Identifier
Mp00064:
Permutations
—reverse⟶
Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
=>
[1]=>[1]=>=>
[1,2]=>[2,1]=>1=>1
[2,1]=>[1,2]=>0=>0
[1,2,3]=>[3,2,1]=>11=>11
[1,3,2]=>[2,3,1]=>10=>01
[2,1,3]=>[3,1,2]=>10=>01
[2,3,1]=>[1,3,2]=>01=>10
[3,1,2]=>[2,1,3]=>10=>01
[3,2,1]=>[1,2,3]=>00=>00
[1,2,3,4]=>[4,3,2,1]=>111=>111
[1,2,4,3]=>[3,4,2,1]=>110=>011
[1,3,2,4]=>[4,2,3,1]=>110=>011
[1,3,4,2]=>[2,4,3,1]=>101=>101
[1,4,2,3]=>[3,2,4,1]=>110=>011
[1,4,3,2]=>[2,3,4,1]=>100=>001
[2,1,3,4]=>[4,3,1,2]=>101=>101
[2,1,4,3]=>[3,4,1,2]=>100=>001
[2,3,1,4]=>[4,1,3,2]=>110=>011
[2,3,4,1]=>[1,4,3,2]=>011=>110
[2,4,1,3]=>[3,1,4,2]=>110=>011
[2,4,3,1]=>[1,3,4,2]=>010=>010
[3,1,2,4]=>[4,2,1,3]=>110=>011
[3,1,4,2]=>[2,4,1,3]=>100=>001
[3,2,1,4]=>[4,1,2,3]=>100=>001
[3,2,4,1]=>[1,4,2,3]=>010=>010
[3,4,1,2]=>[2,1,4,3]=>101=>101
[3,4,2,1]=>[1,2,4,3]=>001=>100
[4,1,2,3]=>[3,2,1,4]=>110=>011
[4,1,3,2]=>[2,3,1,4]=>100=>001
[4,2,1,3]=>[3,1,2,4]=>100=>001
[4,2,3,1]=>[1,3,2,4]=>010=>010
[4,3,1,2]=>[2,1,3,4]=>100=>001
[4,3,2,1]=>[1,2,3,4]=>000=>000
[1,2,3,4,5]=>[5,4,3,2,1]=>1111=>1111
[1,2,3,5,4]=>[4,5,3,2,1]=>1110=>0111
[1,2,4,3,5]=>[5,3,4,2,1]=>1110=>0111
[1,2,4,5,3]=>[3,5,4,2,1]=>1101=>1011
[1,2,5,3,4]=>[4,3,5,2,1]=>1110=>0111
[1,2,5,4,3]=>[3,4,5,2,1]=>1100=>0011
[1,3,2,4,5]=>[5,4,2,3,1]=>1101=>1011
[1,3,2,5,4]=>[4,5,2,3,1]=>1100=>0011
[1,3,4,2,5]=>[5,2,4,3,1]=>1110=>0111
[1,3,4,5,2]=>[2,5,4,3,1]=>1011=>1101
[1,3,5,2,4]=>[4,2,5,3,1]=>1110=>0111
[1,3,5,4,2]=>[2,4,5,3,1]=>1010=>0101
[1,4,2,3,5]=>[5,3,2,4,1]=>1110=>0111
[1,4,2,5,3]=>[3,5,2,4,1]=>1100=>0011
[1,4,3,2,5]=>[5,2,3,4,1]=>1100=>0011
[1,4,3,5,2]=>[2,5,3,4,1]=>1010=>0101
[1,4,5,2,3]=>[3,2,5,4,1]=>1101=>1011
[1,4,5,3,2]=>[2,3,5,4,1]=>1001=>1001
[1,5,2,3,4]=>[4,3,2,5,1]=>1110=>0111
[1,5,2,4,3]=>[3,4,2,5,1]=>1100=>0011
[1,5,3,2,4]=>[4,2,3,5,1]=>1100=>0011
[1,5,3,4,2]=>[2,4,3,5,1]=>1010=>0101
[1,5,4,2,3]=>[3,2,4,5,1]=>1100=>0011
[1,5,4,3,2]=>[2,3,4,5,1]=>1000=>0001
[2,1,3,4,5]=>[5,4,3,1,2]=>1011=>1101
[2,1,3,5,4]=>[4,5,3,1,2]=>1010=>0101
[2,1,4,3,5]=>[5,3,4,1,2]=>1010=>0101
[2,1,4,5,3]=>[3,5,4,1,2]=>1001=>1001
[2,1,5,3,4]=>[4,3,5,1,2]=>1010=>0101
[2,1,5,4,3]=>[3,4,5,1,2]=>1000=>0001
[2,3,1,4,5]=>[5,4,1,3,2]=>1101=>1011
[2,3,1,5,4]=>[4,5,1,3,2]=>1100=>0011
[2,3,4,1,5]=>[5,1,4,3,2]=>1110=>0111
[2,3,4,5,1]=>[1,5,4,3,2]=>0111=>1110
[2,3,5,1,4]=>[4,1,5,3,2]=>1110=>0111
[2,3,5,4,1]=>[1,4,5,3,2]=>0110=>0110
[2,4,1,3,5]=>[5,3,1,4,2]=>1110=>0111
[2,4,1,5,3]=>[3,5,1,4,2]=>1100=>0011
[2,4,3,1,5]=>[5,1,3,4,2]=>1100=>0011
[2,4,3,5,1]=>[1,5,3,4,2]=>0110=>0110
[2,4,5,1,3]=>[3,1,5,4,2]=>1101=>1011
[2,4,5,3,1]=>[1,3,5,4,2]=>0101=>1010
[2,5,1,3,4]=>[4,3,1,5,2]=>1110=>0111
[2,5,1,4,3]=>[3,4,1,5,2]=>1100=>0011
[2,5,3,1,4]=>[4,1,3,5,2]=>1100=>0011
[2,5,3,4,1]=>[1,4,3,5,2]=>0110=>0110
[2,5,4,1,3]=>[3,1,4,5,2]=>1100=>0011
[2,5,4,3,1]=>[1,3,4,5,2]=>0100=>0010
[3,1,2,4,5]=>[5,4,2,1,3]=>1101=>1011
[3,1,2,5,4]=>[4,5,2,1,3]=>1100=>0011
[3,1,4,2,5]=>[5,2,4,1,3]=>1100=>0011
[3,1,4,5,2]=>[2,5,4,1,3]=>1001=>1001
[3,1,5,2,4]=>[4,2,5,1,3]=>1100=>0011
[3,1,5,4,2]=>[2,4,5,1,3]=>1000=>0001
[3,2,1,4,5]=>[5,4,1,2,3]=>1001=>1001
[3,2,1,5,4]=>[4,5,1,2,3]=>1000=>0001
[3,2,4,1,5]=>[5,1,4,2,3]=>1100=>0011
[3,2,4,5,1]=>[1,5,4,2,3]=>0101=>1010
[3,2,5,1,4]=>[4,1,5,2,3]=>1100=>0011
[3,2,5,4,1]=>[1,4,5,2,3]=>0100=>0010
[3,4,1,2,5]=>[5,2,1,4,3]=>1110=>0111
[3,4,1,5,2]=>[2,5,1,4,3]=>1010=>0101
[3,4,2,1,5]=>[5,1,2,4,3]=>1010=>0101
[3,4,2,5,1]=>[1,5,2,4,3]=>0110=>0110
[3,4,5,1,2]=>[2,1,5,4,3]=>1011=>1101
[3,4,5,2,1]=>[1,2,5,4,3]=>0011=>1100
[3,5,1,2,4]=>[4,2,1,5,3]=>1110=>0111
[3,5,1,4,2]=>[2,4,1,5,3]=>1010=>0101
[3,5,2,1,4]=>[4,1,2,5,3]=>1010=>0101
[3,5,2,4,1]=>[1,4,2,5,3]=>0110=>0110
[3,5,4,1,2]=>[2,1,4,5,3]=>1010=>0101
[3,5,4,2,1]=>[1,2,4,5,3]=>0010=>0100
[4,1,2,3,5]=>[5,3,2,1,4]=>1110=>0111
[4,1,2,5,3]=>[3,5,2,1,4]=>1100=>0011
[4,1,3,2,5]=>[5,2,3,1,4]=>1100=>0011
[4,1,3,5,2]=>[2,5,3,1,4]=>1010=>0101
[4,1,5,2,3]=>[3,2,5,1,4]=>1100=>0011
[4,1,5,3,2]=>[2,3,5,1,4]=>1000=>0001
[4,2,1,3,5]=>[5,3,1,2,4]=>1010=>0101
[4,2,1,5,3]=>[3,5,1,2,4]=>1000=>0001
[4,2,3,1,5]=>[5,1,3,2,4]=>1100=>0011
[4,2,3,5,1]=>[1,5,3,2,4]=>0110=>0110
[4,2,5,1,3]=>[3,1,5,2,4]=>1100=>0011
[4,2,5,3,1]=>[1,3,5,2,4]=>0100=>0010
[4,3,1,2,5]=>[5,2,1,3,4]=>1100=>0011
[4,3,1,5,2]=>[2,5,1,3,4]=>1000=>0001
[4,3,2,1,5]=>[5,1,2,3,4]=>1000=>0001
[4,3,2,5,1]=>[1,5,2,3,4]=>0100=>0010
[4,3,5,1,2]=>[2,1,5,3,4]=>1010=>0101
[4,3,5,2,1]=>[1,2,5,3,4]=>0010=>0100
[4,5,1,2,3]=>[3,2,1,5,4]=>1101=>1011
[4,5,1,3,2]=>[2,3,1,5,4]=>1001=>1001
[4,5,2,1,3]=>[3,1,2,5,4]=>1001=>1001
[4,5,2,3,1]=>[1,3,2,5,4]=>0101=>1010
[4,5,3,1,2]=>[2,1,3,5,4]=>1001=>1001
[4,5,3,2,1]=>[1,2,3,5,4]=>0001=>1000
[5,1,2,3,4]=>[4,3,2,1,5]=>1110=>0111
[5,1,2,4,3]=>[3,4,2,1,5]=>1100=>0011
[5,1,3,2,4]=>[4,2,3,1,5]=>1100=>0011
[5,1,3,4,2]=>[2,4,3,1,5]=>1010=>0101
[5,1,4,2,3]=>[3,2,4,1,5]=>1100=>0011
[5,1,4,3,2]=>[2,3,4,1,5]=>1000=>0001
[5,2,1,3,4]=>[4,3,1,2,5]=>1010=>0101
[5,2,1,4,3]=>[3,4,1,2,5]=>1000=>0001
[5,2,3,1,4]=>[4,1,3,2,5]=>1100=>0011
[5,2,3,4,1]=>[1,4,3,2,5]=>0110=>0110
[5,2,4,1,3]=>[3,1,4,2,5]=>1100=>0011
[5,2,4,3,1]=>[1,3,4,2,5]=>0100=>0010
[5,3,1,2,4]=>[4,2,1,3,5]=>1100=>0011
[5,3,1,4,2]=>[2,4,1,3,5]=>1000=>0001
[5,3,2,1,4]=>[4,1,2,3,5]=>1000=>0001
[5,3,2,4,1]=>[1,4,2,3,5]=>0100=>0010
[5,3,4,1,2]=>[2,1,4,3,5]=>1010=>0101
[5,3,4,2,1]=>[1,2,4,3,5]=>0010=>0100
[5,4,1,2,3]=>[3,2,1,4,5]=>1100=>0011
[5,4,1,3,2]=>[2,3,1,4,5]=>1000=>0001
[5,4,2,1,3]=>[3,1,2,4,5]=>1000=>0001
[5,4,2,3,1]=>[1,3,2,4,5]=>0100=>0010
[5,4,3,1,2]=>[2,1,3,4,5]=>1000=>0001
[5,4,3,2,1]=>[1,2,3,4,5]=>0000=>0000
[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>11111=>11111
[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>11110=>01111
[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>11110=>01111
[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>11101=>10111
[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>11110=>01111
[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>11100=>00111
[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>11101=>10111
[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>11100=>00111
[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>11110=>01111
[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>11011=>11011
[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>11110=>01111
[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>11010=>01011
[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>11110=>01111
[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>11100=>00111
[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>11100=>00111
[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>11010=>01011
[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>11101=>10111
[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>11001=>10011
[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>11110=>01111
[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>11100=>00111
[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>11100=>00111
[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>11010=>01011
[1,2,6,5,3,4]=>[4,3,5,6,2,1]=>11100=>00111
[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>11000=>00011
[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>11011=>11011
[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>11010=>01011
[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>11010=>01011
[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>11001=>10011
[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>11010=>01011
[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>11000=>00011
[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>11101=>10111
[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>11100=>00111
[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>11110=>01111
[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>10111=>11101
[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>11110=>01111
[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>10110=>01101
[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>11110=>01111
[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>11100=>00111
[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>11100=>00111
[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>10110=>01101
[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>11101=>10111
[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>10101=>10101
[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>11110=>01111
[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>11100=>00111
[1,3,6,4,2,5]=>[5,2,4,6,3,1]=>11100=>00111
[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>10110=>01101
[1,3,6,5,2,4]=>[4,2,5,6,3,1]=>11100=>00111
[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>10100=>00101
[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>11101=>10111
[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>11100=>00111
[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>11100=>00111
[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>11001=>10011
[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>11100=>00111
[1,4,2,6,5,3]=>[3,5,6,2,4,1]=>11000=>00011
[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>11001=>10011
[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>11000=>00011
[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>11100=>00111
[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>10101=>10101
[1,4,3,6,2,5]=>[5,2,6,3,4,1]=>11100=>00111
[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>10100=>00101
[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>11110=>01111
[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>11010=>01011
[1,4,5,3,2,6]=>[6,2,3,5,4,1]=>11010=>01011
[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>10110=>01101
[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>11011=>11011
[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>10011=>11001
[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>11110=>01111
[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>11010=>01011
[1,4,6,3,2,5]=>[5,2,3,6,4,1]=>11010=>01011
[1,4,6,3,5,2]=>[2,5,3,6,4,1]=>10110=>01101
[1,4,6,5,2,3]=>[3,2,5,6,4,1]=>11010=>01011
[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>10010=>01001
[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>11110=>01111
[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>11100=>00111
[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>11100=>00111
[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>11010=>01011
[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>11100=>00111
[1,5,2,6,4,3]=>[3,4,6,2,5,1]=>11000=>00011
[1,5,3,2,4,6]=>[6,4,2,3,5,1]=>11010=>01011
[1,5,3,2,6,4]=>[4,6,2,3,5,1]=>11000=>00011
[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>11100=>00111
[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>10110=>01101
[1,5,3,6,2,4]=>[4,2,6,3,5,1]=>11100=>00111
[1,5,3,6,4,2]=>[2,4,6,3,5,1]=>10100=>00101
[1,5,4,2,3,6]=>[6,3,2,4,5,1]=>11100=>00111
[1,5,4,2,6,3]=>[3,6,2,4,5,1]=>11000=>00011
[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>11000=>00011
[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>10100=>00101
[1,5,4,6,2,3]=>[3,2,6,4,5,1]=>11010=>01011
[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>10010=>01001
[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>11101=>10111
[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>11001=>10011
[1,5,6,3,2,4]=>[4,2,3,6,5,1]=>11001=>10011
[1,5,6,3,4,2]=>[2,4,3,6,5,1]=>10101=>10101
[1,5,6,4,2,3]=>[3,2,4,6,5,1]=>11001=>10011
[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>10001=>10001
[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>11110=>01111
[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>11100=>00111
[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>11100=>00111
[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>11010=>01011
[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>11100=>00111
[1,6,2,5,4,3]=>[3,4,5,2,6,1]=>11000=>00011
[1,6,3,2,4,5]=>[5,4,2,3,6,1]=>11010=>01011
[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>11000=>00011
[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>11100=>00111
[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>10110=>01101
[1,6,3,5,2,4]=>[4,2,5,3,6,1]=>11100=>00111
[1,6,3,5,4,2]=>[2,4,5,3,6,1]=>10100=>00101
[1,6,4,2,3,5]=>[5,3,2,4,6,1]=>11100=>00111
[1,6,4,2,5,3]=>[3,5,2,4,6,1]=>11000=>00011
[1,6,4,3,2,5]=>[5,2,3,4,6,1]=>11000=>00011
[1,6,4,3,5,2]=>[2,5,3,4,6,1]=>10100=>00101
[1,6,4,5,2,3]=>[3,2,5,4,6,1]=>11010=>01011
[1,6,4,5,3,2]=>[2,3,5,4,6,1]=>10010=>01001
[1,6,5,2,3,4]=>[4,3,2,5,6,1]=>11100=>00111
[1,6,5,2,4,3]=>[3,4,2,5,6,1]=>11000=>00011
[1,6,5,3,2,4]=>[4,2,3,5,6,1]=>11000=>00011
[1,6,5,3,4,2]=>[2,4,3,5,6,1]=>10100=>00101
[1,6,5,4,2,3]=>[3,2,4,5,6,1]=>11000=>00011
[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>10000=>00001
[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>10111=>11101
[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>10110=>01101
[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>10110=>01101
[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>10101=>10101
[2,1,3,6,4,5]=>[5,4,6,3,1,2]=>10110=>01101
[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>10100=>00101
[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>10101=>10101
[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>10100=>00101
[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>10110=>01101
[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>10011=>11001
[2,1,4,6,3,5]=>[5,3,6,4,1,2]=>10110=>01101
[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>10010=>01001
[2,1,5,3,4,6]=>[6,4,3,5,1,2]=>10110=>01101
[2,1,5,3,6,4]=>[4,6,3,5,1,2]=>10100=>00101
[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>10100=>00101
[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>10010=>01001
[2,1,5,6,3,4]=>[4,3,6,5,1,2]=>10101=>10101
[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>10001=>10001
[2,1,6,3,4,5]=>[5,4,3,6,1,2]=>10110=>01101
[2,1,6,3,5,4]=>[4,5,3,6,1,2]=>10100=>00101
[2,1,6,4,3,5]=>[5,3,4,6,1,2]=>10100=>00101
[2,1,6,4,5,3]=>[3,5,4,6,1,2]=>10010=>01001
[2,1,6,5,3,4]=>[4,3,5,6,1,2]=>10100=>00101
[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>10000=>00001
[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>11011=>11011
[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>11010=>01011
[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>11010=>01011
[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>11001=>10011
[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>11010=>01011
[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>11000=>00011
[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>11101=>10111
[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>11100=>00111
[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>11110=>01111
[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>01111=>11110
[2,3,4,6,1,5]=>[5,1,6,4,3,2]=>11110=>01111
[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>01110=>01110
[2,3,5,1,4,6]=>[6,4,1,5,3,2]=>11110=>01111
[2,3,5,1,6,4]=>[4,6,1,5,3,2]=>11100=>00111
[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>11100=>00111
[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>01110=>01110
[2,3,5,6,1,4]=>[4,1,6,5,3,2]=>11101=>10111
[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>01101=>10110
[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>11110=>01111
[2,3,6,1,5,4]=>[4,5,1,6,3,2]=>11100=>00111
[2,3,6,4,1,5]=>[5,1,4,6,3,2]=>11100=>00111
[2,3,6,4,5,1]=>[1,5,4,6,3,2]=>01110=>01110
[2,3,6,5,1,4]=>[4,1,5,6,3,2]=>11100=>00111
[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>01100=>00110
[2,4,1,3,5,6]=>[6,5,3,1,4,2]=>11101=>10111
[2,4,1,3,6,5]=>[5,6,3,1,4,2]=>11100=>00111
[2,4,1,5,3,6]=>[6,3,5,1,4,2]=>11100=>00111
[2,4,1,5,6,3]=>[3,6,5,1,4,2]=>11001=>10011
[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>11100=>00111
[2,4,1,6,5,3]=>[3,5,6,1,4,2]=>11000=>00011
[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>11001=>10011
[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>11000=>00011
[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>11100=>00111
[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>01101=>10110
[2,4,3,6,1,5]=>[5,1,6,3,4,2]=>11100=>00111
[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>01100=>00110
[2,4,5,1,3,6]=>[6,3,1,5,4,2]=>11110=>01111
[2,4,5,1,6,3]=>[3,6,1,5,4,2]=>11010=>01011
[2,4,5,3,1,6]=>[6,1,3,5,4,2]=>11010=>01011
[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>01110=>01110
[2,4,5,6,1,3]=>[3,1,6,5,4,2]=>11011=>11011
[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>01011=>11010
[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>11110=>01111
[2,4,6,1,5,3]=>[3,5,1,6,4,2]=>11010=>01011
[2,4,6,3,1,5]=>[5,1,3,6,4,2]=>11010=>01011
[2,4,6,3,5,1]=>[1,5,3,6,4,2]=>01110=>01110
[2,4,6,5,1,3]=>[3,1,5,6,4,2]=>11010=>01011
[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>01010=>01010
[2,5,1,3,4,6]=>[6,4,3,1,5,2]=>11110=>01111
[2,5,1,3,6,4]=>[4,6,3,1,5,2]=>11100=>00111
[2,5,1,4,3,6]=>[6,3,4,1,5,2]=>11100=>00111
[2,5,1,4,6,3]=>[3,6,4,1,5,2]=>11010=>01011
[2,5,1,6,3,4]=>[4,3,6,1,5,2]=>11100=>00111
[2,5,1,6,4,3]=>[3,4,6,1,5,2]=>11000=>00011
[2,5,3,1,4,6]=>[6,4,1,3,5,2]=>11010=>01011
[2,5,3,1,6,4]=>[4,6,1,3,5,2]=>11000=>00011
[2,5,3,4,1,6]=>[6,1,4,3,5,2]=>11100=>00111
[2,5,3,4,6,1]=>[1,6,4,3,5,2]=>01110=>01110
[2,5,3,6,1,4]=>[4,1,6,3,5,2]=>11100=>00111
[2,5,3,6,4,1]=>[1,4,6,3,5,2]=>01100=>00110
[2,5,4,1,3,6]=>[6,3,1,4,5,2]=>11100=>00111
[2,5,4,1,6,3]=>[3,6,1,4,5,2]=>11000=>00011
[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>11000=>00011
[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>01100=>00110
[2,5,4,6,1,3]=>[3,1,6,4,5,2]=>11010=>01011
[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>01010=>01010
[2,5,6,1,3,4]=>[4,3,1,6,5,2]=>11101=>10111
[2,5,6,1,4,3]=>[3,4,1,6,5,2]=>11001=>10011
[2,5,6,3,1,4]=>[4,1,3,6,5,2]=>11001=>10011
[2,5,6,3,4,1]=>[1,4,3,6,5,2]=>01101=>10110
[2,5,6,4,1,3]=>[3,1,4,6,5,2]=>11001=>10011
[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>01001=>10010
[2,6,1,3,4,5]=>[5,4,3,1,6,2]=>11110=>01111
[2,6,1,3,5,4]=>[4,5,3,1,6,2]=>11100=>00111
[2,6,1,4,3,5]=>[5,3,4,1,6,2]=>11100=>00111
[2,6,1,4,5,3]=>[3,5,4,1,6,2]=>11010=>01011
[2,6,1,5,3,4]=>[4,3,5,1,6,2]=>11100=>00111
[2,6,1,5,4,3]=>[3,4,5,1,6,2]=>11000=>00011
[2,6,3,1,4,5]=>[5,4,1,3,6,2]=>11010=>01011
[2,6,3,1,5,4]=>[4,5,1,3,6,2]=>11000=>00011
[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>11100=>00111
[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>01110=>01110
[2,6,3,5,1,4]=>[4,1,5,3,6,2]=>11100=>00111
[2,6,3,5,4,1]=>[1,4,5,3,6,2]=>01100=>00110
[2,6,4,1,3,5]=>[5,3,1,4,6,2]=>11100=>00111
[2,6,4,1,5,3]=>[3,5,1,4,6,2]=>11000=>00011
[2,6,4,3,1,5]=>[5,1,3,4,6,2]=>11000=>00011
[2,6,4,3,5,1]=>[1,5,3,4,6,2]=>01100=>00110
[2,6,4,5,1,3]=>[3,1,5,4,6,2]=>11010=>01011
[2,6,4,5,3,1]=>[1,3,5,4,6,2]=>01010=>01010
[2,6,5,1,3,4]=>[4,3,1,5,6,2]=>11100=>00111
[2,6,5,1,4,3]=>[3,4,1,5,6,2]=>11000=>00011
[2,6,5,3,1,4]=>[4,1,3,5,6,2]=>11000=>00011
[2,6,5,3,4,1]=>[1,4,3,5,6,2]=>01100=>00110
[2,6,5,4,1,3]=>[3,1,4,5,6,2]=>11000=>00011
[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>01000=>00010
[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>11011=>11011
[3,1,2,4,6,5]=>[5,6,4,2,1,3]=>11010=>01011
[3,1,2,5,4,6]=>[6,4,5,2,1,3]=>11010=>01011
[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>11001=>10011
[3,1,2,6,4,5]=>[5,4,6,2,1,3]=>11010=>01011
[3,1,2,6,5,4]=>[4,5,6,2,1,3]=>11000=>00011
[3,1,4,2,5,6]=>[6,5,2,4,1,3]=>11001=>10011
[3,1,4,2,6,5]=>[5,6,2,4,1,3]=>11000=>00011
[3,1,4,5,2,6]=>[6,2,5,4,1,3]=>11010=>01011
[3,1,4,5,6,2]=>[2,6,5,4,1,3]=>10011=>11001
[3,1,4,6,2,5]=>[5,2,6,4,1,3]=>11010=>01011
[3,1,4,6,5,2]=>[2,5,6,4,1,3]=>10010=>01001
[3,1,5,2,4,6]=>[6,4,2,5,1,3]=>11010=>01011
[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>11000=>00011
[3,1,5,4,2,6]=>[6,2,4,5,1,3]=>11000=>00011
[3,1,5,4,6,2]=>[2,6,4,5,1,3]=>10010=>01001
[3,1,5,6,2,4]=>[4,2,6,5,1,3]=>11001=>10011
[3,1,5,6,4,2]=>[2,4,6,5,1,3]=>10001=>10001
[3,1,6,2,4,5]=>[5,4,2,6,1,3]=>11010=>01011
[3,1,6,2,5,4]=>[4,5,2,6,1,3]=>11000=>00011
[3,1,6,4,2,5]=>[5,2,4,6,1,3]=>11000=>00011
[3,1,6,4,5,2]=>[2,5,4,6,1,3]=>10010=>01001
[3,1,6,5,2,4]=>[4,2,5,6,1,3]=>11000=>00011
[3,1,6,5,4,2]=>[2,4,5,6,1,3]=>10000=>00001
[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>10011=>11001
[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>10010=>01001
[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>10010=>01001
[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>10001=>10001
[3,2,1,6,4,5]=>[5,4,6,1,2,3]=>10010=>01001
[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>10000=>00001
[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>11001=>10011
[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>11000=>00011
[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>11010=>01011
[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>01011=>11010
[3,2,4,6,1,5]=>[5,1,6,4,2,3]=>11010=>01011
[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>01010=>01010
[3,2,5,1,4,6]=>[6,4,1,5,2,3]=>11010=>01011
[3,2,5,1,6,4]=>[4,6,1,5,2,3]=>11000=>00011
[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>11000=>00011
[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>01010=>01010
[3,2,5,6,1,4]=>[4,1,6,5,2,3]=>11001=>10011
[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>01001=>10010
[3,2,6,1,4,5]=>[5,4,1,6,2,3]=>11010=>01011
[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>11000=>00011
[3,2,6,4,1,5]=>[5,1,4,6,2,3]=>11000=>00011
[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>01010=>01010
[3,2,6,5,1,4]=>[4,1,5,6,2,3]=>11000=>00011
[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>01000=>00010
[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>11101=>10111
[3,4,1,2,6,5]=>[5,6,2,1,4,3]=>11100=>00111
[3,4,1,5,2,6]=>[6,2,5,1,4,3]=>11100=>00111
[3,4,1,5,6,2]=>[2,6,5,1,4,3]=>10101=>10101
[3,4,1,6,2,5]=>[5,2,6,1,4,3]=>11100=>00111
[3,4,1,6,5,2]=>[2,5,6,1,4,3]=>10100=>00101
[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>10101=>10101
[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>10100=>00101
[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>11100=>00111
[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>01101=>10110
[3,4,2,6,1,5]=>[5,1,6,2,4,3]=>11100=>00111
[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>01100=>00110
[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>11110=>01111
[3,4,5,1,6,2]=>[2,6,1,5,4,3]=>10110=>01101
[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>10110=>01101
[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>01110=>01110
[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>10111=>11101
[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>00111=>11100
[3,4,6,1,2,5]=>[5,2,1,6,4,3]=>11110=>01111
[3,4,6,1,5,2]=>[2,5,1,6,4,3]=>10110=>01101
[3,4,6,2,1,5]=>[5,1,2,6,4,3]=>10110=>01101
[3,4,6,2,5,1]=>[1,5,2,6,4,3]=>01110=>01110
[3,4,6,5,1,2]=>[2,1,5,6,4,3]=>10110=>01101
[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>00110=>01100
[3,5,1,2,4,6]=>[6,4,2,1,5,3]=>11110=>01111
[3,5,1,2,6,4]=>[4,6,2,1,5,3]=>11100=>00111
[3,5,1,4,2,6]=>[6,2,4,1,5,3]=>11100=>00111
[3,5,1,4,6,2]=>[2,6,4,1,5,3]=>10110=>01101
[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>11100=>00111
[3,5,1,6,4,2]=>[2,4,6,1,5,3]=>10100=>00101
[3,5,2,1,4,6]=>[6,4,1,2,5,3]=>10110=>01101
[3,5,2,1,6,4]=>[4,6,1,2,5,3]=>10100=>00101
[3,5,2,4,1,6]=>[6,1,4,2,5,3]=>11100=>00111
[3,5,2,4,6,1]=>[1,6,4,2,5,3]=>01110=>01110
[3,5,2,6,1,4]=>[4,1,6,2,5,3]=>11100=>00111
[3,5,2,6,4,1]=>[1,4,6,2,5,3]=>01100=>00110
[3,5,4,1,2,6]=>[6,2,1,4,5,3]=>11100=>00111
[3,5,4,1,6,2]=>[2,6,1,4,5,3]=>10100=>00101
[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>10100=>00101
[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>01100=>00110
[3,5,4,6,1,2]=>[2,1,6,4,5,3]=>10110=>01101
[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>00110=>01100
[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>11101=>10111
[3,5,6,1,4,2]=>[2,4,1,6,5,3]=>10101=>10101
[3,5,6,2,1,4]=>[4,1,2,6,5,3]=>10101=>10101
[3,5,6,2,4,1]=>[1,4,2,6,5,3]=>01101=>10110
[3,5,6,4,1,2]=>[2,1,4,6,5,3]=>10101=>10101
[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>00101=>10100
[3,6,1,2,4,5]=>[5,4,2,1,6,3]=>11110=>01111
[3,6,1,2,5,4]=>[4,5,2,1,6,3]=>11100=>00111
[3,6,1,4,2,5]=>[5,2,4,1,6,3]=>11100=>00111
[3,6,1,4,5,2]=>[2,5,4,1,6,3]=>10110=>01101
[3,6,1,5,2,4]=>[4,2,5,1,6,3]=>11100=>00111
[3,6,1,5,4,2]=>[2,4,5,1,6,3]=>10100=>00101
[3,6,2,1,4,5]=>[5,4,1,2,6,3]=>10110=>01101
[3,6,2,1,5,4]=>[4,5,1,2,6,3]=>10100=>00101
[3,6,2,4,1,5]=>[5,1,4,2,6,3]=>11100=>00111
[3,6,2,4,5,1]=>[1,5,4,2,6,3]=>01110=>01110
[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>11100=>00111
[3,6,2,5,4,1]=>[1,4,5,2,6,3]=>01100=>00110
[3,6,4,1,2,5]=>[5,2,1,4,6,3]=>11100=>00111
[3,6,4,1,5,2]=>[2,5,1,4,6,3]=>10100=>00101
[3,6,4,2,1,5]=>[5,1,2,4,6,3]=>10100=>00101
[3,6,4,2,5,1]=>[1,5,2,4,6,3]=>01100=>00110
[3,6,4,5,1,2]=>[2,1,5,4,6,3]=>10110=>01101
[3,6,4,5,2,1]=>[1,2,5,4,6,3]=>00110=>01100
[3,6,5,1,2,4]=>[4,2,1,5,6,3]=>11100=>00111
[3,6,5,1,4,2]=>[2,4,1,5,6,3]=>10100=>00101
[3,6,5,2,1,4]=>[4,1,2,5,6,3]=>10100=>00101
[3,6,5,2,4,1]=>[1,4,2,5,6,3]=>01100=>00110
[3,6,5,4,1,2]=>[2,1,4,5,6,3]=>10100=>00101
[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>00100=>00100
[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>11101=>10111
[4,1,2,3,6,5]=>[5,6,3,2,1,4]=>11100=>00111
[4,1,2,5,3,6]=>[6,3,5,2,1,4]=>11100=>00111
[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>11001=>10011
[4,1,2,6,3,5]=>[5,3,6,2,1,4]=>11100=>00111
[4,1,2,6,5,3]=>[3,5,6,2,1,4]=>11000=>00011
[4,1,3,2,5,6]=>[6,5,2,3,1,4]=>11001=>10011
[4,1,3,2,6,5]=>[5,6,2,3,1,4]=>11000=>00011
[4,1,3,5,2,6]=>[6,2,5,3,1,4]=>11100=>00111
[4,1,3,5,6,2]=>[2,6,5,3,1,4]=>10101=>10101
[4,1,3,6,2,5]=>[5,2,6,3,1,4]=>11100=>00111
[4,1,3,6,5,2]=>[2,5,6,3,1,4]=>10100=>00101
[4,1,5,2,3,6]=>[6,3,2,5,1,4]=>11100=>00111
[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>11000=>00011
[4,1,5,3,2,6]=>[6,2,3,5,1,4]=>11000=>00011
[4,1,5,3,6,2]=>[2,6,3,5,1,4]=>10100=>00101
[4,1,5,6,2,3]=>[3,2,6,5,1,4]=>11001=>10011
[4,1,5,6,3,2]=>[2,3,6,5,1,4]=>10001=>10001
[4,1,6,2,3,5]=>[5,3,2,6,1,4]=>11100=>00111
[4,1,6,2,5,3]=>[3,5,2,6,1,4]=>11000=>00011
[4,1,6,3,2,5]=>[5,2,3,6,1,4]=>11000=>00011
[4,1,6,3,5,2]=>[2,5,3,6,1,4]=>10100=>00101
[4,1,6,5,2,3]=>[3,2,5,6,1,4]=>11000=>00011
[4,1,6,5,3,2]=>[2,3,5,6,1,4]=>10000=>00001
[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>10101=>10101
[4,2,1,3,6,5]=>[5,6,3,1,2,4]=>10100=>00101
[4,2,1,5,3,6]=>[6,3,5,1,2,4]=>10100=>00101
[4,2,1,5,6,3]=>[3,6,5,1,2,4]=>10001=>10001
[4,2,1,6,3,5]=>[5,3,6,1,2,4]=>10100=>00101
[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>10000=>00001
[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>11001=>10011
[4,2,3,1,6,5]=>[5,6,1,3,2,4]=>11000=>00011
[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>11100=>00111
[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>01101=>10110
[4,2,3,6,1,5]=>[5,1,6,3,2,4]=>11100=>00111
[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>01100=>00110
[4,2,5,1,3,6]=>[6,3,1,5,2,4]=>11100=>00111
[4,2,5,1,6,3]=>[3,6,1,5,2,4]=>11000=>00011
[4,2,5,3,1,6]=>[6,1,3,5,2,4]=>11000=>00011
[4,2,5,3,6,1]=>[1,6,3,5,2,4]=>01100=>00110
[4,2,5,6,1,3]=>[3,1,6,5,2,4]=>11001=>10011
[4,2,5,6,3,1]=>[1,3,6,5,2,4]=>01001=>10010
[4,2,6,1,3,5]=>[5,3,1,6,2,4]=>11100=>00111
[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>11000=>00011
[4,2,6,3,1,5]=>[5,1,3,6,2,4]=>11000=>00011
[4,2,6,3,5,1]=>[1,5,3,6,2,4]=>01100=>00110
[4,2,6,5,1,3]=>[3,1,5,6,2,4]=>11000=>00011
[4,2,6,5,3,1]=>[1,3,5,6,2,4]=>01000=>00010
[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>11001=>10011
[4,3,1,2,6,5]=>[5,6,2,1,3,4]=>11000=>00011
[4,3,1,5,2,6]=>[6,2,5,1,3,4]=>11000=>00011
[4,3,1,5,6,2]=>[2,6,5,1,3,4]=>10001=>10001
[4,3,1,6,2,5]=>[5,2,6,1,3,4]=>11000=>00011
[4,3,1,6,5,2]=>[2,5,6,1,3,4]=>10000=>00001
[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>10001=>10001
[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>10000=>00001
[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>11000=>00011
[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>01001=>10010
[4,3,2,6,1,5]=>[5,1,6,2,3,4]=>11000=>00011
[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>01000=>00010
[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>11100=>00111
[4,3,5,1,6,2]=>[2,6,1,5,3,4]=>10100=>00101
[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>10100=>00101
[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>01100=>00110
[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>10101=>10101
[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>00101=>10100
[4,3,6,1,2,5]=>[5,2,1,6,3,4]=>11100=>00111
[4,3,6,1,5,2]=>[2,5,1,6,3,4]=>10100=>00101
[4,3,6,2,1,5]=>[5,1,2,6,3,4]=>10100=>00101
[4,3,6,2,5,1]=>[1,5,2,6,3,4]=>01100=>00110
[4,3,6,5,1,2]=>[2,1,5,6,3,4]=>10100=>00101
[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>00100=>00100
[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>11110=>01111
[4,5,1,2,6,3]=>[3,6,2,1,5,4]=>11010=>01011
[4,5,1,3,2,6]=>[6,2,3,1,5,4]=>11010=>01011
[4,5,1,3,6,2]=>[2,6,3,1,5,4]=>10110=>01101
[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>11010=>01011
[4,5,1,6,3,2]=>[2,3,6,1,5,4]=>10010=>01001
[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>10110=>01101
[4,5,2,1,6,3]=>[3,6,1,2,5,4]=>10010=>01001
[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>11010=>01011
[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>01110=>01110
[4,5,2,6,1,3]=>[3,1,6,2,5,4]=>11010=>01011
[4,5,2,6,3,1]=>[1,3,6,2,5,4]=>01010=>01010
[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>11010=>01011
[4,5,3,1,6,2]=>[2,6,1,3,5,4]=>10010=>01001
[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>10010=>01001
[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>01010=>01010
[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>10110=>01101
[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>00110=>01100
[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011=>11011
[4,5,6,1,3,2]=>[2,3,1,6,5,4]=>10011=>11001
[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>10011=>11001
[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>01011=>11010
[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>10011=>11001
[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>00011=>11000
[4,6,1,2,3,5]=>[5,3,2,1,6,4]=>11110=>01111
[4,6,1,2,5,3]=>[3,5,2,1,6,4]=>11010=>01011
[4,6,1,3,2,5]=>[5,2,3,1,6,4]=>11010=>01011
[4,6,1,3,5,2]=>[2,5,3,1,6,4]=>10110=>01101
[4,6,1,5,2,3]=>[3,2,5,1,6,4]=>11010=>01011
[4,6,1,5,3,2]=>[2,3,5,1,6,4]=>10010=>01001
[4,6,2,1,3,5]=>[5,3,1,2,6,4]=>10110=>01101
[4,6,2,1,5,3]=>[3,5,1,2,6,4]=>10010=>01001
[4,6,2,3,1,5]=>[5,1,3,2,6,4]=>11010=>01011
[4,6,2,3,5,1]=>[1,5,3,2,6,4]=>01110=>01110
[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>11010=>01011
[4,6,2,5,3,1]=>[1,3,5,2,6,4]=>01010=>01010
[4,6,3,1,2,5]=>[5,2,1,3,6,4]=>11010=>01011
[4,6,3,1,5,2]=>[2,5,1,3,6,4]=>10010=>01001
[4,6,3,2,1,5]=>[5,1,2,3,6,4]=>10010=>01001
[4,6,3,2,5,1]=>[1,5,2,3,6,4]=>01010=>01010
[4,6,3,5,1,2]=>[2,1,5,3,6,4]=>10110=>01101
[4,6,3,5,2,1]=>[1,2,5,3,6,4]=>00110=>01100
[4,6,5,1,2,3]=>[3,2,1,5,6,4]=>11010=>01011
[4,6,5,1,3,2]=>[2,3,1,5,6,4]=>10010=>01001
[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>10010=>01001
[4,6,5,2,3,1]=>[1,3,2,5,6,4]=>01010=>01010
[4,6,5,3,1,2]=>[2,1,3,5,6,4]=>10010=>01001
[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>00010=>01000
[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>11110=>01111
[5,1,2,3,6,4]=>[4,6,3,2,1,5]=>11100=>00111
[5,1,2,4,3,6]=>[6,3,4,2,1,5]=>11100=>00111
[5,1,2,4,6,3]=>[3,6,4,2,1,5]=>11010=>01011
[5,1,2,6,3,4]=>[4,3,6,2,1,5]=>11100=>00111
[5,1,2,6,4,3]=>[3,4,6,2,1,5]=>11000=>00011
[5,1,3,2,4,6]=>[6,4,2,3,1,5]=>11010=>01011
[5,1,3,2,6,4]=>[4,6,2,3,1,5]=>11000=>00011
[5,1,3,4,2,6]=>[6,2,4,3,1,5]=>11100=>00111
[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>10110=>01101
[5,1,3,6,2,4]=>[4,2,6,3,1,5]=>11100=>00111
[5,1,3,6,4,2]=>[2,4,6,3,1,5]=>10100=>00101
[5,1,4,2,3,6]=>[6,3,2,4,1,5]=>11100=>00111
[5,1,4,2,6,3]=>[3,6,2,4,1,5]=>11000=>00011
[5,1,4,3,2,6]=>[6,2,3,4,1,5]=>11000=>00011
[5,1,4,3,6,2]=>[2,6,3,4,1,5]=>10100=>00101
[5,1,4,6,2,3]=>[3,2,6,4,1,5]=>11010=>01011
[5,1,4,6,3,2]=>[2,3,6,4,1,5]=>10010=>01001
[5,1,6,2,3,4]=>[4,3,2,6,1,5]=>11100=>00111
[5,1,6,2,4,3]=>[3,4,2,6,1,5]=>11000=>00011
[5,1,6,3,2,4]=>[4,2,3,6,1,5]=>11000=>00011
[5,1,6,3,4,2]=>[2,4,3,6,1,5]=>10100=>00101
[5,1,6,4,2,3]=>[3,2,4,6,1,5]=>11000=>00011
[5,1,6,4,3,2]=>[2,3,4,6,1,5]=>10000=>00001
[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>10110=>01101
[5,2,1,3,6,4]=>[4,6,3,1,2,5]=>10100=>00101
[5,2,1,4,3,6]=>[6,3,4,1,2,5]=>10100=>00101
[5,2,1,4,6,3]=>[3,6,4,1,2,5]=>10010=>01001
[5,2,1,6,3,4]=>[4,3,6,1,2,5]=>10100=>00101
[5,2,1,6,4,3]=>[3,4,6,1,2,5]=>10000=>00001
[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>11010=>01011
[5,2,3,1,6,4]=>[4,6,1,3,2,5]=>11000=>00011
[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>11100=>00111
[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>01110=>01110
[5,2,3,6,1,4]=>[4,1,6,3,2,5]=>11100=>00111
[5,2,3,6,4,1]=>[1,4,6,3,2,5]=>01100=>00110
[5,2,4,1,3,6]=>[6,3,1,4,2,5]=>11100=>00111
[5,2,4,1,6,3]=>[3,6,1,4,2,5]=>11000=>00011
[5,2,4,3,1,6]=>[6,1,3,4,2,5]=>11000=>00011
[5,2,4,3,6,1]=>[1,6,3,4,2,5]=>01100=>00110
[5,2,4,6,1,3]=>[3,1,6,4,2,5]=>11010=>01011
[5,2,4,6,3,1]=>[1,3,6,4,2,5]=>01010=>01010
[5,2,6,1,3,4]=>[4,3,1,6,2,5]=>11100=>00111
[5,2,6,1,4,3]=>[3,4,1,6,2,5]=>11000=>00011
[5,2,6,3,1,4]=>[4,1,3,6,2,5]=>11000=>00011
[5,2,6,3,4,1]=>[1,4,3,6,2,5]=>01100=>00110
[5,2,6,4,1,3]=>[3,1,4,6,2,5]=>11000=>00011
[5,2,6,4,3,1]=>[1,3,4,6,2,5]=>01000=>00010
[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>11010=>01011
[5,3,1,2,6,4]=>[4,6,2,1,3,5]=>11000=>00011
[5,3,1,4,2,6]=>[6,2,4,1,3,5]=>11000=>00011
[5,3,1,4,6,2]=>[2,6,4,1,3,5]=>10010=>01001
[5,3,1,6,2,4]=>[4,2,6,1,3,5]=>11000=>00011
[5,3,1,6,4,2]=>[2,4,6,1,3,5]=>10000=>00001
[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>10010=>01001
[5,3,2,1,6,4]=>[4,6,1,2,3,5]=>10000=>00001
[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>11000=>00011
[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>01010=>01010
[5,3,2,6,1,4]=>[4,1,6,2,3,5]=>11000=>00011
[5,3,2,6,4,1]=>[1,4,6,2,3,5]=>01000=>00010
[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>11100=>00111
[5,3,4,1,6,2]=>[2,6,1,4,3,5]=>10100=>00101
[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>10100=>00101
[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>01100=>00110
[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10110=>01101
[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>00110=>01100
[5,3,6,1,2,4]=>[4,2,1,6,3,5]=>11100=>00111
[5,3,6,1,4,2]=>[2,4,1,6,3,5]=>10100=>00101
[5,3,6,2,1,4]=>[4,1,2,6,3,5]=>10100=>00101
[5,3,6,2,4,1]=>[1,4,2,6,3,5]=>01100=>00110
[5,3,6,4,1,2]=>[2,1,4,6,3,5]=>10100=>00101
[5,3,6,4,2,1]=>[1,2,4,6,3,5]=>00100=>00100
[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>11100=>00111
[5,4,1,2,6,3]=>[3,6,2,1,4,5]=>11000=>00011
[5,4,1,3,2,6]=>[6,2,3,1,4,5]=>11000=>00011
[5,4,1,3,6,2]=>[2,6,3,1,4,5]=>10100=>00101
[5,4,1,6,2,3]=>[3,2,6,1,4,5]=>11000=>00011
[5,4,1,6,3,2]=>[2,3,6,1,4,5]=>10000=>00001
[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>10100=>00101
[5,4,2,1,6,3]=>[3,6,1,2,4,5]=>10000=>00001
[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>11000=>00011
[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>01100=>00110
[5,4,2,6,1,3]=>[3,1,6,2,4,5]=>11000=>00011
[5,4,2,6,3,1]=>[1,3,6,2,4,5]=>01000=>00010
[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>11000=>00011
[5,4,3,1,6,2]=>[2,6,1,3,4,5]=>10000=>00001
[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>10000=>00001
[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>01000=>00010
[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>10100=>00101
[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>00100=>00100
[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11010=>01011
[5,4,6,1,3,2]=>[2,3,1,6,4,5]=>10010=>01001
[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>10010=>01001
[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>01010=>01010
[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>10010=>01001
[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>00010=>01000
[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101=>10111
[5,6,1,2,4,3]=>[3,4,2,1,6,5]=>11001=>10011
[5,6,1,3,2,4]=>[4,2,3,1,6,5]=>11001=>10011
[5,6,1,3,4,2]=>[2,4,3,1,6,5]=>10101=>10101
[5,6,1,4,2,3]=>[3,2,4,1,6,5]=>11001=>10011
[5,6,1,4,3,2]=>[2,3,4,1,6,5]=>10001=>10001
[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>10101=>10101
[5,6,2,1,4,3]=>[3,4,1,2,6,5]=>10001=>10001
[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>11001=>10011
[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>01101=>10110
[5,6,2,4,1,3]=>[3,1,4,2,6,5]=>11001=>10011
[5,6,2,4,3,1]=>[1,3,4,2,6,5]=>01001=>10010
[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>11001=>10011
[5,6,3,1,4,2]=>[2,4,1,3,6,5]=>10001=>10001
[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>10001=>10001
[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>01001=>10010
[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101=>10101
[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>00101=>10100
[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001=>10011
[5,6,4,1,3,2]=>[2,3,1,4,6,5]=>10001=>10001
[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>10001=>10001
[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>01001=>10010
[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001=>10001
[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>00001=>10000
[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>11110=>01111
[6,1,2,3,5,4]=>[4,5,3,2,1,6]=>11100=>00111
[6,1,2,4,3,5]=>[5,3,4,2,1,6]=>11100=>00111
[6,1,2,4,5,3]=>[3,5,4,2,1,6]=>11010=>01011
[6,1,2,5,3,4]=>[4,3,5,2,1,6]=>11100=>00111
[6,1,2,5,4,3]=>[3,4,5,2,1,6]=>11000=>00011
[6,1,3,2,4,5]=>[5,4,2,3,1,6]=>11010=>01011
[6,1,3,2,5,4]=>[4,5,2,3,1,6]=>11000=>00011
[6,1,3,4,2,5]=>[5,2,4,3,1,6]=>11100=>00111
[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>10110=>01101
[6,1,3,5,2,4]=>[4,2,5,3,1,6]=>11100=>00111
[6,1,3,5,4,2]=>[2,4,5,3,1,6]=>10100=>00101
[6,1,4,2,3,5]=>[5,3,2,4,1,6]=>11100=>00111
[6,1,4,2,5,3]=>[3,5,2,4,1,6]=>11000=>00011
[6,1,4,3,2,5]=>[5,2,3,4,1,6]=>11000=>00011
[6,1,4,3,5,2]=>[2,5,3,4,1,6]=>10100=>00101
[6,1,4,5,2,3]=>[3,2,5,4,1,6]=>11010=>01011
[6,1,4,5,3,2]=>[2,3,5,4,1,6]=>10010=>01001
[6,1,5,2,3,4]=>[4,3,2,5,1,6]=>11100=>00111
[6,1,5,2,4,3]=>[3,4,2,5,1,6]=>11000=>00011
[6,1,5,3,2,4]=>[4,2,3,5,1,6]=>11000=>00011
[6,1,5,3,4,2]=>[2,4,3,5,1,6]=>10100=>00101
[6,1,5,4,2,3]=>[3,2,4,5,1,6]=>11000=>00011
[6,1,5,4,3,2]=>[2,3,4,5,1,6]=>10000=>00001
[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>10110=>01101
[6,2,1,3,5,4]=>[4,5,3,1,2,6]=>10100=>00101
[6,2,1,4,3,5]=>[5,3,4,1,2,6]=>10100=>00101
[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>10010=>01001
[6,2,1,5,3,4]=>[4,3,5,1,2,6]=>10100=>00101
[6,2,1,5,4,3]=>[3,4,5,1,2,6]=>10000=>00001
[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>11010=>01011
[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>11000=>00011
[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>11100=>00111
[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>01110=>01110
[6,2,3,5,1,4]=>[4,1,5,3,2,6]=>11100=>00111
[6,2,3,5,4,1]=>[1,4,5,3,2,6]=>01100=>00110
[6,2,4,1,3,5]=>[5,3,1,4,2,6]=>11100=>00111
[6,2,4,1,5,3]=>[3,5,1,4,2,6]=>11000=>00011
[6,2,4,3,1,5]=>[5,1,3,4,2,6]=>11000=>00011
[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>01100=>00110
[6,2,4,5,1,3]=>[3,1,5,4,2,6]=>11010=>01011
[6,2,4,5,3,1]=>[1,3,5,4,2,6]=>01010=>01010
[6,2,5,1,3,4]=>[4,3,1,5,2,6]=>11100=>00111
[6,2,5,1,4,3]=>[3,4,1,5,2,6]=>11000=>00011
[6,2,5,3,1,4]=>[4,1,3,5,2,6]=>11000=>00011
[6,2,5,3,4,1]=>[1,4,3,5,2,6]=>01100=>00110
[6,2,5,4,1,3]=>[3,1,4,5,2,6]=>11000=>00011
[6,2,5,4,3,1]=>[1,3,4,5,2,6]=>01000=>00010
[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>11010=>01011
[6,3,1,2,5,4]=>[4,5,2,1,3,6]=>11000=>00011
[6,3,1,4,2,5]=>[5,2,4,1,3,6]=>11000=>00011
[6,3,1,4,5,2]=>[2,5,4,1,3,6]=>10010=>01001
[6,3,1,5,2,4]=>[4,2,5,1,3,6]=>11000=>00011
[6,3,1,5,4,2]=>[2,4,5,1,3,6]=>10000=>00001
[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>10010=>01001
[6,3,2,1,5,4]=>[4,5,1,2,3,6]=>10000=>00001
[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>11000=>00011
[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>01010=>01010
[6,3,2,5,1,4]=>[4,1,5,2,3,6]=>11000=>00011
[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>01000=>00010
[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>11100=>00111
[6,3,4,1,5,2]=>[2,5,1,4,3,6]=>10100=>00101
[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>10100=>00101
[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>01100=>00110
[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110=>01101
[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>00110=>01100
[6,3,5,1,2,4]=>[4,2,1,5,3,6]=>11100=>00111
[6,3,5,1,4,2]=>[2,4,1,5,3,6]=>10100=>00101
[6,3,5,2,1,4]=>[4,1,2,5,3,6]=>10100=>00101
[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>01100=>00110
[6,3,5,4,1,2]=>[2,1,4,5,3,6]=>10100=>00101
[6,3,5,4,2,1]=>[1,2,4,5,3,6]=>00100=>00100
[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11100=>00111
[6,4,1,2,5,3]=>[3,5,2,1,4,6]=>11000=>00011
[6,4,1,3,2,5]=>[5,2,3,1,4,6]=>11000=>00011
[6,4,1,3,5,2]=>[2,5,3,1,4,6]=>10100=>00101
[6,4,1,5,2,3]=>[3,2,5,1,4,6]=>11000=>00011
[6,4,1,5,3,2]=>[2,3,5,1,4,6]=>10000=>00001
[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>10100=>00101
[6,4,2,1,5,3]=>[3,5,1,2,4,6]=>10000=>00001
[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>11000=>00011
[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01100=>00110
[6,4,2,5,1,3]=>[3,1,5,2,4,6]=>11000=>00011
[6,4,2,5,3,1]=>[1,3,5,2,4,6]=>01000=>00010
[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>11000=>00011
[6,4,3,1,5,2]=>[2,5,1,3,4,6]=>10000=>00001
[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>10000=>00001
[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>01000=>00010
[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10100=>00101
[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>00100=>00100
[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010=>01011
[6,4,5,1,3,2]=>[2,3,1,5,4,6]=>10010=>01001
[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>10010=>01001
[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010=>01010
[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010=>01001
[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>00010=>01000
[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100=>00111
[6,5,1,2,4,3]=>[3,4,2,1,5,6]=>11000=>00011
[6,5,1,3,2,4]=>[4,2,3,1,5,6]=>11000=>00011
[6,5,1,3,4,2]=>[2,4,3,1,5,6]=>10100=>00101
[6,5,1,4,2,3]=>[3,2,4,1,5,6]=>11000=>00011
[6,5,1,4,3,2]=>[2,3,4,1,5,6]=>10000=>00001
[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>10100=>00101
[6,5,2,1,4,3]=>[3,4,1,2,5,6]=>10000=>00001
[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>11000=>00011
[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>01100=>00110
[6,5,2,4,1,3]=>[3,1,4,2,5,6]=>11000=>00011
[6,5,2,4,3,1]=>[1,3,4,2,5,6]=>01000=>00010
[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>11000=>00011
[6,5,3,1,4,2]=>[2,4,1,3,5,6]=>10000=>00001
[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>10000=>00001
[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>01000=>00010
[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100=>00101
[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>00100=>00100
[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000=>00011
[6,5,4,1,3,2]=>[2,3,1,4,5,6]=>10000=>00001
[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>10000=>00001
[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>01000=>00010
[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>10000=>00001
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>00000=>00000
[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>111111=>111111
[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>111110=>011111
[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>111110=>011111
[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>111101=>101111
[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>111110=>011111
[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>111100=>001111
[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>111101=>101111
[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>111100=>001111
[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>111110=>011111
[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>111011=>110111
[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>111110=>011111
[1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1]=>111010=>010111
[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>111110=>011111
[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>111100=>001111
[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>111100=>001111
[1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1]=>111010=>010111
[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>111101=>101111
[1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1]=>111001=>100111
[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>111110=>011111
[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>111100=>001111
[1,2,3,7,5,4,6]=>[6,4,5,7,3,2,1]=>111100=>001111
[1,2,3,7,5,6,4]=>[4,6,5,7,3,2,1]=>111010=>010111
[1,2,3,7,6,4,5]=>[5,4,6,7,3,2,1]=>111100=>001111
[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>111000=>000111
[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>111011=>110111
[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>111010=>010111
[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>111010=>010111
[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>111001=>100111
[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>111010=>010111
[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>111000=>000111
[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>111101=>101111
[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>111100=>001111
[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>111110=>011111
[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>110111=>111011
[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>111110=>011111
[1,2,4,5,7,6,3]=>[3,6,7,5,4,2,1]=>110110=>011011
[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>111110=>011111
[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>111100=>001111
[1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1]=>111100=>001111
[1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1]=>110110=>011011
[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>111101=>101111
[1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1]=>110101=>101011
[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>111110=>011111
[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>111100=>001111
[1,2,4,7,5,3,6]=>[6,3,5,7,4,2,1]=>111100=>001111
[1,2,4,7,5,6,3]=>[3,6,5,7,4,2,1]=>110110=>011011
[1,2,4,7,6,3,5]=>[5,3,6,7,4,2,1]=>111100=>001111
[1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1]=>110100=>001011
[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>111101=>101111
[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>111100=>001111
[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>111100=>001111
[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>111001=>100111
[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>111100=>001111
[1,2,5,3,7,6,4]=>[4,6,7,3,5,2,1]=>111000=>000111
[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>111001=>100111
[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>111000=>000111
[1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1]=>111100=>001111
[1,2,5,4,6,7,3]=>[3,7,6,4,5,2,1]=>110101=>101011
[1,2,5,4,7,3,6]=>[6,3,7,4,5,2,1]=>111100=>001111
[1,2,5,4,7,6,3]=>[3,6,7,4,5,2,1]=>110100=>001011
[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>111110=>011111
[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>111010=>010111
[1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1]=>111010=>010111
[1,2,5,6,4,7,3]=>[3,7,4,6,5,2,1]=>110110=>011011
[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>111011=>110111
[1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1]=>110011=>110011
[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>111110=>011111
[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>111010=>010111
[1,2,5,7,4,3,6]=>[6,3,4,7,5,2,1]=>111010=>010111
[1,2,5,7,4,6,3]=>[3,6,4,7,5,2,1]=>110110=>011011
[1,2,5,7,6,3,4]=>[4,3,6,7,5,2,1]=>111010=>010111
[1,2,5,7,6,4,3]=>[3,4,6,7,5,2,1]=>110010=>010011
[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>111110=>011111
[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>111100=>001111
[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>111100=>001111
[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>111010=>010111
[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>111100=>001111
[1,2,6,3,7,5,4]=>[4,5,7,3,6,2,1]=>111000=>000111
[1,2,6,4,3,5,7]=>[7,5,3,4,6,2,1]=>111010=>010111
[1,2,6,4,3,7,5]=>[5,7,3,4,6,2,1]=>111000=>000111
[1,2,6,4,5,3,7]=>[7,3,5,4,6,2,1]=>111100=>001111
[1,2,6,4,5,7,3]=>[3,7,5,4,6,2,1]=>110110=>011011
[1,2,6,4,7,3,5]=>[5,3,7,4,6,2,1]=>111100=>001111
[1,2,6,4,7,5,3]=>[3,5,7,4,6,2,1]=>110100=>001011
[1,2,6,5,3,4,7]=>[7,4,3,5,6,2,1]=>111100=>001111
[1,2,6,5,3,7,4]=>[4,7,3,5,6,2,1]=>111000=>000111
[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>111000=>000111
[1,2,6,5,4,7,3]=>[3,7,4,5,6,2,1]=>110100=>001011
[1,2,6,5,7,3,4]=>[4,3,7,5,6,2,1]=>111010=>010111
[1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1]=>110010=>010011
[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>111101=>101111
[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>111001=>100111
[1,2,6,7,4,3,5]=>[5,3,4,7,6,2,1]=>111001=>100111
[1,2,6,7,4,5,3]=>[3,5,4,7,6,2,1]=>110101=>101011
[1,2,6,7,5,3,4]=>[4,3,5,7,6,2,1]=>111001=>100111
[1,2,6,7,5,4,3]=>[3,4,5,7,6,2,1]=>110001=>100011
[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>111110=>011111
[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>111100=>001111
[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>111100=>001111
[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>111010=>010111
[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>111100=>001111
[1,2,7,3,6,5,4]=>[4,5,6,3,7,2,1]=>111000=>000111
[1,2,7,4,3,5,6]=>[6,5,3,4,7,2,1]=>111010=>010111
[1,2,7,4,3,6,5]=>[5,6,3,4,7,2,1]=>111000=>000111
[1,2,7,4,5,3,6]=>[6,3,5,4,7,2,1]=>111100=>001111
[1,2,7,4,5,6,3]=>[3,6,5,4,7,2,1]=>110110=>011011
[1,2,7,4,6,3,5]=>[5,3,6,4,7,2,1]=>111100=>001111
[1,2,7,4,6,5,3]=>[3,5,6,4,7,2,1]=>110100=>001011
[1,2,7,5,3,4,6]=>[6,4,3,5,7,2,1]=>111100=>001111
[1,2,7,5,3,6,4]=>[4,6,3,5,7,2,1]=>111000=>000111
[1,2,7,5,4,3,6]=>[6,3,4,5,7,2,1]=>111000=>000111
[1,2,7,5,4,6,3]=>[3,6,4,5,7,2,1]=>110100=>001011
[1,2,7,5,6,3,4]=>[4,3,6,5,7,2,1]=>111010=>010111
[1,2,7,5,6,4,3]=>[3,4,6,5,7,2,1]=>110010=>010011
[1,2,7,6,3,4,5]=>[5,4,3,6,7,2,1]=>111100=>001111
[1,2,7,6,3,5,4]=>[4,5,3,6,7,2,1]=>111000=>000111
[1,2,7,6,4,3,5]=>[5,3,4,6,7,2,1]=>111000=>000111
[1,2,7,6,4,5,3]=>[3,5,4,6,7,2,1]=>110100=>001011
[1,2,7,6,5,3,4]=>[4,3,5,6,7,2,1]=>111000=>000111
[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>110000=>000011
[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>110111=>111011
[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>110110=>011011
[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>110110=>011011
[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>110101=>101011
[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>110110=>011011
[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>110100=>001011
[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>110101=>101011
[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>110100=>001011
[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>110110=>011011
[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>110011=>110011
[1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1]=>110110=>011011
[1,3,2,5,7,6,4]=>[4,6,7,5,2,3,1]=>110010=>010011
[1,3,2,6,4,5,7]=>[7,5,4,6,2,3,1]=>110110=>011011
[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>110100=>001011
[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>110100=>001011
[1,3,2,6,5,7,4]=>[4,7,5,6,2,3,1]=>110010=>010011
[1,3,2,6,7,4,5]=>[5,4,7,6,2,3,1]=>110101=>101011
[1,3,2,6,7,5,4]=>[4,5,7,6,2,3,1]=>110001=>100011
[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>110110=>011011
[1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1]=>110100=>001011
[1,3,2,7,5,4,6]=>[6,4,5,7,2,3,1]=>110100=>001011
[1,3,2,7,5,6,4]=>[4,6,5,7,2,3,1]=>110010=>010011
[1,3,2,7,6,4,5]=>[5,4,6,7,2,3,1]=>110100=>001011
[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>110000=>000011
[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>111011=>110111
[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>111010=>010111
[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>111010=>010111
[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>111001=>100111
[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>111010=>010111
[1,3,4,2,7,6,5]=>[5,6,7,2,4,3,1]=>111000=>000111
[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>111101=>101111
[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>111100=>001111
[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>111110=>011111
[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>101111=>111101
[1,3,4,5,7,2,6]=>[6,2,7,5,4,3,1]=>111110=>011111
[1,3,4,5,7,6,2]=>[2,6,7,5,4,3,1]=>101110=>011101
[1,3,4,6,2,5,7]=>[7,5,2,6,4,3,1]=>111110=>011111
[1,3,4,6,2,7,5]=>[5,7,2,6,4,3,1]=>111100=>001111
[1,3,4,6,5,2,7]=>[7,2,5,6,4,3,1]=>111100=>001111
[1,3,4,6,5,7,2]=>[2,7,5,6,4,3,1]=>101110=>011101
[1,3,4,6,7,2,5]=>[5,2,7,6,4,3,1]=>111101=>101111
[1,3,4,6,7,5,2]=>[2,5,7,6,4,3,1]=>101101=>101101
[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>111110=>011111
[1,3,4,7,2,6,5]=>[5,6,2,7,4,3,1]=>111100=>001111
[1,3,4,7,5,2,6]=>[6,2,5,7,4,3,1]=>111100=>001111
[1,3,4,7,5,6,2]=>[2,6,5,7,4,3,1]=>101110=>011101
[1,3,4,7,6,2,5]=>[5,2,6,7,4,3,1]=>111100=>001111
[1,3,4,7,6,5,2]=>[2,5,6,7,4,3,1]=>101100=>001101
[1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1]=>111101=>101111
[1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1]=>111100=>001111
[1,3,5,2,6,4,7]=>[7,4,6,2,5,3,1]=>111100=>001111
[1,3,5,2,6,7,4]=>[4,7,6,2,5,3,1]=>111001=>100111
[1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1]=>111100=>001111
[1,3,5,2,7,6,4]=>[4,6,7,2,5,3,1]=>111000=>000111
[1,3,5,4,2,6,7]=>[7,6,2,4,5,3,1]=>111001=>100111
[1,3,5,4,2,7,6]=>[6,7,2,4,5,3,1]=>111000=>000111
[1,3,5,4,6,2,7]=>[7,2,6,4,5,3,1]=>111100=>001111
[1,3,5,4,6,7,2]=>[2,7,6,4,5,3,1]=>101101=>101101
[1,3,5,4,7,2,6]=>[6,2,7,4,5,3,1]=>111100=>001111
[1,3,5,4,7,6,2]=>[2,6,7,4,5,3,1]=>101100=>001101
[1,3,5,6,2,4,7]=>[7,4,2,6,5,3,1]=>111110=>011111
[1,3,5,6,2,7,4]=>[4,7,2,6,5,3,1]=>111010=>010111
[1,3,5,6,4,2,7]=>[7,2,4,6,5,3,1]=>111010=>010111
[1,3,5,6,4,7,2]=>[2,7,4,6,5,3,1]=>101110=>011101
[1,3,5,6,7,2,4]=>[4,2,7,6,5,3,1]=>111011=>110111
[1,3,5,6,7,4,2]=>[2,4,7,6,5,3,1]=>101011=>110101
[1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1]=>111110=>011111
[1,3,5,7,2,6,4]=>[4,6,2,7,5,3,1]=>111010=>010111
[1,3,5,7,4,2,6]=>[6,2,4,7,5,3,1]=>111010=>010111
[1,3,5,7,4,6,2]=>[2,6,4,7,5,3,1]=>101110=>011101
[1,3,5,7,6,2,4]=>[4,2,6,7,5,3,1]=>111010=>010111
[1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1]=>101010=>010101
[1,3,6,2,4,5,7]=>[7,5,4,2,6,3,1]=>111110=>011111
[1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1]=>111100=>001111
[1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1]=>111100=>001111
[1,3,6,2,5,7,4]=>[4,7,5,2,6,3,1]=>111010=>010111
[1,3,6,2,7,4,5]=>[5,4,7,2,6,3,1]=>111100=>001111
[1,3,6,2,7,5,4]=>[4,5,7,2,6,3,1]=>111000=>000111
[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>111010=>010111
[1,3,6,4,2,7,5]=>[5,7,2,4,6,3,1]=>111000=>000111
[1,3,6,4,5,2,7]=>[7,2,5,4,6,3,1]=>111100=>001111
[1,3,6,4,5,7,2]=>[2,7,5,4,6,3,1]=>101110=>011101
[1,3,6,4,7,2,5]=>[5,2,7,4,6,3,1]=>111100=>001111
[1,3,6,4,7,5,2]=>[2,5,7,4,6,3,1]=>101100=>001101
[1,3,6,5,2,4,7]=>[7,4,2,5,6,3,1]=>111100=>001111
[1,3,6,5,2,7,4]=>[4,7,2,5,6,3,1]=>111000=>000111
[1,3,6,5,4,2,7]=>[7,2,4,5,6,3,1]=>111000=>000111
[1,3,6,5,4,7,2]=>[2,7,4,5,6,3,1]=>101100=>001101
[1,3,6,5,7,2,4]=>[4,2,7,5,6,3,1]=>111010=>010111
[1,3,6,5,7,4,2]=>[2,4,7,5,6,3,1]=>101010=>010101
[1,3,6,7,2,4,5]=>[5,4,2,7,6,3,1]=>111101=>101111
[1,3,6,7,2,5,4]=>[4,5,2,7,6,3,1]=>111001=>100111
[1,3,6,7,4,2,5]=>[5,2,4,7,6,3,1]=>111001=>100111
[1,3,6,7,4,5,2]=>[2,5,4,7,6,3,1]=>101101=>101101
[1,3,6,7,5,2,4]=>[4,2,5,7,6,3,1]=>111001=>100111
[1,3,6,7,5,4,2]=>[2,4,5,7,6,3,1]=>101001=>100101
[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>111110=>011111
[1,3,7,2,4,6,5]=>[5,6,4,2,7,3,1]=>111100=>001111
[1,3,7,2,5,4,6]=>[6,4,5,2,7,3,1]=>111100=>001111
[1,3,7,2,5,6,4]=>[4,6,5,2,7,3,1]=>111010=>010111
[1,3,7,2,6,4,5]=>[5,4,6,2,7,3,1]=>111100=>001111
[1,3,7,2,6,5,4]=>[4,5,6,2,7,3,1]=>111000=>000111
[1,3,7,4,2,5,6]=>[6,5,2,4,7,3,1]=>111010=>010111
[1,3,7,4,2,6,5]=>[5,6,2,4,7,3,1]=>111000=>000111
[1,3,7,4,5,2,6]=>[6,2,5,4,7,3,1]=>111100=>001111
[1,3,7,4,5,6,2]=>[2,6,5,4,7,3,1]=>101110=>011101
[1,3,7,4,6,2,5]=>[5,2,6,4,7,3,1]=>111100=>001111
[1,3,7,4,6,5,2]=>[2,5,6,4,7,3,1]=>101100=>001101
[1,3,7,5,2,4,6]=>[6,4,2,5,7,3,1]=>111100=>001111
[1,3,7,5,2,6,4]=>[4,6,2,5,7,3,1]=>111000=>000111
[1,3,7,5,4,2,6]=>[6,2,4,5,7,3,1]=>111000=>000111
[1,3,7,5,4,6,2]=>[2,6,4,5,7,3,1]=>101100=>001101
[1,3,7,5,6,2,4]=>[4,2,6,5,7,3,1]=>111010=>010111
[1,3,7,5,6,4,2]=>[2,4,6,5,7,3,1]=>101010=>010101
[1,3,7,6,2,4,5]=>[5,4,2,6,7,3,1]=>111100=>001111
[1,3,7,6,2,5,4]=>[4,5,2,6,7,3,1]=>111000=>000111
[1,3,7,6,4,2,5]=>[5,2,4,6,7,3,1]=>111000=>000111
[1,3,7,6,4,5,2]=>[2,5,4,6,7,3,1]=>101100=>001101
[1,3,7,6,5,2,4]=>[4,2,5,6,7,3,1]=>111000=>000111
[1,3,7,6,5,4,2]=>[2,4,5,6,7,3,1]=>101000=>000101
[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>111011=>110111
[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>111010=>010111
[1,4,2,3,6,5,7]=>[7,5,6,3,2,4,1]=>111010=>010111
[1,4,2,3,6,7,5]=>[5,7,6,3,2,4,1]=>111001=>100111
[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>111010=>010111
[1,4,2,3,7,6,5]=>[5,6,7,3,2,4,1]=>111000=>000111
[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>111001=>100111
[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>111000=>000111
[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>111010=>010111
[1,4,2,5,6,7,3]=>[3,7,6,5,2,4,1]=>110011=>110011
[1,4,2,5,7,3,6]=>[6,3,7,5,2,4,1]=>111010=>010111
[1,4,2,5,7,6,3]=>[3,6,7,5,2,4,1]=>110010=>010011
[1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1]=>111010=>010111
[1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1]=>111000=>000111
[1,4,2,6,5,3,7]=>[7,3,5,6,2,4,1]=>111000=>000111
[1,4,2,6,5,7,3]=>[3,7,5,6,2,4,1]=>110010=>010011
[1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1]=>111001=>100111
[1,4,2,6,7,5,3]=>[3,5,7,6,2,4,1]=>110001=>100011
[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>111010=>010111
[1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1]=>111000=>000111
[1,4,2,7,5,3,6]=>[6,3,5,7,2,4,1]=>111000=>000111
[1,4,2,7,5,6,3]=>[3,6,5,7,2,4,1]=>110010=>010011
[1,4,2,7,6,3,5]=>[5,3,6,7,2,4,1]=>111000=>000111
[1,4,2,7,6,5,3]=>[3,5,6,7,2,4,1]=>110000=>000011
[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>110011=>110011
[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>110010=>010011
[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>110010=>010011
[1,4,3,2,6,7,5]=>[5,7,6,2,3,4,1]=>110001=>100011
[1,4,3,2,7,5,6]=>[6,5,7,2,3,4,1]=>110010=>010011
[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>110000=>000011
[1,4,3,5,2,6,7]=>[7,6,2,5,3,4,1]=>111001=>100111
[1,4,3,5,2,7,6]=>[6,7,2,5,3,4,1]=>111000=>000111
[1,4,3,5,6,2,7]=>[7,2,6,5,3,4,1]=>111010=>010111
[1,4,3,5,6,7,2]=>[2,7,6,5,3,4,1]=>101011=>110101
[1,4,3,5,7,2,6]=>[6,2,7,5,3,4,1]=>111010=>010111
[1,4,3,5,7,6,2]=>[2,6,7,5,3,4,1]=>101010=>010101
[1,4,3,6,2,5,7]=>[7,5,2,6,3,4,1]=>111010=>010111
[1,4,3,6,2,7,5]=>[5,7,2,6,3,4,1]=>111000=>000111
[1,4,3,6,5,2,7]=>[7,2,5,6,3,4,1]=>111000=>000111
[1,4,3,6,5,7,2]=>[2,7,5,6,3,4,1]=>101010=>010101
[1,4,3,6,7,2,5]=>[5,2,7,6,3,4,1]=>111001=>100111
[1,4,3,6,7,5,2]=>[2,5,7,6,3,4,1]=>101001=>100101
[1,4,3,7,2,5,6]=>[6,5,2,7,3,4,1]=>111010=>010111
[1,4,3,7,2,6,5]=>[5,6,2,7,3,4,1]=>111000=>000111
[1,4,3,7,5,2,6]=>[6,2,5,7,3,4,1]=>111000=>000111
[1,4,3,7,5,6,2]=>[2,6,5,7,3,4,1]=>101010=>010101
[1,4,3,7,6,2,5]=>[5,2,6,7,3,4,1]=>111000=>000111
[1,4,3,7,6,5,2]=>[2,5,6,7,3,4,1]=>101000=>000101
[1,4,5,2,3,6,7]=>[7,6,3,2,5,4,1]=>111101=>101111
[1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1]=>111100=>001111
[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>111100=>001111
[1,4,5,2,6,7,3]=>[3,7,6,2,5,4,1]=>110101=>101011
[1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1]=>111100=>001111
[1,4,5,2,7,6,3]=>[3,6,7,2,5,4,1]=>110100=>001011
[1,4,5,3,2,6,7]=>[7,6,2,3,5,4,1]=>110101=>101011
[1,4,5,3,2,7,6]=>[6,7,2,3,5,4,1]=>110100=>001011
[1,4,5,3,6,2,7]=>[7,2,6,3,5,4,1]=>111100=>001111
[1,4,5,3,6,7,2]=>[2,7,6,3,5,4,1]=>101101=>101101
[1,4,5,3,7,2,6]=>[6,2,7,3,5,4,1]=>111100=>001111
[1,4,5,3,7,6,2]=>[2,6,7,3,5,4,1]=>101100=>001101
[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>111110=>011111
[1,4,5,6,2,7,3]=>[3,7,2,6,5,4,1]=>110110=>011011
[1,4,5,6,3,2,7]=>[7,2,3,6,5,4,1]=>110110=>011011
[1,4,5,6,3,7,2]=>[2,7,3,6,5,4,1]=>101110=>011101
[1,4,5,6,7,2,3]=>[3,2,7,6,5,4,1]=>110111=>111011
[1,4,5,6,7,3,2]=>[2,3,7,6,5,4,1]=>100111=>111001
[1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1]=>111110=>011111
[1,4,5,7,2,6,3]=>[3,6,2,7,5,4,1]=>110110=>011011
[1,4,5,7,3,2,6]=>[6,2,3,7,5,4,1]=>110110=>011011
[1,4,5,7,3,6,2]=>[2,6,3,7,5,4,1]=>101110=>011101
[1,4,5,7,6,2,3]=>[3,2,6,7,5,4,1]=>110110=>011011
[1,4,5,7,6,3,2]=>[2,3,6,7,5,4,1]=>100110=>011001
[1,4,6,2,3,5,7]=>[7,5,3,2,6,4,1]=>111110=>011111
[1,4,6,2,3,7,5]=>[5,7,3,2,6,4,1]=>111100=>001111
[1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1]=>111100=>001111
[1,4,6,2,5,7,3]=>[3,7,5,2,6,4,1]=>110110=>011011
[1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1]=>111100=>001111
[1,4,6,2,7,5,3]=>[3,5,7,2,6,4,1]=>110100=>001011
[1,4,6,3,2,5,7]=>[7,5,2,3,6,4,1]=>110110=>011011
[1,4,6,3,2,7,5]=>[5,7,2,3,6,4,1]=>110100=>001011
[1,4,6,3,5,2,7]=>[7,2,5,3,6,4,1]=>111100=>001111
[1,4,6,3,5,7,2]=>[2,7,5,3,6,4,1]=>101110=>011101
[1,4,6,3,7,2,5]=>[5,2,7,3,6,4,1]=>111100=>001111
[1,4,6,3,7,5,2]=>[2,5,7,3,6,4,1]=>101100=>001101
[1,4,6,5,2,3,7]=>[7,3,2,5,6,4,1]=>111100=>001111
[1,4,6,5,2,7,3]=>[3,7,2,5,6,4,1]=>110100=>001011
[1,4,6,5,3,2,7]=>[7,2,3,5,6,4,1]=>110100=>001011
[1,4,6,5,3,7,2]=>[2,7,3,5,6,4,1]=>101100=>001101
[1,4,6,5,7,2,3]=>[3,2,7,5,6,4,1]=>110110=>011011
[1,4,6,5,7,3,2]=>[2,3,7,5,6,4,1]=>100110=>011001
[1,4,6,7,2,3,5]=>[5,3,2,7,6,4,1]=>111101=>101111
[1,4,6,7,2,5,3]=>[3,5,2,7,6,4,1]=>110101=>101011
[1,4,6,7,3,2,5]=>[5,2,3,7,6,4,1]=>110101=>101011
[1,4,6,7,3,5,2]=>[2,5,3,7,6,4,1]=>101101=>101101
[1,4,6,7,5,2,3]=>[3,2,5,7,6,4,1]=>110101=>101011
[1,4,6,7,5,3,2]=>[2,3,5,7,6,4,1]=>100101=>101001
[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>111110=>011111
[1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1]=>111100=>001111
[1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1]=>111100=>001111
[1,4,7,2,5,6,3]=>[3,6,5,2,7,4,1]=>110110=>011011
[1,4,7,2,6,3,5]=>[5,3,6,2,7,4,1]=>111100=>001111
[1,4,7,2,6,5,3]=>[3,5,6,2,7,4,1]=>110100=>001011
[1,4,7,3,2,5,6]=>[6,5,2,3,7,4,1]=>110110=>011011
[1,4,7,3,2,6,5]=>[5,6,2,3,7,4,1]=>110100=>001011
[1,4,7,3,5,2,6]=>[6,2,5,3,7,4,1]=>111100=>001111
[1,4,7,3,5,6,2]=>[2,6,5,3,7,4,1]=>101110=>011101
[1,4,7,3,6,2,5]=>[5,2,6,3,7,4,1]=>111100=>001111
[1,4,7,3,6,5,2]=>[2,5,6,3,7,4,1]=>101100=>001101
[1,4,7,5,2,3,6]=>[6,3,2,5,7,4,1]=>111100=>001111
[1,4,7,5,2,6,3]=>[3,6,2,5,7,4,1]=>110100=>001011
[1,4,7,5,3,2,6]=>[6,2,3,5,7,4,1]=>110100=>001011
[1,4,7,5,3,6,2]=>[2,6,3,5,7,4,1]=>101100=>001101
[1,4,7,5,6,2,3]=>[3,2,6,5,7,4,1]=>110110=>011011
[1,4,7,5,6,3,2]=>[2,3,6,5,7,4,1]=>100110=>011001
[1,4,7,6,2,3,5]=>[5,3,2,6,7,4,1]=>111100=>001111
[1,4,7,6,2,5,3]=>[3,5,2,6,7,4,1]=>110100=>001011
[1,4,7,6,3,2,5]=>[5,2,3,6,7,4,1]=>110100=>001011
[1,4,7,6,3,5,2]=>[2,5,3,6,7,4,1]=>101100=>001101
[1,4,7,6,5,2,3]=>[3,2,5,6,7,4,1]=>110100=>001011
[1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1]=>100100=>001001
[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>111101=>101111
[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>111100=>001111
[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>111100=>001111
[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>111001=>100111
[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>111100=>001111
[1,5,2,3,7,6,4]=>[4,6,7,3,2,5,1]=>111000=>000111
[1,5,2,4,3,6,7]=>[7,6,3,4,2,5,1]=>111001=>100111
[1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1]=>111000=>000111
[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>111100=>001111
[1,5,2,4,6,7,3]=>[3,7,6,4,2,5,1]=>110101=>101011
[1,5,2,4,7,3,6]=>[6,3,7,4,2,5,1]=>111100=>001111
[1,5,2,4,7,6,3]=>[3,6,7,4,2,5,1]=>110100=>001011
[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>111100=>001111
[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>111000=>000111
[1,5,2,6,4,3,7]=>[7,3,4,6,2,5,1]=>111000=>000111
[1,5,2,6,4,7,3]=>[3,7,4,6,2,5,1]=>110100=>001011
[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>111001=>100111
[1,5,2,6,7,4,3]=>[3,4,7,6,2,5,1]=>110001=>100011
[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>111100=>001111
[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>111000=>000111
[1,5,2,7,4,3,6]=>[6,3,4,7,2,5,1]=>111000=>000111
[1,5,2,7,4,6,3]=>[3,6,4,7,2,5,1]=>110100=>001011
[1,5,2,7,6,3,4]=>[4,3,6,7,2,5,1]=>111000=>000111
[1,5,2,7,6,4,3]=>[3,4,6,7,2,5,1]=>110000=>000011
[1,5,3,2,4,6,7]=>[7,6,4,2,3,5,1]=>110101=>101011
[1,5,3,2,4,7,6]=>[6,7,4,2,3,5,1]=>110100=>001011
[1,5,3,2,6,4,7]=>[7,4,6,2,3,5,1]=>110100=>001011
[1,5,3,2,6,7,4]=>[4,7,6,2,3,5,1]=>110001=>100011
[1,5,3,2,7,4,6]=>[6,4,7,2,3,5,1]=>110100=>001011
[1,5,3,2,7,6,4]=>[4,6,7,2,3,5,1]=>110000=>000011
[1,5,3,4,2,6,7]=>[7,6,2,4,3,5,1]=>111001=>100111
[1,5,3,4,2,7,6]=>[6,7,2,4,3,5,1]=>111000=>000111
[1,5,3,4,6,2,7]=>[7,2,6,4,3,5,1]=>111100=>001111
[1,5,3,4,6,7,2]=>[2,7,6,4,3,5,1]=>101101=>101101
[1,5,3,4,7,2,6]=>[6,2,7,4,3,5,1]=>111100=>001111
[1,5,3,4,7,6,2]=>[2,6,7,4,3,5,1]=>101100=>001101
[1,5,3,6,2,4,7]=>[7,4,2,6,3,5,1]=>111100=>001111
[1,5,3,6,2,7,4]=>[4,7,2,6,3,5,1]=>111000=>000111
[1,5,3,6,4,2,7]=>[7,2,4,6,3,5,1]=>111000=>000111
[1,5,3,6,4,7,2]=>[2,7,4,6,3,5,1]=>101100=>001101
[1,5,3,6,7,2,4]=>[4,2,7,6,3,5,1]=>111001=>100111
[1,5,3,6,7,4,2]=>[2,4,7,6,3,5,1]=>101001=>100101
[1,5,3,7,2,4,6]=>[6,4,2,7,3,5,1]=>111100=>001111
[1,5,3,7,2,6,4]=>[4,6,2,7,3,5,1]=>111000=>000111
[1,5,3,7,4,2,6]=>[6,2,4,7,3,5,1]=>111000=>000111
[1,5,3,7,4,6,2]=>[2,6,4,7,3,5,1]=>101100=>001101
[1,5,3,7,6,2,4]=>[4,2,6,7,3,5,1]=>111000=>000111
[1,5,3,7,6,4,2]=>[2,4,6,7,3,5,1]=>101000=>000101
[1,5,4,2,3,6,7]=>[7,6,3,2,4,5,1]=>111001=>100111
[1,5,4,2,3,7,6]=>[6,7,3,2,4,5,1]=>111000=>000111
[1,5,4,2,6,3,7]=>[7,3,6,2,4,5,1]=>111000=>000111
[1,5,4,2,6,7,3]=>[3,7,6,2,4,5,1]=>110001=>100011
[1,5,4,2,7,3,6]=>[6,3,7,2,4,5,1]=>111000=>000111
[1,5,4,2,7,6,3]=>[3,6,7,2,4,5,1]=>110000=>000011
[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>110001=>100011
[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>110000=>000011
[1,5,4,3,6,2,7]=>[7,2,6,3,4,5,1]=>111000=>000111
[1,5,4,3,6,7,2]=>[2,7,6,3,4,5,1]=>101001=>100101
[1,5,4,3,7,2,6]=>[6,2,7,3,4,5,1]=>111000=>000111
[1,5,4,3,7,6,2]=>[2,6,7,3,4,5,1]=>101000=>000101
[1,5,4,6,2,3,7]=>[7,3,2,6,4,5,1]=>111100=>001111
[1,5,4,6,2,7,3]=>[3,7,2,6,4,5,1]=>110100=>001011
[1,5,4,6,3,2,7]=>[7,2,3,6,4,5,1]=>110100=>001011
[1,5,4,6,3,7,2]=>[2,7,3,6,4,5,1]=>101100=>001101
[1,5,4,6,7,2,3]=>[3,2,7,6,4,5,1]=>110101=>101011
[1,5,4,6,7,3,2]=>[2,3,7,6,4,5,1]=>100101=>101001
[1,5,4,7,2,3,6]=>[6,3,2,7,4,5,1]=>111100=>001111
[1,5,4,7,2,6,3]=>[3,6,2,7,4,5,1]=>110100=>001011
[1,5,4,7,3,2,6]=>[6,2,3,7,4,5,1]=>110100=>001011
[1,5,4,7,3,6,2]=>[2,6,3,7,4,5,1]=>101100=>001101
[1,5,4,7,6,2,3]=>[3,2,6,7,4,5,1]=>110100=>001011
[1,5,4,7,6,3,2]=>[2,3,6,7,4,5,1]=>100100=>001001
[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>111110=>011111
[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>111010=>010111
[1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1]=>111010=>010111
[1,5,6,2,4,7,3]=>[3,7,4,2,6,5,1]=>110110=>011011
[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>111010=>010111
[1,5,6,2,7,4,3]=>[3,4,7,2,6,5,1]=>110010=>010011
[1,5,6,3,2,4,7]=>[7,4,2,3,6,5,1]=>110110=>011011
[1,5,6,3,2,7,4]=>[4,7,2,3,6,5,1]=>110010=>010011
[1,5,6,3,4,2,7]=>[7,2,4,3,6,5,1]=>111010=>010111
[1,5,6,3,4,7,2]=>[2,7,4,3,6,5,1]=>101110=>011101
[1,5,6,3,7,2,4]=>[4,2,7,3,6,5,1]=>111010=>010111
[1,5,6,3,7,4,2]=>[2,4,7,3,6,5,1]=>101010=>010101
[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>111010=>010111
[1,5,6,4,2,7,3]=>[3,7,2,4,6,5,1]=>110010=>010011
[1,5,6,4,3,2,7]=>[7,2,3,4,6,5,1]=>110010=>010011
[1,5,6,4,3,7,2]=>[2,7,3,4,6,5,1]=>101010=>010101
[1,5,6,4,7,2,3]=>[3,2,7,4,6,5,1]=>110110=>011011
[1,5,6,4,7,3,2]=>[2,3,7,4,6,5,1]=>100110=>011001
[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>111011=>110111
[1,5,6,7,2,4,3]=>[3,4,2,7,6,5,1]=>110011=>110011
[1,5,6,7,3,2,4]=>[4,2,3,7,6,5,1]=>110011=>110011
[1,5,6,7,3,4,2]=>[2,4,3,7,6,5,1]=>101011=>110101
[1,5,6,7,4,2,3]=>[3,2,4,7,6,5,1]=>110011=>110011
[1,5,6,7,4,3,2]=>[2,3,4,7,6,5,1]=>100011=>110001
[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>111110=>011111
[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>111010=>010111
[1,5,7,2,4,3,6]=>[6,3,4,2,7,5,1]=>111010=>010111
[1,5,7,2,4,6,3]=>[3,6,4,2,7,5,1]=>110110=>011011
[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>111010=>010111
[1,5,7,2,6,4,3]=>[3,4,6,2,7,5,1]=>110010=>010011
[1,5,7,3,2,4,6]=>[6,4,2,3,7,5,1]=>110110=>011011
[1,5,7,3,2,6,4]=>[4,6,2,3,7,5,1]=>110010=>010011
[1,5,7,3,4,2,6]=>[6,2,4,3,7,5,1]=>111010=>010111
[1,5,7,3,4,6,2]=>[2,6,4,3,7,5,1]=>101110=>011101
[1,5,7,3,6,2,4]=>[4,2,6,3,7,5,1]=>111010=>010111
[1,5,7,3,6,4,2]=>[2,4,6,3,7,5,1]=>101010=>010101
[1,5,7,4,2,3,6]=>[6,3,2,4,7,5,1]=>111010=>010111
[1,5,7,4,2,6,3]=>[3,6,2,4,7,5,1]=>110010=>010011
[1,5,7,4,3,2,6]=>[6,2,3,4,7,5,1]=>110010=>010011
[1,5,7,4,3,6,2]=>[2,6,3,4,7,5,1]=>101010=>010101
[1,5,7,4,6,2,3]=>[3,2,6,4,7,5,1]=>110110=>011011
[1,5,7,4,6,3,2]=>[2,3,6,4,7,5,1]=>100110=>011001
[1,5,7,6,2,3,4]=>[4,3,2,6,7,5,1]=>111010=>010111
[1,5,7,6,2,4,3]=>[3,4,2,6,7,5,1]=>110010=>010011
[1,5,7,6,3,2,4]=>[4,2,3,6,7,5,1]=>110010=>010011
[1,5,7,6,3,4,2]=>[2,4,3,6,7,5,1]=>101010=>010101
[1,5,7,6,4,2,3]=>[3,2,4,6,7,5,1]=>110010=>010011
[1,5,7,6,4,3,2]=>[2,3,4,6,7,5,1]=>100010=>010001
[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>111110=>011111
[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>111100=>001111
[1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1]=>111100=>001111
[1,6,2,3,5,7,4]=>[4,7,5,3,2,6,1]=>111010=>010111
[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>111100=>001111
[1,6,2,3,7,5,4]=>[4,5,7,3,2,6,1]=>111000=>000111
[1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1]=>111010=>010111
[1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1]=>111000=>000111
[1,6,2,4,5,3,7]=>[7,3,5,4,2,6,1]=>111100=>001111
[1,6,2,4,5,7,3]=>[3,7,5,4,2,6,1]=>110110=>011011
[1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1]=>111100=>001111
[1,6,2,4,7,5,3]=>[3,5,7,4,2,6,1]=>110100=>001011
[1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1]=>111100=>001111
[1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1]=>111000=>000111
[1,6,2,5,4,3,7]=>[7,3,4,5,2,6,1]=>111000=>000111
[1,6,2,5,4,7,3]=>[3,7,4,5,2,6,1]=>110100=>001011
[1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1]=>111010=>010111
[1,6,2,5,7,4,3]=>[3,4,7,5,2,6,1]=>110010=>010011
[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>111100=>001111
[1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1]=>111000=>000111
[1,6,2,7,4,3,5]=>[5,3,4,7,2,6,1]=>111000=>000111
[1,6,2,7,4,5,3]=>[3,5,4,7,2,6,1]=>110100=>001011
[1,6,2,7,5,3,4]=>[4,3,5,7,2,6,1]=>111000=>000111
[1,6,2,7,5,4,3]=>[3,4,5,7,2,6,1]=>110000=>000011
[1,6,3,2,4,5,7]=>[7,5,4,2,3,6,1]=>110110=>011011
[1,6,3,2,4,7,5]=>[5,7,4,2,3,6,1]=>110100=>001011
[1,6,3,2,5,4,7]=>[7,4,5,2,3,6,1]=>110100=>001011
[1,6,3,2,5,7,4]=>[4,7,5,2,3,6,1]=>110010=>010011
[1,6,3,2,7,4,5]=>[5,4,7,2,3,6,1]=>110100=>001011
[1,6,3,2,7,5,4]=>[4,5,7,2,3,6,1]=>110000=>000011
[1,6,3,4,2,5,7]=>[7,5,2,4,3,6,1]=>111010=>010111
[1,6,3,4,2,7,5]=>[5,7,2,4,3,6,1]=>111000=>000111
[1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1]=>111100=>001111
[1,6,3,4,5,7,2]=>[2,7,5,4,3,6,1]=>101110=>011101
[1,6,3,4,7,2,5]=>[5,2,7,4,3,6,1]=>111100=>001111
[1,6,3,4,7,5,2]=>[2,5,7,4,3,6,1]=>101100=>001101
[1,6,3,5,2,4,7]=>[7,4,2,5,3,6,1]=>111100=>001111
[1,6,3,5,2,7,4]=>[4,7,2,5,3,6,1]=>111000=>000111
[1,6,3,5,4,2,7]=>[7,2,4,5,3,6,1]=>111000=>000111
[1,6,3,5,4,7,2]=>[2,7,4,5,3,6,1]=>101100=>001101
[1,6,3,5,7,2,4]=>[4,2,7,5,3,6,1]=>111010=>010111
[1,6,3,5,7,4,2]=>[2,4,7,5,3,6,1]=>101010=>010101
[1,6,3,7,2,4,5]=>[5,4,2,7,3,6,1]=>111100=>001111
[1,6,3,7,2,5,4]=>[4,5,2,7,3,6,1]=>111000=>000111
[1,6,3,7,4,2,5]=>[5,2,4,7,3,6,1]=>111000=>000111
[1,6,3,7,4,5,2]=>[2,5,4,7,3,6,1]=>101100=>001101
[1,6,3,7,5,2,4]=>[4,2,5,7,3,6,1]=>111000=>000111
[1,6,3,7,5,4,2]=>[2,4,5,7,3,6,1]=>101000=>000101
[1,6,4,2,3,5,7]=>[7,5,3,2,4,6,1]=>111010=>010111
[1,6,4,2,3,7,5]=>[5,7,3,2,4,6,1]=>111000=>000111
[1,6,4,2,5,3,7]=>[7,3,5,2,4,6,1]=>111000=>000111
[1,6,4,2,5,7,3]=>[3,7,5,2,4,6,1]=>110010=>010011
[1,6,4,2,7,3,5]=>[5,3,7,2,4,6,1]=>111000=>000111
[1,6,4,2,7,5,3]=>[3,5,7,2,4,6,1]=>110000=>000011
[1,6,4,3,2,5,7]=>[7,5,2,3,4,6,1]=>110010=>010011
[1,6,4,3,2,7,5]=>[5,7,2,3,4,6,1]=>110000=>000011
[1,6,4,3,5,2,7]=>[7,2,5,3,4,6,1]=>111000=>000111
[1,6,4,3,5,7,2]=>[2,7,5,3,4,6,1]=>101010=>010101
[1,6,4,3,7,2,5]=>[5,2,7,3,4,6,1]=>111000=>000111
[1,6,4,3,7,5,2]=>[2,5,7,3,4,6,1]=>101000=>000101
[1,6,4,5,2,3,7]=>[7,3,2,5,4,6,1]=>111100=>001111
[1,6,4,5,2,7,3]=>[3,7,2,5,4,6,1]=>110100=>001011
[1,6,4,5,3,2,7]=>[7,2,3,5,4,6,1]=>110100=>001011
[1,6,4,5,3,7,2]=>[2,7,3,5,4,6,1]=>101100=>001101
[1,6,4,5,7,2,3]=>[3,2,7,5,4,6,1]=>110110=>011011
[1,6,4,5,7,3,2]=>[2,3,7,5,4,6,1]=>100110=>011001
[1,6,4,7,2,3,5]=>[5,3,2,7,4,6,1]=>111100=>001111
[1,6,4,7,2,5,3]=>[3,5,2,7,4,6,1]=>110100=>001011
[1,6,4,7,3,2,5]=>[5,2,3,7,4,6,1]=>110100=>001011
[1,6,4,7,3,5,2]=>[2,5,3,7,4,6,1]=>101100=>001101
[1,6,4,7,5,2,3]=>[3,2,5,7,4,6,1]=>110100=>001011
[1,6,4,7,5,3,2]=>[2,3,5,7,4,6,1]=>100100=>001001
[1,6,5,2,3,4,7]=>[7,4,3,2,5,6,1]=>111100=>001111
[1,6,5,2,3,7,4]=>[4,7,3,2,5,6,1]=>111000=>000111
[1,6,5,2,4,3,7]=>[7,3,4,2,5,6,1]=>111000=>000111
[1,6,5,2,4,7,3]=>[3,7,4,2,5,6,1]=>110100=>001011
[1,6,5,2,7,3,4]=>[4,3,7,2,5,6,1]=>111000=>000111
[1,6,5,2,7,4,3]=>[3,4,7,2,5,6,1]=>110000=>000011
[1,6,5,3,2,4,7]=>[7,4,2,3,5,6,1]=>110100=>001011
[1,6,5,3,2,7,4]=>[4,7,2,3,5,6,1]=>110000=>000011
[1,6,5,3,4,2,7]=>[7,2,4,3,5,6,1]=>111000=>000111
[1,6,5,3,4,7,2]=>[2,7,4,3,5,6,1]=>101100=>001101
[1,6,5,3,7,2,4]=>[4,2,7,3,5,6,1]=>111000=>000111
[1,6,5,3,7,4,2]=>[2,4,7,3,5,6,1]=>101000=>000101
[1,6,5,4,2,3,7]=>[7,3,2,4,5,6,1]=>111000=>000111
[1,6,5,4,2,7,3]=>[3,7,2,4,5,6,1]=>110000=>000011
[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>110000=>000011
[1,6,5,4,3,7,2]=>[2,7,3,4,5,6,1]=>101000=>000101
[1,6,5,4,7,2,3]=>[3,2,7,4,5,6,1]=>110100=>001011
[1,6,5,4,7,3,2]=>[2,3,7,4,5,6,1]=>100100=>001001
[1,6,5,7,2,3,4]=>[4,3,2,7,5,6,1]=>111010=>010111
[1,6,5,7,2,4,3]=>[3,4,2,7,5,6,1]=>110010=>010011
[1,6,5,7,3,2,4]=>[4,2,3,7,5,6,1]=>110010=>010011
[1,6,5,7,3,4,2]=>[2,4,3,7,5,6,1]=>101010=>010101
[1,6,5,7,4,2,3]=>[3,2,4,7,5,6,1]=>110010=>010011
[1,6,5,7,4,3,2]=>[2,3,4,7,5,6,1]=>100010=>010001
[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>111101=>101111
[1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1]=>111001=>100111
[1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1]=>111001=>100111
[1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1]=>110101=>101011
[1,6,7,2,5,3,4]=>[4,3,5,2,7,6,1]=>111001=>100111
[1,6,7,2,5,4,3]=>[3,4,5,2,7,6,1]=>110001=>100011
[1,6,7,3,2,4,5]=>[5,4,2,3,7,6,1]=>110101=>101011
[1,6,7,3,2,5,4]=>[4,5,2,3,7,6,1]=>110001=>100011
[1,6,7,3,4,2,5]=>[5,2,4,3,7,6,1]=>111001=>100111
[1,6,7,3,4,5,2]=>[2,5,4,3,7,6,1]=>101101=>101101
[1,6,7,3,5,2,4]=>[4,2,5,3,7,6,1]=>111001=>100111
[1,6,7,3,5,4,2]=>[2,4,5,3,7,6,1]=>101001=>100101
[1,6,7,4,2,3,5]=>[5,3,2,4,7,6,1]=>111001=>100111
[1,6,7,4,2,5,3]=>[3,5,2,4,7,6,1]=>110001=>100011
[1,6,7,4,3,2,5]=>[5,2,3,4,7,6,1]=>110001=>100011
[1,6,7,4,3,5,2]=>[2,5,3,4,7,6,1]=>101001=>100101
[1,6,7,4,5,2,3]=>[3,2,5,4,7,6,1]=>110101=>101011
[1,6,7,4,5,3,2]=>[2,3,5,4,7,6,1]=>100101=>101001
[1,6,7,5,2,3,4]=>[4,3,2,5,7,6,1]=>111001=>100111
[1,6,7,5,2,4,3]=>[3,4,2,5,7,6,1]=>110001=>100011
[1,6,7,5,3,2,4]=>[4,2,3,5,7,6,1]=>110001=>100011
[1,6,7,5,3,4,2]=>[2,4,3,5,7,6,1]=>101001=>100101
[1,6,7,5,4,2,3]=>[3,2,4,5,7,6,1]=>110001=>100011
[1,6,7,5,4,3,2]=>[2,3,4,5,7,6,1]=>100001=>100001
[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>111110=>011111
[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>111100=>001111
[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>111100=>001111
[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>111010=>010111
[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>111100=>001111
[1,7,2,3,6,5,4]=>[4,5,6,3,2,7,1]=>111000=>000111
[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>111010=>010111
[1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1]=>111000=>000111
[1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1]=>111100=>001111
[1,7,2,4,5,6,3]=>[3,6,5,4,2,7,1]=>110110=>011011
[1,7,2,4,6,3,5]=>[5,3,6,4,2,7,1]=>111100=>001111
[1,7,2,4,6,5,3]=>[3,5,6,4,2,7,1]=>110100=>001011
[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>111100=>001111
[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>111000=>000111
[1,7,2,5,4,3,6]=>[6,3,4,5,2,7,1]=>111000=>000111
[1,7,2,5,4,6,3]=>[3,6,4,5,2,7,1]=>110100=>001011
[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>111010=>010111
[1,7,2,5,6,4,3]=>[3,4,6,5,2,7,1]=>110010=>010011
[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>111100=>001111
[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>111000=>000111
[1,7,2,6,4,3,5]=>[5,3,4,6,2,7,1]=>111000=>000111
[1,7,2,6,4,5,3]=>[3,5,4,6,2,7,1]=>110100=>001011
[1,7,2,6,5,3,4]=>[4,3,5,6,2,7,1]=>111000=>000111
[1,7,2,6,5,4,3]=>[3,4,5,6,2,7,1]=>110000=>000011
[1,7,3,2,4,5,6]=>[6,5,4,2,3,7,1]=>110110=>011011
[1,7,3,2,4,6,5]=>[5,6,4,2,3,7,1]=>110100=>001011
[1,7,3,2,5,4,6]=>[6,4,5,2,3,7,1]=>110100=>001011
[1,7,3,2,5,6,4]=>[4,6,5,2,3,7,1]=>110010=>010011
[1,7,3,2,6,4,5]=>[5,4,6,2,3,7,1]=>110100=>001011
[1,7,3,2,6,5,4]=>[4,5,6,2,3,7,1]=>110000=>000011
[1,7,3,4,2,5,6]=>[6,5,2,4,3,7,1]=>111010=>010111
[1,7,3,4,2,6,5]=>[5,6,2,4,3,7,1]=>111000=>000111
[1,7,3,4,5,2,6]=>[6,2,5,4,3,7,1]=>111100=>001111
[1,7,3,4,5,6,2]=>[2,6,5,4,3,7,1]=>101110=>011101
[1,7,3,4,6,2,5]=>[5,2,6,4,3,7,1]=>111100=>001111
[1,7,3,4,6,5,2]=>[2,5,6,4,3,7,1]=>101100=>001101
[1,7,3,5,2,4,6]=>[6,4,2,5,3,7,1]=>111100=>001111
[1,7,3,5,2,6,4]=>[4,6,2,5,3,7,1]=>111000=>000111
[1,7,3,5,4,2,6]=>[6,2,4,5,3,7,1]=>111000=>000111
[1,7,3,5,4,6,2]=>[2,6,4,5,3,7,1]=>101100=>001101
[1,7,3,5,6,2,4]=>[4,2,6,5,3,7,1]=>111010=>010111
[1,7,3,5,6,4,2]=>[2,4,6,5,3,7,1]=>101010=>010101
[1,7,3,6,2,4,5]=>[5,4,2,6,3,7,1]=>111100=>001111
[1,7,3,6,2,5,4]=>[4,5,2,6,3,7,1]=>111000=>000111
[1,7,3,6,4,2,5]=>[5,2,4,6,3,7,1]=>111000=>000111
[1,7,3,6,4,5,2]=>[2,5,4,6,3,7,1]=>101100=>001101
[1,7,3,6,5,2,4]=>[4,2,5,6,3,7,1]=>111000=>000111
[1,7,3,6,5,4,2]=>[2,4,5,6,3,7,1]=>101000=>000101
[1,7,4,2,3,5,6]=>[6,5,3,2,4,7,1]=>111010=>010111
[1,7,4,2,3,6,5]=>[5,6,3,2,4,7,1]=>111000=>000111
[1,7,4,2,5,3,6]=>[6,3,5,2,4,7,1]=>111000=>000111
[1,7,4,2,5,6,3]=>[3,6,5,2,4,7,1]=>110010=>010011
[1,7,4,2,6,3,5]=>[5,3,6,2,4,7,1]=>111000=>000111
[1,7,4,2,6,5,3]=>[3,5,6,2,4,7,1]=>110000=>000011
[1,7,4,3,2,5,6]=>[6,5,2,3,4,7,1]=>110010=>010011
[1,7,4,3,2,6,5]=>[5,6,2,3,4,7,1]=>110000=>000011
[1,7,4,3,5,2,6]=>[6,2,5,3,4,7,1]=>111000=>000111
[1,7,4,3,5,6,2]=>[2,6,5,3,4,7,1]=>101010=>010101
[1,7,4,3,6,2,5]=>[5,2,6,3,4,7,1]=>111000=>000111
[1,7,4,3,6,5,2]=>[2,5,6,3,4,7,1]=>101000=>000101
[1,7,4,5,2,3,6]=>[6,3,2,5,4,7,1]=>111100=>001111
[1,7,4,5,2,6,3]=>[3,6,2,5,4,7,1]=>110100=>001011
[1,7,4,5,3,2,6]=>[6,2,3,5,4,7,1]=>110100=>001011
[1,7,4,5,3,6,2]=>[2,6,3,5,4,7,1]=>101100=>001101
[1,7,4,5,6,2,3]=>[3,2,6,5,4,7,1]=>110110=>011011
[1,7,4,5,6,3,2]=>[2,3,6,5,4,7,1]=>100110=>011001
[1,7,4,6,2,3,5]=>[5,3,2,6,4,7,1]=>111100=>001111
[1,7,4,6,2,5,3]=>[3,5,2,6,4,7,1]=>110100=>001011
[1,7,4,6,3,2,5]=>[5,2,3,6,4,7,1]=>110100=>001011
[1,7,4,6,3,5,2]=>[2,5,3,6,4,7,1]=>101100=>001101
[1,7,4,6,5,2,3]=>[3,2,5,6,4,7,1]=>110100=>001011
[1,7,4,6,5,3,2]=>[2,3,5,6,4,7,1]=>100100=>001001
[1,7,5,2,3,4,6]=>[6,4,3,2,5,7,1]=>111100=>001111
[1,7,5,2,3,6,4]=>[4,6,3,2,5,7,1]=>111000=>000111
[1,7,5,2,4,3,6]=>[6,3,4,2,5,7,1]=>111000=>000111
[1,7,5,2,4,6,3]=>[3,6,4,2,5,7,1]=>110100=>001011
[1,7,5,2,6,3,4]=>[4,3,6,2,5,7,1]=>111000=>000111
[1,7,5,2,6,4,3]=>[3,4,6,2,5,7,1]=>110000=>000011
[1,7,5,3,2,4,6]=>[6,4,2,3,5,7,1]=>110100=>001011
[1,7,5,3,2,6,4]=>[4,6,2,3,5,7,1]=>110000=>000011
[1,7,5,3,4,2,6]=>[6,2,4,3,5,7,1]=>111000=>000111
[1,7,5,3,4,6,2]=>[2,6,4,3,5,7,1]=>101100=>001101
[1,7,5,3,6,2,4]=>[4,2,6,3,5,7,1]=>111000=>000111
[1,7,5,3,6,4,2]=>[2,4,6,3,5,7,1]=>101000=>000101
[1,7,5,4,2,3,6]=>[6,3,2,4,5,7,1]=>111000=>000111
[1,7,5,4,2,6,3]=>[3,6,2,4,5,7,1]=>110000=>000011
[1,7,5,4,3,2,6]=>[6,2,3,4,5,7,1]=>110000=>000011
[1,7,5,4,3,6,2]=>[2,6,3,4,5,7,1]=>101000=>000101
[1,7,5,4,6,2,3]=>[3,2,6,4,5,7,1]=>110100=>001011
[1,7,5,4,6,3,2]=>[2,3,6,4,5,7,1]=>100100=>001001
[1,7,5,6,2,3,4]=>[4,3,2,6,5,7,1]=>111010=>010111
[1,7,5,6,2,4,3]=>[3,4,2,6,5,7,1]=>110010=>010011
[1,7,5,6,3,2,4]=>[4,2,3,6,5,7,1]=>110010=>010011
[1,7,5,6,3,4,2]=>[2,4,3,6,5,7,1]=>101010=>010101
[1,7,5,6,4,2,3]=>[3,2,4,6,5,7,1]=>110010=>010011
[1,7,5,6,4,3,2]=>[2,3,4,6,5,7,1]=>100010=>010001
[1,7,6,2,3,4,5]=>[5,4,3,2,6,7,1]=>111100=>001111
[1,7,6,2,3,5,4]=>[4,5,3,2,6,7,1]=>111000=>000111
[1,7,6,2,4,3,5]=>[5,3,4,2,6,7,1]=>111000=>000111
[1,7,6,2,4,5,3]=>[3,5,4,2,6,7,1]=>110100=>001011
[1,7,6,2,5,3,4]=>[4,3,5,2,6,7,1]=>111000=>000111
[1,7,6,2,5,4,3]=>[3,4,5,2,6,7,1]=>110000=>000011
[1,7,6,3,2,4,5]=>[5,4,2,3,6,7,1]=>110100=>001011
[1,7,6,3,2,5,4]=>[4,5,2,3,6,7,1]=>110000=>000011
[1,7,6,3,4,2,5]=>[5,2,4,3,6,7,1]=>111000=>000111
[1,7,6,3,4,5,2]=>[2,5,4,3,6,7,1]=>101100=>001101
[1,7,6,3,5,2,4]=>[4,2,5,3,6,7,1]=>111000=>000111
[1,7,6,3,5,4,2]=>[2,4,5,3,6,7,1]=>101000=>000101
[1,7,6,4,2,3,5]=>[5,3,2,4,6,7,1]=>111000=>000111
[1,7,6,4,2,5,3]=>[3,5,2,4,6,7,1]=>110000=>000011
[1,7,6,4,3,2,5]=>[5,2,3,4,6,7,1]=>110000=>000011
[1,7,6,4,3,5,2]=>[2,5,3,4,6,7,1]=>101000=>000101
[1,7,6,4,5,2,3]=>[3,2,5,4,6,7,1]=>110100=>001011
[1,7,6,4,5,3,2]=>[2,3,5,4,6,7,1]=>100100=>001001
[1,7,6,5,2,3,4]=>[4,3,2,5,6,7,1]=>111000=>000111
[1,7,6,5,2,4,3]=>[3,4,2,5,6,7,1]=>110000=>000011
[1,7,6,5,3,2,4]=>[4,2,3,5,6,7,1]=>110000=>000011
[1,7,6,5,3,4,2]=>[2,4,3,5,6,7,1]=>101000=>000101
[1,7,6,5,4,2,3]=>[3,2,4,5,6,7,1]=>110000=>000011
[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>100000=>000001
[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>101111=>111101
[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>101110=>011101
[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>101110=>011101
[2,1,3,4,6,7,5]=>[5,7,6,4,3,1,2]=>101101=>101101
[2,1,3,4,7,5,6]=>[6,5,7,4,3,1,2]=>101110=>011101
[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>101100=>001101
[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>101101=>101101
[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>101100=>001101
[2,1,3,5,6,4,7]=>[7,4,6,5,3,1,2]=>101110=>011101
[2,1,3,5,6,7,4]=>[4,7,6,5,3,1,2]=>101011=>110101
[2,1,3,5,7,4,6]=>[6,4,7,5,3,1,2]=>101110=>011101
[2,1,3,5,7,6,4]=>[4,6,7,5,3,1,2]=>101010=>010101
[2,1,3,6,4,5,7]=>[7,5,4,6,3,1,2]=>101110=>011101
[2,1,3,6,4,7,5]=>[5,7,4,6,3,1,2]=>101100=>001101
[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>101100=>001101
[2,1,3,6,5,7,4]=>[4,7,5,6,3,1,2]=>101010=>010101
[2,1,3,6,7,4,5]=>[5,4,7,6,3,1,2]=>101101=>101101
[2,1,3,6,7,5,4]=>[4,5,7,6,3,1,2]=>101001=>100101
[2,1,3,7,4,5,6]=>[6,5,4,7,3,1,2]=>101110=>011101
[2,1,3,7,4,6,5]=>[5,6,4,7,3,1,2]=>101100=>001101
[2,1,3,7,5,4,6]=>[6,4,5,7,3,1,2]=>101100=>001101
[2,1,3,7,5,6,4]=>[4,6,5,7,3,1,2]=>101010=>010101
[2,1,3,7,6,4,5]=>[5,4,6,7,3,1,2]=>101100=>001101
[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>101000=>000101
[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>101011=>110101
[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>101010=>010101
[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>101010=>010101
[2,1,4,3,6,7,5]=>[5,7,6,3,4,1,2]=>101001=>100101
[2,1,4,3,7,5,6]=>[6,5,7,3,4,1,2]=>101010=>010101
[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>101000=>000101
[2,1,4,5,3,6,7]=>[7,6,3,5,4,1,2]=>101101=>101101
[2,1,4,5,3,7,6]=>[6,7,3,5,4,1,2]=>101100=>001101
[2,1,4,5,6,3,7]=>[7,3,6,5,4,1,2]=>101110=>011101
[2,1,4,5,6,7,3]=>[3,7,6,5,4,1,2]=>100111=>111001
[2,1,4,5,7,3,6]=>[6,3,7,5,4,1,2]=>101110=>011101
[2,1,4,5,7,6,3]=>[3,6,7,5,4,1,2]=>100110=>011001
[2,1,4,6,3,5,7]=>[7,5,3,6,4,1,2]=>101110=>011101
[2,1,4,6,3,7,5]=>[5,7,3,6,4,1,2]=>101100=>001101
[2,1,4,6,5,3,7]=>[7,3,5,6,4,1,2]=>101100=>001101
[2,1,4,6,5,7,3]=>[3,7,5,6,4,1,2]=>100110=>011001
[2,1,4,6,7,3,5]=>[5,3,7,6,4,1,2]=>101101=>101101
[2,1,4,6,7,5,3]=>[3,5,7,6,4,1,2]=>100101=>101001
[2,1,4,7,3,5,6]=>[6,5,3,7,4,1,2]=>101110=>011101
[2,1,4,7,3,6,5]=>[5,6,3,7,4,1,2]=>101100=>001101
[2,1,4,7,5,3,6]=>[6,3,5,7,4,1,2]=>101100=>001101
[2,1,4,7,5,6,3]=>[3,6,5,7,4,1,2]=>100110=>011001
[2,1,4,7,6,3,5]=>[5,3,6,7,4,1,2]=>101100=>001101
[2,1,4,7,6,5,3]=>[3,5,6,7,4,1,2]=>100100=>001001
[2,1,5,3,4,6,7]=>[7,6,4,3,5,1,2]=>101101=>101101
[2,1,5,3,4,7,6]=>[6,7,4,3,5,1,2]=>101100=>001101
[2,1,5,3,6,4,7]=>[7,4,6,3,5,1,2]=>101100=>001101
[2,1,5,3,6,7,4]=>[4,7,6,3,5,1,2]=>101001=>100101
[2,1,5,3,7,4,6]=>[6,4,7,3,5,1,2]=>101100=>001101
[2,1,5,3,7,6,4]=>[4,6,7,3,5,1,2]=>101000=>000101
[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>101001=>100101
[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>101000=>000101
[2,1,5,4,6,3,7]=>[7,3,6,4,5,1,2]=>101100=>001101
[2,1,5,4,6,7,3]=>[3,7,6,4,5,1,2]=>100101=>101001
[2,1,5,4,7,3,6]=>[6,3,7,4,5,1,2]=>101100=>001101
[2,1,5,4,7,6,3]=>[3,6,7,4,5,1,2]=>100100=>001001
[2,1,5,6,3,4,7]=>[7,4,3,6,5,1,2]=>101110=>011101
[2,1,5,6,3,7,4]=>[4,7,3,6,5,1,2]=>101010=>010101
[2,1,5,6,4,3,7]=>[7,3,4,6,5,1,2]=>101010=>010101
[2,1,5,6,4,7,3]=>[3,7,4,6,5,1,2]=>100110=>011001
[2,1,5,6,7,3,4]=>[4,3,7,6,5,1,2]=>101011=>110101
[2,1,5,6,7,4,3]=>[3,4,7,6,5,1,2]=>100011=>110001
[2,1,5,7,3,4,6]=>[6,4,3,7,5,1,2]=>101110=>011101
[2,1,5,7,3,6,4]=>[4,6,3,7,5,1,2]=>101010=>010101
[2,1,5,7,4,3,6]=>[6,3,4,7,5,1,2]=>101010=>010101
[2,1,5,7,4,6,3]=>[3,6,4,7,5,1,2]=>100110=>011001
[2,1,5,7,6,3,4]=>[4,3,6,7,5,1,2]=>101010=>010101
[2,1,5,7,6,4,3]=>[3,4,6,7,5,1,2]=>100010=>010001
[2,1,6,3,4,5,7]=>[7,5,4,3,6,1,2]=>101110=>011101
[2,1,6,3,4,7,5]=>[5,7,4,3,6,1,2]=>101100=>001101
[2,1,6,3,5,4,7]=>[7,4,5,3,6,1,2]=>101100=>001101
[2,1,6,3,5,7,4]=>[4,7,5,3,6,1,2]=>101010=>010101
[2,1,6,3,7,4,5]=>[5,4,7,3,6,1,2]=>101100=>001101
[2,1,6,3,7,5,4]=>[4,5,7,3,6,1,2]=>101000=>000101
[2,1,6,4,3,5,7]=>[7,5,3,4,6,1,2]=>101010=>010101
[2,1,6,4,3,7,5]=>[5,7,3,4,6,1,2]=>101000=>000101
[2,1,6,4,5,3,7]=>[7,3,5,4,6,1,2]=>101100=>001101
[2,1,6,4,5,7,3]=>[3,7,5,4,6,1,2]=>100110=>011001
[2,1,6,4,7,3,5]=>[5,3,7,4,6,1,2]=>101100=>001101
[2,1,6,4,7,5,3]=>[3,5,7,4,6,1,2]=>100100=>001001
[2,1,6,5,3,4,7]=>[7,4,3,5,6,1,2]=>101100=>001101
[2,1,6,5,3,7,4]=>[4,7,3,5,6,1,2]=>101000=>000101
[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>101000=>000101
[2,1,6,5,4,7,3]=>[3,7,4,5,6,1,2]=>100100=>001001
[2,1,6,5,7,3,4]=>[4,3,7,5,6,1,2]=>101010=>010101
[2,1,6,5,7,4,3]=>[3,4,7,5,6,1,2]=>100010=>010001
[2,1,6,7,3,4,5]=>[5,4,3,7,6,1,2]=>101101=>101101
[2,1,6,7,3,5,4]=>[4,5,3,7,6,1,2]=>101001=>100101
[2,1,6,7,4,3,5]=>[5,3,4,7,6,1,2]=>101001=>100101
[2,1,6,7,4,5,3]=>[3,5,4,7,6,1,2]=>100101=>101001
[2,1,6,7,5,3,4]=>[4,3,5,7,6,1,2]=>101001=>100101
[2,1,6,7,5,4,3]=>[3,4,5,7,6,1,2]=>100001=>100001
[2,1,7,3,4,5,6]=>[6,5,4,3,7,1,2]=>101110=>011101
[2,1,7,3,4,6,5]=>[5,6,4,3,7,1,2]=>101100=>001101
[2,1,7,3,5,4,6]=>[6,4,5,3,7,1,2]=>101100=>001101
[2,1,7,3,5,6,4]=>[4,6,5,3,7,1,2]=>101010=>010101
[2,1,7,3,6,4,5]=>[5,4,6,3,7,1,2]=>101100=>001101
[2,1,7,3,6,5,4]=>[4,5,6,3,7,1,2]=>101000=>000101
[2,1,7,4,3,5,6]=>[6,5,3,4,7,1,2]=>101010=>010101
[2,1,7,4,3,6,5]=>[5,6,3,4,7,1,2]=>101000=>000101
[2,1,7,4,5,3,6]=>[6,3,5,4,7,1,2]=>101100=>001101
[2,1,7,4,5,6,3]=>[3,6,5,4,7,1,2]=>100110=>011001
[2,1,7,4,6,3,5]=>[5,3,6,4,7,1,2]=>101100=>001101
[2,1,7,4,6,5,3]=>[3,5,6,4,7,1,2]=>100100=>001001
[2,1,7,5,3,4,6]=>[6,4,3,5,7,1,2]=>101100=>001101
[2,1,7,5,3,6,4]=>[4,6,3,5,7,1,2]=>101000=>000101
[2,1,7,5,4,3,6]=>[6,3,4,5,7,1,2]=>101000=>000101
[2,1,7,5,4,6,3]=>[3,6,4,5,7,1,2]=>100100=>001001
[2,1,7,5,6,3,4]=>[4,3,6,5,7,1,2]=>101010=>010101
[2,1,7,5,6,4,3]=>[3,4,6,5,7,1,2]=>100010=>010001
[2,1,7,6,3,4,5]=>[5,4,3,6,7,1,2]=>101100=>001101
[2,1,7,6,3,5,4]=>[4,5,3,6,7,1,2]=>101000=>000101
[2,1,7,6,4,3,5]=>[5,3,4,6,7,1,2]=>101000=>000101
[2,1,7,6,4,5,3]=>[3,5,4,6,7,1,2]=>100100=>001001
[2,1,7,6,5,3,4]=>[4,3,5,6,7,1,2]=>101000=>000101
[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>100000=>000001
[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>110111=>111011
[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>110110=>011011
[2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2]=>110110=>011011
[2,3,1,4,6,7,5]=>[5,7,6,4,1,3,2]=>110101=>101011
[2,3,1,4,7,5,6]=>[6,5,7,4,1,3,2]=>110110=>011011
[2,3,1,4,7,6,5]=>[5,6,7,4,1,3,2]=>110100=>001011
[2,3,1,5,4,6,7]=>[7,6,4,5,1,3,2]=>110101=>101011
[2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2]=>110100=>001011
[2,3,1,5,6,4,7]=>[7,4,6,5,1,3,2]=>110110=>011011
[2,3,1,5,6,7,4]=>[4,7,6,5,1,3,2]=>110011=>110011
[2,3,1,5,7,4,6]=>[6,4,7,5,1,3,2]=>110110=>011011
[2,3,1,5,7,6,4]=>[4,6,7,5,1,3,2]=>110010=>010011
[2,3,1,6,4,5,7]=>[7,5,4,6,1,3,2]=>110110=>011011
[2,3,1,6,4,7,5]=>[5,7,4,6,1,3,2]=>110100=>001011
[2,3,1,6,5,4,7]=>[7,4,5,6,1,3,2]=>110100=>001011
[2,3,1,6,5,7,4]=>[4,7,5,6,1,3,2]=>110010=>010011
[2,3,1,6,7,4,5]=>[5,4,7,6,1,3,2]=>110101=>101011
[2,3,1,6,7,5,4]=>[4,5,7,6,1,3,2]=>110001=>100011
[2,3,1,7,4,5,6]=>[6,5,4,7,1,3,2]=>110110=>011011
[2,3,1,7,4,6,5]=>[5,6,4,7,1,3,2]=>110100=>001011
[2,3,1,7,5,4,6]=>[6,4,5,7,1,3,2]=>110100=>001011
[2,3,1,7,5,6,4]=>[4,6,5,7,1,3,2]=>110010=>010011
[2,3,1,7,6,4,5]=>[5,4,6,7,1,3,2]=>110100=>001011
[2,3,1,7,6,5,4]=>[4,5,6,7,1,3,2]=>110000=>000011
[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>111011=>110111
[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>111010=>010111
[2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2]=>111010=>010111
[2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2]=>111001=>100111
[2,3,4,1,7,5,6]=>[6,5,7,1,4,3,2]=>111010=>010111
[2,3,4,1,7,6,5]=>[5,6,7,1,4,3,2]=>111000=>000111
[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>111101=>101111
[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>111100=>001111
[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>111110=>011111
[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>011111=>111110
[2,3,4,5,7,1,6]=>[6,1,7,5,4,3,2]=>111110=>011111
[2,3,4,5,7,6,1]=>[1,6,7,5,4,3,2]=>011110=>011110
[2,3,4,6,1,5,7]=>[7,5,1,6,4,3,2]=>111110=>011111
[2,3,4,6,1,7,5]=>[5,7,1,6,4,3,2]=>111100=>001111
[2,3,4,6,5,1,7]=>[7,1,5,6,4,3,2]=>111100=>001111
[2,3,4,6,5,7,1]=>[1,7,5,6,4,3,2]=>011110=>011110
[2,3,4,6,7,1,5]=>[5,1,7,6,4,3,2]=>111101=>101111
[2,3,4,6,7,5,1]=>[1,5,7,6,4,3,2]=>011101=>101110
[2,3,4,7,1,5,6]=>[6,5,1,7,4,3,2]=>111110=>011111
[2,3,4,7,1,6,5]=>[5,6,1,7,4,3,2]=>111100=>001111
[2,3,4,7,5,1,6]=>[6,1,5,7,4,3,2]=>111100=>001111
[2,3,4,7,5,6,1]=>[1,6,5,7,4,3,2]=>011110=>011110
[2,3,4,7,6,1,5]=>[5,1,6,7,4,3,2]=>111100=>001111
[2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2]=>011100=>001110
[2,3,5,1,4,6,7]=>[7,6,4,1,5,3,2]=>111101=>101111
[2,3,5,1,4,7,6]=>[6,7,4,1,5,3,2]=>111100=>001111
[2,3,5,1,6,4,7]=>[7,4,6,1,5,3,2]=>111100=>001111
[2,3,5,1,6,7,4]=>[4,7,6,1,5,3,2]=>111001=>100111
[2,3,5,1,7,4,6]=>[6,4,7,1,5,3,2]=>111100=>001111
[2,3,5,1,7,6,4]=>[4,6,7,1,5,3,2]=>111000=>000111
[2,3,5,4,1,6,7]=>[7,6,1,4,5,3,2]=>111001=>100111
[2,3,5,4,1,7,6]=>[6,7,1,4,5,3,2]=>111000=>000111
[2,3,5,4,6,1,7]=>[7,1,6,4,5,3,2]=>111100=>001111
[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>011101=>101110
[2,3,5,4,7,1,6]=>[6,1,7,4,5,3,2]=>111100=>001111
[2,3,5,4,7,6,1]=>[1,6,7,4,5,3,2]=>011100=>001110
[2,3,5,6,1,4,7]=>[7,4,1,6,5,3,2]=>111110=>011111
[2,3,5,6,1,7,4]=>[4,7,1,6,5,3,2]=>111010=>010111
[2,3,5,6,4,1,7]=>[7,1,4,6,5,3,2]=>111010=>010111
[2,3,5,6,4,7,1]=>[1,7,4,6,5,3,2]=>011110=>011110
[2,3,5,6,7,1,4]=>[4,1,7,6,5,3,2]=>111011=>110111
[2,3,5,6,7,4,1]=>[1,4,7,6,5,3,2]=>011011=>110110
[2,3,5,7,1,4,6]=>[6,4,1,7,5,3,2]=>111110=>011111
[2,3,5,7,1,6,4]=>[4,6,1,7,5,3,2]=>111010=>010111
[2,3,5,7,4,1,6]=>[6,1,4,7,5,3,2]=>111010=>010111
[2,3,5,7,4,6,1]=>[1,6,4,7,5,3,2]=>011110=>011110
[2,3,5,7,6,1,4]=>[4,1,6,7,5,3,2]=>111010=>010111
[2,3,5,7,6,4,1]=>[1,4,6,7,5,3,2]=>011010=>010110
[2,3,6,1,4,5,7]=>[7,5,4,1,6,3,2]=>111110=>011111
[2,3,6,1,4,7,5]=>[5,7,4,1,6,3,2]=>111100=>001111
[2,3,6,1,5,4,7]=>[7,4,5,1,6,3,2]=>111100=>001111
[2,3,6,1,5,7,4]=>[4,7,5,1,6,3,2]=>111010=>010111
[2,3,6,1,7,4,5]=>[5,4,7,1,6,3,2]=>111100=>001111
[2,3,6,1,7,5,4]=>[4,5,7,1,6,3,2]=>111000=>000111
[2,3,6,4,1,5,7]=>[7,5,1,4,6,3,2]=>111010=>010111
[2,3,6,4,1,7,5]=>[5,7,1,4,6,3,2]=>111000=>000111
[2,3,6,4,5,1,7]=>[7,1,5,4,6,3,2]=>111100=>001111
[2,3,6,4,5,7,1]=>[1,7,5,4,6,3,2]=>011110=>011110
[2,3,6,4,7,1,5]=>[5,1,7,4,6,3,2]=>111100=>001111
[2,3,6,4,7,5,1]=>[1,5,7,4,6,3,2]=>011100=>001110
[2,3,6,5,1,4,7]=>[7,4,1,5,6,3,2]=>111100=>001111
[2,3,6,5,1,7,4]=>[4,7,1,5,6,3,2]=>111000=>000111
[2,3,6,5,4,1,7]=>[7,1,4,5,6,3,2]=>111000=>000111
[2,3,6,5,4,7,1]=>[1,7,4,5,6,3,2]=>011100=>001110
[2,3,6,5,7,1,4]=>[4,1,7,5,6,3,2]=>111010=>010111
[2,3,6,5,7,4,1]=>[1,4,7,5,6,3,2]=>011010=>010110
[2,3,6,7,1,4,5]=>[5,4,1,7,6,3,2]=>111101=>101111
[2,3,6,7,1,5,4]=>[4,5,1,7,6,3,2]=>111001=>100111
[2,3,6,7,4,1,5]=>[5,1,4,7,6,3,2]=>111001=>100111
[2,3,6,7,4,5,1]=>[1,5,4,7,6,3,2]=>011101=>101110
[2,3,6,7,5,1,4]=>[4,1,5,7,6,3,2]=>111001=>100111
[2,3,6,7,5,4,1]=>[1,4,5,7,6,3,2]=>011001=>100110
[2,3,7,1,4,5,6]=>[6,5,4,1,7,3,2]=>111110=>011111
[2,3,7,1,4,6,5]=>[5,6,4,1,7,3,2]=>111100=>001111
[2,3,7,1,5,4,6]=>[6,4,5,1,7,3,2]=>111100=>001111
[2,3,7,1,5,6,4]=>[4,6,5,1,7,3,2]=>111010=>010111
[2,3,7,1,6,4,5]=>[5,4,6,1,7,3,2]=>111100=>001111
[2,3,7,1,6,5,4]=>[4,5,6,1,7,3,2]=>111000=>000111
[2,3,7,4,1,5,6]=>[6,5,1,4,7,3,2]=>111010=>010111
[2,3,7,4,1,6,5]=>[5,6,1,4,7,3,2]=>111000=>000111
[2,3,7,4,5,1,6]=>[6,1,5,4,7,3,2]=>111100=>001111
[2,3,7,4,5,6,1]=>[1,6,5,4,7,3,2]=>011110=>011110
[2,3,7,4,6,1,5]=>[5,1,6,4,7,3,2]=>111100=>001111
[2,3,7,4,6,5,1]=>[1,5,6,4,7,3,2]=>011100=>001110
[2,3,7,5,1,4,6]=>[6,4,1,5,7,3,2]=>111100=>001111
[2,3,7,5,1,6,4]=>[4,6,1,5,7,3,2]=>111000=>000111
[2,3,7,5,4,1,6]=>[6,1,4,5,7,3,2]=>111000=>000111
[2,3,7,5,4,6,1]=>[1,6,4,5,7,3,2]=>011100=>001110
[2,3,7,5,6,1,4]=>[4,1,6,5,7,3,2]=>111010=>010111
[2,3,7,5,6,4,1]=>[1,4,6,5,7,3,2]=>011010=>010110
[2,3,7,6,1,4,5]=>[5,4,1,6,7,3,2]=>111100=>001111
[2,3,7,6,1,5,4]=>[4,5,1,6,7,3,2]=>111000=>000111
[2,3,7,6,4,1,5]=>[5,1,4,6,7,3,2]=>111000=>000111
[2,3,7,6,4,5,1]=>[1,5,4,6,7,3,2]=>011100=>001110
[2,3,7,6,5,1,4]=>[4,1,5,6,7,3,2]=>111000=>000111
[2,3,7,6,5,4,1]=>[1,4,5,6,7,3,2]=>011000=>000110
[2,4,1,3,5,6,7]=>[7,6,5,3,1,4,2]=>111011=>110111
[2,4,1,3,5,7,6]=>[6,7,5,3,1,4,2]=>111010=>010111
[2,4,1,3,6,5,7]=>[7,5,6,3,1,4,2]=>111010=>010111
[2,4,1,3,6,7,5]=>[5,7,6,3,1,4,2]=>111001=>100111
[2,4,1,3,7,5,6]=>[6,5,7,3,1,4,2]=>111010=>010111
[2,4,1,3,7,6,5]=>[5,6,7,3,1,4,2]=>111000=>000111
[2,4,1,5,3,6,7]=>[7,6,3,5,1,4,2]=>111001=>100111
[2,4,1,5,3,7,6]=>[6,7,3,5,1,4,2]=>111000=>000111
[2,4,1,5,6,3,7]=>[7,3,6,5,1,4,2]=>111010=>010111
[2,4,1,5,6,7,3]=>[3,7,6,5,1,4,2]=>110011=>110011
[2,4,1,5,7,3,6]=>[6,3,7,5,1,4,2]=>111010=>010111
[2,4,1,5,7,6,3]=>[3,6,7,5,1,4,2]=>110010=>010011
[2,4,1,6,3,5,7]=>[7,5,3,6,1,4,2]=>111010=>010111
[2,4,1,6,3,7,5]=>[5,7,3,6,1,4,2]=>111000=>000111
[2,4,1,6,5,3,7]=>[7,3,5,6,1,4,2]=>111000=>000111
[2,4,1,6,5,7,3]=>[3,7,5,6,1,4,2]=>110010=>010011
[2,4,1,6,7,3,5]=>[5,3,7,6,1,4,2]=>111001=>100111
[2,4,1,6,7,5,3]=>[3,5,7,6,1,4,2]=>110001=>100011
[2,4,1,7,3,5,6]=>[6,5,3,7,1,4,2]=>111010=>010111
[2,4,1,7,3,6,5]=>[5,6,3,7,1,4,2]=>111000=>000111
[2,4,1,7,5,3,6]=>[6,3,5,7,1,4,2]=>111000=>000111
[2,4,1,7,5,6,3]=>[3,6,5,7,1,4,2]=>110010=>010011
[2,4,1,7,6,3,5]=>[5,3,6,7,1,4,2]=>111000=>000111
[2,4,1,7,6,5,3]=>[3,5,6,7,1,4,2]=>110000=>000011
[2,4,3,1,5,6,7]=>[7,6,5,1,3,4,2]=>110011=>110011
[2,4,3,1,5,7,6]=>[6,7,5,1,3,4,2]=>110010=>010011
[2,4,3,1,6,5,7]=>[7,5,6,1,3,4,2]=>110010=>010011
[2,4,3,1,6,7,5]=>[5,7,6,1,3,4,2]=>110001=>100011
[2,4,3,1,7,5,6]=>[6,5,7,1,3,4,2]=>110010=>010011
[2,4,3,1,7,6,5]=>[5,6,7,1,3,4,2]=>110000=>000011
[2,4,3,5,1,6,7]=>[7,6,1,5,3,4,2]=>111001=>100111
[2,4,3,5,1,7,6]=>[6,7,1,5,3,4,2]=>111000=>000111
[2,4,3,5,6,1,7]=>[7,1,6,5,3,4,2]=>111010=>010111
[2,4,3,5,6,7,1]=>[1,7,6,5,3,4,2]=>011011=>110110
[2,4,3,5,7,1,6]=>[6,1,7,5,3,4,2]=>111010=>010111
[2,4,3,5,7,6,1]=>[1,6,7,5,3,4,2]=>011010=>010110
[2,4,3,6,1,5,7]=>[7,5,1,6,3,4,2]=>111010=>010111
[2,4,3,6,1,7,5]=>[5,7,1,6,3,4,2]=>111000=>000111
[2,4,3,6,5,1,7]=>[7,1,5,6,3,4,2]=>111000=>000111
[2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2]=>011010=>010110
[2,4,3,6,7,1,5]=>[5,1,7,6,3,4,2]=>111001=>100111
[2,4,3,6,7,5,1]=>[1,5,7,6,3,4,2]=>011001=>100110
[2,4,3,7,1,5,6]=>[6,5,1,7,3,4,2]=>111010=>010111
[2,4,3,7,1,6,5]=>[5,6,1,7,3,4,2]=>111000=>000111
[2,4,3,7,5,1,6]=>[6,1,5,7,3,4,2]=>111000=>000111
[2,4,3,7,5,6,1]=>[1,6,5,7,3,4,2]=>011010=>010110
[2,4,3,7,6,1,5]=>[5,1,6,7,3,4,2]=>111000=>000111
[2,4,3,7,6,5,1]=>[1,5,6,7,3,4,2]=>011000=>000110
[2,4,5,1,3,6,7]=>[7,6,3,1,5,4,2]=>111101=>101111
[2,4,5,1,3,7,6]=>[6,7,3,1,5,4,2]=>111100=>001111
[2,4,5,1,6,3,7]=>[7,3,6,1,5,4,2]=>111100=>001111
[2,4,5,1,6,7,3]=>[3,7,6,1,5,4,2]=>110101=>101011
[2,4,5,1,7,3,6]=>[6,3,7,1,5,4,2]=>111100=>001111
[2,4,5,1,7,6,3]=>[3,6,7,1,5,4,2]=>110100=>001011
[2,4,5,3,1,6,7]=>[7,6,1,3,5,4,2]=>110101=>101011
[2,4,5,3,1,7,6]=>[6,7,1,3,5,4,2]=>110100=>001011
[2,4,5,3,6,1,7]=>[7,1,6,3,5,4,2]=>111100=>001111
[2,4,5,3,6,7,1]=>[1,7,6,3,5,4,2]=>011101=>101110
[2,4,5,3,7,1,6]=>[6,1,7,3,5,4,2]=>111100=>001111
[2,4,5,3,7,6,1]=>[1,6,7,3,5,4,2]=>011100=>001110
[2,4,5,6,1,3,7]=>[7,3,1,6,5,4,2]=>111110=>011111
[2,4,5,6,1,7,3]=>[3,7,1,6,5,4,2]=>110110=>011011
[2,4,5,6,3,1,7]=>[7,1,3,6,5,4,2]=>110110=>011011
[2,4,5,6,3,7,1]=>[1,7,3,6,5,4,2]=>011110=>011110
[2,4,5,6,7,1,3]=>[3,1,7,6,5,4,2]=>110111=>111011
[2,4,5,6,7,3,1]=>[1,3,7,6,5,4,2]=>010111=>111010
[2,4,5,7,1,3,6]=>[6,3,1,7,5,4,2]=>111110=>011111
[2,4,5,7,1,6,3]=>[3,6,1,7,5,4,2]=>110110=>011011
[2,4,5,7,3,1,6]=>[6,1,3,7,5,4,2]=>110110=>011011
[2,4,5,7,3,6,1]=>[1,6,3,7,5,4,2]=>011110=>011110
[2,4,5,7,6,1,3]=>[3,1,6,7,5,4,2]=>110110=>011011
[2,4,5,7,6,3,1]=>[1,3,6,7,5,4,2]=>010110=>011010
[2,4,6,1,3,5,7]=>[7,5,3,1,6,4,2]=>111110=>011111
[2,4,6,1,3,7,5]=>[5,7,3,1,6,4,2]=>111100=>001111
[2,4,6,1,5,3,7]=>[7,3,5,1,6,4,2]=>111100=>001111
[2,4,6,1,5,7,3]=>[3,7,5,1,6,4,2]=>110110=>011011
[2,4,6,1,7,3,5]=>[5,3,7,1,6,4,2]=>111100=>001111
[2,4,6,1,7,5,3]=>[3,5,7,1,6,4,2]=>110100=>001011
[2,4,6,3,1,5,7]=>[7,5,1,3,6,4,2]=>110110=>011011
[2,4,6,3,1,7,5]=>[5,7,1,3,6,4,2]=>110100=>001011
[2,4,6,3,5,1,7]=>[7,1,5,3,6,4,2]=>111100=>001111
[2,4,6,3,5,7,1]=>[1,7,5,3,6,4,2]=>011110=>011110
[2,4,6,3,7,1,5]=>[5,1,7,3,6,4,2]=>111100=>001111
[2,4,6,3,7,5,1]=>[1,5,7,3,6,4,2]=>011100=>001110
[2,4,6,5,1,3,7]=>[7,3,1,5,6,4,2]=>111100=>001111
[2,4,6,5,1,7,3]=>[3,7,1,5,6,4,2]=>110100=>001011
[2,4,6,5,3,1,7]=>[7,1,3,5,6,4,2]=>110100=>001011
[2,4,6,5,3,7,1]=>[1,7,3,5,6,4,2]=>011100=>001110
[2,4,6,5,7,1,3]=>[3,1,7,5,6,4,2]=>110110=>011011
[2,4,6,5,7,3,1]=>[1,3,7,5,6,4,2]=>010110=>011010
[2,4,6,7,1,3,5]=>[5,3,1,7,6,4,2]=>111101=>101111
[2,4,6,7,1,5,3]=>[3,5,1,7,6,4,2]=>110101=>101011
[2,4,6,7,3,1,5]=>[5,1,3,7,6,4,2]=>110101=>101011
[2,4,6,7,3,5,1]=>[1,5,3,7,6,4,2]=>011101=>101110
[2,4,6,7,5,1,3]=>[3,1,5,7,6,4,2]=>110101=>101011
[2,4,6,7,5,3,1]=>[1,3,5,7,6,4,2]=>010101=>101010
[2,4,7,1,3,5,6]=>[6,5,3,1,7,4,2]=>111110=>011111
[2,4,7,1,3,6,5]=>[5,6,3,1,7,4,2]=>111100=>001111
[2,4,7,1,5,3,6]=>[6,3,5,1,7,4,2]=>111100=>001111
[2,4,7,1,5,6,3]=>[3,6,5,1,7,4,2]=>110110=>011011
[2,4,7,1,6,3,5]=>[5,3,6,1,7,4,2]=>111100=>001111
[2,4,7,1,6,5,3]=>[3,5,6,1,7,4,2]=>110100=>001011
[2,4,7,3,1,5,6]=>[6,5,1,3,7,4,2]=>110110=>011011
[2,4,7,3,1,6,5]=>[5,6,1,3,7,4,2]=>110100=>001011
[2,4,7,3,5,1,6]=>[6,1,5,3,7,4,2]=>111100=>001111
[2,4,7,3,5,6,1]=>[1,6,5,3,7,4,2]=>011110=>011110
[2,4,7,3,6,1,5]=>[5,1,6,3,7,4,2]=>111100=>001111
[2,4,7,3,6,5,1]=>[1,5,6,3,7,4,2]=>011100=>001110
[2,4,7,5,1,3,6]=>[6,3,1,5,7,4,2]=>111100=>001111
[2,4,7,5,1,6,3]=>[3,6,1,5,7,4,2]=>110100=>001011
[2,4,7,5,3,1,6]=>[6,1,3,5,7,4,2]=>110100=>001011
[2,4,7,5,3,6,1]=>[1,6,3,5,7,4,2]=>011100=>001110
[2,4,7,5,6,1,3]=>[3,1,6,5,7,4,2]=>110110=>011011
[2,4,7,5,6,3,1]=>[1,3,6,5,7,4,2]=>010110=>011010
[2,4,7,6,1,3,5]=>[5,3,1,6,7,4,2]=>111100=>001111
[2,4,7,6,1,5,3]=>[3,5,1,6,7,4,2]=>110100=>001011
[2,4,7,6,3,1,5]=>[5,1,3,6,7,4,2]=>110100=>001011
[2,4,7,6,3,5,1]=>[1,5,3,6,7,4,2]=>011100=>001110
[2,4,7,6,5,1,3]=>[3,1,5,6,7,4,2]=>110100=>001011
[2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2]=>010100=>001010
[2,5,1,3,4,6,7]=>[7,6,4,3,1,5,2]=>111101=>101111
[2,5,1,3,4,7,6]=>[6,7,4,3,1,5,2]=>111100=>001111
[2,5,1,3,6,4,7]=>[7,4,6,3,1,5,2]=>111100=>001111
[2,5,1,3,6,7,4]=>[4,7,6,3,1,5,2]=>111001=>100111
[2,5,1,3,7,4,6]=>[6,4,7,3,1,5,2]=>111100=>001111
[2,5,1,3,7,6,4]=>[4,6,7,3,1,5,2]=>111000=>000111
[2,5,1,4,3,6,7]=>[7,6,3,4,1,5,2]=>111001=>100111
[2,5,1,4,3,7,6]=>[6,7,3,4,1,5,2]=>111000=>000111
[2,5,1,4,6,3,7]=>[7,3,6,4,1,5,2]=>111100=>001111
[2,5,1,4,6,7,3]=>[3,7,6,4,1,5,2]=>110101=>101011
[2,5,1,4,7,3,6]=>[6,3,7,4,1,5,2]=>111100=>001111
[2,5,1,4,7,6,3]=>[3,6,7,4,1,5,2]=>110100=>001011
[2,5,1,6,3,4,7]=>[7,4,3,6,1,5,2]=>111100=>001111
[2,5,1,6,3,7,4]=>[4,7,3,6,1,5,2]=>111000=>000111
[2,5,1,6,4,3,7]=>[7,3,4,6,1,5,2]=>111000=>000111
[2,5,1,6,4,7,3]=>[3,7,4,6,1,5,2]=>110100=>001011
[2,5,1,6,7,3,4]=>[4,3,7,6,1,5,2]=>111001=>100111
[2,5,1,6,7,4,3]=>[3,4,7,6,1,5,2]=>110001=>100011
[2,5,1,7,3,4,6]=>[6,4,3,7,1,5,2]=>111100=>001111
[2,5,1,7,3,6,4]=>[4,6,3,7,1,5,2]=>111000=>000111
[2,5,1,7,4,3,6]=>[6,3,4,7,1,5,2]=>111000=>000111
[2,5,1,7,4,6,3]=>[3,6,4,7,1,5,2]=>110100=>001011
[2,5,1,7,6,3,4]=>[4,3,6,7,1,5,2]=>111000=>000111
[2,5,1,7,6,4,3]=>[3,4,6,7,1,5,2]=>110000=>000011
[2,5,3,1,4,6,7]=>[7,6,4,1,3,5,2]=>110101=>101011
[2,5,3,1,4,7,6]=>[6,7,4,1,3,5,2]=>110100=>001011
[2,5,3,1,6,4,7]=>[7,4,6,1,3,5,2]=>110100=>001011
[2,5,3,1,6,7,4]=>[4,7,6,1,3,5,2]=>110001=>100011
[2,5,3,1,7,4,6]=>[6,4,7,1,3,5,2]=>110100=>001011
[2,5,3,1,7,6,4]=>[4,6,7,1,3,5,2]=>110000=>000011
[2,5,3,4,1,6,7]=>[7,6,1,4,3,5,2]=>111001=>100111
[2,5,3,4,1,7,6]=>[6,7,1,4,3,5,2]=>111000=>000111
[2,5,3,4,6,1,7]=>[7,1,6,4,3,5,2]=>111100=>001111
[2,5,3,4,6,7,1]=>[1,7,6,4,3,5,2]=>011101=>101110
[2,5,3,4,7,1,6]=>[6,1,7,4,3,5,2]=>111100=>001111
[2,5,3,4,7,6,1]=>[1,6,7,4,3,5,2]=>011100=>001110
[2,5,3,6,1,4,7]=>[7,4,1,6,3,5,2]=>111100=>001111
[2,5,3,6,1,7,4]=>[4,7,1,6,3,5,2]=>111000=>000111
[2,5,3,6,4,1,7]=>[7,1,4,6,3,5,2]=>111000=>000111
[2,5,3,6,4,7,1]=>[1,7,4,6,3,5,2]=>011100=>001110
[2,5,3,6,7,1,4]=>[4,1,7,6,3,5,2]=>111001=>100111
[2,5,3,6,7,4,1]=>[1,4,7,6,3,5,2]=>011001=>100110
[2,5,3,7,1,4,6]=>[6,4,1,7,3,5,2]=>111100=>001111
[2,5,3,7,1,6,4]=>[4,6,1,7,3,5,2]=>111000=>000111
[2,5,3,7,4,1,6]=>[6,1,4,7,3,5,2]=>111000=>000111
[2,5,3,7,4,6,1]=>[1,6,4,7,3,5,2]=>011100=>001110
[2,5,3,7,6,1,4]=>[4,1,6,7,3,5,2]=>111000=>000111
[2,5,3,7,6,4,1]=>[1,4,6,7,3,5,2]=>011000=>000110
[2,5,4,1,3,6,7]=>[7,6,3,1,4,5,2]=>111001=>100111
[2,5,4,1,3,7,6]=>[6,7,3,1,4,5,2]=>111000=>000111
[2,5,4,1,6,3,7]=>[7,3,6,1,4,5,2]=>111000=>000111
[2,5,4,1,6,7,3]=>[3,7,6,1,4,5,2]=>110001=>100011
[2,5,4,1,7,3,6]=>[6,3,7,1,4,5,2]=>111000=>000111
[2,5,4,1,7,6,3]=>[3,6,7,1,4,5,2]=>110000=>000011
[2,5,4,3,1,6,7]=>[7,6,1,3,4,5,2]=>110001=>100011
[2,5,4,3,1,7,6]=>[6,7,1,3,4,5,2]=>110000=>000011
[2,5,4,3,6,1,7]=>[7,1,6,3,4,5,2]=>111000=>000111
[2,5,4,3,6,7,1]=>[1,7,6,3,4,5,2]=>011001=>100110
[2,5,4,3,7,1,6]=>[6,1,7,3,4,5,2]=>111000=>000111
[2,5,4,3,7,6,1]=>[1,6,7,3,4,5,2]=>011000=>000110
[2,5,4,6,1,3,7]=>[7,3,1,6,4,5,2]=>111100=>001111
[2,5,4,6,1,7,3]=>[3,7,1,6,4,5,2]=>110100=>001011
[2,5,4,6,3,1,7]=>[7,1,3,6,4,5,2]=>110100=>001011
[2,5,4,6,3,7,1]=>[1,7,3,6,4,5,2]=>011100=>001110
[2,5,4,6,7,1,3]=>[3,1,7,6,4,5,2]=>110101=>101011
[2,5,4,6,7,3,1]=>[1,3,7,6,4,5,2]=>010101=>101010
[2,5,4,7,1,3,6]=>[6,3,1,7,4,5,2]=>111100=>001111
[2,5,4,7,1,6,3]=>[3,6,1,7,4,5,2]=>110100=>001011
[2,5,4,7,3,1,6]=>[6,1,3,7,4,5,2]=>110100=>001011
[2,5,4,7,3,6,1]=>[1,6,3,7,4,5,2]=>011100=>001110
[2,5,4,7,6,1,3]=>[3,1,6,7,4,5,2]=>110100=>001011
[2,5,4,7,6,3,1]=>[1,3,6,7,4,5,2]=>010100=>001010
[2,5,6,1,3,4,7]=>[7,4,3,1,6,5,2]=>111110=>011111
[2,5,6,1,3,7,4]=>[4,7,3,1,6,5,2]=>111010=>010111
[2,5,6,1,4,3,7]=>[7,3,4,1,6,5,2]=>111010=>010111
[2,5,6,1,4,7,3]=>[3,7,4,1,6,5,2]=>110110=>011011
[2,5,6,1,7,3,4]=>[4,3,7,1,6,5,2]=>111010=>010111
[2,5,6,1,7,4,3]=>[3,4,7,1,6,5,2]=>110010=>010011
[2,5,6,3,1,4,7]=>[7,4,1,3,6,5,2]=>110110=>011011
[2,5,6,3,1,7,4]=>[4,7,1,3,6,5,2]=>110010=>010011
[2,5,6,3,4,1,7]=>[7,1,4,3,6,5,2]=>111010=>010111
[2,5,6,3,4,7,1]=>[1,7,4,3,6,5,2]=>011110=>011110
[2,5,6,3,7,1,4]=>[4,1,7,3,6,5,2]=>111010=>010111
[2,5,6,3,7,4,1]=>[1,4,7,3,6,5,2]=>011010=>010110
[2,5,6,4,1,3,7]=>[7,3,1,4,6,5,2]=>111010=>010111
[2,5,6,4,1,7,3]=>[3,7,1,4,6,5,2]=>110010=>010011
[2,5,6,4,3,1,7]=>[7,1,3,4,6,5,2]=>110010=>010011
[2,5,6,4,3,7,1]=>[1,7,3,4,6,5,2]=>011010=>010110
[2,5,6,4,7,1,3]=>[3,1,7,4,6,5,2]=>110110=>011011
[2,5,6,4,7,3,1]=>[1,3,7,4,6,5,2]=>010110=>011010
[2,5,6,7,1,3,4]=>[4,3,1,7,6,5,2]=>111011=>110111
[2,5,6,7,1,4,3]=>[3,4,1,7,6,5,2]=>110011=>110011
[2,5,6,7,3,1,4]=>[4,1,3,7,6,5,2]=>110011=>110011
[2,5,6,7,3,4,1]=>[1,4,3,7,6,5,2]=>011011=>110110
[2,5,6,7,4,1,3]=>[3,1,4,7,6,5,2]=>110011=>110011
[2,5,6,7,4,3,1]=>[1,3,4,7,6,5,2]=>010011=>110010
[2,5,7,1,3,4,6]=>[6,4,3,1,7,5,2]=>111110=>011111
[2,5,7,1,3,6,4]=>[4,6,3,1,7,5,2]=>111010=>010111
[2,5,7,1,4,3,6]=>[6,3,4,1,7,5,2]=>111010=>010111
[2,5,7,1,4,6,3]=>[3,6,4,1,7,5,2]=>110110=>011011
[2,5,7,1,6,3,4]=>[4,3,6,1,7,5,2]=>111010=>010111
[2,5,7,1,6,4,3]=>[3,4,6,1,7,5,2]=>110010=>010011
[2,5,7,3,1,4,6]=>[6,4,1,3,7,5,2]=>110110=>011011
[2,5,7,3,1,6,4]=>[4,6,1,3,7,5,2]=>110010=>010011
[2,5,7,3,4,1,6]=>[6,1,4,3,7,5,2]=>111010=>010111
[2,5,7,3,4,6,1]=>[1,6,4,3,7,5,2]=>011110=>011110
[2,5,7,3,6,1,4]=>[4,1,6,3,7,5,2]=>111010=>010111
[2,5,7,3,6,4,1]=>[1,4,6,3,7,5,2]=>011010=>010110
[2,5,7,4,1,3,6]=>[6,3,1,4,7,5,2]=>111010=>010111
[2,5,7,4,1,6,3]=>[3,6,1,4,7,5,2]=>110010=>010011
[2,5,7,4,3,1,6]=>[6,1,3,4,7,5,2]=>110010=>010011
[2,5,7,4,3,6,1]=>[1,6,3,4,7,5,2]=>011010=>010110
[2,5,7,4,6,1,3]=>[3,1,6,4,7,5,2]=>110110=>011011
[2,5,7,4,6,3,1]=>[1,3,6,4,7,5,2]=>010110=>011010
[2,5,7,6,1,3,4]=>[4,3,1,6,7,5,2]=>111010=>010111
[2,5,7,6,1,4,3]=>[3,4,1,6,7,5,2]=>110010=>010011
[2,5,7,6,3,1,4]=>[4,1,3,6,7,5,2]=>110010=>010011
[2,5,7,6,3,4,1]=>[1,4,3,6,7,5,2]=>011010=>010110
[2,5,7,6,4,1,3]=>[3,1,4,6,7,5,2]=>110010=>010011
[2,5,7,6,4,3,1]=>[1,3,4,6,7,5,2]=>010010=>010010
[2,6,1,3,4,5,7]=>[7,5,4,3,1,6,2]=>111110=>011111
[2,6,1,3,4,7,5]=>[5,7,4,3,1,6,2]=>111100=>001111
[2,6,1,3,5,4,7]=>[7,4,5,3,1,6,2]=>111100=>001111
[2,6,1,3,5,7,4]=>[4,7,5,3,1,6,2]=>111010=>010111
[2,6,1,3,7,4,5]=>[5,4,7,3,1,6,2]=>111100=>001111
[2,6,1,3,7,5,4]=>[4,5,7,3,1,6,2]=>111000=>000111
[2,6,1,4,3,5,7]=>[7,5,3,4,1,6,2]=>111010=>010111
[2,6,1,4,3,7,5]=>[5,7,3,4,1,6,2]=>111000=>000111
[2,6,1,4,5,3,7]=>[7,3,5,4,1,6,2]=>111100=>001111
[2,6,1,4,5,7,3]=>[3,7,5,4,1,6,2]=>110110=>011011
[2,6,1,4,7,3,5]=>[5,3,7,4,1,6,2]=>111100=>001111
[2,6,1,4,7,5,3]=>[3,5,7,4,1,6,2]=>110100=>001011
[2,6,1,5,3,4,7]=>[7,4,3,5,1,6,2]=>111100=>001111
[2,6,1,5,3,7,4]=>[4,7,3,5,1,6,2]=>111000=>000111
[2,6,1,5,4,3,7]=>[7,3,4,5,1,6,2]=>111000=>000111
[2,6,1,5,4,7,3]=>[3,7,4,5,1,6,2]=>110100=>001011
[2,6,1,5,7,3,4]=>[4,3,7,5,1,6,2]=>111010=>010111
[2,6,1,5,7,4,3]=>[3,4,7,5,1,6,2]=>110010=>010011
[2,6,1,7,3,4,5]=>[5,4,3,7,1,6,2]=>111100=>001111
[2,6,1,7,3,5,4]=>[4,5,3,7,1,6,2]=>111000=>000111
[2,6,1,7,4,3,5]=>[5,3,4,7,1,6,2]=>111000=>000111
[2,6,1,7,4,5,3]=>[3,5,4,7,1,6,2]=>110100=>001011
[2,6,1,7,5,3,4]=>[4,3,5,7,1,6,2]=>111000=>000111
[2,6,1,7,5,4,3]=>[3,4,5,7,1,6,2]=>110000=>000011
[2,6,3,1,4,5,7]=>[7,5,4,1,3,6,2]=>110110=>011011
[2,6,3,1,4,7,5]=>[5,7,4,1,3,6,2]=>110100=>001011
[2,6,3,1,5,4,7]=>[7,4,5,1,3,6,2]=>110100=>001011
[2,6,3,1,5,7,4]=>[4,7,5,1,3,6,2]=>110010=>010011
[2,6,3,1,7,4,5]=>[5,4,7,1,3,6,2]=>110100=>001011
[2,6,3,1,7,5,4]=>[4,5,7,1,3,6,2]=>110000=>000011
[2,6,3,4,1,5,7]=>[7,5,1,4,3,6,2]=>111010=>010111
[2,6,3,4,1,7,5]=>[5,7,1,4,3,6,2]=>111000=>000111
[2,6,3,4,5,1,7]=>[7,1,5,4,3,6,2]=>111100=>001111
[2,6,3,4,5,7,1]=>[1,7,5,4,3,6,2]=>011110=>011110
[2,6,3,4,7,1,5]=>[5,1,7,4,3,6,2]=>111100=>001111
[2,6,3,4,7,5,1]=>[1,5,7,4,3,6,2]=>011100=>001110
[2,6,3,5,1,4,7]=>[7,4,1,5,3,6,2]=>111100=>001111
[2,6,3,5,1,7,4]=>[4,7,1,5,3,6,2]=>111000=>000111
[2,6,3,5,4,1,7]=>[7,1,4,5,3,6,2]=>111000=>000111
[2,6,3,5,4,7,1]=>[1,7,4,5,3,6,2]=>011100=>001110
[2,6,3,5,7,1,4]=>[4,1,7,5,3,6,2]=>111010=>010111
[2,6,3,5,7,4,1]=>[1,4,7,5,3,6,2]=>011010=>010110
[2,6,3,7,1,4,5]=>[5,4,1,7,3,6,2]=>111100=>001111
[2,6,3,7,1,5,4]=>[4,5,1,7,3,6,2]=>111000=>000111
[2,6,3,7,4,1,5]=>[5,1,4,7,3,6,2]=>111000=>000111
[2,6,3,7,4,5,1]=>[1,5,4,7,3,6,2]=>011100=>001110
[2,6,3,7,5,1,4]=>[4,1,5,7,3,6,2]=>111000=>000111
[2,6,3,7,5,4,1]=>[1,4,5,7,3,6,2]=>011000=>000110
[2,6,4,1,3,5,7]=>[7,5,3,1,4,6,2]=>111010=>010111
[2,6,4,1,3,7,5]=>[5,7,3,1,4,6,2]=>111000=>000111
[2,6,4,1,5,3,7]=>[7,3,5,1,4,6,2]=>111000=>000111
[2,6,4,1,5,7,3]=>[3,7,5,1,4,6,2]=>110010=>010011
[2,6,4,1,7,3,5]=>[5,3,7,1,4,6,2]=>111000=>000111
[2,6,4,1,7,5,3]=>[3,5,7,1,4,6,2]=>110000=>000011
[2,6,4,3,1,5,7]=>[7,5,1,3,4,6,2]=>110010=>010011
[2,6,4,3,1,7,5]=>[5,7,1,3,4,6,2]=>110000=>000011
[2,6,4,3,5,1,7]=>[7,1,5,3,4,6,2]=>111000=>000111
[2,6,4,3,5,7,1]=>[1,7,5,3,4,6,2]=>011010=>010110
[2,6,4,3,7,1,5]=>[5,1,7,3,4,6,2]=>111000=>000111
[2,6,4,3,7,5,1]=>[1,5,7,3,4,6,2]=>011000=>000110
[2,6,4,5,1,3,7]=>[7,3,1,5,4,6,2]=>111100=>001111
[2,6,4,5,1,7,3]=>[3,7,1,5,4,6,2]=>110100=>001011
[2,6,4,5,3,1,7]=>[7,1,3,5,4,6,2]=>110100=>001011
[2,6,4,5,3,7,1]=>[1,7,3,5,4,6,2]=>011100=>001110
[2,6,4,5,7,1,3]=>[3,1,7,5,4,6,2]=>110110=>011011
[2,6,4,5,7,3,1]=>[1,3,7,5,4,6,2]=>010110=>011010
[2,6,4,7,1,3,5]=>[5,3,1,7,4,6,2]=>111100=>001111
[2,6,4,7,1,5,3]=>[3,5,1,7,4,6,2]=>110100=>001011
[2,6,4,7,3,1,5]=>[5,1,3,7,4,6,2]=>110100=>001011
[2,6,4,7,3,5,1]=>[1,5,3,7,4,6,2]=>011100=>001110
[2,6,4,7,5,1,3]=>[3,1,5,7,4,6,2]=>110100=>001011
[2,6,4,7,5,3,1]=>[1,3,5,7,4,6,2]=>010100=>001010
[2,6,5,1,3,4,7]=>[7,4,3,1,5,6,2]=>111100=>001111
[2,6,5,1,3,7,4]=>[4,7,3,1,5,6,2]=>111000=>000111
[2,6,5,1,4,3,7]=>[7,3,4,1,5,6,2]=>111000=>000111
[2,6,5,1,4,7,3]=>[3,7,4,1,5,6,2]=>110100=>001011
[2,6,5,1,7,3,4]=>[4,3,7,1,5,6,2]=>111000=>000111
[2,6,5,1,7,4,3]=>[3,4,7,1,5,6,2]=>110000=>000011
[2,6,5,3,1,4,7]=>[7,4,1,3,5,6,2]=>110100=>001011
[2,6,5,3,1,7,4]=>[4,7,1,3,5,6,2]=>110000=>000011
[2,6,5,3,4,1,7]=>[7,1,4,3,5,6,2]=>111000=>000111
[2,6,5,3,4,7,1]=>[1,7,4,3,5,6,2]=>011100=>001110
[2,6,5,3,7,1,4]=>[4,1,7,3,5,6,2]=>111000=>000111
[2,6,5,3,7,4,1]=>[1,4,7,3,5,6,2]=>011000=>000110
[2,6,5,4,1,3,7]=>[7,3,1,4,5,6,2]=>111000=>000111
[2,6,5,4,1,7,3]=>[3,7,1,4,5,6,2]=>110000=>000011
[2,6,5,4,3,1,7]=>[7,1,3,4,5,6,2]=>110000=>000011
[2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2]=>011000=>000110
[2,6,5,4,7,1,3]=>[3,1,7,4,5,6,2]=>110100=>001011
[2,6,5,4,7,3,1]=>[1,3,7,4,5,6,2]=>010100=>001010
[2,6,5,7,1,3,4]=>[4,3,1,7,5,6,2]=>111010=>010111
[2,6,5,7,1,4,3]=>[3,4,1,7,5,6,2]=>110010=>010011
[2,6,5,7,3,1,4]=>[4,1,3,7,5,6,2]=>110010=>010011
[2,6,5,7,3,4,1]=>[1,4,3,7,5,6,2]=>011010=>010110
[2,6,5,7,4,1,3]=>[3,1,4,7,5,6,2]=>110010=>010011
[2,6,5,7,4,3,1]=>[1,3,4,7,5,6,2]=>010010=>010010
[2,6,7,1,3,4,5]=>[5,4,3,1,7,6,2]=>111101=>101111
[2,6,7,1,3,5,4]=>[4,5,3,1,7,6,2]=>111001=>100111
[2,6,7,1,4,3,5]=>[5,3,4,1,7,6,2]=>111001=>100111
[2,6,7,1,4,5,3]=>[3,5,4,1,7,6,2]=>110101=>101011
[2,6,7,1,5,3,4]=>[4,3,5,1,7,6,2]=>111001=>100111
[2,6,7,1,5,4,3]=>[3,4,5,1,7,6,2]=>110001=>100011
[2,6,7,3,1,4,5]=>[5,4,1,3,7,6,2]=>110101=>101011
[2,6,7,3,1,5,4]=>[4,5,1,3,7,6,2]=>110001=>100011
[2,6,7,3,4,1,5]=>[5,1,4,3,7,6,2]=>111001=>100111
[2,6,7,3,4,5,1]=>[1,5,4,3,7,6,2]=>011101=>101110
[2,6,7,3,5,1,4]=>[4,1,5,3,7,6,2]=>111001=>100111
[2,6,7,3,5,4,1]=>[1,4,5,3,7,6,2]=>011001=>100110
[2,6,7,4,1,3,5]=>[5,3,1,4,7,6,2]=>111001=>100111
[2,6,7,4,1,5,3]=>[3,5,1,4,7,6,2]=>110001=>100011
[2,6,7,4,3,1,5]=>[5,1,3,4,7,6,2]=>110001=>100011
[2,6,7,4,3,5,1]=>[1,5,3,4,7,6,2]=>011001=>100110
[2,6,7,4,5,1,3]=>[3,1,5,4,7,6,2]=>110101=>101011
[2,6,7,4,5,3,1]=>[1,3,5,4,7,6,2]=>010101=>101010
[2,6,7,5,1,3,4]=>[4,3,1,5,7,6,2]=>111001=>100111
[2,6,7,5,1,4,3]=>[3,4,1,5,7,6,2]=>110001=>100011
[2,6,7,5,3,1,4]=>[4,1,3,5,7,6,2]=>110001=>100011
[2,6,7,5,3,4,1]=>[1,4,3,5,7,6,2]=>011001=>100110
[2,6,7,5,4,1,3]=>[3,1,4,5,7,6,2]=>110001=>100011
[2,6,7,5,4,3,1]=>[1,3,4,5,7,6,2]=>010001=>100010
[2,7,1,3,4,5,6]=>[6,5,4,3,1,7,2]=>111110=>011111
[2,7,1,3,4,6,5]=>[5,6,4,3,1,7,2]=>111100=>001111
[2,7,1,3,5,4,6]=>[6,4,5,3,1,7,2]=>111100=>001111
[2,7,1,3,5,6,4]=>[4,6,5,3,1,7,2]=>111010=>010111
[2,7,1,3,6,4,5]=>[5,4,6,3,1,7,2]=>111100=>001111
[2,7,1,3,6,5,4]=>[4,5,6,3,1,7,2]=>111000=>000111
[2,7,1,4,3,5,6]=>[6,5,3,4,1,7,2]=>111010=>010111
[2,7,1,4,3,6,5]=>[5,6,3,4,1,7,2]=>111000=>000111
[2,7,1,4,5,3,6]=>[6,3,5,4,1,7,2]=>111100=>001111
[2,7,1,4,5,6,3]=>[3,6,5,4,1,7,2]=>110110=>011011
[2,7,1,4,6,3,5]=>[5,3,6,4,1,7,2]=>111100=>001111
[2,7,1,4,6,5,3]=>[3,5,6,4,1,7,2]=>110100=>001011
[2,7,1,5,3,4,6]=>[6,4,3,5,1,7,2]=>111100=>001111
[2,7,1,5,3,6,4]=>[4,6,3,5,1,7,2]=>111000=>000111
[2,7,1,5,4,3,6]=>[6,3,4,5,1,7,2]=>111000=>000111
[2,7,1,5,4,6,3]=>[3,6,4,5,1,7,2]=>110100=>001011
[2,7,1,5,6,3,4]=>[4,3,6,5,1,7,2]=>111010=>010111
[2,7,1,5,6,4,3]=>[3,4,6,5,1,7,2]=>110010=>010011
[2,7,1,6,3,4,5]=>[5,4,3,6,1,7,2]=>111100=>001111
[2,7,1,6,3,5,4]=>[4,5,3,6,1,7,2]=>111000=>000111
[2,7,1,6,4,3,5]=>[5,3,4,6,1,7,2]=>111000=>000111
[2,7,1,6,4,5,3]=>[3,5,4,6,1,7,2]=>110100=>001011
[2,7,1,6,5,3,4]=>[4,3,5,6,1,7,2]=>111000=>000111
[2,7,1,6,5,4,3]=>[3,4,5,6,1,7,2]=>110000=>000011
[2,7,3,1,4,5,6]=>[6,5,4,1,3,7,2]=>110110=>011011
[2,7,3,1,4,6,5]=>[5,6,4,1,3,7,2]=>110100=>001011
[2,7,3,1,5,4,6]=>[6,4,5,1,3,7,2]=>110100=>001011
[2,7,3,1,5,6,4]=>[4,6,5,1,3,7,2]=>110010=>010011
[2,7,3,1,6,4,5]=>[5,4,6,1,3,7,2]=>110100=>001011
[2,7,3,1,6,5,4]=>[4,5,6,1,3,7,2]=>110000=>000011
[2,7,3,4,1,5,6]=>[6,5,1,4,3,7,2]=>111010=>010111
[2,7,3,4,1,6,5]=>[5,6,1,4,3,7,2]=>111000=>000111
[2,7,3,4,5,1,6]=>[6,1,5,4,3,7,2]=>111100=>001111
[2,7,3,4,5,6,1]=>[1,6,5,4,3,7,2]=>011110=>011110
[2,7,3,4,6,1,5]=>[5,1,6,4,3,7,2]=>111100=>001111
[2,7,3,4,6,5,1]=>[1,5,6,4,3,7,2]=>011100=>001110
[2,7,3,5,1,4,6]=>[6,4,1,5,3,7,2]=>111100=>001111
[2,7,3,5,1,6,4]=>[4,6,1,5,3,7,2]=>111000=>000111
[2,7,3,5,4,1,6]=>[6,1,4,5,3,7,2]=>111000=>000111
[2,7,3,5,4,6,1]=>[1,6,4,5,3,7,2]=>011100=>001110
[2,7,3,5,6,1,4]=>[4,1,6,5,3,7,2]=>111010=>010111
[2,7,3,5,6,4,1]=>[1,4,6,5,3,7,2]=>011010=>010110
[2,7,3,6,1,4,5]=>[5,4,1,6,3,7,2]=>111100=>001111
[2,7,3,6,1,5,4]=>[4,5,1,6,3,7,2]=>111000=>000111
[2,7,3,6,4,1,5]=>[5,1,4,6,3,7,2]=>111000=>000111
[2,7,3,6,4,5,1]=>[1,5,4,6,3,7,2]=>011100=>001110
[2,7,3,6,5,1,4]=>[4,1,5,6,3,7,2]=>111000=>000111
[2,7,3,6,5,4,1]=>[1,4,5,6,3,7,2]=>011000=>000110
[2,7,4,1,3,5,6]=>[6,5,3,1,4,7,2]=>111010=>010111
[2,7,4,1,3,6,5]=>[5,6,3,1,4,7,2]=>111000=>000111
[2,7,4,1,5,3,6]=>[6,3,5,1,4,7,2]=>111000=>000111
[2,7,4,1,5,6,3]=>[3,6,5,1,4,7,2]=>110010=>010011
[2,7,4,1,6,3,5]=>[5,3,6,1,4,7,2]=>111000=>000111
[2,7,4,1,6,5,3]=>[3,5,6,1,4,7,2]=>110000=>000011
[2,7,4,3,1,5,6]=>[6,5,1,3,4,7,2]=>110010=>010011
[2,7,4,3,1,6,5]=>[5,6,1,3,4,7,2]=>110000=>000011
[2,7,4,3,5,1,6]=>[6,1,5,3,4,7,2]=>111000=>000111
[2,7,4,3,5,6,1]=>[1,6,5,3,4,7,2]=>011010=>010110
[2,7,4,3,6,1,5]=>[5,1,6,3,4,7,2]=>111000=>000111
[2,7,4,3,6,5,1]=>[1,5,6,3,4,7,2]=>011000=>000110
[2,7,4,5,1,3,6]=>[6,3,1,5,4,7,2]=>111100=>001111
[2,7,4,5,1,6,3]=>[3,6,1,5,4,7,2]=>110100=>001011
[2,7,4,5,3,1,6]=>[6,1,3,5,4,7,2]=>110100=>001011
[2,7,4,5,3,6,1]=>[1,6,3,5,4,7,2]=>011100=>001110
[2,7,4,5,6,1,3]=>[3,1,6,5,4,7,2]=>110110=>011011
[2,7,4,5,6,3,1]=>[1,3,6,5,4,7,2]=>010110=>011010
[2,7,4,6,1,3,5]=>[5,3,1,6,4,7,2]=>111100=>001111
[2,7,4,6,1,5,3]=>[3,5,1,6,4,7,2]=>110100=>001011
[2,7,4,6,3,1,5]=>[5,1,3,6,4,7,2]=>110100=>001011
[2,7,4,6,3,5,1]=>[1,5,3,6,4,7,2]=>011100=>001110
[2,7,4,6,5,1,3]=>[3,1,5,6,4,7,2]=>110100=>001011
[2,7,4,6,5,3,1]=>[1,3,5,6,4,7,2]=>010100=>001010
[2,7,5,1,3,4,6]=>[6,4,3,1,5,7,2]=>111100=>001111
[2,7,5,1,3,6,4]=>[4,6,3,1,5,7,2]=>111000=>000111
[2,7,5,1,4,3,6]=>[6,3,4,1,5,7,2]=>111000=>000111
[2,7,5,1,4,6,3]=>[3,6,4,1,5,7,2]=>110100=>001011
[2,7,5,1,6,3,4]=>[4,3,6,1,5,7,2]=>111000=>000111
[2,7,5,1,6,4,3]=>[3,4,6,1,5,7,2]=>110000=>000011
[2,7,5,3,1,4,6]=>[6,4,1,3,5,7,2]=>110100=>001011
[2,7,5,3,1,6,4]=>[4,6,1,3,5,7,2]=>110000=>000011
[2,7,5,3,4,1,6]=>[6,1,4,3,5,7,2]=>111000=>000111
[2,7,5,3,4,6,1]=>[1,6,4,3,5,7,2]=>011100=>001110
[2,7,5,3,6,1,4]=>[4,1,6,3,5,7,2]=>111000=>000111
[2,7,5,3,6,4,1]=>[1,4,6,3,5,7,2]=>011000=>000110
[2,7,5,4,1,3,6]=>[6,3,1,4,5,7,2]=>111000=>000111
[2,7,5,4,1,6,3]=>[3,6,1,4,5,7,2]=>110000=>000011
[2,7,5,4,3,1,6]=>[6,1,3,4,5,7,2]=>110000=>000011
[2,7,5,4,3,6,1]=>[1,6,3,4,5,7,2]=>011000=>000110
[2,7,5,4,6,1,3]=>[3,1,6,4,5,7,2]=>110100=>001011
[2,7,5,4,6,3,1]=>[1,3,6,4,5,7,2]=>010100=>001010
[2,7,5,6,1,3,4]=>[4,3,1,6,5,7,2]=>111010=>010111
[2,7,5,6,1,4,3]=>[3,4,1,6,5,7,2]=>110010=>010011
[2,7,5,6,3,1,4]=>[4,1,3,6,5,7,2]=>110010=>010011
[2,7,5,6,3,4,1]=>[1,4,3,6,5,7,2]=>011010=>010110
[2,7,5,6,4,1,3]=>[3,1,4,6,5,7,2]=>110010=>010011
[2,7,5,6,4,3,1]=>[1,3,4,6,5,7,2]=>010010=>010010
[2,7,6,1,3,4,5]=>[5,4,3,1,6,7,2]=>111100=>001111
[2,7,6,1,3,5,4]=>[4,5,3,1,6,7,2]=>111000=>000111
[2,7,6,1,4,3,5]=>[5,3,4,1,6,7,2]=>111000=>000111
[2,7,6,1,4,5,3]=>[3,5,4,1,6,7,2]=>110100=>001011
[2,7,6,1,5,3,4]=>[4,3,5,1,6,7,2]=>111000=>000111
[2,7,6,1,5,4,3]=>[3,4,5,1,6,7,2]=>110000=>000011
[2,7,6,3,1,4,5]=>[5,4,1,3,6,7,2]=>110100=>001011
[2,7,6,3,1,5,4]=>[4,5,1,3,6,7,2]=>110000=>000011
[2,7,6,3,4,1,5]=>[5,1,4,3,6,7,2]=>111000=>000111
[2,7,6,3,4,5,1]=>[1,5,4,3,6,7,2]=>011100=>001110
[2,7,6,3,5,1,4]=>[4,1,5,3,6,7,2]=>111000=>000111
[2,7,6,3,5,4,1]=>[1,4,5,3,6,7,2]=>011000=>000110
[2,7,6,4,1,3,5]=>[5,3,1,4,6,7,2]=>111000=>000111
[2,7,6,4,1,5,3]=>[3,5,1,4,6,7,2]=>110000=>000011
[2,7,6,4,3,1,5]=>[5,1,3,4,6,7,2]=>110000=>000011
[2,7,6,4,3,5,1]=>[1,5,3,4,6,7,2]=>011000=>000110
[2,7,6,4,5,1,3]=>[3,1,5,4,6,7,2]=>110100=>001011
[2,7,6,4,5,3,1]=>[1,3,5,4,6,7,2]=>010100=>001010
[2,7,6,5,1,3,4]=>[4,3,1,5,6,7,2]=>111000=>000111
[2,7,6,5,1,4,3]=>[3,4,1,5,6,7,2]=>110000=>000011
[2,7,6,5,3,1,4]=>[4,1,3,5,6,7,2]=>110000=>000011
[2,7,6,5,3,4,1]=>[1,4,3,5,6,7,2]=>011000=>000110
[2,7,6,5,4,1,3]=>[3,1,4,5,6,7,2]=>110000=>000011
[2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2]=>010000=>000010
[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>110111=>111011
[3,1,2,4,5,7,6]=>[6,7,5,4,2,1,3]=>110110=>011011
[3,1,2,4,6,5,7]=>[7,5,6,4,2,1,3]=>110110=>011011
[3,1,2,4,6,7,5]=>[5,7,6,4,2,1,3]=>110101=>101011
[3,1,2,4,7,5,6]=>[6,5,7,4,2,1,3]=>110110=>011011
[3,1,2,4,7,6,5]=>[5,6,7,4,2,1,3]=>110100=>001011
[3,1,2,5,4,6,7]=>[7,6,4,5,2,1,3]=>110101=>101011
[3,1,2,5,4,7,6]=>[6,7,4,5,2,1,3]=>110100=>001011
[3,1,2,5,6,4,7]=>[7,4,6,5,2,1,3]=>110110=>011011
[3,1,2,5,6,7,4]=>[4,7,6,5,2,1,3]=>110011=>110011
[3,1,2,5,7,4,6]=>[6,4,7,5,2,1,3]=>110110=>011011
[3,1,2,5,7,6,4]=>[4,6,7,5,2,1,3]=>110010=>010011
[3,1,2,6,4,5,7]=>[7,5,4,6,2,1,3]=>110110=>011011
[3,1,2,6,4,7,5]=>[5,7,4,6,2,1,3]=>110100=>001011
[3,1,2,6,5,4,7]=>[7,4,5,6,2,1,3]=>110100=>001011
[3,1,2,6,5,7,4]=>[4,7,5,6,2,1,3]=>110010=>010011
[3,1,2,6,7,4,5]=>[5,4,7,6,2,1,3]=>110101=>101011
[3,1,2,6,7,5,4]=>[4,5,7,6,2,1,3]=>110001=>100011
[3,1,2,7,4,5,6]=>[6,5,4,7,2,1,3]=>110110=>011011
[3,1,2,7,4,6,5]=>[5,6,4,7,2,1,3]=>110100=>001011
[3,1,2,7,5,4,6]=>[6,4,5,7,2,1,3]=>110100=>001011
[3,1,2,7,5,6,4]=>[4,6,5,7,2,1,3]=>110010=>010011
[3,1,2,7,6,4,5]=>[5,4,6,7,2,1,3]=>110100=>001011
[3,1,2,7,6,5,4]=>[4,5,6,7,2,1,3]=>110000=>000011
[3,1,4,2,5,6,7]=>[7,6,5,2,4,1,3]=>110011=>110011
[3,1,4,2,5,7,6]=>[6,7,5,2,4,1,3]=>110010=>010011
[3,1,4,2,6,5,7]=>[7,5,6,2,4,1,3]=>110010=>010011
[3,1,4,2,6,7,5]=>[5,7,6,2,4,1,3]=>110001=>100011
[3,1,4,2,7,5,6]=>[6,5,7,2,4,1,3]=>110010=>010011
[3,1,4,2,7,6,5]=>[5,6,7,2,4,1,3]=>110000=>000011
