111000
[1,4,2,3,6,7,8,5]=>[1,4,2,3,8,7,6,5]=>0100111=>1011000
[1,2,4,6,3,7,8,5]=>[1,2,8,7,6,4,3,5]=>0011011=>1100100
[1,2,4,6,7,3,8,5]=>[1,2,8,7,4,3,6,5]=>0011101=>1100010
[1,2,4,6,7,8,3,5]=>[1,2,8,4,3,7,6,5]=>0011110=>1100001
[4,7,1,2,8,3,5,6]=>[8,1,4,2,3,7,5,6]=>1100100=>0011011
[4,7,1,8,2,3,5,6]=>[8,1,7,4,2,3,5,6]=>1101000=>0010111
[4,7,8,1,2,3,5,6]=>[8,1,7,2,4,3,5,6]=>1110000=>0001111
[4,1,7,2,3,8,5,6]=>[8,1,2,4,3,5,7,6]=>1010010=>0101101
[4,7,1,2,3,8,5,6]=>[8,1,4,2,3,5,7,6]=>1100010=>0011101
[1,4,2,7,3,8,5,6]=>[1,8,4,2,3,5,7,6]=>0101010=>1010101
[4,1,2,7,8,3,5,6]=>[8,4,1,2,3,7,5,6]=>1001100=>0110011
[1,4,2,7,8,3,5,6]=>[1,8,4,2,3,7,5,6]=>0101100=>1010011
[1,4,7,2,8,3,5,6]=>[1,8,2,4,3,7,5,6]=>0110100=>1001011
[1,4,7,8,2,3,5,6]=>[1,8,2,7,4,3,5,6]=>0111000=>1000111
[4,1,7,2,3,5,8,6]=>[8,7,1,2,4,3,5,6]=>1010001=>0101110
[4,7,1,2,3,5,8,6]=>[8,7,1,4,2,3,5,6]=>1100001=>0011110
[4,1,2,7,3,5,8,6]=>[8,7,4,1,2,3,5,6]=>1001001=>0110110
[1,4,2,7,3,5,8,6]=>[1,8,7,4,2,3,5,6]=>0101001=>1010110
[4,1,2,3,7,5,8,6]=>[4,1,2,3,8,7,5,6]=>1000101=>0111010
[1,4,2,3,7,5,8,6]=>[1,4,2,3,8,7,5,6]=>0100101=>1011010
[1,2,4,3,7,5,8,6]=>[1,2,4,3,8,7,5,6]=>0010101=>1101010
[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,5,7,6]=>1000110=>0111001
[1,4,2,3,7,8,5,6]=>[1,4,2,3,8,5,7,6]=>0100110=>1011001
[1,2,4,3,7,8,5,6]=>[1,2,4,3,8,5,7,6]=>0010110=>1101001
[1,2,4,7,3,8,5,6]=>[1,2,8,4,3,5,7,6]=>0011010=>1100101
[1,2,4,7,8,3,5,6]=>[1,2,8,4,3,7,5,6]=>0011100=>1100011
[4,1,7,2,3,5,6,8]=>[7,1,2,4,3,5,6,8]=>1010000=>0101111
[4,7,1,2,3,5,6,8]=>[7,1,4,2,3,5,6,8]=>1100000=>0011111
[4,1,2,7,3,5,6,8]=>[7,4,1,2,3,5,6,8]=>1001000=>0110111
[1,4,2,7,3,5,6,8]=>[1,7,4,2,3,5,6,8]=>0101000=>1010111
[1,4,7,2,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>0110000=>1001111
[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>1000100=>0111011
[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>0100100=>1011011
[1,2,4,3,7,5,6,8]=>[1,2,4,3,7,5,6,8]=>0010100=>1101011
[1,2,4,7,3,5,6,8]=>[1,2,7,4,3,5,6,8]=>0011000=>1100111
[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>1000010=>0111101
[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>0100010=>1011101
[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>1000011=>0111100
[1,4,2,3,5,7,8,6]=>[1,4,2,3,5,8,7,6]=>0100011=>1011100
[1,2,4,5,7,3,8,6]=>[1,2,8,7,5,4,3,6]=>0011101=>1100010
[4,1,8,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]=>1010000=>0101111
[4,8,1,2,3,5,6,7]=>[8,1,4,2,3,5,6,7]=>1100000=>0011111
[4,1,2,8,3,5,6,7]=>[8,4,1,2,3,5,6,7]=>1001000=>0110111
[1,4,2,8,3,5,6,7]=>[1,8,4,2,3,5,6,7]=>0101000=>1010111
[1,4,8,2,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>0110000=>1001111
[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>1000100=>0111011
[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>0100100=>1011011
[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>0010100=>1101011
[1,2,4,8,3,5,6,7]=>[1,2,8,4,3,5,6,7]=>0011000=>1100111
[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>1000010=>0111101
[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>0100010=>1011101
[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,6,7]=>0010010=>1101101
[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>0011010=>1100101
[1,2,4,5,8,3,6,7]=>[1,2,8,5,4,3,6,7]=>0011100=>1100011
[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>1000001=>0111110
[1,4,2,3,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>0100001=>1011110
[1,2,4,5,6,8,3,7]=>[1,2,8,6,5,4,3,7]=>0011110=>1100001
[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>0100000=>1011111
[5,1,6,2,7,3,8,4]=>[8,7,1,2,6,5,3,4]=>1010101=>0101010
[5,6,1,2,7,3,8,4]=>[8,7,1,6,5,2,3,4]=>1100101=>0011010
[5,6,1,7,2,3,8,4]=>[8,7,1,6,2,3,5,4]=>1101001=>0010110
[5,6,7,1,2,3,8,4]=>[8,7,1,6,2,5,3,4]=>1110001=>0001110
[5,6,1,2,7,8,3,4]=>[8,1,7,6,5,2,3,4]=>1100110=>0011001
[5,1,6,7,2,8,3,4]=>[8,1,2,7,6,3,5,4]=>1011010=>0100101
[5,1,6,7,8,2,3,4]=>[8,1,2,7,3,6,5,4]=>1011100=>0100011
[5,6,1,7,8,2,3,4]=>[8,1,7,2,3,6,5,4]=>1101100=>0010011
[5,1,6,2,7,3,4,8]=>[7,1,2,6,5,3,4,8]=>1010100=>0101011
[5,1,2,6,3,7,4,8]=>[7,6,1,2,3,5,4,8]=>1001010=>0110101
[5,1,2,6,7,3,4,8]=>[7,1,2,3,6,5,4,8]=>1001100=>0110011
[1,5,6,7,2,3,4,8]=>[1,7,2,6,3,5,4,8]=>0111000=>1000111
[5,1,6,2,3,7,8,4]=>[8,7,6,1,2,5,3,4]=>1010011=>0101100
[5,6,1,2,3,7,8,4]=>[8,7,6,1,5,2,3,4]=>1100011=>0011100
[5,1,2,6,3,7,8,4]=>[8,7,6,1,2,3,5,4]=>1001011=>0110100
[5,1,2,6,7,3,8,4]=>[8,7,1,2,3,6,5,4]=>1001101=>0110010
[1,5,6,7,2,3,8,4]=>[1,8,7,2,6,3,5,4]=>0111001=>1000110
[5,1,2,6,7,8,3,4]=>[8,1,2,3,7,6,5,4]=>1001110=>0110001
[1,5,2,6,7,8,3,4]=>[1,8,2,3,7,6,5,4]=>0101110=>1010001
[1,5,6,7,2,8,3,4]=>[1,8,2,7,6,3,5,4]=>0111010=>1000101
[1,5,6,7,8,2,3,4]=>[1,8,2,7,3,6,5,4]=>0111100=>1000011
[5,1,6,2,8,3,4,7]=>[8,1,2,6,5,3,4,7]=>1010100=>0101011
[5,6,1,2,8,3,4,7]=>[8,1,6,5,2,3,4,7]=>1100100=>0011011
[5,6,1,8,2,3,4,7]=>[8,1,6,2,3,5,4,7]=>1101000=>0010111
[5,1,6,2,3,8,4,7]=>[8,6,1,2,5,3,4,7]=>1010010=>0101101
[5,6,1,2,3,8,4,7]=>[8,6,1,5,2,3,4,7]=>1100010=>0011101
[5,1,2,6,3,8,4,7]=>[8,6,1,2,3,5,4,7]=>1001010=>0110101
[1,5,6,2,3,8,4,7]=>[1,8,6,2,5,3,4,7]=>0110010=>1001101
[5,1,2,6,8,3,4,7]=>[8,1,2,3,6,5,4,7]=>1001100=>0110011
[1,5,2,6,8,3,4,7]=>[1,8,2,3,6,5,4,7]=>0101100=>1010011
[1,5,6,2,8,3,4,7]=>[1,8,2,6,5,3,4,7]=>0110100=>1001011
[1,5,6,8,2,3,4,7]=>[1,8,2,6,3,5,4,7]=>0111000=>1000111
[5,6,1,2,3,4,8,7]=>[6,1,5,2,3,4,8,7]=>1100001=>0011110
[1,5,6,2,3,4,8,7]=>[1,6,2,5,3,4,8,7]=>0110001=>1001110
[1,5,2,3,6,4,8,7]=>[1,6,5,2,3,4,8,7]=>0100101=>1011010
[5,1,2,3,6,8,4,7]=>[8,6,5,1,2,3,4,7]=>1000110=>0111001
[1,2,5,6,8,3,4,7]=>[1,2,8,3,6,5,4,7]=>0011100=>1100011
[5,1,6,2,3,4,7,8]=>[6,1,2,5,3,4,7,8]=>1010000=>0101111
[5,1,2,6,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>1001000=>0110111
[1,5,6,2,3,4,7,8]=>[1,6,2,5,3,4,7,8]=>0110000=>1001111
[1,2,5,3,6,4,7,8]=>[1,2,6,5,3,4,7,8]=>0010100=>1101011
[1,2,5,6,3,4,7,8]=>[1,2,6,3,5,4,7,8]=>0011000=>1100111
[5,1,2,3,6,7,4,8]=>[7,6,5,1,2,3,4,8]=>1000110=>0111001
[5,1,2,3,6,7,8,4]=>[8,7,6,5,1,2,3,4]=>1000111=>0111000
[1,5,2,3,6,7,8,4]=>[1,8,7,6,5,2,3,4]=>0100111=>1011000
[1,2,5,3,6,7,8,4]=>[1,2,8,7,6,5,3,4]=>0010111=>1101000
[1,2,5,6,3,7,8,4]=>[1,2,8,7,6,3,5,4]=>0011011=>1100100
[1,2,5,6,7,3,8,4]=>[1,2,8,7,3,6,5,4]=>0011101=>1100010
[1,2,5,6,7,8,3,4]=>[1,2,8,3,7,6,5,4]=>0011110=>1100001
[5,1,7,8,2,3,4,6]=>[8,1,2,7,3,5,4,6]=>1011000=>0100111
[5,7,8,1,2,3,4,6]=>[8,1,7,2,5,3,4,6]=>1110000=>0001111
[5,1,7,2,3,8,4,6]=>[8,1,2,5,3,4,7,6]=>1010010=>0101101
[5,1,2,7,3,8,4,6]=>[8,1,2,3,5,4,7,6]=>1001010=>0110101
[1,5,7,2,3,8,4,6]=>[1,8,2,5,3,4,7,6]=>0110010=>1001101
[5,1,2,7,8,3,4,6]=>[8,1,2,3,7,5,4,6]=>1001100=>0110011
[1,5,2,7,8,3,4,6]=>[1,8,2,3,7,5,4,6]=>0101100=>1010011
[1,5,7,2,8,3,4,6]=>[1,8,2,7,5,3,4,6]=>0110100=>1001011
[1,5,7,8,2,3,4,6]=>[1,8,2,7,3,5,4,6]=>0111000=>1000111
[5,1,7,2,3,4,8,6]=>[8,7,1,2,5,3,4,6]=>1010001=>0101110
[5,7,1,2,3,4,8,6]=>[8,7,1,5,2,3,4,6]=>1100001=>0011110
[1,5,2,7,3,4,8,6]=>[1,8,7,2,3,5,4,6]=>0101001=>1010110
[1,5,7,2,3,4,8,6]=>[1,8,7,2,5,3,4,6]=>0110001=>1001110
[5,1,2,3,7,4,8,6]=>[8,7,5,1,2,3,4,6]=>1000101=>0111010
[1,5,2,3,7,4,8,6]=>[1,8,7,5,2,3,4,6]=>0100101=>1011010
[1,2,5,7,3,4,8,6]=>[1,2,8,7,3,5,4,6]=>0011001=>1100110
[1,5,2,3,7,8,4,6]=>[1,8,5,2,3,4,7,6]=>0100110=>1011001
[1,2,5,7,3,8,4,6]=>[1,2,8,3,5,4,7,6]=>0011010=>1100101
[1,2,5,7,8,3,4,6]=>[1,2,8,3,7,5,4,6]=>0011100=>1100011
[5,1,7,2,3,4,6,8]=>[7,1,2,5,3,4,6,8]=>1010000=>0101111
[5,1,2,7,3,4,6,8]=>[7,1,2,3,5,4,6,8]=>1001000=>0110111
[1,5,2,7,3,4,6,8]=>[1,7,2,3,5,4,6,8]=>0101000=>1010111
[1,5,7,2,3,4,6,8]=>[1,7,2,5,3,4,6,8]=>0110000=>1001111
[5,1,2,3,7,4,6,8]=>[7,5,1,2,3,4,6,8]=>1000100=>0111011
[1,5,2,3,7,4,6,8]=>[1,7,5,2,3,4,6,8]=>0100100=>1011011
[1,2,5,3,7,4,6,8]=>[1,2,7,5,3,4,6,8]=>0010100=>1101011
[1,2,5,7,3,4,6,8]=>[1,2,7,3,5,4,6,8]=>0011000=>1100111
[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>0100010=>1011101
[1,2,5,3,4,7,6,8]=>[1,2,5,3,4,7,6,8]=>0010010=>1101101
[1,2,3,5,7,4,6,8]=>[1,2,3,7,5,4,6,8]=>0001100=>1110011
[5,1,2,3,4,7,8,6]=>[5,1,2,3,4,8,7,6]=>1000011=>0111100
[1,5,2,3,4,7,8,6]=>[1,5,2,3,4,8,7,6]=>0100011=>1011100
[1,2,5,3,4,7,8,6]=>[1,2,5,3,4,8,7,6]=>0010011=>1101100
[1,2,3,5,7,4,8,6]=>[1,2,3,8,7,5,4,6]=>0001101=>1110010
[1,2,3,5,7,8,4,6]=>[1,2,3,8,5,4,7,6]=>0001110=>1110001
[5,1,8,2,3,4,6,7]=>[8,1,2,5,3,4,6,7]=>1010000=>0101111
[5,8,1,2,3,4,6,7]=>[8,1,5,2,3,4,6,7]=>1100000=>0011111
[5,1,2,8,3,4,6,7]=>[8,1,2,3,5,4,6,7]=>1001000=>0110111
[1,5,2,8,3,4,6,7]=>[1,8,2,3,5,4,6,7]=>0101000=>1010111
[1,5,8,2,3,4,6,7]=>[1,8,2,5,3,4,6,7]=>0110000=>1001111
[5,1,2,3,8,4,6,7]=>[8,5,1,2,3,4,6,7]=>1000100=>0111011
[1,2,5,3,8,4,6,7]=>[1,2,8,5,3,4,6,7]=>0010100=>1101011
[1,2,5,8,3,4,6,7]=>[1,2,8,3,5,4,6,7]=>0011000=>1100111
[5,1,2,3,4,8,6,7]=>[5,1,2,3,4,8,6,7]=>1000010=>0111101
[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>0100010=>1011101
[1,2,5,3,4,8,6,7]=>[1,2,5,3,4,8,6,7]=>0010010=>1101101
[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>0001010=>1110101
[1,2,3,5,8,4,6,7]=>[1,2,3,8,5,4,6,7]=>0001100=>1110011
[5,1,2,3,4,6,8,7]=>[5,1,2,3,4,6,8,7]=>1000001=>0111110
[1,5,2,3,4,6,8,7]=>[1,5,2,3,4,6,8,7]=>0100001=>1011110
[1,2,5,3,4,6,8,7]=>[1,2,5,3,4,6,8,7]=>0010001=>1101110
[1,2,3,5,6,8,4,7]=>[1,2,3,8,6,5,4,7]=>0001110=>1110001
[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>0100000=>1011111
[1,2,5,3,4,6,7,8]=>[1,2,5,3,4,6,7,8]=>0010000=>1101111
[6,1,7,2,8,3,4,5]=>[8,1,2,7,3,4,6,5]=>1010100=>0101011
[6,1,7,8,2,3,4,5]=>[8,1,2,7,3,6,4,5]=>1011000=>0100111
[6,7,1,8,2,3,4,5]=>[8,1,7,2,3,6,4,5]=>1101000=>0010111
[6,1,7,2,3,8,4,5]=>[8,1,2,7,6,3,4,5]=>1010010=>0101101
[6,7,1,2,3,8,4,5]=>[8,1,7,6,2,3,4,5]=>1100010=>0011101
[1,6,2,7,3,8,4,5]=>[1,8,2,3,7,6,4,5]=>0101010=>1010101
[1,6,7,2,3,8,4,5]=>[1,8,2,7,6,3,4,5]=>0110010=>1001101
[1,6,7,2,8,3,4,5]=>[1,8,2,7,3,4,6,5]=>0110100=>1001011
[1,6,7,8,2,3,4,5]=>[1,8,2,7,3,6,4,5]=>0111000=>1000111
[6,1,7,2,3,4,8,5]=>[8,7,1,2,6,3,4,5]=>1010001=>0101110
[6,7,1,2,3,4,8,5]=>[8,7,1,6,2,3,4,5]=>1100001=>0011110
[6,1,2,7,3,4,8,5]=>[8,7,1,2,3,6,4,5]=>1001001=>0110110
[1,6,2,7,3,4,8,5]=>[1,8,7,2,3,6,4,5]=>0101001=>1010110
[1,6,7,2,3,4,8,5]=>[1,8,7,2,6,3,4,5]=>0110001=>1001110
[6,1,2,3,7,4,8,5]=>[8,7,1,2,3,4,6,5]=>1000101=>0111010
[1,6,2,3,7,4,8,5]=>[1,8,7,2,3,4,6,5]=>0100101=>1011010
[1,2,6,3,7,4,8,5]=>[1,2,8,7,3,4,6,5]=>0010101=>1101010
[6,1,2,3,7,8,4,5]=>[8,1,2,3,4,7,6,5]=>1000110=>0111001
[1,6,2,3,7,8,4,5]=>[1,8,2,3,4,7,6,5]=>0100110=>1011001
[1,2,6,3,7,8,4,5]=>[1,2,8,3,4,7,6,5]=>0010110=>1101001
[1,2,6,7,3,8,4,5]=>[1,2,8,3,7,6,4,5]=>0011010=>1100101
[1,2,6,7,8,3,4,5]=>[1,2,8,3,7,4,6,5]=>0011100=>1100011
[6,1,7,2,3,4,5,8]=>[7,1,2,6,3,4,5,8]=>1010000=>0101111
[6,1,2,7,3,4,5,8]=>[7,1,2,3,6,4,5,8]=>1001000=>0110111
[1,6,2,7,3,4,5,8]=>[1,7,2,3,6,4,5,8]=>0101000=>1010111
[1,6,7,2,3,4,5,8]=>[1,7,2,6,3,4,5,8]=>0110000=>1001111
[6,1,2,3,7,4,5,8]=>[7,1,2,3,4,6,5,8]=>1000100=>0111011
[1,6,2,3,7,4,5,8]=>[1,7,2,3,4,6,5,8]=>0100100=>1011011
[1,2,6,3,7,4,5,8]=>[1,2,7,3,4,6,5,8]=>0010100=>1101011
[1,2,6,7,3,4,5,8]=>[1,2,7,3,6,4,5,8]=>0011000=>1100111
[6,1,2,3,4,7,5,8]=>[7,6,1,2,3,4,5,8]=>1000010=>0111101
[1,6,2,3,4,7,5,8]=>[1,7,6,2,3,4,5,8]=>0100010=>1011101
[1,2,6,3,4,7,5,8]=>[1,2,7,6,3,4,5,8]=>0010010=>1101101
[1,2,3,6,4,7,5,8]=>[1,2,3,7,6,4,5,8]=>0001010=>1110101
[1,2,3,6,7,4,5,8]=>[1,2,3,7,4,6,5,8]=>0001100=>1110011
[6,1,2,3,4,7,8,5]=>[8,7,6,1,2,3,4,5]=>1000011=>0111100
[1,6,2,3,4,7,8,5]=>[1,8,7,6,2,3,4,5]=>0100011=>1011100
[1,2,6,3,4,7,8,5]=>[1,2,8,7,6,3,4,5]=>0010011=>1101100
[1,2,3,6,4,7,8,5]=>[1,2,3,8,7,6,4,5]=>0001011=>1110100
[1,2,3,6,7,4,8,5]=>[1,2,3,8,7,4,6,5]=>0001101=>1110010
[1,2,3,6,7,8,4,5]=>[1,2,3,8,4,7,6,5]=>0001110=>1110001
[6,1,8,2,3,4,5,7]=>[8,1,2,6,3,4,5,7]=>1010000=>0101111
[6,8,1,2,3,4,5,7]=>[8,1,6,2,3,4,5,7]=>1100000=>0011111
[6,1,2,8,3,4,5,7]=>[8,1,2,3,6,4,5,7]=>1001000=>0110111
[1,6,2,8,3,4,5,7]=>[1,8,2,3,6,4,5,7]=>0101000=>1010111
[1,6,8,2,3,4,5,7]=>[1,8,2,6,3,4,5,7]=>0110000=>1001111
[6,1,2,3,8,4,5,7]=>[8,1,2,3,4,6,5,7]=>1000100=>0111011
[1,6,2,3,8,4,5,7]=>[1,8,2,3,4,6,5,7]=>0100100=>1011011
[1,2,6,3,8,4,5,7]=>[1,2,8,3,4,6,5,7]=>0010100=>1101011
[1,2,6,8,3,4,5,7]=>[1,2,8,3,6,4,5,7]=>0011000=>1100111
[6,1,2,3,4,8,5,7]=>[8,6,1,2,3,4,5,7]=>1000010=>0111101
[1,6,2,3,4,8,5,7]=>[1,8,6,2,3,4,5,7]=>0100010=>1011101
[1,2,6,3,4,8,5,7]=>[1,2,8,6,3,4,5,7]=>0010010=>1101101
[1,2,3,6,4,8,5,7]=>[1,2,3,8,6,4,5,7]=>0001010=>1110101
[1,2,3,6,8,4,5,7]=>[1,2,3,8,4,6,5,7]=>0001100=>1110011
[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>1000001=>0111110
[1,6,2,3,4,5,8,7]=>[1,6,2,3,4,5,8,7]=>0100001=>1011110
[1,2,6,3,4,5,8,7]=>[1,2,6,3,4,5,8,7]=>0010001=>1101110
[1,2,3,6,4,5,8,7]=>[1,2,3,6,4,5,8,7]=>0001001=>1110110
[1,2,3,4,6,8,5,7]=>[1,2,3,4,8,6,5,7]=>0000110=>1111001
[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>0100000=>1011111
[1,2,6,3,4,5,7,8]=>[1,2,6,3,4,5,7,8]=>0010000=>1101111
[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>0001000=>1110111
[7,1,8,2,3,4,5,6]=>[8,1,2,7,3,4,5,6]=>1010000=>0101111
[7,1,2,8,3,4,5,6]=>[8,1,2,3,7,4,5,6]=>1001000=>0110111
[1,7,8,2,3,4,5,6]=>[1,8,2,7,3,4,5,6]=>0110000=>1001111
[7,1,2,3,8,4,5,6]=>[8,1,2,3,4,7,5,6]=>1000100=>0111011
[1,7,2,3,8,4,5,6]=>[1,8,2,3,4,7,5,6]=>0100100=>1011011
[1,2,7,8,3,4,5,6]=>[1,2,8,3,7,4,5,6]=>0011000=>1100111
[7,1,2,3,4,8,5,6]=>[8,1,2,3,4,5,7,6]=>1000010=>0111101
[1,7,2,3,4,8,5,6]=>[1,8,2,3,4,5,7,6]=>0100010=>1011101
[1,2,7,3,4,8,5,6]=>[1,2,8,3,4,5,7,6]=>0010010=>1101101
[1,2,3,7,4,8,5,6]=>[1,2,3,8,4,5,7,6]=>0001010=>1110101
[1,2,3,7,8,4,5,6]=>[1,2,3,8,4,7,5,6]=>0001100=>1110011
[7,1,2,3,4,5,8,6]=>[8,7,1,2,3,4,5,6]=>1000001=>0111110
[1,7,2,3,4,5,8,6]=>[1,8,7,2,3,4,5,6]=>0100001=>1011110
[1,2,7,3,4,5,8,6]=>[1,2,8,7,3,4,5,6]=>0010001=>1101110
[1,2,3,7,4,5,8,6]=>[1,2,3,8,7,4,5,6]=>0001001=>1110110
[1,2,3,4,7,5,8,6]=>[1,2,3,4,8,7,5,6]=>0000101=>1111010
[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,5,7,6]=>0000110=>1111001
[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>0100000=>1011111
[1,2,7,3,4,5,6,8]=>[1,2,7,3,4,5,6,8]=>0010000=>1101111
[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>0001000=>1110111
[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,5,6,8]=>0000100=>1111011
[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>0100000=>1011111
[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]=>0010000=>1101111
[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>0001000=>1110111
[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>0000100=>1111011
[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>0000010=>1111101
[5,3,2,6,1,4,8,7]=>[3,2,6,1,5,4,8,7]=>1101001=>0010110
[7,3,2,5,4,8,1,6]=>[3,2,5,4,8,1,7,6]=>1101010=>0010101
[8,4,5,2,3,7,6,1]=>[5,2,4,3,7,6,8,1]=>1110010=>0001101
[7,4,5,2,3,8,1,6]=>[5,2,4,3,8,1,7,6]=>1110010=>0001101
[6,4,5,2,3,1,8,7]=>[5,2,4,3,6,1,8,7]=>1110001=>0001110
[5,4,6,2,1,3,8,7]=>[6,2,4,1,5,3,8,7]=>1110001=>0001110
[3,6,1,5,4,2,8,7]=>[5,4,6,1,3,2,8,7]=>1101001=>0010110
[4,6,5,1,3,2,8,7]=>[5,1,6,3,4,2,8,7]=>1110001=>0001110
[5,6,4,3,1,2,8,7]=>[4,3,6,1,5,2,8,7]=>1110001=>0001110
[7,5,4,3,2,8,1,6]=>[4,3,5,2,8,1,7,6]=>1110010=>0001101
[8,6,4,3,7,2,5,1]=>[4,3,7,2,6,5,8,1]=>1110100=>0001011
[7,6,4,3,8,2,1,5]=>[4,3,8,2,6,1,7,5]=>1110100=>0001011
[6,7,4,3,8,1,2,5]=>[4,3,8,1,7,2,6,5]=>1110100=>0001011
[5,7,4,3,1,8,2,6]=>[4,3,8,1,5,2,7,6]=>1110010=>0001101
[4,7,5,1,3,8,2,6]=>[5,1,8,3,4,2,7,6]=>1110010=>0001101
[3,7,1,5,4,8,2,6]=>[5,4,8,1,3,2,7,6]=>1101010=>0010101
[2,1,7,5,4,8,3,6]=>[2,1,5,4,8,3,7,6]=>1011010=>0100101
[3,8,1,5,4,7,6,2]=>[5,4,7,6,8,1,3,2]=>1101010=>0010101
[4,8,5,1,3,7,6,2]=>[5,1,7,6,8,3,4,2]=>1110010=>0001101
[5,8,4,3,1,7,6,2]=>[4,3,7,6,8,1,5,2]=>1110010=>0001101
[6,8,4,3,7,1,5,2]=>[4,3,7,1,8,5,6,2]=>1110100=>0001011
[7,8,4,3,6,5,1,2]=>[4,3,6,5,8,1,7,2]=>1110100=>0001011
[6,8,5,7,3,1,4,2]=>[7,3,5,1,8,4,6,2]=>1111000=>0000111
[5,8,6,7,1,3,4,2]=>[7,1,6,3,8,4,5,2]=>1111000=>0000111
[4,8,6,1,7,3,5,2]=>[7,1,6,5,8,3,4,2]=>1110100=>0001011
[3,8,1,6,7,4,5,2]=>[7,4,6,5,8,1,3,2]=>1101100=>0010011
[2,1,8,6,7,4,5,3]=>[2,1,7,4,6,5,8,3]=>1011100=>0100011
[2,1,7,6,8,4,3,5]=>[2,1,8,4,6,3,7,5]=>1011100=>0100011
[3,7,1,6,8,4,2,5]=>[8,4,6,1,3,2,7,5]=>1101100=>0010011
[4,7,6,1,8,3,2,5]=>[8,1,6,3,4,2,7,5]=>1110100=>0001011
[5,7,6,8,1,3,2,4]=>[8,1,6,3,7,2,5,4]=>1111000=>0000111
[5,4,7,2,1,8,3,6]=>[8,2,4,1,5,3,7,6]=>1110010=>0001101
[6,4,7,2,8,1,3,5]=>[8,2,4,1,7,3,6,5]=>1110100=>0001011
[7,4,6,2,8,3,1,5]=>[8,2,4,3,6,1,7,5]=>1110100=>0001011
[8,4,6,2,7,3,5,1]=>[7,2,4,3,6,5,8,1]=>1110100=>0001011
[8,3,2,6,7,4,5,1]=>[3,2,7,4,6,5,8,1]=>1101100=>0010011
[7,3,2,6,8,4,1,5]=>[3,2,8,4,6,1,7,5]=>1101100=>0010011
[6,3,2,7,8,1,4,5]=>[3,2,8,1,7,4,6,5]=>1101100=>0010011
[5,3,2,7,1,8,4,6]=>[3,2,8,1,5,4,7,6]=>1101010=>0010101
[4,3,2,1,7,8,5,6]=>[3,2,4,1,8,5,7,6]=>1100110=>0011001
[3,4,1,2,8,7,6,5]=>[4,1,3,2,7,6,8,5]=>1100110=>0011001
[5,3,2,8,1,7,6,4]=>[3,2,7,6,8,1,5,4]=>1101010=>0010101
[6,3,2,8,7,1,5,4]=>[3,2,7,1,8,5,6,4]=>1101100=>0010011
[7,3,2,8,6,5,1,4]=>[3,2,6,5,8,1,7,4]=>1101100=>0010011
[8,4,7,2,6,5,3,1]=>[6,5,7,2,4,3,8,1]=>1110100=>0001011
[7,4,8,2,6,5,1,3]=>[6,5,8,2,4,1,7,3]=>1110100=>0001011
[6,4,8,2,7,1,5,3]=>[7,2,4,1,8,5,6,3]=>1110100=>0001011
[5,4,8,2,1,7,6,3]=>[7,6,8,2,4,1,5,3]=>1110010=>0001101
[4,5,8,1,2,7,6,3]=>[7,6,8,1,5,2,4,3]=>1110010=>0001101
[3,5,1,8,2,7,6,4]=>[7,6,8,1,3,2,5,4]=>1101010=>0010101
[2,1,5,8,3,7,6,4]=>[2,1,7,6,8,3,5,4]=>1011010=>0100101
[2,1,6,8,7,3,5,4]=>[2,1,7,3,8,5,6,4]=>1011100=>0100011
[3,6,1,8,7,2,5,4]=>[7,1,3,2,8,5,6,4]=>1101100=>0010011
[4,6,8,1,7,2,5,3]=>[7,1,8,5,6,2,4,3]=>1110100=>0001011
[5,6,8,7,1,2,4,3]=>[7,1,8,2,6,4,5,3]=>1111000=>0000111
[6,5,8,7,2,1,4,3]=>[7,2,8,1,5,4,6,3]=>1111000=>0000111
[7,5,8,6,2,4,1,3]=>[6,2,8,4,5,1,7,3]=>1111000=>0000111
[8,5,7,6,2,4,3,1]=>[6,2,7,4,5,3,8,1]=>1111000=>0000111
[5,7,8,6,1,4,2,3]=>[6,1,8,4,7,2,5,3]=>1111000=>0000111
[4,7,8,1,6,5,2,3]=>[6,5,8,1,7,2,4,3]=>1110100=>0001011
[3,7,1,8,6,5,2,4]=>[6,5,8,1,3,2,7,4]=>1101100=>0010011
[2,1,7,8,6,5,3,4]=>[2,1,6,5,8,3,7,4]=>1011100=>0100011
[3,8,1,7,6,5,4,2]=>[6,5,7,4,8,1,3,2]=>1101100=>0010011
[4,8,7,1,6,5,3,2]=>[6,5,7,1,8,3,4,2]=>1110100=>0001011
[5,8,7,6,1,4,3,2]=>[6,1,7,4,8,3,5,2]=>1111000=>0000111
[6,8,7,5,4,1,3,2]=>[5,4,7,1,8,3,6,2]=>1111000=>0000111
[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>101010101=>010101010
[3,4,1,2,6,5,8,7,10,9]=>[4,1,3,2,6,5,8,7,10,9]=>110010101=>001101010
[4,3,2,1,6,5,8,7,10,9]=>[3,2,4,1,6,5,8,7,10,9]=>110010101=>001101010
[6,3,2,5,4,1,8,7,10,9]=>[3,2,5,4,6,1,8,7,10,9]=>110100101=>001011010
[8,3,2,5,4,7,6,1,10,9]=>[3,2,5,4,7,6,8,1,10,9]=>110101001=>001010110
[10,3,2,5,4,7,6,9,8,1]=>[3,2,5,4,7,6,9,8,10,1]=>110101010=>001010101
[2,1,5,6,3,4,8,7,10,9]=>[2,1,6,3,5,4,8,7,10,9]=>101100101=>010011010
[2,1,6,5,4,3,8,7,10,9]=>[2,1,5,4,6,3,8,7,10,9]=>101100101=>010011010
[6,5,4,3,2,1,8,7,10,9]=>[4,3,5,2,6,1,8,7,10,9]=>111000101=>000111010
[8,5,4,3,2,7,6,1,10,9]=>[4,3,5,2,7,6,8,1,10,9]=>111001001=>000110110
[10,5,4,3,2,7,6,9,8,1]=>[4,3,5,2,7,6,9,8,10,1]=>111001010=>000110101
[2,1,8,5,4,7,6,3,10,9]=>[2,1,5,4,7,6,8,3,10,9]=>101101001=>010010110
[8,7,4,3,6,5,2,1,10,9]=>[4,3,6,5,7,2,8,1,10,9]=>111010001=>000101110
[10,7,4,3,6,5,2,9,8,1]=>[4,3,6,5,7,2,9,8,10,1]=>111010010=>000101101
[2,1,10,5,4,7,6,9,8,3]=>[2,1,5,4,7,6,9,8,10,3]=>101101010=>010010101
[10,9,4,3,6,5,8,7,2,1]=>[4,3,6,5,8,7,9,2,10,1]=>111010100=>000101011
[3,4,1,2,7,8,5,6,10,9]=>[4,1,3,2,8,5,7,6,10,9]=>110011001=>001100110
[2,1,4,3,7,8,5,6,10,9]=>[2,1,4,3,8,5,7,6,10,9]=>101011001=>010100110
[2,1,4,3,8,7,6,5,10,9]=>[2,1,4,3,7,6,8,5,10,9]=>101011001=>010100110
[4,3,2,1,8,7,6,5,10,9]=>[3,2,4,1,7,6,8,5,10,9]=>110011001=>001100110
[8,3,2,7,6,5,4,1,10,9]=>[3,2,6,5,7,4,8,1,10,9]=>110110001=>001001110
[10,3,2,7,6,5,4,9,8,1]=>[3,2,6,5,7,4,9,8,10,1]=>110110010=>001001101
[2,1,8,7,6,5,4,3,10,9]=>[2,1,6,5,7,4,8,3,10,9]=>101110001=>010001110
[8,7,6,5,4,3,2,1,10,9]=>[5,4,6,3,7,2,8,1,10,9]=>111100001=>000011110
[10,7,6,5,4,3,2,9,8,1]=>[5,4,6,3,7,2,9,8,10,1]=>111100010=>000011101
[2,1,10,7,6,5,4,9,8,3]=>[2,1,6,5,7,4,9,8,10,3]=>101110010=>010001101
[10,9,6,5,4,3,8,7,2,1]=>[5,4,6,3,8,7,9,2,10,1]=>111100100=>000011011
[2,1,4,3,10,7,6,9,8,5]=>[2,1,4,3,7,6,9,8,10,5]=>101011010=>010100101
[4,3,2,1,10,7,6,9,8,5]=>[3,2,4,1,7,6,9,8,10,5]=>110011010=>001100101
[10,3,2,9,6,5,8,7,4,1]=>[3,2,6,5,8,7,9,4,10,1]=>110110100=>001001011
[2,1,10,9,6,5,8,7,4,3]=>[2,1,6,5,8,7,9,4,10,3]=>101110100=>010001011
[10,9,8,5,4,7,6,3,2,1]=>[5,4,7,6,8,3,9,2,10,1]=>111101000=>000010111
[6,7,8,9,10,1,2,3,4,5]=>[10,1,9,2,8,3,7,4,6,5]=>111110000=>000001111
[3,5,1,7,2,9,4,10,6,8]=>[10,1,3,2,5,4,7,6,9,8]=>110101010=>001010101
[2,1,5,6,3,4,9,10,7,8]=>[2,1,6,3,5,4,10,7,9,8]=>101100110=>010011001
[3,4,1,2,6,5,9,10,7,8]=>[4,1,3,2,6,5,10,7,9,8]=>110010110=>001101001
[2,1,4,3,6,5,9,10,7,8]=>[2,1,4,3,6,5,10,7,9,8]=>101010110=>010101001
[2,1,4,3,6,5,10,9,8,7]=>[2,1,4,3,6,5,9,8,10,7]=>101010110=>010101001
[4,3,2,1,6,5,10,9,8,7]=>[3,2,4,1,6,5,9,8,10,7]=>110010110=>001101001
[6,3,2,5,4,1,10,9,8,7]=>[3,2,5,4,6,1,9,8,10,7]=>110100110=>001011001
[10,3,2,5,4,9,8,7,6,1]=>[3,2,5,4,8,7,9,6,10,1]=>110101100=>001010011
[2,1,6,5,4,3,10,9,8,7]=>[2,1,5,4,6,3,9,8,10,7]=>101100110=>010011001
[6,5,4,3,2,1,10,9,8,7]=>[4,3,5,2,6,1,9,8,10,7]=>111000110=>000111001
[10,5,4,3,2,9,8,7,6,1]=>[4,3,5,2,8,7,9,6,10,1]=>111001100=>000110011
[2,1,10,5,4,9,8,7,6,3]=>[2,1,5,4,8,7,9,6,10,3]=>101101100=>010010011
[10,9,4,3,8,7,6,5,2,1]=>[4,3,7,6,8,5,9,2,10,1]=>111011000=>000100111
[2,1,4,3,10,9,8,7,6,5]=>[2,1,4,3,8,7,9,6,10,5]=>101011100=>010100011
[4,3,2,1,10,9,8,7,6,5]=>[3,2,4,1,8,7,9,6,10,5]=>110011100=>001100011
[10,3,2,9,8,7,6,5,4,1]=>[3,2,7,6,8,5,9,4,10,1]=>110111000=>001000111
[2,1,10,9,8,7,6,5,4,3]=>[2,1,7,6,8,5,9,4,10,3]=>101111000=>010000111
[9,10,8,7,6,5,4,3,1,2]=>[6,5,7,4,8,3,10,1,9,2]=>111110000=>000001111
[10,9,8,7,6,5,4,3,2,1]=>[6,5,7,4,8,3,9,2,10,1]=>111110000=>000001111
[5,2,4,1,3,6,7,8]=>[2,4,1,5,3,6,7,8]=>1010000=>0101111
[4,2,6,1,3,5,7,8]=>[2,6,1,4,3,5,7,8]=>1010000=>0101111
[6,2,4,1,3,5,7,8]=>[2,4,1,6,3,5,7,8]=>1010000=>0101111
[6,3,5,1,2,4,7,8]=>[5,3,1,6,2,4,7,8]=>1110000=>0001111
[5,2,7,1,3,4,6,8]=>[2,7,1,5,3,4,6,8]=>1010000=>0101111
[5,3,7,1,2,4,6,8]=>[7,3,1,5,2,4,6,8]=>1110000=>0001111
[5,4,7,1,2,3,6,8]=>[7,1,4,2,5,3,6,8]=>1110000=>0001111
[6,4,7,1,2,3,5,8]=>[7,1,4,2,6,3,5,8]=>1110000=>0001111
[7,3,5,1,2,4,6,8]=>[5,3,1,7,2,4,6,8]=>1110000=>0001111
[3,2,8,1,4,5,6,7]=>[2,8,3,1,4,5,6,7]=>1010000=>0101111
[5,2,8,1,3,4,6,7]=>[2,8,1,5,3,4,6,7]=>1010000=>0101111
[5,4,8,1,2,3,6,7]=>[8,1,4,2,5,3,6,7]=>1110000=>0001111
[6,2,8,1,3,4,5,7]=>[2,8,1,6,3,4,5,7]=>1010000=>0101111
[6,3,8,1,2,4,5,7]=>[8,3,1,6,2,4,5,7]=>1110000=>0001111
[6,5,8,1,2,3,4,7]=>[8,1,5,2,6,3,4,7]=>1110000=>0001111
[7,2,8,1,3,4,5,6]=>[2,8,1,7,3,4,5,6]=>1010000=>0101111
[7,3,8,1,2,4,5,6]=>[8,3,1,7,2,4,5,6]=>1110000=>0001111
[7,4,8,1,2,3,5,6]=>[8,1,4,2,7,3,5,6]=>1110000=>0001111
[7,5,8,1,2,3,4,6]=>[8,1,5,2,7,3,4,6]=>1110000=>0001111
[8,2,4,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>1010000=>0101111
[8,3,5,1,2,4,6,7]=>[5,3,1,8,2,4,6,7]=>1110000=>0001111
[8,3,6,1,2,4,5,7]=>[6,3,1,8,2,4,5,7]=>1110000=>0001111
[8,3,7,1,2,4,5,6]=>[7,3,1,8,2,4,5,6]=>1110000=>0001111
[8,5,7,1,2,3,4,6]=>[7,1,5,2,8,3,4,6]=>1110000=>0001111
[3,2,5,7,1,4,6,8]=>[2,7,3,1,5,4,6,8]=>1011000=>0100111
[4,2,5,7,1,3,6,8]=>[2,7,1,5,4,3,6,8]=>1011000=>0100111
[4,3,5,7,1,2,6,8]=>[7,3,1,5,4,2,6,8]=>1111000=>0000111
[5,2,6,7,1,3,4,8]=>[2,7,1,6,3,5,4,8]=>1011000=>0100111
[5,3,6,7,1,2,4,8]=>[7,3,1,6,2,5,4,8]=>1111000=>0000111
[6,3,5,7,1,2,4,8]=>[7,3,1,5,2,6,4,8]=>1111000=>0000111
[7,2,4,6,1,3,5,8]=>[2,6,4,1,7,3,5,8]=>1011000=>0100111
[7,3,4,6,1,2,5,8]=>[6,4,3,1,7,2,5,8]=>1111000=>0000111
[3,2,5,8,1,4,6,7]=>[2,8,3,1,5,4,6,7]=>1011000=>0100111
[5,2,4,8,1,3,6,7]=>[2,8,4,1,5,3,6,7]=>1011000=>0100111
[3,2,6,8,1,4,5,7]=>[2,8,3,1,6,4,5,7]=>1011000=>0100111
[4,2,6,8,1,3,5,7]=>[2,8,1,6,4,3,5,7]=>1011000=>0100111
[4,3,6,8,1,2,5,7]=>[8,3,1,6,4,2,5,7]=>1111000=>0000111
[6,2,4,8,1,3,5,7]=>[2,8,4,1,6,3,5,7]=>1011000=>0100111
[6,3,4,8,1,2,5,7]=>[8,4,3,1,6,2,5,7]=>1111000=>0000111
[6,4,5,8,1,2,3,7]=>[8,1,5,4,2,6,3,7]=>1111000=>0000111
[4,3,7,8,1,2,5,6]=>[8,3,1,7,4,2,5,6]=>1111000=>0000111
[5,3,7,8,1,2,4,6]=>[8,3,1,7,2,5,4,6]=>1111000=>0000111
[5,4,7,8,1,2,3,6]=>[8,1,7,4,2,5,3,6]=>1111000=>0000111
[6,2,7,8,1,3,4,5]=>[2,8,1,7,3,6,4,5]=>1011000=>0100111
[6,3,7,8,1,2,4,5]=>[8,3,1,7,2,6,4,5]=>1111000=>0000111
[6,4,7,8,1,2,3,5]=>[8,1,7,4,2,6,3,5]=>1111000=>0000111
[7,2,4,8,1,3,5,6]=>[2,8,4,1,7,3,5,6]=>1011000=>0100111
[7,3,5,8,1,2,4,6]=>[8,3,1,5,2,7,4,6]=>1111000=>0000111
[7,4,5,8,1,2,3,6]=>[8,1,5,4,2,7,3,6]=>1111000=>0000111
[7,4,6,8,1,2,3,5]=>[8,1,6,4,2,7,3,5]=>1111000=>0000111
[8,2,4,6,1,3,5,7]=>[2,6,4,1,8,3,5,7]=>1011000=>0100111
[8,3,4,6,1,2,5,7]=>[6,4,3,1,8,2,5,7]=>1111000=>0000111
[8,2,5,6,1,3,4,7]=>[2,6,1,5,3,8,4,7]=>1011000=>0100111
[8,3,5,6,1,2,4,7]=>[6,3,1,5,2,8,4,7]=>1111000=>0000111
[8,2,4,7,1,3,5,6]=>[2,7,4,1,8,3,5,6]=>1011000=>0100111
[8,3,5,7,1,2,4,6]=>[7,3,1,5,2,8,4,6]=>1111000=>0000111
[4,6,2,5,1,3,7,8]=>[5,2,6,4,1,3,7,8]=>1101000=>0010111
[4,6,3,5,1,2,7,8]=>[3,5,1,6,4,2,7,8]=>1101000=>0010111
[5,6,2,4,1,3,7,8]=>[4,6,2,5,1,3,7,8]=>1100000=>0011111
[5,7,3,4,1,2,6,8]=>[3,4,7,1,5,2,6,8]=>1100000=>0011111
[4,7,3,6,1,2,5,8]=>[3,6,1,7,4,2,5,8]=>1101000=>0010111
[6,7,2,5,1,3,4,8]=>[5,2,7,1,3,6,4,8]=>1101000=>0010111
[4,8,2,5,1,3,6,7]=>[5,2,8,4,1,3,6,7]=>1101000=>0010111
[5,8,2,4,1,3,6,7]=>[4,8,2,5,1,3,6,7]=>1100000=>0011111
[5,8,3,4,1,2,6,7]=>[3,4,8,1,5,2,6,7]=>1100000=>0011111
[4,8,2,6,1,3,5,7]=>[6,2,8,4,1,3,5,7]=>1101000=>0010111
[6,8,2,4,1,3,5,7]=>[4,8,2,6,1,3,5,7]=>1100000=>0011111
[6,8,3,4,1,2,5,7]=>[3,4,8,1,6,2,5,7]=>1100000=>0011111
[6,8,3,5,1,2,4,7]=>[3,5,1,8,2,6,4,7]=>1101000=>0010111
[6,8,4,5,1,2,3,7]=>[5,4,1,8,2,6,3,7]=>1111000=>0000111
[3,8,2,7,1,4,5,6]=>[7,2,3,1,8,4,5,6]=>1101000=>0010111
[4,8,2,7,1,3,5,6]=>[7,2,8,4,1,3,5,6]=>1101000=>0010111
[4,8,3,7,1,2,5,6]=>[3,7,1,8,4,2,5,6]=>1101000=>0010111
[5,8,4,7,1,2,3,6]=>[7,4,1,8,2,5,3,6]=>1111000=>0000111
[6,8,2,7,1,3,4,5]=>[7,2,8,1,3,6,4,5]=>1101000=>0010111
[6,8,5,7,1,2,3,4]=>[7,1,5,2,8,3,6,4]=>1111000=>0000111
[7,8,2,4,1,3,5,6]=>[4,8,2,7,1,3,5,6]=>1100000=>0011111
[7,8,2,5,1,3,4,6]=>[5,2,8,1,3,7,4,6]=>1101000=>0010111
[7,8,3,5,1,2,4,6]=>[3,5,1,8,2,7,4,6]=>1101000=>0010111
[4,3,2,6,1,5,7,8]=>[3,2,6,4,1,5,7,8]=>1101000=>0010111
[5,3,2,6,1,4,7,8]=>[3,2,6,1,5,4,7,8]=>1101000=>0010111
[5,4,2,6,1,3,7,8]=>[6,4,2,5,1,3,7,8]=>1101000=>0010111
[6,3,2,5,1,4,7,8]=>[3,2,5,1,6,4,7,8]=>1101000=>0010111
[6,4,2,5,1,3,7,8]=>[5,4,2,6,1,3,7,8]=>1101000=>0010111
[6,5,2,4,1,3,7,8]=>[4,5,2,6,1,3,7,8]=>1100000=>0011111
[5,3,2,7,1,4,6,8]=>[3,2,7,1,5,4,6,8]=>1101000=>0010111
[6,3,2,7,1,4,5,8]=>[3,2,7,1,6,4,5,8]=>1101000=>0010111
[6,4,2,7,1,3,5,8]=>[7,4,2,6,1,3,5,8]=>1101000=>0010111
[6,5,2,7,1,3,4,8]=>[7,2,5,1,3,6,4,8]=>1101000=>0010111
[6,5,3,7,1,2,4,8]=>[3,7,1,5,2,6,4,8]=>1101000=>0010111
[7,3,2,5,1,4,6,8]=>[3,2,5,1,7,4,6,8]=>1101000=>0010111
[7,3,2,6,1,4,5,8]=>[3,2,6,1,7,4,5,8]=>1101000=>0010111
[7,4,2,6,1,3,5,8]=>[6,4,2,7,1,3,5,8]=>1101000=>0010111
[7,4,3,6,1,2,5,8]=>[3,6,4,1,7,2,5,8]=>1101000=>0010111
[7,5,2,6,1,3,4,8]=>[6,2,5,1,3,7,4,8]=>1101000=>0010111
[7,6,3,5,1,2,4,8]=>[3,5,1,6,2,7,4,8]=>1101000=>0010111
[5,3,2,8,1,4,6,7]=>[3,2,8,1,5,4,6,7]=>1101000=>0010111
[5,4,3,8,1,2,6,7]=>[3,8,4,1,5,2,6,7]=>1101000=>0010111
[6,3,2,8,1,4,5,7]=>[3,2,8,1,6,4,5,7]=>1101000=>0010111
[6,4,2,8,1,3,5,7]=>[8,4,2,6,1,3,5,7]=>1101000=>0010111
[6,5,2,8,1,3,4,7]=>[8,2,5,1,3,6,4,7]=>1101000=>0010111
[6,5,3,8,1,2,4,7]=>[3,8,1,5,2,6,4,7]=>1101000=>0010111
[6,5,4,8,1,2,3,7]=>[8,4,1,5,2,6,3,7]=>1111000=>0000111
[7,4,2,8,1,3,5,6]=>[8,4,2,7,1,3,5,6]=>1101000=>0010111
[7,5,3,8,1,2,4,6]=>[3,8,1,5,2,7,4,6]=>1101000=>0010111
[7,5,4,8,1,2,3,6]=>[8,4,1,5,2,7,3,6]=>1111000=>0000111
[7,6,4,8,1,2,3,5]=>[8,4,1,6,2,7,3,5]=>1111000=>0000111
[8,3,2,5,1,4,6,7]=>[3,2,5,1,8,4,6,7]=>1101000=>0010111
[8,4,2,6,1,3,5,7]=>[6,4,2,8,1,3,5,7]=>1101000=>0010111
[8,6,2,4,1,3,5,7]=>[4,6,2,8,1,3,5,7]=>1100000=>0011111
[8,4,2,7,1,3,5,6]=>[7,4,2,8,1,3,5,6]=>1101000=>0010111
[8,4,3,7,1,2,5,6]=>[3,7,4,1,8,2,5,6]=>1101000=>0010111
[8,5,3,7,1,2,4,6]=>[3,7,1,5,2,8,4,6]=>1101000=>0010111
[8,6,3,7,1,2,4,5]=>[3,7,1,6,2,8,4,5]=>1101000=>0010111
[8,7,2,4,1,3,5,6]=>[4,7,2,8,1,3,5,6]=>1100000=>0011111
[8,7,2,5,1,3,4,6]=>[5,2,7,1,3,8,4,6]=>1101000=>0010111
[8,7,3,5,1,2,4,6]=>[3,5,1,7,2,8,4,6]=>1101000=>0010111
[8,7,3,6,1,2,4,5]=>[3,6,1,7,2,8,4,5]=>1101000=>0010111
[3,6,2,5,8,1,4,7]=>[8,5,2,3,1,6,4,7]=>1101100=>0010011
[4,6,3,5,8,1,2,7]=>[3,8,5,1,6,4,2,7]=>1101100=>0010011
[5,6,2,4,8,1,3,7]=>[4,8,2,6,5,1,3,7]=>1100100=>0011011
[4,7,2,5,8,1,3,6]=>[8,5,2,7,4,1,3,6]=>1101100=>0010011
[5,7,2,4,8,1,3,6]=>[4,8,2,7,5,1,3,6]=>1100100=>0011011
[3,7,2,6,8,1,4,5]=>[8,2,3,1,6,4,7,5]=>1101100=>0010011
[4,7,3,6,8,1,2,5]=>[3,8,1,6,4,2,7,5]=>1101100=>0010011
[5,7,4,6,8,1,2,3]=>[8,4,1,6,2,7,5,3]=>1111100=>0000011
[6,7,3,4,8,1,2,5]=>[3,4,8,1,7,2,6,5]=>1100100=>0011011
[4,8,2,5,7,1,3,6]=>[7,5,2,8,4,1,3,6]=>1101100=>0010011
[4,8,3,6,7,1,2,5]=>[3,7,1,6,4,2,8,5]=>1101100=>0010011
[5,8,3,6,7,1,2,4]=>[3,7,1,6,2,8,5,4]=>1101100=>0010011
[5,8,4,6,7,1,2,3]=>[7,4,1,6,2,8,5,3]=>1111100=>0000011
[6,8,3,5,7,1,2,4]=>[3,7,5,1,8,2,6,4]=>1101100=>0010011
[6,8,4,5,7,1,2,3]=>[7,5,4,1,8,2,6,3]=>1111100=>0000011
[7,8,2,4,6,1,3,5]=>[4,6,2,8,1,3,7,5]=>1100100=>0011011
[7,8,3,4,6,1,2,5]=>[3,4,6,1,8,2,7,5]=>1100100=>0011011
[7,8,3,5,6,1,2,4]=>[3,6,5,1,8,2,7,4]=>1101100=>0010011
[4,3,2,6,8,1,5,7]=>[3,2,8,4,1,6,5,7]=>1101100=>0010011
[5,3,2,6,8,1,4,7]=>[3,2,8,1,6,5,4,7]=>1101100=>0010011
[5,4,2,6,8,1,3,7]=>[8,4,2,6,5,1,3,7]=>1101100=>0010011
[5,4,3,6,8,1,2,7]=>[3,8,4,1,6,5,2,7]=>1101100=>0010011
[6,3,2,5,8,1,4,7]=>[3,2,8,5,1,6,4,7]=>1101100=>0010011
[6,5,2,4,8,1,3,7]=>[4,8,5,2,6,1,3,7]=>1100100=>0011011
[5,3,2,7,8,1,4,6]=>[3,2,8,1,7,5,4,6]=>1101100=>0010011
[5,4,2,7,8,1,3,6]=>[8,4,2,7,5,1,3,6]=>1101100=>0010011
[5,4,3,7,8,1,2,6]=>[3,8,4,1,7,5,2,6]=>1101100=>0010011
[6,4,2,7,8,1,3,5]=>[8,4,2,7,1,3,6,5]=>1101100=>0010011
[6,4,3,7,8,1,2,5]=>[3,8,4,1,7,2,6,5]=>1101100=>0010011
[7,4,3,5,8,1,2,6]=>[3,8,5,4,1,7,2,6]=>1101100=>0010011
[7,3,2,6,8,1,4,5]=>[3,2,8,1,6,4,7,5]=>1101100=>0010011
[7,5,2,6,8,1,3,4]=>[8,2,6,5,1,3,7,4]=>1101100=>0010011
[7,5,3,6,8,1,2,4]=>[3,8,1,6,5,2,7,4]=>1101100=>0010011
[7,6,3,5,8,1,2,4]=>[3,8,5,1,6,2,7,4]=>1101100=>0010011
[8,3,2,5,7,1,4,6]=>[3,2,7,5,1,8,4,6]=>1101100=>0010011
[8,4,2,5,7,1,3,6]=>[7,5,4,2,8,1,3,6]=>1101100=>0010011
[8,5,2,4,7,1,3,6]=>[4,7,5,2,8,1,3,6]=>1100100=>0011011
[8,3,2,6,7,1,4,5]=>[3,2,7,1,6,4,8,5]=>1101100=>0010011
[8,5,3,6,7,1,2,4]=>[3,7,1,6,5,2,8,4]=>1101100=>0010011
[8,6,2,4,7,1,3,5]=>[4,7,2,6,1,3,8,5]=>1100100=>0011011
[8,7,2,4,6,1,3,5]=>[4,6,2,7,1,3,8,5]=>1100100=>0011011
[8,7,3,4,6,1,2,5]=>[3,4,6,1,7,2,8,5]=>1100100=>0011011
[8,7,2,5,6,1,3,4]=>[6,5,2,7,1,3,8,4]=>1101100=>0010011
[8,7,3,5,6,1,2,4]=>[3,6,5,1,7,2,8,4]=>1101100=>0010011
[5,3,7,2,6,1,4,8]=>[6,3,2,7,5,1,4,8]=>1110100=>0001011
[6,4,7,2,5,1,3,8]=>[5,7,2,4,1,6,3,8]=>1110000=>0001111
[6,4,7,3,5,1,2,8]=>[5,7,3,4,1,6,2,8]=>1110000=>0001111
[7,3,6,2,5,1,4,8]=>[5,6,3,2,7,1,4,8]=>1110000=>0001111
[5,3,8,2,6,1,4,7]=>[6,3,2,8,5,1,4,7]=>1110100=>0001011
[5,4,8,2,6,1,3,7]=>[6,2,4,1,8,5,3,7]=>1110100=>0001011
[5,4,8,3,6,1,2,7]=>[6,3,4,1,8,5,2,7]=>1110100=>0001011
[6,3,8,2,5,1,4,7]=>[5,8,3,2,6,1,4,7]=>1110000=>0001111
[6,4,8,2,5,1,3,7]=>[5,8,2,4,1,6,3,7]=>1110000=>0001111
[6,4,8,3,5,1,2,7]=>[5,8,3,4,1,6,2,7]=>1110000=>0001111
[6,5,8,2,4,1,3,7]=>[8,2,4,5,1,6,3,7]=>1110000=>0001111
[5,3,8,2,7,1,4,6]=>[7,3,2,8,5,1,4,6]=>1110100=>0001011
[5,4,8,2,7,1,3,6]=>[7,2,4,1,8,5,3,6]=>1110100=>0001011
[5,4,8,3,7,1,2,6]=>[7,3,4,1,8,5,2,6]=>1110100=>0001011
[6,3,8,2,7,1,4,5]=>[7,3,2,8,1,4,6,5]=>1110100=>0001011
[6,4,8,2,7,1,3,5]=>[7,2,4,1,8,3,6,5]=>1110100=>0001011
[6,5,8,2,7,1,3,4]=>[7,2,8,5,1,6,3,4]=>1110100=>0001011
[7,3,8,2,5,1,4,6]=>[5,8,3,2,7,1,4,6]=>1110000=>0001111
[7,4,8,3,5,1,2,6]=>[5,8,3,4,1,7,2,6]=>1110000=>0001111
[7,5,8,2,4,1,3,6]=>[8,2,4,5,1,7,3,6]=>1110000=>0001111
[7,5,8,3,4,1,2,6]=>[8,3,4,5,1,7,2,6]=>1110000=>0001111
[7,3,8,2,6,1,4,5]=>[6,3,2,8,1,4,7,5]=>1110100=>0001011
[7,4,8,2,6,1,3,5]=>[6,2,4,1,8,3,7,5]=>1110100=>0001011
[7,5,8,2,6,1,3,4]=>[6,2,8,5,1,7,3,4]=>1110100=>0001011
[7,6,8,2,5,1,3,4]=>[5,8,2,6,1,7,3,4]=>1110000=>0001111
[8,3,6,2,5,1,4,7]=>[5,6,3,2,8,1,4,7]=>1110000=>0001111
[8,4,6,2,5,1,3,7]=>[5,6,2,4,1,8,3,7]=>1110000=>0001111
[8,5,6,2,4,1,3,7]=>[6,2,4,5,1,8,3,7]=>1110000=>0001111
[8,3,7,2,5,1,4,6]=>[5,7,3,2,8,1,4,6]=>1110000=>0001111
[8,4,7,3,5,1,2,6]=>[5,7,3,4,1,8,2,6]=>1110000=>0001111
[8,5,7,2,4,1,3,6]=>[7,2,4,5,1,8,3,6]=>1110000=>0001111
[8,3,7,2,6,1,4,5]=>[6,3,2,7,1,4,8,5]=>1110100=>0001011
[8,4,7,2,6,1,3,5]=>[6,2,4,1,7,3,8,5]=>1110100=>0001011
[8,4,7,3,6,1,2,5]=>[6,3,4,1,7,2,8,5]=>1110100=>0001011
[8,5,7,2,6,1,3,4]=>[6,2,7,5,1,8,3,4]=>1110100=>0001011
[8,6,7,2,4,1,3,5]=>[7,2,4,6,1,8,3,5]=>1110000=>0001111
[8,6,7,2,5,1,3,4]=>[5,7,2,6,1,8,3,4]=>1110000=>0001111
[7,5,3,2,6,1,4,8]=>[3,6,5,2,7,1,4,8]=>1100100=>0011011
[7,5,4,2,6,1,3,8]=>[4,2,6,5,1,7,3,8]=>1110100=>0001011
[7,6,3,2,5,1,4,8]=>[3,5,6,2,7,1,4,8]=>1100000=>0011111
[6,5,4,2,8,1,3,7]=>[4,2,8,5,1,6,3,7]=>1110100=>0001011
[7,6,4,3,8,1,2,5]=>[4,3,8,1,6,2,7,5]=>1110100=>0001011
[7,6,5,2,8,1,3,4]=>[8,5,2,6,1,7,3,4]=>1110100=>0001011
[7,6,5,3,8,1,2,4]=>[8,5,3,6,1,7,2,4]=>1110100=>0001011
[8,5,3,2,6,1,4,7]=>[3,6,5,2,8,1,4,7]=>1100100=>0011011
[8,5,4,2,6,1,3,7]=>[4,2,6,5,1,8,3,7]=>1110100=>0001011
[8,6,3,2,5,1,4,7]=>[3,5,6,2,8,1,4,7]=>1100000=>0011111
[8,6,4,2,5,1,3,7]=>[4,2,5,6,1,8,3,7]=>1110000=>0001111
[8,5,3,2,7,1,4,6]=>[3,7,5,2,8,1,4,6]=>1100100=>0011011
[8,6,4,2,7,1,3,5]=>[4,2,7,1,6,3,8,5]=>1110100=>0001011
[8,6,4,3,7,1,2,5]=>[4,3,7,1,6,2,8,5]=>1110100=>0001011
[8,6,5,3,7,1,2,4]=>[7,5,3,6,1,8,2,4]=>1110100=>0001011
[8,7,3,2,5,1,4,6]=>[3,5,7,2,8,1,4,6]=>1100000=>0011111
[8,7,3,2,6,1,4,5]=>[3,6,2,7,1,4,8,5]=>1100100=>0011011
[8,7,4,2,6,1,3,5]=>[4,2,6,1,7,3,8,5]=>1110100=>0001011
[8,7,4,3,6,1,2,5]=>[4,3,6,1,7,2,8,5]=>1110100=>0001011
[8,7,5,2,6,1,3,4]=>[6,5,2,7,1,8,3,4]=>1110100=>0001011
[8,7,5,3,6,1,2,4]=>[6,5,3,7,1,8,2,4]=>1110100=>0001011
[8,7,6,2,5,1,3,4]=>[5,6,2,7,1,8,3,4]=>1110000=>0001111
[8,7,6,3,5,1,2,4]=>[5,6,3,7,1,8,2,4]=>1110000=>0001111
[4,8,3,7,2,6,1,5]=>[3,6,7,2,8,4,1,5]=>1101000=>0010111
[5,8,3,7,2,6,1,4]=>[3,6,7,2,8,1,5,4]=>1101000=>0010111
[5,8,4,7,2,6,1,3]=>[6,7,4,2,8,1,5,3]=>1111000=>0000111
[5,8,4,7,3,6,1,2]=>[6,7,4,3,8,1,5,2]=>1111000=>0000111
[6,8,4,7,2,5,1,3]=>[7,4,2,5,8,1,6,3]=>1111000=>0000111
[6,8,4,7,3,5,1,2]=>[7,4,3,5,8,1,6,2]=>1111000=>0000111
[6,8,5,7,2,4,1,3]=>[7,2,5,4,8,1,6,3]=>1111000=>0000111
[6,8,5,7,3,4,1,2]=>[7,3,5,4,8,1,6,2]=>1111000=>0000111
[7,8,3,6,2,5,1,4]=>[3,6,2,5,8,1,7,4]=>1101000=>0010111
[7,8,4,6,2,5,1,3]=>[6,4,2,5,8,1,7,3]=>1111000=>0000111
[7,8,4,6,3,5,1,2]=>[6,4,3,5,8,1,7,2]=>1111000=>0000111
[5,4,3,8,2,7,1,6]=>[3,7,4,2,5,1,8,6]=>1101010=>0010101
[6,5,3,8,2,7,1,4]=>[3,7,2,5,1,8,6,4]=>1101010=>0010101
[6,5,4,8,2,7,1,3]=>[7,4,2,5,1,8,6,3]=>1111010=>0000101
[7,4,3,8,2,6,1,5]=>[3,6,8,4,2,7,1,5]=>1101000=>0010111
[7,5,3,8,2,6,1,4]=>[3,6,8,2,5,1,7,4]=>1101000=>0010111
[7,5,4,8,2,6,1,3]=>[6,8,4,2,5,1,7,3]=>1111000=>0000111
[7,6,3,8,2,5,1,4]=>[3,8,2,5,6,1,7,4]=>1101000=>0010111
[7,6,4,8,2,5,1,3]=>[8,4,2,5,6,1,7,3]=>1111000=>0000111
[8,5,3,7,2,6,1,4]=>[3,6,7,2,5,1,8,4]=>1101000=>0010111
[8,5,4,7,2,6,1,3]=>[6,7,4,2,5,1,8,3]=>1111000=>0000111
[8,5,4,7,3,6,1,2]=>[6,7,4,3,5,1,8,2]=>1111000=>0000111
[8,6,3,7,2,5,1,4]=>[3,7,2,5,6,1,8,4]=>1101000=>0010111
[8,6,4,7,3,5,1,2]=>[7,4,3,5,6,1,8,2]=>1111000=>0000111
[8,6,5,7,2,4,1,3]=>[7,2,5,4,6,1,8,3]=>1111000=>0000111
[8,7,4,6,2,5,1,3]=>[6,4,2,5,7,1,8,3]=>1111000=>0000111
[8,7,4,6,3,5,1,2]=>[6,4,3,5,7,1,8,2]=>1111000=>0000111
[8,7,5,6,2,4,1,3]=>[6,2,5,4,7,1,8,3]=>1111000=>0000111
[6,5,4,3,2,8,1,7]=>[4,3,5,2,8,6,1,7]=>1110010=>0001101
[7,6,4,3,2,8,1,5]=>[4,3,8,6,2,7,1,5]=>1110010=>0001101
[7,6,5,4,2,8,1,3]=>[4,5,2,8,6,1,7,3]=>1110010=>0001101
[8,5,4,3,2,7,1,6]=>[4,3,5,2,7,1,8,6]=>1110010=>0001101
[8,6,5,4,2,7,1,3]=>[4,5,2,7,6,1,8,3]=>1110010=>0001101
[8,7,4,3,2,6,1,5]=>[4,3,6,7,2,8,1,5]=>1110000=>0001111
[8,7,5,4,2,6,1,3]=>[4,5,2,6,7,1,8,3]=>1110000=>0001111
[8,7,6,3,2,5,1,4]=>[6,3,5,7,2,8,1,4]=>1110000=>0001111
[8,7,6,5,2,4,1,3]=>[5,2,6,4,7,1,8,3]=>1111000=>0000111
[8,1,2,3,4,7,5,6]=>[7,1,2,3,4,5,8,6]=>1000010=>0111101
[8,1,2,3,6,4,5,7]=>[6,1,2,3,4,8,5,7]=>1000100=>0111011
[8,1,2,3,7,4,5,6]=>[7,1,2,3,4,8,5,6]=>1000100=>0111011
[7,1,2,3,6,4,8,5]=>[6,1,2,3,4,8,7,5]=>1000101=>0111010
[5,1,2,3,8,7,4,6]=>[7,5,1,2,3,4,8,6]=>1000110=>0111001
[8,1,2,3,6,7,4,5]=>[7,6,1,2,3,4,8,5]=>1000110=>0111001
[4,1,2,8,3,7,5,6]=>[7,4,1,2,3,5,8,6]=>1001010=>0110101
[8,1,2,5,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>1001000=>0110111
[7,1,2,5,3,4,8,6]=>[5,1,2,3,8,7,4,6]=>1001001=>0110110
[8,1,2,6,3,4,5,7]=>[6,1,2,3,8,4,5,7]=>1001000=>0110111
[7,1,2,6,3,4,8,5]=>[6,1,2,3,8,7,4,5]=>1001001=>0110110
[6,1,2,5,3,8,4,7]=>[5,1,2,3,8,6,4,7]=>1001010=>0110101
[8,1,2,5,3,7,4,6]=>[5,1,2,3,7,4,8,6]=>1001010=>0110101
[8,1,2,6,3,7,4,5]=>[7,6,1,2,3,8,4,5]=>1001010=>0110101
[6,1,2,5,3,7,8,4]=>[5,1,2,3,8,7,6,4]=>1001011=>0110100
[4,1,2,8,6,3,5,7]=>[6,4,1,2,3,8,5,7]=>1001100=>0110011
[4,1,2,8,7,3,5,6]=>[7,4,1,2,3,8,5,6]=>1001100=>0110011
[4,1,2,7,6,3,8,5]=>[6,4,1,2,3,8,7,5]=>1001101=>0110010
[8,1,2,5,6,3,4,7]=>[6,5,1,2,3,8,4,7]=>1001100=>0110011
[8,1,2,5,7,3,4,6]=>[7,5,1,2,3,8,4,6]=>1001100=>0110011
[8,1,2,7,6,3,4,5]=>[6,1,2,3,7,4,8,5]=>1001100=>0110011
[7,1,2,5,6,3,8,4]=>[6,5,1,2,3,8,7,4]=>1001101=>0110010
[4,1,2,5,8,7,3,6]=>[7,5,4,1,2,3,8,6]=>1001110=>0110001
[4,1,2,8,6,7,3,5]=>[7,6,4,1,2,3,8,5]=>1001110=>0110001
[8,1,2,5,6,7,3,4]=>[7,6,5,1,2,3,8,4]=>1001110=>0110001
[3,1,8,2,4,7,5,6]=>[7,3,1,2,4,5,8,6]=>1010010=>0101101
[3,1,8,2,6,4,5,7]=>[6,3,1,2,4,8,5,7]=>1010100=>0101011
[3,1,7,2,6,4,8,5]=>[6,3,1,2,4,8,7,5]=>1010101=>0101010
[3,1,5,2,8,7,4,6]=>[7,5,3,1,2,4,8,6]=>1010110=>0101001
[3,1,8,2,6,7,4,5]=>[7,6,3,1,2,4,8,5]=>1010110=>0101001
[8,1,4,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>1010000=>0101111
[7,1,4,2,3,5,8,6]=>[4,1,2,8,7,3,5,6]=>1010001=>0101110
[6,1,4,2,3,8,5,7]=>[4,1,2,8,6,3,5,7]=>1010010=>0101101
[8,1,4,2,3,7,5,6]=>[4,1,2,7,3,5,8,6]=>1010010=>0101101
[8,1,5,2,3,4,6,7]=>[5,1,2,8,3,4,6,7]=>1010000=>0101111
[8,1,7,2,3,4,5,6]=>[7,1,2,8,3,4,5,6]=>1010000=>0101111
[6,1,5,2,3,8,4,7]=>[5,1,2,8,6,3,4,7]=>1010010=>0101101
[8,1,5,2,3,7,4,6]=>[5,1,2,7,3,4,8,6]=>1010010=>0101101
[6,1,5,2,3,7,8,4]=>[5,1,2,8,7,6,3,4]=>1010011=>0101100
[5,1,4,2,8,3,6,7]=>[4,1,2,8,5,3,6,7]=>1010100=>0101011
[5,1,4,2,7,3,8,6]=>[4,1,2,8,7,5,3,6]=>1010101=>0101010
[8,1,4,2,6,3,5,7]=>[4,1,2,6,3,8,5,7]=>1010100=>0101011
[7,1,4,2,6,3,8,5]=>[4,1,2,6,3,8,7,5]=>1010101=>0101010
[8,1,5,2,6,3,4,7]=>[6,5,1,2,8,3,4,7]=>1010100=>0101011
[8,1,5,2,7,3,4,6]=>[7,5,1,2,8,3,4,6]=>1010100=>0101011
[7,1,8,2,6,3,4,5]=>[6,1,2,8,3,4,7,5]=>1010100=>0101011
[7,1,5,2,6,3,8,4]=>[6,5,1,2,8,7,3,4]=>1010101=>0101010
[8,1,4,2,6,7,3,5]=>[4,1,2,7,6,3,8,5]=>1010110=>0101001
[8,1,5,2,6,7,3,4]=>[7,6,5,1,2,8,3,4]=>1010110=>0101001
[5,1,4,2,6,7,8,3]=>[4,1,2,8,7,6,5,3]=>1010111=>0101000
[3,1,8,5,2,4,6,7]=>[5,3,1,2,8,4,6,7]=>1011000=>0100111
[3,1,7,5,2,4,8,6]=>[5,3,1,2,8,7,4,6]=>1011001=>0100110
[3,1,8,6,2,4,5,7]=>[6,3,1,2,8,4,5,7]=>1011000=>0100111
[3,1,7,6,2,4,8,5]=>[6,3,1,2,8,7,4,5]=>1011001=>0100110
[3,1,6,5,2,8,4,7]=>[5,3,1,2,8,6,4,7]=>1011010=>0100101
[3,1,8,5,2,7,4,6]=>[5,3,1,2,7,4,8,6]=>1011010=>0100101
[3,1,8,6,2,7,4,5]=>[7,6,3,1,2,8,4,5]=>1011010=>0100101
[8,1,4,5,2,3,6,7]=>[5,4,1,2,8,3,6,7]=>1011000=>0100111
[7,1,4,5,2,3,8,6]=>[5,4,1,2,8,7,3,6]=>1011001=>0100110
[8,1,4,6,2,3,5,7]=>[6,4,1,2,8,3,5,7]=>1011000=>0100111
[7,1,4,8,2,3,5,6]=>[8,4,1,2,7,3,5,6]=>1011000=>0100111
[7,1,4,6,2,3,8,5]=>[6,4,1,2,8,7,3,5]=>1011001=>0100110
[8,1,6,5,2,3,4,7]=>[5,1,2,6,3,8,4,7]=>1011000=>0100111
[7,1,8,6,2,3,4,5]=>[6,1,2,8,3,7,4,5]=>1011000=>0100111
[7,1,6,5,2,3,8,4]=>[5,1,2,6,3,8,7,4]=>1011001=>0100110
[8,1,4,5,2,7,3,6]=>[5,4,1,2,7,3,8,6]=>1011010=>0100101
[6,1,4,5,2,7,8,3]=>[5,4,1,2,8,7,6,3]=>1011011=>0100100
[3,1,4,8,6,2,5,7]=>[6,4,3,1,2,8,5,7]=>1011100=>0100011
[3,1,4,8,7,2,5,6]=>[7,4,3,1,2,8,5,6]=>1011100=>0100011
[3,1,4,7,6,2,8,5]=>[6,4,3,1,2,8,7,5]=>1011101=>0100010
[3,1,8,5,6,2,4,7]=>[6,5,3,1,2,8,4,7]=>1011100=>0100011
[3,1,8,5,7,2,4,6]=>[7,5,3,1,2,8,4,6]=>1011100=>0100011
[3,1,8,7,6,2,4,5]=>[6,3,1,2,7,4,8,5]=>1011100=>0100011
[8,1,4,5,6,2,3,7]=>[6,5,4,1,2,8,3,7]=>1011100=>0100011
[8,1,4,5,7,2,3,6]=>[7,5,4,1,2,8,3,6]=>1011100=>0100011
[8,1,4,7,6,2,3,5]=>[6,4,1,2,7,3,8,5]=>1011100=>0100011
[8,1,7,5,6,2,3,4]=>[6,5,1,2,7,3,8,4]=>1011100=>0100011
[3,1,4,8,6,7,2,5]=>[7,6,4,3,1,2,8,5]=>1011110=>0100001
[3,1,8,5,6,7,2,4]=>[7,6,5,3,1,2,8,4]=>1011110=>0100001
[8,1,4,5,6,7,2,3]=>[7,6,5,4,1,2,8,3]=>1011110=>0100001
[2,8,1,3,4,7,5,6]=>[7,2,1,3,4,5,8,6]=>1100010=>0011101
[2,8,1,3,7,4,5,6]=>[7,2,1,3,4,8,5,6]=>1100100=>0011011
[2,7,1,3,6,4,8,5]=>[6,2,1,3,4,8,7,5]=>1100101=>0011010
[2,8,1,5,3,4,6,7]=>[5,2,1,3,8,4,6,7]=>1101000=>0010111
[2,7,1,5,3,4,8,6]=>[5,2,1,3,8,7,4,6]=>1101001=>0010110
[2,8,1,6,3,4,5,7]=>[6,2,1,3,8,4,5,7]=>1101000=>0010111
[2,6,1,5,3,7,8,4]=>[5,2,1,3,8,7,6,4]=>1101011=>0010100
[2,4,1,8,6,3,5,7]=>[6,4,2,1,3,8,5,7]=>1101100=>0010011
[2,4,1,8,7,3,5,6]=>[7,4,2,1,3,8,5,6]=>1101100=>0010011
[2,4,1,7,6,3,8,5]=>[6,4,2,1,3,8,7,5]=>1101101=>0010010
[2,8,1,5,6,3,4,7]=>[6,5,2,1,3,8,4,7]=>1101100=>0010011
[2,8,1,5,7,3,4,6]=>[7,5,2,1,3,8,4,6]=>1101100=>0010011
[2,8,1,7,6,3,4,5]=>[6,2,1,3,7,4,8,5]=>1101100=>0010011
[2,7,1,5,6,3,8,4]=>[6,5,2,1,3,8,7,4]=>1101101=>0010010
[2,4,1,8,6,7,3,5]=>[7,6,4,2,1,3,8,5]=>1101110=>0010001
[7,3,1,2,4,5,8,6]=>[3,1,8,7,2,4,5,6]=>1100001=>0011110
[6,3,1,2,4,8,5,7]=>[3,1,8,6,2,4,5,7]=>1100010=>0011101
[8,3,1,2,4,7,5,6]=>[3,1,7,2,4,5,8,6]=>1100010=>0011101
[6,3,1,2,4,7,8,5]=>[3,1,8,7,6,2,4,5]=>1100011=>0011100
[5,3,1,2,8,4,6,7]=>[3,1,8,5,2,4,6,7]=>1100100=>0011011
[5,3,1,2,7,4,8,6]=>[3,1,8,7,5,2,4,6]=>1100101=>0011010
[8,3,1,2,6,4,5,7]=>[3,1,6,2,4,8,5,7]=>1100100=>0011011
[7,3,1,2,6,4,8,5]=>[3,1,6,2,4,8,7,5]=>1100101=>0011010
[5,3,1,2,8,7,4,6]=>[3,1,7,5,2,4,8,6]=>1100110=>0011001
[8,3,1,2,6,7,4,5]=>[3,1,7,6,2,4,8,5]=>1100110=>0011001
[5,3,1,2,6,7,8,4]=>[3,1,8,7,6,5,2,4]=>1100111=>0011000
[7,4,1,2,3,5,8,6]=>[4,1,8,7,2,3,5,6]=>1100001=>0011110
[6,4,1,2,3,8,5,7]=>[4,1,8,6,2,3,5,7]=>1100010=>0011101
[8,4,1,2,3,7,5,6]=>[4,1,7,2,3,5,8,6]=>1100010=>0011101
[6,4,1,2,3,7,8,5]=>[4,1,8,7,6,2,3,5]=>1100011=>0011100
[7,6,1,2,3,4,8,5]=>[6,1,8,7,2,3,4,5]=>1100001=>0011110
[5,8,1,2,3,7,4,6]=>[7,1,5,2,3,4,8,6]=>1100010=>0011101
[8,6,1,2,3,7,4,5]=>[7,6,1,8,2,3,4,5]=>1100010=>0011101
[5,4,1,2,8,3,6,7]=>[4,1,8,5,2,3,6,7]=>1100100=>0011011
[5,4,1,2,7,3,8,6]=>[4,1,8,7,5,2,3,6]=>1100101=>0011010
[8,4,1,2,6,3,5,7]=>[4,1,6,2,3,8,5,7]=>1100100=>0011011
[8,4,1,2,7,3,5,6]=>[4,1,7,2,3,8,5,6]=>1100100=>0011011
[7,4,1,2,6,3,8,5]=>[4,1,6,2,3,8,7,5]=>1100101=>0011010
[5,8,1,2,6,3,4,7]=>[6,1,8,5,2,3,4,7]=>1100100=>0011011
[5,8,1,2,7,3,4,6]=>[7,1,8,5,2,3,4,6]=>1100100=>0011011
[8,7,1,2,6,3,4,5]=>[6,1,7,2,3,4,8,5]=>1100100=>0011011
[5,7,1,2,6,3,8,4]=>[6,1,8,7,5,2,3,4]=>1100101=>0011010
[5,4,1,2,8,7,3,6]=>[4,1,7,5,2,3,8,6]=>1100110=>0011001
[8,4,1,2,6,7,3,5]=>[4,1,7,6,2,3,8,5]=>1100110=>0011001
[5,8,1,2,6,7,3,4]=>[7,6,1,8,5,2,3,4]=>1100110=>0011001
[5,4,1,2,6,7,8,3]=>[4,1,8,7,6,5,2,3]=>1100111=>0011000
[4,3,1,8,2,5,6,7]=>[3,1,8,4,2,5,6,7]=>1101000=>0010111
[4,3,1,8,2,7,5,6]=>[3,1,7,4,2,5,8,6]=>1101010=>0010101
[4,3,1,6,2,7,8,5]=>[3,1,8,7,6,4,2,5]=>1101011=>0010100
[8,3,1,5,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>1101000=>0010111
[7,3,1,5,2,4,8,6]=>[3,1,5,2,8,7,4,6]=>1101001=>0010110
[8,3,1,6,2,4,5,7]=>[3,1,6,2,8,4,5,7]=>1101000=>0010111
[7,3,1,8,2,4,5,6]=>[3,1,8,2,7,4,5,6]=>1101000=>0010111
[7,3,1,6,2,4,8,5]=>[3,1,6,2,8,7,4,5]=>1101001=>0010110
[8,3,1,5,2,7,4,6]=>[3,1,5,2,7,4,8,6]=>1101010=>0010101
[6,3,1,5,2,7,8,4]=>[3,1,5,2,8,7,6,4]=>1101011=>0010100
[8,4,1,5,2,3,6,7]=>[5,4,1,8,2,3,6,7]=>1101000=>0010111
[7,4,1,5,2,3,8,6]=>[5,4,1,8,7,2,3,6]=>1101001=>0010110
[8,4,1,6,2,3,5,7]=>[6,4,1,8,2,3,5,7]=>1101000=>0010111
[7,4,1,8,2,3,5,6]=>[8,4,1,7,2,3,5,6]=>1101000=>0010111
[8,7,1,5,2,3,4,6]=>[5,1,7,2,3,8,4,6]=>1101000=>0010111
[8,7,1,6,2,3,4,5]=>[6,1,7,2,3,8,4,5]=>1101000=>0010111
[6,7,1,5,2,3,8,4]=>[5,1,8,7,2,3,6,4]=>1101001=>0010110
[8,4,1,6,2,7,3,5]=>[7,6,4,1,8,2,3,5]=>1101010=>0010101
[6,8,1,5,2,7,3,4]=>[5,1,7,2,3,8,6,4]=>1101010=>0010101
[6,4,1,5,2,7,8,3]=>[5,4,1,8,7,6,2,3]=>1101011=>0010100
[4,3,1,5,8,2,6,7]=>[3,1,8,5,4,2,6,7]=>1101100=>0010011
[4,3,1,5,7,2,8,6]=>[3,1,8,7,5,4,2,6]=>1101101=>0010010
[4,3,1,8,6,2,5,7]=>[3,1,6,4,2,8,5,7]=>1101100=>0010011
[8,3,1,5,6,2,4,7]=>[3,1,6,5,2,8,4,7]=>1101100=>0010011
[8,3,1,5,7,2,4,6]=>[3,1,7,5,2,8,4,6]=>1101100=>0010011
[8,3,1,7,6,2,4,5]=>[3,1,6,2,7,4,8,5]=>1101100=>0010011
[7,3,1,5,6,2,8,4]=>[3,1,6,5,2,8,7,4]=>1101101=>0010010
[8,4,1,5,7,2,3,6]=>[7,5,4,1,8,2,3,6]=>1101100=>0010011
[8,4,1,7,6,2,3,5]=>[6,4,1,7,2,3,8,5]=>1101100=>0010011
[7,4,1,5,6,2,8,3]=>[6,5,4,1,8,7,2,3]=>1101101=>0010010
[4,3,1,5,6,8,2,7]=>[3,1,8,6,5,4,2,7]=>1101110=>0010001
[4,3,1,5,8,7,2,6]=>[3,1,7,5,4,2,8,6]=>1101110=>0010001
[4,3,1,8,6,7,2,5]=>[3,1,7,6,4,2,8,5]=>1101110=>0010001
[8,3,1,5,6,7,2,4]=>[3,1,7,6,5,2,8,4]=>1101110=>0010001
[8,4,1,5,6,7,2,3]=>[7,6,5,4,1,8,2,3]=>1101110=>0010001
[4,3,1,5,6,7,8,2]=>[3,1,8,7,6,5,4,2]=>1101111=>0010000
[2,3,8,1,4,7,5,6]=>[7,3,2,1,4,5,8,6]=>1110010=>0001101
[2,3,8,1,6,4,5,7]=>[6,3,2,1,4,8,5,7]=>1110100=>0001011
[2,3,7,1,6,4,8,5]=>[6,3,2,1,4,8,7,5]=>1110101=>0001010
[2,8,4,1,3,5,6,7]=>[4,2,1,8,3,5,6,7]=>1110000=>0001111
[2,7,4,1,3,5,8,6]=>[4,2,1,8,7,3,5,6]=>1110001=>0001110
[2,6,4,1,3,8,5,7]=>[4,2,1,8,6,3,5,7]=>1110010=>0001101
[2,8,4,1,3,7,5,6]=>[4,2,1,7,3,5,8,6]=>1110010=>0001101
[2,6,4,1,3,7,8,5]=>[4,2,1,8,7,6,3,5]=>1110011=>0001100
[2,8,5,1,3,4,6,7]=>[5,2,1,8,3,4,6,7]=>1110000=>0001111
[2,7,5,1,3,4,8,6]=>[5,2,1,8,7,3,4,6]=>1110001=>0001110
[2,8,7,1,3,4,5,6]=>[7,2,1,8,3,4,5,6]=>1110000=>0001111
[2,8,5,1,3,7,4,6]=>[5,2,1,7,3,4,8,6]=>1110010=>0001101
[2,6,8,1,3,7,4,5]=>[7,2,1,8,6,3,4,5]=>1110010=>0001101
[2,6,5,1,3,7,8,4]=>[5,2,1,8,7,6,3,4]=>1110011=>0001100
[2,5,4,1,8,3,6,7]=>[4,2,1,8,5,3,6,7]=>1110100=>0001011
[2,8,4,1,6,3,5,7]=>[4,2,1,6,3,8,5,7]=>1110100=>0001011
[2,8,4,1,7,3,5,6]=>[4,2,1,7,3,8,5,6]=>1110100=>0001011
[2,7,4,1,6,3,8,5]=>[4,2,1,6,3,8,7,5]=>1110101=>0001010
[2,8,5,1,6,3,4,7]=>[6,5,2,1,8,3,4,7]=>1110100=>0001011
[2,8,5,1,7,3,4,6]=>[7,5,2,1,8,3,4,6]=>1110100=>0001011
[2,7,8,1,6,3,4,5]=>[6,2,1,8,3,4,7,5]=>1110100=>0001011
[2,7,5,1,6,3,8,4]=>[6,5,2,1,8,7,3,4]=>1110101=>0001010
[2,5,4,1,6,8,3,7]=>[4,2,1,8,6,5,3,7]=>1110110=>0001001
[2,5,4,1,6,7,8,3]=>[4,2,1,8,7,6,5,3]=>1110111=>0001000
[7,3,4,1,2,5,8,6]=>[4,3,1,8,7,2,5,6]=>1110001=>0001110
[6,3,4,1,2,8,5,7]=>[4,3,1,8,6,2,5,7]=>1110010=>0001101
[8,3,4,1,2,7,5,6]=>[4,3,1,7,2,5,8,6]=>1110010=>0001101
[7,3,5,1,2,4,8,6]=>[5,3,1,8,7,2,4,6]=>1110001=>0001110
[6,3,7,1,2,4,8,5]=>[8,7,3,1,6,2,4,5]=>1110001=>0001110
[6,3,5,1,2,8,4,7]=>[5,3,1,8,6,2,4,7]=>1110010=>0001101
[6,3,8,1,2,7,4,5]=>[7,3,1,8,6,2,4,5]=>1110010=>0001101
[7,5,4,1,2,3,8,6]=>[4,1,5,2,8,7,3,6]=>1110001=>0001110
[6,8,4,1,2,3,5,7]=>[4,1,8,2,6,3,5,7]=>1110000=>0001111
[6,7,4,1,2,3,8,5]=>[4,1,8,7,2,6,3,5]=>1110001=>0001110
[6,7,5,1,2,3,8,4]=>[5,1,8,7,2,6,3,4]=>1110001=>0001110
[8,5,4,1,2,7,3,6]=>[4,1,5,2,7,3,8,6]=>1110010=>0001101
[6,8,5,1,2,7,3,4]=>[5,1,7,2,8,6,3,4]=>1110010=>0001101
[6,5,4,1,2,7,8,3]=>[4,1,5,2,8,7,6,3]=>1110011=>0001100
[5,3,4,1,8,2,6,7]=>[4,3,1,8,5,2,6,7]=>1110100=>0001011
[5,3,4,1,7,2,8,6]=>[4,3,1,8,7,5,2,6]=>1110101=>0001010
[8,3,4,1,6,2,5,7]=>[4,3,1,6,2,8,5,7]=>1110100=>0001011
[8,3,4,1,7,2,5,6]=>[4,3,1,7,2,8,5,6]=>1110100=>0001011
[8,3,5,1,6,2,4,7]=>[6,5,3,1,8,2,4,7]=>1110100=>0001011
[8,3,5,1,7,2,4,6]=>[7,5,3,1,8,2,4,6]=>1110100=>0001011
[7,3,8,1,6,2,4,5]=>[6,3,1,8,2,4,7,5]=>1110100=>0001011
[7,8,4,1,6,2,3,5]=>[4,1,6,2,8,3,7,5]=>1110100=>0001011
[7,8,5,1,6,2,3,4]=>[6,5,1,8,2,7,3,4]=>1110100=>0001011
[5,3,4,1,8,7,2,6]=>[4,3,1,7,5,2,8,6]=>1110110=>0001001
[8,3,4,1,6,7,2,5]=>[4,3,1,7,6,2,8,5]=>1110110=>0001001
[8,3,5,1,6,7,2,4]=>[7,6,5,3,1,8,2,4]=>1110110=>0001001
[8,5,4,1,6,7,2,3]=>[4,1,7,6,5,2,8,3]=>1110110=>0001001
[5,3,4,1,6,7,8,2]=>[4,3,1,8,7,6,5,2]=>1110111=>0001000
[2,3,4,8,1,7,5,6]=>[7,4,3,2,1,5,8,6]=>1111010=>0000101
[2,3,8,5,1,4,6,7]=>[5,3,2,1,8,4,6,7]=>1111000=>0000111
[2,3,8,6,1,4,5,7]=>[6,3,2,1,8,4,5,7]=>1111000=>0000111
[2,3,7,6,1,4,8,5]=>[6,3,2,1,8,7,4,5]=>1111001=>0000110
[2,3,6,5,1,8,4,7]=>[5,3,2,1,8,6,4,7]=>1111010=>0000101
[2,3,8,5,1,7,4,6]=>[5,3,2,1,7,4,8,6]=>1111010=>0000101
[2,3,8,6,1,7,4,5]=>[7,6,3,2,1,8,4,5]=>1111010=>0000101
[2,3,6,5,1,7,8,4]=>[5,3,2,1,8,7,6,4]=>1111011=>0000100
[2,8,4,5,1,3,6,7]=>[5,4,2,1,8,3,6,7]=>1111000=>0000111
[2,7,4,5,1,3,8,6]=>[5,4,2,1,8,7,3,6]=>1111001=>0000110
[2,8,4,6,1,3,5,7]=>[6,4,2,1,8,3,5,7]=>1111000=>0000111
[2,7,4,8,1,3,5,6]=>[8,4,2,1,7,3,5,6]=>1111000=>0000111
[2,8,6,5,1,3,4,7]=>[5,2,1,6,3,8,4,7]=>1111000=>0000111
[2,7,8,6,1,3,4,5]=>[6,2,1,8,3,7,4,5]=>1111000=>0000111
[2,7,6,5,1,3,8,4]=>[5,2,1,6,3,8,7,4]=>1111001=>0000110
[2,8,4,6,1,7,3,5]=>[7,6,4,2,1,8,3,5]=>1111010=>0000101
[2,8,6,5,1,7,3,4]=>[5,2,1,7,6,3,8,4]=>1111010=>0000101
[2,6,4,5,1,7,8,3]=>[5,4,2,1,8,7,6,3]=>1111011=>0000100
[7,3,4,5,1,2,8,6]=>[5,4,3,1,8,7,2,6]=>1111001=>0000110
[8,3,6,5,1,2,4,7]=>[5,3,1,6,2,8,4,7]=>1111000=>0000111
[7,3,8,5,1,2,4,6]=>[5,3,1,8,2,7,4,6]=>1111000=>0000111
[7,3,8,6,1,2,4,5]=>[6,3,1,8,2,7,4,5]=>1111000=>0000111
[8,3,4,5,1,7,2,6]=>[5,4,3,1,7,2,8,6]=>1111010=>0000101
[8,3,4,6,1,7,2,5]=>[7,6,4,3,1,8,2,5]=>1111010=>0000101
[8,6,4,5,1,7,2,3]=>[5,4,1,7,6,2,8,3]=>1111010=>0000101
[6,3,4,5,1,7,8,2]=>[5,4,3,1,8,7,6,2]=>1111011=>0000100
[2,3,4,8,6,1,5,7]=>[6,4,3,2,1,8,5,7]=>1111100=>0000011
[2,3,4,8,7,1,5,6]=>[7,4,3,2,1,8,5,6]=>1111100=>0000011
[2,3,4,7,6,1,8,5]=>[6,4,3,2,1,8,7,5]=>1111101=>0000010
[2,3,8,5,7,1,4,6]=>[7,5,3,2,1,8,4,6]=>1111100=>0000011
[2,3,8,7,6,1,4,5]=>[6,3,2,1,7,4,8,5]=>1111100=>0000011
[2,3,7,5,6,1,8,4]=>[6,5,3,2,1,8,7,4]=>1111101=>0000010
[2,8,4,5,7,1,3,6]=>[7,5,4,2,1,8,3,6]=>1111100=>0000011
[2,8,4,7,6,1,3,5]=>[6,4,2,1,7,3,8,5]=>1111100=>0000011
[2,8,7,5,6,1,3,4]=>[6,5,2,1,7,3,8,4]=>1111100=>0000011
[8,3,4,5,7,1,2,6]=>[7,5,4,3,1,8,2,6]=>1111100=>0000011
[8,3,4,7,6,1,2,5]=>[6,4,3,1,7,2,8,5]=>1111100=>0000011
[8,3,7,5,6,1,2,4]=>[6,5,3,1,7,2,8,4]=>1111100=>0000011
[7,3,4,5,6,1,8,2]=>[6,5,4,3,1,8,7,2]=>1111101=>0000010
[2,3,4,5,8,7,1,6]=>[7,5,4,3,2,1,8,6]=>1111110=>0000001
[2,3,4,8,6,7,1,5]=>[7,6,4,3,2,1,8,5]=>1111110=>0000001
[2,3,8,5,6,7,1,4]=>[7,6,5,3,2,1,8,4]=>1111110=>0000001
[2,8,4,5,6,7,1,3]=>[7,6,5,4,2,1,8,3]=>1111110=>0000001
[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>10000000=>01111111
[8,1,2,3,4,5,6,9,7]=>[9,8,1,2,3,4,5,6,7]=>10000001=>01111110
[7,1,2,3,4,5,9,6,8]=>[9,7,1,2,3,4,5,6,8]=>10000010=>01111101
[9,1,2,3,4,5,8,6,7]=>[8,1,2,3,4,5,6,9,7]=>10000010=>01111101
[7,1,2,3,4,5,8,9,6]=>[9,8,7,1,2,3,4,5,6]=>10000011=>01111100
[6,1,2,3,4,9,5,7,8]=>[9,6,1,2,3,4,5,7,8]=>10000100=>01111011
[6,1,2,3,4,8,5,9,7]=>[9,8,6,1,2,3,4,5,7]=>10000101=>01111010
[9,1,2,3,4,7,5,6,8]=>[7,1,2,3,4,5,9,6,8]=>10000100=>01111011
[9,1,2,3,4,8,5,6,7]=>[8,1,2,3,4,5,9,6,7]=>10000100=>01111011
[6,1,2,3,4,9,8,5,7]=>[8,6,1,2,3,4,5,9,7]=>10000110=>01111001
[9,1,2,3,4,7,8,5,6]=>[8,7,1,2,3,4,5,9,6]=>10000110=>01111001
[6,1,2,3,4,7,8,9,5]=>[9,8,7,6,1,2,3,4,5]=>10000111=>01111000
[9,1,2,3,6,4,5,7,8]=>[6,1,2,3,4,9,5,7,8]=>10001000=>01110111
[8,1,2,3,9,4,5,6,7]=>[9,1,2,3,4,8,5,6,7]=>10001000=>01110111
[5,1,2,3,6,7,8,9,4]=>[9,8,7,6,5,1,2,3,4]=>10001111=>01110000
[4,1,2,8,3,5,6,9,7]=>[9,8,4,1,2,3,5,6,7]=>10010001=>01101110
[9,1,2,5,3,4,6,7,8]=>[5,1,2,3,9,4,6,7,8]=>10010000=>01101111
[9,1,2,8,3,4,5,6,7]=>[8,1,2,3,9,4,5,6,7]=>10010000=>01101111
[7,1,2,8,3,4,5,9,6]=>[9,8,1,2,3,7,4,5,6]=>10010001=>01101110
[4,1,2,5,9,3,6,7,8]=>[9,5,4,1,2,3,6,7,8]=>10011000=>01100111
[4,1,2,5,6,7,8,9,3]=>[9,8,7,6,5,4,1,2,3]=>10011111=>01100000
[3,1,9,2,4,5,6,7,8]=>[9,3,1,2,4,5,6,7,8]=>10100000=>01011111
[3,1,9,2,4,5,8,6,7]=>[8,3,1,2,4,5,6,9,7]=>10100010=>01011101
[3,1,5,2,7,4,9,6,8]=>[9,7,5,3,1,2,4,6,8]=>10101010=>01010101
[9,1,4,2,3,5,8,6,7]=>[4,1,2,8,3,5,6,9,7]=>10100010=>01011101
[9,1,8,2,3,4,5,6,7]=>[8,1,2,9,3,4,5,6,7]=>10100000=>01011111
[9,1,4,5,2,3,6,7,8]=>[5,4,1,2,9,3,6,7,8]=>10110000=>01001111
[9,1,4,8,2,3,5,6,7]=>[8,4,1,2,9,3,5,6,7]=>10110000=>01001111
[3,1,4,5,6,7,9,2,8]=>[9,7,6,5,4,3,1,2,8]=>10111110=>01000001
[3,1,4,5,6,7,8,9,2]=>[9,8,7,6,5,4,3,1,2]=>10111111=>01000000
[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]=>11000000=>00111111
[2,9,1,3,4,5,8,6,7]=>[8,2,1,3,4,5,6,9,7]=>11000010=>00111101
[2,5,1,3,6,7,8,9,4]=>[9,8,7,6,5,2,1,3,4]=>11001111=>00110000
[2,4,1,5,6,7,8,9,3]=>[9,8,7,6,5,4,2,1,3]=>11011111=>00100000
[9,3,1,2,4,5,6,7,8]=>[3,1,9,2,4,5,6,7,8]=>11000000=>00111111
[8,3,1,2,4,5,6,9,7]=>[3,1,9,8,2,4,5,6,7]=>11000001=>00111110
[9,3,1,2,4,5,8,6,7]=>[3,1,8,2,4,5,6,9,7]=>11000010=>00111101
[9,7,1,2,3,4,5,6,8]=>[7,1,9,2,3,4,5,6,8]=>11000000=>00111111
[8,9,1,2,3,4,5,6,7]=>[9,1,8,2,3,4,5,6,7]=>11000000=>00111111
[9,7,1,2,3,4,8,5,6]=>[8,7,1,9,2,3,4,5,6]=>11000010=>00111101
[9,8,1,2,3,7,4,5,6]=>[7,1,8,2,3,4,5,9,6]=>11000100=>00111011
[4,3,1,5,6,7,8,9,2]=>[3,1,9,8,7,6,5,4,2]=>11011111=>00100000
[2,3,5,1,6,7,8,9,4]=>[9,8,7,6,5,3,2,1,4]=>11101111=>00010000
[9,3,4,1,2,5,6,7,8]=>[4,3,1,9,2,5,6,7,8]=>11100000=>00011111
[2,3,4,6,1,7,8,9,5]=>[9,8,7,6,4,3,2,1,5]=>11110111=>00001000
[7,3,4,5,1,2,8,9,6]=>[5,4,3,1,9,8,7,2,6]=>11110011=>00001100
[2,3,4,5,9,1,6,7,8]=>[9,5,4,3,2,1,6,7,8]=>11111000=>00000111
[2,3,4,5,8,1,6,9,7]=>[9,8,5,4,3,2,1,6,7]=>11111001=>00000110
[2,3,4,5,7,1,8,9,6]=>[9,8,7,5,4,3,2,1,6]=>11111011=>00000100
[2,3,4,5,6,9,1,7,8]=>[9,6,5,4,3,2,1,7,8]=>11111100=>00000011
[2,3,4,5,6,8,1,9,7]=>[9,8,6,5,4,3,2,1,7]=>11111101=>00000010
[2,3,4,5,6,7,9,1,8]=>[9,7,6,5,4,3,2,1,8]=>11111110=>00000001
[2,3,4,5,6,9,8,1,7]=>[8,6,5,4,3,2,1,9,7]=>11111110=>00000001
[2,3,4,5,9,7,8,1,6]=>[8,7,5,4,3,2,1,9,6]=>11111110=>00000001
[2,3,4,9,6,7,8,1,5]=>[8,7,6,4,3,2,1,9,5]=>11111110=>00000001
[2,3,9,5,6,7,8,1,4]=>[8,7,6,5,3,2,1,9,4]=>11111110=>00000001
[2,9,4,5,6,7,8,1,3]=>[8,7,6,5,4,2,1,9,3]=>11111110=>00000001
[9,3,4,5,6,7,8,1,2]=>[8,7,6,5,4,3,1,9,2]=>11111110=>00000001
[2,3,4,5,6,7,8,9,1]=>[9,8,7,6,5,4,3,2,1]=>11111111=>00000000
[]=>[]=>=>
[3,5,2,6,1,4,8,7]=>[6,2,3,1,5,4,8,7]=>1101001=>0010110
[3,5,2,6,4,1,8,7]=>[6,4,5,2,3,1,8,7]=>1101001=>0010110
[3,5,2,7,4,8,1,6]=>[8,4,5,2,3,1,7,6]=>1101010=>0010101
[3,5,2,7,4,8,6,1]=>[8,6,7,4,5,2,3,1]=>1101010=>0010101
[4,5,7,2,3,8,6,1]=>[8,6,7,2,5,3,4,1]=>1110010=>0001101
[4,5,7,2,3,8,1,6]=>[8,2,5,3,4,1,7,6]=>1110010=>0001101
[4,5,6,2,3,1,8,7]=>[6,2,5,3,4,1,8,7]=>1110001=>0001110
[4,5,6,2,1,3,8,7]=>[6,2,5,1,4,3,8,7]=>1110001=>0001110
[3,5,1,6,4,2,8,7]=>[6,4,5,1,3,2,8,7]=>1101001=>0010110
[4,5,6,1,3,2,8,7]=>[6,1,5,3,4,2,8,7]=>1110001=>0001110
[4,5,6,3,1,2,8,7]=>[6,3,5,1,4,2,8,7]=>1110001=>0001110
[4,5,7,3,2,8,1,6]=>[8,3,5,2,4,1,7,6]=>1110010=>0001101
[4,5,7,3,2,8,6,1]=>[8,6,7,3,5,2,4,1]=>1110010=>0001101
[4,6,7,3,8,2,5,1]=>[8,3,7,5,6,2,4,1]=>1110100=>0001011
[4,6,7,3,8,2,1,5]=>[8,3,7,2,4,1,6,5]=>1110100=>0001011
[4,6,7,3,8,1,2,5]=>[8,3,7,1,4,2,6,5]=>1110100=>0001011
[4,5,7,3,1,8,2,6]=>[8,3,5,1,4,2,7,6]=>1110010=>0001101
[4,5,7,1,3,8,2,6]=>[8,1,5,3,4,2,7,6]=>1110010=>0001101
[3,5,1,7,4,8,2,6]=>[8,4,5,1,3,2,7,6]=>1101010=>0010101
[2,1,5,7,4,8,3,6]=>[2,1,8,4,5,3,7,6]=>1011010=>0100101
[2,1,5,7,4,8,6,3]=>[2,1,8,6,7,4,5,3]=>1011010=>0100101
[3,5,1,7,4,8,6,2]=>[8,6,7,4,5,1,3,2]=>1101010=>0010101
[4,5,7,1,3,8,6,2]=>[8,6,7,1,5,3,4,2]=>1110010=>0001101
[4,5,7,3,1,8,6,2]=>[8,6,7,3,5,1,4,2]=>1110010=>0001101
[4,6,7,3,8,1,5,2]=>[8,3,7,5,6,1,4,2]=>1110100=>0001011
[4,6,7,3,8,5,1,2]=>[8,5,7,3,6,1,4,2]=>1110100=>0001011
[4,6,7,3,8,5,2,1]=>[8,5,7,3,6,2,4,1]=>1110100=>0001011
[5,6,7,8,3,1,4,2]=>[8,3,7,1,6,4,5,2]=>1111000=>0000111
[5,6,7,8,1,3,4,2]=>[8,1,7,3,6,4,5,2]=>1111000=>0000111
[4,6,7,1,8,3,5,2]=>[8,1,7,5,6,3,4,2]=>1110100=>0001011
[3,6,1,7,8,4,5,2]=>[8,4,7,5,6,1,3,2]=>1101100=>0010011
[2,1,6,7,8,4,5,3]=>[2,1,8,4,7,5,6,3]=>1011100=>0100011
[2,1,6,7,8,4,3,5]=>[2,1,8,4,7,3,6,5]=>1011100=>0100011
[3,6,1,7,8,4,2,5]=>[8,4,7,1,3,2,6,5]=>1101100=>0010011
[4,6,7,1,8,3,2,5]=>[8,1,7,3,4,2,6,5]=>1110100=>0001011
[5,6,7,8,1,3,2,4]=>[8,1,7,3,6,2,5,4]=>1111000=>0000111
[4,5,7,2,1,8,3,6]=>[8,2,5,1,4,3,7,6]=>1110010=>0001101
[4,6,7,2,8,1,3,5]=>[8,2,7,1,4,3,6,5]=>1110100=>0001011
[4,6,7,2,8,3,1,5]=>[8,2,7,3,4,1,6,5]=>1110100=>0001011
[4,6,7,2,8,3,5,1]=>[8,2,7,5,6,3,4,1]=>1110100=>0001011
[3,6,2,7,8,4,5,1]=>[8,4,7,5,6,2,3,1]=>1101100=>0010011
[3,6,2,7,8,4,1,5]=>[8,4,7,2,3,1,6,5]=>1101100=>0010011
[3,6,2,7,8,1,4,5]=>[8,2,3,1,7,4,6,5]=>1101100=>0010011
[3,5,2,7,1,8,4,6]=>[8,2,3,1,5,4,7,6]=>1101010=>0010101
[3,4,2,1,7,8,5,6]=>[4,2,3,1,8,5,7,6]=>1100110=>0011001
[3,4,1,2,7,8,6,5]=>[4,1,3,2,8,6,7,5]=>1100110=>0011001
[3,5,2,7,1,8,6,4]=>[8,6,7,2,3,1,5,4]=>1101010=>0010101
[3,6,2,7,8,1,5,4]=>[8,2,3,1,7,5,6,4]=>1101100=>0010011
[3,6,2,7,8,5,1,4]=>[8,5,7,2,3,1,6,4]=>1101100=>0010011
[3,6,2,7,8,5,4,1]=>[8,5,7,4,6,2,3,1]=>1101100=>0010011
[4,6,7,2,8,5,3,1]=>[8,5,7,2,6,3,4,1]=>1110100=>0001011
[4,6,7,2,8,5,1,3]=>[8,5,7,2,6,1,4,3]=>1110100=>0001011
[4,6,7,2,8,1,5,3]=>[8,2,7,5,6,1,4,3]=>1110100=>0001011
[4,5,7,2,1,8,6,3]=>[8,6,7,2,5,1,4,3]=>1110010=>0001101
[4,5,7,1,2,8,6,3]=>[8,6,7,1,5,2,4,3]=>1110010=>0001101
[3,5,1,7,2,8,6,4]=>[8,6,7,1,3,2,5,4]=>1101010=>0010101
[2,1,5,7,3,8,6,4]=>[2,1,8,6,7,3,5,4]=>1011010=>0100101
[2,1,6,7,8,3,5,4]=>[2,1,8,3,7,5,6,4]=>1011100=>0100011
[3,6,1,7,8,2,5,4]=>[8,1,3,2,7,5,6,4]=>1101100=>0010011
[4,6,7,1,8,2,5,3]=>[8,1,7,5,6,2,4,3]=>1110100=>0001011
[5,6,7,8,1,2,4,3]=>[8,1,7,2,6,4,5,3]=>1111000=>0000111
[5,6,7,8,2,1,4,3]=>[8,2,7,1,6,4,5,3]=>1111000=>0000111
[5,6,7,8,2,4,1,3]=>[8,2,7,4,6,1,5,3]=>1111000=>0000111
[5,6,7,8,2,4,3,1]=>[8,2,7,4,6,3,5,1]=>1111000=>0000111
[5,6,7,8,1,4,2,3]=>[8,1,7,4,6,2,5,3]=>1111000=>0000111
[4,6,7,1,8,5,2,3]=>[8,5,7,1,6,2,4,3]=>1110100=>0001011
[3,6,1,7,8,5,2,4]=>[8,5,7,1,3,2,6,4]=>1101100=>0010011
[2,1,6,7,8,5,3,4]=>[2,1,8,5,7,3,6,4]=>1011100=>0100011
[3,6,1,7,8,5,4,2]=>[8,5,7,4,6,1,3,2]=>1101100=>0010011
[4,6,7,1,8,5,3,2]=>[8,5,7,1,6,3,4,2]=>1110100=>0001011
[5,6,7,8,1,4,3,2]=>[8,1,7,4,6,3,5,2]=>1111000=>0000111
[5,6,7,8,4,1,3,2]=>[8,4,7,1,6,3,5,2]=>1111000=>0000111
[3,5,2,7,4,9,6,10,8,1]=>[10,8,9,6,7,4,5,2,3,1]=>110101010=>001010101
[6,7,8,9,10,5,4,3,2,1]=>[10,5,9,4,8,3,7,2,6,1]=>111110000=>000001111
[6,5,8,7,3,4,1,2]=>[7,3,8,4,5,1,6,2]=>1111000=>0000111
[3,6,7,4,5,8,1,2]=>[4,5,8,1,7,6,3,2]=>1110010=>0001101
[2,6,7,4,5,1,8,3]=>[4,5,8,7,2,1,6,3]=>1110001=>0001110
[1,6,7,4,5,2,3,8]=>[1,4,5,7,2,6,3,8]=>0110000=>1001111
[1,5,4,7,6,2,3,8]=>[1,6,4,2,7,5,3,8]=>0111100=>1000011
[2,5,4,7,6,1,8,3]=>[6,4,2,1,8,7,5,3]=>1111101=>0000010
[3,5,4,7,6,8,1,2]=>[8,6,4,1,7,5,3,2]=>1111110=>0000001
[4,5,3,7,8,6,1,2]=>[3,6,8,1,7,5,4,2]=>1101100=>0010011
[5,4,3,8,7,6,1,2]=>[3,6,7,4,1,8,5,2]=>1101100=>0010011
[6,4,8,3,7,5,1,2]=>[7,5,8,3,4,1,6,2]=>1110100=>0001011
[6,3,8,4,5,7,1,2]=>[4,5,7,3,1,8,6,2]=>1110010=>0001101
[5,3,4,8,6,7,1,2]=>[7,6,4,3,1,8,5,2]=>1111110=>0000001
[4,3,5,6,8,7,1,2]=>[7,3,1,8,6,5,4,2]=>1111110=>0000001
[3,2,5,6,1,8,7,4]=>[2,7,8,6,3,1,5,4]=>1011010=>0100101
[4,2,5,6,8,1,7,3]=>[2,7,8,1,6,5,4,3]=>1011100=>0100011
[5,2,4,8,6,1,7,3]=>[2,6,4,1,7,8,5,3]=>1011100=>0100011
[6,2,8,4,5,1,7,3]=>[2,4,5,7,8,1,6,3]=>1010000=>0101111
[7,8,2,4,5,1,6,3]=>[4,5,8,2,6,7,1,3]=>1100000=>0011111
[7,8,1,4,5,2,3,6]=>[4,5,8,1,7,2,3,6]=>1100000=>0011111
[6,1,8,4,5,2,3,7]=>[4,5,8,1,2,6,3,7]=>1010000=>0101111
[5,1,4,8,6,2,3,7]=>[6,4,1,2,8,5,3,7]=>1011100=>0100011
[4,1,3,2,8,6,5,7]=>[3,4,1,2,6,8,5,7]=>1000100=>0111011
[5,1,3,8,2,6,4,7]=>[3,6,8,1,2,5,4,7]=>1001000=>0110111
[6,1,8,3,2,5,4,7]=>[8,3,5,6,1,2,4,7]=>1010000=>0101111
[7,8,1,3,2,5,4,6]=>[8,1,3,5,7,2,4,6]=>1100000=>0011111
[7,8,2,3,1,5,6,4]=>[8,2,3,5,6,7,1,4]=>1100000=>0011111
[6,2,8,3,1,5,7,4]=>[2,7,8,3,5,6,1,4]=>1010000=>0101111
[5,2,3,8,1,6,7,4]=>[2,3,6,7,8,1,5,4]=>1001000=>0110111
[6,3,8,2,1,7,5,4]=>[7,3,2,5,8,6,1,4]=>1110010=>0001101
[7,8,3,2,1,6,5,4]=>[3,6,8,2,5,7,1,4]=>1100000=>0011111
[7,8,4,2,6,1,5,3]=>[4,2,6,1,8,5,7,3]=>1110100=>0001011
[5,4,2,8,7,1,6,3]=>[7,4,2,6,8,5,1,3]=>1101100=>0010011
[4,5,2,7,8,1,6,3]=>[8,2,6,7,5,4,1,3]=>1101100=>0010011
[2,5,3,7,1,6,8,4]=>[3,6,8,7,2,1,5,4]=>1101001=>0010110
[1,5,3,7,2,6,4,8]=>[1,3,6,7,2,5,4,8]=>0101000=>1010111
[1,6,7,3,2,5,4,8]=>[1,7,3,5,6,2,4,8]=>0110000=>1001111
[2,6,7,3,1,5,8,4]=>[8,7,3,5,6,2,1,4]=>1110001=>0001110
[3,6,7,2,1,8,5,4]=>[8,2,5,7,6,3,1,4]=>1110010=>0001101
[7,8,5,6,2,1,4,3]=>[6,2,5,1,8,4,7,3]=>1111000=>0000111
[6,5,8,7,1,2,3,4]=>[7,1,8,2,5,3,6,4]=>1111000=>0000111
[5,4,1,8,7,2,3,6]=>[7,4,1,8,5,2,3,6]=>1101100=>0010011
[6,4,8,1,7,2,3,5]=>[7,1,4,2,8,3,6,5]=>1110100=>0001011
[7,8,3,1,2,6,4,5]=>[3,6,8,1,7,2,4,5]=>1100000=>0011111
[5,3,1,8,2,7,4,6]=>[3,1,7,2,5,4,8,6]=>1101010=>0010101
[4,3,1,2,8,7,5,6]=>[3,1,4,2,7,5,8,6]=>1100110=>0011001
[4,2,1,3,8,5,7,6]=>[2,4,1,3,7,8,5,6]=>1000100=>0111011
[5,2,1,8,3,4,7,6]=>[2,7,8,1,3,5,4,6]=>1001000=>0110111
[6,2,8,1,3,4,7,5]=>[2,7,8,1,6,3,4,5]=>1010000=>0101111
[7,8,2,1,3,4,6,5]=>[8,2,6,7,1,3,4,5]=>1100000=>0011111
[4,3,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>1100101=>0011010
[5,3,1,6,2,4,8,7]=>[3,1,6,2,5,4,8,7]=>1101001=>0010110
[6,3,1,5,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>1101001=>0010110
[7,3,1,5,2,8,4,6]=>[3,1,5,2,8,4,7,6]=>1101010=>0010101
[8,4,5,1,2,7,3,6]=>[5,1,4,2,7,3,8,6]=>1110010=>0001101
[7,4,5,1,2,8,3,6]=>[5,1,4,2,8,3,7,6]=>1110010=>0001101
[6,4,5,1,2,3,8,7]=>[5,1,4,2,6,3,8,7]=>1110001=>0001110
[5,4,6,1,2,3,8,7]=>[6,1,4,2,5,3,8,7]=>1110001=>0001110
[2,1,6,5,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>1011001=>0100110
[3,6,1,5,2,4,8,7]=>[5,1,3,2,6,4,8,7]=>1101001=>0010110
[4,6,5,1,2,3,8,7]=>[5,1,6,2,4,3,8,7]=>1110001=>0001110
[5,6,4,1,2,3,8,7]=>[4,1,6,2,5,3,8,7]=>1110001=>0001110
[6,5,4,1,2,3,8,7]=>[4,1,5,2,6,3,8,7]=>1110001=>0001110
[7,5,4,1,2,8,3,6]=>[4,1,5,2,8,3,7,6]=>1110010=>0001101
[8,6,4,1,7,2,3,5]=>[4,1,7,2,6,3,8,5]=>1110100=>0001011
[7,6,4,1,8,2,3,5]=>[4,1,8,2,6,3,7,5]=>1110100=>0001011
[5,7,4,1,2,8,3,6]=>[4,1,8,2,5,3,7,6]=>1110010=>0001101
[3,7,1,5,2,8,4,6]=>[5,1,3,2,8,4,7,6]=>1101010=>0010101
[2,1,7,5,3,8,4,6]=>[2,1,5,3,8,4,7,6]=>1011010=>0100101
[2,1,8,5,3,7,4,6]=>[2,1,5,3,7,4,8,6]=>1011010=>0100101
[3,8,1,5,2,7,4,6]=>[5,1,3,2,7,4,8,6]=>1101010=>0010101
[4,8,5,1,2,7,3,6]=>[5,1,7,2,4,3,8,6]=>1110010=>0001101
[5,8,4,1,2,7,3,6]=>[4,1,7,2,5,3,8,6]=>1110010=>0001101
[6,8,4,1,7,2,3,5]=>[4,1,7,2,8,3,6,5]=>1110100=>0001011
[8,7,4,1,6,2,3,5]=>[4,1,6,2,7,3,8,5]=>1110100=>0001011
[3,8,1,6,7,2,4,5]=>[7,1,3,2,6,4,8,5]=>1101100=>0010011
[2,1,8,6,7,3,4,5]=>[2,1,7,3,6,4,8,5]=>1011100=>0100011
[2,1,7,6,8,3,4,5]=>[2,1,8,3,6,4,7,5]=>1011100=>0100011
[3,7,1,6,8,2,4,5]=>[8,1,3,2,6,4,7,5]=>1101100=>0010011
[5,4,7,1,2,8,3,6]=>[8,1,4,2,5,3,7,6]=>1110010=>0001101
[6,4,7,1,8,2,3,5]=>[8,1,4,2,7,3,6,5]=>1110100=>0001011
[7,4,6,1,8,2,3,5]=>[8,1,4,2,6,3,7,5]=>1110100=>0001011
[8,4,6,1,7,2,3,5]=>[7,1,4,2,6,3,8,5]=>1110100=>0001011
[8,3,1,6,7,2,4,5]=>[3,1,7,2,6,4,8,5]=>1101100=>0010011
[7,3,1,6,8,2,4,5]=>[3,1,8,2,6,4,7,5]=>1101100=>0010011
[6,3,1,7,8,2,4,5]=>[3,1,8,2,7,4,6,5]=>1101100=>0010011
[5,3,1,7,2,8,4,6]=>[3,1,8,2,5,4,7,6]=>1101010=>0010101
[4,3,1,2,7,8,5,6]=>[3,1,4,2,8,5,7,6]=>1100110=>0011001
[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,5,8,6]=>1010110=>0101001
[3,4,1,2,8,7,5,6]=>[4,1,3,2,7,5,8,6]=>1100110=>0011001
[6,3,1,8,7,2,4,5]=>[3,1,7,2,8,4,6,5]=>1101100=>0010011
[7,3,1,8,6,2,4,5]=>[3,1,6,2,8,4,7,5]=>1101100=>0010011
[8,4,7,1,6,2,3,5]=>[6,1,4,2,7,3,8,5]=>1110100=>0001011
[7,4,8,1,6,2,3,5]=>[6,1,4,2,8,3,7,5]=>1110100=>0001011
[5,4,8,1,2,7,3,6]=>[7,1,4,2,5,3,8,6]=>1110010=>0001101
[3,5,1,8,2,7,4,6]=>[7,1,3,2,5,4,8,6]=>1101010=>0010101
[2,1,5,8,3,7,4,6]=>[2,1,7,3,5,4,8,6]=>1011010=>0100101
[2,1,6,8,7,3,4,5]=>[2,1,7,3,8,4,6,5]=>1011100=>0100011
[4,6,8,1,7,2,3,5]=>[7,1,8,2,4,3,6,5]=>1110100=>0001011
[3,7,1,8,6,2,4,5]=>[6,1,3,2,8,4,7,5]=>1101100=>0010011
[2,1,7,8,6,3,4,5]=>[2,1,6,3,8,4,7,5]=>1011100=>0100011
[2,1,8,7,6,3,4,5]=>[2,1,6,3,7,4,8,5]=>1011100=>0100011
[3,8,1,7,6,2,4,5]=>[6,1,3,2,7,4,8,5]=>1101100=>0010011
[5,8,7,6,1,2,3,4]=>[6,1,7,2,8,3,5,4]=>1111000=>0000111
[6,8,7,5,1,2,3,4]=>[5,1,7,2,8,3,6,4]=>1111000=>0000111
[6,4,7,3,8,5,1,2]=>[8,5,7,3,4,1,6,2]=>1110100=>0001011
[6,4,7,3,5,8,1,2]=>[5,8,3,4,1,7,6,2]=>1110010=>0001101
[6,4,7,2,5,1,8,3]=>[5,8,7,2,4,1,6,3]=>1110001=>0001110
[5,4,2,7,6,1,3,8]=>[6,4,2,7,5,1,3,8]=>1101100=>0010011
[5,4,2,7,6,1,8,3]=>[6,4,2,8,7,5,1,3]=>1101101=>0010010
[5,4,3,7,6,8,1,2]=>[3,8,6,4,1,7,5,2]=>1101110=>0010001
[5,4,3,7,8,6,1,2]=>[3,6,8,4,1,7,5,2]=>1101100=>0010011
[6,4,8,3,5,7,1,2]=>[5,7,3,4,1,8,6,2]=>1110010=>0001101
[5,4,3,8,6,7,1,2]=>[3,7,6,4,1,8,5,2]=>1101110=>0010001
[5,4,3,6,8,7,1,2]=>[3,7,4,1,8,6,5,2]=>1101110=>0010001
[5,4,2,6,7,1,8,3]=>[8,7,4,2,6,5,1,3]=>1101101=>0010010
[5,4,2,6,7,1,3,8]=>[7,4,2,6,5,1,3,8]=>1101100=>0010011
[5,3,2,6,1,7,4,8]=>[3,2,7,6,1,5,4,8]=>1101010=>0010101
[5,3,2,6,1,7,8,4]=>[3,2,8,7,6,1,5,4]=>1101011=>0010100
[5,3,2,6,1,8,7,4]=>[3,2,7,8,6,1,5,4]=>1101010=>0010101
[5,4,2,6,8,1,7,3]=>[7,8,4,2,6,5,1,3]=>1101100=>0010011
[5,4,2,8,6,1,7,3]=>[6,4,2,7,8,5,1,3]=>1101100=>0010011
[6,4,8,2,5,1,7,3]=>[5,7,8,2,4,1,6,3]=>1110000=>0001111
[7,8,4,2,5,1,6,3]=>[4,2,5,8,1,6,7,3]=>1110000=>0001111
[7,8,4,2,5,1,3,6]=>[4,2,5,8,1,7,3,6]=>1110000=>0001111
[5,4,2,8,6,1,3,7]=>[6,4,2,8,5,1,3,7]=>1101100=>0010011
[5,3,2,6,1,8,4,7]=>[3,2,8,6,1,5,4,7]=>1101010=>0010101
[4,3,2,1,6,8,5,7]=>[3,2,4,1,8,6,5,7]=>1100110=>0011001
[4,3,2,1,8,6,5,7]=>[3,2,4,1,6,8,5,7]=>1100100=>0011011
[5,3,2,8,1,6,4,7]=>[3,2,6,8,1,5,4,7]=>1101000=>0010111
[6,3,8,2,1,5,4,7]=>[8,3,2,5,6,1,4,7]=>1110000=>0001111
[7,8,3,2,1,5,4,6]=>[3,8,2,5,7,1,4,6]=>1100000=>0011111
[7,8,3,2,1,5,6,4]=>[3,8,2,5,6,7,1,4]=>1100000=>0011111
[6,3,8,2,1,5,7,4]=>[7,8,3,2,5,6,1,4]=>1110000=>0001111
[5,3,2,8,1,6,7,4]=>[3,2,6,7,8,1,5,4]=>1101000=>0010111
[5,4,2,7,8,1,6,3]=>[8,4,2,6,7,5,1,3]=>1101100=>0010011
[5,3,2,7,1,8,6,4]=>[3,2,8,6,7,1,5,4]=>1101010=>0010101
[5,3,2,7,1,6,8,4]=>[3,2,6,8,7,1,5,4]=>1101001=>0010110
[5,3,2,7,1,6,4,8]=>[3,2,6,7,1,5,4,8]=>1101000=>0010111
[6,3,7,2,1,5,4,8]=>[7,3,2,5,6,1,4,8]=>1110000=>0001111
[6,3,7,2,1,5,8,4]=>[8,7,3,2,5,6,1,4]=>1110001=>0001110
[6,3,7,2,1,8,5,4]=>[8,3,2,5,7,6,1,4]=>1110010=>0001101
[6,4,7,2,8,1,5,3]=>[8,2,4,1,7,5,6,3]=>1110100=>0001011
[6,5,7,8,2,1,4,3]=>[8,2,7,1,5,4,6,3]=>1111000=>0000111
[6,5,8,7,2,1,3,4]=>[7,2,8,1,5,3,6,4]=>1111000=>0000111
[6,3,7,2,1,8,4,5]=>[8,3,2,7,6,1,4,5]=>1110010=>0001101
[6,3,7,2,1,4,8,5]=>[8,7,3,2,6,1,4,5]=>1110001=>0001110
[6,3,7,2,1,4,5,8]=>[7,3,2,6,1,4,5,8]=>1110000=>0001111
[5,3,2,7,1,4,8,6]=>[3,2,8,7,1,5,4,6]=>1101001=>0010110
[5,4,2,8,7,1,3,6]=>[7,4,2,8,5,1,3,6]=>1101100=>0010011
[7,8,4,2,6,1,3,5]=>[4,2,6,1,8,3,7,5]=>1110100=>0001011
[7,8,3,2,1,6,4,5]=>[3,6,8,2,7,1,4,5]=>1100000=>0011111
[6,3,8,2,1,7,4,5]=>[7,3,2,8,6,1,4,5]=>1110010=>0001101
[5,3,2,8,1,7,4,6]=>[3,2,7,1,5,4,8,6]=>1101010=>0010101
[4,3,2,1,8,7,5,6]=>[3,2,4,1,7,5,8,6]=>1100110=>0011001
[4,3,2,1,7,5,8,6]=>[3,2,4,1,8,7,5,6]=>1100101=>0011010
[4,3,2,1,7,5,6,8]=>[3,2,4,1,7,5,6,8]=>1100100=>0011011
[4,3,2,1,8,5,7,6]=>[3,2,4,1,7,8,5,6]=>1100100=>0011011
[5,3,2,8,1,4,7,6]=>[3,2,7,8,1,5,4,6]=>1101000=>0010111
[6,3,8,2,1,4,7,5]=>[7,8,3,2,6,1,4,5]=>1110000=>0001111
[7,8,3,2,1,4,6,5]=>[3,8,2,6,7,1,4,5]=>1100000=>0011111
[6,3,8,2,1,4,5,7]=>[8,3,2,6,1,4,5,7]=>1110000=>0001111
[4,3,2,1,8,5,6,7]=>[3,2,4,1,8,5,6,7]=>1100100=>0011011
[4,3,2,1,5,8,6,7]=>[3,2,4,1,5,8,6,7]=>1100010=>0011101
[7,8,5,6,1,2,4,3]=>[6,1,5,2,8,4,7,3]=>1111000=>0000111
[7,8,4,1,6,2,5,3]=>[4,1,6,2,8,5,7,3]=>1110100=>0001011
[7,8,1,4,6,2,5,3]=>[4,6,1,8,5,7,2,3]=>1100100=>0011011
[6,1,8,4,7,2,5,3]=>[4,7,1,2,8,5,6,3]=>1010100=>0101011
[1,6,8,4,7,2,5,3]=>[1,4,7,2,8,5,6,3]=>0110100=>1001011
[1,6,8,3,2,7,5,4]=>[1,7,3,5,8,6,2,4]=>0110010=>1001101
[6,1,8,3,2,7,5,4]=>[7,3,5,8,6,1,2,4]=>1010010=>0101101
[7,8,1,3,2,6,5,4]=>[6,8,1,3,5,7,2,4]=>1100000=>0011111
[7,8,3,1,2,6,5,4]=>[3,6,8,1,5,7,2,4]=>1100000=>0011111
[7,8,3,4,6,5,1,2]=>[3,4,6,5,8,1,7,2]=>1100100=>0011011
[7,8,2,4,6,1,5,3]=>[4,6,2,8,5,7,1,3]=>1100100=>0011011
[7,8,2,3,1,6,5,4]=>[6,8,2,3,5,7,1,4]=>1100000=>0011111
[7,8,2,1,3,6,5,4]=>[6,8,2,5,7,1,3,4]=>1100000=>0011111
[7,8,1,2,3,6,5,4]=>[6,8,1,5,7,2,3,4]=>1100000=>0011111
[6,1,8,2,3,7,5,4]=>[7,1,2,5,8,6,3,4]=>1010010=>0101101
[1,6,8,2,3,7,5,4]=>[1,7,2,5,8,6,3,4]=>0110010=>1001101
[1,5,2,8,3,7,6,4]=>[1,7,6,8,2,3,5,4]=>0101010=>1010101
[5,1,2,8,3,7,6,4]=>[7,6,8,1,2,3,5,4]=>1001010=>0110101
[5,2,1,8,3,7,6,4]=>[2,7,6,8,1,3,5,4]=>1001010=>0110101
[6,2,8,1,3,7,5,4]=>[2,7,1,5,8,6,3,4]=>1010010=>0101101
[6,2,8,3,1,7,5,4]=>[2,7,3,5,8,6,1,4]=>1010010=>0101101
[6,2,8,4,7,1,5,3]=>[2,4,7,1,8,5,6,3]=>1010100=>0101011
[6,3,8,4,7,5,1,2]=>[4,7,5,8,3,1,6,2]=>1110100=>0001011
[3,6,8,4,7,5,1,2]=>[4,7,5,8,1,6,3,2]=>1110100=>0001011
[2,6,8,4,7,1,5,3]=>[4,7,2,1,8,5,6,3]=>1110100=>0001011
[2,6,8,3,1,7,5,4]=>[7,3,5,8,6,2,1,4]=>1110010=>0001101
[2,6,8,1,3,7,5,4]=>[7,2,1,5,8,6,3,4]=>1110010=>0001101
[2,5,1,8,3,7,6,4]=>[7,6,8,2,1,3,5,4]=>1101010=>0010101
[1,2,5,8,3,7,6,4]=>[1,2,7,6,8,3,5,4]=>0011010=>1100101
[2,4,1,3,8,7,6,5]=>[4,2,1,3,7,6,8,5]=>1100110=>0011001
[2,5,3,8,1,7,6,4]=>[3,7,6,8,2,1,5,4]=>1101010=>0010101
[2,5,4,8,7,1,6,3]=>[7,4,2,1,6,8,5,3]=>1111100=>0000011
[3,5,4,8,7,6,1,2]=>[6,7,4,1,8,5,3,2]=>1111100=>0000011
[5,3,4,8,7,6,1,2]=>[6,7,4,3,1,8,5,2]=>1111100=>0000011
[5,2,4,8,7,1,6,3]=>[2,7,4,1,6,8,5,3]=>1011100=>0100011
[5,2,3,8,1,7,6,4]=>[2,3,7,6,8,1,5,4]=>1001010=>0110101
[4,2,1,3,8,7,6,5]=>[2,4,1,3,7,6,8,5]=>1000110=>0111001
[4,1,2,3,8,7,6,5]=>[4,1,2,3,7,6,8,5]=>1000110=>0111001
[1,4,2,3,8,7,6,5]=>[1,4,2,3,7,6,8,5]=>0100110=>1011001
[4,1,3,2,8,7,6,5]=>[3,4,1,2,7,6,8,5]=>1000110=>0111001
[4,3,1,2,8,7,6,5]=>[3,1,4,2,7,6,8,5]=>1100110=>0011001
[6,3,8,1,2,7,5,4]=>[7,3,1,5,8,6,2,4]=>1110010=>0001101
[5,3,1,8,2,7,6,4]=>[3,1,7,6,8,2,5,4]=>1101010=>0010101
[5,1,3,8,2,7,6,4]=>[3,7,6,8,1,2,5,4]=>1001010=>0110101
[1,5,3,8,2,7,6,4]=>[1,3,7,6,8,2,5,4]=>0101010=>1010101
[1,5,4,8,7,2,6,3]=>[1,7,4,2,6,8,5,3]=>0111100=>1000011
[5,1,4,8,7,2,6,3]=>[7,4,1,2,6,8,5,3]=>1011100=>0100011
[5,4,1,8,7,2,6,3]=>[7,4,1,6,8,5,2,3]=>1101100=>0010011
[6,4,8,1,7,2,5,3]=>[7,1,4,2,8,5,6,3]=>1110100=>0001011
[6,5,8,7,1,2,4,3]=>[7,1,8,2,5,4,6,3]=>1111000=>0000111
[5,6,8,7,3,4,1,2]=>[7,3,8,4,6,1,5,2]=>1111000=>0000111
[5,6,8,7,2,1,4,3]=>[7,2,8,1,6,4,5,3]=>1111000=>0000111
[4,5,1,8,7,2,6,3]=>[7,1,6,8,5,4,2,3]=>1101100=>0010011
[4,1,5,8,7,2,6,3]=>[7,1,2,6,8,5,4,3]=>1011100=>0100011
[1,4,5,8,7,2,6,3]=>[1,7,2,6,8,5,4,3]=>0111100=>1000011
[1,3,5,8,2,7,6,4]=>[1,7,6,8,3,2,5,4]=>0111010=>1000101
[3,1,5,8,2,7,6,4]=>[7,6,8,3,1,2,5,4]=>1011010=>0100101
[3,6,8,1,2,7,5,4]=>[7,1,5,8,6,3,2,4]=>1110010=>0001101
[3,6,8,2,1,7,5,4]=>[7,2,5,8,6,3,1,4]=>1110010=>0001101
[4,6,8,2,7,1,5,3]=>[7,2,8,5,6,1,4,3]=>1110100=>0001011
[4,6,8,3,7,5,1,2]=>[7,5,8,3,6,1,4,2]=>1110100=>0001011
[4,5,3,8,7,6,1,2]=>[3,6,7,1,8,5,4,2]=>1101100=>0010011
[4,5,2,8,7,1,6,3]=>[7,2,6,8,5,4,1,3]=>1101100=>0010011
[3,5,2,8,1,7,6,4]=>[7,6,8,2,3,1,5,4]=>1101010=>0010101
[3,1,4,2,8,7,6,5]=>[4,3,1,2,7,6,8,5]=>1010110=>0101001
[3,1,2,4,8,7,6,5]=>[3,1,2,4,7,6,8,5]=>1000110=>0111001
[3,2,5,8,1,7,6,4]=>[2,7,6,8,3,1,5,4]=>1011010=>0100101
[4,2,5,8,7,1,6,3]=>[2,7,1,6,8,5,4,3]=>1011100=>0100011
[4,3,5,8,7,6,1,2]=>[6,7,3,1,8,5,4,2]=>1111100=>0000011
[3,4,5,8,7,6,1,2]=>[6,7,1,8,5,4,3,2]=>1111100=>0000011
[2,4,5,8,7,1,6,3]=>[7,2,1,6,8,5,4,3]=>1111100=>0000011
[2,3,5,8,1,7,6,4]=>[7,6,8,3,2,1,5,4]=>1111010=>0000101
[4,1,3,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>1000101=>0111010
[5,1,3,2,6,4,8,7]=>[3,6,5,1,2,4,8,7]=>1000101=>0111010
[6,1,3,2,5,4,8,7]=>[3,5,6,1,2,4,8,7]=>1000001=>0111110
[7,1,3,2,5,4,8,6]=>[3,5,8,7,1,2,4,6]=>1000001=>0111110
[8,1,3,2,5,4,7,6]=>[3,5,7,8,1,2,4,6]=>1000000=>0111111
[8,1,4,2,5,3,7,6]=>[4,1,2,5,7,8,3,6]=>1010000=>0101111
[7,1,4,2,5,3,8,6]=>[4,1,2,5,8,7,3,6]=>1010001=>0101110
[6,1,4,2,5,3,8,7]=>[4,1,2,5,6,3,8,7]=>1010001=>0101110
[5,1,4,2,6,3,8,7]=>[4,1,2,6,5,3,8,7]=>1010101=>0101010
[2,1,6,3,5,4,8,7]=>[2,1,5,6,3,4,8,7]=>1010001=>0101110
[3,1,6,2,5,4,8,7]=>[5,6,3,1,2,4,8,7]=>1010001=>0101110
[4,1,6,2,5,3,8,7]=>[5,6,1,2,4,3,8,7]=>1010001=>0101110
[6,2,5,1,4,3,8,7]=>[2,5,1,4,6,3,8,7]=>1010001=>0101110
[5,2,6,1,4,3,8,7]=>[2,6,1,4,5,3,8,7]=>1010001=>0101110
[5,2,7,1,4,3,8,6]=>[2,8,7,1,4,5,3,6]=>1010001=>0101110
[5,2,8,1,4,3,7,6]=>[2,7,8,1,4,5,3,6]=>1010000=>0101111
[6,2,8,1,4,3,7,5]=>[2,7,8,1,4,6,3,5]=>1010000=>0101111
[6,2,7,1,4,3,8,5]=>[2,8,7,1,4,6,3,5]=>1010001=>0101110
[7,2,6,1,4,3,8,5]=>[2,6,1,4,8,7,3,5]=>1010001=>0101110
[7,2,5,1,4,3,8,6]=>[2,5,1,4,8,7,3,6]=>1010001=>0101110
[4,1,7,2,5,3,8,6]=>[5,8,7,1,2,4,3,6]=>1010001=>0101110
[3,1,7,2,5,4,8,6]=>[5,8,7,3,1,2,4,6]=>1010001=>0101110
[2,1,7,3,5,4,8,6]=>[2,1,5,8,7,3,4,6]=>1010001=>0101110
[2,1,8,3,5,4,7,6]=>[2,1,5,7,8,3,4,6]=>1010000=>0101111
[3,1,8,2,5,4,7,6]=>[5,7,8,3,1,2,4,6]=>1010000=>0101111
[4,1,8,2,5,3,7,6]=>[5,7,8,1,2,4,3,6]=>1010000=>0101111
[8,2,5,1,4,3,7,6]=>[2,5,1,4,7,8,3,6]=>1010000=>0101111
[8,2,6,1,4,3,7,5]=>[2,6,1,4,7,8,3,5]=>1010000=>0101111
[7,1,4,3,8,2,6,5]=>[4,3,8,1,2,6,7,5]=>1010100=>0101011
[8,1,4,3,7,2,6,5]=>[4,3,7,1,2,6,8,5]=>1010100=>0101011
[8,1,5,3,7,2,6,4]=>[7,5,3,6,8,1,2,4]=>1010100=>0101011
[7,1,5,3,8,2,6,4]=>[8,5,3,6,7,1,2,4]=>1010100=>0101011
[8,2,6,1,5,3,7,4]=>[2,5,6,1,7,8,3,4]=>1010000=>0101111
[5,1,8,2,6,3,7,4]=>[6,1,2,7,8,5,3,4]=>1010100=>0101011
[4,1,8,2,6,3,7,5]=>[6,1,2,4,3,7,8,5]=>1010100=>0101011
[3,1,8,2,6,4,7,5]=>[6,3,1,2,4,7,8,5]=>1010100=>0101011
[2,1,8,3,6,4,7,5]=>[2,1,6,3,4,7,8,5]=>1010100=>0101011
[2,1,7,3,6,4,8,5]=>[2,1,6,3,4,8,7,5]=>1010101=>0101010
[4,1,7,2,6,3,8,5]=>[6,1,2,4,3,8,7,5]=>1010101=>0101010
[5,1,7,2,6,3,8,4]=>[6,1,2,8,7,5,3,4]=>1010101=>0101010
[7,2,6,1,5,3,8,4]=>[2,5,6,1,8,7,3,4]=>1010001=>0101110
[6,2,7,1,5,3,8,4]=>[2,5,8,7,1,6,3,4]=>1010001=>0101110
[6,2,8,1,5,3,7,4]=>[2,5,7,8,1,6,3,4]=>1010000=>0101111
[8,1,5,2,6,3,7,4]=>[6,5,1,2,7,8,3,4]=>1010100=>0101011
[6,1,5,2,7,3,8,4]=>[8,7,5,1,2,6,3,4]=>1010101=>0101010
[6,1,4,2,7,3,8,5]=>[4,1,2,8,7,3,6,5]=>1010101=>0101010
[8,1,4,2,6,3,7,5]=>[4,1,2,6,3,7,8,5]=>1010100=>0101011
[8,1,3,2,6,4,7,5]=>[3,6,1,2,4,7,8,5]=>1000100=>0111011
[7,1,3,2,6,4,8,5]=>[3,6,1,2,4,8,7,5]=>1000101=>0111010
[6,1,3,2,7,4,8,5]=>[3,8,7,1,2,4,6,5]=>1000101=>0111010
[5,1,3,2,7,4,8,6]=>[3,8,7,5,1,2,4,6]=>1000101=>0111010
[4,1,3,2,7,5,8,6]=>[3,4,1,2,8,7,5,6]=>1000101=>0111010
[2,1,4,3,8,5,7,6]=>[2,1,4,3,7,8,5,6]=>1010100=>0101011
[3,1,4,2,8,5,7,6]=>[4,3,1,2,7,8,5,6]=>1010100=>0101011
[4,1,3,2,8,5,7,6]=>[3,4,1,2,7,8,5,6]=>1000100=>0111011
[5,1,3,2,8,4,7,6]=>[3,7,8,5,1,2,4,6]=>1000100=>0111011
[6,1,3,2,8,4,7,5]=>[3,7,8,1,2,4,6,5]=>1000100=>0111011
[8,4,7,1,3,2,6,5]=>[7,1,4,3,6,8,2,5]=>1110000=>0001111
[7,4,8,1,3,2,6,5]=>[8,1,4,3,6,7,2,5]=>1110000=>0001111
[7,3,8,1,4,2,6,5]=>[8,3,1,4,6,7,2,5]=>1110000=>0001111
[8,3,7,1,4,2,6,5]=>[7,3,1,4,6,8,2,5]=>1110000=>0001111
[6,1,4,2,8,3,7,5]=>[4,1,2,7,8,3,6,5]=>1010100=>0101011
[5,1,4,2,8,3,7,6]=>[4,1,2,7,8,5,3,6]=>1010100=>0101011
[4,1,5,2,8,3,7,6]=>[7,8,5,1,2,4,3,6]=>1010100=>0101011
[3,1,5,2,8,4,7,6]=>[7,8,5,3,1,2,4,6]=>1010100=>0101011
[2,1,5,3,8,4,7,6]=>[2,1,7,8,5,3,4,6]=>1010100=>0101011
[2,1,6,3,8,4,7,5]=>[2,1,7,8,3,4,6,5]=>1010100=>0101011
[3,1,6,2,8,4,7,5]=>[7,8,3,1,2,4,6,5]=>1010100=>0101011
[4,1,6,2,8,3,7,5]=>[7,8,1,2,4,3,6,5]=>1010100=>0101011
[5,1,6,2,8,3,7,4]=>[7,8,1,2,6,5,3,4]=>1010100=>0101011
[6,1,5,2,8,3,7,4]=>[7,8,5,1,2,6,3,4]=>1010100=>0101011
[8,3,7,1,5,2,6,4]=>[5,7,3,1,6,8,2,4]=>1110000=>0001111
[7,3,8,1,5,2,6,4]=>[5,8,3,1,6,7,2,4]=>1110000=>0001111
[6,2,7,3,8,1,5,4]=>[2,8,3,7,5,6,1,4]=>1010100=>0101011
[6,2,8,3,7,1,5,4]=>[2,7,3,8,5,6,1,4]=>1010100=>0101011
[8,3,7,2,6,1,5,4]=>[6,3,2,7,5,8,1,4]=>1110100=>0001011
[5,1,8,3,7,2,6,4]=>[7,3,6,8,5,1,2,4]=>1010100=>0101011
[4,1,8,3,7,2,6,5]=>[7,3,4,1,2,6,8,5]=>1010100=>0101011
[3,1,8,4,7,2,6,5]=>[4,7,3,1,2,6,8,5]=>1010100=>0101011
[2,1,8,4,7,3,6,5]=>[2,1,4,7,3,6,8,5]=>1010100=>0101011
[2,1,7,4,8,3,6,5]=>[2,1,4,8,3,6,7,5]=>1010100=>0101011
[3,1,7,4,8,2,6,5]=>[4,8,3,1,2,6,7,5]=>1010100=>0101011
[4,1,7,3,8,2,6,5]=>[8,3,4,1,2,6,7,5]=>1010100=>0101011
[5,1,7,3,8,2,6,4]=>[8,3,6,7,5,1,2,4]=>1010100=>0101011
[7,3,8,2,6,1,5,4]=>[6,3,2,8,5,7,1,4]=>1110100=>0001011
[8,2,6,3,7,1,5,4]=>[2,7,3,6,5,8,1,4]=>1010100=>0101011
[7,2,6,3,8,1,5,4]=>[2,8,3,6,5,7,1,4]=>1010100=>0101011
[3,4,2,6,8,1,5,7]=>[8,4,2,3,1,6,5,7]=>1101100=>0010011
[5,3,6,2,8,1,4,7]=>[8,3,2,6,5,1,4,7]=>1110100=>0001011
[5,3,6,2,4,8,1,7]=>[8,6,3,2,4,5,1,7]=>1110010=>0001101
[5,7,3,8,2,4,1,6]=>[3,8,2,7,4,5,1,6]=>1101000=>0010111
[5,7,3,8,2,4,6,1]=>[3,8,2,6,7,4,5,1]=>1101000=>0010111
[7,4,2,5,8,3,6,1]=>[8,5,4,2,3,6,7,1]=>1101100=>0010011
[7,4,2,5,8,3,1,6]=>[8,5,4,2,3,7,1,6]=>1101100=>0010011
[4,5,2,6,3,8,1,7]=>[8,6,2,3,5,4,1,7]=>1101010=>0010101
[4,5,2,1,6,8,3,7]=>[8,6,5,2,4,1,3,7]=>1100110=>0011001
[5,3,1,6,8,2,4,7]=>[3,1,8,2,6,5,4,7]=>1101100=>0010011
[5,6,2,8,1,3,4,7]=>[8,2,6,1,3,5,4,7]=>1101000=>0010111
[3,5,6,1,4,8,2,7]=>[8,6,1,4,5,3,2,7]=>1110010=>0001101
[4,1,5,6,3,8,2,7]=>[8,6,3,5,4,1,2,7]=>1011010=>0100101
[4,5,1,6,3,8,2,7]=>[8,6,1,3,5,4,2,7]=>1101010=>0010101
[4,5,6,3,2,8,1,7]=>[8,6,3,5,2,4,1,7]=>1110010=>0001101
[7,4,5,3,8,2,1,6]=>[8,5,3,4,2,7,1,6]=>1110100=>0001011
[7,4,5,3,8,2,6,1]=>[8,5,3,4,2,6,7,1]=>1110100=>0001011
[6,7,4,8,3,2,5,1]=>[8,4,3,7,2,5,6,1]=>1111000=>0000111
[6,7,4,8,3,2,1,5]=>[8,4,3,7,2,6,1,5]=>1111000=>0000111
[6,7,4,1,8,3,2,5]=>[4,1,8,3,7,2,6,5]=>1110100=>0001011
[7,4,5,3,1,8,2,6]=>[5,3,4,1,8,2,7,6]=>1110010=>0001101
[4,7,1,5,8,3,2,6]=>[8,5,1,3,7,4,2,6]=>1101100=>0010011
[5,3,7,8,1,4,2,6]=>[8,3,1,7,4,5,2,6]=>1111000=>0000111
[7,5,8,2,4,6,1,3]=>[6,8,2,4,5,1,7,3]=>1110000=>0001111
[7,3,5,8,1,4,6,2]=>[8,3,1,5,4,6,7,2]=>1111000=>0000111
[4,5,1,7,8,3,6,2]=>[8,1,3,6,7,5,4,2]=>1101100=>0010011
[7,4,1,5,8,3,6,2]=>[8,5,4,1,3,6,7,2]=>1101100=>0010011
[6,7,4,3,8,1,5,2]=>[4,3,8,1,7,5,6,2]=>1110100=>0001011
[6,7,4,8,3,1,5,2]=>[8,4,3,7,1,5,6,2]=>1111000=>0000111
[6,7,4,8,3,5,2,1]=>[8,4,3,5,7,2,6,1]=>1111000=>0000111
[5,6,7,3,8,4,2,1]=>[8,3,4,7,2,6,5,1]=>1110100=>0001011
[5,6,7,3,1,8,4,2]=>[8,3,7,6,1,4,5,2]=>1110010=>0001101
[5,6,1,7,3,8,4,2]=>[8,1,3,7,6,4,5,2]=>1101010=>0010101
[5,1,6,7,3,8,4,2]=>[8,3,7,6,4,5,1,2]=>1011010=>0100101
[6,4,7,1,8,3,5,2]=>[8,1,4,3,7,5,6,2]=>1110100=>0001011
[6,7,8,3,1,4,5,2]=>[8,3,7,1,4,5,6,2]=>1110000=>0001111
[6,7,2,8,4,5,1,3]=>[8,4,5,7,2,6,1,3]=>1101000=>0010111
[6,7,2,8,4,1,3,5]=>[8,4,7,2,6,1,3,5]=>1101000=>0010111
[6,1,7,4,8,3,2,5]=>[4,8,3,7,1,2,6,5]=>1010100=>0101011
[5,1,6,7,3,2,8,4]=>[8,7,3,6,1,2,5,4]=>1011001=>0100110
[5,6,1,7,3,2,8,4]=>[8,7,1,3,6,2,5,4]=>1101001=>0010110
[5,6,7,3,2,1,8,4]=>[8,7,3,6,2,5,1,4]=>1110001=>0001110
[5,6,7,3,2,8,4,1]=>[8,3,7,6,2,4,5,1]=>1110010=>0001101
[5,6,2,7,3,8,4,1]=>[8,2,3,7,6,4,5,1]=>1101010=>0010101
[5,6,2,7,3,1,8,4]=>[8,7,2,3,6,1,5,4]=>1101001=>0010110
[5,6,2,1,7,3,8,4]=>[8,7,2,6,5,1,3,4]=>1100101=>0011010
[6,1,7,4,2,8,3,5]=>[4,8,1,2,7,6,3,5]=>1010010=>0101101
[6,7,2,1,8,3,4,5]=>[8,2,7,1,3,4,6,5]=>1100100=>0011011
[7,5,8,2,1,3,4,6]=>[8,2,5,1,7,3,4,6]=>1110000=>0001111
[5,7,3,1,8,2,4,6]=>[3,8,1,7,5,2,4,6]=>1100100=>0011011
[4,7,1,5,2,8,3,6]=>[5,1,8,4,2,3,7,6]=>1101010=>0010101
[7,4,2,5,1,8,3,6]=>[5,4,2,8,1,3,7,6]=>1101010=>0010101
[6,7,4,2,1,8,3,5]=>[4,2,8,1,7,6,3,5]=>1110010=>0001101
[6,7,4,2,8,3,1,5]=>[4,2,8,3,7,1,6,5]=>1110100=>0001011
[6,7,4,2,8,3,5,1]=>[4,2,8,3,7,5,6,1]=>1110100=>0001011
[3,6,7,2,8,4,5,1]=>[8,2,4,7,5,6,3,1]=>1110100=>0001011
[3,6,7,2,8,4,1,5]=>[8,2,4,7,3,1,6,5]=>1110100=>0001011
[3,6,7,2,1,8,4,5]=>[8,2,7,6,3,1,4,5]=>1110010=>0001101
[5,7,3,8,2,1,4,6]=>[3,8,2,7,1,5,4,6]=>1101000=>0010111
[3,4,7,8,2,1,5,6]=>[8,2,7,4,3,1,5,6]=>1111000=>0000111
[3,7,8,1,4,6,2,5]=>[6,8,1,4,7,3,2,5]=>1110000=>0001111
[3,4,7,8,2,6,1,5]=>[6,8,2,7,4,3,1,5]=>1111000=>0000111
[5,7,3,8,2,6,1,4]=>[3,6,8,2,7,1,5,4]=>1101000=>0010111
[3,6,7,2,8,5,1,4]=>[8,5,7,2,6,3,1,4]=>1110100=>0001011
[3,6,7,8,5,2,1,4]=>[5,8,2,7,3,1,6,4]=>1111000=>0000111
[3,6,7,8,5,2,4,1]=>[5,8,2,7,4,6,3,1]=>1111000=>0000111
[6,4,7,8,2,5,3,1]=>[8,2,5,7,4,3,6,1]=>1111000=>0000111
[6,4,7,8,2,1,5,3]=>[8,2,7,4,1,5,6,3]=>1111000=>0000111
[4,1,5,7,8,2,6,3]=>[8,1,2,6,7,5,4,3]=>1011100=>0100011
[5,3,7,8,1,6,2,4]=>[6,8,3,1,7,2,5,4]=>1111000=>0000111
[6,7,2,8,5,1,3,4]=>[5,8,2,7,1,3,6,4]=>1101000=>0010111
[6,4,1,7,8,2,5,3]=>[8,4,1,7,5,6,2,3]=>1101100=>0010011
[5,1,6,2,7,8,4,3]=>[8,1,2,4,7,6,5,3]=>1010110=>0101001
[5,6,2,1,7,8,4,3]=>[8,2,4,7,6,5,1,3]=>1100110=>0011001
[5,6,2,7,1,8,4,3]=>[8,2,7,6,4,5,1,3]=>1101010=>0010101
[5,6,2,7,8,4,3,1]=>[8,4,7,2,3,6,5,1]=>1101100=>0010011
[5,6,7,2,8,4,3,1]=>[8,2,4,7,3,6,5,1]=>1110100=>0001011
[5,6,7,2,1,8,4,3]=>[8,2,7,6,1,4,5,3]=>1110010=>0001101
[5,6,1,7,2,8,4,3]=>[8,1,7,6,4,5,2,3]=>1101010=>0010101
[5,1,6,7,2,8,4,3]=>[8,1,2,7,6,4,5,3]=>1011010=>0100101
[6,4,7,1,8,2,5,3]=>[8,1,4,2,7,5,6,3]=>1110100=>0001011
[3,6,7,1,8,5,2,4]=>[8,5,7,1,6,3,2,4]=>1110100=>0001011
[6,7,8,5,2,4,1,3]=>[5,2,8,4,7,1,6,3]=>1111000=>0000111
[6,7,8,3,5,1,4,2]=>[5,8,3,7,1,4,6,2]=>1110000=>0001111
[4,6,7,8,1,5,3,2]=>[8,1,5,7,3,6,4,2]=>1111000=>0000111
[5,1,6,7,8,4,3,2]=>[8,4,7,3,6,5,1,2]=>1011100=>0100011
[5,6,1,7,8,4,3,2]=>[8,4,7,1,3,6,5,2]=>1101100=>0010011
[5,6,7,1,8,4,3,2]=>[8,1,4,7,3,6,5,2]=>1110100=>0001011
[8,6,1,3,4,2,5,7]=>[6,1,3,4,8,2,5,7]=>1100000=>0011111
[8,3,2,5,1,6,4,7]=>[3,2,5,1,6,8,4,7]=>1101000=>0010111
[8,5,3,6,2,4,1,7]=>[3,6,2,5,4,8,1,7]=>1101000=>0010111
[5,3,2,7,4,1,8,6]=>[3,2,8,7,4,5,1,6]=>1101001=>0010110
[7,5,3,8,2,4,6,1]=>[3,8,2,5,4,6,7,1]=>1101000=>0010111
[7,2,4,5,8,3,6,1]=>[2,8,5,4,3,6,7,1]=>1011100=>0100011
[2,4,5,3,7,1,8,6]=>[8,7,5,3,4,2,1,6]=>1110101=>0001010
[8,2,4,5,6,3,1,7]=>[2,6,5,4,3,8,1,7]=>1011100=>0100011
[8,2,4,5,6,1,3,7]=>[2,6,5,4,1,8,3,7]=>1011100=>0100011
[8,1,2,4,5,6,3,7]=>[4,5,6,8,1,2,3,7]=>1000000=>0111111
[8,2,5,1,3,6,4,7]=>[2,5,1,6,8,3,4,7]=>1010000=>0101111
[8,5,6,2,1,4,3,7]=>[6,2,5,1,4,8,3,7]=>1110000=>0001111
[8,5,3,6,4,1,2,7]=>[3,6,4,5,1,8,2,7]=>1101000=>0010111
[8,4,1,5,6,3,2,7]=>[6,5,4,1,3,8,2,7]=>1101100=>0010011
[8,1,4,5,6,3,2,7]=>[6,5,4,3,8,1,2,7]=>1011100=>0100011
[4,5,3,7,2,1,8,6]=>[3,8,7,2,5,4,1,6]=>1101001=>0010110
[7,4,5,8,3,2,6,1]=>[8,3,5,4,2,6,7,1]=>1111000=>0000111
[4,3,6,7,2,8,5,1]=>[8,3,2,5,7,6,4,1]=>1111010=>0000101
[4,3,6,7,2,8,1,5]=>[8,3,2,7,6,4,1,5]=>1111010=>0000101
[1,4,3,6,7,2,8,5]=>[1,3,8,7,4,2,6,5]=>0101101=>1010010
[4,5,3,7,1,8,2,6]=>[3,8,1,5,4,2,7,6]=>1101010=>0010101
[4,1,5,3,7,2,8,6]=>[8,7,5,3,4,1,2,6]=>1010101=>0101010
[5,3,4,7,1,2,8,6]=>[8,7,4,3,1,5,2,6]=>1111001=>0000110
[7,5,8,2,1,4,6,3]=>[8,2,5,1,4,6,7,3]=>1110000=>0001111
[7,5,3,8,4,1,6,2]=>[3,8,4,5,1,6,7,2]=>1101000=>0010111
[7,4,5,8,3,6,1,2]=>[6,8,3,5,4,1,7,2]=>1111000=>0000111
[4,3,6,7,8,1,5,2]=>[8,3,1,7,5,6,4,2]=>1111100=>0000011
[1,6,4,7,8,3,5,2]=>[1,8,4,3,7,5,6,2]=>0111100=>1000011
[6,4,7,8,3,5,2,1]=>[8,3,5,7,4,2,6,1]=>1111000=>0000111
[3,5,6,7,8,4,1,2]=>[8,4,7,1,6,5,3,2]=>1111100=>0000011
[3,1,5,6,7,8,4,2]=>[8,4,7,6,5,3,1,2]=>1011110=>0100001
[4,6,1,7,8,3,5,2]=>[8,1,3,7,5,6,4,2]=>1101100=>0010011
[3,6,7,1,4,8,5,2]=>[8,1,4,5,7,6,3,2]=>1110010=>0001101
[6,2,4,1,7,8,5,3]=>[2,4,1,8,5,7,6,3]=>1010110=>0101001
[2,6,7,1,4,8,3,5]=>[8,2,1,4,7,6,3,5]=>1110010=>0001101
[4,3,6,7,8,1,2,5]=>[8,3,1,7,4,2,6,5]=>1111100=>0000011
[1,5,3,6,7,8,2,4]=>[1,3,8,2,7,6,5,4]=>0101110=>1010001
[3,5,6,7,8,2,1,4]=>[8,2,7,3,1,6,5,4]=>1111100=>0000011
[3,5,6,7,8,2,4,1]=>[8,2,7,4,6,5,3,1]=>1111100=>0000011
[5,2,7,1,3,8,4,6]=>[2,8,1,5,3,4,7,6]=>1010010=>0101101
[5,3,1,7,8,2,4,6]=>[3,1,8,2,7,5,4,6]=>1101100=>0010011
[4,5,2,7,8,1,3,6]=>[8,2,7,5,4,1,3,6]=>1101100=>0010011
[4,2,6,7,8,3,1,5]=>[2,8,3,7,4,1,6,5]=>1011100=>0100011
[4,2,6,7,8,3,5,1]=>[2,8,3,7,5,6,4,1]=>1011100=>0100011
[3,6,2,7,4,8,5,1]=>[8,4,5,7,6,2,3,1]=>1101010=>0010101
[3,6,2,7,4,8,1,5]=>[8,4,7,6,2,3,1,5]=>1101010=>0010101
[3,2,1,6,4,7,8,5]=>[2,3,1,8,7,6,4,5]=>1001011=>0110100
[3,7,4,2,1,5,8,6]=>[4,2,8,7,3,1,5,6]=>1110001=>0001110
[1,7,3,4,2,5,8,6]=>[1,3,4,8,7,2,5,6]=>0100001=>1011110
[4,7,2,1,3,5,8,6]=>[8,7,2,4,1,3,5,6]=>1100001=>0011110
[7,8,4,2,1,3,6,5]=>[4,2,8,1,6,7,3,5]=>1110000=>0001111
[7,8,1,3,4,2,6,5]=>[8,1,3,4,6,7,2,5]=>1100000=>0011111
[7,8,3,4,2,1,6,5]=>[3,4,8,2,6,7,1,5]=>1100000=>0011111
[6,3,2,7,1,8,5,4]=>[3,2,8,1,5,7,6,4]=>1101010=>0010101
[3,6,2,7,1,8,5,4]=>[8,2,3,1,5,7,6,4]=>1101010=>0010101
[6,7,3,8,2,5,4,1]=>[3,8,2,5,7,4,6,1]=>1101000=>0010111
[6,4,7,8,5,2,3,1]=>[5,8,2,7,4,3,6,1]=>1111000=>0000111
[2,6,4,7,8,1,5,3]=>[8,4,2,1,7,5,6,3]=>1111100=>0000011
[4,6,2,7,8,1,5,3]=>[8,2,7,5,6,4,1,3]=>1101100=>0010011
[7,4,5,8,6,2,1,3]=>[6,2,8,5,4,1,7,3]=>1111100=>0000011
[7,4,1,5,8,6,2,3]=>[6,8,5,4,1,7,2,3]=>1101100=>0010011
[7,5,3,8,6,1,2,4]=>[3,6,1,8,5,2,7,4]=>1101100=>0010011
[7,5,8,2,1,6,3,4]=>[6,8,2,5,1,7,3,4]=>1110000=>0001111
[6,2,7,1,3,8,5,4]=>[2,8,1,5,7,6,3,4]=>1010010=>0101101
[6,3,1,7,8,2,5,4]=>[3,1,8,2,7,5,6,4]=>1101100=>0010011
[4,6,1,7,8,5,2,3]=>[8,5,7,1,6,4,2,3]=>1101100=>0010011
[5,1,2,6,7,8,4,3]=>[8,4,7,6,5,1,2,3]=>1001110=>0110001
[5,2,6,7,8,4,1,3]=>[2,8,4,7,1,6,5,3]=>1011100=>0100011
[5,2,6,7,8,4,3,1]=>[2,8,4,7,3,6,5,1]=>1011100=>0100011
[2,5,6,7,8,4,1,3]=>[8,4,7,2,1,6,5,3]=>1111100=>0000011
[1,5,2,6,7,8,4,3]=>[1,8,4,7,6,5,2,3]=>0101110=>1010001
[1,6,4,7,8,5,2,3]=>[1,8,5,7,4,2,6,3]=>0111100=>1000011
[2,6,7,1,3,8,5,4]=>[8,2,1,5,7,6,3,4]=>1110010=>0001101
[6,7,8,2,1,5,4,3]=>[8,2,5,7,1,4,6,3]=>1110000=>0001111
[6,7,3,8,5,1,4,2]=>[3,5,8,1,7,4,6,2]=>1101000=>0010111
[6,4,7,8,5,3,1,2]=>[5,8,3,7,4,1,6,2]=>1111000=>0000111
[4,5,2,3,7,6,1,8]=>[6,7,5,2,3,4,1,8]=>1100100=>0011011
[8,4,3,6,5,1,2,7]=>[3,5,6,4,1,8,2,7]=>1101000=>0010111
[1,5,6,3,4,8,7,2]=>[1,7,8,6,3,4,5,2]=>0110010=>1001101
[4,6,2,7,3,5,1,8]=>[7,2,3,5,6,4,1,8]=>1101000=>0010111
[4,7,2,6,5,3,1,8]=>[5,6,2,3,7,4,1,8]=>1101000=>0010111
[8,7,5,4,1,3,2,6]=>[4,5,1,7,3,8,2,6]=>1110000=>0001111
[6,8,5,4,2,1,3,7]=>[4,5,2,8,1,6,3,7]=>1110000=>0001111
[5,8,6,2,4,1,3,7]=>[6,2,4,8,1,5,3,7]=>1110000=>0001111
[4,1,2,6,5,8,7,3]=>[5,7,8,6,4,1,2,3]=>1001010=>0110101
[5,1,6,2,4,8,7,3]=>[7,8,6,1,2,4,5,3]=>1010010=>0101101
[6,1,5,4,2,8,7,3]=>[4,5,1,2,7,8,6,3]=>1010010=>0101101
[8,1,5,4,7,6,2,3]=>[4,6,7,5,1,2,8,3]=>1010100=>0101011
[1,8,6,7,4,5,3,2]=>[1,7,4,5,6,3,8,2]=>0111000=>1000111
[8,1,6,7,4,5,2,3]=>[7,4,5,6,1,2,8,3]=>1011000=>0100111
[6,1,7,8,2,4,5,3]=>[8,1,2,7,4,5,6,3]=>1011000=>0100111
[5,1,7,2,8,4,6,3]=>[8,1,2,4,6,7,5,3]=>1010100=>0101011
[4,1,2,7,8,5,6,3]=>[8,5,6,7,4,1,2,3]=>1001100=>0110011
[3,2,1,7,8,5,6,4]=>[2,3,1,8,5,6,7,4]=>1001100=>0110011
[3,2,8,7,1,5,4,6]=>[2,7,3,1,5,8,4,6]=>1011000=>0100111
[4,8,2,7,1,5,3,6]=>[7,2,5,8,4,1,3,6]=>1101000=>0010111
[6,8,7,1,2,4,3,5]=>[7,1,8,2,4,6,3,5]=>1110000=>0001111
[7,8,6,1,4,2,3,5]=>[6,1,4,8,2,7,3,5]=>1110000=>0001111
[1,7,6,8,4,3,5,2]=>[1,8,4,6,3,5,7,2]=>0111000=>1000111
[7,6,8,1,3,2,4,5]=>[8,1,6,3,7,2,4,5]=>1110000=>0001111
[5,7,8,2,1,3,4,6]=>[8,2,7,1,5,3,4,6]=>1110000=>0001111
[4,7,2,8,1,3,5,6]=>[8,2,7,4,1,3,5,6]=>1101000=>0010111
[3,2,6,8,4,1,5,7]=>[2,8,4,6,3,1,5,7]=>1011000=>0100111
[4,6,2,8,3,1,5,7]=>[8,2,3,6,4,1,5,7]=>1101000=>0010111
[5,6,8,2,3,1,4,7]=>[8,2,6,3,5,1,4,7]=>1110000=>0001111
[6,5,8,3,2,1,4,7]=>[8,3,5,2,6,1,4,7]=>1110000=>0001111
[7,5,8,3,1,2,4,6]=>[8,3,5,1,7,2,4,6]=>1110000=>0001111
[1,5,7,3,8,4,6,2]=>[1,8,3,4,6,7,5,2]=>0110100=>1001011
[1,4,3,7,8,5,6,2]=>[1,3,8,5,6,7,4,2]=>0101100=>1010011
[6,4,3,8,2,1,5,7]=>[3,8,4,2,6,1,5,7]=>1101000=>0010111
[3,2,5,4,8,1,6,7]=>[2,4,8,5,3,1,6,7]=>1010100=>0101011
[4,5,2,3,1,8,7,6]=>[5,2,3,4,1,7,8,6]=>1100010=>0011101
[6,4,3,1,2,8,7,5]=>[3,4,1,7,8,6,2,5]=>1100010=>0011101
[7,4,3,1,8,2,6,5]=>[3,4,1,8,2,6,7,5]=>1100100=>0011011
[8,4,3,1,7,6,2,5]=>[3,4,1,6,7,2,8,5]=>1100100=>0011011
[1,5,8,3,7,6,4,2]=>[1,6,7,3,4,8,5,2]=>0110100=>1001011
[6,5,1,3,2,8,7,4]=>[5,1,3,7,8,6,2,4]=>1100010=>0011101
[5,6,1,2,3,8,7,4]=>[7,8,6,1,5,2,3,4]=>1100010=>0011101
[4,6,2,1,3,8,7,5]=>[7,8,6,2,4,1,3,5]=>1100010=>0011101
[3,2,6,1,4,8,7,5]=>[2,7,8,6,3,1,4,5]=>1010010=>0101101
[3,2,7,1,8,4,6,5]=>[2,8,3,1,4,6,7,5]=>1010100=>0101011
[5,7,1,2,8,3,6,4]=>[8,1,6,7,5,2,3,4]=>1100100=>0011011
[7,8,1,6,5,2,3,4]=>[5,6,1,8,2,3,7,4]=>1101000=>0010111
[5,8,1,2,7,6,3,4]=>[6,7,1,8,5,2,3,4]=>1100100=>0011011
[3,2,8,1,7,6,4,5]=>[2,6,7,3,1,4,8,5]=>1010100=>0101011
[4,1,2,8,7,6,5,3]=>[6,7,5,8,4,1,2,3]=>1001100=>0110011
[5,1,8,2,7,6,4,3]=>[6,7,1,2,4,8,5,3]=>1010100=>0101011
[3,1,2,6,5,8,7,4]=>[3,1,2,5,7,8,6,4]=>1001010=>0110101
[3,1,6,2,4,8,7,5]=>[7,8,6,3,1,2,4,5]=>1010010=>0101101
[3,1,5,2,4,8,7,6]=>[5,3,1,2,4,7,8,6]=>1010010=>0101101
[4,5,1,2,3,8,7,6]=>[5,1,4,2,3,7,8,6]=>1100010=>0011101
[4,6,1,2,3,8,7,5]=>[7,8,6,1,4,2,3,5]=>1100010=>0011101
[1,6,5,3,4,8,7,2]=>[1,5,3,4,7,8,6,2]=>0110010=>1001101
[6,5,1,2,3,8,7,4]=>[5,1,7,8,6,2,3,4]=>1100010=>0011101
[6,4,1,2,3,8,7,5]=>[4,1,7,8,6,2,3,5]=>1100010=>0011101
[5,4,1,2,3,8,7,6]=>[4,1,5,2,3,7,8,6]=>1100010=>0011101
[6,4,1,7,2,3,5,8]=>[7,4,1,6,2,3,5,8]=>1101000=>0010111
[6,4,1,8,2,3,5,7]=>[8,4,1,6,2,3,5,7]=>1101000=>0010111
[7,5,1,2,8,3,6,4]=>[8,5,1,6,7,2,3,4]=>1100100=>0011011
[7,1,5,2,8,4,6,3]=>[8,5,1,2,4,6,7,3]=>1010100=>0101011
[1,7,5,3,8,4,6,2]=>[1,8,5,3,4,6,7,2]=>0110100=>1001011
[1,8,5,3,7,4,6,2]=>[1,7,5,3,4,6,8,2]=>0110100=>1001011
[8,5,1,2,7,3,6,4]=>[7,5,1,6,8,2,3,4]=>1100100=>0011011
[8,4,1,2,7,3,6,5]=>[4,1,7,2,3,6,8,5]=>1100100=>0011011
[8,4,1,7,2,3,5,6]=>[7,4,1,8,2,3,5,6]=>1101000=>0010111
[7,4,1,6,2,3,5,8]=>[6,4,1,7,2,3,5,8]=>1101000=>0010111
[1,7,6,8,3,4,5,2]=>[1,8,3,6,4,5,7,2]=>0111000=>1000111
[4,7,1,2,8,3,6,5]=>[8,1,4,2,3,6,7,5]=>1100100=>0011011
[3,1,7,2,8,4,6,5]=>[8,3,1,2,4,6,7,5]=>1010100=>0101011
[1,4,3,8,7,5,6,2]=>[1,3,7,5,6,8,4,2]=>0101100=>1010011
[4,1,2,8,7,5,6,3]=>[7,5,6,8,4,1,2,3]=>1001100=>0110011
[3,1,2,8,7,5,6,4]=>[3,1,2,7,5,6,8,4]=>1001100=>0110011
[3,1,8,2,7,4,6,5]=>[7,3,1,2,4,6,8,5]=>1010100=>0101011
[3,1,8,7,2,4,5,6]=>[7,3,1,2,8,4,5,6]=>1011000=>0100111
[4,8,1,6,2,3,5,7]=>[6,1,8,4,2,3,5,7]=>1101000=>0010111
[4,8,1,7,2,3,5,6]=>[7,1,8,4,2,3,5,6]=>1101000=>0010111
[4,8,1,2,7,3,6,5]=>[7,1,4,2,3,6,8,5]=>1100100=>0011011
[5,8,1,2,7,3,6,4]=>[7,1,6,8,5,2,3,4]=>1100100=>0011011
[5,1,8,2,7,4,6,3]=>[7,1,2,4,6,8,5,3]=>1010100=>0101011
[6,1,8,7,2,4,5,3]=>[7,1,2,8,4,5,6,3]=>1011000=>0100111
[6,8,1,7,2,3,5,4]=>[7,1,8,2,3,5,6,4]=>1101000=>0010111
[6,8,7,1,2,3,4,5]=>[7,1,8,2,6,3,4,5]=>1110000=>0001111
[5,8,7,1,2,3,4,6]=>[7,1,8,2,5,3,4,6]=>1110000=>0001111
[5,8,6,1,2,3,4,7]=>[6,1,8,2,5,3,4,7]=>1110000=>0001111
[7,1,8,6,2,4,5,3]=>[6,1,2,8,4,5,7,3]=>1011000=>0100111
[1,7,8,6,3,4,5,2]=>[1,6,3,8,4,5,7,2]=>0111000=>1000111
[1,8,7,6,3,4,5,2]=>[1,6,3,7,4,5,8,2]=>0111000=>1000111
[8,1,7,6,2,4,5,3]=>[6,1,2,7,4,5,8,3]=>1011000=>0100111
[3,2,5,1,6,4,8,7]=>[2,6,5,3,1,4,8,7]=>1010101=>0101010
[3,2,5,4,7,1,8,6]=>[2,4,8,7,5,3,1,6]=>1010101=>0101010
[4,2,5,3,7,6,8,1]=>[2,6,8,7,5,3,4,1]=>1010101=>0101010
[4,2,5,3,7,1,8,6]=>[2,8,7,5,3,4,1,6]=>1010101=>0101010
[4,2,5,3,6,1,8,7]=>[2,6,5,3,4,1,8,7]=>1010101=>0101010
[4,2,5,1,6,3,8,7]=>[2,6,5,1,4,3,8,7]=>1010101=>0101010
[3,1,5,4,6,2,8,7]=>[4,6,5,3,1,2,8,7]=>1010101=>0101010
[4,1,5,3,6,2,8,7]=>[6,5,3,4,1,2,8,7]=>1010101=>0101010
[4,3,5,1,6,2,8,7]=>[6,5,3,1,4,2,8,7]=>1110101=>0001010
[4,3,5,2,7,1,8,6]=>[8,7,5,3,2,4,1,6]=>1110101=>0001010
[4,3,6,2,7,5,8,1]=>[8,7,5,6,3,2,4,1]=>1110101=>0001010
[4,3,6,2,7,1,8,5]=>[8,7,3,2,4,1,6,5]=>1110101=>0001010
[4,3,6,1,7,2,8,5]=>[8,7,3,1,4,2,6,5]=>1110101=>0001010
[4,3,5,1,7,2,8,6]=>[8,7,5,3,1,4,2,6]=>1110101=>0001010
[3,1,5,4,7,2,8,6]=>[4,8,7,5,3,1,2,6]=>1010101=>0101010
[2,1,5,4,7,3,8,6]=>[2,1,4,8,7,5,3,6]=>1010101=>0101010
[3,1,5,4,7,6,8,2]=>[4,6,8,7,5,3,1,2]=>1010101=>0101010
[4,1,5,3,7,6,8,2]=>[6,8,7,5,3,4,1,2]=>1010101=>0101010
[4,3,5,1,7,6,8,2]=>[6,8,7,5,3,1,4,2]=>1110101=>0001010
[4,3,6,1,7,5,8,2]=>[8,7,5,6,3,1,4,2]=>1110101=>0001010
[4,3,6,5,7,1,8,2]=>[8,7,5,3,1,6,4,2]=>1111101=>0000010
[5,3,6,4,7,2,8,1]=>[4,8,7,3,2,6,5,1]=>1110101=>0001010
[5,3,6,4,7,1,8,2]=>[4,8,7,3,1,6,5,2]=>1110101=>0001010
[5,3,6,1,7,4,8,2]=>[8,7,3,1,4,6,5,2]=>1110101=>0001010
[5,1,6,3,7,4,8,2]=>[8,7,3,4,6,5,1,2]=>1010101=>0101010
[4,1,6,3,7,5,8,2]=>[8,7,5,6,3,4,1,2]=>1010101=>0101010
[3,1,6,4,7,5,8,2]=>[4,8,7,5,6,3,1,2]=>1010101=>0101010
[2,1,6,4,7,5,8,3]=>[2,1,4,8,7,5,6,3]=>1010101=>0101010
[2,1,6,4,7,3,8,5]=>[2,1,4,8,7,3,6,5]=>1010101=>0101010
[3,1,6,4,7,2,8,5]=>[4,8,7,3,1,2,6,5]=>1010101=>0101010
[4,1,6,3,7,2,8,5]=>[8,7,3,4,1,2,6,5]=>1010101=>0101010
[5,1,6,3,7,2,8,4]=>[8,7,3,6,5,1,2,4]=>1010101=>0101010
[5,3,6,1,7,2,8,4]=>[8,7,3,1,6,5,2,4]=>1110101=>0001010
[5,3,6,2,7,1,8,4]=>[8,7,3,2,6,5,1,4]=>1110101=>0001010
[5,3,6,2,7,4,8,1]=>[8,7,3,2,4,6,5,1]=>1110101=>0001010
[5,2,6,3,7,4,8,1]=>[2,8,7,3,4,6,5,1]=>1010101=>0101010
[5,2,6,3,7,1,8,4]=>[2,8,7,3,6,5,1,4]=>1010101=>0101010
[5,2,6,1,7,3,8,4]=>[2,8,7,1,6,5,3,4]=>1010101=>0101010
[4,2,5,1,7,3,8,6]=>[2,8,7,5,1,4,3,6]=>1010101=>0101010
[4,2,6,1,7,3,8,5]=>[2,8,7,1,4,3,6,5]=>1010101=>0101010
[4,2,6,3,7,1,8,5]=>[2,8,7,3,4,1,6,5]=>1010101=>0101010
[4,2,6,3,7,5,8,1]=>[2,8,7,5,6,3,4,1]=>1010101=>0101010
[3,2,6,4,7,5,8,1]=>[2,4,8,7,5,6,3,1]=>1010101=>0101010
[3,2,6,4,7,1,8,5]=>[2,4,8,7,3,1,6,5]=>1010101=>0101010
[3,2,6,1,7,4,8,5]=>[2,8,7,3,1,4,6,5]=>1010101=>0101010
[3,2,5,1,7,4,8,6]=>[2,8,7,5,3,1,4,6]=>1010101=>0101010
[3,2,4,1,7,5,8,6]=>[2,4,3,1,8,7,5,6]=>1010101=>0101010
[3,1,4,2,7,6,8,5]=>[4,3,1,2,6,8,7,5]=>1010101=>0101010
[3,2,5,1,7,6,8,4]=>[2,6,8,7,5,3,1,4]=>1010101=>0101010
[3,2,6,1,7,5,8,4]=>[2,8,7,5,6,3,1,4]=>1010101=>0101010
[3,2,6,5,7,1,8,4]=>[2,8,7,5,3,1,6,4]=>1011101=>0100010
[4,2,6,5,7,3,8,1]=>[2,8,7,5,3,6,4,1]=>1011101=>0100010
[4,2,6,5,7,1,8,3]=>[2,8,7,5,1,6,4,3]=>1011101=>0100010
[4,2,6,1,7,5,8,3]=>[2,8,7,5,6,1,4,3]=>1010101=>0101010
[4,2,5,1,7,6,8,3]=>[2,6,8,7,5,1,4,3]=>1010101=>0101010
[4,1,5,2,7,6,8,3]=>[6,8,7,5,1,2,4,3]=>1010101=>0101010
[3,1,5,2,7,6,8,4]=>[6,8,7,5,3,1,2,4]=>1010101=>0101010
[2,1,5,3,7,6,8,4]=>[2,1,6,8,7,5,3,4]=>1010101=>0101010
[2,1,6,3,7,5,8,4]=>[2,1,8,7,5,6,3,4]=>1010101=>0101010
[3,1,6,2,7,5,8,4]=>[8,7,5,6,3,1,2,4]=>1010101=>0101010
[4,1,6,2,7,5,8,3]=>[8,7,5,6,1,2,4,3]=>1010101=>0101010
[5,1,6,2,7,4,8,3]=>[8,7,1,2,4,6,5,3]=>1010101=>0101010
[5,2,6,1,7,4,8,3]=>[2,8,7,1,4,6,5,3]=>1010101=>0101010
[5,2,6,4,7,1,8,3]=>[2,4,8,7,1,6,5,3]=>1010101=>0101010
[5,2,6,4,7,3,8,1]=>[2,4,8,7,3,6,5,1]=>1010101=>0101010
[5,4,6,2,7,3,8,1]=>[8,7,2,4,3,6,5,1]=>1110101=>0001010
[5,4,6,2,7,1,8,3]=>[8,7,2,4,1,6,5,3]=>1110101=>0001010
[5,4,6,1,7,2,8,3]=>[8,7,1,4,2,6,5,3]=>1110101=>0001010
[5,1,6,4,7,2,8,3]=>[4,8,7,1,2,6,5,3]=>1010101=>0101010
[4,1,6,5,7,2,8,3]=>[8,7,5,1,2,6,4,3]=>1011101=>0100010
[3,1,6,5,7,2,8,4]=>[8,7,5,3,1,2,6,4]=>1011101=>0100010
[2,1,6,5,7,3,8,4]=>[2,1,8,7,5,3,6,4]=>1011101=>0100010
[3,1,6,5,7,4,8,2]=>[8,7,5,4,6,3,1,2]=>1011101=>0100010
[4,1,6,5,7,3,8,2]=>[8,7,5,3,6,4,1,2]=>1011101=>0100010
[5,1,6,4,7,3,8,2]=>[4,8,7,3,6,5,1,2]=>1010101=>0101010
[5,4,6,1,7,3,8,2]=>[8,7,1,4,3,6,5,2]=>1110101=>0001010
[5,4,6,3,7,1,8,2]=>[8,7,3,4,1,6,5,2]=>1110101=>0001010
[8,3,5,2,1,6,4,7]=>[5,3,2,6,8,1,4,7]=>1110000=>0001111
[8,6,3,5,2,4,1,7]=>[3,5,2,6,4,8,1,7]=>1101000=>0010111
[3,7,5,2,4,1,8,6]=>[5,2,4,8,7,3,1,6]=>1110001=>0001110
[8,3,7,5,2,4,6,1]=>[5,3,2,7,4,6,8,1]=>1111000=>0000111
[8,2,4,5,7,3,6,1]=>[2,7,5,4,3,6,8,1]=>1011100=>0100011
[2,4,5,7,3,1,8,6]=>[8,7,3,5,4,2,1,6]=>1111001=>0000110
[8,2,4,6,5,3,1,7]=>[2,5,6,4,3,8,1,7]=>1011000=>0100111
[8,2,5,4,6,1,3,7]=>[2,4,6,5,1,8,3,7]=>1010100=>0101011
[8,6,3,5,1,4,2,7]=>[3,5,1,6,4,8,2,7]=>1101000=>0010111
[8,6,1,4,5,3,2,7]=>[4,5,6,1,3,8,2,7]=>1100000=>0011111
[8,1,5,6,4,3,2,7]=>[6,4,5,3,8,1,2,7]=>1011000=>0100111
[5,7,4,3,2,1,8,6]=>[4,3,8,7,2,5,1,6]=>1110001=>0001110
[8,5,7,4,3,2,6,1]=>[4,7,3,5,2,6,8,1]=>1110000=>0001111
[4,6,8,3,2,7,5,1]=>[7,3,5,8,6,2,4,1]=>1110010=>0001101
[4,7,6,3,2,8,1,5]=>[8,6,3,7,2,4,1,5]=>1110010=>0001101
[1,4,6,7,3,2,8,5]=>[1,8,7,3,6,4,2,5]=>0111001=>1000110
[5,4,7,3,1,8,2,6]=>[8,3,4,1,5,2,7,6]=>1110010=>0001101
[1,7,4,5,3,2,8,6]=>[1,5,4,3,8,7,2,6]=>0111001=>1000110
[3,7,5,1,4,2,8,6]=>[5,1,4,8,7,3,2,6]=>1110001=>0001110
[5,7,4,2,1,3,8,6]=>[4,2,8,7,1,5,3,6]=>1110001=>0001110
[8,5,7,4,2,1,6,3]=>[4,7,2,5,1,6,8,3]=>1110000=>0001111
[8,3,7,5,1,4,6,2]=>[5,3,1,7,4,6,8,2]=>1111000=>0000111
[8,4,1,7,5,3,6,2]=>[5,7,4,1,3,6,8,2]=>1101000=>0010111
[4,6,3,8,7,1,5,2]=>[3,7,1,8,5,6,4,2]=>1101100=>0010011
[1,7,4,8,6,3,5,2]=>[1,6,4,3,8,5,7,2]=>0111100=>1000011
[8,4,7,6,3,5,2,1]=>[6,3,5,7,4,2,8,1]=>1111000=>0000111
[3,6,5,8,7,4,1,2]=>[7,4,8,5,1,6,3,2]=>1111100=>0000011
[3,1,5,8,6,7,4,2]=>[7,6,4,8,5,3,1,2]=>1011110=>0100001
[4,8,1,6,7,3,5,2]=>[7,1,3,6,5,8,4,2]=>1101100=>0010011
[3,6,4,1,8,7,5,2]=>[4,1,7,5,8,6,3,2]=>1110110=>0001001
[8,2,6,1,4,7,5,3]=>[2,7,6,1,4,5,8,3]=>1010010=>0101101
[2,7,6,8,1,4,3,5]=>[8,2,1,6,4,7,3,5]=>1111000=>0000111
[3,7,1,6,4,8,2,5]=>[8,6,4,7,1,3,2,5]=>1101010=>0010101
[1,7,3,5,6,8,2,4]=>[1,3,8,6,5,2,7,4]=>0101110=>1010001
[1,3,6,7,5,8,2,4]=>[1,5,8,3,2,7,6,4]=>0111010=>1000101
[3,7,6,5,8,2,1,4]=>[8,5,2,6,3,1,7,4]=>1111100=>0000011
[3,6,8,5,7,2,4,1]=>[7,5,2,8,4,6,3,1]=>1111100=>0000011
[2,3,5,7,6,8,1,4]=>[8,6,3,2,1,7,5,4]=>1111110=>0000001
[2,1,6,5,7,8,3,4]=>[2,1,8,5,3,7,6,4]=>1011110=>0100001
[4,2,7,6,8,3,1,5]=>[2,8,3,6,4,1,7,5]=>1011100=>0100011
[4,2,6,8,7,3,5,1]=>[2,7,3,8,5,6,4,1]=>1011100=>0100011
[3,8,2,4,6,7,5,1]=>[4,7,6,5,8,2,3,1]=>1100110=>0011001
[3,7,2,6,4,8,1,5]=>[8,6,4,7,2,3,1,5]=>1101010=>0010101
[3,2,6,1,4,7,8,5]=>[2,8,7,6,3,1,4,5]=>1010011=>0101100
[5,3,7,2,1,8,4,6]=>[8,3,2,5,1,4,7,6]=>1110010=>0001101
[4,7,3,2,1,5,8,6]=>[3,8,7,2,4,1,5,6]=>1100001=>0011110
[8,7,6,1,3,4,2,5]=>[6,1,7,3,4,8,2,5]=>1110000=>0001111
[8,5,7,3,2,1,6,4]=>[7,3,5,2,6,8,1,4]=>1110000=>0001111
[8,3,6,7,2,1,5,4]=>[7,3,2,6,1,5,8,4]=>1111000=>0000111
[3,7,8,6,2,1,5,4]=>[6,2,8,3,1,5,7,4]=>1111000=>0000111
[8,7,6,3,5,2,4,1]=>[5,6,3,7,2,4,8,1]=>1110000=>0001111
[2,7,4,8,1,6,5,3]=>[6,8,4,2,1,5,7,3]=>1111000=>0000111
[4,6,8,2,1,7,5,3]=>[7,2,5,8,6,1,4,3]=>1110010=>0001101
[8,4,1,5,7,2,6,3]=>[7,5,4,1,6,8,2,3]=>1101100=>0010011
[8,5,3,7,1,6,2,4]=>[3,6,7,1,5,2,8,4]=>1101000=>0010111
[8,5,7,2,1,3,6,4]=>[7,2,5,1,6,8,3,4]=>1110000=>0001111
[8,2,6,7,1,3,5,4]=>[2,7,1,6,3,5,8,4]=>1011000=>0100111
[8,3,6,1,7,5,2,4]=>[7,5,6,3,1,8,2,4]=>1110100=>0001011
[4,6,1,8,7,2,5,3]=>[7,1,8,5,6,4,2,3]=>1101100=>0010011
[8,1,2,5,6,7,4,3]=>[7,6,5,4,8,1,2,3]=>1001110=>0110001
[8,2,6,5,7,4,1,3]=>[2,7,5,4,6,1,8,3]=>1011100=>0100011
[2,1,7,8,5,6,4,3]=>[2,1,5,6,8,4,7,3]=>1011000=>0100111
[8,2,5,7,6,4,3,1]=>[2,6,4,7,5,3,8,1]=>1011100=>0100011
[2,7,6,8,5,4,1,3]=>[5,8,4,6,2,1,7,3]=>1111000=>0000111
[1,7,2,5,8,6,4,3]=>[1,6,8,5,4,7,2,3]=>0101100=>1010011
[1,7,4,8,2,6,5,3]=>[1,6,8,4,2,5,7,3]=>0111000=>1000111
[3,7,8,1,6,5,2,4]=>[6,5,8,1,7,3,2,4]=>1110100=>0001011
[2,7,8,6,1,3,5,4]=>[6,2,1,8,3,5,7,4]=>1111000=>0000111
[8,7,6,3,5,1,4,2]=>[5,6,3,7,1,4,8,2]=>1110000=>0001111
[8,4,7,6,5,1,3,2]=>[5,6,1,7,4,3,8,2]=>1111000=>0000111
[8,7,1,5,6,4,3,2]=>[6,5,4,7,1,3,8,2]=>1101100=>0010011
[8,1,6,7,5,4,3,2]=>[5,7,4,6,3,8,1,2]=>1011000=>0100111
[6,5,3,1,2,4,8,7]=>[3,5,1,6,2,4,8,7]=>1100001=>0011110
[4,6,3,5,1,2,8,7]=>[3,5,1,6,4,2,8,7]=>1101001=>0010110
[8,5,3,7,2,1,4,6]=>[3,7,2,5,1,8,4,6]=>1101000=>0010111
[6,8,1,4,5,7,3,2]=>[4,5,7,1,3,8,6,2]=>1100010=>0011101
[8,7,2,4,5,1,3,6]=>[4,5,7,2,8,1,3,6]=>1100000=>0011111
[3,6,2,4,5,1,8,7]=>[4,5,6,2,3,1,8,7]=>1100001=>0011110
[2,6,1,4,5,3,8,7]=>[4,5,6,2,1,3,8,7]=>1100001=>0011110
[6,1,2,4,5,3,8,7]=>[4,5,6,1,2,3,8,7]=>1000001=>0111110
[5,6,3,2,1,4,8,7]=>[3,6,2,5,1,4,8,7]=>1100001=>0011110
[5,4,3,6,1,2,8,7]=>[3,6,4,1,5,2,8,7]=>1101001=>0010110
[6,3,1,4,5,2,8,7]=>[3,1,4,5,6,2,8,7]=>1100001=>0011110
[3,1,6,4,5,2,8,7]=>[4,5,6,3,1,2,8,7]=>1010001=>0101110
[8,3,7,4,5,1,2,6]=>[4,5,7,3,1,8,2,6]=>1110000=>0001111
[5,8,7,4,2,6,3,1]=>[4,6,7,2,8,3,5,1]=>1110000=>0001111
[2,1,8,7,5,3,4,6]=>[2,1,5,7,3,8,4,6]=>1011000=>0100111
[2,1,6,8,5,7,3,4]=>[2,1,5,7,3,8,6,4]=>1011010=>0100101
[5,6,3,8,1,7,2,4]=>[3,7,1,8,6,2,5,4]=>1101010=>0010101
[5,1,8,4,7,6,2,3]=>[4,6,7,1,2,8,5,3]=>1010100=>0101011
[2,4,8,3,5,6,7,1]=>[5,6,7,8,3,4,2,1]=>1110000=>0001111
[4,1,8,3,5,6,7,2]=>[5,6,7,8,3,4,1,2]=>1010000=>0101111
[3,8,4,2,5,6,7,1]=>[4,2,5,6,7,8,3,1]=>1110000=>0001111
[7,5,8,4,3,6,1,2]=>[4,6,8,3,5,1,7,2]=>1110000=>0001111
[6,5,3,8,4,1,7,2]=>[3,7,8,4,5,1,6,2]=>1101000=>0010111
[2,1,5,8,4,6,7,3]=>[2,1,6,7,8,4,5,3]=>1011000=>0100111
[2,1,4,8,3,6,7,5]=>[2,1,6,7,8,4,3,5]=>1011000=>0100111
[6,4,3,8,2,1,7,5]=>[3,7,8,4,2,6,1,5]=>1101000=>0010111
[8,3,1,2,5,6,7,4]=>[3,1,5,6,7,8,2,4]=>1100000=>0011111
[3,1,8,2,5,6,7,4]=>[5,6,7,8,3,1,2,4]=>1010000=>0101111
[2,3,8,1,5,6,7,4]=>[5,6,7,8,3,2,1,4]=>1110000=>0001111
[4,3,8,2,5,6,7,1]=>[5,6,7,8,3,2,4,1]=>1110000=>0001111
[4,8,2,3,5,6,7,1]=>[5,6,7,8,2,3,4,1]=>1100000=>0011111
[3,8,2,1,5,6,7,4]=>[5,6,7,8,2,3,1,4]=>1100000=>0011111
[2,8,1,3,5,6,7,4]=>[5,6,7,8,2,1,3,4]=>1100000=>0011111
[8,1,2,3,5,6,7,4]=>[5,6,7,8,1,2,3,4]=>1000000=>0111111
[6,8,3,2,4,1,7,5]=>[3,7,8,2,4,6,1,5]=>1100000=>0011111
[2,1,8,3,4,6,7,5]=>[2,1,6,7,8,3,4,5]=>1010000=>0101111
[2,1,7,8,5,4,3,6]=>[2,1,5,8,4,7,3,6]=>1011000=>0100111
[3,8,7,4,2,6,1,5]=>[4,6,7,2,8,3,1,5]=>1110000=>0001111
[5,7,8,4,3,6,2,1]=>[4,6,8,3,7,2,5,1]=>1110000=>0001111
[4,8,3,6,2,1,7,5]=>[3,6,2,7,8,4,1,5]=>1101000=>0010111
[2,4,3,1,8,5,7,6]=>[3,4,2,1,7,8,5,6]=>1100100=>0011011
[4,1,3,2,6,8,7,5]=>[3,4,1,2,7,8,6,5]=>1000110=>0111001
[8,6,3,5,1,2,7,4]=>[3,5,1,6,2,7,8,4]=>1101000=>0010111
[5,8,3,2,6,1,7,4]=>[3,6,2,7,8,5,1,4]=>1100100=>0011011
[4,5,3,8,6,2,7,1]=>[3,6,2,7,8,5,4,1]=>1101100=>0010011
[3,5,8,4,7,6,2,1]=>[4,6,7,2,8,5,3,1]=>1110100=>0001011
[5,8,2,4,7,6,1,3]=>[4,6,7,2,8,5,1,3]=>1100100=>0011011
[8,7,5,4,1,6,2,3]=>[4,5,1,6,7,2,8,3]=>1110000=>0001111
[5,7,3,6,1,8,2,4]=>[3,8,6,1,7,2,5,4]=>1101010=>0010101
[2,1,7,6,5,8,3,4]=>[2,1,5,8,6,3,7,4]=>1011010=>0100101
[2,1,8,5,3,6,7,4]=>[2,1,5,3,6,7,8,4]=>1011000=>0100111
[6,8,3,5,2,1,7,4]=>[3,5,2,7,8,1,6,4]=>1101000=>0010111
[7,8,5,4,2,6,1,3]=>[4,5,2,6,8,1,7,3]=>1110000=>0001111
[8,1,4,2,5,6,7,3]=>[4,1,2,5,6,7,8,3]=>1010000=>0101111
[2,8,4,1,5,6,7,3]=>[4,2,1,5,6,7,8,3]=>1110000=>0001111
[4,8,1,2,5,6,7,3]=>[5,6,7,8,1,4,2,3]=>1100000=>0011111
[3,4,8,1,5,6,7,2]=>[5,6,7,8,1,4,3,2]=>1110000=>0001111
[3,4,2,8,5,6,7,1]=>[5,6,7,8,4,2,3,1]=>1101000=>0010111
[2,4,1,8,5,6,7,3]=>[5,6,7,8,4,2,1,3]=>1101000=>0010111
[4,1,2,8,5,6,7,3]=>[5,6,7,8,4,1,2,3]=>1001000=>0110111
[8,4,2,1,5,6,7,3]=>[4,2,5,6,7,8,1,3]=>1100000=>0011111
[7,5,2,4,8,6,1,3]=>[4,6,8,5,2,7,1,3]=>1100100=>0011011
[6,5,3,2,8,1,7,4]=>[3,7,8,5,2,6,1,4]=>1100100=>0011011
[2,1,5,3,8,6,7,4]=>[2,1,6,7,8,5,3,4]=>1010100=>0101011
[6,4,3,5,8,1,7,2]=>[3,7,8,5,4,1,6,2]=>1101100=>0010011
[8,3,4,1,5,6,7,2]=>[4,3,1,5,6,7,8,2]=>1110000=>0001111
[4,3,1,8,5,6,7,2]=>[3,1,5,6,7,8,4,2]=>1101000=>0010111
[3,1,4,8,5,6,7,2]=>[5,6,7,8,4,3,1,2]=>1011000=>0100111
[6,5,3,7,2,8,4,1]=>[3,8,2,5,4,7,6,1]=>1101010=>0010101
[6,3,7,4,5,8,2,1]=>[4,5,8,3,2,7,6,1]=>1110010=>0001101
[5,1,7,4,8,6,3,2]=>[4,6,8,3,7,5,1,2]=>1010100=>0101011
[2,5,7,4,8,6,3,1]=>[4,6,8,3,7,5,2,1]=>1110100=>0001011
[5,6,3,7,1,8,4,2]=>[3,8,1,7,6,4,5,2]=>1101010=>0010101
[5,7,1,4,8,6,2,3]=>[4,6,8,1,7,5,2,3]=>1100100=>0011011
[5,6,3,1,8,2,7,4]=>[3,7,8,1,6,5,2,4]=>1100100=>0011011
[3,7,8,4,1,6,2,5]=>[4,6,8,1,7,3,2,5]=>1110000=>0001111
[3,2,5,1,6,8,4,7]=>[2,8,6,5,3,1,4,7]=>1010110=>0101001
[3,6,2,5,4,8,1,7]=>[5,4,8,6,2,3,1,7]=>1101010=>0010101
[3,5,2,4,7,1,8,6]=>[4,8,7,5,2,3,1,6]=>1100101=>0011010
[3,5,8,2,4,7,6,1]=>[7,6,8,2,4,5,3,1]=>1110010=>0001101
[4,2,5,8,3,7,6,1]=>[2,7,6,8,3,5,4,1]=>1011010=>0100101
[4,2,6,5,3,8,1,7]=>[2,5,3,8,6,4,1,7]=>1011010=>0100101
[5,4,2,1,6,8,3,7]=>[4,2,8,6,5,1,3,7]=>1100110=>0011001
[6,3,5,1,4,8,2,7]=>[5,3,1,4,8,6,2,7]=>1110010=>0001101
[4,6,1,5,3,8,2,7]=>[5,1,3,8,6,4,2,7]=>1101010=>0010101
[5,1,6,4,3,8,2,7]=>[4,8,6,3,5,1,2,7]=>1010010=>0101101
[5,4,3,2,7,1,8,6]=>[3,4,2,8,7,5,1,6]=>1100101=>0011010
[5,4,3,8,2,7,6,1]=>[3,7,6,8,4,2,5,1]=>1101010=>0010101
[4,3,6,2,8,7,5,1]=>[7,5,8,6,3,2,4,1]=>1110110=>0001001
[4,3,7,6,2,1,8,5]=>[6,3,2,8,7,4,1,5]=>1111001=>0000110
[6,4,3,1,7,2,8,5]=>[3,4,1,8,7,2,6,5]=>1100101=>0011010
[7,5,4,3,1,8,2,6]=>[4,3,5,1,8,2,7,6]=>1110010=>0001101
[1,4,7,5,8,3,2,6]=>[1,8,5,3,7,4,2,6]=>0111100=>1000011
[7,1,3,5,8,4,2,6]=>[3,8,5,4,7,1,2,6]=>1001100=>0110011
[7,2,5,8,4,1,3,6]=>[2,8,4,5,1,7,3,6]=>1011000=>0100111
[2,8,5,7,4,6,1,3]=>[6,7,4,5,2,1,8,3]=>1111000=>0000111
[3,5,8,7,1,4,6,2]=>[7,1,6,8,4,5,3,2]=>1111000=>0000111
[1,4,5,8,7,3,6,2]=>[1,7,3,6,8,5,4,2]=>0111100=>1000011
[1,5,4,8,7,3,6,2]=>[1,7,4,3,6,8,5,2]=>0111100=>1000011
[6,4,3,8,1,7,5,2]=>[3,7,4,1,5,8,6,2]=>1101010=>0010101
[4,3,7,1,8,6,5,2]=>[6,8,5,7,3,1,4,2]=>1110100=>0001011
[4,8,3,7,6,5,2,1]=>[3,6,5,7,2,8,4,1]=>1101100=>0010011
[5,3,8,7,6,4,2,1]=>[6,4,7,3,2,8,5,1]=>1111100=>0000011
[7,5,3,1,8,6,4,2]=>[3,6,8,5,1,4,7,2]=>1100100=>0011011
[1,8,6,5,3,7,4,2]=>[1,5,3,7,6,4,8,2]=>0111010=>1000101
[1,5,8,6,3,7,4,2]=>[1,7,6,3,8,4,5,2]=>0111010=>1000101
[4,6,1,8,7,3,5,2]=>[7,1,3,8,5,6,4,2]=>1101100=>0010011
[6,8,7,3,1,4,5,2]=>[7,3,8,1,4,5,6,2]=>1110000=>0001111
[6,2,8,7,4,5,1,3]=>[2,7,4,5,8,1,6,3]=>1011000=>0100111
[7,6,2,8,4,1,3,5]=>[8,4,6,2,7,1,3,5]=>1101000=>0010111
[7,3,1,6,8,4,2,5]=>[3,1,8,4,6,2,7,5]=>1101100=>0010011
[1,7,6,4,8,3,2,5]=>[1,4,8,3,6,2,7,5]=>0110100=>1001011
[5,7,1,6,3,2,8,4]=>[6,1,3,8,7,2,5,4]=>1101001=>0010110
[6,1,7,5,3,2,8,4]=>[5,3,8,7,1,2,6,4]=>1011001=>0100110
[7,6,5,3,2,1,8,4]=>[5,3,6,2,8,7,1,4]=>1110001=>0001110
[6,5,3,2,8,7,4,1]=>[3,7,5,2,4,8,6,1]=>1100110=>0011001
[5,2,6,3,8,7,4,1]=>[2,7,3,4,8,6,5,1]=>1010110=>0101001
[5,2,7,6,3,1,8,4]=>[2,6,3,8,7,1,5,4]=>1011001=>0100110
[6,5,2,1,7,3,8,4]=>[8,7,5,2,6,1,3,4]=>1100101=>0011010
[5,2,7,4,1,8,3,6]=>[2,4,8,1,5,3,7,6]=>1010010=>0101101
[4,7,2,6,3,1,8,5]=>[6,2,3,8,7,4,1,5]=>1101001=>0010110
[2,4,8,6,3,7,5,1]=>[7,6,3,5,8,4,2,1]=>1111010=>0000101
[3,8,6,2,4,7,5,1]=>[7,6,2,4,5,8,3,1]=>1110010=>0001101
[7,3,6,2,4,1,8,5]=>[6,3,2,4,8,7,1,5]=>1110001=>0001110
[3,6,7,2,1,4,8,5]=>[8,7,2,6,3,1,4,5]=>1110001=>0001110
[4,3,7,8,2,1,5,6]=>[8,3,2,7,4,1,5,6]=>1111000=>0000111
[8,3,7,1,4,6,2,5]=>[6,7,3,1,4,8,2,5]=>1110000=>0001111
[3,8,2,5,7,1,6,4]=>[7,5,2,3,1,6,8,4]=>1101100=>0010011
[8,3,6,2,7,1,5,4]=>[7,3,2,6,5,8,1,4]=>1110100=>0001011
[7,8,3,6,2,1,5,4]=>[3,6,2,8,1,5,7,4]=>1101000=>0010111
[8,7,3,6,2,5,4,1]=>[3,6,2,5,7,4,8,1]=>1101000=>0010111
[4,7,8,2,1,6,5,3]=>[6,8,2,5,7,1,4,3]=>1110000=>0001111
[4,2,6,8,1,7,5,3]=>[2,7,1,5,8,6,4,3]=>1011010=>0100101
[5,4,8,2,7,1,6,3]=>[7,2,4,1,6,8,5,3]=>1110100=>0001011
[4,8,1,5,7,2,6,3]=>[7,5,1,6,8,4,2,3]=>1101100=>0010011
[5,8,3,7,1,6,2,4]=>[3,6,7,1,8,2,5,4]=>1101000=>0010111
[5,8,7,2,6,1,3,4]=>[6,2,7,1,8,5,3,4]=>1110100=>0001011
[8,6,2,7,5,1,3,4]=>[5,7,2,6,1,3,8,4]=>1101000=>0010111
[3,6,8,1,7,5,2,4]=>[7,5,8,1,6,3,2,4]=>1110100=>0001011
[5,1,6,8,2,7,4,3]=>[7,1,2,8,6,4,5,3]=>1011010=>0100101
[6,5,2,8,1,7,4,3]=>[7,2,5,4,8,6,1,3]=>1101010=>0010101
[5,2,7,1,8,6,4,3]=>[2,6,8,1,4,7,5,3]=>1010100=>0101011
[5,8,2,7,6,4,3,1]=>[6,4,7,2,3,8,5,1]=>1101100=>0010011
[6,2,8,7,5,4,3,1]=>[2,5,7,4,8,3,6,1]=>1011000=>0100111
[7,6,2,1,8,5,4,3]=>[8,5,6,2,4,7,1,3]=>1100100=>0011011
[6,1,7,2,8,5,4,3]=>[8,5,7,1,2,4,6,3]=>1010100=>0101011
[7,5,1,8,2,6,4,3]=>[6,8,1,5,4,7,2,3]=>1101000=>0010111
[4,7,1,8,6,2,5,3]=>[6,1,8,5,7,4,2,3]=>1101100=>0010011
[7,8,3,1,6,5,2,4]=>[3,6,5,8,1,7,2,4]=>1100100=>0011011
[8,7,4,6,1,5,3,2]=>[6,4,1,5,7,3,8,2]=>1111000=>0000111
[8,5,7,1,6,4,3,2]=>[6,1,4,7,5,3,8,2]=>1110100=>0001011
[6,8,1,7,5,4,3,2]=>[5,7,4,8,1,3,6,2]=>1101000=>0010111
[7,1,8,6,5,4,3,2]=>[5,6,4,8,3,7,1,2]=>1011000=>0100111
[8,4,2,6,3,1,5,7]=>[6,4,2,3,8,1,5,7]=>1101000=>0010111
[3,2,7,6,4,5,1,8]=>[2,6,4,5,7,3,1,8]=>1011000=>0100111
[5,7,6,2,3,4,1,8]=>[6,2,7,3,4,5,1,8]=>1110000=>0001111
[1,6,5,2,3,8,4,7]=>[1,5,2,8,6,3,4,7]=>0110010=>1001101
[1,7,5,2,8,3,4,6]=>[1,8,5,2,7,3,4,6]=>0110100=>1001011
[5,8,6,2,3,1,4,7]=>[6,2,8,3,5,1,4,7]=>1110000=>0001111
[4,8,2,6,3,1,5,7]=>[6,2,3,8,4,1,5,7]=>1101000=>0010111
[3,2,1,6,4,8,5,7]=>[2,3,1,8,6,4,5,7]=>1001010=>0110101
[7,1,5,2,8,3,4,6]=>[8,5,1,2,7,3,4,6]=>1010100=>0101011
[1,8,5,2,7,3,4,6]=>[1,7,5,2,8,3,4,6]=>0110100=>1001011
[1,8,6,7,2,3,4,5]=>[1,7,2,6,3,8,4,5]=>0111000=>1000111
[7,1,6,8,2,3,4,5]=>[8,1,2,6,3,7,4,5]=>1011000=>0100111
[3,2,1,7,8,4,5,6]=>[2,3,1,8,4,7,5,6]=>1001100=>0110011
[3,2,8,7,1,4,5,6]=>[2,7,3,1,8,4,5,6]=>1011000=>0100111
[5,8,7,2,1,3,4,6]=>[7,2,8,1,5,3,4,6]=>1110000=>0001111
[1,7,6,8,2,3,4,5]=>[1,8,2,6,3,7,4,5]=>0111000=>1000111
[8,5,7,2,1,3,4,6]=>[7,2,5,1,8,3,4,6]=>1110000=>0001111
[6,4,2,8,3,1,5,7]=>[8,4,2,3,6,1,5,7]=>1101000=>0010111
[5,4,2,3,8,1,6,7]=>[4,2,3,8,5,1,6,7]=>1100100=>0011011
[3,2,5,4,1,8,6,7]=>[2,4,5,3,1,8,6,7]=>1010010=>0101101
[4,5,2,3,1,8,6,7]=>[5,2,3,4,1,8,6,7]=>1100010=>0011101
[6,4,2,1,3,8,5,7]=>[4,2,8,6,1,3,5,7]=>1100010=>0011101
[8,4,2,1,7,3,5,6]=>[4,2,7,1,3,8,5,6]=>1100100=>0011011
[1,5,8,2,7,3,4,6]=>[1,7,2,8,5,3,4,6]=>0110100=>1001011
[7,5,1,2,8,3,4,6]=>[8,5,1,7,2,3,4,6]=>1100100=>0011011
[6,5,1,2,3,8,4,7]=>[5,1,8,6,2,3,4,7]=>1100010=>0011101
[4,6,2,1,3,8,5,7]=>[8,6,2,4,1,3,5,7]=>1100010=>0011101
[3,2,6,1,4,8,5,7]=>[2,8,6,3,1,4,5,7]=>1010010=>0101101
[4,7,2,1,8,3,5,6]=>[8,2,4,1,3,7,5,6]=>1100100=>0011011
[8,6,1,7,2,3,4,5]=>[7,1,6,2,3,8,4,5]=>1101000=>0010111
[1,6,8,7,2,3,4,5]=>[1,7,2,8,3,6,4,5]=>0111000=>1000111
[1,7,8,6,2,3,4,5]=>[1,6,2,8,3,7,4,5]=>0111000=>1000111
[7,8,1,6,2,3,4,5]=>[6,1,8,2,3,7,4,5]=>1101000=>0010111
[3,2,8,1,7,4,5,6]=>[2,7,3,1,4,8,5,6]=>1010100=>0101011
[3,2,1,8,7,4,5,6]=>[2,3,1,7,4,8,5,6]=>1001100=>0110011
[5,1,8,2,7,3,4,6]=>[7,1,2,8,5,3,4,6]=>1010100=>0101011
[6,1,8,7,2,3,4,5]=>[7,1,2,8,3,6,4,5]=>1011000=>0100111
[8,1,7,6,2,3,4,5]=>[6,1,2,7,3,8,4,5]=>1011000=>0100111
[1,8,7,6,2,3,4,5]=>[1,6,2,7,3,8,4,5]=>0111000=>1000111
[6,3,5,1,2,4,8,7]=>[5,3,1,6,2,4,8,7]=>1110001=>0001110
[4,3,5,6,1,2,8,7]=>[6,3,1,5,4,2,8,7]=>1111001=>0000110
[8,3,7,5,2,1,4,6]=>[5,3,2,7,1,8,4,6]=>1111000=>0000111
[6,3,7,5,1,8,4,2]=>[5,3,1,8,4,7,6,2]=>1111010=>0000101
[6,5,2,7,1,8,3,4]=>[8,2,5,1,3,7,6,4]=>1101010=>0010101
[8,5,2,7,4,1,3,6]=>[7,4,5,2,8,1,3,6]=>1101000=>0010111
[2,6,1,5,4,3,8,7]=>[5,4,6,2,1,3,8,7]=>1101001=>0010110
[5,3,1,4,6,2,8,7]=>[3,1,4,6,5,2,8,7]=>1100101=>0011010
[3,1,4,6,5,2,8,7]=>[5,6,4,3,1,2,8,7]=>1011001=>0100110
[5,7,4,6,2,8,3,1]=>[8,6,4,2,7,3,5,1]=>1111010=>0000101
[3,4,7,8,5,2,1,6]=>[5,8,2,7,4,3,1,6]=>1111000=>0000111
[2,1,8,5,7,3,4,6]=>[2,1,7,5,3,8,4,6]=>1011100=>0100011
[5,8,2,4,6,7,3,1]=>[4,7,6,2,3,8,5,1]=>1100110=>0011001
[3,4,8,6,5,7,1,2]=>[5,7,6,1,8,4,3,2]=>1111010=>0000101
[7,5,4,8,1,6,3,2]=>[6,8,4,1,5,3,7,2]=>1111000=>0000111
[5,1,4,6,8,2,7,3]=>[7,8,4,1,2,6,5,3]=>1011100=>0100011
[2,4,6,3,7,5,8,1]=>[8,7,5,6,3,4,2,1]=>1110101=>0001010
[4,1,6,3,8,5,7,2]=>[7,8,5,6,3,4,1,2]=>1010100=>0101011
[3,7,4,2,8,6,5,1]=>[4,2,6,8,5,7,3,1]=>1110100=>0001011
[7,4,1,3,5,8,6,2]=>[4,1,3,5,8,6,7,2]=>1100010=>0011101
[2,1,4,8,3,7,6,5]=>[2,1,7,6,8,4,3,5]=>1011010=>0100101
[8,3,1,2,5,7,6,4]=>[3,1,5,7,6,8,2,4]=>1100010=>0011101
[3,1,8,2,7,6,5,4]=>[6,7,5,8,3,1,2,4]=>1010100=>0101011
[2,3,8,1,6,7,5,4]=>[7,6,5,8,3,2,1,4]=>1110110=>0001001
[4,3,7,2,6,8,5,1]=>[8,6,5,7,3,2,4,1]=>1110110=>0001001
[4,7,2,3,8,5,6,1]=>[8,5,6,7,2,3,4,1]=>1100100=>0011011
[3,8,2,1,7,5,6,4]=>[7,5,6,8,2,3,1,4]=>1100100=>0011011
[2,8,1,3,6,5,7,4]=>[6,5,7,8,2,1,3,4]=>1100100=>0011011
[8,7,1,6,3,4,2,5]=>[6,1,3,7,4,8,2,5]=>1101000=>0010111
[3,8,6,7,2,4,1,5]=>[7,2,6,4,8,3,1,5]=>1111000=>0000111
[4,3,8,7,2,1,6,5]=>[7,3,2,6,8,4,1,5]=>1111000=>0000111
[7,3,5,8,2,4,1,6]=>[8,3,2,5,4,7,1,6]=>1111000=>0000111
[2,3,4,1,8,5,7,6]=>[4,3,2,1,7,8,5,6]=>1110100=>0001011
[4,1,3,2,6,7,8,5]=>[3,4,1,2,8,7,6,5]=>1000111=>0111000
[5,6,2,8,7,4,1,3]=>[7,4,8,2,6,5,1,3]=>1101100=>0010011
[8,1,6,4,5,7,2,3]=>[4,5,7,6,1,2,8,3]=>1010010=>0101101
[5,8,3,6,1,7,2,4]=>[3,7,6,1,8,2,5,4]=>1101010=>0010101
[2,1,8,6,5,7,3,4]=>[2,1,5,7,6,3,8,4]=>1011010=>0100101
[2,1,7,5,3,6,8,4]=>[2,1,5,3,6,8,7,4]=>1011001=>0100110
[7,1,4,2,5,6,8,3]=>[4,1,2,5,6,8,7,3]=>1010001=>0101110
[2,7,4,1,6,5,8,3]=>[4,2,1,6,5,8,7,3]=>1110101=>0001010
[4,6,1,2,8,7,3,5]=>[7,1,4,2,3,8,6,5]=>1100110=>0011001
[2,4,1,5,8,7,6,3]=>[7,6,8,5,4,2,1,3]=>1101110=>0010001
[4,1,2,5,8,6,7,3]=>[6,7,8,5,4,1,2,3]=>1001100=>0110011
[6,4,2,1,5,8,7,3]=>[4,2,5,7,8,6,1,3]=>1100010=>0011101
[8,5,2,4,6,1,7,3]=>[4,6,5,2,7,8,1,3]=>1100100=>0011011
[7,5,3,2,6,8,1,4]=>[3,8,6,5,2,7,1,4]=>1100110=>0011001
[2,1,5,3,6,8,7,4]=>[2,1,7,8,6,5,3,4]=>1010110=>0101001
[7,3,5,4,6,1,8,2]=>[4,6,5,3,1,8,7,2]=>1110101=>0001010
[4,3,1,5,7,6,8,2]=>[3,1,6,8,7,5,4,2]=>1101101=>0010010
[3,1,4,5,6,8,7,2]=>[7,8,6,5,4,3,1,2]=>1011110=>0100001
[4,5,2,6,3,1,8,7]=>[6,2,3,5,4,1,8,7]=>1101001=>0010110
[6,5,2,1,4,3,8,7]=>[5,2,4,6,1,3,8,7]=>1100001=>0011110
[6,5,2,7,4,8,3,1]=>[8,4,5,2,3,7,6,1]=>1101010=>0010101
[8,5,2,7,4,1,6,3]=>[7,4,5,2,6,8,1,3]=>1101000=>0010111
[8,3,7,5,2,1,6,4]=>[5,3,2,7,1,6,8,4]=>1111000=>0000111
[6,3,7,5,2,8,4,1]=>[5,3,2,8,4,7,6,1]=>1111010=>0000101
[3,1,6,5,4,2,8,7]=>[5,4,6,3,1,2,8,7]=>1011001=>0100110
[5,6,3,2,4,1,8,7]=>[3,6,2,4,5,1,8,7]=>1100001=>0011110
[3,6,2,4,1,5,8,7]=>[4,6,2,3,1,5,8,7]=>1100001=>0011110
[2,6,1,3,5,4,8,7]=>[5,6,2,1,3,4,8,7]=>1100001=>0011110
[6,7,2,3,4,8,5,1]=>[8,2,3,4,5,7,6,1]=>1100010=>0011101
[8,7,2,3,4,1,6,5]=>[7,2,3,4,6,8,1,5]=>1100000=>0011111
[5,1,7,3,8,4,6,2]=>[8,3,4,6,7,5,1,2]=>1010100=>0101011
[5,6,3,7,4,8,1,2]=>[3,8,4,7,6,1,5,2]=>1101010=>0010101
[2,1,6,7,4,8,5,3]=>[2,1,8,4,5,7,6,3]=>1011010=>0100101
[2,1,8,7,4,3,6,5]=>[2,1,7,4,6,8,3,5]=>1011000=>0100111
[5,8,3,7,4,2,6,1]=>[3,7,4,6,8,2,5,1]=>1101000=>0010111
[7,8,1,3,5,2,6,4]=>[5,8,1,3,6,7,2,4]=>1100000=>0011111
[5,8,7,3,2,6,1,4]=>[6,7,3,8,2,5,1,4]=>1110000=>0001111
[2,8,6,3,1,5,7,4]=>[6,3,5,7,8,2,1,4]=>1110000=>0001111
[8,1,6,3,2,5,4,7]=>[6,3,5,8,1,2,4,7]=>1010000=>0101111
[2,8,4,1,6,3,7,5]=>[4,2,1,6,3,7,8,5]=>1110100=>0001011
[4,8,1,2,7,6,3,5]=>[6,7,1,4,2,3,8,5]=>1100100=>0011011
[3,8,4,2,5,7,1,6]=>[4,2,5,7,3,1,8,6]=>1110010=>0001101
[6,8,3,5,2,7,4,1]=>[3,5,2,7,4,8,6,1]=>1101010=>0010101
[2,1,5,3,8,7,6,4]=>[2,1,7,6,8,5,3,4]=>1010110=>0101001
[6,5,3,2,8,7,1,4]=>[3,7,5,2,8,6,1,4]=>1100110=>0011001
[3,4,2,8,5,7,6,1]=>[5,7,6,8,4,2,3,1]=>1101010=>0010101
[2,4,1,8,7,6,5,3]=>[6,7,5,8,4,2,1,3]=>1101100=>0010011
[4,3,1,8,6,7,5,2]=>[3,1,7,6,5,8,4,2]=>1101110=>0010001
[3,1,4,8,6,5,7,2]=>[6,5,7,8,4,3,1,2]=>1011100=>0100011
[3,7,5,6,8,4,2,1]=>[8,4,6,5,2,7,3,1]=>1111100=>0000011
[5,6,2,1,8,7,3,4]=>[7,2,8,6,5,1,3,4]=>1100110=>0011001
[4,6,2,5,8,3,7,1]=>[7,8,5,2,3,6,4,1]=>1101100=>0010011
[7,5,2,6,3,8,1,4]=>[8,6,2,3,5,1,7,4]=>1101010=>0010101
[4,1,2,3,6,8,7,5]=>[4,1,2,3,7,8,6,5]=>1000110=>0111001
[2,4,3,1,8,5,6,7]=>[3,4,2,1,8,5,6,7]=>1100100=>0011011
[7,5,2,8,3,4,6,1]=>[8,2,3,5,4,6,7,1]=>1101000=>0010111
[5,6,2,8,4,3,1,7]=>[8,4,6,2,3,5,1,7]=>1101000=>0010111
[8,7,2,1,4,5,6,3]=>[7,2,4,5,6,8,1,3]=>1100000=>0011111
[7,1,8,5,4,3,6,2]=>[5,4,8,3,6,7,1,2]=>1011000=>0100111
[2,7,8,4,5,3,6,1]=>[4,5,8,3,6,7,2,1]=>1110000=>0001111
[5,7,3,8,1,4,6,2]=>[3,8,1,6,7,4,5,2]=>1101000=>0010111
[2,1,7,8,5,4,6,3]=>[2,1,5,8,4,6,7,3]=>1011000=>0100111
[2,1,5,8,4,6,3,7]=>[2,1,6,8,4,5,3,7]=>1011000=>0100111
[6,5,3,8,4,1,2,7]=>[3,8,4,5,1,6,2,7]=>1101000=>0010111
[7,5,8,4,3,6,2,1]=>[4,6,8,3,5,2,7,1]=>1110000=>0001111
[2,4,8,3,5,6,1,7]=>[5,6,8,3,4,2,1,7]=>1110000=>0001111
[4,1,8,3,6,5,2,7]=>[6,5,8,3,4,1,2,7]=>1010100=>0101011
[3,1,8,2,4,7,6,5]=>[7,6,8,3,1,2,4,5]=>1010010=>0101101
[2,3,8,1,4,6,7,5]=>[6,7,8,3,2,1,4,5]=>1110000=>0001111
[4,3,8,2,5,1,7,6]=>[5,7,8,3,2,4,1,6]=>1110000=>0001111
[6,3,8,4,2,5,7,1]=>[4,7,8,3,2,5,6,1]=>1110000=>0001111
[7,4,3,8,2,5,1,6]=>[3,8,4,2,5,7,1,6]=>1101000=>0010111
[2,1,4,8,3,5,7,6]=>[2,1,7,8,4,3,5,6]=>1011000=>0100111
[6,8,2,4,3,5,1,7]=>[4,8,2,3,5,6,1,7]=>1100000=>0011111
[4,8,2,3,5,1,6,7]=>[5,8,2,3,4,1,6,7]=>1100000=>0011111
[3,8,2,1,4,6,5,7]=>[6,8,2,3,1,4,5,7]=>1100000=>0011111
[2,8,1,3,4,5,7,6]=>[7,8,2,1,3,4,5,6]=>1100000=>0011111
[2,8,4,1,6,5,3,7]=>[4,2,1,6,5,8,3,7]=>1110100=>0001011
[2,8,4,1,6,5,7,3]=>[4,2,1,6,5,7,8,3]=>1110100=>0001011
[2,8,7,6,1,4,3,5]=>[6,2,1,7,4,8,3,5]=>1111000=>0000111
[7,5,8,6,1,4,2,3]=>[6,1,8,4,5,2,7,3]=>1111000=>0000111
[3,5,7,2,4,1,6,8]=>[7,2,4,5,3,1,6,8]=>1110000=>0001111
[7,5,8,2,4,1,6,3]=>[8,2,4,5,1,6,7,3]=>1110000=>0001111
[2,8,5,3,4,1,7,6]=>[5,3,4,7,8,2,1,6]=>1110000=>0001111
[2,8,5,3,6,1,7,4]=>[6,5,3,7,8,2,1,4]=>1110100=>0001011
[2,8,5,6,7,4,1,3]=>[7,4,6,5,2,1,8,3]=>1111100=>0000011
[2,8,5,3,4,6,1,7]=>[5,3,4,6,8,2,1,7]=>1110000=>0001111
[2,8,5,3,4,6,7,1]=>[5,3,4,6,7,8,2,1]=>1110000=>0001111
[3,5,7,2,4,6,1,8]=>[6,7,2,4,5,3,1,8]=>1110000=>0001111
[7,5,8,2,4,6,3,1]=>[6,8,2,4,5,3,7,1]=>1110000=>0001111
[7,5,8,6,1,4,3,2]=>[6,1,8,4,5,3,7,2]=>1111000=>0000111
[6,5,8,2,1,3,7,4]=>[7,8,2,5,1,6,3,4]=>1110000=>0001111
[3,5,6,2,1,8,7,4]=>[7,8,6,2,5,3,1,4]=>1110010=>0001101
[3,5,7,6,1,4,8,2]=>[6,1,8,7,4,5,3,2]=>1111001=>0000110
[3,5,7,2,4,1,8,6]=>[8,7,2,4,5,3,1,6]=>1110001=>0001110
[3,5,7,2,4,6,8,1]=>[6,8,7,2,4,5,3,1]=>1110001=>0001110
[4,5,2,6,3,1,7,8]=>[6,2,3,5,4,1,7,8]=>1101000=>0010111
[4,1,2,3,7,6,8,5]=>[4,1,2,3,6,8,7,5]=>1000101=>0111010
[6,5,2,7,3,4,8,1]=>[8,7,2,3,5,4,6,1]=>1101001=>0010110
[5,1,6,7,4,3,8,2]=>[8,7,4,6,3,5,1,2]=>1011001=>0100110
[5,1,6,8,7,3,4,2]=>[7,3,8,4,6,5,1,2]=>1011100=>0100011
[6,5,2,8,3,7,4,1]=>[7,2,3,5,4,8,6,1]=>1101010=>0010101
[4,1,2,3,8,7,5,6]=>[4,1,2,3,7,5,8,6]=>1000110=>0111001
[4,1,2,3,8,6,5,7]=>[4,1,2,3,6,8,5,7]=>1000100=>0111011
[4,1,2,3,8,6,7,5]=>[4,1,2,3,6,7,8,5]=>1000100=>0111011
[4,1,2,3,7,6,5,8]=>[4,1,2,3,6,7,5,8]=>1000100=>0111011
[4,1,2,3,8,5,7,6]=>[4,1,2,3,7,8,5,6]=>1000100=>0111011
[6,1,2,8,4,5,7,3]=>[7,8,4,5,6,1,2,3]=>1001000=>0110111
[5,6,8,2,3,1,7,4]=>[7,8,2,6,3,5,1,4]=>1110000=>0001111
[7,5,2,8,3,4,1,6]=>[8,2,3,5,4,7,1,6]=>1101000=>0010111
[6,5,2,8,3,7,1,4]=>[7,2,3,5,1,8,6,4]=>1101010=>0010101
[6,5,2,7,3,4,1,8]=>[7,2,3,5,4,6,1,8]=>1101000=>0010111
[5,1,6,8,7,3,2,4]=>[7,3,8,1,2,6,5,4]=>1011100=>0100011
[7,1,6,8,4,3,2,5]=>[8,4,6,3,7,1,2,5]=>1011000=>0100111
[5,7,8,6,3,4,2,1]=>[6,3,8,4,7,2,5,1]=>1111000=>0000111
[4,1,8,3,6,5,7,2]=>[6,5,7,8,3,4,1,2]=>1010100=>0101011
[4,1,8,3,6,2,7,5]=>[6,3,4,1,2,7,8,5]=>1010100=>0101011
[3,1,4,8,6,2,7,5]=>[6,4,3,1,2,7,8,5]=>1011100=>0100011
[3,1,4,8,6,5,2,7]=>[6,5,8,4,3,1,2,7]=>1011100=>0100011
[4,1,6,5,7,3,2,8]=>[7,5,3,6,4,1,2,8]=>1011100=>0100011
[4,5,2,6,3,7,1,8]=>[7,6,2,3,5,4,1,8]=>1101010=>0010101
[4,5,2,7,3,8,1,6]=>[8,2,3,5,4,1,7,6]=>1101010=>0010101
[3,5,6,2,4,8,1,7]=>[8,6,2,4,5,3,1,7]=>1110010=>0001101
[6,1,2,5,8,4,7,3]=>[7,8,5,4,6,1,2,3]=>1001100=>0110011
[4,1,2,3,5,8,7,6]=>[4,1,2,3,5,7,8,6]=>1000010=>0111101
[4,1,2,3,7,8,6,5]=>[4,1,2,3,8,6,7,5]=>1000110=>0111001
[4,5,2,7,3,8,6,1]=>[8,6,7,2,3,5,4,1]=>1101010=>0010101
[4,1,2,6,8,5,7,3]=>[7,8,5,6,4,1,2,3]=>1001100=>0110011
[4,1,2,5,6,8,7,3]=>[7,8,6,5,4,1,2,3]=>1001110=>0110001
[4,5,2,6,3,7,8,1]=>[8,7,6,2,3,5,4,1]=>1101011=>0010100
[7,8,4,2,1,5,3,6]=>[4,2,8,1,5,7,3,6]=>1110000=>0001111
[7,8,2,1,6,5,3,4]=>[6,5,8,2,7,1,3,4]=>1100100=>0011011
[6,4,1,2,5,7,3,8]=>[4,1,5,7,6,2,3,8]=>1100010=>0011101
[2,4,8,1,5,7,3,6]=>[5,7,2,1,4,3,8,6]=>1110010=>0001101
[7,8,3,4,5,1,6,2]=>[3,4,5,8,1,6,7,2]=>1100000=>0011111
[7,8,4,1,2,3,6,5]=>[4,1,8,2,6,7,3,5]=>1110000=>0001111
[7,8,3,6,5,4,1,2]=>[3,5,6,4,8,1,7,2]=>1101000=>0010111
[7,8,2,1,5,3,4,6]=>[5,8,2,7,1,3,4,6]=>1100000=>0011111
[7,8,2,6,4,1,3,5]=>[6,4,8,2,7,1,3,5]=>1101000=>0010111
[7,8,2,5,6,4,1,3]=>[6,5,4,8,2,7,1,3]=>1101100=>0010011
[6,2,1,7,5,4,3,8]=>[2,5,7,4,6,1,3,8]=>1001000=>0110111
[2,1,8,7,5,4,3,6]=>[2,1,5,7,4,8,3,6]=>1011000=>0100111
[1,3,8,2,6,4,7,5]=>[1,6,3,2,4,7,8,5]=>0110100=>1001011
[5,3,7,1,6,4,8,2]=>[6,3,1,4,8,7,5,2]=>1110101=>0001010
[6,1,2,5,8,7,4,3]=>[7,5,4,8,6,1,2,3]=>1001110=>0110001
[6,3,1,8,4,2,7,5]=>[3,1,7,8,4,6,2,5]=>1101000=>0010111
[6,4,2,1,5,3,8,7]=>[4,2,5,6,1,3,8,7]=>1100001=>0011110
[4,3,8,7,5,6,1,2]=>[5,6,7,3,1,8,4,2]=>1111000=>0000111
[2,1,7,5,6,8,4,3]=>[2,1,8,6,5,4,7,3]=>1011110=>0100001
[3,7,2,8,6,4,1,5]=>[6,4,8,2,3,1,7,5]=>1101100=>0010011
[1,8,5,7,3,6,4,2]=>[1,6,7,3,5,4,8,2]=>0111000=>1000111
[2,7,5,8,3,6,1,4]=>[6,8,3,5,2,1,7,4]=>1111000=>0000111
[1,5,6,8,2,4,7,3]=>[1,7,8,2,6,4,5,3]=>0111000=>1000111
[2,6,8,5,3,1,4,7]=>[5,3,8,2,1,6,4,7]=>1111000=>0000111
[2,6,1,4,7,3,5,8]=>[4,7,2,1,3,6,5,8]=>1100100=>0011011
[5,6,7,3,8,4,1,2]=>[8,3,4,7,1,6,5,2]=>1110100=>0001011
[5,2,8,1,4,7,3,6]=>[2,7,1,4,5,3,8,6]=>1010010=>0101101
[4,6,7,5,2,1,3,8]=>[5,2,7,1,6,4,3,8]=>1111000=>0000111
[4,5,6,7,2,8,1,3]=>[8,2,7,6,1,5,4,3]=>1111010=>0000101
[4,5,7,6,1,8,3,2]=>[8,6,1,7,3,5,4,2]=>1111010=>0000101
[1,5,8,6,2,7,3,4]=>[1,7,6,2,8,3,5,4]=>0111010=>1000101
[1,6,5,8,3,2,7,4]=>[1,7,8,3,5,2,6,4]=>0111000=>1000111
[5,7,1,4,2,3,8,6]=>[4,8,7,1,5,2,3,6]=>1100001=>0011110
[5,7,6,4,3,8,1,2]=>[4,8,6,3,7,1,5,2]=>1110010=>0001101
[6,3,4,5,8,7,1,2]=>[7,5,4,3,1,8,6,2]=>1111110=>0000001
[6,2,4,1,8,3,7,5]=>[2,4,1,7,8,3,6,5]=>1010100=>0101011
[6,1,3,4,5,8,7,2]=>[3,4,5,7,8,6,1,2]=>1000010=>0111101
[5,1,4,2,7,6,8,3]=>[4,1,2,6,8,7,5,3]=>1010101=>0101010
[1,6,2,4,7,8,3,5]=>[1,4,8,2,3,7,6,5]=>0100110=>1011001
[5,7,2,4,1,6,3,8]=>[4,6,7,2,5,1,3,8]=>1100000=>0011111
[6,7,5,8,1,4,3,2]=>[8,1,5,4,7,3,6,2]=>1111000=>0000111
[5,8,7,6,3,4,1,2]=>[6,3,7,4,8,1,5,2]=>1111000=>0000111
[5,8,7,6,2,3,1,4]=>[6,2,7,3,8,1,5,4]=>1111000=>0000111
[4,8,2,1,5,6,3,7]=>[5,6,8,2,4,1,3,7]=>1100000=>0011111
[2,1,8,7,6,5,3,4]=>[2,1,6,5,7,3,8,4]=>1011100=>0100011
[3,1,4,7,8,2,6,5]=>[8,4,3,1,2,6,7,5]=>1011100=>0100011
[3,1,7,4,5,6,8,2]=>[4,5,6,8,7,3,1,2]=>1010001=>0101110
[4,2,7,1,6,3,8,5]=>[2,6,1,4,3,8,7,5]=>1010101=>0101010
[4,8,6,3,5,7,1,2]=>[5,7,6,3,8,1,4,2]=>1110010=>0001101
[3,8,6,5,2,4,1,7]=>[5,2,6,4,8,3,1,7]=>1111000=>0000111
[5,2,8,7,1,6,4,3]=>[2,6,7,1,8,4,5,3]=>1011000=>0100111
[1,6,8,7,5,2,4,3]=>[1,5,7,2,8,4,6,3]=>0111000=>1000111
[3,7,6,8,5,2,1,4]=>[5,8,2,6,3,1,7,4]=>1111000=>0000111
[3,7,8,5,1,2,4,6]=>[5,1,8,3,2,7,4,6]=>1111000=>0000111
[4,1,8,6,2,3,5,7]=>[6,1,2,8,4,3,5,7]=>1011000=>0100111
[4,7,8,6,3,5,1,2]=>[6,3,5,8,1,7,4,2]=>1111000=>0000111
[3,8,7,6,5,4,1,2]=>[5,6,4,7,1,8,3,2]=>1111000=>0000111
[2,1,7,6,5,3,4,8]=>[2,1,5,6,3,7,4,8]=>1011000=>0100111
[2,8,7,5,1,4,3,6]=>[5,2,1,7,4,8,3,6]=>1111000=>0000111
[2,8,6,7,5,1,3,4]=>[5,7,2,1,6,3,8,4]=>1111000=>0000111
[2,7,8,6,5,4,1,3]=>[5,6,4,8,2,1,7,3]=>1111000=>0000111
[6,3,1,2,7,4,8,5]=>[3,1,8,7,2,4,6,5]=>1100101=>0011010
[6,4,2,7,1,3,8,5]=>[8,7,4,2,6,1,3,5]=>1101001=>0010110
[7,4,2,5,1,3,8,6]=>[5,4,2,8,7,1,3,6]=>1101001=>0010110
[7,5,3,6,1,8,2,4]=>[3,8,6,1,5,2,7,4]=>1101010=>0010101
[8,5,3,6,1,7,2,4]=>[3,7,6,1,5,2,8,4]=>1101010=>0010101
[8,3,6,2,4,7,1,5]=>[7,6,3,2,4,8,1,5]=>1110010=>0001101
[7,3,6,2,4,8,1,5]=>[8,6,3,2,4,7,1,5]=>1110010=>0001101
[4,3,7,1,2,5,8,6]=>[8,7,3,1,4,2,5,6]=>1110001=>0001110
[3,6,2,7,1,4,8,5]=>[8,7,2,3,1,6,4,5]=>1101001=>0010110
[5,3,6,7,1,2,8,4]=>[8,7,3,1,6,2,5,4]=>1111001=>0000110
[6,3,7,4,1,2,8,5]=>[4,8,7,3,1,6,2,5]=>1110001=>0001110
[4,7,1,5,2,3,8,6]=>[5,1,8,7,4,2,3,6]=>1101001=>0010110
[8,6,4,2,3,7,1,5]=>[4,2,7,6,3,8,1,5]=>1110010=>0001101
[4,7,6,3,8,1,2,5]=>[8,3,6,1,4,2,7,5]=>1110100=>0001011
[5,7,4,2,3,8,1,6]=>[4,2,8,3,5,1,7,6]=>1110010=>0001101
[3,7,6,1,4,8,2,5]=>[8,6,1,4,7,3,2,5]=>1110010=>0001101
[5,7,2,6,1,8,3,4]=>[8,6,2,7,1,3,5,4]=>1101010=>0010101
[6,4,7,5,2,8,1,3]=>[5,2,8,4,1,7,6,3]=>1111010=>0000101
[7,4,8,5,2,6,1,3]=>[5,2,6,8,4,1,7,3]=>1111000=>0000111
[3,8,6,1,2,7,4,5]=>[7,6,1,8,3,2,4,5]=>1110010=>0001101
[3,8,6,2,4,7,1,5]=>[7,6,2,4,8,3,1,5]=>1110010=>0001101
[6,8,5,3,7,1,2,4]=>[7,5,3,8,1,6,2,4]=>1110100=>0001011
[2,8,5,7,1,3,4,6]=>[7,2,1,5,3,8,4,6]=>1111000=>0000111
[4,8,6,2,7,1,3,5]=>[7,2,6,1,4,3,8,5]=>1110100=>0001011
[7,3,8,5,6,1,2,4]=>[6,5,3,1,8,2,7,4]=>1111100=>0000011
[6,3,7,5,8,1,2,4]=>[8,5,3,1,7,2,6,4]=>1111100=>0000011
[2,7,6,4,8,1,3,5]=>[4,8,2,1,6,3,7,5]=>1110100=>0001011
[2,5,7,4,8,1,3,6]=>[4,8,2,1,7,5,3,6]=>1110100=>0001011
[5,4,6,7,2,8,1,3]=>[8,2,7,6,4,1,5,3]=>1111010=>0000101
[4,6,3,7,1,8,2,5]=>[3,8,1,7,6,4,2,5]=>1101010=>0010101
[3,5,7,1,4,8,2,6]=>[8,1,4,5,3,2,7,6]=>1110010=>0001101
[8,4,6,3,7,1,2,5]=>[7,3,4,1,6,2,8,5]=>1110100=>0001011
[8,4,1,6,7,2,3,5]=>[7,4,1,6,2,3,8,5]=>1101100=>0010011
[7,4,1,6,8,2,3,5]=>[8,4,1,6,2,3,7,5]=>1101100=>0010011
[5,4,1,7,8,2,3,6]=>[8,4,1,7,5,2,3,6]=>1101100=>0010011
[6,5,3,7,1,8,2,4]=>[3,8,1,5,2,7,6,4]=>1101010=>0010101
[5,3,6,4,7,8,1,2]=>[4,8,3,1,7,6,5,2]=>1110110=>0001001
[6,3,7,4,8,5,1,2]=>[4,8,5,7,3,1,6,2]=>1110100=>0001011
[4,7,1,5,8,6,2,3]=>[6,8,5,1,7,4,2,3]=>1101100=>0010011
[7,5,1,2,8,6,3,4]=>[6,8,5,1,7,2,3,4]=>1100100=>0011011
[7,4,1,8,6,2,3,5]=>[6,4,1,8,2,3,7,5]=>1101100=>0010011
[8,6,1,7,5,2,3,4]=>[5,7,1,6,2,3,8,4]=>1101000=>0010111
[5,7,2,8,1,6,3,4]=>[6,8,2,7,1,3,5,4]=>1101000=>0010111
[2,4,8,7,1,3,5,6]=>[7,2,1,8,4,3,5,6]=>1111000=>0000111
[4,3,8,7,1,2,5,6]=>[7,3,1,8,4,2,5,6]=>1111000=>0000111
[8,4,7,6,1,2,3,5]=>[6,1,7,4,2,8,3,5]=>1111000=>0000111
[5,4,8,7,1,2,3,6]=>[7,1,8,4,2,5,3,6]=>1111000=>0000111
[3,5,8,7,1,2,4,6]=>[7,1,8,3,2,5,4,6]=>1111000=>0000111
[4,6,8,2,7,1,3,5]=>[7,2,8,1,4,3,6,5]=>1110100=>0001011
[6,8,4,7,5,1,2,3]=>[5,7,4,1,8,2,6,3]=>1111000=>0000111
[2,8,7,6,1,3,4,5]=>[6,2,1,7,3,8,4,5]=>1111000=>0000111
[3,8,7,6,1,2,4,5]=>[6,1,7,3,2,8,4,5]=>1111000=>0000111
[4,8,7,6,1,2,3,5]=>[6,1,7,2,8,4,3,5]=>1111000=>0000111
[5,6,3,1,4,2,8,7]=>[3,6,1,4,5,2,8,7]=>1100001=>0011110
[7,5,3,8,2,1,6,4]=>[3,8,2,5,1,6,7,4]=>1101000=>0010111
[6,7,1,4,5,8,2,3]=>[4,5,8,1,7,6,2,3]=>1100010=>0011101
[2,1,7,8,5,3,6,4]=>[2,1,5,8,3,6,7,4]=>1011000=>0100111
[8,7,1,4,5,3,2,6]=>[4,5,7,1,3,8,2,6]=>1100000=>0011111
[2,7,8,4,1,6,5,3]=>[4,6,8,2,1,5,7,3]=>1110000=>0001111
[7,5,1,4,8,6,3,2]=>[4,6,8,5,1,3,7,2]=>1100100=>0011011
[6,5,3,1,8,4,7,2]=>[3,7,8,5,1,4,6,2]=>1100100=>0011011
[6,4,3,8,1,5,7,2]=>[3,7,8,4,1,5,6,2]=>1101000=>0010111
[8,6,3,1,2,5,7,4]=>[3,6,1,5,7,8,2,4]=>1100000=>0011111
[7,3,8,4,1,6,5,2]=>[4,6,8,3,1,5,7,2]=>1110000=>0001111
[2,3,4,5,6,7,8,1,9]=>[8,7,6,5,4,3,2,1,9]=>11111110=>00000001
[2,3,4,5,6,8,9,1,7]=>[9,6,5,4,3,2,1,8,7]=>11111110=>00000001
[2,3,4,6,7,8,9,1,5]=>[9,4,3,2,1,8,7,6,5]=>11111110=>00000001
[2,4,5,6,7,8,9,1,3]=>[9,2,1,8,7,6,5,4,3]=>11111110=>00000001
[3,4,5,6,7,8,9,1,2]=>[9,1,8,7,6,5,4,3,2]=>11111110=>00000001
[2,3,4,5,6,7,8,9,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111=>000000000
[2,3,4,5,6,7,8,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110=>000000001
[2,3,4,5,6,7,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>11111100=>00000011
[2,3,4,5,6,7,8,10,1,9]=>[10,8,7,6,5,4,3,2,1,9]=>111111110=>000000001
[2,3,4,5,6,7,9,10,1,8]=>[10,7,6,5,4,3,2,1,9,8]=>111111110=>000000001
[1,4,5,6,7,8,9,2,3]=>[1,9,2,8,7,6,5,4,3]=>01111110=>10000001
[2,4,5,6,7,8,9,10,1,3]=>[10,2,1,9,8,7,6,5,4,3]=>111111110=>000000001
[3,4,5,6,7,8,9,10,1,2]=>[10,1,9,8,7,6,5,4,3,2]=>111111110=>000000001
[5,3,2,7,4,6,8,1]=>[3,2,6,8,7,4,5,1]=>1101001=>0010110
[6,3,2,5,1,8,4,7]=>[3,2,5,1,8,6,4,7]=>1101010=>0010101
[7,2,6,3,4,5,8,1]=>[2,6,3,4,5,8,7,1]=>1010001=>0101110
[6,2,7,3,4,5,8,1]=>[2,8,7,3,4,5,6,1]=>1010001=>0101110
[3,6,2,7,4,5,8,1]=>[8,7,4,5,6,2,3,1]=>1101001=>0010110
[5,4,7,6,2,3,8,1]=>[6,2,8,7,4,3,5,1]=>1111001=>0000110
[3,7,6,2,4,5,8,1]=>[6,2,4,5,8,7,3,1]=>1110001=>0001110
[2,7,6,3,4,5,8,1]=>[6,3,4,5,8,7,2,1]=>1110001=>0001110
[6,5,3,1,2,8,4,7]=>[3,5,1,8,6,2,4,7]=>1100010=>0011101
[7,5,2,1,8,3,4,6]=>[8,5,2,7,1,3,4,6]=>1100100=>0011011
[1,6,3,2,8,4,5,7]=>[1,3,8,2,4,6,5,7]=>0100100=>1011011
[5,7,3,1,2,8,4,6]=>[3,8,1,5,2,4,7,6]=>1100010=>0011101
[5,6,2,3,1,8,4,7]=>[8,6,2,3,5,1,4,7]=>1100010=>0011101
[4,2,6,5,1,8,3,7]=>[2,5,1,8,6,4,3,7]=>1011010=>0100101
[5,4,8,6,2,7,1,3]=>[7,6,2,8,4,1,5,3]=>1111010=>0000101
[6,8,3,5,2,7,1,4]=>[3,5,2,7,1,8,6,4]=>1101010=>0010101
[7,8,5,2,3,6,1,4]=>[5,2,6,8,3,7,1,4]=>1110000=>0001111
[1,8,2,7,3,4,5,6]=>[1,7,2,3,8,4,5,6]=>0101000=>1010111
[3,8,6,1,7,2,4,5]=>[7,1,6,3,2,4,8,5]=>1110100=>0001011
[4,2,8,3,7,1,5,6]=>[2,7,3,4,1,8,5,6]=>1010100=>0101011
[4,1,7,5,8,2,3,6]=>[8,5,1,2,7,4,3,6]=>1011100=>0100011
[8,1,2,7,3,4,5,6]=>[7,1,2,3,8,4,5,6]=>1001000=>0110111
[3,6,2,7,1,8,4,5]=>[8,2,3,1,7,6,4,5]=>1101010=>0010101
[6,3,7,1,2,8,4,5]=>[8,3,1,7,6,2,4,5]=>1110010=>0001101
[7,2,6,1,8,3,4,5]=>[2,8,1,6,3,4,7,5]=>1010100=>0101011
[8,2,6,1,7,3,4,5]=>[2,7,1,6,3,4,8,5]=>1010100=>0101011
[7,3,1,5,8,2,4,6]=>[3,1,8,5,2,7,4,6]=>1101100=>0010011
[3,2,1,5,8,4,6,7]=>[2,3,1,8,5,4,6,7]=>1001100=>0110011
[1,5,3,4,6,8,2,7]=>[1,3,4,8,6,5,2,7]=>0100110=>1011001
[5,4,6,3,8,7,1,2]=>[7,3,4,1,8,6,5,2]=>1110110=>0001001
[3,6,4,5,8,7,1,2]=>[7,5,4,1,8,6,3,2]=>1111110=>0000001
[6,5,3,4,8,7,1,2]=>[3,4,7,5,1,8,6,2]=>1100110=>0011001
[5,3,2,8,7,1,4,6]=>[3,2,7,1,8,5,4,6]=>1101100=>0010011
[5,3,1,8,7,2,4,6]=>[3,1,7,2,8,5,4,6]=>1101100=>0010011
[8,5,3,7,6,1,2,4]=>[3,6,1,7,5,2,8,4]=>1101100=>0010011
[6,1,8,3,7,2,4,5]=>[7,3,8,1,2,4,6,5]=>1010100=>0101011
[7,6,8,2,3,5,1,4]=>[8,2,5,6,3,7,1,4]=>1110000=>0001111
[6,7,3,8,2,5,1,4]=>[3,8,2,5,7,1,6,4]=>1101000=>0010111
[5,4,7,8,2,6,1,3]=>[6,8,2,7,4,1,5,3]=>1111000=>0000111
[3,6,2,8,7,1,4,5]=>[7,2,3,1,8,4,6,5]=>1101100=>0010011
[3,7,8,1,6,2,4,5]=>[6,1,8,3,2,4,7,5]=>1110100=>0001011
[2,3,8,7,1,4,5,6]=>[7,3,2,1,8,4,5,6]=>1111000=>0000111
[7,2,8,6,1,3,4,5]=>[2,6,1,8,3,7,4,5]=>1011000=>0100111
[2,1,8,7,3,4,5,6]=>[2,1,7,3,8,4,5,6]=>1011000=>0100111
[8,2,7,6,1,3,4,5]=>[2,6,1,7,3,8,4,5]=>1011000=>0100111
[1,2,8,7,3,4,5,6]=>[1,2,7,3,8,4,5,6]=>0011000=>1100111
[1,3,8,7,2,4,5,6]=>[1,7,3,2,8,4,5,6]=>0111000=>1000111
[1,7,8,3,6,2,4,5]=>[1,6,3,8,2,4,7,5]=>0110100=>1001011
[5,4,8,7,6,1,2,3]=>[6,1,7,4,2,8,5,3]=>1111100=>0000011
[6,8,3,7,5,1,2,4]=>[3,5,7,1,8,2,6,4]=>1101000=>0010111
[7,8,6,2,5,1,3,4]=>[5,6,2,8,1,7,3,4]=>1110000=>0001111
[8,1,6,7,3,2,4,5]=>[7,3,6,1,2,8,4,5]=>1011000=>0100111
[8,1,5,3,7,2,4,6]=>[7,5,3,8,1,2,4,6]=>1010100=>0101011
[8,1,5,3,6,2,4,7]=>[6,5,3,8,1,2,4,7]=>1010100=>0101011
[7,4,1,3,2,6,5,8]=>[4,1,3,6,7,2,5,8]=>1100000=>0011111
[8,1,4,3,2,6,5,7]=>[4,3,6,8,1,2,5,7]=>1010000=>0101111
[8,1,4,3,2,7,5,6]=>[4,3,7,1,2,5,8,6]=>1010010=>0101101
[8,1,4,3,2,7,6,5]=>[4,3,7,6,8,1,2,5]=>1010010=>0101101
[8,1,5,4,6,7,2,3]=>[4,7,6,5,1,2,8,3]=>1010110=>0101001
[8,1,4,3,2,6,7,5]=>[4,3,6,7,8,1,2,5]=>1010000=>0101111
[8,1,4,3,2,5,7,6]=>[4,3,7,8,1,2,5,6]=>1010000=>0101111
[7,4,8,3,2,5,6,1]=>[8,3,4,2,5,6,7,1]=>1110000=>0001111
[6,4,3,8,2,5,7,1]=>[3,7,8,4,2,5,6,1]=>1101000=>0010111
[6,4,3,1,2,5,8,7]=>[3,4,1,6,2,5,8,7]=>1100001=>0011110
[7,5,8,3,6,2,1,4]=>[6,3,8,5,2,7,1,4]=>1110100=>0001011
[7,4,8,3,2,6,1,5]=>[6,8,3,4,2,7,1,5]=>1110000=>0001111
[6,5,4,8,7,1,2,3]=>[7,4,1,8,5,2,6,3]=>1111100=>0000011
[6,5,4,1,7,8,2,3]=>[4,1,8,5,2,7,6,3]=>1110110=>0001001
[6,5,3,1,7,2,8,4]=>[3,8,7,5,1,6,2,4]=>1100101=>0011010
[6,4,3,1,2,7,8,5]=>[3,4,1,8,7,6,2,5]=>1100011=>0011100
[5,4,3,2,1,8,6,7]=>[3,4,2,5,1,8,6,7]=>1100010=>0011101
[6,5,3,1,8,2,7,4]=>[3,7,8,5,1,6,2,4]=>1100100=>0011011
[6,5,4,1,8,7,2,3]=>[4,1,7,5,2,8,6,3]=>1110110=>0001001
[6,4,3,8,2,7,5,1]=>[3,7,4,2,5,8,6,1]=>1101010=>0010101
[6,5,3,1,7,2,4,8]=>[3,7,5,1,6,2,4,8]=>1100100=>0011011
[7,5,1,3,8,2,4,6]=>[8,5,1,3,7,2,4,6]=>1100100=>0011011
[7,6,8,1,4,5,2,3]=>[8,1,4,5,6,2,7,3]=>1110000=>0001111
[7,6,8,1,3,2,5,4]=>[8,1,6,3,5,7,2,4]=>1110000=>0001111
[6,5,3,7,8,2,4,1]=>[3,8,2,7,5,4,6,1]=>1101100=>0010011
[6,4,3,7,2,1,5,8]=>[3,7,4,2,6,1,5,8]=>1101000=>0010111
[7,4,8,3,2,1,6,5]=>[8,3,4,2,6,7,1,5]=>1110000=>0001111
[7,5,8,3,1,2,6,4]=>[8,3,5,1,6,7,2,4]=>1110000=>0001111
[7,5,8,4,1,6,2,3]=>[4,6,8,1,5,2,7,3]=>1110000=>0001111
[6,5,4,8,1,7,2,3]=>[7,4,1,5,2,8,6,3]=>1111010=>0000101
[6,5,3,8,1,2,7,4]=>[3,7,8,1,5,2,6,4]=>1101000=>0010111
[6,4,3,7,2,1,8,5]=>[3,8,7,4,2,6,1,5]=>1101001=>0010110
[6,5,4,7,1,8,2,3]=>[8,4,1,5,2,7,6,3]=>1111010=>0000101
[5,4,3,2,7,8,1,6]=>[3,4,2,8,5,1,7,6]=>1100110=>0011001
[5,6,2,1,3,4,8,7]=>[6,2,5,1,3,4,8,7]=>1100001=>0011110
[5,3,7,8,2,1,4,6]=>[8,3,2,7,1,5,4,6]=>1111000=>0000111
[7,6,1,2,5,8,3,4]=>[5,8,6,1,7,2,3,4]=>1100010=>0011101
[7,8,1,2,5,4,6,3]=>[5,8,1,4,6,7,2,3]=>1100000=>0011111
[2,6,8,3,1,4,7,5]=>[7,8,3,6,2,1,4,5]=>1110000=>0001111
[6,1,8,3,2,4,5,7]=>[8,3,6,1,2,4,5,7]=>1010000=>0101111
[8,4,1,3,7,6,2,5]=>[4,1,3,6,7,2,8,5]=>1100100=>0011011
[5,8,7,4,2,1,6,3]=>[4,7,2,6,8,1,5,3]=>1110000=>0001111
[6,5,2,1,8,7,4,3]=>[7,5,2,4,8,6,1,3]=>1100110=>0011001
[3,4,7,1,8,2,6,5]=>[8,1,4,3,2,6,7,5]=>1110100=>0001011
[1,8,2,4,3,5,6,7]=>[1,4,8,2,3,5,6,7]=>0100000=>1011111
[1,7,2,4,3,5,6,8]=>[1,4,7,2,3,5,6,8]=>0100000=>1011111
[1,6,2,4,3,5,7,8]=>[1,4,6,2,3,5,7,8]=>0100000=>1011111
[1,5,2,4,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>0100000=>1011111
[1,6,2,5,3,4,7,8]=>[1,5,2,3,6,4,7,8]=>0101000=>1010111
[1,7,2,5,3,4,6,8]=>[1,5,2,3,7,4,6,8]=>0101000=>1010111
[1,8,2,5,3,4,6,7]=>[1,5,2,3,8,4,6,7]=>0101000=>1010111
[1,8,2,6,3,4,5,7]=>[1,6,2,3,8,4,5,7]=>0101000=>1010111
[1,7,2,6,3,4,5,8]=>[1,6,2,3,7,4,5,8]=>0101000=>1010111
[1,8,2,7,3,5,4,6]=>[1,7,2,3,5,8,4,6]=>0101000=>1010111
[1,7,2,8,3,5,4,6]=>[1,8,2,3,5,7,4,6]=>0101000=>1010111
[1,6,2,8,3,5,4,7]=>[1,8,2,3,5,6,4,7]=>0101000=>1010111
[1,5,2,8,3,6,4,7]=>[1,6,8,2,3,5,4,7]=>0101000=>1010111
[1,3,2,8,4,6,5,7]=>[1,3,2,6,8,4,5,7]=>0101000=>1010111
[1,2,3,8,4,6,5,7]=>[1,2,3,6,8,4,5,7]=>0001000=>1110111
[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,4,5,8]=>0001000=>1110111
[1,3,2,7,4,6,5,8]=>[1,3,2,6,7,4,5,8]=>0101000=>1010111
[1,5,2,7,3,6,4,8]=>[1,6,7,2,3,5,4,8]=>0101000=>1010111
[1,8,2,6,3,5,4,7]=>[1,6,2,3,5,8,4,7]=>0101000=>1010111
[1,8,2,5,3,6,4,7]=>[1,5,2,3,6,8,4,7]=>0101000=>1010111
[1,7,2,5,3,6,4,8]=>[1,5,2,3,6,7,4,8]=>0101000=>1010111
[1,5,2,4,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>0100010=>1011101
[1,6,2,4,3,7,5,8]=>[1,4,7,6,2,3,5,8]=>0100010=>1011101
[1,7,2,4,3,6,5,8]=>[1,4,6,7,2,3,5,8]=>0100000=>1011111
[1,8,2,4,3,6,5,7]=>[1,4,6,8,2,3,5,7]=>0100000=>1011111
[1,8,2,3,4,6,5,7]=>[1,6,8,2,3,4,5,7]=>0100000=>1011111
[1,7,2,3,4,6,5,8]=>[1,6,7,2,3,4,5,8]=>0100000=>1011111
[1,8,2,3,4,7,5,6]=>[1,7,2,3,4,5,8,6]=>0100010=>1011101
[1,8,2,4,3,7,5,6]=>[1,4,7,2,3,5,8,6]=>0100010=>1011101
[1,7,2,4,3,8,5,6]=>[1,4,8,2,3,5,7,6]=>0100010=>1011101
[1,6,2,4,3,8,5,7]=>[1,4,8,6,2,3,5,7]=>0100010=>1011101
[1,5,2,4,3,8,6,7]=>[1,4,5,2,3,8,6,7]=>0100010=>1011101
[1,7,2,5,3,8,4,6]=>[1,5,2,3,8,4,7,6]=>0101010=>1010101
[1,8,2,5,3,7,4,6]=>[1,5,2,3,7,4,8,6]=>0101010=>1010101
[1,8,2,6,3,7,4,5]=>[1,7,6,2,3,8,4,5]=>0101010=>1010101
[1,7,2,6,3,8,4,5]=>[1,8,6,2,3,7,4,5]=>0101010=>1010101
[1,2,3,8,4,7,5,6]=>[1,2,3,7,4,5,8,6]=>0001010=>1110101
[1,4,2,8,3,7,5,6]=>[1,7,4,2,3,5,8,6]=>0101010=>1010101
[1,5,2,8,3,7,4,6]=>[1,7,2,3,5,4,8,6]=>0101010=>1010101
[1,6,2,8,3,7,4,5]=>[1,7,2,3,8,6,4,5]=>0101010=>1010101
[1,7,2,8,3,6,4,5]=>[1,6,8,2,3,7,4,5]=>0101000=>1010111
[1,8,2,7,3,6,4,5]=>[1,6,7,2,3,8,4,5]=>0101000=>1010111
[4,6,3,7,2,5,1,8]=>[3,7,2,5,6,4,1,8]=>1101000=>0010111
[4,6,3,7,5,2,1,8]=>[3,5,7,2,6,4,1,8]=>1101000=>0010111
[4,6,3,8,5,1,7,2]=>[3,5,7,8,1,6,4,2]=>1101000=>0010111
[5,6,8,3,4,1,2,7]=>[8,3,4,6,1,5,2,7]=>1110000=>0001111
[5,6,8,3,4,1,7,2]=>[7,8,3,4,6,1,5,2]=>1110000=>0001111
[5,6,8,4,3,1,7,2]=>[4,7,8,3,6,1,5,2]=>1110000=>0001111
[5,6,8,4,3,1,2,7]=>[4,8,3,6,1,5,2,7]=>1110000=>0001111
[5,7,8,4,1,6,2,3]=>[4,6,8,1,7,2,5,3]=>1110000=>0001111
[5,7,8,4,1,6,3,2]=>[4,6,8,1,7,3,5,2]=>1110000=>0001111
[5,7,8,4,1,3,6,2]=>[4,8,1,6,7,3,5,2]=>1110000=>0001111
[5,6,8,4,2,1,7,3]=>[4,7,8,2,6,1,5,3]=>1110000=>0001111
[5,6,8,2,4,1,7,3]=>[7,8,2,4,6,1,5,3]=>1110000=>0001111
[4,6,2,8,5,1,7,3]=>[5,7,8,2,6,4,1,3]=>1101000=>0010111
[3,2,6,8,5,1,7,4]=>[2,5,7,8,3,1,6,4]=>1011000=>0100111
[4,6,2,8,5,1,3,7]=>[5,8,2,6,4,1,3,7]=>1101000=>0010111
[5,6,8,2,4,1,3,7]=>[8,2,4,6,1,5,3,7]=>1110000=>0001111
[5,6,8,4,2,1,3,7]=>[4,8,2,6,1,5,3,7]=>1110000=>0001111
[5,7,8,4,1,3,2,6]=>[4,8,1,7,3,5,2,6]=>1110000=>0001111
[5,7,8,4,1,2,6,3]=>[4,8,1,6,7,2,5,3]=>1110000=>0001111
[5,7,8,4,1,2,3,6]=>[4,8,1,7,2,5,3,6]=>1110000=>0001111
[6,7,8,1,5,2,3,4]=>[5,8,1,7,2,6,3,4]=>1110000=>0001111
[6,7,8,1,5,2,4,3]=>[5,8,1,7,2,4,6,3]=>1110000=>0001111
[6,7,8,1,5,3,2,4]=>[5,8,1,7,3,6,2,4]=>1110000=>0001111
[6,7,8,1,3,5,2,4]=>[8,1,5,7,3,6,2,4]=>1110000=>0001111
[5,7,8,2,1,6,3,4]=>[6,8,2,7,1,5,3,4]=>1110000=>0001111
[3,2,7,8,1,6,4,5]=>[2,6,8,3,1,7,4,5]=>1011000=>0100111
[3,2,7,8,1,6,5,4]=>[2,6,8,3,1,5,7,4]=>1011000=>0100111
[4,7,2,8,1,6,5,3]=>[6,8,2,5,7,4,1,3]=>1101000=>0010111
[5,7,8,2,1,6,4,3]=>[6,8,2,7,1,4,5,3]=>1110000=>0001111
[6,7,8,1,3,5,4,2]=>[8,1,5,7,3,4,6,2]=>1110000=>0001111
[6,7,8,1,5,3,4,2]=>[5,8,1,7,3,4,6,2]=>1110000=>0001111
[6,7,8,1,5,4,3,2]=>[5,8,1,4,7,3,6,2]=>1110000=>0001111
[6,7,8,1,5,4,2,3]=>[5,8,1,4,7,2,6,3]=>1110000=>0001111
[6,7,8,1,4,5,3,2]=>[8,1,4,5,7,3,6,2]=>1110000=>0001111
[6,7,8,1,4,3,5,2]=>[8,1,4,7,3,5,6,2]=>1110000=>0001111
[6,7,8,1,3,4,5,2]=>[8,1,7,3,4,5,6,2]=>1110000=>0001111
[5,7,8,2,1,4,6,3]=>[8,2,6,7,1,4,5,3]=>1110000=>0001111
[4,7,2,8,1,5,6,3]=>[8,2,5,6,7,4,1,3]=>1101000=>0010111
[3,2,7,8,1,5,6,4]=>[2,8,3,1,5,6,7,4]=>1011000=>0100111
[3,2,6,8,4,1,7,5]=>[2,7,8,4,6,3,1,5]=>1011000=>0100111
[5,6,8,3,2,1,7,4]=>[7,8,3,6,2,5,1,4]=>1110000=>0001111
[5,7,8,3,1,6,2,4]=>[6,8,3,7,1,5,2,4]=>1110000=>0001111
[4,7,3,8,1,6,2,5]=>[3,6,8,1,7,4,2,5]=>1101000=>0010111
[4,7,3,8,1,6,5,2]=>[3,6,8,1,5,7,4,2]=>1101000=>0010111
[4,7,3,8,1,5,6,2]=>[3,8,1,5,6,7,4,2]=>1101000=>0010111
[4,6,3,8,2,1,7,5]=>[3,7,8,2,6,4,1,5]=>1101000=>0010111
[4,5,3,2,8,1,7,6]=>[3,7,8,5,2,4,1,6]=>1100100=>0011011
[4,5,2,3,8,1,7,6]=>[7,8,5,2,3,4,1,6]=>1100100=>0011011
[3,2,5,4,8,1,7,6]=>[2,4,7,8,5,3,1,6]=>1010100=>0101011
[4,7,3,8,1,2,6,5]=>[3,8,1,6,7,4,2,5]=>1101000=>0010111
[5,7,8,3,1,2,4,6]=>[8,3,7,1,5,2,4,6]=>1110000=>0001111
[5,6,8,3,2,1,4,7]=>[8,3,6,2,5,1,4,7]=>1110000=>0001111
[3,2,7,8,1,5,4,6]=>[2,8,3,1,5,7,4,6]=>1011000=>0100111
[6,7,8,1,3,4,2,5]=>[8,1,7,3,4,6,2,5]=>1110000=>0001111
[6,7,8,1,4,3,2,5]=>[8,1,4,7,3,6,2,5]=>1110000=>0001111
[6,7,8,1,4,2,5,3]=>[8,1,4,7,2,5,6,3]=>1110000=>0001111
[6,7,8,1,4,2,3,5]=>[8,1,4,7,2,6,3,5]=>1110000=>0001111
[6,7,8,1,2,5,4,3]=>[8,1,5,7,2,4,6,3]=>1110000=>0001111
[6,7,8,1,2,4,5,3]=>[8,1,7,2,4,5,6,3]=>1110000=>0001111
[6,7,8,1,3,2,5,4]=>[8,1,7,3,5,6,2,4]=>1110000=>0001111
[5,7,8,2,1,3,6,4]=>[8,2,6,7,1,5,3,4]=>1110000=>0001111
[3,2,7,8,1,4,6,5]=>[2,8,3,1,6,7,4,5]=>1011000=>0100111
[6,7,8,1,3,2,4,5]=>[8,1,7,3,6,2,4,5]=>1110000=>0001111
[6,7,8,1,2,4,3,5]=>[8,1,7,2,4,6,3,5]=>1110000=>0001111
[6,7,8,1,2,3,5,4]=>[8,1,7,2,5,6,3,4]=>1110000=>0001111
[7,2,8,5,1,6,4,3]=>[2,5,1,6,8,4,7,3]=>1011000=>0100111
[1,3,7,5,2,6,4,8]=>[1,5,3,2,6,7,4,8]=>0111000=>1000111
[7,2,8,5,4,1,6,3]=>[2,5,4,8,1,6,7,3]=>1011000=>0100111
[2,8,4,5,6,1,7,3]=>[6,5,4,2,1,7,8,3]=>1111100=>0000011
[7,2,8,4,5,6,1,3]=>[2,4,5,6,8,1,7,3]=>1010000=>0101111
[1,6,3,7,5,2,4,8]=>[1,3,5,7,2,6,4,8]=>0101000=>1010111
[6,2,3,8,5,1,7,4]=>[2,3,5,7,8,1,6,4]=>1001000=>0110111
[7,4,8,2,5,6,3,1]=>[5,6,8,2,4,3,7,1]=>1110000=>0001111
[7,4,8,5,2,1,3,6]=>[5,2,8,4,1,7,3,6]=>1111000=>0000111
[6,4,8,5,1,3,7,2]=>[5,1,7,8,4,3,6,2]=>1111000=>0000111
[6,3,7,5,2,1,8,4]=>[5,3,2,8,7,1,6,4]=>1111001=>0000110
[4,3,7,5,1,2,8,6]=>[5,3,1,8,7,4,2,6]=>1111001=>0000110
[4,3,7,1,5,6,8,2]=>[5,6,8,7,3,1,4,2]=>1110001=>0001110
[3,4,1,2,7,6,8,5]=>[4,1,3,2,6,8,7,5]=>1100101=>0011010
[3,4,2,1,7,5,8,6]=>[4,2,3,1,8,7,5,6]=>1100101=>0011010
[3,6,5,7,1,4,8,2]=>[8,7,1,5,4,6,3,2]=>1111001=>0000110
[6,5,2,7,4,1,8,3]=>[8,7,4,5,2,6,1,3]=>1101001=>0010110
[5,3,1,8,6,4,7,2]=>[3,1,6,4,7,8,5,2]=>1101100=>0010011
[5,6,1,8,7,2,4,3]=>[7,1,8,4,6,5,2,3]=>1101100=>0010011
[6,3,5,8,2,7,4,1]=>[7,3,2,5,4,8,6,1]=>1111010=>0000101
[1,6,5,7,3,4,2,8]=>[1,7,3,5,4,6,2,8]=>0111000=>1000111
[1,5,2,7,4,6,3,8]=>[1,6,7,4,5,2,3,8]=>0101000=>1010111
[5,2,1,8,7,6,3,4]=>[2,6,7,1,3,8,5,4]=>1001100=>0110011
[2,3,4,8,6,1,7,5]=>[6,4,3,2,1,7,8,5]=>1111100=>0000011
[2,3,4,8,6,5,1,7]=>[6,5,8,4,3,2,1,7]=>1111100=>0000011
[2,7,3,5,8,6,1,4]=>[3,6,8,5,2,1,7,4]=>1101100=>0010011
[3,2,4,7,8,6,1,5]=>[2,6,8,4,3,1,7,5]=>1011100=>0100011
[1,5,4,6,2,7,3,8]=>[1,7,6,4,2,5,3,8]=>0111010=>1000101
[5,2,4,7,1,8,3,6]=>[2,8,4,1,5,3,7,6]=>1011010=>0100101
[6,3,5,1,8,2,7,4]=>[7,8,5,3,1,6,2,4]=>1110100=>0001011
[2,7,6,5,8,3,4,1]=>[8,5,3,6,4,7,2,1]=>1111100=>0000011
[3,2,4,1,7,8,5,6]=>[2,4,3,1,8,5,7,6]=>1010110=>0101001
[3,1,4,2,7,8,6,5]=>[4,3,1,2,8,6,7,5]=>1010110=>0101001
[3,1,4,6,8,5,7,2]=>[7,8,5,6,4,3,1,2]=>1011100=>0100011
[6,3,4,5,7,1,8,2]=>[8,7,5,4,3,1,6,2]=>1111101=>0000010
[2,5,4,6,1,7,8,3]=>[8,7,6,4,2,1,5,3]=>1111011=>0000100
[7,2,1,4,3,6,5,8]=>[2,4,6,7,1,3,5,8]=>1000000=>0111111
[7,3,4,1,2,6,5,8]=>[4,3,1,6,7,2,5,8]=>1110000=>0001111
[7,4,3,2,1,6,5,8]=>[3,4,2,6,7,1,5,8]=>1100000=>0011111
[7,6,3,2,5,4,1,8]=>[3,5,6,2,4,7,1,8]=>1100000=>0011111
[6,7,3,2,5,4,8,1]=>[3,5,8,7,2,4,6,1]=>1100001=>0011110
[1,8,3,2,5,4,7,6]=>[1,3,5,7,8,2,4,6]=>0100000=>1011111
[1,8,4,5,2,3,7,6]=>[1,5,4,2,7,8,3,6]=>0111000=>1000111
[7,3,5,1,6,2,4,8]=>[6,5,3,1,7,2,4,8]=>1110100=>0001011
[7,2,1,5,6,3,4,8]=>[2,6,5,1,3,7,4,8]=>1001100=>0110011
[7,2,1,6,5,4,3,8]=>[2,5,6,4,7,1,3,8]=>1001000=>0110111
[1,8,5,4,3,2,7,6]=>[1,4,5,3,7,8,2,6]=>0110000=>1001111
[1,8,6,4,3,7,2,5]=>[1,4,7,6,3,8,2,5]=>0110010=>1001101
[6,5,7,4,3,1,8,2]=>[4,8,7,3,5,1,6,2]=>1110001=>0001110
[6,4,7,5,1,3,8,2]=>[5,1,8,7,4,3,6,2]=>1111001=>0000110
[6,3,7,1,5,4,8,2]=>[5,8,7,3,1,4,6,2]=>1110001=>0001110
[6,2,1,7,5,4,8,3]=>[2,5,8,7,4,6,1,3]=>1001001=>0110110
[3,2,1,8,5,4,7,6]=>[2,3,1,5,7,8,4,6]=>1001000=>0110111
[2,3,8,1,5,4,7,6]=>[5,7,8,3,2,1,4,6]=>1110000=>0001111
[2,5,8,4,3,1,7,6]=>[4,7,8,3,5,2,1,6]=>1110000=>0001111
[2,6,8,4,3,7,1,5]=>[4,7,3,8,6,2,1,5]=>1110010=>0001101
[2,7,8,4,3,6,5,1]=>[4,6,8,3,5,7,2,1]=>1110000=>0001111
[1,8,7,4,3,6,5,2]=>[1,4,6,7,3,5,8,2]=>0110000=>1001111
[2,7,8,5,6,3,4,1]=>[6,5,3,8,4,7,2,1]=>1111100=>0000011
[2,6,8,5,7,3,1,4]=>[7,5,3,8,2,1,6,4]=>1111100=>0000011
[2,5,8,6,7,1,3,4]=>[7,2,1,6,3,8,5,4]=>1111100=>0000011
[2,4,8,6,1,7,3,5]=>[7,6,2,1,8,4,3,5]=>1111010=>0000101
[3,2,1,8,6,7,4,5]=>[2,3,1,7,6,4,8,5]=>1001110=>0110001
[5,2,1,7,6,8,4,3]=>[2,8,6,4,7,5,1,3]=>1001110=>0110001
[5,3,7,1,6,8,4,2]=>[8,6,3,1,4,7,5,2]=>1110110=>0001001
[4,5,7,6,8,1,3,2]=>[8,1,6,3,7,5,4,2]=>1111100=>0000011
[4,6,7,5,8,3,1,2]=>[8,5,3,7,1,6,4,2]=>1111100=>0000011
[1,8,6,5,7,3,2,4]=>[1,7,5,3,6,2,8,4]=>0111100=>1000011
[4,6,5,7,8,2,1,3]=>[8,2,7,5,1,6,4,3]=>1111100=>0000011
[5,4,6,7,1,8,2,3]=>[8,1,7,6,4,2,5,3]=>1111010=>0000101
[5,3,6,1,7,8,2,4]=>[8,3,1,7,6,5,2,4]=>1110110=>0001001
[5,2,1,6,7,8,3,4]=>[2,8,1,3,7,6,5,4]=>1001110=>0110001
[6,5,4,7,2,1,8,3]=>[8,7,4,2,5,1,6,3]=>1111001=>0000110
[5,6,4,7,2,8,1,3]=>[8,4,2,7,6,1,5,3]=>1111010=>0000101
[1,8,4,6,2,7,3,5]=>[1,7,6,4,2,8,3,5]=>0111010=>1000101
[1,8,3,2,6,7,4,5]=>[1,3,7,6,2,4,8,5]=>0100110=>1011001
[5,7,3,2,6,8,4,1]=>[3,8,6,2,4,7,5,1]=>1100110=>0011001
[5,6,3,2,7,8,1,4]=>[3,8,2,7,6,5,1,4]=>1100110=>0011001
[6,5,3,2,7,1,8,4]=>[3,8,7,5,2,6,1,4]=>1100101=>0011010
[6,4,3,2,1,7,8,5]=>[3,4,2,8,7,6,1,5]=>1100011=>0011100
[6,2,1,4,3,7,8,5]=>[2,4,8,7,6,1,3,5]=>1000011=>0111100
[5,2,1,4,3,8,7,6]=>[2,4,5,1,3,7,8,6]=>1000010=>0111101
[5,3,4,1,2,8,7,6]=>[4,3,1,5,2,7,8,6]=>1110010=>0001101
[4,6,3,2,8,7,1,5]=>[3,7,2,4,1,8,6,5]=>1100110=>0011001
[4,7,3,2,8,6,5,1]=>[3,6,8,5,7,2,4,1]=>1100100=>0011011
[1,8,3,2,7,6,5,4]=>[1,3,6,7,5,8,2,4]=>0100100=>1011011
[1,8,4,7,2,6,5,3]=>[1,6,7,4,2,5,8,3]=>0111000=>1000111
[3,7,4,8,2,6,5,1]=>[6,8,4,2,5,7,3,1]=>1111000=>0000111
[3,6,4,8,2,7,1,5]=>[7,4,2,8,6,3,1,5]=>1111010=>0000101
[3,5,4,8,2,1,7,6]=>[7,8,4,2,5,3,1,6]=>1111000=>0000111
[4,3,5,1,8,2,7,6]=>[7,8,5,3,1,4,2,6]=>1110100=>0001011
[4,2,1,5,8,3,7,6]=>[2,7,8,5,4,1,3,6]=>1001100=>0110011
[4,3,6,1,8,7,2,5]=>[7,3,1,4,2,8,6,5]=>1110110=>0001001
[3,4,6,8,1,7,2,5]=>[7,1,8,6,4,3,2,5]=>1111010=>0000101
[3,5,6,8,7,1,2,4]=>[7,1,8,3,2,6,5,4]=>1111100=>0000011
[3,6,5,8,7,2,1,4]=>[7,2,8,5,3,1,6,4]=>1111100=>0000011
[3,7,5,8,6,2,4,1]=>[6,2,8,5,4,7,3,1]=>1111100=>0000011
[3,6,7,8,5,4,1,2]=>[5,8,4,7,1,6,3,2]=>1111000=>0000111
[3,5,7,8,6,1,4,2]=>[6,1,8,4,7,5,3,2]=>1111100=>0000011
[4,2,1,7,8,6,5,3]=>[2,6,8,5,7,4,1,3]=>1001100=>0110011
[2,3,8,1,7,6,5,4]=>[6,7,5,8,3,2,1,4]=>1110100=>0001011
[2,4,8,7,1,6,5,3]=>[6,7,2,1,5,8,4,3]=>1111000=>0000111
[2,6,8,7,5,4,1,3]=>[5,7,4,8,2,1,6,3]=>1111000=>0000111
[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=>01010101010
[2,1,4,3,6,5,8,7,12,11,10,9]=>[2,1,4,3,6,5,8,7,11,10,12,9]=>10101010110=>01010101001
[2,1,4,3,6,5,10,9,8,7,12,11]=>[2,1,4,3,6,5,9,8,10,7,12,11]=>10101011001=>01010100110
[2,1,4,3,6,5,12,9,8,11,10,7]=>[2,1,4,3,6,5,9,8,11,10,12,7]=>10101011010=>01010100101
[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,4,3,6,5,10,9,11,8,12,7]=>10101011100=>01010100011
[2,1,4,3,8,7,6,5,10,9,12,11]=>[2,1,4,3,7,6,8,5,10,9,12,11]=>10101100101=>01010011010
[2,1,4,3,8,7,6,5,12,11,10,9]=>[2,1,4,3,7,6,8,5,11,10,12,9]=>10101100110=>01010011001
[2,1,4,3,10,7,6,9,8,5,12,11]=>[2,1,4,3,7,6,9,8,10,5,12,11]=>10101101001=>01010010110
[2,1,4,3,12,7,6,9,8,11,10,5]=>[2,1,4,3,7,6,9,8,11,10,12,5]=>10101101010=>01010010101
[2,1,4,3,12,7,6,11,10,9,8,5]=>[2,1,4,3,7,6,10,9,11,8,12,5]=>10101101100=>01010010011
[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,4,3,8,7,9,6,10,5,12,11]=>10101110001=>01010001110
[2,1,4,3,12,9,8,7,6,11,10,5]=>[2,1,4,3,8,7,9,6,11,10,12,5]=>10101110010=>01010001101
[2,1,4,3,12,11,8,7,10,9,6,5]=>[2,1,4,3,8,7,10,9,11,6,12,5]=>10101110100=>01010001011
[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,4,3,9,8,10,7,11,6,12,5]=>10101111000=>01010000111
[2,1,6,5,4,3,8,7,10,9,12,11]=>[2,1,5,4,6,3,8,7,10,9,12,11]=>10110010101=>01001101010
[2,1,6,5,4,3,8,7,12,11,10,9]=>[2,1,5,4,6,3,8,7,11,10,12,9]=>10110010110=>01001101001
[2,1,6,5,4,3,10,9,8,7,12,11]=>[2,1,5,4,6,3,9,8,10,7,12,11]=>10110011001=>01001100110
[2,1,6,5,4,3,12,9,8,11,10,7]=>[2,1,5,4,6,3,9,8,11,10,12,7]=>10110011010=>01001100101
[2,1,6,5,4,3,12,11,10,9,8,7]=>[2,1,5,4,6,3,10,9,11,8,12,7]=>10110011100=>01001100011
[2,1,8,5,4,7,6,3,10,9,12,11]=>[2,1,5,4,7,6,8,3,10,9,12,11]=>10110100101=>01001011010
[2,1,8,5,4,7,6,3,12,11,10,9]=>[2,1,5,4,7,6,8,3,11,10,12,9]=>10110100110=>01001011001
[2,1,10,5,4,7,6,9,8,3,12,11]=>[2,1,5,4,7,6,9,8,10,3,12,11]=>10110101001=>01001010110
[2,1,12,5,4,7,6,9,8,11,10,3]=>[2,1,5,4,7,6,9,8,11,10,12,3]=>10110101010=>01001010101
[2,1,12,5,4,7,6,11,10,9,8,3]=>[2,1,5,4,7,6,10,9,11,8,12,3]=>10110101100=>01001010011
[2,1,10,5,4,9,8,7,6,3,12,11]=>[2,1,5,4,8,7,9,6,10,3,12,11]=>10110110001=>01001001110
[2,1,12,5,4,9,8,7,6,11,10,3]=>[2,1,5,4,8,7,9,6,11,10,12,3]=>10110110010=>01001001101
[2,1,12,5,4,11,8,7,10,9,6,3]=>[2,1,5,4,8,7,10,9,11,6,12,3]=>10110110100=>01001001011
[2,1,12,5,4,11,10,9,8,7,6,3]=>[2,1,5,4,9,8,10,7,11,6,12,3]=>10110111000=>01001000111
[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,6,5,7,4,8,3,10,9,12,11]=>10111000101=>01000111010
[2,1,8,7,6,5,4,3,12,11,10,9]=>[2,1,6,5,7,4,8,3,11,10,12,9]=>10111000110=>01000111001
[2,1,10,7,6,5,4,9,8,3,12,11]=>[2,1,6,5,7,4,9,8,10,3,12,11]=>10111001001=>01000110110
[2,1,12,7,6,5,4,9,8,11,10,3]=>[2,1,6,5,7,4,9,8,11,10,12,3]=>10111001010=>01000110101
[2,1,12,7,6,5,4,11,10,9,8,3]=>[2,1,6,5,7,4,10,9,11,8,12,3]=>10111001100=>01000110011
[2,1,10,9,6,5,8,7,4,3,12,11]=>[2,1,6,5,8,7,9,4,10,3,12,11]=>10111010001=>01000101110
[2,1,12,9,6,5,8,7,4,11,10,3]=>[2,1,6,5,8,7,9,4,11,10,12,3]=>10111010010=>01000101101
[2,1,12,11,6,5,8,7,10,9,4,3]=>[2,1,6,5,8,7,10,9,11,4,12,3]=>10111010100=>01000101011
[2,1,12,11,6,5,10,9,8,7,4,3]=>[2,1,6,5,9,8,10,7,11,4,12,3]=>10111011000=>01000100111
[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,7,6,8,5,9,4,10,3,12,11]=>10111100001=>01000011110
[2,1,12,9,8,7,6,5,4,11,10,3]=>[2,1,7,6,8,5,9,4,11,10,12,3]=>10111100010=>01000011101
[2,1,12,11,8,7,6,5,10,9,4,3]=>[2,1,7,6,8,5,10,9,11,4,12,3]=>10111100100=>01000011011
[2,1,12,11,10,7,6,9,8,5,4,3]=>[2,1,7,6,9,8,10,5,11,4,12,3]=>10111101000=>01000010111
[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,8,7,9,6,10,5,11,4,12,3]=>10111110000=>01000001111
[4,3,2,1,6,5,8,7,10,9,12,11]=>[3,2,4,1,6,5,8,7,10,9,12,11]=>11001010101=>00110101010
[4,3,2,1,6,5,8,7,12,11,10,9]=>[3,2,4,1,6,5,8,7,11,10,12,9]=>11001010110=>00110101001
[4,3,2,1,6,5,10,9,8,7,12,11]=>[3,2,4,1,6,5,9,8,10,7,12,11]=>11001011001=>00110100110
[4,3,2,1,6,5,12,9,8,11,10,7]=>[3,2,4,1,6,5,9,8,11,10,12,7]=>11001011010=>00110100101
[4,3,2,1,6,5,12,11,10,9,8,7]=>[3,2,4,1,6,5,10,9,11,8,12,7]=>11001011100=>00110100011
[4,3,2,1,8,7,6,5,10,9,12,11]=>[3,2,4,1,7,6,8,5,10,9,12,11]=>11001100101=>00110011010
[4,3,2,1,8,7,6,5,12,11,10,9]=>[3,2,4,1,7,6,8,5,11,10,12,9]=>11001100110=>00110011001
[4,3,2,1,10,7,6,9,8,5,12,11]=>[3,2,4,1,7,6,9,8,10,5,12,11]=>11001101001=>00110010110
[4,3,2,1,12,7,6,9,8,11,10,5]=>[3,2,4,1,7,6,9,8,11,10,12,5]=>11001101010=>00110010101
[4,3,2,1,12,7,6,11,10,9,8,5]=>[3,2,4,1,7,6,10,9,11,8,12,5]=>11001101100=>00110010011
[4,3,2,1,10,9,8,7,6,5,12,11]=>[3,2,4,1,8,7,9,6,10,5,12,11]=>11001110001=>00110001110
[4,3,2,1,12,9,8,7,6,11,10,5]=>[3,2,4,1,8,7,9,6,11,10,12,5]=>11001110010=>00110001101
[4,3,2,1,12,11,8,7,10,9,6,5]=>[3,2,4,1,8,7,10,9,11,6,12,5]=>11001110100=>00110001011
[4,3,2,1,12,11,10,9,8,7,6,5]=>[3,2,4,1,9,8,10,7,11,6,12,5]=>11001111000=>00110000111
[6,3,2,5,4,1,8,7,10,9,12,11]=>[3,2,5,4,6,1,8,7,10,9,12,11]=>11010010101=>00101101010
[6,3,2,5,4,1,8,7,12,11,10,9]=>[3,2,5,4,6,1,8,7,11,10,12,9]=>11010010110=>00101101001
[6,3,2,5,4,1,10,9,8,7,12,11]=>[3,2,5,4,6,1,9,8,10,7,12,11]=>11010011001=>00101100110
[6,3,2,5,4,1,12,9,8,11,10,7]=>[3,2,5,4,6,1,9,8,11,10,12,7]=>11010011010=>00101100101
[6,3,2,5,4,1,12,11,10,9,8,7]=>[3,2,5,4,6,1,10,9,11,8,12,7]=>11010011100=>00101100011
[8,3,2,5,4,7,6,1,10,9,12,11]=>[3,2,5,4,7,6,8,1,10,9,12,11]=>11010100101=>00101011010
[8,3,2,5,4,7,6,1,12,11,10,9]=>[3,2,5,4,7,6,8,1,11,10,12,9]=>11010100110=>00101011001
[10,3,2,5,4,7,6,9,8,1,12,11]=>[3,2,5,4,7,6,9,8,10,1,12,11]=>11010101001=>00101010110
[12,3,2,5,4,7,6,9,8,11,10,1]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>11010101010=>00101010101
[12,3,2,5,4,7,6,11,10,9,8,1]=>[3,2,5,4,7,6,10,9,11,8,12,1]=>11010101100=>00101010011
[10,3,2,5,4,9,8,7,6,1,12,11]=>[3,2,5,4,8,7,9,6,10,1,12,11]=>11010110001=>00101001110
[12,3,2,5,4,9,8,7,6,11,10,1]=>[3,2,5,4,8,7,9,6,11,10,12,1]=>11010110010=>00101001101
[12,3,2,5,4,11,8,7,10,9,6,1]=>[3,2,5,4,8,7,10,9,11,6,12,1]=>11010110100=>00101001011
[12,3,2,5,4,11,10,9,8,7,6,1]=>[3,2,5,4,9,8,10,7,11,6,12,1]=>11010111000=>00101000111
[8,3,2,7,6,5,4,1,10,9,12,11]=>[3,2,6,5,7,4,8,1,10,9,12,11]=>11011000101=>00100111010
[8,3,2,7,6,5,4,1,12,11,10,9]=>[3,2,6,5,7,4,8,1,11,10,12,9]=>11011000110=>00100111001
[10,3,2,7,6,5,4,9,8,1,12,11]=>[3,2,6,5,7,4,9,8,10,1,12,11]=>11011001001=>00100110110
[12,3,2,7,6,5,4,9,8,11,10,1]=>[3,2,6,5,7,4,9,8,11,10,12,1]=>11011001010=>00100110101
[12,3,2,7,6,5,4,11,10,9,8,1]=>[3,2,6,5,7,4,10,9,11,8,12,1]=>11011001100=>00100110011
[10,3,2,9,6,5,8,7,4,1,12,11]=>[3,2,6,5,8,7,9,4,10,1,12,11]=>11011010001=>00100101110
[12,3,2,9,6,5,8,7,4,11,10,1]=>[3,2,6,5,8,7,9,4,11,10,12,1]=>11011010010=>00100101101
[12,3,2,11,6,5,8,7,10,9,4,1]=>[3,2,6,5,8,7,10,9,11,4,12,1]=>11011010100=>00100101011
[12,3,2,11,6,5,10,9,8,7,4,1]=>[3,2,6,5,9,8,10,7,11,4,12,1]=>11011011000=>00100100111
[10,3,2,9,8,7,6,5,4,1,12,11]=>[3,2,7,6,8,5,9,4,10,1,12,11]=>11011100001=>00100011110
[12,3,2,9,8,7,6,5,4,11,10,1]=>[3,2,7,6,8,5,9,4,11,10,12,1]=>11011100010=>00100011101
[12,3,2,11,8,7,6,5,10,9,4,1]=>[3,2,7,6,8,5,10,9,11,4,12,1]=>11011100100=>00100011011
[12,3,2,11,10,7,6,9,8,5,4,1]=>[3,2,7,6,9,8,10,5,11,4,12,1]=>11011101000=>00100010111
[12,3,2,11,10,9,8,7,6,5,4,1]=>[3,2,8,7,9,6,10,5,11,4,12,1]=>11011110000=>00100001111
[6,5,4,3,2,1,8,7,10,9,12,11]=>[4,3,5,2,6,1,8,7,10,9,12,11]=>11100010101=>00011101010
[6,5,4,3,2,1,8,7,12,11,10,9]=>[4,3,5,2,6,1,8,7,11,10,12,9]=>11100010110=>00011101001
[6,5,4,3,2,1,10,9,8,7,12,11]=>[4,3,5,2,6,1,9,8,10,7,12,11]=>11100011001=>00011100110
[6,5,4,3,2,1,12,9,8,11,10,7]=>[4,3,5,2,6,1,9,8,11,10,12,7]=>11100011010=>00011100101
[6,5,4,3,2,1,12,11,10,9,8,7]=>[4,3,5,2,6,1,10,9,11,8,12,7]=>11100011100=>00011100011
[8,5,4,3,2,7,6,1,10,9,12,11]=>[4,3,5,2,7,6,8,1,10,9,12,11]=>11100100101=>00011011010
[8,5,4,3,2,7,6,1,12,11,10,9]=>[4,3,5,2,7,6,8,1,11,10,12,9]=>11100100110=>00011011001
[10,5,4,3,2,7,6,9,8,1,12,11]=>[4,3,5,2,7,6,9,8,10,1,12,11]=>11100101001=>00011010110
[12,5,4,3,2,7,6,9,8,11,10,1]=>[4,3,5,2,7,6,9,8,11,10,12,1]=>11100101010=>00011010101
[12,5,4,3,2,7,6,11,10,9,8,1]=>[4,3,5,2,7,6,10,9,11,8,12,1]=>11100101100=>00011010011
[10,5,4,3,2,9,8,7,6,1,12,11]=>[4,3,5,2,8,7,9,6,10,1,12,11]=>11100110001=>00011001110
[12,5,4,3,2,9,8,7,6,11,10,1]=>[4,3,5,2,8,7,9,6,11,10,12,1]=>11100110010=>00011001101
[12,5,4,3,2,11,8,7,10,9,6,1]=>[4,3,5,2,8,7,10,9,11,6,12,1]=>11100110100=>00011001011
[12,5,4,3,2,11,10,9,8,7,6,1]=>[4,3,5,2,9,8,10,7,11,6,12,1]=>11100111000=>00011000111
[8,7,4,3,6,5,2,1,10,9,12,11]=>[4,3,6,5,7,2,8,1,10,9,12,11]=>11101000101=>00010111010
[8,7,4,3,6,5,2,1,12,11,10,9]=>[4,3,6,5,7,2,8,1,11,10,12,9]=>11101000110=>00010111001
[10,7,4,3,6,5,2,9,8,1,12,11]=>[4,3,6,5,7,2,9,8,10,1,12,11]=>11101001001=>00010110110
[12,7,4,3,6,5,2,9,8,11,10,1]=>[4,3,6,5,7,2,9,8,11,10,12,1]=>11101001010=>00010110101
[12,7,4,3,6,5,2,11,10,9,8,1]=>[4,3,6,5,7,2,10,9,11,8,12,1]=>11101001100=>00010110011
[10,9,4,3,6,5,8,7,2,1,12,11]=>[4,3,6,5,8,7,9,2,10,1,12,11]=>11101010001=>00010101110
[12,9,4,3,6,5,8,7,2,11,10,1]=>[4,3,6,5,8,7,9,2,11,10,12,1]=>11101010010=>00010101101
[12,11,4,3,6,5,8,7,10,9,2,1]=>[4,3,6,5,8,7,10,9,11,2,12,1]=>11101010100=>00010101011
[12,11,4,3,6,5,10,9,8,7,2,1]=>[4,3,6,5,9,8,10,7,11,2,12,1]=>11101011000=>00010100111
[10,9,4,3,8,7,6,5,2,1,12,11]=>[4,3,7,6,8,5,9,2,10,1,12,11]=>11101100001=>00010011110
[12,9,4,3,8,7,6,5,2,11,10,1]=>[4,3,7,6,8,5,9,2,11,10,12,1]=>11101100010=>00010011101
[12,11,4,3,8,7,6,5,10,9,2,1]=>[4,3,7,6,8,5,10,9,11,2,12,1]=>11101100100=>00010011011
[12,11,4,3,10,7,6,9,8,5,2,1]=>[4,3,7,6,9,8,10,5,11,2,12,1]=>11101101000=>00010010111
[12,11,4,3,10,9,8,7,6,5,2,1]=>[4,3,8,7,9,6,10,5,11,2,12,1]=>11101110000=>00010001111
[8,7,6,5,4,3,2,1,10,9,12,11]=>[5,4,6,3,7,2,8,1,10,9,12,11]=>11110000101=>00001111010
[8,7,6,5,4,3,2,1,12,11,10,9]=>[5,4,6,3,7,2,8,1,11,10,12,9]=>11110000110=>00001111001
[10,7,6,5,4,3,2,9,8,1,12,11]=>[5,4,6,3,7,2,9,8,10,1,12,11]=>11110001001=>00001110110
[12,7,6,5,4,3,2,9,8,11,10,1]=>[5,4,6,3,7,2,9,8,11,10,12,1]=>11110001010=>00001110101
[12,7,6,5,4,3,2,11,10,9,8,1]=>[5,4,6,3,7,2,10,9,11,8,12,1]=>11110001100=>00001110011
[10,9,6,5,4,3,8,7,2,1,12,11]=>[5,4,6,3,8,7,9,2,10,1,12,11]=>11110010001=>00001101110
[12,9,6,5,4,3,8,7,2,11,10,1]=>[5,4,6,3,8,7,9,2,11,10,12,1]=>11110010010=>00001101101
[12,11,6,5,4,3,8,7,10,9,2,1]=>[5,4,6,3,8,7,10,9,11,2,12,1]=>11110010100=>00001101011
[12,11,6,5,4,3,10,9,8,7,2,1]=>[5,4,6,3,9,8,10,7,11,2,12,1]=>11110011000=>00001100111
[10,9,8,5,4,7,6,3,2,1,12,11]=>[5,4,7,6,8,3,9,2,10,1,12,11]=>11110100001=>00001011110
[12,9,8,5,4,7,6,3,2,11,10,1]=>[5,4,7,6,8,3,9,2,11,10,12,1]=>11110100010=>00001011101
[12,11,8,5,4,7,6,3,10,9,2,1]=>[5,4,7,6,8,3,10,9,11,2,12,1]=>11110100100=>00001011011
[12,11,10,5,4,7,6,9,8,3,2,1]=>[5,4,7,6,9,8,10,3,11,2,12,1]=>11110101000=>00001010111
[12,11,10,5,4,9,8,7,6,3,2,1]=>[5,4,8,7,9,6,10,3,11,2,12,1]=>11110110000=>00001001111
[10,9,8,7,6,5,4,3,2,1,12,11]=>[6,5,7,4,8,3,9,2,10,1,12,11]=>11111000001=>00000111110
[12,9,8,7,6,5,4,3,2,11,10,1]=>[6,5,7,4,8,3,9,2,11,10,12,1]=>11111000010=>00000111101
[12,11,8,7,6,5,4,3,10,9,2,1]=>[6,5,7,4,8,3,10,9,11,2,12,1]=>11111000100=>00000111011
[12,11,10,7,6,5,4,9,8,3,2,1]=>[6,5,7,4,9,8,10,3,11,2,12,1]=>11111001000=>00000110111
[12,11,10,9,6,5,8,7,4,3,2,1]=>[6,5,8,7,9,4,10,3,11,2,12,1]=>11111010000=>00000101111
[12,11,10,9,8,7,6,5,4,3,2,1]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>11111100000=>00000011111