[3,1,4,5,2,6,7]=>[7,6,2,5,4,1,3]=>110101=>101011
[3,1,4,5,2,7,6]=>[6,7,2,5,4,1,3]=>110100=>001011
[3,1,4,5,6,2,7]=>[7,2,6,5,4,1,3]=>110110=>011011
[3,1,4,5,6,7,2]=>[2,7,6,5,4,1,3]=>100111=>111001
[3,1,4,5,7,2,6]=>[6,2,7,5,4,1,3]=>110110=>011011
[3,1,4,5,7,6,2]=>[2,6,7,5,4,1,3]=>100110=>011001
[3,1,4,6,2,5,7]=>[7,5,2,6,4,1,3]=>110110=>011011
[3,1,4,6,2,7,5]=>[5,7,2,6,4,1,3]=>110100=>001011
[3,1,4,6,5,2,7]=>[7,2,5,6,4,1,3]=>110100=>001011
[3,1,4,6,5,7,2]=>[2,7,5,6,4,1,3]=>100110=>011001
[3,1,4,6,7,2,5]=>[5,2,7,6,4,1,3]=>110101=>101011
[3,1,4,6,7,5,2]=>[2,5,7,6,4,1,3]=>100101=>101001
[3,1,4,7,2,5,6]=>[6,5,2,7,4,1,3]=>110110=>011011
[3,1,4,7,2,6,5]=>[5,6,2,7,4,1,3]=>110100=>001011
[3,1,4,7,5,2,6]=>[6,2,5,7,4,1,3]=>110100=>001011
[3,1,4,7,5,6,2]=>[2,6,5,7,4,1,3]=>100110=>011001
[3,1,4,7,6,2,5]=>[5,2,6,7,4,1,3]=>110100=>001011
[3,1,4,7,6,5,2]=>[2,5,6,7,4,1,3]=>100100=>001001
[3,1,5,2,4,6,7]=>[7,6,4,2,5,1,3]=>110101=>101011
[3,1,5,2,4,7,6]=>[6,7,4,2,5,1,3]=>110100=>001011
[3,1,5,2,6,4,7]=>[7,4,6,2,5,1,3]=>110100=>001011
[3,1,5,2,6,7,4]=>[4,7,6,2,5,1,3]=>110001=>100011
[3,1,5,2,7,4,6]=>[6,4,7,2,5,1,3]=>110100=>001011
[3,1,5,2,7,6,4]=>[4,6,7,2,5,1,3]=>110000=>000011
[3,1,5,4,2,6,7]=>[7,6,2,4,5,1,3]=>110001=>100011
[3,1,5,4,2,7,6]=>[6,7,2,4,5,1,3]=>110000=>000011
[3,1,5,4,6,2,7]=>[7,2,6,4,5,1,3]=>110100=>001011
[3,1,5,4,6,7,2]=>[2,7,6,4,5,1,3]=>100101=>101001
[3,1,5,4,7,2,6]=>[6,2,7,4,5,1,3]=>110100=>001011
[3,1,5,4,7,6,2]=>[2,6,7,4,5,1,3]=>100100=>001001
[3,1,5,6,2,4,7]=>[7,4,2,6,5,1,3]=>110110=>011011
[3,1,5,6,2,7,4]=>[4,7,2,6,5,1,3]=>110010=>010011
[3,1,5,6,4,2,7]=>[7,2,4,6,5,1,3]=>110010=>010011
[3,1,5,6,4,7,2]=>[2,7,4,6,5,1,3]=>100110=>011001
[3,1,5,6,7,2,4]=>[4,2,7,6,5,1,3]=>110011=>110011
[3,1,5,6,7,4,2]=>[2,4,7,6,5,1,3]=>100011=>110001
[3,1,5,7,2,4,6]=>[6,4,2,7,5,1,3]=>110110=>011011
[3,1,5,7,2,6,4]=>[4,6,2,7,5,1,3]=>110010=>010011
[3,1,5,7,4,2,6]=>[6,2,4,7,5,1,3]=>110010=>010011
[3,1,5,7,4,6,2]=>[2,6,4,7,5,1,3]=>100110=>011001
[3,1,5,7,6,2,4]=>[4,2,6,7,5,1,3]=>110010=>010011
[3,1,5,7,6,4,2]=>[2,4,6,7,5,1,3]=>100010=>010001
[3,1,6,2,4,5,7]=>[7,5,4,2,6,1,3]=>110110=>011011
[3,1,6,2,4,7,5]=>[5,7,4,2,6,1,3]=>110100=>001011
[3,1,6,2,5,4,7]=>[7,4,5,2,6,1,3]=>110100=>001011
[3,1,6,2,5,7,4]=>[4,7,5,2,6,1,3]=>110010=>010011
[3,1,6,2,7,4,5]=>[5,4,7,2,6,1,3]=>110100=>001011
[3,1,6,2,7,5,4]=>[4,5,7,2,6,1,3]=>110000=>000011
[3,1,6,4,2,5,7]=>[7,5,2,4,6,1,3]=>110010=>010011
[3,1,6,4,2,7,5]=>[5,7,2,4,6,1,3]=>110000=>000011
[3,1,6,4,5,2,7]=>[7,2,5,4,6,1,3]=>110100=>001011
[3,1,6,4,5,7,2]=>[2,7,5,4,6,1,3]=>100110=>011001
[3,1,6,4,7,2,5]=>[5,2,7,4,6,1,3]=>110100=>001011
[3,1,6,4,7,5,2]=>[2,5,7,4,6,1,3]=>100100=>001001
[3,1,6,5,2,4,7]=>[7,4,2,5,6,1,3]=>110100=>001011
[3,1,6,5,2,7,4]=>[4,7,2,5,6,1,3]=>110000=>000011
[3,1,6,5,4,2,7]=>[7,2,4,5,6,1,3]=>110000=>000011
[3,1,6,5,4,7,2]=>[2,7,4,5,6,1,3]=>100100=>001001
[3,1,6,5,7,2,4]=>[4,2,7,5,6,1,3]=>110010=>010011
[3,1,6,5,7,4,2]=>[2,4,7,5,6,1,3]=>100010=>010001
[3,1,6,7,2,4,5]=>[5,4,2,7,6,1,3]=>110101=>101011
[3,1,6,7,2,5,4]=>[4,5,2,7,6,1,3]=>110001=>100011
[3,1,6,7,4,2,5]=>[5,2,4,7,6,1,3]=>110001=>100011
[3,1,6,7,4,5,2]=>[2,5,4,7,6,1,3]=>100101=>101001
[3,1,6,7,5,2,4]=>[4,2,5,7,6,1,3]=>110001=>100011
[3,1,6,7,5,4,2]=>[2,4,5,7,6,1,3]=>100001=>100001
[3,1,7,2,4,5,6]=>[6,5,4,2,7,1,3]=>110110=>011011
[3,1,7,2,4,6,5]=>[5,6,4,2,7,1,3]=>110100=>001011
[3,1,7,2,5,4,6]=>[6,4,5,2,7,1,3]=>110100=>001011
[3,1,7,2,5,6,4]=>[4,6,5,2,7,1,3]=>110010=>010011
[3,1,7,2,6,4,5]=>[5,4,6,2,7,1,3]=>110100=>001011
[3,1,7,2,6,5,4]=>[4,5,6,2,7,1,3]=>110000=>000011
[3,1,7,4,2,5,6]=>[6,5,2,4,7,1,3]=>110010=>010011
[3,1,7,4,2,6,5]=>[5,6,2,4,7,1,3]=>110000=>000011
[3,1,7,4,5,2,6]=>[6,2,5,4,7,1,3]=>110100=>001011
[3,1,7,4,5,6,2]=>[2,6,5,4,7,1,3]=>100110=>011001
[3,1,7,4,6,2,5]=>[5,2,6,4,7,1,3]=>110100=>001011
[3,1,7,4,6,5,2]=>[2,5,6,4,7,1,3]=>100100=>001001
[3,1,7,5,2,4,6]=>[6,4,2,5,7,1,3]=>110100=>001011
[3,1,7,5,2,6,4]=>[4,6,2,5,7,1,3]=>110000=>000011
[3,1,7,5,4,2,6]=>[6,2,4,5,7,1,3]=>110000=>000011
[3,1,7,5,4,6,2]=>[2,6,4,5,7,1,3]=>100100=>001001
[3,1,7,5,6,2,4]=>[4,2,6,5,7,1,3]=>110010=>010011
[3,1,7,5,6,4,2]=>[2,4,6,5,7,1,3]=>100010=>010001
[3,1,7,6,2,4,5]=>[5,4,2,6,7,1,3]=>110100=>001011
[3,1,7,6,2,5,4]=>[4,5,2,6,7,1,3]=>110000=>000011
[3,1,7,6,4,2,5]=>[5,2,4,6,7,1,3]=>110000=>000011
[3,1,7,6,4,5,2]=>[2,5,4,6,7,1,3]=>100100=>001001
[3,1,7,6,5,2,4]=>[4,2,5,6,7,1,3]=>110000=>000011
[3,1,7,6,5,4,2]=>[2,4,5,6,7,1,3]=>100000=>000001
[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>100111=>111001
[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>100110=>011001
[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>100110=>011001
[3,2,1,4,6,7,5]=>[5,7,6,4,1,2,3]=>100101=>101001
[3,2,1,4,7,5,6]=>[6,5,7,4,1,2,3]=>100110=>011001
[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>100100=>001001
[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>100101=>101001
[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>100100=>001001
[3,2,1,5,6,4,7]=>[7,4,6,5,1,2,3]=>100110=>011001
[3,2,1,5,6,7,4]=>[4,7,6,5,1,2,3]=>100011=>110001
[3,2,1,5,7,4,6]=>[6,4,7,5,1,2,3]=>100110=>011001
[3,2,1,5,7,6,4]=>[4,6,7,5,1,2,3]=>100010=>010001
[3,2,1,6,4,5,7]=>[7,5,4,6,1,2,3]=>100110=>011001
[3,2,1,6,4,7,5]=>[5,7,4,6,1,2,3]=>100100=>001001
[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>100100=>001001
[3,2,1,6,5,7,4]=>[4,7,5,6,1,2,3]=>100010=>010001
[3,2,1,6,7,4,5]=>[5,4,7,6,1,2,3]=>100101=>101001
[3,2,1,6,7,5,4]=>[4,5,7,6,1,2,3]=>100001=>100001
[3,2,1,7,4,5,6]=>[6,5,4,7,1,2,3]=>100110=>011001
[3,2,1,7,4,6,5]=>[5,6,4,7,1,2,3]=>100100=>001001
[3,2,1,7,5,4,6]=>[6,4,5,7,1,2,3]=>100100=>001001
[3,2,1,7,5,6,4]=>[4,6,5,7,1,2,3]=>100010=>010001
[3,2,1,7,6,4,5]=>[5,4,6,7,1,2,3]=>100100=>001001
[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>100000=>000001
[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>110011=>110011
[3,2,4,1,5,7,6]=>[6,7,5,1,4,2,3]=>110010=>010011
[3,2,4,1,6,5,7]=>[7,5,6,1,4,2,3]=>110010=>010011
[3,2,4,1,6,7,5]=>[5,7,6,1,4,2,3]=>110001=>100011
[3,2,4,1,7,5,6]=>[6,5,7,1,4,2,3]=>110010=>010011
[3,2,4,1,7,6,5]=>[5,6,7,1,4,2,3]=>110000=>000011
[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>110101=>101011
[3,2,4,5,1,7,6]=>[6,7,1,5,4,2,3]=>110100=>001011
[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>110110=>011011
[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>010111=>111010
[3,2,4,5,7,1,6]=>[6,1,7,5,4,2,3]=>110110=>011011
[3,2,4,5,7,6,1]=>[1,6,7,5,4,2,3]=>010110=>011010
[3,2,4,6,1,5,7]=>[7,5,1,6,4,2,3]=>110110=>011011
[3,2,4,6,1,7,5]=>[5,7,1,6,4,2,3]=>110100=>001011
[3,2,4,6,5,1,7]=>[7,1,5,6,4,2,3]=>110100=>001011
[3,2,4,6,5,7,1]=>[1,7,5,6,4,2,3]=>010110=>011010
[3,2,4,6,7,1,5]=>[5,1,7,6,4,2,3]=>110101=>101011
[3,2,4,6,7,5,1]=>[1,5,7,6,4,2,3]=>010101=>101010
[3,2,4,7,1,5,6]=>[6,5,1,7,4,2,3]=>110110=>011011
[3,2,4,7,1,6,5]=>[5,6,1,7,4,2,3]=>110100=>001011
[3,2,4,7,5,1,6]=>[6,1,5,7,4,2,3]=>110100=>001011
[3,2,4,7,5,6,1]=>[1,6,5,7,4,2,3]=>010110=>011010
[3,2,4,7,6,1,5]=>[5,1,6,7,4,2,3]=>110100=>001011
[3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3]=>010100=>001010
[3,2,5,1,4,6,7]=>[7,6,4,1,5,2,3]=>110101=>101011
[3,2,5,1,4,7,6]=>[6,7,4,1,5,2,3]=>110100=>001011
[3,2,5,1,6,4,7]=>[7,4,6,1,5,2,3]=>110100=>001011
[3,2,5,1,6,7,4]=>[4,7,6,1,5,2,3]=>110001=>100011
[3,2,5,1,7,4,6]=>[6,4,7,1,5,2,3]=>110100=>001011
[3,2,5,1,7,6,4]=>[4,6,7,1,5,2,3]=>110000=>000011
[3,2,5,4,1,6,7]=>[7,6,1,4,5,2,3]=>110001=>100011
[3,2,5,4,1,7,6]=>[6,7,1,4,5,2,3]=>110000=>000011
[3,2,5,4,6,1,7]=>[7,1,6,4,5,2,3]=>110100=>001011
[3,2,5,4,6,7,1]=>[1,7,6,4,5,2,3]=>010101=>101010
[3,2,5,4,7,1,6]=>[6,1,7,4,5,2,3]=>110100=>001011
[3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3]=>010100=>001010
[3,2,5,6,1,4,7]=>[7,4,1,6,5,2,3]=>110110=>011011
[3,2,5,6,1,7,4]=>[4,7,1,6,5,2,3]=>110010=>010011
[3,2,5,6,4,1,7]=>[7,1,4,6,5,2,3]=>110010=>010011
[3,2,5,6,4,7,1]=>[1,7,4,6,5,2,3]=>010110=>011010
[3,2,5,6,7,1,4]=>[4,1,7,6,5,2,3]=>110011=>110011
[3,2,5,6,7,4,1]=>[1,4,7,6,5,2,3]=>010011=>110010
[3,2,5,7,1,4,6]=>[6,4,1,7,5,2,3]=>110110=>011011
[3,2,5,7,1,6,4]=>[4,6,1,7,5,2,3]=>110010=>010011
[3,2,5,7,4,1,6]=>[6,1,4,7,5,2,3]=>110010=>010011
[3,2,5,7,4,6,1]=>[1,6,4,7,5,2,3]=>010110=>011010
[3,2,5,7,6,1,4]=>[4,1,6,7,5,2,3]=>110010=>010011
[3,2,5,7,6,4,1]=>[1,4,6,7,5,2,3]=>010010=>010010
[3,2,6,1,4,5,7]=>[7,5,4,1,6,2,3]=>110110=>011011
[3,2,6,1,4,7,5]=>[5,7,4,1,6,2,3]=>110100=>001011
[3,2,6,1,5,4,7]=>[7,4,5,1,6,2,3]=>110100=>001011
[3,2,6,1,5,7,4]=>[4,7,5,1,6,2,3]=>110010=>010011
[3,2,6,1,7,4,5]=>[5,4,7,1,6,2,3]=>110100=>001011
[3,2,6,1,7,5,4]=>[4,5,7,1,6,2,3]=>110000=>000011
[3,2,6,4,1,5,7]=>[7,5,1,4,6,2,3]=>110010=>010011
[3,2,6,4,1,7,5]=>[5,7,1,4,6,2,3]=>110000=>000011
[3,2,6,4,5,1,7]=>[7,1,5,4,6,2,3]=>110100=>001011
[3,2,6,4,5,7,1]=>[1,7,5,4,6,2,3]=>010110=>011010
[3,2,6,4,7,1,5]=>[5,1,7,4,6,2,3]=>110100=>001011
[3,2,6,4,7,5,1]=>[1,5,7,4,6,2,3]=>010100=>001010
[3,2,6,5,1,4,7]=>[7,4,1,5,6,2,3]=>110100=>001011
[3,2,6,5,1,7,4]=>[4,7,1,5,6,2,3]=>110000=>000011
[3,2,6,5,4,1,7]=>[7,1,4,5,6,2,3]=>110000=>000011
[3,2,6,5,4,7,1]=>[1,7,4,5,6,2,3]=>010100=>001010
[3,2,6,5,7,1,4]=>[4,1,7,5,6,2,3]=>110010=>010011
[3,2,6,5,7,4,1]=>[1,4,7,5,6,2,3]=>010010=>010010
[3,2,6,7,1,4,5]=>[5,4,1,7,6,2,3]=>110101=>101011
[3,2,6,7,1,5,4]=>[4,5,1,7,6,2,3]=>110001=>100011
[3,2,6,7,4,1,5]=>[5,1,4,7,6,2,3]=>110001=>100011
[3,2,6,7,4,5,1]=>[1,5,4,7,6,2,3]=>010101=>101010
[3,2,6,7,5,1,4]=>[4,1,5,7,6,2,3]=>110001=>100011
[3,2,6,7,5,4,1]=>[1,4,5,7,6,2,3]=>010001=>100010
[3,2,7,1,4,5,6]=>[6,5,4,1,7,2,3]=>110110=>011011
[3,2,7,1,4,6,5]=>[5,6,4,1,7,2,3]=>110100=>001011
[3,2,7,1,5,4,6]=>[6,4,5,1,7,2,3]=>110100=>001011
[3,2,7,1,5,6,4]=>[4,6,5,1,7,2,3]=>110010=>010011
[3,2,7,1,6,4,5]=>[5,4,6,1,7,2,3]=>110100=>001011
[3,2,7,1,6,5,4]=>[4,5,6,1,7,2,3]=>110000=>000011
[3,2,7,4,1,5,6]=>[6,5,1,4,7,2,3]=>110010=>010011
[3,2,7,4,1,6,5]=>[5,6,1,4,7,2,3]=>110000=>000011
[3,2,7,4,5,1,6]=>[6,1,5,4,7,2,3]=>110100=>001011
[3,2,7,4,5,6,1]=>[1,6,5,4,7,2,3]=>010110=>011010
[3,2,7,4,6,1,5]=>[5,1,6,4,7,2,3]=>110100=>001011
[3,2,7,4,6,5,1]=>[1,5,6,4,7,2,3]=>010100=>001010
[3,2,7,5,1,4,6]=>[6,4,1,5,7,2,3]=>110100=>001011
[3,2,7,5,1,6,4]=>[4,6,1,5,7,2,3]=>110000=>000011
[3,2,7,5,4,1,6]=>[6,1,4,5,7,2,3]=>110000=>000011
[3,2,7,5,4,6,1]=>[1,6,4,5,7,2,3]=>010100=>001010
[3,2,7,5,6,1,4]=>[4,1,6,5,7,2,3]=>110010=>010011
[3,2,7,5,6,4,1]=>[1,4,6,5,7,2,3]=>010010=>010010
[3,2,7,6,1,4,5]=>[5,4,1,6,7,2,3]=>110100=>001011
[3,2,7,6,1,5,4]=>[4,5,1,6,7,2,3]=>110000=>000011
[3,2,7,6,4,1,5]=>[5,1,4,6,7,2,3]=>110000=>000011
[3,2,7,6,4,5,1]=>[1,5,4,6,7,2,3]=>010100=>001010
[3,2,7,6,5,1,4]=>[4,1,5,6,7,2,3]=>110000=>000011
[3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3]=>010000=>000010
[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>111011=>110111
[3,4,1,2,5,7,6]=>[6,7,5,2,1,4,3]=>111010=>010111
[3,4,1,2,6,5,7]=>[7,5,6,2,1,4,3]=>111010=>010111
[3,4,1,2,6,7,5]=>[5,7,6,2,1,4,3]=>111001=>100111
[3,4,1,2,7,5,6]=>[6,5,7,2,1,4,3]=>111010=>010111
[3,4,1,2,7,6,5]=>[5,6,7,2,1,4,3]=>111000=>000111
[3,4,1,5,2,6,7]=>[7,6,2,5,1,4,3]=>111001=>100111
[3,4,1,5,2,7,6]=>[6,7,2,5,1,4,3]=>111000=>000111
[3,4,1,5,6,2,7]=>[7,2,6,5,1,4,3]=>111010=>010111
[3,4,1,5,6,7,2]=>[2,7,6,5,1,4,3]=>101011=>110101
[3,4,1,5,7,2,6]=>[6,2,7,5,1,4,3]=>111010=>010111
[3,4,1,5,7,6,2]=>[2,6,7,5,1,4,3]=>101010=>010101
[3,4,1,6,2,5,7]=>[7,5,2,6,1,4,3]=>111010=>010111
[3,4,1,6,2,7,5]=>[5,7,2,6,1,4,3]=>111000=>000111
[3,4,1,6,5,2,7]=>[7,2,5,6,1,4,3]=>111000=>000111
[3,4,1,6,5,7,2]=>[2,7,5,6,1,4,3]=>101010=>010101
[3,4,1,6,7,2,5]=>[5,2,7,6,1,4,3]=>111001=>100111
[3,4,1,6,7,5,2]=>[2,5,7,6,1,4,3]=>101001=>100101
[3,4,1,7,2,5,6]=>[6,5,2,7,1,4,3]=>111010=>010111
[3,4,1,7,2,6,5]=>[5,6,2,7,1,4,3]=>111000=>000111
[3,4,1,7,5,2,6]=>[6,2,5,7,1,4,3]=>111000=>000111
[3,4,1,7,5,6,2]=>[2,6,5,7,1,4,3]=>101010=>010101
[3,4,1,7,6,2,5]=>[5,2,6,7,1,4,3]=>111000=>000111
[3,4,1,7,6,5,2]=>[2,5,6,7,1,4,3]=>101000=>000101
[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>101011=>110101
[3,4,2,1,5,7,6]=>[6,7,5,1,2,4,3]=>101010=>010101
[3,4,2,1,6,5,7]=>[7,5,6,1,2,4,3]=>101010=>010101
[3,4,2,1,6,7,5]=>[5,7,6,1,2,4,3]=>101001=>100101
[3,4,2,1,7,5,6]=>[6,5,7,1,2,4,3]=>101010=>010101
[3,4,2,1,7,6,5]=>[5,6,7,1,2,4,3]=>101000=>000101
[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>111001=>100111
[3,4,2,5,1,7,6]=>[6,7,1,5,2,4,3]=>111000=>000111
[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>111010=>010111
[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>011011=>110110
[3,4,2,5,7,1,6]=>[6,1,7,5,2,4,3]=>111010=>010111
[3,4,2,5,7,6,1]=>[1,6,7,5,2,4,3]=>011010=>010110
[3,4,2,6,1,5,7]=>[7,5,1,6,2,4,3]=>111010=>010111
[3,4,2,6,1,7,5]=>[5,7,1,6,2,4,3]=>111000=>000111
[3,4,2,6,5,1,7]=>[7,1,5,6,2,4,3]=>111000=>000111
[3,4,2,6,5,7,1]=>[1,7,5,6,2,4,3]=>011010=>010110
[3,4,2,6,7,1,5]=>[5,1,7,6,2,4,3]=>111001=>100111
[3,4,2,6,7,5,1]=>[1,5,7,6,2,4,3]=>011001=>100110
[3,4,2,7,1,5,6]=>[6,5,1,7,2,4,3]=>111010=>010111
[3,4,2,7,1,6,5]=>[5,6,1,7,2,4,3]=>111000=>000111
[3,4,2,7,5,1,6]=>[6,1,5,7,2,4,3]=>111000=>000111
[3,4,2,7,5,6,1]=>[1,6,5,7,2,4,3]=>011010=>010110
[3,4,2,7,6,1,5]=>[5,1,6,7,2,4,3]=>111000=>000111
[3,4,2,7,6,5,1]=>[1,5,6,7,2,4,3]=>011000=>000110
[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>111101=>101111
[3,4,5,1,2,7,6]=>[6,7,2,1,5,4,3]=>111100=>001111
[3,4,5,1,6,2,7]=>[7,2,6,1,5,4,3]=>111100=>001111
[3,4,5,1,6,7,2]=>[2,7,6,1,5,4,3]=>101101=>101101
[3,4,5,1,7,2,6]=>[6,2,7,1,5,4,3]=>111100=>001111
[3,4,5,1,7,6,2]=>[2,6,7,1,5,4,3]=>101100=>001101
[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>101101=>101101
[3,4,5,2,1,7,6]=>[6,7,1,2,5,4,3]=>101100=>001101
[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>111100=>001111
[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>011101=>101110
[3,4,5,2,7,1,6]=>[6,1,7,2,5,4,3]=>111100=>001111
[3,4,5,2,7,6,1]=>[1,6,7,2,5,4,3]=>011100=>001110
[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>111110=>011111
[3,4,5,6,1,7,2]=>[2,7,1,6,5,4,3]=>101110=>011101
[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>101110=>011101
[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>011110=>011110
[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>101111=>111101
[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>001111=>111100
[3,4,5,7,1,2,6]=>[6,2,1,7,5,4,3]=>111110=>011111
[3,4,5,7,1,6,2]=>[2,6,1,7,5,4,3]=>101110=>011101
[3,4,5,7,2,1,6]=>[6,1,2,7,5,4,3]=>101110=>011101
[3,4,5,7,2,6,1]=>[1,6,2,7,5,4,3]=>011110=>011110
[3,4,5,7,6,1,2]=>[2,1,6,7,5,4,3]=>101110=>011101
[3,4,5,7,6,2,1]=>[1,2,6,7,5,4,3]=>001110=>011100
[3,4,6,1,2,5,7]=>[7,5,2,1,6,4,3]=>111110=>011111
[3,4,6,1,2,7,5]=>[5,7,2,1,6,4,3]=>111100=>001111
[3,4,6,1,5,2,7]=>[7,2,5,1,6,4,3]=>111100=>001111
[3,4,6,1,5,7,2]=>[2,7,5,1,6,4,3]=>101110=>011101
[3,4,6,1,7,2,5]=>[5,2,7,1,6,4,3]=>111100=>001111
[3,4,6,1,7,5,2]=>[2,5,7,1,6,4,3]=>101100=>001101
[3,4,6,2,1,5,7]=>[7,5,1,2,6,4,3]=>101110=>011101
[3,4,6,2,1,7,5]=>[5,7,1,2,6,4,3]=>101100=>001101
[3,4,6,2,5,1,7]=>[7,1,5,2,6,4,3]=>111100=>001111
[3,4,6,2,5,7,1]=>[1,7,5,2,6,4,3]=>011110=>011110
[3,4,6,2,7,1,5]=>[5,1,7,2,6,4,3]=>111100=>001111
[3,4,6,2,7,5,1]=>[1,5,7,2,6,4,3]=>011100=>001110
[3,4,6,5,1,2,7]=>[7,2,1,5,6,4,3]=>111100=>001111
[3,4,6,5,1,7,2]=>[2,7,1,5,6,4,3]=>101100=>001101
[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>101100=>001101
[3,4,6,5,2,7,1]=>[1,7,2,5,6,4,3]=>011100=>001110
[3,4,6,5,7,1,2]=>[2,1,7,5,6,4,3]=>101110=>011101
[3,4,6,5,7,2,1]=>[1,2,7,5,6,4,3]=>001110=>011100
[3,4,6,7,1,2,5]=>[5,2,1,7,6,4,3]=>111101=>101111
[3,4,6,7,1,5,2]=>[2,5,1,7,6,4,3]=>101101=>101101
[3,4,6,7,2,1,5]=>[5,1,2,7,6,4,3]=>101101=>101101
[3,4,6,7,2,5,1]=>[1,5,2,7,6,4,3]=>011101=>101110
[3,4,6,7,5,1,2]=>[2,1,5,7,6,4,3]=>101101=>101101
[3,4,6,7,5,2,1]=>[1,2,5,7,6,4,3]=>001101=>101100
[3,4,7,1,2,5,6]=>[6,5,2,1,7,4,3]=>111110=>011111
[3,4,7,1,2,6,5]=>[5,6,2,1,7,4,3]=>111100=>001111
[3,4,7,1,5,2,6]=>[6,2,5,1,7,4,3]=>111100=>001111
[3,4,7,1,5,6,2]=>[2,6,5,1,7,4,3]=>101110=>011101
[3,4,7,1,6,2,5]=>[5,2,6,1,7,4,3]=>111100=>001111
[3,4,7,1,6,5,2]=>[2,5,6,1,7,4,3]=>101100=>001101
[3,4,7,2,1,5,6]=>[6,5,1,2,7,4,3]=>101110=>011101
[3,4,7,2,1,6,5]=>[5,6,1,2,7,4,3]=>101100=>001101
[3,4,7,2,5,1,6]=>[6,1,5,2,7,4,3]=>111100=>001111
[3,4,7,2,5,6,1]=>[1,6,5,2,7,4,3]=>011110=>011110
[3,4,7,2,6,1,5]=>[5,1,6,2,7,4,3]=>111100=>001111
[3,4,7,2,6,5,1]=>[1,5,6,2,7,4,3]=>011100=>001110
[3,4,7,5,1,2,6]=>[6,2,1,5,7,4,3]=>111100=>001111
[3,4,7,5,1,6,2]=>[2,6,1,5,7,4,3]=>101100=>001101
[3,4,7,5,2,1,6]=>[6,1,2,5,7,4,3]=>101100=>001101
[3,4,7,5,2,6,1]=>[1,6,2,5,7,4,3]=>011100=>001110
[3,4,7,5,6,1,2]=>[2,1,6,5,7,4,3]=>101110=>011101
[3,4,7,5,6,2,1]=>[1,2,6,5,7,4,3]=>001110=>011100
[3,4,7,6,1,2,5]=>[5,2,1,6,7,4,3]=>111100=>001111
[3,4,7,6,1,5,2]=>[2,5,1,6,7,4,3]=>101100=>001101
[3,4,7,6,2,1,5]=>[5,1,2,6,7,4,3]=>101100=>001101
[3,4,7,6,2,5,1]=>[1,5,2,6,7,4,3]=>011100=>001110
[3,4,7,6,5,1,2]=>[2,1,5,6,7,4,3]=>101100=>001101
[3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3]=>001100=>001100
[3,5,1,2,4,6,7]=>[7,6,4,2,1,5,3]=>111101=>101111
[3,5,1,2,4,7,6]=>[6,7,4,2,1,5,3]=>111100=>001111
[3,5,1,2,6,4,7]=>[7,4,6,2,1,5,3]=>111100=>001111
[3,5,1,2,6,7,4]=>[4,7,6,2,1,5,3]=>111001=>100111
[3,5,1,2,7,4,6]=>[6,4,7,2,1,5,3]=>111100=>001111
[3,5,1,2,7,6,4]=>[4,6,7,2,1,5,3]=>111000=>000111
[3,5,1,4,2,6,7]=>[7,6,2,4,1,5,3]=>111001=>100111
[3,5,1,4,2,7,6]=>[6,7,2,4,1,5,3]=>111000=>000111
[3,5,1,4,6,2,7]=>[7,2,6,4,1,5,3]=>111100=>001111
[3,5,1,4,6,7,2]=>[2,7,6,4,1,5,3]=>101101=>101101
[3,5,1,4,7,2,6]=>[6,2,7,4,1,5,3]=>111100=>001111
[3,5,1,4,7,6,2]=>[2,6,7,4,1,5,3]=>101100=>001101
[3,5,1,6,2,4,7]=>[7,4,2,6,1,5,3]=>111100=>001111
[3,5,1,6,2,7,4]=>[4,7,2,6,1,5,3]=>111000=>000111
[3,5,1,6,4,2,7]=>[7,2,4,6,1,5,3]=>111000=>000111
[3,5,1,6,4,7,2]=>[2,7,4,6,1,5,3]=>101100=>001101
[3,5,1,6,7,2,4]=>[4,2,7,6,1,5,3]=>111001=>100111
[3,5,1,6,7,4,2]=>[2,4,7,6,1,5,3]=>101001=>100101
[3,5,1,7,2,4,6]=>[6,4,2,7,1,5,3]=>111100=>001111
[3,5,1,7,2,6,4]=>[4,6,2,7,1,5,3]=>111000=>000111
[3,5,1,7,4,2,6]=>[6,2,4,7,1,5,3]=>111000=>000111
[3,5,1,7,4,6,2]=>[2,6,4,7,1,5,3]=>101100=>001101
[3,5,1,7,6,2,4]=>[4,2,6,7,1,5,3]=>111000=>000111
[3,5,1,7,6,4,2]=>[2,4,6,7,1,5,3]=>101000=>000101
[3,5,2,1,4,6,7]=>[7,6,4,1,2,5,3]=>101101=>101101
[3,5,2,1,4,7,6]=>[6,7,4,1,2,5,3]=>101100=>001101
[3,5,2,1,6,4,7]=>[7,4,6,1,2,5,3]=>101100=>001101
[3,5,2,1,6,7,4]=>[4,7,6,1,2,5,3]=>101001=>100101
[3,5,2,1,7,4,6]=>[6,4,7,1,2,5,3]=>101100=>001101
[3,5,2,1,7,6,4]=>[4,6,7,1,2,5,3]=>101000=>000101
[3,5,2,4,1,6,7]=>[7,6,1,4,2,5,3]=>111001=>100111
[3,5,2,4,1,7,6]=>[6,7,1,4,2,5,3]=>111000=>000111
[3,5,2,4,6,1,7]=>[7,1,6,4,2,5,3]=>111100=>001111
[3,5,2,4,6,7,1]=>[1,7,6,4,2,5,3]=>011101=>101110
[3,5,2,4,7,1,6]=>[6,1,7,4,2,5,3]=>111100=>001111
[3,5,2,4,7,6,1]=>[1,6,7,4,2,5,3]=>011100=>001110
[3,5,2,6,1,4,7]=>[7,4,1,6,2,5,3]=>111100=>001111
[3,5,2,6,1,7,4]=>[4,7,1,6,2,5,3]=>111000=>000111
[3,5,2,6,4,1,7]=>[7,1,4,6,2,5,3]=>111000=>000111
[3,5,2,6,4,7,1]=>[1,7,4,6,2,5,3]=>011100=>001110
[3,5,2,6,7,1,4]=>[4,1,7,6,2,5,3]=>111001=>100111
[3,5,2,6,7,4,1]=>[1,4,7,6,2,5,3]=>011001=>100110
[3,5,2,7,1,4,6]=>[6,4,1,7,2,5,3]=>111100=>001111
[3,5,2,7,1,6,4]=>[4,6,1,7,2,5,3]=>111000=>000111
[3,5,2,7,4,1,6]=>[6,1,4,7,2,5,3]=>111000=>000111
[3,5,2,7,4,6,1]=>[1,6,4,7,2,5,3]=>011100=>001110
[3,5,2,7,6,1,4]=>[4,1,6,7,2,5,3]=>111000=>000111
[3,5,2,7,6,4,1]=>[1,4,6,7,2,5,3]=>011000=>000110
[3,5,4,1,2,6,7]=>[7,6,2,1,4,5,3]=>111001=>100111
[3,5,4,1,2,7,6]=>[6,7,2,1,4,5,3]=>111000=>000111
[3,5,4,1,6,2,7]=>[7,2,6,1,4,5,3]=>111000=>000111
[3,5,4,1,6,7,2]=>[2,7,6,1,4,5,3]=>101001=>100101
[3,5,4,1,7,2,6]=>[6,2,7,1,4,5,3]=>111000=>000111
[3,5,4,1,7,6,2]=>[2,6,7,1,4,5,3]=>101000=>000101
[3,5,4,2,1,6,7]=>[7,6,1,2,4,5,3]=>101001=>100101
[3,5,4,2,1,7,6]=>[6,7,1,2,4,5,3]=>101000=>000101
[3,5,4,2,6,1,7]=>[7,1,6,2,4,5,3]=>111000=>000111
[3,5,4,2,6,7,1]=>[1,7,6,2,4,5,3]=>011001=>100110
[3,5,4,2,7,1,6]=>[6,1,7,2,4,5,3]=>111000=>000111
[3,5,4,2,7,6,1]=>[1,6,7,2,4,5,3]=>011000=>000110
[3,5,4,6,1,2,7]=>[7,2,1,6,4,5,3]=>111100=>001111
[3,5,4,6,1,7,2]=>[2,7,1,6,4,5,3]=>101100=>001101
[3,5,4,6,2,1,7]=>[7,1,2,6,4,5,3]=>101100=>001101
[3,5,4,6,2,7,1]=>[1,7,2,6,4,5,3]=>011100=>001110
[3,5,4,6,7,1,2]=>[2,1,7,6,4,5,3]=>101101=>101101
[3,5,4,6,7,2,1]=>[1,2,7,6,4,5,3]=>001101=>101100
[3,5,4,7,1,2,6]=>[6,2,1,7,4,5,3]=>111100=>001111
[3,5,4,7,1,6,2]=>[2,6,1,7,4,5,3]=>101100=>001101
[3,5,4,7,2,1,6]=>[6,1,2,7,4,5,3]=>101100=>001101
[3,5,4,7,2,6,1]=>[1,6,2,7,4,5,3]=>011100=>001110
[3,5,4,7,6,1,2]=>[2,1,6,7,4,5,3]=>101100=>001101
[3,5,4,7,6,2,1]=>[1,2,6,7,4,5,3]=>001100=>001100
[3,5,6,1,2,4,7]=>[7,4,2,1,6,5,3]=>111110=>011111
[3,5,6,1,2,7,4]=>[4,7,2,1,6,5,3]=>111010=>010111
[3,5,6,1,4,2,7]=>[7,2,4,1,6,5,3]=>111010=>010111
[3,5,6,1,4,7,2]=>[2,7,4,1,6,5,3]=>101110=>011101
[3,5,6,1,7,2,4]=>[4,2,7,1,6,5,3]=>111010=>010111
[3,5,6,1,7,4,2]=>[2,4,7,1,6,5,3]=>101010=>010101
[3,5,6,2,1,4,7]=>[7,4,1,2,6,5,3]=>101110=>011101
[3,5,6,2,1,7,4]=>[4,7,1,2,6,5,3]=>101010=>010101
[3,5,6,2,4,1,7]=>[7,1,4,2,6,5,3]=>111010=>010111
[3,5,6,2,4,7,1]=>[1,7,4,2,6,5,3]=>011110=>011110
[3,5,6,2,7,1,4]=>[4,1,7,2,6,5,3]=>111010=>010111
[3,5,6,2,7,4,1]=>[1,4,7,2,6,5,3]=>011010=>010110
[3,5,6,4,1,2,7]=>[7,2,1,4,6,5,3]=>111010=>010111
[3,5,6,4,1,7,2]=>[2,7,1,4,6,5,3]=>101010=>010101
[3,5,6,4,2,1,7]=>[7,1,2,4,6,5,3]=>101010=>010101
[3,5,6,4,2,7,1]=>[1,7,2,4,6,5,3]=>011010=>010110
[3,5,6,4,7,1,2]=>[2,1,7,4,6,5,3]=>101110=>011101
[3,5,6,4,7,2,1]=>[1,2,7,4,6,5,3]=>001110=>011100
[3,5,6,7,1,2,4]=>[4,2,1,7,6,5,3]=>111011=>110111
[3,5,6,7,1,4,2]=>[2,4,1,7,6,5,3]=>101011=>110101
[3,5,6,7,2,1,4]=>[4,1,2,7,6,5,3]=>101011=>110101
[3,5,6,7,2,4,1]=>[1,4,2,7,6,5,3]=>011011=>110110
[3,5,6,7,4,1,2]=>[2,1,4,7,6,5,3]=>101011=>110101
[3,5,6,7,4,2,1]=>[1,2,4,7,6,5,3]=>001011=>110100
[3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3]=>111110=>011111
[3,5,7,1,2,6,4]=>[4,6,2,1,7,5,3]=>111010=>010111
[3,5,7,1,4,2,6]=>[6,2,4,1,7,5,3]=>111010=>010111
[3,5,7,1,4,6,2]=>[2,6,4,1,7,5,3]=>101110=>011101
[3,5,7,1,6,2,4]=>[4,2,6,1,7,5,3]=>111010=>010111
[3,5,7,1,6,4,2]=>[2,4,6,1,7,5,3]=>101010=>010101
[3,5,7,2,1,4,6]=>[6,4,1,2,7,5,3]=>101110=>011101
[3,5,7,2,1,6,4]=>[4,6,1,2,7,5,3]=>101010=>010101
[3,5,7,2,4,1,6]=>[6,1,4,2,7,5,3]=>111010=>010111
[3,5,7,2,4,6,1]=>[1,6,4,2,7,5,3]=>011110=>011110
[3,5,7,2,6,1,4]=>[4,1,6,2,7,5,3]=>111010=>010111
[3,5,7,2,6,4,1]=>[1,4,6,2,7,5,3]=>011010=>010110
[3,5,7,4,1,2,6]=>[6,2,1,4,7,5,3]=>111010=>010111
[3,5,7,4,1,6,2]=>[2,6,1,4,7,5,3]=>101010=>010101
[3,5,7,4,2,1,6]=>[6,1,2,4,7,5,3]=>101010=>010101
[3,5,7,4,2,6,1]=>[1,6,2,4,7,5,3]=>011010=>010110
[3,5,7,4,6,1,2]=>[2,1,6,4,7,5,3]=>101110=>011101
[3,5,7,4,6,2,1]=>[1,2,6,4,7,5,3]=>001110=>011100
[3,5,7,6,1,2,4]=>[4,2,1,6,7,5,3]=>111010=>010111
[3,5,7,6,1,4,2]=>[2,4,1,6,7,5,3]=>101010=>010101
[3,5,7,6,2,1,4]=>[4,1,2,6,7,5,3]=>101010=>010101
[3,5,7,6,2,4,1]=>[1,4,2,6,7,5,3]=>011010=>010110
[3,5,7,6,4,1,2]=>[2,1,4,6,7,5,3]=>101010=>010101
[3,5,7,6,4,2,1]=>[1,2,4,6,7,5,3]=>001010=>010100
[3,6,1,2,4,5,7]=>[7,5,4,2,1,6,3]=>111110=>011111
[3,6,1,2,4,7,5]=>[5,7,4,2,1,6,3]=>111100=>001111
[3,6,1,2,5,4,7]=>[7,4,5,2,1,6,3]=>111100=>001111
[3,6,1,2,5,7,4]=>[4,7,5,2,1,6,3]=>111010=>010111
[3,6,1,2,7,4,5]=>[5,4,7,2,1,6,3]=>111100=>001111
[3,6,1,2,7,5,4]=>[4,5,7,2,1,6,3]=>111000=>000111
[3,6,1,4,2,5,7]=>[7,5,2,4,1,6,3]=>111010=>010111
[3,6,1,4,2,7,5]=>[5,7,2,4,1,6,3]=>111000=>000111
[3,6,1,4,5,2,7]=>[7,2,5,4,1,6,3]=>111100=>001111
[3,6,1,4,5,7,2]=>[2,7,5,4,1,6,3]=>101110=>011101
[3,6,1,4,7,2,5]=>[5,2,7,4,1,6,3]=>111100=>001111
[3,6,1,4,7,5,2]=>[2,5,7,4,1,6,3]=>101100=>001101
[3,6,1,5,2,4,7]=>[7,4,2,5,1,6,3]=>111100=>001111
[3,6,1,5,2,7,4]=>[4,7,2,5,1,6,3]=>111000=>000111
[3,6,1,5,4,2,7]=>[7,2,4,5,1,6,3]=>111000=>000111
[3,6,1,5,4,7,2]=>[2,7,4,5,1,6,3]=>101100=>001101
[3,6,1,5,7,2,4]=>[4,2,7,5,1,6,3]=>111010=>010111
[3,6,1,5,7,4,2]=>[2,4,7,5,1,6,3]=>101010=>010101
[3,6,1,7,2,4,5]=>[5,4,2,7,1,6,3]=>111100=>001111
[3,6,1,7,2,5,4]=>[4,5,2,7,1,6,3]=>111000=>000111
[3,6,1,7,4,2,5]=>[5,2,4,7,1,6,3]=>111000=>000111
[3,6,1,7,4,5,2]=>[2,5,4,7,1,6,3]=>101100=>001101
[3,6,1,7,5,2,4]=>[4,2,5,7,1,6,3]=>111000=>000111
[3,6,1,7,5,4,2]=>[2,4,5,7,1,6,3]=>101000=>000101
[3,6,2,1,4,5,7]=>[7,5,4,1,2,6,3]=>101110=>011101
[3,6,2,1,4,7,5]=>[5,7,4,1,2,6,3]=>101100=>001101
[3,6,2,1,5,4,7]=>[7,4,5,1,2,6,3]=>101100=>001101
[3,6,2,1,5,7,4]=>[4,7,5,1,2,6,3]=>101010=>010101
[3,6,2,1,7,4,5]=>[5,4,7,1,2,6,3]=>101100=>001101
[3,6,2,1,7,5,4]=>[4,5,7,1,2,6,3]=>101000=>000101
[3,6,2,4,1,5,7]=>[7,5,1,4,2,6,3]=>111010=>010111
[3,6,2,4,1,7,5]=>[5,7,1,4,2,6,3]=>111000=>000111
[3,6,2,4,5,1,7]=>[7,1,5,4,2,6,3]=>111100=>001111
[3,6,2,4,5,7,1]=>[1,7,5,4,2,6,3]=>011110=>011110
[3,6,2,4,7,1,5]=>[5,1,7,4,2,6,3]=>111100=>001111
[3,6,2,4,7,5,1]=>[1,5,7,4,2,6,3]=>011100=>001110
[3,6,2,5,1,4,7]=>[7,4,1,5,2,6,3]=>111100=>001111
[3,6,2,5,1,7,4]=>[4,7,1,5,2,6,3]=>111000=>000111
[3,6,2,5,4,1,7]=>[7,1,4,5,2,6,3]=>111000=>000111
[3,6,2,5,4,7,1]=>[1,7,4,5,2,6,3]=>011100=>001110
[3,6,2,5,7,1,4]=>[4,1,7,5,2,6,3]=>111010=>010111
[3,6,2,5,7,4,1]=>[1,4,7,5,2,6,3]=>011010=>010110
[3,6,2,7,1,4,5]=>[5,4,1,7,2,6,3]=>111100=>001111
[3,6,2,7,1,5,4]=>[4,5,1,7,2,6,3]=>111000=>000111
[3,6,2,7,4,1,5]=>[5,1,4,7,2,6,3]=>111000=>000111
[3,6,2,7,4,5,1]=>[1,5,4,7,2,6,3]=>011100=>001110
[3,6,2,7,5,1,4]=>[4,1,5,7,2,6,3]=>111000=>000111
[3,6,2,7,5,4,1]=>[1,4,5,7,2,6,3]=>011000=>000110
[3,6,4,1,2,5,7]=>[7,5,2,1,4,6,3]=>111010=>010111
[3,6,4,1,2,7,5]=>[5,7,2,1,4,6,3]=>111000=>000111
[3,6,4,1,5,2,7]=>[7,2,5,1,4,6,3]=>111000=>000111
[3,6,4,1,5,7,2]=>[2,7,5,1,4,6,3]=>101010=>010101
[3,6,4,1,7,2,5]=>[5,2,7,1,4,6,3]=>111000=>000111
[3,6,4,1,7,5,2]=>[2,5,7,1,4,6,3]=>101000=>000101
[3,6,4,2,1,5,7]=>[7,5,1,2,4,6,3]=>101010=>010101
[3,6,4,2,1,7,5]=>[5,7,1,2,4,6,3]=>101000=>000101
[3,6,4,2,5,1,7]=>[7,1,5,2,4,6,3]=>111000=>000111
[3,6,4,2,5,7,1]=>[1,7,5,2,4,6,3]=>011010=>010110
[3,6,4,2,7,1,5]=>[5,1,7,2,4,6,3]=>111000=>000111
[3,6,4,2,7,5,1]=>[1,5,7,2,4,6,3]=>011000=>000110
[3,6,4,5,1,2,7]=>[7,2,1,5,4,6,3]=>111100=>001111
[3,6,4,5,1,7,2]=>[2,7,1,5,4,6,3]=>101100=>001101
[3,6,4,5,2,1,7]=>[7,1,2,5,4,6,3]=>101100=>001101
[3,6,4,5,2,7,1]=>[1,7,2,5,4,6,3]=>011100=>001110
[3,6,4,5,7,1,2]=>[2,1,7,5,4,6,3]=>101110=>011101
[3,6,4,5,7,2,1]=>[1,2,7,5,4,6,3]=>001110=>011100
[3,6,4,7,1,2,5]=>[5,2,1,7,4,6,3]=>111100=>001111
[3,6,4,7,1,5,2]=>[2,5,1,7,4,6,3]=>101100=>001101
[3,6,4,7,2,1,5]=>[5,1,2,7,4,6,3]=>101100=>001101
[3,6,4,7,2,5,1]=>[1,5,2,7,4,6,3]=>011100=>001110
[3,6,4,7,5,1,2]=>[2,1,5,7,4,6,3]=>101100=>001101
[3,6,4,7,5,2,1]=>[1,2,5,7,4,6,3]=>001100=>001100
[3,6,5,1,2,4,7]=>[7,4,2,1,5,6,3]=>111100=>001111
[3,6,5,1,2,7,4]=>[4,7,2,1,5,6,3]=>111000=>000111
[3,6,5,1,4,2,7]=>[7,2,4,1,5,6,3]=>111000=>000111
[3,6,5,1,4,7,2]=>[2,7,4,1,5,6,3]=>101100=>001101
[3,6,5,1,7,2,4]=>[4,2,7,1,5,6,3]=>111000=>000111
[3,6,5,1,7,4,2]=>[2,4,7,1,5,6,3]=>101000=>000101
[3,6,5,2,1,4,7]=>[7,4,1,2,5,6,3]=>101100=>001101
[3,6,5,2,1,7,4]=>[4,7,1,2,5,6,3]=>101000=>000101
[3,6,5,2,4,1,7]=>[7,1,4,2,5,6,3]=>111000=>000111
[3,6,5,2,4,7,1]=>[1,7,4,2,5,6,3]=>011100=>001110
[3,6,5,2,7,1,4]=>[4,1,7,2,5,6,3]=>111000=>000111
[3,6,5,2,7,4,1]=>[1,4,7,2,5,6,3]=>011000=>000110
[3,6,5,4,1,2,7]=>[7,2,1,4,5,6,3]=>111000=>000111
[3,6,5,4,1,7,2]=>[2,7,1,4,5,6,3]=>101000=>000101
[3,6,5,4,2,1,7]=>[7,1,2,4,5,6,3]=>101000=>000101
[3,6,5,4,2,7,1]=>[1,7,2,4,5,6,3]=>011000=>000110
[3,6,5,4,7,1,2]=>[2,1,7,4,5,6,3]=>101100=>001101
[3,6,5,4,7,2,1]=>[1,2,7,4,5,6,3]=>001100=>001100
[3,6,5,7,1,2,4]=>[4,2,1,7,5,6,3]=>111010=>010111
[3,6,5,7,1,4,2]=>[2,4,1,7,5,6,3]=>101010=>010101
[3,6,5,7,2,1,4]=>[4,1,2,7,5,6,3]=>101010=>010101
[3,6,5,7,2,4,1]=>[1,4,2,7,5,6,3]=>011010=>010110
[3,6,5,7,4,1,2]=>[2,1,4,7,5,6,3]=>101010=>010101
[3,6,5,7,4,2,1]=>[1,2,4,7,5,6,3]=>001010=>010100
[3,6,7,1,2,4,5]=>[5,4,2,1,7,6,3]=>111101=>101111
[3,6,7,1,2,5,4]=>[4,5,2,1,7,6,3]=>111001=>100111
[3,6,7,1,4,2,5]=>[5,2,4,1,7,6,3]=>111001=>100111
[3,6,7,1,4,5,2]=>[2,5,4,1,7,6,3]=>101101=>101101
[3,6,7,1,5,2,4]=>[4,2,5,1,7,6,3]=>111001=>100111
[3,6,7,1,5,4,2]=>[2,4,5,1,7,6,3]=>101001=>100101
[3,6,7,2,1,4,5]=>[5,4,1,2,7,6,3]=>101101=>101101
[3,6,7,2,1,5,4]=>[4,5,1,2,7,6,3]=>101001=>100101
[3,6,7,2,4,1,5]=>[5,1,4,2,7,6,3]=>111001=>100111
[3,6,7,2,4,5,1]=>[1,5,4,2,7,6,3]=>011101=>101110
[3,6,7,2,5,1,4]=>[4,1,5,2,7,6,3]=>111001=>100111
[3,6,7,2,5,4,1]=>[1,4,5,2,7,6,3]=>011001=>100110
[3,6,7,4,1,2,5]=>[5,2,1,4,7,6,3]=>111001=>100111
[3,6,7,4,1,5,2]=>[2,5,1,4,7,6,3]=>101001=>100101
[3,6,7,4,2,1,5]=>[5,1,2,4,7,6,3]=>101001=>100101
[3,6,7,4,2,5,1]=>[1,5,2,4,7,6,3]=>011001=>100110
[3,6,7,4,5,1,2]=>[2,1,5,4,7,6,3]=>101101=>101101
[3,6,7,4,5,2,1]=>[1,2,5,4,7,6,3]=>001101=>101100
[3,6,7,5,1,2,4]=>[4,2,1,5,7,6,3]=>111001=>100111
[3,6,7,5,1,4,2]=>[2,4,1,5,7,6,3]=>101001=>100101
[3,6,7,5,2,1,4]=>[4,1,2,5,7,6,3]=>101001=>100101
[3,6,7,5,2,4,1]=>[1,4,2,5,7,6,3]=>011001=>100110
[3,6,7,5,4,1,2]=>[2,1,4,5,7,6,3]=>101001=>100101
[3,6,7,5,4,2,1]=>[1,2,4,5,7,6,3]=>001001=>100100
[3,7,1,2,4,5,6]=>[6,5,4,2,1,7,3]=>111110=>011111
[3,7,1,2,4,6,5]=>[5,6,4,2,1,7,3]=>111100=>001111
[3,7,1,2,5,4,6]=>[6,4,5,2,1,7,3]=>111100=>001111
[3,7,1,2,5,6,4]=>[4,6,5,2,1,7,3]=>111010=>010111
[3,7,1,2,6,4,5]=>[5,4,6,2,1,7,3]=>111100=>001111
[3,7,1,2,6,5,4]=>[4,5,6,2,1,7,3]=>111000=>000111
[3,7,1,4,2,5,6]=>[6,5,2,4,1,7,3]=>111010=>010111
[3,7,1,4,2,6,5]=>[5,6,2,4,1,7,3]=>111000=>000111
[3,7,1,4,5,2,6]=>[6,2,5,4,1,7,3]=>111100=>001111
[3,7,1,4,5,6,2]=>[2,6,5,4,1,7,3]=>101110=>011101
[3,7,1,4,6,2,5]=>[5,2,6,4,1,7,3]=>111100=>001111
[3,7,1,4,6,5,2]=>[2,5,6,4,1,7,3]=>101100=>001101
[3,7,1,5,2,4,6]=>[6,4,2,5,1,7,3]=>111100=>001111
[3,7,1,5,2,6,4]=>[4,6,2,5,1,7,3]=>111000=>000111
[3,7,1,5,4,2,6]=>[6,2,4,5,1,7,3]=>111000=>000111
[3,7,1,5,4,6,2]=>[2,6,4,5,1,7,3]=>101100=>001101
[3,7,1,5,6,2,4]=>[4,2,6,5,1,7,3]=>111010=>010111
[3,7,1,5,6,4,2]=>[2,4,6,5,1,7,3]=>101010=>010101
[3,7,1,6,2,4,5]=>[5,4,2,6,1,7,3]=>111100=>001111
[3,7,1,6,2,5,4]=>[4,5,2,6,1,7,3]=>111000=>000111
[3,7,1,6,4,2,5]=>[5,2,4,6,1,7,3]=>111000=>000111
[3,7,1,6,4,5,2]=>[2,5,4,6,1,7,3]=>101100=>001101
[3,7,1,6,5,2,4]=>[4,2,5,6,1,7,3]=>111000=>000111
[3,7,1,6,5,4,2]=>[2,4,5,6,1,7,3]=>101000=>000101
[3,7,2,1,4,5,6]=>[6,5,4,1,2,7,3]=>101110=>011101
[3,7,2,1,4,6,5]=>[5,6,4,1,2,7,3]=>101100=>001101
[3,7,2,1,5,4,6]=>[6,4,5,1,2,7,3]=>101100=>001101
[3,7,2,1,5,6,4]=>[4,6,5,1,2,7,3]=>101010=>010101
[3,7,2,1,6,4,5]=>[5,4,6,1,2,7,3]=>101100=>001101
[3,7,2,1,6,5,4]=>[4,5,6,1,2,7,3]=>101000=>000101
[3,7,2,4,1,5,6]=>[6,5,1,4,2,7,3]=>111010=>010111
[3,7,2,4,1,6,5]=>[5,6,1,4,2,7,3]=>111000=>000111
[3,7,2,4,5,1,6]=>[6,1,5,4,2,7,3]=>111100=>001111
[3,7,2,4,5,6,1]=>[1,6,5,4,2,7,3]=>011110=>011110
[3,7,2,4,6,1,5]=>[5,1,6,4,2,7,3]=>111100=>001111
[3,7,2,4,6,5,1]=>[1,5,6,4,2,7,3]=>011100=>001110
[3,7,2,5,1,4,6]=>[6,4,1,5,2,7,3]=>111100=>001111
[3,7,2,5,1,6,4]=>[4,6,1,5,2,7,3]=>111000=>000111
[3,7,2,5,4,1,6]=>[6,1,4,5,2,7,3]=>111000=>000111
[3,7,2,5,4,6,1]=>[1,6,4,5,2,7,3]=>011100=>001110
[3,7,2,5,6,1,4]=>[4,1,6,5,2,7,3]=>111010=>010111
[3,7,2,5,6,4,1]=>[1,4,6,5,2,7,3]=>011010=>010110
[3,7,2,6,1,4,5]=>[5,4,1,6,2,7,3]=>111100=>001111
[3,7,2,6,1,5,4]=>[4,5,1,6,2,7,3]=>111000=>000111
[3,7,2,6,4,1,5]=>[5,1,4,6,2,7,3]=>111000=>000111
[3,7,2,6,4,5,1]=>[1,5,4,6,2,7,3]=>011100=>001110
[3,7,2,6,5,1,4]=>[4,1,5,6,2,7,3]=>111000=>000111
[3,7,2,6,5,4,1]=>[1,4,5,6,2,7,3]=>011000=>000110
[3,7,4,1,2,5,6]=>[6,5,2,1,4,7,3]=>111010=>010111
[3,7,4,1,2,6,5]=>[5,6,2,1,4,7,3]=>111000=>000111
[3,7,4,1,5,2,6]=>[6,2,5,1,4,7,3]=>111000=>000111
[3,7,4,1,5,6,2]=>[2,6,5,1,4,7,3]=>101010=>010101
[3,7,4,1,6,2,5]=>[5,2,6,1,4,7,3]=>111000=>000111
[3,7,4,1,6,5,2]=>[2,5,6,1,4,7,3]=>101000=>000101
[3,7,4,2,1,5,6]=>[6,5,1,2,4,7,3]=>101010=>010101
[3,7,4,2,1,6,5]=>[5,6,1,2,4,7,3]=>101000=>000101
[3,7,4,2,5,1,6]=>[6,1,5,2,4,7,3]=>111000=>000111
[3,7,4,2,5,6,1]=>[1,6,5,2,4,7,3]=>011010=>010110
[3,7,4,2,6,1,5]=>[5,1,6,2,4,7,3]=>111000=>000111
[3,7,4,2,6,5,1]=>[1,5,6,2,4,7,3]=>011000=>000110
[3,7,4,5,1,2,6]=>[6,2,1,5,4,7,3]=>111100=>001111
[3,7,4,5,1,6,2]=>[2,6,1,5,4,7,3]=>101100=>001101
[3,7,4,5,2,1,6]=>[6,1,2,5,4,7,3]=>101100=>001101
[3,7,4,5,2,6,1]=>[1,6,2,5,4,7,3]=>011100=>001110
[3,7,4,5,6,1,2]=>[2,1,6,5,4,7,3]=>101110=>011101
[3,7,4,5,6,2,1]=>[1,2,6,5,4,7,3]=>001110=>011100
[3,7,4,6,1,2,5]=>[5,2,1,6,4,7,3]=>111100=>001111
[3,7,4,6,1,5,2]=>[2,5,1,6,4,7,3]=>101100=>001101
[3,7,4,6,2,1,5]=>[5,1,2,6,4,7,3]=>101100=>001101
[3,7,4,6,2,5,1]=>[1,5,2,6,4,7,3]=>011100=>001110
[3,7,4,6,5,1,2]=>[2,1,5,6,4,7,3]=>101100=>001101
[3,7,4,6,5,2,1]=>[1,2,5,6,4,7,3]=>001100=>001100
[3,7,5,1,2,4,6]=>[6,4,2,1,5,7,3]=>111100=>001111
[3,7,5,1,2,6,4]=>[4,6,2,1,5,7,3]=>111000=>000111
[3,7,5,1,4,2,6]=>[6,2,4,1,5,7,3]=>111000=>000111
[3,7,5,1,4,6,2]=>[2,6,4,1,5,7,3]=>101100=>001101
[3,7,5,1,6,2,4]=>[4,2,6,1,5,7,3]=>111000=>000111
[3,7,5,1,6,4,2]=>[2,4,6,1,5,7,3]=>101000=>000101
[3,7,5,2,1,4,6]=>[6,4,1,2,5,7,3]=>101100=>001101
[3,7,5,2,1,6,4]=>[4,6,1,2,5,7,3]=>101000=>000101
[3,7,5,2,4,1,6]=>[6,1,4,2,5,7,3]=>111000=>000111
[3,7,5,2,4,6,1]=>[1,6,4,2,5,7,3]=>011100=>001110
[3,7,5,2,6,1,4]=>[4,1,6,2,5,7,3]=>111000=>000111
[3,7,5,2,6,4,1]=>[1,4,6,2,5,7,3]=>011000=>000110
[3,7,5,4,1,2,6]=>[6,2,1,4,5,7,3]=>111000=>000111
[3,7,5,4,1,6,2]=>[2,6,1,4,5,7,3]=>101000=>000101
[3,7,5,4,2,1,6]=>[6,1,2,4,5,7,3]=>101000=>000101
[3,7,5,4,2,6,1]=>[1,6,2,4,5,7,3]=>011000=>000110
[3,7,5,4,6,1,2]=>[2,1,6,4,5,7,3]=>101100=>001101
[3,7,5,4,6,2,1]=>[1,2,6,4,5,7,3]=>001100=>001100
[3,7,5,6,1,2,4]=>[4,2,1,6,5,7,3]=>111010=>010111
[3,7,5,6,1,4,2]=>[2,4,1,6,5,7,3]=>101010=>010101
[3,7,5,6,2,1,4]=>[4,1,2,6,5,7,3]=>101010=>010101
[3,7,5,6,2,4,1]=>[1,4,2,6,5,7,3]=>011010=>010110
[3,7,5,6,4,1,2]=>[2,1,4,6,5,7,3]=>101010=>010101
[3,7,5,6,4,2,1]=>[1,2,4,6,5,7,3]=>001010=>010100
[3,7,6,1,2,4,5]=>[5,4,2,1,6,7,3]=>111100=>001111
[3,7,6,1,2,5,4]=>[4,5,2,1,6,7,3]=>111000=>000111
[3,7,6,1,4,2,5]=>[5,2,4,1,6,7,3]=>111000=>000111
[3,7,6,1,4,5,2]=>[2,5,4,1,6,7,3]=>101100=>001101
[3,7,6,1,5,2,4]=>[4,2,5,1,6,7,3]=>111000=>000111
[3,7,6,1,5,4,2]=>[2,4,5,1,6,7,3]=>101000=>000101
[3,7,6,2,1,4,5]=>[5,4,1,2,6,7,3]=>101100=>001101
[3,7,6,2,1,5,4]=>[4,5,1,2,6,7,3]=>101000=>000101
[3,7,6,2,4,1,5]=>[5,1,4,2,6,7,3]=>111000=>000111
[3,7,6,2,4,5,1]=>[1,5,4,2,6,7,3]=>011100=>001110
[3,7,6,2,5,1,4]=>[4,1,5,2,6,7,3]=>111000=>000111
[3,7,6,2,5,4,1]=>[1,4,5,2,6,7,3]=>011000=>000110
[3,7,6,4,1,2,5]=>[5,2,1,4,6,7,3]=>111000=>000111
[3,7,6,4,1,5,2]=>[2,5,1,4,6,7,3]=>101000=>000101
[3,7,6,4,2,1,5]=>[5,1,2,4,6,7,3]=>101000=>000101
[3,7,6,4,2,5,1]=>[1,5,2,4,6,7,3]=>011000=>000110
[3,7,6,4,5,1,2]=>[2,1,5,4,6,7,3]=>101100=>001101
[3,7,6,4,5,2,1]=>[1,2,5,4,6,7,3]=>001100=>001100
[3,7,6,5,1,2,4]=>[4,2,1,5,6,7,3]=>111000=>000111
[3,7,6,5,1,4,2]=>[2,4,1,5,6,7,3]=>101000=>000101
[3,7,6,5,2,1,4]=>[4,1,2,5,6,7,3]=>101000=>000101
[3,7,6,5,2,4,1]=>[1,4,2,5,6,7,3]=>011000=>000110
[3,7,6,5,4,1,2]=>[2,1,4,5,6,7,3]=>101000=>000101
[3,7,6,5,4,2,1]=>[1,2,4,5,6,7,3]=>001000=>000100
[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>111011=>110111
[4,1,2,3,5,7,6]=>[6,7,5,3,2,1,4]=>111010=>010111
[4,1,2,3,6,5,7]=>[7,5,6,3,2,1,4]=>111010=>010111
[4,1,2,3,6,7,5]=>[5,7,6,3,2,1,4]=>111001=>100111
[4,1,2,3,7,5,6]=>[6,5,7,3,2,1,4]=>111010=>010111
[4,1,2,3,7,6,5]=>[5,6,7,3,2,1,4]=>111000=>000111
[4,1,2,5,3,6,7]=>[7,6,3,5,2,1,4]=>111001=>100111
[4,1,2,5,3,7,6]=>[6,7,3,5,2,1,4]=>111000=>000111
[4,1,2,5,6,3,7]=>[7,3,6,5,2,1,4]=>111010=>010111
[4,1,2,5,6,7,3]=>[3,7,6,5,2,1,4]=>110011=>110011
[4,1,2,5,7,3,6]=>[6,3,7,5,2,1,4]=>111010=>010111
[4,1,2,5,7,6,3]=>[3,6,7,5,2,1,4]=>110010=>010011
[4,1,2,6,3,5,7]=>[7,5,3,6,2,1,4]=>111010=>010111
[4,1,2,6,3,7,5]=>[5,7,3,6,2,1,4]=>111000=>000111
[4,1,2,6,5,3,7]=>[7,3,5,6,2,1,4]=>111000=>000111
[4,1,2,6,5,7,3]=>[3,7,5,6,2,1,4]=>110010=>010011
[4,1,2,6,7,3,5]=>[5,3,7,6,2,1,4]=>111001=>100111
[4,1,2,6,7,5,3]=>[3,5,7,6,2,1,4]=>110001=>100011
[4,1,2,7,3,5,6]=>[6,5,3,7,2,1,4]=>111010=>010111
[4,1,2,7,3,6,5]=>[5,6,3,7,2,1,4]=>111000=>000111
[4,1,2,7,5,3,6]=>[6,3,5,7,2,1,4]=>111000=>000111
[4,1,2,7,5,6,3]=>[3,6,5,7,2,1,4]=>110010=>010011
[4,1,2,7,6,3,5]=>[5,3,6,7,2,1,4]=>111000=>000111
[4,1,2,7,6,5,3]=>[3,5,6,7,2,1,4]=>110000=>000011
[4,1,3,2,5,6,7]=>[7,6,5,2,3,1,4]=>110011=>110011
[4,1,3,2,5,7,6]=>[6,7,5,2,3,1,4]=>110010=>010011
[4,1,3,2,6,5,7]=>[7,5,6,2,3,1,4]=>110010=>010011
[4,1,3,2,6,7,5]=>[5,7,6,2,3,1,4]=>110001=>100011
[4,1,3,2,7,5,6]=>[6,5,7,2,3,1,4]=>110010=>010011
[4,1,3,2,7,6,5]=>[5,6,7,2,3,1,4]=>110000=>000011
[4,1,3,5,2,6,7]=>[7,6,2,5,3,1,4]=>111001=>100111
[4,1,3,5,2,7,6]=>[6,7,2,5,3,1,4]=>111000=>000111
[4,1,3,5,6,2,7]=>[7,2,6,5,3,1,4]=>111010=>010111
[4,1,3,5,6,7,2]=>[2,7,6,5,3,1,4]=>101011=>110101
[4,1,3,5,7,2,6]=>[6,2,7,5,3,1,4]=>111010=>010111
[4,1,3,5,7,6,2]=>[2,6,7,5,3,1,4]=>101010=>010101
[4,1,3,6,2,5,7]=>[7,5,2,6,3,1,4]=>111010=>010111
[4,1,3,6,2,7,5]=>[5,7,2,6,3,1,4]=>111000=>000111
[4,1,3,6,5,2,7]=>[7,2,5,6,3,1,4]=>111000=>000111
[4,1,3,6,5,7,2]=>[2,7,5,6,3,1,4]=>101010=>010101
[4,1,3,6,7,2,5]=>[5,2,7,6,3,1,4]=>111001=>100111
[4,1,3,6,7,5,2]=>[2,5,7,6,3,1,4]=>101001=>100101
[4,1,3,7,2,5,6]=>[6,5,2,7,3,1,4]=>111010=>010111
[4,1,3,7,2,6,5]=>[5,6,2,7,3,1,4]=>111000=>000111
[4,1,3,7,5,2,6]=>[6,2,5,7,3,1,4]=>111000=>000111
[4,1,3,7,5,6,2]=>[2,6,5,7,3,1,4]=>101010=>010101
[4,1,3,7,6,2,5]=>[5,2,6,7,3,1,4]=>111000=>000111
[4,1,3,7,6,5,2]=>[2,5,6,7,3,1,4]=>101000=>000101
[4,1,5,2,3,6,7]=>[7,6,3,2,5,1,4]=>111001=>100111
[4,1,5,2,3,7,6]=>[6,7,3,2,5,1,4]=>111000=>000111
[4,1,5,2,6,3,7]=>[7,3,6,2,5,1,4]=>111000=>000111
[4,1,5,2,6,7,3]=>[3,7,6,2,5,1,4]=>110001=>100011
[4,1,5,2,7,3,6]=>[6,3,7,2,5,1,4]=>111000=>000111
[4,1,5,2,7,6,3]=>[3,6,7,2,5,1,4]=>110000=>000011
[4,1,5,3,2,6,7]=>[7,6,2,3,5,1,4]=>110001=>100011
[4,1,5,3,2,7,6]=>[6,7,2,3,5,1,4]=>110000=>000011
[4,1,5,3,6,2,7]=>[7,2,6,3,5,1,4]=>111000=>000111
[4,1,5,3,6,7,2]=>[2,7,6,3,5,1,4]=>101001=>100101
[4,1,5,3,7,2,6]=>[6,2,7,3,5,1,4]=>111000=>000111
[4,1,5,3,7,6,2]=>[2,6,7,3,5,1,4]=>101000=>000101
[4,1,5,6,2,3,7]=>[7,3,2,6,5,1,4]=>111010=>010111
[4,1,5,6,2,7,3]=>[3,7,2,6,5,1,4]=>110010=>010011
[4,1,5,6,3,2,7]=>[7,2,3,6,5,1,4]=>110010=>010011
[4,1,5,6,3,7,2]=>[2,7,3,6,5,1,4]=>101010=>010101
[4,1,5,6,7,2,3]=>[3,2,7,6,5,1,4]=>110011=>110011
[4,1,5,6,7,3,2]=>[2,3,7,6,5,1,4]=>100011=>110001
[4,1,5,7,2,3,6]=>[6,3,2,7,5,1,4]=>111010=>010111
[4,1,5,7,2,6,3]=>[3,6,2,7,5,1,4]=>110010=>010011
[4,1,5,7,3,2,6]=>[6,2,3,7,5,1,4]=>110010=>010011
[4,1,5,7,3,6,2]=>[2,6,3,7,5,1,4]=>101010=>010101
[4,1,5,7,6,2,3]=>[3,2,6,7,5,1,4]=>110010=>010011
[4,1,5,7,6,3,2]=>[2,3,6,7,5,1,4]=>100010=>010001
[4,1,6,2,3,5,7]=>[7,5,3,2,6,1,4]=>111010=>010111
[4,1,6,2,3,7,5]=>[5,7,3,2,6,1,4]=>111000=>000111
[4,1,6,2,5,3,7]=>[7,3,5,2,6,1,4]=>111000=>000111
[4,1,6,2,5,7,3]=>[3,7,5,2,6,1,4]=>110010=>010011
[4,1,6,2,7,3,5]=>[5,3,7,2,6,1,4]=>111000=>000111
[4,1,6,2,7,5,3]=>[3,5,7,2,6,1,4]=>110000=>000011
[4,1,6,3,2,5,7]=>[7,5,2,3,6,1,4]=>110010=>010011
[4,1,6,3,2,7,5]=>[5,7,2,3,6,1,4]=>110000=>000011
[4,1,6,3,5,2,7]=>[7,2,5,3,6,1,4]=>111000=>000111
[4,1,6,3,5,7,2]=>[2,7,5,3,6,1,4]=>101010=>010101
[4,1,6,3,7,2,5]=>[5,2,7,3,6,1,4]=>111000=>000111
[4,1,6,3,7,5,2]=>[2,5,7,3,6,1,4]=>101000=>000101
[4,1,6,5,2,3,7]=>[7,3,2,5,6,1,4]=>111000=>000111
[4,1,6,5,2,7,3]=>[3,7,2,5,6,1,4]=>110000=>000011
[4,1,6,5,3,2,7]=>[7,2,3,5,6,1,4]=>110000=>000011
[4,1,6,5,3,7,2]=>[2,7,3,5,6,1,4]=>101000=>000101
[4,1,6,5,7,2,3]=>[3,2,7,5,6,1,4]=>110010=>010011
[4,1,6,5,7,3,2]=>[2,3,7,5,6,1,4]=>100010=>010001
[4,1,6,7,2,3,5]=>[5,3,2,7,6,1,4]=>111001=>100111
[4,1,6,7,2,5,3]=>[3,5,2,7,6,1,4]=>110001=>100011
[4,1,6,7,3,2,5]=>[5,2,3,7,6,1,4]=>110001=>100011
[4,1,6,7,3,5,2]=>[2,5,3,7,6,1,4]=>101001=>100101
[4,1,6,7,5,2,3]=>[3,2,5,7,6,1,4]=>110001=>100011
[4,1,6,7,5,3,2]=>[2,3,5,7,6,1,4]=>100001=>100001
[4,1,7,2,3,5,6]=>[6,5,3,2,7,1,4]=>111010=>010111
[4,1,7,2,3,6,5]=>[5,6,3,2,7,1,4]=>111000=>000111
[4,1,7,2,5,3,6]=>[6,3,5,2,7,1,4]=>111000=>000111
[4,1,7,2,5,6,3]=>[3,6,5,2,7,1,4]=>110010=>010011
[4,1,7,2,6,3,5]=>[5,3,6,2,7,1,4]=>111000=>000111
[4,1,7,2,6,5,3]=>[3,5,6,2,7,1,4]=>110000=>000011
[4,1,7,3,2,5,6]=>[6,5,2,3,7,1,4]=>110010=>010011
[4,1,7,3,2,6,5]=>[5,6,2,3,7,1,4]=>110000=>000011
[4,1,7,3,5,2,6]=>[6,2,5,3,7,1,4]=>111000=>000111
[4,1,7,3,5,6,2]=>[2,6,5,3,7,1,4]=>101010=>010101
[4,1,7,3,6,2,5]=>[5,2,6,3,7,1,4]=>111000=>000111
[4,1,7,3,6,5,2]=>[2,5,6,3,7,1,4]=>101000=>000101
[4,1,7,5,2,3,6]=>[6,3,2,5,7,1,4]=>111000=>000111
[4,1,7,5,2,6,3]=>[3,6,2,5,7,1,4]=>110000=>000011
[4,1,7,5,3,2,6]=>[6,2,3,5,7,1,4]=>110000=>000011
[4,1,7,5,3,6,2]=>[2,6,3,5,7,1,4]=>101000=>000101
[4,1,7,5,6,2,3]=>[3,2,6,5,7,1,4]=>110010=>010011
[4,1,7,5,6,3,2]=>[2,3,6,5,7,1,4]=>100010=>010001
[4,1,7,6,2,3,5]=>[5,3,2,6,7,1,4]=>111000=>000111
[4,1,7,6,2,5,3]=>[3,5,2,6,7,1,4]=>110000=>000011
[4,1,7,6,3,2,5]=>[5,2,3,6,7,1,4]=>110000=>000011
[4,1,7,6,3,5,2]=>[2,5,3,6,7,1,4]=>101000=>000101
[4,1,7,6,5,2,3]=>[3,2,5,6,7,1,4]=>110000=>000011
[4,1,7,6,5,3,2]=>[2,3,5,6,7,1,4]=>100000=>000001
[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>101011=>110101
[4,2,1,3,5,7,6]=>[6,7,5,3,1,2,4]=>101010=>010101
[4,2,1,3,6,5,7]=>[7,5,6,3,1,2,4]=>101010=>010101
[4,2,1,3,6,7,5]=>[5,7,6,3,1,2,4]=>101001=>100101
[4,2,1,3,7,5,6]=>[6,5,7,3,1,2,4]=>101010=>010101
[4,2,1,3,7,6,5]=>[5,6,7,3,1,2,4]=>101000=>000101
[4,2,1,5,3,6,7]=>[7,6,3,5,1,2,4]=>101001=>100101
[4,2,1,5,3,7,6]=>[6,7,3,5,1,2,4]=>101000=>000101
[4,2,1,5,6,3,7]=>[7,3,6,5,1,2,4]=>101010=>010101
[4,2,1,5,6,7,3]=>[3,7,6,5,1,2,4]=>100011=>110001
[4,2,1,5,7,3,6]=>[6,3,7,5,1,2,4]=>101010=>010101
[4,2,1,5,7,6,3]=>[3,6,7,5,1,2,4]=>100010=>010001
[4,2,1,6,3,5,7]=>[7,5,3,6,1,2,4]=>101010=>010101
[4,2,1,6,3,7,5]=>[5,7,3,6,1,2,4]=>101000=>000101
[4,2,1,6,5,3,7]=>[7,3,5,6,1,2,4]=>101000=>000101
[4,2,1,6,5,7,3]=>[3,7,5,6,1,2,4]=>100010=>010001
[4,2,1,6,7,3,5]=>[5,3,7,6,1,2,4]=>101001=>100101
[4,2,1,6,7,5,3]=>[3,5,7,6,1,2,4]=>100001=>100001
[4,2,1,7,3,5,6]=>[6,5,3,7,1,2,4]=>101010=>010101
[4,2,1,7,3,6,5]=>[5,6,3,7,1,2,4]=>101000=>000101
[4,2,1,7,5,3,6]=>[6,3,5,7,1,2,4]=>101000=>000101
[4,2,1,7,5,6,3]=>[3,6,5,7,1,2,4]=>100010=>010001
[4,2,1,7,6,3,5]=>[5,3,6,7,1,2,4]=>101000=>000101
[4,2,1,7,6,5,3]=>[3,5,6,7,1,2,4]=>100000=>000001
[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>110011=>110011
[4,2,3,1,5,7,6]=>[6,7,5,1,3,2,4]=>110010=>010011
[4,2,3,1,6,5,7]=>[7,5,6,1,3,2,4]=>110010=>010011
[4,2,3,1,6,7,5]=>[5,7,6,1,3,2,4]=>110001=>100011
[4,2,3,1,7,5,6]=>[6,5,7,1,3,2,4]=>110010=>010011
[4,2,3,1,7,6,5]=>[5,6,7,1,3,2,4]=>110000=>000011
[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>111001=>100111
[4,2,3,5,1,7,6]=>[6,7,1,5,3,2,4]=>111000=>000111
[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>111010=>010111
[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>011011=>110110
[4,2,3,5,7,1,6]=>[6,1,7,5,3,2,4]=>111010=>010111
[4,2,3,5,7,6,1]=>[1,6,7,5,3,2,4]=>011010=>010110
[4,2,3,6,1,5,7]=>[7,5,1,6,3,2,4]=>111010=>010111
[4,2,3,6,1,7,5]=>[5,7,1,6,3,2,4]=>111000=>000111
[4,2,3,6,5,1,7]=>[7,1,5,6,3,2,4]=>111000=>000111
[4,2,3,6,5,7,1]=>[1,7,5,6,3,2,4]=>011010=>010110
[4,2,3,6,7,1,5]=>[5,1,7,6,3,2,4]=>111001=>100111
[4,2,3,6,7,5,1]=>[1,5,7,6,3,2,4]=>011001=>100110
[4,2,3,7,1,5,6]=>[6,5,1,7,3,2,4]=>111010=>010111
[4,2,3,7,1,6,5]=>[5,6,1,7,3,2,4]=>111000=>000111
[4,2,3,7,5,1,6]=>[6,1,5,7,3,2,4]=>111000=>000111
[4,2,3,7,5,6,1]=>[1,6,5,7,3,2,4]=>011010=>010110
[4,2,3,7,6,1,5]=>[5,1,6,7,3,2,4]=>111000=>000111
[4,2,3,7,6,5,1]=>[1,5,6,7,3,2,4]=>011000=>000110
[4,2,5,1,3,6,7]=>[7,6,3,1,5,2,4]=>111001=>100111
[4,2,5,1,3,7,6]=>[6,7,3,1,5,2,4]=>111000=>000111
[4,2,5,1,6,3,7]=>[7,3,6,1,5,2,4]=>111000=>000111
[4,2,5,1,6,7,3]=>[3,7,6,1,5,2,4]=>110001=>100011
[4,2,5,1,7,3,6]=>[6,3,7,1,5,2,4]=>111000=>000111
[4,2,5,1,7,6,3]=>[3,6,7,1,5,2,4]=>110000=>000011
[4,2,5,3,1,6,7]=>[7,6,1,3,5,2,4]=>110001=>100011
[4,2,5,3,1,7,6]=>[6,7,1,3,5,2,4]=>110000=>000011
[4,2,5,3,6,1,7]=>[7,1,6,3,5,2,4]=>111000=>000111
[4,2,5,3,6,7,1]=>[1,7,6,3,5,2,4]=>011001=>100110
[4,2,5,3,7,1,6]=>[6,1,7,3,5,2,4]=>111000=>000111
[4,2,5,3,7,6,1]=>[1,6,7,3,5,2,4]=>011000=>000110
[4,2,5,6,1,3,7]=>[7,3,1,6,5,2,4]=>111010=>010111
[4,2,5,6,1,7,3]=>[3,7,1,6,5,2,4]=>110010=>010011
[4,2,5,6,3,1,7]=>[7,1,3,6,5,2,4]=>110010=>010011
[4,2,5,6,3,7,1]=>[1,7,3,6,5,2,4]=>011010=>010110
[4,2,5,6,7,1,3]=>[3,1,7,6,5,2,4]=>110011=>110011
[4,2,5,6,7,3,1]=>[1,3,7,6,5,2,4]=>010011=>110010
[4,2,5,7,1,3,6]=>[6,3,1,7,5,2,4]=>111010=>010111
[4,2,5,7,1,6,3]=>[3,6,1,7,5,2,4]=>110010=>010011
[4,2,5,7,3,1,6]=>[6,1,3,7,5,2,4]=>110010=>010011
[4,2,5,7,3,6,1]=>[1,6,3,7,5,2,4]=>011010=>010110
[4,2,5,7,6,1,3]=>[3,1,6,7,5,2,4]=>110010=>010011
[4,2,5,7,6,3,1]=>[1,3,6,7,5,2,4]=>010010=>010010
[4,2,6,1,3,5,7]=>[7,5,3,1,6,2,4]=>111010=>010111
[4,2,6,1,3,7,5]=>[5,7,3,1,6,2,4]=>111000=>000111
[4,2,6,1,5,3,7]=>[7,3,5,1,6,2,4]=>111000=>000111
[4,2,6,1,5,7,3]=>[3,7,5,1,6,2,4]=>110010=>010011
[4,2,6,1,7,3,5]=>[5,3,7,1,6,2,4]=>111000=>000111
[4,2,6,1,7,5,3]=>[3,5,7,1,6,2,4]=>110000=>000011
[4,2,6,3,1,5,7]=>[7,5,1,3,6,2,4]=>110010=>010011
[4,2,6,3,1,7,5]=>[5,7,1,3,6,2,4]=>110000=>000011
[4,2,6,3,5,1,7]=>[7,1,5,3,6,2,4]=>111000=>000111
[4,2,6,3,5,7,1]=>[1,7,5,3,6,2,4]=>011010=>010110
[4,2,6,3,7,1,5]=>[5,1,7,3,6,2,4]=>111000=>000111
[4,2,6,3,7,5,1]=>[1,5,7,3,6,2,4]=>011000=>000110
[4,2,6,5,1,3,7]=>[7,3,1,5,6,2,4]=>111000=>000111
[4,2,6,5,1,7,3]=>[3,7,1,5,6,2,4]=>110000=>000011
[4,2,6,5,3,1,7]=>[7,1,3,5,6,2,4]=>110000=>000011
[4,2,6,5,3,7,1]=>[1,7,3,5,6,2,4]=>011000=>000110
[4,2,6,5,7,1,3]=>[3,1,7,5,6,2,4]=>110010=>010011
[4,2,6,5,7,3,1]=>[1,3,7,5,6,2,4]=>010010=>010010
[4,2,6,7,1,3,5]=>[5,3,1,7,6,2,4]=>111001=>100111
[4,2,6,7,1,5,3]=>[3,5,1,7,6,2,4]=>110001=>100011
[4,2,6,7,3,1,5]=>[5,1,3,7,6,2,4]=>110001=>100011
[4,2,6,7,3,5,1]=>[1,5,3,7,6,2,4]=>011001=>100110
[4,2,6,7,5,1,3]=>[3,1,5,7,6,2,4]=>110001=>100011
[4,2,6,7,5,3,1]=>[1,3,5,7,6,2,4]=>010001=>100010
[4,2,7,1,3,5,6]=>[6,5,3,1,7,2,4]=>111010=>010111
[4,2,7,1,3,6,5]=>[5,6,3,1,7,2,4]=>111000=>000111
[4,2,7,1,5,3,6]=>[6,3,5,1,7,2,4]=>111000=>000111
[4,2,7,1,5,6,3]=>[3,6,5,1,7,2,4]=>110010=>010011
[4,2,7,1,6,3,5]=>[5,3,6,1,7,2,4]=>111000=>000111
[4,2,7,1,6,5,3]=>[3,5,6,1,7,2,4]=>110000=>000011
[4,2,7,3,1,5,6]=>[6,5,1,3,7,2,4]=>110010=>010011
[4,2,7,3,1,6,5]=>[5,6,1,3,7,2,4]=>110000=>000011
[4,2,7,3,5,1,6]=>[6,1,5,3,7,2,4]=>111000=>000111
[4,2,7,3,5,6,1]=>[1,6,5,3,7,2,4]=>011010=>010110
[4,2,7,3,6,1,5]=>[5,1,6,3,7,2,4]=>111000=>000111
[4,2,7,3,6,5,1]=>[1,5,6,3,7,2,4]=>011000=>000110
[4,2,7,5,1,3,6]=>[6,3,1,5,7,2,4]=>111000=>000111
[4,2,7,5,1,6,3]=>[3,6,1,5,7,2,4]=>110000=>000011
[4,2,7,5,3,1,6]=>[6,1,3,5,7,2,4]=>110000=>000011
[4,2,7,5,3,6,1]=>[1,6,3,5,7,2,4]=>011000=>000110
[4,2,7,5,6,1,3]=>[3,1,6,5,7,2,4]=>110010=>010011
[4,2,7,5,6,3,1]=>[1,3,6,5,7,2,4]=>010010=>010010
[4,2,7,6,1,3,5]=>[5,3,1,6,7,2,4]=>111000=>000111
[4,2,7,6,1,5,3]=>[3,5,1,6,7,2,4]=>110000=>000011
[4,2,7,6,3,1,5]=>[5,1,3,6,7,2,4]=>110000=>000011
[4,2,7,6,3,5,1]=>[1,5,3,6,7,2,4]=>011000=>000110
[4,2,7,6,5,1,3]=>[3,1,5,6,7,2,4]=>110000=>000011
[4,2,7,6,5,3,1]=>[1,3,5,6,7,2,4]=>010000=>000010
[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>110011=>110011
[4,3,1,2,5,7,6]=>[6,7,5,2,1,3,4]=>110010=>010011
[4,3,1,2,6,5,7]=>[7,5,6,2,1,3,4]=>110010=>010011
[4,3,1,2,6,7,5]=>[5,7,6,2,1,3,4]=>110001=>100011
[4,3,1,2,7,5,6]=>[6,5,7,2,1,3,4]=>110010=>010011
[4,3,1,2,7,6,5]=>[5,6,7,2,1,3,4]=>110000=>000011
[4,3,1,5,2,6,7]=>[7,6,2,5,1,3,4]=>110001=>100011
[4,3,1,5,2,7,6]=>[6,7,2,5,1,3,4]=>110000=>000011
[4,3,1,5,6,2,7]=>[7,2,6,5,1,3,4]=>110010=>010011
[4,3,1,5,6,7,2]=>[2,7,6,5,1,3,4]=>100011=>110001
[4,3,1,5,7,2,6]=>[6,2,7,5,1,3,4]=>110010=>010011
[4,3,1,5,7,6,2]=>[2,6,7,5,1,3,4]=>100010=>010001
[4,3,1,6,2,5,7]=>[7,5,2,6,1,3,4]=>110010=>010011
[4,3,1,6,2,7,5]=>[5,7,2,6,1,3,4]=>110000=>000011
[4,3,1,6,5,2,7]=>[7,2,5,6,1,3,4]=>110000=>000011
[4,3,1,6,5,7,2]=>[2,7,5,6,1,3,4]=>100010=>010001
[4,3,1,6,7,2,5]=>[5,2,7,6,1,3,4]=>110001=>100011
[4,3,1,6,7,5,2]=>[2,5,7,6,1,3,4]=>100001=>100001
[4,3,1,7,2,5,6]=>[6,5,2,7,1,3,4]=>110010=>010011
[4,3,1,7,2,6,5]=>[5,6,2,7,1,3,4]=>110000=>000011
[4,3,1,7,5,2,6]=>[6,2,5,7,1,3,4]=>110000=>000011
[4,3,1,7,5,6,2]=>[2,6,5,7,1,3,4]=>100010=>010001
[4,3,1,7,6,2,5]=>[5,2,6,7,1,3,4]=>110000=>000011
[4,3,1,7,6,5,2]=>[2,5,6,7,1,3,4]=>100000=>000001
[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>100011=>110001
[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>100010=>010001
[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>100010=>010001
[4,3,2,1,6,7,5]=>[5,7,6,1,2,3,4]=>100001=>100001
[4,3,2,1,7,5,6]=>[6,5,7,1,2,3,4]=>100010=>010001
[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>100000=>000001
[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>110001=>100011
[4,3,2,5,1,7,6]=>[6,7,1,5,2,3,4]=>110000=>000011
[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>110010=>010011
[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>010011=>110010
[4,3,2,5,7,1,6]=>[6,1,7,5,2,3,4]=>110010=>010011
[4,3,2,5,7,6,1]=>[1,6,7,5,2,3,4]=>010010=>010010
[4,3,2,6,1,5,7]=>[7,5,1,6,2,3,4]=>110010=>010011
[4,3,2,6,1,7,5]=>[5,7,1,6,2,3,4]=>110000=>000011
[4,3,2,6,5,1,7]=>[7,1,5,6,2,3,4]=>110000=>000011
[4,3,2,6,5,7,1]=>[1,7,5,6,2,3,4]=>010010=>010010
[4,3,2,6,7,1,5]=>[5,1,7,6,2,3,4]=>110001=>100011
[4,3,2,6,7,5,1]=>[1,5,7,6,2,3,4]=>010001=>100010
[4,3,2,7,1,5,6]=>[6,5,1,7,2,3,4]=>110010=>010011
[4,3,2,7,1,6,5]=>[5,6,1,7,2,3,4]=>110000=>000011
[4,3,2,7,5,1,6]=>[6,1,5,7,2,3,4]=>110000=>000011
[4,3,2,7,5,6,1]=>[1,6,5,7,2,3,4]=>010010=>010010
[4,3,2,7,6,1,5]=>[5,1,6,7,2,3,4]=>110000=>000011
[4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4]=>010000=>000010
[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>111001=>100111
[4,3,5,1,2,7,6]=>[6,7,2,1,5,3,4]=>111000=>000111
[4,3,5,1,6,2,7]=>[7,2,6,1,5,3,4]=>111000=>000111
[4,3,5,1,6,7,2]=>[2,7,6,1,5,3,4]=>101001=>100101
[4,3,5,1,7,2,6]=>[6,2,7,1,5,3,4]=>111000=>000111
[4,3,5,1,7,6,2]=>[2,6,7,1,5,3,4]=>101000=>000101
[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>101001=>100101
[4,3,5,2,1,7,6]=>[6,7,1,2,5,3,4]=>101000=>000101
[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>111000=>000111
[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>011001=>100110
[4,3,5,2,7,1,6]=>[6,1,7,2,5,3,4]=>111000=>000111
[4,3,5,2,7,6,1]=>[1,6,7,2,5,3,4]=>011000=>000110
[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>111010=>010111
[4,3,5,6,1,7,2]=>[2,7,1,6,5,3,4]=>101010=>010101
[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>101010=>010101
[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>011010=>010110
[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>101011=>110101
[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>001011=>110100
[4,3,5,7,1,2,6]=>[6,2,1,7,5,3,4]=>111010=>010111
[4,3,5,7,1,6,2]=>[2,6,1,7,5,3,4]=>101010=>010101
[4,3,5,7,2,1,6]=>[6,1,2,7,5,3,4]=>101010=>010101
[4,3,5,7,2,6,1]=>[1,6,2,7,5,3,4]=>011010=>010110
[4,3,5,7,6,1,2]=>[2,1,6,7,5,3,4]=>101010=>010101
[4,3,5,7,6,2,1]=>[1,2,6,7,5,3,4]=>001010=>010100
[4,3,6,1,2,5,7]=>[7,5,2,1,6,3,4]=>111010=>010111
[4,3,6,1,2,7,5]=>[5,7,2,1,6,3,4]=>111000=>000111
[4,3,6,1,5,2,7]=>[7,2,5,1,6,3,4]=>111000=>000111
[4,3,6,1,5,7,2]=>[2,7,5,1,6,3,4]=>101010=>010101
[4,3,6,1,7,2,5]=>[5,2,7,1,6,3,4]=>111000=>000111
[4,3,6,1,7,5,2]=>[2,5,7,1,6,3,4]=>101000=>000101
[4,3,6,2,1,5,7]=>[7,5,1,2,6,3,4]=>101010=>010101
[4,3,6,2,1,7,5]=>[5,7,1,2,6,3,4]=>101000=>000101
[4,3,6,2,5,1,7]=>[7,1,5,2,6,3,4]=>111000=>000111
[4,3,6,2,5,7,1]=>[1,7,5,2,6,3,4]=>011010=>010110
[4,3,6,2,7,1,5]=>[5,1,7,2,6,3,4]=>111000=>000111
[4,3,6,2,7,5,1]=>[1,5,7,2,6,3,4]=>011000=>000110
[4,3,6,5,1,2,7]=>[7,2,1,5,6,3,4]=>111000=>000111
[4,3,6,5,1,7,2]=>[2,7,1,5,6,3,4]=>101000=>000101
[4,3,6,5,2,1,7]=>[7,1,2,5,6,3,4]=>101000=>000101
[4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4]=>011000=>000110
[4,3,6,5,7,1,2]=>[2,1,7,5,6,3,4]=>101010=>010101
[4,3,6,5,7,2,1]=>[1,2,7,5,6,3,4]=>001010=>010100
[4,3,6,7,1,2,5]=>[5,2,1,7,6,3,4]=>111001=>100111
[4,3,6,7,1,5,2]=>[2,5,1,7,6,3,4]=>101001=>100101
[4,3,6,7,2,1,5]=>[5,1,2,7,6,3,4]=>101001=>100101
[4,3,6,7,2,5,1]=>[1,5,2,7,6,3,4]=>011001=>100110
[4,3,6,7,5,1,2]=>[2,1,5,7,6,3,4]=>101001=>100101
[4,3,6,7,5,2,1]=>[1,2,5,7,6,3,4]=>001001=>100100
[4,3,7,1,2,5,6]=>[6,5,2,1,7,3,4]=>111010=>010111
[4,3,7,1,2,6,5]=>[5,6,2,1,7,3,4]=>111000=>000111
[4,3,7,1,5,2,6]=>[6,2,5,1,7,3,4]=>111000=>000111
[4,3,7,1,5,6,2]=>[2,6,5,1,7,3,4]=>101010=>010101
[4,3,7,1,6,2,5]=>[5,2,6,1,7,3,4]=>111000=>000111
[4,3,7,1,6,5,2]=>[2,5,6,1,7,3,4]=>101000=>000101
[4,3,7,2,1,5,6]=>[6,5,1,2,7,3,4]=>101010=>010101
[4,3,7,2,1,6,5]=>[5,6,1,2,7,3,4]=>101000=>000101
[4,3,7,2,5,1,6]=>[6,1,5,2,7,3,4]=>111000=>000111
[4,3,7,2,5,6,1]=>[1,6,5,2,7,3,4]=>011010=>010110
[4,3,7,2,6,1,5]=>[5,1,6,2,7,3,4]=>111000=>000111
[4,3,7,2,6,5,1]=>[1,5,6,2,7,3,4]=>011000=>000110
[4,3,7,5,1,2,6]=>[6,2,1,5,7,3,4]=>111000=>000111
[4,3,7,5,1,6,2]=>[2,6,1,5,7,3,4]=>101000=>000101
[4,3,7,5,2,1,6]=>[6,1,2,5,7,3,4]=>101000=>000101
[4,3,7,5,2,6,1]=>[1,6,2,5,7,3,4]=>011000=>000110
[4,3,7,5,6,1,2]=>[2,1,6,5,7,3,4]=>101010=>010101
[4,3,7,5,6,2,1]=>[1,2,6,5,7,3,4]=>001010=>010100
[4,3,7,6,1,2,5]=>[5,2,1,6,7,3,4]=>111000=>000111
[4,3,7,6,1,5,2]=>[2,5,1,6,7,3,4]=>101000=>000101
[4,3,7,6,2,1,5]=>[5,1,2,6,7,3,4]=>101000=>000101
[4,3,7,6,2,5,1]=>[1,5,2,6,7,3,4]=>011000=>000110
[4,3,7,6,5,1,2]=>[2,1,5,6,7,3,4]=>101000=>000101
[4,3,7,6,5,2,1]=>[1,2,5,6,7,3,4]=>001000=>000100
[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>111101=>101111
[4,5,1,2,3,7,6]=>[6,7,3,2,1,5,4]=>111100=>001111
[4,5,1,2,6,3,7]=>[7,3,6,2,1,5,4]=>111100=>001111
[4,5,1,2,6,7,3]=>[3,7,6,2,1,5,4]=>110101=>101011
[4,5,1,2,7,3,6]=>[6,3,7,2,1,5,4]=>111100=>001111
[4,5,1,2,7,6,3]=>[3,6,7,2,1,5,4]=>110100=>001011
[4,5,1,3,2,6,7]=>[7,6,2,3,1,5,4]=>110101=>101011
[4,5,1,3,2,7,6]=>[6,7,2,3,1,5,4]=>110100=>001011
[4,5,1,3,6,2,7]=>[7,2,6,3,1,5,4]=>111100=>001111
[4,5,1,3,6,7,2]=>[2,7,6,3,1,5,4]=>101101=>101101
[4,5,1,3,7,2,6]=>[6,2,7,3,1,5,4]=>111100=>001111
[4,5,1,3,7,6,2]=>[2,6,7,3,1,5,4]=>101100=>001101
[4,5,1,6,2,3,7]=>[7,3,2,6,1,5,4]=>111100=>001111
[4,5,1,6,2,7,3]=>[3,7,2,6,1,5,4]=>110100=>001011
[4,5,1,6,3,2,7]=>[7,2,3,6,1,5,4]=>110100=>001011
[4,5,1,6,3,7,2]=>[2,7,3,6,1,5,4]=>101100=>001101
[4,5,1,6,7,2,3]=>[3,2,7,6,1,5,4]=>110101=>101011
[4,5,1,6,7,3,2]=>[2,3,7,6,1,5,4]=>100101=>101001
[4,5,1,7,2,3,6]=>[6,3,2,7,1,5,4]=>111100=>001111
[4,5,1,7,2,6,3]=>[3,6,2,7,1,5,4]=>110100=>001011
[4,5,1,7,3,2,6]=>[6,2,3,7,1,5,4]=>110100=>001011
[4,5,1,7,3,6,2]=>[2,6,3,7,1,5,4]=>101100=>001101
[4,5,1,7,6,2,3]=>[3,2,6,7,1,5,4]=>110100=>001011
[4,5,1,7,6,3,2]=>[2,3,6,7,1,5,4]=>100100=>001001
[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>101101=>101101
[4,5,2,1,3,7,6]=>[6,7,3,1,2,5,4]=>101100=>001101
[4,5,2,1,6,3,7]=>[7,3,6,1,2,5,4]=>101100=>001101
[4,5,2,1,6,7,3]=>[3,7,6,1,2,5,4]=>100101=>101001
[4,5,2,1,7,3,6]=>[6,3,7,1,2,5,4]=>101100=>001101
[4,5,2,1,7,6,3]=>[3,6,7,1,2,5,4]=>100100=>001001
[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>110101=>101011
[4,5,2,3,1,7,6]=>[6,7,1,3,2,5,4]=>110100=>001011
[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>111100=>001111
[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>011101=>101110
[4,5,2,3,7,1,6]=>[6,1,7,3,2,5,4]=>111100=>001111
[4,5,2,3,7,6,1]=>[1,6,7,3,2,5,4]=>011100=>001110
[4,5,2,6,1,3,7]=>[7,3,1,6,2,5,4]=>111100=>001111
[4,5,2,6,1,7,3]=>[3,7,1,6,2,5,4]=>110100=>001011
[4,5,2,6,3,1,7]=>[7,1,3,6,2,5,4]=>110100=>001011
[4,5,2,6,3,7,1]=>[1,7,3,6,2,5,4]=>011100=>001110
[4,5,2,6,7,1,3]=>[3,1,7,6,2,5,4]=>110101=>101011
[4,5,2,6,7,3,1]=>[1,3,7,6,2,5,4]=>010101=>101010
[4,5,2,7,1,3,6]=>[6,3,1,7,2,5,4]=>111100=>001111
[4,5,2,7,1,6,3]=>[3,6,1,7,2,5,4]=>110100=>001011
[4,5,2,7,3,1,6]=>[6,1,3,7,2,5,4]=>110100=>001011
[4,5,2,7,3,6,1]=>[1,6,3,7,2,5,4]=>011100=>001110
[4,5,2,7,6,1,3]=>[3,1,6,7,2,5,4]=>110100=>001011
[4,5,2,7,6,3,1]=>[1,3,6,7,2,5,4]=>010100=>001010
[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>110101=>101011
[4,5,3,1,2,7,6]=>[6,7,2,1,3,5,4]=>110100=>001011
[4,5,3,1,6,2,7]=>[7,2,6,1,3,5,4]=>110100=>001011
[4,5,3,1,6,7,2]=>[2,7,6,1,3,5,4]=>100101=>101001
[4,5,3,1,7,2,6]=>[6,2,7,1,3,5,4]=>110100=>001011
[4,5,3,1,7,6,2]=>[2,6,7,1,3,5,4]=>100100=>001001
[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>100101=>101001
[4,5,3,2,1,7,6]=>[6,7,1,2,3,5,4]=>100100=>001001
[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>110100=>001011
[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>010101=>101010
[4,5,3,2,7,1,6]=>[6,1,7,2,3,5,4]=>110100=>001011
[4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4]=>010100=>001010
[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>111100=>001111
[4,5,3,6,1,7,2]=>[2,7,1,6,3,5,4]=>101100=>001101
[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>101100=>001101
[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>011100=>001110
[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>101101=>101101
[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>001101=>101100
[4,5,3,7,1,2,6]=>[6,2,1,7,3,5,4]=>111100=>001111
[4,5,3,7,1,6,2]=>[2,6,1,7,3,5,4]=>101100=>001101
[4,5,3,7,2,1,6]=>[6,1,2,7,3,5,4]=>101100=>001101
[4,5,3,7,2,6,1]=>[1,6,2,7,3,5,4]=>011100=>001110
[4,5,3,7,6,1,2]=>[2,1,6,7,3,5,4]=>101100=>001101
[4,5,3,7,6,2,1]=>[1,2,6,7,3,5,4]=>001100=>001100
[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>111110=>011111
[4,5,6,1,2,7,3]=>[3,7,2,1,6,5,4]=>110110=>011011
[4,5,6,1,3,2,7]=>[7,2,3,1,6,5,4]=>110110=>011011
[4,5,6,1,3,7,2]=>[2,7,3,1,6,5,4]=>101110=>011101
[4,5,6,1,7,2,3]=>[3,2,7,1,6,5,4]=>110110=>011011
[4,5,6,1,7,3,2]=>[2,3,7,1,6,5,4]=>100110=>011001
[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>101110=>011101
[4,5,6,2,1,7,3]=>[3,7,1,2,6,5,4]=>100110=>011001
[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>110110=>011011
[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>011110=>011110
[4,5,6,2,7,1,3]=>[3,1,7,2,6,5,4]=>110110=>011011
[4,5,6,2,7,3,1]=>[1,3,7,2,6,5,4]=>010110=>011010
[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>110110=>011011
[4,5,6,3,1,7,2]=>[2,7,1,3,6,5,4]=>100110=>011001
[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>100110=>011001
[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>010110=>011010
[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>101110=>011101
[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>001110=>011100
[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111=>111011
[4,5,6,7,1,3,2]=>[2,3,1,7,6,5,4]=>100111=>111001
[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>100111=>111001
[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>010111=>111010
[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>100111=>111001
[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>000111=>111000
[4,5,7,1,2,3,6]=>[6,3,2,1,7,5,4]=>111110=>011111
[4,5,7,1,2,6,3]=>[3,6,2,1,7,5,4]=>110110=>011011
[4,5,7,1,3,2,6]=>[6,2,3,1,7,5,4]=>110110=>011011
[4,5,7,1,3,6,2]=>[2,6,3,1,7,5,4]=>101110=>011101
[4,5,7,1,6,2,3]=>[3,2,6,1,7,5,4]=>110110=>011011
[4,5,7,1,6,3,2]=>[2,3,6,1,7,5,4]=>100110=>011001
[4,5,7,2,1,3,6]=>[6,3,1,2,7,5,4]=>101110=>011101
[4,5,7,2,1,6,3]=>[3,6,1,2,7,5,4]=>100110=>011001
[4,5,7,2,3,1,6]=>[6,1,3,2,7,5,4]=>110110=>011011
[4,5,7,2,3,6,1]=>[1,6,3,2,7,5,4]=>011110=>011110
[4,5,7,2,6,1,3]=>[3,1,6,2,7,5,4]=>110110=>011011
[4,5,7,2,6,3,1]=>[1,3,6,2,7,5,4]=>010110=>011010
[4,5,7,3,1,2,6]=>[6,2,1,3,7,5,4]=>110110=>011011
[4,5,7,3,1,6,2]=>[2,6,1,3,7,5,4]=>100110=>011001
[4,5,7,3,2,1,6]=>[6,1,2,3,7,5,4]=>100110=>011001
[4,5,7,3,2,6,1]=>[1,6,2,3,7,5,4]=>010110=>011010
[4,5,7,3,6,1,2]=>[2,1,6,3,7,5,4]=>101110=>011101
[4,5,7,3,6,2,1]=>[1,2,6,3,7,5,4]=>001110=>011100
[4,5,7,6,1,2,3]=>[3,2,1,6,7,5,4]=>110110=>011011
[4,5,7,6,1,3,2]=>[2,3,1,6,7,5,4]=>100110=>011001
[4,5,7,6,2,1,3]=>[3,1,2,6,7,5,4]=>100110=>011001
[4,5,7,6,2,3,1]=>[1,3,2,6,7,5,4]=>010110=>011010
[4,5,7,6,3,1,2]=>[2,1,3,6,7,5,4]=>100110=>011001
[4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4]=>000110=>011000
[4,6,1,2,3,5,7]=>[7,5,3,2,1,6,4]=>111110=>011111
[4,6,1,2,3,7,5]=>[5,7,3,2,1,6,4]=>111100=>001111
[4,6,1,2,5,3,7]=>[7,3,5,2,1,6,4]=>111100=>001111
[4,6,1,2,5,7,3]=>[3,7,5,2,1,6,4]=>110110=>011011
[4,6,1,2,7,3,5]=>[5,3,7,2,1,6,4]=>111100=>001111
[4,6,1,2,7,5,3]=>[3,5,7,2,1,6,4]=>110100=>001011
[4,6,1,3,2,5,7]=>[7,5,2,3,1,6,4]=>110110=>011011
[4,6,1,3,2,7,5]=>[5,7,2,3,1,6,4]=>110100=>001011
[4,6,1,3,5,2,7]=>[7,2,5,3,1,6,4]=>111100=>001111
[4,6,1,3,5,7,2]=>[2,7,5,3,1,6,4]=>101110=>011101
[4,6,1,3,7,2,5]=>[5,2,7,3,1,6,4]=>111100=>001111
[4,6,1,3,7,5,2]=>[2,5,7,3,1,6,4]=>101100=>001101
[4,6,1,5,2,3,7]=>[7,3,2,5,1,6,4]=>111100=>001111
[4,6,1,5,2,7,3]=>[3,7,2,5,1,6,4]=>110100=>001011
[4,6,1,5,3,2,7]=>[7,2,3,5,1,6,4]=>110100=>001011
[4,6,1,5,3,7,2]=>[2,7,3,5,1,6,4]=>101100=>001101
[4,6,1,5,7,2,3]=>[3,2,7,5,1,6,4]=>110110=>011011
[4,6,1,5,7,3,2]=>[2,3,7,5,1,6,4]=>100110=>011001
[4,6,1,7,2,3,5]=>[5,3,2,7,1,6,4]=>111100=>001111
[4,6,1,7,2,5,3]=>[3,5,2,7,1,6,4]=>110100=>001011
[4,6,1,7,3,2,5]=>[5,2,3,7,1,6,4]=>110100=>001011
[4,6,1,7,3,5,2]=>[2,5,3,7,1,6,4]=>101100=>001101
[4,6,1,7,5,2,3]=>[3,2,5,7,1,6,4]=>110100=>001011
[4,6,1,7,5,3,2]=>[2,3,5,7,1,6,4]=>100100=>001001
[4,6,2,1,3,5,7]=>[7,5,3,1,2,6,4]=>101110=>011101
[4,6,2,1,3,7,5]=>[5,7,3,1,2,6,4]=>101100=>001101
[4,6,2,1,5,3,7]=>[7,3,5,1,2,6,4]=>101100=>001101
[4,6,2,1,5,7,3]=>[3,7,5,1,2,6,4]=>100110=>011001
[4,6,2,1,7,3,5]=>[5,3,7,1,2,6,4]=>101100=>001101
[4,6,2,1,7,5,3]=>[3,5,7,1,2,6,4]=>100100=>001001
[4,6,2,3,1,5,7]=>[7,5,1,3,2,6,4]=>110110=>011011
[4,6,2,3,1,7,5]=>[5,7,1,3,2,6,4]=>110100=>001011
[4,6,2,3,5,1,7]=>[7,1,5,3,2,6,4]=>111100=>001111
[4,6,2,3,5,7,1]=>[1,7,5,3,2,6,4]=>011110=>011110
[4,6,2,3,7,1,5]=>[5,1,7,3,2,6,4]=>111100=>001111
[4,6,2,3,7,5,1]=>[1,5,7,3,2,6,4]=>011100=>001110
[4,6,2,5,1,3,7]=>[7,3,1,5,2,6,4]=>111100=>001111
[4,6,2,5,1,7,3]=>[3,7,1,5,2,6,4]=>110100=>001011
[4,6,2,5,3,1,7]=>[7,1,3,5,2,6,4]=>110100=>001011
[4,6,2,5,3,7,1]=>[1,7,3,5,2,6,4]=>011100=>001110
[4,6,2,5,7,1,3]=>[3,1,7,5,2,6,4]=>110110=>011011
[4,6,2,5,7,3,1]=>[1,3,7,5,2,6,4]=>010110=>011010
[4,6,2,7,1,3,5]=>[5,3,1,7,2,6,4]=>111100=>001111
[4,6,2,7,1,5,3]=>[3,5,1,7,2,6,4]=>110100=>001011
[4,6,2,7,3,1,5]=>[5,1,3,7,2,6,4]=>110100=>001011
[4,6,2,7,3,5,1]=>[1,5,3,7,2,6,4]=>011100=>001110
[4,6,2,7,5,1,3]=>[3,1,5,7,2,6,4]=>110100=>001011
[4,6,2,7,5,3,1]=>[1,3,5,7,2,6,4]=>010100=>001010
[4,6,3,1,2,5,7]=>[7,5,2,1,3,6,4]=>110110=>011011
[4,6,3,1,2,7,5]=>[5,7,2,1,3,6,4]=>110100=>001011
[4,6,3,1,5,2,7]=>[7,2,5,1,3,6,4]=>110100=>001011
[4,6,3,1,5,7,2]=>[2,7,5,1,3,6,4]=>100110=>011001
[4,6,3,1,7,2,5]=>[5,2,7,1,3,6,4]=>110100=>001011
[4,6,3,1,7,5,2]=>[2,5,7,1,3,6,4]=>100100=>001001
[4,6,3,2,1,5,7]=>[7,5,1,2,3,6,4]=>100110=>011001
[4,6,3,2,1,7,5]=>[5,7,1,2,3,6,4]=>100100=>001001
[4,6,3,2,5,1,7]=>[7,1,5,2,3,6,4]=>110100=>001011
[4,6,3,2,5,7,1]=>[1,7,5,2,3,6,4]=>010110=>011010
[4,6,3,2,7,1,5]=>[5,1,7,2,3,6,4]=>110100=>001011
[4,6,3,2,7,5,1]=>[1,5,7,2,3,6,4]=>010100=>001010
[4,6,3,5,1,2,7]=>[7,2,1,5,3,6,4]=>111100=>001111
[4,6,3,5,1,7,2]=>[2,7,1,5,3,6,4]=>101100=>001101
[4,6,3,5,2,1,7]=>[7,1,2,5,3,6,4]=>101100=>001101
[4,6,3,5,2,7,1]=>[1,7,2,5,3,6,4]=>011100=>001110
[4,6,3,5,7,1,2]=>[2,1,7,5,3,6,4]=>101110=>011101
[4,6,3,5,7,2,1]=>[1,2,7,5,3,6,4]=>001110=>011100
[4,6,3,7,1,2,5]=>[5,2,1,7,3,6,4]=>111100=>001111
[4,6,3,7,1,5,2]=>[2,5,1,7,3,6,4]=>101100=>001101
[4,6,3,7,2,1,5]=>[5,1,2,7,3,6,4]=>101100=>001101
[4,6,3,7,2,5,1]=>[1,5,2,7,3,6,4]=>011100=>001110
[4,6,3,7,5,1,2]=>[2,1,5,7,3,6,4]=>101100=>001101
[4,6,3,7,5,2,1]=>[1,2,5,7,3,6,4]=>001100=>001100
[4,6,5,1,2,3,7]=>[7,3,2,1,5,6,4]=>111100=>001111
[4,6,5,1,2,7,3]=>[3,7,2,1,5,6,4]=>110100=>001011
[4,6,5,1,3,2,7]=>[7,2,3,1,5,6,4]=>110100=>001011
[4,6,5,1,3,7,2]=>[2,7,3,1,5,6,4]=>101100=>001101
[4,6,5,1,7,2,3]=>[3,2,7,1,5,6,4]=>110100=>001011
[4,6,5,1,7,3,2]=>[2,3,7,1,5,6,4]=>100100=>001001
[4,6,5,2,1,3,7]=>[7,3,1,2,5,6,4]=>101100=>001101
[4,6,5,2,1,7,3]=>[3,7,1,2,5,6,4]=>100100=>001001
[4,6,5,2,3,1,7]=>[7,1,3,2,5,6,4]=>110100=>001011
[4,6,5,2,3,7,1]=>[1,7,3,2,5,6,4]=>011100=>001110
[4,6,5,2,7,1,3]=>[3,1,7,2,5,6,4]=>110100=>001011
[4,6,5,2,7,3,1]=>[1,3,7,2,5,6,4]=>010100=>001010
[4,6,5,3,1,2,7]=>[7,2,1,3,5,6,4]=>110100=>001011
[4,6,5,3,1,7,2]=>[2,7,1,3,5,6,4]=>100100=>001001
[4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4]=>100100=>001001
[4,6,5,3,2,7,1]=>[1,7,2,3,5,6,4]=>010100=>001010
[4,6,5,3,7,1,2]=>[2,1,7,3,5,6,4]=>101100=>001101
[4,6,5,3,7,2,1]=>[1,2,7,3,5,6,4]=>001100=>001100
[4,6,5,7,1,2,3]=>[3,2,1,7,5,6,4]=>110110=>011011
[4,6,5,7,1,3,2]=>[2,3,1,7,5,6,4]=>100110=>011001
[4,6,5,7,2,1,3]=>[3,1,2,7,5,6,4]=>100110=>011001
[4,6,5,7,2,3,1]=>[1,3,2,7,5,6,4]=>010110=>011010
[4,6,5,7,3,1,2]=>[2,1,3,7,5,6,4]=>100110=>011001
[4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4]=>000110=>011000
[4,6,7,1,2,3,5]=>[5,3,2,1,7,6,4]=>111101=>101111
[4,6,7,1,2,5,3]=>[3,5,2,1,7,6,4]=>110101=>101011
[4,6,7,1,3,2,5]=>[5,2,3,1,7,6,4]=>110101=>101011
[4,6,7,1,3,5,2]=>[2,5,3,1,7,6,4]=>101101=>101101
[4,6,7,1,5,2,3]=>[3,2,5,1,7,6,4]=>110101=>101011
[4,6,7,1,5,3,2]=>[2,3,5,1,7,6,4]=>100101=>101001
[4,6,7,2,1,3,5]=>[5,3,1,2,7,6,4]=>101101=>101101
[4,6,7,2,1,5,3]=>[3,5,1,2,7,6,4]=>100101=>101001
[4,6,7,2,3,1,5]=>[5,1,3,2,7,6,4]=>110101=>101011
[4,6,7,2,3,5,1]=>[1,5,3,2,7,6,4]=>011101=>101110
[4,6,7,2,5,1,3]=>[3,1,5,2,7,6,4]=>110101=>101011
[4,6,7,2,5,3,1]=>[1,3,5,2,7,6,4]=>010101=>101010
[4,6,7,3,1,2,5]=>[5,2,1,3,7,6,4]=>110101=>101011
[4,6,7,3,1,5,2]=>[2,5,1,3,7,6,4]=>100101=>101001
[4,6,7,3,2,1,5]=>[5,1,2,3,7,6,4]=>100101=>101001
[4,6,7,3,2,5,1]=>[1,5,2,3,7,6,4]=>010101=>101010
[4,6,7,3,5,1,2]=>[2,1,5,3,7,6,4]=>101101=>101101
[4,6,7,3,5,2,1]=>[1,2,5,3,7,6,4]=>001101=>101100
[4,6,7,5,1,2,3]=>[3,2,1,5,7,6,4]=>110101=>101011
[4,6,7,5,1,3,2]=>[2,3,1,5,7,6,4]=>100101=>101001
[4,6,7,5,2,1,3]=>[3,1,2,5,7,6,4]=>100101=>101001
[4,6,7,5,2,3,1]=>[1,3,2,5,7,6,4]=>010101=>101010
[4,6,7,5,3,1,2]=>[2,1,3,5,7,6,4]=>100101=>101001
[4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4]=>000101=>101000
[4,7,1,2,3,5,6]=>[6,5,3,2,1,7,4]=>111110=>011111
[4,7,1,2,3,6,5]=>[5,6,3,2,1,7,4]=>111100=>001111
[4,7,1,2,5,3,6]=>[6,3,5,2,1,7,4]=>111100=>001111
[4,7,1,2,5,6,3]=>[3,6,5,2,1,7,4]=>110110=>011011
[4,7,1,2,6,3,5]=>[5,3,6,2,1,7,4]=>111100=>001111
[4,7,1,2,6,5,3]=>[3,5,6,2,1,7,4]=>110100=>001011
[4,7,1,3,2,5,6]=>[6,5,2,3,1,7,4]=>110110=>011011
[4,7,1,3,2,6,5]=>[5,6,2,3,1,7,4]=>110100=>001011
[4,7,1,3,5,2,6]=>[6,2,5,3,1,7,4]=>111100=>001111
[4,7,1,3,5,6,2]=>[2,6,5,3,1,7,4]=>101110=>011101
[4,7,1,3,6,2,5]=>[5,2,6,3,1,7,4]=>111100=>001111
[4,7,1,3,6,5,2]=>[2,5,6,3,1,7,4]=>101100=>001101
[4,7,1,5,2,3,6]=>[6,3,2,5,1,7,4]=>111100=>001111
[4,7,1,5,2,6,3]=>[3,6,2,5,1,7,4]=>110100=>001011
[4,7,1,5,3,2,6]=>[6,2,3,5,1,7,4]=>110100=>001011
[4,7,1,5,3,6,2]=>[2,6,3,5,1,7,4]=>101100=>001101
[4,7,1,5,6,2,3]=>[3,2,6,5,1,7,4]=>110110=>011011
[4,7,1,5,6,3,2]=>[2,3,6,5,1,7,4]=>100110=>011001
[4,7,1,6,2,3,5]=>[5,3,2,6,1,7,4]=>111100=>001111
[4,7,1,6,2,5,3]=>[3,5,2,6,1,7,4]=>110100=>001011
[4,7,1,6,3,2,5]=>[5,2,3,6,1,7,4]=>110100=>001011
[4,7,1,6,3,5,2]=>[2,5,3,6,1,7,4]=>101100=>001101
[4,7,1,6,5,2,3]=>[3,2,5,6,1,7,4]=>110100=>001011
[4,7,1,6,5,3,2]=>[2,3,5,6,1,7,4]=>100100=>001001
[4,7,2,1,3,5,6]=>[6,5,3,1,2,7,4]=>101110=>011101
[4,7,2,1,3,6,5]=>[5,6,3,1,2,7,4]=>101100=>001101
[4,7,2,1,5,3,6]=>[6,3,5,1,2,7,4]=>101100=>001101
[4,7,2,1,5,6,3]=>[3,6,5,1,2,7,4]=>100110=>011001
[4,7,2,1,6,3,5]=>[5,3,6,1,2,7,4]=>101100=>001101
[4,7,2,1,6,5,3]=>[3,5,6,1,2,7,4]=>100100=>001001
[4,7,2,3,1,5,6]=>[6,5,1,3,2,7,4]=>110110=>011011
[4,7,2,3,1,6,5]=>[5,6,1,3,2,7,4]=>110100=>001011
[4,7,2,3,5,1,6]=>[6,1,5,3,2,7,4]=>111100=>001111
[4,7,2,3,5,6,1]=>[1,6,5,3,2,7,4]=>011110=>011110
[4,7,2,3,6,1,5]=>[5,1,6,3,2,7,4]=>111100=>001111
[4,7,2,3,6,5,1]=>[1,5,6,3,2,7,4]=>011100=>001110
[4,7,2,5,1,3,6]=>[6,3,1,5,2,7,4]=>111100=>001111
[4,7,2,5,1,6,3]=>[3,6,1,5,2,7,4]=>110100=>001011
[4,7,2,5,3,1,6]=>[6,1,3,5,2,7,4]=>110100=>001011
[4,7,2,5,3,6,1]=>[1,6,3,5,2,7,4]=>011100=>001110
[4,7,2,5,6,1,3]=>[3,1,6,5,2,7,4]=>110110=>011011
[4,7,2,5,6,3,1]=>[1,3,6,5,2,7,4]=>010110=>011010
[4,7,2,6,1,3,5]=>[5,3,1,6,2,7,4]=>111100=>001111
[4,7,2,6,1,5,3]=>[3,5,1,6,2,7,4]=>110100=>001011
[4,7,2,6,3,1,5]=>[5,1,3,6,2,7,4]=>110100=>001011
[4,7,2,6,3,5,1]=>[1,5,3,6,2,7,4]=>011100=>001110
[4,7,2,6,5,1,3]=>[3,1,5,6,2,7,4]=>110100=>001011
[4,7,2,6,5,3,1]=>[1,3,5,6,2,7,4]=>010100=>001010
[4,7,3,1,2,5,6]=>[6,5,2,1,3,7,4]=>110110=>011011
[4,7,3,1,2,6,5]=>[5,6,2,1,3,7,4]=>110100=>001011
[4,7,3,1,5,2,6]=>[6,2,5,1,3,7,4]=>110100=>001011
[4,7,3,1,5,6,2]=>[2,6,5,1,3,7,4]=>100110=>011001
[4,7,3,1,6,2,5]=>[5,2,6,1,3,7,4]=>110100=>001011
[4,7,3,1,6,5,2]=>[2,5,6,1,3,7,4]=>100100=>001001
[4,7,3,2,1,5,6]=>[6,5,1,2,3,7,4]=>100110=>011001
[4,7,3,2,1,6,5]=>[5,6,1,2,3,7,4]=>100100=>001001
[4,7,3,2,5,1,6]=>[6,1,5,2,3,7,4]=>110100=>001011
[4,7,3,2,5,6,1]=>[1,6,5,2,3,7,4]=>010110=>011010
[4,7,3,2,6,1,5]=>[5,1,6,2,3,7,4]=>110100=>001011
[4,7,3,2,6,5,1]=>[1,5,6,2,3,7,4]=>010100=>001010
[4,7,3,5,1,2,6]=>[6,2,1,5,3,7,4]=>111100=>001111
[4,7,3,5,1,6,2]=>[2,6,1,5,3,7,4]=>101100=>001101
[4,7,3,5,2,1,6]=>[6,1,2,5,3,7,4]=>101100=>001101
[4,7,3,5,2,6,1]=>[1,6,2,5,3,7,4]=>011100=>001110
[4,7,3,5,6,1,2]=>[2,1,6,5,3,7,4]=>101110=>011101
[4,7,3,5,6,2,1]=>[1,2,6,5,3,7,4]=>001110=>011100
[4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4]=>111100=>001111
[4,7,3,6,1,5,2]=>[2,5,1,6,3,7,4]=>101100=>001101
[4,7,3,6,2,1,5]=>[5,1,2,6,3,7,4]=>101100=>001101
[4,7,3,6,2,5,1]=>[1,5,2,6,3,7,4]=>011100=>001110
[4,7,3,6,5,1,2]=>[2,1,5,6,3,7,4]=>101100=>001101
[4,7,3,6,5,2,1]=>[1,2,5,6,3,7,4]=>001100=>001100
[4,7,5,1,2,3,6]=>[6,3,2,1,5,7,4]=>111100=>001111
[4,7,5,1,2,6,3]=>[3,6,2,1,5,7,4]=>110100=>001011
[4,7,5,1,3,2,6]=>[6,2,3,1,5,7,4]=>110100=>001011
[4,7,5,1,3,6,2]=>[2,6,3,1,5,7,4]=>101100=>001101
[4,7,5,1,6,2,3]=>[3,2,6,1,5,7,4]=>110100=>001011
[4,7,5,1,6,3,2]=>[2,3,6,1,5,7,4]=>100100=>001001
[4,7,5,2,1,3,6]=>[6,3,1,2,5,7,4]=>101100=>001101
[4,7,5,2,1,6,3]=>[3,6,1,2,5,7,4]=>100100=>001001
[4,7,5,2,3,1,6]=>[6,1,3,2,5,7,4]=>110100=>001011
[4,7,5,2,3,6,1]=>[1,6,3,2,5,7,4]=>011100=>001110
[4,7,5,2,6,1,3]=>[3,1,6,2,5,7,4]=>110100=>001011
[4,7,5,2,6,3,1]=>[1,3,6,2,5,7,4]=>010100=>001010
[4,7,5,3,1,2,6]=>[6,2,1,3,5,7,4]=>110100=>001011
[4,7,5,3,1,6,2]=>[2,6,1,3,5,7,4]=>100100=>001001
[4,7,5,3,2,1,6]=>[6,1,2,3,5,7,4]=>100100=>001001
[4,7,5,3,2,6,1]=>[1,6,2,3,5,7,4]=>010100=>001010
[4,7,5,3,6,1,2]=>[2,1,6,3,5,7,4]=>101100=>001101
[4,7,5,3,6,2,1]=>[1,2,6,3,5,7,4]=>001100=>001100
[4,7,5,6,1,2,3]=>[3,2,1,6,5,7,4]=>110110=>011011
[4,7,5,6,1,3,2]=>[2,3,1,6,5,7,4]=>100110=>011001
[4,7,5,6,2,1,3]=>[3,1,2,6,5,7,4]=>100110=>011001
[4,7,5,6,2,3,1]=>[1,3,2,6,5,7,4]=>010110=>011010
[4,7,5,6,3,1,2]=>[2,1,3,6,5,7,4]=>100110=>011001
[4,7,5,6,3,2,1]=>[1,2,3,6,5,7,4]=>000110=>011000
[4,7,6,1,2,3,5]=>[5,3,2,1,6,7,4]=>111100=>001111
[4,7,6,1,2,5,3]=>[3,5,2,1,6,7,4]=>110100=>001011
[4,7,6,1,3,2,5]=>[5,2,3,1,6,7,4]=>110100=>001011
[4,7,6,1,3,5,2]=>[2,5,3,1,6,7,4]=>101100=>001101
[4,7,6,1,5,2,3]=>[3,2,5,1,6,7,4]=>110100=>001011
[4,7,6,1,5,3,2]=>[2,3,5,1,6,7,4]=>100100=>001001
[4,7,6,2,1,3,5]=>[5,3,1,2,6,7,4]=>101100=>001101
[4,7,6,2,1,5,3]=>[3,5,1,2,6,7,4]=>100100=>001001
[4,7,6,2,3,1,5]=>[5,1,3,2,6,7,4]=>110100=>001011
[4,7,6,2,3,5,1]=>[1,5,3,2,6,7,4]=>011100=>001110
[4,7,6,2,5,1,3]=>[3,1,5,2,6,7,4]=>110100=>001011
[4,7,6,2,5,3,1]=>[1,3,5,2,6,7,4]=>010100=>001010
[4,7,6,3,1,2,5]=>[5,2,1,3,6,7,4]=>110100=>001011
[4,7,6,3,1,5,2]=>[2,5,1,3,6,7,4]=>100100=>001001
[4,7,6,3,2,1,5]=>[5,1,2,3,6,7,4]=>100100=>001001
[4,7,6,3,2,5,1]=>[1,5,2,3,6,7,4]=>010100=>001010
[4,7,6,3,5,1,2]=>[2,1,5,3,6,7,4]=>101100=>001101
[4,7,6,3,5,2,1]=>[1,2,5,3,6,7,4]=>001100=>001100
[4,7,6,5,1,2,3]=>[3,2,1,5,6,7,4]=>110100=>001011
[4,7,6,5,1,3,2]=>[2,3,1,5,6,7,4]=>100100=>001001
[4,7,6,5,2,1,3]=>[3,1,2,5,6,7,4]=>100100=>001001
[4,7,6,5,2,3,1]=>[1,3,2,5,6,7,4]=>010100=>001010
[4,7,6,5,3,1,2]=>[2,1,3,5,6,7,4]=>100100=>001001
[4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4]=>000100=>001000
[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>111101=>101111
[5,1,2,3,4,7,6]=>[6,7,4,3,2,1,5]=>111100=>001111
[5,1,2,3,6,4,7]=>[7,4,6,3,2,1,5]=>111100=>001111
[5,1,2,3,6,7,4]=>[4,7,6,3,2,1,5]=>111001=>100111
[5,1,2,3,7,4,6]=>[6,4,7,3,2,1,5]=>111100=>001111
[5,1,2,3,7,6,4]=>[4,6,7,3,2,1,5]=>111000=>000111
[5,1,2,4,3,6,7]=>[7,6,3,4,2,1,5]=>111001=>100111
[5,1,2,4,3,7,6]=>[6,7,3,4,2,1,5]=>111000=>000111
[5,1,2,4,6,3,7]=>[7,3,6,4,2,1,5]=>111100=>001111
[5,1,2,4,6,7,3]=>[3,7,6,4,2,1,5]=>110101=>101011
[5,1,2,4,7,3,6]=>[6,3,7,4,2,1,5]=>111100=>001111
[5,1,2,4,7,6,3]=>[3,6,7,4,2,1,5]=>110100=>001011
[5,1,2,6,3,4,7]=>[7,4,3,6,2,1,5]=>111100=>001111
[5,1,2,6,3,7,4]=>[4,7,3,6,2,1,5]=>111000=>000111
[5,1,2,6,4,3,7]=>[7,3,4,6,2,1,5]=>111000=>000111
[5,1,2,6,4,7,3]=>[3,7,4,6,2,1,5]=>110100=>001011
[5,1,2,6,7,3,4]=>[4,3,7,6,2,1,5]=>111001=>100111
[5,1,2,6,7,4,3]=>[3,4,7,6,2,1,5]=>110001=>100011
[5,1,2,7,3,4,6]=>[6,4,3,7,2,1,5]=>111100=>001111
[5,1,2,7,3,6,4]=>[4,6,3,7,2,1,5]=>111000=>000111
[5,1,2,7,4,3,6]=>[6,3,4,7,2,1,5]=>111000=>000111
[5,1,2,7,4,6,3]=>[3,6,4,7,2,1,5]=>110100=>001011
[5,1,2,7,6,3,4]=>[4,3,6,7,2,1,5]=>111000=>000111
[5,1,2,7,6,4,3]=>[3,4,6,7,2,1,5]=>110000=>000011
[5,1,3,2,4,6,7]=>[7,6,4,2,3,1,5]=>110101=>101011
[5,1,3,2,4,7,6]=>[6,7,4,2,3,1,5]=>110100=>001011
[5,1,3,2,6,4,7]=>[7,4,6,2,3,1,5]=>110100=>001011
[5,1,3,2,6,7,4]=>[4,7,6,2,3,1,5]=>110001=>100011
[5,1,3,2,7,4,6]=>[6,4,7,2,3,1,5]=>110100=>001011
[5,1,3,2,7,6,4]=>[4,6,7,2,3,1,5]=>110000=>000011
[5,1,3,4,2,6,7]=>[7,6,2,4,3,1,5]=>111001=>100111
[5,1,3,4,2,7,6]=>[6,7,2,4,3,1,5]=>111000=>000111
[5,1,3,4,6,2,7]=>[7,2,6,4,3,1,5]=>111100=>001111
[5,1,3,4,6,7,2]=>[2,7,6,4,3,1,5]=>101101=>101101
[5,1,3,4,7,2,6]=>[6,2,7,4,3,1,5]=>111100=>001111
[5,1,3,4,7,6,2]=>[2,6,7,4,3,1,5]=>101100=>001101
[5,1,3,6,2,4,7]=>[7,4,2,6,3,1,5]=>111100=>001111
[5,1,3,6,2,7,4]=>[4,7,2,6,3,1,5]=>111000=>000111
[5,1,3,6,4,2,7]=>[7,2,4,6,3,1,5]=>111000=>000111
[5,1,3,6,4,7,2]=>[2,7,4,6,3,1,5]=>101100=>001101
[5,1,3,6,7,2,4]=>[4,2,7,6,3,1,5]=>111001=>100111
[5,1,3,6,7,4,2]=>[2,4,7,6,3,1,5]=>101001=>100101
[5,1,3,7,2,4,6]=>[6,4,2,7,3,1,5]=>111100=>001111
[5,1,3,7,2,6,4]=>[4,6,2,7,3,1,5]=>111000=>000111
[5,1,3,7,4,2,6]=>[6,2,4,7,3,1,5]=>111000=>000111
[5,1,3,7,4,6,2]=>[2,6,4,7,3,1,5]=>101100=>001101
[5,1,3,7,6,2,4]=>[4,2,6,7,3,1,5]=>111000=>000111
[5,1,3,7,6,4,2]=>[2,4,6,7,3,1,5]=>101000=>000101
[5,1,4,2,3,6,7]=>[7,6,3,2,4,1,5]=>111001=>100111
[5,1,4,2,3,7,6]=>[6,7,3,2,4,1,5]=>111000=>000111
[5,1,4,2,6,3,7]=>[7,3,6,2,4,1,5]=>111000=>000111
[5,1,4,2,6,7,3]=>[3,7,6,2,4,1,5]=>110001=>100011
[5,1,4,2,7,3,6]=>[6,3,7,2,4,1,5]=>111000=>000111
[5,1,4,2,7,6,3]=>[3,6,7,2,4,1,5]=>110000=>000011
[5,1,4,3,2,6,7]=>[7,6,2,3,4,1,5]=>110001=>100011
[5,1,4,3,2,7,6]=>[6,7,2,3,4,1,5]=>110000=>000011
[5,1,4,3,6,2,7]=>[7,2,6,3,4,1,5]=>111000=>000111
[5,1,4,3,6,7,2]=>[2,7,6,3,4,1,5]=>101001=>100101
[5,1,4,3,7,2,6]=>[6,2,7,3,4,1,5]=>111000=>000111
[5,1,4,3,7,6,2]=>[2,6,7,3,4,1,5]=>101000=>000101
[5,1,4,6,2,3,7]=>[7,3,2,6,4,1,5]=>111100=>001111
[5,1,4,6,2,7,3]=>[3,7,2,6,4,1,5]=>110100=>001011
[5,1,4,6,3,2,7]=>[7,2,3,6,4,1,5]=>110100=>001011
[5,1,4,6,3,7,2]=>[2,7,3,6,4,1,5]=>101100=>001101
[5,1,4,6,7,2,3]=>[3,2,7,6,4,1,5]=>110101=>101011
[5,1,4,6,7,3,2]=>[2,3,7,6,4,1,5]=>100101=>101001
[5,1,4,7,2,3,6]=>[6,3,2,7,4,1,5]=>111100=>001111
[5,1,4,7,2,6,3]=>[3,6,2,7,4,1,5]=>110100=>001011
[5,1,4,7,3,2,6]=>[6,2,3,7,4,1,5]=>110100=>001011
[5,1,4,7,3,6,2]=>[2,6,3,7,4,1,5]=>101100=>001101
[5,1,4,7,6,2,3]=>[3,2,6,7,4,1,5]=>110100=>001011
[5,1,4,7,6,3,2]=>[2,3,6,7,4,1,5]=>100100=>001001
[5,1,6,2,3,4,7]=>[7,4,3,2,6,1,5]=>111100=>001111
[5,1,6,2,3,7,4]=>[4,7,3,2,6,1,5]=>111000=>000111
[5,1,6,2,4,3,7]=>[7,3,4,2,6,1,5]=>111000=>000111
[5,1,6,2,4,7,3]=>[3,7,4,2,6,1,5]=>110100=>001011
[5,1,6,2,7,3,4]=>[4,3,7,2,6,1,5]=>111000=>000111
[5,1,6,2,7,4,3]=>[3,4,7,2,6,1,5]=>110000=>000011
[5,1,6,3,2,4,7]=>[7,4,2,3,6,1,5]=>110100=>001011
[5,1,6,3,2,7,4]=>[4,7,2,3,6,1,5]=>110000=>000011
[5,1,6,3,4,2,7]=>[7,2,4,3,6,1,5]=>111000=>000111
[5,1,6,3,4,7,2]=>[2,7,4,3,6,1,5]=>101100=>001101
[5,1,6,3,7,2,4]=>[4,2,7,3,6,1,5]=>111000=>000111
[5,1,6,3,7,4,2]=>[2,4,7,3,6,1,5]=>101000=>000101
[5,1,6,4,2,3,7]=>[7,3,2,4,6,1,5]=>111000=>000111
[5,1,6,4,2,7,3]=>[3,7,2,4,6,1,5]=>110000=>000011
[5,1,6,4,3,2,7]=>[7,2,3,4,6,1,5]=>110000=>000011
[5,1,6,4,3,7,2]=>[2,7,3,4,6,1,5]=>101000=>000101
[5,1,6,4,7,2,3]=>[3,2,7,4,6,1,5]=>110100=>001011
[5,1,6,4,7,3,2]=>[2,3,7,4,6,1,5]=>100100=>001001
[5,1,6,7,2,3,4]=>[4,3,2,7,6,1,5]=>111001=>100111
[5,1,6,7,2,4,3]=>[3,4,2,7,6,1,5]=>110001=>100011
[5,1,6,7,3,2,4]=>[4,2,3,7,6,1,5]=>110001=>100011
[5,1,6,7,3,4,2]=>[2,4,3,7,6,1,5]=>101001=>100101
[5,1,6,7,4,2,3]=>[3,2,4,7,6,1,5]=>110001=>100011
[5,1,6,7,4,3,2]=>[2,3,4,7,6,1,5]=>100001=>100001
[5,1,7,2,3,4,6]=>[6,4,3,2,7,1,5]=>111100=>001111
[5,1,7,2,3,6,4]=>[4,6,3,2,7,1,5]=>111000=>000111
[5,1,7,2,4,3,6]=>[6,3,4,2,7,1,5]=>111000=>000111
[5,1,7,2,4,6,3]=>[3,6,4,2,7,1,5]=>110100=>001011
[5,1,7,2,6,3,4]=>[4,3,6,2,7,1,5]=>111000=>000111
[5,1,7,2,6,4,3]=>[3,4,6,2,7,1,5]=>110000=>000011
[5,1,7,3,2,4,6]=>[6,4,2,3,7,1,5]=>110100=>001011
[5,1,7,3,2,6,4]=>[4,6,2,3,7,1,5]=>110000=>000011
[5,1,7,3,4,2,6]=>[6,2,4,3,7,1,5]=>111000=>000111
[5,1,7,3,4,6,2]=>[2,6,4,3,7,1,5]=>101100=>001101
[5,1,7,3,6,2,4]=>[4,2,6,3,7,1,5]=>111000=>000111
[5,1,7,3,6,4,2]=>[2,4,6,3,7,1,5]=>101000=>000101
[5,1,7,4,2,3,6]=>[6,3,2,4,7,1,5]=>111000=>000111
[5,1,7,4,2,6,3]=>[3,6,2,4,7,1,5]=>110000=>000011
[5,1,7,4,3,2,6]=>[6,2,3,4,7,1,5]=>110000=>000011
[5,1,7,4,3,6,2]=>[2,6,3,4,7,1,5]=>101000=>000101
[5,1,7,4,6,2,3]=>[3,2,6,4,7,1,5]=>110100=>001011
[5,1,7,4,6,3,2]=>[2,3,6,4,7,1,5]=>100100=>001001
[5,1,7,6,2,3,4]=>[4,3,2,6,7,1,5]=>111000=>000111
[5,1,7,6,2,4,3]=>[3,4,2,6,7,1,5]=>110000=>000011
[5,1,7,6,3,2,4]=>[4,2,3,6,7,1,5]=>110000=>000011
[5,1,7,6,3,4,2]=>[2,4,3,6,7,1,5]=>101000=>000101
[5,1,7,6,4,2,3]=>[3,2,4,6,7,1,5]=>110000=>000011
[5,1,7,6,4,3,2]=>[2,3,4,6,7,1,5]=>100000=>000001
[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>101101=>101101
[5,2,1,3,4,7,6]=>[6,7,4,3,1,2,5]=>101100=>001101
[5,2,1,3,6,4,7]=>[7,4,6,3,1,2,5]=>101100=>001101
[5,2,1,3,6,7,4]=>[4,7,6,3,1,2,5]=>101001=>100101
[5,2,1,3,7,4,6]=>[6,4,7,3,1,2,5]=>101100=>001101
[5,2,1,3,7,6,4]=>[4,6,7,3,1,2,5]=>101000=>000101
[5,2,1,4,3,6,7]=>[7,6,3,4,1,2,5]=>101001=>100101
[5,2,1,4,3,7,6]=>[6,7,3,4,1,2,5]=>101000=>000101
[5,2,1,4,6,3,7]=>[7,3,6,4,1,2,5]=>101100=>001101
[5,2,1,4,6,7,3]=>[3,7,6,4,1,2,5]=>100101=>101001
[5,2,1,4,7,3,6]=>[6,3,7,4,1,2,5]=>101100=>001101
[5,2,1,4,7,6,3]=>[3,6,7,4,1,2,5]=>100100=>001001
[5,2,1,6,3,4,7]=>[7,4,3,6,1,2,5]=>101100=>001101
[5,2,1,6,3,7,4]=>[4,7,3,6,1,2,5]=>101000=>000101
[5,2,1,6,4,3,7]=>[7,3,4,6,1,2,5]=>101000=>000101
[5,2,1,6,4,7,3]=>[3,7,4,6,1,2,5]=>100100=>001001
[5,2,1,6,7,3,4]=>[4,3,7,6,1,2,5]=>101001=>100101
[5,2,1,6,7,4,3]=>[3,4,7,6,1,2,5]=>100001=>100001
[5,2,1,7,3,4,6]=>[6,4,3,7,1,2,5]=>101100=>001101
[5,2,1,7,3,6,4]=>[4,6,3,7,1,2,5]=>101000=>000101
[5,2,1,7,4,3,6]=>[6,3,4,7,1,2,5]=>101000=>000101
[5,2,1,7,4,6,3]=>[3,6,4,7,1,2,5]=>100100=>001001
[5,2,1,7,6,3,4]=>[4,3,6,7,1,2,5]=>101000=>000101
[5,2,1,7,6,4,3]=>[3,4,6,7,1,2,5]=>100000=>000001
[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>110101=>101011
[5,2,3,1,4,7,6]=>[6,7,4,1,3,2,5]=>110100=>001011
[5,2,3,1,6,4,7]=>[7,4,6,1,3,2,5]=>110100=>001011
[5,2,3,1,6,7,4]=>[4,7,6,1,3,2,5]=>110001=>100011
[5,2,3,1,7,4,6]=>[6,4,7,1,3,2,5]=>110100=>001011
[5,2,3,1,7,6,4]=>[4,6,7,1,3,2,5]=>110000=>000011
[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>111001=>100111
[5,2,3,4,1,7,6]=>[6,7,1,4,3,2,5]=>111000=>000111
[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>111100=>001111
[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>011101=>101110
[5,2,3,4,7,1,6]=>[6,1,7,4,3,2,5]=>111100=>001111
[5,2,3,4,7,6,1]=>[1,6,7,4,3,2,5]=>011100=>001110
[5,2,3,6,1,4,7]=>[7,4,1,6,3,2,5]=>111100=>001111
[5,2,3,6,1,7,4]=>[4,7,1,6,3,2,5]=>111000=>000111
[5,2,3,6,4,1,7]=>[7,1,4,6,3,2,5]=>111000=>000111
[5,2,3,6,4,7,1]=>[1,7,4,6,3,2,5]=>011100=>001110
[5,2,3,6,7,1,4]=>[4,1,7,6,3,2,5]=>111001=>100111
[5,2,3,6,7,4,1]=>[1,4,7,6,3,2,5]=>011001=>100110
[5,2,3,7,1,4,6]=>[6,4,1,7,3,2,5]=>111100=>001111
[5,2,3,7,1,6,4]=>[4,6,1,7,3,2,5]=>111000=>000111
[5,2,3,7,4,1,6]=>[6,1,4,7,3,2,5]=>111000=>000111
[5,2,3,7,4,6,1]=>[1,6,4,7,3,2,5]=>011100=>001110
[5,2,3,7,6,1,4]=>[4,1,6,7,3,2,5]=>111000=>000111
[5,2,3,7,6,4,1]=>[1,4,6,7,3,2,5]=>011000=>000110
[5,2,4,1,3,6,7]=>[7,6,3,1,4,2,5]=>111001=>100111
[5,2,4,1,3,7,6]=>[6,7,3,1,4,2,5]=>111000=>000111
[5,2,4,1,6,3,7]=>[7,3,6,1,4,2,5]=>111000=>000111
[5,2,4,1,6,7,3]=>[3,7,6,1,4,2,5]=>110001=>100011
[5,2,4,1,7,3,6]=>[6,3,7,1,4,2,5]=>111000=>000111
[5,2,4,1,7,6,3]=>[3,6,7,1,4,2,5]=>110000=>000011
[5,2,4,3,1,6,7]=>[7,6,1,3,4,2,5]=>110001=>100011
[5,2,4,3,1,7,6]=>[6,7,1,3,4,2,5]=>110000=>000011
[5,2,4,3,6,1,7]=>[7,1,6,3,4,2,5]=>111000=>000111
[5,2,4,3,6,7,1]=>[1,7,6,3,4,2,5]=>011001=>100110
[5,2,4,3,7,1,6]=>[6,1,7,3,4,2,5]=>111000=>000111
[5,2,4,3,7,6,1]=>[1,6,7,3,4,2,5]=>011000=>000110
[5,2,4,6,1,3,7]=>[7,3,1,6,4,2,5]=>111100=>001111
[5,2,4,6,1,7,3]=>[3,7,1,6,4,2,5]=>110100=>001011
[5,2,4,6,3,1,7]=>[7,1,3,6,4,2,5]=>110100=>001011
[5,2,4,6,3,7,1]=>[1,7,3,6,4,2,5]=>011100=>001110
[5,2,4,6,7,1,3]=>[3,1,7,6,4,2,5]=>110101=>101011
[5,2,4,6,7,3,1]=>[1,3,7,6,4,2,5]=>010101=>101010
[5,2,4,7,1,3,6]=>[6,3,1,7,4,2,5]=>111100=>001111
[5,2,4,7,1,6,3]=>[3,6,1,7,4,2,5]=>110100=>001011
[5,2,4,7,3,1,6]=>[6,1,3,7,4,2,5]=>110100=>001011
[5,2,4,7,3,6,1]=>[1,6,3,7,4,2,5]=>011100=>001110
[5,2,4,7,6,1,3]=>[3,1,6,7,4,2,5]=>110100=>001011
[5,2,4,7,6,3,1]=>[1,3,6,7,4,2,5]=>010100=>001010
[5,2,6,1,3,4,7]=>[7,4,3,1,6,2,5]=>111100=>001111
[5,2,6,1,3,7,4]=>[4,7,3,1,6,2,5]=>111000=>000111
[5,2,6,1,4,3,7]=>[7,3,4,1,6,2,5]=>111000=>000111
[5,2,6,1,4,7,3]=>[3,7,4,1,6,2,5]=>110100=>001011
[5,2,6,1,7,3,4]=>[4,3,7,1,6,2,5]=>111000=>000111
[5,2,6,1,7,4,3]=>[3,4,7,1,6,2,5]=>110000=>000011
[5,2,6,3,1,4,7]=>[7,4,1,3,6,2,5]=>110100=>001011
[5,2,6,3,1,7,4]=>[4,7,1,3,6,2,5]=>110000=>000011
[5,2,6,3,4,1,7]=>[7,1,4,3,6,2,5]=>111000=>000111
[5,2,6,3,4,7,1]=>[1,7,4,3,6,2,5]=>011100=>001110
[5,2,6,3,7,1,4]=>[4,1,7,3,6,2,5]=>111000=>000111
[5,2,6,3,7,4,1]=>[1,4,7,3,6,2,5]=>011000=>000110
[5,2,6,4,1,3,7]=>[7,3,1,4,6,2,5]=>111000=>000111
[5,2,6,4,1,7,3]=>[3,7,1,4,6,2,5]=>110000=>000011
[5,2,6,4,3,1,7]=>[7,1,3,4,6,2,5]=>110000=>000011
[5,2,6,4,3,7,1]=>[1,7,3,4,6,2,5]=>011000=>000110
[5,2,6,4,7,1,3]=>[3,1,7,4,6,2,5]=>110100=>001011
[5,2,6,4,7,3,1]=>[1,3,7,4,6,2,5]=>010100=>001010
[5,2,6,7,1,3,4]=>[4,3,1,7,6,2,5]=>111001=>100111
[5,2,6,7,1,4,3]=>[3,4,1,7,6,2,5]=>110001=>100011
[5,2,6,7,3,1,4]=>[4,1,3,7,6,2,5]=>110001=>100011
[5,2,6,7,3,4,1]=>[1,4,3,7,6,2,5]=>011001=>100110
[5,2,6,7,4,1,3]=>[3,1,4,7,6,2,5]=>110001=>100011
[5,2,6,7,4,3,1]=>[1,3,4,7,6,2,5]=>010001=>100010
[5,2,7,1,3,4,6]=>[6,4,3,1,7,2,5]=>111100=>001111
[5,2,7,1,3,6,4]=>[4,6,3,1,7,2,5]=>111000=>000111
[5,2,7,1,4,3,6]=>[6,3,4,1,7,2,5]=>111000=>000111
[5,2,7,1,4,6,3]=>[3,6,4,1,7,2,5]=>110100=>001011
[5,2,7,1,6,3,4]=>[4,3,6,1,7,2,5]=>111000=>000111
[5,2,7,1,6,4,3]=>[3,4,6,1,7,2,5]=>110000=>000011
[5,2,7,3,1,4,6]=>[6,4,1,3,7,2,5]=>110100=>001011
[5,2,7,3,1,6,4]=>[4,6,1,3,7,2,5]=>110000=>000011
[5,2,7,3,4,1,6]=>[6,1,4,3,7,2,5]=>111000=>000111
[5,2,7,3,4,6,1]=>[1,6,4,3,7,2,5]=>011100=>001110
[5,2,7,3,6,1,4]=>[4,1,6,3,7,2,5]=>111000=>000111
[5,2,7,3,6,4,1]=>[1,4,6,3,7,2,5]=>011000=>000110
[5,2,7,4,1,3,6]=>[6,3,1,4,7,2,5]=>111000=>000111
[5,2,7,4,1,6,3]=>[3,6,1,4,7,2,5]=>110000=>000011
[5,2,7,4,3,1,6]=>[6,1,3,4,7,2,5]=>110000=>000011
[5,2,7,4,3,6,1]=>[1,6,3,4,7,2,5]=>011000=>000110
[5,2,7,4,6,1,3]=>[3,1,6,4,7,2,5]=>110100=>001011
[5,2,7,4,6,3,1]=>[1,3,6,4,7,2,5]=>010100=>001010
[5,2,7,6,1,3,4]=>[4,3,1,6,7,2,5]=>111000=>000111
[5,2,7,6,1,4,3]=>[3,4,1,6,7,2,5]=>110000=>000011
[5,2,7,6,3,1,4]=>[4,1,3,6,7,2,5]=>110000=>000011
[5,2,7,6,3,4,1]=>[1,4,3,6,7,2,5]=>011000=>000110
[5,2,7,6,4,1,3]=>[3,1,4,6,7,2,5]=>110000=>000011
[5,2,7,6,4,3,1]=>[1,3,4,6,7,2,5]=>010000=>000010
[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>110101=>101011
[5,3,1,2,4,7,6]=>[6,7,4,2,1,3,5]=>110100=>001011
[5,3,1,2,6,4,7]=>[7,4,6,2,1,3,5]=>110100=>001011
[5,3,1,2,6,7,4]=>[4,7,6,2,1,3,5]=>110001=>100011
[5,3,1,2,7,4,6]=>[6,4,7,2,1,3,5]=>110100=>001011
[5,3,1,2,7,6,4]=>[4,6,7,2,1,3,5]=>110000=>000011
[5,3,1,4,2,6,7]=>[7,6,2,4,1,3,5]=>110001=>100011
[5,3,1,4,2,7,6]=>[6,7,2,4,1,3,5]=>110000=>000011
[5,3,1,4,6,2,7]=>[7,2,6,4,1,3,5]=>110100=>001011
[5,3,1,4,6,7,2]=>[2,7,6,4,1,3,5]=>100101=>101001
[5,3,1,4,7,2,6]=>[6,2,7,4,1,3,5]=>110100=>001011
[5,3,1,4,7,6,2]=>[2,6,7,4,1,3,5]=>100100=>001001
[5,3,1,6,2,4,7]=>[7,4,2,6,1,3,5]=>110100=>001011
[5,3,1,6,2,7,4]=>[4,7,2,6,1,3,5]=>110000=>000011
[5,3,1,6,4,2,7]=>[7,2,4,6,1,3,5]=>110000=>000011
[5,3,1,6,4,7,2]=>[2,7,4,6,1,3,5]=>100100=>001001
[5,3,1,6,7,2,4]=>[4,2,7,6,1,3,5]=>110001=>100011
[5,3,1,6,7,4,2]=>[2,4,7,6,1,3,5]=>100001=>100001
[5,3,1,7,2,4,6]=>[6,4,2,7,1,3,5]=>110100=>001011
[5,3,1,7,2,6,4]=>[4,6,2,7,1,3,5]=>110000=>000011
[5,3,1,7,4,2,6]=>[6,2,4,7,1,3,5]=>110000=>000011
[5,3,1,7,4,6,2]=>[2,6,4,7,1,3,5]=>100100=>001001
[5,3,1,7,6,2,4]=>[4,2,6,7,1,3,5]=>110000=>000011
[5,3,1,7,6,4,2]=>[2,4,6,7,1,3,5]=>100000=>000001
[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>100101=>101001
[5,3,2,1,4,7,6]=>[6,7,4,1,2,3,5]=>100100=>001001
[5,3,2,1,6,4,7]=>[7,4,6,1,2,3,5]=>100100=>001001
[5,3,2,1,6,7,4]=>[4,7,6,1,2,3,5]=>100001=>100001
[5,3,2,1,7,4,6]=>[6,4,7,1,2,3,5]=>100100=>001001
[5,3,2,1,7,6,4]=>[4,6,7,1,2,3,5]=>100000=>000001
[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>110001=>100011
[5,3,2,4,1,7,6]=>[6,7,1,4,2,3,5]=>110000=>000011
[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>110100=>001011
[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>010101=>101010
[5,3,2,4,7,1,6]=>[6,1,7,4,2,3,5]=>110100=>001011
[5,3,2,4,7,6,1]=>[1,6,7,4,2,3,5]=>010100=>001010
[5,3,2,6,1,4,7]=>[7,4,1,6,2,3,5]=>110100=>001011
[5,3,2,6,1,7,4]=>[4,7,1,6,2,3,5]=>110000=>000011
[5,3,2,6,4,1,7]=>[7,1,4,6,2,3,5]=>110000=>000011
[5,3,2,6,4,7,1]=>[1,7,4,6,2,3,5]=>010100=>001010
[5,3,2,6,7,1,4]=>[4,1,7,6,2,3,5]=>110001=>100011
[5,3,2,6,7,4,1]=>[1,4,7,6,2,3,5]=>010001=>100010
[5,3,2,7,1,4,6]=>[6,4,1,7,2,3,5]=>110100=>001011
[5,3,2,7,1,6,4]=>[4,6,1,7,2,3,5]=>110000=>000011
[5,3,2,7,4,1,6]=>[6,1,4,7,2,3,5]=>110000=>000011
[5,3,2,7,4,6,1]=>[1,6,4,7,2,3,5]=>010100=>001010
[5,3,2,7,6,1,4]=>[4,1,6,7,2,3,5]=>110000=>000011
[5,3,2,7,6,4,1]=>[1,4,6,7,2,3,5]=>010000=>000010
[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>111001=>100111
[5,3,4,1,2,7,6]=>[6,7,2,1,4,3,5]=>111000=>000111
[5,3,4,1,6,2,7]=>[7,2,6,1,4,3,5]=>111000=>000111
[5,3,4,1,6,7,2]=>[2,7,6,1,4,3,5]=>101001=>100101
[5,3,4,1,7,2,6]=>[6,2,7,1,4,3,5]=>111000=>000111
[5,3,4,1,7,6,2]=>[2,6,7,1,4,3,5]=>101000=>000101
[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>101001=>100101
[5,3,4,2,1,7,6]=>[6,7,1,2,4,3,5]=>101000=>000101
[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>111000=>000111
[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>011001=>100110
[5,3,4,2,7,1,6]=>[6,1,7,2,4,3,5]=>111000=>000111
[5,3,4,2,7,6,1]=>[1,6,7,2,4,3,5]=>011000=>000110
[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>111100=>001111
[5,3,4,6,1,7,2]=>[2,7,1,6,4,3,5]=>101100=>001101
[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>101100=>001101
[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>011100=>001110
[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101101=>101101
[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>001101=>101100
[5,3,4,7,1,2,6]=>[6,2,1,7,4,3,5]=>111100=>001111
[5,3,4,7,1,6,2]=>[2,6,1,7,4,3,5]=>101100=>001101
[5,3,4,7,2,1,6]=>[6,1,2,7,4,3,5]=>101100=>001101
[5,3,4,7,2,6,1]=>[1,6,2,7,4,3,5]=>011100=>001110
[5,3,4,7,6,1,2]=>[2,1,6,7,4,3,5]=>101100=>001101
[5,3,4,7,6,2,1]=>[1,2,6,7,4,3,5]=>001100=>001100
[5,3,6,1,2,4,7]=>[7,4,2,1,6,3,5]=>111100=>001111
[5,3,6,1,2,7,4]=>[4,7,2,1,6,3,5]=>111000=>000111
[5,3,6,1,4,2,7]=>[7,2,4,1,6,3,5]=>111000=>000111
[5,3,6,1,4,7,2]=>[2,7,4,1,6,3,5]=>101100=>001101
[5,3,6,1,7,2,4]=>[4,2,7,1,6,3,5]=>111000=>000111
[5,3,6,1,7,4,2]=>[2,4,7,1,6,3,5]=>101000=>000101
[5,3,6,2,1,4,7]=>[7,4,1,2,6,3,5]=>101100=>001101
[5,3,6,2,1,7,4]=>[4,7,1,2,6,3,5]=>101000=>000101
[5,3,6,2,4,1,7]=>[7,1,4,2,6,3,5]=>111000=>000111
[5,3,6,2,4,7,1]=>[1,7,4,2,6,3,5]=>011100=>001110
[5,3,6,2,7,1,4]=>[4,1,7,2,6,3,5]=>111000=>000111
[5,3,6,2,7,4,1]=>[1,4,7,2,6,3,5]=>011000=>000110
[5,3,6,4,1,2,7]=>[7,2,1,4,6,3,5]=>111000=>000111
[5,3,6,4,1,7,2]=>[2,7,1,4,6,3,5]=>101000=>000101
[5,3,6,4,2,1,7]=>[7,1,2,4,6,3,5]=>101000=>000101
[5,3,6,4,2,7,1]=>[1,7,2,4,6,3,5]=>011000=>000110
[5,3,6,4,7,1,2]=>[2,1,7,4,6,3,5]=>101100=>001101
[5,3,6,4,7,2,1]=>[1,2,7,4,6,3,5]=>001100=>001100
[5,3,6,7,1,2,4]=>[4,2,1,7,6,3,5]=>111001=>100111
[5,3,6,7,1,4,2]=>[2,4,1,7,6,3,5]=>101001=>100101
[5,3,6,7,2,1,4]=>[4,1,2,7,6,3,5]=>101001=>100101
[5,3,6,7,2,4,1]=>[1,4,2,7,6,3,5]=>011001=>100110
[5,3,6,7,4,1,2]=>[2,1,4,7,6,3,5]=>101001=>100101
[5,3,6,7,4,2,1]=>[1,2,4,7,6,3,5]=>001001=>100100
[5,3,7,1,2,4,6]=>[6,4,2,1,7,3,5]=>111100=>001111
[5,3,7,1,2,6,4]=>[4,6,2,1,7,3,5]=>111000=>000111
[5,3,7,1,4,2,6]=>[6,2,4,1,7,3,5]=>111000=>000111
[5,3,7,1,4,6,2]=>[2,6,4,1,7,3,5]=>101100=>001101
[5,3,7,1,6,2,4]=>[4,2,6,1,7,3,5]=>111000=>000111
[5,3,7,1,6,4,2]=>[2,4,6,1,7,3,5]=>101000=>000101
[5,3,7,2,1,4,6]=>[6,4,1,2,7,3,5]=>101100=>001101
[5,3,7,2,1,6,4]=>[4,6,1,2,7,3,5]=>101000=>000101
[5,3,7,2,4,1,6]=>[6,1,4,2,7,3,5]=>111000=>000111
[5,3,7,2,4,6,1]=>[1,6,4,2,7,3,5]=>011100=>001110
[5,3,7,2,6,1,4]=>[4,1,6,2,7,3,5]=>111000=>000111
[5,3,7,2,6,4,1]=>[1,4,6,2,7,3,5]=>011000=>000110
[5,3,7,4,1,2,6]=>[6,2,1,4,7,3,5]=>111000=>000111
[5,3,7,4,1,6,2]=>[2,6,1,4,7,3,5]=>101000=>000101
[5,3,7,4,2,1,6]=>[6,1,2,4,7,3,5]=>101000=>000101
[5,3,7,4,2,6,1]=>[1,6,2,4,7,3,5]=>011000=>000110
[5,3,7,4,6,1,2]=>[2,1,6,4,7,3,5]=>101100=>001101
[5,3,7,4,6,2,1]=>[1,2,6,4,7,3,5]=>001100=>001100
[5,3,7,6,1,2,4]=>[4,2,1,6,7,3,5]=>111000=>000111
[5,3,7,6,1,4,2]=>[2,4,1,6,7,3,5]=>101000=>000101
[5,3,7,6,2,1,4]=>[4,1,2,6,7,3,5]=>101000=>000101
[5,3,7,6,2,4,1]=>[1,4,2,6,7,3,5]=>011000=>000110
[5,3,7,6,4,1,2]=>[2,1,4,6,7,3,5]=>101000=>000101
[5,3,7,6,4,2,1]=>[1,2,4,6,7,3,5]=>001000=>000100
[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>111001=>100111
[5,4,1,2,3,7,6]=>[6,7,3,2,1,4,5]=>111000=>000111
[5,4,1,2,6,3,7]=>[7,3,6,2,1,4,5]=>111000=>000111
[5,4,1,2,6,7,3]=>[3,7,6,2,1,4,5]=>110001=>100011
[5,4,1,2,7,3,6]=>[6,3,7,2,1,4,5]=>111000=>000111
[5,4,1,2,7,6,3]=>[3,6,7,2,1,4,5]=>110000=>000011
[5,4,1,3,2,6,7]=>[7,6,2,3,1,4,5]=>110001=>100011
[5,4,1,3,2,7,6]=>[6,7,2,3,1,4,5]=>110000=>000011
[5,4,1,3,6,2,7]=>[7,2,6,3,1,4,5]=>111000=>000111
[5,4,1,3,6,7,2]=>[2,7,6,3,1,4,5]=>101001=>100101
[5,4,1,3,7,2,6]=>[6,2,7,3,1,4,5]=>111000=>000111
[5,4,1,3,7,6,2]=>[2,6,7,3,1,4,5]=>101000=>000101
[5,4,1,6,2,3,7]=>[7,3,2,6,1,4,5]=>111000=>000111
[5,4,1,6,2,7,3]=>[3,7,2,6,1,4,5]=>110000=>000011
[5,4,1,6,3,2,7]=>[7,2,3,6,1,4,5]=>110000=>000011
[5,4,1,6,3,7,2]=>[2,7,3,6,1,4,5]=>101000=>000101
[5,4,1,6,7,2,3]=>[3,2,7,6,1,4,5]=>110001=>100011
[5,4,1,6,7,3,2]=>[2,3,7,6,1,4,5]=>100001=>100001
[5,4,1,7,2,3,6]=>[6,3,2,7,1,4,5]=>111000=>000111
[5,4,1,7,2,6,3]=>[3,6,2,7,1,4,5]=>110000=>000011
[5,4,1,7,3,2,6]=>[6,2,3,7,1,4,5]=>110000=>000011
[5,4,1,7,3,6,2]=>[2,6,3,7,1,4,5]=>101000=>000101
[5,4,1,7,6,2,3]=>[3,2,6,7,1,4,5]=>110000=>000011
[5,4,1,7,6,3,2]=>[2,3,6,7,1,4,5]=>100000=>000001
[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>101001=>100101
[5,4,2,1,3,7,6]=>[6,7,3,1,2,4,5]=>101000=>000101
[5,4,2,1,6,3,7]=>[7,3,6,1,2,4,5]=>101000=>000101
[5,4,2,1,6,7,3]=>[3,7,6,1,2,4,5]=>100001=>100001
[5,4,2,1,7,3,6]=>[6,3,7,1,2,4,5]=>101000=>000101
[5,4,2,1,7,6,3]=>[3,6,7,1,2,4,5]=>100000=>000001
[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>110001=>100011
[5,4,2,3,1,7,6]=>[6,7,1,3,2,4,5]=>110000=>000011
[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>111000=>000111
[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>011001=>100110
[5,4,2,3,7,1,6]=>[6,1,7,3,2,4,5]=>111000=>000111
[5,4,2,3,7,6,1]=>[1,6,7,3,2,4,5]=>011000=>000110
[5,4,2,6,1,3,7]=>[7,3,1,6,2,4,5]=>111000=>000111
[5,4,2,6,1,7,3]=>[3,7,1,6,2,4,5]=>110000=>000011
[5,4,2,6,3,1,7]=>[7,1,3,6,2,4,5]=>110000=>000011
[5,4,2,6,3,7,1]=>[1,7,3,6,2,4,5]=>011000=>000110
[5,4,2,6,7,1,3]=>[3,1,7,6,2,4,5]=>110001=>100011
[5,4,2,6,7,3,1]=>[1,3,7,6,2,4,5]=>010001=>100010
[5,4,2,7,1,3,6]=>[6,3,1,7,2,4,5]=>111000=>000111
[5,4,2,7,1,6,3]=>[3,6,1,7,2,4,5]=>110000=>000011
[5,4,2,7,3,1,6]=>[6,1,3,7,2,4,5]=>110000=>000011
[5,4,2,7,3,6,1]=>[1,6,3,7,2,4,5]=>011000=>000110
[5,4,2,7,6,1,3]=>[3,1,6,7,2,4,5]=>110000=>000011
[5,4,2,7,6,3,1]=>[1,3,6,7,2,4,5]=>010000=>000010
[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>110001=>100011
[5,4,3,1,2,7,6]=>[6,7,2,1,3,4,5]=>110000=>000011
[5,4,3,1,6,2,7]=>[7,2,6,1,3,4,5]=>110000=>000011
[5,4,3,1,6,7,2]=>[2,7,6,1,3,4,5]=>100001=>100001
[5,4,3,1,7,2,6]=>[6,2,7,1,3,4,5]=>110000=>000011
[5,4,3,1,7,6,2]=>[2,6,7,1,3,4,5]=>100000=>000001
[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>100001=>100001
[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>100000=>000001
[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>110000=>000011
[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>010001=>100010
[5,4,3,2,7,1,6]=>[6,1,7,2,3,4,5]=>110000=>000011
[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>010000=>000010
[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>111000=>000111
[5,4,3,6,1,7,2]=>[2,7,1,6,3,4,5]=>101000=>000101
[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>101000=>000101
[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>011000=>000110
[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>101001=>100101
[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>001001=>100100
[5,4,3,7,1,2,6]=>[6,2,1,7,3,4,5]=>111000=>000111
[5,4,3,7,1,6,2]=>[2,6,1,7,3,4,5]=>101000=>000101
[5,4,3,7,2,1,6]=>[6,1,2,7,3,4,5]=>101000=>000101
[5,4,3,7,2,6,1]=>[1,6,2,7,3,4,5]=>011000=>000110
[5,4,3,7,6,1,2]=>[2,1,6,7,3,4,5]=>101000=>000101
[5,4,3,7,6,2,1]=>[1,2,6,7,3,4,5]=>001000=>000100
[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>111100=>001111
[5,4,6,1,2,7,3]=>[3,7,2,1,6,4,5]=>110100=>001011
[5,4,6,1,3,2,7]=>[7,2,3,1,6,4,5]=>110100=>001011
[5,4,6,1,3,7,2]=>[2,7,3,1,6,4,5]=>101100=>001101
[5,4,6,1,7,2,3]=>[3,2,7,1,6,4,5]=>110100=>001011
[5,4,6,1,7,3,2]=>[2,3,7,1,6,4,5]=>100100=>001001
[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>101100=>001101
[5,4,6,2,1,7,3]=>[3,7,1,2,6,4,5]=>100100=>001001
[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>110100=>001011
[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>011100=>001110
[5,4,6,2,7,1,3]=>[3,1,7,2,6,4,5]=>110100=>001011
[5,4,6,2,7,3,1]=>[1,3,7,2,6,4,5]=>010100=>001010
[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>110100=>001011
[5,4,6,3,1,7,2]=>[2,7,1,3,6,4,5]=>100100=>001001
[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>100100=>001001
[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>010100=>001010
[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>101100=>001101
[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>001100=>001100
[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110101=>101011
[5,4,6,7,1,3,2]=>[2,3,1,7,6,4,5]=>100101=>101001
[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>100101=>101001
[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>010101=>101010
[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>100101=>101001
[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>000101=>101000
[5,4,7,1,2,3,6]=>[6,3,2,1,7,4,5]=>111100=>001111
[5,4,7,1,2,6,3]=>[3,6,2,1,7,4,5]=>110100=>001011
[5,4,7,1,3,2,6]=>[6,2,3,1,7,4,5]=>110100=>001011
[5,4,7,1,3,6,2]=>[2,6,3,1,7,4,5]=>101100=>001101
[5,4,7,1,6,2,3]=>[3,2,6,1,7,4,5]=>110100=>001011
[5,4,7,1,6,3,2]=>[2,3,6,1,7,4,5]=>100100=>001001
[5,4,7,2,1,3,6]=>[6,3,1,2,7,4,5]=>101100=>001101
[5,4,7,2,1,6,3]=>[3,6,1,2,7,4,5]=>100100=>001001
[5,4,7,2,3,1,6]=>[6,1,3,2,7,4,5]=>110100=>001011
[5,4,7,2,3,6,1]=>[1,6,3,2,7,4,5]=>011100=>001110
[5,4,7,2,6,1,3]=>[3,1,6,2,7,4,5]=>110100=>001011
[5,4,7,2,6,3,1]=>[1,3,6,2,7,4,5]=>010100=>001010
[5,4,7,3,1,2,6]=>[6,2,1,3,7,4,5]=>110100=>001011
[5,4,7,3,1,6,2]=>[2,6,1,3,7,4,5]=>100100=>001001
[5,4,7,3,2,1,6]=>[6,1,2,3,7,4,5]=>100100=>001001
[5,4,7,3,2,6,1]=>[1,6,2,3,7,4,5]=>010100=>001010
[5,4,7,3,6,1,2]=>[2,1,6,3,7,4,5]=>101100=>001101
[5,4,7,3,6,2,1]=>[1,2,6,3,7,4,5]=>001100=>001100
[5,4,7,6,1,2,3]=>[3,2,1,6,7,4,5]=>110100=>001011
[5,4,7,6,1,3,2]=>[2,3,1,6,7,4,5]=>100100=>001001
[5,4,7,6,2,1,3]=>[3,1,2,6,7,4,5]=>100100=>001001
[5,4,7,6,2,3,1]=>[1,3,2,6,7,4,5]=>010100=>001010
[5,4,7,6,3,1,2]=>[2,1,3,6,7,4,5]=>100100=>001001
[5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5]=>000100=>001000
[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111110=>011111
[5,6,1,2,3,7,4]=>[4,7,3,2,1,6,5]=>111010=>010111
[5,6,1,2,4,3,7]=>[7,3,4,2,1,6,5]=>111010=>010111
[5,6,1,2,4,7,3]=>[3,7,4,2,1,6,5]=>110110=>011011
[5,6,1,2,7,3,4]=>[4,3,7,2,1,6,5]=>111010=>010111
[5,6,1,2,7,4,3]=>[3,4,7,2,1,6,5]=>110010=>010011
[5,6,1,3,2,4,7]=>[7,4,2,3,1,6,5]=>110110=>011011
[5,6,1,3,2,7,4]=>[4,7,2,3,1,6,5]=>110010=>010011
[5,6,1,3,4,2,7]=>[7,2,4,3,1,6,5]=>111010=>010111
[5,6,1,3,4,7,2]=>[2,7,4,3,1,6,5]=>101110=>011101
[5,6,1,3,7,2,4]=>[4,2,7,3,1,6,5]=>111010=>010111
[5,6,1,3,7,4,2]=>[2,4,7,3,1,6,5]=>101010=>010101
[5,6,1,4,2,3,7]=>[7,3,2,4,1,6,5]=>111010=>010111
[5,6,1,4,2,7,3]=>[3,7,2,4,1,6,5]=>110010=>010011
[5,6,1,4,3,2,7]=>[7,2,3,4,1,6,5]=>110010=>010011
[5,6,1,4,3,7,2]=>[2,7,3,4,1,6,5]=>101010=>010101
[5,6,1,4,7,2,3]=>[3,2,7,4,1,6,5]=>110110=>011011
[5,6,1,4,7,3,2]=>[2,3,7,4,1,6,5]=>100110=>011001
[5,6,1,7,2,3,4]=>[4,3,2,7,1,6,5]=>111010=>010111
[5,6,1,7,2,4,3]=>[3,4,2,7,1,6,5]=>110010=>010011
[5,6,1,7,3,2,4]=>[4,2,3,7,1,6,5]=>110010=>010011
[5,6,1,7,3,4,2]=>[2,4,3,7,1,6,5]=>101010=>010101
[5,6,1,7,4,2,3]=>[3,2,4,7,1,6,5]=>110010=>010011
[5,6,1,7,4,3,2]=>[2,3,4,7,1,6,5]=>100010=>010001
[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>101110=>011101
[5,6,2,1,3,7,4]=>[4,7,3,1,2,6,5]=>101010=>010101
[5,6,2,1,4,3,7]=>[7,3,4,1,2,6,5]=>101010=>010101
[5,6,2,1,4,7,3]=>[3,7,4,1,2,6,5]=>100110=>011001
[5,6,2,1,7,3,4]=>[4,3,7,1,2,6,5]=>101010=>010101
[5,6,2,1,7,4,3]=>[3,4,7,1,2,6,5]=>100010=>010001
[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>110110=>011011
[5,6,2,3,1,7,4]=>[4,7,1,3,2,6,5]=>110010=>010011
[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>111010=>010111
[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>011110=>011110
[5,6,2,3,7,1,4]=>[4,1,7,3,2,6,5]=>111010=>010111
[5,6,2,3,7,4,1]=>[1,4,7,3,2,6,5]=>011010=>010110
[5,6,2,4,1,3,7]=>[7,3,1,4,2,6,5]=>111010=>010111
[5,6,2,4,1,7,3]=>[3,7,1,4,2,6,5]=>110010=>010011
[5,6,2,4,3,1,7]=>[7,1,3,4,2,6,5]=>110010=>010011
[5,6,2,4,3,7,1]=>[1,7,3,4,2,6,5]=>011010=>010110
[5,6,2,4,7,1,3]=>[3,1,7,4,2,6,5]=>110110=>011011
[5,6,2,4,7,3,1]=>[1,3,7,4,2,6,5]=>010110=>011010
[5,6,2,7,1,3,4]=>[4,3,1,7,2,6,5]=>111010=>010111
[5,6,2,7,1,4,3]=>[3,4,1,7,2,6,5]=>110010=>010011
[5,6,2,7,3,1,4]=>[4,1,3,7,2,6,5]=>110010=>010011
[5,6,2,7,3,4,1]=>[1,4,3,7,2,6,5]=>011010=>010110
[5,6,2,7,4,1,3]=>[3,1,4,7,2,6,5]=>110010=>010011
[5,6,2,7,4,3,1]=>[1,3,4,7,2,6,5]=>010010=>010010
[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>110110=>011011
[5,6,3,1,2,7,4]=>[4,7,2,1,3,6,5]=>110010=>010011
[5,6,3,1,4,2,7]=>[7,2,4,1,3,6,5]=>110010=>010011
[5,6,3,1,4,7,2]=>[2,7,4,1,3,6,5]=>100110=>011001
[5,6,3,1,7,2,4]=>[4,2,7,1,3,6,5]=>110010=>010011
[5,6,3,1,7,4,2]=>[2,4,7,1,3,6,5]=>100010=>010001
[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>100110=>011001
[5,6,3,2,1,7,4]=>[4,7,1,2,3,6,5]=>100010=>010001
[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>110010=>010011
[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>010110=>011010
[5,6,3,2,7,1,4]=>[4,1,7,2,3,6,5]=>110010=>010011
[5,6,3,2,7,4,1]=>[1,4,7,2,3,6,5]=>010010=>010010
[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>111010=>010111
[5,6,3,4,1,7,2]=>[2,7,1,4,3,6,5]=>101010=>010101
[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>101010=>010101
[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>011010=>010110
[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101110=>011101
[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>001110=>011100
[5,6,3,7,1,2,4]=>[4,2,1,7,3,6,5]=>111010=>010111
[5,6,3,7,1,4,2]=>[2,4,1,7,3,6,5]=>101010=>010101
[5,6,3,7,2,1,4]=>[4,1,2,7,3,6,5]=>101010=>010101
[5,6,3,7,2,4,1]=>[1,4,2,7,3,6,5]=>011010=>010110
[5,6,3,7,4,1,2]=>[2,1,4,7,3,6,5]=>101010=>010101
[5,6,3,7,4,2,1]=>[1,2,4,7,3,6,5]=>001010=>010100
[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>111010=>010111
[5,6,4,1,2,7,3]=>[3,7,2,1,4,6,5]=>110010=>010011
[5,6,4,1,3,2,7]=>[7,2,3,1,4,6,5]=>110010=>010011
[5,6,4,1,3,7,2]=>[2,7,3,1,4,6,5]=>101010=>010101
[5,6,4,1,7,2,3]=>[3,2,7,1,4,6,5]=>110010=>010011
[5,6,4,1,7,3,2]=>[2,3,7,1,4,6,5]=>100010=>010001
[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>101010=>010101
[5,6,4,2,1,7,3]=>[3,7,1,2,4,6,5]=>100010=>010001
[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>110010=>010011
[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>011010=>010110
[5,6,4,2,7,1,3]=>[3,1,7,2,4,6,5]=>110010=>010011
[5,6,4,2,7,3,1]=>[1,3,7,2,4,6,5]=>010010=>010010
[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>110010=>010011
[5,6,4,3,1,7,2]=>[2,7,1,3,4,6,5]=>100010=>010001
[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>100010=>010001
[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>010010=>010010
[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>101010=>010101
[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>001010=>010100
[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110110=>011011
[5,6,4,7,1,3,2]=>[2,3,1,7,4,6,5]=>100110=>011001
[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>100110=>011001
[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>010110=>011010
[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>100110=>011001
[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>000110=>011000
[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011=>110111
[5,6,7,1,2,4,3]=>[3,4,2,1,7,6,5]=>110011=>110011
[5,6,7,1,3,2,4]=>[4,2,3,1,7,6,5]=>110011=>110011
[5,6,7,1,3,4,2]=>[2,4,3,1,7,6,5]=>101011=>110101
[5,6,7,1,4,2,3]=>[3,2,4,1,7,6,5]=>110011=>110011
[5,6,7,1,4,3,2]=>[2,3,4,1,7,6,5]=>100011=>110001
[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>101011=>110101
[5,6,7,2,1,4,3]=>[3,4,1,2,7,6,5]=>100011=>110001
[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>110011=>110011
[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011=>110110
[5,6,7,2,4,1,3]=>[3,1,4,2,7,6,5]=>110011=>110011
[5,6,7,2,4,3,1]=>[1,3,4,2,7,6,5]=>010011=>110010
[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>110011=>110011
[5,6,7,3,1,4,2]=>[2,4,1,3,7,6,5]=>100011=>110001
[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>100011=>110001
[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>010011=>110010
[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011=>110101
[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>001011=>110100
[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011=>110011
[5,6,7,4,1,3,2]=>[2,3,1,4,7,6,5]=>100011=>110001
[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>100011=>110001
[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>010011=>110010
[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>100011=>110001
[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>000011=>110000
[5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5]=>111110=>011111
[5,7,1,2,3,6,4]=>[4,6,3,2,1,7,5]=>111010=>010111
[5,7,1,2,4,3,6]=>[6,3,4,2,1,7,5]=>111010=>010111
[5,7,1,2,4,6,3]=>[3,6,4,2,1,7,5]=>110110=>011011
[5,7,1,2,6,3,4]=>[4,3,6,2,1,7,5]=>111010=>010111
[5,7,1,2,6,4,3]=>[3,4,6,2,1,7,5]=>110010=>010011
[5,7,1,3,2,4,6]=>[6,4,2,3,1,7,5]=>110110=>011011
[5,7,1,3,2,6,4]=>[4,6,2,3,1,7,5]=>110010=>010011
[5,7,1,3,4,2,6]=>[6,2,4,3,1,7,5]=>111010=>010111
[5,7,1,3,4,6,2]=>[2,6,4,3,1,7,5]=>101110=>011101
[5,7,1,3,6,2,4]=>[4,2,6,3,1,7,5]=>111010=>010111
[5,7,1,3,6,4,2]=>[2,4,6,3,1,7,5]=>101010=>010101
[5,7,1,4,2,3,6]=>[6,3,2,4,1,7,5]=>111010=>010111
[5,7,1,4,2,6,3]=>[3,6,2,4,1,7,5]=>110010=>010011
[5,7,1,4,3,2,6]=>[6,2,3,4,1,7,5]=>110010=>010011
[5,7,1,4,3,6,2]=>[2,6,3,4,1,7,5]=>101010=>010101
[5,7,1,4,6,2,3]=>[3,2,6,4,1,7,5]=>110110=>011011
[5,7,1,4,6,3,2]=>[2,3,6,4,1,7,5]=>100110=>011001
[5,7,1,6,2,3,4]=>[4,3,2,6,1,7,5]=>111010=>010111
[5,7,1,6,2,4,3]=>[3,4,2,6,1,7,5]=>110010=>010011
[5,7,1,6,3,2,4]=>[4,2,3,6,1,7,5]=>110010=>010011
[5,7,1,6,3,4,2]=>[2,4,3,6,1,7,5]=>101010=>010101
[5,7,1,6,4,2,3]=>[3,2,4,6,1,7,5]=>110010=>010011
[5,7,1,6,4,3,2]=>[2,3,4,6,1,7,5]=>100010=>010001
[5,7,2,1,3,4,6]=>[6,4,3,1,2,7,5]=>101110=>011101
[5,7,2,1,3,6,4]=>[4,6,3,1,2,7,5]=>101010=>010101
[5,7,2,1,4,3,6]=>[6,3,4,1,2,7,5]=>101010=>010101
[5,7,2,1,4,6,3]=>[3,6,4,1,2,7,5]=>100110=>011001
[5,7,2,1,6,3,4]=>[4,3,6,1,2,7,5]=>101010=>010101
[5,7,2,1,6,4,3]=>[3,4,6,1,2,7,5]=>100010=>010001
[5,7,2,3,1,4,6]=>[6,4,1,3,2,7,5]=>110110=>011011
[5,7,2,3,1,6,4]=>[4,6,1,3,2,7,5]=>110010=>010011
[5,7,2,3,4,1,6]=>[6,1,4,3,2,7,5]=>111010=>010111
[5,7,2,3,4,6,1]=>[1,6,4,3,2,7,5]=>011110=>011110
[5,7,2,3,6,1,4]=>[4,1,6,3,2,7,5]=>111010=>010111
[5,7,2,3,6,4,1]=>[1,4,6,3,2,7,5]=>011010=>010110
[5,7,2,4,1,3,6]=>[6,3,1,4,2,7,5]=>111010=>010111
[5,7,2,4,1,6,3]=>[3,6,1,4,2,7,5]=>110010=>010011
[5,7,2,4,3,1,6]=>[6,1,3,4,2,7,5]=>110010=>010011
[5,7,2,4,3,6,1]=>[1,6,3,4,2,7,5]=>011010=>010110
[5,7,2,4,6,1,3]=>[3,1,6,4,2,7,5]=>110110=>011011
[5,7,2,4,6,3,1]=>[1,3,6,4,2,7,5]=>010110=>011010
[5,7,2,6,1,3,4]=>[4,3,1,6,2,7,5]=>111010=>010111
[5,7,2,6,1,4,3]=>[3,4,1,6,2,7,5]=>110010=>010011
[5,7,2,6,3,1,4]=>[4,1,3,6,2,7,5]=>110010=>010011
[5,7,2,6,3,4,1]=>[1,4,3,6,2,7,5]=>011010=>010110
[5,7,2,6,4,1,3]=>[3,1,4,6,2,7,5]=>110010=>010011
[5,7,2,6,4,3,1]=>[1,3,4,6,2,7,5]=>010010=>010010
[5,7,3,1,2,4,6]=>[6,4,2,1,3,7,5]=>110110=>011011
[5,7,3,1,2,6,4]=>[4,6,2,1,3,7,5]=>110010=>010011
[5,7,3,1,4,2,6]=>[6,2,4,1,3,7,5]=>110010=>010011
[5,7,3,1,4,6,2]=>[2,6,4,1,3,7,5]=>100110=>011001
[5,7,3,1,6,2,4]=>[4,2,6,1,3,7,5]=>110010=>010011
[5,7,3,1,6,4,2]=>[2,4,6,1,3,7,5]=>100010=>010001
[5,7,3,2,1,4,6]=>[6,4,1,2,3,7,5]=>100110=>011001
[5,7,3,2,1,6,4]=>[4,6,1,2,3,7,5]=>100010=>010001
[5,7,3,2,4,1,6]=>[6,1,4,2,3,7,5]=>110010=>010011
[5,7,3,2,4,6,1]=>[1,6,4,2,3,7,5]=>010110=>011010
[5,7,3,2,6,1,4]=>[4,1,6,2,3,7,5]=>110010=>010011
[5,7,3,2,6,4,1]=>[1,4,6,2,3,7,5]=>010010=>010010
[5,7,3,4,1,2,6]=>[6,2,1,4,3,7,5]=>111010=>010111
[5,7,3,4,1,6,2]=>[2,6,1,4,3,7,5]=>101010=>010101
[5,7,3,4,2,1,6]=>[6,1,2,4,3,7,5]=>101010=>010101
[5,7,3,4,2,6,1]=>[1,6,2,4,3,7,5]=>011010=>010110
[5,7,3,4,6,1,2]=>[2,1,6,4,3,7,5]=>101110=>011101
[5,7,3,4,6,2,1]=>[1,2,6,4,3,7,5]=>001110=>011100
[5,7,3,6,1,2,4]=>[4,2,1,6,3,7,5]=>111010=>010111
[5,7,3,6,1,4,2]=>[2,4,1,6,3,7,5]=>101010=>010101
[5,7,3,6,2,1,4]=>[4,1,2,6,3,7,5]=>101010=>010101
[5,7,3,6,2,4,1]=>[1,4,2,6,3,7,5]=>011010=>010110
[5,7,3,6,4,1,2]=>[2,1,4,6,3,7,5]=>101010=>010101
[5,7,3,6,4,2,1]=>[1,2,4,6,3,7,5]=>001010=>010100
[5,7,4,1,2,3,6]=>[6,3,2,1,4,7,5]=>111010=>010111
[5,7,4,1,2,6,3]=>[3,6,2,1,4,7,5]=>110010=>010011
[5,7,4,1,3,2,6]=>[6,2,3,1,4,7,5]=>110010=>010011
[5,7,4,1,3,6,2]=>[2,6,3,1,4,7,5]=>101010=>010101
[5,7,4,1,6,2,3]=>[3,2,6,1,4,7,5]=>110010=>010011
[5,7,4,1,6,3,2]=>[2,3,6,1,4,7,5]=>100010=>010001
[5,7,4,2,1,3,6]=>[6,3,1,2,4,7,5]=>101010=>010101
[5,7,4,2,1,6,3]=>[3,6,1,2,4,7,5]=>100010=>010001
[5,7,4,2,3,1,6]=>[6,1,3,2,4,7,5]=>110010=>010011
[5,7,4,2,3,6,1]=>[1,6,3,2,4,7,5]=>011010=>010110
[5,7,4,2,6,1,3]=>[3,1,6,2,4,7,5]=>110010=>010011
[5,7,4,2,6,3,1]=>[1,3,6,2,4,7,5]=>010010=>010010
[5,7,4,3,1,2,6]=>[6,2,1,3,4,7,5]=>110010=>010011
[5,7,4,3,1,6,2]=>[2,6,1,3,4,7,5]=>100010=>010001
[5,7,4,3,2,1,6]=>[6,1,2,3,4,7,5]=>100010=>010001
[5,7,4,3,2,6,1]=>[1,6,2,3,4,7,5]=>010010=>010010
[5,7,4,3,6,1,2]=>[2,1,6,3,4,7,5]=>101010=>010101
[5,7,4,3,6,2,1]=>[1,2,6,3,4,7,5]=>001010=>010100
[5,7,4,6,1,2,3]=>[3,2,1,6,4,7,5]=>110110=>011011
[5,7,4,6,1,3,2]=>[2,3,1,6,4,7,5]=>100110=>011001
[5,7,4,6,2,1,3]=>[3,1,2,6,4,7,5]=>100110=>011001
[5,7,4,6,2,3,1]=>[1,3,2,6,4,7,5]=>010110=>011010
[5,7,4,6,3,1,2]=>[2,1,3,6,4,7,5]=>100110=>011001
[5,7,4,6,3,2,1]=>[1,2,3,6,4,7,5]=>000110=>011000
[5,7,6,1,2,3,4]=>[4,3,2,1,6,7,5]=>111010=>010111
[5,7,6,1,2,4,3]=>[3,4,2,1,6,7,5]=>110010=>010011
[5,7,6,1,3,2,4]=>[4,2,3,1,6,7,5]=>110010=>010011
[5,7,6,1,3,4,2]=>[2,4,3,1,6,7,5]=>101010=>010101
[5,7,6,1,4,2,3]=>[3,2,4,1,6,7,5]=>110010=>010011
[5,7,6,1,4,3,2]=>[2,3,4,1,6,7,5]=>100010=>010001
[5,7,6,2,1,3,4]=>[4,3,1,2,6,7,5]=>101010=>010101
[5,7,6,2,1,4,3]=>[3,4,1,2,6,7,5]=>100010=>010001
[5,7,6,2,3,1,4]=>[4,1,3,2,6,7,5]=>110010=>010011
[5,7,6,2,3,4,1]=>[1,4,3,2,6,7,5]=>011010=>010110
[5,7,6,2,4,1,3]=>[3,1,4,2,6,7,5]=>110010=>010011
[5,7,6,2,4,3,1]=>[1,3,4,2,6,7,5]=>010010=>010010
[5,7,6,3,1,2,4]=>[4,2,1,3,6,7,5]=>110010=>010011
[5,7,6,3,1,4,2]=>[2,4,1,3,6,7,5]=>100010=>010001
[5,7,6,3,2,1,4]=>[4,1,2,3,6,7,5]=>100010=>010001
[5,7,6,3,2,4,1]=>[1,4,2,3,6,7,5]=>010010=>010010
[5,7,6,3,4,1,2]=>[2,1,4,3,6,7,5]=>101010=>010101
[5,7,6,3,4,2,1]=>[1,2,4,3,6,7,5]=>001010=>010100
[5,7,6,4,1,2,3]=>[3,2,1,4,6,7,5]=>110010=>010011
[5,7,6,4,1,3,2]=>[2,3,1,4,6,7,5]=>100010=>010001
[5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5]=>100010=>010001
[5,7,6,4,2,3,1]=>[1,3,2,4,6,7,5]=>010010=>010010
[5,7,6,4,3,1,2]=>[2,1,3,4,6,7,5]=>100010=>010001
[5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5]=>000010=>010000
[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>111110=>011111
[6,1,2,3,4,7,5]=>[5,7,4,3,2,1,6]=>111100=>001111
[6,1,2,3,5,4,7]=>[7,4,5,3,2,1,6]=>111100=>001111
[6,1,2,3,5,7,4]=>[4,7,5,3,2,1,6]=>111010=>010111
[6,1,2,3,7,4,5]=>[5,4,7,3,2,1,6]=>111100=>001111
[6,1,2,3,7,5,4]=>[4,5,7,3,2,1,6]=>111000=>000111
[6,1,2,4,3,5,7]=>[7,5,3,4,2,1,6]=>111010=>010111
[6,1,2,4,3,7,5]=>[5,7,3,4,2,1,6]=>111000=>000111
[6,1,2,4,5,3,7]=>[7,3,5,4,2,1,6]=>111100=>001111
[6,1,2,4,5,7,3]=>[3,7,5,4,2,1,6]=>110110=>011011
[6,1,2,4,7,3,5]=>[5,3,7,4,2,1,6]=>111100=>001111
[6,1,2,4,7,5,3]=>[3,5,7,4,2,1,6]=>110100=>001011
[6,1,2,5,3,4,7]=>[7,4,3,5,2,1,6]=>111100=>001111
[6,1,2,5,3,7,4]=>[4,7,3,5,2,1,6]=>111000=>000111
[6,1,2,5,4,3,7]=>[7,3,4,5,2,1,6]=>111000=>000111
[6,1,2,5,4,7,3]=>[3,7,4,5,2,1,6]=>110100=>001011
[6,1,2,5,7,3,4]=>[4,3,7,5,2,1,6]=>111010=>010111
[6,1,2,5,7,4,3]=>[3,4,7,5,2,1,6]=>110010=>010011
[6,1,2,7,3,4,5]=>[5,4,3,7,2,1,6]=>111100=>001111
[6,1,2,7,3,5,4]=>[4,5,3,7,2,1,6]=>111000=>000111
[6,1,2,7,4,3,5]=>[5,3,4,7,2,1,6]=>111000=>000111
[6,1,2,7,4,5,3]=>[3,5,4,7,2,1,6]=>110100=>001011
[6,1,2,7,5,3,4]=>[4,3,5,7,2,1,6]=>111000=>000111
[6,1,2,7,5,4,3]=>[3,4,5,7,2,1,6]=>110000=>000011
[6,1,3,2,4,5,7]=>[7,5,4,2,3,1,6]=>110110=>011011
[6,1,3,2,4,7,5]=>[5,7,4,2,3,1,6]=>110100=>001011
[6,1,3,2,5,4,7]=>[7,4,5,2,3,1,6]=>110100=>001011
[6,1,3,2,5,7,4]=>[4,7,5,2,3,1,6]=>110010=>010011
[6,1,3,2,7,4,5]=>[5,4,7,2,3,1,6]=>110100=>001011
[6,1,3,2,7,5,4]=>[4,5,7,2,3,1,6]=>110000=>000011
[6,1,3,4,2,5,7]=>[7,5,2,4,3,1,6]=>111010=>010111
[6,1,3,4,2,7,5]=>[5,7,2,4,3,1,6]=>111000=>000111
[6,1,3,4,5,2,7]=>[7,2,5,4,3,1,6]=>111100=>001111
[6,1,3,4,5,7,2]=>[2,7,5,4,3,1,6]=>101110=>011101
[6,1,3,4,7,2,5]=>[5,2,7,4,3,1,6]=>111100=>001111
[6,1,3,4,7,5,2]=>[2,5,7,4,3,1,6]=>101100=>001101
[6,1,3,5,2,4,7]=>[7,4,2,5,3,1,6]=>111100=>001111
[6,1,3,5,2,7,4]=>[4,7,2,5,3,1,6]=>111000=>000111
[6,1,3,5,4,2,7]=>[7,2,4,5,3,1,6]=>111000=>000111
[6,1,3,5,4,7,2]=>[2,7,4,5,3,1,6]=>101100=>001101
[6,1,3,5,7,2,4]=>[4,2,7,5,3,1,6]=>111010=>010111
[6,1,3,5,7,4,2]=>[2,4,7,5,3,1,6]=>101010=>010101
[6,1,3,7,2,4,5]=>[5,4,2,7,3,1,6]=>111100=>001111
[6,1,3,7,2,5,4]=>[4,5,2,7,3,1,6]=>111000=>000111
[6,1,3,7,4,2,5]=>[5,2,4,7,3,1,6]=>111000=>000111
[6,1,3,7,4,5,2]=>[2,5,4,7,3,1,6]=>101100=>001101
[6,1,3,7,5,2,4]=>[4,2,5,7,3,1,6]=>111000=>000111
[6,1,3,7,5,4,2]=>[2,4,5,7,3,1,6]=>101000=>000101
[6,1,4,2,3,5,7]=>[7,5,3,2,4,1,6]=>111010=>010111
[6,1,4,2,3,7,5]=>[5,7,3,2,4,1,6]=>111000=>000111
[6,1,4,2,5,3,7]=>[7,3,5,2,4,1,6]=>111000=>000111
[6,1,4,2,5,7,3]=>[3,7,5,2,4,1,6]=>110010=>010011
[6,1,4,2,7,3,5]=>[5,3,7,2,4,1,6]=>111000=>000111
[6,1,4,2,7,5,3]=>[3,5,7,2,4,1,6]=>110000=>000011
[6,1,4,3,2,5,7]=>[7,5,2,3,4,1,6]=>110010=>010011
[6,1,4,3,2,7,5]=>[5,7,2,3,4,1,6]=>110000=>000011
[6,1,4,3,5,2,7]=>[7,2,5,3,4,1,6]=>111000=>000111
[6,1,4,3,5,7,2]=>[2,7,5,3,4,1,6]=>101010=>010101
[6,1,4,3,7,2,5]=>[5,2,7,3,4,1,6]=>111000=>000111
[6,1,4,3,7,5,2]=>[2,5,7,3,4,1,6]=>101000=>000101
[6,1,4,5,2,3,7]=>[7,3,2,5,4,1,6]=>111100=>001111
[6,1,4,5,2,7,3]=>[3,7,2,5,4,1,6]=>110100=>001011
[6,1,4,5,3,2,7]=>[7,2,3,5,4,1,6]=>110100=>001011
[6,1,4,5,3,7,2]=>[2,7,3,5,4,1,6]=>101100=>001101
[6,1,4,5,7,2,3]=>[3,2,7,5,4,1,6]=>110110=>011011
[6,1,4,5,7,3,2]=>[2,3,7,5,4,1,6]=>100110=>011001
[6,1,4,7,2,3,5]=>[5,3,2,7,4,1,6]=>111100=>001111
[6,1,4,7,2,5,3]=>[3,5,2,7,4,1,6]=>110100=>001011
[6,1,4,7,3,2,5]=>[5,2,3,7,4,1,6]=>110100=>001011
[6,1,4,7,3,5,2]=>[2,5,3,7,4,1,6]=>101100=>001101
[6,1,4,7,5,2,3]=>[3,2,5,7,4,1,6]=>110100=>001011
[6,1,4,7,5,3,2]=>[2,3,5,7,4,1,6]=>100100=>001001
[6,1,5,2,3,4,7]=>[7,4,3,2,5,1,6]=>111100=>001111
[6,1,5,2,3,7,4]=>[4,7,3,2,5,1,6]=>111000=>000111
[6,1,5,2,4,3,7]=>[7,3,4,2,5,1,6]=>111000=>000111
[6,1,5,2,4,7,3]=>[3,7,4,2,5,1,6]=>110100=>001011
[6,1,5,2,7,3,4]=>[4,3,7,2,5,1,6]=>111000=>000111
[6,1,5,2,7,4,3]=>[3,4,7,2,5,1,6]=>110000=>000011
[6,1,5,3,2,4,7]=>[7,4,2,3,5,1,6]=>110100=>001011
[6,1,5,3,2,7,4]=>[4,7,2,3,5,1,6]=>110000=>000011
[6,1,5,3,4,2,7]=>[7,2,4,3,5,1,6]=>111000=>000111
[6,1,5,3,4,7,2]=>[2,7,4,3,5,1,6]=>101100=>001101
[6,1,5,3,7,2,4]=>[4,2,7,3,5,1,6]=>111000=>000111
[6,1,5,3,7,4,2]=>[2,4,7,3,5,1,6]=>101000=>000101
[6,1,5,4,2,3,7]=>[7,3,2,4,5,1,6]=>111000=>000111
[6,1,5,4,2,7,3]=>[3,7,2,4,5,1,6]=>110000=>000011
[6,1,5,4,3,2,7]=>[7,2,3,4,5,1,6]=>110000=>000011
[6,1,5,4,3,7,2]=>[2,7,3,4,5,1,6]=>101000=>000101
[6,1,5,4,7,2,3]=>[3,2,7,4,5,1,6]=>110100=>001011
[6,1,5,4,7,3,2]=>[2,3,7,4,5,1,6]=>100100=>001001
[6,1,5,7,2,3,4]=>[4,3,2,7,5,1,6]=>111010=>010111
[6,1,5,7,2,4,3]=>[3,4,2,7,5,1,6]=>110010=>010011
[6,1,5,7,3,2,4]=>[4,2,3,7,5,1,6]=>110010=>010011
[6,1,5,7,3,4,2]=>[2,4,3,7,5,1,6]=>101010=>010101
[6,1,5,7,4,2,3]=>[3,2,4,7,5,1,6]=>110010=>010011
[6,1,5,7,4,3,2]=>[2,3,4,7,5,1,6]=>100010=>010001
[6,1,7,2,3,4,5]=>[5,4,3,2,7,1,6]=>111100=>001111
[6,1,7,2,3,5,4]=>[4,5,3,2,7,1,6]=>111000=>000111
[6,1,7,2,4,3,5]=>[5,3,4,2,7,1,6]=>111000=>000111
[6,1,7,2,4,5,3]=>[3,5,4,2,7,1,6]=>110100=>001011
[6,1,7,2,5,3,4]=>[4,3,5,2,7,1,6]=>111000=>000111
[6,1,7,2,5,4,3]=>[3,4,5,2,7,1,6]=>110000=>000011
[6,1,7,3,2,4,5]=>[5,4,2,3,7,1,6]=>110100=>001011
[6,1,7,3,2,5,4]=>[4,5,2,3,7,1,6]=>110000=>000011
[6,1,7,3,4,2,5]=>[5,2,4,3,7,1,6]=>111000=>000111
[6,1,7,3,4,5,2]=>[2,5,4,3,7,1,6]=>101100=>001101
[6,1,7,3,5,2,4]=>[4,2,5,3,7,1,6]=>111000=>000111
[6,1,7,3,5,4,2]=>[2,4,5,3,7,1,6]=>101000=>000101
[6,1,7,4,2,3,5]=>[5,3,2,4,7,1,6]=>111000=>000111
[6,1,7,4,2,5,3]=>[3,5,2,4,7,1,6]=>110000=>000011
[6,1,7,4,3,2,5]=>[5,2,3,4,7,1,6]=>110000=>000011
[6,1,7,4,3,5,2]=>[2,5,3,4,7,1,6]=>101000=>000101
[6,1,7,4,5,2,3]=>[3,2,5,4,7,1,6]=>110100=>001011
[6,1,7,4,5,3,2]=>[2,3,5,4,7,1,6]=>100100=>001001
[6,1,7,5,2,3,4]=>[4,3,2,5,7,1,6]=>111000=>000111
[6,1,7,5,2,4,3]=>[3,4,2,5,7,1,6]=>110000=>000011
[6,1,7,5,3,2,4]=>[4,2,3,5,7,1,6]=>110000=>000011
[6,1,7,5,3,4,2]=>[2,4,3,5,7,1,6]=>101000=>000101
[6,1,7,5,4,2,3]=>[3,2,4,5,7,1,6]=>110000=>000011
[6,1,7,5,4,3,2]=>[2,3,4,5,7,1,6]=>100000=>000001
[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>101110=>011101
[6,2,1,3,4,7,5]=>[5,7,4,3,1,2,6]=>101100=>001101
[6,2,1,3,5,4,7]=>[7,4,5,3,1,2,6]=>101100=>001101
[6,2,1,3,5,7,4]=>[4,7,5,3,1,2,6]=>101010=>010101
[6,2,1,3,7,4,5]=>[5,4,7,3,1,2,6]=>101100=>001101
[6,2,1,3,7,5,4]=>[4,5,7,3,1,2,6]=>101000=>000101
[6,2,1,4,3,5,7]=>[7,5,3,4,1,2,6]=>101010=>010101
[6,2,1,4,3,7,5]=>[5,7,3,4,1,2,6]=>101000=>000101
[6,2,1,4,5,3,7]=>[7,3,5,4,1,2,6]=>101100=>001101
[6,2,1,4,5,7,3]=>[3,7,5,4,1,2,6]=>100110=>011001
[6,2,1,4,7,3,5]=>[5,3,7,4,1,2,6]=>101100=>001101
[6,2,1,4,7,5,3]=>[3,5,7,4,1,2,6]=>100100=>001001
[6,2,1,5,3,4,7]=>[7,4,3,5,1,2,6]=>101100=>001101
[6,2,1,5,3,7,4]=>[4,7,3,5,1,2,6]=>101000=>000101
[6,2,1,5,4,3,7]=>[7,3,4,5,1,2,6]=>101000=>000101
[6,2,1,5,4,7,3]=>[3,7,4,5,1,2,6]=>100100=>001001
[6,2,1,5,7,3,4]=>[4,3,7,5,1,2,6]=>101010=>010101
[6,2,1,5,7,4,3]=>[3,4,7,5,1,2,6]=>100010=>010001
[6,2,1,7,3,4,5]=>[5,4,3,7,1,2,6]=>101100=>001101
[6,2,1,7,3,5,4]=>[4,5,3,7,1,2,6]=>101000=>000101
[6,2,1,7,4,3,5]=>[5,3,4,7,1,2,6]=>101000=>000101
[6,2,1,7,4,5,3]=>[3,5,4,7,1,2,6]=>100100=>001001
[6,2,1,7,5,3,4]=>[4,3,5,7,1,2,6]=>101000=>000101
[6,2,1,7,5,4,3]=>[3,4,5,7,1,2,6]=>100000=>000001
[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>110110=>011011
[6,2,3,1,4,7,5]=>[5,7,4,1,3,2,6]=>110100=>001011
[6,2,3,1,5,4,7]=>[7,4,5,1,3,2,6]=>110100=>001011
[6,2,3,1,5,7,4]=>[4,7,5,1,3,2,6]=>110010=>010011
[6,2,3,1,7,4,5]=>[5,4,7,1,3,2,6]=>110100=>001011
[6,2,3,1,7,5,4]=>[4,5,7,1,3,2,6]=>110000=>000011
[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>111010=>010111
[6,2,3,4,1,7,5]=>[5,7,1,4,3,2,6]=>111000=>000111
[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>111100=>001111
[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>011110=>011110
[6,2,3,4,7,1,5]=>[5,1,7,4,3,2,6]=>111100=>001111
[6,2,3,4,7,5,1]=>[1,5,7,4,3,2,6]=>011100=>001110
[6,2,3,5,1,4,7]=>[7,4,1,5,3,2,6]=>111100=>001111
[6,2,3,5,1,7,4]=>[4,7,1,5,3,2,6]=>111000=>000111
[6,2,3,5,4,1,7]=>[7,1,4,5,3,2,6]=>111000=>000111
[6,2,3,5,4,7,1]=>[1,7,4,5,3,2,6]=>011100=>001110
[6,2,3,5,7,1,4]=>[4,1,7,5,3,2,6]=>111010=>010111
[6,2,3,5,7,4,1]=>[1,4,7,5,3,2,6]=>011010=>010110
[6,2,3,7,1,4,5]=>[5,4,1,7,3,2,6]=>111100=>001111
[6,2,3,7,1,5,4]=>[4,5,1,7,3,2,6]=>111000=>000111
[6,2,3,7,4,1,5]=>[5,1,4,7,3,2,6]=>111000=>000111
[6,2,3,7,4,5,1]=>[1,5,4,7,3,2,6]=>011100=>001110
[6,2,3,7,5,1,4]=>[4,1,5,7,3,2,6]=>111000=>000111
[6,2,3,7,5,4,1]=>[1,4,5,7,3,2,6]=>011000=>000110
[6,2,4,1,3,5,7]=>[7,5,3,1,4,2,6]=>111010=>010111
[6,2,4,1,3,7,5]=>[5,7,3,1,4,2,6]=>111000=>000111
[6,2,4,1,5,3,7]=>[7,3,5,1,4,2,6]=>111000=>000111
[6,2,4,1,5,7,3]=>[3,7,5,1,4,2,6]=>110010=>010011
[6,2,4,1,7,3,5]=>[5,3,7,1,4,2,6]=>111000=>000111
[6,2,4,1,7,5,3]=>[3,5,7,1,4,2,6]=>110000=>000011
[6,2,4,3,1,5,7]=>[7,5,1,3,4,2,6]=>110010=>010011
[6,2,4,3,1,7,5]=>[5,7,1,3,4,2,6]=>110000=>000011
[6,2,4,3,5,1,7]=>[7,1,5,3,4,2,6]=>111000=>000111
[6,2,4,3,5,7,1]=>[1,7,5,3,4,2,6]=>011010=>010110
[6,2,4,3,7,1,5]=>[5,1,7,3,4,2,6]=>111000=>000111
[6,2,4,3,7,5,1]=>[1,5,7,3,4,2,6]=>011000=>000110
[6,2,4,5,1,3,7]=>[7,3,1,5,4,2,6]=>111100=>001111
[6,2,4,5,1,7,3]=>[3,7,1,5,4,2,6]=>110100=>001011
[6,2,4,5,3,1,7]=>[7,1,3,5,4,2,6]=>110100=>001011
[6,2,4,5,3,7,1]=>[1,7,3,5,4,2,6]=>011100=>001110
[6,2,4,5,7,1,3]=>[3,1,7,5,4,2,6]=>110110=>011011
[6,2,4,5,7,3,1]=>[1,3,7,5,4,2,6]=>010110=>011010
[6,2,4,7,1,3,5]=>[5,3,1,7,4,2,6]=>111100=>001111
[6,2,4,7,1,5,3]=>[3,5,1,7,4,2,6]=>110100=>001011
[6,2,4,7,3,1,5]=>[5,1,3,7,4,2,6]=>110100=>001011
[6,2,4,7,3,5,1]=>[1,5,3,7,4,2,6]=>011100=>001110
[6,2,4,7,5,1,3]=>[3,1,5,7,4,2,6]=>110100=>001011
[6,2,4,7,5,3,1]=>[1,3,5,7,4,2,6]=>010100=>001010
[6,2,5,1,3,4,7]=>[7,4,3,1,5,2,6]=>111100=>001111
[6,2,5,1,3,7,4]=>[4,7,3,1,5,2,6]=>111000=>000111
[6,2,5,1,4,3,7]=>[7,3,4,1,5,2,6]=>111000=>000111
[6,2,5,1,4,7,3]=>[3,7,4,1,5,2,6]=>110100=>001011
[6,2,5,1,7,3,4]=>[4,3,7,1,5,2,6]=>111000=>000111
[6,2,5,1,7,4,3]=>[3,4,7,1,5,2,6]=>110000=>000011
[6,2,5,3,1,4,7]=>[7,4,1,3,5,2,6]=>110100=>001011
[6,2,5,3,1,7,4]=>[4,7,1,3,5,2,6]=>110000=>000011
[6,2,5,3,4,1,7]=>[7,1,4,3,5,2,6]=>111000=>000111
[6,2,5,3,4,7,1]=>[1,7,4,3,5,2,6]=>011100=>001110
[6,2,5,3,7,1,4]=>[4,1,7,3,5,2,6]=>111000=>000111
[6,2,5,3,7,4,1]=>[1,4,7,3,5,2,6]=>011000=>000110
[6,2,5,4,1,3,7]=>[7,3,1,4,5,2,6]=>111000=>000111
[6,2,5,4,1,7,3]=>[3,7,1,4,5,2,6]=>110000=>000011
[6,2,5,4,3,1,7]=>[7,1,3,4,5,2,6]=>110000=>000011
[6,2,5,4,3,7,1]=>[1,7,3,4,5,2,6]=>011000=>000110
[6,2,5,4,7,1,3]=>[3,1,7,4,5,2,6]=>110100=>001011
[6,2,5,4,7,3,1]=>[1,3,7,4,5,2,6]=>010100=>001010
[6,2,5,7,1,3,4]=>[4,3,1,7,5,2,6]=>111010=>010111
[6,2,5,7,1,4,3]=>[3,4,1,7,5,2,6]=>110010=>010011
[6,2,5,7,3,1,4]=>[4,1,3,7,5,2,6]=>110010=>010011
[6,2,5,7,3,4,1]=>[1,4,3,7,5,2,6]=>011010=>010110
[6,2,5,7,4,1,3]=>[3,1,4,7,5,2,6]=>110010=>010011
[6,2,5,7,4,3,1]=>[1,3,4,7,5,2,6]=>010010=>010010
[6,2,7,1,3,4,5]=>[5,4,3,1,7,2,6]=>111100=>001111
[6,2,7,1,3,5,4]=>[4,5,3,1,7,2,6]=>111000=>000111
[6,2,7,1,4,3,5]=>[5,3,4,1,7,2,6]=>111000=>000111
[6,2,7,1,4,5,3]=>[3,5,4,1,7,2,6]=>110100=>001011
[6,2,7,1,5,3,4]=>[4,3,5,1,7,2,6]=>111000=>000111
[6,2,7,1,5,4,3]=>[3,4,5,1,7,2,6]=>110000=>000011
[6,2,7,3,1,4,5]=>[5,4,1,3,7,2,6]=>110100=>001011
[6,2,7,3,1,5,4]=>[4,5,1,3,7,2,6]=>110000=>000011
[6,2,7,3,4,1,5]=>[5,1,4,3,7,2,6]=>111000=>000111
[6,2,7,3,4,5,1]=>[1,5,4,3,7,2,6]=>011100=>001110
[6,2,7,3,5,1,4]=>[4,1,5,3,7,2,6]=>111000=>000111
[6,2,7,3,5,4,1]=>[1,4,5,3,7,2,6]=>011000=>000110
[6,2,7,4,1,3,5]=>[5,3,1,4,7,2,6]=>111000=>000111
[6,2,7,4,1,5,3]=>[3,5,1,4,7,2,6]=>110000=>000011
[6,2,7,4,3,1,5]=>[5,1,3,4,7,2,6]=>110000=>000011
[6,2,7,4,3,5,1]=>[1,5,3,4,7,2,6]=>011000=>000110
[6,2,7,4,5,1,3]=>[3,1,5,4,7,2,6]=>110100=>001011
[6,2,7,4,5,3,1]=>[1,3,5,4,7,2,6]=>010100=>001010
[6,2,7,5,1,3,4]=>[4,3,1,5,7,2,6]=>111000=>000111
[6,2,7,5,1,4,3]=>[3,4,1,5,7,2,6]=>110000=>000011
[6,2,7,5,3,1,4]=>[4,1,3,5,7,2,6]=>110000=>000011
[6,2,7,5,3,4,1]=>[1,4,3,5,7,2,6]=>011000=>000110
[6,2,7,5,4,1,3]=>[3,1,4,5,7,2,6]=>110000=>000011
[6,2,7,5,4,3,1]=>[1,3,4,5,7,2,6]=>010000=>000010
[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>110110=>011011
[6,3,1,2,4,7,5]=>[5,7,4,2,1,3,6]=>110100=>001011
[6,3,1,2,5,4,7]=>[7,4,5,2,1,3,6]=>110100=>001011
[6,3,1,2,5,7,4]=>[4,7,5,2,1,3,6]=>110010=>010011
[6,3,1,2,7,4,5]=>[5,4,7,2,1,3,6]=>110100=>001011
[6,3,1,2,7,5,4]=>[4,5,7,2,1,3,6]=>110000=>000011
[6,3,1,4,2,5,7]=>[7,5,2,4,1,3,6]=>110010=>010011
[6,3,1,4,2,7,5]=>[5,7,2,4,1,3,6]=>110000=>000011
[6,3,1,4,5,2,7]=>[7,2,5,4,1,3,6]=>110100=>001011
[6,3,1,4,5,7,2]=>[2,7,5,4,1,3,6]=>100110=>011001
[6,3,1,4,7,2,5]=>[5,2,7,4,1,3,6]=>110100=>001011