[7,4,6,1,8,3,5,2]=>[8,1,4,3,6,5,7,2]=>1110100=>0001011
[8,3,5,1,7,4,6,2]=>[7,5,3,1,4,6,8,2]=>1110100=>0001011
[8,3,4,1,7,5,6,2]=>[4,3,1,7,5,6,8,2]=>1110100=>0001011
[4,6,2,1,7,5,8,3]=>[8,7,5,6,2,4,1,3]=>1100101=>0011010
[1,7,5,2,6,8,4,3]=>[1,8,6,5,2,4,7,3]=>0110110=>1001001
[7,5,2,1,6,8,4,3]=>[8,6,5,2,4,7,1,3]=>1100110=>0011001
[6,8,4,3,1,7,5,2]=>[4,3,7,1,5,8,6,2]=>1110010=>0001101
[3,6,7,5,1,8,4,2]=>[5,1,8,4,7,6,3,2]=>1111010=>0000101
[7,5,6,1,8,3,4,2]=>[8,1,6,5,3,4,7,2]=>1110100=>0001011
[3,4,6,5,7,1,8,2]=>[8,7,5,1,6,4,3,2]=>1111101=>0000010
[6,7,5,1,8,4,3,2]=>[8,5,1,4,7,3,6,2]=>1110100=>0001011
[6,8,4,1,7,5,3,2]=>[4,1,7,5,8,3,6,2]=>1110100=>0001011
[6,7,5,3,1,8,4,2]=>[5,3,8,1,4,7,6,2]=>1110010=>0001101
[8,4,2,1,6,7,5,3]=>[4,2,7,6,5,8,1,3]=>1100110=>0011001
[1,8,4,2,6,7,5,3]=>[1,4,2,7,6,5,8,3]=>0110110=>1001001
[1,5,3,2,7,6,8,4]=>[1,3,6,8,7,5,2,4]=>0100101=>1011010
[2,5,3,1,7,6,8,4]=>[3,6,8,7,5,2,1,4]=>1100101=>0011010
[2,4,6,1,7,5,8,3]=>[8,7,5,6,2,1,4,3]=>1110101=>0001010
[4,8,2,6,5,7,1,3]=>[5,7,6,2,8,4,1,3]=>1101010=>0010101
[4,6,1,2,7,5,8,3]=>[8,7,5,6,1,4,2,3]=>1100101=>0011010
[8,4,1,2,6,7,5,3]=>[4,1,7,6,5,8,2,3]=>1100110=>0011001
[5,3,1,2,7,6,8,4]=>[3,1,6,8,7,5,2,4]=>1100101=>0011010
[1,2,5,3,7,6,8,4]=>[1,2,6,8,7,5,3,4]=>0010101=>1101010
[4,3,1,2,7,6,8,5]=>[3,1,4,2,6,8,7,5]=>1100101=>0011010
[3,5,1,2,7,6,8,4]=>[6,8,7,5,1,3,2,4]=>1100101=>0011010
[2,3,5,1,7,6,8,4]=>[6,8,7,5,3,2,1,4]=>1110101=>0001010
[7,5,1,6,8,4,2,3]=>[8,4,6,5,1,7,2,3]=>1101100=>0010011
[5,2,3,1,7,6,8,4]=>[2,3,6,8,7,5,1,4]=>1000101=>0111010
[3,5,2,1,7,6,8,4]=>[6,8,7,5,2,3,1,4]=>1100101=>0011010
[1,3,5,2,7,6,8,4]=>[1,6,8,7,5,3,2,4]=>0110101=>1001010
[1,7,6,2,5,8,3,4]=>[1,5,8,6,2,7,3,4]=>0110010=>1001101
[8,3,1,5,7,6,2,4]=>[3,1,6,7,5,2,8,4]=>1101100=>0010011
[7,1,6,4,8,2,5,3]=>[4,8,1,2,6,5,7,3]=>1010100=>0101011
[8,2,6,4,7,1,5,3]=>[2,4,7,1,6,5,8,3]=>1010100=>0101011
[6,1,5,2,7,4,8,3]=>[8,7,5,1,2,4,6,3]=>1010101=>0101010
[7,6,2,5,8,3,1,4]=>[8,5,2,3,6,1,7,4]=>1101100=>0010011
[8,3,5,7,6,2,1,4]=>[6,3,2,7,5,1,8,4]=>1111100=>0000011
[1,8,3,5,7,6,2,4]=>[1,3,6,7,5,2,8,4]=>0101100=>1010011
[1,5,2,3,7,6,8,4]=>[1,6,8,7,5,2,3,4]=>0100101=>1011010
[5,2,1,3,7,6,8,4]=>[2,6,8,7,5,1,3,4]=>1000101=>0111010
[6,1,4,2,7,5,8,3]=>[4,1,2,8,7,5,6,3]=>1010101=>0101010
[4,1,3,2,7,6,8,5]=>[3,4,1,2,6,8,7,5]=>1000101=>0111010
[4,2,1,3,7,6,8,5]=>[2,4,1,3,6,8,7,5]=>1000101=>0111010
[1,4,2,3,7,6,8,5]=>[1,4,2,3,6,8,7,5]=>0100101=>1011010
[2,4,1,3,7,6,8,5]=>[4,2,1,3,6,8,7,5]=>1100101=>0011010
[2,5,1,3,7,6,8,4]=>[6,8,7,5,2,1,3,4]=>1100101=>0011010
[2,8,3,5,7,6,1,4]=>[3,6,7,5,2,1,8,4]=>1101100=>0010011
[6,8,2,3,5,7,1,4]=>[5,7,2,3,8,6,1,4]=>1100010=>0011101
[6,7,1,3,5,8,2,4]=>[5,8,1,3,7,6,2,4]=>1100010=>0011101
[8,3,5,7,6,1,2,4]=>[6,3,1,7,5,2,8,4]=>1111100=>0000011
[5,1,2,3,7,6,8,4]=>[6,8,7,5,1,2,3,4]=>1000101=>0111010
[3,1,2,4,7,6,8,5]=>[3,1,2,4,6,8,7,5]=>1000101=>0111010
[8,1,2,4,3,6,5,7]=>[4,6,8,1,2,3,5,7]=>1000000=>0111111
[8,1,3,4,2,6,7,5]=>[3,4,6,7,8,1,2,5]=>1000000=>0111111
[8,1,3,2,4,5,7,6]=>[3,7,8,1,2,4,5,6]=>1000000=>0111111
[2,7,8,3,4,5,6,1]=>[8,3,4,5,6,7,2,1]=>1110000=>0001111
[2,6,3,8,4,5,7,1]=>[3,7,8,4,5,6,2,1]=>1101000=>0010111
[6,3,2,1,4,5,8,7]=>[3,2,6,1,4,5,8,7]=>1100001=>0011110
[7,3,1,4,2,6,8,5]=>[3,1,4,6,8,7,2,5]=>1100001=>0011110
[7,4,1,5,6,8,2,3]=>[8,6,5,4,1,7,2,3]=>1101110=>0010001
[4,7,8,5,6,1,2,3]=>[6,5,1,8,2,7,4,3]=>1111100=>0000011
[3,7,8,5,6,2,1,4]=>[6,5,2,8,3,1,7,4]=>1111100=>0000011
[3,7,8,4,2,6,1,5]=>[4,6,8,2,7,3,1,5]=>1110000=>0001111
[3,7,8,2,4,5,1,6]=>[8,2,4,5,7,3,1,6]=>1110000=>0001111
[3,6,2,8,4,5,1,7]=>[8,4,5,6,2,3,1,7]=>1101000=>0010111
[2,3,6,7,4,5,8,1]=>[8,7,4,5,6,3,2,1]=>1111001=>0000110
[3,5,4,2,8,7,1,6]=>[4,2,7,5,3,1,8,6]=>1110110=>0001001
[7,4,1,2,3,8,5,6]=>[4,1,8,2,3,5,7,6]=>1100010=>0011101
[2,6,4,8,3,7,5,1]=>[7,4,3,5,8,6,2,1]=>1111010=>0000101
[2,6,5,8,7,3,4,1]=>[7,3,8,5,4,6,2,1]=>1111100=>0000011
[2,5,6,7,8,3,4,1]=>[8,3,7,4,6,5,2,1]=>1111100=>0000011
[2,4,6,7,3,8,5,1]=>[8,3,5,7,6,4,2,1]=>1111010=>0000101
[4,7,8,2,3,1,5,6]=>[8,2,7,3,4,1,5,6]=>1110000=>0001111
[3,4,6,7,2,8,1,5]=>[8,2,7,6,4,3,1,5]=>1111010=>0000101
[3,4,5,2,7,8,1,6]=>[8,5,2,4,3,1,7,6]=>1110110=>0001001
[3,4,2,5,6,8,1,7]=>[8,6,5,4,2,3,1,7]=>1101110=>0010001
[5,2,7,8,6,4,1,3]=>[2,6,4,8,1,7,5,3]=>1011100=>0100011
[5,1,2,7,8,6,4,3]=>[6,8,4,7,5,1,2,3]=>1001100=>0110011
[4,7,1,2,8,6,5,3]=>[6,8,5,7,1,4,2,3]=>1100100=>0011011
[6,8,7,1,5,3,2,4]=>[5,7,1,8,3,6,2,4]=>1110000=>0001111
[6,8,7,3,5,1,2,4]=>[5,7,3,8,1,6,2,4]=>1110000=>0001111
[7,8,1,6,3,5,2,4]=>[6,1,3,5,8,2,7,4]=>1101000=>0010111
[7,8,1,3,6,5,2,4]=>[6,5,8,1,3,7,2,4]=>1100100=>0011011
[7,8,3,6,5,2,1,4]=>[3,5,6,2,8,1,7,4]=>1101000=>0010111
[7,8,2,3,6,5,1,4]=>[6,5,8,2,3,7,1,4]=>1100100=>0011011
[8,5,7,1,6,2,3,4]=>[6,1,7,5,2,8,3,4]=>1110100=>0001011
[8,5,7,1,2,6,3,4]=>[6,7,1,5,2,8,3,4]=>1110000=>0001111
[6,2,4,8,1,7,5,3]=>[2,7,4,1,5,8,6,3]=>1011010=>0100101
[6,8,7,2,3,5,1,4]=>[7,2,5,8,3,6,1,4]=>1110000=>0001111
[6,8,2,1,7,3,5,4]=>[7,2,8,5,6,1,3,4]=>1100100=>0011011
[8,5,7,2,1,6,3,4]=>[6,7,2,5,1,8,3,4]=>1110000=>0001111
[8,5,7,1,2,3,6,4]=>[7,1,5,2,6,8,3,4]=>1110000=>0001111
[8,5,7,2,3,1,6,4]=>[7,2,5,3,6,8,1,4]=>1110000=>0001111
[1,8,7,3,5,4,6,2]=>[1,5,7,3,4,6,8,2]=>0110000=>1001111
[8,2,5,4,7,1,6,3]=>[2,4,7,5,1,6,8,3]=>1010100=>0101011
[8,7,6,1,4,2,3,5]=>[6,1,4,7,2,8,3,5]=>1110000=>0001111
[8,7,6,4,1,3,2,5]=>[4,6,1,7,3,8,2,5]=>1110000=>0001111
[1,8,7,5,4,3,6,2]=>[1,5,4,7,3,6,8,2]=>0111000=>1000111
[1,6,8,4,3,7,5,2]=>[1,4,7,3,5,8,6,2]=>0110010=>1001101
[6,8,7,3,2,5,1,4]=>[7,3,5,8,2,6,1,4]=>1110000=>0001111
[8,5,7,3,1,6,2,4]=>[6,7,3,5,1,8,2,4]=>1110000=>0001111
[8,5,7,1,3,2,6,4]=>[7,1,5,3,6,8,2,4]=>1110000=>0001111
[8,5,7,3,1,2,6,4]=>[7,3,5,1,6,8,2,4]=>1110000=>0001111
[5,8,4,7,1,2,6,3]=>[7,4,1,6,8,2,5,3]=>1111000=>0000111
[5,8,4,1,7,2,6,3]=>[4,1,7,2,6,8,5,3]=>1110100=>0001011
[5,8,4,7,1,6,2,3]=>[6,7,4,1,8,2,5,3]=>1111000=>0000111
[8,1,2,6,5,7,4,3]=>[5,7,6,4,8,1,2,3]=>1001010=>0110101
[8,2,5,6,7,4,1,3]=>[2,7,4,6,5,1,8,3]=>1011100=>0100011
[4,8,5,7,1,6,2,3]=>[6,7,1,5,2,8,4,3]=>1111000=>0000111
[4,8,5,7,1,2,6,3]=>[7,1,5,2,6,8,4,3]=>1111000=>0000111
[4,8,5,1,7,2,6,3]=>[7,5,1,6,8,2,4,3]=>1110100=>0001011
[8,5,3,1,7,2,6,4]=>[3,7,5,1,6,8,2,4]=>1100100=>0011011
[8,5,3,7,1,2,6,4]=>[3,7,1,5,2,6,8,4]=>1101000=>0010111
[6,8,1,3,7,2,5,4]=>[7,1,3,8,5,6,2,4]=>1100100=>0011011
[4,6,2,8,1,7,5,3]=>[7,2,5,8,6,4,1,3]=>1101010=>0010101
[1,8,7,4,5,3,6,2]=>[1,4,5,7,3,6,8,2]=>0110000=>1001111
[8,7,6,3,1,4,2,5]=>[6,3,7,1,4,8,2,5]=>1110000=>0001111
[8,7,6,1,3,2,4,5]=>[6,1,7,3,8,2,4,5]=>1110000=>0001111
[8,5,3,2,7,1,6,4]=>[3,7,5,2,6,8,1,4]=>1100100=>0011011
[4,8,5,2,7,1,6,3]=>[7,5,2,6,8,1,4,3]=>1110100=>0001011
[1,8,7,4,3,5,6,2]=>[1,4,7,3,5,6,8,2]=>0110000=>1001111
[1,8,7,3,4,5,6,2]=>[1,7,3,4,5,6,8,2]=>0110000=>1001111
[6,3,1,5,4,2,8,7]=>[3,1,5,4,6,2,8,7]=>1101001=>0010110
[8,3,1,5,2,7,6,4]=>[3,1,5,2,7,6,8,4]=>1101010=>0010101
[8,5,4,2,1,7,3,6]=>[4,2,5,1,7,3,8,6]=>1110010=>0001101
[8,5,4,2,1,7,6,3]=>[4,2,5,1,7,6,8,3]=>1110010=>0001101
[6,5,4,2,1,3,8,7]=>[4,2,5,1,6,3,8,7]=>1110001=>0001110
[6,5,4,2,3,1,8,7]=>[4,2,5,3,6,1,8,7]=>1110001=>0001110
[6,3,2,5,1,4,8,7]=>[3,2,5,1,6,4,8,7]=>1101001=>0010110
[6,5,4,3,1,2,8,7]=>[4,3,5,1,6,2,8,7]=>1110001=>0001110
[6,5,4,1,3,2,8,7]=>[4,1,5,3,6,2,8,7]=>1110001=>0001110
[8,5,4,1,2,7,6,3]=>[4,1,5,2,7,6,8,3]=>1110010=>0001101
[8,7,4,1,6,3,2,5]=>[4,1,6,3,7,2,8,5]=>1110100=>0001011
[8,7,4,1,6,3,5,2]=>[4,1,6,3,7,5,8,2]=>1110100=>0001011
[8,7,4,1,6,5,3,2]=>[4,1,6,5,7,3,8,2]=>1110100=>0001011
[8,5,4,1,3,7,6,2]=>[4,1,5,3,7,6,8,2]=>1110010=>0001101
[8,5,4,3,1,7,6,2]=>[4,3,5,1,7,6,8,2]=>1110010=>0001101
[8,3,2,5,1,7,6,4]=>[3,2,5,1,7,6,8,4]=>1101010=>0010101
[2,1,8,5,3,7,6,4]=>[2,1,5,3,7,6,8,4]=>1011010=>0100101
[8,3,2,5,1,7,4,6]=>[3,2,5,1,7,4,8,6]=>1101010=>0010101
[8,5,4,3,1,7,2,6]=>[4,3,5,1,7,2,8,6]=>1110010=>0001101
[8,5,4,1,3,7,2,6]=>[4,1,5,3,7,2,8,6]=>1110010=>0001101
[8,7,4,1,6,5,2,3]=>[4,1,6,5,7,2,8,3]=>1110100=>0001011
[8,7,4,1,6,2,5,3]=>[4,1,6,2,7,5,8,3]=>1110100=>0001011
[8,7,6,5,2,1,4,3]=>[5,2,6,1,7,4,8,3]=>1111000=>0000111
[8,7,4,3,6,2,1,5]=>[4,3,6,2,7,1,8,5]=>1110100=>0001011
[8,3,2,7,6,4,1,5]=>[3,2,6,4,7,1,8,5]=>1101100=>0010011
[2,1,8,7,6,4,3,5]=>[2,1,6,4,7,3,8,5]=>1011100=>0100011
[2,1,8,7,6,4,5,3]=>[2,1,6,4,7,5,8,3]=>1011100=>0100011
[8,3,2,7,6,4,5,1]=>[3,2,6,4,7,5,8,1]=>1101100=>0010011
[8,7,4,3,6,2,5,1]=>[4,3,6,2,7,5,8,1]=>1110100=>0001011
[8,7,6,5,2,4,3,1]=>[5,2,6,4,7,3,8,1]=>1111000=>0000111
[8,5,4,2,3,7,6,1]=>[4,2,5,3,7,6,8,1]=>1110010=>0001101
[8,7,4,2,6,5,3,1]=>[4,2,6,5,7,3,8,1]=>1110100=>0001011
[8,7,4,2,6,3,5,1]=>[4,2,6,3,7,5,8,1]=>1110100=>0001011
[8,7,4,2,6,3,1,5]=>[4,2,6,3,7,1,8,5]=>1110100=>0001011
[8,3,1,7,6,4,2,5]=>[3,1,6,4,7,2,8,5]=>1101100=>0010011
[8,3,1,7,6,4,5,2]=>[3,1,6,4,7,5,8,2]=>1101100=>0010011
[8,3,1,7,6,5,4,2]=>[3,1,6,5,7,4,8,2]=>1101100=>0010011
[8,3,1,5,4,7,6,2]=>[3,1,5,4,7,6,8,2]=>1101010=>0010101
[8,3,1,5,4,7,2,6]=>[3,1,5,4,7,2,8,6]=>1101010=>0010101
[8,3,1,7,6,5,2,4]=>[3,1,6,5,7,2,8,4]=>1101100=>0010011
[8,3,1,7,6,2,5,4]=>[3,1,6,2,7,5,8,4]=>1101100=>0010011
[8,7,4,2,6,1,5,3]=>[4,2,6,1,7,5,8,3]=>1110100=>0001011
[8,7,4,2,6,5,1,3]=>[4,2,6,5,7,1,8,3]=>1110100=>0001011
[8,5,4,2,3,7,1,6]=>[4,2,5,3,7,1,8,6]=>1110010=>0001101
[8,3,2,5,4,7,1,6]=>[3,2,5,4,7,1,8,6]=>1101010=>0010101
[2,1,8,5,4,7,3,6]=>[2,1,5,4,7,3,8,6]=>1011010=>0100101
[8,3,2,7,6,5,1,4]=>[3,2,6,5,7,1,8,4]=>1101100=>0010011
[8,7,4,3,6,5,1,2]=>[4,3,6,5,7,1,8,2]=>1110100=>0001011
[8,7,6,5,3,1,4,2]=>[5,3,6,1,7,4,8,2]=>1111000=>0000111
[8,7,6,5,1,3,2,4]=>[5,1,6,3,7,2,8,4]=>1111000=>0000111
[8,7,6,5,1,3,4,2]=>[5,1,6,3,7,4,8,2]=>1111000=>0000111
[8,7,6,5,1,4,3,2]=>[5,1,6,4,7,3,8,2]=>1111000=>0000111
[8,7,6,5,4,1,3,2]=>[5,4,6,1,7,3,8,2]=>1111000=>0000111
[8,7,4,3,6,1,5,2]=>[4,3,6,1,7,5,8,2]=>1110100=>0001011
[8,3,2,7,6,1,5,4]=>[3,2,6,1,7,5,8,4]=>1101100=>0010011
[2,1,8,7,6,3,5,4]=>[2,1,6,3,7,5,8,4]=>1011100=>0100011
[8,3,2,7,6,1,4,5]=>[3,2,6,1,7,4,8,5]=>1101100=>0010011
[8,7,6,5,1,4,2,3]=>[5,1,6,4,7,2,8,3]=>1111000=>0000111
[8,7,6,5,1,2,4,3]=>[5,1,6,2,7,4,8,3]=>1111000=>0000111
[7,3,5,1,8,4,6,2]=>[8,5,3,1,4,6,7,2]=>1110100=>0001011
[7,3,4,1,8,5,6,2]=>[4,3,1,8,5,6,7,2]=>1110100=>0001011
[1,6,5,2,7,4,3,8]=>[1,7,5,2,4,6,3,8]=>0110100=>1001011
[6,4,2,1,8,7,5,3]=>[4,2,7,5,8,6,1,3]=>1100110=>0011001
[1,5,3,2,7,6,4,8]=>[1,3,6,7,5,2,4,8]=>0100100=>1011011
[5,3,2,1,8,7,6,4]=>[3,2,7,6,8,5,1,4]=>1100110=>0011001
[2,5,3,1,7,8,6,4]=>[3,8,6,7,5,2,1,4]=>1100110=>0011001
[2,6,5,1,7,8,4,3]=>[8,5,2,1,4,7,6,3]=>1110110=>0001001
[4,5,7,1,6,8,2,3]=>[8,6,1,7,5,2,4,3]=>1110110=>0001001
[6,4,1,2,8,5,3,7]=>[4,1,8,5,6,2,3,7]=>1100100=>0011011
[5,3,1,2,8,6,4,7]=>[3,1,6,8,5,2,4,7]=>1100100=>0011011
[4,3,1,2,8,6,5,7]=>[3,1,4,2,6,8,5,7]=>1100100=>0011011
[7,1,5,6,8,2,3,4]=>[8,1,2,6,5,3,7,4]=>1011100=>0100011
[7,4,1,6,8,5,2,3]=>[8,5,6,4,1,7,2,3]=>1101100=>0010011
[5,2,3,1,8,6,7,4]=>[2,3,6,7,8,5,1,4]=>1000100=>0111011
[3,5,2,1,6,8,7,4]=>[7,8,6,5,2,3,1,4]=>1100110=>0011001
[1,6,2,5,7,3,4,8]=>[1,7,5,2,3,6,4,8]=>0101100=>1010011
[6,2,1,5,8,7,3,4]=>[2,7,5,1,3,8,6,4]=>1001110=>0110001
[7,3,1,5,8,6,2,4]=>[3,1,6,8,5,2,7,4]=>1101100=>0010011
[6,2,4,1,8,5,7,3]=>[2,4,1,7,8,5,6,3]=>1010100=>0101011
[6,2,5,1,8,4,7,3]=>[2,7,8,5,1,4,6,3]=>1010100=>0101011
[7,3,1,4,8,6,2,5]=>[3,1,4,6,8,2,7,5]=>1100100=>0011011
[6,2,1,4,8,7,3,5]=>[2,4,7,1,3,8,6,5]=>1000110=>0111001
[1,6,2,4,7,3,5,8]=>[1,4,7,2,3,6,5,8]=>0100100=>1011011
[5,2,1,3,8,7,4,6]=>[2,7,5,1,3,4,8,6]=>1000110=>0111001
[3,6,7,1,4,8,2,5]=>[8,1,4,7,6,3,2,5]=>1110010=>0001101
[7,6,1,4,8,3,2,5]=>[4,8,1,3,6,2,7,5]=>1100100=>0011011
[4,2,1,3,8,7,5,6]=>[2,4,1,3,7,5,8,6]=>1000110=>0111001
[2,6,1,4,7,8,3,5]=>[4,8,2,1,3,7,6,5]=>1100110=>0011001
[7,1,4,6,8,2,3,5]=>[8,4,1,2,6,3,7,5]=>1011100=>0100011
[6,1,2,4,8,3,5,7]=>[4,8,1,2,3,6,5,7]=>1000100=>0111011
[5,2,3,1,6,4,8,7]=>[2,3,6,5,1,4,8,7]=>1000101=>0111010
[6,3,5,2,4,1,8,7]=>[5,3,2,4,6,1,8,7]=>1110001=>0001110
[5,2,4,1,6,3,8,7]=>[2,4,1,6,5,3,8,7]=>1010101=>0101010
[4,1,6,3,5,2,8,7]=>[5,6,3,4,1,2,8,7]=>1010001=>0101110
[6,3,4,1,5,2,8,7]=>[4,3,1,5,6,2,8,7]=>1110001=>0001110
[5,2,7,3,4,1,8,6]=>[2,8,7,3,4,5,1,6]=>1010001=>0101110
[6,2,7,3,4,1,8,5]=>[2,8,7,3,4,6,1,5]=>1010001=>0101110
[7,3,4,1,5,2,8,6]=>[4,3,1,5,8,7,2,6]=>1110001=>0001110
[4,1,7,3,5,2,8,6]=>[5,8,7,3,4,1,2,6]=>1010001=>0101110
[3,1,7,4,5,2,8,6]=>[4,5,8,7,3,1,2,6]=>1010001=>0101110
[2,1,7,4,5,3,8,6]=>[2,1,4,5,8,7,3,6]=>1010001=>0101110
[8,6,7,3,4,1,5,2]=>[7,3,4,6,1,5,8,2]=>1110000=>0001111
[8,5,7,3,4,1,6,2]=>[7,3,4,5,1,6,8,2]=>1110000=>0001111
[8,4,7,3,5,1,6,2]=>[5,7,3,4,1,6,8,2]=>1110000=>0001111
[4,1,8,5,7,3,6,2]=>[7,5,3,6,8,4,1,2]=>1011100=>0100011
[2,1,8,5,7,4,6,3]=>[2,1,7,5,4,6,8,3]=>1011100=>0100011
[2,1,7,4,6,3,8,5]=>[2,1,4,6,3,8,7,5]=>1010101=>0101010
[3,1,7,4,6,2,8,5]=>[4,6,3,1,2,8,7,5]=>1010101=>0101010
[4,1,7,3,6,2,8,5]=>[6,3,4,1,2,8,7,5]=>1010101=>0101010
[5,1,7,3,6,2,8,4]=>[6,3,8,7,5,1,2,4]=>1010101=>0101010
[6,2,7,3,5,1,8,4]=>[2,5,8,7,3,6,1,4]=>1010001=>0101110
[6,2,8,4,7,3,5,1]=>[2,4,7,3,8,5,6,1]=>1010100=>0101011
[7,3,6,2,5,1,8,4]=>[5,6,3,2,8,7,1,4]=>1110001=>0001110
[6,2,5,1,7,3,8,4]=>[2,8,7,5,1,6,3,4]=>1010101=>0101010
[6,2,4,1,7,3,8,5]=>[2,4,1,8,7,3,6,5]=>1010101=>0101010
[8,5,7,3,6,2,4,1]=>[6,3,7,5,2,4,8,1]=>1110100=>0001011
[6,2,3,1,7,4,8,5]=>[2,3,8,7,1,4,6,5]=>1000101=>0111010
[4,2,3,1,7,5,8,6]=>[2,3,4,1,8,7,5,6]=>1000101=>0111010
[3,1,4,2,8,6,7,5]=>[4,3,1,2,6,7,8,5]=>1010100=>0101011
[6,2,3,1,8,5,7,4]=>[2,3,7,8,5,6,1,4]=>1000100=>0111011
[7,4,8,5,6,2,3,1]=>[6,5,2,8,4,3,7,1]=>1111100=>0000011
[8,5,6,2,4,1,7,3]=>[6,2,4,5,1,7,8,3]=>1110000=>0001111
[5,2,4,1,8,6,7,3]=>[2,4,1,6,7,8,5,3]=>1010100=>0101011
[4,1,5,2,8,6,7,3]=>[6,7,8,5,1,2,4,3]=>1010100=>0101011
[2,1,6,3,8,5,7,4]=>[2,1,7,8,5,6,3,4]=>1010100=>0101011
[3,1,6,2,8,5,7,4]=>[7,8,5,6,3,1,2,4]=>1010100=>0101011
[4,1,6,2,8,5,7,3]=>[7,8,5,6,1,2,4,3]=>1010100=>0101011
[5,1,6,2,8,4,7,3]=>[7,8,1,2,4,6,5,3]=>1010100=>0101011
[8,4,6,2,5,1,7,3]=>[5,6,2,4,1,7,8,3]=>1110000=>0001111
[7,3,8,4,6,2,5,1]=>[4,6,3,2,8,5,7,1]=>1110100=>0001011
[6,2,7,3,8,4,5,1]=>[2,8,3,4,7,5,6,1]=>1010100=>0101011
[8,4,5,1,6,2,7,3]=>[6,5,1,4,2,7,8,3]=>1110100=>0001011
[5,1,8,4,6,2,7,3]=>[4,6,1,2,7,8,5,3]=>1010100=>0101011
[4,1,8,5,6,2,7,3]=>[6,5,1,2,7,8,4,3]=>1011100=>0100011
[3,1,8,5,6,2,7,4]=>[6,5,3,1,2,7,8,4]=>1011100=>0100011
[2,1,8,5,6,3,7,4]=>[2,1,6,5,3,7,8,4]=>1011100=>0100011
[2,1,7,4,8,5,6,3]=>[2,1,4,8,5,6,7,3]=>1010100=>0101011
[3,1,7,4,8,5,6,2]=>[4,8,5,6,7,3,1,2]=>1010100=>0101011
[4,1,7,3,8,5,6,2]=>[8,5,6,7,3,4,1,2]=>1010100=>0101011
[7,3,8,4,5,1,6,2]=>[4,5,8,3,1,6,7,2]=>1110000=>0001111
[7,3,6,2,8,4,5,1]=>[8,3,2,4,6,5,7,1]=>1110100=>0001011
[7,8,5,6,1,3,4,2]=>[6,1,5,3,8,4,7,2]=>1111000=>0000111
[7,8,1,3,6,2,5,4]=>[6,1,3,8,5,7,2,4]=>1100100=>0011011
[1,3,8,4,7,2,5,6]=>[1,4,7,3,2,8,5,6]=>0110100=>1001011
[3,6,1,4,7,2,5,8]=>[4,7,1,3,2,6,5,8]=>1100100=>0011011
[1,4,8,2,5,7,3,6]=>[1,5,7,2,4,3,8,6]=>0110010=>1001101
[7,8,1,5,4,6,3,2]=>[5,4,6,8,1,3,7,2]=>1101000=>0010111
[7,8,2,1,6,3,4,5]=>[6,2,8,1,3,4,7,5]=>1100100=>0011011
[7,8,3,5,6,4,1,2]=>[3,6,5,4,8,1,7,2]=>1101100=>0010011
[7,8,5,1,4,2,6,3]=>[5,1,4,8,2,6,7,3]=>1110000=>0001111
[7,8,4,5,3,1,6,2]=>[5,4,3,8,1,6,7,2]=>1111000=>0000111
[1,5,8,4,3,2,7,6]=>[1,4,7,8,3,5,2,6]=>0110000=>1001111
[5,6,1,4,3,2,7,8]=>[4,6,1,3,5,2,7,8]=>1100000=>0011111
[2,6,4,8,3,7,1,5]=>[7,4,3,8,6,2,1,5]=>1111010=>0000101
[1,4,6,8,3,7,5,2]=>[1,7,3,5,8,6,4,2]=>0111010=>1000101
[2,4,8,5,3,1,6,7]=>[5,3,8,4,2,1,6,7]=>1111000=>0000111
[3,5,8,4,7,6,1,2]=>[4,6,7,1,8,5,3,2]=>1110100=>0001011
[1,6,2,4,7,3,8,5]=>[1,4,8,7,2,3,6,5]=>0100101=>1011010
[5,6,2,1,4,7,8,3]=>[8,7,6,2,4,5,1,3]=>1100011=>0011100
[4,6,2,5,3,1,8,7]=>[5,2,3,6,4,1,8,7]=>1101001=>0010110
[4,7,5,1,3,6,8,2]=>[5,1,6,8,7,3,4,2]=>1110001=>0001110
[7,5,3,6,2,4,1,8]=>[3,6,2,5,4,7,1,8]=>1101000=>0010111
[5,7,3,6,1,4,8,2]=>[3,6,1,8,7,4,5,2]=>1101001=>0010110
[5,3,6,7,2,1,8,4]=>[8,7,3,2,6,1,5,4]=>1111001=>0000110
[6,3,1,2,4,5,8,7]=>[3,1,6,2,4,5,8,7]=>1100001=>0011110
[1,4,7,2,5,3,8,6]=>[1,5,8,7,2,4,3,6]=>0110001=>1001110
[3,6,1,8,4,2,5,7]=>[8,4,6,1,3,2,5,7]=>1101000=>0010111
[1,6,7,5,8,2,4,3]=>[1,8,5,2,7,4,6,3]=>0111100=>1000011
[3,5,6,7,8,1,4,2]=>[8,1,7,4,6,5,3,2]=>1111100=>0000011
[3,6,5,7,8,2,1,4]=>[8,2,7,5,3,1,6,4]=>1111100=>0000011
[2,5,7,6,8,1,3,4]=>[8,2,1,6,3,7,5,4]=>1111100=>0000011
[2,7,5,6,8,4,1,3]=>[8,4,6,5,2,1,7,3]=>1111100=>0000011
[3,7,6,8,5,4,1,2]=>[5,8,4,6,1,7,3,2]=>1111000=>0000111
[4,3,8,5,6,7,1,2]=>[7,6,5,3,1,8,4,2]=>1111110=>0000001
[4,2,8,1,6,3,7,5]=>[2,6,1,4,3,7,8,5]=>1010100=>0101011
[3,1,8,5,4,6,7,2]=>[5,4,6,7,8,3,1,2]=>1011000=>0100111
[3,2,8,4,5,6,1,7]=>[2,4,5,6,8,3,1,7]=>1010000=>0101111
[3,4,7,1,5,2,6,8]=>[5,7,1,4,3,2,6,8]=>1110000=>0001111
[4,3,7,8,1,2,6,5]=>[8,3,1,6,7,4,2,5]=>1111000=>0000111
[1,7,3,8,5,2,6,4]=>[1,3,5,8,2,6,7,4]=>0101000=>1010111
[4,1,8,3,6,2,5,7]=>[6,3,4,1,2,8,5,7]=>1010100=>0101011
[5,7,8,6,3,2,1,4]=>[6,3,8,2,7,1,5,4]=>1111000=>0000111
[7,6,5,8,1,3,4,2]=>[8,1,5,3,6,4,7,2]=>1111000=>0000111
[1,6,4,3,8,2,5,7]=>[1,4,3,8,2,6,5,7]=>0110100=>1001011
[7,1,3,4,8,2,6,5]=>[3,4,8,1,2,6,7,5]=>1000100=>0111011
[3,6,5,4,1,2,7,8]=>[4,5,1,6,3,2,7,8]=>1110000=>0001111
[2,4,5,1,7,8,6,3]=>[8,6,7,5,2,1,4,3]=>1110110=>0001001
[2,6,3,4,5,8,1,7]=>[3,4,5,8,6,2,1,7]=>1100010=>0011101
[2,6,4,1,8,3,7,5]=>[4,2,1,7,8,3,6,5]=>1110100=>0001011
[7,3,6,4,8,5,1,2]=>[4,8,5,6,3,1,7,2]=>1110100=>0001011
[7,2,1,4,8,3,5,6]=>[2,4,8,1,3,7,5,6]=>1000100=>0111011
[7,2,5,6,3,8,1,4]=>[2,8,6,3,5,1,7,4]=>1011010=>0100101
[6,5,2,7,1,8,4,3]=>[8,2,5,4,7,6,1,3]=>1101010=>0010101
[5,6,7,4,2,8,1,3]=>[4,8,2,7,6,1,5,3]=>1110010=>0001101
[5,7,6,4,1,8,3,2]=>[4,8,6,1,7,3,5,2]=>1110010=>0001101
[1,7,5,2,4,8,3,6]=>[1,5,2,4,8,3,7,6]=>0110010=>1001101
[6,1,5,2,8,3,4,7]=>[8,5,1,2,6,3,4,7]=>1010100=>0101011
[1,6,5,4,2,3,8,7]=>[1,4,5,2,6,3,8,7]=>0110001=>1001110
[7,1,5,3,4,2,8,6]=>[5,3,4,8,7,1,2,6]=>1010001=>0101110
[7,5,6,4,1,2,8,3]=>[4,6,1,5,2,8,7,3]=>1110001=>0001110
[7,5,2,4,3,1,6,8]=>[4,5,2,3,7,1,6,8]=>1100000=>0011111
[7,1,4,2,5,3,6,8]=>[4,1,2,5,7,3,6,8]=>1010000=>0101111
[6,8,1,4,2,5,7,3]=>[4,7,8,1,5,6,2,3]=>1100000=>0011111
[1,6,4,2,5,7,3,8]=>[1,4,2,5,7,6,3,8]=>0110010=>1001101
[1,6,3,7,5,4,2,8]=>[1,3,5,7,4,6,2,8]=>0101000=>1010111
[7,3,1,6,4,5,2,8]=>[3,1,6,4,5,7,2,8]=>1101000=>0010111
[6,8,1,2,3,4,7,5]=>[7,8,1,6,2,3,4,5]=>1100000=>0011111
[1,5,7,2,3,8,6,4]=>[1,8,6,7,2,5,3,4]=>0110010=>1001101
[5,1,8,2,3,6,7,4]=>[6,7,8,1,2,5,3,4]=>1010000=>0101111
[5,8,2,3,7,6,4,1]=>[6,7,2,3,4,8,5,1]=>1100100=>0011011
[6,8,2,4,1,5,7,3]=>[4,7,8,2,5,6,1,3]=>1100000=>0011111
[6,8,3,1,2,4,7,5]=>[3,7,8,1,6,2,4,5]=>1100000=>0011111
[2,6,4,1,5,7,3,8]=>[4,2,1,5,7,6,3,8]=>1110010=>0001101
[2,1,4,7,8,5,6,3]=>[2,1,8,5,6,7,4,3]=>1011100=>0100011
[2,5,7,8,1,4,6,3]=>[8,2,1,6,7,4,5,3]=>1111000=>0000111
[5,3,4,1,8,6,7,2]=>[4,3,1,6,7,8,5,2]=>1110100=>0001011
[5,2,1,8,6,3,7,4]=>[2,6,1,3,7,8,5,4]=>1001100=>0110011
[4,2,8,6,5,3,7,1]=>[2,5,6,3,7,8,4,1]=>1011000=>0100111
[4,2,8,5,7,6,3,1]=>[2,6,7,5,3,8,4,1]=>1011100=>0100011
[1,4,2,7,5,8,6,3]=>[1,5,8,6,7,4,2,3]=>0101010=>1010101
[4,1,8,6,7,5,3,2]=>[7,5,6,3,8,4,1,2]=>1011100=>0100011
[5,8,7,4,3,6,1,2]=>[4,6,7,3,8,1,5,2]=>1110000=>0001111
[6,4,8,3,1,7,2,5]=>[7,3,4,1,8,6,2,5]=>1110010=>0001101
[6,4,2,8,7,1,3,5]=>[7,4,2,8,1,3,6,5]=>1101100=>0010011
[6,3,8,7,2,5,1,4]=>[7,3,2,5,8,1,6,4]=>1111000=>0000111
[1,5,3,7,8,6,2,4]=>[1,3,6,8,2,7,5,4]=>0101100=>1010011
[1,5,7,6,4,2,8,3]=>[1,6,4,8,7,2,5,3]=>0111001=>1000110
[5,8,7,4,1,6,2,3]=>[4,6,7,1,8,2,5,3]=>1110000=>0001111
[6,4,8,1,2,7,3,5]=>[7,1,4,2,8,6,3,5]=>1110010=>0001101
[6,8,5,3,1,2,7,4]=>[5,3,7,8,1,6,2,4]=>1110000=>0001111
[4,5,1,2,6,8,7,3]=>[7,8,6,5,1,4,2,3]=>1100110=>0011001
[3,5,6,1,8,4,7,2]=>[7,8,1,4,6,5,3,2]=>1110100=>0001011
[3,5,7,1,2,8,6,4]=>[8,6,7,1,5,3,2,4]=>1110010=>0001101
[3,6,2,7,5,1,4,8]=>[5,7,2,3,1,6,4,8]=>1101000=>0010111
[4,2,6,1,7,3,5,8]=>[2,7,1,4,3,6,5,8]=>1010100=>0101011
[4,6,3,1,2,7,5,8]=>[3,7,6,1,4,2,5,8]=>1100010=>0011101
[3,4,6,5,8,7,1,2]=>[7,5,1,8,6,4,3,2]=>1111110=>0000001
[3,1,4,5,8,6,7,2]=>[6,7,8,5,4,3,1,2]=>1011100=>0100011
[2,1,7,5,8,6,4,3]=>[2,1,6,8,5,4,7,3]=>1011100=>0100011
[1,2,7,5,3,8,6,4]=>[1,2,5,3,8,6,7,4]=>0011010=>1100101
[6,4,1,7,5,2,3,8]=>[5,7,4,1,6,2,3,8]=>1101000=>0010111
[6,1,3,7,5,2,4,8]=>[3,5,7,1,2,6,4,8]=>1001000=>0110111
[3,1,2,6,8,5,4,7]=>[3,1,2,8,5,6,4,7]=>1001100=>0110011
[1,3,7,2,4,8,6,5]=>[1,8,6,7,3,2,4,5]=>0110010=>1001101
[2,4,1,7,8,6,5,3]=>[6,8,5,7,4,2,1,3]=>1101100=>0010011
[3,4,7,5,1,8,6,2]=>[5,1,8,6,7,4,3,2]=>1111010=>0000101
[2,7,4,1,5,8,6,3]=>[4,2,1,5,8,6,7,3]=>1110010=>0001101
[2,3,7,1,5,8,6,4]=>[5,8,6,7,3,2,1,4]=>1110010=>0001101
[5,2,8,1,3,7,4,6]=>[2,7,1,5,3,4,8,6]=>1010010=>0101101
[2,1,6,8,3,4,7,5]=>[2,1,7,8,3,6,4,5]=>1011000=>0100111
[2,6,8,3,1,5,7,4]=>[7,8,3,5,6,2,1,4]=>1110000=>0001111
[2,8,6,4,1,5,7,3]=>[4,6,2,1,5,7,8,3]=>1110000=>0001111
[3,6,4,8,5,1,7,2]=>[5,7,8,4,1,6,3,2]=>1111000=>0000111
[6,3,7,4,5,1,8,2]=>[4,5,8,7,3,1,6,2]=>1110001=>0001110
[5,2,1,7,8,3,4,6]=>[2,8,1,3,7,5,4,6]=>1001100=>0110011
[4,7,2,3,6,8,1,5]=>[8,6,2,3,4,1,7,5]=>1100110=>0011001
[5,7,4,6,2,8,1,3]=>[8,6,4,2,7,1,5,3]=>1111010=>0000101
[5,7,3,4,6,1,8,2]=>[3,4,6,1,8,7,5,2]=>1100101=>0011010
[5,3,8,4,6,1,7,2]=>[4,6,3,1,7,8,5,2]=>1110100=>0001011
[8,5,2,4,1,6,7,3]=>[4,5,2,6,7,8,1,3]=>1100000=>0011111
[8,2,3,5,1,6,7,4]=>[2,3,5,1,6,7,8,4]=>1001000=>0110111
[4,2,8,3,6,7,1,5]=>[2,7,6,3,4,1,8,5]=>1010110=>0101001
[4,8,3,1,7,2,5,6]=>[3,7,1,4,2,8,5,6]=>1100100=>0011011
[4,6,8,3,1,7,5,2]=>[7,3,5,8,6,1,4,2]=>1110010=>0001101
[6,3,8,2,7,1,5,4]=>[7,3,2,8,5,6,1,4]=>1110100=>0001011
[6,3,1,8,2,4,7,5]=>[3,1,7,8,2,6,4,5]=>1101000=>0010111
[5,3,8,1,2,6,4,7]=>[6,8,3,1,5,2,4,7]=>1110000=>0001111
[5,7,4,1,6,2,3,8]=>[4,1,6,2,7,5,3,8]=>1110100=>0001011
[8,5,4,1,2,6,3,7]=>[4,1,5,2,6,8,3,7]=>1110000=>0001111
[5,1,8,4,2,7,3,6]=>[4,7,1,2,5,3,8,6]=>1010010=>0101101
[1,6,2,8,5,3,7,4]=>[1,5,7,8,2,3,6,4]=>0101000=>1010111
[6,8,5,3,1,7,4,2]=>[5,3,7,1,4,8,6,2]=>1110010=>0001101
[8,4,5,1,2,6,3,7]=>[5,1,4,2,6,8,3,7]=>1110000=>0001111
[5,6,3,7,1,2,4,8]=>[3,7,1,6,2,5,4,8]=>1101000=>0010111
[1,6,3,7,2,8,4,5]=>[1,3,8,2,7,6,4,5]=>0101010=>1010101
[6,3,2,7,8,5,1,4]=>[3,2,8,5,7,1,6,4]=>1101100=>0010011
[4,5,7,8,3,1,6,2]=>[8,3,6,7,1,5,4,2]=>1111000=>0000111
[4,7,2,5,8,1,6,3]=>[8,5,2,6,7,4,1,3]=>1101100=>0010011
[3,8,2,4,6,7,1,5]=>[4,7,6,2,3,1,8,5]=>1100110=>0011001
[3,5,6,8,2,7,1,4]=>[7,2,8,6,3,1,5,4]=>1111010=>0000101
[2,4,5,6,8,1,7,3]=>[7,8,2,1,6,5,4,3]=>1111100=>0000011
[6,8,7,3,4,1,2,5]=>[7,3,4,8,1,6,2,5]=>1110000=>0001111
[6,8,4,7,1,5,3,2]=>[7,4,1,5,8,3,6,2]=>1111000=>0000111
[6,8,4,7,2,5,3,1]=>[7,4,2,5,8,3,6,1]=>1111000=>0000111
[5,4,8,7,1,6,3,2]=>[6,7,1,8,4,3,5,2]=>1111000=>0000111
[5,3,8,7,6,1,2,4]=>[6,3,1,7,2,8,5,4]=>1111100=>0000011
[4,3,8,7,6,1,2,5]=>[6,3,1,7,4,2,8,5]=>1111100=>0000011
[4,8,3,7,5,1,2,6]=>[3,5,7,1,8,4,2,6]=>1101000=>0010111
[8,3,4,6,5,1,2,7]=>[5,6,4,3,1,8,2,7]=>1111000=>0000111
[3,8,4,7,5,1,2,6]=>[5,7,4,1,8,3,2,6]=>1111000=>0000111
[3,4,8,7,6,1,2,5]=>[6,1,7,4,3,2,8,5]=>1111100=>0000011
[3,5,8,7,6,1,2,4]=>[6,1,7,3,2,8,5,4]=>1111100=>0000011
[4,5,8,7,6,1,2,3]=>[6,1,7,2,8,5,4,3]=>1111100=>0000011
[4,5,8,7,2,6,3,1]=>[6,7,2,8,3,5,4,1]=>1111000=>0000111
[3,5,8,2,7,6,4,1]=>[6,7,2,4,8,5,3,1]=>1110100=>0001011
[3,5,8,1,7,6,4,2]=>[6,7,1,4,8,5,3,2]=>1110100=>0001011
[2,5,8,7,1,6,3,4]=>[6,7,2,1,8,3,5,4]=>1111000=>0000111
[2,4,8,7,1,6,3,5]=>[6,7,2,1,8,4,3,5]=>1111000=>0000111
[2,8,4,7,1,5,3,6]=>[7,4,2,1,5,8,3,6]=>1111000=>0000111
[8,2,4,6,1,5,3,7]=>[2,6,4,1,5,8,3,7]=>1011000=>0100111
[8,1,4,6,2,5,3,7]=>[6,4,1,2,5,8,3,7]=>1011000=>0100111
[1,8,4,7,2,5,3,6]=>[1,7,4,2,5,8,3,6]=>0111000=>1000111
[1,4,8,7,2,6,3,5]=>[1,6,7,2,8,4,3,5]=>0111000=>1000111
[1,5,8,2,7,6,4,3]=>[1,6,7,2,4,8,5,3]=>0110100=>1001011
[2,5,8,3,7,6,4,1]=>[6,7,3,4,8,5,2,1]=>1110100=>0001011
[1,4,2,8,7,6,5,3]=>[1,6,7,5,8,4,2,3]=>0101100=>1010011
[1,3,8,2,7,6,4,5]=>[1,6,7,3,2,4,8,5]=>0110100=>1001011
[1,8,3,2,7,5,4,6]=>[1,3,7,5,8,2,4,6]=>0100100=>1011011
[8,1,3,2,6,5,4,7]=>[3,6,5,8,1,2,4,7]=>1000100=>0111011
[8,2,3,1,6,5,4,7]=>[2,3,6,5,8,1,4,7]=>1000100=>0111011
[2,8,3,1,7,5,4,6]=>[3,7,5,8,2,1,4,6]=>1100100=>0011011
[2,3,8,1,7,6,4,5]=>[6,7,3,2,1,4,8,5]=>1110100=>0001011
[3,4,1,8,7,6,5,2]=>[6,7,5,8,4,1,3,2]=>1101100=>0010011
[4,3,1,8,7,6,5,2]=>[3,1,6,7,5,8,4,2]=>1101100=>0010011
[3,8,2,1,7,5,4,6]=>[7,5,8,2,3,1,4,6]=>1100100=>0011011
[5,3,8,1,7,6,4,2]=>[6,7,3,1,4,8,5,2]=>1110100=>0001011
[5,3,8,2,7,6,4,1]=>[6,7,3,2,4,8,5,1]=>1110100=>0001011
[6,8,3,2,7,5,4,1]=>[3,7,5,8,2,4,6,1]=>1100100=>0011011
[6,8,3,1,7,5,4,2]=>[3,7,5,8,1,4,6,2]=>1100100=>0011011
[6,8,2,1,7,5,4,3]=>[7,5,8,2,4,6,1,3]=>1100100=>0011011
[6,8,2,7,1,5,3,4]=>[7,2,5,8,1,3,6,4]=>1101000=>0010111
[6,8,7,2,1,4,3,5]=>[7,2,8,1,4,6,3,5]=>1110000=>0001111
[8,5,6,1,2,4,3,7]=>[6,1,5,2,4,8,3,7]=>1110000=>0001111
[5,8,7,1,2,4,3,6]=>[7,1,8,2,4,5,3,6]=>1110000=>0001111
[5,2,8,3,7,6,4,1]=>[2,6,7,3,4,8,5,1]=>1010100=>0101011
[5,1,8,3,7,6,4,2]=>[6,7,3,4,8,5,1,2]=>1010100=>0101011
[5,1,8,7,2,6,3,4]=>[6,7,1,2,8,3,5,4]=>1011000=>0100111
[4,1,8,7,2,6,3,5]=>[6,7,1,2,8,4,3,5]=>1011000=>0100111
[4,8,1,7,2,5,3,6]=>[7,1,5,8,4,2,3,6]=>1101000=>0010111
[8,3,1,2,6,5,4,7]=>[3,1,6,5,8,2,4,7]=>1100100=>0011011
[3,8,1,2,7,5,4,6]=>[7,5,8,1,3,2,4,6]=>1100100=>0011011
[3,1,8,2,7,6,4,5]=>[6,7,3,1,2,4,8,5]=>1010100=>0101011
[3,1,2,8,7,6,5,4]=>[3,1,2,6,7,5,8,4]=>1001100=>0110011
[4,1,3,8,7,6,5,2]=>[3,6,7,5,8,4,1,2]=>1001100=>0110011
[3,1,4,8,7,6,5,2]=>[6,7,5,8,4,3,1,2]=>1011100=>0100011
[2,1,8,3,7,6,4,5]=>[2,1,6,7,3,4,8,5]=>1010100=>0101011
[2,8,1,3,7,5,4,6]=>[7,5,8,2,1,3,4,6]=>1100100=>0011011
[8,2,1,3,6,5,4,7]=>[2,6,5,8,1,3,4,7]=>1000100=>0111011
[8,1,2,3,6,5,4,7]=>[6,5,8,1,2,3,4,7]=>1000100=>0111011
[1,8,2,3,7,5,4,6]=>[1,7,5,8,2,3,4,6]=>0100100=>1011011
[1,2,8,3,7,6,4,5]=>[1,2,6,7,3,4,8,5]=>0010100=>1101011
[1,4,3,6,8,2,5,7]=>[1,3,8,4,2,6,5,7]=>0101100=>1010011
[3,1,6,2,5,8,4,7]=>[5,8,6,3,1,2,4,7]=>1010010=>0101101
[3,5,1,8,2,4,7,6]=>[7,8,1,3,2,5,4,6]=>1101000=>0010111
[1,4,2,6,5,8,3,7]=>[1,5,8,6,4,2,3,7]=>0101010=>1010101
[1,5,4,2,6,8,3,7]=>[1,4,2,8,6,5,3,7]=>0110110=>1001001
[1,6,4,2,5,8,3,7]=>[1,4,2,5,8,6,3,7]=>0110010=>1001101
[1,5,2,6,4,8,3,7]=>[1,8,6,4,5,2,3,7]=>0101010=>1010101
[1,2,6,5,4,8,3,7]=>[1,2,5,4,8,6,3,7]=>0011010=>1100101
[1,2,5,4,7,3,8,6]=>[1,2,4,8,7,5,3,6]=>0010101=>1101010
[4,1,2,6,3,8,7,5]=>[7,8,6,4,1,2,3,5]=>1001010=>0110101
[7,1,5,4,2,8,3,6]=>[4,5,1,2,8,3,7,6]=>1010010=>0101101
[1,4,7,5,2,8,3,6]=>[1,5,2,8,4,3,7,6]=>0111010=>1000101
[7,1,3,5,2,8,4,6]=>[3,5,1,2,8,4,7,6]=>1001010=>0110101
[7,2,5,1,8,3,4,6]=>[2,8,5,1,7,3,4,6]=>1010100=>0101011
[1,4,5,2,8,7,3,6]=>[1,7,5,2,4,3,8,6]=>0110110=>1001001
[1,6,4,2,8,3,7,5]=>[1,4,2,7,8,3,6,5]=>0110100=>1001011
[1,4,2,8,3,7,6,5]=>[1,7,6,8,4,2,3,5]=>0101010=>1010101
[1,2,8,6,5,3,7,4]=>[1,2,5,6,3,7,8,4]=>0011000=>1100111
[1,5,2,8,6,3,7,4]=>[1,6,2,3,7,8,5,4]=>0101100=>1010011
[1,6,4,2,8,7,3,5]=>[1,4,2,7,3,8,6,5]=>0110110=>1001001
[6,2,1,8,7,3,4,5]=>[2,7,1,3,8,4,6,5]=>1001100=>0110011
[7,3,1,6,2,8,4,5]=>[3,1,8,6,2,7,4,5]=>1101010=>0010101
[1,7,6,4,2,8,3,5]=>[1,4,8,6,2,7,3,5]=>0110010=>1001101
[1,7,5,2,6,3,8,4]=>[1,6,5,2,8,7,3,4]=>0110101=>1001010
[1,6,2,7,5,3,8,4]=>[1,5,8,7,2,3,6,4]=>0101001=>1010110
[1,2,7,6,5,3,8,4]=>[1,2,5,6,3,8,7,4]=>0011001=>1100110
[1,2,6,5,3,8,7,4]=>[1,2,5,3,7,8,6,4]=>0011010=>1100101
[1,5,2,6,3,8,7,4]=>[1,7,8,6,2,3,5,4]=>0101010=>1010101
[1,5,2,7,6,3,8,4]=>[1,6,2,3,8,7,5,4]=>0101101=>1010010
[1,6,5,2,7,3,8,4]=>[1,8,7,5,2,6,3,4]=>0110101=>1001010
[4,1,2,8,6,3,7,5]=>[6,4,1,2,3,7,8,5]=>1001100=>0110011
[3,1,8,6,2,4,7,5]=>[6,3,1,2,7,8,4,5]=>1011000=>0100111
[1,4,2,8,7,3,6,5]=>[1,7,4,2,3,6,8,5]=>0101100=>1010011
[8,1,5,4,2,7,3,6]=>[4,5,1,2,7,3,8,6]=>1010010=>0101101
[1,4,8,5,2,7,3,6]=>[1,5,2,7,4,3,8,6]=>0111010=>1000101
[8,5,3,1,7,2,4,6]=>[3,7,5,1,8,2,4,6]=>1100100=>0011011
[8,6,2,1,7,3,4,5]=>[7,2,6,1,3,4,8,5]=>1100100=>0011011
[1,8,6,4,2,7,3,5]=>[1,4,7,6,2,8,3,5]=>0110010=>1001101
[1,2,8,5,3,7,6,4]=>[1,2,5,3,7,6,8,4]=>0011010=>1100101
[1,2,6,3,8,7,5,4]=>[1,2,7,5,8,6,3,4]=>0010110=>1101001
[1,2,7,6,3,8,5,4]=>[1,2,8,6,3,5,7,4]=>0011010=>1100101
[1,7,2,8,5,3,6,4]=>[1,5,8,2,3,6,7,4]=>0101000=>1010111
[1,7,4,2,8,6,3,5]=>[1,4,2,6,8,3,7,5]=>0110100=>1001011
[7,1,8,3,2,6,4,5]=>[6,8,3,7,1,2,4,5]=>1010000=>0101111
[7,2,1,8,6,3,4,5]=>[2,6,1,3,8,4,7,5]=>1001100=>0110011
[1,4,2,8,7,6,3,5]=>[1,6,7,4,2,3,8,5]=>0101100=>1010011
[1,2,8,7,5,3,6,4]=>[1,2,5,7,3,6,8,4]=>0011000=>1100111
[1,2,8,6,3,7,5,4]=>[1,2,7,6,3,5,8,4]=>0011010=>1100101
[1,2,7,3,8,6,5,4]=>[1,2,6,8,5,7,3,4]=>0010100=>1101011
[4,1,7,3,6,5,8,2]=>[6,5,8,7,3,4,1,2]=>1010101=>0101010
[5,1,8,7,6,2,4,3]=>[6,1,2,7,4,8,5,3]=>1011100=>0100011
[8,1,7,6,3,4,5,2]=>[6,3,7,4,5,8,1,2]=>1011000=>0100111
[5,7,8,6,2,4,1,3]=>[6,2,8,4,7,1,5,3]=>1111000=>0000111
[5,7,1,6,2,4,3,8]=>[6,1,7,4,5,2,3,8]=>1101000=>0010111
[8,1,4,5,3,7,6,2]=>[5,4,3,7,6,8,1,2]=>1011010=>0100101
[6,1,4,5,3,8,7,2]=>[5,4,3,7,8,6,1,2]=>1011010=>0100101
[6,1,4,5,3,7,8,2]=>[5,4,3,8,7,6,1,2]=>1011011=>0100100
[5,1,7,8,6,2,4,3]=>[6,1,2,8,4,7,5,3]=>1011100=>0100011
[6,1,4,8,3,5,7,2]=>[7,8,4,3,5,6,1,2]=>1011000=>0100111
[7,1,8,6,3,4,5,2]=>[6,3,8,4,5,7,1,2]=>1011000=>0100111
[7,1,4,5,3,8,6,2]=>[5,4,3,8,6,7,1,2]=>1011010=>0100101
[7,1,4,5,3,6,8,2]=>[5,4,3,6,8,7,1,2]=>1011001=>0100110
[8,1,4,5,3,6,7,2]=>[5,4,3,6,7,8,1,2]=>1011000=>0100111
[7,4,1,5,2,6,3,8]=>[5,4,1,6,7,2,3,8]=>1101000=>0010111
[6,3,5,7,2,1,4,8]=>[7,3,2,5,1,6,4,8]=>1111000=>0000111
[6,3,5,7,2,1,8,4]=>[8,7,3,2,5,1,6,4]=>1111001=>0000110
[6,4,5,8,3,7,2,1]=>[7,3,5,4,2,8,6,1]=>1111010=>0000101
[5,8,7,6,2,4,1,3]=>[6,2,7,4,8,1,5,3]=>1111000=>0000111
[5,4,8,6,3,1,7,2]=>[6,3,7,8,4,1,5,2]=>1111000=>0000111
[5,4,1,8,2,3,7,6]=>[7,8,4,1,5,2,3,6]=>1101000=>0010111
[5,8,1,6,2,4,3,7]=>[6,1,8,4,5,2,3,7]=>1101000=>0010111
[8,4,1,5,2,6,3,7]=>[5,4,1,6,8,2,3,7]=>1101000=>0010111
[6,3,5,8,2,1,4,7]=>[8,3,2,5,1,6,4,7]=>1111000=>0000111
[2,3,4,1,8,6,5,7]=>[4,3,2,1,6,8,5,7]=>1110100=>0001011
[8,3,5,6,2,1,4,7]=>[6,3,2,5,1,8,4,7]=>1111000=>0000111
[2,3,8,5,1,4,7,6]=>[5,3,2,1,7,8,4,6]=>1111000=>0000111
[2,8,6,7,1,3,5,4]=>[7,2,1,6,3,5,8,4]=>1111000=>0000111
[8,3,5,7,2,1,6,4]=>[7,3,2,5,1,6,8,4]=>1111000=>0000111
[2,3,8,5,6,1,7,4]=>[6,5,3,2,1,7,8,4]=>1111100=>0000011
[8,4,5,6,3,1,7,2]=>[6,3,5,4,1,7,8,2]=>1111000=>0000111
[7,3,5,8,2,1,6,4]=>[8,3,2,5,1,6,7,4]=>1111000=>0000111
[7,3,5,6,2,1,4,8]=>[6,3,2,5,1,7,4,8]=>1111000=>0000111
[2,7,6,5,1,3,4,8]=>[5,2,1,6,3,7,4,8]=>1111000=>0000111
[2,7,6,8,1,3,5,4]=>[8,2,1,6,3,5,7,4]=>1111000=>0000111
[2,7,6,5,8,3,1,4]=>[8,5,3,6,2,1,7,4]=>1111100=>0000011
[8,7,5,6,1,4,2,3]=>[6,1,5,4,7,2,8,3]=>1111000=>0000111
[2,6,4,1,8,5,7,3]=>[4,2,1,7,8,5,6,3]=>1110100=>0001011
[2,6,1,3,8,5,7,4]=>[7,8,5,6,2,1,3,4]=>1100100=>0011011
[2,7,1,3,6,5,8,4]=>[6,5,8,7,2,1,3,4]=>1100101=>0011010
[2,7,6,8,4,3,1,5]=>[8,4,6,3,7,2,1,5]=>1111000=>0000111
[7,3,5,1,2,8,4,6]=>[5,3,1,8,2,4,7,6]=>1110010=>0001101
[8,4,1,5,2,3,7,6]=>[5,4,1,7,8,2,3,6]=>1101000=>0010111
[6,4,1,8,3,2,7,5]=>[7,8,4,1,3,6,2,5]=>1101000=>0010111
[2,3,8,6,4,1,7,5]=>[6,4,7,8,3,2,1,5]=>1111000=>0000111
[2,8,6,7,4,3,1,5]=>[7,4,6,3,8,2,1,5]=>1111000=>0000111
[8,3,5,7,2,4,1,6]=>[7,3,2,5,4,8,1,6]=>1111000=>0000111
[2,3,4,1,8,7,5,6]=>[4,3,2,1,7,5,8,6]=>1110110=>0001001
[2,8,6,1,7,3,4,5]=>[7,2,1,6,3,4,8,5]=>1110100=>0001011
[2,3,8,1,6,4,7,5]=>[6,3,2,1,4,7,8,5]=>1110100=>0001011
[2,3,8,1,4,5,7,6]=>[7,8,3,2,1,4,5,6]=>1110000=>0001111
[2,8,6,1,4,3,5,7]=>[6,2,1,4,8,3,5,7]=>1110000=>0001111
[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>00000001=>11111110
[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000=>01111111
[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>000000001=>111111110
[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000=>011111111
[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001=>1111111110
[9,1,2,3,4,5,6,7,10,8]=>[10,9,1,2,3,4,5,6,7,8]=>100000001=>011111110
[7,1,2,3,4,5,6,9,8]=>[7,1,2,3,4,5,6,9,8]=>10000001=>01111110
[2,1,9,3,4,5,6,7,8]=>[2,1,9,3,4,5,6,7,8]=>10100000=>01011111
[2,8,1,3,4,5,6,7,9]=>[8,2,1,3,4,5,6,7,9]=>11000000=>00111111
[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]=>110000000=>001111111
[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000=>0111111111
[8,4,3,6,5,1,7,2]=>[3,5,6,4,1,7,8,2]=>1101000=>0010111
[8,5,6,3,4,1,7,2]=>[6,3,4,5,1,7,8,2]=>1110000=>0001111
[1,7,6,5,4,2,3,8]=>[1,5,4,6,2,7,3,8]=>0111000=>1000111
[1,8,6,5,2,7,3,4]=>[1,5,2,7,6,3,8,4]=>0111010=>1000101
[8,7,5,4,1,6,3,2]=>[4,5,1,6,7,3,8,2]=>1110000=>0001111
[6,8,5,4,2,1,7,3]=>[4,5,2,7,8,1,6,3]=>1110000=>0001111
[5,8,6,2,4,1,7,3]=>[6,2,4,7,8,1,5,3]=>1110000=>0001111
[4,8,2,6,5,1,7,3]=>[5,6,2,7,8,4,1,3]=>1101000=>0010111
[3,2,8,6,5,1,7,4]=>[2,5,6,3,1,7,8,4]=>1011000=>0100111
[3,2,1,7,6,4,5,8]=>[2,3,1,6,4,7,5,8]=>1001100=>0110011
[4,1,3,7,6,2,5,8]=>[3,6,4,1,2,7,5,8]=>1001100=>0110011
[8,1,6,5,2,3,7,4]=>[5,1,2,6,3,7,8,4]=>1011000=>0100111
[1,2,7,6,3,4,5,8]=>[1,2,6,3,7,4,5,8]=>0011000=>1100111
[1,2,8,3,7,4,5,6]=>[1,2,7,3,4,8,5,6]=>0010100=>1101011
[8,1,7,2,6,3,5,4]=>[6,1,2,7,5,8,3,4]=>1010100=>0101011
[7,1,8,2,6,4,3,5]=>[6,1,2,4,8,3,7,5]=>1010100=>0101011
[5,1,8,3,2,7,4,6]=>[7,3,5,1,2,4,8,6]=>1010010=>0101101
[4,1,3,8,2,7,5,6]=>[3,7,4,1,2,5,8,6]=>1001010=>0110101
[3,2,1,8,4,7,5,6]=>[2,3,1,7,4,5,8,6]=>1001010=>0110101
[3,2,8,7,1,6,5,4]=>[2,6,7,3,1,5,8,4]=>1011000=>0100111
[4,8,2,7,1,6,5,3]=>[6,7,2,5,8,4,1,3]=>1101000=>0010111
[6,8,7,1,3,5,4,2]=>[7,1,5,8,3,4,6,2]=>1110000=>0001111
[8,7,6,1,5,4,3,2]=>[5,6,1,4,7,3,8,2]=>1110000=>0001111
[1,8,7,2,6,5,3,4]=>[1,6,5,7,2,8,3,4]=>0110100=>1001011
[1,7,8,2,5,6,3,4]=>[1,5,6,8,2,7,3,4]=>0110000=>1001111
[7,6,8,1,4,3,5,2]=>[8,1,4,6,3,5,7,2]=>1110000=>0001111
[6,5,8,3,2,1,7,4]=>[7,8,3,5,2,6,1,4]=>1110000=>0001111
[7,5,8,3,1,4,6,2]=>[8,3,5,1,4,6,7,2]=>1110000=>0001111
[8,5,7,3,1,6,4,2]=>[6,7,3,5,1,4,8,2]=>1110000=>0001111
[1,6,8,4,2,7,3,5]=>[1,4,7,2,8,6,3,5]=>0110010=>1001101
[1,5,4,8,2,7,3,6]=>[1,7,4,2,5,3,8,6]=>0111010=>1000101
[8,4,3,7,1,6,5,2]=>[3,6,7,4,1,5,8,2]=>1101000=>0010111
[7,4,3,8,1,5,6,2]=>[3,8,4,1,5,6,7,2]=>1101000=>0010111
[6,4,3,1,5,2,7,8]=>[3,4,1,5,6,2,7,8]=>1100000=>0011111
[7,4,3,1,2,6,5,8]=>[3,4,1,6,7,2,5,8]=>1100000=>0011111
[1,5,4,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>0110000=>1001111
[8,5,1,4,2,3,7,6]=>[4,5,1,7,8,2,3,6]=>1100000=>0011111
[7,5,1,4,2,6,3,8]=>[4,5,1,6,7,2,3,8]=>1100000=>0011111
[5,6,1,3,4,2,7,8]=>[6,1,3,4,5,2,7,8]=>1100000=>0011111
[4,6,2,1,5,3,7,8]=>[5,6,2,4,1,3,7,8]=>1100000=>0011111
[3,2,7,1,4,6,5,8]=>[2,6,7,3,1,4,5,8]=>1010000=>0101111
[7,6,1,2,5,4,3,8]=>[5,6,1,4,7,2,3,8]=>1100000=>0011111
[8,6,1,2,5,3,7,4]=>[5,6,1,7,8,2,3,4]=>1100000=>0011111
[1,7,2,3,6,4,5,8]=>[1,6,2,3,4,7,5,8]=>0100100=>1011011
[8,7,1,2,3,6,5,4]=>[6,7,1,5,8,2,3,4]=>1100000=>0011111
[7,8,1,2,3,5,6,4]=>[8,1,5,6,7,2,3,4]=>1100000=>0011111
[6,8,1,2,4,3,7,5]=>[7,8,1,4,6,2,3,5]=>1100000=>0011111
[5,8,1,3,2,4,7,6]=>[7,8,1,3,5,2,4,6]=>1100000=>0011111
[4,8,2,1,3,5,7,6]=>[7,8,2,4,1,3,5,6]=>1100000=>0011111
[3,2,8,1,4,5,7,6]=>[2,7,8,3,1,4,5,6]=>1010000=>0101111
[4,1,3,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>1000000=>0111111
[5,1,2,4,3,6,7,8]=>[4,5,1,2,3,6,7,8]=>1000000=>0111111
[7,1,2,3,4,6,5,8]=>[6,7,1,2,3,4,5,8]=>1000000=>0111111
[8,1,2,3,4,5,7,6]=>[7,8,1,2,3,4,5,6]=>1000000=>0111111
[5,4,7,6,8,1,2,3]=>[8,1,6,4,2,7,5,3]=>1111100=>0000011
[5,3,7,8,6,1,2,4]=>[6,3,1,8,2,7,5,4]=>1111100=>0000011
[3,8,4,5,7,1,2,6]=>[7,5,4,1,8,3,2,6]=>1111100=>0000011
[4,5,6,7,1,8,3,2]=>[8,1,7,6,3,5,4,2]=>1111010=>0000101
[3,5,6,2,7,4,8,1]=>[8,7,2,4,6,5,3,1]=>1110101=>0001010
[3,5,6,1,7,8,4,2]=>[8,1,4,7,6,5,3,2]=>1110110=>0001001
[2,5,6,1,8,7,4,3]=>[7,2,1,4,8,6,5,3]=>1110110=>0001001
[8,2,4,5,1,6,3,7]=>[2,5,4,1,6,8,3,7]=>1011000=>0100111
[1,4,8,6,2,3,7,5]=>[1,6,2,7,8,4,3,5]=>0111000=>1000111
[1,5,6,2,8,4,7,3]=>[1,7,8,2,4,6,5,3]=>0110100=>1001011
[2,5,6,3,4,7,8,1]=>[8,7,6,3,4,5,2,1]=>1110011=>0001100
[1,4,2,6,8,5,7,3]=>[1,7,8,5,6,4,2,3]=>0101100=>1010011
[8,2,3,1,5,6,4,7]=>[2,3,5,6,8,1,4,7]=>1000000=>0111111
[2,8,3,1,5,7,4,6]=>[3,5,7,2,1,4,8,6]=>1100010=>0011101
[2,4,1,6,8,7,5,3]=>[7,5,8,6,4,2,1,3]=>1101110=>0010001
[3,4,1,6,7,8,5,2]=>[8,5,7,6,4,1,3,2]=>1101110=>0010001
[5,3,7,2,6,4,8,1]=>[6,3,2,4,8,7,5,1]=>1110101=>0001010
[6,7,2,8,1,5,3,4]=>[8,2,5,7,1,3,6,4]=>1101000=>0010111
[6,7,8,2,1,4,3,5]=>[8,2,7,1,4,6,3,5]=>1110000=>0001111
[6,7,1,3,4,8,5,2]=>[8,1,3,4,5,7,6,2]=>1100010=>0011101
[5,2,7,3,4,6,8,1]=>[2,6,8,7,3,4,5,1]=>1010001=>0101110
[5,1,7,3,4,8,6,2]=>[8,6,7,3,4,5,1,2]=>1010010=>0101101
[5,1,7,8,2,3,6,4]=>[8,1,2,6,7,3,5,4]=>1011000=>0100111
[3,8,1,2,7,4,5,6]=>[7,1,3,2,4,8,5,6]=>1100100=>0011011
[4,1,3,7,5,8,6,2]=>[3,5,8,6,7,4,1,2]=>1001010=>0110101
[3,1,4,5,7,8,6,2]=>[8,6,7,5,4,3,1,2]=>1011110=>0100001
[2,1,8,3,4,7,6,5]=>[2,1,7,6,8,3,4,5]=>1010010=>0101101
[8,2,1,3,4,6,5,7]=>[2,6,8,1,3,4,5,7]=>1000000=>0111111
[1,8,2,3,4,5,7,6]=>[1,7,8,2,3,4,5,6]=>0100000=>1011111
[1,2,8,3,4,6,7,5]=>[1,2,6,7,8,3,4,5]=>0010000=>1101111
[4,2,1,6,5,8,7,3]=>[2,5,7,8,6,4,1,3]=>1001010=>0110101
[5,2,6,4,1,8,7,3]=>[2,4,7,8,6,1,5,3]=>1010010=>0101101
[5,2,7,4,8,6,1,3]=>[2,4,6,8,1,7,5,3]=>1010100=>0101011
[5,7,2,3,8,6,1,4]=>[6,8,2,3,7,5,1,4]=>1100100=>0011011
[5,7,2,3,8,1,6,4]=>[8,2,3,6,7,5,1,4]=>1100100=>0011011
[5,6,2,3,1,8,7,4]=>[7,8,6,2,3,5,1,4]=>1100010=>0011101
[5,6,2,1,3,8,7,4]=>[7,8,6,2,5,1,3,4]=>1100010=>0011101
[5,1,6,4,2,8,7,3]=>[4,7,8,6,1,2,5,3]=>1010010=>0101101
[5,6,1,3,2,8,7,4]=>[7,8,6,1,3,5,2,4]=>1100010=>0011101
[5,7,3,2,8,1,6,4]=>[3,8,2,6,7,5,1,4]=>1100100=>0011011
[5,7,3,2,8,6,1,4]=>[3,6,8,2,7,5,1,4]=>1100100=>0011011
[6,7,3,8,2,1,5,4]=>[3,8,2,7,1,5,6,4]=>1101000=>0010111
[6,7,3,8,1,2,5,4]=>[3,8,1,7,2,5,6,4]=>1101000=>0010111
[5,7,3,1,8,2,6,4]=>[3,8,1,6,7,5,2,4]=>1100100=>0011011
[5,1,7,4,8,2,6,3]=>[4,8,1,2,6,7,5,3]=>1010100=>0101011
[1,5,7,4,8,3,6,2]=>[1,4,8,3,6,7,5,2]=>0110100=>1001011
[1,5,7,4,8,6,3,2]=>[1,4,6,8,3,7,5,2]=>0110100=>1001011
[5,1,7,4,8,6,2,3]=>[4,6,8,1,2,7,5,3]=>1010100=>0101011
[5,7,1,3,8,6,2,4]=>[6,8,1,3,7,5,2,4]=>1100100=>0011011
[5,7,3,1,8,6,2,4]=>[3,6,8,1,7,5,2,4]=>1100100=>0011011
[6,7,3,8,1,5,2,4]=>[3,8,1,5,7,2,6,4]=>1101000=>0010111
[6,7,3,8,5,2,1,4]=>[3,5,8,2,7,1,6,4]=>1101000=>0010111
[6,7,8,3,1,4,2,5]=>[8,3,7,1,4,6,2,5]=>1110000=>0001111
[6,7,1,8,3,5,2,4]=>[8,1,3,5,7,2,6,4]=>1101000=>0010111
[6,1,7,8,4,2,5,3]=>[8,4,7,1,2,5,6,3]=>1011000=>0100111
[6,7,1,8,3,2,5,4]=>[8,1,3,7,2,5,6,4]=>1101000=>0010111
[5,7,2,1,8,3,6,4]=>[8,2,6,7,5,1,3,4]=>1100100=>0011011
[6,7,2,8,3,1,5,4]=>[8,2,3,7,1,5,6,4]=>1101000=>0010111
[6,7,2,8,3,5,1,4]=>[8,2,3,5,7,1,6,4]=>1101000=>0010111
[6,2,7,8,4,5,1,3]=>[2,8,4,5,7,1,6,3]=>1011000=>0100111
[4,2,1,7,8,5,6,3]=>[2,8,5,6,7,4,1,3]=>1001100=>0110011
[4,1,2,7,8,6,5,3]=>[6,8,5,7,4,1,2,3]=>1001100=>0110011
[6,2,7,8,5,1,4,3]=>[2,5,8,1,7,4,6,3]=>1011000=>0100111
[6,2,7,8,5,4,1,3]=>[2,5,8,4,7,1,6,3]=>1011000=>0100111
[5,7,1,2,8,6,3,4]=>[6,8,1,7,5,2,3,4]=>1100100=>0011011
[5,1,7,2,8,6,4,3]=>[6,8,1,2,4,7,5,3]=>1010100=>0101011
[1,5,7,3,8,6,4,2]=>[1,6,8,3,4,7,5,2]=>0110100=>1001011
[1,6,7,8,3,5,4,2]=>[1,8,3,5,7,4,6,2]=>0111000=>1000111
[6,1,7,8,2,5,4,3]=>[8,1,2,5,7,4,6,3]=>1011000=>0100111
[6,7,1,8,2,5,3,4]=>[8,1,5,7,2,3,6,4]=>1101000=>0010111
[6,7,8,2,4,3,1,5]=>[8,2,4,7,3,6,1,5]=>1110000=>0001111
[1,6,7,8,5,3,4,2]=>[1,5,8,3,7,4,6,2]=>0111000=>1000111
[6,1,7,8,5,4,2,3]=>[5,8,4,7,1,2,6,3]=>1011000=>0100111
[6,7,1,8,5,3,2,4]=>[5,8,1,3,7,2,6,4]=>1101000=>0010111
[6,7,8,4,1,3,2,5]=>[4,8,1,7,3,6,2,5]=>1110000=>0001111
[6,3,8,5,2,7,4,1]=>[5,3,2,7,4,8,6,1]=>1111010=>0000101
[6,5,2,8,4,7,3,1]=>[7,4,5,2,3,8,6,1]=>1101010=>0010101
[6,3,4,5,8,7,2,1]=>[7,5,4,3,2,8,6,1]=>1111110=>0000001
[5,8,1,4,7,2,3,6]=>[4,7,1,8,5,2,3,6]=>1100100=>0011011
[5,6,1,4,8,7,3,2]=>[4,7,1,3,8,6,5,2]=>1100110=>0011001
[3,6,4,8,5,7,1,2]=>[5,7,4,1,8,6,3,2]=>1111010=>0000101
[5,1,4,8,6,3,7,2]=>[6,4,3,7,8,5,1,2]=>1011100=>0100011
[3,4,7,1,8,6,5,2]=>[6,8,5,7,1,4,3,2]=>1110100=>0001011
[6,3,8,4,2,7,1,5]=>[4,7,3,2,8,6,1,5]=>1110010=>0001101
[3,6,8,7,1,4,2,5]=>[7,1,8,4,6,3,2,5]=>1111000=>0000111
[5,3,7,1,6,8,2,4]=>[8,6,3,1,7,5,2,4]=>1110110=>0001001
[4,3,8,5,6,7,2,1]=>[7,6,5,3,2,8,4,1]=>1111110=>0000001
[5,8,1,7,6,2,4,3]=>[6,1,7,4,8,5,2,3]=>1101100=>0010011
[4,6,1,2,7,8,5,3]=>[8,5,7,6,1,4,2,3]=>1100110=>0011001
[3,6,4,2,8,7,5,1]=>[4,2,7,5,8,6,3,1]=>1110110=>0001001
[6,3,7,5,2,8,1,4]=>[5,3,2,8,1,7,6,4]=>1111010=>0000101
[6,5,2,7,4,8,1,3]=>[8,4,5,2,7,6,1,3]=>1101010=>0010101
[5,7,1,4,8,3,2,6]=>[4,8,1,3,7,5,2,6]=>1100100=>0011011
[7,8,3,5,1,4,6,2]=>[3,5,1,8,4,6,7,2]=>1101000=>0010111
[6,3,7,4,2,8,5,1]=>[4,8,3,2,5,7,6,1]=>1110010=>0001101
[8,7,1,6,2,4,5,3]=>[6,1,7,4,5,8,2,3]=>1101000=>0010111
[3,8,6,7,1,4,5,2]=>[7,1,6,4,5,8,3,2]=>1111000=>0000111
[5,3,8,7,4,1,2,6]=>[7,4,8,3,1,5,2,6]=>1111000=>0000111
[4,3,8,7,1,5,6,2]=>[7,3,1,5,6,8,4,2]=>1111000=>0000111
[5,6,1,8,7,3,2,4]=>[7,1,3,8,2,6,5,4]=>1101100=>0010011
[5,4,2,7,3,6,8,1]=>[6,8,7,4,2,3,5,1]=>1101001=>0010110
[7,5,3,6,4,2,8,1]=>[3,6,4,5,2,8,7,1]=>1101001=>0010110
[6,4,1,5,3,8,2,7]=>[5,4,1,3,8,6,2,7]=>1101010=>0010101
[8,5,2,6,4,7,3,1]=>[7,6,4,5,2,3,8,1]=>1101010=>0010101
[8,2,6,3,4,7,5,1]=>[2,7,6,3,4,5,8,1]=>1010010=>0101101
[7,2,6,3,5,4,8,1]=>[2,5,6,3,4,8,7,1]=>1010001=>0101110
[6,2,7,4,3,5,8,1]=>[2,4,8,7,3,5,6,1]=>1010001=>0101110
[5,7,3,6,4,2,8,1]=>[3,6,4,8,7,2,5,1]=>1101001=>0010110
[3,7,6,4,5,2,8,1]=>[4,5,6,2,8,7,3,1]=>1110001=>0001110
[2,7,6,5,3,4,8,1]=>[5,3,6,4,8,7,2,1]=>1111001=>0000110
[6,5,4,3,1,8,2,7]=>[4,3,5,1,8,6,2,7]=>1110010=>0001101
[8,6,5,4,2,7,3,1]=>[4,5,2,7,6,3,8,1]=>1110010=>0001101
[8,5,4,1,7,2,6,3]=>[4,1,7,5,2,6,8,3]=>1110100=>0001011
[1,6,5,2,8,3,4,7]=>[1,8,5,2,6,3,4,7]=>0110100=>1001011
[5,7,4,2,1,8,3,6]=>[4,2,8,1,5,3,7,6]=>1110010=>0001101
[1,6,5,3,4,8,2,7]=>[1,5,3,4,8,6,2,7]=>0110010=>1001101
[5,4,6,3,1,8,2,7]=>[8,6,3,4,1,5,2,7]=>1110010=>0001101
[6,5,8,4,2,7,3,1]=>[4,7,2,5,3,8,6,1]=>1110010=>0001101
[5,8,2,6,4,7,3,1]=>[7,6,4,8,2,3,5,1]=>1101010=>0010101
[3,8,6,2,5,7,4,1]=>[5,7,6,2,4,8,3,1]=>1110010=>0001101
[7,8,5,3,2,6,4,1]=>[5,3,6,8,2,4,7,1]=>1110000=>0001111
[6,8,3,1,7,2,5,4]=>[3,7,1,8,5,6,2,4]=>1100100=>0011011
[1,8,6,3,7,5,2,4]=>[1,7,5,6,3,8,2,4]=>0110100=>1001011
[2,8,1,7,3,5,6,4]=>[7,2,1,3,5,6,8,4]=>1101000=>0010111
[3,8,6,1,7,4,5,2]=>[7,1,4,6,5,8,3,2]=>1110100=>0001011
[4,8,1,3,7,2,6,5]=>[7,1,3,4,2,6,8,5]=>1100100=>0011011
[3,7,1,5,8,4,2,6]=>[8,5,4,7,1,3,2,6]=>1101100=>0010011
[6,7,3,1,8,4,2,5]=>[3,8,1,4,7,2,6,5]=>1100100=>0011011
[1,7,3,8,4,5,2,6]=>[1,3,8,4,5,7,2,6]=>0101000=>1010111
[1,7,2,8,5,3,4,6]=>[1,5,8,2,3,7,4,6]=>0101000=>1010111
[7,6,1,8,4,3,2,5]=>[8,4,6,1,3,7,2,5]=>1101000=>0010111
[8,1,2,7,3,4,6,5]=>[7,1,2,3,6,8,4,5]=>1001000=>0110111
[7,1,2,8,3,5,4,6]=>[8,1,2,3,5,7,4,6]=>1001000=>0110111
[8,2,6,1,7,3,5,4]=>[2,7,1,6,5,8,3,4]=>1010100=>0101011
[7,3,1,5,8,4,2,6]=>[3,1,8,5,4,7,2,6]=>1101100=>0010011
[4,2,1,5,8,3,6,7]=>[2,8,5,4,1,3,6,7]=>1001100=>0110011
[5,4,2,7,1,8,3,6]=>[8,4,2,5,1,3,7,6]=>1101010=>0010101
[6,5,2,8,7,3,4,1]=>[7,2,3,8,5,4,6,1]=>1101100=>0010011
[6,5,1,8,7,4,2,3]=>[7,4,8,5,1,6,2,3]=>1101100=>0010011
[8,6,4,7,5,3,2,1]=>[5,7,4,3,6,2,8,1]=>1111000=>0000111
[5,1,8,3,7,6,2,4]=>[6,7,3,8,5,1,2,4]=>1010100=>0101011
[3,6,8,2,4,7,5,1]=>[7,2,4,5,8,6,3,1]=>1110010=>0001101
[5,4,6,8,2,7,3,1]=>[7,2,8,6,4,3,5,1]=>1111010=>0000101
[5,2,6,8,7,3,4,1]=>[2,7,3,8,4,6,5,1]=>1011100=>0100011
[4,7,2,8,6,3,5,1]=>[6,2,3,8,5,7,4,1]=>1101100=>0010011
[2,3,8,7,4,5,6,1]=>[7,4,5,6,8,3,2,1]=>1111000=>0000111
[7,2,8,6,4,3,5,1]=>[2,6,4,8,3,5,7,1]=>1011000=>0100111
[2,1,8,7,5,6,3,4]=>[2,1,5,6,7,3,8,4]=>1011000=>0100111
[8,1,7,6,5,2,4,3]=>[5,6,1,2,7,4,8,3]=>1011000=>0100111
[7,1,8,6,5,3,2,4]=>[5,6,3,8,1,2,7,4]=>1011000=>0100111
[1,2,8,7,6,3,4,5]=>[1,2,6,3,7,4,8,5]=>0011100=>1100011
[1,3,8,7,4,6,2,5]=>[1,6,7,4,8,3,2,5]=>0111000=>1000111
[1,5,8,3,7,6,2,4]=>[1,6,7,3,8,5,2,4]=>0110100=>1001011
[6,8,4,7,5,3,2,1]=>[5,7,4,3,8,2,6,1]=>1111000=>0000111
[6,8,7,2,5,4,3,1]=>[5,7,2,4,8,3,6,1]=>1110000=>0001111
[2,8,7,6,5,3,4,1]=>[5,6,3,7,4,8,2,1]=>1111000=>0000111
[5,8,6,7,3,4,1,2]=>[7,3,6,4,8,1,5,2]=>1111000=>0000111
[4,8,6,7,3,5,1,2]=>[7,3,5,6,1,8,4,2]=>1111000=>0000111
[3,8,6,7,4,5,1,2]=>[7,4,5,6,1,8,3,2]=>1111000=>0000111
[2,8,6,7,4,5,1,3]=>[7,4,5,6,2,1,8,3]=>1111000=>0000111
[1,8,5,7,4,6,2,3]=>[1,6,7,4,5,2,8,3]=>0111000=>1000111
[3,8,5,7,4,6,1,2]=>[6,7,4,5,1,8,3,2]=>1111000=>0000111
[6,8,3,7,4,5,1,2]=>[3,7,4,5,8,1,6,2]=>1101000=>0010111
[5,8,3,7,4,6,1,2]=>[3,6,7,4,8,1,5,2]=>1101000=>0010111
[3,7,4,8,5,6,1,2]=>[5,6,8,4,1,7,3,2]=>1111000=>0000111
[4,7,2,8,5,6,1,3]=>[5,6,8,2,7,4,1,3]=>1101000=>0010111
[3,7,1,8,5,6,2,4]=>[5,6,8,1,3,2,7,4]=>1101000=>0010111
[3,7,2,8,5,6,1,4]=>[5,6,8,2,3,1,7,4]=>1101000=>0010111
[2,7,3,8,5,6,1,4]=>[3,5,6,8,2,1,7,4]=>1101000=>0010111
[2,7,4,8,5,6,1,3]=>[5,6,8,4,2,1,7,3]=>1111000=>0000111
[5,8,2,7,4,6,1,3]=>[6,7,4,8,2,5,1,3]=>1101000=>0010111
[7,8,1,6,4,5,2,3]=>[6,4,5,8,1,7,2,3]=>1101000=>0010111
[6,8,1,7,4,5,2,3]=>[7,4,5,8,1,6,2,3]=>1101000=>0010111
[5,8,1,7,4,6,2,3]=>[6,7,4,8,1,5,2,3]=>1101000=>0010111
[1,7,4,8,5,6,2,3]=>[1,5,6,8,4,2,7,3]=>0111000=>1000111
[1,8,5,6,2,7,3,4]=>[1,7,6,2,5,3,8,4]=>0111010=>1000101
[4,8,1,7,3,6,2,5]=>[6,7,1,3,8,4,2,5]=>1101000=>0010111
[6,8,1,7,3,5,2,4]=>[7,1,3,5,8,2,6,4]=>1101000=>0010111
[7,8,2,6,3,5,1,4]=>[6,2,3,5,8,1,7,4]=>1101000=>0010111
[6,8,2,7,3,5,1,4]=>[7,2,3,5,8,1,6,4]=>1101000=>0010111
[4,8,2,7,3,6,1,5]=>[6,7,2,3,8,4,1,5]=>1101000=>0010111
[2,7,3,8,4,6,1,5]=>[3,6,8,4,7,2,1,5]=>1101000=>0010111
[3,7,2,8,4,6,1,5]=>[6,8,4,7,2,3,1,5]=>1101000=>0010111
[3,7,1,8,4,6,2,5]=>[6,8,4,7,1,3,2,5]=>1101000=>0010111
[1,8,4,7,3,6,2,5]=>[1,6,7,4,3,8,2,5]=>0111000=>1000111
[3,8,4,7,2,6,1,5]=>[6,7,4,2,8,3,1,5]=>1111000=>0000111
[4,8,5,7,2,6,1,3]=>[6,7,2,5,1,8,4,3]=>1111000=>0000111
[2,8,5,7,3,6,1,4]=>[6,7,3,5,2,1,8,4]=>1111000=>0000111
[1,8,6,7,3,5,2,4]=>[1,7,3,5,6,2,8,4]=>0111000=>1000111
[6,8,5,7,1,4,2,3]=>[7,1,5,4,8,2,6,3]=>1111000=>0000111
[5,8,6,7,1,4,2,3]=>[7,1,6,4,8,2,5,3]=>1111000=>0000111
[3,8,6,7,1,5,2,4]=>[7,1,5,6,3,2,8,4]=>1111000=>0000111
[1,5,2,8,6,7,3,4]=>[1,7,6,2,3,8,5,4]=>0101110=>1010001
[1,6,2,8,5,7,3,4]=>[1,5,7,2,3,8,6,4]=>0101010=>1010101
[6,8,4,7,1,5,2,3]=>[7,4,1,5,8,2,6,3]=>1111000=>0000111
[7,8,4,6,1,5,2,3]=>[6,4,1,5,8,2,7,3]=>1111000=>0000111
[6,8,3,7,1,5,2,4]=>[3,7,1,5,8,2,6,4]=>1101000=>0010111
[4,8,3,7,1,6,2,5]=>[3,6,7,1,8,4,2,5]=>1101000=>0010111
[3,8,4,7,1,6,2,5]=>[6,7,4,1,8,3,2,5]=>1111000=>0000111
[1,6,2,8,4,7,3,5]=>[1,7,4,8,6,2,3,5]=>0101010=>1010101
[2,6,1,8,4,7,3,5]=>[7,4,8,6,2,1,3,5]=>1101010=>0010101
[3,7,2,6,1,8,4,5]=>[8,6,2,3,1,7,4,5]=>1101010=>0010101
[3,7,1,6,2,8,4,5]=>[8,6,1,3,2,7,4,5]=>1101010=>0010101
[4,8,1,6,2,7,3,5]=>[7,6,1,8,4,2,3,5]=>1101010=>0010101
[5,8,1,6,2,7,3,4]=>[7,6,1,8,2,3,5,4]=>1101010=>0010101
[7,8,2,5,1,6,3,4]=>[5,2,6,8,1,3,7,4]=>1101000=>0010111
[6,8,2,5,1,7,3,4]=>[5,2,7,1,3,8,6,4]=>1101010=>0010101
[4,8,2,6,1,7,3,5]=>[7,6,2,8,4,1,3,5]=>1101010=>0010101
[1,7,3,6,2,8,4,5]=>[1,3,8,6,2,7,4,5]=>0101010=>1010101
[2,7,3,6,1,8,4,5]=>[3,8,6,2,1,7,4,5]=>1101010=>0010101
[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000=>11111111
[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>00000011=>11111100
[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,8,7,6]=>00000111=>11111000
[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,8,7,6,5]=>00001111=>11110000
[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,8,7,6,5,4]=>00011111=>11100000
[1,2,4,5,6,7,8,9,3]=>[1,2,9,8,7,6,5,4,3]=>00111111=>11000000
[1,3,4,5,6,7,8,9,2]=>[1,9,8,7,6,5,4,3,2]=>01111111=>10000000
[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000=>111111111
[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]=>00000010=>11111101
[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>000000011=>111111100
[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,7,9,8,6]=>00000101=>11111010
[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,9,8,7]=>000000111=>111111000
[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,6,9,8,7,5]=>00001011=>11110100
[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,9,8,7,6]=>000001111=>111110000
[1,2,3,6,5,7,8,9,4]=>[1,2,3,5,9,8,7,6,4]=>00010111=>11101000
[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,9,8,7,6,5]=>000011111=>111100000
[1,2,5,4,6,7,8,9,3]=>[1,2,4,9,8,7,6,5,3]=>00101111=>11010000
[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,9,8,7,6,5,4]=>000111111=>111000000
[1,4,3,5,6,7,8,9,2]=>[1,3,9,8,7,6,5,4,2]=>01011111=>10100000
[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,9,8,7,6,5,4,3]=>001111111=>110000000
[3,2,4,5,6,7,8,9,1]=>[2,9,8,7,6,5,4,3,1]=>10111111=>01000000
[1,3,4,5,6,7,8,9,10,2]=>[1,10,9,8,7,6,5,4,3,2]=>011111111=>100000000
[6,7,4,8,3,5,1,2]=>[8,4,3,5,7,1,6,2]=>1111000=>0000111
[6,7,4,5,2,8,1,3]=>[5,4,2,8,1,7,6,3]=>1111010=>0000101
[5,7,4,6,2,3,1,8]=>[6,4,2,7,3,5,1,8]=>1111000=>0000111
[5,7,4,6,3,8,1,2]=>[8,6,4,3,7,1,5,2]=>1111010=>0000101
[5,7,4,8,3,6,1,2]=>[6,8,4,3,7,1,5,2]=>1111000=>0000111
[5,8,4,6,3,7,1,2]=>[7,6,4,3,8,1,5,2]=>1111010=>0000101
[5,6,4,8,3,7,1,2]=>[7,4,3,8,6,1,5,2]=>1111010=>0000101
[5,6,3,7,2,8,1,4]=>[3,8,2,7,6,1,5,4]=>1101010=>0010101
[5,6,3,8,2,7,1,4]=>[3,7,2,8,6,1,5,4]=>1101010=>0010101
[5,6,4,8,2,7,1,3]=>[7,4,2,8,6,1,5,3]=>1111010=>0000101
[5,8,4,6,2,7,1,3]=>[7,6,4,2,8,1,5,3]=>1111010=>0000101
[6,8,4,5,2,7,1,3]=>[5,4,2,7,1,8,6,3]=>1111010=>0000101
[7,8,4,5,2,6,1,3]=>[5,4,2,6,8,1,7,3]=>1111000=>0000111
[6,8,4,5,2,3,1,7]=>[5,4,2,8,3,6,1,7]=>1111000=>0000111
[5,8,4,6,2,3,1,7]=>[6,4,2,8,3,5,1,7]=>1111000=>0000111
[5,6,4,8,2,3,1,7]=>[8,4,2,6,3,5,1,7]=>1111000=>0000111
[4,6,3,5,2,7,1,8]=>[3,5,2,7,6,4,1,8]=>1101010=>0010101
[4,6,3,5,2,8,1,7]=>[3,5,2,8,6,4,1,7]=>1101010=>0010101
[5,8,3,6,2,4,1,7]=>[3,6,2,8,4,5,1,7]=>1101000=>0010111
[6,8,3,5,2,4,1,7]=>[3,5,2,8,4,6,1,7]=>1101000=>0010111
[7,8,3,5,2,4,1,6]=>[3,5,2,8,4,7,1,6]=>1101000=>0010111
[7,8,3,5,2,6,1,4]=>[3,5,2,6,8,1,7,4]=>1101000=>0010111
[4,6,3,8,2,7,1,5]=>[3,7,2,8,6,4,1,5]=>1101010=>0010101
[4,6,3,7,2,8,1,5]=>[3,8,2,7,6,4,1,5]=>1101010=>0010101
[4,7,3,6,2,8,1,5]=>[3,8,6,2,7,4,1,5]=>1101010=>0010101
[4,7,3,8,2,6,1,5]=>[3,6,8,2,7,4,1,5]=>1101000=>0010111
[5,7,4,8,2,6,1,3]=>[6,8,4,2,7,1,5,3]=>1111000=>0000111
[5,7,3,6,2,8,1,4]=>[3,8,6,2,7,1,5,4]=>1101010=>0010101
[5,7,3,6,2,4,1,8]=>[3,6,2,7,4,5,1,8]=>1101000=>0010111
[6,7,3,5,2,4,1,8]=>[3,5,2,7,4,6,1,8]=>1101000=>0010111
[6,7,3,5,2,8,1,4]=>[3,5,2,8,1,7,6,4]=>1101010=>0010101
[6,7,4,8,2,5,1,3]=>[8,4,2,5,7,1,6,3]=>1111000=>0000111
[6,7,5,8,2,4,1,3]=>[8,2,5,4,7,1,6,3]=>1111000=>0000111
[6,7,3,8,2,4,1,5]=>[3,8,2,7,4,6,1,5]=>1101000=>0010111
[6,7,3,4,2,8,1,5]=>[3,4,8,2,7,6,1,5]=>1100010=>0011101
[5,7,3,4,2,8,1,6]=>[3,4,8,2,5,1,7,6]=>1100010=>0011101
[5,8,4,7,2,3,1,6]=>[7,4,2,8,3,5,1,6]=>1111000=>0000111
[7,8,3,6,2,4,1,5]=>[3,6,2,8,4,7,1,5]=>1101000=>0010111
[6,8,3,7,2,4,1,5]=>[3,7,2,8,4,6,1,5]=>1101000=>0010111
[4,5,3,7,2,8,1,6]=>[3,8,2,5,4,1,7,6]=>1101010=>0010101
[4,8,3,5,2,7,1,6]=>[3,5,2,7,4,1,8,6]=>1101010=>0010101
[5,8,3,4,2,7,1,6]=>[3,4,7,2,5,1,8,6]=>1100010=>0011101
[6,8,3,4,2,7,1,5]=>[3,4,7,2,8,6,1,5]=>1100010=>0011101
[7,8,3,4,2,6,1,5]=>[3,4,6,8,2,7,1,5]=>1100000=>0011111
[6,8,3,4,2,5,1,7]=>[3,4,8,2,5,6,1,7]=>1100000=>0011111
[4,8,3,5,2,6,1,7]=>[3,5,2,6,8,4,1,7]=>1101000=>0010111
[4,7,5,2,1,8,3,6]=>[5,2,8,1,4,3,7,6]=>1110010=>0001101
[4,6,5,2,1,3,8,7]=>[5,2,6,1,4,3,8,7]=>1110001=>0001110
[5,6,4,2,3,1,8,7]=>[4,2,6,3,5,1,8,7]=>1110001=>0001110
[5,4,6,1,3,2,8,7]=>[6,1,4,3,5,2,8,7]=>1110001=>0001110
[4,6,8,1,7,3,2,5]=>[7,1,8,3,4,2,6,5]=>1110100=>0001011
[7,4,8,1,6,5,3,2]=>[6,5,8,1,4,3,7,2]=>1110100=>0001011
[5,4,8,1,3,7,6,2]=>[7,6,8,1,4,3,5,2]=>1110010=>0001101
[8,4,5,3,1,7,6,2]=>[5,3,4,1,7,6,8,2]=>1110010=>0001101
[5,4,7,1,3,8,2,6]=>[8,1,4,3,5,2,7,6]=>1110010=>0001101
[5,6,8,7,2,1,3,4]=>[7,2,8,1,6,3,5,4]=>1111000=>0000111
[8,5,7,6,4,2,1,3]=>[6,4,7,2,5,1,8,3]=>1111000=>0000111
[8,4,6,3,7,2,1,5]=>[7,3,4,2,6,1,8,5]=>1110100=>0001011
[6,3,2,8,7,4,1,5]=>[3,2,7,4,8,1,6,5]=>1101100=>0010011
[2,1,6,8,7,4,3,5]=>[2,1,7,4,8,3,6,5]=>1011100=>0100011
[2,1,7,8,6,4,5,3]=>[2,1,6,4,8,5,7,3]=>1011100=>0100011
[7,3,2,8,6,4,5,1]=>[3,2,6,4,8,5,7,1]=>1101100=>0010011
[7,6,8,5,2,4,3,1]=>[5,2,8,4,6,3,7,1]=>1111000=>0000111
[5,7,8,6,2,3,1,4]=>[6,2,8,3,7,1,5,4]=>1111000=>0000111
[5,8,7,6,3,2,1,4]=>[6,3,7,2,8,1,5,4]=>1111000=>0000111
[6,8,7,5,3,2,4,1]=>[5,3,7,2,8,4,6,1]=>1111000=>0000111
[7,8,4,2,6,5,3,1]=>[4,2,6,5,8,3,7,1]=>1110100=>0001011
[4,8,6,2,7,3,1,5]=>[7,2,6,3,4,1,8,5]=>1110100=>0001011
[3,6,1,8,7,4,2,5]=>[7,4,8,1,3,2,6,5]=>1101100=>0010011
[3,8,1,6,7,5,2,4]=>[7,5,6,1,3,2,8,4]=>1101100=>0010011
[3,7,1,6,8,2,5,4]=>[8,1,3,2,6,5,7,4]=>1101100=>0010011
[4,7,6,2,8,1,3,5]=>[8,2,6,1,4,3,7,5]=>1110100=>0001011
[6,7,4,2,8,1,5,3]=>[4,2,8,1,7,5,6,3]=>1110100=>0001011
[2,1,8,6,7,5,3,4]=>[2,1,7,5,6,3,8,4]=>1011100=>0100011
[8,3,2,6,7,5,1,4]=>[3,2,7,5,6,1,8,4]=>1101100=>0010011
[8,6,4,3,7,5,1,2]=>[4,3,7,5,6,1,8,2]=>1110100=>0001011
[6,7,5,8,1,3,4,2]=>[8,1,5,3,7,4,6,2]=>1111000=>0000111
[7,6,5,8,1,4,3,2]=>[8,1,5,4,6,3,7,2]=>1111000=>0000111
[8,6,5,7,4,1,3,2]=>[7,4,5,1,6,3,8,2]=>1111000=>0000111
[7,6,4,3,8,1,5,2]=>[4,3,8,1,6,5,7,2]=>1110100=>0001011
[7,3,2,6,8,1,5,4]=>[3,2,8,1,6,5,7,4]=>1101100=>0010011
[2,1,7,6,8,3,5,4]=>[2,1,8,3,6,5,7,4]=>1011100=>0100011
[6,5,7,8,1,2,4,3]=>[8,1,7,2,5,4,6,3]=>1111000=>0000111
[8,1,3,7,4,6,5,2]=>[3,6,7,4,5,8,1,2]=>1001000=>0110111
[1,6,2,5,4,7,3,8]=>[1,5,4,7,6,2,3,8]=>0101010=>1010101
[6,2,7,5,4,8,3,1]=>[2,5,4,8,3,7,6,1]=>1011010=>0100101
[8,1,3,5,4,7,6,2]=>[3,5,4,7,6,8,1,2]=>1001010=>0110101
[6,1,5,4,3,8,7,2]=>[4,5,3,7,8,6,1,2]=>1010010=>0101101
[6,1,8,3,4,5,7,2]=>[7,8,3,4,5,6,1,2]=>1010000=>0101111
[7,1,5,3,4,8,6,2]=>[5,3,4,8,6,7,1,2]=>1010010=>0101101
[7,1,4,3,5,6,8,2]=>[4,3,5,6,8,7,1,2]=>1010001=>0101110
[8,1,3,4,5,6,7,2]=>[3,4,5,6,7,8,1,2]=>1000000=>0111111
[1,7,2,4,5,6,3,8]=>[1,4,5,6,7,2,3,8]=>0100000=>1011111
[6,3,2,7,5,1,8,4]=>[3,2,5,8,7,1,6,4]=>1101001=>0010110
[8,4,7,2,5,6,1,3]=>[5,6,7,2,4,1,8,3]=>1110000=>0001111
[8,5,2,1,4,3,7,6]=>[5,2,4,7,8,1,3,6]=>1100000=>0011111
[6,5,2,8,4,1,3,7]=>[8,4,5,2,6,1,3,7]=>1101000=>0010111
[5,6,2,1,4,8,3,7]=>[8,6,2,4,5,1,3,7]=>1100010=>0011101
[3,6,1,8,5,2,4,7]=>[5,8,1,3,2,6,4,7]=>1101000=>0010111
[1,2,6,3,5,4,7,8]=>[1,2,5,6,3,4,7,8]=>0010000=>1101111
[4,3,1,2,6,8,5,7]=>[3,1,4,2,8,6,5,7]=>1100110=>0011001
[5,8,1,6,3,2,4,7]=>[6,1,3,8,2,5,4,7]=>1101000=>0010111
[6,3,8,5,2,1,4,7]=>[5,3,2,8,1,6,4,7]=>1111000=>0000111
[8,3,1,5,2,4,7,6]=>[3,1,5,2,7,8,4,6]=>1101000=>0010111
[3,8,2,6,1,5,7,4]=>[6,2,3,1,5,7,8,4]=>1101000=>0010111
[8,5,6,4,2,1,7,3]=>[4,6,2,5,1,7,8,3]=>1110000=>0001111
[1,7,5,6,3,2,4,8]=>[1,6,3,5,2,7,4,8]=>0111000=>1000111
[6,1,2,3,8,5,7,4]=>[7,8,5,6,1,2,3,4]=>1000100=>0111011
[7,1,2,3,6,5,8,4]=>[6,5,8,7,1,2,3,4]=>1000101=>0111010
[1,5,7,3,2,4,6,8]=>[1,7,3,5,2,4,6,8]=>0110000=>1001111
[5,2,7,3,1,8,4,6]=>[2,8,3,5,1,4,7,6]=>1010010=>0101101
[5,8,2,4,1,3,7,6]=>[4,7,8,2,5,1,3,6]=>1100000=>0011111
[8,7,2,6,3,4,1,5]=>[6,2,3,7,4,8,1,5]=>1101000=>0010111
[3,1,8,6,4,2,7,5]=>[6,4,7,8,3,1,2,5]=>1011000=>0100111
[8,1,6,7,4,3,2,5]=>[7,4,6,3,8,1,2,5]=>1011000=>0100111
[3,5,8,7,2,4,1,6]=>[7,2,8,4,5,3,1,6]=>1111000=>0000111
[4,2,1,3,7,8,5,6]=>[2,4,1,3,8,5,7,6]=>1000110=>0111001
[2,4,1,3,8,7,5,6]=>[4,2,1,3,7,5,8,6]=>1100110=>0011001
[2,8,1,3,6,4,7,5]=>[6,2,1,3,4,7,8,5]=>1100100=>0011011
[6,8,2,3,4,1,5,7]=>[8,2,3,4,6,1,5,7]=>1100000=>0011111
[5,1,8,3,2,4,6,7]=>[8,3,5,1,2,4,6,7]=>1010000=>0101111
[9,8,7,6,5,4,3,2,1]=>[5,6,4,7,3,8,2,9,1]=>11110000=>00001111
[8,9,7,6,5,4,3,2,1]=>[5,6,4,7,3,9,2,8,1]=>11110000=>00001111
[8,7,6,5,4,3,2,1,9]=>[5,4,6,3,7,2,8,1,9]=>11110000=>00001111
[9,10,8,7,6,5,4,3,2,1]=>[6,5,7,4,8,3,10,2,9,1]=>111110000=>000001111
[9,8,7,6,5,4,3,2,1,10]=>[5,6,4,7,3,8,2,9,1,10]=>111100000=>000011111
[1,4,2,7,8,6,3,5]=>[1,6,8,4,2,3,7,5]=>0101100=>1010011
[1,6,2,4,8,5,3,7]=>[1,4,8,5,6,2,3,7]=>0100100=>1011011
[1,7,3,8,5,2,4,6]=>[1,3,5,8,2,7,4,6]=>0101000=>1010111
[1,7,3,2,8,6,4,5]=>[1,3,6,8,2,4,7,5]=>0100100=>1011011
[4,2,5,7,8,6,1,3]=>[2,6,8,1,7,5,4,3]=>1011100=>0100011
[7,2,3,1,8,5,6,4]=>[2,3,8,5,6,7,1,4]=>1000100=>0111011
[8,2,5,1,7,3,4,6]=>[2,7,5,1,8,3,4,6]=>1010100=>0101011
[6,2,1,8,3,4,7,5]=>[2,7,8,1,3,6,4,5]=>1001000=>0110111
[6,2,8,3,5,1,7,4]=>[2,5,7,8,3,6,1,4]=>1010000=>0101111
[6,2,4,8,5,7,1,3]=>[2,5,7,4,1,8,6,3]=>1011010=>0100101
[1,3,6,4,8,5,7,2]=>[1,4,7,8,5,6,3,2]=>0110100=>1001011
[6,2,4,7,5,8,1,3]=>[2,5,8,4,1,7,6,3]=>1011010=>0100101
[7,8,2,1,4,3,5,6]=>[8,2,4,7,1,3,5,6]=>1100000=>0011111
[7,6,4,2,3,1,8,5]=>[4,2,6,3,8,7,1,5]=>1110001=>0001110
[5,7,2,3,1,6,8,4]=>[6,8,7,2,3,5,1,4]=>1100001=>0011110
[7,5,4,2,6,8,1,3]=>[4,2,8,6,5,1,7,3]=>1110110=>0001001
[8,2,6,4,3,1,7,5]=>[2,4,6,3,7,8,1,5]=>1010000=>0101111
[8,2,7,4,1,3,5,6]=>[2,4,7,1,8,3,5,6]=>1010000=>0101111
[1,2,8,4,3,5,6,7]=>[1,2,4,8,3,5,6,7]=>0010000=>1101111
[1,7,4,2,3,5,6,8]=>[1,4,2,7,3,5,6,8]=>0110000=>1001111
[6,8,4,1,3,2,5,7]=>[4,1,8,3,6,2,5,7]=>1110000=>0001111
[1,8,7,4,3,2,5,6]=>[1,4,7,3,8,2,5,6]=>0110000=>1001111
[1,6,3,8,2,4,7,5]=>[1,3,7,8,2,6,4,5]=>0101000=>1010111
[5,3,8,1,2,7,4,6]=>[7,3,1,5,2,4,8,6]=>1110010=>0001101
[5,1,8,3,2,6,4,7]=>[6,8,3,5,1,2,4,7]=>1010000=>0101111
[1,7,5,4,2,6,3,8]=>[1,4,5,2,6,7,3,8]=>0110000=>1001111
[1,5,8,4,2,7,3,6]=>[1,4,7,2,5,3,8,6]=>0110010=>1001101
[1,4,6,2,8,3,7,5]=>[1,7,8,2,4,3,6,5]=>0110100=>1001011
[5,3,6,1,2,8,4,7]=>[8,6,3,1,5,2,4,7]=>1110010=>0001101
[1,6,3,2,7,8,4,5]=>[1,3,8,2,4,7,6,5]=>0100110=>1011001
[6,3,4,1,2,5,8,7]=>[4,3,1,6,2,5,8,7]=>1110001=>0001110
[6,3,1,4,2,7,5,8]=>[3,1,4,7,6,2,5,8]=>1100010=>0011101
[1,8,3,2,4,5,6,7]=>[1,3,8,2,4,5,6,7]=>0100000=>1011111
[8,6,3,2,4,1,7,5]=>[3,6,2,4,7,8,1,5]=>1100000=>0011111
[8,5,3,2,6,7,1,4]=>[3,7,6,5,2,8,1,4]=>1100110=>0011001
[4,5,2,6,8,1,7,3]=>[7,8,2,6,5,4,1,3]=>1101100=>0010011
[4,2,5,6,7,8,1,3]=>[2,8,1,7,6,5,4,3]=>1011110=>0100001
[5,2,3,6,7,1,8,4]=>[2,3,8,7,1,6,5,4]=>1001101=>0110010
[6,2,3,4,1,7,8,5]=>[2,3,4,8,7,6,1,5]=>1000011=>0111100
[7,2,3,1,4,5,8,6]=>[2,3,8,7,1,4,5,6]=>1000001=>0111110
[8,3,1,6,5,2,4,7]=>[3,1,5,6,2,8,4,7]=>1101000=>0010111
[3,7,5,1,8,2,4,6]=>[8,5,1,7,3,2,4,6]=>1110100=>0001011
[4,1,5,2,8,7,3,6]=>[7,5,1,2,4,3,8,6]=>1010110=>0101001
[8,2,6,5,1,3,4,7]=>[2,5,1,6,3,8,4,7]=>1011000=>0100111
[8,3,1,6,2,5,4,7]=>[3,1,6,2,5,8,4,7]=>1101000=>0010111
[8,1,2,6,4,5,3,7]=>[6,4,5,8,1,2,3,7]=>1001000=>0110111
[8,1,2,5,6,4,3,7]=>[6,5,4,8,1,2,3,7]=>1001100=>0110011
[1,7,5,4,2,8,3,6]=>[1,4,5,2,8,3,7,6]=>0110010=>1001101
[1,4,7,6,2,8,3,5]=>[1,8,6,2,7,4,3,5]=>0111010=>1000101
[5,1,4,7,2,8,3,6]=>[8,4,1,2,5,3,7,6]=>1011010=>0100101
[1,7,4,5,2,8,3,6]=>[1,5,4,2,8,3,7,6]=>0111010=>1000101
[3,7,5,1,2,8,4,6]=>[5,1,8,3,2,4,7,6]=>1110010=>0001101
[5,2,8,7,1,3,4,6]=>[2,7,1,8,3,5,4,6]=>1011000=>0100111
[1,4,6,2,8,7,3,5]=>[1,7,2,4,3,8,6,5]=>0110110=>1001001
[3,1,2,6,4,8,7,5]=>[3,1,2,7,8,6,4,5]=>1001010=>0110101
[1,4,7,2,6,8,3,5]=>[1,8,6,2,4,3,7,5]=>0110110=>1001001
[1,2,3,6,8,5,7,4]=>[1,2,3,7,8,5,6,4]=>0001100=>1110011
[5,1,4,2,7,8,3,6]=>[4,1,2,8,5,3,7,6]=>1010110=>0101001
[1,4,2,7,6,8,3,5]=>[1,8,6,4,2,3,7,5]=>0101110=>1010001
[3,1,2,8,4,6,7,5]=>[3,1,2,6,7,8,4,5]=>1001000=>0110111
[3,1,2,7,6,4,8,5]=>[3,1,2,6,4,8,7,5]=>1001101=>0110010
[1,7,4,3,2,5,8,6]=>[1,4,3,8,7,2,5,6]=>0110001=>1001110
[1,8,7,3,4,2,5,6]=>[1,7,3,4,8,2,5,6]=>0110000=>1001111
[3,1,7,8,2,6,4,5]=>[6,8,3,1,2,7,4,5]=>1011000=>0100111
[1,4,2,7,8,3,6,5]=>[1,8,4,2,3,6,7,5]=>0101100=>1010011
[5,2,8,1,3,4,7,6]=>[2,7,8,1,5,3,4,6]=>1010000=>0101111
[2,1,8,6,3,4,7,5]=>[2,1,6,3,7,8,4,5]=>1011000=>0100111
[1,4,2,6,8,3,7,5]=>[1,7,8,4,2,3,6,5]=>0101100=>1010011
[1,2,3,7,8,5,6,4]=>[1,2,3,8,5,6,7,4]=>0001100=>1110011
[1,2,3,7,5,8,6,4]=>[1,2,3,5,8,6,7,4]=>0001010=>1110101
[1,4,2,7,3,8,6,5]=>[1,8,6,7,4,2,3,5]=>0101010=>1010101
[3,1,7,2,8,6,4,5]=>[6,8,3,1,2,4,7,5]=>1010100=>0101011
[2,1,7,8,3,4,6,5]=>[2,1,8,3,6,7,4,5]=>1011000=>0100111
[1,2,3,8,7,5,6,4]=>[1,2,3,7,5,6,8,4]=>0001100=>1110011
[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>100000000=>011111111
[10,1,2,3,4,5,6,9,7,8]=>[9,1,2,3,4,5,6,7,10,8]=>100000010=>011111101
[10,1,2,3,4,5,9,6,7,8]=>[9,1,2,3,4,5,6,10,7,8]=>100000100=>011111011
[9,1,2,3,4,10,5,6,7,8]=>[10,1,2,3,4,5,9,6,7,8]=>100001000=>011110111
[10,1,2,3,9,4,5,6,7,8]=>[9,1,2,3,4,10,5,6,7,8]=>100010000=>011101111
[10,1,2,9,3,4,5,6,7,8]=>[9,1,2,3,10,4,5,6,7,8]=>100100000=>011011111
[9,1,10,2,3,4,5,6,7,8]=>[10,1,2,9,3,4,5,6,7,8]=>101000000=>010111111
[10,9,1,2,3,4,5,6,7,8]=>[9,1,10,2,3,4,5,6,7,8]=>110000000=>001111111
[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000=>0111111111
[10,1,2,3,4,5,6,7,8,11,9]=>[11,10,1,2,3,4,5,6,7,8,9]=>1000000001=>0111111110
[8,1,2,3,4,5,6,9,10,7]=>[10,9,8,1,2,3,4,5,6,7]=>100000011=>011111100
[11,1,2,3,4,5,6,7,10,8,9]=>[10,1,2,3,4,5,6,7,8,11,9]=>1000000010=>0111111101
[7,1,2,3,4,5,10,9,6,8]=>[9,7,1,2,3,4,5,6,10,8]=>100000110=>011111001
[11,1,2,3,4,5,6,10,7,8,9]=>[10,1,2,3,4,5,6,7,11,8,9]=>1000000100=>0111111011
[10,1,2,3,4,5,11,6,7,8,9]=>[11,1,2,3,4,5,6,10,7,8,9]=>1000001000=>0111110111
[11,1,2,3,4,10,5,6,7,8,9]=>[10,1,2,3,4,5,11,6,7,8,9]=>1000010000=>0111101111
[10,1,2,11,3,4,5,6,7,8,9]=>[11,1,2,3,10,4,5,6,7,8,9]=>1001000000=>0110111111
[11,1,10,2,3,4,5,6,7,8,9]=>[10,1,2,11,3,4,5,6,7,8,9]=>1010000000=>0101111111
[11,10,1,2,3,4,5,6,7,8,9]=>[10,1,11,2,3,4,5,6,7,8,9]=>1100000000=>0011111111
[4,7,8,5,6,2,1,3]=>[6,5,2,8,1,7,4,3]=>1111100=>0000011
[5,7,8,4,2,6,1,3]=>[4,6,8,2,7,1,5,3]=>1110000=>0001111
[6,7,8,4,2,5,1,3]=>[4,8,2,5,7,1,6,3]=>1110000=>0001111
[7,6,3,8,2,1,5,4]=>[3,8,2,6,1,5,7,4]=>1101000=>0010111
[6,7,8,3,2,1,5,4]=>[8,3,7,2,5,6,1,4]=>1110000=>0001111
[2,7,8,4,3,5,6,1]=>[4,8,3,5,6,7,2,1]=>1110000=>0001111
[3,7,8,4,2,5,1,6]=>[4,8,2,5,7,3,1,6]=>1110000=>0001111
[4,7,8,3,2,1,5,6]=>[8,3,7,2,4,1,5,6]=>1110000=>0001111
[5,7,8,3,2,1,4,6]=>[8,3,7,2,5,1,4,6]=>1110000=>0001111
[7,6,3,8,2,1,4,5]=>[3,8,2,6,1,7,4,5]=>1101000=>0010111
[8,6,3,7,2,1,4,5]=>[3,7,2,6,1,8,4,5]=>1101000=>0010111
[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]=>1111001=>0000110
[3,6,4,7,2,5,1,8]=>[7,4,2,5,6,3,1,8]=>1111000=>0000111
[5,6,3,7,2,1,4,8]=>[3,7,2,6,1,5,4,8]=>1101000=>0010111
[8,4,3,2,1,6,5,7]=>[3,4,2,6,8,1,5,7]=>1100000=>0011111
[4,5,3,2,7,1,6,8]=>[3,7,5,2,4,1,6,8]=>1100100=>0011011
[3,5,4,2,8,6,1,7]=>[4,2,6,8,5,3,1,7]=>1110100=>0001011
[6,4,3,2,1,8,5,7]=>[3,4,2,8,6,1,5,7]=>1100010=>0011101
[7,4,3,2,1,8,6,5]=>[3,4,2,8,6,7,1,5]=>1100010=>0011101
[6,4,3,2,1,8,7,5]=>[3,4,2,7,8,6,1,5]=>1100010=>0011101
[7,5,3,2,8,1,6,4]=>[3,8,5,2,6,7,1,4]=>1100100=>0011011
[8,5,4,2,7,6,1,3]=>[4,2,6,7,5,1,8,3]=>1110100=>0001011
[7,5,4,2,8,6,1,3]=>[4,2,6,8,5,1,7,3]=>1110100=>0001011
[6,5,4,2,8,7,1,3]=>[4,2,7,5,1,8,6,3]=>1110110=>0001001
[4,6,5,8,7,2,1,3]=>[7,2,8,5,1,6,4,3]=>1111100=>0000011
[2,6,5,7,8,3,4,1]=>[8,3,7,5,4,6,2,1]=>1111100=>0000011
[6,5,4,2,7,8,1,3]=>[4,2,8,5,1,7,6,3]=>1110110=>0001001
[8,5,3,2,6,1,7,4]=>[3,6,5,2,7,8,1,4]=>1100100=>0011011
[5,6,3,7,2,1,8,4]=>[3,8,7,2,6,1,5,4]=>1101001=>0010110
[4,6,3,7,2,1,8,5]=>[3,8,7,2,6,4,1,5]=>1101001=>0010110
[3,6,4,7,2,8,1,5]=>[8,4,2,7,6,3,1,5]=>1111010=>0000101
[2,6,4,7,3,8,5,1]=>[8,4,3,5,7,6,2,1]=>1111010=>0000101
[3,5,4,2,7,8,1,6]=>[4,2,8,5,3,1,7,6]=>1110110=>0001001
[7,4,3,2,1,6,8,5]=>[3,4,2,6,8,7,1,5]=>1100001=>0011110
[8,4,3,2,1,6,7,5]=>[3,4,2,6,7,8,1,5]=>1100000=>0011111
[8,4,3,2,1,5,7,6]=>[3,4,2,7,8,1,5,6]=>1100000=>0011111
[8,5,7,4,2,6,3,1]=>[4,6,7,2,5,3,8,1]=>1110000=>0001111
[2,1,7,8,5,6,3,4]=>[2,1,5,6,8,3,7,4]=>1011000=>0100111
[6,8,3,7,5,1,4,2]=>[3,5,7,1,8,4,6,2]=>1101000=>0010111
[5,7,3,8,1,6,2,4]=>[3,6,8,1,7,2,5,4]=>1101000=>0010111
[3,2,6,4,8,5,1,7]=>[2,4,8,5,6,3,1,7]=>1010100=>0101011
[3,2,5,8,4,6,1,7]=>[2,6,8,4,5,3,1,7]=>1011000=>0100111
[3,5,2,4,1,7,6,8]=>[4,5,2,3,1,7,6,8]=>1100010=>0011101
[4,2,1,5,7,3,6,8]=>[2,7,5,4,1,3,6,8]=>1001100=>0110011
[4,5,2,3,7,1,6,8]=>[7,5,2,3,4,1,6,8]=>1100100=>0011011
[4,2,5,3,8,1,6,7]=>[2,8,5,3,4,1,6,7]=>1010100=>0101011
[4,2,5,8,3,1,6,7]=>[2,8,3,5,4,1,6,7]=>1011000=>0100111
[3,1,5,4,2,8,6,7]=>[4,5,3,1,2,8,6,7]=>1010010=>0101101
[4,1,5,3,8,2,6,7]=>[8,5,3,4,1,2,6,7]=>1010100=>0101011
[4,7,3,5,2,1,6,8]=>[3,5,2,7,4,1,6,8]=>1101000=>0010111
[4,3,2,7,5,1,6,8]=>[3,2,5,7,4,1,6,8]=>1101000=>0010111
[4,3,6,2,5,1,7,8]=>[5,6,3,2,4,1,7,8]=>1110000=>0001111
[4,6,3,2,5,1,7,8]=>[3,5,6,2,4,1,7,8]=>1100000=>0011111
[4,6,7,1,3,2,5,8]=>[7,1,6,3,4,2,5,8]=>1110000=>0001111
[4,5,1,3,7,2,6,8]=>[7,5,1,3,4,2,6,8]=>1100100=>0011011
[3,5,1,4,2,7,6,8]=>[4,5,1,3,2,7,6,8]=>1100010=>0011101
[2,5,1,4,3,7,8,6]=>[4,5,2,1,3,8,7,6]=>1100011=>0011100
[5,2,1,4,3,7,8,6]=>[2,4,5,1,3,8,7,6]=>1000011=>0111100
[5,3,1,4,2,7,6,8]=>[3,1,4,5,2,7,6,8]=>1100010=>0011101
[4,3,1,5,7,2,6,8]=>[3,1,7,5,4,2,6,8]=>1101100=>0010011
[4,3,6,1,5,2,7,8]=>[5,6,3,1,4,2,7,8]=>1110000=>0001111
[4,6,3,1,5,2,7,8]=>[3,5,6,1,4,2,7,8]=>1100000=>0011111
[5,3,6,4,1,2,7,8]=>[4,6,3,1,5,2,7,8]=>1110000=>0001111
[4,3,6,1,7,2,5,8]=>[7,3,1,4,2,6,5,8]=>1110100=>0001011
[6,3,4,1,2,7,5,8]=>[4,3,1,7,6,2,5,8]=>1110010=>0001101
[6,2,4,1,3,7,8,5]=>[2,4,1,8,7,6,3,5]=>1010011=>0101100
[4,6,3,1,7,2,5,8]=>[3,7,1,4,2,6,5,8]=>1100100=>0011011
[5,3,6,2,1,4,7,8]=>[6,3,2,5,1,4,7,8]=>1110000=>0001111
[4,5,2,7,3,1,6,8]=>[7,2,3,5,4,1,6,8]=>1101000=>0010111
[4,6,7,2,3,1,5,8]=>[7,2,6,3,4,1,5,8]=>1110000=>0001111
[3,2,6,1,4,7,5,8]=>[2,7,6,3,1,4,5,8]=>1010010=>0101101
[3,6,2,1,4,7,5,8]=>[7,6,2,3,1,4,5,8]=>1100010=>0011101
[3,5,2,7,4,6,1,8]=>[6,7,4,5,2,3,1,8]=>1101000=>0010111
[7,2,1,4,6,3,8,5]=>[2,4,6,1,3,8,7,5]=>1000101=>0111010
[7,3,1,4,6,8,2,5]=>[3,1,4,8,6,2,7,5]=>1100110=>0011001
[3,2,6,1,5,7,4,8]=>[2,5,7,6,3,1,4,8]=>1010010=>0101101
[3,6,2,1,5,7,4,8]=>[5,7,6,2,3,1,4,8]=>1100010=>0011101
[6,3,2,1,5,7,4,8]=>[3,2,5,7,6,1,4,8]=>1100010=>0011101
[4,2,6,1,5,3,7,8]=>[2,5,6,1,4,3,7,8]=>1010000=>0101111
[4,2,1,7,5,3,6,8]=>[2,5,7,4,1,3,6,8]=>1001000=>0110111
[7,4,1,5,6,2,3,8]=>[6,5,4,1,7,2,3,8]=>1101100=>0010011
[7,2,1,5,3,6,8,4]=>[2,5,1,3,6,8,7,4]=>1001001=>0110110
[6,2,5,1,3,7,8,4]=>[2,5,1,8,7,6,3,4]=>1010011=>0101100
[6,4,5,1,7,2,3,8]=>[7,5,1,4,2,6,3,8]=>1110100=>0001011
[5,2,6,4,1,3,7,8]=>[2,4,6,1,5,3,7,8]=>1010000=>0101111
[6,5,2,1,4,7,8,3]=>[5,2,4,8,7,6,1,3]=>1100011=>0011100
[2,3,1,8,5,4,7,6]=>[3,2,1,5,7,8,4,6]=>1101000=>0010111
[2,4,1,5,8,3,7,6]=>[7,8,5,4,2,1,3,6]=>1101100=>0010011
[2,4,1,5,3,8,7,6]=>[5,4,2,1,3,7,8,6]=>1101010=>0010101
[3,4,5,1,2,8,7,6]=>[5,1,4,3,2,7,8,6]=>1110010=>0001101
[1,8,4,5,3,2,7,6]=>[1,5,4,3,7,8,2,6]=>0111000=>1000111
[2,4,8,5,3,1,7,6]=>[5,3,7,8,4,2,1,6]=>1111000=>0000111
[3,4,5,8,2,1,7,6]=>[7,8,2,5,4,3,1,6]=>1111000=>0000111
[3,4,6,2,1,7,8,5]=>[8,7,6,2,4,3,1,5]=>1110011=>0001100
[3,4,6,2,1,7,5,8]=>[7,6,2,4,3,1,5,8]=>1110010=>0001101
[3,5,6,2,7,1,4,8]=>[7,2,6,5,3,1,4,8]=>1110100=>0001011
[3,4,6,8,2,7,1,5]=>[7,2,8,6,4,3,1,5]=>1111010=>0000101
[2,4,8,6,3,7,1,5]=>[7,6,3,8,4,2,1,5]=>1111010=>0000101
[1,8,4,6,3,7,2,5]=>[1,7,6,4,3,8,2,5]=>0111010=>1000101
[1,8,4,6,3,7,5,2]=>[1,7,6,4,3,5,8,2]=>0111010=>1000101
[3,5,6,2,7,8,4,1]=>[8,2,4,7,6,5,3,1]=>1110110=>0001001
[3,5,6,2,7,4,1,8]=>[7,2,4,6,5,3,1,8]=>1110100=>0001011
[4,5,6,7,2,8,3,1]=>[8,2,7,6,3,5,4,1]=>1111010=>0000101
[1,8,5,6,7,3,4,2]=>[1,7,3,6,5,4,8,2]=>0111100=>1000011
[1,8,5,6,7,3,2,4]=>[1,7,3,6,5,2,8,4]=>0111100=>1000011
[2,5,8,6,7,3,1,4]=>[7,3,6,2,1,8,5,4]=>1111100=>0000011
[4,5,6,7,2,1,8,3]=>[8,7,2,6,1,5,4,3]=>1111001=>0000110
[2,3,1,8,6,7,4,5]=>[3,2,1,7,6,4,8,5]=>1101110=>0010001
[1,8,3,2,6,7,5,4]=>[1,3,7,6,5,8,2,4]=>0100110=>1011001
[2,5,1,6,7,8,4,3]=>[8,4,7,6,5,2,1,3]=>1101110=>0010001
[2,5,1,6,7,4,8,3]=>[8,7,4,6,5,2,1,3]=>1101101=>0010010
[3,5,6,1,7,4,2,8]=>[7,1,4,6,5,3,2,8]=>1110100=>0001011
[3,5,6,1,7,4,8,2]=>[8,7,1,4,6,5,3,2]=>1110101=>0001010
[3,4,6,1,8,7,5,2]=>[7,5,8,6,1,4,3,2]=>1110110=>0001001
[3,4,6,8,1,7,5,2]=>[7,1,5,8,6,4,3,2]=>1111010=>0000101
[2,4,8,6,1,7,5,3]=>[7,6,2,1,5,8,4,3]=>1111010=>0000101
[2,5,8,6,7,1,4,3]=>[7,2,1,6,4,8,5,3]=>1111100=>0000011
[3,5,6,8,7,1,4,2]=>[7,1,8,4,6,5,3,2]=>1111100=>0000011
[4,5,6,7,8,1,3,2]=>[8,1,7,3,6,5,4,2]=>1111100=>0000011
[4,5,6,7,1,3,8,2]=>[8,7,1,6,3,5,4,2]=>1111001=>0000110
[4,5,6,7,1,3,2,8]=>[7,1,6,3,5,4,2,8]=>1111000=>0000111
[4,5,6,7,3,1,8,2]=>[8,7,3,6,1,5,4,2]=>1111001=>0000110
[3,5,6,8,7,4,1,2]=>[7,4,8,1,6,5,3,2]=>1111100=>0000011
[2,5,8,6,7,4,3,1]=>[7,4,6,3,8,5,2,1]=>1111100=>0000011
[8,2,5,3,7,1,6,4]=>[2,7,5,3,6,8,1,4]=>1010100=>0101011
[8,2,4,3,7,1,6,5]=>[2,4,3,7,1,6,8,5]=>1010100=>0101011
[5,8,2,4,3,7,1,6]=>[4,7,2,3,5,1,8,6]=>1100010=>0011101
[4,2,5,6,1,7,3,8]=>[2,7,6,1,5,4,3,8]=>1011010=>0100101
[6,1,5,7,3,2,4,8]=>[7,3,5,1,2,6,4,8]=>1011000=>0100111
[6,1,5,8,3,2,4,7]=>[8,3,5,1,2,6,4,7]=>1011000=>0100111
[3,8,2,4,7,1,5,6]=>[4,7,2,3,1,8,5,6]=>1100100=>0011011
[3,6,8,2,4,7,1,5]=>[7,2,4,8,6,3,1,5]=>1110010=>0001101
[4,3,5,6,7,1,8,2]=>[8,7,3,1,6,5,4,2]=>1111101=>0000010
[3,7,1,5,6,8,2,4]=>[8,6,5,1,3,2,7,4]=>1101110=>0010001
[3,2,5,1,8,4,6,7]=>[2,8,5,3,1,4,6,7]=>1010100=>0101011
[3,2,5,1,7,8,4,6]=>[2,8,5,3,1,4,7,6]=>1010110=>0101001
[7,8,3,2,4,6,1,5]=>[3,6,8,2,4,7,1,5]=>1100000=>0011111
[6,1,5,7,8,3,2,4]=>[8,3,7,5,1,2,6,4]=>1011100=>0100011
[4,2,5,6,1,7,8,3]=>[2,8,7,6,1,5,4,3]=>1011011=>0100100
[6,1,5,8,7,3,2,4]=>[7,3,8,5,1,2,6,4]=>1011100=>0100011
[8,7,3,2,4,6,1,5]=>[3,6,7,2,4,8,1,5]=>1100000=>0011111
[3,2,5,1,8,7,4,6]=>[2,7,5,3,1,4,8,6]=>1010110=>0101001
[3,2,5,1,6,8,7,4]=>[2,7,8,6,5,3,1,4]=>1010110=>0101001
[3,8,6,5,1,7,4,2]=>[5,1,7,6,4,8,3,2]=>1111010=>0000101
[6,5,1,7,8,4,2,3]=>[8,4,7,5,1,6,2,3]=>1101100=>0010011
[3,2,4,1,8,5,6,7]=>[2,4,3,1,8,5,6,7]=>1010100=>0101011
[3,2,4,1,6,8,5,7]=>[2,4,3,1,8,6,5,7]=>1010110=>0101001
[3,2,4,1,8,5,7,6]=>[2,4,3,1,7,8,5,6]=>1010100=>0101011
[3,2,5,1,6,7,4,8]=>[2,7,6,5,3,1,4,8]=>1010110=>0101001
[4,2,6,1,8,3,7,5]=>[2,7,8,1,4,3,6,5]=>1010100=>0101011
[5,2,6,1,8,3,7,4]=>[2,7,8,1,6,5,3,4]=>1010100=>0101011
[8,4,6,1,7,3,5,2]=>[7,1,4,3,6,5,8,2]=>1110100=>0001011
[7,4,2,3,8,5,1,6]=>[4,2,3,8,5,7,1,6]=>1100100=>0011011
[7,5,1,6,4,2,3,8]=>[6,4,5,1,7,2,3,8]=>1101000=>0010111
[3,2,5,1,8,6,4,7]=>[2,6,8,5,3,1,4,7]=>1010100=>0101011
[8,6,1,5,7,3,2,4]=>[7,5,1,3,6,2,8,4]=>1101100=>0010011
[4,2,6,1,8,5,7,3]=>[2,7,8,5,6,1,4,3]=>1010100=>0101011
[8,5,6,1,7,3,4,2]=>[7,1,6,5,3,4,8,2]=>1110100=>0001011
[3,6,8,5,1,7,4,2]=>[5,1,7,4,8,6,3,2]=>1111010=>0000101
[8,5,1,6,7,4,2,3]=>[7,4,6,5,1,8,2,3]=>1101100=>0010011
[3,2,5,1,8,6,7,4]=>[2,6,7,8,5,3,1,4]=>1010100=>0101011
[3,2,4,1,8,6,5,7]=>[2,4,3,1,6,8,5,7]=>1010100=>0101011
[3,2,4,1,5,8,6,7]=>[2,4,3,1,5,8,6,7]=>1010010=>0101101
[3,2,5,1,7,8,6,4]=>[2,8,6,7,5,3,1,4]=>1010110=>0101001
[3,8,5,1,7,6,4,2]=>[6,7,5,1,4,8,3,2]=>1110100=>0001011
[3,2,5,1,8,7,6,4]=>[2,7,6,8,5,3,1,4]=>1010110=>0101001
[4,6,3,7,1,8,5,2]=>[3,8,1,5,7,6,4,2]=>1101010=>0010101
[2,5,7,4,1,6,8,3]=>[4,6,8,7,2,1,5,3]=>1110001=>0001110
[5,4,7,3,6,1,8,2]=>[6,3,4,1,8,7,5,2]=>1110101=>0001010
[4,3,7,5,1,8,6,2]=>[5,3,1,8,6,7,4,2]=>1111010=>0000101
[6,4,3,8,5,1,7,2]=>[3,5,7,8,4,1,6,2]=>1101000=>0010111
[5,8,4,3,6,1,7,2]=>[4,3,6,1,7,8,5,2]=>1110100=>0001011
[5,4,3,6,7,1,8,2]=>[3,8,7,4,1,6,5,2]=>1101101=>0010010
[2,5,4,6,1,7,3,8]=>[7,6,4,2,1,5,3,8]=>1111010=>0000101
[2,5,4,6,8,1,7,3]=>[7,8,4,2,1,6,5,3]=>1111100=>0000011
[5,2,8,4,1,6,7,3]=>[2,4,6,7,8,1,5,3]=>1010000=>0101111
[4,6,2,1,8,5,7,3]=>[7,8,5,6,2,4,1,3]=>1100100=>0011011
[2,4,1,7,5,8,6,3]=>[5,8,6,7,4,2,1,3]=>1101010=>0010101
[2,4,1,7,5,3,8,6]=>[5,8,7,4,2,1,3,6]=>1101001=>0010110
[2,6,4,1,8,5,3,7]=>[4,2,1,8,5,6,3,7]=>1110100=>0001011
[3,2,5,6,1,8,4,7]=>[2,8,6,3,1,5,4,7]=>1011010=>0100101
[4,8,3,2,6,1,5,7]=>[3,6,2,4,1,8,5,7]=>1100100=>0011011
[3,5,2,8,1,6,4,7]=>[6,8,2,3,1,5,4,7]=>1101000=>0010111
[3,2,1,6,8,5,4,7]=>[2,3,1,8,5,6,4,7]=>1001100=>0110011
[3,2,7,1,5,4,8,6]=>[2,5,8,7,3,1,4,6]=>1010001=>0101110
[3,2,7,1,5,8,6,4]=>[2,5,8,6,7,3,1,4]=>1010010=>0101101
[3,8,2,5,1,6,7,4]=>[5,2,3,1,6,7,8,4]=>1101000=>0010111
[4,8,3,2,6,7,1,5]=>[3,7,6,2,4,1,8,5]=>1100110=>0011001
[4,3,8,2,6,7,1,5]=>[7,6,3,2,4,1,8,5]=>1110110=>0001001
[4,3,2,6,7,8,1,5]=>[3,2,8,4,1,7,6,5]=>1101110=>0010001
[4,3,2,6,7,1,5,8]=>[3,2,7,4,1,6,5,8]=>1101100=>0010011
[4,3,7,2,6,8,1,5]=>[8,6,3,2,4,1,7,5]=>1110110=>0001001
[2,5,7,4,8,1,6,3]=>[4,8,2,1,6,7,5,3]=>1110100=>0001011
[3,2,5,7,8,1,6,4]=>[2,8,3,1,6,7,5,4]=>1011100=>0100011
[3,2,5,7,1,6,4,8]=>[2,6,7,3,1,5,4,8]=>1011000=>0100111
[6,3,2,7,1,5,8,4]=>[3,2,8,7,1,5,6,4]=>1101001=>0010110
[6,3,2,7,8,1,5,4]=>[3,2,8,1,7,5,6,4]=>1101100=>0010011
[2,1,7,5,3,8,6,4]=>[2,1,5,3,8,6,7,4]=>1011010=>0100101
[6,3,2,7,1,4,8,5]=>[3,2,8,7,1,6,4,5]=>1101001=>0010110
[6,3,2,1,4,7,8,5]=>[3,2,8,7,6,1,4,5]=>1100011=>0011100
[6,3,2,1,4,7,5,8]=>[3,2,7,6,1,4,5,8]=>1100010=>0011101
[3,5,2,1,7,4,6,8]=>[7,5,2,3,1,4,6,8]=>1100100=>0011011
[5,8,4,2,1,7,3,6]=>[4,2,7,1,5,3,8,6]=>1110010=>0001101
[4,6,2,1,8,3,7,5]=>[7,8,2,4,1,3,6,5]=>1100100=>0011011
[2,4,1,7,3,8,6,5]=>[8,6,7,4,2,1,3,5]=>1101010=>0010101
[4,8,3,7,2,1,5,6]=>[3,7,2,8,4,1,5,6]=>1101000=>0010111
[4,3,7,2,8,1,5,6]=>[8,3,2,4,1,7,5,6]=>1110100=>0001011
[6,3,2,8,1,4,7,5]=>[3,2,7,8,1,6,4,5]=>1101000=>0010111
[5,3,2,1,8,4,6,7]=>[3,2,8,5,1,4,6,7]=>1100100=>0011011
[1,9,8,7,6,5,4,3,2]=>[1,6,5,7,4,8,3,9,2]=>01111000=>10000111
[8,7,6,4,5,3,2,1,9]=>[4,5,6,3,7,2,8,1,9]=>11100000=>00011111
[1,9,8,7,5,6,4,3,2]=>[1,5,6,7,4,8,3,9,2]=>01110000=>10001111
[1,10,9,8,7,6,5,4,3,2]=>[1,6,7,5,8,4,9,3,10,2]=>011110000=>100001111
[10,9,8,7,6,5,4,3,2,1,11]=>[6,5,7,4,8,3,9,2,10,1,11]=>1111100000=>0000011111
[1,11,10,9,8,7,6,5,4,3,2]=>[1,7,6,8,5,9,4,10,3,11,2]=>0111110000=>1000001111
[6,2,3,1,5,4,8,7]=>[2,3,5,6,1,4,8,7]=>1000001=>0111110
[8,4,5,2,3,1,7,6]=>[5,2,4,3,7,8,1,6]=>1110000=>0001111
[8,6,7,2,5,3,4,1]=>[5,7,2,6,3,4,8,1]=>1110000=>0001111
[6,1,5,2,4,3,8,7]=>[5,1,2,4,6,3,8,7]=>1010001=>0101110
[6,4,5,1,3,2,8,7]=>[5,1,4,3,6,2,8,7]=>1110001=>0001110
[6,3,5,1,4,2,8,7]=>[5,3,1,4,6,2,8,7]=>1110001=>0001110
[8,3,7,5,6,2,4,1]=>[6,5,3,2,7,4,8,1]=>1111100=>0000011
[8,3,7,2,4,1,6,5]=>[7,3,2,4,6,8,1,5]=>1110000=>0001111
[8,3,5,1,4,2,7,6]=>[5,3,1,4,7,8,2,6]=>1110000=>0001111
[8,1,5,3,4,2,7,6]=>[5,3,4,7,8,1,2,6]=>1010000=>0101111
[2,1,8,4,5,3,7,6]=>[2,1,4,5,7,8,3,6]=>1010000=>0101111
[8,6,7,4,5,1,3,2]=>[4,5,7,1,6,3,8,2]=>1110000=>0001111
[8,6,7,3,5,1,4,2]=>[5,7,3,6,1,4,8,2]=>1110000=>0001111
[8,5,7,3,6,1,4,2]=>[6,3,7,5,1,4,8,2]=>1110100=>0001011
[8,3,7,1,6,4,5,2]=>[6,3,1,4,7,5,8,2]=>1110100=>0001011
[8,1,7,3,6,4,5,2]=>[6,3,4,7,5,8,1,2]=>1010100=>0101011
[8,4,7,5,6,1,3,2]=>[6,5,1,7,4,3,8,2]=>1111100=>0000011
[8,1,7,3,4,2,6,5]=>[7,3,4,6,8,1,2,5]=>1010000=>0101111
[8,1,7,3,6,2,5,4]=>[6,3,7,5,8,1,2,4]=>1010100=>0101011
[8,3,7,1,6,2,5,4]=>[6,3,1,7,5,8,2,4]=>1110100=>0001011
[8,3,7,2,6,4,5,1]=>[6,3,2,4,7,5,8,1]=>1110100=>0001011
[8,2,7,3,6,4,5,1]=>[2,6,3,4,7,5,8,1]=>1010100=>0101011
[8,2,7,3,6,1,5,4]=>[2,6,3,7,5,8,1,4]=>1010100=>0101011
[8,2,7,1,6,3,5,4]=>[2,6,1,7,5,8,3,4]=>1010100=>0101011
[2,1,8,3,7,4,6,5]=>[2,1,7,3,4,6,8,5]=>1010100=>0101011
[8,1,5,2,4,3,7,6]=>[5,1,2,4,7,8,3,6]=>1010000=>0101111
[8,2,7,5,6,3,4,1]=>[2,6,5,3,7,4,8,1]=>1011100=>0100011
[8,4,7,5,6,2,3,1]=>[6,5,2,7,4,3,8,1]=>1111100=>0000011
[8,2,3,1,5,4,7,6]=>[2,3,5,7,8,1,4,6]=>1000000=>0111111
[4,2,3,1,8,5,7,6]=>[2,3,4,1,7,8,5,6]=>1000100=>0111011
[4,1,3,2,8,6,7,5]=>[3,4,1,2,6,7,8,5]=>1000100=>0111011
[8,2,3,1,7,5,6,4]=>[2,3,7,5,6,8,1,4]=>1000100=>0111011
[8,5,7,2,6,1,4,3]=>[6,2,7,5,1,4,8,3]=>1110100=>0001011
[8,6,7,2,5,1,4,3]=>[5,7,2,6,1,4,8,3]=>1110000=>0001111
[8,6,7,1,3,2,5,4]=>[7,1,6,3,5,8,2,4]=>1110000=>0001111
[2,1,8,6,7,3,5,4]=>[2,1,7,3,6,5,8,4]=>1011100=>0100011
[2,1,8,3,7,5,6,4]=>[2,1,7,5,6,8,3,4]=>1010100=>0101011
[8,1,3,2,7,5,6,4]=>[3,7,5,6,8,1,2,4]=>1000100=>0111011
[8,1,7,5,6,2,4,3]=>[6,5,1,2,7,4,8,3]=>1011100=>0100011
[8,2,7,1,6,4,5,3]=>[2,6,1,4,7,5,8,3]=>1010100=>0101011
[8,2,7,4,6,1,5,3]=>[2,4,6,1,7,5,8,3]=>1010100=>0101011
[8,2,7,4,6,3,5,1]=>[2,4,6,3,7,5,8,1]=>1010100=>0101011
[8,4,7,2,6,3,5,1]=>[6,2,4,3,7,5,8,1]=>1110100=>0001011
[8,4,7,2,6,1,5,3]=>[6,2,4,1,7,5,8,3]=>1110100=>0001011
[8,4,7,1,6,2,5,3]=>[6,1,4,2,7,5,8,3]=>1110100=>0001011
[8,1,7,4,6,2,5,3]=>[4,6,1,2,7,5,8,3]=>1010100=>0101011
[8,5,7,1,6,2,4,3]=>[6,1,7,5,2,4,8,3]=>1110100=>0001011
[2,1,8,5,7,3,6,4]=>[2,1,7,5,3,6,8,4]=>1011100=>0100011
[8,1,7,4,6,3,5,2]=>[4,6,3,7,5,8,1,2]=>1010100=>0101011
[8,4,7,1,6,3,5,2]=>[6,1,4,3,7,5,8,2]=>1110100=>0001011
[2,4,8,3,6,1,7,5]=>[6,3,4,2,1,7,8,5]=>1110100=>0001011
[6,5,8,1,3,2,7,4]=>[7,8,1,5,3,6,2,4]=>1110000=>0001111
[4,5,8,6,3,2,7,1]=>[6,3,7,8,2,5,4,1]=>1111000=>0000111
[6,5,8,7,3,1,2,4]=>[7,3,8,1,5,2,6,4]=>1111000=>0000111
[1,5,8,7,3,6,2,4]=>[1,6,7,3,8,2,5,4]=>0111000=>1000111
[6,7,2,8,4,1,5,3]=>[8,4,7,2,5,6,1,3]=>1101000=>0010111
[3,6,2,8,4,5,7,1]=>[7,8,4,5,6,2,3,1]=>1101000=>0010111
[3,1,6,8,4,5,7,2]=>[7,8,4,5,6,3,1,2]=>1011000=>0100111
[6,3,7,8,4,1,5,2]=>[8,4,7,3,1,5,6,2]=>1111000=>0000111
[1,5,7,8,2,4,6,3]=>[1,8,2,6,7,4,5,3]=>0111000=>1000111
[5,1,7,8,2,4,6,3]=>[8,1,2,6,7,4,5,3]=>1011000=>0100111
[3,6,7,8,4,2,5,1]=>[8,4,7,2,5,6,3,1]=>1111000=>0000111
[5,6,8,7,3,2,1,4]=>[7,3,8,2,6,1,5,4]=>1111000=>0000111
[2,8,3,7,1,6,5,4]=>[3,6,7,2,1,5,8,4]=>1101000=>0010111
[5,2,8,7,3,6,1,4]=>[2,6,7,3,8,1,5,4]=>1011000=>0100111
[7,2,1,8,4,6,5,3]=>[2,6,8,4,5,7,1,3]=>1001000=>0110111
[3,2,7,8,4,6,5,1]=>[2,6,8,4,5,7,3,1]=>1011000=>0100111
[5,2,7,8,1,4,6,3]=>[2,8,1,6,7,4,5,3]=>1011000=>0100111
[4,2,1,3,8,5,6,7]=>[2,4,1,3,8,5,6,7]=>1000100=>0111011
[6,2,8,5,4,3,1,7]=>[2,5,4,8,3,6,1,7]=>1011000=>0100111
[2,8,4,5,3,1,6,7]=>[5,4,3,8,2,1,6,7]=>1111000=>0000111
[4,3,1,2,8,5,6,7]=>[3,1,4,2,8,5,6,7]=>1100100=>0011011
[3,4,2,1,8,5,6,7]=>[4,2,3,1,8,5,6,7]=>1100100=>0011011
[5,7,1,8,3,4,6,2]=>[8,1,3,6,7,4,5,2]=>1101000=>0010111
[3,7,5,8,1,4,6,2]=>[8,1,5,4,6,7,3,2]=>1111000=>0000111
[1,7,5,8,3,4,6,2]=>[1,8,3,5,4,6,7,2]=>0111000=>1000111
[5,6,8,1,4,3,2,7]=>[8,1,4,6,3,5,2,7]=>1110000=>0001111
[7,5,8,6,3,4,2,1]=>[6,3,8,4,5,2,7,1]=>1111000=>0000111
[2,4,8,3,6,5,1,7]=>[6,5,8,3,4,2,1,7]=>1110100=>0001011
[4,1,8,3,5,6,2,7]=>[5,6,8,3,4,1,2,7]=>1010000=>0101111
[5,6,8,4,1,3,2,7]=>[4,8,1,6,3,5,2,7]=>1110000=>0001111
[4,6,8,1,5,3,2,7]=>[5,8,1,6,3,4,2,7]=>1110000=>0001111
[1,6,8,4,5,3,2,7]=>[1,4,5,8,3,6,2,7]=>0110000=>1001111
[1,7,3,8,5,4,6,2]=>[1,3,5,8,4,6,7,2]=>0101000=>1010111
[3,7,1,8,5,4,6,2]=>[5,8,4,6,7,1,3,2]=>1101000=>0010111
[2,7,3,8,4,6,5,1]=>[3,6,8,4,5,7,2,1]=>1101000=>0010111
[7,1,3,8,4,6,5,2]=>[3,6,8,4,5,7,1,2]=>1001000=>0110111
[5,7,8,4,3,6,1,2]=>[4,6,8,3,7,1,5,2]=>1110000=>0001111
[2,8,7,4,1,6,5,3]=>[4,6,7,2,1,5,8,3]=>1110000=>0001111
[2,8,5,4,3,1,6,7]=>[4,5,3,8,2,1,6,7]=>1110000=>0001111
[4,1,3,2,8,5,6,7]=>[3,4,1,2,8,5,6,7]=>1000100=>0111011
[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]=>0100100=>1011011
[6,4,8,2,5,3,1,7]=>[5,8,2,4,3,6,1,7]=>1110000=>0001111
[2,8,4,3,5,1,6,7]=>[4,3,5,8,2,1,6,7]=>1110000=>0001111
[6,2,8,4,5,3,1,7]=>[2,4,5,8,3,6,1,7]=>1010000=>0101111
[7,2,3,8,5,4,6,1]=>[2,3,5,8,4,6,7,1]=>1001000=>0110111
[4,2,3,1,8,5,6,7]=>[2,3,4,1,8,5,6,7]=>1000100=>0111011
[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,5,6,7]=>1000100=>0111011
[5,1,3,2,4,8,6,7]=>[3,5,1,2,4,8,6,7]=>1000010=>0111101
[1,2,8,4,5,3,7,6]=>[1,2,4,5,7,8,3,6]=>0010000=>1101111
[1,4,2,8,5,3,6,7]=>[1,5,8,4,2,3,6,7]=>0101000=>1010111
[1,8,4,2,5,3,6,7]=>[1,4,2,5,8,3,6,7]=>0110000=>1001111
[3,5,1,4,8,2,6,7]=>[4,8,5,1,3,2,6,7]=>1100100=>0011011
[1,5,2,8,4,3,6,7]=>[1,8,4,5,2,3,6,7]=>0101000=>1010111
[1,2,8,5,4,3,6,7]=>[1,2,5,4,8,3,6,7]=>0011000=>1100111
[1,2,5,4,3,8,6,7]=>[1,2,4,5,3,8,6,7]=>0010010=>1101101
[1,2,4,8,5,3,7,6]=>[1,2,5,7,8,4,3,6]=>0011000=>1100111
[1,2,7,4,8,5,3,6]=>[1,2,4,8,5,7,3,6]=>0010100=>1101011
[1,5,2,7,8,4,3,6]=>[1,8,4,7,5,2,3,6]=>0101100=>1010011
[8,3,5,1,4,7,2,6]=>[5,3,1,4,7,2,8,6]=>1110010=>0001101
[2,8,1,5,4,7,3,6]=>[5,4,7,2,1,3,8,6]=>1101010=>0010101
[1,2,8,5,7,4,3,6]=>[1,2,7,5,4,8,3,6]=>0011100=>1100011
[1,2,4,8,7,5,3,6]=>[1,2,7,5,8,4,3,6]=>0011100=>1100011
[7,6,1,4,2,8,3,5]=>[4,8,6,1,7,2,3,5]=>1100010=>0011101
[7,1,6,2,8,4,3,5]=>[8,1,2,4,6,3,7,5]=>1010100=>0101011
[1,6,7,2,8,4,3,5]=>[1,8,2,4,7,3,6,5]=>0110100=>1001011
[6,7,1,4,2,8,3,5]=>[4,8,1,7,6,2,3,5]=>1100010=>0011101
[6,3,7,1,4,8,2,5]=>[8,3,1,4,7,6,2,5]=>1110010=>0001101
[7,1,2,8,5,3,4,6]=>[5,8,1,2,3,7,4,6]=>1001000=>0110111
[1,7,2,8,4,5,3,6]=>[1,8,4,5,7,2,3,6]=>0101000=>1010111
[1,4,2,7,8,5,3,6]=>[1,8,5,7,4,2,3,6]=>0101100=>1010011
[6,1,2,8,4,3,7,5]=>[7,8,4,6,1,2,3,5]=>1001000=>0110111
[6,4,1,2,8,3,7,5]=>[4,1,7,8,2,3,6,5]=>1100100=>0011011
[7,6,1,3,2,4,8,5]=>[6,1,3,8,7,2,4,5]=>1100001=>0011110
[6,7,1,3,2,4,8,5]=>[8,7,1,3,6,2,4,5]=>1100001=>0011110
[1,2,7,3,5,8,4,6]=>[1,2,5,8,3,4,7,6]=>0010010=>1101101
[1,2,7,5,8,3,4,6]=>[1,2,8,5,3,7,4,6]=>0011100=>1100011
[5,8,1,3,7,2,4,6]=>[7,1,3,8,5,2,4,6]=>1100100=>0011011
[1,2,5,8,7,3,4,6]=>[1,2,7,3,8,5,4,6]=>0011100=>1100011
[1,2,5,8,3,7,4,6]=>[1,2,7,3,5,4,8,6]=>0011010=>1100101
[2,8,1,7,3,5,4,6]=>[7,2,1,3,5,8,4,6]=>1101000=>0010111
[4,2,8,1,7,3,6,5]=>[2,7,1,4,3,6,8,5]=>1010100=>0101011
[2,8,1,7,4,3,6,5]=>[7,4,6,8,2,1,3,5]=>1101000=>0010111
[7,1,2,8,4,3,6,5]=>[8,4,6,7,1,2,3,5]=>1001000=>0110111
[1,2,8,4,7,5,3,6]=>[1,2,4,7,5,8,3,6]=>0010100=>1101011
[1,2,8,7,4,5,3,6]=>[1,2,7,4,5,8,3,6]=>0011000=>1100111
[2,8,1,7,5,3,4,6]=>[5,7,2,1,3,8,4,6]=>1101000=>0010111
[8,3,7,1,5,2,4,6]=>[5,7,3,1,8,2,4,6]=>1110000=>0001111
[3,8,6,1,4,7,2,5]=>[7,6,1,4,8,3,2,5]=>1110010=>0001101
[8,6,1,4,2,7,3,5]=>[4,7,6,1,8,2,3,5]=>1100010=>0011101
[8,1,6,2,7,4,3,5]=>[7,1,2,4,6,3,8,5]=>1010100=>0101011
[7,1,2,8,6,4,3,5]=>[6,4,8,1,2,3,7,5]=>1001100=>0110011
[7,4,1,2,8,6,3,5]=>[4,1,6,8,2,3,7,5]=>1100100=>0011011
[3,7,4,8,1,6,2,5]=>[6,8,4,1,7,3,2,5]=>1111000=>0000111
[4,2,8,1,7,6,3,5]=>[2,6,7,1,4,3,8,5]=>1010100=>0101011
[2,8,1,7,6,4,3,5]=>[6,4,7,2,1,3,8,5]=>1101100=>0010011
[7,8,3,4,1,6,2,5]=>[3,4,6,8,1,7,2,5]=>1100000=>0011111
[6,8,3,4,1,7,2,5]=>[3,4,7,1,8,6,2,5]=>1100010=>0011101
[6,7,3,4,1,8,2,5]=>[3,4,8,1,7,6,2,5]=>1100010=>0011101
[5,7,3,4,1,8,2,6]=>[3,4,8,1,5,2,7,6]=>1100010=>0011101
[5,8,3,4,1,7,2,6]=>[3,4,7,1,5,2,8,6]=>1100010=>0011101
[5,8,3,4,1,6,2,7]=>[3,4,6,8,1,5,2,7]=>1100000=>0011111
[6,7,3,4,1,5,2,8]=>[3,4,7,1,5,6,2,8]=>1100000=>0011111
[4,7,3,5,1,6,2,8]=>[3,5,1,6,7,4,2,8]=>1101000=>0010111
[4,7,3,5,1,8,2,6]=>[3,5,1,8,4,2,7,6]=>1101010=>0010101
[5,6,2,3,1,7,4,8]=>[7,6,2,3,5,1,4,8]=>1100010=>0011101
[4,6,2,5,1,8,3,7]=>[5,2,8,6,4,1,3,7]=>1101010=>0010101
[4,5,1,8,3,7,2,6]=>[7,1,3,5,4,2,8,6]=>1101010=>0010101
[5,6,2,7,4,8,1,3]=>[8,4,7,6,2,5,1,3]=>1101010=>0010101
[5,6,3,8,4,7,1,2]=>[3,7,4,8,6,1,5,2]=>1101010=>0010101
[5,6,2,8,3,7,1,4]=>[7,2,3,8,6,1,5,4]=>1101010=>0010101
[4,6,2,8,3,7,1,5]=>[7,2,3,8,6,4,1,5]=>1101010=>0010101
[9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,8]=>10000000=>01111111
[10,2,1,3,4,5,6,7,8,9]=>[2,10,1,3,4,5,6,7,8,9]=>100000000=>011111111
[9,2,3,1,4,5,6,7,8]=>[2,3,9,1,4,5,6,7,8]=>10000000=>01111111
[4,2,3,5,6,7,8,9,1]=>[2,3,9,8,7,6,5,4,1]=>10011111=>01100000
[3,4,2,5,6,7,8,9,1]=>[9,8,7,6,5,4,2,3,1]=>11011111=>00100000
[3,2,4,5,6,7,8,9,10,1]=>[2,10,9,8,7,6,5,4,3,1]=>101111111=>010000000
[2,3,4,5,6,7,8,9,10,11,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>1111111111=>0000000000
[6,5,3,2,1,4,8,7]=>[3,5,2,6,1,4,8,7]=>1100001=>0011110
[4,6,3,5,2,1,8,7]=>[3,5,2,6,4,1,8,7]=>1101001=>0010110
[6,8,2,4,5,7,3,1]=>[4,5,7,2,3,8,6,1]=>1100010=>0011101
[8,7,2,4,5,3,1,6]=>[4,5,7,2,3,8,1,6]=>1100000=>0011111
[3,6,1,4,5,2,8,7]=>[4,5,6,1,3,2,8,7]=>1100001=>0011110
[6,3,8,4,5,7,2,1]=>[4,5,7,3,2,8,6,1]=>1110010=>0001101
[5,8,7,4,3,6,2,1]=>[4,6,7,3,8,2,5,1]=>1110000=>0001111
[2,8,7,4,3,6,1,5]=>[4,6,7,3,8,2,1,5]=>1110000=>0001111
[8,7,3,5,1,4,2,6]=>[3,5,1,7,4,8,2,6]=>1101000=>0010111
[2,1,6,8,5,7,4,3]=>[2,1,5,7,4,8,6,3]=>1011010=>0100101
[6,8,3,5,1,7,4,2]=>[3,5,1,7,4,8,6,2]=>1101010=>0010101
[5,1,8,4,7,6,3,2]=>[4,6,7,3,8,5,1,2]=>1010100=>0101011
[2,5,8,4,7,6,3,1]=>[4,6,7,3,8,5,2,1]=>1110100=>0001011
[4,3,8,1,5,6,7,2]=>[5,6,7,8,3,1,4,2]=>1110000=>0001111
[4,8,1,3,5,6,7,2]=>[5,6,7,8,1,3,4,2]=>1100000=>0011111
[5,8,7,4,1,6,3,2]=>[4,6,7,1,8,3,5,2]=>1110000=>0001111
[5,8,3,6,1,4,7,2]=>[3,6,1,7,8,4,5,2]=>1101000=>0010111
[4,8,3,6,1,2,7,5]=>[3,6,1,7,8,4,2,5]=>1101000=>0010111
[3,8,7,4,1,6,2,5]=>[4,6,7,1,8,3,2,5]=>1110000=>0001111
[3,8,1,2,5,6,7,4]=>[5,6,7,8,1,3,2,4]=>1100000=>0011111
[8,6,3,1,2,4,7,5]=>[3,6,1,7,8,2,4,5]=>1100000=>0011111
[8,1,7,4,5,2,3,6]=>[4,5,7,1,2,8,3,6]=>1010000=>0101111
[8,6,3,2,1,4,7,5]=>[3,6,2,7,8,1,4,5]=>1100000=>0011111
[5,8,3,6,2,1,7,4]=>[3,6,2,7,8,1,5,4]=>1101000=>0010111
[2,6,8,4,5,7,1,3]=>[4,5,7,2,1,8,6,3]=>1110010=>0001101
[6,1,8,4,5,7,2,3]=>[4,5,7,1,2,8,6,3]=>1010010=>0101101
[6,8,3,5,1,7,2,4]=>[3,5,1,7,2,8,6,4]=>1101010=>0010101
[2,1,5,8,3,6,7,4]=>[2,1,6,7,8,3,5,4]=>1011000=>0100111
[4,1,8,2,5,6,7,3]=>[5,6,7,8,1,2,4,3]=>1010000=>0101111
[2,4,8,1,5,6,7,3]=>[5,6,7,8,2,1,4,3]=>1110000=>0001111
[4,8,2,1,5,6,7,3]=>[5,6,7,8,2,4,1,3]=>1100000=>0011111
[3,4,8,2,5,6,7,1]=>[5,6,7,8,2,4,3,1]=>1110000=>0001111
[5,8,1,4,7,6,2,3]=>[4,6,7,1,8,5,2,3]=>1100100=>0011011
[5,8,3,1,6,2,7,4]=>[3,6,1,7,8,5,2,4]=>1100100=>0011011
[3,4,1,8,5,6,7,2]=>[5,6,7,8,4,1,3,2]=>1101000=>0010111
[4,5,7,6,2,3,8,1]=>[6,2,8,7,3,5,4,1]=>1111001=>0000110
[3,5,7,2,6,4,8,1]=>[6,2,4,8,7,5,3,1]=>1110101=>0001010
[5,2,7,3,6,4,8,1]=>[2,6,3,4,8,7,5,1]=>1010101=>0101010
[8,3,4,7,6,1,5,2]=>[6,4,3,1,7,5,8,2]=>1111100=>0000011
[3,1,4,7,6,8,5,2]=>[8,6,5,7,4,3,1,2]=>1011110=>0100001
[4,1,3,7,6,8,5,2]=>[3,8,6,5,7,4,1,2]=>1001110=>0110001
[6,7,1,3,5,8,4,2]=>[5,8,1,3,4,7,6,2]=>1100010=>0011101
[5,8,7,3,6,1,4,2]=>[6,3,7,1,4,8,5,2]=>1110100=>0001011
[3,8,4,7,6,1,5,2]=>[6,4,1,7,5,8,3,2]=>1111100=>0000011
[2,8,4,7,1,6,5,3]=>[6,7,4,2,1,5,8,3]=>1111000=>0000111
[8,1,4,7,2,6,5,3]=>[6,7,4,1,2,5,8,3]=>1011000=>0100111
[8,1,3,2,7,6,5,4]=>[3,6,7,5,8,1,2,4]=>1000100=>0111011
[2,8,3,1,7,6,5,4]=>[3,6,7,5,8,2,1,4]=>1100100=>0011011
[3,8,2,1,7,6,5,4]=>[6,7,5,8,2,3,1,4]=>1100100=>0011011
[8,2,3,1,7,6,5,4]=>[2,3,6,7,5,8,1,4]=>1000100=>0111011
[8,3,2,1,7,6,5,4]=>[3,2,6,7,5,8,1,4]=>1100100=>0011011
[3,4,1,7,6,8,5,2]=>[8,6,5,7,4,1,3,2]=>1101110=>0010001
[6,7,4,5,8,1,3,2]=>[8,5,4,1,7,3,6,2]=>1111100=>0000011
[5,4,7,6,8,1,3,2]=>[8,1,6,4,3,7,5,2]=>1111100=>0000011
[2,5,7,8,1,6,4,3]=>[6,8,2,1,7,4,5,3]=>1111000=>0000111
[1,5,7,8,2,6,4,3]=>[1,6,8,2,7,4,5,3]=>0111000=>1000111
[8,5,7,1,2,6,4,3]=>[6,7,1,5,2,4,8,3]=>1110000=>0001111
[1,4,8,7,2,6,5,3]=>[1,6,7,2,5,8,4,3]=>0111000=>1000111
[3,4,8,7,6,1,5,2]=>[6,1,7,5,8,4,3,2]=>1111100=>0000011
[5,3,7,8,6,1,4,2]=>[6,3,1,8,4,7,5,2]=>1111100=>0000011
[6,7,2,8,1,5,4,3]=>[8,2,5,7,4,6,1,3]=>1101000=>0010111
[4,2,8,7,1,6,5,3]=>[2,6,7,1,5,8,4,3]=>1011000=>0100111
[1,3,8,2,7,6,5,4]=>[1,6,7,5,8,3,2,4]=>0110100=>1001011
[8,3,1,2,7,6,5,4]=>[3,1,6,7,5,8,2,4]=>1100100=>0011011
[8,2,1,3,7,6,5,4]=>[2,6,7,5,8,1,3,4]=>1000100=>0111011
[1,2,8,3,7,6,5,4]=>[1,2,6,7,5,8,3,4]=>0010100=>1101011
[2,1,8,3,7,6,5,4]=>[2,1,6,7,5,8,3,4]=>1010100=>0101011
[5,1,7,8,2,6,4,3]=>[6,8,1,2,7,4,5,3]=>1011000=>0100111
[3,8,1,2,7,6,5,4]=>[6,7,5,8,1,3,2,4]=>1100100=>0011011
[2,8,1,3,7,6,5,4]=>[6,7,5,8,2,1,3,4]=>1100100=>0011011
[1,8,2,3,7,6,5,4]=>[1,6,7,5,8,2,3,4]=>0100100=>1011011
[8,1,2,3,7,6,5,4]=>[6,7,5,8,1,2,3,4]=>1000100=>0111011
[3,1,4,5,6,7,8,9,10,2]=>[10,9,8,7,6,5,4,3,1,2]=>101111111=>010000000
[2,3,4,5,6,7,8,9,11,1,10]=>[11,9,8,7,6,5,4,3,2,1,10]=>1111111110=>0000000001
[3,1,4,5,6,7,8,9,10,11,2]=>[11,10,9,8,7,6,5,4,3,1,2]=>1011111111=>0100000000
[2,3,4,5,6,7,8,9,10,12,1,11]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>11111111110=>00000000001
[3,7,1,5,8,2,6,4]=>[8,5,1,3,2,6,7,4]=>1101100=>0010011
[3,6,5,1,8,2,7,4]=>[7,8,5,1,6,3,2,4]=>1110100=>0001011
[4,6,5,1,8,7,2,3]=>[7,5,1,8,6,2,4,3]=>1110110=>0001001
[5,6,4,1,8,7,2,3]=>[4,1,7,2,8,6,5,3]=>1110110=>0001001
[8,1,4,5,7,6,2,3]=>[6,7,5,4,1,2,8,3]=>1011100=>0100011
[6,4,5,1,8,7,2,3]=>[7,5,1,4,2,8,6,3]=>1110110=>0001001
[5,4,6,1,8,7,2,3]=>[7,1,4,2,8,6,5,3]=>1110110=>0001001
[4,5,6,1,8,7,2,3]=>[7,1,8,6,5,2,4,3]=>1110110=>0001001
[3,5,6,1,8,2,7,4]=>[7,8,1,6,5,3,2,4]=>1110100=>0001011
[2,5,6,1,8,3,7,4]=>[7,8,2,1,6,5,3,4]=>1110100=>0001011
[2,4,6,1,3,8,7,5]=>[7,8,6,2,1,4,3,5]=>1110010=>0001101
[3,4,6,1,2,8,7,5]=>[7,8,6,1,4,3,2,5]=>1110010=>0001101
[4,3,6,1,2,8,7,5]=>[7,8,6,3,1,4,2,5]=>1110010=>0001101
[5,3,6,1,8,2,7,4]=>[7,8,3,1,6,5,2,4]=>1110100=>0001011
[8,1,3,5,7,2,6,4]=>[3,7,5,1,2,6,8,4]=>1001100=>0110011
[4,2,6,1,3,8,7,5]=>[2,7,8,6,1,4,3,5]=>1010010=>0101101
[2,3,6,1,4,8,7,5]=>[7,8,6,3,2,1,4,5]=>1110010=>0001101
[6,2,4,1,3,8,7,5]=>[2,4,1,7,8,6,3,5]=>1010010=>0101101
[7,2,1,4,3,8,6,5]=>[2,4,8,6,7,1,3,5]=>1000010=>0111101
[8,1,3,4,2,7,6,5]=>[3,4,7,6,8,1,2,5]=>1000010=>0111101
[7,3,1,4,2,8,6,5]=>[3,1,4,8,6,7,2,5]=>1100010=>0011101
[4,6,3,1,2,8,7,5]=>[3,7,8,6,1,4,2,5]=>1100010=>0011101
[3,6,4,1,2,8,7,5]=>[4,1,7,8,6,3,2,5]=>1110010=>0001101
[2,6,4,1,3,8,7,5]=>[4,2,1,7,8,6,3,5]=>1110010=>0001101
[2,7,1,4,3,8,6,5]=>[4,8,6,7,2,1,3,5]=>1100010=>0011101
[3,7,1,4,2,8,6,5]=>[4,8,6,7,1,3,2,5]=>1100010=>0011101
[4,7,1,3,2,8,6,5]=>[8,6,7,1,3,4,2,5]=>1100010=>0011101
[4,7,1,2,3,8,6,5]=>[8,6,7,1,4,2,3,5]=>1100010=>0011101
[2,7,1,3,4,8,6,5]=>[8,6,7,2,1,3,4,5]=>1100010=>0011101
[2,6,3,1,4,8,7,5]=>[3,7,8,6,2,1,4,5]=>1100010=>0011101
[3,6,2,1,4,8,7,5]=>[7,8,6,2,3,1,4,5]=>1100010=>0011101
[5,6,2,1,8,3,7,4]=>[7,8,2,6,5,1,3,4]=>1100100=>0011011
[8,1,5,2,7,3,6,4]=>[7,5,1,2,6,8,3,4]=>1010100=>0101011
[6,4,2,1,3,8,7,5]=>[4,2,7,8,6,1,3,5]=>1100010=>0011101
[5,4,2,3,1,8,7,6]=>[4,2,3,5,1,7,8,6]=>1100010=>0011101
[3,5,2,4,1,8,7,6]=>[4,5,2,3,1,7,8,6]=>1100010=>0011101
[6,3,2,1,4,8,7,5]=>[3,2,7,8,6,1,4,5]=>1100010=>0011101
[7,3,1,2,4,8,6,5]=>[3,1,8,6,7,2,4,5]=>1100010=>0011101
[8,1,2,3,4,7,6,5]=>[7,6,8,1,2,3,4,5]=>1000010=>0111101
[2,4,3,6,1,5,8,7]=>[3,6,4,2,1,5,8,7]=>1101001=>0010110
[2,4,3,6,5,8,1,7]=>[3,5,8,6,4,2,1,7]=>1101010=>0010101
[2,4,6,3,5,8,7,1]=>[5,7,8,6,3,4,2,1]=>1110010=>0001101
[2,4,6,3,5,8,1,7]=>[5,8,6,3,4,2,1,7]=>1110010=>0001101
[2,4,6,3,5,1,8,7]=>[5,6,3,4,2,1,8,7]=>1110001=>0001110
[2,4,6,3,1,5,8,7]=>[6,3,4,2,1,5,8,7]=>1110001=>0001110
[2,4,1,6,5,3,8,7]=>[5,6,4,2,1,3,8,7]=>1101001=>0010110
[4,2,6,5,1,3,8,7]=>[2,5,1,6,4,3,8,7]=>1011001=>0100110
[4,2,6,5,1,8,7,3]=>[2,5,1,7,8,6,4,3]=>1011010=>0100101
[4,2,6,5,8,1,3,7]=>[2,8,5,1,6,4,3,7]=>1011100=>0100011
[2,4,6,1,5,8,3,7]=>[5,8,6,2,1,4,3,7]=>1110010=>0001101
[2,4,1,6,5,8,3,7]=>[5,8,6,4,2,1,3,7]=>1101010=>0010101
[2,1,4,6,5,8,3,7]=>[2,1,5,8,6,4,3,7]=>1011010=>0100101
[2,4,1,6,5,8,7,3]=>[5,7,8,6,4,2,1,3]=>1101010=>0010101
[2,4,6,1,5,8,7,3]=>[5,7,8,6,2,1,4,3]=>1110010=>0001101
[4,2,6,5,3,8,7,1]=>[2,5,3,7,8,6,4,1]=>1011010=>0100101
[2,6,4,3,8,7,1,5]=>[4,3,7,2,1,8,6,5]=>1110110=>0001001
[2,6,4,3,8,7,5,1]=>[4,3,7,5,8,6,2,1]=>1110110=>0001001
[2,4,6,8,1,5,7,3]=>[7,8,2,1,5,6,4,3]=>1111000=>0000111
[2,4,6,1,8,5,7,3]=>[7,8,5,6,2,1,4,3]=>1110100=>0001011
[2,4,1,6,8,5,7,3]=>[7,8,5,6,4,2,1,3]=>1101100=>0010011
[2,1,4,6,8,5,7,3]=>[2,1,7,8,5,6,4,3]=>1011100=>0100011
[2,1,4,6,8,5,3,7]=>[2,1,8,5,6,4,3,7]=>1011100=>0100011
[2,4,1,6,8,5,3,7]=>[8,5,6,4,2,1,3,7]=>1101100=>0010011
[2,4,6,1,8,5,3,7]=>[8,5,6,2,1,4,3,7]=>1110100=>0001011
[2,4,6,8,1,5,3,7]=>[8,2,1,5,6,4,3,7]=>1111000=>0000111
[4,2,6,8,5,1,7,3]=>[2,5,7,8,1,6,4,3]=>1011000=>0100111
[2,4,6,8,3,1,5,7]=>[8,3,6,4,2,1,5,7]=>1111000=>0000111
[2,4,6,3,1,8,5,7]=>[8,6,3,4,2,1,5,7]=>1110010=>0001101
[2,4,6,3,8,1,5,7]=>[8,3,4,2,1,6,5,7]=>1110100=>0001011
[2,4,6,3,8,5,1,7]=>[8,5,6,3,4,2,1,7]=>1110100=>0001011
[2,4,6,3,8,5,7,1]=>[7,8,5,6,3,4,2,1]=>1110100=>0001011
[2,4,3,6,8,5,7,1]=>[3,7,8,5,6,4,2,1]=>1101100=>0010011
[2,4,3,6,8,5,1,7]=>[3,8,5,6,4,2,1,7]=>1101100=>0010011
[2,4,3,6,1,8,5,7]=>[3,8,6,4,2,1,5,7]=>1101010=>0010101
[2,4,3,1,6,8,5,7]=>[3,4,2,1,8,6,5,7]=>1100110=>0011001
[2,4,1,3,6,8,7,5]=>[4,2,1,3,7,8,6,5]=>1100110=>0011001
[2,4,3,6,1,8,7,5]=>[3,7,8,6,4,2,1,5]=>1101010=>0010101
[2,4,3,6,8,1,7,5]=>[3,7,8,4,2,1,6,5]=>1101100=>0010011
[4,6,5,2,8,7,3,1]=>[7,5,2,8,6,3,4,1]=>1110110=>0001001
[4,6,5,2,8,7,1,3]=>[7,5,2,8,6,1,4,3]=>1110110=>0001001
[4,6,2,5,8,7,1,3]=>[7,5,2,8,6,4,1,3]=>1101110=>0010001
[4,6,2,5,8,7,3,1]=>[7,5,2,3,8,6,4,1]=>1101110=>0010001
[2,4,6,3,8,1,7,5]=>[7,8,3,4,2,1,6,5]=>1110100=>0001011
[2,4,6,3,1,8,7,5]=>[7,8,6,3,4,2,1,5]=>1110010=>0001101
[2,4,1,6,3,8,7,5]=>[7,8,6,4,2,1,3,5]=>1101010=>0010101
[2,1,4,6,3,8,7,5]=>[2,1,7,8,6,4,3,5]=>1011010=>0100101
[2,4,1,6,8,3,7,5]=>[7,8,4,2,1,3,6,5]=>1101100=>0010011
[2,4,6,1,8,3,7,5]=>[7,8,2,1,4,3,6,5]=>1110100=>0001011
[2,4,6,8,3,1,7,5]=>[7,8,3,6,4,2,1,5]=>1111000=>0000111
[4,6,2,8,5,7,1,3]=>[5,7,2,8,6,4,1,3]=>1101010=>0010101
[6,2,4,8,7,1,3,5]=>[2,7,4,1,8,3,6,5]=>1011100=>0100011
[6,4,2,8,7,5,3,1]=>[7,5,8,4,2,3,6,1]=>1101100=>0010011
[2,6,4,8,1,7,5,3]=>[7,4,2,1,5,8,6,3]=>1111010=>0000101
[2,6,1,4,8,7,5,3]=>[4,7,5,8,6,2,1,3]=>1100110=>0011001
[2,1,6,4,8,7,5,3]=>[2,1,4,7,5,8,6,3]=>1010110=>0101001
[2,6,1,4,8,7,3,5]=>[4,7,2,1,3,8,6,5]=>1100110=>0011001
[2,6,4,1,8,7,3,5]=>[4,2,1,7,3,8,6,5]=>1110110=>0001001
[2,6,4,8,1,7,3,5]=>[7,4,2,1,8,6,3,5]=>1111010=>0000101
[6,4,2,8,7,5,1,3]=>[7,5,8,4,2,6,1,3]=>1101100=>0010011
[6,2,4,8,7,3,5,1]=>[2,7,4,3,8,5,6,1]=>1011100=>0100011
[1,6,4,7,3,8,2,5]=>[1,8,4,3,7,6,2,5]=>0111010=>1000101
[1,3,7,4,5,8,2,6]=>[1,4,5,8,3,2,7,6]=>0110010=>1001101
[5,2,4,7,3,6,8,1]=>[2,6,8,7,4,3,5,1]=>1011001=>0100110
[1,7,6,3,4,8,2,5]=>[1,8,6,3,4,7,2,5]=>0110010=>1001101
[8,1,6,3,7,2,4,5]=>[7,3,6,1,2,4,8,5]=>1010100=>0101011
[7,1,6,3,8,2,4,5]=>[8,3,6,1,2,4,7,5]=>1010100=>0101011
[6,1,7,3,4,8,2,5]=>[8,3,4,7,6,1,2,5]=>1010010=>0101101
[2,1,7,4,5,8,3,6]=>[2,1,4,5,8,3,7,6]=>1010010=>0101101
[6,8,1,3,7,2,4,5]=>[7,1,3,8,2,4,6,5]=>1100100=>0011011
[5,8,2,1,7,3,4,6]=>[7,2,8,5,1,3,4,6]=>1100100=>0011011
[5,7,2,1,8,3,4,6]=>[8,2,7,5,1,3,4,6]=>1100100=>0011011
[6,7,1,3,8,2,4,5]=>[8,1,3,7,2,4,6,5]=>1100100=>0011011
[5,1,2,4,8,3,6,7]=>[4,8,5,1,2,3,6,7]=>1000100=>0111011
[2,6,1,4,5,8,3,7]=>[4,5,8,6,2,1,3,7]=>1100010=>0011101
[1,6,2,4,8,3,5,7]=>[1,4,8,2,3,6,5,7]=>0100100=>1011011
[8,5,1,3,7,2,4,6]=>[7,5,1,3,8,2,4,6]=>1100100=>0011011
[1,5,3,2,8,4,6,7]=>[1,3,8,5,2,4,6,7]=>0100100=>1011011
[2,5,3,4,1,8,6,7]=>[3,4,5,2,1,8,6,7]=>1100010=>0011101
[2,6,4,8,7,1,3,5]=>[7,4,2,1,8,3,6,5]=>1111100=>0000011
[1,6,4,8,7,2,3,5]=>[1,7,4,2,8,3,6,5]=>0111100=>1000011
[2,7,8,3,6,1,4,5]=>[6,3,8,2,1,4,7,5]=>1110100=>0001011
[5,1,4,8,7,2,3,6]=>[7,4,1,2,8,5,3,6]=>1011100=>0100011
[4,8,2,5,1,3,7,6]=>[5,2,7,8,4,1,3,6]=>1101000=>0010111
[3,8,2,1,5,4,7,6]=>[5,7,8,2,3,1,4,6]=>1100000=>0011111
[8,3,2,1,5,4,6,7]=>[3,2,5,8,1,4,6,7]=>1100000=>0011111
[8,3,2,1,6,4,5,7]=>[3,2,6,1,4,8,5,7]=>1100100=>0011011
[8,4,2,5,1,6,3,7]=>[5,4,2,6,8,1,3,7]=>1101000=>0010111
[8,3,2,1,5,6,4,7]=>[3,2,5,6,8,1,4,7]=>1100000=>0011111
[8,3,2,1,4,6,5,7]=>[3,2,6,8,1,4,5,7]=>1100000=>0011111
[3,8,2,1,4,5,7,6]=>[7,8,2,3,1,4,5,6]=>1100000=>0011111
[3,7,2,1,4,5,8,6]=>[8,7,2,3,1,4,5,6]=>1100001=>0011110
[3,2,7,1,4,6,8,5]=>[2,6,8,7,3,1,4,5]=>1010001=>0101110
[3,2,8,1,4,6,7,5]=>[2,6,7,8,3,1,4,5]=>1010000=>0101111
[3,2,8,1,4,7,6,5]=>[2,7,6,8,3,1,4,5]=>1010010=>0101101
[3,8,2,1,4,7,5,6]=>[7,2,3,1,4,5,8,6]=>1100010=>0011101
[3,8,2,1,5,7,4,6]=>[5,7,2,3,1,4,8,6]=>1100010=>0011101
[4,8,2,5,1,7,3,6]=>[5,2,7,4,1,3,8,6]=>1101010=>0010101
[4,7,2,5,1,8,3,6]=>[5,2,8,4,1,3,7,6]=>1101010=>0010101
[3,7,2,1,4,8,5,6]=>[8,2,3,1,4,5,7,6]=>1100010=>0011101
[3,2,1,7,5,8,6,4]=>[2,3,1,5,8,6,7,4]=>1001010=>0110101
[3,2,7,1,6,8,4,5]=>[2,8,6,3,1,4,7,5]=>1010110=>0101001
[4,2,7,6,1,8,3,5]=>[2,8,6,1,7,4,3,5]=>1011010=>0100101
[4,2,8,6,1,7,3,5]=>[2,7,6,1,8,4,3,5]=>1011010=>0100101
[3,2,8,1,6,7,4,5]=>[2,7,6,3,1,4,8,5]=>1010110=>0101001
[3,2,8,1,7,4,6,5]=>[2,7,3,1,4,6,8,5]=>1010100=>0101011
[3,2,8,1,6,4,7,5]=>[2,6,3,1,4,7,8,5]=>1010100=>0101011
[3,2,7,1,6,4,8,5]=>[2,6,3,1,4,8,7,5]=>1010101=>0101010
[4,2,7,6,1,3,8,5]=>[2,6,1,8,7,4,3,5]=>1011001=>0100110
[4,7,3,8,5,1,2,6]=>[3,5,8,1,7,4,2,6]=>1101000=>0010111
[4,3,7,8,6,1,2,5]=>[6,3,1,8,4,2,7,5]=>1111100=>0000011
[3,2,7,1,8,6,4,5]=>[2,6,8,3,1,4,7,5]=>1010100=>0101011
[3,2,1,6,8,5,7,4]=>[2,3,1,7,8,5,6,4]=>1001100=>0110011
[3,2,6,1,8,7,4,5]=>[2,7,3,1,4,8,6,5]=>1010110=>0101001
[4,3,6,8,7,1,2,5]=>[7,3,1,8,4,2,6,5]=>1111100=>0000011
[4,2,6,7,1,8,3,5]=>[2,8,1,7,6,4,3,5]=>1011010=>0100101
[3,4,6,8,7,5,1,2]=>[7,5,8,1,6,4,3,2]=>1111100=>0000011
[5,3,6,4,8,7,1,2]=>[4,7,3,1,8,6,5,2]=>1110110=>0001001
[1,4,6,2,7,8,5,3]=>[1,8,5,7,6,2,4,3]=>0110110=>1001001
[3,1,8,5,4,2,6,7]=>[5,4,8,3,1,2,6,7]=>1011000=>0100111
[1,2,7,5,4,8,6,3]=>[1,2,5,4,8,6,7,3]=>0011010=>1100101
[6,3,7,5,4,8,1,2]=>[5,4,8,3,1,7,6,2]=>1111010=>0000101
[7,3,8,5,4,6,1,2]=>[5,4,6,8,3,1,7,2]=>1111000=>0000111
[3,8,7,5,4,6,1,2]=>[5,4,6,7,1,8,3,2]=>1111000=>0000111
[4,3,6,7,8,5,1,2]=>[8,5,7,3,1,6,4,2]=>1111100=>0000011
[4,5,6,3,8,7,1,2]=>[7,3,8,6,5,1,4,2]=>1110110=>0001001
[3,6,8,5,4,7,1,2]=>[5,4,7,1,8,6,3,2]=>1111010=>0000101
[6,8,3,5,4,7,1,2]=>[3,5,4,7,1,8,6,2]=>1101010=>0010101
[7,6,3,5,4,8,1,2]=>[3,5,4,8,6,1,7,2]=>1101010=>0010101
[1,6,2,5,4,8,7,3]=>[1,5,4,7,8,6,2,3]=>0101010=>1010101
[7,1,2,5,8,3,6,4]=>[8,5,1,2,3,6,7,4]=>1001100=>0110011
[1,8,2,5,7,3,6,4]=>[1,7,5,2,3,6,8,4]=>0101100=>1010011
[6,2,1,5,4,8,7,3]=>[2,5,4,7,8,6,1,3]=>1001010=>0110101
[4,1,6,2,8,7,5,3]=>[7,5,8,6,1,2,4,3]=>1010110=>0101001
[7,8,1,2,4,6,5,3]=>[6,8,1,4,5,7,2,3]=>1100000=>0011111
[7,8,3,1,4,2,6,5]=>[3,8,1,4,6,7,2,5]=>1100000=>0011111
[4,3,6,1,8,2,7,5]=>[7,8,3,1,4,2,6,5]=>1110100=>0001011
[2,3,8,5,4,1,6,7]=>[5,4,8,3,2,1,6,7]=>1111000=>0000111
[4,8,1,5,2,3,7,6]=>[5,1,7,8,4,2,3,6]=>1101000=>0010111
[1,5,8,6,4,3,2,7]=>[1,6,4,8,3,5,2,7]=>0111000=>1000111
[3,4,6,1,5,8,2,7]=>[5,8,6,1,4,3,2,7]=>1110010=>0001101
[7,8,5,1,6,3,2,4]=>[6,5,1,8,3,7,2,4]=>1110100=>0001011
[2,6,1,5,7,3,8,4]=>[8,7,5,2,1,3,6,4]=>1101101=>0010010
[1,6,8,7,4,3,2,5]=>[1,7,4,8,3,6,2,5]=>0111000=>1000111
[6,8,1,7,4,3,2,5]=>[7,4,8,1,3,6,2,5]=>1101000=>0010111
[5,6,1,7,4,3,2,8]=>[7,4,6,1,3,5,2,8]=>1101000=>0010111
[5,1,7,6,4,3,2,8]=>[6,4,7,3,5,1,2,8]=>1011000=>0100111
[6,1,7,8,4,3,2,5]=>[8,4,7,3,6,1,2,5]=>1011000=>0100111
[7,1,8,6,4,3,2,5]=>[6,4,8,3,7,1,2,5]=>1011000=>0100111
[1,8,7,6,4,3,2,5]=>[1,6,4,7,3,8,2,5]=>0111000=>1000111
[2,1,7,5,6,3,8,4]=>[2,1,6,5,3,8,7,4]=>1011101=>0100010
[3,1,6,7,5,8,2,4]=>[5,8,3,1,2,7,6,4]=>1011010=>0100101
[2,8,1,5,4,6,7,3]=>[5,4,6,7,8,2,1,3]=>1101000=>0010111
[7,2,1,5,4,6,8,3]=>[2,5,4,6,8,7,1,3]=>1001001=>0110110
[1,2,8,5,6,3,7,4]=>[1,2,6,5,3,7,8,4]=>0011100=>1100011
[6,1,2,5,7,3,8,4]=>[8,7,5,1,2,3,6,4]=>1001101=>0110010
[4,2,1,5,6,3,7,8]=>[2,6,5,4,1,3,7,8]=>1001100=>0110011
[1,3,6,8,5,7,2,4]=>[1,5,7,3,2,8,6,4]=>0111010=>1000101
[1,3,6,4,8,7,2,5]=>[1,4,7,3,2,8,6,5]=>0110110=>1001001
[5,4,6,1,3,7,2,8]=>[7,6,1,4,3,5,2,8]=>1110010=>0001101
[6,4,1,5,2,3,7,8]=>[5,4,1,6,2,3,7,8]=>1101000=>0010111
[1,2,4,5,8,3,7,6]=>[1,2,7,8,5,4,3,6]=>0011100=>1100011
[7,2,3,5,4,1,8,6]=>[2,3,5,4,8,7,1,6]=>1001001=>0110110
[7,8,2,3,4,1,6,5]=>[8,2,3,4,6,7,1,5]=>1100000=>0011111
[7,8,1,4,6,3,2,5]=>[4,6,1,3,8,2,7,5]=>1100100=>0011011
[3,1,6,4,7,8,2,5]=>[4,8,3,1,2,7,6,5]=>1010110=>0101001
[7,1,5,8,4,3,2,6]=>[8,4,5,3,7,1,2,6]=>1011000=>0100111
[5,1,8,7,4,3,2,6]=>[7,4,8,3,5,1,2,6]=>1011000=>0100111
[6,5,7,1,4,3,2,8]=>[7,1,4,5,3,6,2,8]=>1110000=>0001111
[7,5,8,1,4,3,2,6]=>[8,1,4,5,3,7,2,6]=>1110000=>0001111
[5,8,7,1,4,3,2,6]=>[7,1,4,8,3,5,2,6]=>1110000=>0001111
[1,5,7,8,4,3,2,6]=>[1,8,4,7,3,5,2,6]=>0111000=>1000111
[2,4,7,5,1,3,8,6]=>[5,2,1,8,7,4,3,6]=>1111001=>0000110
[7,8,5,4,1,3,2,6]=>[4,5,1,8,3,7,2,6]=>1110000=>0001111
[3,5,6,4,1,8,2,7]=>[4,8,6,1,5,3,2,7]=>1110010=>0001101
[1,6,5,8,4,3,2,7]=>[1,8,4,5,3,6,2,7]=>0111000=>1000111
[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8]=>00000010=>11111101
[1,4,2,5,6,7,8,9,3]=>[1,9,8,7,6,5,4,2,3]=>01011111=>10100000
[9,8,1,2,3,4,5,6,7]=>[8,1,9,2,3,4,5,6,7]=>11000000=>00111111
[9,8,7,1,2,3,4,5,6]=>[7,1,8,2,9,3,4,5,6]=>11100000=>00011111
[6,7,8,9,1,2,3,4,5]=>[9,1,8,2,7,3,6,4,5]=>11110000=>00001111
[9,8,7,6,1,2,3,4,5]=>[6,1,7,2,8,3,9,4,5]=>11110000=>00001111
[9,8,7,6,5,1,2,3,4]=>[5,6,1,7,2,8,3,9,4]=>11110000=>00001111
[9,8,7,4,5,6,1,2,3]=>[4,5,6,7,1,8,2,9,3]=>11100000=>00011111
[8,9,10,1,2,3,4,5,6,7]=>[10,1,9,2,8,3,4,5,6,7]=>111000000=>000111111
[10,9,8,1,2,3,4,5,6,7]=>[8,1,9,2,10,3,4,5,6,7]=>111000000=>000111111
[10,9,8,7,1,2,3,4,5,6]=>[7,1,8,2,9,3,10,4,5,6]=>111100000=>000011111
[10,9,8,7,6,1,2,3,4,5]=>[6,1,7,2,8,3,9,4,10,5]=>111110000=>000001111
[10,9,8,7,5,6,1,2,3,4]=>[5,6,7,1,8,2,9,3,10,4]=>111100000=>000011111
[10,9,8,7,5,6,3,4,1,2]=>[5,6,7,3,8,4,9,1,10,2]=>111100000=>000011111
[3,4,6,2,7,1,5,8]=>[7,2,4,3,1,6,5,8]=>1110100=>0001011
[3,6,2,5,4,1,7,8]=>[5,4,6,2,3,1,7,8]=>1101000=>0010111
[6,1,2,5,4,7,8,3]=>[5,4,8,7,6,1,2,3]=>1001011=>0110100
[6,2,4,5,1,3,7,8]=>[2,5,4,1,6,3,7,8]=>1011000=>0100111
[4,3,6,8,1,7,2,5]=>[7,3,1,8,6,4,2,5]=>1111010=>0000101
[6,2,1,5,8,3,7,4]=>[2,7,8,5,1,3,6,4]=>1001100=>0110011
[1,6,7,4,8,3,5,2]=>[1,4,8,3,7,5,6,2]=>0110100=>1001011
[1,4,6,3,7,5,8,2]=>[1,8,7,5,6,3,4,2]=>0110101=>1001010
[4,6,7,2,5,8,1,3]=>[5,8,2,7,6,1,4,3]=>1110010=>0001101
[2,7,5,4,1,6,3,8]=>[4,5,2,1,6,7,3,8]=>1110000=>0001111
[7,5,4,6,2,8,1,3]=>[8,6,4,2,5,1,7,3]=>1111010=>0000101
[1,7,5,4,3,8,6,2]=>[1,4,5,3,8,6,7,2]=>0110010=>1001101
[1,4,6,3,5,8,7,2]=>[1,5,7,8,6,3,4,2]=>0110010=>1001101
[1,5,8,4,3,6,7,2]=>[1,4,6,7,8,3,5,2]=>0110000=>1001111
[5,4,6,2,7,8,1,3]=>[8,2,4,1,7,6,5,3]=>1110110=>0001001
[5,6,3,2,7,1,8,4]=>[3,8,7,2,6,5,1,4]=>1100101=>0011010
[5,4,6,2,8,1,7,3]=>[7,8,2,4,1,6,5,3]=>1110100=>0001011
[2,4,1,7,8,5,3,6]=>[8,5,7,4,2,1,3,6]=>1101100=>0010011
[2,5,4,1,6,3,8,7]=>[4,2,1,6,5,3,8,7]=>1110101=>0001010
[6,8,4,3,2,1,5,7]=>[4,3,8,2,6,1,5,7]=>1110000=>0001111
[5,3,8,2,1,6,4,7]=>[6,8,3,2,5,1,4,7]=>1110000=>0001111
[3,7,5,8,2,1,4,6]=>[8,2,5,3,1,7,4,6]=>1111000=>0000111
[7,3,2,8,5,1,6,4]=>[3,2,5,8,1,6,7,4]=>1101000=>0010111
[8,4,6,3,2,1,7,5]=>[6,3,4,2,7,8,1,5]=>1110000=>0001111
[8,6,4,3,2,1,7,5]=>[4,3,6,2,7,8,1,5]=>1110000=>0001111
[7,6,4,3,2,1,8,5]=>[4,3,6,2,8,7,1,5]=>1110001=>0001110
[7,8,4,3,2,1,6,5]=>[4,3,8,2,6,7,1,5]=>1110000=>0001111
[5,4,7,2,1,8,6,3]=>[8,6,7,2,4,1,5,3]=>1110010=>0001101
[7,5,8,3,2,6,1,4]=>[6,8,3,5,2,7,1,4]=>1110000=>0001111
[5,7,3,2,1,6,8,4]=>[3,6,8,7,2,5,1,4]=>1100001=>0011110
[5,7,3,2,1,6,4,8]=>[3,6,7,2,5,1,4,8]=>1100000=>0011111
[6,3,7,2,5,1,8,4]=>[5,8,7,3,2,6,1,4]=>1110001=>0001110
[6,7,8,3,5,2,1,4]=>[5,8,3,7,2,6,1,4]=>1110000=>0001111
[2,1,5,7,8,6,3,4]=>[2,1,6,8,3,7,5,4]=>1011100=>0100011
[7,3,5,2,1,8,4,6]=>[5,3,2,8,1,4,7,6]=>1110010=>0001101
[2,4,1,7,8,3,6,5]=>[8,4,2,1,3,6,7,5]=>1101100=>0010011
[3,7,2,8,6,1,4,5]=>[6,2,3,1,8,4,7,5]=>1101100=>0010011
[3,6,8,2,1,7,4,5]=>[7,2,8,6,3,1,4,5]=>1110010=>0001101
[5,3,8,2,1,4,7,6]=>[7,8,3,2,5,1,4,6]=>1110000=>0001111
[4,8,7,3,2,1,5,6]=>[7,3,8,2,4,1,5,6]=>1110000=>0001111
[8,3,5,2,1,4,7,6]=>[5,3,2,7,8,1,4,6]=>1110000=>0001111
[7,3,2,8,6,1,4,5]=>[3,2,6,1,8,4,7,5]=>1101100=>0010011
[3,5,2,1,4,6,8,7]=>[5,2,3,1,4,6,8,7]=>1100001=>0011110
[7,8,6,5,4,3,2,1,9]=>[5,4,6,3,8,2,7,1,9]=>11110000=>00001111
[8,6,3,7,5,2,4,1]=>[3,5,7,2,6,4,8,1]=>1101000=>0010111
[5,4,1,6,2,3,8,7]=>[6,4,1,5,2,3,8,7]=>1101001=>0010110
[5,7,1,6,2,8,3,4]=>[8,6,1,7,2,3,5,4]=>1101010=>0010101
[5,7,1,6,2,8,4,3]=>[8,6,1,7,4,5,2,3]=>1101010=>0010101
[2,7,6,5,1,8,3,4]=>[5,2,1,8,6,3,7,4]=>1111010=>0000101
[2,3,6,5,1,4,8,7]=>[5,3,2,1,6,4,8,7]=>1111001=>0000110
[2,3,6,4,1,5,8,7]=>[4,6,3,2,1,5,8,7]=>1110001=>0001110
[2,3,6,1,5,4,8,7]=>[5,6,3,2,1,4,8,7]=>1110001=>0001110
[2,7,6,4,1,8,5,3]=>[4,8,6,2,1,5,7,3]=>1110010=>0001101
[2,1,7,6,3,8,5,4]=>[2,1,8,6,3,5,7,4]=>1011010=>0100101
[2,1,7,6,3,8,4,5]=>[2,1,8,6,3,7,4,5]=>1011010=>0100101
[5,7,3,6,2,8,4,1]=>[3,8,6,2,7,4,5,1]=>1101010=>0010101
[2,7,6,4,1,8,3,5]=>[4,8,6,2,1,7,3,5]=>1110010=>0001101
[7,3,5,1,8,6,2,4]=>[6,8,5,3,1,7,2,4]=>1110100=>0001011
[6,3,5,1,8,2,4,7]=>[8,5,3,1,6,2,4,7]=>1110100=>0001011
[2,3,4,8,7,6,1,5]=>[6,7,4,3,2,1,8,5]=>1111100=>0000011
[2,3,4,8,5,7,1,6]=>[5,7,4,3,2,1,8,6]=>1111010=>0000101
[7,3,5,4,8,1,2,6]=>[4,8,5,3,1,7,2,6]=>1110100=>0001011
[2,1,4,5,8,7,3,6]=>[2,1,7,5,4,3,8,6]=>1011110=>0100001
[6,4,3,5,8,7,1,2]=>[3,7,5,4,1,8,6,2]=>1101110=>0010001
[7,3,5,4,8,1,6,2]=>[4,8,5,3,1,6,7,2]=>1110100=>0001011
[2,3,4,8,7,5,6,1]=>[7,5,6,8,4,3,2,1]=>1111100=>0000011
[2,3,4,8,7,5,1,6]=>[7,5,8,4,3,2,1,6]=>1111100=>0000011
[7,3,5,6,8,4,1,2]=>[8,4,6,5,3,1,7,2]=>1111100=>0000011
[6,4,1,5,8,7,3,2]=>[7,5,4,1,3,8,6,2]=>1101110=>0010001
[6,4,1,5,8,3,7,2]=>[7,8,5,4,1,3,6,2]=>1101100=>0010011
[5,7,1,6,3,8,2,4]=>[8,6,1,3,7,2,5,4]=>1101010=>0010101
[6,4,1,5,8,3,2,7]=>[8,5,4,1,3,6,2,7]=>1101100=>0010011
[7,4,1,5,8,2,3,6]=>[8,5,4,1,7,2,3,6]=>1101100=>0010011
[7,4,1,5,8,2,6,3]=>[8,5,4,1,6,7,2,3]=>1101100=>0010011
[2,7,6,4,5,8,3,1]=>[4,5,8,6,3,7,2,1]=>1110010=>0001101
[5,7,3,6,1,8,4,2]=>[3,8,6,1,7,4,5,2]=>1101010=>0010101
[2,1,4,5,8,6,3,7]=>[2,1,6,8,5,4,3,7]=>1011100=>0100011
[7,3,5,4,8,6,2,1]=>[4,6,8,5,3,2,7,1]=>1110100=>0001011
[2,3,4,8,5,6,1,7]=>[5,6,8,4,3,2,1,7]=>1111000=>0000111
[2,3,4,8,7,1,6,5]=>[7,4,3,2,1,6,8,5]=>1111100=>0000011
[2,3,4,8,1,7,6,5]=>[7,6,8,4,3,2,1,5]=>1111010=>0000101
[2,3,4,8,1,6,7,5]=>[6,7,8,4,3,2,1,5]=>1111000=>0000111
[2,3,4,8,5,1,7,6]=>[5,7,8,4,3,2,1,6]=>1111000=>0000111
[2,1,4,5,8,3,7,6]=>[2,1,7,8,5,4,3,6]=>1011100=>0100011
[6,3,5,4,8,2,1,7]=>[4,8,5,3,2,6,1,7]=>1110100=>0001011
[2,3,4,8,5,1,6,7]=>[5,8,4,3,2,1,6,7]=>1111000=>0000111
[2,3,4,8,1,6,5,7]=>[6,8,4,3,2,1,5,7]=>1111000=>0000111
[2,3,4,8,1,5,7,6]=>[7,8,4,3,2,1,5,6]=>1111000=>0000111
[7,8,1,6,2,5,3,4]=>[6,1,5,8,2,3,7,4]=>1101000=>0010111
[5,8,1,7,2,6,3,4]=>[6,7,1,8,2,3,5,4]=>1101000=>0010111
[5,8,2,7,1,6,3,4]=>[6,7,2,8,1,3,5,4]=>1101000=>0010111
[2,8,6,7,1,5,3,4]=>[7,2,1,5,6,3,8,4]=>1111000=>0000111
[2,8,5,7,1,6,3,4]=>[6,7,2,1,5,3,8,4]=>1111000=>0000111
[2,8,1,7,5,6,3,4]=>[5,6,7,2,1,3,8,4]=>1101000=>0010111
[1,8,2,7,5,6,3,4]=>[1,5,6,7,2,3,8,4]=>0101000=>1010111
[1,8,2,7,4,6,3,5]=>[1,6,7,4,8,2,3,5]=>0101000=>1010111
[2,8,1,7,4,6,3,5]=>[6,7,4,8,2,1,3,5]=>1101000=>0010111
[2,8,4,7,1,6,3,5]=>[6,7,4,2,1,8,3,5]=>1111000=>0000111
[4,8,2,7,1,6,3,5]=>[6,7,2,8,4,1,3,5]=>1101000=>0010111
[4,8,1,7,2,6,3,5]=>[6,7,1,8,4,2,3,5]=>1101000=>0010111
[1,8,4,7,2,6,3,5]=>[1,6,7,4,2,8,3,5]=>0111000=>1000111
[4,8,1,7,5,6,2,3]=>[5,6,7,1,8,4,2,3]=>1101000=>0010111
[1,8,3,7,5,6,2,4]=>[1,3,5,6,7,2,8,4]=>0101000=>1010111
[3,8,1,7,5,6,2,4]=>[5,6,7,1,3,2,8,4]=>1101000=>0010111
[3,8,1,7,4,6,2,5]=>[6,7,4,8,1,3,2,5]=>1101000=>0010111
[3,8,1,7,2,6,4,5]=>[6,7,1,3,2,8,4,5]=>1101000=>0010111
[3,8,2,7,1,6,4,5]=>[6,7,2,3,1,8,4,5]=>1101000=>0010111
[3,8,2,7,4,6,1,5]=>[6,7,4,8,2,3,1,5]=>1101000=>0010111
[3,8,2,7,5,6,1,4]=>[5,6,7,2,3,1,8,4]=>1101000=>0010111
[4,8,2,7,5,6,1,3]=>[5,6,7,2,8,4,1,3]=>1101000=>0010111
[4,8,3,7,5,6,1,2]=>[3,5,6,7,1,8,4,2]=>1101000=>0010111
[2,8,3,7,1,6,4,5]=>[3,6,7,2,1,8,4,5]=>1101000=>0010111
[2,8,1,7,3,6,4,5]=>[6,7,2,1,3,8,4,5]=>1101000=>0010111
[7,5,2,8,6,4,1,3]=>[6,4,8,5,2,7,1,3]=>1101100=>0010011
[7,4,8,6,1,5,2,3]=>[6,1,5,8,4,2,7,3]=>1111000=>0000111
[7,1,8,4,5,2,6,3]=>[4,5,8,1,2,6,7,3]=>1010000=>0101111
[6,8,1,7,4,2,5,3]=>[7,4,8,1,5,6,2,3]=>1101000=>0010111
[1,6,7,3,8,5,2,4]=>[1,8,5,7,3,6,2,4]=>0110100=>1001011
[7,3,8,6,2,5,1,4]=>[6,3,2,5,8,1,7,4]=>1111000=>0000111
[7,4,2,8,6,1,3,5]=>[6,4,2,8,1,3,7,5]=>1101100=>0010011
[7,3,1,8,4,2,5,6]=>[3,1,8,4,7,2,5,6]=>1101000=>0010111
[7,2,8,4,1,5,3,6]=>[2,4,8,1,5,7,3,6]=>1010000=>0101111
[7,2,8,3,4,6,1,5]=>[2,6,8,3,4,7,1,5]=>1010000=>0101111
[6,2,3,8,5,7,4,1]=>[2,3,5,7,4,8,6,1]=>1001010=>0110101
[6,3,1,4,8,5,2,7]=>[3,1,4,8,5,6,2,7]=>1100100=>0011011
[2,6,3,7,8,5,4,1]=>[3,8,5,7,4,6,2,1]=>1101100=>0010011
[2,6,3,7,8,4,5,1]=>[3,8,4,7,5,6,2,1]=>1101100=>0010011
[2,5,3,7,8,1,6,4]=>[3,8,2,1,6,7,5,4]=>1101100=>0010011
[3,1,5,4,7,8,2,6]=>[4,8,5,3,1,2,7,6]=>1010110=>0101001
[5,2,4,8,6,1,3,7]=>[2,6,4,1,8,5,3,7]=>1011100=>0100011
[4,8,2,3,6,1,7,5]=>[6,2,3,4,1,7,8,5]=>1100100=>0011011
[4,8,2,3,5,7,1,6]=>[5,7,2,3,4,1,8,6]=>1100010=>0011101
[1,4,7,8,3,6,2,5]=>[1,6,8,3,7,4,2,5]=>0111000=>1000111
[4,8,1,3,6,7,2,5]=>[7,6,1,3,4,2,8,5]=>1100110=>0011001
[5,3,8,2,4,7,1,6]=>[7,3,2,4,5,1,8,6]=>1110010=>0001101
[5,4,3,8,1,2,7,6]=>[3,7,8,4,1,5,2,6]=>1101000=>0010111
[6,4,2,8,1,3,7,5]=>[7,8,4,2,6,1,3,5]=>1101000=>0010111
[6,3,8,2,5,1,7,4]=>[5,7,8,3,2,6,1,4]=>1110000=>0001111
[6,3,8,1,4,7,2,5]=>[7,3,1,4,8,6,2,5]=>1110010=>0001101
[1,5,7,4,2,6,8,3]=>[1,4,6,8,7,2,5,3]=>0110001=>1001110
[5,8,4,1,2,7,6,3]=>[4,1,7,6,8,2,5,3]=>1110010=>0001101
[6,5,1,2,8,7,3,4]=>[7,5,1,8,6,2,3,4]=>1100110=>0011001
[6,5,3,1,4,2,8,7]=>[3,5,1,4,6,2,8,7]=>1100001=>0011110
[5,3,1,6,4,2,7,8]=>[3,1,6,4,5,2,7,8]=>1101000=>0010111
[4,6,1,7,5,2,8,3]=>[5,8,7,1,6,4,2,3]=>1101001=>0010110
[3,5,6,1,2,8,7,4]=>[7,8,6,1,5,3,2,4]=>1110010=>0001101
[3,4,7,2,8,6,1,5]=>[6,8,2,4,3,1,7,5]=>1110100=>0001011
[3,4,6,2,8,1,5,7]=>[8,2,4,3,1,6,5,7]=>1110100=>0001011
[3,5,2,6,8,1,7,4]=>[7,8,2,3,1,6,5,4]=>1101100=>0010011
[4,2,5,6,1,3,8,7]=>[2,6,1,5,4,3,8,7]=>1011001=>0100110
[5,3,6,8,4,7,2,1]=>[7,4,8,6,3,2,5,1]=>1111010=>0000101
[3,7,2,5,4,8,6,1]=>[5,4,8,6,7,2,3,1]=>1101010=>0010101
[8,4,2,5,7,3,6,1]=>[7,5,4,2,3,6,8,1]=>1101100=>0010011
[4,7,2,5,8,3,6,1]=>[8,5,2,3,6,7,4,1]=>1101100=>0010011
[3,1,6,5,4,8,2,7]=>[5,4,8,6,3,1,2,7]=>1011010=>0100101
[4,1,6,5,8,3,2,7]=>[8,5,3,6,4,1,2,7]=>1011100=>0100011
[2,7,1,5,4,3,8,6]=>[5,4,8,7,2,1,3,6]=>1101001=>0010110
[8,2,1,5,4,3,7,6]=>[2,5,4,7,8,1,3,6]=>1001000=>0110111
[8,4,1,5,7,3,2,6]=>[7,5,4,1,3,8,2,6]=>1101100=>0010011
[8,3,6,1,4,7,2,5]=>[7,6,3,1,4,8,2,5]=>1110010=>0001101
[2,7,6,1,4,3,8,5]=>[6,2,1,4,8,7,3,5]=>1110001=>0001110
[6,7,8,5,1,3,2,4]=>[5,1,8,3,7,2,6,4]=>1111000=>0000111
[5,7,6,8,2,3,4,1]=>[8,2,6,3,7,4,5,1]=>1111000=>0000111
[5,7,2,8,4,3,6,1]=>[8,4,6,7,2,3,5,1]=>1101000=>0010111
[6,7,8,2,4,3,5,1]=>[8,2,4,7,3,5,6,1]=>1110000=>0001111
[4,7,6,2,8,3,5,1]=>[8,2,6,5,7,3,4,1]=>1110100=>0001011
[8,3,6,2,4,7,5,1]=>[7,6,3,2,4,5,8,1]=>1110010=>0001101
[3,7,6,2,4,8,5,1]=>[8,6,2,4,5,7,3,1]=>1110010=>0001101
[5,7,3,8,4,6,2,1]=>[3,6,8,4,7,2,5,1]=>1101000=>0010111
[4,7,3,5,8,6,2,1]=>[3,6,8,5,2,7,4,1]=>1101100=>0010011
[8,7,2,1,4,3,6,5]=>[7,2,4,6,8,1,3,5]=>1100000=>0011111
[8,7,3,1,4,6,2,5]=>[3,6,7,1,4,8,2,5]=>1100000=>0011111
[8,7,6,3,2,5,4,1]=>[6,3,5,7,2,4,8,1]=>1110000=>0001111
[8,7,3,5,1,6,2,4]=>[3,5,1,6,7,2,8,4]=>1101000=>0010111
[8,2,6,5,1,3,7,4]=>[2,5,1,6,3,7,8,4]=>1011000=>0100111
[5,7,6,8,4,1,2,3]=>[8,4,6,1,7,2,5,3]=>1111000=>0000111
[3,7,6,5,1,8,2,4]=>[5,1,8,6,3,2,7,4]=>1111010=>0000101
[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>10000000=>01111111
[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>01000000=>10111111
[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>100000000=>011111111
[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]=>010000000=>101111111
[10,1,2,3,4,5,6,7,8,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>1000000000=>0111111111
[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,2,3,4,5,6,7,8,9,10]=>0100000000=>1011111111
[3,6,4,8,7,5,1,2]=>[7,5,8,4,1,6,3,2]=>1111100=>0000011
[5,6,4,3,8,7,1,2]=>[4,3,7,1,8,6,5,2]=>1110110=>0001001
[1,6,2,4,7,8,5,3]=>[1,4,8,5,7,6,2,3]=>0100110=>1011001
[3,6,2,4,8,1,5,7]=>[4,8,2,3,1,6,5,7]=>1100100=>0011011
[7,3,8,4,5,6,1,2]=>[4,5,6,8,3,1,7,2]=>1110000=>0001111
[3,5,6,4,8,7,1,2]=>[4,7,1,8,6,5,3,2]=>1110110=>0001001
[4,6,8,5,3,7,1,2]=>[5,3,7,1,8,6,4,2]=>1111010=>0000101
[6,8,5,3,4,7,1,2]=>[5,3,4,7,1,8,6,2]=>1110010=>0001101
[1,8,5,2,7,3,6,4]=>[1,7,5,2,6,8,3,4]=>0110100=>1001011
[4,2,7,5,1,8,6,3]=>[2,5,1,8,6,7,4,3]=>1011010=>0100101
[7,8,1,4,2,6,5,3]=>[4,6,8,1,5,7,2,3]=>1100000=>0011111
[1,3,6,4,8,2,5,7]=>[1,4,8,3,2,6,5,7]=>0110100=>1001011
[4,1,7,5,3,2,6,8]=>[5,3,7,4,1,2,6,8]=>1011000=>0100111
[6,5,1,3,4,2,8,7]=>[5,1,3,4,6,2,8,7]=>1100001=>0011110
[4,8,5,3,1,7,2,6]=>[5,3,7,1,4,2,8,6]=>1110010=>0001101
[5,8,3,6,1,4,2,7]=>[3,6,1,8,4,5,2,7]=>1101000=>0010111
[2,5,8,6,4,1,3,7]=>[6,4,8,2,1,5,3,7]=>1111000=>0000111
[1,4,6,2,5,8,3,7]=>[1,5,8,6,2,4,3,7]=>0110010=>1001101
[7,1,8,6,3,4,2,5]=>[6,3,8,4,7,1,2,5]=>1011000=>0100111
[7,2,1,4,5,6,8,3]=>[2,4,5,6,8,7,1,3]=>1000001=>0111110
[6,1,3,2,7,5,8,4]=>[3,8,7,5,6,1,2,4]=>1000101=>0111010
[1,6,3,8,5,7,2,4]=>[1,3,5,7,2,8,6,4]=>0101010=>1010101
[2,6,4,1,7,5,8,3]=>[4,2,1,8,7,5,6,3]=>1110101=>0001010
[7,6,5,8,1,4,2,3]=>[8,1,5,4,6,2,7,3]=>1111000=>0000111
[5,8,6,7,3,2,1,4]=>[7,3,6,2,8,1,5,4]=>1111000=>0000111
[1,6,4,3,7,2,8,5]=>[1,4,3,8,7,2,6,5]=>0110101=>1001010
[2,6,3,4,8,7,1,5]=>[3,4,7,2,1,8,6,5]=>1100110=>0011001
[7,1,3,4,5,2,8,6]=>[3,4,5,8,7,1,2,6]=>1000001=>0111110
[1,8,3,5,4,2,7,6]=>[1,3,5,4,7,8,2,6]=>0101000=>1010111
[3,2,6,4,7,8,1,5]=>[2,4,8,3,1,7,6,5]=>1010110=>0101001
[2,8,5,7,4,3,1,6]=>[7,4,5,3,8,2,1,6]=>1111000=>0000111
[5,3,8,7,1,2,6,4]=>[7,3,1,6,8,2,5,4]=>1111000=>0000111
[6,5,3,8,2,1,7,4]=>[3,7,8,2,5,1,6,4]=>1101000=>0010111
[7,5,8,4,1,2,3,6]=>[4,8,1,5,2,7,3,6]=>1110000=>0001111
[5,8,7,4,1,3,2,6]=>[4,7,1,8,3,5,2,6]=>1110000=>0001111
[1,4,7,5,3,8,2,6]=>[1,5,3,8,4,2,7,6]=>0111010=>1000101
[2,4,6,7,3,1,8,5]=>[8,7,3,6,4,2,1,5]=>1111001=>0000110
[7,8,4,6,3,1,2,5]=>[6,4,3,8,1,7,2,5]=>1111000=>0000111
[3,6,5,8,4,2,1,7]=>[8,4,5,2,6,3,1,7]=>1111000=>0000111
[5,6,8,4,2,3,1,7]=>[4,8,2,6,3,5,1,7]=>1110000=>0001111
[6,1,4,2,8,5,7,3]=>[4,1,2,7,8,5,6,3]=>1010100=>0101011
[4,8,6,5,3,2,7,1]=>[5,3,6,2,7,8,4,1]=>1111000=>0000111
[8,6,5,1,2,4,7,3]=>[5,1,6,2,4,7,8,3]=>1110000=>0001111
[1,7,5,8,2,6,4,3]=>[1,6,8,2,5,4,7,3]=>0111000=>1000111
[6,3,8,5,7,1,2,4]=>[7,5,3,1,8,2,6,4]=>1111100=>0000011
[8,3,1,5,6,2,7,4]=>[3,1,6,5,2,7,8,4]=>1101100=>0010011
[6,8,5,2,1,4,7,3]=>[5,2,7,8,1,4,6,3]=>1110000=>0001111
[3,8,2,5,6,1,7,4]=>[6,5,2,3,1,7,8,4]=>1101100=>0010011
[2,8,1,5,6,3,7,4]=>[6,5,2,1,3,7,8,4]=>1101100=>0010011
[8,1,2,5,6,3,7,4]=>[6,5,1,2,3,7,8,4]=>1001100=>0110011
[1,8,2,5,7,6,3,4]=>[1,6,7,5,2,3,8,4]=>0101100=>1010011
[5,1,8,6,2,7,3,4]=>[7,6,1,2,8,3,5,4]=>1011010=>0100101
[2,5,8,6,1,7,3,4]=>[7,6,2,1,8,3,5,4]=>1111010=>0000101
[8,6,1,5,7,2,3,4]=>[7,5,1,6,2,3,8,4]=>1101100=>0010011
[3,8,6,5,7,1,2,4]=>[7,5,1,6,3,2,8,4]=>1111100=>0000011
[7,6,5,8,1,2,4,3]=>[8,1,5,2,6,4,7,3]=>1111000=>0000111
[5,1,3,7,8,6,2,4]=>[3,6,8,1,2,7,5,4]=>1001100=>0110011
[7,2,5,8,1,6,4,3]=>[2,6,8,1,5,4,7,3]=>1011000=>0100111
[8,2,1,5,7,6,3,4]=>[2,6,7,5,1,3,8,4]=>1001100=>0110011
[4,2,1,3,6,7,8,5]=>[2,4,1,3,8,7,6,5]=>1000111=>0111000
[6,1,3,5,4,7,8,2]=>[3,5,4,8,7,6,1,2]=>1001011=>0110100
[6,1,5,3,4,7,8,2]=>[5,3,4,8,7,6,1,2]=>1010011=>0101100
[7,5,6,2,4,1,8,3]=>[6,2,4,5,1,8,7,3]=>1110001=>0001110
[4,3,1,2,6,7,8,5]=>[3,1,4,2,8,7,6,5]=>1100111=>0011000
[8,1,6,5,7,3,2,4]=>[7,5,3,6,1,2,8,4]=>1011100=>0100011
[5,8,1,6,3,7,2,4]=>[7,6,1,3,8,2,5,4]=>1101010=>0010101
[1,7,6,5,4,2,8,3]=>[1,5,4,6,2,8,7,3]=>0111001=>1000110
[5,7,6,1,4,2,8,3]=>[6,1,4,8,7,2,5,3]=>1110001=>0001110
[7,1,4,2,6,5,8,3]=>[4,1,2,6,5,8,7,3]=>1010101=>0101010
[4,1,7,3,5,6,8,2]=>[5,6,8,7,3,4,1,2]=>1010001=>0101110
[2,7,4,1,5,6,8,3]=>[4,2,1,5,6,8,7,3]=>1110001=>0001110
[5,7,6,4,1,2,8,3]=>[4,6,1,8,7,2,5,3]=>1110001=>0001110
[4,7,6,1,5,2,8,3]=>[5,6,1,8,7,2,4,3]=>1110001=>0001110
[1,8,3,6,5,7,2,4]=>[1,3,5,7,6,2,8,4]=>0101010=>1010101
[3,8,1,6,5,7,2,4]=>[5,7,6,1,3,2,8,4]=>1101010=>0010101
[8,1,3,5,7,6,2,4]=>[3,6,7,5,1,2,8,4]=>1001100=>0110011
[7,8,5,4,1,6,2,3]=>[4,5,1,6,8,2,7,3]=>1110000=>0001111
[6,1,5,4,3,7,8,2]=>[4,5,3,8,7,6,1,2]=>1010011=>0101100
[7,5,6,4,2,1,8,3]=>[4,6,2,5,1,8,7,3]=>1110001=>0001110
[8,3,2,6,5,7,1,4]=>[3,2,5,7,6,1,8,4]=>1101010=>0010101
[7,4,6,2,5,1,8,3]=>[5,6,2,4,1,8,7,3]=>1110001=>0001110
[6,1,4,3,5,7,8,2]=>[4,3,5,8,7,6,1,2]=>1010011=>0101100
[6,1,3,4,5,7,8,2]=>[3,4,5,8,7,6,1,2]=>1000011=>0111100
[7,2,6,4,5,1,8,3]=>[2,4,5,6,1,8,7,3]=>1010001=>0101110
[8,2,3,6,5,7,1,4]=>[2,3,5,7,6,1,8,4]=>1001010=>0110101
[3,4,7,8,5,6,1,2]=>[5,6,8,1,7,4,3,2]=>1111000=>0000111
[1,4,7,2,5,8,3,6]=>[1,5,8,2,4,3,7,6]=>0110010=>1001101
[6,8,3,4,5,7,1,2]=>[3,4,5,7,1,8,6,2]=>1100010=>0011101
[4,3,6,7,5,8,1,2]=>[5,8,3,1,7,6,4,2]=>1111010=>0000101
[7,3,8,6,4,5,1,2]=>[6,4,5,8,3,1,7,2]=>1111000=>0000111
[1,2,7,6,5,8,3,4]=>[1,2,5,8,6,3,7,4]=>0011010=>1100101
[4,8,2,6,1,5,3,7]=>[6,2,5,8,4,1,3,7]=>1101000=>0010111
[4,3,6,2,5,1,8,7]=>[5,6,3,2,4,1,8,7]=>1110001=>0001110
[7,8,1,2,5,6,3,4]=>[5,6,8,1,7,2,3,4]=>1100000=>0011111
[6,1,2,5,8,7,3,4]=>[7,5,1,2,3,8,6,4]=>1001110=>0110001
[7,1,5,8,3,6,2,4]=>[6,8,3,5,1,2,7,4]=>1011000=>0100111
[6,1,5,7,4,2,8,3]=>[8,7,4,5,1,2,6,3]=>1011001=>0100110
[3,1,6,4,7,2,5,8]=>[4,7,3,1,2,6,5,8]=>1010100=>0101011
[2,4,7,5,1,8,3,6]=>[5,2,1,8,4,3,7,6]=>1111010=>0000101
[5,6,8,1,3,2,4,7]=>[8,1,6,3,5,2,4,7]=>1110000=>0001111
[6,8,5,1,3,4,2,7]=>[5,1,8,3,4,6,2,7]=>1110000=>0001111
[4,2,8,3,1,7,5,6]=>[2,7,3,4,1,5,8,6]=>1010010=>0101101
[1,3,7,4,8,2,5,6]=>[1,4,8,3,2,7,5,6]=>0110100=>1001011
[5,3,7,4,1,6,2,8]=>[4,6,7,3,1,5,2,8]=>1110000=>0001111
[2,4,7,3,6,1,8,5]=>[6,3,4,2,1,8,7,5]=>1110101=>0001010
[5,8,7,6,3,1,2,4]=>[6,3,7,1,8,2,5,4]=>1111000=>0000111
[1,2,7,8,5,4,3,6]=>[1,2,5,8,4,7,3,6]=>0011000=>1100111
[6,3,1,2,8,4,5,7]=>[3,1,8,2,4,6,5,7]=>1100100=>0011011
[4,2,1,3,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>1000101=>0111010
[7,2,1,5,4,6,3,8]=>[2,5,4,6,7,1,3,8]=>1001000=>0110111
[4,2,6,1,8,5,3,7]=>[2,8,5,6,1,4,3,7]=>1010100=>0101011
[7,8,4,1,5,3,6,2]=>[4,1,5,8,3,6,7,2]=>1110000=>0001111
[3,4,6,1,5,8,7,2]=>[5,7,8,6,1,4,3,2]=>1110010=>0001101
[7,5,1,6,4,3,8,2]=>[6,4,5,1,3,8,7,2]=>1101001=>0010110
[6,8,1,7,5,2,3,4]=>[5,7,1,8,2,3,6,4]=>1101000=>0010111
[7,6,1,8,5,3,2,4]=>[5,8,1,3,6,2,7,4]=>1101000=>0010111
[5,6,1,7,4,8,2,3]=>[8,4,7,6,1,5,2,3]=>1101010=>0010101
[3,6,1,5,7,4,2,8]=>[7,5,4,6,1,3,2,8]=>1101100=>0010011
[3,1,7,5,6,4,8,2]=>[6,5,4,8,7,3,1,2]=>1011101=>0100010
[5,1,7,6,4,8,3,2]=>[8,6,4,7,3,5,1,2]=>1011010=>0100101
[6,1,7,8,5,3,4,2]=>[5,8,3,7,4,6,1,2]=>1011000=>0100111
[7,1,8,6,5,4,2,3]=>[5,6,4,8,1,2,7,3]=>1011000=>0100111
[2,6,5,7,3,4,8,1]=>[8,7,3,5,4,6,2,1]=>1111001=>0000110
[1,6,4,7,5,8,2,3]=>[1,5,8,4,2,7,6,3]=>0111010=>1000101
[1,3,7,4,6,8,2,5]=>[1,4,8,6,3,2,7,5]=>0110110=>1001001
[4,7,5,6,3,2,8,1]=>[6,3,5,2,8,7,4,1]=>1111001=>0000110
[1,7,6,5,4,8,2,3]=>[1,5,4,8,6,2,7,3]=>0111010=>1000101
[1,2,7,6,8,3,4,5]=>[1,2,8,3,6,4,7,5]=>0011100=>1100011
[5,4,1,7,6,8,2,3]=>[8,6,4,1,7,5,2,3]=>1101110=>0010001
[4,8,5,6,2,7,3,1]=>[7,6,2,5,3,8,4,1]=>1111010=>0000101
[7,8,5,2,4,6,3,1]=>[5,2,4,6,8,3,7,1]=>1110000=>0001111
[7,8,1,6,2,4,5,3]=>[6,1,8,4,5,7,2,3]=>1101000=>0010111
[6,8,1,4,7,2,5,3]=>[4,7,1,8,5,6,2,3]=>1100100=>0011011
[3,7,4,1,8,5,2,6]=>[4,1,8,5,7,3,2,6]=>1110100=>0001011
[6,7,1,4,8,3,2,5]=>[4,8,1,3,7,2,6,5]=>1100100=>0011011
[6,5,1,4,3,8,2,7]=>[4,5,1,3,8,6,2,7]=>1100010=>0011101
[1,6,2,5,8,3,4,7]=>[1,8,5,2,3,6,4,7]=>0101100=>1010011
[7,4,2,1,8,5,3,6]=>[4,2,8,5,7,1,3,6]=>1100100=>0011011
[1,5,4,2,8,3,6,7]=>[1,4,2,8,5,3,6,7]=>0110100=>1001011
[3,4,8,5,6,7,2,1]=>[7,6,5,2,8,4,3,1]=>1111110=>0000001
[6,3,5,8,4,7,2,1]=>[7,4,5,3,2,8,6,1]=>1111010=>0000101
[5,4,3,8,6,7,2,1]=>[3,7,6,4,2,8,5,1]=>1101110=>0010001
[5,4,2,8,7,3,6,1]=>[7,4,2,3,6,8,5,1]=>1101100=>0010011
[1,3,8,7,5,6,2,4]=>[1,5,6,7,3,2,8,4]=>0111000=>1000111
[2,1,8,7,4,6,3,5]=>[2,1,6,7,4,8,3,5]=>1011000=>0100111
[3,1,8,5,7,6,2,4]=>[6,7,5,3,1,2,8,4]=>1011100=>0100011
[5,4,1,8,7,6,2,3]=>[6,7,4,1,8,5,2,3]=>1101100=>0010011
[5,8,6,7,4,3,2,1]=>[7,4,6,3,8,2,5,1]=>1111000=>0000111
[4,8,7,5,6,3,2,1]=>[6,5,3,7,2,8,4,1]=>1111100=>0000011
[4,2,1,6,3,5,8,7]=>[2,6,4,1,3,5,8,7]=>1001001=>0110110
[6,2,1,4,3,5,8,7]=>[2,4,6,1,3,5,8,7]=>1000001=>0111110
[6,2,1,4,3,8,5,7]=>[2,4,8,6,1,3,5,7]=>1000010=>0111101
[8,2,1,4,3,6,5,7]=>[2,4,6,8,1,3,5,7]=>1000000=>0111111
[8,2,4,1,3,6,5,7]=>[2,4,1,6,8,3,5,7]=>1010000=>0101111
[6,2,4,1,3,8,5,7]=>[2,4,1,8,6,3,5,7]=>1010010=>0101101
[6,2,4,1,3,5,8,7]=>[2,4,1,6,3,5,8,7]=>1010001=>0101110
[4,2,6,1,3,5,8,7]=>[2,6,1,4,3,5,8,7]=>1010001=>0101110
[2,1,6,4,3,5,8,7]=>[2,1,4,6,3,5,8,7]=>1010001=>0101110
[2,6,1,4,3,5,8,7]=>[4,6,2,1,3,5,8,7]=>1100001=>0011110
[2,6,4,1,3,5,8,7]=>[4,2,1,6,3,5,8,7]=>1110001=>0001110
[4,6,2,1,3,5,8,7]=>[6,2,4,1,3,5,8,7]=>1100001=>0011110
[6,4,2,1,3,5,8,7]=>[4,2,6,1,3,5,8,7]=>1100001=>0011110
[8,4,2,1,3,6,5,7]=>[4,2,6,8,1,3,5,7]=>1100000=>0011111
[8,4,2,1,6,3,5,7]=>[4,2,6,1,3,8,5,7]=>1100100=>0011011
[6,4,2,1,8,3,5,7]=>[4,2,8,1,3,6,5,7]=>1100100=>0011011
[4,6,2,1,8,3,5,7]=>[8,2,4,1,3,6,5,7]=>1100100=>0011011
[2,6,1,4,3,8,5,7]=>[4,8,6,2,1,3,5,7]=>1100010=>0011101
[2,1,6,4,3,8,5,7]=>[2,1,4,8,6,3,5,7]=>1010010=>0101101
[2,1,8,4,3,6,5,7]=>[2,1,4,6,8,3,5,7]=>1010000=>0101111
[2,8,1,4,3,6,5,7]=>[4,6,8,2,1,3,5,7]=>1100000=>0011111
[2,8,4,1,3,6,5,7]=>[4,2,1,6,8,3,5,7]=>1110000=>0001111
[4,8,2,1,3,6,5,7]=>[6,8,2,4,1,3,5,7]=>1100000=>0011111
[4,8,2,1,6,3,5,7]=>[6,2,4,1,3,8,5,7]=>1100100=>0011011
[6,8,2,1,4,3,5,7]=>[8,2,4,6,1,3,5,7]=>1100000=>0011111
[8,6,2,1,4,3,5,7]=>[6,2,4,8,1,3,5,7]=>1100000=>0011111
[2,8,1,4,6,3,5,7]=>[4,6,2,1,3,8,5,7]=>1100100=>0011011
[2,1,8,4,6,3,5,7]=>[2,1,4,6,3,8,5,7]=>1010100=>0101011
[2,1,6,4,8,3,5,7]=>[2,1,4,8,3,6,5,7]=>1010100=>0101011
[2,6,1,4,8,3,5,7]=>[4,8,2,1,3,6,5,7]=>1100100=>0011011
[2,6,4,1,8,3,5,7]=>[4,2,1,8,3,6,5,7]=>1110100=>0001011
[2,6,4,8,1,3,5,7]=>[8,4,2,1,6,3,5,7]=>1111000=>0000111
[4,6,2,8,1,3,5,7]=>[8,2,6,4,1,3,5,7]=>1101000=>0010111
[4,2,6,1,3,8,5,7]=>[2,8,6,1,4,3,5,7]=>1010010=>0101101
[4,2,6,1,8,3,5,7]=>[2,8,1,4,3,6,5,7]=>1010100=>0101011
[6,2,4,1,8,3,5,7]=>[2,4,1,8,3,6,5,7]=>1010100=>0101011
[8,2,4,1,6,3,5,7]=>[2,4,1,6,3,8,5,7]=>1010100=>0101011
[8,2,1,4,6,3,5,7]=>[2,4,6,1,3,8,5,7]=>1000100=>0111011
[6,2,1,4,8,3,5,7]=>[2,4,8,1,3,6,5,7]=>1000100=>0111011
[4,2,1,6,8,3,5,7]=>[2,8,4,1,3,6,5,7]=>1001100=>0110011
[4,2,1,6,3,8,5,7]=>[2,8,6,4,1,3,5,7]=>1001010=>0110101
[4,2,1,3,6,8,5,7]=>[2,4,1,3,8,6,5,7]=>1000110=>0111001
[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,5,7]=>1010100=>0101011
[2,4,1,3,8,6,5,7]=>[4,2,1,3,6,8,5,7]=>1100100=>0011011
[4,2,1,3,8,6,5,7]=>[2,4,1,3,6,8,5,7]=>1000100=>0111011
[4,2,1,8,3,6,5,7]=>[2,6,8,4,1,3,5,7]=>1001000=>0110111
[4,2,1,8,6,3,5,7]=>[2,6,4,1,3,8,5,7]=>1001100=>0110011
[6,2,1,8,4,3,5,7]=>[2,8,4,6,1,3,5,7]=>1001000=>0110111
[8,2,1,6,4,3,5,7]=>[2,6,4,8,1,3,5,7]=>1001000=>0110111
[8,2,6,1,4,3,5,7]=>[2,6,1,4,8,3,5,7]=>1010000=>0101111
[6,2,8,1,4,3,5,7]=>[2,8,1,4,6,3,5,7]=>1010000=>0101111
[4,2,8,1,6,3,5,7]=>[2,6,1,4,3,8,5,7]=>1010100=>0101011
[4,2,8,1,3,6,5,7]=>[2,6,8,1,4,3,5,7]=>1010000=>0101111
[2,4,8,1,3,6,5,7]=>[6,8,2,1,4,3,5,7]=>1110000=>0001111
[2,4,1,8,3,6,5,7]=>[6,8,4,2,1,3,5,7]=>1101000=>0010111
[2,1,4,8,3,6,5,7]=>[2,1,6,8,4,3,5,7]=>1011000=>0100111
[2,1,4,8,6,3,5,7]=>[2,1,6,4,3,8,5,7]=>1011100=>0100011
[2,4,8,1,6,3,5,7]=>[6,2,1,4,3,8,5,7]=>1110100=>0001011
[2,4,8,6,1,3,5,7]=>[6,2,1,8,4,3,5,7]=>1111000=>0000111
[4,2,8,6,1,3,5,7]=>[2,6,1,8,4,3,5,7]=>1011000=>0100111
[6,2,8,4,1,3,5,7]=>[2,4,8,1,6,3,5,7]=>1010000=>0101111
[8,2,6,4,1,3,5,7]=>[2,4,6,1,8,3,5,7]=>1010000=>0101111
[8,4,6,2,1,3,5,7]=>[6,2,4,1,8,3,5,7]=>1110000=>0001111
[6,4,8,2,1,3,5,7]=>[8,2,4,1,6,3,5,7]=>1110000=>0001111
[4,6,8,2,1,3,5,7]=>[8,2,6,1,4,3,5,7]=>1110000=>0001111
[2,6,8,4,1,3,5,7]=>[4,8,2,1,6,3,5,7]=>1110000=>0001111
[2,6,8,1,4,3,5,7]=>[8,2,1,4,6,3,5,7]=>1110000=>0001111
[2,6,1,8,4,3,5,7]=>[8,4,6,2,1,3,5,7]=>1101000=>0010111
[2,1,6,8,4,3,5,7]=>[2,1,8,4,6,3,5,7]=>1011000=>0100111
[2,1,8,6,4,3,5,7]=>[2,1,6,4,8,3,5,7]=>1011000=>0100111
[2,8,1,6,4,3,5,7]=>[6,4,8,2,1,3,5,7]=>1101000=>0010111
[2,8,6,4,1,3,5,7]=>[4,6,2,1,8,3,5,7]=>1110000=>0001111
[4,8,6,2,1,3,5,7]=>[6,2,8,1,4,3,5,7]=>1110000=>0001111
[6,8,4,2,1,3,5,7]=>[4,2,8,1,6,3,5,7]=>1110000=>0001111
[3,2,6,1,5,4,8,7]=>[2,5,6,3,1,4,8,7]=>1010001=>0101110
[6,2,4,1,5,3,8,7]=>[2,4,1,5,6,3,8,7]=>1010001=>0101110
[4,3,6,1,5,2,8,7]=>[5,6,3,1,4,2,8,7]=>1110001=>0001110
[4,3,7,2,6,5,8,1]=>[6,5,8,7,3,2,4,1]=>1110101=>0001010
[4,3,8,1,7,2,6,5]=>[7,3,1,4,2,6,8,5]=>1110100=>0001011
[4,3,8,1,5,2,7,6]=>[5,7,8,3,1,4,2,6]=>1110000=>0001111
[5,1,8,3,4,2,7,6]=>[7,8,3,4,5,1,2,6]=>1010000=>0101111
[5,4,8,1,3,2,7,6]=>[7,8,1,4,3,5,2,6]=>1110000=>0001111
[2,1,5,4,8,3,7,6]=>[2,1,4,7,8,5,3,6]=>1010100=>0101011
[4,3,7,6,8,1,5,2]=>[8,3,1,6,5,7,4,2]=>1111100=>0000011
[4,3,7,1,8,5,6,2]=>[8,5,6,7,3,1,4,2]=>1110100=>0001011
[4,3,6,5,8,1,7,2]=>[7,8,5,3,1,6,4,2]=>1111100=>0000011
[7,4,6,5,8,1,3,2]=>[8,5,1,6,4,3,7,2]=>1111100=>0000011
[2,1,8,4,6,3,7,5]=>[2,1,4,6,3,7,8,5]=>1010100=>0101011
[8,4,6,1,3,2,7,5]=>[6,1,4,3,7,8,2,5]=>1110000=>0001111
[8,3,5,1,7,2,6,4]=>[7,5,3,1,6,8,2,4]=>1110100=>0001011
[8,3,5,2,6,1,7,4]=>[6,5,3,2,7,8,1,4]=>1110100=>0001011
[8,2,6,3,5,1,7,4]=>[2,5,6,3,7,8,1,4]=>1010000=>0101111
[3,2,8,4,6,1,7,5]=>[2,4,6,3,1,7,8,5]=>1010100=>0101011
[3,2,8,1,5,4,7,6]=>[2,5,7,8,3,1,4,6]=>1010000=>0101111
[3,2,7,6,8,1,5,4]=>[2,8,3,1,6,5,7,4]=>1011100=>0100011
[6,5,7,2,4,3,8,1]=>[8,7,2,4,5,3,6,1]=>1110001=>0001110
[6,5,8,2,4,1,7,3]=>[7,8,2,4,5,1,6,3]=>1110000=>0001111
[7,2,4,1,8,5,6,3]=>[2,4,1,8,5,6,7,3]=>1010100=>0101011
[2,1,7,3,8,5,6,4]=>[2,1,8,5,6,7,3,4]=>1010100=>0101011
[7,1,3,2,8,5,6,4]=>[3,8,5,6,7,1,2,4]=>1000100=>0111011
[7,1,8,5,6,2,4,3]=>[6,5,1,2,8,4,7,3]=>1011100=>0100011
[7,2,8,1,5,4,6,3]=>[2,5,8,1,4,6,7,3]=>1010000=>0101111
[5,4,7,2,6,3,8,1]=>[6,2,4,3,8,7,5,1]=>1110101=>0001010
[5,4,8,2,6,1,7,3]=>[6,2,4,1,7,8,5,3]=>1110100=>0001011
[2,1,6,5,8,3,7,4]=>[2,1,7,8,5,3,6,4]=>1011100=>0100011
[6,1,7,4,8,3,5,2]=>[4,8,3,7,5,6,1,2]=>1010100=>0101011
[5,4,6,3,8,1,7,2]=>[7,8,3,4,1,6,5,2]=>1110100=>0001011
[2,8,3,1,5,4,6,7]=>[3,5,8,2,1,4,6,7]=>1100000=>0011111
[2,5,3,4,7,1,8,6]=>[3,4,8,7,5,2,1,6]=>1100101=>0011010
[2,4,8,3,5,7,6,1]=>[5,7,6,8,3,4,2,1]=>1110010=>0001101
[4,2,5,3,1,8,6,7]=>[2,5,3,4,1,8,6,7]=>1010010=>0101101
[5,4,1,3,8,2,6,7]=>[4,1,3,8,5,2,6,7]=>1100100=>0011011
[1,8,5,4,3,2,6,7]=>[1,4,5,3,8,2,6,7]=>0110000=>1001111
[1,7,4,3,8,5,2,6]=>[1,4,3,8,5,7,2,6]=>0110100=>1001011
[5,1,4,7,8,3,2,6]=>[8,4,3,7,5,1,2,6]=>1011100=>0100011
[8,1,5,3,7,4,6,2]=>[7,5,3,4,6,8,1,2]=>1010100=>0101011
[3,8,4,7,6,5,2,1]=>[6,5,7,4,2,8,3,1]=>1111100=>0000011
[1,6,8,5,3,7,4,2]=>[1,5,3,7,4,8,6,2]=>0111010=>1000101
[6,4,8,1,7,3,5,2]=>[7,1,4,3,8,5,6,2]=>1110100=>0001011
[6,4,8,7,1,5,2,3]=>[7,1,5,8,4,2,6,3]=>1111000=>0000111
[7,6,4,1,3,8,2,5]=>[4,1,8,6,3,7,2,5]=>1110010=>0001101
[1,7,5,6,3,2,8,4]=>[1,6,3,5,2,8,7,4]=>0111001=>1000110
[4,2,1,7,8,5,3,6]=>[2,8,5,7,4,1,3,6]=>1001100=>0110011
[2,7,4,6,3,1,8,5]=>[6,4,3,8,7,2,1,5]=>1111001=>0000110
[2,6,8,4,3,7,5,1]=>[4,7,3,5,8,6,2,1]=>1110010=>0001101
[7,2,6,3,4,1,8,5]=>[2,6,3,4,8,7,1,5]=>1010001=>0101110
[2,7,1,8,3,5,4,6]=>[8,2,1,3,5,7,4,6]=>1101000=>0010111
[8,2,1,7,3,5,6,4]=>[2,7,1,3,5,6,8,4]=>1001000=>0110111
[7,8,2,6,3,1,5,4]=>[6,2,3,8,1,5,7,4]=>1101000=>0010111
[1,2,8,7,4,5,6,3]=>[1,2,7,4,5,6,8,3]=>0011000=>1100111
[8,3,7,1,5,6,2,4]=>[5,6,7,3,1,8,2,4]=>1110000=>0001111
[1,8,5,2,6,7,4,3]=>[1,7,6,5,2,4,8,3]=>0110110=>1001001
[5,2,1,8,6,7,4,3]=>[2,7,6,4,8,5,1,3]=>1001110=>0110001
[1,7,8,5,2,6,4,3]=>[1,5,2,6,8,4,7,3]=>0111000=>1000111
[7,8,1,6,4,2,5,3]=>[6,4,8,1,5,7,2,3]=>1101000=>0010111
[7,8,6,1,5,3,2,4]=>[5,6,1,8,3,7,2,4]=>1110000=>0001111
[8,7,1,6,4,5,3,2]=>[6,4,5,7,1,3,8,2]=>1101000=>0010111
[8,1,7,5,6,4,3,2]=>[6,5,4,7,3,8,1,2]=>1011100=>0100011
[8,5,2,7,4,3,1,6]=>[7,4,5,2,3,8,1,6]=>1101000=>0010111
[4,5,3,6,1,2,8,7]=>[3,6,1,5,4,2,8,7]=>1101001=>0010110
[3,5,1,4,6,2,8,7]=>[4,6,5,1,3,2,8,7]=>1100101=>0011010
[8,3,4,5,7,2,1,6]=>[7,5,4,3,2,8,1,6]=>1111100=>0000011
[5,7,4,6,3,8,2,1]=>[8,6,4,3,7,2,5,1]=>1111010=>0000101
[8,1,4,7,3,6,2,5]=>[6,7,4,3,8,1,2,5]=>1011000=>0100111
[8,5,1,4,7,3,2,6]=>[4,7,5,1,3,8,2,6]=>1100100=>0011011
[8,5,3,7,1,4,2,6]=>[3,7,1,5,4,8,2,6]=>1101000=>0010111
[2,1,8,5,7,4,3,6]=>[2,1,7,5,4,8,3,6]=>1011100=>0100011
[6,5,3,7,1,8,4,2]=>[3,8,1,5,4,7,6,2]=>1101010=>0010101
[6,5,1,4,7,8,3,2]=>[4,8,5,1,3,7,6,2]=>1100110=>0011001
[6,3,4,7,5,8,1,2]=>[5,8,4,3,1,7,6,2]=>1111010=>0000101
[4,7,1,3,5,8,6,2]=>[5,8,6,7,1,3,4,2]=>1100010=>0011101
[4,8,3,7,1,2,6,5]=>[3,7,1,6,8,4,2,5]=>1101000=>0010111
[2,8,7,5,4,1,3,6]=>[5,4,7,2,1,8,3,6]=>1111000=>0000111
[3,8,6,7,4,2,1,5]=>[7,4,6,2,8,3,1,5]=>1111000=>0000111
[5,7,6,8,4,2,3,1]=>[8,4,6,2,7,3,5,1]=>1111000=>0000111
[5,3,7,8,2,4,6,1]=>[8,3,2,6,7,4,5,1]=>1111000=>0000111
[5,3,7,6,2,1,8,4]=>[6,3,2,8,7,1,5,4]=>1111001=>0000110
[5,3,6,2,8,7,1,4]=>[7,3,2,8,6,5,1,4]=>1110110=>0001001
[5,7,8,6,4,2,1,3]=>[6,4,8,2,7,1,5,3]=>1111000=>0000111
[2,6,7,5,4,8,1,3]=>[5,4,8,2,1,7,6,3]=>1111010=>0000101
[6,7,3,5,1,8,2,4]=>[3,5,1,8,2,7,6,4]=>1101010=>0010101
[2,1,6,7,5,8,3,4]=>[2,1,5,8,3,7,6,4]=>1011010=>0100101
[2,1,5,7,3,6,8,4]=>[2,1,6,8,7,3,5,4]=>1011001=>0100110
[5,7,3,6,1,2,8,4]=>[3,6,1,8,7,2,5,4]=>1101001=>0010110
[2,4,7,1,6,5,8,3]=>[6,5,8,7,2,1,4,3]=>1110101=>0001010
[4,6,2,1,8,7,5,3]=>[7,5,8,6,2,4,1,3]=>1100110=>0011001
[3,4,6,2,7,8,5,1]=>[8,5,7,6,2,4,3,1]=>1110110=>0001001
[4,6,1,2,5,8,7,3]=>[5,7,8,6,1,4,2,3]=>1100010=>0011101
[5,6,1,4,8,2,7,3]=>[4,7,8,1,6,5,2,3]=>1100100=>0011011
[5,6,3,1,8,7,2,4]=>[3,7,1,8,6,5,2,4]=>1100110=>0011001
[3,5,6,4,7,1,8,2]=>[4,8,7,1,6,5,3,2]=>1110101=>0001010
[3,4,6,1,5,7,8,2]=>[5,8,7,6,1,4,3,2]=>1110011=>0001100
[3,4,1,5,7,6,8,2]=>[6,8,7,5,4,1,3,2]=>1101101=>0010010
[3,8,2,7,1,6,5,4]=>[6,7,2,3,1,5,8,4]=>1101000=>0010111
[3,8,2,7,6,5,4,1]=>[6,5,7,4,8,2,3,1]=>1101100=>0010011
[4,8,7,2,6,5,3,1]=>[6,5,7,2,8,3,4,1]=>1110100=>0001011
[4,8,7,2,6,1,5,3]=>[6,2,7,5,8,1,4,3]=>1110100=>0001011
[4,8,7,2,1,6,5,3]=>[6,7,2,5,8,1,4,3]=>1110000=>0001111
[4,8,7,3,2,6,1,5]=>[6,7,3,8,2,4,1,5]=>1110000=>0001111
[4,8,7,3,6,2,5,1]=>[6,3,7,5,8,2,4,1]=>1110100=>0001011
[4,8,7,3,6,5,1,2]=>[6,5,7,3,8,1,4,2]=>1110100=>0001011
[4,8,7,3,6,5,2,1]=>[6,5,7,3,8,2,4,1]=>1110100=>0001011
[5,8,7,6,3,4,2,1]=>[6,3,7,4,8,2,5,1]=>1111000=>0000111
[5,8,7,6,3,1,4,2]=>[6,3,7,1,8,4,5,2]=>1111000=>0000111
[5,8,7,6,3,2,4,1]=>[6,3,7,2,8,4,5,1]=>1111000=>0000111
[5,8,7,6,2,1,4,3]=>[6,2,7,1,8,4,5,3]=>1111000=>0000111
[5,8,7,6,4,2,1,3]=>[6,4,7,2,8,1,5,3]=>1111000=>0000111
[5,8,7,6,4,1,3,2]=>[6,4,7,1,8,3,5,2]=>1111000=>0000111
[5,8,7,6,4,3,1,2]=>[6,4,7,3,8,1,5,2]=>1111000=>0000111
[7,3,4,2,1,6,5,8]=>[4,3,2,6,7,1,5,8]=>1110000=>0001111
[7,3,5,2,6,1,4,8]=>[6,5,3,2,7,1,4,8]=>1110100=>0001011
[7,3,5,2,6,4,1,8]=>[6,5,3,2,4,7,1,8]=>1110100=>0001011
[6,3,5,2,7,4,8,1]=>[8,7,5,3,2,4,6,1]=>1110101=>0001010
[7,2,1,5,6,4,3,8]=>[2,6,5,4,7,1,3,8]=>1001100=>0110011
[7,3,5,1,6,4,2,8]=>[6,5,3,1,4,7,2,8]=>1110100=>0001011
[1,4,5,7,3,2,8,6]=>[1,8,7,3,5,4,2,6]=>0111001=>1000110
[6,3,5,1,7,4,8,2]=>[8,7,5,3,1,4,6,2]=>1110101=>0001010
[6,2,1,5,7,4,8,3]=>[2,8,7,5,4,6,1,3]=>1001101=>0110010
[3,2,1,5,7,4,8,6]=>[2,3,1,8,7,5,4,6]=>1001101=>0110010
[2,4,6,7,3,8,1,5]=>[8,3,7,6,4,2,1,5]=>1111010=>0000101
[1,4,6,7,3,8,5,2]=>[1,8,3,5,7,6,4,2]=>0111010=>1000101
[1,5,6,7,8,3,4,2]=>[1,8,3,7,4,6,5,2]=>0111100=>1000011
[2,5,6,7,8,3,1,4]=>[8,3,7,2,1,6,5,4]=>1111100=>0000011
[3,2,1,6,7,8,4,5]=>[2,3,1,8,4,7,6,5]=>1001110=>0110001
[5,4,6,7,1,8,3,2]=>[8,1,7,6,4,3,5,2]=>1111010=>0000101
[1,5,6,7,8,3,2,4]=>[1,8,3,7,2,6,5,4]=>0111100=>1000011
[5,3,6,2,7,8,4,1]=>[8,3,2,4,7,6,5,1]=>1110110=>0001001
[5,3,6,2,7,8,1,4]=>[8,3,2,7,6,5,1,4]=>1110110=>0001001
[6,3,5,2,7,1,8,4]=>[8,7,5,3,2,6,1,4]=>1110101=>0001010
[6,3,4,2,1,7,8,5]=>[4,3,2,8,7,6,1,5]=>1110011=>0001100
[4,3,6,2,7,8,5,1]=>[8,5,7,6,3,2,4,1]=>1110110=>0001001
[1,3,6,2,7,8,5,4]=>[1,8,5,7,6,3,2,4]=>0110110=>1001001
[1,4,6,7,2,8,5,3]=>[1,8,2,5,7,6,4,3]=>0111010=>1000101
[3,4,6,7,2,8,5,1]=>[8,2,5,7,6,4,3,1]=>1111010=>0000101
[3,4,5,7,2,1,8,6]=>[8,7,2,5,4,3,1,6]=>1111001=>0000110
[4,2,1,5,7,3,8,6]=>[2,8,7,5,4,1,3,6]=>1001101=>0110010
[4,2,1,6,7,8,3,5]=>[2,8,4,1,3,7,6,5]=>1001110=>0110001
[1,5,6,7,8,2,4,3]=>[1,8,2,7,4,6,5,3]=>0111100=>1000011
[1,5,6,7,8,4,2,3]=>[1,8,4,7,2,6,5,3]=>0111100=>1000011
[4,3,6,1,7,8,5,2]=>[8,5,7,6,3,1,4,2]=>1110110=>0001001
[4,2,1,6,7,8,5,3]=>[2,8,5,7,6,4,1,3]=>1001110=>0110001
[2,3,6,1,7,8,5,4]=>[8,5,7,6,3,2,1,4]=>1110110=>0001001
[2,4,6,7,1,8,5,3]=>[8,2,1,5,7,6,4,3]=>1111010=>0000101
[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>10101010=>01010101
[2,4,1,3,6,5,8,7,9]=>[4,2,1,3,6,5,8,7,9]=>11001010=>00110101
[2,4,1,6,3,8,5,7,9]=>[8,6,4,2,1,3,5,7,9]=>11010100=>00101011
[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>11010101=>00101010
[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>01010101=>10101010
[2,4,1,3,6,5,8,7,10,9]=>[4,2,1,3,6,5,8,7,10,9]=>110010101=>001101010
[2,4,6,1,3,5,8,7,9]=>[6,2,1,4,3,5,8,7,9]=>11100010=>00011101
[2,4,1,6,3,8,5,10,7,9]=>[10,8,6,4,2,1,3,5,7,9]=>110101010=>001010101
[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>110101010=>001010101
[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>010101010=>101010101
[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>10000000=>01111111
[1,4,3,6,2,5,7,8]=>[1,3,6,4,2,5,7,8]=>0101000=>1010111
[1,4,3,7,2,6,5,8]=>[1,3,6,7,4,2,5,8]=>0101000=>1010111
[1,3,2,6,5,8,4,7]=>[1,3,2,5,8,6,4,7]=>0101010=>1010101
[1,5,4,8,2,6,3,7]=>[1,6,8,4,2,5,3,7]=>0111000=>1000111
[1,5,4,8,3,7,2,6]=>[1,7,4,3,5,2,8,6]=>0111010=>1000101
[1,2,3,6,5,8,4,7]=>[1,2,3,5,8,6,4,7]=>0001010=>1110101
[6,8,2,4,5,7,1,3]=>[4,5,7,2,8,6,1,3]=>1100010=>0011101
[3,7,8,4,5,2,6,1]=>[4,5,8,2,6,7,3,1]=>1110000=>0001111
[3,8,7,4,1,6,5,2]=>[4,6,7,1,5,8,3,2]=>1110000=>0001111
[4,8,3,6,1,5,7,2]=>[3,6,1,5,7,8,4,2]=>1101000=>0010111
[5,8,3,1,6,4,7,2]=>[3,6,1,4,7,8,5,2]=>1100100=>0011011
[5,8,1,4,7,6,3,2]=>[4,6,7,1,3,8,5,2]=>1100100=>0011011
[7,4,1,8,2,6,3,5]=>[6,8,4,1,7,2,3,5]=>1101000=>0010111
[6,1,3,8,5,2,4,7]=>[3,5,8,1,2,6,4,7]=>1001000=>0110111
[7,1,8,3,6,2,5,4]=>[6,3,8,5,7,1,2,4]=>1010100=>0101011
[7,2,8,4,1,6,5,3]=>[2,4,6,8,1,5,7,3]=>1010000=>0101111
[7,2,8,3,6,5,1,4]=>[2,6,5,8,3,7,1,4]=>1010100=>0101011
[6,1,2,8,3,5,4,7]=>[8,1,2,3,5,6,4,7]=>1001000=>0110111
[5,1,2,3,8,4,7,6]=>[7,8,5,1,2,3,4,6]=>1000100=>0111011
[5,2,3,8,1,4,7,6]=>[2,3,7,8,1,5,4,6]=>1001000=>0110111
[6,2,8,1,3,5,4,7]=>[2,8,1,5,6,3,4,7]=>1010000=>0101111
[6,2,4,1,8,7,3,5]=>[2,4,1,7,3,8,6,5]=>1010110=>0101001
[6,3,1,4,2,8,5,7]=>[3,1,4,8,6,2,5,7]=>1100010=>0011101
[2,6,3,8,7,1,5,4]=>[3,7,2,1,8,5,6,4]=>1101100=>0010011
[2,5,1,8,3,4,7,6]=>[7,8,2,1,3,5,4,6]=>1101000=>0010111
[2,5,1,3,8,4,7,6]=>[7,8,5,2,1,3,4,6]=>1100100=>0011011
[1,2,5,3,8,4,7,6]=>[1,2,7,8,5,3,4,6]=>0010100=>1101011
[1,2,4,8,3,7,6,5]=>[1,2,7,6,8,4,3,5]=>0011010=>1100101
[2,4,8,3,7,6,1,5]=>[6,7,3,4,2,1,8,5]=>1110100=>0001011
[2,5,3,8,1,7,4,6]=>[3,7,2,1,5,4,8,6]=>1101010=>0010101
[2,5,4,1,3,8,7,6]=>[4,2,1,5,3,7,8,6]=>1110010=>0001101
[3,1,5,4,8,2,7,6]=>[4,7,8,5,3,1,2,6]=>1010100=>0101011
[5,3,1,4,8,2,7,6]=>[3,1,4,7,8,5,2,6]=>1100100=>0011011
[4,8,2,3,7,6,1,5]=>[6,7,2,3,4,1,8,5]=>1100100=>0011011
[4,8,2,3,7,1,6,5]=>[7,2,3,4,1,6,8,5]=>1100100=>0011011
[4,8,1,2,3,7,6,5]=>[7,6,8,1,4,2,3,5]=>1100010=>0011101
[1,4,8,2,3,7,6,5]=>[1,7,6,8,2,4,3,5]=>0110010=>1001101
[1,4,8,3,7,2,6,5]=>[1,7,3,4,2,6,8,5]=>0110100=>1001011
[5,3,8,1,2,4,7,6]=>[7,8,3,1,5,2,4,6]=>1110000=>0001111
[1,5,3,8,2,4,7,6]=>[1,3,7,8,2,5,4,6]=>0101000=>1010111
[6,5,1,2,8,7,4,3]=>[7,5,1,4,8,6,2,3]=>1100110=>0011001
[5,3,1,6,4,2,8,7]=>[3,1,6,4,5,2,8,7]=>1101001=>0010110
[5,1,6,2,8,7,4,3]=>[7,1,2,4,8,6,5,3]=>1010110=>0101001
[4,1,5,8,2,7,6,3]=>[7,6,8,1,2,5,4,3]=>1011010=>0100101
[4,1,2,5,8,7,6,3]=>[7,6,8,5,4,1,2,3]=>1001110=>0110001
[1,4,2,5,8,7,6,3]=>[1,7,6,8,5,4,2,3]=>0101110=>1010001
[1,3,5,2,8,7,4,6]=>[1,7,5,3,2,4,8,6]=>0110110=>1001001
[3,5,1,2,8,7,4,6]=>[7,5,1,3,2,4,8,6]=>1100110=>0011001
[4,2,6,1,8,7,3,5]=>[2,7,1,4,3,8,6,5]=>1010110=>0101001
[4,3,1,5,8,2,7,6]=>[3,1,7,8,5,4,2,6]=>1101100=>0010011
[3,4,8,7,2,6,1,5]=>[6,7,2,8,4,3,1,5]=>1111000=>0000111
[3,4,8,7,1,2,6,5]=>[7,1,6,8,4,3,2,5]=>1111000=>0000111
[1,3,4,8,7,2,6,5]=>[1,7,4,3,2,6,8,5]=>0111100=>1000011
[1,3,4,8,2,7,6,5]=>[1,7,6,8,4,3,2,5]=>0111010=>1000101
[3,4,8,1,2,7,6,5]=>[7,6,8,1,4,3,2,5]=>1110010=>0001101
[4,2,5,8,1,7,6,3]=>[2,7,6,8,1,5,4,3]=>1011010=>0100101
[4,3,1,2,5,8,7,6]=>[3,1,4,2,5,7,8,6]=>1100010=>0011101
[2,3,5,1,8,7,6,4]=>[7,6,8,5,3,2,1,4]=>1110110=>0001001
[7,8,2,1,5,3,6,4]=>[5,8,2,6,7,1,3,4]=>1100000=>0011111
[2,3,7,5,4,1,8,6]=>[5,4,8,7,3,2,1,6]=>1111001=>0000110
[7,8,3,5,4,1,6,2]=>[3,5,4,8,1,6,7,2]=>1101000=>0010111
[7,8,2,5,4,1,3,6]=>[5,4,8,2,7,1,3,6]=>1101000=>0010111
[7,8,2,5,4,6,1,3]=>[5,4,6,8,2,7,1,3]=>1101000=>0010111
[6,2,1,5,4,7,3,8]=>[2,5,4,7,6,1,3,8]=>1001010=>0110101
[5,3,6,2,4,7,1,8]=>[7,6,3,2,4,5,1,8]=>1110010=>0001101
[6,4,2,1,7,3,8,5]=>[4,2,8,7,1,3,6,5]=>1100101=>0011010
[4,3,7,5,8,6,1,2]=>[6,8,5,3,1,7,4,2]=>1111100=>0000011
[3,2,6,7,4,8,1,5]=>[2,8,4,7,6,3,1,5]=>1011010=>0100101
[1,7,6,5,2,4,8,3]=>[1,5,2,6,4,8,7,3]=>0111001=>1000110
[2,7,1,4,8,3,5,6]=>[4,8,2,1,3,7,5,6]=>1100100=>0011011
[3,7,6,4,8,5,1,2]=>[4,8,5,6,1,7,3,2]=>1110100=>0001011
[4,7,6,5,1,8,3,2]=>[5,1,8,6,3,7,4,2]=>1111010=>0000101
[1,7,6,5,2,8,3,4]=>[1,5,2,8,6,3,7,4]=>0111010=>1000101
[1,7,6,5,3,2,8,4]=>[1,5,3,6,2,8,7,4]=>0111001=>1000110
[4,7,6,5,1,2,8,3]=>[5,1,6,2,8,7,4,3]=>1111001=>0000110
[4,7,6,5,3,1,8,2]=>[5,3,6,1,8,7,4,2]=>1111001=>0000110
[6,1,3,5,4,8,7,2]=>[3,5,4,7,8,6,1,2]=>1001010=>0110101
[5,2,6,3,4,1,7,8]=>[2,6,3,4,5,1,7,8]=>1010000=>0101111
[5,1,6,2,4,7,8,3]=>[8,7,6,1,2,4,5,3]=>1010011=>0101100
[1,2,6,3,4,8,7,5]=>[1,2,7,8,6,3,4,5]=>0010010=>1101101
[1,7,2,4,8,3,6,5]=>[1,4,8,2,3,6,7,5]=>0100100=>1011011
[6,1,4,2,8,3,5,7]=>[4,1,2,8,3,6,5,7]=>1010100=>0101011
[4,7,2,1,5,3,6,8]=>[5,7,2,4,1,3,6,8]=>1100000=>0011111
[4,7,1,6,2,3,8,5]=>[6,1,8,7,4,2,3,5]=>1101001=>0010110
[1,7,2,6,8,3,5,4]=>[1,8,2,3,6,5,7,4]=>0101100=>1010011
[4,7,1,2,5,3,8,6]=>[5,8,7,1,4,2,3,6]=>1100001=>0011110
[3,7,6,5,2,4,1,8]=>[5,2,6,4,7,3,1,8]=>1111000=>0000111
[3,7,6,5,2,1,8,4]=>[5,2,6,3,1,8,7,4]=>1111001=>0000110
[3,7,6,5,1,2,4,8]=>[5,1,6,3,2,7,4,8]=>1111000=>0000111
[3,1,6,8,4,2,5,7]=>[8,4,6,3,1,2,5,7]=>1011000=>0100111
[4,7,6,8,3,5,1,2]=>[8,3,5,6,1,7,4,2]=>1111000=>0000111
[2,7,6,5,1,4,3,8]=>[5,2,1,6,4,7,3,8]=>1111000=>0000111
[2,7,6,5,8,1,3,4]=>[8,5,2,1,6,3,7,4]=>1111100=>0000011
[6,3,2,1,7,4,8,5]=>[3,2,8,7,1,4,6,5]=>1100101=>0011010
[4,2,1,7,3,5,8,6]=>[2,8,7,4,1,3,5,6]=>1001001=>0110110
[7,3,1,5,4,2,8,6]=>[3,1,5,4,8,7,2,6]=>1101001=>0010110
[8,4,1,5,2,7,6,3]=>[5,4,1,7,6,8,2,3]=>1101010=>0010101
[8,2,5,1,3,7,6,4]=>[2,5,1,7,6,8,3,4]=>1010010=>0101101
[4,3,7,2,1,5,8,6]=>[8,7,3,2,4,1,5,6]=>1110001=>0001110
[6,3,7,4,2,1,8,5]=>[4,8,7,3,2,6,1,5]=>1110001=>0001110
[4,7,2,5,3,1,8,6]=>[5,2,3,8,7,4,1,6]=>1101001=>0010110
[2,7,5,4,1,3,8,6]=>[4,5,2,1,8,7,3,6]=>1110001=>0001110
[7,5,4,3,2,1,8,6]=>[4,3,5,2,8,7,1,6]=>1110001=>0001110
[6,5,2,1,8,4,3,7]=>[8,5,2,4,6,1,3,7]=>1100100=>0011011
[5,7,4,3,2,8,1,6]=>[4,3,8,2,5,1,7,6]=>1110010=>0001101
[1,7,6,2,4,8,3,5]=>[1,8,6,2,4,7,3,5]=>0110010=>1001101
[2,7,3,6,4,8,1,5]=>[3,8,6,4,7,2,1,5]=>1101010=>0010101
[6,2,7,5,3,8,1,4]=>[2,5,3,8,1,7,6,4]=>1011010=>0100101
[7,1,8,5,3,6,4,2]=>[5,3,6,8,4,7,1,2]=>1011000=>0100111
[5,8,1,6,2,7,4,3]=>[7,6,1,8,4,5,2,3]=>1101010=>0010101
[1,8,6,2,3,7,5,4]=>[1,7,6,2,5,8,3,4]=>0110010=>1001101
[1,8,6,3,2,7,5,4]=>[1,7,6,3,5,8,2,4]=>0110010=>1001101
[5,8,3,2,7,1,6,4]=>[3,7,2,6,8,5,1,4]=>1100100=>0011011
[8,7,3,1,6,5,4,2]=>[3,6,5,7,1,4,8,2]=>1100100=>0011011
[1,8,5,7,4,3,6,2]=>[1,7,4,5,3,6,8,2]=>0111000=>1000111
[1,8,5,7,2,4,6,3]=>[1,7,2,5,4,6,8,3]=>0111000=>1000111
[3,8,6,1,7,2,5,4]=>[7,1,6,5,8,3,2,4]=>1110100=>0001011
[5,8,4,6,7,1,3,2]=>[7,4,1,6,3,8,5,2]=>1111100=>0000011
[6,3,7,5,8,2,1,4]=>[8,5,3,2,7,1,6,4]=>1111100=>0000011
[3,7,2,6,8,4,1,5]=>[8,4,6,2,3,1,7,5]=>1101100=>0010011
[2,6,5,8,4,1,3,7]=>[8,4,5,2,1,6,3,7]=>1111000=>0000111
[6,5,4,8,3,2,1,7]=>[8,4,3,5,2,6,1,7]=>1111000=>0000111
[8,4,3,7,2,1,6,5]=>[3,7,4,2,6,8,1,5]=>1101000=>0010111
[8,2,4,7,1,3,6,5]=>[2,7,4,1,6,8,3,5]=>1011000=>0100111
[4,3,6,8,2,1,5,7]=>[8,3,2,6,4,1,5,7]=>1111000=>0000111
[8,4,1,5,7,3,6,2]=>[7,5,4,1,3,6,8,2]=>1101100=>0010011
[6,4,2,5,8,3,1,7]=>[8,5,4,2,3,6,1,7]=>1101100=>0010011
[5,4,1,6,8,2,3,7]=>[8,4,1,6,5,2,3,7]=>1101100=>0010011
[6,5,2,1,7,8,3,4]=>[8,5,2,7,6,1,3,4]=>1100110=>0011001
[4,7,2,5,8,6,3,1]=>[6,8,5,2,3,7,4,1]=>1101100=>0010011
[6,5,3,8,7,4,1,2]=>[3,7,4,8,5,1,6,2]=>1101100=>0010011
[8,5,3,7,6,4,2,1]=>[3,6,4,7,5,2,8,1]=>1101100=>0010011
[5,4,8,1,7,6,2,3]=>[6,7,1,4,2,8,5,3]=>1110100=>0001011
[6,4,8,2,1,7,5,3]=>[7,2,4,1,5,8,6,3]=>1110010=>0001101
[5,7,3,8,1,6,4,2]=>[3,6,8,1,7,4,5,2]=>1101000=>0010111
[6,3,7,8,5,2,4,1]=>[5,8,3,2,7,4,6,1]=>1111000=>0000111
[2,5,8,7,1,3,6,4]=>[7,2,1,6,8,3,5,4]=>1111000=>0000111
[5,3,8,7,2,1,6,4]=>[7,3,2,6,8,1,5,4]=>1111000=>0000111
[8,2,7,6,5,1,4,3]=>[2,5,6,1,7,4,8,3]=>1011000=>0100111
[4,3,8,7,6,2,1,5]=>[6,3,2,7,4,1,8,5]=>1111100=>0000011
[2,4,8,7,6,1,3,5]=>[6,2,1,7,4,3,8,5]=>1111100=>0000011
[3,5,8,7,2,6,1,4]=>[6,7,2,8,3,1,5,4]=>1111000=>0000111
[4,7,3,8,6,5,1,2]=>[3,6,5,8,1,7,4,2]=>1101100=>0010011
[7,5,8,6,4,3,2,1]=>[6,4,8,3,5,2,7,1]=>1111000=>0000111
[5,8,7,3,6,4,2,1]=>[6,3,4,7,2,8,5,1]=>1110100=>0001011
[3,4,1,2,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>11000000=>00111111
[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>10000000=>01111111
[4,3,2,1,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>11000000=>00111111
[5,4,3,2,1,6,7,8,9]=>[3,4,2,5,1,6,7,8,9]=>11000000=>00111111
[6,5,4,3,2,1,7,8,9]=>[4,3,5,2,6,1,7,8,9]=>11100000=>00011111
[7,6,5,4,3,2,1,8,9]=>[4,5,3,6,2,7,1,8,9]=>11100000=>00011111
[3,4,1,2,5,6,7,8,9,10]=>[4,1,3,2,5,6,7,8,9,10]=>110000000=>001111111
[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>100000000=>011111111
[4,3,2,1,5,6,7,8,9,10]=>[3,2,4,1,5,6,7,8,9,10]=>110000000=>001111111
[5,4,3,2,1,6,7,8,9,10]=>[3,4,2,5,1,6,7,8,9,10]=>110000000=>001111111
[6,5,4,3,2,1,7,8,9,10]=>[4,3,5,2,6,1,7,8,9,10]=>111000000=>000111111
[7,6,5,4,3,2,1,8,9,10]=>[4,5,3,6,2,7,1,8,9,10]=>111000000=>000111111
[8,7,6,5,4,3,2,1,9,10]=>[5,4,6,3,7,2,8,1,9,10]=>111100000=>000011111
[3,6,5,1,2,4,8,7]=>[5,1,6,3,2,4,8,7]=>1110001=>0001110
[3,7,5,8,2,4,1,6]=>[8,2,5,4,7,3,1,6]=>1111000=>0000111
[5,1,7,8,4,3,2,6]=>[8,4,7,3,5,1,2,6]=>1011000=>0100111
[5,1,2,6,4,3,8,7]=>[6,4,5,1,2,3,8,7]=>1001001=>0110110
[6,1,2,5,4,3,8,7]=>[5,4,6,1,2,3,8,7]=>1001001=>0110110
[5,1,2,4,6,3,8,7]=>[4,6,5,1,2,3,8,7]=>1000101=>0111010
[4,1,2,6,5,3,8,7]=>[5,6,4,1,2,3,8,7]=>1001001=>0110110
[4,1,5,7,8,3,2,6]=>[8,3,7,5,4,1,2,6]=>1011100=>0100011
[4,1,5,8,7,3,2,6]=>[7,3,8,5,4,1,2,6]=>1011100=>0100011
[4,1,7,8,5,2,3,6]=>[5,8,1,2,7,4,3,6]=>1011000=>0100111
[5,1,7,4,8,2,3,6]=>[4,8,1,2,7,5,3,6]=>1010100=>0101011
[7,5,3,8,1,4,2,6]=>[3,8,1,5,4,7,2,6]=>1101000=>0010111
[2,1,5,8,7,3,4,6]=>[2,1,7,3,8,5,4,6]=>1011100=>0100011
[5,1,8,4,7,2,3,6]=>[4,7,1,2,8,5,3,6]=>1010100=>0101011
[6,1,2,3,7,5,8,4]=>[8,7,5,6,1,2,3,4]=>1000101=>0111010
[7,1,2,3,8,6,5,4]=>[6,8,5,7,1,2,3,4]=>1000100=>0111011
[7,1,2,3,5,8,6,4]=>[5,8,6,7,1,2,3,4]=>1000010=>0111101
[8,7,3,2,4,1,6,5]=>[3,7,2,4,6,8,1,5]=>1100000=>0011111
[2,1,7,3,4,8,6,5]=>[2,1,8,6,7,3,4,5]=>1010010=>0101101
[7,8,3,2,4,1,6,5]=>[3,8,2,4,6,7,1,5]=>1100000=>0011111
[6,7,1,4,3,8,2,5]=>[4,8,1,3,7,6,2,5]=>1100010=>0011101
[8,1,2,3,5,7,6,4]=>[5,7,6,8,1,2,3,4]=>1000010=>0111101
[8,1,2,3,6,7,5,4]=>[7,6,5,8,1,2,3,4]=>1000110=>0111001
[7,1,2,3,6,8,5,4]=>[8,6,5,7,1,2,3,4]=>1000110=>0111001
[7,1,2,3,8,5,6,4]=>[8,5,6,7,1,2,3,4]=>1000100=>0111011
[8,1,2,3,7,5,6,4]=>[7,5,6,8,1,2,3,4]=>1000100=>0111011
[8,1,2,3,6,5,7,4]=>[6,5,7,8,1,2,3,4]=>1000100=>0111011
[7,1,8,5,4,3,2,6]=>[5,4,8,3,7,1,2,6]=>1011000=>0100111
[6,8,2,7,3,4,1,5]=>[7,2,3,8,4,6,1,5]=>1101000=>0010111
[6,7,2,8,3,4,1,5]=>[8,2,3,7,4,6,1,5]=>1101000=>0010111
[3,7,8,1,4,2,6,5]=>[8,1,4,6,7,3,2,5]=>1110000=>0001111
[3,6,8,1,4,2,7,5]=>[7,8,1,4,6,3,2,5]=>1110000=>0001111
[3,5,7,8,2,4,1,6]=>[8,2,7,4,5,3,1,6]=>1111000=>0000111
[3,6,7,1,4,2,8,5]=>[8,7,1,4,6,3,2,5]=>1110001=>0001110
[8,6,2,7,3,1,4,5]=>[7,2,3,6,1,8,4,5]=>1101000=>0010111
[8,1,7,5,4,3,2,6]=>[5,4,7,3,8,1,2,6]=>1011000=>0100111
[5,8,3,7,1,4,2,6]=>[3,7,1,8,4,5,2,6]=>1101000=>0010111
[2,1,7,3,4,6,8,5]=>[2,1,6,8,7,3,4,5]=>1010001=>0101110
[6,7,3,2,4,1,8,5]=>[3,8,7,2,4,6,1,5]=>1100001=>0011110
[8,7,2,4,3,6,1,5]=>[4,6,7,2,3,8,1,5]=>1100000=>0011111
[7,1,2,3,5,6,8,4]=>[5,6,8,7,1,2,3,4]=>1000001=>0111110
[6,1,2,3,8,7,4,5]=>[7,1,2,3,4,8,6,5]=>1000110=>0111001
[5,1,2,3,7,8,6,4]=>[8,6,7,5,1,2,3,4]=>1000110=>0111001
[5,1,2,3,8,7,6,4]=>[7,6,8,5,1,2,3,4]=>1000110=>0111001
[5,1,2,3,8,6,7,4]=>[6,7,8,5,1,2,3,4]=>1000100=>0111011
[6,1,2,3,5,8,7,4]=>[5,7,8,6,1,2,3,4]=>1000010=>0111101
[8,6,2,4,3,1,7,5]=>[4,6,2,3,7,8,1,5]=>1100000=>0011111
[7,6,3,2,4,8,1,5]=>[3,8,6,2,4,7,1,5]=>1100010=>0011101
[2,1,6,3,4,8,7,5]=>[2,1,7,8,6,3,4,5]=>1010010=>0101101
[8,6,3,2,4,7,1,5]=>[3,7,6,2,4,8,1,5]=>1100010=>0011101
[6,1,2,3,5,7,8,4]=>[5,8,7,6,1,2,3,4]=>1000011=>0111100
[5,1,2,3,6,8,7,4]=>[7,8,6,5,1,2,3,4]=>1000110=>0111001
[7,8,1,2,6,3,5,4]=>[6,1,8,5,7,2,3,4]=>1100100=>0011011
[1,4,8,2,7,3,5,6]=>[1,7,2,4,3,8,5,6]=>0110100=>1001011
[1,2,8,5,4,7,3,6]=>[1,2,5,4,7,3,8,6]=>0011010=>1100101
[3,4,8,5,7,6,1,2]=>[6,7,5,1,8,4,3,2]=>1111100=>0000011
[1,2,6,8,4,5,7,3]=>[1,2,7,8,4,5,6,3]=>0011000=>1100111
[7,5,1,2,4,3,6,8]=>[5,1,4,7,2,3,6,8]=>1100000=>0011111
[7,4,6,1,5,2,3,8]=>[5,6,1,4,2,7,3,8]=>1110000=>0001111
[7,1,4,2,6,3,5,8]=>[4,1,2,6,3,7,5,8]=>1010100=>0101011
[1,6,4,2,8,3,5,7]=>[1,4,2,8,3,6,5,7]=>0110100=>1001011
[7,2,1,4,6,3,5,8]=>[2,4,6,1,3,7,5,8]=>1000100=>0111011
[7,2,3,6,5,1,4,8]=>[2,3,5,6,1,7,4,8]=>1001000=>0110111
[7,1,2,3,6,5,4,8]=>[6,5,7,1,2,3,4,8]=>1000100=>0111011
[6,8,1,2,7,3,5,4]=>[7,1,8,5,6,2,3,4]=>1100100=>0011011
[1,6,2,3,8,5,4,7]=>[1,8,5,6,2,3,4,7]=>0100100=>1011011
[5,1,8,2,7,6,3,4]=>[6,7,1,2,8,5,3,4]=>1010100=>0101011
[5,8,2,7,6,3,4,1]=>[6,2,3,7,4,8,5,1]=>1101100=>0010011
[6,2,8,1,7,3,5,4]=>[2,7,1,8,5,6,3,4]=>1010100=>0101011
[6,8,2,1,7,4,3,5]=>[7,2,4,8,1,3,6,5]=>1100100=>0011011
[2,5,1,8,7,6,3,4]=>[6,7,2,1,3,8,5,4]=>1101100=>0010011
[1,2,5,3,8,7,4,6]=>[1,2,7,5,3,4,8,6]=>0010110=>1101001
[2,4,8,7,6,5,1,3]=>[6,5,7,2,1,8,4,3]=>1111100=>0000011
[2,5,8,4,1,7,6,3]=>[4,7,6,8,2,1,5,3]=>1110010=>0001101
[3,5,8,7,1,4,2,6]=>[7,1,8,4,5,3,2,6]=>1111000=>0000111
[5,3,8,4,1,7,6,2]=>[4,7,6,8,3,1,5,2]=>1110010=>0001101
[4,2,8,7,6,3,5,1]=>[2,6,3,7,5,8,4,1]=>1011100=>0100011
[4,2,8,7,6,5,3,1]=>[2,6,5,7,3,8,4,1]=>1011100=>0100011
[4,1,8,7,6,5,3,2]=>[6,5,7,3,8,4,1,2]=>1011100=>0100011
[4,3,8,7,6,5,1,2]=>[6,5,7,3,1,8,4,2]=>1111100=>0000011
[6,3,1,8,7,2,5,4]=>[3,1,7,2,8,5,6,4]=>1101100=>0010011
[1,5,8,4,7,2,6,3]=>[1,4,7,2,6,8,5,3]=>0110100=>1001011
[6,8,5,1,2,4,7,3]=>[5,1,7,8,2,4,6,3]=>1110000=>0001111
[5,6,3,1,2,4,8,7]=>[3,6,1,5,2,4,8,7]=>1100001=>0011110
[5,6,2,4,3,1,8,7]=>[4,6,2,3,5,1,8,7]=>1100001=>0011110
[4,5,8,1,7,2,6,3]=>[7,1,6,8,5,2,4,3]=>1110100=>0001011
[1,3,2,5,8,7,4,6]=>[1,3,2,7,5,4,8,6]=>0101110=>1010001
[3,5,1,8,7,4,6,2]=>[7,4,6,8,5,1,3,2]=>1101100=>0010011
[3,5,1,8,7,2,6,4]=>[7,1,3,2,6,8,5,4]=>1101100=>0010011
[4,3,6,1,2,8,5,7]=>[8,6,3,1,4,2,5,7]=>1110010=>0001101
[4,5,8,3,1,7,2,6]=>[7,3,5,1,4,2,8,6]=>1110010=>0001101
[4,5,2,8,7,1,3,6]=>[7,2,8,5,4,1,3,6]=>1101100=>0010011
[3,4,8,7,6,5,1,2]=>[6,5,7,1,8,4,3,2]=>1111100=>0000011
[1,3,4,8,7,6,2,5]=>[1,6,7,4,3,2,8,5]=>0111100=>1000011
[3,2,5,8,7,4,6,1]=>[2,7,4,6,8,5,3,1]=>1011100=>0100011
[4,5,8,3,1,7,6,2]=>[7,6,8,3,5,1,4,2]=>1110010=>0001101
[2,1,3,5,8,7,4,6]=>[2,1,3,7,5,4,8,6]=>1001110=>0110001
[1,2,7,5,8,6,4,3]=>[1,2,6,8,5,4,7,3]=>0011100=>1100011
[7,1,4,8,2,6,5,3]=>[6,8,4,1,2,5,7,3]=>1011000=>0100111
[6,8,1,3,7,5,2,4]=>[7,5,8,1,3,6,2,4]=>1100100=>0011011
[3,7,8,1,2,6,5,4]=>[6,8,1,5,7,3,2,4]=>1110000=>0001111
[1,3,7,8,2,6,5,4]=>[1,6,8,3,2,5,7,4]=>0111000=>1000111
[2,7,8,1,3,6,5,4]=>[6,8,2,1,5,7,3,4]=>1110000=>0001111
[8,1,2,6,7,3,5,4]=>[7,1,2,3,6,5,8,4]=>1001100=>0110011
[8,1,2,6,7,5,3,4]=>[7,5,6,1,2,3,8,4]=>1001100=>0110011
[8,2,5,7,1,3,6,4]=>[2,7,1,5,3,6,8,4]=>1011000=>0100111
[2,6,8,3,7,1,5,4]=>[7,3,8,5,6,2,1,4]=>1110100=>0001011
[2,8,6,4,7,1,5,3]=>[4,7,2,1,6,5,8,3]=>1110100=>0001011
[6,8,3,4,1,7,5,2]=>[3,4,7,1,5,8,6,2]=>1100010=>0011101
[2,6,8,3,7,5,1,4]=>[7,5,8,3,6,2,1,4]=>1110100=>0001011
[2,8,1,6,7,5,3,4]=>[7,5,6,2,1,3,8,4]=>1101100=>0010011
[8,4,7,2,3,6,1,5]=>[6,7,2,4,3,8,1,5]=>1110000=>0001111
[8,5,7,4,2,6,1,3]=>[4,6,7,2,5,1,8,3]=>1110000=>0001111
[8,3,5,7,4,1,6,2]=>[7,4,5,3,1,6,8,2]=>1111000=>0000111
[8,2,4,7,3,6,1,5]=>[2,6,7,4,3,8,1,5]=>1011000=>0100111
[8,2,7,1,4,6,3,5]=>[2,6,7,1,4,8,3,5]=>1010000=>0101111
[8,7,1,4,6,2,3,5]=>[4,6,1,7,2,3,8,5]=>1100100=>0011011
[8,4,7,1,3,6,2,5]=>[6,7,1,4,3,8,2,5]=>1110000=>0001111
[1,6,8,3,7,2,5,4]=>[1,7,3,8,5,6,2,4]=>0110100=>1001011
[5,8,7,1,3,6,2,4]=>[6,7,1,8,3,5,2,4]=>1110000=>0001111
[8,5,4,7,1,6,2,3]=>[6,7,4,1,5,2,8,3]=>1111000=>0000111
[8,5,4,7,1,2,6,3]=>[7,4,1,5,2,6,8,3]=>1111000=>0000111
[8,5,1,4,7,2,6,3]=>[4,7,5,1,6,8,2,3]=>1100100=>0011011
[1,4,6,8,2,7,5,3]=>[1,7,2,5,8,6,4,3]=>0111010=>1000101
[8,5,6,3,1,7,4,2]=>[7,6,3,5,1,4,8,2]=>1110010=>0001101
[5,6,2,8,1,7,4,3]=>[7,2,8,6,4,5,1,3]=>1101010=>0010101
[5,8,7,3,6,1,2,4]=>[6,3,7,1,8,5,2,4]=>1110100=>0001011
[8,3,5,7,1,6,2,4]=>[6,7,3,1,5,2,8,4]=>1111000=>0000111
[6,3,8,2,7,5,1,4]=>[7,5,8,3,2,6,1,4]=>1110100=>0001011
[6,8,4,2,7,1,5,3]=>[4,2,7,1,8,5,6,3]=>1110100=>0001011
[8,4,5,7,3,1,6,2]=>[7,3,5,4,1,6,8,2]=>1111000=>0000111
[8,4,2,5,7,1,6,3]=>[7,5,4,2,6,8,1,3]=>1101100=>0010011
[8,7,1,3,4,6,2,5]=>[6,7,1,3,4,8,2,5]=>1100000=>0011111
[8,3,7,2,4,6,1,5]=>[6,7,3,2,4,8,1,5]=>1110000=>0001111
[2,8,4,5,7,1,6,3]=>[7,5,4,2,1,6,8,3]=>1111100=>0000011
[8,7,4,5,2,6,1,3]=>[5,4,2,6,7,1,8,3]=>1111000=>0000111
[5,8,7,2,3,6,1,4]=>[6,7,2,8,3,5,1,4]=>1110000=>0001111
[8,7,2,3,4,6,1,5]=>[6,7,2,3,4,8,1,5]=>1100000=>0011111
[1,3,2,8,5,4,7,6]=>[1,3,2,5,7,8,4,6]=>0101000=>1010111
[4,2,8,5,3,7,1,6]=>[2,5,3,7,4,1,8,6]=>1011010=>0100101
[5,2,1,8,4,3,7,6]=>[2,7,8,4,5,1,3,6]=>1001000=>0110111
[6,2,8,4,3,7,5,1]=>[2,4,7,3,5,8,6,1]=>1010010=>0101101
[7,2,8,4,3,1,6,5]=>[2,4,8,3,6,7,1,5]=>1010000=>0101111
[7,3,4,8,2,1,6,5]=>[8,4,3,2,6,7,1,5]=>1111000=>0000111
[5,3,4,1,8,2,7,6]=>[4,3,1,7,8,5,2,6]=>1110100=>0001011
[8,1,4,5,2,3,7,6]=>[5,4,1,2,7,8,3,6]=>1011000=>0100111
[8,1,5,4,3,2,7,6]=>[4,5,3,7,8,1,2,6]=>1010000=>0101111
[3,5,4,2,8,1,7,6]=>[4,2,7,8,5,3,1,6]=>1110100=>0001011
[4,5,3,2,8,7,1,6]=>[3,7,5,2,4,1,8,6]=>1100110=>0011001
[6,4,3,2,8,7,5,1]=>[3,4,2,7,5,8,6,1]=>1100110=>0011001
[5,6,3,2,7,8,4,1]=>[3,8,2,4,7,6,5,1]=>1100110=>0011001
[4,1,6,3,2,7,8,5]=>[8,7,6,3,4,1,2,5]=>1010011=>0101100
[3,6,4,2,7,8,1,5]=>[4,2,8,3,1,7,6,5]=>1110110=>0001001
[8,1,6,4,3,7,2,5]=>[4,7,6,3,8,1,2,5]=>1010010=>0101101
[8,1,7,4,3,6,5,2]=>[4,6,7,3,5,8,1,2]=>1010000=>0101111
[2,7,4,1,3,6,5,8]=>[4,2,1,6,7,3,5,8]=>1110000=>0001111
[3,7,4,2,6,1,5,8]=>[4,2,6,3,1,7,5,8]=>1110100=>0001011
[4,1,7,3,2,6,5,8]=>[6,7,3,4,1,2,5,8]=>1010000=>0101111
[6,7,3,2,5,4,1,8]=>[3,5,7,2,4,6,1,8]=>1100000=>0011111
[7,6,3,2,1,5,4,8]=>[3,6,2,5,7,1,4,8]=>1100000=>0011111
[3,1,7,5,6,2,4,8]=>[6,5,3,1,2,7,4,8]=>1011100=>0100011
[2,7,5,6,1,3,4,8]=>[6,2,1,5,3,7,4,8]=>1111000=>0000111
[2,6,5,7,1,3,8,4]=>[8,7,2,1,5,3,6,4]=>1111001=>0000110
[4,6,5,7,2,8,1,3]=>[8,2,5,1,7,6,4,3]=>1111010=>0000101
[7,5,4,6,2,1,8,3]=>[6,4,2,5,1,8,7,3]=>1111001=>0000110
[6,4,5,7,1,8,2,3]=>[8,1,5,4,2,7,6,3]=>1111010=>0000101
[8,1,5,6,7,2,3,4]=>[7,1,2,6,5,3,8,4]=>1011100=>0100011
[2,1,4,6,8,7,3,5]=>[2,1,7,4,3,8,6,5]=>1011110=>0100001
[3,4,6,8,7,1,2,5]=>[7,1,8,4,3,2,6,5]=>1111100=>0000011
[4,3,1,6,8,7,2,5]=>[3,1,7,4,2,8,6,5]=>1101110=>0010001
[5,3,6,8,7,2,4,1]=>[7,3,2,8,4,6,5,1]=>1111100=>0000011
[6,3,5,1,8,7,2,4]=>[7,5,3,1,8,6,2,4]=>1110110=>0001001
[7,3,5,8,6,2,1,4]=>[6,3,2,8,5,1,7,4]=>1111100=>0000011
[7,2,8,5,6,3,1,4]=>[2,6,5,3,8,1,7,4]=>1011100=>0100011
[6,2,8,5,1,7,3,4]=>[2,5,1,7,3,8,6,4]=>1011010=>0100101
[4,2,1,8,6,7,3,5]=>[2,7,6,4,1,3,8,5]=>1001110=>0110001
[2,3,8,6,7,1,4,5]=>[7,3,2,1,6,4,8,5]=>1111100=>0000011
[8,1,3,2,6,7,4,5]=>[3,7,6,1,2,4,8,5]=>1000110=>0111001
[4,2,8,7,6,1,5,3]=>[2,6,1,7,5,8,4,3]=>1011100=>0100011
[5,2,8,7,6,4,1,3]=>[2,6,4,7,1,8,5,3]=>1011100=>0100011
[7,2,1,8,6,5,4,3]=>[2,6,5,8,4,7,1,3]=>1001100=>0110011
[6,3,7,8,5,4,2,1]=>[5,8,4,7,3,2,6,1]=>1111000=>0000111
[5,3,7,8,6,4,1,2]=>[6,4,8,3,1,7,5,2]=>1111100=>0000011
[4,3,1,7,8,6,5,2]=>[3,1,6,8,5,7,4,2]=>1101100=>0010011
[3,4,7,8,6,1,5,2]=>[6,1,8,5,7,4,3,2]=>1111100=>0000011
[3,5,7,6,8,1,4,2]=>[8,1,6,4,7,5,3,2]=>1111100=>0000011
[5,4,1,7,6,8,3,2]=>[8,6,4,1,3,7,5,2]=>1101110=>0010001
[6,4,7,5,8,3,2,1]=>[8,5,3,7,4,2,6,1]=>1111100=>0000011
[7,5,6,4,3,1,8,2]=>[4,6,3,5,1,8,7,2]=>1110001=>0001110
[6,5,1,7,4,3,8,2]=>[8,7,4,5,1,3,6,2]=>1101001=>0010110
[4,6,7,5,3,8,1,2]=>[5,3,8,1,7,6,4,2]=>1111010=>0000101
[3,6,7,5,1,4,8,2]=>[5,1,8,7,4,6,3,2]=>1111001=>0000110
[8,1,7,6,5,4,3,2]=>[5,6,4,7,3,8,1,2]=>1011000=>0100111
[8,6,4,3,1,5,7,2]=>[4,3,6,1,5,7,8,2]=>1110000=>0001111
[8,6,5,1,3,2,7,4]=>[5,1,6,3,7,8,2,4]=>1110000=>0001111
[8,6,3,1,7,2,4,5]=>[3,7,1,6,2,4,8,5]=>1100100=>0011011
[5,3,1,7,2,4,6,8]=>[3,1,7,2,5,4,6,8]=>1101000=>0010111
[8,7,1,2,4,5,3,6]=>[7,1,4,5,8,2,3,6]=>1100000=>0011111
[8,6,1,2,4,7,3,5]=>[7,6,1,4,8,2,3,5]=>1100010=>0011101
[8,5,1,2,6,7,3,4]=>[7,6,5,1,8,2,3,4]=>1100110=>0011001
[8,5,1,6,4,2,7,3]=>[6,4,5,1,7,8,2,3]=>1101000=>0010111
[8,6,1,5,2,4,7,3]=>[5,1,6,4,7,8,2,3]=>1101000=>0010111
[8,6,1,2,5,7,3,4]=>[5,7,6,1,8,2,3,4]=>1100010=>0011101
[8,6,1,2,7,4,3,5]=>[7,1,4,6,2,3,8,5]=>1100100=>0011011
[8,7,1,2,5,4,3,6]=>[5,7,1,4,8,2,3,6]=>1100000=>0011111
[5,1,4,2,3,8,6,7]=>[4,1,2,5,3,8,6,7]=>1010010=>0101101
[7,1,5,8,2,6,3,4]=>[6,8,1,2,5,3,7,4]=>1011000=>0100111
[5,7,8,1,2,4,6,3]=>[8,1,6,7,2,4,5,3]=>1110000=>0001111
[8,4,1,2,7,6,3,5]=>[4,1,6,7,2,3,8,5]=>1100100=>0011011
[1,4,2,3,8,7,5,6]=>[1,4,2,3,7,5,8,6]=>0100110=>1011001
[1,4,2,7,6,3,5,8]=>[1,6,4,2,3,7,5,8]=>0101100=>1010011
[6,1,2,8,7,5,3,4]=>[7,5,8,1,2,3,6,4]=>1001100=>0110011
[6,1,2,4,8,7,5,3]=>[4,7,5,8,6,1,2,3]=>1000110=>0111001
[3,1,7,6,4,8,5,2]=>[8,6,4,5,7,3,1,2]=>1011010=>0100101
[7,1,2,4,6,8,5,3]=>[4,8,6,5,7,1,2,3]=>1000110=>0111001
[6,1,2,7,8,5,3,4]=>[8,5,7,1,2,3,6,4]=>1001100=>0110011
[6,1,2,7,4,8,5,3]=>[8,4,5,7,6,1,2,3]=>1001010=>0110101
[3,1,6,4,7,8,5,2]=>[4,8,5,7,6,3,1,2]=>1010110=>0101001
[5,7,1,3,8,4,6,2]=>[8,1,3,4,6,7,5,2]=>1100100=>0011011
[5,7,1,8,4,2,6,3]=>[8,4,6,7,1,5,2,3]=>1101000=>0010111
[7,1,4,5,2,8,6,3]=>[5,4,1,2,8,6,7,3]=>1011010=>0100101
[4,7,3,1,5,8,6,2]=>[3,5,8,6,7,1,4,2]=>1100010=>0011101
[4,8,7,3,1,5,6,2]=>[7,3,5,6,8,1,4,2]=>1110000=>0001111
[8,1,7,4,5,2,6,3]=>[4,5,7,1,2,6,8,3]=>1010000=>0101111
[8,1,7,5,3,2,6,4]=>[5,3,7,1,2,6,8,4]=>1011000=>0100111
[8,3,7,1,2,6,4,5]=>[6,7,3,1,8,2,4,5]=>1110000=>0001111
[3,1,7,2,6,4,5,8]=>[6,3,1,2,4,7,5,8]=>1010100=>0101011
[1,4,2,3,8,5,7,6]=>[1,4,2,3,7,8,5,6]=>0100100=>1011011
[5,8,1,3,4,7,6,2]=>[7,6,8,1,3,4,5,2]=>1100010=>0011101
[3,1,8,6,4,7,5,2]=>[7,6,4,5,8,3,1,2]=>1011010=>0100101
[8,1,2,6,7,4,5,3]=>[7,4,6,5,8,1,2,3]=>1001100=>0110011
[6,1,2,8,7,3,5,4]=>[7,1,2,3,8,5,6,4]=>1001100=>0110011
[1,2,3,5,8,4,7,6]=>[1,2,3,7,8,5,4,6]=>0001100=>1110011
[1,2,3,5,8,6,4,7]=>[1,2,3,6,8,5,4,7]=>0001100=>1110011
[7,1,2,8,6,4,5,3]=>[6,4,8,5,7,1,2,3]=>1001100=>0110011
[3,1,8,7,6,4,5,2]=>[6,4,7,5,8,3,1,2]=>1011100=>0100011
[8,1,2,7,4,6,5,3]=>[6,7,4,5,8,1,2,3]=>1001000=>0110111
[8,1,2,7,3,6,5,4]=>[6,7,1,2,3,5,8,4]=>1001000=>0110111
[1,2,3,5,8,7,4,6]=>[1,2,3,7,5,4,8,6]=>0001110=>1110001
[1,2,3,6,8,5,4,7]=>[1,2,3,8,5,6,4,7]=>0001100=>1110011
[7,8,5,6,3,1,4,2]=>[6,3,5,1,8,4,7,2]=>1111000=>0000111
[7,8,5,3,6,1,2,4]=>[6,5,3,8,1,7,2,4]=>1110100=>0001011
[7,5,8,3,1,4,2,6]=>[8,3,5,1,4,7,2,6]=>1110000=>0001111
[7,8,5,3,1,4,2,6]=>[5,3,8,1,4,7,2,6]=>1110000=>0001111
[7,8,5,3,1,6,2,4]=>[5,3,6,8,1,7,2,4]=>1110000=>0001111
[7,8,5,3,1,6,4,2]=>[5,3,6,8,1,4,7,2]=>1110000=>0001111
[7,8,5,3,6,1,4,2]=>[6,5,3,8,1,4,7,2]=>1110100=>0001011
[7,8,5,3,6,4,1,2]=>[6,5,3,4,8,1,7,2]=>1110100=>0001011
[7,8,5,3,4,1,6,2]=>[5,3,4,8,1,6,7,2]=>1110000=>0001111
[7,8,5,3,1,4,6,2]=>[5,3,8,1,4,6,7,2]=>1110000=>0001111
[7,8,5,3,1,2,6,4]=>[5,3,8,1,6,7,2,4]=>1110000=>0001111
[7,5,8,3,4,1,6,2]=>[8,3,4,5,1,6,7,2]=>1110000=>0001111
[7,5,8,3,4,6,1,2]=>[6,8,3,4,5,1,7,2]=>1110000=>0001111
[7,5,6,3,1,2,8,4]=>[6,3,5,1,8,7,2,4]=>1110001=>0001110
[7,5,3,4,1,2,8,6]=>[3,4,5,1,8,7,2,6]=>1100001=>0011110
[7,5,3,1,4,2,6,8]=>[3,5,1,4,7,2,6,8]=>1100000=>0011111
[7,5,3,1,4,2,8,6]=>[3,5,1,4,8,7,2,6]=>1100001=>0011110
[7,5,3,1,6,4,8,2]=>[3,6,5,1,4,8,7,2]=>1100101=>0011010
[7,5,3,6,1,4,8,2]=>[3,6,1,5,4,8,7,2]=>1101001=>0010110
[7,5,3,6,4,1,8,2]=>[3,6,4,5,1,8,7,2]=>1101001=>0010110
[7,5,3,6,4,8,1,2]=>[3,8,6,4,5,1,7,2]=>1101010=>0010101