[6,3,1,4,7,5,2]=>[2,5,7,4,1,3,6]=>100100=>001001
[6,3,1,5,2,4,7]=>[7,4,2,5,1,3,6]=>110100=>001011
[6,3,1,5,2,7,4]=>[4,7,2,5,1,3,6]=>110000=>000011
[6,3,1,5,4,2,7]=>[7,2,4,5,1,3,6]=>110000=>000011
[6,3,1,5,4,7,2]=>[2,7,4,5,1,3,6]=>100100=>001001
[6,3,1,5,7,2,4]=>[4,2,7,5,1,3,6]=>110010=>010011
[6,3,1,5,7,4,2]=>[2,4,7,5,1,3,6]=>100010=>010001
[6,3,1,7,2,4,5]=>[5,4,2,7,1,3,6]=>110100=>001011
[6,3,1,7,2,5,4]=>[4,5,2,7,1,3,6]=>110000=>000011
[6,3,1,7,4,2,5]=>[5,2,4,7,1,3,6]=>110000=>000011
[6,3,1,7,4,5,2]=>[2,5,4,7,1,3,6]=>100100=>001001
[6,3,1,7,5,2,4]=>[4,2,5,7,1,3,6]=>110000=>000011
[6,3,1,7,5,4,2]=>[2,4,5,7,1,3,6]=>100000=>000001
[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>100110=>011001
[6,3,2,1,4,7,5]=>[5,7,4,1,2,3,6]=>100100=>001001
[6,3,2,1,5,4,7]=>[7,4,5,1,2,3,6]=>100100=>001001
[6,3,2,1,5,7,4]=>[4,7,5,1,2,3,6]=>100010=>010001
[6,3,2,1,7,4,5]=>[5,4,7,1,2,3,6]=>100100=>001001
[6,3,2,1,7,5,4]=>[4,5,7,1,2,3,6]=>100000=>000001
[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>110010=>010011
[6,3,2,4,1,7,5]=>[5,7,1,4,2,3,6]=>110000=>000011
[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>110100=>001011
[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>010110=>011010
[6,3,2,4,7,1,5]=>[5,1,7,4,2,3,6]=>110100=>001011
[6,3,2,4,7,5,1]=>[1,5,7,4,2,3,6]=>010100=>001010
[6,3,2,5,1,4,7]=>[7,4,1,5,2,3,6]=>110100=>001011
[6,3,2,5,1,7,4]=>[4,7,1,5,2,3,6]=>110000=>000011
[6,3,2,5,4,1,7]=>[7,1,4,5,2,3,6]=>110000=>000011
[6,3,2,5,4,7,1]=>[1,7,4,5,2,3,6]=>010100=>001010
[6,3,2,5,7,1,4]=>[4,1,7,5,2,3,6]=>110010=>010011
[6,3,2,5,7,4,1]=>[1,4,7,5,2,3,6]=>010010=>010010
[6,3,2,7,1,4,5]=>[5,4,1,7,2,3,6]=>110100=>001011
[6,3,2,7,1,5,4]=>[4,5,1,7,2,3,6]=>110000=>000011
[6,3,2,7,4,1,5]=>[5,1,4,7,2,3,6]=>110000=>000011
[6,3,2,7,4,5,1]=>[1,5,4,7,2,3,6]=>010100=>001010
[6,3,2,7,5,1,4]=>[4,1,5,7,2,3,6]=>110000=>000011
[6,3,2,7,5,4,1]=>[1,4,5,7,2,3,6]=>010000=>000010
[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>111010=>010111
[6,3,4,1,2,7,5]=>[5,7,2,1,4,3,6]=>111000=>000111
[6,3,4,1,5,2,7]=>[7,2,5,1,4,3,6]=>111000=>000111
[6,3,4,1,5,7,2]=>[2,7,5,1,4,3,6]=>101010=>010101
[6,3,4,1,7,2,5]=>[5,2,7,1,4,3,6]=>111000=>000111
[6,3,4,1,7,5,2]=>[2,5,7,1,4,3,6]=>101000=>000101
[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>101010=>010101
[6,3,4,2,1,7,5]=>[5,7,1,2,4,3,6]=>101000=>000101
[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>111000=>000111
[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>011010=>010110
[6,3,4,2,7,1,5]=>[5,1,7,2,4,3,6]=>111000=>000111
[6,3,4,2,7,5,1]=>[1,5,7,2,4,3,6]=>011000=>000110
[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>111100=>001111
[6,3,4,5,1,7,2]=>[2,7,1,5,4,3,6]=>101100=>001101
[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>101100=>001101
[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>011100=>001110
[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101110=>011101
[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>001110=>011100
[6,3,4,7,1,2,5]=>[5,2,1,7,4,3,6]=>111100=>001111
[6,3,4,7,1,5,2]=>[2,5,1,7,4,3,6]=>101100=>001101
[6,3,4,7,2,1,5]=>[5,1,2,7,4,3,6]=>101100=>001101
[6,3,4,7,2,5,1]=>[1,5,2,7,4,3,6]=>011100=>001110
[6,3,4,7,5,1,2]=>[2,1,5,7,4,3,6]=>101100=>001101
[6,3,4,7,5,2,1]=>[1,2,5,7,4,3,6]=>001100=>001100
[6,3,5,1,2,4,7]=>[7,4,2,1,5,3,6]=>111100=>001111
[6,3,5,1,2,7,4]=>[4,7,2,1,5,3,6]=>111000=>000111
[6,3,5,1,4,2,7]=>[7,2,4,1,5,3,6]=>111000=>000111
[6,3,5,1,4,7,2]=>[2,7,4,1,5,3,6]=>101100=>001101
[6,3,5,1,7,2,4]=>[4,2,7,1,5,3,6]=>111000=>000111
[6,3,5,1,7,4,2]=>[2,4,7,1,5,3,6]=>101000=>000101
[6,3,5,2,1,4,7]=>[7,4,1,2,5,3,6]=>101100=>001101
[6,3,5,2,1,7,4]=>[4,7,1,2,5,3,6]=>101000=>000101
[6,3,5,2,4,1,7]=>[7,1,4,2,5,3,6]=>111000=>000111
[6,3,5,2,4,7,1]=>[1,7,4,2,5,3,6]=>011100=>001110
[6,3,5,2,7,1,4]=>[4,1,7,2,5,3,6]=>111000=>000111
[6,3,5,2,7,4,1]=>[1,4,7,2,5,3,6]=>011000=>000110
[6,3,5,4,1,2,7]=>[7,2,1,4,5,3,6]=>111000=>000111
[6,3,5,4,1,7,2]=>[2,7,1,4,5,3,6]=>101000=>000101
[6,3,5,4,2,1,7]=>[7,1,2,4,5,3,6]=>101000=>000101
[6,3,5,4,2,7,1]=>[1,7,2,4,5,3,6]=>011000=>000110
[6,3,5,4,7,1,2]=>[2,1,7,4,5,3,6]=>101100=>001101
[6,3,5,4,7,2,1]=>[1,2,7,4,5,3,6]=>001100=>001100
[6,3,5,7,1,2,4]=>[4,2,1,7,5,3,6]=>111010=>010111
[6,3,5,7,1,4,2]=>[2,4,1,7,5,3,6]=>101010=>010101
[6,3,5,7,2,1,4]=>[4,1,2,7,5,3,6]=>101010=>010101
[6,3,5,7,2,4,1]=>[1,4,2,7,5,3,6]=>011010=>010110
[6,3,5,7,4,1,2]=>[2,1,4,7,5,3,6]=>101010=>010101
[6,3,5,7,4,2,1]=>[1,2,4,7,5,3,6]=>001010=>010100
[6,3,7,1,2,4,5]=>[5,4,2,1,7,3,6]=>111100=>001111
[6,3,7,1,2,5,4]=>[4,5,2,1,7,3,6]=>111000=>000111
[6,3,7,1,4,2,5]=>[5,2,4,1,7,3,6]=>111000=>000111
[6,3,7,1,4,5,2]=>[2,5,4,1,7,3,6]=>101100=>001101
[6,3,7,1,5,2,4]=>[4,2,5,1,7,3,6]=>111000=>000111
[6,3,7,1,5,4,2]=>[2,4,5,1,7,3,6]=>101000=>000101
[6,3,7,2,1,4,5]=>[5,4,1,2,7,3,6]=>101100=>001101
[6,3,7,2,1,5,4]=>[4,5,1,2,7,3,6]=>101000=>000101
[6,3,7,2,4,1,5]=>[5,1,4,2,7,3,6]=>111000=>000111
[6,3,7,2,4,5,1]=>[1,5,4,2,7,3,6]=>011100=>001110
[6,3,7,2,5,1,4]=>[4,1,5,2,7,3,6]=>111000=>000111
[6,3,7,2,5,4,1]=>[1,4,5,2,7,3,6]=>011000=>000110
[6,3,7,4,1,2,5]=>[5,2,1,4,7,3,6]=>111000=>000111
[6,3,7,4,1,5,2]=>[2,5,1,4,7,3,6]=>101000=>000101
[6,3,7,4,2,1,5]=>[5,1,2,4,7,3,6]=>101000=>000101
[6,3,7,4,2,5,1]=>[1,5,2,4,7,3,6]=>011000=>000110
[6,3,7,4,5,1,2]=>[2,1,5,4,7,3,6]=>101100=>001101
[6,3,7,4,5,2,1]=>[1,2,5,4,7,3,6]=>001100=>001100
[6,3,7,5,1,2,4]=>[4,2,1,5,7,3,6]=>111000=>000111
[6,3,7,5,1,4,2]=>[2,4,1,5,7,3,6]=>101000=>000101
[6,3,7,5,2,1,4]=>[4,1,2,5,7,3,6]=>101000=>000101
[6,3,7,5,2,4,1]=>[1,4,2,5,7,3,6]=>011000=>000110
[6,3,7,5,4,1,2]=>[2,1,4,5,7,3,6]=>101000=>000101
[6,3,7,5,4,2,1]=>[1,2,4,5,7,3,6]=>001000=>000100
[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>111010=>010111
[6,4,1,2,3,7,5]=>[5,7,3,2,1,4,6]=>111000=>000111
[6,4,1,2,5,3,7]=>[7,3,5,2,1,4,6]=>111000=>000111
[6,4,1,2,5,7,3]=>[3,7,5,2,1,4,6]=>110010=>010011
[6,4,1,2,7,3,5]=>[5,3,7,2,1,4,6]=>111000=>000111
[6,4,1,2,7,5,3]=>[3,5,7,2,1,4,6]=>110000=>000011
[6,4,1,3,2,5,7]=>[7,5,2,3,1,4,6]=>110010=>010011
[6,4,1,3,2,7,5]=>[5,7,2,3,1,4,6]=>110000=>000011
[6,4,1,3,5,2,7]=>[7,2,5,3,1,4,6]=>111000=>000111
[6,4,1,3,5,7,2]=>[2,7,5,3,1,4,6]=>101010=>010101
[6,4,1,3,7,2,5]=>[5,2,7,3,1,4,6]=>111000=>000111
[6,4,1,3,7,5,2]=>[2,5,7,3,1,4,6]=>101000=>000101
[6,4,1,5,2,3,7]=>[7,3,2,5,1,4,6]=>111000=>000111
[6,4,1,5,2,7,3]=>[3,7,2,5,1,4,6]=>110000=>000011
[6,4,1,5,3,2,7]=>[7,2,3,5,1,4,6]=>110000=>000011
[6,4,1,5,3,7,2]=>[2,7,3,5,1,4,6]=>101000=>000101
[6,4,1,5,7,2,3]=>[3,2,7,5,1,4,6]=>110010=>010011
[6,4,1,5,7,3,2]=>[2,3,7,5,1,4,6]=>100010=>010001
[6,4,1,7,2,3,5]=>[5,3,2,7,1,4,6]=>111000=>000111
[6,4,1,7,2,5,3]=>[3,5,2,7,1,4,6]=>110000=>000011
[6,4,1,7,3,2,5]=>[5,2,3,7,1,4,6]=>110000=>000011
[6,4,1,7,3,5,2]=>[2,5,3,7,1,4,6]=>101000=>000101
[6,4,1,7,5,2,3]=>[3,2,5,7,1,4,6]=>110000=>000011
[6,4,1,7,5,3,2]=>[2,3,5,7,1,4,6]=>100000=>000001
[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>101010=>010101
[6,4,2,1,3,7,5]=>[5,7,3,1,2,4,6]=>101000=>000101
[6,4,2,1,5,3,7]=>[7,3,5,1,2,4,6]=>101000=>000101
[6,4,2,1,5,7,3]=>[3,7,5,1,2,4,6]=>100010=>010001
[6,4,2,1,7,3,5]=>[5,3,7,1,2,4,6]=>101000=>000101
[6,4,2,1,7,5,3]=>[3,5,7,1,2,4,6]=>100000=>000001
[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>110010=>010011
[6,4,2,3,1,7,5]=>[5,7,1,3,2,4,6]=>110000=>000011
[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>111000=>000111
[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>011010=>010110
[6,4,2,3,7,1,5]=>[5,1,7,3,2,4,6]=>111000=>000111
[6,4,2,3,7,5,1]=>[1,5,7,3,2,4,6]=>011000=>000110
[6,4,2,5,1,3,7]=>[7,3,1,5,2,4,6]=>111000=>000111
[6,4,2,5,1,7,3]=>[3,7,1,5,2,4,6]=>110000=>000011
[6,4,2,5,3,1,7]=>[7,1,3,5,2,4,6]=>110000=>000011
[6,4,2,5,3,7,1]=>[1,7,3,5,2,4,6]=>011000=>000110
[6,4,2,5,7,1,3]=>[3,1,7,5,2,4,6]=>110010=>010011
[6,4,2,5,7,3,1]=>[1,3,7,5,2,4,6]=>010010=>010010
[6,4,2,7,1,3,5]=>[5,3,1,7,2,4,6]=>111000=>000111
[6,4,2,7,1,5,3]=>[3,5,1,7,2,4,6]=>110000=>000011
[6,4,2,7,3,1,5]=>[5,1,3,7,2,4,6]=>110000=>000011
[6,4,2,7,3,5,1]=>[1,5,3,7,2,4,6]=>011000=>000110
[6,4,2,7,5,1,3]=>[3,1,5,7,2,4,6]=>110000=>000011
[6,4,2,7,5,3,1]=>[1,3,5,7,2,4,6]=>010000=>000010
[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>110010=>010011
[6,4,3,1,2,7,5]=>[5,7,2,1,3,4,6]=>110000=>000011
[6,4,3,1,5,2,7]=>[7,2,5,1,3,4,6]=>110000=>000011
[6,4,3,1,5,7,2]=>[2,7,5,1,3,4,6]=>100010=>010001
[6,4,3,1,7,2,5]=>[5,2,7,1,3,4,6]=>110000=>000011
[6,4,3,1,7,5,2]=>[2,5,7,1,3,4,6]=>100000=>000001
[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>100010=>010001
[6,4,3,2,1,7,5]=>[5,7,1,2,3,4,6]=>100000=>000001
[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>110000=>000011
[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>010010=>010010
[6,4,3,2,7,1,5]=>[5,1,7,2,3,4,6]=>110000=>000011
[6,4,3,2,7,5,1]=>[1,5,7,2,3,4,6]=>010000=>000010
[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>111000=>000111
[6,4,3,5,1,7,2]=>[2,7,1,5,3,4,6]=>101000=>000101
[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>101000=>000101
[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>011000=>000110
[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>101010=>010101
[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>001010=>010100
[6,4,3,7,1,2,5]=>[5,2,1,7,3,4,6]=>111000=>000111
[6,4,3,7,1,5,2]=>[2,5,1,7,3,4,6]=>101000=>000101
[6,4,3,7,2,1,5]=>[5,1,2,7,3,4,6]=>101000=>000101
[6,4,3,7,2,5,1]=>[1,5,2,7,3,4,6]=>011000=>000110
[6,4,3,7,5,1,2]=>[2,1,5,7,3,4,6]=>101000=>000101
[6,4,3,7,5,2,1]=>[1,2,5,7,3,4,6]=>001000=>000100
[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>111100=>001111
[6,4,5,1,2,7,3]=>[3,7,2,1,5,4,6]=>110100=>001011
[6,4,5,1,3,2,7]=>[7,2,3,1,5,4,6]=>110100=>001011
[6,4,5,1,3,7,2]=>[2,7,3,1,5,4,6]=>101100=>001101
[6,4,5,1,7,2,3]=>[3,2,7,1,5,4,6]=>110100=>001011
[6,4,5,1,7,3,2]=>[2,3,7,1,5,4,6]=>100100=>001001
[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>101100=>001101
[6,4,5,2,1,7,3]=>[3,7,1,2,5,4,6]=>100100=>001001
[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>110100=>001011
[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>011100=>001110
[6,4,5,2,7,1,3]=>[3,1,7,2,5,4,6]=>110100=>001011
[6,4,5,2,7,3,1]=>[1,3,7,2,5,4,6]=>010100=>001010
[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>110100=>001011
[6,4,5,3,1,7,2]=>[2,7,1,3,5,4,6]=>100100=>001001
[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>100100=>001001
[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>010100=>001010
[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>101100=>001101
[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>001100=>001100
[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110110=>011011
[6,4,5,7,1,3,2]=>[2,3,1,7,5,4,6]=>100110=>011001
[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>100110=>011001
[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010110=>011010
[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100110=>011001
[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>000110=>011000
[6,4,7,1,2,3,5]=>[5,3,2,1,7,4,6]=>111100=>001111
[6,4,7,1,2,5,3]=>[3,5,2,1,7,4,6]=>110100=>001011
[6,4,7,1,3,2,5]=>[5,2,3,1,7,4,6]=>110100=>001011
[6,4,7,1,3,5,2]=>[2,5,3,1,7,4,6]=>101100=>001101
[6,4,7,1,5,2,3]=>[3,2,5,1,7,4,6]=>110100=>001011
[6,4,7,1,5,3,2]=>[2,3,5,1,7,4,6]=>100100=>001001
[6,4,7,2,1,3,5]=>[5,3,1,2,7,4,6]=>101100=>001101
[6,4,7,2,1,5,3]=>[3,5,1,2,7,4,6]=>100100=>001001
[6,4,7,2,3,1,5]=>[5,1,3,2,7,4,6]=>110100=>001011
[6,4,7,2,3,5,1]=>[1,5,3,2,7,4,6]=>011100=>001110
[6,4,7,2,5,1,3]=>[3,1,5,2,7,4,6]=>110100=>001011
[6,4,7,2,5,3,1]=>[1,3,5,2,7,4,6]=>010100=>001010
[6,4,7,3,1,2,5]=>[5,2,1,3,7,4,6]=>110100=>001011
[6,4,7,3,1,5,2]=>[2,5,1,3,7,4,6]=>100100=>001001
[6,4,7,3,2,1,5]=>[5,1,2,3,7,4,6]=>100100=>001001
[6,4,7,3,2,5,1]=>[1,5,2,3,7,4,6]=>010100=>001010
[6,4,7,3,5,1,2]=>[2,1,5,3,7,4,6]=>101100=>001101
[6,4,7,3,5,2,1]=>[1,2,5,3,7,4,6]=>001100=>001100
[6,4,7,5,1,2,3]=>[3,2,1,5,7,4,6]=>110100=>001011
[6,4,7,5,1,3,2]=>[2,3,1,5,7,4,6]=>100100=>001001
[6,4,7,5,2,1,3]=>[3,1,2,5,7,4,6]=>100100=>001001
[6,4,7,5,2,3,1]=>[1,3,2,5,7,4,6]=>010100=>001010
[6,4,7,5,3,1,2]=>[2,1,3,5,7,4,6]=>100100=>001001
[6,4,7,5,3,2,1]=>[1,2,3,5,7,4,6]=>000100=>001000
[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111100=>001111
[6,5,1,2,3,7,4]=>[4,7,3,2,1,5,6]=>111000=>000111
[6,5,1,2,4,3,7]=>[7,3,4,2,1,5,6]=>111000=>000111
[6,5,1,2,4,7,3]=>[3,7,4,2,1,5,6]=>110100=>001011
[6,5,1,2,7,3,4]=>[4,3,7,2,1,5,6]=>111000=>000111
[6,5,1,2,7,4,3]=>[3,4,7,2,1,5,6]=>110000=>000011
[6,5,1,3,2,4,7]=>[7,4,2,3,1,5,6]=>110100=>001011
[6,5,1,3,2,7,4]=>[4,7,2,3,1,5,6]=>110000=>000011
[6,5,1,3,4,2,7]=>[7,2,4,3,1,5,6]=>111000=>000111
[6,5,1,3,4,7,2]=>[2,7,4,3,1,5,6]=>101100=>001101
[6,5,1,3,7,2,4]=>[4,2,7,3,1,5,6]=>111000=>000111
[6,5,1,3,7,4,2]=>[2,4,7,3,1,5,6]=>101000=>000101
[6,5,1,4,2,3,7]=>[7,3,2,4,1,5,6]=>111000=>000111
[6,5,1,4,2,7,3]=>[3,7,2,4,1,5,6]=>110000=>000011
[6,5,1,4,3,2,7]=>[7,2,3,4,1,5,6]=>110000=>000011
[6,5,1,4,3,7,2]=>[2,7,3,4,1,5,6]=>101000=>000101
[6,5,1,4,7,2,3]=>[3,2,7,4,1,5,6]=>110100=>001011
[6,5,1,4,7,3,2]=>[2,3,7,4,1,5,6]=>100100=>001001
[6,5,1,7,2,3,4]=>[4,3,2,7,1,5,6]=>111000=>000111
[6,5,1,7,2,4,3]=>[3,4,2,7,1,5,6]=>110000=>000011
[6,5,1,7,3,2,4]=>[4,2,3,7,1,5,6]=>110000=>000011
[6,5,1,7,3,4,2]=>[2,4,3,7,1,5,6]=>101000=>000101
[6,5,1,7,4,2,3]=>[3,2,4,7,1,5,6]=>110000=>000011
[6,5,1,7,4,3,2]=>[2,3,4,7,1,5,6]=>100000=>000001
[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>101100=>001101
[6,5,2,1,3,7,4]=>[4,7,3,1,2,5,6]=>101000=>000101
[6,5,2,1,4,3,7]=>[7,3,4,1,2,5,6]=>101000=>000101
[6,5,2,1,4,7,3]=>[3,7,4,1,2,5,6]=>100100=>001001
[6,5,2,1,7,3,4]=>[4,3,7,1,2,5,6]=>101000=>000101
[6,5,2,1,7,4,3]=>[3,4,7,1,2,5,6]=>100000=>000001
[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>110100=>001011
[6,5,2,3,1,7,4]=>[4,7,1,3,2,5,6]=>110000=>000011
[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>111000=>000111
[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>011100=>001110
[6,5,2,3,7,1,4]=>[4,1,7,3,2,5,6]=>111000=>000111
[6,5,2,3,7,4,1]=>[1,4,7,3,2,5,6]=>011000=>000110
[6,5,2,4,1,3,7]=>[7,3,1,4,2,5,6]=>111000=>000111
[6,5,2,4,1,7,3]=>[3,7,1,4,2,5,6]=>110000=>000011
[6,5,2,4,3,1,7]=>[7,1,3,4,2,5,6]=>110000=>000011
[6,5,2,4,3,7,1]=>[1,7,3,4,2,5,6]=>011000=>000110
[6,5,2,4,7,1,3]=>[3,1,7,4,2,5,6]=>110100=>001011
[6,5,2,4,7,3,1]=>[1,3,7,4,2,5,6]=>010100=>001010
[6,5,2,7,1,3,4]=>[4,3,1,7,2,5,6]=>111000=>000111
[6,5,2,7,1,4,3]=>[3,4,1,7,2,5,6]=>110000=>000011
[6,5,2,7,3,1,4]=>[4,1,3,7,2,5,6]=>110000=>000011
[6,5,2,7,3,4,1]=>[1,4,3,7,2,5,6]=>011000=>000110
[6,5,2,7,4,1,3]=>[3,1,4,7,2,5,6]=>110000=>000011
[6,5,2,7,4,3,1]=>[1,3,4,7,2,5,6]=>010000=>000010
[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>110100=>001011
[6,5,3,1,2,7,4]=>[4,7,2,1,3,5,6]=>110000=>000011
[6,5,3,1,4,2,7]=>[7,2,4,1,3,5,6]=>110000=>000011
[6,5,3,1,4,7,2]=>[2,7,4,1,3,5,6]=>100100=>001001
[6,5,3,1,7,2,4]=>[4,2,7,1,3,5,6]=>110000=>000011
[6,5,3,1,7,4,2]=>[2,4,7,1,3,5,6]=>100000=>000001
[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>100100=>001001
[6,5,3,2,1,7,4]=>[4,7,1,2,3,5,6]=>100000=>000001
[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>110000=>000011
[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>010100=>001010
[6,5,3,2,7,1,4]=>[4,1,7,2,3,5,6]=>110000=>000011
[6,5,3,2,7,4,1]=>[1,4,7,2,3,5,6]=>010000=>000010
[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>111000=>000111
[6,5,3,4,1,7,2]=>[2,7,1,4,3,5,6]=>101000=>000101
[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>101000=>000101
[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>011000=>000110
[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101100=>001101
[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>001100=>001100
[6,5,3,7,1,2,4]=>[4,2,1,7,3,5,6]=>111000=>000111
[6,5,3,7,1,4,2]=>[2,4,1,7,3,5,6]=>101000=>000101
[6,5,3,7,2,1,4]=>[4,1,2,7,3,5,6]=>101000=>000101
[6,5,3,7,2,4,1]=>[1,4,2,7,3,5,6]=>011000=>000110
[6,5,3,7,4,1,2]=>[2,1,4,7,3,5,6]=>101000=>000101
[6,5,3,7,4,2,1]=>[1,2,4,7,3,5,6]=>001000=>000100
[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>111000=>000111
[6,5,4,1,2,7,3]=>[3,7,2,1,4,5,6]=>110000=>000011
[6,5,4,1,3,2,7]=>[7,2,3,1,4,5,6]=>110000=>000011
[6,5,4,1,3,7,2]=>[2,7,3,1,4,5,6]=>101000=>000101
[6,5,4,1,7,2,3]=>[3,2,7,1,4,5,6]=>110000=>000011
[6,5,4,1,7,3,2]=>[2,3,7,1,4,5,6]=>100000=>000001
[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>101000=>000101
[6,5,4,2,1,7,3]=>[3,7,1,2,4,5,6]=>100000=>000001
[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>110000=>000011
[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>011000=>000110
[6,5,4,2,7,1,3]=>[3,1,7,2,4,5,6]=>110000=>000011
[6,5,4,2,7,3,1]=>[1,3,7,2,4,5,6]=>010000=>000010
[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>110000=>000011
[6,5,4,3,1,7,2]=>[2,7,1,3,4,5,6]=>100000=>000001
[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>100000=>000001
[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>010000=>000010
[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>101000=>000101
[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>001000=>000100
[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110100=>001011
[6,5,4,7,1,3,2]=>[2,3,1,7,4,5,6]=>100100=>001001
[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>100100=>001001
[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>010100=>001010
[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>100100=>001001
[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>000100=>001000
[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111010=>010111
[6,5,7,1,2,4,3]=>[3,4,2,1,7,5,6]=>110010=>010011
[6,5,7,1,3,2,4]=>[4,2,3,1,7,5,6]=>110010=>010011
[6,5,7,1,3,4,2]=>[2,4,3,1,7,5,6]=>101010=>010101
[6,5,7,1,4,2,3]=>[3,2,4,1,7,5,6]=>110010=>010011
[6,5,7,1,4,3,2]=>[2,3,4,1,7,5,6]=>100010=>010001
[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>101010=>010101
[6,5,7,2,1,4,3]=>[3,4,1,2,7,5,6]=>100010=>010001
[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>110010=>010011
[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011010=>010110
[6,5,7,2,4,1,3]=>[3,1,4,2,7,5,6]=>110010=>010011
[6,5,7,2,4,3,1]=>[1,3,4,2,7,5,6]=>010010=>010010
[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>110010=>010011
[6,5,7,3,1,4,2]=>[2,4,1,3,7,5,6]=>100010=>010001
[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>100010=>010001
[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>010010=>010010
[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101010=>010101
[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>001010=>010100
[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110010=>010011
[6,5,7,4,1,3,2]=>[2,3,1,4,7,5,6]=>100010=>010001
[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>100010=>010001
[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>010010=>010010
[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>100010=>010001
[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>000010=>010000
[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101=>101111
[6,7,1,2,3,5,4]=>[4,5,3,2,1,7,6]=>111001=>100111
[6,7,1,2,4,3,5]=>[5,3,4,2,1,7,6]=>111001=>100111
[6,7,1,2,4,5,3]=>[3,5,4,2,1,7,6]=>110101=>101011
[6,7,1,2,5,3,4]=>[4,3,5,2,1,7,6]=>111001=>100111
[6,7,1,2,5,4,3]=>[3,4,5,2,1,7,6]=>110001=>100011
[6,7,1,3,2,4,5]=>[5,4,2,3,1,7,6]=>110101=>101011
[6,7,1,3,2,5,4]=>[4,5,2,3,1,7,6]=>110001=>100011
[6,7,1,3,4,2,5]=>[5,2,4,3,1,7,6]=>111001=>100111
[6,7,1,3,4,5,2]=>[2,5,4,3,1,7,6]=>101101=>101101
[6,7,1,3,5,2,4]=>[4,2,5,3,1,7,6]=>111001=>100111
[6,7,1,3,5,4,2]=>[2,4,5,3,1,7,6]=>101001=>100101
[6,7,1,4,2,3,5]=>[5,3,2,4,1,7,6]=>111001=>100111
[6,7,1,4,2,5,3]=>[3,5,2,4,1,7,6]=>110001=>100011
[6,7,1,4,3,2,5]=>[5,2,3,4,1,7,6]=>110001=>100011
[6,7,1,4,3,5,2]=>[2,5,3,4,1,7,6]=>101001=>100101
[6,7,1,4,5,2,3]=>[3,2,5,4,1,7,6]=>110101=>101011
[6,7,1,4,5,3,2]=>[2,3,5,4,1,7,6]=>100101=>101001
[6,7,1,5,2,3,4]=>[4,3,2,5,1,7,6]=>111001=>100111
[6,7,1,5,2,4,3]=>[3,4,2,5,1,7,6]=>110001=>100011
[6,7,1,5,3,2,4]=>[4,2,3,5,1,7,6]=>110001=>100011
[6,7,1,5,3,4,2]=>[2,4,3,5,1,7,6]=>101001=>100101
[6,7,1,5,4,2,3]=>[3,2,4,5,1,7,6]=>110001=>100011
[6,7,1,5,4,3,2]=>[2,3,4,5,1,7,6]=>100001=>100001
[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>101101=>101101
[6,7,2,1,3,5,4]=>[4,5,3,1,2,7,6]=>101001=>100101
[6,7,2,1,4,3,5]=>[5,3,4,1,2,7,6]=>101001=>100101
[6,7,2,1,4,5,3]=>[3,5,4,1,2,7,6]=>100101=>101001
[6,7,2,1,5,3,4]=>[4,3,5,1,2,7,6]=>101001=>100101
[6,7,2,1,5,4,3]=>[3,4,5,1,2,7,6]=>100001=>100001
[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>110101=>101011
[6,7,2,3,1,5,4]=>[4,5,1,3,2,7,6]=>110001=>100011
[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>111001=>100111
[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101=>101110
[6,7,2,3,5,1,4]=>[4,1,5,3,2,7,6]=>111001=>100111
[6,7,2,3,5,4,1]=>[1,4,5,3,2,7,6]=>011001=>100110
[6,7,2,4,1,3,5]=>[5,3,1,4,2,7,6]=>111001=>100111
[6,7,2,4,1,5,3]=>[3,5,1,4,2,7,6]=>110001=>100011
[6,7,2,4,3,1,5]=>[5,1,3,4,2,7,6]=>110001=>100011
[6,7,2,4,3,5,1]=>[1,5,3,4,2,7,6]=>011001=>100110
[6,7,2,4,5,1,3]=>[3,1,5,4,2,7,6]=>110101=>101011
[6,7,2,4,5,3,1]=>[1,3,5,4,2,7,6]=>010101=>101010
[6,7,2,5,1,3,4]=>[4,3,1,5,2,7,6]=>111001=>100111
[6,7,2,5,1,4,3]=>[3,4,1,5,2,7,6]=>110001=>100011
[6,7,2,5,3,1,4]=>[4,1,3,5,2,7,6]=>110001=>100011
[6,7,2,5,3,4,1]=>[1,4,3,5,2,7,6]=>011001=>100110
[6,7,2,5,4,1,3]=>[3,1,4,5,2,7,6]=>110001=>100011
[6,7,2,5,4,3,1]=>[1,3,4,5,2,7,6]=>010001=>100010
[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>110101=>101011
[6,7,3,1,2,5,4]=>[4,5,2,1,3,7,6]=>110001=>100011
[6,7,3,1,4,2,5]=>[5,2,4,1,3,7,6]=>110001=>100011
[6,7,3,1,4,5,2]=>[2,5,4,1,3,7,6]=>100101=>101001
[6,7,3,1,5,2,4]=>[4,2,5,1,3,7,6]=>110001=>100011
[6,7,3,1,5,4,2]=>[2,4,5,1,3,7,6]=>100001=>100001
[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>100101=>101001
[6,7,3,2,1,5,4]=>[4,5,1,2,3,7,6]=>100001=>100001
[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>110001=>100011
[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>010101=>101010
[6,7,3,2,5,1,4]=>[4,1,5,2,3,7,6]=>110001=>100011
[6,7,3,2,5,4,1]=>[1,4,5,2,3,7,6]=>010001=>100010
[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>111001=>100111
[6,7,3,4,1,5,2]=>[2,5,1,4,3,7,6]=>101001=>100101
[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>101001=>100101
[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>011001=>100110
[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101=>101101
[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>001101=>101100
[6,7,3,5,1,2,4]=>[4,2,1,5,3,7,6]=>111001=>100111
[6,7,3,5,1,4,2]=>[2,4,1,5,3,7,6]=>101001=>100101
[6,7,3,5,2,1,4]=>[4,1,2,5,3,7,6]=>101001=>100101
[6,7,3,5,2,4,1]=>[1,4,2,5,3,7,6]=>011001=>100110
[6,7,3,5,4,1,2]=>[2,1,4,5,3,7,6]=>101001=>100101
[6,7,3,5,4,2,1]=>[1,2,4,5,3,7,6]=>001001=>100100
[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>111001=>100111
[6,7,4,1,2,5,3]=>[3,5,2,1,4,7,6]=>110001=>100011
[6,7,4,1,3,2,5]=>[5,2,3,1,4,7,6]=>110001=>100011
[6,7,4,1,3,5,2]=>[2,5,3,1,4,7,6]=>101001=>100101
[6,7,4,1,5,2,3]=>[3,2,5,1,4,7,6]=>110001=>100011
[6,7,4,1,5,3,2]=>[2,3,5,1,4,7,6]=>100001=>100001
[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>101001=>100101
[6,7,4,2,1,5,3]=>[3,5,1,2,4,7,6]=>100001=>100001
[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>110001=>100011
[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>011001=>100110
[6,7,4,2,5,1,3]=>[3,1,5,2,4,7,6]=>110001=>100011
[6,7,4,2,5,3,1]=>[1,3,5,2,4,7,6]=>010001=>100010
[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>110001=>100011
[6,7,4,3,1,5,2]=>[2,5,1,3,4,7,6]=>100001=>100001
[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>100001=>100001
[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>010001=>100010
[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>101001=>100101
[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>001001=>100100
[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101=>101011
[6,7,4,5,1,3,2]=>[2,3,1,5,4,7,6]=>100101=>101001
[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>100101=>101001
[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101=>101010
[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101=>101001
[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>000101=>101000
[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001=>100111
[6,7,5,1,2,4,3]=>[3,4,2,1,5,7,6]=>110001=>100011
[6,7,5,1,3,2,4]=>[4,2,3,1,5,7,6]=>110001=>100011
[6,7,5,1,3,4,2]=>[2,4,3,1,5,7,6]=>101001=>100101
[6,7,5,1,4,2,3]=>[3,2,4,1,5,7,6]=>110001=>100011
[6,7,5,1,4,3,2]=>[2,3,4,1,5,7,6]=>100001=>100001
[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>101001=>100101
[6,7,5,2,1,4,3]=>[3,4,1,2,5,7,6]=>100001=>100001
[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>110001=>100011
[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001=>100110
[6,7,5,2,4,1,3]=>[3,1,4,2,5,7,6]=>110001=>100011
[6,7,5,2,4,3,1]=>[1,3,4,2,5,7,6]=>010001=>100010
[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>110001=>100011
[6,7,5,3,1,4,2]=>[2,4,1,3,5,7,6]=>100001=>100001
[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>100001=>100001
[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>010001=>100010
[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001=>100101
[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>001001=>100100
[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001=>100011
[6,7,5,4,1,3,2]=>[2,3,1,4,5,7,6]=>100001=>100001
[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>100001=>100001
[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>010001=>100010
[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001=>100001
[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>000001=>100000
[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>111110=>011111
[7,1,2,3,4,6,5]=>[5,6,4,3,2,1,7]=>111100=>001111
[7,1,2,3,5,4,6]=>[6,4,5,3,2,1,7]=>111100=>001111
[7,1,2,3,5,6,4]=>[4,6,5,3,2,1,7]=>111010=>010111
[7,1,2,3,6,4,5]=>[5,4,6,3,2,1,7]=>111100=>001111
[7,1,2,3,6,5,4]=>[4,5,6,3,2,1,7]=>111000=>000111
[7,1,2,4,3,5,6]=>[6,5,3,4,2,1,7]=>111010=>010111
[7,1,2,4,3,6,5]=>[5,6,3,4,2,1,7]=>111000=>000111
[7,1,2,4,5,3,6]=>[6,3,5,4,2,1,7]=>111100=>001111
[7,1,2,4,5,6,3]=>[3,6,5,4,2,1,7]=>110110=>011011
[7,1,2,4,6,3,5]=>[5,3,6,4,2,1,7]=>111100=>001111
[7,1,2,4,6,5,3]=>[3,5,6,4,2,1,7]=>110100=>001011
[7,1,2,5,3,4,6]=>[6,4,3,5,2,1,7]=>111100=>001111
[7,1,2,5,3,6,4]=>[4,6,3,5,2,1,7]=>111000=>000111
[7,1,2,5,4,3,6]=>[6,3,4,5,2,1,7]=>111000=>000111
[7,1,2,5,4,6,3]=>[3,6,4,5,2,1,7]=>110100=>001011
[7,1,2,5,6,3,4]=>[4,3,6,5,2,1,7]=>111010=>010111
[7,1,2,5,6,4,3]=>[3,4,6,5,2,1,7]=>110010=>010011
[7,1,2,6,3,4,5]=>[5,4,3,6,2,1,7]=>111100=>001111
[7,1,2,6,3,5,4]=>[4,5,3,6,2,1,7]=>111000=>000111
[7,1,2,6,4,3,5]=>[5,3,4,6,2,1,7]=>111000=>000111
[7,1,2,6,4,5,3]=>[3,5,4,6,2,1,7]=>110100=>001011
[7,1,2,6,5,3,4]=>[4,3,5,6,2,1,7]=>111000=>000111
[7,1,2,6,5,4,3]=>[3,4,5,6,2,1,7]=>110000=>000011
[7,1,3,2,4,5,6]=>[6,5,4,2,3,1,7]=>110110=>011011
[7,1,3,2,4,6,5]=>[5,6,4,2,3,1,7]=>110100=>001011
[7,1,3,2,5,4,6]=>[6,4,5,2,3,1,7]=>110100=>001011
[7,1,3,2,5,6,4]=>[4,6,5,2,3,1,7]=>110010=>010011
[7,1,3,2,6,4,5]=>[5,4,6,2,3,1,7]=>110100=>001011
[7,1,3,2,6,5,4]=>[4,5,6,2,3,1,7]=>110000=>000011
[7,1,3,4,2,5,6]=>[6,5,2,4,3,1,7]=>111010=>010111
[7,1,3,4,2,6,5]=>[5,6,2,4,3,1,7]=>111000=>000111
[7,1,3,4,5,2,6]=>[6,2,5,4,3,1,7]=>111100=>001111
[7,1,3,4,5,6,2]=>[2,6,5,4,3,1,7]=>101110=>011101
[7,1,3,4,6,2,5]=>[5,2,6,4,3,1,7]=>111100=>001111
[7,1,3,4,6,5,2]=>[2,5,6,4,3,1,7]=>101100=>001101
[7,1,3,5,2,4,6]=>[6,4,2,5,3,1,7]=>111100=>001111
[7,1,3,5,2,6,4]=>[4,6,2,5,3,1,7]=>111000=>000111
[7,1,3,5,4,2,6]=>[6,2,4,5,3,1,7]=>111000=>000111
[7,1,3,5,4,6,2]=>[2,6,4,5,3,1,7]=>101100=>001101
[7,1,3,5,6,2,4]=>[4,2,6,5,3,1,7]=>111010=>010111
[7,1,3,5,6,4,2]=>[2,4,6,5,3,1,7]=>101010=>010101
[7,1,3,6,2,4,5]=>[5,4,2,6,3,1,7]=>111100=>001111
[7,1,3,6,2,5,4]=>[4,5,2,6,3,1,7]=>111000=>000111
[7,1,3,6,4,2,5]=>[5,2,4,6,3,1,7]=>111000=>000111
[7,1,3,6,4,5,2]=>[2,5,4,6,3,1,7]=>101100=>001101
[7,1,3,6,5,2,4]=>[4,2,5,6,3,1,7]=>111000=>000111
[7,1,3,6,5,4,2]=>[2,4,5,6,3,1,7]=>101000=>000101
[7,1,4,2,3,5,6]=>[6,5,3,2,4,1,7]=>111010=>010111
[7,1,4,2,3,6,5]=>[5,6,3,2,4,1,7]=>111000=>000111
[7,1,4,2,5,3,6]=>[6,3,5,2,4,1,7]=>111000=>000111
[7,1,4,2,5,6,3]=>[3,6,5,2,4,1,7]=>110010=>010011
[7,1,4,2,6,3,5]=>[5,3,6,2,4,1,7]=>111000=>000111
[7,1,4,2,6,5,3]=>[3,5,6,2,4,1,7]=>110000=>000011
[7,1,4,3,2,5,6]=>[6,5,2,3,4,1,7]=>110010=>010011
[7,1,4,3,2,6,5]=>[5,6,2,3,4,1,7]=>110000=>000011
[7,1,4,3,5,2,6]=>[6,2,5,3,4,1,7]=>111000=>000111
[7,1,4,3,5,6,2]=>[2,6,5,3,4,1,7]=>101010=>010101
[7,1,4,3,6,2,5]=>[5,2,6,3,4,1,7]=>111000=>000111
[7,1,4,3,6,5,2]=>[2,5,6,3,4,1,7]=>101000=>000101
[7,1,4,5,2,3,6]=>[6,3,2,5,4,1,7]=>111100=>001111
[7,1,4,5,2,6,3]=>[3,6,2,5,4,1,7]=>110100=>001011
[7,1,4,5,3,2,6]=>[6,2,3,5,4,1,7]=>110100=>001011
[7,1,4,5,3,6,2]=>[2,6,3,5,4,1,7]=>101100=>001101
[7,1,4,5,6,2,3]=>[3,2,6,5,4,1,7]=>110110=>011011
[7,1,4,5,6,3,2]=>[2,3,6,5,4,1,7]=>100110=>011001
[7,1,4,6,2,3,5]=>[5,3,2,6,4,1,7]=>111100=>001111
[7,1,4,6,2,5,3]=>[3,5,2,6,4,1,7]=>110100=>001011
[7,1,4,6,3,2,5]=>[5,2,3,6,4,1,7]=>110100=>001011
[7,1,4,6,3,5,2]=>[2,5,3,6,4,1,7]=>101100=>001101
[7,1,4,6,5,2,3]=>[3,2,5,6,4,1,7]=>110100=>001011
[7,1,4,6,5,3,2]=>[2,3,5,6,4,1,7]=>100100=>001001
[7,1,5,2,3,4,6]=>[6,4,3,2,5,1,7]=>111100=>001111
[7,1,5,2,3,6,4]=>[4,6,3,2,5,1,7]=>111000=>000111
[7,1,5,2,4,3,6]=>[6,3,4,2,5,1,7]=>111000=>000111
[7,1,5,2,4,6,3]=>[3,6,4,2,5,1,7]=>110100=>001011
[7,1,5,2,6,3,4]=>[4,3,6,2,5,1,7]=>111000=>000111
[7,1,5,2,6,4,3]=>[3,4,6,2,5,1,7]=>110000=>000011
[7,1,5,3,2,4,6]=>[6,4,2,3,5,1,7]=>110100=>001011
[7,1,5,3,2,6,4]=>[4,6,2,3,5,1,7]=>110000=>000011
[7,1,5,3,4,2,6]=>[6,2,4,3,5,1,7]=>111000=>000111
[7,1,5,3,4,6,2]=>[2,6,4,3,5,1,7]=>101100=>001101
[7,1,5,3,6,2,4]=>[4,2,6,3,5,1,7]=>111000=>000111
[7,1,5,3,6,4,2]=>[2,4,6,3,5,1,7]=>101000=>000101
[7,1,5,4,2,3,6]=>[6,3,2,4,5,1,7]=>111000=>000111
[7,1,5,4,2,6,3]=>[3,6,2,4,5,1,7]=>110000=>000011
[7,1,5,4,3,2,6]=>[6,2,3,4,5,1,7]=>110000=>000011
[7,1,5,4,3,6,2]=>[2,6,3,4,5,1,7]=>101000=>000101
[7,1,5,4,6,2,3]=>[3,2,6,4,5,1,7]=>110100=>001011
[7,1,5,4,6,3,2]=>[2,3,6,4,5,1,7]=>100100=>001001
[7,1,5,6,2,3,4]=>[4,3,2,6,5,1,7]=>111010=>010111
[7,1,5,6,2,4,3]=>[3,4,2,6,5,1,7]=>110010=>010011
[7,1,5,6,3,2,4]=>[4,2,3,6,5,1,7]=>110010=>010011
[7,1,5,6,3,4,2]=>[2,4,3,6,5,1,7]=>101010=>010101
[7,1,5,6,4,2,3]=>[3,2,4,6,5,1,7]=>110010=>010011
[7,1,5,6,4,3,2]=>[2,3,4,6,5,1,7]=>100010=>010001
[7,1,6,2,3,4,5]=>[5,4,3,2,6,1,7]=>111100=>001111
[7,1,6,2,3,5,4]=>[4,5,3,2,6,1,7]=>111000=>000111
[7,1,6,2,4,3,5]=>[5,3,4,2,6,1,7]=>111000=>000111
[7,1,6,2,4,5,3]=>[3,5,4,2,6,1,7]=>110100=>001011
[7,1,6,2,5,3,4]=>[4,3,5,2,6,1,7]=>111000=>000111
[7,1,6,2,5,4,3]=>[3,4,5,2,6,1,7]=>110000=>000011
[7,1,6,3,2,4,5]=>[5,4,2,3,6,1,7]=>110100=>001011
[7,1,6,3,2,5,4]=>[4,5,2,3,6,1,7]=>110000=>000011
[7,1,6,3,4,2,5]=>[5,2,4,3,6,1,7]=>111000=>000111
[7,1,6,3,4,5,2]=>[2,5,4,3,6,1,7]=>101100=>001101
[7,1,6,3,5,2,4]=>[4,2,5,3,6,1,7]=>111000=>000111
[7,1,6,3,5,4,2]=>[2,4,5,3,6,1,7]=>101000=>000101
[7,1,6,4,2,3,5]=>[5,3,2,4,6,1,7]=>111000=>000111
[7,1,6,4,2,5,3]=>[3,5,2,4,6,1,7]=>110000=>000011
[7,1,6,4,3,2,5]=>[5,2,3,4,6,1,7]=>110000=>000011
[7,1,6,4,3,5,2]=>[2,5,3,4,6,1,7]=>101000=>000101
[7,1,6,4,5,2,3]=>[3,2,5,4,6,1,7]=>110100=>001011
[7,1,6,4,5,3,2]=>[2,3,5,4,6,1,7]=>100100=>001001
[7,1,6,5,2,3,4]=>[4,3,2,5,6,1,7]=>111000=>000111
[7,1,6,5,2,4,3]=>[3,4,2,5,6,1,7]=>110000=>000011
[7,1,6,5,3,2,4]=>[4,2,3,5,6,1,7]=>110000=>000011
[7,1,6,5,3,4,2]=>[2,4,3,5,6,1,7]=>101000=>000101
[7,1,6,5,4,2,3]=>[3,2,4,5,6,1,7]=>110000=>000011
[7,1,6,5,4,3,2]=>[2,3,4,5,6,1,7]=>100000=>000001
[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>101110=>011101
[7,2,1,3,4,6,5]=>[5,6,4,3,1,2,7]=>101100=>001101
[7,2,1,3,5,4,6]=>[6,4,5,3,1,2,7]=>101100=>001101
[7,2,1,3,5,6,4]=>[4,6,5,3,1,2,7]=>101010=>010101
[7,2,1,3,6,4,5]=>[5,4,6,3,1,2,7]=>101100=>001101
[7,2,1,3,6,5,4]=>[4,5,6,3,1,2,7]=>101000=>000101
[7,2,1,4,3,5,6]=>[6,5,3,4,1,2,7]=>101010=>010101
[7,2,1,4,3,6,5]=>[5,6,3,4,1,2,7]=>101000=>000101
[7,2,1,4,5,3,6]=>[6,3,5,4,1,2,7]=>101100=>001101
[7,2,1,4,5,6,3]=>[3,6,5,4,1,2,7]=>100110=>011001
[7,2,1,4,6,3,5]=>[5,3,6,4,1,2,7]=>101100=>001101
[7,2,1,4,6,5,3]=>[3,5,6,4,1,2,7]=>100100=>001001
[7,2,1,5,3,4,6]=>[6,4,3,5,1,2,7]=>101100=>001101
[7,2,1,5,3,6,4]=>[4,6,3,5,1,2,7]=>101000=>000101
[7,2,1,5,4,3,6]=>[6,3,4,5,1,2,7]=>101000=>000101
[7,2,1,5,4,6,3]=>[3,6,4,5,1,2,7]=>100100=>001001
[7,2,1,5,6,3,4]=>[4,3,6,5,1,2,7]=>101010=>010101
[7,2,1,5,6,4,3]=>[3,4,6,5,1,2,7]=>100010=>010001
[7,2,1,6,3,4,5]=>[5,4,3,6,1,2,7]=>101100=>001101
[7,2,1,6,3,5,4]=>[4,5,3,6,1,2,7]=>101000=>000101
[7,2,1,6,4,3,5]=>[5,3,4,6,1,2,7]=>101000=>000101
[7,2,1,6,4,5,3]=>[3,5,4,6,1,2,7]=>100100=>001001
[7,2,1,6,5,3,4]=>[4,3,5,6,1,2,7]=>101000=>000101
[7,2,1,6,5,4,3]=>[3,4,5,6,1,2,7]=>100000=>000001
[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>110110=>011011
[7,2,3,1,4,6,5]=>[5,6,4,1,3,2,7]=>110100=>001011
[7,2,3,1,5,4,6]=>[6,4,5,1,3,2,7]=>110100=>001011
[7,2,3,1,5,6,4]=>[4,6,5,1,3,2,7]=>110010=>010011
[7,2,3,1,6,4,5]=>[5,4,6,1,3,2,7]=>110100=>001011
[7,2,3,1,6,5,4]=>[4,5,6,1,3,2,7]=>110000=>000011
[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>111010=>010111
[7,2,3,4,1,6,5]=>[5,6,1,4,3,2,7]=>111000=>000111
[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>111100=>001111
[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110=>011110
[7,2,3,4,6,1,5]=>[5,1,6,4,3,2,7]=>111100=>001111
[7,2,3,4,6,5,1]=>[1,5,6,4,3,2,7]=>011100=>001110
[7,2,3,5,1,4,6]=>[6,4,1,5,3,2,7]=>111100=>001111
[7,2,3,5,1,6,4]=>[4,6,1,5,3,2,7]=>111000=>000111
[7,2,3,5,4,1,6]=>[6,1,4,5,3,2,7]=>111000=>000111
[7,2,3,5,4,6,1]=>[1,6,4,5,3,2,7]=>011100=>001110
[7,2,3,5,6,1,4]=>[4,1,6,5,3,2,7]=>111010=>010111
[7,2,3,5,6,4,1]=>[1,4,6,5,3,2,7]=>011010=>010110
[7,2,3,6,1,4,5]=>[5,4,1,6,3,2,7]=>111100=>001111
[7,2,3,6,1,5,4]=>[4,5,1,6,3,2,7]=>111000=>000111
[7,2,3,6,4,1,5]=>[5,1,4,6,3,2,7]=>111000=>000111
[7,2,3,6,4,5,1]=>[1,5,4,6,3,2,7]=>011100=>001110
[7,2,3,6,5,1,4]=>[4,1,5,6,3,2,7]=>111000=>000111
[7,2,3,6,5,4,1]=>[1,4,5,6,3,2,7]=>011000=>000110
[7,2,4,1,3,5,6]=>[6,5,3,1,4,2,7]=>111010=>010111
[7,2,4,1,3,6,5]=>[5,6,3,1,4,2,7]=>111000=>000111
[7,2,4,1,5,3,6]=>[6,3,5,1,4,2,7]=>111000=>000111
[7,2,4,1,5,6,3]=>[3,6,5,1,4,2,7]=>110010=>010011
[7,2,4,1,6,3,5]=>[5,3,6,1,4,2,7]=>111000=>000111
[7,2,4,1,6,5,3]=>[3,5,6,1,4,2,7]=>110000=>000011
[7,2,4,3,1,5,6]=>[6,5,1,3,4,2,7]=>110010=>010011
[7,2,4,3,1,6,5]=>[5,6,1,3,4,2,7]=>110000=>000011
[7,2,4,3,5,1,6]=>[6,1,5,3,4,2,7]=>111000=>000111
[7,2,4,3,5,6,1]=>[1,6,5,3,4,2,7]=>011010=>010110
[7,2,4,3,6,1,5]=>[5,1,6,3,4,2,7]=>111000=>000111
[7,2,4,3,6,5,1]=>[1,5,6,3,4,2,7]=>011000=>000110
[7,2,4,5,1,3,6]=>[6,3,1,5,4,2,7]=>111100=>001111
[7,2,4,5,1,6,3]=>[3,6,1,5,4,2,7]=>110100=>001011
[7,2,4,5,3,1,6]=>[6,1,3,5,4,2,7]=>110100=>001011
[7,2,4,5,3,6,1]=>[1,6,3,5,4,2,7]=>011100=>001110
[7,2,4,5,6,1,3]=>[3,1,6,5,4,2,7]=>110110=>011011
[7,2,4,5,6,3,1]=>[1,3,6,5,4,2,7]=>010110=>011010
[7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7]=>111100=>001111
[7,2,4,6,1,5,3]=>[3,5,1,6,4,2,7]=>110100=>001011
[7,2,4,6,3,1,5]=>[5,1,3,6,4,2,7]=>110100=>001011
[7,2,4,6,3,5,1]=>[1,5,3,6,4,2,7]=>011100=>001110
[7,2,4,6,5,1,3]=>[3,1,5,6,4,2,7]=>110100=>001011
[7,2,4,6,5,3,1]=>[1,3,5,6,4,2,7]=>010100=>001010
[7,2,5,1,3,4,6]=>[6,4,3,1,5,2,7]=>111100=>001111
[7,2,5,1,3,6,4]=>[4,6,3,1,5,2,7]=>111000=>000111
[7,2,5,1,4,3,6]=>[6,3,4,1,5,2,7]=>111000=>000111
[7,2,5,1,4,6,3]=>[3,6,4,1,5,2,7]=>110100=>001011
[7,2,5,1,6,3,4]=>[4,3,6,1,5,2,7]=>111000=>000111
[7,2,5,1,6,4,3]=>[3,4,6,1,5,2,7]=>110000=>000011
[7,2,5,3,1,4,6]=>[6,4,1,3,5,2,7]=>110100=>001011
[7,2,5,3,1,6,4]=>[4,6,1,3,5,2,7]=>110000=>000011
[7,2,5,3,4,1,6]=>[6,1,4,3,5,2,7]=>111000=>000111
[7,2,5,3,4,6,1]=>[1,6,4,3,5,2,7]=>011100=>001110
[7,2,5,3,6,1,4]=>[4,1,6,3,5,2,7]=>111000=>000111
[7,2,5,3,6,4,1]=>[1,4,6,3,5,2,7]=>011000=>000110
[7,2,5,4,1,3,6]=>[6,3,1,4,5,2,7]=>111000=>000111
[7,2,5,4,1,6,3]=>[3,6,1,4,5,2,7]=>110000=>000011
[7,2,5,4,3,1,6]=>[6,1,3,4,5,2,7]=>110000=>000011
[7,2,5,4,3,6,1]=>[1,6,3,4,5,2,7]=>011000=>000110
[7,2,5,4,6,1,3]=>[3,1,6,4,5,2,7]=>110100=>001011
[7,2,5,4,6,3,1]=>[1,3,6,4,5,2,7]=>010100=>001010
[7,2,5,6,1,3,4]=>[4,3,1,6,5,2,7]=>111010=>010111
[7,2,5,6,1,4,3]=>[3,4,1,6,5,2,7]=>110010=>010011
[7,2,5,6,3,1,4]=>[4,1,3,6,5,2,7]=>110010=>010011
[7,2,5,6,3,4,1]=>[1,4,3,6,5,2,7]=>011010=>010110
[7,2,5,6,4,1,3]=>[3,1,4,6,5,2,7]=>110010=>010011
[7,2,5,6,4,3,1]=>[1,3,4,6,5,2,7]=>010010=>010010
[7,2,6,1,3,4,5]=>[5,4,3,1,6,2,7]=>111100=>001111
[7,2,6,1,3,5,4]=>[4,5,3,1,6,2,7]=>111000=>000111
[7,2,6,1,4,3,5]=>[5,3,4,1,6,2,7]=>111000=>000111
[7,2,6,1,4,5,3]=>[3,5,4,1,6,2,7]=>110100=>001011
[7,2,6,1,5,3,4]=>[4,3,5,1,6,2,7]=>111000=>000111
[7,2,6,1,5,4,3]=>[3,4,5,1,6,2,7]=>110000=>000011
[7,2,6,3,1,4,5]=>[5,4,1,3,6,2,7]=>110100=>001011
[7,2,6,3,1,5,4]=>[4,5,1,3,6,2,7]=>110000=>000011
[7,2,6,3,4,1,5]=>[5,1,4,3,6,2,7]=>111000=>000111
[7,2,6,3,4,5,1]=>[1,5,4,3,6,2,7]=>011100=>001110
[7,2,6,3,5,1,4]=>[4,1,5,3,6,2,7]=>111000=>000111
[7,2,6,3,5,4,1]=>[1,4,5,3,6,2,7]=>011000=>000110
[7,2,6,4,1,3,5]=>[5,3,1,4,6,2,7]=>111000=>000111
[7,2,6,4,1,5,3]=>[3,5,1,4,6,2,7]=>110000=>000011
[7,2,6,4,3,1,5]=>[5,1,3,4,6,2,7]=>110000=>000011
[7,2,6,4,3,5,1]=>[1,5,3,4,6,2,7]=>011000=>000110
[7,2,6,4,5,1,3]=>[3,1,5,4,6,2,7]=>110100=>001011
[7,2,6,4,5,3,1]=>[1,3,5,4,6,2,7]=>010100=>001010
[7,2,6,5,1,3,4]=>[4,3,1,5,6,2,7]=>111000=>000111
[7,2,6,5,1,4,3]=>[3,4,1,5,6,2,7]=>110000=>000011
[7,2,6,5,3,1,4]=>[4,1,3,5,6,2,7]=>110000=>000011
[7,2,6,5,3,4,1]=>[1,4,3,5,6,2,7]=>011000=>000110
[7,2,6,5,4,1,3]=>[3,1,4,5,6,2,7]=>110000=>000011
[7,2,6,5,4,3,1]=>[1,3,4,5,6,2,7]=>010000=>000010
[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>110110=>011011
[7,3,1,2,4,6,5]=>[5,6,4,2,1,3,7]=>110100=>001011
[7,3,1,2,5,4,6]=>[6,4,5,2,1,3,7]=>110100=>001011
[7,3,1,2,5,6,4]=>[4,6,5,2,1,3,7]=>110010=>010011
[7,3,1,2,6,4,5]=>[5,4,6,2,1,3,7]=>110100=>001011
[7,3,1,2,6,5,4]=>[4,5,6,2,1,3,7]=>110000=>000011
[7,3,1,4,2,5,6]=>[6,5,2,4,1,3,7]=>110010=>010011
[7,3,1,4,2,6,5]=>[5,6,2,4,1,3,7]=>110000=>000011
[7,3,1,4,5,2,6]=>[6,2,5,4,1,3,7]=>110100=>001011
[7,3,1,4,5,6,2]=>[2,6,5,4,1,3,7]=>100110=>011001
[7,3,1,4,6,2,5]=>[5,2,6,4,1,3,7]=>110100=>001011
[7,3,1,4,6,5,2]=>[2,5,6,4,1,3,7]=>100100=>001001
[7,3,1,5,2,4,6]=>[6,4,2,5,1,3,7]=>110100=>001011
[7,3,1,5,2,6,4]=>[4,6,2,5,1,3,7]=>110000=>000011
[7,3,1,5,4,2,6]=>[6,2,4,5,1,3,7]=>110000=>000011
[7,3,1,5,4,6,2]=>[2,6,4,5,1,3,7]=>100100=>001001
[7,3,1,5,6,2,4]=>[4,2,6,5,1,3,7]=>110010=>010011
[7,3,1,5,6,4,2]=>[2,4,6,5,1,3,7]=>100010=>010001
[7,3,1,6,2,4,5]=>[5,4,2,6,1,3,7]=>110100=>001011
[7,3,1,6,2,5,4]=>[4,5,2,6,1,3,7]=>110000=>000011
[7,3,1,6,4,2,5]=>[5,2,4,6,1,3,7]=>110000=>000011
[7,3,1,6,4,5,2]=>[2,5,4,6,1,3,7]=>100100=>001001
[7,3,1,6,5,2,4]=>[4,2,5,6,1,3,7]=>110000=>000011
[7,3,1,6,5,4,2]=>[2,4,5,6,1,3,7]=>100000=>000001
[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>100110=>011001
[7,3,2,1,4,6,5]=>[5,6,4,1,2,3,7]=>100100=>001001
[7,3,2,1,5,4,6]=>[6,4,5,1,2,3,7]=>100100=>001001
[7,3,2,1,5,6,4]=>[4,6,5,1,2,3,7]=>100010=>010001
[7,3,2,1,6,4,5]=>[5,4,6,1,2,3,7]=>100100=>001001
[7,3,2,1,6,5,4]=>[4,5,6,1,2,3,7]=>100000=>000001
[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>110010=>010011
[7,3,2,4,1,6,5]=>[5,6,1,4,2,3,7]=>110000=>000011
[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>110100=>001011
[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>010110=>011010
[7,3,2,4,6,1,5]=>[5,1,6,4,2,3,7]=>110100=>001011
[7,3,2,4,6,5,1]=>[1,5,6,4,2,3,7]=>010100=>001010
[7,3,2,5,1,4,6]=>[6,4,1,5,2,3,7]=>110100=>001011
[7,3,2,5,1,6,4]=>[4,6,1,5,2,3,7]=>110000=>000011
[7,3,2,5,4,1,6]=>[6,1,4,5,2,3,7]=>110000=>000011
[7,3,2,5,4,6,1]=>[1,6,4,5,2,3,7]=>010100=>001010
[7,3,2,5,6,1,4]=>[4,1,6,5,2,3,7]=>110010=>010011
[7,3,2,5,6,4,1]=>[1,4,6,5,2,3,7]=>010010=>010010
[7,3,2,6,1,4,5]=>[5,4,1,6,2,3,7]=>110100=>001011
[7,3,2,6,1,5,4]=>[4,5,1,6,2,3,7]=>110000=>000011
[7,3,2,6,4,1,5]=>[5,1,4,6,2,3,7]=>110000=>000011
[7,3,2,6,4,5,1]=>[1,5,4,6,2,3,7]=>010100=>001010
[7,3,2,6,5,1,4]=>[4,1,5,6,2,3,7]=>110000=>000011
[7,3,2,6,5,4,1]=>[1,4,5,6,2,3,7]=>010000=>000010
[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>111010=>010111
[7,3,4,1,2,6,5]=>[5,6,2,1,4,3,7]=>111000=>000111
[7,3,4,1,5,2,6]=>[6,2,5,1,4,3,7]=>111000=>000111
[7,3,4,1,5,6,2]=>[2,6,5,1,4,3,7]=>101010=>010101
[7,3,4,1,6,2,5]=>[5,2,6,1,4,3,7]=>111000=>000111
[7,3,4,1,6,5,2]=>[2,5,6,1,4,3,7]=>101000=>000101
[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>101010=>010101
[7,3,4,2,1,6,5]=>[5,6,1,2,4,3,7]=>101000=>000101
[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>111000=>000111
[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>011010=>010110
[7,3,4,2,6,1,5]=>[5,1,6,2,4,3,7]=>111000=>000111
[7,3,4,2,6,5,1]=>[1,5,6,2,4,3,7]=>011000=>000110
[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>111100=>001111
[7,3,4,5,1,6,2]=>[2,6,1,5,4,3,7]=>101100=>001101
[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>101100=>001101
[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>011100=>001110
[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110=>011101
[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>001110=>011100
[7,3,4,6,1,2,5]=>[5,2,1,6,4,3,7]=>111100=>001111
[7,3,4,6,1,5,2]=>[2,5,1,6,4,3,7]=>101100=>001101
[7,3,4,6,2,1,5]=>[5,1,2,6,4,3,7]=>101100=>001101
[7,3,4,6,2,5,1]=>[1,5,2,6,4,3,7]=>011100=>001110
[7,3,4,6,5,1,2]=>[2,1,5,6,4,3,7]=>101100=>001101
[7,3,4,6,5,2,1]=>[1,2,5,6,4,3,7]=>001100=>001100
[7,3,5,1,2,4,6]=>[6,4,2,1,5,3,7]=>111100=>001111
[7,3,5,1,2,6,4]=>[4,6,2,1,5,3,7]=>111000=>000111
[7,3,5,1,4,2,6]=>[6,2,4,1,5,3,7]=>111000=>000111
[7,3,5,1,4,6,2]=>[2,6,4,1,5,3,7]=>101100=>001101
[7,3,5,1,6,2,4]=>[4,2,6,1,5,3,7]=>111000=>000111
[7,3,5,1,6,4,2]=>[2,4,6,1,5,3,7]=>101000=>000101
[7,3,5,2,1,4,6]=>[6,4,1,2,5,3,7]=>101100=>001101
[7,3,5,2,1,6,4]=>[4,6,1,2,5,3,7]=>101000=>000101
[7,3,5,2,4,1,6]=>[6,1,4,2,5,3,7]=>111000=>000111
[7,3,5,2,4,6,1]=>[1,6,4,2,5,3,7]=>011100=>001110
[7,3,5,2,6,1,4]=>[4,1,6,2,5,3,7]=>111000=>000111
[7,3,5,2,6,4,1]=>[1,4,6,2,5,3,7]=>011000=>000110
[7,3,5,4,1,2,6]=>[6,2,1,4,5,3,7]=>111000=>000111
[7,3,5,4,1,6,2]=>[2,6,1,4,5,3,7]=>101000=>000101
[7,3,5,4,2,1,6]=>[6,1,2,4,5,3,7]=>101000=>000101
[7,3,5,4,2,6,1]=>[1,6,2,4,5,3,7]=>011000=>000110
[7,3,5,4,6,1,2]=>[2,1,6,4,5,3,7]=>101100=>001101
[7,3,5,4,6,2,1]=>[1,2,6,4,5,3,7]=>001100=>001100
[7,3,5,6,1,2,4]=>[4,2,1,6,5,3,7]=>111010=>010111
[7,3,5,6,1,4,2]=>[2,4,1,6,5,3,7]=>101010=>010101
[7,3,5,6,2,1,4]=>[4,1,2,6,5,3,7]=>101010=>010101
[7,3,5,6,2,4,1]=>[1,4,2,6,5,3,7]=>011010=>010110
[7,3,5,6,4,1,2]=>[2,1,4,6,5,3,7]=>101010=>010101
[7,3,5,6,4,2,1]=>[1,2,4,6,5,3,7]=>001010=>010100
[7,3,6,1,2,4,5]=>[5,4,2,1,6,3,7]=>111100=>001111
[7,3,6,1,2,5,4]=>[4,5,2,1,6,3,7]=>111000=>000111
[7,3,6,1,4,2,5]=>[5,2,4,1,6,3,7]=>111000=>000111
[7,3,6,1,4,5,2]=>[2,5,4,1,6,3,7]=>101100=>001101
[7,3,6,1,5,2,4]=>[4,2,5,1,6,3,7]=>111000=>000111
[7,3,6,1,5,4,2]=>[2,4,5,1,6,3,7]=>101000=>000101
[7,3,6,2,1,4,5]=>[5,4,1,2,6,3,7]=>101100=>001101
[7,3,6,2,1,5,4]=>[4,5,1,2,6,3,7]=>101000=>000101
[7,3,6,2,4,1,5]=>[5,1,4,2,6,3,7]=>111000=>000111
[7,3,6,2,4,5,1]=>[1,5,4,2,6,3,7]=>011100=>001110
[7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7]=>111000=>000111
[7,3,6,2,5,4,1]=>[1,4,5,2,6,3,7]=>011000=>000110
[7,3,6,4,1,2,5]=>[5,2,1,4,6,3,7]=>111000=>000111
[7,3,6,4,1,5,2]=>[2,5,1,4,6,3,7]=>101000=>000101
[7,3,6,4,2,1,5]=>[5,1,2,4,6,3,7]=>101000=>000101
[7,3,6,4,2,5,1]=>[1,5,2,4,6,3,7]=>011000=>000110
[7,3,6,4,5,1,2]=>[2,1,5,4,6,3,7]=>101100=>001101
[7,3,6,4,5,2,1]=>[1,2,5,4,6,3,7]=>001100=>001100
[7,3,6,5,1,2,4]=>[4,2,1,5,6,3,7]=>111000=>000111
[7,3,6,5,1,4,2]=>[2,4,1,5,6,3,7]=>101000=>000101
[7,3,6,5,2,1,4]=>[4,1,2,5,6,3,7]=>101000=>000101
[7,3,6,5,2,4,1]=>[1,4,2,5,6,3,7]=>011000=>000110
[7,3,6,5,4,1,2]=>[2,1,4,5,6,3,7]=>101000=>000101
[7,3,6,5,4,2,1]=>[1,2,4,5,6,3,7]=>001000=>000100
[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>111010=>010111
[7,4,1,2,3,6,5]=>[5,6,3,2,1,4,7]=>111000=>000111
[7,4,1,2,5,3,6]=>[6,3,5,2,1,4,7]=>111000=>000111
[7,4,1,2,5,6,3]=>[3,6,5,2,1,4,7]=>110010=>010011
[7,4,1,2,6,3,5]=>[5,3,6,2,1,4,7]=>111000=>000111
[7,4,1,2,6,5,3]=>[3,5,6,2,1,4,7]=>110000=>000011
[7,4,1,3,2,5,6]=>[6,5,2,3,1,4,7]=>110010=>010011
[7,4,1,3,2,6,5]=>[5,6,2,3,1,4,7]=>110000=>000011
[7,4,1,3,5,2,6]=>[6,2,5,3,1,4,7]=>111000=>000111
[7,4,1,3,5,6,2]=>[2,6,5,3,1,4,7]=>101010=>010101
[7,4,1,3,6,2,5]=>[5,2,6,3,1,4,7]=>111000=>000111
[7,4,1,3,6,5,2]=>[2,5,6,3,1,4,7]=>101000=>000101
[7,4,1,5,2,3,6]=>[6,3,2,5,1,4,7]=>111000=>000111
[7,4,1,5,2,6,3]=>[3,6,2,5,1,4,7]=>110000=>000011
[7,4,1,5,3,2,6]=>[6,2,3,5,1,4,7]=>110000=>000011
[7,4,1,5,3,6,2]=>[2,6,3,5,1,4,7]=>101000=>000101
[7,4,1,5,6,2,3]=>[3,2,6,5,1,4,7]=>110010=>010011
[7,4,1,5,6,3,2]=>[2,3,6,5,1,4,7]=>100010=>010001
[7,4,1,6,2,3,5]=>[5,3,2,6,1,4,7]=>111000=>000111
[7,4,1,6,2,5,3]=>[3,5,2,6,1,4,7]=>110000=>000011
[7,4,1,6,3,2,5]=>[5,2,3,6,1,4,7]=>110000=>000011
[7,4,1,6,3,5,2]=>[2,5,3,6,1,4,7]=>101000=>000101
[7,4,1,6,5,2,3]=>[3,2,5,6,1,4,7]=>110000=>000011
[7,4,1,6,5,3,2]=>[2,3,5,6,1,4,7]=>100000=>000001
[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>101010=>010101
[7,4,2,1,3,6,5]=>[5,6,3,1,2,4,7]=>101000=>000101
[7,4,2,1,5,3,6]=>[6,3,5,1,2,4,7]=>101000=>000101
[7,4,2,1,5,6,3]=>[3,6,5,1,2,4,7]=>100010=>010001
[7,4,2,1,6,3,5]=>[5,3,6,1,2,4,7]=>101000=>000101
[7,4,2,1,6,5,3]=>[3,5,6,1,2,4,7]=>100000=>000001
[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>110010=>010011
[7,4,2,3,1,6,5]=>[5,6,1,3,2,4,7]=>110000=>000011
[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>111000=>000111
[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>011010=>010110
[7,4,2,3,6,1,5]=>[5,1,6,3,2,4,7]=>111000=>000111
[7,4,2,3,6,5,1]=>[1,5,6,3,2,4,7]=>011000=>000110
[7,4,2,5,1,3,6]=>[6,3,1,5,2,4,7]=>111000=>000111
[7,4,2,5,1,6,3]=>[3,6,1,5,2,4,7]=>110000=>000011
[7,4,2,5,3,1,6]=>[6,1,3,5,2,4,7]=>110000=>000011
[7,4,2,5,3,6,1]=>[1,6,3,5,2,4,7]=>011000=>000110
[7,4,2,5,6,1,3]=>[3,1,6,5,2,4,7]=>110010=>010011
[7,4,2,5,6,3,1]=>[1,3,6,5,2,4,7]=>010010=>010010
[7,4,2,6,1,3,5]=>[5,3,1,6,2,4,7]=>111000=>000111
[7,4,2,6,1,5,3]=>[3,5,1,6,2,4,7]=>110000=>000011
[7,4,2,6,3,1,5]=>[5,1,3,6,2,4,7]=>110000=>000011
[7,4,2,6,3,5,1]=>[1,5,3,6,2,4,7]=>011000=>000110
[7,4,2,6,5,1,3]=>[3,1,5,6,2,4,7]=>110000=>000011
[7,4,2,6,5,3,1]=>[1,3,5,6,2,4,7]=>010000=>000010
[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>110010=>010011
[7,4,3,1,2,6,5]=>[5,6,2,1,3,4,7]=>110000=>000011
[7,4,3,1,5,2,6]=>[6,2,5,1,3,4,7]=>110000=>000011
[7,4,3,1,5,6,2]=>[2,6,5,1,3,4,7]=>100010=>010001
[7,4,3,1,6,2,5]=>[5,2,6,1,3,4,7]=>110000=>000011
[7,4,3,1,6,5,2]=>[2,5,6,1,3,4,7]=>100000=>000001
[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>100010=>010001
[7,4,3,2,1,6,5]=>[5,6,1,2,3,4,7]=>100000=>000001
[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>110000=>000011
[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>010010=>010010
[7,4,3,2,6,1,5]=>[5,1,6,2,3,4,7]=>110000=>000011
[7,4,3,2,6,5,1]=>[1,5,6,2,3,4,7]=>010000=>000010
[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>111000=>000111
[7,4,3,5,1,6,2]=>[2,6,1,5,3,4,7]=>101000=>000101
[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>101000=>000101
[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>011000=>000110
[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>101010=>010101
[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>001010=>010100
[7,4,3,6,1,2,5]=>[5,2,1,6,3,4,7]=>111000=>000111
[7,4,3,6,1,5,2]=>[2,5,1,6,3,4,7]=>101000=>000101
[7,4,3,6,2,1,5]=>[5,1,2,6,3,4,7]=>101000=>000101
[7,4,3,6,2,5,1]=>[1,5,2,6,3,4,7]=>011000=>000110
[7,4,3,6,5,1,2]=>[2,1,5,6,3,4,7]=>101000=>000101
[7,4,3,6,5,2,1]=>[1,2,5,6,3,4,7]=>001000=>000100
[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>111100=>001111
[7,4,5,1,2,6,3]=>[3,6,2,1,5,4,7]=>110100=>001011
[7,4,5,1,3,2,6]=>[6,2,3,1,5,4,7]=>110100=>001011
[7,4,5,1,3,6,2]=>[2,6,3,1,5,4,7]=>101100=>001101
[7,4,5,1,6,2,3]=>[3,2,6,1,5,4,7]=>110100=>001011
[7,4,5,1,6,3,2]=>[2,3,6,1,5,4,7]=>100100=>001001
[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>101100=>001101
[7,4,5,2,1,6,3]=>[3,6,1,2,5,4,7]=>100100=>001001
[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>110100=>001011
[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>011100=>001110
[7,4,5,2,6,1,3]=>[3,1,6,2,5,4,7]=>110100=>001011
[7,4,5,2,6,3,1]=>[1,3,6,2,5,4,7]=>010100=>001010
[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>110100=>001011
[7,4,5,3,1,6,2]=>[2,6,1,3,5,4,7]=>100100=>001001
[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>100100=>001001
[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>010100=>001010
[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>101100=>001101
[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>001100=>001100
[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110=>011011
[7,4,5,6,1,3,2]=>[2,3,1,6,5,4,7]=>100110=>011001
[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>100110=>011001
[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110=>011010
[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110=>011001
[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>000110=>011000
[7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7]=>111100=>001111
[7,4,6,1,2,5,3]=>[3,5,2,1,6,4,7]=>110100=>001011
[7,4,6,1,3,2,5]=>[5,2,3,1,6,4,7]=>110100=>001011
[7,4,6,1,3,5,2]=>[2,5,3,1,6,4,7]=>101100=>001101
[7,4,6,1,5,2,3]=>[3,2,5,1,6,4,7]=>110100=>001011
[7,4,6,1,5,3,2]=>[2,3,5,1,6,4,7]=>100100=>001001
[7,4,6,2,1,3,5]=>[5,3,1,2,6,4,7]=>101100=>001101
[7,4,6,2,1,5,3]=>[3,5,1,2,6,4,7]=>100100=>001001
[7,4,6,2,3,1,5]=>[5,1,3,2,6,4,7]=>110100=>001011
[7,4,6,2,3,5,1]=>[1,5,3,2,6,4,7]=>011100=>001110
[7,4,6,2,5,1,3]=>[3,1,5,2,6,4,7]=>110100=>001011
[7,4,6,2,5,3,1]=>[1,3,5,2,6,4,7]=>010100=>001010
[7,4,6,3,1,2,5]=>[5,2,1,3,6,4,7]=>110100=>001011
[7,4,6,3,1,5,2]=>[2,5,1,3,6,4,7]=>100100=>001001
[7,4,6,3,2,1,5]=>[5,1,2,3,6,4,7]=>100100=>001001
[7,4,6,3,2,5,1]=>[1,5,2,3,6,4,7]=>010100=>001010
[7,4,6,3,5,1,2]=>[2,1,5,3,6,4,7]=>101100=>001101
[7,4,6,3,5,2,1]=>[1,2,5,3,6,4,7]=>001100=>001100
[7,4,6,5,1,2,3]=>[3,2,1,5,6,4,7]=>110100=>001011
[7,4,6,5,1,3,2]=>[2,3,1,5,6,4,7]=>100100=>001001
[7,4,6,5,2,1,3]=>[3,1,2,5,6,4,7]=>100100=>001001
[7,4,6,5,2,3,1]=>[1,3,2,5,6,4,7]=>010100=>001010
[7,4,6,5,3,1,2]=>[2,1,3,5,6,4,7]=>100100=>001001
[7,4,6,5,3,2,1]=>[1,2,3,5,6,4,7]=>000100=>001000
[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111100=>001111
[7,5,1,2,3,6,4]=>[4,6,3,2,1,5,7]=>111000=>000111
[7,5,1,2,4,3,6]=>[6,3,4,2,1,5,7]=>111000=>000111
[7,5,1,2,4,6,3]=>[3,6,4,2,1,5,7]=>110100=>001011
[7,5,1,2,6,3,4]=>[4,3,6,2,1,5,7]=>111000=>000111
[7,5,1,2,6,4,3]=>[3,4,6,2,1,5,7]=>110000=>000011
[7,5,1,3,2,4,6]=>[6,4,2,3,1,5,7]=>110100=>001011
[7,5,1,3,2,6,4]=>[4,6,2,3,1,5,7]=>110000=>000011
[7,5,1,3,4,2,6]=>[6,2,4,3,1,5,7]=>111000=>000111
[7,5,1,3,4,6,2]=>[2,6,4,3,1,5,7]=>101100=>001101
[7,5,1,3,6,2,4]=>[4,2,6,3,1,5,7]=>111000=>000111
[7,5,1,3,6,4,2]=>[2,4,6,3,1,5,7]=>101000=>000101
[7,5,1,4,2,3,6]=>[6,3,2,4,1,5,7]=>111000=>000111
[7,5,1,4,2,6,3]=>[3,6,2,4,1,5,7]=>110000=>000011
[7,5,1,4,3,2,6]=>[6,2,3,4,1,5,7]=>110000=>000011
[7,5,1,4,3,6,2]=>[2,6,3,4,1,5,7]=>101000=>000101
[7,5,1,4,6,2,3]=>[3,2,6,4,1,5,7]=>110100=>001011
[7,5,1,4,6,3,2]=>[2,3,6,4,1,5,7]=>100100=>001001
[7,5,1,6,2,3,4]=>[4,3,2,6,1,5,7]=>111000=>000111
[7,5,1,6,2,4,3]=>[3,4,2,6,1,5,7]=>110000=>000011
[7,5,1,6,3,2,4]=>[4,2,3,6,1,5,7]=>110000=>000011
[7,5,1,6,3,4,2]=>[2,4,3,6,1,5,7]=>101000=>000101
[7,5,1,6,4,2,3]=>[3,2,4,6,1,5,7]=>110000=>000011
[7,5,1,6,4,3,2]=>[2,3,4,6,1,5,7]=>100000=>000001
[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>101100=>001101
[7,5,2,1,3,6,4]=>[4,6,3,1,2,5,7]=>101000=>000101
[7,5,2,1,4,3,6]=>[6,3,4,1,2,5,7]=>101000=>000101
[7,5,2,1,4,6,3]=>[3,6,4,1,2,5,7]=>100100=>001001
[7,5,2,1,6,3,4]=>[4,3,6,1,2,5,7]=>101000=>000101
[7,5,2,1,6,4,3]=>[3,4,6,1,2,5,7]=>100000=>000001
[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>110100=>001011
[7,5,2,3,1,6,4]=>[4,6,1,3,2,5,7]=>110000=>000011
[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>111000=>000111
[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011100=>001110
[7,5,2,3,6,1,4]=>[4,1,6,3,2,5,7]=>111000=>000111
[7,5,2,3,6,4,1]=>[1,4,6,3,2,5,7]=>011000=>000110
[7,5,2,4,1,3,6]=>[6,3,1,4,2,5,7]=>111000=>000111
[7,5,2,4,1,6,3]=>[3,6,1,4,2,5,7]=>110000=>000011
[7,5,2,4,3,1,6]=>[6,1,3,4,2,5,7]=>110000=>000011
[7,5,2,4,3,6,1]=>[1,6,3,4,2,5,7]=>011000=>000110
[7,5,2,4,6,1,3]=>[3,1,6,4,2,5,7]=>110100=>001011
[7,5,2,4,6,3,1]=>[1,3,6,4,2,5,7]=>010100=>001010
[7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7]=>111000=>000111
[7,5,2,6,1,4,3]=>[3,4,1,6,2,5,7]=>110000=>000011
[7,5,2,6,3,1,4]=>[4,1,3,6,2,5,7]=>110000=>000011
[7,5,2,6,3,4,1]=>[1,4,3,6,2,5,7]=>011000=>000110
[7,5,2,6,4,1,3]=>[3,1,4,6,2,5,7]=>110000=>000011
[7,5,2,6,4,3,1]=>[1,3,4,6,2,5,7]=>010000=>000010
[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>110100=>001011
[7,5,3,1,2,6,4]=>[4,6,2,1,3,5,7]=>110000=>000011
[7,5,3,1,4,2,6]=>[6,2,4,1,3,5,7]=>110000=>000011
[7,5,3,1,4,6,2]=>[2,6,4,1,3,5,7]=>100100=>001001
[7,5,3,1,6,2,4]=>[4,2,6,1,3,5,7]=>110000=>000011
[7,5,3,1,6,4,2]=>[2,4,6,1,3,5,7]=>100000=>000001
[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>100100=>001001
[7,5,3,2,1,6,4]=>[4,6,1,2,3,5,7]=>100000=>000001
[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>110000=>000011
[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>010100=>001010
[7,5,3,2,6,1,4]=>[4,1,6,2,3,5,7]=>110000=>000011
[7,5,3,2,6,4,1]=>[1,4,6,2,3,5,7]=>010000=>000010
[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>111000=>000111
[7,5,3,4,1,6,2]=>[2,6,1,4,3,5,7]=>101000=>000101
[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>101000=>000101
[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>011000=>000110
[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101100=>001101
[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001100=>001100
[7,5,3,6,1,2,4]=>[4,2,1,6,3,5,7]=>111000=>000111
[7,5,3,6,1,4,2]=>[2,4,1,6,3,5,7]=>101000=>000101
[7,5,3,6,2,1,4]=>[4,1,2,6,3,5,7]=>101000=>000101
[7,5,3,6,2,4,1]=>[1,4,2,6,3,5,7]=>011000=>000110
[7,5,3,6,4,1,2]=>[2,1,4,6,3,5,7]=>101000=>000101
[7,5,3,6,4,2,1]=>[1,2,4,6,3,5,7]=>001000=>000100
[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>111000=>000111
[7,5,4,1,2,6,3]=>[3,6,2,1,4,5,7]=>110000=>000011
[7,5,4,1,3,2,6]=>[6,2,3,1,4,5,7]=>110000=>000011
[7,5,4,1,3,6,2]=>[2,6,3,1,4,5,7]=>101000=>000101
[7,5,4,1,6,2,3]=>[3,2,6,1,4,5,7]=>110000=>000011
[7,5,4,1,6,3,2]=>[2,3,6,1,4,5,7]=>100000=>000001
[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>101000=>000101
[7,5,4,2,1,6,3]=>[3,6,1,2,4,5,7]=>100000=>000001
[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>110000=>000011
[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>011000=>000110
[7,5,4,2,6,1,3]=>[3,1,6,2,4,5,7]=>110000=>000011
[7,5,4,2,6,3,1]=>[1,3,6,2,4,5,7]=>010000=>000010
[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>110000=>000011
[7,5,4,3,1,6,2]=>[2,6,1,3,4,5,7]=>100000=>000001
[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>100000=>000001
[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>010000=>000010
[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>101000=>000101
[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>001000=>000100
[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110100=>001011
[7,5,4,6,1,3,2]=>[2,3,1,6,4,5,7]=>100100=>001001
[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>100100=>001001
[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010100=>001010
[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100100=>001001
[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>000100=>001000
[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010=>010111
[7,5,6,1,2,4,3]=>[3,4,2,1,6,5,7]=>110010=>010011
[7,5,6,1,3,2,4]=>[4,2,3,1,6,5,7]=>110010=>010011
[7,5,6,1,3,4,2]=>[2,4,3,1,6,5,7]=>101010=>010101
[7,5,6,1,4,2,3]=>[3,2,4,1,6,5,7]=>110010=>010011
[7,5,6,1,4,3,2]=>[2,3,4,1,6,5,7]=>100010=>010001
[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>101010=>010101
[7,5,6,2,1,4,3]=>[3,4,1,2,6,5,7]=>100010=>010001
[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>110010=>010011
[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010=>010110
[7,5,6,2,4,1,3]=>[3,1,4,2,6,5,7]=>110010=>010011
[7,5,6,2,4,3,1]=>[1,3,4,2,6,5,7]=>010010=>010010
[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>110010=>010011
[7,5,6,3,1,4,2]=>[2,4,1,3,6,5,7]=>100010=>010001
[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>100010=>010001
[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>010010=>010010
[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010=>010101
[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010=>010100
[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010=>010011
[7,5,6,4,1,3,2]=>[2,3,1,4,6,5,7]=>100010=>010001
[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>100010=>010001
[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010=>010010
[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010=>010001
[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>000010=>010000
[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100=>001111
[7,6,1,2,3,5,4]=>[4,5,3,2,1,6,7]=>111000=>000111
[7,6,1,2,4,3,5]=>[5,3,4,2,1,6,7]=>111000=>000111
[7,6,1,2,4,5,3]=>[3,5,4,2,1,6,7]=>110100=>001011
[7,6,1,2,5,3,4]=>[4,3,5,2,1,6,7]=>111000=>000111
[7,6,1,2,5,4,3]=>[3,4,5,2,1,6,7]=>110000=>000011
[7,6,1,3,2,4,5]=>[5,4,2,3,1,6,7]=>110100=>001011
[7,6,1,3,2,5,4]=>[4,5,2,3,1,6,7]=>110000=>000011
[7,6,1,3,4,2,5]=>[5,2,4,3,1,6,7]=>111000=>000111
[7,6,1,3,4,5,2]=>[2,5,4,3,1,6,7]=>101100=>001101
[7,6,1,3,5,2,4]=>[4,2,5,3,1,6,7]=>111000=>000111
[7,6,1,3,5,4,2]=>[2,4,5,3,1,6,7]=>101000=>000101
[7,6,1,4,2,3,5]=>[5,3,2,4,1,6,7]=>111000=>000111
[7,6,1,4,2,5,3]=>[3,5,2,4,1,6,7]=>110000=>000011
[7,6,1,4,3,2,5]=>[5,2,3,4,1,6,7]=>110000=>000011
[7,6,1,4,3,5,2]=>[2,5,3,4,1,6,7]=>101000=>000101
[7,6,1,4,5,2,3]=>[3,2,5,4,1,6,7]=>110100=>001011
[7,6,1,4,5,3,2]=>[2,3,5,4,1,6,7]=>100100=>001001
[7,6,1,5,2,3,4]=>[4,3,2,5,1,6,7]=>111000=>000111
[7,6,1,5,2,4,3]=>[3,4,2,5,1,6,7]=>110000=>000011
[7,6,1,5,3,2,4]=>[4,2,3,5,1,6,7]=>110000=>000011
[7,6,1,5,3,4,2]=>[2,4,3,5,1,6,7]=>101000=>000101
[7,6,1,5,4,2,3]=>[3,2,4,5,1,6,7]=>110000=>000011
[7,6,1,5,4,3,2]=>[2,3,4,5,1,6,7]=>100000=>000001
[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>101100=>001101
[7,6,2,1,3,5,4]=>[4,5,3,1,2,6,7]=>101000=>000101
[7,6,2,1,4,3,5]=>[5,3,4,1,2,6,7]=>101000=>000101
[7,6,2,1,4,5,3]=>[3,5,4,1,2,6,7]=>100100=>001001
[7,6,2,1,5,3,4]=>[4,3,5,1,2,6,7]=>101000=>000101
[7,6,2,1,5,4,3]=>[3,4,5,1,2,6,7]=>100000=>000001
[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>110100=>001011
[7,6,2,3,1,5,4]=>[4,5,1,3,2,6,7]=>110000=>000011
[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>111000=>000111
[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100=>001110
[7,6,2,3,5,1,4]=>[4,1,5,3,2,6,7]=>111000=>000111
[7,6,2,3,5,4,1]=>[1,4,5,3,2,6,7]=>011000=>000110
[7,6,2,4,1,3,5]=>[5,3,1,4,2,6,7]=>111000=>000111
[7,6,2,4,1,5,3]=>[3,5,1,4,2,6,7]=>110000=>000011
[7,6,2,4,3,1,5]=>[5,1,3,4,2,6,7]=>110000=>000011
[7,6,2,4,3,5,1]=>[1,5,3,4,2,6,7]=>011000=>000110
[7,6,2,4,5,1,3]=>[3,1,5,4,2,6,7]=>110100=>001011
[7,6,2,4,5,3,1]=>[1,3,5,4,2,6,7]=>010100=>001010
[7,6,2,5,1,3,4]=>[4,3,1,5,2,6,7]=>111000=>000111
[7,6,2,5,1,4,3]=>[3,4,1,5,2,6,7]=>110000=>000011
[7,6,2,5,3,1,4]=>[4,1,3,5,2,6,7]=>110000=>000011
[7,6,2,5,3,4,1]=>[1,4,3,5,2,6,7]=>011000=>000110
[7,6,2,5,4,1,3]=>[3,1,4,5,2,6,7]=>110000=>000011
[7,6,2,5,4,3,1]=>[1,3,4,5,2,6,7]=>010000=>000010
[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>110100=>001011
[7,6,3,1,2,5,4]=>[4,5,2,1,3,6,7]=>110000=>000011
[7,6,3,1,4,2,5]=>[5,2,4,1,3,6,7]=>110000=>000011
[7,6,3,1,4,5,2]=>[2,5,4,1,3,6,7]=>100100=>001001
[7,6,3,1,5,2,4]=>[4,2,5,1,3,6,7]=>110000=>000011
[7,6,3,1,5,4,2]=>[2,4,5,1,3,6,7]=>100000=>000001
[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>100100=>001001
[7,6,3,2,1,5,4]=>[4,5,1,2,3,6,7]=>100000=>000001
[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>110000=>000011
[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>010100=>001010
[7,6,3,2,5,1,4]=>[4,1,5,2,3,6,7]=>110000=>000011
[7,6,3,2,5,4,1]=>[1,4,5,2,3,6,7]=>010000=>000010
[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>111000=>000111
[7,6,3,4,1,5,2]=>[2,5,1,4,3,6,7]=>101000=>000101
[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>101000=>000101
[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>011000=>000110
[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100=>001101
[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100=>001100
[7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7]=>111000=>000111
[7,6,3,5,1,4,2]=>[2,4,1,5,3,6,7]=>101000=>000101
[7,6,3,5,2,1,4]=>[4,1,2,5,3,6,7]=>101000=>000101
[7,6,3,5,2,4,1]=>[1,4,2,5,3,6,7]=>011000=>000110
[7,6,3,5,4,1,2]=>[2,1,4,5,3,6,7]=>101000=>000101
[7,6,3,5,4,2,1]=>[1,2,4,5,3,6,7]=>001000=>000100
[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>111000=>000111
[7,6,4,1,2,5,3]=>[3,5,2,1,4,6,7]=>110000=>000011
[7,6,4,1,3,2,5]=>[5,2,3,1,4,6,7]=>110000=>000011
[7,6,4,1,3,5,2]=>[2,5,3,1,4,6,7]=>101000=>000101
[7,6,4,1,5,2,3]=>[3,2,5,1,4,6,7]=>110000=>000011
[7,6,4,1,5,3,2]=>[2,3,5,1,4,6,7]=>100000=>000001
[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>101000=>000101
[7,6,4,2,1,5,3]=>[3,5,1,2,4,6,7]=>100000=>000001
[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>110000=>000011
[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>011000=>000110
[7,6,4,2,5,1,3]=>[3,1,5,2,4,6,7]=>110000=>000011
[7,6,4,2,5,3,1]=>[1,3,5,2,4,6,7]=>010000=>000010
[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>110000=>000011
[7,6,4,3,1,5,2]=>[2,5,1,3,4,6,7]=>100000=>000001
[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>100000=>000001
[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>010000=>000010
[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>101000=>000101
[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>001000=>000100
[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100=>001011
[7,6,4,5,1,3,2]=>[2,3,1,5,4,6,7]=>100100=>001001
[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>100100=>001001
[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100=>001010
[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100=>001001
[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>000100=>001000
[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000=>000111
[7,6,5,1,2,4,3]=>[3,4,2,1,5,6,7]=>110000=>000011
[7,6,5,1,3,2,4]=>[4,2,3,1,5,6,7]=>110000=>000011
[7,6,5,1,3,4,2]=>[2,4,3,1,5,6,7]=>101000=>000101
[7,6,5,1,4,2,3]=>[3,2,4,1,5,6,7]=>110000=>000011
[7,6,5,1,4,3,2]=>[2,3,4,1,5,6,7]=>100000=>000001
[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>101000=>000101
[7,6,5,2,1,4,3]=>[3,4,1,2,5,6,7]=>100000=>000001
[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>110000=>000011
[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000=>000110
[7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7]=>110000=>000011
[7,6,5,2,4,3,1]=>[1,3,4,2,5,6,7]=>010000=>000010
[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>110000=>000011
[7,6,5,3,1,4,2]=>[2,4,1,3,5,6,7]=>100000=>000001
[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>100000=>000001
[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>010000=>000010
[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000=>000101
[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>001000=>000100
[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000=>000011
[7,6,5,4,1,3,2]=>[2,3,1,4,5,6,7]=>100000=>000001
[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>100000=>000001
[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>010000=>000010
[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>100000=>000001
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>000000=>000000
[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>0000000=>0000000
[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>0000001=>1000000
[8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8]=>0000010=>0100000
[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>0000010=>0100000
[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6]=>0000011=>1100000
[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>0000100=>0010000
[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>0000101=>1010000
[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>0000100=>0010000
[8,5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5,8]=>0000110=>0110000
[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>0000100=>0010000
[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>0000110=>0110000
[7,5,6,8,4,3,2,1]=>[1,2,3,4,8,6,5,7]=>0000110=>0110000
[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>0000101=>1010000
[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000
[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>0001000=>0001000
[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010=>0101000
[7,6,8,4,5,3,2,1]=>[1,2,3,5,4,8,6,7]=>0001010=>0101000
[6,7,8,4,5,3,2,1]=>[1,2,3,5,4,8,7,6]=>0001011=>1101000
[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>0001000=>0001000
[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>0001001=>1001000
[7,8,4,5,6,3,2,1]=>[1,2,3,6,5,4,8,7]=>0001101=>1011000
[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>0001000=>0001000
[8,5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5,8]=>0001100=>0011000
[8,6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6,8]=>0001100=>0011000
[8,5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5,8]=>0001010=>0101000
[8,4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4,8]=>0001110=>0111000
[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>0001000=>0001000
[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>0001010=>0101000
[7,5,6,4,8,3,2,1]=>[1,2,3,8,4,6,5,7]=>0001100=>0011000
[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>0001100=>0011000
[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>0001110=>0111000
[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>0001100=>0011000
[6,7,4,5,8,3,2,1]=>[1,2,3,8,5,4,7,6]=>0001110=>0111000
[7,5,4,6,8,3,2,1]=>[1,2,3,8,6,4,5,7]=>0001010=>0101000
[7,4,5,6,8,3,2,1]=>[1,2,3,8,6,5,4,7]=>0001110=>0111000
[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>0001001=>1001000
[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>0001101=>1011000
[6,4,5,7,8,3,2,1]=>[1,2,3,8,7,5,4,6]=>0001101=>1011000
[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>0001011=>1101000
[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>0001111=>1111000
[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>0010000=>0000100
[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>0010001=>1000100
[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>0010010=>0100100
[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100=>0010100
[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>0010101=>1010100
[7,6,5,8,3,4,2,1]=>[1,2,4,3,8,5,6,7]=>0010100=>0010100
[6,7,5,8,3,4,2,1]=>[1,2,4,3,8,5,7,6]=>0010110=>0110100
[7,5,6,8,3,4,2,1]=>[1,2,4,3,8,6,5,7]=>0010110=>0110100
[5,6,7,8,3,4,2,1]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100
[7,6,8,4,3,5,2,1]=>[1,2,5,3,4,8,6,7]=>0010010=>0100100
[6,7,8,4,3,5,2,1]=>[1,2,5,3,4,8,7,6]=>0010011=>1100100
[7,8,6,3,4,5,2,1]=>[1,2,5,4,3,6,8,7]=>0011001=>1001100
[7,6,8,3,4,5,2,1]=>[1,2,5,4,3,8,6,7]=>0011010=>0101100
[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0010000=>0000100
[7,8,5,4,3,6,2,1]=>[1,2,6,3,4,5,8,7]=>0010001=>1000100
[8,7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7,8]=>0010100=>0010100
[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>0011100=>0011100
[8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8]=>0010000=>0000100
[8,5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5,8]=>0011010=>0101100
[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>0010000=>0000100
[6,7,5,4,3,8,2,1]=>[1,2,8,3,4,5,7,6]=>0010010=>0100100
[7,6,4,5,3,8,2,1]=>[1,2,8,3,5,4,6,7]=>0011000=>0001100
[6,7,4,5,3,8,2,1]=>[1,2,8,3,5,4,7,6]=>0011010=>0101100
[7,5,4,6,3,8,2,1]=>[1,2,8,3,6,4,5,7]=>0011000=>0001100
[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>0011000=>0001100
[6,4,5,7,3,8,2,1]=>[1,2,8,3,7,5,4,6]=>0011100=>0011100
[5,4,6,7,3,8,2,1]=>[1,2,8,3,7,6,4,5]=>0011010=>0101100
[4,5,6,7,3,8,2,1]=>[1,2,8,3,7,6,5,4]=>0011110=>0111100
[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>0011000=>0001100
[6,7,5,3,4,8,2,1]=>[1,2,8,4,3,5,7,6]=>0011010=>0101100
[6,5,7,3,4,8,2,1]=>[1,2,8,4,3,7,5,6]=>0011100=>0011100
[5,6,7,3,4,8,2,1]=>[1,2,8,4,3,7,6,5]=>0011110=>0111100
[7,6,4,3,5,8,2,1]=>[1,2,8,5,3,4,6,7]=>0010100=>0010100
[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>0011100=>0011100
[7,5,3,4,6,8,2,1]=>[1,2,8,6,4,3,5,7]=>0011010=>0101100
[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>0010001=>1000100
[6,4,5,3,7,8,2,1]=>[1,2,8,7,3,5,4,6]=>0011001=>1001100
[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>0011101=>1011100
[5,6,3,4,7,8,2,1]=>[1,2,8,7,4,3,6,5]=>0011101=>1011100
[6,3,4,5,7,8,2,1]=>[1,2,8,7,5,4,3,6]=>0011101=>1011100
[4,5,3,6,7,8,2,1]=>[1,2,8,7,6,3,5,4]=>0011011=>1101100
[5,3,4,6,7,8,2,1]=>[1,2,8,7,6,4,3,5]=>0011011=>1101100
[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>0011111=>1111100
[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>0100000=>0000010
[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010=>0100010
[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>0100010=>0100010
[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>0100101=>1010010
[8,5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5,8]=>0100110=>0110010
[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>0100100=>0010010
[6,7,5,8,4,2,3,1]=>[1,3,2,4,8,5,7,6]=>0100110=>0110010
[7,5,6,8,4,2,3,1]=>[1,3,2,4,8,6,5,7]=>0100110=>0110010
[5,6,7,8,4,2,3,1]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010
[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000=>0001010
[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010=>0101010
[7,6,8,4,5,2,3,1]=>[1,3,2,5,4,8,6,7]=>0101010=>0101010
[6,7,8,4,5,2,3,1]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010
[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0101000=>0001010
[8,5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5,8]=>0101100=>0011010
[8,6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6,8]=>0101100=>0011010
[7,6,5,4,8,2,3,1]=>[1,3,2,8,4,5,6,7]=>0101000=>0001010
[7,5,6,4,8,2,3,1]=>[1,3,2,8,4,6,5,7]=>0101100=>0011010
[6,5,7,4,8,2,3,1]=>[1,3,2,8,4,7,5,6]=>0101100=>0011010
[7,6,4,5,8,2,3,1]=>[1,3,2,8,5,4,6,7]=>0101100=>0011010
[7,4,5,6,8,2,3,1]=>[1,3,2,8,6,5,4,7]=>0101110=>0111010
[6,5,4,7,8,2,3,1]=>[1,3,2,8,7,4,5,6]=>0101001=>1001010
[5,4,6,7,8,2,3,1]=>[1,3,2,8,7,6,4,5]=>0101011=>1101010
[4,5,6,7,8,2,3,1]=>[1,3,2,8,7,6,5,4]=>0101111=>1111010
[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0100000=>0000010
[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0100001=>1000010
[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0100010=>0100010
[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>0100010=>0100010
[6,7,8,5,3,2,4,1]=>[1,4,2,3,5,8,7,6]=>0100011=>1100010
[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0100100=>0010010
[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0100101=>1010010
[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0100100=>0010010
[7,6,5,8,3,2,4,1]=>[1,4,2,3,8,5,6,7]=>0100100=>0010010
[6,7,5,8,3,2,4,1]=>[1,4,2,3,8,5,7,6]=>0100110=>0110010
[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>0100110=>0110010
[6,5,7,8,3,2,4,1]=>[1,4,2,3,8,7,5,6]=>0100101=>1010010
[5,6,7,8,3,2,4,1]=>[1,4,2,3,8,7,6,5]=>0100111=>1110010
[8,7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7,8]=>0110000=>0000110
[8,6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6,8]=>0110010=>0100110
[7,6,8,5,2,3,4,1]=>[1,4,3,2,5,8,6,7]=>0110010=>0100110
[6,7,8,5,2,3,4,1]=>[1,4,3,2,5,8,7,6]=>0110011=>1100110
[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>0110110=>0110110
[7,6,5,8,2,3,4,1]=>[1,4,3,2,8,5,6,7]=>0110100=>0010110
[7,5,6,8,2,3,4,1]=>[1,4,3,2,8,6,5,7]=>0110110=>0110110
[5,6,7,8,2,3,4,1]=>[1,4,3,2,8,7,6,5]=>0110111=>1110110
[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0100000=>0000010
[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>0100001=>1000010
[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0100010=>0100010
[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>0100010=>0100010
[6,7,8,4,3,2,5,1]=>[1,5,2,3,4,8,7,6]=>0100011=>1100010
[8,7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7,8]=>0110000=>0000110
[7,8,6,3,4,2,5,1]=>[1,5,2,4,3,6,8,7]=>0110001=>1000110
[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>0110010=>0100110
[7,6,8,3,4,2,5,1]=>[1,5,2,4,3,8,6,7]=>0110010=>0100110
[6,7,8,3,4,2,5,1]=>[1,5,2,4,3,8,7,6]=>0110011=>1100110
[8,7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7,8]=>0110000=>0000110
[7,8,6,4,2,3,5,1]=>[1,5,3,2,4,6,8,7]=>0110001=>1000110
[8,6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6,8]=>0110010=>0100110
[7,6,8,4,2,3,5,1]=>[1,5,3,2,4,8,6,7]=>0110010=>0100110
[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>0110011=>1100110
[8,7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7,8]=>0101000=>0001010
[7,8,6,3,2,4,5,1]=>[1,5,4,2,3,6,8,7]=>0101001=>1001010
[7,6,8,3,2,4,5,1]=>[1,5,4,2,3,8,6,7]=>0101010=>0101010
[6,7,8,3,2,4,5,1]=>[1,5,4,2,3,8,7,6]=>0101011=>1101010
[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0100000=>0000010
[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>0100001=>1000010
[8,7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7,8]=>0110000=>0000110
[8,7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7,8]=>0101000=>0001010
[7,8,5,3,2,4,6,1]=>[1,6,4,2,3,5,8,7]=>0101001=>1001010
[8,7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7,8]=>0111000=>0001110
[7,8,4,3,2,5,6,1]=>[1,6,5,2,3,4,8,7]=>0100101=>1010010
[8,7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7,8]=>0110100=>0010110
[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>0100000=>0000010
[8,5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5,8]=>0110100=>0010110
[8,6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6,8]=>0110000=>0000110
[8,6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6,8]=>0111000=>0001110
[8,4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4,8]=>0111000=>0001110
[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>0110000=>0000110
[8,5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5,8]=>0110100=>0010110
[8,6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6,8]=>0111000=>0001110
[8,6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6,8]=>0111000=>0001110
[8,6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6,8]=>0110100=>0010110
[8,5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5,8]=>0100010=>0100010
[8,5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5,8]=>0110010=>0100110
[8,5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5,8]=>0110010=>0100110
[8,5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5,8]=>0101010=>0101010
[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>0100000=>0000010
[5,6,7,4,3,2,8,1]=>[1,8,2,3,4,7,6,5]=>0100110=>0110010
[7,6,4,5,3,2,8,1]=>[1,8,2,3,5,4,6,7]=>0101000=>0001010
[7,5,4,6,3,2,8,1]=>[1,8,2,3,6,4,5,7]=>0101000=>0001010
[7,4,5,6,3,2,8,1]=>[1,8,2,3,6,5,4,7]=>0101100=>0011010
[6,4,5,7,3,2,8,1]=>[1,8,2,3,7,5,4,6]=>0101100=>0011010
[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>0101110=>0111010
[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>0110000=>0000110
[7,5,6,3,4,2,8,1]=>[1,8,2,4,3,6,5,7]=>0110100=>0010110
[6,5,7,3,4,2,8,1]=>[1,8,2,4,3,7,5,6]=>0110100=>0010110
[7,6,4,3,5,2,8,1]=>[1,8,2,5,3,4,6,7]=>0110000=>0000110
[7,5,4,3,6,2,8,1]=>[1,8,2,6,3,4,5,7]=>0110000=>0000110
[7,4,5,3,6,2,8,1]=>[1,8,2,6,3,5,4,7]=>0111000=>0001110
[7,4,3,5,6,2,8,1]=>[1,8,2,6,5,3,4,7]=>0110100=>0010110
[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>0110000=>0000110
[6,4,5,3,7,2,8,1]=>[1,8,2,7,3,5,4,6]=>0111000=>0001110
[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>0111000=>0001110
[4,5,6,3,7,2,8,1]=>[1,8,2,7,3,6,5,4]=>0111100=>0011110
[6,5,3,4,7,2,8,1]=>[1,8,2,7,4,3,5,6]=>0111000=>0001110
[6,3,4,5,7,2,8,1]=>[1,8,2,7,5,4,3,6]=>0111100=>0011110
[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>0110010=>0100110
[4,5,3,6,7,2,8,1]=>[1,8,2,7,6,3,5,4]=>0111010=>0101110
[5,3,4,6,7,2,8,1]=>[1,8,2,7,6,4,3,5]=>0111010=>0101110
[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>0111110=>0111110
[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>0110000=>0000110
[7,6,4,5,2,3,8,1]=>[1,8,3,2,5,4,6,7]=>0111000=>0001110
[6,7,4,5,2,3,8,1]=>[1,8,3,2,5,4,7,6]=>0111010=>0101110
[7,5,4,6,2,3,8,1]=>[1,8,3,2,6,4,5,7]=>0111000=>0001110
[5,4,6,7,2,3,8,1]=>[1,8,3,2,7,6,4,5]=>0111010=>0101110
[4,5,6,7,2,3,8,1]=>[1,8,3,2,7,6,5,4]=>0111110=>0111110
[7,6,5,3,2,4,8,1]=>[1,8,4,2,3,5,6,7]=>0101000=>0001010
[6,7,5,3,2,4,8,1]=>[1,8,4,2,3,5,7,6]=>0101010=>0101010
[6,5,7,3,2,4,8,1]=>[1,8,4,2,3,7,5,6]=>0101100=>0011010
[5,6,7,3,2,4,8,1]=>[1,8,4,2,3,7,6,5]=>0101110=>0111010
[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>0111000=>0001110
[5,6,7,2,3,4,8,1]=>[1,8,4,3,2,7,6,5]=>0111110=>0111110
[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>0110100=>0010110
[6,7,4,2,3,5,8,1]=>[1,8,5,3,2,4,7,6]=>0110110=>0110110
[6,7,3,2,4,5,8,1]=>[1,8,5,4,2,3,7,6]=>0101110=>0111010
[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>0111110=>0111110
[7,5,4,3,2,6,8,1]=>[1,8,6,2,3,4,5,7]=>0100010=>0100010
[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>0110010=>0100110
[7,5,3,2,4,6,8,1]=>[1,8,6,4,2,3,5,7]=>0101010=>0101010
[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>0100001=>1000010
[5,4,6,3,2,7,8,1]=>[1,8,7,2,3,6,4,5]=>0101001=>1001010
[4,5,6,3,2,7,8,1]=>[1,8,7,2,3,6,5,4]=>0101101=>1011010
[6,4,3,5,2,7,8,1]=>[1,8,7,2,5,3,4,6]=>0110001=>1000110
[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>0110001=>1000110
[4,5,3,6,2,7,8,1]=>[1,8,7,2,6,3,5,4]=>0111001=>1001110
[3,4,5,6,2,7,8,1]=>[1,8,7,2,6,5,4,3]=>0111101=>1011110
[6,5,4,2,3,7,8,1]=>[1,8,7,3,2,4,5,6]=>0110001=>1000110
[5,6,4,2,3,7,8,1]=>[1,8,7,3,2,4,6,5]=>0110101=>1010110
[6,4,5,2,3,7,8,1]=>[1,8,7,3,2,5,4,6]=>0111001=>1001110
[5,4,6,2,3,7,8,1]=>[1,8,7,3,2,6,4,5]=>0111001=>1001110
[6,5,3,2,4,7,8,1]=>[1,8,7,4,2,3,5,6]=>0101001=>1001010
[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>0111001=>1001110
[6,4,3,2,5,7,8,1]=>[1,8,7,5,2,3,4,6]=>0100101=>1010010
[6,4,2,3,5,7,8,1]=>[1,8,7,5,3,2,4,6]=>0110101=>1010110
[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>0111101=>1011110
[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>0100011=>1100010
[5,3,4,2,6,7,8,1]=>[1,8,7,6,2,4,3,5]=>0110011=>1100110
[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>0111011=>1101110
[5,4,2,3,6,7,8,1]=>[1,8,7,6,3,2,4,5]=>0110011=>1100110
[4,5,2,3,6,7,8,1]=>[1,8,7,6,3,2,5,4]=>0111011=>1101110
[5,3,2,4,6,7,8,1]=>[1,8,7,6,4,2,3,5]=>0101011=>1101010
[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>0111011=>1101110
[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>0100111=>1110010
[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>0110111=>1110110
[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>0111111=>1111110
[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>1000000=>0000001
[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>1000001=>1000001
[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100=>0010001
[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101=>1010001
[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>1000100=>0010001
[6,7,5,8,4,3,1,2]=>[2,1,3,4,8,5,7,6]=>1000110=>0110001
[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>1000110=>0110001
[6,5,7,8,4,3,1,2]=>[2,1,3,4,8,7,5,6]=>1000101=>1010001
[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>1000111=>1110001
[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001=>1001001
[6,7,8,4,5,3,1,2]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001
[7,8,4,5,6,3,1,2]=>[2,1,3,6,5,4,8,7]=>1001101=>1011001
[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>1001000=>0001001
[6,7,5,4,8,3,1,2]=>[2,1,3,8,4,5,7,6]=>1001010=>0101001
[6,5,7,4,8,3,1,2]=>[2,1,3,8,4,7,5,6]=>1001100=>0011001
[5,6,7,4,8,3,1,2]=>[2,1,3,8,4,7,6,5]=>1001110=>0111001
[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>1001110=>0111001
[6,5,4,7,8,3,1,2]=>[2,1,3,8,7,4,5,6]=>1001001=>1001001
[5,6,4,7,8,3,1,2]=>[2,1,3,8,7,4,6,5]=>1001101=>1011001
[6,4,5,7,8,3,1,2]=>[2,1,3,8,7,5,4,6]=>1001101=>1011001
[5,4,6,7,8,3,1,2]=>[2,1,3,8,7,6,4,5]=>1001011=>1101001
[4,5,6,7,8,3,1,2]=>[2,1,3,8,7,6,5,4]=>1001111=>1111001
[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000=>0000101
[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001=>1000101
[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100=>0010101
[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101
[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010100=>0010101
[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>1010110=>0110101
[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010110=>0110101
[6,5,7,8,3,4,1,2]=>[2,1,4,3,8,7,5,6]=>1010101=>1010101
[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101
[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1010001=>1000101
[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>1011001=>1001101
[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1010001=>1000101
[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>1011001=>1001101
[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1011001=>1001101
[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>1010101=>1010101
[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>1011101=>1011101
[8,5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5,8]=>1011000=>0001101
[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>1010000=>0000101
[5,6,7,4,3,8,1,2]=>[2,1,8,3,4,7,6,5]=>1010110=>0110101
[6,7,4,5,3,8,1,2]=>[2,1,8,3,5,4,7,6]=>1011010=>0101101
[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>1011000=>0001101
[6,5,4,7,3,8,1,2]=>[2,1,8,3,7,4,5,6]=>1011000=>0001101
[5,6,4,7,3,8,1,2]=>[2,1,8,3,7,4,6,5]=>1011100=>0011101
[6,4,5,7,3,8,1,2]=>[2,1,8,3,7,5,4,6]=>1011100=>0011101
[5,4,6,7,3,8,1,2]=>[2,1,8,3,7,6,4,5]=>1011010=>0101101
[4,5,6,7,3,8,1,2]=>[2,1,8,3,7,6,5,4]=>1011110=>0111101
[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>1011010=>0101101
[6,5,7,3,4,8,1,2]=>[2,1,8,4,3,7,5,6]=>1011100=>0011101
[7,6,3,4,5,8,1,2]=>[2,1,8,5,4,3,6,7]=>1011100=>0011101
[6,7,3,4,5,8,1,2]=>[2,1,8,5,4,3,7,6]=>1011110=>0111101
[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1011010=>0101101
[6,5,4,3,7,8,1,2]=>[2,1,8,7,3,4,5,6]=>1010001=>1000101
[5,6,4,3,7,8,1,2]=>[2,1,8,7,3,4,6,5]=>1010101=>1010101
[6,4,5,3,7,8,1,2]=>[2,1,8,7,3,5,4,6]=>1011001=>1001101
[6,5,3,4,7,8,1,2]=>[2,1,8,7,4,3,5,6]=>1011001=>1001101
[5,6,3,4,7,8,1,2]=>[2,1,8,7,4,3,6,5]=>1011101=>1011101
[6,4,3,5,7,8,1,2]=>[2,1,8,7,5,3,4,6]=>1010101=>1010101
[6,3,4,5,7,8,1,2]=>[2,1,8,7,5,4,3,6]=>1011101=>1011101
[5,4,3,6,7,8,1,2]=>[2,1,8,7,6,3,4,5]=>1010011=>1100101
[4,5,3,6,7,8,1,2]=>[2,1,8,7,6,3,5,4]=>1011011=>1101101
[5,3,4,6,7,8,1,2]=>[2,1,8,7,6,4,3,5]=>1011011=>1101101
[4,3,5,6,7,8,1,2]=>[2,1,8,7,6,5,3,4]=>1010111=>1110101
[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>1011111=>1111101
[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>1000000=>0000001
[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>1000010=>0100001
[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>1000100=>0010001
[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>1000100=>0010001
[6,7,5,8,4,2,1,3]=>[3,1,2,4,8,5,7,6]=>1000110=>0110001
[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>1000110=>0110001
[6,5,7,8,4,2,1,3]=>[3,1,2,4,8,7,5,6]=>1000101=>1010001
[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>1000111=>1110001
[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>1001001=>1001001
[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>1001010=>0101001
[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>1001001=>1001001
[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>1001100=>0011001
[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>1001010=>0101001
[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>1001000=>0001001
[6,7,5,4,8,2,1,3]=>[3,1,2,8,4,5,7,6]=>1001010=>0101001
[6,5,7,4,8,2,1,3]=>[3,1,2,8,4,7,5,6]=>1001100=>0011001
[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>1001010=>0101001
[7,4,5,6,8,2,1,3]=>[3,1,2,8,6,5,4,7]=>1001110=>0111001
[6,5,4,7,8,2,1,3]=>[3,1,2,8,7,4,5,6]=>1001001=>1001001
[5,6,4,7,8,2,1,3]=>[3,1,2,8,7,4,6,5]=>1001101=>1011001
[6,4,5,7,8,2,1,3]=>[3,1,2,8,7,5,4,6]=>1001101=>1011001
[5,4,6,7,8,2,1,3]=>[3,1,2,8,7,6,4,5]=>1001011=>1101001
[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>1001111=>1111001
[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000=>0000011
[7,6,8,5,4,1,2,3]=>[3,2,1,4,5,8,6,7]=>1100010=>0100011
[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>1100011=>1100011
[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110=>0110011
[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>1100100=>0010011
[6,7,5,8,4,1,2,3]=>[3,2,1,4,8,5,7,6]=>1100110=>0110011
[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>1100110=>0110011
[6,5,7,8,4,1,2,3]=>[3,2,1,4,8,7,5,6]=>1100101=>1010011
[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>1100111=>1110011
[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010=>0101011
[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1101000=>0001011
[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>1101000=>0001011
[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>1101000=>0001011
[6,7,5,4,8,1,2,3]=>[3,2,1,8,4,5,7,6]=>1101010=>0101011
[6,5,7,4,8,1,2,3]=>[3,2,1,8,4,7,5,6]=>1101100=>0011011
[5,6,7,4,8,1,2,3]=>[3,2,1,8,4,7,6,5]=>1101110=>0111011
[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>1101100=>0011011
[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>1101110=>0111011
[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>1101010=>0101011
[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>1101110=>0111011
[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>1101001=>1001011
[5,6,4,7,8,1,2,3]=>[3,2,1,8,7,4,6,5]=>1101101=>1011011
[5,4,6,7,8,1,2,3]=>[3,2,1,8,7,6,4,5]=>1101011=>1101011
[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>1101111=>1111011
[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>1000000=>0000001
[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>1000001=>1000001
[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>1000010=>0100001
[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>1000010=>0100001
[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>1000011=>1100001
[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>1000100=>0010001
[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>1000101=>1010001
[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>1000100=>0010001
[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>1000110=>0110001
[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>1000100=>0010001
[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>1000110=>0110001
[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>1000110=>0110001
[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>1000101=>1010001
[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>1000111=>1110001
[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>1100000=>0000011
[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>1100101=>1010011
[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>1100100=>0010011
[6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6]=>1100110=>0110011
[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>1100110=>0110011
[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>1100111=>1110011
[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1100000=>0000011
[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1100001=>1000011
[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1100010=>0100011
[7,6,8,5,3,1,2,4]=>[4,2,1,3,5,8,6,7]=>1100010=>0100011
[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>1100011=>1100011
[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1100100=>0010011
[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1100101=>1010011
[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1100100=>0010011
[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1100110=>0110011
[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>1100100=>0010011
[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>1100110=>0110011
[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1100110=>0110011
[6,5,7,8,3,1,2,4]=>[4,2,1,3,8,7,5,6]=>1100101=>1010011
[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>1100111=>1110011
[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>1010000=>0000101
[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>1010010=>0100101
[6,7,8,5,2,1,3,4]=>[4,3,1,2,5,8,7,6]=>1010011=>1100101
[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>1010100=>0010101
[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>1010101=>1010101
[7,6,5,8,2,1,3,4]=>[4,3,1,2,8,5,6,7]=>1010100=>0010101
[6,7,5,8,2,1,3,4]=>[4,3,1,2,8,5,7,6]=>1010110=>0110101
[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>1010110=>0110101
[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>1010101=>1010101
[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>1010111=>1110101
[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000=>0000111
[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>1110001=>1000111
[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010=>0100111
[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>1110010=>0100111
[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>1110011=>1100111
[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100=>0010111
[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101=>1010111
[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110100=>0010111
[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110=>0110111
[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>1110100=>0010111
[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>1110110=>0110111
[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>1110110=>0110111
[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>1110101=>1010111
[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111=>1110111
[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>1000000=>0000001
[6,7,8,4,3,2,1,5]=>[5,1,2,3,4,8,7,6]=>1000011=>1100001
[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>1010000=>0000101
[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>1010001=>1000101
[6,7,8,3,4,2,1,5]=>[5,1,2,4,3,8,7,6]=>1010011=>1100101
[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>1100000=>0000011
[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>1100001=>1000011
[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>1100010=>0100011
[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>1100010=>0100011
[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>1100011=>1100011
[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>1100000=>0000011
[7,6,8,3,2,4,1,5]=>[5,1,4,2,3,8,6,7]=>1100010=>0100011
[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>1100011=>1100011
[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>1110000=>0000111
[6,7,8,2,3,4,1,5]=>[5,1,4,3,2,8,7,6]=>1110011=>1100111
[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1100000=>0000011
[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>1100011=>1100011
[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1110000=>0000111
[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>1110001=>1000111
[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1110011=>1100111
[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>1010000=>0000101
[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>1010001=>1000101
[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>1010010=>0100101
[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>1010010=>0100101
[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>1010011=>1100101
[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1110000=>0000111
[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>1110010=>0100111
[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1110011=>1100111
[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>1001000=>0001001
[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>1001010=>0101001
[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>1001011=>1101001
[8,7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7,8]=>1101000=>0001011
[6,7,8,2,3,1,4,5]=>[5,4,1,3,2,8,7,6]=>1101011=>1101011
[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1101000=>0001011
[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>1101011=>1101011
[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>1011000=>0001101
[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>1011010=>0101101
[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>1011011=>1101101
[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000=>0001111
[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>1111001=>1001111
[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010=>0101111
[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>1111010=>0101111
[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>1111011=>1101111
[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>1000001=>1000001
[7,8,4,5,2,3,1,6]=>[6,1,3,2,5,4,8,7]=>1101001=>1001011
[7,8,5,3,2,4,1,6]=>[6,1,4,2,3,5,8,7]=>1100001=>1000011
[7,8,4,3,2,5,1,6]=>[6,1,5,2,3,4,8,7]=>1100001=>1000011
[7,8,3,4,2,5,1,6]=>[6,1,5,2,4,3,8,7]=>1110001=>1000111
[7,8,3,2,4,5,1,6]=>[6,1,5,4,2,3,8,7]=>1101001=>1001011
[7,8,2,3,4,5,1,6]=>[6,1,5,4,3,2,8,7]=>1111001=>1001111
[8,7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7,8]=>1111000=>0001111
[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>1010001=>1000101
[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1111000=>0001111
[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1101000=>0001011
[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1101001=>1001011
[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>1011000=>0001101
[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>1011001=>1001101
[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1111000=>0001111
[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1111001=>1001111
[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>1000101=>1010001
[7,8,3,4,2,1,5,6]=>[6,5,1,2,4,3,8,7]=>1010101=>1010101
[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>1110101=>1010111
[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>1010101=>1010101
[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1110101=>1010111
[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>1001101=>1011001
[7,8,2,3,1,4,5,6]=>[6,5,4,1,3,2,8,7]=>1101101=>1011011
[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>1101101=>1011011
[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>1011100=>0011101
[7,8,2,1,3,4,5,6]=>[6,5,4,3,1,2,8,7]=>1011101=>1011101
[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>1111101=>1011111
[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>1000000=>0000001
[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>1001100=>0011001
[8,5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5,8]=>1010000=>0000101
[8,4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4,8]=>1011000=>0001101
[8,5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5,8]=>1011000=>0001101
[8,4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4,8]=>1010100=>0010101
[8,3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3,8]=>1011100=>0011101
[8,6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6,8]=>1101000=>0001011
[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>1110000=>0000111
[8,6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6,8]=>1110000=>0000111
[8,6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6,8]=>1101000=>0001011
[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>1100000=>0000011
[8,4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4,8]=>1110000=>0000111
[8,5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5,8]=>1101000=>0001011
[8,4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4,8]=>1110100=>0010111
[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>1110100=>0010111
[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1111000=>0001111
[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>1111000=>0001111
[8,4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4,8]=>1110100=>0010111
[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>1010000=>0000101
[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>1010100=>0010101
[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>1011000=>0001101
[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>1110100=>0010111
[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>1111000=>0001111
[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>1101000=>0001011
[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>1101100=>0011011
[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>1011000=>0001101
[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>1011100=>0011101
[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1111000=>0001111
[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1111100=>0011111
[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>1000100=>0010001
[8,6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6,8]=>1010100=>0010101
[8,6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6,8]=>1100100=>0010011
[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>1010100=>0010101
[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1110100=>0010111
[8,6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6,8]=>1101100=>0011011
[8,4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4,8]=>1001010=>0101001
[8,3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3,8]=>1011010=>0101101
[8,5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5,8]=>1100010=>0100011
[8,5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5,8]=>1110010=>0100111
[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1110010=>0100111
[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1101010=>0101011
[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1111010=>0101111
[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>1000110=>0110001
[8,3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3,8]=>1010110=>0110101
[8,4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4,8]=>1100110=>0110011
[8,3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3,8]=>1100110=>0110011
[8,2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2,8]=>1110110=>0110111
[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1100110=>0110011
[8,3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3,8]=>1110110=>0110111
[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>1001110=>0111001
[8,2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2,8]=>1101110=>0111011
[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>1111110=>0111111
[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>1000000=>0000001
[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>1000110=>0110001
[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>1001000=>0001001
[6,7,4,5,3,2,1,8]=>[8,1,2,3,5,4,7,6]=>1001010=>0101001
[7,4,5,6,3,2,1,8]=>[8,1,2,3,6,5,4,7]=>1001100=>0011001
[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>1001000=>0001001
[6,4,5,7,3,2,1,8]=>[8,1,2,3,7,5,4,6]=>1001100=>0011001
[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>1001110=>0111001
[6,7,5,3,4,2,1,8]=>[8,1,2,4,3,5,7,6]=>1010010=>0100101
[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>1010100=>0010101
[5,6,7,3,4,2,1,8]=>[8,1,2,4,3,7,6,5]=>1010110=>0110101
[7,6,4,3,5,2,1,8]=>[8,1,2,5,3,4,6,7]=>1010000=>0000101
[7,6,3,4,5,2,1,8]=>[8,1,2,5,4,3,6,7]=>1011000=>0001101
[7,4,3,5,6,2,1,8]=>[8,1,2,6,5,3,4,7]=>1010100=>0010101
[7,3,4,5,6,2,1,8]=>[8,1,2,6,5,4,3,7]=>1011100=>0011101
[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>1010000=>0000101
[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>1011000=>0001101
[4,5,6,3,7,2,1,8]=>[8,1,2,7,3,6,5,4]=>1011100=>0011101
[6,3,4,5,7,2,1,8]=>[8,1,2,7,5,4,3,6]=>1011100=>0011101
[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>1010010=>0100101
[4,5,3,6,7,2,1,8]=>[8,1,2,7,6,3,5,4]=>1011010=>0101101
[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>1011110=>0111101
[7,5,6,4,2,3,1,8]=>[8,1,3,2,4,6,5,7]=>1100100=>0010011
[5,6,7,4,2,3,1,8]=>[8,1,3,2,4,7,6,5]=>1100110=>0110011
[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>1101000=>0001011
[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>1101010=>0101011
[7,4,5,6,2,3,1,8]=>[8,1,3,2,6,5,4,7]=>1101100=>0011011
[5,6,4,7,2,3,1,8]=>[8,1,3,2,7,4,6,5]=>1101100=>0011011
[6,4,5,7,2,3,1,8]=>[8,1,3,2,7,5,4,6]=>1101100=>0011011
[5,4,6,7,2,3,1,8]=>[8,1,3,2,7,6,4,5]=>1101010=>0101011
[7,6,5,3,2,4,1,8]=>[8,1,4,2,3,5,6,7]=>1100000=>0000011
[6,7,5,3,2,4,1,8]=>[8,1,4,2,3,5,7,6]=>1100010=>0100011
[5,6,7,3,2,4,1,8]=>[8,1,4,2,3,7,6,5]=>1100110=>0110011
[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>1110000=>0000111
[6,7,5,2,3,4,1,8]=>[8,1,4,3,2,5,7,6]=>1110010=>0100111
[7,5,6,2,3,4,1,8]=>[8,1,4,3,2,6,5,7]=>1110100=>0010111
[6,5,7,2,3,4,1,8]=>[8,1,4,3,2,7,5,6]=>1110100=>0010111
[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>1110110=>0110111
[7,6,4,2,3,5,1,8]=>[8,1,5,3,2,4,6,7]=>1110000=>0000111
[6,7,4,2,3,5,1,8]=>[8,1,5,3,2,4,7,6]=>1110010=>0100111
[7,6,3,2,4,5,1,8]=>[8,1,5,4,2,3,6,7]=>1101000=>0001011
[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>1111000=>0001111
[7,5,4,3,2,6,1,8]=>[8,1,6,2,3,4,5,7]=>1100000=>0000011
[7,5,3,4,2,6,1,8]=>[8,1,6,2,4,3,5,7]=>1110000=>0000111
[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>1111000=>0001111
[7,5,3,2,4,6,1,8]=>[8,1,6,4,2,3,5,7]=>1101000=>0001011
[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>1101000=>0001011
[4,5,6,3,2,7,1,8]=>[8,1,7,2,3,6,5,4]=>1101100=>0011011
[5,6,3,4,2,7,1,8]=>[8,1,7,2,4,3,6,5]=>1110100=>0010111
[6,4,3,5,2,7,1,8]=>[8,1,7,2,5,3,4,6]=>1110000=>0000111
[6,3,4,5,2,7,1,8]=>[8,1,7,2,5,4,3,6]=>1111000=>0001111
[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>1110000=>0000111
[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>1111000=>0001111
[5,3,4,6,2,7,1,8]=>[8,1,7,2,6,4,3,5]=>1111000=>0001111
[3,4,5,6,2,7,1,8]=>[8,1,7,2,6,5,4,3]=>1111100=>0011111
[4,5,6,2,3,7,1,8]=>[8,1,7,3,2,6,5,4]=>1111100=>0011111
[6,5,3,2,4,7,1,8]=>[8,1,7,4,2,3,5,6]=>1101000=>0001011
[5,6,3,2,4,7,1,8]=>[8,1,7,4,2,3,6,5]=>1101100=>0011011
[5,6,2,3,4,7,1,8]=>[8,1,7,4,3,2,6,5]=>1111100=>0011111
[6,3,4,2,5,7,1,8]=>[8,1,7,5,2,4,3,6]=>1110100=>0010111
[6,4,2,3,5,7,1,8]=>[8,1,7,5,3,2,4,6]=>1110100=>0010111
[6,3,2,4,5,7,1,8]=>[8,1,7,5,4,2,3,6]=>1101100=>0011011
[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>1100010=>0100011
[5,3,4,2,6,7,1,8]=>[8,1,7,6,2,4,3,5]=>1110010=>0100111
[3,4,5,2,6,7,1,8]=>[8,1,7,6,2,5,4,3]=>1111010=>0101111
[5,4,2,3,6,7,1,8]=>[8,1,7,6,3,2,4,5]=>1110010=>0100111
[5,2,3,4,6,7,1,8]=>[8,1,7,6,4,3,2,5]=>1111010=>0101111
[4,3,2,5,6,7,1,8]=>[8,1,7,6,5,2,3,4]=>1100110=>0110011
[4,2,3,5,6,7,1,8]=>[8,1,7,6,5,3,2,4]=>1110110=>0110111
[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>1111110=>0111111
[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>1101100=>0011011
[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1110100=>0010111
[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1111000=>0001111
[7,4,3,5,6,1,2,8]=>[8,2,1,6,5,3,4,7]=>1110100=>0010111
[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>1110000=>0000111
[6,4,3,5,7,1,2,8]=>[8,2,1,7,5,3,4,6]=>1110100=>0010111
[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>1111100=>0011111
[5,4,3,6,7,1,2,8]=>[8,2,1,7,6,3,4,5]=>1110010=>0100111
[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>1111110=>0111111
[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>1010000=>0000101
[6,7,5,4,2,1,3,8]=>[8,3,1,2,4,5,7,6]=>1010010=>0100101
[7,5,6,4,2,1,3,8]=>[8,3,1,2,4,6,5,7]=>1010100=>0010101
[7,6,4,5,2,1,3,8]=>[8,3,1,2,5,4,6,7]=>1011000=>0001101
[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>1011010=>0101101
[7,4,5,6,2,1,3,8]=>[8,3,1,2,6,5,4,7]=>1011100=>0011101
[4,5,6,7,2,1,3,8]=>[8,3,1,2,7,6,5,4]=>1011110=>0111101
[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1110000=>0000111
[6,7,5,4,1,2,3,8]=>[8,3,2,1,4,5,7,6]=>1110010=>0100111
[7,5,6,4,1,2,3,8]=>[8,3,2,1,4,6,5,7]=>1110100=>0010111
[5,6,7,4,1,2,3,8]=>[8,3,2,1,4,7,6,5]=>1110110=>0110111
[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>1111000=>0001111
[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>1111010=>0101111
[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>1111000=>0001111
[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>1111100=>0011111
[6,5,4,7,1,2,3,8]=>[8,3,2,1,7,4,5,6]=>1111000=>0001111
[5,6,4,7,1,2,3,8]=>[8,3,2,1,7,4,6,5]=>1111100=>0011111
[5,4,6,7,1,2,3,8]=>[8,3,2,1,7,6,4,5]=>1111010=>0101111
[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>1111110=>0111111
[7,6,5,2,3,1,4,8]=>[8,4,1,3,2,5,6,7]=>1101000=>0001011
[6,7,5,2,3,1,4,8]=>[8,4,1,3,2,5,7,6]=>1101010=>0101011
[7,5,6,2,3,1,4,8]=>[8,4,1,3,2,6,5,7]=>1101100=>0011011
[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1101000=>0001011
[6,7,5,3,1,2,4,8]=>[8,4,2,1,3,5,7,6]=>1101010=>0101011
[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1101100=>0011011
[5,6,7,3,1,2,4,8]=>[8,4,2,1,3,7,6,5]=>1101110=>0111011
[7,5,6,2,1,3,4,8]=>[8,4,3,1,2,6,5,7]=>1011100=>0011101
[5,6,7,2,1,3,4,8]=>[8,4,3,1,2,7,6,5]=>1011110=>0111101
[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1111000=>0001111
[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>1111010=>0101111
[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>1111100=>0011111
[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>1111100=>0011111
[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>1111110=>0111111
[7,6,3,4,2,1,5,8]=>[8,5,1,2,4,3,6,7]=>1010100=>0010101
[6,7,3,4,2,1,5,8]=>[8,5,1,2,4,3,7,6]=>1010110=>0110101
[7,6,4,2,3,1,5,8]=>[8,5,1,3,2,4,6,7]=>1100100=>0010011
[6,7,4,2,3,1,5,8]=>[8,5,1,3,2,4,7,6]=>1100110=>0110011
[7,6,3,2,4,1,5,8]=>[8,5,1,4,2,3,6,7]=>1100100=>0010011
[6,7,3,2,4,1,5,8]=>[8,5,1,4,2,3,7,6]=>1100110=>0110011
[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>1110110=>0110111
[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1110100=>0010111
[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1110110=>0110111
[6,7,3,2,1,4,5,8]=>[8,5,4,1,2,3,7,6]=>1001110=>0111001
[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1101100=>0011011
[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>1111110=>0111111
[7,4,5,3,2,1,6,8]=>[8,6,1,2,3,5,4,7]=>1001010=>0101001
[7,5,3,4,2,1,6,8]=>[8,6,1,2,4,3,5,7]=>1010010=>0100101
[7,4,3,5,2,1,6,8]=>[8,6,1,2,5,3,4,7]=>1010010=>0100101
[7,3,4,5,2,1,6,8]=>[8,6,1,2,5,4,3,7]=>1011010=>0101101
[7,5,3,2,4,1,6,8]=>[8,6,1,4,2,3,5,7]=>1100010=>0100011
[7,5,2,3,4,1,6,8]=>[8,6,1,4,3,2,5,7]=>1110010=>0100111
[7,4,3,2,5,1,6,8]=>[8,6,1,5,2,3,4,7]=>1100010=>0100011
[7,3,4,2,5,1,6,8]=>[8,6,1,5,2,4,3,7]=>1110010=>0100111
[7,4,2,3,5,1,6,8]=>[8,6,1,5,3,2,4,7]=>1110010=>0100111
[7,2,3,4,5,1,6,8]=>[8,6,1,5,4,3,2,7]=>1111010=>0101111
[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1110010=>0100111
[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>1110010=>0100111
[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>1111010=>0101111
[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1110010=>0100111
[7,5,2,3,1,4,6,8]=>[8,6,4,1,3,2,5,7]=>1101010=>0101011
[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1101010=>0101011
[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1111010=>0101111
[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>1000110=>0110001
[7,3,4,2,1,5,6,8]=>[8,6,5,1,2,4,3,7]=>1010110=>0110101
[7,4,2,3,1,5,6,8]=>[8,6,5,1,3,2,4,7]=>1100110=>0110011
[7,2,3,4,1,5,6,8]=>[8,6,5,1,4,3,2,7]=>1110110=>0110111
[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>1100110=>0110011
[7,2,3,1,4,5,6,8]=>[8,6,5,4,1,3,2,7]=>1101110=>0111011
[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>1101110=>0111011
[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>1111110=>0111111
[5,6,4,3,2,1,7,8]=>[8,7,1,2,3,4,6,5]=>1000101=>1010001
[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>1001001=>1001001
[6,5,3,4,2,1,7,8]=>[8,7,1,2,4,3,5,6]=>1010001=>1000101
[5,6,3,4,2,1,7,8]=>[8,7,1,2,4,3,6,5]=>1010101=>1010101
[6,3,4,5,2,1,7,8]=>[8,7,1,2,5,4,3,6]=>1011001=>1001101
[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>1010001=>1000101
[4,3,5,6,2,1,7,8]=>[8,7,1,2,6,5,3,4]=>1010101=>1010101
[3,4,5,6,2,1,7,8]=>[8,7,1,2,6,5,4,3]=>1011101=>1011101
[5,6,4,2,3,1,7,8]=>[8,7,1,3,2,4,6,5]=>1100101=>1010011
[6,4,5,2,3,1,7,8]=>[8,7,1,3,2,5,4,6]=>1101001=>1001011
[5,4,6,2,3,1,7,8]=>[8,7,1,3,2,6,4,5]=>1101001=>1001011
[6,3,2,4,5,1,7,8]=>[8,7,1,5,4,2,3,6]=>1101001=>1001011
[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>1100001=>1000011
[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>1101001=>1001011
[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>1111001=>1001111
[5,3,2,4,6,1,7,8]=>[8,7,1,6,4,2,3,5]=>1101001=>1001011
[5,2,3,4,6,1,7,8]=>[8,7,1,6,4,3,2,5]=>1111001=>1001111
[4,3,2,5,6,1,7,8]=>[8,7,1,6,5,2,3,4]=>1100101=>1010011
[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>1111101=>1011111
[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>1100001=>1000011
[5,6,4,3,1,2,7,8]=>[8,7,2,1,3,4,6,5]=>1100101=>1010011
[6,4,5,3,1,2,7,8]=>[8,7,2,1,3,5,4,6]=>1101001=>1001011
[5,4,6,3,1,2,7,8]=>[8,7,2,1,3,6,4,5]=>1101001=>1001011
[4,5,6,3,1,2,7,8]=>[8,7,2,1,3,6,5,4]=>1101101=>1011011
[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>1110101=>1010111
[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>1110001=>1000111
[5,6,4,2,1,3,7,8]=>[8,7,3,1,2,4,6,5]=>1010101=>1010101
[5,4,6,2,1,3,7,8]=>[8,7,3,1,2,6,4,5]=>1011001=>1001101
[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>1110001=>1000111
[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>1110101=>1010111
[5,4,6,1,2,3,7,8]=>[8,7,3,2,1,6,4,5]=>1111001=>1001111
[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>1111101=>1011111
[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>1001101=>1011001
[5,6,3,1,2,4,7,8]=>[8,7,4,2,1,3,6,5]=>1101101=>1011011
[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>1000101=>1010001
[6,3,4,2,1,5,7,8]=>[8,7,5,1,2,4,3,6]=>1010101=>1010101
[6,3,2,4,1,5,7,8]=>[8,7,5,1,4,2,3,6]=>1100101=>1010011
[6,2,3,4,1,5,7,8]=>[8,7,5,1,4,3,2,6]=>1110101=>1010111
[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>1100101=>1010011
[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>1010101=>1010101
[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>1110101=>1010111
[6,2,3,1,4,5,7,8]=>[8,7,5,4,1,3,2,6]=>1101101=>1011011
[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>1011101=>1011101
[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>1111101=>1011111
[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>1000011=>1100001
[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>1001011=>1101001
[5,3,4,2,1,6,7,8]=>[8,7,6,1,2,4,3,5]=>1010011=>1100101
[4,3,5,2,1,6,7,8]=>[8,7,6,1,2,5,3,4]=>1010011=>1100101
[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>1011011=>1101101
[5,4,2,3,1,6,7,8]=>[8,7,6,1,3,2,4,5]=>1100011=>1100011
[4,5,2,3,1,6,7,8]=>[8,7,6,1,3,2,5,4]=>1101011=>1101011
[5,3,2,4,1,6,7,8]=>[8,7,6,1,4,2,3,5]=>1100011=>1100011
[5,2,3,4,1,6,7,8]=>[8,7,6,1,4,3,2,5]=>1110011=>1100111
[4,3,2,5,1,6,7,8]=>[8,7,6,1,5,2,3,4]=>1100011=>1100011
[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>1110011=>1100111
[4,2,3,5,1,6,7,8]=>[8,7,6,1,5,3,2,4]=>1110011=>1100111
[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>1101011=>1101011
[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>1111011=>1101111
[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>1100011=>1100011
[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>1110011=>1100111
[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>1010011=>1100101
[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>1110011=>1100111
[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>1001011=>1101001
[5,2,3,1,4,6,7,8]=>[8,7,6,4,1,3,2,5]=>1101011=>1101011
[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>1101011=>1101011
[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>1011011=>1101101
[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>1111011=>1101111
[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>1000111=>1110001
[3,4,2,1,5,6,7,8]=>[8,7,6,5,1,2,4,3]=>1010111=>1110101
[4,2,3,1,5,6,7,8]=>[8,7,6,5,1,3,2,4]=>1100111=>1110011
[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>1100111=>1110011
[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>1110111=>1110111
[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>1100111=>1110011
[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>1110111=>1110111
[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>1010111=>1110101
[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>1110111=>1110111
[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>1001111=>1111001
[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>1101111=>1111011
[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>1101111=>1111011
[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>1011111=>1111101
[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>1111111=>1111111
[6,8,7,5,4,3,2,1]=>[1,2,3,4,5,7,8,6]=>0000010=>0100000
[5,8,7,6,4,3,2,1]=>[1,2,3,4,6,7,8,5]=>0000100=>0010000
[5,7,8,6,4,3,2,1]=>[1,2,3,4,6,8,7,5]=>0000101=>1010000
[6,5,8,7,4,3,2,1]=>[1,2,3,4,7,8,5,6]=>0000100=>0010000
[5,6,8,7,4,3,2,1]=>[1,2,3,4,7,8,6,5]=>0000110=>0110000
[5,7,6,8,4,3,2,1]=>[1,2,3,4,8,6,7,5]=>0000110=>0110000
[4,8,7,6,5,3,2,1]=>[1,2,3,5,6,7,8,4]=>0001000=>0001000
[4,7,8,6,5,3,2,1]=>[1,2,3,5,6,8,7,4]=>0001001=>1001000
[4,6,8,7,5,3,2,1]=>[1,2,3,5,7,8,6,4]=>0001010=>0101000
[4,7,6,8,5,3,2,1]=>[1,2,3,5,8,6,7,4]=>0001010=>0101000
[4,6,7,8,5,3,2,1]=>[1,2,3,5,8,7,6,4]=>0001011=>1101000
[5,4,8,7,6,3,2,1]=>[1,2,3,6,7,8,4,5]=>0001000=>0001000
[5,4,7,8,6,3,2,1]=>[1,2,3,6,8,7,4,5]=>0001001=>1001000
[4,5,8,7,6,3,2,1]=>[1,2,3,6,7,8,5,4]=>0001100=>0011000
[4,5,7,8,6,3,2,1]=>[1,2,3,6,8,7,5,4]=>0001101=>1011000
[6,5,4,8,7,3,2,1]=>[1,2,3,7,8,4,5,6]=>0001000=>0001000
[5,6,4,8,7,3,2,1]=>[1,2,3,7,8,4,6,5]=>0001100=>0011000
[4,6,5,8,7,3,2,1]=>[1,2,3,7,8,5,6,4]=>0001100=>0011000
[5,4,6,8,7,3,2,1]=>[1,2,3,7,8,6,4,5]=>0001010=>0101000
[4,5,6,8,7,3,2,1]=>[1,2,3,7,8,6,5,4]=>0001110=>0111000
[5,7,6,4,8,3,2,1]=>[1,2,3,8,4,6,7,5]=>0001100=>0011000
[4,7,6,5,8,3,2,1]=>[1,2,3,8,5,6,7,4]=>0001100=>0011000
[4,6,7,5,8,3,2,1]=>[1,2,3,8,5,7,6,4]=>0001110=>0111000
[5,4,7,6,8,3,2,1]=>[1,2,3,8,6,7,4,5]=>0001010=>0101000
[4,5,7,6,8,3,2,1]=>[1,2,3,8,6,7,5,4]=>0001110=>0111000
[4,6,5,7,8,3,2,1]=>[1,2,3,8,7,5,6,4]=>0001101=>1011000
[3,6,8,7,5,4,2,1]=>[1,2,4,5,7,8,6,3]=>0010010=>0100100
[3,7,6,8,5,4,2,1]=>[1,2,4,5,8,6,7,3]=>0010010=>0100100
[3,5,8,7,6,4,2,1]=>[1,2,4,6,7,8,5,3]=>0010100=>0010100
[3,5,7,8,6,4,2,1]=>[1,2,4,6,8,7,5,3]=>0010101=>1010100
[3,5,6,8,7,4,2,1]=>[1,2,4,7,8,6,5,3]=>0010110=>0110100
[3,7,6,5,8,4,2,1]=>[1,2,4,8,5,6,7,3]=>0010100=>0010100
[3,5,6,7,8,4,2,1]=>[1,2,4,8,7,6,5,3]=>0010111=>1110100
[4,3,8,7,6,5,2,1]=>[1,2,5,6,7,8,3,4]=>0010000=>0000100
[4,3,7,8,6,5,2,1]=>[1,2,5,6,8,7,3,4]=>0010001=>1000100
[4,3,6,8,7,5,2,1]=>[1,2,5,7,8,6,3,4]=>0010010=>0100100
[4,3,6,7,8,5,2,1]=>[1,2,5,8,7,6,3,4]=>0010011=>1100100
[3,4,7,6,8,5,2,1]=>[1,2,5,8,6,7,4,3]=>0011010=>0101100
[5,4,3,8,7,6,2,1]=>[1,2,6,7,8,3,4,5]=>0010000=>0000100
[5,4,3,7,8,6,2,1]=>[1,2,6,8,7,3,4,5]=>0010001=>1000100
[4,5,3,8,7,6,2,1]=>[1,2,6,7,8,3,5,4]=>0011000=>0001100
[4,5,3,7,8,6,2,1]=>[1,2,6,8,7,3,5,4]=>0011001=>1001100
[3,5,4,7,8,6,2,1]=>[1,2,6,8,7,4,5,3]=>0011001=>1001100
[4,3,5,8,7,6,2,1]=>[1,2,6,7,8,5,3,4]=>0010100=>0010100
[4,3,5,7,8,6,2,1]=>[1,2,6,8,7,5,3,4]=>0010101=>1010100
[3,4,5,8,7,6,2,1]=>[1,2,6,7,8,5,4,3]=>0011100=>0011100
[6,5,4,3,8,7,2,1]=>[1,2,7,8,3,4,5,6]=>0010000=>0000100
[5,6,4,3,8,7,2,1]=>[1,2,7,8,3,4,6,5]=>0010100=>0010100
[4,6,5,3,8,7,2,1]=>[1,2,7,8,3,5,6,4]=>0011000=>0001100
[5,4,6,3,8,7,2,1]=>[1,2,7,8,3,6,4,5]=>0011000=>0001100
[4,5,6,3,8,7,2,1]=>[1,2,7,8,3,6,5,4]=>0011100=>0011100
[4,3,6,5,8,7,2,1]=>[1,2,7,8,5,6,3,4]=>0010100=>0010100
[5,4,3,6,8,7,2,1]=>[1,2,7,8,6,3,4,5]=>0010010=>0100100
[4,5,3,6,8,7,2,1]=>[1,2,7,8,6,3,5,4]=>0011010=>0101100
[3,5,4,6,8,7,2,1]=>[1,2,7,8,6,4,5,3]=>0011010=>0101100
[4,3,5,6,8,7,2,1]=>[1,2,7,8,6,5,3,4]=>0010110=>0110100
[5,7,6,4,3,8,2,1]=>[1,2,8,3,4,6,7,5]=>0010100=>0010100
[4,7,6,5,3,8,2,1]=>[1,2,8,3,5,6,7,4]=>0011000=>0001100
[4,6,7,5,3,8,2,1]=>[1,2,8,3,5,7,6,4]=>0011010=>0101100
[3,7,6,5,4,8,2,1]=>[1,2,8,4,5,6,7,3]=>0011000=>0001100
[3,5,7,6,4,8,2,1]=>[1,2,8,4,6,7,5,3]=>0011100=>0011100
[3,5,6,7,4,8,2,1]=>[1,2,8,4,7,6,5,3]=>0011110=>0111100
[4,3,7,6,5,8,2,1]=>[1,2,8,5,6,7,3,4]=>0010100=>0010100
[4,5,3,7,6,8,2,1]=>[1,2,8,6,7,3,5,4]=>0011010=>0101100
[4,3,5,7,6,8,2,1]=>[1,2,8,6,7,5,3,4]=>0010110=>0110100
[3,4,5,7,6,8,2,1]=>[1,2,8,6,7,5,4,3]=>0011110=>0111100
[4,3,6,5,7,8,2,1]=>[1,2,8,7,5,6,3,4]=>0010101=>1010100
[3,4,6,5,7,8,2,1]=>[1,2,8,7,5,6,4,3]=>0011101=>1011100
[2,7,6,8,5,4,3,1]=>[1,3,4,5,8,6,7,2]=>0100010=>0100010
[2,6,7,8,5,4,3,1]=>[1,3,4,5,8,7,6,2]=>0100011=>1100010
[2,5,8,7,6,4,3,1]=>[1,3,4,6,7,8,5,2]=>0100100=>0010010
[2,7,6,5,8,4,3,1]=>[1,3,4,8,5,6,7,2]=>0100100=>0010010
[2,5,6,7,8,4,3,1]=>[1,3,4,8,7,6,5,2]=>0100111=>1110010
[2,4,8,7,6,5,3,1]=>[1,3,5,6,7,8,4,2]=>0101000=>0001010
[2,4,6,8,7,5,3,1]=>[1,3,5,7,8,6,4,2]=>0101010=>0101010
[2,4,6,7,8,5,3,1]=>[1,3,5,8,7,6,4,2]=>0101011=>1101010
[2,4,5,8,7,6,3,1]=>[1,3,6,7,8,5,4,2]=>0101100=>0011010
[2,4,5,7,8,6,3,1]=>[1,3,6,8,7,5,4,2]=>0101101=>1011010
[2,5,6,4,8,7,3,1]=>[1,3,7,8,4,6,5,2]=>0101100=>0011010
[2,4,6,5,8,7,3,1]=>[1,3,7,8,5,6,4,2]=>0101100=>0011010
[2,7,6,5,4,8,3,1]=>[1,3,8,4,5,6,7,2]=>0101000=>0001010
[2,5,7,6,4,8,3,1]=>[1,3,8,4,6,7,5,2]=>0101100=>0011010
[2,4,7,6,5,8,3,1]=>[1,3,8,5,6,7,4,2]=>0101100=>0011010
[2,4,6,7,5,8,3,1]=>[1,3,8,5,7,6,4,2]=>0101110=>0111010
[2,4,6,5,7,8,3,1]=>[1,3,8,7,5,6,4,2]=>0101101=>1011010
[2,4,5,6,7,8,3,1]=>[1,3,8,7,6,5,4,2]=>0101111=>1111010
[3,2,6,7,8,5,4,1]=>[1,4,5,8,7,6,2,3]=>0100011=>1100010
[3,2,7,6,5,8,4,1]=>[1,4,8,5,6,7,2,3]=>0100100=>0010010
[2,3,6,8,7,5,4,1]=>[1,4,5,7,8,6,3,2]=>0110010=>0100110
[2,3,7,6,8,5,4,1]=>[1,4,5,8,6,7,3,2]=>0110010=>0100110
[2,3,5,8,7,6,4,1]=>[1,4,6,7,8,5,3,2]=>0110100=>0010110
[2,3,5,7,8,6,4,1]=>[1,4,6,8,7,5,3,2]=>0110101=>1010110
[2,3,5,6,8,7,4,1]=>[1,4,7,8,6,5,3,2]=>0110110=>0110110
[2,3,7,6,5,8,4,1]=>[1,4,8,5,6,7,3,2]=>0110100=>0010110
[2,3,6,7,5,8,4,1]=>[1,4,8,5,7,6,3,2]=>0110110=>0110110
[2,3,5,7,6,8,4,1]=>[1,4,8,6,7,5,3,2]=>0110110=>0110110
[2,3,5,6,7,8,4,1]=>[1,4,8,7,6,5,3,2]=>0110111=>1110110
[4,3,2,8,7,6,5,1]=>[1,5,6,7,8,2,3,4]=>0100000=>0000010
[4,3,2,7,8,6,5,1]=>[1,5,6,8,7,2,3,4]=>0100001=>1000010
[4,3,2,6,8,7,5,1]=>[1,5,7,8,6,2,3,4]=>0100010=>0100010
[4,3,2,6,7,8,5,1]=>[1,5,8,7,6,2,3,4]=>0100011=>1100010
[3,4,2,8,7,6,5,1]=>[1,5,6,7,8,2,4,3]=>0110000=>0000110
[3,4,2,6,7,8,5,1]=>[1,5,8,7,6,2,4,3]=>0110011=>1100110
[2,4,3,8,7,6,5,1]=>[1,5,6,7,8,3,4,2]=>0110000=>0000110
[2,4,3,6,8,7,5,1]=>[1,5,7,8,6,3,4,2]=>0110010=>0100110
[2,4,3,7,6,8,5,1]=>[1,5,8,6,7,3,4,2]=>0110010=>0100110
[2,4,3,6,7,8,5,1]=>[1,5,8,7,6,3,4,2]=>0110011=>1100110
[3,2,4,8,7,6,5,1]=>[1,5,6,7,8,4,2,3]=>0101000=>0001010
[3,2,4,6,8,7,5,1]=>[1,5,7,8,6,4,2,3]=>0101010=>0101010
[2,3,4,8,7,6,5,1]=>[1,5,6,7,8,4,3,2]=>0111000=>0001110
[5,4,3,2,8,7,6,1]=>[1,6,7,8,2,3,4,5]=>0100000=>0000010
[5,4,3,2,7,8,6,1]=>[1,6,8,7,2,3,4,5]=>0100001=>1000010
[4,5,3,2,8,7,6,1]=>[1,6,7,8,2,3,5,4]=>0101000=>0001010
[4,3,5,2,8,7,6,1]=>[1,6,7,8,2,5,3,4]=>0110000=>0000110
[3,4,5,2,7,8,6,1]=>[1,6,8,7,2,5,4,3]=>0111001=>1001110
[2,5,4,3,8,7,6,1]=>[1,6,7,8,3,4,5,2]=>0110000=>0000110
[2,5,4,3,7,8,6,1]=>[1,6,8,7,3,4,5,2]=>0110001=>1000110
[2,4,5,3,8,7,6,1]=>[1,6,7,8,3,5,4,2]=>0111000=>0001110
[2,3,5,4,8,7,6,1]=>[1,6,7,8,4,5,3,2]=>0111000=>0001110
[2,3,5,4,7,8,6,1]=>[1,6,8,7,4,5,3,2]=>0111001=>1001110
[4,3,2,5,8,7,6,1]=>[1,6,7,8,5,2,3,4]=>0100100=>0010010
[4,3,2,5,7,8,6,1]=>[1,6,8,7,5,2,3,4]=>0100101=>1010010
[2,4,3,5,8,7,6,1]=>[1,6,7,8,5,3,4,2]=>0110100=>0010110
[2,4,3,5,7,8,6,1]=>[1,6,8,7,5,3,4,2]=>0110101=>1010110
[2,3,4,5,8,7,6,1]=>[1,6,7,8,5,4,3,2]=>0111100=>0011110
[2,3,4,5,7,8,6,1]=>[1,6,8,7,5,4,3,2]=>0111101=>1011110
[6,5,4,3,2,8,7,1]=>[1,7,8,2,3,4,5,6]=>0100000=>0000010
[5,4,6,3,2,8,7,1]=>[1,7,8,2,3,6,4,5]=>0101000=>0001010
[4,5,6,3,2,8,7,1]=>[1,7,8,2,3,6,5,4]=>0101100=>0011010
[3,6,5,4,2,8,7,1]=>[1,7,8,2,4,5,6,3]=>0110000=>0000110
[3,5,4,6,2,8,7,1]=>[1,7,8,2,6,4,5,3]=>0111000=>0001110
[2,6,5,4,3,8,7,1]=>[1,7,8,3,4,5,6,2]=>0110000=>0000110
[2,4,6,5,3,8,7,1]=>[1,7,8,3,5,6,4,2]=>0111000=>0001110
[2,4,5,6,3,8,7,1]=>[1,7,8,3,6,5,4,2]=>0111100=>0011110
[3,2,6,5,4,8,7,1]=>[1,7,8,4,5,6,2,3]=>0101000=>0001010