[7,5,3,8,4,6,1,2]=>[3,6,8,4,5,1,7,2]=>1101000=>0010111
[7,5,3,8,1,4,6,2]=>[3,8,1,5,4,6,7,2]=>1101000=>0010111
[7,5,3,1,8,2,6,4]=>[3,8,5,1,6,7,2,4]=>1100100=>0011011
[7,5,3,1,8,2,4,6]=>[3,8,5,1,7,2,4,6]=>1100100=>0011011
[7,5,3,1,6,2,4,8]=>[3,6,5,1,7,2,4,8]=>1100100=>0011011
[7,5,3,1,6,4,2,8]=>[3,6,5,1,4,7,2,8]=>1100100=>0011011
[7,5,3,1,8,4,2,6]=>[3,8,5,1,4,7,2,6]=>1100100=>0011011
[7,5,3,8,1,6,4,2]=>[3,6,8,1,5,4,7,2]=>1101000=>0010111
[7,5,3,8,6,1,4,2]=>[3,6,1,8,5,4,7,2]=>1101100=>0010011
[7,5,3,8,6,4,1,2]=>[3,6,4,8,5,1,7,2]=>1101100=>0010011
[7,5,8,3,6,4,1,2]=>[6,3,4,8,5,1,7,2]=>1110100=>0001011
[7,5,8,3,1,6,4,2]=>[6,8,3,5,1,4,7,2]=>1110000=>0001111
[7,5,8,3,1,6,2,4]=>[6,8,3,5,1,7,2,4]=>1110000=>0001111
[7,5,3,6,1,4,2,8]=>[3,6,1,5,4,7,2,8]=>1101000=>0010111
[7,5,3,6,4,1,2,8]=>[3,6,4,5,1,7,2,8]=>1101000=>0010111
[7,5,8,6,3,1,2,4]=>[6,3,8,1,5,2,7,4]=>1111000=>0000111
[7,5,8,6,3,1,4,2]=>[6,3,8,1,5,4,7,2]=>1111000=>0000111
[7,5,8,6,3,4,1,2]=>[6,3,8,4,5,1,7,2]=>1111000=>0000111
[7,5,6,3,8,1,2,4]=>[8,3,6,5,1,7,2,4]=>1110100=>0001011
[7,5,3,4,1,6,2,8]=>[3,4,5,1,6,7,2,8]=>1100000=>0011111
[7,5,3,4,1,8,2,6]=>[3,4,5,1,8,2,7,6]=>1100010=>0011101
[7,5,6,3,1,8,2,4]=>[8,6,3,5,1,7,2,4]=>1110010=>0001101
[7,5,6,3,8,4,1,2]=>[8,3,4,6,5,1,7,2]=>1110100=>0001011
[7,5,3,6,8,1,4,2]=>[3,8,1,6,5,4,7,2]=>1101100=>0010011
[7,5,3,1,6,8,4,2]=>[3,8,6,5,1,4,7,2]=>1100110=>0011001
[7,5,3,1,6,8,2,4]=>[3,8,6,5,1,7,2,4]=>1100110=>0011001
[7,5,3,1,4,8,2,6]=>[3,5,1,4,8,2,7,6]=>1100010=>0011101
[7,5,3,1,4,6,2,8]=>[3,5,1,4,6,7,2,8]=>1100000=>0011111
[7,5,3,1,2,6,4,8]=>[3,5,1,6,7,2,4,8]=>1100000=>0011111
[7,5,3,1,2,8,4,6]=>[3,5,1,8,2,4,7,6]=>1100010=>0011101
[7,5,3,4,1,8,6,2]=>[3,4,5,1,8,6,7,2]=>1100010=>0011101
[7,5,3,4,8,1,6,2]=>[3,4,8,5,1,6,7,2]=>1100100=>0011011
[7,5,3,4,8,6,1,2]=>[3,4,6,8,5,1,7,2]=>1100100=>0011011
[7,5,3,4,6,1,8,2]=>[3,4,6,5,1,8,7,2]=>1100101=>0011010
[7,5,3,4,1,6,8,2]=>[3,4,5,1,6,8,7,2]=>1100001=>0011110
[7,5,3,1,2,6,8,4]=>[3,5,1,6,8,7,2,4]=>1100001=>0011110
[7,5,3,1,2,4,8,6]=>[3,5,1,8,7,2,4,6]=>1100001=>0011110
[3,5,2,8,4,7,6,1]=>[7,6,8,4,5,2,3,1]=>1101010=>0010101
[5,4,7,3,2,8,6,1]=>[8,6,7,3,4,2,5,1]=>1110010=>0001101
[5,4,8,3,2,7,6,1]=>[7,6,8,3,4,2,5,1]=>1110010=>0001101
[4,5,8,3,2,7,6,1]=>[7,6,8,3,5,2,4,1]=>1110010=>0001101
[4,7,6,3,8,5,2,1]=>[8,5,6,3,7,2,4,1]=>1110100=>0001011
[4,8,6,3,7,5,2,1]=>[7,5,6,3,8,2,4,1]=>1110100=>0001011
[4,8,5,3,2,7,6,1]=>[5,3,7,6,8,2,4,1]=>1110010=>0001101
[5,8,4,3,2,7,6,1]=>[4,3,7,6,8,2,5,1]=>1110010=>0001101
[5,3,2,8,4,7,6,1]=>[3,2,7,6,8,4,5,1]=>1101010=>0010101
[2,1,5,8,4,7,6,3]=>[2,1,7,6,8,4,5,3]=>1011010=>0100101
[5,3,2,7,4,8,6,1]=>[3,2,8,6,7,4,5,1]=>1101010=>0010101
[4,7,5,3,2,8,6,1]=>[5,3,8,6,7,2,4,1]=>1110010=>0001101
[4,7,8,3,6,5,2,1]=>[6,5,8,3,7,2,4,1]=>1110100=>0001011
[4,6,8,3,7,5,2,1]=>[7,5,8,3,6,2,4,1]=>1110100=>0001011
[7,6,4,3,8,5,2,1]=>[4,3,8,5,6,2,7,1]=>1110100=>0001011
[2,1,8,6,7,5,4,3]=>[2,1,7,5,6,4,8,3]=>1011100=>0100011
[8,3,2,6,7,5,4,1]=>[3,2,7,5,6,4,8,1]=>1101100=>0010011
[8,6,4,3,7,5,2,1]=>[4,3,7,5,6,2,8,1]=>1110100=>0001011
[8,5,7,6,4,3,2,1]=>[6,4,7,3,5,2,8,1]=>1111000=>0000111
[8,4,7,3,6,5,2,1]=>[6,5,7,3,4,2,8,1]=>1110100=>0001011
[8,4,6,3,7,5,2,1]=>[7,5,6,3,4,2,8,1]=>1110100=>0001011
[7,4,6,3,8,5,2,1]=>[8,5,6,3,4,2,7,1]=>1110100=>0001011
[3,7,2,6,8,5,4,1]=>[8,5,6,4,7,2,3,1]=>1101100=>0010011
[3,8,2,6,7,5,4,1]=>[7,5,6,4,8,2,3,1]=>1101100=>0010011
[3,8,2,5,4,7,6,1]=>[5,4,7,6,8,2,3,1]=>1101010=>0010101
[3,7,2,8,6,5,4,1]=>[6,5,8,4,7,2,3,1]=>1101100=>0010011
[3,6,2,8,7,5,4,1]=>[7,5,8,4,6,2,3,1]=>1101100=>0010011
[6,4,7,3,8,5,2,1]=>[8,5,7,3,4,2,6,1]=>1110100=>0001011
[6,4,8,3,7,5,2,1]=>[7,5,8,3,4,2,6,1]=>1110100=>0001011
[7,4,8,3,6,5,2,1]=>[6,5,8,3,4,2,7,1]=>1110100=>0001011
[7,5,4,3,2,8,6,1]=>[4,3,5,2,8,6,7,1]=>1110010=>0001101
[7,3,2,5,4,8,6,1]=>[3,2,5,4,8,6,7,1]=>1101010=>0010101
[7,3,2,8,6,5,4,1]=>[3,2,6,5,8,4,7,1]=>1101100=>0010011
[6,8,5,7,4,3,2,1]=>[7,4,5,3,8,2,6,1]=>1111000=>0000111
[6,8,4,3,7,5,2,1]=>[4,3,7,5,8,2,6,1]=>1110100=>0001011
[6,3,2,7,8,5,4,1]=>[3,2,8,5,7,4,6,1]=>1101100=>0010011
[6,7,4,3,8,5,2,1]=>[4,3,8,5,7,2,6,1]=>1110100=>0001011
[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000=>00111111
[2,3,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000=>00011111
[2,3,4,5,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000=>00001111
[2,3,4,5,6,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>11111000=>00000111
[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000=>001111111
[2,4,3,1,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>11000000=>00111111
[2,3,4,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>111000000=>000111111
[2,3,5,4,1,6,7,8,9]=>[4,5,3,2,1,6,7,8,9]=>11100000=>00011111
[2,3,4,5,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>111100000=>000011111
[2,3,4,6,5,1,7,8,9]=>[5,6,4,3,2,1,7,8,9]=>11110000=>00001111
[2,3,4,5,6,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>111110000=>000001111
[2,3,4,5,7,6,1,8,9]=>[6,7,5,4,3,2,1,8,9]=>11111000=>00000111
[2,3,4,5,6,7,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>111111000=>000000111
[2,3,4,5,6,8,7,1,9]=>[7,8,6,5,4,3,2,1,9]=>11111100=>00000011
[2,3,4,5,6,7,8,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>111111100=>000000011
[2,3,4,5,6,7,9,8,1]=>[8,9,7,6,5,4,3,2,1]=>11111110=>00000001
[4,6,8,3,5,7,1,2]=>[5,7,3,8,6,1,4,2]=>1110010=>0001101
[6,8,1,2,4,5,7,3]=>[7,8,1,4,5,6,2,3]=>1100000=>0011111
[8,3,5,2,4,1,6,7]=>[5,3,2,4,8,1,6,7]=>1110000=>0001111
[4,2,5,7,3,6,1,8]=>[2,6,7,3,5,4,1,8]=>1011000=>0100111
[4,2,5,8,3,7,1,6]=>[2,7,3,5,4,1,8,6]=>1011010=>0100101
[2,1,6,8,4,7,3,5]=>[2,1,7,4,8,6,3,5]=>1011010=>0100101
[1,2,5,8,3,6,7,4]=>[1,2,6,7,8,3,5,4]=>0011000=>1100111
[5,3,6,8,4,7,1,2]=>[7,4,8,6,3,1,5,2]=>1111010=>0000101
[3,1,2,6,8,5,7,4]=>[3,1,2,7,8,5,6,4]=>1001100=>0110011
[4,6,3,2,1,8,5,7]=>[3,8,6,2,4,1,5,7]=>1100010=>0011101
[4,1,7,3,2,5,8,6]=>[8,7,3,4,1,2,5,6]=>1010001=>0101110
[3,5,1,2,7,8,6,4]=>[8,6,7,5,1,3,2,4]=>1100110=>0011001
[7,5,1,4,8,2,6,3]=>[4,8,5,1,6,7,2,3]=>1100100=>0011011
[5,4,7,3,8,6,1,2]=>[6,8,3,4,1,7,5,2]=>1110100=>0001011
[8,3,5,1,2,7,6,4]=>[5,3,1,7,6,8,2,4]=>1110010=>0001101
[4,8,3,1,7,2,6,5]=>[3,7,1,4,2,6,8,5]=>1100100=>0011011
[1,8,4,3,5,2,7,6]=>[1,4,3,5,7,8,2,6]=>0110000=>1001111
[4,7,3,6,5,2,1,8]=>[3,5,6,2,7,4,1,8]=>1101000=>0010111
[5,3,7,6,4,2,1,8]=>[6,4,7,3,2,5,1,8]=>1111000=>0000111
[6,4,8,7,5,3,1,2]=>[5,7,3,8,4,1,6,2]=>1111000=>0000111
[7,6,4,3,8,5,1,2]=>[4,3,8,5,6,1,7,2]=>1110100=>0001011
[7,1,3,2,6,8,5,4]=>[3,8,6,5,7,1,2,4]=>1000110=>0111001
[1,5,3,2,7,4,8,6]=>[1,3,8,7,5,2,4,6]=>0100101=>1011010
[6,3,2,1,8,5,4,7]=>[3,2,8,5,6,1,4,7]=>1100100=>0011011
[6,5,3,2,7,4,1,8]=>[3,7,5,2,4,6,1,8]=>1100100=>0011011
[2,8,5,3,1,6,4,7]=>[5,3,6,8,2,1,4,7]=>1110000=>0001111
[2,1,7,3,8,5,4,6]=>[2,1,8,5,7,3,4,6]=>1010100=>0101011
[1,6,2,3,7,8,5,4]=>[1,8,5,7,6,2,3,4]=>0100110=>1011001
[1,6,7,2,8,4,5,3]=>[1,8,2,4,7,5,6,3]=>0110100=>1001011
[5,7,1,8,2,4,6,3]=>[8,1,6,7,4,5,2,3]=>1101000=>0010111
[5,1,2,7,8,3,6,4]=>[8,1,2,3,6,7,5,4]=>1001100=>0110011
[2,4,1,7,8,6,3,5]=>[6,8,4,2,1,3,7,5]=>1101100=>0010011
[4,2,1,7,3,8,5,6]=>[2,8,4,1,3,5,7,6]=>1001010=>0110101
[6,2,8,4,3,1,5,7]=>[2,4,8,3,6,1,5,7]=>1010000=>0101111
[7,8,3,2,5,6,1,4]=>[3,5,6,8,2,7,1,4]=>1100000=>0011111
[7,1,8,2,4,5,6,3]=>[8,1,2,4,5,6,7,3]=>1010000=>0101111
[8,3,7,6,2,1,4,5]=>[6,3,2,7,1,8,4,5]=>1111000=>0000111
[3,2,8,7,5,1,4,6]=>[2,5,7,3,1,8,4,6]=>1011000=>0100111
[8,3,6,5,2,1,4,7]=>[5,3,2,6,1,8,4,7]=>1111000=>0000111
[7,6,3,5,2,4,1,8]=>[3,5,2,6,4,7,1,8]=>1101000=>0010111
[7,4,6,2,5,3,1,8]=>[5,6,2,4,3,7,1,8]=>1110000=>0001111
[8,2,4,1,6,5,3,7]=>[2,4,1,6,5,8,3,7]=>1010100=>0101011
[4,2,8,1,7,5,3,6]=>[2,7,5,8,1,4,3,6]=>1010100=>0101011
[8,2,4,1,7,6,3,5]=>[2,4,1,6,7,3,8,5]=>1010100=>0101011
[6,8,3,7,5,4,1,2]=>[3,5,7,4,8,1,6,2]=>1101000=>0010111
[8,1,2,6,4,3,7,5]=>[6,4,7,8,1,2,3,5]=>1001000=>0110111
[2,8,1,7,5,4,3,6]=>[5,7,4,8,2,1,3,6]=>1101000=>0010111
[6,2,7,5,4,3,1,8]=>[2,5,4,7,3,6,1,8]=>1011000=>0100111
[2,1,8,6,5,4,3,7]=>[2,1,5,6,4,8,3,7]=>1011000=>0100111
[1,2,7,5,4,3,8,6]=>[1,2,5,4,8,7,3,6]=>0011001=>1100110
[1,7,2,4,3,8,6,5]=>[1,4,8,6,7,2,3,5]=>0100010=>1011101
[1,7,2,8,3,6,5,4]=>[1,6,8,2,3,5,7,4]=>0101000=>1010111
[1,7,8,6,5,2,4,3]=>[1,5,6,2,8,4,7,3]=>0111000=>1000111
[7,3,8,6,5,4,1,2]=>[5,6,4,8,3,1,7,2]=>1111000=>0000111
[8,1,7,3,2,6,5,4]=>[6,7,3,5,8,1,2,4]=>1010000=>0101111
[8,6,5,3,2,1,7,4]=>[5,3,6,2,7,8,1,4]=>1110000=>0001111
[8,6,5,4,1,7,2,3]=>[4,5,1,7,6,2,8,3]=>1110010=>0001101
[8,6,5,1,7,3,2,4]=>[7,5,1,6,3,8,2,4]=>1110100=>0001011
[4,6,3,2,7,5,1,8]=>[3,7,5,6,2,4,1,8]=>1100100=>0011011
[7,4,8,3,1,6,2,5]=>[6,8,3,4,1,7,2,5]=>1110000=>0001111
[5,7,4,1,8,2,6,3]=>[4,1,8,2,6,7,5,3]=>1110100=>0001011
[5,7,4,3,1,8,6,2]=>[4,3,8,6,7,1,5,2]=>1110010=>0001101
[1,8,7,2,5,4,6,3]=>[1,5,7,2,4,6,8,3]=>0110000=>1001111
[4,3,1,8,7,5,2,6]=>[3,1,7,5,8,4,2,6]=>1101100=>0010011
[1,4,8,6,3,5,2,7]=>[1,6,3,5,8,4,2,7]=>0111000=>1000111
[7,4,6,3,5,2,1,8]=>[5,6,3,4,2,7,1,8]=>1110000=>0001111
[1,3,5,6,8,4,2,7]=>[1,8,4,6,5,3,2,7]=>0111100=>1000011
[1,6,3,8,7,2,5,4]=>[1,3,7,2,8,5,6,4]=>0101100=>1010011
[1,6,2,4,8,7,5,3]=>[1,4,7,5,8,6,2,3]=>0100110=>1011001
[8,4,1,6,7,5,3,2]=>[7,5,6,4,1,3,8,2]=>1101100=>0010011
[7,1,6,4,8,5,2,3]=>[4,8,5,6,1,2,7,3]=>1010100=>0101011
[7,3,6,8,5,1,2,4]=>[5,8,3,1,6,2,7,4]=>1111000=>0000111
[1,3,7,2,6,8,4,5]=>[1,8,6,3,2,4,7,5]=>0110110=>1001001
[4,2,6,3,8,1,5,7]=>[2,8,3,4,1,6,5,7]=>1010100=>0101011
[3,6,2,4,7,5,1,8]=>[4,7,5,6,2,3,1,8]=>1100100=>0011011
[3,6,2,4,1,8,5,7]=>[4,8,6,2,3,1,5,7]=>1100010=>0011101
[8,7,6,4,1,5,2,3]=>[4,6,1,5,7,2,8,3]=>1110000=>0001111
[4,2,8,1,5,7,3,6]=>[2,5,7,1,4,3,8,6]=>1010010=>0101101
[8,6,1,7,5,4,2,3]=>[5,7,4,6,1,8,2,3]=>1101000=>0010111
[1,8,2,4,6,7,3,5]=>[1,4,7,6,2,3,8,5]=>0100110=>1011001
[2,8,5,4,7,1,3,6]=>[4,7,5,2,1,8,3,6]=>1110100=>0001011
[2,1,5,8,6,4,3,7]=>[2,1,6,4,8,5,3,7]=>1011100=>0100011
[1,2,5,7,8,4,3,6]=>[1,2,8,4,7,5,3,6]=>0011100=>1100011
[1,2,7,4,8,6,3,5]=>[1,2,4,6,8,3,7,5]=>0010100=>1101011
[7,1,8,6,3,5,4,2]=>[6,3,5,8,4,7,1,2]=>1011000=>0100111
[1,8,7,6,3,5,2,4]=>[1,6,3,5,7,2,8,4]=>0111000=>1000111
[1,8,7,4,6,3,2,5]=>[1,4,6,3,7,2,8,5]=>0110100=>1001011
[7,1,5,8,3,4,6,2]=>[8,3,5,4,6,7,1,2]=>1011000=>0100111
[7,1,6,4,2,3,5,8]=>[4,6,1,2,7,3,5,8]=>1010000=>0101111
[8,6,2,4,7,3,5,1]=>[4,7,2,3,6,5,8,1]=>1100100=>0011011
[8,6,2,4,5,7,3,1]=>[4,5,7,6,2,3,8,1]=>1100010=>0011101
[2,7,1,4,5,8,3,6]=>[4,5,8,2,1,3,7,6]=>1100010=>0011101
[7,1,6,4,5,2,3,8]=>[4,5,6,1,2,7,3,8]=>1010000=>0101111
[7,1,4,5,6,8,2,3]=>[8,6,5,4,1,2,7,3]=>1011110=>0100001
[7,1,4,6,5,8,3,2]=>[5,8,6,4,3,7,1,2]=>1011010=>0100101
[7,1,2,3,8,5,4,6]=>[8,5,7,1,2,3,4,6]=>1000100=>0111011
[7,1,5,4,3,8,2,6]=>[4,5,3,8,1,2,7,6]=>1010010=>0101101
[7,1,3,4,2,6,8,5]=>[3,4,6,8,7,1,2,5]=>1000001=>0111110
[7,1,5,6,4,3,8,2]=>[6,4,5,3,8,7,1,2]=>1011001=>0100110
[8,6,2,5,4,3,7,1]=>[5,4,6,2,3,7,8,1]=>1101000=>0010111
[2,5,1,7,4,3,6,8]=>[7,4,5,2,1,3,6,8]=>1101000=>0010111
[3,5,1,4,8,6,2,7]=>[4,6,8,5,1,3,2,7]=>1100100=>0011011
[5,6,2,4,8,7,1,3]=>[4,7,2,8,6,5,1,3]=>1100110=>0011001
[6,3,8,2,4,7,1,5]=>[7,3,2,4,8,6,1,5]=>1110010=>0001101
[6,5,8,7,2,3,1,4]=>[7,2,8,3,5,1,6,4]=>1111000=>0000111
[6,5,7,8,2,4,1,3]=>[8,2,7,4,5,1,6,3]=>1111000=>0000111
[3,4,7,2,5,8,1,6]=>[5,8,2,4,3,1,7,6]=>1110010=>0001101
[4,3,8,1,2,7,5,6]=>[7,3,1,4,2,5,8,6]=>1110010=>0001101
[3,6,4,1,7,2,5,8]=>[4,1,7,3,2,6,5,8]=>1110100=>0001011
[2,8,3,1,5,6,4,7]=>[3,5,6,8,2,1,4,7]=>1100000=>0011111
[3,8,7,1,5,4,2,6]=>[5,7,1,4,8,3,2,6]=>1110000=>0001111
[4,3,1,7,6,8,2,5]=>[3,1,8,6,4,2,7,5]=>1101110=>0010001
[8,4,7,2,5,3,6,1]=>[5,7,2,4,3,6,8,1]=>1110000=>0001111
[4,7,8,1,2,3,6,5]=>[8,1,6,7,2,4,3,5]=>1110000=>0001111
[2,8,6,1,5,3,7,4]=>[5,6,2,1,7,8,3,4]=>1110000=>0001111
[7,2,6,4,1,3,8,5]=>[2,4,6,1,8,7,3,5]=>1010001=>0101110
[6,7,5,2,1,3,8,4]=>[5,2,8,7,1,6,3,4]=>1110001=>0001110
[4,7,5,2,8,1,6,3]=>[8,5,2,6,7,1,4,3]=>1110100=>0001011
[7,2,3,4,1,6,5,8]=>[2,3,4,6,7,1,5,8]=>1000000=>0111111
[4,8,5,2,7,1,3,6]=>[7,5,2,8,1,4,3,6]=>1110100=>0001011
[6,3,5,2,1,7,4,8]=>[5,3,2,7,6,1,4,8]=>1110010=>0001101
[6,8,5,3,1,4,2,7]=>[5,3,8,1,4,6,2,7]=>1110000=>0001111
[1,6,8,2,4,3,7,5]=>[1,7,8,2,4,6,3,5]=>0110000=>1001111
[1,5,6,2,4,7,3,8]=>[1,7,6,2,4,5,3,8]=>0110010=>1001101
[1,5,6,2,4,7,8,3]=>[1,8,7,6,2,4,5,3]=>0110011=>1001100
[1,6,5,7,2,4,3,8]=>[1,7,2,5,4,6,3,8]=>0111000=>1000111
[1,6,7,2,4,3,8,5]=>[1,8,7,2,4,6,3,5]=>0110001=>1001110
[1,5,6,7,2,4,8,3]=>[1,8,7,2,6,4,5,3]=>0111001=>1000110
[1,5,8,2,4,6,7,3]=>[1,6,7,8,2,4,5,3]=>0110000=>1001111
[1,5,7,8,3,2,4,6]=>[1,8,3,7,2,5,4,6]=>0111000=>1000111
[1,7,6,2,8,3,4,5]=>[1,8,2,6,3,4,7,5]=>0110100=>1001011
[1,5,8,7,3,2,4,6]=>[1,7,3,8,2,5,4,6]=>0111000=>1000111
[1,4,2,3,5,8,7,6]=>[1,4,2,3,5,7,8,6]=>0100010=>1011101
[1,5,2,3,4,8,7,6]=>[1,5,2,3,4,7,8,6]=>0100010=>1011101
[1,6,5,2,3,8,7,4]=>[1,5,2,7,8,6,3,4]=>0110010=>1001101
[1,7,4,2,8,6,5,3]=>[1,4,2,6,8,5,7,3]=>0110100=>1001011
[1,7,6,5,2,8,4,3]=>[1,5,2,8,6,4,7,3]=>0111010=>1000101
[1,5,8,3,2,4,7,6]=>[1,7,8,3,5,2,4,6]=>0110000=>1001111
[1,6,5,2,3,7,4,8]=>[1,5,2,7,6,3,4,8]=>0110010=>1001101
[1,6,5,2,3,7,8,4]=>[1,5,2,8,7,6,3,4]=>0110011=>1001100
[1,7,4,6,2,8,3,5]=>[1,8,6,4,2,7,3,5]=>0111010=>1000101
[1,7,3,5,2,8,4,6]=>[1,3,5,2,8,4,7,6]=>0101010=>1010101
[1,6,8,5,2,3,7,4]=>[1,5,2,7,8,3,6,4]=>0111000=>1000111
[1,6,4,2,3,7,8,5]=>[1,4,2,8,7,6,3,5]=>0110011=>1001100
[1,6,4,2,3,7,5,8]=>[1,4,2,7,6,3,5,8]=>0110010=>1001101
[1,5,8,6,2,4,7,3]=>[1,6,2,7,8,4,5,3]=>0111000=>1000111
[1,7,3,4,2,8,5,6]=>[1,3,4,8,2,5,7,6]=>0100010=>1011101
[1,7,4,2,8,5,3,6]=>[1,4,2,8,5,7,3,6]=>0110100=>1001011
[1,6,7,4,2,3,8,5]=>[1,4,8,7,2,6,3,5]=>0110001=>1001110
[1,6,4,2,3,8,5,7]=>[1,4,2,8,6,3,5,7]=>0110010=>1001101
[1,6,4,2,3,8,7,5]=>[1,4,2,7,8,6,3,5]=>0110010=>1001101
[7,3,5,6,1,4,8,2]=>[6,3,1,5,4,8,7,2]=>1111001=>0000110
[3,6,1,4,2,8,5,7]=>[4,8,6,1,3,2,5,7]=>1100010=>0011101
[1,6,7,4,3,5,8,2]=>[1,4,8,7,3,5,6,2]=>0110001=>1001110
[6,7,1,4,3,5,8,2]=>[4,8,7,1,3,5,6,2]=>1100001=>0011110
[7,6,1,4,3,5,8,2]=>[4,6,1,3,5,8,7,2]=>1100001=>0011110
[3,5,4,1,6,7,8,2]=>[4,1,8,7,6,5,3,2]=>1110111=>0001000
[4,7,1,6,3,5,8,2]=>[6,1,3,5,8,7,4,2]=>1101001=>0010110
[3,1,4,7,6,5,8,2]=>[6,5,8,7,4,3,1,2]=>1011101=>0100010
[6,1,7,4,3,5,8,2]=>[4,8,7,3,5,6,1,2]=>1010001=>0101110
[7,1,6,4,3,5,8,2]=>[4,6,3,5,8,7,1,2]=>1010001=>0101110
[1,7,6,4,3,5,8,2]=>[1,4,6,3,5,8,7,2]=>0110001=>1001110
[8,1,6,4,2,7,5,3]=>[4,7,6,1,2,5,8,3]=>1010010=>0101101
[7,4,1,3,8,2,5,6]=>[4,1,3,8,2,7,5,6]=>1100100=>0011011
[1,3,6,4,2,8,5,7]=>[1,4,8,6,3,2,5,7]=>0110010=>1001101
[4,7,3,1,2,8,5,6]=>[3,8,1,4,2,5,7,6]=>1100010=>0011101
[6,8,1,4,2,7,5,3]=>[4,7,1,5,8,6,2,3]=>1100010=>0011101
[1,8,6,4,2,7,5,3]=>[1,4,7,6,2,5,8,3]=>0110010=>1001101
[4,8,1,3,7,2,5,6]=>[7,1,3,4,2,8,5,6]=>1100100=>0011011
[8,7,1,3,6,2,5,4]=>[6,1,3,7,5,8,2,4]=>1100100=>0011011
[3,7,8,4,6,2,1,5]=>[4,6,2,8,3,1,7,5]=>1110100=>0001011
[3,7,4,6,8,2,1,5]=>[8,4,2,6,3,1,7,5]=>1111100=>0000011
[1,4,7,3,8,2,5,6]=>[1,8,3,4,2,7,5,6]=>0110100=>1001011
[5,7,6,8,3,2,1,4]=>[8,3,6,2,7,1,5,4]=>1111000=>0000111
[3,7,5,4,8,2,1,6]=>[4,8,5,2,7,3,1,6]=>1110100=>0001011
[7,1,3,4,2,8,5,6]=>[3,4,8,1,2,5,7,6]=>1000010=>0111101
[4,1,7,3,8,2,5,6]=>[8,3,4,1,2,7,5,6]=>1010100=>0101011
[8,1,4,3,7,2,5,6]=>[4,3,7,1,2,8,5,6]=>1010100=>0101011
[4,2,3,7,8,6,1,5]=>[2,3,6,8,4,1,7,5]=>1001100=>0110011
[5,2,3,4,8,6,1,7]=>[2,3,4,6,8,5,1,7]=>1000100=>0111011
[2,7,5,6,3,8,1,4]=>[8,6,3,5,2,1,7,4]=>1111010=>0000101
[5,7,2,6,3,8,1,4]=>[8,6,2,3,7,1,5,4]=>1101010=>0010101
[7,2,5,6,8,4,1,3]=>[2,8,4,6,5,1,7,3]=>1011100=>0100011
[5,2,3,8,7,6,1,4]=>[2,3,6,7,1,8,5,4]=>1001100=>0110011
[8,2,3,7,5,6,1,4]=>[2,3,5,6,7,1,8,4]=>1001000=>0110111
[6,1,8,3,7,2,5,4]=>[7,3,8,5,6,1,2,4]=>1010100=>0101011
[1,7,8,4,2,6,5,3]=>[1,4,6,8,2,5,7,3]=>0110000=>1001111
[4,7,1,8,2,5,6,3]=>[8,1,5,6,7,4,2,3]=>1101000=>0010111
[3,7,4,8,5,2,1,6]=>[5,8,4,2,7,3,1,6]=>1111000=>0000111
[2,4,3,8,5,6,1,7]=>[3,5,6,8,4,2,1,7]=>1101000=>0010111
[7,5,8,6,3,2,1,4]=>[6,3,8,2,5,1,7,4]=>1111000=>0000111
[6,5,8,7,3,2,1,4]=>[7,3,8,2,5,1,6,4]=>1111000=>0000111
[8,5,7,6,3,2,1,4]=>[6,3,7,2,5,1,8,4]=>1111000=>0000111
[2,5,3,8,7,6,1,4]=>[3,6,7,2,1,8,5,4]=>1101100=>0010011
[3,7,5,8,6,2,1,4]=>[6,2,8,5,3,1,7,4]=>1111100=>0000011
[3,7,8,6,5,2,1,4]=>[5,6,2,8,3,1,7,4]=>1111000=>0000111
[1,8,7,3,6,2,5,4]=>[1,6,3,7,5,8,2,4]=>0110100=>1001011
[6,8,7,5,3,2,1,4]=>[5,3,7,2,8,1,6,4]=>1111000=>0000111
[1,5,4,7,6,8,2,3]=>[1,8,6,4,2,7,5,3]=>0111110=>1000001
[3,5,4,8,6,7,1,2]=>[7,6,4,1,8,5,3,2]=>1111110=>0000001
[3,8,4,6,5,7,1,2]=>[5,7,6,4,1,8,3,2]=>1111010=>0000101
[3,6,4,7,5,8,1,2]=>[5,8,4,1,7,6,3,2]=>1111010=>0000101
[1,6,2,7,5,8,3,4]=>[1,5,8,2,3,7,6,4]=>0101010=>1010101
[1,6,4,8,5,7,2,3]=>[1,5,7,4,2,8,6,3]=>0111010=>1000101
[1,8,4,6,5,7,2,3]=>[1,5,7,6,4,2,8,3]=>0111010=>1000101
[1,5,4,8,6,7,2,3]=>[1,7,6,4,2,8,5,3]=>0111110=>1000001
[7,8,1,5,4,6,2,3]=>[5,4,6,8,1,7,2,3]=>1101000=>0010111
[7,8,1,5,2,4,3,6]=>[5,1,8,4,7,2,3,6]=>1101000=>0010111
[1,8,2,6,5,7,3,4]=>[1,5,7,6,2,3,8,4]=>0101010=>1010101
[1,7,2,8,5,6,3,4]=>[1,5,6,8,2,3,7,4]=>0101000=>1010111
[1,7,2,6,5,8,3,4]=>[1,5,8,6,2,3,7,4]=>0101010=>1010101
[1,5,2,7,6,8,3,4]=>[1,8,6,2,3,7,5,4]=>0101110=>1010001
[1,7,6,8,2,5,3,4]=>[1,8,2,5,6,3,7,4]=>0111000=>1000111
[1,7,6,8,4,5,2,3]=>[1,8,4,5,6,2,7,3]=>0111000=>1000111
[5,7,6,8,1,4,2,3]=>[8,1,6,4,7,2,5,3]=>1111000=>0000111
[7,8,5,6,1,3,2,4]=>[6,1,5,3,8,2,7,4]=>1111000=>0000111
[7,8,1,3,2,6,4,5]=>[6,8,1,3,7,2,4,5]=>1100000=>0011111
[7,8,1,6,2,4,3,5]=>[6,1,8,4,7,2,3,5]=>1101000=>0010111
[7,8,1,4,2,6,3,5]=>[4,6,8,1,7,2,3,5]=>1100000=>0011111
[7,8,1,4,2,5,3,6]=>[4,8,1,5,7,2,3,6]=>1100000=>0011111
[7,8,2,1,4,3,6,5]=>[8,2,4,6,7,1,3,5]=>1100000=>0011111
[7,8,1,2,4,3,5,6]=>[8,1,4,7,2,3,5,6]=>1100000=>0011111
[4,3,6,5,8,7,1,2]=>[7,5,3,1,8,6,4,2]=>1111110=>0000001
[3,4,6,5,7,8,1,2]=>[8,5,1,7,6,4,3,2]=>1111110=>0000001
[3,4,1,5,6,7,8,9,2]=>[9,8,7,6,5,4,1,3,2]=>11011111=>00100000
[3,4,5,1,6,7,8,9,2]=>[9,8,7,6,5,1,4,3,2]=>11101111=>00010000
[3,4,5,6,1,7,8,9,2]=>[9,8,7,6,1,5,4,3,2]=>11110111=>00001000
[3,4,5,6,7,1,8,9,2]=>[9,8,7,1,6,5,4,3,2]=>11111011=>00000100
[3,4,5,6,7,8,1,9,2]=>[9,8,1,7,6,5,4,3,2]=>11111101=>00000010
[3,4,1,5,6,7,8,9,10,2]=>[10,9,8,7,6,5,4,1,3,2]=>110111111=>001000000
[3,4,5,1,6,7,8,9,10,2]=>[10,9,8,7,6,5,1,4,3,2]=>111011111=>000100000
[3,4,5,6,1,7,8,9,10,2]=>[10,9,8,7,6,1,5,4,3,2]=>111101111=>000010000
[3,4,5,6,7,1,8,9,10,2]=>[10,9,8,7,1,6,5,4,3,2]=>111110111=>000001000
[3,4,5,6,7,8,1,9,10,2]=>[10,9,8,1,7,6,5,4,3,2]=>111111011=>000000100
[3,4,5,6,7,8,9,1,10,2]=>[10,9,1,8,7,6,5,4,3,2]=>111111101=>000000010
[1,6,2,3,8,7,4,5]=>[1,7,2,3,4,8,6,5]=>0100110=>1011001
[1,2,6,5,3,7,4,8]=>[1,2,5,3,7,6,4,8]=>0011010=>1100101
[1,2,6,5,3,7,8,4]=>[1,2,5,3,8,7,6,4]=>0011011=>1100100
[1,3,7,5,2,6,8,4]=>[1,5,3,2,6,8,7,4]=>0111001=>1000110
[1,2,6,4,3,7,8,5]=>[1,2,4,8,7,6,3,5]=>0010011=>1101100
[1,4,7,3,2,5,8,6]=>[1,8,7,3,4,2,5,6]=>0110001=>1001110
[1,4,3,2,5,8,6,7]=>[1,3,4,2,5,8,6,7]=>0100010=>1011101
[1,5,3,2,4,8,6,7]=>[1,3,5,2,4,8,6,7]=>0100010=>1011101
[1,7,5,3,2,8,6,4]=>[1,5,3,8,6,7,2,4]=>0110010=>1001101
[1,5,3,2,4,8,7,6]=>[1,3,5,2,4,7,8,6]=>0100010=>1011101
[6,8,5,4,3,2,1,7]=>[4,5,3,8,2,6,1,7]=>1110000=>0001111
[7,1,5,4,3,8,6,2]=>[4,5,3,8,6,7,1,2]=>1010010=>0101101
[3,6,5,4,8,1,7,2]=>[4,7,8,5,1,6,3,2]=>1110100=>0001011
[6,8,1,4,3,2,7,5]=>[4,7,8,1,3,6,2,5]=>1100000=>0011111
[2,8,5,4,3,7,1,6]=>[4,5,3,7,2,1,8,6]=>1110010=>0001101
[7,6,1,4,3,8,5,2]=>[4,8,6,1,3,5,7,2]=>1100010=>0011101
[4,6,5,8,3,1,7,2]=>[7,8,3,5,1,6,4,2]=>1111000=>0000111
[1,8,2,4,3,7,6,5]=>[1,4,7,6,8,2,3,5]=>0100010=>1011101
[7,6,5,1,3,8,4,2]=>[5,1,8,6,3,4,7,2]=>1110010=>0001101
[1,6,3,4,8,7,5,2]=>[1,3,4,7,5,8,6,2]=>0100110=>1011001
[1,4,5,8,3,7,6,2]=>[1,7,6,8,3,5,4,2]=>0111010=>1000101
[1,8,5,2,3,7,6,4]=>[1,5,2,7,6,8,3,4]=>0110010=>1001101
[7,5,8,4,3,2,1,6]=>[4,8,3,5,2,7,1,6]=>1110000=>0001111
[5,1,7,6,8,4,3,2]=>[8,4,6,3,7,5,1,2]=>1011100=>0100011
[6,4,8,5,2,7,1,3]=>[5,2,7,4,1,8,6,3]=>1111010=>0000101
[5,1,8,6,7,4,3,2]=>[7,4,6,3,8,5,1,2]=>1011100=>0100011
[8,4,7,5,2,6,1,3]=>[5,2,6,7,4,1,8,3]=>1111000=>0000111
[5,4,6,8,2,1,7,3]=>[7,8,2,6,4,1,5,3]=>1111000=>0000111
[6,4,5,8,1,2,7,3]=>[7,8,1,5,4,2,6,3]=>1111000=>0000111
[7,4,6,5,2,1,8,3]=>[5,2,6,4,1,8,7,3]=>1111001=>0000110
[8,4,6,5,2,1,7,3]=>[5,2,6,4,1,7,8,3]=>1111000=>0000111
[5,2,3,6,4,1,8,7]=>[2,3,6,4,5,1,8,7]=>1001001=>0110110
[6,1,4,5,3,2,8,7]=>[5,4,3,6,1,2,8,7]=>1011001=>0100110
[5,7,1,2,4,3,8,6]=>[8,7,1,4,5,2,3,6]=>1100001=>0011110
[4,3,7,6,8,2,5,1]=>[8,3,2,6,5,7,4,1]=>1111100=>0000011
[5,3,6,8,1,7,2,4]=>[7,3,1,8,6,2,5,4]=>1111010=>0000101
[3,2,6,8,5,7,1,4]=>[2,5,7,3,1,8,6,4]=>1011010=>0100101
[7,4,8,6,5,2,1,3]=>[5,6,2,8,4,1,7,3]=>1111000=>0000111
[7,1,8,2,5,4,3,6]=>[5,8,1,2,4,7,3,6]=>1010000=>0101111
[2,5,3,7,4,1,8,6]=>[3,8,7,4,5,2,1,6]=>1101001=>0010110
[3,6,4,7,5,1,8,2]=>[5,8,7,4,1,6,3,2]=>1111001=>0000110
[8,4,7,6,2,3,1,5]=>[6,2,7,4,3,8,1,5]=>1111000=>0000111
[8,4,7,1,2,5,6,3]=>[7,1,4,2,5,6,8,3]=>1110000=>0001111
[8,1,7,4,2,5,6,3]=>[4,7,1,2,5,6,8,3]=>1010000=>0101111
[7,4,3,8,2,5,6,1]=>[3,8,4,2,5,6,7,1]=>1101000=>0010111
[6,4,1,5,8,2,7,3]=>[7,8,5,4,1,6,2,3]=>1101100=>0010011
[2,5,8,7,3,6,1,4]=>[6,7,3,8,2,1,5,4]=>1111000=>0000111
[7,4,3,2,8,5,6,1]=>[3,4,2,8,5,6,7,1]=>1100100=>0011011
[4,2,7,1,8,5,6,3]=>[2,8,5,6,7,1,4,3]=>1010100=>0101011
[2,4,8,7,3,5,6,1]=>[7,3,5,6,8,4,2,1]=>1111000=>0000111
[3,4,7,2,8,5,6,1]=>[8,5,6,7,2,4,3,1]=>1110100=>0001011
[3,7,1,4,8,5,6,2]=>[4,8,5,6,7,1,3,2]=>1100100=>0011011
[7,2,3,4,8,5,6,1]=>[2,3,4,8,5,6,7,1]=>1000100=>0111011
[6,1,8,5,2,7,4,3]=>[5,1,2,7,4,8,6,3]=>1011010=>0100101
[2,1,7,4,5,8,6,3]=>[2,1,4,5,8,6,7,3]=>1010010=>0101101
[2,1,8,3,6,7,5,4]=>[2,1,7,6,5,8,3,4]=>1010110=>0101001
[8,2,1,6,4,7,5,3]=>[2,7,6,4,5,8,1,3]=>1001010=>0110101
[7,8,2,6,4,1,5,3]=>[6,4,8,2,5,7,1,3]=>1101000=>0010111
[2,6,3,5,8,7,1,4]=>[3,7,5,2,1,8,6,4]=>1101110=>0010001
[7,6,2,1,5,8,4,3]=>[5,8,6,2,4,7,1,3]=>1100010=>0011101
[4,5,2,7,6,1,8,3]=>[6,2,8,7,5,4,1,3]=>1101101=>0010010
[5,1,6,8,4,7,2,3]=>[7,4,8,6,1,2,5,3]=>1011010=>0100101
[7,4,8,6,5,2,3,1]=>[5,6,2,8,4,3,7,1]=>1111000=>0000111
[8,1,6,4,7,3,2,5]=>[4,7,3,6,1,2,8,5]=>1010100=>0101011
[2,6,4,8,5,3,7,1]=>[5,7,8,4,3,6,2,1]=>1111000=>0000111
[3,2,5,8,4,1,7,6]=>[2,7,8,4,5,3,1,6]=>1011000=>0100111
[4,8,7,5,6,1,2,3]=>[6,5,1,7,2,8,4,3]=>1111100=>0000011
[6,1,4,8,7,3,5,2]=>[7,4,3,8,5,6,1,2]=>1011100=>0100011
[7,2,8,4,3,5,6,1]=>[2,4,8,3,5,6,7,1]=>1010000=>0101111
[4,7,8,1,3,5,6,2]=>[8,1,5,6,7,3,4,2]=>1110000=>0001111
[8,7,3,4,1,5,6,2]=>[3,4,7,1,5,6,8,2]=>1100000=>0011111
[4,8,2,7,3,5,6,1]=>[7,2,3,5,6,8,4,1]=>1101000=>0010111
[3,8,1,7,2,5,6,4]=>[7,1,3,2,5,6,8,4]=>1101000=>0010111
[6,4,8,7,1,3,2,5]=>[7,1,8,4,3,6,2,5]=>1111000=>0000111
[2,8,4,6,7,3,1,5]=>[7,4,3,6,2,1,8,5]=>1111100=>0000011
[4,3,8,2,7,6,1,5]=>[6,7,3,2,4,1,8,5]=>1110100=>0001011
[6,8,4,2,1,3,7,5]=>[4,2,7,8,1,6,3,5]=>1110000=>0001111
[7,8,2,4,3,5,6,1]=>[4,8,2,3,5,6,7,1]=>1100000=>0011111
[2,8,3,7,1,5,6,4]=>[3,7,2,1,5,6,8,4]=>1101000=>0010111
[8,1,2,7,3,5,6,4]=>[7,1,2,3,5,6,8,4]=>1001000=>0110111
[6,4,1,3,2,8,5,7]=>[4,1,3,8,6,2,5,7]=>1100010=>0011101
[6,8,5,2,7,4,3,1]=>[7,5,2,4,8,3,6,1]=>1110100=>0001011
[7,2,5,4,3,8,1,6]=>[2,4,5,3,8,1,7,6]=>1010010=>0101101
[3,6,8,1,4,5,2,7]=>[8,1,4,5,6,3,2,7]=>1110000=>0001111
[6,8,1,2,4,5,3,7]=>[8,1,4,5,6,2,3,7]=>1100000=>0011111
[3,8,6,1,2,5,4,7]=>[6,1,5,8,3,2,4,7]=>1110000=>0001111
[4,1,6,5,8,2,3,7]=>[8,5,1,2,6,4,3,7]=>1011100=>0100011
[4,3,8,6,2,5,1,7]=>[6,3,2,5,8,4,1,7]=>1111000=>0000111
[8,3,6,1,4,5,2,7]=>[6,3,1,4,5,8,2,7]=>1110000=>0001111
[2,3,6,8,4,5,1,7]=>[8,4,5,6,3,2,1,7]=>1111000=>0000111
[2,7,5,4,3,8,1,6]=>[4,5,3,8,2,1,7,6]=>1110010=>0001101
[6,3,8,7,4,2,5,1]=>[7,4,8,3,2,5,6,1]=>1111000=>0000111
[5,8,4,3,7,6,1,2]=>[4,3,6,7,1,8,5,2]=>1110100=>0001011
[8,7,4,3,1,6,2,5]=>[4,3,6,7,1,8,2,5]=>1110000=>0001111
[7,1,5,3,4,8,2,6]=>[5,3,4,8,1,2,7,6]=>1010010=>0101101
[4,8,6,5,7,2,1,3]=>[7,5,2,6,1,8,4,3]=>1111100=>0000011
[6,1,8,7,4,3,5,2]=>[7,4,8,3,5,6,1,2]=>1011000=>0100111
[8,5,4,3,1,6,7,2]=>[4,3,5,1,6,7,8,2]=>1110000=>0001111
[2,5,8,6,3,4,7,1]=>[6,3,7,8,4,5,2,1]=>1111000=>0000111
[4,1,3,8,5,6,7,2]=>[3,5,6,7,8,4,1,2]=>1001000=>0110111
[6,5,8,4,3,1,7,2]=>[4,7,8,3,5,1,6,2]=>1110000=>0001111
[7,2,8,1,3,6,4,5]=>[2,6,8,1,7,3,4,5]=>1010000=>0101111
[1,8,5,2,3,6,7,4]=>[1,5,2,6,7,8,3,4]=>0110000=>1001111
[1,8,3,2,5,6,7,4]=>[1,3,5,6,7,8,2,4]=>0100000=>1011111
[2,8,3,1,5,6,7,4]=>[3,5,6,7,8,2,1,4]=>1100000=>0011111
[4,8,3,2,5,6,7,1]=>[3,5,6,7,8,2,4,1]=>1100000=>0011111
[8,2,3,1,5,6,7,4]=>[2,3,5,6,7,8,1,4]=>1000000=>0111111
[2,1,8,3,5,6,7,4]=>[2,1,5,6,7,8,3,4]=>1010000=>0101111
[1,4,8,2,3,6,7,5]=>[1,6,7,8,2,4,3,5]=>0110000=>1001111
[3,1,2,7,8,6,4,5]=>[3,1,2,6,8,4,7,5]=>1001100=>0110011
[7,5,1,8,2,4,3,6]=>[8,1,5,4,7,2,3,6]=>1101000=>0010111
[3,5,8,1,2,4,7,6]=>[7,8,1,5,3,2,4,6]=>1110000=>0001111
[4,5,8,1,2,3,7,6]=>[7,8,1,5,2,4,3,6]=>1110000=>0001111
[4,2,7,1,8,6,3,5]=>[2,6,8,1,4,3,7,5]=>1010100=>0101011
[3,8,4,1,2,6,7,5]=>[4,1,6,7,8,3,2,5]=>1110000=>0001111
[5,4,8,2,3,6,7,1]=>[6,7,8,2,4,3,5,1]=>1110000=>0001111
[2,7,1,4,3,8,5,6]=>[4,8,2,1,3,5,7,6]=>1100010=>0011101
[2,4,1,8,6,3,7,5]=>[6,4,2,1,3,7,8,5]=>1101100=>0010011
[7,3,6,5,8,2,1,4]=>[8,5,3,2,6,1,7,4]=>1111100=>0000011
[7,6,3,5,8,2,1,4]=>[3,8,5,2,6,1,7,4]=>1101100=>0010011
[3,5,2,8,6,1,7,4]=>[6,2,3,1,7,8,5,4]=>1101100=>0010011
[8,2,5,6,1,4,7,3]=>[2,6,1,5,4,7,8,3]=>1011000=>0100111
[8,6,5,4,1,2,7,3]=>[4,5,1,6,2,7,8,3]=>1110000=>0001111
[2,6,1,8,3,7,5,4]=>[7,2,1,3,5,8,6,4]=>1101010=>0010101
[6,1,5,3,8,7,2,4]=>[7,5,3,8,6,1,2,4]=>1010110=>0101001
[2,8,6,3,7,1,5,4]=>[7,3,6,5,8,2,1,4]=>1110100=>0001011
[3,6,8,5,1,2,7,4]=>[5,1,7,8,3,2,6,4]=>1111000=>0000111
[4,8,2,5,1,6,7,3]=>[5,2,6,7,8,4,1,3]=>1101000=>0010111
[3,4,8,5,2,6,7,1]=>[5,2,6,7,8,4,3,1]=>1111000=>0000111
[4,2,1,8,5,6,7,3]=>[2,5,6,7,8,4,1,3]=>1001000=>0110111
[1,5,4,8,2,6,7,3]=>[1,6,7,8,4,2,5,3]=>0111000=>1000111
[7,2,1,5,8,6,3,4]=>[2,6,8,5,1,3,7,4]=>1001100=>0110011
[2,8,4,5,1,6,7,3]=>[5,4,2,1,6,7,8,3]=>1111000=>0000111
[3,1,5,8,6,2,7,4]=>[6,3,1,2,7,8,5,4]=>1011100=>0100011
[6,3,4,8,5,1,7,2]=>[5,7,8,4,3,1,6,2]=>1111000=>0000111
[5,3,4,8,1,6,7,2]=>[6,7,8,4,3,1,5,2]=>1111000=>0000111
[7,5,8,4,1,2,6,3]=>[4,8,1,5,2,6,7,3]=>1110000=>0001111
[7,5,8,4,6,1,3,2]=>[4,6,1,8,5,3,7,2]=>1110100=>0001011
[6,5,4,8,7,1,3,2]=>[7,4,1,8,5,3,6,2]=>1111100=>0000011
[7,5,1,6,8,2,4,3]=>[8,1,6,5,4,7,2,3]=>1101100=>0010011
[6,5,4,7,1,2,8,3]=>[8,7,4,1,5,2,6,3]=>1111001=>0000110
[6,5,4,7,8,1,3,2]=>[8,4,1,7,5,3,6,2]=>1111100=>0000011
[6,5,3,7,1,4,2,8]=>[3,7,1,5,4,6,2,8]=>1101000=>0010111
[7,5,1,4,8,3,2,6]=>[4,8,5,1,3,7,2,6]=>1100100=>0011011
[8,1,6,4,7,3,5,2]=>[4,7,3,6,5,8,1,2]=>1010100=>0101011
[6,5,3,7,1,4,8,2]=>[3,8,7,1,5,4,6,2]=>1101001=>0010110
[8,1,5,4,3,7,6,2]=>[4,5,3,7,6,8,1,2]=>1010010=>0101101
[8,1,5,4,3,7,2,6]=>[4,5,3,7,1,2,8,6]=>1010010=>0101101
[7,4,1,5,3,2,6,8]=>[5,4,1,3,7,2,6,8]=>1101000=>0010111
[8,1,6,4,2,5,3,7]=>[4,6,1,2,5,8,3,7]=>1010000=>0101111
[6,5,3,8,1,4,2,7]=>[3,8,1,5,4,6,2,7]=>1101000=>0010111
[7,6,8,1,4,3,2,5]=>[8,1,4,6,3,7,2,5]=>1110000=>0001111
[6,5,3,8,1,4,7,2]=>[3,7,8,1,5,4,6,2]=>1101000=>0010111
[6,5,3,1,2,7,8,4]=>[3,5,1,8,7,6,2,4]=>1100011=>0011100
[7,5,1,4,2,6,8,3]=>[4,5,1,6,8,7,2,3]=>1100001=>0011110
[8,1,6,4,2,5,7,3]=>[4,6,1,2,5,7,8,3]=>1010000=>0101111
[6,4,3,1,5,2,8,7]=>[3,4,1,5,6,2,8,7]=>1100001=>0011110
[6,4,3,1,5,7,2,8]=>[3,4,1,5,7,6,2,8]=>1100010=>0011101
[7,4,1,5,3,6,2,8]=>[5,4,1,3,6,7,2,8]=>1101000=>0010111
[8,1,5,4,3,6,2,7]=>[4,5,3,6,8,1,2,7]=>1010000=>0101111
[8,1,5,4,3,6,7,2]=>[4,5,3,6,7,8,1,2]=>1010000=>0101111
[7,4,1,5,3,6,8,2]=>[5,4,1,3,6,8,7,2]=>1101001=>0010110
[6,7,4,5,1,8,2,3]=>[5,4,1,8,2,7,6,3]=>1111010=>0000101
[4,7,5,6,2,3,1,8]=>[6,2,5,3,7,4,1,8]=>1111000=>0000111
[4,7,5,6,1,8,2,3]=>[8,6,1,5,2,7,4,3]=>1111010=>0000101
[4,7,5,6,3,8,1,2]=>[8,6,3,5,1,7,4,2]=>1111010=>0000101
[4,5,3,8,6,7,1,2]=>[3,7,6,1,8,5,4,2]=>1101110=>0010001
[4,8,3,6,5,7,1,2]=>[3,5,7,6,1,8,4,2]=>1101010=>0010101
[5,6,1,8,2,7,3,4]=>[7,1,8,6,2,3,5,4]=>1101010=>0010101
[5,6,1,8,4,7,2,3]=>[7,4,8,6,1,5,2,3]=>1101010=>0010101
[4,5,1,8,6,7,2,3]=>[7,6,1,8,5,4,2,3]=>1101110=>0010001
[7,8,4,5,1,6,2,3]=>[5,4,1,6,8,2,7,3]=>1111000=>0000111
[4,8,2,3,1,6,5,7]=>[6,8,2,3,4,1,5,7]=>1100000=>0011111
[5,6,2,8,1,4,3,7]=>[8,2,6,4,5,1,3,7]=>1101000=>0010111
[3,6,4,5,1,8,2,7]=>[5,4,1,8,6,3,2,7]=>1111010=>0000101
[2,6,4,8,1,5,3,7]=>[8,4,2,1,5,6,3,7]=>1111000=>0000111
[2,8,3,6,1,5,4,7]=>[3,6,2,1,5,8,4,7]=>1101000=>0010111
[2,8,3,4,1,6,5,7]=>[3,4,6,8,2,1,5,7]=>1100000=>0011111
[7,8,2,5,3,4,1,6]=>[5,2,3,8,4,7,1,6]=>1101000=>0010111
[1,5,3,8,6,7,2,4]=>[1,3,7,6,2,8,5,4]=>0101110=>1010001
[1,8,3,6,2,7,4,5]=>[1,3,7,6,2,8,4,5]=>0101010=>1010101
[1,6,4,8,2,7,3,5]=>[1,7,4,2,8,6,3,5]=>0111010=>1000101
[1,7,3,6,4,8,2,5]=>[1,3,8,6,4,7,2,5]=>0101010=>1010101
[1,7,2,8,4,6,3,5]=>[1,6,8,4,7,2,3,5]=>0101000=>1010111
[1,7,5,8,4,6,2,3]=>[1,6,8,4,5,2,7,3]=>0111000=>1000111
[1,7,5,8,2,6,3,4]=>[1,6,8,2,5,3,7,4]=>0111000=>1000111
[1,7,5,6,3,8,2,4]=>[1,8,6,3,5,2,7,4]=>0111010=>1000101
[2,7,5,6,3,4,1,8]=>[6,3,5,4,7,2,1,8]=>1111000=>0000111
[6,7,2,5,3,4,1,8]=>[5,2,3,7,4,6,1,8]=>1101000=>0010111
[6,7,1,5,3,8,2,4]=>[5,1,3,8,2,7,6,4]=>1101010=>0010101
[6,7,5,8,1,4,2,3]=>[8,1,5,4,7,2,6,3]=>1111000=>0000111
[5,8,6,7,2,3,1,4]=>[7,2,6,3,8,1,5,4]=>1111000=>0000111
[6,7,2,8,1,4,3,5]=>[8,2,7,4,6,1,3,5]=>1101000=>0010111
[3,4,2,7,5,6,1,8]=>[5,6,7,4,2,3,1,8]=>1101000=>0010111
[3,4,1,7,5,8,2,6]=>[5,8,4,1,3,2,7,6]=>1101010=>0010101
[2,3,1,8,4,7,5,6]=>[3,2,1,7,4,5,8,6]=>1101010=>0010101
[7,8,2,6,1,4,3,5]=>[6,2,8,4,7,1,3,5]=>1101000=>0010111
[2,8,6,7,1,4,3,5]=>[7,2,1,6,4,8,3,5]=>1111000=>0000111
[2,8,1,4,3,7,5,6]=>[4,7,2,1,3,5,8,6]=>1100010=>0011101
[3,7,2,5,4,6,1,8]=>[5,4,6,7,2,3,1,8]=>1101000=>0010111
[3,4,1,8,2,7,5,6]=>[7,4,1,3,2,5,8,6]=>1101010=>0010101
[3,4,1,8,6,7,2,5]=>[7,6,4,1,3,2,8,5]=>1101110=>0010001
[3,4,2,5,1,8,6,7]=>[5,4,2,3,1,8,6,7]=>1101010=>0010101
[3,4,2,8,1,6,5,7]=>[6,8,4,2,3,1,5,7]=>1101000=>0010111
[7,1,5,8,4,6,2,3]=>[6,8,4,5,1,2,7,3]=>1011000=>0100111
[7,6,1,8,3,5,2,4]=>[8,1,3,5,6,2,7,4]=>1101000=>0010111
[8,7,1,5,2,6,3,4]=>[5,1,6,7,2,3,8,4]=>1101000=>0010111
[8,7,1,5,2,3,6,4]=>[5,1,7,2,3,6,8,4]=>1101000=>0010111
[8,4,2,1,7,6,3,5]=>[4,2,6,7,1,3,8,5]=>1100100=>0011011
[8,5,7,2,1,4,3,6]=>[7,2,5,1,4,8,3,6]=>1110000=>0001111
[5,8,7,3,1,4,2,6]=>[7,3,8,1,4,5,2,6]=>1110000=>0001111
[8,5,2,7,1,3,6,4]=>[7,2,5,1,3,6,8,4]=>1101000=>0010111
[8,4,2,1,3,7,6,5]=>[4,2,7,6,8,1,3,5]=>1100010=>0011101
[8,7,4,1,2,3,6,5]=>[4,1,7,2,6,8,3,5]=>1110000=>0001111
[8,7,4,1,2,6,3,5]=>[4,1,6,7,2,8,3,5]=>1110000=>0001111
[8,4,3,1,7,2,6,5]=>[3,4,1,7,2,6,8,5]=>1100100=>0011011
[8,4,3,1,2,7,6,5]=>[3,4,1,7,6,8,2,5]=>1100010=>0011101
[8,5,7,4,1,2,6,3]=>[4,7,1,5,2,6,8,3]=>1110000=>0001111
[8,1,5,4,2,7,6,3]=>[4,5,1,2,7,6,8,3]=>1010010=>0101101
[8,1,6,4,7,2,5,3]=>[4,7,1,2,6,5,8,3]=>1010100=>0101011
[5,8,3,6,4,1,2,7]=>[3,6,4,8,1,5,2,7]=>1101000=>0010111
[5,2,8,6,4,1,3,7]=>[2,6,4,8,1,5,3,7]=>1011000=>0100111
[8,4,7,5,1,6,2,3]=>[5,1,6,7,4,2,8,3]=>1111000=>0000111
[8,4,7,5,1,2,6,3]=>[5,1,7,4,2,6,8,3]=>1111000=>0000111
[8,7,3,5,1,2,6,4]=>[3,5,1,7,2,6,8,4]=>1101000=>0010111
[8,3,2,6,5,1,4,7]=>[3,2,5,6,1,8,4,7]=>1101000=>0010111
[4,8,6,3,5,1,2,7]=>[5,6,3,8,1,4,2,7]=>1110000=>0001111
[4,8,7,3,1,5,2,6]=>[7,3,5,8,1,4,2,6]=>1110000=>0001111
[8,3,2,7,1,5,4,6]=>[3,2,7,1,5,8,4,6]=>1101000=>0010111
[8,7,3,1,4,2,6,5]=>[3,7,1,4,6,8,2,5]=>1100000=>0011111
[8,7,3,1,6,2,4,5]=>[3,6,1,7,2,4,8,5]=>1100100=>0011011
[8,7,3,1,2,4,6,5]=>[3,7,1,6,8,2,4,5]=>1100000=>0011111
[8,3,2,1,4,7,6,5]=>[3,2,7,6,8,1,4,5]=>1100010=>0011101
[8,3,2,1,7,4,6,5]=>[3,2,7,1,4,6,8,5]=>1100100=>0011011
[3,8,7,4,1,2,5,6]=>[4,7,1,8,3,2,5,6]=>1110000=>0001111
[8,7,2,1,6,3,4,5]=>[6,2,7,1,3,4,8,5]=>1100100=>0011011
[8,7,2,1,3,6,4,5]=>[6,7,2,8,1,3,4,5]=>1100000=>0011111
[3,6,5,4,1,2,8,7]=>[4,5,1,6,3,2,8,7]=>1110001=>0001110
[3,8,5,6,7,4,1,2]=>[7,4,6,5,1,8,3,2]=>1111100=>0000011
[4,7,5,8,6,2,1,3]=>[6,2,8,5,1,7,4,3]=>1111100=>0000011
[4,8,5,7,6,3,1,2]=>[6,3,7,5,1,8,4,2]=>1111100=>0000011
[4,6,3,2,1,5,8,7]=>[3,6,2,4,1,5,8,7]=>1100001=>0011110
[6,2,1,5,3,4,8,7]=>[2,5,1,3,6,4,8,7]=>1001001=>0110110
[5,8,1,3,7,6,4,2]=>[6,7,1,3,4,8,5,2]=>1100100=>0011011
[3,7,4,2,8,1,5,6]=>[4,2,8,3,1,7,5,6]=>1110100=>0001011
[4,2,6,8,5,7,3,1]=>[2,5,7,3,8,6,4,1]=>1011010=>0100101
[6,4,2,7,3,8,5,1]=>[8,4,2,3,5,7,6,1]=>1101010=>0010101
[8,1,6,7,5,3,4,2]=>[5,7,3,6,4,8,1,2]=>1011000=>0100111
[2,1,5,8,7,6,3,4]=>[2,1,6,7,3,8,5,4]=>1011100=>0100011
[2,1,4,7,6,3,8,5]=>[2,1,6,4,3,8,7,5]=>1011101=>0100010
[6,4,7,8,5,3,2,1]=>[5,8,3,7,4,2,6,1]=>1111000=>0000111
[4,1,3,7,6,2,8,5]=>[3,6,4,1,2,8,7,5]=>1001101=>0110010
[8,4,6,1,3,2,5,7]=>[6,1,4,3,8,2,5,7]=>1110000=>0001111
[4,2,8,6,7,3,1,5]=>[2,7,3,6,4,1,8,5]=>1011100=>0100011
[7,4,3,8,2,1,5,6]=>[3,8,4,2,7,1,5,6]=>1101000=>0010111
[6,4,3,2,7,8,1,5]=>[3,4,2,8,1,7,6,5]=>1100110=>0011001
[4,2,5,1,6,7,8,3]=>[2,8,7,6,5,1,4,3]=>1010111=>0101000
[2,4,8,5,7,1,3,6]=>[7,5,2,1,8,4,3,6]=>1111100=>0000011
[3,7,1,4,6,8,5,2]=>[4,8,6,5,7,1,3,2]=>1100110=>0011001
[7,8,2,5,6,1,4,3]=>[6,5,2,8,4,7,1,3]=>1101100=>0010011
[2,4,3,8,7,5,6,1]=>[3,7,5,6,8,4,2,1]=>1101100=>0010011
[8,5,7,1,6,3,2,4]=>[6,1,7,5,3,8,2,4]=>1110100=>0001011
[3,4,8,6,5,2,1,7]=>[5,6,2,8,4,3,1,7]=>1111000=>0000111
[4,1,6,3,5,8,7,2]=>[5,7,8,6,3,4,1,2]=>1010010=>0101101
[6,2,5,8,4,3,7,1]=>[2,7,8,4,5,3,6,1]=>1011000=>0100111
[8,6,7,1,5,4,3,2]=>[5,7,1,4,6,3,8,2]=>1110000=>0001111
[2,1,6,5,8,4,7,3]=>[2,1,7,8,5,4,6,3]=>1011100=>0100011
[2,1,6,8,5,4,3,7]=>[2,1,5,8,4,6,3,7]=>1011000=>0100111
[4,1,8,5,6,2,3,7]=>[6,5,1,2,8,4,3,7]=>1011100=>0100011
[2,6,4,8,7,3,5,1]=>[7,4,3,8,5,6,2,1]=>1111100=>0000011
[6,2,8,4,3,5,1,7]=>[2,4,8,3,5,6,1,7]=>1010000=>0101111
[3,1,8,2,7,5,4,6]=>[7,5,8,3,1,2,4,6]=>1010100=>0101011
[3,8,1,2,6,7,4,5]=>[7,6,1,3,2,4,8,5]=>1100110=>0011001
[5,8,4,3,2,7,1,6]=>[4,3,7,2,5,1,8,6]=>1110010=>0001101
[7,4,8,6,3,2,5,1]=>[6,3,8,4,2,5,7,1]=>1111000=>0000111
[5,8,4,7,2,1,3,6]=>[7,4,2,8,1,5,3,6]=>1111000=>0000111
[2,1,8,4,3,7,5,6]=>[2,1,4,7,3,5,8,6]=>1010010=>0101101
[6,3,8,2,4,5,7,1]=>[7,8,3,2,4,5,6,1]=>1110000=>0001111
[5,8,2,4,3,1,6,7]=>[4,8,2,3,5,1,6,7]=>1100000=>0011111
[2,8,3,1,6,4,5,7]=>[3,6,2,1,4,8,5,7]=>1100100=>0011011
[8,2,1,3,4,7,5,6]=>[2,7,1,3,4,5,8,6]=>1000010=>0111101
[1,4,8,2,6,3,5,7]=>[1,6,2,4,3,8,5,7]=>0110100=>1001011
[1,2,7,3,5,4,8,6]=>[1,2,5,8,7,3,4,6]=>0010001=>1101110
[1,2,3,8,4,5,7,6]=>[1,2,3,7,8,4,5,6]=>0001000=>1110111
[1,2,8,3,4,5,7,6]=>[1,2,7,8,3,4,5,6]=>0010000=>1101111
[1,5,7,2,3,6,4,8]=>[1,6,7,2,5,3,4,8]=>0110000=>1001111
[1,7,2,3,5,4,8,6]=>[1,5,8,7,2,3,4,6]=>0100001=>1011110
[1,2,3,8,4,6,7,5]=>[1,2,3,6,7,8,4,5]=>0001000=>1110111
[1,8,2,3,5,4,6,7]=>[1,5,8,2,3,4,6,7]=>0100000=>1011111
[1,7,8,2,3,6,4,5]=>[1,6,8,2,7,3,4,5]=>0110000=>1001111
[1,6,7,8,2,3,5,4]=>[1,8,2,7,3,5,6,4]=>0111000=>1000111
[1,2,8,3,6,4,5,7]=>[1,2,6,3,4,8,5,7]=>0010100=>1101011
[1,8,2,3,6,4,5,7]=>[1,6,2,3,4,8,5,7]=>0100100=>1011011
[1,2,8,3,5,4,6,7]=>[1,2,5,8,3,4,6,7]=>0010000=>1101111
[1,2,7,8,3,6,4,5]=>[1,2,6,8,3,7,4,5]=>0011000=>1100111
[1,5,2,7,8,3,6,4]=>[1,8,2,3,6,7,5,4]=>0101100=>1010011
[1,3,2,8,4,6,7,5]=>[1,3,2,6,7,8,4,5]=>0101000=>1010111
[1,8,2,3,4,6,7,5]=>[1,6,7,8,2,3,4,5]=>0100000=>1011111
[1,7,8,2,4,3,6,5]=>[1,8,2,4,6,7,3,5]=>0110000=>1001111
[7,6,3,1,5,2,4,8]=>[3,5,6,1,7,2,4,8]=>1100000=>0011111
[6,7,3,1,5,2,8,4]=>[3,5,8,7,1,6,2,4]=>1100001=>0011110
[6,8,3,1,5,2,7,4]=>[3,5,7,8,1,6,2,4]=>1100000=>0011111
[6,8,4,5,1,2,7,3]=>[5,4,1,7,8,2,6,3]=>1111000=>0000111
[6,7,4,5,1,2,8,3]=>[5,4,1,8,7,2,6,3]=>1111001=>0000110
[7,2,1,6,5,3,4,8]=>[2,5,6,1,3,7,4,8]=>1001000=>0110111
[7,4,6,5,1,2,3,8]=>[5,1,6,4,2,7,3,8]=>1111000=>0000111
[6,7,5,4,1,2,8,3]=>[4,5,1,8,7,2,6,3]=>1110001=>0001110
[5,8,6,4,1,7,2,3]=>[4,7,6,1,8,2,5,3]=>1110010=>0001101
[5,7,6,4,1,8,2,3]=>[4,8,6,1,7,2,5,3]=>1110010=>0001101
[5,6,7,4,1,8,2,3]=>[4,8,1,7,6,2,5,3]=>1110010=>0001101
[6,5,7,4,1,2,8,3]=>[4,8,7,1,5,2,6,3]=>1110001=>0001110
[6,4,7,5,1,2,8,3]=>[5,1,8,7,4,2,6,3]=>1111001=>0000110
[6,2,1,7,5,3,8,4]=>[2,5,8,7,1,3,6,4]=>1001001=>0110110
[6,3,8,1,5,2,7,4]=>[5,7,8,3,1,6,2,4]=>1110000=>0001111
[6,4,8,5,1,2,7,3]=>[5,1,7,8,4,2,6,3]=>1111000=>0000111
[5,6,8,4,1,7,2,3]=>[4,7,1,8,6,2,5,3]=>1110010=>0001101
[4,6,8,5,7,1,2,3]=>[7,5,1,8,2,6,4,3]=>1111100=>0000011
[4,5,8,6,7,1,2,3]=>[7,1,6,2,8,5,4,3]=>1111100=>0000011
[5,4,8,6,1,7,2,3]=>[7,6,1,8,4,2,5,3]=>1111010=>0000101
[5,3,8,1,6,7,2,4]=>[7,6,3,1,8,5,2,4]=>1110110=>0001001
[5,2,1,8,6,7,3,4]=>[2,7,6,1,3,8,5,4]=>1001110=>0110001
[5,4,7,6,1,8,2,3]=>[8,6,1,7,4,2,5,3]=>1111010=>0000101
[4,8,6,5,7,1,2,3]=>[7,5,1,6,2,8,4,3]=>1111100=>0000011
[4,7,5,6,8,1,2,3]=>[8,1,6,5,2,7,4,3]=>1111100=>0000011
[5,7,4,6,1,8,2,3]=>[8,6,4,1,7,2,5,3]=>1111010=>0000101
[5,8,4,6,1,7,2,3]=>[7,6,4,1,8,2,5,3]=>1111010=>0000101
[5,8,3,1,6,7,2,4]=>[3,7,6,1,8,5,2,4]=>1100110=>0011001
[5,7,3,1,6,8,2,4]=>[3,8,6,1,7,5,2,4]=>1100110=>0011001
[6,2,1,4,3,8,7,5]=>[2,4,7,8,6,1,3,5]=>1000010=>0111101
[5,8,3,1,7,6,2,4]=>[3,6,7,1,8,5,2,4]=>1100100=>0011011
[5,7,4,8,1,6,2,3]=>[6,8,4,1,7,2,5,3]=>1111000=>0000111
[5,2,1,6,8,7,3,4]=>[2,7,1,3,8,6,5,4]=>1001110=>0110001
[4,5,6,8,7,1,2,3]=>[7,1,8,2,6,5,4,3]=>1111100=>0000011
[4,7,5,8,6,1,2,3]=>[6,1,8,5,2,7,4,3]=>1111100=>0000011
[4,8,5,7,6,1,2,3]=>[6,1,7,5,2,8,4,3]=>1111100=>0000011
[4,8,6,7,5,1,2,3]=>[5,7,1,6,2,8,4,3]=>1111000=>0000111
[4,7,6,8,5,1,2,3]=>[5,8,1,6,2,7,4,3]=>1111000=>0000111
[4,6,7,8,5,1,2,3]=>[5,8,1,7,2,6,4,3]=>1111000=>0000111
[4,5,7,8,6,1,2,3]=>[6,1,8,2,7,5,4,3]=>1111100=>0000011
[5,4,7,8,1,6,2,3]=>[6,8,1,7,4,2,5,3]=>1111000=>0000111
[5,3,7,1,8,6,2,4]=>[6,8,3,1,7,5,2,4]=>1110100=>0001011
[5,2,1,7,8,6,3,4]=>[2,6,8,1,3,7,5,4]=>1001100=>0110011
[5,3,8,1,7,6,2,4]=>[6,7,3,1,8,5,2,4]=>1110100=>0001011
[4,6,8,7,5,1,2,3]=>[5,7,1,8,2,6,4,3]=>1111000=>0000111
[4,7,8,6,5,1,2,3]=>[5,6,1,8,2,7,4,3]=>1111000=>0000111
[4,8,7,6,5,1,2,3]=>[5,6,1,7,2,8,4,3]=>1111000=>0000111
[2,5,4,7,3,6,1,8]=>[6,7,4,3,5,2,1,8]=>1111000=>0000111
[2,4,6,3,7,5,1,8]=>[7,5,6,3,4,2,1,8]=>1110100=>0001011
[4,2,7,3,6,5,1,8]=>[2,6,5,7,3,4,1,8]=>1010100=>0101011
[2,5,3,1,6,4,8,7]=>[3,6,5,2,1,4,8,7]=>1100101=>0011010
[2,5,3,7,6,4,1,8]=>[3,6,4,7,5,2,1,8]=>1101100=>0010011
[2,6,3,7,5,4,1,8]=>[3,5,7,4,6,2,1,8]=>1101000=>0010111
[1,7,5,2,3,8,4,6]=>[1,5,2,8,3,4,7,6]=>0110010=>1001101
[2,1,3,7,5,4,8,6]=>[2,1,3,5,8,7,4,6]=>1001001=>0110110
[2,3,1,8,6,5,4,7]=>[3,2,1,6,5,8,4,7]=>1101100=>0010011
[8,3,2,6,4,1,5,7]=>[3,2,6,4,8,1,5,7]=>1101000=>0010111
[1,2,6,3,8,7,4,5]=>[1,2,7,3,4,8,6,5]=>0010110=>1101001
[1,2,8,3,6,4,7,5]=>[1,2,6,3,4,7,8,5]=>0010100=>1101011
[1,2,7,6,3,4,8,5]=>[1,2,6,3,8,7,4,5]=>0011001=>1100110
[2,1,3,8,7,5,4,6]=>[2,1,3,7,5,8,4,6]=>1001100=>0110011
[1,2,3,8,6,4,7,5]=>[1,2,3,6,4,7,8,5]=>0001100=>1110011
[1,2,3,7,4,8,6,5]=>[1,2,3,8,6,7,4,5]=>0001010=>1110101
[1,2,7,6,3,8,4,5]=>[1,2,8,6,3,7,4,5]=>0011010=>1100101
[1,2,3,6,4,8,7,5]=>[1,2,3,7,8,6,4,5]=>0001010=>1110101
[1,2,3,7,6,4,8,5]=>[1,2,3,6,4,8,7,5]=>0001101=>1110010
[7,1,8,4,2,3,5,6]=>[4,8,1,2,7,3,5,6]=>1010000=>0101111
[2,1,8,4,3,5,7,6]=>[2,1,4,7,8,3,5,6]=>1010000=>0101111
[5,4,2,8,3,1,6,7]=>[8,4,2,3,5,1,6,7]=>1101000=>0010111
[3,5,8,2,4,1,6,7]=>[8,2,4,5,3,1,6,7]=>1110000=>0001111
[2,5,4,8,3,1,6,7]=>[8,4,3,5,2,1,6,7]=>1111000=>0000111
[4,2,1,8,3,5,7,6]=>[2,7,8,4,1,3,5,6]=>1001000=>0110111
[1,8,7,4,2,3,5,6]=>[1,4,7,2,8,3,5,6]=>0110000=>1001111
[1,5,2,8,7,3,4,6]=>[1,7,2,3,8,5,4,6]=>0101100=>1010011
[1,2,7,3,6,4,8,5]=>[1,2,6,3,4,8,7,5]=>0010101=>1101010
[1,2,8,6,3,7,4,5]=>[1,2,7,6,3,8,4,5]=>0011010=>1100101
[1,2,7,3,8,6,4,5]=>[1,2,6,8,3,4,7,5]=>0010100=>1101011
[1,2,3,8,4,7,6,5]=>[1,2,3,7,6,8,4,5]=>0001010=>1110101
[1,2,6,3,8,4,7,5]=>[1,2,7,8,3,4,6,5]=>0010100=>1101011
[1,5,2,3,8,7,4,6]=>[1,7,5,2,3,4,8,6]=>0100110=>1011001
[4,2,1,8,3,7,5,6]=>[2,7,4,1,3,5,8,6]=>1001010=>0110101
[8,3,2,1,7,4,5,6]=>[3,2,7,1,4,8,5,6]=>1100100=>0011011
[1,8,4,2,7,3,5,6]=>[1,4,2,7,3,8,5,6]=>0110100=>1001011
[1,2,8,6,3,4,7,5]=>[1,2,6,3,7,8,4,5]=>0011000=>1100111
[1,2,7,3,8,4,6,5]=>[1,2,8,3,4,6,7,5]=>0010100=>1101011
[1,2,3,8,7,4,6,5]=>[1,2,3,7,4,6,8,5]=>0001100=>1110011
[1,2,3,8,7,6,4,5]=>[1,2,3,6,7,4,8,5]=>0001100=>1110011
[2,5,3,8,1,6,4,7]=>[3,6,8,2,1,5,4,7]=>1101000=>0010111
[2,6,4,7,1,5,3,8]=>[7,4,2,1,5,6,3,8]=>1111000=>0000111
[2,6,5,7,1,4,3,8]=>[7,2,1,5,4,6,3,8]=>1111000=>0000111
[3,8,5,7,1,2,6,4]=>[7,1,5,3,2,6,8,4]=>1111000=>0000111
[3,4,8,6,1,2,5,7]=>[6,1,8,4,3,2,5,7]=>1111000=>0000111
[2,4,8,1,5,7,6,3]=>[5,7,6,8,2,1,4,3]=>1110010=>0001101
[2,4,3,8,1,6,5,7]=>[3,6,8,4,2,1,5,7]=>1101000=>0010111
[2,8,1,7,5,6,4,3]=>[5,6,7,4,8,2,1,3]=>1101000=>0010111
[2,3,8,1,6,5,7,4]=>[6,5,7,8,3,2,1,4]=>1110100=>0001011
[2,4,8,1,3,5,7,6]=>[7,8,2,1,4,3,5,6]=>1110000=>0001111
[3,5,7,6,2,4,8,1]=>[6,2,8,7,4,5,3,1]=>1111001=>0000110
[4,8,6,7,1,2,3,5]=>[7,1,6,2,8,4,3,5]=>1111000=>0000111
[4,8,6,7,1,3,5,2]=>[7,1,6,3,5,8,4,2]=>1111000=>0000111
[3,4,8,6,1,5,7,2]=>[6,1,5,7,8,4,3,2]=>1111000=>0000111
[3,2,8,5,6,1,7,4]=>[2,6,5,3,1,7,8,4]=>1011100=>0100011
[3,4,8,6,2,1,5,7]=>[6,2,8,4,3,1,5,7]=>1111000=>0000111
[3,5,7,6,2,1,4,8]=>[6,2,7,3,1,5,4,8]=>1111000=>0000111
[4,8,6,7,2,1,3,5]=>[7,2,6,1,8,4,3,5]=>1111000=>0000111
[5,8,6,7,3,4,2,1]=>[7,3,6,4,8,2,5,1]=>1111000=>0000111
[4,3,2,8,5,1,7,6]=>[3,2,5,7,8,4,1,6]=>1101000=>0010111
[4,3,8,5,1,6,7,2]=>[5,3,1,6,7,8,4,2]=>1111000=>0000111
[4,8,6,7,1,5,3,2]=>[7,1,5,6,3,8,4,2]=>1111000=>0000111
[5,8,6,7,1,4,3,2]=>[7,1,6,4,8,3,5,2]=>1111000=>0000111
[5,8,6,7,1,2,4,3]=>[7,1,6,2,8,4,5,3]=>1111000=>0000111
[3,4,2,8,5,6,1,7]=>[5,6,8,4,2,3,1,7]=>1101000=>0010111
[3,2,4,8,6,1,5,7]=>[2,6,4,3,1,8,5,7]=>1011100=>0100011
[3,2,5,7,6,1,4,8]=>[2,6,3,1,7,5,4,8]=>1011100=>0100011
[4,3,8,5,1,2,6,7]=>[5,3,1,8,4,2,6,7]=>1111000=>0000111
[3,8,5,7,1,4,2,6]=>[7,1,5,4,8,3,2,6]=>1111000=>0000111
[3,8,4,7,1,5,2,6]=>[7,4,1,5,8,3,2,6]=>1111000=>0000111
[3,5,2,8,4,6,1,7]=>[6,8,4,5,2,3,1,7]=>1101000=>0010111
[3,5,1,7,4,6,2,8]=>[6,7,4,5,1,3,2,8]=>1101000=>0010111
[3,8,4,7,2,5,1,6]=>[7,4,2,5,8,3,1,6]=>1111000=>0000111
[4,1,3,8,5,2,6,7]=>[3,5,8,4,1,2,6,7]=>1001000=>0110111
[4,1,2,6,7,5,3,8]=>[7,5,6,4,1,2,3,8]=>1001100=>0110011
[4,2,6,7,5,3,8,1]=>[2,5,8,7,3,6,4,1]=>1011001=>0100110
[4,8,6,7,2,3,1,5]=>[7,2,6,3,8,4,1,5]=>1111000=>0000111
[5,8,6,7,3,2,4,1]=>[7,3,6,2,8,4,5,1]=>1111000=>0000111
[5,8,6,7,4,2,3,1]=>[7,4,6,2,8,3,5,1]=>1111000=>0000111
[5,8,6,7,4,1,3,2]=>[7,4,6,1,8,3,5,2]=>1111000=>0000111
[5,8,6,7,3,1,4,2]=>[7,3,6,1,8,4,5,2]=>1111000=>0000111
[4,8,6,7,3,1,5,2]=>[7,3,6,1,5,8,4,2]=>1111000=>0000111
[4,1,7,5,3,2,8,6]=>[5,3,8,7,4,1,2,6]=>1011001=>0100110
[4,8,6,7,3,2,1,5]=>[7,3,6,2,8,4,1,5]=>1111000=>0000111
[5,8,6,7,4,2,1,3]=>[7,4,6,2,8,1,5,3]=>1111000=>0000111
[5,8,6,7,4,3,1,2]=>[7,4,6,3,8,1,5,2]=>1111000=>0000111
[7,3,5,8,1,4,2,6]=>[8,3,1,5,4,7,2,6]=>1111000=>0000111
[3,8,7,6,1,4,2,5]=>[6,1,7,4,8,3,2,5]=>1111000=>0000111
[5,1,8,3,6,7,2,4]=>[7,6,3,8,5,1,2,4]=>1010110=>0101001
[1,4,7,8,5,6,2,3]=>[1,5,6,8,2,7,4,3]=>0111000=>1000111
[3,4,7,1,5,8,6,2]=>[5,8,6,7,1,4,3,2]=>1110010=>0001101
[3,6,1,4,7,8,5,2]=>[4,8,5,7,6,1,3,2]=>1100110=>0011001
[1,6,8,4,7,5,2,3]=>[1,4,7,5,8,2,6,3]=>0110100=>1001011
[6,8,1,3,5,7,2,4]=>[5,7,1,3,8,6,2,4]=>1100010=>0011101
[3,8,1,6,5,4,2,7]=>[5,6,4,8,1,3,2,7]=>1101000=>0010111
[4,1,3,7,5,8,2,6]=>[3,5,8,4,1,2,7,6]=>1001010=>0110101
[6,1,7,3,8,4,2,5]=>[8,3,4,7,1,2,6,5]=>1010100=>0101011
[8,2,7,6,5,3,4,1]=>[2,5,6,3,7,4,8,1]=>1011000=>0100111
[8,4,2,6,7,5,3,1]=>[7,5,6,4,2,3,8,1]=>1101100=>0010011
[4,8,1,6,7,5,3,2]=>[7,5,6,1,3,8,4,2]=>1101100=>0010011
[1,3,8,6,2,7,5,4]=>[1,7,6,3,2,5,8,4]=>0111010=>1000101
[6,1,3,2,7,8,4,5]=>[3,8,1,2,4,7,6,5]=>1000110=>0111001
[1,8,6,2,5,3,4,7]=>[1,5,6,2,8,3,4,7]=>0110000=>1001111
[4,7,2,6,8,1,5,3]=>[8,2,6,5,7,4,1,3]=>1101100=>0010011
[8,7,3,6,4,5,2,1]=>[3,6,4,5,7,2,8,1]=>1101000=>0010111
[5,7,8,6,2,1,4,3]=>[6,2,8,1,7,4,5,3]=>1111000=>0000111
[2,7,4,1,6,8,3,5]=>[4,2,1,8,6,3,7,5]=>1110110=>0001001
[1,8,6,4,5,2,3,7]=>[1,4,5,6,2,8,3,7]=>0110000=>1001111
[2,8,4,6,5,1,3,7]=>[5,6,4,2,1,8,3,7]=>1111000=>0000111
[3,4,1,7,5,2,6,8]=>[5,7,4,1,3,2,6,8]=>1101000=>0010111
[5,6,8,7,3,1,4,2]=>[7,3,8,1,6,4,5,2]=>1111000=>0000111
[3,8,5,4,6,2,1,7]=>[4,6,5,2,8,3,1,7]=>1110100=>0001011
[6,4,1,2,7,5,8,3]=>[4,1,8,7,5,6,2,3]=>1100101=>0011010
[4,1,8,3,6,7,5,2]=>[7,6,5,8,3,4,1,2]=>1010110=>0101001
[8,3,7,4,5,2,6,1]=>[4,5,7,3,2,6,8,1]=>1110000=>0001111
[4,3,7,8,5,1,6,2]=>[5,8,3,1,6,7,4,2]=>1111000=>0000111
[5,4,8,2,7,6,1,3]=>[6,7,2,4,1,8,5,3]=>1110100=>0001011
[1,2,7,3,6,5,8,4]=>[1,2,6,5,8,7,3,4]=>0010101=>1101010
[2,8,7,6,3,4,1,5]=>[6,3,7,4,8,2,1,5]=>1111000=>0000111
[5,8,2,6,3,4,1,7]=>[6,2,3,8,4,5,1,7]=>1101000=>0010111
[4,1,7,5,8,6,2,3]=>[6,8,5,1,2,7,4,3]=>1011100=>0100011
[1,4,3,5,7,8,2,6]=>[1,3,8,5,4,2,7,6]=>0101110=>1010001
[6,5,8,7,1,3,4,2]=>[7,1,8,3,5,4,6,2]=>1111000=>0000111
[3,6,7,2,4,8,1,5]=>[8,2,4,7,6,3,1,5]=>1110010=>0001101
[1,5,2,7,4,3,8,6]=>[1,8,7,4,5,2,3,6]=>0101001=>1010110
[2,8,5,6,4,3,1,7]=>[6,4,5,3,8,2,1,7]=>1111000=>0000111
[1,8,6,5,4,3,2,7]=>[1,5,4,6,3,8,2,7]=>0111000=>1000111
[4,6,1,8,5,7,2,3]=>[5,7,1,8,6,4,2,3]=>1101010=>0010101
[4,7,1,2,8,5,6,3]=>[8,5,6,7,1,4,2,3]=>1100100=>0011011
[1,4,7,2,8,5,6,3]=>[1,8,5,6,7,2,4,3]=>0110100=>1001011
[1,7,3,5,8,6,2,4]=>[1,3,6,8,5,2,7,4]=>0101100=>1010011
[7,3,5,8,6,1,2,4]=>[6,3,1,8,5,2,7,4]=>1111100=>0000011
[3,6,8,1,5,7,2,4]=>[5,7,1,8,6,3,2,4]=>1110010=>0001101
[3,4,6,5,8,1,7,2]=>[7,8,5,1,6,4,3,2]=>1111100=>0000011
[6,8,1,5,7,2,3,4]=>[7,5,1,8,2,3,6,4]=>1101100=>0010011
[7,1,2,5,8,6,3,4]=>[6,8,5,1,2,3,7,4]=>1001100=>0110011
[1,7,2,5,8,6,3,4]=>[1,6,8,5,2,3,7,4]=>0101100=>1010011
[7,6,8,1,2,3,5,4]=>[8,1,6,2,5,7,3,4]=>1110000=>0001111
[2,4,7,1,8,5,6,3]=>[8,5,6,7,2,1,4,3]=>1110100=>0001011
[7,6,8,2,1,3,5,4]=>[8,2,6,1,5,7,3,4]=>1110000=>0001111
[1,2,7,6,8,3,5,4]=>[1,2,8,3,6,5,7,4]=>0011100=>1100011
[3,7,6,8,2,1,5,4]=>[8,2,6,3,1,5,7,4]=>1111000=>0000111
[7,4,2,1,6,8,5,3]=>[4,2,8,6,5,7,1,3]=>1100110=>0011001
[6,7,4,1,8,5,3,2]=>[4,1,8,5,7,3,6,2]=>1110100=>0001011
[6,7,4,3,1,8,5,2]=>[4,3,8,1,5,7,6,2]=>1110010=>0001101
[2,3,7,6,8,1,5,4]=>[8,3,2,1,6,5,7,4]=>1111100=>0000011
[7,3,2,5,8,6,1,4]=>[3,2,6,8,5,1,7,4]=>1101100=>0010011
[3,7,6,8,1,2,5,4]=>[8,1,6,3,2,5,7,4]=>1111000=>0000111
[1,7,4,2,6,8,5,3]=>[1,4,2,8,6,5,7,3]=>0110110=>1001001
[7,1,4,2,8,5,6,3]=>[4,1,2,8,5,6,7,3]=>1010100=>0101011
[7,3,8,4,6,1,5,2]=>[4,6,3,1,8,5,7,2]=>1110100=>0001011
[7,1,6,8,5,4,2,3]=>[5,8,4,6,1,2,7,3]=>1011000=>0100111
[7,1,2,6,8,5,4,3]=>[8,5,6,4,7,1,2,3]=>1001100=>0110011
[1,7,2,6,8,5,4,3]=>[1,8,5,6,4,7,2,3]=>0101100=>1010011
[7,6,8,3,1,2,5,4]=>[8,3,6,1,5,7,2,4]=>1110000=>0001111
[7,2,5,8,6,3,1,4]=>[2,6,3,8,5,1,7,4]=>1011100=>0100011
[3,6,7,1,8,5,4,2]=>[8,5,7,1,4,6,3,2]=>1110100=>0001011
[7,2,6,8,5,4,1,3]=>[2,5,8,4,6,1,7,3]=>1011000=>0100111
[7,6,8,2,3,1,5,4]=>[8,2,6,3,5,7,1,4]=>1110000=>0001111
[6,7,1,8,5,4,3,2]=>[5,8,4,7,1,3,6,2]=>1101000=>0010111
[4,7,8,5,6,1,3,2]=>[6,5,1,8,3,7,4,2]=>1111100=>0000011
[4,6,5,8,7,1,3,2]=>[7,1,8,5,3,6,4,2]=>1111100=>0000011
[5,6,4,8,1,2,7,3]=>[7,8,4,1,6,2,5,3]=>1111000=>0000111
[6,4,5,1,8,2,7,3]=>[7,8,5,1,4,2,6,3]=>1110100=>0001011
[5,3,6,7,1,4,2,8]=>[7,3,1,6,4,5,2,8]=>1111000=>0000111
[8,1,3,6,7,4,5,2]=>[3,7,4,6,5,8,1,2]=>1001100=>0110011
[5,2,6,7,1,4,8,3]=>[2,8,7,1,6,4,5,3]=>1011001=>0100110
[8,1,4,5,3,7,2,6]=>[5,4,3,7,1,2,8,6]=>1011010=>0100101
[7,3,1,5,4,8,2,6]=>[3,1,5,4,8,2,7,6]=>1101010=>0010101
[5,3,4,2,1,8,6,7]=>[4,3,2,5,1,8,6,7]=>1110010=>0001101
[4,3,5,2,7,1,6,8]=>[7,5,3,2,4,1,6,8]=>1110100=>0001011
[5,6,3,8,1,4,2,7]=>[3,8,1,6,4,5,2,7]=>1101000=>0010111
[8,1,7,2,4,5,6,3]=>[7,1,2,4,5,6,8,3]=>1010000=>0101111
[5,6,2,8,1,4,7,3]=>[7,8,2,6,4,5,1,3]=>1101000=>0010111
[6,5,2,1,3,7,8,4]=>[5,2,8,7,6,1,3,4]=>1100011=>0011100
[5,4,2,3,1,6,8,7]=>[4,2,3,5,1,6,8,7]=>1100001=>0011110
[7,3,1,4,5,6,2,8]=>[3,1,4,5,6,7,2,8]=>1100000=>0011111
[7,8,4,2,1,5,6,3]=>[4,2,8,1,5,6,7,3]=>1110000=>0001111
[6,2,3,4,8,7,1,5]=>[2,3,4,7,1,8,6,5]=>1000110=>0111001
[6,2,3,4,7,8,1,5]=>[2,3,4,8,1,7,6,5]=>1000110=>0111001
[7,8,3,4,6,2,1,5]=>[3,4,6,2,8,1,7,5]=>1100100=>0011011
[7,8,3,6,4,2,1,5]=>[3,6,4,8,2,7,1,5]=>1101000=>0010111
[7,8,3,5,6,2,1,4]=>[3,6,5,2,8,1,7,4]=>1101100=>0010011
[6,2,3,7,8,5,1,4]=>[2,3,8,5,7,1,6,4]=>1001100=>0110011
[5,2,6,3,8,1,7,4]=>[2,7,8,3,6,5,1,4]=>1010100=>0101011
[6,3,2,5,8,7,1,4]=>[3,2,7,5,1,8,6,4]=>1101110=>0010001
[6,3,2,8,4,7,1,5]=>[3,2,7,4,8,6,1,5]=>1101010=>0010101
[6,3,2,7,4,8,1,5]=>[3,2,8,4,7,6,1,5]=>1101010=>0010101
[5,7,2,3,6,1,8,4]=>[6,2,3,8,7,5,1,4]=>1100101=>0011010
[5,8,2,3,6,1,7,4]=>[6,2,3,7,8,5,1,4]=>1100100=>0011011
[4,7,5,8,3,2,1,6]=>[8,3,5,2,7,4,1,6]=>1111000=>0000111
[4,5,6,8,3,2,1,7]=>[8,3,6,2,5,4,1,7]=>1111000=>0000111
[5,6,8,4,3,7,1,2]=>[4,7,3,8,6,1,5,2]=>1110010=>0001101
[5,6,1,4,2,3,8,7]=>[4,6,1,5,2,3,8,7]=>1100001=>0011110
[5,2,8,3,4,1,7,6]=>[2,7,8,3,4,5,1,6]=>1010000=>0101111
[4,5,8,6,3,2,1,7]=>[6,3,8,2,5,4,1,7]=>1111000=>0000111
[4,7,5,6,3,2,1,8]=>[6,3,5,2,7,4,1,8]=>1111000=>0000111
[6,2,3,4,5,8,1,7]=>[2,3,4,5,8,6,1,7]=>1000010=>0111101
[5,1,4,3,8,2,7,6]=>[4,3,7,8,5,1,2,6]=>1010100=>0101011
[5,6,2,4,1,8,7,3]=>[4,7,8,6,2,5,1,3]=>1100010=>0011101
[5,7,2,4,1,8,6,3]=>[4,8,6,7,2,5,1,3]=>1100010=>0011101
[6,1,4,2,7,8,5,3]=>[4,1,2,8,5,7,6,3]=>1010110=>0101001
[5,8,2,4,1,7,6,3]=>[4,7,6,8,2,5,1,3]=>1100010=>0011101
[5,2,7,4,1,6,8,3]=>[2,4,6,8,7,1,5,3]=>1010001=>0101110
[5,4,1,3,7,2,6,8]=>[4,1,3,7,5,2,6,8]=>1100100=>0011011
[5,1,4,3,6,2,7,8]=>[4,3,6,5,1,2,7,8]=>1010100=>0101011
[5,8,6,4,3,7,1,2]=>[4,7,6,3,8,1,5,2]=>1110010=>0001101
[4,8,6,5,3,2,1,7]=>[5,3,6,2,8,4,1,7]=>1111000=>0000111
[4,6,8,7,3,2,1,5]=>[7,3,8,2,6,4,1,5]=>1111000=>0000111
[4,6,7,8,3,2,1,5]=>[8,3,7,2,6,4,1,5]=>1111000=>0000111
[5,1,8,4,2,3,6,7]=>[4,8,1,2,5,3,6,7]=>1010000=>0101111
[5,1,7,4,2,3,6,8]=>[4,7,1,2,5,3,6,8]=>1010000=>0101111
[5,8,1,3,4,2,6,7]=>[8,1,3,4,5,2,6,7]=>1100000=>0011111
[4,8,7,5,3,2,1,6]=>[5,3,7,2,8,4,1,6]=>1111000=>0000111
[4,7,8,6,3,2,1,5]=>[6,3,8,2,7,4,1,5]=>1111000=>0000111
[4,8,7,6,3,2,1,5]=>[6,3,7,2,8,4,1,5]=>1111000=>0000111
[4,8,2,6,3,7,5,1]=>[7,6,2,3,5,8,4,1]=>1101010=>0010101
[4,8,2,3,6,7,5,1]=>[7,6,5,8,2,3,4,1]=>1100110=>0011001
[4,8,3,1,6,7,5,2]=>[3,7,6,5,8,1,4,2]=>1100110=>0011001
[4,3,8,1,6,2,5,7]=>[6,3,1,4,2,8,5,7]=>1110100=>0001011
[1,4,8,7,3,5,2,6]=>[1,7,3,5,8,4,2,6]=>0111000=>1000111
[5,8,4,3,7,1,6,2]=>[4,3,7,1,6,8,5,2]=>1110100=>0001011
[5,8,1,4,7,2,6,3]=>[4,7,1,6,8,5,2,3]=>1100100=>0011011
[5,8,1,7,4,2,3,6]=>[7,4,8,1,5,2,3,6]=>1101000=>0010111
[6,8,1,2,4,3,5,7]=>[8,1,4,6,2,3,5,7]=>1100000=>0011111
[5,8,7,1,3,4,2,6]=>[7,1,8,3,4,5,2,6]=>1110000=>0001111
[4,8,7,6,3,1,2,5]=>[6,3,7,1,8,4,2,5]=>1111000=>0000111
[5,8,4,7,3,1,2,6]=>[7,4,3,8,1,5,2,6]=>1111000=>0000111
[1,4,8,3,7,5,6,2]=>[1,7,5,6,8,3,4,2]=>0110100=>1001011
[4,3,2,8,1,6,5,7]=>[3,2,6,8,4,1,5,7]=>1101000=>0010111
[4,1,3,8,2,6,5,7]=>[3,6,8,4,1,2,5,7]=>1001000=>0110111
[4,1,8,3,7,5,6,2]=>[7,5,6,8,3,4,1,2]=>1010100=>0101011
[4,1,8,7,3,5,2,6]=>[7,3,5,8,4,1,2,6]=>1011000=>0100111
[3,7,8,1,5,4,2,6]=>[5,8,1,4,7,3,2,6]=>1110000=>0001111
[7,3,8,1,5,4,6,2]=>[5,8,3,1,4,6,7,2]=>1110000=>0001111
[3,4,8,1,6,2,5,7]=>[6,1,4,3,2,8,5,7]=>1110100=>0001011
[3,4,8,7,2,5,1,6]=>[7,2,5,8,4,3,1,6]=>1111000=>0000111
[1,2,4,8,3,6,5,7]=>[1,2,6,8,4,3,5,7]=>0011000=>1100111
[1,2,4,3,8,6,5,7]=>[1,2,4,3,6,8,5,7]=>0010100=>1101011
[3,4,2,1,8,6,5,7]=>[4,2,3,1,6,8,5,7]=>1100100=>0011011
[3,4,1,8,2,6,5,7]=>[6,8,4,1,3,2,5,7]=>1101000=>0010111
[4,1,2,8,3,6,5,7]=>[6,8,4,1,2,3,5,7]=>1001000=>0110111
[4,2,3,1,8,6,5,7]=>[2,3,4,1,6,8,5,7]=>1000100=>0111011
[3,7,6,8,4,2,1,5]=>[8,4,6,2,7,3,1,5]=>1111000=>0000111
[4,7,1,8,5,2,3,6]=>[5,8,1,7,4,2,3,6]=>1101000=>0010111
[2,6,8,7,4,3,1,5]=>[7,4,8,3,6,2,1,5]=>1111000=>0000111
[4,2,3,8,1,6,5,7]=>[2,3,6,8,4,1,5,7]=>1001000=>0110111
[4,3,1,8,2,6,5,7]=>[3,1,6,8,4,2,5,7]=>1101000=>0010111
[1,4,7,8,5,3,2,6]=>[1,5,8,3,7,4,2,6]=>0111000=>1000111
[3,7,2,8,4,6,5,1]=>[6,8,4,5,7,2,3,1]=>1101000=>0010111
[4,2,8,6,3,1,5,7]=>[2,6,3,8,4,1,5,7]=>1011000=>0100111
[2,4,8,6,3,1,5,7]=>[6,3,8,4,2,1,5,7]=>1111000=>0000111
[1,7,3,8,4,6,5,2]=>[1,3,6,8,4,5,7,2]=>0101000=>1010111
[1,3,4,8,2,6,5,7]=>[1,6,8,4,3,2,5,7]=>0111000=>1000111
[7,3,8,6,2,4,1,5]=>[6,3,2,8,4,7,1,5]=>1111000=>0000111
[2,4,8,3,6,1,5,7]=>[6,3,4,2,1,8,5,7]=>1110100=>0001011
[6,2,8,7,4,3,5,1]=>[2,7,4,8,3,5,6,1]=>1011000=>0100111
[7,4,1,8,5,2,6,3]=>[5,8,4,1,6,7,2,3]=>1101000=>0010111
[2,4,3,1,8,6,5,7]=>[3,4,2,1,6,8,5,7]=>1100100=>0011011
[1,3,2,4,8,6,5,7]=>[1,3,2,4,6,8,5,7]=>0100100=>1011011
[3,1,2,4,8,6,5,7]=>[3,1,2,4,6,8,5,7]=>1000100=>0111011
[3,1,4,2,8,6,5,7]=>[4,3,1,2,6,8,5,7]=>1010100=>0101011
[7,3,4,8,5,1,6,2]=>[5,8,4,3,1,6,7,2]=>1111000=>0000111
[2,3,1,4,8,6,5,7]=>[3,2,1,4,6,8,5,7]=>1100100=>0011011
[1,2,3,4,8,6,5,7]=>[1,2,3,4,6,8,5,7]=>0000100=>1111011
[5,3,8,7,2,4,6,1]=>[7,3,2,6,8,4,5,1]=>1111000=>0000111
[2,8,4,5,7,3,6,1]=>[7,5,4,3,6,8,2,1]=>1111100=>0000011
[2,4,5,7,3,8,1,6]=>[8,3,5,4,2,1,7,6]=>1111010=>0000101
[6,2,4,5,8,3,1,7]=>[2,8,5,4,3,6,1,7]=>1011100=>0100011
[4,8,1,2,5,6,3,7]=>[5,6,8,1,4,2,3,7]=>1100000=>0011111
[8,1,3,5,2,6,4,7]=>[3,5,1,2,6,8,4,7]=>1001000=>0110111
[5,2,1,6,3,8,4,7]=>[2,8,6,1,3,5,4,7]=>1001010=>0110101
[6,1,4,5,8,3,2,7]=>[8,5,4,3,6,1,2,7]=>1011100=>0100011
[5,6,4,8,1,3,2,7]=>[8,4,1,6,3,5,2,7]=>1111000=>0000111
[6,5,4,3,8,2,1,7]=>[4,3,8,5,2,6,1,7]=>1110100=>0001011
[5,4,3,7,2,8,1,6]=>[3,8,4,2,5,1,7,6]=>1101010=>0010101
[5,8,4,3,7,2,6,1]=>[4,3,7,2,6,8,5,1]=>1110100=>0001011
[4,6,8,3,7,2,5,1]=>[7,3,8,5,6,2,4,1]=>1110100=>0001011
[1,4,3,6,2,7,8,5]=>[1,3,8,7,6,4,2,5]=>0101011=>1010100
[4,3,8,1,6,7,5,2]=>[7,6,5,8,3,1,4,2]=>1110110=>0001001
[4,7,8,3,6,1,5,2]=>[6,3,8,5,7,1,4,2]=>1110100=>0001011
[5,3,8,6,7,4,1,2]=>[7,4,6,3,1,8,5,2]=>1111100=>0000011
[1,3,8,6,4,7,5,2]=>[1,7,6,4,5,8,3,2]=>0111010=>1000101
[7,6,2,1,4,3,8,5]=>[6,2,4,8,7,1,3,5]=>1100001=>0011110
[1,6,7,3,2,5,8,4]=>[1,8,7,3,5,6,2,4]=>0110001=>1001110
[3,2,6,8,5,7,4,1]=>[2,5,7,4,8,6,3,1]=>1011010=>0100101
[5,8,2,3,6,7,4,1]=>[7,6,2,3,4,8,5,1]=>1100110=>0011001
[1,6,4,7,2,3,8,5]=>[1,8,7,4,2,6,3,5]=>0111001=>1000110
[3,1,7,5,2,8,4,6]=>[5,3,1,2,8,4,7,6]=>1011010=>0100101
[4,2,6,1,7,8,3,5]=>[2,8,1,4,3,7,6,5]=>1010110=>0101001
[6,4,8,7,2,3,5,1]=>[7,2,8,4,3,5,6,1]=>1111000=>0000111
[3,2,7,4,1,6,8,5]=>[2,4,6,8,7,3,1,5]=>1010001=>0101110
[6,3,2,1,7,8,4,5]=>[3,2,8,1,4,7,6,5]=>1100110=>0011001
[3,7,1,8,4,2,5,6]=>[8,4,7,1,3,2,5,6]=>1101000=>0010111
[4,2,1,3,7,5,8,6]=>[2,4,1,3,8,7,5,6]=>1000101=>0111010
[3,6,2,8,7,1,5,4]=>[7,2,3,1,8,5,6,4]=>1101100=>0010011
[7,3,2,8,1,6,5,4]=>[3,2,6,8,1,5,7,4]=>1101000=>0010111
[4,2,7,8,6,1,5,3]=>[2,6,1,8,5,7,4,3]=>1011100=>0100011
[6,8,2,4,7,1,5,3]=>[4,7,2,8,5,6,1,3]=>1100100=>0011011
[5,2,1,8,7,3,6,4]=>[2,7,1,3,6,8,5,4]=>1001100=>0110011
[8,2,1,6,3,7,5,4]=>[2,7,6,1,3,5,8,4]=>1001010=>0110101
[6,8,3,1,7,5,2,4]=>[3,7,5,8,1,6,2,4]=>1100100=>0011011
[5,8,1,6,7,2,4,3]=>[7,1,6,4,8,5,2,3]=>1101100=>0010011
[6,2,8,1,5,7,4,3]=>[2,5,7,1,4,8,6,3]=>1010010=>0101101
[8,7,2,5,6,4,3,1]=>[6,5,4,7,2,3,8,1]=>1101100=>0010011
[7,2,6,8,1,5,4,3]=>[2,8,1,5,6,4,7,3]=>1011000=>0100111
[1,2,7,8,5,6,4,3]=>[1,2,5,6,8,4,7,3]=>0011000=>1100111
[7,4,8,1,6,2,5,3]=>[6,1,4,2,8,5,7,3]=>1110100=>0001011
[3,7,1,8,2,6,5,4]=>[6,8,1,3,2,5,7,4]=>1101000=>0010111
[2,1,7,3,8,6,5,4]=>[2,1,6,8,5,7,3,4]=>1010100=>0101011
[8,1,4,7,6,5,3,2]=>[6,5,7,4,3,8,1,2]=>1011100=>0100011
[5,8,4,3,2,1,6,7]=>[4,3,8,2,5,1,6,7]=>1110000=>0001111
[5,8,3,6,2,1,4,7]=>[3,6,2,8,1,5,4,7]=>1101000=>0010111
[6,3,7,8,2,1,4,5]=>[8,3,2,7,1,6,4,5]=>1111000=>0000111
[5,3,7,6,2,1,4,8]=>[6,3,2,7,1,5,4,8]=>1111000=>0000111
[5,8,4,2,6,1,3,7]=>[4,2,6,1,8,5,3,7]=>1110100=>0001011
[4,8,7,2,5,1,3,6]=>[5,7,2,8,1,4,3,6]=>1110000=>0001111
[5,8,3,2,6,1,4,7]=>[3,6,2,8,5,1,4,7]=>1100100=>0011011
[4,8,3,2,5,1,7,6]=>[3,5,7,8,2,4,1,6]=>1100000=>0011111
[4,3,7,2,5,1,8,6]=>[5,8,7,3,2,4,1,6]=>1110001=>0001110
[6,4,2,7,5,1,3,8]=>[5,7,4,2,6,1,3,8]=>1101000=>0010111
[6,3,2,7,5,1,4,8]=>[3,2,5,7,1,6,4,8]=>1101000=>0010111
[3,8,2,6,5,1,4,7]=>[5,6,2,3,1,8,4,7]=>1101000=>0010111
[6,2,7,8,5,1,3,4]=>[2,5,8,1,7,3,6,4]=>1011000=>0100111
[4,2,7,6,5,1,3,8]=>[2,5,6,1,7,4,3,8]=>1011000=>0100111
[2,8,7,6,5,1,3,4]=>[5,6,2,1,7,3,8,4]=>1111000=>0000111
[6,4,7,3,1,5,8,2]=>[8,7,3,4,1,5,6,2]=>1110001=>0001110
[5,4,7,3,1,8,6,2]=>[8,6,7,3,4,1,5,2]=>1110010=>0001101
[5,4,3,6,1,8,7,2]=>[3,7,8,6,4,1,5,2]=>1101010=>0010101
[5,3,7,6,1,4,8,2]=>[6,3,1,8,7,4,5,2]=>1111001=>0000110
[3,8,7,6,1,4,5,2]=>[6,1,7,4,5,8,3,2]=>1111000=>0000111
[4,8,3,2,1,5,7,6]=>[3,7,8,2,4,1,5,6]=>1100000=>0011111
[3,8,7,2,1,4,5,6]=>[7,2,8,3,1,4,5,6]=>1110000=>0001111
[6,5,2,7,1,4,3,8]=>[7,2,5,4,6,1,3,8]=>1101000=>0010111
[5,8,2,6,1,4,3,7]=>[6,2,8,4,5,1,3,7]=>1101000=>0010111
[6,4,2,7,1,5,3,8]=>[7,4,2,5,6,1,3,8]=>1101000=>0010111
[5,4,2,6,1,8,3,7]=>[8,6,4,2,5,1,3,7]=>1101010=>0010101
[6,2,7,8,1,4,3,5]=>[2,8,1,7,4,6,3,5]=>1011000=>0100111
[4,2,7,6,1,5,3,8]=>[2,6,1,5,7,4,3,8]=>1011000=>0100111
[3,2,7,6,1,4,5,8]=>[2,6,3,1,7,4,5,8]=>1011000=>0100111
[5,8,4,1,6,7,3,2]=>[4,1,7,6,3,8,5,2]=>1110110=>0001001
[5,4,7,1,6,8,3,2]=>[8,6,1,4,3,7,5,2]=>1110110=>0001001
[4,8,7,1,5,6,3,2]=>[5,6,7,1,8,3,4,2]=>1110000=>0001111
[5,4,3,1,6,8,7,2]=>[3,4,1,7,8,6,5,2]=>1100110=>0011001
[4,8,3,1,5,6,7,2]=>[3,5,6,7,8,1,4,2]=>1100000=>0011111
[3,8,7,1,5,4,6,2]=>[5,7,1,4,6,8,3,2]=>1110000=>0001111
[5,8,2,1,6,4,3,7]=>[6,2,4,8,5,1,3,7]=>1100100=>0011011
[3,8,2,1,5,4,6,7]=>[5,8,2,3,1,4,6,7]=>1100000=>0011111
[6,2,7,1,5,4,3,8]=>[2,5,7,1,4,6,3,8]=>1010000=>0101111
[5,2,7,1,6,4,3,8]=>[2,6,1,4,7,5,3,8]=>1010100=>0101011
[3,2,7,1,5,4,6,8]=>[2,5,7,3,1,4,6,8]=>1010000=>0101111
[6,4,1,7,5,8,3,2]=>[5,8,4,1,3,7,6,2]=>1101010=>0010101
[5,4,1,6,7,8,3,2]=>[8,4,1,3,7,6,5,2]=>1101110=>0010001
[4,8,1,6,5,7,3,2]=>[5,7,6,1,3,8,4,2]=>1101010=>0010101
[3,8,1,6,5,4,7,2]=>[5,6,4,7,8,1,3,2]=>1101000=>0010111
[6,1,7,8,5,4,3,2]=>[5,8,4,7,3,6,1,2]=>1011000=>0100111
[4,5,8,1,2,6,3,7]=>[6,8,1,5,2,4,3,7]=>1110000=>0001111
[1,7,3,5,6,2,4,8]=>[1,3,6,5,2,7,4,8]=>0101100=>1010011
[8,1,3,5,7,2,4,6]=>[3,7,5,1,2,8,4,6]=>1001100=>0110011
[3,6,8,1,7,2,4,5]=>[7,1,8,3,2,4,6,5]=>1110100=>0001011
[3,4,5,6,8,1,7,2]=>[7,8,1,6,5,4,3,2]=>1111100=>0000011
[4,5,8,2,6,7,1,3]=>[7,6,2,8,5,1,4,3]=>1110110=>0001001
[8,2,3,5,6,7,1,4]=>[2,3,7,6,5,1,8,4]=>1001110=>0110001
[1,7,2,3,5,4,6,8]=>[1,5,7,2,3,4,6,8]=>0100000=>1011111
[8,1,2,3,5,4,6,7]=>[5,8,1,2,3,4,6,7]=>1000000=>0111111
[2,7,8,1,3,5,4,6]=>[8,2,1,5,7,3,4,6]=>1110000=>0001111
[2,7,8,3,5,6,1,4]=>[5,6,8,3,7,2,1,4]=>1110000=>0001111
[2,4,5,7,8,1,6,3]=>[8,2,1,6,7,5,4,3]=>1111100=>0000011
[4,5,8,1,7,6,3,2]=>[6,7,1,8,5,3,4,2]=>1110100=>0001011
[4,5,8,7,2,1,6,3]=>[7,2,6,8,1,5,4,3]=>1111000=>0000111
[3,6,8,1,2,5,4,7]=>[8,1,5,6,3,2,4,7]=>1110000=>0001111
[1,3,6,7,2,5,4,8]=>[1,7,3,2,5,6,4,8]=>0111000=>1000111
[7,1,4,2,8,3,6,5]=>[4,1,2,8,3,6,7,5]=>1010100=>0101011
[7,1,8,2,5,3,6,4]=>[5,8,1,2,6,7,3,4]=>1010000=>0101111
[8,1,7,5,4,2,3,6]=>[5,4,7,1,2,8,3,6]=>1011000=>0100111
[1,7,2,6,5,4,3,8]=>[1,5,6,4,7,2,3,8]=>0101000=>1010111
[8,6,3,1,2,5,4,7]=>[3,6,1,5,8,2,4,7]=>1100000=>0011111
[8,1,7,6,3,2,4,5]=>[6,3,7,1,2,8,4,5]=>1011000=>0100111
[8,2,5,7,6,3,1,4]=>[2,6,3,7,5,1,8,4]=>1011100=>0100011
[3,6,8,1,7,5,4,2]=>[7,5,8,1,4,6,3,2]=>1110100=>0001011
[2,7,8,6,3,1,5,4]=>[6,3,8,2,1,5,7,4]=>1111000=>0000111
[8,7,2,1,6,5,4,3]=>[6,5,7,2,4,8,1,3]=>1100100=>0011011
[8,7,6,3,2,1,5,4]=>[6,3,7,2,5,8,1,4]=>1110000=>0001111
[2,1,8,6,3,7,4,5]=>[2,1,7,6,3,8,4,5]=>1011010=>0100101
[8,5,1,7,4,2,6,3]=>[7,4,5,1,6,8,2,3]=>1101000=>0010111
[2,1,7,5,4,3,8,6]=>[2,1,5,4,8,7,3,6]=>1011001=>0100110
[2,1,8,4,5,3,6,7]=>[2,1,4,5,8,3,6,7]=>1010000=>0101111
[2,1,7,8,3,6,5,4]=>[2,1,6,8,3,5,7,4]=>1011000=>0100111
[2,1,8,5,7,6,3,4]=>[2,1,6,7,5,3,8,4]=>1011100=>0100011
[2,1,4,8,5,7,3,6]=>[2,1,5,7,4,3,8,6]=>1011010=>0100101
[2,1,5,4,6,8,3,7]=>[2,1,4,8,6,5,3,7]=>1010110=>0101001
[8,5,3,1,6,2,4,7]=>[3,6,5,1,8,2,4,7]=>1100100=>0011011
[7,5,1,4,6,8,3,2]=>[4,8,6,5,1,3,7,2]=>1100110=>0011001
[6,4,1,5,2,3,8,7]=>[5,4,1,6,2,3,8,7]=>1101001=>0010110
[8,3,7,5,2,6,1,4]=>[5,3,2,6,7,1,8,4]=>1111000=>0000111
[5,8,3,7,6,2,1,4]=>[3,6,2,7,1,8,5,4]=>1101100=>0010011
[5,2,4,8,6,3,1,7]=>[2,6,4,3,8,5,1,7]=>1011100=>0100011
[3,8,2,4,7,5,1,6]=>[4,7,5,8,2,3,1,6]=>1100100=>0011011
[3,6,8,7,5,4,1,2]=>[5,7,4,8,1,6,3,2]=>1111000=>0000111
[8,5,2,7,4,6,1,3]=>[6,7,4,5,2,8,1,3]=>1101000=>0010111
[5,8,2,1,7,6,4,3]=>[6,7,2,4,8,5,1,3]=>1100100=>0011011
[6,3,8,1,5,7,4,2]=>[5,7,3,1,4,8,6,2]=>1110010=>0001101
[7,4,2,3,1,8,6,5]=>[4,2,3,8,6,7,1,5]=>1100010=>0011101
[7,8,3,1,5,4,6,2]=>[3,5,8,1,4,6,7,2]=>1100000=>0011111
[7,2,8,1,4,6,5,3]=>[2,6,8,1,4,5,7,3]=>1010000=>0101111
[6,2,3,1,4,5,8,7]=>[2,3,6,1,4,5,8,7]=>1000001=>0111110
[5,6,1,4,3,2,8,7]=>[4,6,1,3,5,2,8,7]=>1100001=>0011110
[5,7,1,8,3,6,2,4]=>[6,8,1,3,7,2,5,4]=>1101000=>0010111
[6,8,1,4,5,3,2,7]=>[4,5,8,1,3,6,2,7]=>1100000=>0011111
[8,7,5,1,3,4,2,6]=>[5,1,7,3,4,8,2,6]=>1110000=>0001111
[6,5,7,1,3,8,2,4]=>[8,1,5,3,7,6,2,4]=>1110010=>0001101
[8,2,6,1,4,7,3,5]=>[2,7,6,1,4,8,3,5]=>1010010=>0101101
[8,3,5,6,1,7,4,2]=>[7,6,3,1,5,4,8,2]=>1111010=>0000101
[7,5,4,8,2,1,3,6]=>[8,4,2,5,1,7,3,6]=>1111000=>0000111
[7,3,6,5,4,1,8,2]=>[5,4,6,3,1,8,7,2]=>1111001=>0000110
[8,3,6,4,5,1,2,7]=>[4,5,6,3,1,8,2,7]=>1110000=>0001111
[7,3,5,8,1,6,2,4]=>[6,8,3,1,5,2,7,4]=>1111000=>0000111
[2,7,8,5,1,6,4,3]=>[5,2,1,6,8,4,7,3]=>1111000=>0000111
[8,7,3,6,5,1,4,2]=>[3,5,6,1,7,4,8,2]=>1101000=>0010111
[2,8,3,4,6,1,5,7]=>[3,4,6,2,1,8,5,7]=>1100100=>0011011
[2,7,4,3,6,1,8,5]=>[4,3,6,2,1,8,7,5]=>1110101=>0001010
[3,4,7,2,8,1,5,6]=>[8,2,4,3,1,7,5,6]=>1110100=>0001011
[4,3,2,5,7,1,8,6]=>[3,2,8,7,5,4,1,6]=>1101101=>0010010
[4,2,3,5,8,1,6,7]=>[2,3,8,5,4,1,6,7]=>1001100=>0110011
[8,2,4,7,5,1,6,3]=>[2,5,7,4,1,6,8,3]=>1011000=>0100111
[3,8,4,7,1,6,5,2]=>[6,7,4,1,5,8,3,2]=>1111000=>0000111
[3,2,4,6,1,5,8,7]=>[2,6,4,3,1,5,8,7]=>1011001=>0100110
[8,3,4,5,7,6,1,2]=>[6,7,5,4,3,1,8,2]=>1111100=>0000011
[2,4,3,5,8,7,1,6]=>[3,7,5,4,2,1,8,6]=>1101110=>0010001
[3,2,4,5,6,8,1,7]=>[2,8,6,5,4,3,1,7]=>1011110=>0100001
[5,6,8,1,4,2,7,3]=>[7,8,1,4,6,2,5,3]=>1110000=>0001111
[1,3,5,7,8,6,2,4]=>[1,6,8,3,2,7,5,4]=>0111100=>1000011
[3,5,7,8,6,1,2,4]=>[6,1,8,3,2,7,5,4]=>1111100=>0000011
[3,5,1,6,8,2,7,4]=>[7,8,1,3,2,6,5,4]=>1101100=>0010011
[2,3,5,6,8,1,7,4]=>[7,8,3,2,1,6,5,4]=>1111100=>0000011
[5,6,4,8,2,1,7,3]=>[7,8,4,2,6,1,5,3]=>1111000=>0000111
[5,1,6,3,8,4,7,2]=>[7,8,3,4,6,5,1,2]=>1010100=>0101011
[2,5,1,6,8,3,7,4]=>[7,8,2,1,3,6,5,4]=>1101100=>0010011
[5,1,2,6,8,3,7,4]=>[7,8,1,2,3,6,5,4]=>1001100=>0110011
[5,7,1,8,6,2,3,4]=>[6,1,8,2,3,7,5,4]=>1101100=>0010011
[1,5,2,7,8,6,3,4]=>[1,6,8,2,3,7,5,4]=>0101100=>1010011
[1,6,7,5,2,8,3,4]=>[1,5,2,8,3,7,6,4]=>0111010=>1000101
[6,1,7,5,2,8,3,4]=>[5,1,2,8,3,7,6,4]=>1011010=>0100101
[5,7,2,8,6,1,3,4]=>[6,2,8,1,3,7,5,4]=>1101100=>0010011
[5,1,7,8,6,3,4,2]=>[6,3,8,4,7,5,1,2]=>1011100=>0100011
[5,1,3,7,8,6,4,2]=>[3,6,8,4,7,5,1,2]=>1001100=>0110011
[5,2,7,8,4,6,1,3]=>[2,6,8,4,7,1,5,3]=>1011000=>0100111
[1,2,6,7,5,8,3,4]=>[1,2,5,8,3,7,6,4]=>0011010=>1100101
[6,2,7,5,4,1,8,3]=>[2,5,4,8,7,1,6,3]=>1011001=>0100110
[6,7,5,2,4,1,8,3]=>[5,2,4,8,7,1,6,3]=>1110001=>0001110
[6,7,4,5,2,1,8,3]=>[5,4,2,8,7,1,6,3]=>1111001=>0000110
[5,1,7,8,6,4,3,2]=>[6,4,8,3,7,5,1,2]=>1011100=>0100011
[2,5,7,8,6,3,1,4]=>[6,3,8,2,1,7,5,4]=>1111100=>0000011
[5,1,7,8,6,3,2,4]=>[6,3,8,1,2,7,5,4]=>1011100=>0100011
[6,3,7,5,1,8,2,4]=>[5,3,1,8,2,7,6,4]=>1111010=>0000101
[6,7,5,1,4,2,8,3]=>[5,1,4,8,7,2,6,3]=>1110001=>0001110
[5,7,8,6,4,1,2,3]=>[6,4,8,1,7,2,5,3]=>1111000=>0000111
[4,1,7,2,6,5,8,3]=>[6,5,8,7,1,2,4,3]=>1010101=>0101010
[2,4,7,1,5,6,8,3]=>[5,6,8,7,2,1,4,3]=>1110001=>0001110
[1,6,7,4,5,2,8,3]=>[1,4,5,8,7,2,6,3]=>0110001=>1001110
[1,6,3,7,5,8,2,4]=>[1,3,5,8,2,7,6,4]=>0101010=>1010101
[6,7,5,4,2,1,8,3]=>[4,5,2,8,7,1,6,3]=>1110001=>0001110
[6,3,2,7,5,8,1,4]=>[3,2,5,8,1,7,6,4]=>1101010=>0010101
[6,7,4,2,5,1,8,3]=>[4,2,5,8,7,1,6,3]=>1110001=>0001110
[6,2,7,4,5,1,8,3]=>[2,4,5,8,7,1,6,3]=>1010001=>0101110
[4,5,1,6,3,2,8,7]=>[6,1,3,5,4,2,8,7]=>1101001=>0010110
[7,5,1,6,3,8,2,4]=>[8,6,1,3,5,2,7,4]=>1101010=>0010101
[7,5,1,6,3,8,4,2]=>[8,6,1,3,5,4,7,2]=>1101010=>0010101
[2,7,6,1,3,8,4,5]=>[8,6,2,1,7,3,4,5]=>1110010=>0001101
[2,7,6,1,3,8,5,4]=>[8,6,2,1,5,7,3,4]=>1110010=>0001101
[7,3,5,1,8,2,4,6]=>[8,5,3,1,7,2,4,6]=>1110100=>0001011
[3,7,5,1,8,6,2,4]=>[6,8,5,1,7,3,2,4]=>1110100=>0001011
[2,6,7,1,5,8,3,4]=>[5,8,2,1,7,6,3,4]=>1110010=>0001101
[2,6,7,4,1,8,3,5]=>[4,8,2,1,7,6,3,5]=>1110010=>0001101
[2,1,6,7,3,8,5,4]=>[2,1,8,3,5,7,6,4]=>1011010=>0100101
[2,6,7,1,5,8,4,3]=>[5,8,2,1,4,7,6,3]=>1110010=>0001101
[3,6,5,1,8,4,7,2]=>[7,8,5,1,4,6,3,2]=>1110100=>0001011
[3,6,5,1,8,4,2,7]=>[8,5,1,4,6,3,2,7]=>1110100=>0001011
[3,7,5,4,8,1,6,2]=>[4,8,5,1,6,7,3,2]=>1110100=>0001011
[4,6,1,5,8,7,3,2]=>[7,5,1,3,8,6,4,2]=>1101110=>0010001
[4,6,1,5,8,2,7,3]=>[7,8,5,1,6,4,2,3]=>1101100=>0010011
[7,5,1,6,2,8,4,3]=>[8,6,1,5,4,7,2,3]=>1101010=>0010101
[4,6,1,5,8,2,3,7]=>[8,5,1,6,4,2,3,7]=>1101100=>0010011
[2,3,4,7,8,1,6,5]=>[8,4,3,2,1,6,7,5]=>1111100=>0000011
[6,8,5,4,3,2,7,1]=>[4,5,3,7,8,2,6,1]=>1110000=>0001111
[6,8,5,4,3,7,2,1]=>[4,5,3,7,2,8,6,1]=>1110010=>0001101
[5,8,4,3,2,1,7,6]=>[4,3,7,8,2,5,1,6]=>1110000=>0001111
[6,5,4,3,1,8,7,2]=>[4,3,5,1,7,8,6,2]=>1110010=>0001101
[8,7,5,4,3,1,6,2]=>[4,5,3,7,1,6,8,2]=>1110000=>0001111
[3,5,6,2,1,8,4,7]=>[8,6,2,5,3,1,4,7]=>1110010=>0001101
[7,5,3,2,8,4,1,6]=>[3,8,5,2,4,7,1,6]=>1100100=>0011011
[7,5,3,2,8,4,6,1]=>[3,8,5,2,4,6,7,1]=>1100100=>0011011
[2,4,5,7,3,8,6,1]=>[8,6,7,3,5,4,2,1]=>1111010=>0000101
[2,5,6,1,8,4,3,7]=>[8,2,1,4,6,5,3,7]=>1110100=>0001011
[4,5,3,7,2,8,6,1]=>[3,8,6,7,2,5,4,1]=>1101010=>0010101
[6,1,4,7,3,2,8,5]=>[8,7,4,3,6,1,2,5]=>1011001=>0100110
[5,1,7,3,8,4,2,6]=>[8,3,4,7,5,1,2,6]=>1010100=>0101011
[2,5,7,4,1,8,6,3]=>[4,8,6,7,2,1,5,3]=>1110010=>0001101
[6,4,3,1,7,8,5,2]=>[3,4,1,8,5,7,6,2]=>1100110=>0011001
[5,6,1,7,8,3,4,2]=>[8,1,3,7,4,6,5,2]=>1101100=>0010011
[6,7,2,1,4,3,8,5]=>[8,7,2,4,6,1,3,5]=>1100001=>0011110
[5,6,1,3,2,7,8,4]=>[8,7,6,1,3,5,2,4]=>1100011=>0011100
[5,6,3,2,1,7,8,4]=>[3,8,7,6,2,5,1,4]=>1100011=>0011100
[2,5,6,3,7,8,4,1]=>[8,3,4,7,6,5,2,1]=>1110110=>0001001
[2,5,6,3,1,7,8,4]=>[8,7,6,3,5,2,1,4]=>1110011=>0001100
[2,6,4,7,3,1,8,5]=>[8,7,4,3,6,2,1,5]=>1111001=>0000110
[6,3,7,2,8,4,1,5]=>[8,3,2,4,7,1,6,5]=>1110100=>0001011
[6,3,2,7,1,8,4,5]=>[3,2,8,1,7,6,4,5]=>1101010=>0010101
[7,3,8,4,2,1,5,6]=>[4,8,3,2,7,1,5,6]=>1110000=>0001111
[4,7,2,1,3,8,6,5]=>[8,6,7,2,4,1,3,5]=>1100010=>0011101
[1,3,7,8,6,4,2,5]=>[1,6,4,8,3,2,7,5]=>0111100=>1000011
[6,3,7,8,5,2,1,4]=>[5,8,3,2,7,1,6,4]=>1111000=>0000111
[4,6,2,7,8,5,3,1]=>[8,5,7,2,3,6,4,1]=>1101100=>0010011
[2,5,1,7,3,8,6,4]=>[8,6,7,2,1,3,5,4]=>1101010=>0010101
[5,1,6,7,8,2,4,3]=>[8,1,2,7,4,6,5,3]=>1011100=>0100011
[6,3,7,1,8,5,2,4]=>[8,5,7,3,1,6,2,4]=>1110100=>0001011
[4,2,3,6,8,1,5,7]=>[2,3,8,4,1,6,5,7]=>1001100=>0110011
[5,3,2,1,8,4,7,6]=>[3,2,7,8,5,1,4,6]=>1100100=>0011011
[3,6,5,8,2,1,7,4]=>[7,8,2,5,3,1,6,4]=>1111000=>0000111
[4,5,2,1,3,8,7,6]=>[5,2,4,1,3,7,8,6]=>1100010=>0011101
[3,2,6,4,5,8,1,7]=>[2,4,5,8,6,3,1,7]=>1010010=>0101101
[2,4,6,5,8,1,3,7]=>[8,5,2,1,6,4,3,7]=>1111100=>0000011
[1,6,2,4,5,8,3,7]=>[1,4,5,8,6,2,3,7]=>0100010=>1011101
[5,3,2,1,6,8,4,7]=>[3,2,8,6,5,1,4,7]=>1100110=>0011001
[6,2,4,5,8,1,3,7]=>[2,8,5,4,1,6,3,7]=>1011100=>0100011
[1,3,4,6,5,8,2,7]=>[1,5,8,6,4,3,2,7]=>0111010=>1000101
[1,6,3,4,5,8,2,7]=>[1,3,4,5,8,6,2,7]=>0100010=>1011101
[3,4,1,8,5,2,7,6]=>[5,7,8,4,1,3,2,6]=>1101000=>0010111
[8,1,4,2,7,3,6,5]=>[4,1,2,7,3,6,8,5]=>1010100=>0101011
[1,5,3,2,8,7,4,6]=>[1,3,7,5,2,4,8,6]=>0100110=>1011001
[8,2,1,7,5,3,4,6]=>[2,5,7,1,3,8,4,6]=>1001000=>0110111
[5,8,7,4,6,2,1,3]=>[4,6,2,7,1,8,5,3]=>1110100=>0001011
[2,4,8,6,7,1,3,5]=>[7,2,1,6,4,3,8,5]=>1111100=>0000011
[4,3,6,2,8,1,7,5]=>[7,8,3,2,4,1,6,5]=>1110100=>0001011
[3,7,4,8,2,1,6,5]=>[8,4,2,6,7,3,1,5]=>1111000=>0000111
[2,3,5,8,6,7,1,4]=>[7,6,3,2,1,8,5,4]=>1111110=>0000001
[2,1,8,5,6,7,3,4]=>[2,1,7,6,5,3,8,4]=>1011110=>0100001
[1,2,8,3,5,6,7,4]=>[1,2,5,6,7,8,3,4]=>0010000=>1101111
[3,2,6,4,8,1,7,5]=>[2,4,7,8,3,1,6,5]=>1010100=>0101011
[8,2,1,6,7,3,4,5]=>[2,7,1,3,6,4,8,5]=>1001100=>0110011
[2,7,8,5,4,1,3,6]=>[5,4,8,2,1,7,3,6]=>1111000=>0000111
[1,7,5,3,8,4,2,6]=>[1,8,5,3,4,7,2,6]=>0110100=>1001011
[4,7,5,3,1,2,8,6]=>[5,3,8,7,1,4,2,6]=>1110001=>0001110
[7,2,4,8,5,3,1,6]=>[2,5,8,4,3,7,1,6]=>1011000=>0100111
[4,8,3,1,2,7,6,5]=>[3,7,6,8,1,4,2,5]=>1100010=>0011101
[3,5,2,7,4,1,8,6]=>[8,7,4,5,2,3,1,6]=>1101001=>0010110
[2,8,4,7,1,3,5,6]=>[7,4,2,1,8,3,5,6]=>1111000=>0000111
[8,2,4,6,7,1,3,5]=>[2,7,4,1,6,3,8,5]=>1011100=>0100011
[4,8,2,3,6,7,1,5]=>[7,6,2,3,4,1,8,5]=>1100110=>0011001
[1,6,3,2,5,8,7,4]=>[1,3,5,7,8,6,2,4]=>0100010=>1011101
[5,8,3,2,1,6,7,4]=>[3,6,7,8,2,5,1,4]=>1100000=>0011111
[5,3,7,1,6,2,8,4]=>[6,3,1,8,7,5,2,4]=>1110101=>0001010
[6,3,2,1,8,5,7,4]=>[3,2,7,8,5,6,1,4]=>1100100=>0011011
[2,7,5,4,1,8,6,3]=>[4,5,2,1,8,6,7,3]=>1110010=>0001101
[4,2,5,6,8,7,1,3]=>[2,7,1,8,6,5,4,3]=>1011110=>0100001
[1,8,4,2,5,6,7,3]=>[1,4,2,5,6,7,8,3]=>0110000=>1001111
[3,8,4,1,5,6,7,2]=>[4,1,5,6,7,8,3,2]=>1110000=>0001111
[4,2,8,5,6,7,1,3]=>[2,7,6,5,1,8,4,3]=>1011110=>0100001
[5,3,4,7,1,8,6,2]=>[8,6,7,4,3,1,5,2]=>1111010=>0000101
[8,1,3,6,5,2,4,7]=>[3,5,6,1,2,8,4,7]=>1001000=>0110111
[3,6,5,2,1,8,7,4]=>[5,2,7,8,6,3,1,4]=>1110010=>0001101
[8,3,2,4,6,5,1,7]=>[3,2,4,6,5,8,1,7]=>1100100=>0011011
[8,4,2,1,6,5,3,7]=>[4,2,6,5,8,1,3,7]=>1100100=>0011011
[8,4,1,2,6,5,3,7]=>[4,1,6,5,8,2,3,7]=>1100100=>0011011
[8,6,4,2,1,5,3,7]=>[4,2,6,1,5,8,3,7]=>1110000=>0001111
[8,2,6,3,4,5,1,7]=>[2,6,3,4,5,8,1,7]=>1010000=>0101111
[5,8,4,7,6,2,3,1]=>[6,4,2,7,3,8,5,1]=>1111100=>0000011
[1,3,4,7,5,8,2,6]=>[1,5,8,4,3,2,7,6]=>0111010=>1000101
[1,3,5,2,4,8,7,6]=>[1,5,3,2,4,7,8,6]=>0110010=>1001101
[2,6,5,1,3,8,7,4]=>[5,2,1,7,8,6,3,4]=>1110010=>0001101
[5,4,8,7,6,3,1,2]=>[6,3,7,4,1,8,5,2]=>1111100=>0000011
[4,1,3,5,8,6,7,2]=>[3,6,7,8,5,4,1,2]=>1001100=>0110011
[6,5,3,8,4,7,1,2]=>[3,7,4,5,1,8,6,2]=>1101010=>0010101
[5,4,2,1,6,8,7,3]=>[4,2,7,8,6,5,1,3]=>1100110=>0011001
[6,8,4,3,2,7,1,5]=>[4,3,7,2,8,6,1,5]=>1110010=>0001101
[5,1,3,2,8,6,7,4]=>[3,6,7,8,5,1,2,4]=>1000100=>0111011
[5,3,2,1,8,6,7,4]=>[3,2,6,7,8,5,1,4]=>1100100=>0011011
[5,2,1,3,6,8,7,4]=>[2,7,8,6,5,1,3,4]=>1000110=>0111001
[6,3,8,2,7,4,1,5]=>[7,3,2,4,8,1,6,5]=>1110100=>0001011
[8,2,1,3,6,4,7,5]=>[2,6,1,3,4,7,8,5]=>1000100=>0111011
[3,5,1,7,8,4,2,6]=>[8,4,7,5,1,3,2,6]=>1101100=>0010011
[2,7,4,5,8,3,1,6]=>[8,5,4,3,7,2,1,6]=>1111100=>0000011
[3,4,8,7,2,1,6,5]=>[7,2,6,8,4,3,1,5]=>1111000=>0000111
[6,3,8,7,4,1,2,5]=>[7,4,8,3,1,6,2,5]=>1111000=>0000111
[3,5,7,2,4,8,1,6]=>[8,2,4,5,3,1,7,6]=>1110010=>0001101
[8,4,7,2,3,1,5,6]=>[7,2,4,3,8,1,5,6]=>1110000=>0001111
[8,4,7,2,1,3,5,6]=>[7,2,4,1,8,3,5,6]=>1110000=>0001111
[8,6,4,2,1,3,7,5]=>[4,2,6,1,7,8,3,5]=>1110000=>0001111
[8,6,4,1,3,2,7,5]=>[4,1,6,3,7,8,2,5]=>1110000=>0001111
[8,6,4,2,3,1,7,5]=>[4,2,6,3,7,8,1,5]=>1110000=>0001111
[3,5,7,2,6,1,8,4]=>[6,2,8,7,5,3,1,4]=>1110101=>0001010
[6,1,3,8,5,7,2,4]=>[3,5,7,1,2,8,6,4]=>1001010=>0110101
[5,8,3,2,6,7,1,4]=>[3,7,6,2,8,5,1,4]=>1100110=>0011001
[4,8,5,3,6,2,7,1]=>[6,5,3,7,8,2,4,1]=>1110100=>0001011
[2,8,1,5,4,7,6,3]=>[5,4,7,6,8,2,1,3]=>1101010=>0010101
[1,5,8,7,4,6,2,3]=>[1,6,7,4,8,2,5,3]=>0111000=>1000111
[2,1,7,6,4,5,8,3]=>[2,1,6,4,5,8,7,3]=>1011001=>0100110
[3,5,1,7,6,8,2,4]=>[8,6,1,3,2,7,5,4]=>1101110=>0010001
[5,8,2,6,1,3,7,4]=>[6,2,7,8,1,3,5,4]=>1101000=>0010111
[6,3,5,8,7,2,1,4]=>[7,3,2,8,5,1,6,4]=>1111100=>0000011
[4,2,8,1,5,6,7,3]=>[2,5,6,7,8,1,4,3]=>1010000=>0101111
[4,1,5,2,6,8,7,3]=>[7,8,6,5,1,2,4,3]=>1010110=>0101001
[3,4,5,1,6,8,7,2]=>[7,8,6,5,1,4,3,2]=>1110110=>0001001
[4,2,8,5,1,6,7,3]=>[2,5,1,6,7,8,4,3]=>1011000=>0100111
[4,1,8,5,2,6,7,3]=>[5,1,2,6,7,8,4,3]=>1011000=>0100111
[2,7,1,8,5,4,6,3]=>[5,8,4,6,7,2,1,3]=>1101000=>0010111
[5,8,6,2,1,3,7,4]=>[6,2,7,8,1,5,3,4]=>1110000=>0001111
[8,2,4,1,5,6,7,3]=>[2,4,1,5,6,7,8,3]=>1010000=>0101111
[4,6,3,5,8,1,7,2]=>[3,7,8,5,1,6,4,2]=>1101100=>0010011
[1,7,8,3,5,4,6,2]=>[1,5,8,3,4,6,7,2]=>0110000=>1001111
[3,4,5,1,8,6,7,2]=>[6,7,8,5,1,4,3,2]=>1110100=>0001011
[3,8,1,4,5,6,7,2]=>[4,5,6,7,8,1,3,2]=>1100000=>0011111
[3,4,5,6,8,2,1,7]=>[8,2,6,5,4,3,1,7]=>1111100=>0000011
[3,4,5,7,1,8,6,2]=>[8,6,7,1,5,4,3,2]=>1111010=>0000101
[3,4,5,7,8,2,6,1]=>[8,2,6,7,5,4,3,1]=>1111100=>0000011
[3,4,6,8,1,5,2,7]=>[8,1,5,6,4,3,2,7]=>1111000=>0000111
[3,4,7,8,1,5,6,2]=>[8,1,5,6,7,4,3,2]=>1111000=>0000111
[3,5,2,6,7,8,1,4]=>[8,2,3,1,7,6,5,4]=>1101110=>0010001
[3,5,2,7,8,4,6,1]=>[8,4,6,7,5,2,3,1]=>1101100=>0010011
[3,5,2,8,4,1,6,7]=>[8,4,5,2,3,1,6,7]=>1101000=>0010111
[3,5,6,2,8,4,1,7]=>[8,2,4,6,5,3,1,7]=>1110100=>0001011
[3,5,7,2,4,8,6,1]=>[8,6,7,2,4,5,3,1]=>1110010=>0001101
[3,5,7,2,8,4,6,1]=>[8,2,4,6,7,5,3,1]=>1110100=>0001011
[3,5,7,8,4,1,6,2]=>[8,4,6,7,1,5,3,2]=>1111000=>0000111
[3,6,2,1,7,8,5,4]=>[8,5,7,6,2,3,1,4]=>1100110=>0011001
[3,6,2,1,8,5,4,7]=>[8,5,6,2,3,1,4,7]=>1100100=>0011011
[3,6,7,2,4,8,5,1]=>[8,2,4,5,7,6,3,1]=>1110010=>0001101
[3,6,7,2,8,5,4,1]=>[8,5,7,2,4,6,3,1]=>1110100=>0001011
[3,6,7,8,4,5,1,2]=>[8,4,5,7,1,6,3,2]=>1111000=>0000111
[3,6,8,2,4,5,1,7]=>[8,2,4,5,6,3,1,7]=>1110000=>0001111
[3,7,2,1,4,8,6,5]=>[8,6,7,2,3,1,4,5]=>1100010=>0011101
[3,7,2,1,8,5,6,4]=>[8,5,6,7,2,3,1,4]=>1100100=>0011011
[3,7,2,8,4,5,6,1]=>[8,4,5,6,7,2,3,1]=>1101000=>0010111
[3,7,8,2,4,5,6,1]=>[8,2,4,5,6,7,3,1]=>1110000=>0001111
[3,8,2,1,4,5,6,7]=>[8,2,3,1,4,5,6,7]=>1100000=>0011111
[4,1,6,3,7,8,5,2]=>[8,5,7,6,3,4,1,2]=>1010110=>0101001
[4,1,6,3,8,5,2,7]=>[8,5,6,3,4,1,2,7]=>1010100=>0101011
[4,1,6,7,8,5,2,3]=>[8,5,7,1,2,6,4,3]=>1011100=>0100011
[4,1,7,3,2,8,6,5]=>[8,6,7,3,4,1,2,5]=>1010010=>0101101
[4,1,7,8,3,5,6,2]=>[8,3,5,6,7,4,1,2]=>1011000=>0100111
[4,1,8,3,2,5,6,7]=>[8,3,4,1,2,5,6,7]=>1010000=>0101111
[4,5,2,6,7,8,3,1]=>[8,2,3,7,6,5,4,1]=>1101110=>0010001
[4,5,2,6,8,1,3,7]=>[8,2,6,5,4,1,3,7]=>1101100=>0010011
[4,5,6,8,3,1,2,7]=>[8,3,6,1,5,4,2,7]=>1111000=>0000111
[4,5,8,3,2,1,6,7]=>[8,3,5,2,4,1,6,7]=>1110000=>0001111
[4,6,2,3,7,8,5,1]=>[8,5,7,6,2,3,4,1]=>1100110=>0011001
[4,6,2,3,8,5,1,7]=>[8,5,6,2,3,4,1,7]=>1100100=>0011011
[4,6,2,7,3,8,5,1]=>[8,2,3,5,7,6,4,1]=>1101010=>0010101
[4,6,7,3,2,8,5,1]=>[8,3,5,7,6,2,4,1]=>1110010=>0001101
[4,6,8,3,2,5,1,7]=>[8,3,5,6,2,4,1,7]=>1110000=>0001111
[4,7,2,3,1,8,6,5]=>[8,6,7,2,3,4,1,5]=>1100010=>0011101
[4,7,2,8,3,5,6,1]=>[8,2,3,5,6,7,4,1]=>1101000=>0010111
[4,8,2,3,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>1100000=>0011111
[5,1,2,7,4,8,6,3]=>[8,6,7,4,5,1,2,3]=>1001010=>0110101
[5,1,2,7,8,4,6,3]=>[8,4,6,7,5,1,2,3]=>1001100=>0110011
[5,1,2,8,4,3,6,7]=>[8,4,5,1,2,3,6,7]=>1001000=>0110111
[5,1,6,3,8,4,2,7]=>[8,3,4,6,5,1,2,7]=>1010100=>0101011
[5,1,6,7,4,8,2,3]=>[8,4,7,6,1,2,5,3]=>1011010=>0100101
[5,1,6,7,8,4,2,3]=>[8,4,7,1,2,6,5,3]=>1011100=>0100011
[5,1,8,3,4,2,6,7]=>[8,3,4,5,1,2,6,7]=>1010000=>0101111
[5,6,2,7,8,4,1,3]=>[8,4,7,2,6,5,1,3]=>1101100=>0010011
[5,7,2,3,4,8,6,1]=>[8,6,7,2,3,4,5,1]=>1100010=>0011101
[5,8,2,3,4,1,6,7]=>[8,2,3,4,5,1,6,7]=>1100000=>0011111
[6,1,2,3,7,8,5,4]=>[8,5,7,6,1,2,3,4]=>1000110=>0111001
[6,1,2,3,8,5,4,7]=>[8,5,6,1,2,3,4,7]=>1000100=>0111011
[6,1,2,8,4,5,3,7]=>[8,4,5,6,1,2,3,7]=>1001000=>0110111
[6,1,7,3,4,8,5,2]=>[8,3,4,5,7,6,1,2]=>1010010=>0101101
[6,1,7,8,4,5,3,2]=>[8,4,5,7,3,6,1,2]=>1011000=>0100111
[6,1,8,3,4,5,2,7]=>[8,3,4,5,6,1,2,7]=>1010000=>0101111
[6,8,2,3,4,5,1,7]=>[8,2,3,4,5,6,1,7]=>1100000=>0011111
[7,1,2,3,4,8,6,5]=>[8,6,7,1,2,3,4,5]=>1000010=>0111101
[7,1,2,8,4,5,6,3]=>[8,4,5,6,7,1,2,3]=>1001000=>0110111
[7,1,8,3,4,5,6,2]=>[8,3,4,5,6,7,1,2]=>1010000=>0101111
[1,3,5,7,2,6,4,8]=>[1,6,7,3,2,5,4,8]=>0111000=>1000111
[3,5,8,6,1,2,4,7]=>[6,1,8,3,2,5,4,7]=>1111000=>0000111
[3,1,6,8,2,4,7,5]=>[7,8,3,1,2,6,4,5]=>1011000=>0100111
[3,6,2,8,1,5,7,4]=>[7,8,2,3,1,5,6,4]=>1101000=>0010111
[2,6,1,3,8,4,7,5]=>[7,8,2,1,3,4,6,5]=>1100100=>0011011
[7,6,5,2,4,8,1,3]=>[5,2,4,8,6,1,7,3]=>1110010=>0001101
[7,1,8,6,3,2,4,5]=>[6,3,8,1,2,7,4,5]=>1011000=>0100111
[6,8,1,5,3,2,4,7]=>[5,1,3,8,2,6,4,7]=>1101000=>0010111
[1,6,7,5,3,2,4,8]=>[1,5,3,7,2,6,4,8]=>0111000=>1000111
[8,4,1,2,5,6,3,7]=>[4,1,5,6,8,2,3,7]=>1100000=>0011111
[1,7,3,6,5,2,4,8]=>[1,3,5,6,2,7,4,8]=>0101000=>1010111
[7,3,2,6,5,1,8,4]=>[3,2,5,6,1,8,7,4]=>1101001=>0010110
[8,2,3,6,5,1,7,4]=>[2,3,5,6,1,7,8,4]=>1001000=>0110111
[3,8,7,5,4,6,2,1]=>[5,4,6,7,2,8,3,1]=>1111000=>0000111
[4,8,5,6,7,3,2,1]=>[7,3,6,5,2,8,4,1]=>1111100=>0000011
[3,8,7,4,5,6,2,1]=>[4,5,6,7,2,8,3,1]=>1110000=>0001111
[1,8,7,6,5,3,2,4]=>[1,5,6,3,7,2,8,4]=>0111000=>1000111
[2,8,7,6,3,4,5,1]=>[6,3,7,4,5,8,2,1]=>1111000=>0000111
[7,2,8,6,5,4,1,3]=>[2,5,6,4,8,1,7,3]=>1011000=>0100111
[7,2,8,5,4,6,1,3]=>[2,5,4,6,8,1,7,3]=>1011000=>0100111
[6,3,2,8,5,1,7,4]=>[3,2,5,7,8,1,6,4]=>1101000=>0010111
[6,8,5,4,3,1,7,2]=>[4,5,3,7,8,1,6,2]=>1110000=>0001111
[5,8,6,4,1,3,7,2]=>[4,6,1,7,8,3,5,2]=>1110000=>0001111
[4,8,6,1,5,3,7,2]=>[5,6,1,7,8,3,4,2]=>1110000=>0001111
[3,6,1,8,5,2,7,4]=>[5,7,8,1,3,2,6,4]=>1101000=>0010111
[3,4,1,2,8,6,7,5]=>[4,1,3,2,6,7,8,5]=>1100100=>0011011
[7,6,3,8,5,2,1,4]=>[3,5,8,2,6,1,7,4]=>1101000=>0010111
[7,2,6,4,8,3,1,5]=>[2,4,8,3,6,1,7,5]=>1010100=>0101011
[4,2,3,1,7,8,5,6]=>[2,3,4,1,8,5,7,6]=>1000110=>0111001
[8,6,3,4,7,2,5,1]=>[3,4,7,2,6,5,8,1]=>1100100=>0011011
[6,8,3,4,5,1,7,2]=>[3,4,5,7,8,1,6,2]=>1100000=>0011111
[6,3,7,1,5,8,4,2]=>[5,8,3,1,4,7,6,2]=>1110010=>0001101
[6,2,5,4,8,1,3,7]=>[2,4,8,5,1,6,3,7]=>1010100=>0101011
[6,1,3,4,5,8,2,7]=>[3,4,5,8,6,1,2,7]=>1000010=>0111101
[8,3,4,1,5,2,7,6]=>[4,3,1,5,7,8,2,6]=>1110000=>0001111
[7,5,4,2,6,8,3,1]=>[4,2,8,6,5,3,7,1]=>1110110=>0001001
[8,2,6,4,1,7,3,5]=>[2,4,7,6,1,8,3,5]=>1010010=>0101101
[7,3,8,4,5,2,1,6]=>[4,5,8,3,2,7,1,6]=>1110000=>0001111
[7,2,5,1,8,4,3,6]=>[2,8,5,1,4,7,3,6]=>1010100=>0101011
[1,7,3,2,5,4,8,6]=>[1,3,5,8,7,2,4,6]=>0100001=>1011110
[8,7,2,1,5,3,4,6]=>[5,7,2,8,1,3,4,6]=>1100000=>0011111
[3,6,1,5,8,7,4,2]=>[7,5,4,8,6,1,3,2]=>1101110=>0010001
[8,3,6,4,5,1,7,2]=>[4,5,6,3,1,7,8,2]=>1110000=>0001111
[5,4,6,8,1,2,7,3]=>[7,8,1,6,4,2,5,3]=>1111000=>0000111
[6,4,7,2,3,5,8,1]=>[8,7,2,4,3,5,6,1]=>1110001=>0001110
[6,8,4,1,3,5,7,2]=>[4,1,7,8,3,5,6,2]=>1110000=>0001111
[4,1,3,5,7,8,6,2]=>[3,8,6,7,5,4,1,2]=>1001110=>0110001
[6,5,1,8,4,7,3,2]=>[7,4,5,1,3,8,6,2]=>1101010=>0010101
[8,2,7,4,6,1,3,5]=>[2,4,6,1,7,3,8,5]=>1010100=>0101011
[4,7,3,2,8,1,6,5]=>[3,8,2,4,1,6,7,5]=>1100100=>0011011
[6,3,1,4,7,2,8,5]=>[3,1,4,8,7,2,6,5]=>1100101=>0011010
[8,7,3,6,1,5,2,4]=>[3,6,1,5,7,2,8,4]=>1101000=>0010111
[2,4,7,3,8,5,6,1]=>[8,5,6,7,3,4,2,1]=>1110100=>0001011
[1,8,3,4,2,7,6,5]=>[1,3,4,7,6,8,2,5]=>0100010=>1011101
[4,1,3,6,7,8,2,5]=>[3,8,4,1,2,7,6,5]=>1001110=>0110001
[7,1,5,2,8,6,4,3]=>[6,8,5,1,2,4,7,3]=>1010100=>0101011
[1,8,6,4,5,2,7,3]=>[1,4,5,6,2,7,8,3]=>0110000=>1001111
[3,6,2,1,7,5,8,4]=>[8,7,5,6,2,3,1,4]=>1100101=>0011010
[4,7,2,6,5,8,1,3]=>[5,8,6,2,7,4,1,3]=>1101010=>0010101
[6,8,1,4,2,7,3,5]=>[4,7,1,8,6,2,3,5]=>1100010=>0011101
[6,3,4,7,1,8,2,5]=>[8,4,3,1,7,6,2,5]=>1111010=>0000101
[3,4,7,8,2,5,6,1]=>[8,2,5,6,7,4,3,1]=>1111000=>0000111
[1,8,2,4,5,6,7,3]=>[1,4,5,6,7,8,2,3]=>0100000=>1011111
[5,2,4,1,6,8,7,3]=>[2,4,1,7,8,6,5,3]=>1010110=>0101001
[4,3,5,6,1,8,7,2]=>[7,8,6,3,1,5,4,2]=>1111010=>0000101
[5,3,4,1,7,6,8,2]=>[4,3,1,6,8,7,5,2]=>1110101=>0001010
[3,1,4,6,5,7,8,2]=>[5,8,7,6,4,3,1,2]=>1011011=>0100100
[1,4,2,5,8,3,7,6]=>[1,7,8,5,4,2,3,6]=>0101100=>1010011
[1,4,2,7,8,5,6,3]=>[1,8,5,6,7,4,2,3]=>0101100=>1010011
[4,1,2,6,8,5,3,7]=>[8,5,6,4,1,2,3,7]=>1001100=>0110011
[1,5,2,4,8,7,6,3]=>[1,4,7,6,8,5,2,3]=>0100110=>1011001
[1,2,6,4,8,7,5,3]=>[1,2,4,7,5,8,6,3]=>0010110=>1101001
[1,2,7,4,8,6,5,3]=>[1,2,4,6,8,5,7,3]=>0010100=>1101011
[1,3,2,8,5,7,4,6]=>[1,3,2,5,7,4,8,6]=>0101010=>1010101
[1,5,2,4,8,7,3,6]=>[1,4,7,5,2,3,8,6]=>0100110=>1011001
[1,2,6,4,8,7,3,5]=>[1,2,4,7,3,8,6,5]=>0010110=>1101001
[1,2,7,8,5,6,3,4]=>[1,2,5,6,8,3,7,4]=>0011000=>1100111
[1,2,6,8,5,7,3,4]=>[1,2,5,7,3,8,6,4]=>0011010=>1100101
[1,5,6,8,2,7,3,4]=>[1,7,2,8,6,3,5,4]=>0111010=>1000101
[1,3,8,2,6,7,4,5]=>[1,7,6,3,2,4,8,5]=>0110110=>1001001
[1,4,7,2,8,6,3,5]=>[1,6,8,2,4,3,7,5]=>0110100=>1001011
[1,6,7,8,2,5,3,4]=>[1,8,2,5,7,3,6,4]=>0111000=>1000111
[1,2,6,8,3,7,5,4]=>[1,2,7,3,5,8,6,4]=>0011010=>1100101
[1,5,2,7,8,4,6,3]=>[1,8,4,6,7,5,2,3]=>0101100=>1010011
[1,3,6,2,4,8,7,5]=>[1,7,8,6,3,2,4,5]=>0110010=>1001101
[1,5,3,7,4,8,6,2]=>[1,3,8,6,7,4,5,2]=>0101010=>1010101
[2,8,4,1,5,3,7,6]=>[4,2,1,5,7,8,3,6]=>1110000=>0001111
[3,8,4,1,5,7,2,6]=>[4,1,5,7,3,2,8,6]=>1110010=>0001101
[1,3,7,4,2,8,6,5]=>[1,4,8,6,7,3,2,5]=>0110010=>1001101
[1,3,8,4,2,7,6,5]=>[1,4,7,6,8,3,2,5]=>0110010=>1001101
[1,2,7,4,8,3,6,5]=>[1,2,4,8,3,6,7,5]=>0010100=>1101011
[1,5,2,4,8,3,7,6]=>[1,4,7,8,5,2,3,6]=>0100100=>1011011
[1,8,4,5,7,2,3,6]=>[1,7,5,4,2,8,3,6]=>0111100=>1000011
[1,8,3,5,2,7,4,6]=>[1,3,5,2,7,4,8,6]=>0101010=>1010101
[2,8,3,5,1,4,7,6]=>[3,5,2,1,7,8,4,6]=>1101000=>0010111
[2,3,8,6,1,4,7,5]=>[6,3,2,1,7,8,4,5]=>1111000=>0000111
[1,3,8,6,2,7,4,5]=>[1,7,6,3,2,8,4,5]=>0111010=>1000101
[1,5,6,8,7,2,3,4]=>[1,7,2,8,3,6,5,4]=>0111100=>1000011
[1,2,6,8,5,3,7,4]=>[1,2,5,7,8,3,6,4]=>0011000=>1100111
[1,2,7,8,5,3,6,4]=>[1,2,5,8,3,6,7,4]=>0011000=>1100111
[1,2,5,8,7,3,6,4]=>[1,2,7,3,6,8,5,4]=>0011100=>1100011
[1,2,6,8,7,3,5,4]=>[1,2,7,3,8,5,6,4]=>0011100=>1100011
[1,2,7,8,6,3,5,4]=>[1,2,6,3,8,5,7,4]=>0011100=>1100011
[1,6,7,8,5,2,3,4]=>[1,5,8,2,7,3,6,4]=>0111000=>1000111
[1,3,7,6,2,8,4,5]=>[1,8,6,3,2,7,4,5]=>0111010=>1000101
[1,2,8,4,7,6,3,5]=>[1,2,4,6,7,3,8,5]=>0010100=>1101011
[1,2,5,8,7,6,3,4]=>[1,2,6,7,3,8,5,4]=>0011100=>1100011
[1,2,6,8,7,5,3,4]=>[1,2,7,5,8,3,6,4]=>0011100=>1100011
[1,2,7,8,6,5,3,4]=>[1,2,6,5,8,3,7,4]=>0011100=>1100011
[5,2,4,7,6,3,8,1]=>[2,6,4,3,8,7,5,1]=>1011101=>0100010
[5,6,2,1,7,8,3,4]=>[8,2,7,6,5,1,3,4]=>1100110=>0011001
[2,6,1,4,5,8,7,3]=>[4,5,7,8,6,2,1,3]=>1100010=>0011101
[5,4,2,7,6,3,8,1]=>[6,4,2,3,8,7,5,1]=>1101101=>0010010
[2,6,1,7,5,8,3,4]=>[5,8,2,1,3,7,6,4]=>1101010=>0010101
[5,1,2,7,8,4,3,6]=>[8,4,7,5,1,2,3,6]=>1001100=>0110011
[2,6,1,7,4,8,3,5]=>[8,4,7,6,2,1,3,5]=>1101010=>0010101
[3,6,4,1,7,8,2,5]=>[4,1,8,3,2,7,6,5]=>1110110=>0001001
[5,4,6,1,3,8,7,2]=>[7,8,6,1,4,3,5,2]=>1110010=>0001101
[3,6,4,1,5,8,7,2]=>[4,1,5,7,8,6,3,2]=>1110010=>0001101
[2,6,1,5,4,8,7,3]=>[5,4,7,8,6,2,1,3]=>1101010=>0010101
[2,6,1,4,7,8,5,3]=>[4,8,5,7,6,2,1,3]=>1100110=>0011001
[5,1,2,4,8,6,7,3]=>[4,6,7,8,5,1,2,3]=>1000100=>0111011
[5,1,2,4,8,7,6,3]=>[4,7,6,8,5,1,2,3]=>1000110=>0111001
[1,2,3,8,5,4,7,6]=>[1,2,3,5,7,8,4,6]=>0001000=>1110111
[4,3,1,2,8,5,7,6]=>[3,1,4,2,7,8,5,6]=>1100100=>0011011
[2,1,5,3,8,6,4,7]=>[2,1,6,8,5,3,4,7]=>1010100=>0101011
[1,2,3,8,5,6,4,7]=>[1,2,3,5,6,8,4,7]=>0001000=>1110111
[1,2,3,8,6,4,5,7]=>[1,2,3,6,4,8,5,7]=>0001100=>1110011
[1,2,3,8,6,5,4,7]=>[1,2,3,6,5,8,4,7]=>0001100=>1110011
[1,2,3,8,5,4,6,7]=>[1,2,3,5,8,4,6,7]=>0001000=>1110111
[2,6,1,5,4,8,3,7]=>[5,4,8,6,2,1,3,7]=>1101010=>0010101
[5,1,2,4,8,6,3,7]=>[4,6,8,5,1,2,3,7]=>1000100=>0111011
[2,5,4,3,1,8,6,7]=>[4,3,5,2,1,8,6,7]=>1110010=>0001101
[5,2,6,1,7,8,4,3]=>[2,8,1,4,7,6,5,3]=>1010110=>0101001
[2,1,3,7,8,5,6,4]=>[2,1,3,8,5,6,7,4]=>1001100=>0110011
[5,2,4,1,7,8,6,3]=>[2,4,1,8,6,7,5,3]=>1010110=>0101001
[4,3,1,2,8,6,7,5]=>[3,1,4,2,6,7,8,5]=>1100100=>0011011
[5,1,4,2,8,6,7,3]=>[4,1,2,6,7,8,5,3]=>1010100=>0101011
[2,1,3,6,8,5,7,4]=>[2,1,3,7,8,5,6,4]=>1001100=>0110011
[1,2,3,8,6,7,4,5]=>[1,2,3,7,6,4,8,5]=>0001110=>1110001
[1,2,3,8,7,5,4,6]=>[1,2,3,7,5,8,4,6]=>0001100=>1110011
[1,2,3,8,7,4,5,6]=>[1,2,3,7,4,8,5,6]=>0001100=>1110011
[1,2,3,8,5,7,4,6]=>[1,2,3,5,7,4,8,6]=>0001010=>1110101
[2,1,3,6,8,7,4,5]=>[2,1,3,7,4,8,6,5]=>1001110=>0110001
[3,1,6,2,8,7,5,4]=>[7,5,8,6,3,1,2,4]=>1010110=>0101001
[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,6,7,8]=>00000100=>11111011
[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,5,6,7,8]=>00001000=>11110111
[1,2,3,9,4,5,6,7,8]=>[1,2,3,9,4,5,6,7,8]=>00010000=>11101111
[1,2,9,3,4,5,6,7,8]=>[1,2,9,3,4,5,6,7,8]=>00100000=>11011111
[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,8,9]=>000000010=>111111101
[1,2,3,4,5,9,7,6,8]=>[1,2,3,4,5,7,9,6,8]=>00000100=>11111011
[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,7,8,9]=>000000100=>111111011
[1,2,3,4,9,6,5,7,8]=>[1,2,3,4,6,9,5,7,8]=>00001000=>11110111
[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,10,6,7,8,9]=>000001000=>111110111
[1,2,3,9,5,4,6,7,8]=>[1,2,3,5,9,4,6,7,8]=>00010000=>11101111
[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,10,5,6,7,8,9]=>000010000=>111101111
[1,8,3,4,2,5,6,7]=>[1,3,4,8,2,5,6,7]=>0100000=>1011111
[1,2,9,4,3,5,6,7,8]=>[1,2,4,9,3,5,6,7,8]=>00100000=>11011111
[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,10,4,5,6,7,8,9]=>000100000=>111011111
[1,8,4,3,2,5,6,7]=>[1,4,3,8,2,5,6,7]=>0110000=>1001111
[1,9,3,2,4,5,6,7,8]=>[1,3,9,2,4,5,6,7,8]=>01000000=>10111111
[1,2,10,3,4,5,6,7,8,9]=>[1,2,10,3,4,5,6,7,8,9]=>001000000=>110111111
[8,5,7,4,6,3,2,1]=>[4,6,3,7,5,2,8,1]=>1110100=>0001011
[8,7,6,3,5,4,2,1]=>[5,6,3,4,7,2,8,1]=>1110000=>0001111
[8,6,7,3,5,4,2,1]=>[5,7,3,4,6,2,8,1]=>1110000=>0001111
[8,1,7,4,6,5,3,2]=>[4,6,5,7,3,8,1,2]=>1010100=>0101011
[8,2,7,3,6,5,4,1]=>[2,6,5,7,3,4,8,1]=>1010100=>0101011
[8,3,7,2,6,5,4,1]=>[6,5,7,3,2,4,8,1]=>1110100=>0001011
[8,7,6,2,5,4,3,1]=>[5,6,2,4,7,3,8,1]=>1110000=>0001111
[8,4,7,1,6,5,3,2]=>[6,5,7,1,4,3,8,2]=>1110100=>0001011
[8,2,7,1,6,5,4,3]=>[2,6,5,7,1,4,8,3]=>1010100=>0101011
[8,7,6,2,5,3,4,1]=>[5,6,2,7,3,4,8,1]=>1110000=>0001111
[8,1,7,6,5,3,4,2]=>[5,6,3,7,4,8,1,2]=>1011000=>0100111
[8,4,7,6,5,2,3,1]=>[5,6,2,7,4,3,8,1]=>1111000=>0000111
[8,5,7,6,4,2,3,1]=>[6,4,7,2,5,3,8,1]=>1111000=>0000111
[8,5,7,6,4,1,3,2]=>[6,4,7,1,5,3,8,2]=>1111000=>0000111
[8,3,7,6,5,1,4,2]=>[5,6,3,1,7,4,8,2]=>1111000=>0000111
[8,7,6,4,5,1,3,2]=>[4,5,6,1,7,3,8,2]=>1110000=>0001111
[8,7,6,2,5,1,4,3]=>[5,6,2,7,1,4,8,3]=>1110000=>0001111
[8,7,6,1,5,2,4,3]=>[5,6,1,7,2,4,8,3]=>1110000=>0001111
[6,8,1,4,2,5,3,7]=>[4,8,1,5,6,2,3,7]=>1100000=>0011111
[7,8,3,6,1,4,2,5]=>[3,6,1,8,4,7,2,5]=>1101000=>0010111
[7,8,2,5,1,4,3,6]=>[5,2,8,4,7,1,3,6]=>1101000=>0010111
[6,8,2,5,3,7,1,4]=>[5,2,3,7,1,8,6,4]=>1101010=>0010101
[6,8,2,5,4,7,1,3]=>[5,4,7,2,8,6,1,3]=>1101010=>0010101
[2,5,4,7,6,8,1,3]=>[8,6,4,2,1,7,5,3]=>1111110=>0000001
[2,5,1,4,3,7,6,8]=>[4,5,2,1,3,7,6,8]=>1100010=>0011101
[2,6,1,5,3,7,4,8]=>[5,2,1,3,7,6,4,8]=>1101010=>0010101
[2,6,4,7,5,8,1,3]=>[5,8,4,2,1,7,6,3]=>1111010=>0000101
[5,8,2,6,4,7,1,3]=>[7,6,4,8,2,5,1,3]=>1101010=>0010101
[4,8,2,6,3,7,1,5]=>[7,6,2,3,8,4,1,5]=>1101010=>0010101
[4,8,1,5,2,6,3,7]=>[5,1,6,8,4,2,3,7]=>1101000=>0010111
[4,8,3,7,1,5,2,6]=>[3,7,1,5,8,4,2,6]=>1101000=>0010111
[6,8,3,7,1,4,2,5]=>[3,7,1,8,4,6,2,5]=>1101000=>0010111
[5,8,4,7,1,3,2,6]=>[7,4,1,8,3,5,2,6]=>1111000=>0000111
[6,8,5,7,1,3,2,4]=>[7,1,5,3,8,2,6,4]=>1111000=>0000111
[5,7,6,8,2,4,1,3]=>[8,2,6,4,7,1,5,3]=>1111000=>0000111
[4,7,6,8,1,3,2,5]=>[8,1,6,3,7,4,2,5]=>1111000=>0000111
[4,7,5,8,1,3,2,6]=>[8,1,5,3,7,4,2,6]=>1111000=>0000111
[3,7,1,4,2,6,5,8]=>[4,6,7,1,3,2,5,8]=>1100000=>0011111
[3,7,5,8,1,4,2,6]=>[8,1,5,4,7,3,2,6]=>1111000=>0000111
[3,7,6,8,1,4,2,5]=>[8,1,6,4,7,3,2,5]=>1111000=>0000111
[3,7,6,8,2,5,1,4]=>[8,2,5,6,3,1,7,4]=>1111000=>0000111
[4,7,6,8,2,5,1,3]=>[8,2,5,6,1,7,4,3]=>1111000=>0000111
[4,7,5,8,3,6,1,2]=>[6,8,3,5,1,7,4,2]=>1111000=>0000111
[4,7,5,8,2,6,1,3]=>[6,8,2,5,1,7,4,3]=>1111000=>0000111
[3,7,4,8,2,6,1,5]=>[6,8,4,2,7,3,1,5]=>1111000=>0000111
[3,7,4,8,1,5,2,6]=>[8,4,1,5,7,3,2,6]=>1111000=>0000111
[3,7,2,6,5,8,1,4]=>[5,8,6,2,3,1,7,4]=>1101010=>0010101
[4,7,3,6,5,8,1,2]=>[3,5,8,6,1,7,4,2]=>1101010=>0010101
[2,6,5,8,4,7,1,3]=>[7,4,5,2,1,8,6,3]=>1111010=>0000101
[2,6,5,8,3,7,1,4]=>[7,3,5,2,1,8,6,4]=>1111010=>0000101
[2,6,3,7,1,5,4,8]=>[3,7,2,1,5,6,4,8]=>1101000=>0010111
[7,6,4,2,8,5,3,1]=>[4,2,8,5,6,3,7,1]=>1110100=>0001011
[7,6,4,3,8,2,5,1]=>[4,3,8,2,6,5,7,1]=>1110100=>0001011
[6,7,3,5,4,8,2,1]=>[3,5,4,8,2,7,6,1]=>1101010=>0010101
[6,8,3,7,5,2,4,1]=>[3,5,7,2,8,4,6,1]=>1101000=>0010111
[7,6,8,3,5,2,4,1]=>[5,8,3,6,2,4,7,1]=>1110000=>0001111
[7,6,3,5,8,2,4,1]=>[3,8,5,2,6,4,7,1]=>1101100=>0010011
[7,6,3,5,2,4,8,1]=>[3,5,2,6,4,8,7,1]=>1101001=>0010110
[7,6,4,2,5,1,8,3]=>[4,2,5,6,1,8,7,3]=>1110001=>0001110
[7,6,2,8,4,1,5,3]=>[8,4,6,2,5,7,1,3]=>1101000=>0010111
[7,6,3,8,2,4,1,5]=>[3,8,2,6,4,7,1,5]=>1101000=>0010111
[7,6,3,4,8,2,5,1]=>[3,4,8,2,6,5,7,1]=>1100100=>0011011
[5,7,8,3,6,2,1,4]=>[6,3,8,2,7,5,1,4]=>1110100=>0001011
[6,3,4,8,7,2,5,1]=>[7,4,3,2,8,5,6,1]=>1111100=>0000011
[6,3,8,4,7,2,1,5]=>[4,7,3,2,8,1,6,5]=>1110100=>0001011
[6,2,8,4,1,7,5,3]=>[2,4,7,1,5,8,6,3]=>1010010=>0101101
[6,3,4,7,5,8,2,1]=>[5,8,4,3,2,7,6,1]=>1111010=>0000101
[5,6,8,3,7,2,1,4]=>[7,3,8,2,6,5,1,4]=>1110100=>0001011
[4,6,7,8,3,5,2,1]=>[8,3,5,7,2,6,4,1]=>1111000=>0000111
[4,6,8,3,5,7,2,1]=>[5,7,3,8,6,2,4,1]=>1110010=>0001101
[4,7,3,5,6,8,2,1]=>[3,8,6,5,2,7,4,1]=>1101110=>0010001
[4,7,3,5,8,2,6,1]=>[3,8,5,2,6,7,4,1]=>1101100=>0010011
[5,3,4,7,8,2,1,6]=>[8,4,3,2,7,5,1,6]=>1111100=>0000011
[4,8,3,6,2,5,7,1]=>[3,6,2,5,7,8,4,1]=>1101000=>0010111
[4,8,3,5,7,2,6,1]=>[3,7,5,2,6,8,4,1]=>1101100=>0010011
[4,7,8,3,5,6,2,1]=>[5,6,8,3,7,2,4,1]=>1110000=>0001111
[4,7,8,3,6,2,5,1]=>[6,3,8,5,7,2,4,1]=>1110100=>0001011
[5,3,4,8,2,7,6,1]=>[7,6,8,4,3,2,5,1]=>1111010=>0000101
[5,2,8,4,1,7,3,6]=>[2,4,7,1,5,3,8,6]=>1010010=>0101101
[6,4,2,5,1,8,7,3]=>[5,4,2,7,8,6,1,3]=>1101010=>0010101
[6,3,5,8,7,2,4,1]=>[7,3,2,8,5,4,6,1]=>1111100=>0000011
[5,8,3,7,2,6,4,1]=>[3,6,7,2,8,4,5,1]=>1101000=>0010111
[5,7,3,4,8,2,1,6]=>[3,4,8,2,7,5,1,6]=>1100100=>0011011
[6,4,8,5,3,7,2,1]=>[5,3,7,4,2,8,6,1]=>1111010=>0000101
[6,4,3,8,5,7,2,1]=>[3,5,7,4,2,8,6,1]=>1101010=>0010101
[6,4,2,8,5,3,1,7]=>[5,8,4,2,3,6,1,7]=>1101000=>0010111
[6,4,2,7,3,1,8,5]=>[8,7,4,2,3,6,1,5]=>1101001=>0010110
[6,4,5,3,7,1,8,2]=>[8,7,5,3,4,1,6,2]=>1110101=>0001010
[5,7,4,2,3,1,6,8]=>[4,2,7,3,5,1,6,8]=>1110000=>0001111
[5,6,3,7,1,8,2,4]=>[3,8,1,7,6,2,5,4]=>1101010=>0010101
[5,6,3,4,7,1,8,2]=>[3,4,8,7,1,6,5,2]=>1100101=>0011010
[6,3,5,7,4,8,2,1]=>[8,4,5,3,2,7,6,1]=>1111010=>0000101
[6,3,5,4,7,8,2,1]=>[4,8,5,3,2,7,6,1]=>1110110=>0001001
[6,4,2,5,1,7,3,8]=>[5,4,2,7,6,1,3,8]=>1101010=>0010101
[5,3,4,7,2,6,1,8]=>[6,7,4,3,2,5,1,8]=>1111000=>0000111
[4,7,3,6,2,5,8,1]=>[3,6,2,5,8,7,4,1]=>1101001=>0010110
[4,6,7,3,5,8,2,1]=>[5,8,3,7,6,2,4,1]=>1110010=>0001101
[4,5,7,8,3,6,2,1]=>[6,8,3,7,2,5,4,1]=>1111000=>0000111
[4,5,8,3,7,2,6,1]=>[7,3,6,8,5,2,4,1]=>1110100=>0001011
[5,3,6,8,2,1,4,7]=>[8,3,2,6,1,5,4,7]=>1111000=>0000111
[5,3,6,7,1,8,2,4]=>[8,3,1,7,6,2,5,4]=>1111010=>0000101
[4,5,7,3,6,8,2,1]=>[8,6,3,7,5,2,4,1]=>1110110=>0001001
[5,7,4,8,6,3,2,1]=>[6,4,3,8,2,7,5,1]=>1111100=>0000011
[3,2,6,5,1,8,7,4]=>[2,5,3,1,7,8,6,4]=>1011010=>0100101
[3,5,6,7,2,8,4,1]=>[8,2,7,6,4,5,3,1]=>1111010=>0000101
[3,4,5,6,7,8,9,2,1]=>[9,2,8,7,6,5,4,3,1]=>11111110=>00000001
[3,4,5,6,7,8,9,10,2,1]=>[10,2,9,8,7,6,5,4,3,1]=>111111110=>000000001
[2,4,6,1,8,3,9,5,10,7]=>[10,9,2,1,4,3,6,5,8,7]=>111010101=>000101010
[1,6,2,5,3,4,8,7]=>[1,5,2,3,6,4,8,7]=>0101001=>1010110
[1,3,8,2,4,6,5,7]=>[1,6,8,3,2,4,5,7]=>0110000=>1001111
[1,7,2,3,6,4,8,5]=>[1,6,2,3,4,8,7,5]=>0100101=>1011010
[1,6,8,2,5,3,7,4]=>[1,5,7,8,2,6,3,4]=>0110000=>1001111
[1,8,2,5,3,4,7,6]=>[1,5,2,3,7,8,4,6]=>0101000=>1010111
[1,8,2,3,6,4,7,5]=>[1,6,2,3,4,7,8,5]=>0100100=>1011011
[1,2,7,3,5,4,6,8]=>[1,2,5,7,3,4,6,8]=>0010000=>1101111
[1,8,2,7,3,4,6,5]=>[1,7,2,3,6,8,4,5]=>0101000=>1010111
[1,5,8,2,3,7,4,6]=>[1,7,2,5,3,4,8,6]=>0110010=>1001101
[1,6,8,2,3,5,4,7]=>[1,8,2,5,6,3,4,7]=>0110000=>1001111
[5,3,6,1,2,4,8,7]=>[6,3,1,5,2,4,8,7]=>1110001=>0001110
[7,1,5,8,4,2,3,6]=>[8,4,5,1,2,7,3,6]=>1011000=>0100111
[7,1,4,5,8,2,3,6]=>[8,5,4,1,2,7,3,6]=>1011100=>0100011
[8,1,4,7,5,2,3,6]=>[5,7,4,1,2,8,3,6]=>1011000=>0100111
[8,1,5,4,7,2,3,6]=>[4,7,5,1,2,8,3,6]=>1010100=>0101011
[2,1,7,5,8,3,4,6]=>[2,1,8,5,3,7,4,6]=>1011100=>0100011
[7,1,5,4,8,2,3,6]=>[4,8,5,1,2,7,3,6]=>1010100=>0101011
[7,1,4,8,5,2,3,6]=>[5,8,4,1,2,7,3,6]=>1011000=>0100111
[7,8,3,1,2,4,6,5]=>[3,8,1,6,7,2,4,5]=>1100000=>0011111
[8,3,7,1,2,4,6,5]=>[7,3,1,6,8,2,4,5]=>1110000=>0001111
[8,3,7,5,1,2,4,6]=>[5,3,1,7,2,8,4,6]=>1111000=>0000111
[6,7,1,8,4,2,3,5]=>[8,4,7,1,6,2,3,5]=>1101000=>0010111
[6,8,1,7,4,2,3,5]=>[7,4,8,1,6,2,3,5]=>1101000=>0010111
[7,1,8,5,4,2,3,6]=>[5,4,8,1,2,7,3,6]=>1011000=>0100111
[7,1,8,4,5,2,3,6]=>[4,5,8,1,2,7,3,6]=>1010000=>0101111
[2,1,7,8,5,3,4,6]=>[2,1,5,8,3,7,4,6]=>1011000=>0100111
[6,1,2,3,8,7,5,4]=>[7,5,8,6,1,2,3,4]=>1000110=>0111001
[6,8,1,4,2,3,7,5]=>[4,7,8,1,6,2,3,5]=>1100000=>0011111
[6,8,3,1,2,7,4,5]=>[3,7,1,8,6,2,4,5]=>1100010=>0011101
[6,7,3,1,2,8,4,5]=>[3,8,1,7,6,2,4,5]=>1100010=>0011101
[6,7,1,4,2,3,8,5]=>[4,8,7,1,6,2,3,5]=>1100001=>0011110
[4,3,6,8,5,7,1,2]=>[5,7,3,1,8,6,4,2]=>1111010=>0000101
[6,1,2,5,4,8,3,7]=>[5,4,8,6,1,2,3,7]=>1001010=>0110101
[3,2,8,5,4,1,7,6]=>[2,5,4,7,8,3,1,6]=>1011000=>0100111
[7,2,1,5,8,3,4,6]=>[2,8,5,1,3,7,4,6]=>1001100=>0110011
[3,5,6,1,8,4,2,7]=>[8,1,4,6,5,3,2,7]=>1110100=>0001011
[1,3,6,8,7,4,2,5]=>[1,7,4,8,3,2,6,5]=>0111100=>1000011
[1,2,8,5,7,3,4,6]=>[1,2,7,5,3,8,4,6]=>0011100=>1100011
[4,8,1,2,5,7,3,6]=>[5,7,1,4,2,3,8,6]=>1100010=>0011101
[3,8,1,4,7,2,5,6]=>[4,7,1,3,2,8,5,6]=>1100100=>0011011
[1,7,8,4,6,2,5,3]=>[1,4,6,2,8,5,7,3]=>0110100=>1001011
[3,7,4,8,5,1,6,2]=>[5,8,4,1,6,7,3,2]=>1111000=>0000111
[2,7,3,1,5,8,4,6]=>[3,5,8,2,1,4,7,6]=>1100010=>0011101
[2,7,5,8,6,4,1,3]=>[6,4,8,5,2,1,7,3]=>1111100=>0000011
[8,2,6,7,5,4,3,1]=>[2,5,7,4,6,3,8,1]=>1011000=>0100111
[3,4,2,7,8,1,6,5]=>[8,4,2,3,1,6,7,5]=>1101100=>0010011
[4,1,3,7,5,6,8,2]=>[3,5,6,8,7,4,1,2]=>1001001=>0110110
[6,5,8,7,1,4,2,3]=>[7,1,8,4,5,2,6,3]=>1111000=>0000111
[1,6,7,4,5,3,8,2]=>[1,4,5,8,7,3,6,2]=>0110001=>1001110
[6,1,7,3,5,4,8,2]=>[5,8,7,3,4,6,1,2]=>1010001=>0101110
[6,3,1,2,5,8,4,7]=>[3,1,5,8,6,2,4,7]=>1100010=>0011101
[1,4,7,2,8,5,3,6]=>[1,8,5,7,2,4,3,6]=>0110100=>1001011
[5,6,8,7,2,4,1,3]=>[7,2,8,4,6,1,5,3]=>1111000=>0000111
[6,8,5,7,1,2,4,3]=>[7,1,5,2,8,4,6,3]=>1111000=>0000111
[2,8,4,1,7,5,6,3]=>[4,2,1,7,5,6,8,3]=>1110100=>0001011
[8,2,4,3,7,5,6,1]=>[2,4,3,7,5,6,8,1]=>1010100=>0101011
[6,8,2,1,5,7,3,4]=>[5,7,2,8,6,1,3,4]=>1100010=>0011101
[7,2,8,4,1,6,3,5]=>[2,4,6,8,1,7,3,5]=>1010000=>0101111
[4,8,2,5,7,1,6,3]=>[7,5,2,6,8,4,1,3]=>1101100=>0010011
[4,1,6,8,5,3,7,2]=>[5,7,8,3,6,4,1,2]=>1011000=>0100111
[5,2,6,4,8,3,1,7]=>[2,4,8,3,6,5,1,7]=>1010100=>0101011
[6,7,1,3,4,5,8,2]=>[8,7,1,3,4,5,6,2]=>1100001=>0011110
[1,7,3,2,4,8,5,6]=>[1,3,8,2,4,5,7,6]=>0100010=>1011101
[1,3,6,5,2,8,4,7]=>[1,5,3,2,8,6,4,7]=>0111010=>1000101
[7,1,6,5,3,4,8,2]=>[5,3,6,4,8,7,1,2]=>1011001=>0100110
[4,3,8,7,5,2,6,1]=>[5,7,3,2,6,8,4,1]=>1111000=>0000111
[6,8,7,4,2,3,5,1]=>[4,7,2,8,3,5,6,1]=>1110000=>0001111
[2,5,6,3,4,8,7,1]=>[7,8,6,3,4,5,2,1]=>1110010=>0001101
[3,8,7,2,6,4,5,1]=>[6,2,4,7,5,8,3,1]=>1110100=>0001011
[6,3,5,4,8,7,2,1]=>[4,7,5,3,2,8,6,1]=>1110110=>0001001
[4,3,8,6,1,5,2,7]=>[6,3,1,5,8,4,2,7]=>1111000=>0000111
[7,5,2,6,8,1,4,3]=>[8,2,6,5,4,7,1,3]=>1101100=>0010011
[1,8,5,3,6,2,4,7]=>[1,6,5,3,8,2,4,7]=>0110100=>1001011
[5,1,7,2,4,3,8,6]=>[8,7,1,2,4,5,3,6]=>1010001=>0101110
[5,4,1,3,8,6,2,7]=>[4,1,3,6,8,5,2,7]=>1100100=>0011011
[5,1,8,6,3,4,2,7]=>[6,3,8,4,5,1,2,7]=>1011000=>0100111
[8,2,3,7,6,4,5,1]=>[2,3,6,4,7,5,8,1]=>1001100=>0110011
[5,8,2,4,7,6,3,1]=>[4,6,7,2,3,8,5,1]=>1100100=>0011011
[7,2,5,6,4,8,1,3]=>[2,8,6,4,5,1,7,3]=>1011010=>0100101
[7,1,3,5,8,2,6,4]=>[3,8,5,1,2,6,7,4]=>1001100=>0110011
[8,2,1,3,5,6,7,4]=>[2,5,6,7,8,1,3,4]=>1000000=>0111111
[4,1,3,8,2,6,7,5]=>[3,6,7,8,4,1,2,5]=>1001000=>0110111
[3,1,7,2,8,5,4,6]=>[8,5,7,3,1,2,4,6]=>1010100=>0101011
[3,6,1,4,7,2,8,5]=>[4,8,7,1,3,2,6,5]=>1100101=>0011010
[1,5,8,4,7,2,3,6]=>[1,4,7,2,8,5,3,6]=>0110100=>1001011
[7,1,3,6,2,8,4,5]=>[3,8,6,1,2,7,4,5]=>1001010=>0110101
[6,2,7,4,5,8,1,3]=>[2,4,5,8,1,7,6,3]=>1010010=>0101101
[2,1,8,4,5,7,3,6]=>[2,1,4,5,7,3,8,6]=>1010010=>0101101
[1,8,5,7,3,2,4,6]=>[1,7,3,5,2,8,4,6]=>0111000=>1000111
[2,7,4,1,5,3,8,6]=>[4,2,1,5,8,7,3,6]=>1110001=>0001110
[7,4,8,6,2,3,1,5]=>[6,2,8,4,3,7,1,5]=>1111000=>0000111
[2,7,1,4,6,3,8,5]=>[4,6,2,1,3,8,7,5]=>1100101=>0011010
[7,1,3,2,8,5,4,6]=>[3,8,5,7,1,2,4,6]=>1000100=>0111011
[5,1,7,4,2,3,8,6]=>[4,8,7,1,2,5,3,6]=>1010001=>0101110
[1,3,4,8,6,5,2,7]=>[1,6,5,8,4,3,2,7]=>0111100=>1000011
[4,1,8,6,5,3,2,7]=>[5,6,3,8,4,1,2,7]=>1011000=>0100111
[7,2,8,5,3,6,4,1]=>[2,5,3,6,8,4,7,1]=>1011000=>0100111
[5,2,8,4,3,7,6,1]=>[2,4,7,6,8,3,5,1]=>1010010=>0101101
[8,4,7,5,2,3,6,1]=>[5,2,7,4,3,6,8,1]=>1111000=>0000111
[7,5,2,8,4,6,1,3]=>[6,8,4,5,2,7,1,3]=>1101000=>0010111
[5,7,4,3,6,2,8,1]=>[4,3,6,2,8,7,5,1]=>1110101=>0001010
[6,7,5,1,2,8,3,4]=>[5,1,8,2,7,6,3,4]=>1110010=>0001101
[5,2,6,8,3,4,7,1]=>[2,7,8,3,6,4,5,1]=>1011000=>0100111
[3,6,8,4,7,2,5,1]=>[4,7,2,8,5,6,3,1]=>1110100=>0001011
[2,6,3,8,4,7,5,1]=>[3,7,4,5,8,6,2,1]=>1101010=>0010101
[7,2,3,6,5,8,4,1]=>[2,3,5,8,6,4,7,1]=>1001010=>0110101
[2,1,5,6,8,3,7,4]=>[2,1,7,8,3,6,5,4]=>1011100=>0100011
[5,8,1,2,6,4,7,3]=>[6,1,4,7,8,5,2,3]=>1100100=>0011011
[1,6,8,3,2,7,4,5]=>[1,7,3,8,6,2,4,5]=>0110010=>1001101
[5,4,8,3,6,2,7,1]=>[6,3,4,2,7,8,5,1]=>1110100=>0001011
[6,4,5,8,2,7,3,1]=>[7,2,5,4,3,8,6,1]=>1111010=>0000101
[1,5,6,4,8,2,7,3]=>[1,4,7,8,2,6,5,3]=>0110100=>1001011
[3,1,5,6,4,8,7,2]=>[7,8,6,4,5,3,1,2]=>1011010=>0100101
[1,3,6,2,5,7,8,4]=>[1,5,8,7,6,3,2,4]=>0110011=>1001100
[1,4,6,3,5,7,8,2]=>[1,5,8,7,6,3,4,2]=>0110011=>1001100
[3,5,1,6,4,7,8,2]=>[8,7,6,4,5,1,3,2]=>1101011=>0010100
[3,6,1,4,2,7,8,5]=>[4,8,7,6,1,3,2,5]=>1100011=>0011100
[2,4,6,3,1,7,8,5]=>[8,7,6,3,4,2,1,5]=>1110011=>0001100
[1,3,6,5,2,7,8,4]=>[1,5,3,2,8,7,6,4]=>0111011=>1000100
[1,2,6,4,3,8,5,7]=>[1,2,4,8,6,3,5,7]=>0010010=>1101101
[1,2,6,3,5,8,7,4]=>[1,2,5,7,8,6,3,4]=>0010010=>1101101
[2,3,5,1,8,4,7,6]=>[7,8,5,3,2,1,4,6]=>1110100=>0001011
[2,3,6,1,8,5,4,7]=>[8,5,6,3,2,1,4,7]=>1110100=>0001011
[1,2,7,4,6,8,3,5]=>[1,2,4,8,6,3,7,5]=>0010110=>1101001
[2,3,7,5,1,8,4,6]=>[5,3,2,1,8,4,7,6]=>1111010=>0000101
[4,7,2,5,3,8,6,1]=>[5,2,3,8,6,7,4,1]=>1101010=>0010101
[3,1,7,5,4,8,6,2]=>[5,4,8,6,7,3,1,2]=>1011010=>0100101
[1,2,7,6,4,8,5,3]=>[1,2,8,6,4,5,7,3]=>0011010=>1100101
[1,2,7,3,6,8,5,4]=>[1,2,8,6,5,7,3,4]=>0010110=>1101001
[2,3,6,1,8,5,7,4]=>[7,8,5,6,3,2,1,4]=>1110100=>0001011
[3,1,5,4,8,7,6,2]=>[4,7,6,8,5,3,1,2]=>1010110=>0101001
[1,2,5,8,4,7,3,6]=>[1,2,7,4,5,3,8,6]=>0011010=>1100101
[1,2,6,8,5,4,7,3]=>[1,2,5,7,8,4,6,3]=>0011000=>1100111
[3,5,7,4,8,2,1,6]=>[4,8,2,7,5,3,1,6]=>1110100=>0001011
[1,2,6,8,5,4,3,7]=>[1,2,5,8,4,6,3,7]=>0011000=>1100111
[1,2,5,8,4,3,7,6]=>[1,2,7,8,4,5,3,6]=>0011000=>1100111
[1,3,5,8,2,4,7,6]=>[1,7,8,3,2,5,4,6]=>0111000=>1000111
[1,3,6,8,2,5,4,7]=>[1,8,3,2,5,6,4,7]=>0111000=>1000111
[3,5,7,4,8,1,2,6]=>[4,8,1,7,5,3,2,6]=>1110100=>0001011
[4,6,1,7,5,8,2,3]=>[5,8,1,7,6,4,2,3]=>1101010=>0010101
[2,3,6,7,5,8,1,4]=>[5,8,3,2,1,7,6,4]=>1111010=>0000101
[1,3,7,5,6,8,2,4]=>[1,8,6,5,3,2,7,4]=>0111110=>1000001
[2,3,6,5,8,1,7,4]=>[7,8,5,3,2,1,6,4]=>1111100=>0000011
[3,4,6,2,8,1,7,5]=>[7,8,2,4,3,1,6,5]=>1110100=>0001011
[3,5,4,6,8,2,1,7]=>[8,4,2,6,5,3,1,7]=>1111100=>0000011
[3,5,4,6,8,1,2,7]=>[8,4,1,6,5,3,2,7]=>1111100=>0000011
[1,2,4,7,5,8,3,6]=>[1,2,5,8,4,3,7,6]=>0011010=>1100101
[1,2,6,7,4,8,3,5]=>[1,2,8,4,7,6,3,5]=>0011010=>1100101
[3,6,4,7,1,8,5,2]=>[8,4,1,5,7,6,3,2]=>1111010=>0000101
[1,2,6,7,3,8,5,4]=>[1,2,8,3,5,7,6,4]=>0011010=>1100101
[1,2,5,7,3,8,6,4]=>[1,2,8,6,7,3,5,4]=>0011010=>1100101
[3,1,5,7,6,8,4,2]=>[8,6,4,7,5,3,1,2]=>1011110=>0100001
[3,5,4,6,8,2,7,1]=>[7,8,4,2,6,5,3,1]=>1111100=>0000011
[3,1,6,5,8,7,4,2]=>[7,5,4,8,6,3,1,2]=>1011110=>0100001
[2,3,6,5,8,7,1,4]=>[7,5,3,2,1,8,6,4]=>1111110=>0000001
[1,2,7,4,6,8,5,3]=>[1,2,4,8,6,5,7,3]=>0010110=>1101001
[1,2,7,5,6,8,4,3]=>[1,2,8,6,5,4,7,3]=>0011110=>1100001
[3,1,6,7,5,8,4,2]=>[5,8,4,7,6,3,1,2]=>1011010=>0100101
[4,6,2,7,5,8,3,1]=>[5,8,2,3,7,6,4,1]=>1101010=>0010101
[3,5,7,4,8,2,6,1]=>[4,8,2,6,7,5,3,1]=>1110100=>0001011
[2,4,7,6,8,3,5,1]=>[8,3,6,5,7,4,2,1]=>1111100=>0000011
[1,4,6,8,3,5,7,2]=>[1,7,8,3,5,6,4,2]=>0111000=>1000111
[1,3,6,8,2,5,7,4]=>[1,7,8,3,2,5,6,4]=>0111000=>1000111
[1,3,5,8,2,7,4,6]=>[1,7,3,2,5,4,8,6]=>0111010=>1000101
[1,2,5,8,4,7,6,3]=>[1,2,7,6,8,4,5,3]=>0011010=>1100101
[1,2,4,8,7,3,6,5]=>[1,2,7,4,3,6,8,5]=>0011100=>1100011
[1,2,5,8,7,4,3,6]=>[1,2,7,4,8,5,3,6]=>0011100=>1100011
[1,3,5,8,7,2,4,6]=>[1,7,3,2,8,5,4,6]=>0111100=>1000011
[5,7,1,2,8,6,4,3]=>[6,8,1,4,7,5,2,3]=>1100100=>0011011
[3,1,7,6,8,5,4,2]=>[8,5,6,4,7,3,1,2]=>1011100=>0100011
[1,2,6,8,5,7,4,3]=>[1,2,5,7,4,8,6,3]=>0011010=>1100101
[1,2,5,8,7,4,6,3]=>[1,2,7,4,6,8,5,3]=>0011100=>1100011
[1,2,4,8,7,6,3,5]=>[1,2,6,7,4,3,8,5]=>0011100=>1100011
[6,4,5,7,2,8,1,3]=>[8,2,5,4,1,7,6,3]=>1111010=>0000101
[5,3,4,7,2,8,1,6]=>[8,4,3,2,5,1,7,6]=>1111010=>0000101
[3,2,7,4,6,8,1,5]=>[2,4,8,6,3,1,7,5]=>1010110=>0101001
[5,3,6,2,7,1,4,8]=>[7,3,2,6,5,1,4,8]=>1110100=>0001011
[2,6,3,4,7,1,5,8]=>[3,4,7,2,1,6,5,8]=>1100100=>0011011
[2,7,3,4,5,8,1,6]=>[3,4,5,8,2,1,7,6]=>1100010=>0011101
[2,5,7,3,6,8,1,4]=>[8,6,3,7,5,2,1,4]=>1110110=>0001001
[4,7,6,2,3,8,1,5]=>[8,6,2,7,3,4,1,5]=>1110010=>0001101
[7,3,5,2,4,8,1,6]=>[5,3,2,4,8,1,7,6]=>1110010=>0001101
[6,5,2,3,4,8,1,7]=>[5,2,3,4,8,6,1,7]=>1100010=>0011101
[5,3,1,2,8,4,7,6]=>[3,1,7,8,5,2,4,6]=>1100100=>0011011
[5,2,1,8,3,4,6,7]=>[2,8,1,3,5,4,6,7]=>1001000=>0110111
[6,2,3,1,8,4,7,5]=>[2,3,7,8,1,4,6,5]=>1000100=>0111011
[8,3,5,2,7,1,4,6]=>[7,5,3,2,8,1,4,6]=>1110100=>0001011
[8,6,2,4,7,1,5,3]=>[4,7,2,6,5,8,1,3]=>1100100=>0011011
[8,2,1,7,3,4,5,6]=>[2,7,1,3,8,4,5,6]=>1001000=>0110111
[7,1,6,2,3,4,5,8]=>[6,1,2,7,3,4,5,8]=>1010000=>0101111
[8,1,6,2,3,4,5,7]=>[6,1,2,8,3,4,5,7]=>1010000=>0101111
[8,1,7,3,4,5,6,2]=>[7,3,4,5,6,8,1,2]=>1010000=>0101111
[8,6,1,7,2,4,5,3]=>[7,1,6,4,5,8,2,3]=>1101000=>0010111
[8,1,5,7,2,3,6,4]=>[7,1,2,5,3,6,8,4]=>1011000=>0100111
[1,7,5,8,2,3,6,4]=>[1,8,2,5,3,6,7,4]=>0111000=>1000111
[7,2,1,8,3,4,5,6]=>[2,8,1,3,7,4,5,6]=>1001000=>0110111
[7,3,8,2,4,5,6,1]=>[8,3,2,4,5,6,7,1]=>1110000=>0001111
[7,2,8,3,4,5,6,1]=>[2,8,3,4,5,6,7,1]=>1010000=>0101111
[1,7,8,3,4,5,6,2]=>[1,8,3,4,5,6,7,2]=>0110000=>1001111
[1,4,5,8,3,6,7,2]=>[1,6,7,8,3,5,4,2]=>0111000=>1000111
[1,6,2,8,4,5,7,3]=>[1,7,8,4,5,6,2,3]=>0101000=>1010111
[4,1,3,6,8,2,7,5]=>[3,7,8,4,1,2,6,5]=>1001100=>0110011
[5,3,4,6,8,2,7,1]=>[7,8,4,3,2,6,5,1]=>1111100=>0000011
[5,3,4,8,7,1,2,6]=>[7,4,3,1,8,5,2,6]=>1111100=>0000011
[1,8,3,7,2,4,5,6]=>[1,3,7,2,8,4,5,6]=>0101000=>1010111
[3,8,1,7,2,4,5,6]=>[7,1,3,2,8,4,5,6]=>1101000=>0010111
[4,7,8,2,6,1,3,5]=>[6,2,8,1,4,3,7,5]=>1110100=>0001011
[6,2,8,7,1,4,5,3]=>[2,7,1,8,4,5,6,3]=>1011000=>0100111
[3,8,7,1,4,5,6,2]=>[7,1,4,5,6,8,3,2]=>1110000=>0001111
[1,7,6,2,3,4,5,8]=>[1,6,2,7,3,4,5,8]=>0110000=>1001111
[1,8,6,2,3,4,5,7]=>[1,6,2,8,3,4,5,7]=>0110000=>1001111
[2,8,7,3,4,5,6,1]=>[7,3,4,5,6,8,2,1]=>1110000=>0001111
[3,8,7,2,4,5,6,1]=>[7,2,4,5,6,8,3,1]=>1110000=>0001111
[7,8,3,6,2,4,5,1]=>[3,6,2,8,4,5,7,1]=>1101000=>0010111
[1,5,8,7,2,3,6,4]=>[1,7,2,6,8,3,5,4]=>0111000=>1000111
[8,7,6,1,3,4,5,2]=>[6,1,7,3,4,5,8,2]=>1110000=>0001111
[3,4,7,2,5,1,8,6]=>[5,8,7,2,4,3,1,6]=>1110001=>0001110
[4,1,8,5,3,2,7,6]=>[5,3,7,8,4,1,2,6]=>1011000=>0100111
[3,6,2,5,7,1,4,8]=>[7,5,2,3,1,6,4,8]=>1101100=>0010011
[1,2,8,3,7,5,4,6]=>[1,2,7,5,8,3,4,6]=>0010100=>1101011
[6,1,3,2,8,5,4,7]=>[3,8,5,6,1,2,4,7]=>1000100=>0111011
[1,6,3,8,7,4,2,5]=>[1,3,7,4,8,2,6,5]=>0101100=>1010011
[4,3,8,1,2,6,7,5]=>[6,7,8,3,1,4,2,5]=>1110000=>0001111
[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>10000000=>01111111
[2,3,4,5,6,8,1,7,9]=>[8,6,5,4,3,2,1,7,9]=>11111100=>00000011
[6,2,8,5,4,7,1,3]=>[2,5,4,7,1,8,6,3]=>1011010=>0100101
[3,5,1,2,4,8,7,6]=>[5,1,3,2,4,7,8,6]=>1100010=>0011101
[3,7,5,2,1,4,6,8]=>[5,2,7,3,1,4,6,8]=>1110000=>0001111
[3,8,5,2,7,4,1,6]=>[7,5,2,4,8,3,1,6]=>1110100=>0001011
[5,2,8,4,7,3,1,6]=>[2,4,7,3,8,5,1,6]=>1010100=>0101011
[5,2,7,4,1,3,6,8]=>[2,4,7,1,5,3,6,8]=>1010000=>0101111
[4,3,5,1,2,8,7,6]=>[5,3,1,4,2,7,8,6]=>1110010=>0001101
[1,4,6,5,2,8,7,3]=>[1,5,2,7,8,6,4,3]=>0111010=>1000101
[3,4,5,6,1,8,7,2]=>[7,8,6,1,5,4,3,2]=>1111010=>0000101
[1,4,7,2,6,3,5,8]=>[1,6,2,4,3,7,5,8]=>0110100=>1001011
[8,4,7,5,2,1,6,3]=>[5,2,7,4,1,6,8,3]=>1111000=>0000111
[8,1,4,7,2,3,6,5]=>[7,4,1,2,6,8,3,5]=>1011000=>0100111
[6,3,5,1,7,4,2,8]=>[7,5,3,1,4,6,2,8]=>1110100=>0001011
[6,1,4,8,7,3,2,5]=>[7,4,3,8,1,2,6,5]=>1011100=>0100011
[6,4,8,5,7,1,2,3]=>[7,5,1,8,4,2,6,3]=>1111100=>0000011
[5,4,8,1,6,3,2,7]=>[6,1,4,3,8,5,2,7]=>1110100=>0001011
[5,4,7,6,3,8,1,2]=>[8,6,3,7,4,1,5,2]=>1111010=>0000101
[4,6,3,7,5,8,1,2]=>[3,5,8,1,7,6,4,2]=>1101010=>0010101
[1,4,8,3,7,6,5,2]=>[1,6,7,5,8,3,4,2]=>0110100=>1001011
[4,3,8,2,1,6,5,7]=>[6,8,3,2,4,1,5,7]=>1110000=>0001111
[3,7,2,6,8,5,1,4]=>[8,5,6,2,3,1,7,4]=>1101100=>0010011
[7,2,3,8,5,6,1,4]=>[2,3,5,6,8,1,7,4]=>1001000=>0110111
[8,2,1,7,5,6,4,3]=>[2,5,6,7,4,8,1,3]=>1001000=>0110111
[8,1,3,6,5,7,4,2]=>[3,5,7,6,4,8,1,2]=>1001010=>0110101
[8,2,4,3,6,1,5,7]=>[2,4,3,6,1,8,5,7]=>1010100=>0101011
[3,4,1,8,5,7,6,2]=>[5,7,6,8,4,1,3,2]=>1101010=>0010101
[3,6,5,1,2,8,4,7]=>[5,1,8,6,3,2,4,7]=>1110010=>0001101
[8,5,6,1,4,2,3,7]=>[6,1,4,5,2,8,3,7]=>1110000=>0001111
[1,6,4,5,7,2,3,8]=>[1,7,5,4,2,6,3,8]=>0111100=>1000011
[8,3,6,1,7,2,4,5]=>[7,3,1,6,2,4,8,5]=>1110100=>0001011
[1,8,6,5,7,3,4,2]=>[1,7,5,3,6,4,8,2]=>0111100=>1000011
[7,4,1,6,5,8,3,2]=>[5,8,6,4,1,3,7,2]=>1101010=>0010101
[4,1,5,8,7,6,3,2]=>[6,7,3,8,5,4,1,2]=>1011100=>0100011
[1,2,5,8,6,7,3,4]=>[1,2,7,6,3,8,5,4]=>0011110=>1100001
[4,2,1,5,8,7,3,6]=>[2,7,5,4,1,3,8,6]=>1001110=>0110001
[3,5,4,6,1,8,2,7]=>[8,6,4,1,5,3,2,7]=>1111010=>0000101
[8,6,2,5,4,1,7,3]=>[5,4,6,2,7,8,1,3]=>1101000=>0010111
[3,7,2,6,5,4,1,8]=>[5,6,4,7,2,3,1,8]=>1101000=>0010111
[7,6,2,5,4,3,1,8]=>[5,4,6,2,3,7,1,8]=>1101000=>0010111
[4,7,5,2,6,3,1,8]=>[6,5,2,7,3,4,1,8]=>1110100=>0001011
[1,3,4,7,6,2,8,5]=>[1,6,4,3,2,8,7,5]=>0111101=>1000010
[2,8,3,6,1,7,5,4]=>[3,7,6,2,1,5,8,4]=>1101010=>0010101
[8,7,2,5,1,6,4,3]=>[5,2,6,7,4,8,1,3]=>1101000=>0010111
[3,8,2,6,5,1,7,4]=>[5,6,2,3,1,7,8,4]=>1101000=>0010111
[4,8,5,2,6,1,7,3]=>[6,5,2,7,8,1,4,3]=>1110100=>0001011
[6,1,3,7,5,2,8,4]=>[3,5,8,7,1,2,6,4]=>1001001=>0110110
[7,1,3,6,2,8,5,4]=>[3,8,6,1,2,5,7,4]=>1001010=>0110101
[7,1,8,2,6,5,4,3]=>[6,5,8,1,2,4,7,3]=>1010100=>0101011
[4,1,7,8,2,6,5,3]=>[6,8,1,2,5,7,4,3]=>1011000=>0100111
[5,6,1,8,2,7,4,3]=>[7,1,8,6,4,5,2,3]=>1101010=>0010101
[4,2,7,8,1,6,5,3]=>[2,6,8,1,5,7,4,3]=>1011000=>0100111
[3,2,8,6,1,7,5,4]=>[2,7,6,3,1,5,8,4]=>1011010=>0100101
[2,8,7,1,6,5,4,3]=>[6,5,7,2,1,4,8,3]=>1110100=>0001011
[4,8,7,5,1,6,3,2]=>[5,1,6,7,3,8,4,2]=>1111000=>0000111
[6,7,8,5,1,4,3,2]=>[5,1,8,4,7,3,6,2]=>1111000=>0000111
[3,4,8,6,5,1,7,2]=>[5,6,1,7,8,4,3,2]=>1111000=>0000111
[8,3,7,5,1,6,4,2]=>[5,3,1,6,7,4,8,2]=>1111000=>0000111
[1,4,8,6,2,7,5,3]=>[1,7,6,2,5,8,4,3]=>0111010=>1000101
[8,4,6,7,1,5,3,2]=>[7,1,5,6,4,3,8,2]=>1111000=>0000111
[5,6,4,7,8,1,3,2]=>[8,4,1,7,3,6,5,2]=>1111100=>0000011
[3,4,6,5,1,2,8,7]=>[5,1,6,4,3,2,8,7]=>1111001=>0000110
[1,4,6,2,3,8,7,5]=>[1,7,8,6,2,4,3,5]=>0110010=>1001101
[1,3,2,7,4,8,6,5]=>[1,3,2,8,6,7,4,5]=>0101010=>1010101
[7,2,1,6,3,8,5,4]=>[2,8,6,1,3,5,7,4]=>1001010=>0110101
[5,6,7,1,2,8,4,3]=>[8,1,7,6,2,4,5,3]=>1110010=>0001101
[3,7,1,6,2,8,5,4]=>[8,6,1,3,2,5,7,4]=>1101010=>0010101
[7,6,1,2,8,5,4,3]=>[8,5,6,1,4,7,2,3]=>1100100=>0011011
[2,7,1,3,8,6,5,4]=>[6,8,5,7,2,1,3,4]=>1100100=>0011011
[8,6,1,2,7,5,4,3]=>[7,5,6,1,4,8,2,3]=>1100100=>0011011
[1,7,2,3,8,6,5,4]=>[1,6,8,5,7,2,3,4]=>0100100=>1011011
[5,6,8,1,2,7,4,3]=>[7,1,8,6,2,4,5,3]=>1110010=>0001101
[2,1,3,7,4,8,6,5]=>[2,1,3,8,6,7,4,5]=>1001010=>0110101
[4,2,7,3,6,8,1,5]=>[2,8,6,3,4,1,7,5]=>1010110=>0101001
[4,1,5,3,8,2,7,6]=>[7,8,5,3,4,1,2,6]=>1010100=>0101011
[2,6,3,4,7,5,1,8]=>[3,4,7,5,6,2,1,8]=>1100100=>0011011
[2,7,4,3,5,8,1,6]=>[4,3,5,8,2,1,7,6]=>1110010=>0001101
[7,6,4,5,2,8,1,3]=>[5,4,2,8,6,1,7,3]=>1111010=>0000101
[5,4,3,1,8,2,7,6]=>[3,4,1,7,8,5,2,6]=>1100100=>0011011
[5,4,1,8,3,2,6,7]=>[8,4,1,3,5,2,6,7]=>1101000=>0010111
[6,5,2,8,3,4,7,1]=>[7,8,2,3,5,4,6,1]=>1101000=>0010111
[7,4,2,1,8,3,6,5]=>[4,2,8,1,3,6,7,5]=>1100100=>0011011
[6,5,3,4,8,2,7,1]=>[3,4,7,8,5,2,6,1]=>1100100=>0011011
[6,1,5,3,8,2,7,4]=>[7,8,5,3,6,1,2,4]=>1010100=>0101011
[4,6,3,1,8,2,7,5]=>[3,7,8,1,4,2,6,5]=>1100100=>0011011
[5,8,4,2,7,3,1,6]=>[4,2,7,3,8,5,1,6]=>1110100=>0001011
[8,2,6,4,7,3,1,5]=>[2,4,7,3,6,1,8,5]=>1010100=>0101011
[8,6,2,5,7,4,1,3]=>[7,5,4,6,2,8,1,3]=>1101100=>0010011
[8,5,3,2,6,4,1,7]=>[3,6,5,2,4,8,1,7]=>1100100=>0011011
[8,3,1,7,2,5,4,6]=>[3,1,7,2,5,8,4,6]=>1101000=>0010111
[8,1,7,3,5,6,4,2]=>[5,6,7,3,4,8,1,2]=>1010000=>0101111
[8,6,1,7,4,5,2,3]=>[7,4,5,6,1,8,2,3]=>1101000=>0010111
[8,1,3,7,2,6,5,4]=>[3,6,7,1,2,5,8,4]=>1001000=>0110111
[1,7,6,8,3,2,4,5]=>[1,8,3,6,2,7,4,5]=>0111000=>1000111
[7,1,5,8,4,2,6,3]=>[8,4,5,1,2,6,7,3]=>1011000=>0100111
[6,1,7,4,2,5,3,8]=>[4,7,1,2,5,6,3,8]=>1010000=>0101111
[1,2,7,3,4,6,5,8]=>[1,2,6,7,3,4,5,8]=>0010000=>1101111
[1,6,2,8,3,5,7,4]=>[1,7,8,2,3,5,6,4]=>0101000=>1010111
[5,4,8,2,7,3,1,6]=>[7,2,4,3,8,5,1,6]=>1110100=>0001011
[6,4,7,5,3,2,1,8]=>[5,3,7,4,2,6,1,8]=>1111000=>0000111
[1,8,3,7,6,2,4,5]=>[1,3,6,2,7,4,8,5]=>0101100=>1010011
[6,8,2,4,7,5,1,3]=>[4,7,5,8,2,6,1,3]=>1100100=>0011011
[2,6,8,7,3,4,1,5]=>[7,3,8,4,6,2,1,5]=>1111000=>0000111
[7,2,8,6,3,5,1,4]=>[2,6,3,5,8,1,7,4]=>1011000=>0100111
[6,8,1,7,2,5,4,3]=>[7,1,5,8,4,6,2,3]=>1101000=>0010111
[3,8,7,4,5,6,1,2]=>[4,5,6,7,1,8,3,2]=>1110000=>0001111
[2,8,6,4,3,5,1,7]=>[4,6,3,5,8,2,1,7]=>1110000=>0001111
[1,7,6,5,2,4,3,8]=>[1,5,2,6,4,7,3,8]=>0111000=>1000111
[3,8,7,4,6,2,5,1]=>[4,6,2,7,5,8,3,1]=>1110100=>0001011
[5,8,3,7,6,2,4,1]=>[3,6,2,7,4,8,5,1]=>1101100=>0010011
[7,1,8,6,5,2,3,4]=>[5,6,1,2,8,3,7,4]=>1011000=>0100111
[8,4,7,5,3,2,1,6]=>[5,3,7,4,2,8,1,6]=>1111000=>0000111
[6,8,3,2,5,4,7,1]=>[3,5,7,8,2,4,6,1]=>1100000=>0011111
[6,8,4,5,2,3,7,1]=>[5,4,2,7,8,3,6,1]=>1111000=>0000111
[1,5,7,8,4,3,6,2]=>[1,8,4,6,7,3,5,2]=>0111000=>1000111
[6,3,8,1,5,4,7,2]=>[5,7,8,3,1,4,6,2]=>1110000=>0001111
[6,2,1,8,5,4,7,3]=>[2,5,7,8,4,6,1,3]=>1001000=>0110111
[2,6,3,1,7,5,4,8]=>[3,7,5,6,2,1,4,8]=>1100100=>0011011
[2,4,7,5,8,1,6,3]=>[8,5,2,1,6,7,4,3]=>1111100=>0000011
[2,5,4,7,1,8,6,3]=>[8,6,7,4,2,1,5,3]=>1111010=>0000101
[5,2,1,8,7,6,4,3]=>[2,6,7,4,8,5,1,3]=>1001100=>0110011
[4,8,5,7,6,1,3,2]=>[6,1,7,5,3,8,4,2]=>1111100=>0000011
[4,8,6,7,5,3,1,2]=>[5,7,3,6,1,8,4,2]=>1111000=>0000111
[6,5,4,8,2,1,7,3]=>[7,8,4,2,5,1,6,3]=>1111000=>0000111
[5,8,4,7,2,6,3,1]=>[6,7,4,2,8,3,5,1]=>1111000=>0000111
[1,5,7,4,8,2,6,3]=>[1,4,8,2,6,7,5,3]=>0110100=>1001011
[1,5,7,3,2,8,6,4]=>[1,8,6,7,3,5,2,4]=>0110010=>1001101
[5,8,3,2,7,6,4,1]=>[3,6,7,2,4,8,5,1]=>1100100=>0011011
[5,2,1,4,3,6,7,8]=>[2,4,5,1,3,6,7,8]=>1000000=>0111111
[3,5,7,4,2,6,1,8]=>[4,6,7,2,5,3,1,8]=>1110000=>0001111
[3,6,4,5,1,2,7,8]=>[5,4,1,6,3,2,7,8]=>1111000=>0000111
[4,2,1,6,5,3,7,8]=>[2,5,6,4,1,3,7,8]=>1001000=>0110111
[4,2,1,5,7,6,3,8]=>[2,6,7,5,4,1,3,8]=>1001100=>0110011
[3,4,7,5,6,1,2,8]=>[6,5,1,7,4,3,2,8]=>1111100=>0000011
[3,4,5,8,6,7,1,2]=>[7,6,1,8,5,4,3,2]=>1111110=>0000001
[4,2,1,5,6,8,7,3]=>[2,7,8,6,5,4,1,3]=>1001110=>0110001
[2,1,4,3,6,5,10,9,7,8]=>[2,1,4,3,6,5,9,7,10,8]=>101010110=>010101001
[2,1,4,3,8,7,5,6,10,9]=>[2,1,4,3,7,5,8,6,10,9]=>101011001=>010100110
[2,1,4,3,10,7,5,9,6,8]=>[2,1,4,3,7,5,9,6,10,8]=>101011010=>010100101
[2,1,4,3,10,9,8,5,6,7]=>[2,1,4,3,8,5,9,6,10,7]=>101011100=>010100011
[2,1,6,5,3,4,8,7,10,9]=>[2,1,5,3,6,4,8,7,10,9]=>101100101=>010011010
[2,1,6,5,3,4,10,9,7,8]=>[2,1,5,3,6,4,9,7,10,8]=>101100110=>010011001
[2,1,8,5,3,7,4,6,10,9]=>[2,1,5,3,7,4,8,6,10,9]=>101101001=>010010110
[2,1,10,5,3,7,4,9,6,8]=>[2,1,5,3,7,4,9,6,10,8]=>101101010=>010010101
[2,1,10,5,3,9,8,4,6,7]=>[2,1,5,3,8,4,9,6,10,7]=>101101100=>010010011
[2,1,8,7,6,3,4,5,10,9]=>[2,1,6,3,7,4,8,5,10,9]=>101110001=>010001110
[2,1,10,7,6,3,4,9,5,8]=>[2,1,6,3,7,4,9,5,10,8]=>101110010=>010001101
[2,1,10,9,6,3,8,4,5,7]=>[2,1,6,3,8,4,9,5,10,7]=>101110100=>010001011
[2,1,10,9,8,7,3,4,5,6]=>[2,1,7,3,8,4,9,5,10,6]=>101111000=>010000111
[4,3,1,2,6,5,8,7,10,9]=>[3,1,4,2,6,5,8,7,10,9]=>110010101=>001101010
[4,3,1,2,6,5,10,9,7,8]=>[3,1,4,2,6,5,9,7,10,8]=>110010110=>001101001
[4,3,1,2,8,7,5,6,10,9]=>[3,1,4,2,7,5,8,6,10,9]=>110011001=>001100110
[4,3,1,2,10,7,5,9,6,8]=>[3,1,4,2,7,5,9,6,10,8]=>110011010=>001100101
[4,3,1,2,10,9,8,5,6,7]=>[3,1,4,2,8,5,9,6,10,7]=>110011100=>001100011
[6,3,1,5,2,4,8,7,10,9]=>[3,1,5,2,6,4,8,7,10,9]=>110100101=>001011010
[6,3,1,5,2,4,10,9,7,8]=>[3,1,5,2,6,4,9,7,10,8]=>110100110=>001011001
[8,3,1,5,2,7,4,6,10,9]=>[3,1,5,2,7,4,8,6,10,9]=>110101001=>001010110
[10,3,1,5,2,7,4,9,6,8]=>[3,1,5,2,7,4,9,6,10,8]=>110101010=>001010101
[10,3,1,5,2,9,8,4,6,7]=>[3,1,5,2,8,4,9,6,10,7]=>110101100=>001010011
[8,3,1,7,6,2,4,5,10,9]=>[3,1,6,2,7,4,8,5,10,9]=>110110001=>001001110
[10,3,1,7,6,2,4,9,5,8]=>[3,1,6,2,7,4,9,5,10,8]=>110110010=>001001101
[10,3,1,9,6,2,8,4,5,7]=>[3,1,6,2,8,4,9,5,10,7]=>110110100=>001001011
[10,3,1,9,8,7,2,4,5,6]=>[3,1,7,2,8,4,9,5,10,6]=>110111000=>001000111
[6,5,4,1,2,3,8,7,10,9]=>[4,1,5,2,6,3,8,7,10,9]=>111000101=>000111010
[6,5,4,1,2,3,10,9,7,8]=>[4,1,5,2,6,3,9,7,10,8]=>111000110=>000111001
[8,5,4,1,2,7,3,6,10,9]=>[4,1,5,2,7,3,8,6,10,9]=>111001001=>000110110
[10,5,4,1,2,7,3,9,6,8]=>[4,1,5,2,7,3,9,6,10,8]=>111001010=>000110101
[10,5,4,1,2,9,8,3,6,7]=>[4,1,5,2,8,3,9,6,10,7]=>111001100=>000110011
[8,7,4,1,6,2,3,5,10,9]=>[4,1,6,2,7,3,8,5,10,9]=>111010001=>000101110
[10,7,4,1,6,2,3,9,5,8]=>[4,1,6,2,7,3,9,5,10,8]=>111010010=>000101101
[10,9,4,1,6,2,8,3,5,7]=>[4,1,6,2,8,3,9,5,10,7]=>111010100=>000101011
[10,9,4,1,8,7,2,3,5,6]=>[4,1,7,2,8,3,9,5,10,6]=>111011000=>000100111
[8,7,6,5,1,2,3,4,10,9]=>[5,1,6,2,7,3,8,4,10,9]=>111100001=>000011110
[10,7,6,5,1,2,3,9,4,8]=>[5,1,6,2,7,3,9,4,10,8]=>111100010=>000011101
[10,9,6,5,1,2,8,3,4,7]=>[5,1,6,2,8,3,9,4,10,7]=>111100100=>000011011
[10,9,8,5,1,7,2,3,4,6]=>[5,1,7,2,8,3,9,4,10,6]=>111101000=>000010111
[2,1,4,3,6,5,8,7,12,11,9,10]=>[2,1,4,3,6,5,8,7,11,9,12,10]=>10101010110=>01010101001
[2,1,4,3,6,5,10,9,7,8,12,11]=>[2,1,4,3,6,5,9,7,10,8,12,11]=>10101011001=>01010100110
[2,1,4,3,6,5,12,9,7,11,8,10]=>[2,1,4,3,6,5,9,7,11,8,12,10]=>10101011010=>01010100101
[2,1,4,3,6,5,12,11,10,7,8,9]=>[2,1,4,3,6,5,10,7,11,8,12,9]=>10101011100=>01010100011
[2,1,4,3,8,7,5,6,10,9,12,11]=>[2,1,4,3,7,5,8,6,10,9,12,11]=>10101100101=>01010011010
[2,1,4,3,8,7,5,6,12,11,9,10]=>[2,1,4,3,7,5,8,6,11,9,12,10]=>10101100110=>01010011001
[2,1,4,3,10,7,5,9,6,8,12,11]=>[2,1,4,3,7,5,9,6,10,8,12,11]=>10101101001=>01010010110
[2,1,4,3,12,7,5,9,6,11,8,10]=>[2,1,4,3,7,5,9,6,11,8,12,10]=>10101101010=>01010010101
[2,1,4,3,12,7,5,11,10,6,8,9]=>[2,1,4,3,7,5,10,6,11,8,12,9]=>10101101100=>01010010011
[2,1,4,3,10,9,8,5,6,7,12,11]=>[2,1,4,3,8,5,9,6,10,7,12,11]=>10101110001=>01010001110
[2,1,4,3,12,9,8,5,6,11,7,10]=>[2,1,4,3,8,5,9,6,11,7,12,10]=>10101110010=>01010001101
[2,1,4,3,12,11,8,5,10,6,7,9]=>[2,1,4,3,8,5,10,6,11,7,12,9]=>10101110100=>01010001011
[2,1,4,3,12,11,10,9,5,6,7,8]=>[2,1,4,3,9,5,10,6,11,7,12,8]=>10101111000=>01010000111
[2,1,6,5,3,4,8,7,10,9,12,11]=>[2,1,5,3,6,4,8,7,10,9,12,11]=>10110010101=>01001101010
[2,1,6,5,3,4,8,7,12,11,9,10]=>[2,1,5,3,6,4,8,7,11,9,12,10]=>10110010110=>01001101001
[2,1,6,5,3,4,10,9,7,8,12,11]=>[2,1,5,3,6,4,9,7,10,8,12,11]=>10110011001=>01001100110
[2,1,6,5,3,4,12,9,7,11,8,10]=>[2,1,5,3,6,4,9,7,11,8,12,10]=>10110011010=>01001100101
[2,1,6,5,3,4,12,11,10,7,8,9]=>[2,1,5,3,6,4,10,7,11,8,12,9]=>10110011100=>01001100011
[2,1,8,5,3,7,4,6,10,9,12,11]=>[2,1,5,3,7,4,8,6,10,9,12,11]=>10110100101=>01001011010
[2,1,8,5,3,7,4,6,12,11,9,10]=>[2,1,5,3,7,4,8,6,11,9,12,10]=>10110100110=>01001011001
[2,1,10,5,3,7,4,9,6,8,12,11]=>[2,1,5,3,7,4,9,6,10,8,12,11]=>10110101001=>01001010110
[2,1,12,5,3,7,4,9,6,11,8,10]=>[2,1,5,3,7,4,9,6,11,8,12,10]=>10110101010=>01001010101
[2,1,12,5,3,7,4,11,10,6,8,9]=>[2,1,5,3,7,4,10,6,11,8,12,9]=>10110101100=>01001010011
[2,1,10,5,3,9,8,4,6,7,12,11]=>[2,1,5,3,8,4,9,6,10,7,12,11]=>10110110001=>01001001110
[2,1,12,5,3,9,8,4,6,11,7,10]=>[2,1,5,3,8,4,9,6,11,7,12,10]=>10110110010=>01001001101
[2,1,12,5,3,11,8,4,10,6,7,9]=>[2,1,5,3,8,4,10,6,11,7,12,9]=>10110110100=>01001001011
[2,1,12,5,3,11,10,9,4,6,7,8]=>[2,1,5,3,9,4,10,6,11,7,12,8]=>10110111000=>01001000111
[2,1,8,7,6,3,4,5,10,9,12,11]=>[2,1,6,3,7,4,8,5,10,9,12,11]=>10111000101=>01000111010
[2,1,8,7,6,3,4,5,12,11,9,10]=>[2,1,6,3,7,4,8,5,11,9,12,10]=>10111000110=>01000111001
[2,1,10,7,6,3,4,9,5,8,12,11]=>[2,1,6,3,7,4,9,5,10,8,12,11]=>10111001001=>01000110110
[2,1,12,7,6,3,4,9,5,11,8,10]=>[2,1,6,3,7,4,9,5,11,8,12,10]=>10111001010=>01000110101
[2,1,12,7,6,3,4,11,10,5,8,9]=>[2,1,6,3,7,4,10,5,11,8,12,9]=>10111001100=>01000110011
[2,1,10,9,6,3,8,4,5,7,12,11]=>[2,1,6,3,8,4,9,5,10,7,12,11]=>10111010001=>01000101110
[2,1,12,9,6,3,8,4,5,11,7,10]=>[2,1,6,3,8,4,9,5,11,7,12,10]=>10111010010=>01000101101
[2,1,12,11,6,3,8,4,10,5,7,9]=>[2,1,6,3,8,4,10,5,11,7,12,9]=>10111010100=>01000101011
[2,1,12,11,6,3,10,9,4,5,7,8]=>[2,1,6,3,9,4,10,5,11,7,12,8]=>10111011000=>01000100111
[2,1,10,9,8,7,3,4,5,6,12,11]=>[2,1,7,3,8,4,9,5,10,6,12,11]=>10111100001=>01000011110
[2,1,12,9,8,7,3,4,5,11,6,10]=>[2,1,7,3,8,4,9,5,11,6,12,10]=>10111100010=>01000011101
[2,1,12,11,8,7,3,4,10,5,6,9]=>[2,1,7,3,8,4,10,5,11,6,12,9]=>10111100100=>01000011011
[2,1,12,11,10,7,3,9,4,5,6,8]=>[2,1,7,3,9,4,10,5,11,6,12,8]=>10111101000=>01000010111
[2,1,12,11,10,9,8,3,4,5,6,7]=>[2,1,8,3,9,4,10,5,11,6,12,7]=>10111110000=>01000001111
[4,3,1,2,6,5,8,7,10,9,12,11]=>[3,1,4,2,6,5,8,7,10,9,12,11]=>11001010101=>00110101010
[4,3,1,2,6,5,8,7,12,11,9,10]=>[3,1,4,2,6,5,8,7,11,9,12,10]=>11001010110=>00110101001
[4,3,1,2,6,5,10,9,7,8,12,11]=>[3,1,4,2,6,5,9,7,10,8,12,11]=>11001011001=>00110100110
[4,3,1,2,6,5,12,9,7,11,8,10]=>[3,1,4,2,6,5,9,7,11,8,12,10]=>11001011010=>00110100101
[4,3,1,2,6,5,12,11,10,7,8,9]=>[3,1,4,2,6,5,10,7,11,8,12,9]=>11001011100=>00110100011
[4,3,1,2,8,7,5,6,10,9,12,11]=>[3,1,4,2,7,5,8,6,10,9,12,11]=>11001100101=>00110011010
[4,3,1,2,8,7,5,6,12,11,9,10]=>[3,1,4,2,7,5,8,6,11,9,12,10]=>11001100110=>00110011001
[4,3,1,2,10,7,5,9,6,8,12,11]=>[3,1,4,2,7,5,9,6,10,8,12,11]=>11001101001=>00110010110
[4,3,1,2,12,7,5,9,6,11,8,10]=>[3,1,4,2,7,5,9,6,11,8,12,10]=>11001101010=>00110010101
[4,3,1,2,12,7,5,11,10,6,8,9]=>[3,1,4,2,7,5,10,6,11,8,12,9]=>11001101100=>00110010011
[4,3,1,2,10,9,8,5,6,7,12,11]=>[3,1,4,2,8,5,9,6,10,7,12,11]=>11001110001=>00110001110
[4,3,1,2,12,9,8,5,6,11,7,10]=>[3,1,4,2,8,5,9,6,11,7,12,10]=>11001110010=>00110001101
[4,3,1,2,12,11,8,5,10,6,7,9]=>[3,1,4,2,8,5,10,6,11,7,12,9]=>11001110100=>00110001011
[4,3,1,2,12,11,10,9,5,6,7,8]=>[3,1,4,2,9,5,10,6,11,7,12,8]=>11001111000=>00110000111
[6,3,1,5,2,4,8,7,10,9,12,11]=>[3,1,5,2,6,4,8,7,10,9,12,11]=>11010010101=>00101101010
[6,3,1,5,2,4,8,7,12,11,9,10]=>[3,1,5,2,6,4,8,7,11,9,12,10]=>11010010110=>00101101001
[6,3,1,5,2,4,10,9,7,8,12,11]=>[3,1,5,2,6,4,9,7,10,8,12,11]=>11010011001=>00101100110
[6,3,1,5,2,4,12,9,7,11,8,10]=>[3,1,5,2,6,4,9,7,11,8,12,10]=>11010011010=>00101100101
[6,3,1,5,2,4,12,11,10,7,8,9]=>[3,1,5,2,6,4,10,7,11,8,12,9]=>11010011100=>00101100011
[8,3,1,5,2,7,4,6,10,9,12,11]=>[3,1,5,2,7,4,8,6,10,9,12,11]=>11010100101=>00101011010
[8,3,1,5,2,7,4,6,12,11,9,10]=>[3,1,5,2,7,4,8,6,11,9,12,10]=>11010100110=>00101011001
[10,3,1,5,2,7,4,9,6,8,12,11]=>[3,1,5,2,7,4,9,6,10,8,12,11]=>11010101001=>00101010110
[12,3,1,5,2,7,4,9,6,11,8,10]=>[3,1,5,2,7,4,9,6,11,8,12,10]=>11010101010=>00101010101
[12,3,1,5,2,7,4,11,10,6,8,9]=>[3,1,5,2,7,4,10,6,11,8,12,9]=>11010101100=>00101010011
[10,3,1,5,2,9,8,4,6,7,12,11]=>[3,1,5,2,8,4,9,6,10,7,12,11]=>11010110001=>00101001110
[12,3,1,5,2,9,8,4,6,11,7,10]=>[3,1,5,2,8,4,9,6,11,7,12,10]=>11010110010=>00101001101
[12,3,1,5,2,11,8,4,10,6,7,9]=>[3,1,5,2,8,4,10,6,11,7,12,9]=>11010110100=>00101001011
[12,3,1,5,2,11,10,9,4,6,7,8]=>[3,1,5,2,9,4,10,6,11,7,12,8]=>11010111000=>00101000111
[8,3,1,7,6,2,4,5,10,9,12,11]=>[3,1,6,2,7,4,8,5,10,9,12,11]=>11011000101=>00100111010
[8,3,1,7,6,2,4,5,12,11,9,10]=>[3,1,6,2,7,4,8,5,11,9,12,10]=>11011000110=>00100111001
[10,3,1,7,6,2,4,9,5,8,12,11]=>[3,1,6,2,7,4,9,5,10,8,12,11]=>11011001001=>00100110110
[12,3,1,7,6,2,4,9,5,11,8,10]=>[3,1,6,2,7,4,9,5,11,8,12,10]=>11011001010=>00100110101
[12,3,1,7,6,2,4,11,10,5,8,9]=>[3,1,6,2,7,4,10,5,11,8,12,9]=>11011001100=>00100110011
[10,3,1,9,6,2,8,4,5,7,12,11]=>[3,1,6,2,8,4,9,5,10,7,12,11]=>11011010001=>00100101110
[12,3,1,9,6,2,8,4,5,11,7,10]=>[3,1,6,2,8,4,9,5,11,7,12,10]=>11011010010=>00100101101
[12,3,1,11,6,2,8,4,10,5,7,9]=>[3,1,6,2,8,4,10,5,11,7,12,9]=>11011010100=>00100101011
[12,3,1,11,6,2,10,9,4,5,7,8]=>[3,1,6,2,9,4,10,5,11,7,12,8]=>11011011000=>00100100111
[10,3,1,9,8,7,2,4,5,6,12,11]=>[3,1,7,2,8,4,9,5,10,6,12,11]=>11011100001=>00100011110
[12,3,1,9,8,7,2,4,5,11,6,10]=>[3,1,7,2,8,4,9,5,11,6,12,10]=>11011100010=>00100011101
[12,3,1,11,8,7,2,4,10,5,6,9]=>[3,1,7,2,8,4,10,5,11,6,12,9]=>11011100100=>00100011011
[12,3,1,11,10,7,2,9,4,5,6,8]=>[3,1,7,2,9,4,10,5,11,6,12,8]=>11011101000=>00100010111
[12,3,1,11,10,9,8,2,4,5,6,7]=>[3,1,8,2,9,4,10,5,11,6,12,7]=>11011110000=>00100001111
[6,5,4,1,2,3,8,7,10,9,12,11]=>[4,1,5,2,6,3,8,7,10,9,12,11]=>11100010101=>00011101010
[6,5,4,1,2,3,8,7,12,11,9,10]=>[4,1,5,2,6,3,8,7,11,9,12,10]=>11100010110=>00011101001
[6,5,4,1,2,3,10,9,7,8,12,11]=>[4,1,5,2,6,3,9,7,10,8,12,11]=>11100011001=>00011100110
[6,5,4,1,2,3,12,9,7,11,8,10]=>[4,1,5,2,6,3,9,7,11,8,12,10]=>11100011010=>00011100101
[6,5,4,1,2,3,12,11,10,7,8,9]=>[4,1,5,2,6,3,10,7,11,8,12,9]=>11100011100=>00011100011
[8,5,4,1,2,7,3,6,10,9,12,11]=>[4,1,5,2,7,3,8,6,10,9,12,11]=>11100100101=>00011011010
[8,5,4,1,2,7,3,6,12,11,9,10]=>[4,1,5,2,7,3,8,6,11,9,12,10]=>11100100110=>00011011001
[10,5,4,1,2,7,3,9,6,8,12,11]=>[4,1,5,2,7,3,9,6,10,8,12,11]=>11100101001=>00011010110
[12,5,4,1,2,7,3,9,6,11,8,10]=>[4,1,5,2,7,3,9,6,11,8,12,10]=>11100101010=>00011010101
[12,5,4,1,2,7,3,11,10,6,8,9]=>[4,1,5,2,7,3,10,6,11,8,12,9]=>11100101100=>00011010011
[10,5,4,1,2,9,8,3,6,7,12,11]=>[4,1,5,2,8,3,9,6,10,7,12,11]=>11100110001=>00011001110
[12,5,4,1,2,9,8,3,6,11,7,10]=>[4,1,5,2,8,3,9,6,11,7,12,10]=>11100110010=>00011001101
[12,5,4,1,2,11,8,3,10,6,7,9]=>[4,1,5,2,8,3,10,6,11,7,12,9]=>11100110100=>00011001011
[12,5,4,1,2,11,10,9,3,6,7,8]=>[4,1,5,2,9,3,10,6,11,7,12,8]=>11100111000=>00011000111
[8,7,4,1,6,2,3,5,10,9,12,11]=>[4,1,6,2,7,3,8,5,10,9,12,11]=>11101000101=>00010111010
[8,7,4,1,6,2,3,5,12,11,9,10]=>[4,1,6,2,7,3,8,5,11,9,12,10]=>11101000110=>00010111001
[10,7,4,1,6,2,3,9,5,8,12,11]=>[4,1,6,2,7,3,9,5,10,8,12,11]=>11101001001=>00010110110
[12,7,4,1,6,2,3,9,5,11,8,10]=>[4,1,6,2,7,3,9,5,11,8,12,10]=>11101001010=>00010110101
[12,7,4,1,6,2,3,11,10,5,8,9]=>[4,1,6,2,7,3,10,5,11,8,12,9]=>11101001100=>00010110011
[10,9,4,1,6,2,8,3,5,7,12,11]=>[4,1,6,2,8,3,9,5,10,7,12,11]=>11101010001=>00010101110
[12,9,4,1,6,2,8,3,5,11,7,10]=>[4,1,6,2,8,3,9,5,11,7,12,10]=>11101010010=>00010101101
[12,11,4,1,6,2,8,3,10,5,7,9]=>[4,1,6,2,8,3,10,5,11,7,12,9]=>11101010100=>00010101011
[12,11,4,1,6,2,10,9,3,5,7,8]=>[4,1,6,2,9,3,10,5,11,7,12,8]=>11101011000=>00010100111
[10,9,4,1,8,7,2,3,5,6,12,11]=>[4,1,7,2,8,3,9,5,10,6,12,11]=>11101100001=>00010011110
[12,9,4,1,8,7,2,3,5,11,6,10]=>[4,1,7,2,8,3,9,5,11,6,12,10]=>11101100010=>00010011101
[12,11,4,1,8,7,2,3,10,5,6,9]=>[4,1,7,2,8,3,10,5,11,6,12,9]=>11101100100=>00010011011
[12,11,4,1,10,7,2,9,3,5,6,8]=>[4,1,7,2,9,3,10,5,11,6,12,8]=>11101101000=>00010010111
[12,11,4,1,10,9,8,2,3,5,6,7]=>[4,1,8,2,9,3,10,5,11,6,12,7]=>11101110000=>00010001111
[8,7,6,5,1,2,3,4,10,9,12,11]=>[5,1,6,2,7,3,8,4,10,9,12,11]=>11110000101=>00001111010
[8,7,6,5,1,2,3,4,12,11,9,10]=>[5,1,6,2,7,3,8,4,11,9,12,10]=>11110000110=>00001111001
[10,7,6,5,1,2,3,9,4,8,12,11]=>[5,1,6,2,7,3,9,4,10,8,12,11]=>11110001001=>00001110110
[12,7,6,5,1,2,3,9,4,11,8,10]=>[5,1,6,2,7,3,9,4,11,8,12,10]=>11110001010=>00001110101
[12,7,6,5,1,2,3,11,10,4,8,9]=>[5,1,6,2,7,3,10,4,11,8,12,9]=>11110001100=>00001110011
[10,9,6,5,1,2,8,3,4,7,12,11]=>[5,1,6,2,8,3,9,4,10,7,12,11]=>11110010001=>00001101110
[12,9,6,5,1,2,8,3,4,11,7,10]=>[5,1,6,2,8,3,9,4,11,7,12,10]=>11110010010=>00001101101
[12,11,6,5,1,2,8,3,10,4,7,9]=>[5,1,6,2,8,3,10,4,11,7,12,9]=>11110010100=>00001101011
[12,11,6,5,1,2,10,9,3,4,7,8]=>[5,1,6,2,9,3,10,4,11,7,12,8]=>11110011000=>00001100111
[10,9,8,5,1,7,2,3,4,6,12,11]=>[5,1,7,2,8,3,9,4,10,6,12,11]=>11110100001=>00001011110
[12,9,8,5,1,7,2,3,4,11,6,10]=>[5,1,7,2,8,3,9,4,11,6,12,10]=>11110100010=>00001011101
[12,11,8,5,1,7,2,3,10,4,6,9]=>[5,1,7,2,8,3,10,4,11,6,12,9]=>11110100100=>00001011011
[12,11,10,5,1,7,2,9,3,4,6,8]=>[5,1,7,2,9,3,10,4,11,6,12,8]=>11110101000=>00001010111
[12,11,10,5,1,9,8,2,3,4,6,7]=>[5,1,8,2,9,3,10,4,11,6,12,7]=>11110110000=>00001001111
[10,9,8,7,6,1,2,3,4,5,12,11]=>[6,1,7,2,8,3,9,4,10,5,12,11]=>11111000001=>00000111110
[12,9,8,7,6,1,2,3,4,11,5,10]=>[6,1,7,2,8,3,9,4,11,5,12,10]=>11111000010=>00000111101
[12,11,8,7,6,1,2,3,10,4,5,9]=>[6,1,7,2,8,3,10,4,11,5,12,9]=>11111000100=>00000111011
[12,11,10,7,6,1,2,9,3,4,5,8]=>[6,1,7,2,9,3,10,4,11,5,12,8]=>11111001000=>00000110111
[12,11,10,9,6,1,8,2,3,4,5,7]=>[6,1,8,2,9,3,10,4,11,5,12,7]=>11111010000=>00000101111
[12,11,10,9,8,7,1,2,3,4,5,6]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>11111100000=>00000011111
[2,1,7,3,8,4,6,5]=>[2,1,8,3,4,6,7,5]=>1010100=>0101011
[4,1,7,2,8,3,6,5]=>[8,1,2,4,3,6,7,5]=>1010100=>0101011
[7,1,8,2,4,3,6,5]=>[8,1,2,4,6,7,3,5]=>1010000=>0101111
[8,1,7,2,5,3,6,4]=>[5,7,1,2,6,8,3,4]=>1010000=>0101111
[7,1,5,2,8,3,6,4]=>[8,5,1,2,6,7,3,4]=>1010100=>0101011
[5,1,7,2,8,3,6,4]=>[8,1,2,6,7,5,3,4]=>1010100=>0101011
[5,1,8,2,7,3,6,4]=>[7,1,2,6,8,5,3,4]=>1010100=>0101011
[8,1,6,2,4,3,7,5]=>[6,1,2,4,7,8,3,5]=>1010000=>0101111
[6,1,8,2,4,3,7,5]=>[7,8,1,2,4,6,3,5]=>1010000=>0101111
[6,1,8,2,5,3,7,4]=>[5,7,8,1,2,6,3,4]=>1010000=>0101111
[8,1,6,2,5,3,7,4]=>[5,6,1,2,7,8,3,4]=>1010000=>0101111
[8,1,6,2,7,3,5,4]=>[7,1,2,6,5,8,3,4]=>1010100=>0101011
[6,1,8,2,7,3,5,4]=>[7,1,2,8,5,6,3,4]=>1010100=>0101011
[6,1,7,2,8,3,5,4]=>[8,1,2,7,5,6,3,4]=>1010100=>0101011
[6,1,7,2,5,3,8,4]=>[5,8,7,1,2,6,3,4]=>1010001=>0101110
[6,1,7,2,4,3,8,5]=>[8,7,1,2,4,6,3,5]=>1010001=>0101110
[5,1,6,2,4,3,8,7]=>[6,1,2,4,5,3,8,7]=>1010001=>0101110
[7,1,5,2,4,3,8,6]=>[5,1,2,4,8,7,3,6]=>1010001=>0101110
[7,1,6,2,8,3,5,4]=>[8,1,2,6,5,7,3,4]=>1010100=>0101011
[7,1,8,2,6,3,5,4]=>[6,1,2,8,5,7,3,4]=>1010100=>0101011
[1,8,4,2,6,3,5,7]=>[1,4,2,6,3,8,5,7]=>0110100=>1001011
[7,4,8,1,5,2,3,6]=>[5,8,1,4,2,7,3,6]=>1110000=>0001111
[7,5,8,3,2,4,1,6]=>[8,3,5,2,4,7,1,6]=>1110000=>0001111
[1,8,5,4,3,7,2,6]=>[1,4,5,3,7,2,8,6]=>0110010=>1001101
[1,8,5,4,7,2,6,3]=>[1,4,7,5,2,6,8,3]=>0110100=>1001011
[1,8,4,2,5,3,7,6]=>[1,4,2,5,7,8,3,6]=>0110000=>1001111
[1,8,5,4,2,6,7,3]=>[1,4,5,2,6,7,8,3]=>0110000=>1001111
[7,4,8,2,1,3,5,6]=>[8,2,4,1,7,3,5,6]=>1110000=>0001111
[4,1,7,3,2,5,6,8]=>[7,3,4,1,2,5,6,8]=>1010000=>0101111
[7,5,4,8,2,3,6,1]=>[8,4,2,5,3,6,7,1]=>1111000=>0000111
[7,3,8,1,5,6,2,4]=>[5,6,8,3,1,7,2,4]=>1110000=>0001111
[3,1,7,2,6,8,4,5]=>[8,6,3,1,2,4,7,5]=>1010110=>0101001
[4,1,6,3,2,5,8,7]=>[6,3,4,1,2,5,8,7]=>1010001=>0101110
[5,4,3,7,1,2,8,6]=>[3,8,7,4,1,5,2,6]=>1101001=>0010110
[6,5,4,3,7,1,8,2]=>[4,3,8,7,5,1,6,2]=>1110101=>0001010
[5,4,2,7,1,6,8,3]=>[6,8,7,4,2,5,1,3]=>1101001=>0010110
[6,5,1,7,3,8,2,4]=>[8,1,3,5,2,7,6,4]=>1101010=>0010101
[6,3,2,8,5,7,1,4]=>[3,2,5,7,1,8,6,4]=>1101010=>0010101
[6,5,4,3,8,7,1,2]=>[4,3,7,5,1,8,6,2]=>1110110=>0001001
[7,5,4,8,6,1,3,2]=>[6,4,1,8,5,3,7,2]=>1111100=>0000011
[7,6,3,8,5,4,1,2]=>[3,5,8,4,6,1,7,2]=>1101000=>0010111
[6,3,8,1,7,5,2,4]=>[7,5,8,3,1,6,2,4]=>1110100=>0001011
[6,5,8,3,1,7,4,2]=>[7,3,5,1,4,8,6,2]=>1110010=>0001101
[5,4,8,2,1,7,3,6]=>[7,2,4,1,5,3,8,6]=>1110010=>0001101
[5,4,3,8,1,6,2,7]=>[3,6,8,4,1,5,2,7]=>1101000=>0010111
[6,4,2,8,5,1,3,7]=>[5,8,4,2,6,1,3,7]=>1101000=>0010111
[7,6,4,8,5,1,2,3]=>[5,8,4,1,6,2,7,3]=>1111000=>0000111
[7,2,8,6,3,1,4,5]=>[2,6,3,8,1,7,4,5]=>1011000=>0100111
[2,1,7,8,3,6,4,5]=>[2,1,6,8,3,7,4,5]=>1011000=>0100111
[6,4,1,7,8,2,3,5]=>[8,4,1,7,2,3,6,5]=>1101100=>0010011
[4,2,1,6,7,3,5,8]=>[2,7,4,1,3,6,5,8]=>1001100=>0110011
[4,1,5,3,2,8,6,7]=>[5,3,4,1,2,8,6,7]=>1010010=>0101101
[3,1,6,2,8,7,4,5]=>[7,3,1,2,4,8,6,5]=>1010110=>0101001
[6,3,1,7,8,5,2,4]=>[3,1,8,5,7,2,6,4]=>1101100=>0010011
[5,4,1,7,8,2,6,3]=>[8,4,1,6,7,5,2,3]=>1101100=>0010011
[5,4,2,6,1,8,7,3]=>[7,8,6,4,2,5,1,3]=>1101010=>0010101
[6,5,4,2,7,8,3,1]=>[4,2,8,5,3,7,6,1]=>1110110=>0001001
[5,4,2,1,6,7,8,3]=>[4,2,8,7,6,5,1,3]=>1100111=>0011000
[5,4,3,1,6,7,8,2]=>[3,4,1,8,7,6,5,2]=>1100111=>0011000
[6,3,8,1,2,5,7,4]=>[7,8,3,1,5,6,2,4]=>1110000=>0001111
[3,6,7,1,2,5,8,4]=>[8,7,1,5,6,3,2,4]=>1110001=>0001110
[7,8,3,1,2,5,6,4]=>[3,8,1,5,6,7,2,4]=>1100000=>0011111
[7,8,1,3,2,4,6,5]=>[8,1,3,6,7,2,4,5]=>1100000=>0011111
[7,8,2,1,3,5,4,6]=>[8,2,5,7,1,3,4,6]=>1100000=>0011111
[5,2,3,7,1,8,6,4]=>[2,3,8,6,7,1,5,4]=>1001010=>0110101
[2,5,3,6,1,8,7,4]=>[3,7,8,6,2,1,5,4]=>1101010=>0010101
[2,6,7,3,1,8,4,5]=>[8,3,7,6,2,1,4,5]=>1110010=>0001101
[2,6,7,1,3,5,4,8]=>[7,2,1,5,6,3,4,8]=>1110000=>0001111
[3,2,5,7,1,8,4,6]=>[2,8,3,1,5,4,7,6]=>1011010=>0100101
[4,3,1,2,7,8,6,5]=>[3,1,4,2,8,6,7,5]=>1100110=>0011001
[5,1,4,7,8,2,3,6]=>[8,4,1,2,7,5,3,6]=>1011100=>0100011
[5,3,4,7,8,6,1,2]=>[6,8,4,3,1,7,5,2]=>1111100=>0000011
[3,5,4,6,8,7,1,2]=>[7,4,1,8,6,5,3,2]=>1111110=>0000001
[1,5,4,6,8,2,3,7]=>[1,8,4,2,6,5,3,7]=>0111100=>1000011
[1,6,7,3,2,4,8,5]=>[1,8,7,3,6,2,4,5]=>0110001=>1001110
[1,5,3,6,2,7,8,4]=>[1,3,8,7,6,2,5,4]=>0101011=>1010100
[5,1,3,7,2,6,8,4]=>[3,6,8,7,1,2,5,4]=>1001001=>0110110
[5,2,4,7,8,1,6,3]=>[2,8,4,1,6,7,5,3]=>1011100=>0100011
[4,5,2,8,6,1,7,3]=>[6,2,7,8,5,4,1,3]=>1101100=>0010011
[4,3,5,7,6,8,1,2]=>[8,6,3,1,7,5,4,2]=>1111110=>0000001
[4,1,5,7,6,2,3,8]=>[6,1,2,7,5,4,3,8]=>1011100=>0100011
[3,4,2,1,8,7,5,6]=>[4,2,3,1,7,5,8,6]=>1100110=>0011001
[7,6,5,4,2,1,8,3]=>[4,5,2,6,1,8,7,3]=>1110001=>0001110
[7,6,5,4,1,8,3,2]=>[4,5,1,8,6,3,7,2]=>1110010=>0001101
[7,6,5,2,8,1,4,3]=>[8,5,2,6,1,4,7,3]=>1110100=>0001011
[8,7,4,3,2,1,6,5]=>[4,3,7,2,6,8,1,5]=>1110000=>0001111
[7,8,1,3,2,4,5,6]=>[8,1,3,7,2,4,5,6]=>1100000=>0011111
[7,8,4,1,5,2,3,6]=>[4,1,5,8,2,7,3,6]=>1110000=>0001111
[5,2,3,6,1,4,7,8]=>[2,3,6,1,5,4,7,8]=>1001000=>0110111
[2,5,3,6,1,4,7,8]=>[3,6,2,1,5,4,7,8]=>1101000=>0010111
[2,6,7,3,1,4,5,8]=>[7,3,6,2,1,4,5,8]=>1110000=>0001111
[4,6,7,1,5,2,3,8]=>[5,7,1,6,2,4,3,8]=>1110000=>0001111
[4,6,7,3,5,8,1,2]=>[5,8,3,7,6,1,4,2]=>1110010=>0001101
[6,4,7,1,5,2,3,8]=>[5,7,1,4,2,6,3,8]=>1110000=>0001111
[6,2,7,3,1,4,5,8]=>[2,7,3,6,1,4,5,8]=>1010000=>0101111
[3,2,5,6,1,4,7,8]=>[2,6,3,1,5,4,7,8]=>1011000=>0100111
[3,5,2,6,1,4,7,8]=>[6,2,3,1,5,4,7,8]=>1101000=>0010111
[5,1,4,6,7,2,3,8]=>[7,4,1,2,6,5,3,8]=>1011100=>0100011
[3,5,4,6,7,8,1,2]=>[8,4,1,7,6,5,3,2]=>1111110=>0000001
[1,5,4,6,7,2,3,8]=>[1,7,4,2,6,5,3,8]=>0111100=>1000011
[1,6,7,3,2,4,5,8]=>[1,7,3,6,2,4,5,8]=>0110000=>1001111
[5,2,4,6,7,1,3,8]=>[2,7,4,1,6,5,3,8]=>1011100=>0100011
[2,5,4,6,7,1,3,8]=>[7,4,2,1,6,5,3,8]=>1111100=>0000011
[2,6,7,4,5,1,3,8]=>[4,5,7,2,1,6,3,8]=>1110000=>0001111
[5,3,1,6,2,4,7,8]=>[3,1,6,2,5,4,7,8]=>1101000=>0010111
[6,1,7,3,2,4,5,8]=>[7,3,6,1,2,4,5,8]=>1010000=>0101111
[6,1,7,4,5,2,3,8]=>[4,5,7,1,2,6,3,8]=>1010000=>0101111
[6,3,7,4,5,8,1,2]=>[4,5,8,3,1,7,6,2]=>1110010=>0001101
[5,4,1,6,7,2,3,8]=>[7,4,1,6,5,2,3,8]=>1101100=>0010011
[5,2,1,6,3,4,7,8]=>[2,6,1,3,5,4,7,8]=>1001000=>0110111
[7,3,2,5,4,1,6,8]=>[3,2,5,4,7,1,6,8]=>1101000=>0010111
[7,3,5,4,2,1,6,8]=>[4,5,3,2,7,1,6,8]=>1110000=>0001111
[7,3,5,2,4,1,6,8]=>[5,3,2,4,7,1,6,8]=>1110000=>0001111
[1,3,6,7,5,2,8,4]=>[1,5,8,7,3,2,6,4]=>0111001=>1000110
[7,3,4,1,6,2,5,8]=>[4,3,1,6,2,7,5,8]=>1110100=>0001011
[7,3,2,5,1,6,4,8]=>[3,2,5,1,6,7,4,8]=>1101000=>0010111
[7,6,5,4,1,3,2,8]=>[4,5,1,6,3,7,2,8]=>1110000=>0001111
[7,3,4,1,5,2,6,8]=>[4,3,1,5,7,2,6,8]=>1110000=>0001111
[1,3,6,7,2,5,8,4]=>[1,8,7,3,2,5,6,4]=>0111001=>1000110
[1,7,4,6,2,8,5,3]=>[1,8,6,4,2,5,7,3]=>0111010=>1000101
[4,3,1,7,2,6,8,5]=>[3,1,6,8,7,4,2,5]=>1101001=>0010110
[5,3,2,1,7,4,8,6]=>[3,2,8,7,5,1,4,6]=>1100101=>0011010
[1,3,4,5,8,7,2,6]=>[1,7,5,4,3,2,8,6]=>0111110=>1000001
[6,3,4,5,8,1,7,2]=>[7,8,5,4,3,1,6,2]=>1111100=>0000011
[2,4,5,1,6,8,7,3]=>[7,8,6,5,2,1,4,3]=>1110110=>0001001
[4,3,2,5,6,8,1,7]=>[3,2,8,6,5,4,1,7]=>1101110=>0010001
[3,7,5,4,6,8,1,2]=>[4,8,6,5,1,7,3,2]=>1110110=>0001001
[2,3,4,5,8,6,1,7]=>[6,8,5,4,3,2,1,7]=>1111100=>0000011
[2,3,4,5,8,1,7,6]=>[7,8,5,4,3,2,1,6]=>1111100=>0000011
[4,3,1,7,6,5,8,2]=>[3,1,6,5,8,7,4,2]=>1101101=>0010010
[3,1,4,6,7,8,5,2]=>[8,5,7,6,4,3,1,2]=>1011110=>0100001
[1,4,5,2,6,8,7,3]=>[1,7,8,6,5,2,4,3]=>0110110=>1001001
[3,7,5,2,6,8,1,4]=>[8,6,5,2,7,3,1,4]=>1110110=>0001001
[5,6,1,2,7,4,8,3]=>[8,7,1,4,6,5,2,3]=>1100101=>0011010
[5,3,2,1,4,7,8,6]=>[3,2,5,1,4,8,7,6]=>1100011=>0011100
[5,3,1,4,2,7,8,6]=>[3,1,4,5,2,8,7,6]=>1100011=>0011100
[5,3,1,2,4,7,8,6]=>[3,1,5,2,4,8,7,6]=>1100011=>0011100
[7,1,5,2,6,8,4,3]=>[8,6,5,1,2,4,7,3]=>1010110=>0101001
[1,7,4,6,5,8,3,2]=>[1,5,8,6,4,3,7,2]=>0111010=>1000101
[2,7,4,6,1,8,3,5]=>[8,6,4,2,1,7,3,5]=>1111010=>0000101
[2,7,4,6,1,8,5,3]=>[8,6,4,2,1,5,7,3]=>1111010=>0000101
[2,3,6,7,1,5,8,4]=>[8,7,3,2,1,5,6,4]=>1111001=>0000110
[2,3,6,7,5,1,8,4]=>[5,8,7,3,2,1,6,4]=>1111001=>0000110
[7,3,2,5,6,8,1,4]=>[3,2,8,6,5,1,7,4]=>1101110=>0010001
[7,1,5,4,6,8,2,3]=>[4,8,6,5,1,2,7,3]=>1010110=>0101001
[2,7,4,6,5,8,1,3]=>[5,8,6,4,2,1,7,3]=>1111010=>0000101
[7,3,4,5,8,6,1,2]=>[6,8,5,4,3,1,7,2]=>1111100=>0000011
[7,3,4,5,8,1,6,2]=>[8,5,4,3,1,6,7,2]=>1111100=>0000011
[7,3,4,5,8,1,2,6]=>[8,5,4,3,1,7,2,6]=>1111100=>0000011
[1,3,4,5,8,6,2,7]=>[1,6,8,5,4,3,2,7]=>0111100=>1000011
[1,3,4,5,8,2,7,6]=>[1,7,8,5,4,3,2,6]=>0111100=>1000011
[6,3,4,5,8,2,1,7]=>[8,5,4,3,2,6,1,7]=>1111100=>0000011
[6,3,4,5,8,2,7,1]=>[7,8,5,4,3,2,6,1]=>1111100=>0000011
[7,3,4,5,8,6,2,1]=>[6,8,5,4,3,2,7,1]=>1111100=>0000011
[7,3,4,5,8,2,1,6]=>[8,5,4,3,2,7,1,6]=>1111100=>0000011
[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]=>1111100=>0000011
[4,7,6,1,8,2,5,3]=>[8,1,6,5,7,2,4,3]=>1110100=>0001011
[8,6,4,2,7,5,3,1]=>[4,2,7,5,6,3,8,1]=>1110100=>0001011
[8,4,6,1,7,5,3,2]=>[7,5,6,1,4,3,8,2]=>1110100=>0001011
[6,4,7,1,8,3,2,5]=>[8,1,4,3,7,2,6,5]=>1110100=>0001011
[7,4,8,3,6,1,5,2]=>[6,3,4,1,8,5,7,2]=>1110100=>0001011
[6,2,1,7,3,5,4,8]=>[2,7,1,3,5,6,4,8]=>1001000=>0110111
[2,1,8,6,3,5,4,7]=>[2,1,6,3,5,8,4,7]=>1011000=>0100111
[2,7,3,1,5,4,6,8]=>[3,5,7,2,1,4,6,8]=>1100000=>0011111
[2,6,3,1,4,8,5,7]=>[3,8,6,2,1,4,5,7]=>1100010=>0011101
[4,2,1,8,3,6,7,5]=>[2,6,7,8,4,1,3,5]=>1001000=>0110111
[2,1,8,6,3,5,7,4]=>[2,1,6,3,5,7,8,4]=>1011000=>0100111
[6,2,1,7,3,5,8,4]=>[2,8,7,1,3,5,6,4]=>1001001=>0110110
[2,7,3,1,4,8,5,6]=>[3,8,2,1,4,5,7,6]=>1100010=>0011101
[3,2,1,6,4,5,7,8]=>[2,3,1,6,4,5,7,8]=>1001000=>0110111
[3,2,1,5,7,8,4,6]=>[2,3,1,8,5,4,7,6]=>1001110=>0110001
[2,1,7,3,6,8,4,5]=>[2,1,8,6,3,4,7,5]=>1010110=>0101001
[2,7,3,1,5,6,8,4]=>[3,5,6,8,7,2,1,4]=>1100001=>0011110
[2,4,7,5,1,6,8,3]=>[5,2,1,6,8,7,4,3]=>1111001=>0000110
[4,3,7,5,6,1,8,2]=>[6,5,3,1,8,7,4,2]=>1111101=>0000010
[4,3,6,8,5,1,7,2]=>[5,7,8,3,1,6,4,2]=>1111000=>0000111
[2,1,6,8,3,7,4,5]=>[2,1,7,3,8,6,4,5]=>1011010=>0100101
[2,1,8,3,5,7,4,6]=>[2,1,5,7,3,4,8,6]=>1010010=>0101101
[3,2,1,5,6,8,4,7]=>[2,3,1,8,6,5,4,7]=>1001110=>0110001
[8,2,4,1,7,5,6,3]=>[2,4,1,7,5,6,8,3]=>1010100=>0101011
[3,8,4,7,5,1,6,2]=>[5,7,4,1,6,8,3,2]=>1111000=>0000111
[8,4,3,6,1,7,5,2]=>[3,7,6,4,1,5,8,2]=>1101010=>0010101
[2,6,1,8,3,5,4,7]=>[8,2,1,3,5,6,4,7]=>1101000=>0010111
[2,4,7,5,1,6,3,8]=>[5,2,1,6,7,4,3,8]=>1111000=>0000111
[8,2,4,1,7,5,3,6]=>[2,4,1,7,5,8,3,6]=>1010100=>0101011
[5,8,6,3,1,7,4,2]=>[7,6,3,8,1,4,5,2]=>1110010=>0001101
[2,4,7,1,8,5,3,6]=>[8,5,7,2,1,4,3,6]=>1110100=>0001011
[6,2,1,7,3,4,8,5]=>[2,8,7,1,3,6,4,5]=>1001001=>0110110
[6,2,1,7,8,3,5,4]=>[2,8,1,3,7,5,6,4]=>1001100=>0110011
[2,7,1,8,3,5,6,4]=>[8,2,1,3,5,6,7,4]=>1101000=>0010111
[2,1,8,3,6,4,5,7]=>[2,1,6,3,4,8,5,7]=>1010100=>0101011
[3,2,1,6,8,4,5,7]=>[2,3,1,8,4,6,5,7]=>1001100=>0110011
[2,1,8,3,7,4,5,6]=>[2,1,7,3,4,8,5,6]=>1010100=>0101011
[2,1,8,3,6,7,4,5]=>[2,1,7,6,3,4,8,5]=>1010110=>0101001
[2,4,8,5,1,6,7,3]=>[5,2,1,6,7,8,4,3]=>1111000=>0000111
[4,3,8,5,6,1,7,2]=>[6,5,3,1,7,8,4,2]=>1111100=>0000011
[3,2,1,8,4,5,6,7]=>[2,3,1,8,4,5,6,7]=>1001000=>0110111
[1,6,8,3,7,2,4,5]=>[1,7,3,8,2,4,6,5]=>0110100=>1001011
[1,2,6,8,4,7,3,5]=>[1,2,7,4,8,6,3,5]=>0011010=>1100101
[6,1,5,8,2,4,7,3]=>[7,8,1,2,5,4,6,3]=>1011000=>0100111
[1,2,4,8,3,6,7,5]=>[1,2,6,7,8,4,3,5]=>0011000=>1100111
[4,1,2,7,8,3,6,5]=>[8,4,1,2,3,6,7,5]=>1001100=>0110011
[5,3,8,4,7,6,1,2]=>[4,6,7,3,1,8,5,2]=>1110100=>0001011
[8,7,1,2,5,4,6,3]=>[5,7,1,4,6,8,2,3]=>1100000=>0011111
[5,8,1,2,3,7,6,4]=>[7,6,8,1,5,2,3,4]=>1100010=>0011101
[1,2,8,4,3,5,7,6]=>[1,2,4,7,8,3,5,6]=>0010000=>1101111
[1,2,5,3,7,6,4,8]=>[1,2,6,7,5,3,4,8]=>0010100=>1101011
[6,1,2,8,7,4,5,3]=>[7,4,8,5,6,1,2,3]=>1001100=>0110011
[7,1,6,2,8,4,5,3]=>[8,1,2,4,6,5,7,3]=>1010100=>0101011
[1,2,6,3,8,5,4,7]=>[1,2,8,5,6,3,4,7]=>0010100=>1101011
[1,2,7,3,8,5,4,6]=>[1,2,8,5,7,3,4,6]=>0010100=>1101011
[4,1,2,7,8,6,3,5]=>[6,8,4,1,2,3,7,5]=>1001100=>0110011
[1,6,4,2,7,3,5,8]=>[1,4,2,7,3,6,5,8]=>0110100=>1001011
[1,7,3,2,8,4,5,6]=>[1,3,8,2,4,7,5,6]=>0100100=>1011011
[3,1,7,8,6,2,4,5]=>[6,3,1,2,8,4,7,5]=>1011100=>0100011
[1,8,7,2,4,5,6,3]=>[1,7,2,4,5,6,8,3]=>0110000=>1001111
[1,8,7,3,5,6,2,4]=>[1,5,6,7,3,8,2,4]=>0110000=>1001111
[1,3,2,8,7,4,5,6]=>[1,3,2,7,4,8,5,6]=>0101100=>1010011
[1,8,3,2,6,4,5,7]=>[1,3,6,2,4,8,5,7]=>0100100=>1011011
[1,7,6,3,2,4,5,8]=>[1,6,3,7,2,4,5,8]=>0110000=>1001111
[1,2,8,4,3,7,5,6]=>[1,2,4,7,3,5,8,6]=>0010010=>1101101
[8,5,1,7,2,4,6,3]=>[7,1,5,4,6,8,2,3]=>1101000=>0010111
[5,3,8,7,4,6,1,2]=>[6,7,4,8,3,1,5,2]=>1111000=>0000111
[3,8,6,4,7,5,1,2]=>[4,7,5,6,1,8,3,2]=>1110100=>0001011
[6,1,8,2,7,4,5,3]=>[7,1,2,4,8,5,6,3]=>1010100=>0101011
[1,2,5,3,8,6,4,7]=>[1,2,6,8,5,3,4,7]=>0010100=>1101011
[1,2,7,5,3,6,4,8]=>[1,2,5,3,6,7,4,8]=>0011000=>1100111
[1,2,6,3,7,5,4,8]=>[1,2,7,5,6,3,4,8]=>0010100=>1101011
[1,2,3,7,5,4,8,6]=>[1,2,3,5,8,7,4,6]=>0001001=>1110110
[3,7,4,8,6,5,1,2]=>[6,5,8,4,1,7,3,2]=>1111100=>0000011
[1,8,2,7,6,4,5,3]=>[1,6,4,7,5,8,2,3]=>0101100=>1010011
[7,1,6,3,2,5,4,8]=>[6,3,5,7,1,2,4,8]=>1010000=>0101111
[2,7,6,3,1,5,8,4]=>[6,3,5,8,7,2,1,4]=>1110001=>0001110
[1,8,4,3,6,5,2,7]=>[1,4,3,6,5,8,2,7]=>0110100=>1001011
[7,6,1,4,3,5,2,8]=>[4,6,1,3,5,7,2,8]=>1100000=>0011111
[7,3,1,2,4,6,5,8]=>[3,1,6,7,2,4,5,8]=>1100000=>0011111
[1,8,6,3,4,5,2,7]=>[1,6,3,4,5,8,2,7]=>0110000=>1001111
[3,1,7,2,4,6,8,5]=>[6,8,7,3,1,2,4,5]=>1010001=>0101110
[3,4,7,1,5,2,8,6]=>[5,8,7,1,4,3,2,6]=>1110001=>0001110
[3,6,7,4,1,5,8,2]=>[4,8,7,1,5,6,3,2]=>1110001=>0001110
[4,3,2,7,1,5,8,6]=>[3,2,8,7,4,1,5,6]=>1101001=>0010110
[3,1,2,8,6,5,4,7]=>[3,1,2,6,5,8,4,7]=>1001100=>0110011
[5,6,8,7,4,3,1,2]=>[7,4,8,3,6,1,5,2]=>1111000=>0000111
[6,5,8,2,3,7,1,4]=>[7,2,5,3,8,6,1,4]=>1110010=>0001101
[6,4,8,5,3,1,7,2]=>[5,3,7,8,4,1,6,2]=>1111000=>0000111
[5,7,8,6,1,3,2,4]=>[6,1,8,3,7,2,5,4]=>1111000=>0000111
[2,4,8,1,6,3,7,5]=>[6,2,1,4,3,7,8,5]=>1110100=>0001011
[3,1,2,8,6,4,7,5]=>[3,1,2,6,4,7,8,5]=>1001100=>0110011
[5,3,2,6,4,8,1,7]=>[3,2,8,6,4,5,1,7]=>1101010=>0010101
[4,1,6,3,5,8,2,7]=>[5,8,6,3,4,1,2,7]=>1010010=>0101101
[2,4,5,3,8,6,1,7]=>[6,8,5,3,4,2,1,7]=>1110100=>0001011
[4,1,2,7,6,5,8,3]=>[6,5,8,7,4,1,2,3]=>1001101=>0110010
[2,4,1,6,7,8,5,3]=>[8,5,7,6,4,2,1,3]=>1101110=>0010001
[1,8,4,3,6,2,7,5]=>[1,4,3,6,2,7,8,5]=>0110100=>1001011
[5,6,7,3,2,8,1,4]=>[8,3,7,6,2,5,1,4]=>1110010=>0001101
[3,4,7,8,1,2,6,5]=>[8,1,6,7,4,3,2,5]=>1111000=>0000111
[3,6,2,8,1,5,4,7]=>[8,2,3,1,5,6,4,7]=>1101000=>0010111
[2,3,6,8,5,1,4,7]=>[5,8,3,2,1,6,4,7]=>1111000=>0000111
[3,1,6,4,8,2,5,7]=>[4,8,3,1,2,6,5,7]=>1010100=>0101011
[7,3,2,6,8,5,1,4]=>[3,2,8,5,6,1,7,4]=>1101100=>0010011
[7,3,5,8,4,6,1,2]=>[6,8,4,5,3,1,7,2]=>1111000=>0000111
[7,4,5,8,2,1,3,6]=>[8,2,5,4,1,7,3,6]=>1111000=>0000111
[1,8,5,2,4,6,3,7]=>[1,5,2,4,6,8,3,7]=>0110000=>1001111
[1,8,4,2,3,5,7,6]=>[1,4,2,7,8,3,5,6]=>0110000=>1001111
[6,3,4,8,2,5,7,1]=>[7,8,4,3,2,5,6,1]=>1111000=>0000111
[7,5,4,8,3,6,2,1]=>[6,8,4,3,5,2,7,1]=>1111000=>0000111
[2,7,4,8,5,3,6,1]=>[5,8,4,3,6,7,2,1]=>1111000=>0000111
[7,1,5,4,8,3,6,2]=>[4,8,5,3,6,7,1,2]=>1010100=>0101011
[7,3,2,5,8,4,6,1]=>[3,2,8,5,4,6,7,1]=>1101100=>0010011
[8,4,6,3,7,2,5,1]=>[7,3,4,2,6,5,8,1]=>1110100=>0001011
[7,4,6,3,8,5,1,2]=>[8,5,6,3,4,1,7,2]=>1110100=>0001011
[2,5,6,8,3,4,1,7]=>[8,3,6,4,5,2,1,7]=>1111000=>0000111
[8,4,6,2,7,5,3,1]=>[7,5,6,2,4,3,8,1]=>1110100=>0001011
[8,5,6,7,2,4,3,1]=>[7,2,6,4,5,3,8,1]=>1111000=>0000111
[2,5,7,8,4,1,3,6]=>[8,4,7,2,1,5,3,6]=>1111000=>0000111
[6,5,7,8,4,1,3,2]=>[8,4,7,1,5,3,6,2]=>1111000=>0000111
[7,5,6,8,2,4,1,3]=>[8,2,6,4,5,1,7,3]=>1111000=>0000111
[7,4,6,2,8,5,1,3]=>[8,5,6,2,4,1,7,3]=>1110100=>0001011
[3,6,7,8,1,4,2,5]=>[8,1,7,4,6,3,2,5]=>1111000=>0000111
[3,5,7,8,2,1,4,6]=>[8,2,7,3,1,5,4,6]=>1111000=>0000111
[2,6,7,8,1,4,3,5]=>[8,2,1,7,4,6,3,5]=>1111000=>0000111
[6,5,7,8,3,1,4,2]=>[8,3,7,1,5,4,6,2]=>1111000=>0000111
[2,5,7,8,3,1,4,6]=>[8,3,7,2,1,5,4,6]=>1111000=>0000111
[2,4,7,3,8,1,5,6]=>[8,3,4,2,1,7,5,6]=>1110100=>0001011
[6,4,7,3,8,1,5,2]=>[8,3,4,1,7,5,6,2]=>1110100=>0001011
[7,4,6,3,8,2,1,5]=>[8,3,4,2,6,1,7,5]=>1110100=>0001011
[6,3,2,5,4,8,1,7]=>[3,2,5,4,8,6,1,7]=>1101010=>0010101
[6,4,5,2,3,8,1,7]=>[5,2,4,3,8,6,1,7]=>1110010=>0001101
[5,4,7,3,8,1,6,2]=>[8,3,4,1,6,7,5,2]=>1110100=>0001011
[2,5,7,8,3,1,6,4]=>[8,3,6,7,2,1,5,4]=>1111000=>0000111
[4,5,6,8,2,3,1,7]=>[8,2,6,3,5,4,1,7]=>1111000=>0000111
[5,4,6,2,8,3,1,7]=>[8,2,4,3,6,5,1,7]=>1110100=>0001011
[5,3,2,6,8,4,1,7]=>[3,2,8,4,6,5,1,7]=>1101100=>0010011
[5,4,7,2,8,1,3,6]=>[8,2,4,1,7,5,3,6]=>1110100=>0001011
[4,5,7,8,2,1,3,6]=>[8,2,7,1,5,4,3,6]=>1111000=>0000111
[4,6,7,8,1,3,2,5]=>[8,1,7,3,6,4,2,5]=>1111000=>0000111
[4,6,7,8,1,3,5,2]=>[8,1,7,3,5,6,4,2]=>1111000=>0000111
[2,6,7,8,1,3,5,4]=>[8,2,1,7,3,5,6,4]=>1111000=>0000111
[4,6,7,8,1,5,2,3]=>[8,1,5,7,2,6,4,3]=>1111000=>0000111
[4,6,7,8,1,2,5,3]=>[8,1,7,2,5,6,4,3]=>1111000=>0000111
[5,4,7,2,8,1,6,3]=>[8,2,4,1,6,7,5,3]=>1110100=>0001011
[3,5,7,8,2,1,6,4]=>[8,2,6,7,3,1,5,4]=>1111000=>0000111
[3,6,7,8,1,2,5,4]=>[8,1,7,3,2,5,6,4]=>1111000=>0000111
[3,6,7,8,1,5,2,4]=>[8,1,5,7,3,2,6,4]=>1111000=>0000111
[3,6,7,8,1,5,4,2]=>[8,1,5,7,4,6,3,2]=>1111000=>0000111
[2,3,4,5,6,7,8,9,10,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110=>0000000001
[2,4,5,6,7,8,1,3,9]=>[8,2,1,7,6,5,4,3,9]=>11111100=>00000011
[1,4,5,6,7,8,2,9,3]=>[1,9,8,2,7,6,5,4,3]=>01111101=>10000010
[1,3,4,5,6,7,8,9,10,11,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111=>1000000000
[4,2,7,1,5,3,8,6]=>[2,5,8,7,1,4,3,6]=>1010001=>0101110
[2,7,1,3,5,4,8,6]=>[5,8,7,2,1,3,4,6]=>1100001=>0011110
[4,7,2,1,5,8,6,3]=>[5,8,6,7,2,4,1,3]=>1100010=>0011101
[7,2,1,3,5,8,6,4]=>[2,5,8,6,7,1,3,4]=>1000010=>0111101
[2,3,6,4,7,1,5,8]=>[4,7,3,2,1,6,5,8]=>1110100=>0001011
[1,3,4,8,2,7,5,6]=>[1,7,4,3,2,5,8,6]=>0111010=>1000101
[3,1,4,8,2,6,7,5]=>[6,7,8,4,3,1,2,5]=>1011000=>0100111
[8,3,1,6,2,5,7,4]=>[3,1,6,2,5,7,8,4]=>1101000=>0010111
[4,8,3,6,5,1,7,2]=>[3,5,6,1,7,8,4,2]=>1101000=>0010111
[6,4,7,3,5,1,8,2]=>[5,8,7,3,4,1,6,2]=>1110001=>0001110
[6,4,7,5,1,8,2,3]=>[5,1,8,4,2,7,6,3]=>1111010=>0000101
[4,7,3,5,6,1,8,2]=>[3,6,5,1,8,7,4,2]=>1101101=>0010010
[4,6,8,2,1,5,7,3]=>[7,8,2,5,6,1,4,3]=>1110000=>0001111
[6,8,2,1,3,5,7,4]=>[7,8,2,5,6,1,3,4]=>1100000=>0011111
[1,8,2,3,5,7,4,6]=>[1,5,7,2,3,4,8,6]=>0100010=>1011101
[2,7,3,6,1,4,5,8]=>[3,6,2,1,7,4,5,8]=>1101000=>0010111
[4,7,5,2,6,1,3,8]=>[6,5,2,7,1,4,3,8]=>1110100=>0001011
[8,4,1,2,7,5,3,6]=>[4,1,7,5,8,2,3,6]=>1100100=>0011011
[8,5,1,2,6,3,4,7]=>[6,5,1,8,2,3,4,7]=>1100100=>0011011
[1,6,2,7,4,8,3,5]=>[1,8,4,7,6,2,3,5]=>0101010=>1010101
[2,7,8,4,1,5,6,3]=>[4,8,2,1,5,6,7,3]=>1110000=>0001111
[8,2,5,1,6,7,3,4]=>[2,7,6,5,1,8,3,4]=>1010110=>0101001
[8,2,4,5,1,6,7,3]=>[2,5,4,1,6,7,8,3]=>1011000=>0100111
[3,8,4,5,6,1,7,2]=>[6,5,4,1,7,8,3,2]=>1111100=>0000011
[4,5,8,3,6,7,1,2]=>[7,6,3,8,5,1,4,2]=>1110110=>0001001
[4,5,8,3,7,6,1,2]=>[6,7,3,8,5,1,4,2]=>1110100=>0001011
[7,2,3,4,8,1,6,5]=>[2,3,4,8,1,6,7,5]=>1000100=>0111011
[7,2,3,4,8,1,5,6]=>[2,3,4,8,1,7,5,6]=>1000100=>0111011
[7,6,3,4,8,5,1,2]=>[3,4,8,5,6,1,7,2]=>1100100=>0011011
[7,6,3,8,4,5,1,2]=>[3,8,4,5,6,1,7,2]=>1101000=>0010111
[7,2,3,8,5,1,6,4]=>[2,3,5,8,1,6,7,4]=>1001000=>0110111
[2,6,4,8,1,5,7,3]=>[7,8,4,2,1,5,6,3]=>1111000=>0000111
[7,2,3,5,8,1,4,6]=>[2,3,8,5,1,7,4,6]=>1001100=>0110011
[7,2,3,5,8,1,6,4]=>[2,3,8,5,1,6,7,4]=>1001100=>0110011
[2,6,4,8,1,3,7,5]=>[7,8,4,2,1,6,3,5]=>1111000=>0000111
[3,6,4,8,1,7,5,2]=>[7,4,1,5,8,6,3,2]=>1111010=>0000101
[7,6,5,1,2,3,8,4]=>[5,1,6,2,8,7,3,4]=>1110001=>0001110
[7,6,5,1,4,2,8,3]=>[5,1,4,6,2,8,7,3]=>1110001=>0001110
[2,6,4,5,1,8,7,3]=>[5,4,2,1,7,8,6,3]=>1111010=>0000101
[3,5,6,4,1,2,8,7]=>[4,6,1,5,3,2,8,7]=>1110001=>0001110
[7,6,5,1,2,4,8,3]=>[5,1,6,2,4,8,7,3]=>1110001=>0001110
[7,6,5,1,3,2,8,4]=>[5,1,6,3,8,7,2,4]=>1110001=>0001110
[7,2,3,4,5,1,8,6]=>[2,3,4,5,8,7,1,6]=>1000001=>0111110
[3,5,8,4,1,2,7,6]=>[4,7,8,1,5,3,2,6]=>1110000=>0001111
[3,5,8,4,1,6,2,7]=>[4,6,8,1,5,3,2,7]=>1110000=>0001111
[3,5,8,4,1,6,7,2]=>[4,6,7,8,1,5,3,2]=>1110000=>0001111
[2,5,8,4,1,7,3,6]=>[4,7,2,1,5,3,8,6]=>1110010=>0001101
[3,6,4,2,1,7,8,5]=>[4,2,8,7,6,3,1,5]=>1110011=>0001100
[3,6,4,2,1,7,5,8]=>[4,2,7,6,3,1,5,8]=>1110010=>0001101
[2,6,4,5,1,3,7,8]=>[5,4,2,1,6,3,7,8]=>1111000=>0000111
[7,6,5,1,2,8,3,4]=>[5,1,8,6,2,7,3,4]=>1110010=>0001101
[7,6,5,1,8,2,3,4]=>[8,5,1,6,2,7,3,4]=>1110100=>0001011
[7,6,5,1,8,3,2,4]=>[8,5,1,6,3,7,2,4]=>1110100=>0001011
[7,6,5,1,4,8,2,3]=>[5,1,4,8,6,2,7,3]=>1110010=>0001101
[3,6,4,5,1,7,2,8]=>[5,4,1,7,6,3,2,8]=>1111010=>0000101
[2,5,6,4,1,7,8,3]=>[4,8,7,6,2,1,5,3]=>1110011=>0001100
[3,6,4,5,1,7,8,2]=>[5,4,1,8,7,6,3,2]=>1111011=>0000100
[7,6,5,1,4,8,3,2]=>[5,1,4,8,6,3,7,2]=>1110010=>0001101
[7,6,5,1,8,3,4,2]=>[8,5,1,6,3,4,7,2]=>1110100=>0001011
[7,8,6,2,1,3,5,4]=>[6,2,8,1,5,7,3,4]=>1110000=>0001111
[2,6,4,5,7,8,1,3]=>[8,5,4,2,1,7,6,3]=>1111110=>0000001
[8,7,1,6,5,2,4,3]=>[5,6,1,7,4,8,2,3]=>1101000=>0010111
[7,2,5,6,8,1,3,4]=>[2,8,1,6,5,3,7,4]=>1011100=>0100011
[6,1,3,4,2,8,7,5]=>[3,4,7,8,6,1,2,5]=>1000010=>0111101
[2,4,5,6,1,8,7,3]=>[7,8,6,2,1,5,4,3]=>1111010=>0000101
[8,4,1,6,5,7,3,2]=>[5,7,6,4,1,3,8,2]=>1101010=>0010101
[2,8,3,4,7,5,1,6]=>[3,4,7,5,8,2,1,6]=>1100100=>0011011
[6,8,2,7,4,3,5,1]=>[7,4,8,2,3,5,6,1]=>1101000=>0010111
[4,7,8,5,1,6,3,2]=>[5,1,6,8,3,7,4,2]=>1111000=>0000111
[4,8,6,1,7,3,2,5]=>[7,1,6,3,4,2,8,5]=>1110100=>0001011
[8,3,7,4,6,1,2,5]=>[4,6,3,1,7,2,8,5]=>1110100=>0001011
[7,1,3,8,6,4,5,2]=>[3,6,4,8,5,7,1,2]=>1001100=>0110011
[2,3,5,8,6,7,4,1]=>[7,6,4,8,5,3,2,1]=>1111110=>0000001
[7,4,2,1,8,6,5,3]=>[4,2,6,8,5,7,1,3]=>1100100=>0011011
[4,6,7,2,5,8,3,1]=>[5,8,2,7,6,3,4,1]=>1110010=>0001101
[6,2,1,3,4,8,7,5]=>[2,7,8,6,1,3,4,5]=>1000010=>0111101
[6,5,4,2,8,3,1,7]=>[4,2,8,5,3,6,1,7]=>1110100=>0001011
[4,7,6,2,8,1,5,3]=>[8,2,6,5,7,1,4,3]=>1110100=>0001011
[6,4,5,1,7,8,3,2]=>[8,5,1,4,3,7,6,2]=>1110110=>0001001
[4,2,3,1,7,8,6,5]=>[2,3,4,1,8,6,7,5]=>1000110=>0111001
[3,4,2,1,8,6,7,5]=>[4,2,3,1,6,7,8,5]=>1100100=>0011011
[2,7,6,8,1,5,3,4]=>[8,2,1,5,6,3,7,4]=>1111000=>0000111
[6,4,5,8,3,1,2,7]=>[8,3,5,4,1,6,2,7]=>1111000=>0000111
[8,1,3,2,5,6,7,4]=>[3,5,6,7,8,1,2,4]=>1000000=>0111111
[3,6,8,1,5,2,4,7]=>[5,8,1,6,3,2,4,7]=>1110000=>0001111
[3,2,8,7,4,5,1,6]=>[2,7,4,5,8,3,1,6]=>1011000=>0100111
[6,3,8,5,7,4,2,1]=>[7,5,4,8,3,2,6,1]=>1111100=>0000011
[2,1,6,8,3,7,5,4]=>[2,1,7,3,5,8,6,4]=>1011010=>0100101
[6,2,8,1,7,5,4,3]=>[2,7,5,8,1,4,6,3]=>1010100=>0101011
[6,5,3,4,8,1,7,2]=>[3,4,7,8,5,1,6,2]=>1100100=>0011011
[5,1,8,2,6,4,3,7]=>[6,1,2,4,8,5,3,7]=>1010100=>0101011
[7,4,8,6,2,1,3,5]=>[6,2,8,4,1,7,3,5]=>1111000=>0000111
[5,8,4,1,6,3,7,2]=>[4,1,6,3,7,8,5,2]=>1110100=>0001011
[4,8,1,3,5,7,6,2]=>[5,7,6,8,1,3,4,2]=>1100010=>0011101
[3,8,1,4,5,6,2,7]=>[4,5,6,8,1,3,2,7]=>1100000=>0011111
[7,6,8,3,5,1,4,2]=>[5,8,3,6,1,4,7,2]=>1110000=>0001111
[7,8,6,3,5,1,4,2]=>[5,6,3,8,1,4,7,2]=>1110000=>0001111
[5,3,8,7,6,1,4,2]=>[6,3,1,7,4,8,5,2]=>1111100=>0000011
[6,5,8,4,7,1,3,2]=>[4,7,1,8,5,3,6,2]=>1110100=>0001011
[6,7,4,2,5,3,1,8]=>[4,2,5,7,3,6,1,8]=>1110000=>0001111
[7,4,8,5,6,1,3,2]=>[6,5,1,8,4,3,7,2]=>1111100=>0000011
[4,2,7,5,6,3,1,8]=>[2,6,5,3,7,4,1,8]=>1011100=>0100011
[3,4,7,5,6,2,1,8]=>[6,5,2,7,4,3,1,8]=>1111100=>0000011
[3,7,2,5,6,4,1,8]=>[6,5,4,7,2,3,1,8]=>1101100=>0010011
[7,8,3,5,6,1,4,2]=>[3,6,5,1,8,4,7,2]=>1101100=>0010011
[1,6,8,5,2,7,4,3]=>[1,5,2,7,4,8,6,3]=>0111010=>1000101
[6,2,8,5,1,7,4,3]=>[2,5,1,7,4,8,6,3]=>1011010=>0100101
[6,7,4,8,2,1,5,3]=>[8,4,2,7,1,5,6,3]=>1111000=>0000111
[6,8,4,1,2,3,7,5]=>[4,1,7,8,2,6,3,5]=>1110000=>0001111
[4,1,8,5,6,3,2,7]=>[6,5,3,8,4,1,2,7]=>1011100=>0100011
[1,8,2,5,6,4,3,7]=>[1,6,5,4,8,2,3,7]=>0101100=>1010011
[6,1,8,5,3,7,4,2]=>[5,3,7,4,8,6,1,2]=>1011010=>0100101
[3,8,1,5,2,7,6,4]=>[5,1,3,2,7,6,8,4]=>1101010=>0010101
[8,2,1,5,3,7,6,4]=>[2,5,1,3,7,6,8,4]=>1001010=>0110101
[4,1,5,3,6,7,8,2]=>[8,7,6,5,3,4,1,2]=>1010111=>0101000
[8,1,6,5,3,7,2,4]=>[5,3,7,6,1,2,8,4]=>1011010=>0100101
[7,1,4,6,3,2,8,5]=>[6,4,3,8,7,1,2,5]=>1011001=>0100110
[7,6,4,3,1,2,8,5]=>[4,3,6,1,8,7,2,5]=>1110001=>0001110
[8,6,3,5,1,7,2,4]=>[3,5,1,7,6,2,8,4]=>1101010=>0010101
[4,5,3,1,6,7,8,2]=>[3,8,7,6,5,1,4,2]=>1100111=>0011000
[3,5,2,1,6,7,8,4]=>[8,7,6,5,2,3,1,4]=>1100111=>0011000
[5,2,3,1,6,7,8,4]=>[2,3,8,7,6,5,1,4]=>1000111=>0111000
[1,5,3,2,6,7,8,4]=>[1,3,8,7,6,5,2,4]=>0100111=>1011000
[8,4,6,5,1,7,2,3]=>[5,1,7,6,4,2,8,3]=>1111010=>0000101
[7,5,4,6,1,2,8,3]=>[6,4,1,5,2,8,7,3]=>1111001=>0000110
[3,2,5,6,1,7,8,4]=>[2,8,7,6,3,1,5,4]=>1011011=>0100100
[3,2,8,7,6,1,4,5]=>[2,6,3,1,7,4,8,5]=>1011100=>0100011
[1,7,4,6,2,3,8,5]=>[1,6,4,2,8,7,3,5]=>0111001=>1000110
[7,6,4,2,1,5,8,3]=>[4,2,6,1,5,8,7,3]=>1110001=>0001110
[5,7,4,6,1,3,8,2]=>[6,4,1,8,7,3,5,2]=>1111001=>0000110
[3,5,4,2,7,1,8,6]=>[4,2,8,7,5,3,1,6]=>1110101=>0001010
[8,6,4,1,3,5,2,7]=>[4,1,6,3,5,8,2,7]=>1110000=>0001111
[7,5,4,1,2,6,8,3]=>[4,1,5,2,6,8,7,3]=>1110001=>0001110
[1,7,4,2,3,6,8,5]=>[1,4,2,6,8,7,3,5]=>0110001=>1001110
[1,8,2,5,3,7,6,4]=>[1,5,2,3,7,6,8,4]=>0101010=>1010101
[6,8,1,5,4,7,3,2]=>[5,4,7,1,3,8,6,2]=>1101010=>0010101
[8,2,1,5,6,4,3,7]=>[2,6,5,4,8,1,3,7]=>1001100=>0110011
[6,8,4,1,2,5,3,7]=>[4,1,8,2,5,6,3,7]=>1110000=>0001111
[3,2,8,1,6,5,4,7]=>[2,6,5,8,3,1,4,7]=>1010100=>0101011
[3,2,6,1,5,7,8,4]=>[2,5,8,7,6,3,1,4]=>1010011=>0101100
[8,6,1,5,4,7,2,3]=>[5,4,7,6,1,8,2,3]=>1101010=>0010101
[3,5,1,4,6,7,8,2]=>[4,8,7,6,5,1,3,2]=>1100111=>0011000
[5,2,1,4,6,7,8,3]=>[2,4,8,7,6,5,1,3]=>1000111=>0111000
[5,4,1,3,6,7,8,2]=>[4,1,3,8,7,6,5,2]=>1100111=>0011000
[8,4,1,5,3,7,2,6]=>[5,4,1,3,7,2,8,6]=>1101010=>0010101
[7,1,4,3,5,2,8,6]=>[4,3,5,8,7,1,2,6]=>1010001=>0101110
[8,1,3,5,4,7,2,6]=>[3,5,4,7,1,2,8,6]=>1001010=>0110101
[5,1,3,4,6,7,8,2]=>[3,4,8,7,6,5,1,2]=>1000111=>0111000
[3,1,8,2,5,7,4,6]=>[5,7,3,1,2,4,8,6]=>1010010=>0101101
[8,3,2,6,1,4,7,5]=>[3,2,6,1,7,8,4,5]=>1101000=>0010111
[2,8,1,6,4,3,7,5]=>[6,4,7,8,2,1,3,5]=>1101000=>0010111
[2,6,1,3,8,7,5,4]=>[7,5,8,6,2,1,3,4]=>1100110=>0011001
[2,6,8,1,5,7,4,3]=>[5,7,2,1,4,8,6,3]=>1110010=>0001101
[2,7,1,6,4,8,3,5]=>[8,6,4,7,2,1,3,5]=>1101010=>0010101
[2,7,1,6,5,3,8,4]=>[5,6,2,1,3,8,7,4]=>1101001=>0010110
[2,8,1,7,6,5,4,3]=>[6,5,7,4,8,2,1,3]=>1101100=>0010011
[4,1,8,7,3,2,6,5]=>[7,3,6,8,4,1,2,5]=>1011000=>0100111
[4,1,7,2,8,6,5,3]=>[6,8,5,7,1,2,4,3]=>1010100=>0101011
[3,7,1,8,6,5,4,2]=>[6,5,8,4,7,1,3,2]=>1101100=>0010011
[7,3,5,8,2,1,4,6]=>[8,3,2,5,1,7,4,6]=>1111000=>0000111
[7,3,6,2,1,4,5,8]=>[6,3,2,7,1,4,5,8]=>1110000=>0001111
[7,3,6,2,1,5,4,8]=>[6,3,2,5,7,1,4,8]=>1110000=>0001111
[6,8,4,5,2,1,7,3]=>[5,4,2,7,8,1,6,3]=>1111000=>0000111
[4,6,8,5,1,7,3,2]=>[5,1,7,3,8,6,4,2]=>1111010=>0000101
[4,7,5,1,3,8,6,2]=>[5,1,8,6,7,3,4,2]=>1110010=>0001101
[4,7,6,1,5,3,2,8]=>[5,6,1,7,3,4,2,8]=>1110000=>0001111
[5,1,7,6,4,2,8,3]=>[6,4,8,7,1,2,5,3]=>1011001=>0100110
[5,1,8,7,6,4,3,2]=>[6,4,7,3,8,5,1,2]=>1011100=>0100011
[8,5,2,1,6,3,7,4]=>[6,5,2,7,8,1,3,4]=>1100100=>0011011
[5,1,8,6,3,2,7,4]=>[6,3,7,8,1,2,5,4]=>1011000=>0100111
[8,4,2,5,7,3,1,6]=>[7,5,4,2,3,8,1,6]=>1101100=>0010011
[5,4,8,7,3,6,1,2]=>[6,7,3,8,4,1,5,2]=>1111000=>0000111
[6,4,3,8,7,1,2,5]=>[3,7,4,1,8,2,6,5]=>1101100=>0010011
[6,3,7,2,4,8,1,5]=>[8,3,2,4,7,6,1,5]=>1110010=>0001101
[5,6,8,4,2,7,3,1]=>[4,7,2,8,6,3,5,1]=>1110010=>0001101
[5,7,4,2,8,1,3,6]=>[4,2,8,1,7,5,3,6]=>1110100=>0001011
[6,5,2,7,1,3,8,4]=>[8,7,2,5,1,3,6,4]=>1101001=>0010110
[5,7,4,3,8,6,1,2]=>[4,3,6,8,1,7,5,2]=>1110100=>0001011
[7,5,8,4,6,3,2,1]=>[4,6,3,8,5,2,7,1]=>1110100=>0001011
[7,6,4,8,3,5,2,1]=>[8,4,3,5,6,2,7,1]=>1111000=>0000111
[7,6,5,3,8,2,4,1]=>[8,5,3,6,2,4,7,1]=>1110100=>0001011
[4,3,2,1,6,5,8,7,9]=>[3,2,4,1,6,5,8,7,9]=>11001010=>00110101
[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]=>10010101=>01101010
[3,2,1,5,4,6,7,8,9]=>[2,3,1,5,4,6,7,8,9]=>10010000=>01101111
[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>10101000=>01010111
[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>10100000=>01011111
[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]=>100101010=>011010101
[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>101010100=>010101011
[2,1,4,3,6,5,7,8,9,10]=>[2,1,4,3,6,5,7,8,9,10]=>101010000=>010101111
[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>101000000=>010111111
[6,4,8,1,3,2,5,7]=>[8,1,4,3,6,2,5,7]=>1110000=>0001111
[3,7,2,4,6,5,1,8]=>[4,6,5,7,2,3,1,8]=>1100100=>0011011
[8,1,3,4,5,2,6,7]=>[3,4,5,8,1,2,6,7]=>1000000=>0111111
[1,6,8,4,2,5,3,7]=>[1,4,8,2,5,6,3,7]=>0110000=>1001111
[6,7,4,8,5,1,2,3]=>[5,8,4,1,7,2,6,3]=>1111000=>0000111
[3,2,7,8,5,1,6,4]=>[2,5,8,3,1,6,7,4]=>1011000=>0100111
[3,2,8,1,5,4,6,7]=>[2,5,8,3,1,4,6,7]=>1010000=>0101111
[6,1,4,8,5,3,7,2]=>[5,7,8,4,3,6,1,2]=>1011000=>0100111
[1,4,8,5,2,6,7,3]=>[1,5,2,6,7,8,4,3]=>0111000=>1000111
[4,1,5,3,6,8,2,7]=>[8,6,5,3,4,1,2,7]=>1010110=>0101001
[3,5,2,1,8,7,6,4]=>[7,6,8,5,2,3,1,4]=>1100110=>0011001
[1,5,3,2,8,6,4,7]=>[1,3,6,8,5,2,4,7]=>0100100=>1011011
[5,4,2,1,7,8,6,3]=>[4,2,8,6,7,5,1,3]=>1100110=>0011001
[8,6,2,7,1,4,5,3]=>[7,2,6,4,5,8,1,3]=>1101000=>0010111
[5,2,3,4,7,1,8,6]=>[2,3,4,8,7,5,1,6]=>1000101=>0111010
[8,6,3,1,4,5,7,2]=>[3,6,1,4,5,7,8,2]=>1100000=>0011111
[6,7,3,1,5,4,2,8]=>[3,5,7,1,4,6,2,8]=>1100000=>0011111
[5,8,3,1,2,4,7,6]=>[3,7,8,1,5,2,4,6]=>1100000=>0011111
[8,1,3,2,4,5,6,7]=>[3,8,1,2,4,5,6,7]=>1000000=>0111111
[8,4,1,7,2,3,6,5]=>[7,4,1,6,8,2,3,5]=>1101000=>0010111
[3,8,1,5,6,4,7,2]=>[6,5,4,7,8,1,3,2]=>1101100=>0010011
[6,8,4,1,2,5,7,3]=>[4,1,7,8,2,5,6,3]=>1110000=>0001111
[3,2,8,1,6,5,7,4]=>[2,6,5,7,8,3,1,4]=>1010100=>0101011
[4,5,8,2,1,3,7,6]=>[7,8,2,5,1,4,3,6]=>1110000=>0001111
[5,8,2,3,1,4,6,7]=>[8,2,3,5,1,4,6,7]=>1100000=>0011111
[4,2,1,3,5,8,7,6]=>[2,4,1,3,5,7,8,6]=>1000010=>0111101
[5,4,1,3,6,2,8,7]=>[4,1,3,6,5,2,8,7]=>1100101=>0011010
[8,5,4,1,3,6,2,7]=>[4,1,5,3,6,8,2,7]=>1110000=>0001111
[8,1,4,3,5,6,7,2]=>[4,3,5,6,7,8,1,2]=>1010000=>0101111
[5,1,3,4,6,2,7,8]=>[3,4,6,5,1,2,7,8]=>1000100=>0111011
[4,1,3,2,5,7,6,8]=>[3,4,1,2,5,7,6,8]=>1000010=>0111101
[3,1,4,2,6,5,8,7,9]=>[4,3,1,2,6,5,8,7,9]=>10101010=>01010101
[3,1,5,2,6,4,8,7,9]=>[6,5,3,1,2,4,8,7,9]=>10101010=>01010101
[3,1,5,2,7,4,8,6,9]=>[8,7,5,3,1,2,4,6,9]=>10101010=>01010101
[3,1,5,2,7,4,6,9,8]=>[7,5,3,1,2,4,6,9,8]=>10101001=>01010110
[3,1,5,2,4,7,6,9,8]=>[5,3,1,2,4,7,6,9,8]=>10100101=>01011010
[3,1,2,5,4,7,6,9,8]=>[3,1,2,5,4,7,6,9,8]=>10010101=>01101010
[3,1,4,2,6,5,8,7,10,9]=>[4,3,1,2,6,5,8,7,10,9]=>101010101=>010101010
[3,1,5,2,6,4,8,7,10,9]=>[6,5,3,1,2,4,8,7,10,9]=>101010101=>010101010
[3,1,5,2,7,4,8,6,10,9]=>[8,7,5,3,1,2,4,6,10,9]=>101010101=>010101010
[3,1,5,2,7,4,9,6,10,8]=>[10,9,7,5,3,1,2,4,6,8]=>101010101=>010101010
[3,1,5,2,7,4,6,8,9]=>[7,5,3,1,2,4,6,8,9]=>10101000=>01010111
[3,1,5,2,7,4,9,6,8,10]=>[9,7,5,3,1,2,4,6,8,10]=>101010100=>010101011
[3,1,5,2,4,7,9,6,8]=>[5,3,1,2,4,9,7,6,8]=>10100110=>01011001
[3,1,5,2,7,4,6,9,8,10]=>[7,5,3,1,2,4,6,9,8,10]=>101010010=>010101101
[3,1,2,5,7,4,6,9,8]=>[3,1,2,7,5,4,6,9,8]=>10011001=>01100110