[3,2,5,6,4,8,7,1]=>[1,7,8,4,6,5,2,3]=>0101100=>0011010
[2,4,3,6,5,8,7,1]=>[1,7,8,5,6,3,4,2]=>0110100=>0010110
[3,2,4,6,5,8,7,1]=>[1,7,8,5,6,4,2,3]=>0101100=>0011010
[5,4,3,2,6,8,7,1]=>[1,7,8,6,2,3,4,5]=>0100010=>0100010
[3,4,5,2,6,8,7,1]=>[1,7,8,6,2,5,4,3]=>0111010=>0101110
[2,5,4,3,6,8,7,1]=>[1,7,8,6,3,4,5,2]=>0110010=>0100110
[2,4,5,3,6,8,7,1]=>[1,7,8,6,3,5,4,2]=>0111010=>0101110
[2,3,5,4,6,8,7,1]=>[1,7,8,6,4,5,3,2]=>0111010=>0101110
[2,3,4,5,6,8,7,1]=>[1,7,8,6,5,4,3,2]=>0111110=>0111110
[5,7,6,4,3,2,8,1]=>[1,8,2,3,4,6,7,5]=>0100100=>0010010
[4,7,6,5,3,2,8,1]=>[1,8,2,3,5,6,7,4]=>0101000=>0001010
[3,7,6,5,4,2,8,1]=>[1,8,2,4,5,6,7,3]=>0110000=>0000110
[3,6,7,5,4,2,8,1]=>[1,8,2,4,5,7,6,3]=>0110010=>0100110
[3,6,5,7,4,2,8,1]=>[1,8,2,4,7,5,6,3]=>0110100=>0010110
[3,5,6,7,4,2,8,1]=>[1,8,2,4,7,6,5,3]=>0110110=>0110110
[4,3,7,6,5,2,8,1]=>[1,8,2,5,6,7,3,4]=>0110000=>0000110
[4,3,6,7,5,2,8,1]=>[1,8,2,5,7,6,3,4]=>0110010=>0100110
[3,4,7,6,5,2,8,1]=>[1,8,2,5,6,7,4,3]=>0111000=>0001110
[3,4,6,7,5,2,8,1]=>[1,8,2,5,7,6,4,3]=>0111010=>0101110
[3,6,5,4,7,2,8,1]=>[1,8,2,7,4,5,6,3]=>0111000=>0001110
[4,3,6,5,7,2,8,1]=>[1,8,2,7,5,6,3,4]=>0110100=>0010110
[3,5,4,6,7,2,8,1]=>[1,8,2,7,6,4,5,3]=>0111010=>0101110
[2,5,7,6,4,3,8,1]=>[1,8,3,4,6,7,5,2]=>0110100=>0010110
[2,4,6,7,5,3,8,1]=>[1,8,3,5,7,6,4,2]=>0111010=>0101110
[2,5,4,7,6,3,8,1]=>[1,8,3,6,7,4,5,2]=>0111000=>0001110
[2,4,6,5,7,3,8,1]=>[1,8,3,7,5,6,4,2]=>0111100=>0011110
[2,5,4,6,7,3,8,1]=>[1,8,3,7,6,4,5,2]=>0111010=>0101110
[2,4,5,6,7,3,8,1]=>[1,8,3,7,6,5,4,2]=>0111110=>0111110
[3,2,7,6,5,4,8,1]=>[1,8,4,5,6,7,2,3]=>0101000=>0001010
[3,2,6,7,5,4,8,1]=>[1,8,4,5,7,6,2,3]=>0101010=>0101010
[3,2,5,7,6,4,8,1]=>[1,8,4,6,7,5,2,3]=>0101100=>0011010
[3,2,6,5,7,4,8,1]=>[1,8,4,7,5,6,2,3]=>0101100=>0011010
[3,2,5,6,7,4,8,1]=>[1,8,4,7,6,5,2,3]=>0101110=>0111010
[2,3,7,6,5,4,8,1]=>[1,8,4,5,6,7,3,2]=>0111000=>0001110
[2,3,5,7,6,4,8,1]=>[1,8,4,6,7,5,3,2]=>0111100=>0011110
[2,3,5,6,7,4,8,1]=>[1,8,4,7,6,5,3,2]=>0111110=>0111110
[4,3,2,7,6,5,8,1]=>[1,8,5,6,7,2,3,4]=>0100100=>0010010
[4,3,2,6,7,5,8,1]=>[1,8,5,7,6,2,3,4]=>0100110=>0110010
[3,4,2,7,6,5,8,1]=>[1,8,5,6,7,2,4,3]=>0110100=>0010110
[2,4,3,7,6,5,8,1]=>[1,8,5,6,7,3,4,2]=>0110100=>0010110
[3,2,4,7,6,5,8,1]=>[1,8,5,6,7,4,2,3]=>0101100=>0011010
[2,3,4,7,6,5,8,1]=>[1,8,5,6,7,4,3,2]=>0111100=>0011110
[5,4,3,2,7,6,8,1]=>[1,8,6,7,2,3,4,5]=>0100010=>0100010
[4,3,5,2,7,6,8,1]=>[1,8,6,7,2,5,3,4]=>0110010=>0100110
[3,4,5,2,7,6,8,1]=>[1,8,6,7,2,5,4,3]=>0111010=>0101110
[2,5,4,3,7,6,8,1]=>[1,8,6,7,3,4,5,2]=>0110010=>0100110
[3,2,5,4,7,6,8,1]=>[1,8,6,7,4,5,2,3]=>0101010=>0101010
[2,3,5,4,7,6,8,1]=>[1,8,6,7,4,5,3,2]=>0111010=>0101110
[4,3,2,5,7,6,8,1]=>[1,8,6,7,5,2,3,4]=>0100110=>0110010
[2,4,3,5,7,6,8,1]=>[1,8,6,7,5,3,4,2]=>0110110=>0110110
[2,3,4,5,7,6,8,1]=>[1,8,6,7,5,4,3,2]=>0111110=>0111110
[3,6,5,4,2,7,8,1]=>[1,8,7,2,4,5,6,3]=>0110001=>1000110
[3,5,4,6,2,7,8,1]=>[1,8,7,2,6,4,5,3]=>0111001=>1001110
[2,6,5,4,3,7,8,1]=>[1,8,7,3,4,5,6,2]=>0110001=>1000110
[2,5,6,4,3,7,8,1]=>[1,8,7,3,4,6,5,2]=>0110101=>1010110
[2,5,4,6,3,7,8,1]=>[1,8,7,3,6,4,5,2]=>0111001=>1001110
[3,2,6,5,4,7,8,1]=>[1,8,7,4,5,6,2,3]=>0101001=>1001010
[2,3,5,6,4,7,8,1]=>[1,8,7,4,6,5,3,2]=>0111101=>1011110
[2,4,3,6,5,7,8,1]=>[1,8,7,5,6,3,4,2]=>0110101=>1010110
[2,3,4,6,5,7,8,1]=>[1,8,7,5,6,4,3,2]=>0111101=>1011110
[2,5,4,3,6,7,8,1]=>[1,8,7,6,3,4,5,2]=>0110011=>1100110
[2,3,5,4,6,7,8,1]=>[1,8,7,6,4,5,3,2]=>0111011=>1101110
[1,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,1]=>1000000=>0000001
[1,7,8,6,5,4,3,2]=>[2,3,4,5,6,8,7,1]=>1000001=>1000001
[1,7,6,8,5,4,3,2]=>[2,3,4,5,8,6,7,1]=>1000010=>0100001
[1,6,7,8,5,4,3,2]=>[2,3,4,5,8,7,6,1]=>1000011=>1100001
[1,5,8,7,6,4,3,2]=>[2,3,4,6,7,8,5,1]=>1000100=>0010001
[1,7,6,5,8,4,3,2]=>[2,3,4,8,5,6,7,1]=>1000100=>0010001
[1,6,7,5,8,4,3,2]=>[2,3,4,8,5,7,6,1]=>1000110=>0110001
[1,5,7,6,8,4,3,2]=>[2,3,4,8,6,7,5,1]=>1000110=>0110001
[1,6,5,7,8,4,3,2]=>[2,3,4,8,7,5,6,1]=>1000101=>1010001
[1,5,6,7,8,4,3,2]=>[2,3,4,8,7,6,5,1]=>1000111=>1110001
[1,4,8,7,6,5,3,2]=>[2,3,5,6,7,8,4,1]=>1001000=>0001001
[1,4,6,8,7,5,3,2]=>[2,3,5,7,8,6,4,1]=>1001010=>0101001
[1,4,7,6,8,5,3,2]=>[2,3,5,8,6,7,4,1]=>1001010=>0101001
[1,4,6,7,8,5,3,2]=>[2,3,5,8,7,6,4,1]=>1001011=>1101001
[1,5,4,7,8,6,3,2]=>[2,3,6,8,7,4,5,1]=>1001001=>1001001
[1,4,5,8,7,6,3,2]=>[2,3,6,7,8,5,4,1]=>1001100=>0011001
[1,5,4,6,8,7,3,2]=>[2,3,7,8,6,4,5,1]=>1001010=>0101001
[1,7,6,5,4,8,3,2]=>[2,3,8,4,5,6,7,1]=>1001000=>0001001
[1,4,6,7,5,8,3,2]=>[2,3,8,5,7,6,4,1]=>1001110=>0111001
[1,6,5,4,7,8,3,2]=>[2,3,8,7,4,5,6,1]=>1001001=>1001001
[1,4,5,6,7,8,3,2]=>[2,3,8,7,6,5,4,1]=>1001111=>1111001
[1,3,6,8,7,5,4,2]=>[2,4,5,7,8,6,3,1]=>1010010=>0100101
[1,3,5,8,7,6,4,2]=>[2,4,6,7,8,5,3,1]=>1010100=>0010101
[1,3,5,7,8,6,4,2]=>[2,4,6,8,7,5,3,1]=>1010101=>1010101
[1,3,6,5,8,7,4,2]=>[2,4,7,8,5,6,3,1]=>1010100=>0010101
[1,3,7,6,5,8,4,2]=>[2,4,8,5,6,7,3,1]=>1010100=>0010101
[1,3,6,7,5,8,4,2]=>[2,4,8,5,7,6,3,1]=>1010110=>0110101
[1,3,5,7,6,8,4,2]=>[2,4,8,6,7,5,3,1]=>1010110=>0110101
[1,3,6,5,7,8,4,2]=>[2,4,8,7,5,6,3,1]=>1010101=>1010101
[1,3,5,6,7,8,4,2]=>[2,4,8,7,6,5,3,1]=>1010111=>1110101
[1,4,3,8,7,6,5,2]=>[2,5,6,7,8,3,4,1]=>1010000=>0000101
[1,4,3,7,8,6,5,2]=>[2,5,6,8,7,3,4,1]=>1010001=>1000101
[1,4,3,7,6,8,5,2]=>[2,5,8,6,7,3,4,1]=>1010010=>0100101
[1,3,4,8,7,6,5,2]=>[2,5,6,7,8,4,3,1]=>1011000=>0001101
[1,3,4,7,6,8,5,2]=>[2,5,8,6,7,4,3,1]=>1011010=>0101101
[1,3,5,4,7,8,6,2]=>[2,6,8,7,4,5,3,1]=>1011001=>1001101
[1,4,3,5,8,7,6,2]=>[2,6,7,8,5,3,4,1]=>1010100=>0010101
[1,5,6,4,3,8,7,2]=>[2,7,8,3,4,6,5,1]=>1010100=>0010101
[1,5,4,6,3,8,7,2]=>[2,7,8,3,6,4,5,1]=>1011000=>0001101
[1,3,6,5,4,8,7,2]=>[2,7,8,4,5,6,3,1]=>1011000=>0001101
[1,4,3,6,5,8,7,2]=>[2,7,8,5,6,3,4,1]=>1010100=>0010101
[1,4,5,3,6,8,7,2]=>[2,7,8,6,3,5,4,1]=>1011010=>0101101
[1,4,6,7,5,3,8,2]=>[2,8,3,5,7,6,4,1]=>1011010=>0101101
[1,6,5,4,7,3,8,2]=>[2,8,3,7,4,5,6,1]=>1011000=>0001101
[1,5,6,4,7,3,8,2]=>[2,8,3,7,4,6,5,1]=>1011100=>0011101
[1,4,6,5,7,3,8,2]=>[2,8,3,7,5,6,4,1]=>1011100=>0011101
[1,3,5,7,6,4,8,2]=>[2,8,4,6,7,5,3,1]=>1011100=>0011101
[1,3,4,7,6,5,8,2]=>[2,8,5,6,7,4,3,1]=>1011100=>0011101
[1,3,5,4,7,6,8,2]=>[2,8,6,7,4,5,3,1]=>1011010=>0101101
[1,6,5,4,3,7,8,2]=>[2,8,7,3,4,5,6,1]=>1010001=>1000101
[1,3,4,6,5,7,8,2]=>[2,8,7,5,6,4,3,1]=>1011101=>1011101
[1,5,4,3,6,7,8,2]=>[2,8,7,6,3,4,5,1]=>1010011=>1100101
[1,3,4,5,6,7,8,2]=>[2,8,7,6,5,4,3,1]=>1011111=>1111101
[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2]=>1000000=>0000001
[2,1,7,8,6,5,4,3]=>[3,4,5,6,8,7,1,2]=>1000001=>1000001
[2,1,6,8,7,5,4,3]=>[3,4,5,7,8,6,1,2]=>1000010=>0100001
[2,1,7,6,8,5,4,3]=>[3,4,5,8,6,7,1,2]=>1000010=>0100001
[2,1,6,7,8,5,4,3]=>[3,4,5,8,7,6,1,2]=>1000011=>1100001
[2,1,5,8,7,6,4,3]=>[3,4,6,7,8,5,1,2]=>1000100=>0010001
[2,1,5,7,8,6,4,3]=>[3,4,6,8,7,5,1,2]=>1000101=>1010001
[2,1,7,6,5,8,4,3]=>[3,4,8,5,6,7,1,2]=>1000100=>0010001
[2,1,6,7,5,8,4,3]=>[3,4,8,5,7,6,1,2]=>1000110=>0110001
[2,1,6,5,7,8,4,3]=>[3,4,8,7,5,6,1,2]=>1000101=>1010001
[2,1,5,6,7,8,4,3]=>[3,4,8,7,6,5,1,2]=>1000111=>1110001
[2,1,4,8,7,6,5,3]=>[3,5,6,7,8,4,1,2]=>1001000=>0001001
[2,1,4,7,8,6,5,3]=>[3,5,6,8,7,4,1,2]=>1001001=>1001001
[2,1,4,6,8,7,5,3]=>[3,5,7,8,6,4,1,2]=>1001010=>0101001
[2,1,4,7,6,8,5,3]=>[3,5,8,6,7,4,1,2]=>1001010=>0101001
[2,1,4,5,8,7,6,3]=>[3,6,7,8,5,4,1,2]=>1001100=>0011001
[2,1,4,6,5,8,7,3]=>[3,7,8,5,6,4,1,2]=>1001100=>0011001
[2,1,6,5,7,4,8,3]=>[3,8,4,7,5,6,1,2]=>1001100=>0011001
[2,1,5,4,7,6,8,3]=>[3,8,6,7,4,5,1,2]=>1001010=>0101001
[2,1,6,5,4,7,8,3]=>[3,8,7,4,5,6,1,2]=>1001001=>1001001
[2,1,4,5,6,7,8,3]=>[3,8,7,6,5,4,1,2]=>1001111=>1111001
[1,2,6,8,7,5,4,3]=>[3,4,5,7,8,6,2,1]=>1100010=>0100011
[1,2,7,6,8,5,4,3]=>[3,4,5,8,6,7,2,1]=>1100010=>0100011
[1,2,5,8,7,6,4,3]=>[3,4,6,7,8,5,2,1]=>1100100=>0010011
[1,2,7,6,5,8,4,3]=>[3,4,8,5,6,7,2,1]=>1100100=>0010011
[1,2,6,5,7,8,4,3]=>[3,4,8,7,5,6,2,1]=>1100101=>1010011
[1,2,5,6,7,8,4,3]=>[3,4,8,7,6,5,2,1]=>1100111=>1110011
[1,2,4,8,7,6,5,3]=>[3,5,6,7,8,4,2,1]=>1101000=>0001011
[1,2,4,7,8,6,5,3]=>[3,5,6,8,7,4,2,1]=>1101001=>1001011
[1,2,4,6,8,7,5,3]=>[3,5,7,8,6,4,2,1]=>1101010=>0101011
[1,2,4,7,6,8,5,3]=>[3,5,8,6,7,4,2,1]=>1101010=>0101011
[1,2,4,6,7,8,5,3]=>[3,5,8,7,6,4,2,1]=>1101011=>1101011
[1,2,5,4,8,7,6,3]=>[3,6,7,8,4,5,2,1]=>1101000=>0001011
[1,2,6,5,4,8,7,3]=>[3,7,8,4,5,6,2,1]=>1101000=>0001011
[1,2,4,6,5,8,7,3]=>[3,7,8,5,6,4,2,1]=>1101100=>0011011
[1,2,7,6,5,4,8,3]=>[3,8,4,5,6,7,2,1]=>1101000=>0001011
[1,2,4,6,7,5,8,3]=>[3,8,5,7,6,4,2,1]=>1101110=>0111011
[1,2,6,5,4,7,8,3]=>[3,8,7,4,5,6,2,1]=>1101001=>1001011
[1,2,4,6,5,7,8,3]=>[3,8,7,5,6,4,2,1]=>1101101=>1011011
[1,2,4,5,6,7,8,3]=>[3,8,7,6,5,4,2,1]=>1101111=>1111011
[3,2,1,8,7,6,5,4]=>[4,5,6,7,8,1,2,3]=>1000000=>0000001
[3,2,1,7,8,6,5,4]=>[4,5,6,8,7,1,2,3]=>1000001=>1000001
[3,2,1,6,8,7,5,4]=>[4,5,7,8,6,1,2,3]=>1000010=>0100001
[3,2,1,7,6,8,5,4]=>[4,5,8,6,7,1,2,3]=>1000010=>0100001
[3,2,1,6,7,8,5,4]=>[4,5,8,7,6,1,2,3]=>1000011=>1100001
[3,2,1,5,8,7,6,4]=>[4,6,7,8,5,1,2,3]=>1000100=>0010001
[3,2,1,5,7,8,6,4]=>[4,6,8,7,5,1,2,3]=>1000101=>1010001
[3,2,1,6,5,8,7,4]=>[4,7,8,5,6,1,2,3]=>1000100=>0010001
[3,2,1,5,6,8,7,4]=>[4,7,8,6,5,1,2,3]=>1000110=>0110001
[3,2,1,7,6,5,8,4]=>[4,8,5,6,7,1,2,3]=>1000100=>0010001
[3,2,1,6,7,5,8,4]=>[4,8,5,7,6,1,2,3]=>1000110=>0110001
[3,2,1,5,7,6,8,4]=>[4,8,6,7,5,1,2,3]=>1000110=>0110001
[3,2,1,6,5,7,8,4]=>[4,8,7,5,6,1,2,3]=>1000101=>1010001
[3,2,1,5,6,7,8,4]=>[4,8,7,6,5,1,2,3]=>1000111=>1110001
[2,3,1,8,7,6,5,4]=>[4,5,6,7,8,1,3,2]=>1100000=>0000011
[2,3,1,7,6,8,5,4]=>[4,5,8,6,7,1,3,2]=>1100010=>0100011
[2,3,1,6,7,8,5,4]=>[4,5,8,7,6,1,3,2]=>1100011=>1100011
[2,3,1,5,8,7,6,4]=>[4,6,7,8,5,1,3,2]=>1100100=>0010011
[2,3,1,6,5,8,7,4]=>[4,7,8,5,6,1,3,2]=>1100100=>0010011
[2,3,1,7,6,5,8,4]=>[4,8,5,6,7,1,3,2]=>1100100=>0010011
[2,3,1,5,7,6,8,4]=>[4,8,6,7,5,1,3,2]=>1100110=>0110011
[2,3,1,6,5,7,8,4]=>[4,8,7,5,6,1,3,2]=>1100101=>1010011
[2,3,1,5,6,7,8,4]=>[4,8,7,6,5,1,3,2]=>1100111=>1110011
[1,3,2,8,7,6,5,4]=>[4,5,6,7,8,2,3,1]=>1100000=>0000011
[1,3,2,5,7,8,6,4]=>[4,6,8,7,5,2,3,1]=>1100101=>1010011
[1,3,2,7,6,5,8,4]=>[4,8,5,6,7,2,3,1]=>1100100=>0010011
[1,3,2,5,7,6,8,4]=>[4,8,6,7,5,2,3,1]=>1100110=>0110011
[1,3,2,5,6,7,8,4]=>[4,8,7,6,5,2,3,1]=>1100111=>1110011
[2,1,3,8,7,6,5,4]=>[4,5,6,7,8,3,1,2]=>1010000=>0000101
[2,1,3,7,8,6,5,4]=>[4,5,6,8,7,3,1,2]=>1010001=>1000101
[2,1,3,6,8,7,5,4]=>[4,5,7,8,6,3,1,2]=>1010010=>0100101
[2,1,3,5,7,8,6,4]=>[4,6,8,7,5,3,1,2]=>1010101=>1010101
[2,1,3,7,6,5,8,4]=>[4,8,5,6,7,3,1,2]=>1010100=>0010101
[2,1,3,5,7,6,8,4]=>[4,8,6,7,5,3,1,2]=>1010110=>0110101
[2,1,3,5,6,7,8,4]=>[4,8,7,6,5,3,1,2]=>1010111=>1110101
[1,2,3,8,7,6,5,4]=>[4,5,6,7,8,3,2,1]=>1110000=>0000111
[1,2,3,7,8,6,5,4]=>[4,5,6,8,7,3,2,1]=>1110001=>1000111
[1,2,3,6,8,7,5,4]=>[4,5,7,8,6,3,2,1]=>1110010=>0100111
[1,2,3,7,6,8,5,4]=>[4,5,8,6,7,3,2,1]=>1110010=>0100111
[1,2,3,6,7,8,5,4]=>[4,5,8,7,6,3,2,1]=>1110011=>1100111
[1,2,3,5,8,7,6,4]=>[4,6,7,8,5,3,2,1]=>1110100=>0010111
[1,2,3,5,7,8,6,4]=>[4,6,8,7,5,3,2,1]=>1110101=>1010111
[1,2,3,6,5,8,7,4]=>[4,7,8,5,6,3,2,1]=>1110100=>0010111
[1,2,3,5,6,8,7,4]=>[4,7,8,6,5,3,2,1]=>1110110=>0110111
[1,2,3,7,6,5,8,4]=>[4,8,5,6,7,3,2,1]=>1110100=>0010111
[1,2,3,6,7,5,8,4]=>[4,8,5,7,6,3,2,1]=>1110110=>0110111
[1,2,3,5,7,6,8,4]=>[4,8,6,7,5,3,2,1]=>1110110=>0110111
[1,2,3,6,5,7,8,4]=>[4,8,7,5,6,3,2,1]=>1110101=>1010111
[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>1110111=>1110111
[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>1000000=>0000001
[4,3,2,1,7,8,6,5]=>[5,6,8,7,1,2,3,4]=>1000001=>1000001
[4,3,2,1,6,8,7,5]=>[5,7,8,6,1,2,3,4]=>1000010=>0100001
[4,3,2,1,7,6,8,5]=>[5,8,6,7,1,2,3,4]=>1000010=>0100001
[4,3,2,1,6,7,8,5]=>[5,8,7,6,1,2,3,4]=>1000011=>1100001
[3,4,2,1,8,7,6,5]=>[5,6,7,8,1,2,4,3]=>1010000=>0000101
[3,4,2,1,7,8,6,5]=>[5,6,8,7,1,2,4,3]=>1010001=>1000101
[3,4,2,1,7,6,8,5]=>[5,8,6,7,1,2,4,3]=>1010010=>0100101
[3,4,2,1,6,7,8,5]=>[5,8,7,6,1,2,4,3]=>1010011=>1100101
[2,4,3,1,8,7,6,5]=>[5,6,7,8,1,3,4,2]=>1100000=>0000011
[2,4,3,1,7,8,6,5]=>[5,6,8,7,1,3,4,2]=>1100001=>1000011
[2,4,3,1,6,8,7,5]=>[5,7,8,6,1,3,4,2]=>1100010=>0100011
[2,4,3,1,7,6,8,5]=>[5,8,6,7,1,3,4,2]=>1100010=>0100011
[2,4,3,1,6,7,8,5]=>[5,8,7,6,1,3,4,2]=>1100011=>1100011
[3,2,4,1,8,7,6,5]=>[5,6,7,8,1,4,2,3]=>1100000=>0000011
[3,2,4,1,7,8,6,5]=>[5,6,8,7,1,4,2,3]=>1100001=>1000011
[3,2,4,1,6,8,7,5]=>[5,7,8,6,1,4,2,3]=>1100010=>0100011
[3,2,4,1,7,6,8,5]=>[5,8,6,7,1,4,2,3]=>1100010=>0100011
[3,2,4,1,6,7,8,5]=>[5,8,7,6,1,4,2,3]=>1100011=>1100011
[2,3,4,1,8,7,6,5]=>[5,6,7,8,1,4,3,2]=>1110000=>0000111
[2,3,4,1,7,8,6,5]=>[5,6,8,7,1,4,3,2]=>1110001=>1000111
[2,3,4,1,6,8,7,5]=>[5,7,8,6,1,4,3,2]=>1110010=>0100111
[2,3,4,1,7,6,8,5]=>[5,8,6,7,1,4,3,2]=>1110010=>0100111
[2,3,4,1,6,7,8,5]=>[5,8,7,6,1,4,3,2]=>1110011=>1100111
[1,4,3,2,8,7,6,5]=>[5,6,7,8,2,3,4,1]=>1100000=>0000011
[1,4,3,2,6,8,7,5]=>[5,7,8,6,2,3,4,1]=>1100010=>0100011
[1,4,3,2,7,6,8,5]=>[5,8,6,7,2,3,4,1]=>1100010=>0100011
[1,4,3,2,6,7,8,5]=>[5,8,7,6,2,3,4,1]=>1100011=>1100011
[1,3,4,2,8,7,6,5]=>[5,6,7,8,2,4,3,1]=>1110000=>0000111
[1,3,4,2,7,8,6,5]=>[5,6,8,7,2,4,3,1]=>1110001=>1000111
[1,3,4,2,7,6,8,5]=>[5,8,6,7,2,4,3,1]=>1110010=>0100111
[1,3,4,2,6,7,8,5]=>[5,8,7,6,2,4,3,1]=>1110011=>1100111
[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2]=>1010000=>0000101
[2,1,4,3,7,8,6,5]=>[5,6,8,7,3,4,1,2]=>1010001=>1000101
[2,1,4,3,6,8,7,5]=>[5,7,8,6,3,4,1,2]=>1010010=>0100101
[2,1,4,3,7,6,8,5]=>[5,8,6,7,3,4,1,2]=>1010010=>0100101
[2,1,4,3,6,7,8,5]=>[5,8,7,6,3,4,1,2]=>1010011=>1100101
[1,2,4,3,8,7,6,5]=>[5,6,7,8,3,4,2,1]=>1110000=>0000111
[1,2,4,3,6,8,7,5]=>[5,7,8,6,3,4,2,1]=>1110010=>0100111
[1,2,4,3,7,6,8,5]=>[5,8,6,7,3,4,2,1]=>1110010=>0100111
[1,2,4,3,6,7,8,5]=>[5,8,7,6,3,4,2,1]=>1110011=>1100111
[3,2,1,4,8,7,6,5]=>[5,6,7,8,4,1,2,3]=>1001000=>0001001
[3,2,1,4,7,8,6,5]=>[5,6,8,7,4,1,2,3]=>1001001=>1001001
[3,2,1,4,6,8,7,5]=>[5,7,8,6,4,1,2,3]=>1001010=>0101001
[3,2,1,4,7,6,8,5]=>[5,8,6,7,4,1,2,3]=>1001010=>0101001
[3,2,1,4,6,7,8,5]=>[5,8,7,6,4,1,2,3]=>1001011=>1101001
[2,3,1,4,8,7,6,5]=>[5,6,7,8,4,1,3,2]=>1101000=>0001011
[2,3,1,4,7,6,8,5]=>[5,8,6,7,4,1,3,2]=>1101010=>0101011
[2,3,1,4,6,7,8,5]=>[5,8,7,6,4,1,3,2]=>1101011=>1101011
[1,3,2,4,8,7,6,5]=>[5,6,7,8,4,2,3,1]=>1101000=>0001011
[1,3,2,4,6,8,7,5]=>[5,7,8,6,4,2,3,1]=>1101010=>0101011
[1,3,2,4,7,6,8,5]=>[5,8,6,7,4,2,3,1]=>1101010=>0101011
[1,3,2,4,6,7,8,5]=>[5,8,7,6,4,2,3,1]=>1101011=>1101011
[2,1,3,4,8,7,6,5]=>[5,6,7,8,4,3,1,2]=>1011000=>0001101
[2,1,3,4,7,8,6,5]=>[5,6,8,7,4,3,1,2]=>1011001=>1001101
[2,1,3,4,7,6,8,5]=>[5,8,6,7,4,3,1,2]=>1011010=>0101101
[2,1,3,4,6,7,8,5]=>[5,8,7,6,4,3,1,2]=>1011011=>1101101
[1,2,3,4,8,7,6,5]=>[5,6,7,8,4,3,2,1]=>1111000=>0001111
[1,2,3,4,7,8,6,5]=>[5,6,8,7,4,3,2,1]=>1111001=>1001111
[1,2,3,4,6,8,7,5]=>[5,7,8,6,4,3,2,1]=>1111010=>0101111
[1,2,3,4,7,6,8,5]=>[5,8,6,7,4,3,2,1]=>1111010=>0101111
[1,2,3,4,6,7,8,5]=>[5,8,7,6,4,3,2,1]=>1111011=>1101111
[5,4,3,2,1,8,7,6]=>[6,7,8,1,2,3,4,5]=>1000000=>0000001
[5,4,3,2,1,7,8,6]=>[6,8,7,1,2,3,4,5]=>1000001=>1000001
[4,5,3,2,1,8,7,6]=>[6,7,8,1,2,3,5,4]=>1001000=>0001001
[3,5,4,2,1,8,7,6]=>[6,7,8,1,2,4,5,3]=>1010000=>0000101
[4,3,5,2,1,8,7,6]=>[6,7,8,1,2,5,3,4]=>1010000=>0000101
[3,4,5,2,1,8,7,6]=>[6,7,8,1,2,5,4,3]=>1011000=>0001101
[2,5,4,3,1,8,7,6]=>[6,7,8,1,3,4,5,2]=>1100000=>0000011
[2,5,4,3,1,7,8,6]=>[6,8,7,1,3,4,5,2]=>1100001=>1000011
[2,4,5,3,1,8,7,6]=>[6,7,8,1,3,5,4,2]=>1101000=>0001011
[3,2,5,4,1,8,7,6]=>[6,7,8,1,4,5,2,3]=>1100000=>0000011
[2,3,5,4,1,8,7,6]=>[6,7,8,1,4,5,3,2]=>1110000=>0000111
[4,3,2,5,1,8,7,6]=>[6,7,8,1,5,2,3,4]=>1100000=>0000011
[4,3,2,5,1,7,8,6]=>[6,8,7,1,5,2,3,4]=>1100001=>1000011
[3,4,2,5,1,8,7,6]=>[6,7,8,1,5,2,4,3]=>1110000=>0000111
[2,4,3,5,1,8,7,6]=>[6,7,8,1,5,3,4,2]=>1110000=>0000111
[2,4,3,5,1,7,8,6]=>[6,8,7,1,5,3,4,2]=>1110001=>1000111
[2,3,4,5,1,8,7,6]=>[6,7,8,1,5,4,3,2]=>1111000=>0001111
[2,3,4,5,1,7,8,6]=>[6,8,7,1,5,4,3,2]=>1111001=>1001111
[1,5,4,3,2,8,7,6]=>[6,7,8,2,3,4,5,1]=>1100000=>0000011
[1,5,4,3,2,7,8,6]=>[6,8,7,2,3,4,5,1]=>1100001=>1000011
[1,4,5,3,2,8,7,6]=>[6,7,8,2,3,5,4,1]=>1101000=>0001011
[1,3,5,4,2,7,8,6]=>[6,8,7,2,4,5,3,1]=>1110001=>1000111
[1,3,4,5,2,8,7,6]=>[6,7,8,2,5,4,3,1]=>1111000=>0001111
[1,3,4,5,2,7,8,6]=>[6,8,7,2,5,4,3,1]=>1111001=>1001111
[1,2,5,4,3,8,7,6]=>[6,7,8,3,4,5,2,1]=>1110000=>0000111
[1,2,5,4,3,7,8,6]=>[6,8,7,3,4,5,2,1]=>1110001=>1000111
[1,2,4,5,3,8,7,6]=>[6,7,8,3,5,4,2,1]=>1111000=>0001111
[1,3,2,5,4,8,7,6]=>[6,7,8,4,5,2,3,1]=>1101000=>0001011
[1,3,2,5,4,7,8,6]=>[6,8,7,4,5,2,3,1]=>1101001=>1001011
[2,1,3,5,4,7,8,6]=>[6,8,7,4,5,3,1,2]=>1011001=>1001101
[4,3,2,1,5,8,7,6]=>[6,7,8,5,1,2,3,4]=>1000100=>0010001
[4,3,2,1,5,7,8,6]=>[6,8,7,5,1,2,3,4]=>1000101=>1010001
[3,4,2,1,5,8,7,6]=>[6,7,8,5,1,2,4,3]=>1010100=>0010101
[3,4,2,1,5,7,8,6]=>[6,8,7,5,1,2,4,3]=>1010101=>1010101
[3,2,4,1,5,8,7,6]=>[6,7,8,5,1,4,2,3]=>1100100=>0010011
[3,2,4,1,5,7,8,6]=>[6,8,7,5,1,4,2,3]=>1100101=>1010011
[2,3,4,1,5,8,7,6]=>[6,7,8,5,1,4,3,2]=>1110100=>0010111
[2,3,4,1,5,7,8,6]=>[6,8,7,5,1,4,3,2]=>1110101=>1010111
[1,4,3,2,5,8,7,6]=>[6,7,8,5,2,3,4,1]=>1100100=>0010011
[2,1,4,3,5,8,7,6]=>[6,7,8,5,3,4,1,2]=>1010100=>0010101
[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>1001100=>0011001
[3,2,1,4,5,7,8,6]=>[6,8,7,5,4,1,2,3]=>1001101=>1011001
[2,3,1,4,5,7,8,6]=>[6,8,7,5,4,1,3,2]=>1101101=>1011011
[1,2,3,4,5,8,7,6]=>[6,7,8,5,4,3,2,1]=>1111100=>0011111
[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>1111101=>1011111
[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6]=>1000000=>0000001
[5,6,4,3,2,1,8,7]=>[7,8,1,2,3,4,6,5]=>1000100=>0010001
[4,6,5,3,2,1,8,7]=>[7,8,1,2,3,5,6,4]=>1001000=>0001001
[5,4,6,3,2,1,8,7]=>[7,8,1,2,3,6,4,5]=>1001000=>0001001
[4,5,6,3,2,1,8,7]=>[7,8,1,2,3,6,5,4]=>1001100=>0011001
[3,6,5,4,2,1,8,7]=>[7,8,1,2,4,5,6,3]=>1010000=>0000101
[3,5,6,4,2,1,8,7]=>[7,8,1,2,4,6,5,3]=>1010100=>0010101
[4,3,6,5,2,1,8,7]=>[7,8,1,2,5,6,3,4]=>1010000=>0000101
[5,4,3,6,2,1,8,7]=>[7,8,1,2,6,3,4,5]=>1010000=>0000101
[4,5,3,6,2,1,8,7]=>[7,8,1,2,6,3,5,4]=>1011000=>0001101
[4,3,5,6,2,1,8,7]=>[7,8,1,2,6,5,3,4]=>1010100=>0010101
[3,4,5,6,2,1,8,7]=>[7,8,1,2,6,5,4,3]=>1011100=>0011101
[2,6,5,4,3,1,8,7]=>[7,8,1,3,4,5,6,2]=>1100000=>0000011
[2,4,6,5,3,1,8,7]=>[7,8,1,3,5,6,4,2]=>1101000=>0001011
[2,3,6,5,4,1,8,7]=>[7,8,1,4,5,6,3,2]=>1110000=>0000111
[2,4,3,6,5,1,8,7]=>[7,8,1,5,6,3,4,2]=>1110000=>0000111
[5,4,3,2,6,1,8,7]=>[7,8,1,6,2,3,4,5]=>1100000=>0000011
[4,5,3,2,6,1,8,7]=>[7,8,1,6,2,3,5,4]=>1101000=>0001011
[3,5,4,2,6,1,8,7]=>[7,8,1,6,2,4,5,3]=>1110000=>0000111
[4,3,5,2,6,1,8,7]=>[7,8,1,6,2,5,3,4]=>1110000=>0000111
[3,4,5,2,6,1,8,7]=>[7,8,1,6,2,5,4,3]=>1111000=>0001111
[2,4,5,3,6,1,8,7]=>[7,8,1,6,3,5,4,2]=>1111000=>0001111
[3,2,5,4,6,1,8,7]=>[7,8,1,6,4,5,2,3]=>1101000=>0001011
[4,3,2,5,6,1,8,7]=>[7,8,1,6,5,2,3,4]=>1100100=>0010011
[2,3,4,5,6,1,8,7]=>[7,8,1,6,5,4,3,2]=>1111100=>0011111
[1,4,5,3,6,2,8,7]=>[7,8,2,6,3,5,4,1]=>1111000=>0001111
[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>1010000=>0000101
[2,1,5,6,4,3,8,7]=>[7,8,3,4,6,5,1,2]=>1010100=>0010101
[2,1,4,6,5,3,8,7]=>[7,8,3,5,6,4,1,2]=>1011000=>0001101
[2,1,5,4,6,3,8,7]=>[7,8,3,6,4,5,1,2]=>1011000=>0001101
[2,1,4,5,6,3,8,7]=>[7,8,3,6,5,4,1,2]=>1011100=>0011101
[1,2,5,6,4,3,8,7]=>[7,8,3,4,6,5,2,1]=>1110100=>0010111
[2,1,3,6,5,4,8,7]=>[7,8,4,5,6,3,1,2]=>1011000=>0001101
[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4]=>1000100=>0010001
[3,4,2,1,6,5,8,7]=>[7,8,5,6,1,2,4,3]=>1010100=>0010101
[2,4,3,1,6,5,8,7]=>[7,8,5,6,1,3,4,2]=>1100100=>0010011
[3,2,4,1,6,5,8,7]=>[7,8,5,6,1,4,2,3]=>1100100=>0010011
[2,3,4,1,6,5,8,7]=>[7,8,5,6,1,4,3,2]=>1110100=>0010111
[1,4,3,2,6,5,8,7]=>[7,8,5,6,2,3,4,1]=>1100100=>0010011
[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>1010100=>0010101
[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1]=>1110100=>0010111
[3,2,1,4,6,5,8,7]=>[7,8,5,6,4,1,2,3]=>1001100=>0011001
[2,3,1,4,6,5,8,7]=>[7,8,5,6,4,1,3,2]=>1101100=>0011011
[2,1,3,4,6,5,8,7]=>[7,8,5,6,4,3,1,2]=>1011100=>0011101
[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>1111100=>0011111
[5,4,3,2,1,6,8,7]=>[7,8,6,1,2,3,4,5]=>1000010=>0100001
[2,5,4,3,1,6,8,7]=>[7,8,6,1,3,4,5,2]=>1100010=>0100011
[2,4,5,3,1,6,8,7]=>[7,8,6,1,3,5,4,2]=>1101010=>0101011
[3,2,5,4,1,6,8,7]=>[7,8,6,1,4,5,2,3]=>1100010=>0100011
[4,3,2,5,1,6,8,7]=>[7,8,6,1,5,2,3,4]=>1100010=>0100011
[2,3,4,5,1,6,8,7]=>[7,8,6,1,5,4,3,2]=>1111010=>0101111
[1,5,4,3,2,6,8,7]=>[7,8,6,2,3,4,5,1]=>1100010=>0100011
[1,4,5,3,2,6,8,7]=>[7,8,6,2,3,5,4,1]=>1101010=>0101011
[2,1,5,4,3,6,8,7]=>[7,8,6,3,4,5,1,2]=>1010010=>0100101
[1,2,5,4,3,6,8,7]=>[7,8,6,3,4,5,2,1]=>1110010=>0100111
[1,2,4,5,3,6,8,7]=>[7,8,6,3,5,4,2,1]=>1111010=>0101111
[2,1,3,5,4,6,8,7]=>[7,8,6,4,5,3,1,2]=>1011010=>0101101
[4,3,2,1,5,6,8,7]=>[7,8,6,5,1,2,3,4]=>1000110=>0110001
[3,2,4,1,5,6,8,7]=>[7,8,6,5,1,4,2,3]=>1100110=>0110011
[2,3,4,1,5,6,8,7]=>[7,8,6,5,1,4,3,2]=>1110110=>0110111
[1,3,4,2,5,6,8,7]=>[7,8,6,5,2,4,3,1]=>1110110=>0110111
[2,1,4,3,5,6,8,7]=>[7,8,6,5,3,4,1,2]=>1010110=>0110101
[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>1110110=>0110111
[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>1011110=>0111101
[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>1111110=>0111111
[5,7,6,4,3,2,1,8]=>[8,1,2,3,4,6,7,5]=>1000100=>0010001
[4,7,6,5,3,2,1,8]=>[8,1,2,3,5,6,7,4]=>1001000=>0001001
[4,6,7,5,3,2,1,8]=>[8,1,2,3,5,7,6,4]=>1001010=>0101001
[4,5,7,6,3,2,1,8]=>[8,1,2,3,6,7,5,4]=>1001100=>0011001
[4,6,5,7,3,2,1,8]=>[8,1,2,3,7,5,6,4]=>1001100=>0011001
[3,7,6,5,4,2,1,8]=>[8,1,2,4,5,6,7,3]=>1010000=>0000101
[3,5,6,7,4,2,1,8]=>[8,1,2,4,7,6,5,3]=>1010110=>0110101
[4,3,7,6,5,2,1,8]=>[8,1,2,5,6,7,3,4]=>1010000=>0000101
[3,4,7,6,5,2,1,8]=>[8,1,2,5,6,7,4,3]=>1011000=>0001101
[4,5,3,7,6,2,1,8]=>[8,1,2,6,7,3,5,4]=>1011000=>0001101
[3,5,4,7,6,2,1,8]=>[8,1,2,6,7,4,5,3]=>1011000=>0001101
[4,3,5,7,6,2,1,8]=>[8,1,2,6,7,5,3,4]=>1010100=>0010101
[3,4,5,7,6,2,1,8]=>[8,1,2,6,7,5,4,3]=>1011100=>0011101
[4,6,5,3,7,2,1,8]=>[8,1,2,7,3,5,6,4]=>1011000=>0001101
[3,5,6,4,7,2,1,8]=>[8,1,2,7,4,6,5,3]=>1011100=>0011101
[2,4,7,6,5,3,1,8]=>[8,1,3,5,6,7,4,2]=>1101000=>0001011
[2,4,6,7,5,3,1,8]=>[8,1,3,5,7,6,4,2]=>1101010=>0101011
[2,5,4,7,6,3,1,8]=>[8,1,3,6,7,4,5,2]=>1101000=>0001011
[2,4,5,7,6,3,1,8]=>[8,1,3,6,7,5,4,2]=>1101100=>0011011
[2,6,5,4,7,3,1,8]=>[8,1,3,7,4,5,6,2]=>1101000=>0001011
[2,5,6,4,7,3,1,8]=>[8,1,3,7,4,6,5,2]=>1101100=>0011011
[2,4,6,5,7,3,1,8]=>[8,1,3,7,5,6,4,2]=>1101100=>0011011
[2,5,4,6,7,3,1,8]=>[8,1,3,7,6,4,5,2]=>1101010=>0101011
[3,2,7,6,5,4,1,8]=>[8,1,4,5,6,7,2,3]=>1100000=>0000011
[3,2,6,7,5,4,1,8]=>[8,1,4,5,7,6,2,3]=>1100010=>0100011
[3,2,5,7,6,4,1,8]=>[8,1,4,6,7,5,2,3]=>1100100=>0010011
[3,2,5,6,7,4,1,8]=>[8,1,4,7,6,5,2,3]=>1100110=>0110011
[2,3,7,6,5,4,1,8]=>[8,1,4,5,6,7,3,2]=>1110000=>0000111
[2,3,6,7,5,4,1,8]=>[8,1,4,5,7,6,3,2]=>1110010=>0100111
[4,3,2,7,6,5,1,8]=>[8,1,5,6,7,2,3,4]=>1100000=>0000011
[4,3,2,6,7,5,1,8]=>[8,1,5,7,6,2,3,4]=>1100010=>0100011
[2,3,4,7,6,5,1,8]=>[8,1,5,6,7,4,3,2]=>1111000=>0001111
[5,4,3,2,7,6,1,8]=>[8,1,6,7,2,3,4,5]=>1100000=>0000011
[4,5,3,2,7,6,1,8]=>[8,1,6,7,2,3,5,4]=>1101000=>0001011
[3,5,4,2,7,6,1,8]=>[8,1,6,7,2,4,5,3]=>1110000=>0000111
[3,4,5,2,7,6,1,8]=>[8,1,6,7,2,5,4,3]=>1111000=>0001111
[3,2,5,4,7,6,1,8]=>[8,1,6,7,4,5,2,3]=>1101000=>0001011
[4,3,2,5,7,6,1,8]=>[8,1,6,7,5,2,3,4]=>1100100=>0010011
[2,3,4,5,7,6,1,8]=>[8,1,6,7,5,4,3,2]=>1111100=>0011111
[3,6,5,4,2,7,1,8]=>[8,1,7,2,4,5,6,3]=>1110000=>0000111
[3,5,6,4,2,7,1,8]=>[8,1,7,2,4,6,5,3]=>1110100=>0010111
[4,3,6,5,2,7,1,8]=>[8,1,7,2,5,6,3,4]=>1110000=>0000111
[3,4,6,5,2,7,1,8]=>[8,1,7,2,5,6,4,3]=>1111000=>0001111
[3,5,4,6,2,7,1,8]=>[8,1,7,2,6,4,5,3]=>1111000=>0001111
[2,5,4,6,3,7,1,8]=>[8,1,7,3,6,4,5,2]=>1111000=>0001111
[3,2,6,5,4,7,1,8]=>[8,1,7,4,5,6,2,3]=>1101000=>0001011
[2,3,5,6,4,7,1,8]=>[8,1,7,4,6,5,3,2]=>1111100=>0011111
[2,4,3,6,5,7,1,8]=>[8,1,7,5,6,3,4,2]=>1110100=>0010111
[3,2,4,6,5,7,1,8]=>[8,1,7,5,6,4,2,3]=>1101100=>0011011
[2,3,4,6,5,7,1,8]=>[8,1,7,5,6,4,3,2]=>1111100=>0011111
[3,5,4,2,6,7,1,8]=>[8,1,7,6,2,4,5,3]=>1110010=>0100111
[3,2,5,4,6,7,1,8]=>[8,1,7,6,4,5,2,3]=>1101010=>0101011
[2,3,5,4,6,7,1,8]=>[8,1,7,6,4,5,3,2]=>1111010=>0101111
[1,5,6,7,4,3,2,8]=>[8,2,3,4,7,6,5,1]=>1100110=>0110011
[1,6,5,4,7,3,2,8]=>[8,2,3,7,4,5,6,1]=>1101000=>0001011
[1,4,6,5,7,3,2,8]=>[8,2,3,7,5,6,4,1]=>1101100=>0011011
[1,5,4,6,7,3,2,8]=>[8,2,3,7,6,4,5,1]=>1101010=>0101011
[1,4,5,6,7,3,2,8]=>[8,2,3,7,6,5,4,1]=>1101110=>0111011
[1,3,5,7,6,4,2,8]=>[8,2,4,6,7,5,3,1]=>1110100=>0010111
[1,3,6,5,7,4,2,8]=>[8,2,4,7,5,6,3,1]=>1110100=>0010111
[1,3,5,6,7,4,2,8]=>[8,2,4,7,6,5,3,1]=>1110110=>0110111
[1,3,4,7,6,5,2,8]=>[8,2,5,6,7,4,3,1]=>1111000=>0001111
[1,3,5,4,7,6,2,8]=>[8,2,6,7,4,5,3,1]=>1111000=>0001111
[1,4,3,5,7,6,2,8]=>[8,2,6,7,5,3,4,1]=>1110100=>0010111
[1,6,5,4,3,7,2,8]=>[8,2,7,3,4,5,6,1]=>1110000=>0000111
[1,5,4,6,3,7,2,8]=>[8,2,7,3,6,4,5,1]=>1111000=>0001111
[1,3,6,5,4,7,2,8]=>[8,2,7,4,5,6,3,1]=>1111000=>0001111
[1,3,5,6,4,7,2,8]=>[8,2,7,4,6,5,3,1]=>1111100=>0011111
[1,4,3,6,5,7,2,8]=>[8,2,7,5,6,3,4,1]=>1110100=>0010111
[1,3,4,6,5,7,2,8]=>[8,2,7,5,6,4,3,1]=>1111100=>0011111
[1,5,4,3,6,7,2,8]=>[8,2,7,6,3,4,5,1]=>1110010=>0100111
[1,3,4,5,6,7,2,8]=>[8,2,7,6,5,4,3,1]=>1111110=>0111111
[2,1,6,5,4,7,3,8]=>[8,3,7,4,5,6,1,2]=>1011000=>0001101
[2,1,5,4,6,7,3,8]=>[8,3,7,6,4,5,1,2]=>1011010=>0101101
[1,2,4,6,7,5,3,8]=>[8,3,5,7,6,4,2,1]=>1111010=>0101111
[1,2,6,5,4,7,3,8]=>[8,3,7,4,5,6,2,1]=>1111000=>0001111
[1,2,4,6,5,7,3,8]=>[8,3,7,5,6,4,2,1]=>1111100=>0011111
[3,2,1,5,6,7,4,8]=>[8,4,7,6,5,1,2,3]=>1001110=>0111001
[2,3,1,5,7,6,4,8]=>[8,4,6,7,5,1,3,2]=>1101100=>0011011
[2,3,1,5,6,7,4,8]=>[8,4,7,6,5,1,3,2]=>1101110=>0111011
[1,3,2,6,7,5,4,8]=>[8,4,5,7,6,2,3,1]=>1101010=>0101011
[1,3,2,5,7,6,4,8]=>[8,4,6,7,5,2,3,1]=>1101100=>0011011
[1,3,2,6,5,7,4,8]=>[8,4,7,5,6,2,3,1]=>1101100=>0011011
[1,3,2,5,6,7,4,8]=>[8,4,7,6,5,2,3,1]=>1101110=>0111011
[2,1,3,5,7,6,4,8]=>[8,4,6,7,5,3,1,2]=>1011100=>0011101
[2,1,3,5,6,7,4,8]=>[8,4,7,6,5,3,1,2]=>1011110=>0111101
[1,2,3,6,5,7,4,8]=>[8,4,7,5,6,3,2,1]=>1111100=>0011111
[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>1111110=>0111111
[4,3,2,1,7,6,5,8]=>[8,5,6,7,1,2,3,4]=>1000100=>0010001
[4,3,2,1,6,7,5,8]=>[8,5,7,6,1,2,3,4]=>1000110=>0110001
[3,4,2,1,6,7,5,8]=>[8,5,7,6,1,2,4,3]=>1010110=>0110101
[3,2,4,1,7,6,5,8]=>[8,5,6,7,1,4,2,3]=>1100100=>0010011
[3,2,4,1,6,7,5,8]=>[8,5,7,6,1,4,2,3]=>1100110=>0110011
[2,3,4,1,7,6,5,8]=>[8,5,6,7,1,4,3,2]=>1110100=>0010111
[2,3,4,1,6,7,5,8]=>[8,5,7,6,1,4,3,2]=>1110110=>0110111
[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>1100100=>0010011
[1,4,3,2,6,7,5,8]=>[8,5,7,6,2,3,4,1]=>1100110=>0110011
[1,3,4,2,7,6,5,8]=>[8,5,6,7,2,4,3,1]=>1110100=>0010111
[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>1110110=>0110111
[2,1,4,3,7,6,5,8]=>[8,5,6,7,3,4,1,2]=>1010100=>0010101
[1,2,4,3,7,6,5,8]=>[8,5,6,7,3,4,2,1]=>1110100=>0010111
[3,2,1,4,7,6,5,8]=>[8,5,6,7,4,1,2,3]=>1001100=>0011001
[3,2,1,4,6,7,5,8]=>[8,5,7,6,4,1,2,3]=>1001110=>0111001
[2,3,1,4,6,7,5,8]=>[8,5,7,6,4,1,3,2]=>1101110=>0111011
[1,3,2,4,7,6,5,8]=>[8,5,6,7,4,2,3,1]=>1101100=>0011011
[1,3,2,4,6,7,5,8]=>[8,5,7,6,4,2,3,1]=>1101110=>0111011
[2,1,3,4,6,7,5,8]=>[8,5,7,6,4,3,1,2]=>1011110=>0111101
[1,2,3,4,7,6,5,8]=>[8,5,6,7,4,3,2,1]=>1111100=>0011111
[1,2,3,4,6,7,5,8]=>[8,5,7,6,4,3,2,1]=>1111110=>0111111
[5,4,3,2,1,7,6,8]=>[8,6,7,1,2,3,4,5]=>1000010=>0100001
[2,3,5,4,1,7,6,8]=>[8,6,7,1,4,5,3,2]=>1110010=>0100111
[4,3,2,5,1,7,6,8]=>[8,6,7,1,5,2,3,4]=>1100010=>0100011
[3,4,2,5,1,7,6,8]=>[8,6,7,1,5,2,4,3]=>1110010=>0100111
[2,3,4,5,1,7,6,8]=>[8,6,7,1,5,4,3,2]=>1111010=>0101111
[1,5,4,3,2,7,6,8]=>[8,6,7,2,3,4,5,1]=>1100010=>0100011
[1,4,5,3,2,7,6,8]=>[8,6,7,2,3,5,4,1]=>1101010=>0101011
[1,3,5,4,2,7,6,8]=>[8,6,7,2,4,5,3,1]=>1110010=>0100111
[1,4,3,5,2,7,6,8]=>[8,6,7,2,5,3,4,1]=>1110010=>0100111
[1,3,4,5,2,7,6,8]=>[8,6,7,2,5,4,3,1]=>1111010=>0101111
[1,2,5,4,3,7,6,8]=>[8,6,7,3,4,5,2,1]=>1110010=>0100111
[1,2,4,5,3,7,6,8]=>[8,6,7,3,5,4,2,1]=>1111010=>0101111
[3,2,1,5,4,7,6,8]=>[8,6,7,4,5,1,2,3]=>1001010=>0101001
[2,3,1,5,4,7,6,8]=>[8,6,7,4,5,1,3,2]=>1101010=>0101011
[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>1101010=>0101011
[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>1111010=>0101111
[4,3,2,1,5,7,6,8]=>[8,6,7,5,1,2,3,4]=>1000110=>0110001
[3,2,4,1,5,7,6,8]=>[8,6,7,5,1,4,2,3]=>1100110=>0110011
[2,3,4,1,5,7,6,8]=>[8,6,7,5,1,4,3,2]=>1110110=>0110111
[1,4,3,2,5,7,6,8]=>[8,6,7,5,2,3,4,1]=>1100110=>0110011
[2,3,1,4,5,7,6,8]=>[8,6,7,5,4,1,3,2]=>1101110=>0111011
[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>1101110=>0111011
[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>1111110=>0111111
[3,6,5,4,2,1,7,8]=>[8,7,1,2,4,5,6,3]=>1010001=>1000101
[2,4,5,6,3,1,7,8]=>[8,7,1,3,6,5,4,2]=>1101101=>1011011
[3,2,6,5,4,1,7,8]=>[8,7,1,4,5,6,2,3]=>1100001=>1000011
[3,2,5,6,4,1,7,8]=>[8,7,1,4,6,5,2,3]=>1100101=>1010011
[2,3,6,5,4,1,7,8]=>[8,7,1,4,5,6,3,2]=>1110001=>1000111
[4,3,2,6,5,1,7,8]=>[8,7,1,5,6,2,3,4]=>1100001=>1000011
[2,3,4,6,5,1,7,8]=>[8,7,1,5,6,4,3,2]=>1111001=>1001111
[3,5,4,2,6,1,7,8]=>[8,7,1,6,2,4,5,3]=>1110001=>1000111
[1,3,6,5,4,2,7,8]=>[8,7,2,4,5,6,3,1]=>1110001=>1000111
[1,3,5,4,6,2,7,8]=>[8,7,2,6,4,5,3,1]=>1111001=>1001111
[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>1110001=>1000111
[1,2,5,6,4,3,7,8]=>[8,7,3,4,6,5,2,1]=>1110101=>1010111
[1,2,4,6,5,3,7,8]=>[8,7,3,5,6,4,2,1]=>1111001=>1001111
[1,2,5,4,6,3,7,8]=>[8,7,3,6,4,5,2,1]=>1111001=>1001111
[1,2,4,5,6,3,7,8]=>[8,7,3,6,5,4,2,1]=>1111101=>1011111
[2,3,1,6,5,4,7,8]=>[8,7,4,5,6,1,3,2]=>1101001=>1001011
[2,3,1,5,6,4,7,8]=>[8,7,4,6,5,1,3,2]=>1101101=>1011011
[1,3,2,6,5,4,7,8]=>[8,7,4,5,6,2,3,1]=>1101001=>1001011
[4,3,2,1,6,5,7,8]=>[8,7,5,6,1,2,3,4]=>1000101=>1010001
[2,4,3,1,6,5,7,8]=>[8,7,5,6,1,3,4,2]=>1100101=>1010011
[3,2,4,1,6,5,7,8]=>[8,7,5,6,1,4,2,3]=>1100101=>1010011
[2,3,4,1,6,5,7,8]=>[8,7,5,6,1,4,3,2]=>1110101=>1010111
[1,4,3,2,6,5,7,8]=>[8,7,5,6,2,3,4,1]=>1100101=>1010011
[2,1,4,3,6,5,7,8]=>[8,7,5,6,3,4,1,2]=>1010101=>1010101
[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>1110101=>1010111
[2,3,1,4,6,5,7,8]=>[8,7,5,6,4,1,3,2]=>1101101=>1011011
[2,1,3,4,6,5,7,8]=>[8,7,5,6,4,3,1,2]=>1011101=>1011101
[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>1111101=>1011111
[3,5,4,2,1,6,7,8]=>[8,7,6,1,2,4,5,3]=>1010011=>1100101
[2,5,4,3,1,6,7,8]=>[8,7,6,1,3,4,5,2]=>1100011=>1100011
[2,4,5,3,1,6,7,8]=>[8,7,6,1,3,5,4,2]=>1101011=>1101011
[3,2,5,4,1,6,7,8]=>[8,7,6,1,4,5,2,3]=>1100011=>1100011
[2,3,5,4,1,6,7,8]=>[8,7,6,1,4,5,3,2]=>1110011=>1100111
[2,4,3,5,1,6,7,8]=>[8,7,6,1,5,3,4,2]=>1110011=>1100111
[1,5,4,3,2,6,7,8]=>[8,7,6,2,3,4,5,1]=>1100011=>1100011
[1,4,3,5,2,6,7,8]=>[8,7,6,2,5,3,4,1]=>1110011=>1100111
[1,3,4,5,2,6,7,8]=>[8,7,6,2,5,4,3,1]=>1111011=>1101111
[2,1,5,4,3,6,7,8]=>[8,7,6,3,4,5,1,2]=>1010011=>1100101
[2,1,4,5,3,6,7,8]=>[8,7,6,3,5,4,1,2]=>1011011=>1101101
[1,2,5,4,3,6,7,8]=>[8,7,6,3,4,5,2,1]=>1110011=>1100111
[1,2,4,5,3,6,7,8]=>[8,7,6,3,5,4,2,1]=>1111011=>1101111
[2,3,1,5,4,6,7,8]=>[8,7,6,4,5,1,3,2]=>1101011=>1101011
[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>1101011=>1101011
[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>1111011=>1101111
[2,4,3,1,5,6,7,8]=>[8,7,6,5,1,3,4,2]=>1100111=>1110011
[1,4,3,2,5,6,7,8]=>[8,7,6,5,2,3,4,1]=>1100111=>1110011
[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>1110111=>1110111
[2,1,4,3,5,6,7,8]=>[8,7,6,5,3,4,1,2]=>1010111=>1110101
[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>1110111=>1110111
[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>1101111=>1111011
[1,2,3,4,8,6,7,5]=>[5,7,6,8,4,3,2,1]=>1111010=>0101111
[1,2,3,5,8,6,7,4]=>[4,7,6,8,5,3,2,1]=>1110110=>0110111
[1,2,3,7,5,6,8,4]=>[4,8,6,5,7,3,2,1]=>1110110=>0110111
[1,2,3,8,5,6,7,4]=>[4,7,6,5,8,3,2,1]=>1110110=>0110111
[1,2,3,8,5,7,6,4]=>[4,6,7,5,8,3,2,1]=>1110100=>0010111
[1,2,3,8,6,5,7,4]=>[4,7,5,6,8,3,2,1]=>1110100=>0010111
[1,2,3,8,6,7,5,4]=>[4,5,7,6,8,3,2,1]=>1110010=>0100111
[1,2,4,8,5,6,7,3]=>[3,7,6,5,8,4,2,1]=>1101110=>0111011
[1,2,4,8,5,7,6,3]=>[3,6,7,5,8,4,2,1]=>1101100=>0011011
[1,2,4,8,6,5,7,3]=>[3,7,5,6,8,4,2,1]=>1101100=>0011011
[1,2,5,4,8,6,7,3]=>[3,7,6,8,4,5,2,1]=>1101010=>0101011
[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>1111001=>1001111
[1,2,6,4,5,8,7,3]=>[3,7,8,5,4,6,2,1]=>1101100=>0011011
[1,2,7,4,6,5,8,3]=>[3,8,5,6,4,7,2,1]=>1101100=>0011011
[1,2,8,5,4,6,7,3]=>[3,7,6,4,5,8,2,1]=>1101010=>0101011
[1,2,8,5,4,7,6,3]=>[3,6,7,4,5,8,2,1]=>1101000=>0001011
[1,2,8,5,6,7,4,3]=>[3,4,7,6,5,8,2,1]=>1100110=>0110011
[1,2,8,6,5,7,4,3]=>[3,4,7,5,6,8,2,1]=>1100100=>0010011
[1,2,8,7,5,6,4,3]=>[3,4,6,5,7,8,2,1]=>1100100=>0010011
[1,3,4,5,8,6,7,2]=>[2,7,6,8,5,4,3,1]=>1011110=>0111101
[1,3,4,7,5,6,2,8]=>[8,2,6,5,7,4,3,1]=>1111100=>0011111
[1,3,4,7,5,6,8,2]=>[2,8,6,5,7,4,3,1]=>1011110=>0111101
[1,3,4,8,6,5,7,2]=>[2,7,5,6,8,4,3,1]=>1011100=>0011101
[1,3,6,4,5,7,2,8]=>[8,2,7,5,4,6,3,1]=>1111100=>0011111
[1,3,6,4,5,7,8,2]=>[2,8,7,5,4,6,3,1]=>1011101=>1011101
[1,3,6,4,5,8,7,2]=>[2,7,8,5,4,6,3,1]=>1011100=>0011101
[1,3,8,4,5,6,7,2]=>[2,7,6,5,4,8,3,1]=>1011110=>0111101
[1,3,8,4,5,7,6,2]=>[2,6,7,5,4,8,3,1]=>1011100=>0011101
[1,3,7,5,4,6,2,8]=>[8,2,6,4,5,7,3,1]=>1111000=>0001111
[1,3,8,5,4,6,7,2]=>[2,7,6,4,5,8,3,1]=>1011010=>0101101
[1,3,8,5,4,7,6,2]=>[2,6,7,4,5,8,3,1]=>1011000=>0001101
[1,3,8,5,6,4,7,2]=>[2,7,4,6,5,8,3,1]=>1011100=>0011101
[1,3,8,5,6,7,4,2]=>[2,4,7,6,5,8,3,1]=>1010110=>0110101
[1,3,8,6,5,7,4,2]=>[2,4,7,5,6,8,3,1]=>1010100=>0010101
[1,4,3,7,5,6,2,8]=>[8,2,6,5,7,3,4,1]=>1110100=>0010111
[1,4,3,8,6,5,7,2]=>[2,7,5,6,8,3,4,1]=>1010100=>0010101
[1,5,3,4,2,8,7,6]=>[6,7,8,2,4,3,5,1]=>1110000=>0000111
[1,5,3,4,7,6,8,2]=>[2,8,6,7,4,3,5,1]=>1011010=>0101101
[1,7,3,4,5,6,2,8]=>[8,2,6,5,4,3,7,1]=>1111100=>0011111
[1,8,3,4,6,5,7,2]=>[2,7,5,6,4,3,8,1]=>1011100=>0011101
[1,7,3,5,4,6,2,8]=>[8,2,6,4,5,3,7,1]=>1111000=>0001111
[1,8,3,6,5,4,7,2]=>[2,7,4,5,6,3,8,1]=>1011000=>0001101
[1,8,3,6,5,7,4,2]=>[2,4,7,5,6,3,8,1]=>1010100=>0010101
[1,8,3,7,5,6,4,2]=>[2,4,6,5,7,3,8,1]=>1010100=>0010101
[1,8,3,7,6,5,4,2]=>[2,4,5,6,7,3,8,1]=>1010000=>0000101
[1,6,4,5,3,2,8,7]=>[7,8,2,3,5,4,6,1]=>1101000=>0001011
[1,8,4,5,6,7,3,2]=>[2,3,7,6,5,4,8,1]=>1001110=>0111001
[1,8,4,6,5,3,7,2]=>[2,7,3,5,6,4,8,1]=>1011000=>0001101
[1,8,4,6,5,7,3,2]=>[2,3,7,5,6,4,8,1]=>1001100=>0011001
[1,8,5,4,3,6,7,2]=>[2,7,6,3,4,5,8,1]=>1010010=>0100101
[1,8,5,4,6,7,3,2]=>[2,3,7,6,4,5,8,1]=>1001010=>0101001
[1,8,5,4,7,6,3,2]=>[2,3,6,7,4,5,8,1]=>1001000=>0001001
[1,8,6,4,5,3,7,2]=>[2,7,3,5,4,6,8,1]=>1011000=>0001101
[1,8,6,4,5,7,3,2]=>[2,3,7,5,4,6,8,1]=>1001100=>0011001
[1,8,7,4,5,6,3,2]=>[2,3,6,5,4,7,8,1]=>1001100=>0011001
[1,8,7,4,6,5,3,2]=>[2,3,5,6,4,7,8,1]=>1001000=>0001001
[1,8,6,5,4,7,3,2]=>[2,3,7,4,5,6,8,1]=>1001000=>0001001
[1,8,7,5,4,6,3,2]=>[2,3,6,4,5,7,8,1]=>1001000=>0001001
[1,8,7,5,6,4,3,2]=>[2,3,4,6,5,7,8,1]=>1000100=>0010001
[2,1,3,5,8,6,7,4]=>[4,7,6,8,5,3,1,2]=>1010110=>0110101
[2,1,3,8,5,7,6,4]=>[4,6,7,5,8,3,1,2]=>1010100=>0010101
[2,1,3,8,6,5,7,4]=>[4,7,5,6,8,3,1,2]=>1010100=>0010101
[2,1,3,8,6,7,5,4]=>[4,5,7,6,8,3,1,2]=>1010010=>0100101
[2,1,4,3,8,6,7,5]=>[5,7,6,8,3,4,1,2]=>1010010=>0100101
[2,1,4,5,8,6,7,3]=>[3,7,6,8,5,4,1,2]=>1001110=>0111001
[2,1,4,8,5,7,6,3]=>[3,6,7,5,8,4,1,2]=>1001100=>0011001
[2,1,4,8,6,5,7,3]=>[3,7,5,6,8,4,1,2]=>1001100=>0011001
[2,1,4,8,6,7,5,3]=>[3,5,7,6,8,4,1,2]=>1001010=>0101001
[2,1,5,4,8,6,7,3]=>[3,7,6,8,4,5,1,2]=>1001010=>0101001
[2,1,6,4,5,3,8,7]=>[7,8,3,5,4,6,1,2]=>1011000=>0001101
[2,1,6,4,5,7,8,3]=>[3,8,7,5,4,6,1,2]=>1001101=>1011001
[2,1,6,4,5,8,7,3]=>[3,7,8,5,4,6,1,2]=>1001100=>0011001
[2,1,8,4,6,7,5,3]=>[3,5,7,6,4,8,1,2]=>1001010=>0101001
[2,1,7,5,4,6,8,3]=>[3,8,6,4,5,7,1,2]=>1001010=>0101001
[2,1,8,5,4,6,7,3]=>[3,7,6,4,5,8,1,2]=>1001010=>0101001
[2,1,8,5,4,7,6,3]=>[3,6,7,4,5,8,1,2]=>1001000=>0001001
[2,1,7,5,6,4,8,3]=>[3,8,4,6,5,7,1,2]=>1001100=>0011001
[2,1,8,5,6,4,7,3]=>[3,7,4,6,5,8,1,2]=>1001100=>0011001
[2,1,8,6,5,4,7,3]=>[3,7,4,5,6,8,1,2]=>1001000=>0001001
[2,1,8,7,5,6,4,3]=>[3,4,6,5,7,8,1,2]=>1000100=>0010001
[2,3,1,4,8,6,7,5]=>[5,7,6,8,4,1,3,2]=>1101010=>0101011
[2,3,1,5,8,6,7,4]=>[4,7,6,8,5,1,3,2]=>1100110=>0110011
[2,3,1,7,5,6,8,4]=>[4,8,6,5,7,1,3,2]=>1100110=>0110011
[2,3,1,8,6,7,5,4]=>[4,5,7,6,8,1,3,2]=>1100010=>0100011
[2,3,4,1,8,6,7,5]=>[5,7,6,8,1,4,3,2]=>1110010=>0100111
[2,3,4,5,8,6,7,1]=>[1,7,6,8,5,4,3,2]=>0111110=>0111110
[2,3,4,8,5,6,7,1]=>[1,7,6,5,8,4,3,2]=>0111110=>0111110
[2,3,4,8,5,7,6,1]=>[1,6,7,5,8,4,3,2]=>0111100=>0011110
[2,3,4,8,6,5,7,1]=>[1,7,5,6,8,4,3,2]=>0111100=>0011110
[2,3,4,8,6,7,5,1]=>[1,5,7,6,8,4,3,2]=>0111010=>0101110
[2,3,5,4,8,6,7,1]=>[1,7,6,8,4,5,3,2]=>0111010=>0101110
[2,3,6,4,5,1,8,7]=>[7,8,1,5,4,6,3,2]=>1111000=>0001111
[2,3,7,4,5,6,8,1]=>[1,8,6,5,4,7,3,2]=>0111110=>0111110
[2,3,7,4,6,5,8,1]=>[1,8,5,6,4,7,3,2]=>0111100=>0011110
[2,3,7,5,4,6,8,1]=>[1,8,6,4,5,7,3,2]=>0111010=>0101110
[2,3,8,5,4,6,7,1]=>[1,7,6,4,5,8,3,2]=>0111010=>0101110
[2,3,7,5,6,4,8,1]=>[1,8,4,6,5,7,3,2]=>0111100=>0011110
[2,3,8,5,6,4,7,1]=>[1,7,4,6,5,8,3,2]=>0111100=>0011110
[2,3,8,5,6,7,4,1]=>[1,4,7,6,5,8,3,2]=>0110110=>0110110
[2,3,8,6,5,4,7,1]=>[1,7,4,5,6,8,3,2]=>0111000=>0001110
[2,4,3,1,8,6,7,5]=>[5,7,6,8,1,3,4,2]=>1100010=>0100011
[2,4,3,7,5,6,1,8]=>[8,1,6,5,7,3,4,2]=>1110100=>0010111
[2,4,3,8,5,6,7,1]=>[1,7,6,5,8,3,4,2]=>0110110=>0110110
[2,4,3,8,5,7,6,1]=>[1,6,7,5,8,3,4,2]=>0110100=>0010110
[2,4,3,8,6,5,7,1]=>[1,7,5,6,8,3,4,2]=>0110100=>0010110
[2,4,3,8,6,7,5,1]=>[1,5,7,6,8,3,4,2]=>0110010=>0100110
[2,5,3,4,1,6,7,8]=>[8,7,6,1,4,3,5,2]=>1110011=>1100111
[2,5,3,4,1,7,6,8]=>[8,6,7,1,4,3,5,2]=>1110010=>0100111
[2,5,3,4,6,1,7,8]=>[8,7,1,6,4,3,5,2]=>1111001=>1001111
[2,5,3,4,6,7,1,8]=>[8,1,7,6,4,3,5,2]=>1111010=>0101111
[2,5,3,4,8,7,6,1]=>[1,6,7,8,4,3,5,2]=>0111000=>0001110
[2,6,3,4,5,7,8,1]=>[1,8,7,5,4,3,6,2]=>0111101=>1011110
[2,6,3,4,5,8,7,1]=>[1,7,8,5,4,3,6,2]=>0111100=>0011110
[2,8,3,4,5,7,6,1]=>[1,6,7,5,4,3,8,2]=>0111100=>0011110
[2,7,3,4,6,5,8,1]=>[1,8,5,6,4,3,7,2]=>0111100=>0011110
[2,6,3,5,4,1,7,8]=>[8,7,1,4,5,3,6,2]=>1110001=>1000111
[2,6,3,5,4,1,8,7]=>[7,8,1,4,5,3,6,2]=>1110000=>0000111
[2,6,3,5,4,7,8,1]=>[1,8,7,4,5,3,6,2]=>0111001=>1001110
[2,6,3,5,4,8,7,1]=>[1,7,8,4,5,3,6,2]=>0111000=>0001110
[2,7,3,6,5,4,1,8]=>[8,1,4,5,6,3,7,2]=>1110000=>0000111
[2,7,3,6,5,4,8,1]=>[1,8,4,5,6,3,7,2]=>0111000=>0001110
[2,5,4,3,8,6,7,1]=>[1,7,6,8,3,4,5,2]=>0110010=>0100110
[2,6,4,3,5,7,8,1]=>[1,8,7,5,3,4,6,2]=>0110101=>1010110
[2,7,4,3,5,6,1,8]=>[8,1,6,5,3,4,7,2]=>1110100=>0010111
[2,8,4,3,6,7,5,1]=>[1,5,7,6,3,4,8,2]=>0110010=>0100110
[2,8,4,3,7,6,5,1]=>[1,5,6,7,3,4,8,2]=>0110000=>0000110
[2,6,4,5,3,1,8,7]=>[7,8,1,3,5,4,6,2]=>1101000=>0001011
[2,6,4,5,3,7,8,1]=>[1,8,7,3,5,4,6,2]=>0111001=>1001110
[2,6,4,5,3,8,7,1]=>[1,7,8,3,5,4,6,2]=>0111000=>0001110
[2,8,4,5,3,6,7,1]=>[1,7,6,3,5,4,8,2]=>0111010=>0101110
[2,7,4,5,6,3,8,1]=>[1,8,3,6,5,4,7,2]=>0111100=>0011110
[2,7,4,6,5,3,1,8]=>[8,1,3,5,6,4,7,2]=>1101000=>0001011
[2,7,4,6,5,3,8,1]=>[1,8,3,5,6,4,7,2]=>0111000=>0001110
[2,8,5,4,3,6,7,1]=>[1,7,6,3,4,5,8,2]=>0110010=>0100110
[2,8,5,4,3,7,6,1]=>[1,6,7,3,4,5,8,2]=>0110000=>0000110
[2,7,5,4,6,3,8,1]=>[1,8,3,6,4,5,7,2]=>0111000=>0001110
[2,8,5,4,7,6,3,1]=>[1,3,6,7,4,5,8,2]=>0101000=>0001010
[3,2,1,5,8,6,7,4]=>[4,7,6,8,5,1,2,3]=>1000110=>0110001
[3,2,1,7,5,6,4,8]=>[8,4,6,5,7,1,2,3]=>1001100=>0011001
[3,2,1,7,5,6,8,4]=>[4,8,6,5,7,1,2,3]=>1000110=>0110001
[3,2,1,8,5,6,7,4]=>[4,7,6,5,8,1,2,3]=>1000110=>0110001
[3,2,1,8,5,7,6,4]=>[4,6,7,5,8,1,2,3]=>1000100=>0010001
[3,2,1,8,6,5,7,4]=>[4,7,5,6,8,1,2,3]=>1000100=>0010001
[3,2,1,8,6,7,5,4]=>[4,5,7,6,8,1,2,3]=>1000010=>0100001
[3,2,4,1,8,6,7,5]=>[5,7,6,8,1,4,2,3]=>1100010=>0100011
[3,2,4,5,8,6,7,1]=>[1,7,6,8,5,4,2,3]=>0101110=>0111010
[3,2,4,8,5,7,6,1]=>[1,6,7,5,8,4,2,3]=>0101100=>0011010
[3,2,4,8,6,7,5,1]=>[1,5,7,6,8,4,2,3]=>0101010=>0101010
[3,2,5,4,8,6,7,1]=>[1,7,6,8,4,5,2,3]=>0101010=>0101010
[3,2,6,4,5,1,7,8]=>[8,7,1,5,4,6,2,3]=>1101001=>1001011
[3,2,6,4,5,1,8,7]=>[7,8,1,5,4,6,2,3]=>1101000=>0001011
[3,2,6,4,5,7,1,8]=>[8,1,7,5,4,6,2,3]=>1101100=>0011011
[3,2,8,4,7,6,5,1]=>[1,5,6,7,4,8,2,3]=>0101000=>0001010
[3,2,7,5,4,6,1,8]=>[8,1,6,4,5,7,2,3]=>1101000=>0001011
[3,2,7,5,4,6,8,1]=>[1,8,6,4,5,7,2,3]=>0101010=>0101010
[3,2,7,5,6,4,8,1]=>[1,8,4,6,5,7,2,3]=>0101100=>0011010
[3,2,8,5,6,4,7,1]=>[1,7,4,6,5,8,2,3]=>0101100=>0011010
[3,2,8,6,5,4,7,1]=>[1,7,4,5,6,8,2,3]=>0101000=>0001010
[4,2,3,1,5,7,8,6]=>[6,8,7,5,1,3,2,4]=>1100101=>1010011
[4,2,3,1,5,8,7,6]=>[6,7,8,5,1,3,2,4]=>1100100=>0010011
[4,2,3,1,6,5,8,7]=>[7,8,5,6,1,3,2,4]=>1100100=>0010011
[4,2,3,1,6,7,8,5]=>[5,8,7,6,1,3,2,4]=>1100011=>1100011
[4,2,3,1,6,8,7,5]=>[5,7,8,6,1,3,2,4]=>1100010=>0100011
[4,2,3,1,7,6,8,5]=>[5,8,6,7,1,3,2,4]=>1100010=>0100011
[4,2,3,1,8,6,7,5]=>[5,7,6,8,1,3,2,4]=>1100010=>0100011
[4,2,3,1,8,7,6,5]=>[5,6,7,8,1,3,2,4]=>1100000=>0000011
[4,2,3,5,1,7,8,6]=>[6,8,7,1,5,3,2,4]=>1110001=>1000111
[4,2,3,5,1,8,7,6]=>[6,7,8,1,5,3,2,4]=>1110000=>0000111
[4,2,3,5,6,1,8,7]=>[7,8,1,6,5,3,2,4]=>1110100=>0010111
[4,2,3,6,5,1,7,8]=>[8,7,1,5,6,3,2,4]=>1110001=>1000111
[4,2,3,6,5,1,8,7]=>[7,8,1,5,6,3,2,4]=>1110000=>0000111
[4,2,3,6,5,8,7,1]=>[1,7,8,5,6,3,2,4]=>0110100=>0010110
[4,2,3,7,5,6,1,8]=>[8,1,6,5,7,3,2,4]=>1110100=>0010111
[4,2,3,7,6,5,8,1]=>[1,8,5,6,7,3,2,4]=>0110100=>0010110
[4,2,3,8,6,7,5,1]=>[1,5,7,6,8,3,2,4]=>0110010=>0100110
[4,2,3,8,7,6,5,1]=>[1,5,6,7,8,3,2,4]=>0110000=>0000110
[5,2,3,4,1,6,8,7]=>[7,8,6,1,4,3,2,5]=>1110010=>0100111
[5,2,3,4,1,7,6,8]=>[8,6,7,1,4,3,2,5]=>1110010=>0100111
[5,2,3,4,1,8,7,6]=>[6,7,8,1,4,3,2,5]=>1110000=>0000111
[5,2,3,4,7,6,1,8]=>[8,1,6,7,4,3,2,5]=>1111000=>0001111
[5,2,3,4,8,7,6,1]=>[1,6,7,8,4,3,2,5]=>0111000=>0001110
[7,2,3,4,6,5,1,8]=>[8,1,5,6,4,3,2,7]=>1111000=>0001111
[8,2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2,8]=>0111000=>0001110
[6,2,3,5,4,1,7,8]=>[8,7,1,4,5,3,2,6]=>1110001=>1000111
[6,2,3,5,4,1,8,7]=>[7,8,1,4,5,3,2,6]=>1110000=>0000111
[6,2,3,5,4,7,1,8]=>[8,1,7,4,5,3,2,6]=>1111000=>0001111
[6,2,3,5,4,8,7,1]=>[1,7,8,4,5,3,2,6]=>0111000=>0001110
[7,2,3,5,6,4,8,1]=>[1,8,4,6,5,3,2,7]=>0111100=>0011110
[7,2,3,6,5,4,1,8]=>[8,1,4,5,6,3,2,7]=>1110000=>0000111
[7,2,3,6,5,4,8,1]=>[1,8,4,5,6,3,2,7]=>0111000=>0001110
[8,2,3,7,5,6,4,1]=>[1,4,6,5,7,3,2,8]=>0110100=>0010110
[5,2,4,3,1,6,7,8]=>[8,7,6,1,3,4,2,5]=>1100011=>1100011
[5,2,4,3,1,7,6,8]=>[8,6,7,1,3,4,2,5]=>1100010=>0100011
[5,2,4,3,1,8,7,6]=>[6,7,8,1,3,4,2,5]=>1100000=>0000011
[5,2,4,3,6,1,7,8]=>[8,7,1,6,3,4,2,5]=>1110001=>1000111
[5,2,4,3,6,1,8,7]=>[7,8,1,6,3,4,2,5]=>1110000=>0000111
[5,2,4,3,6,7,8,1]=>[1,8,7,6,3,4,2,5]=>0110011=>1100110
[5,2,4,3,6,8,7,1]=>[1,7,8,6,3,4,2,5]=>0110010=>0100110
[5,2,4,3,7,6,1,8]=>[8,1,6,7,3,4,2,5]=>1110000=>0000111
[5,2,4,3,7,6,8,1]=>[1,8,6,7,3,4,2,5]=>0110010=>0100110
[5,2,4,3,8,6,7,1]=>[1,7,6,8,3,4,2,5]=>0110010=>0100110
[5,2,4,3,8,7,6,1]=>[1,6,7,8,3,4,2,5]=>0110000=>0000110
[7,2,4,3,6,5,8,1]=>[1,8,5,6,3,4,2,7]=>0110100=>0010110
[6,2,4,5,3,1,8,7]=>[7,8,1,3,5,4,2,6]=>1101000=>0001011
[6,2,4,5,3,7,1,8]=>[8,1,7,3,5,4,2,6]=>1111000=>0001111
[6,2,4,5,3,7,8,1]=>[1,8,7,3,5,4,2,6]=>0111001=>1001110
[6,2,4,5,3,8,7,1]=>[1,7,8,3,5,4,2,6]=>0111000=>0001110
[7,2,4,5,3,6,8,1]=>[1,8,6,3,5,4,2,7]=>0111010=>0101110
[7,2,4,5,6,3,1,8]=>[8,1,3,6,5,4,2,7]=>1101100=>0011011
[7,2,4,6,5,3,1,8]=>[8,1,3,5,6,4,2,7]=>1101000=>0001011
[8,2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2,8]=>0101000=>0001010
[6,2,5,4,3,7,1,8]=>[8,1,7,3,4,5,2,6]=>1110000=>0000111
[6,2,5,4,3,7,8,1]=>[1,8,7,3,4,5,2,6]=>0110001=>1000110
[6,2,5,4,3,8,7,1]=>[1,7,8,3,4,5,2,6]=>0110000=>0000110
[7,2,5,4,6,3,1,8]=>[8,1,3,6,4,5,2,7]=>1101000=>0001011
[8,2,7,4,5,6,3,1]=>[1,3,6,5,4,7,2,8]=>0101100=>0011010
[8,2,7,5,4,6,3,1]=>[1,3,6,4,5,7,2,8]=>0101000=>0001010
[8,2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2,8]=>0100000=>0000010
[4,3,2,1,8,6,7,5]=>[5,7,6,8,1,2,3,4]=>1000010=>0100001
[4,3,2,7,5,6,8,1]=>[1,8,6,5,7,2,3,4]=>0100110=>0110010
[4,3,2,8,5,6,7,1]=>[1,7,6,5,8,2,3,4]=>0100110=>0110010
[4,3,2,8,5,7,6,1]=>[1,6,7,5,8,2,3,4]=>0100100=>0010010
[5,3,2,4,1,8,7,6]=>[6,7,8,1,4,2,3,5]=>1100000=>0000011
[5,3,2,4,6,1,8,7]=>[7,8,1,6,4,2,3,5]=>1101000=>0001011
[5,3,2,4,7,6,1,8]=>[8,1,6,7,4,2,3,5]=>1101000=>0001011
[5,3,2,4,7,6,8,1]=>[1,8,6,7,4,2,3,5]=>0101010=>0101010
[5,3,2,4,8,6,7,1]=>[1,7,6,8,4,2,3,5]=>0101010=>0101010
[5,3,2,4,8,7,6,1]=>[1,6,7,8,4,2,3,5]=>0101000=>0001010
[7,3,2,4,6,5,8,1]=>[1,8,5,6,4,2,3,7]=>0101100=>0011010
[8,3,2,4,6,7,5,1]=>[1,5,7,6,4,2,3,8]=>0101010=>0101010
[8,3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3,8]=>0101000=>0001010
[6,3,2,5,4,1,7,8]=>[8,7,1,4,5,2,3,6]=>1100001=>1000011
[6,3,2,5,4,1,8,7]=>[7,8,1,4,5,2,3,6]=>1100000=>0000011
[6,3,2,5,4,7,1,8]=>[8,1,7,4,5,2,3,6]=>1101000=>0001011
[6,3,2,5,4,7,8,1]=>[1,8,7,4,5,2,3,6]=>0101001=>1001010
[7,3,2,5,4,6,1,8]=>[8,1,6,4,5,2,3,7]=>1101000=>0001011
[7,3,2,5,4,6,8,1]=>[1,8,6,4,5,2,3,7]=>0101010=>0101010
[8,3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3,8]=>0101000=>0001010
[7,3,2,6,5,4,8,1]=>[1,8,4,5,6,2,3,7]=>0101000=>0001010
[8,3,2,7,5,6,4,1]=>[1,4,6,5,7,2,3,8]=>0100100=>0010010
[8,3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3,8]=>0100000=>0000010
[5,3,4,2,1,7,8,6]=>[6,8,7,1,2,4,3,5]=>1010001=>1000101
[5,3,4,2,1,8,7,6]=>[6,7,8,1,2,4,3,5]=>1010000=>0000101
[5,3,4,2,6,1,8,7]=>[7,8,1,6,2,4,3,5]=>1110000=>0000111
[5,3,4,2,7,6,8,1]=>[1,8,6,7,2,4,3,5]=>0110010=>0100110
[5,3,4,2,8,6,7,1]=>[1,7,6,8,2,4,3,5]=>0110010=>0100110
[5,3,4,2,8,7,6,1]=>[1,6,7,8,2,4,3,5]=>0110000=>0000110
[6,3,4,2,5,1,8,7]=>[7,8,1,5,2,4,3,6]=>1110000=>0000111
[7,3,4,2,6,5,1,8]=>[8,1,5,6,2,4,3,7]=>1110000=>0000111
[7,3,4,2,6,5,8,1]=>[1,8,5,6,2,4,3,7]=>0110100=>0010110
[8,3,4,2,7,6,5,1]=>[1,5,6,7,2,4,3,8]=>0110000=>0000110
[6,3,4,5,2,8,7,1]=>[1,7,8,2,5,4,3,6]=>0111000=>0001110
[7,3,4,6,5,2,1,8]=>[8,1,2,5,6,4,3,7]=>1011000=>0001101
[7,3,4,6,5,2,8,1]=>[1,8,2,5,6,4,3,7]=>0111000=>0001110
[8,3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3,8]=>0011000=>0001100
[6,3,5,4,2,1,7,8]=>[8,7,1,2,4,5,3,6]=>1010001=>1000101
[6,3,5,4,2,7,1,8]=>[8,1,7,2,4,5,3,6]=>1110000=>0000111
[6,3,5,4,2,8,7,1]=>[1,7,8,2,4,5,3,6]=>0110000=>0000110
[7,3,5,4,2,6,1,8]=>[8,1,6,2,4,5,3,7]=>1110000=>0000111
[7,3,5,4,6,2,1,8]=>[8,1,2,6,4,5,3,7]=>1011000=>0001101
[7,3,6,4,5,2,1,8]=>[8,1,2,5,4,6,3,7]=>1011000=>0001101
[8,3,7,4,6,5,2,1]=>[1,2,5,6,4,7,3,8]=>0011000=>0001100
[7,3,6,5,4,2,1,8]=>[8,1,2,4,5,6,3,7]=>1010000=>0000101
[5,4,3,2,8,6,7,1]=>[1,7,6,8,2,3,4,5]=>0100010=>0100010
[7,4,3,2,6,5,8,1]=>[1,8,5,6,2,3,4,7]=>0100100=>0010010
[8,4,3,2,6,7,5,1]=>[1,5,7,6,2,3,4,8]=>0100010=>0100010
[8,4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4,8]=>0100000=>0000010
[6,4,3,5,2,1,8,7]=>[7,8,1,2,5,3,4,6]=>1010000=>0000101
[6,4,3,5,2,8,7,1]=>[1,7,8,2,5,3,4,6]=>0110000=>0000110
[7,4,3,6,5,2,1,8]=>[8,1,2,5,6,3,4,7]=>1010000=>0000101
[7,4,3,6,5,2,8,1]=>[1,8,2,5,6,3,4,7]=>0110000=>0000110
[8,4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4,8]=>0110000=>0000110
[6,5,3,4,2,1,8,7]=>[7,8,1,2,4,3,5,6]=>1010000=>0000101
[8,5,3,4,2,7,6,1]=>[1,6,7,2,4,3,5,8]=>0110000=>0000110
[8,7,3,4,6,5,2,1]=>[1,2,5,6,4,3,7,8]=>0011000=>0001100
[7,6,3,5,4,2,1,8]=>[8,1,2,4,5,3,6,7]=>1010000=>0000101
[8,6,3,5,4,2,7,1]=>[1,7,2,4,5,3,6,8]=>0110000=>0000110
[8,7,3,5,4,6,2,1]=>[1,2,6,4,5,3,7,8]=>0011000=>0001100
[8,7,3,6,5,4,2,1]=>[1,2,4,5,6,3,7,8]=>0010000=>0000100
[8,5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5,8]=>0100000=>0000010
[8,7,4,3,6,5,2,1]=>[1,2,5,6,3,4,7,8]=>0010000=>0000100
[8,7,4,6,5,3,2,1]=>[1,2,3,5,6,4,7,8]=>0001000=>0001000
[2,4,1,3,6,5,8,7]=>[7,8,5,6,3,1,4,2]=>1110100=>0010111
[2,1,4,6,3,5,8,7]=>[7,8,5,3,6,4,1,2]=>1011100=>0011101
[2,4,1,6,3,5,8,7]=>[7,8,5,3,6,1,4,2]=>1110100=>0010111
[2,4,6,1,3,5,8,7]=>[7,8,5,3,1,6,4,2]=>1111100=>0011111
[2,1,4,3,6,8,5,7]=>[7,5,8,6,3,4,1,2]=>1010110=>0110101
[2,4,1,3,6,8,5,7]=>[7,5,8,6,3,1,4,2]=>1110110=>0110111
[2,1,4,6,3,8,5,7]=>[7,5,8,3,6,4,1,2]=>1011100=>0011101
[2,4,1,6,3,8,5,7]=>[7,5,8,3,6,1,4,2]=>1110100=>0010111
[2,4,6,1,3,8,5,7]=>[7,5,8,3,1,6,4,2]=>1111100=>0011111
[2,1,4,6,8,3,5,7]=>[7,5,3,8,6,4,1,2]=>1011110=>0111101
[2,4,1,6,8,3,5,7]=>[7,5,3,8,6,1,4,2]=>1110110=>0110111
[2,4,6,1,8,3,5,7]=>[7,5,3,8,1,6,4,2]=>1111100=>0011111
[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]=>1111110=>0111111
[2,4,6,1,3,5,7,8]=>[8,7,5,3,1,6,4,2]=>1111101=>1011111
[2,4,1,3,6,7,5,8]=>[8,5,7,6,3,1,4,2]=>1110110=>0110111
[2,4,1,6,3,7,5,8]=>[8,5,7,3,6,1,4,2]=>1110100=>0010111
[2,4,1,6,7,3,5,8]=>[8,5,3,7,6,1,4,2]=>1110110=>0110111
[2,4,6,1,7,3,5,8]=>[8,5,3,7,1,6,4,2]=>1111100=>0011111
[2,4,1,3,6,7,8,5]=>[5,8,7,6,3,1,4,2]=>1110011=>1100111
[2,4,1,6,3,7,8,5]=>[5,8,7,3,6,1,4,2]=>1110001=>1000111
[2,4,6,1,3,7,8,5]=>[5,8,7,3,1,6,4,2]=>1111001=>1001111
[2,4,1,6,7,3,8,5]=>[5,8,3,7,6,1,4,2]=>1110010=>0100111
[2,4,6,1,7,3,8,5]=>[5,8,3,7,1,6,4,2]=>1111000=>0001111
[2,4,6,7,1,3,8,5]=>[5,8,3,1,7,6,4,2]=>1111010=>0101111
[2,4,6,1,7,8,3,5]=>[5,3,8,7,1,6,4,2]=>1111001=>1001111
[2,4,6,7,1,8,3,5]=>[5,3,8,1,7,6,4,2]=>1111010=>0101111
[2,4,6,7,8,1,3,5]=>[5,3,1,8,7,6,4,2]=>1111011=>1101111
[2,1,4,3,7,5,8,6]=>[6,8,5,7,3,4,1,2]=>1010100=>0010101
[2,4,1,3,7,5,8,6]=>[6,8,5,7,3,1,4,2]=>1110100=>0010111
[2,4,7,1,3,5,8,6]=>[6,8,5,3,1,7,4,2]=>1111100=>0011111
[2,1,4,3,7,8,5,6]=>[6,5,8,7,3,4,1,2]=>1010101=>1010101
[2,4,1,3,7,8,5,6]=>[6,5,8,7,3,1,4,2]=>1110101=>1010111
[2,4,1,7,3,8,5,6]=>[6,5,8,3,7,1,4,2]=>1110100=>0010111
[2,4,7,1,3,8,5,6]=>[6,5,8,3,1,7,4,2]=>1111100=>0011111
[2,4,1,7,8,3,5,6]=>[6,5,3,8,7,1,4,2]=>1110101=>1010111
[2,4,7,8,1,3,5,6]=>[6,5,3,1,8,7,4,2]=>1111101=>1011111
[2,4,1,3,5,7,6,8]=>[8,6,7,5,3,1,4,2]=>1110110=>0110111
[2,4,1,5,3,7,6,8]=>[8,6,7,3,5,1,4,2]=>1110010=>0100111
[2,4,1,5,7,3,6,8]=>[8,6,3,7,5,1,4,2]=>1110110=>0110111
[2,4,5,1,7,3,6,8]=>[8,6,3,7,1,5,4,2]=>1111010=>0101111
[2,4,5,7,1,3,6,8]=>[8,6,3,1,7,5,4,2]=>1111110=>0111111
[2,4,1,5,3,7,8,6]=>[6,8,7,3,5,1,4,2]=>1110001=>1000111
[2,4,5,1,3,7,8,6]=>[6,8,7,3,1,5,4,2]=>1111001=>1001111
[2,4,1,5,7,3,8,6]=>[6,8,3,7,5,1,4,2]=>1110100=>0010111
[2,4,5,1,7,3,8,6]=>[6,8,3,7,1,5,4,2]=>1111000=>0001111
[2,4,5,7,1,3,8,6]=>[6,8,3,1,7,5,4,2]=>1111100=>0011111
[2,1,4,5,7,8,3,6]=>[6,3,8,7,5,4,1,2]=>1011101=>1011101
[2,4,5,7,8,1,3,6]=>[6,3,1,8,7,5,4,2]=>1111101=>1011111
[2,1,4,3,8,5,6,7]=>[7,6,5,8,3,4,1,2]=>1010110=>0110101
[2,4,1,3,8,5,6,7]=>[7,6,5,8,3,1,4,2]=>1110110=>0110111
[2,4,5,1,3,8,6,7]=>[7,6,8,3,1,5,4,2]=>1111010=>0101111
[2,1,4,5,8,3,6,7]=>[7,6,3,8,5,4,1,2]=>1011110=>0111101
[2,4,5,6,1,3,8,7]=>[7,8,3,1,6,5,4,2]=>1111100=>0011111
[2,1,4,5,6,8,3,7]=>[7,3,8,6,5,4,1,2]=>1011110=>0111101
[2,4,5,1,6,8,3,7]=>[7,3,8,6,1,5,4,2]=>1111010=>0101111
[2,4,5,6,1,8,3,7]=>[7,3,8,1,6,5,4,2]=>1111100=>0011111
[2,4,5,6,8,1,3,7]=>[7,3,1,8,6,5,4,2]=>1111110=>0111111
[2,4,1,3,5,6,7,8]=>[8,7,6,5,3,1,4,2]=>1110111=>1110111
[2,4,1,5,3,6,7,8]=>[8,7,6,3,5,1,4,2]=>1110011=>1100111
[2,4,1,5,6,3,7,8]=>[8,7,3,6,5,1,4,2]=>1110101=>1010111
[2,4,5,1,6,3,7,8]=>[8,7,3,6,1,5,4,2]=>1111001=>1001111
[2,4,1,5,6,7,3,8]=>[8,3,7,6,5,1,4,2]=>1110110=>0110111
[2,4,5,1,6,7,3,8]=>[8,3,7,6,1,5,4,2]=>1111010=>0101111
[2,4,5,6,1,7,3,8]=>[8,3,7,1,6,5,4,2]=>1111100=>0011111
[2,4,5,6,7,1,3,8]=>[8,3,1,7,6,5,4,2]=>1111110=>0111111
[2,4,1,5,6,7,8,3]=>[3,8,7,6,5,1,4,2]=>1100111=>1110011
[2,4,5,1,6,7,8,3]=>[3,8,7,6,1,5,4,2]=>1101011=>1101011
[2,4,5,6,1,7,8,3]=>[3,8,7,1,6,5,4,2]=>1101101=>1011011
[2,4,5,6,7,1,8,3]=>[3,8,1,7,6,5,4,2]=>1101110=>0111011
[2,4,5,6,7,8,1,3]=>[3,1,8,7,6,5,4,2]=>1101111=>1111011
[2,1,5,3,6,4,8,7]=>[7,8,4,6,3,5,1,2]=>1011000=>0001101
[2,1,5,6,3,4,8,7]=>[7,8,4,3,6,5,1,2]=>1011100=>0011101
[2,5,1,6,3,4,8,7]=>[7,8,4,3,6,1,5,2]=>1111000=>0001111
[2,1,5,3,6,8,4,7]=>[7,4,8,6,3,5,1,2]=>1011010=>0101101
[2,1,5,6,3,8,4,7]=>[7,4,8,3,6,5,1,2]=>1011100=>0011101
[2,5,1,6,3,8,4,7]=>[7,4,8,3,6,1,5,2]=>1111000=>0001111
[2,5,6,1,3,8,4,7]=>[7,4,8,3,1,6,5,2]=>1111100=>0011111
[2,5,1,6,8,3,4,7]=>[7,4,3,8,6,1,5,2]=>1111010=>0101111
[2,5,6,1,8,3,4,7]=>[7,4,3,8,1,6,5,2]=>1111100=>0011111
[2,5,6,8,1,3,4,7]=>[7,4,3,1,8,6,5,2]=>1111110=>0111111
[2,1,5,3,6,4,7,8]=>[8,7,4,6,3,5,1,2]=>1011001=>1001101
[2,1,5,6,3,4,7,8]=>[8,7,4,3,6,5,1,2]=>1011101=>1011101
[2,5,1,6,3,4,7,8]=>[8,7,4,3,6,1,5,2]=>1111001=>1001111
[2,1,5,3,6,7,4,8]=>[8,4,7,6,3,5,1,2]=>1011010=>0101101
[2,5,1,3,6,7,4,8]=>[8,4,7,6,3,1,5,2]=>1111010=>0101111
[2,1,5,6,3,7,4,8]=>[8,4,7,3,6,5,1,2]=>1011100=>0011101
[2,5,1,6,3,7,4,8]=>[8,4,7,3,6,1,5,2]=>1111000=>0001111
[2,5,6,1,3,7,4,8]=>[8,4,7,3,1,6,5,2]=>1111100=>0011111
[2,5,1,6,7,3,4,8]=>[8,4,3,7,6,1,5,2]=>1111010=>0101111
[2,5,6,1,7,3,4,8]=>[8,4,3,7,1,6,5,2]=>1111100=>0011111
[2,5,6,7,1,3,4,8]=>[8,4,3,1,7,6,5,2]=>1111110=>0111111
[2,5,1,3,6,7,8,4]=>[4,8,7,6,3,1,5,2]=>1110011=>1100111
[2,1,5,6,3,7,8,4]=>[4,8,7,3,6,5,1,2]=>1010101=>1010101
[2,5,1,6,3,7,8,4]=>[4,8,7,3,6,1,5,2]=>1110001=>1000111
[2,5,6,1,3,7,8,4]=>[4,8,7,3,1,6,5,2]=>1110101=>1010111
[2,5,1,6,7,3,8,4]=>[4,8,3,7,6,1,5,2]=>1110010=>0100111
[2,5,6,1,7,3,8,4]=>[4,8,3,7,1,6,5,2]=>1110100=>0010111
[2,5,6,7,1,3,8,4]=>[4,8,3,1,7,6,5,2]=>1110110=>0110111
[2,1,5,6,7,8,3,4]=>[4,3,8,7,6,5,1,2]=>1010111=>1110101
[2,5,1,6,7,8,3,4]=>[4,3,8,7,6,1,5,2]=>1110011=>1100111
[2,5,6,1,7,8,3,4]=>[4,3,8,7,1,6,5,2]=>1110101=>1010111
[2,5,6,7,1,8,3,4]=>[4,3,8,1,7,6,5,2]=>1110110=>0110111
[2,5,6,7,8,1,3,4]=>[4,3,1,8,7,6,5,2]=>1110111=>1110111
[2,1,5,3,7,4,8,6]=>[6,8,4,7,3,5,1,2]=>1011000=>0001101
[2,5,1,3,7,4,8,6]=>[6,8,4,7,3,1,5,2]=>1111000=>0001111
[2,1,5,7,3,4,8,6]=>[6,8,4,3,7,5,1,2]=>1011100=>0011101
[2,5,1,7,3,4,8,6]=>[6,8,4,3,7,1,5,2]=>1111000=>0001111
[2,5,7,1,3,4,8,6]=>[6,8,4,3,1,7,5,2]=>1111100=>0011111
[2,1,5,7,3,8,4,6]=>[6,4,8,3,7,5,1,2]=>1011100=>0011101
[2,5,1,7,3,8,4,6]=>[6,4,8,3,7,1,5,2]=>1111000=>0001111
[2,5,7,1,3,8,4,6]=>[6,4,8,3,1,7,5,2]=>1111100=>0011111
[2,1,5,7,8,3,4,6]=>[6,4,3,8,7,5,1,2]=>1011101=>1011101
[2,5,1,7,8,3,4,6]=>[6,4,3,8,7,1,5,2]=>1111001=>1001111
[2,5,1,3,7,4,6,8]=>[8,6,4,7,3,1,5,2]=>1111010=>0101111
[2,3,5,1,4,7,6,8]=>[8,6,7,4,1,5,3,2]=>1111010=>0101111
[2,1,3,5,7,4,6,8]=>[8,6,4,7,5,3,1,2]=>1011110=>0111101
[2,3,5,7,1,4,6,8]=>[8,6,4,1,7,5,3,2]=>1111110=>0111111
[2,1,3,5,7,4,8,6]=>[6,8,4,7,5,3,1,2]=>1011100=>0011101
[2,3,1,5,7,4,8,6]=>[6,8,4,7,5,1,3,2]=>1101100=>0011011
[2,3,5,1,7,4,8,6]=>[6,8,4,7,1,5,3,2]=>1111000=>0001111
[2,3,5,7,1,4,8,6]=>[6,8,4,1,7,5,3,2]=>1111100=>0011111
[2,1,3,5,7,8,4,6]=>[6,4,8,7,5,3,1,2]=>1011101=>1011101
[2,3,5,7,1,8,4,6]=>[6,4,8,1,7,5,3,2]=>1111100=>0011111
[2,3,5,7,8,1,4,6]=>[6,4,1,8,7,5,3,2]=>1111101=>1011111
[2,5,1,3,8,4,6,7]=>[7,6,4,8,3,1,5,2]=>1111010=>0101111
[2,3,1,5,8,4,6,7]=>[7,6,4,8,5,1,3,2]=>1101110=>0111011
[2,3,5,8,1,4,6,7]=>[7,6,4,1,8,5,3,2]=>1111110=>0111111
[2,3,5,6,1,4,8,7]=>[7,8,4,1,6,5,3,2]=>1111100=>0011111
[2,1,3,5,6,8,4,7]=>[7,4,8,6,5,3,1,2]=>1011110=>0111101
[2,3,5,6,1,8,4,7]=>[7,4,8,1,6,5,3,2]=>1111100=>0011111
[2,3,5,6,8,1,4,7]=>[7,4,1,8,6,5,3,2]=>1111110=>0111111
[2,3,5,1,6,4,7,8]=>[8,7,4,6,1,5,3,2]=>1111001=>1001111
[2,3,5,6,1,4,7,8]=>[8,7,4,1,6,5,3,2]=>1111101=>1011111
[2,3,5,6,1,7,4,8]=>[8,4,7,1,6,5,3,2]=>1111100=>0011111
[2,3,5,6,7,1,4,8]=>[8,4,1,7,6,5,3,2]=>1111110=>0111111
[2,3,5,1,6,7,8,4]=>[4,8,7,6,1,5,3,2]=>1110011=>1100111
[2,3,5,6,1,7,8,4]=>[4,8,7,1,6,5,3,2]=>1110101=>1010111
[2,3,5,6,7,1,8,4]=>[4,8,1,7,6,5,3,2]=>1110110=>0110111
[2,3,5,6,7,8,1,4]=>[4,1,8,7,6,5,3,2]=>1110111=>1110111
[2,1,6,3,7,4,8,5]=>[5,8,4,7,3,6,1,2]=>1011000=>0001101
[2,6,1,3,7,4,8,5]=>[5,8,4,7,3,1,6,2]=>1111000=>0001111
[2,1,6,7,3,4,8,5]=>[5,8,4,3,7,6,1,2]=>1011010=>0101101
[2,6,1,7,3,4,8,5]=>[5,8,4,3,7,1,6,2]=>1111000=>0001111
[2,6,7,1,3,4,8,5]=>[5,8,4,3,1,7,6,2]=>1111010=>0101111
[2,1,6,7,3,8,4,5]=>[5,4,8,3,7,6,1,2]=>1011010=>0101101
[2,1,6,7,8,3,4,5]=>[5,4,3,8,7,6,1,2]=>1011011=>1101101
[2,6,7,1,8,3,4,5]=>[5,4,3,8,1,7,6,2]=>1111010=>0101111
[2,6,7,1,3,4,5,8]=>[8,5,4,3,1,7,6,2]=>1111110=>0111111
[2,1,6,3,4,7,5,8]=>[8,5,7,4,3,6,1,2]=>1011100=>0011101
[2,3,1,6,4,7,5,8]=>[8,5,7,4,6,1,3,2]=>1101100=>0011011
[2,3,6,1,4,7,5,8]=>[8,5,7,4,1,6,3,2]=>1111100=>0011111
[2,1,3,6,7,4,5,8]=>[8,5,4,7,6,3,1,2]=>1011110=>0111101
[2,3,1,6,7,4,5,8]=>[8,5,4,7,6,1,3,2]=>1101110=>0111011
[2,3,6,1,7,4,5,8]=>[8,5,4,7,1,6,3,2]=>1111100=>0011111
[2,3,6,7,1,4,5,8]=>[8,5,4,1,7,6,3,2]=>1111110=>0111111
[2,1,6,3,4,7,8,5]=>[5,8,7,4,3,6,1,2]=>1011001=>1001101
[2,3,1,6,4,7,8,5]=>[5,8,7,4,6,1,3,2]=>1101001=>1001011
[2,3,6,1,4,7,8,5]=>[5,8,7,4,1,6,3,2]=>1111001=>1001111
[2,1,3,6,7,4,8,5]=>[5,8,4,7,6,3,1,2]=>1011010=>0101101
[2,3,6,1,7,4,8,5]=>[5,8,4,7,1,6,3,2]=>1111000=>0001111
[2,3,6,7,1,4,8,5]=>[5,8,4,1,7,6,3,2]=>1111010=>0101111
[2,1,3,6,7,8,4,5]=>[5,4,8,7,6,3,1,2]=>1011011=>1101101
[2,3,6,1,7,8,4,5]=>[5,4,8,7,1,6,3,2]=>1111001=>1001111
[2,3,6,7,1,8,4,5]=>[5,4,8,1,7,6,3,2]=>1111010=>0101111
[2,3,6,7,8,1,4,5]=>[5,4,1,8,7,6,3,2]=>1111011=>1101111
[2,1,6,3,4,8,5,7]=>[7,5,8,4,3,6,1,2]=>1011100=>0011101
[2,3,1,6,4,8,5,7]=>[7,5,8,4,6,1,3,2]=>1101100=>0011011
[2,3,6,1,4,8,5,7]=>[7,5,8,4,1,6,3,2]=>1111100=>0011111
[2,1,3,6,8,4,5,7]=>[7,5,4,8,6,3,1,2]=>1011110=>0111101
[2,3,1,6,8,4,5,7]=>[7,5,4,8,6,1,3,2]=>1101110=>0111011
[2,3,6,8,1,4,5,7]=>[7,5,4,1,8,6,3,2]=>1111110=>0111111
[2,1,6,3,4,5,8,7]=>[7,8,5,4,3,6,1,2]=>1011100=>0011101
[2,3,6,1,4,5,8,7]=>[7,8,5,4,1,6,3,2]=>1111100=>0011111
[2,3,4,6,1,5,8,7]=>[7,8,5,1,6,4,3,2]=>1111100=>0011111
[2,3,1,4,6,8,5,7]=>[7,5,8,6,4,1,3,2]=>1101110=>0111011
[2,3,4,1,6,8,5,7]=>[7,5,8,6,1,4,3,2]=>1110110=>0110111
[2,3,4,6,1,8,5,7]=>[7,5,8,1,6,4,3,2]=>1111100=>0011111
[2,3,4,6,8,1,5,7]=>[7,5,1,8,6,4,3,2]=>1111110=>0111111
[2,6,1,3,4,5,7,8]=>[8,7,5,4,3,1,6,2]=>1111101=>1011111
[2,1,3,6,4,5,7,8]=>[8,7,5,4,6,3,1,2]=>1011101=>1011101
[2,3,6,1,4,5,7,8]=>[8,7,5,4,1,6,3,2]=>1111101=>1011111
[2,3,4,6,1,5,7,8]=>[8,7,5,1,6,4,3,2]=>1111101=>1011111
[2,3,4,6,1,7,5,8]=>[8,5,7,1,6,4,3,2]=>1111100=>0011111
[2,3,4,6,7,1,5,8]=>[8,5,1,7,6,4,3,2]=>1111110=>0111111
[2,3,4,6,1,7,8,5]=>[5,8,7,1,6,4,3,2]=>1111001=>1001111
[2,3,4,6,7,1,8,5]=>[5,8,1,7,6,4,3,2]=>1111010=>0101111
[2,3,4,6,7,8,1,5]=>[5,1,8,7,6,4,3,2]=>1111011=>1101111
[2,1,7,8,3,4,5,6]=>[6,5,4,3,8,7,1,2]=>1011101=>1011101
[2,7,1,8,3,4,5,6]=>[6,5,4,3,8,1,7,2]=>1111100=>0011111
[2,7,8,1,3,4,5,6]=>[6,5,4,3,1,8,7,2]=>1111101=>1011111
[2,7,1,3,4,8,5,6]=>[6,5,8,4,3,1,7,2]=>1111100=>0011111
[2,3,1,7,4,8,5,6]=>[6,5,8,4,7,1,3,2]=>1101100=>0011011
[2,3,1,7,8,4,5,6]=>[6,5,4,8,7,1,3,2]=>1101101=>1011011
[2,3,7,8,1,4,5,6]=>[6,5,4,1,8,7,3,2]=>1111101=>1011111
[2,7,1,3,4,5,8,6]=>[6,8,5,4,3,1,7,2]=>1111100=>0011111
[2,3,4,1,7,5,8,6]=>[6,8,5,7,1,4,3,2]=>1110100=>0010111
[2,3,4,7,1,5,8,6]=>[6,8,5,1,7,4,3,2]=>1111100=>0011111
[2,1,3,4,7,8,5,6]=>[6,5,8,7,4,3,1,2]=>1011101=>1011101
[2,3,1,4,7,8,5,6]=>[6,5,8,7,4,1,3,2]=>1101101=>1011011
[2,3,4,1,7,8,5,6]=>[6,5,8,7,1,4,3,2]=>1110101=>1010111
[2,3,4,7,1,8,5,6]=>[6,5,8,1,7,4,3,2]=>1111100=>0011111
[2,3,4,7,8,1,5,6]=>[6,5,1,8,7,4,3,2]=>1111101=>1011111
[2,7,1,3,4,5,6,8]=>[8,6,5,4,3,1,7,2]=>1111110=>0111111
[2,3,1,4,7,5,6,8]=>[8,6,5,7,4,1,3,2]=>1101110=>0111011
[2,3,4,1,7,5,6,8]=>[8,6,5,7,1,4,3,2]=>1110110=>0110111
[2,3,4,7,1,5,6,8]=>[8,6,5,1,7,4,3,2]=>1111110=>0111111
[2,3,4,5,7,1,6,8]=>[8,6,1,7,5,4,3,2]=>1111110=>0111111
[2,3,4,5,7,1,8,6]=>[6,8,1,7,5,4,3,2]=>1111100=>0011111
[2,3,4,5,7,8,1,6]=>[6,1,8,7,5,4,3,2]=>1111101=>1011111
[2,1,8,3,4,5,6,7]=>[7,6,5,4,3,8,1,2]=>1011110=>0111101
[2,1,3,4,8,5,6,7]=>[7,6,5,8,4,3,1,2]=>1011110=>0111101
[2,3,1,4,8,5,6,7]=>[7,6,5,8,4,1,3,2]=>1101110=>0111011
[2,3,4,1,8,5,6,7]=>[7,6,5,8,1,4,3,2]=>1110110=>0110111
[2,3,4,8,1,5,6,7]=>[7,6,5,1,8,4,3,2]=>1111110=>0111111
[2,3,4,1,5,8,6,7]=>[7,6,8,5,1,4,3,2]=>1110110=>0110111
[2,3,4,5,1,8,6,7]=>[7,6,8,1,5,4,3,2]=>1111010=>0101111
[2,3,4,5,8,1,6,7]=>[7,6,1,8,5,4,3,2]=>1111110=>0111111
[2,3,4,5,6,8,1,7]=>[7,1,8,6,5,4,3,2]=>1111110=>0111111
[3,1,4,2,6,5,8,7]=>[7,8,5,6,2,4,1,3]=>1100100=>0010011
[3,4,1,2,6,5,8,7]=>[7,8,5,6,2,1,4,3]=>1110100=>0010111
[3,4,6,1,2,5,8,7]=>[7,8,5,2,1,6,4,3]=>1111100=>0011111
[3,1,4,2,6,8,5,7]=>[7,5,8,6,2,4,1,3]=>1100110=>0110011
[3,4,1,2,6,8,5,7]=>[7,5,8,6,2,1,4,3]=>1110110=>0110111
[3,1,4,6,2,8,5,7]=>[7,5,8,2,6,4,1,3]=>1101100=>0011011
[3,4,1,6,2,8,5,7]=>[7,5,8,2,6,1,4,3]=>1110100=>0010111
[3,4,6,1,2,8,5,7]=>[7,5,8,2,1,6,4,3]=>1111100=>0011111
[3,1,4,6,8,2,5,7]=>[7,5,2,8,6,4,1,3]=>1101110=>0111011
[3,4,1,6,8,2,5,7]=>[7,5,2,8,6,1,4,3]=>1110110=>0110111
[3,4,6,8,1,2,5,7]=>[7,5,2,1,8,6,4,3]=>1111110=>0111111
[3,1,4,2,6,5,7,8]=>[8,7,5,6,2,4,1,3]=>1100101=>1010011
[3,4,1,2,6,5,7,8]=>[8,7,5,6,2,1,4,3]=>1110101=>1010111
[3,4,6,1,2,5,7,8]=>[8,7,5,2,1,6,4,3]=>1111101=>1011111
[3,4,1,2,6,7,5,8]=>[8,5,7,6,2,1,4,3]=>1110110=>0110111
[3,4,1,6,2,7,5,8]=>[8,5,7,2,6,1,4,3]=>1110100=>0010111
[3,4,6,1,2,7,5,8]=>[8,5,7,2,1,6,4,3]=>1111100=>0011111
[3,4,6,1,7,2,5,8]=>[8,5,2,7,1,6,4,3]=>1111100=>0011111
[3,1,4,2,6,7,8,5]=>[5,8,7,6,2,4,1,3]=>1100011=>1100011
[3,4,1,2,6,7,8,5]=>[5,8,7,6,2,1,4,3]=>1110011=>1100111
[3,1,4,6,2,7,8,5]=>[5,8,7,2,6,4,1,3]=>1101001=>1001011
[3,4,1,6,2,7,8,5]=>[5,8,7,2,6,1,4,3]=>1110001=>1000111
[3,4,6,1,2,7,8,5]=>[5,8,7,2,1,6,4,3]=>1111001=>1001111
[3,1,4,6,7,2,8,5]=>[5,8,2,7,6,4,1,3]=>1101010=>0101011
[3,4,1,6,7,2,8,5]=>[5,8,2,7,6,1,4,3]=>1110010=>0100111
[3,4,6,1,7,2,8,5]=>[5,8,2,7,1,6,4,3]=>1111000=>0001111
[3,4,6,7,1,2,8,5]=>[5,8,2,1,7,6,4,3]=>1111010=>0101111
[3,1,4,6,7,8,2,5]=>[5,2,8,7,6,4,1,3]=>1101011=>1101011
[3,4,1,6,7,8,2,5]=>[5,2,8,7,6,1,4,3]=>1110011=>1100111
[3,4,6,1,7,8,2,5]=>[5,2,8,7,1,6,4,3]=>1111001=>1001111
[3,4,6,7,1,8,2,5]=>[5,2,8,1,7,6,4,3]=>1111010=>0101111
[3,1,4,2,7,5,8,6]=>[6,8,5,7,2,4,1,3]=>1100100=>0010011
[3,4,1,2,7,5,8,6]=>[6,8,5,7,2,1,4,3]=>1110100=>0010111
[3,1,4,7,2,5,8,6]=>[6,8,5,2,7,4,1,3]=>1101100=>0011011
[3,4,1,7,2,5,8,6]=>[6,8,5,2,7,1,4,3]=>1110100=>0010111
[3,1,4,2,7,8,5,6]=>[6,5,8,7,2,4,1,3]=>1100101=>1010011
[3,4,1,2,7,8,5,6]=>[6,5,8,7,2,1,4,3]=>1110101=>1010111
[3,1,4,7,2,8,5,6]=>[6,5,8,2,7,4,1,3]=>1101100=>0011011
[3,4,1,7,2,8,5,6]=>[6,5,8,2,7,1,4,3]=>1110100=>0010111
[3,4,7,1,2,8,5,6]=>[6,5,8,2,1,7,4,3]=>1111100=>0011111
[3,4,7,1,8,2,5,6]=>[6,5,2,8,1,7,4,3]=>1111100=>0011111
[3,4,7,8,1,2,5,6]=>[6,5,2,1,8,7,4,3]=>1111101=>1011111
[3,1,4,2,7,5,6,8]=>[8,6,5,7,2,4,1,3]=>1100110=>0110011
[3,4,1,2,7,5,6,8]=>[8,6,5,7,2,1,4,3]=>1110110=>0110111
[3,4,1,7,2,5,6,8]=>[8,6,5,2,7,1,4,3]=>1110110=>0110111
[3,4,7,1,2,5,6,8]=>[8,6,5,2,1,7,4,3]=>1111110=>0111111
[3,4,1,2,5,7,6,8]=>[8,6,7,5,2,1,4,3]=>1110110=>0110111
[3,4,1,5,2,7,6,8]=>[8,6,7,2,5,1,4,3]=>1110010=>0100111
[3,4,5,1,7,2,6,8]=>[8,6,2,7,1,5,4,3]=>1111010=>0101111
[3,1,4,2,5,7,8,6]=>[6,8,7,5,2,4,1,3]=>1100101=>1010011
[3,4,1,2,5,7,8,6]=>[6,8,7,5,2,1,4,3]=>1110101=>1010111
[3,1,4,5,2,7,8,6]=>[6,8,7,2,5,4,1,3]=>1101001=>1001011
[3,4,5,1,2,7,8,6]=>[6,8,7,2,1,5,4,3]=>1111001=>1001111
[3,1,4,5,7,2,8,6]=>[6,8,2,7,5,4,1,3]=>1101100=>0011011
[3,4,1,5,7,2,8,6]=>[6,8,2,7,5,1,4,3]=>1110100=>0010111
[3,4,5,7,1,2,8,6]=>[6,8,2,1,7,5,4,3]=>1111100=>0011111
[3,1,4,5,7,8,2,6]=>[6,2,8,7,5,4,1,3]=>1101101=>1011011
[3,4,1,5,7,8,2,6]=>[6,2,8,7,5,1,4,3]=>1110101=>1010111
[3,4,5,7,1,8,2,6]=>[6,2,8,1,7,5,4,3]=>1111100=>0011111
[3,4,5,7,8,1,2,6]=>[6,2,1,8,7,5,4,3]=>1111101=>1011111
[3,1,4,2,8,5,6,7]=>[7,6,5,8,2,4,1,3]=>1100110=>0110011
[3,4,1,2,8,5,6,7]=>[7,6,5,8,2,1,4,3]=>1110110=>0110111
[3,1,4,8,2,5,6,7]=>[7,6,5,2,8,4,1,3]=>1101110=>0111011
[3,4,8,1,2,5,6,7]=>[7,6,5,2,1,8,4,3]=>1111110=>0111111
[3,1,4,2,5,8,6,7]=>[7,6,8,5,2,4,1,3]=>1100110=>0110011
[3,4,1,2,5,8,6,7]=>[7,6,8,5,2,1,4,3]=>1110110=>0110111
[3,4,1,5,8,2,6,7]=>[7,6,2,8,5,1,4,3]=>1110110=>0110111
[3,4,1,2,5,6,8,7]=>[7,8,6,5,2,1,4,3]=>1110110=>0110111
[3,1,4,5,6,2,8,7]=>[7,8,2,6,5,4,1,3]=>1101100=>0011011
[3,4,1,5,6,2,8,7]=>[7,8,2,6,5,1,4,3]=>1110100=>0010111
[3,4,5,1,6,2,8,7]=>[7,8,2,6,1,5,4,3]=>1111000=>0001111
[3,4,5,6,1,2,8,7]=>[7,8,2,1,6,5,4,3]=>1111100=>0011111
[3,1,4,5,6,8,2,7]=>[7,2,8,6,5,4,1,3]=>1101110=>0111011
[3,4,1,5,6,8,2,7]=>[7,2,8,6,5,1,4,3]=>1110110=>0110111
[3,4,5,6,1,8,2,7]=>[7,2,8,1,6,5,4,3]=>1111100=>0011111
[3,1,4,2,5,6,7,8]=>[8,7,6,5,2,4,1,3]=>1100111=>1110011
[3,4,1,5,2,6,7,8]=>[8,7,6,2,5,1,4,3]=>1110011=>1100111
[3,4,1,5,6,2,7,8]=>[8,7,2,6,5,1,4,3]=>1110101=>1010111
[3,4,5,1,6,2,7,8]=>[8,7,2,6,1,5,4,3]=>1111001=>1001111
[3,1,4,5,6,7,2,8]=>[8,2,7,6,5,4,1,3]=>1101110=>0111011
[3,4,1,5,6,7,2,8]=>[8,2,7,6,5,1,4,3]=>1110110=>0110111
[3,4,5,6,1,7,2,8]=>[8,2,7,1,6,5,4,3]=>1111100=>0011111
[3,1,4,5,6,7,8,2]=>[2,8,7,6,5,4,1,3]=>1001111=>1111001
[3,4,1,5,6,7,8,2]=>[2,8,7,6,5,1,4,3]=>1010111=>1110101
[3,4,5,1,6,7,8,2]=>[2,8,7,6,1,5,4,3]=>1011011=>1101101
[3,4,5,6,1,7,8,2]=>[2,8,7,1,6,5,4,3]=>1011101=>1011101
[3,4,5,6,7,1,8,2]=>[2,8,1,7,6,5,4,3]=>1011110=>0111101
[3,1,5,2,6,4,8,7]=>[7,8,4,6,2,5,1,3]=>1101000=>0001011
[3,1,5,6,2,4,8,7]=>[7,8,4,2,6,5,1,3]=>1101100=>0011011
[3,5,1,6,2,4,8,7]=>[7,8,4,2,6,1,5,3]=>1111000=>0001111
[3,5,6,1,2,4,8,7]=>[7,8,4,2,1,6,5,3]=>1111100=>0011111
[3,1,5,6,2,8,4,7]=>[7,4,8,2,6,5,1,3]=>1101100=>0011011
[3,5,1,6,2,8,4,7]=>[7,4,8,2,6,1,5,3]=>1111000=>0001111
[3,1,5,6,8,2,4,7]=>[7,4,2,8,6,5,1,3]=>1101110=>0111011
[3,5,1,6,8,2,4,7]=>[7,4,2,8,6,1,5,3]=>1111010=>0101111
[3,5,6,1,8,2,4,7]=>[7,4,2,8,1,6,5,3]=>1111100=>0011111
[3,5,6,8,1,2,4,7]=>[7,4,2,1,8,6,5,3]=>1111110=>0111111
[3,1,5,6,2,4,7,8]=>[8,7,4,2,6,5,1,3]=>1101101=>1011011
[3,5,1,6,2,4,7,8]=>[8,7,4,2,6,1,5,3]=>1111001=>1001111
[3,1,5,2,6,7,4,8]=>[8,4,7,6,2,5,1,3]=>1101010=>0101011
[3,5,1,2,6,7,4,8]=>[8,4,7,6,2,1,5,3]=>1111010=>0101111
[3,5,1,6,2,7,4,8]=>[8,4,7,2,6,1,5,3]=>1111000=>0001111
[3,5,6,1,2,7,4,8]=>[8,4,7,2,1,6,5,3]=>1111100=>0011111
[3,1,5,6,7,2,4,8]=>[8,4,2,7,6,5,1,3]=>1101110=>0111011
[3,5,1,6,7,2,4,8]=>[8,4,2,7,6,1,5,3]=>1111010=>0101111
[3,5,6,1,7,2,4,8]=>[8,4,2,7,1,6,5,3]=>1111100=>0011111
[3,5,6,7,1,2,4,8]=>[8,4,2,1,7,6,5,3]=>1111110=>0111111
[3,5,1,6,2,7,8,4]=>[4,8,7,2,6,1,5,3]=>1110001=>1000111
[3,5,6,1,2,7,8,4]=>[4,8,7,2,1,6,5,3]=>1110101=>1010111
[3,1,5,6,7,2,8,4]=>[4,8,2,7,6,5,1,3]=>1100110=>0110011
[3,5,1,6,7,2,8,4]=>[4,8,2,7,6,1,5,3]=>1110010=>0100111
[3,5,6,1,7,2,8,4]=>[4,8,2,7,1,6,5,3]=>1110100=>0010111
[3,5,6,7,1,2,8,4]=>[4,8,2,1,7,6,5,3]=>1110110=>0110111
[3,1,5,6,7,8,2,4]=>[4,2,8,7,6,5,1,3]=>1100111=>1110011
[3,5,6,1,7,8,2,4]=>[4,2,8,7,1,6,5,3]=>1110101=>1010111
[3,5,6,7,1,8,2,4]=>[4,2,8,1,7,6,5,3]=>1110110=>0110111
[3,5,6,7,8,1,2,4]=>[4,2,1,8,7,6,5,3]=>1110111=>1110111
[3,1,5,2,7,4,8,6]=>[6,8,4,7,2,5,1,3]=>1101000=>0001011
[3,5,1,2,7,4,8,6]=>[6,8,4,7,2,1,5,3]=>1111000=>0001111
[3,1,5,7,2,4,8,6]=>[6,8,4,2,7,5,1,3]=>1101100=>0011011
[3,5,1,7,2,4,8,6]=>[6,8,4,2,7,1,5,3]=>1111000=>0001111
[3,5,7,1,2,4,8,6]=>[6,8,4,2,1,7,5,3]=>1111100=>0011111
[3,5,1,2,7,8,4,6]=>[6,4,8,7,2,1,5,3]=>1111001=>1001111
[3,1,5,7,2,8,4,6]=>[6,4,8,2,7,5,1,3]=>1101100=>0011011
[3,5,1,7,2,8,4,6]=>[6,4,8,2,7,1,5,3]=>1111000=>0001111
[3,5,7,1,2,8,4,6]=>[6,4,8,2,1,7,5,3]=>1111100=>0011111
[3,1,5,7,8,2,4,6]=>[6,4,2,8,7,5,1,3]=>1101101=>1011011
[3,5,1,7,8,2,4,6]=>[6,4,2,8,7,1,5,3]=>1111001=>1001111
[3,5,7,8,1,2,4,6]=>[6,4,2,1,8,7,5,3]=>1111101=>1011111
[3,1,5,2,7,4,6,8]=>[8,6,4,7,2,5,1,3]=>1101010=>0101011
[3,1,5,7,2,4,6,8]=>[8,6,4,2,7,5,1,3]=>1101110=>0111011
[3,5,7,1,2,4,6,8]=>[8,6,4,2,1,7,5,3]=>1111110=>0111111
[1,3,5,2,4,7,6,8]=>[8,6,7,4,2,5,3,1]=>1111010=>0101111
[3,1,2,5,7,4,6,8]=>[8,6,4,7,5,2,1,3]=>1101110=>0111011
[1,3,2,5,7,4,6,8]=>[8,6,4,7,5,2,3,1]=>1101110=>0111011
[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>1111010=>0101111
[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>1111110=>0111111
[3,1,5,2,4,7,8,6]=>[6,8,7,4,2,5,1,3]=>1101001=>1001011
[1,3,5,2,4,7,8,6]=>[6,8,7,4,2,5,3,1]=>1111001=>1001111
[1,3,2,5,7,4,8,6]=>[6,8,4,7,5,2,3,1]=>1101100=>0011011
[1,3,5,2,7,4,8,6]=>[6,8,4,7,2,5,3,1]=>1111000=>0001111
[1,3,5,7,2,4,8,6]=>[6,8,4,2,7,5,3,1]=>1111100=>0011111
[3,1,2,5,7,8,4,6]=>[6,4,8,7,5,2,1,3]=>1101101=>1011011
[1,3,2,5,7,8,4,6]=>[6,4,8,7,5,2,3,1]=>1101101=>1011011
[1,3,5,2,7,8,4,6]=>[6,4,8,7,2,5,3,1]=>1111001=>1001111
[1,3,5,7,2,8,4,6]=>[6,4,8,2,7,5,3,1]=>1111100=>0011111
[1,3,5,7,8,2,4,6]=>[6,4,2,8,7,5,3,1]=>1111101=>1011111
[3,1,5,2,8,4,6,7]=>[7,6,4,8,2,5,1,3]=>1101010=>0101011
[3,5,1,8,2,4,6,7]=>[7,6,4,2,8,1,5,3]=>1111010=>0101111
[3,1,2,5,4,8,6,7]=>[7,6,8,4,5,2,1,3]=>1101010=>0101011
[1,3,2,5,4,8,6,7]=>[7,6,8,4,5,2,3,1]=>1101010=>0101011
[1,3,5,2,4,8,6,7]=>[7,6,8,4,2,5,3,1]=>1111010=>0101111
[3,1,2,5,8,4,6,7]=>[7,6,4,8,5,2,1,3]=>1101110=>0111011
[1,3,2,5,8,4,6,7]=>[7,6,4,8,5,2,3,1]=>1101110=>0111011
[1,3,5,8,2,4,6,7]=>[7,6,4,2,8,5,3,1]=>1111110=>0111111
[3,1,5,2,4,6,8,7]=>[7,8,6,4,2,5,1,3]=>1101010=>0101011
[1,3,5,6,2,4,8,7]=>[7,8,4,2,6,5,3,1]=>1111100=>0011111
[3,1,2,5,6,8,4,7]=>[7,4,8,6,5,2,1,3]=>1101110=>0111011
[1,3,2,5,6,8,4,7]=>[7,4,8,6,5,2,3,1]=>1101110=>0111011
[1,3,5,2,6,8,4,7]=>[7,4,8,6,2,5,3,1]=>1111010=>0101111
[1,3,5,6,8,2,4,7]=>[7,4,2,8,6,5,3,1]=>1111110=>0111111
[1,3,5,2,4,6,7,8]=>[8,7,6,4,2,5,3,1]=>1111011=>1101111
[1,3,5,6,2,4,7,8]=>[8,7,4,2,6,5,3,1]=>1111101=>1011111
[3,1,2,5,6,7,4,8]=>[8,4,7,6,5,2,1,3]=>1101110=>0111011
[1,3,5,2,6,7,4,8]=>[8,4,7,6,2,5,3,1]=>1111010=>0101111
[1,3,5,6,2,7,4,8]=>[8,4,7,2,6,5,3,1]=>1111100=>0011111
[3,1,2,5,6,7,8,4]=>[4,8,7,6,5,2,1,3]=>1100111=>1110011
[1,3,5,6,2,7,8,4]=>[4,8,7,2,6,5,3,1]=>1110101=>1010111
[1,3,5,6,7,2,8,4]=>[4,8,2,7,6,5,3,1]=>1110110=>0110111
[1,3,5,6,7,8,2,4]=>[4,2,8,7,6,5,3,1]=>1110111=>1110111
[3,1,6,2,7,4,8,5]=>[5,8,4,7,2,6,1,3]=>1101000=>0001011
[3,6,1,2,7,4,8,5]=>[5,8,4,7,2,1,6,3]=>1111000=>0001111
[3,6,1,7,2,4,8,5]=>[5,8,4,2,7,1,6,3]=>1111000=>0001111
[3,6,1,7,2,8,4,5]=>[5,4,8,2,7,1,6,3]=>1111000=>0001111
[3,6,7,1,2,8,4,5]=>[5,4,8,2,1,7,6,3]=>1111010=>0101111
[3,1,6,7,8,2,4,5]=>[5,4,2,8,7,6,1,3]=>1101011=>1101011
[3,6,1,7,8,2,4,5]=>[5,4,2,8,7,1,6,3]=>1111001=>1001111
[3,6,7,1,8,2,4,5]=>[5,4,2,8,1,7,6,3]=>1111010=>0101111
[3,6,7,8,1,2,4,5]=>[5,4,2,1,8,7,6,3]=>1111011=>1101111
[3,1,6,7,2,4,5,8]=>[8,5,4,2,7,6,1,3]=>1101110=>0111011
[3,6,7,1,2,4,5,8]=>[8,5,4,2,1,7,6,3]=>1111110=>0111111
[3,1,6,2,4,7,5,8]=>[8,5,7,4,2,6,1,3]=>1101100=>0011011
[3,6,1,2,4,7,5,8]=>[8,5,7,4,2,1,6,3]=>1111100=>0011111
[3,1,2,6,4,7,5,8]=>[8,5,7,4,6,2,1,3]=>1101100=>0011011
[1,3,2,6,4,7,5,8]=>[8,5,7,4,6,2,3,1]=>1101100=>0011011
[1,3,6,2,4,7,5,8]=>[8,5,7,4,2,6,3,1]=>1111100=>0011111
[3,1,2,6,7,4,5,8]=>[8,5,4,7,6,2,1,3]=>1101110=>0111011
[1,3,6,7,2,4,5,8]=>[8,5,4,2,7,6,3,1]=>1111110=>0111111
[3,1,6,2,4,7,8,5]=>[5,8,7,4,2,6,1,3]=>1101001=>1001011
[3,1,2,6,4,7,8,5]=>[5,8,7,4,6,2,1,3]=>1101001=>1001011
[1,3,2,6,4,7,8,5]=>[5,8,7,4,6,2,3,1]=>1101001=>1001011
[1,3,6,2,4,7,8,5]=>[5,8,7,4,2,6,3,1]=>1111001=>1001111
[3,1,2,6,7,4,8,5]=>[5,8,4,7,6,2,1,3]=>1101010=>0101011
[1,3,2,6,7,4,8,5]=>[5,8,4,7,6,2,3,1]=>1101010=>0101011
[1,3,6,2,7,4,8,5]=>[5,8,4,7,2,6,3,1]=>1111000=>0001111
[1,3,2,6,7,8,4,5]=>[5,4,8,7,6,2,3,1]=>1101011=>1101011
[1,3,6,2,7,8,4,5]=>[5,4,8,7,2,6,3,1]=>1111001=>1001111
[3,1,6,2,8,4,5,7]=>[7,5,4,8,2,6,1,3]=>1101100=>0011011
[3,1,6,8,2,4,5,7]=>[7,5,4,2,8,6,1,3]=>1101110=>0111011
[3,6,8,1,2,4,5,7]=>[7,5,4,2,1,8,6,3]=>1111110=>0111111
[3,1,6,2,4,8,5,7]=>[7,5,8,4,2,6,1,3]=>1101100=>0011011
[1,3,2,6,4,8,5,7]=>[7,5,8,4,6,2,3,1]=>1101100=>0011011
[1,3,6,2,4,8,5,7]=>[7,5,8,4,2,6,3,1]=>1111100=>0011111
[3,1,6,2,4,5,8,7]=>[7,8,5,4,2,6,1,3]=>1101100=>0011011
[1,3,4,6,2,5,8,7]=>[7,8,5,2,6,4,3,1]=>1111100=>0011111
[3,1,2,4,6,8,5,7]=>[7,5,8,6,4,2,1,3]=>1101110=>0111011
[3,1,6,2,4,5,7,8]=>[8,7,5,4,2,6,1,3]=>1101101=>1011011
[1,3,2,6,4,5,7,8]=>[8,7,5,4,6,2,3,1]=>1101101=>1011011
[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>1111101=>1011111
[3,1,2,4,6,7,5,8]=>[8,5,7,6,4,2,1,3]=>1101110=>0111011
[1,3,4,6,2,7,5,8]=>[8,5,7,2,6,4,3,1]=>1111100=>0011111
[3,1,2,4,6,7,8,5]=>[5,8,7,6,4,2,1,3]=>1101011=>1101011
[1,3,4,6,2,7,8,5]=>[5,8,7,2,6,4,3,1]=>1111001=>1001111
[1,3,4,6,7,2,8,5]=>[5,8,2,7,6,4,3,1]=>1111010=>0101111
[1,3,4,6,7,8,2,5]=>[5,2,8,7,6,4,3,1]=>1111011=>1101111
[3,1,7,2,8,4,5,6]=>[6,5,4,8,2,7,1,3]=>1101100=>0011011
[3,7,1,2,8,4,5,6]=>[6,5,4,8,2,1,7,3]=>1111100=>0011111
[3,1,7,8,2,4,5,6]=>[6,5,4,2,8,7,1,3]=>1101101=>1011011
[1,3,2,7,4,8,5,6]=>[6,5,8,4,7,2,3,1]=>1101100=>0011011
[3,1,2,7,8,4,5,6]=>[6,5,4,8,7,2,1,3]=>1101101=>1011011
[1,3,7,2,8,4,5,6]=>[6,5,4,8,2,7,3,1]=>1111100=>0011111
[3,1,7,2,4,5,8,6]=>[6,8,5,4,2,7,1,3]=>1101100=>0011011
[3,7,1,2,4,5,8,6]=>[6,8,5,4,2,1,7,3]=>1111100=>0011111
[3,1,2,4,7,5,8,6]=>[6,8,5,7,4,2,1,3]=>1101100=>0011011
[1,3,2,4,7,5,8,6]=>[6,8,5,7,4,2,3,1]=>1101100=>0011011
[1,3,4,7,2,5,8,6]=>[6,8,5,2,7,4,3,1]=>1111100=>0011111
[3,1,2,4,7,8,5,6]=>[6,5,8,7,4,2,1,3]=>1101101=>1011011
[1,3,2,4,7,8,5,6]=>[6,5,8,7,4,2,3,1]=>1101101=>1011011
[1,3,4,2,7,8,5,6]=>[6,5,8,7,2,4,3,1]=>1110101=>1010111
[1,3,2,7,4,5,6,8]=>[8,6,5,4,7,2,3,1]=>1101110=>0111011
[1,3,4,5,7,2,8,6]=>[6,8,2,7,5,4,3,1]=>1111100=>0011111
[1,3,4,5,7,8,2,6]=>[6,2,8,7,5,4,3,1]=>1111101=>1011111
[3,1,2,4,8,5,6,7]=>[7,6,5,8,4,2,1,3]=>1101110=>0111011
[1,3,2,4,8,5,6,7]=>[7,6,5,8,4,2,3,1]=>1101110=>0111011
[1,3,4,2,8,5,6,7]=>[7,6,5,8,2,4,3,1]=>1110110=>0110111
[3,1,2,4,5,8,6,7]=>[7,6,8,5,4,2,1,3]=>1101110=>0111011
[1,3,2,4,5,8,6,7]=>[7,6,8,5,4,2,3,1]=>1101110=>0111011
[1,3,4,2,5,8,6,7]=>[7,6,8,5,2,4,3,1]=>1110110=>0110111
[1,3,4,5,6,8,2,7]=>[7,2,8,6,5,4,3,1]=>1111110=>0111111
[4,1,5,2,6,3,8,7]=>[7,8,3,6,2,5,1,4]=>1110000=>0000111
[4,5,1,2,6,3,8,7]=>[7,8,3,6,2,1,5,4]=>1111000=>0001111
[4,5,6,1,2,3,8,7]=>[7,8,3,2,1,6,5,4]=>1111100=>0011111
[4,1,5,2,6,8,3,7]=>[7,3,8,6,2,5,1,4]=>1110010=>0100111
[4,1,5,6,2,8,3,7]=>[7,3,8,2,6,5,1,4]=>1110100=>0010111
[4,1,5,6,8,2,3,7]=>[7,3,2,8,6,5,1,4]=>1110110=>0110111
[4,5,6,1,8,2,3,7]=>[7,3,2,8,1,6,5,4]=>1111100=>0011111
[4,5,6,8,1,2,3,7]=>[7,3,2,1,8,6,5,4]=>1111110=>0111111
[4,1,5,2,6,3,7,8]=>[8,7,3,6,2,5,1,4]=>1110001=>1000111
[4,1,5,6,2,3,7,8]=>[8,7,3,2,6,5,1,4]=>1110101=>1010111
[4,5,1,6,2,3,7,8]=>[8,7,3,2,6,1,5,4]=>1111001=>1001111
[4,1,5,6,2,7,3,8]=>[8,3,7,2,6,5,1,4]=>1110100=>0010111
[4,5,1,6,2,7,3,8]=>[8,3,7,2,6,1,5,4]=>1111000=>0001111
[4,5,6,1,2,7,3,8]=>[8,3,7,2,1,6,5,4]=>1111100=>0011111
[4,1,5,6,7,2,3,8]=>[8,3,2,7,6,5,1,4]=>1110110=>0110111
[4,5,1,6,7,2,3,8]=>[8,3,2,7,6,1,5,4]=>1111010=>0101111
[4,5,6,1,7,2,3,8]=>[8,3,2,7,1,6,5,4]=>1111100=>0011111
[4,1,5,2,6,7,8,3]=>[3,8,7,6,2,5,1,4]=>1100011=>1100011
[4,5,1,2,6,7,8,3]=>[3,8,7,6,2,1,5,4]=>1101011=>1101011
[4,1,5,6,2,7,8,3]=>[3,8,7,2,6,5,1,4]=>1100101=>1010011
[4,5,1,6,2,7,8,3]=>[3,8,7,2,6,1,5,4]=>1101001=>1001011
[4,5,6,1,2,7,8,3]=>[3,8,7,2,1,6,5,4]=>1101101=>1011011
[4,1,5,6,7,2,8,3]=>[3,8,2,7,6,5,1,4]=>1100110=>0110011
[4,5,1,6,7,2,8,3]=>[3,8,2,7,6,1,5,4]=>1101010=>0101011
[4,5,6,1,7,2,8,3]=>[3,8,2,7,1,6,5,4]=>1101100=>0011011
[4,5,6,7,1,2,8,3]=>[3,8,2,1,7,6,5,4]=>1101110=>0111011
[4,1,5,6,7,8,2,3]=>[3,2,8,7,6,5,1,4]=>1100111=>1110011
[4,5,1,6,7,8,2,3]=>[3,2,8,7,6,1,5,4]=>1101011=>1101011
[4,5,6,1,7,8,2,3]=>[3,2,8,7,1,6,5,4]=>1101101=>1011011
[4,5,6,7,1,8,2,3]=>[3,2,8,1,7,6,5,4]=>1101110=>0111011
[4,1,5,2,7,3,8,6]=>[6,8,3,7,2,5,1,4]=>1110000=>0000111
[4,5,1,2,7,3,8,6]=>[6,8,3,7,2,1,5,4]=>1111000=>0001111
[4,1,5,7,2,3,8,6]=>[6,8,3,2,7,5,1,4]=>1110100=>0010111
[4,5,1,7,2,3,8,6]=>[6,8,3,2,7,1,5,4]=>1111000=>0001111
[4,1,5,2,7,8,3,6]=>[6,3,8,7,2,5,1,4]=>1110001=>1000111
[4,1,5,7,2,8,3,6]=>[6,3,8,2,7,5,1,4]=>1110100=>0010111
[4,5,1,7,2,8,3,6]=>[6,3,8,2,7,1,5,4]=>1111000=>0001111
[4,5,7,1,2,8,3,6]=>[6,3,8,2,1,7,5,4]=>1111100=>0011111
[4,5,1,7,8,2,3,6]=>[6,3,2,8,7,1,5,4]=>1111001=>1001111
[4,5,7,1,8,2,3,6]=>[6,3,2,8,1,7,5,4]=>1111100=>0011111
[4,1,5,2,7,3,6,8]=>[8,6,3,7,2,5,1,4]=>1110010=>0100111
[4,5,1,2,7,3,6,8]=>[8,6,3,7,2,1,5,4]=>1111010=>0101111
[4,1,5,7,2,3,6,8]=>[8,6,3,2,7,5,1,4]=>1110110=>0110111
[4,1,2,5,3,7,6,8]=>[8,6,7,3,5,2,1,4]=>1110010=>0100111
[1,4,2,5,3,7,6,8]=>[8,6,7,3,5,2,4,1]=>1110010=>0100111
[4,1,2,5,7,3,6,8]=>[8,6,3,7,5,2,1,4]=>1110110=>0110111
[1,4,2,5,7,3,6,8]=>[8,6,3,7,5,2,4,1]=>1110110=>0110111
[4,1,5,2,3,7,8,6]=>[6,8,7,3,2,5,1,4]=>1110001=>1000111
[4,5,1,2,3,7,8,6]=>[6,8,7,3,2,1,5,4]=>1111001=>1001111
[4,1,2,5,3,7,8,6]=>[6,8,7,3,5,2,1,4]=>1110001=>1000111
[1,4,2,5,3,7,8,6]=>[6,8,7,3,5,2,4,1]=>1110001=>1000111
[4,1,2,5,7,3,8,6]=>[6,8,3,7,5,2,1,4]=>1110100=>0010111
[1,4,2,5,7,3,8,6]=>[6,8,3,7,5,2,4,1]=>1110100=>0010111
[1,4,5,2,7,3,8,6]=>[6,8,3,7,2,5,4,1]=>1111000=>0001111
[1,4,5,7,2,3,8,6]=>[6,8,3,2,7,5,4,1]=>1111100=>0011111
[4,1,2,5,7,8,3,6]=>[6,3,8,7,5,2,1,4]=>1110101=>1010111
[1,4,5,7,8,2,3,6]=>[6,3,2,8,7,5,4,1]=>1111101=>1011111
[4,1,5,2,8,3,6,7]=>[7,6,3,8,2,5,1,4]=>1110010=>0100111
[4,5,1,2,8,3,6,7]=>[7,6,3,8,2,1,5,4]=>1111010=>0101111
[4,1,5,8,2,3,6,7]=>[7,6,3,2,8,5,1,4]=>1110110=>0110111
[4,5,8,1,2,3,6,7]=>[7,6,3,2,1,8,5,4]=>1111110=>0111111
[4,5,1,2,3,8,6,7]=>[7,6,8,3,2,1,5,4]=>1111010=>0101111
[4,1,2,5,3,8,6,7]=>[7,6,8,3,5,2,1,4]=>1110010=>0100111
[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>1110010=>0100111
[4,1,2,5,8,3,6,7]=>[7,6,3,8,5,2,1,4]=>1110110=>0110111
[4,1,2,5,6,3,8,7]=>[7,8,3,6,5,2,1,4]=>1110100=>0010111
[1,4,5,6,8,2,3,7]=>[7,3,2,8,6,5,4,1]=>1111110=>0111111
[4,1,5,2,3,6,7,8]=>[8,7,6,3,2,5,1,4]=>1110011=>1100111
[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>1110011=>1100111
[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>1111011=>1101111
[4,1,2,5,6,3,7,8]=>[8,7,3,6,5,2,1,4]=>1110101=>1010111
[1,4,2,5,6,3,7,8]=>[8,7,3,6,5,2,4,1]=>1110101=>1010111
[1,4,5,2,6,3,7,8]=>[8,7,3,6,2,5,4,1]=>1111001=>1001111
[1,4,2,5,6,7,3,8]=>[8,3,7,6,5,2,4,1]=>1110110=>0110111
[1,4,5,6,2,7,3,8]=>[8,3,7,2,6,5,4,1]=>1111100=>0011111
[1,4,5,6,7,2,3,8]=>[8,3,2,7,6,5,4,1]=>1111110=>0111111
[4,1,2,5,6,7,8,3]=>[3,8,7,6,5,2,1,4]=>1100111=>1110011
[1,4,2,5,6,7,8,3]=>[3,8,7,6,5,2,4,1]=>1100111=>1110011
[1,4,5,6,2,7,8,3]=>[3,8,7,2,6,5,4,1]=>1101101=>1011011
[1,4,5,6,7,2,8,3]=>[3,8,2,7,6,5,4,1]=>1101110=>0111011
[1,4,5,6,7,8,2,3]=>[3,2,8,7,6,5,4,1]=>1101111=>1111011
[4,1,6,2,7,3,8,5]=>[5,8,3,7,2,6,1,4]=>1110000=>0000111
[4,6,1,2,7,3,8,5]=>[5,8,3,7,2,1,6,4]=>1111000=>0001111
[4,1,6,7,2,3,8,5]=>[5,8,3,2,7,6,1,4]=>1110010=>0100111
[4,6,1,7,2,3,8,5]=>[5,8,3,2,7,1,6,4]=>1111000=>0001111
[4,6,7,1,2,3,8,5]=>[5,8,3,2,1,7,6,4]=>1111010=>0101111
[4,6,1,2,7,8,3,5]=>[5,3,8,7,2,1,6,4]=>1111001=>1001111
[4,1,6,7,2,8,3,5]=>[5,3,8,2,7,6,1,4]=>1110010=>0100111
[4,6,1,7,2,8,3,5]=>[5,3,8,2,7,1,6,4]=>1111000=>0001111
[4,6,7,1,2,8,3,5]=>[5,3,8,2,1,7,6,4]=>1111010=>0101111
[4,6,1,7,8,2,3,5]=>[5,3,2,8,7,1,6,4]=>1111001=>1001111
[4,6,7,1,8,2,3,5]=>[5,3,2,8,1,7,6,4]=>1111010=>0101111
[4,1,6,2,7,3,5,8]=>[8,5,3,7,2,6,1,4]=>1110100=>0010111
[4,6,1,2,7,3,5,8]=>[8,5,3,7,2,1,6,4]=>1111100=>0011111
[4,1,6,7,2,3,5,8]=>[8,5,3,2,7,6,1,4]=>1110110=>0110111
[4,6,1,7,2,3,5,8]=>[8,5,3,2,7,1,6,4]=>1111100=>0011111
[4,6,1,2,3,7,5,8]=>[8,5,7,3,2,1,6,4]=>1111100=>0011111
[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>1110100=>0010111
[1,4,2,6,7,3,5,8]=>[8,5,3,7,6,2,4,1]=>1110110=>0110111
[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>1111100=>0011111
[4,1,6,2,3,7,8,5]=>[5,8,7,3,2,6,1,4]=>1110001=>1000111
[4,6,1,2,3,7,8,5]=>[5,8,7,3,2,1,6,4]=>1111001=>1001111
[1,4,6,2,3,7,8,5]=>[5,8,7,3,2,6,4,1]=>1111001=>1001111
[4,1,2,6,7,3,8,5]=>[5,8,3,7,6,2,1,4]=>1110010=>0100111
[1,4,2,6,7,3,8,5]=>[5,8,3,7,6,2,4,1]=>1110010=>0100111
[1,4,6,2,7,3,8,5]=>[5,8,3,7,2,6,4,1]=>1111000=>0001111
[1,4,6,7,2,3,8,5]=>[5,8,3,2,7,6,4,1]=>1111010=>0101111
[4,1,2,6,7,8,3,5]=>[5,3,8,7,6,2,1,4]=>1110011=>1100111
[1,4,2,6,7,8,3,5]=>[5,3,8,7,6,2,4,1]=>1110011=>1100111
[1,4,6,2,7,8,3,5]=>[5,3,8,7,2,6,4,1]=>1111001=>1001111
[1,4,6,7,2,8,3,5]=>[5,3,8,2,7,6,4,1]=>1111010=>0101111
[1,4,6,7,8,2,3,5]=>[5,3,2,8,7,6,4,1]=>1111011=>1101111
[4,1,6,2,8,3,5,7]=>[7,5,3,8,2,6,1,4]=>1110100=>0010111
[4,6,1,2,8,3,5,7]=>[7,5,3,8,2,1,6,4]=>1111100=>0011111
[4,1,6,8,2,3,5,7]=>[7,5,3,2,8,6,1,4]=>1110110=>0110111
[4,6,1,8,2,3,5,7]=>[7,5,3,2,8,1,6,4]=>1111100=>0011111
[4,6,8,1,2,3,5,7]=>[7,5,3,2,1,8,6,4]=>1111110=>0111111
[4,1,6,2,3,8,5,7]=>[7,5,8,3,2,6,1,4]=>1110100=>0010111
[4,6,1,2,3,8,5,7]=>[7,5,8,3,2,1,6,4]=>1111100=>0011111
[4,1,2,6,3,8,5,7]=>[7,5,8,3,6,2,1,4]=>1110100=>0010111
[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>1110100=>0010111
[1,4,2,6,8,3,5,7]=>[7,5,3,8,6,2,4,1]=>1110110=>0110111
[1,4,6,2,8,3,5,7]=>[7,5,3,8,2,6,4,1]=>1111100=>0011111
[1,4,6,8,2,3,5,7]=>[7,5,3,2,8,6,4,1]=>1111110=>0111111
[4,1,6,2,3,5,8,7]=>[7,8,5,3,2,6,1,4]=>1110100=>0010111
[4,6,1,2,3,5,8,7]=>[7,8,5,3,2,1,6,4]=>1111100=>0011111
[4,1,2,6,3,5,8,7]=>[7,8,5,3,6,2,1,4]=>1110100=>0010111
[4,1,2,3,6,5,8,7]=>[7,8,5,6,3,2,1,4]=>1110100=>0010111
[1,2,4,6,3,5,8,7]=>[7,8,5,3,6,4,2,1]=>1111100=>0011111
[4,1,2,3,6,8,5,7]=>[7,5,8,6,3,2,1,4]=>1110110=>0110111
[1,4,2,3,6,8,5,7]=>[7,5,8,6,3,2,4,1]=>1110110=>0110111
[1,2,4,3,6,8,5,7]=>[7,5,8,6,3,4,2,1]=>1110110=>0110111
[4,1,6,2,3,5,7,8]=>[8,7,5,3,2,6,1,4]=>1110101=>1010111
[4,6,1,2,3,5,7,8]=>[8,7,5,3,2,1,6,4]=>1111101=>1011111
[1,4,2,6,3,5,7,8]=>[8,7,5,3,6,2,4,1]=>1110101=>1010111
[1,4,6,2,3,5,7,8]=>[8,7,5,3,2,6,4,1]=>1111101=>1011111
[4,1,2,3,6,5,7,8]=>[8,7,5,6,3,2,1,4]=>1110101=>1010111
[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>1111101=>1011111
[4,1,2,3,6,7,5,8]=>[8,5,7,6,3,2,1,4]=>1110110=>0110111
[1,2,4,6,3,7,5,8]=>[8,5,7,3,6,4,2,1]=>1111100=>0011111
[4,1,2,3,6,7,8,5]=>[5,8,7,6,3,2,1,4]=>1110011=>1100111
[1,4,2,3,6,7,8,5]=>[5,8,7,6,3,2,4,1]=>1110011=>1100111
[1,2,4,6,3,7,8,5]=>[5,8,7,3,6,4,2,1]=>1111001=>1001111
[4,1,7,2,8,3,5,6]=>[6,5,3,8,2,7,1,4]=>1110100=>0010111
[4,7,1,2,8,3,5,6]=>[6,5,3,8,2,1,7,4]=>1111100=>0011111
[4,1,7,8,2,3,5,6]=>[6,5,3,2,8,7,1,4]=>1110101=>1010111
[4,7,1,8,2,3,5,6]=>[6,5,3,2,8,1,7,4]=>1111100=>0011111
[4,7,8,1,2,3,5,6]=>[6,5,3,2,1,8,7,4]=>1111101=>1011111
[4,7,1,2,3,8,5,6]=>[6,5,8,3,2,1,7,4]=>1111100=>0011111
[1,4,2,7,3,8,5,6]=>[6,5,8,3,7,2,4,1]=>1110100=>0010111
[4,1,2,7,8,3,5,6]=>[6,5,3,8,7,2,1,4]=>1110101=>1010111
[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>1110101=>1010111
[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>1111100=>0011111
[4,1,2,7,3,5,8,6]=>[6,8,5,3,7,2,1,4]=>1110100=>0010111
[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>1110100=>0010111
[4,1,2,3,7,5,8,6]=>[6,8,5,7,3,2,1,4]=>1110100=>0010111
[1,2,4,3,7,5,8,6]=>[6,8,5,7,3,4,2,1]=>1110100=>0010111
[4,1,2,3,7,8,5,6]=>[6,5,8,7,3,2,1,4]=>1110101=>1010111
[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>1110101=>1010111
[1,2,4,3,7,8,5,6]=>[6,5,8,7,3,4,2,1]=>1110101=>1010111
[1,2,4,7,3,8,5,6]=>[6,5,8,3,7,4,2,1]=>1111100=>0011111
[4,7,1,2,3,5,6,8]=>[8,6,5,3,2,1,7,4]=>1111110=>0111111
[4,1,2,7,3,5,6,8]=>[8,6,5,3,7,2,1,4]=>1110110=>0110111
[1,4,2,7,3,5,6,8]=>[8,6,5,3,7,2,4,1]=>1110110=>0110111
[4,1,2,3,7,5,6,8]=>[8,6,5,7,3,2,1,4]=>1110110=>0110111
[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>1110110=>0110111
[4,1,2,3,5,7,6,8]=>[8,6,7,5,3,2,1,4]=>1110110=>0110111
[1,4,2,3,5,7,6,8]=>[8,6,7,5,3,2,4,1]=>1110110=>0110111
[4,1,2,3,5,7,8,6]=>[6,8,7,5,3,2,1,4]=>1110101=>1010111
[1,4,2,3,5,7,8,6]=>[6,8,7,5,3,2,4,1]=>1110101=>1010111
[1,2,4,5,7,8,3,6]=>[6,3,8,7,5,4,2,1]=>1111101=>1011111
[4,1,2,3,8,5,6,7]=>[7,6,5,8,3,2,1,4]=>1110110=>0110111
[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>1110110=>0110111
[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>1110110=>0110111
[4,1,2,3,5,8,6,7]=>[7,6,8,5,3,2,1,4]=>1110110=>0110111
[1,4,2,3,5,8,6,7]=>[7,6,8,5,3,2,4,1]=>1110110=>0110111
[1,2,4,3,5,8,6,7]=>[7,6,8,5,3,4,2,1]=>1110110=>0110111
[1,2,4,5,8,3,6,7]=>[7,6,3,8,5,4,2,1]=>1111110=>0111111
[4,1,2,3,5,6,8,7]=>[7,8,6,5,3,2,1,4]=>1110110=>0110111
[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>1110110=>0110111
[1,4,2,3,5,6,7,8]=>[8,7,6,5,3,2,4,1]=>1110111=>1110111
[5,1,6,2,7,3,8,4]=>[4,8,3,7,2,6,1,5]=>1110000=>0000111
[5,6,1,2,7,3,8,4]=>[4,8,3,7,2,1,6,5]=>1110100=>0010111
[5,1,6,7,2,3,8,4]=>[4,8,3,2,7,6,1,5]=>1110010=>0100111
[5,6,7,1,2,3,8,4]=>[4,8,3,2,1,7,6,5]=>1110110=>0110111
[5,1,6,2,7,8,3,4]=>[4,3,8,7,2,6,1,5]=>1110001=>1000111
[5,1,6,7,2,8,3,4]=>[4,3,8,2,7,6,1,5]=>1110010=>0100111
[5,6,1,7,2,8,3,4]=>[4,3,8,2,7,1,6,5]=>1110100=>0010111
[5,1,6,7,8,2,3,4]=>[4,3,2,8,7,6,1,5]=>1110011=>1100111
[5,1,6,2,7,3,4,8]=>[8,4,3,7,2,6,1,5]=>1111000=>0001111
[5,1,6,7,2,3,4,8]=>[8,4,3,2,7,6,1,5]=>1111010=>0101111
[5,1,2,6,3,7,4,8]=>[8,4,7,3,6,2,1,5]=>1111000=>0001111
[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>1111000=>0001111
[5,1,2,6,7,3,4,8]=>[8,4,3,7,6,2,1,5]=>1111010=>0101111
[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>1111110=>0111111
[5,1,6,2,3,7,8,4]=>[4,8,7,3,2,6,1,5]=>1110001=>1000111
[5,6,1,2,3,7,8,4]=>[4,8,7,3,2,1,6,5]=>1110101=>1010111
[5,1,2,6,3,7,8,4]=>[4,8,7,3,6,2,1,5]=>1110001=>1000111
[1,5,2,6,3,7,8,4]=>[4,8,7,3,6,2,5,1]=>1110001=>1000111
[1,5,6,2,3,7,8,4]=>[4,8,7,3,2,6,5,1]=>1110101=>1010111
[1,5,2,6,7,3,8,4]=>[4,8,3,7,6,2,5,1]=>1110010=>0100111
[1,5,6,7,2,3,8,4]=>[4,8,3,2,7,6,5,1]=>1110110=>0110111
[5,1,2,6,7,8,3,4]=>[4,3,8,7,6,2,1,5]=>1110011=>1100111
[1,5,2,6,7,8,3,4]=>[4,3,8,7,6,2,5,1]=>1110011=>1100111
[1,5,6,2,7,8,3,4]=>[4,3,8,7,2,6,5,1]=>1110101=>1010111
[1,5,6,7,2,8,3,4]=>[4,3,8,2,7,6,5,1]=>1110110=>0110111
[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>1110111=>1110111
[5,1,6,2,8,3,4,7]=>[7,4,3,8,2,6,1,5]=>1111000=>0001111
[5,1,6,8,2,3,4,7]=>[7,4,3,2,8,6,1,5]=>1111010=>0101111
[5,6,1,8,2,3,4,7]=>[7,4,3,2,8,1,6,5]=>1111100=>0011111
[5,6,8,1,2,3,4,7]=>[7,4,3,2,1,8,6,5]=>1111110=>0111111
[5,1,6,2,3,8,4,7]=>[7,4,8,3,2,6,1,5]=>1111000=>0001111
[5,6,1,2,3,8,4,7]=>[7,4,8,3,2,1,6,5]=>1111100=>0011111
[5,1,2,6,3,8,4,7]=>[7,4,8,3,6,2,1,5]=>1111000=>0001111
[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>1111000=>0001111
[1,5,6,2,3,8,4,7]=>[7,4,8,3,2,6,5,1]=>1111100=>0011111
[5,1,2,6,8,3,4,7]=>[7,4,3,8,6,2,1,5]=>1111010=>0101111
[1,5,2,6,8,3,4,7]=>[7,4,3,8,6,2,5,1]=>1111010=>0101111
[5,6,1,2,3,4,8,7]=>[7,8,4,3,2,1,6,5]=>1111100=>0011111
[5,1,2,6,3,4,8,7]=>[7,8,4,3,6,2,1,5]=>1111000=>0001111
[1,5,2,6,3,4,8,7]=>[7,8,4,3,6,2,5,1]=>1111000=>0001111
[1,2,5,6,3,4,8,7]=>[7,8,4,3,6,5,2,1]=>1111100=>0011111
[1,5,2,3,6,8,4,7]=>[7,4,8,6,3,2,5,1]=>1111010=>0101111
[1,2,5,6,3,8,4,7]=>[7,4,8,3,6,5,2,1]=>1111100=>0011111
[5,1,6,2,3,4,7,8]=>[8,7,4,3,2,6,1,5]=>1111001=>1001111
[5,1,2,6,3,4,7,8]=>[8,7,4,3,6,2,1,5]=>1111001=>1001111
[1,5,2,6,3,4,7,8]=>[8,7,4,3,6,2,5,1]=>1111001=>1001111
[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>1111001=>1001111
[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>1111101=>1011111
[5,1,2,3,6,7,4,8]=>[8,4,7,6,3,2,1,5]=>1111010=>0101111
[1,2,5,3,6,7,4,8]=>[8,4,7,6,3,5,2,1]=>1111010=>0101111
[1,2,5,6,3,7,4,8]=>[8,4,7,3,6,5,2,1]=>1111100=>0011111
[5,1,2,3,6,7,8,4]=>[4,8,7,6,3,2,1,5]=>1110011=>1100111
[1,5,2,3,6,7,8,4]=>[4,8,7,6,3,2,5,1]=>1110011=>1100111
[1,2,5,3,6,7,8,4]=>[4,8,7,6,3,5,2,1]=>1110011=>1100111
[1,2,5,6,3,7,8,4]=>[4,8,7,3,6,5,2,1]=>1110101=>1010111
[1,2,5,6,7,3,8,4]=>[4,8,3,7,6,5,2,1]=>1110110=>0110111
[5,1,7,2,8,3,4,6]=>[6,4,3,8,2,7,1,5]=>1111000=>0001111
[5,7,1,8,2,3,4,6]=>[6,4,3,2,8,1,7,5]=>1111100=>0011111
[5,7,8,1,2,3,4,6]=>[6,4,3,2,1,8,7,5]=>1111101=>1011111
[5,1,7,2,3,8,4,6]=>[6,4,8,3,2,7,1,5]=>1111000=>0001111
[5,1,2,7,3,8,4,6]=>[6,4,8,3,7,2,1,5]=>1111000=>0001111
[1,5,2,7,3,8,4,6]=>[6,4,8,3,7,2,5,1]=>1111000=>0001111
[5,1,2,7,8,3,4,6]=>[6,4,3,8,7,2,1,5]=>1111001=>1001111
[1,5,2,7,8,3,4,6]=>[6,4,3,8,7,2,5,1]=>1111001=>1001111
[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>1111100=>0011111
[5,1,7,2,3,4,8,6]=>[6,8,4,3,2,7,1,5]=>1111000=>0001111
[5,7,1,2,3,4,8,6]=>[6,8,4,3,2,1,7,5]=>1111100=>0011111
[5,1,2,7,3,4,8,6]=>[6,8,4,3,7,2,1,5]=>1111000=>0001111
[1,5,7,2,3,4,8,6]=>[6,8,4,3,2,7,5,1]=>1111100=>0011111
[5,1,2,3,7,4,8,6]=>[6,8,4,7,3,2,1,5]=>1111000=>0001111
[1,5,2,3,7,4,8,6]=>[6,8,4,7,3,2,5,1]=>1111000=>0001111
[1,2,5,3,7,4,8,6]=>[6,8,4,7,3,5,2,1]=>1111000=>0001111
[1,2,5,7,3,4,8,6]=>[6,8,4,3,7,5,2,1]=>1111100=>0011111
[5,1,2,3,7,8,4,6]=>[6,4,8,7,3,2,1,5]=>1111001=>1001111
[1,2,5,3,7,8,4,6]=>[6,4,8,7,3,5,2,1]=>1111001=>1001111
[1,2,5,7,3,8,4,6]=>[6,4,8,3,7,5,2,1]=>1111100=>0011111
[5,7,1,2,3,4,6,8]=>[8,6,4,3,2,1,7,5]=>1111110=>0111111
[5,1,2,7,3,4,6,8]=>[8,6,4,3,7,2,1,5]=>1111010=>0101111
[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>1111010=>0101111
[1,2,5,7,3,4,6,8]=>[8,6,4,3,7,5,2,1]=>1111110=>0111111
[5,1,2,3,4,7,6,8]=>[8,6,7,4,3,2,1,5]=>1111010=>0101111
[1,5,2,3,4,7,6,8]=>[8,6,7,4,3,2,5,1]=>1111010=>0101111
[1,2,3,5,7,4,6,8]=>[8,6,4,7,5,3,2,1]=>1111110=>0111111
[5,1,2,3,4,7,8,6]=>[6,8,7,4,3,2,1,5]=>1111001=>1001111
[1,5,2,3,4,7,8,6]=>[6,8,7,4,3,2,5,1]=>1111001=>1001111
[5,1,8,2,3,4,6,7]=>[7,6,4,3,2,8,1,5]=>1111010=>0101111
[5,8,1,2,3,4,6,7]=>[7,6,4,3,2,1,8,5]=>1111110=>0111111
[5,1,2,8,3,4,6,7]=>[7,6,4,3,8,2,1,5]=>1111010=>0101111
[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>1111010=>0101111
[1,2,5,8,3,4,6,7]=>[7,6,4,3,8,5,2,1]=>1111110=>0111111
[5,1,2,3,4,8,6,7]=>[7,6,8,4,3,2,1,5]=>1111010=>0101111
[1,5,2,3,4,8,6,7]=>[7,6,8,4,3,2,5,1]=>1111010=>0101111
[1,2,5,3,4,8,6,7]=>[7,6,8,4,3,5,2,1]=>1111010=>0101111
[1,2,3,5,4,8,6,7]=>[7,6,8,4,5,3,2,1]=>1111010=>0101111
[5,1,2,3,4,6,8,7]=>[7,8,6,4,3,2,1,5]=>1111010=>0101111
[1,5,2,3,4,6,8,7]=>[7,8,6,4,3,2,5,1]=>1111010=>0101111
[1,2,5,3,4,6,8,7]=>[7,8,6,4,3,5,2,1]=>1111010=>0101111
[1,2,3,5,6,8,4,7]=>[7,4,8,6,5,3,2,1]=>1111110=>0111111
[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>1111011=>1101111
[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>1111011=>1101111
[6,7,1,2,8,3,4,5]=>[5,4,3,8,2,1,7,6]=>1111010=>0101111
[6,1,7,8,2,3,4,5]=>[5,4,3,2,8,7,1,6]=>1111001=>1001111
[6,7,1,8,2,3,4,5]=>[5,4,3,2,8,1,7,6]=>1111010=>0101111
[6,1,7,2,3,8,4,5]=>[5,4,8,3,2,7,1,6]=>1111000=>0001111
[6,7,1,2,3,8,4,5]=>[5,4,8,3,2,1,7,6]=>1111010=>0101111
[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>1111000=>0001111
[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>1111010=>0101111
[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>1111010=>0101111
[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>1111011=>1101111
[6,7,1,2,3,4,8,5]=>[5,8,4,3,2,1,7,6]=>1111010=>0101111
[1,6,7,2,3,4,8,5]=>[5,8,4,3,2,7,6,1]=>1111010=>0101111
[1,2,6,3,7,4,8,5]=>[5,8,4,7,3,6,2,1]=>1111000=>0001111
[1,2,6,7,3,4,8,5]=>[5,8,4,3,7,6,2,1]=>1111010=>0101111
[6,1,2,3,7,8,4,5]=>[5,4,8,7,3,2,1,6]=>1111001=>1001111
[6,1,7,2,3,4,5,8]=>[8,5,4,3,2,7,1,6]=>1111100=>0011111
[6,1,2,7,3,4,5,8]=>[8,5,4,3,7,2,1,6]=>1111100=>0011111
[1,6,2,7,3,4,5,8]=>[8,5,4,3,7,2,6,1]=>1111100=>0011111
[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>1111110=>0111111
[1,2,6,7,3,4,5,8]=>[8,5,4,3,7,6,2,1]=>1111110=>0111111
[6,1,2,3,4,7,5,8]=>[8,5,7,4,3,2,1,6]=>1111100=>0011111
[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>1111100=>0011111
[1,2,6,3,4,7,5,8]=>[8,5,7,4,3,6,2,1]=>1111100=>0011111
[1,2,3,6,4,7,5,8]=>[8,5,7,4,6,3,2,1]=>1111100=>0011111
[6,1,2,3,4,7,8,5]=>[5,8,7,4,3,2,1,6]=>1111001=>1001111
[1,2,6,3,4,7,8,5]=>[5,8,7,4,3,6,2,1]=>1111001=>1001111
[6,1,8,2,3,4,5,7]=>[7,5,4,3,2,8,1,6]=>1111100=>0011111
[6,1,2,8,3,4,5,7]=>[7,5,4,3,8,2,1,6]=>1111100=>0011111
[1,6,8,2,3,4,5,7]=>[7,5,4,3,2,8,6,1]=>1111110=>0111111
[1,6,2,3,8,4,5,7]=>[7,5,4,8,3,2,6,1]=>1111100=>0011111
[1,2,6,3,8,4,5,7]=>[7,5,4,8,3,6,2,1]=>1111100=>0011111
[6,1,2,3,4,8,5,7]=>[7,5,8,4,3,2,1,6]=>1111100=>0011111
[1,6,2,3,4,8,5,7]=>[7,5,8,4,3,2,6,1]=>1111100=>0011111
[1,2,6,3,4,8,5,7]=>[7,5,8,4,3,6,2,1]=>1111100=>0011111
[1,2,3,6,4,8,5,7]=>[7,5,8,4,6,3,2,1]=>1111100=>0011111
[6,1,2,3,4,5,8,7]=>[7,8,5,4,3,2,1,6]=>1111100=>0011111
[1,2,6,3,4,5,8,7]=>[7,8,5,4,3,6,2,1]=>1111100=>0011111
[1,2,3,4,6,8,5,7]=>[7,5,8,6,4,3,2,1]=>1111110=>0111111
[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>1111101=>1011111
[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>1111101=>1011111
[7,1,8,2,3,4,5,6]=>[6,5,4,3,2,8,1,7]=>1111100=>0011111
[7,1,2,8,3,4,5,6]=>[6,5,4,3,8,2,1,7]=>1111100=>0011111
[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>1111100=>0011111
[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>1111101=>1011111
[7,1,2,3,4,8,5,6]=>[6,5,8,4,3,2,1,7]=>1111100=>0011111
[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>1111100=>0011111
[7,1,2,3,4,5,8,6]=>[6,8,5,4,3,2,1,7]=>1111100=>0011111
[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>1111100=>0011111
[1,2,3,4,7,5,8,6]=>[6,8,5,7,4,3,2,1]=>1111100=>0011111
[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>1111101=>1011111
[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>1111110=>0111111
[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>1111110=>0111111
[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>1111110=>0111111
[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>1111110=>0111111
[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>1111110=>0111111
[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>1111110=>0111111
[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>1111110=>0111111
[5,3,2,6,1,4,8,7]=>[7,8,4,1,6,2,3,5]=>1101000=>0001011
[7,3,2,5,4,8,1,6]=>[6,1,8,4,5,2,3,7]=>1101000=>0001011
[8,4,5,2,3,7,6,1]=>[1,6,7,3,2,5,4,8]=>0111000=>0001110
[7,4,5,2,3,8,1,6]=>[6,1,8,3,2,5,4,7]=>1111000=>0001111
[6,4,5,2,3,1,8,7]=>[7,8,1,3,2,5,4,6]=>1101000=>0001011
[5,4,6,2,1,3,8,7]=>[7,8,3,1,2,6,4,5]=>1011000=>0001101
[3,6,1,5,4,2,8,7]=>[7,8,2,4,5,1,6,3]=>1110000=>0000111
[4,6,5,1,3,2,8,7]=>[7,8,2,3,1,5,6,4]=>1101000=>0001011
[5,6,4,3,1,2,8,7]=>[7,8,2,1,3,4,6,5]=>1100100=>0010011
[7,5,4,3,2,8,1,6]=>[6,1,8,2,3,4,5,7]=>1100000=>0000011
[8,6,4,3,7,2,5,1]=>[1,5,2,7,3,4,6,8]=>0110000=>0000110
[7,6,4,3,8,2,1,5]=>[5,1,2,8,3,4,6,7]=>1010000=>0000101
[6,7,4,3,8,1,2,5]=>[5,2,1,8,3,4,7,6]=>1110010=>0100111
[5,7,4,3,1,8,2,6]=>[6,2,8,1,3,4,7,5]=>1100100=>0010011
[4,7,5,1,3,8,2,6]=>[6,2,8,3,1,5,7,4]=>1111000=>0001111
[3,7,1,5,4,8,2,6]=>[6,2,8,4,5,1,7,3]=>1111000=>0001111
[2,1,7,5,4,8,3,6]=>[6,3,8,4,5,7,1,2]=>1011000=>0001101
[3,8,1,5,4,7,6,2]=>[2,6,7,4,5,1,8,3]=>1011000=>0001101
[4,8,5,1,3,7,6,2]=>[2,6,7,3,1,5,8,4]=>1011000=>0001101
[5,8,4,3,1,7,6,2]=>[2,6,7,1,3,4,8,5]=>1000100=>0010001
[6,8,4,3,7,1,5,2]=>[2,5,1,7,3,4,8,6]=>1010010=>0100101
[7,8,4,3,6,5,1,2]=>[2,1,5,6,3,4,8,7]=>1010001=>1000101
[6,8,5,7,3,1,4,2]=>[2,4,1,3,7,5,8,6]=>1000110=>0110001
[5,8,6,7,1,3,4,2]=>[2,4,3,1,7,6,8,5]=>1010110=>0110101
[4,8,6,1,7,3,5,2]=>[2,5,3,7,1,6,8,4]=>1011000=>0001101
[3,8,1,6,7,4,5,2]=>[2,5,4,7,6,1,8,3]=>1011010=>0101101
[2,1,8,6,7,4,5,3]=>[3,5,4,7,6,8,1,2]=>1001010=>0101001
[2,1,7,6,8,4,3,5]=>[5,3,4,8,6,7,1,2]=>1010010=>0100101
[3,7,1,6,8,4,2,5]=>[5,2,4,8,6,1,7,3]=>1110010=>0100111
[4,7,6,1,8,3,2,5]=>[5,2,3,8,1,6,7,4]=>1101000=>0001011
[5,7,6,8,1,3,2,4]=>[4,2,3,1,8,6,7,5]=>1100110=>0110011
[5,4,7,2,1,8,3,6]=>[6,3,8,1,2,7,4,5]=>1011000=>0001101
[6,4,7,2,8,1,3,5]=>[5,3,1,8,2,7,4,6]=>1111000=>0001111
[7,4,6,2,8,3,1,5]=>[5,1,3,8,2,6,4,7]=>1101000=>0001011
[8,4,6,2,7,3,5,1]=>[1,5,3,7,2,6,4,8]=>0111000=>0001110
[8,3,2,6,7,4,5,1]=>[1,5,4,7,6,2,3,8]=>0101010=>0101010
[7,3,2,6,8,4,1,5]=>[5,1,4,8,6,2,3,7]=>1100010=>0100011
[6,3,2,7,8,1,4,5]=>[5,4,1,8,7,2,3,6]=>1101001=>1001011
[5,3,2,7,1,8,4,6]=>[6,4,8,1,7,2,3,5]=>1101000=>0001011
[4,3,2,1,7,8,5,6]=>[6,5,8,7,1,2,3,4]=>1000101=>1010001
[3,4,1,2,8,7,6,5]=>[5,6,7,8,2,1,4,3]=>1110000=>0000111
[5,3,2,8,1,7,6,4]=>[4,6,7,1,8,2,3,5]=>1100000=>0000011
[6,3,2,8,7,1,5,4]=>[4,5,1,7,8,2,3,6]=>1100000=>0000011
[7,3,2,8,6,5,1,4]=>[4,1,5,6,8,2,3,7]=>1100000=>0000011
[8,4,7,2,6,5,3,1]=>[1,3,5,6,2,7,4,8]=>0101000=>0001010
[7,4,8,2,6,5,1,3]=>[3,1,5,6,2,8,4,7]=>1101000=>0001011
[6,4,8,2,7,1,5,3]=>[3,5,1,7,2,8,4,6]=>1101000=>0001011
[5,4,8,2,1,7,6,3]=>[3,6,7,1,2,8,4,5]=>1001000=>0001001
[4,5,8,1,2,7,6,3]=>[3,6,7,2,1,8,5,4]=>1101100=>0011011
[3,5,1,8,2,7,6,4]=>[4,6,7,2,8,1,5,3]=>1110000=>0000111
[2,1,5,8,3,7,6,4]=>[4,6,7,3,8,5,1,2]=>1010100=>0010101
[2,1,6,8,7,3,5,4]=>[4,5,3,7,8,6,1,2]=>1010010=>0100101
[3,6,1,8,7,2,5,4]=>[4,5,2,7,8,1,6,3]=>1110000=>0000111
[4,6,8,1,7,2,5,3]=>[3,5,2,7,1,8,6,4]=>1101010=>0101011
[5,6,8,7,1,2,4,3]=>[3,4,2,1,7,8,6,5]=>1100110=>0110011
[6,5,8,7,2,1,4,3]=>[3,4,1,2,7,8,5,6]=>1000100=>0010001
[7,5,8,6,2,4,1,3]=>[3,1,4,2,6,8,5,7]=>1100100=>0010011
[8,5,7,6,2,4,3,1]=>[1,3,4,2,6,7,5,8]=>0100100=>0010010
[5,7,8,6,1,4,2,3]=>[3,2,4,1,6,8,7,5]=>1100101=>1010011
[4,7,8,1,6,5,2,3]=>[3,2,5,6,1,8,7,4]=>1101001=>1001011
[3,7,1,8,6,5,2,4]=>[4,2,5,6,8,1,7,3]=>1110000=>0000111
[2,1,7,8,6,5,3,4]=>[4,3,5,6,8,7,1,2]=>1010001=>1000101
[3,8,1,7,6,5,4,2]=>[2,4,5,6,7,1,8,3]=>1010000=>0000101
[4,8,7,1,6,5,3,2]=>[2,3,5,6,1,7,8,4]=>1001000=>0001001
[5,8,7,6,1,4,3,2]=>[2,3,4,1,6,7,8,5]=>1000100=>0010001
[6,8,7,5,4,1,3,2]=>[2,3,1,4,5,7,8,6]=>1000010=>0100001
[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2]=>101010100=>001010101
[3,2,5,1,4,6,7,8]=>[8,7,6,4,1,5,2,3]=>1101011=>1101011
[5,2,4,1,3,6,7,8]=>[8,7,6,3,1,4,2,5]=>1110011=>1100111
[5,2,6,1,3,4,7,8]=>[8,7,4,3,1,6,2,5]=>1111001=>1001111
[6,2,5,1,3,4,7,8]=>[8,7,4,3,1,5,2,6]=>1111001=>1001111
[6,3,5,1,2,4,7,8]=>[8,7,4,2,1,5,3,6]=>1111001=>1001111
[6,2,7,1,3,4,5,8]=>[8,5,4,3,1,7,2,6]=>1111100=>0011111
[6,3,7,1,2,4,5,8]=>[8,5,4,2,1,7,3,6]=>1111100=>0011111
[7,3,5,1,2,4,6,8]=>[8,6,4,2,1,5,3,7]=>1111010=>0101111
[7,4,6,1,2,3,5,8]=>[8,5,3,2,1,6,4,7]=>1111100=>0011111
[5,2,8,1,3,4,6,7]=>[7,6,4,3,1,8,2,5]=>1111010=>0101111
[5,3,8,1,2,4,6,7]=>[7,6,4,2,1,8,3,5]=>1111010=>0101111
[5,4,8,1,2,3,6,7]=>[7,6,3,2,1,8,4,5]=>1111010=>0101111
[6,4,8,1,2,3,5,7]=>[7,5,3,2,1,8,4,6]=>1111100=>0011111
[6,5,8,1,2,3,4,7]=>[7,4,3,2,1,8,5,6]=>1111100=>0011111
[7,5,8,1,2,3,4,6]=>[6,4,3,2,1,8,5,7]=>1111100=>0011111
[8,3,5,1,2,4,6,7]=>[7,6,4,2,1,5,3,8]=>1111010=>0101111
[8,5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5,8]=>1111100=>0011111
[3,2,5,7,1,4,6,8]=>[8,6,4,1,7,5,2,3]=>1101110=>0111011
[4,2,5,7,1,3,6,8]=>[8,6,3,1,7,5,2,4]=>1110110=>0110111
[5,2,4,7,1,3,6,8]=>[8,6,3,1,7,4,2,5]=>1111010=>0101111
[3,2,6,7,1,4,5,8]=>[8,5,4,1,7,6,2,3]=>1101110=>0111011
[5,2,6,7,1,3,4,8]=>[8,4,3,1,7,6,2,5]=>1111010=>0101111
[5,3,6,7,1,2,4,8]=>[8,4,2,1,7,6,3,5]=>1111010=>0101111
[6,3,4,7,1,2,5,8]=>[8,5,2,1,7,4,3,6]=>1111100=>0011111
[6,2,5,7,1,3,4,8]=>[8,4,3,1,7,5,2,6]=>1111100=>0011111
[6,3,5,7,1,2,4,8]=>[8,4,2,1,7,5,3,6]=>1111100=>0011111
[7,2,4,6,1,3,5,8]=>[8,5,3,1,6,4,2,7]=>1111100=>0011111
[7,3,4,6,1,2,5,8]=>[8,5,2,1,6,4,3,7]=>1111100=>0011111
[7,3,5,6,1,2,4,8]=>[8,4,2,1,6,5,3,7]=>1111100=>0011111
[3,2,5,8,1,4,6,7]=>[7,6,4,1,8,5,2,3]=>1101110=>0111011
[4,2,5,8,1,3,6,7]=>[7,6,3,1,8,5,2,4]=>1110110=>0110111
[5,2,4,8,1,3,6,7]=>[7,6,3,1,8,4,2,5]=>1111010=>0101111
[5,3,4,8,1,2,6,7]=>[7,6,2,1,8,4,3,5]=>1111010=>0101111
[4,2,6,8,1,3,5,7]=>[7,5,3,1,8,6,2,4]=>1110110=>0110111
[4,3,6,8,1,2,5,7]=>[7,5,2,1,8,6,3,4]=>1110110=>0110111
[5,2,6,8,1,3,4,7]=>[7,4,3,1,8,6,2,5]=>1111010=>0101111
[5,3,6,8,1,2,4,7]=>[7,4,2,1,8,6,3,5]=>1111010=>0101111
[6,2,4,8,1,3,5,7]=>[7,5,3,1,8,4,2,6]=>1111100=>0011111
[6,3,5,8,1,2,4,7]=>[7,4,2,1,8,5,3,6]=>1111100=>0011111
[3,2,7,8,1,4,5,6]=>[6,5,4,1,8,7,2,3]=>1101101=>1011011
[4,3,7,8,1,2,5,6]=>[6,5,2,1,8,7,3,4]=>1110101=>1010111
[5,4,7,8,1,2,3,6]=>[6,3,2,1,8,7,4,5]=>1111001=>1001111
[7,2,4,8,1,3,5,6]=>[6,5,3,1,8,4,2,7]=>1111100=>0011111
[7,2,5,8,1,3,4,6]=>[6,4,3,1,8,5,2,7]=>1111100=>0011111
[7,3,5,8,1,2,4,6]=>[6,4,2,1,8,5,3,7]=>1111100=>0011111
[7,4,6,8,1,2,3,5]=>[5,3,2,1,8,6,4,7]=>1111010=>0101111
[8,2,4,6,1,3,5,7]=>[7,5,3,1,6,4,2,8]=>1111100=>0011111
[8,2,5,6,1,3,4,7]=>[7,4,3,1,6,5,2,8]=>1111100=>0011111
[8,3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3,8]=>1111100=>0011111
[3,6,2,5,1,4,7,8]=>[8,7,4,1,5,2,6,3]=>1111001=>1001111
[4,6,2,5,1,3,7,8]=>[8,7,3,1,5,2,6,4]=>1111001=>1001111
[4,6,3,5,1,2,7,8]=>[8,7,2,1,5,3,6,4]=>1111001=>1001111
[5,6,2,4,1,3,7,8]=>[8,7,3,1,4,2,6,5]=>1110101=>1010111
[3,7,2,5,1,4,6,8]=>[8,6,4,1,5,2,7,3]=>1111010=>0101111
[5,7,2,4,1,3,6,8]=>[8,6,3,1,4,2,7,5]=>1110110=>0110111
[3,7,2,6,1,4,5,8]=>[8,5,4,1,6,2,7,3]=>1111100=>0011111
[4,7,3,6,1,2,5,8]=>[8,5,2,1,6,3,7,4]=>1111100=>0011111
[5,7,4,6,1,2,3,8]=>[8,3,2,1,6,4,7,5]=>1111100=>0011111
[5,8,2,4,1,3,6,7]=>[7,6,3,1,4,2,8,5]=>1110110=>0110111
[5,8,3,4,1,2,6,7]=>[7,6,2,1,4,3,8,5]=>1110110=>0110111
[3,8,2,6,1,4,5,7]=>[7,5,4,1,6,2,8,3]=>1111100=>0011111
[5,8,2,6,1,3,4,7]=>[7,4,3,1,6,2,8,5]=>1111100=>0011111
[5,8,4,6,1,2,3,7]=>[7,3,2,1,6,4,8,5]=>1111100=>0011111
[6,8,3,4,1,2,5,7]=>[7,5,2,1,4,3,8,6]=>1110110=>0110111
[6,8,4,5,1,2,3,7]=>[7,3,2,1,5,4,8,6]=>1111010=>0101111
[3,8,2,7,1,4,5,6]=>[6,5,4,1,7,2,8,3]=>1111100=>0011111
[4,8,2,7,1,3,5,6]=>[6,5,3,1,7,2,8,4]=>1111100=>0011111
[4,8,3,7,1,2,5,6]=>[6,5,2,1,7,3,8,4]=>1111100=>0011111
[5,8,2,7,1,3,4,6]=>[6,4,3,1,7,2,8,5]=>1111100=>0011111
[5,8,3,7,1,2,4,6]=>[6,4,2,1,7,3,8,5]=>1111100=>0011111
[5,8,4,7,1,2,3,6]=>[6,3,2,1,7,4,8,5]=>1111100=>0011111
[6,8,2,7,1,3,4,5]=>[5,4,3,1,7,2,8,6]=>1111010=>0101111
[6,8,4,7,1,2,3,5]=>[5,3,2,1,7,4,8,6]=>1111010=>0101111
[6,8,5,7,1,2,3,4]=>[4,3,2,1,7,5,8,6]=>1110110=>0110111
[7,8,2,4,1,3,5,6]=>[6,5,3,1,4,2,8,7]=>1110101=>1010111
[7,8,2,5,1,3,4,6]=>[6,4,3,1,5,2,8,7]=>1111001=>1001111
[7,8,3,5,1,2,4,6]=>[6,4,2,1,5,3,8,7]=>1111001=>1001111
[4,3,2,6,1,5,7,8]=>[8,7,5,1,6,2,3,4]=>1100101=>1010011
[5,3,2,6,1,4,7,8]=>[8,7,4,1,6,2,3,5]=>1101001=>1001011
[5,4,2,6,1,3,7,8]=>[8,7,3,1,6,2,4,5]=>1110001=>1000111
[6,3,2,5,1,4,7,8]=>[8,7,4,1,5,2,3,6]=>1101001=>1001011
[6,4,2,5,1,3,7,8]=>[8,7,3,1,5,2,4,6]=>1110001=>1000111
[6,5,2,4,1,3,7,8]=>[8,7,3,1,4,2,5,6]=>1110001=>1000111
[5,3,2,7,1,4,6,8]=>[8,6,4,1,7,2,3,5]=>1101010=>0101011
[5,4,2,7,1,3,6,8]=>[8,6,3,1,7,2,4,5]=>1110010=>0100111
[5,4,3,7,1,2,6,8]=>[8,6,2,1,7,3,4,5]=>1110010=>0100111
[6,4,2,7,1,3,5,8]=>[8,5,3,1,7,2,4,6]=>1110100=>0010111
[6,4,3,7,1,2,5,8]=>[8,5,2,1,7,3,4,6]=>1110100=>0010111
[6,5,3,7,1,2,4,8]=>[8,4,2,1,7,3,5,6]=>1111000=>0001111
[7,3,2,5,1,4,6,8]=>[8,6,4,1,5,2,3,7]=>1101010=>0101011
[7,4,2,5,1,3,6,8]=>[8,6,3,1,5,2,4,7]=>1110010=>0100111
[7,3,2,6,1,4,5,8]=>[8,5,4,1,6,2,3,7]=>1101100=>0011011
[7,5,3,6,1,2,4,8]=>[8,4,2,1,6,3,5,7]=>1111000=>0001111
[7,6,3,5,1,2,4,8]=>[8,4,2,1,5,3,6,7]=>1111000=>0001111
[4,3,2,8,1,5,6,7]=>[7,6,5,1,8,2,3,4]=>1100110=>0110011
[5,3,2,8,1,4,6,7]=>[7,6,4,1,8,2,3,5]=>1101010=>0101011
[5,4,2,8,1,3,6,7]=>[7,6,3,1,8,2,4,5]=>1110010=>0100111
[5,4,3,8,1,2,6,7]=>[7,6,2,1,8,3,4,5]=>1110010=>0100111
[6,3,2,8,1,4,5,7]=>[7,5,4,1,8,2,3,6]=>1101100=>0011011
[6,4,3,8,1,2,5,7]=>[7,5,2,1,8,3,4,6]=>1110100=>0010111
[6,5,2,8,1,3,4,7]=>[7,4,3,1,8,2,5,6]=>1111000=>0001111
[6,5,3,8,1,2,4,7]=>[7,4,2,1,8,3,5,6]=>1111000=>0001111
[6,5,4,8,1,2,3,7]=>[7,3,2,1,8,4,5,6]=>1111000=>0001111
[7,4,2,8,1,3,5,6]=>[6,5,3,1,8,2,4,7]=>1110100=>0010111
[7,4,3,8,1,2,5,6]=>[6,5,2,1,8,3,4,7]=>1110100=>0010111
[7,5,2,8,1,3,4,6]=>[6,4,3,1,8,2,5,7]=>1111000=>0001111
[7,5,3,8,1,2,4,6]=>[6,4,2,1,8,3,5,7]=>1111000=>0001111
[7,5,4,8,1,2,3,6]=>[6,3,2,1,8,4,5,7]=>1111000=>0001111
[7,6,4,8,1,2,3,5]=>[5,3,2,1,8,4,6,7]=>1111000=>0001111
[8,4,2,5,1,3,6,7]=>[7,6,3,1,5,2,4,8]=>1110010=>0100111
[8,5,2,4,1,3,6,7]=>[7,6,3,1,4,2,5,8]=>1110010=>0100111
[8,3,2,6,1,4,5,7]=>[7,5,4,1,6,2,3,8]=>1101100=>0011011
[8,4,2,6,1,3,5,7]=>[7,5,3,1,6,2,4,8]=>1110100=>0010111
[8,4,2,7,1,3,5,6]=>[6,5,3,1,7,2,4,8]=>1110100=>0010111
[8,5,2,7,1,3,4,6]=>[6,4,3,1,7,2,5,8]=>1111000=>0001111
[8,5,3,7,1,2,4,6]=>[6,4,2,1,7,3,5,8]=>1111000=>0001111
[8,5,4,7,1,2,3,6]=>[6,3,2,1,7,4,5,8]=>1111000=>0001111
[8,6,3,7,1,2,4,5]=>[5,4,2,1,7,3,6,8]=>1111000=>0001111
[8,7,2,4,1,3,5,6]=>[6,5,3,1,4,2,7,8]=>1110100=>0010111
[8,7,2,5,1,3,4,6]=>[6,4,3,1,5,2,7,8]=>1111000=>0001111
[8,7,3,5,1,2,4,6]=>[6,4,2,1,5,3,7,8]=>1111000=>0001111
[8,7,2,6,1,3,4,5]=>[5,4,3,1,6,2,7,8]=>1111000=>0001111
[8,7,3,6,1,2,4,5]=>[5,4,2,1,6,3,7,8]=>1111000=>0001111
[8,7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7,8]=>1111000=>0001111
[3,6,2,5,8,1,4,7]=>[7,4,1,8,5,2,6,3]=>1111100=>0011111
[5,6,2,4,8,1,3,7]=>[7,3,1,8,4,2,6,5]=>1111100=>0011111
[3,7,2,5,8,1,4,6]=>[6,4,1,8,5,2,7,3]=>1111100=>0011111
[4,7,2,5,8,1,3,6]=>[6,3,1,8,5,2,7,4]=>1111100=>0011111
[4,7,3,5,8,1,2,6]=>[6,2,1,8,5,3,7,4]=>1111100=>0011111
[5,7,2,4,8,1,3,6]=>[6,3,1,8,4,2,7,5]=>1111100=>0011111
[5,7,3,4,8,1,2,6]=>[6,2,1,8,4,3,7,5]=>1111100=>0011111
[4,7,3,6,8,1,2,5]=>[5,2,1,8,6,3,7,4]=>1111010=>0101111
[5,7,2,6,8,1,3,4]=>[4,3,1,8,6,2,7,5]=>1110110=>0110111
[5,7,4,6,8,1,2,3]=>[3,2,1,8,6,4,7,5]=>1101110=>0111011
[6,7,2,5,8,1,3,4]=>[4,3,1,8,5,2,7,6]=>1110110=>0110111
[3,8,2,5,7,1,4,6]=>[6,4,1,7,5,2,8,3]=>1111100=>0011111
[4,8,2,5,7,1,3,6]=>[6,3,1,7,5,2,8,4]=>1111100=>0011111
[4,8,3,5,7,1,2,6]=>[6,2,1,7,5,3,8,4]=>1111100=>0011111
[5,8,2,4,7,1,3,6]=>[6,3,1,7,4,2,8,5]=>1111100=>0011111
[5,8,3,4,7,1,2,6]=>[6,2,1,7,4,3,8,5]=>1111100=>0011111
[3,8,2,6,7,1,4,5]=>[5,4,1,7,6,2,8,3]=>1111010=>0101111
[4,8,3,6,7,1,2,5]=>[5,2,1,7,6,3,8,4]=>1111010=>0101111
[5,8,2,6,7,1,3,4]=>[4,3,1,7,6,2,8,5]=>1110110=>0110111
[5,8,4,6,7,1,2,3]=>[3,2,1,7,6,4,8,5]=>1101110=>0111011
[6,8,2,5,7,1,3,4]=>[4,3,1,7,5,2,8,6]=>1110110=>0110111
[6,8,4,5,7,1,2,3]=>[3,2,1,7,5,4,8,6]=>1101110=>0111011
[7,8,2,4,6,1,3,5]=>[5,3,1,6,4,2,8,7]=>1111001=>1001111
[7,8,3,5,6,1,2,4]=>[4,2,1,6,5,3,8,7]=>1110101=>1010111
[5,3,2,6,8,1,4,7]=>[7,4,1,8,6,2,3,5]=>1101010=>0101011
[5,4,2,6,8,1,3,7]=>[7,3,1,8,6,2,4,5]=>1110010=>0100111
[5,4,3,6,8,1,2,7]=>[7,2,1,8,6,3,4,5]=>1110010=>0100111
[6,4,3,5,8,1,2,7]=>[7,2,1,8,5,3,4,6]=>1110100=>0010111
[4,3,2,7,8,1,5,6]=>[6,5,1,8,7,2,3,4]=>1100101=>1010011
[5,4,2,7,8,1,3,6]=>[6,3,1,8,7,2,4,5]=>1110001=>1000111
[5,4,3,7,8,1,2,6]=>[6,2,1,8,7,3,4,5]=>1110001=>1000111
[6,4,2,7,8,1,3,5]=>[5,3,1,8,7,2,4,6]=>1110001=>1000111
[6,5,2,7,8,1,3,4]=>[4,3,1,8,7,2,5,6]=>1110001=>1000111
[6,5,3,7,8,1,2,4]=>[4,2,1,8,7,3,5,6]=>1110001=>1000111
[7,4,2,6,8,1,3,5]=>[5,3,1,8,6,2,4,7]=>1110010=>0100111
[7,5,3,6,8,1,2,4]=>[4,2,1,8,6,3,5,7]=>1110010=>0100111
[7,6,2,5,8,1,3,4]=>[4,3,1,8,5,2,6,7]=>1110100=>0010111
[8,4,2,5,7,1,3,6]=>[6,3,1,7,5,2,4,8]=>1110100=>0010111
[8,4,3,6,7,1,2,5]=>[5,2,1,7,6,3,4,8]=>1110010=>0100111
[8,5,2,6,7,1,3,4]=>[4,3,1,7,6,2,5,8]=>1110010=>0100111
[8,6,2,5,7,1,3,4]=>[4,3,1,7,5,2,6,8]=>1110100=>0010111
[8,6,3,5,7,1,2,4]=>[4,2,1,7,5,3,6,8]=>1110100=>0010111
[8,7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7,8]=>1111000=>0001111
[8,7,3,4,6,1,2,5]=>[5,2,1,6,4,3,7,8]=>1111000=>0001111
[8,7,2,5,6,1,3,4]=>[4,3,1,6,5,2,7,8]=>1110100=>0010111
[8,7,3,5,6,1,2,4]=>[4,2,1,6,5,3,7,8]=>1110100=>0010111
[5,3,7,2,6,1,4,8]=>[8,4,1,6,2,7,3,5]=>1111000=>0001111
[5,4,7,2,6,1,3,8]=>[8,3,1,6,2,7,4,5]=>1111000=>0001111
[6,4,7,2,5,1,3,8]=>[8,3,1,5,2,7,4,6]=>1111000=>0001111
[7,3,6,2,5,1,4,8]=>[8,4,1,5,2,6,3,7]=>1111000=>0001111
[7,5,6,2,4,1,3,8]=>[8,3,1,4,2,6,5,7]=>1110100=>0010111
[4,3,8,2,6,1,5,7]=>[7,5,1,6,2,8,3,4]=>1110100=>0010111
[5,3,8,2,6,1,4,7]=>[7,4,1,6,2,8,3,5]=>1111000=>0001111
[5,4,8,2,6,1,3,7]=>[7,3,1,6,2,8,4,5]=>1111000=>0001111
[6,4,8,2,5,1,3,7]=>[7,3,1,5,2,8,4,6]=>1111000=>0001111
[6,4,8,3,5,1,2,7]=>[7,2,1,5,3,8,4,6]=>1111000=>0001111
[4,3,8,2,7,1,5,6]=>[6,5,1,7,2,8,3,4]=>1110100=>0010111
[6,4,8,2,7,1,3,5]=>[5,3,1,7,2,8,4,6]=>1111000=>0001111
[6,4,8,3,7,1,2,5]=>[5,2,1,7,3,8,4,6]=>1111000=>0001111
[6,5,8,2,7,1,3,4]=>[4,3,1,7,2,8,5,6]=>1110100=>0010111
[6,5,8,3,7,1,2,4]=>[4,2,1,7,3,8,5,6]=>1110100=>0010111
[6,5,8,4,7,1,2,3]=>[3,2,1,7,4,8,5,6]=>1101100=>0011011
[7,3,8,2,5,1,4,6]=>[6,4,1,5,2,8,3,7]=>1111000=>0001111
[7,4,8,3,5,1,2,6]=>[6,2,1,5,3,8,4,7]=>1111000=>0001111
[7,5,8,2,4,1,3,6]=>[6,3,1,4,2,8,5,7]=>1110100=>0010111
[7,5,8,3,4,1,2,6]=>[6,2,1,4,3,8,5,7]=>1110100=>0010111
[7,3,8,2,6,1,4,5]=>[5,4,1,6,2,8,3,7]=>1111000=>0001111
[7,4,8,2,6,1,3,5]=>[5,3,1,6,2,8,4,7]=>1111000=>0001111
[7,4,8,3,6,1,2,5]=>[5,2,1,6,3,8,4,7]=>1111000=>0001111
[7,5,8,2,6,1,3,4]=>[4,3,1,6,2,8,5,7]=>1110100=>0010111
[7,5,8,3,6,1,2,4]=>[4,2,1,6,3,8,5,7]=>1110100=>0010111
[7,5,8,4,6,1,2,3]=>[3,2,1,6,4,8,5,7]=>1101100=>0011011
[8,3,6,2,5,1,4,7]=>[7,4,1,5,2,6,3,8]=>1111000=>0001111
[8,4,6,2,5,1,3,7]=>[7,3,1,5,2,6,4,8]=>1111000=>0001111
[8,5,6,2,4,1,3,7]=>[7,3,1,4,2,6,5,8]=>1110100=>0010111
[8,3,7,2,5,1,4,6]=>[6,4,1,5,2,7,3,8]=>1111000=>0001111
[8,4,7,3,5,1,2,6]=>[6,2,1,5,3,7,4,8]=>1111000=>0001111
[8,5,7,2,4,1,3,6]=>[6,3,1,4,2,7,5,8]=>1110100=>0010111
[8,3,7,2,6,1,4,5]=>[5,4,1,6,2,7,3,8]=>1111000=>0001111
[8,4,7,2,6,1,3,5]=>[5,3,1,6,2,7,4,8]=>1111000=>0001111
[8,4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4,8]=>1111000=>0001111
[8,5,7,2,6,1,3,4]=>[4,3,1,6,2,7,5,8]=>1110100=>0010111
[8,5,7,3,6,1,2,4]=>[4,2,1,6,3,7,5,8]=>1110100=>0010111
[8,5,7,4,6,1,2,3]=>[3,2,1,6,4,7,5,8]=>1101100=>0011011
[8,6,7,2,4,1,3,5]=>[5,3,1,4,2,7,6,8]=>1110010=>0100111
[8,6,7,2,5,1,3,4]=>[4,3,1,5,2,7,6,8]=>1110010=>0100111
[8,6,7,3,5,1,2,4]=>[4,2,1,5,3,7,6,8]=>1110010=>0100111
[5,4,3,2,7,1,6,8]=>[8,6,1,7,2,3,4,5]=>1100010=>0100011
[6,5,3,2,7,1,4,8]=>[8,4,1,7,2,3,5,6]=>1101000=>0001011
[6,5,4,2,7,1,3,8]=>[8,3,1,7,2,4,5,6]=>1110000=>0000111
[7,4,3,2,6,1,5,8]=>[8,5,1,6,2,3,4,7]=>1100100=>0010011
[7,5,3,2,6,1,4,8]=>[8,4,1,6,2,3,5,7]=>1101000=>0001011
[7,5,4,2,6,1,3,8]=>[8,3,1,6,2,4,5,7]=>1110000=>0000111
[7,6,4,2,5,1,3,8]=>[8,3,1,5,2,4,6,7]=>1110000=>0000111
[5,4,3,2,8,1,6,7]=>[7,6,1,8,2,3,4,5]=>1100010=>0100011
[6,5,3,2,8,1,4,7]=>[7,4,1,8,2,3,5,6]=>1101000=>0001011
[6,5,4,3,8,1,2,7]=>[7,2,1,8,3,4,5,6]=>1110000=>0000111
[7,4,3,2,8,1,5,6]=>[6,5,1,8,2,3,4,7]=>1100100=>0010011
[7,5,3,2,8,1,4,6]=>[6,4,1,8,2,3,5,7]=>1101000=>0001011
[7,6,3,2,8,1,4,5]=>[5,4,1,8,2,3,6,7]=>1101000=>0001011
[7,6,4,2,8,1,3,5]=>[5,3,1,8,2,4,6,7]=>1110000=>0000111
[7,6,4,3,8,1,2,5]=>[5,2,1,8,3,4,6,7]=>1110000=>0000111
[7,6,5,2,8,1,3,4]=>[4,3,1,8,2,5,6,7]=>1110000=>0000111
[7,6,5,3,8,1,2,4]=>[4,2,1,8,3,5,6,7]=>1110000=>0000111
[8,5,3,2,6,1,4,7]=>[7,4,1,6,2,3,5,8]=>1101000=>0001011
[8,6,3,2,5,1,4,7]=>[7,4,1,5,2,3,6,8]=>1101000=>0001011
[8,6,4,2,5,1,3,7]=>[7,3,1,5,2,4,6,8]=>1110000=>0000111
[8,5,3,2,7,1,4,6]=>[6,4,1,7,2,3,5,8]=>1101000=>0001011
[8,6,4,2,7,1,3,5]=>[5,3,1,7,2,4,6,8]=>1110000=>0000111
[8,6,4,3,7,1,2,5]=>[5,2,1,7,3,4,6,8]=>1110000=>0000111
[8,6,5,3,7,1,2,4]=>[4,2,1,7,3,5,6,8]=>1110000=>0000111
[8,7,3,2,5,1,4,6]=>[6,4,1,5,2,3,7,8]=>1101000=>0001011
[8,7,3,2,6,1,4,5]=>[5,4,1,6,2,3,7,8]=>1101000=>0001011
[8,7,4,2,6,1,3,5]=>[5,3,1,6,2,4,7,8]=>1110000=>0000111
[8,7,4,3,6,1,2,5]=>[5,2,1,6,3,4,7,8]=>1110000=>0000111
[8,7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7,8]=>1110000=>0000111
[8,7,5,3,6,1,2,4]=>[4,2,1,6,3,5,7,8]=>1110000=>0000111
[8,7,6,2,4,1,3,5]=>[5,3,1,4,2,6,7,8]=>1110000=>0000111
[4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4]=>1111000=>0001111
[5,8,3,7,2,6,1,4]=>[4,1,6,2,7,3,8,5]=>1110100=>0010111
[5,8,4,7,2,6,1,3]=>[3,1,6,2,7,4,8,5]=>1101100=>0011011
[5,8,4,7,3,6,1,2]=>[2,1,6,3,7,4,8,5]=>1011100=>0011101
[6,8,3,7,2,5,1,4]=>[4,1,5,2,7,3,8,6]=>1110010=>0100111
[6,8,4,7,2,5,1,3]=>[3,1,5,2,7,4,8,6]=>1101010=>0101011
[6,8,4,7,3,5,1,2]=>[2,1,5,3,7,4,8,6]=>1011010=>0101101
[6,8,5,7,2,4,1,3]=>[3,1,4,2,7,5,8,6]=>1100110=>0110011
[6,8,5,7,3,4,1,2]=>[2,1,4,3,7,5,8,6]=>1010110=>0110101
[7,8,3,6,2,5,1,4]=>[4,1,5,2,6,3,8,7]=>1110001=>1000111
[7,8,4,6,2,5,1,3]=>[3,1,5,2,6,4,8,7]=>1101001=>1001011
[7,8,4,6,3,5,1,2]=>[2,1,5,3,6,4,8,7]=>1011001=>1001101
[7,8,5,6,2,4,1,3]=>[3,1,4,2,6,5,8,7]=>1100101=>1010011
[5,4,3,8,2,7,1,6]=>[6,1,7,2,8,3,4,5]=>1110000=>0000111
[6,4,3,8,2,7,1,5]=>[5,1,7,2,8,3,4,6]=>1110000=>0000111
[6,5,3,8,2,7,1,4]=>[4,1,7,2,8,3,5,6]=>1110000=>0000111
[7,4,3,8,2,6,1,5]=>[5,1,6,2,8,3,4,7]=>1110000=>0000111
[7,5,3,8,2,6,1,4]=>[4,1,6,2,8,3,5,7]=>1110000=>0000111
[7,5,4,8,2,6,1,3]=>[3,1,6,2,8,4,5,7]=>1101000=>0001011
[7,6,3,8,2,5,1,4]=>[4,1,5,2,8,3,6,7]=>1110000=>0000111
[7,6,4,8,2,5,1,3]=>[3,1,5,2,8,4,6,7]=>1101000=>0001011
[7,6,4,8,3,5,1,2]=>[2,1,5,3,8,4,6,7]=>1011000=>0001101
[7,6,5,8,2,4,1,3]=>[3,1,4,2,8,5,6,7]=>1100100=>0010011
[8,4,3,7,2,6,1,5]=>[5,1,6,2,7,3,4,8]=>1110000=>0000111
[8,5,3,7,2,6,1,4]=>[4,1,6,2,7,3,5,8]=>1110000=>0000111
[8,6,3,7,2,5,1,4]=>[4,1,5,2,7,3,6,8]=>1110000=>0000111
[8,6,4,7,2,5,1,3]=>[3,1,5,2,7,4,6,8]=>1101000=>0001011
[8,6,5,7,2,4,1,3]=>[3,1,4,2,7,5,6,8]=>1100100=>0010011
[8,7,5,6,2,4,1,3]=>[3,1,4,2,6,5,7,8]=>1100100=>0010011
[7,6,5,4,2,8,1,3]=>[3,1,8,2,4,5,6,7]=>1100000=>0000011
[8,5,4,3,2,7,1,6]=>[6,1,7,2,3,4,5,8]=>1100000=>0000011
[8,7,4,3,2,6,1,5]=>[5,1,6,2,3,4,7,8]=>1100000=>0000011
[8,7,5,4,2,6,1,3]=>[3,1,6,2,4,5,7,8]=>1100000=>0000011
[8,7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7,8]=>1100000=>0000011
[8,1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1,8]=>1111100=>0011111
[8,1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1,8]=>1111100=>0011111
[8,1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1,8]=>1111000=>0001111
[8,1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1,8]=>1111000=>0001111
[6,1,2,5,3,7,8,4]=>[4,8,7,3,5,2,1,6]=>1110001=>1000111
[4,1,2,8,6,3,5,7]=>[7,5,3,6,8,2,1,4]=>1110100=>0010111
[4,1,2,8,7,3,5,6]=>[6,5,3,7,8,2,1,4]=>1110100=>0010111
[4,1,2,7,6,3,8,5]=>[5,8,3,6,7,2,1,4]=>1110000=>0000111
[8,1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1,8]=>1111100=>0011111
[8,1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1,8]=>1111100=>0011111
[8,1,2,7,6,3,4,5]=>[5,4,3,6,7,2,1,8]=>1111000=>0001111
[7,1,2,5,6,3,8,4]=>[4,8,3,6,5,2,1,7]=>1110100=>0010111
[4,1,2,5,8,7,3,6]=>[6,3,7,8,5,2,1,4]=>1110100=>0010111
[3,1,8,2,6,4,5,7]=>[7,5,4,6,2,8,1,3]=>1101100=>0011011
[3,1,7,2,6,4,8,5]=>[5,8,4,6,2,7,1,3]=>1101000=>0001011
[3,1,5,2,8,7,4,6]=>[6,4,7,8,2,5,1,3]=>1101000=>0001011
[3,1,8,2,6,7,4,5]=>[5,4,7,6,2,8,1,3]=>1101010=>0101011
[6,1,4,2,3,8,5,7]=>[7,5,8,3,2,4,1,6]=>1110100=>0010111
[6,1,4,2,3,7,8,5]=>[5,8,7,3,2,4,1,6]=>1110001=>1000111
[6,1,5,2,3,8,4,7]=>[7,4,8,3,2,5,1,6]=>1111000=>0001111
[8,1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1,8]=>1111000=>0001111
[5,1,4,2,8,3,6,7]=>[7,6,3,8,2,4,1,5]=>1110010=>0100111
[5,1,4,2,7,3,8,6]=>[6,8,3,7,2,4,1,5]=>1110000=>0000111
[8,1,4,2,6,3,5,7]=>[7,5,3,6,2,4,1,8]=>1110100=>0010111
[8,1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1,8]=>1110100=>0010111
[7,1,4,2,6,3,8,5]=>[5,8,3,6,2,4,1,7]=>1110000=>0000111
[8,1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1,8]=>1111000=>0001111
[7,1,5,2,6,3,8,4]=>[4,8,3,6,2,5,1,7]=>1110000=>0000111
[5,1,4,2,6,8,3,7]=>[7,3,8,6,2,4,1,5]=>1110010=>0100111
[5,1,4,2,8,7,3,6]=>[6,3,7,8,2,4,1,5]=>1110000=>0000111
[8,1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1,8]=>1110010=>0100111
[5,1,4,2,6,7,8,3]=>[3,8,7,6,2,4,1,5]=>1100011=>1100011
[3,1,8,6,2,4,5,7]=>[7,5,4,2,6,8,1,3]=>1101100=>0011011
[3,1,6,5,2,8,4,7]=>[7,4,8,2,5,6,1,3]=>1101000=>0001011
[3,1,8,6,2,7,4,5]=>[5,4,7,2,6,8,1,3]=>1101000=>0001011
[3,1,6,5,2,7,8,4]=>[4,8,7,2,5,6,1,3]=>1100001=>1000011
[7,1,4,6,2,3,8,5]=>[5,8,3,2,6,4,1,7]=>1111000=>0001111
[7,1,8,6,2,3,4,5]=>[5,4,3,2,6,8,1,7]=>1111000=>0001111
[7,1,6,5,2,3,8,4]=>[4,8,3,2,5,6,1,7]=>1110000=>0000111
[6,1,4,5,2,8,3,7]=>[7,3,8,2,5,4,1,6]=>1111000=>0001111
[8,1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1,8]=>1111000=>0001111
[8,1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1,8]=>1111000=>0001111
[8,1,6,5,2,7,3,4]=>[4,3,7,2,5,6,1,8]=>1110000=>0000111
[6,1,4,5,2,7,8,3]=>[3,8,7,2,5,4,1,6]=>1101001=>1001011
[3,1,4,8,6,2,5,7]=>[7,5,2,6,8,4,1,3]=>1101100=>0011011
[3,1,8,5,7,2,4,6]=>[6,4,2,7,5,8,1,3]=>1101100=>0011011
[3,1,7,5,6,2,8,4]=>[4,8,2,6,5,7,1,3]=>1100100=>0010011
[8,1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1,8]=>1111100=>0011111
[8,1,4,7,6,2,3,5]=>[5,3,2,6,7,4,1,8]=>1111000=>0001111
[7,1,4,5,6,2,8,3]=>[3,8,2,6,5,4,1,7]=>1101100=>0011011
[3,1,4,5,8,7,2,6]=>[6,2,7,8,5,4,1,3]=>1101100=>0011011
[8,1,4,5,6,7,2,3]=>[3,2,7,6,5,4,1,8]=>1101110=>0111011
[2,5,1,3,8,7,4,6]=>[6,4,7,8,3,1,5,2]=>1111000=>0001111
[2,4,1,8,3,7,5,6]=>[6,5,7,3,8,1,4,2]=>1110100=>0010111
[2,7,1,6,3,4,8,5]=>[5,8,4,3,6,1,7,2]=>1111000=>0001111
[2,8,1,6,3,7,4,5]=>[5,4,7,3,6,1,8,2]=>1111000=>0001111
[2,4,1,8,6,3,5,7]=>[7,5,3,6,8,1,4,2]=>1110100=>0010111
[2,8,1,5,7,3,4,6]=>[6,4,3,7,5,1,8,2]=>1111100=>0011111
[2,8,1,7,6,3,4,5]=>[5,4,3,6,7,1,8,2]=>1111000=>0001111
[2,7,1,5,6,3,8,4]=>[4,8,3,6,5,1,7,2]=>1110100=>0010111
[2,8,1,5,6,7,3,4]=>[4,3,7,6,5,1,8,2]=>1110110=>0110111
[6,3,1,2,4,7,8,5]=>[5,8,7,4,2,1,3,6]=>1101001=>1001011
[5,3,1,2,8,4,6,7]=>[7,6,4,8,2,1,3,5]=>1101010=>0101011
[5,3,1,2,7,4,8,6]=>[6,8,4,7,2,1,3,5]=>1101000=>0001011
[5,3,1,2,8,7,4,6]=>[6,4,7,8,2,1,3,5]=>1101000=>0001011
[5,3,1,2,6,7,8,4]=>[4,8,7,6,2,1,3,5]=>1100011=>1100011
[5,8,1,2,3,7,4,6]=>[6,4,7,3,2,1,8,5]=>1111100=>0011111
[5,4,1,2,8,3,6,7]=>[7,6,3,8,2,1,4,5]=>1110010=>0100111
[5,4,1,2,7,3,8,6]=>[6,8,3,7,2,1,4,5]=>1110000=>0000111
[8,4,1,2,6,3,5,7]=>[7,5,3,6,2,1,4,8]=>1110100=>0010111
[8,4,1,2,7,3,5,6]=>[6,5,3,7,2,1,4,8]=>1110100=>0010111
[7,4,1,2,6,3,8,5]=>[5,8,3,6,2,1,4,7]=>1110000=>0000111
[5,8,1,2,6,3,4,7]=>[7,4,3,6,2,1,8,5]=>1111100=>0011111
[5,8,1,2,7,3,4,6]=>[6,4,3,7,2,1,8,5]=>1111100=>0011111
[8,7,1,2,6,3,4,5]=>[5,4,3,6,2,1,7,8]=>1111000=>0001111
[5,7,1,2,6,3,8,4]=>[4,8,3,6,2,1,7,5]=>1110100=>0010111
[5,4,1,2,6,8,3,7]=>[7,3,8,6,2,1,4,5]=>1110010=>0100111
[5,4,1,2,8,7,3,6]=>[6,3,7,8,2,1,4,5]=>1110000=>0000111
[8,4,1,2,6,7,3,5]=>[5,3,7,6,2,1,4,8]=>1110010=>0100111
[5,8,1,2,6,7,3,4]=>[4,3,7,6,2,1,8,5]=>1110110=>0110111
[5,4,1,2,6,7,8,3]=>[3,8,7,6,2,1,4,5]=>1100011=>1100011
[4,3,1,6,2,8,5,7]=>[7,5,8,2,6,1,3,4]=>1100100=>0010011
[4,3,1,6,2,7,8,5]=>[5,8,7,2,6,1,3,4]=>1100001=>1000011
[7,3,1,6,2,4,8,5]=>[5,8,4,2,6,1,3,7]=>1101000=>0001011
[8,3,1,5,2,7,4,6]=>[6,4,7,2,5,1,3,8]=>1101000=>0001011
[8,3,1,6,2,7,4,5]=>[5,4,7,2,6,1,3,8]=>1101000=>0001011
[6,3,1,5,2,7,8,4]=>[4,8,7,2,5,1,3,6]=>1100001=>1000011
[7,4,1,5,2,3,8,6]=>[6,8,3,2,5,1,4,7]=>1110000=>0000111
[8,4,1,6,2,3,5,7]=>[7,5,3,2,6,1,4,8]=>1110100=>0010111
[7,4,1,8,2,3,5,6]=>[6,5,3,2,8,1,4,7]=>1110100=>0010111
[7,4,1,6,2,3,8,5]=>[5,8,3,2,6,1,4,7]=>1110000=>0000111
[8,7,1,5,2,3,4,6]=>[6,4,3,2,5,1,7,8]=>1111000=>0001111
[8,7,1,6,2,3,4,5]=>[5,4,3,2,6,1,7,8]=>1111000=>0001111
[6,7,1,5,2,3,8,4]=>[4,8,3,2,5,1,7,6]=>1110010=>0100111
[6,4,1,5,2,8,3,7]=>[7,3,8,2,5,1,4,6]=>1110000=>0000111
[8,4,1,5,2,7,3,6]=>[6,3,7,2,5,1,4,8]=>1110000=>0000111
[8,4,1,6,2,7,3,5]=>[5,3,7,2,6,1,4,8]=>1110000=>0000111
[6,8,1,5,2,7,3,4]=>[4,3,7,2,5,1,8,6]=>1110010=>0100111
[4,3,1,8,7,2,5,6]=>[6,5,2,7,8,1,3,4]=>1100100=>0010011
[8,3,1,5,6,2,4,7]=>[7,4,2,6,5,1,3,8]=>1101100=>0011011
[8,3,1,5,7,2,4,6]=>[6,4,2,7,5,1,3,8]=>1101100=>0011011
[8,3,1,7,6,2,4,5]=>[5,4,2,6,7,1,3,8]=>1101000=>0001011
[7,3,1,5,6,2,8,4]=>[4,8,2,6,5,1,3,7]=>1100100=>0010011
[4,3,1,5,6,8,2,7]=>[7,2,8,6,5,1,3,4]=>1100110=>0110011
[4,3,1,5,8,7,2,6]=>[6,2,7,8,5,1,3,4]=>1100100=>0010011
[4,3,1,5,6,7,8,2]=>[2,8,7,6,5,1,3,4]=>1000111=>1110001
[2,3,7,1,6,4,8,5]=>[5,8,4,6,1,7,3,2]=>1111000=>0001111
[2,3,5,1,8,7,4,6]=>[6,4,7,8,1,5,3,2]=>1111000=>0001111
[2,3,8,1,6,7,4,5]=>[5,4,7,6,1,8,3,2]=>1111010=>0101111
[2,6,4,1,3,8,5,7]=>[7,5,8,3,1,4,6,2]=>1110100=>0010111
[2,6,4,1,3,7,8,5]=>[5,8,7,3,1,4,6,2]=>1110001=>1000111
[2,7,5,1,3,4,8,6]=>[6,8,4,3,1,5,7,2]=>1111000=>0001111
[2,6,5,1,3,8,4,7]=>[7,4,8,3,1,5,6,2]=>1111000=>0001111
[2,8,5,1,3,7,4,6]=>[6,4,7,3,1,5,8,2]=>1111000=>0001111
[2,6,8,1,3,7,4,5]=>[5,4,7,3,1,8,6,2]=>1111010=>0101111
[2,6,5,1,3,7,8,4]=>[4,8,7,3,1,5,6,2]=>1110001=>1000111
[2,5,4,1,8,3,6,7]=>[7,6,3,8,1,4,5,2]=>1110010=>0100111
[2,8,4,1,6,3,5,7]=>[7,5,3,6,1,4,8,2]=>1110100=>0010111
[2,8,4,1,7,3,5,6]=>[6,5,3,7,1,4,8,2]=>1110100=>0010111
[2,7,4,1,6,3,8,5]=>[5,8,3,6,1,4,7,2]=>1110000=>0000111
[2,8,5,1,7,3,4,6]=>[6,4,3,7,1,5,8,2]=>1111000=>0001111
[2,7,5,1,6,3,8,4]=>[4,8,3,6,1,5,7,2]=>1110000=>0000111
[2,8,4,1,6,7,3,5]=>[5,3,7,6,1,4,8,2]=>1110010=>0100111
[2,8,5,1,6,7,3,4]=>[4,3,7,6,1,5,8,2]=>1110010=>0100111
[2,5,4,1,6,7,8,3]=>[3,8,7,6,1,4,5,2]=>1100011=>1100011
[6,3,4,1,2,8,5,7]=>[7,5,8,2,1,4,3,6]=>1110100=>0010111
[6,3,4,1,2,7,8,5]=>[5,8,7,2,1,4,3,6]=>1110001=>1000111
[7,3,5,1,2,4,8,6]=>[6,8,4,2,1,5,3,7]=>1111000=>0001111
[6,3,7,1,2,4,8,5]=>[5,8,4,2,1,7,3,6]=>1111000=>0001111
[6,3,5,1,2,8,4,7]=>[7,4,8,2,1,5,3,6]=>1111000=>0001111
[8,3,5,1,2,7,4,6]=>[6,4,7,2,1,5,3,8]=>1111000=>0001111
[6,3,8,1,2,7,4,5]=>[5,4,7,2,1,8,3,6]=>1111000=>0001111
[7,5,4,1,2,3,8,6]=>[6,8,3,2,1,4,5,7]=>1110000=>0000111
[6,7,4,1,2,3,8,5]=>[5,8,3,2,1,4,7,6]=>1110010=>0100111
[6,8,5,1,2,3,4,7]=>[7,4,3,2,1,5,8,6]=>1111010=>0101111
[8,5,4,1,2,7,3,6]=>[6,3,7,2,1,4,5,8]=>1110000=>0000111
[8,3,4,1,7,2,5,6]=>[6,5,2,7,1,4,3,8]=>1110100=>0010111
[7,3,4,1,6,2,8,5]=>[5,8,2,6,1,4,3,7]=>1110000=>0000111
[8,3,5,1,6,2,4,7]=>[7,4,2,6,1,5,3,8]=>1111000=>0001111
[8,3,5,1,7,2,4,6]=>[6,4,2,7,1,5,3,8]=>1111000=>0001111
[7,3,5,1,6,2,8,4]=>[4,8,2,6,1,5,3,7]=>1110000=>0000111
[8,5,4,1,6,2,3,7]=>[7,3,2,6,1,4,5,8]=>1110000=>0000111
[8,5,4,1,7,2,3,6]=>[6,3,2,7,1,4,5,8]=>1110000=>0000111
[7,8,4,1,6,2,3,5]=>[5,3,2,6,1,4,8,7]=>1110001=>1000111
[8,3,4,1,6,7,2,5]=>[5,2,7,6,1,4,3,8]=>1110010=>0100111
[5,3,4,1,6,7,8,2]=>[2,8,7,6,1,4,3,5]=>1010011=>1100101
[2,3,4,8,1,7,5,6]=>[6,5,7,1,8,4,3,2]=>1111100=>0011111
[2,3,7,5,1,4,8,6]=>[6,8,4,1,5,7,3,2]=>1111000=>0001111
[2,3,7,6,1,4,8,5]=>[5,8,4,1,6,7,3,2]=>1111000=>0001111
[2,3,6,5,1,8,4,7]=>[7,4,8,1,5,6,3,2]=>1111000=>0001111
[2,3,8,5,1,7,4,6]=>[6,4,7,1,5,8,3,2]=>1111000=>0001111
[2,3,6,5,1,7,8,4]=>[4,8,7,1,5,6,3,2]=>1110001=>1000111
[2,8,4,6,1,3,5,7]=>[7,5,3,1,6,4,8,2]=>1111100=>0011111
[2,7,4,8,1,3,5,6]=>[6,5,3,1,8,4,7,2]=>1111100=>0011111
[2,7,4,6,1,3,8,5]=>[5,8,3,1,6,4,7,2]=>1111000=>0001111
[2,8,6,5,1,3,4,7]=>[7,4,3,1,5,6,8,2]=>1111000=>0001111
[2,7,8,5,1,3,4,6]=>[6,4,3,1,5,8,7,2]=>1111001=>1001111
[2,6,4,5,1,8,3,7]=>[7,3,8,1,5,4,6,2]=>1111000=>0001111
[2,8,4,6,1,7,3,5]=>[5,3,7,1,6,4,8,2]=>1111000=>0001111
[2,8,6,5,1,7,3,4]=>[4,3,7,1,5,6,8,2]=>1110000=>0000111
[7,3,4,6,1,2,8,5]=>[5,8,2,1,6,4,3,7]=>1111000=>0001111
[8,3,6,5,1,2,4,7]=>[7,4,2,1,5,6,3,8]=>1111000=>0001111
[7,3,8,5,1,2,4,6]=>[6,4,2,1,5,8,3,7]=>1111000=>0001111
[7,3,6,5,1,2,8,4]=>[4,8,2,1,5,6,3,7]=>1110000=>0000111
[7,6,4,5,1,2,8,3]=>[3,8,2,1,5,4,6,7]=>1101000=>0001011
[8,3,4,5,1,7,2,6]=>[6,2,7,1,5,4,3,8]=>1111000=>0001111
[8,3,6,5,1,7,2,4]=>[4,2,7,1,5,6,3,8]=>1110000=>0000111
[8,6,4,5,1,7,2,3]=>[3,2,7,1,5,4,6,8]=>1101000=>0001011
[6,3,4,5,1,7,8,2]=>[2,8,7,1,5,4,3,6]=>1011001=>1001101
[2,3,4,8,6,1,5,7]=>[7,5,1,6,8,4,3,2]=>1111100=>0011111
[2,3,4,8,7,1,5,6]=>[6,5,1,7,8,4,3,2]=>1111100=>0011111
[2,3,8,5,6,1,4,7]=>[7,4,1,6,5,8,3,2]=>1111100=>0011111
[2,3,8,7,6,1,4,5]=>[5,4,1,6,7,8,3,2]=>1111000=>0001111
[2,8,7,5,6,1,3,4]=>[4,3,1,6,5,7,8,2]=>1110100=>0010111
[8,3,4,7,6,1,2,5]=>[5,2,1,6,7,4,3,8]=>1111000=>0001111
[8,3,7,5,6,1,2,4]=>[4,2,1,6,5,7,3,8]=>1110100=>0010111
[7,3,4,5,6,1,8,2]=>[2,8,1,6,5,4,3,7]=>1011100=>0011101
[2,3,4,5,8,7,1,6]=>[6,1,7,8,5,4,3,2]=>1111100=>0011111
[2,3,4,8,6,7,1,5]=>[5,1,7,6,8,4,3,2]=>1111010=>0101111
[2,3,8,5,6,7,1,4]=>[4,1,7,6,5,8,3,2]=>1110110=>0110111