[3,1,5,2,4,7,6,9,8,10]=>[5,3,1,2,4,7,6,9,8,10]=>101001010=>010110101
[1,3,5,2,4,7,6,9,8]=>[1,5,3,2,4,7,6,9,8]=>01100101=>10011010
[3,1,2,5,4,7,6,9,8,10]=>[3,1,2,5,4,7,6,9,8,10]=>100101010=>011010101
[4,6,7,3,1,5,2,8]=>[7,3,5,6,1,4,2,8]=>1110000=>0001111
[5,8,1,2,4,7,3,6]=>[7,1,4,5,2,3,8,6]=>1100010=>0011101
[6,1,8,2,3,4,7,5]=>[7,8,1,2,6,3,4,5]=>1010000=>0101111
[4,1,8,3,5,7,2,6]=>[5,7,3,4,1,2,8,6]=>1010010=>0101101
[3,4,7,2,6,1,8,5]=>[6,2,4,3,1,8,7,5]=>1110101=>0001010
[4,5,7,3,2,6,8,1]=>[6,8,7,3,5,2,4,1]=>1110001=>0001110
[2,6,3,4,7,5,8,1]=>[3,4,8,7,5,6,2,1]=>1100101=>0011010
[4,5,2,7,1,6,8,3]=>[6,8,7,2,5,4,1,3]=>1101001=>0010110
[3,4,1,6,5,8,2,7]=>[5,8,6,4,1,3,2,7]=>1101010=>0010101
[4,1,2,8,5,7,3,6]=>[5,7,4,1,2,3,8,6]=>1001010=>0110101
[7,3,1,4,8,5,6,2]=>[3,1,4,8,5,6,7,2]=>1100100=>0011011
[7,3,4,1,8,5,2,6]=>[4,3,1,8,5,7,2,6]=>1110100=>0001011
[6,4,2,8,7,1,5,3]=>[7,4,2,8,5,6,1,3]=>1101100=>0010011
[2,6,3,7,5,1,4,8]=>[3,5,7,2,1,6,4,8]=>1101000=>0010111
[7,1,3,8,5,2,4,6]=>[3,5,8,1,2,7,4,6]=>1001000=>0110111
[3,2,6,7,1,8,4,5]=>[2,8,3,1,7,6,4,5]=>1011010=>0100101
[4,6,3,1,7,8,5,2]=>[3,8,5,7,6,1,4,2]=>1100110=>0011001
[5,3,1,6,7,8,4,2]=>[3,1,8,4,7,6,5,2]=>1101110=>0010001
[4,1,6,2,7,8,5,3]=>[8,5,7,6,1,2,4,3]=>1010110=>0101001
[2,1,3,4,8,7,5,6]=>[2,1,3,4,7,5,8,6]=>1000110=>0111001
[7,8,9,4,5,6,3,2,1]=>[4,5,6,9,3,8,2,7,1]=>11100000=>00011111
[8,9,6,7,4,5,3,2,1]=>[7,4,5,6,3,9,2,8,1]=>11110000=>00001111
[8,9,6,7,5,4,3,2,1]=>[5,7,4,6,3,9,2,8,1]=>11110000=>00001111
[7,8,9,10,4,5,6,3,2,1]=>[10,4,5,6,9,3,8,2,7,1]=>111100000=>000011111
[9,10,7,8,5,6,4,3,2,1]=>[5,6,8,4,7,3,10,2,9,1]=>111100000=>000011111
[9,10,7,8,6,5,4,3,2,1]=>[6,5,8,4,7,3,10,2,9,1]=>111110000=>000001111
[4,8,3,7,6,5,1,2]=>[3,6,5,7,1,8,4,2]=>1101100=>0010011
[6,3,8,7,5,4,1,2]=>[5,7,4,8,3,1,6,2]=>1111000=>0000111
[2,8,7,6,1,5,4,3]=>[6,2,1,5,7,4,8,3]=>1111000=>0000111
[5,2,8,7,6,1,4,3]=>[2,6,1,7,4,8,5,3]=>1011100=>0100011
[7,8,2,6,5,1,4,3]=>[5,6,2,8,4,7,1,3]=>1101000=>0010111
[6,1,8,7,5,4,3,2]=>[5,7,4,8,3,6,1,2]=>1011000=>0100111
[3,1,8,7,6,5,4,2]=>[6,5,7,4,8,3,1,2]=>1011100=>0100011
[6,2,8,7,1,5,4,3]=>[2,7,1,5,8,4,6,3]=>1011000=>0100111
[4,2,8,1,7,6,5,3]=>[2,6,7,5,8,1,4,3]=>1010100=>0101011
[4,8,2,7,6,1,5,3]=>[6,2,7,5,8,4,1,3]=>1101100=>0010011
[6,5,8,7,1,4,3,2]=>[7,1,8,4,5,3,6,2]=>1111000=>0000111
[4,8,1,7,6,5,3,2]=>[6,5,7,1,3,8,4,2]=>1101100=>0010011
[7,8,4,1,6,5,3,2]=>[4,1,6,5,8,3,7,2]=>1110100=>0001011
[7,8,3,1,6,5,4,2]=>[3,6,5,8,1,4,7,2]=>1100100=>0011011
[6,3,8,1,7,5,4,2]=>[7,5,8,3,1,4,6,2]=>1110100=>0001011
[5,3,1,8,7,6,4,2]=>[3,1,6,7,4,8,5,2]=>1101100=>0010011
[6,5,3,1,8,7,4,2]=>[3,7,5,1,4,8,6,2]=>1100110=>0011001
[6,4,3,1,8,7,5,2]=>[3,4,1,7,5,8,6,2]=>1100110=>0011001
[5,4,3,1,8,7,6,2]=>[3,4,1,7,6,8,5,2]=>1100110=>0011001
[5,4,2,1,8,7,6,3]=>[4,2,7,6,8,5,1,3]=>1100110=>0011001
[7,3,2,1,8,6,5,4]=>[3,2,6,8,5,7,1,4]=>1100100=>0011011
[6,3,2,1,8,7,5,4]=>[3,2,7,5,8,6,1,4]=>1100110=>0011001
[6,1,4,2,3,5,8,7]=>[4,1,2,6,3,5,8,7]=>1010001=>0101110
[8,6,1,4,2,3,5,7]=>[4,6,1,8,2,3,5,7]=>1100000=>0011111
[6,8,1,4,2,3,5,7]=>[4,8,1,6,2,3,5,7]=>1100000=>0011111
[4,1,8,2,3,6,5,7]=>[6,8,1,2,4,3,5,7]=>1010000=>0101111
[8,2,3,6,1,4,5,7]=>[2,3,6,1,8,4,5,7]=>1001000=>0110111
[6,2,3,8,1,4,5,7]=>[2,3,8,1,6,4,5,7]=>1001000=>0110111
[4,8,2,3,6,1,5,7]=>[6,2,3,4,1,8,5,7]=>1100100=>0011011
[8,2,3,6,4,1,5,7]=>[2,3,6,4,8,1,5,7]=>1001000=>0110111
[8,4,2,3,6,1,5,7]=>[4,2,3,6,1,8,5,7]=>1100100=>0011011
[6,4,2,3,8,1,5,7]=>[4,2,3,8,1,6,5,7]=>1100100=>0011011
[2,6,4,3,8,1,5,7]=>[4,3,8,2,1,6,5,7]=>1110100=>0001011
[2,8,4,3,6,1,5,7]=>[4,3,6,2,1,8,5,7]=>1110100=>0001011
[2,6,3,8,4,1,5,7]=>[3,8,4,6,2,1,5,7]=>1101000=>0010111
[6,3,8,4,2,1,5,7]=>[4,8,3,2,6,1,5,7]=>1110000=>0001111
[2,6,3,8,1,4,5,7]=>[3,8,2,1,6,4,5,7]=>1101000=>0010111
[8,3,6,4,2,1,5,7]=>[4,6,3,2,8,1,5,7]=>1110000=>0001111
[2,8,3,6,4,1,5,7]=>[3,6,4,8,2,1,5,7]=>1101000=>0010111
[8,3,6,2,4,1,5,7]=>[6,3,2,4,8,1,5,7]=>1110000=>0001111
[8,3,6,2,1,4,5,7]=>[6,3,2,8,1,4,5,7]=>1110000=>0001111
[8,2,1,3,6,4,5,7]=>[2,6,1,3,4,8,5,7]=>1000100=>0111011
[6,3,8,2,4,1,5,7]=>[8,3,2,4,6,1,5,7]=>1110000=>0001111
[6,2,4,3,8,1,5,7]=>[2,4,3,8,1,6,5,7]=>1010100=>0101011
[3,6,4,7,8,5,1,2]=>[8,5,7,4,1,6,3,2]=>1111100=>0000011
[3,6,4,2,7,1,5,8]=>[4,2,7,3,1,6,5,8]=>1110100=>0001011
[6,4,8,5,3,7,1,2]=>[5,3,7,4,1,8,6,2]=>1111010=>0000101
[1,6,5,4,2,7,8,3]=>[1,4,5,2,8,7,6,3]=>0110011=>1001100
[4,2,5,3,6,1,7,8]=>[2,6,5,3,4,1,7,8]=>1010100=>0101011
[7,1,5,3,6,2,8,4]=>[6,5,3,8,7,1,2,4]=>1010101=>0101010
[1,6,5,2,4,8,7,3]=>[1,5,2,4,7,8,6,3]=>0110010=>1001101
[7,8,1,4,2,5,6,3]=>[4,8,1,5,6,7,2,3]=>1100000=>0011111
[3,4,8,5,2,1,6,7]=>[5,2,8,4,3,1,6,7]=>1111000=>0000111
[4,8,5,3,1,6,2,7]=>[5,3,6,8,1,4,2,7]=>1110000=>0001111
[6,1,3,5,8,2,7,4]=>[3,7,8,5,1,2,6,4]=>1001100=>0110011
[1,8,2,5,4,7,6,3]=>[1,5,4,7,6,8,2,3]=>0101010=>1010101
[7,1,2,4,5,8,6,3]=>[4,5,8,6,7,1,2,3]=>1000010=>0111101
[1,2,7,3,5,8,6,4]=>[1,2,5,8,6,7,3,4]=>0010010=>1101101
[6,1,3,2,5,7,8,4]=>[3,5,8,7,6,1,2,4]=>1000011=>0111100
[1,6,3,7,8,5,2,4]=>[1,3,8,5,7,2,6,4]=>0101100=>1010011
[4,2,1,3,5,7,8,6]=>[2,4,1,3,5,8,7,6]=>1000011=>0111100
[7,3,2,4,5,1,8,6]=>[3,2,4,5,8,7,1,6]=>1100001=>0011110
[7,8,4,2,6,3,1,5]=>[4,2,6,3,8,1,7,5]=>1110100=>0001011
[5,8,2,7,4,3,1,6]=>[7,4,8,2,3,5,1,6]=>1101000=>0010111
[6,4,3,5,2,8,1,7]=>[3,5,4,2,8,6,1,7]=>1101010=>0010101
[3,8,1,7,5,6,4,2]=>[5,6,7,4,8,1,3,2]=>1101000=>0010111
[1,8,6,7,5,3,4,2]=>[1,5,7,3,6,4,8,2]=>0111000=>1000111
[8,2,6,7,5,3,4,1]=>[2,5,7,3,6,4,8,1]=>1011000=>0100111
[1,5,8,7,2,6,4,3]=>[1,6,7,2,8,4,5,3]=>0111000=>1000111
[5,4,8,6,2,3,7,1]=>[6,2,7,8,4,3,5,1]=>1111000=>0000111
[2,7,6,1,3,5,4,8]=>[6,2,1,5,7,3,4,8]=>1110000=>0001111
[6,4,1,8,2,5,7,3]=>[7,8,4,1,5,6,2,3]=>1101000=>0010111
[2,8,6,1,3,5,4,7]=>[6,2,1,5,8,3,4,7]=>1110000=>0001111
[4,1,3,6,5,8,7,2]=>[3,5,7,8,6,4,1,2]=>1001010=>0110101
[2,1,6,3,5,8,7,4]=>[2,1,5,7,8,6,3,4]=>1010010=>0101101
[2,4,1,3,8,5,7,6]=>[4,2,1,3,7,8,5,6]=>1100100=>0011011
[2,4,1,3,5,8,7,6]=>[4,2,1,3,5,7,8,6]=>1100010=>0011101
[4,6,1,3,5,8,7,2]=>[5,7,8,6,1,3,4,2]=>1100010=>0011101
[6,4,1,3,5,8,7,2]=>[4,1,3,5,7,8,6,2]=>1100010=>0011101
[4,2,1,3,6,5,7,8]=>[2,4,1,3,6,5,7,8]=>1000100=>0111011
[4,2,1,6,3,5,7,8]=>[2,6,4,1,3,5,7,8]=>1001000=>0110111
[6,2,1,3,8,5,7,4]=>[2,7,8,5,6,1,3,4]=>1000100=>0111011
[1,6,4,3,8,5,7,2]=>[1,4,3,7,8,5,6,2]=>0110100=>1001011
[8,1,4,3,6,5,7,2]=>[4,3,6,5,7,8,1,2]=>1010100=>0101011
[8,4,1,3,6,5,7,2]=>[4,1,3,6,5,7,8,2]=>1100100=>0011011
[8,2,1,4,3,5,7,6]=>[2,4,7,8,1,3,5,6]=>1000000=>0111111
[6,2,1,4,3,5,7,8]=>[2,4,6,1,3,5,7,8]=>1000000=>0111111
[8,2,4,1,3,5,7,6]=>[2,4,1,7,8,3,5,6]=>1010000=>0101111
[8,2,6,1,3,5,7,4]=>[2,6,1,5,7,8,3,4]=>1010000=>0101111
[8,4,6,1,3,5,7,2]=>[6,1,4,3,5,7,8,2]=>1110000=>0001111
[8,1,4,6,3,5,7,2]=>[6,4,3,5,7,8,1,2]=>1011000=>0100111
[1,6,4,8,3,5,7,2]=>[1,7,8,4,3,5,6,2]=>0111000=>1000111
[6,4,1,8,3,5,7,2]=>[7,8,4,1,3,5,6,2]=>1101000=>0010111
[6,4,8,1,3,5,7,2]=>[7,8,1,4,3,5,6,2]=>1110000=>0001111
[6,2,8,1,3,5,7,4]=>[2,7,8,1,5,6,3,4]=>1010000=>0101111
[4,6,8,1,3,5,7,2]=>[7,8,1,5,6,3,4,2]=>1110000=>0001111
[4,6,1,8,3,5,7,2]=>[7,8,1,3,5,6,4,2]=>1101000=>0010111
[4,1,6,8,3,5,7,2]=>[7,8,3,5,6,4,1,2]=>1011000=>0100111
[1,4,6,3,8,5,7,2]=>[1,7,8,5,6,3,4,2]=>0110100=>1001011
[4,6,1,3,8,5,7,2]=>[7,8,5,6,1,3,4,2]=>1100100=>0011011
[2,4,1,8,3,5,7,6]=>[7,8,4,2,1,3,5,6]=>1101000=>0010111
[4,1,3,6,8,5,7,2]=>[3,7,8,5,6,4,1,2]=>1001100=>0110011
[1,4,3,6,8,5,7,2]=>[1,3,7,8,5,6,4,2]=>0101100=>1010011
[2,1,8,3,6,5,7,4]=>[2,1,6,5,7,8,3,4]=>1010100=>0101011
[2,1,6,4,3,5,7,8]=>[2,1,4,6,3,5,7,8]=>1010000=>0101111
[2,6,1,4,3,5,7,8]=>[4,6,2,1,3,5,7,8]=>1100000=>0011111
[2,8,1,4,3,5,7,6]=>[4,7,8,2,1,3,5,6]=>1100000=>0011111
[4,8,1,3,6,5,7,2]=>[6,5,7,8,1,3,4,2]=>1100100=>0011011
[1,4,8,3,6,5,7,2]=>[1,6,5,7,8,3,4,2]=>0110100=>1001011
[1,4,8,6,3,5,7,2]=>[1,6,3,5,7,8,4,2]=>0111000=>1000111
[4,8,6,1,3,5,7,2]=>[6,1,5,7,8,3,4,2]=>1110000=>0001111
[2,8,4,1,3,5,7,6]=>[4,2,1,7,8,3,5,6]=>1110000=>0001111
[2,6,4,1,3,5,7,8]=>[4,2,1,6,3,5,7,8]=>1110000=>0001111
[4,6,2,1,3,5,7,8]=>[6,2,4,1,3,5,7,8]=>1100000=>0011111
[6,8,1,4,3,5,7,2]=>[4,7,8,1,3,5,6,2]=>1100000=>0011111
[6,1,8,4,3,5,7,2]=>[4,7,8,3,5,6,1,2]=>1010000=>0101111
[1,8,6,4,3,5,7,2]=>[1,4,6,3,5,7,8,2]=>0110000=>1001111
[8,1,6,4,3,5,7,2]=>[4,6,3,5,7,8,1,2]=>1010000=>0101111
[8,6,4,1,3,5,7,2]=>[4,1,6,3,5,7,8,2]=>1110000=>0001111
[8,6,2,1,3,5,7,4]=>[6,2,5,7,8,1,3,4]=>1100000=>0011111
[7,8,6,5,2,1,4,3]=>[5,2,6,1,8,4,7,3]=>1111000=>0000111
[5,7,4,1,8,6,3,2]=>[4,1,6,8,3,7,5,2]=>1110100=>0001011
[5,6,4,2,8,3,7,1]=>[4,2,7,8,3,6,5,1]=>1110100=>0001011
[5,6,4,2,7,3,1,8]=>[4,2,7,3,6,5,1,8]=>1110100=>0001011
[5,8,1,4,6,3,7,2]=>[4,6,1,3,7,8,5,2]=>1100100=>0011011
[3,5,7,4,6,8,2,1]=>[4,8,6,2,7,5,3,1]=>1110110=>0001001
[6,8,4,1,7,2,5,3]=>[4,1,7,2,8,5,6,3]=>1110100=>0001011
[5,4,6,1,7,8,3,2]=>[8,1,4,3,7,6,5,2]=>1110110=>0001001
[3,7,8,4,5,6,2,1]=>[4,5,6,8,2,7,3,1]=>1110000=>0001111
[3,8,1,5,4,6,7,2]=>[5,4,6,7,8,1,3,2]=>1101000=>0010111
[5,7,1,4,6,3,8,2]=>[4,6,1,3,8,7,5,2]=>1100101=>0011010
[5,6,4,2,7,3,8,1]=>[4,2,8,7,3,6,5,1]=>1110101=>0001010
[5,4,7,2,8,3,1,6]=>[8,2,4,3,7,5,1,6]=>1110100=>0001011
[5,4,7,2,8,3,6,1]=>[8,2,4,3,6,7,5,1]=>1110100=>0001011
[5,6,4,2,8,3,1,7]=>[4,2,8,3,6,5,1,7]=>1110100=>0001011
[5,8,1,4,6,3,2,7]=>[4,6,1,3,8,5,2,7]=>1100100=>0011011
[3,8,1,5,4,6,2,7]=>[5,4,6,8,1,3,2,7]=>1101000=>0010111
[3,6,1,5,4,2,7,8]=>[5,4,6,1,3,2,7,8]=>1101000=>0010111
[6,8,3,1,4,2,5,7]=>[3,8,1,4,6,2,5,7]=>1100000=>0011111
[7,3,8,1,4,2,5,6]=>[8,3,1,4,7,2,5,6]=>1110000=>0001111
[3,6,1,5,4,7,8,2]=>[5,4,8,7,6,1,3,2]=>1101011=>0010100
[6,4,7,2,8,5,1,3]=>[8,5,7,2,4,1,6,3]=>1110100=>0001011
[7,8,1,4,5,3,2,6]=>[4,5,8,1,3,7,2,6]=>1100000=>0011111
[3,8,1,5,4,7,2,6]=>[5,4,7,1,3,2,8,6]=>1101010=>0010101
[3,6,1,5,4,8,7,2]=>[5,4,7,8,6,1,3,2]=>1101010=>0010101
[6,8,3,1,4,2,7,5]=>[3,7,8,1,4,6,2,5]=>1100000=>0011111
[7,8,4,2,6,5,1,3]=>[4,2,6,5,8,1,7,3]=>1110100=>0001011
[6,5,8,7,3,4,2,1]=>[7,3,8,4,5,2,6,1]=>1111000=>0000111
[6,7,3,1,4,5,2,8]=>[3,7,1,4,5,6,2,8]=>1100000=>0011111
[3,7,1,5,4,2,6,8]=>[5,4,7,1,3,2,6,8]=>1101000=>0010111
[3,8,1,5,4,2,7,6]=>[5,4,7,8,1,3,2,6]=>1101000=>0010111
[6,8,4,2,7,5,3,1]=>[4,2,7,5,8,3,6,1]=>1110100=>0001011
[6,4,7,2,8,5,3,1]=>[8,5,7,2,4,3,6,1]=>1110100=>0001011
[6,3,7,1,4,8,5,2]=>[8,3,1,4,5,7,6,2]=>1110010=>0001101
[3,4,1,2,8,5,7,6]=>[4,1,3,2,7,8,5,6]=>1100100=>0011011
[3,4,1,2,5,8,7,6]=>[4,1,3,2,5,7,8,6]=>1100010=>0011101
[3,7,1,5,4,2,8,6]=>[5,4,8,7,1,3,2,6]=>1101001=>0010110
[6,7,3,1,4,5,8,2]=>[3,8,7,1,4,5,6,2]=>1100001=>0011110
[7,3,8,1,4,5,2,6]=>[8,3,1,4,5,7,2,6]=>1110000=>0001111
[7,3,8,1,4,5,6,2]=>[8,3,1,4,5,6,7,2]=>1110000=>0001111
[6,8,3,1,4,5,2,7]=>[3,8,1,4,5,6,2,7]=>1100000=>0011111
[3,8,1,5,4,2,6,7]=>[5,4,8,1,3,2,6,7]=>1101000=>0010111
[8,7,6,3,5,2,1,4]=>[5,6,3,7,2,8,1,4]=>1110000=>0001111
[8,7,4,6,3,2,1,5]=>[6,4,3,7,2,8,1,5]=>1111000=>0000111
[8,5,7,4,3,2,1,6]=>[4,7,3,5,2,8,1,6]=>1110000=>0001111
[9,7,6,5,4,3,2,1,8]=>[5,4,6,3,7,2,9,1,8]=>11110000=>00001111
[8,7,6,2,5,4,1,3]=>[5,6,2,4,7,1,8,3]=>1110000=>0001111
[8,5,4,7,3,2,1,6]=>[7,4,3,5,2,8,1,6]=>1111000=>0000111
[8,7,3,6,5,2,1,4]=>[3,5,6,2,7,1,8,4]=>1101000=>0010111
[6,5,8,4,3,2,1,7]=>[4,8,3,5,2,6,1,7]=>1110000=>0001111
[5,8,7,4,3,2,1,6]=>[4,7,3,8,2,5,1,6]=>1110000=>0001111
[10,8,7,6,5,4,3,2,1,9]=>[5,6,4,7,3,8,2,10,1,9]=>111100000=>000011111
[5,8,6,2,3,4,7,1]=>[6,2,7,8,3,4,5,1]=>1110000=>0001111
[4,5,2,7,3,1,8,6]=>[8,7,2,3,5,4,1,6]=>1101001=>0010110
[4,3,7,8,6,5,1,2]=>[6,5,8,3,1,7,4,2]=>1111100=>0000011
[4,1,7,2,5,8,6,3]=>[5,8,6,7,1,2,4,3]=>1010010=>0101101
[7,8,2,1,5,6,4,3]=>[5,6,8,2,4,7,1,3]=>1100000=>0011111
[1,6,2,5,8,4,3,7]=>[1,8,5,4,6,2,3,7]=>0101100=>1010011
[2,1,8,7,4,5,3,6]=>[2,1,7,4,5,8,3,6]=>1011000=>0100111
[7,3,1,6,8,5,2,4]=>[3,1,8,5,6,2,7,4]=>1101100=>0010011
[5,2,7,1,8,6,3,4]=>[2,6,8,1,7,5,3,4]=>1010100=>0101011
[2,6,1,3,8,7,4,5]=>[7,2,1,3,4,8,6,5]=>1100110=>0011001
[2,8,3,5,1,7,4,6]=>[3,5,2,1,7,4,8,6]=>1101010=>0010101
[5,4,3,8,7,1,6,2]=>[3,7,4,1,6,8,5,2]=>1101100=>0010011
[8,3,7,4,2,6,5,1]=>[4,6,7,3,2,5,8,1]=>1110000=>0001111
[2,8,6,5,1,7,4,3]=>[5,2,1,7,6,4,8,3]=>1111010=>0000101
[6,3,2,8,4,1,7,5]=>[3,2,7,8,4,6,1,5]=>1101000=>0010111
[2,8,3,4,1,7,5,6]=>[3,4,7,2,1,5,8,6]=>1100010=>0011101
[2,8,4,3,1,7,6,5]=>[4,3,7,6,8,2,1,5]=>1110010=>0001101
[2,8,5,3,1,7,6,4]=>[5,3,7,6,8,2,1,4]=>1110010=>0001101
[3,8,7,5,1,6,4,2]=>[5,1,6,7,4,8,3,2]=>1111000=>0000111
[8,3,7,5,2,6,4,1]=>[5,3,2,6,7,4,8,1]=>1111000=>0000111
[8,4,7,6,2,5,3,1]=>[6,2,5,7,4,3,8,1]=>1111000=>0000111
[4,8,7,6,1,5,3,2]=>[6,1,5,7,3,8,4,2]=>1111000=>0000111
[7,4,8,6,2,1,5,3]=>[6,2,8,4,1,5,7,3]=>1111000=>0000111
[7,3,8,5,2,1,6,4]=>[5,3,2,8,1,6,7,4]=>1111000=>0000111
[7,3,8,4,2,1,6,5]=>[4,8,3,2,6,7,1,5]=>1110000=>0001111
[7,5,4,3,8,2,1,6]=>[4,3,8,5,2,7,1,6]=>1110100=>0001011
[3,7,8,4,1,2,6,5]=>[4,8,1,6,7,3,2,5]=>1110000=>0001111
[3,7,8,5,1,2,6,4]=>[5,1,8,3,2,6,7,4]=>1111000=>0000111
[8,7,4,6,3,5,2,1]=>[6,4,3,5,7,2,8,1]=>1111000=>0000111
[5,7,8,6,1,2,4,3]=>[6,1,8,2,7,4,5,3]=>1111000=>0000111
[6,4,7,8,3,1,2,5]=>[8,3,7,4,1,6,2,5]=>1111000=>0000111
[7,5,8,6,2,1,4,3]=>[6,2,8,1,5,4,7,3]=>1111000=>0000111
[6,5,8,7,3,1,4,2]=>[7,3,8,1,5,4,6,2]=>1111000=>0000111
[2,4,8,3,1,5,7,6]=>[7,8,3,4,2,1,5,6]=>1110000=>0001111
[6,3,2,4,8,1,5,7]=>[3,2,4,8,1,6,5,7]=>1100100=>0011011
[2,3,8,4,1,6,7,5]=>[4,6,7,8,3,2,1,5]=>1110000=>0001111
[2,3,8,5,1,6,7,4]=>[5,3,2,1,6,7,8,4]=>1111000=>0000111
[6,4,8,7,3,1,5,2]=>[7,3,8,4,1,5,6,2]=>1111000=>0000111
[8,6,4,7,3,2,5,1]=>[7,4,3,6,2,5,8,1]=>1111000=>0000111
[3,4,8,7,1,5,6,2]=>[7,1,5,6,8,4,3,2]=>1111000=>0000111
[2,5,8,6,1,4,7,3]=>[6,2,1,7,8,4,5,3]=>1111000=>0000111
[8,4,6,7,2,3,5,1]=>[7,2,6,4,3,5,8,1]=>1111000=>0000111
[4,6,8,7,1,3,5,2]=>[7,1,8,3,5,6,4,2]=>1111000=>0000111
[7,4,6,8,2,1,3,5]=>[8,2,6,4,1,7,3,5]=>1111000=>0000111
[2,3,5,4,1,8,6,7]=>[4,5,3,2,1,8,6,7]=>1110010=>0001101
[1,8,4,6,3,5,2,7]=>[1,6,4,3,5,8,2,7]=>0111000=>1000111
[5,4,8,6,2,1,3,7]=>[6,2,8,4,1,5,3,7]=>1111000=>0000111
[2,3,6,8,1,5,4,7]=>[8,3,2,1,5,6,4,7]=>1111000=>0000111
[2,7,6,1,8,5,4,3]=>[8,5,6,2,1,4,7,3]=>1110100=>0001011
[1,8,7,6,3,2,4,5]=>[1,6,3,7,2,8,4,5]=>0111000=>1000111
[5,7,8,6,2,3,4,1]=>[6,2,8,3,7,4,5,1]=>1111000=>0000111
[6,3,5,1,7,2,4,8]=>[7,5,3,1,6,2,4,8]=>1110100=>0001011
[2,3,4,7,6,1,5,8]=>[6,4,3,2,1,7,5,8]=>1111100=>0000011
[7,3,5,8,4,1,2,6]=>[8,4,5,3,1,7,2,6]=>1111000=>0000111
[7,3,5,8,4,1,6,2]=>[8,4,5,3,1,6,7,2]=>1111000=>0000111
[6,3,5,4,7,1,8,2]=>[4,8,7,5,3,1,6,2]=>1110101=>0001010
[6,3,5,4,7,1,2,8]=>[4,7,5,3,1,6,2,8]=>1110100=>0001011
[3,4,1,5,6,8,7,2]=>[7,8,6,5,4,1,3,2]=>1101110=>0010001
[3,7,1,6,8,5,2,4]=>[8,5,6,1,3,2,7,4]=>1101100=>0010011
[2,3,1,8,6,4,7,5]=>[3,2,1,6,4,7,8,5]=>1101100=>0010011
[2,3,1,8,6,4,5,7]=>[3,2,1,6,4,8,5,7]=>1101100=>0010011
[7,3,5,4,6,8,2,1]=>[4,8,6,5,3,2,7,1]=>1110110=>0001001
[1,8,4,5,2,6,3,7]=>[1,5,4,2,6,8,3,7]=>0111000=>1000111
[6,4,8,5,3,1,2,7]=>[5,3,8,4,1,6,2,7]=>1111000=>0000111
[2,3,4,6,5,8,1,7]=>[5,8,6,4,3,2,1,7]=>1111010=>0000101
[2,3,4,7,5,1,8,6]=>[5,8,7,4,3,2,1,6]=>1111001=>0000110
[2,3,4,7,1,6,5,8]=>[6,7,4,3,2,1,5,8]=>1111000=>0000111
[2,3,4,7,1,6,8,5]=>[6,8,7,4,3,2,1,5]=>1111001=>0000110
[2,3,4,6,1,8,7,5]=>[7,8,6,4,3,2,1,5]=>1111010=>0000101
[1,8,4,5,2,3,6,7]=>[1,5,4,2,8,3,6,7]=>0111000=>1000111
[7,4,8,5,3,2,6,1]=>[5,3,8,4,2,6,7,1]=>1111000=>0000111
[5,2,4,6,8,3,7,1]=>[2,7,8,4,3,6,5,1]=>1011100=>0100011
[1,5,7,4,6,3,2,8]=>[1,4,6,3,7,5,2,8]=>0110100=>1001011
[5,2,8,4,6,3,7,1]=>[2,4,6,3,7,8,5,1]=>1010100=>0101011
[3,8,5,4,6,7,2,1]=>[4,7,6,5,2,8,3,1]=>1110110=>0001001
[6,8,3,4,5,7,2,1]=>[3,4,5,7,2,8,6,1]=>1100010=>0011101
[2,5,7,4,6,3,8,1]=>[4,6,3,8,7,5,2,1]=>1110101=>0001010
[5,4,1,7,8,3,2,6]=>[8,4,1,3,7,5,2,6]=>1101100=>0010011
[5,4,2,7,8,3,6,1]=>[8,4,2,3,6,7,5,1]=>1101100=>0010011
[5,1,4,6,8,3,2,7]=>[8,4,3,6,5,1,2,7]=>1011100=>0100011
[5,1,8,4,6,3,2,7]=>[4,6,3,8,5,1,2,7]=>1010100=>0101011
[8,1,6,4,5,3,2,7]=>[4,5,6,3,8,1,2,7]=>1010000=>0101111
[8,1,3,5,4,6,2,7]=>[3,5,4,6,8,1,2,7]=>1001000=>0110111
[8,1,6,2,4,3,5,7]=>[6,1,2,4,8,3,5,7]=>1010000=>0101111
[8,7,1,2,4,3,5,6]=>[7,1,4,8,2,3,5,6]=>1100000=>0011111
[1,7,6,2,4,3,5,8]=>[1,6,2,4,7,3,5,8]=>0110000=>1001111
[8,7,3,2,4,6,5,1]=>[3,6,7,2,4,5,8,1]=>1100000=>0011111
[8,2,6,3,4,5,7,1]=>[2,6,3,4,5,7,8,1]=>1010000=>0101111
[8,7,2,4,5,3,6,1]=>[4,5,7,2,3,6,8,1]=>1100000=>0011111
[8,7,1,3,4,5,2,6]=>[7,1,3,4,5,8,2,6]=>1100000=>0011111
[8,1,6,3,4,5,2,7]=>[6,3,4,5,8,1,2,7]=>1010000=>0101111
[8,1,2,5,4,3,6,7]=>[5,4,8,1,2,3,6,7]=>1001000=>0110111
[3,2,8,6,1,5,4,7]=>[2,6,3,1,5,8,4,7]=>1011000=>0100111
[8,6,1,2,4,3,5,7]=>[6,1,4,8,2,3,5,7]=>1100000=>0011111
[8,7,2,4,5,6,3,1]=>[4,5,6,7,2,3,8,1]=>1100000=>0011111
[5,3,6,2,4,8,7,1]=>[7,8,6,3,2,4,5,1]=>1110010=>0001101
[3,5,2,8,6,1,4,7]=>[6,2,3,1,8,5,4,7]=>1101100=>0010011
[5,1,8,6,2,3,4,7]=>[6,1,2,8,3,5,4,7]=>1011000=>0100111
[2,5,4,1,8,6,3,7]=>[4,2,1,6,8,5,3,7]=>1110100=>0001011
[3,7,6,1,8,2,5,4]=>[8,1,6,5,7,3,2,4]=>1110100=>0001011
[8,2,3,6,1,4,7,5]=>[2,3,6,1,7,8,4,5]=>1001000=>0110111
[1,8,2,6,3,4,7,5]=>[1,6,2,3,7,8,4,5]=>0101000=>1010111
[8,1,3,6,4,7,2,5]=>[3,7,6,4,8,1,2,5]=>1001010=>0110101
[7,1,3,6,4,8,2,5]=>[3,8,6,4,7,1,2,5]=>1001010=>0110101
[8,2,1,3,5,7,4,6]=>[2,5,7,1,3,4,8,6]=>1000010=>0111101
[8,2,6,3,1,4,7,5]=>[2,6,3,7,8,1,4,5]=>1010000=>0101111
[7,5,4,1,3,8,2,6]=>[4,1,5,3,8,2,7,6]=>1110010=>0001101
[7,3,8,5,4,1,2,6]=>[5,4,8,3,1,7,2,6]=>1111000=>0000111
[1,3,7,2,5,8,4,6]=>[1,5,8,3,2,4,7,6]=>0110010=>1001101
[1,7,2,3,5,8,4,6]=>[1,5,8,2,3,4,7,6]=>0100010=>1011101
[7,4,8,1,3,6,2,5]=>[6,8,1,4,3,7,2,5]=>1110000=>0001111
[8,1,2,3,5,7,4,6]=>[5,7,1,2,3,4,8,6]=>1000010=>0111101
[7,1,2,3,5,8,4,6]=>[5,8,1,2,3,4,7,6]=>1000010=>0111101
[2,6,3,7,1,4,8,5]=>[3,8,7,2,1,6,4,5]=>1101001=>0010110
[2,6,3,8,1,4,7,5]=>[3,7,8,2,1,6,4,5]=>1101000=>0010111
[7,5,4,8,1,3,2,6]=>[8,4,1,5,3,7,2,6]=>1111000=>0000111
[8,5,4,7,1,3,2,6]=>[7,4,1,5,3,8,2,6]=>1111000=>0000111
[2,3,1,8,5,4,6,7]=>[3,2,1,5,8,4,6,7]=>1101000=>0010111
[8,6,5,1,3,4,2,7]=>[5,1,6,3,4,8,2,7]=>1110000=>0001111
[3,5,2,6,7,1,8,4]=>[8,7,2,3,1,6,5,4]=>1101101=>0010010
[3,2,8,4,7,5,1,6]=>[2,4,7,5,8,3,1,6]=>1010100=>0101011
[8,4,7,5,1,3,2,6]=>[5,1,7,4,3,8,2,6]=>1111000=>0000111
[3,8,1,6,5,2,7,4]=>[5,6,1,3,2,7,8,4]=>1101000=>0010111
[6,1,2,8,3,4,7,5]=>[7,8,1,2,3,6,4,5]=>1001000=>0110111
[3,7,2,5,6,1,8,4]=>[6,5,2,3,1,8,7,4]=>1101101=>0010010
[6,8,4,2,5,1,7,3]=>[4,2,5,7,8,1,6,3]=>1110000=>0001111
[8,3,2,1,5,7,4,6]=>[3,2,5,7,1,4,8,6]=>1100010=>0011101
[2,8,3,6,4,7,1,5]=>[3,7,6,4,8,2,1,5]=>1101010=>0010101
[7,3,6,4,8,1,2,5]=>[4,8,3,1,6,2,7,5]=>1110100=>0001011
[1,2,8,3,5,7,4,6]=>[1,2,5,7,3,4,8,6]=>0010010=>1101101
[1,8,3,2,5,7,4,6]=>[1,3,5,7,2,4,8,6]=>0100010=>1011101
[6,5,1,7,4,2,8,3]=>[8,7,4,5,1,6,2,3]=>1101001=>0010110
[7,3,6,4,8,2,1,5]=>[4,8,3,2,6,1,7,5]=>1110100=>0001011
[4,6,1,7,3,5,2,8]=>[7,1,3,5,6,4,2,8]=>1101000=>0010111
[5,6,1,7,3,4,2,8]=>[7,1,3,6,4,5,2,8]=>1101000=>0010111
[6,1,7,3,4,2,8,5]=>[8,7,3,4,6,1,2,5]=>1010001=>0101110
[5,1,7,4,2,8,6,3]=>[4,8,6,7,1,2,5,3]=>1010010=>0101101
[4,2,8,6,5,1,7,3]=>[2,5,6,1,7,8,4,3]=>1011000=>0100111
[6,4,2,8,5,1,7,3]=>[5,7,8,4,2,6,1,3]=>1101000=>0010111
[8,6,4,7,1,5,2,3]=>[7,4,1,5,6,2,8,3]=>1111000=>0000111
[7,6,4,8,1,5,2,3]=>[8,4,1,5,6,2,7,3]=>1111000=>0000111
[2,4,3,8,1,6,7,5]=>[3,6,7,8,4,2,1,5]=>1101000=>0010111
[5,1,6,4,2,3,7,8]=>[4,6,1,2,5,3,7,8]=>1010000=>0101111
[6,4,7,8,1,5,2,3]=>[8,1,5,7,4,2,6,3]=>1111000=>0000111
[8,7,4,6,1,5,2,3]=>[6,4,1,5,7,2,8,3]=>1111000=>0000111
[6,5,7,8,1,4,2,3]=>[8,1,7,4,5,2,6,3]=>1111000=>0000111
[4,7,8,6,1,5,2,3]=>[6,1,5,8,2,7,4,3]=>1111000=>0000111
[8,6,5,7,1,4,2,3]=>[7,1,5,4,6,2,8,3]=>1111000=>0000111
[5,1,6,7,4,2,3,8]=>[7,4,6,1,2,5,3,8]=>1011000=>0100111
[6,7,4,8,1,5,2,3]=>[8,4,1,5,7,2,6,3]=>1111000=>0000111
[8,4,7,6,1,5,2,3]=>[6,1,5,7,4,2,8,3]=>1111000=>0000111
[2,4,7,1,5,8,6,3]=>[5,8,6,7,2,1,4,3]=>1110010=>0001101
[3,2,4,7,6,1,5,8]=>[2,6,4,3,1,7,5,8]=>1011100=>0100011
[8,5,6,7,1,4,2,3]=>[7,1,6,4,5,2,8,3]=>1111000=>0000111
[7,6,8,5,1,4,2,3]=>[5,1,8,4,6,2,7,3]=>1111000=>0000111
[6,8,7,5,1,4,2,3]=>[5,1,7,4,8,2,6,3]=>1111000=>0000111
[4,6,8,7,1,5,2,3]=>[7,1,5,8,2,6,4,3]=>1111000=>0000111
[3,2,4,6,1,5,7,8]=>[2,6,4,3,1,5,7,8]=>1011000=>0100111
[6,7,8,5,1,4,2,3]=>[5,1,8,4,7,2,6,3]=>1111000=>0000111
[3,1,7,5,4,2,8,6]=>[5,4,8,7,3,1,2,6]=>1011001=>0100110
[4,1,8,5,2,3,6,7]=>[5,1,2,8,4,3,6,7]=>1011000=>0100111
[5,4,1,3,6,7,2,8]=>[4,1,3,7,6,5,2,8]=>1100110=>0011001
[8,4,1,2,6,3,7,5]=>[4,1,6,2,3,7,8,5]=>1100100=>0011011
[8,2,7,1,5,3,4,6]=>[2,5,7,1,8,3,4,6]=>1010000=>0101111
[3,2,7,1,5,8,4,6]=>[2,5,8,3,1,4,7,6]=>1010010=>0101101
[6,3,7,1,5,4,2,8]=>[5,7,3,1,4,6,2,8]=>1110000=>0001111
[4,5,1,3,6,8,2,7]=>[8,6,5,1,3,4,2,7]=>1100110=>0011001
[3,6,8,1,5,4,2,7]=>[5,8,1,4,6,3,2,7]=>1110000=>0001111
[3,6,2,1,5,8,4,7]=>[5,8,6,2,3,1,4,7]=>1100010=>0011101
[8,6,2,1,5,3,4,7]=>[5,6,2,8,1,3,4,7]=>1100000=>0011111
[4,8,2,1,7,5,3,6]=>[7,5,8,2,4,1,3,6]=>1100100=>0011011
[7,1,3,2,8,6,4,5]=>[3,6,8,1,2,4,7,5]=>1000100=>0111011
[2,7,8,1,5,3,4,6]=>[5,8,2,1,7,3,4,6]=>1110000=>0001111
[6,7,2,1,5,3,4,8]=>[5,7,2,6,1,3,4,8]=>1100000=>0011111
[4,7,2,1,8,5,3,6]=>[8,5,7,2,4,1,3,6]=>1100100=>0011011
[8,7,5,6,1,4,3,2]=>[6,1,5,4,7,3,8,2]=>1111000=>0000111
[5,7,8,6,1,4,3,2]=>[6,1,8,4,7,3,5,2]=>1111000=>0000111
[2,7,4,1,6,5,3,8]=>[4,2,1,6,5,7,3,8]=>1110100=>0001011
[5,6,8,7,1,4,3,2]=>[7,1,8,4,6,3,5,2]=>1111000=>0000111
[6,8,5,7,1,4,3,2]=>[7,1,5,4,8,3,6,2]=>1111000=>0000111
[8,6,5,7,1,4,3,2]=>[7,1,5,4,6,3,8,2]=>1111000=>0000111
[8,5,7,6,1,4,3,2]=>[6,1,7,4,5,3,8,2]=>1111000=>0000111
[7,2,3,1,5,6,4,8]=>[2,3,5,6,7,1,4,8]=>1000000=>0111111
[4,2,8,1,6,5,3,7]=>[2,6,5,8,1,4,3,7]=>1010100=>0101011
[6,2,4,1,8,5,3,7]=>[2,4,1,8,5,6,3,7]=>1010100=>0101011
[8,3,1,4,5,6,7,2]=>[3,1,4,5,6,7,8,2]=>1100000=>0011111
[5,3,1,4,8,6,7,2]=>[3,1,4,6,7,8,5,2]=>1100100=>0011011
[7,5,1,6,3,4,8,2]=>[6,1,3,5,4,8,7,2]=>1101001=>0010110
[5,3,1,8,4,6,7,2]=>[3,1,6,7,8,4,5,2]=>1101000=>0010111
[8,3,1,5,4,6,7,2]=>[3,1,5,4,6,7,8,2]=>1101000=>0010111
[8,2,6,1,4,5,3,7]=>[2,6,1,4,5,8,3,7]=>1010000=>0101111
[6,2,8,1,4,5,3,7]=>[2,8,1,4,5,6,3,7]=>1010000=>0101111
[7,2,6,1,5,3,4,8]=>[2,5,6,1,7,3,4,8]=>1010000=>0101111
[2,8,6,1,5,3,4,7]=>[5,6,2,1,8,3,4,7]=>1110000=>0001111
[4,2,1,5,6,3,8,7]=>[2,6,5,4,1,3,8,7]=>1001101=>0110010
[7,1,2,5,8,3,4,6]=>[8,5,1,2,3,7,4,6]=>1001100=>0110011
[7,1,4,5,6,8,3,2]=>[8,6,5,4,3,7,1,2]=>1011110=>0100001
[7,6,8,5,1,4,3,2]=>[5,1,8,4,6,3,7,2]=>1111000=>0000111
[6,8,7,5,1,4,3,2]=>[5,1,7,4,8,3,6,2]=>1111000=>0000111
[2,6,7,1,4,5,3,8]=>[7,2,1,4,5,6,3,8]=>1110000=>0001111
[3,5,1,7,4,6,8,2]=>[6,8,7,4,5,1,3,2]=>1101001=>0010110
[7,1,6,5,4,8,3,2]=>[5,4,8,6,3,7,1,2]=>1011010=>0100101
[5,7,6,8,1,4,3,2]=>[8,1,6,4,7,3,5,2]=>1111000=>0000111
[4,3,1,6,5,8,7,2]=>[3,1,5,7,8,6,4,2]=>1101010=>0010101
[5,3,1,2,4,8,7,6]=>[3,1,5,2,4,7,8,6]=>1100010=>0011101
[5,3,7,2,1,4,6,8]=>[7,3,2,5,1,4,6,8]=>1110000=>0001111
[7,2,4,5,8,3,1,6]=>[2,8,5,4,3,7,1,6]=>1011100=>0100011
[6,2,4,5,1,8,7,3]=>[2,5,4,1,7,8,6,3]=>1011010=>0100101
[1,7,4,2,6,3,5,8]=>[1,4,2,6,3,7,5,8]=>0110100=>1001011
[8,7,4,5,2,1,6,3]=>[5,4,2,7,1,6,8,3]=>1111000=>0000111
[6,3,7,1,8,4,2,5]=>[8,3,1,4,7,2,6,5]=>1110100=>0001011
[5,7,4,1,6,3,2,8]=>[4,1,6,3,7,5,2,8]=>1110100=>0001011
[1,7,4,8,6,3,2,5]=>[1,6,4,3,8,2,7,5]=>0111100=>1000011
[5,7,4,8,6,3,1,2]=>[6,4,3,8,1,7,5,2]=>1111100=>0000011
[4,8,3,5,6,7,1,2]=>[3,7,6,5,1,8,4,2]=>1101110=>0010001
[4,8,1,5,6,7,2,3]=>[7,6,5,1,8,4,2,3]=>1101110=>0010001
[5,8,4,3,6,1,2,7]=>[4,3,6,1,8,5,2,7]=>1110100=>0001011
[5,3,8,4,1,7,2,6]=>[4,7,3,1,5,2,8,6]=>1110010=>0001101
[1,4,8,3,6,7,5,2]=>[1,7,6,5,8,3,4,2]=>0110110=>1001001
[3,8,4,2,6,1,5,7]=>[4,2,6,3,1,8,5,7]=>1110100=>0001011
[1,8,2,5,6,7,4,3]=>[1,7,6,5,4,8,2,3]=>0101110=>1010001
[3,8,1,5,6,7,4,2]=>[7,6,5,4,8,1,3,2]=>1101110=>0010001
[8,2,1,5,6,7,4,3]=>[2,7,6,5,4,8,1,3]=>1001110=>0110001
[7,1,4,3,6,2,5,8]=>[4,3,6,1,2,7,5,8]=>1010100=>0101011
[7,8,4,3,6,2,1,5]=>[4,3,6,2,8,1,7,5]=>1110100=>0001011
[4,3,1,8,5,7,6,2]=>[3,1,5,7,6,8,4,2]=>1101010=>0010101
[4,3,1,6,8,7,5,2]=>[3,1,7,5,8,6,4,2]=>1101110=>0010001
[6,3,1,8,2,7,4,5]=>[3,1,7,2,8,6,4,5]=>1101010=>0010101
[6,3,5,8,2,7,1,4]=>[7,3,2,5,1,8,6,4]=>1111010=>0000101
[7,5,4,8,6,2,1,3]=>[6,4,2,8,5,1,7,3]=>1111100=>0000011
[7,1,4,8,6,2,3,5]=>[6,4,1,2,8,3,7,5]=>1011100=>0100011
[7,5,4,1,6,2,3,8]=>[4,1,6,5,2,7,3,8]=>1110100=>0001011
[7,6,4,5,8,1,3,2]=>[8,5,4,1,6,3,7,2]=>1111100=>0000011
[1,6,4,5,8,2,3,7]=>[1,8,5,4,2,6,3,7]=>0111100=>1000011
[7,3,6,1,8,2,4,5]=>[8,3,1,6,2,4,7,5]=>1110100=>0001011
[8,3,5,2,1,7,4,6]=>[5,3,2,7,1,4,8,6]=>1110010=>0001101
[8,4,2,5,6,7,1,3]=>[7,6,5,4,2,8,1,3]=>1101110=>0010001
[4,1,8,5,6,7,3,2]=>[7,6,5,3,8,4,1,2]=>1011110=>0100001
[1,2,8,5,6,7,3,4]=>[1,2,7,6,5,3,8,4]=>0011110=>1100001
[4,2,1,5,6,7,3,8]=>[2,7,6,5,4,1,3,8]=>1001110=>0110001
[1,5,3,8,6,7,4,2]=>[1,3,7,6,4,8,5,2]=>0101110=>1010001
[4,3,5,8,1,7,2,6]=>[7,3,1,5,4,2,8,6]=>1111010=>0000101
[3,5,4,8,6,1,2,7]=>[6,4,1,8,5,3,2,7]=>1111100=>0000011
[1,4,8,5,6,7,2,3]=>[1,7,6,5,2,8,4,3]=>0111110=>1000001
[3,4,8,5,6,7,1,2]=>[7,6,5,1,8,4,3,2]=>1111110=>0000001
[2,7,1,5,6,3,4,8]=>[6,5,2,1,3,7,4,8]=>1101100=>0010011
[2,7,1,4,3,6,5,8]=>[4,6,7,2,1,3,5,8]=>1100000=>0011111
[2,6,3,1,4,5,8,7]=>[3,6,2,1,4,5,8,7]=>1100001=>0011110
[3,7,1,5,6,2,8,4]=>[6,5,1,3,2,8,7,4]=>1101101=>0010010
[4,7,1,5,6,8,2,3]=>[8,6,5,1,7,4,2,3]=>1101110=>0010001
[8,4,2,6,3,7,1,5]=>[7,6,4,2,3,8,1,5]=>1101010=>0010101
[4,7,3,2,5,6,1,8]=>[3,5,6,7,2,4,1,8]=>1100000=>0011111
[5,3,4,6,2,8,1,7]=>[8,6,4,3,2,5,1,7]=>1111010=>0000101
[5,3,7,4,2,8,1,6]=>[4,8,3,2,5,1,7,6]=>1110010=>0001101
[6,4,7,2,3,8,1,5]=>[8,2,4,3,7,6,1,5]=>1110010=>0001101
[5,3,7,2,4,8,6,1]=>[8,6,7,3,2,4,5,1]=>1110010=>0001101
[2,6,5,1,8,3,4,7]=>[8,5,2,1,6,3,4,7]=>1110100=>0001011
[8,7,6,1,3,2,5,4]=>[6,1,7,3,5,8,2,4]=>1110000=>0001111
[8,7,2,4,3,1,6,5]=>[4,7,2,3,6,8,1,5]=>1100000=>0011111
[8,7,4,5,1,6,2,3]=>[5,4,1,6,7,2,8,3]=>1111000=>0000111
[8,5,6,4,1,7,2,3]=>[4,7,6,1,5,2,8,3]=>1110010=>0001101
[8,5,6,3,1,2,7,4]=>[6,3,5,1,7,8,2,4]=>1110000=>0001111
[8,3,5,4,2,1,7,6]=>[4,5,3,2,7,8,1,6]=>1110000=>0001111
[5,7,3,4,2,1,8,6]=>[3,4,8,7,2,5,1,6]=>1100001=>0011110
[6,7,4,2,3,1,8,5]=>[4,2,8,7,3,6,1,5]=>1110001=>0001110
[6,7,5,3,1,2,8,4]=>[5,3,8,7,1,6,2,4]=>1110001=>0001110
[6,7,5,4,1,8,2,3]=>[4,5,1,8,2,7,6,3]=>1110010=>0001101
[5,10,1,2,3,4,6,7,8,9]=>[10,1,5,2,3,4,6,7,8,9]=>110000000=>001111111
[2,11,1,3,4,5,6,7,8,9,10]=>[11,2,1,3,4,5,6,7,8,9,10]=>1100000000=>0011111111
[7,3,5,4,1,8,6,2]=>[4,5,3,1,8,6,7,2]=>1110010=>0001101
[2,6,5,7,3,1,4,8]=>[7,3,5,2,1,6,4,8]=>1111000=>0000111
[2,6,5,7,3,1,8,4]=>[8,7,3,5,2,1,6,4]=>1111001=>0000110
[6,3,2,4,7,5,8,1]=>[3,2,4,8,7,5,6,1]=>1100101=>0011010
[4,2,1,6,3,7,8,5]=>[2,8,7,6,4,1,3,5]=>1001011=>0110100
[7,4,3,5,8,6,1,2]=>[3,6,8,5,4,1,7,2]=>1101100=>0010011
[2,7,6,8,3,1,4,5]=>[8,3,6,2,1,7,4,5]=>1111000=>0000111
[7,4,3,5,8,6,2,1]=>[3,6,8,5,4,2,7,1]=>1101100=>0010011
[4,2,1,7,3,8,6,5]=>[2,8,6,7,4,1,3,5]=>1001010=>0110101
[4,2,1,3,7,8,6,5]=>[2,4,1,3,8,6,7,5]=>1000110=>0111001
[3,7,8,6,2,1,4,5]=>[6,2,8,3,1,7,4,5]=>1111000=>0000111
[4,2,1,8,3,5,6,7]=>[2,8,4,1,3,5,6,7]=>1001000=>0110111
[4,2,1,3,6,8,7,5]=>[2,4,1,3,7,8,6,5]=>1000110=>0111001
[4,2,1,6,3,8,7,5]=>[2,7,8,6,4,1,3,5]=>1001010=>0110101
[3,6,7,5,2,1,4,8]=>[5,2,7,3,1,6,4,8]=>1111000=>0000111
[4,8,6,2,7,3,5,1]=>[7,2,6,5,8,3,4,1]=>1110100=>0001011
[3,7,6,8,4,2,5,1]=>[8,4,6,2,5,7,3,1]=>1111000=>0000111
[5,8,1,7,4,2,6,3]=>[7,4,6,8,1,5,2,3]=>1101000=>0010111
[3,7,8,6,2,4,5,1]=>[6,2,8,4,5,7,3,1]=>1111000=>0000111
[4,2,1,3,8,6,7,5]=>[2,4,1,3,6,7,8,5]=>1000100=>0111011
[4,8,1,7,3,6,5,2]=>[6,7,1,3,5,8,4,2]=>1101000=>0010111
[4,7,8,6,3,5,2,1]=>[6,3,5,8,2,7,4,1]=>1111000=>0000111
[2,6,1,5,4,7,8,3]=>[5,4,8,7,6,2,1,3]=>1101011=>0010100
[4,6,3,5,8,7,1,2]=>[3,7,5,1,8,6,4,2]=>1101110=>0010001
[3,5,6,1,4,8,7,2]=>[7,8,6,1,4,5,3,2]=>1110010=>0001101
[2,7,5,1,8,3,4,6]=>[8,5,2,1,7,3,4,6]=>1110100=>0001011
[4,7,5,2,1,3,6,8]=>[5,2,7,1,4,3,6,8]=>1110000=>0001111
[3,5,6,2,4,1,7,8]=>[6,2,4,5,3,1,7,8]=>1110000=>0001111
[6,7,8,4,1,5,3,2]=>[4,8,1,5,7,3,6,2]=>1110000=>0001111
[7,4,6,5,2,8,1,3]=>[5,2,8,6,4,1,7,3]=>1111010=>0000101
[7,1,5,6,4,2,3,8]=>[6,4,5,1,2,7,3,8]=>1011000=>0100111
[5,7,4,6,8,1,3,2]=>[8,4,1,6,3,7,5,2]=>1111100=>0000011
[5,7,8,1,4,6,3,2]=>[6,8,1,4,7,3,5,2]=>1110000=>0001111
[8,1,5,7,4,6,3,2]=>[6,7,4,5,3,8,1,2]=>1011000=>0100111
[6,1,8,4,7,5,3,2]=>[4,7,5,8,3,6,1,2]=>1010100=>0101011
[4,8,5,1,6,7,3,2]=>[7,6,5,1,8,3,4,2]=>1110110=>0001001
[8,1,4,5,6,7,3,2]=>[7,6,5,4,3,8,1,2]=>1011110=>0100001
[4,8,5,2,1,6,7,3]=>[5,2,6,7,8,1,4,3]=>1110000=>0001111
[5,1,8,4,2,6,3,7]=>[4,6,8,1,2,5,3,7]=>1010000=>0101111
[1,8,4,6,2,5,3,7]=>[1,6,4,2,5,8,3,7]=>0111000=>1000111
[6,1,5,2,3,4,7,8]=>[5,1,2,6,3,4,7,8]=>1010000=>0101111
[8,3,1,4,6,2,5,7]=>[3,1,4,6,2,8,5,7]=>1100100=>0011011
[3,5,1,8,2,6,4,7]=>[6,8,1,3,2,5,4,7]=>1101000=>0010111
[3,5,1,2,8,4,7,6]=>[7,8,5,1,3,2,4,6]=>1100100=>0011011
[2,3,5,8,6,1,7,4]=>[6,3,2,1,7,8,5,4]=>1111100=>0000011
[8,2,4,3,6,7,1,5]=>[2,4,3,7,6,1,8,5]=>1010110=>0101001
[3,6,2,8,5,1,7,4]=>[5,7,8,2,3,1,6,4]=>1101000=>0010111
[8,2,7,1,5,4,6,3]=>[2,5,7,1,4,6,8,3]=>1010000=>0101111
[7,2,5,3,6,8,1,4]=>[2,8,6,5,3,7,1,4]=>1010110=>0101001
[7,3,1,5,6,2,4,8]=>[3,1,6,5,2,7,4,8]=>1101100=>0010011
[8,7,2,4,1,6,5,3]=>[4,6,7,2,5,8,1,3]=>1100000=>0011111
[1,8,7,2,3,6,5,4]=>[1,6,7,2,5,8,3,4]=>0110000=>1001111
[1,7,8,2,6,4,3,5]=>[1,6,2,4,8,3,7,5]=>0110100=>1001011
[1,7,3,8,2,6,4,5]=>[1,3,6,8,2,7,4,5]=>0101000=>1010111
[1,2,7,3,6,4,5,8]=>[1,2,6,3,4,7,5,8]=>0010100=>1101011
[7,1,5,8,3,2,4,6]=>[8,3,5,1,2,7,4,6]=>1011000=>0100111
[1,6,2,8,4,3,7,5]=>[1,7,8,4,6,2,3,5]=>0101000=>1010111
[1,3,8,7,2,4,6,5]=>[1,7,3,2,6,8,4,5]=>0111000=>1000111
[1,8,3,7,2,5,4,6]=>[1,3,7,2,5,8,4,6]=>0101000=>1010111
[8,1,4,7,3,2,5,6]=>[7,4,3,8,1,2,5,6]=>1011000=>0100111
[7,1,4,2,3,5,6,8]=>[4,1,2,7,3,5,6,8]=>1010000=>0101111
[8,2,1,4,7,3,5,6]=>[2,4,7,1,3,8,5,6]=>1000100=>0111011
[2,1,3,8,4,6,7,5]=>[2,1,3,6,7,8,4,5]=>1001000=>0110111
[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,5,6]=>0000100=>1111011
[2,4,8,7,5,6,3,1]=>[5,6,7,3,8,4,2,1]=>1111000=>0000111
[2,5,3,8,4,7,6,1]=>[3,7,6,8,4,5,2,1]=>1101010=>0010101
[2,8,5,7,3,6,4,1]=>[6,7,3,5,4,8,2,1]=>1111000=>0000111
[3,1,8,5,2,7,6,4]=>[5,3,1,2,7,6,8,4]=>1011010=>0100101
[8,3,5,7,1,6,4,2]=>[6,7,3,1,5,4,8,2]=>1111000=>0000111
[8,3,6,1,4,5,7,2]=>[6,3,1,4,5,7,8,2]=>1110000=>0001111
[2,8,6,3,4,5,7,1]=>[6,3,4,5,7,8,2,1]=>1110000=>0001111
[2,6,8,3,4,5,7,1]=>[7,8,3,4,5,6,2,1]=>1110000=>0001111
[2,5,7,3,4,8,6,1]=>[8,6,7,3,4,5,2,1]=>1110010=>0001101
[2,7,8,5,3,6,4,1]=>[5,3,6,8,4,7,2,1]=>1111000=>0000111
[3,1,8,7,2,6,4,5]=>[6,7,3,1,2,8,4,5]=>1011000=>0100111
[3,1,7,8,2,5,6,4]=>[8,3,1,2,5,6,7,4]=>1011000=>0100111
[3,1,6,5,8,2,7,4]=>[7,8,5,3,1,2,6,4]=>1011100=>0100011
[7,3,8,5,1,6,4,2]=>[5,3,1,6,8,4,7,2]=>1111000=>0000111
[7,3,6,1,4,8,5,2]=>[8,6,3,1,4,5,7,2]=>1110010=>0001101
[7,4,8,1,2,3,6,5]=>[8,1,4,2,6,7,3,5]=>1110000=>0001111
[7,5,1,2,3,4,8,6]=>[5,1,8,7,2,3,4,6]=>1100001=>0011110
[7,4,6,1,2,8,3,5]=>[8,6,1,4,2,7,3,5]=>1110010=>0001101
[3,6,8,1,2,7,4,5]=>[7,1,8,6,3,2,4,5]=>1110010=>0001101
[4,8,6,1,2,3,7,5]=>[6,1,7,8,2,4,3,5]=>1110000=>0001111
[8,4,6,1,2,3,7,5]=>[6,1,4,2,7,8,3,5]=>1110000=>0001111
[4,8,1,5,2,7,3,6]=>[5,1,7,4,2,3,8,6]=>1101010=>0010101
[4,1,2,5,3,8,7,6]=>[5,4,1,2,3,7,8,6]=>1001010=>0110101
[4,3,6,8,7,5,1,2]=>[7,5,8,3,1,6,4,2]=>1111100=>0000011
[5,4,1,8,2,7,6,3]=>[7,6,8,4,1,5,2,3]=>1101010=>0010101
[5,4,1,8,2,7,3,6]=>[7,4,1,5,2,3,8,6]=>1101010=>0010101
[6,4,8,1,2,5,3,7]=>[8,1,4,2,5,6,3,7]=>1110000=>0001111
[5,4,1,6,8,2,7,3]=>[7,8,4,1,6,5,2,3]=>1101100=>0010011
[5,4,7,1,2,8,6,3]=>[8,6,7,1,4,2,5,3]=>1110010=>0001101
[6,5,1,2,3,7,8,4]=>[5,1,8,7,6,2,3,4]=>1100011=>0011100
[6,5,1,2,3,4,8,7]=>[5,1,6,2,3,4,8,7]=>1100001=>0011110
[8,6,5,1,2,3,7,4]=>[5,1,6,2,7,8,3,4]=>1110000=>0001111
[2,4,6,3,5,7,1,8]=>[5,7,6,3,4,2,1,8]=>1110010=>0001101
[1,4,6,3,7,2,5,8]=>[1,7,3,4,2,6,5,8]=>0110100=>1001011
[8,6,2,5,3,1,7,4]=>[5,2,3,6,1,7,8,4]=>1101000=>0010111
[8,2,3,4,5,1,7,6]=>[2,3,4,5,7,8,1,6]=>1000000=>0111111
[1,8,3,4,2,7,5,6]=>[1,3,4,7,2,5,8,6]=>0100010=>1011101
[2,8,3,4,1,6,7,5]=>[3,4,6,7,8,2,1,5]=>1100000=>0011111
[7,8,2,4,3,1,6,5]=>[4,8,2,3,6,7,1,5]=>1100000=>0011111
[4,5,8,2,3,1,7,6]=>[7,8,2,5,3,4,1,6]=>1110000=>0001111
[6,1,3,5,7,2,4,8]=>[3,7,5,1,2,6,4,8]=>1001100=>0110011
[8,1,3,6,2,4,7,5]=>[3,6,1,2,7,8,4,5]=>1001000=>0110111
[2,1,8,3,7,5,4,6]=>[2,1,7,5,8,3,4,6]=>1010100=>0101011
[6,2,5,8,1,4,7,3]=>[2,7,8,1,5,4,6,3]=>1011000=>0100111
[8,2,7,1,4,6,5,3]=>[2,6,7,1,4,5,8,3]=>1010000=>0101111
[1,3,8,2,5,7,4,6]=>[1,5,7,3,2,4,8,6]=>0110010=>1001101
[2,8,7,1,6,4,5,3]=>[6,2,1,4,7,5,8,3]=>1110100=>0001011
[3,4,8,5,6,1,7,2]=>[6,5,1,7,8,4,3,2]=>1111100=>0000011
[1,4,8,6,2,7,3,5]=>[1,7,6,2,8,4,3,5]=>0111010=>1000101
[6,2,3,1,5,4,7,8]=>[2,3,5,6,1,4,7,8]=>1000000=>0111111
[7,2,3,1,4,6,5,8]=>[2,3,6,7,1,4,5,8]=>1000000=>0111111
[8,2,3,1,4,5,7,6]=>[2,3,7,8,1,4,5,6]=>1000000=>0111111
[2,6,1,4,5,3,7,8]=>[4,5,6,2,1,3,7,8]=>1100000=>0011111
[3,6,4,1,5,2,7,8]=>[4,1,5,6,3,2,7,8]=>1110000=>0001111
[2,7,1,3,5,6,4,8]=>[5,6,7,2,1,3,4,8]=>1100000=>0011111
[8,6,1,2,4,3,7,5]=>[6,1,4,7,8,2,3,5]=>1100000=>0011111
[2,8,1,3,4,6,7,5]=>[6,7,8,2,1,3,4,5]=>1100000=>0011111
[7,8,1,2,5,3,6,4]=>[5,8,1,6,7,2,3,4]=>1100000=>0011111
[3,8,4,1,2,5,7,6]=>[4,1,7,8,3,2,5,6]=>1110000=>0001111
[1,2,6,7,5,3,8,4]=>[1,2,5,8,7,3,6,4]=>0011001=>1100110
[1,7,5,3,2,8,4,6]=>[1,5,3,8,2,4,7,6]=>0110010=>1001101
[1,6,7,5,3,8,4,2]=>[1,5,3,8,4,7,6,2]=>0111010=>1000101
[1,3,8,2,6,5,7,4]=>[1,6,5,7,8,3,2,4]=>0110100=>1001011
[1,2,5,7,6,3,4,8]=>[1,2,6,3,7,5,4,8]=>0011100=>1100011
[1,5,7,6,2,3,4,8]=>[1,6,2,7,3,5,4,8]=>0111000=>1000111
[1,5,3,8,2,6,4,7]=>[1,3,6,8,2,5,4,7]=>0101000=>1010111
[1,4,8,3,2,5,7,6]=>[1,7,8,3,4,2,5,6]=>0110000=>1001111
[1,4,8,3,5,7,6,2]=>[1,5,7,6,8,3,4,2]=>0110010=>1001101
[1,2,4,8,3,5,7,6]=>[1,2,7,8,4,3,5,6]=>0011000=>1100111
[1,3,8,4,2,6,7,5]=>[1,4,6,7,8,3,2,5]=>0110000=>1001111
[1,4,8,2,3,5,7,6]=>[1,7,8,2,4,3,5,6]=>0110000=>1001111
[6,5,7,3,8,2,4,1]=>[8,3,7,5,2,4,6,1]=>1110100=>0001011
[4,2,6,7,5,8,3,1]=>[2,5,8,3,7,6,4,1]=>1011010=>0100101
[5,6,8,3,1,7,2,4]=>[7,3,8,6,1,5,2,4]=>1110010=>0001101
[3,4,7,1,8,6,2,5]=>[6,8,1,4,3,2,7,5]=>1110100=>0001011
[3,5,2,8,6,4,1,7]=>[6,4,8,5,2,3,1,7]=>1101100=>0010011
[7,4,2,5,3,8,1,6]=>[5,4,2,3,8,1,7,6]=>1101010=>0010101
[3,1,2,8,5,6,4,7]=>[3,1,2,5,6,8,4,7]=>1001000=>0110111
[5,2,1,6,8,3,4,7]=>[2,8,1,3,6,5,4,7]=>1001100=>0110011
[5,2,6,8,4,1,3,7]=>[2,8,4,6,1,5,3,7]=>1011000=>0100111
[1,5,6,8,3,4,2,7]=>[1,8,3,6,4,5,2,7]=>0111000=>1000111
[4,5,1,6,8,3,2,7]=>[8,1,3,6,5,4,2,7]=>1101100=>0010011
[4,5,7,3,8,2,6,1]=>[8,3,6,7,5,2,4,1]=>1110100=>0001011
[7,1,3,5,4,8,2,6]=>[3,5,4,8,1,2,7,6]=>1001010=>0110101
[5,7,3,8,4,6,1,2]=>[3,6,8,4,7,1,5,2]=>1101000=>0010111
[4,6,3,7,8,5,2,1]=>[3,8,5,7,2,6,4,1]=>1101100=>0010011
[4,6,1,7,3,8,5,2]=>[8,1,3,5,7,6,4,2]=>1101010=>0010101
[6,3,7,1,8,4,5,2]=>[8,3,1,4,7,5,6,2]=>1110100=>0001011
[6,7,2,4,8,1,5,3]=>[4,8,2,7,5,6,1,3]=>1100100=>0011011
[3,2,5,6,7,8,1,4]=>[2,8,3,1,7,6,5,4]=>1011110=>0100001
[6,7,1,3,2,8,4,5]=>[8,1,3,7,6,2,4,5]=>1100010=>0011101
[6,2,7,1,3,4,8,5]=>[2,8,7,1,6,3,4,5]=>1010001=>0101110
[5,2,1,7,3,8,4,6]=>[2,8,1,3,5,4,7,6]=>1001010=>0110101
[6,4,2,7,1,8,3,5]=>[8,4,2,7,6,1,3,5]=>1101010=>0010101
[4,2,6,3,7,8,1,5]=>[2,8,3,4,1,7,6,5]=>1010110=>0101001
[4,2,6,3,7,8,5,1]=>[2,8,5,7,6,3,4,1]=>1010110=>0101001
[3,6,2,7,4,1,8,5]=>[8,7,4,6,2,3,1,5]=>1101001=>0010110
[6,7,3,2,1,4,8,5]=>[3,8,7,2,6,1,4,5]=>1100001=>0011110
[7,2,4,1,8,3,5,6]=>[2,4,1,8,3,7,5,6]=>1010100=>0101011
[7,2,4,8,6,1,3,5]=>[2,6,4,1,8,3,7,5]=>1011100=>0100011
[7,3,4,8,6,2,1,5]=>[6,4,3,2,8,1,7,5]=>1111100=>0000011
[3,5,7,2,1,8,6,4]=>[8,6,7,2,5,3,1,4]=>1110010=>0001101
[6,2,4,7,1,8,5,3]=>[2,8,4,1,5,7,6,3]=>1011010=>0100101
[1,7,4,8,5,2,6,3]=>[1,5,8,4,2,6,7,3]=>0111000=>1000111
[1,3,7,8,5,2,6,4]=>[1,5,8,3,2,6,7,4]=>0111000=>1000111
[2,5,7,8,1,6,3,4]=>[6,8,2,1,7,3,5,4]=>1111000=>0000111
[6,3,7,1,8,2,5,4]=>[8,3,1,7,5,6,2,4]=>1110100=>0001011
[5,6,1,2,7,8,4,3]=>[8,1,4,7,6,5,2,3]=>1100110=>0011001
[6,7,2,1,8,5,3,4]=>[8,5,7,2,6,1,3,4]=>1100100=>0011011
[6,7,2,8,5,4,1,3]=>[5,8,4,7,2,6,1,3]=>1101000=>0010111
[1,8,2,4,6,3,5,7]=>[1,4,6,2,3,8,5,7]=>0100100=>1011011
[1,3,7,4,6,2,5,8]=>[1,4,6,3,2,7,5,8]=>0110100=>1001011
[1,5,7,4,3,6,2,8]=>[1,4,6,7,3,5,2,8]=>0110000=>1001111
[1,8,4,5,3,6,2,7]=>[1,5,4,3,6,8,2,7]=>0111000=>1000111
[1,8,2,4,6,3,7,5]=>[1,4,6,2,3,7,8,5]=>0100100=>1011011
[1,8,2,5,4,6,7,3]=>[1,5,4,6,7,8,2,3]=>0101000=>1010111
[1,3,7,4,6,2,8,5]=>[1,4,6,3,2,8,7,5]=>0110101=>1001010
[1,4,7,5,2,6,8,3]=>[1,5,2,6,8,7,4,3]=>0111001=>1000110
[4,5,2,7,1,3,8,6]=>[8,7,2,5,4,1,3,6]=>1101001=>0010110
[2,5,4,7,1,6,8,3]=>[6,8,7,4,2,1,5,3]=>1111001=>0000110
[6,2,4,8,5,1,7,3]=>[2,5,7,8,4,1,6,3]=>1011000=>0100111
[6,2,5,4,8,3,7,1]=>[2,4,7,8,5,3,6,1]=>1010100=>0101011
[6,4,3,5,8,2,7,1]=>[3,7,8,5,4,2,6,1]=>1101100=>0010011
[5,2,3,4,8,1,6,7]=>[2,3,4,8,5,1,6,7]=>1000100=>0111011
[5,3,4,8,1,6,2,7]=>[6,8,4,3,1,5,2,7]=>1111000=>0000111
[6,2,4,8,5,1,3,7]=>[2,5,8,4,1,6,3,7]=>1011000=>0100111
[1,4,3,7,8,2,5,6]=>[1,3,8,4,2,7,5,6]=>0101100=>1010011
[1,5,7,4,2,8,6,3]=>[1,4,8,6,7,2,5,3]=>0110010=>1001101
[1,3,7,2,8,6,4,5]=>[1,6,8,3,2,4,7,5]=>0110100=>1001011
[1,5,3,6,8,2,7,4]=>[1,3,7,8,2,6,5,4]=>0101100=>1010011
[5,2,6,4,7,8,3,1]=>[2,4,8,3,7,6,5,1]=>1010110=>0101001
[4,2,6,7,3,8,5,1]=>[2,8,3,5,7,6,4,1]=>1011010=>0100101
[4,6,5,2,3,1,8,7]=>[5,2,6,3,4,1,8,7]=>1110001=>0001110
[6,4,2,5,3,1,8,7]=>[5,4,2,3,6,1,8,7]=>1101001=>0010110
[6,4,2,5,3,8,7,1]=>[5,4,2,3,7,8,6,1]=>1101010=>0010101
[8,6,4,7,5,2,3,1]=>[5,7,4,2,6,3,8,1]=>1111000=>0000111
[8,6,2,7,4,5,3,1]=>[7,4,5,6,2,3,8,1]=>1101000=>0010111
[4,6,5,2,3,8,7,1]=>[5,2,7,8,6,3,4,1]=>1110010=>0001101
[6,8,7,4,5,2,3,1]=>[4,5,7,2,8,3,6,1]=>1110000=>0001111
[4,8,6,7,5,2,3,1]=>[5,7,2,6,3,8,4,1]=>1111000=>0000111
[6,8,4,7,5,2,3,1]=>[5,7,4,2,8,3,6,1]=>1111000=>0000111
[8,6,4,7,2,5,3,1]=>[7,4,2,5,6,3,8,1]=>1111000=>0000111
[8,6,2,4,7,5,3,1]=>[4,7,5,6,2,3,8,1]=>1100100=>0011011
[4,8,2,6,7,5,3,1]=>[7,5,6,2,3,8,4,1]=>1101100=>0010011
[2,8,4,6,7,5,3,1]=>[7,5,6,4,3,8,2,1]=>1111100=>0000011
[2,8,6,7,4,5,3,1]=>[7,4,5,6,3,8,2,1]=>1111000=>0000111
[6,8,7,2,4,5,3,1]=>[7,2,4,5,8,3,6,1]=>1110000=>0001111
[2,6,4,5,8,7,3,1]=>[7,5,4,3,8,6,2,1]=>1111110=>0000001
[2,6,4,8,7,5,3,1]=>[7,5,8,4,3,6,2,1]=>1111100=>0000011
[8,2,4,6,7,5,3,1]=>[2,7,5,6,4,3,8,1]=>1011100=>0100011
[6,2,4,8,7,5,3,1]=>[2,7,5,8,4,3,6,1]=>1011100=>0100011
[4,2,6,8,7,5,3,1]=>[2,7,5,8,3,6,4,1]=>1011100=>0100011
[4,2,6,5,8,7,3,1]=>[2,7,5,3,8,6,4,1]=>1011110=>0100001
[6,2,4,5,8,7,3,1]=>[2,7,5,4,3,8,6,1]=>1011110=>0100001
[8,2,6,7,4,5,3,1]=>[2,7,4,5,6,3,8,1]=>1011000=>0100111
[6,4,5,2,8,7,3,1]=>[7,5,2,4,3,8,6,1]=>1110110=>0001001
[6,4,5,8,7,2,3,1]=>[7,2,8,5,4,3,6,1]=>1111100=>0000011
[8,6,7,4,2,5,3,1]=>[4,7,2,5,6,3,8,1]=>1110000=>0001111
[6,2,8,7,4,5,3,1]=>[2,7,4,5,8,3,6,1]=>1011000=>0100111
[6,4,8,7,5,2,3,1]=>[5,7,2,8,4,3,6,1]=>1111000=>0000111
[4,6,8,7,5,2,3,1]=>[5,7,2,8,3,6,4,1]=>1111000=>0000111
[4,6,5,8,7,2,3,1]=>[7,2,8,5,3,6,4,1]=>1111100=>0000011
[2,1,6,8,7,4,5,3]=>[2,1,7,4,8,5,6,3]=>1011100=>0100011
[2,6,8,7,4,5,3,1]=>[7,4,5,8,3,6,2,1]=>1111000=>0000111
[2,4,8,6,7,5,3,1]=>[7,5,6,3,8,4,2,1]=>1111100=>0000011
[4,2,8,6,7,5,3,1]=>[2,7,5,6,3,8,4,1]=>1011100=>0100011
[6,2,8,4,7,5,3,1]=>[2,4,7,5,8,3,6,1]=>1010100=>0101011
[8,2,6,4,7,5,3,1]=>[2,4,7,5,6,3,8,1]=>1010100=>0101011
[6,4,8,2,7,5,3,1]=>[7,5,8,2,4,3,6,1]=>1110100=>0001011
[4,6,8,2,7,5,3,1]=>[7,5,8,2,6,3,4,1]=>1110100=>0001011
[2,6,8,4,7,5,3,1]=>[4,7,5,8,3,6,2,1]=>1110100=>0001011
[4,6,5,8,2,7,3,1]=>[7,2,5,3,8,6,4,1]=>1111010=>0000101
[2,1,6,8,4,7,5,3]=>[2,1,7,4,5,8,6,3]=>1011010=>0100101
[2,1,8,6,4,7,5,3]=>[2,1,7,6,4,5,8,3]=>1011010=>0100101
[6,8,7,4,2,5,3,1]=>[4,7,2,5,8,3,6,1]=>1110000=>0001111
[2,8,6,4,7,5,3,1]=>[4,7,5,6,3,8,2,1]=>1110100=>0001011
[4,8,6,2,7,5,3,1]=>[7,5,6,2,8,3,4,1]=>1110100=>0001011
[4,2,5,6,3,8,1,7]=>[2,8,6,3,5,4,1,7]=>1011010=>0100101
[8,5,2,1,4,7,6,3]=>[5,2,4,7,6,8,1,3]=>1100010=>0011101
[6,7,3,2,5,8,4,1]=>[3,5,8,2,4,7,6,1]=>1100010=>0011101
[3,2,6,4,8,1,5,7]=>[2,4,8,3,1,6,5,7]=>1010100=>0101011
[2,3,6,4,7,8,5,1]=>[4,8,5,7,6,3,2,1]=>1110110=>0001001
[5,7,8,2,6,3,4,1]=>[6,2,8,3,4,7,5,1]=>1110100=>0001011
[7,3,1,2,5,8,6,4]=>[3,1,5,8,6,7,2,4]=>1100010=>0011101
[1,6,3,5,2,4,8,7]=>[1,3,5,2,6,4,8,7]=>0101001=>1010110
[3,4,8,2,7,5,1,6]=>[7,5,8,2,4,3,1,6]=>1110100=>0001011
[6,3,2,8,5,7,4,1]=>[3,2,5,7,4,8,6,1]=>1101010=>0010101
[2,4,8,1,5,3,7,6]=>[5,7,8,2,1,4,3,6]=>1110000=>0001111
[3,4,8,1,6,2,7,5]=>[6,1,4,3,2,7,8,5]=>1110100=>0001011
[1,8,4,6,7,3,5,2]=>[1,7,4,3,6,5,8,2]=>0111100=>1000011
[8,1,6,3,4,5,7,2]=>[6,3,4,5,7,8,1,2]=>1010000=>0101111
[7,6,5,4,1,2,8,3]=>[4,5,1,6,2,8,7,3]=>1110001=>0001110
[5,7,6,8,3,4,2,1]=>[8,3,6,4,7,2,5,1]=>1111000=>0000111
[2,8,1,6,5,7,4,3]=>[5,7,6,4,8,2,1,3]=>1101010=>0010101
[4,6,8,2,5,3,7,1]=>[5,7,8,2,6,3,4,1]=>1110000=>0001111
[5,2,3,7,6,1,8,4]=>[2,3,6,1,8,7,5,4]=>1001101=>0110010
[8,1,2,4,6,7,3,5]=>[4,7,6,1,2,3,8,5]=>1000110=>0111001
[5,2,6,8,4,3,1,7]=>[2,8,4,6,3,5,1,7]=>1011000=>0100111
[7,8,1,5,4,3,6,2]=>[5,4,8,1,3,6,7,2]=>1101000=>0010111
[3,7,5,1,8,4,6,2]=>[8,5,1,4,6,7,3,2]=>1110100=>0001011
[2,7,8,5,4,6,1,3]=>[5,4,6,8,2,1,7,3]=>1111000=>0000111
[8,3,1,7,4,2,5,6]=>[3,1,7,4,8,2,5,6]=>1101000=>0010111
[3,1,8,2,4,5,7,6]=>[7,8,3,1,2,4,5,6]=>1010000=>0101111
[8,1,3,7,6,2,4,5]=>[3,6,1,2,7,4,8,5]=>1001100=>0110011
[4,3,2,8,5,7,1,6]=>[3,2,5,7,4,1,8,6]=>1101010=>0010101
[4,7,3,2,5,1,8,6]=>[3,5,8,7,2,4,1,6]=>1100001=>0011110
[3,2,4,7,5,8,6,1]=>[2,5,8,6,7,4,3,1]=>1011010=>0100101
[4,2,3,8,6,5,1,7]=>[2,3,6,5,8,4,1,7]=>1001100=>0110011
[3,7,8,5,6,1,2,4]=>[6,5,1,8,3,2,7,4]=>1111100=>0000011
[3,6,1,8,4,7,2,5]=>[7,4,8,6,1,3,2,5]=>1101010=>0010101
[3,1,6,8,4,7,2,5]=>[7,4,8,6,3,1,2,5]=>1011010=>0100101
[4,6,1,8,3,2,7,5]=>[7,8,1,3,6,4,2,5]=>1101000=>0010111
[4,7,8,1,3,2,6,5]=>[8,1,6,7,3,4,2,5]=>1110000=>0001111
[2,7,8,3,4,6,5,1]=>[6,8,3,4,5,7,2,1]=>1110000=>0001111
[4,6,1,8,2,3,7,5]=>[7,8,1,6,4,2,3,5]=>1101000=>0010111
[4,5,2,1,8,3,7,6]=>[7,8,5,2,4,1,3,6]=>1100100=>0011011
[4,6,2,8,1,3,7,5]=>[7,8,2,6,4,1,3,5]=>1101000=>0010111
[3,6,2,8,4,7,1,5]=>[7,4,8,6,2,3,1,5]=>1101010=>0010101
[2,3,6,8,4,7,5,1]=>[7,4,5,8,6,3,2,1]=>1111010=>0000101
[3,2,6,8,4,7,1,5]=>[2,7,4,8,6,3,1,5]=>1011010=>0100101
[4,2,5,1,8,3,7,6]=>[2,7,8,5,1,4,3,6]=>1010100=>0101011
[4,1,2,5,8,3,7,6]=>[7,8,5,4,1,2,3,6]=>1001100=>0110011
[5,2,4,1,3,8,7,6]=>[2,4,1,5,3,7,8,6]=>1010010=>0101101
[5,4,2,1,3,8,7,6]=>[4,2,5,1,3,7,8,6]=>1100010=>0011101
[5,1,4,2,3,8,7,6]=>[4,1,2,5,3,7,8,6]=>1010010=>0101101
[5,4,1,3,2,8,7,6]=>[4,1,3,5,2,7,8,6]=>1100010=>0011101
[4,5,3,1,8,2,7,6]=>[3,7,8,5,1,4,2,6]=>1100100=>0011011
[4,5,1,3,8,2,7,6]=>[7,8,5,1,3,4,2,6]=>1100100=>0011011
[3,1,5,4,8,7,2,6]=>[4,7,5,3,1,2,8,6]=>1010110=>0101001
[3,5,4,1,8,7,2,6]=>[4,1,7,5,3,2,8,6]=>1110110=>0001001
[3,6,5,8,7,1,2,4]=>[7,1,8,5,3,2,6,4]=>1111100=>0000011
[3,4,5,1,8,7,2,6]=>[7,5,1,4,3,2,8,6]=>1110110=>0001001
[3,4,1,5,8,7,2,6]=>[7,5,4,1,3,2,8,6]=>1101110=>0010001
[4,1,3,5,8,2,7,6]=>[3,7,8,5,4,1,2,6]=>1001100=>0110011
[5,3,1,4,2,8,7,6]=>[3,1,4,5,2,7,8,6]=>1100010=>0011101
[5,1,3,4,2,8,7,6]=>[3,4,5,1,2,7,8,6]=>1000010=>0111101
[5,1,3,2,4,8,7,6]=>[3,5,1,2,4,7,8,6]=>1000010=>0111101
[5,3,2,1,4,8,7,6]=>[3,2,5,1,4,7,8,6]=>1100010=>0011101
[4,3,2,5,8,1,7,6]=>[3,2,7,8,5,4,1,6]=>1101100=>0010011
[3,4,2,5,8,7,1,6]=>[7,5,4,2,3,1,8,6]=>1101110=>0010001
[4,2,3,5,8,1,7,6]=>[2,3,7,8,5,4,1,6]=>1001100=>0110011
[5,1,2,3,4,8,7,6]=>[5,1,2,3,4,7,8,6]=>1000010=>0111101
[6,7,5,3,8,2,4,1]=>[8,5,3,7,2,4,6,1]=>1110100=>0001011
[8,2,1,6,3,4,5,7]=>[2,6,1,3,8,4,5,7]=>1001000=>0110111
[8,3,5,6,2,4,1,7]=>[6,3,2,5,4,8,1,7]=>1111000=>0000111
[8,6,2,1,3,5,4,7]=>[6,2,5,8,1,3,4,7]=>1100000=>0011111
[8,1,2,3,4,6,5,7]=>[6,8,1,2,3,4,5,7]=>1000000=>0111111
[6,2,3,7,8,4,5,1]=>[2,3,8,4,7,5,6,1]=>1001100=>0110011
[7,3,1,6,5,8,4,2]=>[3,1,5,8,6,4,7,2]=>1101010=>0010101
[1,5,6,7,3,4,8,2]=>[1,8,7,3,6,4,5,2]=>0111001=>1000110
[6,7,8,2,1,4,5,3]=>[8,2,7,1,4,5,6,3]=>1110000=>0001111
[5,3,8,4,7,2,6,1]=>[4,7,3,2,6,8,5,1]=>1110100=>0001011
[8,1,3,7,6,4,2,5]=>[3,6,4,7,1,2,8,5]=>1001100=>0110011
[5,3,1,7,8,6,2,4]=>[3,1,6,8,2,7,5,4]=>1101100=>0010011
[3,5,8,2,7,1,6,4]=>[7,2,6,8,5,3,1,4]=>1110100=>0001011
[6,2,8,5,3,1,7,4]=>[2,5,3,7,8,1,6,4]=>1011000=>0100111
[8,2,6,4,7,1,3,5]=>[2,4,7,1,6,3,8,5]=>1010100=>0101011
[3,8,6,5,2,1,7,4]=>[5,2,6,3,1,7,8,4]=>1111000=>0000111
[8,3,7,4,2,5,6,1]=>[4,7,3,2,5,6,8,1]=>1110000=>0001111
[4,8,5,7,2,1,3,6]=>[7,2,5,1,8,4,3,6]=>1111000=>0000111
[3,4,1,8,2,6,7,5]=>[6,7,8,4,1,3,2,5]=>1101000=>0010111
[8,4,6,3,7,1,5,2]=>[7,3,4,1,6,5,8,2]=>1110100=>0001011
[6,8,3,4,1,5,7,2]=>[3,4,7,8,1,5,6,2]=>1100000=>0011111
[5,1,7,6,2,8,4,3]=>[8,6,1,2,7,4,5,3]=>1011010=>0100101
[6,8,2,5,7,4,1,3]=>[7,5,4,8,2,6,1,3]=>1101100=>0010011
[2,5,7,6,3,1,8,4]=>[6,3,8,7,2,1,5,4]=>1111001=>0000110
[4,2,8,3,1,5,6,7]=>[2,8,3,4,1,5,6,7]=>1010000=>0101111
[4,2,7,1,8,5,3,6]=>[2,8,5,7,1,4,3,6]=>1010100=>0101011
[4,2,1,8,7,5,6,3]=>[2,7,5,6,8,4,1,3]=>1001100=>0110011
[5,7,8,4,3,1,6,2]=>[4,8,3,6,7,1,5,2]=>1110000=>0001111
[2,7,4,5,8,3,6,1]=>[8,5,4,3,6,7,2,1]=>1111100=>0000011
[3,5,7,1,4,8,6,2]=>[8,6,7,1,4,5,3,2]=>1110010=>0001101
[7,2,8,5,1,4,6,3]=>[2,5,1,8,4,6,7,3]=>1011000=>0100111
[1,6,5,3,8,4,2,7]=>[1,8,5,3,4,6,2,7]=>0110100=>1001011
[4,8,6,1,3,5,2,7]=>[6,1,5,8,3,4,2,7]=>1110000=>0001111
[1,8,3,2,4,7,5,6]=>[1,3,7,2,4,5,8,6]=>0100010=>1011101
[4,3,7,2,5,8,1,6]=>[5,8,3,2,4,1,7,6]=>1110010=>0001101
[3,2,4,7,8,5,6,1]=>[2,8,5,6,7,4,3,1]=>1011100=>0100011
[8,2,1,3,4,5,7,6]=>[2,7,8,1,3,4,5,6]=>1000000=>0111111
[4,6,8,3,2,1,5,7]=>[8,3,6,2,4,1,5,7]=>1110000=>0001111
[3,2,6,8,5,4,1,7]=>[2,5,8,4,6,3,1,7]=>1011000=>0100111
[4,2,5,3,8,7,6,1]=>[2,7,6,8,5,3,4,1]=>1010110=>0101001
[4,8,2,6,5,3,1,7]=>[5,6,2,3,8,4,1,7]=>1101000=>0010111
[2,6,8,5,4,1,3,7]=>[5,4,8,2,1,6,3,7]=>1111000=>0000111
[3,1,8,6,5,4,2,7]=>[5,6,4,8,3,1,2,7]=>1011000=>0100111
[6,4,8,3,7,2,5,1]=>[7,3,4,2,8,5,6,1]=>1110100=>0001011
[4,7,3,6,2,1,8,5]=>[3,6,2,8,7,4,1,5]=>1101001=>0010110
[5,4,3,7,1,8,2,6]=>[3,8,4,1,5,2,7,6]=>1101010=>0010101
[7,3,8,5,1,4,2,6]=>[5,3,1,8,4,7,2,6]=>1111000=>0000111
[5,4,8,7,6,2,1,3]=>[6,2,7,4,1,8,5,3]=>1111100=>0000011
[4,8,5,7,3,1,6,2]=>[7,3,5,1,6,8,4,2]=>1111000=>0000111
[1,5,4,8,3,7,6,2]=>[1,7,6,8,4,3,5,2]=>0111010=>1000101
[4,7,8,3,1,6,5,2]=>[6,8,3,5,7,1,4,2]=>1110000=>0001111
[8,7,5,3,6,4,2,1]=>[6,5,3,4,7,2,8,1]=>1110100=>0001011
[4,6,1,3,8,7,5,2]=>[7,5,8,6,1,3,4,2]=>1100110=>0011001
[3,7,1,6,4,2,8,5]=>[6,4,8,7,1,3,2,5]=>1101001=>0010110
[3,1,2,7,5,6,8,4]=>[3,1,2,5,6,8,7,4]=>1001001=>0110110
[8,5,2,3,6,7,4,1]=>[7,6,5,2,3,4,8,1]=>1100110=>0011001
[6,3,2,4,8,7,5,1]=>[3,2,4,7,5,8,6,1]=>1100110=>0011001
[6,3,2,8,7,5,1,4]=>[3,2,7,5,8,1,6,4]=>1101100=>0010011
[7,3,8,2,6,5,1,4]=>[6,5,8,3,2,7,1,4]=>1110100=>0001011
[5,2,8,1,7,6,3,4]=>[2,6,7,1,8,5,3,4]=>1010100=>0101011
[5,6,1,2,8,7,4,3]=>[7,1,4,8,6,5,2,3]=>1100110=>0011001
[7,5,2,8,1,6,4,3]=>[6,8,2,5,4,7,1,3]=>1101000=>0010111
[2,7,6,8,1,5,4,3]=>[8,2,1,5,6,4,7,3]=>1111000=>0000111
[7,2,1,8,3,6,5,4]=>[2,6,8,1,3,5,7,4]=>1001000=>0110111
[9,6,5,4,3,2,8,1,7]=>[4,5,3,6,2,8,1,9,7]=>11100010=>00011101
[6,5,4,8,3,2,7,1]=>[7,8,4,3,5,2,6,1]=>1111000=>0000111
[7,3,1,4,8,2,5,6]=>[3,1,4,8,2,7,5,6]=>1100100=>0011011
[6,7,4,2,5,1,3,8]=>[4,2,5,7,1,6,3,8]=>1110000=>0001111
[4,7,5,1,6,2,8,3]=>[6,5,1,8,7,2,4,3]=>1110101=>0001010
[5,7,4,6,3,1,8,2]=>[6,4,3,8,7,1,5,2]=>1111001=>0000110
[7,5,1,4,3,2,8,6]=>[4,5,1,3,8,7,2,6]=>1100001=>0011110
[8,6,4,2,3,7,5,1]=>[4,2,7,6,3,5,8,1]=>1110010=>0001101
[6,4,7,1,3,8,5,2]=>[8,1,4,3,5,7,6,2]=>1110010=>0001101
[5,4,2,7,3,1,6,8]=>[7,4,2,3,5,1,6,8]=>1101000=>0010111
[4,5,1,2,7,6,8,3]=>[6,8,7,5,1,4,2,3]=>1100101=>0011010
[5,4,6,8,3,1,2,7]=>[8,3,6,4,1,5,2,7]=>1111000=>0000111
[1,3,8,4,5,7,2,6]=>[1,4,5,7,3,2,8,6]=>0110010=>1001101
[1,3,7,4,2,8,5,6]=>[1,4,8,3,2,5,7,6]=>0110010=>1001101
[7,5,8,6,2,1,3,4]=>[6,2,8,1,5,3,7,4]=>1111000=>0000111
[2,8,7,3,5,4,1,6]=>[5,7,3,4,8,2,1,6]=>1110000=>0001111
[7,3,8,4,1,2,6,5]=>[4,8,3,1,6,7,2,5]=>1110000=>0001111
[6,8,3,2,7,1,5,4]=>[3,7,2,8,5,6,1,4]=>1100100=>0011011
[2,8,5,6,3,7,1,4]=>[7,6,3,5,2,1,8,4]=>1111010=>0000101
[7,4,2,5,8,1,6,3]=>[8,5,4,2,6,7,1,3]=>1101100=>0010011
[2,7,8,3,4,5,1,6]=>[8,3,4,5,7,2,1,6]=>1110000=>0001111
[7,5,6,8,2,1,4,3]=>[8,2,6,1,5,4,7,3]=>1111000=>0000111
[2,8,6,5,3,4,1,7]=>[5,3,6,4,8,2,1,7]=>1111000=>0000111
[1,7,2,3,5,6,8,4]=>[1,5,6,8,7,2,3,4]=>0100001=>1011110
[3,7,4,2,1,5,6,8]=>[4,2,7,3,1,5,6,8]=>1110000=>0001111
[3,4,6,2,8,5,7,1]=>[7,8,5,6,2,4,3,1]=>1110100=>0001011
[4,2,1,7,5,8,3,6]=>[2,5,8,4,1,3,7,6]=>1001010=>0110101
[3,7,4,1,2,5,8,6]=>[4,1,8,7,3,2,5,6]=>1110001=>0001110
[4,7,3,6,5,1,8,2]=>[3,5,6,1,8,7,4,2]=>1101001=>0010110
[4,2,6,8,7,3,1,5]=>[2,7,3,8,4,1,6,5]=>1011100=>0100011
[3,4,6,1,8,5,2,7]=>[8,5,6,1,4,3,2,7]=>1110100=>0001011
[4,1,6,7,5,8,2,3]=>[5,8,1,2,7,6,4,3]=>1011010=>0100101
[4,3,7,1,6,8,2,5]=>[8,6,3,1,4,2,7,5]=>1110110=>0001001
[4,1,7,3,6,5,2,8]=>[6,5,7,3,4,1,2,8]=>1010100=>0101011
[4,1,7,3,6,2,5,8]=>[6,3,4,1,2,7,5,8]=>1010100=>0101011
[5,8,7,6,1,2,4,3]=>[6,1,7,2,8,4,5,3]=>1111000=>0000111
[5,8,7,6,2,1,3,4]=>[6,2,7,1,8,3,5,4]=>1111000=>0000111
[4,2,7,3,6,5,8,1]=>[2,6,5,8,7,3,4,1]=>1010101=>0101010
[3,8,2,4,5,6,7,1]=>[4,5,6,7,8,2,3,1]=>1100000=>0011111
[3,8,2,4,1,6,7,5]=>[4,6,7,8,2,3,1,5]=>1100000=>0011111
[2,8,6,5,3,7,1,4]=>[5,3,7,6,2,1,8,4]=>1111010=>0000101
[3,8,2,1,4,6,7,5]=>[6,7,8,2,3,1,4,5]=>1100000=>0011111
[4,2,7,5,6,1,8,3]=>[2,6,5,1,8,7,4,3]=>1011101=>0100010
[3,2,6,1,4,5,8,7]=>[2,6,3,1,4,5,8,7]=>1010001=>0101110
[2,8,7,3,4,5,1,6]=>[7,3,4,5,8,2,1,6]=>1110000=>0001111
[5,8,7,6,1,3,4,2]=>[6,1,7,3,8,4,5,2]=>1111000=>0000111
[5,8,7,6,2,3,4,1]=>[6,2,7,3,8,4,5,1]=>1111000=>0000111
[3,8,1,5,2,6,4,7]=>[5,1,3,2,6,8,4,7]=>1101000=>0010111
[2,8,7,5,3,4,1,6]=>[5,3,7,4,8,2,1,6]=>1111000=>0000111
[2,8,7,5,4,3,1,6]=>[5,4,7,3,8,2,1,6]=>1111000=>0000111
[5,8,7,6,1,3,2,4]=>[6,1,7,3,8,2,5,4]=>1111000=>0000111
[5,8,7,6,4,1,2,3]=>[6,4,7,1,8,2,5,3]=>1111000=>0000111
[5,4,2,3,7,6,8,1]=>[4,2,3,6,8,7,5,1]=>1100101=>0011010
[7,4,3,5,2,8,1,6]=>[3,5,4,2,8,1,7,6]=>1101010=>0010101
[8,4,3,7,5,1,6,2]=>[3,5,7,4,1,6,8,2]=>1101000=>0010111
[3,6,4,7,5,2,8,1]=>[5,8,7,4,2,6,3,1]=>1111001=>0000110
[4,7,5,6,1,3,8,2]=>[6,1,5,3,8,7,4,2]=>1111001=>0000110
[5,7,6,4,3,1,8,2]=>[4,6,3,8,7,1,5,2]=>1110001=>0001110
[6,7,1,3,8,4,2,5]=>[8,1,3,4,7,2,6,5]=>1100100=>0011011
[7,6,1,3,4,8,5,2]=>[8,6,1,3,4,5,7,2]=>1100010=>0011101
[3,6,5,2,7,8,1,4]=>[8,5,2,7,6,3,1,4]=>1110110=>0001001
[4,8,3,6,5,2,1,7]=>[3,5,6,2,8,4,1,7]=>1101000=>0010111
[1,8,6,5,4,2,3,7]=>[1,5,4,6,2,8,3,7]=>0111000=>1000111
[1,8,7,2,3,5,4,6]=>[1,7,2,5,8,3,4,6]=>0110000=>1001111
[1,8,7,2,5,3,4,6]=>[1,5,7,2,8,3,4,6]=>0110000=>1001111
[3,6,8,5,1,2,4,7]=>[5,1,8,3,2,6,4,7]=>1111000=>0000111
[7,1,2,8,3,5,6,4]=>[8,1,2,3,5,6,7,4]=>1001000=>0110111
[6,1,7,8,2,5,3,4]=>[8,1,2,5,7,3,6,4]=>1011000=>0100111
[7,1,4,5,8,6,2,3]=>[6,8,5,4,1,2,7,3]=>1011100=>0100011
[5,7,6,4,2,8,1,3]=>[4,8,6,2,7,1,5,3]=>1110010=>0001101
[7,5,6,1,2,8,4,3]=>[8,6,1,5,2,4,7,3]=>1110010=>0001101
[4,1,3,7,8,6,2,5]=>[3,6,8,4,1,2,7,5]=>1001100=>0110011
[5,1,4,3,6,8,7,2]=>[4,3,7,8,6,5,1,2]=>1010110=>0101001
[4,5,7,6,8,2,1,3]=>[8,2,6,1,7,5,4,3]=>1111100=>0000011
[5,6,8,4,7,3,2,1]=>[4,7,3,8,2,6,5,1]=>1110100=>0001011
[6,4,7,8,5,2,1,3]=>[5,8,2,7,4,1,6,3]=>1111000=>0000111
[3,6,4,8,5,1,2,7]=>[5,8,4,1,6,3,2,7]=>1111000=>0000111
[3,7,4,8,1,2,5,6]=>[8,4,1,7,3,2,5,6]=>1111000=>0000111
[8,7,1,3,5,4,6,2]=>[5,7,1,3,4,6,8,2]=>1100000=>0011111
[3,1,4,8,2,5,7,6]=>[7,8,4,3,1,2,5,6]=>1011000=>0100111
[6,8,2,3,7,4,1,5]=>[7,2,3,4,8,1,6,5]=>1100100=>0011011
[8,1,3,6,2,5,4,7]=>[3,6,1,2,5,8,4,7]=>1001000=>0110111
[8,1,5,6,2,3,7,4]=>[6,1,2,5,3,7,8,4]=>1011000=>0100111
[8,1,4,5,3,2,6,7]=>[5,4,3,8,1,2,6,7]=>1011000=>0100111
[8,1,4,3,5,2,6,7]=>[4,3,5,8,1,2,6,7]=>1010000=>0101111
[2,6,3,1,5,4,7,8]=>[3,5,6,2,1,4,7,8]=>1100000=>0011111
[6,3,2,1,5,4,7,8]=>[3,2,5,6,1,4,7,8]=>1100000=>0011111
[7,3,1,5,4,2,6,8]=>[3,1,5,4,7,2,6,8]=>1101000=>0010111
[2,3,6,1,5,4,7,8]=>[5,6,3,2,1,4,7,8]=>1110000=>0001111
[3,5,2,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>1100000=>0011111
[6,2,4,1,5,3,7,8]=>[2,4,1,5,6,3,7,8]=>1010000=>0101111
[2,6,4,1,5,3,7,8]=>[4,2,1,5,6,3,7,8]=>1110000=>0001111
[2,6,5,1,3,7,4,8]=>[5,2,1,7,6,3,4,8]=>1110010=>0001101
[7,6,1,2,4,5,3,8]=>[6,1,4,5,7,2,3,8]=>1100000=>0011111
[6,7,1,2,8,3,5,4]=>[8,1,7,5,6,2,3,4]=>1100100=>0011011
[2,4,6,1,5,3,7,8]=>[5,6,2,1,4,3,7,8]=>1110000=>0001111
[4,7,1,3,5,2,6,8]=>[5,7,1,3,4,2,6,8]=>1100000=>0011111
[5,7,1,4,2,6,3,8]=>[4,6,7,1,5,2,3,8]=>1100000=>0011111
[5,7,1,6,2,3,8,4]=>[6,1,8,7,2,3,5,4]=>1101001=>0010110
[5,6,3,1,2,7,4,8]=>[3,7,6,1,5,2,4,8]=>1100010=>0011101
[4,2,5,3,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>1010000=>0101111
[5,3,6,1,2,7,4,8]=>[7,6,3,1,5,2,4,8]=>1110010=>0001101
[3,4,6,1,5,2,7,8]=>[5,6,1,4,3,2,7,8]=>1110000=>0001111
[8,2,7,5,4,1,3,6]=>[2,5,4,7,1,8,3,6]=>1011000=>0100111
[6,8,5,2,3,4,1,7]=>[5,2,8,3,4,6,1,7]=>1110000=>0001111
[2,6,8,7,1,5,3,4]=>[7,2,1,5,8,3,6,4]=>1111000=>0000111
[5,7,6,4,1,3,8,2]=>[4,6,1,8,7,3,5,2]=>1110001=>0001110
[6,1,7,5,3,8,4,2]=>[5,3,8,4,7,6,1,2]=>1011010=>0100101
[8,6,7,5,3,1,4,2]=>[5,3,7,1,6,4,8,2]=>1111000=>0000111
[8,5,2,7,1,6,4,3]=>[6,7,2,5,4,8,1,3]=>1101000=>0010111
[5,6,2,4,7,8,1,3]=>[4,8,2,7,6,5,1,3]=>1100110=>0011001
[3,4,6,1,7,8,5,2]=>[8,5,7,6,1,4,3,2]=>1110110=>0001001
[3,4,8,6,7,1,5,2]=>[7,1,6,5,8,4,3,2]=>1111100=>0000011
[5,8,6,4,1,2,7,3]=>[4,6,1,7,8,2,5,3]=>1110000=>0001111
[5,8,7,3,2,6,4,1]=>[6,7,3,8,2,4,5,1]=>1110000=>0001111
[5,8,1,7,2,6,4,3]=>[6,7,1,8,4,5,2,3]=>1101000=>0010111
[8,1,5,7,2,6,4,3]=>[6,7,1,2,5,4,8,3]=>1011000=>0100111
[8,1,7,2,5,6,3,4]=>[5,6,7,1,2,8,3,4]=>1010000=>0101111
[6,8,7,2,5,1,3,4]=>[5,7,2,8,1,6,3,4]=>1110000=>0001111
[5,8,7,2,1,6,3,4]=>[6,7,2,8,1,5,3,4]=>1110000=>0001111
[4,8,1,5,2,6,7,3]=>[5,1,6,7,8,4,2,3]=>1101000=>0010111
[3,7,8,5,1,6,2,4]=>[5,1,6,8,3,2,7,4]=>1111000=>0000111
[6,5,2,7,8,1,4,3]=>[8,2,7,5,4,6,1,3]=>1101100=>0010011
[7,1,2,8,5,6,3,4]=>[5,6,8,1,2,3,7,4]=>1001000=>0110111
[8,7,2,1,5,6,3,4]=>[5,6,7,2,8,1,3,4]=>1100000=>0011111
[8,6,7,1,5,2,3,4]=>[5,7,1,6,2,8,3,4]=>1110000=>0001111
[6,1,7,8,5,2,3,4]=>[5,8,1,2,7,3,6,4]=>1011000=>0100111
[8,7,5,2,1,6,4,3]=>[5,2,6,7,1,4,8,3]=>1110000=>0001111
[7,1,3,5,8,6,2,4]=>[3,6,8,5,1,2,7,4]=>1001100=>0110011
[5,1,3,4,6,8,7,2]=>[3,4,7,8,6,5,1,2]=>1000110=>0111001
[5,6,3,4,8,1,7,2]=>[3,4,7,8,1,6,5,2]=>1100100=>0011011
[4,6,7,8,5,1,3,2]=>[5,8,1,7,3,6,4,2]=>1111000=>0000111
[8,4,3,1,2,6,7,5]=>[3,4,1,6,7,8,2,5]=>1100000=>0011111
[8,5,1,6,3,4,7,2]=>[6,1,3,5,4,7,8,2]=>1101000=>0010111
[4,6,8,1,5,3,7,2]=>[5,7,8,1,6,3,4,2]=>1110000=>0001111
[6,5,8,1,3,4,7,2]=>[7,8,1,5,3,4,6,2]=>1110000=>0001111
[5,6,8,3,1,2,7,4]=>[7,8,3,6,1,5,2,4]=>1110000=>0001111
[6,1,8,3,5,2,7,4]=>[5,7,8,3,6,1,2,4]=>1010000=>0101111
[7,6,8,3,5,2,1,4]=>[5,8,3,6,2,7,1,4]=>1110000=>0001111
[8,7,1,3,5,6,2,4]=>[5,6,7,1,3,8,2,4]=>1100000=>0011111
[6,7,8,3,5,1,2,4]=>[5,8,3,7,1,6,2,4]=>1110000=>0001111
[3,4,8,1,2,6,7,5]=>[6,7,8,1,4,3,2,5]=>1110000=>0001111
[5,8,2,4,3,6,7,1]=>[4,6,7,8,2,3,5,1]=>1100000=>0011111
[6,8,2,3,5,1,7,4]=>[5,7,8,2,3,6,1,4]=>1100000=>0011111
[7,8,2,3,5,6,1,4]=>[5,6,8,2,3,7,1,4]=>1100000=>0011111
[8,6,5,1,4,3,7,2]=>[5,1,4,6,3,7,8,2]=>1110000=>0001111
[2,4,8,6,1,3,7,5]=>[6,2,1,7,8,4,3,5]=>1111000=>0000111
[2,7,3,8,1,6,4,5]=>[3,6,8,2,1,7,4,5]=>1101000=>0010111
[7,5,1,8,2,4,6,3]=>[8,1,5,4,6,7,2,3]=>1101000=>0010111
[2,6,5,4,1,3,8,7]=>[4,5,2,1,6,3,8,7]=>1110001=>0001110
[4,1,7,6,3,8,2,5]=>[8,6,3,7,4,1,2,5]=>1011010=>0100101
[4,8,2,5,7,6,3,1]=>[6,7,5,2,3,8,4,1]=>1101100=>0010011
[3,4,6,5,1,8,2,7]=>[5,1,8,6,4,3,2,7]=>1111010=>0000101
[4,6,1,5,2,3,8,7]=>[5,1,6,4,2,3,8,7]=>1101001=>0010110
[6,2,3,5,1,4,8,7]=>[2,3,5,1,6,4,8,7]=>1001001=>0110110
[8,6,1,2,5,3,4,7]=>[5,6,1,8,2,3,4,7]=>1100000=>0011111
[6,2,5,1,8,3,4,7]=>[2,8,5,1,6,3,4,7]=>1010100=>0101011
[7,6,5,2,8,3,4,1]=>[8,5,2,6,3,4,7,1]=>1110100=>0001011
[2,6,3,5,1,8,7,4]=>[3,5,2,1,7,8,6,4]=>1101010=>0010101
[2,1,4,8,7,6,3,5]=>[2,1,6,7,4,3,8,5]=>1011100=>0100011
[8,1,3,5,7,4,6,2]=>[3,7,5,4,6,8,1,2]=>1001100=>0110011
[4,8,5,1,6,7,2,3]=>[7,6,5,1,8,2,4,3]=>1110110=>0001001
[3,8,5,1,6,7,2,4]=>[7,6,5,1,8,3,2,4]=>1110110=>0001001
[7,8,6,1,3,5,2,4]=>[6,1,5,8,3,7,2,4]=>1110000=>0001111
[2,5,1,8,6,7,4,3]=>[7,6,4,8,5,2,1,3]=>1101110=>0010001
[3,5,1,8,6,7,4,2]=>[7,6,4,8,5,1,3,2]=>1101110=>0010001
[8,3,5,4,6,7,1,2]=>[4,7,6,5,3,1,8,2]=>1110110=>0001001
[5,1,3,8,6,7,4,2]=>[3,7,6,4,8,5,1,2]=>1001110=>0110001
[3,2,5,8,6,7,4,1]=>[2,7,6,4,8,5,3,1]=>1011110=>0100001
[6,2,1,5,3,8,7,4]=>[2,5,1,3,7,8,6,4]=>1001010=>0110101
[5,6,3,2,8,1,4,7]=>[3,8,2,6,5,1,4,7]=>1100100=>0011011
[8,1,6,3,5,2,7,4]=>[5,6,3,7,8,1,2,4]=>1010000=>0101111
[8,7,6,2,5,3,1,4]=>[5,6,2,7,3,8,1,4]=>1110000=>0001111
[2,7,5,8,1,3,4,6]=>[8,2,1,5,3,7,4,6]=>1111000=>0000111
[7,6,2,8,5,1,4,3]=>[5,8,2,6,4,7,1,3]=>1101000=>0010111
[8,1,3,7,5,2,6,4]=>[3,5,7,1,2,6,8,4]=>1001000=>0110111
[3,4,8,7,5,1,6,2]=>[5,7,1,6,8,4,3,2]=>1111000=>0000111
[6,3,8,1,4,2,5,7]=>[8,3,1,4,6,2,5,7]=>1110000=>0001111
[7,4,6,8,5,1,3,2]=>[5,8,1,6,4,3,7,2]=>1111000=>0000111
[2,1,4,8,7,5,6,3]=>[2,1,7,5,6,8,4,3]=>1011100=>0100011
[7,1,5,8,2,6,4,3]=>[6,8,1,2,5,4,7,3]=>1011000=>0100111
[3,6,8,2,4,1,7,5]=>[7,8,2,4,6,3,1,5]=>1110000=>0001111
[4,5,8,2,6,7,3,1]=>[7,6,2,8,5,3,4,1]=>1110110=>0001001
[5,2,8,1,6,7,3,4]=>[2,7,6,1,8,5,3,4]=>1010110=>0101001
[2,5,8,4,6,7,3,1]=>[4,7,6,3,8,5,2,1]=>1110110=>0001001
[4,2,8,1,6,7,3,5]=>[2,7,6,1,4,3,8,5]=>1010110=>0101001
[2,4,8,1,6,7,3,5]=>[7,6,2,1,4,3,8,5]=>1110110=>0001001
[3,4,8,7,2,1,5,6]=>[7,2,8,4,3,1,5,6]=>1111000=>0000111
[7,8,5,3,6,4,2,1]=>[6,5,3,4,8,2,7,1]=>1110100=>0001011
[5,8,4,1,6,7,2,3]=>[4,1,7,6,2,8,5,3]=>1110110=>0001001
[3,8,1,4,6,7,2,5]=>[4,7,6,1,3,2,8,5]=>1100110=>0011001
[8,2,3,4,6,7,1,5]=>[2,3,4,7,6,1,8,5]=>1000110=>0111001
[8,4,2,6,5,3,1,7]=>[5,6,4,2,3,8,1,7]=>1101000=>0010111
[5,4,8,3,2,6,1,7]=>[6,8,3,4,2,5,1,7]=>1110000=>0001111
[5,8,3,6,4,2,1,7]=>[3,6,4,8,2,5,1,7]=>1101000=>0010111
[4,8,6,2,5,3,1,7]=>[5,6,2,8,3,4,1,7]=>1110000=>0001111
[1,6,4,3,2,8,7,5]=>[1,4,3,7,8,6,2,5]=>0110010=>1001101
[1,5,3,2,8,4,7,6]=>[1,3,7,8,5,2,4,6]=>0100100=>1011011
[5,7,4,3,1,2,6,8]=>[4,3,7,1,5,2,6,8]=>1110000=>0001111
[2,8,7,3,5,1,4,6]=>[5,7,3,8,2,1,4,6]=>1110000=>0001111
[7,3,8,6,4,1,2,5]=>[6,4,8,3,1,7,2,5]=>1111000=>0000111
[6,1,2,7,3,8,5,4]=>[8,1,2,3,5,7,6,4]=>1001010=>0110101
[2,1,7,4,3,8,6,5]=>[2,1,4,8,6,7,3,5]=>1010010=>0101101
[6,1,4,3,8,2,7,5]=>[4,3,7,8,1,2,6,5]=>1010100=>0101011
[5,1,3,2,8,7,4,6]=>[3,7,5,1,2,4,8,6]=>1000110=>0111001
[1,8,3,7,2,6,5,4]=>[1,3,6,7,2,5,8,4]=>0101000=>1010111
[2,1,6,8,5,4,7,3]=>[2,1,5,7,8,4,6,3]=>1011000=>0100111
[8,3,1,6,7,2,5,4]=>[3,1,7,2,6,5,8,4]=>1101100=>0010011
[7,4,8,6,1,3,2,5]=>[6,1,8,4,3,7,2,5]=>1111000=>0000111
[4,7,6,1,2,5,3,8]=>[6,1,5,7,2,4,3,8]=>1110000=>0001111
[1,5,4,8,3,2,7,6]=>[1,7,8,4,3,5,2,6]=>0111000=>1000111
[7,3,6,1,2,5,4,8]=>[6,3,1,5,7,2,4,8]=>1110000=>0001111
[4,6,8,2,5,1,3,7]=>[5,8,2,6,1,4,3,7]=>1110000=>0001111
[1,2,6,3,8,5,7,4]=>[1,2,7,8,5,6,3,4]=>0010100=>1101011
[1,5,2,6,8,4,7,3]=>[1,7,8,4,6,5,2,3]=>0101100=>1010011
[6,4,7,5,8,1,2,3]=>[8,5,1,7,4,2,6,3]=>1111100=>0000011
[8,6,4,2,1,7,5,3]=>[4,2,7,6,1,5,8,3]=>1110010=>0001101
[7,4,2,1,5,8,6,3]=>[4,2,5,8,6,7,1,3]=>1100010=>0011101
[7,6,4,1,8,5,2,3]=>[4,1,8,5,6,2,7,3]=>1110100=>0001011
[1,6,4,8,7,5,3,2]=>[1,7,5,8,4,3,6,2]=>0111100=>1000011
[7,5,1,3,2,8,6,4]=>[5,1,3,8,6,7,2,4]=>1100010=>0011101
[4,7,1,2,5,8,6,3]=>[5,8,6,7,1,4,2,3]=>1100010=>0011101
[6,8,4,1,2,7,5,3]=>[4,1,7,2,5,8,6,3]=>1110010=>0001101
[7,4,8,1,6,3,5,2]=>[6,1,4,3,8,5,7,2]=>1110100=>0001011
[5,8,2,1,7,3,6,4]=>[7,2,6,8,5,1,3,4]=>1100100=>0011011
[3,6,1,8,2,4,7,5]=>[7,8,1,3,2,6,4,5]=>1101000=>0010111
[1,3,8,7,6,2,5,4]=>[1,6,3,2,7,5,8,4]=>0111100=>1000011
[5,4,1,8,7,3,2,6]=>[7,4,1,3,8,5,2,6]=>1101100=>0010011
[3,5,1,8,7,2,4,6]=>[7,1,3,2,8,5,4,6]=>1101100=>0010011
[4,7,1,2,8,6,3,5]=>[6,8,1,4,2,3,7,5]=>1100100=>0011011
[7,6,8,1,5,4,2,3]=>[5,8,1,4,6,2,7,3]=>1110000=>0001111
[8,6,1,7,5,4,3,2]=>[5,7,4,6,1,3,8,2]=>1101000=>0010111
[7,1,5,8,6,4,3,2]=>[6,4,8,5,3,7,1,2]=>1011100=>0100011
[5,1,8,7,3,6,4,2]=>[6,7,3,8,4,5,1,2]=>1011000=>0100111
[4,1,8,7,6,2,5,3]=>[6,1,2,7,5,8,4,3]=>1011100=>0100011
[1,6,4,5,2,3,7,8]=>[1,5,4,2,6,3,7,8]=>0111000=>1000111
[1,7,4,5,2,3,6,8]=>[1,5,4,2,7,3,6,8]=>0111000=>1000111
[1,7,3,5,2,4,6,8]=>[1,3,5,2,7,4,6,8]=>0101000=>1010111
[1,6,3,5,2,4,7,8]=>[1,3,5,2,6,4,7,8]=>0101000=>1010111
[1,6,3,4,2,5,7,8]=>[1,3,4,6,2,5,7,8]=>0100000=>1011111
[1,7,3,4,2,5,6,8]=>[1,3,4,7,2,5,6,8]=>0100000=>1011111
[1,8,6,7,3,4,2,5]=>[1,7,3,6,4,8,2,5]=>0111000=>1000111
[1,8,5,7,3,4,2,6]=>[1,7,3,5,4,8,2,6]=>0111000=>1000111
[1,7,3,4,2,6,5,8]=>[1,3,4,6,7,2,5,8]=>0100000=>1011111
[1,5,2,8,4,7,3,6]=>[1,7,4,5,2,3,8,6]=>0101010=>1010101
[1,4,2,8,5,7,3,6]=>[1,5,7,4,2,3,8,6]=>0101010=>1010101
[1,7,3,5,2,6,4,8]=>[1,3,5,2,6,7,4,8]=>0101000=>1010111
[1,7,3,6,2,4,5,8]=>[1,3,6,2,7,4,5,8]=>0101000=>1010111
[1,7,4,6,2,3,5,8]=>[1,6,4,2,7,3,5,8]=>0111000=>1000111
[1,8,5,6,2,3,4,7]=>[1,6,2,5,3,8,4,7]=>0111000=>1000111
[1,8,5,6,2,4,3,7]=>[1,6,2,5,4,8,3,7]=>0111000=>1000111
[1,4,2,8,5,6,3,7]=>[1,5,6,8,4,2,3,7]=>0101000=>1010111
[1,5,2,8,4,6,3,7]=>[1,6,8,4,5,2,3,7]=>0101000=>1010111
[1,6,2,8,4,5,3,7]=>[1,8,4,5,6,2,3,7]=>0101000=>1010111
[9,1,2,3,5,4,6,7,8]=>[5,9,1,2,3,4,6,7,8]=>10000000=>01111111
[8,1,2,4,5,3,6,7]=>[4,5,8,1,2,3,6,7]=>1000000=>0111111
[2,3,4,6,5,7,8,9,1]=>[5,9,8,7,6,4,3,2,1]=>11110111=>00001000
[10,1,2,3,4,6,5,7,8,9]=>[6,10,1,2,3,4,5,7,8,9]=>100000000=>011111111
[2,3,4,6,7,5,8,9,1]=>[9,8,7,5,6,4,3,2,1]=>11111011=>00000100
[2,3,4,5,7,6,8,9,10,1]=>[6,10,9,8,7,5,4,3,2,1]=>111110111=>000001000
[9,10,3,4,5,6,7,8,1,2]=>[3,4,5,6,7,8,10,1,9,2]=>110000000=>001111111
[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=>11111111111
[1,6,4,7,2,8,3,5]=>[1,8,4,2,7,6,3,5]=>0111010=>1000101
[1,4,7,3,5,8,2,6]=>[1,5,8,3,4,2,7,6]=>0110010=>1001101
[5,4,8,2,3,6,1,7]=>[6,8,2,4,3,5,1,7]=>1110000=>0001111
[7,4,8,5,2,3,1,6]=>[5,2,8,4,3,7,1,6]=>1111000=>0000111
[3,8,6,2,4,5,1,7]=>[6,2,4,5,8,3,1,7]=>1110000=>0001111
[4,8,6,2,3,5,1,7]=>[6,2,5,8,3,4,1,7]=>1110000=>0001111
[1,7,6,4,8,2,3,5]=>[1,4,8,2,6,3,7,5]=>0110100=>1001011
[5,8,7,4,1,2,3,6]=>[4,7,1,8,2,5,3,6]=>1110000=>0001111
[6,8,5,3,4,1,2,7]=>[5,3,4,8,1,6,2,7]=>1110000=>0001111
[6,8,3,7,2,1,4,5]=>[3,7,2,8,1,6,4,5]=>1101000=>0010111
[8,5,1,6,3,7,2,4]=>[7,6,1,3,5,2,8,4]=>1101010=>0010101
[7,1,6,4,8,2,3,5]=>[4,8,1,2,6,3,7,5]=>1010100=>0101011
[1,8,5,7,2,3,4,6]=>[1,7,2,5,3,8,4,6]=>0111000=>1000111
[5,1,7,3,8,2,4,6]=>[8,3,7,5,1,2,4,6]=>1010100=>0101011
[7,4,8,6,1,2,3,5]=>[6,1,8,4,2,7,3,5]=>1111000=>0000111
[3,8,7,5,1,2,4,6]=>[5,1,7,3,2,8,4,6]=>1111000=>0000111
[3,7,6,1,2,4,5,8]=>[6,1,7,3,2,4,5,8]=>1110000=>0001111
[1,6,5,8,2,3,4,7]=>[1,8,2,5,3,6,4,7]=>0111000=>1000111
[6,5,8,4,1,2,3,7]=>[4,8,1,5,2,6,3,7]=>1110000=>0001111
[8,5,7,4,1,2,3,6]=>[4,7,1,5,2,8,3,6]=>1110000=>0001111
[1,5,7,4,8,2,3,6]=>[1,4,8,2,7,5,3,6]=>0110100=>1001011
[7,6,2,3,8,1,4,5]=>[8,2,3,6,1,4,7,5]=>1100100=>0011011
[7,4,8,5,1,6,2,3]=>[5,1,6,8,4,2,7,3]=>1111000=>0000111
[8,6,2,3,1,7,4,5]=>[7,6,2,3,8,1,4,5]=>1100010=>0011101
[8,6,4,1,2,7,3,5]=>[4,1,7,6,2,8,3,5]=>1110010=>0001101
[7,6,1,3,8,2,4,5]=>[8,1,3,6,2,4,7,5]=>1100100=>0011011
[7,5,8,1,3,6,2,4]=>[6,8,1,5,3,7,2,4]=>1110000=>0001111
[5,4,1,8,2,3,6,7]=>[8,4,1,5,2,3,6,7]=>1101000=>0010111
[1,4,8,7,2,3,5,6]=>[1,7,2,8,4,3,5,6]=>0111000=>1000111
[1,5,8,7,2,3,4,6]=>[1,7,2,8,3,5,4,6]=>0111000=>1000111
[7,6,8,1,5,2,3,4]=>[5,8,1,6,2,7,3,4]=>1110000=>0001111
[7,1,5,8,6,2,3,4]=>[6,1,2,8,5,3,7,4]=>1011100=>0100011
[5,1,8,7,2,3,4,6]=>[7,1,2,8,3,5,4,6]=>1011000=>0100111
[1,8,7,6,4,5,3,2]=>[1,6,4,5,7,3,8,2]=>0111000=>1000111
[9,8,7,6,4,5,3,2,1,10]=>[6,4,5,7,3,8,2,9,1,10]=>111100000=>000011111
[1,8,7,3,6,5,4,2]=>[1,6,5,7,3,4,8,2]=>0110100=>1001011
[7,1,5,8,3,4,2,6]=>[8,3,5,4,7,1,2,6]=>1011000=>0100111
[6,4,2,7,5,8,3,1]=>[5,8,4,2,3,7,6,1]=>1101010=>0010101
[2,4,1,7,5,8,3,6]=>[5,8,4,2,1,3,7,6]=>1101010=>0010101
[7,1,4,6,5,2,3,8]=>[5,6,4,1,2,7,3,8]=>1011000=>0100111
[7,1,4,6,5,8,2,3]=>[5,8,6,4,1,2,7,3]=>1011010=>0100101
[7,1,4,6,3,8,2,5]=>[8,6,4,3,7,1,2,5]=>1011010=>0100101
[7,1,4,3,2,5,8,6]=>[4,3,8,7,1,2,5,6]=>1010001=>0101110
[7,1,4,6,5,3,8,2]=>[5,6,4,3,8,7,1,2]=>1011001=>0100110
[3,4,7,2,6,8,5,1]=>[8,6,5,7,2,4,3,1]=>1110110=>0001001
[3,4,7,1,6,8,2,5]=>[8,6,1,4,3,2,7,5]=>1110110=>0001001
[3,4,7,1,6,8,5,2]=>[8,6,5,7,1,4,3,2]=>1110110=>0001001
[2,4,1,7,5,3,6,8]=>[5,7,4,2,1,3,6,8]=>1101000=>0010111
[6,4,2,3,8,5,1,7]=>[4,2,3,8,5,6,1,7]=>1100100=>0011011
[3,4,7,2,6,8,1,5]=>[8,6,2,4,3,1,7,5]=>1110110=>0001001
[3,4,7,2,6,5,1,8]=>[6,5,7,2,4,3,1,8]=>1110100=>0001011
[4,8,3,2,5,6,1,7]=>[3,5,6,8,2,4,1,7]=>1100000=>0011111
[4,8,7,3,5,1,2,6]=>[5,7,3,8,1,4,2,6]=>1110000=>0001111
[4,8,7,1,3,5,2,6]=>[7,1,5,8,3,4,2,6]=>1110000=>0001111
[3,4,7,2,6,5,8,1]=>[6,5,8,7,2,4,3,1]=>1110101=>0001010
[4,8,3,1,2,6,7,5]=>[3,6,7,8,1,4,2,5]=>1100000=>0011111
[5,8,1,6,3,4,2,7]=>[6,1,3,8,4,5,2,7]=>1101000=>0010111
[6,8,5,1,3,7,2,4]=>[5,1,7,3,8,6,2,4]=>1110010=>0001101
[6,8,5,1,3,4,7,2]=>[5,1,7,8,3,4,6,2]=>1110000=>0001111
[5,8,3,4,2,6,7,1]=>[3,4,6,7,8,2,5,1]=>1100000=>0011111
[5,4,7,3,6,2,8,1]=>[6,3,4,2,8,7,5,1]=>1110101=>0001010
[6,4,3,7,5,1,2,8]=>[3,5,7,4,1,6,2,8]=>1101000=>0010111
[6,4,3,7,5,1,8,2]=>[3,5,8,7,4,1,6,2]=>1101001=>0010110
[6,2,4,3,1,5,8,7]=>[2,4,3,6,1,5,8,7]=>1010001=>0101110
[3,8,7,4,1,5,2,6]=>[4,7,1,5,8,3,2,6]=>1110000=>0001111
[5,8,3,2,1,6,4,7]=>[3,6,8,2,5,1,4,7]=>1100000=>0011111
[5,8,7,4,3,1,2,6]=>[4,7,3,8,1,5,2,6]=>1110000=>0001111
[6,5,2,8,4,3,1,7]=>[8,4,5,2,3,6,1,7]=>1101000=>0010111
[4,3,2,8,6,5,1,7]=>[3,2,6,5,8,4,1,7]=>1101100=>0010011
[4,3,8,7,5,1,6,2]=>[5,7,3,1,6,8,4,2]=>1111000=>0000111
[3,2,5,8,6,1,4,7]=>[2,6,3,1,8,5,4,7]=>1011100=>0100011
[8,4,3,7,5,2,6,1]=>[3,5,7,4,2,6,8,1]=>1101000=>0010111
[5,3,7,8,4,1,2,6]=>[8,4,7,3,1,5,2,6]=>1111000=>0000111
[6,2,5,8,3,1,4,7]=>[2,8,3,5,1,6,4,7]=>1011000=>0100111
[6,2,4,8,3,1,5,7]=>[2,8,4,3,6,1,5,7]=>1011000=>0100111
[5,3,2,8,6,4,1,7]=>[3,2,6,4,8,5,1,7]=>1101100=>0010011
[8,7,5,3,6,2,4,1]=>[6,5,3,7,2,4,8,1]=>1110100=>0001011
[8,6,5,3,7,2,4,1]=>[7,5,3,6,2,4,8,1]=>1110100=>0001011
[7,5,4,3,8,2,6,1]=>[4,3,8,5,2,6,7,1]=>1110100=>0001011
[6,4,5,3,8,2,7,1]=>[7,8,5,3,4,2,6,1]=>1110100=>0001011
[7,4,6,3,8,2,5,1]=>[8,3,4,2,6,5,7,1]=>1110100=>0001011
[7,4,6,3,5,2,8,1]=>[5,6,3,4,2,8,7,1]=>1110001=>0001110
[8,4,7,3,5,2,6,1]=>[5,7,3,4,2,6,8,1]=>1110000=>0001111
[7,5,8,3,4,2,6,1]=>[8,3,4,5,2,6,7,1]=>1110000=>0001111
[7,5,8,4,6,2,3,1]=>[4,6,2,8,5,3,7,1]=>1110100=>0001011
[7,4,8,3,5,2,6,1]=>[5,8,3,4,2,6,7,1]=>1110000=>0001111
[6,4,8,3,5,2,7,1]=>[5,7,8,3,4,2,6,1]=>1110000=>0001111
[6,4,7,3,5,2,8,1]=>[5,8,7,3,4,2,6,1]=>1110001=>0001110
[5,4,8,3,7,2,6,1]=>[7,3,4,2,6,8,5,1]=>1110100=>0001011
[6,5,8,3,7,2,4,1]=>[7,3,8,5,2,4,6,1]=>1110100=>0001011
[6,4,7,3,8,2,5,1]=>[8,3,4,2,7,5,6,1]=>1110100=>0001011
[5,3,6,2,4,7,8,1]=>[8,7,6,3,2,4,5,1]=>1110011=>0001100
[5,3,6,1,4,8,7,2]=>[7,8,6,3,1,4,5,2]=>1110010=>0001101
[5,3,7,2,4,6,8,1]=>[6,8,7,3,2,4,5,1]=>1110001=>0001110
[4,2,1,5,8,6,3,7]=>[2,6,8,5,4,1,3,7]=>1001100=>0110011
[4,2,1,5,8,7,6,3]=>[2,7,6,8,5,4,1,3]=>1001110=>0110001
[4,3,1,5,7,8,6,2]=>[3,1,8,6,7,5,4,2]=>1101110=>0010001
[4,3,1,7,5,8,6,2]=>[3,1,5,8,6,7,4,2]=>1101010=>0010101
[4,3,1,5,7,8,2,6]=>[3,1,8,5,4,2,7,6]=>1101110=>0010001
[3,2,1,8,7,5,4,6]=>[2,3,1,7,5,8,4,6]=>1001100=>0110011
[6,7,2,1,8,4,3,5]=>[8,2,4,7,1,3,6,5]=>1100100=>0011011
[3,2,1,8,5,6,4,7]=>[2,3,1,5,6,8,4,7]=>1001000=>0110111
[4,3,1,6,7,8,5,2]=>[3,1,8,5,7,6,4,2]=>1101110=>0010001
[4,2,1,6,8,7,5,3]=>[2,7,5,8,6,4,1,3]=>1001110=>0110001
[5,2,6,1,8,7,3,4]=>[2,7,1,8,6,5,3,4]=>1010110=>0101001
[4,2,1,6,8,3,7,5]=>[2,7,8,4,1,3,6,5]=>1001100=>0110011
[4,3,1,6,7,8,2,5]=>[3,1,8,4,2,7,6,5]=>1101110=>0010001
[6,7,3,1,5,8,2,4]=>[3,5,8,1,7,6,2,4]=>1100010=>0011101
[4,2,1,7,8,6,3,5]=>[2,6,8,4,1,3,7,5]=>1001100=>0110011
[3,2,1,8,6,4,5,7]=>[2,3,1,6,4,8,5,7]=>1001100=>0110011
[3,2,1,8,4,6,5,7]=>[2,3,1,6,8,4,5,7]=>1001000=>0110111
[3,2,1,8,4,6,7,5]=>[2,3,1,6,7,8,4,5]=>1001000=>0110111
[3,2,1,8,4,7,6,5]=>[2,3,1,7,6,8,4,5]=>1001010=>0110101
[4,2,1,7,8,3,6,5]=>[2,8,4,1,3,6,7,5]=>1001100=>0110011
[5,2,7,1,8,3,6,4]=>[2,8,1,6,7,5,3,4]=>1010100=>0101011
[6,7,2,1,8,3,5,4]=>[8,2,7,5,6,1,3,4]=>1100100=>0011011
[5,2,7,1,8,3,4,6]=>[2,8,1,7,5,3,4,6]=>1010100=>0101011
[4,2,1,7,8,3,5,6]=>[2,8,4,1,3,7,5,6]=>1001100=>0110011
[3,2,1,8,4,5,7,6]=>[2,3,1,7,8,4,5,6]=>1001000=>0110111
[7,5,2,8,6,3,4,1]=>[6,2,3,8,5,4,7,1]=>1101100=>0010011
[7,4,8,6,2,5,3,1]=>[6,2,5,8,4,3,7,1]=>1111000=>0000111
[7,3,8,6,2,4,5,1]=>[6,3,2,8,4,5,7,1]=>1111000=>0000111
[7,4,3,1,8,2,5,6]=>[3,4,1,8,2,7,5,6]=>1100100=>0011011
[7,4,2,8,5,6,1,3]=>[5,6,8,4,2,7,1,3]=>1101000=>0010111
[6,3,8,2,4,5,1,7]=>[8,3,2,4,5,6,1,7]=>1110000=>0001111
[6,3,8,2,5,7,4,1]=>[5,7,3,2,4,8,6,1]=>1110010=>0001101
[5,3,8,2,4,6,7,1]=>[6,7,8,3,2,4,5,1]=>1110000=>0001111
[6,4,8,2,7,5,1,3]=>[7,5,8,2,4,1,6,3]=>1110100=>0001011
[5,7,4,2,6,1,3,8]=>[4,2,6,1,7,5,3,8]=>1110100=>0001011
[5,6,3,8,2,4,7,1]=>[3,7,8,2,6,4,5,1]=>1101000=>0010111
[6,3,7,2,5,8,4,1]=>[5,8,3,2,4,7,6,1]=>1110010=>0001101
[5,4,6,2,3,8,1,7]=>[8,6,2,4,3,5,1,7]=>1110010=>0001101
[5,3,6,7,8,2,4,1]=>[8,3,2,7,4,6,5,1]=>1111100=>0000011
[3,6,4,2,1,5,8,7]=>[4,2,6,3,1,5,8,7]=>1110001=>0001110
[3,5,8,6,4,2,1,7]=>[6,4,8,2,5,3,1,7]=>1111000=>0000111
[6,3,4,2,1,5,8,7]=>[4,3,2,6,1,5,8,7]=>1110001=>0001110
[5,6,4,2,1,3,8,7]=>[4,2,6,1,5,3,8,7]=>1110001=>0001110
[2,8,5,4,1,6,3,7]=>[4,5,2,1,6,8,3,7]=>1110000=>0001111
[2,8,6,3,5,4,1,7]=>[5,6,3,4,8,2,1,7]=>1110000=>0001111
[5,8,6,4,2,1,3,7]=>[4,6,2,8,1,5,3,7]=>1110000=>0001111
[2,7,8,6,3,5,4,1]=>[6,3,5,8,4,7,2,1]=>1111000=>0000111
[4,3,8,5,7,6,2,1]=>[6,7,5,3,2,8,4,1]=>1111100=>0000011
[7,6,2,1,8,4,3,5]=>[8,2,4,6,1,3,7,5]=>1100100=>0011011
[2,1,8,5,6,4,3,7]=>[2,1,6,5,4,8,3,7]=>1011100=>0100011
[6,3,4,2,1,8,5,7]=>[4,3,2,8,6,1,5,7]=>1110010=>0001101
[3,7,8,5,6,4,2,1]=>[6,5,4,8,2,7,3,1]=>1111100=>0000011
[3,8,5,6,4,2,1,7]=>[6,4,5,2,8,3,1,7]=>1111000=>0000111
[3,6,4,2,1,8,5,7]=>[4,2,8,6,3,1,5,7]=>1110010=>0001101
[3,8,6,4,2,1,5,7]=>[4,6,2,8,3,1,5,7]=>1110000=>0001111
[3,7,8,6,4,2,1,5]=>[6,4,8,2,7,3,1,5]=>1111000=>0000111
[8,5,3,7,6,2,4,1]=>[3,6,2,7,5,4,8,1]=>1101100=>0010011
[7,6,2,4,1,8,5,3]=>[4,8,6,2,5,7,1,3]=>1100010=>0011101
[2,1,7,8,6,4,3,5]=>[2,1,6,4,8,3,7,5]=>1011100=>0100011
[2,1,6,4,3,7,8,5]=>[2,1,4,8,7,6,3,5]=>1010011=>0101100
[6,3,7,8,4,2,1,5]=>[8,4,7,3,2,6,1,5]=>1111000=>0000111
[7,8,4,2,1,6,3,5]=>[4,2,6,8,1,7,3,5]=>1110000=>0001111
[5,7,6,2,3,8,4,1]=>[8,6,2,7,3,4,5,1]=>1110010=>0001101
[2,6,1,7,5,8,4,3]=>[5,8,4,7,6,2,1,3]=>1101010=>0010101
[8,4,2,3,7,5,6,1]=>[4,2,3,7,5,6,8,1]=>1100100=>0011011
[4,7,6,2,1,3,8,5]=>[6,2,8,7,1,4,3,5]=>1110001=>0001110
[7,5,6,1,8,4,2,3]=>[8,1,4,6,5,2,7,3]=>1110100=>0001011
[6,4,7,8,3,2,1,5]=>[8,3,7,4,2,6,1,5]=>1111000=>0000111
[6,4,3,7,5,2,1,8]=>[3,5,7,4,2,6,1,8]=>1101000=>0010111
[6,5,3,2,8,4,1,7]=>[3,8,5,2,4,6,1,7]=>1100100=>0011011
[6,5,2,7,8,4,1,3]=>[8,4,7,5,2,6,1,3]=>1101100=>0010011
[6,3,7,2,5,4,1,8]=>[5,7,3,2,4,6,1,8]=>1110000=>0001111
[6,3,2,7,5,4,1,8]=>[3,2,5,7,4,6,1,8]=>1101000=>0010111
[8,4,2,6,3,1,7,5]=>[6,4,2,3,7,8,1,5]=>1101000=>0010111
[1,8,6,3,2,5,7,4]=>[1,6,3,5,7,8,2,4]=>0110000=>1001111
[8,7,5,2,1,4,6,3]=>[5,2,7,1,4,6,8,3]=>1110000=>0001111
[7,8,5,2,1,4,6,3]=>[5,2,8,1,4,6,7,3]=>1110000=>0001111
[6,8,5,2,3,1,7,4]=>[5,2,7,8,3,6,1,4]=>1110000=>0001111
[3,2,8,6,4,1,7,5]=>[2,6,4,7,8,3,1,5]=>1011000=>0100111
[4,1,3,7,5,2,8,6]=>[3,5,8,7,4,1,2,6]=>1001001=>0110110
[5,1,7,3,4,2,8,6]=>[8,7,3,4,5,1,2,6]=>1010001=>0101110
[7,1,6,3,2,5,8,4]=>[6,3,5,8,7,1,2,4]=>1010001=>0101110
[6,1,8,2,4,5,7,3]=>[7,8,1,2,4,5,6,3]=>1010000=>0101111
[5,1,8,3,2,6,7,4]=>[6,7,8,3,5,1,2,4]=>1010000=>0101111
[3,2,8,7,1,5,6,4]=>[2,7,3,1,5,6,8,4]=>1011000=>0100111
[4,8,2,7,1,5,6,3]=>[7,2,5,6,8,4,1,3]=>1101000=>0010111
[6,8,7,1,3,4,5,2]=>[7,1,8,3,4,5,6,2]=>1110000=>0001111
[7,8,6,1,3,4,5,2]=>[6,1,8,3,4,5,7,2]=>1110000=>0001111
[1,7,8,2,4,5,6,3]=>[1,8,2,4,5,6,7,3]=>0110000=>1001111
[7,6,8,1,3,4,5,2]=>[8,1,6,3,4,5,7,2]=>1110000=>0001111
[6,5,8,2,3,1,7,4]=>[7,8,2,5,3,6,1,4]=>1110000=>0001111
[1,6,8,3,2,5,7,4]=>[1,7,8,3,5,6,2,4]=>0110000=>1001111
[7,4,2,8,1,5,6,3]=>[8,4,2,5,6,7,1,3]=>1101000=>0010111
[5,4,2,3,8,1,7,6]=>[4,2,3,7,8,5,1,6]=>1100100=>0011011
[4,5,2,3,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>1100001=>0011110
[7,4,2,1,3,6,8,5]=>[4,2,6,8,7,1,3,5]=>1100001=>0011110
[8,4,2,1,3,6,7,5]=>[4,2,6,7,8,1,3,5]=>1100000=>0011111
[1,5,3,2,4,7,8,6]=>[1,3,5,2,4,8,7,6]=>0100011=>1011100
[6,7,1,2,4,5,8,3]=>[8,7,1,4,5,6,2,3]=>1100001=>0011110
[8,6,1,2,4,5,7,3]=>[6,1,4,5,7,8,2,3]=>1100000=>0011111
[1,8,2,3,5,6,7,4]=>[1,5,6,7,8,2,3,4]=>0100000=>1011111
[8,7,1,2,4,5,6,3]=>[7,1,4,5,6,8,2,3]=>1100000=>0011111
[7,8,1,2,4,5,6,3]=>[8,1,4,5,6,7,2,3]=>1100000=>0011111
[5,8,1,3,2,6,7,4]=>[6,7,8,1,3,5,2,4]=>1100000=>0011111
[4,8,2,1,3,6,7,5]=>[6,7,8,2,4,1,3,5]=>1100000=>0011111
[4,1,3,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>1000011=>0111100
[5,1,2,4,3,7,8,6]=>[4,5,1,2,3,8,7,6]=>1000011=>0111100
[5,4,8,1,2,3,7,6]=>[7,8,1,4,2,5,3,6]=>1110000=>0001111
[1,4,7,6,3,2,5,8]=>[1,6,3,7,4,2,5,8]=>0111000=>1000111
[4,8,3,2,7,6,1,5]=>[3,6,7,2,4,1,8,5]=>1100100=>0011011
[1,4,7,3,6,2,5,8]=>[1,6,3,4,2,7,5,8]=>0110100=>1001011
[4,3,2,8,1,7,6,5]=>[3,2,7,6,8,4,1,5]=>1101010=>0010101
[4,1,8,7,3,2,5,6]=>[7,3,8,4,1,2,5,6]=>1011000=>0100111
[2,3,6,7,4,1,8,5]=>[8,7,4,6,3,2,1,5]=>1111001=>0000110
[2,6,3,4,7,8,1,5]=>[3,4,8,2,1,7,6,5]=>1100110=>0011001
[3,1,7,8,4,2,5,6]=>[8,4,7,3,1,2,5,6]=>1011000=>0100111
[4,1,3,2,8,7,5,6]=>[3,4,1,2,7,5,8,6]=>1000110=>0111001
[4,3,1,8,2,5,7,6]=>[3,1,7,8,4,2,5,6]=>1101000=>0010111
[3,2,7,8,4,1,6,5]=>[2,8,4,6,7,3,1,5]=>1011000=>0100111
[3,7,2,4,8,6,1,5]=>[4,6,8,2,3,1,7,5]=>1100100=>0011011
[3,2,7,4,8,1,6,5]=>[2,4,8,3,1,6,7,5]=>1010100=>0101011
[3,2,4,7,1,8,6,5]=>[2,8,6,7,4,3,1,5]=>1011010=>0100101
[3,7,4,2,6,8,1,5]=>[4,2,8,6,3,1,7,5]=>1110110=>0001001
[3,7,4,6,2,8,1,5]=>[8,6,4,2,7,3,1,5]=>1111010=>0000101
[3,7,6,4,8,2,1,5]=>[4,8,2,6,3,1,7,5]=>1110100=>0001011
[2,3,6,4,7,1,8,5]=>[4,8,7,3,2,1,6,5]=>1110101=>0001010
[8,7,5,2,6,3,4,1]=>[6,5,2,7,3,4,8,1]=>1110100=>0001011
[8,6,5,2,7,3,4,1]=>[7,5,2,6,3,4,8,1]=>1110100=>0001011
[7,4,8,5,6,3,2,1]=>[6,5,3,8,4,2,7,1]=>1111100=>0000011
[3,4,6,7,8,5,1,2]=>[8,5,7,1,6,4,3,2]=>1111100=>0000011
[3,1,7,5,4,2,6,8]=>[5,4,7,3,1,2,6,8]=>1011000=>0100111
[6,3,8,5,4,7,1,2]=>[5,4,7,3,1,8,6,2]=>1111010=>0000101
[1,6,2,5,4,7,8,3]=>[1,5,4,8,7,6,2,3]=>0101011=>1010100
[1,8,2,5,6,3,7,4]=>[1,6,5,2,3,7,8,4]=>0101100=>1010011
[1,2,6,4,8,5,7,3]=>[1,2,4,7,8,5,6,3]=>0010100=>1101011
[7,8,3,1,4,2,5,6]=>[3,8,1,4,7,2,5,6]=>1100000=>0011111
[4,8,1,5,2,3,6,7]=>[5,1,8,4,2,3,6,7]=>1101000=>0010111
[5,6,1,8,4,3,2,7]=>[8,4,6,1,3,5,2,7]=>1101000=>0010111
[5,1,8,6,4,3,2,7]=>[6,4,8,3,5,1,2,7]=>1011000=>0100111
[5,1,6,3,8,7,2,4]=>[7,3,8,6,5,1,2,4]=>1010110=>0101001
[7,1,2,5,4,8,6,3]=>[5,4,8,6,7,1,2,3]=>1001010=>0110101
[4,1,6,3,7,5,2,8]=>[7,5,6,3,4,1,2,8]=>1010100=>0101011
[3,1,6,4,8,2,7,5]=>[4,7,8,3,1,2,6,5]=>1010100=>0101011
[7,8,4,1,6,3,2,5]=>[4,1,6,3,8,2,7,5]=>1110100=>0001011
[4,1,8,5,2,3,7,6]=>[5,1,2,7,8,4,3,6]=>1011000=>0100111
[4,1,6,8,3,7,2,5]=>[7,3,8,6,4,1,2,5]=>1011010=>0100101
[5,4,6,1,3,8,2,7]=>[8,6,1,4,3,5,2,7]=>1110010=>0001101
[6,5,8,1,4,3,2,7]=>[8,1,4,5,3,6,2,7]=>1110000=>0001111
[1,3,5,7,6,8,2,4]=>[1,8,6,3,2,7,5,4]=>0111110=>1000001
[1,3,5,2,7,6,4,8]=>[1,6,7,5,3,2,4,8]=>0110100=>1001011
[1,3,5,7,6,2,4,8]=>[1,6,3,2,7,5,4,8]=>0111100=>1000011
[1,3,5,7,4,6,8,2]=>[1,6,8,7,4,5,3,2]=>0111001=>1000110
[1,3,5,7,4,6,2,8]=>[1,6,7,4,5,3,2,8]=>0111000=>1000111
[1,3,5,7,4,2,6,8]=>[1,7,4,5,3,2,6,8]=>0111000=>1000111
[1,3,5,4,7,2,6,8]=>[1,4,7,5,3,2,6,8]=>0110100=>1001011
[1,3,5,4,7,8,2,6]=>[1,4,8,5,3,2,7,6]=>0110110=>1001001
[1,3,5,4,7,2,8,6]=>[1,4,8,7,5,3,2,6]=>0110101=>1001010
[1,3,5,7,4,2,8,6]=>[1,8,7,4,5,3,2,6]=>0111001=>1000110
[1,3,5,7,4,8,2,6]=>[1,8,4,5,3,2,7,6]=>0111010=>1000101
[1,3,5,7,4,8,6,2]=>[1,8,6,7,4,5,3,2]=>0111010=>1000101
[1,3,5,7,8,4,6,2]=>[1,8,4,6,7,5,3,2]=>0111100=>1000011
[1,3,5,7,8,4,2,6]=>[1,8,4,7,5,3,2,6]=>0111100=>1000011
[1,3,5,2,7,8,6,4]=>[1,8,6,7,5,3,2,4]=>0110110=>1001001
[1,3,5,7,8,2,6,4]=>[1,8,3,2,6,7,5,4]=>0111100=>1000011
[1,6,3,2,7,4,8,5]=>[1,3,8,7,2,4,6,5]=>0100101=>1011010
[3,5,1,6,2,8,7,4]=>[7,8,6,1,3,2,5,4]=>1101010=>0010101
[1,3,7,2,5,4,8,6]=>[1,5,8,7,3,2,4,6]=>0110001=>1001110
[1,3,7,5,2,4,8,6]=>[1,5,3,2,8,7,4,6]=>0111001=>1000110
[1,4,7,2,3,8,6,5]=>[1,8,6,7,2,4,3,5]=>0110010=>1001101
[1,4,7,3,8,2,6,5]=>[1,8,3,4,2,6,7,5]=>0110100=>1001011
[2,5,1,7,8,4,6,3]=>[8,4,6,7,5,2,1,3]=>1101100=>0010011
[3,2,6,7,8,1,5,4]=>[2,8,3,1,7,5,6,4]=>1011100=>0100011
[3,5,2,7,8,4,1,6]=>[8,4,7,5,2,3,1,6]=>1101100=>0010011
[1,5,7,4,8,3,2,6]=>[1,4,8,3,7,5,2,6]=>0110100=>1001011
[4,6,2,1,7,8,3,5]=>[8,2,4,1,3,7,6,5]=>1100110=>0011001
[5,3,6,4,7,8,2,1]=>[4,8,3,2,7,6,5,1]=>1110110=>0001001
[2,5,4,6,8,7,1,3]=>[7,4,2,1,8,6,5,3]=>1111110=>0000001
[1,3,6,2,8,7,5,4]=>[1,7,5,8,6,3,2,4]=>0110110=>1001001
[1,4,6,3,8,7,2,5]=>[1,7,3,4,2,8,6,5]=>0110110=>1001001
[2,5,7,4,3,8,6,1]=>[4,8,6,7,3,5,2,1]=>1110010=>0001101
[4,3,6,7,8,2,5,1]=>[8,3,2,7,5,6,4,1]=>1111100=>0000011
[1,4,7,3,8,6,2,5]=>[1,6,8,3,4,2,7,5]=>0110100=>1001011
[2,5,4,7,8,6,1,3]=>[6,8,4,2,1,7,5,3]=>1111100=>0000011
[5,1,6,8,2,4,3,7]=>[8,1,2,6,4,5,3,7]=>1011000=>0100111
[5,3,7,8,2,4,1,6]=>[8,3,2,7,4,5,1,6]=>1111000=>0000111
[8,5,3,7,2,4,1,6]=>[3,7,2,5,4,8,1,6]=>1101000=>0010111
[8,2,4,7,3,1,5,6]=>[2,7,4,3,8,1,5,6]=>1011000=>0100111
[5,2,4,3,8,1,6,7]=>[2,4,3,8,5,1,6,7]=>1010100=>0101011
[3,2,4,6,8,1,5,7]=>[2,8,4,3,1,6,5,7]=>1011100=>0100011
[8,1,5,7,3,2,4,6]=>[7,3,5,1,2,8,4,6]=>1011000=>0100111
[8,4,6,7,2,3,1,5]=>[7,2,6,4,3,8,1,5]=>1111000=>0000111
[7,2,4,8,3,1,5,6]=>[2,8,4,3,7,1,5,6]=>1011000=>0100111
[5,3,8,7,2,4,1,6]=>[7,3,2,8,4,5,1,6]=>1111000=>0000111
[2,4,8,7,3,1,5,6]=>[7,3,8,4,2,1,5,6]=>1111000=>0000111
[8,7,4,6,2,3,1,5]=>[6,4,2,7,3,8,1,5]=>1111000=>0000111
[5,6,8,7,2,3,1,4]=>[7,2,8,3,6,1,5,4]=>1111000=>0000111
[6,4,8,7,2,3,1,5]=>[7,2,8,4,3,6,1,5]=>1111000=>0000111
[3,1,7,4,2,8,6,5]=>[4,8,6,7,3,1,2,5]=>1010010=>0101101
[3,2,8,4,1,7,6,5]=>[2,4,7,6,8,3,1,5]=>1010010=>0101101
[7,6,4,8,2,3,1,5]=>[8,4,2,6,3,7,1,5]=>1111000=>0000111
[5,7,6,8,2,3,1,4]=>[8,2,6,3,7,1,5,4]=>1111000=>0000111
[4,7,6,8,2,3,1,5]=>[8,2,6,3,7,4,1,5]=>1111000=>0000111
[3,7,4,8,2,5,1,6]=>[8,4,2,5,7,3,1,6]=>1111000=>0000111
[2,3,7,4,1,6,8,5]=>[4,6,8,7,3,2,1,5]=>1110001=>0001110
[8,1,6,4,2,3,7,5]=>[4,6,1,2,7,8,3,5]=>1010000=>0101111
[4,7,8,6,2,3,1,5]=>[6,2,8,3,7,4,1,5]=>1111000=>0000111
[2,4,7,3,1,5,8,6]=>[8,7,3,4,2,1,5,6]=>1110001=>0001110
[8,5,7,6,2,3,1,4]=>[6,2,7,3,5,1,8,4]=>1111000=>0000111
[7,5,8,6,2,3,1,4]=>[6,2,8,3,5,1,7,4]=>1111000=>0000111
[7,1,6,4,2,3,8,5]=>[4,6,1,2,8,7,3,5]=>1010001=>0101110
[4,8,7,6,2,3,1,5]=>[6,2,7,3,8,4,1,5]=>1111000=>0000111
[4,3,6,1,5,8,7,2]=>[5,7,8,6,3,1,4,2]=>1110010=>0001101
[4,3,6,5,1,8,7,2]=>[5,3,1,7,8,6,4,2]=>1111010=>0000101
[4,6,3,5,1,8,7,2]=>[3,5,1,7,8,6,4,2]=>1101010=>0010101
[4,6,3,1,5,8,7,2]=>[3,5,7,8,6,1,4,2]=>1100010=>0011101
[4,1,6,5,3,8,7,2]=>[5,3,7,8,6,4,1,2]=>1011010=>0100101
[4,6,1,5,3,8,7,2]=>[5,1,3,7,8,6,4,2]=>1101010=>0010101
[2,6,5,1,8,7,3,4]=>[7,5,2,1,8,6,3,4]=>1110110=>0001001
[2,6,5,8,1,7,3,4]=>[7,2,1,5,3,8,6,4]=>1111010=>0000101
[2,6,5,8,1,3,7,4]=>[7,8,2,1,5,3,6,4]=>1111000=>0000111
[2,6,5,8,3,1,7,4]=>[7,8,3,5,2,1,6,4]=>1111000=>0000111
[2,6,5,3,8,1,7,4]=>[7,8,5,3,6,2,1,4]=>1110100=>0001011
[4,6,1,5,8,3,7,2]=>[7,8,5,1,3,6,4,2]=>1101100=>0010011
[4,1,6,5,8,3,7,2]=>[7,8,5,3,6,4,1,2]=>1011100=>0100011
[1,4,6,5,8,3,7,2]=>[1,7,8,5,3,6,4,2]=>0111100=>1000011
[4,1,6,5,8,7,3,2]=>[7,5,3,8,6,4,1,2]=>1011110=>0100001
[2,6,5,3,8,7,1,4]=>[7,5,3,8,6,2,1,4]=>1110110=>0001001
[6,4,3,8,7,1,5,2]=>[3,7,4,1,8,5,6,2]=>1101100=>0010011
[6,4,8,3,7,1,5,2]=>[7,3,4,1,8,5,6,2]=>1110100=>0001011
[2,6,8,5,3,7,1,4]=>[5,3,7,2,1,8,6,4]=>1111010=>0000101
[4,6,8,1,5,7,3,2]=>[5,7,1,8,6,3,4,2]=>1110010=>0001101
[4,6,1,8,5,7,3,2]=>[5,7,1,3,8,6,4,2]=>1101010=>0010101
[4,1,6,8,5,7,3,2]=>[5,7,3,8,6,4,1,2]=>1011010=>0100101
[1,4,6,8,5,7,3,2]=>[1,5,7,3,8,6,4,2]=>0111010=>1000101
[1,4,6,8,5,3,7,2]=>[1,5,7,8,3,6,4,2]=>0111000=>1000111
[4,6,1,8,5,3,7,2]=>[5,7,8,1,3,6,4,2]=>1101000=>0010111
[2,6,8,5,3,1,7,4]=>[5,3,7,8,2,1,6,4]=>1111000=>0000111
[4,6,8,3,5,1,7,2]=>[5,7,8,3,6,1,4,2]=>1110000=>0001111
[4,6,8,3,1,5,7,2]=>[7,8,3,5,6,1,4,2]=>1110000=>0001111
[4,6,3,1,8,5,7,2]=>[3,7,8,5,6,1,4,2]=>1100100=>0011011
[4,6,3,8,1,5,7,2]=>[3,7,8,1,5,6,4,2]=>1101000=>0010111
[4,6,3,8,5,7,1,2]=>[3,5,7,1,8,6,4,2]=>1101010=>0010101
[4,3,6,8,1,5,7,2]=>[7,8,3,1,5,6,4,2]=>1111000=>0000111
[4,3,6,1,8,5,7,2]=>[7,8,5,6,3,1,4,2]=>1110100=>0001011
[4,3,1,6,8,5,7,2]=>[3,1,7,8,5,6,4,2]=>1101100=>0010011
[4,1,3,6,8,7,5,2]=>[3,7,5,8,6,4,1,2]=>1001110=>0110001
[4,3,6,1,8,7,5,2]=>[7,5,8,6,3,1,4,2]=>1110110=>0001001
[4,3,6,8,1,7,5,2]=>[7,3,1,5,8,6,4,2]=>1111010=>0000101
[6,5,2,8,7,3,1,4]=>[7,2,3,8,5,1,6,4]=>1101100=>0010011
[6,5,2,8,7,1,3,4]=>[7,2,8,5,1,3,6,4]=>1101100=>0010011
[6,2,5,8,7,3,1,4]=>[2,7,3,8,5,1,6,4]=>1011100=>0100011
[4,6,3,8,1,7,5,2]=>[3,7,1,5,8,6,4,2]=>1101010=>0010101
[4,6,3,1,8,7,5,2]=>[3,7,5,8,6,1,4,2]=>1100110=>0011001
[4,1,6,3,8,7,5,2]=>[7,5,8,6,3,4,1,2]=>1010110=>0101001
[1,4,6,3,8,7,5,2]=>[1,7,5,8,6,3,4,2]=>0110110=>1001001
[4,1,6,8,3,7,5,2]=>[7,3,5,8,6,4,1,2]=>1011010=>0100101
[4,6,1,8,3,7,5,2]=>[7,1,3,5,8,6,4,2]=>1101010=>0010101
[4,6,8,1,3,7,5,2]=>[7,1,5,8,6,3,4,2]=>1110010=>0001101
[6,2,8,5,7,1,3,4]=>[2,7,5,1,8,3,6,4]=>1011100=>0100011
[2,4,8,7,1,5,3,6]=>[7,2,1,5,8,4,3,6]=>1111000=>0000111
[4,2,8,7,5,3,1,6]=>[2,5,7,3,8,4,1,6]=>1011000=>0100111
[6,4,1,8,7,5,3,2]=>[7,5,8,4,1,3,6,2]=>1101100=>0010011
[6,1,4,8,7,5,3,2]=>[7,5,8,4,3,6,1,2]=>1011100=>0100011
[6,4,1,8,7,3,5,2]=>[7,4,1,3,8,5,6,2]=>1101100=>0010011
[4,2,8,7,5,1,3,6]=>[2,5,7,1,8,4,3,6]=>1011000=>0100111
[2,4,8,7,3,5,1,6]=>[7,3,5,8,4,2,1,6]=>1111000=>0000111
[2,3,4,5,6,8,9,7,1]=>[9,7,8,6,5,4,3,2,1]=>11111110=>00000001
[2,3,4,7,1,8,6,5]=>[8,6,7,4,3,2,1,5]=>1111010=>0000101
[2,4,5,6,7,8,9,3,1]=>[9,3,8,7,6,5,4,2,1]=>11111110=>00000001
[2,3,4,5,6,7,9,10,8,1]=>[10,8,9,7,6,5,4,3,2,1]=>111111110=>000000001
[2,3,4,7,8,5,6,1]=>[8,5,6,7,4,3,2,1]=>1111100=>0000011
[2,3,4,5,8,1,9,7,6]=>[9,7,8,5,4,3,2,1,6]=>11111010=>00000101
[2,3,6,7,4,8,5,1]=>[8,4,5,7,6,3,2,1]=>1111010=>0000101
[2,3,7,1,4,8,6,5]=>[8,6,7,3,2,1,4,5]=>1110010=>0001101
[2,6,1,3,7,8,5,4]=>[8,5,7,6,2,1,3,4]=>1100110=>0011001
[2,3,4,5,6,7,10,1,8,9]=>[10,7,6,5,4,3,2,1,8,9]=>111111100=>000000011
[2,3,4,5,6,7,8,10,11,9,1]=>[11,9,10,8,7,6,5,4,3,2,1]=>1111111110=>0000000001
[2,3,4,5,8,9,6,7,1]=>[9,6,7,8,5,4,3,2,1]=>11111100=>00000011
[2,3,4,5,6,9,1,10,8,7]=>[10,8,9,6,5,4,3,2,1,7]=>111111010=>000000101
[2,5,6,7,4,8,1,3]=>[8,4,7,6,2,1,5,3]=>1111010=>0000101
[2,3,4,8,1,5,9,7,6]=>[9,7,8,4,3,2,1,5,6]=>11110010=>00001101
[2,3,7,8,4,5,6,1]=>[8,4,5,6,7,3,2,1]=>1111000=>0000111
[2,6,7,3,4,8,5,1]=>[8,3,4,5,7,6,2,1]=>1110010=>0001101
[1,5,3,2,6,4,7,8]=>[1,3,6,5,2,4,7,8]=>0100100=>1011011
[1,5,3,2,6,7,4,8]=>[1,3,7,6,5,2,4,8]=>0100110=>1011001
[1,7,3,2,5,8,4,6]=>[1,3,5,8,2,4,7,6]=>0100010=>1011101
[1,3,2,7,5,4,8,6]=>[1,3,2,5,8,7,4,6]=>0101001=>1010110
[6,5,2,4,3,7,1,8]=>[4,5,2,3,7,6,1,8]=>1100010=>0011101
[6,4,2,5,3,7,1,8]=>[5,4,2,3,7,6,1,8]=>1101010=>0010101
[3,6,4,8,2,1,5,7]=>[8,4,2,6,3,1,5,7]=>1111000=>0000111
[1,6,2,8,5,3,4,7]=>[1,5,8,2,3,6,4,7]=>0101000=>1010111
[4,6,2,3,7,5,1,8]=>[7,5,6,2,3,4,1,8]=>1100100=>0011011
[4,7,2,3,6,5,1,8]=>[6,5,7,2,3,4,1,8]=>1100100=>0011011
[4,7,2,3,5,6,1,8]=>[5,6,7,2,3,4,1,8]=>1100000=>0011111
[5,3,2,7,4,6,1,8]=>[3,2,6,7,4,5,1,8]=>1101000=>0010111
[5,3,2,6,4,7,1,8]=>[3,2,7,6,4,5,1,8]=>1101010=>0010101
[4,6,2,3,5,7,1,8]=>[5,7,6,2,3,4,1,8]=>1100010=>0011101
[3,5,2,1,6,8,4,7]=>[8,6,5,2,3,1,4,7]=>1100110=>0011001
[3,5,2,1,8,6,4,7]=>[6,8,5,2,3,1,4,7]=>1100100=>0011011
[3,6,8,4,2,1,5,7]=>[4,8,2,6,3,1,5,7]=>1110000=>0001111
[4,3,2,6,1,8,5,7]=>[3,2,8,6,4,1,5,7]=>1101010=>0010101
[1,5,8,2,7,4,3,6]=>[1,7,2,4,8,5,3,6]=>0110100=>1001011
[1,7,2,3,4,8,6,5]=>[1,8,6,7,2,3,4,5]=>0100010=>1011101
[6,8,2,3,4,1,7,5]=>[7,8,2,3,4,6,1,5]=>1100000=>0011111
[4,1,8,2,3,5,7,6]=>[7,8,1,2,4,3,5,6]=>1010000=>0101111
[2,3,1,8,4,5,7,6]=>[3,2,1,7,8,4,5,6]=>1101000=>0010111
[7,3,2,1,4,5,8,6]=>[3,2,8,7,1,4,5,6]=>1100001=>0011110
[7,8,1,4,3,5,2,6]=>[4,8,1,3,5,7,2,6]=>1100000=>0011111
[7,1,2,3,4,6,8,5]=>[6,8,7,1,2,3,4,5]=>1000001=>0111110
[6,1,2,3,4,8,7,5]=>[7,8,6,1,2,3,4,5]=>1000010=>0111101
[1,8,2,3,4,7,6,5]=>[1,7,6,8,2,3,4,5]=>0100010=>1011101
[8,1,2,3,4,6,7,5]=>[6,7,8,1,2,3,4,5]=>1000000=>0111111
[2,8,1,3,5,4,7,6]=>[5,7,8,2,1,3,4,6]=>1100000=>0011111
[8,3,2,1,4,5,7,6]=>[3,2,7,8,1,4,5,6]=>1100000=>0011111
[3,8,2,1,5,6,4,7]=>[5,6,8,2,3,1,4,7]=>1100000=>0011111
[3,8,2,1,6,5,4,7]=>[6,5,8,2,3,1,4,7]=>1100100=>0011011
[1,7,8,3,5,4,2,6]=>[1,5,8,3,4,7,2,6]=>0110000=>1001111
[3,8,4,6,2,1,5,7]=>[6,4,2,8,3,1,5,7]=>1111000=>0000111
[8,4,2,5,3,1,6,7]=>[5,4,2,3,8,1,6,7]=>1101000=>0010111
[8,5,2,4,3,1,6,7]=>[4,5,2,3,8,1,6,7]=>1100000=>0011111
[8,3,2,5,4,1,6,7]=>[3,2,5,4,8,1,6,7]=>1101000=>0010111
[4,3,2,5,1,8,6,7]=>[3,2,5,4,1,8,6,7]=>1101010=>0010101
[3,5,2,4,1,8,6,7]=>[4,5,2,3,1,8,6,7]=>1100010=>0011101
[1,8,7,3,5,4,2,6]=>[1,5,7,3,4,8,2,6]=>0110000=>1001111
[6,3,2,1,8,4,5,7]=>[3,2,8,1,4,6,5,7]=>1100100=>0011011
[7,3,2,8,4,5,1,6]=>[3,2,8,4,5,7,1,6]=>1101000=>0010111
[7,8,2,3,4,6,1,5]=>[6,8,2,3,4,7,1,5]=>1100000=>0011111
[1,7,2,3,4,6,8,5]=>[1,6,8,7,2,3,4,5]=>0100001=>1011110
[1,6,2,3,4,8,7,5]=>[1,7,8,6,2,3,4,5]=>0100010=>1011101
[7,6,2,3,4,1,8,5]=>[6,2,3,4,8,7,1,5]=>1100001=>0011110
[8,6,2,3,4,1,7,5]=>[6,2,3,4,7,8,1,5]=>1100000=>0011111
[8,1,7,3,5,4,2,6]=>[5,7,3,4,8,1,2,6]=>1010000=>0101111
[8,3,2,7,4,5,1,6]=>[3,2,7,4,5,8,1,6]=>1101000=>0010111
[6,7,2,3,4,1,8,5]=>[8,7,2,3,4,6,1,5]=>1100001=>0011110
[7,6,2,3,4,8,1,5]=>[8,6,2,3,4,7,1,5]=>1100010=>0011101
[8,6,2,3,4,7,1,5]=>[7,6,2,3,4,8,1,5]=>1100010=>0011101
[6,3,4,8,7,5,1,2]=>[7,5,8,4,3,1,6,2]=>1111100=>0000011
[4,8,7,5,3,6,1,2]=>[5,3,6,7,1,8,4,2]=>1111000=>0000111
[5,8,4,2,1,6,7,3]=>[4,2,6,7,8,1,5,3]=>1110000=>0001111
[5,8,4,1,2,6,7,3]=>[4,1,6,7,8,2,5,3]=>1110000=>0001111
[5,3,7,2,6,1,8,4]=>[6,3,2,8,7,5,1,4]=>1110101=>0001010
[5,2,8,1,6,3,7,4]=>[2,6,1,7,8,5,3,4]=>1010100=>0101011
[5,8,2,1,4,7,6,3]=>[7,6,8,2,4,5,1,3]=>1100010=>0011101
[4,8,2,5,1,7,6,3]=>[5,2,7,6,8,4,1,3]=>1101010=>0010101
[4,8,1,5,2,7,6,3]=>[5,1,7,6,8,4,2,3]=>1101010=>0010101
[5,8,1,2,4,7,6,3]=>[7,6,8,1,4,5,2,3]=>1100010=>0011101
[5,2,8,3,6,7,1,4]=>[2,7,6,3,8,5,1,4]=>1010110=>0101001
[3,8,7,6,2,4,1,5]=>[6,2,7,4,8,3,1,5]=>1111000=>0000111
[2,8,7,6,4,1,3,5]=>[6,4,7,2,1,8,3,5]=>1111000=>0000111
[7,8,2,6,5,1,3,4]=>[5,6,2,8,1,3,7,4]=>1101000=>0010111
[1,8,7,6,4,2,3,5]=>[1,6,4,7,2,8,3,5]=>0111000=>1000111
[2,8,7,6,3,1,4,5]=>[6,3,7,2,1,8,4,5]=>1111000=>0000111
[1,8,7,6,2,4,3,5]=>[1,6,2,7,4,8,3,5]=>0111000=>1000111
[2,8,1,4,5,6,7,3]=>[4,5,6,7,8,2,1,3]=>1100000=>0011111
[2,1,7,3,6,5,8,4]=>[2,1,6,5,8,7,3,4]=>1010101=>0101010
[3,1,7,2,6,5,8,4]=>[6,5,8,7,3,1,2,4]=>1010101=>0101010
[3,2,7,1,6,5,8,4]=>[2,6,5,8,7,3,1,4]=>1010101=>0101010
[6,1,2,8,5,7,3,4]=>[5,7,1,2,3,8,6,4]=>1001010=>0110101
[6,2,1,8,5,7,3,4]=>[2,5,7,1,3,8,6,4]=>1001010=>0110101
[6,3,1,8,5,7,2,4]=>[3,1,5,7,2,8,6,4]=>1101010=>0010101
[6,1,3,8,5,2,7,4]=>[3,5,7,8,1,2,6,4]=>1001000=>0110111
[2,3,7,1,6,8,5,4]=>[8,6,5,7,3,2,1,4]=>1110110=>0001001
[1,3,7,2,6,8,5,4]=>[1,8,6,5,7,3,2,4]=>0110110=>1001001
[3,2,6,7,5,8,1,4]=>[2,5,8,3,1,7,6,4]=>1011010=>0100101
[1,2,7,5,6,3,8,4]=>[1,2,6,5,3,8,7,4]=>0011101=>1100010
[2,8,7,6,4,3,1,5]=>[6,4,7,3,8,2,1,5]=>1111000=>0000111
[3,8,7,6,2,1,5,4]=>[6,2,7,3,1,5,8,4]=>1111000=>0000111
[4,8,7,6,2,1,3,5]=>[6,2,7,1,8,4,3,5]=>1111000=>0000111
[4,8,7,6,1,3,2,5]=>[6,1,7,3,8,4,2,5]=>1111000=>0000111
[3,8,7,6,4,1,2,5]=>[6,4,7,1,8,3,2,5]=>1111000=>0000111
[7,8,3,6,5,1,2,4]=>[3,5,6,1,8,2,7,4]=>1101000=>0010111
[2,3,7,5,6,8,1,4]=>[8,6,5,3,2,1,7,4]=>1111110=>0000001
[3,8,7,6,4,2,1,5]=>[6,4,7,2,8,3,1,5]=>1111000=>0000111
[5,1,4,6,8,2,3,7]=>[8,4,1,2,6,5,3,7]=>1011100=>0100011
[1,7,6,3,5,4,8,2]=>[1,5,6,3,4,8,7,2]=>0110001=>1001110
[4,3,7,2,6,5,1,8]=>[6,5,7,3,2,4,1,8]=>1110100=>0001011
[3,4,6,1,5,7,2,8]=>[5,7,6,1,4,3,2,8]=>1110010=>0001101
[1,6,8,5,7,3,4,2]=>[1,7,5,3,8,4,6,2]=>0111100=>1000011
[2,4,1,5,8,6,3,7]=>[6,8,5,4,2,1,3,7]=>1101100=>0010011
[5,6,7,2,1,4,8,3]=>[8,7,2,6,1,4,5,3]=>1110001=>0001110
[7,8,6,5,1,2,4,3]=>[5,1,6,2,8,4,7,3]=>1111000=>0000111
[1,3,6,5,7,8,2,4]=>[1,8,5,3,2,7,6,4]=>0111110=>1000001
[7,4,8,5,3,1,6,2]=>[5,3,8,4,1,6,7,2]=>1111000=>0000111
[6,8,5,2,4,1,7,3]=>[5,2,4,7,8,1,6,3]=>1110000=>0001111
[2,3,1,6,8,5,7,4]=>[3,2,1,7,8,5,6,4]=>1101100=>0010011
[7,3,2,5,1,4,8,6]=>[3,2,5,1,8,7,4,6]=>1101001=>0010110
[1,5,8,3,4,6,7,2]=>[1,6,7,8,3,4,5,2]=>0110000=>1001111
[8,3,1,2,4,7,6,5]=>[3,1,7,6,8,2,4,5]=>1100010=>0011101
[2,3,8,1,6,5,4,7]=>[6,5,8,3,2,1,4,7]=>1110100=>0001011
[8,1,4,7,2,5,3,6]=>[7,4,1,2,5,8,3,6]=>1011000=>0100111
[3,5,2,4,1,7,8,6]=>[4,5,2,3,1,8,7,6]=>1100011=>0011100
[3,4,7,8,6,2,1,5]=>[6,2,8,4,3,1,7,5]=>1111100=>0000011
[3,4,8,6,2,7,1,5]=>[7,6,2,8,4,3,1,5]=>1111010=>0000101
[5,8,2,1,6,7,3,4]=>[7,6,2,8,5,1,3,4]=>1100110=>0011001
[7,3,2,8,6,4,1,5]=>[3,2,6,4,8,1,7,5]=>1101100=>0010011
[2,7,8,4,6,3,1,5]=>[4,6,3,8,2,1,7,5]=>1110100=>0001011
[1,4,5,7,2,6,8,3]=>[1,6,8,7,2,5,4,3]=>0111001=>1000110
[7,3,5,2,6,1,8,4]=>[6,5,3,2,8,7,1,4]=>1110101=>0001010
[8,5,2,3,6,1,7,4]=>[6,5,2,3,7,8,1,4]=>1100100=>0011011
[8,1,6,3,5,7,2,4]=>[5,7,6,3,8,1,2,4]=>1010010=>0101101
[2,8,6,4,3,7,1,5]=>[4,7,6,3,8,2,1,5]=>1110010=>0001101
[4,2,8,7,3,6,1,5]=>[2,6,7,3,8,4,1,5]=>1011000=>0100111
[4,5,8,7,1,2,6,3]=>[7,1,6,8,2,5,4,3]=>1111000=>0000111
[1,5,8,7,3,2,6,4]=>[1,7,3,6,8,2,5,4]=>0111000=>1000111
[4,5,8,7,3,2,1,6]=>[7,3,8,2,5,4,1,6]=>1111000=>0000111
[2,6,8,1,7,5,4,3]=>[7,5,8,2,1,4,6,3]=>1110100=>0001011
[3,6,8,4,7,2,1,5]=>[4,7,2,8,3,1,6,5]=>1110100=>0001011
[2,5,8,3,7,6,1,4]=>[6,7,3,8,5,2,1,4]=>1110100=>0001011
[3,2,8,4,7,6,1,5]=>[2,4,6,7,3,1,8,5]=>1010100=>0101011
[5,6,8,2,3,7,1,4]=>[7,2,8,6,3,5,1,4]=>1110010=>0001101
[1,6,8,4,2,7,5,3]=>[1,4,7,2,5,8,6,3]=>0110010=>1001101
[1,5,8,2,3,7,6,4]=>[1,7,6,8,2,5,3,4]=>0110010=>1001101
[5,6,8,1,3,2,7,4]=>[7,8,1,6,3,5,2,4]=>1110000=>0001111
[1,6,8,4,3,2,7,5]=>[1,4,7,8,3,6,2,5]=>0110000=>1001111
[5,6,8,4,3,2,1,7]=>[4,8,3,6,2,5,1,7]=>1110000=>0001111
[7,3,1,8,6,2,5,4]=>[3,1,6,2,8,5,7,4]=>1101100=>0010011
[7,2,4,8,3,6,1,5]=>[2,6,8,4,3,7,1,5]=>1011000=>0100111
[7,4,5,8,3,2,1,6]=>[8,3,5,4,2,7,1,6]=>1111000=>0000111
[1,6,2,8,7,5,4,3]=>[1,7,5,8,4,6,2,3]=>0101100=>1010011
[1,6,4,8,7,2,5,3]=>[1,7,4,2,8,5,6,3]=>0111100=>1000011
[3,2,5,8,7,6,1,4]=>[2,6,7,3,1,8,5,4]=>1011100=>0100011
[1,6,4,8,2,7,5,3]=>[1,7,4,2,5,8,6,3]=>0111010=>1000101
[1,4,5,8,2,7,6,3]=>[1,7,6,8,2,5,4,3]=>0111010=>1000101
[2,4,5,8,3,7,1,6]=>[7,3,5,4,2,1,8,6]=>1111010=>0000101
[1,6,4,8,3,2,7,5]=>[1,7,8,4,3,6,2,5]=>0111000=>1000111
[1,4,5,8,3,2,7,6]=>[1,7,8,3,5,4,2,6]=>0111000=>1000111
[7,6,1,4,8,2,5,3]=>[4,8,1,6,5,7,2,3]=>1100100=>0011011
[7,6,3,4,8,2,1,5]=>[3,4,8,2,6,1,7,5]=>1100100=>0011011
[7,2,5,1,8,6,4,3]=>[2,6,8,5,1,4,7,3]=>1010100=>0101011
[7,2,5,3,8,6,1,4]=>[2,6,8,5,3,7,1,4]=>1010100=>0101011
[7,2,1,4,8,6,5,3]=>[2,4,6,8,5,7,1,3]=>1000100=>0111011
[7,2,1,3,8,6,5,4]=>[2,6,8,5,7,1,3,4]=>1000100=>0111011
[7,2,3,4,8,6,1,5]=>[2,3,4,6,8,1,7,5]=>1000100=>0111011
[7,3,5,4,8,2,1,6]=>[4,8,5,3,2,7,1,6]=>1110100=>0001011
[1,6,5,3,8,2,7,4]=>[1,7,8,5,3,6,2,4]=>0110100=>1001011
[1,6,3,4,8,2,7,5]=>[1,3,4,7,8,2,6,5]=>0100100=>1011011
[1,3,5,4,8,2,7,6]=>[1,4,7,8,5,3,2,6]=>0110100=>1001011
[7,6,5,2,3,8,1,4]=>[5,2,8,6,3,7,1,4]=>1110010=>0001101
[7,6,1,2,3,8,5,4]=>[8,6,1,5,7,2,3,4]=>1100010=>0011101
[7,1,5,4,2,8,6,3]=>[4,5,1,2,8,6,7,3]=>1010010=>0101101
[7,1,5,2,3,8,6,4]=>[5,1,2,8,6,7,3,4]=>1010010=>0101101
[7,1,2,4,3,8,6,5]=>[4,8,6,7,1,2,3,5]=>1000010=>0111101
[7,1,5,4,3,2,8,6]=>[4,5,3,8,7,1,2,6]=>1010001=>0101110
[3,1,4,2,6,8,7,5]=>[4,3,1,2,7,8,6,5]=>1010110=>0101001
[8,3,4,2,6,1,7,5]=>[4,3,2,6,1,7,8,5]=>1110100=>0001011
[4,8,1,2,7,5,3,6]=>[7,5,8,1,4,2,3,6]=>1100100=>0011011
[7,4,1,2,8,5,3,6]=>[4,1,8,5,7,2,3,6]=>1100100=>0011011
[8,7,4,2,1,5,3,6]=>[4,2,7,1,5,8,3,6]=>1110000=>0001111
[7,4,3,1,5,6,8,2]=>[3,4,1,5,6,8,7,2]=>1100001=>0011110
[6,7,4,1,5,8,3,2]=>[4,1,5,8,3,7,6,2]=>1110010=>0001101
[4,6,1,2,8,5,3,7]=>[8,5,6,1,4,2,3,7]=>1100100=>0011011
[8,4,3,1,5,6,7,2]=>[3,4,1,5,6,7,8,2]=>1100000=>0011111
[4,5,3,1,8,6,7,2]=>[3,6,7,8,5,1,4,2]=>1100100=>0011011
[5,1,3,4,8,6,7,2]=>[3,4,6,7,8,5,1,2]=>1000100=>0111011
[5,4,3,8,1,6,7,2]=>[3,6,7,8,4,1,5,2]=>1101000=>0010111
[8,5,3,4,1,6,7,2]=>[3,4,5,1,6,7,8,2]=>1100000=>0011111
[6,7,3,2,5,1,4,8]=>[3,5,7,2,6,1,4,8]=>1100000=>0011111
[6,8,3,2,5,1,4,7]=>[3,5,8,2,6,1,4,7]=>1100000=>0011111
[5,1,3,4,7,6,8,2]=>[3,4,6,8,7,5,1,2]=>1000101=>0111010
[6,1,4,2,7,5,3,8]=>[4,1,2,7,5,6,3,8]=>1010100=>0101011
[7,6,4,2,1,5,3,8]=>[4,2,6,1,5,7,3,8]=>1110000=>0001111
[8,2,7,6,5,4,1,3]=>[2,5,6,4,7,1,8,3]=>1011000=>0100111
[7,2,8,6,5,4,3,1]=>[2,5,6,4,8,3,7,1]=>1011000=>0100111
[8,7,2,6,5,4,1,3]=>[5,6,4,7,2,8,1,3]=>1101000=>0010111
[3,2,8,7,6,5,1,4]=>[2,6,5,7,3,1,8,4]=>1011100=>0100011
[4,8,7,6,5,3,1,2]=>[5,6,3,7,1,8,4,2]=>1111000=>0000111
[4,8,5,7,6,3,2,1]=>[6,3,7,5,2,8,4,1]=>1111100=>0000011
[2,8,7,6,3,5,4,1]=>[6,3,5,7,4,8,2,1]=>1111000=>0000111
[8,5,6,1,3,2,4,7]=>[6,1,5,3,8,2,4,7]=>1110000=>0001111
[7,8,1,5,3,2,4,6]=>[5,1,3,8,2,7,4,6]=>1101000=>0010111
[8,1,7,5,3,2,4,6]=>[5,3,7,1,2,8,4,6]=>1011000=>0100111
[8,6,1,4,5,2,3,7]=>[4,5,6,1,8,2,3,7]=>1100000=>0011111
[8,6,3,1,5,2,4,7]=>[3,5,6,1,8,2,4,7]=>1100000=>0011111
[8,6,2,1,5,4,3,7]=>[5,6,2,4,8,1,3,7]=>1100000=>0011111
[8,5,2,6,1,4,3,7]=>[6,2,5,4,8,1,3,7]=>1101000=>0010111
[7,8,2,1,5,4,3,6]=>[5,8,2,4,7,1,3,6]=>1100000=>0011111
[7,8,3,1,5,2,4,6]=>[3,5,8,1,7,2,4,6]=>1100000=>0011111
[8,2,7,5,1,3,4,6]=>[2,5,1,7,3,8,4,6]=>1011000=>0100111
[8,2,6,1,7,4,3,5]=>[2,7,1,4,6,3,8,5]=>1010100=>0101011
[8,1,7,4,3,2,6,5]=>[4,7,3,6,8,1,2,5]=>1010000=>0101111
[5,8,1,6,7,2,3,4]=>[7,1,6,2,3,8,5,4]=>1101100=>0010011
[5,7,6,1,8,2,3,4]=>[8,1,6,2,7,5,3,4]=>1110100=>0001011
[6,7,2,5,1,8,3,4]=>[5,2,8,1,3,7,6,4]=>1101010=>0010101
[7,5,1,6,8,2,3,4]=>[8,1,6,5,2,3,7,4]=>1101100=>0010011
[6,7,3,8,1,2,4,5]=>[3,8,1,7,2,6,4,5]=>1101000=>0010111
[7,6,1,4,8,2,3,5]=>[4,8,1,6,2,3,7,5]=>1100100=>0011011
[8,1,6,4,7,2,3,5]=>[4,7,1,2,6,3,8,5]=>1010100=>0101011
[7,5,8,1,3,2,4,6]=>[8,1,5,3,7,2,4,6]=>1110000=>0001111
[7,8,4,1,3,2,5,6]=>[4,1,8,3,7,2,5,6]=>1110000=>0001111
[8,3,7,4,1,2,5,6]=>[4,7,3,1,8,2,5,6]=>1110000=>0001111
[8,5,1,7,3,2,4,6]=>[7,1,3,5,2,8,4,6]=>1101000=>0010111
[6,8,1,7,3,2,4,5]=>[7,1,3,8,2,6,4,5]=>1101000=>0010111
[7,1,8,4,3,6,2,5]=>[4,6,8,3,7,1,2,5]=>1010000=>0101111
[7,3,1,8,6,4,2,5]=>[3,1,6,4,8,2,7,5]=>1101100=>0010011
[7,3,1,8,5,6,2,4]=>[3,1,5,6,8,2,7,4]=>1101000=>0010111
[6,2,7,8,3,1,5,4]=>[2,8,3,7,1,5,6,4]=>1011000=>0100111
[5,8,1,7,3,2,6,4]=>[7,1,3,6,8,2,5,4]=>1101000=>0010111
[8,4,1,7,3,2,6,5]=>[7,4,1,3,6,8,2,5]=>1101000=>0010111
[8,2,7,4,1,3,6,5]=>[2,4,7,1,6,8,3,5]=>1010000=>0101111
[7,4,8,2,1,3,6,5]=>[8,2,4,1,6,7,3,5]=>1110000=>0001111
[8,2,3,6,7,1,5,4]=>[2,3,7,1,6,5,8,4]=>1001100=>0110011
[2,6,8,7,1,5,4,3]=>[7,2,1,5,8,4,6,3]=>1111000=>0000111
[7,8,5,2,3,6,4,1]=>[5,2,6,8,3,4,7,1]=>1110000=>0001111
[8,7,5,2,3,1,6,4]=>[5,2,7,3,6,8,1,4]=>1110000=>0001111
[3,5,2,6,8,1,4,7]=>[8,2,3,1,6,5,4,7]=>1101100=>0010011
[2,4,5,7,3,6,8,1]=>[6,8,7,3,5,4,2,1]=>1111001=>0000110
[2,4,5,3,6,8,1,7]=>[8,6,5,3,4,2,1,7]=>1110110=>0001001
[5,2,4,6,8,1,3,7]=>[2,8,4,1,6,5,3,7]=>1011100=>0100011
[4,3,5,2,6,8,1,7]=>[8,6,5,3,2,4,1,7]=>1110110=>0001001
[5,7,1,3,4,6,8,2]=>[6,8,7,1,3,4,5,2]=>1100001=>0011110
[4,5,7,1,3,6,8,2]=>[6,8,7,1,5,3,4,2]=>1110001=>0001110
[4,6,3,5,7,2,8,1]=>[3,8,7,5,2,6,4,1]=>1101101=>0010010
[3,5,6,4,1,7,8,2]=>[4,8,7,6,1,5,3,2]=>1110011=>0001100
[3,1,5,6,7,4,8,2]=>[8,7,4,6,5,3,1,2]=>1011101=>0100010
[6,4,7,1,3,5,8,2]=>[8,7,1,4,3,5,6,2]=>1110001=>0001110
[1,6,7,3,4,5,8,2]=>[1,8,7,3,4,5,6,2]=>0110001=>1001110
[2,6,7,4,5,8,1,3]=>[4,5,8,2,1,7,6,3]=>1110010=>0001101
[5,3,6,1,2,7,8,4]=>[8,7,6,3,1,5,2,4]=>1110011=>0001100
[3,5,2,6,7,4,8,1]=>[8,7,4,6,5,2,3,1]=>1101101=>0010010
[5,2,6,1,3,7,8,4]=>[2,8,7,6,1,5,3,4]=>1010011=>0101100
[7,2,4,6,8,1,3,5]=>[2,8,4,1,6,3,7,5]=>1011100=>0100011
[3,7,2,4,6,8,1,5]=>[4,8,6,2,3,1,7,5]=>1100110=>0011001
[3,5,7,2,6,8,1,4]=>[8,6,2,7,5,3,1,4]=>1110110=>0001001
[6,3,7,2,5,8,1,4]=>[5,8,3,2,7,6,1,4]=>1110010=>0001101
[6,3,5,7,2,8,1,4]=>[8,3,2,5,1,7,6,4]=>1111010=>0000101
[6,3,5,7,2,4,8,1]=>[8,7,3,2,5,4,6,1]=>1111001=>0000110
[6,2,4,5,1,7,8,3]=>[2,5,4,1,8,7,6,3]=>1011011=>0100100
[4,7,1,2,5,6,8,3]=>[5,6,8,7,1,4,2,3]=>1100001=>0011110
[4,6,7,1,2,5,8,3]=>[8,7,1,5,6,2,4,3]=>1110001=>0001110
[5,4,2,6,7,3,8,1]=>[8,7,4,2,3,6,5,1]=>1101101=>0010010
[5,4,2,6,1,7,8,3]=>[8,7,6,4,2,5,1,3]=>1101011=>0010100
[5,6,4,1,2,7,8,3]=>[4,1,8,7,6,2,5,3]=>1110011=>0001100
[6,4,5,1,2,7,8,3]=>[5,1,4,2,8,7,6,3]=>1110011=>0001100
[5,6,4,7,1,3,8,2]=>[8,7,4,1,6,3,5,2]=>1111001=>0000110
[5,4,6,3,1,7,8,2]=>[8,7,6,3,4,1,5,2]=>1110011=>0001100
[7,5,3,2,4,8,1,6]=>[3,5,2,4,8,1,7,6]=>1100010=>0011101
[8,4,5,2,6,1,3,7]=>[6,5,2,4,1,8,3,7]=>1110100=>0001011
[8,5,4,2,1,6,3,7]=>[4,2,5,1,6,8,3,7]=>1110000=>0001111
[8,4,5,3,1,6,2,7]=>[5,3,4,1,6,8,2,7]=>1110000=>0001111
[7,5,4,2,1,8,3,6]=>[4,2,5,1,8,3,7,6]=>1110010=>0001101
[7,5,4,2,1,6,8,3]=>[4,2,5,1,6,8,7,3]=>1110001=>0001110
[7,4,3,5,6,1,8,2]=>[3,6,5,4,1,8,7,2]=>1101101=>0010010
[6,7,3,4,1,5,8,2]=>[3,4,8,7,1,5,6,2]=>1100001=>0011110
[5,6,3,7,8,1,2,4]=>[3,8,1,7,2,6,5,4]=>1101100=>0010011
[5,6,3,7,2,4,8,1]=>[3,8,7,2,6,4,5,1]=>1101001=>0010110
[7,6,4,2,1,3,8,5]=>[4,2,6,1,8,7,3,5]=>1110001=>0001110
[7,6,3,4,1,2,8,5]=>[3,4,6,1,8,7,2,5]=>1100001=>0011110
[7,6,3,2,4,1,8,5]=>[3,6,2,4,8,7,1,5]=>1100001=>0011110
[6,7,3,2,5,1,8,4]=>[3,5,8,7,2,6,1,4]=>1100001=>0011110
[6,5,3,2,7,8,1,4]=>[3,8,5,2,7,6,1,4]=>1100110=>0011001
[6,4,5,2,7,3,8,1]=>[8,7,5,2,4,3,6,1]=>1110101=>0001010
[7,4,5,6,1,2,8,3]=>[6,1,5,4,2,8,7,3]=>1111001=>0000110
[7,5,6,2,1,3,8,4]=>[6,2,5,1,8,7,3,4]=>1110001=>0001110
[6,7,3,5,1,2,8,4]=>[3,5,1,8,7,2,6,4]=>1101001=>0010110
[5,6,7,2,4,1,8,3]=>[8,7,2,4,6,1,5,3]=>1110001=>0001110
[5,6,4,2,7,8,1,3]=>[4,2,8,1,7,6,5,3]=>1110110=>0001001
[6,5,7,2,1,8,3,4]=>[8,2,5,1,7,6,3,4]=>1110010=>0001101
[6,5,7,2,1,4,8,3]=>[8,7,2,5,1,4,6,3]=>1110001=>0001110
[3,7,8,5,6,1,4,2]=>[6,5,1,8,4,7,3,2]=>1111100=>0000011
[1,7,8,5,6,3,4,2]=>[1,6,5,3,8,4,7,2]=>0111100=>1000011
[3,7,5,8,6,1,4,2]=>[6,1,8,5,4,7,3,2]=>1111100=>0000011
[3,7,5,8,6,4,1,2]=>[6,4,8,5,1,7,3,2]=>1111100=>0000011
[5,7,3,8,6,4,1,2]=>[3,6,4,8,1,7,5,2]=>1101100=>0010011
[7,3,5,8,6,4,1,2]=>[6,4,8,5,3,1,7,2]=>1111100=>0000011
[3,5,7,8,6,4,1,2]=>[6,4,8,1,7,5,3,2]=>1111100=>0000011
[1,5,7,8,3,6,4,2]=>[1,6,8,3,7,4,5,2]=>0111000=>1000111
[7,3,5,8,6,1,4,2]=>[6,3,1,8,5,4,7,2]=>1111100=>0000011
[7,3,8,5,6,1,4,2]=>[6,5,3,1,8,4,7,2]=>1111100=>0000011
[7,8,1,5,6,3,4,2]=>[6,5,1,3,8,4,7,2]=>1101100=>0010011
[7,1,8,5,6,3,4,2]=>[6,5,3,8,4,7,1,2]=>1011100=>0100011
[7,1,5,8,6,3,4,2]=>[6,3,8,5,4,7,1,2]=>1011100=>0100011
[5,1,7,8,3,6,4,2]=>[6,8,3,7,4,5,1,2]=>1011000=>0100111
[3,1,7,8,5,6,4,2]=>[5,6,8,4,7,3,1,2]=>1011000=>0100111
[1,3,7,8,5,6,4,2]=>[1,5,6,8,4,7,3,2]=>0111000=>1000111
[7,1,5,3,8,6,4,2]=>[6,8,5,3,4,7,1,2]=>1010100=>0101011
[7,1,5,8,3,6,4,2]=>[6,8,3,5,4,7,1,2]=>1011000=>0100111
[7,8,3,5,1,6,4,2]=>[3,5,1,6,8,4,7,2]=>1101000=>0010111
[7,3,5,8,1,6,4,2]=>[6,8,3,1,5,4,7,2]=>1111000=>0000111
[5,3,7,1,8,6,4,2]=>[6,8,3,1,4,7,5,2]=>1110100=>0001011
[5,7,3,1,8,6,4,2]=>[3,6,8,1,4,7,5,2]=>1100100=>0011011
[3,7,5,8,1,6,4,2]=>[6,8,1,5,4,7,3,2]=>1111000=>0000111
[1,7,8,5,3,6,4,2]=>[1,5,3,6,8,4,7,2]=>0111000=>1000111
[3,7,8,5,1,6,4,2]=>[5,1,6,8,4,7,3,2]=>1111000=>0000111
[5,7,8,3,6,1,4,2]=>[6,3,8,1,4,7,5,2]=>1110100=>0001011
[7,5,8,6,1,3,4,2]=>[6,1,8,3,5,4,7,2]=>1111000=>0000111
[5,7,8,1,6,3,4,2]=>[6,1,8,3,4,7,5,2]=>1110100=>0001011
[1,7,3,8,5,6,4,2]=>[1,3,5,6,8,4,7,2]=>0101000=>1010111
[5,7,1,8,3,6,4,2]=>[6,8,1,3,7,4,5,2]=>1101000=>0010111
[7,5,1,8,6,3,4,2]=>[6,1,3,8,5,4,7,2]=>1101100=>0010011
[7,5,8,1,6,3,4,2]=>[6,1,8,5,3,4,7,2]=>1110100=>0001011
[7,8,5,1,6,3,4,2]=>[6,5,1,8,3,4,7,2]=>1110100=>0001011
[7,8,5,1,3,6,4,2]=>[5,1,6,8,3,4,7,2]=>1110000=>0001111
[7,5,1,8,3,6,4,2]=>[6,8,1,3,5,4,7,2]=>1101000=>0010111
[7,5,1,3,8,6,4,2]=>[6,8,5,1,3,4,7,2]=>1100100=>0011011
[3,7,1,5,8,6,4,2]=>[6,8,5,4,7,1,3,2]=>1101100=>0010011
[1,5,3,7,8,6,4,2]=>[1,3,6,8,4,7,5,2]=>0101100=>1010011
[3,5,1,7,8,6,4,2]=>[6,8,4,7,5,1,3,2]=>1101100=>0010011
[5,3,1,7,8,6,4,2]=>[3,1,6,8,4,7,5,2]=>1101100=>0010011
[7,3,1,5,8,6,4,2]=>[3,1,6,8,5,4,7,2]=>1101100=>0010011
[7,8,1,3,5,6,4,2]=>[5,6,8,1,3,4,7,2]=>1100000=>0011111
[7,1,3,8,5,6,4,2]=>[3,5,6,8,4,7,1,2]=>1001000=>0110111
[7,1,3,5,8,6,4,2]=>[3,6,8,5,4,7,1,2]=>1001100=>0110011
[3,1,5,7,8,6,4,2]=>[6,8,4,7,5,3,1,2]=>1011100=>0100011
[5,7,3,4,8,6,1,2]=>[3,4,6,8,1,7,5,2]=>1100100=>0011011
[5,7,3,4,1,8,6,2]=>[3,4,8,6,7,1,5,2]=>1100010=>0011101
[5,7,3,4,1,6,8,2]=>[3,4,6,8,7,1,5,2]=>1100001=>0011110
[5,7,3,1,4,8,6,2]=>[3,8,6,7,1,4,5,2]=>1100010=>0011101
[5,3,7,4,1,2,8,6]=>[4,8,7,3,1,5,2,6]=>1110001=>0001110
[5,3,7,1,4,2,6,8]=>[7,3,1,4,5,2,6,8]=>1110000=>0001111
[5,3,7,1,4,2,8,6]=>[8,7,3,1,4,5,2,6]=>1110001=>0001110
[7,3,8,5,1,2,6,4]=>[5,3,1,8,2,6,7,4]=>1111000=>0000111
[7,3,5,8,1,2,6,4]=>[8,3,1,5,2,6,7,4]=>1111000=>0000111
[3,7,5,1,2,6,4,8]=>[5,1,6,7,3,2,4,8]=>1110000=>0001111
[3,7,5,1,2,6,8,4]=>[5,1,6,8,7,3,2,4]=>1110001=>0001110
[6,1,4,3,5,2,8,7]=>[4,3,5,6,1,2,8,7]=>1010001=>0101110
[4,7,2,5,8,3,1,6]=>[8,5,2,3,7,4,1,6]=>1101100=>0010011
[6,2,4,5,1,3,8,7]=>[2,5,4,1,6,3,8,7]=>1011001=>0100110
[5,1,4,6,3,2,8,7]=>[6,4,3,5,1,2,8,7]=>1011001=>0100110
[3,5,6,2,4,1,8,7]=>[6,2,4,5,3,1,8,7]=>1110001=>0001110
[3,8,6,7,5,4,1,2]=>[5,7,4,6,1,8,3,2]=>1111000=>0000111
[6,2,7,8,3,4,1,5]=>[2,8,3,7,4,6,1,5]=>1011000=>0100111
[2,5,3,4,8,1,7,6]=>[3,4,7,8,5,2,1,6]=>1100100=>0011011
[8,7,1,2,5,3,4,6]=>[5,7,1,8,2,3,4,6]=>1100000=>0011111
[5,1,8,2,3,4,7,6]=>[7,8,1,2,5,3,4,6]=>1010000=>0101111
[5,4,7,6,2,8,1,3]=>[8,6,2,7,4,1,5,3]=>1111010=>0000101
[7,1,3,4,6,8,5,2]=>[3,4,8,6,5,7,1,2]=>1000110=>0111001
[8,3,6,5,7,1,4,2]=>[7,5,3,1,6,4,8,2]=>1111100=>0000011
[4,7,6,1,8,3,5,2]=>[8,1,6,5,7,3,4,2]=>1110100=>0001011
[4,7,2,6,3,8,5,1]=>[8,6,2,3,5,7,4,1]=>1101010=>0010101
[2,1,8,4,6,7,3,5]=>[2,1,4,7,6,3,8,5]=>1010110=>0101001
[4,7,8,6,3,1,2,5]=>[6,3,8,1,7,4,2,5]=>1111000=>0000111
[3,8,1,5,6,7,2,4]=>[7,6,5,1,3,2,8,4]=>1101110=>0010001
[2,8,3,6,7,5,1,4]=>[3,7,5,6,2,1,8,4]=>1101100=>0010011
[3,2,4,5,8,1,7,6]=>[2,7,8,5,4,3,1,6]=>1011100=>0100011
[4,7,3,2,1,8,6,5]=>[3,8,6,7,2,4,1,5]=>1100010=>0011101
[6,4,8,1,7,3,2,5]=>[7,1,4,3,8,2,6,5]=>1110100=>0001011
[4,8,7,2,3,1,5,6]=>[7,2,8,3,4,1,5,6]=>1110000=>0001111
[4,2,3,1,8,7,5,6]=>[2,3,4,1,7,5,8,6]=>1000110=>0111001
[6,7,5,2,3,1,8,4]=>[5,2,8,7,3,6,1,4]=>1110001=>0001110
[4,7,2,6,5,1,8,3]=>[5,6,2,8,7,4,1,3]=>1101001=>0010110
[6,4,2,1,8,5,7,3]=>[4,2,7,8,5,6,1,3]=>1100100=>0011011
[7,2,1,5,6,8,4,3]=>[2,8,6,5,4,7,1,3]=>1001110=>0110001
[8,7,2,6,4,1,5,3]=>[6,4,7,2,5,8,1,3]=>1101000=>0010111
[6,7,8,2,5,3,1,4]=>[5,8,2,7,3,6,1,4]=>1110000=>0001111
[2,1,7,3,6,8,5,4]=>[2,1,8,6,5,7,3,4]=>1010110=>0101001
[2,1,5,7,8,4,6,3]=>[2,1,8,4,6,7,5,3]=>1011100=>0100011
[2,5,7,8,3,6,1,4]=>[6,8,3,7,2,1,5,4]=>1111000=>0000111
[6,4,1,5,7,2,8,3]=>[8,7,5,4,1,6,2,3]=>1101101=>0010010
[7,4,8,1,2,5,6,3]=>[8,1,4,2,5,6,7,3]=>1110000=>0001111
[6,1,7,4,3,2,8,5]=>[4,8,7,3,6,1,2,5]=>1010001=>0101110
[6,8,3,4,2,1,7,5]=>[3,4,7,8,2,6,1,5]=>1100000=>0011111
[4,2,6,1,5,7,8,3]=>[2,5,8,7,6,1,4,3]=>1010011=>0101100
[2,4,6,7,3,5,8,1]=>[8,7,3,5,6,4,2,1]=>1111001=>0000110
[6,5,8,3,7,4,1,2]=>[7,3,4,8,5,1,6,2]=>1110100=>0001011
[7,1,4,8,3,5,6,2]=>[8,4,3,5,6,7,1,2]=>1011000=>0100111
[6,8,7,5,3,4,1,2]=>[5,3,7,4,8,1,6,2]=>1111000=>0000111
[4,8,6,3,1,5,7,2]=>[6,3,5,7,8,1,4,2]=>1110000=>0001111
[3,6,8,7,2,5,1,4]=>[7,2,5,8,3,1,6,4]=>1111000=>0000111
[3,5,7,2,8,6,1,4]=>[6,8,2,7,5,3,1,4]=>1110100=>0001011
[2,5,7,4,8,6,1,3]=>[4,6,8,2,1,7,5,3]=>1110100=>0001011
[1,6,3,7,5,2,8,4]=>[1,3,5,8,7,2,6,4]=>0101001=>1010110
[2,6,3,7,5,1,8,4]=>[3,5,8,7,2,1,6,4]=>1101001=>0010110
[2,6,4,8,7,5,1,3]=>[7,5,8,4,2,1,6,3]=>1111100=>0000011
[6,3,7,2,8,5,1,4]=>[8,5,7,3,2,6,1,4]=>1110100=>0001011
[3,6,2,5,8,7,1,4]=>[7,5,2,3,1,8,6,4]=>1101110=>0010001
[5,2,8,4,7,6,1,3]=>[2,4,6,7,1,8,5,3]=>1010100=>0101011
[2,4,5,8,7,6,1,3]=>[6,7,2,1,8,5,4,3]=>1111100=>0000011
[2,3,5,7,6,1,8,4]=>[6,3,2,1,8,7,5,4]=>1111101=>0000010
[1,3,4,6,2,8,7,5]=>[1,7,8,6,4,3,2,5]=>0111010=>1000101
[4,2,7,3,8,1,6,5]=>[2,8,3,4,1,6,7,5]=>1010100=>0101011
[2,5,1,4,7,3,8,6]=>[4,8,7,5,2,1,3,6]=>1100101=>0011010
[6,1,3,8,7,2,5,4]=>[3,7,1,2,8,5,6,4]=>1001100=>0110011
[3,1,5,6,2,8,7,4]=>[7,8,6,3,1,2,5,4]=>1011010=>0100101
[1,2,4,6,3,8,7,5]=>[1,2,7,8,6,4,3,5]=>0011010=>1100101
[7,1,4,2,8,6,5,3]=>[4,1,2,6,8,5,7,3]=>1010100=>0101011
[4,1,5,3,2,8,7,6]=>[5,3,4,1,2,7,8,6]=>1010010=>0101101
[3,6,2,4,1,8,7,5]=>[4,7,8,6,2,3,1,5]=>1100010=>0011101
[7,3,4,1,8,6,5,2]=>[4,3,1,6,8,5,7,2]=>1110100=>0001011
[6,3,4,1,8,7,5,2]=>[4,3,1,7,5,8,6,2]=>1110110=>0001001
[3,4,5,1,8,7,6,2]=>[7,6,8,5,1,4,3,2]=>1110110=>0001001
[1,4,5,2,8,7,6,3]=>[1,7,6,8,5,2,4,3]=>0110110=>1001001
[1,6,4,2,8,7,5,3]=>[1,4,2,7,5,8,6,3]=>0110110=>1001001
[5,6,3,1,8,7,4,2]=>[3,7,1,4,8,6,5,2]=>1100110=>0011001
[4,6,2,7,5,1,8,3]=>[5,8,7,2,6,4,1,3]=>1101001=>0010110
[2,5,8,3,1,7,6,4]=>[7,6,8,3,5,2,1,4]=>1110010=>0001101
[4,5,8,2,1,7,6,3]=>[7,6,8,2,5,1,4,3]=>1110010=>0001101
[5,2,8,4,1,3,7,6]=>[2,4,7,8,1,5,3,6]=>1010000=>0101111
[2,5,8,1,3,7,6,4]=>[7,6,8,2,1,5,3,4]=>1110010=>0001101
[2,3,8,1,4,7,6,5]=>[7,6,8,3,2,1,4,5]=>1110010=>0001101
[1,3,8,2,4,7,6,5]=>[1,7,6,8,3,2,4,5]=>0110010=>1001101
[3,5,2,1,7,4,8,6]=>[8,7,5,2,3,1,4,6]=>1100101=>0011010
[6,3,1,7,2,8,5,4]=>[3,1,8,2,5,7,6,4]=>1101010=>0010101
[4,6,1,2,8,7,5,3]=>[7,5,8,6,1,4,2,3]=>1100110=>0011001
[4,5,1,2,8,7,6,3]=>[7,6,8,5,1,4,2,3]=>1100110=>0011001
[6,4,1,2,8,7,5,3]=>[4,1,7,5,8,6,2,3]=>1100110=>0011001
[5,2,8,1,3,7,6,4]=>[2,7,6,8,1,5,3,4]=>1010010=>0101101
[4,1,2,8,3,7,6,5]=>[7,6,8,4,1,2,3,5]=>1001010=>0110101
[8,6,4,7,5,3,1,2]=>[5,7,4,3,6,1,8,2]=>1111000=>0000111
[7,5,2,6,4,1,3,8]=>[6,4,5,2,7,1,3,8]=>1101000=>0010111
[1,3,7,4,5,8,6,2]=>[1,4,5,8,6,7,3,2]=>0110010=>1001101
[7,2,6,3,4,1,5,8]=>[2,6,3,4,7,1,5,8]=>1010000=>0101111
[6,8,4,7,5,3,1,2]=>[5,7,4,3,8,1,6,2]=>1111000=>0000111
[4,8,7,5,6,3,1,2]=>[6,5,3,7,1,8,4,2]=>1111100=>0000011
[1,6,5,2,8,3,7,4]=>[1,7,8,5,2,6,3,4]=>0110100=>1001011
[8,6,5,2,1,4,3,7]=>[5,2,6,1,4,8,3,7]=>1110000=>0001111
[2,7,6,3,1,4,5,8]=>[6,3,7,2,1,4,5,8]=>1110000=>0001111
[6,8,5,3,2,1,4,7]=>[5,3,8,2,6,1,4,7]=>1110000=>0001111
[2,7,6,4,5,1,3,8]=>[4,5,6,2,1,7,3,8]=>1110000=>0001111
[5,7,2,6,4,1,3,8]=>[6,4,7,2,5,1,3,8]=>1101000=>0010111
[6,1,3,7,5,8,4,2]=>[3,5,8,4,7,6,1,2]=>1001010=>0110101
[4,1,7,3,6,8,5,2]=>[8,6,5,7,3,4,1,2]=>1010110=>0101001
[8,1,6,4,3,7,5,2]=>[4,7,6,3,5,8,1,2]=>1010010=>0101101
[2,1,7,4,8,6,3,5]=>[2,1,4,6,8,3,7,5]=>1010100=>0101011
[1,8,6,3,7,5,4,2]=>[1,7,5,6,3,4,8,2]=>0110100=>1001011
[1,8,2,7,3,6,5,4]=>[1,6,7,2,3,5,8,4]=>0101000=>1010111
[8,1,2,7,4,3,6,5]=>[7,4,6,8,1,2,3,5]=>1001000=>0110111
[5,3,1,6,8,4,7,2]=>[3,1,7,8,4,6,5,2]=>1101100=>0010011
[6,2,8,7,1,4,3,5]=>[2,7,1,8,4,6,3,5]=>1011000=>0100111
[8,7,2,1,5,4,3,6]=>[5,7,2,4,8,1,3,6]=>1100000=>0011111
[8,2,3,1,4,6,5,7]=>[2,3,6,8,1,4,5,7]=>1000000=>0111111
[2,4,8,3,1,5,6,7]=>[8,3,4,2,1,5,6,7]=>1110000=>0001111
[1,3,7,2,8,4,6,5]=>[1,8,3,2,4,6,7,5]=>0110100=>1001011
[6,5,3,8,2,1,4,7]=>[3,8,2,5,1,6,4,7]=>1101000=>0010111
[2,6,4,5,7,1,3,8]=>[7,5,4,2,1,6,3,8]=>1111100=>0000011
[5,4,6,2,7,1,3,8]=>[7,2,4,1,6,5,3,8]=>1110100=>0001011
[7,6,2,1,8,5,3,4]=>[8,5,6,2,7,1,3,4]=>1100100=>0011011
[1,7,5,8,6,4,3,2]=>[1,6,4,8,5,3,7,2]=>0111100=>1000011
[6,5,1,2,8,3,7,4]=>[7,8,5,1,6,2,3,4]=>1100100=>0011011
[6,8,4,1,3,7,5,2]=>[4,1,7,3,5,8,6,2]=>1110010=>0001101
[5,8,3,1,7,4,6,2]=>[3,7,1,4,6,8,5,2]=>1100100=>0011011
[8,3,1,7,5,4,6,2]=>[3,1,5,7,4,6,8,2]=>1101000=>0010111
[1,2,8,7,6,3,5,4]=>[1,2,6,3,7,5,8,4]=>0011100=>1100011
[8,2,1,7,6,4,3,5]=>[2,6,4,7,1,3,8,5]=>1001100=>0110011
[2,3,1,8,7,4,5,6]=>[3,2,1,7,4,8,5,6]=>1101100=>0010011
[2,4,1,8,5,7,3,6]=>[5,7,4,2,1,3,8,6]=>1101010=>0010101
[5,8,2,1,7,6,3,4]=>[6,7,2,8,5,1,3,4]=>1100100=>0011011
[6,2,7,1,8,5,3,4]=>[2,8,5,7,1,6,3,4]=>1010100=>0101011
[8,7,1,6,5,4,3,2]=>[5,6,4,7,1,3,8,2]=>1101000=>0010111
[4,1,8,7,5,6,3,2]=>[5,6,7,3,8,4,1,2]=>1011000=>0100111
[8,1,2,3,4,5,9,6,7]=>[9,1,2,3,4,5,6,8,7]=>10000010=>01111101
[8,1,2,3,4,9,5,6,7]=>[9,1,2,3,4,5,8,6,7]=>10000100=>01111011
[8,1,9,2,3,4,5,6,7]=>[9,1,2,8,3,4,5,6,7]=>10100000=>01011111
[6,1,2,3,4,5,8,9,7]=>[6,1,2,3,4,5,9,8,7]=>10000011=>01111100
[9,1,2,3,4,5,6,10,7,8]=>[10,1,2,3,4,5,6,7,9,8]=>100000010=>011111101
[9,1,2,3,4,5,10,6,7,8]=>[10,1,2,3,4,5,6,9,7,8]=>100000100=>011111011
[9,1,2,10,3,4,5,6,7,8]=>[10,1,2,3,9,4,5,6,7,8]=>100100000=>011011111
[2,1,7,8,4,6,3,5]=>[2,1,6,8,4,7,3,5]=>1011000=>0100111
[3,5,8,7,2,6,4,1]=>[6,7,2,8,4,5,3,1]=>1111000=>0000111
[5,8,2,7,1,6,4,3]=>[6,7,2,8,4,5,1,3]=>1101000=>0010111
[2,1,6,4,5,8,3,7]=>[2,1,4,5,8,6,3,7]=>1010010=>0101101
[8,6,3,7,5,2,1,4]=>[3,5,7,2,6,1,8,4]=>1101000=>0010111
[4,6,3,7,5,2,8,1]=>[3,5,8,7,2,6,4,1]=>1101001=>0010110
[3,5,7,8,2,6,1,4]=>[6,8,2,7,3,1,5,4]=>1111000=>0000111
[8,2,3,4,6,1,5,7]=>[2,3,4,6,1,8,5,7]=>1000100=>0111011
[7,2,3,4,6,1,8,5]=>[2,3,4,6,1,8,7,5]=>1000101=>0111010
[8,2,3,4,7,5,1,6]=>[2,3,4,7,5,8,1,6]=>1000100=>0111011
[7,2,3,4,6,8,5,1]=>[2,3,4,8,6,5,7,1]=>1000110=>0111001
[7,8,3,6,5,1,4,2]=>[3,5,6,1,8,4,7,2]=>1101000=>0010111
[4,2,3,6,1,5,8,7]=>[2,3,6,4,1,5,8,7]=>1001001=>0110110
[4,8,3,7,5,1,6,2]=>[3,5,7,1,6,8,4,2]=>1101000=>0010111
[5,2,3,4,7,8,6,1]=>[2,3,4,8,6,7,5,1]=>1000110=>0111001
[8,2,3,4,7,1,6,5]=>[2,3,4,7,1,6,8,5]=>1000100=>0111011
[5,2,3,4,8,7,1,6]=>[2,3,4,7,5,1,8,6]=>1000110=>0111001
[5,2,3,4,6,8,1,7]=>[2,3,4,8,6,5,1,7]=>1000110=>0111001
[4,2,8,5,7,6,1,3]=>[2,6,7,5,1,8,4,3]=>1011100=>0100011
[3,7,6,4,5,1,8,2]=>[4,5,6,1,8,7,3,2]=>1110001=>0001110
[4,8,3,7,5,2,1,6]=>[3,5,7,2,8,4,1,6]=>1101000=>0010111
[8,7,3,6,5,1,2,4]=>[3,5,6,1,7,2,8,4]=>1101000=>0010111
[8,2,7,5,1,6,3,4]=>[2,5,1,6,7,3,8,4]=>1011000=>0100111
[5,8,1,7,3,6,4,2]=>[6,7,1,3,8,4,5,2]=>1101000=>0010111
[5,2,7,8,4,6,3,1]=>[2,6,8,4,7,3,5,1]=>1011000=>0100111
[6,8,3,2,5,7,1,4]=>[3,5,7,2,8,6,1,4]=>1100010=>0011101
[6,7,3,8,5,4,2,1]=>[3,5,8,4,7,2,6,1]=>1101000=>0010111
[6,2,3,4,7,5,8,1]=>[2,3,4,8,7,5,6,1]=>1000101=>0111010
[6,2,3,4,8,5,1,7]=>[2,3,4,8,5,6,1,7]=>1000100=>0111011
[8,2,3,4,1,7,5,6]=>[2,3,4,7,1,5,8,6]=>1000010=>0111101
[6,2,3,4,1,8,5,7]=>[2,3,4,8,6,1,5,7]=>1000010=>0111101
[6,2,3,4,8,7,5,1]=>[2,3,4,7,5,8,6,1]=>1000110=>0111001
[6,8,3,1,5,7,4,2]=>[3,5,7,1,4,8,6,2]=>1100010=>0011101
[7,2,3,4,1,8,6,5]=>[2,3,4,8,6,7,1,5]=>1000010=>0111101
[7,2,3,4,1,5,8,6]=>[2,3,4,8,7,1,5,6]=>1000001=>0111110
[1,2,3,4,8,7,5,6]=>[1,2,3,4,7,5,8,6]=>0000110=>1111001
[1,2,8,5,3,4,6,7]=>[1,2,5,3,8,4,6,7]=>0011000=>1100111
[1,8,4,2,3,5,6,7]=>[1,4,2,8,3,5,6,7]=>0110000=>1001111
[4,8,6,7,5,1,3,2]=>[5,7,1,6,3,8,4,2]=>1111000=>0000111
[7,1,8,4,6,5,2,3]=>[4,6,5,8,1,2,7,3]=>1010100=>0101011
[8,7,1,5,4,6,2,3]=>[5,4,6,7,1,8,2,3]=>1101000=>0010111
[8,5,7,1,4,6,3,2]=>[6,7,1,4,5,3,8,2]=>1110000=>0001111
[6,4,8,5,1,7,3,2]=>[5,1,7,4,3,8,6,2]=>1111010=>0000101
[8,7,1,4,5,6,3,2]=>[4,5,6,7,1,3,8,2]=>1100000=>0011111
[8,7,5,1,4,6,2,3]=>[5,1,4,6,7,2,8,3]=>1110000=>0001111
[8,7,2,5,1,4,6,3]=>[5,2,7,4,6,8,1,3]=>1101000=>0010111
[1,6,4,8,5,2,7,3]=>[1,5,7,8,4,2,6,3]=>0111000=>1000111
[8,7,1,4,2,5,6,3]=>[4,7,1,5,6,8,2,3]=>1100000=>0011111
[8,7,5,1,2,4,6,3]=>[5,1,7,2,4,6,8,3]=>1110000=>0001111
[7,1,8,5,6,2,3,4]=>[6,5,1,2,8,3,7,4]=>1011100=>0100011
[2,3,8,5,7,1,6,4]=>[7,5,3,2,1,6,8,4]=>1111100=>0000011
[3,8,7,1,5,6,2,4]=>[5,6,7,1,8,3,2,4]=>1110000=>0001111
[3,5,8,7,1,6,2,4]=>[6,7,1,8,3,2,5,4]=>1111000=>0000111
[1,3,8,6,7,5,2,4]=>[1,7,5,6,3,2,8,4]=>0111100=>1000011
[5,7,1,8,2,6,3,4]=>[6,8,1,7,2,3,5,4]=>1101000=>0010111
[2,8,7,1,5,6,3,4]=>[5,6,7,2,1,8,3,4]=>1110000=>0001111
[7,1,8,2,4,6,5,3]=>[6,8,1,2,4,5,7,3]=>1010000=>0101111
[1,8,3,7,2,5,6,4]=>[1,3,7,2,5,6,8,4]=>0101000=>1010111
[5,7,1,8,2,3,6,4]=>[8,1,6,7,2,3,5,4]=>1101000=>0010111
[7,1,8,2,3,5,6,4]=>[8,1,2,5,6,7,3,4]=>1010000=>0101111
[8,6,3,7,4,1,5,2]=>[3,7,4,6,1,5,8,2]=>1101000=>0010111
[4,2,8,6,7,5,1,3]=>[2,7,5,6,1,8,4,3]=>1011100=>0100011
[8,4,2,7,5,6,1,3]=>[5,6,7,4,2,8,1,3]=>1101000=>0010111
[4,8,3,6,1,7,5,2]=>[3,7,6,1,5,8,4,2]=>1101010=>0010101
[8,3,7,4,5,1,6,2]=>[4,5,7,3,1,6,8,2]=>1110000=>0001111
[8,7,4,2,5,6,1,3]=>[4,2,5,6,7,1,8,3]=>1110000=>0001111
[8,7,5,1,6,2,3,4]=>[6,5,1,7,2,8,3,4]=>1110100=>0001011
[8,7,2,4,1,5,6,3]=>[4,7,2,5,6,8,1,3]=>1100000=>0011111
[4,8,6,1,7,2,5,3]=>[7,1,6,5,8,2,4,3]=>1110100=>0001011
[8,7,4,1,2,5,6,3]=>[4,1,7,2,5,6,8,3]=>1110000=>0001111
[8,2,7,1,6,3,4,5]=>[2,6,1,7,3,4,8,5]=>1010100=>0101011
[8,2,7,1,3,6,4,5]=>[2,6,7,1,8,3,4,5]=>1010000=>0101111
[8,7,2,1,3,5,6,4]=>[7,2,5,6,8,1,3,4]=>1100000=>0011111
[1,8,7,2,3,6,4,5]=>[1,6,7,2,8,3,4,5]=>0110000=>1001111
[1,8,7,2,6,3,4,5]=>[1,6,2,7,3,4,8,5]=>0110100=>1001011
[8,2,7,3,6,1,4,5]=>[2,6,3,7,1,4,8,5]=>1010100=>0101011
[1,8,7,3,6,2,4,5]=>[1,6,3,7,2,4,8,5]=>0110100=>1001011
[1,8,2,7,6,3,4,5]=>[1,6,2,3,7,4,8,5]=>0101100=>1010011
[8,2,7,4,1,5,6,3]=>[2,4,7,1,5,6,8,3]=>1010000=>0101111
[8,2,1,7,5,6,3,4]=>[2,5,6,7,1,3,8,4]=>1001000=>0110111
[8,7,3,1,5,6,2,4]=>[3,5,6,7,1,8,2,4]=>1100000=>0011111
[2,8,7,3,5,6,1,4]=>[5,6,7,3,8,2,1,4]=>1110000=>0001111
[8,3,1,6,7,5,2,4]=>[3,1,7,5,6,2,8,4]=>1101100=>0010011
[8,5,2,1,6,7,4,3]=>[7,6,5,2,4,8,1,3]=>1100110=>0011001
[1,2,8,6,7,5,3,4]=>[1,2,7,5,6,3,8,4]=>0011100=>1100011
[1,8,3,6,7,5,2,4]=>[1,3,7,5,6,2,8,4]=>0101100=>1010011
[8,2,3,6,7,5,1,4]=>[2,3,7,5,6,1,8,4]=>1001100=>0110011
[8,3,7,2,5,6,1,4]=>[5,6,7,3,2,8,1,4]=>1110000=>0001111
[8,1,3,7,5,6,2,4]=>[3,5,6,7,1,2,8,4]=>1001000=>0110111
[8,4,1,2,7,5,6,3]=>[4,1,7,5,6,8,2,3]=>1100100=>0011011
[8,1,4,2,6,7,5,3]=>[4,1,2,7,6,5,8,3]=>1010110=>0101001
[1,2,8,6,7,3,5,4]=>[1,2,7,3,6,5,8,4]=>0011100=>1100011
[8,1,2,7,3,6,4,5]=>[6,7,1,2,3,8,4,5]=>1001000=>0110111
[8,1,7,3,6,2,4,5]=>[6,3,7,1,2,4,8,5]=>1010100=>0101011
[8,1,7,2,6,3,4,5]=>[6,1,2,7,3,4,8,5]=>1010100=>0101011
[8,1,7,2,3,6,4,5]=>[6,7,1,2,8,3,4,5]=>1010000=>0101111
[1,8,3,6,7,2,5,4]=>[1,3,7,2,6,5,8,4]=>0101100=>1010011
[8,7,1,2,3,6,4,5]=>[6,7,1,8,2,3,4,5]=>1100000=>0011111
[2,8,5,7,4,6,3,1]=>[6,7,4,5,3,8,2,1]=>1111000=>0000111
[2,8,6,4,3,5,7,1]=>[4,6,3,5,7,8,2,1]=>1110000=>0001111
[2,6,8,3,5,4,7,1]=>[5,7,8,3,4,6,2,1]=>1110000=>0001111
[8,4,2,7,6,1,3,5]=>[6,4,2,7,1,3,8,5]=>1101100=>0010011
[4,8,1,7,6,3,2,5]=>[6,1,3,7,4,2,8,5]=>1101100=>0010011
[3,7,1,8,6,2,5,4]=>[6,1,3,2,8,5,7,4]=>1101100=>0010011
[3,1,7,5,8,4,2,6]=>[8,5,4,7,3,1,2,6]=>1011100=>0100011
[3,1,6,8,7,5,2,4]=>[7,5,8,3,1,2,6,4]=>1011100=>0100011
[6,3,8,7,5,2,4,1]=>[5,7,3,2,8,4,6,1]=>1111000=>0000111
[7,3,5,8,4,2,6,1]=>[8,4,5,3,2,6,7,1]=>1111000=>0000111
[7,4,8,2,1,6,3,5]=>[6,8,2,4,1,7,3,5]=>1110000=>0001111
[8,7,4,6,3,2,5,1]=>[6,4,3,7,2,5,8,1]=>1111000=>0000111
[7,8,5,2,1,4,3,6]=>[5,2,8,1,4,7,3,6]=>1110000=>0001111
[7,5,2,3,1,4,8,6]=>[5,2,3,8,7,1,4,6]=>1100001=>0011110
[4,7,1,5,3,8,2,6]=>[5,1,3,8,4,2,7,6]=>1101010=>0010101
[4,7,8,1,3,6,2,5]=>[6,8,1,7,3,4,2,5]=>1110000=>0001111
[5,8,1,3,2,4,6,7]=>[8,1,3,5,2,4,6,7]=>1100000=>0011111
[5,4,8,7,2,3,6,1]=>[7,2,6,8,4,3,5,1]=>1111000=>0000111
[5,4,8,7,3,1,2,6]=>[7,3,8,4,1,5,2,6]=>1111000=>0000111
[6,8,3,7,2,5,4,1]=>[3,7,2,5,8,4,6,1]=>1101000=>0010111
[5,4,6,8,2,3,7,1]=>[7,8,2,6,4,3,5,1]=>1111000=>0000111
[5,7,4,2,8,3,6,1]=>[4,2,8,3,6,7,5,1]=>1110100=>0001011
[6,4,7,2,1,8,3,5]=>[8,2,4,1,7,6,3,5]=>1110010=>0001101
[6,5,3,4,1,2,8,7]=>[3,4,5,1,6,2,8,7]=>1100001=>0011110
[6,8,5,4,1,3,2,7]=>[4,5,1,8,3,6,2,7]=>1110000=>0001111
[6,4,3,7,1,5,2,8]=>[3,7,4,1,5,6,2,8]=>1101000=>0010111
[9,6,7,5,4,3,2,1,8]=>[5,4,7,3,6,2,9,1,8]=>11110000=>00001111
[7,4,2,5,6,1,3,8]=>[6,5,4,2,7,1,3,8]=>1101100=>0010011
[6,4,2,8,1,5,7,3]=>[7,8,4,2,5,6,1,3]=>1101000=>0010111
[7,4,3,1,5,6,2,8]=>[3,4,1,5,6,7,2,8]=>1100000=>0011111
[5,3,7,2,8,6,4,1]=>[6,8,3,2,4,7,5,1]=>1110100=>0001011
[6,3,8,2,5,4,7,1]=>[5,7,8,3,2,4,6,1]=>1110000=>0001111
[4,7,8,5,6,3,2,1]=>[6,5,3,8,2,7,4,1]=>1111100=>0000011
[5,7,8,4,6,2,1,3]=>[4,6,2,8,1,7,5,3]=>1110100=>0001011
[5,8,4,3,6,7,1,2]=>[4,3,7,6,1,8,5,2]=>1110110=>0001001
[5,3,8,6,2,7,4,1]=>[7,6,3,2,8,4,5,1]=>1111010=>0000101
[4,7,5,8,6,3,2,1]=>[6,3,8,5,2,7,4,1]=>1111100=>0000011
[4,8,6,7,5,3,2,1]=>[5,7,3,6,2,8,4,1]=>1111000=>0000111
[6,3,8,7,2,4,1,5]=>[7,3,2,8,4,6,1,5]=>1111000=>0000111
[5,3,8,7,2,6,4,1]=>[6,7,3,2,8,4,5,1]=>1111000=>0000111
[6,4,2,8,1,7,3,5]=>[7,4,2,8,6,1,3,5]=>1101010=>0010101
[5,6,3,8,7,2,4,1]=>[3,7,2,8,4,6,5,1]=>1101100=>0010011
[5,7,3,8,6,2,4,1]=>[3,6,2,8,4,7,5,1]=>1101100=>0010011
[4,6,8,5,7,3,2,1]=>[7,5,3,8,2,6,4,1]=>1111100=>0000011
[5,7,8,2,6,4,1,3]=>[6,2,4,8,1,7,5,3]=>1110100=>0001011
[3,6,8,5,7,1,4,2]=>[7,5,1,8,4,6,3,2]=>1111100=>0000011
[1,7,4,8,6,2,3,5]=>[1,6,4,2,8,3,7,5]=>0111100=>1000011
[3,6,2,5,7,8,1,4]=>[8,5,2,3,1,7,6,4]=>1101110=>0010001
[5,2,7,4,6,8,1,3]=>[2,4,8,6,1,7,5,3]=>1010110=>0101001
[5,3,6,7,1,8,4,2]=>[8,3,1,7,6,4,5,2]=>1111010=>0000101
[4,2,5,6,7,1,8,3]=>[2,8,7,1,6,5,4,3]=>1011101=>0100010
[8,1,4,2,5,6,3,7]=>[4,1,2,5,6,8,3,7]=>1010000=>0101111
[8,1,4,2,7,5,3,6]=>[4,1,2,7,5,8,3,6]=>1010100=>0101011
[3,6,2,4,1,7,8,5]=>[4,8,7,6,2,3,1,5]=>1100011=>0011100
[6,2,7,3,1,5,8,4]=>[2,8,7,3,5,6,1,4]=>1010001=>0101110
[7,3,4,1,5,8,6,2]=>[4,3,1,5,8,6,7,2]=>1110010=>0001101
[1,7,5,2,8,6,3,4]=>[1,6,8,5,2,7,3,4]=>0110100=>1001011
[3,7,4,1,8,5,6,2]=>[4,1,8,5,6,7,3,2]=>1110100=>0001011
[5,6,3,1,7,8,4,2]=>[3,8,1,4,7,6,5,2]=>1100110=>0011001
[3,6,4,8,1,5,7,2]=>[7,8,4,1,5,6,3,2]=>1111000=>0000111
[4,5,1,8,2,3,7,6]=>[7,8,1,5,4,2,3,6]=>1101000=>0010111
[4,7,1,8,2,6,3,5]=>[6,8,1,7,4,2,3,5]=>1101000=>0010111
[7,5,1,2,3,8,6,4]=>[5,1,8,6,7,2,3,4]=>1100010=>0011101
[6,4,1,2,7,3,8,5]=>[4,1,8,7,2,3,6,5]=>1100101=>0011010
[5,2,6,1,3,4,8,7]=>[2,6,1,5,3,4,8,7]=>1010001=>0101110
[6,7,1,4,3,5,2,8]=>[4,7,1,3,5,6,2,8]=>1100000=>0011111
[7,8,2,3,1,5,4,6]=>[8,2,3,5,7,1,4,6]=>1100000=>0011111
[7,8,2,4,3,5,1,6]=>[4,8,2,3,5,7,1,6]=>1100000=>0011111
[7,8,2,4,1,5,3,6]=>[4,8,2,5,7,1,3,6]=>1100000=>0011111
[1,4,2,6,5,7,3,8]=>[1,5,7,6,4,2,3,8]=>0101010=>1010101
[6,7,2,4,3,5,1,8]=>[4,7,2,3,5,6,1,8]=>1100000=>0011111
[2,4,1,6,5,7,3,8]=>[5,7,6,4,2,1,3,8]=>1101010=>0010101
[2,5,1,6,4,7,3,8]=>[7,6,4,5,2,1,3,8]=>1101010=>0010101
[4,5,3,6,1,7,2,8]=>[3,7,6,1,5,4,2,8]=>1101010=>0010101
[5,6,1,3,2,7,4,8]=>[7,6,1,3,5,2,4,8]=>1100010=>0011101
[5,6,4,7,1,3,2,8]=>[7,4,1,6,3,5,2,8]=>1111000=>0000111
[6,7,5,8,1,3,2,4]=>[8,1,5,3,7,2,6,4]=>1111000=>0000111
[4,5,1,3,2,7,6,8]=>[5,1,3,4,2,7,6,8]=>1100010=>0011101
[4,6,5,7,1,3,2,8]=>[7,1,5,3,6,4,2,8]=>1111000=>0000111
[4,6,1,3,2,7,5,8]=>[7,6,1,3,4,2,5,8]=>1100010=>0011101
[1,4,3,6,2,7,5,8]=>[1,3,7,6,4,2,5,8]=>0101010=>1010101
[4,6,5,7,3,8,1,2]=>[8,3,5,1,7,6,4,2]=>1111010=>0000101
[4,6,5,7,2,3,1,8]=>[7,2,5,3,6,4,1,8]=>1111000=>0000111
[3,5,2,6,4,7,1,8]=>[7,6,4,5,2,3,1,8]=>1101010=>0010101
[3,4,2,6,1,7,5,8]=>[7,6,4,2,3,1,5,8]=>1101010=>0010101
[4,6,2,3,1,7,5,8]=>[7,6,2,3,4,1,5,8]=>1100010=>0011101
[3,6,2,7,5,4,8,1]=>[5,8,7,4,6,2,3,1]=>1101001=>0010110
[4,6,1,7,3,8,2,5]=>[8,1,3,7,6,4,2,5]=>1101010=>0010101
[2,4,7,1,3,8,6,5]=>[8,6,7,2,1,4,3,5]=>1110010=>0001101
[5,2,6,7,4,3,8,1]=>[2,8,7,4,6,3,5,1]=>1011001=>0100110
[3,5,2,7,6,4,8,1]=>[6,4,8,7,5,2,3,1]=>1101101=>0010010
[2,5,7,3,1,8,6,4]=>[8,6,7,3,5,2,1,4]=>1110010=>0001101
[2,5,7,3,1,8,4,6]=>[8,3,5,2,1,4,7,6]=>1110010=>0001101
[1,5,7,3,4,8,2,6]=>[1,8,3,4,5,2,7,6]=>0110010=>1001101
[1,3,7,2,8,5,6,4]=>[1,8,5,6,7,3,2,4]=>0110100=>1001011
[2,3,1,5,8,4,7,6]=>[3,2,1,7,8,5,4,6]=>1101100=>0010011
[2,1,5,6,8,4,3,7]=>[2,1,8,4,6,5,3,7]=>1011100=>0100011
[2,3,1,5,8,6,4,7]=>[3,2,1,6,8,5,4,7]=>1101100=>0010011
[1,3,7,2,8,5,4,6]=>[1,8,5,7,3,2,4,6]=>0110100=>1001011
[2,3,1,6,8,5,4,7]=>[3,2,1,8,5,6,4,7]=>1101100=>0010011
[4,6,2,7,1,8,3,5]=>[8,2,7,6,4,1,3,5]=>1101010=>0010101
[1,6,4,5,7,8,3,2]=>[1,8,5,4,3,7,6,2]=>0111110=>1000001
[1,3,6,2,8,7,4,5]=>[1,7,3,2,4,8,6,5]=>0110110=>1001001
[2,1,5,6,8,4,7,3]=>[2,1,7,8,4,6,5,3]=>1011100=>0100011
[2,1,5,6,8,7,3,4]=>[2,1,7,3,8,6,5,4]=>1011110=>0100001
[6,2,4,7,5,8,3,1]=>[2,5,8,4,3,7,6,1]=>1011010=>0100101
[1,5,7,8,4,2,6,3]=>[1,8,4,6,7,2,5,3]=>0111000=>1000111
[3,7,4,1,8,6,2,5]=>[4,1,6,8,3,2,7,5]=>1110100=>0001011
[3,4,6,8,5,7,2,1]=>[5,7,2,8,6,4,3,1]=>1111010=>0000101
[4,2,5,7,3,1,8,6]=>[2,8,7,3,5,4,1,6]=>1011001=>0100110
[4,5,6,2,8,7,3,1]=>[7,2,8,6,5,3,4,1]=>1110110=>0001001
[2,5,6,8,1,7,4,3]=>[7,2,1,8,6,4,5,3]=>1111010=>0000101
[4,5,6,3,1,8,7,2]=>[7,8,6,3,5,1,4,2]=>1110010=>0001101
[4,3,6,2,1,7,5,8]=>[7,6,3,2,4,1,5,8]=>1110010=>0001101
[4,6,3,1,7,5,2,8]=>[3,7,5,6,1,4,2,8]=>1100100=>0011011
[4,5,3,7,6,1,8,2]=>[3,6,1,8,7,5,4,2]=>1101101=>0010010
[2,5,7,1,4,3,8,6]=>[8,7,2,1,4,5,3,6]=>1110001=>0001110
[4,3,5,7,6,1,8,2]=>[6,3,1,8,7,5,4,2]=>1111101=>0000010
[4,3,6,1,7,5,2,8]=>[7,5,6,3,1,4,2,8]=>1110100=>0001011
[4,3,2,6,1,7,5,8]=>[3,2,7,6,4,1,5,8]=>1101010=>0010101
[5,1,6,3,2,7,4,8]=>[7,6,3,5,1,2,4,8]=>1010010=>0101101
[3,6,1,7,4,2,5,8]=>[7,4,6,1,3,2,5,8]=>1101000=>0010111
[5,3,6,4,2,1,7,8]=>[4,6,3,2,5,1,7,8]=>1110000=>0001111
[5,2,1,6,3,7,4,8]=>[2,7,6,1,3,5,4,8]=>1001010=>0110101
[4,2,6,3,1,7,8,5]=>[2,8,7,6,3,4,1,5]=>1010011=>0101100
[3,6,2,1,7,4,5,8]=>[7,2,3,1,4,6,5,8]=>1100100=>0011011
[3,5,7,2,8,6,4,1]=>[6,8,2,4,7,5,3,1]=>1110100=>0001011
[2,6,1,3,7,5,4,8]=>[7,5,6,2,1,3,4,8]=>1100100=>0011011
[3,6,1,7,5,2,4,8]=>[5,7,1,3,2,6,4,8]=>1101000=>0010111
[5,2,6,4,3,1,7,8]=>[2,4,6,3,5,1,7,8]=>1010000=>0101111
[5,2,1,6,4,3,7,8]=>[2,6,4,5,1,3,7,8]=>1001000=>0110111
[5,4,2,1,6,3,7,8]=>[4,2,6,5,1,3,7,8]=>1100100=>0011011
[5,4,1,6,2,7,3,8]=>[7,6,4,1,5,2,3,8]=>1101010=>0010101
[5,1,6,4,2,7,3,8]=>[4,7,6,1,2,5,3,8]=>1010010=>0101101
[3,6,1,7,5,4,8,2]=>[5,8,7,4,6,1,3,2]=>1101001=>0010110
[2,6,1,5,4,3,7,8]=>[5,4,6,2,1,3,7,8]=>1101000=>0010111
[5,1,6,4,3,2,7,8]=>[4,6,3,5,1,2,7,8]=>1010000=>0101111
[5,4,1,6,3,2,7,8]=>[6,4,1,3,5,2,7,8]=>1101000=>0010111
[7,3,1,6,5,4,8,2]=>[3,1,5,6,4,8,7,2]=>1101001=>0010110
[4,2,7,6,5,8,1,3]=>[2,5,8,6,1,7,4,3]=>1011010=>0100101
[3,8,2,6,5,4,1,7]=>[5,6,4,8,2,3,1,7]=>1101000=>0010111
[7,3,2,1,5,4,6,8]=>[3,2,5,7,1,4,6,8]=>1100000=>0011111
[7,2,8,6,1,4,3,5]=>[2,6,1,8,4,7,3,5]=>1011000=>0100111
[5,2,7,6,8,4,1,3]=>[2,8,4,6,1,7,5,3]=>1011100=>0100011
[7,5,1,6,8,4,3,2]=>[8,4,6,5,1,3,7,2]=>1101100=>0010011
[7,4,2,1,5,6,3,8]=>[4,2,5,6,7,1,3,8]=>1100000=>0011111
[7,2,8,6,5,1,3,4]=>[2,5,6,1,8,3,7,4]=>1011000=>0100111
[5,3,2,6,7,4,1,8]=>[3,2,7,4,6,5,1,8]=>1101100=>0010011
[4,3,7,2,5,6,1,8]=>[5,6,7,3,2,4,1,8]=>1110000=>0001111
[3,7,1,6,5,2,4,8]=>[5,6,1,3,2,7,4,8]=>1101000=>0010111
[3,5,6,2,4,7,1,8]=>[7,6,2,4,5,3,1,8]=>1110010=>0001101
[3,5,8,7,2,4,6,1]=>[7,2,6,8,4,5,3,1]=>1111000=>0000111
[1,7,8,2,5,4,3,6]=>[1,5,8,2,4,7,3,6]=>0110000=>1001111
[8,7,2,5,4,3,6,1]=>[5,4,7,2,3,6,8,1]=>1101000=>0010111
[4,5,3,8,7,2,6,1]=>[3,7,2,6,8,5,4,1]=>1101100=>0010011
[1,4,8,2,7,6,3,5]=>[1,6,7,2,4,3,8,5]=>0110100=>1001011
[4,7,3,5,1,8,6,2]=>[3,5,1,8,6,7,4,2]=>1101010=>0010101
[2,5,8,7,4,6,1,3]=>[6,7,4,8,2,1,5,3]=>1111000=>0000111
[5,4,2,1,7,8,3,6]=>[4,2,8,5,1,3,7,6]=>1100110=>0011001
[4,7,8,3,5,2,1,6]=>[5,8,3,7,2,4,1,6]=>1110000=>0001111
[8,3,6,2,1,7,5,4]=>[7,6,3,2,5,8,1,4]=>1110010=>0001101
[2,3,1,8,4,7,6,5]=>[3,2,1,7,6,8,4,5]=>1101010=>0010101
[2,7,4,8,6,5,1,3]=>[6,5,8,4,2,1,7,3]=>1111100=>0000011
[6,3,7,2,8,5,4,1]=>[8,5,7,3,2,4,6,1]=>1110100=>0001011
[1,6,3,8,2,7,5,4]=>[1,3,7,2,5,8,6,4]=>0101010=>1010101
[6,2,7,4,1,8,5,3]=>[2,4,8,1,5,7,6,3]=>1010010=>0101101
[2,7,5,1,3,8,6,4]=>[5,2,1,8,6,7,3,4]=>1110010=>0001101
[1,7,6,4,3,8,2,5]=>[1,4,8,6,3,7,2,5]=>0110010=>1001101
[3,7,2,4,8,6,5,1]=>[4,6,8,5,7,2,3,1]=>1100100=>0011011
[3,4,2,8,7,6,1,5]=>[6,7,4,2,3,1,8,5]=>1101100=>0010011
[5,1,4,3,2,7,8,6]=>[4,3,5,1,2,8,7,6]=>1010011=>0101100
[3,7,8,5,2,4,1,6]=>[5,2,8,4,7,3,1,6]=>1111000=>0000111
[3,7,6,2,4,1,8,5]=>[6,2,4,8,7,3,1,5]=>1110001=>0001110
[1,6,8,2,5,7,4,3]=>[1,5,7,2,4,8,6,3]=>0110010=>1001101
[5,3,1,7,8,4,2,6]=>[3,1,8,4,7,5,2,6]=>1101100=>0010011
[4,1,7,6,3,2,8,5]=>[6,3,8,7,4,1,2,5]=>1011001=>0100110
[6,3,1,7,5,2,8,4]=>[3,1,5,8,7,2,6,4]=>1101001=>0010110
[6,2,7,5,3,1,8,4]=>[2,5,3,8,7,1,6,4]=>1011001=>0100110
[5,7,3,1,8,4,6,2]=>[3,8,1,4,6,7,5,2]=>1100100=>0011011
[8,4,7,3,1,6,5,2]=>[6,7,3,4,1,5,8,2]=>1110000=>0001111
[6,5,2,1,7,4,8,3]=>[8,7,5,2,4,6,1,3]=>1100101=>0011010
[5,7,4,6,2,1,8,3]=>[6,4,2,8,7,1,5,3]=>1111001=>0000110
[5,6,4,8,3,7,2,1]=>[7,4,3,8,6,2,5,1]=>1111010=>0000101
[6,7,2,4,3,8,1,5]=>[4,8,2,3,7,6,1,5]=>1100010=>0011101
[2,3,1,8,5,6,4,7]=>[3,2,1,5,6,8,4,7]=>1101000=>0010111
[5,7,3,6,4,8,1,2]=>[3,8,6,4,7,1,5,2]=>1101010=>0010101
[4,7,1,5,3,6,2,8]=>[5,1,3,6,7,4,2,8]=>1101000=>0010111
[4,6,3,5,1,7,2,8]=>[3,5,1,7,6,4,2,8]=>1101010=>0010101
[6,7,3,5,1,4,2,8]=>[3,5,1,7,4,6,2,8]=>1101000=>0010111
[5,7,1,6,3,4,2,8]=>[6,1,3,7,4,5,2,8]=>1101000=>0010111
[1,8,5,6,4,7,2,3]=>[1,7,6,4,5,2,8,3]=>0111010=>1000101
[5,7,1,6,4,8,2,3]=>[8,6,4,7,1,5,2,3]=>1101010=>0010101
[4,6,5,8,1,7,2,3]=>[7,1,5,2,8,6,4,3]=>1111010=>0000101
[3,7,1,4,2,8,5,6]=>[4,8,1,3,2,5,7,6]=>1100010=>0011101
[3,5,1,4,2,8,6,7]=>[4,5,1,3,2,8,6,7]=>1100010=>0011101
[4,6,5,8,3,7,1,2]=>[7,3,5,1,8,6,4,2]=>1111010=>0000101
[4,6,5,8,2,3,1,7]=>[8,2,5,3,6,4,1,7]=>1111000=>0000111
[3,4,2,6,5,8,1,7]=>[5,8,6,4,2,3,1,7]=>1101010=>0010101
[3,5,4,6,2,8,1,7]=>[8,6,4,2,5,3,1,7]=>1111010=>0000101
[1,8,3,5,4,7,2,6]=>[1,3,5,4,7,2,8,6]=>0101010=>1010101
[3,4,2,7,1,8,5,6]=>[8,4,2,3,1,5,7,6]=>1101010=>0010101
[4,7,2,3,1,8,5,6]=>[8,2,3,4,1,5,7,6]=>1100010=>0011101
[2,4,3,8,1,7,5,6]=>[3,7,4,2,1,5,8,6]=>1101010=>0010101
[2,5,3,8,4,7,1,6]=>[3,7,4,5,2,1,8,6]=>1101010=>0010101
[2,6,3,8,1,7,4,5]=>[3,7,2,1,8,6,4,5]=>1101010=>0010101
[1,2,8,7,4,6,3,5]=>[1,2,6,7,4,8,3,5]=>0011000=>1100111
[3,7,4,8,6,1,5,2]=>[6,4,1,8,5,7,3,2]=>1111100=>0000011
[4,5,1,8,7,6,2,3]=>[6,7,1,8,5,4,2,3]=>1101100=>0010011
[1,5,2,8,7,6,3,4]=>[1,6,7,2,3,8,5,4]=>0101100=>1010011
[4,1,5,8,7,6,2,3]=>[6,7,1,2,8,5,4,3]=>1011100=>0100011
[2,3,6,8,7,4,5,1]=>[7,4,8,5,6,3,2,1]=>1111100=>0000011
[4,5,7,8,2,6,3,1]=>[6,8,2,7,3,5,4,1]=>1111000=>0000111
[3,1,6,8,7,4,5,2]=>[7,4,8,5,6,3,1,2]=>1011100=>0100011
[6,1,4,8,7,2,5,3]=>[7,4,1,2,8,5,6,3]=>1011100=>0100011
[6,1,8,4,7,3,5,2]=>[4,7,3,8,5,6,1,2]=>1010100=>0101011
[5,8,3,4,7,1,6,2]=>[3,4,7,1,6,8,5,2]=>1100100=>0011011
[6,8,3,5,7,1,4,2]=>[3,7,5,1,8,4,6,2]=>1101100=>0010011
[3,1,7,8,6,4,5,2]=>[6,4,8,5,7,3,1,2]=>1011100=>0100011
[5,2,7,8,3,6,4,1]=>[2,6,8,3,7,4,5,1]=>1011000=>0100111
[4,6,7,8,2,5,3,1]=>[8,2,5,7,3,6,4,1]=>1111000=>0000111
[7,4,5,2,8,6,3,1]=>[6,8,5,2,4,3,7,1]=>1110100=>0001011
[7,5,8,4,2,6,3,1]=>[4,6,8,2,5,3,7,1]=>1110000=>0001111
[6,8,4,5,2,7,3,1]=>[5,4,2,7,3,8,6,1]=>1111010=>0000101
[6,8,2,5,3,7,4,1]=>[5,2,3,7,4,8,6,1]=>1101010=>0010101
[6,3,8,4,2,7,5,1]=>[4,7,3,2,5,8,6,1]=>1110010=>0001101
[3,4,7,5,8,6,2,1]=>[6,8,5,2,7,4,3,1]=>1111100=>0000011
[3,6,7,4,8,5,2,1]=>[4,8,5,7,2,6,3,1]=>1110100=>0001011
[6,7,4,2,8,5,3,1]=>[4,2,8,5,7,3,6,1]=>1110100=>0001011
[4,7,5,2,8,6,3,1]=>[6,8,5,2,7,3,4,1]=>1110100=>0001011
[5,6,2,8,3,7,4,1]=>[7,2,3,8,6,4,5,1]=>1101010=>0010101
[5,6,8,3,2,7,4,1]=>[7,3,8,6,2,4,5,1]=>1110010=>0001101
[3,6,8,4,2,7,5,1]=>[4,7,2,5,8,6,3,1]=>1110010=>0001101
[5,6,8,1,3,7,4,2]=>[7,1,8,6,3,4,5,2]=>1110010=>0001101
[6,7,4,8,1,5,3,2]=>[8,4,1,5,7,3,6,2]=>1111000=>0000111
[6,8,5,3,7,2,4,1]=>[7,5,3,8,2,4,6,1]=>1110100=>0001011
[7,5,3,8,2,6,4,1]=>[3,6,8,2,5,4,7,1]=>1101000=>0010111
[7,5,2,3,8,6,4,1]=>[6,8,5,2,3,4,7,1]=>1100100=>0011011
[3,7,4,5,8,6,2,1]=>[6,8,5,4,2,7,3,1]=>1111100=>0000011
[6,7,3,4,8,5,2,1]=>[3,4,8,5,7,2,6,1]=>1100100=>0011011
[3,6,4,7,8,5,2,1]=>[8,5,7,4,2,6,3,1]=>1111100=>0000011
[7,4,2,5,8,6,3,1]=>[6,8,5,4,2,3,7,1]=>1101100=>0010011
[6,1,8,3,4,7,5,2]=>[7,3,4,5,8,6,1,2]=>1010010=>0101101
[6,8,4,2,5,7,3,1]=>[4,2,5,7,3,8,6,1]=>1110010=>0001101
[6,3,4,7,8,5,2,1]=>[8,5,7,4,3,2,6,1]=>1111100=>0000011
[7,8,2,3,4,5,6,9,1]=>[9,8,2,3,4,5,6,7,1]=>11000001=>00111110
[6,1,7,3,4,5,8,2]=>[8,7,3,4,5,6,1,2]=>1010001=>0101110
[5,7,2,3,4,1,8,6]=>[8,7,2,3,4,5,1,6]=>1100001=>0011110
[2,7,1,8,4,5,6,3]=>[8,4,5,6,7,2,1,3]=>1101000=>0010111
[2,6,8,3,4,5,1,7]=>[8,3,4,5,6,2,1,7]=>1110000=>0001111
[2,8,9,3,4,5,6,7,1]=>[9,3,4,5,6,7,8,2,1]=>11100000=>00011111
[8,9,2,3,4,5,6,7,10,1]=>[10,9,2,3,4,5,6,7,8,1]=>110000001=>001111110
[7,1,8,3,4,5,6,9,2]=>[9,8,3,4,5,6,7,1,2]=>10100001=>01011110
[6,8,2,3,4,5,1,9,7]=>[9,8,2,3,4,5,6,1,7]=>11000001=>00111110
[6,1,2,7,4,5,8,3]=>[8,7,4,5,6,1,2,3]=>1001001=>0110110
[4,7,2,3,1,5,8,6]=>[8,7,2,3,4,1,5,6]=>1100001=>0011110
[2,7,1,3,8,5,6,4]=>[8,5,6,7,2,1,3,4]=>1100100=>0011011
[2,6,7,8,4,5,3,1]=>[8,4,5,7,3,6,2,1]=>1111000=>0000111
[2,8,1,9,4,5,6,7,3]=>[9,4,5,6,7,8,2,1,3]=>11010000=>00101111
[2,5,8,3,4,1,6,7]=>[8,3,4,5,2,1,6,7]=>1110000=>0001111
[2,7,9,3,4,5,6,1,8]=>[9,3,4,5,6,7,2,1,8]=>11100000=>00011111
[2,9,10,3,4,5,6,7,8,1]=>[10,3,4,5,6,7,8,9,2,1]=>111000000=>000111111
[11,1,2,3,4,5,6,7,8,9,12,10]=>[12,11,1,2,3,4,5,6,7,8,9,10]=>10000000001=>01111111110
[9,10,2,3,4,5,6,7,8,11,1]=>[11,10,2,3,4,5,6,7,8,9,1]=>1100000001=>0011111110
[8,1,9,3,4,5,6,7,10,2]=>[10,9,3,4,5,6,7,8,1,2]=>101000001=>010111110
[7,9,2,3,4,5,6,1,10,8]=>[10,9,2,3,4,5,6,7,1,8]=>110000001=>001111110
[7,1,2,8,4,5,6,9,3]=>[9,8,4,5,6,7,1,2,3]=>10010001=>01101110
[5,8,2,3,4,1,6,9,7]=>[9,8,2,3,4,5,1,6,7]=>11000001=>00111110
[5,6,2,7,4,3,8,1]=>[8,7,4,6,2,3,5,1]=>1101001=>0010110
[4,6,7,3,2,5,8,1]=>[8,7,3,5,6,2,4,1]=>1110001=>0001110
[2,6,7,3,8,5,4,1]=>[8,5,7,3,4,6,2,1]=>1110100=>0001011
[2,8,1,3,9,5,6,7,4]=>[9,5,6,7,8,2,1,3,4]=>11001000=>00110111
[2,6,1,8,4,5,3,7]=>[8,4,5,6,2,1,3,7]=>1101000=>0010111
[2,5,7,8,4,3,6,1]=>[8,4,6,7,3,5,2,1]=>1111000=>0000111
[2,9,1,10,4,5,6,7,8,3]=>[10,4,5,6,7,8,9,2,1,3]=>110100000=>001011111
[2,6,9,3,4,5,1,7,8]=>[9,3,4,5,6,2,1,7,8]=>11100000=>00011111
[2,8,10,3,4,5,6,7,1,9]=>[10,3,4,5,6,7,8,2,1,9]=>111000000=>000111111
[2,10,11,3,4,5,6,7,8,9,1]=>[11,3,4,5,6,7,8,9,10,2,1]=>1110000000=>0001111111
[2,12,1,3,4,5,6,7,8,9,10,11]=>[12,2,1,3,4,5,6,7,8,9,10,11]=>11000000000=>00111111111
[1,6,8,4,7,2,3,5]=>[1,4,7,2,8,3,6,5]=>0110100=>1001011
[1,4,5,7,8,2,6,3]=>[1,8,2,6,7,5,4,3]=>0111100=>1000011
[3,4,5,7,8,6,1,2]=>[6,8,1,7,5,4,3,2]=>1111100=>0000011
[3,4,5,7,6,8,1,2]=>[8,6,1,7,5,4,3,2]=>1111110=>0000001
[3,6,7,4,8,5,1,2]=>[4,8,5,7,1,6,3,2]=>1110100=>0001011
[3,4,5,6,8,7,1,2]=>[7,1,8,6,5,4,3,2]=>1111110=>0000001
[1,4,5,8,7,2,3,6]=>[1,7,2,8,5,4,3,6]=>0111100=>1000011
[1,2,5,8,3,6,4,7]=>[1,2,6,8,3,5,4,7]=>0011000=>1100111
[1,4,5,8,6,2,3,7]=>[1,6,2,8,5,4,3,7]=>0111100=>1000011
[7,8,1,4,6,2,3,5]=>[4,6,1,8,2,3,7,5]=>1100100=>0011011
[1,2,5,8,3,4,7,6]=>[1,2,7,8,3,5,4,6]=>0011000=>1100111
[1,6,7,2,3,5,8,4]=>[1,8,7,2,5,6,3,4]=>0110001=>1001110
[1,6,7,2,3,5,4,8]=>[1,7,2,5,6,3,4,8]=>0110000=>1001111
[1,2,5,7,3,6,4,8]=>[1,2,6,7,3,5,4,8]=>0011000=>1100111
[1,2,5,7,3,6,8,4]=>[1,2,6,8,7,3,5,4]=>0011001=>1100110
[1,6,8,2,3,5,7,4]=>[1,7,8,2,5,6,3,4]=>0110000=>1001111
[1,6,8,4,5,2,3,7]=>[1,4,5,8,2,6,3,7]=>0110000=>1001111
[1,6,8,4,5,2,7,3]=>[1,4,5,7,8,2,6,3]=>0110000=>1001111
[1,6,8,2,3,7,4,5]=>[1,7,2,8,6,3,4,5]=>0110010=>1001101
[1,4,5,7,6,2,8,3]=>[1,6,2,8,7,5,4,3]=>0111101=>1000010
[7,8,1,4,5,2,6,3]=>[4,5,8,1,6,7,2,3]=>1100000=>0011111
[7,8,1,2,3,4,6,5]=>[8,1,6,7,2,3,4,5]=>1100000=>0011111
[7,8,1,2,3,6,4,5]=>[6,8,1,7,2,3,4,5]=>1100000=>0011111
[1,6,7,2,3,8,5,4]=>[1,8,2,5,7,6,3,4]=>0110010=>1001101
[1,2,5,6,3,8,7,4]=>[1,2,7,8,6,3,5,4]=>0011010=>1100101
[4,2,1,6,5,3,8,7]=>[2,5,6,4,1,3,8,7]=>1001001=>0110110
[8,2,4,3,1,6,5,7]=>[2,4,3,6,8,1,5,7]=>1010000=>0101111
[6,2,4,3,1,8,7,5]=>[2,4,3,7,8,6,1,5]=>1010010=>0101101
[4,2,6,3,5,1,8,7]=>[2,5,6,3,4,1,8,7]=>1010001=>0101110
[4,6,2,1,5,8,7,3]=>[5,7,8,6,2,4,1,3]=>1100010=>0011101
[2,1,6,4,3,8,7,5]=>[2,1,4,7,8,6,3,5]=>1010010=>0101101
[6,8,2,1,4,3,7,5]=>[7,8,2,4,6,1,3,5]=>1100000=>0011111
[8,6,2,4,3,1,5,7]=>[4,6,2,3,8,1,5,7]=>1100000=>0011111
[6,8,7,2,4,3,1,5]=>[7,2,4,8,3,6,1,5]=>1110000=>0001111
[2,1,8,4,6,5,3,7]=>[2,1,4,6,5,8,3,7]=>1010100=>0101011
[2,1,6,4,8,5,7,3]=>[2,1,4,7,8,5,6,3]=>1010100=>0101011
[2,6,4,5,8,3,7,1]=>[7,8,5,4,3,6,2,1]=>1111100=>0000011
[6,4,2,8,3,5,7,1]=>[7,8,4,2,3,5,6,1]=>1101000=>0010111
[8,4,2,6,3,5,1,7]=>[6,4,2,3,5,8,1,7]=>1101000=>0010111
[6,2,4,8,5,3,7,1]=>[2,5,7,8,4,3,6,1]=>1011000=>0100111
[4,2,6,3,5,8,7,1]=>[2,5,7,8,6,3,4,1]=>1010010=>0101101
[4,2,6,3,8,7,5,1]=>[2,7,5,8,6,3,4,1]=>1010110=>0101001
[6,2,4,3,8,5,7,1]=>[2,4,3,7,8,5,6,1]=>1010100=>0101011
[8,2,4,3,6,5,1,7]=>[2,4,3,6,5,8,1,7]=>1010100=>0101011
[8,2,1,4,6,5,3,7]=>[2,4,6,5,8,1,3,7]=>1000100=>0111011
[6,2,1,4,8,5,7,3]=>[2,4,7,8,5,6,1,3]=>1000100=>0111011
[6,2,1,8,7,4,3,5]=>[2,7,4,8,1,3,6,5]=>1001100=>0110011
[6,2,1,8,4,3,7,5]=>[2,7,8,4,6,1,3,5]=>1001000=>0110111
[6,4,8,5,2,1,7,3]=>[5,2,7,8,4,1,6,3]=>1111000=>0000111
[6,4,8,5,7,2,1,3]=>[7,5,2,8,4,1,6,3]=>1111100=>0000011
[2,4,8,6,7,5,1,3]=>[7,5,6,2,1,8,4,3]=>1111100=>0000011
[8,2,6,4,5,1,3,7]=>[2,4,5,6,1,8,3,7]=>1010000=>0101111
[4,6,8,7,2,1,5,3]=>[7,2,8,1,5,6,4,3]=>1111000=>0000111
[6,8,7,4,2,1,3,5]=>[4,7,2,8,1,6,3,5]=>1110000=>0001111
[2,8,6,4,7,1,3,5]=>[4,7,2,1,6,3,8,5]=>1110100=>0001011
[4,8,6,2,1,7,3,5]=>[7,6,2,8,1,4,3,5]=>1110010=>0001101
[2,8,5,3,1,4,6,7]=>[5,3,8,2,1,4,6,7]=>1110000=>0001111
[2,7,4,8,3,5,6,1]=>[8,4,3,5,6,7,2,1]=>1111000=>0000111
[7,2,8,4,3,5,1,6]=>[2,4,8,3,5,7,1,6]=>1010000=>0101111
[8,4,2,1,5,3,6,7]=>[4,2,5,8,1,3,6,7]=>1100000=>0011111
[8,5,1,4,2,3,6,7]=>[4,5,1,8,2,3,6,7]=>1100000=>0011111
[8,4,1,5,3,2,6,7]=>[5,4,1,3,8,2,6,7]=>1101000=>0010111
[6,7,3,8,4,2,5,1]=>[3,8,4,7,2,5,6,1]=>1101000=>0010111
[6,7,3,8,4,2,1,5]=>[3,8,4,7,2,6,1,5]=>1101000=>0010111
[7,1,8,4,3,5,2,6]=>[4,8,3,5,7,1,2,6]=>1010000=>0101111
[7,4,8,1,5,6,2,3]=>[5,6,8,1,4,2,7,3]=>1110000=>0001111
[7,1,8,4,3,5,6,2]=>[4,8,3,5,6,7,1,2]=>1010000=>0101111
[6,7,3,8,4,5,2,1]=>[3,8,4,5,7,2,6,1]=>1101000=>0010111
[6,7,1,4,8,3,5,2]=>[4,8,1,3,7,5,6,2]=>1100100=>0011011
[1,6,7,8,4,3,2,5]=>[1,8,4,7,3,6,2,5]=>0111000=>1000111
[7,2,1,8,4,5,3,6]=>[2,8,4,5,7,1,3,6]=>1001000=>0110111
[6,2,7,8,4,3,1,5]=>[2,8,4,7,3,6,1,5]=>1011000=>0100111
[6,2,7,8,4,3,5,1]=>[2,8,4,7,3,5,6,1]=>1011000=>0100111
[2,6,7,4,8,3,5,1]=>[4,8,3,7,5,6,2,1]=>1110100=>0001011
[2,6,7,4,8,3,1,5]=>[4,8,3,7,2,1,6,5]=>1110100=>0001011
[1,2,7,8,6,3,4,5]=>[1,2,6,3,8,4,7,5]=>0011100=>1100011
[2,6,7,1,8,5,3,4]=>[8,5,7,2,1,6,3,4]=>1110100=>0001011
[2,6,7,8,5,3,1,4]=>[5,8,3,7,2,1,6,4]=>1111000=>0000111
[2,6,7,8,5,3,4,1]=>[5,8,3,7,4,6,2,1]=>1111000=>0000111
[6,2,7,8,4,5,3,1]=>[2,8,4,5,7,3,6,1]=>1011000=>0100111
[7,2,1,8,4,5,6,3]=>[2,8,4,5,6,7,1,3]=>1001000=>0110111
[1,7,2,8,4,5,6,3]=>[1,8,4,5,6,7,2,3]=>0101000=>1010111
[3,7,8,1,5,6,2,4]=>[5,6,8,1,7,3,2,4]=>1110000=>0001111
[6,3,7,8,1,5,2,4]=>[8,3,1,5,7,2,6,4]=>1111000=>0000111
[6,7,1,2,8,5,3,4]=>[8,5,7,1,6,2,3,4]=>1100100=>0011011
[3,1,2,7,6,5,8,4]=>[3,1,2,6,5,8,7,4]=>1001101=>0110010
[6,1,2,4,7,3,8,5]=>[4,8,7,1,2,3,6,5]=>1000101=>0111010
[1,7,5,3,6,4,8,2]=>[1,6,5,3,4,8,7,2]=>0110101=>1001010
[4,1,5,7,3,2,6,8]=>[7,3,5,4,1,2,6,8]=>1011000=>0100111
[4,7,1,8,3,5,2,6]=>[8,1,3,5,7,4,2,6]=>1101000=>0010111
[4,1,7,8,6,2,3,5]=>[6,1,2,8,4,3,7,5]=>1011100=>0100011
[1,6,5,8,7,3,4,2]=>[1,7,3,8,5,4,6,2]=>0111100=>1000011
[4,1,8,7,6,2,3,5]=>[6,1,2,7,4,3,8,5]=>1011100=>0100011
[4,8,1,7,3,5,2,6]=>[7,1,3,5,8,4,2,6]=>1101000=>0010111
[4,7,1,6,3,2,5,8]=>[6,1,3,7,4,2,5,8]=>1101000=>0010111
[6,1,2,3,7,5,4,8]=>[7,5,6,1,2,3,4,8]=>1000100=>0111011
[6,8,1,5,3,7,2,4]=>[5,1,3,7,2,8,6,4]=>1101010=>0010101
[1,5,7,3,4,8,6,2]=>[1,8,6,7,3,4,5,2]=>0110010=>1001101
[1,5,8,3,4,7,6,2]=>[1,7,6,8,3,4,5,2]=>0110010=>1001101
[7,8,5,2,4,1,6,3]=>[5,2,4,8,1,6,7,3]=>1110000=>0001111
[7,1,2,3,5,6,4,8]=>[5,6,7,1,2,3,4,8]=>1000000=>0111111
[8,1,2,3,5,6,4,7]=>[5,6,8,1,2,3,4,7]=>1000000=>0111111
[8,1,2,3,5,4,7,6]=>[5,7,8,1,2,3,4,6]=>1000000=>0111111
[7,1,8,4,6,3,2,5]=>[4,6,3,8,1,2,7,5]=>1010100=>0101011
[6,8,2,4,3,1,5,7]=>[4,8,2,3,6,1,5,7]=>1100000=>0011111
[3,8,1,2,4,5,7,6]=>[7,8,1,3,2,4,5,6]=>1100000=>0011111
[3,7,1,8,6,4,2,5]=>[6,4,8,1,3,2,7,5]=>1101100=>0010011
[1,6,4,3,7,5,8,2]=>[1,4,3,8,7,5,6,2]=>0110101=>1001010
[3,1,2,6,7,5,8,4]=>[3,1,2,8,7,5,6,4]=>1001101=>0110010
[3,8,1,7,6,4,2,5]=>[6,4,7,1,3,2,8,5]=>1101100=>0010011
[8,1,7,4,6,3,2,5]=>[4,6,3,7,1,2,8,5]=>1010100=>0101011
[1,5,7,3,4,6,8,2]=>[1,6,8,7,3,4,5,2]=>0110001=>1001110
[8,7,2,5,3,6,1,4]=>[5,2,3,6,7,1,8,4]=>1101000=>0010111
[7,1,2,3,5,4,8,6]=>[5,8,7,1,2,3,4,6]=>1000001=>0111110
[6,1,2,3,5,8,4,7]=>[5,8,6,1,2,3,4,7]=>1000010=>0111101
[6,1,2,3,5,7,4,8]=>[5,7,6,1,2,3,4,8]=>1000010=>0111101
[5,1,2,3,7,6,4,8]=>[6,7,5,1,2,3,4,8]=>1000100=>0111011
[5,1,2,3,8,6,4,7]=>[6,8,5,1,2,3,4,7]=>1000100=>0111011
[1,5,6,3,4,7,8,2]=>[1,8,7,6,3,4,5,2]=>0110011=>1001100
[7,6,2,5,3,1,8,4]=>[5,2,3,6,1,8,7,4]=>1101001=>0010110
[7,2,3,4,5,8,6,1]=>[2,3,4,5,8,6,7,1]=>1000010=>0111101
[8,2,3,4,5,7,1,6]=>[2,3,4,5,7,1,8,6]=>1000010=>0111101
[7,3,4,6,8,5,1,2]=>[8,5,6,4,3,1,7,2]=>1111100=>0000011
[4,7,3,2,8,6,1,5]=>[3,6,8,2,4,1,7,5]=>1100100=>0011011
[3,8,2,6,7,4,5,1]=>[7,4,6,5,8,2,3,1]=>1101100=>0010011
[4,8,1,5,6,7,3,2]=>[7,6,5,1,3,8,4,2]=>1101110=>0010001
[5,8,2,4,6,7,1,3]=>[4,7,6,2,8,5,1,3]=>1100110=>0011001
[3,7,6,1,8,5,2,4]=>[8,5,6,1,7,3,2,4]=>1110100=>0001011
[7,1,3,6,4,8,5,2]=>[3,8,6,4,5,7,1,2]=>1001010=>0110101
[6,2,3,7,8,5,4,1]=>[2,3,8,5,7,4,6,1]=>1001100=>0110011
[8,2,3,5,7,1,4,6]=>[2,3,7,5,1,8,4,6]=>1001100=>0110011
[5,4,8,3,6,7,1,2]=>[7,6,3,4,1,8,5,2]=>1110110=>0001001
[4,8,2,3,5,6,1,7]=>[5,6,8,2,3,4,1,7]=>1100000=>0011111
[6,8,2,3,1,4,5,7]=>[8,2,3,6,1,4,5,7]=>1100000=>0011111
[3,7,5,2,8,4,1,6]=>[8,5,2,4,7,3,1,6]=>1110100=>0001011
[6,3,2,4,1,8,7,5]=>[3,2,4,7,8,6,1,5]=>1100010=>0011101
[7,2,3,4,8,5,1,6]=>[2,3,4,8,5,7,1,6]=>1000100=>0111011
[5,7,3,1,4,2,6,8]=>[3,7,1,4,5,2,6,8]=>1100000=>0011111
[6,3,7,4,8,1,2,5]=>[4,8,3,1,7,2,6,5]=>1110100=>0001011
[8,3,7,4,2,6,1,5]=>[4,6,7,3,2,8,1,5]=>1110000=>0001111
[1,8,3,2,4,5,7,6]=>[1,3,7,8,2,4,5,6]=>0100000=>1011111
[8,4,1,6,3,7,5,2]=>[7,6,4,1,3,5,8,2]=>1101010=>0010101
[8,7,4,2,1,6,3,5]=>[4,2,6,7,1,8,3,5]=>1110000=>0001111
[8,3,5,2,7,4,1,6]=>[7,5,3,2,4,8,1,6]=>1110100=>0001011
[1,5,3,8,7,6,4,2]=>[1,3,6,7,4,8,5,2]=>0101100=>1010011
[7,2,4,8,1,3,6,5]=>[2,8,4,1,6,7,3,5]=>1011000=>0100111
[1,2,8,7,5,6,3,4]=>[1,2,5,6,7,3,8,4]=>0011000=>1100111
[3,1,8,6,7,5,2,4]=>[7,5,6,3,1,2,8,4]=>1011100=>0100011
[1,4,8,6,5,7,2,3]=>[1,5,7,6,2,8,4,3]=>0111010=>1000101
[1,6,5,4,8,2,3,7]=>[1,4,8,5,2,6,3,7]=>0110100=>1001011
[6,2,5,1,7,4,3,8]=>[2,7,5,1,4,6,3,8]=>1010100=>0101011
[5,2,8,3,4,6,1,7]=>[2,6,8,3,4,5,1,7]=>1010000=>0101111
[7,2,8,1,3,6,5,4]=>[2,6,8,1,5,7,3,4]=>1010000=>0101111
[7,3,8,1,4,6,2,5]=>[6,8,3,1,4,7,2,5]=>1110000=>0001111
[5,3,8,4,1,2,7,6]=>[4,7,8,3,1,5,2,6]=>1110000=>0001111
[5,8,4,3,6,2,1,7]=>[4,3,6,2,8,5,1,7]=>1110100=>0001011
[1,8,3,6,5,2,7,4]=>[1,3,5,6,2,7,8,4]=>0101000=>1010111
[3,8,1,4,6,7,5,2]=>[4,7,6,5,8,1,3,2]=>1100110=>0011001
[3,8,2,5,1,7,6,4]=>[5,2,3,1,7,6,8,4]=>1101010=>0010101
[4,3,8,2,5,1,6,7]=>[5,8,3,2,4,1,6,7]=>1110000=>0001111
[8,2,4,3,5,1,7,6]=>[2,4,3,5,7,8,1,6]=>1010000=>0101111
[8,2,1,4,6,5,7,3]=>[2,4,6,5,7,8,1,3]=>1000100=>0111011
[8,1,3,4,5,7,6,2]=>[3,4,5,7,6,8,1,2]=>1000010=>0111101
[6,1,5,2,4,7,8,3]=>[5,1,2,4,8,7,6,3]=>1010011=>0101100
[4,1,8,5,2,7,6,3]=>[5,1,2,7,6,8,4,3]=>1011010=>0100101
[4,8,5,1,3,6,2,7]=>[5,1,6,8,3,4,2,7]=>1110000=>0001111
[6,3,1,2,8,5,7,4]=>[3,1,7,8,5,6,2,4]=>1100100=>0011011
[5,3,8,7,2,1,4,6]=>[7,3,2,8,1,5,4,6]=>1111000=>0000111
[6,7,3,5,1,4,8,2]=>[3,5,1,8,7,4,6,2]=>1101001=>0010110
[5,7,8,4,2,6,3,1]=>[4,6,8,2,7,3,5,1]=>1110000=>0001111
[5,7,4,1,6,8,3,2]=>[4,1,8,6,3,7,5,2]=>1110110=>0001001
[5,8,4,6,1,7,3,2]=>[7,6,4,1,8,3,5,2]=>1111010=>0000101
[5,6,1,4,7,8,3,2]=>[4,8,1,3,7,6,5,2]=>1100110=>0011001
[5,6,8,2,4,7,3,1]=>[7,2,4,8,6,3,5,1]=>1110010=>0001101
[5,6,3,8,4,7,2,1]=>[3,7,4,8,6,2,5,1]=>1101010=>0010101
[4,6,3,2,8,7,5,1]=>[3,7,5,8,6,2,4,1]=>1100110=>0011001
[5,6,3,8,2,7,4,1]=>[3,7,2,8,6,4,5,1]=>1101010=>0010101
[3,6,5,8,7,2,4,1]=>[7,2,8,5,4,6,3,1]=>1111100=>0000011
[5,3,6,8,2,7,4,1]=>[7,3,2,8,6,4,5,1]=>1111010=>0000101
[5,4,7,2,6,8,3,1]=>[8,6,2,4,3,7,5,1]=>1110110=>0001001
[6,7,3,8,5,2,4,1]=>[3,5,8,2,7,4,6,1]=>1101000=>0010111
[6,3,2,7,5,4,8,1]=>[3,2,5,8,7,4,6,1]=>1101001=>0010110
[6,4,7,2,5,3,8,1]=>[5,8,7,2,4,3,6,1]=>1110001=>0001110
[6,2,7,5,1,4,8,3]=>[2,5,1,8,7,4,6,3]=>1011001=>0100110
[6,3,7,8,4,2,5,1]=>[8,4,7,3,2,5,6,1]=>1111000=>0000111
[3,5,7,8,4,6,2,1]=>[6,8,4,7,2,5,3,1]=>1111000=>0000111
[5,3,7,8,4,6,2,1]=>[6,8,4,7,3,2,5,1]=>1111000=>0000111
[5,7,8,2,4,6,3,1]=>[6,8,2,4,7,3,5,1]=>1110000=>0001111
[2,6,8,4,7,3,5,1]=>[4,7,3,8,5,6,2,1]=>1110100=>0001011
[3,7,4,8,6,2,1,5]=>[6,4,2,8,3,1,7,5]=>1111100=>0000011
[3,6,4,8,7,2,5,1]=>[7,4,2,8,5,6,3,1]=>1111100=>0000011
[3,5,4,8,2,7,6,1]=>[7,6,8,4,2,5,3,1]=>1111010=>0000101
[4,5,7,3,8,6,2,1]=>[6,8,3,7,5,2,4,1]=>1110100=>0001011
[3,5,6,8,4,7,2,1]=>[7,4,8,6,2,5,3,1]=>1111010=>0000101
[5,4,8,1,7,6,3,2]=>[6,7,1,4,3,8,5,2]=>1110100=>0001011
[5,8,4,1,7,6,3,2]=>[4,1,6,7,3,8,5,2]=>1110100=>0001011
[7,5,4,1,8,6,3,2]=>[4,1,6,8,5,3,7,2]=>1110100=>0001011
[8,5,4,1,7,6,3,2]=>[4,1,6,7,5,3,8,2]=>1110100=>0001011
[1,8,2,5,6,3,4,7]=>[1,6,5,2,3,8,4,7]=>0101100=>1010011
[1,3,7,5,6,2,4,8]=>[1,6,5,3,2,7,4,8]=>0111100=>1000011
[1,8,5,2,3,7,4,6]=>[1,5,2,7,3,4,8,6]=>0110010=>1001101
[1,8,2,5,3,6,7,4]=>[1,5,2,3,6,7,8,4]=>0101000=>1010111
[2,6,8,4,3,5,7,1]=>[4,7,8,3,5,6,2,1]=>1110000=>0001111
[7,2,8,4,1,5,6,3]=>[2,4,8,1,5,6,7,3]=>1010000=>0101111
[7,5,8,1,2,6,3,4]=>[6,8,1,5,2,7,3,4]=>1110000=>0001111
[1,6,7,4,3,2,8,5]=>[1,4,8,7,3,6,2,5]=>0110001=>1001110
[1,5,2,6,4,7,8,3]=>[1,8,7,6,4,5,2,3]=>0101011=>1010100
[1,5,4,6,2,3,7,8]=>[1,6,4,2,5,3,7,8]=>0111000=>1000111
[6,5,4,3,8,1,7,2]=>[4,3,7,8,5,1,6,2]=>1110100=>0001011
[2,7,8,3,6,5,1,4]=>[6,5,8,3,7,2,1,4]=>1110100=>0001011
[2,6,5,7,3,4,1,8]=>[7,3,5,4,6,2,1,8]=>1111000=>0000111
[6,2,5,8,4,1,3,7]=>[2,8,4,5,1,6,3,7]=>1011000=>0100111
[2,7,8,4,6,1,3,5]=>[4,6,2,1,8,3,7,5]=>1110100=>0001011
[6,1,2,8,3,7,4,5]=>[7,1,2,3,8,6,4,5]=>1001010=>0110101
[6,2,5,7,8,1,3,4]=>[2,8,1,7,5,3,6,4]=>1011100=>0100011
[1,6,2,7,5,8,4,3]=>[1,5,8,4,7,6,2,3]=>0101010=>1010101
[1,6,2,4,8,7,3,5]=>[1,4,7,2,3,8,6,5]=>0100110=>1011001
[2,6,5,3,7,8,4,1]=>[8,5,3,4,7,6,2,1]=>1110110=>0001001
[6,5,2,3,8,7,1,4]=>[7,5,2,3,8,6,1,4]=>1100110=>0011001
[5,4,1,2,3,8,6,7]=>[4,1,5,2,3,8,6,7]=>1100010=>0011101
[5,1,4,2,3,7,8,6]=>[4,1,2,5,3,8,7,6]=>1010011=>0101100
[1,5,4,2,6,3,8,7]=>[1,4,2,6,5,3,8,7]=>0110101=>1001010
[5,1,6,3,8,2,7,4]=>[7,8,3,6,5,1,2,4]=>1010100=>0101011
[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,8,7,9,6]=>00000110=>11111001
[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>00010101=>11101010
[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>00000101=>11111010
[1,2,4,3,7,6,5,10,9,8]=>[1,2,4,3,6,7,5,9,10,8]=>001010010=>110101101
[1,3,2,5,4,7,6,10,9,8]=>[1,3,2,5,4,7,6,9,10,8]=>010101010=>101010101
[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,9,10,8]=>000000010=>111111101
[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>001010101=>110101010
[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]=>000010101=>111101010
[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>000000101=>111111010
[5,8,3,4,1,6,7,2]=>[3,4,6,7,8,1,5,2]=>1100000=>0011111
[1,7,8,4,5,6,2,3]=>[1,4,5,6,8,2,7,3]=>0110000=>1001111
[1,6,3,8,5,2,7,4]=>[1,3,5,7,8,2,6,4]=>0101000=>1010111
[5,2,3,7,1,6,4,8]=>[2,3,6,7,1,5,4,8]=>1001000=>0110111
[6,2,3,7,5,1,4,8]=>[2,3,5,7,1,6,4,8]=>1001000=>0110111
[6,2,3,4,8,1,7,5]=>[2,3,4,7,8,1,6,5]=>1000100=>0111011
[8,7,3,2,1,6,5,4]=>[3,6,7,2,5,8,1,4]=>1100000=>0011111
[9,8,3,1,5,2,7,4,6]=>[3,5,7,8,1,9,2,4,6]=>11000000=>00111111
[2,4,1,8,5,3,7,6]=>[5,7,8,4,2,1,3,6]=>1101000=>0010111
[2,4,8,6,3,1,7,5]=>[6,3,7,8,4,2,1,5]=>1111000=>0000111
[3,4,1,5,8,2,7,6]=>[7,8,5,4,1,3,2,6]=>1101100=>0010011
[8,1,4,5,3,2,7,6]=>[5,4,3,7,8,1,2,6]=>1011000=>0100111
[3,5,6,2,1,7,8,4]=>[8,7,6,2,5,3,1,4]=>1110011=>0001100
[8,1,4,6,3,7,2,5]=>[7,6,4,3,8,1,2,5]=>1011010=>0100101
[8,1,4,6,3,7,5,2]=>[7,6,4,3,5,8,1,2]=>1011010=>0100101
[3,5,6,2,1,7,4,8]=>[7,6,2,5,3,1,4,8]=>1110010=>0001101
[8,1,5,6,7,3,2,4]=>[7,3,6,5,1,2,8,4]=>1011100=>0100011
[3,4,1,6,8,7,2,5]=>[7,4,1,3,2,8,6,5]=>1101110=>0010001
[3,5,6,1,8,7,2,4]=>[7,1,8,6,5,3,2,4]=>1110110=>0001001
[8,1,3,2,6,7,5,4]=>[3,7,6,5,8,1,2,4]=>1000110=>0111001
[2,3,8,6,7,1,5,4]=>[7,3,2,1,6,5,8,4]=>1111100=>0000011
[2,4,1,8,6,7,5,3]=>[7,6,5,8,4,2,1,3]=>1101110=>0010001
[3,4,1,6,8,7,5,2]=>[7,5,8,6,4,1,3,2]=>1101110=>0010001
[8,1,4,6,2,7,5,3]=>[7,6,4,1,2,5,8,3]=>1011010=>0100101
[3,5,1,6,7,8,4,2]=>[8,4,7,6,5,1,3,2]=>1101110=>0010001
[4,5,6,1,7,8,3,2]=>[8,1,7,6,5,3,4,2]=>1110110=>0001001
[3,5,1,6,7,4,8,2]=>[8,7,4,6,5,1,3,2]=>1101101=>0010010
[3,5,1,6,7,4,2,8]=>[7,4,6,5,1,3,2,8]=>1101100=>0010011
[6,4,2,7,8,5,1,3]=>[8,5,7,4,2,6,1,3]=>1101100=>0010011
[6,1,4,8,7,5,2,3]=>[7,5,8,4,1,2,6,3]=>1011100=>0100011
[1,8,6,2,4,7,3,5]=>[1,7,6,2,4,8,3,5]=>0110010=>1001101
[8,1,6,2,4,7,3,5]=>[7,6,1,2,4,8,3,5]=>1010010=>0101101
[7,6,2,1,4,8,3,5]=>[8,6,2,4,7,1,3,5]=>1100010=>0011101
[6,4,1,7,8,5,2,3]=>[8,5,7,4,1,6,2,3]=>1101100=>0010011
[1,8,6,3,4,7,2,5]=>[1,7,6,3,4,8,2,5]=>0110010=>1001101
[1,7,2,5,4,8,3,6]=>[1,5,4,8,2,3,7,6]=>0101010=>1010101
[7,1,2,5,4,8,3,6]=>[5,4,8,1,2,3,7,6]=>1001010=>0110101
[2,7,1,5,4,8,3,6]=>[5,4,8,2,1,3,7,6]=>1101010=>0010101
[2,8,6,3,4,7,1,5]=>[7,6,3,4,8,2,1,5]=>1110010=>0001101
[2,8,6,1,4,7,3,5]=>[7,6,2,1,4,8,3,5]=>1110010=>0001101
[7,2,1,5,4,8,3,6]=>[2,5,4,8,1,3,7,6]=>1001010=>0110101
[1,2,7,5,4,8,3,6]=>[1,2,5,4,8,3,7,6]=>0011010=>1100101
[3,2,7,5,4,8,1,6]=>[2,5,4,8,3,1,7,6]=>1011010=>0100101
[2,5,8,4,7,3,1,6]=>[4,7,3,8,5,2,1,6]=>1110100=>0001011
[2,3,7,5,4,8,1,6]=>[5,4,8,3,2,1,7,6]=>1111010=>0000101
[6,8,3,2,4,7,1,5]=>[3,7,2,4,8,6,1,5]=>1100010=>0011101
[3,7,2,5,4,8,1,6]=>[5,4,8,2,3,1,7,6]=>1101010=>0010101
[1,3,7,5,4,8,2,6]=>[1,5,4,8,3,2,7,6]=>0111010=>1000101
[5,1,8,4,7,3,2,6]=>[4,7,3,8,5,1,2,6]=>1010100=>0101011
[5,8,2,4,7,3,1,6]=>[4,7,2,3,8,5,1,6]=>1100100=>0011011
[8,7,5,6,2,1,4,3]=>[6,2,5,1,7,4,8,3]=>1111000=>0000111
[8,1,5,4,7,3,2,6]=>[4,7,5,3,8,1,2,6]=>1010100=>0101011
[1,8,5,4,7,3,2,6]=>[1,4,7,5,3,8,2,6]=>0110100=>1001011
[1,7,3,5,4,8,2,6]=>[1,3,5,4,8,2,7,6]=>0101010=>1010101
[8,6,3,1,4,7,2,5]=>[3,7,6,1,4,8,2,5]=>1100010=>0011101
[8,6,4,2,7,5,1,3]=>[4,2,7,5,6,1,8,3]=>1110100=>0001011
[8,6,4,1,7,2,5,3]=>[4,1,7,2,6,5,8,3]=>1110100=>0001011
[4,1,3,2,7,8,5,6]=>[3,4,1,2,8,5,7,6]=>1000110=>0111001
[1,4,3,2,7,8,5,6]=>[1,3,4,2,8,5,7,6]=>0100110=>1011001
[2,7,3,5,4,8,1,6]=>[3,5,4,8,2,1,7,6]=>1101010=>0010101
[2,8,5,4,7,3,1,6]=>[4,7,5,3,8,2,1,6]=>1110100=>0001011
[3,2,1,4,7,8,5,6]=>[2,3,1,4,8,5,7,6]=>1000110=>0111001
[8,1,7,6,4,3,5,2]=>[6,4,7,3,5,8,1,2]=>1011000=>0100111
[8,6,4,5,2,7,1,3]=>[5,4,2,7,6,1,8,3]=>1111010=>0000101
[7,1,8,6,4,3,5,2]=>[6,4,8,3,5,7,1,2]=>1011000=>0100111
[7,3,6,5,2,1,4,8]=>[5,3,2,6,1,7,4,8]=>1111000=>0000111
[5,4,2,8,1,3,7,6]=>[7,8,4,2,5,1,3,6]=>1101000=>0010111
[6,4,2,5,1,8,3,7]=>[5,4,2,8,6,1,3,7]=>1101010=>0010101
[6,3,5,2,1,4,7,8]=>[5,3,2,6,1,4,7,8]=>1110000=>0001111
[2,5,8,6,3,1,4,7]=>[6,3,8,2,1,5,4,7]=>1111000=>0000111
[2,3,5,8,1,4,7,6]=>[7,8,3,2,1,5,4,6]=>1111000=>0000111
[6,3,8,5,2,7,1,4]=>[5,3,2,7,1,8,6,4]=>1111010=>0000101
[2,5,7,6,3,1,4,8]=>[6,3,7,2,1,5,4,8]=>1111000=>0000111
[2,5,8,7,6,3,1,4]=>[6,3,7,2,1,8,5,4]=>1111100=>0000011
[7,3,5,2,1,4,6,8]=>[5,3,2,7,1,4,6,8]=>1110000=>0001111
[8,4,2,5,1,3,7,6]=>[5,4,2,7,8,1,3,6]=>1101000=>0010111
[2,3,6,8,1,4,7,5]=>[7,8,3,2,1,6,4,5]=>1111000=>0000111
[2,7,8,6,3,1,4,5]=>[6,3,8,2,1,7,4,5]=>1111000=>0000111
[7,3,8,5,2,1,4,6]=>[5,3,2,8,1,7,4,6]=>1111000=>0000111
[2,3,6,1,8,4,7,5]=>[7,8,3,2,1,4,6,5]=>1110100=>0001011
[2,8,6,3,1,4,5,7]=>[6,3,8,2,1,4,5,7]=>1110000=>0001111
[8,3,5,2,1,4,6,7]=>[5,3,2,8,1,4,6,7]=>1110000=>0001111
[2,4,8,1,3,7,5,6]=>[7,2,1,4,3,5,8,6]=>1110010=>0001101
[8,3,6,1,4,7,5,2]=>[7,6,3,1,4,5,8,2]=>1110010=>0001101
[3,8,6,1,4,7,5,2]=>[7,6,1,4,5,8,3,2]=>1110010=>0001101
[2,6,8,1,5,7,3,4]=>[5,7,2,1,8,6,3,4]=>1110010=>0001101
[2,7,1,6,3,8,4,5]=>[8,6,2,1,3,7,4,5]=>1101010=>0010101
[4,7,6,1,8,5,2,3]=>[8,5,6,1,7,2,4,3]=>1110100=>0001011
[3,7,5,8,1,2,6,4]=>[8,1,5,3,2,6,7,4]=>1111000=>0000111
[7,3,6,1,2,8,4,5]=>[8,6,3,1,7,2,4,5]=>1110010=>0001101
[7,4,8,1,6,5,2,3]=>[6,5,8,1,4,2,7,3]=>1110100=>0001011
[7,4,6,1,8,2,5,3]=>[8,1,4,2,6,5,7,3]=>1110100=>0001011
[6,8,4,5,1,7,2,3]=>[5,4,1,7,2,8,6,3]=>1111010=>0000101
[4,6,8,5,1,7,2,3]=>[5,1,7,2,8,6,4,3]=>1111010=>0000101
[5,1,7,6,2,3,8,4]=>[6,1,2,8,7,3,5,4]=>1011001=>0100110
[5,1,7,6,2,8,3,4]=>[8,6,1,2,7,3,5,4]=>1011010=>0100101
[5,1,8,7,6,2,3,4]=>[6,1,2,7,3,8,5,4]=>1011100=>0100011
[8,5,1,6,2,7,3,4]=>[7,6,1,5,2,3,8,4]=>1101010=>0010101
[3,6,1,8,4,7,5,2]=>[7,4,5,8,6,1,3,2]=>1101010=>0010101
[4,6,1,8,7,5,2,3]=>[7,5,8,1,6,4,2,3]=>1101100=>0010011
[4,8,5,1,7,2,3,6]=>[7,5,1,8,2,4,3,6]=>1110100=>0001011
[4,5,1,8,7,2,3,6]=>[7,1,8,5,4,2,3,6]=>1101100=>0010011
[5,8,4,1,7,2,3,6]=>[4,1,7,2,8,5,3,6]=>1110100=>0001011
[8,6,4,7,1,2,5,3]=>[7,4,1,6,2,5,8,3]=>1111000=>0000111
[6,4,8,7,1,2,5,3]=>[7,1,8,4,2,5,6,3]=>1111000=>0000111
[6,4,7,1,2,8,5,3]=>[8,1,4,2,5,7,6,3]=>1110010=>0001101
[6,5,1,2,7,3,8,4]=>[8,7,5,1,6,2,3,4]=>1100101=>0011010
[6,5,1,8,2,7,3,4]=>[7,1,5,2,3,8,6,4]=>1101010=>0010101
[8,6,5,1,7,2,3,4]=>[7,5,1,6,2,8,3,4]=>1110100=>0001011
[6,5,1,7,2,8,3,4]=>[8,1,5,2,3,7,6,4]=>1101010=>0010101
[6,5,1,7,2,3,8,4]=>[8,7,1,5,2,3,6,4]=>1101001=>0010110
[5,7,4,1,8,2,3,6]=>[4,1,8,2,7,5,3,6]=>1110100=>0001011
[5,6,8,7,4,1,2,3]=>[7,4,8,1,6,2,5,3]=>1111000=>0000111
[7,3,8,1,5,2,4,6]=>[5,8,3,1,7,2,4,6]=>1110000=>0001111
[1,8,4,2,3,6,7,5]=>[1,4,2,6,7,8,3,5]=>0110000=>1001111
[2,5,8,3,4,6,7,1]=>[6,7,8,3,4,5,2,1]=>1110000=>0001111
[4,1,7,2,3,6,8,5]=>[6,8,7,1,2,4,3,5]=>1010001=>0101110
[4,6,2,1,5,7,8,3]=>[5,8,7,6,2,4,1,3]=>1100011=>0011100
[4,5,2,3,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>1100011=>0011100
[3,2,6,7,4,1,8,5]=>[2,8,7,4,6,3,1,5]=>1011001=>0100110
[5,6,2,7,1,4,8,3]=>[8,7,2,6,4,5,1,3]=>1101001=>0010110
[6,2,3,8,1,7,4,5]=>[2,3,7,1,8,6,4,5]=>1001010=>0110101
[2,6,8,3,4,7,1,5]=>[7,3,4,8,6,2,1,5]=>1110010=>0001101
[4,6,2,7,5,1,3,8]=>[5,7,2,6,4,1,3,8]=>1101000=>0010111
[2,6,3,1,8,4,5,7]=>[3,8,2,1,4,6,5,7]=>1100100=>0011011
[5,1,2,7,6,8,4,3]=>[8,6,4,7,5,1,2,3]=>1001110=>0110001
[2,6,3,1,8,7,4,5]=>[3,7,2,1,4,8,6,5]=>1100110=>0011001
[3,5,6,4,7,8,1,2]=>[4,8,1,7,6,5,3,2]=>1110110=>0001001
[5,4,2,3,7,8,6,1]=>[4,2,3,8,6,7,5,1]=>1100110=>0011001
[4,1,8,2,5,7,3,6]=>[5,7,1,2,4,3,8,6]=>1010010=>0101101
[3,1,8,4,7,2,5,6]=>[4,7,3,1,2,8,5,6]=>1010100=>0101011
[6,2,3,8,4,1,7,5]=>[2,3,7,8,4,6,1,5]=>1001000=>0110111
[2,6,4,1,5,3,8,7]=>[4,2,1,5,6,3,8,7]=>1110001=>0001110
[3,2,7,6,4,1,8,5]=>[2,6,4,8,7,3,1,5]=>1011001=>0100110
[2,5,4,1,7,6,8,3]=>[4,2,1,6,8,7,5,3]=>1110101=>0001010
[6,2,1,4,7,8,3,5]=>[2,4,8,1,3,7,6,5]=>1000110=>0111001
[2,6,5,1,7,8,3,4]=>[8,5,2,1,7,6,3,4]=>1110110=>0001001
[4,2,3,7,8,1,6,5]=>[2,3,8,4,1,6,7,5]=>1001100=>0110011
[5,8,3,1,7,2,4,6]=>[3,7,1,8,5,2,4,6]=>1100100=>0011011
[4,2,7,1,6,3,5,8]=>[2,6,1,4,3,7,5,8]=>1010100=>0101011
[6,8,4,2,1,5,3,7]=>[4,2,8,1,5,6,3,7]=>1110000=>0001111
[6,8,5,2,1,7,3,4]=>[5,2,7,1,8,6,3,4]=>1110010=>0001101
[6,8,3,2,5,1,7,4]=>[3,5,7,8,2,6,1,4]=>1100000=>0011111
[6,8,3,2,1,4,5,7]=>[3,8,2,6,1,4,5,7]=>1100000=>0011111
[5,1,7,3,2,4,6,8]=>[7,3,5,1,2,4,6,8]=>1010000=>0101111
[5,2,1,8,3,6,7,4]=>[2,6,7,8,1,3,5,4]=>1001000=>0110111
[4,3,8,1,6,2,7,5]=>[6,3,1,4,2,7,8,5]=>1110100=>0001011
[5,3,1,7,2,6,8,4]=>[3,1,6,8,7,2,5,4]=>1101001=>0010110
[4,2,1,6,5,8,3,7]=>[2,5,8,6,4,1,3,7]=>1001010=>0110101
[4,2,1,8,5,7,3,6]=>[2,5,7,4,1,3,8,6]=>1001010=>0110101
[7,4,3,1,8,5,6,2]=>[3,4,1,8,5,6,7,2]=>1100100=>0011011
[7,4,2,1,8,5,6,3]=>[4,2,8,5,6,7,1,3]=>1100100=>0011011
[6,3,2,1,7,4,5,8]=>[3,2,7,1,4,6,5,8]=>1100100=>0011011
[7,5,2,1,8,6,3,4]=>[6,8,5,2,7,1,3,4]=>1100100=>0011011
[6,1,8,4,2,7,3,5]=>[4,7,1,2,8,6,3,5]=>1010010=>0101101
[5,2,1,7,3,6,4,8]=>[2,6,7,1,3,5,4,8]=>1001000=>0110111
[6,3,2,8,7,1,4,5]=>[3,2,7,1,8,4,6,5]=>1101100=>0010011
[4,2,8,1,7,3,5,6]=>[2,7,1,4,3,8,5,6]=>1010100=>0101011
[4,3,2,5,8,1,6,7]=>[3,2,8,5,4,1,6,7]=>1101100=>0010011
[4,3,2,5,7,1,6,8]=>[3,2,7,5,4,1,6,8]=>1101100=>0010011
[6,4,2,1,7,8,3,5]=>[4,2,8,1,3,7,6,5]=>1100110=>0011001
[5,4,2,1,6,7,3,8]=>[4,2,7,6,5,1,3,8]=>1100110=>0011001
[5,3,2,1,6,7,4,8]=>[3,2,7,6,5,1,4,8]=>1100110=>0011001
[6,4,2,1,7,8,5,3]=>[4,2,8,5,7,6,1,3]=>1100110=>0011001
[5,3,2,6,8,1,7,4]=>[3,2,7,8,1,6,5,4]=>1101100=>0010011
[3,2,1,4,6,8,5,7]=>[2,3,1,4,8,6,5,7]=>1000110=>0111001
[4,3,2,6,1,7,8,5]=>[3,2,8,7,6,4,1,5]=>1101011=>0010100
[5,3,2,1,6,7,8,4]=>[3,2,8,7,6,5,1,4]=>1100111=>0011000
[8,6,1,4,5,7,2,3]=>[4,5,7,6,1,8,2,3]=>1100010=>0011101
[3,8,6,4,5,7,1,2]=>[4,5,7,6,1,8,3,2]=>1110010=>0001101
[6,2,8,5,4,7,3,1]=>[2,5,4,7,3,8,6,1]=>1011010=>0100101
[1,8,6,5,7,2,3,4]=>[1,7,5,2,6,3,8,4]=>0111100=>1000011
[5,2,8,4,3,6,7,1]=>[2,4,6,7,8,3,5,1]=>1010000=>0101111
[5,4,2,7,3,6,1,8]=>[6,7,4,2,3,5,1,8]=>1101000=>0010111
[6,4,3,7,1,2,8,5]=>[3,8,7,4,1,6,2,5]=>1101001=>0010110
[6,4,3,8,1,2,7,5]=>[3,7,8,4,1,6,2,5]=>1101000=>0010111
[7,2,8,5,1,6,3,4]=>[2,5,1,6,8,3,7,4]=>1011000=>0100111
[7,2,8,4,3,1,5,6]=>[2,4,8,3,7,1,5,6]=>1010000=>0101111
[7,5,3,8,4,2,6,1]=>[3,8,4,5,2,6,7,1]=>1101000=>0010111
[5,3,1,7,8,4,6,2]=>[3,1,8,4,6,7,5,2]=>1101100=>0010011
[6,3,1,7,8,4,2,5]=>[3,1,8,4,7,2,6,5]=>1101100=>0010011
[6,1,5,4,3,2,8,7]=>[4,5,3,6,1,2,8,7]=>1010001=>0101110
[8,7,6,1,3,5,2,4]=>[6,1,5,7,3,8,2,4]=>1110000=>0001111
[8,1,6,5,7,3,4,2]=>[7,5,3,6,4,8,1,2]=>1011100=>0100011
[8,4,1,5,7,6,2,3]=>[6,7,5,4,1,8,2,3]=>1101100=>0010011
[7,8,6,2,5,3,1,4]=>[5,6,2,8,3,7,1,4]=>1110000=>0001111
[8,1,3,7,4,2,5,6]=>[3,7,4,8,1,2,5,6]=>1001000=>0110111
[4,3,8,7,5,2,1,6]=>[5,7,3,2,8,4,1,6]=>1111000=>0000111
[6,5,2,7,1,4,8,3]=>[8,7,2,5,4,6,1,3]=>1101001=>0010110
[7,4,6,1,3,2,8,5]=>[6,1,4,3,8,7,2,5]=>1110001=>0001110
[7,5,2,1,3,8,4,6]=>[5,2,8,1,3,4,7,6]=>1100010=>0011101
[3,4,7,5,6,1,8,2]=>[6,5,1,8,7,4,3,2]=>1111101=>0000010
[3,5,6,7,1,4,8,2]=>[8,7,1,6,4,5,3,2]=>1111001=>0000110
[2,7,6,1,3,4,8,5]=>[6,2,1,8,7,3,4,5]=>1110001=>0001110
[5,7,2,1,6,3,8,4]=>[6,2,8,7,5,1,3,4]=>1100101=>0011010
[2,7,4,5,3,8,1,6]=>[5,4,3,8,2,1,7,6]=>1111010=>0000101
[6,8,7,1,3,2,5,4]=>[7,1,8,3,5,6,2,4]=>1110000=>0001111
[2,8,6,5,7,1,4,3]=>[7,5,2,1,6,4,8,3]=>1111100=>0000011
[5,8,4,3,2,6,7,1]=>[4,3,6,7,8,2,5,1]=>1110000=>0001111
[1,8,5,6,2,4,7,3]=>[1,6,2,5,4,7,8,3]=>0111000=>1000111
[8,1,5,6,2,4,7,3]=>[6,1,2,5,4,7,8,3]=>1011000=>0100111
[6,4,8,1,3,2,7,5]=>[7,8,1,4,3,6,2,5]=>1110000=>0001111
[2,3,1,7,8,6,4,5]=>[3,2,1,6,8,4,7,5]=>1101100=>0010011
[3,5,7,6,2,8,1,4]=>[8,6,2,7,3,1,5,4]=>1111010=>0000101
[5,4,1,2,8,6,7,3]=>[4,1,6,7,8,5,2,3]=>1100100=>0011011
[8,4,5,2,1,6,7,3]=>[5,2,4,1,6,7,8,3]=>1110000=>0001111
[3,1,2,6,8,4,7,5]=>[3,1,2,7,8,4,6,5]=>1001100=>0110011
[5,1,3,2,7,8,4,6]=>[3,8,5,1,2,4,7,6]=>1000110=>0111001
[1,5,4,2,7,8,3,6]=>[1,4,2,8,5,3,7,6]=>0110110=>1001001
[7,6,2,8,4,3,1,5]=>[8,4,6,2,3,7,1,5]=>1101000=>0010111
[5,2,8,6,3,4,7,1]=>[2,6,3,7,8,4,5,1]=>1011000=>0100111
[5,6,8,4,3,2,7,1]=>[4,7,8,3,6,2,5,1]=>1110000=>0001111
[3,6,7,8,4,2,1,5]=>[8,4,7,2,6,3,1,5]=>1111000=>0000111
[6,5,1,8,4,3,7,2]=>[7,8,4,5,1,3,6,2]=>1101000=>0010111
[2,5,8,3,1,6,7,4]=>[6,7,8,3,5,2,1,4]=>1110000=>0001111
[3,5,8,1,2,6,7,4]=>[6,7,8,1,5,3,2,4]=>1110000=>0001111
[3,2,8,1,5,6,7,4]=>[2,5,6,7,8,3,1,4]=>1010000=>0101111
[1,3,8,6,2,4,7,5]=>[1,6,3,2,7,8,4,5]=>0111000=>1000111
[3,2,7,8,4,6,1,5]=>[2,6,8,4,7,3,1,5]=>1011000=>0100111
[5,1,8,3,4,6,7,2]=>[6,7,8,3,4,5,1,2]=>1010000=>0101111
[4,8,7,2,1,6,3,5]=>[6,7,2,8,1,4,3,5]=>1110000=>0001111
[2,8,1,6,3,4,7,5]=>[6,2,1,3,7,8,4,5]=>1101000=>0010111
[8,3,4,2,1,6,5,7]=>[4,3,2,6,8,1,5,7]=>1110000=>0001111
[6,4,7,2,5,8,1,3]=>[5,8,2,4,1,7,6,3]=>1110010=>0001101
[3,5,8,1,2,6,4,7]=>[6,8,1,5,3,2,4,7]=>1110000=>0001111
[5,8,6,1,3,4,2