[6,5,8,7,3,4,1,2]=>[2,1,4,3,7,8,5,6]=>1010100=>0010101
[4,6,7,3,8,5,1,2]=>[2,1,5,8,3,7,6,4]=>1011010=>0101101
[3,6,7,4,5,8,1,2]=>[2,1,8,5,4,7,6,3]=>1011110=>0111101
[2,6,7,4,5,1,8,3]=>[3,8,1,5,4,7,6,2]=>1101010=>0101011
[1,6,7,4,5,2,3,8]=>[8,3,2,5,4,7,6,1]=>1111010=>0101111
[1,5,4,7,6,2,3,8]=>[8,3,2,6,7,4,5,1]=>1111000=>0001111
[2,5,4,7,6,1,8,3]=>[3,8,1,6,7,4,5,2]=>1101000=>0001011
[3,5,4,7,6,8,1,2]=>[2,1,8,6,7,4,5,3]=>1011010=>0101101
[4,5,3,7,8,6,1,2]=>[2,1,6,8,7,3,5,4]=>1011001=>1001101
[5,4,3,8,7,6,1,2]=>[2,1,6,7,8,3,4,5]=>1010000=>0000101
[6,4,8,3,7,5,1,2]=>[2,1,5,7,3,8,4,6]=>1011000=>0001101
[6,3,8,4,5,7,1,2]=>[2,1,7,5,4,8,3,6]=>1011100=>0011101
[5,3,4,8,6,7,1,2]=>[2,1,7,6,8,4,3,5]=>1011010=>0101101
[4,3,5,6,8,7,1,2]=>[2,1,7,8,6,5,3,4]=>1010110=>0110101
[3,2,5,6,1,8,7,4]=>[4,7,8,1,6,5,2,3]=>1100100=>0010011
[4,2,5,6,8,1,7,3]=>[3,7,1,8,6,5,2,4]=>1100110=>0110011
[5,2,4,8,6,1,7,3]=>[3,7,1,6,8,4,2,5]=>1101000=>0001011
[6,2,8,4,5,1,7,3]=>[3,7,1,5,4,8,2,6]=>1101000=>0001011
[7,8,2,4,5,1,6,3]=>[3,6,1,5,4,2,8,7]=>1101001=>1001011
[7,8,1,4,5,2,3,6]=>[6,3,2,5,4,1,8,7]=>1111001=>1001111
[6,1,8,4,5,2,3,7]=>[7,3,2,5,4,8,1,6]=>1111000=>0001111
[5,1,4,8,6,2,3,7]=>[7,3,2,6,8,4,1,5]=>1111000=>0001111
[4,1,3,2,8,6,5,7]=>[7,5,6,8,2,3,1,4]=>1100100=>0010011
[5,1,3,8,2,6,4,7]=>[7,4,6,2,8,3,1,5]=>1111000=>0001111
[6,1,8,3,2,5,4,7]=>[7,4,5,2,3,8,1,6]=>1101000=>0001011
[7,8,1,3,2,5,4,6]=>[6,4,5,2,3,1,8,7]=>1101001=>1001011
[6,2,8,3,1,5,7,4]=>[4,7,5,1,3,8,2,6]=>1100100=>0010011
[5,2,3,8,1,6,7,4]=>[4,7,6,1,8,3,2,5]=>1110010=>0100111
[6,3,8,2,1,7,5,4]=>[4,5,7,1,2,8,3,6]=>1010000=>0000101
[7,8,3,2,1,6,5,4]=>[4,5,6,1,2,3,8,7]=>1000001=>1000001
[7,8,4,2,6,1,5,3]=>[3,5,1,6,2,4,8,7]=>1100001=>1000011
[5,4,2,8,7,1,6,3]=>[3,6,1,7,8,2,4,5]=>1100000=>0000011
[4,5,2,7,8,1,6,3]=>[3,6,1,8,7,2,5,4]=>1101001=>1001011
[3,5,2,7,1,8,6,4]=>[4,6,8,1,7,2,5,3]=>1110000=>0000111
[2,5,3,7,1,6,8,4]=>[4,8,6,1,7,3,5,2]=>1110010=>0100111
[1,5,3,7,2,6,4,8]=>[8,4,6,2,7,3,5,1]=>1111000=>0001111
[1,6,7,3,2,5,4,8]=>[8,4,5,2,3,7,6,1]=>1101010=>0101011
[2,6,7,3,1,5,8,4]=>[4,8,5,1,3,7,6,2]=>1100110=>0110011
[3,6,7,2,1,8,5,4]=>[4,5,8,1,2,7,6,3]=>1010010=>0100101
[4,6,7,2,8,1,5,3]=>[3,5,1,8,2,7,6,4]=>1101010=>0101011
[5,6,7,8,2,1,4,3]=>[3,4,1,2,8,7,6,5]=>1000111=>1110001
[7,8,5,6,2,1,4,3]=>[3,4,1,2,6,5,8,7]=>1000101=>1010001
[6,5,8,7,1,2,3,4]=>[4,3,2,1,7,8,5,6]=>1110100=>0010111
[5,4,1,8,7,2,3,6]=>[6,3,2,7,8,1,4,5]=>1110000=>0000111
[6,4,8,1,7,2,3,5]=>[5,3,2,7,1,8,4,6]=>1111000=>0001111
[7,8,3,1,2,6,4,5]=>[5,4,6,2,1,3,8,7]=>1101001=>1001011
[5,3,1,8,2,7,4,6]=>[6,4,7,2,8,1,3,5]=>1101000=>0001011
[4,3,1,2,8,7,5,6]=>[6,5,7,8,2,1,3,4]=>1100100=>0010011
[4,2,1,3,8,5,7,6]=>[6,7,5,8,3,1,2,4]=>1010100=>0010101
[6,2,8,1,3,4,7,5]=>[5,7,4,3,1,8,2,6]=>1111000=>0001111
[7,8,2,1,3,4,6,5]=>[5,6,4,3,1,2,8,7]=>1011001=>1001101
[4,5,2,3,7,6,1,8]=>[8,1,6,7,3,2,5,4]=>1111000=>0001111
[6,4,3,7,2,5,1,8]=>[8,1,5,2,7,3,4,6]=>1110000=>0000111
[8,4,3,6,5,1,2,7]=>[7,2,1,5,6,3,4,8]=>1110000=>0000111
[1,5,6,3,4,8,7,2]=>[2,7,8,4,3,6,5,1]=>1011100=>0011101
[4,6,2,7,3,5,1,8]=>[8,1,5,3,7,2,6,4]=>1111000=>0001111
[3,2,6,7,4,5,1,8]=>[8,1,5,4,7,6,2,3]=>1101010=>0101011
[4,7,2,6,5,3,1,8]=>[8,1,3,5,6,2,7,4]=>1101000=>0001011
[6,8,5,4,2,1,3,7]=>[7,3,1,2,4,5,8,6]=>1010010=>0100101
[4,8,2,6,5,1,3,7]=>[7,3,1,5,6,2,8,4]=>1111000=>0001111
[4,1,2,6,5,8,7,3]=>[3,7,8,5,6,2,1,4]=>1100100=>0010011
[5,1,6,2,4,8,7,3]=>[3,7,8,4,2,6,1,5]=>1101000=>0001011
[6,1,5,4,2,8,7,3]=>[3,7,8,2,4,5,1,6]=>1100000=>0000011
[7,1,5,4,8,2,6,3]=>[3,6,2,8,4,5,1,7]=>1101000=>0001011
[8,1,5,4,7,6,2,3]=>[3,2,6,7,4,5,1,8]=>1101000=>0001011
[1,8,6,7,4,5,3,2]=>[2,3,5,4,7,6,8,1]=>1001010=>0101001
[8,1,6,7,4,5,2,3]=>[3,2,5,4,7,6,1,8]=>1101010=>0101011
[7,1,6,8,4,2,5,3]=>[3,5,2,4,8,6,1,7]=>1100010=>0100011
[6,1,7,8,2,4,5,3]=>[3,5,4,2,8,7,1,6]=>1101001=>1001011
[5,1,7,2,8,4,6,3]=>[3,6,4,8,2,7,1,5]=>1101000=>0001011
[4,1,2,7,8,5,6,3]=>[3,6,5,8,7,2,1,4]=>1100101=>1010011
[3,2,1,7,8,5,6,4]=>[4,6,5,8,7,1,2,3]=>1000101=>1010001
[3,2,8,7,1,5,4,6]=>[6,4,5,1,7,8,2,3]=>1101000=>0001011
[4,8,2,7,1,5,3,6]=>[6,3,5,1,7,2,8,4]=>1111000=>0001111
[5,8,7,2,1,4,3,6]=>[6,3,4,1,2,7,8,5]=>1010100=>0010101
[6,8,7,1,2,4,3,5]=>[5,3,4,2,1,7,8,6]=>1110010=>0100111
[7,8,6,1,4,2,3,5]=>[5,3,2,4,1,6,8,7]=>1110001=>1000111
[8,7,6,1,4,3,2,5]=>[5,2,3,4,1,6,7,8]=>1100000=>0000011
[1,6,7,8,3,4,5,2]=>[2,5,4,3,8,7,6,1]=>1011011=>1101101
[8,6,7,1,3,4,2,5]=>[5,2,4,3,1,7,6,8]=>1110010=>0100111
[7,6,8,1,3,2,4,5]=>[5,4,2,3,1,8,6,7]=>1101010=>0101011
[5,7,8,2,1,3,4,6]=>[6,4,3,1,2,8,7,5]=>1011101=>1011101
[4,7,2,8,1,3,5,6]=>[6,5,3,1,8,2,7,4]=>1111100=>0011111
[3,2,6,8,4,1,5,7]=>[7,5,1,4,8,6,2,3]=>1100110=>0110011
[4,6,2,8,3,1,5,7]=>[7,5,1,3,8,2,6,4]=>1101100=>0011011
[5,6,8,2,3,1,4,7]=>[7,4,1,3,2,8,6,5]=>1101110=>0111011
[6,5,8,3,2,1,4,7]=>[7,4,1,2,3,8,5,6]=>1001100=>0011001
[7,5,8,3,1,2,4,6]=>[6,4,2,1,3,8,5,7]=>1101100=>0011011
[1,5,7,3,8,4,6,2]=>[2,6,4,8,3,7,5,1]=>1011100=>0011101
[1,4,3,7,8,5,6,2]=>[2,6,5,8,7,3,4,1]=>1010101=>1010101
[6,4,3,8,2,1,5,7]=>[7,5,1,2,8,3,4,6]=>1010100=>0010101
[4,5,2,3,8,1,6,7]=>[7,6,1,8,3,2,5,4]=>1111010=>0101111
[3,2,5,4,8,1,6,7]=>[7,6,1,8,4,5,2,3]=>1101010=>0101011
[4,5,2,3,1,8,7,6]=>[6,7,8,1,3,2,5,4]=>1101000=>0001011
[6,4,3,1,2,8,7,5]=>[5,7,8,2,1,3,4,6]=>1100000=>0000011
[7,4,3,1,8,2,6,5]=>[5,6,2,8,1,3,4,7]=>1100000=>0000011
[8,4,3,1,7,6,2,5]=>[5,2,6,7,1,3,4,8]=>1100000=>0000011
[1,5,8,3,7,6,4,2]=>[2,4,6,7,3,8,5,1]=>1010100=>0010101
[8,5,1,3,7,6,2,4]=>[4,2,6,7,3,1,5,8]=>1110000=>0000111
[7,5,1,3,8,2,6,4]=>[4,6,2,8,3,1,5,7]=>1110000=>0000111
[6,5,1,3,2,8,7,4]=>[4,7,8,2,3,1,5,6]=>1100000=>0000011
[5,6,1,2,3,8,7,4]=>[4,7,8,3,2,1,6,5]=>1110100=>0010111
[4,6,2,1,3,8,7,5]=>[5,7,8,3,1,2,6,4]=>1011000=>0001101
[3,2,6,1,4,8,7,5]=>[5,7,8,4,1,6,2,3]=>1101000=>0001011
[3,2,7,1,8,4,6,5]=>[5,6,4,8,1,7,2,3]=>1101000=>0001011
[5,7,1,2,8,3,6,4]=>[4,6,3,8,2,1,7,5]=>1110100=>0010111
[6,7,1,8,2,3,5,4]=>[4,5,3,2,8,1,7,6]=>1110010=>0100111
[7,6,1,8,3,2,5,4]=>[4,5,2,3,8,1,6,7]=>1100000=>0000011
[8,6,1,7,3,5,2,4]=>[4,2,5,3,7,1,6,8]=>1110000=>0000111
[1,7,8,6,5,3,4,2]=>[2,4,3,5,6,8,7,1]=>1010001=>1000101
[6,8,1,7,2,5,3,4]=>[4,3,5,2,7,1,8,6]=>1110010=>0100111
[4,8,2,1,7,6,3,5]=>[5,3,6,7,1,2,8,4]=>1011000=>0001101
[3,2,8,1,7,6,4,5]=>[5,4,6,7,1,8,2,3]=>1101000=>0001011
[4,1,2,8,7,6,5,3]=>[3,5,6,7,8,2,1,4]=>1100000=>0000011
[5,1,8,2,7,6,4,3]=>[3,4,6,7,2,8,1,5]=>1100000=>0000011
[3,2,5,1,6,4,8,7]=>[7,8,4,6,1,5,2,3]=>1101000=>0001011
[3,2,5,4,7,1,8,6]=>[6,8,1,7,4,5,2,3]=>1101000=>0001011
[4,2,5,3,7,6,8,1]=>[1,8,6,7,3,5,2,4]=>0110010=>0100110
[4,2,5,3,7,1,8,6]=>[6,8,1,7,3,5,2,4]=>1110000=>0000111
[4,2,5,3,6,1,8,7]=>[7,8,1,6,3,5,2,4]=>1110000=>0000111
[4,2,5,1,6,3,8,7]=>[7,8,3,6,1,5,2,4]=>1110000=>0000111
[3,1,5,4,6,2,8,7]=>[7,8,2,6,4,5,1,3]=>1101000=>0001011
[4,1,5,3,6,2,8,7]=>[7,8,2,6,3,5,1,4]=>1110000=>0000111
[4,3,5,1,6,2,8,7]=>[7,8,2,6,1,5,3,4]=>1110000=>0000111
[4,3,5,2,7,1,8,6]=>[6,8,1,7,2,5,3,4]=>1110000=>0000111
[4,3,6,2,7,5,8,1]=>[1,8,5,7,2,6,3,4]=>0110100=>0010110
[4,3,6,2,7,1,8,5]=>[5,8,1,7,2,6,3,4]=>1110000=>0000111
[4,3,6,1,7,2,8,5]=>[5,8,2,7,1,6,3,4]=>1110000=>0000111
[4,3,5,1,7,2,8,6]=>[6,8,2,7,1,5,3,4]=>1110000=>0000111
[4,1,5,3,7,2,8,6]=>[6,8,2,7,3,5,1,4]=>1110000=>0000111
[3,1,5,4,7,2,8,6]=>[6,8,2,7,4,5,1,3]=>1101000=>0001011
[2,1,5,4,7,3,8,6]=>[6,8,3,7,4,5,1,2]=>1011000=>0001101
[3,1,5,4,7,6,8,2]=>[2,8,6,7,4,5,1,3]=>1001010=>0101001
[4,1,5,3,7,6,8,2]=>[2,8,6,7,3,5,1,4]=>1010010=>0100101
[4,3,5,1,7,6,8,2]=>[2,8,6,7,1,5,3,4]=>1010010=>0100101
[4,3,6,1,7,5,8,2]=>[2,8,5,7,1,6,3,4]=>1010100=>0010101
[4,3,6,5,7,1,8,2]=>[2,8,1,7,5,6,3,4]=>1010100=>0010101
[5,3,6,4,7,2,8,1]=>[1,8,2,7,4,6,3,5]=>0111000=>0001110
[5,3,6,4,7,1,8,2]=>[2,8,1,7,4,6,3,5]=>1011000=>0001101
[5,3,6,1,7,4,8,2]=>[2,8,4,7,1,6,3,5]=>1011000=>0001101
[5,1,6,3,7,4,8,2]=>[2,8,4,7,3,6,1,5]=>1011000=>0001101
[4,1,6,3,7,5,8,2]=>[2,8,5,7,3,6,1,4]=>1010100=>0010101
[3,1,6,4,7,5,8,2]=>[2,8,5,7,4,6,1,3]=>1001100=>0011001
[2,1,6,4,7,5,8,3]=>[3,8,5,7,4,6,1,2]=>1001100=>0011001
[2,1,6,4,7,3,8,5]=>[5,8,3,7,4,6,1,2]=>1011000=>0001101
[3,1,6,4,7,2,8,5]=>[5,8,2,7,4,6,1,3]=>1101000=>0001011
[4,1,6,3,7,2,8,5]=>[5,8,2,7,3,6,1,4]=>1110000=>0000111
[5,1,6,3,7,2,8,4]=>[4,8,2,7,3,6,1,5]=>1110000=>0000111
[5,3,6,1,7,2,8,4]=>[4,8,2,7,1,6,3,5]=>1110000=>0000111
[5,3,6,2,7,1,8,4]=>[4,8,1,7,2,6,3,5]=>1110000=>0000111
[5,3,6,2,7,4,8,1]=>[1,8,4,7,2,6,3,5]=>0111000=>0001110
[5,2,6,3,7,4,8,1]=>[1,8,4,7,3,6,2,5]=>0111000=>0001110
[5,2,6,3,7,1,8,4]=>[4,8,1,7,3,6,2,5]=>1110000=>0000111
[5,2,6,1,7,3,8,4]=>[4,8,3,7,1,6,2,5]=>1110000=>0000111
[4,2,5,1,7,3,8,6]=>[6,8,3,7,1,5,2,4]=>1110000=>0000111
[4,2,6,1,7,3,8,5]=>[5,8,3,7,1,6,2,4]=>1110000=>0000111
[4,2,6,3,7,1,8,5]=>[5,8,1,7,3,6,2,4]=>1110000=>0000111
[4,2,6,3,7,5,8,1]=>[1,8,5,7,3,6,2,4]=>0110100=>0010110
[3,2,6,4,7,5,8,1]=>[1,8,5,7,4,6,2,3]=>0101100=>0011010
[3,2,6,4,7,1,8,5]=>[5,8,1,7,4,6,2,3]=>1101000=>0001011
[3,2,6,1,7,4,8,5]=>[5,8,4,7,1,6,2,3]=>1101000=>0001011
[3,2,5,1,7,4,8,6]=>[6,8,4,7,1,5,2,3]=>1101000=>0001011
[3,2,4,1,7,5,8,6]=>[6,8,5,7,1,4,2,3]=>1100100=>0010011
[3,1,4,2,7,6,8,5]=>[5,8,6,7,2,4,1,3]=>1100010=>0100011
[3,2,5,1,7,6,8,4]=>[4,8,6,7,1,5,2,3]=>1100010=>0100011
[3,2,6,1,7,5,8,4]=>[4,8,5,7,1,6,2,3]=>1100100=>0010011
[3,2,6,5,7,1,8,4]=>[4,8,1,7,5,6,2,3]=>1100100=>0010011
[4,2,6,5,7,3,8,1]=>[1,8,3,7,5,6,2,4]=>0110100=>0010110
[4,2,6,5,7,1,8,3]=>[3,8,1,7,5,6,2,4]=>1100100=>0010011
[4,2,6,1,7,5,8,3]=>[3,8,5,7,1,6,2,4]=>1100100=>0010011
[4,2,5,1,7,6,8,3]=>[3,8,6,7,1,5,2,4]=>1100010=>0100011
[4,1,5,2,7,6,8,3]=>[3,8,6,7,2,5,1,4]=>1100010=>0100011
[3,1,5,2,7,6,8,4]=>[4,8,6,7,2,5,1,3]=>1100010=>0100011
[2,1,5,3,7,6,8,4]=>[4,8,6,7,3,5,1,2]=>1010010=>0100101
[2,1,6,3,7,5,8,4]=>[4,8,5,7,3,6,1,2]=>1010100=>0010101
[3,1,6,2,7,5,8,4]=>[4,8,5,7,2,6,1,3]=>1100100=>0010011
[4,1,6,2,7,5,8,3]=>[3,8,5,7,2,6,1,4]=>1100100=>0010011
[5,1,6,2,7,4,8,3]=>[3,8,4,7,2,6,1,5]=>1101000=>0001011
[5,2,6,1,7,4,8,3]=>[3,8,4,7,1,6,2,5]=>1101000=>0001011
[5,2,6,4,7,1,8,3]=>[3,8,1,7,4,6,2,5]=>1101000=>0001011
[5,2,6,4,7,3,8,1]=>[1,8,3,7,4,6,2,5]=>0111000=>0001110
[5,4,6,2,7,3,8,1]=>[1,8,3,7,2,6,4,5]=>0111000=>0001110
[5,4,6,2,7,1,8,3]=>[3,8,1,7,2,6,4,5]=>1101000=>0001011
[5,4,6,1,7,2,8,3]=>[3,8,2,7,1,6,4,5]=>1101000=>0001011
[5,1,6,4,7,2,8,3]=>[3,8,2,7,4,6,1,5]=>1101000=>0001011
[4,1,6,5,7,2,8,3]=>[3,8,2,7,5,6,1,4]=>1100100=>0010011
[3,1,6,5,7,2,8,4]=>[4,8,2,7,5,6,1,3]=>1100100=>0010011
[2,1,6,5,7,3,8,4]=>[4,8,3,7,5,6,1,2]=>1010100=>0010101
[3,1,6,5,7,4,8,2]=>[2,8,4,7,5,6,1,3]=>1001100=>0011001
[4,1,6,5,7,3,8,2]=>[2,8,3,7,5,6,1,4]=>1010100=>0010101
[5,1,6,4,7,3,8,2]=>[2,8,3,7,4,6,1,5]=>1011000=>0001101
[5,4,6,1,7,3,8,2]=>[2,8,3,7,1,6,4,5]=>1011000=>0001101
[5,4,6,3,7,1,8,2]=>[2,8,1,7,3,6,4,5]=>1011000=>0001101
[8,6,1,3,4,2,5,7]=>[7,5,2,4,3,1,6,8]=>1110100=>0010111
[2,4,5,7,3,1,8,6]=>[6,8,1,3,7,5,4,2]=>1101100=>0011011
[8,1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1,8]=>1111100=>0011111
[8,2,5,1,3,6,4,7]=>[7,4,6,3,1,5,2,8]=>1111000=>0001111
[8,6,1,4,5,3,2,7]=>[7,2,3,5,4,1,6,8]=>1101000=>0001011
[5,7,4,3,2,1,8,6]=>[6,8,1,2,3,4,7,5]=>1000100=>0010001
[8,5,7,4,3,2,6,1]=>[1,6,2,3,4,7,5,8]=>0100100=>0010010
[8,5,7,4,2,1,6,3]=>[3,6,1,2,4,7,5,8]=>1000100=>0010001
[4,6,3,8,7,1,5,2]=>[2,5,1,7,8,3,6,4]=>1011000=>0001101
[1,7,4,8,6,3,5,2]=>[2,5,3,6,8,4,7,1]=>1011000=>0001101
[3,6,5,8,7,4,1,2]=>[2,1,4,7,8,5,6,3]=>1010100=>0010101
[3,6,4,1,8,7,5,2]=>[2,5,7,8,1,4,6,3]=>1010000=>0000101
[8,2,6,1,4,7,5,3]=>[3,5,7,4,1,6,2,8]=>1101000=>0001011
[3,7,1,6,4,8,2,5]=>[5,2,8,4,6,1,7,3]=>1111000=>0001111
[1,3,6,7,5,8,2,4]=>[4,2,8,5,7,6,3,1]=>1110110=>0110111
[3,7,6,5,8,2,1,4]=>[4,1,2,8,5,6,7,3]=>1010100=>0010101
[3,6,8,5,7,2,4,1]=>[1,4,2,7,5,8,6,3]=>0110110=>0110110
[2,3,5,7,6,8,1,4]=>[4,1,8,6,7,5,3,2]=>1110110=>0110111
[2,1,6,5,7,8,3,4]=>[4,3,8,7,5,6,1,2]=>1010101=>1010101
[5,2,7,1,3,8,4,6]=>[6,4,8,3,1,7,2,5]=>1111000=>0001111
[5,3,1,7,8,2,4,6]=>[6,4,2,8,7,1,3,5]=>1101001=>1001011
[3,2,6,1,4,7,8,5]=>[5,8,7,4,1,6,2,3]=>1101001=>1001011
[1,7,3,4,2,5,8,6]=>[6,8,5,2,4,3,7,1]=>1110100=>0010111
[4,7,2,1,3,5,8,6]=>[6,8,5,3,1,2,7,4]=>1011100=>0011101
[8,7,6,1,3,4,2,5]=>[5,2,4,3,1,6,7,8]=>1110000=>0000111
[8,5,7,3,2,1,6,4]=>[4,6,1,2,3,7,5,8]=>1000100=>0010001
[8,3,6,7,2,1,5,4]=>[4,5,1,2,7,6,3,8]=>1010010=>0100101
[3,7,8,6,2,1,5,4]=>[4,5,1,2,6,8,7,3]=>1010001=>1000101
[8,7,6,3,5,2,4,1]=>[1,4,2,5,3,6,7,8]=>0110000=>0000110
[2,7,4,8,1,6,5,3]=>[3,5,6,1,8,4,7,2]=>1101000=>0001011
[4,6,8,2,1,7,5,3]=>[3,5,7,1,2,8,6,4]=>1001010=>0101001
[8,5,3,7,1,6,2,4]=>[4,2,6,1,7,3,5,8]=>1110000=>0000111
[8,5,7,2,1,3,6,4]=>[4,6,3,1,2,7,5,8]=>1010100=>0010101
[4,6,1,8,7,2,5,3]=>[3,5,2,7,8,1,6,4]=>1101000=>0001011
[8,1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1,8]=>1100110=>0110011
[8,2,6,5,7,4,1,3]=>[3,1,4,7,5,6,2,8]=>1100100=>0010011
[2,7,6,8,5,4,1,3]=>[3,1,4,5,8,6,7,2]=>1100010=>0100011
[1,7,2,5,8,6,4,3]=>[3,4,6,8,5,2,7,1]=>1100100=>0010011
[3,7,8,1,6,5,2,4]=>[4,2,5,6,1,8,7,3]=>1110001=>1000111
[8,4,7,6,5,1,3,2]=>[2,3,1,5,6,7,4,8]=>1001000=>0001001
[3,2,5,1,6,8,4,7]=>[7,4,8,6,1,5,2,3]=>1101010=>0101011
[3,6,2,5,4,8,1,7]=>[7,1,8,4,5,2,6,3]=>1111000=>0001111
[3,5,8,2,4,7,6,1]=>[1,6,7,4,2,8,5,3]=>0111100=>0011110
[4,2,5,8,3,7,6,1]=>[1,6,7,3,8,5,2,4]=>0110100=>0010110
[4,2,6,5,3,8,1,7]=>[7,1,8,3,5,6,2,4]=>1110000=>0000111
[5,3,1,6,8,2,4,7]=>[7,4,2,8,6,1,3,5]=>1101010=>0101011
[5,6,2,8,1,3,4,7]=>[7,4,3,1,8,2,6,5]=>1111100=>0011111
[5,4,3,2,7,1,8,6]=>[6,8,1,7,2,3,4,5]=>1100000=>0000011
[5,4,3,8,2,7,6,1]=>[1,6,7,2,8,3,4,5]=>0110000=>0000110
[4,3,6,2,8,7,5,1]=>[1,5,7,8,2,6,3,4]=>0110000=>0000110
[4,3,7,6,2,1,8,5]=>[5,8,1,2,6,7,3,4]=>1010000=>0000101
[6,4,3,1,7,2,8,5]=>[5,8,2,7,1,3,4,6]=>1100000=>0000011
[7,5,4,3,1,8,2,6]=>[6,2,8,1,3,4,5,7]=>1100000=>0000011
[1,4,5,8,7,3,6,2]=>[2,6,3,7,8,5,4,1]=>1011100=>0011101
[4,3,7,1,8,6,5,2]=>[2,5,6,8,1,7,3,4]=>1010000=>0000101
[7,5,3,1,8,6,4,2]=>[2,4,6,8,1,3,5,7]=>1000000=>0000001
[4,6,1,8,7,3,5,2]=>[2,5,3,7,8,1,6,4]=>1011000=>0001101
[6,8,7,3,1,4,5,2]=>[2,5,4,1,3,7,8,6]=>1001010=>0101001
[6,2,8,7,4,5,1,3]=>[3,1,5,4,7,8,2,6]=>1101000=>0001011
[7,6,2,8,4,1,3,5]=>[5,3,1,4,8,2,6,7]=>1110000=>0000111
[7,3,1,6,8,4,2,5]=>[5,2,4,8,6,1,3,7]=>1100010=>0100011
[7,6,5,3,2,1,8,4]=>[4,8,1,2,3,5,6,7]=>1000000=>0000001
[5,2,7,6,3,1,8,4]=>[4,8,1,3,6,7,2,5]=>1100000=>0000011
[6,5,2,1,7,3,8,4]=>[4,8,3,7,1,2,5,6]=>1010000=>0000101
[6,1,7,4,2,8,3,5]=>[5,3,8,2,4,7,1,6]=>1110000=>0000111
[6,7,2,1,8,3,4,5]=>[5,4,3,8,1,2,7,6]=>1011010=>0101101
[7,5,8,2,1,3,4,6]=>[6,4,3,1,2,8,5,7]=>1011100=>0011101
[5,7,3,1,8,2,4,6]=>[6,4,2,8,1,3,7,5]=>1101100=>0011011
[4,7,1,5,2,8,3,6]=>[6,3,8,2,5,1,7,4]=>1111000=>0001111
[5,2,7,4,1,8,3,6]=>[6,3,8,1,4,7,2,5]=>1110000=>0000111
[2,4,8,6,3,7,5,1]=>[1,5,7,3,6,8,4,2]=>0111000=>0001110
[3,8,6,2,4,7,5,1]=>[1,5,7,4,2,6,8,3]=>0111000=>0001110
[7,3,6,2,4,1,8,5]=>[5,8,1,4,2,6,3,7]=>1110000=>0000111
[3,6,7,2,1,4,8,5]=>[5,8,4,1,2,7,6,3]=>1011010=>0101101
[3,5,2,7,1,8,4,6]=>[6,4,8,1,7,2,5,3]=>1111000=>0001111
[4,3,7,8,2,1,5,6]=>[6,5,1,2,8,7,3,4]=>1010101=>1010101
[8,3,7,1,4,6,2,5]=>[5,2,6,4,1,7,3,8]=>1111000=>0001111
[3,8,2,5,7,1,6,4]=>[4,6,1,7,5,2,8,3]=>1110100=>0010111
[7,8,3,6,2,1,5,4]=>[4,5,1,2,6,3,8,7]=>1010001=>1000101
[8,7,3,6,2,5,4,1]=>[1,4,5,2,6,3,7,8]=>0110000=>0000110
[4,7,8,2,1,6,5,3]=>[3,5,6,1,2,8,7,4]=>1001001=>1001001
[4,2,6,8,1,7,5,3]=>[3,5,7,1,8,6,2,4]=>1100010=>0100011
[5,4,8,2,7,1,6,3]=>[3,6,1,7,2,8,4,5]=>1101000=>0001011
[4,8,1,5,7,2,6,3]=>[3,6,2,7,5,1,8,4]=>1101100=>0011011
[5,8,3,7,1,6,2,4]=>[4,2,6,1,7,3,8,5]=>1110100=>0010111
[5,8,7,2,6,1,3,4]=>[4,3,1,6,2,7,8,5]=>1110100=>0010111
[8,6,2,7,5,1,3,4]=>[4,3,1,5,7,2,6,8]=>1110000=>0000111
[6,4,8,1,7,2,5,3]=>[3,5,2,7,1,8,4,6]=>1101000=>0001011
[5,1,6,8,2,7,4,3]=>[3,4,7,2,8,6,1,5]=>1100010=>0100011
[6,5,2,8,1,7,4,3]=>[3,4,7,1,8,2,5,6]=>1100000=>0000011
[5,2,7,1,8,6,4,3]=>[3,4,6,8,1,7,2,5]=>1100000=>0000011
[5,8,2,7,6,4,3,1]=>[1,3,4,6,7,2,8,5]=>0100100=>0010010
[6,2,8,7,5,4,3,1]=>[1,3,4,5,7,8,2,6]=>0100000=>0000010
[7,6,2,1,8,5,4,3]=>[3,4,5,8,1,2,6,7]=>1000000=>0000001
[6,1,7,2,8,5,4,3]=>[3,4,5,8,2,7,1,6]=>1100000=>0000011
[7,5,1,8,2,6,4,3]=>[3,4,6,2,8,1,5,7]=>1100000=>0000011
[4,7,1,8,6,2,5,3]=>[3,5,2,6,8,1,7,4]=>1101000=>0001011
[4,1,3,2,6,5,8,7]=>[7,8,5,6,2,3,1,4]=>1100100=>0010011
[6,3,5,1,2,4,8,7]=>[7,8,4,2,1,5,3,6]=>1111000=>0001111
[4,3,5,6,1,2,8,7]=>[7,8,2,1,6,5,3,4]=>1110100=>0010111
[8,3,7,5,2,1,4,6]=>[6,4,1,2,5,7,3,8]=>1011000=>0001101
[6,5,2,7,1,8,3,4]=>[4,3,8,1,7,2,5,6]=>1110000=>0000111
[8,5,2,7,4,1,3,6]=>[6,3,1,4,7,2,5,8]=>1110000=>0000111
[3,5,2,6,4,1,8,7]=>[7,8,1,4,6,2,5,3]=>1110000=>0000111
[6,1,2,4,5,3,8,7]=>[7,8,3,5,4,2,1,6]=>1111000=>0001111
[5,6,3,2,1,4,8,7]=>[7,8,4,1,2,3,6,5]=>1001100=>0011001
[2,1,6,3,5,4,8,7]=>[7,8,4,5,3,6,1,2]=>1011000=>0001101
[5,3,1,4,6,2,8,7]=>[7,8,2,6,4,1,3,5]=>1101000=>0001011
[5,7,4,6,2,8,3,1]=>[1,3,8,2,6,4,7,5]=>0101100=>0011010
[3,4,7,8,5,2,1,6]=>[6,1,2,5,8,7,4,3]=>1011001=>1001101
[2,1,8,5,7,3,4,6]=>[6,4,3,7,5,8,1,2]=>1011100=>0011101
[8,6,3,5,1,7,4,2]=>[2,4,7,1,5,3,6,8]=>1010000=>0000101
[7,5,4,8,1,6,3,2]=>[2,3,6,1,8,4,5,7]=>1001000=>0001001
[5,1,4,6,8,2,7,3]=>[3,7,2,8,6,4,1,5]=>1101010=>0101011
[2,5,4,6,7,1,8,3]=>[3,8,1,7,6,4,5,2]=>1101010=>0101011
[2,4,6,3,7,5,8,1]=>[1,8,5,7,3,6,4,2]=>0111100=>0011110
[4,1,6,3,8,5,7,2]=>[2,7,5,8,3,6,1,4]=>1010100=>0010101
[3,7,4,2,8,6,5,1]=>[1,5,6,8,2,4,7,3]=>0110000=>0000110
[8,5,3,7,4,1,6,2]=>[2,6,1,4,7,3,5,8]=>1010000=>0000101
[2,1,5,7,4,8,6,3]=>[3,6,8,4,7,5,1,2]=>1001100=>0011001
[2,1,4,8,3,7,6,5]=>[5,6,7,3,8,4,1,2]=>1011000=>0001101
[7,4,3,8,2,1,6,5]=>[5,6,1,2,8,3,4,7]=>1010000=>0000101
[3,1,8,2,7,6,5,4]=>[4,5,6,7,2,8,1,3]=>1100000=>0000011
[2,3,8,1,6,7,5,4]=>[4,5,7,6,1,8,3,2]=>1110010=>0100111
[4,3,7,2,6,8,5,1]=>[1,5,8,6,2,7,3,4]=>0110010=>0100110
[2,8,1,3,6,5,7,4]=>[4,7,5,6,3,1,8,2]=>1110100=>0010111
[8,1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1,8]=>1110110=>0110111
[7,8,2,4,3,6,1,5]=>[5,1,6,3,4,2,8,7]=>1110001=>1000111
[6,8,3,2,4,1,7,5]=>[5,7,1,4,2,3,8,6]=>1100010=>0100011
[2,1,8,3,4,6,7,5]=>[5,7,6,4,3,8,1,2]=>1011010=>0101101
[2,1,7,8,5,4,3,6]=>[6,3,4,5,8,7,1,2]=>1010001=>1000101
[5,7,3,8,1,4,2,6]=>[6,2,4,1,8,3,7,5]=>1110100=>0010111
[7,1,8,4,5,3,2,6]=>[6,2,3,5,4,8,1,7]=>1101000=>0001011
[8,7,1,6,3,4,2,5]=>[5,2,4,3,6,1,7,8]=>1110000=>0000111
[3,8,6,7,2,4,1,5]=>[5,1,4,2,7,6,8,3]=>1110010=>0100111
[5,3,8,7,4,2,6,1]=>[1,6,2,4,7,8,3,5]=>0110000=>0000110
[8,3,6,1,4,2,7,5]=>[5,7,2,4,1,6,3,8]=>1110000=>0000111
[7,3,5,8,2,4,1,6]=>[6,1,4,2,8,5,3,7]=>1110100=>0010111
[2,3,4,1,8,5,7,6]=>[6,7,5,8,1,4,3,2]=>1110100=>0010111
[4,1,3,2,8,5,7,6]=>[6,7,5,8,2,3,1,4]=>1100100=>0010011
[2,1,4,3,8,5,7,6]=>[6,7,5,8,3,4,1,2]=>1010100=>0010101
[4,1,3,2,6,7,8,5]=>[5,8,7,6,2,3,1,4]=>1100011=>1100011
[8,3,5,6,2,7,1,4]=>[4,1,7,2,6,5,3,8]=>1110100=>0010111
[5,3,6,1,8,7,2,4]=>[4,2,7,8,1,6,3,5]=>1110000=>0000111
[7,8,5,6,1,4,2,3]=>[3,2,4,1,6,5,8,7]=>1100101=>1010011
[5,8,3,6,1,7,2,4]=>[4,2,7,1,6,3,8,5]=>1110100=>0010111
[2,1,8,6,5,7,3,4]=>[4,3,7,5,6,8,1,2]=>1010100=>0010101
[7,1,4,2,5,6,8,3]=>[3,8,6,5,2,4,1,7]=>1100110=>0110011
[2,7,4,1,6,5,8,3]=>[3,8,5,6,1,4,7,2]=>1100100=>0010011
[4,6,1,2,8,7,3,5]=>[5,3,7,8,2,1,6,4]=>1111000=>0001111
[2,4,1,5,8,7,6,3]=>[3,6,7,8,5,1,4,2]=>1100100=>0010011
[6,4,2,1,5,8,7,3]=>[3,7,8,5,1,2,4,6]=>1000100=>0010001
[7,5,3,2,6,8,1,4]=>[4,1,8,6,2,3,5,7]=>1100010=>0100011
[2,1,5,3,6,8,7,4]=>[4,7,8,6,3,5,1,2]=>1010010=>0100101
[4,3,1,5,7,6,8,2]=>[2,8,6,7,5,1,3,4]=>1000110=>0110001
[4,5,2,6,3,1,8,7]=>[7,8,1,3,6,2,5,4]=>1101000=>0001011
[6,5,2,1,4,3,8,7]=>[7,8,3,4,1,2,5,6]=>1010000=>0000101
[6,5,2,7,4,8,3,1]=>[1,3,8,4,7,2,5,6]=>0101000=>0001010
[8,3,7,5,2,1,6,4]=>[4,6,1,2,5,7,3,8]=>1010000=>0000101
[6,3,7,5,2,8,4,1]=>[1,4,8,2,5,7,3,6]=>0110000=>0000110
[6,3,1,5,2,4,8,7]=>[7,8,4,2,5,1,3,6]=>1101000=>0001011
[5,4,3,6,1,2,8,7]=>[7,8,2,1,6,3,4,5]=>1110000=>0000111
[2,6,1,3,5,4,8,7]=>[7,8,4,5,3,1,6,2]=>1111000=>0001111
[5,1,7,3,8,4,6,2]=>[2,6,4,8,3,7,1,5]=>1011000=>0001101
[2,5,7,3,8,6,4,1]=>[1,4,6,8,3,7,5,2]=>0110100=>0010110
[3,6,7,4,1,8,5,2]=>[2,5,8,1,4,7,6,3]=>1010010=>0100101
[5,6,3,7,4,8,1,2]=>[2,1,8,4,7,3,6,5]=>1011100=>0011101
[2,1,6,7,4,8,5,3]=>[3,5,8,4,7,6,1,2]=>1001010=>0101001
[2,1,8,7,4,3,6,5]=>[5,6,3,4,7,8,1,2]=>1010000=>0000101
[5,8,3,7,4,2,6,1]=>[1,6,2,4,7,3,8,5]=>0110100=>0010110
[3,8,7,4,1,2,6,5]=>[5,6,2,1,4,7,8,3]=>1110000=>0000111
[7,8,1,3,5,2,6,4]=>[4,6,2,5,3,1,8,7]=>1110001=>1000111
[5,8,7,3,2,6,1,4]=>[4,1,6,2,3,7,8,5]=>1100100=>0010011
[2,8,6,3,1,5,7,4]=>[4,7,5,1,3,6,8,2]=>1100100=>0010011
[8,1,6,3,2,5,4,7]=>[7,4,5,2,3,6,1,8]=>1101000=>0001011
[2,8,4,1,6,3,7,5]=>[5,7,3,6,1,4,8,2]=>1110000=>0000111
[4,8,1,2,7,6,3,5]=>[5,3,6,7,2,1,8,4]=>1111000=>0001111
[6,8,3,5,2,7,4,1]=>[1,4,7,2,5,3,8,6]=>0110010=>0100110
[2,1,8,5,3,7,4,6]=>[6,4,7,3,5,8,1,2]=>1011000=>0001101
[2,4,1,8,7,6,5,3]=>[3,5,6,7,8,1,4,2]=>1100000=>0000011
[4,1,2,8,7,5,6,3]=>[3,6,5,7,8,2,1,4]=>1100100=>0010011
[3,1,4,8,6,5,7,2]=>[2,7,5,6,8,4,1,3]=>1001100=>0011001
[7,3,5,4,8,6,1,2]=>[2,1,6,8,4,5,3,7]=>1011000=>0001101
[6,4,3,5,8,1,7,2]=>[2,7,1,8,5,3,4,6]=>1010100=>0010101
[2,1,7,6,5,8,3,4]=>[4,3,8,5,6,7,1,2]=>1010100=>0010101
[5,7,3,6,1,8,2,4]=>[4,2,8,1,6,3,7,5]=>1110100=>0010111
[2,7,6,4,5,8,1,3]=>[3,1,8,5,4,6,7,2]=>1101100=>0011011
[3,7,5,6,8,4,2,1]=>[1,2,4,8,6,5,7,3]=>0010110=>0110100
[5,7,1,6,8,2,4,3]=>[3,4,2,8,6,1,7,5]=>1100110=>0110011
[4,6,2,5,8,3,7,1]=>[1,7,3,8,5,2,6,4]=>0111100=>0011110
[7,5,2,6,3,8,1,4]=>[4,1,8,3,6,2,5,7]=>1110000=>0000111
[4,1,2,3,6,8,7,5]=>[5,7,8,6,3,2,1,4]=>1110010=>0100111
[2,4,3,1,8,5,6,7]=>[7,6,5,8,1,3,4,2]=>1100110=>0110011
[7,5,2,8,3,4,6,1]=>[1,6,4,3,8,2,5,7]=>0111000=>0001110
[4,7,2,8,1,5,3,6]=>[6,3,5,1,8,2,7,4]=>1111000=>0001111
[5,7,8,6,3,4,1,2]=>[2,1,4,3,6,8,7,5]=>1010101=>1010101
[7,1,8,5,4,3,6,2]=>[2,6,3,4,5,8,1,7]=>1010000=>0000101
[2,7,8,4,5,3,6,1]=>[1,6,3,5,4,8,7,2]=>0111001=>1001110
[5,7,3,8,1,4,6,2]=>[2,6,4,1,8,3,7,5]=>1011100=>0011101
[2,1,7,8,5,4,6,3]=>[3,6,4,5,8,7,1,2]=>1001001=>1001001
[6,5,3,8,4,1,2,7]=>[7,2,1,4,8,3,5,6]=>1110000=>0000111
[7,5,8,4,3,6,2,1]=>[1,2,6,3,4,8,5,7]=>0010100=>0010100
[2,4,8,3,5,6,1,7]=>[7,1,6,5,3,8,4,2]=>1111100=>0011111
[4,1,8,3,6,5,2,7]=>[7,2,5,6,3,8,1,4]=>1110000=>0000111
[8,4,1,3,7,2,6,5]=>[5,6,2,7,3,1,4,8]=>1110000=>0000111
[2,3,8,1,4,6,7,5]=>[5,7,6,4,1,8,3,2]=>1111010=>0101111
[4,3,8,2,5,1,7,6]=>[6,7,1,5,2,8,3,4]=>1110000=>0000111
[7,4,3,8,2,5,1,6]=>[6,1,5,2,8,3,4,7]=>1110000=>0000111
[7,8,5,6,1,4,3,2]=>[2,3,4,1,6,5,8,7]=>1000101=>1010001
[7,8,4,2,1,5,3,6]=>[6,3,5,1,2,4,8,7]=>1010001=>1000101
[7,8,2,1,6,5,3,4]=>[4,3,5,6,1,2,8,7]=>1010001=>1000101
[6,4,1,2,5,7,3,8]=>[8,3,7,5,2,1,4,6]=>1110100=>0010111
[2,4,8,1,5,7,3,6]=>[6,3,7,5,1,8,4,2]=>1111100=>0011111
[4,3,8,1,7,2,5,6]=>[6,5,2,7,1,8,3,4]=>1110100=>0010111
[7,8,1,4,6,2,5,3]=>[3,5,2,6,4,1,8,7]=>1101001=>1001011
[7,8,3,5,4,2,1,6]=>[6,1,2,4,5,3,8,7]=>1010001=>1000101
[7,8,4,1,2,3,6,5]=>[5,6,3,2,1,4,8,7]=>1110001=>1000111
[7,8,3,6,5,4,1,2]=>[2,1,4,5,6,3,8,7]=>1010001=>1000101
[7,8,2,1,5,3,4,6]=>[6,4,3,5,1,2,8,7]=>1011001=>1001101
[7,8,2,6,4,1,3,5]=>[5,3,1,4,6,2,8,7]=>1110001=>1000111
[7,8,1,6,5,4,3,2]=>[2,3,4,5,6,1,8,7]=>1000001=>1000001
[2,1,8,7,5,4,3,6]=>[6,3,4,5,7,8,1,2]=>1010000=>0000101
[1,3,8,2,6,4,7,5]=>[5,7,4,6,2,8,3,1]=>1111000=>0001111
[5,3,7,1,6,4,8,2]=>[2,8,4,6,1,7,3,5]=>1011000=>0001101
[6,1,2,5,8,7,4,3]=>[3,4,7,8,5,2,1,6]=>1100100=>0010011
[6,4,2,1,5,3,8,7]=>[7,8,3,5,1,2,4,6]=>1010000=>0000101
[6,4,3,7,5,8,1,2]=>[2,1,8,5,7,3,4,6]=>1010100=>0010101
[4,3,8,7,5,6,1,2]=>[2,1,6,5,7,8,3,4]=>1010100=>0010101
[2,4,7,1,5,3,6,8]=>[8,6,3,5,1,7,4,2]=>1111010=>0101111
[2,1,7,5,6,8,4,3]=>[3,4,8,6,5,7,1,2]=>1000110=>0110001
[3,7,2,8,6,4,1,5]=>[5,1,4,6,8,2,7,3]=>1110000=>0000111
[3,8,1,7,6,4,5,2]=>[2,5,4,6,7,1,8,3]=>1011000=>0001101
[1,8,5,7,3,6,4,2]=>[2,4,6,3,7,5,8,1]=>1010100=>0010101
[2,7,5,8,3,6,1,4]=>[4,1,6,3,8,5,7,2]=>1110100=>0010111
[1,5,6,8,2,4,7,3]=>[3,7,4,2,8,6,5,1]=>1101110=>0111011
[2,6,1,4,7,3,5,8]=>[8,5,3,7,4,1,6,2]=>1111100=>0011111
[3,6,8,4,7,5,1,2]=>[2,1,5,7,4,8,6,3]=>1011010=>0101101
[4,5,6,7,2,8,1,3]=>[3,1,8,2,7,6,5,4]=>1101110=>0111011
[4,5,7,6,1,8,3,2]=>[2,3,8,1,6,7,5,4]=>1001100=>0011001
[1,5,8,6,2,7,3,4]=>[4,3,7,2,6,8,5,1]=>1110100=>0010111
[4,7,5,6,3,1,8,2]=>[2,8,1,3,6,5,7,4]=>1001100=>0011001
[5,1,6,3,4,2,8,7]=>[7,8,2,4,3,6,1,5]=>1110000=>0000111
[5,7,1,4,2,3,8,6]=>[6,8,3,2,4,1,7,5]=>1110100=>0010111
[5,7,6,4,3,8,1,2]=>[2,1,8,3,4,6,7,5]=>1010100=>0010101
[6,3,4,5,8,7,1,2]=>[2,1,7,8,5,4,3,6]=>1011100=>0011101
[6,2,4,1,8,3,7,5]=>[5,7,3,8,1,4,2,6]=>1110000=>0000111
[6,2,3,5,4,8,1,7]=>[7,1,8,4,5,3,2,6]=>1111000=>0001111
[1,6,2,4,7,8,3,5]=>[5,3,8,7,4,2,6,1]=>1111001=>1001111
[5,7,2,4,1,6,3,8]=>[8,3,6,1,4,2,7,5]=>1110100=>0010111
[6,1,4,2,8,5,3,7]=>[7,3,5,8,2,4,1,6]=>1110000=>0000111
[6,7,5,8,1,4,3,2]=>[2,3,4,1,8,5,7,6]=>1000110=>0110001
[5,8,7,6,3,4,1,2]=>[2,1,4,3,6,7,8,5]=>1010100=>0010101
[5,8,7,6,2,3,1,4]=>[4,1,3,2,6,7,8,5]=>1100100=>0010011
[4,1,7,2,6,5,3,8]=>[8,3,5,6,2,7,1,4]=>1110000=>0000111
[4,2,7,8,1,6,3,5]=>[5,3,6,1,8,7,2,4]=>1110001=>1000111
[2,1,8,7,6,5,3,4]=>[4,3,5,6,7,8,1,2]=>1010000=>0000101
[3,1,4,7,8,2,6,5]=>[5,6,2,8,7,4,1,3]=>1101001=>1001011
[4,3,7,5,6,8,1,2]=>[2,1,8,6,5,7,3,4]=>1010110=>0110101
[4,8,6,3,5,7,1,2]=>[2,1,7,5,3,6,8,4]=>1011100=>0011101
[3,8,6,5,2,4,1,7]=>[7,1,4,2,5,6,8,3]=>1110000=>0000111
[3,8,5,6,1,4,7,2]=>[2,7,4,1,6,5,8,3]=>1011100=>0011101
[5,2,8,7,1,6,4,3]=>[3,4,6,1,7,8,2,5]=>1100000=>0000011
[3,7,6,8,5,2,1,4]=>[4,1,2,5,8,6,7,3]=>1010010=>0100101
[3,8,7,6,5,4,1,2]=>[2,1,4,5,6,7,8,3]=>1010000=>0000101
[2,1,7,6,5,3,4,8]=>[8,4,3,5,6,7,1,2]=>1011000=>0001101
[2,8,1,6,4,5,3,7]=>[7,3,5,4,6,1,8,2]=>1111000=>0001111
[2,8,7,5,1,4,3,6]=>[6,3,4,1,5,7,8,2]=>1110000=>0000111
[2,7,8,6,5,4,1,3]=>[3,1,4,5,6,8,7,2]=>1100001=>1000011
[5,3,7,8,2,1,4,6]=>[6,4,1,2,8,7,3,5]=>1011001=>1001101
[7,6,1,2,5,8,3,4]=>[4,3,8,5,2,1,6,7]=>1110100=>0010111
[2,1,7,8,4,3,5,6]=>[6,5,3,4,8,7,1,2]=>1010101=>1010101
[7,8,1,2,5,4,6,3]=>[3,6,4,5,2,1,8,7]=>1101001=>1001011
[6,1,8,3,2,4,5,7]=>[7,5,4,2,3,8,1,6]=>1101100=>0011011
[5,8,7,4,2,1,6,3]=>[3,6,1,2,4,7,8,5]=>1000100=>0010001
[4,7,2,8,1,3,6,5]=>[5,6,3,1,8,2,7,4]=>1111000=>0001111
[7,3,8,6,1,2,5,4]=>[4,5,2,1,6,8,3,7]=>1110000=>0000111
[3,4,7,1,8,2,6,5]=>[5,6,2,8,1,7,4,3]=>1111000=>0001111
[1,6,2,4,3,5,7,8]=>[8,7,5,3,4,2,6,1]=>1110101=>1010111
[1,5,2,4,3,6,7,8]=>[8,7,6,3,4,2,5,1]=>1110011=>1100111
[1,7,2,5,3,4,6,8]=>[8,6,4,3,5,2,7,1]=>1111010=>0101111
[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>1111100=>0011111
[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>1111000=>0001111
[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>1111000=>0001111
[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>1111000=>0001111
[1,4,2,8,3,6,5,7]=>[7,5,6,3,8,2,4,1]=>1110100=>0010111
[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>1111100=>0011111
[1,2,3,7,4,6,5,8]=>[8,5,6,4,7,3,2,1]=>1111100=>0011111
[1,3,2,7,4,6,5,8]=>[8,5,6,4,7,2,3,1]=>1101100=>0011011
[1,4,2,7,3,6,5,8]=>[8,5,6,3,7,2,4,1]=>1110100=>0010111
[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>1111000=>0001111
[1,6,2,7,3,5,4,8]=>[8,4,5,3,7,2,6,1]=>1111000=>0001111
[1,7,2,6,3,5,4,8]=>[8,4,5,3,6,2,7,1]=>1111000=>0001111
[1,6,2,5,3,7,4,8]=>[8,4,7,3,5,2,6,1]=>1111000=>0001111
[1,5,2,4,3,7,6,8]=>[8,6,7,3,4,2,5,1]=>1110010=>0100111
[1,6,2,4,3,7,5,8]=>[8,5,7,3,4,2,6,1]=>1110100=>0010111
[1,6,2,4,3,8,5,7]=>[7,5,8,3,4,2,6,1]=>1110100=>0010111
[1,5,2,4,3,8,6,7]=>[7,6,8,3,4,2,5,1]=>1110010=>0100111
[1,6,2,5,3,8,4,7]=>[7,4,8,3,5,2,6,1]=>1111000=>0001111
[1,7,2,5,3,8,4,6]=>[6,4,8,3,5,2,7,1]=>1111000=>0001111
[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>1111000=>0001111
[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>1111100=>0011111
[1,3,2,8,4,7,5,6]=>[6,5,7,4,8,2,3,1]=>1101100=>0011011
[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>1110100=>0010111
[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>1111000=>0001111
[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>1111000=>0001111
[2,8,4,1,6,5,3,7]=>[7,3,5,6,1,4,8,2]=>1110000=>0000111
[2,8,4,1,5,6,7,3]=>[3,7,6,5,1,4,8,2]=>1100110=>0110011
[2,8,7,4,1,6,3,5]=>[5,3,6,1,4,7,8,2]=>1110000=>0000111
[7,2,8,5,1,6,4,3]=>[3,4,6,1,5,8,2,7]=>1100000=>0000011
[2,8,5,4,3,1,7,6]=>[6,7,1,3,4,5,8,2]=>1100000=>0000011
[2,8,5,3,4,1,6,7]=>[7,6,1,4,3,5,8,2]=>1110010=>0100111
[2,8,7,6,1,4,5,3]=>[3,5,4,1,6,7,8,2]=>1101000=>0001011
[2,8,6,5,7,3,1,4]=>[4,1,3,7,5,6,8,2]=>1100100=>0010011
[2,8,4,5,3,7,1,6]=>[6,1,7,3,5,4,8,2]=>1111000=>0001111
[6,2,3,8,5,1,7,4]=>[4,7,1,5,8,3,2,6]=>1110000=>0000111
[6,3,2,8,5,1,4,7]=>[7,4,1,5,8,2,3,6]=>1101000=>0001011
[6,4,8,5,1,3,7,2]=>[2,7,3,1,5,8,4,6]=>1011000=>0001101
[6,3,7,5,2,1,8,4]=>[4,8,1,2,5,7,3,6]=>1010000=>0000101
[4,3,7,5,1,2,8,6]=>[6,8,2,1,5,7,3,4]=>1110000=>0000111
[3,6,1,7,5,2,8,4]=>[4,8,2,5,7,1,6,3]=>1110000=>0000111
[3,4,1,2,7,6,8,5]=>[5,8,6,7,2,1,4,3]=>1110010=>0100111
[3,4,2,1,7,5,8,6]=>[6,8,5,7,1,2,4,3]=>1010100=>0010101
[3,5,2,6,4,8,7,1]=>[1,7,8,4,6,2,5,3]=>0111000=>0001110
[5,6,1,8,7,2,4,3]=>[3,4,2,7,8,1,6,5]=>1100100=>0010011
[6,3,5,8,2,7,4,1]=>[1,4,7,2,8,5,3,6]=>0110100=>0010110
[4,3,2,1,8,6,5,7]=>[7,5,6,8,1,2,3,4]=>1000100=>0010001
[4,2,1,3,8,7,6,5]=>[5,6,7,8,3,1,2,4]=>1010000=>0000101
[7,1,6,8,4,3,5,2]=>[2,5,3,4,8,6,1,7]=>1010010=>0100101
[6,1,2,8,4,5,7,3]=>[3,7,5,4,8,2,1,6]=>1101100=>0011011
[5,6,8,2,3,1,7,4]=>[4,7,1,3,2,8,6,5]=>1100110=>0110011
[6,5,8,2,4,3,1,7]=>[7,1,3,4,2,8,5,6]=>1100100=>0010011
[6,5,8,4,2,3,7,1]=>[1,7,3,2,4,8,5,6]=>0110100=>0010110
[7,5,3,8,2,4,1,6]=>[6,1,4,2,8,3,5,7]=>1110000=>0000111
[6,2,5,8,3,7,1,4]=>[4,1,7,3,8,5,2,6]=>1110100=>0010111
[1,6,5,7,3,4,2,8]=>[8,2,4,3,7,5,6,1]=>1110100=>0010111
[5,2,1,8,7,6,3,4]=>[4,3,6,7,8,1,2,5]=>1010000=>0000101
[7,1,3,8,4,6,2,5]=>[5,2,6,4,8,3,1,7]=>1111000=>0001111
[5,7,8,4,3,6,2,1]=>[1,2,6,3,4,8,7,5]=>0010101=>1010100
[4,1,8,3,5,6,7,2]=>[2,7,6,5,3,8,1,4]=>1010110=>0110101
[4,1,8,3,6,2,7,5]=>[5,7,2,6,3,8,1,4]=>1110000=>0000111
[2,3,4,8,6,1,7,5]=>[5,7,1,6,8,4,3,2]=>1111000=>0001111
[2,3,4,8,6,5,1,7]=>[7,1,5,6,8,4,3,2]=>1111000=>0001111
[2,7,3,5,8,6,1,4]=>[4,1,6,8,5,3,7,2]=>1110100=>0010111
[1,5,4,6,2,7,3,8]=>[8,3,7,2,6,4,5,1]=>1111000=>0001111
[5,3,6,4,1,8,7,2]=>[2,7,8,1,4,6,3,5]=>1010000=>0000101
[5,3,6,1,4,8,2,7]=>[7,2,8,4,1,6,3,5]=>1111000=>0001111
[7,3,5,6,8,4,2,1]=>[1,2,4,8,6,5,3,7]=>0010110=>0110100
[6,3,5,1,8,2,7,4]=>[4,7,2,8,1,5,3,6]=>1110000=>0000111
[2,6,1,5,8,4,7,3]=>[3,7,4,8,5,1,6,2]=>1101100=>0011011
[2,7,6,5,8,3,4,1]=>[1,4,3,8,5,6,7,2]=>0110100=>0010110
[5,7,1,6,3,8,4,2]=>[2,4,8,3,6,1,7,5]=>1010100=>0010101
[3,2,4,1,7,8,5,6]=>[6,5,8,7,1,4,2,3]=>1100101=>1010011
[3,1,4,2,7,8,6,5]=>[5,6,8,7,2,4,1,3]=>1100001=>1000011
[3,1,4,6,8,5,7,2]=>[2,7,5,8,6,4,1,3]=>1001110=>0111001
[6,3,4,5,7,1,8,2]=>[2,8,1,7,5,4,3,6]=>1011100=>0011101
[2,5,4,6,1,7,8,3]=>[3,8,7,1,6,4,5,2]=>1101001=>1001011
[7,2,1,4,3,6,5,8]=>[8,5,6,3,4,1,2,7]=>1010100=>0010101
[7,3,4,1,2,6,5,8]=>[8,5,6,2,1,4,3,7]=>1110100=>0010111
[7,4,3,2,1,6,5,8]=>[8,5,6,1,2,3,4,7]=>1000100=>0010001
[7,6,3,2,5,4,1,8]=>[8,1,4,5,2,3,6,7]=>1100000=>0000011
[6,7,3,2,5,4,8,1]=>[1,8,4,5,2,3,7,6]=>0101010=>0101010
[1,8,3,2,5,4,7,6]=>[6,7,4,5,2,3,8,1]=>1101000=>0001011
[1,8,4,5,2,3,7,6]=>[6,7,3,2,5,4,8,1]=>1111000=>0001111
[7,3,5,1,6,2,4,8]=>[8,4,2,6,1,5,3,7]=>1111000=>0001111
[7,2,1,5,6,3,4,8]=>[8,4,3,6,5,1,2,7]=>1011100=>0011101
[7,2,1,6,5,4,3,8]=>[8,3,4,5,6,1,2,7]=>1010000=>0000101
[7,3,6,1,5,4,2,8]=>[8,2,4,5,1,6,3,7]=>1110000=>0000111
[1,8,5,4,3,2,7,6]=>[6,7,2,3,4,5,8,1]=>1100000=>0000011
[3,2,1,8,5,4,7,6]=>[6,7,4,5,8,1,2,3]=>1001000=>0001001
[2,3,8,1,5,4,7,6]=>[6,7,4,5,1,8,3,2]=>1111000=>0001111
[2,4,8,5,1,3,7,6]=>[6,7,3,1,5,8,4,2]=>1111000=>0001111
[2,5,8,4,3,1,7,6]=>[6,7,1,3,4,8,5,2]=>1100100=>0010011
[2,6,8,4,3,7,1,5]=>[5,1,7,3,4,8,6,2]=>1110010=>0100111
[2,7,8,4,3,6,5,1]=>[1,5,6,3,4,8,7,2]=>0110001=>1000110
[1,8,7,5,6,3,4,2]=>[2,4,3,6,5,7,8,1]=>1010100=>0010101
[2,7,8,5,6,3,4,1]=>[1,4,3,6,5,8,7,2]=>0110101=>1010110
[2,6,8,5,7,3,1,4]=>[4,1,3,7,5,8,6,2]=>1100110=>0110011
[2,5,8,6,7,1,3,4]=>[4,3,1,7,6,8,5,2]=>1110110=>0110111
[2,4,8,6,1,7,3,5]=>[5,3,7,1,6,8,4,2]=>1111000=>0001111
[3,2,1,8,6,7,4,5]=>[5,4,7,6,8,1,2,3]=>1001010=>0101001
[5,3,7,1,6,8,4,2]=>[2,4,8,6,1,7,3,5]=>1010010=>0100101
[5,4,7,6,1,8,3,2]=>[2,3,8,1,6,7,4,5]=>1001000=>0001001
[4,5,7,6,8,1,3,2]=>[2,3,1,8,6,7,5,4]=>1001110=>0111001
[1,8,5,6,7,2,3,4]=>[4,3,2,7,6,5,8,1]=>1110110=>0110111
[4,6,5,7,8,2,1,3]=>[3,1,2,8,7,5,6,4]=>1001101=>1011001
[5,4,6,7,1,8,2,3]=>[3,2,8,1,7,6,4,5]=>1101010=>0101011
[5,3,6,1,7,8,2,4]=>[4,2,8,7,1,6,3,5]=>1110001=>1000111
[5,2,1,6,7,8,3,4]=>[4,3,8,7,6,1,2,5]=>1010011=>1100101
[6,2,1,5,7,3,8,4]=>[4,8,3,7,5,1,2,6]=>1010100=>0010101
[6,3,5,1,7,2,8,4]=>[4,8,2,7,1,5,3,6]=>1110000=>0000111
[6,4,5,7,1,2,8,3]=>[3,8,2,1,7,5,4,6]=>1101100=>0011011
[6,5,4,7,2,1,8,3]=>[3,8,1,2,7,4,5,6]=>1001000=>0001001
[1,8,4,6,2,7,3,5]=>[5,3,7,2,6,4,8,1]=>1111000=>0001111
[1,8,3,2,6,7,4,5]=>[5,4,7,6,2,3,8,1]=>1101010=>0101011
[5,7,3,2,6,8,4,1]=>[1,4,8,6,2,3,7,5]=>0100110=>0110010
[6,5,3,2,7,1,8,4]=>[4,8,1,7,2,3,5,6]=>1100000=>0000011
[6,4,3,2,1,7,8,5]=>[5,8,7,1,2,3,4,6]=>1000001=>1000001
[6,2,1,4,3,7,8,5]=>[5,8,7,3,4,1,2,6]=>1010001=>1000101
[5,2,1,4,3,8,7,6]=>[6,7,8,3,4,1,2,5]=>1010000=>0000101
[5,3,4,1,2,8,7,6]=>[6,7,8,2,1,4,3,5]=>1110000=>0000111
[4,5,3,2,8,1,7,6]=>[6,7,1,8,2,3,5,4]=>1101000=>0001011
[4,6,3,2,8,7,1,5]=>[5,1,7,8,2,3,6,4]=>1101000=>0001011
[4,7,3,2,8,6,5,1]=>[1,5,6,8,2,3,7,4]=>0101000=>0001010
[1,8,3,2,7,6,5,4]=>[4,5,6,7,2,3,8,1]=>1100000=>0000011
[1,8,4,7,2,6,5,3]=>[3,5,6,2,7,4,8,1]=>1101000=>0001011
[3,7,4,8,2,6,5,1]=>[1,5,6,2,8,4,7,3]=>0111000=>0001110
[3,6,4,8,2,7,1,5]=>[5,1,7,2,8,4,6,3]=>1111000=>0001111
[3,5,4,8,2,1,7,6]=>[6,7,1,2,8,4,5,3]=>1011000=>0001101
[3,4,5,8,1,2,7,6]=>[6,7,2,1,8,5,4,3]=>1111100=>0011111
[4,3,5,1,8,2,7,6]=>[6,7,2,8,1,5,3,4]=>1110000=>0000111
[4,2,1,5,8,3,7,6]=>[6,7,3,8,5,1,2,4]=>1010100=>0010101
[4,2,1,6,8,7,3,5]=>[5,3,7,8,6,1,2,4]=>1010010=>0100101
[4,3,6,1,8,7,2,5]=>[5,2,7,8,1,6,3,4]=>1110000=>0000111
[3,4,6,8,1,7,2,5]=>[5,2,7,1,8,6,4,3]=>1111010=>0101111
[3,5,6,8,7,1,2,4]=>[4,2,1,7,8,6,5,3]=>1110110=>0110111
[3,6,5,8,7,2,1,4]=>[4,1,2,7,8,5,6,3]=>1010100=>0010101
[3,7,5,8,6,2,4,1]=>[1,4,2,6,8,5,7,3]=>0110100=>0010110
[1,8,6,7,5,4,2,3]=>[3,2,4,5,7,6,8,1]=>1100010=>0100011
[3,6,7,8,5,4,1,2]=>[2,1,4,5,8,7,6,3]=>1010011=>1100101
[3,5,7,8,6,1,4,2]=>[2,4,1,6,8,7,5,3]=>1010101=>1010101
[4,2,1,7,8,6,5,3]=>[3,5,6,8,7,1,2,4]=>1000001=>1000001
[2,3,8,1,7,6,5,4]=>[4,5,6,7,1,8,3,2]=>1110000=>0000111
[2,4,8,7,1,6,5,3]=>[3,5,6,1,7,8,4,2]=>1101000=>0001011
[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>10101010100=>00101010101
[8,1,6,7,3,2,5,4]=>[4,5,2,3,7,6,1,8]=>1100010=>0100011
[8,1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1,8]=>1111010=>0101111
[8,1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1,8]=>1110100=>0010111
[8,1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1,8]=>1100000=>0000011
[8,1,5,3,7,2,6,4]=>[4,6,2,7,3,5,1,8]=>1110000=>0000111
[2,7,8,3,4,5,6,1]=>[1,6,5,4,3,8,7,2]=>0111101=>1011110
[6,3,2,1,4,5,8,7]=>[7,8,5,4,1,2,3,6]=>1001100=>0011001
[7,3,1,4,2,6,8,5]=>[5,8,6,2,4,1,3,7]=>1100010=>0100011
[4,7,8,5,6,1,2,3]=>[3,2,1,6,5,8,7,4]=>1101101=>1011011
[3,7,8,5,6,2,1,4]=>[4,1,2,6,5,8,7,3]=>1010101=>1010101
[3,7,8,4,2,6,1,5]=>[5,1,6,2,4,8,7,3]=>1110001=>1000111
[3,7,8,2,4,5,1,6]=>[6,1,5,4,2,8,7,3]=>1111001=>1001111
[3,6,2,8,4,5,1,7]=>[7,1,5,4,8,2,6,3]=>1111000=>0001111
[2,3,6,7,4,5,8,1]=>[1,8,5,4,7,6,3,2]=>0111110=>0111110
[3,5,4,2,8,7,1,6]=>[6,1,7,8,2,4,5,3]=>1110000=>0000111
[4,6,5,8,7,1,2,3]=>[3,2,1,7,8,5,6,4]=>1101100=>0011011
[6,4,5,1,7,8,2,3]=>[3,2,8,7,1,5,4,6]=>1101001=>1001011
[5,4,2,3,1,8,6,7]=>[7,6,8,1,3,2,4,5]=>1100010=>0100011
[6,5,3,1,8,2,7,4]=>[4,7,2,8,1,3,5,6]=>1100000=>0000011
[6,5,4,1,8,7,2,3]=>[3,2,7,8,1,4,5,6]=>1100000=>0000011
[7,5,1,4,8,6,2,3]=>[3,2,6,8,4,1,5,7]=>1101000=>0001011
[7,4,1,3,2,8,6,5]=>[5,6,8,2,3,1,4,7]=>1100000=>0000011
[6,4,2,1,3,8,5,7]=>[7,5,8,3,1,2,4,6]=>1010100=>0010101
[6,2,4,1,3,7,5,8]=>[8,5,7,3,1,4,2,6]=>1110100=>0010111
[2,6,4,8,3,7,5,1]=>[1,5,7,3,8,4,6,2]=>0111000=>0001110
[2,6,5,8,7,3,4,1]=>[1,4,3,7,8,5,6,2]=>0110100=>0010110
[7,5,1,2,8,3,4,6]=>[6,4,3,8,2,1,5,7]=>1111000=>0001111
[7,6,1,8,2,3,4,5]=>[5,4,3,2,8,1,6,7]=>1111000=>0001111
[7,6,1,8,4,5,2,3]=>[3,2,5,4,8,1,6,7]=>1101000=>0001011
[6,7,8,1,4,5,2,3]=>[3,2,5,4,1,8,7,6]=>1101011=>1101011
[6,7,8,1,3,2,5,4]=>[4,5,2,3,1,8,7,6]=>1100011=>1100011
[2,5,6,7,8,3,4,1]=>[1,4,3,8,7,6,5,2]=>0110111=>1110110
[2,4,6,7,3,8,5,1]=>[1,5,8,3,7,6,4,2]=>0111010=>0101110
[4,7,8,3,2,1,6,5]=>[5,6,1,2,3,8,7,4]=>1001001=>1001001
[5,7,8,3,1,2,6,4]=>[4,6,2,1,3,8,7,5]=>1100101=>1010011
[5,7,8,4,1,6,2,3]=>[3,2,6,1,4,8,7,5]=>1100101=>1010011
[5,6,4,8,1,7,2,3]=>[3,2,7,1,8,4,6,5]=>1101100=>0011011
[4,6,3,8,2,1,7,5]=>[5,7,1,2,8,3,6,4]=>1011000=>0001101
[4,3,6,7,2,1,8,5]=>[5,8,1,2,7,6,3,4]=>1010010=>0100101
[5,3,6,7,1,2,8,4]=>[4,8,2,1,7,6,3,5]=>1110010=>0100111
[3,5,6,7,8,2,1,4]=>[4,1,2,8,7,6,5,3]=>1010111=>1110101
[3,4,6,7,2,8,1,5]=>[5,1,8,2,7,6,4,3]=>1111010=>0101111
[3,4,5,2,7,8,1,6]=>[6,1,8,7,2,5,4,3]=>1111001=>1001111
[7,4,6,1,8,3,5,2]=>[2,5,3,8,1,6,4,7]=>1011000=>0001101
[7,3,5,1,8,4,6,2]=>[2,6,4,8,1,5,3,7]=>1011000=>0001101
[7,3,4,1,8,5,6,2]=>[2,6,5,8,1,4,3,7]=>1010100=>0010101
[4,5,7,3,1,8,6,2]=>[2,6,8,1,3,7,5,4]=>1001100=>0011001
[4,5,6,2,1,8,7,3]=>[3,7,8,1,2,6,5,4]=>1001100=>0011001
[1,6,5,2,7,4,3,8]=>[8,3,4,7,2,5,6,1]=>1110000=>0000111
[3,6,7,5,1,8,4,2]=>[2,4,8,1,5,7,6,3]=>1010010=>0100101
[7,5,6,1,8,3,4,2]=>[2,4,3,8,1,6,5,7]=>1010100=>0010101
[7,6,5,1,8,4,3,2]=>[2,3,4,8,1,5,6,7]=>1000000=>0000001
[7,6,4,1,8,5,3,2]=>[2,3,5,8,1,4,6,7]=>1000000=>0000001
[6,4,2,1,8,7,5,3]=>[3,5,7,8,1,2,4,6]=>1000000=>0000001
[1,5,3,2,7,6,4,8]=>[8,4,6,7,2,3,5,1]=>1101000=>0001011
[5,3,2,1,8,7,6,4]=>[4,6,7,8,1,2,3,5]=>1000000=>0000001
[2,6,4,1,7,8,5,3]=>[3,5,8,7,1,4,6,2]=>1100001=>1000011
[2,6,5,1,7,8,4,3]=>[3,4,8,7,1,5,6,2]=>1100001=>1000011
[4,5,7,1,6,8,2,3]=>[3,2,8,6,1,7,5,4]=>1101110=>0111011
[4,5,7,1,3,8,2,6]=>[6,2,8,3,1,7,5,4]=>1111100=>0011111
[6,5,1,2,8,4,3,7]=>[7,3,4,8,2,1,5,6]=>1110000=>0000111
[4,3,1,2,8,6,5,7]=>[7,5,6,8,2,1,3,4]=>1100100=>0010011
[6,1,2,5,8,3,4,7]=>[7,4,3,8,5,2,1,6]=>1111100=>0011111
[7,1,3,4,8,2,5,6]=>[6,5,2,8,4,3,1,7]=>1111100=>0011111
[2,6,1,5,7,8,3,4]=>[4,3,8,7,5,1,6,2]=>1110101=>1010111
[7,6,1,5,8,3,2,4]=>[4,2,3,8,5,1,6,7]=>1100100=>0010011
[3,6,7,1,5,8,2,4]=>[4,2,8,5,1,7,6,3]=>1110110=>0110111
[7,1,6,5,8,2,4,3]=>[3,4,2,8,5,6,1,7]=>1100100=>0010011
[7,5,1,6,8,4,2,3]=>[3,2,4,8,6,1,5,7]=>1100010=>0100011
[7,4,1,6,8,5,2,3]=>[3,2,5,8,6,1,4,7]=>1100010=>0100011
[5,2,3,1,8,6,7,4]=>[4,7,6,8,1,3,2,5]=>1100010=>0100011
[1,6,2,5,7,3,4,8]=>[8,4,3,7,5,2,6,1]=>1111100=>0011111
[6,2,1,5,8,7,3,4]=>[4,3,7,8,5,1,2,6]=>1010100=>0010101
[7,3,1,5,8,6,2,4]=>[4,2,6,8,5,1,3,7]=>1100100=>0010011
[6,2,4,1,8,5,7,3]=>[3,7,5,8,1,4,2,6]=>1100100=>0010011
[6,2,5,1,8,4,7,3]=>[3,7,4,8,1,5,2,6]=>1101000=>0001011
[7,1,6,4,8,2,5,3]=>[3,5,2,8,4,6,1,7]=>1101000=>0001011
[7,1,5,3,8,2,6,4]=>[4,6,2,8,3,5,1,7]=>1110000=>0000111
[6,1,5,2,8,3,7,4]=>[4,7,3,8,2,5,1,6]=>1110000=>0000111
[7,3,1,4,8,6,2,5]=>[5,2,6,8,4,1,3,7]=>1101000=>0001011
[6,2,1,4,8,7,3,5]=>[5,3,7,8,4,1,2,6]=>1011000=>0001101
[6,1,4,2,8,3,7,5]=>[5,7,3,8,2,4,1,6]=>1110000=>0000111
[7,1,4,3,8,2,6,5]=>[5,6,2,8,3,4,1,7]=>1110000=>0000111
[5,1,3,2,8,4,7,6]=>[6,7,4,8,2,3,1,5]=>1101000=>0001011
[4,2,1,3,8,7,5,6]=>[6,5,7,8,3,1,2,4]=>1010100=>0010101
[2,6,1,4,7,8,3,5]=>[5,3,8,7,4,1,6,2]=>1111001=>1001111
[7,1,3,5,8,2,4,6]=>[6,4,2,8,5,3,1,7]=>1111100=>0011111
[7,8,5,6,1,3,4,2]=>[2,4,3,1,6,5,8,7]=>1010101=>1010101
[7,8,1,3,6,2,5,4]=>[4,5,2,6,3,1,8,7]=>1110001=>1000111
[1,3,8,4,7,2,5,6]=>[6,5,2,7,4,8,3,1]=>1111100=>0011111
[4,6,1,2,5,7,3,8]=>[8,3,7,5,2,1,6,4]=>1111100=>0011111
[1,4,8,2,5,7,3,6]=>[6,3,7,5,2,8,4,1]=>1111100=>0011111
[7,8,4,2,5,1,3,6]=>[6,3,1,5,2,4,8,7]=>1110001=>1000111
[7,8,2,4,5,6,1,3]=>[3,1,6,5,4,2,8,7]=>1101101=>1011011
[7,8,1,5,4,6,3,2]=>[2,3,6,4,5,1,8,7]=>1001001=>1001001
[7,8,2,1,6,3,4,5]=>[5,4,3,6,1,2,8,7]=>1011001=>1001101
[7,8,3,5,6,4,1,2]=>[2,1,4,6,5,3,8,7]=>1010101=>1010101
[7,8,1,4,2,3,6,5]=>[5,6,3,2,4,1,8,7]=>1110001=>1000111
[1,5,8,4,3,2,7,6]=>[6,7,2,3,4,8,5,1]=>1100100=>0010011
[5,6,1,4,3,2,7,8]=>[8,7,2,3,4,1,6,5]=>1100101=>1010011
[2,6,4,8,3,7,1,5]=>[5,1,7,3,8,4,6,2]=>1111000=>0001111
[1,4,6,8,3,7,5,2]=>[2,5,7,3,8,6,4,1]=>1011010=>0101101
[2,1,8,4,7,3,6,5]=>[5,6,3,7,4,8,1,2]=>1011000=>0001101
[3,5,8,4,7,6,1,2]=>[2,1,6,7,4,8,5,3]=>1011100=>0011101
[1,6,2,4,7,3,8,5]=>[5,8,3,7,4,2,6,1]=>1111000=>0001111
[4,6,2,5,3,1,8,7]=>[7,8,1,3,5,2,6,4]=>1101000=>0001011
[4,7,5,1,3,6,8,2]=>[2,8,6,3,1,5,7,4]=>1011010=>0101101
[7,5,3,6,2,4,1,8]=>[8,1,4,2,6,3,5,7]=>1110000=>0000111
[5,7,3,6,1,4,8,2]=>[2,8,4,1,6,3,7,5]=>1011100=>0011101
[5,3,6,7,2,1,8,4]=>[4,8,1,2,7,6,3,5]=>1010010=>0100101
[6,3,1,2,4,5,8,7]=>[7,8,5,4,2,1,3,6]=>1101100=>0011011
[1,4,7,2,5,3,8,6]=>[6,8,3,5,2,7,4,1]=>1111000=>0001111
[6,4,7,3,5,8,1,2]=>[2,1,8,5,3,7,4,6]=>1011100=>0011101
[3,5,6,7,8,1,4,2]=>[2,4,1,8,7,6,5,3]=>1010111=>1110101
[3,6,5,7,8,2,1,4]=>[4,1,2,8,7,5,6,3]=>1010101=>1010101
[2,5,7,6,8,1,3,4]=>[4,3,1,8,6,7,5,2]=>1110110=>0110111
[2,1,6,8,4,5,3,7]=>[7,3,5,4,8,6,1,2]=>1011010=>0101101
[2,7,1,8,5,3,4,6]=>[6,4,3,5,8,1,7,2]=>1111000=>0001111
[3,7,6,8,5,4,1,2]=>[2,1,4,5,8,6,7,3]=>1010010=>0100101
[4,3,8,5,6,7,1,2]=>[2,1,7,6,5,8,3,4]=>1010110=>0110101
[4,2,8,1,6,3,7,5]=>[5,7,3,6,1,8,2,4]=>1110000=>0000111
[3,1,8,5,4,6,7,2]=>[2,7,6,4,5,8,1,3]=>1001010=>0101001
[3,4,2,8,6,1,7,5]=>[5,7,1,6,8,2,4,3]=>1110000=>0000111
[3,4,7,1,5,2,6,8]=>[8,6,2,5,1,7,4,3]=>1111010=>0101111
[4,1,8,3,6,2,5,7]=>[7,5,2,6,3,8,1,4]=>1110100=>0010111
[5,7,8,6,3,2,1,4]=>[4,1,2,3,6,8,7,5]=>1000101=>1010001
[5,7,8,6,1,3,4,2]=>[2,4,3,1,6,8,7,5]=>1010101=>1010101
[7,6,5,8,1,3,4,2]=>[2,4,3,1,8,5,6,7]=>1010100=>0010101
[1,6,4,3,8,2,5,7]=>[7,5,2,8,3,4,6,1]=>1110100=>0010111
[3,6,5,4,1,2,7,8]=>[8,7,2,1,4,5,6,3]=>1110001=>1000111
[2,4,5,1,7,8,6,3]=>[3,6,8,7,1,5,4,2]=>1101001=>1001011
[2,6,4,1,8,3,7,5]=>[5,7,3,8,1,4,6,2]=>1110000=>0000111
[3,6,4,5,8,7,1,2]=>[2,1,7,8,5,4,6,3]=>1011100=>0011101
[7,1,6,5,3,8,4,2]=>[2,4,8,3,5,6,1,7]=>1010000=>0000101
[7,2,5,6,3,8,1,4]=>[4,1,8,3,6,5,2,7]=>1110100=>0010111
[5,6,2,7,3,1,4,8]=>[8,4,1,3,7,2,6,5]=>1101100=>0011011
[6,7,1,5,2,8,3,4]=>[4,3,8,2,5,1,7,6]=>1110010=>0100111
[6,7,5,3,8,4,1,2]=>[2,1,4,8,3,5,7,6]=>1010010=>0100101
[1,6,5,4,2,3,8,7]=>[7,8,3,2,4,5,6,1]=>1110000=>0000111
[7,1,5,3,4,2,8,6]=>[6,8,2,4,3,5,1,7]=>1110000=>0000111
[7,6,1,5,3,2,8,4]=>[4,8,2,3,5,1,6,7]=>1100000=>0000011
[7,5,2,4,3,1,6,8]=>[8,6,1,3,4,2,5,7]=>1100010=>0100011
[7,4,6,1,2,5,3,8]=>[8,3,5,2,1,6,4,7]=>1111000=>0001111
[7,1,4,2,5,3,6,8]=>[8,6,3,5,2,4,1,7]=>1110010=>0100111
[6,8,1,3,7,5,4,2]=>[2,4,5,7,3,1,8,6]=>1010010=>0100101
[7,1,3,5,6,4,2,8]=>[8,2,4,6,5,3,1,7]=>1110100=>0010111
[7,4,2,6,5,1,3,8]=>[8,3,1,5,6,2,4,7]=>1110000=>0000111
[7,2,3,5,4,1,6,8]=>[8,6,1,4,5,3,2,7]=>1110010=>0100111
[2,5,1,7,8,3,6,4]=>[4,6,3,8,7,1,5,2]=>1110001=>1000111
[2,5,3,6,8,4,7,1]=>[1,7,4,8,6,3,5,2]=>0111010=>0101110
[2,4,7,6,8,5,1,3]=>[3,1,5,8,6,7,4,2]=>1101010=>0101011
[2,5,3,7,6,1,8,4]=>[4,8,1,6,7,3,5,2]=>1110000=>0000111
[2,5,7,8,1,4,6,3]=>[3,6,4,1,8,7,5,2]=>1101101=>1011011
[3,5,7,4,1,6,2,8]=>[8,2,6,1,4,7,5,3]=>1110100=>0010111
[5,3,4,1,8,6,7,2]=>[2,7,6,8,1,4,3,5]=>1010010=>0100101
[5,2,1,8,6,3,7,4]=>[4,7,3,6,8,1,2,5]=>1010000=>0000101
[4,2,8,6,5,3,7,1]=>[1,7,3,5,6,8,2,4]=>0110000=>0000110
[4,1,2,8,5,6,7,3]=>[3,7,6,5,8,2,1,4]=>1100110=>0110011
[1,4,2,7,5,8,6,3]=>[3,6,8,5,7,2,4,1]=>1100100=>0010011
[4,1,8,6,7,5,3,2]=>[2,3,5,7,6,8,1,4]=>1000010=>0100001
[5,3,8,7,6,2,4,1]=>[1,4,2,6,7,8,3,5]=>0110000=>0000110
[5,8,4,7,6,2,1,3]=>[3,1,2,6,7,4,8,5]=>1001100=>0011001
[5,8,7,4,3,6,1,2]=>[2,1,6,3,4,7,8,5]=>1010100=>0010101
[6,4,8,3,1,7,2,5]=>[5,2,7,1,3,8,4,6]=>1101000=>0001011
[6,4,2,8,7,1,3,5]=>[5,3,1,7,8,2,4,6]=>1110000=>0000111
[6,3,8,7,2,5,1,4]=>[4,1,5,2,7,8,3,6]=>1110000=>0000111
[6,3,1,8,7,2,4,5]=>[5,4,2,7,8,1,3,6]=>1101000=>0001011
[5,8,3,7,1,6,4,2]=>[2,4,6,1,7,3,8,5]=>1010100=>0010101
[5,1,8,4,6,2,7,3]=>[3,7,2,6,4,8,1,5]=>1101000=>0001011
[5,8,7,4,1,6,2,3]=>[3,2,6,1,4,7,8,5]=>1100100=>0010011
[6,4,8,1,2,7,3,5]=>[5,3,7,2,1,8,4,6]=>1111000=>0001111
[6,8,5,1,2,3,7,4]=>[4,7,3,2,1,5,8,6]=>1110010=>0100111
[6,8,5,3,1,2,7,4]=>[4,7,2,1,3,5,8,6]=>1100010=>0100011
[4,5,1,2,6,8,7,3]=>[3,7,8,6,2,1,5,4]=>1101010=>0101011
[3,5,6,1,8,4,7,2]=>[2,7,4,8,1,6,5,3]=>1011100=>0011101
[4,2,6,1,7,3,5,8]=>[8,5,3,7,1,6,2,4]=>1110100=>0010111
[4,6,3,1,2,7,5,8]=>[8,5,7,2,1,3,6,4]=>1101100=>0011011
[3,5,2,7,8,1,6,4]=>[4,6,1,8,7,2,5,3]=>1110001=>1000111
[3,1,4,7,5,6,2,8]=>[8,2,6,5,7,4,1,3]=>1101100=>0011011
[3,4,6,5,8,7,1,2]=>[2,1,7,8,5,6,4,3]=>1011100=>0011101
[3,1,4,5,8,6,7,2]=>[2,7,6,8,5,4,1,3]=>1001110=>0111001
[3,4,6,8,5,2,7,1]=>[1,7,2,5,8,6,4,3]=>0111010=>0101110
[4,2,5,6,1,8,7,3]=>[3,7,8,1,6,5,2,4]=>1100100=>0010011
[2,1,7,5,8,6,4,3]=>[3,4,6,8,5,7,1,2]=>1000100=>0010001
[1,2,7,5,3,8,6,4]=>[4,6,8,3,5,7,2,1]=>1110000=>0000111
[4,1,2,7,3,8,6,5]=>[5,6,8,3,7,2,1,4]=>1110000=>0000111
[7,1,4,2,5,3,8,6]=>[6,8,3,5,2,4,1,7]=>1110000=>0000111
[3,1,2,6,8,5,4,7]=>[7,4,5,8,6,2,1,3]=>1101010=>0101011
[3,7,1,2,5,4,8,6]=>[6,8,4,5,2,1,7,3]=>1111000=>0001111
[1,3,7,2,4,8,6,5]=>[5,6,8,4,2,7,3,1]=>1111000=>0001111
[3,2,7,8,1,6,5,4]=>[4,5,6,1,8,7,2,3]=>1100001=>1000011
[2,4,1,7,8,6,5,3]=>[3,5,6,8,7,1,4,2]=>1100001=>1000011
[2,3,7,1,5,8,6,4]=>[4,6,8,5,1,7,3,2]=>1110100=>0010111
[5,2,8,1,3,7,4,6]=>[6,4,7,3,1,8,2,5]=>1111000=>0001111
[2,6,8,3,1,5,7,4]=>[4,7,5,1,3,8,6,2]=>1100110=>0110011
[6,3,7,4,5,1,8,2]=>[2,8,1,5,4,7,3,6]=>1011000=>0001101
[6,4,7,5,2,8,1,3]=>[3,1,8,2,5,7,4,6]=>1101000=>0001011
[5,7,4,6,2,8,1,3]=>[3,1,8,2,6,4,7,5]=>1101100=>0011011
[8,4,1,3,6,2,5,7]=>[7,5,2,6,3,1,4,8]=>1110100=>0010111
[4,8,3,1,7,2,5,6]=>[6,5,2,7,1,3,8,4]=>1101100=>0011011
[5,2,8,4,7,1,6,3]=>[3,6,1,7,4,8,2,5]=>1101000=>0001011
[5,8,4,7,3,1,6,2]=>[2,6,1,3,7,4,8,5]=>1001100=>0011001
[4,6,8,3,1,7,5,2]=>[2,5,7,1,3,8,6,4]=>1001010=>0101001
[6,3,8,2,7,1,5,4]=>[4,5,1,7,2,8,3,6]=>1110000=>0000111
[3,5,1,8,2,7,4,6]=>[6,4,7,2,8,1,5,3]=>1111000=>0001111
[5,3,8,1,2,6,4,7]=>[7,4,6,2,1,8,3,5]=>1111000=>0001111
[7,5,1,3,6,2,4,8]=>[8,4,2,6,3,1,5,7]=>1111000=>0001111
[5,7,4,1,6,2,3,8]=>[8,3,2,6,1,4,7,5]=>1110100=>0010111
[5,1,8,4,2,7,3,6]=>[6,3,7,2,4,8,1,5]=>1110000=>0000111
[4,1,6,2,8,3,7,5]=>[5,7,3,8,2,6,1,4]=>1110000=>0000111
[1,6,2,8,5,3,7,4]=>[4,7,3,5,8,2,6,1]=>1110000=>0000111
[6,8,5,3,1,7,4,2]=>[2,4,7,1,3,5,8,6]=>1000010=>0100001
[5,6,7,3,1,8,4,2]=>[2,4,8,1,3,7,6,5]=>1000110=>0110001
[5,6,2,1,7,8,4,3]=>[3,4,8,7,1,2,6,5]=>1000101=>1010001
[5,6,3,7,1,2,4,8]=>[8,4,2,1,7,3,6,5]=>1111100=>0011111
[6,3,2,7,8,5,1,4]=>[4,1,5,8,7,2,3,6]=>1100001=>1000011
[6,4,7,2,8,1,5,3]=>[3,5,1,8,2,7,4,6]=>1101000=>0001011
[6,7,4,8,3,1,5,2]=>[2,5,1,3,8,4,7,6]=>1001010=>0101001
[4,5,7,8,3,1,6,2]=>[2,6,1,3,8,7,5,4]=>1001101=>1011001
[4,7,2,5,8,1,6,3]=>[3,6,1,8,5,2,7,4]=>1101100=>0011011
[5,7,3,8,2,6,1,4]=>[4,1,6,2,8,3,7,5]=>1110100=>0010111
[3,4,7,8,2,6,1,5]=>[5,1,6,2,8,7,4,3]=>1111001=>1001111
[3,8,2,4,6,7,1,5]=>[5,1,7,6,4,2,8,3]=>1111010=>0101111
[4,8,3,5,6,1,7,2]=>[2,7,1,6,5,3,8,4]=>1011100=>0011101
[8,4,3,6,5,1,7,2]=>[2,7,1,5,6,3,4,8]=>1010000=>0000101
[8,7,5,4,1,6,3,2]=>[2,3,6,1,4,5,7,8]=>1000000=>0000001
[6,8,5,4,2,1,7,3]=>[3,7,1,2,4,5,8,6]=>1000010=>0100001
[8,1,6,5,2,3,7,4]=>[4,7,3,2,5,6,1,8]=>1110000=>0000111
[8,1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1,8]=>1110000=>0000111
[3,2,1,8,4,7,5,6]=>[6,5,7,4,8,1,2,3]=>1001100=>0011001
[4,8,2,7,1,6,5,3]=>[3,5,6,1,7,2,8,4]=>1101000=>0001011
[5,8,7,2,1,6,4,3]=>[3,4,6,1,2,7,8,5]=>1000100=>0010001
[8,7,6,1,5,4,3,2]=>[2,3,4,5,1,6,7,8]=>1000000=>0000001
[1,7,8,2,5,6,3,4]=>[4,3,6,5,2,8,7,1]=>1110101=>1010111
[7,6,8,1,4,3,5,2]=>[2,5,3,4,1,8,6,7]=>1010010=>0100101
[6,7,8,1,3,4,5,2]=>[2,5,4,3,1,8,7,6]=>1011011=>1101101
[5,7,8,2,1,4,6,3]=>[3,6,4,1,2,8,7,5]=>1001101=>1011001
[4,7,2,8,1,5,6,3]=>[3,6,5,1,8,2,7,4]=>1101100=>0011011
[3,2,7,8,1,5,6,4]=>[4,6,5,1,8,7,2,3]=>1100101=>1010011
[3,2,6,8,4,1,7,5]=>[5,7,1,4,8,6,2,3]=>1100010=>0100011
[4,6,2,8,3,1,7,5]=>[5,7,1,3,8,2,6,4]=>1101000=>0001011
[7,5,8,3,1,4,6,2]=>[2,6,4,1,3,8,5,7]=>1001100=>0011001
[8,5,7,3,1,6,4,2]=>[2,4,6,1,3,7,5,8]=>1000100=>0010001
[1,5,4,8,2,7,3,6]=>[6,3,7,2,8,4,5,1]=>1111000=>0001111
[6,4,3,8,2,1,7,5]=>[5,7,1,2,8,3,4,6]=>1010000=>0000101
[5,4,3,2,8,1,7,6]=>[6,7,1,8,2,3,4,5]=>1100000=>0000011
[4,5,2,3,8,1,7,6]=>[6,7,1,8,3,2,5,4]=>1111000=>0001111
[3,2,5,4,8,1,7,6]=>[6,7,1,8,4,5,2,3]=>1101000=>0001011
[6,4,3,1,5,2,7,8]=>[8,7,2,5,1,3,4,6]=>1100001=>1000011
[7,4,3,1,2,6,5,8]=>[8,5,6,2,1,3,4,7]=>1100100=>0010011
[7,5,1,4,2,6,3,8]=>[8,3,6,2,4,1,5,7]=>1110000=>0000111
[4,6,2,1,5,3,7,8]=>[8,7,3,5,1,2,6,4]=>1011001=>1001101
[3,2,6,1,5,4,7,8]=>[8,7,4,5,1,6,2,3]=>1101001=>1001011
[3,2,7,1,4,6,5,8]=>[8,5,6,4,1,7,2,3]=>1101100=>0011011
[5,7,1,3,2,6,4,8]=>[8,4,6,2,3,1,7,5]=>1101100=>0011011
[6,7,1,2,4,5,3,8]=>[8,3,5,4,2,1,7,6]=>1111010=>0101111
[7,6,1,2,5,4,3,8]=>[8,3,4,5,2,1,6,7]=>1110000=>0000111
[8,6,1,2,5,3,7,4]=>[4,7,3,5,2,1,6,8]=>1110000=>0000111
[8,7,1,2,3,6,5,4]=>[4,5,6,3,2,1,7,8]=>1110000=>0000111
[7,8,1,2,3,5,6,4]=>[4,6,5,3,2,1,8,7]=>1110101=>1010111
[4,1,3,2,5,6,7,8]=>[8,7,6,5,2,3,1,4]=>1100111=>1110011
[5,1,2,4,3,6,7,8]=>[8,7,6,3,4,2,1,5]=>1110011=>1100111
[7,1,2,3,4,6,5,8]=>[8,5,6,4,3,2,1,7]=>1111100=>0011111
[8,1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1,8]=>1111100=>0011111
[5,8,7,3,4,1,2,6]=>[6,2,1,4,3,7,8,5]=>1110100=>0010111
[6,7,3,8,5,1,2,4]=>[4,2,1,5,8,3,7,6]=>1110010=>0100111
[6,7,4,5,1,8,3,2]=>[2,3,8,1,5,4,7,6]=>1001010=>0101001
[5,4,7,6,2,3,8,1]=>[1,8,3,2,6,7,4,5]=>0111000=>0001110
[5,4,7,6,8,1,2,3]=>[3,2,1,8,6,7,4,5]=>1101010=>0101011
[5,3,7,8,6,1,2,4]=>[4,2,1,6,8,7,3,5]=>1110001=>1000111
[4,3,8,7,6,1,2,5]=>[5,2,1,6,7,8,3,4]=>1110000=>0000111
[4,8,3,7,5,1,2,6]=>[6,2,1,5,7,3,8,4]=>1111000=>0001111
[3,4,8,6,7,1,2,5]=>[5,2,1,7,6,8,4,3]=>1111010=>0101111
[4,5,6,7,1,8,3,2]=>[2,3,8,1,7,6,5,4]=>1001110=>0111001
[3,5,6,2,7,4,8,1]=>[1,8,4,7,2,6,5,3]=>0111100=>0011110
[3,5,6,1,7,8,4,2]=>[2,4,8,7,1,6,5,3]=>1010101=>1010101
[2,5,6,8,1,7,3,4]=>[4,3,7,1,8,6,5,2]=>1110110=>0110111
[1,4,8,6,2,3,7,5]=>[5,7,3,2,6,8,4,1]=>1111000=>0001111
[1,5,6,8,2,3,7,4]=>[4,7,3,2,8,6,5,1]=>1110110=>0110111
[8,1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1,8]=>1101010=>0101011
[2,8,3,1,5,7,4,6]=>[6,4,7,5,1,3,8,2]=>1101100=>0011011
[2,4,1,6,8,7,5,3]=>[3,5,7,8,6,1,4,2]=>1100010=>0100011
[4,3,1,7,6,8,5,2]=>[2,5,8,6,7,1,3,4]=>1000010=>0100001
[3,8,2,1,7,5,4,6]=>[6,4,5,7,1,2,8,3]=>1011000=>0001101
[8,3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3,8]=>1001000=>0001001
[8,4,2,6,1,5,3,7]=>[7,3,5,1,6,2,4,8]=>1110000=>0000111
[4,2,8,7,1,6,3,5]=>[5,3,6,1,7,8,2,4]=>1110000=>0000111
[5,3,7,2,6,4,8,1]=>[1,8,4,6,2,7,3,5]=>0111000=>0001110
[6,7,3,1,5,8,4,2]=>[2,4,8,5,1,3,7,6]=>1000110=>0110001
[6,7,2,1,8,5,4,3]=>[3,4,5,8,1,2,7,6]=>1000010=>0100001
[6,7,2,8,1,5,3,4]=>[4,3,5,1,8,2,7,6]=>1110010=>0100111
[6,7,8,2,1,4,3,5]=>[5,3,4,1,2,8,7,6]=>1010011=>1100101
[8,5,6,2,1,4,3,7]=>[7,3,4,1,2,6,5,8]=>1010100=>0010101
[5,8,7,1,2,3,4,6]=>[6,4,3,2,1,7,8,5]=>1111100=>0011111
[5,1,7,3,4,8,6,2]=>[2,6,8,4,3,7,1,5]=>1011000=>0001101
[5,1,7,8,2,3,6,4]=>[4,6,3,2,8,7,1,5]=>1110001=>1000111
[4,8,1,7,2,3,5,6]=>[6,5,3,2,7,1,8,4]=>1111100=>0011111
[3,1,8,2,7,4,6,5]=>[5,6,4,7,2,8,1,3]=>1101000=>0001011
[3,1,2,8,7,5,6,4]=>[4,6,5,7,8,2,1,3]=>1100100=>0010011
[2,1,8,3,4,7,6,5]=>[5,6,7,4,3,8,1,2]=>1011000=>0001101
[1,2,8,3,4,6,7,5]=>[5,7,6,4,3,8,2,1]=>1111010=>0101111
[6,3,8,5,2,7,4,1]=>[1,4,7,2,5,8,3,6]=>0110000=>0000110
[6,5,2,8,4,7,3,1]=>[1,3,7,4,8,2,5,6]=>0101000=>0001010
[5,6,1,4,8,7,3,2]=>[2,3,7,8,4,1,6,5]=>1001100=>0011001
[3,6,4,8,5,7,1,2]=>[2,1,7,5,8,4,6,3]=>1011100=>0011101
[3,4,7,1,8,6,5,2]=>[2,5,6,8,1,7,4,3]=>1011000=>0001101
[3,6,8,7,1,4,2,5]=>[5,2,4,1,7,8,6,3]=>1110010=>0100111
[5,3,7,1,6,8,2,4]=>[4,2,8,6,1,7,3,5]=>1110010=>0100111
[3,6,4,2,8,7,5,1]=>[1,5,7,8,2,4,6,3]=>0110000=>0000110
[6,3,7,5,2,8,1,4]=>[4,1,8,2,5,7,3,6]=>1110000=>0000111
[6,5,2,7,4,8,1,3]=>[3,1,8,4,7,2,5,6]=>1101000=>0001011
[7,8,3,5,1,4,6,2]=>[2,6,4,1,5,3,8,7]=>1011001=>1001101
[6,5,8,4,3,7,2,1]=>[1,2,7,3,4,8,5,6]=>0010100=>0010100
[6,3,7,4,2,8,5,1]=>[1,5,8,2,4,7,3,6]=>0110000=>0000110
[8,7,1,6,2,4,5,3]=>[3,5,4,2,6,1,7,8]=>1101000=>0001011
[5,3,8,7,4,1,2,6]=>[6,2,1,4,7,8,3,5]=>1110000=>0000111
[3,6,4,5,7,2,8,1]=>[1,8,2,7,5,4,6,3]=>0111100=>0011110
[5,4,2,7,3,6,8,1]=>[1,8,6,3,7,2,4,5]=>0110010=>0100110
[6,2,7,4,3,5,8,1]=>[1,8,5,3,4,7,2,6]=>0110100=>0010110
[3,6,2,7,4,5,8,1]=>[1,8,5,4,7,2,6,3]=>0111100=>0011110
[4,2,5,7,3,6,8,1]=>[1,8,6,3,7,5,2,4]=>0110110=>0110110
[3,7,6,4,5,2,8,1]=>[1,8,2,5,4,6,7,3]=>0111000=>0001110
[2,7,6,5,3,4,8,1]=>[1,8,4,3,5,6,7,2]=>0111000=>0001110
[1,6,5,2,8,3,4,7]=>[7,4,3,8,2,5,6,1]=>1111000=>0001111
[1,6,5,3,4,8,2,7]=>[7,2,8,4,3,5,6,1]=>1111000=>0001111
[5,4,6,3,1,8,2,7]=>[7,2,8,1,3,6,4,5]=>1101000=>0001011
[6,5,8,4,2,7,3,1]=>[1,3,7,2,4,8,5,6]=>0100100=>0010010
[3,8,6,2,5,7,4,1]=>[1,4,7,5,2,6,8,3]=>0110100=>0010110
[1,8,6,3,7,5,2,4]=>[4,2,5,7,3,6,8,1]=>1110000=>0000111
[2,8,1,7,3,5,6,4]=>[4,6,5,3,7,1,8,2]=>1110100=>0010111
[4,8,1,3,7,2,6,5]=>[5,6,2,7,3,1,8,4]=>1111000=>0001111
[4,2,8,5,7,3,6,1]=>[1,6,3,7,5,8,2,4]=>0110100=>0010110
[6,7,3,1,8,4,2,5]=>[5,2,4,8,1,3,7,6]=>1100010=>0100011
[1,7,3,8,4,5,2,6]=>[6,2,5,4,8,3,7,1]=>1111000=>0001111
[8,6,1,7,4,2,5,3]=>[3,5,2,4,7,1,6,8]=>1100000=>0000011
[7,1,2,8,3,5,4,6]=>[6,4,5,3,8,2,1,7]=>1111000=>0001111
[4,2,5,7,1,8,3,6]=>[6,3,8,1,7,5,2,4]=>1110100=>0010111
[3,6,2,7,1,8,4,5]=>[5,4,8,1,7,2,6,3]=>1111000=>0001111
[6,3,7,2,1,8,4,5]=>[5,4,8,1,2,7,3,6]=>1011000=>0001101
[7,3,1,5,8,4,2,6]=>[6,2,4,8,5,1,3,7]=>1100100=>0010011
[4,2,1,5,8,3,6,7]=>[7,6,3,8,5,1,2,4]=>1010110=>0110101
[5,4,2,7,1,8,3,6]=>[6,3,8,1,7,2,4,5]=>1110000=>0000111
[5,4,3,1,6,8,2,7]=>[7,2,8,6,1,3,4,5]=>1100010=>0100011
[1,5,3,4,6,8,2,7]=>[7,2,8,6,4,3,5,1]=>1111010=>0101111
[4,3,5,1,6,8,2,7]=>[7,2,8,6,1,5,3,4]=>1110010=>0100111
[4,7,5,6,8,3,2,1]=>[1,2,3,8,6,5,7,4]=>0001110=>0111000
[6,5,4,8,2,7,3,1]=>[1,3,7,2,8,4,5,6]=>0101000=>0001010
[6,5,1,8,7,4,2,3]=>[3,2,4,7,8,1,5,6]=>1100000=>0000011
[8,6,4,7,5,3,2,1]=>[1,2,3,5,7,4,6,8]=>0001000=>0001000
[5,1,8,3,7,6,2,4]=>[4,2,6,7,3,8,1,5]=>1110000=>0000111
[5,4,8,1,7,2,6,3]=>[3,6,2,7,1,8,4,5]=>1101000=>0001011
[7,5,8,3,2,6,4,1]=>[1,4,6,2,3,8,5,7]=>0100100=>0010010
[3,6,8,2,4,7,5,1]=>[1,5,7,4,2,8,6,3]=>0111010=>0101110
[5,7,3,8,2,6,4,1]=>[1,4,6,2,8,3,7,5]=>0110100=>0010110
[5,4,6,8,2,7,3,1]=>[1,3,7,2,8,6,4,5]=>0101010=>0101010
[4,7,2,8,6,3,5,1]=>[1,5,3,6,8,2,7,4]=>0111000=>0001110
[3,6,8,1,7,2,5,4]=>[4,5,2,7,1,8,6,3]=>1110010=>0100111
[2,3,8,7,4,5,6,1]=>[1,6,5,4,7,8,3,2]=>0111100=>0011110
[7,2,8,6,4,3,5,1]=>[1,5,3,4,6,8,2,7]=>0110000=>0000110
[2,1,8,7,5,6,3,4]=>[4,3,6,5,7,8,1,2]=>1010100=>0010101
[7,1,8,6,5,3,2,4]=>[4,2,3,5,6,8,1,7]=>1100000=>0000011
[1,3,8,7,4,6,2,5]=>[5,2,6,4,7,8,3,1]=>1111000=>0001111
[1,5,8,3,7,6,2,4]=>[4,2,6,7,3,8,5,1]=>1110100=>0010111
[4,7,1,8,6,5,2,3]=>[3,2,5,6,8,1,7,4]=>1101000=>0001011
[5,1,6,8,7,4,2,3]=>[3,2,4,7,8,6,1,5]=>1100010=>0100011
[6,8,4,7,5,3,2,1]=>[1,2,3,5,7,4,8,6]=>0001010=>0101000
[6,8,7,2,5,4,3,1]=>[1,3,4,5,2,7,8,6]=>0100010=>0100010
[1,8,7,6,5,4,2,3]=>[3,2,4,5,6,7,8,1]=>1100000=>0000011
[6,7,4,8,3,5,1,2]=>[2,1,5,3,8,4,7,6]=>1011010=>0101101
[6,7,4,5,2,8,1,3]=>[3,1,8,2,5,4,7,6]=>1101010=>0101011
[5,7,4,6,2,3,1,8]=>[8,1,3,2,6,4,7,5]=>1101100=>0011011
[5,7,4,6,3,8,1,2]=>[2,1,8,3,6,4,7,5]=>1011100=>0011101
[5,7,4,8,3,6,1,2]=>[2,1,6,3,8,4,7,5]=>1011100=>0011101
[6,8,4,5,3,7,1,2]=>[2,1,7,3,5,4,8,6]=>1011010=>0101101
[5,8,4,6,3,7,1,2]=>[2,1,7,3,6,4,8,5]=>1011100=>0011101
[5,6,4,8,3,7,1,2]=>[2,1,7,3,8,4,6,5]=>1011100=>0011101
[5,6,3,7,2,4,1,8]=>[8,1,4,2,7,3,6,5]=>1110100=>0010111
[5,6,3,8,2,7,1,4]=>[4,1,7,2,8,3,6,5]=>1110100=>0010111
[5,6,4,8,2,7,1,3]=>[3,1,7,2,8,4,6,5]=>1101100=>0011011
[5,8,4,6,2,7,1,3]=>[3,1,7,2,6,4,8,5]=>1101100=>0011011
[6,8,4,5,2,7,1,3]=>[3,1,7,2,5,4,8,6]=>1101010=>0101011
[7,8,4,5,2,6,1,3]=>[3,1,6,2,5,4,8,7]=>1101001=>1001011
[6,8,4,5,2,3,1,7]=>[7,1,3,2,5,4,8,6]=>1101010=>0101011
[5,8,4,6,2,3,1,7]=>[7,1,3,2,6,4,8,5]=>1101100=>0011011
[5,6,3,4,2,8,1,7]=>[7,1,8,2,4,3,6,5]=>1110100=>0010111
[4,6,3,5,2,8,1,7]=>[7,1,8,2,5,3,6,4]=>1111000=>0001111
[4,6,3,8,2,5,1,7]=>[7,1,5,2,8,3,6,4]=>1111000=>0001111
[4,8,3,6,2,5,1,7]=>[7,1,5,2,6,3,8,4]=>1111000=>0001111
[5,8,3,6,2,4,1,7]=>[7,1,4,2,6,3,8,5]=>1110100=>0010111
[6,8,3,5,2,4,1,7]=>[7,1,4,2,5,3,8,6]=>1110010=>0100111
[7,8,3,5,2,4,1,6]=>[6,1,4,2,5,3,8,7]=>1110001=>1000111
[7,8,3,5,2,6,1,4]=>[4,1,6,2,5,3,8,7]=>1110001=>1000111
[6,8,3,5,2,7,1,4]=>[4,1,7,2,5,3,8,6]=>1110010=>0100111
[5,8,3,6,2,7,1,4]=>[4,1,7,2,6,3,8,5]=>1110100=>0010111
[4,6,3,8,2,7,1,5]=>[5,1,7,2,8,3,6,4]=>1111000=>0001111
[4,6,3,7,2,5,1,8]=>[8,1,5,2,7,3,6,4]=>1111000=>0001111
[4,7,3,6,2,5,1,8]=>[8,1,5,2,6,3,7,4]=>1111000=>0001111
[4,7,3,6,2,8,1,5]=>[5,1,8,2,6,3,7,4]=>1111000=>0001111
[5,7,4,8,2,6,1,3]=>[3,1,6,2,8,4,7,5]=>1101100=>0011011
[5,7,3,6,2,8,1,4]=>[4,1,8,2,6,3,7,5]=>1110100=>0010111
[5,7,3,6,2,4,1,8]=>[8,1,4,2,6,3,7,5]=>1110100=>0010111
[6,7,3,5,2,4,1,8]=>[8,1,4,2,5,3,7,6]=>1110010=>0100111
[6,7,3,5,2,8,1,4]=>[4,1,8,2,5,3,7,6]=>1110010=>0100111
[6,7,3,8,2,5,1,4]=>[4,1,5,2,8,3,7,6]=>1110010=>0100111
[6,7,4,8,2,5,1,3]=>[3,1,5,2,8,4,7,6]=>1101010=>0101011
[6,7,5,8,2,4,1,3]=>[3,1,4,2,8,5,7,6]=>1100110=>0110011
[6,8,5,7,2,3,1,4]=>[4,1,3,2,7,5,8,6]=>1100110=>0110011
[6,7,4,8,2,3,1,5]=>[5,1,3,2,8,4,7,6]=>1101010=>0101011
[6,7,3,8,2,4,1,5]=>[5,1,4,2,8,3,7,6]=>1110010=>0100111
[5,7,3,8,2,4,1,6]=>[6,1,4,2,8,3,7,5]=>1110100=>0010111
[5,8,4,7,2,3,1,6]=>[6,1,3,2,7,4,8,5]=>1101100=>0011011
[6,8,4,7,2,3,1,5]=>[5,1,3,2,7,4,8,6]=>1101010=>0101011
[7,8,3,6,2,4,1,5]=>[5,1,4,2,6,3,8,7]=>1110001=>1000111
[6,8,3,7,2,4,1,5]=>[5,1,4,2,7,3,8,6]=>1110010=>0100111
[5,8,3,7,2,4,1,6]=>[6,1,4,2,7,3,8,5]=>1110100=>0010111
[4,8,3,7,2,5,1,6]=>[6,1,5,2,7,3,8,4]=>1111000=>0001111
[4,7,3,8,2,5,1,6]=>[6,1,5,2,8,3,7,4]=>1111000=>0001111
[4,5,3,8,2,7,1,6]=>[6,1,7,2,8,3,5,4]=>1111000=>0001111
[7,8,3,4,2,6,1,5]=>[5,1,6,2,4,3,8,7]=>1110001=>1000111
[4,6,5,2,1,3,8,7]=>[7,8,3,1,2,5,6,4]=>1011000=>0001101
[5,6,4,2,3,1,8,7]=>[7,8,1,3,2,4,6,5]=>1100100=>0010011
[5,4,6,1,3,2,8,7]=>[7,8,2,3,1,6,4,5]=>1101000=>0001011
[4,7,8,1,6,3,5,2]=>[2,5,3,6,1,8,7,4]=>1011001=>1001101
[7,4,8,1,6,5,3,2]=>[2,3,5,6,1,8,4,7]=>1001000=>0001001
[7,4,5,3,1,8,2,6]=>[6,2,8,1,3,5,4,7]=>1101000=>0001011
[5,4,7,1,3,8,2,6]=>[6,2,8,3,1,7,4,5]=>1111000=>0001111
[6,4,8,1,7,5,2,3]=>[3,2,5,7,1,8,4,6]=>1101000=>0001011
[6,4,7,1,8,2,5,3]=>[3,5,2,8,1,7,4,6]=>1101000=>0001011
[5,6,8,7,2,1,3,4]=>[4,3,1,2,7,8,6,5]=>1010110=>0110101
[8,5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5,8]=>1000100=>0010001
[2,1,6,8,7,4,3,5]=>[5,3,4,7,8,6,1,2]=>1010010=>0100101
[8,4,7,3,6,2,5,1]=>[1,5,2,6,3,7,4,8]=>0111000=>0001110
[7,6,8,5,2,4,3,1]=>[1,3,4,2,5,8,6,7]=>0100010=>0100010
[5,7,8,6,2,3,1,4]=>[4,1,3,2,6,8,7,5]=>1100101=>1010011
[5,8,7,6,3,2,1,4]=>[4,1,2,3,6,7,8,5]=>1000100=>0010001
[6,8,7,5,3,2,4,1]=>[1,4,2,3,5,7,8,6]=>0100010=>0100010
[7,8,4,2,6,5,3,1]=>[1,3,5,6,2,4,8,7]=>0100001=>1000010
[4,8,6,2,7,3,1,5]=>[5,1,3,7,2,6,8,4]=>1101000=>0001011
[3,6,1,8,7,4,2,5]=>[5,2,4,7,8,1,6,3]=>1110000=>0000111
[3,7,1,8,6,4,5,2]=>[2,5,4,6,8,1,7,3]=>1011000=>0001101
[3,8,1,6,7,5,2,4]=>[4,2,5,7,6,1,8,3]=>1110010=>0100111
[6,7,4,2,8,1,5,3]=>[3,5,1,8,2,4,7,6]=>1100010=>0100011
[6,8,4,2,7,5,1,3]=>[3,1,5,7,2,4,8,6]=>1100010=>0100011
[5,7,4,2,3,8,1,6]=>[6,1,8,3,2,4,7,5]=>1110100=>0010111
[2,1,8,6,7,5,3,4]=>[4,3,5,7,6,8,1,2]=>1010010=>0100101
[8,6,4,3,7,5,1,2]=>[2,1,5,7,3,4,6,8]=>1010000=>0000101
[5,8,6,7,3,1,2,4]=>[4,2,1,3,7,6,8,5]=>1100110=>0110011
[6,7,5,8,1,3,4,2]=>[2,4,3,1,8,5,7,6]=>1010110=>0110101
[7,6,5,8,1,4,3,2]=>[2,3,4,1,8,5,6,7]=>1000100=>0010001
[7,6,4,3,8,1,5,2]=>[2,5,1,8,3,4,6,7]=>1010000=>0000101
[2,1,7,6,8,3,5,4]=>[4,5,3,8,6,7,1,2]=>1010010=>0100101
[7,4,6,3,8,1,2,5]=>[5,2,1,8,3,6,4,7]=>1111000=>0001111
[7,5,6,8,1,4,2,3]=>[3,2,4,1,8,6,5,7]=>1100110=>0110011
[6,5,7,8,1,2,4,3]=>[3,4,2,1,8,7,5,6]=>1100101=>1010011
[4,1,7,3,6,5,8,2]=>[2,8,5,6,3,7,1,4]=>1010100=>0010101
[5,1,8,4,7,6,2,3]=>[3,2,6,7,4,8,1,5]=>1101000=>0001011
[5,2,8,7,4,6,1,3]=>[3,1,6,4,7,8,2,5]=>1101000=>0001011
[8,1,3,5,4,7,6,2]=>[2,6,7,4,5,3,1,8]=>1011000=>0001101
[6,1,4,5,3,7,8,2]=>[2,8,7,3,5,4,1,6]=>1011001=>1001101
[5,1,7,8,6,2,4,3]=>[3,4,2,6,8,7,1,5]=>1100001=>1000011
[6,1,8,3,4,5,7,2]=>[2,7,5,4,3,8,1,6]=>1011100=>0011101
[6,3,2,7,5,1,8,4]=>[4,8,1,5,7,2,3,6]=>1100000=>0000011
[6,5,8,2,4,7,3,1]=>[1,3,7,4,2,8,5,6]=>0101100=>0011010
[6,5,2,8,4,1,3,7]=>[7,3,1,4,8,2,5,6]=>1110000=>0000111
[5,6,2,1,4,8,3,7]=>[7,3,8,4,1,2,6,5]=>1011100=>0011101
[3,4,1,2,8,6,5,7]=>[7,5,6,8,2,1,4,3]=>1110100=>0010111
[4,3,1,2,6,8,5,7]=>[7,5,8,6,2,1,3,4]=>1100110=>0110011
[6,3,8,5,2,1,4,7]=>[7,4,1,2,5,8,3,6]=>1011000=>0001101
[8,5,2,7,3,1,6,4]=>[4,6,1,3,7,2,5,8]=>1100000=>0000011
[2,3,8,5,6,1,7,4]=>[4,7,1,6,5,8,3,2]=>1110100=>0010111
[7,4,5,6,3,1,8,2]=>[2,8,1,3,6,5,4,7]=>1001100=>0011001
[8,5,6,4,2,1,7,3]=>[3,7,1,2,4,6,5,8]=>1000100=>0010001
[7,5,3,6,2,8,1,4]=>[4,1,8,2,6,3,5,7]=>1110000=>0000111
[8,7,5,4,1,6,2,3]=>[3,2,6,1,4,5,7,8]=>1100000=>0000011
[2,6,4,1,8,5,7,3]=>[3,7,5,8,1,4,6,2]=>1100100=>0010011
[6,1,2,3,8,5,7,4]=>[4,7,5,8,3,2,1,6]=>1110100=>0010111
[7,1,2,3,6,5,8,4]=>[4,8,5,6,3,2,1,7]=>1110100=>0010111
[1,5,7,3,2,4,6,8]=>[8,6,4,2,3,7,5,1]=>1101110=>0111011
[5,8,2,4,1,3,7,6]=>[6,7,3,1,4,2,8,5]=>1110100=>0010111
[8,7,2,6,3,4,1,5]=>[5,1,4,3,6,2,7,8]=>1110000=>0000111
[4,8,1,6,3,2,7,5]=>[5,7,2,3,6,1,8,4]=>1101000=>0001011
[3,5,8,7,2,4,1,6]=>[6,1,4,2,7,8,5,3]=>1110100=>0010111
[4,2,1,3,7,8,5,6]=>[6,5,8,7,3,1,2,4]=>1010101=>1010101
[2,4,1,3,8,7,5,6]=>[6,5,7,8,3,1,4,2]=>1110100=>0010111
[2,5,8,3,1,7,4,6]=>[6,4,7,1,3,8,5,2]=>1101100=>0011011
[5,1,8,3,2,4,6,7]=>[7,6,4,2,3,8,1,5]=>1101010=>0101011
[5,2,7,8,6,4,1,3]=>[3,1,4,6,8,7,2,5]=>1100001=>1000011
[1,4,2,7,8,6,3,5]=>[5,3,6,8,7,2,4,1]=>1110001=>1000111
[1,6,2,4,7,5,3,8]=>[8,3,5,7,4,2,6,1]=>1111000=>0001111
[7,8,3,6,5,2,1,4]=>[4,1,2,5,6,3,8,7]=>1010001=>1000101
[4,7,2,8,6,1,5,3]=>[3,5,1,6,8,2,7,4]=>1101000=>0001011
[6,2,1,8,3,4,7,5]=>[5,7,4,3,8,1,2,6]=>1011000=>0001101
[6,2,4,7,5,8,1,3]=>[3,1,8,5,7,4,2,6]=>1101100=>0011011
[6,2,7,3,5,1,8,4]=>[4,8,1,5,3,7,2,6]=>1110000=>0000111
[6,2,1,3,7,8,4,5]=>[5,4,8,7,3,1,2,6]=>1011001=>1001101
[7,2,5,1,8,3,4,6]=>[6,4,3,8,1,5,2,7]=>1111000=>0001111
[7,5,4,2,6,8,1,3]=>[3,1,8,6,2,4,5,7]=>1100010=>0100011
[5,2,6,3,1,8,7,4]=>[4,7,8,1,3,6,2,5]=>1100000=>0000011
[8,2,7,4,1,3,5,6]=>[6,5,3,1,4,7,2,8]=>1110100=>0010111
[1,8,7,4,3,2,5,6]=>[6,5,2,3,4,7,8,1]=>1100100=>0010011
[5,8,4,7,2,1,6,3]=>[3,6,1,2,7,4,8,5]=>1001100=>0011001
[1,8,7,5,4,3,6,2]=>[2,6,3,4,5,7,8,1]=>1010000=>0000101
[1,6,8,4,3,7,5,2]=>[2,5,7,3,4,8,6,1]=>1010010=>0100101
[6,8,7,3,2,5,1,4]=>[4,1,5,2,3,7,8,6]=>1100010=>0100011
[1,6,3,8,2,4,7,5]=>[5,7,4,2,8,3,6,1]=>1111000=>0001111
[5,3,8,1,2,7,4,6]=>[6,4,7,2,1,8,3,5]=>1111000=>0001111
[5,7,3,1,2,6,4,8]=>[8,4,6,2,1,3,7,5]=>1101100=>0011011
[1,7,5,4,2,6,3,8]=>[8,3,6,2,4,5,7,1]=>1110000=>0000111
[1,5,8,2,4,6,3,7]=>[7,3,6,4,2,8,5,1]=>1111100=>0011111
[1,5,8,4,2,7,3,6]=>[6,3,7,2,4,8,5,1]=>1110100=>0010111
[1,4,6,2,8,3,7,5]=>[5,7,3,8,2,6,4,1]=>1111000=>0001111
[5,2,6,7,8,4,1,3]=>[3,1,4,8,7,6,2,5]=>1100011=>1100011
[6,7,3,8,5,2,1,4]=>[4,1,2,5,8,3,7,6]=>1010010=>0100101
[4,6,2,7,8,1,5,3]=>[3,5,1,8,7,2,6,4]=>1101001=>1001011
[1,6,4,7,8,3,5,2]=>[2,5,3,8,7,4,6,1]=>1011001=>1001101
[4,5,7,2,1,8,6,3]=>[3,6,8,1,2,7,5,4]=>1001100=>0011001
[7,8,3,4,2,1,6,5]=>[5,6,1,2,4,3,8,7]=>1010001=>1000101
[4,2,5,6,7,8,1,3]=>[3,1,8,7,6,5,2,4]=>1100111=>1110011
[5,2,3,6,7,1,8,4]=>[4,8,1,7,6,3,2,5]=>1110010=>0100111
[6,2,3,4,1,7,8,5]=>[5,8,7,1,4,3,2,6]=>1110001=>1000111
[10,9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9,10]=>111100000=>000001111
[9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9]=>101010101=>101010101
[5,6,3,4,1,2,8,7]=>[7,8,2,1,4,3,6,5]=>1110100=>0010111
[7,8,3,5,4,6,1,2]=>[2,1,6,4,5,3,8,7]=>1011001=>1001101
[6,8,3,7,5,1,4,2]=>[2,4,1,5,7,3,8,6]=>1010010=>0100101
[2,1,7,8,5,6,3,4]=>[4,3,6,5,8,7,1,2]=>1010101=>1010101
[5,7,3,8,1,6,2,4]=>[4,2,6,1,8,3,7,5]=>1110100=>0010111
[7,5,8,4,2,6,1,3]=>[3,1,6,2,4,8,5,7]=>1100100=>0010011
[8,6,3,7,5,2,4,1]=>[1,4,2,5,7,3,6,8]=>0110000=>0000110
[8,5,3,7,2,6,4,1]=>[1,4,6,2,7,3,5,8]=>0110000=>0000110
[8,5,7,4,2,6,3,1]=>[1,3,6,2,4,7,5,8]=>0100100=>0010010
[6,8,1,7,4,5,2,3]=>[3,2,5,4,7,1,8,6]=>1101010=>0101011
[1,8,6,7,4,5,2,3]=>[3,2,5,4,7,6,8,1]=>1101010=>0101011
[1,8,6,7,3,5,2,4]=>[4,2,5,3,7,6,8,1]=>1110010=>0100111
[7,8,1,6,3,5,2,4]=>[4,2,5,3,6,1,8,7]=>1110001=>1000111
[7,8,3,6,4,5,1,2]=>[2,1,5,4,6,3,8,7]=>1011001=>1001101
[7,8,2,6,3,5,1,4]=>[4,1,5,3,6,2,8,7]=>1110001=>1000111
[7,8,1,6,2,5,3,4]=>[4,3,5,2,6,1,8,7]=>1110001=>1000111
[6,8,2,7,1,5,3,4]=>[4,3,5,1,7,2,8,6]=>1110010=>0100111
[6,8,2,7,3,5,1,4]=>[4,1,5,3,7,2,8,6]=>1110010=>0100111
[6,8,3,7,4,5,1,2]=>[2,1,5,4,7,3,8,6]=>1011010=>0101101
[3,8,6,7,4,5,1,2]=>[2,1,5,4,7,6,8,3]=>1011010=>0101101
[2,8,1,7,5,6,3,4]=>[4,3,6,5,7,1,8,2]=>1110100=>0010111
[2,8,1,7,4,6,3,5]=>[5,3,6,4,7,1,8,2]=>1111000=>0001111
[2,8,5,7,3,6,1,4]=>[4,1,6,3,7,5,8,2]=>1110100=>0010111
[3,8,5,7,4,6,1,2]=>[2,1,6,4,7,5,8,3]=>1011100=>0011101
[5,8,3,7,4,6,1,2]=>[2,1,6,4,7,3,8,5]=>1011100=>0011101
[5,8,2,7,4,6,1,3]=>[3,1,6,4,7,2,8,5]=>1101100=>0011011
[5,8,2,7,3,6,1,4]=>[4,1,6,3,7,2,8,5]=>1110100=>0010111
[1,8,4,7,2,6,3,5]=>[5,3,6,2,7,4,8,1]=>1111000=>0001111
[1,8,4,7,3,6,2,5]=>[5,2,6,3,7,4,8,1]=>1111000=>0001111
[4,8,1,7,3,6,2,5]=>[5,2,6,3,7,1,8,4]=>1111000=>0001111
[4,8,3,7,1,6,2,5]=>[5,2,6,1,7,3,8,4]=>1111000=>0001111
[5,8,1,7,3,6,2,4]=>[4,2,6,3,7,1,8,5]=>1110100=>0010111
[1,8,5,7,3,6,2,4]=>[4,2,6,3,7,5,8,1]=>1110100=>0010111
[1,8,5,7,4,6,2,3]=>[3,2,6,4,7,5,8,1]=>1101100=>0011011
[5,8,1,7,4,6,2,3]=>[3,2,6,4,7,1,8,5]=>1101100=>0011011
[5,8,4,7,1,6,2,3]=>[3,2,6,1,7,4,8,5]=>1101100=>0011011
[6,8,4,7,1,5,2,3]=>[3,2,5,1,7,4,8,6]=>1101010=>0101011
[6,8,5,7,1,4,2,3]=>[3,2,4,1,7,5,8,6]=>1100110=>0110011
[5,8,6,7,3,4,1,2]=>[2,1,4,3,7,6,8,5]=>1010110=>0110101
[5,8,6,7,2,4,1,3]=>[3,1,4,2,7,6,8,5]=>1100110=>0110011
[5,8,6,7,1,4,2,3]=>[3,2,4,1,7,6,8,5]=>1100110=>0110011
[4,8,6,7,1,5,2,3]=>[3,2,5,1,7,6,8,4]=>1101010=>0101011
[4,8,5,7,1,6,2,3]=>[3,2,6,1,7,5,8,4]=>1101100=>0011011
[3,8,5,7,1,6,2,4]=>[4,2,6,1,7,5,8,3]=>1110100=>0010111
[4,8,6,7,2,5,1,3]=>[3,1,5,2,7,6,8,4]=>1101010=>0101011
[4,8,6,7,3,5,1,2]=>[2,1,5,3,7,6,8,4]=>1011010=>0101101
[4,8,5,7,3,6,1,2]=>[2,1,6,3,7,5,8,4]=>1011100=>0011101
[4,8,5,7,2,6,1,3]=>[3,1,6,2,7,5,8,4]=>1101100=>0011011
[3,8,5,7,2,6,1,4]=>[4,1,6,2,7,5,8,3]=>1110100=>0010111
[3,8,4,7,2,6,1,5]=>[5,1,6,2,7,4,8,3]=>1111000=>0001111
[3,8,4,7,1,6,2,5]=>[5,2,6,1,7,4,8,3]=>1111000=>0001111
[3,8,1,7,2,6,4,5]=>[5,4,6,2,7,1,8,3]=>1111000=>0001111
[3,8,2,7,4,6,1,5]=>[5,1,6,4,7,2,8,3]=>1111000=>0001111
[4,8,2,7,5,6,1,3]=>[3,1,6,5,7,2,8,4]=>1101100=>0011011
[3,8,4,7,5,6,1,2]=>[2,1,6,5,7,4,8,3]=>1011100=>0011101
[2,8,4,7,5,6,1,3]=>[3,1,6,5,7,4,8,2]=>1101100=>0011011
[2,8,3,7,5,6,1,4]=>[4,1,6,5,7,3,8,2]=>1110100=>0010111
[2,8,3,7,4,6,1,5]=>[5,1,6,4,7,3,8,2]=>1111000=>0001111
[7,5,2,8,6,4,1,3]=>[3,1,4,6,8,2,5,7]=>1100000=>0000011
[7,5,1,8,6,2,3,4]=>[4,3,2,6,8,1,5,7]=>1110000=>0000111
[7,4,8,6,1,5,2,3]=>[3,2,5,1,6,8,4,7]=>1101000=>0001011
[7,1,8,4,5,2,6,3]=>[3,6,2,5,4,8,1,7]=>1101000=>0001011
[6,8,1,7,4,2,5,3]=>[3,5,2,4,7,1,8,6]=>1100010=>0100011
[1,6,7,4,2,8,5,3]=>[3,5,8,2,4,7,6,1]=>1100010=>0100011
[7,1,8,3,5,6,2,4]=>[4,2,6,5,3,8,1,7]=>1110100=>0010111
[7,3,8,6,2,5,1,4]=>[4,1,5,2,6,8,3,7]=>1110000=>0000111
[7,4,2,8,6,1,3,5]=>[5,3,1,6,8,2,4,7]=>1110000=>0000111
[7,3,1,8,4,2,5,6]=>[6,5,2,4,8,1,3,7]=>1100100=>0010011
[6,8,1,7,2,3,4,5]=>[5,4,3,2,7,1,8,6]=>1111010=>0101111
[1,5,7,8,2,6,3,4]=>[4,3,6,2,8,7,5,1]=>1110101=>1010111
[6,2,3,8,5,7,4,1]=>[1,4,7,5,8,3,2,6]=>0110100=>0010110
[6,3,1,4,8,5,2,7]=>[7,2,5,8,4,1,3,6]=>1101000=>0001011
[2,4,7,3,6,8,5,1]=>[1,5,8,6,3,7,4,2]=>0111010=>0101110
[3,1,5,4,7,8,2,6]=>[6,2,8,7,4,5,1,3]=>1101001=>1001011
[4,8,2,3,5,7,1,6]=>[6,1,7,5,3,2,8,4]=>1111100=>0011111
[1,4,7,8,3,6,2,5]=>[5,2,6,3,8,7,4,1]=>1111001=>1001111
[5,3,8,2,4,7,1,6]=>[6,1,7,4,2,8,3,5]=>1111000=>0001111
[5,4,3,8,1,2,7,6]=>[6,7,2,1,8,3,4,5]=>1110000=>0000111
[6,4,3,1,2,8,5,7]=>[7,5,8,2,1,3,4,6]=>1100100=>0010011
[6,4,2,8,1,3,7,5]=>[5,7,3,1,8,2,4,6]=>1110000=>0000111
[6,3,8,2,5,1,7,4]=>[4,7,1,5,2,8,3,6]=>1110000=>0000111
[1,5,7,3,6,8,4,2]=>[2,4,8,6,3,7,5,1]=>1010110=>0110101
[1,5,7,4,2,6,8,3]=>[3,8,6,2,4,7,5,1]=>1100110=>0110011
[6,5,1,2,8,7,3,4]=>[4,3,7,8,2,1,5,6]=>1110000=>0000111
[6,5,3,1,4,2,8,7]=>[7,8,2,4,1,3,5,6]=>1100000=>0000011
[5,3,1,6,4,2,7,8]=>[8,7,2,4,6,1,3,5]=>1100001=>1000011
[5,2,6,4,1,7,3,8]=>[8,3,7,1,4,6,2,5]=>1110000=>0000111
[4,6,1,7,5,2,8,3]=>[3,8,2,5,7,1,6,4]=>1101000=>0001011
[4,3,1,5,7,2,6,8]=>[8,6,2,7,5,1,3,4]=>1100110=>0110011
[3,4,7,2,8,6,1,5]=>[5,1,6,8,2,7,4,3]=>1111000=>0001111
[3,4,5,8,2,7,1,6]=>[6,1,7,2,8,5,4,3]=>1111100=>0011111
[3,5,2,6,8,1,7,4]=>[4,7,1,8,6,2,5,3]=>1110010=>0100111
[4,2,5,6,1,3,8,7]=>[7,8,3,1,6,5,2,4]=>1110100=>0010111
[5,3,6,8,4,7,2,1]=>[1,2,7,4,8,6,3,5]=>0011010=>0101100
[3,7,2,5,4,8,6,1]=>[1,6,8,4,5,2,7,3]=>0111000=>0001110
[4,7,2,5,8,3,6,1]=>[1,6,3,8,5,2,7,4]=>0111100=>0011110
[4,2,6,5,8,3,7,1]=>[1,7,3,8,5,6,2,4]=>0110100=>0010110
[3,1,6,5,4,8,2,7]=>[7,2,8,4,5,6,1,3]=>1101000=>0001011
[8,5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5,8]=>0001000=>0001000
[6,7,8,1,4,3,2,5]=>[5,2,3,4,1,8,7,6]=>1100011=>1100011
[4,7,1,5,8,3,2,6]=>[6,2,3,8,5,1,7,4]=>1101100=>0011011
[2,7,1,5,4,3,8,6]=>[6,8,3,4,5,1,7,2]=>1110000=>0000111
[8,2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2,8]=>1010000=>0000101
[8,3,1,5,4,7,2,6]=>[6,2,7,4,5,1,3,8]=>1101000=>0001011
[8,4,1,5,7,3,2,6]=>[6,2,3,7,5,1,4,8]=>1100100=>0010011
[8,3,6,1,4,7,2,5]=>[5,2,7,4,1,6,3,8]=>1111000=>0001111
[8,2,6,1,4,3,7,5]=>[5,7,3,4,1,6,2,8]=>1110000=>0000111
[3,7,6,1,4,8,2,5]=>[5,2,8,4,1,6,7,3]=>1111000=>0001111
[6,7,8,2,4,3,5,1]=>[1,5,3,4,2,8,7,6]=>0110011=>1100110
[4,7,6,2,8,3,5,1]=>[1,5,3,8,2,6,7,4]=>0111000=>0001110
[3,7,6,2,4,8,5,1]=>[1,5,8,4,2,6,7,3]=>0111000=>0001110
[5,7,3,8,4,6,2,1]=>[1,2,6,4,8,3,7,5]=>0011100=>0011100
[4,7,3,5,8,6,2,1]=>[1,2,6,8,5,3,7,4]=>0011100=>0011100
[8,7,2,1,4,3,6,5]=>[5,6,3,4,1,2,7,8]=>1010000=>0000101
[8,7,3,1,4,6,2,5]=>[5,2,6,4,1,3,7,8]=>1101000=>0001011
[8,7,6,3,2,5,4,1]=>[1,4,5,2,3,6,7,8]=>0100000=>0000010
[8,7,3,5,1,6,2,4]=>[4,2,6,1,5,3,7,8]=>1110000=>0000111
[8,7,2,5,1,3,6,4]=>[4,6,3,1,5,2,7,8]=>1110000=>0000111
[8,4,6,5,7,1,2,3]=>[3,2,1,7,5,6,4,8]=>1101100=>0011011
[5,7,6,8,4,1,2,3]=>[3,2,1,4,8,6,7,5]=>1100110=>0110011
[4,7,6,5,8,1,2,3]=>[3,2,1,8,5,6,7,4]=>1101100=>0011011
[3,7,6,5,1,8,2,4]=>[4,2,8,1,5,6,7,3]=>1110000=>0000111
[8,7,6,5,2,1,4,3]=>[3,4,1,2,5,6,7,8]=>1000000=>0000001
[3,6,4,8,7,5,1,2]=>[2,1,5,7,8,4,6,3]=>1011000=>0001101
[5,6,4,3,8,7,1,2]=>[2,1,7,8,3,4,6,5]=>1010100=>0010101
[3,6,2,4,8,1,5,7]=>[7,5,1,8,4,2,6,3]=>1111100=>0011111
[3,4,7,2,8,1,6,5]=>[5,6,1,8,2,7,4,3]=>1111000=>0001111
[1,4,7,2,5,8,6,3]=>[3,6,8,5,2,7,4,1]=>1101100=>0011011
[7,3,8,4,5,6,1,2]=>[2,1,6,5,4,8,3,7]=>1011100=>0011101
[3,8,7,5,4,6,1,2]=>[2,1,6,4,5,7,8,3]=>1011000=>0001101
[4,3,6,7,8,5,1,2]=>[2,1,5,8,7,6,3,4]=>1010011=>1100101
[4,6,8,5,3,7,1,2]=>[2,1,7,3,5,8,6,4]=>1011010=>0101101
[6,5,2,1,4,7,8,3]=>[3,8,7,4,1,2,5,6]=>1001001=>1001001
[4,2,7,5,1,8,6,3]=>[3,6,8,1,5,7,2,4]=>1100000=>0000011
[2,1,6,4,8,7,5,3]=>[3,5,7,8,4,6,1,2]=>1001000=>0001001
[7,8,1,4,2,6,5,3]=>[3,5,6,2,4,1,8,7]=>1100001=>1000011
[1,3,6,4,8,2,5,7]=>[7,5,2,8,4,6,3,1]=>1111100=>0011111
[6,5,1,3,4,2,8,7]=>[7,8,2,4,3,1,5,6]=>1110000=>0000111
[3,6,2,5,8,1,7,4]=>[4,7,1,8,5,2,6,3]=>1110100=>0010111
[7,6,1,8,3,2,4,5]=>[5,4,2,3,8,1,6,7]=>1101000=>0001011
[1,8,7,6,4,3,2,5]=>[5,2,3,4,6,7,8,1]=>1100000=>0000011
[7,8,1,6,5,3,2,4]=>[4,2,3,5,6,1,8,7]=>1100001=>1000011
[4,2,6,1,8,5,7,3]=>[3,7,5,8,1,6,2,4]=>1100100=>0010011
[2,8,1,5,4,6,7,3]=>[3,7,6,4,5,1,8,2]=>1101010=>0101011
[1,2,8,3,6,5,7,4]=>[4,7,5,6,3,8,2,1]=>1110100=>0010111
[1,6,3,8,5,7,2,4]=>[4,2,7,5,8,3,6,1]=>1110100=>0010111
[7,6,5,8,1,4,2,3]=>[3,2,4,1,8,5,6,7]=>1100100=>0010011
[5,8,6,7,3,2,1,4]=>[4,1,2,3,7,6,8,5]=>1000110=>0110001
[1,6,4,3,7,2,8,5]=>[5,8,2,7,3,4,6,1]=>1110000=>0000111
[4,6,3,8,1,2,7,5]=>[5,7,2,1,8,3,6,4]=>1111000=>0001111
[4,3,7,1,2,5,8,6]=>[6,8,5,2,1,7,3,4]=>1110100=>0010111
[7,8,1,3,4,2,6,5]=>[5,6,2,4,3,1,8,7]=>1110001=>1000111
[5,3,8,7,1,2,6,4]=>[4,6,2,1,7,8,3,5]=>1110000=>0000111
[6,5,3,8,2,1,7,4]=>[4,7,1,2,8,3,5,6]=>1010000=>0000101
[7,5,8,4,1,2,3,6]=>[6,3,2,1,4,8,5,7]=>1110100=>0010111
[2,6,4,5,3,8,1,7]=>[7,1,8,3,5,4,6,2]=>1111000=>0001111
[3,6,5,8,4,2,1,7]=>[7,1,2,4,8,5,6,3]=>1010100=>0010101
[5,4,7,3,6,8,1,2]=>[2,1,8,6,3,7,4,5]=>1011010=>0101101
[3,4,7,8,5,6,1,2]=>[2,1,6,5,8,7,4,3]=>1011101=>1011101
[3,4,7,2,5,1,6,8]=>[8,6,1,5,2,7,4,3]=>1111010=>0101111
[1,4,7,2,5,8,3,6]=>[6,3,8,5,2,7,4,1]=>1111100=>0011111
[3,6,2,4,7,1,5,8]=>[8,5,1,7,4,2,6,3]=>1111100=>0011111
[4,5,6,3,8,7,1,2]=>[2,1,7,8,3,6,5,4]=>1011100=>0011101
[6,3,7,5,8,4,1,2]=>[2,1,4,8,5,7,3,6]=>1010100=>0010101
[3,2,7,6,5,1,4,8]=>[8,4,1,5,6,7,2,3]=>1101000=>0001011
[4,8,2,6,1,5,3,7]=>[7,3,5,1,6,2,8,4]=>1111000=>0001111
[4,3,6,2,5,1,8,7]=>[7,8,1,5,2,6,3,4]=>1110000=>0000111
[7,8,3,2,5,1,4,6]=>[6,4,1,5,2,3,8,7]=>1101001=>1001011
[7,8,1,2,5,6,3,4]=>[4,3,6,5,2,1,8,7]=>1110101=>1010111
[2,1,8,6,4,7,3,5]=>[5,3,7,4,6,8,1,2]=>1011000=>0001101
[1,8,3,6,7,4,5,2]=>[2,5,4,7,6,3,8,1]=>1011010=>0101101
[7,1,5,8,3,6,2,4]=>[4,2,6,3,8,5,1,7]=>1110100=>0010111
[5,8,7,1,2,4,3,6]=>[6,3,4,2,1,7,8,5]=>1110100=>0010111
[1,5,7,8,2,4,6,3]=>[3,6,4,2,8,7,5,1]=>1101101=>1011011
[7,6,5,1,4,3,2,8]=>[8,2,3,4,1,5,6,7]=>1100000=>0000011
[2,6,4,5,1,3,8,7]=>[7,8,3,1,5,4,6,2]=>1111000=>0001111
[3,5,6,4,1,8,2,7]=>[7,2,8,1,4,6,5,3]=>1110100=>0010111
[4,2,6,3,8,1,7,5]=>[5,7,1,8,3,6,2,4]=>1110000=>0000111
[7,2,3,5,4,1,8,6]=>[6,8,1,4,5,3,2,7]=>1110000=>0000111
[1,3,7,4,8,2,5,6]=>[6,5,2,8,4,7,3,1]=>1111100=>0011111
[5,3,7,4,1,6,2,8]=>[8,2,6,1,4,7,3,5]=>1110000=>0000111
[5,8,7,6,3,1,2,4]=>[4,2,1,3,6,7,8,5]=>1100100=>0010011
[7,5,6,8,1,4,3,2]=>[2,3,4,1,8,6,5,7]=>1000110=>0110001
[5,2,7,1,8,4,6,3]=>[3,6,4,8,1,7,2,5]=>1101000=>0001011
[1,2,7,8,5,4,3,6]=>[6,3,4,5,8,7,2,1]=>1110001=>1000111
[4,2,1,3,6,5,8,7]=>[7,8,5,6,3,1,2,4]=>1010100=>0010101
[7,8,2,1,4,5,3,6]=>[6,3,5,4,1,2,8,7]=>1011001=>1001101
[6,5,1,8,2,7,4,3]=>[3,4,7,2,8,1,5,6]=>1100000=>0000011
[7,6,1,8,5,3,2,4]=>[4,2,3,5,8,1,6,7]=>1100000=>0000011
[2,5,6,1,7,4,8,3]=>[3,8,4,7,1,6,5,2]=>1101100=>0011011
[7,8,5,1,6,4,2,3]=>[3,2,4,6,1,5,8,7]=>1100001=>1000011
[2,6,5,7,3,4,8,1]=>[1,8,4,3,7,5,6,2]=>0111100=>0011110
[1,6,4,7,5,8,2,3]=>[3,2,8,5,7,4,6,1]=>1101100=>0011011
[1,3,7,4,6,8,2,5]=>[5,2,8,6,4,7,3,1]=>1111010=>0101111
[5,2,4,7,3,6,8,1]=>[1,8,6,3,7,4,2,5]=>0111010=>0101110
[8,1,6,5,7,2,4,3]=>[3,4,2,7,5,6,1,8]=>1100100=>0010011
[7,1,6,5,8,3,2,4]=>[4,2,3,8,5,6,1,7]=>1100100=>0010011
[1,2,7,6,8,3,4,5]=>[5,4,3,8,6,7,2,1]=>1111010=>0101111
[6,1,7,5,3,8,2,4]=>[4,2,8,3,5,7,1,6]=>1110000=>0000111
[2,1,7,5,6,8,3,4]=>[4,3,8,6,5,7,1,2]=>1010110=>0110101
[4,8,5,6,2,7,3,1]=>[1,3,7,2,6,5,8,4]=>0101100=>0011010
[3,8,6,4,2,7,5,1]=>[1,5,7,2,4,6,8,3]=>0110000=>0000110
[7,8,5,2,4,6,3,1]=>[1,3,6,4,2,5,8,7]=>0101001=>1001010
[7,8,1,6,2,4,5,3]=>[3,5,4,2,6,1,8,7]=>1101001=>1001011
[2,8,1,7,4,3,6,5]=>[5,6,3,4,7,1,8,2]=>1110000=>0000111
[6,8,1,4,7,2,5,3]=>[3,5,2,7,4,1,8,6]=>1101010=>0101011
[3,8,4,1,7,2,6,5]=>[5,6,2,7,1,4,8,3]=>1110000=>0000111
[3,7,4,1,8,5,2,6]=>[6,2,5,8,1,4,7,3]=>1110000=>0000111
[6,7,1,4,8,3,2,5]=>[5,2,3,8,4,1,7,6]=>1101010=>0101011
[2,7,1,8,4,5,3,6]=>[6,3,5,4,8,1,7,2]=>1111000=>0001111
[6,1,2,8,4,3,5,7]=>[7,5,3,4,8,2,1,6]=>1110100=>0010111
[5,1,2,4,8,3,6,7]=>[7,6,3,8,4,2,1,5]=>1111010=>0101111
[4,1,3,2,8,5,6,7]=>[7,6,5,8,2,3,1,4]=>1100110=>0110011
[3,2,1,4,8,5,6,7]=>[7,6,5,8,4,1,2,3]=>1001110=>0111001
[4,3,6,1,5,8,2,7]=>[7,2,8,5,1,6,3,4]=>1110100=>0010111
[2,6,1,4,5,8,3,7]=>[7,3,8,5,4,1,6,2]=>1111100=>0011111
[1,6,2,5,8,3,4,7]=>[7,4,3,8,5,2,6,1]=>1111100=>0011111
[8,4,2,1,7,3,6,5]=>[5,6,3,7,1,2,4,8]=>1010000=>0000101
[7,4,2,1,8,5,3,6]=>[6,3,5,8,1,2,4,7]=>1010000=>0000101
[6,4,3,1,5,8,2,7]=>[7,2,8,5,1,3,4,6]=>1100100=>0010011
[5,4,3,2,1,8,6,7]=>[7,6,8,1,2,3,4,5]=>1000010=>0100001
[2,5,3,4,1,8,6,7]=>[7,6,8,1,4,3,5,2]=>1110010=>0100111
[4,3,5,2,1,8,6,7]=>[7,6,8,1,2,5,3,4]=>1010010=>0100101
[3,7,6,8,4,5,2,1]=>[1,2,5,4,8,6,7,3]=>0011010=>0101100
[1,4,8,6,7,5,2,3]=>[3,2,5,7,6,8,4,1]=>1101010=>0101011
[2,4,8,6,7,3,5,1]=>[1,5,3,7,6,8,4,2]=>0111010=>0101110
[7,3,8,5,4,6,2,1]=>[1,2,6,4,5,8,3,7]=>0011000=>0001100
[3,4,8,5,6,7,2,1]=>[1,2,7,6,5,8,4,3]=>0011110=>0111100
[6,3,5,8,4,7,2,1]=>[1,2,7,4,8,5,3,6]=>0011100=>0011100
[5,4,3,8,6,7,2,1]=>[1,2,7,6,8,3,4,5]=>0010010=>0100100
[5,4,2,8,7,3,6,1]=>[1,6,3,7,8,2,4,5]=>0110000=>0000110
[3,2,8,5,7,4,6,1]=>[1,6,4,7,5,8,2,3]=>0101100=>0011010
[2,1,8,7,4,6,3,5]=>[5,3,6,4,7,8,1,2]=>1011000=>0001101
[5,4,1,8,7,6,2,3]=>[3,2,6,7,8,1,4,5]=>1100000=>0000011
[5,8,6,7,4,3,2,1]=>[1,2,3,4,7,6,8,5]=>0000110=>0110000
[4,8,7,5,6,3,2,1]=>[1,2,3,6,5,7,8,4]=>0001100=>0011000
[4,2,1,6,3,5,8,7]=>[7,8,5,3,6,1,2,4]=>1010100=>0010101
[6,2,1,4,3,5,8,7]=>[7,8,5,3,4,1,2,6]=>1010100=>0010101
[6,2,1,4,3,8,5,7]=>[7,5,8,3,4,1,2,6]=>1010100=>0010101
[8,2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2,8]=>1010100=>0010101
[8,2,4,1,3,6,5,7]=>[7,5,6,3,1,4,2,8]=>1110100=>0010111
[6,2,4,1,3,8,5,7]=>[7,5,8,3,1,4,2,6]=>1110100=>0010111
[6,2,4,1,3,5,8,7]=>[7,8,5,3,1,4,2,6]=>1110100=>0010111
[4,2,6,1,3,5,8,7]=>[7,8,5,3,1,6,2,4]=>1110100=>0010111
[2,1,6,4,3,5,8,7]=>[7,8,5,3,4,6,1,2]=>1010100=>0010101
[2,6,1,4,3,5,8,7]=>[7,8,5,3,4,1,6,2]=>1110100=>0010111
[2,6,4,1,3,5,8,7]=>[7,8,5,3,1,4,6,2]=>1110100=>0010111
[6,4,2,1,3,5,8,7]=>[7,8,5,3,1,2,4,6]=>1010100=>0010101
[8,4,2,1,3,6,5,7]=>[7,5,6,3,1,2,4,8]=>1010100=>0010101
[8,4,2,1,6,3,5,7]=>[7,5,3,6,1,2,4,8]=>1010100=>0010101
[6,4,2,1,8,3,5,7]=>[7,5,3,8,1,2,4,6]=>1010100=>0010101
[4,6,2,1,3,8,5,7]=>[7,5,8,3,1,2,6,4]=>1011100=>0011101
[2,6,1,4,3,8,5,7]=>[7,5,8,3,4,1,6,2]=>1110100=>0010111
[2,1,6,4,3,8,5,7]=>[7,5,8,3,4,6,1,2]=>1010100=>0010101
[2,1,8,4,3,6,5,7]=>[7,5,6,3,4,8,1,2]=>1010100=>0010101
[2,8,1,4,3,6,5,7]=>[7,5,6,3,4,1,8,2]=>1110100=>0010111
[2,8,4,1,3,6,5,7]=>[7,5,6,3,1,4,8,2]=>1110100=>0010111
[8,6,2,1,4,3,5,7]=>[7,5,3,4,1,2,6,8]=>1010100=>0010101
[2,8,1,4,6,3,5,7]=>[7,5,3,6,4,1,8,2]=>1111100=>0011111
[2,1,8,4,6,3,5,7]=>[7,5,3,6,4,8,1,2]=>1011100=>0011101
[2,1,6,4,8,3,5,7]=>[7,5,3,8,4,6,1,2]=>1011100=>0011101
[2,6,1,4,8,3,5,7]=>[7,5,3,8,4,1,6,2]=>1111100=>0011111
[2,6,4,1,8,3,5,7]=>[7,5,3,8,1,4,6,2]=>1110100=>0010111
[2,6,4,8,1,3,5,7]=>[7,5,3,1,8,4,6,2]=>1111100=>0011111
[4,6,2,8,1,3,5,7]=>[7,5,3,1,8,2,6,4]=>1111100=>0011111
[4,2,6,1,3,8,5,7]=>[7,5,8,3,1,6,2,4]=>1110100=>0010111
[4,2,6,1,8,3,5,7]=>[7,5,3,8,1,6,2,4]=>1110100=>0010111
[6,2,4,1,8,3,5,7]=>[7,5,3,8,1,4,2,6]=>1110100=>0010111
[8,2,4,1,6,3,5,7]=>[7,5,3,6,1,4,2,8]=>1110100=>0010111
[8,2,1,4,6,3,5,7]=>[7,5,3,6,4,1,2,8]=>1011100=>0011101
[6,2,1,4,8,3,5,7]=>[7,5,3,8,4,1,2,6]=>1011100=>0011101
[4,2,1,6,8,3,5,7]=>[7,5,3,8,6,1,2,4]=>1010110=>0110101
[4,2,1,6,3,8,5,7]=>[7,5,8,3,6,1,2,4]=>1010100=>0010101
[4,2,1,3,6,8,5,7]=>[7,5,8,6,3,1,2,4]=>1010110=>0110101
[2,1,4,3,8,6,5,7]=>[7,5,6,8,3,4,1,2]=>1010100=>0010101
[2,4,1,3,8,6,5,7]=>[7,5,6,8,3,1,4,2]=>1110100=>0010111
[4,2,1,3,8,6,5,7]=>[7,5,6,8,3,1,2,4]=>1010100=>0010101
[4,2,1,8,3,6,5,7]=>[7,5,6,3,8,1,2,4]=>1010100=>0010101
[4,2,1,8,6,3,5,7]=>[7,5,3,6,8,1,2,4]=>1010100=>0010101
[8,2,1,6,4,3,5,7]=>[7,5,3,4,6,1,2,8]=>1010100=>0010101
[4,2,8,1,6,3,5,7]=>[7,5,3,6,1,8,2,4]=>1110100=>0010111
[4,2,8,1,3,6,5,7]=>[7,5,6,3,1,8,2,4]=>1110100=>0010111
[2,4,8,1,3,6,5,7]=>[7,5,6,3,1,8,4,2]=>1111100=>0011111
[2,4,1,8,3,6,5,7]=>[7,5,6,3,8,1,4,2]=>1110100=>0010111
[2,1,4,8,3,6,5,7]=>[7,5,6,3,8,4,1,2]=>1011100=>0011101
[2,1,4,8,6,3,5,7]=>[7,5,3,6,8,4,1,2]=>1011100=>0011101
[2,4,8,1,6,3,5,7]=>[7,5,3,6,1,8,4,2]=>1111100=>0011111
[2,4,8,6,1,3,5,7]=>[7,5,3,1,6,8,4,2]=>1111100=>0011111
[4,2,8,6,1,3,5,7]=>[7,5,3,1,6,8,2,4]=>1110100=>0010111
[4,6,8,2,1,3,5,7]=>[7,5,3,1,2,8,6,4]=>1011110=>0111101
[2,1,8,6,4,3,5,7]=>[7,5,3,4,6,8,1,2]=>1010100=>0010101
[2,8,6,1,4,3,5,7]=>[7,5,3,4,1,6,8,2]=>1110100=>0010111
[3,2,6,1,5,4,8,7]=>[7,8,4,5,1,6,2,3]=>1101000=>0001011
[5,2,4,3,8,1,7,6]=>[6,7,1,8,3,4,2,5]=>1110000=>0000111
[6,1,5,2,4,3,8,7]=>[7,8,3,4,2,5,1,6]=>1110000=>0000111
[6,1,3,2,5,4,8,7]=>[7,8,4,5,2,3,1,6]=>1101000=>0001011
[4,3,6,1,5,2,8,7]=>[7,8,2,5,1,6,3,4]=>1110000=>0000111
[4,3,5,2,8,1,7,6]=>[6,7,1,8,2,5,3,4]=>1110000=>0000111
[4,3,7,2,6,5,8,1]=>[1,8,5,6,2,7,3,4]=>0110100=>0010110
[4,3,8,2,6,1,7,5]=>[5,7,1,6,2,8,3,4]=>1110000=>0000111
[4,3,8,1,7,2,6,5]=>[5,6,2,7,1,8,3,4]=>1110000=>0000111
[4,3,8,1,5,2,7,6]=>[6,7,2,5,1,8,3,4]=>1110000=>0000111
[5,1,8,3,4,2,7,6]=>[6,7,2,4,3,8,1,5]=>1110000=>0000111
[5,4,8,1,3,2,7,6]=>[6,7,2,3,1,8,4,5]=>1101000=>0001011
[2,1,5,4,8,3,7,6]=>[6,7,3,8,4,5,1,2]=>1011000=>0001101
[5,4,7,6,8,1,3,2]=>[2,3,1,8,6,7,4,5]=>1001010=>0101001
[4,3,7,6,8,1,5,2]=>[2,5,1,8,6,7,3,4]=>1010010=>0100101
[4,3,7,1,8,5,6,2]=>[2,6,5,8,1,7,3,4]=>1010100=>0010101
[4,3,6,5,8,1,7,2]=>[2,7,1,8,5,6,3,4]=>1010100=>0010101
[6,3,5,4,7,2,8,1]=>[1,8,2,7,4,5,3,6]=>0111000=>0001110
[6,3,5,4,8,1,7,2]=>[2,7,1,8,4,5,3,6]=>1011000=>0001101
[7,1,6,5,8,3,4,2]=>[2,4,3,8,5,6,1,7]=>1010100=>0010101
[7,4,6,5,8,1,3,2]=>[2,3,1,8,5,6,4,7]=>1001100=>0011001
[8,3,5,1,7,2,6,4]=>[4,6,2,7,1,5,3,8]=>1110000=>0000111
[8,3,5,2,6,1,7,4]=>[4,7,1,6,2,5,3,8]=>1110000=>0000111
[7,3,5,2,6,4,8,1]=>[1,8,4,6,2,5,3,7]=>0111000=>0001110
[8,2,7,1,5,3,6,4]=>[4,6,3,5,1,7,2,8]=>1110000=>0000111
[8,1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1,8]=>1110000=>0000111
[8,1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1,8]=>1101000=>0001011
[2,1,8,3,7,4,6,5]=>[5,6,4,7,3,8,1,2]=>1011000=>0001101
[2,1,8,3,5,4,7,6]=>[6,7,4,5,3,8,1,2]=>1011000=>0001101
[8,1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1,8]=>1101000=>0001011
[8,1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1,8]=>1110000=>0000111
[8,2,4,1,7,3,6,5]=>[5,6,3,7,1,4,2,8]=>1110000=>0000111
[3,2,8,1,7,4,6,5]=>[5,6,4,7,1,8,2,3]=>1101000=>0001011
[3,2,8,1,5,4,7,6]=>[6,7,4,5,1,8,2,3]=>1101000=>0001011
[3,2,4,1,8,5,7,6]=>[6,7,5,8,1,4,2,3]=>1100100=>0010011
[4,1,3,2,7,6,8,5]=>[5,8,6,7,2,3,1,4]=>1100010=>0100011
[3,2,7,6,8,1,5,4]=>[4,5,1,8,6,7,2,3]=>1100010=>0100011
[3,2,6,5,8,1,7,4]=>[4,7,1,8,5,6,2,3]=>1100100=>0010011
[6,5,7,2,4,3,8,1]=>[1,8,3,4,2,7,5,6]=>0110100=>0010110
[7,2,4,1,8,5,6,3]=>[3,6,5,8,1,4,2,7]=>1100100=>0010011
[7,6,8,1,5,2,4,3]=>[3,4,2,5,1,8,6,7]=>1100010=>0100011
[7,6,8,1,3,2,5,4]=>[4,5,2,3,1,8,6,7]=>1100010=>0100011
[7,1,8,5,6,2,4,3]=>[3,4,2,6,5,8,1,7]=>1100100=>0010011
[7,1,8,2,6,4,5,3]=>[3,5,4,6,2,8,1,7]=>1101000=>0001011
[7,2,8,1,5,4,6,3]=>[3,6,4,5,1,8,2,7]=>1101000=>0001011
[5,4,8,2,6,1,7,3]=>[3,7,1,6,2,8,4,5]=>1101000=>0001011
[6,1,8,4,7,2,5,3]=>[3,5,2,7,4,8,1,6]=>1101000=>0001011
[6,5,8,1,3,2,7,4]=>[4,7,2,3,1,8,5,6]=>1100100=>0010011
[2,1,6,5,8,3,7,4]=>[4,7,3,8,5,6,1,2]=>1010100=>0010101
[6,5,7,4,8,1,3,2]=>[2,3,1,8,4,7,5,6]=>1001100=>0011001
[6,5,7,1,8,3,4,2]=>[2,4,3,8,1,7,5,6]=>1010100=>0010101
[3,2,1,5,8,4,6,7]=>[7,6,4,8,5,1,2,3]=>1001110=>0111001
[2,8,3,1,5,4,6,7]=>[7,6,4,5,1,3,8,2]=>1101010=>0101011
[2,4,8,3,5,7,6,1]=>[1,6,7,5,3,8,4,2]=>0111100=>0011110
[4,2,1,8,5,3,6,7]=>[7,6,3,5,8,1,2,4]=>1010010=>0100101
[1,8,4,2,5,3,6,7]=>[7,6,3,5,2,4,8,1]=>1110010=>0100111
[8,1,5,3,2,4,6,7]=>[7,6,4,2,3,5,1,8]=>1101010=>0101011
[3,8,1,5,2,4,6,7]=>[7,6,4,2,5,1,8,3]=>1111010=>0101111
[5,4,1,3,8,2,6,7]=>[7,6,2,8,3,1,4,5]=>1110010=>0100111
[1,5,7,3,8,4,2,6]=>[6,2,4,8,3,7,5,1]=>1110100=>0010111
[4,8,1,5,7,3,6,2]=>[2,6,3,7,5,1,8,4]=>1011100=>0011101
[1,4,3,8,7,5,6,2]=>[2,6,5,7,8,3,4,1]=>1010100=>0010101
[3,8,4,7,6,5,2,1]=>[1,2,5,6,7,4,8,3]=>0011000=>0001100
[6,4,8,7,1,5,2,3]=>[3,2,5,1,7,8,4,6]=>1101000=>0001011
[7,1,6,8,4,3,2,5]=>[5,2,3,4,8,6,1,7]=>1100010=>0100011
[1,6,7,2,8,4,3,5]=>[5,3,4,8,2,7,6,1]=>1110010=>0100111
[6,7,1,4,2,8,3,5]=>[5,3,8,2,4,1,7,6]=>1110010=>0100111
[6,3,7,1,4,8,2,5]=>[5,2,8,4,1,7,3,6]=>1111000=>0001111
[3,7,8,1,5,2,4,6]=>[6,4,2,5,1,8,7,3]=>1111001=>1001111
[7,1,2,8,5,3,4,6]=>[6,4,3,5,8,2,1,7]=>1111000=>0001111
[1,7,2,8,4,5,3,6]=>[6,3,5,4,8,2,7,1]=>1111000=>0001111
[4,2,1,7,8,5,3,6]=>[6,3,5,8,7,1,2,4]=>1010001=>1000101
[2,6,8,4,3,7,5,1]=>[1,5,7,3,4,8,6,2]=>0110010=>0100110
[6,2,4,8,3,7,5,1]=>[1,5,7,3,8,4,2,6]=>0111000=>0001110
[2,6,7,3,1,4,8,5]=>[5,8,4,1,3,7,6,2]=>1101010=>0101011
[2,7,1,8,3,5,4,6]=>[6,4,5,3,8,1,7,2]=>1111000=>0001111
[2,1,7,3,5,8,4,6]=>[6,4,8,5,3,7,1,2]=>1011100=>0011101
[1,2,7,5,8,3,4,6]=>[6,4,3,8,5,7,2,1]=>1111100=>0011111
[8,7,1,3,6,2,4,5]=>[5,4,2,6,3,1,7,8]=>1111000=>0001111
[8,2,1,7,3,5,6,4]=>[4,6,5,3,7,1,2,8]=>1010100=>0010101
[2,7,8,4,1,6,5,3]=>[3,5,6,1,4,8,7,2]=>1100001=>1000011
[2,8,4,1,6,7,5,3]=>[3,5,7,6,1,4,8,2]=>1100010=>0100011
[2,1,8,4,7,5,6,3]=>[3,6,5,7,4,8,1,2]=>1001100=>0011001
[8,3,7,1,5,6,2,4]=>[4,2,6,5,1,7,3,8]=>1110100=>0010111
[8,6,1,2,7,5,3,4]=>[4,3,5,7,2,1,6,8]=>1110000=>0000111
[8,1,6,2,7,4,5,3]=>[3,5,4,7,2,6,1,8]=>1101000=>0001011
[1,8,5,2,6,7,4,3]=>[3,4,7,6,2,5,8,1]=>1100010=>0100011
[5,2,1,8,6,7,4,3]=>[3,4,7,6,8,1,2,5]=>1000010=>0100001
[8,7,6,5,1,4,2,3]=>[3,2,4,1,5,6,7,8]=>1100000=>0000011
[8,7,6,1,5,3,4,2]=>[2,4,3,5,1,6,7,8]=>1010000=>0000101
[1,8,6,7,5,4,3,2]=>[2,3,4,5,7,6,8,1]=>1000010=>0100001
[6,3,5,2,1,4,8,7]=>[7,8,4,1,2,5,3,6]=>1011000=>0001101
[8,3,5,7,2,4,1,6]=>[6,1,4,2,7,5,3,8]=>1110100=>0010111
[6,5,3,1,2,4,8,7]=>[7,8,4,2,1,3,5,6]=>1101000=>0001011
[4,5,3,6,1,2,8,7]=>[7,8,2,1,6,3,5,4]=>1111000=>0001111
[3,5,1,4,6,2,8,7]=>[7,8,2,6,4,1,5,3]=>1111000=>0001111
[5,7,4,6,3,8,2,1]=>[1,2,8,3,6,4,7,5]=>0011100=>0011100
[2,8,4,6,3,7,1,5]=>[5,1,7,3,6,4,8,2]=>1111000=>0001111
[8,1,4,7,3,6,2,5]=>[5,2,6,3,7,4,1,8]=>1111000=>0001111
[8,5,1,4,7,3,2,6]=>[6,2,3,7,4,1,5,8]=>1101000=>0001011
[8,5,3,7,1,4,2,6]=>[6,2,4,1,7,3,5,8]=>1110000=>0000111
[2,1,8,5,7,4,3,6]=>[6,3,4,7,5,8,1,2]=>1010100=>0010101
[5,1,4,6,8,3,7,2]=>[2,7,3,8,6,4,1,5]=>1011010=>0101101
[4,7,1,3,5,8,6,2]=>[2,6,8,5,3,1,7,4]=>1011100=>0011101
[4,8,3,7,1,2,6,5]=>[5,6,2,1,7,3,8,4]=>1111000=>0001111
[8,7,1,4,2,6,3,5]=>[5,3,6,2,4,1,7,8]=>1110000=>0000111
[8,6,3,1,2,4,7,5]=>[5,7,4,2,1,3,6,8]=>1101000=>0001011
[2,1,8,7,5,3,4,6]=>[6,4,3,5,7,8,1,2]=>1011000=>0001101
[8,1,7,4,5,2,3,6]=>[6,3,2,5,4,7,1,8]=>1111000=>0001111
[8,7,2,6,4,1,3,5]=>[5,3,1,4,6,2,7,8]=>1110000=>0000111
[3,8,6,7,4,2,1,5]=>[5,1,2,4,7,6,8,3]=>1010010=>0100101
[5,3,7,8,2,4,6,1]=>[1,6,4,2,8,7,3,5]=>0111001=>1001110
[5,3,7,6,2,1,8,4]=>[4,8,1,2,6,7,3,5]=>1010000=>0000101
[5,7,8,6,4,2,1,3]=>[3,1,2,4,6,8,7,5]=>1000101=>1010001
[6,7,3,5,1,8,2,4]=>[4,2,8,1,5,3,7,6]=>1110010=>0100111
[2,1,6,7,5,8,3,4]=>[4,3,8,5,7,6,1,2]=>1010110=>0110101
[2,1,5,7,3,6,8,4]=>[4,8,6,3,7,5,1,2]=>1010110=>0110101
[4,1,7,2,5,6,8,3]=>[3,8,6,5,2,7,1,4]=>1100110=>0110011
[2,4,7,1,6,5,8,3]=>[3,8,5,6,1,7,4,2]=>1101100=>0011011
[3,4,6,2,7,8,5,1]=>[1,5,8,7,2,6,4,3]=>0111001=>1001110
[4,6,1,2,5,8,7,3]=>[3,7,8,5,2,1,6,4]=>1101100=>0011011
[5,6,3,1,8,7,2,4]=>[4,2,7,8,1,3,6,5]=>1100100=>0010011
[6,3,2,1,7,4,8,5]=>[5,8,4,7,1,2,3,6]=>1001000=>0001001
[4,2,1,7,3,5,8,6]=>[6,8,5,3,7,1,2,4]=>1010100=>0010101
[7,3,1,5,4,2,8,6]=>[6,8,2,4,5,1,3,7]=>1100000=>0000011
[7,2,5,1,4,3,8,6]=>[6,8,3,4,1,5,2,7]=>1110000=>0000111
[4,3,7,2,1,5,8,6]=>[6,8,5,1,2,7,3,4]=>1010100=>0010101
[3,6,2,7,1,4,8,5]=>[5,8,4,1,7,2,6,3]=>1111000=>0001111
[2,7,5,4,1,3,8,6]=>[6,8,3,1,4,5,7,2]=>1110000=>0000111
[6,4,3,2,1,8,5,7]=>[7,5,8,1,2,3,4,6]=>1000100=>0010001
[1,7,6,2,4,8,3,5]=>[5,3,8,4,2,6,7,1]=>1111000=>0001111
[6,2,7,5,3,8,1,4]=>[4,1,8,3,5,7,2,6]=>1110000=>0000111
[7,1,8,5,3,6,4,2]=>[2,4,6,3,5,8,1,7]=>1010000=>0000101
[1,8,6,3,2,7,5,4]=>[4,5,7,2,3,6,8,1]=>1100000=>0000011
[8,7,3,1,6,5,4,2]=>[2,4,5,6,1,3,7,8]=>1000000=>0000001
[8,7,2,6,1,5,4,3]=>[3,4,5,1,6,2,7,8]=>1100000=>0000011
[1,8,5,7,4,3,6,2]=>[2,6,3,4,7,5,8,1]=>1010100=>0010101
[3,8,6,1,7,2,5,4]=>[4,5,2,7,1,6,8,3]=>1110000=>0000111
[5,8,4,6,7,1,3,2]=>[2,3,1,7,6,4,8,5]=>1001110=>0111001
[7,2,8,5,6,1,4,3]=>[3,4,1,6,5,8,2,7]=>1100100=>0010011
[3,6,5,8,1,4,2,7]=>[7,2,4,1,8,5,6,3]=>1110100=>0010111
[2,6,5,8,4,1,3,7]=>[7,3,1,4,8,5,6,2]=>1110100=>0010111
[6,5,4,8,3,2,1,7]=>[7,1,2,3,8,4,5,6]=>1001000=>0001001
[4,3,6,8,2,1,5,7]=>[7,5,1,2,8,6,3,4]=>1010110=>0110101
[4,3,6,7,8,1,2,5]=>[5,2,1,8,7,6,3,4]=>1110011=>1100111
[5,4,6,7,2,8,1,3]=>[3,1,8,2,7,6,4,5]=>1101010=>0101011
[4,6,3,7,1,8,2,5]=>[5,2,8,1,7,3,6,4]=>1111000=>0001111
[3,5,7,1,4,8,2,6]=>[6,2,8,4,1,7,5,3]=>1111100=>0011111
[8,1,5,2,7,4,6,3]=>[3,6,4,7,2,5,1,8]=>1101000=>0001011
[5,4,1,6,8,2,3,7]=>[7,3,2,8,6,1,4,5]=>1110010=>0100111
[5,3,1,7,2,8,4,6]=>[6,4,8,2,7,1,3,5]=>1101000=>0001011
[6,5,2,1,7,8,3,4]=>[4,3,8,7,1,2,5,6]=>1010001=>1000101
[5,3,6,4,7,8,1,2]=>[2,1,8,7,4,6,3,5]=>1011001=>1001101
[6,3,7,4,8,5,2,1]=>[1,2,5,8,4,7,3,6]=>0011000=>0001100
[4,7,2,5,8,6,3,1]=>[1,3,6,8,5,2,7,4]=>0101100=>0011010
[6,3,1,8,4,7,5,2]=>[2,5,7,4,8,1,3,6]=>1001000=>0001001
[5,2,8,1,7,3,6,4]=>[4,6,3,7,1,8,2,5]=>1110000=>0000111
[3,6,8,1,4,7,5,2]=>[2,5,7,4,1,8,6,3]=>1011010=>0101101
[5,7,3,8,1,6,4,2]=>[2,4,6,1,8,3,7,5]=>1010100=>0010101
[6,4,7,8,1,5,3,2]=>[2,3,5,1,8,7,4,6]=>1001001=>1001001
[4,6,8,2,7,1,5,3]=>[3,5,1,7,2,8,6,4]=>1101010=>0101011
[2,5,8,7,1,3,6,4]=>[4,6,3,1,7,8,5,2]=>1110100=>0010111
[5,3,8,7,2,1,6,4]=>[4,6,1,2,7,8,3,5]=>1010000=>0000101
[8,2,7,6,5,1,4,3]=>[3,4,1,5,6,7,2,8]=>1100000=>0000011
[4,3,8,7,6,2,1,5]=>[5,1,2,6,7,8,3,4]=>1010000=>0000101
[2,4,8,7,6,1,3,5]=>[5,3,1,6,7,8,4,2]=>1111000=>0001111
[3,5,8,7,2,6,1,4]=>[4,1,6,2,7,8,5,3]=>1110100=>0010111
[4,7,3,8,6,5,1,2]=>[2,1,5,6,8,3,7,4]=>1011000=>0001101
[7,5,8,6,4,3,2,1]=>[1,2,3,4,6,8,5,7]=>0000100=>0010000
[3,8,7,6,5,1,4,2]=>[2,4,1,5,6,7,8,3]=>1010000=>0000101
[2,8,7,6,5,4,1,3]=>[3,1,4,5,6,7,8,2]=>1100000=>0000011
[5,4,3,2,1,6,7,8,9,10]=>[10,9,8,7,6,1,2,3,4,5]=>100001111=>111100001
[6,4,3,2,7,1,5,8,9,10]=>[10,9,8,5,1,7,2,3,4,6]=>110010011=>110010011
[7,5,3,8,2,6,1,4,9,10]=>[10,9,4,1,6,2,8,3,5,7]=>111100001=>100001111
[8,6,9,4,7,2,5,1,3,10]=>[10,3,1,5,2,7,4,9,6,8]=>111101000=>000101111
[7,8,5,6,3,1,4,2]=>[2,4,1,3,6,5,8,7]=>1000101=>1010001
[7,8,5,3,6,1,2,4]=>[4,2,1,6,3,5,8,7]=>1110001=>1000111
[7,5,8,3,1,4,2,6]=>[6,2,4,1,3,8,5,7]=>1100100=>0010011
[7,8,5,3,1,6,4,2]=>[2,4,6,1,3,5,8,7]=>1000001=>1000001
[7,8,5,3,6,1,4,2]=>[2,4,1,6,3,5,8,7]=>1010001=>1000101
[7,8,5,3,6,4,1,2]=>[2,1,4,6,3,5,8,7]=>1010001=>1000101
[7,5,8,3,1,2,6,4]=>[4,6,2,1,3,8,5,7]=>1100100=>0010011
[7,5,8,3,4,1,6,2]=>[2,6,1,4,3,8,5,7]=>1010100=>0010101
[7,5,8,3,4,6,1,2]=>[2,1,6,4,3,8,5,7]=>1011100=>0011101
[7,5,6,3,1,2,8,4]=>[4,8,2,1,3,6,5,7]=>1100100=>0010011
[7,5,3,4,1,2,8,6]=>[6,8,2,1,4,3,5,7]=>1110000=>0000111
[7,5,3,1,4,2,8,6]=>[6,8,2,4,1,3,5,7]=>1100000=>0000011
[7,5,3,6,4,1,8,2]=>[2,8,1,4,6,3,5,7]=>1010000=>0000101
[7,5,3,8,4,1,6,2]=>[2,6,1,4,8,3,5,7]=>1010000=>0000101
[7,5,3,8,1,4,6,2]=>[2,6,4,1,8,3,5,7]=>1011000=>0001101
[7,5,3,1,8,4,6,2]=>[2,6,4,8,1,3,5,7]=>1001000=>0001001
[7,5,3,1,8,2,6,4]=>[4,6,2,8,1,3,5,7]=>1100000=>0000011
[7,5,3,1,6,2,4,8]=>[8,4,2,6,1,3,5,7]=>1101000=>0001011
[7,5,3,1,8,4,2,6]=>[6,2,4,8,1,3,5,7]=>1100000=>0000011
[7,5,3,1,8,6,2,4]=>[4,2,6,8,1,3,5,7]=>1100000=>0000011
[7,5,3,8,1,6,4,2]=>[2,4,6,1,8,3,5,7]=>1010000=>0000101
[7,5,3,8,6,1,4,2]=>[2,4,1,6,8,3,5,7]=>1010000=>0000101
[7,5,3,8,6,4,1,2]=>[2,1,4,6,8,3,5,7]=>1010000=>0000101
[7,5,8,3,6,4,1,2]=>[2,1,4,6,3,8,5,7]=>1010100=>0010101
[7,5,8,3,6,1,4,2]=>[2,4,1,6,3,8,5,7]=>1010100=>0010101
[7,5,8,3,1,6,4,2]=>[2,4,6,1,3,8,5,7]=>1000100=>0010001
[7,5,3,8,1,6,2,4]=>[4,2,6,1,8,3,5,7]=>1110000=>0000111
[7,5,3,8,1,4,2,6]=>[6,2,4,1,8,3,5,7]=>1110000=>0000111
[7,5,3,8,6,1,2,4]=>[4,2,1,6,8,3,5,7]=>1110000=>0000111
[7,5,8,6,3,1,2,4]=>[4,2,1,3,6,8,5,7]=>1100100=>0010011
[7,5,8,6,3,1,4,2]=>[2,4,1,3,6,8,5,7]=>1000100=>0010001
[7,5,8,6,3,4,1,2]=>[2,1,4,3,6,8,5,7]=>1010100=>0010101
[7,5,6,8,3,1,4,2]=>[2,4,1,3,8,6,5,7]=>1000110=>0110001
[7,5,6,3,8,1,2,4]=>[4,2,1,8,3,6,5,7]=>1110100=>0010111
[7,5,3,6,1,8,2,4]=>[4,2,8,1,6,3,5,7]=>1110000=>0000111
[7,5,6,3,8,1,4,2]=>[2,4,1,8,3,6,5,7]=>1010100=>0010101
[7,5,6,3,8,4,1,2]=>[2,1,4,8,3,6,5,7]=>1010100=>0010101
[7,5,3,6,8,1,4,2]=>[2,4,1,8,6,3,5,7]=>1010010=>0100101
[7,5,3,6,1,8,4,2]=>[2,4,8,1,6,3,5,7]=>1010000=>0000101
[7,5,3,1,6,8,4,2]=>[2,4,8,6,1,3,5,7]=>1000010=>0100001
[7,5,3,1,6,8,2,4]=>[4,2,8,6,1,3,5,7]=>1100010=>0100011
[7,5,3,4,1,6,8,2]=>[2,8,6,1,4,3,5,7]=>1010010=>0100101
[7,5,3,1,4,6,8,2]=>[2,8,6,4,1,3,5,7]=>1001010=>0101001
[7,5,3,1,2,6,8,4]=>[4,8,6,2,1,3,5,7]=>1100010=>0100011
[4,6,8,3,5,7,1,2]=>[2,1,7,5,3,8,6,4]=>1011110=>0111101
[6,8,1,2,4,5,7,3]=>[3,7,5,4,2,1,8,6]=>1101110=>0111011
[3,6,8,2,5,7,1,4]=>[4,1,7,5,2,8,6,3]=>1110110=>0110111
[3,5,8,2,4,7,1,6]=>[6,1,7,4,2,8,5,3]=>1111100=>0011111
[3,5,7,2,4,6,1,8]=>[8,1,6,4,2,7,5,3]=>1111100=>0011111
[4,2,5,8,3,7,1,6]=>[6,1,7,3,8,5,2,4]=>1110100=>0010111
[1,2,5,8,3,6,7,4]=>[4,7,6,3,8,5,2,1]=>1110110=>0110111
[1,4,3,8,2,6,7,5]=>[5,7,6,2,8,3,4,1]=>1110010=>0100111
[5,4,8,3,2,1,6,7]=>[7,6,1,2,3,8,4,5]=>1001010=>0101001
[4,6,3,2,1,8,5,7]=>[7,5,8,1,2,3,6,4]=>1001100=>0011001
[5,4,7,3,8,6,1,2]=>[2,1,6,8,3,7,4,5]=>1011000=>0001101
[5,8,4,7,6,3,1,2]=>[2,1,3,6,7,4,8,5]=>1001100=>0011001
[4,8,3,1,7,2,6,5]=>[5,6,2,7,1,3,8,4]=>1101000=>0001011
[4,7,3,6,5,2,1,8]=>[8,1,2,5,6,3,7,4]=>1011000=>0001101
[5,3,1,6,4,2,8,7]=>[7,8,2,4,6,1,3,5]=>1100000=>0000011
[1,3,8,5,4,2,7,6]=>[6,7,2,4,5,8,3,1]=>1110000=>0000111
[1,6,3,4,2,8,7,5]=>[5,7,8,2,4,3,6,1]=>1110000=>0000111
[1,6,8,7,4,2,5,3]=>[3,5,2,4,7,8,6,1]=>1100010=>0100011
[7,6,4,3,8,5,1,2]=>[2,1,5,8,3,4,6,7]=>1010000=>0000101
[1,7,6,2,8,4,5,3]=>[3,5,4,8,2,6,7,1]=>1101000=>0001011
[3,1,2,7,6,4,8,5]=>[5,8,4,6,7,2,1,3]=>1101000=>0001011
[6,3,2,1,8,5,4,7]=>[7,4,5,8,1,2,3,6]=>1001000=>0001001
[5,2,6,3,7,4,1,8]=>[8,1,4,7,3,6,2,5]=>1110000=>0000111
[1,6,7,2,8,4,5,3]=>[3,5,4,8,2,7,6,1]=>1101010=>0101011
[6,3,7,4,8,5,1,2]=>[2,1,5,8,4,7,3,6]=>1011000=>0001101
[5,1,2,7,8,3,6,4]=>[4,6,3,8,7,2,1,5]=>1110001=>1000111
[2,4,1,7,8,6,3,5]=>[5,3,6,8,7,1,4,2]=>1110001=>1000111
[6,4,2,7,3,5,1,8]=>[8,1,5,3,7,2,4,6]=>1110000=>0000111
[7,3,2,1,8,4,5,6]=>[6,5,4,8,1,2,3,7]=>1001100=>0011001
[7,8,3,2,5,6,1,4]=>[4,1,6,5,2,3,8,7]=>1100101=>1010011
[7,1,8,2,4,5,6,3]=>[3,6,5,4,2,8,1,7]=>1101100=>0011011
[8,7,6,1,2,4,5,3]=>[3,5,4,2,1,6,7,8]=>1101000=>0001011
[8,3,7,6,2,1,4,5]=>[5,4,1,2,6,7,3,8]=>1011000=>0001101
[3,2,8,7,5,1,4,6]=>[6,4,1,5,7,8,2,3]=>1101000=>0001011
[8,3,6,5,2,1,4,7]=>[7,4,1,2,5,6,3,8]=>1011000=>0001101
[7,6,3,5,2,4,1,8]=>[8,1,4,2,5,3,6,7]=>1110000=>0000111
[7,4,6,2,5,3,1,8]=>[8,1,3,5,2,6,4,7]=>1101000=>0001011
[8,5,1,2,7,3,6,4]=>[4,6,3,7,2,1,5,8]=>1110000=>0000111
[6,8,3,7,5,4,1,2]=>[2,1,4,5,7,3,8,6]=>1010010=>0100101
[6,1,8,2,3,7,5,4]=>[4,5,7,3,2,8,1,6]=>1110000=>0000111
[1,2,7,5,4,3,8,6]=>[6,8,3,4,5,7,2,1]=>1110000=>0000111
[1,7,2,4,3,8,6,5]=>[5,6,8,3,4,2,7,1]=>1110000=>0000111
[1,7,8,6,5,2,4,3]=>[3,4,2,5,6,8,7,1]=>1100001=>1000011
[7,3,8,6,5,4,1,2]=>[2,1,4,5,6,8,3,7]=>1010000=>0000101
[1,8,7,6,5,2,4,3]=>[3,4,2,5,6,7,8,1]=>1100000=>0000011
[4,3,1,2,8,7,6,5]=>[5,6,7,8,2,1,3,4]=>1100000=>0000011
[5,1,4,3,2,8,7,6]=>[6,7,8,2,3,4,1,5]=>1100000=>0000011
[8,6,3,2,1,7,4,5]=>[5,4,7,1,2,3,6,8]=>1001000=>0001001
[8,7,2,4,5,3,1,6]=>[6,1,3,5,4,2,7,8]=>1101000=>0001011
[4,6,3,2,7,5,1,8]=>[8,1,5,7,2,3,6,4]=>1101000=>0001011
[7,1,5,8,3,2,6,4]=>[4,6,2,3,8,5,1,7]=>1100100=>0010011
[8,5,7,4,6,1,3,2]=>[2,3,1,6,4,7,5,8]=>1001100=>0011001
[1,8,5,3,7,2,6,4]=>[4,6,2,7,3,5,8,1]=>1110000=>0000111
[4,3,1,8,7,5,2,6]=>[6,2,5,7,8,1,3,4]=>1100000=>0000011
[3,1,4,6,8,7,2,5]=>[5,2,7,8,6,4,1,3]=>1101010=>0101011
[7,1,6,4,8,5,2,3]=>[3,2,5,8,4,6,1,7]=>1101000=>0001011
[7,3,6,8,5,1,2,4]=>[4,2,1,5,8,6,3,7]=>1110010=>0100111
[1,3,7,2,6,8,4,5]=>[5,4,8,6,2,7,3,1]=>1111010=>0101111
[3,6,5,2,8,1,4,7]=>[7,4,1,8,2,5,6,3]=>1111000=>0001111
[3,6,5,7,2,4,1,8]=>[8,1,4,2,7,5,6,3]=>1110100=>0010111
[5,7,1,8,4,2,6,3]=>[3,6,2,4,8,1,7,5]=>1100100=>0010011
[5,7,1,2,8,6,3,4]=>[4,3,6,8,2,1,7,5]=>1110100=>0010111
[3,6,2,4,7,5,1,8]=>[8,1,5,7,4,2,6,3]=>1111000=>0001111
[4,7,3,1,5,8,6,2]=>[2,6,8,5,1,3,7,4]=>1001100=>0011001
[8,7,6,4,3,1,5,2]=>[2,5,1,3,4,6,7,8]=>1000000=>0000001
[8,7,6,4,1,5,2,3]=>[3,2,5,1,4,6,7,8]=>1100000=>0000011
[3,6,8,2,1,5,4,7]=>[7,4,5,1,2,8,6,3]=>1011010=>0101101
[2,4,8,1,6,5,3,7]=>[7,3,5,6,1,8,4,2]=>1111000=>0001111
[4,2,8,1,5,7,3,6]=>[6,3,7,5,1,8,2,4]=>1110100=>0010111
[8,5,7,6,1,4,2,3]=>[3,2,4,1,6,7,5,8]=>1100100=>0010011
[1,2,7,4,8,6,3,5]=>[5,3,6,8,4,7,2,1]=>1111000=>0001111
[1,2,7,8,3,6,5,4]=>[4,5,6,3,8,7,2,1]=>1110001=>1000111
[1,8,7,6,3,5,2,4]=>[4,2,5,3,6,7,8,1]=>1110000=>0000111
[1,6,8,5,4,3,2,7]=>[7,2,3,4,5,8,6,1]=>1100010=>0100011
[7,1,2,5,8,3,6,4]=>[4,6,3,8,5,2,1,7]=>1110100=>0010111
[2,7,1,4,8,3,5,6]=>[6,5,3,8,4,1,7,2]=>1111100=>0011111
[8,6,2,4,7,3,5,1]=>[1,5,3,7,4,2,6,8]=>0111000=>0001110
[8,6,2,4,5,7,3,1]=>[1,3,7,5,4,2,6,8]=>0101100=>0011010
[7,1,4,5,6,8,2,3]=>[3,2,8,6,5,4,1,7]=>1101110=>0111011
[3,6,7,1,4,8,5,2]=>[2,5,8,4,1,7,6,3]=>1011010=>0101101
[3,6,2,4,7,8,1,5]=>[5,1,8,7,4,2,6,3]=>1111001=>1001111
[6,5,8,7,2,3,1,4]=>[4,1,3,2,7,8,5,6]=>1100100=>0010011
[3,4,7,2,5,8,1,6]=>[6,1,8,5,2,7,4,3]=>1111100=>0011111
[5,6,7,8,1,3,4,2]=>[2,4,3,1,8,7,6,5]=>1010111=>1110101
[5,7,8,6,1,2,3,4]=>[4,3,2,1,6,8,7,5]=>1110101=>1010111
[2,8,3,1,5,6,4,7]=>[7,4,6,5,1,3,8,2]=>1101100=>0011011
[4,3,1,7,6,8,2,5]=>[5,2,8,6,7,1,3,4]=>1100010=>0100011
[3,4,1,7,5,6,8,2]=>[2,8,6,5,7,1,4,3]=>1010110=>0110101
[2,4,6,1,7,5,8,3]=>[3,8,5,7,1,6,4,2]=>1101100=>0011011
[3,7,4,1,6,2,8,5]=>[5,8,2,6,1,4,7,3]=>1110000=>0000111
[8,4,7,2,5,3,6,1]=>[1,6,3,5,2,7,4,8]=>0111000=>0001110
[4,7,8,1,2,3,6,5]=>[5,6,3,2,1,8,7,4]=>1111001=>1001111
[4,2,1,5,6,3,7,8]=>[8,7,3,6,5,1,2,4]=>1010101=>1010101
[5,8,1,6,3,7,2,4]=>[4,2,7,3,6,1,8,5]=>1110100=>0010111
[8,4,5,3,7,2,6,1]=>[1,6,2,7,3,5,4,8]=>0111000=>0001110
[4,6,3,8,5,1,7,2]=>[2,7,1,5,8,3,6,4]=>1011000=>0001101
[3,6,4,8,1,7,2,5]=>[5,2,7,1,8,4,6,3]=>1111000=>0001111
[7,3,8,4,1,5,2,6]=>[6,2,5,1,4,8,3,7]=>1110000=>0000111
[7,2,3,4,1,6,5,8]=>[8,5,6,1,4,3,2,7]=>1110100=>0010111
[4,2,8,3,6,1,5,7]=>[7,5,1,6,3,8,2,4]=>1110100=>0010111
[6,7,5,8,2,1,4,3]=>[3,4,1,2,8,5,7,6]=>1000110=>0110001
[4,8,5,2,7,1,3,6]=>[6,3,1,7,2,5,8,4]=>1111000=>0001111
[6,3,5,2,1,7,4,8]=>[8,4,7,1,2,5,3,6]=>1011000=>0001101
[3,6,5,4,2,8,1,7]=>[7,1,8,2,4,5,6,3]=>1110000=>0000111
[7,4,5,3,8,2,1,6]=>[6,1,2,8,3,5,4,7]=>1011000=>0001101
[1,6,4,7,2,5,3,8]=>[8,3,5,2,7,4,6,1]=>1111000=>0001111
[1,4,3,7,2,6,5,8]=>[8,5,6,2,7,3,4,1]=>1110100=>0010111
[1,5,7,2,4,8,3,6]=>[6,3,8,4,2,7,5,1]=>1111100=>0011111
[1,6,5,7,2,4,3,8]=>[8,3,4,2,7,5,6,1]=>1110100=>0010111
[1,7,6,2,8,3,4,5]=>[5,4,3,8,2,6,7,1]=>1111000=>0001111
[1,4,2,3,5,8,7,6]=>[6,7,8,5,3,2,4,1]=>1110100=>0010111
[1,5,2,3,4,8,7,6]=>[6,7,8,4,3,2,5,1]=>1111000=>0001111
[1,6,5,2,3,8,7,4]=>[4,7,8,3,2,5,6,1]=>1110000=>0000111
[1,7,4,3,2,8,6,5]=>[5,6,8,2,3,4,7,1]=>1100000=>0000011
[1,7,6,5,2,8,4,3]=>[3,4,8,2,5,6,7,1]=>1100000=>0000011
[1,6,5,2,3,8,4,7]=>[7,4,8,3,2,5,6,1]=>1111000=>0001111
[1,6,7,5,2,3,8,4]=>[4,8,3,2,5,7,6,1]=>1110010=>0100111
[1,7,5,2,8,4,3,6]=>[6,3,4,8,2,5,7,1]=>1110000=>0000111
[1,7,5,6,2,8,3,4]=>[4,3,8,2,6,5,7,1]=>1110100=>0010111
[1,5,7,6,2,4,8,3]=>[3,8,4,2,6,7,5,1]=>1101100=>0011011
[1,3,7,5,2,6,8,4]=>[4,8,6,2,5,7,3,1]=>1110010=>0100111
[1,7,4,6,2,8,3,5]=>[5,3,8,2,6,4,7,1]=>1111000=>0001111
[1,7,3,5,2,8,4,6]=>[6,4,8,2,5,3,7,1]=>1111000=>0001111
[1,2,6,4,3,7,8,5]=>[5,8,7,3,4,6,2,1]=>1110001=>1000111
[1,4,7,3,2,5,8,6]=>[6,8,5,2,3,7,4,1]=>1101100=>0011011
[1,5,7,3,2,4,8,6]=>[6,8,4,2,3,7,5,1]=>1101100=>0011011
[1,7,3,4,2,8,5,6]=>[6,5,8,2,4,3,7,1]=>1110100=>0010111
[1,7,4,2,8,5,3,6]=>[6,3,5,8,2,4,7,1]=>1110000=>0000111
[1,6,7,4,2,3,8,5]=>[5,8,3,2,4,7,6,1]=>1110010=>0100111
[1,4,3,2,5,8,6,7]=>[7,6,8,5,2,3,4,1]=>1100110=>0110011
[1,5,3,2,4,8,6,7]=>[7,6,8,4,2,3,5,1]=>1101010=>0101011
[1,6,4,2,3,8,5,7]=>[7,5,8,3,2,4,6,1]=>1110100=>0010111
[1,7,6,4,2,8,5,3]=>[3,5,8,2,4,6,7,1]=>1100000=>0000011
[1,7,5,3,2,8,6,4]=>[4,6,8,2,3,5,7,1]=>1100000=>0000011
[1,6,4,2,3,8,7,5]=>[5,7,8,3,2,4,6,1]=>1110000=>0000111
[1,5,3,2,4,8,7,6]=>[6,7,8,4,2,3,5,1]=>1101000=>0001011
[7,6,5,4,3,1,8,2]=>[2,8,1,3,4,5,6,7]=>1000000=>0000001
[7,6,1,4,3,8,5,2]=>[2,5,8,3,4,1,6,7]=>1010000=>0000101
[7,6,5,1,3,8,4,2]=>[2,4,8,3,1,5,6,7]=>1010000=>0000101
[7,3,5,4,8,1,6,2]=>[2,6,1,8,4,5,3,7]=>1011000=>0001101
[1,4,5,8,3,7,6,2]=>[2,6,7,3,8,5,4,1]=>1011100=>0011101
[5,6,8,4,3,1,7,2]=>[2,7,1,3,4,8,6,5]=>1000110=>0110001
[6,8,5,4,1,2,7,3]=>[3,7,2,1,4,5,8,6]=>1100010=>0100011
[1,8,5,2,3,7,6,4]=>[4,6,7,3,2,5,8,1]=>1110000=>0000111
[6,8,2,4,3,7,1,5]=>[5,1,7,3,4,2,8,6]=>1110010=>0100111
[1,8,3,4,7,2,6,5]=>[5,6,2,7,4,3,8,1]=>1111000=>0001111
[4,8,5,7,3,2,1,6]=>[6,1,2,3,7,5,8,4]=>1001100=>0011001
[7,8,1,2,4,3,5,6]=>[6,5,3,4,2,1,8,7]=>1110101=>1010111
[7,8,2,1,4,3,6,5]=>[5,6,3,4,1,2,8,7]=>1010001=>1000101
[3,4,6,5,7,8,1,2]=>[2,1,8,7,5,6,4,3]=>1011101=>1011101
[4,3,6,5,8,7,1,2]=>[2,1,7,8,5,6,3,4]=>1010100=>0010101
[4,2,6,1,8,3,7,5]=>[5,7,3,8,1,6,2,4]=>1110000=>0000111
[6,7,3,8,4,5,1,2]=>[2,1,5,4,8,3,7,6]=>1011010=>0101101
[4,7,5,6,2,3,1,8]=>[8,1,3,2,6,5,7,4]=>1101100=>0011011
[4,7,5,6,3,8,1,2]=>[2,1,8,3,6,5,7,4]=>1011100=>0011101
[4,5,3,8,6,7,1,2]=>[2,1,7,6,8,3,5,4]=>1011010=>0101101
[4,8,3,6,5,7,1,2]=>[2,1,7,5,6,3,8,4]=>1011100=>0011101
[5,6,3,8,4,7,1,2]=>[2,1,7,4,8,3,6,5]=>1011100=>0011101
[5,6,4,7,1,8,2,3]=>[3,2,8,1,7,4,6,5]=>1101100=>0011011
[5,6,2,7,3,4,1,8]=>[8,1,4,3,7,2,6,5]=>1110100=>0010111
[5,6,1,7,3,8,2,4]=>[4,2,8,3,7,1,6,5]=>1110100=>0010111
[4,8,1,6,5,7,2,3]=>[3,2,7,5,6,1,8,4]=>1101100=>0011011
[4,5,1,8,6,7,2,3]=>[3,2,7,6,8,1,5,4]=>1101010=>0101011
[7,8,4,5,1,6,2,3]=>[3,2,6,1,5,4,8,7]=>1101001=>1001011
[4,5,2,3,1,8,6,7]=>[7,6,8,1,3,2,5,4]=>1101010=>0101011
[5,6,2,3,1,8,4,7]=>[7,4,8,1,3,2,6,5]=>1101100=>0011011
[5,6,3,4,1,8,2,7]=>[7,2,8,1,4,3,6,5]=>1110100=>0010111
[3,6,4,5,2,7,1,8]=>[8,1,7,2,5,4,6,3]=>1111000=>0001111
[3,6,4,5,1,8,2,7]=>[7,2,8,1,5,4,6,3]=>1111000=>0001111
[2,6,4,8,1,5,3,7]=>[7,3,5,1,8,4,6,2]=>1111000=>0001111
[2,8,3,4,1,6,5,7]=>[7,5,6,1,4,3,8,2]=>1110100=>0010111
[7,8,2,5,3,4,1,6]=>[6,1,4,3,5,2,8,7]=>1110001=>1000111
[1,8,3,6,5,7,2,4]=>[4,2,7,5,6,3,8,1]=>1110100=>0010111
[1,8,3,6,2,7,4,5]=>[5,4,7,2,6,3,8,1]=>1111000=>0001111
[1,6,4,8,2,7,3,5]=>[5,3,7,2,8,4,6,1]=>1111000=>0001111
[1,6,4,7,3,8,2,5]=>[5,2,8,3,7,4,6,1]=>1111000=>0001111
[2,6,4,7,3,5,1,8]=>[8,1,5,3,7,4,6,2]=>1111000=>0001111
[2,7,5,6,3,4,1,8]=>[8,1,4,3,6,5,7,2]=>1110100=>0010111
[6,7,2,5,3,4,1,8]=>[8,1,4,3,5,2,7,6]=>1110010=>0100111
[6,7,1,5,3,8,2,4]=>[4,2,8,3,5,1,7,6]=>1110010=>0100111
[6,7,1,8,2,5,3,4]=>[4,3,5,2,8,1,7,6]=>1110010=>0100111
[6,7,1,8,4,5,2,3]=>[3,2,5,4,8,1,7,6]=>1101010=>0101011
[6,7,5,8,1,4,2,3]=>[3,2,4,1,8,5,7,6]=>1100110=>0110011
[5,8,6,7,2,3,1,4]=>[4,1,3,2,7,6,8,5]=>1100110=>0110011
[6,7,2,8,1,4,3,5]=>[5,3,4,1,8,2,7,6]=>1110010=>0100111
[6,7,3,4,1,8,2,5]=>[5,2,8,1,4,3,7,6]=>1110010=>0100111
[3,4,2,7,5,6,1,8]=>[8,1,6,5,7,2,4,3]=>1110100=>0010111
[2,3,1,8,4,7,5,6]=>[6,5,7,4,8,1,3,2]=>1101100=>0011011
[2,3,1,8,6,7,4,5]=>[5,4,7,6,8,1,3,2]=>1101010=>0101011
[7,8,2,3,1,6,4,5]=>[5,4,6,1,3,2,8,7]=>1101001=>1001011
[2,8,1,7,3,5,4,6]=>[6,4,5,3,7,1,8,2]=>1111000=>0001111
[4,5,1,7,3,8,2,6]=>[6,2,8,3,7,1,5,4]=>1111000=>0001111
[4,5,1,8,2,7,3,6]=>[6,3,7,2,8,1,5,4]=>1111000=>0001111
[3,8,1,5,2,7,4,6]=>[6,4,7,2,5,1,8,3]=>1111000=>0001111
[7,8,3,4,1,6,2,5]=>[5,2,6,1,4,3,8,7]=>1110001=>1000111
[3,4,2,5,1,8,6,7]=>[7,6,8,1,5,2,4,3]=>1110010=>0100111
[4,5,3,6,1,8,2,7]=>[7,2,8,1,6,3,5,4]=>1111000=>0001111
[3,6,5,4,1,2,8,7]=>[7,8,2,1,4,5,6,3]=>1110000=>0000111
[3,8,5,6,7,4,1,2]=>[2,1,4,7,6,5,8,3]=>1010110=>0110101
[4,7,5,8,6,2,1,3]=>[3,1,2,6,8,5,7,4]=>1001100=>0011001
[2,5,7,8,6,3,4,1]=>[1,4,3,6,8,7,5,2]=>0110101=>1010110
[3,6,5,1,2,4,8,7]=>[7,8,4,2,1,5,6,3]=>1111000=>0001111
[5,2,3,6,4,1,8,7]=>[7,8,1,4,6,3,2,5]=>1110000=>0000111
[6,1,4,5,3,2,8,7]=>[7,8,2,3,5,4,1,6]=>1101000=>0001011
[5,6,7,8,1,4,3,2]=>[2,3,4,1,8,7,6,5]=>1000111=>1110001
[4,2,6,8,5,7,3,1]=>[1,3,7,5,8,6,2,4]=>0100110=>0110010
[2,1,5,8,7,6,3,4]=>[4,3,6,7,8,5,1,2]=>1010100=>0010101
[2,1,4,7,6,3,8,5]=>[5,8,3,6,7,4,1,2]=>1011000=>0001101
[6,4,7,8,5,3,2,1]=>[1,2,3,5,8,7,4,6]=>0001001=>1001000
[6,3,7,1,5,2,8,4]=>[4,8,2,5,1,7,3,6]=>1110000=>0000111
[3,2,6,8,4,7,5,1]=>[1,5,7,4,8,6,2,3]=>0101010=>0101010
[8,4,6,1,3,2,5,7]=>[7,5,2,3,1,6,4,8]=>1101100=>0011011
[2,4,1,5,8,3,7,6]=>[6,7,3,8,5,1,4,2]=>1110100=>0010111
[4,7,5,8,1,6,3,2]=>[2,3,6,1,8,5,7,4]=>1001100=>0011001
[2,1,5,8,7,3,4,6]=>[6,4,3,7,8,5,1,2]=>1011100=>0011101
[8,5,7,3,6,1,4,2]=>[2,4,1,6,3,7,5,8]=>1010100=>0010101
[6,4,3,2,7,8,1,5]=>[5,1,8,7,2,3,4,6]=>1100001=>1000011
[3,7,1,4,6,8,5,2]=>[2,5,8,6,4,1,7,3]=>1011010=>0101101
[7,2,3,4,8,5,6,1]=>[1,6,5,8,4,3,2,7]=>0111100=>0011110
[6,1,8,5,2,7,4,3]=>[3,4,7,2,5,8,1,6]=>1100000=>0000011
[2,1,7,4,5,8,6,3]=>[3,6,8,5,4,7,1,2]=>1001100=>0011001
[6,8,7,2,5,3,1,4]=>[4,1,3,5,2,7,8,6]=>1100010=>0100011
[8,2,1,6,4,7,5,3]=>[3,5,7,4,6,1,2,8]=>1001000=>0001001
[2,4,3,8,7,5,6,1]=>[1,6,5,7,8,3,4,2]=>0110100=>0010110
[7,8,4,2,5,1,6,3]=>[3,6,1,5,2,4,8,7]=>1100001=>1000011
[6,1,2,3,7,5,8,4]=>[4,8,5,7,3,2,1,6]=>1110100=>0010111
[2,6,7,3,5,1,8,4]=>[4,8,1,5,3,7,6,2]=>1110010=>0100111
[7,6,8,4,2,5,3,1]=>[1,3,5,2,4,8,6,7]=>0100010=>0100010
[4,1,2,3,7,6,8,5]=>[5,8,6,7,3,2,1,4]=>1110010=>0100111
[3,2,4,1,8,5,6,7]=>[7,6,5,8,1,4,2,3]=>1100110=>0110011
[6,5,8,2,1,7,3,4]=>[4,3,7,1,2,8,5,6]=>1010100=>0010101
[7,4,3,5,1,6,8,2]=>[2,8,6,1,5,3,4,7]=>1010010=>0100101
[4,1,6,3,5,8,7,2]=>[2,7,8,5,3,6,1,4]=>1010100=>0010101
[2,1,6,5,8,4,7,3]=>[3,7,4,8,5,6,1,2]=>1001100=>0011001
[2,1,6,8,5,4,3,7]=>[7,3,4,5,8,6,1,2]=>1010010=>0100101
[2,6,4,8,7,3,5,1]=>[1,5,3,7,8,4,6,2]=>0111000=>0001110
[6,2,8,4,3,5,1,7]=>[7,1,5,3,4,8,2,6]=>1110000=>0000111
[3,1,8,2,7,5,4,6]=>[6,4,5,7,2,8,1,3]=>1101000=>0001011
[8,2,3,1,7,4,6,5]=>[5,6,4,7,1,3,2,8]=>1101000=>0001011
[5,8,4,3,2,7,1,6]=>[6,1,7,2,3,4,8,5]=>1100100=>0010011
[7,4,8,6,3,2,5,1]=>[1,5,2,3,6,8,4,7]=>0101000=>0001010
[5,8,4,7,2,1,3,6]=>[6,3,1,2,7,4,8,5]=>1011100=>0011101
[6,3,8,2,4,5,7,1]=>[1,7,5,4,2,8,3,6]=>0111100=>0011110
[5,8,4,2,3,6,1,7]=>[7,1,6,3,2,4,8,5]=>1110100=>0010111
[7,3,5,8,1,4,2,6]=>[6,2,4,1,8,5,3,7]=>1110100=>0010111
[3,8,7,6,1,4,2,5]=>[5,2,4,1,6,7,8,3]=>1110000=>0000111
[3,4,7,1,5,8,6,2]=>[2,6,8,5,1,7,4,3]=>1011100=>0011101
[6,8,1,3,5,7,2,4]=>[4,2,7,5,3,1,8,6]=>1110110=>0110111
[4,1,3,7,5,8,2,6]=>[6,2,8,5,7,3,1,4]=>1110100=>0010111
[3,1,7,6,5,8,4,2]=>[2,4,8,5,6,7,1,3]=>1000100=>0010001
[8,4,2,6,7,5,3,1]=>[1,3,5,7,6,2,4,8]=>0100010=>0100010
[4,8,1,6,7,5,3,2]=>[2,3,5,7,6,1,8,4]=>1001010=>0101001
[7,4,1,6,8,2,5,3]=>[3,5,2,8,6,1,4,7]=>1100010=>0100011
[4,7,1,2,5,3,8,6]=>[6,8,3,5,2,1,7,4]=>1111000=>0001111
[5,7,8,6,2,1,4,3]=>[3,4,1,2,6,8,7,5]=>1000101=>1010001
[3,4,1,7,5,2,6,8]=>[8,6,2,5,7,1,4,3]=>1110010=>0100111
[1,4,7,2,6,8,3,5]=>[5,3,8,6,2,7,4,1]=>1111010=>0101111
[2,5,4,3,6,8,1,7]=>[7,1,8,6,3,4,5,2]=>1110010=>0100111
[4,3,7,8,5,1,6,2]=>[2,6,1,5,8,7,3,4]=>1010001=>1000101
[5,4,8,2,7,6,1,3]=>[3,1,6,7,2,8,4,5]=>1101000=>0001011
[4,1,7,5,8,6,2,3]=>[3,2,6,8,5,7,1,4]=>1100100=>0010011
[6,5,8,7,1,3,4,2]=>[2,4,3,1,7,8,5,6]=>1010100=>0010101
[3,6,7,2,4,8,1,5]=>[5,1,8,4,2,7,6,3]=>1111010=>0101111
[7,6,1,2,8,3,5,4]=>[4,5,3,8,2,1,6,7]=>1110000=>0000111
[6,7,8,1,5,2,4,3]=>[3,4,2,5,1,8,7,6]=>1100011=>1100011
[5,7,8,4,1,2,6,3]=>[3,6,2,1,4,8,7,5]=>1100101=>1010011
[4,7,8,5,6,1,3,2]=>[2,3,1,6,5,8,7,4]=>1001101=>1011001
[4,6,5,8,7,1,3,2]=>[2,3,1,7,8,5,6,4]=>1001100=>0011001
[5,6,4,8,1,2,7,3]=>[3,7,2,1,8,4,6,5]=>1101100=>0011011
[6,5,4,1,2,3,8,7]=>[7,8,3,2,1,4,5,6]=>1110000=>0000111
[7,5,1,6,2,3,8,4]=>[4,8,3,2,6,1,5,7]=>1110000=>0000111
[6,4,5,1,8,2,7,3]=>[3,7,2,8,1,5,4,6]=>1101000=>0001011
[4,5,6,7,8,1,3,2]=>[2,3,1,8,7,6,5,4]=>1001111=>1111001
[5,3,6,7,1,4,2,8]=>[8,2,4,1,7,6,3,5]=>1110010=>0100111
[4,2,6,7,3,1,8,5]=>[5,8,1,3,7,6,2,4]=>1100010=>0100011
[6,2,4,1,5,8,7,3]=>[3,7,8,5,1,4,2,6]=>1100100=>0010011
[7,3,1,5,4,8,2,6]=>[6,2,8,4,5,1,3,7]=>1101000=>0001011
[4,5,3,2,8,1,6,7]=>[7,6,1,8,2,3,5,4]=>1101010=>0101011
[7,4,1,5,3,2,6,8]=>[8,6,2,3,5,1,4,7]=>1100010=>0100011
[8,1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1,8]=>1100010=>0100011
[8,1,6,4,2,5,3,7]=>[7,3,5,2,4,6,1,8]=>1110000=>0000111
[6,5,3,1,2,7,4,8]=>[8,4,7,2,1,3,5,6]=>1101000=>0001011
[5,6,3,8,1,4,2,7]=>[7,2,4,1,8,3,6,5]=>1110100=>0010111
[4,6,3,8,2,1,5,7]=>[7,5,1,2,8,3,6,4]=>1011100=>0011101
[4,7,8,3,2,1,5,6]=>[6,5,1,2,3,8,7,4]=>1001101=>1011001
[5,7,8,3,1,4,2,6]=>[6,2,4,1,3,8,7,5]=>1100101=>1010011
[8,1,7,2,5,4,3,6]=>[6,3,4,5,2,7,1,8]=>1110000=>0000111
[8,1,7,2,4,5,6,3]=>[3,6,5,4,2,7,1,8]=>1101100=>0011011
[7,6,1,2,4,5,8,3]=>[3,8,5,4,2,1,6,7]=>1101100=>0011011
[4,7,8,2,3,1,6,5]=>[5,6,1,3,2,8,7,4]=>1101001=>1001011
[7,5,1,3,2,6,8,4]=>[4,8,6,2,3,1,5,7]=>1100010=>0100011
[8,1,6,3,2,5,7,4]=>[4,7,5,2,3,6,1,8]=>1100100=>0010011
[8,1,5,3,4,2,7,6]=>[6,7,2,4,3,5,1,8]=>1110000=>0000111
[5,4,2,3,1,6,8,7]=>[7,8,6,1,3,2,4,5]=>1100010=>0100011
[6,3,2,1,5,7,4,8]=>[8,4,7,5,1,2,3,6]=>1001100=>0011001
[7,3,1,4,5,6,2,8]=>[8,2,6,5,4,1,3,7]=>1101100=>0011011
[6,2,3,1,5,7,8,4]=>[4,8,7,5,1,3,2,6]=>1100101=>1010011
[3,5,8,2,6,1,4,7]=>[7,4,1,6,2,8,5,3]=>1111100=>0011111
[3,6,5,8,2,4,1,7]=>[7,1,4,2,8,5,6,3]=>1110100=>0010111
[5,3,7,2,4,8,1,6]=>[6,1,8,4,2,7,3,5]=>1111000=>0001111
[5,3,8,7,2,4,6,1]=>[1,6,4,2,7,8,3,5]=>0111000=>0001110
[4,8,1,2,5,6,3,7]=>[7,3,6,5,2,1,8,4]=>1111100=>0011111
[3,6,1,5,8,4,2,7]=>[7,2,4,8,5,1,6,3]=>1110100=>0010111
[6,1,4,5,8,3,2,7]=>[7,2,3,8,5,4,1,6]=>1101100=>0011011
[6,5,4,3,8,2,1,7]=>[7,1,2,8,3,4,5,6]=>1010000=>0000101
[5,4,3,7,2,8,1,6]=>[6,1,8,2,7,3,4,5]=>1110000=>0000111
[5,8,4,3,7,2,6,1]=>[1,6,2,7,3,4,8,5]=>0110100=>0010110
[4,6,8,3,7,2,5,1]=>[1,5,2,7,3,8,6,4]=>0111010=>0101110
[1,4,3,6,2,7,8,5]=>[5,8,7,2,6,3,4,1]=>1110001=>1000111
[5,7,3,4,1,2,8,6]=>[6,8,2,1,4,3,7,5]=>1110100=>0010111
[8,4,6,1,7,3,5,2]=>[2,5,3,7,1,6,4,8]=>1011000=>0001101
[1,3,8,6,4,7,5,2]=>[2,5,7,4,6,8,3,1]=>1011000=>0001101
[8,6,2,7,4,1,5,3]=>[3,5,1,4,7,2,6,8]=>1100000=>0000011
[7,6,2,1,4,3,8,5]=>[5,8,3,4,1,2,6,7]=>1010000=>0000101
[7,6,1,3,4,2,8,5]=>[5,8,2,4,3,1,6,7]=>1110000=>0000111
[7,6,8,1,4,3,2,5]=>[5,2,3,4,1,8,6,7]=>1100010=>0100011
[1,5,7,3,2,6,8,4]=>[4,8,6,2,3,7,5,1]=>1100110=>0110011
[1,6,4,7,2,3,8,5]=>[5,8,3,2,7,4,6,1]=>1111000=>0001111
[3,1,7,5,2,8,4,6]=>[6,4,8,2,5,7,1,3]=>1101000=>0001011
[1,7,4,5,2,8,3,6]=>[6,3,8,2,5,4,7,1]=>1111000=>0001111
[4,2,7,6,3,8,1,5]=>[5,1,8,3,6,7,2,4]=>1110000=>0000111
[6,4,8,7,2,3,5,1]=>[1,5,3,2,7,8,4,6]=>0111000=>0001110
[3,2,6,8,7,4,5,1]=>[1,5,4,7,8,6,2,3]=>0101010=>0101010
[6,3,2,1,7,8,4,5]=>[5,4,8,7,1,2,3,6]=>1001001=>1001001
[5,7,3,8,2,1,4,6]=>[6,4,1,2,8,3,7,5]=>1011100=>0011101
[3,7,1,8,4,2,5,6]=>[6,5,2,4,8,1,7,3]=>1110100=>0010111
[8,4,2,1,3,7,6,5]=>[5,6,7,3,1,2,4,8]=>1010000=>0000101
[8,4,3,7,6,2,1,5]=>[5,1,2,6,7,3,4,8]=>1010000=>0000101
[5,8,4,2,7,1,6,3]=>[3,6,1,7,2,4,8,5]=>1100100=>0010011
[8,5,3,1,7,2,6,4]=>[4,6,2,7,1,3,5,8]=>1100000=>0000011
[1,4,6,8,2,7,5,3]=>[3,5,7,2,8,6,4,1]=>1101010=>0101011
[8,6,7,5,2,4,3,1]=>[1,3,4,2,5,7,6,8]=>0100010=>0100010
[8,2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2,8]=>1000000=>0000001
[8,1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1,8]=>1001000=>0001001
[8,6,7,5,1,4,3,2]=>[2,3,4,1,5,7,6,8]=>1000010=>0100001
[5,8,4,3,2,1,6,7]=>[7,6,1,2,3,4,8,5]=>1000110=>0110001
[5,4,7,3,2,1,6,8]=>[8,6,1,2,3,7,4,5]=>1001010=>0101001
[4,8,7,3,2,1,6,5]=>[5,6,1,2,3,7,8,4]=>1001000=>0001001
[6,5,3,7,2,1,4,8]=>[8,4,1,2,7,3,5,6]=>1011000=>0001101
[5,8,3,6,2,1,4,7]=>[7,4,1,2,6,3,8,5]=>1011100=>0011101
[6,4,3,7,2,1,8,5]=>[5,8,1,2,7,3,4,6]=>1010000=>0000101
[4,8,3,6,2,1,7,5]=>[5,7,1,2,6,3,8,4]=>1011000=>0001101
[5,3,7,6,2,1,4,8]=>[8,4,1,2,6,7,3,5]=>1011000=>0001101
[3,8,7,6,2,1,4,5]=>[5,4,1,2,6,7,8,3]=>1011000=>0001101
[5,8,4,2,6,1,3,7]=>[7,3,1,6,2,4,8,5]=>1110100=>0010111
[4,8,7,2,5,1,3,6]=>[6,3,1,5,2,7,8,4]=>1111000=>0001111
[5,8,3,2,6,1,4,7]=>[7,4,1,6,2,3,8,5]=>1101100=>0011011
[4,8,3,2,5,1,7,6]=>[6,7,1,5,2,3,8,4]=>1101000=>0001011
[4,3,7,2,5,1,8,6]=>[6,8,1,5,2,7,3,4]=>1110000=>0000111
[3,8,7,2,5,1,4,6]=>[6,4,1,5,2,7,8,3]=>1111000=>0001111
[6,4,2,7,5,1,3,8]=>[8,3,1,5,7,2,4,6]=>1110000=>0000111
[5,4,2,6,7,1,3,8]=>[8,3,1,7,6,2,4,5]=>1110010=>0100111
[2,8,7,6,5,1,3,4]=>[4,3,1,5,6,7,8,2]=>1110000=>0000111
[5,4,7,3,1,8,6,2]=>[2,6,8,1,3,7,4,5]=>1001000=>0001001
[4,8,7,3,1,5,6,2]=>[2,6,5,1,3,7,8,4]=>1001100=>0011001
[6,5,3,7,1,4,8,2]=>[2,8,4,1,7,3,5,6]=>1011000=>0001101
[5,8,3,6,1,4,7,2]=>[2,7,4,1,6,3,8,5]=>1011100=>0011101
[6,4,3,7,1,5,8,2]=>[2,8,5,1,7,3,4,6]=>1010100=>0010101
[4,8,3,6,1,5,7,2]=>[2,7,5,1,6,3,8,4]=>1011100=>0011101
[5,3,7,6,1,4,8,2]=>[2,8,4,1,6,7,3,5]=>1011000=>0001101
[3,8,7,6,1,4,5,2]=>[2,5,4,1,6,7,8,3]=>1011000=>0001101
[5,8,4,2,1,7,3,6]=>[6,3,7,1,2,4,8,5]=>1010100=>0010101
[6,4,7,2,1,5,3,8]=>[8,3,5,1,2,7,4,6]=>1011000=>0001101
[5,8,3,2,1,4,7,6]=>[6,7,4,1,2,3,8,5]=>1001100=>0011001
[6,3,7,2,1,4,5,8]=>[8,5,4,1,2,7,3,6]=>1011100=>0011101
[5,3,7,2,1,4,8,6]=>[6,8,4,1,2,7,3,5]=>1011000=>0001101
[6,5,2,7,1,4,3,8]=>[8,3,4,1,7,2,5,6]=>1110000=>0000111
[4,3,2,6,1,5,8,7]=>[7,8,5,1,6,2,3,4]=>1100100=>0010011
[2,8,7,6,1,4,3,5]=>[5,3,4,1,6,7,8,2]=>1110000=>0000111
[6,5,4,1,8,7,3,2]=>[2,3,7,8,1,4,5,6]=>1000000=>0000001
[5,8,4,1,6,7,3,2]=>[2,3,7,6,1,4,8,5]=>1000110=>0110001
[4,8,7,1,5,6,3,2]=>[2,3,6,5,1,7,8,4]=>1001100=>0011001
[6,5,3,1,8,4,7,2]=>[2,7,4,8,1,3,5,6]=>1001000=>0001001
[5,8,3,1,6,4,7,2]=>[2,7,4,6,1,3,8,5]=>1001100=>0011001
[6,4,3,1,5,8,7,2]=>[2,7,8,5,1,3,4,6]=>1000100=>0010001
[4,8,3,1,5,6,7,2]=>[2,7,6,5,1,3,8,4]=>1001110=>0111001
[6,4,2,1,5,8,3,7]=>[7,3,8,5,1,2,4,6]=>1010100=>0010101
[5,3,2,1,6,4,8,7]=>[7,8,4,6,1,2,3,5]=>1001000=>0001001
[3,2,7,1,5,4,6,8]=>[8,6,4,5,1,7,2,3]=>1101010=>0101011
[6,5,1,7,8,4,3,2]=>[2,3,4,8,7,1,5,6]=>1000001=>1000001
[5,8,1,6,7,4,3,2]=>[2,3,4,7,6,1,8,5]=>1000110=>0110001
[6,4,1,7,5,8,3,2]=>[2,3,8,5,7,1,4,6]=>1000100=>0010001
[4,8,1,6,5,7,3,2]=>[2,3,7,5,6,1,8,4]=>1001100=>0011001
[5,3,1,6,7,4,8,2]=>[2,8,4,7,6,1,3,5]=>1001010=>0101001
[4,3,1,6,5,7,8,2]=>[2,8,7,5,6,1,3,4]=>1000101=>1010001
[5,2,1,6,7,4,3,8]=>[8,3,4,7,6,1,2,5]=>1010010=>0100101
[4,2,1,6,5,7,3,8]=>[8,3,7,5,6,1,2,4]=>1010100=>0010101
[6,1,7,8,5,4,3,2]=>[2,3,4,5,8,7,1,6]=>1000001=>1000001
[5,1,7,6,8,4,3,2]=>[2,3,4,8,6,7,1,5]=>1000010=>0100001
[3,1,7,6,5,4,8,2]=>[2,8,4,5,6,7,1,3]=>1001000=>0001001
[4,5,8,1,7,2,3,6]=>[6,3,2,7,1,8,5,4]=>1111100=>0011111
[8,1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1,8]=>1111100=>0011111
[8,1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1,8]=>1111010=>0101111
[2,7,8,1,3,5,4,6]=>[6,4,5,3,1,8,7,2]=>1111001=>1001111
[2,7,8,3,5,6,1,4]=>[4,1,6,5,3,8,7,2]=>1110101=>1010111
[2,4,5,7,8,1,6,3]=>[3,6,1,8,7,5,4,2]=>1101101=>1011011
[8,7,3,5,6,2,1,4]=>[4,1,2,6,5,3,7,8]=>1010100=>0010101
[8,7,2,1,6,3,4,5]=>[5,4,3,6,1,2,7,8]=>1011000=>0001101
[8,6,4,1,7,5,3,2]=>[2,3,5,7,1,4,6,8]=>1000000=>0000001
[7,4,2,6,8,5,1,3]=>[3,1,5,8,6,2,4,7]=>1100010=>0100011
[7,3,2,5,8,6,1,4]=>[4,1,6,8,5,2,3,7]=>1100100=>0010011
[7,3,1,8,6,2,4,5]=>[5,4,2,6,8,1,3,7]=>1101000=>0001011
[3,1,7,2,5,4,8,6]=>[6,8,4,5,2,7,1,3]=>1101000=>0001011
[3,6,8,1,2,5,4,7]=>[7,4,5,2,1,8,6,3]=>1111010=>0101111
[7,4,1,8,5,2,3,6]=>[6,3,2,5,8,1,4,7]=>1110000=>0000111
[7,1,8,2,5,3,6,4]=>[4,6,3,5,2,8,1,7]=>1110000=>0000111
[7,3,8,4,5,1,6,2]=>[2,6,1,5,4,8,3,7]=>1011000=>0001101
[8,3,7,4,6,1,5,2]=>[2,5,1,6,4,7,3,8]=>1011000=>0001101
[8,2,7,1,6,4,5,3]=>[3,5,4,6,1,7,2,8]=>1101000=>0001011
[8,1,7,5,4,2,3,6]=>[6,3,2,4,5,7,1,8]=>1110000=>0000111
[8,1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1,8]=>1110000=>0000111
[8,2,7,5,6,1,4,3]=>[3,4,1,6,5,7,2,8]=>1100100=>0010011
[8,6,7,2,3,1,5,4]=>[4,5,1,3,2,7,6,8]=>1100010=>0100011
[2,7,8,6,3,1,5,4]=>[4,5,1,3,6,8,7,2]=>1100001=>1000011
[7,3,1,8,6,5,4,2]=>[2,4,5,6,8,1,3,7]=>1000000=>0000001
[8,7,6,3,2,1,5,4]=>[4,5,1,2,3,6,7,8]=>1000000=>0000001
[2,1,8,6,3,7,4,5]=>[5,4,7,3,6,8,1,2]=>1011000=>0001101
[8,6,1,5,2,7,4,3]=>[3,4,7,2,5,1,6,8]=>1100000=>0000011
[8,5,1,7,4,2,6,3]=>[3,6,2,4,7,1,5,8]=>1100000=>0000011
[2,1,8,4,5,3,6,7]=>[7,6,3,5,4,8,1,2]=>1011010=>0101101
[2,1,7,8,3,6,5,4]=>[4,5,6,3,8,7,1,2]=>1010001=>1000101
[2,1,4,8,5,7,3,6]=>[6,3,7,5,8,4,1,2]=>1011100=>0011101
[7,8,1,5,2,6,3,4]=>[4,3,6,2,5,1,8,7]=>1110001=>1000111
[8,3,7,5,2,6,1,4]=>[4,1,6,2,5,7,3,8]=>1110000=>0000111
[5,8,3,7,6,2,1,4]=>[4,1,2,6,7,3,8,5]=>1010100=>0010101
[5,2,4,8,6,3,1,7]=>[7,1,3,6,8,4,2,5]=>1101000=>0001011
[4,2,6,3,8,5,1,7]=>[7,1,5,8,3,6,2,4]=>1110000=>0000111
[3,6,8,7,5,4,1,2]=>[2,1,4,5,7,8,6,3]=>1010010=>0100101
[8,5,2,7,4,6,1,3]=>[3,1,6,4,7,2,5,8]=>1101000=>0001011
[6,3,4,2,1,7,8,5]=>[5,8,7,1,2,4,3,6]=>1010001=>1000101
[7,2,4,3,1,5,8,6]=>[6,8,5,1,3,4,2,7]=>1100100=>0010011
[7,8,3,1,5,4,6,2]=>[2,6,4,5,1,3,8,7]=>1001001=>1001001
[7,2,8,1,4,6,5,3]=>[3,5,6,4,1,8,2,7]=>1101000=>0001011
[6,2,3,1,4,5,8,7]=>[7,8,5,4,1,3,2,6]=>1101100=>0011011
[5,7,1,8,3,6,2,4]=>[4,2,6,3,8,1,7,5]=>1110100=>0010111
[6,8,1,4,5,3,2,7]=>[7,2,3,5,4,1,8,6]=>1101010=>0101011
[8,7,5,1,3,4,2,6]=>[6,2,4,3,1,5,7,8]=>1110000=>0000111
[6,5,7,1,3,8,2,4]=>[4,2,8,3,1,7,5,6]=>1110100=>0010111
[8,2,6,1,4,7,3,5]=>[5,3,7,4,1,6,2,8]=>1111000=>0001111
[5,8,1,6,3,7,4,2]=>[2,4,7,3,6,1,8,5]=>1010100=>0010101
[4,2,1,3,6,7,8,5]=>[5,8,7,6,3,1,2,4]=>1010011=>1100101
[2,3,4,1,8,6,5,7]=>[7,5,6,8,1,4,3,2]=>1110100=>0010111
[8,3,5,6,1,7,4,2]=>[2,4,7,1,6,5,3,8]=>1010100=>0010101
[7,3,5,8,1,6,2,4]=>[4,2,6,1,8,5,3,7]=>1110100=>0010111
[6,3,5,4,1,2,8,7]=>[7,8,2,1,4,5,3,6]=>1110000=>0000111
[2,6,3,5,1,4,8,7]=>[7,8,4,1,5,3,6,2]=>1111000=>0001111
[8,7,3,6,5,1,4,2]=>[2,4,1,5,6,3,7,8]=>1010000=>0000101
[2,8,3,4,6,1,5,7]=>[7,5,1,6,4,3,8,2]=>1111100=>0011111
[2,7,4,3,6,1,8,5]=>[5,8,1,6,3,4,7,2]=>1110000=>0000111
[4,3,2,5,7,1,8,6]=>[6,8,1,7,5,2,3,4]=>1100100=>0010011
[3,2,8,4,7,1,6,5]=>[5,6,1,7,4,8,2,3]=>1101000=>0001011
[3,2,4,6,1,5,8,7]=>[7,8,5,1,6,4,2,3]=>1101100=>0011011
[6,8,5,4,3,7,2,1]=>[1,2,7,3,4,5,8,6]=>0010010=>0100100
[5,8,4,3,2,1,7,6]=>[6,7,1,2,3,4,8,5]=>1000100=>0010001
[6,5,4,3,1,8,7,2]=>[2,7,8,1,3,4,5,6]=>1000000=>0000001
[3,4,5,7,1,8,6,2]=>[2,6,8,1,7,5,4,3]=>1011100=>0011101
[3,4,6,2,8,5,1,7]=>[7,1,5,8,2,6,4,3]=>1111000=>0001111
[3,4,6,7,1,8,5,2]=>[2,5,8,1,7,6,4,3]=>1011010=>0101101
[3,4,7,2,1,8,6,5]=>[5,6,8,1,2,7,4,3]=>1011000=>0001101
[3,4,7,2,8,5,6,1]=>[1,6,5,8,2,7,4,3]=>0111100=>0011110
[3,4,8,2,1,5,6,7]=>[7,6,5,1,2,8,4,3]=>1011110=>0111101
[3,5,2,6,8,4,1,7]=>[7,1,4,8,6,2,5,3]=>1110010=>0100111
[3,5,2,7,4,8,6,1]=>[1,6,8,4,7,2,5,3]=>0111000=>0001110
[3,5,2,7,8,4,6,1]=>[1,6,4,8,7,2,5,3]=>0111001=>1001110
[3,5,2,8,4,1,6,7]=>[7,6,1,4,8,2,5,3]=>1110010=>0100111
[3,5,6,2,7,8,1,4]=>[4,1,8,7,2,6,5,3]=>1110101=>1010111
[3,5,6,2,8,4,1,7]=>[7,1,4,8,2,6,5,3]=>1110100=>0010111
[3,5,6,8,4,1,2,7]=>[7,2,1,4,8,6,5,3]=>1110110=>0110111
[3,5,7,2,4,8,6,1]=>[1,6,8,4,2,7,5,3]=>0111100=>0011110
[3,5,7,2,8,4,6,1]=>[1,6,4,8,2,7,5,3]=>0111100=>0011110
[3,5,7,8,4,1,6,2]=>[2,6,1,4,8,7,5,3]=>1010101=>1010101
[3,6,2,1,7,8,5,4]=>[4,5,8,7,1,2,6,3]=>1010001=>1000101
[3,6,2,1,8,5,4,7]=>[7,4,5,8,1,2,6,3]=>1011000=>0001101
[3,6,2,7,4,8,5,1]=>[1,5,8,4,7,2,6,3]=>0111000=>0001110
[3,6,2,7,8,5,4,1]=>[1,4,5,8,7,2,6,3]=>0110001=>1000110
[3,6,7,2,4,8,5,1]=>[1,5,8,4,2,7,6,3]=>0111010=>0101110
[4,1,5,6,7,8,3,2]=>[2,3,8,7,6,5,1,4]=>1000111=>1110001
[4,1,5,7,3,8,6,2]=>[2,6,8,3,7,5,1,4]=>1010100=>0010101
[4,1,5,7,8,2,6,3]=>[3,6,2,8,7,5,1,4]=>1100101=>1010011
[4,1,5,8,3,2,6,7]=>[7,6,2,3,8,5,1,4]=>1100110=>0110011
[4,1,6,3,7,8,5,2]=>[2,5,8,7,3,6,1,4]=>1010001=>1000101
[4,1,6,7,3,8,5,2]=>[2,5,8,3,7,6,1,4]=>1010010=>0100101
[4,1,6,8,3,5,2,7]=>[7,2,5,3,8,6,1,4]=>1110010=>0100111
[4,1,7,3,8,5,6,2]=>[2,6,5,8,3,7,1,4]=>1010100=>0010101
[4,1,7,8,3,5,6,2]=>[2,6,5,3,8,7,1,4]=>1010101=>1010101
[4,5,2,6,8,1,3,7]=>[7,3,1,8,6,2,5,4]=>1111010=>0101111
[4,5,2,7,3,8,6,1]=>[1,6,8,3,7,2,5,4]=>0111000=>0001110
[4,5,6,8,3,1,2,7]=>[7,2,1,3,8,6,5,4]=>1101110=>0111011
[4,5,7,3,2,8,6,1]=>[1,6,8,2,3,7,5,4]=>0101100=>0011010
[4,5,7,3,8,1,6,2]=>[2,6,1,8,3,7,5,4]=>1011100=>0011101
[4,6,2,3,7,8,5,1]=>[1,5,8,7,3,2,6,4]=>0111001=>1001110
[4,6,2,3,8,5,1,7]=>[7,1,5,8,3,2,6,4]=>1111000=>0001111
[4,6,2,7,3,8,5,1]=>[1,5,8,3,7,2,6,4]=>0111000=>0001110
[4,6,2,8,3,5,1,7]=>[7,1,5,3,8,2,6,4]=>1111000=>0001111
[4,6,8,3,2,5,1,7]=>[7,1,5,2,3,8,6,4]=>1101010=>0101011
[4,7,8,3,2,5,6,1]=>[1,6,5,2,3,8,7,4]=>0101101=>1011010
[4,8,2,3,1,5,6,7]=>[7,6,5,1,3,2,8,4]=>1101110=>0111011
[5,1,2,6,8,4,3,7]=>[7,3,4,8,6,2,1,5]=>1110010=>0100111
[5,1,2,8,4,3,6,7]=>[7,6,3,4,8,2,1,5]=>1110010=>0100111
[5,1,6,7,4,8,2,3]=>[3,2,8,4,7,6,1,5]=>1101010=>0101011
[5,1,6,7,8,4,2,3]=>[3,2,4,8,7,6,1,5]=>1100011=>1100011
[5,6,2,7,4,8,1,3]=>[3,1,8,4,7,2,6,5]=>1101100=>0011011
[5,6,2,7,8,4,1,3]=>[3,1,4,8,7,2,6,5]=>1100101=>1010011
[5,6,8,3,4,2,1,7]=>[7,1,2,4,3,8,6,5]=>1010110=>0110101
[5,7,8,3,4,2,6,1]=>[1,6,2,4,3,8,7,5]=>0110101=>1010110
[6,1,2,3,7,8,5,4]=>[4,5,8,7,3,2,1,6]=>1110001=>1000111
[6,1,7,3,8,5,4,2]=>[2,4,5,8,3,7,1,6]=>1010000=>0000101
[6,1,8,3,4,5,2,7]=>[7,2,5,4,3,8,1,6]=>1111000=>0001111
[6,7,2,3,8,5,4,1]=>[1,4,5,8,3,2,7,6]=>0110010=>0100110
[6,7,2,8,4,5,3,1]=>[1,3,5,4,8,2,7,6]=>0101010=>0101010
[7,1,2,3,4,8,6,5]=>[5,6,8,4,3,2,1,7]=>1111000=>0001111
[7,1,2,3,8,5,6,4]=>[4,6,5,8,3,2,1,7]=>1110100=>0010111
[7,1,8,3,4,5,6,2]=>[2,6,5,4,3,8,1,7]=>1011100=>0011101
[2,4,6,1,8,5,7,3]=>[3,7,5,8,1,6,4,2]=>1101100=>0011011
[6,4,1,8,2,3,7,5]=>[5,7,3,2,8,1,4,6]=>1110000=>0000111
[5,8,1,6,2,4,3,7]=>[7,3,4,2,6,1,8,5]=>1110100=>0010111
[1,3,5,7,2,6,4,8]=>[8,4,6,2,7,5,3,1]=>1111100=>0011111
[3,5,8,6,1,2,4,7]=>[7,4,2,1,6,8,5,3]=>1111100=>0011111
[3,5,1,8,2,4,7,6]=>[6,7,4,2,8,1,5,3]=>1111000=>0001111
[2,3,5,6,8,1,7,4]=>[4,7,1,8,6,5,3,2]=>1110110=>0110111
[5,6,4,8,2,1,7,3]=>[3,7,1,2,8,4,6,5]=>1001100=>0011001
[7,1,8,6,3,4,5,2]=>[2,5,4,3,6,8,1,7]=>1011000=>0001101
[8,2,1,3,7,6,4,5]=>[5,4,6,7,3,1,2,8]=>1011000=>0001101
[8,2,7,5,3,1,6,4]=>[4,6,1,3,5,7,2,8]=>1100000=>0000011
[6,7,4,5,2,1,8,3]=>[3,8,1,2,5,4,7,6]=>1001010=>0101001
[5,1,7,8,6,4,3,2]=>[2,3,4,6,8,7,1,5]=>1000001=>1000001
[2,5,7,8,6,3,1,4]=>[4,1,3,6,8,7,5,2]=>1100101=>1010011
[7,1,8,6,3,2,4,5]=>[5,4,2,3,6,8,1,7]=>1101000=>0001011
[6,5,1,2,4,8,3,7]=>[7,3,8,4,2,1,5,6]=>1111000=>0001111
[7,8,1,6,4,2,3,5]=>[5,3,2,4,6,1,8,7]=>1110001=>1000111
[2,4,8,1,5,6,7,3]=>[3,7,6,5,1,8,4,2]=>1101110=>0111011
[8,4,1,2,5,6,3,7]=>[7,3,6,5,2,1,4,8]=>1110100=>0010111
[8,3,1,6,5,2,4,7]=>[7,4,2,5,6,1,3,8]=>1101000=>0001011
[2,5,3,8,7,6,1,4]=>[4,1,6,7,8,3,5,2]=>1110000=>0000111
[5,8,7,4,2,6,1,3]=>[3,1,6,2,4,7,8,5]=>1100100=>0010011
[5,1,8,4,7,6,3,2]=>[2,3,6,7,4,8,1,5]=>1001000=>0001001
[8,2,7,4,5,6,1,3]=>[3,1,6,5,4,7,2,8]=>1101100=>0011011
[4,8,6,5,7,3,2,1]=>[1,2,3,7,5,6,8,4]=>0001100=>0011000
[4,8,5,6,7,3,2,1]=>[1,2,3,7,6,5,8,4]=>0001110=>0111000
[3,8,7,4,5,6,2,1]=>[1,2,6,5,4,7,8,3]=>0011100=>0011100
[2,8,7,6,3,4,5,1]=>[1,5,4,3,6,7,8,2]=>0111000=>0001110
[1,8,7,6,5,2,3,4]=>[4,3,2,5,6,7,8,1]=>1110000=>0000111
[8,4,7,2,5,6,3,1]=>[1,3,6,5,2,7,4,8]=>0101100=>0011010
[3,6,1,8,5,2,7,4]=>[4,7,2,5,8,1,6,3]=>1110000=>0000111
[3,4,1,2,8,6,7,5]=>[5,7,6,8,2,1,4,3]=>1110010=>0100111
[7,2,5,8,3,6,1,4]=>[4,1,6,3,8,5,2,7]=>1110100=>0010111
[1,7,5,6,3,4,2,8]=>[8,2,4,3,6,5,7,1]=>1110100=>0010111
[7,6,3,8,5,2,1,4]=>[4,1,2,5,8,3,6,7]=>1010000=>0000101
[5,8,7,4,1,6,3,2]=>[2,3,6,1,4,7,8,5]=>1000100=>0010001
[4,2,3,1,7,8,5,6]=>[6,5,8,7,1,3,2,4]=>1100101=>1010011
[5,2,8,4,1,7,6,3]=>[3,6,7,1,4,8,2,5]=>1100000=>0000011
[8,6,3,4,7,2,5,1]=>[1,5,2,7,4,3,6,8]=>0111000=>0001110
[5,2,8,4,1,6,7,3]=>[3,7,6,1,4,8,2,5]=>1100010=>0100011
[4,1,3,6,8,2,5,7]=>[7,5,2,8,6,3,1,4]=>1110110=>0110111
[5,3,6,2,4,8,1,7]=>[7,1,8,4,2,6,3,5]=>1111000=>0001111
[5,3,2,1,6,8,4,7]=>[7,4,8,6,1,2,3,5]=>1001010=>0101001
[2,6,5,8,1,3,4,7]=>[7,4,3,1,8,5,6,2]=>1111100=>0011111
[4,3,1,6,5,8,2,7]=>[7,2,8,5,6,1,3,4]=>1100100=>0010011
[3,4,6,5,7,1,8,2]=>[2,8,1,7,5,6,4,3]=>1011100=>0011101
[7,5,4,2,6,8,3,1]=>[1,3,8,6,2,4,5,7]=>0100010=>0100010
[7,3,8,4,5,2,1,6]=>[6,1,2,5,4,8,3,7]=>1011000=>0001101
[8,7,2,1,5,3,4,6]=>[6,4,3,5,1,2,7,8]=>1011000=>0001101
[6,4,7,2,3,5,8,1]=>[1,8,5,3,2,7,4,6]=>0111100=>0011110
[6,8,4,1,3,5,7,2]=>[2,7,5,3,1,4,8,6]=>1010110=>0110101
[3,4,7,8,6,2,5,1]=>[1,5,2,6,8,7,4,3]=>0111001=>1001110
[4,1,3,5,7,8,6,2]=>[2,6,8,7,5,3,1,4]=>1010101=>1010101
[5,3,1,8,4,7,6,2]=>[2,6,7,4,8,1,3,5]=>1001000=>0001001
[7,5,8,2,4,6,1,3]=>[3,1,6,4,2,8,5,7]=>1101100=>0011011
[8,2,7,4,6,1,3,5]=>[5,3,1,6,4,7,2,8]=>1111000=>0001111
[4,7,3,2,8,1,6,5]=>[5,6,1,8,2,3,7,4]=>1101000=>0001011
[8,7,3,6,1,5,2,4]=>[4,2,5,1,6,3,7,8]=>1110000=>0000111
[7,4,3,6,8,2,5,1]=>[1,5,2,8,6,3,4,7]=>0110010=>0100110
[8,3,2,5,7,6,1,4]=>[4,1,6,7,5,2,3,8]=>1100100=>0010011
[1,2,8,3,5,6,7,4]=>[4,7,6,5,3,8,2,1]=>1110110=>0110111
[3,2,6,4,8,1,7,5]=>[5,7,1,8,4,6,2,3]=>1101000=>0001011
[5,6,7,3,8,4,2,1]=>[1,2,4,8,3,7,6,5]=>0010110=>0110100
[5,7,3,2,4,1,8,6]=>[6,8,1,4,2,3,7,5]=>1100100=>0010011
[8,4,1,3,7,2,5,6]=>[6,5,2,7,3,1,4,8]=>1110100=>0010111
[4,3,5,6,7,1,8,2]=>[2,8,1,7,6,5,3,4]=>1010110=>0110101
[6,5,4,8,7,2,1,3]=>[3,1,2,7,8,4,5,6]=>1001000=>0001001
[1,8,5,3,6,2,7,4]=>[4,7,2,6,3,5,8,1]=>1110000=>0000111
[6,5,8,7,2,1,3,4]=>[4,3,1,2,7,8,5,6]=>1010100=>0010101
[2,5,4,1,8,7,6,3]=>[3,6,7,8,1,4,5,2]=>1100000=>0000011
[4,7,2,6,5,8,1,3]=>[3,1,8,5,6,2,7,4]=>1101100=>0011011
[6,8,1,4,2,7,3,5]=>[5,3,7,2,4,1,8,6]=>1110010=>0100111
[3,4,7,8,2,5,6,1]=>[1,6,5,2,8,7,4,3]=>0111101=>1011110
[2,1,4,6,8,5,7,3]=>[3,7,5,8,6,4,1,2]=>1001110=>0111001
[5,2,4,1,6,8,7,3]=>[3,7,8,6,1,4,2,5]=>1100010=>0100011
[3,1,4,6,5,7,8,2]=>[2,8,7,5,6,4,1,3]=>1001101=>1011001
[1,2,3,4,8,6,5,7]=>[7,5,6,8,4,3,2,1]=>1111100=>0011111
[1,2,3,8,5,4,6,7]=>[7,6,4,5,8,3,2,1]=>1111010=>0101111
[1,2,3,8,5,6,4,7]=>[7,4,6,5,8,3,2,1]=>1111100=>0011111
[1,2,3,8,6,5,4,7]=>[7,4,5,6,8,3,2,1]=>1111000=>0001111
[1,2,8,5,4,3,6,7]=>[7,6,3,4,5,8,2,1]=>1110010=>0100111
[1,8,4,3,2,5,6,7]=>[7,6,5,2,3,4,8,1]=>1100110=>0110011
[8,5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5,8]=>0000100=>0010000
[8,4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4,8]=>0001000=>0001000
[8,4,7,5,6,3,2,1]=>[1,2,3,6,5,7,4,8]=>0001100=>0011000
[8,5,7,4,6,3,2,1]=>[1,2,3,6,4,7,5,8]=>0001100=>0011000
[8,4,7,3,6,5,2,1]=>[1,2,5,6,3,7,4,8]=>0011000=>0001100
[8,6,7,2,5,4,3,1]=>[1,3,4,5,2,7,6,8]=>0100010=>0100010
[8,7,6,2,5,4,3,1]=>[1,3,4,5,2,6,7,8]=>0100000=>0000010
[8,4,7,1,6,5,3,2]=>[2,3,5,6,1,7,4,8]=>1001000=>0001001
[8,2,7,1,6,5,4,3]=>[3,4,5,6,1,7,2,8]=>1100000=>0000011
[8,1,7,2,6,5,4,3]=>[3,4,5,6,2,7,1,8]=>1100000=>0000011
[8,1,7,2,6,4,5,3]=>[3,5,4,6,2,7,1,8]=>1101000=>0001011
[8,3,7,1,6,4,5,2]=>[2,5,4,6,1,7,3,8]=>1011000=>0001101
[8,4,7,1,6,3,5,2]=>[2,5,3,6,1,7,4,8]=>1011000=>0001101
[8,5,7,1,6,3,4,2]=>[2,4,3,6,1,7,5,8]=>1010100=>0010101
[8,6,7,1,5,3,4,2]=>[2,4,3,5,1,7,6,8]=>1010010=>0100101
[8,6,7,2,5,3,4,1]=>[1,4,3,5,2,7,6,8]=>0110010=>0100110
[8,5,7,2,6,3,4,1]=>[1,4,3,6,2,7,5,8]=>0110100=>0010110
[8,4,7,2,6,3,5,1]=>[1,5,3,6,2,7,4,8]=>0111000=>0001110
[8,3,7,2,6,4,5,1]=>[1,5,4,6,2,7,3,8]=>0111000=>0001110
[8,2,7,3,6,4,5,1]=>[1,5,4,6,3,7,2,8]=>0111000=>0001110
[8,1,7,3,6,4,5,2]=>[2,5,4,6,3,7,1,8]=>1011000=>0001101
[8,1,7,4,6,3,5,2]=>[2,5,3,6,4,7,1,8]=>1011000=>0001101
[8,2,7,4,6,3,5,1]=>[1,5,3,6,4,7,2,8]=>0111000=>0001110
[8,3,7,4,6,2,5,1]=>[1,5,2,6,4,7,3,8]=>0111000=>0001110
[8,5,7,3,6,2,4,1]=>[1,4,2,6,3,7,5,8]=>0110100=>0010110
[8,6,7,3,5,2,4,1]=>[1,4,2,5,3,7,6,8]=>0110010=>0100110
[8,5,7,4,6,2,3,1]=>[1,3,2,6,4,7,5,8]=>0101100=>0011010
[8,4,7,5,6,2,3,1]=>[1,3,2,6,5,7,4,8]=>0101100=>0011010
[8,3,7,5,6,2,4,1]=>[1,4,2,6,5,7,3,8]=>0110100=>0010110
[8,2,7,5,6,3,4,1]=>[1,4,3,6,5,7,2,8]=>0110100=>0010110
[8,1,7,5,6,3,4,2]=>[2,4,3,6,5,7,1,8]=>1010100=>0010101
[8,3,7,6,5,2,4,1]=>[1,4,2,5,6,7,3,8]=>0110000=>0000110
[8,4,7,6,5,2,3,1]=>[1,3,2,5,6,7,4,8]=>0101000=>0001010
[8,7,6,5,4,1,3,2]=>[2,3,1,4,5,6,7,8]=>1000000=>0000001
[8,5,7,6,4,1,3,2]=>[2,3,1,4,6,7,5,8]=>1000100=>0010001
[8,1,7,5,6,2,4,3]=>[3,4,2,6,5,7,1,8]=>1100100=>0010011
[8,3,7,5,6,1,4,2]=>[2,4,1,6,5,7,3,8]=>1010100=>0010101
[8,4,7,5,6,1,3,2]=>[2,3,1,6,5,7,4,8]=>1001100=>0011001
[8,6,7,4,5,1,3,2]=>[2,3,1,5,4,7,6,8]=>1001010=>0101001
[8,6,7,3,5,1,4,2]=>[2,4,1,5,3,7,6,8]=>1010010=>0100101
[8,4,7,3,6,1,5,2]=>[2,5,1,6,3,7,4,8]=>1011000=>0001101
[8,2,7,4,6,1,5,3]=>[3,5,1,6,4,7,2,8]=>1101000=>0001011
[8,1,7,4,6,2,5,3]=>[3,5,2,6,4,7,1,8]=>1101000=>0001011
[8,1,7,3,6,2,5,4]=>[4,5,2,6,3,7,1,8]=>1110000=>0000111
[8,2,7,3,6,1,5,4]=>[4,5,1,6,3,7,2,8]=>1110000=>0000111
[8,3,7,2,6,1,5,4]=>[4,5,1,6,2,7,3,8]=>1110000=>0000111
[8,4,7,2,6,1,5,3]=>[3,5,1,6,2,7,4,8]=>1101000=>0001011
[8,5,7,2,6,1,4,3]=>[3,4,1,6,2,7,5,8]=>1100100=>0010011
[8,6,7,2,5,1,4,3]=>[3,4,1,5,2,7,6,8]=>1100010=>0100011
[8,7,6,1,5,2,4,3]=>[3,4,2,5,1,6,7,8]=>1100000=>0000011
[8,6,7,1,5,2,4,3]=>[3,4,2,5,1,7,6,8]=>1100010=>0100011
[8,5,7,1,6,2,4,3]=>[3,4,2,6,1,7,5,8]=>1100100=>0010011
[8,4,7,1,6,2,5,3]=>[3,5,2,6,1,7,4,8]=>1101000=>0001011
[8,3,7,1,6,2,5,4]=>[4,5,2,6,1,7,3,8]=>1110000=>0000111
[8,2,7,1,6,3,5,4]=>[4,5,3,6,1,7,2,8]=>1110000=>0000111
[5,7,4,8,6,3,2,1]=>[1,2,3,6,8,4,7,5]=>0001100=>0011000
[4,6,7,3,8,5,2,1]=>[1,2,5,8,3,7,6,4]=>0011010=>0101100
[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,5,10,9,8,7,6]=>000001111=>111100000
[5,7,8,9,4,10,6,3,2,1]=>[1,2,3,6,10,4,9,8,7,5]=>000110110=>011011000
[4,6,8,3,9,5,10,7,2,1]=>[1,2,7,10,5,9,3,8,6,4]=>001111000=>000111100
[3,5,2,7,4,9,6,10,8,1]=>[1,8,10,6,9,4,7,2,5,3]=>011101000=>000101110
[1,6,2,5,3,4,8,7]=>[7,8,4,3,5,2,6,1]=>1111000=>0001111
[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>1111100=>0011111
[1,7,2,3,6,4,8,5]=>[5,8,4,6,3,2,7,1]=>1111000=>0001111
[1,5,2,3,8,4,7,6]=>[6,7,4,8,3,2,5,1]=>1111000=>0001111
[1,3,5,2,8,4,7,6]=>[6,7,4,8,2,5,3,1]=>1111000=>0001111
[1,5,8,2,3,7,4,6]=>[6,4,7,3,2,8,5,1]=>1111100=>0011111
[1,6,8,2,3,5,4,7]=>[7,4,5,3,2,8,6,1]=>1111010=>0101111
[5,7,2,6,3,8,1,4]=>[4,1,8,3,6,2,7,5]=>1110100=>0010111
[5,7,1,6,8,4,3,2]=>[2,3,4,8,6,1,7,5]=>1000110=>0110001
[8,4,6,2,5,7,3,1]=>[1,3,7,5,2,6,4,8]=>0101100=>0011010
[3,8,1,4,7,2,5,6]=>[6,5,2,7,4,1,8,3]=>1111100=>0011111
[1,7,8,4,6,2,5,3]=>[3,5,2,6,4,8,7,1]=>1101001=>1001011
[3,7,5,4,8,2,1,6]=>[6,1,2,8,4,5,7,3]=>1011000=>0001101
[4,7,1,3,2,8,6,5]=>[5,6,8,2,3,1,7,4]=>1101000=>0001011
[2,7,3,1,5,8,4,6]=>[6,4,8,5,1,3,7,2]=>1101100=>0011011
[3,8,7,1,6,4,5,2]=>[2,5,4,6,1,7,8,3]=>1011000=>0001101
[4,3,2,1,5,8,6,7]=>[7,6,8,5,1,2,3,4]=>1000110=>0110001
[4,1,3,7,5,6,8,2]=>[2,8,6,5,7,3,1,4]=>1010110=>0110101
[3,4,6,1,5,8,2,7]=>[7,2,8,5,1,6,4,3]=>1111100=>0011111
[6,3,8,1,7,4,2,5]=>[5,2,4,7,1,8,3,6]=>1110000=>0000111
[6,5,8,7,1,4,2,3]=>[3,2,4,1,7,8,5,6]=>1100100=>0010011
[6,3,1,2,5,8,4,7]=>[7,4,8,5,2,1,3,6]=>1101100=>0011011
[1,4,7,2,8,5,3,6]=>[6,3,5,8,2,7,4,1]=>1111000=>0001111
[7,1,3,4,2,8,5,6]=>[6,5,8,2,4,3,1,7]=>1110100=>0010111
[7,6,1,4,3,5,8,2]=>[2,8,5,3,4,1,6,7]=>1010100=>0010101
[3,5,4,1,6,7,8,2]=>[2,8,7,6,1,4,5,3]=>1010011=>1100101
[2,5,3,4,8,6,1,7]=>[7,1,6,8,4,3,5,2]=>1111000=>0001111
[2,4,8,3,6,1,7,5]=>[5,7,1,6,3,8,4,2]=>1111000=>0001111
[8,2,4,3,7,5,6,1]=>[1,6,5,7,3,4,2,8]=>0110100=>0010110
[6,8,2,1,5,7,3,4]=>[4,3,7,5,1,2,8,6]=>1010110=>0110101
[7,2,8,4,1,6,3,5]=>[5,3,6,1,4,8,2,7]=>1110000=>0000111
[1,2,4,8,6,5,3,7]=>[7,3,5,6,8,4,2,1]=>1111000=>0001111
[7,1,5,6,8,4,3,2]=>[2,3,4,8,6,5,1,7]=>1000110=>0110001
[3,7,6,5,1,4,8,2]=>[2,8,4,1,5,6,7,3]=>1011000=>0001101
[2,7,6,5,3,8,1,4]=>[4,1,8,3,5,6,7,2]=>1110000=>0000111
[2,7,8,1,4,6,3,5]=>[5,3,6,4,1,8,7,2]=>1111001=>1001111
[4,8,2,5,7,1,6,3]=>[3,6,1,7,5,2,8,4]=>1101100=>0011011
[4,1,6,8,5,3,7,2]=>[2,7,3,5,8,6,1,4]=>1010010=>0100101
[5,2,6,4,8,3,1,7]=>[7,1,3,8,4,6,2,5]=>1101000=>0001011
[1,2,6,3,4,8,7,5]=>[5,7,8,4,3,6,2,1]=>1111000=>0001111
[5,3,6,1,4,7,8,2]=>[2,8,7,4,1,6,3,5]=>1011001=>1001101
[1,7,3,2,4,8,5,6]=>[6,5,8,4,2,3,7,1]=>1101100=>0011011
[6,1,4,2,8,3,5,7]=>[7,5,3,8,2,4,1,6]=>1110100=>0010111
[5,8,6,7,2,1,4,3]=>[3,4,1,2,7,6,8,5]=>1000110=>0110001
[7,4,1,5,8,2,3,6]=>[6,3,2,8,5,1,4,7]=>1110100=>0010111
[6,3,4,2,8,7,5,1]=>[1,5,7,8,2,4,3,6]=>0110000=>0000110
[6,8,7,4,2,3,5,1]=>[1,5,3,2,4,7,8,6]=>0110010=>0100110
[2,7,6,3,4,5,8,1]=>[1,8,5,4,3,6,7,2]=>0111100=>0011110
[3,8,7,2,6,4,5,1]=>[1,5,4,6,2,7,8,3]=>0111000=>0001110
[4,5,8,7,2,6,3,1]=>[1,3,6,2,7,8,5,4]=>0101100=>0011010
[6,3,5,4,8,7,2,1]=>[1,2,7,8,4,5,3,6]=>0011000=>0001100
[1,5,3,4,8,6,2,7]=>[7,2,6,8,4,3,5,1]=>1111000=>0001111
[4,5,2,8,3,7,6,1]=>[1,6,7,3,8,2,5,4]=>0111000=>0001110
[5,8,2,4,7,6,3,1]=>[1,3,6,7,4,2,8,5]=>0101100=>0011010
[3,7,5,8,2,6,1,4]=>[4,1,6,2,8,5,7,3]=>1110100=>0010111
[1,6,7,4,8,2,3,5]=>[5,3,2,8,4,7,6,1]=>1111010=>0101111
[6,3,1,4,7,5,8,2]=>[2,8,5,7,4,1,3,6]=>1001100=>0011001
[4,1,3,8,2,6,7,5]=>[5,7,6,2,8,3,1,4]=>1110010=>0100111
[3,6,1,4,7,2,8,5]=>[5,8,2,7,4,1,6,3]=>1111000=>0001111
[6,2,7,4,5,8,1,3]=>[3,1,8,5,4,7,2,6]=>1101100=>0011011
[2,1,8,4,5,7,3,6]=>[6,3,7,5,4,8,1,2]=>1011100=>0011101
[3,2,1,6,4,8,5,7]=>[7,5,8,4,6,1,2,3]=>1001100=>0011001
[2,1,8,5,4,3,6,7]=>[7,6,3,4,5,8,1,2]=>1010010=>0100101
[7,4,8,6,2,3,1,5]=>[5,1,3,2,6,8,4,7]=>1101000=>0001011
[7,3,2,4,8,6,1,5]=>[5,1,6,8,4,2,3,7]=>1101000=>0001011
[2,7,1,4,6,3,8,5]=>[5,8,3,6,4,1,7,2]=>1111000=>0001111
[7,1,3,2,8,5,4,6]=>[6,4,5,8,2,3,1,7]=>1101000=>0001011
[5,1,7,4,2,3,8,6]=>[6,8,3,2,4,7,1,5]=>1110000=>0000111
[8,4,7,5,2,3,6,1]=>[1,6,3,2,5,7,4,8]=>0111000=>0001110
[7,5,2,8,4,6,1,3]=>[3,1,6,4,8,2,5,7]=>1101000=>0001011
[5,7,4,3,6,2,8,1]=>[1,8,2,6,3,4,7,5]=>0110100=>0010110
[6,7,5,1,2,8,3,4]=>[4,3,8,2,1,5,7,6]=>1110010=>0100111
[7,5,1,4,2,6,8,3]=>[3,8,6,2,4,1,5,7]=>1100010=>0100011
[5,2,6,8,3,4,7,1]=>[1,7,4,3,8,6,2,5]=>0111010=>0101110
[7,6,2,4,5,8,3,1]=>[1,3,8,5,4,2,6,7]=>0101100=>0011010
[3,6,8,4,7,2,5,1]=>[1,5,2,7,4,8,6,3]=>0111010=>0101110
[2,6,3,8,4,7,5,1]=>[1,5,7,4,8,3,6,2]=>0111000=>0001110
[2,1,5,6,8,3,7,4]=>[4,7,3,8,6,5,1,2]=>1010110=>0110101
[5,8,1,2,6,4,7,3]=>[3,7,4,6,2,1,8,5]=>1101100=>0011011
[1,2,7,4,8,3,6,5]=>[5,6,3,8,4,7,2,1]=>1111000=>0001111
[1,6,7,5,2,8,3,4]=>[4,3,8,2,5,7,6,1]=>1110010=>0100111
[7,5,1,2,8,4,6,3]=>[3,6,4,8,2,1,5,7]=>1101000=>0001011
[5,4,8,3,6,2,7,1]=>[1,7,2,6,3,8,4,5]=>0111000=>0001110
[5,7,3,8,2,4,6,1]=>[1,6,4,2,8,3,7,5]=>0111100=>0011110
[6,4,5,8,2,7,3,1]=>[1,3,7,2,8,5,4,6]=>0101100=>0011010
[5,7,3,6,4,8,2,1]=>[1,2,8,4,6,3,7,5]=>0011100=>0011100
[1,5,6,4,8,2,7,3]=>[3,7,2,8,4,6,5,1]=>1101100=>0011011
[3,6,2,4,7,1,8,5]=>[5,8,1,7,4,2,6,3]=>1111000=>0001111
[3,4,7,2,5,1,8,6]=>[6,8,1,5,2,7,4,3]=>1111000=>0001111
[2,1,6,4,8,5,3,7]=>[7,3,5,8,4,6,1,2]=>1011000=>0001101
[1,2,8,3,7,5,4,6]=>[6,4,5,7,3,8,2,1]=>1111000=>0001111
[5,6,1,2,8,4,3,7]=>[7,3,4,8,2,1,6,5]=>1110100=>0010111
[6,4,5,8,1,2,7,3]=>[3,7,2,1,8,5,4,6]=>1101100=>0011011
[3,8,5,7,1,4,2,6]=>[6,2,4,1,7,5,8,3]=>1110100=>0010111
[4,7,2,5,1,3,8,6]=>[6,8,3,1,5,2,7,4]=>1111000=>0001111
[5,1,7,4,8,6,3,2]=>[2,3,6,8,4,7,1,5]=>1001000=>0001001
[3,4,1,6,5,8,7,2]=>[2,7,8,5,6,1,4,3]=>1010100=>0010101
[3,5,1,2,4,8,7,6]=>[6,7,8,4,2,1,5,3]=>1111000=>0001111
[3,7,5,2,1,4,6,8]=>[8,6,4,1,2,5,7,3]=>1011010=>0101101
[3,8,5,2,7,4,1,6]=>[6,1,4,7,2,5,8,3]=>1110000=>0000111
[5,2,8,4,7,3,1,6]=>[6,1,3,7,4,8,2,5]=>1101000=>0001011
[5,2,7,4,1,3,6,8]=>[8,6,3,1,4,7,2,5]=>1110010=>0100111
[5,2,6,4,1,8,7,3]=>[3,7,8,1,4,6,2,5]=>1100000=>0000011
[6,3,2,1,4,8,7,5]=>[5,7,8,4,1,2,3,6]=>1001000=>0001001
[4,3,5,1,2,8,7,6]=>[6,7,8,2,1,5,3,4]=>1110000=>0000111
[3,1,4,6,2,8,7,5]=>[5,7,8,2,6,4,1,3]=>1101000=>0001011
[3,4,5,8,7,2,1,6]=>[6,1,2,7,8,5,4,3]=>1011100=>0011101
[8,1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1,8]=>1111000=>0001111
[1,8,5,7,3,4,6,2]=>[2,6,4,3,7,5,8,1]=>1011100=>0011101
[6,4,8,5,7,1,2,3]=>[3,2,1,7,5,8,4,6]=>1101100=>0011011
[5,4,7,6,3,8,1,2]=>[2,1,8,3,6,7,4,5]=>1011000=>0001101
[4,6,3,7,5,8,1,2]=>[2,1,8,5,7,3,6,4]=>1011100=>0011101
[1,5,7,4,8,6,3,2]=>[2,3,6,8,4,7,5,1]=>1001100=>0011001
[3,1,2,5,7,6,4,8]=>[8,4,6,7,5,2,1,3]=>1101100=>0011011
[7,2,3,8,5,6,1,4]=>[4,1,6,5,8,3,2,7]=>1110100=>0010111
[1,7,8,5,4,3,6,2]=>[2,6,3,4,5,8,7,1]=>1010001=>1000101
[7,3,8,1,4,2,6,5]=>[5,6,2,4,1,8,3,7]=>1110000=>0000111
[1,8,4,5,3,2,6,7]=>[7,6,2,3,5,4,8,1]=>1101010=>0101011
[7,8,5,4,3,1,6,2]=>[2,6,1,3,4,5,8,7]=>1000001=>1000001
[3,8,7,4,2,6,1,5]=>[5,1,6,2,4,7,8,3]=>1110000=>0000111
[3,7,8,1,2,6,5,4]=>[4,5,6,2,1,8,7,3]=>1110001=>1000111
[3,5,6,2,7,1,4,8]=>[8,4,1,7,2,6,5,3]=>1111100=>0011111
[3,6,5,1,2,8,4,7]=>[7,4,8,2,1,5,6,3]=>1111000=>0001111
[3,7,1,6,8,2,4,5]=>[5,4,2,8,6,1,7,3]=>1111010=>0101111
[7,3,5,2,1,8,4,6]=>[6,4,8,1,2,5,3,7]=>1011000=>0001101
[6,4,2,8,7,5,1,3]=>[3,1,5,7,8,2,4,6]=>1100000=>0000011
[5,2,4,6,1,7,3,8]=>[8,3,7,1,6,4,2,5]=>1111000=>0001111
[3,5,4,6,1,8,2,7]=>[7,2,8,1,6,4,5,3]=>1111000=>0001111
[3,1,5,7,6,8,2,4]=>[4,2,8,6,7,5,1,3]=>1100110=>0110011
[6,4,5,7,2,8,1,3]=>[3,1,8,2,7,5,4,6]=>1101100=>0011011
[4,1,5,3,8,2,7,6]=>[6,7,2,8,3,5,1,4]=>1110000=>0000111
[2,6,3,5,4,8,1,7]=>[7,1,8,4,5,3,6,2]=>1111000=>0001111
[7,6,4,5,2,8,1,3]=>[3,1,8,2,5,4,6,7]=>1101000=>0001011
[5,4,3,1,8,2,7,6]=>[6,7,2,8,1,3,4,5]=>1100000=>0000011
[6,5,4,2,7,3,1,8]=>[8,1,3,7,2,4,5,6]=>1100000=>0000011
[6,5,2,8,3,4,7,1]=>[1,7,4,3,8,2,5,6]=>0111000=>0001110
[6,5,3,4,8,2,7,1]=>[1,7,2,8,4,3,5,6]=>0111000=>0001110
[4,6,3,1,8,2,7,5]=>[5,7,2,8,1,3,6,4]=>1101000=>0001011
[8,3,1,7,2,5,4,6]=>[6,4,5,2,7,1,3,8]=>1101000=>0001011
[7,5,2,6,4,3,1,8]=>[8,1,3,4,6,2,5,7]=>1100000=>0000011
[8,6,1,7,4,5,2,3]=>[3,2,5,4,7,1,6,8]=>1101000=>0001011
[8,1,3,7,2,6,5,4]=>[4,5,6,2,7,3,1,8]=>1110000=>0000111
[7,3,8,4,5,2,6,1]=>[1,6,2,5,4,8,3,7]=>0111000=>0001110
[6,1,7,4,2,5,3,8]=>[8,3,5,2,4,7,1,6]=>1110000=>0000111
[1,7,8,4,3,5,6,2]=>[2,6,5,3,4,8,7,1]=>1010101=>1010101
[3,1,6,8,4,5,7,2]=>[2,7,5,4,8,6,1,3]=>1001110=>0111001
[1,4,5,8,3,6,7,2]=>[2,7,6,3,8,5,4,1]=>1011110=>0111101
[2,5,7,1,8,3,6,4]=>[4,6,3,8,1,7,5,2]=>1110100=>0010111
[6,2,7,1,8,4,5,3]=>[3,5,4,8,1,7,2,6]=>1101000=>0001011
[4,7,1,3,8,5,6,2]=>[2,6,5,8,3,1,7,4]=>1011100=>0011101
[3,7,2,1,8,4,5,6]=>[6,5,4,8,1,2,7,3]=>1011100=>0011101
[2,1,5,8,3,6,7,4]=>[4,7,6,3,8,5,1,2]=>1010110=>0110101
[4,2,7,1,8,3,6,5]=>[5,6,3,8,1,7,2,4]=>1110000=>0000111
[4,3,1,6,8,2,7,5]=>[5,7,2,8,6,1,3,4]=>1100010=>0100011
[3,5,1,6,8,2,7,4]=>[4,7,2,8,6,1,5,3]=>1110010=>0100111
[6,4,7,5,3,2,1,8]=>[8,1,2,3,5,7,4,6]=>1001000=>0001001
[4,6,8,2,7,3,1,5]=>[5,1,3,7,2,8,6,4]=>1101010=>0101011
[2,7,6,3,5,4,1,8]=>[8,1,4,5,3,6,7,2]=>1110000=>0000111
[3,8,7,4,6,2,5,1]=>[1,5,2,6,4,7,8,3]=>0111000=>0001110
[7,1,8,6,5,2,3,4]=>[4,3,2,5,6,8,1,7]=>1110000=>0000111
[8,4,7,5,3,2,1,6]=>[6,1,2,3,5,7,4,8]=>1001000=>0001001
[5,8,7,4,3,6,2,1]=>[1,2,6,3,4,7,8,5]=>0010100=>0010100
[6,2,1,8,5,4,7,3]=>[3,7,4,5,8,1,2,6]=>1001000=>0001001
[2,6,4,7,1,5,3,8]=>[8,3,5,1,7,4,6,2]=>1111000=>0001111
[2,5,6,8,4,3,7,1]=>[1,7,3,4,8,6,5,2]=>0110110=>0110110
[2,4,7,5,8,1,6,3]=>[3,6,1,8,5,7,4,2]=>1101100=>0011011
[5,2,1,8,7,6,4,3]=>[3,4,6,7,8,1,2,5]=>1000000=>0000001
[5,3,8,1,7,6,4,2]=>[2,4,6,7,1,8,3,5]=>1010000=>0000101
[5,4,8,7,1,6,3,2]=>[2,3,6,1,7,8,4,5]=>1001000=>0001001
[4,8,7,5,6,2,3,1]=>[1,3,2,6,5,7,8,4]=>0101100=>0011010
[4,8,5,6,7,1,2,3]=>[3,2,1,7,6,5,8,4]=>1101110=>0111011
[5,4,8,6,1,7,2,3]=>[3,2,7,1,6,8,4,5]=>1101000=>0001011
[5,3,8,1,6,7,2,4]=>[4,2,7,6,1,8,3,5]=>1110010=>0100111
[5,2,1,8,6,7,3,4]=>[4,3,7,6,8,1,2,5]=>1010010=>0100101
[6,2,1,5,8,3,7,4]=>[4,7,3,8,5,1,2,6]=>1010100=>0010101
[6,5,4,8,2,1,7,3]=>[3,7,1,2,8,4,5,6]=>1001000=>0001001
[5,8,4,7,2,6,3,1]=>[1,3,6,2,7,4,8,5]=>0101100=>0011010
[1,5,7,4,8,2,6,3]=>[3,6,2,8,4,7,5,1]=>1101100=>0011011
[6,5,3,2,8,1,7,4]=>[4,7,1,8,2,3,5,6]=>1100000=>0000011
[6,4,3,2,1,8,7,5]=>[5,7,8,1,2,3,4,6]=>1000000=>0000001
[6,3,4,1,2,8,7,5]=>[5,7,8,2,1,4,3,6]=>1110000=>0000111
[6,2,1,4,3,8,7,5]=>[5,7,8,3,4,1,2,6]=>1010000=>0000101
[5,2,1,4,3,6,7,8]=>[8,7,6,3,4,1,2,5]=>1010011=>1100101
[4,6,3,2,5,1,7,8]=>[8,7,1,5,2,3,6,4]=>1101001=>1001011
[3,5,7,4,2,6,1,8]=>[8,1,6,2,4,7,5,3]=>1110100=>0010111
[4,3,6,1,5,2,7,8]=>[8,7,2,5,1,6,3,4]=>1110001=>1000111
[4,2,1,6,5,3,7,8]=>[8,7,3,5,6,1,2,4]=>1010001=>1000101
[4,2,1,5,7,6,3,8]=>[8,3,6,7,5,1,2,4]=>1010100=>0010101
[3,4,5,8,6,7,1,2]=>[2,1,7,6,8,5,4,3]=>1011110=>0111101
[3,4,6,5,8,1,7,2]=>[2,7,1,8,5,6,4,3]=>1011100=>0011101
[2,1,5,3,8,4,7,6]=>[6,7,4,8,3,5,1,2]=>1011000=>0001101
[3,1,8,2,5,4,7,6]=>[6,7,4,5,2,8,1,3]=>1101000=>0001011
[8,1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1,8]=>1101000=>0001011
[3,1,8,2,6,4,7,5]=>[5,7,4,6,2,8,1,3]=>1101000=>0001011
[2,1,8,3,6,4,7,5]=>[5,7,4,6,3,8,1,2]=>1011000=>0001101
[2,1,6,3,8,4,7,5]=>[5,7,4,8,3,6,1,2]=>1011000=>0001101
[2,1,7,3,5,4,8,6]=>[6,8,4,5,3,7,1,2]=>1011000=>0001101
[2,1,7,3,6,4,8,5]=>[5,8,4,6,3,7,1,2]=>1011000=>0001101
[2,1,7,3,8,4,6,5]=>[5,6,4,8,3,7,1,2]=>1011000=>0001101
[4,1,8,2,7,3,6,5]=>[5,6,3,7,2,8,1,4]=>1110000=>0000111
[3,1,7,2,8,4,6,5]=>[5,6,4,8,2,7,1,3]=>1101000=>0001011
[3,1,6,2,5,4,8,7]=>[7,8,4,5,2,6,1,3]=>1101000=>0001011
[7,1,3,2,5,4,8,6]=>[6,8,4,5,2,3,1,7]=>1101000=>0001011
[7,1,3,2,6,4,8,5]=>[5,8,4,6,2,3,1,7]=>1101000=>0001011
[7,1,8,2,4,3,6,5]=>[5,6,3,4,2,8,1,7]=>1110000=>0000111
[6,1,4,2,5,3,8,7]=>[7,8,3,5,2,4,1,6]=>1110000=>0000111
[4,1,6,2,5,3,8,7]=>[7,8,3,5,2,6,1,4]=>1110000=>0000111
[4,1,7,2,5,3,8,6]=>[6,8,3,5,2,7,1,4]=>1110000=>0000111
[4,1,7,2,6,3,8,5]=>[5,8,3,6,2,7,1,4]=>1110000=>0000111
[5,1,7,2,6,3,8,4]=>[4,8,3,6,2,7,1,5]=>1110000=>0000111
[5,1,8,2,7,3,6,4]=>[4,6,3,7,2,8,1,5]=>1110000=>0000111
[8,1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1,8]=>1110000=>0000111
[8,1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1,8]=>1110000=>0000111
[5,1,8,2,6,3,7,4]=>[4,7,3,6,2,8,1,5]=>1110000=>0000111
[5,1,6,2,8,3,7,4]=>[4,7,3,8,2,6,1,5]=>1110000=>0000111
[3,1,6,2,8,4,7,5]=>[5,7,4,8,2,6,1,3]=>1101000=>0001011
[4,1,8,2,6,3,7,5]=>[5,7,3,6,2,8,1,4]=>1110000=>0000111
[8,1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1,8]=>1110000=>0000111
[8,1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1,8]=>1110000=>0000111
[4,1,8,2,5,3,7,6]=>[6,7,3,5,2,8,1,4]=>1110000=>0000111
[4,1,5,2,8,3,7,6]=>[6,7,3,8,2,5,1,4]=>1110000=>0000111
[3,1,5,2,8,4,7,6]=>[6,7,4,8,2,5,1,3]=>1101000=>0001011
[3,1,4,2,8,5,7,6]=>[6,7,5,8,2,4,1,3]=>1100100=>0010011
[4,1,3,2,7,5,8,6]=>[6,8,5,7,2,3,1,4]=>1100100=>0010011
[5,1,4,2,8,3,7,6]=>[6,7,3,8,2,4,1,5]=>1110000=>0000111
[6,1,3,2,8,4,7,5]=>[5,7,4,8,2,3,1,6]=>1101000=>0001011
[6,1,3,2,7,4,8,5]=>[5,8,4,7,2,3,1,6]=>1101000=>0001011
[5,1,3,2,7,4,8,6]=>[6,8,4,7,2,3,1,5]=>1101000=>0001011
[5,1,3,2,6,4,8,7]=>[7,8,4,6,2,3,1,5]=>1101000=>0001011
[5,1,4,2,6,3,8,7]=>[7,8,3,6,2,4,1,5]=>1110000=>0000111
[6,1,4,2,7,3,8,5]=>[5,8,3,7,2,4,1,6]=>1110000=>0000111
[6,1,5,2,7,3,8,4]=>[4,8,3,7,2,5,1,6]=>1110000=>0000111
[8,1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1,8]=>1110000=>0000111
[7,1,6,2,4,3,8,5]=>[5,8,3,4,2,6,1,7]=>1110000=>0000111
[7,1,8,2,6,3,5,4]=>[4,5,3,6,2,8,1,7]=>1110000=>0000111
[6,3,8,1,2,5,7,4]=>[4,7,5,2,1,8,3,6]=>1110100=>0010111
[7,8,3,1,2,5,6,4]=>[4,6,5,2,1,3,8,7]=>1100101=>1010011
[7,8,1,3,2,4,6,5]=>[5,6,4,2,3,1,8,7]=>1101001=>1001011
[7,8,2,1,3,5,4,6]=>[6,4,5,3,1,2,8,7]=>1011001=>1001101
[2,5,3,6,1,8,7,4]=>[4,7,8,1,6,3,5,2]=>1110000=>0000111
[6,2,8,1,3,5,4,7]=>[7,4,5,3,1,8,2,6]=>1111000=>0001111
[3,2,5,7,1,8,4,6]=>[6,4,8,1,7,5,2,3]=>1101100=>0011011
[3,5,2,8,1,7,4,6]=>[6,4,7,1,8,2,5,3]=>1111000=>0001111
[5,3,4,7,8,6,1,2]=>[2,1,6,8,7,4,3,5]=>1011001=>1001101
[3,5,4,6,8,7,1,2]=>[2,1,7,8,6,4,5,3]=>1011010=>0101101
[4,1,3,2,6,8,7,5]=>[5,7,8,6,2,3,1,4]=>1100010=>0100011
[5,1,3,7,2,6,8,4]=>[4,8,6,2,7,3,1,5]=>1110010=>0100111
[5,2,4,7,8,1,6,3]=>[3,6,1,8,7,4,2,5]=>1101001=>1001011
[5,3,1,8,2,6,7,4]=>[4,7,6,2,8,1,3,5]=>1100010=>0100011
[6,1,8,3,2,4,7,5]=>[5,7,4,2,3,8,1,6]=>1101000=>0001011
[4,3,5,7,6,8,1,2]=>[2,1,8,6,7,5,3,4]=>1010110=>0110101
[4,2,1,3,7,6,8,5]=>[5,8,6,7,3,1,2,4]=>1010010=>0100101
[2,4,3,1,8,5,7,6]=>[6,7,5,8,1,3,4,2]=>1100100=>0010011
[5,2,1,8,3,6,4,7]=>[7,4,6,3,8,1,2,5]=>1011000=>0001101
[3,2,4,1,8,6,5,7]=>[7,5,6,8,1,4,2,3]=>1100100=>0010011
[7,6,5,4,8,1,3,2]=>[2,3,1,8,4,5,6,7]=>1001000=>0001001
[7,6,5,8,2,1,4,3]=>[3,4,1,2,8,5,6,7]=>1000100=>0010001
[7,6,8,3,2,1,5,4]=>[4,5,1,2,3,8,6,7]=>1000010=>0100001
[8,5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5,8]=>1000000=>0000001
[7,6,5,4,1,8,3,2]=>[2,3,8,1,4,5,6,7]=>1000000=>0000001
[7,6,5,2,8,1,4,3]=>[3,4,1,8,2,5,6,7]=>1100000=>0000011
[7,6,3,8,2,1,5,4]=>[4,5,1,2,8,3,6,7]=>1010000=>0000101
[7,6,5,8,4,1,3,2]=>[2,3,1,4,8,5,6,7]=>1000100=>0010001
[7,4,8,3,2,1,6,5]=>[5,6,1,2,3,8,4,7]=>1001000=>0001001
[7,6,8,5,2,1,4,3]=>[3,4,1,2,5,8,6,7]=>1000010=>0100001
[4,8,6,1,7,5,2,3]=>[3,2,5,7,1,6,8,4]=>1101000=>0001011
[4,8,7,2,6,5,1,3]=>[3,1,5,6,2,7,8,4]=>1101000=>0001011
[4,7,8,2,6,1,5,3]=>[3,5,1,6,2,8,7,4]=>1101001=>1001011
[4,6,8,2,7,1,3,5]=>[5,3,1,7,2,8,6,4]=>1111010=>0101111
[7,6,4,2,8,3,5,1]=>[1,5,3,8,2,4,6,7]=>0110000=>0000110
[8,6,4,2,7,5,3,1]=>[1,3,5,7,2,4,6,8]=>0100000=>0000010
[8,4,7,3,6,5,1,2]=>[2,1,5,6,3,7,4,8]=>1011000=>0001101
[6,4,7,1,8,3,2,5]=>[5,2,3,8,1,7,4,6]=>1101000=>0001011
[7,4,8,3,6,1,5,2]=>[2,5,1,6,3,8,4,7]=>1011000=>0001101
[7,8,4,3,6,2,5,1]=>[1,5,2,6,3,4,8,7]=>0110001=>1000110
[6,8,4,3,7,2,1,5]=>[5,1,2,7,3,4,8,6]=>1010010=>0100101
[6,7,4,2,8,3,1,5]=>[5,1,3,8,2,4,7,6]=>1100010=>0100011
[7,3,2,5,4,1,6,8]=>[8,6,1,4,5,2,3,7]=>1100010=>0100011
[7,1,4,2,6,3,5,8]=>[8,5,3,6,2,4,1,7]=>1110100=>0010111
[7,3,2,5,1,6,4,8]=>[8,4,6,1,5,2,3,7]=>1101000=>0001011
[7,4,1,3,5,2,6,8]=>[8,6,2,5,3,1,4,7]=>1110010=>0100111
[7,3,1,2,4,6,5,8]=>[8,5,6,4,2,1,3,7]=>1101100=>0011011
[1,8,6,7,4,2,5,3]=>[3,5,2,4,7,6,8,1]=>1100010=>0100011
[3,6,2,1,4,8,5,7]=>[7,5,8,4,1,2,6,3]=>1011100=>0011101
[2,3,6,1,4,8,7,5]=>[5,7,8,4,1,6,3,2]=>1111000=>0001111
[3,4,7,1,5,2,8,6]=>[6,8,2,5,1,7,4,3]=>1111000=>0001111
[3,6,7,4,1,5,8,2]=>[2,8,5,1,4,7,6,3]=>1010110=>0110101
[4,3,2,7,1,5,8,6]=>[6,8,5,1,7,2,3,4]=>1100100=>0010011
[5,6,8,2,4,1,3,7]=>[7,3,1,4,2,8,6,5]=>1110110=>0110111
[1,8,2,7,4,3,6,5]=>[5,6,3,4,7,2,8,1]=>1110000=>0000111
[6,5,8,2,3,7,1,4]=>[4,1,7,3,2,8,5,6]=>1110100=>0010111
[5,7,8,6,1,3,2,4]=>[4,2,3,1,6,8,7,5]=>1100101=>1010011
[2,4,8,1,6,3,7,5]=>[5,7,3,6,1,8,4,2]=>1111000=>0001111
[3,7,5,4,6,8,2,1]=>[1,2,8,6,4,5,7,3]=>0011010=>0101100
[5,3,2,1,7,6,8,4]=>[4,8,6,7,1,2,3,5]=>1000010=>0100001
[4,3,1,7,5,6,8,2]=>[2,8,6,5,7,1,3,4]=>1000110=>0110001
[5,6,7,3,2,8,1,4]=>[4,1,8,2,3,7,6,5]=>1100110=>0110011
[5,3,2,1,4,8,6,7]=>[7,6,8,4,1,2,3,5]=>1001010=>0101001
[2,3,6,8,5,1,4,7]=>[7,4,1,5,8,6,3,2]=>1111010=>0101111
[7,3,2,6,8,5,1,4]=>[4,1,5,8,6,2,3,7]=>1100010=>0100011
[7,3,5,8,4,6,1,2]=>[2,1,6,4,8,5,3,7]=>1011100=>0011101
[1,8,4,2,3,5,7,6]=>[6,7,5,3,2,4,8,1]=>1110100=>0010111
[6,3,4,8,2,5,7,1]=>[1,7,5,2,8,4,3,6]=>0111100=>0011110
[7,5,4,8,3,6,2,1]=>[1,2,6,3,8,4,5,7]=>0011000=>0001100
[5,7,8,3,1,4,6,2]=>[2,6,4,1,3,8,7,5]=>1001101=>1011001
[7,4,8,3,2,5,1,6]=>[6,1,5,2,3,8,4,7]=>1101000=>0001011
[4,2,7,1,5,3,8,6]=>[6,8,3,5,1,7,2,4]=>1110000=>0000111
[4,2,8,6,1,5,3,7]=>[7,3,5,1,6,8,2,4]=>1110000=>0000111
[3,2,6,7,5,1,4,8]=>[8,4,1,5,7,6,2,3]=>1101010=>0101011
[4,7,2,1,5,8,6,3]=>[3,6,8,5,1,2,7,4]=>1001100=>0011001
[7,2,1,3,5,8,6,4]=>[4,6,8,5,3,1,2,7]=>1010100=>0010101
[2,3,4,8,1,6,5,7]=>[7,5,6,1,8,4,3,2]=>1111100=>0011111
[4,8,6,2,1,5,7,3]=>[3,7,5,1,2,6,8,4]=>1001100=>0011001
[7,3,1,6,8,2,4,5]=>[5,4,2,8,6,1,3,7]=>1101010=>0101011
[4,7,3,5,6,1,8,2]=>[2,8,1,6,5,3,7,4]=>1011100=>0011101
[4,6,8,2,1,5,7,3]=>[3,7,5,1,2,8,6,4]=>1001110=>0111001
[6,8,2,1,3,5,7,4]=>[4,7,5,3,1,2,8,6]=>1010110=>0110101
[1,2,5,8,3,7,4,6]=>[6,4,7,3,8,5,2,1]=>1111100=>0011111
[8,2,4,1,7,5,6,3]=>[3,6,5,7,1,4,2,8]=>1100100=>0010011
[3,8,4,7,5,1,6,2]=>[2,6,1,5,7,4,8,3]=>1011000=>0001101
[8,4,3,6,1,7,5,2]=>[2,5,7,1,6,3,4,8]=>1010000=>0000101
[2,1,8,6,7,3,5,4]=>[4,5,3,7,6,8,1,2]=>1010010=>0100101
[7,3,2,5,6,1,4,8]=>[8,4,1,6,5,2,3,7]=>1101100=>0011011
[4,6,2,8,1,5,3,7]=>[7,3,5,1,8,2,6,4]=>1111000=>0001111
[8,4,1,2,7,5,3,6]=>[6,3,5,7,2,1,4,8]=>1110000=>0000111
[1,5,2,8,6,3,7,4]=>[4,7,3,6,8,2,5,1]=>1110000=>0000111
[5,8,6,3,1,7,4,2]=>[2,4,7,1,3,6,8,5]=>1000100=>0010001
[7,8,1,4,2,5,3,6]=>[6,3,5,2,4,1,8,7]=>1110001=>1000111
[4,5,6,2,7,1,3,8]=>[8,3,1,7,2,6,5,4]=>1111100=>0011111
[5,6,2,7,1,3,4,8]=>[8,4,3,1,7,2,6,5]=>1111100=>0011111
[8,5,1,2,6,3,4,7]=>[7,4,3,6,2,1,5,8]=>1111000=>0001111
[6,7,3,8,4,1,5,2]=>[2,5,1,4,8,3,7,6]=>1010010=>0100101
[2,7,1,8,5,6,3,4]=>[4,3,6,5,8,1,7,2]=>1110100=>0010111
[2,1,7,8,6,3,4,5]=>[5,4,3,6,8,7,1,2]=>1011001=>1001101
[7,8,6,2,1,3,5,4]=>[4,5,3,1,2,6,8,7]=>1010001=>1000101
[5,2,6,3,4,1,8,7]=>[7,8,1,4,3,6,2,5]=>1110000=>0000111
[4,1,2,6,5,3,8,7]=>[7,8,3,5,6,2,1,4]=>1110000=>0000111
[2,6,5,3,1,4,8,7]=>[7,8,4,1,3,5,6,2]=>1101000=>0001011
[3,6,1,4,2,5,8,7]=>[7,8,5,2,4,1,6,3]=>1110100=>0010111
[4,7,8,5,1,6,3,2]=>[2,3,6,1,5,8,7,4]=>1001001=>1001001
[8,2,6,4,7,3,5,1]=>[1,5,3,7,4,6,2,8]=>0111000=>0001110
[4,8,6,1,7,3,2,5]=>[5,2,3,7,1,6,8,4]=>1101000=>0001011
[3,8,5,1,7,2,4,6]=>[6,4,2,7,1,5,8,3]=>1111000=>0001111
[6,8,7,1,3,2,4,5]=>[5,4,2,3,1,7,8,6]=>1101010=>0101011
[2,1,7,4,8,5,6,3]=>[3,6,5,8,4,7,1,2]=>1001100=>0011001
[2,5,1,8,7,4,6,3]=>[3,6,4,7,8,1,5,2]=>1101000=>0001011
[6,2,3,8,4,7,5,1]=>[1,5,7,4,8,3,2,6]=>0111000=>0001110
[8,6,4,3,1,7,2,5]=>[5,2,7,1,3,4,6,8]=>1100000=>0000011
[8,3,7,4,6,1,2,5]=>[5,2,1,6,4,7,3,8]=>1111000=>0001111
[2,1,6,3,4,8,7,5]=>[5,7,8,4,3,6,1,2]=>1011000=>0001101
[7,6,2,5,3,8,1,4]=>[4,1,8,3,5,2,6,7]=>1110000=>0000111
[6,5,4,2,8,3,1,7]=>[7,1,3,8,2,4,5,6]=>1100000=>0000011
[8,1,4,2,5,6,7,3]=>[3,7,6,5,2,4,1,8]=>1100110=>0110011
[6,1,4,3,8,5,2,7]=>[7,2,5,8,3,4,1,6]=>1110000=>0000111
[4,2,3,1,7,8,6,5]=>[5,6,8,7,1,3,2,4]=>1100001=>1000011
[2,7,6,8,1,5,3,4]=>[4,3,5,1,8,6,7,2]=>1110010=>0100111
[3,6,8,1,5,2,4,7]=>[7,4,2,5,1,8,6,3]=>1111010=>0101111
[6,3,8,5,7,4,2,1]=>[1,2,4,7,5,8,3,6]=>0010100=>0010100
[7,4,6,8,5,1,2,3]=>[3,2,1,5,8,6,4,7]=>1101010=>0101011
[2,6,5,4,8,1,3,7]=>[7,3,1,8,4,5,6,2]=>1111000=>0001111
[2,1,5,8,3,6,4,7]=>[7,4,6,3,8,5,1,2]=>1011100=>0011101
[3,8,1,4,5,6,2,7]=>[7,2,6,5,4,1,8,3]=>1111100=>0011111
[5,8,7,3,6,1,4,2]=>[2,4,1,6,3,7,8,5]=>1010100=>0010101
[7,6,8,3,5,1,4,2]=>[2,4,1,5,3,8,6,7]=>1010010=>0100101
[5,8,3,7,6,1,4,2]=>[2,4,1,6,7,3,8,5]=>1010100=>0010101
[5,3,8,7,6,1,4,2]=>[2,4,1,6,7,8,3,5]=>1010000=>0000101
[7,5,8,4,6,1,3,2]=>[2,3,1,6,4,8,5,7]=>1001100=>0011001
[2,4,8,1,3,7,6,5]=>[5,6,7,3,1,8,4,2]=>1111000=>0001111
[2,5,1,3,8,4,7,6]=>[6,7,4,8,3,1,5,2]=>1111000=>0001111
[2,8,1,5,4,7,3,6]=>[6,3,7,4,5,1,8,2]=>1111000=>0001111
[3,1,8,2,5,7,4,6]=>[6,4,7,5,2,8,1,3]=>1101100=>0011011
[2,8,1,6,4,3,7,5]=>[5,7,3,4,6,1,8,2]=>1110000=>0000111
[2,6,1,3,8,7,5,4]=>[4,5,7,8,3,1,6,2]=>1110000=>0000111
[2,7,1,5,8,4,6,3]=>[3,6,4,8,5,1,7,2]=>1101100=>0011011
[2,7,1,6,5,3,8,4]=>[4,8,3,5,6,1,7,2]=>1110000=>0000111
[7,3,5,8,2,1,4,6]=>[6,4,1,2,8,5,3,7]=>1011100=>0011101
[7,3,6,2,1,4,5,8]=>[8,5,4,1,2,6,3,7]=>1011100=>0011101
[7,3,6,2,1,5,4,8]=>[8,4,5,1,2,6,3,7]=>1011000=>0001101
[7,4,2,8,1,6,5,3]=>[3,5,6,1,8,2,4,7]=>1100000=>0000011
[7,4,5,8,6,2,1,3]=>[3,1,2,6,8,5,4,7]=>1001100=>0011001
[6,8,4,5,2,1,7,3]=>[3,7,1,2,5,4,8,6]=>1001010=>0101001
[4,7,5,1,3,8,6,2]=>[2,6,8,3,1,5,7,4]=>1011000=>0001101
[5,1,7,6,3,8,2,4]=>[4,2,8,3,6,7,1,5]=>1110000=>0000111
[5,1,7,6,4,2,8,3]=>[3,8,2,4,6,7,1,5]=>1100000=>0000011
[5,1,8,7,6,4,3,2]=>[2,3,4,6,7,8,1,5]=>1000000=>0000001
[5,1,6,2,8,7,4,3]=>[3,4,7,8,2,6,1,5]=>1100000=>0000011
[3,5,6,8,7,1,4,2]=>[2,4,1,7,8,6,5,3]=>1010110=>0110101
[3,6,1,7,4,8,2,5]=>[5,2,8,4,7,1,6,3]=>1111000=>0001111
[8,4,2,5,7,3,1,6]=>[6,1,3,7,5,2,4,8]=>1100100=>0010011
[4,1,8,5,7,3,6,2]=>[2,6,3,7,5,8,1,4]=>1010100=>0010101
[4,1,5,8,7,2,3,6]=>[6,3,2,7,8,5,1,4]=>1110100=>0010111
[3,4,8,7,1,2,6,5]=>[5,6,2,1,7,8,4,3]=>1111000=>0001111
[3,4,6,8,5,7,1,2]=>[2,1,7,5,8,6,4,3]=>1011110=>0111101
[4,6,8,3,5,7,2,1]=>[1,2,7,5,3,8,6,4]=>0011110=>0111100
[4,7,3,5,8,2,6,1]=>[1,6,2,8,5,3,7,4]=>0111100=>0011110
[5,4,8,2,7,3,6,1]=>[1,6,3,7,2,8,4,5]=>0111000=>0001110
[5,4,8,7,3,6,1,2]=>[2,1,6,3,7,8,4,5]=>1011000=>0001101
[6,4,3,8,7,1,2,5]=>[5,2,1,7,8,3,4,6]=>1110000=>0000111
[6,3,7,2,4,8,1,5]=>[5,1,8,4,2,7,3,6]=>1111000=>0001111
[5,6,8,3,7,2,1,4]=>[4,1,2,7,3,8,6,5]=>1010110=>0110101
[5,6,8,4,2,7,3,1]=>[1,3,7,2,4,8,6,5]=>0100110=>0110010
[5,7,4,2,8,1,3,6]=>[6,3,1,8,2,4,7,5]=>1110100=>0010111
[6,5,2,7,1,3,8,4]=>[4,8,3,1,7,2,5,6]=>1110000=>0000111
[8,6,5,4,2,1,7,3]=>[3,7,1,2,4,5,6,8]=>1000000=>0000001
[6,5,4,1,7,2,8,3]=>[3,8,2,7,1,4,5,6]=>1100000=>0000011
[6,8,5,7,4,3,2,1]=>[1,2,3,4,7,5,8,6]=>0000110=>0110000
[7,5,8,4,6,3,2,1]=>[1,2,3,6,4,8,5,7]=>0001100=>0011000
[7,6,4,8,3,5,2,1]=>[1,2,5,3,8,4,6,7]=>0011000=>0001100
[7,6,5,3,8,2,4,1]=>[1,4,2,8,3,5,6,7]=>0110000=>0000110
[6,1,3,8,5,2,4,7]=>[7,4,2,5,8,3,1,6]=>1111000=>0001111
[7,4,8,6,3,1,5,2]=>[2,5,1,3,6,8,4,7]=>1001000=>0001001
[7,4,2,6,3,5,1,8]=>[8,1,5,3,6,2,4,7]=>1110000=>0000111
[3,4,7,5,6,2,1,8]=>[8,1,2,6,5,7,4,3]=>1011100=>0011101
[8,1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1,8]=>1111010=>0101111
[6,2,8,4,1,5,7,3]=>[3,7,5,1,4,8,2,6]=>1100100=>0010011
[3,6,8,4,1,7,5,2]=>[2,5,7,1,4,8,6,3]=>1010010=>0100101
[8,7,2,3,6,1,4,5]=>[5,4,1,6,3,2,7,8]=>1111000=>0001111
[3,2,7,8,5,1,6,4]=>[4,6,1,5,8,7,2,3]=>1100001=>1000011
[3,2,8,1,5,4,6,7]=>[7,6,4,5,1,8,2,3]=>1101010=>0101011
[8,1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1,8]=>1110100=>0010111
[3,7,1,4,2,5,8,6]=>[6,8,5,2,4,1,7,3]=>1110100=>0010111
[1,5,2,4,8,7,3,6]=>[6,3,7,8,4,2,5,1]=>1111000=>0001111
[3,5,2,1,8,7,6,4]=>[4,6,7,8,1,2,5,3]=>1010000=>0000101
[3,2,8,7,6,1,4,5]=>[5,4,1,6,7,8,2,3]=>1101000=>0001011
[3,8,7,5,6,1,2,4]=>[4,2,1,6,5,7,8,3]=>1110100=>0010111
[4,8,6,7,1,5,3,2]=>[2,3,5,1,7,6,8,4]=>1001010=>0101001
[8,6,2,7,1,4,5,3]=>[3,5,4,1,7,2,6,8]=>1101000=>0001011
[1,8,6,7,2,3,4,5]=>[5,4,3,2,7,6,8,1]=>1111010=>0101111
[7,6,3,2,1,8,5,4]=>[4,5,8,1,2,3,6,7]=>1000000=>0000001
[5,2,3,4,7,1,8,6]=>[6,8,1,7,4,3,2,5]=>1111000=>0001111
[8,6,3,1,4,5,7,2]=>[2,7,5,4,1,3,6,8]=>1001100=>0011001
[5,8,3,1,2,4,7,6]=>[6,7,4,2,1,3,8,5]=>1101100=>0011011
[8,4,1,7,2,3,6,5]=>[5,6,3,2,7,1,4,8]=>1110000=>0000111
[3,2,8,1,6,5,7,4]=>[4,7,5,6,1,8,2,3]=>1100100=>0010011
[3,2,6,1,5,7,4,8]=>[8,4,7,5,1,6,2,3]=>1101100=>0011011
[3,5,1,4,6,7,2,8]=>[8,2,7,6,4,1,5,3]=>1111010=>0101111
[7,4,1,5,3,6,8,2]=>[2,8,6,3,5,1,4,7]=>1010010=>0100101
[4,1,3,2,5,7,6,8]=>[8,6,7,5,2,3,1,4]=>1100110=>0110011
[6,8,5,3,7,1,2,4]=>[4,2,1,7,3,5,8,6]=>1110010=>0100111
[6,8,2,4,5,1,3,7]=>[7,3,1,5,4,2,8,6]=>1111010=>0101111
[3,6,7,2,5,1,4,8]=>[8,4,1,5,2,7,6,3]=>1111010=>0101111
[6,8,3,4,1,5,2,7]=>[7,2,5,1,4,3,8,6]=>1110010=>0100111
[5,8,4,1,7,2,6,3]=>[3,6,2,7,1,4,8,5]=>1100100=>0010011
[6,8,3,1,4,5,7,2]=>[2,7,5,4,1,3,8,6]=>1001110=>0111001
[5,3,8,4,2,6,7,1]=>[1,7,6,2,4,8,3,5]=>0110010=>0100110
[5,1,8,4,6,3,7,2]=>[2,7,3,6,4,8,1,5]=>1011000=>0001101
[4,1,8,3,5,7,2,6]=>[6,2,7,5,3,8,1,4]=>1110100=>0010111
[2,4,6,3,5,8,1,7]=>[7,1,8,5,3,6,4,2]=>1111100=>0011111
[2,6,3,4,7,5,8,1]=>[1,8,5,7,4,3,6,2]=>0111100=>0011110
[3,4,1,6,5,8,2,7]=>[7,2,8,5,6,1,4,3]=>1110100=>0010111
[7,5,1,2,8,6,3,4]=>[4,3,6,8,2,1,5,7]=>1110000=>0000111
[6,4,2,8,7,1,5,3]=>[3,5,1,7,8,2,4,6]=>1100000=>0000011
[3,1,8,2,7,6,4,5]=>[5,4,6,7,2,8,1,3]=>1101000=>0001011
[6,2,8,4,1,7,5,3]=>[3,5,7,1,4,8,2,6]=>1100000=>0000011
[2,6,3,7,5,1,4,8]=>[8,4,1,5,7,3,6,2]=>1111000=>0001111
[7,1,3,8,5,2,4,6]=>[6,4,2,5,8,3,1,7]=>1111000=>0001111
[7,3,2,8,6,1,4,5]=>[5,4,1,6,8,2,3,7]=>1101000=>0001011
[4,3,8,7,1,2,5,6]=>[6,5,2,1,7,8,3,4]=>1110100=>0010111
[1,2,5,8,4,7,3,6]=>[6,3,7,4,8,5,2,1]=>1111100=>0011111
[1,3,6,8,5,2,7,4]=>[4,7,2,5,8,6,3,1]=>1110010=>0100111
[3,2,6,7,1,8,4,5]=>[5,4,8,1,7,6,2,3]=>1101010=>0101011
[2,4,6,1,8,3,7,5]=>[5,7,3,8,1,6,4,2]=>1111000=>0001111
[1,4,2,5,8,7,3,6]=>[6,3,7,8,5,2,4,1]=>1110100=>0010111
[3,5,1,7,2,8,6,4]=>[4,6,8,2,7,1,5,3]=>1110000=>0000111
[4,6,3,1,7,8,5,2]=>[2,5,8,7,1,3,6,4]=>1001001=>1001001
[5,3,1,6,7,8,4,2]=>[2,4,8,7,6,1,3,5]=>1000011=>1100001
[4,1,6,2,7,8,5,3]=>[3,5,8,7,2,6,1,4]=>1100001=>1000011
[4,8,7,3,6,5,1,2]=>[2,1,5,6,3,7,8,4]=>1011000=>0001101
[4,8,3,7,6,5,1,2]=>[2,1,5,6,7,3,8,4]=>1011000=>0001101
[4,3,8,7,6,5,1,2]=>[2,1,5,6,7,8,3,4]=>1010000=>0000101
[2,8,7,6,1,5,4,3]=>[3,4,5,1,6,7,8,2]=>1100000=>0000011
[4,2,8,7,6,1,5,3]=>[3,5,1,6,7,8,2,4]=>1100000=>0000011
[6,2,8,7,5,1,4,3]=>[3,4,1,5,7,8,2,6]=>1100000=>0000011
[4,1,8,7,6,5,3,2]=>[2,3,5,6,7,8,1,4]=>1000000=>0000001
[7,8,2,6,1,5,4,3]=>[3,4,5,1,6,2,8,7]=>1100001=>1000011
[6,2,8,7,1,5,4,3]=>[3,4,5,1,7,8,2,6]=>1100000=>0000011
[3,2,8,1,7,6,5,4]=>[4,5,6,7,1,8,2,3]=>1100000=>0000011
[2,8,7,1,6,5,4,3]=>[3,4,5,6,1,7,8,2]=>1100000=>0000011
[3,8,2,1,7,6,5,4]=>[4,5,6,7,1,2,8,3]=>1010000=>0000101
[4,8,2,7,6,1,5,3]=>[3,5,1,6,7,2,8,4]=>1101000=>0001011
[3,8,2,7,1,6,5,4]=>[4,5,6,1,7,2,8,3]=>1110000=>0000111
[4,8,7,2,6,1,5,3]=>[3,5,1,6,2,7,8,4]=>1101000=>0001011
[5,8,7,6,2,1,4,3]=>[3,4,1,2,6,7,8,5]=>1000100=>0010001
[6,5,8,7,1,4,3,2]=>[2,3,4,1,7,8,5,6]=>1000100=>0010001
[4,8,1,7,6,5,3,2]=>[2,3,5,6,7,1,8,4]=>1001000=>0001001
[5,4,1,8,7,6,3,2]=>[2,3,6,7,8,1,4,5]=>1000000=>0000001
[6,4,8,1,7,5,3,2]=>[2,3,5,7,1,8,4,6]=>1001000=>0001001
[7,8,4,1,6,5,3,2]=>[2,3,5,6,1,4,8,7]=>1000001=>1000001
[5,3,1,8,7,6,4,2]=>[2,4,6,7,8,1,3,5]=>1000000=>0000001
[4,3,1,8,7,6,5,2]=>[2,5,6,7,8,1,3,4]=>1000000=>0000001
[4,2,1,8,7,6,5,3]=>[3,5,6,7,8,1,2,4]=>1000000=>0000001
[7,8,2,1,6,5,4,3]=>[3,4,5,6,1,2,8,7]=>1000001=>1000001
[5,4,3,1,8,7,6,2]=>[2,6,7,8,1,3,4,5]=>1000000=>0000001
[5,4,2,1,8,7,6,3]=>[3,6,7,8,1,2,4,5]=>1000000=>0000001
[7,3,2,1,8,6,5,4]=>[4,5,6,8,1,2,3,7]=>1000000=>0000001
[9,7,5,3,1,10,8,6,4,2]=>[2,4,6,8,10,1,3,5,7,9]=>100000000=>000000001
[11,9,7,5,3,1,12,10,8,6,4,2]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>10000000000=>00000000001
[6,8,1,4,2,3,5,7]=>[7,5,3,2,4,1,8,6]=>1110110=>0110111
[8,2,3,6,1,4,5,7]=>[7,5,4,1,6,3,2,8]=>1111100=>0011111
[4,6,2,3,8,1,5,7]=>[7,5,1,8,3,2,6,4]=>1111100=>0011111
[6,2,3,8,4,1,5,7]=>[7,5,1,4,8,3,2,6]=>1110100=>0010111
[2,8,4,3,6,1,5,7]=>[7,5,1,6,3,4,8,2]=>1110100=>0010111
[2,6,3,8,4,1,5,7]=>[7,5,1,4,8,3,6,2]=>1110100=>0010111
[2,4,8,3,6,1,5,7]=>[7,5,1,6,3,8,4,2]=>1111100=>0011111
[2,4,6,3,8,1,5,7]=>[7,5,1,8,3,6,4,2]=>1111100=>0011111
[8,3,6,2,4,1,5,7]=>[7,5,1,4,2,6,3,8]=>1110100=>0010111
[2,1,8,3,6,4,5,7]=>[7,5,4,6,3,8,1,2]=>1011100=>0011101
[6,3,8,2,1,4,5,7]=>[7,5,4,1,2,8,3,6]=>1011100=>0011101
[6,2,4,3,8,1,5,7]=>[7,5,1,8,3,4,2,6]=>1110100=>0010111
[3,6,4,7,8,5,1,2]=>[2,1,5,8,7,4,6,3]=>1011001=>1001101
[3,6,4,2,7,1,5,8]=>[8,5,1,7,2,4,6,3]=>1110100=>0010111
[1,4,7,2,5,6,8,3]=>[3,8,6,5,2,7,4,1]=>1101110=>0111011
[3,4,6,8,7,5,1,2]=>[2,1,5,7,8,6,4,3]=>1011010=>0101101
[5,4,6,3,8,7,1,2]=>[2,1,7,8,3,6,4,5]=>1011000=>0001101
[6,4,8,5,3,7,1,2]=>[2,1,7,3,5,8,4,6]=>1011000=>0001101
[1,6,5,4,2,7,8,3]=>[3,8,7,2,4,5,6,1]=>1100001=>1000011
[7,1,5,3,6,2,8,4]=>[4,8,2,6,3,5,1,7]=>1110000=>0000111
[1,8,5,2,6,3,7,4]=>[4,7,3,6,2,5,8,1]=>1110000=>0000111
[3,6,5,2,4,1,8,7]=>[7,8,1,4,2,5,6,3]=>1110000=>0000111
[5,2,8,6,4,1,3,7]=>[7,3,1,4,6,8,2,5]=>1110000=>0000111
[5,1,6,2,8,7,3,4]=>[4,3,7,8,2,6,1,5]=>1110000=>0000111
[1,3,6,8,7,5,2,4]=>[4,2,5,7,8,6,3,1]=>1110010=>0100111
[7,8,1,2,4,6,5,3]=>[3,5,6,4,2,1,8,7]=>1101001=>1001011
[1,2,6,4,8,7,5,3]=>[3,5,7,8,4,6,2,1]=>1101000=>0001011
[6,1,3,2,5,7,8,4]=>[4,8,7,5,2,3,1,6]=>1100101=>1010011
[4,6,2,1,7,5,3,8]=>[8,3,5,7,1,2,6,4]=>1011000=>0001101
[7,8,3,2,4,1,6,5]=>[5,6,1,4,2,3,8,7]=>1100001=>1000011
[7,5,2,8,3,4,1,6]=>[6,1,4,3,8,2,5,7]=>1110000=>0000111
[4,3,6,8,1,2,7,5]=>[5,7,2,1,8,6,3,4]=>1110010=>0100111
[6,4,3,5,2,8,1,7]=>[7,1,8,2,5,3,4,6]=>1110000=>0000111
[6,5,3,8,4,2,1,7]=>[7,1,2,4,8,3,5,6]=>1010000=>0000101
[6,5,8,4,2,3,1,7]=>[7,1,3,2,4,8,5,6]=>1100100=>0010011
[2,4,1,3,8,5,7,6]=>[6,7,5,8,3,1,4,2]=>1110100=>0010111
[6,2,1,3,5,8,7,4]=>[4,7,8,5,3,1,2,6]=>1010100=>0010101
[4,2,1,6,3,5,7,8]=>[8,7,5,3,6,1,2,4]=>1010101=>1010101
[6,2,1,8,3,5,7,4]=>[4,7,5,3,8,1,2,6]=>1010100=>0010101
[6,2,1,3,8,5,7,4]=>[4,7,5,8,3,1,2,6]=>1010100=>0010101
[6,1,4,3,8,5,7,2]=>[2,7,5,8,3,4,1,6]=>1010100=>0010101
[6,2,1,4,3,5,7,8]=>[8,7,5,3,4,1,2,6]=>1010101=>1010101
[8,1,4,6,3,5,7,2]=>[2,7,5,3,6,4,1,8]=>1011100=>0011101
[6,1,4,8,3,5,7,2]=>[2,7,5,3,8,4,1,6]=>1011100=>0011101
[6,4,1,8,3,5,7,2]=>[2,7,5,3,8,1,4,6]=>1010100=>0010101
[6,4,8,1,3,5,7,2]=>[2,7,5,3,1,8,4,6]=>1011100=>0011101
[2,4,8,1,3,5,7,6]=>[6,7,5,3,1,8,4,2]=>1111100=>0011111
[1,4,6,8,3,5,7,2]=>[2,7,5,3,8,6,4,1]=>1011110=>0111101
[2,6,1,3,8,5,7,4]=>[4,7,5,8,3,1,6,2]=>1110100=>0010111
[2,6,1,8,3,5,7,4]=>[4,7,5,3,8,1,6,2]=>1110100=>0010111
[2,1,6,3,8,5,7,4]=>[4,7,5,8,3,6,1,2]=>1010100=>0010101
[2,1,3,6,8,5,7,4]=>[4,7,5,8,6,3,1,2]=>1010110=>0110101
[1,4,3,6,8,5,7,2]=>[2,7,5,8,6,3,4,1]=>1010110=>0110101
[4,1,3,8,6,5,7,2]=>[2,7,5,6,8,3,1,4]=>1010100=>0010101
[2,1,8,6,3,5,7,4]=>[4,7,5,3,6,8,1,2]=>1010100=>0010101
[4,1,8,3,6,5,7,2]=>[2,7,5,6,3,8,1,4]=>1010100=>0010101
[1,4,8,3,6,5,7,2]=>[2,7,5,6,3,8,4,1]=>1011100=>0011101
[4,1,8,6,3,5,7,2]=>[2,7,5,3,6,8,1,4]=>1010100=>0010101
[8,7,6,5,1,4,3,2]=>[2,3,4,1,5,6,7,8]=>1000000=>0000001
[8,7,4,3,6,2,1,5]=>[5,1,2,6,3,4,7,8]=>1010000=>0000101
[8,7,3,6,5,2,1,4]=>[4,1,2,5,6,3,7,8]=>1010000=>0000101
[8,4,7,6,3,2,1,5]=>[5,1,2,3,6,7,4,8]=>1001000=>0001001
[5,8,7,4,3,2,1,6]=>[6,1,2,3,4,7,8,5]=>1000100=>0010001
[4,5,2,7,3,1,8,6]=>[6,8,1,3,7,2,5,4]=>1101000=>0001011
[4,8,2,6,3,5,7,1]=>[1,7,5,3,6,2,8,4]=>0111100=>0011110
[4,3,7,8,6,5,1,2]=>[2,1,5,6,8,7,3,4]=>1010001=>1000101
[4,6,2,1,7,8,5,3]=>[3,5,8,7,1,2,6,4]=>1001001=>1001001
[7,8,2,1,5,6,4,3]=>[3,4,6,5,1,2,8,7]=>1000101=>1010001
[1,5,8,6,2,3,7,4]=>[4,7,3,2,6,8,5,1]=>1110100=>0010111
[2,4,8,3,1,6,5,7]=>[7,5,6,1,3,8,4,2]=>1101100=>0011011
[5,2,7,1,8,6,3,4]=>[4,3,6,8,1,7,2,5]=>1110000=>0000111
[1,2,8,3,7,6,5,4]=>[4,5,6,7,3,8,2,1]=>1110000=>0000111
[2,6,1,3,8,7,4,5]=>[5,4,7,8,3,1,6,2]=>1111000=>0001111
[6,5,2,8,1,7,3,4]=>[4,3,7,1,8,2,5,6]=>1110000=>0000111
[2,8,3,5,1,7,4,6]=>[6,4,7,1,5,3,8,2]=>1111000=>0001111
[2,8,5,6,1,7,3,4]=>[4,3,7,1,6,5,8,2]=>1110100=>0010111
[5,4,2,8,6,1,7,3]=>[3,7,1,6,8,2,4,5]=>1100000=>0000011
[5,4,3,8,7,1,6,2]=>[2,6,1,7,8,3,4,5]=>1010000=>0000101
[8,5,4,3,7,2,6,1]=>[1,6,2,7,3,4,5,8]=>0110000=>0000110
[8,3,7,4,2,6,5,1]=>[1,5,6,2,4,7,3,8]=>0110000=>0000110
[3,8,7,4,1,6,5,2]=>[2,5,6,1,4,7,8,3]=>1010000=>0000101
[2,8,6,5,1,7,4,3]=>[3,4,7,1,5,6,8,2]=>1100000=>0000011
[5,4,2,8,3,1,7,6]=>[6,7,1,3,8,2,4,5]=>1100000=>0000011
[2,8,5,3,1,7,6,4]=>[4,6,7,1,3,5,8,2]=>1100000=>0000011
[2,8,6,4,1,7,5,3]=>[3,5,7,1,4,6,8,2]=>1100000=>0000011
[8,4,7,6,2,5,3,1]=>[1,3,5,2,6,7,4,8]=>0101000=>0001010
[4,8,7,6,1,5,3,2]=>[2,3,5,1,6,7,8,4]=>1001000=>0001001
[7,4,8,6,2,1,5,3]=>[3,5,1,2,6,8,4,7]=>1001000=>0001001
[7,3,8,5,2,1,6,4]=>[4,6,1,2,5,8,3,7]=>1010000=>0000101
[7,5,4,3,8,2,1,6]=>[6,1,2,8,3,4,5,7]=>1010000=>0000101
[5,4,2,3,8,1,6,7]=>[7,6,1,8,3,2,4,5]=>1110010=>0100111
[3,7,8,4,1,2,6,5]=>[5,6,2,1,4,8,7,3]=>1110001=>1000111
[5,7,8,6,1,2,4,3]=>[3,4,2,1,6,8,7,5]=>1100101=>1010011
[7,5,8,6,2,1,4,3]=>[3,4,1,2,6,8,5,7]=>1000100=>0010001
[6,5,8,7,3,1,4,2]=>[2,4,1,3,7,8,5,6]=>1000100=>0010001
[2,4,3,8,1,6,5,7]=>[7,5,6,1,8,3,4,2]=>1110100=>0010111
[2,3,8,5,1,6,7,4]=>[4,7,6,1,5,8,3,2]=>1110010=>0100111
[6,4,8,7,3,1,5,2]=>[2,5,1,3,7,8,4,6]=>1001000=>0001001
[8,3,4,7,2,5,6,1]=>[1,6,5,2,7,4,3,8]=>0111100=>0011110
[3,4,8,7,1,5,6,2]=>[2,6,5,1,7,8,4,3]=>1011100=>0011101
[2,5,3,8,1,6,4,7]=>[7,4,6,1,8,3,5,2]=>1111000=>0001111
[8,4,6,7,2,3,5,1]=>[1,5,3,2,7,6,4,8]=>0111010=>0101110
[2,6,8,5,1,3,7,4]=>[4,7,3,1,5,8,6,2]=>1110010=>0100111
[2,6,8,4,1,3,7,5]=>[5,7,3,1,4,8,6,2]=>1110010=>0100111
[2,6,5,8,1,4,3,7]=>[7,3,4,1,8,5,6,2]=>1110100=>0010111
[7,4,6,8,2,1,3,5]=>[5,3,1,2,8,6,4,7]=>1011010=>0101101
[8,7,4,1,6,2,5,3]=>[3,5,2,6,1,4,7,8]=>1100000=>0000011
[5,2,8,4,6,3,7,1]=>[1,7,3,6,4,8,2,5]=>0111000=>0001110
[6,3,7,4,5,8,2,1]=>[1,2,8,5,4,7,3,6]=>0011100=>0011100
[3,5,7,4,6,8,2,1]=>[1,2,8,6,4,7,5,3]=>0011110=>0111100
[6,8,4,1,7,2,5,3]=>[3,5,2,7,1,4,8,6]=>1100010=>0100011
[6,8,3,4,5,7,2,1]=>[1,2,7,5,4,3,8,6]=>0011110=>0111100
[2,5,7,4,6,3,8,1]=>[1,8,3,6,4,7,5,2]=>0111100=>0011110
[8,1,6,2,4,3,5,7]=>[7,5,3,4,2,6,1,8]=>1110100=>0010111
[8,7,1,2,4,3,5,6]=>[6,5,3,4,2,1,7,8]=>1110100=>0010111
[6,8,3,1,4,7,2,5]=>[5,2,7,4,1,3,8,6]=>1101010=>0101011
[6,4,7,2,8,5,1,3]=>[3,1,5,8,2,7,4,6]=>1101000=>0001011
[5,8,1,4,7,3,2,6]=>[6,2,3,7,4,1,8,5]=>1101100=>0011011
[8,7,1,4,5,3,2,6]=>[6,2,3,5,4,1,7,8]=>1101000=>0001011
[1,7,6,2,4,3,5,8]=>[8,5,3,4,2,6,7,1]=>1110100=>0010111
[8,7,4,2,6,5,1,3]=>[3,1,5,6,2,4,7,8]=>1100000=>0000011
[8,7,3,2,4,6,5,1]=>[1,5,6,4,2,3,7,8]=>0101000=>0001010
[1,7,2,5,4,3,6,8]=>[8,6,3,4,5,2,7,1]=>1110010=>0100111
[8,7,2,4,5,3,6,1]=>[1,6,3,5,4,2,7,8]=>0111000=>0001110
[6,8,4,3,7,5,2,1]=>[1,2,5,7,3,4,8,6]=>0010010=>0100100
[6,4,7,3,8,5,2,1]=>[1,2,5,8,3,7,4,6]=>0011000=>0001100
[6,8,3,2,4,7,5,1]=>[1,5,7,4,2,3,8,6]=>0101010=>0101010
[8,1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1,8]=>1111000=>0001111
[8,1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1,8]=>1110010=>0100111
[2,7,1,5,6,3,4,8]=>[8,4,3,6,5,1,7,2]=>1111100=>0011111
[4,3,7,2,5,6,8,1]=>[1,8,6,5,2,7,3,4]=>0110110=>0110110
[2,6,3,1,4,5,8,7]=>[7,8,5,4,1,3,6,2]=>1101100=>0011011
[3,7,1,4,2,6,8,5]=>[5,8,6,2,4,1,7,3]=>1110010=>0100111
[4,7,1,5,6,8,2,3]=>[3,2,8,6,5,1,7,4]=>1101110=>0111011
[8,4,2,6,3,7,1,5]=>[5,1,7,3,6,2,4,8]=>1110000=>0000111
[4,7,3,2,5,6,1,8]=>[8,1,6,5,2,3,7,4]=>1101100=>0011011
[5,3,4,6,2,8,1,7]=>[7,1,8,2,6,4,3,5]=>1111000=>0001111
[6,4,7,2,3,8,1,5]=>[5,1,8,3,2,7,4,6]=>1111000=>0001111
[3,6,5,1,8,2,7,4]=>[4,7,2,8,1,5,6,3]=>1110000=>0000111
[4,6,5,1,8,7,2,3]=>[3,2,7,8,1,5,6,4]=>1101000=>0001011
[5,7,1,4,8,6,2,3]=>[3,2,6,8,4,1,7,5]=>1101100=>0011011
[5,7,1,3,8,2,6,4]=>[4,6,2,8,3,1,7,5]=>1110100=>0010111
[6,7,1,8,3,2,5,4]=>[4,5,2,3,8,1,7,6]=>1100010=>0100011
[8,7,6,1,4,5,2,3]=>[3,2,5,4,1,6,7,8]=>1101000=>0001011
[8,7,6,1,3,2,5,4]=>[4,5,2,3,1,6,7,8]=>1100000=>0000011
[8,7,3,5,1,2,6,4]=>[4,6,2,1,5,3,7,8]=>1110000=>0000111
[8,7,4,5,1,6,2,3]=>[3,2,6,1,5,4,7,8]=>1101000=>0001011
[8,4,6,2,3,1,7,5]=>[5,7,1,3,2,6,4,8]=>1101000=>0001011
[5,7,3,4,2,1,8,6]=>[6,8,1,2,4,3,7,5]=>1010100=>0010101
[6,7,5,4,1,8,2,3]=>[3,2,8,1,4,5,7,6]=>1100010=>0100011
[6,7,8,4,1,5,3,2]=>[2,3,5,1,4,8,7,6]=>1000011=>1100001
[7,5,1,6,4,2,3,8]=>[8,3,2,4,6,1,5,7]=>1110000=>0000111
[5,7,8,1,4,6,3,2]=>[2,3,6,4,1,8,7,5]=>1001101=>1011001
[4,5,8,6,1,7,3,2]=>[2,3,7,1,6,8,5,4]=>1001100=>0011001
[8,1,4,5,6,7,3,2]=>[2,3,7,6,5,4,1,8]=>1001110=>0111001
[5,1,8,4,2,6,3,7]=>[7,3,6,2,4,8,1,5]=>1110000=>0000111
[1,8,4,6,2,5,3,7]=>[7,3,5,2,6,4,8,1]=>1111000=>0001111
[8,5,6,1,2,4,3,7]=>[7,3,4,2,1,6,5,8]=>1110100=>0010111
[6,1,5,2,3,4,7,8]=>[8,7,4,3,2,5,1,6]=>1111001=>1001111
[3,5,1,2,8,4,7,6]=>[6,7,4,8,2,1,5,3]=>1111000=>0001111
[2,8,3,1,5,6,7,4]=>[4,7,6,5,1,3,8,2]=>1100110=>0110011
[8,3,2,7,1,5,6,4]=>[4,6,5,1,7,2,3,8]=>1100100=>0010011
[6,2,1,8,4,7,5,3]=>[3,5,7,4,8,1,2,6]=>1001000=>0001001
[8,2,7,1,5,4,6,3]=>[3,6,4,5,1,7,2,8]=>1101000=>0001011
[7,3,1,5,6,2,4,8]=>[8,4,2,6,5,1,3,7]=>1101100=>0011011
[7,2,8,1,6,4,5,3]=>[3,5,4,6,1,8,2,7]=>1101000=>0001011
[7,8,2,6,4,1,5,3]=>[3,5,1,4,6,2,8,7]=>1100001=>1000011
[8,7,2,4,1,6,5,3]=>[3,5,6,1,4,2,7,8]=>1100000=>0000011
[1,2,8,6,3,7,5,4]=>[4,5,7,3,6,8,2,1]=>1110000=>0000111
[1,7,3,8,2,6,4,5]=>[5,4,6,2,8,3,7,1]=>1111000=>0001111
[2,1,7,3,6,8,4,5]=>[5,4,8,6,3,7,1,2]=>1011010=>0101101
[7,1,5,8,3,2,4,6]=>[6,4,2,3,8,5,1,7]=>1101100=>0011011
[4,7,8,1,3,2,5,6]=>[6,5,2,3,1,8,7,4]=>1101101=>1011011
[7,1,4,2,3,5,6,8]=>[8,6,5,3,2,4,1,7]=>1110110=>0110111
[2,1,8,3,5,7,4,6]=>[6,4,7,5,3,8,1,2]=>1011100=>0011101
[1,2,3,4,8,5,7,6]=>[6,7,5,8,4,3,2,1]=>1111100=>0011111
[8,3,5,2,4,1,7,6]=>[6,7,1,4,2,5,3,8]=>1110000=>0000111
[8,6,2,5,3,1,7,4]=>[4,7,1,3,5,2,6,8]=>1100000=>0000011
[3,7,2,5,6,4,1,8]=>[8,1,4,6,5,2,7,3]=>1110100=>0010111
[7,6,2,5,4,3,1,8]=>[8,1,3,4,5,2,6,7]=>1100000=>0000011
[5,6,7,2,4,3,1,8]=>[8,1,3,4,2,7,6,5]=>1100110=>0110011
[8,7,2,3,1,6,5,4]=>[4,5,6,1,3,2,7,8]=>1100000=>0000011
[7,8,2,4,3,1,6,5]=>[5,6,1,3,4,2,8,7]=>1100001=>1000011
[4,5,8,2,3,1,7,6]=>[6,7,1,3,2,8,5,4]=>1101100=>0011011
[5,1,4,3,7,2,6,8]=>[8,6,2,7,3,4,1,5]=>1110010=>0100111
[6,1,3,5,7,2,4,8]=>[8,4,2,7,5,3,1,6]=>1111100=>0011111
[8,1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1,8]=>1111000=>0001111
[4,5,2,8,1,6,7,3]=>[3,7,6,1,8,2,5,4]=>1101010=>0101011
[6,2,5,8,1,4,7,3]=>[3,7,4,1,8,5,2,6]=>1101100=>0011011
[2,3,8,1,5,6,7,4]=>[4,7,6,5,1,8,3,2]=>1110110=>0110111
[3,8,7,1,5,6,4,2]=>[2,4,6,5,1,7,8,3]=>1010100=>0010101
[4,8,7,5,1,6,3,2]=>[2,3,6,1,5,7,8,4]=>1001000=>0001001
[5,8,6,7,1,4,3,2]=>[2,3,4,1,7,6,8,5]=>1000110=>0110001
[6,7,8,5,1,4,3,2]=>[2,3,4,1,5,8,7,6]=>1000011=>1100001
[7,3,8,5,4,1,6,2]=>[2,6,1,4,5,8,3,7]=>1010000=>0000101
[8,3,7,4,1,6,5,2]=>[2,5,6,1,4,7,3,8]=>1010000=>0000101
[6,2,3,1,5,4,7,8]=>[8,7,4,5,1,3,2,6]=>1101001=>1001011
[7,5,1,3,2,6,4,8]=>[8,4,6,2,3,1,5,7]=>1101000=>0001011
[3,6,4,1,5,2,7,8]=>[8,7,2,5,1,4,6,3]=>1110001=>1000111
[3,7,4,1,2,6,5,8]=>[8,5,6,2,1,4,7,3]=>1110100=>0010111
[6,7,1,4,2,5,3,8]=>[8,3,5,2,4,1,7,6]=>1110010=>0100111
[2,7,1,3,5,6,4,8]=>[8,4,6,5,3,1,7,2]=>1111100=>0011111
[7,8,1,2,5,3,6,4]=>[4,6,3,5,2,1,8,7]=>1110001=>1000111
[6,8,1,4,2,3,7,5]=>[5,7,3,2,4,1,8,6]=>1110010=>0100111
[1,8,2,7,5,4,6,3]=>[3,6,4,5,7,2,8,1]=>1101000=>0001011
[1,8,6,3,7,2,4,5]=>[5,4,2,7,3,6,8,1]=>1111000=>0001111
[7,2,8,3,5,1,4,6]=>[6,4,1,5,3,8,2,7]=>1111000=>0001111
[1,5,7,4,3,6,2,8]=>[8,2,6,3,4,7,5,1]=>1110100=>0010111
[1,8,5,4,7,2,6,3]=>[3,6,2,7,4,5,8,1]=>1101000=>0001011
[7,2,8,4,3,5,6,1]=>[1,6,5,3,4,8,2,7]=>0110100=>0010110
[4,5,2,7,1,3,8,6]=>[6,8,3,1,7,2,5,4]=>1111000=>0001111
[4,5,2,3,6,1,8,7]=>[7,8,1,6,3,2,5,4]=>1111000=>0001111
[4,6,5,3,7,1,8,2]=>[2,8,1,7,3,5,6,4]=>1011000=>0001101
[5,6,2,7,3,1,8,4]=>[4,8,1,3,7,2,6,5]=>1100100=>0010011
[1,6,3,7,5,8,2,4]=>[4,2,8,5,7,3,6,1]=>1110100=>0010111
[5,2,4,8,1,3,7,6]=>[6,7,3,1,8,4,2,5]=>1111000=>0001111
[6,2,5,4,8,3,7,1]=>[1,7,3,8,4,5,2,6]=>0111000=>0001110
[6,4,3,5,8,2,7,1]=>[1,7,2,8,5,3,4,6]=>0110100=>0010110
[5,2,3,4,8,1,6,7]=>[7,6,1,8,4,3,2,5]=>1111010=>0101111
[6,4,5,3,8,2,1,7]=>[7,1,2,8,3,5,4,6]=>1011000=>0001101
[6,5,3,4,8,7,1,2]=>[2,1,7,8,4,3,5,6]=>1011000=>0001101
[7,5,4,8,6,1,3,2]=>[2,3,1,6,8,4,5,7]=>1001000=>0001001
[7,6,3,8,5,4,1,2]=>[2,1,4,5,8,3,6,7]=>1010000=>0000101
[6,3,8,1,7,5,2,4]=>[4,2,5,7,1,8,3,6]=>1110000=>0000111
[6,5,8,3,1,7,4,2]=>[2,4,7,1,3,8,5,6]=>1000100=>0010001
[5,4,8,1,2,7,3,6]=>[6,3,7,2,1,8,4,5]=>1111000=>0001111
[4,5,3,7,1,6,2,8]=>[8,2,6,1,7,3,5,4]=>1111000=>0001111
[7,6,3,8,5,1,2,4]=>[4,2,1,5,8,3,6,7]=>1110000=>0000111
[6,3,8,1,7,2,4,5]=>[5,4,2,7,1,8,3,6]=>1111000=>0001111
[7,2,8,6,1,3,4,5]=>[5,4,3,1,6,8,2,7]=>1111000=>0001111
[7,2,8,6,1,5,3,4]=>[4,3,5,1,6,8,2,7]=>1110000=>0000111
[3,2,4,7,8,1,5,6]=>[6,5,1,8,7,4,2,3]=>1101101=>1011011
[4,2,6,7,3,8,1,5]=>[5,1,8,3,7,6,2,4]=>1110010=>0100111
[1,3,7,2,8,6,4,5]=>[5,4,6,8,2,7,3,1]=>1111000=>0001111
[4,3,6,5,7,8,1,2]=>[2,1,8,7,5,6,3,4]=>1010101=>1010101
[4,2,3,5,6,8,1,7]=>[7,1,8,6,5,3,2,4]=>1110110=>0110111
[5,2,6,4,7,8,3,1]=>[1,3,8,7,4,6,2,5]=>0101001=>1001010
[3,2,5,6,8,1,7,4]=>[4,7,1,8,6,5,2,3]=>1100110=>0110011
[4,2,3,6,8,1,5,7]=>[7,5,1,8,6,3,2,4]=>1110110=>0110111
[2,6,1,5,4,8,3,7]=>[7,3,8,4,5,1,6,2]=>1111000=>0001111
[8,5,2,1,4,7,6,3]=>[3,6,7,4,1,2,5,8]=>1001000=>0001001
[3,2,1,8,7,5,6,4]=>[4,6,5,7,8,1,2,3]=>1000100=>0010001
[6,7,3,2,5,8,4,1]=>[1,4,8,5,2,3,7,6]=>0100110=>0110010
[3,1,6,2,5,8,4,7]=>[7,4,8,5,2,6,1,3]=>1101100=>0011011
[6,5,1,3,4,8,2,7]=>[7,2,8,4,3,1,5,6]=>1111000=>0001111
[2,3,4,8,1,7,6,5]=>[5,6,7,1,8,4,3,2]=>1111000=>0001111
[6,2,7,8,4,5,1,3]=>[3,1,5,4,8,7,2,6]=>1101001=>1001011
[3,1,4,8,7,6,2,5]=>[5,2,6,7,8,4,1,3]=>1101000=>0001011
[2,3,6,5,8,7,1,4]=>[4,1,7,8,5,6,3,2]=>1110100=>0010111
[6,3,2,8,5,7,4,1]=>[1,4,7,5,8,2,3,6]=>0100100=>0010010
[3,2,6,8,5,1,7,4]=>[4,7,1,5,8,6,2,3]=>1100010=>0100011
[5,2,4,1,7,8,6,3]=>[3,6,8,7,1,4,2,5]=>1100001=>1000011
[3,8,4,7,2,5,6,1]=>[1,6,5,2,7,4,8,3]=>0111100=>0011110
[1,8,7,2,4,5,6,3]=>[3,6,5,4,2,7,8,1]=>1101100=>0011011
[1,8,4,6,7,3,5,2]=>[2,5,3,7,6,4,8,1]=>1011010=>0101101
[5,3,7,1,6,2,8,4]=>[4,8,2,6,1,7,3,5]=>1110000=>0000111
[7,6,5,4,1,2,8,3]=>[3,8,2,1,4,5,6,7]=>1100000=>0000011
[7,5,1,2,6,8,4,3]=>[3,4,8,6,2,1,5,7]=>1100010=>0100011
[1,2,5,3,8,7,6,4]=>[4,6,7,8,3,5,2,1]=>1110000=>0000111
[2,8,1,6,5,7,4,3]=>[3,4,7,5,6,1,8,2]=>1100100=>0010011
[2,8,1,5,6,3,7,4]=>[4,7,3,6,5,1,8,2]=>1110100=>0010111
[5,2,3,7,6,1,8,4]=>[4,8,1,6,7,3,2,5]=>1110000=>0000111
[8,1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1,8]=>1111010=>0101111
[7,2,4,8,5,3,6,1]=>[1,6,3,5,8,4,2,7]=>0111000=>0001110
[3,7,5,1,8,4,6,2]=>[2,6,4,8,1,5,7,3]=>1011000=>0001101
[2,7,8,5,4,6,1,3]=>[3,1,6,4,5,8,7,2]=>1101001=>1001011
[6,5,3,1,8,4,2,7]=>[7,2,4,8,1,3,5,6]=>1100000=>0000011
[5,7,4,3,8,6,2,1]=>[1,2,6,8,3,4,7,5]=>0010100=>0010100
[4,2,3,8,5,6,1,7]=>[7,1,6,5,8,3,2,4]=>1110100=>0010111
[8,3,1,7,4,2,5,6]=>[6,5,2,4,7,1,3,8]=>1100100=>0010011
[4,3,2,8,5,7,1,6]=>[6,1,7,5,8,2,3,4]=>1100100=>0010011
[3,6,4,2,8,5,7,1]=>[1,7,5,8,2,4,6,3]=>0110100=>0010110
[2,4,8,7,1,3,5,6]=>[6,5,3,1,7,8,4,2]=>1111100=>0011111
[8,6,2,5,4,1,3,7]=>[7,3,1,4,5,2,6,8]=>1110000=>0000111
[8,3,5,7,6,2,1,4]=>[4,1,2,6,7,5,3,8]=>1010100=>0010101
[8,1,5,4,3,6,2,7]=>[7,2,6,3,4,5,1,8]=>1110000=>0000111
[8,6,4,2,1,5,3,7]=>[7,3,5,1,2,4,6,8]=>1010000=>0000101
[8,3,5,6,2,4,1,7]=>[7,1,4,2,6,5,3,8]=>1110100=>0010111
[8,3,2,4,6,1,5,7]=>[7,5,1,6,4,2,3,8]=>1101100=>0011011
[8,1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1,8]=>1111100=>0011111
[8,2,3,4,7,6,1,5]=>[5,1,6,7,4,3,2,8]=>1111000=>0001111
[5,7,1,8,3,4,6,2]=>[2,6,4,3,8,1,7,5]=>1011100=>0011101
[1,5,6,7,3,4,8,2]=>[2,8,4,3,7,6,5,1]=>1011110=>0111101
[5,3,8,4,7,2,6,1]=>[1,6,2,7,4,8,3,5]=>0111000=>0001110
[4,8,1,2,7,3,6,5]=>[5,6,3,7,2,1,8,4]=>1111000=>0001111
[2,5,7,8,4,1,3,6]=>[6,3,1,4,8,7,5,2]=>1110101=>1010111
[6,3,5,8,7,2,4,1]=>[1,4,2,7,8,5,3,6]=>0110100=>0010110
[5,2,8,7,1,3,4,6]=>[6,4,3,1,7,8,2,5]=>1111000=>0001111
[5,2,7,4,8,1,6,3]=>[3,6,1,8,4,7,2,5]=>1101000=>0001011
[8,1,7,4,5,2,6,3]=>[3,6,2,5,4,7,1,8]=>1101000=>0001011
[1,7,8,3,5,4,6,2]=>[2,6,4,5,3,8,7,1]=>1011001=>1001101
[3,5,1,7,6,8,2,4]=>[4,2,8,6,7,1,5,3]=>1110010=>0100111
[1,7,6,5,2,4,8,3]=>[3,8,4,2,5,6,7,1]=>1101000=>0001011
[5,1,7,6,2,8,4,3]=>[3,4,8,2,6,7,1,5]=>1100000=>0000011
[2,8,5,6,7,1,3,4]=>[4,3,1,7,6,5,8,2]=>1110110=>0110111
[4,6,2,5,3,8,7,1]=>[1,7,8,3,5,2,6,4]=>0111000=>0001110
[8,6,4,2,3,1,7,5]=>[5,7,1,3,2,4,6,8]=>1100000=>0000011
[8,6,4,2,1,3,7,5]=>[5,7,3,1,2,4,6,8]=>1010000=>0000101
[4,2,8,3,1,5,6,7]=>[7,6,5,1,3,8,2,4]=>1100110=>0110011
[2,5,7,3,8,4,6,1]=>[1,6,4,8,3,7,5,2]=>0111100=>0011110
[8,3,6,7,1,5,4,2]=>[2,4,5,1,7,6,3,8]=>1010010=>0100101
[1,3,7,5,8,6,4,2]=>[2,4,6,8,5,7,3,1]=>1010100=>0010101
[3,5,7,1,4,8,6,2]=>[2,6,8,4,1,7,5,3]=>1011100=>0011101
[5,7,4,8,3,6,2,1]=>[1,2,6,3,8,4,7,5]=>0011100=>0011100
[3,4,1,2,8,5,7,6]=>[6,7,5,8,2,1,4,3]=>1110100=>0010111
[1,8,3,2,4,7,5,6]=>[6,5,7,4,2,3,8,1]=>1101100=>0011011
[6,2,3,1,4,8,7,5]=>[5,7,8,4,1,3,2,6]=>1101000=>0001011
[8,4,3,2,5,7,1,6]=>[6,1,7,5,2,3,4,8]=>1100100=>0010011
[3,6,4,8,2,5,7,1]=>[1,7,5,2,8,4,6,3]=>0111100=>0011110
[4,3,7,2,5,8,1,6]=>[6,1,8,5,2,7,3,4]=>1110100=>0010111
[3,2,4,7,8,5,6,1]=>[1,6,5,8,7,4,2,3]=>0101101=>1011010
[2,6,4,3,8,5,1,7]=>[7,1,5,8,3,4,6,2]=>1110000=>0000111
[3,8,2,1,6,4,5,7]=>[7,5,4,6,1,2,8,3]=>1011100=>0011101
[5,3,6,8,2,1,4,7]=>[7,4,1,2,8,6,3,5]=>1011010=>0101101
[3,2,6,8,5,4,1,7]=>[7,1,4,5,8,6,2,3]=>1100010=>0100011
[7,4,2,5,8,3,1,6]=>[6,1,3,8,5,2,4,7]=>1100100=>0010011
[3,1,8,6,5,4,2,7]=>[7,2,4,5,6,8,1,3]=>1100000=>0000011
[5,6,8,1,4,3,2,7]=>[7,2,3,4,1,8,6,5]=>1100110=>0110011
[6,4,8,3,7,2,5,1]=>[1,5,2,7,3,8,4,6]=>0111000=>0001110
[7,8,4,1,5,3,2,6]=>[6,2,3,5,1,4,8,7]=>1100001=>1000011
[4,7,8,3,1,6,5,2]=>[2,5,6,1,3,8,7,4]=>1001001=>1001001
[8,7,5,3,6,4,2,1]=>[1,2,4,6,3,5,7,8]=>0010000=>0000100
[4,6,1,3,8,7,5,2]=>[2,5,7,8,3,1,6,4]=>1011000=>0001101
[6,8,2,1,7,4,5,3]=>[3,5,4,7,1,2,8,6]=>1001010=>0101001
[3,1,2,7,5,6,8,4]=>[4,8,6,5,7,2,1,3]=>1100110=>0110011
[3,6,1,2,7,5,8,4]=>[4,8,5,7,2,1,6,3]=>1110100=>0010111
[3,7,6,2,5,8,1,4]=>[4,1,8,5,2,6,7,3]=>1110100=>0010111
[8,5,2,3,6,7,4,1]=>[1,4,7,6,3,2,5,8]=>0110010=>0100110
[2,7,3,1,5,6,8,4]=>[4,8,6,5,1,3,7,2]=>1100110=>0110011
[4,8,2,6,3,7,5,1]=>[1,5,7,3,6,2,8,4]=>0111000=>0001110
[6,3,2,4,8,7,5,1]=>[1,5,7,8,4,2,3,6]=>0101000=>0001010
[7,2,4,1,8,3,5,6]=>[6,5,3,8,1,4,2,7]=>1110100=>0010111
[4,8,7,6,3,2,1,5]=>[5,1,2,3,6,7,8,4]=>1001000=>0001001
[7,3,8,2,6,5,1,4]=>[4,1,5,6,2,8,3,7]=>1110000=>0000111
[7,8,2,4,6,1,5,3]=>[3,5,1,6,4,2,8,7]=>1101001=>1001011
[6,4,8,7,2,5,1,3]=>[3,1,5,2,7,8,4,6]=>1101000=>0001011
[3,5,1,8,7,2,6,4]=>[4,6,2,7,8,1,5,3]=>1110000=>0000111
[5,2,8,1,7,6,3,4]=>[4,3,6,7,1,8,2,5]=>1110000=>0000111
[6,2,1,3,8,7,5,4]=>[4,5,7,8,3,1,2,6]=>1010000=>0000101
[5,6,1,2,8,7,4,3]=>[3,4,7,8,2,1,6,5]=>1100100=>0010011
[2,7,6,8,1,5,4,3]=>[3,4,5,1,8,6,7,2]=>1100010=>0100011
[6,7,8,1,2,5,4,3]=>[3,4,5,2,1,8,7,6]=>1100011=>1100011
[7,4,8,6,1,2,5,3]=>[3,5,2,1,6,8,4,7]=>1101000=>0001011
[6,8,7,5,1,4,3,2]=>[2,3,4,1,5,7,8,6]=>1000010=>0100001
[8,6,4,3,2,1,7,5]=>[5,7,1,2,3,4,6,8]=>1000000=>0000001
[6,5,4,3,8,2,7,1]=>[1,7,2,8,3,4,5,6]=>0110000=>0000110
[7,5,4,3,2,8,6,1]=>[1,6,8,2,3,4,5,7]=>0100000=>0000010
[8,4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4,8]=>1000000=>0000001
[3,7,5,8,1,4,6,2]=>[2,6,4,1,8,5,7,3]=>1011100=>0011101
[4,7,5,8,3,2,1,6]=>[6,1,2,3,8,5,7,4]=>1001100=>0011001
[7,4,1,2,5,8,3,6]=>[6,3,8,5,2,1,4,7]=>1110100=>0010111
[5,7,2,4,6,8,1,3]=>[3,1,8,6,4,2,7,5]=>1101110=>0111011
[4,7,1,6,5,8,3,2]=>[2,3,8,5,6,1,7,4]=>1001100=>0011001
[2,7,5,4,3,8,1,6]=>[6,1,8,3,4,5,7,2]=>1110000=>0000111
[8,6,4,2,3,7,5,1]=>[1,5,7,3,2,4,6,8]=>0110000=>0000110
[7,6,4,2,3,8,1,5]=>[5,1,8,3,2,4,6,7]=>1110000=>0000111
[5,4,2,7,3,1,6,8]=>[8,6,1,3,7,2,4,5]=>1100010=>0100011
[3,1,2,4,8,7,6,5]=>[5,6,7,8,4,2,1,3]=>1101000=>0001011
[5,4,6,8,3,1,2,7]=>[7,2,1,3,8,6,4,5]=>1101010=>0101011
[6,4,8,1,3,7,2,5]=>[5,2,7,3,1,8,4,6]=>1111000=>0001111
[6,5,8,7,3,1,2,4]=>[4,2,1,3,7,8,5,6]=>1100100=>0010011
[5,6,7,8,1,4,2,3]=>[3,2,4,1,8,7,6,5]=>1100111=>1110011
[2,8,1,3,6,5,4,7]=>[7,4,5,6,3,1,8,2]=>1111000=>0001111
[2,8,7,3,5,4,1,6]=>[6,1,4,5,3,7,8,2]=>1110000=>0000111
[3,4,2,6,8,7,1,5]=>[5,1,7,8,6,2,4,3]=>1110010=>0100111
[6,1,4,2,7,8,5,3]=>[3,5,8,7,2,4,1,6]=>1100001=>1000011
[8,4,2,3,6,5,7,1]=>[1,7,5,6,3,2,4,8]=>0110100=>0010110
[7,3,8,4,1,2,6,5]=>[5,6,2,1,4,8,3,7]=>1110000=>0000111
[6,8,3,2,7,1,5,4]=>[4,5,1,7,2,3,8,6]=>1100010=>0100011
[4,8,5,6,3,2,1,7]=>[7,1,2,3,6,5,8,4]=>1001100=>0011001
[2,8,5,6,3,7,1,4]=>[4,1,7,3,6,5,8,2]=>1110100=>0010111
[6,7,3,1,4,2,8,5]=>[5,8,2,4,1,3,7,6]=>1100010=>0100011
[7,4,2,5,8,1,6,3]=>[3,6,1,8,5,2,4,7]=>1100100=>0010011
[3,2,6,7,4,8,1,5]=>[5,1,8,4,7,6,2,3]=>1101010=>0101011
[2,7,8,3,4,5,1,6]=>[6,1,5,4,3,8,7,2]=>1111001=>1001111
[3,7,1,2,4,6,5,8]=>[8,5,6,4,2,1,7,3]=>1111100=>0011111
[4,1,8,2,6,3,5,7]=>[7,5,3,6,2,8,1,4]=>1110100=>0010111
[7,5,6,8,2,1,4,3]=>[3,4,1,2,8,6,5,7]=>1000110=>0110001
[5,8,6,7,1,2,3,4]=>[4,3,2,1,7,6,8,5]=>1110110=>0110111
[4,8,1,5,7,2,3,6]=>[6,3,2,7,5,1,8,4]=>1111100=>0011111
[5,3,2,7,1,6,8,4]=>[4,8,6,1,7,2,3,5]=>1100010=>0100011
[5,1,7,2,4,6,8,3]=>[3,8,6,4,2,7,1,5]=>1101010=>0101011
[5,4,1,7,3,6,8,2]=>[2,8,6,3,7,1,4,5]=>1010010=>0100101
[3,4,7,6,2,5,8,1]=>[1,8,5,2,6,7,4,3]=>0111100=>0011110
[5,7,6,3,1,4,8,2]=>[2,8,4,1,3,6,7,5]=>1001100=>0011001
[4,8,3,6,5,2,1,7]=>[7,1,2,5,6,3,8,4]=>1011000=>0001101
[8,1,7,4,2,5,6,3]=>[3,6,5,2,4,7,1,8]=>1100100=>0010011
[4,8,1,5,2,6,3,7]=>[7,3,6,2,5,1,8,4]=>1111000=>0001111
[3,6,8,5,1,2,4,7]=>[7,4,2,1,5,8,6,3]=>1111010=>0101111
[1,5,2,7,8,4,6,3]=>[3,6,4,8,7,2,5,1]=>1101001=>1001011
[6,7,2,8,5,3,1,4]=>[4,1,3,5,8,2,7,6]=>1100010=>0100011
[6,7,2,8,3,1,5,4]=>[4,5,1,3,8,2,7,6]=>1100010=>0100011
[7,1,2,8,3,5,6,4]=>[4,6,5,3,8,2,1,7]=>1110100=>0010111
[7,1,4,5,8,6,2,3]=>[3,2,6,8,5,4,1,7]=>1101100=>0011011
[7,4,6,1,8,2,3,5]=>[5,3,2,8,1,6,4,7]=>1111000=>0001111
[5,7,6,8,4,2,1,3]=>[3,1,2,4,8,6,7,5]=>1000110=>0110001
[5,1,6,8,4,2,7,3]=>[3,7,2,4,8,6,1,5]=>1100010=>0100011
[7,4,8,2,3,6,5,1]=>[1,5,6,3,2,8,4,7]=>0111000=>0001110
[5,6,8,4,7,3,2,1]=>[1,2,3,7,4,8,6,5]=>0001110=>0111000
[3,6,4,8,5,1,2,7]=>[7,2,1,5,8,4,6,3]=>1111000=>0001111
[7,4,3,8,2,6,5,1]=>[1,5,6,2,8,3,4,7]=>0110000=>0000110
[7,5,8,6,3,4,2,1]=>[1,2,4,3,6,8,5,7]=>0010100=>0010100
[5,7,8,3,1,6,4,2]=>[2,4,6,1,3,8,7,5]=>1000101=>1010001
[7,6,8,3,2,5,4,1]=>[1,4,5,2,3,8,6,7]=>0100010=>0100010
[7,5,8,3,2,4,1,6]=>[6,1,4,2,3,8,5,7]=>1100100=>0010011
[8,7,1,3,5,4,6,2]=>[2,6,4,5,3,1,7,8]=>1011000=>0001101
[7,1,8,3,4,2,6,5]=>[5,6,2,4,3,8,1,7]=>1110000=>0000111
[7,6,8,3,1,4,5,2]=>[2,5,4,1,3,8,6,7]=>1001010=>0101001
[6,4,1,8,2,5,7,3]=>[3,7,5,2,8,1,4,6]=>1100100=>0010011
[3,6,5,1,8,4,7,2]=>[2,7,4,8,1,5,6,3]=>1011000=>0001101
[6,8,5,2,3,4,1,7]=>[7,1,4,3,2,5,8,6]=>1110010=>0100111
[2,6,8,7,1,5,3,4]=>[4,3,5,1,7,8,6,2]=>1110010=>0100111
[3,7,2,4,8,5,1,6]=>[6,1,5,8,4,2,7,3]=>1111000=>0001111
[7,4,3,2,8,5,1,6]=>[6,1,5,8,2,3,4,7]=>1100000=>0000011
[5,3,2,8,4,6,1,7]=>[7,1,6,4,8,2,3,5]=>1101000=>0001011
[7,4,2,5,3,1,6,8]=>[8,6,1,3,5,2,4,7]=>1100010=>0100011
[1,5,2,6,3,8,7,4]=>[4,7,8,3,6,2,5,1]=>1110000=>0000111
[1,3,6,2,4,8,7,5]=>[5,7,8,4,2,6,3,1]=>1111000=>0001111
[7,3,5,2,4,1,6,8]=>[8,6,1,4,2,5,3,7]=>1110010=>0100111
[3,5,8,2,4,6,1,7]=>[7,1,6,4,2,8,5,3]=>1111100=>0011111
[7,4,8,5,3,2,1,6]=>[6,1,2,3,5,8,4,7]=>1001000=>0001001
[5,8,3,6,4,2,1,7]=>[7,1,2,4,6,3,8,5]=>1010100=>0010101
[1,5,3,2,8,4,7,6]=>[6,7,4,8,2,3,5,1]=>1101000=>0001011
[3,8,4,7,5,1,2,6]=>[6,2,1,5,7,4,8,3]=>1111000=>0001111
[2,1,7,3,4,8,6,5]=>[5,6,8,4,3,7,1,2]=>1011000=>0001101
[5,1,3,2,8,7,4,6]=>[6,4,7,8,2,3,1,5]=>1101000=>0001011
[1,8,3,7,2,6,5,4]=>[4,5,6,2,7,3,8,1]=>1110000=>0000111
[5,1,4,8,3,7,2,6]=>[6,2,7,3,8,4,1,5]=>1111000=>0001111
[8,3,1,6,7,2,5,4]=>[4,5,2,7,6,1,3,8]=>1100010=>0100011
[4,8,3,7,1,5,2,6]=>[6,2,5,1,7,3,8,4]=>1111000=>0001111
[3,7,6,1,5,2,4,8]=>[8,4,2,5,1,6,7,3]=>1111000=>0001111
[1,5,4,8,3,2,7,6]=>[6,7,2,3,8,4,5,1]=>1101000=>0001011
[1,3,5,8,2,4,7,6]=>[6,7,4,2,8,5,3,1]=>1111100=>0011111
[5,4,7,1,3,2,6,8]=>[8,6,2,3,1,7,4,5]=>1101010=>0101011
[5,7,4,8,2,1,3,6]=>[6,3,1,2,8,4,7,5]=>1011100=>0011101
[4,6,8,2,5,1,3,7]=>[7,3,1,5,2,8,6,4]=>1111010=>0101111
[5,3,7,2,1,4,6,8]=>[8,6,4,1,2,7,3,5]=>1011010=>0101101
[7,4,6,2,1,5,3,8]=>[8,3,5,1,2,6,4,7]=>1011000=>0001101
[1,5,2,6,8,4,7,3]=>[3,7,4,8,6,2,5,1]=>1101010=>0101011
[5,7,2,3,8,1,4,6]=>[6,4,1,8,3,2,7,5]=>1111100=>0011111
[6,4,7,5,8,1,2,3]=>[3,2,1,8,5,7,4,6]=>1101100=>0011011
[7,4,8,5,1,6,3,2]=>[2,3,6,1,5,8,4,7]=>1001000=>0001001
[5,8,3,6,1,7,4,2]=>[2,4,7,1,6,3,8,5]=>1010100=>0010101
[8,6,4,2,1,7,5,3]=>[3,5,7,1,2,4,6,8]=>1000000=>0000001
[7,4,2,1,5,8,6,3]=>[3,6,8,5,1,2,4,7]=>1000100=>0010001
[7,6,4,1,8,5,2,3]=>[3,2,5,8,1,4,6,7]=>1100000=>0000011
[6,3,1,2,8,4,7,5]=>[5,7,4,8,2,1,3,6]=>1101000=>0001011
[6,8,4,1,2,7,5,3]=>[3,5,7,2,1,4,8,6]=>1100010=>0100011
[7,5,8,1,2,6,4,3]=>[3,4,6,2,1,8,5,7]=>1100100=>0010011
[3,6,1,8,2,4,7,5]=>[5,7,4,2,8,1,6,3]=>1111000=>0001111
[6,4,1,8,3,2,7,5]=>[5,7,2,3,8,1,4,6]=>1100000=>0000011
[1,4,8,7,2,6,5,3]=>[3,5,6,2,7,8,4,1]=>1101000=>0001011
[5,4,1,8,7,3,2,6]=>[6,2,3,7,8,1,4,5]=>1100000=>0000011
[8,1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1,8]=>1111010=>0101111
[1,8,7,6,4,5,3,2]=>[2,3,5,4,6,7,8,1]=>1001000=>0001001
[2,6,8,1,3,7,5,4]=>[4,5,7,3,1,8,6,2]=>1110010=>0100111
[2,4,8,1,5,7,6,3]=>[3,6,7,5,1,8,4,2]=>1101100=>0011011
[3,2,8,6,1,7,5,4]=>[4,5,7,1,6,8,2,3]=>1100000=>0000011
[6,2,8,3,1,7,5,4]=>[4,5,7,1,3,8,2,6]=>1100000=>0000011
[7,4,3,8,5,2,1,6]=>[6,1,2,5,8,3,4,7]=>1010000=>0000101
[6,5,2,8,4,3,1,7]=>[7,1,3,4,8,2,5,6]=>1100000=>0000011
[4,3,8,7,5,1,6,2]=>[2,6,1,5,7,8,3,4]=>1010000=>0000101
[4,2,3,8,5,1,6,7]=>[7,6,1,5,8,3,2,4]=>1110010=>0100111
[4,2,8,5,1,7,6,3]=>[3,6,7,1,5,8,2,4]=>1100000=>0000011
[3,4,2,8,5,6,1,7]=>[7,1,6,5,8,2,4,3]=>1110100=>0010111
[3,2,4,8,6,1,5,7]=>[7,5,1,6,8,4,2,3]=>1101100=>0011011
[3,2,5,8,6,1,4,7]=>[7,4,1,6,8,5,2,3]=>1101100=>0011011
[4,2,6,8,5,1,3,7]=>[7,3,1,5,8,6,2,4]=>1110010=>0100111
[3,5,2,8,4,6,1,7]=>[7,1,6,4,8,2,5,3]=>1111000=>0001111
[5,2,6,8,4,1,3,7]=>[7,3,1,4,8,6,2,5]=>1110010=>0100111
[5,3,7,8,4,1,2,6]=>[6,2,1,4,8,7,3,5]=>1110001=>1000111
[5,6,2,8,3,4,1,7]=>[7,1,4,3,8,2,6,5]=>1110100=>0010111
[5,2,3,8,4,1,6,7]=>[7,6,1,4,8,3,2,5]=>1110010=>0100111
[5,3,8,7,4,1,6,2]=>[2,6,1,4,7,8,3,5]=>1010000=>0000101
[6,4,2,8,5,3,1,7]=>[7,1,3,5,8,2,4,6]=>1100000=>0000011
[8,7,4,3,6,2,5,1]=>[1,5,2,6,3,4,7,8]=>0110000=>0000110
[8,6,5,3,7,2,4,1]=>[1,4,2,7,3,5,6,8]=>0110000=>0000110
[7,6,4,3,8,2,5,1]=>[1,5,2,8,3,4,6,7]=>0110000=>0000110
[7,5,4,3,8,2,6,1]=>[1,6,2,8,3,4,5,7]=>0110000=>0000110
[6,4,5,3,8,2,7,1]=>[1,7,2,8,3,5,4,6]=>0111000=>0001110
[7,4,5,3,8,2,6,1]=>[1,6,2,8,3,5,4,7]=>0111000=>0001110
[7,4,6,3,8,2,5,1]=>[1,5,2,8,3,6,4,7]=>0111000=>0001110
[7,5,6,3,8,2,4,1]=>[1,4,2,8,3,6,5,7]=>0110100=>0010110
[8,5,6,3,7,2,4,1]=>[1,4,2,7,3,6,5,8]=>0110100=>0010110
[8,4,6,3,7,2,5,1]=>[1,5,2,7,3,6,4,8]=>0111000=>0001110
[7,4,6,3,5,2,8,1]=>[1,8,2,5,3,6,4,7]=>0111000=>0001110
[8,4,6,3,5,2,7,1]=>[1,7,2,5,3,6,4,8]=>0111000=>0001110
[8,4,7,3,5,2,6,1]=>[1,6,2,5,3,7,4,8]=>0111000=>0001110
[8,5,7,3,4,2,6,1]=>[1,6,2,4,3,7,5,8]=>0110100=>0010110
[7,5,8,4,3,2,6,1]=>[1,6,2,3,4,8,5,7]=>0100100=>0010010
[6,5,8,3,4,2,7,1]=>[1,7,2,4,3,8,5,6]=>0110100=>0010110
[7,5,8,3,4,2,6,1]=>[1,6,2,4,3,8,5,7]=>0110100=>0010110
[7,6,8,3,5,2,4,1]=>[1,4,2,5,3,8,6,7]=>0110010=>0100110
[7,5,8,4,6,2,3,1]=>[1,3,2,6,4,8,5,7]=>0101100=>0011010
[7,5,8,3,6,2,4,1]=>[1,4,2,6,3,8,5,7]=>0110100=>0010110
[7,4,8,3,6,2,5,1]=>[1,5,2,6,3,8,4,7]=>0111000=>0001110
[7,4,8,3,5,2,6,1]=>[1,6,2,5,3,8,4,7]=>0111000=>0001110
[6,4,8,3,5,2,7,1]=>[1,7,2,5,3,8,4,6]=>0111000=>0001110
[6,4,7,3,5,2,8,1]=>[1,8,2,5,3,7,4,6]=>0111000=>0001110
[5,4,7,3,6,2,8,1]=>[1,8,2,6,3,7,4,5]=>0111000=>0001110
[5,4,8,3,7,2,6,1]=>[1,6,2,7,3,8,4,5]=>0111000=>0001110
[6,5,8,3,7,2,4,1]=>[1,4,2,7,3,8,5,6]=>0110100=>0010110
[6,5,8,4,7,2,3,1]=>[1,3,2,7,4,8,5,6]=>0101100=>0011010
[6,5,8,4,7,3,2,1]=>[1,2,3,7,4,8,5,6]=>0001100=>0011000
[6,5,7,3,8,2,4,1]=>[1,4,2,8,3,7,5,6]=>0110100=>0010110
[6,4,7,3,8,2,5,1]=>[1,5,2,8,3,7,4,6]=>0111000=>0001110
[5,4,7,3,8,2,6,1]=>[1,6,2,8,3,7,4,5]=>0111000=>0001110
[5,4,6,3,8,2,7,1]=>[1,7,2,8,3,6,4,5]=>0111000=>0001110
[6,5,3,7,8,2,1,4]=>[4,1,2,8,7,3,5,6]=>1010001=>1000101
[6,5,4,2,8,7,1,3]=>[3,1,7,8,2,4,5,6]=>1100000=>0000011
[6,3,7,8,5,2,1,4]=>[4,1,2,5,8,7,3,6]=>1010001=>1000101
[6,3,2,7,5,4,1,8]=>[8,1,4,5,7,2,3,6]=>1100000=>0000011
[5,8,4,1,2,7,3,6]=>[6,3,7,2,1,4,8,5]=>1110100=>0010111
[5,4,8,1,2,3,7,6]=>[6,7,3,2,1,8,4,5]=>1111000=>0001111
[1,4,7,6,3,2,5,8]=>[8,5,2,3,6,7,4,1]=>1101100=>0011011
[4,8,3,2,7,6,1,5]=>[5,1,6,7,2,3,8,4]=>1101000=>0001011
[5,8,1,7,4,2,3,6]=>[6,3,2,4,7,1,8,5]=>1110100=>0010111
[4,8,6,7,2,3,1,5]=>[5,1,3,2,7,6,8,4]=>1101010=>0101011
[4,8,7,3,6,2,1,5]=>[5,1,2,6,3,7,8,4]=>1011000=>0001101
[1,4,7,3,6,2,5,8]=>[8,5,2,6,3,7,4,1]=>1111100=>0011111
[4,3,2,8,1,7,6,5]=>[5,6,7,1,8,2,3,4]=>1100000=>0000011
[4,7,8,1,2,5,3,6]=>[6,3,5,2,1,8,7,4]=>1111001=>1001111
[4,7,5,1,2,8,3,6]=>[6,3,8,2,1,5,7,4]=>1111000=>0001111
[3,4,2,7,1,6,8,5]=>[5,8,6,1,7,2,4,3]=>1110010=>0100111
[2,3,6,7,4,1,8,5]=>[5,8,1,4,7,6,3,2]=>1110010=>0100111
[2,6,3,4,7,8,1,5]=>[5,1,8,7,4,3,6,2]=>1111001=>1001111
[4,1,3,2,8,7,5,6]=>[6,5,7,8,2,3,1,4]=>1100100=>0010011
[4,3,1,2,8,5,7,6]=>[6,7,5,8,2,1,3,4]=>1100100=>0010011
[3,7,6,8,4,2,1,5]=>[5,1,2,4,8,6,7,3]=>1010010=>0100101
[4,2,8,3,6,1,7,5]=>[5,7,1,6,3,8,2,4]=>1110000=>0000111
[2,4,6,8,3,1,7,5]=>[5,7,1,3,8,6,4,2]=>1101010=>0101011
[3,7,2,4,8,6,1,5]=>[5,1,6,8,4,2,7,3]=>1111000=>0001111
[1,3,6,4,7,2,5,8]=>[8,5,2,7,4,6,3,1]=>1111100=>0011111
[2,4,6,3,8,1,7,5]=>[5,7,1,8,3,6,4,2]=>1111000=>0001111
[2,6,4,3,8,7,1,5]=>[5,1,7,8,3,4,6,2]=>1110000=>0000111
[4,7,1,5,8,2,3,6]=>[6,3,2,8,5,1,7,4]=>1111100=>0011111
[2,4,3,6,1,8,7,5]=>[5,7,8,1,6,3,4,2]=>1110000=>0000111
[3,1,7,4,8,2,5,6]=>[6,5,2,8,4,7,1,3]=>1101100=>0011011
[2,6,7,3,8,4,1,5]=>[5,1,4,8,3,7,6,2]=>1110010=>0100111
[2,6,3,7,4,8,1,5]=>[5,1,8,4,7,3,6,2]=>1111000=>0001111
[1,3,5,7,6,8,2,4]=>[4,2,8,6,7,5,3,1]=>1110110=>0110111
[1,3,5,7,6,2,8,4]=>[4,8,2,6,7,5,3,1]=>1110100=>0010111
[1,3,5,7,2,6,8,4]=>[4,8,6,2,7,5,3,1]=>1110110=>0110111
[1,3,5,2,7,6,8,4]=>[4,8,6,7,2,5,3,1]=>1110010=>0100111
[1,3,5,2,7,6,4,8]=>[8,4,6,7,2,5,3,1]=>1111000=>0001111
[1,3,5,7,6,2,4,8]=>[8,4,2,6,7,5,3,1]=>1111100=>0011111
[1,3,5,7,4,6,8,2]=>[2,8,6,4,7,5,3,1]=>1011110=>0111101
[1,3,5,7,4,6,2,8]=>[8,2,6,4,7,5,3,1]=>1111100=>0011111
[1,3,5,7,4,2,6,8]=>[8,6,2,4,7,5,3,1]=>1110110=>0110111
[1,3,5,4,7,2,6,8]=>[8,6,2,7,4,5,3,1]=>1111010=>0101111
[1,3,5,4,7,8,2,6]=>[6,2,8,7,4,5,3,1]=>1111001=>1001111
[1,3,5,4,7,2,8,6]=>[6,8,2,7,4,5,3,1]=>1111000=>0001111
[1,3,5,7,4,2,8,6]=>[6,8,2,4,7,5,3,1]=>1110100=>0010111
[1,3,5,7,4,8,2,6]=>[6,2,8,4,7,5,3,1]=>1111100=>0011111
[1,3,5,7,4,8,6,2]=>[2,6,8,4,7,5,3,1]=>1011100=>0011101
[1,3,5,7,8,4,6,2]=>[2,6,4,8,7,5,3,1]=>1011101=>1011101
[1,3,5,7,8,4,2,6]=>[6,2,4,8,7,5,3,1]=>1110101=>1010111
[1,3,5,2,7,8,6,4]=>[4,6,8,7,2,5,3,1]=>1110001=>1000111
[1,3,5,7,2,8,6,4]=>[4,6,8,2,7,5,3,1]=>1110100=>0010111
[1,3,5,7,8,2,6,4]=>[4,6,2,8,7,5,3,1]=>1110101=>1010111
[1,3,5,7,8,6,2,4]=>[4,2,6,8,7,5,3,1]=>1110101=>1010111
[2,3,6,1,7,8,5,4]=>[4,5,8,7,1,6,3,2]=>1110001=>1000111
[2,3,6,7,4,8,5,1]=>[1,5,8,4,7,6,3,2]=>0111010=>0101110
[2,3,6,8,4,5,1,7]=>[7,1,5,4,8,6,3,2]=>1111010=>0101111
[2,5,7,3,4,8,6,1]=>[1,6,8,4,3,7,5,2]=>0111100=>0011110
[2,6,7,3,4,8,5,1]=>[1,5,8,4,3,7,6,2]=>0111010=>0101110
[2,5,4,6,7,1,3,8]=>[8,3,1,7,6,4,5,2]=>1111010=>0101111
[5,1,4,6,8,2,3,7]=>[7,3,2,8,6,4,1,5]=>1111010=>0101111
[2,4,6,3,7,5,1,8]=>[8,1,5,7,3,6,4,2]=>1111000=>0001111
[5,3,2,7,4,6,1,8]=>[8,1,6,4,7,2,3,5]=>1101000=>0001011
[3,4,6,1,5,7,2,8]=>[8,2,7,5,1,6,4,3]=>1111100=>0011111
[4,1,2,5,8,3,7,6]=>[6,7,3,8,5,2,1,4]=>1110100=>0010111
[2,4,1,5,8,6,3,7]=>[7,3,6,8,5,1,4,2]=>1110100=>0010111
[4,6,1,2,5,8,3,7]=>[7,3,8,5,2,1,6,4]=>1111100=>0011111
[4,1,7,2,6,5,8,3]=>[3,8,5,6,2,7,1,4]=>1100100=>0010011
[5,6,7,2,1,4,8,3]=>[3,8,4,1,2,7,6,5]=>1001110=>0111001
[6,4,5,7,1,3,8,2]=>[2,8,3,1,7,5,4,6]=>1011100=>0011101
[5,7,6,8,1,4,2,3]=>[3,2,4,1,8,6,7,5]=>1100110=>0110011
[4,1,6,2,8,5,7,3]=>[3,7,5,8,2,6,1,4]=>1100100=>0010011
[6,4,2,1,3,8,7,5]=>[5,7,8,3,1,2,4,6]=>1010000=>0000101
[1,5,8,3,4,6,7,2]=>[2,7,6,4,3,8,5,1]=>1011110=>0111101
[8,1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1,8]=>1111010=>0101111
[8,1,4,7,2,5,3,6]=>[6,3,5,2,7,4,1,8]=>1111000=>0001111
[5,8,2,1,6,7,3,4]=>[4,3,7,6,1,2,8,5]=>1010110=>0110101
[2,6,1,4,7,3,8,5]=>[5,8,3,7,4,1,6,2]=>1111000=>0001111
[2,7,8,4,6,3,1,5]=>[5,1,3,6,4,8,7,2]=>1101001=>1001011
[7,8,2,5,3,6,1,4]=>[4,1,6,3,5,2,8,7]=>1110001=>1000111
[6,3,7,5,1,8,2,4]=>[4,2,8,1,5,7,3,6]=>1110000=>0000111
[7,3,5,2,6,1,8,4]=>[4,8,1,6,2,5,3,7]=>1110000=>0000111
[8,5,2,3,6,1,7,4]=>[4,7,1,6,3,2,5,8]=>1110000=>0000111
[2,8,6,4,3,7,1,5]=>[5,1,7,3,4,6,8,2]=>1110000=>0000111
[5,8,4,6,1,7,2,3]=>[3,2,7,1,6,4,8,5]=>1101100=>0011011
[1,5,8,7,2,6,4,3]=>[3,4,6,2,7,8,5,1]=>1100100=>0010011
[2,5,8,7,3,6,1,4]=>[4,1,6,3,7,8,5,2]=>1110100=>0010111
[4,5,8,7,1,2,6,3]=>[3,6,2,1,7,8,5,4]=>1101100=>0011011
[1,5,8,7,3,2,6,4]=>[4,6,2,3,7,8,5,1]=>1100100=>0010011
[4,5,8,7,3,2,1,6]=>[6,1,2,3,7,8,5,4]=>1001100=>0011001
[2,6,8,3,7,5,1,4]=>[4,1,5,7,3,8,6,2]=>1110010=>0100111
[1,6,8,4,7,2,5,3]=>[3,5,2,7,4,8,6,1]=>1101010=>0101011
[1,6,8,3,7,2,5,4]=>[4,5,2,7,3,8,6,1]=>1110010=>0100111
[2,5,8,1,7,6,4,3]=>[3,4,6,7,1,8,5,2]=>1100100=>0010011
[2,5,8,3,7,6,1,4]=>[4,1,6,7,3,8,5,2]=>1110100=>0010111
[3,2,8,4,7,6,1,5]=>[5,1,6,7,4,8,2,3]=>1101000=>0001011
[1,5,8,4,7,2,6,3]=>[3,6,2,7,4,8,5,1]=>1101100=>0011011
[3,1,8,4,7,2,6,5]=>[5,6,2,7,4,8,1,3]=>1101000=>0001011
[1,6,8,4,2,7,5,3]=>[3,5,7,2,4,8,6,1]=>1100010=>0100011
[1,6,8,2,3,7,5,4]=>[4,5,7,3,2,8,6,1]=>1110010=>0100111
[5,6,8,4,1,2,7,3]=>[3,7,2,1,4,8,6,5]=>1100110=>0110011
[5,6,8,4,3,2,1,7]=>[7,1,2,3,4,8,6,5]=>1000110=>0110001
[7,1,4,8,6,2,5,3]=>[3,5,2,6,8,4,1,7]=>1101000=>0001011
[7,3,4,8,6,2,1,5]=>[5,1,2,6,8,4,3,7]=>1011000=>0001101
[7,1,5,8,2,6,4,3]=>[3,4,6,2,8,5,1,7]=>1100100=>0010011
[7,1,4,8,2,6,5,3]=>[3,5,6,2,8,4,1,7]=>1101000=>0001011
[7,2,4,8,3,6,1,5]=>[5,1,6,3,8,4,2,7]=>1111000=>0001111
[7,4,5,8,1,2,6,3]=>[3,6,2,1,8,5,4,7]=>1101100=>0011011
[7,1,4,8,3,2,6,5]=>[5,6,2,3,8,4,1,7]=>1101000=>0001011
[7,4,5,8,3,2,1,6]=>[6,1,2,3,8,5,4,7]=>1001100=>0011001
[3,6,2,8,7,5,1,4]=>[4,1,5,7,8,2,6,3]=>1110000=>0000111
[1,6,4,8,7,2,5,3]=>[3,5,2,7,8,4,6,1]=>1101000=>0001011
[1,4,5,8,7,2,6,3]=>[3,6,2,7,8,5,4,1]=>1101100=>0011011
[3,1,4,8,7,2,6,5]=>[5,6,2,7,8,4,1,3]=>1101000=>0001011
[1,6,5,8,2,7,4,3]=>[3,4,7,2,8,5,6,1]=>1100100=>0010011
[2,6,5,8,3,7,1,4]=>[4,1,7,3,8,5,6,2]=>1110100=>0010111
[1,6,4,8,2,7,5,3]=>[3,5,7,2,8,4,6,1]=>1101000=>0001011
[4,6,5,8,3,2,1,7]=>[7,1,2,3,8,5,6,4]=>1001100=>0011001
[7,6,2,3,8,5,1,4]=>[4,1,5,8,3,2,6,7]=>1110000=>0000111
[7,6,1,3,8,2,5,4]=>[4,5,2,8,3,1,6,7]=>1110000=>0000111
[7,6,3,4,8,2,1,5]=>[5,1,2,8,4,3,6,7]=>1011000=>0001101
[7,2,5,1,8,6,4,3]=>[3,4,6,8,1,5,2,7]=>1100000=>0000011
[7,2,5,3,8,6,1,4]=>[4,1,6,8,3,5,2,7]=>1110000=>0000111
[7,2,1,4,8,6,5,3]=>[3,5,6,8,4,1,2,7]=>1001000=>0001001
[7,2,3,4,8,6,1,5]=>[5,1,6,8,4,3,2,7]=>1111000=>0001111
[2,6,1,4,8,7,5,3]=>[3,5,7,8,4,1,6,2]=>1101000=>0001011
[2,3,5,4,8,7,1,6]=>[6,1,7,8,4,5,3,2]=>1111000=>0001111
[1,6,5,4,8,2,7,3]=>[3,7,2,8,4,5,6,1]=>1101000=>0001011
[1,6,5,3,8,2,7,4]=>[4,7,2,8,3,5,6,1]=>1110000=>0000111
[1,3,5,4,8,2,7,6]=>[6,7,2,8,4,5,3,1]=>1111000=>0001111
[7,6,5,2,3,8,1,4]=>[4,1,8,3,2,5,6,7]=>1110000=>0000111
[7,6,1,4,2,8,5,3]=>[3,5,8,2,4,1,6,7]=>1100000=>0000011
[7,6,1,2,3,8,5,4]=>[4,5,8,3,2,1,6,7]=>1110000=>0000111
[7,1,5,4,2,8,6,3]=>[3,6,8,2,4,5,1,7]=>1100000=>0000011
[7,1,2,4,3,8,6,5]=>[5,6,8,3,4,2,1,7]=>1110000=>0000111
[1,6,2,4,3,8,7,5]=>[5,7,8,3,4,2,6,1]=>1110000=>0000111
[2,6,5,4,3,8,1,7]=>[7,1,8,3,4,5,6,2]=>1110000=>0000111
[7,6,5,1,3,2,8,4]=>[4,8,2,3,1,5,6,7]=>1100000=>0000011
[7,2,1,8,6,5,4,3]=>[3,4,5,6,8,1,2,7]=>1000000=>0000001
[7,3,8,6,5,4,2,1]=>[1,2,4,5,6,8,3,7]=>0010000=>0000100
[4,8,5,7,6,3,2,1]=>[1,2,3,6,7,5,8,4]=>0001100=>0011000
[3,5,7,2,4,6,8,1]=>[1,8,6,4,2,7,5,3]=>0111110=>0111110
[5,2,4,6,8,1,3,7]=>[7,3,1,8,6,4,2,5]=>1111010=>0101111
[4,3,5,7,2,8,1,6]=>[6,1,8,2,7,5,3,4]=>1110100=>0010111
[5,7,1,3,4,8,2,6]=>[6,2,8,4,3,1,7,5]=>1111100=>0011111
[5,7,1,3,4,6,8,2]=>[2,8,6,4,3,1,7,5]=>1011110=>0111101
[4,6,3,5,1,7,8,2]=>[2,8,7,1,5,3,6,4]=>1011001=>1001101
[4,6,3,5,7,2,8,1]=>[1,8,2,7,5,3,6,4]=>0111100=>0011110
[3,5,6,4,1,7,8,2]=>[2,8,7,1,4,6,5,3]=>1010101=>1010101
[1,6,7,3,4,5,8,2]=>[2,8,5,4,3,7,6,1]=>1011110=>0111101
[2,6,7,4,5,8,1,3]=>[3,1,8,5,4,7,6,2]=>1101110=>0111011
[1,4,6,7,3,8,2,5]=>[5,2,8,3,7,6,4,1]=>1111010=>0101111
[5,3,6,1,2,7,8,4]=>[4,8,7,2,1,6,3,5]=>1110001=>1000111
[3,5,2,6,7,4,8,1]=>[1,8,4,7,6,2,5,3]=>0111010=>0101110
[5,2,6,1,3,7,8,4]=>[4,8,7,3,1,6,2,5]=>1110001=>1000111
[6,3,1,7,8,2,4,5]=>[5,4,2,8,7,1,3,6]=>1101001=>1001011
[5,7,2,8,1,3,4,6]=>[6,4,3,1,8,2,7,5]=>1111100=>0011111
[4,2,6,7,3,5,8,1]=>[1,8,5,3,7,6,2,4]=>0110110=>0110110
[3,5,7,2,8,1,4,6]=>[6,4,1,8,2,7,5,3]=>1111100=>0011111
[3,7,2,4,6,8,1,5]=>[5,1,8,6,4,2,7,3]=>1111010=>0101111
[3,5,7,2,6,8,1,4]=>[4,1,8,6,2,7,5,3]=>1110110=>0110111
[6,3,5,7,2,8,1,4]=>[4,1,8,2,7,5,3,6]=>1110100=>0010111
[6,3,5,7,2,4,8,1]=>[1,8,4,2,7,5,3,6]=>0111100=>0011110
[6,2,4,5,1,7,8,3]=>[3,8,7,1,5,4,2,6]=>1101001=>1001011
[2,4,6,7,1,5,8,3]=>[3,8,5,1,7,6,4,2]=>1101110=>0111011
[2,4,7,1,5,6,8,3]=>[3,8,6,5,1,7,4,2]=>1101110=>0111011
[3,7,1,5,6,8,2,4]=>[4,2,8,6,5,1,7,3]=>1110110=>0110111
[2,6,7,5,8,1,3,4]=>[4,3,1,8,5,7,6,2]=>1110110=>0110111
[1,5,6,7,2,4,8,3]=>[3,8,4,2,7,6,5,1]=>1101110=>0111011
[5,6,2,4,1,7,8,3]=>[3,8,7,1,4,2,6,5]=>1100101=>1010011
[1,5,4,6,2,7,8,3]=>[3,8,7,2,6,4,5,1]=>1101001=>1001011
[6,4,5,1,2,7,8,3]=>[3,8,7,2,1,5,4,6]=>1101001=>1001011
[5,4,6,3,1,7,8,2]=>[2,8,7,1,3,6,4,5]=>1001001=>1001001
[8,4,5,2,6,1,3,7]=>[7,3,1,6,2,5,4,8]=>1111000=>0001111
[6,4,3,7,2,5,8,1]=>[1,8,5,2,7,3,4,6]=>0110100=>0010110
[6,4,3,7,2,8,1,5]=>[5,1,8,2,7,3,4,6]=>1110000=>0000111
[7,4,5,3,1,6,8,2]=>[2,8,6,1,3,5,4,7]=>1001010=>0101001
[6,4,3,7,5,1,8,2]=>[2,8,1,5,7,3,4,6]=>1010000=>0000101
[6,7,3,4,1,5,8,2]=>[2,8,5,1,4,3,7,6]=>1010110=>0110101
[6,7,4,2,1,5,8,3]=>[3,8,5,1,2,4,7,6]=>1000110=>0110001
[6,7,4,2,1,8,3,5]=>[5,3,8,1,2,4,7,6]=>1010010=>0100101
[5,6,7,3,1,8,2,4]=>[4,2,8,1,3,7,6,5]=>1100110=>0110011
[5,6,7,2,3,8,1,4]=>[4,1,8,3,2,7,6,5]=>1110110=>0110111
[6,7,3,2,4,8,1,5]=>[5,1,8,4,2,3,7,6]=>1101010=>0101011
[6,7,3,2,8,1,4,5]=>[5,4,1,8,2,3,7,6]=>1101010=>0101011
[7,6,3,4,1,2,8,5]=>[5,8,2,1,4,3,6,7]=>1110000=>0000111
[7,6,3,2,4,1,8,5]=>[5,8,1,4,2,3,6,7]=>1100000=>0000011
[7,5,3,2,6,1,8,4]=>[4,8,1,6,2,3,5,7]=>1100000=>0000011
[6,7,3,2,5,1,8,4]=>[4,8,1,5,2,3,7,6]=>1100010=>0100011
[6,5,3,2,7,8,1,4]=>[4,1,8,7,2,3,5,6]=>1100001=>1000011
[6,4,5,2,7,3,8,1]=>[1,8,3,7,2,5,4,6]=>0111000=>0001110
[6,4,7,2,5,1,8,3]=>[3,8,1,5,2,7,4,6]=>1101000=>0001011
[7,4,5,6,1,2,8,3]=>[3,8,2,1,6,5,4,7]=>1101100=>0011011
[7,5,6,2,1,3,8,4]=>[4,8,3,1,2,6,5,7]=>1010100=>0010101
[6,4,7,5,1,2,8,3]=>[3,8,2,1,5,7,4,6]=>1101000=>0001011
[5,6,4,2,7,8,1,3]=>[3,1,8,7,2,4,6,5]=>1100101=>1010011
[5,6,4,2,7,3,8,1]=>[1,8,3,7,2,4,6,5]=>0110100=>0010110
[6,4,5,7,1,8,2,3]=>[3,2,8,1,7,5,4,6]=>1101100=>0011011
[6,5,3,7,1,8,2,4]=>[4,2,8,1,7,3,5,6]=>1110000=>0000111
[6,5,7,2,1,8,3,4]=>[4,3,8,1,2,7,5,6]=>1010100=>0010101
[5,7,8,3,6,4,1,2]=>[2,1,4,6,3,8,7,5]=>1010101=>1010101
[3,7,8,5,6,1,4,2]=>[2,4,1,6,5,8,7,3]=>1010101=>1010101
[1,7,8,5,6,3,4,2]=>[2,4,3,6,5,8,7,1]=>1010101=>1010101
[1,7,5,8,6,3,4,2]=>[2,4,3,6,8,5,7,1]=>1010100=>0010101
[3,7,5,8,6,1,4,2]=>[2,4,1,6,8,5,7,3]=>1010100=>0010101
[3,7,5,8,6,4,1,2]=>[2,1,4,6,8,5,7,3]=>1010100=>0010101
[5,7,3,8,6,4,1,2]=>[2,1,4,6,8,3,7,5]=>1010100=>0010101
[7,3,8,5,6,4,1,2]=>[2,1,4,6,5,8,3,7]=>1010100=>0010101
[7,3,5,8,6,4,1,2]=>[2,1,4,6,8,5,3,7]=>1010100=>0010101
[5,3,7,8,6,4,1,2]=>[2,1,4,6,8,7,3,5]=>1010001=>1000101
[3,5,7,8,6,4,1,2]=>[2,1,4,6,8,7,5,3]=>1010101=>1010101
[1,5,7,8,6,3,4,2]=>[2,4,3,6,8,7,5,1]=>1010101=>1010101
[1,5,7,8,3,6,4,2]=>[2,4,6,3,8,7,5,1]=>1010101=>1010101
[3,5,7,8,1,6,4,2]=>[2,4,6,1,8,7,5,3]=>1010101=>1010101
[5,3,7,8,1,6,4,2]=>[2,4,6,1,8,7,3,5]=>1010001=>1000101
[5,3,7,8,6,1,4,2]=>[2,4,1,6,8,7,3,5]=>1010001=>1000101
[7,3,5,8,6,1,4,2]=>[2,4,1,6,8,5,3,7]=>1010100=>0010101
[7,3,8,5,6,1,4,2]=>[2,4,1,6,5,8,3,7]=>1010100=>0010101
[7,8,3,5,6,1,4,2]=>[2,4,1,6,5,3,8,7]=>1010101=>1010101
[7,8,1,5,6,3,4,2]=>[2,4,3,6,5,1,8,7]=>1010101=>1010101
[7,1,8,5,6,3,4,2]=>[2,4,3,6,5,8,1,7]=>1010100=>0010101
[7,1,5,8,6,3,4,2]=>[2,4,3,6,8,5,1,7]=>1010100=>0010101
[5,1,7,8,6,3,4,2]=>[2,4,3,6,8,7,1,5]=>1010001=>1000101
[5,1,7,8,3,6,4,2]=>[2,4,6,3,8,7,1,5]=>1010001=>1000101
[3,1,7,8,5,6,4,2]=>[2,4,6,5,8,7,1,3]=>1000101=>1010001
[1,3,7,8,5,6,4,2]=>[2,4,6,5,8,7,3,1]=>1010101=>1010101
[3,1,7,5,8,6,4,2]=>[2,4,6,8,5,7,1,3]=>1000100=>0010001
[5,1,7,3,8,6,4,2]=>[2,4,6,8,3,7,1,5]=>1010000=>0000101
[7,1,5,3,8,6,4,2]=>[2,4,6,8,3,5,1,7]=>1010000=>0000101
[7,1,5,8,3,6,4,2]=>[2,4,6,3,8,5,1,7]=>1010100=>0010101
[7,8,1,5,3,6,4,2]=>[2,4,6,3,5,1,8,7]=>1010001=>1000101
[7,8,3,5,1,6,4,2]=>[2,4,6,1,5,3,8,7]=>1010001=>1000101
[7,3,8,5,1,6,4,2]=>[2,4,6,1,5,8,3,7]=>1010000=>0000101
[7,3,5,8,1,6,4,2]=>[2,4,6,1,8,5,3,7]=>1010100=>0010101
[7,3,5,1,8,6,4,2]=>[2,4,6,8,1,5,3,7]=>1010000=>0000101
[5,3,7,1,8,6,4,2]=>[2,4,6,8,1,7,3,5]=>1010000=>0000101
[3,5,7,1,8,6,4,2]=>[2,4,6,8,1,7,5,3]=>1010100=>0010101
[1,5,7,3,8,6,4,2]=>[2,4,6,8,3,7,5,1]=>1010100=>0010101
[1,7,5,3,8,6,4,2]=>[2,4,6,8,3,5,7,1]=>1010000=>0000101
[3,7,5,1,8,6,4,2]=>[2,4,6,8,1,5,7,3]=>1010000=>0000101
[5,7,3,1,8,6,4,2]=>[2,4,6,8,1,3,7,5]=>1000100=>0010001
[5,7,3,8,6,1,4,2]=>[2,4,1,6,8,3,7,5]=>1010100=>0010101
[3,7,5,8,1,6,4,2]=>[2,4,6,1,8,5,7,3]=>1010100=>0010101
[1,7,5,8,3,6,4,2]=>[2,4,6,3,8,5,7,1]=>1010100=>0010101
[1,7,8,5,3,6,4,2]=>[2,4,6,3,5,8,7,1]=>1010001=>1000101
[3,7,8,5,1,6,4,2]=>[2,4,6,1,5,8,7,3]=>1010001=>1000101
[5,7,8,3,6,1,4,2]=>[2,4,1,6,3,8,7,5]=>1010101=>1010101
[5,7,8,6,3,1,4,2]=>[2,4,1,3,6,8,7,5]=>1000101=>1010001
[7,5,8,6,1,3,4,2]=>[2,4,3,1,6,8,5,7]=>1010100=>0010101
[5,7,8,1,6,3,4,2]=>[2,4,3,6,1,8,7,5]=>1010101=>1010101
[5,7,8,1,3,6,4,2]=>[2,4,6,3,1,8,7,5]=>1010101=>1010101
[3,7,8,1,5,6,4,2]=>[2,4,6,5,1,8,7,3]=>1010101=>1010101
[1,7,8,3,5,6,4,2]=>[2,4,6,5,3,8,7,1]=>1010101=>1010101
[1,7,3,8,5,6,4,2]=>[2,4,6,5,8,3,7,1]=>1010100=>0010101
[3,7,1,8,5,6,4,2]=>[2,4,6,5,8,1,7,3]=>1010100=>0010101
[5,7,1,8,3,6,4,2]=>[2,4,6,3,8,1,7,5]=>1010100=>0010101
[5,7,1,8,6,3,4,2]=>[2,4,3,6,8,1,7,5]=>1010100=>0010101
[7,5,1,8,6,3,4,2]=>[2,4,3,6,8,1,5,7]=>1010000=>0000101
[7,5,8,1,6,3,4,2]=>[2,4,3,6,1,8,5,7]=>1010100=>0010101
[7,8,5,1,6,3,4,2]=>[2,4,3,6,1,5,8,7]=>1010001=>1000101
[7,8,5,1,3,6,4,2]=>[2,4,6,3,1,5,8,7]=>1010001=>1000101
[7,5,8,1,3,6,4,2]=>[2,4,6,3,1,8,5,7]=>1010100=>0010101
[7,5,1,8,3,6,4,2]=>[2,4,6,3,8,1,5,7]=>1010000=>0000101
[7,5,1,3,8,6,4,2]=>[2,4,6,8,3,1,5,7]=>1010000=>0000101
[5,7,1,3,8,6,4,2]=>[2,4,6,8,3,1,7,5]=>1010100=>0010101
[3,7,1,5,8,6,4,2]=>[2,4,6,8,5,1,7,3]=>1010100=>0010101
[1,7,3,5,8,6,4,2]=>[2,4,6,8,5,3,7,1]=>1010100=>0010101
[1,5,3,7,8,6,4,2]=>[2,4,6,8,7,3,5,1]=>1010001=>1000101
[3,5,1,7,8,6,4,2]=>[2,4,6,8,7,1,5,3]=>1010001=>1000101
[5,3,1,7,8,6,4,2]=>[2,4,6,8,7,1,3,5]=>1000001=>1000001
[7,3,1,5,8,6,4,2]=>[2,4,6,8,5,1,3,7]=>1000100=>0010001
[7,3,1,8,5,6,4,2]=>[2,4,6,5,8,1,3,7]=>1000100=>0010001
[7,3,8,1,5,6,4,2]=>[2,4,6,5,1,8,3,7]=>1010100=>0010101
[7,8,3,1,5,6,4,2]=>[2,4,6,5,1,3,8,7]=>1000101=>1010001
[7,8,1,3,5,6,4,2]=>[2,4,6,5,3,1,8,7]=>1010101=>1010101
[7,1,8,3,5,6,4,2]=>[2,4,6,5,3,8,1,7]=>1010100=>0010101
[7,1,3,8,5,6,4,2]=>[2,4,6,5,8,3,1,7]=>1010100=>0010101
[7,1,3,5,8,6,4,2]=>[2,4,6,8,5,3,1,7]=>1010100=>0010101
[5,1,3,7,8,6,4,2]=>[2,4,6,8,7,3,1,5]=>1010001=>1000101
[3,1,5,7,8,6,4,2]=>[2,4,6,8,7,5,1,3]=>1000101=>1010001
[4,3,1,2,6,5,8,7]=>[7,8,5,6,2,1,3,4]=>1100100=>0010011
[5,4,7,8,6,1,3,2]=>[2,3,1,6,8,7,4,5]=>1001001=>1001001
[7,5,6,2,8,3,1,4]=>[4,1,3,8,2,6,5,7]=>1100100=>0010011
[4,6,3,5,1,2,8,7]=>[7,8,2,1,5,3,6,4]=>1111000=>0001111
[2,3,6,1,5,4,8,7]=>[7,8,4,5,1,6,3,2]=>1111000=>0001111
[2,1,6,5,3,4,8,7]=>[7,8,4,3,5,6,1,2]=>1011000=>0001101
[3,5,6,2,4,1,8,7]=>[7,8,1,4,2,6,5,3]=>1110100=>0010111
[8,7,6,1,3,2,4,5]=>[5,4,2,3,1,6,7,8]=>1101000=>0001011
[2,5,3,4,8,1,7,6]=>[6,7,1,8,4,3,5,2]=>1111000=>0001111
[5,4,7,6,2,8,1,3]=>[3,1,8,2,6,7,4,5]=>1101000=>0001011
[3,7,8,1,5,4,6,2]=>[2,6,4,5,1,8,7,3]=>1011001=>1001101
[5,8,7,1,4,6,2,3]=>[3,2,6,4,1,7,8,5]=>1101100=>0011011
[4,7,6,1,8,3,5,2]=>[2,5,3,8,1,6,7,4]=>1011000=>0001101
[2,1,6,8,5,7,3,4]=>[4,3,7,5,8,6,1,2]=>1010110=>0110101
[4,7,8,6,3,1,2,5]=>[5,2,1,3,6,8,7,4]=>1101001=>1001011
[8,2,3,5,7,1,6,4]=>[4,6,1,7,5,3,2,8]=>1110100=>0010111
[2,8,3,6,7,5,1,4]=>[4,1,5,7,6,3,8,2]=>1110010=>0100111
[6,8,4,2,1,3,7,5]=>[5,7,3,1,2,4,8,6]=>1010010=>0100101
[4,3,8,2,7,6,1,5]=>[5,1,6,7,2,8,3,4]=>1110000=>0000111
[2,1,4,5,8,3,7,6]=>[6,7,3,8,5,4,1,2]=>1011100=>0011101
[8,4,7,1,5,2,3,6]=>[6,3,2,5,1,7,4,8]=>1111000=>0001111
[7,3,5,8,4,2,1,6]=>[6,1,2,4,8,5,3,7]=>1010100=>0010101
[2,4,8,3,5,6,7,1]=>[1,7,6,5,3,8,4,2]=>0111110=>0111110
[6,4,7,5,2,3,8,1]=>[1,8,3,2,5,7,4,6]=>0111000=>0001110
[6,4,8,1,7,3,2,5]=>[5,2,3,7,1,8,4,6]=>1101000=>0001011
[2,1,4,3,8,7,5,6]=>[6,5,7,8,3,4,1,2]=>1010100=>0010101
[4,3,1,2,8,6,7,5]=>[5,7,6,8,2,1,3,4]=>1100010=>0100011
[7,6,8,1,3,5,2,4]=>[4,2,5,3,1,8,6,7]=>1110010=>0100111
[5,1,6,7,8,4,3,2]=>[2,3,4,8,7,6,1,5]=>1000011=>1100001
[6,7,5,2,3,1,8,4]=>[4,8,1,3,2,5,7,6]=>1100010=>0100011
[4,7,2,6,5,1,8,3]=>[3,8,1,5,6,2,7,4]=>1101000=>0001011
[6,4,2,1,8,5,7,3]=>[3,7,5,8,1,2,4,6]=>1000100=>0010001
[2,1,5,7,8,4,6,3]=>[3,6,4,8,7,5,1,2]=>1001101=>1011001
[2,5,7,8,3,6,1,4]=>[4,1,6,3,8,7,5,2]=>1110101=>1010111
[6,8,3,4,2,1,7,5]=>[5,7,1,2,4,3,8,6]=>1010010=>0100101
[4,2,6,1,5,7,8,3]=>[3,8,7,5,1,6,2,4]=>1100101=>1010011
[7,1,4,8,3,5,6,2]=>[2,6,5,3,8,4,1,7]=>1011100=>0011101
[6,5,3,8,4,7,1,2]=>[2,1,7,4,8,3,5,6]=>1011000=>0001101
[1,6,3,7,5,8,4,2]=>[2,4,8,5,7,3,6,1]=>1010100=>0010101
[1,3,7,4,5,8,6,2]=>[2,6,8,5,4,7,3,1]=>1011100=>0011101
[7,3,8,5,4,6,1,2]=>[2,1,6,4,5,8,3,7]=>1011000=>0001101
[3,4,8,5,6,7,1,2]=>[2,1,7,6,5,8,4,3]=>1011110=>0111101
[4,7,3,8,5,6,1,2]=>[2,1,6,5,8,3,7,4]=>1011100=>0011101
[1,7,6,5,3,8,4,2]=>[2,4,8,3,5,6,7,1]=>1010000=>0000101
[1,6,5,2,8,3,7,4]=>[4,7,3,8,2,5,6,1]=>1110000=>0000111
[8,6,5,2,1,4,3,7]=>[7,3,4,1,2,5,6,8]=>1010000=>0000101
[2,7,6,3,1,4,5,8]=>[8,5,4,1,3,6,7,2]=>1101100=>0011011
[2,7,6,4,5,1,3,8]=>[8,3,1,5,4,6,7,2]=>1111000=>0001111
[5,7,2,6,4,1,3,8]=>[8,3,1,4,6,2,7,5]=>1110100=>0010111
[6,1,3,7,5,8,4,2]=>[2,4,8,5,7,3,1,6]=>1010100=>0010101
[2,1,7,4,8,6,3,5]=>[5,3,6,8,4,7,1,2]=>1011000=>0001101
[1,8,2,7,3,6,5,4]=>[4,5,6,3,7,2,8,1]=>1110000=>0000111
[2,1,3,8,4,7,5,6]=>[6,5,7,4,8,3,1,2]=>1011100=>0011101
[3,1,2,8,4,6,7,5]=>[5,7,6,4,8,2,1,3]=>1101010=>0101011
[5,1,2,4,8,3,7,6]=>[6,7,3,8,4,2,1,5]=>1111000=>0001111
[2,8,4,1,5,6,3,7]=>[7,3,6,5,1,4,8,2]=>1110100=>0010111
[1,7,2,8,5,3,6,4]=>[4,6,3,5,8,2,7,1]=>1110000=>0000111
[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>1111100=>0011111
[8,2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2,8]=>1101100=>0011011
[2,4,8,3,1,5,6,7]=>[7,6,5,1,3,8,4,2]=>1101110=>0111011
[3,2,5,6,1,4,7,8]=>[8,7,4,1,6,5,2,3]=>1101101=>1011011
[4,7,3,8,2,1,5,6]=>[6,5,1,2,8,3,7,4]=>1011100=>0011101
[7,4,8,3,2,1,5,6]=>[6,5,1,2,3,8,4,7]=>1001100=>0011001
[5,2,7,3,1,4,6,8]=>[8,6,4,1,3,7,2,5]=>1101010=>0101011
[8,3,7,2,1,5,4,6]=>[6,4,5,1,2,7,3,8]=>1011000=>0001101
[1,3,7,2,8,4,6,5]=>[5,6,4,8,2,7,3,1]=>1111000=>0001111
[6,5,3,8,2,1,4,7]=>[7,4,1,2,8,3,5,6]=>1011000=>0001101
[5,4,6,2,7,1,3,8]=>[8,3,1,7,2,6,4,5]=>1111000=>0001111
[7,6,8,5,1,4,3,2]=>[2,3,4,1,5,8,6,7]=>1000010=>0100001
[7,6,2,1,8,5,3,4]=>[4,3,5,8,1,2,6,7]=>1010000=>0000101
[1,7,5,8,6,4,3,2]=>[2,3,4,6,8,5,7,1]=>1000100=>0010001
[6,5,1,2,8,3,7,4]=>[4,7,3,8,2,1,5,6]=>1110000=>0000111
[6,8,4,1,3,7,5,2]=>[2,5,7,3,1,4,8,6]=>1010010=>0100101
[6,5,7,1,3,8,4,2]=>[2,4,8,3,1,7,5,6]=>1010100=>0010101
[6,3,7,1,8,4,5,2]=>[2,5,4,8,1,7,3,6]=>1011000=>0001101
[5,8,3,1,7,4,6,2]=>[2,6,4,7,1,3,8,5]=>1001100=>0011001
[4,7,1,2,8,3,6,5]=>[5,6,3,8,2,1,7,4]=>1111000=>0001111
[3,4,1,8,5,6,7,2]=>[2,7,6,5,8,1,4,3]=>1010110=>0110101
[8,3,1,7,5,4,6,2]=>[2,6,4,5,7,1,3,8]=>1001000=>0001001
[2,3,1,8,7,4,5,6]=>[6,5,4,7,8,1,3,2]=>1101100=>0011011
[2,6,1,4,8,7,3,5]=>[5,3,7,8,4,1,6,2]=>1111000=>0001111
[6,2,7,1,8,5,3,4]=>[4,3,5,8,1,7,2,6]=>1110000=>0000111
[1,2,3,4,8,7,5,6]=>[6,5,7,8,4,3,2,1]=>1111100=>0011111
[1,2,3,8,6,4,5,7]=>[7,5,4,6,8,3,2,1]=>1111100=>0011111
[2,4,7,5,6,8,3,1]=>[1,3,8,6,5,7,4,2]=>0101110=>0111010
[2,8,5,7,4,6,3,1]=>[1,3,6,4,7,5,8,2]=>0101100=>0011010
[3,1,8,5,7,4,2,6]=>[6,2,4,7,5,8,1,3]=>1100100=>0010011
[8,3,5,7,4,2,6,1]=>[1,6,2,4,7,5,3,8]=>0110100=>0010110
[2,7,5,8,4,6,3,1]=>[1,3,6,4,8,5,7,2]=>0101100=>0011010
[2,7,6,4,5,8,3,1]=>[1,3,8,5,4,6,7,2]=>0101100=>0011010
[4,1,7,6,2,3,5,8]=>[8,5,3,2,6,7,1,4]=>1110100=>0010111
[3,1,7,6,4,5,2,8]=>[8,2,5,4,6,7,1,3]=>1101000=>0001011
[3,1,6,8,7,5,2,4]=>[4,2,5,7,8,6,1,3]=>1100010=>0100011
[6,3,8,7,5,2,4,1]=>[1,4,2,5,7,8,3,6]=>0110000=>0000110
[7,3,5,8,4,2,6,1]=>[1,6,2,4,8,5,3,7]=>0110100=>0010110
[7,8,3,6,2,5,4,1]=>[1,4,5,2,6,3,8,7]=>0110001=>1000110
[7,4,8,2,1,6,3,5]=>[5,3,6,1,2,8,4,7]=>1011000=>0001101
[7,8,5,2,1,4,3,6]=>[6,3,4,1,2,5,8,7]=>1010001=>1000101
[7,4,6,2,3,8,1,5]=>[5,1,8,3,2,6,4,7]=>1111000=>0001111
[6,4,2,5,8,3,7,1]=>[1,7,3,8,5,2,4,6]=>0110100=>0010110
[5,7,1,3,4,6,2,8]=>[8,2,6,4,3,1,7,5]=>1111100=>0011111
[5,7,1,4,2,3,6,8]=>[8,6,3,2,4,1,7,5]=>1110110=>0110111
[5,8,1,3,2,4,6,7]=>[7,6,4,2,3,1,8,5]=>1101110=>0111011
[5,6,1,2,4,3,8,7]=>[7,8,3,4,2,1,6,5]=>1110100=>0010111
[3,6,8,1,2,7,5,4]=>[4,5,7,2,1,8,6,3]=>1110010=>0100111
[8,4,6,2,1,3,7,5]=>[5,7,3,1,2,6,4,8]=>1011000=>0001101
[5,4,8,7,2,3,6,1]=>[1,6,3,2,7,8,4,5]=>0111000=>0001110
[5,4,8,7,3,1,2,6]=>[6,2,1,3,7,8,4,5]=>1101000=>0001011
[6,4,3,8,1,5,2,7]=>[7,2,5,1,8,3,4,6]=>1110000=>0000111
[6,8,3,7,2,5,4,1]=>[1,4,5,2,7,3,8,6]=>0110010=>0100110
[5,3,6,8,7,2,4,1]=>[1,4,2,7,8,6,3,5]=>0110010=>0100110
[5,4,6,8,2,3,7,1]=>[1,7,3,2,8,6,4,5]=>0111010=>0101110
[6,4,7,2,1,8,3,5]=>[5,3,8,1,2,7,4,6]=>1011000=>0001101
[6,5,3,4,1,2,8,7]=>[7,8,2,1,4,3,5,6]=>1110000=>0000111
[6,8,5,4,1,3,2,7]=>[7,2,3,1,4,5,8,6]=>1100010=>0100011
[6,5,3,1,4,7,2,8]=>[8,2,7,4,1,3,5,6]=>1101000=>0001011
[3,6,7,8,2,5,1,4]=>[4,1,5,2,8,7,6,3]=>1110011=>1100111
[5,7,8,2,6,4,1,3]=>[3,1,4,6,2,8,7,5]=>1100101=>1010011
[2,6,8,4,5,7,1,3]=>[3,1,7,5,4,8,6,2]=>1101110=>0111011
[1,7,4,8,6,2,3,5]=>[5,3,2,6,8,4,7,1]=>1111000=>0001111
[6,3,7,2,8,5,1,4]=>[4,1,5,8,2,7,3,6]=>1110000=>0000111
[5,2,7,4,6,8,1,3]=>[3,1,8,6,4,7,2,5]=>1101010=>0101011
[6,1,3,8,2,7,4,5]=>[5,4,7,2,8,3,1,6]=>1111000=>0001111
[2,7,1,4,3,8,5,6]=>[6,5,8,3,4,1,7,2]=>1110100=>0010111
[6,2,7,3,1,5,8,4]=>[4,8,5,1,3,7,2,6]=>1100100=>0010011
[6,3,4,1,8,5,7,2]=>[2,7,5,8,1,4,3,6]=>1010100=>0010101
[5,6,3,1,7,8,4,2]=>[2,4,8,7,1,3,6,5]=>1000101=>1010001
[5,6,3,2,1,8,7,4]=>[4,7,8,1,2,3,6,5]=>1000100=>0010001
[4,5,3,2,7,1,8,6]=>[6,8,1,7,2,3,5,4]=>1101000=>0001011
[6,4,2,8,5,1,7,3]=>[3,7,1,5,8,2,4,6]=>1100000=>0000011
[3,6,4,8,1,5,7,2]=>[2,7,5,1,8,4,6,3]=>1011100=>0011101
[1,8,4,7,2,5,3,6]=>[6,3,5,2,7,4,8,1]=>1111000=>0001111
[3,5,7,4,1,6,8,2]=>[2,8,6,1,4,7,5,3]=>1010110=>0110101
[4,5,8,3,1,7,6,2]=>[2,6,7,1,3,8,5,4]=>1001100=>0011001
[3,4,7,8,2,1,6,5]=>[5,6,1,2,8,7,4,3]=>1011001=>1001101
[4,6,3,5,2,1,8,7]=>[7,8,1,2,5,3,6,4]=>1011000=>0001101
[4,7,1,8,2,6,3,5]=>[5,3,6,2,8,1,7,4]=>1111000=>0001111
[6,3,1,8,5,2,4,7]=>[7,4,2,5,8,1,3,6]=>1101000=>0001011
[3,5,2,1,8,4,6,7]=>[7,6,4,8,1,2,5,3]=>1011010=>0101101
[3,6,2,1,4,7,5,8]=>[8,5,7,4,1,2,6,3]=>1011100=>0011101
[7,4,1,2,8,6,3,5]=>[5,3,6,8,2,1,4,7]=>1110000=>0000111
[4,2,7,6,5,8,1,3]=>[3,1,8,5,6,7,2,4]=>1100100=>0010011
[7,3,8,1,5,4,6,2]=>[2,6,4,5,1,8,3,7]=>1011000=>0001101
[7,2,8,6,5,1,3,4]=>[4,3,1,5,6,8,2,7]=>1110000=>0000111
[6,2,7,8,5,4,1,3]=>[3,1,4,5,8,7,2,6]=>1100001=>1000011
[5,3,2,6,7,4,1,8]=>[8,1,4,7,6,2,3,5]=>1100010=>0100011
[4,8,2,6,5,7,1,3]=>[3,1,7,5,6,2,8,4]=>1101100=>0011011
[3,8,7,6,2,4,1,5]=>[5,1,4,2,6,7,8,3]=>1110000=>0000111
[3,7,1,6,5,2,4,8]=>[8,4,2,5,6,1,7,3]=>1111000=>0001111
[2,7,1,3,6,5,4,8]=>[8,4,5,6,3,1,7,2]=>1111000=>0001111
[5,7,1,4,6,3,2,8]=>[8,2,3,6,4,1,7,5]=>1101100=>0011011
[6,3,7,1,5,4,2,8]=>[8,2,4,5,1,7,3,6]=>1110000=>0000111
[1,4,8,2,7,6,3,5]=>[5,3,6,7,2,8,4,1]=>1111000=>0001111
[4,7,3,5,1,8,6,2]=>[2,6,8,1,5,3,7,4]=>1011000=>0001101
[8,7,3,6,1,5,4,2]=>[2,4,5,1,6,3,7,8]=>1010000=>0000101
[2,5,8,7,4,6,1,3]=>[3,1,6,4,7,8,5,2]=>1101100=>0011011
[5,7,8,3,2,1,4,6]=>[6,4,1,2,3,8,7,5]=>1001101=>1011001
[8,3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3,8]=>1001000=>0001001
[8,5,4,1,7,3,6,2]=>[2,6,3,7,1,4,5,8]=>1010000=>0000101
[1,7,5,3,8,2,6,4]=>[4,6,2,8,3,5,7,1]=>1110000=>0000111
[5,1,7,4,2,8,6,3]=>[3,6,8,2,4,7,1,5]=>1100000=>0000011
[8,6,3,2,7,5,1,4]=>[4,1,5,7,2,3,6,8]=>1100000=>0000011
[2,7,5,1,3,8,6,4]=>[4,6,8,3,1,5,7,2]=>1110000=>0000111
[8,7,4,2,6,1,5,3]=>[3,5,1,6,2,4,7,8]=>1100000=>0000011
[5,2,6,1,8,7,4,3]=>[3,4,7,8,1,6,2,5]=>1100000=>0000011
[1,3,8,2,4,7,6,5]=>[5,6,7,4,2,8,3,1]=>1111000=>0001111
[3,7,2,4,8,6,5,1]=>[1,5,6,8,4,2,7,3]=>0111000=>0001110
[3,4,2,8,7,6,1,5]=>[5,1,6,7,8,2,4,3]=>1110000=>0000111
[6,7,2,5,8,4,3,1]=>[1,3,4,8,5,2,7,6]=>0100110=>0110010
[5,3,1,7,8,4,2,6]=>[6,2,4,8,7,1,3,5]=>1100001=>1000011
[2,7,6,4,1,3,8,5]=>[5,8,3,1,4,6,7,2]=>1110000=>0000111
[6,3,1,7,5,2,8,4]=>[4,8,2,5,7,1,3,6]=>1100000=>0000011
[6,2,7,5,3,1,8,4]=>[4,8,1,3,5,7,2,6]=>1100000=>0000011
[1,5,8,2,7,4,6,3]=>[3,6,4,7,2,8,5,1]=>1101100=>0011011
[5,7,3,1,8,4,6,2]=>[2,6,4,8,1,3,7,5]=>1001100=>0011001
[8,4,7,3,1,6,5,2]=>[2,5,6,1,3,7,4,8]=>1001000=>0001001
[6,5,2,1,7,4,8,3]=>[3,8,4,7,1,2,5,6]=>1001000=>0001001
[5,6,4,8,3,7,2,1]=>[1,2,7,3,8,4,6,5]=>0011100=>0011100
[1,8,6,7,3,4,2,5]=>[5,2,4,3,7,6,8,1]=>1110010=>0100111
[7,8,1,6,3,4,2,5]=>[5,2,4,3,6,1,8,7]=>1110001=>1000111
[7,8,2,5,1,6,3,4]=>[4,3,6,1,5,2,8,7]=>1110001=>1000111
[1,8,5,6,2,7,3,4]=>[4,3,7,2,6,5,8,1]=>1110100=>0010111
[5,7,1,6,2,8,3,4]=>[4,3,8,2,6,1,7,5]=>1110100=>0010111
[5,6,2,7,1,8,3,4]=>[4,3,8,1,7,2,6,5]=>1110100=>0010111
[6,7,2,5,1,8,3,4]=>[4,3,8,1,5,2,7,6]=>1110010=>0100111
[2,5,1,8,6,7,3,4]=>[4,3,7,6,8,1,5,2]=>1110010=>0100111
[2,6,5,8,1,7,3,4]=>[4,3,7,1,8,5,6,2]=>1110100=>0010111
[1,8,2,7,4,5,3,6]=>[6,3,5,4,7,2,8,1]=>1111000=>0001111
[2,5,4,8,3,6,1,7]=>[7,1,6,3,8,4,5,2]=>1111000=>0001111
[2,4,3,8,5,6,1,7]=>[7,1,6,5,8,3,4,2]=>1110100=>0010111
[2,3,1,8,5,6,4,7]=>[7,4,6,5,8,1,3,2]=>1101100=>0011011
[5,7,2,3,1,6,4,8]=>[8,4,6,1,3,2,7,5]=>1101100=>0011011
[5,7,2,4,3,6,1,8]=>[8,1,6,3,4,2,7,5]=>1110100=>0010111
[4,7,1,6,2,5,3,8]=>[8,3,5,2,6,1,7,4]=>1111000=>0001111
[4,6,3,5,1,7,2,8]=>[8,2,7,1,5,3,6,4]=>1111000=>0001111
[6,7,3,5,1,4,2,8]=>[8,2,4,1,5,3,7,6]=>1110010=>0100111
[1,8,5,6,3,4,2,7]=>[7,2,4,3,6,5,8,1]=>1110100=>0010111
[1,8,5,6,4,7,2,3]=>[3,2,7,4,6,5,8,1]=>1101100=>0011011
[5,7,1,6,4,8,2,3]=>[3,2,8,4,6,1,7,5]=>1101100=>0011011
[4,6,5,8,1,7,2,3]=>[3,2,7,1,8,5,6,4]=>1101100=>0011011
[4,7,1,8,5,6,2,3]=>[3,2,6,5,8,1,7,4]=>1101100=>0011011
[3,5,4,6,2,8,1,7]=>[7,1,8,2,6,4,5,3]=>1111000=>0001111
[3,7,1,6,2,8,4,5]=>[5,4,8,2,6,1,7,3]=>1111000=>0001111
[3,5,2,7,4,8,1,6]=>[6,1,8,4,7,2,5,3]=>1111000=>0001111
[4,7,2,3,1,8,5,6]=>[6,5,8,1,3,2,7,4]=>1101100=>0011011
[2,7,1,8,3,6,4,5]=>[5,4,6,3,8,1,7,2]=>1111000=>0001111
[6,1,7,3,4,5,8,2]=>[2,8,5,4,3,7,1,6]=>1011100=>0011101
[2,5,8,3,4,1,6,7]=>[7,6,1,4,3,8,5,2]=>1110110=>0110111
[5,6,2,7,4,3,8,1]=>[1,8,3,4,7,2,6,5]=>0110100=>0010110
[5,1,7,3,4,2,8,6]=>[6,8,2,4,3,7,1,5]=>1110000=>0000111
[3,7,2,1,4,5,8,6]=>[6,8,5,4,1,2,7,3]=>1011100=>0011101
[2,7,1,3,4,8,6,5]=>[5,6,8,4,3,1,7,2]=>1111000=>0001111
[2,6,1,8,4,5,3,7]=>[7,3,5,4,8,1,6,2]=>1111000=>0001111
[4,2,1,6,5,3,8,7]=>[7,8,3,5,6,1,2,4]=>1010000=>0000101
[4,2,6,3,5,1,8,7]=>[7,8,1,5,3,6,2,4]=>1110000=>0000111
[4,6,2,1,5,3,8,7]=>[7,8,3,5,1,2,6,4]=>1011000=>0001101
[8,4,2,1,6,5,3,7]=>[7,3,5,6,1,2,4,8]=>1010000=>0000101
[6,8,7,2,1,4,3,5]=>[5,3,4,1,2,7,8,6]=>1010010=>0100101
[6,8,2,1,7,4,3,5]=>[5,3,4,7,1,2,8,6]=>1010010=>0100101
[4,8,2,1,6,7,3,5]=>[5,3,7,6,1,2,8,4]=>1011010=>0101101
[2,8,6,7,4,3,1,5]=>[5,1,3,4,7,6,8,2]=>1100010=>0100011
[6,8,7,2,4,3,1,5]=>[5,1,3,4,2,7,8,6]=>1100010=>0100011
[2,6,4,5,8,3,7,1]=>[1,7,3,8,5,4,6,2]=>0111100=>0011110
[6,4,2,8,3,5,7,1]=>[1,7,5,3,8,2,4,6]=>0110100=>0010110
[4,2,1,6,8,7,5,3]=>[3,5,7,8,6,1,2,4]=>1000010=>0100001
[4,2,1,6,5,8,7,3]=>[3,7,8,5,6,1,2,4]=>1000100=>0010001
[6,2,1,8,4,3,7,5]=>[5,7,3,4,8,1,2,6]=>1010000=>0000101
[8,4,6,5,2,1,3,7]=>[7,3,1,2,5,6,4,8]=>1011000=>0001101
[6,4,8,5,7,2,1,3]=>[3,1,2,7,5,8,4,6]=>1001100=>0011001
[4,6,5,8,7,2,1,3]=>[3,1,2,7,8,5,6,4]=>1001100=>0011001
[2,4,8,6,7,5,1,3]=>[3,1,5,7,6,8,4,2]=>1101010=>0101011
[6,4,8,2,1,5,7,3]=>[3,7,5,1,2,8,4,6]=>1001100=>0011001
[2,6,8,4,7,1,5,3]=>[3,5,1,7,4,8,6,2]=>1101010=>0101011
[2,1,6,8,4,3,7,5]=>[5,7,3,4,8,6,1,2]=>1010010=>0100101
[6,8,7,4,2,1,3,5]=>[5,3,1,2,4,7,8,6]=>1010010=>0100101
[4,8,6,7,2,1,3,5]=>[5,3,1,2,7,6,8,4]=>1011010=>0101101
[6,2,3,5,1,4,8,7]=>[7,8,4,1,5,3,2,6]=>1111000=>0001111
[7,3,2,5,4,8,6,1]=>[1,6,8,4,5,2,3,7]=>0101000=>0001010
[3,5,1,6,4,2,8,7]=>[7,8,2,4,6,1,5,3]=>1110000=>0000111
[3,6,2,4,5,1,8,7]=>[7,8,1,5,4,2,6,3]=>1111000=>0001111
[7,2,3,4,5,8,6,1]=>[1,6,8,5,4,3,2,7]=>0111100=>0011110
[7,3,4,6,8,5,1,2]=>[2,1,5,8,6,4,3,7]=>1011010=>0101101
[6,7,3,4,8,5,2,1]=>[1,2,5,8,4,3,7,6]=>0011010=>0101100
[5,7,1,3,8,6,2,4]=>[4,2,6,8,3,1,7,5]=>1110100=>0010111
[4,8,1,5,6,7,3,2]=>[2,3,7,6,5,1,8,4]=>1001110=>0111001
[5,8,2,4,6,7,1,3]=>[3,1,7,6,4,2,8,5]=>1101110=>0111011
[7,8,3,4,6,2,1,5]=>[5,1,2,6,4,3,8,7]=>1011001=>1001101
[3,8,2,5,4,7,6,1]=>[1,6,7,4,5,2,8,3]=>0111000=>0001110
[3,7,6,1,8,5,2,4]=>[4,2,5,8,1,6,7,3]=>1110000=>0000111
[4,7,2,3,8,5,1,6]=>[6,1,5,8,3,2,7,4]=>1111000=>0001111
[4,6,7,1,8,5,3,2]=>[2,3,5,8,1,7,6,4]=>1001010=>0101001
[3,6,1,7,8,5,4,2]=>[2,4,5,8,7,1,6,3]=>1010001=>1000101
[2,1,5,7,3,8,6,4]=>[4,6,8,3,7,5,1,2]=>1010100=>0010101
[5,4,7,1,2,8,6,3]=>[3,6,8,2,1,7,4,5]=>1101000=>0001011
[6,4,7,2,8,5,3,1]=>[1,3,5,8,2,7,4,6]=>0101000=>0001010
[7,1,3,6,4,8,5,2]=>[2,5,8,4,6,3,1,7]=>1011000=>0001101
[4,1,2,3,7,8,6,5]=>[5,6,8,7,3,2,1,4]=>1110001=>1000111
[3,4,2,1,8,5,6,7]=>[7,6,5,8,1,2,4,3]=>1010110=>0110101
[7,2,3,6,8,4,1,5]=>[5,1,4,8,6,3,2,7]=>1110010=>0100111
[8,2,3,5,7,1,4,6]=>[6,4,1,7,5,3,2,8]=>1111100=>0011111
[5,4,8,3,6,7,1,2]=>[2,1,7,6,3,8,4,5]=>1011010=>0101101
[4,5,8,3,6,7,2,1]=>[1,2,7,6,3,8,5,4]=>0011110=>0111100
[3,5,1,8,4,6,7,2]=>[2,7,6,4,8,1,5,3]=>1011010=>0101101
[2,1,5,8,4,6,7,3]=>[3,7,6,4,8,5,1,2]=>1001110=>0111001
[3,8,2,4,5,6,7,1]=>[1,7,6,5,4,2,8,3]=>0111110=>0111110
[6,8,2,3,1,4,5,7]=>[7,5,4,1,3,2,8,6]=>1101110=>0111011
[4,3,1,6,5,8,7,2]=>[2,7,8,5,6,1,3,4]=>1000100=>0010001
[3,1,5,2,4,8,7,6]=>[6,7,8,4,2,5,1,3]=>1101000=>0001011
[3,6,4,5,1,8,7,2]=>[2,7,8,1,5,4,6,3]=>1011000=>0001101
[4,3,6,1,2,8,7,5]=>[5,7,8,2,1,6,3,4]=>1110000=>0000111
[6,1,3,5,4,8,7,2]=>[2,7,8,4,5,3,1,6]=>1011000=>0001101
[7,2,3,4,8,5,1,6]=>[6,1,5,8,4,3,2,7]=>1111000=>0001111
[5,7,3,1,4,2,6,8]=>[8,6,2,4,1,3,7,5]=>1100110=>0110011
[1,7,3,8,4,6,2,5]=>[5,2,6,4,8,3,7,1]=>1111000=>0001111
[8,1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1,8]=>1111000=>0001111
[6,8,3,1,4,7,5,2]=>[2,5,7,4,1,3,8,6]=>1001010=>0101001
[1,8,3,2,4,5,7,6]=>[6,7,5,4,2,3,8,1]=>1101100=>0011011
[8,4,2,5,7,1,6,3]=>[3,6,1,7,5,2,4,8]=>1100100=>0010011
[1,8,5,3,7,4,6,2]=>[2,6,4,7,3,5,8,1]=>1011000=>0001101
[5,3,2,8,7,1,4,6]=>[6,4,1,7,8,2,3,5]=>1101000=>0001011
[4,2,8,5,7,6,1,3]=>[3,1,6,7,5,8,2,4]=>1100100=>0010011
[4,2,1,7,5,3,6,8]=>[8,6,3,5,7,1,2,4]=>1010010=>0100101
[1,7,6,5,8,3,4,2]=>[2,4,3,8,5,6,7,1]=>1010100=>0010101
[7,6,4,5,8,1,3,2]=>[2,3,1,8,5,4,6,7]=>1001100=>0011001
[5,1,6,8,3,4,2,7]=>[7,2,4,3,8,6,1,5]=>1110010=>0100111
[4,3,1,8,5,6,7,2]=>[2,7,6,5,8,1,3,4]=>1000110=>0110001
[1,8,5,4,3,6,2,7]=>[7,2,6,3,4,5,8,1]=>1110000=>0000111
[1,8,3,6,5,2,7,4]=>[4,7,2,5,6,3,8,1]=>1110000=>0000111
[4,7,1,8,2,6,5,3]=>[3,5,6,2,8,1,7,4]=>1101000=>0001011
[1,8,2,4,7,6,5,3]=>[3,5,6,7,4,2,8,1]=>1101000=>0001011
[1,4,8,3,5,7,6,2]=>[2,6,7,5,3,8,4,1]=>1011100=>0011101
[6,3,5,1,4,2,8,7]=>[7,8,2,4,1,5,3,6]=>1110000=>0000111
[6,3,1,2,8,5,7,4]=>[4,7,5,8,2,1,3,6]=>1100100=>0010011
[5,3,8,7,2,1,4,6]=>[6,4,1,2,7,8,3,5]=>1011000=>0001101
[7,6,5,4,1,3,2,8]=>[8,2,3,1,4,5,6,7]=>1100000=>0000011
[1,2,3,4,5,10,9,8,7,6]=>[6,7,8,9,10,5,4,3,2,1]=>111110000=>000011111
[4,6,3,1,5,2,7,8]=>[8,7,2,5,1,3,6,4]=>1101001=>1001011
[6,2,7,4,5,1,3,8]=>[8,3,1,5,4,7,2,6]=>1111000=>0001111
[5,2,7,4,1,6,3,8]=>[8,3,6,1,4,7,2,5]=>1110000=>0000111
[5,7,3,4,1,6,2,8]=>[8,2,6,1,4,3,7,5]=>1110100=>0010111
[1,6,8,4,5,2,7,3]=>[3,7,2,5,4,8,6,1]=>1101010=>0101011
[1,5,8,4,2,6,7,3]=>[3,7,6,2,4,8,5,1]=>1100110=>0110011
[1,5,3,8,2,6,7,4]=>[4,7,6,2,8,3,5,1]=>1110010=>0100111
[1,7,3,8,5,6,2,4]=>[4,2,6,5,8,3,7,1]=>1110100=>0010111
[6,2,3,7,5,1,4,8]=>[8,4,1,5,7,3,2,6]=>1111000=>0001111
[4,2,6,1,5,3,7,8]=>[8,7,3,5,1,6,2,4]=>1110001=>1000111
[5,2,6,4,1,3,7,8]=>[8,7,3,1,4,6,2,5]=>1110001=>1000111
[1,2,7,8,5,6,3,4]=>[4,3,6,5,8,7,2,1]=>1110101=>1010111
[1,2,6,8,5,3,7,4]=>[4,7,3,5,8,6,2,1]=>1110010=>0100111
[1,2,6,4,8,3,7,5]=>[5,7,3,8,4,6,2,1]=>1111000=>0001111
[8,7,4,1,6,2,3,5]=>[5,3,2,6,1,4,7,8]=>1110000=>0000111
[8,5,1,7,2,3,4,6]=>[6,4,3,2,7,1,5,8]=>1111000=>0001111
[7,3,8,1,5,2,4,6]=>[6,4,2,5,1,8,3,7]=>1111000=>0001111
[2,5,8,3,4,6,7,1]=>[1,7,6,4,3,8,5,2]=>0111110=>0111110
[3,1,7,5,4,2,8,6]=>[6,8,2,4,5,7,1,3]=>1100000=>0000011
[4,5,2,3,1,7,8,6]=>[6,8,7,1,3,2,5,4]=>1101001=>1001011
[3,2,6,7,4,1,8,5]=>[5,8,1,4,7,6,2,3]=>1100010=>0100011
[6,4,2,8,1,5,7,3]=>[3,7,5,1,8,2,4,6]=>1100100=>0010011
[7,3,6,8,5,2,4,1]=>[1,4,2,5,8,6,3,7]=>0110010=>0100110
[2,7,8,3,6,5,1,4]=>[4,1,5,6,3,8,7,2]=>1110001=>1000111
[2,7,8,5,4,6,3,1]=>[1,3,6,4,5,8,7,2]=>0101001=>1001010
[2,7,8,3,6,1,4,5]=>[5,4,1,6,3,8,7,2]=>1111001=>1001111
[5,3,2,7,4,8,1,6]=>[6,1,8,4,7,2,3,5]=>1101000=>0001011
[2,1,3,7,8,5,6,4]=>[4,6,5,8,7,3,1,2]=>1010101=>1010101
[5,1,2,4,8,7,3,6]=>[6,3,7,8,4,2,1,5]=>1111000=>0001111
[2,6,3,1,8,7,4,5]=>[5,4,7,8,1,3,6,2]=>1101000=>0001011
[2,3,6,1,8,5,7,4]=>[4,7,5,8,1,6,3,2]=>1110100=>0010111
[5,2,6,1,7,8,4,3]=>[3,4,8,7,1,6,2,5]=>1100001=>1000011
[3,6,5,4,1,8,7,2]=>[2,7,8,1,4,5,6,3]=>1010000=>0000101
[5,2,3,4,8,7,1,6]=>[6,1,7,8,4,3,2,5]=>1111000=>0001111
[4,1,8,2,5,7,3,6]=>[6,3,7,5,2,8,1,4]=>1110100=>0010111
[3,1,8,4,7,2,5,6]=>[6,5,2,7,4,8,1,3]=>1101100=>0011011
[3,2,7,6,4,1,8,5]=>[5,8,1,4,6,7,2,3]=>1100000=>0000011
[1,5,8,2,4,7,3,6]=>[6,3,7,4,2,8,5,1]=>1111100=>0011111
[4,2,3,7,8,1,6,5]=>[5,6,1,8,7,3,2,4]=>1110001=>1000111
[3,8,1,4,2,6,5,7]=>[7,5,6,2,4,1,8,3]=>1110100=>0010111
[5,3,2,8,1,6,4,7]=>[7,4,6,1,8,2,3,5]=>1101000=>0001011
[6,4,7,2,5,8,1,3]=>[3,1,8,5,2,7,4,6]=>1101100=>0011011
[8,5,1,2,6,4,3,7]=>[7,3,4,6,2,1,5,8]=>1110000=>0000111
[5,7,4,3,6,1,8,2]=>[2,8,1,6,3,4,7,5]=>1010100=>0010101
[7,6,3,1,5,4,8,2]=>[2,8,4,5,1,3,6,7]=>1001000=>0001001
[2,4,6,5,1,7,8,3]=>[3,8,7,1,5,6,4,2]=>1101001=>1001011
[5,6,1,7,4,2,8,3]=>[3,8,2,4,7,1,6,5]=>1100100=>0010011
[3,7,4,8,1,2,6,5]=>[5,6,2,1,8,4,7,3]=>1111000=>0001111
[1,3,8,6,2,7,4,5]=>[5,4,7,2,6,8,3,1]=>1111000=>0001111
[4,3,7,5,6,1,8,2]=>[2,8,1,6,5,7,3,4]=>1010100=>0010101
[6,4,7,8,2,1,3,5]=>[5,3,1,2,8,7,4,6]=>1011001=>1001101
[2,7,8,3,4,6,1,5]=>[5,1,6,4,3,8,7,2]=>1111001=>1001111
[3,7,8,1,5,4,2,6]=>[6,2,4,5,1,8,7,3]=>1110001=>1000111
[5,7,3,1,6,8,4,2]=>[2,4,8,6,1,3,7,5]=>1000110=>0110001
[4,6,7,2,8,3,1,5]=>[5,1,3,8,2,7,6,4]=>1101010=>0101011
[7,6,8,5,1,3,2,4]=>[4,2,3,1,5,8,6,7]=>1100010=>0100011
[4,5,6,7,3,1,8,2]=>[2,8,1,3,7,6,5,4]=>1001110=>0111001
[8,7,6,4,1,2,5,3]=>[3,5,2,1,4,6,7,8]=>1100000=>0000011
[5,7,2,3,6,8,1,4]=>[4,1,8,6,3,2,7,5]=>1110110=>0110111
[8,5,3,2,7,6,1,4]=>[4,1,6,7,2,3,5,8]=>1100000=>0000011
[2,6,4,5,7,8,3,1]=>[1,3,8,7,5,4,6,2]=>0101101=>1011010
[7,5,2,8,4,1,3,6]=>[6,3,1,4,8,2,5,7]=>1110000=>0000111
[7,3,8,5,2,1,4,6]=>[6,4,1,2,5,8,3,7]=>1011000=>0001101
[5,8,2,1,6,7,4,3]=>[3,4,7,6,1,2,8,5]=>1000110=>0110001
[3,7,6,8,1,2,5,4]=>[4,5,2,1,8,6,7,3]=>1110010=>0100111
[6,5,1,4,2,3,8,7]=>[7,8,3,2,4,1,5,6]=>1110000=>0000111
[4,1,6,3,2,5,8,7]=>[7,8,5,2,3,6,1,4]=>1100100=>0010011
[8,7,6,1,2,3,5,4]=>[4,5,3,2,1,6,7,8]=>1110000=>0000111
[5,4,1,6,2,3,8,7]=>[7,8,3,2,6,1,4,5]=>1110000=>0000111
[2,6,5,3,4,1,8,7]=>[7,8,1,4,3,5,6,2]=>1110000=>0000111
[5,8,7,6,1,2,3,4]=>[4,3,2,1,6,7,8,5]=>1110100=>0010111
[2,1,8,7,3,6,4,5]=>[5,4,6,3,7,8,1,2]=>1011000=>0001101
[2,1,6,3,8,5,4,7]=>[7,4,5,8,3,6,1,2]=>1011000=>0001101
[2,6,3,1,8,5,4,7]=>[7,4,5,8,1,3,6,2]=>1101000=>0001011
[4,6,2,8,5,1,3,7]=>[7,3,1,5,8,2,6,4]=>1111000=>0001111
[5,2,1,8,7,3,4,6]=>[6,4,3,7,8,1,2,5]=>1011000=>0001101
[6,5,2,7,4,3,8,1]=>[1,8,3,4,7,2,5,6]=>0110000=>0000110
[4,6,5,2,7,3,8,1]=>[1,8,3,7,2,5,6,4]=>0111000=>0001110
[2,7,5,4,8,3,6,1]=>[1,6,3,8,4,5,7,2]=>0111000=>0001110
[3,1,6,2,4,8,7,5]=>[5,7,8,4,2,6,1,3]=>1101000=>0001011
[2,1,7,6,3,8,4,5]=>[5,4,8,3,6,7,1,2]=>1011000=>0001101
[7,1,6,2,3,8,5,4]=>[4,5,8,3,2,6,1,7]=>1110000=>0000111
[8,2,3,4,6,7,1,5]=>[5,1,7,6,4,3,2,8]=>1111010=>0101111
[7,4,6,8,5,1,3,2]=>[2,3,1,5,8,6,4,7]=>1001010=>0101001
[6,4,8,3,5,7,1,2]=>[2,1,7,5,3,8,4,6]=>1011100=>0011101
[8,5,7,4,6,2,1,3]=>[3,1,2,6,4,7,5,8]=>1001100=>0011001
[4,6,7,8,2,3,5,1]=>[1,5,3,2,8,7,6,4]=>0111011=>1101110
[5,8,3,2,4,6,1,7]=>[7,1,6,4,2,3,8,5]=>1101100=>0011011
[2,8,4,1,5,3,7,6]=>[6,7,3,5,1,4,8,2]=>1110000=>0000111
[2,1,8,6,4,3,7,5]=>[5,7,3,4,6,8,1,2]=>1010000=>0000101
[2,1,7,6,5,3,8,4]=>[4,8,3,5,6,7,1,2]=>1010000=>0000101
[7,2,5,4,6,1,8,3]=>[3,8,1,6,4,5,2,7]=>1101000=>0001011
[4,7,6,1,2,5,8,3]=>[3,8,5,2,1,6,7,4]=>1101100=>0011011
[3,6,7,1,8,5,2,4]=>[4,2,5,8,1,7,6,3]=>1110010=>0100111
[4,2,3,6,8,7,5,1]=>[1,5,7,8,6,3,2,4]=>0110010=>0100110
[7,5,4,3,1,8,6,2]=>[2,6,8,1,3,4,5,7]=>1000000=>0000001
[6,5,7,3,1,8,4,2]=>[2,4,8,1,3,7,5,6]=>1000100=>0010001
[6,3,5,4,1,7,8,2]=>[2,8,7,1,4,5,3,6]=>1010001=>1000101
[5,4,1,7,6,2,8,3]=>[3,8,2,6,7,1,4,5]=>1100000=>0000011
[4,7,5,2,1,3,8,6]=>[6,8,3,1,2,5,7,4]=>1011000=>0001101
[5,7,2,3,6,4,8,1]=>[1,8,4,6,3,2,7,5]=>0111100=>0011110
[3,1,7,2,5,8,4,6]=>[6,4,8,5,2,7,1,3]=>1101100=>0011011
[7,8,6,1,3,2,5,4]=>[4,5,2,3,1,6,8,7]=>1100001=>1000011
[5,8,6,4,2,3,1,7]=>[7,1,3,2,4,6,8,5]=>1100100=>0010011
[6,8,5,4,2,7,3,1]=>[1,3,7,2,4,5,8,6]=>0100010=>0100010
[4,1,3,8,7,5,6,2]=>[2,6,5,7,8,3,1,4]=>1010100=>0010101
[2,1,4,6,8,3,7,5]=>[5,7,3,8,6,4,1,2]=>1011010=>0101101
[5,4,1,6,3,8,7,2]=>[2,7,8,3,6,1,4,5]=>1010000=>0000101
[3,5,6,2,4,8,7,1]=>[1,7,8,4,2,6,5,3]=>0111100=>0011110
[6,2,7,4,8,1,3,5]=>[5,3,1,8,4,7,2,6]=>1111000=>0001111
[5,4,1,2,8,7,6,3]=>[3,6,7,8,2,1,4,5]=>1100000=>0000011
[5,6,3,7,8,4,2,1]=>[1,2,4,8,7,3,6,5]=>0010101=>1010100
[4,3,2,6,8,1,7,5]=>[5,7,1,8,6,2,3,4]=>1100010=>0100011
[7,1,5,6,3,8,2,4]=>[4,2,8,3,6,5,1,7]=>1110100=>0010111
[1,5,4,2,7,8,3,6]=>[6,3,8,7,2,4,5,1]=>1110001=>1000111
[6,1,2,8,7,4,3,5]=>[5,3,4,7,8,2,1,6]=>1110000=>0000111
[5,1,6,8,4,7,2,3]=>[3,2,7,4,8,6,1,5]=>1101010=>0101011
[7,1,8,4,3,6,5,2]=>[2,5,6,3,4,8,1,7]=>1010000=>0000101
[5,6,8,1,7,3,2,4]=>[4,2,3,7,1,8,6,5]=>1100110=>0110011
[3,2,8,1,4,7,6,5]=>[5,6,7,4,1,8,2,3]=>1101000=>0001011
[6,4,3,8,2,5,7,1]=>[1,7,5,2,8,3,4,6]=>0110100=>0010110
[5,8,2,3,6,4,1,7]=>[7,1,4,6,3,2,8,5]=>1110100=>0010111
[2,1,7,8,3,4,6,5]=>[5,6,4,3,8,7,1,2]=>1011001=>1001101
[3,5,8,7,4,2,6,1]=>[1,6,2,4,7,8,5,3]=>0110100=>0010110
[7,5,1,8,4,2,6,3]=>[3,6,2,4,8,1,5,7]=>1100000=>0000011
[5,6,1,8,2,7,4,3]=>[3,4,7,2,8,1,6,5]=>1100100=>0010011
[3,6,8,5,2,7,4,1]=>[1,4,7,2,5,8,6,3]=>0110010=>0100110
[2,1,6,5,4,8,3,7]=>[7,3,8,4,5,6,1,2]=>1011000=>0001101
[2,1,7,8,4,6,5,3]=>[3,5,6,4,8,7,1,2]=>1001001=>1001001
[2,1,7,3,5,8,6,4]=>[4,6,8,5,3,7,1,2]=>1010100=>0010101
[7,8,1,2,4,5,6,3]=>[3,6,5,4,2,1,8,7]=>1101101=>1011011
[3,8,7,4,1,2,5,6]=>[6,5,2,1,4,7,8,3]=>1110100=>0010111
[3,6,8,1,5,7,2,4]=>[4,2,7,5,1,8,6,3]=>1110110=>0110111
[3,5,7,8,4,6,1,2]=>[2,1,6,4,8,7,5,3]=>1011101=>1011101
[7,8,2,4,3,1,5,6]=>[6,5,1,3,4,2,8,7]=>1100101=>1010011
[6,2,7,1,3,5,8,4]=>[4,8,5,3,1,7,2,6]=>1110100=>0010111
[6,1,8,2,3,5,4,7]=>[7,4,5,3,2,8,1,6]=>1111000=>0001111
[7,2,4,1,6,3,8,5]=>[5,8,3,6,1,4,2,7]=>1110000=>0000111
[7,6,2,8,5,1,4,3]=>[3,4,1,5,8,2,6,7]=>1100000=>0000011
[7,3,8,5,2,6,4,1]=>[1,4,6,2,5,8,3,7]=>0110000=>0000110
[4,3,8,7,1,6,5,2]=>[2,5,6,1,7,8,3,4]=>1010000=>0000101
[5,3,2,4,7,8,6,1]=>[1,6,8,7,4,2,3,5]=>0101001=>1001010
[5,2,4,3,6,8,1,7]=>[7,1,8,6,3,4,2,5]=>1110010=>0100111
[3,7,5,8,1,6,2,4]=>[4,2,6,1,8,5,7,3]=>1110100=>0010111
[3,7,6,4,5,1,8,2]=>[2,8,1,5,4,6,7,3]=>1011000=>0001101
[4,7,5,6,3,8,2,1]=>[1,2,8,3,6,5,7,4]=>0011100=>0011100
[4,8,5,7,2,3,1,6]=>[6,1,3,2,7,5,8,4]=>1101100=>0011011
[3,8,5,7,1,4,6,2]=>[2,6,4,1,7,5,8,3]=>1011100=>0011101
[5,8,2,7,3,4,6,1]=>[1,6,4,3,7,2,8,5]=>0111100=>0011110
[5,7,2,1,8,3,6,4]=>[4,6,3,8,1,2,7,5]=>1010100=>0010101
[7,8,1,2,3,4,6,5]=>[5,6,4,3,2,1,8,7]=>1111001=>1001111
[6,8,5,2,1,7,3,4]=>[4,3,7,1,2,5,8,6]=>1010010=>0100101
[5,7,2,8,3,6,1,4]=>[4,1,6,3,8,2,7,5]=>1110100=>0010111
[5,6,2,4,3,1,8,7]=>[7,8,1,3,4,2,6,5]=>1100100=>0010011
[6,8,3,7,5,4,2,1]=>[1,2,4,5,7,3,8,6]=>0010010=>0100100
[6,1,3,4,7,5,8,2]=>[2,8,5,7,4,3,1,6]=>1011100=>0011101
[4,6,2,1,7,8,3,5]=>[5,3,8,7,1,2,6,4]=>1011001=>1001101
[6,2,1,4,8,7,5,3]=>[3,5,7,8,4,1,2,6]=>1001000=>0001001
[8,7,6,5,1,3,2,4]=>[4,2,3,1,5,6,7,8]=>1100000=>0000011
[8,7,6,2,4,3,1,5]=>[5,1,3,4,2,6,7,8]=>1100000=>0000011
[8,4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4,8]=>1001000=>0001001
[5,4,8,7,6,1,3,2]=>[2,3,1,6,7,8,4,5]=>1001000=>0001001
[7,6,1,8,5,4,3,2]=>[2,3,4,5,8,1,6,7]=>1000000=>0000001
[4,3,8,7,6,1,5,2]=>[2,5,1,6,7,8,3,4]=>1010000=>0000101
[6,5,8,7,4,1,3,2]=>[2,3,1,4,7,8,5,6]=>1000100=>0010001
[7,6,3,1,5,8,4,2]=>[2,4,8,5,1,3,6,7]=>1000100=>0010001
[1,6,3,8,5,2,4,7]=>[7,4,2,5,8,3,6,1]=>1111000=>0001111
[4,6,3,7,5,2,1,8]=>[8,1,2,5,7,3,6,4]=>1011000=>0001101
[3,7,2,6,5,4,1,8]=>[8,1,4,5,6,2,7,3]=>1110000=>0000111
[3,2,1,6,8,4,5,7]=>[7,5,4,8,6,1,2,3]=>1001110=>0111001
[6,2,5,1,7,4,8,3]=>[3,8,4,7,1,5,2,6]=>1101000=>0001011
[3,5,7,4,8,6,1,2]=>[2,1,6,8,4,7,5,3]=>1011100=>0011101
[5,2,7,4,1,6,8,3]=>[3,8,6,1,4,7,2,5]=>1100010=>0100011
[7,4,1,5,3,8,2,6]=>[6,2,8,3,5,1,4,7]=>1110000=>0000111
[3,4,1,2,7,8,6,5]=>[5,6,8,7,2,1,4,3]=>1110001=>1000111
[5,4,8,3,7,1,6,2]=>[2,6,1,7,3,8,4,5]=>1011000=>0001101
[4,1,3,2,8,6,7,5]=>[5,7,6,8,2,3,1,4]=>1100010=>0100011
[3,1,2,4,7,6,8,5]=>[5,8,6,7,4,2,1,3]=>1101010=>0101011
[4,7,1,8,2,5,3,6]=>[6,3,5,2,8,1,7,4]=>1111000=>0001111
[6,7,8,1,4,5,3,2]=>[2,3,5,4,1,8,7,6]=>1001011=>1101001
[8,4,6,1,3,5,2,7]=>[7,2,5,3,1,6,4,8]=>1111000=>0001111
[3,2,5,4,7,8,1,6]=>[6,1,8,7,4,5,2,3]=>1101001=>1001011
[3,1,7,6,5,8,2,4]=>[4,2,8,5,6,7,1,3]=>1100100=>0010011
[5,7,2,3,8,1,6,4]=>[4,6,1,8,3,2,7,5]=>1110100=>0010111
[1,6,3,5,7,2,8,4]=>[4,8,2,7,5,3,6,1]=>1110100=>0010111
[5,4,2,6,8,7,1,3]=>[3,1,7,8,6,2,4,5]=>1100010=>0100011
[6,4,1,2,8,7,3,5]=>[5,3,7,8,2,1,4,6]=>1110000=>0000111
[6,5,1,4,3,2,8,7]=>[7,8,2,3,4,1,5,6]=>1100000=>0000011
[4,3,8,5,2,1,6,7]=>[7,6,1,2,5,8,3,4]=>1010010=>0100101
[3,6,4,5,2,1,8,7]=>[7,8,1,2,5,4,6,3]=>1011000=>0001101
[5,7,4,1,3,8,6,2]=>[2,6,8,3,1,4,7,5]=>1010100=>0010101
[5,2,6,7,3,1,4,8]=>[8,4,1,3,7,6,2,5]=>1101010=>0101011
[5,6,3,1,8,2,7,4]=>[4,7,2,8,1,3,6,5]=>1100100=>0010011
[6,5,4,3,1,2,8,7]=>[7,8,2,1,3,4,5,6]=>1100000=>0000011
[4,5,2,1,6,8,3,7]=>[7,3,8,6,1,2,5,4]=>1011010=>0101101
[5,6,2,8,1,7,4,3]=>[3,4,7,1,8,2,6,5]=>1100100=>0010011
[8,1,3,4,7,2,6,5]=>[5,6,2,7,4,3,1,8]=>1111000=>0001111
[2,1,4,5,8,6,3,7]=>[7,3,6,8,5,4,1,2]=>1011100=>0011101
[5,1,7,3,4,8,2,6]=>[6,2,8,4,3,7,1,5]=>1111000=>0001111
[1,8,3,4,7,6,2,5]=>[5,2,6,7,4,3,8,1]=>1111000=>0001111
[8,7,2,3,6,5,4,1]=>[1,4,5,6,3,2,7,8]=>0110000=>0000110
[4,8,1,6,7,2,5,3]=>[3,5,2,7,6,1,8,4]=>1101010=>0101011
[3,2,1,8,6,5,4,7]=>[7,4,5,6,8,1,2,3]=>1001000=>0001001
[5,2,7,1,8,4,3,6]=>[6,3,4,8,1,7,2,5]=>1110000=>0000111
[6,7,2,1,8,4,3,5]=>[5,3,4,8,1,2,7,6]=>1010010=>0100101
[6,7,3,1,5,8,2,4]=>[4,2,8,5,1,3,7,6]=>1100110=>0110011
[2,4,1,6,8,5,3,7]=>[7,3,5,8,6,1,4,2]=>1110010=>0100111
[5,4,7,6,1,8,2,3]=>[3,2,8,1,6,7,4,5]=>1101000=>0001011
[3,5,6,8,4,7,2,1]=>[1,2,7,4,8,6,5,3]=>0011110=>0111100
[2,5,6,8,7,3,4,1]=>[1,4,3,7,8,6,5,2]=>0110110=>0110110
[8,4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4,8]=>0001100=>0011000
[2,4,8,5,7,3,6,1]=>[1,6,3,7,5,8,4,2]=>0111100=>0011110
[4,3,8,6,5,7,2,1]=>[1,2,7,5,6,8,3,4]=>0010100=>0010100
[5,3,7,8,4,6,2,1]=>[1,2,6,4,8,7,3,5]=>0011001=>1001100
[6,7,3,8,4,5,2,1]=>[1,2,5,4,8,3,7,6]=>0011010=>0101100
[5,2,7,8,6,3,4,1]=>[1,4,3,6,8,7,2,5]=>0110001=>1000110
[2,1,8,7,6,4,3,5]=>[5,3,4,6,7,8,1,2]=>1010000=>0000101
[6,3,8,7,5,1,2,4]=>[4,2,1,5,7,8,3,6]=>1110000=>0000111
[5,4,8,7,1,3,2,6]=>[6,2,3,1,7,8,4,5]=>1101000=>0001011
[4,8,6,1,3,2,5,7]=>[7,5,2,3,1,6,8,4]=>1101100=>0011011
[5,4,2,7,6,8,1,3]=>[3,1,8,6,7,2,4,5]=>1100010=>0100011
[2,5,3,7,6,8,1,4]=>[4,1,8,6,7,3,5,2]=>1110010=>0100111
[8,7,2,3,5,4,1,6]=>[6,1,4,5,3,2,7,8]=>1110000=>0000111
[5,3,1,4,8,7,2,6]=>[6,2,7,8,4,1,3,5]=>1101000=>0001011
[3,4,2,8,6,1,5,7]=>[7,5,1,6,8,2,4,3]=>1110100=>0010111
[2,8,6,1,7,3,5,4]=>[4,5,3,7,1,6,8,2]=>1110000=>0000111
[1,7,6,3,5,8,2,4]=>[4,2,8,5,3,6,7,1]=>1110100=>0010111
[1,8,2,5,7,6,3,4]=>[4,3,6,7,5,2,8,1]=>1110100=>0010111
[4,1,6,8,2,3,7,5]=>[5,7,3,2,8,6,1,4]=>1110010=>0100111
[8,1,5,6,4,7,2,3]=>[3,2,7,4,6,5,1,8]=>1101100=>0011011
[1,7,4,6,8,2,5,3]=>[3,5,2,8,6,4,7,1]=>1101010=>0101011
[6,2,1,8,4,5,3,7]=>[7,3,5,4,8,1,2,6]=>1011000=>0001101
[2,7,4,3,6,8,1,5]=>[5,1,8,6,3,4,7,2]=>1110010=>0100111
[4,7,3,8,5,2,1,6]=>[6,1,2,5,8,3,7,4]=>1011000=>0001101
[3,8,6,2,7,4,1,5]=>[5,1,4,7,2,6,8,3]=>1110000=>0000111
[8,1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1,8]=>1101010=>0101011
[6,4,2,8,5,1,3,7]=>[7,3,1,5,8,2,4,6]=>1110000=>0000111
[4,7,5,1,8,6,3,2]=>[2,3,6,8,1,5,7,4]=>1001000=>0001001
[8,4,5,7,6,1,3,2]=>[2,3,1,6,7,5,4,8]=>1001100=>0011001
[6,7,5,1,4,2,8,3]=>[3,8,2,4,1,5,7,6]=>1100010=>0100011
[4,2,7,6,1,5,8,3]=>[3,8,5,1,6,7,2,4]=>1100100=>0010011
[5,8,4,7,3,2,6,1]=>[1,6,2,3,7,4,8,5]=>0101100=>0011010
[7,2,6,5,8,4,1,3]=>[3,1,4,8,5,6,2,7]=>1100100=>0010011
[6,2,4,1,7,5,8,3]=>[3,8,5,7,1,4,2,6]=>1100100=>0010011
[5,2,1,8,3,6,7,4]=>[4,7,6,3,8,1,2,5]=>1010010=>0100101
[5,7,3,1,6,4,8,2]=>[2,8,4,6,1,3,7,5]=>1001100=>0011001
[6,1,3,7,4,8,5,2]=>[2,5,8,4,7,3,1,6]=>1011000=>0001101
[3,1,5,4,2,8,6,7]=>[7,6,8,2,4,5,1,3]=>1100010=>0100011
[3,7,2,1,5,8,6,4]=>[4,6,8,5,1,2,7,3]=>1010100=>0010101
[3,7,4,2,1,8,5,6]=>[6,5,8,1,2,4,7,3]=>1010100=>0010101
[7,5,1,4,2,8,6,3]=>[3,6,8,2,4,1,5,7]=>1100000=>0000011
[4,3,2,1,8,5,7,6]=>[6,7,5,8,1,2,3,4]=>1000100=>0010001
[5,3,2,1,7,6,4,8]=>[8,4,6,7,1,2,3,5]=>1001000=>0001001
[8,1,6,2,7,4,3,5]=>[5,3,4,7,2,6,1,8]=>1110000=>0000111
[8,6,3,2,7,5,4,1]=>[1,4,5,7,2,3,6,8]=>0100000=>0000010
[7,3,1,6,5,4,2,8]=>[8,2,4,5,6,1,3,7]=>1100000=>0000011
[8,5,7,4,3,6,2,1]=>[1,2,6,3,4,7,5,8]=>0010100=>0010100
[8,5,7,2,4,6,3,1]=>[1,3,6,4,2,7,5,8]=>0101100=>0011010
[2,8,5,6,1,4,3,7]=>[7,3,4,1,6,5,8,2]=>1110100=>0010111
[7,2,6,8,4,1,5,3]=>[3,5,1,4,8,6,2,7]=>1100010=>0100011
[7,6,4,8,3,2,5,1]=>[1,5,2,3,8,4,6,7]=>0101000=>0001010
[6,5,8,4,1,3,7,2]=>[2,7,3,1,4,8,5,6]=>1010100=>0010101
[5,4,8,3,2,1,7,6]=>[6,7,1,2,3,8,4,5]=>1001000=>0001001
[2,4,7,1,3,6,5,8]=>[8,5,6,3,1,7,4,2]=>1111100=>0011111
[3,6,8,2,1,5,7,4]=>[4,7,5,1,2,8,6,3]=>1010110=>0110101
[5,1,7,8,2,4,6,3]=>[3,6,4,2,8,7,1,5]=>1101001=>1001011
[3,6,7,8,1,2,5,4]=>[4,5,2,1,8,7,6,3]=>1110011=>1100111
[4,6,7,2,8,1,3,5]=>[5,3,1,8,2,7,6,4]=>1111010=>0101111
[2,7,4,1,8,3,6,5]=>[5,6,3,8,1,4,7,2]=>1110000=>0000111
[3,5,1,8,4,2,7,6]=>[6,7,2,4,8,1,5,3]=>1110000=>0000111
[4,2,5,8,3,1,7,6]=>[6,7,1,3,8,5,2,4]=>1100100=>0010011
[3,6,4,7,8,1,2,5]=>[5,2,1,8,7,4,6,3]=>1111001=>1001111
[3,7,4,8,5,2,1,6]=>[6,1,2,5,8,4,7,3]=>1011000=>0001101
[7,2,5,8,6,3,1,4]=>[4,1,3,6,8,5,2,7]=>1100100=>0010011
[4,2,8,7,3,5,1,6]=>[6,1,5,3,7,8,2,4]=>1110000=>0000111
[6,8,1,4,7,5,2,3]=>[3,2,5,7,4,1,8,6]=>1101010=>0101011
[5,8,7,1,3,6,4,2]=>[2,4,6,3,1,7,8,5]=>1010100=>0010101
[2,7,6,5,1,4,3,8]=>[8,3,4,1,5,6,7,2]=>1110000=>0000111
[3,8,7,6,2,1,5,4]=>[4,5,1,2,6,7,8,3]=>1010000=>0000101
[5,7,8,4,3,1,2,6]=>[6,2,1,3,4,8,7,5]=>1100101=>1010011
[5,8,6,4,3,2,1,7]=>[7,1,2,3,4,6,8,5]=>1000100=>0010001
[8,1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1,8]=>1111000=>0001111
[3,8,2,7,6,5,4,1]=>[1,4,5,6,7,2,8,3]=>0110000=>0000110
[4,2,8,7,6,5,3,1]=>[1,3,5,6,7,8,2,4]=>0100000=>0000010
[8,3,1,7,6,5,4,2]=>[2,4,5,6,7,1,3,8]=>1000000=>0000001
[8,3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3,8]=>1000000=>0000001
[2,5,8,6,3,1,4,7]=>[7,4,1,3,6,8,5,2]=>1101100=>0011011
[6,8,7,2,4,3,5,1]=>[1,5,3,4,2,7,8,6]=>0110010=>0100110
[8,3,4,6,1,5,2,7]=>[7,2,5,1,6,4,3,8]=>1111000=>0001111
[6,3,4,7,8,2,5,1]=>[1,5,2,8,7,4,3,6]=>0111001=>1001110
[5,3,7,4,8,6,1,2]=>[2,1,6,8,4,7,3,5]=>1011000=>0001101
[2,4,7,6,8,3,5,1]=>[1,5,3,8,6,7,4,2]=>0111010=>0101110
[5,7,6,2,8,4,1,3]=>[3,1,4,8,2,6,7,5]=>1100100=>0010011
[4,8,6,5,7,1,2,3]=>[3,2,1,7,5,6,8,4]=>1101100=>0011011
[7,5,6,4,1,3,8,2]=>[2,8,3,1,4,6,5,7]=>1010100=>0010101
[3,1,2,7,8,6,4,5]=>[5,4,6,8,7,2,1,3]=>1101001=>1001011
[8,4,1,5,2,3,7,6]=>[6,7,3,2,5,1,4,8]=>1110000=>0000111
[3,8,4,1,2,7,6,5]=>[5,6,7,2,1,4,8,3]=>1110000=>0000111
[5,4,7,2,3,6,8,1]=>[1,8,6,3,2,7,4,5]=>0111010=>0101110
[6,3,2,1,8,4,7,5]=>[5,7,4,8,1,2,3,6]=>1001000=>0001001
[2,7,5,8,3,4,1,6]=>[6,1,4,3,8,5,7,2]=>1110100=>0010111
[2,3,7,6,8,1,5,4]=>[4,5,1,8,6,7,3,2]=>1110010=>0100111
[2,7,8,5,1,3,6,4]=>[4,6,3,1,5,8,7,2]=>1110001=>1000111
[4,8,7,6,2,3,5,1]=>[1,5,3,2,6,7,8,4]=>0111000=>0001110
[2,7,1,6,8,3,5,4]=>[4,5,3,8,6,1,7,2]=>1110010=>0100111
[7,8,1,5,3,2,6,4]=>[4,6,2,3,5,1,8,7]=>1100001=>1000011
[6,7,5,4,2,1,8,3]=>[3,8,1,2,4,5,7,6]=>1000010=>0100001
[4,2,1,5,8,7,6,3]=>[3,6,7,8,5,1,2,4]=>1000100=>0010001
[8,5,3,2,6,1,7,4]=>[4,7,1,6,2,3,5,8]=>1100000=>0000011
[7,3,4,6,1,5,8,2]=>[2,8,5,1,6,4,3,7]=>1011100=>0011101
[7,8,4,1,2,5,3,6]=>[6,3,5,2,1,4,8,7]=>1110001=>1000111
[6,1,4,2,7,5,3,8]=>[8,3,5,7,2,4,1,6]=>1110000=>0000111
[6,1,3,4,7,2,5,8]=>[8,5,2,7,4,3,1,6]=>1111100=>0011111
[7,8,2,1,6,3,5,4]=>[4,5,3,6,1,2,8,7]=>1010001=>1000101
[6,2,3,7,4,1,5,8]=>[8,5,1,4,7,3,2,6]=>1110100=>0010111
[6,2,4,1,7,3,5,8]=>[8,5,3,7,1,4,2,6]=>1110100=>0010111
[3,4,8,7,5,6,1,2]=>[2,1,6,5,7,8,4,3]=>1011100=>0011101
[2,7,3,8,6,4,1,5]=>[5,1,4,6,8,3,7,2]=>1110000=>0000111
[2,6,8,5,3,1,7,4]=>[4,7,1,3,5,8,6,2]=>1100010=>0100011
[5,6,2,1,7,3,8,4]=>[4,8,3,7,1,2,6,5]=>1010100=>0010101
[5,3,6,2,4,1,7,8]=>[8,7,1,4,2,6,3,5]=>1110001=>1000111
[5,7,4,2,1,3,6,8]=>[8,6,3,1,2,4,7,5]=>1010110=>0110101
[6,4,2,1,5,3,7,8]=>[8,7,3,5,1,2,4,6]=>1010001=>1000101
[6,3,1,4,5,7,8,2]=>[2,8,7,5,4,1,3,6]=>1001101=>1011001
[1,6,4,2,8,7,3,5]=>[5,3,7,8,2,4,6,1]=>1110000=>0000111
[4,8,1,2,6,7,3,5]=>[5,3,7,6,2,1,8,4]=>1111010=>0101111
[3,1,2,4,6,8,7,5]=>[5,7,8,6,4,2,1,3]=>1101010=>0101011
[3,1,8,4,5,7,6,2]=>[2,6,7,5,4,8,1,3]=>1001100=>0011001
[4,2,8,1,5,3,7,6]=>[6,7,3,5,1,8,2,4]=>1110000=>0000111
[4,3,8,5,7,6,1,2]=>[2,1,6,7,5,8,3,4]=>1010100=>0010101
[4,8,6,3,7,5,1,2]=>[2,1,5,7,3,6,8,4]=>1011000=>0001101
[3,8,6,5,2,7,1,4]=>[4,1,7,2,5,6,8,3]=>1110000=>0000111
[3,8,5,6,1,7,4,2]=>[2,4,7,1,6,5,8,3]=>1010100=>0010101
[3,7,8,5,2,1,6,4]=>[4,6,1,2,5,8,7,3]=>1010001=>1000101
[4,2,7,8,1,3,6,5]=>[5,6,3,1,8,7,2,4]=>1110001=>1000111
[2,1,8,7,6,3,5,4]=>[4,5,3,6,7,8,1,2]=>1010000=>0000101
[2,8,1,7,4,6,5,3]=>[3,5,6,4,7,1,8,2]=>1101000=>0001011
[2,8,7,5,1,6,4,3]=>[3,4,6,1,5,7,8,2]=>1100000=>0000011
[2,8,6,7,5,1,4,3]=>[3,4,1,5,7,6,8,2]=>1100010=>0100011
[5,4,1,6,3,2,8,7]=>[7,8,2,3,6,1,4,5]=>1100000=>0000011
[3,2,6,5,1,4,8,7]=>[7,8,4,1,5,6,2,3]=>1101000=>0001011
[5,1,7,2,8,6,4,3]=>[3,4,6,8,2,7,1,5]=>1100000=>0000011
[2,5,8,1,7,4,3,6]=>[6,3,4,7,1,8,5,2]=>1110100=>0010111
[6,8,2,5,4,7,1,3]=>[3,1,7,4,5,2,8,6]=>1101010=>0101011
[2,1,7,6,3,8,5,4]=>[4,5,8,3,6,7,1,2]=>1010000=>0000101
[7,6,2,8,4,3,1,5]=>[5,1,3,4,8,2,6,7]=>1100000=>0000011
[4,2,1,6,3,8,7,5]=>[5,7,8,3,6,1,2,4]=>1010000=>0000101
[4,2,7,3,1,8,5,6]=>[6,5,8,1,3,7,2,4]=>1100100=>0010011
[5,2,7,3,8,6,1,4]=>[4,1,6,8,3,7,2,5]=>1110000=>0000111
[5,8,3,2,7,6,1,4]=>[4,1,6,7,2,3,8,5]=>1100100=>0010011
[4,8,3,2,1,7,6,5]=>[5,6,7,1,2,3,8,4]=>1001000=>0001001
[3,5,8,2,7,1,4,6]=>[6,4,1,7,2,8,5,3]=>1111100=>0011111
[6,8,3,7,2,1,5,4]=>[4,5,1,2,7,3,8,6]=>1010010=>0100101
[3,5,8,1,7,2,6,4]=>[4,6,2,7,1,8,5,3]=>1110100=>0010111
[5,8,3,1,6,2,7,4]=>[4,7,2,6,1,3,8,5]=>1100100=>0010011
[5,1,7,3,6,2,8,4]=>[4,8,2,6,3,7,1,5]=>1110000=>0000111
[6,8,4,7,1,5,3,2]=>[2,3,5,1,7,4,8,6]=>1001010=>0101001
[4,3,2,1,6,8,5,7]=>[7,5,8,6,1,2,3,4]=>1000110=>0110001
[2,4,1,3,8,7,6,5]=>[5,6,7,8,3,1,4,2]=>1110000=>0000111
[6,5,3,1,7,2,8,4]=>[4,8,2,7,1,3,5,6]=>1100000=>0000011
[3,8,5,4,2,1,7,6]=>[6,7,1,2,4,5,8,3]=>1010000=>0000101
[2,3,8,5,4,1,6,7]=>[7,6,1,4,5,8,3,2]=>1110010=>0100111
[4,8,6,5,2,7,1,3]=>[3,1,7,2,5,6,8,4]=>1101000=>0001011
[2,1,4,8,6,5,3,7]=>[7,3,5,6,8,4,1,2]=>1011000=>0001101
[4,3,2,8,7,6,1,5]=>[5,1,6,7,8,2,3,4]=>1100000=>0000011
[5,4,2,6,3,1,8,7]=>[7,8,1,3,6,2,4,5]=>1100000=>0000011
[6,5,2,1,3,4,8,7]=>[7,8,4,3,1,2,5,6]=>1011000=>0001101
[7,5,2,6,3,8,4,1]=>[1,4,8,3,6,2,5,7]=>0110000=>0000110
[7,3,6,5,2,8,4,1]=>[1,4,8,2,5,6,3,7]=>0110000=>0000110
[5,6,3,1,2,4,8,7]=>[7,8,4,2,1,3,6,5]=>1101100=>0011011
[2,7,5,3,8,6,4,1]=>[1,4,6,8,3,5,7,2]=>0110000=>0000110
[3,7,6,4,2,8,5,1]=>[1,5,8,2,4,6,7,3]=>0110000=>0000110
[5,7,3,6,2,8,4,1]=>[1,4,8,2,6,3,7,5]=>0110100=>0010110
[7,8,2,3,5,1,4,6]=>[6,4,1,5,3,2,8,7]=>1111001=>1001111
[3,8,4,1,5,7,2,6]=>[6,2,7,5,1,4,8,3]=>1110100=>0010111
[5,6,3,1,8,7,4,2]=>[2,4,7,8,1,3,6,5]=>1000100=>0010001
[3,5,7,4,8,6,2,1]=>[1,2,6,8,4,7,5,3]=>0011100=>0011100
[4,5,3,6,8,2,7,1]=>[1,7,2,8,6,3,5,4]=>0111010=>0101110
[5,6,3,7,4,8,2,1]=>[1,2,8,4,7,3,6,5]=>0011100=>0011100
[2,6,7,4,5,8,3,1]=>[1,3,8,5,4,7,6,2]=>0101110=>0111010
[6,3,7,5,8,4,2,1]=>[1,2,4,8,5,7,3,6]=>0010100=>0010100
[7,6,1,5,8,3,4,2]=>[2,4,3,8,5,1,6,7]=>1010100=>0010101
[7,6,8,5,1,4,2,3]=>[3,2,4,1,5,8,6,7]=>1100010=>0100011
[7,1,8,5,4,2,3,6]=>[6,3,2,4,5,8,1,7]=>1110000=>0000111
[2,1,7,8,5,3,4,6]=>[6,4,3,5,8,7,1,2]=>1011001=>1001101
[4,1,8,2,6,5,3,7]=>[7,3,5,6,2,8,1,4]=>1110000=>0000111
[4,7,3,8,1,2,6,5]=>[5,6,2,1,8,3,7,4]=>1111000=>0001111
[3,8,1,2,4,6,5,7]=>[7,5,6,4,2,1,8,3]=>1111100=>0011111
[8,1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1,8]=>1110110=>0110111
[5,8,7,4,6,3,2,1]=>[1,2,3,6,4,7,8,5]=>0001100=>0011000
[4,8,7,6,3,5,2,1]=>[1,2,5,3,6,7,8,4]=>0011000=>0001100
[5,8,4,7,6,3,2,1]=>[1,2,3,6,7,4,8,5]=>0001100=>0011000
[4,8,7,3,6,5,2,1]=>[1,2,5,6,3,7,8,4]=>0011000=>0001100
[6,8,5,4,7,3,2,1]=>[1,2,3,7,4,5,8,6]=>0001010=>0101000
[3,8,7,6,2,5,4,1]=>[1,4,5,2,6,7,8,3]=>0110000=>0000110
[4,8,7,6,3,2,5,1]=>[1,5,2,3,6,7,8,4]=>0101000=>0001010
[3,8,7,6,5,2,1,4]=>[4,1,2,5,6,7,8,3]=>1010000=>0000101
[7,5,8,3,6,2,1,4]=>[4,1,2,6,3,8,5,7]=>1010100=>0010101
[7,5,8,3,2,1,6,4]=>[4,6,1,2,3,8,5,7]=>1000100=>0010001
[9,7,10,5,8,3,6,2,4,1]=>[1,4,2,6,3,8,5,10,7,9]=>011010100=>001010110
[7,6,8,2,5,1,4,3]=>[3,4,1,5,2,8,6,7]=>1100010=>0100011
[6,3,2,7,4,1,8,5]=>[5,8,1,4,7,2,3,6]=>1100000=>0000011
[2,1,7,5,8,4,6,3]=>[3,6,4,8,5,7,1,2]=>1001100=>0011001
[2,7,3,6,8,4,1,5]=>[5,1,4,8,6,3,7,2]=>1110010=>0100111
[2,5,6,8,1,7,4,3]=>[3,4,7,1,8,6,5,2]=>1100110=>0110011
[5,1,7,2,4,8,3,6]=>[6,3,8,4,2,7,1,5]=>1111000=>0001111
[4,2,8,6,1,7,3,5]=>[5,3,7,1,6,8,2,4]=>1110000=>0000111
[3,5,8,7,2,1,6,4]=>[4,6,1,2,7,8,5,3]=>1010100=>0010101
[8,1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1,8]=>1101000=>0001011
[2,6,5,7,1,8,3,4]=>[4,3,8,1,7,5,6,2]=>1110100=>0010111
[8,5,3,6,2,4,1,7]=>[7,1,4,2,6,3,5,8]=>1110000=>0000111
[8,4,1,2,6,5,3,7]=>[7,3,5,6,2,1,4,8]=>1110000=>0000111
[8,3,5,6,2,1,4,7]=>[7,4,1,2,6,5,3,8]=>1011100=>0011101
[8,1,4,6,3,5,2,7]=>[7,2,5,3,6,4,1,8]=>1111000=>0001111
[5,4,7,6,8,2,3,1]=>[1,3,2,8,6,7,4,5]=>0101010=>0101010
[4,1,8,2,3,7,6,5]=>[5,6,7,3,2,8,1,4]=>1110000=>0000111
[3,7,4,5,8,2,1,6]=>[6,1,2,8,5,4,7,3]=>1011100=>0011101
[6,3,8,5,7,4,1,2]=>[2,1,4,7,5,8,3,6]=>1010100=>0010101
[5,2,4,6,8,7,3,1]=>[1,3,7,8,6,4,2,5]=>0101010=>0101010
[1,6,8,3,4,5,7,2]=>[2,7,5,4,3,8,6,1]=>1011110=>0111101
[5,7,4,8,6,1,3,2]=>[2,3,1,6,8,4,7,5]=>1001100=>0011001
[5,4,1,6,8,2,7,3]=>[3,7,2,8,6,1,4,5]=>1100010=>0100011
[7,4,1,8,3,5,6,2]=>[2,6,5,3,8,1,4,7]=>1010100=>0010101
[7,5,8,2,1,4,6,3]=>[3,6,4,1,2,8,5,7]=>1001100=>0011001
[7,4,8,3,2,6,1,5]=>[5,1,6,2,3,8,4,7]=>1101000=>0001011
[7,4,3,2,6,8,5,1]=>[1,5,8,6,2,3,4,7]=>0100010=>0100010
[8,3,7,2,1,5,6,4]=>[4,6,5,1,2,7,3,8]=>1010100=>0010101
[5,1,2,3,6,8,7,4]=>[4,7,8,6,3,2,1,5]=>1110010=>0100111
[6,3,8,2,7,4,1,5]=>[5,1,4,7,2,8,3,6]=>1110000=>0000111
[5,7,8,2,1,4,3,6]=>[6,3,4,1,2,8,7,5]=>1010101=>1010101
[3,5,1,7,8,4,2,6]=>[6,2,4,8,7,1,5,3]=>1110001=>1000111
[8,4,7,3,2,6,1,5]=>[5,1,6,2,3,7,4,8]=>1101000=>0001011
[8,4,7,2,1,3,5,6]=>[6,5,3,1,2,7,4,8]=>1011100=>0011101
[6,4,2,1,3,7,8,5]=>[5,8,7,3,1,2,4,6]=>1010001=>1000101
[7,1,6,3,5,8,2,4]=>[4,2,8,5,3,6,1,7]=>1110100=>0010111
[5,3,6,7,8,4,2,1]=>[1,2,4,8,7,6,3,5]=>0010011=>1100100
[1,5,2,7,8,6,4,3]=>[3,4,6,8,7,2,5,1]=>1100001=>1000011
[2,6,8,5,1,4,7,3]=>[3,7,4,1,5,8,6,2]=>1101010=>0101011
[1,4,2,8,6,5,7,3]=>[3,7,5,6,8,2,4,1]=>1100100=>0010011
[3,5,1,6,8,7,2,4]=>[4,2,7,8,6,1,5,3]=>1110010=>0100111
[5,7,6,2,1,3,8,4]=>[4,8,3,1,2,6,7,5]=>1010100=>0010101
[2,5,8,7,4,1,6,3]=>[3,6,1,4,7,8,5,2]=>1100100=>0010011
[7,6,2,4,5,1,8,3]=>[3,8,1,5,4,2,6,7]=>1101000=>0001011
[4,2,1,5,6,7,8,3]=>[3,8,7,6,5,1,2,4]=>1000111=>1110001
[8,3,4,1,5,6,7,2]=>[2,7,6,5,1,4,3,8]=>1010110=>0110101
[7,3,5,2,4,6,1,8]=>[8,1,6,4,2,5,3,7]=>1111000=>0001111
[3,5,2,7,4,6,1,8]=>[8,1,6,4,7,2,5,3]=>1111000=>0001111
[3,7,5,2,4,6,1,8]=>[8,1,6,4,2,5,7,3]=>1111000=>0001111
[5,7,3,2,4,6,1,8]=>[8,1,6,4,2,3,7,5]=>1101100=>0011011
[5,7,3,2,1,4,6,8]=>[8,6,4,1,2,3,7,5]=>1001110=>0111001
[5,7,3,2,4,1,6,8]=>[8,6,1,4,2,3,7,5]=>1100110=>0110011
[3,7,5,2,4,1,6,8]=>[8,6,1,4,2,5,7,3]=>1110010=>0100111
[3,2,7,5,4,1,6,8]=>[8,6,1,4,5,7,2,3]=>1100010=>0100011
[5,1,3,2,7,4,6,8]=>[8,6,4,7,2,3,1,5]=>1101010=>0101011
[1,7,3,5,2,4,6,8]=>[8,6,4,2,5,3,7,1]=>1111010=>0101111
[3,2,1,5,7,4,6,8]=>[8,6,4,7,5,1,2,3]=>1001110=>0111001
[3,2,7,5,1,4,6,8]=>[8,6,4,1,5,7,2,3]=>1101010=>0101011
[5,7,3,1,2,4,6,8]=>[8,6,4,2,1,3,7,5]=>1101110=>0111011
[1,5,3,7,2,4,6,8]=>[8,6,4,2,7,3,5,1]=>1111010=>0101111
[3,5,7,2,1,4,6,8]=>[8,6,4,1,2,7,5,3]=>1011110=>0111101
[3,5,2,7,1,4,6,8]=>[8,6,4,1,7,2,5,3]=>1111010=>0101111
[3,5,2,7,4,1,6,8]=>[8,6,1,4,7,2,5,3]=>1110010=>0100111
[3,5,7,2,4,1,6,8]=>[8,6,1,4,2,7,5,3]=>1110110=>0110111
[5,3,7,2,4,1,6,8]=>[8,6,1,4,2,7,3,5]=>1110010=>0100111
[7,3,5,2,1,4,6,8]=>[8,6,4,1,2,5,3,7]=>1011010=>0101101
[5,3,2,4,7,1,6,8]=>[8,6,1,7,4,2,3,5]=>1101010=>0101011
[3,5,2,4,1,7,6,8]=>[8,6,7,1,4,2,5,3]=>1110010=>0100111
[1,3,2,7,5,4,6,8]=>[8,6,4,5,7,2,3,1]=>1101010=>0101011
[5,3,1,2,7,4,6,8]=>[8,6,4,7,2,1,3,5]=>1101010=>0101011
[5,3,1,2,4,7,6,8]=>[8,6,7,4,2,1,3,5]=>1101010=>0101011
[3,2,5,1,7,4,6,8]=>[8,6,4,7,1,5,2,3]=>1101010=>0101011
[7,5,1,3,2,4,6,8]=>[8,6,4,2,3,1,5,7]=>1101010=>0101011
[5,7,1,3,2,4,6,8]=>[8,6,4,2,3,1,7,5]=>1101110=>0111011
[3,2,1,7,5,4,6,8]=>[8,6,4,5,7,1,2,3]=>1001010=>0101001
[3,1,7,2,5,4,6,8]=>[8,6,4,5,2,7,1,3]=>1101010=>0101011
[5,1,7,3,2,4,6,8]=>[8,6,4,2,3,7,1,5]=>1101010=>0101011
[7,1,5,3,2,4,6,8]=>[8,6,4,2,3,5,1,7]=>1101010=>0101011
[1,7,5,3,2,4,6,8]=>[8,6,4,2,3,5,7,1]=>1101010=>0101011
[5,8,7,1,2,6,4,3]=>[3,4,6,2,1,7,8,5]=>1100100=>0010011
[6,8,2,1,7,5,4,3]=>[3,4,5,7,1,2,8,6]=>1000010=>0100001
[1,8,7,6,3,2,5,4]=>[4,5,2,3,6,7,8,1]=>1100000=>0000011
[5,8,7,4,1,2,6,3]=>[3,6,2,1,4,7,8,5]=>1100100=>0010011
[6,8,5,1,2,7,4,3]=>[3,4,7,2,1,5,8,6]=>1100010=>0100011
[2,8,7,4,3,6,1,5]=>[5,1,6,3,4,7,8,2]=>1110000=>0000111
[1,8,5,4,2,7,6,3]=>[3,6,7,2,4,5,8,1]=>1100000=>0000011
[7,6,4,2,8,5,3,1]=>[1,3,5,8,2,4,6,7]=>0100000=>0000010
[7,6,4,8,5,1,2,3]=>[3,2,1,5,8,4,6,7]=>1101000=>0001011
[7,6,4,5,1,3,8,2]=>[2,8,3,1,5,4,6,7]=>1011000=>0001101
[1,6,7,5,3,8,4,2]=>[2,4,8,3,5,7,6,1]=>1010010=>0100101
[7,6,4,2,5,1,8,3]=>[3,8,1,5,2,4,6,7]=>1100000=>0000011
[7,6,2,8,3,1,4,5]=>[5,4,1,3,8,2,6,7]=>1101000=>0001011
[6,2,3,8,7,4,1,5]=>[5,1,4,7,8,3,2,6]=>1110000=>0000111
[2,6,5,7,8,3,4,1]=>[1,4,3,8,7,5,6,2]=>0110101=>1010110
[2,4,7,3,5,8,6,1]=>[1,6,8,5,3,7,4,2]=>0111100=>0011110
[2,5,3,7,1,8,4,6]=>[6,4,8,1,7,3,5,2]=>1111000=>0001111
[3,2,5,1,7,8,4,6]=>[6,4,8,7,1,5,2,3]=>1101001=>1001011
[5,2,3,4,8,6,1,7]=>[7,1,6,8,4,3,2,5]=>1111000=>0001111
[5,3,4,8,2,7,6,1]=>[1,6,7,2,8,4,3,5]=>0111000=>0001110
[5,3,8,2,4,1,7,6]=>[6,7,1,4,2,8,3,5]=>1110000=>0000111
[5,2,8,4,1,7,3,6]=>[6,3,7,1,4,8,2,5]=>1110000=>0000111
[6,4,2,5,1,8,7,3]=>[3,7,8,1,5,2,4,6]=>1100000=>0000011
[6,4,3,5,8,2,1,7]=>[7,1,2,8,5,3,4,6]=>1010100=>0010101
[6,3,5,4,8,2,7,1]=>[1,7,2,8,4,5,3,6]=>0111000=>0001110
[6,3,5,8,7,1,2,4]=>[4,2,1,7,8,5,3,6]=>1110100=>0010111
[5,8,1,4,3,6,2,7]=>[7,2,6,3,4,1,8,5]=>1110100=>0010111
[6,4,5,3,8,1,7,2]=>[2,7,1,8,3,5,4,6]=>1011000=>0001101
[6,4,3,8,5,7,2,1]=>[1,2,7,5,8,3,4,6]=>0010100=>0010100
[5,4,2,6,3,1,7,8]=>[8,7,1,3,6,2,4,5]=>1100001=>1000011
[4,5,1,3,6,2,8,7]=>[7,8,2,6,3,1,5,4]=>1111000=>0001111
[3,5,6,1,4,8,7,2]=>[2,7,8,4,1,6,5,3]=>1011100=>0011101
[3,5,7,6,1,4,8,2]=>[2,8,4,1,6,7,5,3]=>1011100=>0011101
[3,6,5,7,4,8,1,2]=>[2,1,8,4,7,5,6,3]=>1011100=>0011101
[4,2,6,5,1,7,3,8]=>[8,3,7,1,5,6,2,4]=>1110000=>0000111
[4,3,5,7,2,1,6,8]=>[8,6,1,2,7,5,3,4]=>1010110=>0110101
[3,5,4,7,2,6,1,8]=>[8,1,6,2,7,4,5,3]=>1111000=>0001111
[3,4,7,6,8,1,2,5]=>[5,2,1,8,6,7,4,3]=>1111010=>0101111
[3,5,2,4,6,1,8,7]=>[7,8,1,6,4,2,5,3]=>1111000=>0001111
[1,8,4,3,7,5,6,2]=>[2,6,5,7,3,4,8,1]=>1010100=>0010101
[5,2,8,6,4,7,3,1]=>[1,3,7,4,6,8,2,5]=>0101000=>0001010
[1,8,6,3,7,4,2,5]=>[5,2,4,7,3,6,8,1]=>1110000=>0000111
[1,8,6,5,7,2,3,4]=>[4,3,2,7,5,6,8,1]=>1110100=>0010111
[1,5,7,2,4,6,8,3]=>[3,8,6,4,2,7,5,1]=>1101110=>0111011
[5,2,3,8,4,1,7,6]=>[6,7,1,4,8,3,2,5]=>1110000=>0000111
[7,5,3,4,8,2,1,6]=>[6,1,2,8,4,3,5,7]=>1011000=>0001101
[7,6,3,8,4,2,1,5]=>[5,1,2,4,8,3,6,7]=>1010000=>0000101
[7,2,8,5,1,6,3,4]=>[4,3,6,1,5,8,2,7]=>1110000=>0000111
[7,4,3,8,5,2,6,1]=>[1,6,2,5,8,3,4,7]=>0110000=>0000110
[7,6,3,8,2,4,5,1]=>[1,5,4,2,8,3,6,7]=>0111000=>0001110
[7,2,8,5,1,3,4,6]=>[6,4,3,1,5,8,2,7]=>1111000=>0001111
[7,6,8,1,2,5,3,4]=>[4,3,5,2,1,8,6,7]=>1110010=>0100111
[1,5,3,7,6,8,4,2]=>[2,4,8,6,7,3,5,1]=>1010010=>0100101
[1,2,7,4,8,5,3,6]=>[6,3,5,8,4,7,2,1]=>1111000=>0001111
[4,2,6,7,5,8,1,3]=>[3,1,8,5,7,6,2,4]=>1100110=>0110011
[3,2,4,7,8,5,1,6]=>[6,1,5,8,7,4,2,3]=>1101001=>1001011
[3,8,4,7,6,1,5,2]=>[2,5,1,6,7,4,8,3]=>1011000=>0001101
[5,7,4,2,6,3,1,8]=>[8,1,3,6,2,4,7,5]=>1100100=>0010011
[4,2,6,3,5,7,1,8]=>[8,1,7,5,3,6,2,4]=>1110100=>0010111
[8,3,4,6,5,1,7,2]=>[2,7,1,5,6,4,3,8]=>1011000=>0001101
[6,1,3,7,4,2,5,8]=>[8,5,2,4,7,3,1,6]=>1110100=>0010111
[2,1,8,3,6,7,4,5]=>[5,4,7,6,3,8,1,2]=>1011010=>0101101
[5,1,8,6,2,7,3,4]=>[4,3,7,2,6,8,1,5]=>1110000=>0000111
[5,7,1,4,2,6,3,8]=>[8,3,6,2,4,1,7,5]=>1110100=>0010111
[8,2,6,1,5,4,7,3]=>[3,7,4,5,1,6,2,8]=>1101000=>0001011
[7,8,5,4,1,6,3,2]=>[2,3,6,1,4,5,8,7]=>1000001=>1000001
[5,7,4,2,8,1,6,3]=>[3,6,1,8,2,4,7,5]=>1100100=>0010011
[7,5,2,8,6,1,4,3]=>[3,4,1,6,8,2,5,7]=>1100000=>0000011
[3,6,2,7,8,1,5,4]=>[4,5,1,8,7,2,6,3]=>1110001=>1000111
[2,6,8,4,1,5,7,3]=>[3,7,5,1,4,8,6,2]=>1100110=>0110011
[5,7,8,4,1,6,3,2]=>[2,3,6,1,4,8,7,5]=>1000101=>1010001
[4,5,6,8,3,1,7,2]=>[2,7,1,3,8,6,5,4]=>1001110=>0111001
[8,4,6,5,3,1,7,2]=>[2,7,1,3,5,6,4,8]=>1001000=>0001001
[5,6,4,8,3,1,7,2]=>[2,7,1,3,8,4,6,5]=>1001100=>0011001
[3,4,8,1,2,5,7,6]=>[6,7,5,2,1,8,4,3]=>1111100=>0011111
[6,3,1,7,5,2,4,8]=>[8,4,2,5,7,1,3,6]=>1101000=>0001011
[4,5,3,1,7,2,6,8]=>[8,6,2,7,1,3,5,4]=>1101010=>0101011
[6,3,1,8,2,7,4,5]=>[5,4,7,2,8,1,3,6]=>1101000=>0001011
[7,8,1,2,4,3,6,5]=>[5,6,3,4,2,1,8,7]=>1110001=>1000111
[5,2,8,1,3,4,7,6]=>[6,7,4,3,1,8,2,5]=>1111000=>0001111
[3,2,1,6,4,7,8,5]=>[5,8,7,4,6,1,2,3]=>1001001=>1001001
[5,1,3,4,2,7,8,6]=>[6,8,7,2,4,3,1,5]=>1110001=>1000111
[8,1,4,2,5,7,6,3]=>[3,6,7,5,2,4,1,8]=>1100100=>0010011
[3,2,6,1,5,7,8,4]=>[4,8,7,5,1,6,2,3]=>1100101=>1010011
[1,4,6,3,5,7,8,2]=>[2,8,7,5,3,6,4,1]=>1011101=>1011101
[3,5,1,6,4,7,8,2]=>[2,8,7,4,6,1,5,3]=>1011001=>1001101
[3,6,4,2,1,7,8,5]=>[5,8,7,1,2,4,6,3]=>1010001=>1000101
[2,6,5,3,1,7,8,4]=>[4,8,7,1,3,5,6,2]=>1100001=>1000011
[1,7,4,3,6,8,2,5]=>[5,2,8,6,3,4,7,1]=>1110010=>0100111
[2,7,6,3,1,8,4,5]=>[5,4,8,1,3,6,7,2]=>1101000=>0001011
[3,8,6,1,4,7,5,2]=>[2,5,7,4,1,6,8,3]=>1011000=>0001101
[2,8,4,6,3,7,5,1]=>[1,5,7,3,6,4,8,2]=>0111000=>0001110
[1,8,3,2,6,7,5,4]=>[4,5,7,6,2,3,8,1]=>1100010=>0100011
[8,7,1,3,6,5,4,2]=>[2,4,5,6,3,1,7,8]=>1010000=>0000101
[1,8,5,7,4,2,6,3]=>[3,6,2,4,7,5,8,1]=>1100100=>0010011
[4,8,6,2,7,1,5,3]=>[3,5,1,7,2,6,8,4]=>1101000=>0001011
[2,7,6,5,8,3,1,4]=>[4,1,3,8,5,6,7,2]=>1100100=>0010011
[1,4,7,6,8,2,3,5]=>[5,3,2,8,6,7,4,1]=>1111010=>0101111
[3,5,7,4,8,1,2,6]=>[6,2,1,8,4,7,5,3]=>1111100=>0011111
[4,6,1,7,5,8,2,3]=>[3,2,8,5,7,1,6,4]=>1101100=>0011011
[2,3,6,7,5,8,1,4]=>[4,1,8,5,7,6,3,2]=>1110110=>0110111
[1,3,7,5,6,8,2,4]=>[4,2,8,6,5,7,3,1]=>1110110=>0110111
[8,2,5,3,7,1,6,4]=>[4,6,1,7,3,5,2,8]=>1110000=>0000111
[2,1,4,7,5,8,3,6]=>[6,3,8,5,7,4,1,2]=>1011100=>0011101
[1,2,6,7,4,8,3,5]=>[5,3,8,4,7,6,2,1]=>1111010=>0101111
[3,6,4,7,8,5,2,1]=>[1,2,5,8,7,4,6,3]=>0011001=>1001100
[6,3,5,8,7,4,1,2]=>[2,1,4,7,8,5,3,6]=>1010100=>0010101
[4,1,8,3,7,5,6,2]=>[2,6,5,7,3,8,1,4]=>1010100=>0010101
[1,4,8,7,3,5,6,2]=>[2,6,5,3,7,8,4,1]=>1011100=>0011101
[3,2,8,7,1,5,6,4]=>[4,6,5,1,7,8,2,3]=>1100100=>0010011
[1,5,8,7,4,6,2,3]=>[3,2,6,4,7,8,5,1]=>1101100=>0011011
[3,6,8,5,7,4,1,2]=>[2,1,4,7,5,8,6,3]=>1010110=>0110101
[4,8,6,7,5,3,2,1]=>[1,2,3,5,7,6,8,4]=>0001010=>0101000
[1,8,7,6,5,3,4,2]=>[2,4,3,5,6,7,8,1]=>1010000=>0000101
[1,7,8,3,5,2,4,6]=>[6,4,2,5,3,8,7,1]=>1111001=>1001111
[8,5,3,7,2,4,6,1]=>[1,6,4,2,7,3,5,8]=>0111000=>0001110
[1,7,2,4,8,5,3,6]=>[6,3,5,8,4,2,7,1]=>1111000=>0001111
[8,2,5,3,1,6,4,7]=>[7,4,6,1,3,5,2,8]=>1101000=>0001011
[8,3,2,1,5,6,4,7]=>[7,4,6,5,1,2,3,8]=>1001100=>0011001
[2,7,6,8,4,3,1,5]=>[5,1,3,4,8,6,7,2]=>1100010=>0100011
[8,1,4,6,7,3,5,2]=>[2,5,3,7,6,4,1,8]=>1011010=>0101101
[3,1,6,5,8,7,4,2]=>[2,4,7,8,5,6,1,3]=>1000100=>0010001
[4,7,1,3,6,8,2,5]=>[5,2,8,6,3,1,7,4]=>1111010=>0101111
[3,1,7,5,6,8,2,4]=>[4,2,8,6,5,7,1,3]=>1100110=>0110011
[2,3,6,4,1,7,8,5]=>[5,8,7,1,4,6,3,2]=>1110001=>1000111
[4,7,2,1,5,3,8,6]=>[6,8,3,5,1,2,7,4]=>1011000=>0001101
[3,1,7,4,5,2,8,6]=>[6,8,2,5,4,7,1,3]=>1101000=>0001011
[3,7,5,4,2,1,8,6]=>[6,8,1,2,4,5,7,3]=>1010000=>0000101
[4,3,7,2,6,8,1,5]=>[5,1,8,6,2,7,3,4]=>1110010=>0100111
[5,4,2,1,3,7,8,6]=>[6,8,7,3,1,2,4,5]=>1010001=>1000101
[8,7,1,5,6,3,2,4]=>[4,2,3,6,5,1,7,8]=>1100100=>0010011
[8,7,2,4,6,5,3,1]=>[1,3,5,6,4,2,7,8]=>0101000=>0001010
[8,7,1,2,4,5,6,3]=>[3,6,5,4,2,1,7,8]=>1101100=>0011011
[8,7,2,5,3,1,6,4]=>[4,6,1,3,5,2,7,8]=>1100000=>0000011
[8,2,6,7,3,1,5,4]=>[4,5,1,3,7,6,2,8]=>1100010=>0100011
[3,7,8,2,1,6,5,4]=>[4,5,6,1,2,8,7,3]=>1010001=>1000101
[8,7,6,5,1,3,4,2]=>[2,4,3,1,5,6,7,8]=>1010000=>0000101
[8,7,6,1,4,5,3,2]=>[2,3,5,4,1,6,7,8]=>1001000=>0001001
[8,7,5,6,1,4,3,2]=>[2,3,4,1,6,5,7,8]=>1000100=>0010001
[8,5,7,6,1,4,3,2]=>[2,3,4,1,6,7,5,8]=>1000100=>0010001
[6,7,8,1,5,4,3,2]=>[2,3,4,5,1,8,7,6]=>1000011=>1100001
[8,5,6,7,1,4,3,2]=>[2,3,4,1,7,6,5,8]=>1000110=>0110001
[8,7,6,5,2,4,3,1]=>[1,3,4,2,5,6,7,8]=>0100000=>0000010
[7,6,5,4,2,8,3,1]=>[1,3,8,2,4,5,6,7]=>0100000=>0000010
[8,7,5,4,2,6,3,1]=>[1,3,6,2,4,5,7,8]=>0100000=>0000010
[4,2,8,7,6,5,1,3]=>[3,1,5,6,7,8,2,4]=>1100000=>0000011
[7,5,8,1,6,4,3,2]=>[2,3,4,6,1,8,5,7]=>1000100=>0010001
[3,5,8,7,6,2,1,4]=>[4,1,2,6,7,8,5,3]=>1010100=>0010101
[7,5,8,4,1,6,3,2]=>[2,3,6,1,4,8,5,7]=>1000100=>0010001
[6,8,5,1,7,4,3,2]=>[2,3,4,7,1,5,8,6]=>1000010=>0100001
[7,3,8,4,6,1,5,2]=>[2,5,1,6,4,8,3,7]=>1011000=>0001101
[4,8,5,7,1,6,3,2]=>[2,3,6,1,7,5,8,4]=>1001100=>0011001
[6,3,7,8,5,1,4,2]=>[2,4,1,5,8,7,3,6]=>1010001=>1000101
[5,4,3,6,7,1,8,2]=>[2,8,1,7,6,3,4,5]=>1010010=>0100101
[4,8,7,3,5,1,6,2]=>[2,6,1,5,3,7,8,4]=>1011000=>0001101
[4,8,7,6,3,1,5,2]=>[2,5,1,3,6,7,8,4]=>1001000=>0001001
[3,4,5,2,8,1,6,7]=>[7,6,1,8,2,5,4,3]=>1111010=>0101111
[3,1,5,7,4,2,8,6]=>[6,8,2,4,7,5,1,3]=>1100100=>0010011
[3,4,2,7,8,5,6,1]=>[1,6,5,8,7,2,4,3]=>0110101=>1010110
[2,4,6,3,1,7,8,5]=>[5,8,7,1,3,6,4,2]=>1101001=>1001011
[6,5,8,4,7,2,1,3]=>[3,1,2,7,4,8,5,6]=>1001100=>0011001
[6,8,5,7,3,2,1,4]=>[4,1,2,3,7,5,8,6]=>1000110=>0110001
[6,5,4,8,3,1,7,2]=>[2,7,1,3,8,4,5,6]=>1001000=>0001001
[6,8,5,3,7,2,1,4]=>[4,1,2,7,3,5,8,6]=>1010010=>0100101
[6,5,8,4,7,3,1,2]=>[2,1,3,7,4,8,5,6]=>1001100=>0011001
[6,8,5,7,4,2,1,3]=>[3,1,2,4,7,5,8,6]=>1000110=>0110001
[2,1,8,7,6,3,4,5]=>[5,4,3,6,7,8,1,2]=>1011000=>0001101
[2,1,8,7,3,6,5,4]=>[4,5,6,3,7,8,1,2]=>1010000=>0000101
[5,8,7,6,2,4,1,3]=>[3,1,4,2,6,7,8,5]=>1100100=>0010011
[6,8,2,7,5,1,4,3]=>[3,4,1,5,7,2,8,6]=>1100010=>0100011
[6,8,7,5,2,4,1,3]=>[3,1,4,2,5,7,8,6]=>1100010=>0100011
[5,8,7,6,4,2,3,1]=>[1,3,2,4,6,7,8,5]=>0100100=>0010010
[2,3,5,7,4,8,6,1]=>[1,6,8,4,7,5,3,2]=>0111100=>0011110
[2,3,5,7,8,4,6,1]=>[1,6,4,8,7,5,3,2]=>0111101=>1011110
[2,3,6,1,7,5,8,4]=>[4,8,5,7,1,6,3,2]=>1110100=>0010111
[2,3,6,1,8,5,4,7]=>[7,4,5,8,1,6,3,2]=>1111000=>0001111
[2,3,7,1,8,5,6,4]=>[4,6,5,8,1,7,3,2]=>1110100=>0010111
[2,4,1,6,7,5,8,3]=>[3,8,5,7,6,1,4,2]=>1100110=>0110011
[2,4,1,7,3,8,6,5]=>[5,6,8,3,7,1,4,2]=>1110000=>0000111
[2,4,1,7,8,5,6,3]=>[3,6,5,8,7,1,4,2]=>1100101=>1010011
[2,4,5,3,7,1,8,6]=>[6,8,1,7,3,5,4,2]=>1111000=>0001111
[2,4,6,3,1,8,5,7]=>[7,5,8,1,3,6,4,2]=>1101100=>0011011
[2,4,6,3,8,5,1,7]=>[7,1,5,8,3,6,4,2]=>1111000=>0001111
[2,4,6,8,3,5,1,7]=>[7,1,5,3,8,6,4,2]=>1111010=>0101111
[2,4,7,3,1,8,6,5]=>[5,6,8,1,3,7,4,2]=>1101000=>0001011
[2,5,1,6,7,4,8,3]=>[3,8,4,7,6,1,5,2]=>1101010=>0101011
[2,5,1,7,4,3,8,6]=>[6,8,3,4,7,1,5,2]=>1110000=>0000111
[2,5,1,7,8,4,6,3]=>[3,6,4,8,7,1,5,2]=>1101001=>1001011
[2,5,6,3,7,4,8,1]=>[1,8,4,7,3,6,5,2]=>0111100=>0011110
[2,5,6,3,8,4,1,7]=>[7,1,4,8,3,6,5,2]=>1110100=>0010111
[2,5,6,7,8,4,1,3]=>[3,1,4,8,7,6,5,2]=>1100111=>1110011
[2,5,6,8,4,3,1,7]=>[7,1,3,4,8,6,5,2]=>1100110=>0110011
[2,5,7,3,4,1,8,6]=>[6,8,1,4,3,7,5,2]=>1110100=>0010111
[2,6,1,7,4,8,5,3]=>[3,5,8,4,7,1,6,2]=>1101000=>0001011
[2,6,7,3,4,5,8,1]=>[1,8,5,4,3,7,6,2]=>0111110=>0111110
[7,6,5,3,8,1,4,2]=>[2,4,1,8,3,5,6,7]=>1010000=>0000101
[7,6,5,2,8,4,1,3]=>[3,1,4,8,2,5,6,7]=>1100000=>0000011
[5,8,4,6,2,1,3,7]=>[7,3,1,2,6,4,8,5]=>1011100=>0011101
[7,4,8,3,5,1,6,2]=>[2,6,1,5,3,8,4,7]=>1011000=>0001101
[7,6,3,8,2,4,1,5]=>[5,1,4,2,8,3,6,7]=>1110000=>0000111
[5,1,2,3,4,8,7,6]=>[6,7,8,4,3,2,1,5]=>1111000=>0001111
[4,1,2,3,7,6,5,8]=>[8,5,6,7,3,2,1,4]=>1110100=>0010111
[7,6,5,8,2,4,3,1]=>[1,3,4,2,8,5,6,7]=>0100100=>0010010
[7,6,8,3,5,4,2,1]=>[1,2,4,5,3,8,6,7]=>0010010=>0100100
[7,8,4,6,5,3,2,1]=>[1,2,3,5,6,4,8,7]=>0001001=>1001000
[6,8,7,4,5,2,3,1]=>[1,3,2,5,4,7,8,6]=>0101010=>0101010
[6,8,4,7,5,2,3,1]=>[1,3,2,5,7,4,8,6]=>0101010=>0101010
[6,8,4,7,2,5,3,1]=>[1,3,5,2,7,4,8,6]=>0101010=>0101010
[6,4,8,7,5,2,3,1]=>[1,3,2,5,7,8,4,6]=>0101000=>0001010
[6,8,4,2,7,5,3,1]=>[1,3,5,7,2,4,8,6]=>0100010=>0100010
[6,8,4,7,2,1,5,3]=>[3,5,1,2,7,4,8,6]=>1001010=>0101001
[6,8,4,7,3,5,2,1]=>[1,2,5,3,7,4,8,6]=>0011010=>0101100
[6,4,8,2,7,5,3,1]=>[1,3,5,7,2,8,4,6]=>0101000=>0001010
[6,8,4,2,7,1,5,3]=>[3,5,1,7,2,4,8,6]=>1100010=>0100011
[6,4,2,8,7,5,3,1]=>[1,3,5,7,8,2,4,6]=>0100000=>0000010
[6,8,4,7,3,2,5,1]=>[1,5,2,3,7,4,8,6]=>0101010=>0101010
[6,8,4,2,1,7,5,3]=>[3,5,7,1,2,4,8,6]=>1000010=>0100001
[6,8,4,7,3,2,1,5]=>[5,1,2,3,7,4,8,6]=>1001010=>0101001
[6,8,5,7,1,4,3,2]=>[2,3,4,1,7,5,8,6]=>1000110=>0110001
[4,8,7,6,2,5,1,3]=>[3,1,5,2,6,7,8,4]=>1101000=>0001011
[1,8,7,6,3,5,4,2]=>[2,4,5,3,6,7,8,1]=>1010000=>0000101
[2,8,7,6,3,5,1,4]=>[4,1,5,3,6,7,8,2]=>1110000=>0000111
[5,8,7,3,6,2,1,4]=>[4,1,2,6,3,7,8,5]=>1010100=>0010101
[1,8,7,4,6,2,5,3]=>[3,5,2,6,4,7,8,1]=>1101000=>0001011
[1,8,7,3,6,2,5,4]=>[4,5,2,6,3,7,8,1]=>1110000=>0000111
[5,8,7,2,3,6,1,4]=>[4,1,6,3,2,7,8,5]=>1110100=>0010111
[6,8,3,7,5,2,1,4]=>[4,1,2,5,7,3,8,6]=>1010010=>0100101
[6,8,1,7,3,5,4,2]=>[2,4,5,3,7,1,8,6]=>1010010=>0100101
[6,8,4,7,3,1,5,2]=>[2,5,1,3,7,4,8,6]=>1001010=>0101001
[6,8,4,7,1,2,5,3]=>[3,5,2,1,7,4,8,6]=>1101010=>0101011
[6,8,1,7,3,2,5,4]=>[4,5,2,3,7,1,8,6]=>1100010=>0100011
[3,8,5,7,6,1,4,2]=>[2,4,1,6,7,5,8,3]=>1010100=>0010101
[3,8,2,7,6,5,1,4]=>[4,1,5,6,7,2,8,3]=>1110000=>0000111
[1,8,4,7,6,2,5,3]=>[3,5,2,6,7,4,8,1]=>1101000=>0001011
[3,8,1,7,6,2,5,4]=>[4,5,2,6,7,1,8,3]=>1110000=>0000111
[3,8,4,7,6,2,1,5]=>[5,1,2,6,7,4,8,3]=>1011000=>0001101
[1,8,4,7,3,6,5,2]=>[2,5,6,3,7,4,8,1]=>1011000=>0001101
[4,8,5,7,1,2,6,3]=>[3,6,2,1,7,5,8,4]=>1101100=>0011011
[1,8,5,7,3,2,6,4]=>[4,6,2,3,7,5,8,1]=>1100100=>0010011
[6,8,5,3,7,1,4,2]=>[2,4,1,7,3,5,8,6]=>1010010=>0100101
[6,8,3,4,7,1,5,2]=>[2,5,1,7,4,3,8,6]=>1011010=>0101101
[6,8,1,3,7,2,5,4]=>[4,5,2,7,3,1,8,6]=>1110010=>0100111
[2,8,1,3,7,6,5,4]=>[4,5,6,7,3,1,8,2]=>1110000=>0000111
[6,8,5,4,1,7,3,2]=>[2,3,7,1,4,5,8,6]=>1000010=>0100001
[6,8,1,4,2,7,5,3]=>[3,5,7,2,4,1,8,6]=>1100010=>0100011
[6,5,4,3,8,7,1,2]=>[2,1,7,8,3,4,5,6]=>1010000=>0000101
[6,5,8,4,3,7,1,2]=>[2,1,7,3,4,8,5,6]=>1010100=>0010101
[3,1,6,8,4,5,2,7]=>[7,2,5,4,8,6,1,3]=>1101010=>0101011
[3,1,7,2,4,8,6,5]=>[5,6,8,4,2,7,1,3]=>1101000=>0001011
[3,1,6,7,8,5,4,2]=>[2,4,5,8,7,6,1,3]=>1000011=>1100001
[3,1,6,7,4,8,5,2]=>[2,5,8,4,7,6,1,3]=>1001010=>0101001
[3,1,5,7,8,4,6,2]=>[2,6,4,8,7,5,1,3]=>1001101=>1011001
[8,6,5,7,1,4,3,2]=>[2,3,4,1,7,5,6,8]=>1000100=>0010001
[8,6,2,7,5,4,3,1]=>[1,3,4,5,7,2,6,8]=>0100000=>0000010
[8,6,7,4,2,5,1,3]=>[3,1,5,2,4,7,6,8]=>1100010=>0100011
[8,6,7,4,2,1,5,3]=>[3,5,1,2,4,7,6,8]=>1000010=>0100001
[8,6,4,2,7,5,1,3]=>[3,1,5,7,2,4,6,8]=>1100000=>0000011
[8,6,4,2,7,1,5,3]=>[3,5,1,7,2,4,6,8]=>1100000=>0000011
[6,4,8,2,7,5,1,3]=>[3,1,5,7,2,8,4,6]=>1101000=>0001011
[3,4,5,6,8,7,1,2]=>[2,1,7,8,6,5,4,3]=>1011110=>0111101
[3,4,5,7,8,6,1,2]=>[2,1,6,8,7,5,4,3]=>1011101=>1011101
[3,4,5,8,7,6,1,2]=>[2,1,6,7,8,5,4,3]=>1011100=>0011101
[7,4,8,6,3,2,1,5]=>[5,1,2,3,6,8,4,7]=>1001000=>0001001
[7,6,5,3,8,2,1,4]=>[4,1,2,8,3,5,6,7]=>1010000=>0000101
[7,4,8,3,5,2,1,6]=>[6,1,2,5,3,8,4,7]=>1011000=>0001101
[5,8,3,6,7,2,1,4]=>[4,1,2,7,6,3,8,5]=>1010110=>0110101
[7,3,8,6,5,2,1,4]=>[4,1,2,5,6,8,3,7]=>1010000=>0000101
[6,4,7,8,2,5,1,3]=>[3,1,5,2,8,7,4,6]=>1101001=>1001011
[6,8,5,3,2,4,1,7]=>[7,1,4,2,3,5,8,6]=>1100010=>0100011
[6,8,4,3,2,5,1,7]=>[7,1,5,2,3,4,8,6]=>1100010=>0100011
[4,8,7,3,2,5,1,6]=>[6,1,5,2,3,7,8,4]=>1101000=>0001011
[6,3,7,8,2,4,1,5]=>[5,1,4,2,8,7,3,6]=>1110001=>1000111
[5,3,7,6,2,4,1,8]=>[8,1,4,2,6,7,3,5]=>1110000=>0000111
[7,5,8,2,6,4,1,3]=>[3,1,4,6,2,8,5,7]=>1100100=>0010011
[7,4,8,2,5,6,1,3]=>[3,1,6,5,2,8,4,7]=>1101100=>0011011
[5,4,7,2,6,8,1,3]=>[3,1,8,6,2,7,4,5]=>1101010=>0101011
[5,4,3,2,6,8,1,7]=>[7,1,8,6,2,3,4,5]=>1100010=>0100011
[4,8,3,2,5,6,1,7]=>[7,1,6,5,2,3,8,4]=>1101100=>0011011
[7,5,2,6,8,4,1,3]=>[3,1,4,8,6,2,5,7]=>1100010=>0100011
[6,4,2,7,5,8,1,3]=>[3,1,8,5,7,2,4,6]=>1100100=>0010011
[7,5,8,4,1,2,6,3]=>[3,6,2,1,4,8,5,7]=>1100100=>0010011
[7,1,8,2,3,6,5,4]=>[4,5,6,3,2,8,1,7]=>1110000=>0000111
[7,1,8,4,2,6,5,3]=>[3,5,6,2,4,8,1,7]=>1100000=>0000011
[7,1,8,3,6,2,5,4]=>[4,5,2,6,3,8,1,7]=>1110000=>0000111
[6,2,3,4,1,7,5,8]=>[8,5,7,1,4,3,2,6]=>1110100=>0010111
[2,8,3,4,5,1,6,7]=>[7,6,1,5,4,3,8,2]=>1111010=>0101111
[2,7,3,4,1,5,6,8]=>[8,6,5,1,4,3,7,2]=>1110110=>0110111
[4,2,1,5,3,6,7,8]=>[8,7,6,3,5,1,2,4]=>1010011=>1100101
[5,3,1,7,2,4,8,6]=>[6,8,4,2,7,1,3,5]=>1101000=>0001011
[5,3,6,1,2,7,4,8]=>[8,4,7,2,1,6,3,5]=>1111000=>0001111
[2,8,5,3,4,6,7,1]=>[1,7,6,4,3,5,8,2]=>0111010=>0101110
[3,6,1,4,8,2,7,5]=>[5,7,2,8,4,1,6,3]=>1111000=>0001111
[4,5,3,1,2,6,8,7]=>[7,8,6,2,1,3,5,4]=>1101010=>0101011
[3,4,1,2,5,8,7,6]=>[6,7,8,5,2,1,4,3]=>1110100=>0010111
[6,7,4,3,2,1,8,5]=>[5,8,1,2,3,4,7,6]=>1000010=>0100001
[4,5,2,1,8,7,6,3]=>[3,6,7,8,1,2,5,4]=>1001000=>0001001
[3,4,1,8,7,6,5,2]=>[2,5,6,7,8,1,4,3]=>1010000=>0000101
[7,1,2,3,4,6,8,5]=>[5,8,6,4,3,2,1,7]=>1111010=>0101111
[6,1,2,3,5,8,7,4]=>[4,7,8,5,3,2,1,6]=>1110100=>0010111
[5,1,2,4,8,6,7,3]=>[3,7,6,8,4,2,1,5]=>1101010=>0101011
[4,1,3,8,5,6,7,2]=>[2,7,6,5,8,3,1,4]=>1010110=>0110101
[7,1,2,3,5,8,6,4]=>[4,6,8,5,3,2,1,7]=>1110100=>0010111
[6,1,2,3,5,7,8,4]=>[4,8,7,5,3,2,1,6]=>1110101=>1010111
[5,1,3,8,4,6,7,2]=>[2,7,6,4,8,3,1,5]=>1011010=>0101101
[5,1,2,4,6,8,7,3]=>[3,7,8,6,4,2,1,5]=>1101010=>0101011
[4,2,8,3,5,6,7,1]=>[1,7,6,5,3,8,2,4]=>0110110=>0110110
[8,6,3,5,2,7,4,1]=>[1,4,7,2,5,3,6,8]=>0110000=>0000110
[7,5,2,8,6,3,4,1]=>[1,4,3,6,8,2,5,7]=>0110000=>0000110
[5,2,8,6,7,3,4,1]=>[1,4,3,7,6,8,2,5]=>0110010=>0100110
[7,5,2,3,8,6,4,1]=>[1,4,6,8,3,2,5,7]=>0110000=>0000110
[5,2,8,3,4,1,6,7]=>[7,6,1,4,3,8,2,5]=>1110010=>0100111
[5,2,3,8,6,7,4,1]=>[1,4,7,6,8,3,2,5]=>0110010=>0100110
[7,4,1,2,6,8,5,3]=>[3,5,8,6,2,1,4,7]=>1100010=>0100011
[5,3,8,4,1,2,6,7]=>[7,6,2,1,4,8,3,5]=>1110010=>0100111
[7,3,5,6,8,4,1,2]=>[2,1,4,8,6,5,3,7]=>1010110=>0110101
[7,4,5,1,2,8,6,3]=>[3,6,8,2,1,5,4,7]=>1101000=>0001011
[6,3,8,4,5,1,2,7]=>[7,2,1,5,4,8,3,6]=>1111000=>0001111
[7,4,5,1,8,6,2,3]=>[3,2,6,8,1,5,4,7]=>1101000=>0001011
[6,2,3,4,8,5,1,7]=>[7,1,5,8,4,3,2,6]=>1111000=>0001111
[7,3,4,5,1,8,6,2]=>[2,6,8,1,5,4,3,7]=>1011000=>0001101
[8,4,5,1,7,3,6,2]=>[2,6,3,7,1,5,4,8]=>1011000=>0001101
[6,2,8,3,4,5,1,7]=>[7,1,5,4,3,8,2,6]=>1111000=>0001111
[7,2,3,4,6,8,5,1]=>[1,5,8,6,4,3,2,7]=>0111010=>0101110
[4,2,7,5,8,6,3,1]=>[1,3,6,8,5,7,2,4]=>0100100=>0010010
[4,2,8,5,6,7,3,1]=>[1,3,7,6,5,8,2,4]=>0100110=>0110010
[7,4,8,5,6,1,2,3]=>[3,2,1,6,5,8,4,7]=>1101100=>0011011
[7,4,5,8,6,1,2,3]=>[3,2,1,6,8,5,4,7]=>1101100=>0011011
[7,5,8,6,1,2,3,4]=>[4,3,2,1,6,8,5,7]=>1110100=>0010111
[6,4,8,5,2,3,1,7]=>[7,1,3,2,5,8,4,6]=>1101000=>0001011
[7,4,6,8,5,2,3,1]=>[1,3,2,5,8,6,4,7]=>0101010=>0101010
[7,2,3,8,4,5,6,1]=>[1,6,5,4,8,3,2,7]=>0111100=>0011110
[8,6,3,1,7,5,2,4]=>[4,2,5,7,1,3,6,8]=>1100000=>0000011
[7,2,8,3,4,5,6,1]=>[1,6,5,4,3,8,2,7]=>0111100=>0011110
[7,4,5,2,8,6,3,1]=>[1,3,6,8,2,5,4,7]=>0101000=>0001010
[8,5,2,7,4,6,3,1]=>[1,3,6,4,7,2,5,8]=>0101000=>0001010
[5,2,4,8,6,7,3,1]=>[1,3,7,6,8,4,2,5]=>0101010=>0101010
[8,5,2,4,6,7,3,1]=>[1,3,7,6,4,2,5,8]=>0101010=>0101010
[5,2,4,8,3,1,6,7]=>[7,6,1,3,8,4,2,5]=>1101010=>0101011
[7,4,5,8,6,2,3,1]=>[1,3,2,6,8,5,4,7]=>0101100=>0011010
[7,4,8,5,6,2,3,1]=>[1,3,2,6,5,8,4,7]=>0101100=>0011010
[4,8,2,5,1,3,7,6]=>[6,7,3,1,5,2,8,4]=>1111000=>0001111
[3,5,4,6,1,7,8,2]=>[2,8,7,1,6,4,5,3]=>1011001=>1001101
[5,2,1,6,3,7,8,4]=>[4,8,7,3,6,1,2,5]=>1010001=>1000101
[4,1,2,8,7,5,3,6]=>[6,3,5,7,8,2,1,4]=>1110000=>0000111
[3,1,5,8,2,6,4,7]=>[7,4,6,2,8,5,1,3]=>1101100=>0011011
[3,1,8,7,4,2,6,5]=>[5,6,2,4,7,8,1,3]=>1100000=>0000011
[2,1,7,8,9,10,6,5,4,3]=>[3,4,5,6,10,9,8,7,1,2]=>100000111=>111000001
[1,5,6,7,8,3,4,2]=>[2,4,3,8,7,6,5,1]=>1010111=>1110101
[1,4,5,7,8,3,6,2]=>[2,6,3,8,7,5,4,1]=>1011101=>1011101
[1,5,6,3,7,8,4,2]=>[2,4,8,7,3,6,5,1]=>1010101=>1010101
[6,1,2,3,4,8,7,5]=>[5,7,8,4,3,2,1,6]=>1111000=>0001111
[5,1,2,3,8,7,6,4]=>[4,6,7,8,3,2,1,5]=>1110000=>0000111
[5,1,2,3,8,6,7,4]=>[4,7,6,8,3,2,1,5]=>1110010=>0100111
[2,8,5,3,1,4,6,7]=>[7,6,4,1,3,5,8,2]=>1101010=>0101011
[2,5,3,6,7,8,1,4]=>[4,1,8,7,6,3,5,2]=>1110011=>1100111
[2,4,3,6,7,8,1,5]=>[5,1,8,7,6,3,4,2]=>1110011=>1100111
[2,5,3,6,7,8,4,1]=>[1,4,8,7,6,3,5,2]=>0110011=>1100110
[2,5,3,6,7,4,8,1]=>[1,8,4,7,6,3,5,2]=>0111010=>0101110
[3,4,5,8,1,6,7,2]=>[2,7,6,1,8,5,4,3]=>1011110=>0111101
[3,4,8,1,5,6,7,2]=>[2,7,6,5,1,8,4,3]=>1011110=>0111101
[3,5,1,6,7,8,4,2]=>[2,4,8,7,6,1,5,3]=>1010011=>1100101
[3,5,1,7,4,8,6,2]=>[2,6,8,4,7,1,5,3]=>1011000=>0001101
[3,5,6,7,4,8,1,2]=>[2,1,8,4,7,6,5,3]=>1011110=>0111101
[3,5,8,4,1,6,7,2]=>[2,7,6,1,4,8,5,3]=>1010110=>0110101
[3,6,7,4,8,5,1,2]=>[2,1,5,8,4,7,6,3]=>1011010=>0101101
[3,6,8,4,5,1,7,2]=>[2,7,1,5,4,8,6,3]=>1011010=>0101101
[4,1,5,7,8,6,3,2]=>[2,3,6,8,7,5,1,4]=>1000101=>1010001
[4,1,5,8,3,6,7,2]=>[2,7,6,3,8,5,1,4]=>1010110=>0110101
[4,1,7,3,5,8,6,2]=>[2,6,8,5,3,7,1,4]=>1010100=>0010101
[4,1,7,8,5,6,3,2]=>[2,3,6,5,8,7,1,4]=>1000101=>1010001
[4,5,7,8,1,6,3,2]=>[2,3,6,1,8,7,5,4]=>1001101=>1011001
[4,5,8,3,1,6,7,2]=>[2,7,6,1,3,8,5,4]=>1001110=>0111001
[4,6,3,1,8,5,7,2]=>[2,7,5,8,1,3,6,4]=>1001100=>0011001
[4,6,3,7,8,5,1,2]=>[2,1,5,8,7,3,6,4]=>1011001=>1001101
[4,6,7,3,5,8,1,2]=>[2,1,8,5,3,7,6,4]=>1011110=>0111101
[4,6,8,3,5,1,7,2]=>[2,7,1,5,3,8,6,4]=>1011010=>0101101
[5,1,3,6,8,4,7,2]=>[2,7,4,8,6,3,1,5]=>1011010=>0101101
[5,1,3,7,4,8,6,2]=>[2,6,8,4,7,3,1,5]=>1011000=>0001101
[5,1,6,4,7,8,3,2]=>[2,3,8,7,4,6,1,5]=>1001001=>1001001
[5,1,6,4,8,3,7,2]=>[2,7,3,8,4,6,1,5]=>1011000=>0001101
[5,1,7,4,3,8,6,2]=>[2,6,8,3,4,7,1,5]=>1010000=>0000101
[5,6,3,7,8,1,4,2]=>[2,4,1,8,7,3,6,5]=>1010101=>1010101
[5,6,7,8,4,1,3,2]=>[2,3,1,4,8,7,6,5]=>1000111=>1110001
[5,7,3,4,1,8,6,2]=>[2,6,8,1,4,3,7,5]=>1010100=>0010101
[5,7,3,8,4,6,1,2]=>[2,1,6,4,8,3,7,5]=>1011100=>0011101
[5,7,8,4,3,6,1,2]=>[2,1,6,3,4,8,7,5]=>1010101=>1010101
[6,1,3,7,8,5,4,2]=>[2,4,5,8,7,3,1,6]=>1010001=>1000101
[6,1,3,8,5,4,7,2]=>[2,7,4,5,8,3,1,6]=>1011000=>0001101
[6,1,7,4,5,8,3,2]=>[2,3,8,5,4,7,1,6]=>1001100=>0011001
[6,1,8,4,5,3,7,2]=>[2,7,3,5,4,8,1,6]=>1011000=>0001101
[6,7,3,8,5,4,1,2]=>[2,1,4,5,8,3,7,6]=>1010010=>0100101
[7,1,3,4,8,6,5,2]=>[2,5,6,8,4,3,1,7]=>1011000=>0001101
[7,1,8,4,5,6,3,2]=>[2,3,6,5,4,8,1,7]=>1001100=>0011001
[8,4,1,3,2,5,6,7]=>[7,6,5,2,3,1,4,8]=>1100110=>0110011
[8,7,1,2,3,4,6,5]=>[5,6,4,3,2,1,7,8]=>1111000=>0001111
[8,5,1,4,2,3,6,7]=>[7,6,3,2,4,1,5,8]=>1110010=>0100111
[8,5,1,4,3,2,6,7]=>[7,6,2,3,4,1,5,8]=>1100010=>0100011
[8,7,1,2,3,6,4,5]=>[5,4,6,3,2,1,7,8]=>1111000=>0001111
[2,5,8,6,1,7,3,4]=>[4,3,7,1,6,8,5,2]=>1110100=>0010111
[6,8,7,2,3,4,1,5]=>[5,1,4,3,2,7,8,6]=>1110010=>0100111
[3,1,8,7,5,2,6,4]=>[4,6,2,5,7,8,1,3]=>1100000=>0000011
[3,1,5,4,6,7,8,2]=>[2,8,7,6,4,5,1,3]=>1001011=>1101001
[4,2,8,6,7,5,3,1]=>[1,3,5,7,6,8,2,4]=>0100010=>0100010
[4,2,8,5,3,1,6,7]=>[7,6,1,3,5,8,2,4]=>1100010=>0100011
[8,1,2,6,5,3,7,4]=>[4,7,3,5,6,2,1,8]=>1110000=>0000111
[1,3,2,4,8,5,7,6]=>[6,7,5,8,4,2,3,1]=>1101100=>0011011
[5,3,1,8,2,4,7,6]=>[6,7,4,2,8,1,3,5]=>1101000=>0001011
[1,5,4,2,8,3,7,6]=>[6,7,3,8,2,4,5,1]=>1110000=>0000111
[1,7,2,5,3,8,6,4]=>[4,6,8,3,5,2,7,1]=>1110000=>0000111
[2,6,1,8,3,7,4,5]=>[5,4,7,3,8,1,6,2]=>1111000=>0001111
[3,5,8,4,1,7,2,6]=>[6,2,7,1,4,8,5,3]=>1110100=>0010111
[5,1,4,6,2,8,7,3]=>[3,7,8,2,6,4,1,5]=>1101000=>0001011
[7,6,2,1,4,8,3,5]=>[5,3,8,4,1,2,6,7]=>1011000=>0001101
[4,6,5,2,7,8,1,3]=>[3,1,8,7,2,5,6,4]=>1101001=>1001011
[1,4,2,7,3,8,6,5]=>[5,6,8,3,7,2,4,1]=>1110000=>0000111
[1,4,2,7,5,3,8,6]=>[6,8,3,5,7,2,4,1]=>1110000=>0000111
[1,2,7,3,8,6,5,4]=>[4,5,6,8,3,7,2,1]=>1110000=>0000111
[3,4,5,1,8,2,7,6]=>[6,7,2,8,1,5,4,3]=>1111000=>0001111
[1,4,2,8,3,5,7,6]=>[6,7,5,3,8,2,4,1]=>1110100=>0010111
[1,5,2,3,8,7,4,6]=>[6,4,7,8,3,2,5,1]=>1111000=>0001111
[4,8,1,2,6,3,7,5]=>[5,7,3,6,2,1,8,4]=>1111000=>0001111
[5,8,1,2,6,3,7,4]=>[4,7,3,6,2,1,8,5]=>1110100=>0010111
[2,8,7,6,3,1,4,5]=>[5,4,1,3,6,7,8,2]=>1101000=>0001011
[7,6,2,3,4,8,1,5]=>[5,1,8,4,3,2,6,7]=>1111000=>0001111
[8,7,6,2,1,4,3,5]=>[5,3,4,1,2,6,7,8]=>1010000=>0000101
[8,7,3,1,4,2,6,5]=>[5,6,2,4,1,3,7,8]=>1100000=>0000011
[1,2,5,3,4,8,7,6]=>[6,7,8,4,3,5,2,1]=>1111000=>0001111
[1,2,3,8,4,7,6,5]=>[5,6,7,4,8,3,2,1]=>1111000=>0001111
[4,5,1,2,8,3,7,6]=>[6,7,3,8,2,1,5,4]=>1111000=>0001111
[1,4,8,2,6,3,7,5]=>[5,7,3,6,2,8,4,1]=>1111000=>0001111
[4,1,2,6,5,7,8,3]=>[3,8,7,5,6,2,1,4]=>1100101=>1010011
[8,4,1,7,3,2,5,6]=>[6,5,2,3,7,1,4,8]=>1100100=>0010011
[1,8,7,3,2,4,6,5]=>[5,6,4,2,3,7,8,1]=>1101000=>0001011
[1,8,4,2,7,3,6,5]=>[5,6,3,7,2,4,8,1]=>1110000=>0000111
[1,7,5,2,3,8,6,4]=>[4,6,8,3,2,5,7,1]=>1110000=>0000111
[8,1,4,7,3,5,2,6]=>[6,2,5,3,7,4,1,8]=>1111000=>0001111
[8,4,3,6,1,7,2,5]=>[5,2,7,1,6,3,4,8]=>1110000=>0000111
[8,3,1,5,6,2,7,4]=>[4,7,2,6,5,1,3,8]=>1100100=>0010011
[3,4,1,6,5,7,2,8]=>[8,2,7,5,6,1,4,3]=>1110100=>0010111
[3,5,1,6,2,8,7,4]=>[4,7,8,2,6,1,5,3]=>1110000=>0000111
[5,4,3,6,1,7,2,8]=>[8,2,7,1,6,3,4,5]=>1110000=>0000111
[4,8,7,6,2,1,5,3]=>[3,5,1,2,6,7,8,4]=>1001000=>0001001
[4,8,7,2,1,6,5,3]=>[3,5,6,1,2,7,8,4]=>1001000=>0001001
[6,8,5,2,1,7,4,3]=>[3,4,7,1,2,5,8,6]=>1000010=>0100001
[7,8,5,3,6,2,4,1]=>[1,4,2,6,3,5,8,7]=>0110001=>1000110
[7,5,8,3,6,4,2,1]=>[1,2,4,6,3,8,5,7]=>0010100=>0010100
[5,8,7,6,3,2,4,1]=>[1,4,2,3,6,7,8,5]=>0100100=>0010010
[7,5,3,8,6,4,2,1]=>[1,2,4,6,8,3,5,7]=>0010000=>0000100
[5,4,8,1,6,3,7,2]=>[2,7,3,6,1,8,4,5]=>1011000=>0001101
[2,1,5,8,3,7,4,6]=>[6,4,7,3,8,5,1,2]=>1011100=>0011101
[2,1,7,4,8,3,6,5]=>[5,6,3,8,4,7,1,2]=>1011000=>0001101
[5,1,4,8,2,7,3,6]=>[6,3,7,2,8,4,1,5]=>1111000=>0001111
[6,1,5,4,7,2,8,3]=>[3,8,2,7,4,5,1,6]=>1101000=>0001011
[6,1,3,5,7,2,8,4]=>[4,8,2,7,5,3,1,6]=>1110100=>0010111
[3,1,2,7,8,4,6,5]=>[5,6,4,8,7,2,1,3]=>1101001=>1001011
[3,4,1,2,8,7,5,6]=>[6,5,7,8,2,1,4,3]=>1110100=>0010111
[2,1,3,4,8,5,7,6]=>[6,7,5,8,4,3,1,2]=>1011100=>0011101
[6,2,5,1,7,3,8,4]=>[4,8,3,7,1,5,2,6]=>1110000=>0000111
[2,4,8,1,3,7,5,6]=>[6,5,7,3,1,8,4,2]=>1111100=>0011111
[1,5,4,8,6,2,7,3]=>[3,7,2,6,8,4,5,1]=>1101000=>0001011
[4,2,5,8,1,7,3,6]=>[6,3,7,1,8,5,2,4]=>1110100=>0010111
[2,6,8,5,1,7,3,4]=>[4,3,7,1,5,8,6,2]=>1110010=>0100111
[6,2,4,5,7,1,8,3]=>[3,8,1,7,5,4,2,6]=>1101100=>0011011
[1,3,2,7,8,5,4,6]=>[6,4,5,8,7,2,3,1]=>1101001=>1001011
[4,1,7,6,5,8,2,3]=>[3,2,8,5,6,7,1,4]=>1100100=>0010011
[5,1,2,3,8,4,7,6]=>[6,7,4,8,3,2,1,5]=>1111000=>0001111
[3,4,5,1,8,7,2,6]=>[6,2,7,8,1,5,4,3]=>1111000=>0001111
[4,1,2,3,8,7,5,6]=>[6,5,7,8,3,2,1,4]=>1110100=>0010111
[7,4,1,6,8,2,3,5]=>[5,3,2,8,6,1,4,7]=>1110010=>0100111
[5,1,4,6,2,7,8,3]=>[3,8,7,2,6,4,1,5]=>1101001=>1001011
[2,3,1,8,5,4,7,6]=>[6,7,4,5,8,1,3,2]=>1101000=>0001011
[5,3,1,8,7,2,4,6]=>[6,4,2,7,8,1,3,5]=>1101000=>0001011
[3,6,1,8,7,2,4,5]=>[5,4,2,7,8,1,6,3]=>1111000=>0001111
[6,3,5,7,1,2,8,4]=>[4,8,2,1,7,5,3,6]=>1110100=>0010111
[1,3,8,4,2,7,6,5]=>[5,6,7,2,4,8,3,1]=>1110000=>0000111
[1,2,3,8,5,7,4,6]=>[6,4,7,5,8,3,2,1]=>1111100=>0011111
[6,1,7,2,5,8,3,4]=>[4,3,8,5,2,7,1,6]=>1110100=>0010111
[4,5,1,8,7,2,3,6]=>[6,3,2,7,8,1,5,4]=>1111000=>0001111
[3,1,5,2,8,6,7,4]=>[4,7,6,8,2,5,1,3]=>1100010=>0100011
[4,3,5,1,6,7,8,2]=>[2,8,7,6,1,5,3,4]=>1010011=>1100101
[7,8,6,5,2,1,4,3]=>[3,4,1,2,5,6,8,7]=>1000001=>1000001
[8,6,7,5,2,1,4,3]=>[3,4,1,2,5,7,6,8]=>1000010=>0100001
[6,7,8,2,1,5,4,3]=>[3,4,5,1,2,8,7,6]=>1000011=>1100001
[8,7,5,6,2,1,4,3]=>[3,4,1,2,6,5,7,8]=>1000100=>0010001
[7,8,4,5,6,1,3,2]=>[2,3,1,6,5,4,8,7]=>1001101=>1011001
[4,2,5,1,8,7,3,6]=>[6,3,7,8,1,5,2,4]=>1110000=>0000111
[7,2,4,5,8,3,6,1]=>[1,6,3,8,5,4,2,7]=>0111100=>0011110
[4,2,7,1,5,6,8,3]=>[3,8,6,5,1,7,2,4]=>1100110=>0110011
[8,1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1,8]=>1100110=>0110011
[4,1,2,8,3,5,7,6]=>[6,7,5,3,8,2,1,4]=>1110100=>0010111
[6,2,5,1,8,3,4,7]=>[7,4,3,8,1,5,2,6]=>1111000=>0001111
[8,2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2,8]=>1110010=>0100111
[1,7,2,4,8,6,5,3]=>[3,5,6,8,4,2,7,1]=>1101000=>0001011
[7,2,8,4,5,3,1,6]=>[6,1,3,5,4,8,2,7]=>1101000=>0001011
[1,5,7,8,4,6,2,3]=>[3,2,6,4,8,7,5,1]=>1101101=>1011011
[6,5,4,8,2,3,1,7]=>[7,1,3,2,8,4,5,6]=>1101000=>0001011
[6,8,4,5,3,2,1,7]=>[7,1,2,3,5,4,8,6]=>1001010=>0101001
[5,1,3,2,8,4,6,7]=>[7,6,4,8,2,3,1,5]=>1101010=>0101011
[7,6,1,3,8,2,4,5]=>[5,4,2,8,3,1,6,7]=>1111000=>0001111
[5,4,1,2,3,8,6,7]=>[7,6,8,3,2,1,4,5]=>1110010=>0100111
[6,5,4,3,2,7,8,9,10,1]=>[1,10,9,8,7,2,3,4,5,6]=>010000111=>111000010
[7,6,8,5,2,4,1,3]=>[3,1,4,2,5,8,6,7]=>1100010=>0100011
[6,7,8,5,2,4,1,3]=>[3,1,4,2,5,8,7,6]=>1100011=>1100011
[3,4,5,7,2,8,1,6]=>[6,1,8,2,7,5,4,3]=>1111100=>0011111
[3,4,5,7,1,6,2,8]=>[8,2,6,1,7,5,4,3]=>1111100=>0011111
[3,4,5,8,2,1,7,6]=>[6,7,1,2,8,5,4,3]=>1011100=>0011101
[3,4,6,2,7,8,1,5]=>[5,1,8,7,2,6,4,3]=>1111001=>1001111
[3,4,6,2,8,1,7,5]=>[5,7,1,8,2,6,4,3]=>1111000=>0001111
[3,4,6,2,1,5,7,8]=>[8,7,5,1,2,6,4,3]=>1011101=>1011101
[3,4,6,7,5,1,2,8]=>[8,2,1,5,7,6,4,3]=>1111010=>0101111
[3,4,6,1,5,2,7,8]=>[8,7,2,5,1,6,4,3]=>1111001=>1001111
[3,4,7,2,1,6,5,8]=>[8,5,6,1,2,7,4,3]=>1011100=>0011101
[3,4,7,1,5,6,2,8]=>[8,2,6,5,1,7,4,3]=>1111100=>0011111
[3,4,8,2,5,1,7,6]=>[6,7,1,5,2,8,4,3]=>1111000=>0001111
[3,5,2,6,1,4,7,8]=>[8,7,4,1,6,2,5,3]=>1111001=>1001111
[3,5,2,7,1,6,4,8]=>[8,4,6,1,7,2,5,3]=>1111000=>0001111
[3,5,6,1,4,2,7,8]=>[8,7,2,4,1,6,5,3]=>1110101=>1010111
[3,5,7,4,8,1,6,2]=>[2,6,1,8,4,7,5,3]=>1011100=>0011101
[3,5,7,8,1,6,2,4]=>[4,2,6,1,8,7,5,3]=>1110101=>1010111
[3,5,8,1,4,6,7,2]=>[2,7,6,4,1,8,5,3]=>1011110=>0111101
[3,6,2,4,8,1,7,5]=>[5,7,1,8,4,2,6,3]=>1111000=>0001111
[3,6,2,7,8,5,1,4]=>[4,1,5,8,7,2,6,3]=>1110001=>1000111
[3,6,2,7,8,1,4,5]=>[5,4,1,8,7,2,6,3]=>1111001=>1001111
[3,6,2,1,5,4,7,8]=>[8,7,4,5,1,2,6,3]=>1011001=>1001101
[3,6,7,8,5,1,2,4]=>[4,2,1,5,8,7,6,3]=>1110011=>1100111
[3,7,2,8,5,1,6,4]=>[4,6,1,5,8,2,7,3]=>1110000=>0000111
[3,7,2,1,5,6,4,8]=>[8,4,6,5,1,2,7,3]=>1011100=>0011101
[3,7,8,4,5,1,6,2]=>[2,6,1,5,4,8,7,3]=>1011001=>1001101
[3,7,8,4,1,6,5,2]=>[2,5,6,1,4,8,7,3]=>1010001=>1000101
[3,8,2,4,1,6,7,5]=>[5,7,6,1,4,2,8,3]=>1110010=>0100111
[3,8,2,1,5,6,7,4]=>[4,7,6,5,1,2,8,3]=>1010110=>0110101
[8,1,5,4,3,6,7,2]=>[2,7,6,3,4,5,1,8]=>1010010=>0100101
[8,1,4,5,3,6,7,2]=>[2,7,6,3,5,4,1,8]=>1011010=>0101101
[4,1,7,3,5,6,8,2]=>[2,8,6,5,3,7,1,4]=>1010110=>0110101
[4,1,3,6,7,8,5,2]=>[2,5,8,7,6,3,1,4]=>1010011=>1100101
[4,6,2,3,5,1,7,8]=>[8,7,1,5,3,2,6,4]=>1111001=>1001111
[3,5,2,4,1,6,7,8]=>[8,7,6,1,4,2,5,3]=>1110011=>1100111
[4,6,2,3,5,7,1,8]=>[8,1,7,5,3,2,6,4]=>1111100=>0011111
[2,3,7,8,1,6,5,4]=>[4,5,6,1,8,7,3,2]=>1110001=>1000111
[2,7,5,1,8,6,3,4]=>[4,3,6,8,1,5,7,2]=>1110000=>0000111
[2,7,6,1,4,8,3,5]=>[5,3,8,4,1,6,7,2]=>1111000=>0001111
[2,4,6,7,8,3,1,5]=>[5,1,3,8,7,6,4,2]=>1101011=>1101011
[2,6,8,1,4,5,7,3]=>[3,7,5,4,1,8,6,2]=>1101110=>0111011
[2,6,5,8,1,3,7,4]=>[4,7,3,1,8,5,6,2]=>1110100=>0010111
[6,4,7,5,8,2,3,1]=>[1,3,2,8,5,7,4,6]=>0101100=>0011010
[6,7,4,1,8,2,3,5]=>[5,3,2,8,1,4,7,6]=>1110010=>0100111
[7,3,6,1,4,8,2,5]=>[5,2,8,4,1,6,3,7]=>1111000=>0001111
[6,7,8,1,4,2,5,3]=>[3,5,2,4,1,8,7,6]=>1100011=>1100011
[6,2,4,5,8,3,7,1]=>[1,7,3,8,5,4,2,6]=>0111100=>0011110
[5,2,6,1,4,8,3,7]=>[7,3,8,4,1,6,2,5]=>1111000=>0001111
[6,2,5,1,8,7,3,4]=>[4,3,7,8,1,5,2,6]=>1110000=>0000111
[7,2,3,5,8,1,4,6]=>[6,4,1,8,5,3,2,7]=>1111100=>0011111
[2,4,7,6,1,8,3,5]=>[5,3,8,1,6,7,4,2]=>1111000=>0001111
[2,3,4,8,1,5,7,6]=>[6,7,5,1,8,4,3,2]=>1111100=>0011111
[2,7,8,5,1,4,6,3]=>[3,6,4,1,5,8,7,2]=>1101001=>1001011
[7,6,4,5,1,8,2,3]=>[3,2,8,1,5,4,6,7]=>1101000=>0001011
[7,4,6,8,1,5,2,3]=>[3,2,5,1,8,6,4,7]=>1101010=>0101011
[2,6,7,8,5,3,1,4]=>[4,1,3,5,8,7,6,2]=>1100011=>1100011
[2,5,6,1,4,8,3,7]=>[7,3,8,4,1,6,5,2]=>1111100=>0011111
[2,5,8,1,4,6,7,3]=>[3,7,6,4,1,8,5,2]=>1101110=>0111011
[7,2,3,8,6,1,5,4]=>[4,5,1,6,8,3,2,7]=>1110000=>0000111
[5,2,3,4,6,8,1,7]=>[7,1,8,6,4,3,2,5]=>1111010=>0101111
[7,2,3,4,8,1,6,5]=>[5,6,1,8,4,3,2,7]=>1111000=>0001111
[3,2,5,7,8,1,6,4]=>[4,6,1,8,7,5,2,3]=>1100101=>1010011
[6,4,1,7,8,2,3,5]=>[5,3,2,8,7,1,4,6]=>1110001=>1000111
[5,7,1,6,2,8,4,3]=>[3,4,8,2,6,1,7,5]=>1100100=>0010011
[5,6,1,8,2,3,7,4]=>[4,7,3,2,8,1,6,5]=>1110100=>0010111
[5,7,6,1,2,8,3,4]=>[4,3,8,2,1,6,7,5]=>1110100=>0010111
[5,7,4,8,2,6,3,1]=>[1,3,6,2,8,4,7,5]=>0101100=>0011010
[5,6,8,1,2,4,7,3]=>[3,7,4,2,1,8,6,5]=>1101110=>0111011
[6,2,3,4,5,8,1,7]=>[7,1,8,5,4,3,2,6]=>1111100=>0011111
[5,4,1,6,7,8,2,3]=>[3,2,8,7,6,1,4,5]=>1100011=>1100011
[7,4,1,5,8,2,6,3]=>[3,6,2,8,5,1,4,7]=>1100100=>0010011
[5,7,1,8,6,2,3,4]=>[4,3,2,6,8,1,7,5]=>1110100=>0010111
[4,6,1,3,5,8,2,7]=>[7,2,8,5,3,1,6,4]=>1111100=>0011111
[4,8,1,3,5,6,7,2]=>[2,7,6,5,3,1,8,4]=>1011110=>0111101
[8,1,2,3,7,5,6,4]=>[4,6,5,7,3,2,1,8]=>1110100=>0010111
[2,1,8,3,7,5,6,4]=>[4,6,5,7,3,8,1,2]=>1010100=>0010101
[8,1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1,8]=>1111100=>0011111
[5,6,7,3,8,2,1,4]=>[4,1,2,8,3,7,6,5]=>1010110=>0110101
[5,6,8,3,1,2,7,4]=>[4,7,2,1,3,8,6,5]=>1100110=>0110011
[5,6,3,7,8,2,1,4]=>[4,1,2,8,7,3,6,5]=>1010101=>1010101
[5,7,3,2,8,6,1,4]=>[4,1,6,8,2,3,7,5]=>1100100=>0010011
[5,7,8,3,1,6,2,4]=>[4,2,6,1,3,8,7,5]=>1100101=>1010011
[5,2,6,8,1,3,7,4]=>[4,7,3,1,8,6,2,5]=>1110010=>0100111
[6,2,3,7,8,5,1,4]=>[4,1,5,8,7,3,2,6]=>1110001=>1000111
[1,5,6,7,8,3,2,4]=>[4,2,3,8,7,6,5,1]=>1100111=>1110011
[6,8,3,2,5,1,7,4]=>[4,7,1,5,2,3,8,6]=>1100010=>0100011
[1,5,8,3,2,6,7,4]=>[4,7,6,2,3,8,5,1]=>1100110=>0110011
[7,2,3,1,8,6,5,4]=>[4,5,6,8,1,3,2,7]=>1100000=>0000011
[1,6,7,8,5,2,3,4]=>[4,3,2,5,8,7,6,1]=>1110011=>1100111
[1,6,8,3,5,2,7,4]=>[4,7,2,5,3,8,6,1]=>1110010=>0100111
[1,7,8,3,5,6,2,4]=>[4,2,6,5,3,8,7,1]=>1110101=>1010111
[6,2,3,7,8,1,4,5]=>[5,4,1,8,7,3,2,6]=>1111001=>1001111
[4,5,7,8,2,6,1,3]=>[3,1,6,2,8,7,5,4]=>1101101=>1011011
[4,6,2,8,5,1,7,3]=>[3,7,1,5,8,2,6,4]=>1101000=>0001011
[4,6,7,1,8,5,2,3]=>[3,2,5,8,1,7,6,4]=>1101010=>0101011
[4,6,8,1,5,2,7,3]=>[3,7,2,5,1,8,6,4]=>1101010=>0101011
[4,7,2,1,8,6,5,3]=>[3,5,6,8,1,2,7,4]=>1001000=>0001001
[4,8,2,1,5,6,7,3]=>[3,7,6,5,1,2,8,4]=>1001110=>0111001
[1,2,8,4,5,3,7,6]=>[6,7,3,5,4,8,2,1]=>1111000=>0001111
[1,2,3,8,5,4,7,6]=>[6,7,4,5,8,3,2,1]=>1111000=>0001111
[5,2,6,7,8,1,4,3]=>[3,4,1,8,7,6,2,5]=>1100011=>1100011
[5,2,7,4,8,6,1,3]=>[3,1,6,8,4,7,2,5]=>1101000=>0001011
[5,2,7,8,4,6,1,3]=>[3,1,6,4,8,7,2,5]=>1101001=>1001011
[7,2,3,8,5,4,1,6]=>[6,1,4,5,8,3,2,7]=>1110000=>0000111
[5,7,2,8,4,6,1,3]=>[3,1,6,4,8,2,7,5]=>1101100=>0011011
[6,2,1,7,8,5,4,3]=>[3,4,5,8,7,1,2,6]=>1000001=>1000001
[6,8,2,4,5,1,7,3]=>[3,7,1,5,4,2,8,6]=>1101010=>0101011
[8,1,2,7,4,5,3,6]=>[6,3,5,4,7,2,1,8]=>1111000=>0001111
[5,1,2,8,3,6,4,7]=>[7,4,6,3,8,2,1,5]=>1111000=>0001111
[7,1,6,3,8,2,4,5]=>[5,4,2,8,3,6,1,7]=>1111000=>0001111
[4,1,7,2,5,8,3,6]=>[6,3,8,5,2,7,1,4]=>1110100=>0010111
[8,1,6,3,4,7,2,5]=>[5,2,7,4,3,6,1,8]=>1111000=>0001111
[7,1,6,8,2,5,3,4]=>[4,3,5,2,8,6,1,7]=>1110010=>0100111
[4,1,8,2,5,6,7,3]=>[3,7,6,5,2,8,1,4]=>1100110=>0110011
[3,8,1,2,7,5,4,6]=>[6,4,5,7,2,1,8,3]=>1111000=>0001111
[3,6,1,2,8,4,7,5]=>[5,7,4,8,2,1,6,3]=>1111000=>0001111
[3,8,1,7,4,2,6,5]=>[5,6,2,4,7,1,8,3]=>1110000=>0000111
[6,4,2,1,8,3,7,5]=>[5,7,3,8,1,2,4,6]=>1010000=>0000101
[6,8,2,7,4,1,3,5]=>[5,3,1,4,7,2,8,6]=>1110010=>0100111
[6,5,2,8,1,3,7,4]=>[4,7,3,1,8,2,5,6]=>1110000=>0000111
[5,4,7,1,2,8,3,6]=>[6,3,8,2,1,7,4,5]=>1111000=>0001111
[8,4,7,1,3,5,2,6]=>[6,2,5,3,1,7,4,8]=>1111000=>0001111
[5,4,7,1,2,3,8,6]=>[6,8,3,2,1,7,4,5]=>1111000=>0001111
[8,4,7,1,3,2,6,5]=>[5,6,2,3,1,7,4,8]=>1101000=>0001011
[8,5,7,3,1,2,6,4]=>[4,6,2,1,3,7,5,8]=>1100100=>0010011
[3,6,1,4,8,2,5,7]=>[7,5,2,8,4,1,6,3]=>1111100=>0011111
[3,8,1,2,4,5,7,6]=>[6,7,5,4,2,1,8,3]=>1111100=>0011111
[3,5,1,6,8,4,2,7]=>[7,2,4,8,6,1,5,3]=>1110010=>0100111
[3,6,1,8,2,7,4,5]=>[5,4,7,2,8,1,6,3]=>1111000=>0001111
[3,7,1,4,5,8,2,6]=>[6,2,8,5,4,1,7,3]=>1111100=>0011111
[3,6,1,4,2,8,5,7]=>[7,5,8,2,4,1,6,3]=>1110100=>0010111
[8,6,2,1,4,5,3,7]=>[7,3,5,4,1,2,6,8]=>1011000=>0001101
[8,6,2,3,7,5,1,4]=>[4,1,5,7,3,2,6,8]=>1110000=>0000111
[7,6,8,1,4,5,2,3]=>[3,2,5,4,1,8,6,7]=>1101010=>0101011
[3,7,1,4,2,8,6,5]=>[5,6,8,2,4,1,7,3]=>1110000=>0000111
[3,7,1,2,8,5,6,4]=>[4,6,5,8,2,1,7,3]=>1110100=>0010111
[2,6,1,5,7,4,8,3]=>[3,8,4,7,5,1,6,2]=>1101100=>0011011
[2,3,6,1,8,4,7,5]=>[5,7,4,8,1,6,3,2]=>1111000=>0001111
[5,2,4,6,3,7,8,1]=>[1,8,7,3,6,4,2,5]=>0111001=>1001110
[2,5,1,7,3,6,8,4]=>[4,8,6,3,7,1,5,2]=>1110010=>0100111
[2,7,1,5,6,8,4,3]=>[3,4,8,6,5,1,7,2]=>1100110=>0110011
[5,2,6,7,3,1,8,4]=>[4,8,1,3,7,6,2,5]=>1100010=>0100011
[5,2,4,7,6,3,8,1]=>[1,8,3,6,7,4,2,5]=>0111000=>0001110
[8,7,6,1,4,3,5,2]=>[2,5,3,4,1,6,7,8]=>1010000=>0000101
[8,7,6,1,3,4,5,2]=>[2,5,4,3,1,6,7,8]=>1011000=>0001101
[8,1,6,5,7,4,3,2]=>[2,3,4,7,5,6,1,8]=>1000100=>0010001
[8,1,5,6,7,4,3,2]=>[2,3,4,7,6,5,1,8]=>1000110=>0110001
[5,8,3,4,1,6,2,7]=>[7,2,6,1,4,3,8,5]=>1110100=>0010111
[4,2,6,1,7,8,5,3]=>[3,5,8,7,1,6,2,4]=>1100001=>1000011
[1,5,2,6,7,8,4,3]=>[3,4,8,7,6,2,5,1]=>1100011=>1100011
[4,5,2,7,8,6,1,3]=>[3,1,6,8,7,2,5,4]=>1101001=>1001011
[4,2,6,8,5,1,7,3]=>[3,7,1,5,8,6,2,4]=>1100010=>0100011
[4,2,7,8,5,6,1,3]=>[3,1,6,5,8,7,2,4]=>1100101=>1010011
[5,2,3,4,7,8,6,1]=>[1,6,8,7,4,3,2,5]=>0111001=>1001110
[4,5,2,6,3,8,7,1]=>[1,7,8,3,6,2,5,4]=>0111000=>0001110
[5,6,2,7,3,8,4,1]=>[1,4,8,3,7,2,6,5]=>0110100=>0010110
[3,5,2,8,4,6,7,1]=>[1,7,6,4,8,2,5,3]=>0111010=>0101110
[3,5,2,4,7,8,6,1]=>[1,6,8,7,4,2,5,3]=>0111001=>1001110
[3,5,2,4,7,8,1,6]=>[6,1,8,7,4,2,5,3]=>1111001=>1001111
[7,2,3,4,6,1,5,8]=>[8,5,1,6,4,3,2,7]=>1111100=>0011111
[3,7,1,5,8,2,4,6]=>[6,4,2,8,5,1,7,3]=>1111100=>0011111
[5,1,3,8,2,4,6,7]=>[7,6,4,2,8,3,1,5]=>1111010=>0101111
[4,2,1,3,8,5,6,7]=>[7,6,5,8,3,1,2,4]=>1010110=>0110101
[1,8,7,6,3,4,5,2]=>[2,5,4,3,6,7,8,1]=>1011000=>0001101
[8,5,7,6,3,4,1,2]=>[2,1,4,3,6,7,5,8]=>1010100=>0010101
[8,5,7,6,3,2,1,4]=>[4,1,2,3,6,7,5,8]=>1000100=>0010001
[7,8,1,4,5,6,3,2]=>[2,3,6,5,4,1,8,7]=>1001101=>1011001
[4,2,8,3,5,1,7,6]=>[6,7,1,5,3,8,2,4]=>1110000=>0000111
[4,2,7,8,1,6,5,3]=>[3,5,6,1,8,7,2,4]=>1100001=>1000011
[7,2,1,4,5,6,3,8]=>[8,3,6,5,4,1,2,7]=>1011100=>0011101
[6,8,1,4,5,3,7,2]=>[2,7,3,5,4,1,8,6]=>1011010=>0101101
[5,1,3,4,2,6,7,8]=>[8,7,6,2,4,3,1,5]=>1110011=>1100111
[4,2,6,8,1,5,7,3]=>[3,7,5,1,8,6,2,4]=>1100110=>0110011
[2,3,4,5,8,1,7,6]=>[6,7,1,8,5,4,3,2]=>1111100=>0011111
[2,3,4,8,1,6,7,5]=>[5,7,6,1,8,4,3,2]=>1111010=>0101111
[5,1,6,3,4,7,8,2]=>[2,8,7,4,3,6,1,5]=>1011001=>1001101
[2,1,7,5,3,8,6,4]=>[4,6,8,3,5,7,1,2]=>1010000=>0000101
[2,1,8,7,5,3,6,4]=>[4,6,3,5,7,8,1,2]=>1010000=>0000101
[7,5,3,2,1,8,6,4]=>[4,6,8,1,2,3,5,7]=>1000000=>0000001
[5,2,3,4,1,8,6,7]=>[7,6,8,1,4,3,2,5]=>1110010=>0100111
[4,2,3,1,7,5,6,8]=>[8,6,5,7,1,3,2,4]=>1100110=>0110011
[3,2,1,6,4,5,7,8]=>[8,7,5,4,6,1,2,3]=>1001101=>1011001
[3,8,1,2,5,4,7,6]=>[6,7,4,5,2,1,8,3]=>1111000=>0001111
[6,4,8,7,5,3,2,1]=>[1,2,3,5,7,8,4,6]=>0001000=>0001000
[6,4,8,5,3,2,1,7]=>[7,1,2,3,5,8,4,6]=>1001000=>0001001
[7,4,6,8,5,3,2,1]=>[1,2,3,5,8,6,4,7]=>0001010=>0101000
[7,5,8,6,3,2,1,4]=>[4,1,2,3,6,8,5,7]=>1000100=>0010001
[7,4,5,8,6,3,2,1]=>[1,2,3,6,8,5,4,7]=>0001100=>0011000
[7,4,8,5,6,3,2,1]=>[1,2,3,6,5,8,4,7]=>0001100=>0011000
[7,5,8,6,4,2,1,3]=>[3,1,2,4,6,8,5,7]=>1000100=>0010001
[6,4,2,1,8,5,3,7]=>[7,3,5,8,1,2,4,6]=>1010000=>0000101
[5,3,8,6,7,4,2,1]=>[1,2,4,7,6,8,3,5]=>0010010=>0100100
[7,4,2,1,6,8,5,3]=>[3,5,8,6,1,2,4,7]=>1000010=>0100001
[5,3,8,4,2,1,6,7]=>[7,6,1,2,4,8,3,5]=>1010010=>0100101
[6,3,5,8,7,4,2,1]=>[1,2,4,7,8,5,3,6]=>0010100=>0010100
[7,4,2,1,8,5,6,3]=>[3,6,5,8,1,2,4,7]=>1000100=>0010001
[6,3,4,8,7,5,2,1]=>[1,2,5,7,8,4,3,6]=>0011000=>0001100
[7,5,2,1,8,6,3,4]=>[4,3,6,8,1,2,5,7]=>1010000=>0000101
[6,3,8,7,4,5,2,1]=>[1,2,5,4,7,8,3,6]=>0011000=>0001100
[6,3,8,4,5,2,1,7]=>[7,1,2,5,4,8,3,6]=>1011000=>0001101
[7,3,6,8,4,5,2,1]=>[1,2,5,4,8,6,3,7]=>0011010=>0101100
[7,4,8,5,6,2,1,3]=>[3,1,2,6,5,8,4,7]=>1001100=>0011001
[7,3,4,5,8,6,2,1]=>[1,2,6,8,5,4,3,7]=>0011100=>0011100
[7,3,8,4,5,6,2,1]=>[1,2,6,5,4,8,3,7]=>0011100=>0011100
[1,8,7,2,6,5,4,3]=>[3,4,5,6,2,7,8,1]=>1100000=>0000011
[1,8,7,6,2,4,5,3]=>[3,5,4,2,6,7,8,1]=>1101000=>0001011
[1,8,7,2,4,6,5,3]=>[3,5,6,4,2,7,8,1]=>1101000=>0001011
[1,8,7,6,2,3,4,5]=>[5,4,3,2,6,7,8,1]=>1111000=>0001111
[1,8,2,5,6,7,4,3]=>[3,4,7,6,5,2,8,1]=>1100110=>0110011
[1,2,8,3,4,6,5,7]=>[7,5,6,4,3,8,2,1]=>1111100=>0011111
[6,4,1,7,2,3,8,5]=>[5,8,3,2,7,1,4,6]=>1110000=>0000111
[7,1,8,2,3,5,4,6]=>[6,4,5,3,2,8,1,7]=>1111000=>0001111
[6,5,1,2,3,8,4,7]=>[7,4,8,3,2,1,5,6]=>1111000=>0001111
[1,8,5,2,3,7,4,6]=>[6,4,7,3,2,5,8,1]=>1111000=>0001111
[6,5,1,2,7,3,8,4]=>[4,8,3,7,2,1,5,6]=>1110000=>0000111
[7,6,4,1,8,2,3,5]=>[5,3,2,8,1,4,6,7]=>1110000=>0000111
[5,3,6,1,2,4,8,7]=>[7,8,4,2,1,6,3,5]=>1111000=>0001111
[5,8,3,1,7,2,4,6]=>[6,4,2,7,1,3,8,5]=>1101100=>0011011
[7,5,4,1,8,2,3,6]=>[6,3,2,8,1,4,5,7]=>1110000=>0000111
[4,1,2,8,6,3,7,5]=>[5,7,3,6,8,2,1,4]=>1110000=>0000111
[5,4,1,6,2,7,8,3]=>[3,8,7,2,6,1,4,5]=>1100001=>1000011
[6,5,3,1,8,2,4,7]=>[7,4,2,8,1,3,5,6]=>1101000=>0001011
[3,8,1,6,7,2,4,5]=>[5,4,2,7,6,1,8,3]=>1111010=>0101111
[6,5,3,7,1,2,8,4]=>[4,8,2,1,7,3,5,6]=>1110000=>0000111
[4,6,1,5,2,8,3,7]=>[7,3,8,2,5,1,6,4]=>1111000=>0001111
[1,6,8,5,2,7,3,4]=>[4,3,7,2,5,8,6,1]=>1110010=>0100111
[3,4,8,1,2,6,5,7]=>[7,5,6,2,1,8,4,3]=>1111100=>0011111
[3,1,8,7,2,6,4,5]=>[5,4,6,2,7,8,1,3]=>1101000=>0001011
[7,3,5,6,1,8,2,4]=>[4,2,8,1,6,5,3,7]=>1110100=>0010111
[1,4,8,2,3,7,6,5]=>[5,6,7,3,2,8,4,1]=>1111000=>0001111
[4,5,1,7,6,8,2,3]=>[3,2,8,6,7,1,5,4]=>1101010=>0101011
[3,1,8,2,5,6,7,4]=>[4,7,6,5,2,8,1,3]=>1100110=>0110011
[5,3,6,7,8,1,2,4]=>[4,2,1,8,7,6,3,5]=>1110011=>1100111
[4,2,5,6,7,8,3,1]=>[1,3,8,7,6,5,2,4]=>0100111=>1110010
[4,2,5,6,7,3,8,1]=>[1,8,3,7,6,5,2,4]=>0110110=>0110110
[7,2,1,8,4,5,6,3]=>[3,6,5,4,8,1,2,7]=>1001100=>0011001
[4,2,7,1,3,8,6,5]=>[5,6,8,3,1,7,2,4]=>1110000=>0000111
[7,2,6,8,1,5,3,4]=>[4,3,5,1,8,6,2,7]=>1110010=>0100111
[5,8,6,3,4,1,7,2]=>[2,7,1,4,3,6,8,5]=>1010100=>0010101
[8,2,6,3,4,7,1,5]=>[5,1,7,4,3,6,2,8]=>1111000=>0001111
[6,2,5,8,1,3,7,4]=>[4,7,3,1,8,5,2,6]=>1110100=>0010111
[7,2,3,4,1,8,6,5]=>[5,6,8,1,4,3,2,7]=>1110000=>0000111
[5,7,2,6,4,8,1,3]=>[3,1,8,4,6,2,7,5]=>1101100=>0011011
[8,2,6,7,4,1,3,5]=>[5,3,1,4,7,6,2,8]=>1110010=>0100111
[2,1,8,6,3,4,5,7]=>[7,5,4,3,6,8,1,2]=>1011100=>0011101
[5,3,1,6,2,7,8,4]=>[4,8,7,2,6,1,3,5]=>1100001=>1000011
[5,2,1,3,6,7,8,4]=>[4,8,7,6,3,1,2,5]=>1010011=>1100101
[6,4,8,7,3,2,1,5]=>[5,1,2,3,7,8,4,6]=>1001000=>0001001
[6,5,3,8,7,2,1,4]=>[4,1,2,7,8,3,5,6]=>1010000=>0000101
[5,4,8,7,3,2,1,6]=>[6,1,2,3,7,8,4,5]=>1001000=>0001001
[6,4,3,8,7,2,1,5]=>[5,1,2,7,8,3,4,6]=>1010000=>0000101
[6,3,8,7,5,2,1,4]=>[4,1,2,5,7,8,3,6]=>1010000=>0000101
[5,6,8,1,4,2,7,3]=>[3,7,2,4,1,8,6,5]=>1100110=>0110011
[5,7,3,8,4,1,6,2]=>[2,6,1,4,8,3,7,5]=>1010100=>0010101
[5,7,3,1,4,6,2,8]=>[8,2,6,4,1,3,7,5]=>1101100=>0011011
[5,7,3,4,8,1,6,2]=>[2,6,1,8,4,3,7,5]=>1011100=>0011101
[5,7,8,1,4,6,2,3]=>[3,2,6,4,1,8,7,5]=>1101101=>1011011
[5,8,3,1,4,6,7,2]=>[2,7,6,4,1,3,8,5]=>1001110=>0111001
[5,8,1,4,3,6,7,2]=>[2,7,6,3,4,1,8,5]=>1010110=>0110101
[5,2,8,4,3,1,7,6]=>[6,7,1,3,4,8,2,5]=>1100000=>0000011
[6,2,7,8,1,5,3,4]=>[4,3,5,1,8,7,2,6]=>1110001=>1000111
[6,2,7,4,1,5,3,8]=>[8,3,5,1,4,7,2,6]=>1110000=>0000111
[6,2,1,4,5,3,7,8]=>[8,7,3,5,4,1,2,6]=>1011001=>1001101
[6,7,3,8,1,5,2,4]=>[4,2,5,1,8,3,7,6]=>1110010=>0100111
[6,7,8,1,5,4,2,3]=>[3,2,4,5,1,8,7,6]=>1100011=>1100011
[4,5,6,7,1,3,2,8]=>[8,2,3,1,7,6,5,4]=>1101110=>0111011
[6,7,1,4,5,3,2,8]=>[8,2,3,5,4,1,7,6]=>1101010=>0101011
[7,2,8,4,1,6,5,3]=>[3,5,6,1,4,8,2,7]=>1100000=>0000011
[7,2,8,4,5,1,6,3]=>[3,6,1,5,4,8,2,7]=>1101000=>0001011
[7,2,8,1,5,6,4,3]=>[3,4,6,5,1,8,2,7]=>1100100=>0010011
[4,6,3,8,1,5,7,2]=>[2,7,5,1,8,3,6,4]=>1011100=>0011101
[4,6,7,3,8,1,2,5]=>[5,2,1,8,3,7,6,4]=>1111010=>0101111
[4,6,7,8,1,5,3,2]=>[2,3,5,1,8,7,6,4]=>1001011=>1101001
[4,6,7,1,5,2,3,8]=>[8,3,2,5,1,7,6,4]=>1111010=>0101111
[4,6,8,3,1,5,7,2]=>[2,7,5,1,3,8,6,4]=>1001110=>0111001
[4,6,1,3,5,2,7,8]=>[8,7,2,5,3,1,6,4]=>1111001=>1001111
[4,7,3,8,1,6,5,2]=>[2,5,6,1,8,3,7,4]=>1011000=>0001101
[4,8,3,2,1,6,7,5]=>[5,7,6,1,2,3,8,4]=>1001010=>0101001
[1,8,4,2,7,3,5,6]=>[6,5,3,7,2,4,8,1]=>1110100=>0010111
[7,4,1,2,6,8,3,5]=>[5,3,8,6,2,1,4,7]=>1110010=>0100111
[1,8,5,2,3,4,7,6]=>[6,7,4,3,2,5,8,1]=>1111000=>0001111
[1,8,3,2,7,4,5,6]=>[6,5,4,7,2,3,8,1]=>1101100=>0011011
[6,1,2,8,3,4,7,5]=>[5,7,4,3,8,2,1,6]=>1111000=>0001111
[5,4,1,2,7,8,3,6]=>[6,3,8,7,2,1,4,5]=>1110001=>1000111
[3,1,8,2,5,4,6,7]=>[7,6,4,5,2,8,1,3]=>1101010=>0101011
[6,3,5,1,8,2,4,7]=>[7,4,2,8,1,5,3,6]=>1111000=>0001111
[6,3,1,5,7,8,2,4]=>[4,2,8,7,5,1,3,6]=>1100101=>1010011
[7,1,3,4,5,8,2,6]=>[6,2,8,5,4,3,1,7]=>1111100=>0011111
[3,8,7,1,4,2,5,6]=>[6,5,2,4,1,7,8,3]=>1110100=>0010111
[7,6,1,3,4,8,2,5]=>[5,2,8,4,3,1,6,7]=>1111000=>0001111
[1,8,7,6,3,2,4,5]=>[5,4,2,3,6,7,8,1]=>1101000=>0001011
[1,8,2,7,5,3,6,4]=>[4,6,3,5,7,2,8,1]=>1110000=>0000111
[1,7,4,5,2,6,8,3]=>[3,8,6,2,5,4,7,1]=>1101010=>0101011
[3,2,1,8,7,6,4,5]=>[5,4,6,7,8,1,2,3]=>1001000=>0001001
[3,2,1,8,7,4,6,5]=>[5,6,4,7,8,1,2,3]=>1001000=>0001001
[3,2,1,8,7,4,5,6]=>[6,5,4,7,8,1,2,3]=>1001100=>0011001
[3,2,1,8,4,7,6,5]=>[5,6,7,4,8,1,2,3]=>1001000=>0001001
[3,2,8,7,6,1,5,4]=>[4,5,1,6,7,8,2,3]=>1100000=>0000011
[6,3,8,7,2,1,5,4]=>[4,5,1,2,7,8,3,6]=>1010000=>0000101
[6,5,8,7,3,2,1,4]=>[4,1,2,3,7,8,5,6]=>1000100=>0010001
[4,5,3,8,6,2,7,1]=>[1,7,2,6,8,3,5,4]=>0111000=>0001110
[4,6,2,8,5,3,7,1]=>[1,7,3,5,8,2,6,4]=>0111000=>0001110
[4,5,8,3,6,2,7,1]=>[1,7,2,6,3,8,5,4]=>0111100=>0011110
[4,7,1,6,2,8,5,3]=>[3,5,8,2,6,1,7,4]=>1101000=>0001011
[6,2,5,3,8,4,7,1]=>[1,7,4,8,3,5,2,6]=>0111000=>0001110
[6,3,7,4,5,2,8,1]=>[1,8,2,5,4,7,3,6]=>0111000=>0001110
[5,7,8,4,3,2,1,6]=>[6,1,2,3,4,8,7,5]=>1000101=>1010001
[4,6,8,7,3,2,1,5]=>[5,1,2,3,7,8,6,4]=>1001010=>0101001
[2,4,8,7,6,5,1,3]=>[3,1,5,6,7,8,4,2]=>1101000=>0001011
[4,7,6,8,3,2,1,5]=>[5,1,2,3,8,6,7,4]=>1001010=>0101001
[4,6,7,8,3,2,1,5]=>[5,1,2,3,8,7,6,4]=>1001011=>1101001
[3,5,6,8,7,2,1,4]=>[4,1,2,7,8,6,5,3]=>1010110=>0110101
[2,3,6,7,8,4,1,5]=>[5,1,4,8,7,6,3,2]=>1110011=>1100111
[2,3,5,7,1,6,8,4]=>[4,8,6,1,7,5,3,2]=>1110110=>0110111
[2,6,4,7,8,3,1,5]=>[5,1,3,8,7,4,6,2]=>1101001=>1001011
[2,5,6,7,3,1,8,4]=>[4,8,1,3,7,6,5,2]=>1100110=>0110011
[2,5,7,6,3,8,4,1]=>[1,4,8,3,6,7,5,2]=>0110100=>0010110
[2,6,7,5,8,3,4,1]=>[1,4,3,8,5,7,6,2]=>0110110=>0110110
[2,4,7,1,5,8,3,6]=>[6,3,8,5,1,7,4,2]=>1111100=>0011111
[2,4,6,1,5,8,3,7]=>[7,3,8,5,1,6,4,2]=>1111100=>0011111
[2,4,5,1,8,7,3,6]=>[6,3,7,8,1,5,4,2]=>1111000=>0001111
[3,4,1,7,6,8,5,2]=>[2,5,8,6,7,1,4,3]=>1010010=>0100101
[3,7,1,5,6,8,4,2]=>[2,4,8,6,5,1,7,3]=>1010110=>0110101
[3,6,1,7,8,4,2,5]=>[5,2,4,8,7,1,6,3]=>1110001=>1000111
[4,3,6,2,8,1,7,5]=>[5,7,1,8,2,6,3,4]=>1110000=>0000111
[5,3,7,6,2,8,4,1]=>[1,4,8,2,6,7,3,5]=>0110000=>0000110
[4,5,7,2,1,8,3,6]=>[6,3,8,1,2,7,5,4]=>1011100=>0011101
[4,6,5,2,8,7,3,1]=>[1,3,7,8,2,5,6,4]=>0101000=>0001010
[5,6,4,8,2,7,3,1]=>[1,3,7,2,8,4,6,5]=>0101100=>0011010
[3,4,1,7,8,2,6,5]=>[5,6,2,8,7,1,4,3]=>1110001=>1000111
[3,6,1,7,2,5,8,4]=>[4,8,5,2,7,1,6,3]=>1110100=>0010111
[3,6,1,8,2,5,7,4]=>[4,7,5,2,8,1,6,3]=>1110100=>0010111
[6,3,4,7,2,5,8,1]=>[1,8,5,2,7,4,3,6]=>0111100=>0011110
[6,3,7,8,2,5,1,4]=>[4,1,5,2,8,7,3,6]=>1110001=>1000111
[4,7,6,5,2,8,3,1]=>[1,3,8,2,5,6,7,4]=>0101000=>0001010
[4,6,8,5,2,1,7,3]=>[3,7,1,2,5,8,6,4]=>1001010=>0101001
[3,6,1,4,5,7,8,2]=>[2,8,7,5,4,1,6,3]=>1011101=>1011101
[4,3,7,5,6,2,8,1]=>[1,8,2,6,5,7,3,4]=>0110100=>0010110
[4,3,5,7,8,2,6,1]=>[1,6,2,8,7,5,3,4]=>0110101=>1010110
[7,3,4,8,6,2,5,1]=>[1,5,2,6,8,4,3,7]=>0111000=>0001110
[4,7,8,5,6,2,1,3]=>[3,1,2,6,5,8,7,4]=>1001101=>1011001
[3,5,1,4,8,7,2,6]=>[6,2,7,8,4,1,5,3]=>1111000=>0001111
[4,5,6,3,8,2,1,7]=>[7,1,2,8,3,6,5,4]=>1011100=>0011101
[4,2,7,3,5,8,1,6]=>[6,1,8,5,3,7,2,4]=>1110100=>0010111
[4,2,6,8,5,3,1,7]=>[7,1,3,5,8,6,2,4]=>1100010=>0100011
[5,1,2,7,8,6,4,3]=>[3,4,6,8,7,2,1,5]=>1100001=>1000011
[4,1,8,7,2,6,3,5]=>[5,3,6,2,7,8,1,4]=>1110000=>0000111
[4,1,5,8,7,3,2,6]=>[6,2,3,7,8,5,1,4]=>1100100=>0010011
[5,1,8,2,7,6,3,4]=>[4,3,6,7,2,8,1,5]=>1110000=>0000111
[7,1,8,2,4,5,3,6]=>[6,3,5,4,2,8,1,7]=>1111000=>0001111
[4,1,5,6,8,2,7,3]=>[3,7,2,8,6,5,1,4]=>1100110=>0110011
[5,2,1,6,8,4,7,3]=>[3,7,4,8,6,1,2,5]=>1001010=>0101001
[4,5,2,8,7,1,6,3]=>[3,6,1,7,8,2,5,4]=>1101000=>0001011
[5,2,8,1,7,4,3,6]=>[6,3,4,7,1,8,2,5]=>1110000=>0000111
[4,2,8,7,1,3,6,5]=>[5,6,3,1,7,8,2,4]=>1110000=>0000111
[5,2,1,3,8,4,7,6]=>[6,7,4,8,3,1,2,5]=>1011000=>0001101
[8,2,1,7,3,5,4,6]=>[6,4,5,3,7,1,2,8]=>1011000=>0001101
[6,2,1,7,8,4,3,5]=>[5,3,4,8,7,1,2,6]=>1010001=>1000101
[5,2,3,6,8,4,7,1]=>[1,7,4,8,6,3,2,5]=>0111010=>0101110
[5,1,8,6,4,7,2,3]=>[3,2,7,4,6,8,1,5]=>1101000=>0001011
[6,1,2,8,3,7,4,5]=>[5,4,7,3,8,2,1,6]=>1111000=>0001111
[5,7,8,3,4,2,1,6]=>[6,1,2,4,3,8,7,5]=>1010101=>1010101
[5,6,7,3,8,1,2,4]=>[4,2,1,8,3,7,6,5]=>1110110=>0110111
[7,1,6,3,4,2,8,5]=>[5,8,2,4,3,6,1,7]=>1110000=>0000111
[6,2,3,8,7,5,1,4]=>[4,1,5,7,8,3,2,6]=>1110000=>0000111
[7,2,3,4,1,5,8,6]=>[6,8,5,1,4,3,2,7]=>1110100=>0010111
[6,2,3,4,7,8,5,1]=>[1,5,8,7,4,3,2,6]=>0111001=>1001110
[3,7,8,1,4,5,2,6]=>[6,2,5,4,1,8,7,3]=>1111001=>1001111
[3,8,5,7,2,4,1,6]=>[6,1,4,2,7,5,8,3]=>1110100=>0010111
[3,6,5,8,2,1,7,4]=>[4,7,1,2,8,5,6,3]=>1010100=>0010101
[4,8,6,7,1,2,3,5]=>[5,3,2,1,7,6,8,4]=>1111010=>0101111
[8,5,7,3,1,6,2,4]=>[4,2,6,1,3,7,5,8]=>1100100=>0010011
[4,6,5,8,2,3,7,1]=>[1,7,3,2,8,5,6,4]=>0111100=>0011110
[3,8,6,1,4,7,2,5]=>[5,2,7,4,1,6,8,3]=>1111000=>0001111
[3,8,7,1,2,5,6,4]=>[4,6,5,2,1,7,8,3]=>1110100=>0010111
[3,4,8,2,5,6,7,1]=>[1,7,6,5,2,8,4,3]=>0111110=>0111110
[3,1,5,4,2,7,6,8]=>[8,6,7,2,4,5,1,3]=>1100010=>0100011
[5,2,7,6,4,1,3,8]=>[8,3,1,4,6,7,2,5]=>1110000=>0000111
[6,3,4,5,1,2,8,7]=>[7,8,2,1,5,4,3,6]=>1111000=>0001111
[6,3,2,5,8,7,4,1]=>[1,4,7,8,5,2,3,6]=>0100100=>0010010
[6,3,4,8,7,5,1,2]=>[2,1,5,7,8,4,3,6]=>1011000=>0001101
[8,5,4,6,2,7,1,3]=>[3,1,7,2,6,4,5,8]=>1101000=>0001011
[4,8,5,6,2,7,1,3]=>[3,1,7,2,6,5,8,4]=>1101100=>0011011
[6,8,4,5,7,2,3,1]=>[1,3,2,7,5,4,8,6]=>0101110=>0111010
[7,3,2,6,8,5,4,1]=>[1,4,5,8,6,2,3,7]=>0100010=>0100010
[4,8,5,3,2,7,6,1]=>[1,6,7,2,3,5,8,4]=>0101000=>0001010
[7,3,5,6,8,1,4,2]=>[2,4,1,8,6,5,3,7]=>1010110=>0110101
[8,3,4,7,6,5,1,2]=>[2,1,5,6,7,4,3,8]=>1011000=>0001101
[7,4,8,3,6,5,2,1]=>[1,2,5,6,3,8,4,7]=>0011000=>0001100
[7,4,6,8,3,5,2,1]=>[1,2,5,3,8,6,4,7]=>0011010=>0101100
[2,4,5,7,6,8,1,3]=>[3,1,8,6,7,5,4,2]=>1101110=>0111011
[7,5,6,3,8,4,2,1]=>[1,2,4,8,3,6,5,7]=>0010100=>0010100
[2,5,4,6,7,8,1,3]=>[3,1,8,7,6,4,5,2]=>1101011=>1101011
[4,8,6,7,3,5,2,1]=>[1,2,5,3,7,6,8,4]=>0011010=>0101100
[3,6,7,5,4,1,8,2]=>[2,8,1,4,5,7,6,3]=>1010010=>0100101
[6,5,4,1,7,3,8,2]=>[2,8,3,7,1,4,5,6]=>1010000=>0000101
[6,3,1,5,7,2,8,4]=>[4,8,2,7,5,1,3,6]=>1100100=>0010011
[4,3,1,2,6,7,8,5]=>[5,8,7,6,2,1,3,4]=>1100011=>1100011
[3,5,4,8,6,7,2,1]=>[1,2,7,6,8,4,5,3]=>0011010=>0101100
[7,4,6,5,8,3,2,1]=>[1,2,3,8,5,6,4,7]=>0001100=>0011000
[5,7,4,2,6,8,3,1]=>[1,3,8,6,2,4,7,5]=>0100110=>0110010
[2,5,8,6,7,3,1,4]=>[4,1,3,7,6,8,5,2]=>1100110=>0110011
[2,3,4,1,8,7,5,6]=>[6,5,7,8,1,4,3,2]=>1110100=>0010111
[4,2,6,5,1,8,7,3]=>[3,7,8,1,5,6,2,4]=>1100000=>0000011
[6,5,4,1,3,2,8,7]=>[7,8,2,3,1,4,5,6]=>1100000=>0000011
[6,5,4,2,1,3,8,7]=>[7,8,3,1,2,4,5,6]=>1010000=>0000101
[8,7,4,3,6,1,5,2]=>[2,5,1,6,3,4,7,8]=>1010000=>0000101
[7,8,4,2,1,5,6,3]=>[3,6,5,1,2,4,8,7]=>1000101=>1010001
[8,3,2,7,4,1,6,5]=>[5,6,1,4,7,2,3,8]=>1100000=>0000011
[7,8,2,3,6,1,5,4]=>[4,5,1,6,3,2,8,7]=>1110001=>1000111
[6,8,2,7,3,5,4,1]=>[1,4,5,3,7,2,8,6]=>0110010=>0100110
[7,5,8,3,2,4,6,1]=>[1,6,4,2,3,8,5,7]=>0101100=>0011010
[7,5,8,1,3,4,6,2]=>[2,6,4,3,1,8,5,7]=>1011100=>0011101
[8,6,7,3,4,1,5,2]=>[2,5,1,4,3,7,6,8]=>1010010=>0100101
[7,3,2,8,4,5,6,1]=>[1,6,5,4,8,2,3,7]=>0101100=>0011010
[8,3,2,7,6,4,1,5]=>[5,1,4,6,7,2,3,8]=>1100000=>0000011
[8,5,4,1,3,7,6,2]=>[2,6,7,3,1,4,5,8]=>1010000=>0000101
[5,8,2,3,4,7,6,1]=>[1,6,7,4,3,2,8,5]=>0111100=>0011110
[6,8,2,7,3,4,1,5]=>[5,1,4,3,7,2,8,6]=>1110010=>0100111
[3,6,5,4,8,7,1,2]=>[2,1,7,8,4,5,6,3]=>1011000=>0001101
[4,5,1,6,3,2,8,7]=>[7,8,2,3,6,1,5,4]=>1101000=>0001011
[2,5,1,4,3,7,6,8]=>[8,6,7,3,4,1,5,2]=>1110010=>0100111
[1,4,5,3,7,2,8,6]=>[6,8,2,7,3,5,4,1]=>1111000=>0001111
[5,1,4,3,7,2,8,6]=>[6,8,2,7,3,4,1,5]=>1110000=>0000111
[1,6,7,4,3,2,8,5]=>[5,8,2,3,4,7,6,1]=>1100010=>0100011
[2,6,7,3,1,4,5,8]=>[8,5,4,1,3,7,6,2]=>1101110=>0111011
[5,1,4,6,7,2,3,8]=>[8,3,2,7,6,4,1,5]=>1111010=>0101111
[1,6,5,2,3,4,8,7]=>[7,8,4,3,2,5,6,1]=>1111000=>0001111
[7,8,1,2,3,6,4,5]=>[5,4,6,3,2,1,8,7]=>1111001=>1001111
[1,3,2,6,5,8,4,7]=>[7,4,8,5,6,2,3,1]=>1101100=>0011011
[2,1,5,7,8,4,3,6]=>[6,3,4,8,7,5,1,2]=>1010101=>1010101
[2,4,1,6,7,5,3,8]=>[8,3,5,7,6,1,4,2]=>1110010=>0100111
[4,3,7,6,5,8,1,2]=>[2,1,8,5,6,7,3,4]=>1010100=>0010101
[1,3,2,7,5,4,8,6]=>[6,8,4,5,7,2,3,1]=>1101000=>0001011
[1,4,5,8,6,2,3,7]=>[7,3,2,6,8,5,4,1]=>1111100=>0011111
[1,6,7,2,3,5,8,4]=>[4,8,5,3,2,7,6,1]=>1110110=>0110111
[2,4,1,8,6,5,3,7]=>[7,3,5,6,8,1,4,2]=>1110000=>0000111
[2,5,4,7,8,6,1,3]=>[3,1,6,8,7,4,5,2]=>1101001=>1001011
[7,1,4,5,8,3,6,2]=>[2,6,3,8,5,4,1,7]=>1011100=>0011101
[3,7,8,5,4,6,1,2]=>[2,1,6,4,5,8,7,3]=>1011001=>1001101
[3,1,7,8,6,4,5,2]=>[2,5,4,6,8,7,1,3]=>1001001=>1001001
[3,6,2,4,7,5,8,1]=>[1,8,5,7,4,2,6,3]=>0111100=>0011110
[3,7,2,8,4,6,5,1]=>[1,5,6,4,8,2,7,3]=>0111000=>0001110
[4,7,5,2,3,6,8,1]=>[1,8,6,3,2,5,7,4]=>0111010=>0101110
[7,3,8,1,2,5,6,4]=>[4,6,5,2,1,8,3,7]=>1110100=>0010111
[4,3,5,8,7,2,6,1]=>[1,6,2,7,8,5,3,4]=>0110100=>0010110
[2,3,4,8,7,5,6,1]=>[1,6,5,7,8,4,3,2]=>0111100=>0011110
[5,6,7,2,4,8,1,3]=>[3,1,8,4,2,7,6,5]=>1101110=>0111011
[6,4,7,5,8,3,2,1]=>[1,2,3,8,5,7,4,6]=>0001100=>0011000
[3,6,7,5,8,1,4,2]=>[2,4,1,8,5,7,6,3]=>1010110=>0110101
[1,8,5,6,7,3,4,2]=>[2,4,3,7,6,5,8,1]=>1010110=>0110101
[7,4,3,2,6,1,8,5]=>[5,8,1,6,2,3,4,7]=>1100000=>0000011
[4,8,3,2,6,7,5,1]=>[1,5,7,6,2,3,8,4]=>0101010=>0101010
[8,2,4,1,6,7,5,3]=>[3,5,7,6,1,4,2,8]=>1100010=>0100011
[3,4,8,7,6,1,5,2]=>[2,5,1,6,7,8,4,3]=>1011000=>0001101
[3,7,8,5,6,4,2,1]=>[1,2,4,6,5,8,7,3]=>0010101=>1010100
[4,3,7,5,8,6,2,1]=>[1,2,6,8,5,7,3,4]=>0010100=>0010100
[3,4,7,5,8,6,1,2]=>[2,1,6,8,5,7,4,3]=>1011100=>0011101
[7,2,4,1,8,6,5,3]=>[3,5,6,8,1,4,2,7]=>1100000=>0000011
[5,4,6,2,3,1,8,7]=>[7,8,1,3,2,6,4,5]=>1101000=>0001011
[6,3,1,5,4,2,8,7]=>[7,8,2,4,5,1,3,6]=>1100000=>0000011
[6,4,5,3,2,1,8,7]=>[7,8,1,2,3,5,4,6]=>1001000=>0001001
[4,8,6,7,5,2,1,3]=>[3,1,2,5,7,6,8,4]=>1001010=>0101001
[7,8,3,4,6,5,1,2]=>[2,1,5,6,4,3,8,7]=>1011001=>1001101
[2,1,7,6,8,4,5,3]=>[3,5,4,8,6,7,1,2]=>1001010=>0101001
[3,4,8,6,7,5,2,1]=>[1,2,5,7,6,8,4,3]=>0011010=>0101100
[3,5,4,7,6,1,8,2]=>[2,8,1,6,7,4,5,3]=>1011000=>0001101
[2,1,8,5,3,7,6,4]=>[4,6,7,3,5,8,1,2]=>1010000=>0000101
[2,8,4,1,7,6,5,3]=>[3,5,6,7,1,4,8,2]=>1100000=>0000011
[3,6,7,5,4,8,1,2]=>[2,1,8,4,5,7,6,3]=>1011010=>0101101
[6,4,7,5,2,8,3,1]=>[1,3,8,2,5,7,4,6]=>0101000=>0001010
[6,5,4,2,7,8,3,1]=>[1,3,8,7,2,4,5,6]=>0100001=>1000010
[2,1,8,6,7,5,4,3]=>[3,4,5,7,6,8,1,2]=>1000010=>0100001
[4,3,1,5,8,7,6,2]=>[2,6,7,8,5,1,3,4]=>1000100=>0010001
[8,6,3,4,2,7,5,1]=>[1,5,7,2,4,3,6,8]=>0110000=>0000110
[7,6,3,4,2,8,1,5]=>[5,1,8,2,4,3,6,7]=>1110000=>0000111
[5,1,3,2,6,4,7,8]=>[8,7,4,6,2,3,1,5]=>1101001=>1001011
[6,3,2,4,5,8,1,7]=>[7,1,8,5,4,2,3,6]=>1101100=>0011011
[3,5,4,2,8,6,1,7]=>[7,1,6,8,2,4,5,3]=>1110000=>0000111
[5,6,8,7,3,2,1,4]=>[4,1,2,3,7,8,6,5]=>1000110=>0110001
[5,1,7,3,2,6,4,8]=>[8,4,6,2,3,7,1,5]=>1101000=>0001011
[4,2,5,7,3,1,6,8]=>[8,6,1,3,7,5,2,4]=>1100110=>0110011
[6,2,7,4,3,1,8,5]=>[5,8,1,3,4,7,2,6]=>1100000=>0000011
[7,4,1,3,2,6,8,5]=>[5,8,6,2,3,1,4,7]=>1100010=>0100011
[1,6,4,2,3,7,8,5]=>[5,8,7,3,2,4,6,1]=>1110001=>1000111
[1,4,5,3,8,2,6,7]=>[7,6,2,8,3,5,4,1]=>1111010=>0101111
[4,1,3,6,2,5,7,8]=>[8,7,5,2,6,3,1,4]=>1110101=>1010111
[6,2,5,1,3,7,4,8]=>[8,4,7,3,1,5,2,6]=>1111000=>0001111
[7,6,5,8,1,2,4,3]=>[3,4,2,1,8,5,6,7]=>1100100=>0010011
[5,7,4,1,3,6,2,8]=>[8,2,6,3,1,4,7,5]=>1110100=>0010111
[7,2,3,6,8,1,4,5]=>[5,4,1,8,6,3,2,7]=>1111010=>0101111
[4,3,8,2,5,6,7,1]=>[1,7,6,5,2,8,3,4]=>0110110=>0110110
[5,4,8,2,3,6,7,1]=>[1,7,6,3,2,8,4,5]=>0111010=>0101110
[3,2,8,1,6,7,4,5]=>[5,4,7,6,1,8,2,3]=>1101010=>0101011
[7,2,6,3,8,1,5,4]=>[4,5,1,8,3,6,2,7]=>1110000=>0000111
[6,3,4,5,8,2,7,1]=>[1,7,2,8,5,4,3,6]=>0111100=>0011110
[5,2,8,3,4,6,7,1]=>[1,7,6,4,3,8,2,5]=>0111010=>0101110
[7,3,8,1,4,5,6,2]=>[2,6,5,4,1,8,3,7]=>1011100=>0011101
[7,3,4,5,8,1,6,2]=>[2,6,1,8,5,4,3,7]=>1011100=>0011101
[7,2,5,3,6,4,8,1]=>[1,8,4,6,3,5,2,7]=>0111000=>0001110
[7,4,8,1,5,6,2,3]=>[3,2,6,5,1,8,4,7]=>1101100=>0011011
[7,2,8,1,6,5,4,3]=>[3,4,5,6,1,8,2,7]=>1100000=>0000011
[8,6,5,7,2,1,4,3]=>[3,4,1,2,7,5,6,8]=>1000100=>0010001
[3,8,5,1,7,6,4,2]=>[2,4,6,7,1,5,8,3]=>1010000=>0000101
[2,8,1,3,5,6,7,4]=>[4,7,6,5,3,1,8,2]=>1110110=>0110111
[2,5,4,8,6,1,7,3]=>[3,7,1,6,8,4,5,2]=>1101000=>0001011
[2,4,5,8,6,1,7,3]=>[3,7,1,6,8,5,4,2]=>1101100=>0011011
[2,4,8,7,5,6,3,1]=>[1,3,6,5,7,8,4,2]=>0101100=>0011010
[3,8,5,2,6,7,4,1]=>[1,4,7,6,2,5,8,3]=>0110010=>0100110
[7,6,3,8,2,5,4,1]=>[1,4,5,2,8,3,6,7]=>0110000=>0000110
[1,2,6,8,7,3,4,5]=>[5,4,3,7,8,6,2,1]=>1111010=>0101111
[1,2,5,3,7,6,8,4]=>[4,8,6,7,3,5,2,1]=>1110010=>0100111
[8,3,7,2,5,6,4,1]=>[1,4,6,5,2,7,3,8]=>0110100=>0010110
[3,7,8,1,5,6,2,4]=>[4,2,6,5,1,8,7,3]=>1110101=>1010111
[1,2,4,8,3,6,5,7]=>[7,5,6,3,8,4,2,1]=>1111100=>0011111
[4,1,3,7,6,8,5,2]=>[2,5,8,6,7,3,1,4]=>1010010=>0100101
[6,5,7,8,1,4,3,2]=>[2,3,4,1,8,7,5,6]=>1000101=>1010001
[1,6,3,8,2,5,4,7]=>[7,4,5,2,8,3,6,1]=>1111000=>0001111
[1,3,7,6,2,5,8,4]=>[4,8,5,2,6,7,3,1]=>1110100=>0010111
[2,8,3,1,7,5,4,6]=>[6,4,5,7,1,3,8,2]=>1101000=>0001011
[4,1,2,6,7,5,3,8]=>[8,3,5,7,6,2,1,4]=>1110010=>0100111
[5,8,7,6,2,1,3,4]=>[4,3,1,2,6,7,8,5]=>1010100=>0010101
[4,8,1,7,5,6,3,2]=>[2,3,6,5,7,1,8,4]=>1001100=>0011001
[4,3,8,5,7,2,6,1]=>[1,6,2,7,5,8,3,4]=>0110100=>0010110
[6,4,8,3,7,5,2,1]=>[1,2,5,7,3,8,4,6]=>0011000=>0001100
[3,6,8,2,5,7,4,1]=>[1,4,7,5,2,8,6,3]=>0110110=>0110110
[5,4,2,6,1,8,7,3]=>[3,7,8,1,6,2,4,5]=>1100000=>0000011
[4,8,7,5,2,6,3,1]=>[1,3,6,2,5,7,8,4]=>0101000=>0001010
[4,8,6,5,2,7,3,1]=>[1,3,7,2,5,6,8,4]=>0101000=>0001010
[8,3,5,6,2,7,4,1]=>[1,4,7,2,6,5,3,8]=>0110100=>0010110
[3,2,8,5,6,1,7,4]=>[4,7,1,6,5,8,2,3]=>1100100=>0010011
[8,7,3,5,2,6,4,1]=>[1,4,6,2,5,3,7,8]=>0110000=>0000110
[3,4,8,1,5,7,6,2]=>[2,6,7,5,1,8,4,3]=>1011100=>0011101
[8,7,3,4,1,6,5,2]=>[2,5,6,1,4,3,7,8]=>1010000=>0000101
[3,5,8,7,4,6,2,1]=>[1,2,6,4,7,8,5,3]=>0011100=>0011100
[3,5,7,6,2,4,8,1]=>[1,8,4,2,6,7,5,3]=>0111100=>0011110
[4,8,5,6,3,7,1,2]=>[2,1,7,3,6,5,8,4]=>1011100=>0011101
[6,4,5,2,8,7,3,1]=>[1,3,7,8,2,5,4,6]=>0101000=>0001010
[6,4,2,7,8,5,3,1]=>[1,3,5,8,7,2,4,6]=>0100001=>1000010
[4,7,8,5,6,2,3,1]=>[1,3,2,6,5,8,7,4]=>0101101=>1011010
[2,4,5,8,6,7,1,3]=>[3,1,7,6,8,5,4,2]=>1101110=>0111011
[3,5,6,7,8,2,4,1]=>[1,4,2,8,7,6,5,3]=>0110111=>1110110
[5,2,4,1,6,7,8,3]=>[3,8,7,6,1,4,2,5]=>1100011=>1100011
[4,5,3,6,1,7,8,2]=>[2,8,7,1,6,3,5,4]=>1011001=>1001101
[7,5,6,8,4,1,3,2]=>[2,3,1,4,8,6,5,7]=>1000110=>0110001
[7,8,4,5,1,6,3,2]=>[2,3,6,1,5,4,8,7]=>1001001=>1001001
[3,5,8,6,4,7,2,1]=>[1,2,7,4,6,8,5,3]=>0011100=>0011100
[7,6,5,3,8,4,2,1]=>[1,2,4,8,3,5,6,7]=>0010000=>0000100
[4,5,6,8,3,7,2,1]=>[1,2,7,3,8,6,5,4]=>0011110=>0111100
[4,8,6,7,5,2,3,1]=>[1,3,2,5,7,6,8,4]=>0101010=>0101010
[8,7,4,3,6,5,1,2]=>[2,1,5,6,3,4,7,8]=>1010000=>0000101
[6,1,2,5,4,3,8,7]=>[7,8,3,4,5,2,1,6]=>1110000=>0000111
[2,8,6,3,4,7,1,5]=>[5,1,7,4,3,6,8,2]=>1111000=>0001111
[8,5,2,1,6,3,4,7]=>[7,4,3,6,1,2,5,8]=>1011000=>0001101
[8,1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1,8]=>1111000=>0001111
[8,1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1,8]=>1110000=>0000111
[2,8,1,6,7,5,3,4]=>[4,3,5,7,6,1,8,2]=>1110010=>0100111
[4,8,5,2,7,1,6,3]=>[3,6,1,7,2,5,8,4]=>1101000=>0001011
[3,7,8,4,6,2,1,5]=>[5,1,2,6,4,8,7,3]=>1011001=>1001101
[8,3,1,5,7,6,2,4]=>[4,2,6,7,5,1,3,8]=>1100100=>0010011
[8,4,5,1,3,6,2,7]=>[7,2,6,3,1,5,4,8]=>1111000=>0001111
[4,5,2,8,6,7,1,3]=>[3,1,7,6,8,2,5,4]=>1101010=>0101011
[8,6,2,1,4,7,3,5]=>[5,3,7,4,1,2,6,8]=>1011000=>0001101
[8,1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1,8]=>1110010=>0100111
[5,4,1,3,2,8,7,6]=>[6,7,8,2,3,1,4,5]=>1100000=>0000011
[5,4,2,1,3,8,7,6]=>[6,7,8,3,1,2,4,5]=>1010000=>0000101
[3,2,7,4,1,6,5,8]=>[8,5,6,1,4,7,2,3]=>1100100=>0010011
[5,7,2,1,3,6,4,8]=>[8,4,6,3,1,2,7,5]=>1011100=>0011101
[7,6,5,2,1,4,3,8]=>[8,3,4,1,2,5,6,7]=>1010000=>0000101
[6,2,7,1,3,5,4,8]=>[8,4,5,3,1,7,2,6]=>1111000=>0001111
[8,7,4,6,1,3,5,2]=>[2,5,3,1,6,4,7,8]=>1011000=>0001101
[6,8,1,5,4,2,3,7]=>[7,3,2,4,5,1,8,6]=>1110010=>0100111
[1,7,6,3,2,4,5,8]=>[8,5,4,2,3,6,7,1]=>1101100=>0011011
[6,8,1,3,2,4,5,7]=>[7,5,4,2,3,1,8,6]=>1101110=>0111011
[5,2,8,1,4,3,7,6]=>[6,7,3,4,1,8,2,5]=>1110000=>0000111
[7,1,6,8,2,4,5,3]=>[3,5,4,2,8,6,1,7]=>1101010=>0101011
[8,6,1,3,7,5,2,4]=>[4,2,5,7,3,1,6,8]=>1110000=>0000111
[5,8,3,1,4,6,2,7]=>[7,2,6,4,1,3,8,5]=>1101100=>0011011
[5,8,6,2,3,1,4,7]=>[7,4,1,3,2,6,8,5]=>1101100=>0011011
[5,8,7,2,3,4,1,6]=>[6,1,4,3,2,7,8,5]=>1110100=>0010111
[5,8,7,3,2,4,6,1]=>[1,6,4,2,3,7,8,5]=>0101100=>0011010
[7,6,2,8,3,5,4,1]=>[1,4,5,3,8,2,6,7]=>0110000=>0000110
[7,6,1,8,3,4,5,2]=>[2,5,4,3,8,1,6,7]=>1011000=>0001101
[8,2,6,3,1,4,7,5]=>[5,7,4,1,3,6,2,8]=>1101000=>0001011
[8,3,2,7,6,1,4,5]=>[5,4,1,6,7,2,3,8]=>1101000=>0001011
[8,6,5,2,3,7,4,1]=>[1,4,7,3,2,5,6,8]=>0110000=>0000110
[3,8,2,7,6,4,1,5]=>[5,1,4,6,7,2,8,3]=>1110000=>0000111
[5,8,4,3,2,7,6,1]=>[1,6,7,2,3,4,8,5]=>0100100=>0010010
[2,4,6,8,7,3,5,1]=>[1,5,3,7,8,6,4,2]=>0111010=>0101110
[6,8,5,7,2,3,4,1]=>[1,4,3,2,7,5,8,6]=>0110110=>0110110
[6,3,5,7,8,2,4,1]=>[1,4,2,8,7,5,3,6]=>0110101=>1010110
[4,6,8,7,5,2,3,1]=>[1,3,2,5,7,8,6,4]=>0101010=>0101010
[5,7,3,6,8,4,2,1]=>[1,2,4,8,6,3,7,5]=>0010110=>0110100
[3,5,6,8,7,2,4,1]=>[1,4,2,7,8,6,5,3]=>0110110=>0110110
[7,5,6,2,8,4,3,1]=>[1,3,4,8,2,6,5,7]=>0100100=>0010010
[3,8,6,5,1,7,2,4]=>[4,2,7,1,5,6,8,3]=>1110000=>0000111
[8,4,6,7,5,2,3,1]=>[1,3,2,5,7,6,4,8]=>0101010=>0101010
[6,5,8,3,7,4,2,1]=>[1,2,4,7,3,8,5,6]=>0010100=>0010100
[6,7,4,3,8,5,2,1]=>[1,2,5,8,3,4,7,6]=>0010010=>0100100
[2,6,8,5,4,7,3,1]=>[1,3,7,4,5,8,6,2]=>0101010=>0101010
[7,2,4,5,8,6,3,1]=>[1,3,6,8,5,4,2,7]=>0101100=>0011010
[2,7,4,6,8,5,3,1]=>[1,3,5,8,6,4,7,2]=>0101010=>0101010
[6,4,7,8,3,5,2,1]=>[1,2,5,3,8,7,4,6]=>0011001=>1001100
[8,4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4,8]=>0001010=>0101000
[5,2,4,1,6,3,8,7]=>[7,8,3,6,1,4,2,5]=>1110000=>0000111
[4,3,7,2,6,1,8,5]=>[5,8,1,6,2,7,3,4]=>1110000=>0000111
[6,3,5,2,7,4,8,1]=>[1,8,4,7,2,5,3,6]=>0111000=>0001110
[4,5,7,2,6,1,8,3]=>[3,8,1,6,2,7,5,4]=>1101100=>0011011
[7,5,4,2,6,1,8,3]=>[3,8,1,6,2,4,5,7]=>1100000=>0000011
[2,1,7,4,6,3,8,5]=>[5,8,3,6,4,7,1,2]=>1011000=>0001101
[4,5,7,3,6,2,8,1]=>[1,8,2,6,3,7,5,4]=>0111100=>0011110
[7,5,4,2,6,3,8,1]=>[1,8,3,6,2,4,5,7]=>0110000=>0000110
[4,5,7,2,6,3,8,1]=>[1,8,3,6,2,7,5,4]=>0111100=>0011110
[7,2,4,3,6,1,8,5]=>[5,8,1,6,3,4,2,7]=>1110000=>0000111
[4,2,7,5,6,1,8,3]=>[3,8,1,6,5,7,2,4]=>1100100=>0010011
[4,2,7,5,6,3,8,1]=>[1,8,3,6,5,7,2,4]=>0110100=>0010110
[6,2,4,3,7,5,8,1]=>[1,8,5,7,3,4,2,6]=>0110100=>0010110
[5,7,6,3,4,8,2,1]=>[1,2,8,4,3,6,7,5]=>0011100=>0011100
[2,7,5,4,8,6,3,1]=>[1,3,6,8,4,5,7,2]=>0101000=>0001010
[7,3,6,4,8,5,2,1]=>[1,2,5,8,4,6,3,7]=>0011000=>0001100
[2,4,7,6,3,5,8,1]=>[1,8,5,3,6,7,4,2]=>0111100=>0011110
[4,3,7,5,8,6,1,2]=>[2,1,6,8,5,7,3,4]=>1010100=>0010101
[6,7,4,8,3,5,2,1]=>[1,2,5,3,8,4,7,6]=>0011010=>0101100
[2,1,5,8,7,4,6,3]=>[3,6,4,7,8,5,1,2]=>1001100=>0011001
[5,8,3,6,4,7,2,1]=>[1,2,7,4,6,3,8,5]=>0011100=>0011100
[3,6,8,5,4,7,1,2]=>[2,1,7,4,5,8,6,3]=>1011010=>0101101
[7,5,3,6,8,4,2,1]=>[1,2,4,8,6,3,5,7]=>0010010=>0100100
[8,4,3,5,7,2,6,1]=>[1,6,2,7,5,3,4,8]=>0110100=>0010110
[4,7,8,6,3,5,2,1]=>[1,2,5,3,6,8,7,4]=>0011001=>1001100
[3,7,6,5,4,8,1,2]=>[2,1,8,4,5,6,7,3]=>1011000=>0001101
[6,8,7,4,5,3,2,1]=>[1,2,3,5,4,7,8,6]=>0001010=>0101000
[2,1,6,5,3,8,7,4]=>[4,7,8,3,5,6,1,2]=>1010000=>0000101
[4,3,1,5,6,8,7,2]=>[2,7,8,6,5,1,3,4]=>1000110=>0110001
[1,6,8,3,2,4,7,5]=>[5,7,4,2,3,8,6,1]=>1101010=>0101011
[1,8,7,6,2,5,3,4]=>[4,3,5,2,6,7,8,1]=>1110000=>0000111
[1,8,7,6,4,5,2,3]=>[3,2,5,4,6,7,8,1]=>1101000=>0001011
[7,1,3,8,4,6,5,2]=>[2,5,6,4,8,3,1,7]=>1011000=>0001101
[8,6,1,2,4,5,7,3]=>[3,7,5,4,2,1,6,8]=>1101100=>0011011
[1,8,6,7,3,4,5,2]=>[2,5,4,3,7,6,8,1]=>1011010=>0101101
[1,7,3,8,2,4,6,5]=>[5,6,4,2,8,3,7,1]=>1111000=>0001111
[8,4,3,1,5,6,7,2]=>[2,7,6,5,1,3,4,8]=>1000110=>0110001
[3,5,2,6,1,4,8,7]=>[7,8,4,1,6,2,5,3]=>1111000=>0001111
[4,5,7,2,3,8,6,1]=>[1,6,8,3,2,7,5,4]=>0111100=>0011110
[4,5,7,2,3,8,1,6]=>[6,1,8,3,2,7,5,4]=>1111100=>0011111
[4,5,6,2,3,1,8,7]=>[7,8,1,3,2,6,5,4]=>1101100=>0011011
[4,5,6,2,1,3,8,7]=>[7,8,3,1,2,6,5,4]=>1011100=>0011101
[4,5,6,1,3,2,8,7]=>[7,8,2,3,1,6,5,4]=>1101100=>0011011
[4,5,6,3,1,2,8,7]=>[7,8,2,1,3,6,5,4]=>1101100=>0011011
[4,5,7,3,2,8,1,6]=>[6,1,8,2,3,7,5,4]=>1101100=>0011011
[4,6,7,3,8,2,5,1]=>[1,5,2,8,3,7,6,4]=>0111010=>0101110
[4,6,7,3,8,2,1,5]=>[5,1,2,8,3,7,6,4]=>1011010=>0101101
[4,5,7,3,1,8,2,6]=>[6,2,8,1,3,7,5,4]=>1101100=>0011011
[3,5,1,7,4,8,2,6]=>[6,2,8,4,7,1,5,3]=>1111000=>0001111
[2,1,5,7,4,8,3,6]=>[6,3,8,4,7,5,1,2]=>1011100=>0011101
[4,5,7,1,3,8,6,2]=>[2,6,8,3,1,7,5,4]=>1011100=>0011101
[4,6,7,3,8,1,5,2]=>[2,5,1,8,3,7,6,4]=>1011010=>0101101
[5,6,7,8,3,1,4,2]=>[2,4,1,3,8,7,6,5]=>1000111=>1110001
[4,6,7,1,8,3,5,2]=>[2,5,3,8,1,7,6,4]=>1011010=>0101101
[3,6,1,7,8,4,5,2]=>[2,5,4,8,7,1,6,3]=>1011001=>1001101
[2,1,6,7,8,4,5,3]=>[3,5,4,8,7,6,1,2]=>1001011=>1101001
[2,1,6,7,8,4,3,5]=>[5,3,4,8,7,6,1,2]=>1010011=>1100101
[4,6,7,1,8,3,2,5]=>[5,2,3,8,1,7,6,4]=>1101010=>0101011
[5,6,7,8,1,3,2,4]=>[4,2,3,1,8,7,6,5]=>1100111=>1110011
[4,6,7,2,8,3,5,1]=>[1,5,3,8,2,7,6,4]=>0111010=>0101110
[3,6,2,7,8,4,5,1]=>[1,5,4,8,7,2,6,3]=>0111001=>1001110
[3,6,2,7,8,4,1,5]=>[5,1,4,8,7,2,6,3]=>1110001=>1000111
[3,4,2,1,7,8,5,6]=>[6,5,8,7,1,2,4,3]=>1010101=>1010101
[4,6,7,2,8,5,3,1]=>[1,3,5,8,2,7,6,4]=>0101010=>0101010
[4,6,7,2,8,5,1,3]=>[3,1,5,8,2,7,6,4]=>1101010=>0101011
[4,5,7,1,2,8,6,3]=>[3,6,8,2,1,7,5,4]=>1101100=>0011011
[2,1,6,7,8,3,5,4]=>[4,5,3,8,7,6,1,2]=>1010011=>1100101
[3,6,1,7,8,2,5,4]=>[4,5,2,8,7,1,6,3]=>1110001=>1000111
[4,6,7,1,8,2,5,3]=>[3,5,2,8,1,7,6,4]=>1101010=>0101011
[5,6,7,8,1,2,4,3]=>[3,4,2,1,8,7,6,5]=>1100111=>1110011
[5,6,7,8,2,4,1,3]=>[3,1,4,2,8,7,6,5]=>1100111=>1110011
[5,6,7,8,2,4,3,1]=>[1,3,4,2,8,7,6,5]=>0100111=>1110010
[3,6,1,7,8,5,2,4]=>[4,2,5,8,7,1,6,3]=>1110001=>1000111
[2,1,6,7,8,5,3,4]=>[4,3,5,8,7,6,1,2]=>1010011=>1100101
[3,4,2,1,6,5,8,7,10,9]=>[9,10,7,8,5,6,1,2,4,3]=>101010100=>001010101
[3,5,2,6,4,1,8,7,10,9]=>[9,10,7,8,1,4,6,2,5,3]=>111000100=>001000111
[3,5,2,7,4,8,6,1,10,9]=>[9,10,1,6,8,4,7,2,5,3]=>111100000=>000001111
[2,1,5,6,4,3,8,7,10,9]=>[9,10,7,8,3,4,6,5,1,2]=>101010100=>001010101
[4,5,6,3,2,1,8,7,10,9]=>[9,10,7,8,1,2,3,6,5,4]=>100110100=>001011001
[4,5,7,3,2,8,6,1,10,9]=>[9,10,1,6,8,2,3,7,5,4]=>110110000=>000011011
[4,5,7,3,2,9,6,10,8,1]=>[1,8,10,6,9,2,3,7,5,4]=>010111000=>000111010
[2,1,5,7,4,8,6,3,10,9]=>[9,10,3,6,8,4,7,5,1,2]=>101110000=>000011101
[4,6,7,3,8,5,2,1,10,9]=>[9,10,1,2,5,8,3,7,6,4]=>101101000=>000101101
[4,6,7,3,9,5,2,10,8,1]=>[1,8,10,2,5,9,3,7,6,4]=>011101000=>000101110
[2,1,5,7,4,9,6,10,8,3]=>[3,8,10,6,9,4,7,5,1,2]=>100111000=>000111001
[2,1,4,3,7,8,6,5,10,9]=>[9,10,5,6,8,7,3,4,1,2]=>101010100=>001010101
[3,4,2,1,7,8,6,5,10,9]=>[9,10,5,6,8,7,1,2,4,3]=>101010100=>001010101
[3,6,2,7,8,5,4,1,10,9]=>[9,10,1,4,5,8,7,2,6,3]=>111000100=>001000111
[3,6,2,7,9,5,4,10,8,1]=>[1,8,10,4,5,9,7,2,6,3]=>011100100=>001001110
[2,1,6,7,8,5,4,3,10,9]=>[9,10,3,4,5,8,7,6,1,2]=>101001100=>001100101
[5,6,7,8,4,3,2,1,10,9]=>[9,10,1,2,3,4,8,7,6,5]=>100011100=>001110001
[5,6,7,9,4,3,2,10,8,1]=>[1,8,10,2,3,4,9,7,6,5]=>010011100=>001110010
[2,1,6,7,9,5,4,10,8,3]=>[3,8,10,4,5,9,7,6,1,2]=>100101100=>001101001
[5,6,8,9,4,3,10,7,2,1]=>[1,2,7,10,3,4,9,8,6,5]=>001011010=>010110100
[2,1,4,3,7,9,6,10,8,5]=>[5,8,10,6,9,7,3,4,1,2]=>101001100=>001100101
[3,4,2,1,7,9,6,10,8,5]=>[5,8,10,6,9,7,1,2,4,3]=>101001100=>001100101
[3,6,2,8,9,5,10,7,4,1]=>[1,4,7,10,5,9,8,2,6,3]=>011010010=>010010110
[2,1,6,8,9,5,10,7,4,3]=>[3,4,7,10,5,9,8,6,1,2]=>100011010=>010110001
[2,1,4,3,6,5,9,10,8,7]=>[7,8,10,9,5,6,3,4,1,2]=>101010001=>100010101
[3,4,2,1,6,5,9,10,8,7]=>[7,8,10,9,5,6,1,2,4,3]=>101010001=>100010101
[3,5,2,6,4,1,9,10,8,7]=>[7,8,10,9,1,4,6,2,5,3]=>111000001=>100000111
[3,5,2,8,4,9,10,7,6,1]=>[1,6,7,10,9,4,8,2,5,3]=>011100001=>100001110
[2,1,5,6,4,3,9,10,8,7]=>[7,8,10,9,3,4,6,5,1,2]=>101010001=>100010101
[4,5,6,3,2,1,9,10,8,7]=>[7,8,10,9,1,2,3,6,5,4]=>100110001=>100011001
[4,5,8,3,2,9,10,7,6,1]=>[1,6,7,10,9,2,3,8,5,4]=>010110001=>100011010
[2,1,5,8,4,9,10,7,6,3]=>[3,6,7,10,9,4,8,5,1,2]=>100110001=>100011001
[4,7,8,3,9,10,6,5,2,1]=>[1,2,5,6,10,9,3,8,7,4]=>001100101=>101001100
[2,1,4,3,8,9,10,7,6,5]=>[5,6,7,10,9,8,3,4,1,2]=>101000011=>110000101
[3,4,2,1,8,9,10,7,6,5]=>[5,6,7,10,9,8,1,2,4,3]=>101000011=>110000101
[3,7,2,8,9,10,6,5,4,1]=>[1,4,5,6,10,9,8,2,7,3]=>011000011=>110000110
[5,3,1,6,2,4,8,7]=>[7,8,4,2,6,1,3,5]=>1101000=>0001011
[7,3,1,5,2,8,4,6]=>[6,4,8,2,5,1,3,7]=>1101000=>0001011
[8,4,5,1,2,7,3,6]=>[6,3,7,2,1,5,4,8]=>1111000=>0001111
[7,4,5,1,2,8,3,6]=>[6,3,8,2,1,5,4,7]=>1111000=>0001111
[6,4,5,1,2,3,8,7]=>[7,8,3,2,1,5,4,6]=>1111000=>0001111
[5,4,6,1,2,3,8,7]=>[7,8,3,2,1,6,4,5]=>1111000=>0001111
[3,6,1,5,2,4,8,7]=>[7,8,4,2,5,1,6,3]=>1111000=>0001111
[4,6,5,1,2,3,8,7]=>[7,8,3,2,1,5,6,4]=>1111000=>0001111
[5,6,4,1,2,3,8,7]=>[7,8,3,2,1,4,6,5]=>1110100=>0010111
[7,5,4,1,2,8,3,6]=>[6,3,8,2,1,4,5,7]=>1110000=>0000111
[8,6,4,1,7,2,3,5]=>[5,3,2,7,1,4,6,8]=>1110000=>0000111
[5,7,4,1,2,8,3,6]=>[6,3,8,2,1,4,7,5]=>1110100=>0010111
[3,7,1,5,2,8,4,6]=>[6,4,8,2,5,1,7,3]=>1111000=>0001111
[2,1,7,5,3,8,4,6]=>[6,4,8,3,5,7,1,2]=>1011000=>0001101
[4,8,5,1,2,7,3,6]=>[6,3,7,2,1,5,8,4]=>1111000=>0001111
[6,8,4,1,7,2,3,5]=>[5,3,2,7,1,4,8,6]=>1110010=>0100111
[4,8,6,1,7,2,3,5]=>[5,3,2,7,1,6,8,4]=>1111000=>0001111
[2,1,8,6,7,3,4,5]=>[5,4,3,7,6,8,1,2]=>1011010=>0101101
[2,1,7,6,8,3,4,5]=>[5,4,3,8,6,7,1,2]=>1011010=>0101101
[4,7,6,1,8,2,3,5]=>[5,3,2,8,1,6,7,4]=>1111000=>0001111
[5,7,6,8,1,2,3,4]=>[4,3,2,1,8,6,7,5]=>1110110=>0110111
[6,4,7,1,8,2,3,5]=>[5,3,2,8,1,7,4,6]=>1111000=>0001111
[8,4,6,1,7,2,3,5]=>[5,3,2,7,1,6,4,8]=>1111000=>0001111
[8,3,1,6,7,2,4,5]=>[5,4,2,7,6,1,3,8]=>1101010=>0101011
[4,3,1,2,7,8,5,6]=>[6,5,8,7,2,1,3,4]=>1100101=>1010011
[8,4,7,1,6,2,3,5]=>[5,3,2,6,1,7,4,8]=>1111000=>0001111
[7,4,8,1,6,2,3,5]=>[5,3,2,6,1,8,4,7]=>1111000=>0001111
[4,5,8,1,2,7,3,6]=>[6,3,7,2,1,8,5,4]=>1111100=>0011111
[2,1,6,8,7,3,4,5]=>[5,4,3,7,8,6,1,2]=>1011010=>0101101
[4,6,8,1,7,2,3,5]=>[5,3,2,7,1,8,6,4]=>1111010=>0101111
[5,6,8,7,1,2,3,4]=>[4,3,2,1,7,8,6,5]=>1110110=>0110111
[8,5,7,6,1,2,3,4]=>[4,3,2,1,6,7,5,8]=>1110100=>0010111
[4,7,8,1,6,2,3,5]=>[5,3,2,6,1,8,7,4]=>1111001=>1001111
[3,7,1,8,6,2,4,5]=>[5,4,2,6,8,1,7,3]=>1111000=>0001111
[3,8,1,7,6,2,4,5]=>[5,4,2,6,7,1,8,3]=>1111000=>0001111
[4,8,7,1,6,2,3,5]=>[5,3,2,6,1,7,8,4]=>1111000=>0001111
[6,8,7,5,1,2,3,4]=>[4,3,2,1,5,7,8,6]=>1110010=>0100111
[6,4,7,3,8,5,1,2]=>[2,1,5,8,3,7,4,6]=>1011000=>0001101
[5,4,2,7,6,1,3,8]=>[8,3,1,6,7,2,4,5]=>1110000=>0000111
[5,4,2,7,6,1,8,3]=>[3,8,1,6,7,2,4,5]=>1100000=>0000011
[5,4,3,7,6,8,1,2]=>[2,1,8,6,7,3,4,5]=>1010010=>0100101
[5,4,3,7,8,6,1,2]=>[2,1,6,8,7,3,4,5]=>1010001=>1000101
[5,4,3,8,6,7,1,2]=>[2,1,7,6,8,3,4,5]=>1010010=>0100101
[5,4,3,6,8,7,1,2]=>[2,1,7,8,6,3,4,5]=>1010010=>0100101
[5,4,2,6,7,1,8,3]=>[3,8,1,7,6,2,4,5]=>1100010=>0100011
[5,3,2,6,1,7,4,8]=>[8,4,7,1,6,2,3,5]=>1101000=>0001011
[5,3,2,6,1,7,8,4]=>[4,8,7,1,6,2,3,5]=>1100001=>1000011
[5,3,2,6,1,8,7,4]=>[4,7,8,1,6,2,3,5]=>1100000=>0000011
[5,4,2,6,8,1,7,3]=>[3,7,1,8,6,2,4,5]=>1100010=>0100011
[6,4,8,2,5,1,7,3]=>[3,7,1,5,2,8,4,6]=>1101000=>0001011
[5,4,2,8,6,1,3,7]=>[7,3,1,6,8,2,4,5]=>1110000=>0000111
[5,3,2,6,1,8,4,7]=>[7,4,8,1,6,2,3,5]=>1101000=>0001011
[6,3,8,2,1,5,4,7]=>[7,4,5,1,2,8,3,6]=>1011000=>0001101
[7,8,3,2,1,5,4,6]=>[6,4,5,1,2,3,8,7]=>1001001=>1001001
[7,8,3,2,1,5,6,4]=>[4,6,5,1,2,3,8,7]=>1000101=>1010001
[6,3,8,2,1,5,7,4]=>[4,7,5,1,2,8,3,6]=>1010100=>0010101
[5,3,2,8,1,6,7,4]=>[4,7,6,1,8,2,3,5]=>1100010=>0100011
[5,4,2,7,8,1,6,3]=>[3,6,1,8,7,2,4,5]=>1100001=>1000011
[5,3,2,7,1,8,6,4]=>[4,6,8,1,7,2,3,5]=>1100000=>0000011
[5,3,2,7,1,6,4,8]=>[8,4,6,1,7,2,3,5]=>1101000=>0001011
[6,3,7,2,1,5,4,8]=>[8,4,5,1,2,7,3,6]=>1011000=>0001101
[6,3,7,2,1,5,8,4]=>[4,8,5,1,2,7,3,6]=>1010100=>0010101
[6,3,7,2,1,8,5,4]=>[4,5,8,1,2,7,3,6]=>1010000=>0000101
[6,5,7,8,2,1,4,3]=>[3,4,1,2,8,7,5,6]=>1000101=>1010001
[6,3,7,2,1,4,8,5]=>[5,8,4,1,2,7,3,6]=>1011000=>0001101
[5,3,2,7,1,4,8,6]=>[6,8,4,1,7,2,3,5]=>1101000=>0001011
[5,4,2,8,7,1,3,6]=>[6,3,1,7,8,2,4,5]=>1110000=>0000111
[7,8,4,2,6,1,3,5]=>[5,3,1,6,2,4,8,7]=>1110001=>1000111
[7,8,3,2,1,6,4,5]=>[5,4,6,1,2,3,8,7]=>1001001=>1001001
[6,3,8,2,1,7,4,5]=>[5,4,7,1,2,8,3,6]=>1011000=>0001101
[5,3,2,8,1,7,4,6]=>[6,4,7,1,8,2,3,5]=>1101000=>0001011
[4,3,2,1,8,7,5,6]=>[6,5,7,8,1,2,3,4]=>1000100=>0010001
[4,3,2,1,7,5,8,6]=>[6,8,5,7,1,2,3,4]=>1000100=>0010001
[4,3,2,1,7,5,6,8]=>[8,6,5,7,1,2,3,4]=>1000110=>0110001
[5,3,2,8,1,4,7,6]=>[6,7,4,1,8,2,3,5]=>1101000=>0001011
[6,3,8,2,1,4,7,5]=>[5,7,4,1,2,8,3,6]=>1011000=>0001101
[7,8,3,2,1,4,6,5]=>[5,6,4,1,2,3,8,7]=>1001001=>1001001
[4,3,2,1,8,5,6,7]=>[7,6,5,8,1,2,3,4]=>1000110=>0110001
[7,8,5,6,1,2,4,3]=>[3,4,2,1,6,5,8,7]=>1100101=>1010011
[7,8,4,1,6,2,5,3]=>[3,5,2,6,1,4,8,7]=>1100001=>1000011
[1,6,8,3,2,7,5,4]=>[4,5,7,2,3,8,6,1]=>1100010=>0100011
[6,1,8,3,2,7,5,4]=>[4,5,7,2,3,8,1,6]=>1100000=>0000011
[7,8,1,3,2,6,5,4]=>[4,5,6,2,3,1,8,7]=>1100001=>1000011
[7,8,3,1,2,6,5,4]=>[4,5,6,2,1,3,8,7]=>1100001=>1000011
[7,8,2,3,1,6,5,4]=>[4,5,6,1,3,2,8,7]=>1100001=>1000011
[7,8,2,1,3,6,5,4]=>[4,5,6,3,1,2,8,7]=>1010001=>1000101
[7,8,1,2,3,6,5,4]=>[4,5,6,3,2,1,8,7]=>1110001=>1000111
[1,5,2,8,3,7,6,4]=>[4,6,7,3,8,2,5,1]=>1110000=>0000111
[5,1,2,8,3,7,6,4]=>[4,6,7,3,8,2,1,5]=>1110000=>0000111
[5,2,1,8,3,7,6,4]=>[4,6,7,3,8,1,2,5]=>1010000=>0000101
[6,2,8,1,3,7,5,4]=>[4,5,7,3,1,8,2,6]=>1110000=>0000111
[6,2,8,4,7,1,5,3]=>[3,5,1,7,4,8,2,6]=>1101000=>0001011
[6,3,8,4,7,5,1,2]=>[2,1,5,7,4,8,3,6]=>1011000=>0001101
[2,6,8,3,1,7,5,4]=>[4,5,7,1,3,8,6,2]=>1100010=>0100011
[2,5,1,8,3,7,6,4]=>[4,6,7,3,8,1,5,2]=>1110000=>0000111
[1,2,5,8,3,7,6,4]=>[4,6,7,3,8,5,2,1]=>1110100=>0010111
[2,5,3,8,1,7,6,4]=>[4,6,7,1,8,3,5,2]=>1110000=>0000111
[2,5,4,8,7,1,6,3]=>[3,6,1,7,8,4,5,2]=>1101000=>0001011
[3,5,4,8,7,6,1,2]=>[2,1,6,7,8,4,5,3]=>1011000=>0001101
[5,3,4,8,7,6,1,2]=>[2,1,6,7,8,4,3,5]=>1011000=>0001101
[5,2,4,8,7,1,6,3]=>[3,6,1,7,8,4,2,5]=>1101000=>0001011
[5,2,3,8,1,7,6,4]=>[4,6,7,1,8,3,2,5]=>1110000=>0000111
[4,1,2,3,8,7,6,5]=>[5,6,7,8,3,2,1,4]=>1110000=>0000111
[1,4,2,3,8,7,6,5]=>[5,6,7,8,3,2,4,1]=>1110000=>0000111
[4,1,3,2,8,7,6,5]=>[5,6,7,8,2,3,1,4]=>1100000=>0000011
[6,3,8,1,2,7,5,4]=>[4,5,7,2,1,8,3,6]=>1110000=>0000111
[5,3,1,8,2,7,6,4]=>[4,6,7,2,8,1,3,5]=>1100000=>0000011
[5,1,3,8,2,7,6,4]=>[4,6,7,2,8,3,1,5]=>1110000=>0000111
[1,5,3,8,2,7,6,4]=>[4,6,7,2,8,3,5,1]=>1110000=>0000111
[1,5,4,8,7,2,6,3]=>[3,6,2,7,8,4,5,1]=>1101000=>0001011
[5,1,4,8,7,2,6,3]=>[3,6,2,7,8,4,1,5]=>1101000=>0001011
[5,4,1,8,7,2,6,3]=>[3,6,2,7,8,1,4,5]=>1100000=>0000011
[6,5,8,7,1,2,4,3]=>[3,4,2,1,7,8,5,6]=>1100100=>0010011
[5,6,8,7,3,4,1,2]=>[2,1,4,3,7,8,6,5]=>1010110=>0110101
[5,6,8,7,2,1,4,3]=>[3,4,1,2,7,8,6,5]=>1000110=>0110001
[4,5,1,8,7,2,6,3]=>[3,6,2,7,8,1,5,4]=>1101000=>0001011
[4,1,5,8,7,2,6,3]=>[3,6,2,7,8,5,1,4]=>1100100=>0010011
[1,3,5,8,2,7,6,4]=>[4,6,7,2,8,5,3,1]=>1110100=>0010111
[3,1,5,8,2,7,6,4]=>[4,6,7,2,8,5,1,3]=>1100100=>0010011
[3,6,8,2,1,7,5,4]=>[4,5,7,1,2,8,6,3]=>1010010=>0100101
[4,6,8,3,7,5,1,2]=>[2,1,5,7,3,8,6,4]=>1011010=>0101101
[4,5,3,8,7,6,1,2]=>[2,1,6,7,8,3,5,4]=>1011000=>0001101
[3,5,2,8,1,7,6,4]=>[4,6,7,1,8,2,5,3]=>1110000=>0000111
[3,1,4,2,8,7,6,5]=>[5,6,7,8,2,4,1,3]=>1100000=>0000011
[3,2,5,8,1,7,6,4]=>[4,6,7,1,8,5,2,3]=>1100100=>0010011
[4,2,5,8,7,1,6,3]=>[3,6,1,7,8,5,2,4]=>1100100=>0010011
[4,3,5,8,7,6,1,2]=>[2,1,6,7,8,5,3,4]=>1010100=>0010101
[2,4,5,8,7,1,6,3]=>[3,6,1,7,8,5,4,2]=>1101100=>0011011
[2,3,5,8,1,7,6,4]=>[4,6,7,1,8,5,3,2]=>1110100=>0010111
[6,2,5,1,4,3,8,7]=>[7,8,3,4,1,5,2,6]=>1110000=>0000111
[5,2,6,1,4,3,8,7]=>[7,8,3,4,1,6,2,5]=>1110000=>0000111
[5,2,7,1,4,3,8,6]=>[6,8,3,4,1,7,2,5]=>1110000=>0000111
[6,2,8,1,4,3,7,5]=>[5,7,3,4,1,8,2,6]=>1110000=>0000111
[6,2,7,1,4,3,8,5]=>[5,8,3,4,1,7,2,6]=>1110000=>0000111
[7,2,6,1,4,3,8,5]=>[5,8,3,4,1,6,2,7]=>1110000=>0000111
[8,2,5,1,4,3,7,6]=>[6,7,3,4,1,5,2,8]=>1110000=>0000111
[8,1,4,3,7,2,6,5]=>[5,6,2,7,3,4,1,8]=>1110000=>0000111
[8,2,6,1,5,3,7,4]=>[4,7,3,5,1,6,2,8]=>1110000=>0000111
[7,2,6,1,5,3,8,4]=>[4,8,3,5,1,6,2,7]=>1110000=>0000111
[6,2,7,1,5,3,8,4]=>[4,8,3,5,1,7,2,6]=>1110000=>0000111
[6,2,8,1,5,3,7,4]=>[4,7,3,5,1,8,2,6]=>1110000=>0000111
[7,4,8,1,3,2,6,5]=>[5,6,2,3,1,8,4,7]=>1101000=>0001011
[8,3,7,1,4,2,6,5]=>[5,6,2,4,1,7,3,8]=>1110000=>0000111
[8,3,7,1,5,2,6,4]=>[4,6,2,5,1,7,3,8]=>1110000=>0000111
[7,3,8,1,5,2,6,4]=>[4,6,2,5,1,8,3,7]=>1110000=>0000111
[6,2,7,3,8,1,5,4]=>[4,5,1,8,3,7,2,6]=>1110000=>0000111
[6,2,8,3,7,1,5,4]=>[4,5,1,7,3,8,2,6]=>1110000=>0000111
[5,1,8,3,7,2,6,4]=>[4,6,2,7,3,8,1,5]=>1110000=>0000111
[4,1,8,3,7,2,6,5]=>[5,6,2,7,3,8,1,4]=>1110000=>0000111
[3,1,7,4,8,2,6,5]=>[5,6,2,8,4,7,1,3]=>1101000=>0001011
[4,1,7,3,8,2,6,5]=>[5,6,2,8,3,7,1,4]=>1110000=>0000111
[5,1,7,3,8,2,6,4]=>[4,6,2,8,3,7,1,5]=>1110000=>0000111
[7,3,8,2,6,1,5,4]=>[4,5,1,6,2,8,3,7]=>1110000=>0000111
[8,2,6,3,7,1,5,4]=>[4,5,1,7,3,6,2,8]=>1110000=>0000111
[3,4,2,6,8,1,5,7]=>[7,5,1,8,6,2,4,3]=>1110110=>0110111
[5,3,6,2,8,1,4,7]=>[7,4,1,8,2,6,3,5]=>1111000=>0001111
[7,4,2,5,8,3,6,1]=>[1,6,3,8,5,2,4,7]=>0110100=>0010110
[4,5,2,6,3,8,1,7]=>[7,1,8,3,6,2,5,4]=>1111000=>0001111
[3,5,6,1,4,8,2,7]=>[7,2,8,4,1,6,5,3]=>1111100=>0011111
[4,1,5,6,3,8,2,7]=>[7,2,8,3,6,5,1,4]=>1110100=>0010111
[4,5,1,6,3,8,2,7]=>[7,2,8,3,6,1,5,4]=>1111000=>0001111
[4,5,6,3,2,8,1,7]=>[7,1,8,2,3,6,5,4]=>1101100=>0011011
[6,7,4,8,3,2,5,1]=>[1,5,2,3,8,4,7,6]=>0101010=>0101010
[6,7,4,8,3,2,1,5]=>[5,1,2,3,8,4,7,6]=>1001010=>0101001
[6,7,4,1,8,3,2,5]=>[5,2,3,8,1,4,7,6]=>1100010=>0100011
[5,3,7,8,1,4,2,6]=>[6,2,4,1,8,7,3,5]=>1110001=>1000111
[7,3,5,8,1,4,6,2]=>[2,6,4,1,8,5,3,7]=>1011100=>0011101
[4,5,1,7,8,3,6,2]=>[2,6,3,8,7,1,5,4]=>1011001=>1001101
[7,4,1,5,8,3,6,2]=>[2,6,3,8,5,1,4,7]=>1010100=>0010101
[6,7,4,3,8,1,5,2]=>[2,5,1,8,3,4,7,6]=>1010010=>0100101
[5,6,1,7,3,8,4,2]=>[2,4,8,3,7,1,6,5]=>1010100=>0010101
[5,1,6,7,3,8,4,2]=>[2,4,8,3,7,6,1,5]=>1010010=>0100101
[6,4,7,1,8,3,5,2]=>[2,5,3,8,1,7,4,6]=>1011000=>0001101
[6,7,8,3,1,4,5,2]=>[2,5,4,1,3,8,7,6]=>1001011=>1101001
[6,7,2,8,4,5,1,3]=>[3,1,5,4,8,2,7,6]=>1101010=>0101011
[6,7,2,8,4,1,3,5]=>[5,3,1,4,8,2,7,6]=>1110010=>0100111
[6,1,7,4,8,3,2,5]=>[5,2,3,8,4,7,1,6]=>1101000=>0001011
[5,1,6,7,3,2,8,4]=>[4,8,2,3,7,6,1,5]=>1100010=>0100011
[5,6,1,7,3,2,8,4]=>[4,8,2,3,7,1,6,5]=>1100100=>0010011
[5,6,7,3,2,1,8,4]=>[4,8,1,2,3,7,6,5]=>1000110=>0110001
[5,6,7,3,2,8,4,1]=>[1,4,8,2,3,7,6,5]=>0100110=>0110010
[7,4,2,5,1,8,3,6]=>[6,3,8,1,5,2,4,7]=>1110000=>0000111
[6,7,4,2,8,3,5,1]=>[1,5,3,8,2,4,7,6]=>0110010=>0100110
[3,6,7,2,8,4,5,1]=>[1,5,4,8,2,7,6,3]=>0111010=>0101110
[3,6,7,2,8,4,1,5]=>[5,1,4,8,2,7,6,3]=>1110010=>0100111
[3,6,7,2,1,8,4,5]=>[5,4,8,1,2,7,6,3]=>1011010=>0101101
[3,4,7,8,2,1,5,6]=>[6,5,1,2,8,7,4,3]=>1011101=>1011101
[3,7,8,1,4,6,2,5]=>[5,2,6,4,1,8,7,3]=>1111001=>1001111
[3,6,7,2,8,5,1,4]=>[4,1,5,8,2,7,6,3]=>1110010=>0100111
[3,6,7,8,5,2,1,4]=>[4,1,2,5,8,7,6,3]=>1010011=>1100101
[3,6,7,8,5,2,4,1]=>[1,4,2,5,8,7,6,3]=>0110011=>1100110
[6,4,7,8,2,5,3,1]=>[1,3,5,2,8,7,4,6]=>0101001=>1001010
[6,4,7,8,2,1,5,3]=>[3,5,1,2,8,7,4,6]=>1001001=>1001001
[5,3,7,8,1,6,2,4]=>[4,2,6,1,8,7,3,5]=>1110001=>1000111
[6,7,2,8,5,1,3,4]=>[4,3,1,5,8,2,7,6]=>1110010=>0100111
[6,4,1,7,8,2,5,3]=>[3,5,2,8,7,1,4,6]=>1100001=>1000011
[5,1,6,2,7,8,4,3]=>[3,4,8,7,2,6,1,5]=>1100001=>1000011
[5,6,2,7,1,8,4,3]=>[3,4,8,1,7,2,6,5]=>1100100=>0010011
[5,6,2,7,8,4,3,1]=>[1,3,4,8,7,2,6,5]=>0100101=>1010010
[5,6,7,2,8,4,3,1]=>[1,3,4,8,2,7,6,5]=>0100110=>0110010
[5,6,7,2,1,8,4,3]=>[3,4,8,1,2,7,6,5]=>1000110=>0110001
[5,6,1,7,2,8,4,3]=>[3,4,8,2,7,1,6,5]=>1100100=>0010011
[5,1,6,7,2,8,4,3]=>[3,4,8,2,7,6,1,5]=>1100010=>0100011
[6,7,8,3,5,1,4,2]=>[2,4,1,5,3,8,7,6]=>1010011=>1100101
[5,6,1,7,8,4,3,2]=>[2,3,4,8,7,1,6,5]=>1000101=>1010001
[5,6,7,1,8,4,3,2]=>[2,3,4,8,1,7,6,5]=>1000110=>0110001
[8,3,2,5,1,6,4,7]=>[7,4,6,1,5,2,3,8]=>1101000=>0001011
[5,3,2,7,4,1,8,6]=>[6,8,1,4,7,2,3,5]=>1100000=>0000011
[7,5,3,8,2,4,6,1]=>[1,6,4,2,8,3,5,7]=>0111000=>0001110
[8,2,4,5,6,3,1,7]=>[7,1,3,6,5,4,2,8]=>1101100=>0011011
[8,2,4,5,6,1,3,7]=>[7,3,1,6,5,4,2,8]=>1111100=>0011111
[8,5,3,6,4,1,2,7]=>[7,2,1,4,6,3,5,8]=>1110000=>0000111
[8,4,1,5,6,3,2,7]=>[7,2,3,6,5,1,4,8]=>1100100=>0010011
[8,1,4,5,6,3,2,7]=>[7,2,3,6,5,4,1,8]=>1101100=>0011011
[4,5,3,7,2,1,8,6]=>[6,8,1,2,7,3,5,4]=>1011000=>0001101
[7,4,5,8,3,2,6,1]=>[1,6,2,3,8,5,4,7]=>0101100=>0011010
[4,3,6,7,2,8,5,1]=>[1,5,8,2,7,6,3,4]=>0110010=>0100110
[4,3,6,7,2,8,1,5]=>[5,1,8,2,7,6,3,4]=>1110010=>0100111
[1,4,3,6,7,2,8,5]=>[5,8,2,7,6,3,4,1]=>1110010=>0100111
[4,5,3,7,1,8,2,6]=>[6,2,8,1,7,3,5,4]=>1111000=>0001111
[5,3,4,7,1,2,8,6]=>[6,8,2,1,7,4,3,5]=>1111000=>0001111
[7,4,5,8,3,6,1,2]=>[2,1,6,3,8,5,4,7]=>1011100=>0011101
[4,3,6,7,8,1,5,2]=>[2,5,1,8,7,6,3,4]=>1010011=>1100101
[3,5,6,7,8,4,1,2]=>[2,1,4,8,7,6,5,3]=>1010111=>1110101
[3,1,5,6,7,8,4,2]=>[2,4,8,7,6,5,1,3]=>1000111=>1110001
[4,6,1,7,8,3,5,2]=>[2,5,3,8,7,1,6,4]=>1011001=>1001101
[6,2,4,1,7,8,5,3]=>[3,5,8,7,1,4,2,6]=>1100001=>1000011
[2,6,7,1,4,8,3,5]=>[5,3,8,4,1,7,6,2]=>1111010=>0101111
[1,5,3,6,7,8,2,4]=>[4,2,8,7,6,3,5,1]=>1110011=>1100111
[4,5,2,7,8,1,3,6]=>[6,3,1,8,7,2,5,4]=>1111001=>1001111
[4,2,6,7,8,3,1,5]=>[5,1,3,8,7,6,2,4]=>1100011=>1100011
[4,2,6,7,8,3,5,1]=>[1,5,3,8,7,6,2,4]=>0110011=>1100110
[3,6,2,7,4,8,1,5]=>[5,1,8,4,7,2,6,3]=>1111000=>0001111
[3,7,4,2,1,5,8,6]=>[6,8,5,1,2,4,7,3]=>1010100=>0010101
[7,8,4,2,1,3,6,5]=>[5,6,3,1,2,4,8,7]=>1010001=>1000101
[6,3,2,7,1,8,5,4]=>[4,5,8,1,7,2,3,6]=>1100000=>0000011
[3,6,2,7,1,8,5,4]=>[4,5,8,1,7,2,6,3]=>1110000=>0000111
[6,7,3,8,2,5,4,1]=>[1,4,5,2,8,3,7,6]=>0110010=>0100110
[6,4,7,8,5,2,3,1]=>[1,3,2,5,8,7,4,6]=>0101001=>1001010
[2,6,4,7,8,1,5,3]=>[3,5,1,8,7,4,6,2]=>1101001=>1001011
[7,4,1,5,8,6,2,3]=>[3,2,6,8,5,1,4,7]=>1100100=>0010011
[7,5,8,2,1,6,3,4]=>[4,3,6,1,2,8,5,7]=>1010100=>0010101
[6,2,7,1,3,8,5,4]=>[4,5,8,3,1,7,2,6]=>1110000=>0000111
[6,3,1,7,8,2,5,4]=>[4,5,2,8,7,1,3,6]=>1100001=>1000011
[4,6,1,7,8,5,2,3]=>[3,2,5,8,7,1,6,4]=>1101001=>1001011
[5,1,2,6,7,8,4,3]=>[3,4,8,7,6,2,1,5]=>1100011=>1100011
[5,2,6,7,8,4,3,1]=>[1,3,4,8,7,6,2,5]=>0100011=>1100010
[1,6,4,7,8,5,2,3]=>[3,2,5,8,7,4,6,1]=>1101001=>1001011
[2,6,7,1,3,8,5,4]=>[4,5,8,3,1,7,6,2]=>1110010=>0100111
[6,7,3,8,5,1,4,2]=>[2,4,1,5,8,3,7,6]=>1010010=>0100101
[6,4,7,8,5,3,1,2]=>[2,1,3,5,8,7,4,6]=>1001001=>1001001
[3,1,2,6,5,8,7,4]=>[4,7,8,5,6,2,1,3]=>1100100=>0010011
[4,5,1,2,3,8,7,6]=>[6,7,8,3,2,1,5,4]=>1111000=>0001111
[4,6,1,2,3,8,7,5]=>[5,7,8,3,2,1,6,4]=>1111000=>0001111
[1,6,5,3,4,8,7,2]=>[2,7,8,4,3,5,6,1]=>1011000=>0001101
[6,1,5,2,4,8,7,3]=>[3,7,8,4,2,5,1,6]=>1101000=>0001011
[6,5,1,2,3,8,7,4]=>[4,7,8,3,2,1,5,6]=>1110000=>0000111
[6,4,1,2,3,8,7,5]=>[5,7,8,3,2,1,4,6]=>1110000=>0000111
[5,4,1,2,3,8,7,6]=>[6,7,8,3,2,1,4,5]=>1110000=>0000111
[5,4,1,2,7,3,6,8]=>[8,6,3,7,2,1,4,5]=>1110010=>0100111
[6,4,1,7,2,3,5,8]=>[8,5,3,2,7,1,4,6]=>1110100=>0010111
[6,4,1,8,2,3,5,7]=>[7,5,3,2,8,1,4,6]=>1110100=>0010111
[7,4,1,2,8,3,6,5]=>[5,6,3,8,2,1,4,7]=>1110000=>0000111
[7,5,1,2,8,3,6,4]=>[4,6,3,8,2,1,5,7]=>1110000=>0000111
[7,1,5,2,8,4,6,3]=>[3,6,4,8,2,5,1,7]=>1101000=>0001011
[1,7,5,3,8,4,6,2]=>[2,6,4,8,3,5,7,1]=>1011000=>0001101
[8,4,1,2,7,3,6,5]=>[5,6,3,7,2,1,4,8]=>1110000=>0000111
[8,4,1,7,2,3,5,6]=>[6,5,3,2,7,1,4,8]=>1110100=>0010111
[7,4,1,6,2,3,5,8]=>[8,5,3,2,6,1,4,7]=>1110100=>0010111
[8,6,1,7,2,3,5,4]=>[4,5,3,2,7,1,6,8]=>1110000=>0000111
[8,1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1,8]=>1101010=>0101011
[1,7,6,8,3,4,5,2]=>[2,5,4,3,8,6,7,1]=>1011010=>0101101
[7,6,1,8,2,3,5,4]=>[4,5,3,2,8,1,6,7]=>1110000=>0000111
[3,1,2,7,8,5,6,4]=>[4,6,5,8,7,2,1,3]=>1100101=>1010011
[3,1,8,7,2,4,5,6]=>[6,5,4,2,7,8,1,3]=>1101100=>0011011
[3,1,7,6,2,4,5,8]=>[8,5,4,2,6,7,1,3]=>1101100=>0011011
[4,7,1,6,2,3,5,8]=>[8,5,3,2,6,1,7,4]=>1111100=>0011111
[4,8,1,6,2,3,5,7]=>[7,5,3,2,6,1,8,4]=>1111100=>0011111
[5,8,1,2,7,3,6,4]=>[4,6,3,7,2,1,8,5]=>1110100=>0010111
[5,1,8,2,7,4,6,3]=>[3,6,4,7,2,8,1,5]=>1101000=>0001011
[1,5,8,3,7,4,6,2]=>[2,6,4,7,3,8,5,1]=>1011100=>0011101
[1,6,8,7,3,4,5,2]=>[2,5,4,3,7,8,6,1]=>1011010=>0101101
[6,1,8,7,2,4,5,3]=>[3,5,4,2,7,8,1,6]=>1101000=>0001011
[6,8,1,7,2,3,5,4]=>[4,5,3,2,7,1,8,6]=>1110010=>0100111
[6,8,7,1,2,3,4,5]=>[5,4,3,2,1,7,8,6]=>1111010=>0101111
[5,8,6,1,2,3,4,7]=>[7,4,3,2,1,6,8,5]=>1111100=>0011111
[5,7,6,1,2,3,4,8]=>[8,4,3,2,1,6,7,5]=>1111100=>0011111
[7,8,1,6,2,3,5,4]=>[4,5,3,2,6,1,8,7]=>1110001=>1000111
[7,1,8,6,2,4,5,3]=>[3,5,4,2,6,8,1,7]=>1101000=>0001011
[1,7,8,6,3,4,5,2]=>[2,5,4,3,6,8,7,1]=>1011001=>1001101
[8,1,7,6,2,4,5,3]=>[3,5,4,2,6,7,1,8]=>1101000=>0001011
[8,7,1,6,2,3,5,4]=>[4,5,3,2,6,1,7,8]=>1110000=>0000111
[8,5,3,7,2,1,4,6]=>[6,4,1,2,7,3,5,8]=>1011000=>0001101
[6,8,1,4,5,7,3,2]=>[2,3,7,5,4,1,8,6]=>1001110=>0111001
[8,7,2,4,5,1,3,6]=>[6,3,1,5,4,2,7,8]=>1111000=>0001111
[2,6,1,4,5,3,8,7]=>[7,8,3,5,4,1,6,2]=>1111000=>0001111
[6,3,1,4,5,2,8,7]=>[7,8,2,5,4,1,3,6]=>1101000=>0001011
[3,1,6,4,5,2,8,7]=>[7,8,2,5,4,6,1,3]=>1101000=>0001011
[8,3,7,4,5,1,2,6]=>[6,2,1,5,4,7,3,8]=>1111000=>0001111
[5,8,7,4,2,6,3,1]=>[1,3,6,2,4,7,8,5]=>0100100=>0010010
[8,1,7,4,2,6,3,5]=>[5,3,6,2,4,7,1,8]=>1110000=>0000111
[3,7,8,4,5,1,2,6]=>[6,2,1,5,4,8,7,3]=>1111001=>1001111
[5,6,3,8,1,7,2,4]=>[4,2,7,1,8,3,6,5]=>1110100=>0010111
[7,6,1,4,5,8,3,2]=>[2,3,8,5,4,1,6,7]=>1001100=>0011001
[3,7,6,4,5,8,2,1]=>[1,2,8,5,4,6,7,3]=>0011100=>0011100
[8,5,7,4,1,6,3,2]=>[2,3,6,1,4,7,5,8]=>1000100=>0010001
[2,5,8,4,7,6,1,3]=>[3,1,6,7,4,8,5,2]=>1101100=>0011011
[3,8,4,2,5,6,7,1]=>[1,7,6,5,2,4,8,3]=>0110110=>0110110
[8,4,1,3,5,6,7,2]=>[2,7,6,5,3,1,4,8]=>1010110=>0110101
[7,5,8,4,3,6,1,2]=>[2,1,6,3,4,8,5,7]=>1010100=>0010101
[6,5,3,8,4,1,7,2]=>[2,7,1,4,8,3,5,6]=>1010000=>0000101
[2,1,4,8,3,6,7,5]=>[5,7,6,3,8,4,1,2]=>1011010=>0101101
[7,3,8,4,2,6,1,5]=>[5,1,6,2,4,8,3,7]=>1110000=>0000111
[8,3,1,2,5,6,7,4]=>[4,7,6,5,2,1,3,8]=>1100110=>0110011
[4,8,2,3,5,6,7,1]=>[1,7,6,5,3,2,8,4]=>0111110=>0111110
[2,7,8,4,5,3,1,6]=>[6,1,3,5,4,8,7,2]=>1101001=>1001011
[8,7,1,4,3,6,2,5]=>[5,2,6,3,4,1,7,8]=>1110000=>0000111
[5,6,3,8,4,2,7,1]=>[1,7,2,4,8,3,6,5]=>0110100=>0010110
[8,6,3,1,4,2,7,5]=>[5,7,2,4,1,3,6,8]=>1100000=>0000011
[8,6,3,5,1,2,7,4]=>[4,7,2,1,5,3,6,8]=>1110000=>0000111
[5,8,3,2,6,1,7,4]=>[4,7,1,6,2,3,8,5]=>1100100=>0010011
[3,5,8,4,7,6,2,1]=>[1,2,6,7,4,8,5,3]=>0011100=>0011100
[5,8,2,4,7,6,1,3]=>[3,1,6,7,4,2,8,5]=>1101100=>0011011
[7,1,6,4,5,8,2,3]=>[3,2,8,5,4,6,1,7]=>1101100=>0011011
[2,1,8,5,3,6,7,4]=>[4,7,6,3,5,8,1,2]=>1010010=>0100101
[6,8,3,5,2,1,7,4]=>[4,7,1,2,5,3,8,6]=>1010010=>0100101
[7,8,5,4,2,6,1,3]=>[3,1,6,2,4,5,8,7]=>1100001=>1000011
[4,8,1,2,5,6,7,3]=>[3,7,6,5,2,1,8,4]=>1101110=>0111011
[3,4,2,8,5,6,7,1]=>[1,7,6,5,8,2,4,3]=>0110110=>0110110
[2,4,1,8,5,6,7,3]=>[3,7,6,5,8,1,4,2]=>1100110=>0110011
[8,4,2,1,5,6,7,3]=>[3,7,6,5,1,2,4,8]=>1000110=>0110001
[7,5,2,4,8,6,1,3]=>[3,1,6,8,4,2,5,7]=>1101000=>0001011
[2,1,5,3,8,6,7,4]=>[4,7,6,8,3,5,1,2]=>1010010=>0100101
[3,1,4,8,5,6,7,2]=>[2,7,6,5,8,4,1,3]=>1001110=>0111001
[6,5,3,7,2,8,4,1]=>[1,4,8,2,7,3,5,6]=>0110000=>0000110
[6,7,2,4,5,8,3,1]=>[1,3,8,5,4,2,7,6]=>0101110=>0111010
[2,5,7,4,8,6,3,1]=>[1,3,6,8,4,7,5,2]=>0101100=>0011010
[5,6,3,7,1,8,4,2]=>[2,4,8,1,7,3,6,5]=>1010100=>0010101
[3,8,7,4,5,2,1,6]=>[6,1,2,5,4,7,8,3]=>1011000=>0001101
[3,7,5,4,8,6,2,1]=>[1,2,6,8,4,5,7,3]=>0011000=>0001100
[4,6,3,5,8,2,7,1]=>[1,7,2,8,5,3,6,4]=>0111100=>0011110
[3,7,8,4,1,6,2,5]=>[5,2,6,1,4,8,7,3]=>1110001=>1000111
[5,4,2,3,7,6,1,8]=>[8,1,6,7,3,2,4,5]=>1110000=>0000111
[3,2,7,6,4,5,1,8]=>[8,1,5,4,6,7,2,3]=>1101000=>0001011
[4,7,2,6,3,5,1,8]=>[8,1,5,3,6,2,7,4]=>1111000=>0001111
[5,7,6,2,3,4,1,8]=>[8,1,4,3,2,6,7,5]=>1110100=>0010111
[1,7,5,2,8,3,4,6]=>[6,4,3,8,2,5,7,1]=>1111000=>0001111
[6,8,5,2,3,1,4,7]=>[7,4,1,3,2,5,8,6]=>1101010=>0101011
[4,8,2,6,3,1,5,7]=>[7,5,1,3,6,2,8,4]=>1101100=>0011011
[3,2,8,6,4,1,5,7]=>[7,5,1,4,6,8,2,3]=>1100100=>0010011
[7,1,5,2,8,3,4,6]=>[6,4,3,8,2,5,1,7]=>1111000=>0001111
[1,8,5,2,7,3,4,6]=>[6,4,3,7,2,5,8,1]=>1111000=>0001111
[7,1,6,8,2,3,4,5]=>[5,4,3,2,8,6,1,7]=>1111010=>0101111
[3,2,1,7,8,4,5,6]=>[6,5,4,8,7,1,2,3]=>1001101=>1011001
[3,2,8,7,1,4,5,6]=>[6,5,4,1,7,8,2,3]=>1101100=>0011011
[5,8,7,2,1,3,4,6]=>[6,4,3,1,2,7,8,5]=>1011100=>0011101
[1,7,6,8,2,3,4,5]=>[5,4,3,2,8,6,7,1]=>1111010=>0101111
[6,5,8,2,3,1,4,7]=>[7,4,1,3,2,8,5,6]=>1101100=>0011011
[8,5,7,2,1,3,4,6]=>[6,4,3,1,2,7,5,8]=>1011100=>0011101
[3,2,5,4,1,8,6,7]=>[7,6,8,1,4,5,2,3]=>1100010=>0100011
[7,4,2,1,8,3,5,6]=>[6,5,3,8,1,2,4,7]=>1010100=>0010101
[8,4,2,1,7,3,5,6]=>[6,5,3,7,1,2,4,8]=>1010100=>0010101
[1,4,2,8,7,3,5,6]=>[6,5,3,7,8,2,4,1]=>1110100=>0010111
[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>1111100=>0011111
[8,5,1,2,7,3,4,6]=>[6,4,3,7,2,1,5,8]=>1111000=>0001111
[3,2,6,1,4,8,5,7]=>[7,5,8,4,1,6,2,3]=>1101100=>0011011
[3,2,7,1,8,4,5,6]=>[6,5,4,8,1,7,2,3]=>1101100=>0011011
[4,7,2,1,8,3,5,6]=>[6,5,3,8,1,2,7,4]=>1011100=>0011101
[8,6,1,7,2,3,4,5]=>[5,4,3,2,7,1,6,8]=>1111000=>0001111
[1,6,8,7,2,3,4,5]=>[5,4,3,2,7,8,6,1]=>1111010=>0101111
[1,7,8,6,2,3,4,5]=>[5,4,3,2,6,8,7,1]=>1111001=>1001111
[7,8,1,6,2,3,4,5]=>[5,4,3,2,6,1,8,7]=>1111001=>1001111
[4,8,2,1,7,3,5,6]=>[6,5,3,7,1,2,8,4]=>1011100=>0011101
[3,2,8,1,7,4,5,6]=>[6,5,4,7,1,8,2,3]=>1101100=>0011011
[5,1,8,2,7,3,4,6]=>[6,4,3,7,2,8,1,5]=>1111000=>0001111
[6,1,8,7,2,3,4,5]=>[5,4,3,2,7,8,1,6]=>1111000=>0001111
[8,1,7,6,2,3,4,5]=>[5,4,3,2,6,7,1,8]=>1111000=>0001111
[2,8,4,1,6,5,7,3]=>[3,7,5,6,1,4,8,2]=>1100100=>0010011
[2,8,5,6,7,4,3,1]=>[1,3,4,7,6,5,8,2]=>0100110=>0110010
[7,5,8,6,1,4,2,3]=>[3,2,4,1,6,8,5,7]=>1100100=>0010011
[3,5,7,6,1,4,2,8]=>[8,2,4,1,6,7,5,3]=>1110100=>0010111
[7,5,8,2,4,1,6,3]=>[3,6,1,4,2,8,5,7]=>1100100=>0010011
[2,8,5,3,4,7,6,1]=>[1,6,7,4,3,5,8,2]=>0111000=>0001110
[2,8,5,3,4,1,7,6]=>[6,7,1,4,3,5,8,2]=>1110000=>0000111
[2,8,5,3,6,1,7,4]=>[4,7,1,6,3,5,8,2]=>1110000=>0000111
[2,8,5,6,7,4,1,3]=>[3,1,4,7,6,5,8,2]=>1100110=>0110011
[2,8,5,3,4,7,1,6]=>[6,1,7,4,3,5,8,2]=>1111000=>0001111
[2,8,5,3,4,6,1,7]=>[7,1,6,4,3,5,8,2]=>1111000=>0001111
[6,5,2,7,3,1,4,8]=>[8,4,1,3,7,2,5,6]=>1101000=>0001011
[6,5,2,8,3,1,7,4]=>[4,7,1,3,8,2,5,6]=>1100000=>0000011
[6,5,2,8,3,1,4,7]=>[7,4,1,3,8,2,5,6]=>1101000=>0001011
[7,5,8,2,4,6,3,1]=>[1,3,6,4,2,8,5,7]=>0101100=>0011010
[7,5,8,6,1,4,3,2]=>[2,3,4,1,6,8,5,7]=>1000100=>0010001
[6,5,8,2,1,3,7,4]=>[4,7,3,1,2,8,5,6]=>1010100=>0010101
[3,5,6,2,1,8,7,4]=>[4,7,8,1,2,6,5,3]=>1010100=>0010101
[3,5,7,2,4,1,8,6]=>[6,8,1,4,2,7,5,3]=>1110100=>0010111
[6,5,2,7,3,1,8,4]=>[4,8,1,3,7,2,5,6]=>1100000=>0000011
[4,5,2,6,3,1,7,8]=>[8,7,1,3,6,2,5,4]=>1101001=>1001011
[6,5,2,7,3,4,8,1]=>[1,8,4,3,7,2,5,6]=>0111000=>0001110
[5,1,6,7,4,3,8,2]=>[2,8,3,4,7,6,1,5]=>1010010=>0100101
[5,1,2,6,4,8,7,3]=>[3,7,8,4,6,2,1,5]=>1101000=>0001011
[5,1,2,8,6,4,7,3]=>[3,7,4,6,8,2,1,5]=>1101000=>0001011
[5,1,6,8,7,3,4,2]=>[2,4,3,7,8,6,1,5]=>1010010=>0100101
[6,5,2,8,3,7,4,1]=>[1,4,7,3,8,2,5,6]=>0110000=>0000110
[4,1,2,3,8,6,5,7]=>[7,5,6,8,3,2,1,4]=>1110100=>0010111
[4,1,2,3,8,6,7,5]=>[5,7,6,8,3,2,1,4]=>1110010=>0100111
[4,1,2,3,8,5,7,6]=>[6,7,5,8,3,2,1,4]=>1110100=>0010111
[6,5,8,2,4,3,7,1]=>[1,7,3,4,2,8,5,6]=>0110100=>0010110
[6,5,2,8,3,7,1,4]=>[4,1,7,3,8,2,5,6]=>1110000=>0000111
[6,5,2,7,3,4,1,8]=>[8,1,4,3,7,2,5,6]=>1110000=>0000111
[5,1,6,7,4,3,2,8]=>[8,2,3,4,7,6,1,5]=>1100010=>0100011
[5,1,6,8,7,3,2,4]=>[4,2,3,7,8,6,1,5]=>1100010=>0100011
[5,7,8,6,3,4,2,1]=>[1,2,4,3,6,8,7,5]=>0010101=>1010100
[3,1,4,8,6,2,7,5]=>[5,7,2,6,8,4,1,3]=>1101000=>0001011
[3,1,4,8,6,5,2,7]=>[7,2,5,6,8,4,1,3]=>1101000=>0001011
[4,1,6,7,8,3,2,5]=>[5,2,3,8,7,6,1,4]=>1100011=>1100011
[4,1,6,5,7,3,2,8]=>[8,2,3,7,5,6,1,4]=>1100100=>0010011
[4,5,2,6,3,7,1,8]=>[8,1,7,3,6,2,5,4]=>1111000=>0001111
[4,5,2,7,3,8,1,6]=>[6,1,8,3,7,2,5,4]=>1111000=>0001111
[3,5,6,2,4,8,1,7]=>[7,1,8,4,2,6,5,3]=>1111100=>0011111
[3,7,5,6,8,4,1,2]=>[2,1,4,8,6,5,7,3]=>1010110=>0110101
[3,6,5,2,8,1,7,4]=>[4,7,1,8,2,5,6,3]=>1110000=>0000111
[6,1,2,5,8,4,7,3]=>[3,7,4,8,5,2,1,6]=>1101100=>0011011
[4,1,2,3,5,8,7,6]=>[6,7,8,5,3,2,1,4]=>1110100=>0010111
[4,1,6,7,8,3,5,2]=>[2,5,3,8,7,6,1,4]=>1010011=>1100101
[4,1,2,6,8,5,7,3]=>[3,7,5,8,6,2,1,4]=>1100110=>0110011
[4,1,2,5,6,8,7,3]=>[3,7,8,6,5,2,1,4]=>1100110=>0110011
[4,5,2,6,3,7,8,1]=>[1,8,7,3,6,2,5,4]=>0111001=>1001110
[6,3,1,2,7,4,8,5]=>[5,8,4,7,2,1,3,6]=>1101000=>0001011
[6,4,2,7,1,3,8,5]=>[5,8,3,1,7,2,4,6]=>1110000=>0000111
[7,4,2,5,1,3,8,6]=>[6,8,3,1,5,2,4,7]=>1110000=>0000111
[8,5,3,6,1,7,2,4]=>[4,2,7,1,6,3,5,8]=>1110000=>0000111
[8,3,6,2,4,7,1,5]=>[5,1,7,4,2,6,3,8]=>1111000=>0001111
[7,3,6,2,4,8,1,5]=>[5,1,8,4,2,6,3,7]=>1111000=>0001111
[6,3,7,4,1,2,8,5]=>[5,8,2,1,4,7,3,6]=>1110000=>0000111
[4,7,1,5,2,3,8,6]=>[6,8,3,2,5,1,7,4]=>1111000=>0001111
[3,7,5,1,2,4,8,6]=>[6,8,4,2,1,5,7,3]=>1111000=>0001111
[8,6,4,2,3,7,1,5]=>[5,1,7,3,2,4,6,8]=>1110000=>0000111
[4,7,6,3,8,1,2,5]=>[5,2,1,8,3,6,7,4]=>1111000=>0001111
[5,7,2,6,1,8,3,4]=>[4,3,8,1,6,2,7,5]=>1110100=>0010111
[7,4,8,5,2,6,1,3]=>[3,1,6,2,5,8,4,7]=>1101000=>0001011
[5,8,2,6,3,7,1,4]=>[4,1,7,3,6,2,8,5]=>1110100=>0010111
[3,8,6,1,2,7,4,5]=>[5,4,7,2,1,6,8,3]=>1111000=>0001111
[3,8,6,2,4,7,1,5]=>[5,1,7,4,2,6,8,3]=>1111000=>0001111
[6,8,4,3,7,1,2,5]=>[5,2,1,7,3,4,8,6]=>1110010=>0100111
[3,8,5,7,1,2,4,6]=>[6,4,2,1,7,5,8,3]=>1111100=>0011111
[2,8,5,7,1,3,4,6]=>[6,4,3,1,7,5,8,2]=>1111100=>0011111
[4,8,6,2,7,1,3,5]=>[5,3,1,7,2,6,8,4]=>1111000=>0001111
[7,3,8,5,6,1,2,4]=>[4,2,1,6,5,8,3,7]=>1110100=>0010111
[6,3,7,5,8,1,2,4]=>[4,2,1,8,5,7,3,6]=>1110100=>0010111
[2,7,6,4,8,1,3,5]=>[5,3,1,8,4,6,7,2]=>1111000=>0001111
[3,6,5,8,1,2,4,7]=>[7,4,2,1,8,5,6,3]=>1111100=>0011111
[5,4,7,3,8,1,2,6]=>[6,2,1,8,3,7,4,5]=>1111000=>0001111
[8,4,6,3,7,1,2,5]=>[5,2,1,7,3,6,4,8]=>1111000=>0001111
[8,4,1,6,7,2,3,5]=>[5,3,2,7,6,1,4,8]=>1110010=>0100111
[5,4,1,7,8,2,3,6]=>[6,3,2,8,7,1,4,5]=>1110001=>1000111
[6,5,1,2,7,8,3,4]=>[4,3,8,7,2,1,5,6]=>1110001=>1000111
[7,4,1,8,6,2,3,5]=>[5,3,2,6,8,1,4,7]=>1110000=>0000111
[7,6,1,8,5,2,3,4]=>[4,3,2,5,8,1,6,7]=>1110000=>0000111
[8,6,1,7,5,2,3,4]=>[4,3,2,5,7,1,6,8]=>1110000=>0000111
[5,7,2,8,1,6,3,4]=>[4,3,6,1,8,2,7,5]=>1110100=>0010111
[6,3,7,8,5,1,2,4]=>[4,2,1,5,8,7,3,6]=>1110001=>1000111
[3,6,8,2,7,1,4,5]=>[5,4,1,7,2,8,6,3]=>1111010=>0101111
[5,3,8,7,1,2,4,6]=>[6,4,2,1,7,8,3,5]=>1111000=>0001111
[8,3,7,6,1,2,4,5]=>[5,4,2,1,6,7,3,8]=>1111000=>0001111
[8,4,7,6,1,2,3,5]=>[5,3,2,1,6,7,4,8]=>1111000=>0001111
[5,4,8,7,1,2,3,6]=>[6,3,2,1,7,8,4,5]=>1111000=>0001111
[3,5,8,7,1,2,4,6]=>[6,4,2,1,7,8,5,3]=>1111100=>0011111
[2,5,8,7,1,3,4,6]=>[6,4,3,1,7,8,5,2]=>1111100=>0011111
[4,7,1,8,6,2,3,5]=>[5,3,2,6,8,1,7,4]=>1111000=>0001111
[7,5,8,6,4,1,2,3]=>[3,2,1,4,6,8,5,7]=>1100100=>0010011
[6,8,4,7,5,1,2,3]=>[3,2,1,5,7,4,8,6]=>1101010=>0101011
[5,8,7,1,6,2,3,4]=>[4,3,2,6,1,7,8,5]=>1110100=>0010111
[2,8,7,6,1,3,4,5]=>[5,4,3,1,6,7,8,2]=>1111000=>0001111
[3,8,7,6,1,2,4,5]=>[5,4,2,1,6,7,8,3]=>1111000=>0001111
[4,8,7,6,1,2,3,5]=>[5,3,2,1,6,7,8,4]=>1111000=>0001111
[5,6,3,1,4,2,8,7]=>[7,8,2,4,1,3,6,5]=>1100100=>0010011
[7,5,3,8,2,1,6,4]=>[4,6,1,2,8,3,5,7]=>1010000=>0000101
[3,8,7,4,5,1,6,2]=>[2,6,1,5,4,7,8,3]=>1011000=>0001101
[6,7,1,4,5,8,2,3]=>[3,2,8,5,4,1,7,6]=>1101110=>0111011
[2,1,7,8,5,3,6,4]=>[4,6,3,5,8,7,1,2]=>1010001=>1000101
[5,7,3,8,1,2,6,4]=>[4,6,2,1,8,3,7,5]=>1110100=>0010111
[7,5,1,4,8,6,3,2]=>[2,3,6,8,4,1,5,7]=>1001000=>0001001
[6,4,3,8,1,5,7,2]=>[2,7,5,1,8,3,4,6]=>1010100=>0010101
[8,6,3,1,2,5,7,4]=>[4,7,5,2,1,3,6,8]=>1100100=>0010011
[8,7,1,4,2,6,5,3]=>[3,5,6,2,4,1,7,8]=>1100000=>0000011
[7,3,8,4,1,6,5,2]=>[2,5,6,1,4,8,3,7]=>1010000=>0000101
[5,3,2,7,4,6,8,1]=>[1,8,6,4,7,2,3,5]=>0101010=>0101010
[7,5,3,6,2,4,8,1]=>[1,8,4,2,6,3,5,7]=>0111000=>0001110
[6,3,2,5,1,8,4,7]=>[7,4,8,1,5,2,3,6]=>1101000=>0001011
[8,5,3,6,2,7,1,4]=>[4,1,7,2,6,3,5,8]=>1110000=>0000111
[7,2,6,3,4,5,8,1]=>[1,8,5,4,3,6,2,7]=>0111100=>0011110
[6,2,7,3,4,5,8,1]=>[1,8,5,4,3,7,2,6]=>0111100=>0011110
[6,7,3,5,2,4,8,1]=>[1,8,4,2,5,3,7,6]=>0111010=>0101110
[3,7,6,2,4,5,8,1]=>[1,8,5,4,2,6,7,3]=>0111100=>0011110
[6,5,3,1,2,8,4,7]=>[7,4,8,2,1,3,5,6]=>1101000=>0001011
[8,6,5,2,3,7,1,4]=>[4,1,7,3,2,5,6,8]=>1110000=>0000111
[8,5,2,1,7,3,4,6]=>[6,4,3,7,1,2,5,8]=>1011000=>0001101
[7,5,2,1,8,3,4,6]=>[6,4,3,8,1,2,5,7]=>1011000=>0001101
[1,6,3,2,8,4,5,7]=>[7,5,4,8,2,3,6,1]=>1101100=>0011011
[5,7,3,1,2,8,4,6]=>[6,4,8,2,1,3,7,5]=>1101100=>0011011
[4,2,6,5,1,8,3,7]=>[7,3,8,1,5,6,2,4]=>1110000=>0000111
[5,4,8,6,2,7,1,3]=>[3,1,7,2,6,8,4,5]=>1101000=>0001011
[7,8,5,2,3,6,1,4]=>[4,1,6,3,2,5,8,7]=>1110001=>1000111
[6,8,2,1,7,3,4,5]=>[5,4,3,7,1,2,8,6]=>1011010=>0101101
[2,8,1,7,3,4,5,6]=>[6,5,4,3,7,1,8,2]=>1111100=>0011111
[3,8,6,1,7,2,4,5]=>[5,4,2,7,1,6,8,3]=>1111000=>0001111
[4,2,8,3,7,1,5,6]=>[6,5,1,7,3,8,2,4]=>1110100=>0010111
[4,1,7,5,8,2,3,6]=>[6,3,2,8,5,7,1,4]=>1110100=>0010111
[1,7,3,8,2,4,5,6]=>[6,5,4,2,8,3,7,1]=>1111100=>0011111
[8,1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1,8]=>1111100=>0011111
[6,3,7,1,2,8,4,5]=>[5,4,8,2,1,7,3,6]=>1111000=>0001111
[7,2,6,1,8,3,4,5]=>[5,4,3,8,1,6,2,7]=>1111000=>0001111
[8,2,6,1,7,3,4,5]=>[5,4,3,7,1,6,2,8]=>1111000=>0001111
[7,3,1,5,8,2,4,6]=>[6,4,2,8,5,1,3,7]=>1101100=>0011011
[5,4,1,3,6,8,2,7]=>[7,2,8,6,3,1,4,5]=>1110010=>0100111
[8,5,3,7,6,1,2,4]=>[4,2,1,6,7,3,5,8]=>1110000=>0000111
[6,1,8,3,7,2,4,5]=>[5,4,2,7,3,8,1,6]=>1111000=>0001111
[7,6,8,2,3,5,1,4]=>[4,1,5,3,2,8,6,7]=>1110010=>0100111
[3,7,8,2,4,6,1,5]=>[5,1,6,4,2,8,7,3]=>1111001=>1001111
[5,4,7,8,2,6,1,3]=>[3,1,6,2,8,7,4,5]=>1101001=>1001011
[4,2,5,8,7,1,3,6]=>[6,3,1,7,8,5,2,4]=>1110100=>0010111
[3,6,2,8,7,1,4,5]=>[5,4,1,7,8,2,6,3]=>1111000=>0001111
[3,7,8,1,6,2,4,5]=>[5,4,2,6,1,8,7,3]=>1111001=>1001111
[2,3,8,7,1,4,5,6]=>[6,5,4,1,7,8,3,2]=>1111100=>0011111
[2,1,8,7,3,4,5,6]=>[6,5,4,3,7,8,1,2]=>1011100=>0011101
[8,2,7,6,1,3,4,5]=>[5,4,3,1,6,7,2,8]=>1111000=>0001111
[1,2,8,7,3,4,5,6]=>[6,5,4,3,7,8,2,1]=>1111100=>0011111
[1,3,8,7,2,4,5,6]=>[6,5,4,2,7,8,3,1]=>1111100=>0011111
[1,7,8,3,6,2,4,5]=>[5,4,2,6,3,8,7,1]=>1111001=>1001111
[5,4,8,7,6,1,2,3]=>[3,2,1,6,7,8,4,5]=>1101000=>0001011
[6,8,3,7,5,1,2,4]=>[4,2,1,5,7,3,8,6]=>1110010=>0100111
[7,8,6,2,5,1,3,4]=>[4,3,1,5,2,6,8,7]=>1110001=>1000111
[8,1,6,7,3,2,4,5]=>[5,4,2,3,7,6,1,8]=>1101010=>0101011
[8,1,5,3,7,2,4,6]=>[6,4,2,7,3,5,1,8]=>1111000=>0001111
[8,1,5,3,6,2,4,7]=>[7,4,2,6,3,5,1,8]=>1111000=>0001111
[7,4,8,3,2,6,5,1]=>[1,5,6,2,3,8,4,7]=>0101000=>0001010
[7,4,1,3,2,6,5,8]=>[8,5,6,2,3,1,4,7]=>1100100=>0010011
[8,1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1,8]=>1100100=>0010011
[8,1,4,3,2,7,5,6]=>[6,5,7,2,3,4,1,8]=>1100100=>0010011
[8,1,5,4,6,7,2,3]=>[3,2,7,6,4,5,1,8]=>1101010=>0101011
[8,1,5,3,6,2,7,4]=>[4,7,2,6,3,5,1,8]=>1110000=>0000111
[8,1,4,3,2,6,7,5]=>[5,7,6,2,3,4,1,8]=>1100010=>0100011
[8,1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1,8]=>1100100=>0010011
[7,4,8,3,2,5,6,1]=>[1,6,5,2,3,8,4,7]=>0101100=>0011010
[6,4,3,1,2,5,8,7]=>[7,8,5,2,1,3,4,6]=>1100100=>0010011
[7,4,1,3,2,5,8,6]=>[6,8,5,2,3,1,4,7]=>1100100=>0010011
[7,5,1,3,6,2,8,4]=>[4,8,2,6,3,1,5,7]=>1110000=>0000111
[7,5,1,4,6,8,2,3]=>[3,2,8,6,4,1,5,7]=>1101010=>0101011
[6,4,3,8,2,5,1,7]=>[7,1,5,2,8,3,4,6]=>1110000=>0000111
[5,4,3,2,8,6,1,7]=>[7,1,6,8,2,3,4,5]=>1100000=>0000011
[5,4,3,2,8,7,1,6]=>[6,1,7,8,2,3,4,5]=>1100000=>0000011
[6,5,4,8,7,1,2,3]=>[3,2,1,7,8,4,5,6]=>1101000=>0001011
[6,5,4,1,7,8,2,3]=>[3,2,8,7,1,4,5,6]=>1100001=>1000011
[6,4,3,1,2,7,8,5]=>[5,8,7,2,1,3,4,6]=>1100001=>1000011
[6,4,3,1,2,7,5,8]=>[8,5,7,2,1,3,4,6]=>1100100=>0010011
[6,4,3,8,2,7,5,1]=>[1,5,7,2,8,3,4,6]=>0110000=>0000110
[6,5,3,8,7,2,4,1]=>[1,4,2,7,8,3,5,6]=>0110000=>0000110
[6,5,3,1,7,2,4,8]=>[8,4,2,7,1,3,5,6]=>1101000=>0001011
[7,5,1,3,8,2,4,6]=>[6,4,2,8,3,1,5,7]=>1111000=>0001111
[6,5,3,7,8,2,4,1]=>[1,4,2,8,7,3,5,6]=>0110001=>1000110
[6,4,3,7,2,8,5,1]=>[1,5,8,2,7,3,4,6]=>0110000=>0000110
[6,4,3,7,2,1,5,8]=>[8,5,1,2,7,3,4,6]=>1010100=>0010101
[7,5,8,4,1,6,2,3]=>[3,2,6,1,4,8,5,7]=>1100100=>0010011
[6,5,4,8,1,7,2,3]=>[3,2,7,1,8,4,5,6]=>1101000=>0001011
[6,5,4,7,1,8,2,3]=>[3,2,8,1,7,4,5,6]=>1101000=>0001011
[5,4,3,2,7,8,1,6]=>[6,1,8,7,2,3,4,5]=>1100001=>1000011
[4,6,3,8,5,1,2,7]=>[7,2,1,5,8,3,6,4]=>1111000=>0001111
[5,6,8,3,4,1,2,7]=>[7,2,1,4,3,8,6,5]=>1110110=>0110111
[5,6,8,3,4,1,7,2]=>[2,7,1,4,3,8,6,5]=>1010110=>0110101
[4,6,2,7,5,3,1,8]=>[8,1,3,5,7,2,6,4]=>1101000=>0001011
[5,6,8,4,3,1,2,7]=>[7,2,1,3,4,8,6,5]=>1100110=>0110011
[5,7,8,4,1,3,6,2]=>[2,6,3,1,4,8,7,5]=>1010101=>1010101
[5,6,8,4,2,1,7,3]=>[3,7,1,2,4,8,6,5]=>1000110=>0110001
[5,6,8,2,4,1,7,3]=>[3,7,1,4,2,8,6,5]=>1100110=>0110011
[3,2,6,8,5,1,4,7]=>[7,4,1,5,8,6,2,3]=>1101010=>0101011
[5,6,8,4,2,1,3,7]=>[7,3,1,2,4,8,6,5]=>1010110=>0110101
[5,7,8,4,1,3,2,6]=>[6,2,3,1,4,8,7,5]=>1100101=>1010011
[5,7,8,4,1,2,3,6]=>[6,3,2,1,4,8,7,5]=>1110101=>1010111
[6,7,8,1,5,2,3,4]=>[4,3,2,5,1,8,7,6]=>1110011=>1100111
[6,7,8,1,5,3,2,4]=>[4,2,3,5,1,8,7,6]=>1100011=>1100011
[6,7,8,1,3,5,2,4]=>[4,2,5,3,1,8,7,6]=>1110011=>1100111
[5,7,8,2,1,6,3,4]=>[4,3,6,1,2,8,7,5]=>1010101=>1010101
[4,7,2,8,1,6,3,5]=>[5,3,6,1,8,2,7,4]=>1111000=>0001111
[3,2,7,8,1,6,4,5]=>[5,4,6,1,8,7,2,3]=>1101001=>1001011
[4,7,2,8,1,6,5,3]=>[3,5,6,1,8,2,7,4]=>1101000=>0001011
[5,7,8,2,1,6,4,3]=>[3,4,6,1,2,8,7,5]=>1000101=>1010001
[6,7,8,1,3,5,4,2]=>[2,4,5,3,1,8,7,6]=>1010011=>1100101
[6,7,8,1,5,3,4,2]=>[2,4,3,5,1,8,7,6]=>1010011=>1100101
[6,7,8,1,4,3,5,2]=>[2,5,3,4,1,8,7,6]=>1010011=>1100101
[5,6,8,3,2,1,7,4]=>[4,7,1,2,3,8,6,5]=>1000110=>0110001
[4,7,3,8,1,6,2,5]=>[5,2,6,1,8,3,7,4]=>1111000=>0001111
[4,7,3,8,1,5,6,2]=>[2,6,5,1,8,3,7,4]=>1011100=>0011101
[4,7,3,8,1,5,2,6]=>[6,2,5,1,8,3,7,4]=>1111000=>0001111
[4,7,3,8,1,2,5,6]=>[6,5,2,1,8,3,7,4]=>1111100=>0011111
[5,7,8,3,1,2,4,6]=>[6,4,2,1,3,8,7,5]=>1101101=>1011011
[5,6,8,3,2,1,4,7]=>[7,4,1,2,3,8,6,5]=>1001110=>0111001
[3,2,7,8,1,5,4,6]=>[6,4,5,1,8,7,2,3]=>1101001=>1001011
[6,7,8,1,3,4,2,5]=>[5,2,4,3,1,8,7,6]=>1110011=>1100111
[6,7,8,1,4,2,3,5]=>[5,3,2,4,1,8,7,6]=>1110011=>1100111
[6,7,8,1,2,5,3,4]=>[4,3,5,2,1,8,7,6]=>1110011=>1100111
[6,7,8,1,2,4,5,3]=>[3,5,4,2,1,8,7,6]=>1101011=>1101011
[5,7,8,2,1,3,6,4]=>[4,6,3,1,2,8,7,5]=>1010101=>1010101
[3,2,7,8,1,4,6,5]=>[5,6,4,1,8,7,2,3]=>1101001=>1001011
[6,7,8,1,3,2,4,5]=>[5,4,2,3,1,8,7,6]=>1101011=>1101011
[6,7,8,1,2,4,3,5]=>[5,3,4,2,1,8,7,6]=>1110011=>1100111
[6,7,8,1,2,3,5,4]=>[4,5,3,2,1,8,7,6]=>1110011=>1100111
[8,3,5,1,7,4,6,2]=>[2,6,4,7,1,5,3,8]=>1011000=>0001101
[8,3,4,1,7,5,6,2]=>[2,6,5,7,1,4,3,8]=>1010100=>0010101
[4,8,3,1,7,5,6,2]=>[2,6,5,7,1,3,8,4]=>1001100=>0011001
[4,6,2,1,7,5,8,3]=>[3,8,5,7,1,2,6,4]=>1001100=>0011001
[1,4,6,2,7,5,8,3]=>[3,8,5,7,2,6,4,1]=>1101100=>0011011
[1,7,5,2,6,8,4,3]=>[3,4,8,6,2,5,7,1]=>1100010=>0100011
[7,5,2,1,6,8,4,3]=>[3,4,8,6,1,2,5,7]=>1000010=>0100001
[6,8,4,3,1,7,5,2]=>[2,5,7,1,3,4,8,6]=>1000010=>0100001
[4,7,5,6,1,8,3,2]=>[2,3,8,1,6,5,7,4]=>1001100=>0011001
[6,7,5,1,8,4,3,2]=>[2,3,4,8,1,5,7,6]=>1000010=>0100001
[6,8,4,1,7,5,3,2]=>[2,3,5,7,1,4,8,6]=>1000010=>0100001
[6,7,5,3,1,8,4,2]=>[2,4,8,1,3,5,7,6]=>1000010=>0100001
[8,4,2,1,6,7,5,3]=>[3,5,7,6,1,2,4,8]=>1000010=>0100001
[1,8,4,2,6,7,5,3]=>[3,5,7,6,2,4,8,1]=>1100010=>0100011
[1,5,3,2,7,6,8,4]=>[4,8,6,7,2,3,5,1]=>1100010=>0100011
[2,5,3,1,7,6,8,4]=>[4,8,6,7,1,3,5,2]=>1100010=>0100011
[2,7,5,1,6,8,4,3]=>[3,4,8,6,1,5,7,2]=>1100010=>0100011
[4,7,1,6,5,8,2,3]=>[3,2,8,5,6,1,7,4]=>1101100=>0011011
[4,6,1,2,7,5,8,3]=>[3,8,5,7,2,1,6,4]=>1101100=>0011011
[8,4,1,2,6,7,5,3]=>[3,5,7,6,2,1,4,8]=>1100010=>0100011
[5,3,1,2,7,6,8,4]=>[4,8,6,7,2,1,3,5]=>1100010=>0100011
[4,3,1,2,7,6,8,5]=>[5,8,6,7,2,1,3,4]=>1100010=>0100011
[3,5,1,2,7,6,8,4]=>[4,8,6,7,2,1,5,3]=>1110010=>0100111
[6,7,1,5,8,2,3,4]=>[4,3,2,8,5,1,7,6]=>1110110=>0110111
[2,7,6,1,5,8,3,4]=>[4,3,8,5,1,6,7,2]=>1110100=>0010111
[2,3,5,1,7,6,8,4]=>[4,8,6,7,1,5,3,2]=>1110010=>0100111
[8,4,1,6,7,5,2,3]=>[3,2,5,7,6,1,4,8]=>1100010=>0100011
[5,2,3,1,7,6,8,4]=>[4,8,6,7,1,3,2,5]=>1100010=>0100011
[3,5,2,1,7,6,8,4]=>[4,8,6,7,1,2,5,3]=>1010010=>0100101
[1,7,6,2,5,8,3,4]=>[4,3,8,5,2,6,7,1]=>1110100=>0010111
[7,6,2,1,5,8,3,4]=>[4,3,8,5,1,2,6,7]=>1010100=>0010101
[8,2,6,4,7,1,5,3]=>[3,5,1,7,4,6,2,8]=>1101000=>0001011
[6,1,5,2,7,4,8,3]=>[3,8,4,7,2,5,1,6]=>1101000=>0001011
[7,6,2,5,8,3,1,4]=>[4,1,3,8,5,2,6,7]=>1100100=>0010011
[1,8,3,5,7,6,2,4]=>[4,2,6,7,5,3,8,1]=>1110100=>0010111
[1,5,2,3,7,6,8,4]=>[4,8,6,7,3,2,5,1]=>1110010=>0100111
[5,2,1,3,7,6,8,4]=>[4,8,6,7,3,1,2,5]=>1010010=>0100101
[8,4,2,6,7,5,1,3]=>[3,1,5,7,6,2,4,8]=>1100010=>0100011
[6,1,4,2,7,5,8,3]=>[3,8,5,7,2,4,1,6]=>1100100=>0010011
[8,2,6,5,7,1,4,3]=>[3,4,1,7,5,6,2,8]=>1100100=>0010011
[5,1,3,2,7,6,8,4]=>[4,8,6,7,2,3,1,5]=>1100010=>0100011
[1,4,2,3,7,6,8,5]=>[5,8,6,7,3,2,4,1]=>1110010=>0100111
[2,4,1,3,7,6,8,5]=>[5,8,6,7,3,1,4,2]=>1110010=>0100111
[2,5,1,3,7,6,8,4]=>[4,8,6,7,3,1,5,2]=>1110010=>0100111
[2,8,3,5,7,6,1,4]=>[4,1,6,7,5,3,8,2]=>1110100=>0010111
[6,8,2,3,5,7,1,4]=>[4,1,7,5,3,2,8,6]=>1110110=>0110111
[6,7,1,3,5,8,2,4]=>[4,2,8,5,3,1,7,6]=>1110110=>0110111
[8,3,5,7,6,1,2,4]=>[4,2,1,6,7,5,3,8]=>1110100=>0010111
[5,1,2,3,7,6,8,4]=>[4,8,6,7,3,2,1,5]=>1110010=>0100111
[4,7,1,2,8,6,5,3]=>[3,5,6,8,2,1,7,4]=>1101000=>0001011
[4,6,8,1,2,7,5,3]=>[3,5,7,2,1,8,6,4]=>1101010=>0101011
[6,8,7,1,5,3,2,4]=>[4,2,3,5,1,7,8,6]=>1100010=>0100011
[6,8,7,3,5,1,2,4]=>[4,2,1,5,3,7,8,6]=>1110010=>0100111
[7,8,1,3,6,5,2,4]=>[4,2,5,6,3,1,8,7]=>1110001=>1000111
[1,7,3,4,8,6,5,2]=>[2,5,6,8,4,3,7,1]=>1011000=>0001101
[4,2,7,1,8,6,5,3]=>[3,5,6,8,1,7,2,4]=>1100000=>0000011
[7,8,2,3,6,5,1,4]=>[4,1,5,6,3,2,8,7]=>1110001=>1000111
[8,5,7,1,6,2,3,4]=>[4,3,2,6,1,7,5,8]=>1110100=>0010111
[8,5,7,1,2,6,3,4]=>[4,3,6,2,1,7,5,8]=>1110100=>0010111
[6,8,2,7,1,3,5,4]=>[4,5,3,1,7,2,8,6]=>1110010=>0100111
[6,2,4,8,7,1,5,3]=>[3,5,1,7,8,4,2,6]=>1101000=>0001011
[1,6,8,3,7,4,5,2]=>[2,5,4,7,3,8,6,1]=>1011010=>0101101
[1,6,8,3,4,7,5,2]=>[2,5,7,4,3,8,6,1]=>1011010=>0101101
[6,2,4,8,1,7,5,3]=>[3,5,7,1,8,4,2,6]=>1101000=>0001011
[6,8,7,2,3,5,1,4]=>[4,1,5,3,2,7,8,6]=>1110010=>0100111
[6,8,2,1,7,3,5,4]=>[4,5,3,7,1,2,8,6]=>1010010=>0100101
[8,5,7,2,1,6,3,4]=>[4,3,6,1,2,7,5,8]=>1010100=>0010101
[8,5,7,1,2,3,6,4]=>[4,6,3,2,1,7,5,8]=>1110100=>0010111
[8,5,7,2,3,1,6,4]=>[4,6,1,3,2,7,5,8]=>1100100=>0010011
[1,8,7,5,3,4,6,2]=>[2,6,4,3,5,7,8,1]=>1011000=>0001101
[1,8,7,3,5,4,6,2]=>[2,6,4,5,3,7,8,1]=>1011000=>0001101
[8,2,5,4,7,1,6,3]=>[3,6,1,7,4,5,2,8]=>1101000=>0001011
[8,7,6,1,2,4,3,5]=>[5,3,4,2,1,6,7,8]=>1110000=>0000111
[8,7,6,1,4,2,3,5]=>[5,3,2,4,1,6,7,8]=>1110000=>0000111
[8,7,6,4,1,3,2,5]=>[5,2,3,1,4,6,7,8]=>1100000=>0000011
[8,5,7,1,3,2,6,4]=>[4,6,2,3,1,7,5,8]=>1100100=>0010011
[5,8,4,7,1,2,6,3]=>[3,6,2,1,7,4,8,5]=>1101100=>0011011
[8,1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1,8]=>1100100=>0010011
[8,2,5,6,7,4,1,3]=>[3,1,4,7,6,5,2,8]=>1100110=>0110011
[4,8,5,1,7,2,6,3]=>[3,6,2,7,1,5,8,4]=>1101000=>0001011
[8,5,3,7,1,2,6,4]=>[4,6,2,1,7,3,5,8]=>1110000=>0000111
[4,6,2,8,1,7,5,3]=>[3,5,7,1,8,2,6,4]=>1101000=>0001011
[1,6,4,8,3,7,5,2]=>[2,5,7,3,8,4,6,1]=>1011000=>0001101
[1,8,7,4,5,3,6,2]=>[2,6,3,5,4,7,8,1]=>1011000=>0001101
[4,8,5,7,2,1,6,3]=>[3,6,1,2,7,5,8,4]=>1001100=>0011001
[8,5,3,7,2,1,6,4]=>[4,6,1,2,7,3,5,8]=>1010000=>0000101
[8,7,6,3,1,4,2,5]=>[5,2,4,1,3,6,7,8]=>1100000=>0000011
[8,5,3,2,7,1,6,4]=>[4,6,1,7,2,3,5,8]=>1100000=>0000011
[1,8,7,4,3,5,6,2]=>[2,6,5,3,4,7,8,1]=>1010100=>0010101
[1,8,7,3,4,5,6,2]=>[2,6,5,4,3,7,8,1]=>1011100=>0011101
[8,2,4,5,7,1,6,3]=>[3,6,1,7,5,4,2,8]=>1101100=>0011011
[8,5,2,3,7,1,6,4]=>[4,6,1,7,3,2,5,8]=>1110000=>0000111
[8,3,1,5,2,7,6,4]=>[4,6,7,2,5,1,3,8]=>1100000=>0000011
[8,5,4,2,1,7,3,6]=>[6,3,7,1,2,4,5,8]=>1010000=>0000101
[8,5,4,2,1,7,6,3]=>[3,6,7,1,2,4,5,8]=>1000000=>0000001
[6,5,4,2,3,1,8,7]=>[7,8,1,3,2,4,5,6]=>1100000=>0000011
[6,3,2,5,1,4,8,7]=>[7,8,4,1,5,2,3,6]=>1101000=>0001011
[8,5,4,1,2,7,6,3]=>[3,6,7,2,1,4,5,8]=>1100000=>0000011
[8,7,4,1,6,3,2,5]=>[5,2,3,6,1,4,7,8]=>1100000=>0000011
[8,7,4,1,6,3,5,2]=>[2,5,3,6,1,4,7,8]=>1010000=>0000101
[8,7,4,1,6,5,3,2]=>[2,3,5,6,1,4,7,8]=>1000000=>0000001
[8,5,4,3,1,7,6,2]=>[2,6,7,1,3,4,5,8]=>1000000=>0000001
[8,3,2,5,1,7,6,4]=>[4,6,7,1,5,2,3,8]=>1100000=>0000011
[8,3,2,5,1,7,4,6]=>[6,4,7,1,5,2,3,8]=>1101000=>0001011
[8,5,4,3,1,7,2,6]=>[6,2,7,1,3,4,5,8]=>1100000=>0000011
[8,5,4,1,3,7,2,6]=>[6,2,7,3,1,4,5,8]=>1110000=>0000111
[8,7,4,1,6,5,2,3]=>[3,2,5,6,1,4,7,8]=>1100000=>0000011
[2,1,8,7,6,4,5,3]=>[3,5,4,6,7,8,1,2]=>1001000=>0001001
[8,3,2,7,6,4,5,1]=>[1,5,4,6,7,2,3,8]=>0101000=>0001010
[8,5,4,2,3,7,6,1]=>[1,6,7,3,2,4,5,8]=>0110000=>0000110
[8,7,4,2,6,5,3,1]=>[1,3,5,6,2,4,7,8]=>0100000=>0000010
[8,7,4,2,6,3,5,1]=>[1,5,3,6,2,4,7,8]=>0110000=>0000110
[8,7,4,2,6,3,1,5]=>[5,1,3,6,2,4,7,8]=>1100000=>0000011
[8,3,1,7,6,4,2,5]=>[5,2,4,6,7,1,3,8]=>1100000=>0000011
[8,3,1,7,6,4,5,2]=>[2,5,4,6,7,1,3,8]=>1001000=>0001001
[8,3,1,5,4,7,6,2]=>[2,6,7,4,5,1,3,8]=>1001000=>0001001
[8,3,1,7,6,5,2,4]=>[4,2,5,6,7,1,3,8]=>1100000=>0000011
[8,3,1,7,6,2,5,4]=>[4,5,2,6,7,1,3,8]=>1100000=>0000011
[8,5,4,2,3,7,1,6]=>[6,1,7,3,2,4,5,8]=>1110000=>0000111
[8,3,2,5,4,7,1,6]=>[6,1,7,4,5,2,3,8]=>1101000=>0001011
[2,1,8,5,4,7,3,6]=>[6,3,7,4,5,8,1,2]=>1011000=>0001101
[8,3,2,7,6,5,1,4]=>[4,1,5,6,7,2,3,8]=>1100000=>0000011
[8,7,6,5,3,1,4,2]=>[2,4,1,3,5,6,7,8]=>1000000=>0000001
[8,3,2,7,6,1,5,4]=>[4,5,1,6,7,2,3,8]=>1100000=>0000011
[8,7,6,5,1,2,4,3]=>[3,4,2,1,5,6,7,8]=>1100000=>0000011
[5,2,3,1,6,4,8,7]=>[7,8,4,6,1,3,2,5]=>1101000=>0001011
[7,4,5,2,3,1,8,6]=>[6,8,1,3,2,5,4,7]=>1101000=>0001011
[7,3,5,2,4,1,8,6]=>[6,8,1,4,2,5,3,7]=>1110000=>0000111
[6,3,5,2,4,1,8,7]=>[7,8,1,4,2,5,3,6]=>1110000=>0000111
[4,1,6,3,5,2,8,7]=>[7,8,2,5,3,6,1,4]=>1110000=>0000111
[6,3,4,1,5,2,8,7]=>[7,8,2,5,1,4,3,6]=>1110000=>0000111
[5,2,7,3,4,1,8,6]=>[6,8,1,4,3,7,2,5]=>1110000=>0000111
[6,2,8,5,7,3,4,1]=>[1,4,3,7,5,8,2,6]=>0110100=>0010110
[6,2,7,3,4,1,8,5]=>[5,8,1,4,3,7,2,6]=>1110000=>0000111
[7,3,4,1,5,2,8,6]=>[6,8,2,5,1,4,3,7]=>1110000=>0000111
[4,1,7,3,5,2,8,6]=>[6,8,2,5,3,7,1,4]=>1110000=>0000111
[2,1,7,4,5,3,8,6]=>[6,8,3,5,4,7,1,2]=>1011000=>0001101
[3,1,8,6,7,4,5,2]=>[2,5,4,7,6,8,1,3]=>1001010=>0101001
[4,1,8,6,7,3,5,2]=>[2,5,3,7,6,8,1,4]=>1010010=>0100101
[8,5,7,3,4,1,6,2]=>[2,6,1,4,3,7,5,8]=>1010100=>0010101
[8,5,6,2,7,3,4,1]=>[1,4,3,7,2,6,5,8]=>0110100=>0010110
[8,4,7,3,5,1,6,2]=>[2,6,1,5,3,7,4,8]=>1011000=>0001101
[5,1,8,4,7,3,6,2]=>[2,6,3,7,4,8,1,5]=>1011000=>0001101
[3,1,8,5,7,4,6,2]=>[2,6,4,7,5,8,1,3]=>1001100=>0011001
[2,1,8,5,7,4,6,3]=>[3,6,4,7,5,8,1,2]=>1001100=>0011001
[3,1,7,4,6,2,8,5]=>[5,8,2,6,4,7,1,3]=>1101000=>0001011
[4,1,7,3,6,2,8,5]=>[5,8,2,6,3,7,1,4]=>1110000=>0000111
[6,2,8,4,7,3,5,1]=>[1,5,3,7,4,8,2,6]=>0111000=>0001110
[7,3,6,2,5,1,8,4]=>[4,8,1,5,2,6,3,7]=>1110000=>0000111
[5,2,4,1,7,3,8,6]=>[6,8,3,7,1,4,2,5]=>1110000=>0000111
[6,2,4,1,7,3,8,5]=>[5,8,3,7,1,4,2,6]=>1110000=>0000111
[7,4,6,2,3,1,8,5]=>[5,8,1,3,2,6,4,7]=>1101000=>0001011
[6,2,3,1,7,4,8,5]=>[5,8,4,7,1,3,2,6]=>1101000=>0001011
[5,2,3,1,7,4,8,6]=>[6,8,4,7,1,3,2,5]=>1101000=>0001011
[4,2,3,1,7,5,8,6]=>[6,8,5,7,1,3,2,4]=>1100100=>0010011
[3,1,4,2,8,6,7,5]=>[5,7,6,8,2,4,1,3]=>1100010=>0100011
[6,2,3,1,8,5,7,4]=>[4,7,5,8,1,3,2,6]=>1100100=>0010011
[8,5,6,2,3,1,7,4]=>[4,7,1,3,2,6,5,8]=>1100100=>0010011
[7,3,8,5,6,2,4,1]=>[1,4,2,6,5,8,3,7]=>0110100=>0010110
[8,5,6,2,4,1,7,3]=>[3,7,1,4,2,6,5,8]=>1100100=>0010011
[5,2,4,1,8,6,7,3]=>[3,7,6,8,1,4,2,5]=>1100010=>0100011
[4,1,5,2,8,6,7,3]=>[3,7,6,8,2,5,1,4]=>1100010=>0100011
[3,1,6,2,8,5,7,4]=>[4,7,5,8,2,6,1,3]=>1100100=>0010011
[5,1,6,2,8,4,7,3]=>[3,7,4,8,2,6,1,5]=>1101000=>0001011
[8,4,6,2,5,1,7,3]=>[3,7,1,5,2,6,4,8]=>1101000=>0001011
[7,3,8,4,6,2,5,1]=>[1,5,2,6,4,8,3,7]=>0111000=>0001110
[6,2,7,3,8,4,5,1]=>[1,5,4,8,3,7,2,6]=>0111000=>0001110
[8,4,5,1,6,2,7,3]=>[3,7,2,6,1,5,4,8]=>1101000=>0001011
[4,1,8,5,6,2,7,3]=>[3,7,2,6,5,8,1,4]=>1100100=>0010011
[3,1,8,5,6,2,7,4]=>[4,7,2,6,5,8,1,3]=>1100100=>0010011
[2,1,8,5,6,3,7,4]=>[4,7,3,6,5,8,1,2]=>1010100=>0010101
[3,1,7,4,8,5,6,2]=>[2,6,5,8,4,7,1,3]=>1001100=>0011001
[7,3,6,2,8,4,5,1]=>[1,5,4,8,2,6,3,7]=>0111000=>0001110
[6,8,7,3,4,1,2,5]=>[5,2,1,4,3,7,8,6]=>1110010=>0100111
[5,4,8,7,2,6,3,1]=>[1,3,6,2,7,8,4,5]=>0101000=>0001010
[5,3,8,7,6,1,2,4]=>[4,2,1,6,7,8,3,5]=>1110000=>0000111
[8,3,4,6,5,1,2,7]=>[7,2,1,5,6,4,3,8]=>1111000=>0001111
[3,4,8,7,6,1,2,5]=>[5,2,1,6,7,8,4,3]=>1111000=>0001111
[3,5,8,7,6,1,2,4]=>[4,2,1,6,7,8,5,3]=>1110100=>0010111
[4,5,8,7,6,1,2,3]=>[3,2,1,6,7,8,5,4]=>1101100=>0011011
[4,5,8,7,1,6,3,2]=>[2,3,6,1,7,8,5,4]=>1001100=>0011001
[3,5,8,2,7,6,4,1]=>[1,4,6,7,2,8,5,3]=>0110100=>0010110
[3,5,8,1,7,6,4,2]=>[2,4,6,7,1,8,5,3]=>1010100=>0010101
[2,5,8,7,1,6,3,4]=>[4,3,6,1,7,8,5,2]=>1110100=>0010111
[2,4,8,7,1,6,3,5]=>[5,3,6,1,7,8,4,2]=>1111000=>0001111
[2,8,4,7,1,5,3,6]=>[6,3,5,1,7,4,8,2]=>1111000=>0001111
[8,2,4,6,1,5,3,7]=>[7,3,5,1,6,4,2,8]=>1111000=>0001111
[8,1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1,8]=>1111000=>0001111
[1,4,8,7,2,6,3,5]=>[5,3,6,2,7,8,4,1]=>1111000=>0001111
[1,5,8,7,2,6,3,4]=>[4,3,6,2,7,8,5,1]=>1110100=>0010111
[1,5,8,2,7,6,4,3]=>[3,4,6,7,2,8,5,1]=>1100100=>0010011
[2,5,8,3,7,6,4,1]=>[1,4,6,7,3,8,5,2]=>0110100=>0010110
[1,4,2,8,7,6,5,3]=>[3,5,6,7,8,2,4,1]=>1100000=>0000011
[1,3,8,2,7,6,4,5]=>[5,4,6,7,2,8,3,1]=>1111000=>0001111
[1,8,3,2,7,5,4,6]=>[6,4,5,7,2,3,8,1]=>1101000=>0001011
[8,2,3,1,6,5,4,7]=>[7,4,5,6,1,3,2,8]=>1101000=>0001011
[2,3,8,1,7,6,4,5]=>[5,4,6,7,1,8,3,2]=>1111000=>0001111
[5,2,8,7,1,6,3,4]=>[4,3,6,1,7,8,2,5]=>1110000=>0000111
[5,2,8,1,7,6,4,3]=>[3,4,6,7,1,8,2,5]=>1100000=>0000011
[5,3,8,2,7,6,4,1]=>[1,4,6,7,2,8,3,5]=>0110000=>0000110
[6,8,3,2,7,5,4,1]=>[1,4,5,7,2,3,8,6]=>0100010=>0100010
[6,8,3,1,7,5,4,2]=>[2,4,5,7,1,3,8,6]=>1000010=>0100001
[6,8,1,2,7,5,4,3]=>[3,4,5,7,2,1,8,6]=>1100010=>0100011
[6,8,2,3,7,5,4,1]=>[1,4,5,7,3,2,8,6]=>0110010=>0100110
[5,2,8,3,7,6,4,1]=>[1,4,6,7,3,8,2,5]=>0110000=>0000110
[5,1,8,3,7,6,4,2]=>[2,4,6,7,3,8,1,5]=>1010000=>0000101
[5,1,8,7,2,6,3,4]=>[4,3,6,2,7,8,1,5]=>1110000=>0000111
[4,8,1,7,2,5,3,6]=>[6,3,5,2,7,1,8,4]=>1111000=>0001111
[8,4,1,6,2,5,3,7]=>[7,3,5,2,6,1,4,8]=>1110000=>0000111
[8,3,1,2,6,5,4,7]=>[7,4,5,6,2,1,3,8]=>1101000=>0001011
[3,1,2,8,7,6,5,4]=>[4,5,6,7,8,2,1,3]=>1100000=>0000011
[4,1,3,8,7,6,5,2]=>[2,5,6,7,8,3,1,4]=>1010000=>0000101
[3,1,4,8,7,6,5,2]=>[2,5,6,7,8,4,1,3]=>1001000=>0001001
[2,1,8,3,7,6,4,5]=>[5,4,6,7,3,8,1,2]=>1011000=>0001101
[2,8,1,3,7,5,4,6]=>[6,4,5,7,3,1,8,2]=>1111000=>0001111
[8,2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2,8]=>1011000=>0001101
[1,8,2,3,7,5,4,6]=>[6,4,5,7,3,2,8,1]=>1111000=>0001111
[1,2,8,3,7,6,4,5]=>[5,4,6,7,3,8,2,1]=>1111000=>0001111
[1,4,3,6,8,2,5,7]=>[7,5,2,8,6,3,4,1]=>1110110=>0110111
[1,4,5,2,8,3,7,6]=>[6,7,3,8,2,5,4,1]=>1111000=>0001111
[1,4,2,6,5,8,3,7]=>[7,3,8,5,6,2,4,1]=>1110100=>0010111
[1,5,4,2,6,8,3,7]=>[7,3,8,6,2,4,5,1]=>1110010=>0100111
[3,1,6,5,8,2,4,7]=>[7,4,2,8,5,6,1,3]=>1101100=>0011011
[1,6,4,2,5,8,3,7]=>[7,3,8,5,2,4,6,1]=>1110100=>0010111
[1,5,2,6,4,8,3,7]=>[7,3,8,4,6,2,5,1]=>1111000=>0001111
[1,2,6,5,4,8,3,7]=>[7,3,8,4,5,6,2,1]=>1111000=>0001111
[1,2,5,4,7,3,8,6]=>[6,8,3,7,4,5,2,1]=>1111000=>0001111
[4,1,2,6,3,8,7,5]=>[5,7,8,3,6,2,1,4]=>1110000=>0000111
[7,1,5,4,2,8,3,6]=>[6,3,8,2,4,5,1,7]=>1110000=>0000111
[1,4,7,5,2,8,3,6]=>[6,3,8,2,5,7,4,1]=>1111000=>0001111
[7,1,3,5,2,8,4,6]=>[6,4,8,2,5,3,1,7]=>1111000=>0001111
[1,4,5,2,8,7,3,6]=>[6,3,7,8,2,5,4,1]=>1111000=>0001111
[1,6,4,2,8,3,7,5]=>[5,7,3,8,2,4,6,1]=>1110000=>0000111
[1,4,2,8,3,7,6,5]=>[5,6,7,3,8,2,4,1]=>1110000=>0000111
[1,2,8,6,5,3,7,4]=>[4,7,3,5,6,8,2,1]=>1110000=>0000111
[6,2,1,8,7,3,4,5]=>[5,4,3,7,8,1,2,6]=>1011000=>0001101
[7,6,2,1,8,3,4,5]=>[5,4,3,8,1,2,6,7]=>1011000=>0001101
[7,3,1,6,2,8,4,5]=>[5,4,8,2,6,1,3,7]=>1101000=>0001011
[1,7,6,4,2,8,3,5]=>[5,3,8,2,4,6,7,1]=>1110000=>0000111
[1,7,5,2,6,3,8,4]=>[4,8,3,6,2,5,7,1]=>1110000=>0000111
[1,6,2,7,5,3,8,4]=>[4,8,3,5,7,2,6,1]=>1110000=>0000111
[1,2,7,6,5,3,8,4]=>[4,8,3,5,6,7,2,1]=>1110000=>0000111
[1,2,6,5,3,8,7,4]=>[4,7,8,3,5,6,2,1]=>1110000=>0000111
[1,5,2,7,6,3,8,4]=>[4,8,3,6,7,2,5,1]=>1110000=>0000111
[1,6,5,2,7,3,8,4]=>[4,8,3,7,2,5,6,1]=>1110000=>0000111
[1,5,7,4,2,8,3,6]=>[6,3,8,2,4,7,5,1]=>1110100=>0010111
[3,1,8,6,2,4,7,5]=>[5,7,4,2,6,8,1,3]=>1101000=>0001011
[4,3,7,1,8,2,5,6]=>[6,5,2,8,1,7,3,4]=>1110100=>0010111
[8,3,1,6,2,4,7,5]=>[5,7,4,2,6,1,3,8]=>1101000=>0001011
[7,1,8,3,2,4,6,5]=>[5,6,4,2,3,8,1,7]=>1101000=>0001011
[1,4,2,8,7,3,6,5]=>[5,6,3,7,8,2,4,1]=>1110000=>0000111
[1,7,4,2,8,3,6,5]=>[5,6,3,8,2,4,7,1]=>1110000=>0000111
[8,1,5,4,2,7,3,6]=>[6,3,7,2,4,5,1,8]=>1110000=>0000111
[1,4,8,5,2,7,3,6]=>[6,3,7,2,5,8,4,1]=>1111000=>0001111
[8,5,3,1,7,2,4,6]=>[6,4,2,7,1,3,5,8]=>1101000=>0001011
[8,6,2,1,7,3,4,5]=>[5,4,3,7,1,2,6,8]=>1011000=>0001101
[1,8,6,4,2,7,3,5]=>[5,3,7,2,4,6,8,1]=>1110000=>0000111
[1,5,2,7,3,8,6,4]=>[4,6,8,3,7,2,5,1]=>1110000=>0000111
[1,2,8,5,3,7,6,4]=>[4,6,7,3,5,8,2,1]=>1110000=>0000111
[1,2,6,3,8,7,5,4]=>[4,5,7,8,3,6,2,1]=>1110000=>0000111
[1,2,7,6,3,8,5,4]=>[4,5,8,3,6,7,2,1]=>1110000=>0000111
[1,6,2,7,3,8,5,4]=>[4,5,8,3,7,2,6,1]=>1110000=>0000111
[1,7,4,2,8,6,3,5]=>[5,3,6,8,2,4,7,1]=>1110000=>0000111
[7,1,8,3,2,6,4,5]=>[5,4,6,2,3,8,1,7]=>1101000=>0001011
[7,2,1,8,6,3,4,5]=>[5,4,3,6,8,1,2,7]=>1011000=>0001101
[1,8,7,3,2,6,4,5]=>[5,4,6,2,3,7,8,1]=>1101000=>0001011
[1,4,2,8,7,6,3,5]=>[5,3,6,7,8,2,4,1]=>1110000=>0000111
[1,2,8,7,5,3,6,4]=>[4,6,3,5,7,8,2,1]=>1110000=>0000111
[5,1,8,7,6,2,4,3]=>[3,4,2,6,7,8,1,5]=>1100000=>0000011
[8,1,7,6,3,4,5,2]=>[2,5,4,3,6,7,1,8]=>1011000=>0001101
[5,7,8,6,2,4,1,3]=>[3,1,4,2,6,8,7,5]=>1100101=>1010011
[5,7,1,6,2,4,3,8]=>[8,3,4,2,6,1,7,5]=>1110100=>0010111
[6,4,1,5,2,7,3,8]=>[8,3,7,2,5,1,4,6]=>1110000=>0000111
[8,1,4,5,3,7,6,2]=>[2,6,7,3,5,4,1,8]=>1011000=>0001101
[6,1,4,5,3,8,7,2]=>[2,7,8,3,5,4,1,6]=>1011000=>0001101
[7,1,4,5,3,8,6,2]=>[2,6,8,3,5,4,1,7]=>1011000=>0001101
[7,1,4,5,3,6,8,2]=>[2,8,6,3,5,4,1,7]=>1011010=>0101101
[7,4,1,5,2,6,3,8]=>[8,3,6,2,5,1,4,7]=>1110000=>0000111
[6,3,5,7,2,1,4,8]=>[8,4,1,2,7,5,3,6]=>1011100=>0011101
[6,3,5,8,2,1,7,4]=>[4,7,1,2,8,5,3,6]=>1010100=>0010101
[6,3,5,7,2,1,8,4]=>[4,8,1,2,7,5,3,6]=>1010100=>0010101
[8,4,5,7,3,6,1,2]=>[2,1,6,3,7,5,4,8]=>1011100=>0011101
[6,4,5,8,3,7,2,1]=>[1,2,7,3,8,5,4,6]=>0011100=>0011100
[5,4,8,6,3,1,7,2]=>[2,7,1,3,6,8,4,5]=>1001000=>0001001
[5,4,1,8,2,3,7,6]=>[6,7,3,2,8,1,4,5]=>1110000=>0000111
[8,4,1,5,2,6,3,7]=>[7,3,6,2,5,1,4,8]=>1110000=>0000111
[6,3,5,8,2,1,4,7]=>[7,4,1,2,8,5,3,6]=>1011100=>0011101
[2,3,8,5,1,4,7,6]=>[6,7,4,1,5,8,3,2]=>1111000=>0001111
[2,3,8,6,1,5,7,4]=>[4,7,5,1,6,8,3,2]=>1110100=>0010111
[2,8,6,7,1,3,5,4]=>[4,5,3,1,7,6,8,2]=>1110010=>0100111
[8,3,5,7,2,1,6,4]=>[4,6,1,2,7,5,3,8]=>1010100=>0010101
[8,4,5,6,3,1,7,2]=>[2,7,1,3,6,5,4,8]=>1001100=>0011001
[7,3,5,6,2,8,1,4]=>[4,1,8,2,6,5,3,7]=>1110100=>0010111
[7,3,5,8,2,1,6,4]=>[4,6,1,2,8,5,3,7]=>1010100=>0010101
[7,3,5,6,2,1,4,8]=>[8,4,1,2,6,5,3,7]=>1011100=>0011101
[2,7,6,5,1,3,4,8]=>[8,4,3,1,5,6,7,2]=>1111000=>0001111
[2,7,6,8,1,3,5,4]=>[4,5,3,1,8,6,7,2]=>1110010=>0100111
[8,7,5,6,1,4,2,3]=>[3,2,4,1,6,5,7,8]=>1100100=>0010011
[2,7,1,3,6,5,8,4]=>[4,8,5,6,3,1,7,2]=>1110100=>0010111
[2,7,6,1,8,3,4,5]=>[5,4,3,8,1,6,7,2]=>1111000=>0001111
[2,7,6,1,4,3,5,8]=>[8,5,3,4,1,6,7,2]=>1110100=>0010111
[7,3,5,1,2,8,4,6]=>[6,4,8,2,1,5,3,7]=>1111000=>0001111
[2,3,8,6,4,1,7,5]=>[5,7,1,4,6,8,3,2]=>1110000=>0000111
[2,8,6,1,7,3,4,5]=>[5,4,3,7,1,6,8,2]=>1111000=>0001111
[2,3,8,1,6,4,7,5]=>[5,7,4,6,1,8,3,2]=>1111000=>0001111
[2,3,8,1,4,5,7,6]=>[6,7,5,4,1,8,3,2]=>1111100=>0011111
[5,7,2,3,8,6,1,4]=>[4,1,6,8,3,2,7,5]=>1110100=>0010111
[5,6,2,3,1,8,7,4]=>[4,7,8,1,3,2,6,5]=>1100100=>0010011
[5,6,2,1,3,8,7,4]=>[4,7,8,3,1,2,6,5]=>1010100=>0010101
[5,1,6,4,2,8,7,3]=>[3,7,8,2,4,6,1,5]=>1100000=>0000011
[5,6,1,3,2,8,7,4]=>[4,7,8,2,3,1,6,5]=>1100100=>0010011
[5,6,3,1,2,8,7,4]=>[4,7,8,2,1,3,6,5]=>1100100=>0010011
[5,7,3,2,8,1,6,4]=>[4,6,1,8,2,3,7,5]=>1100100=>0010011
[6,7,3,8,2,1,5,4]=>[4,5,1,2,8,3,7,6]=>1010010=>0100101
[6,7,3,8,1,2,5,4]=>[4,5,2,1,8,3,7,6]=>1110010=>0100111
[5,7,3,1,8,2,6,4]=>[4,6,2,8,1,3,7,5]=>1100100=>0010011
[5,1,7,4,8,2,6,3]=>[3,6,2,8,4,7,1,5]=>1101000=>0001011
[1,5,7,4,8,3,6,2]=>[2,6,3,8,4,7,5,1]=>1011100=>0011101
[5,1,7,4,8,6,2,3]=>[3,2,6,8,4,7,1,5]=>1101000=>0001011
[5,7,3,1,8,6,2,4]=>[4,2,6,8,1,3,7,5]=>1100100=>0010011
[6,7,8,3,1,4,2,5]=>[5,2,4,1,3,8,7,6]=>1100011=>1100011
[6,7,1,8,3,5,2,4]=>[4,2,5,3,8,1,7,6]=>1110010=>0100111
[6,1,7,8,4,5,2,3]=>[3,2,5,4,8,7,1,6]=>1101001=>1001011
[1,6,7,8,4,5,3,2]=>[2,3,5,4,8,7,6,1]=>1001011=>1101001
[1,6,7,8,4,3,5,2]=>[2,5,3,4,8,7,6,1]=>1010011=>1100101
[6,1,7,8,4,2,5,3]=>[3,5,2,4,8,7,1,6]=>1100001=>1000011
[6,7,2,8,1,3,5,4]=>[4,5,3,1,8,2,7,6]=>1110010=>0100111
[6,7,2,8,3,5,1,4]=>[4,1,5,3,8,2,7,6]=>1110010=>0100111
[6,2,7,8,4,1,5,3]=>[3,5,1,4,8,7,2,6]=>1100001=>1000011
[6,2,7,8,1,4,5,3]=>[3,5,4,1,8,7,2,6]=>1101001=>1001011
[4,2,1,7,8,5,6,3]=>[3,6,5,8,7,1,2,4]=>1000101=>1010001
[4,1,2,7,8,6,5,3]=>[3,5,6,8,7,2,1,4]=>1100001=>1000011
[6,2,7,8,1,5,4,3]=>[3,4,5,1,8,7,2,6]=>1100001=>1000011
[6,2,7,8,5,1,4,3]=>[3,4,1,5,8,7,2,6]=>1100001=>1000011
[5,7,2,1,8,6,3,4]=>[4,3,6,8,1,2,7,5]=>1010100=>0010101
[1,6,7,8,3,5,4,2]=>[2,4,5,3,8,7,6,1]=>1010011=>1100101
[6,1,7,8,2,5,4,3]=>[3,4,5,2,8,7,1,6]=>1100001=>1000011
[6,7,8,2,4,1,3,5]=>[5,3,1,4,2,8,7,6]=>1110011=>1100111
[6,7,8,2,4,3,1,5]=>[5,1,3,4,2,8,7,6]=>1100011=>1100011
[6,7,1,8,5,2,3,4]=>[4,3,2,5,8,1,7,6]=>1110010=>0100111
[6,1,7,8,5,2,4,3]=>[3,4,2,5,8,7,1,6]=>1100001=>1000011
[1,6,7,8,5,3,4,2]=>[2,4,3,5,8,7,6,1]=>1010011=>1100101
[6,1,7,8,5,4,2,3]=>[3,2,4,5,8,7,1,6]=>1100001=>1000011
[6,7,1,8,5,3,2,4]=>[4,2,3,5,8,1,7,6]=>1100010=>0100011
[6,7,8,4,1,3,2,5]=>[5,2,3,1,4,8,7,6]=>1100011=>1100011
[3,7,4,8,5,6,1,2]=>[2,1,6,5,8,4,7,3]=>1011100=>0011101
[3,7,1,8,5,6,2,4]=>[4,2,6,5,8,1,7,3]=>1110100=>0010111
[2,7,3,8,5,6,1,4]=>[4,1,6,5,8,3,7,2]=>1110100=>0010111
[1,7,4,8,5,6,2,3]=>[3,2,6,5,8,4,7,1]=>1101100=>0011011
[3,7,1,8,4,6,2,5]=>[5,2,6,4,8,1,7,3]=>1111000=>0001111
[1,5,2,8,6,7,3,4]=>[4,3,7,6,8,2,5,1]=>1110010=>0100111
[1,6,2,8,5,7,3,4]=>[4,3,7,5,8,2,6,1]=>1110100=>0010111
[1,6,2,8,4,7,3,5]=>[5,3,7,4,8,2,6,1]=>1111000=>0001111
[2,6,1,8,4,7,3,5]=>[5,3,7,4,8,1,6,2]=>1111000=>0001111
[4,8,1,6,2,7,3,5]=>[5,3,7,2,6,1,8,4]=>1111000=>0001111
[5,8,2,6,1,7,3,4]=>[4,3,7,1,6,2,8,5]=>1110100=>0010111
[4,8,2,6,1,7,3,5]=>[5,3,7,1,6,2,8,4]=>1111000=>0001111
[1,7,3,6,2,8,4,5]=>[5,4,8,2,6,3,7,1]=>1111000=>0001111
[8,6,1,4,3,2,5,7]=>[7,5,2,3,4,1,6,8]=>1100100=>0010011
[3,7,5,1,8,2,4,6]=>[6,4,2,8,1,5,7,3]=>1111000=>0001111
[4,1,5,2,8,7,3,6]=>[6,3,7,8,2,5,1,4]=>1110000=>0000111
[8,1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1,8]=>1111000=>0001111
[8,2,6,5,1,3,4,7]=>[7,4,3,1,5,6,2,8]=>1111000=>0001111
[8,3,1,6,2,5,4,7]=>[7,4,5,2,6,1,3,8]=>1101000=>0001011
[8,1,2,6,4,5,3,7]=>[7,3,5,4,6,2,1,8]=>1111000=>0001111
[8,1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1,8]=>1110100=>0010111
[1,7,5,4,2,8,3,6]=>[6,3,8,2,4,5,7,1]=>1110000=>0000111
[1,4,6,8,2,7,3,5]=>[5,3,7,2,8,6,4,1]=>1111010=>0101111
[1,4,7,6,2,8,3,5]=>[5,3,8,2,6,7,4,1]=>1111000=>0001111
[5,1,4,7,2,8,3,6]=>[6,3,8,2,7,4,1,5]=>1111000=>0001111
[3,7,5,1,2,8,4,6]=>[6,4,8,2,1,5,7,3]=>1111000=>0001111
[4,1,5,8,2,7,3,6]=>[6,3,7,2,8,5,1,4]=>1110100=>0010111
[1,4,6,2,8,7,3,5]=>[5,3,7,8,2,6,4,1]=>1111000=>0001111
[1,4,2,8,6,7,3,5]=>[5,3,7,6,8,2,4,1]=>1110010=>0100111
[3,1,2,6,4,8,7,5]=>[5,7,8,4,6,2,1,3]=>1101000=>0001011
[2,1,7,6,3,4,8,5]=>[5,8,4,3,6,7,1,2]=>1011000=>0001101
[3,1,2,7,4,6,8,5]=>[5,8,6,4,7,2,1,3]=>1101010=>0101011
[1,2,3,6,8,5,7,4]=>[4,7,5,8,6,3,2,1]=>1110110=>0110111
[5,1,4,2,7,8,3,6]=>[6,3,8,7,2,4,1,5]=>1110001=>1000111
[1,4,2,7,6,8,3,5]=>[5,3,8,6,7,2,4,1]=>1110010=>0100111
[1,4,2,6,8,7,3,5]=>[5,3,7,8,6,2,4,1]=>1110010=>0100111
[5,3,7,1,8,2,4,6]=>[6,4,2,8,1,7,3,5]=>1111000=>0001111
[1,7,4,3,2,5,8,6]=>[6,8,5,2,3,4,7,1]=>1100100=>0010011
[4,8,7,2,1,3,5,6]=>[6,5,3,1,2,7,8,4]=>1011100=>0011101
[1,8,7,3,4,2,5,6]=>[6,5,2,4,3,7,8,1]=>1110100=>0010111
[3,1,7,8,2,6,4,5]=>[5,4,6,2,8,7,1,3]=>1101001=>1001011
[1,4,2,7,8,3,6,5]=>[5,6,3,8,7,2,4,1]=>1110001=>1000111
[2,1,8,6,3,4,7,5]=>[5,7,4,3,6,8,1,2]=>1011000=>0001101
[1,4,2,6,8,3,7,5]=>[5,7,3,8,6,2,4,1]=>1110010=>0100111
[1,2,3,7,8,5,6,4]=>[4,6,5,8,7,3,2,1]=>1110101=>1010111
[1,2,3,7,5,8,6,4]=>[4,6,8,5,7,3,2,1]=>1110100=>0010111
[3,1,7,2,8,6,4,5]=>[5,4,6,8,2,7,1,3]=>1101000=>0001011
[1,2,3,8,7,5,6,4]=>[4,6,5,7,8,3,2,1]=>1110100=>0010111
[5,7,8,4,2,6,1,3]=>[3,1,6,2,4,8,7,5]=>1100101=>1010011
[6,7,8,4,2,5,1,3]=>[3,1,5,2,4,8,7,6]=>1100011=>1100011
[8,6,3,7,2,1,5,4]=>[4,5,1,2,7,3,6,8]=>1010000=>0000101
[6,7,8,3,2,1,5,4]=>[4,5,1,2,3,8,7,6]=>1000011=>1100001
[5,7,8,3,2,1,6,4]=>[4,6,1,2,3,8,7,5]=>1000101=>1010001
[2,7,8,4,3,5,6,1]=>[1,6,5,3,4,8,7,2]=>0110101=>1010110
[3,7,8,4,2,5,1,6]=>[6,1,5,2,4,8,7,3]=>1110001=>1000111
[7,6,3,8,2,1,4,5]=>[5,4,1,2,8,3,6,7]=>1011000=>0001101
[8,6,3,7,2,1,4,5]=>[5,4,1,2,7,3,6,8]=>1011000=>0001101
[5,6,3,8,2,1,4,7]=>[7,4,1,2,8,3,6,5]=>1011100=>0011101
[3,6,4,8,2,5,1,7]=>[7,1,5,2,8,4,6,3]=>1111000=>0001111
[2,6,4,8,3,5,7,1]=>[1,7,5,3,8,4,6,2]=>0111100=>0011110
[2,6,4,7,3,5,8,1]=>[1,8,5,3,7,4,6,2]=>0111100=>0011110
[5,6,3,7,2,1,4,8]=>[8,4,1,2,7,3,6,5]=>1011100=>0011101
[8,4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4,8]=>1000100=>0010001
[6,4,3,2,1,7,5,8]=>[8,5,7,1,2,3,4,6]=>1000100=>0010001
[4,5,3,2,7,1,6,8]=>[8,6,1,7,2,3,5,4]=>1101010=>0101011
[7,4,3,2,1,8,5,6]=>[6,5,8,1,2,3,4,7]=>1000100=>0010001
[8,4,3,2,1,7,5,6]=>[6,5,7,1,2,3,4,8]=>1000100=>0010001
[7,4,3,2,1,8,6,5]=>[5,6,8,1,2,3,4,7]=>1000000=>0000001
[5,6,3,8,2,1,7,4]=>[4,7,1,2,8,3,6,5]=>1010100=>0010101
[7,5,3,2,8,1,6,4]=>[4,6,1,8,2,3,5,7]=>1100000=>0000011
[8,5,4,2,7,6,1,3]=>[3,1,6,7,2,4,5,8]=>1100000=>0000011
[7,5,4,2,8,6,1,3]=>[3,1,6,8,2,4,5,7]=>1100000=>0000011
[6,5,4,2,7,8,1,3]=>[3,1,8,7,2,4,5,6]=>1100001=>1000011
[8,5,4,2,6,7,1,3]=>[3,1,7,6,2,4,5,8]=>1100010=>0100011
[5,6,3,7,2,1,8,4]=>[4,8,1,2,7,3,6,5]=>1010100=>0010101
[4,6,3,7,2,1,8,5]=>[5,8,1,2,7,3,6,4]=>1011000=>0001101
[3,6,4,7,2,8,1,5]=>[5,1,8,2,7,4,6,3]=>1111000=>0001111
[2,6,4,7,3,8,5,1]=>[1,5,8,3,7,4,6,2]=>0111000=>0001110
[3,5,4,2,7,8,1,6]=>[6,1,8,7,2,4,5,3]=>1110001=>1000111
[7,4,3,2,1,6,8,5]=>[5,8,6,1,2,3,4,7]=>1000010=>0100001
[8,4,3,2,1,6,7,5]=>[5,7,6,1,2,3,4,8]=>1000010=>0100001
[8,4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4,8]=>1000100=>0010001
[7,4,3,2,1,5,8,6]=>[6,8,5,1,2,3,4,7]=>1000100=>0010001
[6,4,3,2,1,5,8,7]=>[7,8,5,1,2,3,4,6]=>1000100=>0010001
[3,5,4,2,6,8,1,7]=>[7,1,8,6,2,4,5,3]=>1110010=>0100111
[3,2,6,4,8,5,1,7]=>[7,1,5,8,4,6,2,3]=>1101000=>0001011
[3,2,5,8,4,6,1,7]=>[7,1,6,4,8,5,2,3]=>1101100=>0011011
[4,2,1,5,7,3,6,8]=>[8,6,3,7,5,1,2,4]=>1010110=>0110101
[4,5,2,3,7,1,6,8]=>[8,6,1,7,3,2,5,4]=>1111010=>0101111
[4,2,5,3,8,1,6,7]=>[7,6,1,8,3,5,2,4]=>1110010=>0100111
[4,2,5,8,3,1,6,7]=>[7,6,1,3,8,5,2,4]=>1100110=>0110011
[4,1,5,3,8,2,6,7]=>[7,6,2,8,3,5,1,4]=>1110010=>0100111
[4,3,2,7,5,1,6,8]=>[8,6,1,5,7,2,3,4]=>1100010=>0100011
[4,3,6,2,5,1,7,8]=>[8,7,1,5,2,6,3,4]=>1110001=>1000111
[4,6,7,1,3,2,5,8]=>[8,5,2,3,1,7,6,4]=>1101110=>0111011
[4,5,1,7,3,2,6,8]=>[8,6,2,3,7,1,5,4]=>1101010=>0101011
[4,5,1,3,7,2,6,8]=>[8,6,2,7,3,1,5,4]=>1111010=>0101111
[3,5,1,4,2,7,6,8]=>[8,6,7,2,4,1,5,3]=>1110010=>0100111
[2,5,1,4,3,7,8,6]=>[6,8,7,3,4,1,5,2]=>1110001=>1000111
[5,2,1,4,3,7,8,6]=>[6,8,7,3,4,1,2,5]=>1010001=>1000101
[5,3,1,4,2,7,6,8]=>[8,6,7,2,4,1,3,5]=>1100010=>0100011
[4,3,1,7,5,2,6,8]=>[8,6,2,5,7,1,3,4]=>1100010=>0100011
[5,3,6,4,1,2,7,8]=>[8,7,2,1,4,6,3,5]=>1110001=>1000111
[4,3,6,1,7,2,5,8]=>[8,5,2,7,1,6,3,4]=>1110100=>0010111
[6,2,4,1,3,7,8,5]=>[5,8,7,3,1,4,2,6]=>1110001=>1000111
[3,6,4,1,2,7,5,8]=>[8,5,7,2,1,4,6,3]=>1110100=>0010111
[4,6,3,1,7,2,5,8]=>[8,5,2,7,1,3,6,4]=>1101100=>0011011
[5,3,6,2,1,4,7,8]=>[8,7,4,1,2,6,3,5]=>1011001=>1001101
[4,5,2,7,3,1,6,8]=>[8,6,1,3,7,2,5,4]=>1101010=>0101011
[4,6,2,1,7,3,5,8]=>[8,5,3,7,1,2,6,4]=>1011100=>0011101
[3,2,6,1,4,7,5,8]=>[8,5,7,4,1,6,2,3]=>1101100=>0011011
[3,6,7,2,4,5,1,8]=>[8,1,5,4,2,7,6,3]=>1111010=>0101111
[7,2,1,4,6,3,8,5]=>[5,8,3,6,4,1,2,7]=>1011000=>0001101
[7,3,1,4,6,8,2,5]=>[5,2,8,6,4,1,3,7]=>1101010=>0101011
[3,6,2,1,5,7,4,8]=>[8,4,7,5,1,2,6,3]=>1011100=>0011101
[7,4,1,5,6,2,3,8]=>[8,3,2,6,5,1,4,7]=>1110100=>0010111
[7,3,1,5,2,6,4,8]=>[8,4,6,2,5,1,3,7]=>1101000=>0001011
[7,2,1,5,3,6,8,4]=>[4,8,6,3,5,1,2,7]=>1010010=>0100101
[6,2,5,1,3,7,8,4]=>[4,8,7,3,1,5,2,6]=>1110001=>1000111
[6,3,5,1,2,7,4,8]=>[8,4,7,2,1,5,3,6]=>1111000=>0001111
[6,4,5,1,7,2,3,8]=>[8,3,2,7,1,5,4,6]=>1111000=>0001111
[4,6,5,1,7,2,3,8]=>[8,3,2,7,1,5,6,4]=>1111000=>0001111
[3,6,5,1,2,7,4,8]=>[8,4,7,2,1,5,6,3]=>1111000=>0001111
[2,4,1,5,3,8,7,6]=>[6,7,8,3,5,1,4,2]=>1110000=>0000111
[3,4,5,1,2,8,7,6]=>[6,7,8,2,1,5,4,3]=>1111000=>0001111
[1,8,4,5,3,2,7,6]=>[6,7,2,3,5,4,8,1]=>1101000=>0001011
[2,4,8,5,3,1,7,6]=>[6,7,1,3,5,8,4,2]=>1101000=>0001011
[3,4,5,2,8,1,7,6]=>[6,7,1,8,2,5,4,3]=>1111000=>0001111
[3,4,6,2,1,7,8,5]=>[5,8,7,1,2,6,4,3]=>1011001=>1001101
[3,4,6,2,1,7,5,8]=>[8,5,7,1,2,6,4,3]=>1011100=>0011101
[3,5,6,2,7,1,8,4]=>[4,8,1,7,2,6,5,3]=>1110100=>0010111
[3,4,6,2,8,7,1,5]=>[5,1,7,8,2,6,4,3]=>1111000=>0001111
[3,4,6,8,2,7,1,5]=>[5,1,7,2,8,6,4,3]=>1111010=>0101111
[2,4,8,6,3,7,1,5]=>[5,1,7,3,6,8,4,2]=>1111000=>0001111
[1,8,4,6,3,7,2,5]=>[5,2,7,3,6,4,8,1]=>1111000=>0001111
[1,8,4,6,3,7,5,2]=>[2,5,7,3,6,4,8,1]=>1011000=>0001101
[3,4,6,8,2,7,5,1]=>[1,5,7,2,8,6,4,3]=>0111010=>0101110
[3,4,6,2,8,7,5,1]=>[1,5,7,8,2,6,4,3]=>0111000=>0001110
[3,5,6,2,7,8,4,1]=>[1,4,8,7,2,6,5,3]=>0110101=>1010110
[3,5,6,2,7,4,1,8]=>[8,1,4,7,2,6,5,3]=>1110100=>0010111
[4,5,6,7,2,8,3,1]=>[1,3,8,2,7,6,5,4]=>0101110=>0111010
[2,5,8,6,7,3,4,1]=>[1,4,3,7,6,8,5,2]=>0110110=>0110110
[1,8,5,6,7,3,2,4]=>[4,2,3,7,6,5,8,1]=>1100110=>0110011
[4,5,6,7,2,1,8,3]=>[3,8,1,2,7,6,5,4]=>1001110=>0111001
[3,4,6,1,8,7,2,5]=>[5,2,7,8,1,6,4,3]=>1111000=>0001111
[2,4,1,6,8,7,3,5]=>[5,3,7,8,6,1,4,2]=>1110010=>0100111
[2,5,1,6,7,8,4,3]=>[3,4,8,7,6,1,5,2]=>1100011=>1100011
[2,5,1,6,7,4,3,8]=>[8,3,4,7,6,1,5,2]=>1110010=>0100111
[3,5,6,1,7,4,2,8]=>[8,2,4,7,1,6,5,3]=>1110100=>0010111
[3,5,6,1,7,4,8,2]=>[2,8,4,7,1,6,5,3]=>1011100=>0011101
[3,4,6,1,8,7,5,2]=>[2,5,7,8,1,6,4,3]=>1011000=>0001101
[2,4,8,6,1,7,5,3]=>[3,5,7,1,6,8,4,2]=>1101000=>0001011
[1,8,4,6,2,7,5,3]=>[3,5,7,2,6,4,8,1]=>1101000=>0001011
[1,8,5,6,7,2,4,3]=>[3,4,2,7,6,5,8,1]=>1100110=>0110011
[2,5,8,6,7,1,4,3]=>[3,4,1,7,6,8,5,2]=>1100110=>0110011
[4,5,6,7,1,3,8,2]=>[2,8,3,1,7,6,5,4]=>1011110=>0111101
[3,5,6,8,7,4,1,2]=>[2,1,4,7,8,6,5,3]=>1010110=>0110101
[2,5,8,6,7,4,1,3]=>[3,1,4,7,6,8,5,2]=>1100110=>0110011
[1,8,5,6,7,4,2,3]=>[3,2,4,7,6,5,8,1]=>1100110=>0110011
[1,8,5,6,7,4,3,2]=>[2,3,4,7,6,5,8,1]=>1000110=>0110001
[2,5,8,6,7,4,3,1]=>[1,3,4,7,6,8,5,2]=>0100110=>0110010
[8,2,4,3,7,1,6,5]=>[5,6,1,7,3,4,2,8]=>1110000=>0000111
[5,8,2,4,3,7,1,6]=>[6,1,7,3,4,2,8,5]=>1110100=>0010111
[4,2,5,6,1,8,3,7]=>[7,3,8,1,6,5,2,4]=>1110100=>0010111
[4,2,5,6,1,7,3,8]=>[8,3,7,1,6,5,2,4]=>1110100=>0010111
[6,1,5,7,3,2,4,8]=>[8,4,2,3,7,5,1,6]=>1101100=>0011011
[6,1,5,8,3,2,4,7]=>[7,4,2,3,8,5,1,6]=>1101100=>0011011
[3,8,2,4,7,1,5,6]=>[6,5,1,7,4,2,8,3]=>1111100=>0011111
[3,6,8,2,4,7,1,5]=>[5,1,7,4,2,8,6,3]=>1111010=>0101111
[7,3,2,4,6,1,5,8]=>[8,5,1,6,4,2,3,7]=>1101100=>0011011
[3,2,5,1,8,4,6,7]=>[7,6,4,8,1,5,2,3]=>1101010=>0101011
[7,8,3,2,4,6,1,5]=>[5,1,6,4,2,3,8,7]=>1101001=>1001011
[6,1,5,7,8,3,2,4]=>[4,2,3,8,7,5,1,6]=>1100101=>1010011
[4,2,5,6,1,7,8,3]=>[3,8,7,1,6,5,2,4]=>1100101=>1010011
[5,7,6,1,8,3,4,2]=>[2,4,3,8,1,6,7,5]=>1010100=>0010101
[5,8,6,1,7,3,4,2]=>[2,4,3,7,1,6,8,5]=>1010100=>0010101
[6,1,5,8,7,3,2,4]=>[4,2,3,7,8,5,1,6]=>1100100=>0010011
[8,7,3,2,4,6,1,5]=>[5,1,6,4,2,3,7,8]=>1101000=>0001011
[3,2,5,1,8,7,4,6]=>[6,4,7,8,1,5,2,3]=>1101000=>0001011
[3,2,5,1,6,4,7,8]=>[8,7,4,6,1,5,2,3]=>1101001=>1001011
[3,2,4,1,8,7,5,6]=>[6,5,7,8,1,4,2,3]=>1100100=>0010011
[3,2,5,1,6,8,7,4]=>[4,7,8,6,1,5,2,3]=>1100010=>0100011
[3,8,6,5,1,7,4,2]=>[2,4,7,1,5,6,8,3]=>1010000=>0000101
[3,7,6,5,1,8,4,2]=>[2,4,8,1,5,6,7,3]=>1010000=>0000101
[6,5,1,7,8,4,2,3]=>[3,2,4,8,7,1,5,6]=>1100001=>1000011
[3,2,5,1,6,7,8,4]=>[4,8,7,6,1,5,2,3]=>1100011=>1100011
[3,2,4,1,7,5,6,8]=>[8,6,5,7,1,4,2,3]=>1100110=>0110011
[3,2,4,1,6,8,5,7]=>[7,5,8,6,1,4,2,3]=>1100110=>0110011
[8,3,2,4,7,6,1,5]=>[5,1,6,7,4,2,3,8]=>1101000=>0001011
[3,2,5,1,8,4,7,6]=>[6,7,4,8,1,5,2,3]=>1101000=>0001011
[3,2,5,1,6,7,4,8]=>[8,4,7,6,1,5,2,3]=>1101010=>0101011
[6,5,1,7,4,2,3,8]=>[8,3,2,4,7,1,5,6]=>1110000=>0000111
[6,5,1,8,4,2,3,7]=>[7,3,2,4,8,1,5,6]=>1110000=>0000111
[8,4,2,3,7,5,1,6]=>[6,1,5,7,3,2,4,8]=>1110000=>0000111
[5,2,6,1,8,3,7,4]=>[4,7,3,8,1,6,2,5]=>1110000=>0000111
[5,2,6,1,8,4,7,3]=>[3,7,4,8,1,6,2,5]=>1101000=>0001011
[7,4,2,3,8,5,1,6]=>[6,1,5,8,3,2,4,7]=>1110000=>0000111
[8,5,1,6,4,2,3,7]=>[7,3,2,4,6,1,5,8]=>1110000=>0000111
[3,2,5,1,7,6,4,8]=>[8,4,6,7,1,5,2,3]=>1101000=>0001011
[3,2,5,1,8,6,4,7]=>[7,4,6,8,1,5,2,3]=>1101000=>0001011
[8,6,1,5,7,3,2,4]=>[4,2,3,7,5,1,6,8]=>1100100=>0010011
[8,5,6,1,7,3,4,2]=>[2,4,3,7,1,6,5,8]=>1010100=>0010101
[3,6,8,5,1,7,4,2]=>[2,4,7,1,5,8,6,3]=>1010010=>0100101
[8,5,1,6,7,4,2,3]=>[3,2,4,7,6,1,5,8]=>1100010=>0100011
[3,2,5,1,8,6,7,4]=>[4,7,6,8,1,5,2,3]=>1100010=>0100011
[3,2,4,1,5,8,6,7]=>[7,6,8,5,1,4,2,3]=>1100110=>0110011
[3,2,5,1,7,8,6,4]=>[4,6,8,7,1,5,2,3]=>1100001=>1000011
[8,7,5,1,6,4,2,3]=>[3,2,4,6,1,5,7,8]=>1100000=>0000011
[3,2,5,1,8,7,6,4]=>[4,6,7,8,1,5,2,3]=>1100000=>0000011
[4,6,3,7,1,8,5,2]=>[2,5,8,1,7,3,6,4]=>1011000=>0001101
[4,6,3,7,5,1,8,2]=>[2,8,1,5,7,3,6,4]=>1011000=>0001101
[4,2,6,1,7,5,3,8]=>[8,3,5,7,1,6,2,4]=>1110000=>0000111
[2,5,7,4,1,6,8,3]=>[3,8,6,1,4,7,5,2]=>1100110=>0110011
[4,3,7,5,1,8,6,2]=>[2,6,8,1,5,7,3,4]=>1010000=>0000101
[6,4,3,8,5,1,7,2]=>[2,7,1,5,8,3,4,6]=>1010000=>0000101
[2,5,4,6,1,7,3,8]=>[8,3,7,1,6,4,5,2]=>1111000=>0001111
[4,6,2,1,8,5,7,3]=>[3,7,5,8,1,2,6,4]=>1001100=>0011001
[2,4,1,7,5,8,6,3]=>[3,6,8,5,7,1,4,2]=>1100100=>0010011
[2,4,1,7,5,3,8,6]=>[6,8,3,5,7,1,4,2]=>1110000=>0000111
[2,6,4,1,8,5,3,7]=>[7,3,5,8,1,4,6,2]=>1110000=>0000111
[5,4,8,2,1,6,3,7]=>[7,3,6,1,2,8,4,5]=>1011000=>0001101
[3,2,5,6,1,8,4,7]=>[7,4,8,1,6,5,2,3]=>1101100=>0011011
[4,8,3,2,6,1,5,7]=>[7,5,1,6,2,3,8,4]=>1101100=>0011011
[3,2,7,1,5,4,8,6]=>[6,8,4,5,1,7,2,3]=>1101000=>0001011
[3,8,2,5,1,6,7,4]=>[4,7,6,1,5,2,8,3]=>1110010=>0100111
[4,3,2,6,7,8,1,5]=>[5,1,8,7,6,2,3,4]=>1100011=>1100011
[4,3,7,8,2,6,1,5]=>[5,1,6,2,8,7,3,4]=>1110001=>1000111
[3,2,5,7,1,6,8,4]=>[4,8,6,1,7,5,2,3]=>1100110=>0110011
[6,3,2,7,1,5,4,8]=>[8,4,5,1,7,2,3,6]=>1101000=>0001011
[6,3,2,7,8,1,5,4]=>[4,5,1,8,7,2,3,6]=>1100001=>1000011
[6,5,2,1,7,8,4,3]=>[3,4,8,7,1,2,5,6]=>1000001=>1000001
[6,2,1,8,5,3,7,4]=>[4,7,3,5,8,1,2,6]=>1010000=>0000101
[6,3,2,1,4,7,8,5]=>[5,8,7,4,1,2,3,6]=>1001001=>1001001
[6,3,2,1,4,7,5,8]=>[8,5,7,4,1,2,3,6]=>1001100=>0011001
[3,5,2,1,7,8,4,6]=>[6,4,8,7,1,2,5,3]=>1011001=>1001101
[4,6,2,1,8,3,7,5]=>[5,7,3,8,1,2,6,4]=>1011000=>0001101
[3,2,7,1,4,8,6,5]=>[5,6,8,4,1,7,2,3]=>1101000=>0001011
[3,5,8,2,1,7,4,6]=>[6,4,7,1,2,8,5,3]=>1011100=>0011101
[4,8,3,7,2,1,5,6]=>[6,5,1,2,7,3,8,4]=>1011100=>0011101
[4,3,7,2,8,1,5,6]=>[6,5,1,8,2,7,3,4]=>1110100=>0010111
[4,8,3,2,7,1,5,6]=>[6,5,1,7,2,3,8,4]=>1101100=>0011011
[3,2,1,4,7,5,8,6]=>[6,8,5,7,4,1,2,3]=>1001100=>0011001
[4,8,3,2,1,5,6,7]=>[7,6,5,1,2,3,8,4]=>1001110=>0111001
[4,3,8,2,1,5,6,7]=>[7,6,5,1,2,8,3,4]=>1010110=>0110101
[6,2,3,1,5,4,8,7]=>[7,8,4,5,1,3,2,6]=>1101000=>0001011
[8,4,5,2,3,1,7,6]=>[6,7,1,3,2,5,4,8]=>1101000=>0001011
[8,2,5,3,4,1,7,6]=>[6,7,1,4,3,5,2,8]=>1110000=>0000111
[6,2,5,3,4,1,8,7]=>[7,8,1,4,3,5,2,6]=>1110000=>0000111
[6,4,5,1,3,2,8,7]=>[7,8,2,3,1,5,4,6]=>1101000=>0001011
[6,1,5,3,4,2,8,7]=>[7,8,2,4,3,5,1,6]=>1110000=>0000111
[8,3,7,2,4,1,6,5]=>[5,6,1,4,2,7,3,8]=>1110000=>0000111
[8,3,5,1,4,2,7,6]=>[6,7,2,4,1,5,3,8]=>1110000=>0000111
[8,4,5,1,3,2,7,6]=>[6,7,2,3,1,5,4,8]=>1101000=>0001011
[2,1,8,4,5,3,7,6]=>[6,7,3,5,4,8,1,2]=>1011000=>0001101
[8,1,7,3,4,2,6,5]=>[5,6,2,4,3,7,1,8]=>1110000=>0000111
[8,2,7,1,4,3,6,5]=>[5,6,3,4,1,7,2,8]=>1110000=>0000111
[8,2,7,3,4,1,6,5]=>[5,6,1,4,3,7,2,8]=>1110000=>0000111
[8,4,7,2,3,1,6,5]=>[5,6,1,3,2,7,4,8]=>1101000=>0001011
[8,2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2,8]=>1101000=>0001011
[4,2,3,1,8,5,7,6]=>[6,7,5,8,1,3,2,4]=>1100100=>0010011
[8,2,3,1,7,5,6,4]=>[4,6,5,7,1,3,2,8]=>1100100=>0010011
[8,6,7,1,3,2,5,4]=>[4,5,2,3,1,7,6,8]=>1100010=>0100011
[8,1,3,2,7,5,6,4]=>[4,6,5,7,2,3,1,8]=>1100100=>0010011
[2,1,8,5,7,3,6,4]=>[4,6,3,7,5,8,1,2]=>1010100=>0010101
[4,5,8,6,3,2,7,1]=>[1,7,2,3,6,8,5,4]=>0101100=>0011010
[1,5,8,7,3,6,2,4]=>[4,2,6,3,7,8,5,1]=>1110100=>0010111
[1,7,2,8,4,6,5,3]=>[3,5,6,4,8,2,7,1]=>1101000=>0001011
[6,7,2,8,4,1,5,3]=>[3,5,1,4,8,2,7,6]=>1100010=>0100011
[3,6,2,8,4,5,7,1]=>[1,7,5,4,8,2,6,3]=>0111100=>0011110
[2,6,1,8,4,5,7,3]=>[3,7,5,4,8,1,6,2]=>1101100=>0011011
[2,8,4,6,1,5,7,3]=>[3,7,5,1,6,4,8,2]=>1101100=>0011011
[6,3,1,8,4,5,7,2]=>[2,7,5,4,8,1,3,6]=>1001100=>0011001
[2,3,6,8,4,5,7,1]=>[1,7,5,4,8,6,3,2]=>0111110=>0111110
[6,3,7,8,4,1,5,2]=>[2,5,1,4,8,7,3,6]=>1010001=>1000101
[1,3,7,8,4,6,5,2]=>[2,5,6,4,8,7,3,1]=>1011001=>1001101
[3,6,7,8,4,2,5,1]=>[1,5,2,4,8,7,6,3]=>0110011=>1100110
[7,6,1,8,4,2,5,3]=>[3,5,2,4,8,1,6,7]=>1100000=>0000011
[2,8,3,7,1,6,5,4]=>[4,5,6,1,7,3,8,2]=>1110000=>0000111
[5,2,8,7,3,6,1,4]=>[4,1,6,3,7,8,2,5]=>1110000=>0000111
[7,2,1,8,4,6,5,3]=>[3,5,6,4,8,1,2,7]=>1001000=>0001001
[3,2,7,8,4,6,5,1]=>[1,5,6,4,8,7,2,3]=>0101001=>1001010
[5,2,7,8,1,4,6,3]=>[3,6,4,1,8,7,2,5]=>1101001=>1001011
[1,2,7,8,5,4,6,3]=>[3,6,4,5,8,7,2,1]=>1101001=>1001011
[7,2,5,8,3,4,6,1]=>[1,6,4,3,8,5,2,7]=>0111100=>0011110
[6,2,8,5,4,3,1,7]=>[7,1,3,4,5,8,2,6]=>1100000=>0000011
[2,8,3,5,4,1,6,7]=>[7,6,1,4,5,3,8,2]=>1110010=>0100111
[2,8,4,5,3,1,6,7]=>[7,6,1,3,5,4,8,2]=>1101010=>0101011
[7,3,5,8,2,4,6,1]=>[1,6,4,2,8,5,3,7]=>0111100=>0011110
[4,3,1,2,8,5,6,7]=>[7,6,5,8,2,1,3,4]=>1100110=>0110011
[2,7,6,8,4,3,5,1]=>[1,5,3,4,8,6,7,2]=>0110010=>0100110
[1,7,5,8,3,4,6,2]=>[2,6,4,3,8,5,7,1]=>1011100=>0011101
[4,6,8,5,1,3,2,7]=>[7,2,3,1,5,8,6,4]=>1101010=>0101011
[2,4,8,3,6,5,1,7]=>[7,1,5,6,3,8,4,2]=>1111000=>0001111
[4,1,8,3,5,6,2,7]=>[7,2,6,5,3,8,1,4]=>1110100=>0010111
[5,6,8,4,1,3,2,7]=>[7,2,3,1,4,8,6,5]=>1100110=>0110011
[4,6,8,1,5,3,2,7]=>[7,2,3,5,1,8,6,4]=>1101010=>0101011
[1,6,8,4,5,3,2,7]=>[7,2,3,5,4,8,6,1]=>1101010=>0101011
[1,7,3,8,5,4,6,2]=>[2,6,4,5,8,3,7,1]=>1011000=>0001101
[3,7,1,8,5,4,6,2]=>[2,6,4,5,8,1,7,3]=>1011000=>0001101
[2,7,3,8,4,6,5,1]=>[1,5,6,4,8,3,7,2]=>0111000=>0001110
[2,8,7,4,1,6,5,3]=>[3,5,6,1,4,7,8,2]=>1100000=>0000011
[2,8,5,4,3,1,6,7]=>[7,6,1,3,4,5,8,2]=>1100010=>0100011
[1,4,3,2,8,5,6,7]=>[7,6,5,8,2,3,4,1]=>1100110=>0110011
[7,3,2,8,5,4,6,1]=>[1,6,4,5,8,2,3,7]=>0101000=>0001010
[6,4,8,2,5,3,1,7]=>[7,1,3,5,2,8,4,6]=>1101000=>0001011
[2,8,4,3,5,1,6,7]=>[7,6,1,5,3,4,8,2]=>1110010=>0100111
[6,2,8,4,5,3,1,7]=>[7,1,3,5,4,8,2,6]=>1101000=>0001011
[7,2,3,8,5,4,6,1]=>[1,6,4,5,8,3,2,7]=>0111000=>0001110
[4,2,3,1,8,5,6,7]=>[7,6,5,8,1,3,2,4]=>1100110=>0110011
[5,1,3,2,4,8,6,7]=>[7,6,8,4,2,3,1,5]=>1101010=>0101011
[2,8,1,5,3,4,7,6]=>[6,7,4,3,5,1,8,2]=>1111000=>0001111
[1,4,2,8,5,3,6,7]=>[7,6,3,5,8,2,4,1]=>1110010=>0100111
[3,5,1,4,8,2,6,7]=>[7,6,2,8,4,1,5,3]=>1111010=>0101111
[1,5,2,8,4,3,6,7]=>[7,6,3,4,8,2,5,1]=>1110010=>0100111
[1,2,5,4,3,8,6,7]=>[7,6,8,3,4,5,2,1]=>1110010=>0100111
[1,2,4,8,5,3,7,6]=>[6,7,3,5,8,4,2,1]=>1111000=>0001111
[1,5,2,7,8,4,3,6]=>[6,3,4,8,7,2,5,1]=>1110001=>1000111
[5,1,2,7,4,8,3,6]=>[6,3,8,4,7,2,1,5]=>1111000=>0001111
[8,3,5,1,4,7,2,6]=>[6,2,7,4,1,5,3,8]=>1111000=>0001111
[1,2,8,5,7,4,3,6]=>[6,3,4,7,5,8,2,1]=>1110100=>0010111
[1,2,4,8,7,5,3,6]=>[6,3,5,7,8,4,2,1]=>1111000=>0001111
[2,8,1,4,3,7,6,5]=>[5,6,7,3,4,1,8,2]=>1110000=>0000111
[7,6,1,4,2,8,3,5]=>[5,3,8,2,4,1,6,7]=>1110000=>0000111
[7,1,6,2,8,4,3,5]=>[5,3,4,8,2,6,1,7]=>1110000=>0000111
[1,4,2,7,8,5,3,6]=>[6,3,5,8,7,2,4,1]=>1110001=>1000111
[6,1,2,8,4,3,7,5]=>[5,7,3,4,8,2,1,6]=>1110000=>0000111
[6,4,1,2,8,3,7,5]=>[5,7,3,8,2,1,4,6]=>1110000=>0000111
[7,6,1,3,2,4,8,5]=>[5,8,4,2,3,1,6,7]=>1101000=>0001011
[6,7,1,3,2,4,8,5]=>[5,8,4,2,3,1,7,6]=>1101010=>0101011
[1,2,7,3,5,8,4,6]=>[6,4,8,5,3,7,2,1]=>1111100=>0011111
[5,8,1,3,7,2,4,6]=>[6,4,2,7,3,1,8,5]=>1111100=>0011111
[1,2,5,8,7,3,4,6]=>[6,4,3,7,8,5,2,1]=>1111100=>0011111
[8,6,1,3,2,4,7,5]=>[5,7,4,2,3,1,6,8]=>1101000=>0001011
[4,2,8,1,7,3,6,5]=>[5,6,3,7,1,8,2,4]=>1110000=>0000111
[7,1,2,8,4,3,6,5]=>[5,6,3,4,8,2,1,7]=>1110000=>0000111
[1,2,8,4,7,5,3,6]=>[6,3,5,7,4,8,2,1]=>1111000=>0001111
[1,2,8,7,4,5,3,6]=>[6,3,5,4,7,8,2,1]=>1111000=>0001111
[2,8,1,7,5,3,4,6]=>[6,4,3,5,7,1,8,2]=>1111000=>0001111
[8,3,7,1,5,2,4,6]=>[6,4,2,5,1,7,3,8]=>1111000=>0001111
[8,6,1,4,2,7,3,5]=>[5,3,7,2,4,1,6,8]=>1110000=>0000111
[7,1,2,8,6,4,3,5]=>[5,3,4,6,8,2,1,7]=>1110000=>0000111
[3,7,4,8,1,6,2,5]=>[5,2,6,1,8,4,7,3]=>1111000=>0001111
[3,4,8,7,1,6,2,5]=>[5,2,6,1,7,8,4,3]=>1111000=>0001111
[4,2,8,1,7,6,3,5]=>[5,3,6,7,1,8,2,4]=>1110000=>0000111
[2,8,1,7,6,4,3,5]=>[5,3,4,6,7,1,8,2]=>1110000=>0000111
[7,8,3,4,1,5,2,6]=>[6,2,5,1,4,3,8,7]=>1110001=>1000111
[6,8,3,4,1,7,2,5]=>[5,2,7,1,4,3,8,6]=>1110010=>0100111
[5,7,3,4,1,8,2,6]=>[6,2,8,1,4,3,7,5]=>1110100=>0010111
[5,8,3,4,1,7,2,6]=>[6,2,7,1,4,3,8,5]=>1110100=>0010111
[4,7,3,5,1,6,2,8]=>[8,2,6,1,5,3,7,4]=>1111000=>0001111
[4,8,3,5,1,6,2,7]=>[7,2,6,1,5,3,8,4]=>1111000=>0001111
[4,8,3,5,1,7,2,6]=>[6,2,7,1,5,3,8,4]=>1111000=>0001111
[4,7,3,5,1,8,2,6]=>[6,2,8,1,5,3,7,4]=>1111000=>0001111
[5,6,2,3,1,7,4,8]=>[8,4,7,1,3,2,6,5]=>1101100=>0011011
[5,6,2,4,1,8,3,7]=>[7,3,8,1,4,2,6,5]=>1110100=>0010111
[5,6,2,4,1,7,3,8]=>[8,3,7,1,4,2,6,5]=>1110100=>0010111
[4,6,2,5,1,7,3,8]=>[8,3,7,1,5,2,6,4]=>1111000=>0001111
[4,6,2,5,1,8,3,7]=>[7,3,8,1,5,2,6,4]=>1111000=>0001111
[4,5,1,8,3,7,2,6]=>[6,2,7,3,8,1,5,4]=>1111000=>0001111
[4,6,2,7,3,8,1,5]=>[5,1,8,3,7,2,6,4]=>1111000=>0001111
[5,6,2,7,3,8,1,4]=>[4,1,8,3,7,2,6,5]=>1110100=>0010111
[5,6,2,8,4,7,1,3]=>[3,1,7,4,8,2,6,5]=>1101100=>0011011
[5,6,2,8,3,7,1,4]=>[4,1,7,3,8,2,6,5]=>1110100=>0010111
[4,6,2,8,3,7,1,5]=>[5,1,7,3,8,2,6,4]=>1111000=>0001111
[4,5,1,8,3,6,2,7]=>[7,2,6,3,8,1,5,4]=>1111000=>0001111
[6,5,3,2,1,4,8,7]=>[7,8,4,1,2,3,5,6]=>1001000=>0001001
[8,7,3,5,2,4,1,6]=>[6,1,4,2,5,3,7,8]=>1110000=>0000111
[6,8,2,4,5,7,3,1]=>[1,3,7,5,4,2,8,6]=>0101110=>0111010
[3,6,1,4,5,2,8,7]=>[7,8,2,5,4,1,6,3]=>1111000=>0001111
[8,3,7,4,5,2,1,6]=>[6,1,2,5,4,7,3,8]=>1011000=>0001101
[6,3,8,4,5,7,2,1]=>[1,2,7,5,4,8,3,6]=>0011100=>0011100
[8,1,7,4,3,6,2,5]=>[5,2,6,3,4,7,1,8]=>1110000=>0000111
[8,7,3,5,1,4,2,6]=>[6,2,4,1,5,3,7,8]=>1110000=>0000111
[2,1,6,8,5,7,4,3]=>[3,4,7,5,8,6,1,2]=>1000110=>0110001
[6,8,3,5,1,7,4,2]=>[2,4,7,1,5,3,8,6]=>1010010=>0100101
[2,5,8,4,7,6,3,1]=>[1,3,6,7,4,8,5,2]=>0101100=>0011010
[4,3,8,1,5,6,7,2]=>[2,7,6,5,1,8,3,4]=>1010110=>0110101
[4,8,3,6,1,2,7,5]=>[5,7,2,1,6,3,8,4]=>1111000=>0001111
[3,8,7,4,1,6,2,5]=>[5,2,6,1,4,7,8,3]=>1110000=>0000111
[3,8,1,2,5,6,7,4]=>[4,7,6,5,2,1,8,3]=>1110110=>0110111
[2,8,7,4,5,1,3,6]=>[6,3,1,5,4,7,8,2]=>1111000=>0001111
[8,7,2,4,1,6,3,5]=>[5,3,6,1,4,2,7,8]=>1110000=>0000111
[5,8,3,6,2,4,7,1]=>[1,7,4,2,6,3,8,5]=>0111100=>0011110
[8,6,3,2,1,4,7,5]=>[5,7,4,1,2,3,6,8]=>1001000=>0001001
[8,7,3,5,2,1,4,6]=>[6,4,1,2,5,3,7,8]=>1011000=>0001101
[5,8,3,6,2,1,7,4]=>[4,7,1,2,6,3,8,5]=>1010100=>0010101
[6,1,8,4,5,7,2,3]=>[3,2,7,5,4,8,1,6]=>1101100=>0011011
[6,8,3,5,1,7,2,4]=>[4,2,7,1,5,3,8,6]=>1110010=>0100111
[5,8,3,6,1,2,7,4]=>[4,7,2,1,6,3,8,5]=>1110100=>0010111
[5,8,1,4,7,6,2,3]=>[3,2,6,7,4,1,8,5]=>1101100=>0011011
[4,5,3,8,6,1,7,2]=>[2,7,1,6,8,3,5,4]=>1011000=>0001101
[4,5,7,6,2,3,8,1]=>[1,8,3,2,6,7,5,4]=>0111100=>0011110
[3,5,7,2,6,4,8,1]=>[1,8,4,6,2,7,5,3]=>0111100=>0011110
[2,5,7,3,6,4,8,1]=>[1,8,4,6,3,7,5,2]=>0111100=>0011110
[8,4,3,7,6,1,5,2]=>[2,5,1,6,7,3,4,8]=>1010000=>0000101
[6,7,2,3,5,4,8,1]=>[1,8,4,5,3,2,7,6]=>0111010=>0101110
[5,2,7,3,6,4,8,1]=>[1,8,4,6,3,7,2,5]=>0111000=>0001110
[8,3,4,7,6,1,5,2]=>[2,5,1,6,7,4,3,8]=>1011000=>0001101
[8,2,4,7,1,6,5,3]=>[3,5,6,1,7,4,2,8]=>1101000=>0001011
[3,1,4,7,6,8,5,2]=>[2,5,8,6,7,4,1,3]=>1001010=>0101001
[5,1,7,3,6,8,4,2]=>[2,4,8,6,3,7,1,5]=>1010010=>0100101
[6,7,1,3,5,8,4,2]=>[2,4,8,5,3,1,7,6]=>1010110=>0110101
[4,8,3,7,6,1,5,2]=>[2,5,1,6,7,3,8,4]=>1011000=>0001101
[2,8,4,7,1,6,5,3]=>[3,5,6,1,7,4,8,2]=>1101000=>0001011
[8,1,4,7,2,6,5,3]=>[3,5,6,2,7,4,1,8]=>1101000=>0001011
[8,1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1,8]=>1100000=>0000011
[2,8,3,1,7,6,5,4]=>[4,5,6,7,1,3,8,2]=>1100000=>0000011
[6,7,1,2,8,5,4,3]=>[3,4,5,8,2,1,7,6]=>1100010=>0100011
[8,2,3,1,7,6,5,4]=>[4,5,6,7,1,3,2,8]=>1100000=>0000011
[1,4,2,7,8,6,5,3]=>[3,5,6,8,7,2,4,1]=>1100001=>1000011
[8,4,2,7,1,6,5,3]=>[3,5,6,1,7,2,4,8]=>1100000=>0000011
[8,5,7,2,1,6,4,3]=>[3,4,6,1,2,7,5,8]=>1000100=>0010001
[1,5,7,2,8,6,4,3]=>[3,4,6,8,2,7,5,1]=>1100100=>0010011
[3,5,7,1,6,8,4,2]=>[2,4,8,6,1,7,5,3]=>1010110=>0110101
[6,7,4,5,8,1,3,2]=>[2,3,1,8,5,4,7,6]=>1001110=>0111001
[2,5,7,8,1,6,4,3]=>[3,4,6,1,8,7,5,2]=>1100101=>1010011
[8,5,7,1,2,6,4,3]=>[3,4,6,2,1,7,5,8]=>1100100=>0010011
[8,4,1,7,2,6,5,3]=>[3,5,6,2,7,1,4,8]=>1100000=>0000011
[6,7,2,8,1,5,4,3]=>[3,4,5,1,8,2,7,6]=>1100010=>0100011
[5,2,7,8,1,6,4,3]=>[3,4,6,1,8,7,2,5]=>1100001=>1000011
[4,2,8,7,1,6,5,3]=>[3,5,6,1,7,8,2,4]=>1100000=>0000011
[1,3,8,2,7,6,5,4]=>[4,5,6,7,2,8,3,1]=>1110000=>0000111
[8,3,1,2,7,6,5,4]=>[4,5,6,7,2,1,3,8]=>1100000=>0000011
[8,2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2,8]=>1010000=>0000101
[2,1,8,3,7,6,5,4]=>[4,5,6,7,3,8,1,2]=>1010000=>0000101
[5,1,7,8,2,6,4,3]=>[3,4,6,2,8,7,1,5]=>1100001=>1000011
[6,7,1,8,2,5,4,3]=>[3,4,5,2,8,1,7,6]=>1100010=>0100011
[4,8,1,7,2,6,5,3]=>[3,5,6,2,7,1,8,4]=>1101000=>0001011
[3,8,1,2,7,6,5,4]=>[4,5,6,7,2,1,8,3]=>1110000=>0000111
[1,8,2,3,7,6,5,4]=>[4,5,6,7,3,2,8,1]=>1110000=>0000111
[3,7,1,5,8,2,6,4]=>[4,6,2,8,5,1,7,3]=>1110100=>0010111
[2,6,5,1,8,3,7,4]=>[4,7,3,8,1,5,6,2]=>1110000=>0000111
[5,6,4,1,8,7,2,3]=>[3,2,7,8,1,4,6,5]=>1100100=>0010011
[8,1,4,5,7,6,2,3]=>[3,2,6,7,5,4,1,8]=>1101100=>0011011
[6,4,5,1,8,7,2,3]=>[3,2,7,8,1,5,4,6]=>1101000=>0001011
[5,4,6,1,8,7,2,3]=>[3,2,7,8,1,6,4,5]=>1101000=>0001011
[3,5,6,1,8,2,7,4]=>[4,7,2,8,1,6,5,3]=>1110100=>0010111
[2,5,6,1,8,3,7,4]=>[4,7,3,8,1,6,5,2]=>1110100=>0010111
[2,4,6,1,3,8,7,5]=>[5,7,8,3,1,6,4,2]=>1111000=>0001111
[3,4,6,1,2,8,7,5]=>[5,7,8,2,1,6,4,3]=>1111000=>0001111
[5,3,6,1,8,2,7,4]=>[4,7,2,8,1,6,3,5]=>1110000=>0000111
[7,3,1,5,8,2,6,4]=>[4,6,2,8,5,1,3,7]=>1100100=>0010011
[8,1,3,5,7,2,6,4]=>[4,6,2,7,5,3,1,8]=>1110100=>0010111
[8,1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1,8]=>1110100=>0010111
[7,2,1,5,8,3,6,4]=>[4,6,3,8,5,1,2,7]=>1010100=>0010101
[6,2,5,1,8,3,7,4]=>[4,7,3,8,1,5,2,6]=>1110000=>0000111
[4,2,6,1,3,8,7,5]=>[5,7,8,3,1,6,2,4]=>1110000=>0000111
[4,2,5,3,1,8,7,6]=>[6,7,8,1,3,5,2,4]=>1100000=>0000011
[6,2,4,1,3,8,7,5]=>[5,7,8,3,1,4,2,6]=>1110000=>0000111
[7,2,1,4,3,8,6,5]=>[5,6,8,3,4,1,2,7]=>1010000=>0000101
[8,1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1,8]=>1110000=>0000111
[8,1,3,4,2,7,6,5]=>[5,6,7,2,4,3,1,8]=>1110000=>0000111
[4,6,3,1,2,8,7,5]=>[5,7,8,2,1,3,6,4]=>1101000=>0001011
[2,6,4,1,3,8,7,5]=>[5,7,8,3,1,4,6,2]=>1110000=>0000111
[2,7,1,4,3,8,6,5]=>[5,6,8,3,4,1,7,2]=>1110000=>0000111
[8,1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1,8]=>1110010=>0100111
[4,7,1,2,3,8,6,5]=>[5,6,8,3,2,1,7,4]=>1111000=>0001111
[3,7,1,2,4,8,6,5]=>[5,6,8,4,2,1,7,3]=>1111000=>0001111
[2,6,3,1,4,8,7,5]=>[5,7,8,4,1,3,6,2]=>1101000=>0001011
[3,6,2,1,4,8,7,5]=>[5,7,8,4,1,2,6,3]=>1011000=>0001101
[5,6,2,1,8,3,7,4]=>[4,7,3,8,1,2,6,5]=>1010100=>0010101
[6,5,2,1,8,3,7,4]=>[4,7,3,8,1,2,5,6]=>1010000=>0000101
[8,1,4,2,3,7,6,5]=>[5,6,7,3,2,4,1,8]=>1110000=>0000111
[5,4,2,3,1,8,7,6]=>[6,7,8,1,3,2,4,5]=>1100000=>0000011
[3,5,2,4,1,8,7,6]=>[6,7,8,1,4,2,5,3]=>1110000=>0000111
[7,3,1,2,4,8,6,5]=>[5,6,8,4,2,1,3,7]=>1101000=>0001011
[8,1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1,8]=>1101000=>0001011
[7,2,1,3,4,8,6,5]=>[5,6,8,4,3,1,2,7]=>1011000=>0001101
[2,4,3,6,1,5,8,7]=>[7,8,5,1,6,3,4,2]=>1110100=>0010111
[2,4,3,6,5,8,1,7]=>[7,1,8,5,6,3,4,2]=>1110100=>0010111
[2,4,6,3,5,8,7,1]=>[1,7,8,5,3,6,4,2]=>0111100=>0011110
[2,4,6,3,5,1,8,7]=>[7,8,1,5,3,6,4,2]=>1111000=>0001111
[2,4,6,3,1,5,8,7]=>[7,8,5,1,3,6,4,2]=>1101100=>0011011
[2,4,1,6,5,3,8,7]=>[7,8,3,5,6,1,4,2]=>1110000=>0000111
[2,4,6,1,5,3,8,7]=>[7,8,3,5,1,6,4,2]=>1111000=>0001111
[4,2,6,5,3,1,8,7]=>[7,8,1,3,5,6,2,4]=>1100000=>0000011
[4,2,6,5,1,3,8,7]=>[7,8,3,1,5,6,2,4]=>1110000=>0000111
[4,2,6,5,8,1,7,3]=>[3,7,1,8,5,6,2,4]=>1100100=>0010011
[4,2,6,5,8,1,3,7]=>[7,3,1,8,5,6,2,4]=>1110100=>0010111
[4,2,6,5,8,3,1,7]=>[7,1,3,8,5,6,2,4]=>1100100=>0010011
[2,4,1,6,5,8,3,7]=>[7,3,8,5,6,1,4,2]=>1110100=>0010111
[2,1,4,6,5,8,3,7]=>[7,3,8,5,6,4,1,2]=>1011100=>0011101
[2,4,1,6,5,8,7,3]=>[3,7,8,5,6,1,4,2]=>1100100=>0010011
[2,4,6,1,5,8,7,3]=>[3,7,8,5,1,6,4,2]=>1101100=>0011011
[4,2,6,5,3,8,7,1]=>[1,7,8,3,5,6,2,4]=>0110000=>0000110
[2,6,4,3,8,7,5,1]=>[1,5,7,8,3,4,6,2]=>0110000=>0000110
[4,2,6,8,5,3,7,1]=>[1,7,3,5,8,6,2,4]=>0110010=>0100110
[2,4,6,8,1,5,7,3]=>[3,7,5,1,8,6,4,2]=>1101110=>0111011
[2,4,1,6,8,5,7,3]=>[3,7,5,8,6,1,4,2]=>1100110=>0110011
[2,1,4,6,8,5,3,7]=>[7,3,5,8,6,4,1,2]=>1011010=>0101101
[2,4,6,1,8,5,3,7]=>[7,3,5,8,1,6,4,2]=>1111000=>0001111
[2,4,6,8,1,5,3,7]=>[7,3,5,1,8,6,4,2]=>1111010=>0101111
[2,4,6,8,3,5,7,1]=>[1,7,5,3,8,6,4,2]=>0111110=>0111110
[2,4,6,8,3,1,5,7]=>[7,5,1,3,8,6,4,2]=>1101110=>0111011
[2,4,6,3,8,5,7,1]=>[1,7,5,8,3,6,4,2]=>0111100=>0011110
[2,4,3,6,8,5,7,1]=>[1,7,5,8,6,3,4,2]=>0110110=>0110110
[2,4,3,6,8,5,1,7]=>[7,1,5,8,6,3,4,2]=>1110010=>0100111
[2,4,3,6,8,1,5,7]=>[7,5,1,8,6,3,4,2]=>1110110=>0110111
[2,4,3,6,1,8,5,7]=>[7,5,8,1,6,3,4,2]=>1110100=>0010111
[2,4,3,1,6,8,5,7]=>[7,5,8,6,1,3,4,2]=>1100110=>0110011
[2,4,1,3,6,8,7,5]=>[5,7,8,6,3,1,4,2]=>1110010=>0100111
[2,4,3,6,8,1,7,5]=>[5,7,1,8,6,3,4,2]=>1110010=>0100111
[4,6,5,2,8,7,1,3]=>[3,1,7,8,2,5,6,4]=>1101000=>0001011
[4,6,2,5,8,7,1,3]=>[3,1,7,8,5,2,6,4]=>1101100=>0011011
[4,6,2,5,8,7,3,1]=>[1,3,7,8,5,2,6,4]=>0101100=>0011010
[2,4,6,3,1,8,7,5]=>[5,7,8,1,3,6,4,2]=>1101000=>0001011
[2,4,1,6,3,8,7,5]=>[5,7,8,3,6,1,4,2]=>1110000=>0000111
[2,1,4,6,3,8,7,5]=>[5,7,8,3,6,4,1,2]=>1011000=>0001101
[2,4,1,6,8,3,7,5]=>[5,7,3,8,6,1,4,2]=>1110010=>0100111
[2,4,6,8,1,3,7,5]=>[5,7,3,1,8,6,4,2]=>1111010=>0101111
[4,6,2,8,5,7,3,1]=>[1,3,7,5,8,2,6,4]=>0101100=>0011010
[4,6,2,8,5,7,1,3]=>[3,1,7,5,8,2,6,4]=>1101100=>0011011
[6,2,4,8,7,1,3,5]=>[5,3,1,7,8,4,2,6]=>1111000=>0001111
[2,6,4,8,1,7,5,3]=>[3,5,7,1,8,4,6,2]=>1101000=>0001011
[2,6,4,1,8,7,5,3]=>[3,5,7,8,1,4,6,2]=>1100000=>0000011
[2,1,6,4,8,7,3,5]=>[5,3,7,8,4,6,1,2]=>1011000=>0001101
[2,6,4,1,8,7,3,5]=>[5,3,7,8,1,4,6,2]=>1110000=>0000111
[2,6,4,8,1,7,3,5]=>[5,3,7,1,8,4,6,2]=>1111000=>0001111
[6,2,4,8,7,3,5,1]=>[1,5,3,7,8,4,2,6]=>0111000=>0001110
[6,2,4,8,7,3,1,5]=>[5,1,3,7,8,4,2,6]=>1101000=>0001011
[1,3,7,4,5,8,2,6]=>[6,2,8,5,4,7,3,1]=>1111100=>0011111
[1,7,6,3,4,8,2,5]=>[5,2,8,4,3,6,7,1]=>1111000=>0001111
[8,1,6,3,7,2,4,5]=>[5,4,2,7,3,6,1,8]=>1111000=>0001111
[1,2,7,4,8,3,5,6]=>[6,5,3,8,4,7,2,1]=>1111100=>0011111
[6,1,7,3,4,8,2,5]=>[5,2,8,4,3,7,1,6]=>1111000=>0001111
[2,1,7,4,5,8,3,6]=>[6,3,8,5,4,7,1,2]=>1011100=>0011101
[5,1,4,7,3,8,2,6]=>[6,2,8,3,7,4,1,5]=>1111000=>0001111
[4,3,1,7,5,8,2,6]=>[6,2,8,5,7,1,3,4]=>1100100=>0010011
[2,8,6,3,7,1,4,5]=>[5,4,1,7,3,6,8,2]=>1111000=>0001111
[6,8,1,3,7,2,4,5]=>[5,4,2,7,3,1,8,6]=>1111010=>0101111
[5,8,2,1,7,3,4,6]=>[6,4,3,7,1,2,8,5]=>1011100=>0011101
[5,7,2,1,8,3,4,6]=>[6,4,3,8,1,2,7,5]=>1011100=>0011101
[6,7,1,3,8,2,4,5]=>[5,4,2,8,3,1,7,6]=>1111010=>0101111
[8,5,1,3,7,2,4,6]=>[6,4,2,7,3,1,5,8]=>1111000=>0001111
[1,5,3,2,8,4,6,7]=>[7,6,4,8,2,3,5,1]=>1101010=>0101011
[2,6,4,8,7,1,3,5]=>[5,3,1,7,8,4,6,2]=>1111000=>0001111
[1,6,4,8,7,2,3,5]=>[5,3,2,7,8,4,6,1]=>1111000=>0001111
[4,3,2,8,7,1,5,6]=>[6,5,1,7,8,2,3,4]=>1100100=>0010011
[5,2,4,8,7,1,3,6]=>[6,3,1,7,8,4,2,5]=>1111000=>0001111
[6,2,8,3,7,1,4,5]=>[5,4,1,7,3,8,2,6]=>1111000=>0001111
[5,1,4,8,7,2,3,6]=>[6,3,2,7,8,4,1,5]=>1111000=>0001111
[3,7,2,1,5,4,8,6]=>[6,8,4,5,1,2,7,3]=>1011000=>0001101
[3,8,2,1,5,4,7,6]=>[6,7,4,5,1,2,8,3]=>1011000=>0001101
[8,3,2,1,6,4,5,7]=>[7,5,4,6,1,2,3,8]=>1001100=>0011001
[8,4,2,5,1,6,3,7]=>[7,3,6,1,5,2,4,8]=>1110000=>0000111
[8,3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3,8]=>1001100=>0011001
[3,8,2,1,4,5,7,6]=>[6,7,5,4,1,2,8,3]=>1011100=>0011101
[3,2,7,1,4,6,8,5]=>[5,8,6,4,1,7,2,3]=>1101010=>0101011
[3,2,8,1,4,6,7,5]=>[5,7,6,4,1,8,2,3]=>1101010=>0101011
[3,8,2,1,4,7,5,6]=>[6,5,7,4,1,2,8,3]=>1011100=>0011101
[3,8,2,1,5,7,4,6]=>[6,4,7,5,1,2,8,3]=>1011100=>0011101
[4,8,2,5,1,7,3,6]=>[6,3,7,1,5,2,8,4]=>1111000=>0001111
[3,7,2,1,5,8,4,6]=>[6,4,8,5,1,2,7,3]=>1011100=>0011101
[3,7,2,1,4,8,5,6]=>[6,5,8,4,1,2,7,3]=>1011100=>0011101
[4,2,7,6,1,8,3,5]=>[5,3,8,1,6,7,2,4]=>1110000=>0000111
[4,3,7,6,8,1,2,5]=>[5,2,1,8,6,7,3,4]=>1110010=>0100111
[3,2,8,1,6,4,7,5]=>[5,7,4,6,1,8,2,3]=>1101000=>0001011
[3,2,7,1,6,4,8,5]=>[5,8,4,6,1,7,2,3]=>1101000=>0001011
[4,2,7,6,1,3,8,5]=>[5,8,3,1,6,7,2,4]=>1110000=>0000111
[4,2,8,6,1,3,7,5]=>[5,7,3,1,6,8,2,4]=>1110000=>0000111
[5,7,8,3,4,1,2,6]=>[6,2,1,4,3,8,7,5]=>1110101=>1010111
[4,2,6,8,1,3,7,5]=>[5,7,3,1,8,6,2,4]=>1110010=>0100111
[4,2,6,7,1,3,8,5]=>[5,8,3,1,7,6,2,4]=>1110010=>0100111
[3,2,6,1,8,4,7,5]=>[5,7,4,8,1,6,2,3]=>1101000=>0001011
[3,7,2,1,8,5,4,6]=>[6,4,5,8,1,2,7,3]=>1011000=>0001101
[4,7,3,8,5,1,2,6]=>[6,2,1,5,8,3,7,4]=>1111000=>0001111
[4,3,7,8,6,1,2,5]=>[5,2,1,6,8,7,3,4]=>1110001=>1000111
[3,2,7,1,8,6,4,5]=>[5,4,6,8,1,7,2,3]=>1101000=>0001011
[3,2,1,6,8,5,7,4]=>[4,7,5,8,6,1,2,3]=>1000110=>0110001
[3,2,6,1,8,7,4,5]=>[5,4,7,8,1,6,2,3]=>1101000=>0001011
[4,2,6,8,1,7,3,5]=>[5,3,7,1,8,6,2,4]=>1110010=>0100111
[4,3,6,8,7,1,2,5]=>[5,2,1,7,8,6,3,4]=>1110010=>0100111
[4,2,6,7,1,8,3,5]=>[5,3,8,1,7,6,2,4]=>1110010=>0100111
[3,2,6,1,7,8,4,5]=>[5,4,8,7,1,6,2,3]=>1101001=>1001011
[1,4,6,2,7,8,5,3]=>[3,5,8,7,2,6,4,1]=>1101001=>1001011
[3,1,8,5,4,2,6,7]=>[7,6,2,4,5,8,1,3]=>1100010=>0100011
[1,2,7,5,4,8,6,3]=>[3,6,8,4,5,7,2,1]=>1101000=>0001011
[6,3,7,5,4,8,1,2]=>[2,1,8,4,5,7,3,6]=>1011000=>0001101
[1,6,2,5,4,8,7,3]=>[3,7,8,4,5,2,6,1]=>1101000=>0001011
[1,8,2,5,7,3,6,4]=>[4,6,3,7,5,2,8,1]=>1110100=>0010111
[6,2,1,5,4,8,7,3]=>[3,7,8,4,5,1,2,6]=>1001000=>0001001
[4,1,6,2,8,7,5,3]=>[3,5,7,8,2,6,1,4]=>1100000=>0000011
[4,3,6,1,8,2,7,5]=>[5,7,2,8,1,6,3,4]=>1110000=>0000111
[7,8,5,1,6,3,2,4]=>[4,2,3,6,1,5,8,7]=>1100001=>1000011
[5,1,7,6,4,3,2,8]=>[8,2,3,4,6,7,1,5]=>1100000=>0000011
[7,2,1,5,4,6,8,3]=>[3,8,6,4,5,1,2,7]=>1001010=>0101001
[6,1,2,5,7,3,8,4]=>[4,8,3,7,5,2,1,6]=>1110100=>0010111
[1,3,6,8,5,7,2,4]=>[4,2,7,5,8,6,3,1]=>1110110=>0110111
[4,1,6,7,3,8,2,5]=>[5,2,8,3,7,6,1,4]=>1110010=>0100111
[5,4,6,1,3,7,2,8]=>[8,2,7,3,1,6,4,5]=>1111000=>0001111
[2,8,3,5,4,1,7,6]=>[6,7,1,4,5,3,8,2]=>1110000=>0000111
[7,8,1,4,6,3,2,5]=>[5,2,3,6,4,1,8,7]=>1101001=>1001011
[5,1,8,7,4,3,2,6]=>[6,2,3,4,7,8,1,5]=>1100000=>0000011
[6,5,1,8,4,3,2,7]=>[7,2,3,4,8,1,5,6]=>1100000=>0000011
[1,6,5,8,4,3,2,7]=>[7,2,3,4,8,5,6,1]=>1100100=>0010011
[3,6,2,5,4,1,7,8]=>[8,7,1,4,5,2,6,3]=>1110001=>1000111
[6,1,2,5,4,7,8,3]=>[3,8,7,4,5,2,1,6]=>1101001=>1001011
[6,2,4,5,1,3,7,8]=>[8,7,3,1,5,4,2,6]=>1111001=>1001111
[4,2,8,5,1,3,7,6]=>[6,7,3,1,5,8,2,4]=>1110000=>0000111
[4,3,6,8,1,7,2,5]=>[5,2,7,1,8,6,3,4]=>1110010=>0100111
[5,3,6,4,1,7,2,8]=>[8,2,7,1,4,6,3,5]=>1110000=>0000111
[4,6,7,2,5,8,1,3]=>[3,1,8,5,2,7,6,4]=>1101110=>0111011
[2,5,4,1,6,7,3,8]=>[8,3,7,6,1,4,5,2]=>1110010=>0100111
[7,3,2,8,5,1,6,4]=>[4,6,1,5,8,2,3,7]=>1100000=>0000011
[6,3,7,2,5,1,8,4]=>[4,8,1,5,2,7,3,6]=>1110000=>0000111
[6,7,8,3,5,2,1,4]=>[4,1,2,5,3,8,7,6]=>1010011=>1100101
[2,1,5,7,8,6,3,4]=>[4,3,6,8,7,5,1,2]=>1010101=>1010101
[3,2,6,1,7,4,5,8]=>[8,5,4,7,1,6,2,3]=>1101100=>0011011
[2,5,8,4,1,3,7,6]=>[6,7,3,1,4,8,5,2]=>1110100=>0010111
[8,3,5,2,1,4,7,6]=>[6,7,4,1,2,5,3,8]=>1011000=>0001101
[2,7,6,5,1,8,3,4]=>[4,3,8,1,5,6,7,2]=>1110000=>0000111
[2,7,6,5,1,8,4,3]=>[3,4,8,1,5,6,7,2]=>1100000=>0000011
[2,3,6,5,1,4,8,7]=>[7,8,4,1,5,6,3,2]=>1111000=>0001111
[2,3,6,4,1,5,8,7]=>[7,8,5,1,4,6,3,2]=>1110100=>0010111
[2,7,6,1,4,8,5,3]=>[3,5,8,4,1,6,7,2]=>1101000=>0001011
[7,3,5,1,8,4,2,6]=>[6,2,4,8,1,5,3,7]=>1110000=>0000111
[2,7,6,1,5,8,4,3]=>[3,4,8,5,1,6,7,2]=>1100100=>0010011
[2,7,6,4,1,8,5,3]=>[3,5,8,1,4,6,7,2]=>1100000=>0000011
[2,7,6,4,1,8,3,5]=>[5,3,8,1,4,6,7,2]=>1110000=>0000111
[7,3,5,1,8,6,2,4]=>[4,2,6,8,1,5,3,7]=>1110000=>0000111
[2,3,4,8,7,6,1,5]=>[5,1,6,7,8,4,3,2]=>1111000=>0001111
[2,3,4,8,5,7,1,6]=>[6,1,7,5,8,4,3,2]=>1111100=>0011111
[7,3,5,4,8,1,2,6]=>[6,2,1,8,4,5,3,7]=>1111000=>0001111
[6,4,3,5,8,7,2,1]=>[1,2,7,8,5,3,4,6]=>0010100=>0010100
[2,1,4,5,8,7,3,6]=>[6,3,7,8,5,4,1,2]=>1011100=>0011101
[6,4,3,5,8,7,1,2]=>[2,1,7,8,5,3,4,6]=>1010100=>0010101
[2,3,4,8,7,5,1,6]=>[6,1,5,7,8,4,3,2]=>1111000=>0001111
[2,7,6,5,4,8,1,3]=>[3,1,8,4,5,6,7,2]=>1101000=>0001011
[7,3,5,6,8,1,2,4]=>[4,2,1,8,6,5,3,7]=>1110110=>0110111
[6,4,1,5,8,7,2,3]=>[3,2,7,8,5,1,4,6]=>1100100=>0010011
[6,4,1,5,8,7,3,2]=>[2,3,7,8,5,1,4,6]=>1000100=>0010001
[6,4,1,5,8,3,7,2]=>[2,7,3,8,5,1,4,6]=>1010100=>0010101
[5,7,1,6,3,8,2,4]=>[4,2,8,3,6,1,7,5]=>1110100=>0010111
[6,4,1,5,8,3,2,7]=>[7,2,3,8,5,1,4,6]=>1100100=>0010011
[6,3,5,7,8,2,1,4]=>[4,1,2,8,7,5,3,6]=>1010101=>1010101
[5,7,3,6,1,8,4,2]=>[2,4,8,1,6,3,7,5]=>1010100=>0010101
[7,3,5,4,8,6,2,1]=>[1,2,6,8,4,5,3,7]=>0011000=>0001100
[2,3,4,8,5,6,1,7]=>[7,1,6,5,8,4,3,2]=>1111100=>0011111
[2,3,4,8,7,1,6,5]=>[5,6,1,7,8,4,3,2]=>1111000=>0001111
[2,3,4,8,5,1,7,6]=>[6,7,1,5,8,4,3,2]=>1111000=>0001111
[7,4,3,5,8,2,1,6]=>[6,1,2,8,5,3,4,7]=>1010100=>0010101
[7,4,3,5,8,2,6,1]=>[1,6,2,8,5,3,4,7]=>0110100=>0010110
[6,3,5,4,8,2,1,7]=>[7,1,2,8,4,5,3,6]=>1011000=>0001101
[2,3,4,8,5,1,6,7]=>[7,6,1,5,8,4,3,2]=>1111010=>0101111
[6,1,4,2,8,5,7,3]=>[3,7,5,8,2,4,1,6]=>1100100=>0010011
[4,8,6,5,3,2,7,1]=>[1,7,2,3,5,6,8,4]=>0101000=>0001010
[8,6,5,1,2,4,7,3]=>[3,7,4,2,1,5,6,8]=>1101000=>0001011
[1,7,5,8,2,6,4,3]=>[3,4,6,2,8,5,7,1]=>1100100=>0010011
[1,3,8,5,7,6,2,4]=>[4,2,6,7,5,8,3,1]=>1110100=>0010111
[6,3,8,5,7,1,2,4]=>[4,2,1,7,5,8,3,6]=>1110100=>0010111
[6,8,5,2,1,4,7,3]=>[3,7,4,1,2,5,8,6]=>1001010=>0101001
[3,8,2,5,6,1,7,4]=>[4,7,1,6,5,2,8,3]=>1110100=>0010111
[8,1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1,8]=>1110100=>0010111
[8,6,1,5,7,2,3,4]=>[4,3,2,7,5,1,6,8]=>1110100=>0010111
[3,8,6,5,7,1,2,4]=>[4,2,1,7,5,6,8,3]=>1110100=>0010111
[5,1,7,6,8,4,2,3]=>[3,2,4,8,6,7,1,5]=>1100010=>0100011
[5,1,3,7,8,6,2,4]=>[4,2,6,8,7,3,1,5]=>1110001=>1000111
[7,2,5,8,1,6,4,3]=>[3,4,6,1,8,5,2,7]=>1100100=>0010011
[3,2,8,5,7,6,1,4]=>[4,1,6,7,5,8,2,3]=>1100100=>0010011
[8,2,1,5,7,6,3,4]=>[4,3,6,7,5,1,2,8]=>1010100=>0010101
[5,2,8,6,1,7,3,4]=>[4,3,7,1,6,8,2,5]=>1110000=>0000111
[1,2,8,6,5,7,3,4]=>[4,3,7,5,6,8,2,1]=>1110100=>0010111
[8,2,5,6,3,7,1,4]=>[4,1,7,3,6,5,2,8]=>1110100=>0010111
[7,2,6,5,4,1,8,3]=>[3,8,1,4,5,6,2,7]=>1100000=>0000011
[6,1,3,5,4,7,8,2]=>[2,8,7,4,5,3,1,6]=>1011001=>1001101
[6,1,5,3,4,7,8,2]=>[2,8,7,4,3,5,1,6]=>1011001=>1001101
[7,5,6,2,4,1,8,3]=>[3,8,1,4,2,6,5,7]=>1100100=>0010011
[8,5,2,6,3,7,1,4]=>[4,1,7,3,6,2,5,8]=>1110000=>0000111
[8,1,6,5,7,3,2,4]=>[4,2,3,7,5,6,1,8]=>1100100=>0010011
[3,5,8,6,2,7,1,4]=>[4,1,7,2,6,8,5,3]=>1110100=>0010111
[1,8,5,6,3,7,2,4]=>[4,2,7,3,6,5,8,1]=>1110100=>0010111
[1,7,6,5,4,2,8,3]=>[3,8,2,4,5,6,7,1]=>1100000=>0000011
[5,7,6,1,4,2,8,3]=>[3,8,2,4,1,6,7,5]=>1100100=>0010011
[7,1,4,2,6,5,8,3]=>[3,8,5,6,2,4,1,7]=>1100100=>0010011
[2,7,4,1,5,6,8,3]=>[3,8,6,5,1,4,7,2]=>1100110=>0110011
[5,7,6,4,1,2,8,3]=>[3,8,2,1,4,6,7,5]=>1100100=>0010011
[4,7,6,1,5,2,8,3]=>[3,8,2,5,1,6,7,4]=>1101000=>0001011
[1,7,6,4,5,2,8,3]=>[3,8,2,5,4,6,7,1]=>1101000=>0001011
[3,8,1,6,5,7,2,4]=>[4,2,7,5,6,1,8,3]=>1110100=>0010111
[8,1,3,5,7,6,2,4]=>[4,2,6,7,5,3,1,8]=>1110100=>0010111
[7,8,5,4,1,6,2,3]=>[3,2,6,1,4,5,8,7]=>1100001=>1000011
[6,1,5,4,3,7,8,2]=>[2,8,7,3,4,5,1,6]=>1010001=>1000101
[7,5,6,4,2,1,8,3]=>[3,8,1,2,4,6,5,7]=>1000100=>0010001
[8,3,2,6,5,7,1,4]=>[4,1,7,5,6,2,3,8]=>1100100=>0010011
[7,4,6,2,5,1,8,3]=>[3,8,1,5,2,6,4,7]=>1101000=>0001011
[6,1,4,3,5,7,8,2]=>[2,8,7,5,3,4,1,6]=>1010101=>1010101
[6,1,3,4,5,7,8,2]=>[2,8,7,5,4,3,1,6]=>1011101=>1011101
[7,2,6,4,5,1,8,3]=>[3,8,1,5,4,6,2,7]=>1101000=>0001011
[8,2,3,6,5,7,1,4]=>[4,1,7,5,6,3,2,8]=>1110100=>0010111
[2,1,4,3,6,5,9,10,8,7,12,11]=>[11,12,7,8,10,9,5,6,3,4,1,2]=>10101010100=>00101010101
[2,1,4,3,7,8,6,5,10,9,12,11]=>[11,12,9,10,5,6,8,7,3,4,1,2]=>10101010100=>00101010101
[2,1,5,6,4,3,8,7,10,9,12,11]=>[11,12,9,10,7,8,3,4,6,5,1,2]=>10101010100=>00101010101
[2,1,5,6,4,3,9,10,8,7,12,11]=>[11,12,7,8,10,9,3,4,6,5,1,2]=>10101010100=>00101010101
[2,1,7,9,10,11,6,12,8,5,4,3]=>[3,4,5,8,12,6,11,10,9,7,1,2]=>10000110110=>01101100001
[3,4,2,1,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,1,2,4,3]=>10101010100=>00101010101
[3,4,2,1,6,5,9,10,8,7,12,11]=>[11,12,7,8,10,9,5,6,1,2,4,3]=>10101010100=>00101010101
[3,4,2,1,7,8,6,5,10,9,12,11]=>[11,12,9,10,5,6,8,7,1,2,4,3]=>10101010100=>00101010101
[3,5,2,7,4,8,6,1,11,12,10,9]=>[9,10,12,11,1,6,8,4,7,2,5,3]=>11110000001=>10000001111
[3,5,2,7,4,9,6,11,8,12,10,1]=>[1,10,12,8,11,6,9,4,7,2,5,3]=>01110101000=>00010101110
[3,6,2,8,9,5,10,7,4,1,12,11]=>[11,12,1,4,7,10,5,9,8,2,6,3]=>11101001000=>00010010111
[4,5,6,3,2,1,8,7,10,9,12,11]=>[11,12,9,10,7,8,1,2,3,6,5,4]=>10011010100=>00101011001
[4,5,6,3,2,1,9,10,8,7,12,11]=>[11,12,7,8,10,9,1,2,3,6,5,4]=>10011010100=>00101011001
[4,5,7,3,2,10,6,11,12,9,8,1]=>[1,8,9,12,11,6,10,2,3,7,5,4]=>01011100001=>10000111010
[4,6,7,3,9,5,2,11,8,12,10,1]=>[1,10,12,8,11,2,5,9,3,7,6,4]=>01110101000=>00010101110
[3,8,2,7,6,1,5,4]=>[4,5,1,6,7,2,8,3]=>1110000=>0000111
[4,8,7,2,6,5,3,1]=>[1,3,5,6,2,7,8,4]=>0101000=>0001010
[4,8,7,3,1,6,5,2]=>[2,5,6,1,3,7,8,4]=>1001000=>0001001
[4,8,7,3,2,6,1,5]=>[5,1,6,2,3,7,8,4]=>1101000=>0001011
[4,8,7,3,2,6,5,1]=>[1,5,6,2,3,7,8,4]=>0101000=>0001010
[4,8,7,3,6,2,5,1]=>[1,5,2,6,3,7,8,4]=>0111000=>0001110
[4,8,7,3,6,1,5,2]=>[2,5,1,6,3,7,8,4]=>1011000=>0001101
[5,8,7,6,3,4,2,1]=>[1,2,4,3,6,7,8,5]=>0010100=>0010100
[5,8,7,6,3,1,4,2]=>[2,4,1,3,6,7,8,5]=>1000100=>0010001
[5,8,7,6,2,4,3,1]=>[1,3,4,2,6,7,8,5]=>0100100=>0010010
[5,8,7,6,4,2,1,3]=>[3,1,2,4,6,7,8,5]=>1000100=>0010001
[5,8,7,6,4,1,3,2]=>[2,3,1,4,6,7,8,5]=>1000100=>0010001
[5,8,7,6,4,3,1,2]=>[2,1,3,4,6,7,8,5]=>1000100=>0010001
[7,3,4,2,1,6,5,8]=>[8,5,6,1,2,4,3,7]=>1010100=>0010101
[7,3,5,2,6,1,4,8]=>[8,4,1,6,2,5,3,7]=>1111000=>0001111
[7,3,5,2,6,4,1,8]=>[8,1,4,6,2,5,3,7]=>1110000=>0000111
[7,2,1,5,6,4,3,8]=>[8,3,4,6,5,1,2,7]=>1010100=>0010101
[7,3,5,1,6,4,2,8]=>[8,2,4,6,1,5,3,7]=>1110000=>0000111
[7,4,5,6,1,3,2,8]=>[8,2,3,1,6,5,4,7]=>1101100=>0011011
[1,4,5,7,3,2,8,6]=>[6,8,2,3,7,5,4,1]=>1101100=>0011011
[6,4,5,7,3,1,8,2]=>[2,8,1,3,7,5,4,6]=>1001100=>0011001
[6,3,5,1,7,4,8,2]=>[2,8,4,7,1,5,3,6]=>1011000=>0001101
[6,2,1,5,7,4,8,3]=>[3,8,4,7,5,1,2,6]=>1001100=>0011001
[3,2,1,5,7,4,8,6]=>[6,8,4,7,5,1,2,3]=>1001100=>0011001
[2,4,6,7,3,8,1,5]=>[5,1,8,3,7,6,4,2]=>1111010=>0101111
[1,4,6,7,3,8,5,2]=>[2,5,8,3,7,6,4,1]=>1011010=>0101101
[2,5,6,7,8,3,1,4]=>[4,1,3,8,7,6,5,2]=>1100111=>1110011
[3,2,1,6,7,8,4,5]=>[5,4,8,7,6,1,2,3]=>1001011=>1101001
[5,2,1,6,7,8,4,3]=>[3,4,8,7,6,1,2,5]=>1000011=>1100001
[5,3,6,1,7,8,4,2]=>[2,4,8,7,1,6,3,5]=>1010001=>1000101
[5,4,6,7,1,8,3,2]=>[2,3,8,1,7,6,4,5]=>1001010=>0101001
[6,4,5,7,2,1,8,3]=>[3,8,1,2,7,5,4,6]=>1001100=>0011001
[5,4,6,7,2,8,3,1]=>[1,3,8,2,7,6,4,5]=>0101010=>0101010
[5,3,6,2,7,8,4,1]=>[1,4,8,7,2,6,3,5]=>0110001=>1000110
[5,3,6,2,7,8,1,4]=>[4,1,8,7,2,6,3,5]=>1110001=>1000111
[6,3,5,2,7,1,8,4]=>[4,8,1,7,2,5,3,6]=>1110000=>0000111
[5,3,4,1,2,7,8,6]=>[6,8,7,2,1,4,3,5]=>1110001=>1000111
[4,3,6,2,7,8,1,5]=>[5,1,8,7,2,6,3,4]=>1110001=>1000111
[4,3,6,2,7,8,5,1]=>[1,5,8,7,2,6,3,4]=>0110001=>1000110
[1,3,6,2,7,8,5,4]=>[4,5,8,7,2,6,3,1]=>1110001=>1000111
[1,4,6,7,2,8,5,3]=>[3,5,8,2,7,6,4,1]=>1101010=>0101011
[3,4,6,7,2,8,5,1]=>[1,5,8,2,7,6,4,3]=>0111010=>0101110
[3,4,5,7,2,1,8,6]=>[6,8,1,2,7,5,4,3]=>1011100=>0011101
[4,2,1,5,7,3,8,6]=>[6,8,3,7,5,1,2,4]=>1010100=>0010101
[4,2,1,6,7,8,3,5]=>[5,3,8,7,6,1,2,4]=>1010011=>1100101
[4,3,6,1,7,8,2,5]=>[5,2,8,7,1,6,3,4]=>1110001=>1000111
[1,5,6,7,8,2,4,3]=>[3,4,2,8,7,6,5,1]=>1100111=>1110011
[1,5,6,7,8,4,2,3]=>[3,2,4,8,7,6,5,1]=>1100111=>1110011
[4,3,6,1,7,8,5,2]=>[2,5,8,7,1,6,3,4]=>1010001=>1000101
[4,2,1,6,7,8,5,3]=>[3,5,8,7,6,1,2,4]=>1000011=>1100001
[2,4,6,7,1,8,5,3]=>[3,5,8,1,7,6,4,2]=>1101010=>0101011
[2,5,6,7,8,1,4,3]=>[3,4,1,8,7,6,5,2]=>1100111=>1110011
[1,4,3,6,2,5,7,8]=>[8,7,5,2,6,3,4,1]=>1110101=>1010111
[1,4,3,7,2,5,6,8]=>[8,6,5,2,7,3,4,1]=>1110110=>0110111
[1,4,3,7,6,8,2,5]=>[5,2,8,6,7,3,4,1]=>1110010=>0100111
[1,4,3,7,5,8,2,6]=>[6,2,8,5,7,3,4,1]=>1110100=>0010111
[1,5,3,7,4,8,2,6]=>[6,2,8,4,7,3,5,1]=>1111000=>0001111
[1,5,4,8,2,6,3,7]=>[7,3,6,2,8,4,5,1]=>1111000=>0001111
[1,5,4,8,3,7,2,6]=>[6,2,7,3,8,4,5,1]=>1111000=>0001111
[1,2,3,6,5,8,4,7]=>[7,4,8,5,6,3,2,1]=>1111100=>0011111
[6,8,2,4,5,7,1,3]=>[3,1,7,5,4,2,8,6]=>1101110=>0111011
[3,7,8,4,5,2,6,1]=>[1,6,2,5,4,8,7,3]=>0111001=>1001110
[7,8,1,4,5,3,6,2]=>[2,6,3,5,4,1,8,7]=>1011001=>1001101
[5,8,1,4,7,6,3,2]=>[2,3,6,7,4,1,8,5]=>1001100=>0011001
[7,5,1,8,6,2,4,3]=>[3,4,2,6,8,1,5,7]=>1100000=>0000011
[7,4,1,8,2,6,3,5]=>[5,3,6,2,8,1,4,7]=>1110000=>0000111
[7,1,8,4,2,6,3,5]=>[5,3,6,2,4,8,1,7]=>1110000=>0000111
[7,3,1,8,4,2,6,5]=>[5,6,2,4,8,1,3,7]=>1100000=>0000011
[7,2,8,3,6,5,1,4]=>[4,1,5,6,3,8,2,7]=>1110000=>0000111
[7,2,8,3,6,1,5,4]=>[4,5,1,6,3,8,2,7]=>1110000=>0000111
[6,1,2,8,3,5,4,7]=>[7,4,5,3,8,2,1,6]=>1111000=>0001111
[5,2,3,8,1,4,7,6]=>[6,7,4,1,8,3,2,5]=>1111000=>0001111
[6,2,4,1,8,7,3,5]=>[5,3,7,8,1,4,2,6]=>1110000=>0000111
[3,1,6,4,2,8,5,7]=>[7,5,8,2,4,6,1,3]=>1100100=>0010011
[2,6,3,8,7,1,5,4]=>[4,5,1,7,8,3,6,2]=>1110000=>0000111
[2,6,3,8,5,1,4,7]=>[7,4,1,5,8,3,6,2]=>1111000=>0001111
[2,5,1,8,3,4,7,6]=>[6,7,4,3,8,1,5,2]=>1111000=>0001111
[1,2,5,3,8,4,7,6]=>[6,7,4,8,3,5,2,1]=>1111000=>0001111
[1,2,4,8,3,7,6,5]=>[5,6,7,3,8,4,2,1]=>1111000=>0001111
[2,4,8,3,7,1,6,5]=>[5,6,1,7,3,8,4,2]=>1111000=>0001111
[2,4,8,3,7,6,1,5]=>[5,1,6,7,3,8,4,2]=>1111000=>0001111
[2,5,3,8,1,7,4,6]=>[6,4,7,1,8,3,5,2]=>1111000=>0001111
[2,5,4,1,3,8,7,6]=>[6,7,8,3,1,4,5,2]=>1110000=>0000111
[3,1,5,4,8,2,7,6]=>[6,7,2,8,4,5,1,3]=>1101000=>0001011
[5,2,3,8,4,7,1,6]=>[6,1,7,4,8,3,2,5]=>1111000=>0001111
[4,8,2,3,7,6,1,5]=>[5,1,6,7,3,2,8,4]=>1111000=>0001111
[4,8,2,3,7,1,6,5]=>[5,6,1,7,3,2,8,4]=>1111000=>0001111
[4,8,1,2,3,7,6,5]=>[5,6,7,3,2,1,8,4]=>1111000=>0001111
[1,4,8,3,7,2,6,5]=>[5,6,2,7,3,8,4,1]=>1111000=>0001111
[6,3,8,1,5,2,4,7]=>[7,4,2,5,1,8,3,6]=>1111000=>0001111
[5,3,8,1,2,4,7,6]=>[6,7,4,2,1,8,3,5]=>1111000=>0001111
[5,1,3,8,2,4,7,6]=>[6,7,4,2,8,3,1,5]=>1111000=>0001111
[1,5,3,8,2,4,7,6]=>[6,7,4,2,8,3,5,1]=>1111000=>0001111
[1,5,4,8,2,7,6,3]=>[3,6,7,2,8,4,5,1]=>1101000=>0001011
[5,1,4,8,2,7,6,3]=>[3,6,7,2,8,4,1,5]=>1101000=>0001011
[5,4,8,1,2,7,6,3]=>[3,6,7,2,1,8,4,5]=>1101000=>0001011
[6,5,1,2,8,7,4,3]=>[3,4,7,8,2,1,5,6]=>1100000=>0000011
[4,1,5,8,2,7,6,3]=>[3,6,7,2,8,5,1,4]=>1100100=>0010011
[4,1,2,5,8,7,6,3]=>[3,6,7,8,5,2,1,4]=>1100100=>0010011
[1,4,2,5,8,7,6,3]=>[3,6,7,8,5,2,4,1]=>1100100=>0010011
[1,3,5,2,8,7,4,6]=>[6,4,7,8,2,5,3,1]=>1111000=>0001111
[3,5,1,2,8,7,4,6]=>[6,4,7,8,2,1,5,3]=>1111000=>0001111
[4,2,6,1,8,7,3,5]=>[5,3,7,8,1,6,2,4]=>1110000=>0000111
[4,3,1,5,8,2,7,6]=>[6,7,2,8,5,1,3,4]=>1100100=>0010011
[3,5,2,8,7,1,4,6]=>[6,4,1,7,8,2,5,3]=>1111000=>0001111
[3,4,8,1,7,2,6,5]=>[5,6,2,7,1,8,4,3]=>1111000=>0001111
[1,3,4,8,7,2,6,5]=>[5,6,2,7,8,4,3,1]=>1111000=>0001111
[1,3,4,8,2,7,6,5]=>[5,6,7,2,8,4,3,1]=>1111000=>0001111
[3,4,8,1,2,7,6,5]=>[5,6,7,2,1,8,4,3]=>1111000=>0001111
[3,4,8,2,7,6,1,5]=>[5,1,6,7,2,8,4,3]=>1111000=>0001111
[4,2,5,8,1,7,6,3]=>[3,6,7,1,8,5,2,4]=>1100100=>0010011
[4,3,1,2,5,8,7,6]=>[6,7,8,5,2,1,3,4]=>1100100=>0010011
[3,1,4,2,5,8,7,6]=>[6,7,8,5,2,4,1,3]=>1100100=>0010011
[7,8,2,1,5,3,6,4]=>[4,6,3,5,1,2,8,7]=>1010001=>1000101
[6,4,1,2,7,3,5,8]=>[8,5,3,7,2,1,4,6]=>1110100=>0010111
[2,3,7,5,4,1,8,6]=>[6,8,1,4,5,7,3,2]=>1110000=>0000111
[6,3,1,5,4,2,7,8]=>[8,7,2,4,5,1,3,6]=>1100001=>1000011
[7,8,1,5,4,2,6,3]=>[3,6,2,4,5,1,8,7]=>1100001=>1000011
[7,8,3,5,4,1,6,2]=>[2,6,1,4,5,3,8,7]=>1010001=>1000101
[7,8,2,5,4,1,3,6]=>[6,3,1,4,5,2,8,7]=>1110001=>1000111
[7,8,2,5,4,6,1,3]=>[3,1,6,4,5,2,8,7]=>1101001=>1001011
[5,3,6,2,4,7,1,8]=>[8,1,7,4,2,6,3,5]=>1111000=>0001111
[6,4,2,1,7,3,8,5]=>[5,8,3,7,1,2,4,6]=>1010000=>0000101
[2,7,6,5,3,1,4,8]=>[8,4,1,3,5,6,7,2]=>1101000=>0001011
[3,7,6,4,8,5,1,2]=>[2,1,5,8,4,6,7,3]=>1011000=>0001101
[5,7,6,3,8,4,1,2]=>[2,1,4,8,3,6,7,5]=>1010100=>0010101
[5,1,6,2,4,8,3,7]=>[7,3,8,4,2,6,1,5]=>1111000=>0001111
[4,7,6,5,2,1,3,8]=>[8,3,1,2,5,6,7,4]=>1011000=>0001101
[4,7,6,5,2,8,1,3]=>[3,1,8,2,5,6,7,4]=>1101000=>0001011
[4,7,6,5,1,8,3,2]=>[2,3,8,1,5,6,7,4]=>1001000=>0001001
[1,7,6,5,2,8,3,4]=>[4,3,8,2,5,6,7,1]=>1110000=>0000111
[1,7,6,5,3,2,8,4]=>[4,8,2,3,5,6,7,1]=>1100000=>0000011
[4,7,6,5,1,2,8,3]=>[3,8,2,1,5,6,7,4]=>1101000=>0001011
[5,2,6,3,4,1,7,8]=>[8,7,1,4,3,6,2,5]=>1110001=>1000111
[5,1,6,2,4,7,8,3]=>[3,8,7,4,2,6,1,5]=>1101001=>1001011
[1,7,2,4,8,3,6,5]=>[5,6,3,8,4,2,7,1]=>1111000=>0001111
[4,7,2,1,5,3,6,8]=>[8,6,3,5,1,2,7,4]=>1011010=>0101101
[4,7,1,6,2,3,8,5]=>[5,8,3,2,6,1,7,4]=>1111000=>0001111
[1,7,2,6,8,3,5,4]=>[4,5,3,8,6,2,7,1]=>1110010=>0100111
[1,2,6,7,4,8,5,3]=>[3,5,8,4,7,6,2,1]=>1101010=>0101011
[3,1,6,7,4,2,8,5]=>[5,8,2,4,7,6,1,3]=>1100010=>0100011
[3,2,8,5,4,6,1,7]=>[7,1,6,4,5,8,2,3]=>1101000=>0001011
[3,7,6,5,2,4,1,8]=>[8,1,4,2,5,6,7,3]=>1110000=>0000111
[1,7,6,5,8,2,4,3]=>[3,4,2,8,5,6,7,1]=>1100100=>0010011
[3,7,6,5,8,1,4,2]=>[2,4,1,8,5,6,7,3]=>1010100=>0010101
[3,7,6,5,1,2,4,8]=>[8,4,2,1,5,6,7,3]=>1111000=>0001111
[3,1,6,8,4,2,5,7]=>[7,5,2,4,8,6,1,3]=>1100110=>0110011
[4,7,6,8,3,5,1,2]=>[2,1,5,3,8,6,7,4]=>1011010=>0101101
[2,7,6,5,8,1,3,4]=>[4,3,1,8,5,6,7,2]=>1110100=>0010111
[2,7,6,5,8,4,1,3]=>[3,1,4,8,5,6,7,2]=>1100100=>0010011
[3,7,5,8,2,4,1,6]=>[6,1,4,2,8,5,7,3]=>1110100=>0010111
[5,1,7,8,4,3,2,6]=>[6,2,3,4,8,7,1,5]=>1100001=>1000011
[5,1,2,6,4,3,8,7]=>[7,8,3,4,6,2,1,5]=>1110000=>0000111
[5,1,2,4,6,3,8,7]=>[7,8,3,6,4,2,1,5]=>1111000=>0001111
[4,1,5,7,8,3,2,6]=>[6,2,3,8,7,5,1,4]=>1100101=>1010011
[4,7,1,8,3,6,2,5]=>[5,2,6,3,8,1,7,4]=>1111000=>0001111
[4,1,7,8,5,2,3,6]=>[6,3,2,5,8,7,1,4]=>1110001=>1000111
[5,1,7,4,8,2,3,6]=>[6,3,2,8,4,7,1,5]=>1111000=>0001111
[5,1,8,4,7,2,3,6]=>[6,3,2,7,4,8,1,5]=>1111000=>0001111
[4,1,8,7,5,2,3,6]=>[6,3,2,5,7,8,1,4]=>1110000=>0000111
[4,7,1,6,3,2,8,5]=>[5,8,2,3,6,1,7,4]=>1101000=>0001011
[7,1,2,3,8,6,5,4]=>[4,5,6,8,3,2,1,7]=>1110000=>0000111
[6,8,1,4,3,7,2,5]=>[5,2,7,3,4,1,8,6]=>1110010=>0100111
[8,7,3,2,4,1,6,5]=>[5,6,1,4,2,3,7,8]=>1100000=>0000011
[6,7,1,4,3,8,2,5]=>[5,2,8,3,4,1,7,6]=>1110010=>0100111
[8,1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1,8]=>1110100=>0010111
[7,1,2,3,6,8,5,4]=>[4,5,8,6,3,2,1,7]=>1110010=>0100111
[7,1,8,5,4,3,2,6]=>[6,2,3,4,5,8,1,7]=>1100000=>0000011
[7,8,2,6,3,4,1,5]=>[5,1,4,3,6,2,8,7]=>1110001=>1000111
[6,7,2,8,3,4,1,5]=>[5,1,4,3,8,2,7,6]=>1110010=>0100111
[3,8,7,1,4,2,6,5]=>[5,6,2,4,1,7,8,3]=>1110000=>0000111
[3,7,8,1,4,2,6,5]=>[5,6,2,4,1,8,7,3]=>1110001=>1000111
[3,6,8,1,4,2,7,5]=>[5,7,2,4,1,8,6,3]=>1110010=>0100111
[3,5,7,8,2,4,1,6]=>[6,1,4,2,8,7,5,3]=>1110101=>1010111
[3,6,7,1,4,2,8,5]=>[5,8,2,4,1,7,6,3]=>1110010=>0100111
[8,6,2,7,3,1,4,5]=>[5,4,1,3,7,2,6,8]=>1101000=>0001011
[8,1,7,5,4,3,2,6]=>[6,2,3,4,5,7,1,8]=>1100000=>0000011
[8,1,7,4,5,3,2,6]=>[6,2,3,5,4,7,1,8]=>1101000=>0001011
[5,8,3,7,1,4,2,6]=>[6,2,4,1,7,3,8,5]=>1110100=>0010111
[2,1,7,3,4,6,8,5]=>[5,8,6,4,3,7,1,2]=>1011010=>0101101
[6,7,3,2,4,1,8,5]=>[5,8,1,4,2,3,7,6]=>1100010=>0100011
[8,7,2,4,3,6,1,5]=>[5,1,6,3,4,2,7,8]=>1110000=>0000111
[7,1,2,3,5,6,8,4]=>[4,8,6,5,3,2,1,7]=>1110110=>0110111
[6,1,2,3,8,7,4,5]=>[5,4,7,8,3,2,1,6]=>1111000=>0001111
[5,1,2,3,7,8,6,4]=>[4,6,8,7,3,2,1,5]=>1110001=>1000111
[8,6,2,4,3,1,7,5]=>[5,7,1,3,4,2,6,8]=>1100000=>0000011
[7,6,3,2,4,8,1,5]=>[5,1,8,4,2,3,6,7]=>1101000=>0001011
[8,6,3,2,4,7,1,5]=>[5,1,7,4,2,3,6,8]=>1101000=>0001011
[7,6,2,4,3,1,8,5]=>[5,8,1,3,4,2,6,7]=>1100000=>0000011
[7,8,1,2,6,3,5,4]=>[4,5,3,6,2,1,8,7]=>1110001=>1000111
[1,4,8,2,7,3,5,6]=>[6,5,3,7,2,8,4,1]=>1111100=>0011111
[1,2,8,5,4,7,3,6]=>[6,3,7,4,5,8,2,1]=>1111000=>0001111
[2,3,6,8,4,7,1,5]=>[5,1,7,4,8,6,3,2]=>1111010=>0101111
[1,3,6,8,4,7,5,2]=>[2,5,7,4,8,6,3,1]=>1011010=>0101101
[2,4,8,1,7,3,6,5]=>[5,6,3,7,1,8,4,2]=>1111000=>0001111
[3,4,8,5,7,6,1,2]=>[2,1,6,7,5,8,4,3]=>1011100=>0011101
[1,2,6,8,4,5,7,3]=>[3,7,5,4,8,6,2,1]=>1101110=>0111011
[7,4,6,1,5,2,3,8]=>[8,3,2,5,1,6,4,7]=>1111000=>0001111
[6,8,1,4,7,2,3,5]=>[5,3,2,7,4,1,8,6]=>1111010=>0101111
[1,6,4,2,8,3,5,7]=>[7,5,3,8,2,4,6,1]=>1110100=>0010111
[1,6,3,8,5,4,2,7]=>[7,2,4,5,8,3,6,1]=>1110000=>0000111
[7,1,3,6,5,4,2,8]=>[8,2,4,5,6,3,1,7]=>1110000=>0000111
[7,2,1,4,6,3,5,8]=>[8,5,3,6,4,1,2,7]=>1011100=>0011101
[7,1,2,3,6,5,4,8]=>[8,4,5,6,3,2,1,7]=>1111000=>0001111
[6,8,1,2,7,3,5,4]=>[4,5,3,7,2,1,8,6]=>1110010=>0100111
[1,6,2,3,8,5,4,7]=>[7,4,5,8,3,2,6,1]=>1111000=>0001111
[6,2,8,1,7,3,5,4]=>[4,5,3,7,1,8,2,6]=>1110000=>0000111
[3,6,4,1,2,8,5,7]=>[7,5,8,2,1,4,6,3]=>1110100=>0010111
[2,5,1,8,7,6,3,4]=>[4,3,6,7,8,1,5,2]=>1110000=>0000111
[1,2,5,3,8,7,4,6]=>[6,4,7,8,3,5,2,1]=>1111000=>0001111
[2,5,3,8,7,1,6,4]=>[4,6,1,7,8,3,5,2]=>1110000=>0000111
[2,5,8,4,1,7,6,3]=>[3,6,7,1,4,8,5,2]=>1100100=>0010011
[3,5,8,7,1,4,2,6]=>[6,2,4,1,7,8,5,3]=>1110100=>0010111
[5,3,8,4,1,7,6,2]=>[2,6,7,1,4,8,3,5]=>1010000=>0000101
[4,2,8,7,6,3,5,1]=>[1,5,3,6,7,8,2,4]=>0110000=>0000110
[6,3,1,8,7,2,5,4]=>[4,5,2,7,8,1,3,6]=>1100000=>0000011
[5,1,3,8,7,6,2,4]=>[4,2,6,7,8,3,1,5]=>1110000=>0000111
[1,5,3,8,7,6,2,4]=>[4,2,6,7,8,3,5,1]=>1110000=>0000111
[5,1,8,4,7,2,6,3]=>[3,6,2,7,4,8,1,5]=>1101000=>0001011
[5,8,7,4,6,1,2,3]=>[3,2,1,6,4,7,8,5]=>1101100=>0011011
[6,8,5,1,2,4,7,3]=>[3,7,4,2,1,5,8,6]=>1101010=>0101011
[4,5,8,1,7,2,6,3]=>[3,6,2,7,1,8,5,4]=>1101100=>0011011
[1,3,2,5,8,7,4,6]=>[6,4,7,8,5,2,3,1]=>1101100=>0011011
[3,5,1,8,7,4,6,2]=>[2,6,4,7,8,1,5,3]=>1011000=>0001101
[4,3,6,1,2,8,5,7]=>[7,5,8,2,1,6,3,4]=>1110100=>0010111
[4,5,8,3,1,7,2,6]=>[6,2,7,1,3,8,5,4]=>1101100=>0011011
[4,5,2,8,7,1,3,6]=>[6,3,1,7,8,2,5,4]=>1111000=>0001111
[3,4,8,7,6,2,1,5]=>[5,1,2,6,7,8,4,3]=>1011000=>0001101
[3,4,8,7,6,5,1,2]=>[2,1,5,6,7,8,4,3]=>1011000=>0001101
[1,3,4,8,7,6,2,5]=>[5,2,6,7,8,4,3,1]=>1111000=>0001111
[3,2,5,8,7,4,6,1]=>[1,6,4,7,8,5,2,3]=>0101100=>0011010
[2,1,3,5,8,7,4,6]=>[6,4,7,8,5,3,1,2]=>1011100=>0011101
[1,2,7,5,8,6,4,3]=>[3,4,6,8,5,7,2,1]=>1100100=>0010011
[6,8,1,3,7,5,2,4]=>[4,2,5,7,3,1,8,6]=>1110010=>0100111
[1,3,7,8,2,6,5,4]=>[4,5,6,2,8,7,3,1]=>1110001=>1000111
[2,7,8,1,3,6,5,4]=>[4,5,6,3,1,8,7,2]=>1110001=>1000111
[8,1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1,8]=>1110010=>0100111
[8,1,2,6,7,5,3,4]=>[4,3,5,7,6,2,1,8]=>1110010=>0100111
[8,2,5,7,1,3,6,4]=>[4,6,3,1,7,5,2,8]=>1110100=>0010111
[2,8,1,6,7,3,5,4]=>[4,5,3,7,6,1,8,2]=>1110010=>0100111
[2,6,8,3,7,1,5,4]=>[4,5,1,7,3,8,6,2]=>1110010=>0100111
[2,8,6,4,7,1,5,3]=>[3,5,1,7,4,6,8,2]=>1101000=>0001011
[6,8,3,4,1,7,5,2]=>[2,5,7,1,4,3,8,6]=>1010010=>0100101
[6,8,3,7,4,1,5,2]=>[2,5,1,4,7,3,8,6]=>1010010=>0100101
[8,2,5,7,1,6,3,4]=>[4,3,6,1,7,5,2,8]=>1110100=>0010111
[8,4,7,2,3,6,1,5]=>[5,1,6,3,2,7,4,8]=>1111000=>0001111
[8,5,7,4,2,6,1,3]=>[3,1,6,2,4,7,5,8]=>1100100=>0010011
[8,3,5,7,4,1,6,2]=>[2,6,1,4,7,5,3,8]=>1010100=>0010101
[8,5,2,4,7,1,6,3]=>[3,6,1,7,4,2,5,8]=>1101000=>0001011
[8,2,4,7,3,6,1,5]=>[5,1,6,3,7,4,2,8]=>1111000=>0001111
[8,2,7,1,4,6,3,5]=>[5,3,6,4,1,7,2,8]=>1111000=>0001111
[8,7,1,2,4,6,3,5]=>[5,3,6,4,2,1,7,8]=>1111000=>0001111
[8,7,1,4,6,2,3,5]=>[5,3,2,6,4,1,7,8]=>1111000=>0001111
[8,4,7,1,3,6,2,5]=>[5,2,6,3,1,7,4,8]=>1111000=>0001111
[8,3,5,7,1,2,6,4]=>[4,6,2,1,7,5,3,8]=>1110100=>0010111
[5,8,7,1,3,6,2,4]=>[4,2,6,3,1,7,8,5]=>1110100=>0010111
[8,5,4,7,1,6,2,3]=>[3,2,6,1,7,4,5,8]=>1101000=>0001011
[8,5,4,7,1,2,6,3]=>[3,6,2,1,7,4,5,8]=>1101000=>0001011
[8,5,1,4,7,2,6,3]=>[3,6,2,7,4,1,5,8]=>1101000=>0001011
[8,5,6,3,1,7,4,2]=>[2,4,7,1,3,6,5,8]=>1000100=>0010001
[1,8,4,5,7,2,6,3]=>[3,6,2,7,5,4,8,1]=>1101100=>0011011
[5,8,7,3,6,1,2,4]=>[4,2,1,6,3,7,8,5]=>1110100=>0010111
[8,3,5,7,1,6,2,4]=>[4,2,6,1,7,5,3,8]=>1110100=>0010111
[1,6,8,3,7,5,2,4]=>[4,2,5,7,3,8,6,1]=>1110010=>0100111
[6,3,8,2,7,5,1,4]=>[4,1,5,7,2,8,3,6]=>1110000=>0000111
[8,6,4,7,3,1,5,2]=>[2,5,1,3,7,4,6,8]=>1001000=>0001001
[8,4,5,7,3,1,6,2]=>[2,6,1,3,7,5,4,8]=>1001100=>0011001
[8,3,4,7,2,6,1,5]=>[5,1,6,2,7,4,3,8]=>1111000=>0001111
[8,7,1,3,4,6,2,5]=>[5,2,6,4,3,1,7,8]=>1111000=>0001111
[8,3,7,2,4,6,1,5]=>[5,1,6,4,2,7,3,8]=>1111000=>0001111
[2,8,4,5,7,1,6,3]=>[3,6,1,7,5,4,8,2]=>1101100=>0011011
[8,7,3,4,5,1,6,2]=>[2,6,1,5,4,3,7,8]=>1011000=>0001101
[8,7,4,5,2,6,1,3]=>[3,1,6,2,5,4,7,8]=>1101000=>0001011
[8,7,2,3,4,6,1,5]=>[5,1,6,4,3,2,7,8]=>1111000=>0001111
[8,7,3,1,5,2,4,6]=>[6,4,2,5,1,3,7,8]=>1101000=>0001011
[8,6,1,2,5,7,3,4]=>[4,3,7,5,2,1,6,8]=>1110100=>0010111
[5,1,4,2,7,3,6,8]=>[8,6,3,7,2,4,1,5]=>1110010=>0100111
[5,7,8,1,3,4,6,2]=>[2,6,4,3,1,8,7,5]=>1011101=>1011101
[5,8,1,7,3,4,6,2]=>[2,6,4,3,7,1,8,5]=>1011100=>0011101
[6,1,2,4,8,7,5,3]=>[3,5,7,8,4,2,1,6]=>1101000=>0001011
[3,1,7,6,4,8,5,2]=>[2,5,8,4,6,7,1,3]=>1001000=>0001001
[7,1,2,4,6,8,5,3]=>[3,5,8,6,4,2,1,7]=>1101010=>0101011
[7,1,5,3,2,8,6,4]=>[4,6,8,2,3,5,1,7]=>1100000=>0000011
[8,1,7,5,3,2,6,4]=>[4,6,2,3,5,7,1,8]=>1100000=>0000011
[1,4,2,3,8,5,7,6]=>[6,7,5,8,3,2,4,1]=>1110100=>0010111
[3,1,8,6,4,7,5,2]=>[2,5,7,4,6,8,1,3]=>1001000=>0001001
[8,1,2,6,7,4,5,3]=>[3,5,4,7,6,2,1,8]=>1101010=>0101011
[1,2,3,5,8,6,4,7]=>[7,4,6,8,5,3,2,1]=>1111100=>0011111
[7,1,2,8,3,6,5,4]=>[4,5,6,3,8,2,1,7]=>1110000=>0000111
[7,1,2,8,6,4,5,3]=>[3,5,4,6,8,2,1,7]=>1101000=>0001011
[3,6,2,5,4,1,8,7]=>[7,8,1,4,5,2,6,3]=>1110000=>0000111
[3,5,2,8,4,7,6,1]=>[1,6,7,4,8,2,5,3]=>0111000=>0001110
[5,4,7,3,2,8,6,1]=>[1,6,8,2,3,7,4,5]=>0101000=>0001010
[5,4,8,3,2,7,6,1]=>[1,6,7,2,3,8,4,5]=>0101000=>0001010
[5,3,2,6,4,1,8,7]=>[7,8,1,4,6,2,3,5]=>1100000=>0000011
[4,5,8,3,2,7,6,1]=>[1,6,7,2,3,8,5,4]=>0101100=>0011010
[4,7,6,3,8,5,2,1]=>[1,2,5,8,3,6,7,4]=>0011000=>0001100
[4,8,6,3,7,5,2,1]=>[1,2,5,7,3,6,8,4]=>0011000=>0001100
[5,3,2,8,4,7,6,1]=>[1,6,7,4,8,2,3,5]=>0101000=>0001010
[2,1,5,8,4,7,6,3]=>[3,6,7,4,8,5,1,2]=>1001100=>0011001
[5,3,2,7,4,8,6,1]=>[1,6,8,4,7,2,3,5]=>0101000=>0001010
[5,7,4,3,2,8,6,1]=>[1,6,8,2,3,4,7,5]=>0100100=>0010010
[4,7,5,3,2,8,6,1]=>[1,6,8,2,3,5,7,4]=>0101000=>0001010
[4,7,8,3,6,5,2,1]=>[1,2,5,6,3,8,7,4]=>0011001=>1001100
[4,6,8,3,7,5,2,1]=>[1,2,5,7,3,8,6,4]=>0011010=>0101100
[7,6,4,3,8,5,2,1]=>[1,2,5,8,3,4,6,7]=>0010000=>0000100
[8,3,2,6,7,5,4,1]=>[1,4,5,7,6,2,3,8]=>0100010=>0100010
[8,6,4,3,7,5,2,1]=>[1,2,5,7,3,4,6,8]=>0010000=>0000100
[8,4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4,8]=>0101000=>0001010
[8,4,6,3,7,5,2,1]=>[1,2,5,7,3,6,4,8]=>0011000=>0001100
[7,4,6,3,8,5,2,1]=>[1,2,5,8,3,6,4,7]=>0011000=>0001100
[3,7,2,6,8,5,4,1]=>[1,4,5,8,6,2,7,3]=>0110010=>0100110
[3,8,2,6,7,5,4,1]=>[1,4,5,7,6,2,8,3]=>0110010=>0100110
[3,7,2,8,6,5,4,1]=>[1,4,5,6,8,2,7,3]=>0110000=>0000110
[3,6,2,8,7,5,4,1]=>[1,4,5,7,8,2,6,3]=>0110000=>0000110
[7,4,5,3,2,8,6,1]=>[1,6,8,2,3,5,4,7]=>0101000=>0001010
[2,1,7,5,4,8,6,3]=>[3,6,8,4,5,7,1,2]=>1001000=>0001001
[7,3,2,8,6,5,4,1]=>[1,4,5,6,8,2,3,7]=>0100000=>0000010
[7,8,4,3,6,5,2,1]=>[1,2,5,6,3,4,8,7]=>0010001=>1000100
[6,3,2,8,7,5,4,1]=>[1,4,5,7,8,2,3,6]=>0100000=>0000010
[6,3,2,7,8,5,4,1]=>[1,4,5,8,7,2,3,6]=>0100001=>1000010
[1,6,4,8,2,5,3,7]=>[7,3,5,2,8,4,6,1]=>1111000=>0001111
[1,6,5,8,2,4,3,7]=>[7,3,4,2,8,5,6,1]=>1110100=>0010111
[1,6,8,2,4,3,7,5]=>[5,7,3,4,2,8,6,1]=>1110010=>0100111
[1,6,2,4,3,7,8,5]=>[5,8,7,3,4,2,6,1]=>1110001=>1000111
[1,5,6,2,4,7,3,8]=>[8,3,7,4,2,6,5,1]=>1111100=>0011111
[1,5,6,2,4,7,8,3]=>[3,8,7,4,2,6,5,1]=>1101101=>1011011
[1,6,7,2,4,3,8,5]=>[5,8,3,4,2,7,6,1]=>1110010=>0100111
[1,5,8,2,4,6,7,3]=>[3,7,6,4,2,8,5,1]=>1101110=>0111011
[1,5,7,8,3,2,4,6]=>[6,4,2,3,8,7,5,1]=>1101101=>1011011
[1,5,8,3,2,4,6,7]=>[7,6,4,2,3,8,5,1]=>1101110=>0111011
[1,5,6,2,4,8,3,7]=>[7,3,8,4,2,6,5,1]=>1111100=>0011111
[1,7,3,4,2,8,6,5]=>[5,6,8,2,4,3,7,1]=>1110000=>0000111
[1,5,6,2,4,8,7,3]=>[3,7,8,4,2,6,5,1]=>1101100=>0011011
[1,5,8,7,3,2,4,6]=>[6,4,2,3,7,8,5,1]=>1101100=>0011011
[1,7,4,2,8,6,5,3]=>[3,5,6,8,2,4,7,1]=>1100000=>0000011
[1,5,8,3,2,4,7,6]=>[6,7,4,2,3,8,5,1]=>1101100=>0011011
[1,6,5,2,3,7,4,8]=>[8,4,7,3,2,5,6,1]=>1111000=>0001111
[1,6,5,2,3,7,8,4]=>[4,8,7,3,2,5,6,1]=>1110001=>1000111
[1,6,8,4,2,3,7,5]=>[5,7,3,2,4,8,6,1]=>1110010=>0100111
[1,6,8,5,2,3,7,4]=>[4,7,3,2,5,8,6,1]=>1110010=>0100111
[1,6,4,2,3,7,5,8]=>[8,5,7,3,2,4,6,1]=>1110100=>0010111
[1,5,8,6,2,4,7,3]=>[3,7,4,2,6,8,5,1]=>1101100=>0011011
[1,7,5,2,8,6,4,3]=>[3,4,6,8,2,5,7,1]=>1100000=>0000011
[3,7,5,6,1,4,8,2]=>[2,8,4,1,6,5,7,3]=>1011100=>0011101
[8,6,1,4,2,7,5,3]=>[3,5,7,2,4,1,6,8]=>1100000=>0000011
[6,7,1,4,3,5,8,2]=>[2,8,5,3,4,1,7,6]=>1010110=>0110101
[3,1,4,7,6,5,8,2]=>[2,8,5,6,7,4,1,3]=>1001100=>0011001
[6,1,7,4,3,5,8,2]=>[2,8,5,3,4,7,1,6]=>1010100=>0010101
[7,1,6,4,3,5,8,2]=>[2,8,5,3,4,6,1,7]=>1010100=>0010101
[1,7,6,4,3,5,8,2]=>[2,8,5,3,4,6,7,1]=>1010100=>0010101
[8,1,6,4,2,7,5,3]=>[3,5,7,2,4,6,1,8]=>1100000=>0000011
[4,7,1,3,8,2,5,6]=>[6,5,2,8,3,1,7,4]=>1111100=>0011111
[7,4,1,3,8,2,5,6]=>[6,5,2,8,3,1,4,7]=>1110100=>0010111
[1,3,6,4,2,8,5,7]=>[7,5,8,2,4,6,3,1]=>1110100=>0010111
[4,7,3,1,2,8,5,6]=>[6,5,8,2,1,3,7,4]=>1101100=>0011011
[4,7,8,1,2,6,5,3]=>[3,5,6,2,1,8,7,4]=>1101001=>1001011
[1,8,6,4,2,7,5,3]=>[3,5,7,2,4,6,8,1]=>1100000=>0000011
[4,8,1,3,7,2,5,6]=>[6,5,2,7,3,1,8,4]=>1111100=>0011111
[8,7,1,3,6,2,5,4]=>[4,5,2,6,3,1,7,8]=>1110000=>0000111
[1,8,4,3,7,2,5,6]=>[6,5,2,7,3,4,8,1]=>1110100=>0010111
[3,7,4,6,8,2,1,5]=>[5,1,2,8,6,4,7,3]=>1011010=>0101101
[2,4,3,7,8,6,1,5]=>[5,1,6,8,7,3,4,2]=>1110001=>1000111
[1,4,7,3,8,2,5,6]=>[6,5,2,8,3,7,4,1]=>1111100=>0011111
[5,7,6,8,3,2,1,4]=>[4,1,2,3,8,6,7,5]=>1000110=>0110001
[6,1,4,3,8,2,5,7]=>[7,5,2,8,3,4,1,6]=>1110100=>0010111
[4,1,7,3,8,2,5,6]=>[6,5,2,8,3,7,1,4]=>1110100=>0010111
[8,1,4,3,7,2,5,6]=>[6,5,2,7,3,4,1,8]=>1110100=>0010111
[4,2,3,7,8,6,1,5]=>[5,1,6,8,7,3,2,4]=>1110001=>1000111
[5,7,2,6,8,4,1,3]=>[3,1,4,8,6,2,7,5]=>1100110=>0110011
[7,2,5,6,8,4,1,3]=>[3,1,4,8,6,5,2,7]=>1100110=>0110011
[5,2,3,8,7,6,1,4]=>[4,1,6,7,8,3,2,5]=>1110000=>0000111
[8,2,3,7,5,6,1,4]=>[4,1,6,5,7,3,2,8]=>1110100=>0010111
[6,1,8,3,7,2,5,4]=>[4,5,2,7,3,8,1,6]=>1110000=>0000111
[1,7,8,4,2,6,5,3]=>[3,5,6,2,4,8,7,1]=>1100001=>1000011
[4,7,1,8,2,5,6,3]=>[3,6,5,2,8,1,7,4]=>1101100=>0011011
[1,4,8,3,6,2,5,7]=>[7,5,2,6,3,8,4,1]=>1111100=>0011111
[3,7,5,8,6,2,1,4]=>[4,1,2,6,8,5,7,3]=>1010100=>0010101
[3,7,8,6,5,2,1,4]=>[4,1,2,5,6,8,7,3]=>1010001=>1000101
[6,8,7,5,3,2,1,4]=>[4,1,2,3,5,7,8,6]=>1000010=>0100001
[5,7,6,8,3,4,1,2]=>[2,1,4,3,8,6,7,5]=>1010110=>0110101
[1,5,4,7,6,8,2,3]=>[3,2,8,6,7,4,5,1]=>1101010=>0101011
[3,5,4,8,6,7,1,2]=>[2,1,7,6,8,4,5,3]=>1011010=>0101101
[3,8,4,6,5,7,1,2]=>[2,1,7,5,6,4,8,3]=>1011100=>0011101
[3,6,4,7,5,8,1,2]=>[2,1,8,5,7,4,6,3]=>1011100=>0011101
[1,8,2,6,5,7,3,4]=>[4,3,7,5,6,2,8,1]=>1110100=>0010111
[1,7,6,8,2,5,3,4]=>[4,3,5,2,8,6,7,1]=>1110010=>0100111
[7,8,5,6,1,3,2,4]=>[4,2,3,1,6,5,8,7]=>1100101=>1010011
[5,8,6,7,1,3,2,4]=>[4,2,3,1,7,6,8,5]=>1100110=>0110011
[1,3,2,8,6,7,4,5]=>[5,4,7,6,8,2,3,1]=>1101010=>0101011
[7,8,1,4,2,6,3,5]=>[5,3,6,2,4,1,8,7]=>1110001=>1000111
[3,8,7,1,4,6,5,2]=>[2,5,6,4,1,7,8,3]=>1011000=>0001101
[5,7,1,2,4,3,8,6]=>[6,8,3,4,2,1,7,5]=>1110100=>0010111
[4,3,7,6,8,2,5,1]=>[1,5,2,8,6,7,3,4]=>0110010=>0100110
[5,3,6,8,1,7,2,4]=>[4,2,7,1,8,6,3,5]=>1110010=>0100111
[3,2,6,8,5,7,1,4]=>[4,1,7,5,8,6,2,3]=>1100110=>0110011
[7,4,8,6,5,2,1,3]=>[3,1,2,5,6,8,4,7]=>1001000=>0001001
[6,4,1,5,8,2,7,3]=>[3,7,2,8,5,1,4,6]=>1100100=>0010011
[7,4,3,2,8,5,6,1]=>[1,6,5,8,2,3,4,7]=>0100100=>0010010
[4,7,8,3,1,5,6,2]=>[2,6,5,1,3,8,7,4]=>1001101=>1011001
[2,6,3,5,8,7,1,4]=>[4,1,7,8,5,3,6,2]=>1110100=>0010111
[8,1,6,4,7,3,2,5]=>[5,2,3,7,4,6,1,8]=>1101000=>0001011
[4,8,7,5,6,1,2,3]=>[3,2,1,6,5,7,8,4]=>1101100=>0011011
[4,7,8,1,3,5,6,2]=>[2,6,5,3,1,8,7,4]=>1011101=>1011101
[6,4,8,7,1,3,2,5]=>[5,2,3,1,7,8,4,6]=>1101000=>0001011
[2,8,3,7,1,5,6,4]=>[4,6,5,1,7,3,8,2]=>1110100=>0010111
[5,3,8,6,2,1,4,7]=>[7,4,1,2,6,8,3,5]=>1011000=>0001101
[4,3,7,5,1,8,2,6]=>[6,2,8,1,5,7,3,4]=>1110000=>0000111
[6,8,5,2,7,4,3,1]=>[1,3,4,7,2,5,8,6]=>0100010=>0100010
[3,6,8,1,4,5,2,7]=>[7,2,5,4,1,8,6,3]=>1111010=>0101111
[4,1,6,5,8,2,3,7]=>[7,3,2,8,5,6,1,4]=>1110100=>0010111
[4,3,8,6,2,5,1,7]=>[7,1,5,2,6,8,3,4]=>1110000=>0000111
[1,7,4,3,8,6,2,5]=>[5,2,6,8,3,4,7,1]=>1110000=>0000111
[2,8,6,1,7,4,5,3]=>[3,5,4,7,1,6,8,2]=>1101000=>0001011
[8,5,4,3,1,6,7,2]=>[2,7,6,1,3,4,5,8]=>1000010=>0100001
[4,2,7,1,8,6,3,5]=>[5,3,6,8,1,7,2,4]=>1110000=>0000111
[5,8,3,6,7,4,1,2]=>[2,1,4,7,6,3,8,5]=>1010110=>0110101
[7,6,3,5,8,2,1,4]=>[4,1,2,8,5,3,6,7]=>1010100=>0010101
[3,6,8,5,1,2,7,4]=>[4,7,2,1,5,8,6,3]=>1110010=>0100111
[6,5,2,4,8,1,7,3]=>[3,7,1,8,4,2,5,6]=>1101000=>0001011
[1,5,4,8,2,6,7,3]=>[3,7,6,2,8,4,5,1]=>1101010=>0101011
[7,2,1,5,8,6,3,4]=>[4,3,6,8,5,1,2,7]=>1010100=>0010101
[5,4,8,3,7,6,1,2]=>[2,1,6,7,3,8,4,5]=>1011000=>0001101
[6,3,4,8,5,1,7,2]=>[2,7,1,5,8,4,3,6]=>1011000=>0001101
[5,3,4,8,1,6,7,2]=>[2,7,6,1,8,4,3,5]=>1011010=>0101101
[6,5,4,8,7,1,3,2]=>[2,3,1,7,8,4,5,6]=>1001000=>0001001
[6,5,4,8,1,2,7,3]=>[3,7,2,1,8,4,5,6]=>1101000=>0001011
[7,5,1,6,8,2,4,3]=>[3,4,2,8,6,1,5,7]=>1100010=>0100011
[6,5,4,1,8,2,7,3]=>[3,7,2,8,1,4,5,6]=>1100000=>0000011
[6,5,4,7,1,2,8,3]=>[3,8,2,1,7,4,5,6]=>1101000=>0001011
[6,5,4,7,8,1,3,2]=>[2,3,1,8,7,4,5,6]=>1001001=>1001001
[6,5,3,7,1,4,2,8]=>[8,2,4,1,7,3,5,6]=>1110000=>0000111
[7,5,1,4,8,3,2,6]=>[6,2,3,8,4,1,5,7]=>1101000=>0001011
[8,1,6,4,7,3,5,2]=>[2,5,3,7,4,6,1,8]=>1011000=>0001101
[7,5,1,4,8,3,6,2]=>[2,6,3,8,4,1,5,7]=>1011000=>0001101
[7,4,1,5,3,8,6,2]=>[2,6,8,3,5,1,4,7]=>1010000=>0000101
[8,1,5,4,3,7,6,2]=>[2,6,7,3,4,5,1,8]=>1010000=>0000101
[8,1,5,4,3,7,2,6]=>[6,2,7,3,4,5,1,8]=>1110000=>0000111
[6,5,3,8,1,4,2,7]=>[7,2,4,1,8,3,5,6]=>1110000=>0000111
[8,1,7,2,5,4,6,3]=>[3,6,4,5,2,7,1,8]=>1101000=>0001011
[7,6,1,2,5,4,8,3]=>[3,8,4,5,2,1,6,7]=>1101000=>0001011
[6,5,3,8,1,4,7,2]=>[2,7,4,1,8,3,5,6]=>1011000=>0001101
[6,5,3,1,2,7,8,4]=>[4,8,7,2,1,3,5,6]=>1100001=>1000011
[8,1,6,4,2,5,7,3]=>[3,7,5,2,4,6,1,8]=>1100100=>0010011
[8,1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1,8]=>1100000=>0000011
[7,4,1,5,3,2,8,6]=>[6,8,2,3,5,1,4,7]=>1100000=>0000011
[6,4,3,1,5,2,8,7]=>[7,8,2,5,1,3,4,6]=>1100000=>0000011
[6,4,3,1,5,7,2,8]=>[8,2,7,5,1,3,4,6]=>1100100=>0010011
[7,4,1,5,3,6,2,8]=>[8,2,6,3,5,1,4,7]=>1110000=>0000111
[6,4,3,1,5,7,8,2]=>[2,8,7,5,1,3,4,6]=>1000101=>1010001
[7,1,5,8,4,6,2,3]=>[3,2,6,4,8,5,1,7]=>1101100=>0011011
[8,6,7,1,4,2,5,3]=>[3,5,2,4,1,7,6,8]=>1100010=>0100011
[8,6,3,7,5,1,2,4]=>[4,2,1,5,7,3,6,8]=>1110000=>0000111
[8,6,1,7,3,2,5,4]=>[4,5,2,3,7,1,6,8]=>1100000=>0000011
[7,6,1,8,3,5,2,4]=>[4,2,5,3,8,1,6,7]=>1110000=>0000111
[7,6,1,3,8,5,2,4]=>[4,2,5,8,3,1,6,7]=>1110000=>0000111
[7,6,2,8,3,5,1,4]=>[4,1,5,3,8,2,6,7]=>1110000=>0000111
[8,7,1,5,2,6,3,4]=>[4,3,6,2,5,1,7,8]=>1110000=>0000111
[8,7,1,5,2,3,6,4]=>[4,6,3,2,5,1,7,8]=>1110000=>0000111
[8,5,2,3,1,7,6,4]=>[4,6,7,1,3,2,5,8]=>1100000=>0000011
[8,6,2,3,7,1,5,4]=>[4,5,1,7,3,2,6,8]=>1110000=>0000111
[8,6,2,7,3,1,5,4]=>[4,5,1,3,7,2,6,8]=>1100000=>0000011
[8,6,7,2,4,1,5,3]=>[3,5,1,4,2,7,6,8]=>1100010=>0100011
[6,8,7,3,4,1,5,2]=>[2,5,1,4,3,7,8,6]=>1010010=>0100101
[8,7,2,5,1,6,3,4]=>[4,3,6,1,5,2,7,8]=>1110000=>0000111
[8,7,2,1,4,6,3,5]=>[5,3,6,4,1,2,7,8]=>1011000=>0001101
[8,4,2,1,7,6,3,5]=>[5,3,6,7,1,2,4,8]=>1010000=>0000101
[8,5,2,7,1,6,3,4]=>[4,3,6,1,7,2,5,8]=>1110000=>0000111
[8,5,7,2,1,4,3,6]=>[6,3,4,1,2,7,5,8]=>1010100=>0010101
[5,8,7,3,1,4,2,6]=>[6,2,4,1,3,7,8,5]=>1100100=>0010011
[8,5,7,2,1,4,6,3]=>[3,6,4,1,2,7,5,8]=>1001100=>0011001
[8,5,2,7,1,3,6,4]=>[4,6,3,1,7,2,5,8]=>1110000=>0000111
[8,7,4,1,2,3,6,5]=>[5,6,3,2,1,4,7,8]=>1110000=>0000111
[8,7,4,1,2,6,3,5]=>[5,3,6,2,1,4,7,8]=>1110000=>0000111
[8,4,3,1,7,2,6,5]=>[5,6,2,7,1,3,4,8]=>1100000=>0000011
[8,4,3,1,2,7,6,5]=>[5,6,7,2,1,3,4,8]=>1100000=>0000011
[8,6,1,3,7,2,5,4]=>[4,5,2,7,3,1,6,8]=>1110000=>0000111
[8,5,1,3,2,7,6,4]=>[4,6,7,2,3,1,5,8]=>1100000=>0000011
[8,5,7,4,1,6,2,3]=>[3,2,6,1,4,7,5,8]=>1100100=>0010011
[8,5,7,4,1,2,6,3]=>[3,6,2,1,4,7,5,8]=>1100100=>0010011
[8,1,5,4,2,7,6,3]=>[3,6,7,2,4,5,1,8]=>1100000=>0000011
[8,1,6,4,7,2,5,3]=>[3,5,2,7,4,6,1,8]=>1101000=>0001011
[6,1,5,8,4,2,7,3]=>[3,7,2,4,8,5,1,6]=>1100100=>0010011
[5,8,3,6,4,1,2,7]=>[7,2,1,4,6,3,8,5]=>1110100=>0010111
[8,4,7,5,1,6,2,3]=>[3,2,6,1,5,7,4,8]=>1101000=>0001011
[8,4,7,5,1,2,6,3]=>[3,6,2,1,5,7,4,8]=>1101000=>0001011
[8,4,7,5,1,2,3,6]=>[6,3,2,1,5,7,4,8]=>1111000=>0001111
[8,3,2,6,5,1,4,7]=>[7,4,1,5,6,2,3,8]=>1101000=>0001011
[4,8,7,3,1,5,2,6]=>[6,2,5,1,3,7,8,4]=>1101000=>0001011
[8,4,7,2,1,5,3,6]=>[6,3,5,1,2,7,4,8]=>1011000=>0001101
[8,3,2,7,1,5,4,6]=>[6,4,5,1,7,2,3,8]=>1101000=>0001011
[8,7,3,1,6,2,4,5]=>[5,4,2,6,1,3,7,8]=>1101000=>0001011
[8,7,3,1,2,4,6,5]=>[5,6,4,2,1,3,7,8]=>1101000=>0001011
[8,3,2,1,7,4,6,5]=>[5,6,4,7,1,2,3,8]=>1001000=>0001001
[8,4,7,2,1,5,6,3]=>[3,6,5,1,2,7,4,8]=>1001100=>0011001
[8,7,2,1,3,6,4,5]=>[5,4,6,3,1,2,7,8]=>1011000=>0001101
[8,7,2,1,3,4,6,5]=>[5,6,4,3,1,2,7,8]=>1011000=>0001101
[1,2,3,8,4,6,7,5]=>[5,7,6,4,8,3,2,1]=>1111010=>0101111
[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>1111001=>1001111
[1,6,7,8,2,3,5,4]=>[4,5,3,2,8,7,6,1]=>1110011=>1100111
[1,7,8,2,5,3,6,4]=>[4,6,3,5,2,8,7,1]=>1110001=>1000111
[1,5,2,7,8,3,6,4]=>[4,6,3,8,7,2,5,1]=>1110001=>1000111
[1,7,8,2,4,3,6,5]=>[5,6,3,4,2,8,7,1]=>1110001=>1000111
[7,6,3,1,5,2,4,8]=>[8,4,2,5,1,3,6,7]=>1101000=>0001011
[6,7,3,1,5,2,8,4]=>[4,8,2,5,1,3,7,6]=>1100010=>0100011
[6,8,3,1,5,2,7,4]=>[4,7,2,5,1,3,8,6]=>1100010=>0100011
[6,8,4,5,1,2,7,3]=>[3,7,2,1,5,4,8,6]=>1101010=>0101011
[6,7,4,5,1,2,8,3]=>[3,8,2,1,5,4,7,6]=>1101010=>0101011
[7,2,1,6,5,3,4,8]=>[8,4,3,5,6,1,2,7]=>1011000=>0001101
[7,3,6,1,5,2,4,8]=>[8,4,2,5,1,6,3,7]=>1111000=>0001111
[7,4,6,5,1,2,3,8]=>[8,3,2,1,5,6,4,7]=>1111000=>0001111
[6,7,5,4,1,2,8,3]=>[3,8,2,1,4,5,7,6]=>1100010=>0100011
[5,8,6,4,1,7,2,3]=>[3,2,7,1,4,6,8,5]=>1100100=>0010011
[5,7,6,4,1,8,2,3]=>[3,2,8,1,4,6,7,5]=>1100100=>0010011
[5,6,7,4,1,8,2,3]=>[3,2,8,1,4,7,6,5]=>1100110=>0110011
[6,5,7,4,1,2,8,3]=>[3,8,2,1,4,7,5,6]=>1100100=>0010011
[6,2,1,7,5,3,8,4]=>[4,8,3,5,7,1,2,6]=>1010000=>0000101
[6,3,8,1,5,2,7,4]=>[4,7,2,5,1,8,3,6]=>1110000=>0000111
[6,4,8,5,1,2,7,3]=>[3,7,2,1,5,8,4,6]=>1101000=>0001011
[6,5,8,4,1,2,7,3]=>[3,7,2,1,4,8,5,6]=>1100100=>0010011
[5,6,8,4,1,7,2,3]=>[3,2,7,1,4,8,6,5]=>1100110=>0110011
[4,6,8,5,7,1,2,3]=>[3,2,1,7,5,8,6,4]=>1101110=>0111011
[4,5,8,6,7,1,2,3]=>[3,2,1,7,6,8,5,4]=>1101110=>0111011
[5,2,1,7,6,8,3,4]=>[4,3,8,6,7,1,2,5]=>1010010=>0100101
[4,5,7,6,8,1,2,3]=>[3,2,1,8,6,7,5,4]=>1101110=>0111011
[4,6,7,5,8,1,2,3]=>[3,2,1,8,5,7,6,4]=>1101110=>0111011
[4,7,5,6,8,1,2,3]=>[3,2,1,8,6,5,7,4]=>1101110=>0111011
[4,6,5,7,8,1,2,3]=>[3,2,1,8,7,5,6,4]=>1101101=>1011011
[5,7,4,6,1,8,2,3]=>[3,2,8,1,6,4,7,5]=>1101100=>0011011
[5,8,3,1,6,7,2,4]=>[4,2,7,6,1,3,8,5]=>1100110=>0110011
[5,7,3,1,6,8,2,4]=>[4,2,8,6,1,3,7,5]=>1100110=>0110011
[5,6,3,1,7,8,2,4]=>[4,2,8,7,1,3,6,5]=>1100101=>1010011
[5,8,3,1,7,6,2,4]=>[4,2,6,7,1,3,8,5]=>1100100=>0010011
[5,7,4,8,1,6,2,3]=>[3,2,6,1,8,4,7,5]=>1101100=>0011011
[5,2,1,6,8,7,3,4]=>[4,3,7,8,6,1,2,5]=>1010010=>0100101
[5,4,6,8,1,7,2,3]=>[3,2,7,1,8,6,4,5]=>1101010=>0101011
[4,5,6,8,7,1,2,3]=>[3,2,1,7,8,6,5,4]=>1101110=>0111011
[4,7,5,8,6,1,2,3]=>[3,2,1,6,8,5,7,4]=>1101100=>0011011
[4,8,5,7,6,1,2,3]=>[3,2,1,6,7,5,8,4]=>1101100=>0011011
[4,8,6,7,5,1,2,3]=>[3,2,1,5,7,6,8,4]=>1101010=>0101011
[4,7,6,8,5,1,2,3]=>[3,2,1,5,8,6,7,4]=>1101010=>0101011
[4,6,7,8,5,1,2,3]=>[3,2,1,5,8,7,6,4]=>1101011=>1101011
[4,5,7,8,6,1,2,3]=>[3,2,1,6,8,7,5,4]=>1101101=>1011011
[5,4,7,8,1,6,2,3]=>[3,2,6,1,8,7,4,5]=>1101001=>1001011
[5,3,7,1,8,6,2,4]=>[4,2,6,8,1,7,3,5]=>1110000=>0000111
[5,2,1,7,8,6,3,4]=>[4,3,6,8,7,1,2,5]=>1010001=>1000101
[5,3,8,1,7,6,2,4]=>[4,2,6,7,1,8,3,5]=>1110000=>0000111
[5,4,8,7,1,6,2,3]=>[3,2,6,1,7,8,4,5]=>1101000=>0001011
[4,6,8,7,5,1,2,3]=>[3,2,1,5,7,8,6,4]=>1101010=>0101011
[4,7,8,6,5,1,2,3]=>[3,2,1,5,6,8,7,4]=>1101001=>1001011
[4,8,7,6,5,1,2,3]=>[3,2,1,5,6,7,8,4]=>1101000=>0001011
[2,5,3,1,6,4,8,7]=>[7,8,4,6,1,3,5,2]=>1101000=>0001011
[4,2,7,6,3,5,1,8]=>[8,1,5,3,6,7,2,4]=>1110000=>0000111
[2,7,5,3,6,4,1,8]=>[8,1,4,6,3,5,7,2]=>1110000=>0000111
[2,3,1,8,6,5,4,7]=>[7,4,5,6,8,1,3,2]=>1101000=>0001011
[1,2,6,3,8,7,4,5]=>[5,4,7,8,3,6,2,1]=>1111000=>0001111
[1,2,7,6,3,4,8,5]=>[5,8,4,3,6,7,2,1]=>1111000=>0001111
[1,2,3,8,6,4,7,5]=>[5,7,4,6,8,3,2,1]=>1111000=>0001111
[1,2,3,6,4,8,7,5]=>[5,7,8,4,6,3,2,1]=>1111000=>0001111
[2,1,3,8,5,4,7,6]=>[6,7,4,5,8,3,1,2]=>1011000=>0001101
[7,1,8,4,2,3,5,6]=>[6,5,3,2,4,8,1,7]=>1110100=>0010111
[4,2,6,3,1,8,5,7]=>[7,5,8,1,3,6,2,4]=>1100100=>0010011
[5,4,2,8,3,1,6,7]=>[7,6,1,3,8,2,4,5]=>1100010=>0100011
[1,5,2,8,7,3,4,6]=>[6,4,3,7,8,2,5,1]=>1111000=>0001111
[1,2,8,6,3,7,4,5]=>[5,4,7,3,6,8,2,1]=>1111000=>0001111
[1,2,3,8,7,4,6,5]=>[5,6,4,7,8,3,2,1]=>1111000=>0001111
[1,2,3,8,7,6,4,5]=>[5,4,6,7,8,3,2,1]=>1111000=>0001111
[2,6,5,7,1,4,3,8]=>[8,3,4,1,7,5,6,2]=>1110100=>0010111
[2,6,5,7,1,3,8,4]=>[4,8,3,1,7,5,6,2]=>1110100=>0010111
[3,8,5,7,2,6,4,1]=>[1,4,6,2,7,5,8,3]=>0110100=>0010110
[3,4,8,6,1,2,5,7]=>[7,5,2,1,6,8,4,3]=>1111100=>0011111
[2,5,7,1,4,8,6,3]=>[3,6,8,4,1,7,5,2]=>1101100=>0011011
[2,8,1,7,5,6,4,3]=>[3,4,6,5,7,1,8,2]=>1100100=>0010011
[2,3,8,1,6,5,7,4]=>[4,7,5,6,1,8,3,2]=>1110100=>0010111
[3,5,7,6,1,2,4,8]=>[8,4,2,1,6,7,5,3]=>1111100=>0011111
[4,8,6,7,2,3,5,1]=>[1,5,3,2,7,6,8,4]=>0111010=>0101110
[4,8,6,7,1,3,5,2]=>[2,5,3,1,7,6,8,4]=>1011010=>0101101
[3,4,8,6,1,5,7,2]=>[2,7,5,1,6,8,4,3]=>1011100=>0011101
[3,8,5,7,1,6,4,2]=>[2,4,6,1,7,5,8,3]=>1010100=>0010101
[3,8,5,7,2,1,6,4]=>[4,6,1,2,7,5,8,3]=>1010100=>0010101
[3,4,8,6,2,1,5,7]=>[7,5,1,2,6,8,4,3]=>1011100=>0011101
[3,5,7,6,2,1,4,8]=>[8,4,1,2,6,7,5,3]=>1011100=>0011101
[5,8,6,7,3,4,2,1]=>[1,2,4,3,7,6,8,5]=>0010110=>0110100
[5,8,6,7,2,1,3,4]=>[4,3,1,2,7,6,8,5]=>1010110=>0110101
[4,3,1,7,5,2,8,6]=>[6,8,2,5,7,1,3,4]=>1100000=>0000011
[4,3,2,8,5,1,7,6]=>[6,7,1,5,8,2,3,4]=>1100000=>0000011
[4,3,8,5,1,6,7,2]=>[2,7,6,1,5,8,3,4]=>1010010=>0100101
[5,8,6,7,2,3,4,1]=>[1,4,3,2,7,6,8,5]=>0110110=>0110110
[5,8,6,7,1,2,4,3]=>[3,4,2,1,7,6,8,5]=>1100110=>0110011
[3,2,5,7,6,1,4,8]=>[8,4,1,6,7,5,2,3]=>1101100=>0011011
[4,8,6,7,1,3,2,5]=>[5,2,3,1,7,6,8,4]=>1101010=>0101011
[4,8,6,7,1,2,5,3]=>[3,5,2,1,7,6,8,4]=>1101010=>0101011
[4,8,6,7,2,5,3,1]=>[1,3,5,2,7,6,8,4]=>0101010=>0101010
[4,3,8,5,2,6,7,1]=>[1,7,6,2,5,8,3,4]=>0110010=>0100110
[4,2,6,7,5,1,3,8]=>[8,3,1,5,7,6,2,4]=>1110010=>0100111
[3,5,1,7,4,6,2,8]=>[8,2,6,4,7,1,5,3]=>1111000=>0001111
[3,8,4,7,2,5,1,6]=>[6,1,5,2,7,4,8,3]=>1111000=>0001111
[4,1,3,8,5,2,6,7]=>[7,6,2,5,8,3,1,4]=>1110010=>0100111
[4,2,6,7,5,3,8,1]=>[1,8,3,5,7,6,2,4]=>0110010=>0100110
[4,8,6,7,3,1,2,5]=>[5,2,1,3,7,6,8,4]=>1101010=>0101011
[3,1,5,7,6,2,4,8]=>[8,4,2,6,7,5,1,3]=>1101100=>0011011
[3,4,1,7,5,6,2,8]=>[8,2,6,5,7,1,4,3]=>1110100=>0010111
[4,1,7,5,2,8,6,3]=>[3,6,8,2,5,7,1,4]=>1100000=>0000011
[4,1,6,7,5,2,3,8]=>[8,3,2,5,7,6,1,4]=>1110010=>0100111
[5,8,6,7,3,2,4,1]=>[1,4,2,3,7,6,8,5]=>0100110=>0110010
[5,8,6,7,4,2,3,1]=>[1,3,2,4,7,6,8,5]=>0100110=>0110010
[5,8,6,7,4,1,2,3]=>[3,2,1,4,7,6,8,5]=>1100110=>0110011
[5,8,6,7,4,1,3,2]=>[2,3,1,4,7,6,8,5]=>1000110=>0110001
[5,8,6,7,3,1,4,2]=>[2,4,1,3,7,6,8,5]=>1000110=>0110001
[4,8,6,7,3,1,5,2]=>[2,5,1,3,7,6,8,4]=>1001010=>0101001
[4,1,6,7,5,3,8,2]=>[2,8,3,5,7,6,1,4]=>1010010=>0100101
[4,1,7,5,3,2,8,6]=>[6,8,2,3,5,7,1,4]=>1100000=>0000011
[4,2,8,5,3,1,7,6]=>[6,7,1,3,5,8,2,4]=>1100000=>0000011
[4,2,1,6,7,5,3,8]=>[8,3,5,7,6,1,2,4]=>1010010=>0100101
[4,8,6,7,3,2,1,5]=>[5,1,2,3,7,6,8,4]=>1001010=>0101001
[5,8,6,7,4,2,1,3]=>[3,1,2,4,7,6,8,5]=>1000110=>0110001
[5,8,6,7,4,3,1,2]=>[2,1,3,4,7,6,8,5]=>1000110=>0110001
[6,1,5,2,8,4,7,3]=>[3,7,4,8,2,5,1,6]=>1101000=>0001011
[4,6,1,8,5,7,2,3]=>[3,2,7,5,8,1,6,4]=>1101100=>0011011
[4,7,1,2,8,5,6,3]=>[3,6,5,8,2,1,7,4]=>1101100=>0011011
[1,4,7,2,8,5,6,3]=>[3,6,5,8,2,7,4,1]=>1101100=>0011011
[1,7,3,5,8,6,2,4]=>[4,2,6,8,5,3,7,1]=>1110100=>0010111
[7,3,5,8,6,1,2,4]=>[4,2,1,6,8,5,3,7]=>1110100=>0010111
[6,8,1,5,7,2,3,4]=>[4,3,2,7,5,1,8,6]=>1110110=>0110111
[7,1,2,5,8,6,3,4]=>[4,3,6,8,5,2,1,7]=>1110100=>0010111
[1,7,2,5,8,6,3,4]=>[4,3,6,8,5,2,7,1]=>1110100=>0010111
[1,7,6,8,2,3,5,4]=>[4,5,3,2,8,6,7,1]=>1110010=>0100111
[7,6,8,1,2,3,5,4]=>[4,5,3,2,1,8,6,7]=>1110010=>0100111
[2,7,1,5,8,6,3,4]=>[4,3,6,8,5,1,7,2]=>1110100=>0010111
[2,4,7,1,8,5,6,3]=>[3,6,5,8,1,7,4,2]=>1101100=>0011011
[4,7,5,8,3,1,6,2]=>[2,6,1,3,8,5,7,4]=>1001100=>0011001
[4,7,2,1,8,5,6,3]=>[3,6,5,8,1,2,7,4]=>1001100=>0011001
[7,3,5,8,6,2,1,4]=>[4,1,2,6,8,5,3,7]=>1010100=>0010101
[7,6,8,2,1,3,5,4]=>[4,5,3,1,2,8,6,7]=>1010010=>0100101
[1,2,7,6,8,3,5,4]=>[4,5,3,8,6,7,2,1]=>1110010=>0100111
[3,7,6,8,2,1,5,4]=>[4,5,1,2,8,6,7,3]=>1010010=>0100101
[6,7,4,1,8,5,3,2]=>[2,3,5,8,1,4,7,6]=>1000010=>0100001
[6,7,4,3,1,8,5,2]=>[2,5,8,1,3,4,7,6]=>1000010=>0100001
[2,7,4,1,6,8,5,3]=>[3,5,8,6,1,4,7,2]=>1100010=>0100011
[3,1,7,6,8,2,5,4]=>[4,5,2,8,6,7,1,3]=>1100010=>0100011
[1,3,7,6,8,2,5,4]=>[4,5,2,8,6,7,3,1]=>1110010=>0100111
[1,7,4,2,6,8,5,3]=>[3,5,8,6,2,4,7,1]=>1100010=>0100011
[7,1,4,2,8,5,6,3]=>[3,6,5,8,2,4,1,7]=>1100100=>0010011
[7,1,8,2,5,4,6,3]=>[3,6,4,5,2,8,1,7]=>1101000=>0001011
[7,1,6,8,5,4,2,3]=>[3,2,4,5,8,6,1,7]=>1100010=>0100011
[7,1,2,6,8,5,4,3]=>[3,4,5,8,6,2,1,7]=>1100010=>0100011
[1,7,2,6,8,5,4,3]=>[3,4,5,8,6,2,7,1]=>1100010=>0100011
[1,7,6,8,3,2,5,4]=>[4,5,2,3,8,6,7,1]=>1100010=>0100011
[7,6,8,3,1,2,5,4]=>[4,5,2,1,3,8,6,7]=>1100010=>0100011
[7,1,5,8,6,3,2,4]=>[4,2,3,6,8,5,1,7]=>1100100=>0010011
[3,6,7,1,8,5,4,2]=>[2,4,5,8,1,7,6,3]=>1010010=>0100101
[7,2,6,8,5,4,1,3]=>[3,1,4,5,8,6,2,7]=>1100010=>0100011
[7,6,8,2,3,1,5,4]=>[4,5,1,3,2,8,6,7]=>1100010=>0100011
[2,7,6,8,3,1,5,4]=>[4,5,1,3,8,6,7,2]=>1100010=>0100011
[2,7,1,6,8,5,4,3]=>[3,4,5,8,6,1,7,2]=>1100010=>0100011
[6,7,3,1,8,5,4,2]=>[2,4,5,8,1,3,7,6]=>1000010=>0100001
[6,7,1,8,5,4,3,2]=>[2,3,4,5,8,1,7,6]=>1000010=>0100001
[7,2,1,6,8,5,4,3]=>[3,4,5,8,6,1,2,7]=>1000010=>0100001
[7,8,4,2,1,6,5,3]=>[3,5,6,1,2,4,8,7]=>1000001=>1000001
[6,2,3,4,8,7,1,5]=>[5,1,7,8,4,3,2,6]=>1111000=>0001111
[6,2,3,4,7,8,1,5]=>[5,1,8,7,4,3,2,6]=>1111001=>1001111
[7,8,3,6,4,2,1,5]=>[5,1,2,4,6,3,8,7]=>1010001=>1000101
[7,8,3,5,6,2,1,4]=>[4,1,2,6,5,3,8,7]=>1010101=>1010101
[5,2,6,3,8,1,7,4]=>[4,7,1,8,3,6,2,5]=>1110000=>0000111
[6,3,2,5,8,7,1,4]=>[4,1,7,8,5,2,3,6]=>1100100=>0010011
[6,3,2,8,4,7,1,5]=>[5,1,7,4,8,2,3,6]=>1101000=>0001011
[6,4,3,8,7,5,1,2]=>[2,1,5,7,8,3,4,6]=>1010000=>0000101
[6,4,3,7,8,5,1,2]=>[2,1,5,8,7,3,4,6]=>1010001=>1000101
[6,3,2,7,4,8,1,5]=>[5,1,8,4,7,2,3,6]=>1101000=>0001011
[6,3,2,5,7,8,1,4]=>[4,1,8,7,5,2,3,6]=>1100101=>1010011
[4,5,6,8,3,2,1,7]=>[7,1,2,3,8,6,5,4]=>1001110=>0111001
[4,6,8,5,3,2,1,7]=>[7,1,2,3,5,8,6,4]=>1001010=>0101001
[5,6,1,4,2,3,7,8]=>[8,7,3,2,4,1,6,5]=>1110101=>1010111
[5,6,8,4,3,7,1,2]=>[2,1,7,3,4,8,6,5]=>1010110=>0110101
[5,6,1,4,2,3,8,7]=>[7,8,3,2,4,1,6,5]=>1110100=>0010111
[5,2,8,3,4,1,7,6]=>[6,7,1,4,3,8,2,5]=>1110000=>0000111
[4,5,8,6,3,2,1,7]=>[7,1,2,3,6,8,5,4]=>1001100=>0011001
[4,7,5,6,3,2,1,8]=>[8,1,2,3,6,5,7,4]=>1001100=>0011001
[5,1,4,3,6,2,8,7]=>[7,8,2,6,3,4,1,5]=>1110000=>0000111
[5,1,4,3,8,2,7,6]=>[6,7,2,8,3,4,1,5]=>1110000=>0000111
[5,6,2,4,1,8,7,3]=>[3,7,8,1,4,2,6,5]=>1100100=>0010011
[5,7,2,4,1,8,6,3]=>[3,6,8,1,4,2,7,5]=>1100100=>0010011
[6,1,4,2,8,7,5,3]=>[3,5,7,8,2,4,1,6]=>1100000=>0000011
[5,8,2,4,1,7,6,3]=>[3,6,7,1,4,2,8,5]=>1100100=>0010011
[5,4,1,3,7,2,6,8]=>[8,6,2,7,3,1,4,5]=>1110010=>0100111
[5,8,1,4,2,3,7,6]=>[6,7,3,2,4,1,8,5]=>1110100=>0010111
[5,1,6,3,4,2,7,8]=>[8,7,2,4,3,6,1,5]=>1110001=>1000111
[4,8,6,5,3,2,1,7]=>[7,1,2,3,5,6,8,4]=>1001000=>0001001
[5,4,7,8,3,2,1,6]=>[6,1,2,3,8,7,4,5]=>1001001=>1001001
[4,7,8,5,3,2,1,6]=>[6,1,2,3,5,8,7,4]=>1001001=>1001001
[5,7,1,3,4,2,6,8]=>[8,6,2,4,3,1,7,5]=>1110110=>0110111
[5,1,8,4,2,3,6,7]=>[7,6,3,2,4,8,1,5]=>1110010=>0100111
[5,1,7,4,2,3,6,8]=>[8,6,3,2,4,7,1,5]=>1110010=>0100111
[5,8,1,3,4,2,6,7]=>[7,6,2,4,3,1,8,5]=>1110110=>0110111
[4,8,7,5,3,2,1,6]=>[6,1,2,3,5,7,8,4]=>1001000=>0001001
[4,7,8,6,3,2,1,5]=>[5,1,2,3,6,8,7,4]=>1001001=>1001001
[4,8,2,3,6,7,5,1]=>[1,5,7,6,3,2,8,4]=>0111010=>0101110
[4,3,8,7,2,5,1,6]=>[6,1,5,2,7,8,3,4]=>1110000=>0000111
[5,8,1,4,7,2,6,3]=>[3,6,2,7,4,1,8,5]=>1101100=>0011011
[4,8,7,6,3,1,2,5]=>[5,2,1,3,6,7,8,4]=>1101000=>0001011
[4,3,8,2,7,5,6,1]=>[1,6,5,7,2,8,3,4]=>0110100=>0010110
[1,4,3,8,2,6,5,7]=>[7,5,6,2,8,3,4,1]=>1110100=>0010111
[3,4,8,1,6,2,5,7]=>[7,5,2,6,1,8,4,3]=>1111100=>0011111
[3,4,8,7,2,5,1,6]=>[6,1,5,2,7,8,4,3]=>1111000=>0001111
[3,4,8,2,7,5,6,1]=>[1,6,5,7,2,8,4,3]=>0111100=>0011110
[4,2,3,1,8,6,5,7]=>[7,5,6,8,1,3,2,4]=>1100100=>0010011
[3,7,8,2,6,4,5,1]=>[1,5,4,6,2,8,7,3]=>0111001=>1001110
[7,3,6,8,4,2,1,5]=>[5,1,2,4,8,6,3,7]=>1010010=>0100101
[3,2,4,8,1,6,5,7]=>[7,5,6,1,8,4,2,3]=>1101100=>0011011
[7,3,8,2,6,4,5,1]=>[1,5,4,6,2,8,3,7]=>0111000=>0001110
[6,2,8,7,4,3,5,1]=>[1,5,3,4,7,8,2,6]=>0110000=>0000110
[7,3,2,8,4,6,5,1]=>[1,5,6,4,8,2,3,7]=>0101000=>0001010
[1,3,2,4,8,6,5,7]=>[7,5,6,8,4,2,3,1]=>1101100=>0011011
[3,1,2,4,8,6,5,7]=>[7,5,6,8,4,2,1,3]=>1101100=>0011011
[3,1,4,2,8,6,5,7]=>[7,5,6,8,2,4,1,3]=>1100100=>0010011
[3,7,4,8,5,1,2,6]=>[6,2,1,5,8,4,7,3]=>1111000=>0001111
[6,7,2,8,3,5,4,1]=>[1,4,5,3,8,2,7,6]=>0110010=>0100110
[2,1,3,4,8,6,5,7]=>[7,5,6,8,4,3,1,2]=>1011100=>0011101
[3,5,7,8,6,1,2,4]=>[4,2,1,6,8,7,5,3]=>1110101=>1010111
[3,1,5,6,8,2,7,4]=>[4,7,2,8,6,5,1,3]=>1100110=>0110011
[5,1,6,3,8,4,7,2]=>[2,7,4,8,3,6,1,5]=>1011000=>0001101
[2,5,1,6,8,3,7,4]=>[4,7,3,8,6,1,5,2]=>1110010=>0100111
[5,1,2,6,8,3,7,4]=>[4,7,3,8,6,2,1,5]=>1110010=>0100111
[1,5,2,7,8,6,3,4]=>[4,3,6,8,7,2,5,1]=>1110001=>1000111
[6,1,7,5,2,8,3,4]=>[4,3,8,2,5,7,1,6]=>1110000=>0000111
[2,6,7,5,1,8,3,4]=>[4,3,8,1,5,7,6,2]=>1110010=>0100111
[5,7,2,8,6,1,3,4]=>[4,3,1,6,8,2,7,5]=>1110100=>0010111
[3,5,7,8,6,2,1,4]=>[4,1,2,6,8,7,5,3]=>1010101=>1010101
[3,2,5,7,8,6,1,4]=>[4,1,6,8,7,5,2,3]=>1100101=>1010011
[6,2,7,5,1,8,3,4]=>[4,3,8,1,5,7,2,6]=>1110000=>0000111
[1,2,6,7,5,8,3,4]=>[4,3,8,5,7,6,2,1]=>1110110=>0110111
[6,2,7,5,4,1,8,3]=>[3,8,1,4,5,7,2,6]=>1100000=>0000011
[6,7,5,2,4,1,8,3]=>[3,8,1,4,2,5,7,6]=>1100010=>0100011
[6,7,2,5,3,8,1,4]=>[4,1,8,3,5,2,7,6]=>1110010=>0100111
[5,1,7,8,6,3,2,4]=>[4,2,3,6,8,7,1,5]=>1100001=>1000011
[1,6,7,5,3,8,2,4]=>[4,2,8,3,5,7,6,1]=>1110010=>0100111
[1,6,7,5,4,2,8,3]=>[3,8,2,4,5,7,6,1]=>1100010=>0100011
[5,7,8,6,4,1,2,3]=>[3,2,1,4,6,8,7,5]=>1100101=>1010011
[6,7,4,1,5,2,8,3]=>[3,8,2,5,1,4,7,6]=>1100010=>0100011
[1,6,7,4,5,2,8,3]=>[3,8,2,5,4,7,6,1]=>1101010=>0101011
[6,3,1,7,5,8,2,4]=>[4,2,8,5,7,1,3,6]=>1100100=>0010011
[2,5,3,7,8,6,1,4]=>[4,1,6,8,7,3,5,2]=>1110001=>1000111
[6,3,2,7,5,8,1,4]=>[4,1,8,5,7,2,3,6]=>1100100=>0010011
[6,7,4,2,5,1,8,3]=>[3,8,1,5,2,4,7,6]=>1100010=>0100011
[6,2,7,4,5,1,8,3]=>[3,8,1,5,4,7,2,6]=>1101000=>0001011
[6,2,3,7,5,8,1,4]=>[4,1,8,5,7,3,2,6]=>1110100=>0010111
[7,5,1,6,3,8,2,4]=>[4,2,8,3,6,1,5,7]=>1110000=>0000111
[7,5,1,6,3,8,4,2]=>[2,4,8,3,6,1,5,7]=>1010000=>0000101
[2,7,6,1,3,8,5,4]=>[4,5,8,3,1,6,7,2]=>1110000=>0000111
[2,6,7,4,1,8,3,5]=>[5,3,8,1,4,7,6,2]=>1110010=>0100111
[2,1,6,7,3,8,5,4]=>[4,5,8,3,7,6,1,2]=>1010010=>0100101
[3,6,5,1,8,4,2,7]=>[7,2,4,8,1,5,6,3]=>1110000=>0000111
[3,7,5,4,8,1,6,2]=>[2,6,1,8,4,5,7,3]=>1011000=>0001101
[4,6,1,5,8,7,3,2]=>[2,3,7,8,5,1,6,4]=>1001100=>0011001
[7,5,1,6,2,8,3,4]=>[4,3,8,2,6,1,5,7]=>1110000=>0000111
[4,6,1,5,8,2,3,7]=>[7,3,2,8,5,1,6,4]=>1111100=>0011111
[4,7,1,5,8,3,6,2]=>[2,6,3,8,5,1,7,4]=>1011100=>0011101
[7,5,3,2,8,4,1,6]=>[6,1,4,8,2,3,5,7]=>1100000=>0000011
[6,4,7,3,2,8,5,1]=>[1,5,8,2,3,7,4,6]=>0101000=>0001010
[6,1,4,7,3,2,8,5]=>[5,8,2,3,7,4,1,6]=>1101000=>0001011
[5,1,7,3,8,4,2,6]=>[6,2,4,8,3,7,1,5]=>1110000=>0000111
[5,3,7,1,4,8,6,2]=>[2,6,8,4,1,7,3,5]=>1011000=>0001101
[6,4,3,1,7,8,5,2]=>[2,5,8,7,1,3,4,6]=>1000001=>1000001
[5,6,1,7,8,3,4,2]=>[2,4,3,8,7,1,6,5]=>1010101=>1010101
[1,6,3,7,4,8,5,2]=>[2,5,8,4,7,3,6,1]=>1011000=>0001101
[6,7,2,4,1,8,5,3]=>[3,5,8,1,4,2,7,6]=>1100010=>0100011
[5,6,3,2,1,7,8,4]=>[4,8,7,1,2,3,6,5]=>1000101=>1010001
[6,3,7,2,8,4,1,5]=>[5,1,4,8,2,7,3,6]=>1110000=>0000111
[4,7,2,1,3,8,6,5]=>[5,6,8,3,1,2,7,4]=>1011000=>0001101
[5,7,3,8,2,1,6,4]=>[4,6,1,2,8,3,7,5]=>1010100=>0010101
[2,5,1,7,3,8,6,4]=>[4,6,8,3,7,1,5,2]=>1110000=>0000111
[6,7,2,1,3,8,5,4]=>[4,5,8,3,1,2,7,6]=>1010010=>0100101
[6,3,7,1,8,5,2,4]=>[4,2,5,8,1,7,3,6]=>1110000=>0000111
[6,2,7,1,8,5,4,3]=>[3,4,5,8,1,7,2,6]=>1100000=>0000011
[6,3,1,7,8,5,4,2]=>[2,4,5,8,7,1,3,6]=>1000001=>1000001
[5,3,2,1,8,4,7,6]=>[6,7,4,8,1,2,3,5]=>1001000=>0001001
[2,4,6,5,8,1,3,7]=>[7,3,1,8,5,6,4,2]=>1111100=>0011111
[3,4,1,8,5,2,7,6]=>[6,7,2,5,8,1,4,3]=>1110000=>0000111
[1,5,3,2,8,7,4,6]=>[6,4,7,8,2,3,5,1]=>1101000=>0001011
[5,8,7,4,6,2,1,3]=>[3,1,2,6,4,7,8,5]=>1001100=>0011001
[4,1,3,5,6,8,7,2]=>[2,7,8,6,5,3,1,4]=>1010110=>0110101
[3,2,5,6,8,7,1,4]=>[4,1,7,8,6,5,2,3]=>1100110=>0110011
[4,8,3,1,2,7,6,5]=>[5,6,7,2,1,3,8,4]=>1101000=>0001011
[5,8,2,7,4,1,6,3]=>[3,6,1,4,7,2,8,5]=>1100100=>0010011
[5,1,4,2,8,7,6,3]=>[3,6,7,8,2,4,1,5]=>1100000=>0000011
[6,3,2,1,8,5,7,4]=>[4,7,5,8,1,2,3,6]=>1000100=>0010001
[3,8,4,1,5,6,7,2]=>[2,7,6,5,1,4,8,3]=>1010110=>0110101
[8,1,3,6,5,2,4,7]=>[7,4,2,5,6,3,1,8]=>1111000=>0001111
[1,3,5,2,4,8,7,6]=>[6,7,8,4,2,5,3,1]=>1111000=>0001111
[2,6,5,1,3,8,7,4]=>[4,7,8,3,1,5,6,2]=>1110000=>0000111
[2,8,5,1,4,7,6,3]=>[3,6,7,4,1,5,8,2]=>1101000=>0001011
[6,8,4,3,2,7,1,5]=>[5,1,7,2,3,4,8,6]=>1100010=>0100011
[5,1,3,2,8,6,7,4]=>[4,7,6,8,2,3,1,5]=>1100010=>0100011
[1,8,4,3,7,2,6,5]=>[5,6,2,7,3,4,8,1]=>1110000=>0000111
[3,4,8,7,2,1,6,5]=>[5,6,1,2,7,8,4,3]=>1011000=>0001101
[5,4,7,8,3,6,2,1]=>[1,2,6,3,8,7,4,5]=>0011001=>1001100
[6,3,8,7,4,1,2,5]=>[5,2,1,4,7,8,3,6]=>1110000=>0000111
[6,1,3,8,5,7,2,4]=>[4,2,7,5,8,3,1,6]=>1110100=>0010111
[1,7,2,4,6,5,8,3]=>[3,8,5,6,4,2,7,1]=>1101100=>0011011
[6,3,5,8,7,2,1,4]=>[4,1,2,7,8,5,3,6]=>1010100=>0010101
[5,8,6,2,1,3,7,4]=>[4,7,3,1,2,6,8,5]=>1010100=>0010101
[1,3,2,7,5,8,6,4]=>[4,6,8,5,7,2,3,1]=>1100100=>0010011
[1,4,2,5,8,3,7,6]=>[6,7,3,8,5,2,4,1]=>1110100=>0010111
[1,4,2,7,8,5,6,3]=>[3,6,5,8,7,2,4,1]=>1100101=>1010011
[5,1,2,6,8,4,7,3]=>[3,7,4,8,6,2,1,5]=>1101010=>0101011
[4,1,2,6,8,5,3,7]=>[7,3,5,8,6,2,1,4]=>1110010=>0100111
[1,5,2,4,8,7,6,3]=>[3,6,7,8,4,2,5,1]=>1101000=>0001011
[1,2,7,4,8,6,5,3]=>[3,5,6,8,4,7,2,1]=>1101000=>0001011
[1,3,2,7,5,8,4,6]=>[6,4,8,5,7,2,3,1]=>1101100=>0011011
[1,3,2,8,5,7,4,6]=>[6,4,7,5,8,2,3,1]=>1101100=>0011011
[1,2,6,4,8,7,3,5]=>[5,3,7,8,4,6,2,1]=>1111000=>0001111
[1,2,6,8,5,7,3,4]=>[4,3,7,5,8,6,2,1]=>1110110=>0110111
[1,5,6,8,2,7,3,4]=>[4,3,7,2,8,6,5,1]=>1110110=>0110111
[1,3,8,2,6,7,4,5]=>[5,4,7,6,2,8,3,1]=>1111010=>0101111
[1,4,7,2,8,6,3,5]=>[5,3,6,8,2,7,4,1]=>1111000=>0001111
[1,6,7,8,2,5,3,4]=>[4,3,5,2,8,7,6,1]=>1110011=>1100111
[1,2,6,8,3,7,5,4]=>[4,5,7,3,8,6,2,1]=>1110010=>0100111
[1,5,7,8,2,3,6,4]=>[4,6,3,2,8,7,5,1]=>1110101=>1010111
[1,4,7,2,8,3,6,5]=>[5,6,3,8,2,7,4,1]=>1111000=>0001111
[1,6,7,3,4,8,5,2]=>[2,5,8,4,3,7,6,1]=>1011010=>0101101
[1,5,3,7,4,8,6,2]=>[2,6,8,4,7,3,5,1]=>1011000=>0001101
[1,3,6,4,2,8,7,5]=>[5,7,8,2,4,6,3,1]=>1110000=>0000111
[1,3,7,4,2,8,6,5]=>[5,6,8,2,4,7,3,1]=>1110000=>0000111
[1,2,8,4,7,3,6,5]=>[5,6,3,7,4,8,2,1]=>1111000=>0001111
[1,5,2,4,8,3,7,6]=>[6,7,3,8,4,2,5,1]=>1111000=>0001111
[1,8,4,5,7,2,3,6]=>[6,3,2,7,5,4,8,1]=>1111100=>0011111
[1,8,3,5,2,7,4,6]=>[6,4,7,2,5,3,8,1]=>1111000=>0001111
[2,8,3,5,1,4,7,6]=>[6,7,4,1,5,3,8,2]=>1111000=>0001111
[2,3,8,6,1,4,7,5]=>[5,7,4,1,6,8,3,2]=>1111000=>0001111
[1,4,8,6,7,2,3,5]=>[5,3,2,7,6,8,4,1]=>1111010=>0101111
[1,5,6,8,7,2,3,4]=>[4,3,2,7,8,6,5,1]=>1110110=>0110111
[1,2,7,8,5,3,6,4]=>[4,6,3,5,8,7,2,1]=>1110001=>1000111
[1,2,5,8,7,3,6,4]=>[4,6,3,7,8,5,2,1]=>1110100=>0010111
[1,2,6,8,7,3,5,4]=>[4,5,3,7,8,6,2,1]=>1110010=>0100111
[1,2,7,8,6,3,5,4]=>[4,5,3,6,8,7,2,1]=>1110001=>1000111
[1,5,7,8,6,2,3,4]=>[4,3,2,6,8,7,5,1]=>1110101=>1010111
[1,3,7,6,2,8,4,5]=>[5,4,8,2,6,7,3,1]=>1111000=>0001111
[1,2,8,4,7,6,3,5]=>[5,3,6,7,4,8,2,1]=>1111000=>0001111
[1,2,5,8,7,6,3,4]=>[4,3,6,7,8,5,2,1]=>1110100=>0010111
[1,2,6,8,7,5,3,4]=>[4,3,5,7,8,6,2,1]=>1110010=>0100111
[1,2,7,8,6,5,3,4]=>[4,3,5,6,8,7,2,1]=>1110001=>1000111
[5,2,6,7,3,4,8,1]=>[1,8,4,3,7,6,2,5]=>0111010=>0101110
[5,6,2,1,7,8,3,4]=>[4,3,8,7,1,2,6,5]=>1010101=>1010101
[5,6,2,1,4,8,7,3]=>[3,7,8,4,1,2,6,5]=>1001100=>0011001
[2,6,1,4,5,8,7,3]=>[3,7,8,5,4,1,6,2]=>1101100=>0011011
[5,4,2,7,6,3,8,1]=>[1,8,3,6,7,2,4,5]=>0110000=>0000110
[2,3,7,6,4,5,8,1]=>[1,8,5,4,6,7,3,2]=>0111100=>0011110
[2,6,1,7,5,8,3,4]=>[4,3,8,5,7,1,6,2]=>1110100=>0010111
[5,1,2,7,8,4,3,6]=>[6,3,4,8,7,2,1,5]=>1110001=>1000111
[2,6,1,7,4,8,3,5]=>[5,3,8,4,7,1,6,2]=>1111000=>0001111
[3,6,4,1,7,8,2,5]=>[5,2,8,7,1,4,6,3]=>1110001=>1000111
[5,4,6,1,7,8,2,3]=>[3,2,8,7,1,6,4,5]=>1101001=>1001011
[5,4,6,1,3,8,7,2]=>[2,7,8,3,1,6,4,5]=>1011000=>0001101
[3,6,4,1,5,8,7,2]=>[2,7,8,5,1,4,6,3]=>1010100=>0010101
[2,6,1,5,4,8,7,3]=>[3,7,8,4,5,1,6,2]=>1101000=>0001011
[2,6,1,4,7,8,5,3]=>[3,5,8,7,4,1,6,2]=>1101001=>1001011
[5,1,2,4,8,7,6,3]=>[3,6,7,8,4,2,1,5]=>1101000=>0001011
[2,1,5,3,8,6,4,7]=>[7,4,6,8,3,5,1,2]=>1011000=>0001101
[5,1,2,4,8,6,3,7]=>[7,3,6,8,4,2,1,5]=>1111000=>0001111
[5,6,3,1,4,8,2,7]=>[7,2,8,4,1,3,6,5]=>1101100=>0011011
[2,5,4,3,1,8,6,7]=>[7,6,8,1,3,4,5,2]=>1100010=>0100011
[5,4,6,3,1,8,7,2]=>[2,7,8,1,3,6,4,5]=>1001000=>0001001
[2,1,3,7,8,6,4,5]=>[5,4,6,8,7,3,1,2]=>1011001=>1001101
[5,1,4,2,8,6,7,3]=>[3,7,6,8,2,4,1,5]=>1100010=>0100011
[1,2,3,8,6,7,4,5]=>[5,4,7,6,8,3,2,1]=>1111010=>0101111
[1,2,3,8,7,5,4,6]=>[6,4,5,7,8,3,2,1]=>1111000=>0001111
[1,2,3,8,7,4,5,6]=>[6,5,4,7,8,3,2,1]=>1111100=>0011111
[2,1,3,6,8,7,4,5]=>[5,4,7,8,6,3,1,2]=>1011010=>0101101
[3,1,6,2,8,7,5,4]=>[4,5,7,8,2,6,1,3]=>1100000=>0000011
[6,8,1,3,2,5,4,7]=>[7,4,5,2,3,1,8,6]=>1101010=>0101011
[5,8,1,4,3,7,2,6]=>[6,2,7,3,4,1,8,5]=>1110100=>0010111
[6,8,2,5,3,7,1,4]=>[4,1,7,3,5,2,8,6]=>1110010=>0100111
[2,5,4,7,6,8,1,3]=>[3,1,8,6,7,4,5,2]=>1101010=>0101011
[2,6,1,4,3,7,5,8]=>[8,5,7,3,4,1,6,2]=>1110100=>0010111
[2,6,1,5,3,7,4,8]=>[8,4,7,3,5,1,6,2]=>1111000=>0001111
[4,7,1,3,2,6,5,8]=>[8,5,6,2,3,1,7,4]=>1101100=>0011011
[3,7,1,4,2,6,5,8]=>[8,5,6,2,4,1,7,3]=>1110100=>0010111
[4,7,5,8,3,6,1,2]=>[2,1,6,3,8,5,7,4]=>1011100=>0011101
[4,7,5,8,2,6,1,3]=>[3,1,6,2,8,5,7,4]=>1101100=>0011011
[3,7,4,8,2,6,1,5]=>[5,1,6,2,8,4,7,3]=>1111000=>0001111
[3,7,1,5,2,6,4,8]=>[8,4,6,2,5,1,7,3]=>1111000=>0001111
[3,7,2,6,1,5,4,8]=>[8,4,5,1,6,2,7,3]=>1111000=>0001111
[3,7,2,6,5,8,1,4]=>[4,1,8,5,6,2,7,3]=>1110100=>0010111
[2,6,3,7,1,5,4,8]=>[8,4,5,1,7,3,6,2]=>1111000=>0001111
[7,6,4,8,5,2,3,1]=>[1,3,2,5,8,4,6,7]=>0101000=>0001010
[6,7,4,3,5,1,8,2]=>[2,8,1,5,3,4,7,6]=>1010010=>0100101
[6,7,3,5,4,8,2,1]=>[1,2,8,4,5,3,7,6]=>0011010=>0101100
[6,8,3,7,5,2,4,1]=>[1,4,2,5,7,3,8,6]=>0110010=>0100110
[7,6,3,5,8,2,4,1]=>[1,4,2,8,5,3,6,7]=>0110100=>0010110
[7,6,2,8,4,1,5,3]=>[3,5,1,4,8,2,6,7]=>1100000=>0000011
[7,6,3,4,8,2,5,1]=>[1,5,2,8,4,3,6,7]=>0111000=>0001110
[6,8,3,7,4,5,2,1]=>[1,2,5,4,7,3,8,6]=>0011010=>0101100
[6,7,3,5,8,4,2,1]=>[1,2,4,8,5,3,7,6]=>0010110=>0110100
[5,7,8,3,6,2,1,4]=>[4,1,2,6,3,8,7,5]=>1010101=>1010101
[6,3,8,4,7,2,1,5]=>[5,1,2,7,4,8,3,6]=>1011000=>0001101
[6,3,4,7,5,8,2,1]=>[1,2,8,5,7,4,3,6]=>0011100=>0011100
[6,3,5,7,8,4,2,1]=>[1,2,4,8,7,5,3,6]=>0010101=>1010100
[5,7,3,6,8,2,1,4]=>[4,1,2,8,6,3,7,5]=>1010110=>0110101
[5,6,7,3,4,1,8,2]=>[2,8,1,4,3,7,6,5]=>1010110=>0110101
[4,6,7,8,3,5,2,1]=>[1,2,5,3,8,7,6,4]=>0011011=>1101100
[4,7,3,5,6,8,2,1]=>[1,2,8,6,5,3,7,4]=>0011110=>0111100
[5,3,4,7,8,2,1,6]=>[6,1,2,8,7,4,3,5]=>1011001=>1001101
[5,3,8,2,4,1,6,7]=>[7,6,1,4,2,8,3,5]=>1110010=>0100111
[5,3,4,8,2,6,1,7]=>[7,1,6,2,8,4,3,5]=>1111000=>0001111
[4,8,3,6,2,5,7,1]=>[1,7,5,2,6,3,8,4]=>0111100=>0011110
[4,8,3,5,7,2,6,1]=>[1,6,2,7,5,3,8,4]=>0111100=>0011110
[4,8,3,5,6,7,2,1]=>[1,2,7,6,5,3,8,4]=>0011110=>0111100
[4,7,8,3,5,6,2,1]=>[1,2,6,5,3,8,7,4]=>0011101=>1011100
[4,7,8,3,6,2,5,1]=>[1,5,2,6,3,8,7,4]=>0111001=>1001110
[4,8,3,6,7,2,5,1]=>[1,5,2,7,6,3,8,4]=>0111010=>0101110
[4,8,3,7,2,5,6,1]=>[1,6,5,2,7,3,8,4]=>0111100=>0011110
[5,8,3,7,2,6,4,1]=>[1,4,6,2,7,3,8,5]=>0110100=>0010110
[5,7,3,4,8,2,1,6]=>[6,1,2,8,4,3,7,5]=>1011100=>0011101
[5,8,4,2,3,1,6,7]=>[7,6,1,3,2,4,8,5]=>1100110=>0110011
[5,8,4,2,3,1,7,6]=>[6,7,1,3,2,4,8,5]=>1100100=>0010011
[6,4,8,5,3,7,2,1]=>[1,2,7,3,5,8,4,6]=>0011000=>0001100
[6,4,2,7,3,1,8,5]=>[5,8,1,3,7,2,4,6]=>1100000=>0000011
[6,4,3,7,8,5,2,1]=>[1,2,5,8,7,3,4,6]=>0010001=>1000100
[6,4,5,3,7,1,8,2]=>[2,8,1,7,3,5,4,6]=>1011000=>0001101
[5,7,4,2,3,1,6,8]=>[8,6,1,3,2,4,7,5]=>1100110=>0110011
[5,6,3,7,1,8,2,4]=>[4,2,8,1,7,3,6,5]=>1110100=>0010111
[5,6,3,4,8,2,1,7]=>[7,1,2,8,4,3,6,5]=>1011100=>0011101
[6,3,5,7,4,8,2,1]=>[1,2,8,4,7,5,3,6]=>0011100=>0011100
[6,3,5,4,7,8,2,1]=>[1,2,8,7,4,5,3,6]=>0011001=>1001100
[6,4,3,5,7,1,8,2]=>[2,8,1,7,5,3,4,6]=>1010100=>0010101
[6,4,2,5,1,7,3,8]=>[8,3,7,1,5,2,4,6]=>1110000=>0000111
[5,3,4,7,2,6,1,8]=>[8,1,6,2,7,4,3,5]=>1111000=>0001111
[4,7,3,6,2,5,8,1]=>[1,8,5,2,6,3,7,4]=>0111100=>0011110
[4,7,3,6,8,2,5,1]=>[1,5,2,8,6,3,7,4]=>0111010=>0101110
[4,6,7,3,5,8,2,1]=>[1,2,8,5,3,7,6,4]=>0011110=>0111100
[4,5,7,8,3,6,2,1]=>[1,2,6,3,8,7,5,4]=>0011101=>1011100
[4,5,8,3,7,2,6,1]=>[1,6,2,7,3,8,5,4]=>0111100=>0011110
[5,3,4,6,8,2,1,7]=>[7,1,2,8,6,4,3,5]=>1011010=>0101101
[5,3,6,7,1,8,2,4]=>[4,2,8,1,7,6,3,5]=>1110010=>0100111
[5,3,4,6,7,1,8,2]=>[2,8,1,7,6,4,3,5]=>1011010=>0101101
[4,6,3,5,7,8,2,1]=>[1,2,8,7,5,3,6,4]=>0011101=>1011100
[4,5,7,3,6,8,2,1]=>[1,2,8,6,3,7,5,4]=>0011110=>0111100
[7,1,5,8,4,2,3,6]=>[6,3,2,4,8,5,1,7]=>1110100=>0010111
[8,1,5,7,4,2,3,6]=>[6,3,2,4,7,5,1,8]=>1110100=>0010111
[7,1,4,5,8,2,3,6]=>[6,3,2,8,5,4,1,7]=>1111100=>0011111
[7,4,1,6,2,8,3,5]=>[5,3,8,2,6,1,4,7]=>1110000=>0000111
[8,4,1,7,2,6,3,5]=>[5,3,6,2,7,1,4,8]=>1110000=>0000111
[8,1,4,7,5,2,3,6]=>[6,3,2,5,7,4,1,8]=>1111000=>0001111
[8,1,5,4,7,2,3,6]=>[6,3,2,7,4,5,1,8]=>1111000=>0001111
[2,1,7,5,8,3,4,6]=>[6,4,3,8,5,7,1,2]=>1011100=>0011101
[7,1,5,4,8,2,3,6]=>[6,3,2,8,4,5,1,7]=>1111000=>0001111
[7,1,4,8,5,2,3,6]=>[6,3,2,5,8,4,1,7]=>1111000=>0001111
[7,8,3,1,2,4,6,5]=>[5,6,4,2,1,3,8,7]=>1101001=>1001011
[8,7,1,6,4,2,3,5]=>[5,3,2,4,6,1,7,8]=>1110000=>0000111
[8,6,1,7,4,2,3,5]=>[5,3,2,4,7,1,6,8]=>1110000=>0000111
[7,6,1,8,4,2,3,5]=>[5,3,2,4,8,1,6,7]=>1110000=>0000111
[7,3,8,1,2,4,6,5]=>[5,6,4,2,1,8,3,7]=>1111000=>0001111
[8,3,7,1,2,4,6,5]=>[5,6,4,2,1,7,3,8]=>1111000=>0001111
[8,3,6,1,2,4,7,5]=>[5,7,4,2,1,6,3,8]=>1111000=>0001111
[8,3,7,5,1,2,4,6]=>[6,4,2,1,5,7,3,8]=>1111000=>0001111
[7,3,6,1,2,4,8,5]=>[5,8,4,2,1,6,3,7]=>1111000=>0001111
[6,7,1,8,4,2,3,5]=>[5,3,2,4,8,1,7,6]=>1110010=>0100111
[6,8,1,7,4,2,3,5]=>[5,3,2,4,7,1,8,6]=>1110010=>0100111
[7,1,8,4,5,2,3,6]=>[6,3,2,5,4,8,1,7]=>1111000=>0001111
[7,6,3,1,2,4,8,5]=>[5,8,4,2,1,3,6,7]=>1101000=>0001011
[6,1,2,3,8,7,5,4]=>[4,5,7,8,3,2,1,6]=>1110000=>0000111
[6,8,3,1,2,7,4,5]=>[5,4,7,2,1,3,8,6]=>1101010=>0101011
[6,7,3,1,2,8,4,5]=>[5,4,8,2,1,3,7,6]=>1101010=>0101011
[6,7,1,4,2,3,8,5]=>[5,8,3,2,4,1,7,6]=>1110010=>0100111
[4,3,6,8,5,7,1,2]=>[2,1,7,5,8,6,3,4]=>1010110=>0110101
[3,2,8,5,4,1,7,6]=>[6,7,1,4,5,8,2,3]=>1100000=>0000011
[7,8,2,1,4,6,3,5]=>[5,3,6,4,1,2,8,7]=>1011001=>1001101
[2,4,8,5,1,3,6,7]=>[7,6,3,1,5,8,4,2]=>1111010=>0101111
[1,3,6,8,7,4,2,5]=>[5,2,4,7,8,6,3,1]=>1110010=>0100111
[3,1,5,6,4,8,7,2]=>[2,7,8,4,6,5,1,3]=>1001100=>0011001
[1,3,6,2,5,7,8,4]=>[4,8,7,5,2,6,3,1]=>1110101=>1010111
[3,6,1,4,2,7,8,5]=>[5,8,7,2,4,1,6,3]=>1110001=>1000111
[1,3,6,5,2,7,8,4]=>[4,8,7,2,5,6,3,1]=>1110001=>1000111
[1,2,6,4,3,8,5,7]=>[7,5,8,3,4,6,2,1]=>1110100=>0010111
[1,2,6,3,5,8,7,4]=>[4,7,8,5,3,6,2,1]=>1110100=>0010111
[2,3,5,1,8,4,7,6]=>[6,7,4,8,1,5,3,2]=>1111000=>0001111
[1,2,7,4,6,8,3,5]=>[5,3,8,6,4,7,2,1]=>1111010=>0101111
[2,3,7,5,1,8,4,6]=>[6,4,8,1,5,7,3,2]=>1111000=>0001111
[4,7,2,5,3,8,6,1]=>[1,6,8,3,5,2,7,4]=>0111000=>0001110
[3,1,7,5,4,8,6,2]=>[2,6,8,4,5,7,1,3]=>1001000=>0001001
[1,2,7,6,4,8,5,3]=>[3,5,8,4,6,7,2,1]=>1101000=>0001011
[1,2,7,3,6,8,5,4]=>[4,5,8,6,3,7,2,1]=>1110010=>0100111
[3,1,5,4,8,7,6,2]=>[2,6,7,8,4,5,1,3]=>1001000=>0001001
[1,2,6,8,5,4,7,3]=>[3,7,4,5,8,6,2,1]=>1101010=>0101011
[3,5,7,4,8,2,1,6]=>[6,1,2,8,4,7,5,3]=>1011100=>0011101
[2,4,7,6,8,3,1,5]=>[5,1,3,8,6,7,4,2]=>1101010=>0101011
[1,4,6,8,3,5,2,7]=>[7,2,5,3,8,6,4,1]=>1111010=>0101111
[1,3,6,8,5,2,4,7]=>[7,4,2,5,8,6,3,1]=>1111010=>0101111
[1,2,6,8,5,4,3,7]=>[7,3,4,5,8,6,2,1]=>1110010=>0100111
[1,2,5,8,4,3,7,6]=>[6,7,3,4,8,5,2,1]=>1110100=>0010111
[1,3,6,8,2,5,4,7]=>[7,4,5,2,8,6,3,1]=>1111010=>0101111
[1,4,6,8,3,2,5,7]=>[7,5,2,3,8,6,4,1]=>1101110=>0111011
[2,3,6,5,8,1,7,4]=>[4,7,1,8,5,6,3,2]=>1110100=>0010111
[3,5,4,6,8,2,1,7]=>[7,1,2,8,6,4,5,3]=>1011010=>0101101
[3,5,4,6,8,1,2,7]=>[7,2,1,8,6,4,5,3]=>1111010=>0101111
[1,2,4,7,5,8,3,6]=>[6,3,8,5,7,4,2,1]=>1111100=>0011111
[3,6,4,7,1,8,5,2]=>[2,5,8,1,7,4,6,3]=>1011000=>0001101
[1,2,6,7,3,8,5,4]=>[4,5,8,3,7,6,2,1]=>1110010=>0100111
[1,2,5,7,3,8,6,4]=>[4,6,8,3,7,5,2,1]=>1110100=>0010111
[3,1,5,7,6,8,4,2]=>[2,4,8,6,7,5,1,3]=>1000110=>0110001
[3,5,4,6,8,2,7,1]=>[1,7,2,8,6,4,5,3]=>0111010=>0101110
[4,2,6,1,8,7,5,3]=>[3,5,7,8,1,6,2,4]=>1100000=>0000011
[1,2,7,4,6,8,5,3]=>[3,5,8,6,4,7,2,1]=>1101010=>0101011
[1,2,7,5,6,8,4,3]=>[3,4,8,6,5,7,2,1]=>1100110=>0110011
[3,1,6,7,5,8,4,2]=>[2,4,8,5,7,6,1,3]=>1000110=>0110001
[4,6,2,7,5,8,3,1]=>[1,3,8,5,7,2,6,4]=>0101100=>0011010
[3,5,7,4,8,2,6,1]=>[1,6,2,8,4,7,5,3]=>0111100=>0011110
[1,3,6,8,2,5,7,4]=>[4,7,5,2,8,6,3,1]=>1110110=>0110111
[1,3,5,8,2,7,4,6]=>[6,4,7,2,8,5,3,1]=>1111100=>0011111
[1,2,5,8,4,7,6,3]=>[3,6,7,4,8,5,2,1]=>1101100=>0011011
[1,2,4,8,7,3,6,5]=>[5,6,3,7,8,4,2,1]=>1111000=>0001111
[1,2,5,8,7,4,3,6]=>[6,3,4,7,8,5,2,1]=>1110100=>0010111
[1,3,5,8,7,2,4,6]=>[6,4,2,7,8,5,3,1]=>1111100=>0011111
[2,3,7,6,8,5,1,4]=>[4,1,5,8,6,7,3,2]=>1110010=>0100111
[5,7,1,2,8,6,4,3]=>[3,4,6,8,2,1,7,5]=>1100100=>0010011
[3,1,7,6,8,5,4,2]=>[2,4,5,8,6,7,1,3]=>1000010=>0100001
[1,2,6,8,5,7,4,3]=>[3,4,7,5,8,6,2,1]=>1100110=>0110011
[1,2,5,8,7,4,6,3]=>[3,6,4,7,8,5,2,1]=>1101100=>0011011
[1,2,4,8,7,6,3,5]=>[5,3,6,7,8,4,2,1]=>1111000=>0001111
[5,3,6,2,7,1,4,8]=>[8,4,1,7,2,6,3,5]=>1111000=>0001111
[2,6,3,4,7,1,5,8]=>[8,5,1,7,4,3,6,2]=>1111100=>0011111
[4,7,6,2,3,8,1,5]=>[5,1,8,3,2,6,7,4]=>1111000=>0001111
[7,6,2,4,5,8,1,3]=>[3,1,8,5,4,2,6,7]=>1101100=>0011011
[5,3,1,2,8,4,7,6]=>[6,7,4,8,2,1,3,5]=>1101000=>0001011
[6,5,2,3,7,1,4,8]=>[8,4,1,7,3,2,5,6]=>1111000=>0001111
[5,2,1,8,3,4,6,7]=>[7,6,4,3,8,1,2,5]=>1011010=>0101101
[6,2,3,1,8,4,7,5]=>[5,7,4,8,1,3,2,6]=>1101000=>0001011
[8,2,1,7,3,4,5,6]=>[6,5,4,3,7,1,2,8]=>1011100=>0011101
[8,6,1,7,2,4,5,3]=>[3,5,4,2,7,1,6,8]=>1101000=>0001011
[7,2,1,8,3,4,5,6]=>[6,5,4,3,8,1,2,7]=>1011100=>0011101
[1,7,8,3,4,5,6,2]=>[2,6,5,4,3,8,7,1]=>1011101=>1011101
[6,4,5,8,7,1,2,3]=>[3,2,1,7,8,5,4,6]=>1101100=>0011011
[6,8,2,3,5,1,4,7]=>[7,4,1,5,3,2,8,6]=>1111010=>0101111
[2,7,6,1,3,4,5,8]=>[8,5,4,3,1,6,7,2]=>1111100=>0011111
[7,8,3,6,2,4,5,1]=>[1,5,4,2,6,3,8,7]=>0111001=>1001110
[1,2,3,4,5,6,12,11,10,9,8,7]=>[7,8,9,10,11,12,6,5,4,3,2,1]=>11111100000=>00000111111
[8,6,2,5,4,1,7,3]=>[3,7,1,4,5,2,6,8]=>1100000=>0000011
[8,7,2,5,1,6,4,3]=>[3,4,6,1,5,2,7,8]=>1100000=>0000011
[3,8,2,6,5,1,7,4]=>[4,7,1,5,6,2,8,3]=>1110000=>0000111
[7,8,2,5,4,1,6,3]=>[3,6,1,4,5,2,8,7]=>1100001=>1000011
[7,1,8,2,6,5,4,3]=>[3,4,5,6,2,8,1,7]=>1100000=>0000011
[3,4,6,5,1,2,8,7]=>[7,8,2,1,5,6,4,3]=>1111000=>0001111
[1,4,6,2,3,8,7,5]=>[5,7,8,3,2,6,4,1]=>1111000=>0001111
[7,2,1,6,3,8,5,4]=>[4,5,8,3,6,1,2,7]=>1010000=>0000101
[5,6,7,1,2,8,4,3]=>[3,4,8,2,1,7,6,5]=>1100110=>0110011
[8,7,1,2,6,5,4,3]=>[3,4,5,6,2,1,7,8]=>1100000=>0000011
[7,8,1,2,6,5,4,3]=>[3,4,5,6,2,1,8,7]=>1100001=>1000011
[4,8,5,1,2,7,6,3]=>[3,6,7,2,1,5,8,4]=>1101000=>0001011
[1,8,2,7,4,3,5,6]=>[6,5,3,4,7,2,8,1]=>1110100=>0010111
[1,8,6,4,7,2,3,5]=>[5,3,2,7,4,6,8,1]=>1111000=>0001111
[1,8,4,2,6,3,5,7]=>[7,5,3,6,2,4,8,1]=>1110100=>0010111
[7,4,8,1,5,2,3,6]=>[6,3,2,5,1,8,4,7]=>1111000=>0001111
[4,1,7,2,6,3,5,8]=>[8,5,3,6,2,7,1,4]=>1110100=>0010111
[1,8,5,4,3,7,2,6]=>[6,2,7,3,4,5,8,1]=>1110000=>0000111
[1,8,4,2,5,3,7,6]=>[6,7,3,5,2,4,8,1]=>1110000=>0000111
[1,8,5,4,2,6,7,3]=>[3,7,6,2,4,5,8,1]=>1100010=>0100011
[7,4,8,2,1,3,5,6]=>[6,5,3,1,2,8,4,7]=>1011100=>0011101
[4,1,7,3,2,5,6,8]=>[8,6,5,2,3,7,1,4]=>1100110=>0110011
[7,5,4,8,2,3,6,1]=>[1,6,3,2,8,4,5,7]=>0111000=>0001110
[6,4,8,2,1,3,7,5]=>[5,7,3,1,2,8,4,6]=>1011000=>0001101
[7,3,8,1,5,6,2,4]=>[4,2,6,5,1,8,3,7]=>1110100=>0010111
[3,1,7,2,6,8,4,5]=>[5,4,8,6,2,7,1,3]=>1101010=>0101011
[5,1,7,4,2,6,8,3]=>[3,8,6,2,4,7,1,5]=>1100010=>0100011
[5,4,3,7,1,2,8,6]=>[6,8,2,1,7,3,4,5]=>1110000=>0000111
[4,3,1,6,2,5,7,8]=>[8,7,5,2,6,1,3,4]=>1100101=>1010011
[6,5,4,3,7,1,8,2]=>[2,8,1,7,3,4,5,6]=>1010000=>0000101
[6,5,1,7,3,8,2,4]=>[4,2,8,3,7,1,5,6]=>1110000=>0000111
[6,3,2,8,5,7,1,4]=>[4,1,7,5,8,2,3,6]=>1100100=>0010011
[6,5,4,2,8,3,7,1]=>[1,7,3,8,2,4,5,6]=>0110000=>0000110
[5,4,8,2,1,7,3,6]=>[6,3,7,1,2,8,4,5]=>1011000=>0001101
[5,4,3,8,1,6,2,7]=>[7,2,6,1,8,3,4,5]=>1110000=>0000111
[5,4,3,7,1,6,2,8]=>[8,2,6,1,7,3,4,5]=>1110000=>0000111
[7,2,8,6,3,1,4,5]=>[5,4,1,3,6,8,2,7]=>1101000=>0001011
[2,1,7,8,3,6,4,5]=>[5,4,6,3,8,7,1,2]=>1011001=>1001101
[4,2,1,6,7,3,5,8]=>[8,5,3,7,6,1,2,4]=>1010110=>0110101
[4,3,1,5,2,7,6,8]=>[8,6,7,2,5,1,3,4]=>1100010=>0100011
[5,4,2,7,3,8,1,6]=>[6,1,8,3,7,2,4,5]=>1110000=>0000111
[3,1,6,2,8,7,4,5]=>[5,4,7,8,2,6,1,3]=>1101000=>0001011
[6,3,1,7,8,5,2,4]=>[4,2,5,8,7,1,3,6]=>1100001=>1000011
[5,4,1,7,8,2,6,3]=>[3,6,2,8,7,1,4,5]=>1100001=>1000011
[6,5,4,1,7,8,3,2]=>[2,3,8,7,1,4,5,6]=>1000001=>1000001
[5,4,3,1,6,7,2,8]=>[8,2,7,6,1,3,4,5]=>1100010=>0100011
[5,4,2,6,3,8,7,1]=>[1,7,8,3,6,2,4,5]=>0110000=>0000110
[4,3,1,5,2,6,8,7]=>[7,8,6,2,5,1,3,4]=>1100010=>0100011
[5,4,2,1,6,7,8,3]=>[3,8,7,6,1,2,4,5]=>1000011=>1100001
[5,4,3,1,6,7,8,2]=>[2,8,7,6,1,3,4,5]=>1000011=>1100001
[7,8,2,4,5,1,3,6]=>[6,3,1,5,4,2,8,7]=>1111001=>1001111
[4,6,7,2,5,1,3,8]=>[8,3,1,5,2,7,6,4]=>1111010=>0101111
[7,8,1,3,2,4,5,6]=>[6,5,4,2,3,1,8,7]=>1101101=>1011011
[7,8,4,1,5,2,3,6]=>[6,3,2,5,1,4,8,7]=>1110001=>1000111
[3,6,7,2,1,4,5,8]=>[8,5,4,1,2,7,6,3]=>1011110=>0111101
[5,2,3,6,1,4,7,8]=>[8,7,4,1,6,3,2,5]=>1111001=>1001111
[2,5,3,6,1,4,7,8]=>[8,7,4,1,6,3,5,2]=>1111001=>1001111
[6,4,7,1,5,2,3,8]=>[8,3,2,5,1,7,4,6]=>1111000=>0001111
[6,2,7,3,1,4,5,8]=>[8,5,4,1,3,7,2,6]=>1101100=>0011011
[3,5,4,6,7,8,1,2]=>[2,1,8,7,6,4,5,3]=>1011011=>1101101
[1,5,4,6,7,2,3,8]=>[8,3,2,7,6,4,5,1]=>1111010=>0101111
[1,6,7,3,2,4,5,8]=>[8,5,4,2,3,7,6,1]=>1101110=>0111011
[1,5,3,6,2,4,7,8]=>[8,7,4,2,6,3,5,1]=>1111001=>1001111
[5,1,3,6,2,4,7,8]=>[8,7,4,2,6,3,1,5]=>1111001=>1001111
[5,2,4,6,7,1,3,8]=>[8,3,1,7,6,4,2,5]=>1111010=>0101111
[2,6,7,4,5,1,3,8]=>[8,3,1,5,4,7,6,2]=>1111010=>0101111
[4,2,5,6,7,1,3,8]=>[8,3,1,7,6,5,2,4]=>1110110=>0110111
[4,5,2,6,7,1,3,8]=>[8,3,1,7,6,2,5,4]=>1111010=>0101111
[5,3,1,6,2,4,7,8]=>[8,7,4,2,6,1,3,5]=>1101001=>1001011
[6,1,7,3,2,4,5,8]=>[8,5,4,2,3,7,1,6]=>1101100=>0011011
[6,1,7,4,5,2,3,8]=>[8,3,2,5,4,7,1,6]=>1111000=>0001111
[6,3,7,4,5,8,1,2]=>[2,1,8,5,4,7,3,6]=>1011100=>0011101
[5,4,1,6,7,2,3,8]=>[8,3,2,7,6,1,4,5]=>1110010=>0100111
[5,2,1,6,3,4,7,8]=>[8,7,4,3,6,1,2,5]=>1011001=>1001101
[1,3,6,7,5,2,8,4]=>[4,8,2,5,7,6,3,1]=>1110010=>0100111
[7,3,4,1,6,2,5,8]=>[8,5,2,6,1,4,3,7]=>1110100=>0010111
[1,3,6,7,2,5,8,4]=>[4,8,5,2,7,6,3,1]=>1110110=>0110111
[5,6,1,4,7,3,8,2]=>[2,8,3,7,4,1,6,5]=>1011100=>0011101
[2,3,4,5,8,6,1,7]=>[7,1,6,8,5,4,3,2]=>1111100=>0011111
[3,7,5,2,6,8,1,4]=>[4,1,8,6,2,5,7,3]=>1110010=>0100111
[5,6,1,2,7,4,8,3]=>[3,8,4,7,2,1,6,5]=>1101100=>0011011
[6,3,5,2,4,7,8,1]=>[1,8,7,4,2,5,3,6]=>0111001=>1001110
[7,1,5,2,6,8,3,4]=>[4,3,8,6,2,5,1,7]=>1110010=>0100111
[4,3,2,6,7,1,8,5]=>[5,8,1,7,6,2,3,4]=>1100010=>0100011
[5,7,4,6,1,8,3,2]=>[2,3,8,1,6,4,7,5]=>1001100=>0011001
[7,3,4,5,8,2,6,1]=>[1,6,2,8,5,4,3,7]=>0111100=>0011110
[6,2,1,7,3,5,4,8]=>[8,4,5,3,7,1,2,6]=>1011000=>0001101
[2,1,8,6,3,5,4,7]=>[7,4,5,3,6,8,1,2]=>1011000=>0001101
[2,7,3,1,5,4,6,8]=>[8,6,4,5,1,3,7,2]=>1101010=>0101011
[2,6,3,1,4,8,5,7]=>[7,5,8,4,1,3,6,2]=>1101100=>0011011
[4,2,1,8,3,6,7,5]=>[5,7,6,3,8,1,2,4]=>1010010=>0100101
[6,2,1,7,3,5,8,4]=>[4,8,5,3,7,1,2,6]=>1010100=>0010101
[2,7,3,1,4,8,5,6]=>[6,5,8,4,1,3,7,2]=>1101100=>0011011
[3,2,1,5,7,8,4,6]=>[6,4,8,7,5,1,2,3]=>1001101=>1011001
[2,4,7,5,1,6,8,3]=>[3,8,6,1,5,7,4,2]=>1101010=>0101011
[4,3,6,8,5,1,7,2]=>[2,7,1,5,8,6,3,4]=>1010010=>0100101
[2,1,6,8,3,7,4,5]=>[5,4,7,3,8,6,1,2]=>1011010=>0101101
[3,2,1,5,6,8,4,7]=>[7,4,8,6,5,1,2,3]=>1001110=>0111001
[2,1,7,3,6,4,5,8]=>[8,5,4,6,3,7,1,2]=>1011100=>0011101
[2,1,6,3,5,8,4,7]=>[7,4,8,5,3,6,1,2]=>1011100=>0011101
[2,6,1,8,3,5,4,7]=>[7,4,5,3,8,1,6,2]=>1111000=>0001111
[2,7,3,1,5,6,4,8]=>[8,4,6,5,1,3,7,2]=>1101100=>0011011
[2,4,7,5,1,6,3,8]=>[8,3,6,1,5,7,4,2]=>1111000=>0001111
[8,2,4,1,7,5,3,6]=>[6,3,5,7,1,4,2,8]=>1110000=>0000111
[2,4,7,1,8,5,3,6]=>[6,3,5,8,1,7,4,2]=>1111000=>0001111
[2,4,8,5,1,6,3,7]=>[7,3,6,1,5,8,4,2]=>1111000=>0001111
[6,2,1,7,3,4,8,5]=>[5,8,4,3,7,1,2,6]=>1011000=>0001101
[6,2,1,7,8,3,5,4]=>[4,5,3,8,7,1,2,6]=>1010001=>1000101
[2,7,1,8,3,5,6,4]=>[4,6,5,3,8,1,7,2]=>1110100=>0010111
[3,2,1,6,7,4,5,8]=>[8,5,4,7,6,1,2,3]=>1001110=>0111001
[3,2,1,7,4,5,6,8]=>[8,6,5,4,7,1,2,3]=>1001110=>0111001
[2,1,8,3,7,4,5,6]=>[6,5,4,7,3,8,1,2]=>1011100=>0011101
[2,4,8,5,1,6,7,3]=>[3,7,6,1,5,8,4,2]=>1101010=>0101011
[4,3,8,5,6,1,7,2]=>[2,7,1,6,5,8,3,4]=>1010100=>0010101
[3,2,1,8,4,5,6,7]=>[7,6,5,4,8,1,2,3]=>1001110=>0111001
[1,6,8,3,7,2,4,5]=>[5,4,2,7,3,8,6,1]=>1111010=>0101111
[1,2,6,8,4,7,3,5]=>[5,3,7,4,8,6,2,1]=>1111010=>0101111
[6,1,5,8,2,4,7,3]=>[3,7,4,2,8,5,1,6]=>1101100=>0011011
[4,1,2,7,8,3,6,5]=>[5,6,3,8,7,2,1,4]=>1110001=>1000111
[5,3,8,4,7,6,1,2]=>[2,1,6,7,4,8,3,5]=>1011000=>0001101
[1,2,5,3,7,6,4,8]=>[8,4,6,7,3,5,2,1]=>1111000=>0001111
[7,1,6,2,8,4,5,3]=>[3,5,4,8,2,6,1,7]=>1101000=>0001011
[1,2,7,3,8,5,4,6]=>[6,4,5,8,3,7,2,1]=>1111000=>0001111
[3,1,7,8,6,2,4,5]=>[5,4,2,6,8,7,1,3]=>1101001=>1001011
[3,8,6,4,7,5,1,2]=>[2,1,5,7,4,6,8,3]=>1011000=>0001101
[1,2,3,7,5,4,8,6]=>[6,8,4,5,7,3,2,1]=>1111000=>0001111
[3,7,4,8,6,5,1,2]=>[2,1,5,6,8,4,7,3]=>1011000=>0001101
[1,8,2,7,6,4,5,3]=>[3,5,4,6,7,2,8,1]=>1101000=>0001011
[8,4,6,2,7,5,3,1]=>[1,3,5,7,2,6,4,8]=>0101000=>0001010
[7,5,6,8,2,4,1,3]=>[3,1,4,2,8,6,5,7]=>1100110=>0110011
[4,3,2,6,8,5,1,7]=>[7,1,5,8,6,2,3,4]=>1100010=>0100011
[3,5,6,8,2,4,1,7]=>[7,1,4,2,8,6,5,3]=>1110110=>0110111
[3,5,7,8,2,1,4,6]=>[6,4,1,2,8,7,5,3]=>1011101=>1011101
[2,5,7,8,3,1,4,6]=>[6,4,1,3,8,7,5,2]=>1101101=>1011011
[6,4,7,3,8,1,5,2]=>[2,5,1,8,3,7,4,6]=>1011000=>0001101
[6,3,2,5,4,8,1,7]=>[7,1,8,4,5,2,3,6]=>1101000=>0001011
[2,5,7,8,3,1,6,4]=>[4,6,1,3,8,7,5,2]=>1100101=>1010011
[4,5,7,8,3,1,2,6]=>[6,2,1,3,8,7,5,4]=>1101101=>1011011
[5,4,6,2,8,3,1,7]=>[7,1,3,8,2,6,4,5]=>1101000=>0001011
[5,3,2,6,8,4,1,7]=>[7,1,4,8,6,2,3,5]=>1100010=>0100011
[5,4,7,2,8,1,3,6]=>[6,3,1,8,2,7,4,5]=>1111000=>0001111
[4,5,7,8,2,1,3,6]=>[6,3,1,2,8,7,5,4]=>1011101=>1011101
[4,6,7,8,1,5,2,3]=>[3,2,5,1,8,7,6,4]=>1101011=>1101011
[4,3,2,7,8,1,6,5]=>[5,6,1,8,7,2,3,4]=>1100001=>1000011
[3,5,7,8,2,1,6,4]=>[4,6,1,2,8,7,5,3]=>1010101=>1010101
[2,6,7,8,1,5,4,3]=>[3,4,5,1,8,7,6,2]=>1100011=>1100011
[4,5,8,3,6,7,1,2]=>[2,1,7,6,3,8,5,4]=>1011110=>0111101
[4,5,8,3,7,6,1,2]=>[2,1,6,7,3,8,5,4]=>1011100=>0011101
[7,2,3,4,8,1,5,6]=>[6,5,1,8,4,3,2,7]=>1111100=>0011111
[7,6,3,4,8,5,1,2]=>[2,1,5,8,4,3,6,7]=>1011000=>0001101
[7,2,3,8,5,1,4,6]=>[6,4,1,5,8,3,2,7]=>1111000=>0001111
[2,6,4,8,1,5,7,3]=>[3,7,5,1,8,4,6,2]=>1101100=>0011011
[7,8,2,3,6,1,4,5]=>[5,4,1,6,3,2,8,7]=>1111001=>1001111
[7,6,5,1,2,3,8,4]=>[4,8,3,2,1,5,6,7]=>1110000=>0000111
[7,8,5,4,1,2,6,3]=>[3,6,2,1,4,5,8,7]=>1100001=>1000011
[3,5,6,4,1,2,8,7]=>[7,8,2,1,4,6,5,3]=>1110100=>0010111
[7,6,5,1,2,4,8,3]=>[3,8,4,2,1,5,6,7]=>1101000=>0001011
[2,6,4,3,1,8,7,5]=>[5,7,8,1,3,4,6,2]=>1100000=>0000011
[2,5,8,4,1,7,3,6]=>[6,3,7,1,4,8,5,2]=>1110100=>0010111
[3,6,4,2,1,7,5,8]=>[8,5,7,1,2,4,6,3]=>1010100=>0010101
[7,6,5,1,2,8,3,4]=>[4,3,8,2,1,5,6,7]=>1110000=>0000111
[7,6,5,1,8,2,4,3]=>[3,4,2,8,1,5,6,7]=>1100000=>0000011
[7,6,5,1,8,2,3,4]=>[4,3,2,8,1,5,6,7]=>1110000=>0000111
[3,6,4,5,1,7,2,8]=>[8,2,7,1,5,4,6,3]=>1111000=>0001111
[2,5,6,4,1,7,8,3]=>[3,8,7,1,4,6,5,2]=>1100101=>1010011
[2,5,6,4,1,7,3,8]=>[8,3,7,1,4,6,5,2]=>1110100=>0010111
[7,6,5,1,8,4,2,3]=>[3,2,4,8,1,5,6,7]=>1100000=>0000011
[7,4,2,5,6,3,1,8]=>[8,1,3,6,5,2,4,7]=>1100100=>0010011
[1,6,8,5,2,7,4,3]=>[3,4,7,2,5,8,6,1]=>1100010=>0100011
[6,2,8,5,1,7,4,3]=>[3,4,7,1,5,8,2,6]=>1100000=>0000011
[3,2,7,8,6,1,5,4]=>[4,5,1,6,8,7,2,3]=>1100001=>1000011
[3,8,1,5,2,7,6,4]=>[4,6,7,2,5,1,8,3]=>1110000=>0000111
[5,2,3,1,6,7,8,4]=>[4,8,7,6,1,3,2,5]=>1100011=>1100011
[7,6,4,2,1,5,8,3]=>[3,8,5,1,2,4,6,7]=>1000100=>0010001
[6,7,4,1,5,3,8,2]=>[2,8,3,5,1,4,7,6]=>1010010=>0100101
[7,5,4,1,2,6,8,3]=>[3,8,6,2,1,4,5,7]=>1100010=>0100011
[5,2,1,4,6,7,8,3]=>[3,8,7,6,4,1,2,5]=>1001011=>1101001
[5,4,1,3,6,7,8,2]=>[2,8,7,6,3,1,4,5]=>1010011=>1100101
[8,4,1,5,3,7,2,6]=>[6,2,7,3,5,1,4,8]=>1110000=>0000111
[7,5,4,1,3,2,8,6]=>[6,8,2,3,1,4,5,7]=>1100000=>0000011
[5,1,3,4,6,7,8,2]=>[2,8,7,6,4,3,1,5]=>1011011=>1101101
[3,8,1,7,5,6,4,2]=>[2,4,6,5,7,1,8,3]=>1010100=>0010101
[8,2,5,7,3,6,4,1]=>[1,4,6,3,7,5,2,8]=>0110100=>0010110
[1,8,6,7,5,3,4,2]=>[2,4,3,5,7,6,8,1]=>1010010=>0100101
[8,2,6,7,5,3,4,1]=>[1,4,3,5,7,6,2,8]=>0110010=>0100110
[5,4,8,6,2,3,7,1]=>[1,7,3,2,6,8,4,5]=>0111000=>0001110
[2,7,6,1,3,5,4,8]=>[8,4,5,3,1,6,7,2]=>1111000=>0001111
[2,8,6,1,3,5,4,7]=>[7,4,5,3,1,6,8,2]=>1111000=>0001111
[5,7,4,1,8,6,3,2]=>[2,3,6,8,1,4,7,5]=>1000100=>0010001
[5,6,4,2,8,3,7,1]=>[1,7,3,8,2,4,6,5]=>0110100=>0010110
[5,6,4,2,7,3,1,8]=>[8,1,3,7,2,4,6,5]=>1100100=>0010011
[5,8,1,4,6,3,7,2]=>[2,7,3,6,4,1,8,5]=>1011100=>0011101
[3,6,7,4,5,8,2,1]=>[1,2,8,5,4,7,6,3]=>0011110=>0111100
[5,4,6,1,7,8,3,2]=>[2,3,8,7,1,6,4,5]=>1001001=>1001001
[5,6,4,1,8,7,3,2]=>[2,3,7,8,1,4,6,5]=>1000100=>0010001
[3,5,8,4,6,7,2,1]=>[1,2,7,6,4,8,5,3]=>0011110=>0111100
[3,6,8,4,5,7,2,1]=>[1,2,7,5,4,8,6,3]=>0011110=>0111100
[3,7,8,4,5,6,2,1]=>[1,2,6,5,4,8,7,3]=>0011101=>1011100
[3,7,1,5,4,6,2,8]=>[8,2,6,4,5,1,7,3]=>1111000=>0001111
[3,8,1,5,4,6,7,2]=>[2,7,6,4,5,1,8,3]=>1011010=>0101101
[3,7,1,5,4,6,8,2]=>[2,8,6,4,5,1,7,3]=>1011010=>0101101
[6,7,1,4,5,3,8,2]=>[2,8,3,5,4,1,7,6]=>1011010=>0101101
[5,7,1,4,6,3,8,2]=>[2,8,3,6,4,1,7,5]=>1011100=>0011101
[5,4,7,2,8,3,1,6]=>[6,1,3,8,2,7,4,5]=>1101000=>0001011
[5,4,7,2,8,3,6,1]=>[1,6,3,8,2,7,4,5]=>0111000=>0001110
[5,6,4,2,8,3,1,7]=>[7,1,3,8,2,4,6,5]=>1100100=>0010011
[5,8,1,4,6,3,2,7]=>[7,2,3,6,4,1,8,5]=>1101100=>0011011
[3,8,1,5,4,6,2,7]=>[7,2,6,4,5,1,8,3]=>1111000=>0001111
[3,6,1,5,4,2,7,8]=>[8,7,2,4,5,1,6,3]=>1110001=>1000111
[3,6,1,5,4,8,2,7]=>[7,2,8,4,5,1,6,3]=>1111000=>0001111
[6,8,3,1,4,2,5,7]=>[7,5,2,4,1,3,8,6]=>1100110=>0110011
[7,3,8,1,4,2,5,6]=>[6,5,2,4,1,8,3,7]=>1110100=>0010111
[3,6,1,5,4,7,8,2]=>[2,8,7,4,5,1,6,3]=>1011001=>1001101
[3,4,1,2,7,6,5,8]=>[8,5,6,7,2,1,4,3]=>1110100=>0010111
[3,4,1,2,6,8,7,5]=>[5,7,8,6,2,1,4,3]=>1110010=>0100111
[7,8,1,4,5,3,2,6]=>[6,2,3,5,4,1,8,7]=>1101001=>1001011
[3,8,1,5,4,7,2,6]=>[6,2,7,4,5,1,8,3]=>1111000=>0001111
[3,6,1,5,4,8,7,2]=>[2,7,8,4,5,1,6,3]=>1011000=>0001101
[3,6,1,5,4,7,2,8]=>[8,2,7,4,5,1,6,3]=>1111000=>0001111
[6,7,3,1,4,2,5,8]=>[8,5,2,4,1,3,7,6]=>1100110=>0110011
[6,8,3,1,4,2,7,5]=>[5,7,2,4,1,3,8,6]=>1100010=>0100011
[7,8,3,1,4,6,2,5]=>[5,2,6,4,1,3,8,7]=>1101001=>1001011
[7,8,4,2,6,5,1,3]=>[3,1,5,6,2,4,8,7]=>1100001=>1000011
[6,5,8,7,3,4,2,1]=>[1,2,4,3,7,8,5,6]=>0010100=>0010100
[7,8,3,1,4,6,5,2]=>[2,5,6,4,1,3,8,7]=>1001001=>1001001
[6,7,3,1,4,5,2,8]=>[8,2,5,4,1,3,7,6]=>1101010=>0101011
[3,7,1,5,4,2,6,8]=>[8,6,2,4,5,1,7,3]=>1110010=>0100111
[3,8,1,5,4,2,7,6]=>[6,7,2,4,5,1,8,3]=>1110000=>0000111
[5,8,1,4,7,3,6,2]=>[2,6,3,7,4,1,8,5]=>1011100=>0011101
[6,3,7,1,4,8,5,2]=>[2,5,8,4,1,7,3,6]=>1011000=>0001101
[3,7,1,5,4,8,6,2]=>[2,6,8,4,5,1,7,3]=>1011000=>0001101
[3,7,1,5,4,2,8,6]=>[6,8,2,4,5,1,7,3]=>1110000=>0000111
[6,7,3,1,4,5,8,2]=>[2,8,5,4,1,3,7,6]=>1001110=>0111001
[7,3,8,1,4,5,2,6]=>[6,2,5,4,1,8,3,7]=>1111000=>0001111
[6,8,3,1,4,5,2,7]=>[7,2,5,4,1,3,8,6]=>1101010=>0101011
[3,8,1,5,4,2,6,7]=>[7,6,2,4,5,1,8,3]=>1110010=>0100111
[2,3,6,4,8,1,5,7]=>[7,5,1,8,4,6,3,2]=>1111100=>0011111
[2,5,6,1,4,7,8,3]=>[3,8,7,4,1,6,5,2]=>1101101=>1011011
[2,5,6,1,4,7,3,8]=>[8,3,7,4,1,6,5,2]=>1111100=>0011111
[7,3,5,8,4,1,2,6]=>[6,2,1,4,8,5,3,7]=>1110100=>0010111
[1,8,4,5,2,7,3,6]=>[6,3,7,2,5,4,8,1]=>1111000=>0001111
[7,3,5,8,4,1,6,2]=>[2,6,1,4,8,5,3,7]=>1010100=>0010101
[6,3,5,4,7,1,8,2]=>[2,8,1,7,4,5,3,6]=>1011000=>0001101
[7,3,5,4,6,8,2,1]=>[1,2,8,6,4,5,3,7]=>0011010=>0101100
[2,7,6,4,8,5,3,1]=>[1,3,5,8,4,6,7,2]=>0101000=>0001010
[1,8,4,5,2,6,3,7]=>[7,3,6,2,5,4,8,1]=>1111000=>0001111
[6,4,8,5,3,1,2,7]=>[7,2,1,3,5,8,4,6]=>1101000=>0001011
[3,2,8,6,1,5,4,7]=>[7,4,5,1,6,8,2,3]=>1101000=>0001011
[8,7,3,6,4,2,5,1]=>[1,5,2,4,6,3,7,8]=>0110000=>0000110
[5,3,6,2,4,8,7,1]=>[1,7,8,4,2,6,3,5]=>0111000=>0001110
[3,5,2,8,6,1,4,7]=>[7,4,1,6,8,2,5,3]=>1111000=>0001111
[3,7,2,5,1,4,8,6]=>[6,8,4,1,5,2,7,3]=>1111000=>0001111
[8,2,3,6,1,4,7,5]=>[5,7,4,1,6,3,2,8]=>1111000=>0001111
[1,8,2,6,3,4,7,5]=>[5,7,4,3,6,2,8,1]=>1111000=>0001111
[7,2,3,6,1,4,8,5]=>[5,8,4,1,6,3,2,7]=>1111000=>0001111
[8,6,1,4,7,3,2,5]=>[5,2,3,7,4,1,6,8]=>1101000=>0001011
[2,3,1,8,5,4,6,7]=>[7,6,4,5,8,1,3,2]=>1101010=>0101011
[8,5,1,7,6,3,4,2]=>[2,4,3,6,7,1,5,8]=>1010000=>0000101
[3,7,2,5,6,1,8,4]=>[4,8,1,6,5,2,7,3]=>1110100=>0010111
[2,7,5,3,8,4,1,6]=>[6,1,4,8,3,5,7,2]=>1110000=>0000111
[1,8,3,2,5,7,4,6]=>[6,4,7,5,2,3,8,1]=>1101100=>0011011
[6,5,1,7,4,2,8,3]=>[3,8,2,4,7,1,5,6]=>1100000=>0000011
[4,6,1,7,3,5,2,8]=>[8,2,5,3,7,1,6,4]=>1111000=>0001111
[6,1,7,3,4,2,8,5]=>[5,8,2,4,3,7,1,6]=>1110000=>0000111
[7,3,8,1,6,5,2,4]=>[4,2,5,6,1,8,3,7]=>1110000=>0000111
[8,3,7,1,6,5,2,4]=>[4,2,5,6,1,7,3,8]=>1110000=>0000111
[2,8,1,7,6,5,3,4]=>[4,3,5,6,7,1,8,2]=>1110000=>0000111
[4,2,8,6,5,1,7,3]=>[3,7,1,5,6,8,2,4]=>1100000=>0000011
[8,6,4,7,1,5,2,3]=>[3,2,5,1,7,4,6,8]=>1101000=>0001011
[7,6,4,8,1,5,2,3]=>[3,2,5,1,8,4,6,7]=>1101000=>0001011
[5,1,6,4,2,3,8,7]=>[7,8,3,2,4,6,1,5]=>1110000=>0000111
[4,2,3,8,7,5,1,6]=>[6,1,5,7,8,3,2,4]=>1110000=>0000111
[3,8,7,1,6,5,2,4]=>[4,2,5,6,1,7,8,3]=>1110000=>0000111
[2,4,3,8,1,6,7,5]=>[5,7,6,1,8,3,4,2]=>1110010=>0100111
[2,4,3,7,1,6,8,5]=>[5,8,6,1,7,3,4,2]=>1110010=>0100111
[4,2,3,7,8,5,1,6]=>[6,1,5,8,7,3,2,4]=>1110001=>1000111
[5,1,6,4,2,3,7,8]=>[8,7,3,2,4,6,1,5]=>1110001=>1000111
[6,4,7,8,1,5,2,3]=>[3,2,5,1,8,7,4,6]=>1101001=>1001011
[8,7,4,6,1,5,2,3]=>[3,2,5,1,6,4,7,8]=>1101000=>0001011
[6,5,7,8,1,4,2,3]=>[3,2,4,1,8,7,5,6]=>1100101=>1010011
[4,7,8,6,1,5,2,3]=>[3,2,5,1,6,8,7,4]=>1101001=>1001011
[3,2,4,8,7,1,5,6]=>[6,5,1,7,8,4,2,3]=>1101100=>0011011
[4,8,7,6,1,5,2,3]=>[3,2,5,1,6,7,8,4]=>1101000=>0001011
[5,8,7,6,1,4,2,3]=>[3,2,4,1,6,7,8,5]=>1100100=>0010011
[8,6,5,7,1,4,2,3]=>[3,2,4,1,7,5,6,8]=>1100100=>0010011
[6,7,4,8,1,5,2,3]=>[3,2,5,1,8,4,7,6]=>1101010=>0101011
[8,4,7,6,1,5,2,3]=>[3,2,5,1,6,7,4,8]=>1101000=>0001011
[8,3,2,4,7,1,5,6]=>[6,5,1,7,4,2,3,8]=>1101100=>0011011
[2,5,3,7,1,6,4,8]=>[8,4,6,1,7,3,5,2]=>1111000=>0001111
[8,4,6,7,1,5,2,3]=>[3,2,5,1,7,6,4,8]=>1101010=>0101011
[5,1,6,8,4,2,3,7]=>[7,3,2,4,8,6,1,5]=>1110010=>0100111
[4,2,3,7,5,1,6,8]=>[8,6,1,5,7,3,2,4]=>1110010=>0100111
[2,4,7,1,5,8,6,3]=>[3,6,8,5,1,7,4,2]=>1101100=>0011011
[3,2,4,7,6,1,5,8]=>[8,5,1,6,7,4,2,3]=>1101100=>0011011
[4,7,6,8,1,5,2,3]=>[3,2,5,1,8,6,7,4]=>1101010=>0101011
[8,5,6,7,1,4,2,3]=>[3,2,4,1,7,6,5,8]=>1100110=>0110011
[8,6,7,5,1,4,2,3]=>[3,2,4,1,5,7,6,8]=>1100010=>0100011
[6,8,7,5,1,4,2,3]=>[3,2,4,1,5,7,8,6]=>1100010=>0100011
[5,6,8,7,1,4,2,3]=>[3,2,4,1,7,8,6,5]=>1100110=>0110011
[4,6,8,7,1,5,2,3]=>[3,2,5,1,7,8,6,4]=>1101010=>0101011
[3,2,4,6,1,5,7,8]=>[8,7,5,1,6,4,2,3]=>1101101=>1011011
[6,7,8,5,1,4,2,3]=>[3,2,4,1,5,8,7,6]=>1100011=>1100011
[7,8,6,5,1,4,2,3]=>[3,2,4,1,5,6,8,7]=>1100001=>1000011
[4,1,8,5,2,3,6,7]=>[7,6,3,2,5,8,1,4]=>1110010=>0100111
[5,4,1,3,6,7,2,8]=>[8,2,7,6,3,1,4,5]=>1110010=>0100111
[8,4,1,2,6,3,7,5]=>[5,7,3,6,2,1,4,8]=>1110000=>0000111
[3,2,7,1,5,8,4,6]=>[6,4,8,5,1,7,2,3]=>1101100=>0011011
[7,3,8,1,5,4,2,6]=>[6,2,4,5,1,8,3,7]=>1110000=>0000111
[4,7,1,2,6,3,8,5]=>[5,8,3,6,2,1,7,4]=>1111000=>0001111
[5,7,8,6,1,4,3,2]=>[2,3,4,1,6,8,7,5]=>1000101=>1010001
[2,7,4,1,6,5,3,8]=>[8,3,5,6,1,4,7,2]=>1110000=>0000111
[5,6,8,7,1,4,3,2]=>[2,3,4,1,7,8,6,5]=>1000110=>0110001
[6,2,4,1,8,5,3,7]=>[7,3,5,8,1,4,2,6]=>1110000=>0000111
[7,5,1,6,3,4,8,2]=>[2,8,4,3,6,1,5,7]=>1011000=>0001101
[5,3,1,8,4,6,7,2]=>[2,7,6,4,8,1,3,5]=>1001010=>0101001
[8,3,1,5,4,6,7,2]=>[2,7,6,4,5,1,3,8]=>1001010=>0101001
[4,2,1,5,6,3,8,7]=>[7,8,3,6,5,1,2,4]=>1010100=>0010101
[7,1,2,5,8,3,4,6]=>[6,4,3,8,5,2,1,7]=>1111100=>0011111
[3,5,1,7,4,6,8,2]=>[2,8,6,4,7,1,5,3]=>1011010=>0101101
[2,7,6,1,4,5,3,8]=>[8,3,5,4,1,6,7,2]=>1111000=>0001111
[5,7,6,8,1,4,3,2]=>[2,3,4,1,8,6,7,5]=>1000110=>0110001
[7,8,6,5,1,4,3,2]=>[2,3,4,1,5,6,8,7]=>1000001=>1000001
[5,3,1,2,4,8,7,6]=>[6,7,8,4,2,1,3,5]=>1101000=>0001011
[5,3,6,2,1,8,7,4]=>[4,7,8,1,2,6,3,5]=>1010000=>0000101
[7,2,4,5,1,3,6,8]=>[8,6,3,1,5,4,2,7]=>1111010=>0101111
[6,2,4,5,1,8,7,3]=>[3,7,8,1,5,4,2,6]=>1101000=>0001011
[1,6,4,5,2,8,7,3]=>[3,7,8,2,5,4,6,1]=>1101000=>0001011
[1,7,4,2,6,3,5,8]=>[8,5,3,6,2,4,7,1]=>1110100=>0010111
[5,7,4,1,6,3,2,8]=>[8,2,3,6,1,4,7,5]=>1100100=>0010011
[5,8,4,3,6,1,2,7]=>[7,2,1,6,3,4,8,5]=>1110100=>0010111
[4,3,8,2,1,7,5,6]=>[6,5,7,1,2,8,3,4]=>1010100=>0010101
[3,8,2,5,6,7,1,4]=>[4,1,7,6,5,2,8,3]=>1110110=>0110111
[8,2,1,5,6,7,4,3]=>[3,4,7,6,5,1,2,8]=>1000110=>0110001
[7,8,4,3,6,2,1,5]=>[5,1,2,6,3,4,8,7]=>1010001=>1000101
[6,3,5,8,2,7,1,4]=>[4,1,7,2,8,5,3,6]=>1110100=>0010111
[7,1,4,8,6,2,3,5]=>[5,3,2,6,8,4,1,7]=>1111000=>0001111
[7,5,4,1,6,2,3,8]=>[8,3,2,6,1,4,5,7]=>1110000=>0000111
[1,6,4,5,8,2,3,7]=>[7,3,2,8,5,4,6,1]=>1111100=>0011111
[8,3,5,2,1,7,4,6]=>[6,4,7,1,2,5,3,8]=>1011000=>0001101
[4,1,8,5,6,7,3,2]=>[2,3,7,6,5,8,1,4]=>1000110=>0110001
[1,5,3,8,6,7,4,2]=>[2,4,7,6,8,3,5,1]=>1010010=>0100101
[6,2,4,3,8,7,5,1]=>[1,5,7,8,3,4,2,6]=>0110000=>0000110
[5,2,7,1,3,4,8,6]=>[6,8,4,3,1,7,2,5]=>1111000=>0001111
[2,6,5,7,3,1,4,8]=>[8,4,1,3,7,5,6,2]=>1101100=>0011011
[2,6,5,7,3,1,8,4]=>[4,8,1,3,7,5,6,2]=>1100100=>0010011
[6,3,1,4,7,8,5,2]=>[2,5,8,7,4,1,3,6]=>1001001=>1001001
[6,3,2,4,7,5,8,1]=>[1,8,5,7,4,2,3,6]=>0101100=>0011010
[6,3,2,4,7,5,1,8]=>[8,1,5,7,4,2,3,6]=>1101000=>0001011
[4,2,1,6,3,7,8,5]=>[5,8,7,3,6,1,2,4]=>1010001=>1000101
[7,4,3,5,8,6,1,2]=>[2,1,6,8,5,3,4,7]=>1010100=>0010101
[7,4,3,5,8,6,2,1]=>[1,2,6,8,5,3,4,7]=>0010100=>0010100
[4,2,1,3,7,8,6,5]=>[5,6,8,7,3,1,2,4]=>1010001=>1000101
[4,2,1,8,3,5,6,7]=>[7,6,5,3,8,1,2,4]=>1010110=>0110101
[7,3,2,4,8,6,5,1]=>[1,5,6,8,4,2,3,7]=>0101000=>0001010
[4,2,1,7,3,5,6,8]=>[8,6,5,3,7,1,2,4]=>1010110=>0110101
[7,3,4,2,6,8,5,1]=>[1,5,8,6,2,4,3,7]=>0110010=>0100110
[4,8,6,2,7,3,5,1]=>[1,5,3,7,2,6,8,4]=>0111000=>0001110
[3,6,7,5,2,4,8,1]=>[1,8,4,2,5,7,6,3]=>0111010=>0101110
[3,7,6,8,4,2,5,1]=>[1,5,2,4,8,6,7,3]=>0110010=>0100110
[5,8,1,7,4,2,6,3]=>[3,6,2,4,7,1,8,5]=>1100100=>0010011
[3,7,8,6,2,4,5,1]=>[1,5,4,2,6,8,7,3]=>0111001=>1001110
[4,2,1,3,8,6,7,5]=>[5,7,6,8,3,1,2,4]=>1010010=>0100101
[4,2,1,8,3,7,6,5]=>[5,6,7,3,8,1,2,4]=>1010000=>0000101
[4,2,1,3,5,6,8,7]=>[7,8,6,5,3,1,2,4]=>1010110=>0110101
[7,8,2,4,1,3,6,5]=>[5,6,3,1,4,2,8,7]=>1110001=>1000111
[2,6,1,5,4,7,8,3]=>[3,8,7,4,5,1,6,2]=>1101001=>1001011
[4,6,3,5,8,7,1,2]=>[2,1,7,8,5,3,6,4]=>1011100=>0011101
[2,3,6,8,4,1,5,7]=>[7,5,1,4,8,6,3,2]=>1110110=>0110111
[2,7,5,1,8,3,4,6]=>[6,4,3,8,1,5,7,2]=>1111000=>0001111
[4,7,5,2,1,3,6,8]=>[8,6,3,1,2,5,7,4]=>1011010=>0101101
[3,5,6,2,4,1,7,8]=>[8,7,1,4,2,6,5,3]=>1110101=>1010111
[2,5,3,8,4,7,6,1]=>[1,6,7,4,8,3,5,2]=>0111000=>0001110
[2,8,5,7,3,6,4,1]=>[1,4,6,3,7,5,8,2]=>0110100=>0010110
[3,1,8,5,2,7,6,4]=>[4,6,7,2,5,8,1,3]=>1100000=>0000011
[8,3,5,7,1,6,4,2]=>[2,4,6,1,7,5,3,8]=>1010100=>0010101
[8,3,6,1,4,5,7,2]=>[2,7,5,4,1,6,3,8]=>1011100=>0011101
[2,8,6,3,4,5,7,1]=>[1,7,5,4,3,6,8,2]=>0111100=>0011110
[2,6,8,3,4,5,7,1]=>[1,7,5,4,3,8,6,2]=>0111110=>0111110
[2,7,8,5,3,6,4,1]=>[1,4,6,3,5,8,7,2]=>0110001=>1000110
[2,7,6,3,4,8,5,1]=>[1,5,8,4,3,6,7,2]=>0111000=>0001110
[8,3,7,6,1,4,5,2]=>[2,5,4,1,6,7,3,8]=>1011000=>0001101
[4,8,1,7,2,3,6,5]=>[5,6,3,2,7,1,8,4]=>1111000=>0001111
[4,1,7,2,3,6,5,8]=>[8,5,6,3,2,7,1,4]=>1110100=>0010111
[3,7,1,8,2,6,4,5]=>[5,4,6,2,8,1,7,3]=>1111000=>0001111
[3,1,7,8,2,5,6,4]=>[4,6,5,2,8,7,1,3]=>1100101=>1010011
[3,1,6,5,8,2,7,4]=>[4,7,2,8,5,6,1,3]=>1100100=>0010011
[6,3,5,8,7,1,4,2]=>[2,4,1,7,8,5,3,6]=>1010100=>0010101
[7,3,6,1,4,8,5,2]=>[2,5,8,4,1,6,3,7]=>1011000=>0001101
[7,8,3,6,1,4,5,2]=>[2,5,4,1,6,3,8,7]=>1011001=>1001101
[7,4,8,1,2,3,6,5]=>[5,6,3,2,1,8,4,7]=>1111000=>0001111
[8,7,4,6,1,2,5,3]=>[3,5,2,1,6,4,7,8]=>1101000=>0001011
[7,5,1,2,3,4,8,6]=>[6,8,4,3,2,1,5,7]=>1111000=>0001111
[7,4,6,1,2,8,3,5]=>[5,3,8,2,1,6,4,7]=>1111000=>0001111
[6,4,1,2,8,5,7,3]=>[3,7,5,8,2,1,4,6]=>1100100=>0010011
[5,7,1,2,3,6,4,8]=>[8,4,6,3,2,1,7,5]=>1111100=>0011111
[3,6,8,1,2,7,4,5]=>[5,4,7,2,1,8,6,3]=>1111010=>0101111
[4,8,6,1,2,3,7,5]=>[5,7,3,2,1,6,8,4]=>1111000=>0001111
[8,4,6,1,2,3,7,5]=>[5,7,3,2,1,6,4,8]=>1111000=>0001111
[4,8,1,5,2,7,3,6]=>[6,3,7,2,5,1,8,4]=>1111000=>0001111
[4,1,2,5,3,8,7,6]=>[6,7,8,3,5,2,1,4]=>1110000=>0000111
[3,1,4,8,7,5,2,6]=>[6,2,5,7,8,4,1,3]=>1101000=>0001011
[4,3,6,8,7,5,1,2]=>[2,1,5,7,8,6,3,4]=>1010010=>0100101
[5,4,1,8,2,7,6,3]=>[3,6,7,2,8,1,4,5]=>1100000=>0000011
[5,4,1,8,2,7,3,6]=>[6,3,7,2,8,1,4,5]=>1110000=>0000111
[8,6,7,4,1,2,5,3]=>[3,5,2,1,4,7,6,8]=>1100010=>0100011
[6,4,8,1,2,5,3,7]=>[7,3,5,2,1,8,4,6]=>1111000=>0001111
[6,7,3,1,4,8,5,2]=>[2,5,8,4,1,3,7,6]=>1001010=>0101001
[5,6,3,8,7,1,4,2]=>[2,4,1,7,8,3,6,5]=>1010100=>0010101
[6,7,4,1,2,8,3,5]=>[5,3,8,2,1,4,7,6]=>1110010=>0100111
[6,5,1,2,3,7,8,4]=>[4,8,7,3,2,1,5,6]=>1110001=>1000111
[6,5,1,2,3,4,8,7]=>[7,8,4,3,2,1,5,6]=>1111000=>0001111
[8,6,5,1,2,3,7,4]=>[4,7,3,2,1,5,6,8]=>1110000=>0000111
[6,5,1,2,3,7,4,8]=>[8,4,7,3,2,1,5,6]=>1111000=>0001111
[6,7,4,1,2,5,3,8]=>[8,3,5,2,1,4,7,6]=>1110010=>0100111
[7,8,6,4,1,2,5,3]=>[3,5,2,1,4,6,8,7]=>1100001=>1000011
[1,2,6,7,5,3,8,4]=>[4,8,3,5,7,6,2,1]=>1110010=>0100111
[1,7,5,3,2,8,4,6]=>[6,4,8,2,3,5,7,1]=>1101000=>0001011
[1,6,5,7,2,3,8,4]=>[4,8,3,2,7,5,6,1]=>1110100=>0010111
[1,3,8,2,6,5,7,4]=>[4,7,5,6,2,8,3,1]=>1110100=>0010111
[1,2,5,7,6,3,4,8]=>[8,4,3,6,7,5,2,1]=>1111100=>0011111
[1,3,4,8,2,5,7,6]=>[6,7,5,2,8,4,3,1]=>1111100=>0011111
[1,5,7,6,2,3,4,8]=>[8,4,3,2,6,7,5,1]=>1111100=>0011111
[1,5,3,8,2,6,4,7]=>[7,4,6,2,8,3,5,1]=>1111000=>0001111
[1,4,8,3,2,5,7,6]=>[6,7,5,2,3,8,4,1]=>1101100=>0011011
[1,2,4,8,3,5,7,6]=>[6,7,5,3,8,4,2,1]=>1111100=>0011111
[1,3,8,4,2,6,7,5]=>[5,7,6,2,4,8,3,1]=>1110010=>0100111
[1,4,8,2,3,5,7,6]=>[6,7,5,3,2,8,4,1]=>1111100=>0011111
[4,2,6,7,5,8,3,1]=>[1,3,8,5,7,6,2,4]=>0100110=>0110010
[6,7,5,2,1,8,4,3]=>[3,4,8,1,2,5,7,6]=>1000010=>0100001
[5,6,8,3,1,7,2,4]=>[4,2,7,1,3,8,6,5]=>1100110=>0110011
[3,4,6,8,2,1,5,7]=>[7,5,1,2,8,6,4,3]=>1011110=>0111101
[3,8,2,5,6,1,4,7]=>[7,4,1,6,5,2,8,3]=>1111100=>0011111
[4,2,5,7,3,8,6,1]=>[1,6,8,3,7,5,2,4]=>0110100=>0010110
[6,4,3,7,8,2,5,1]=>[1,5,2,8,7,3,4,6]=>0110001=>1000110
[6,4,3,1,7,8,2,5]=>[5,2,8,7,1,3,4,6]=>1100001=>1000011
[7,1,3,5,4,8,2,6]=>[6,2,8,4,5,3,1,7]=>1111000=>0001111
[4,6,3,7,8,5,2,1]=>[1,2,5,8,7,3,6,4]=>0011001=>1001100
[1,5,3,6,7,8,4,2]=>[2,4,8,7,6,3,5,1]=>1010011=>1100101
[4,6,1,7,3,8,5,2]=>[2,5,8,3,7,1,6,4]=>1011000=>0001101
[6,4,2,7,1,8,3,5]=>[5,3,8,1,7,2,4,6]=>1110000=>0000111
[4,2,6,3,7,8,5,1]=>[1,5,8,7,3,6,2,4]=>0110001=>1000110
[3,6,2,7,4,1,8,5]=>[5,8,1,4,7,2,6,3]=>1110000=>0000111
[3,5,7,2,1,8,6,4]=>[4,6,8,1,2,7,5,3]=>1010100=>0010101
[6,7,8,3,2,5,1,4]=>[4,1,5,2,3,8,7,6]=>1100011=>1100011
[6,3,7,8,2,5,4,1]=>[1,4,5,2,8,7,3,6]=>0110001=>1000110
[6,2,4,7,1,8,5,3]=>[3,5,8,1,7,4,2,6]=>1101000=>0001011
[1,3,7,8,5,2,6,4]=>[4,6,2,5,8,7,3,1]=>1110001=>1000111
[2,5,7,8,1,6,3,4]=>[4,3,6,1,8,7,5,2]=>1110101=>1010111
[2,5,6,1,7,8,4,3]=>[3,4,8,7,1,6,5,2]=>1100101=>1010011
[5,6,1,2,7,8,4,3]=>[3,4,8,7,2,1,6,5]=>1100101=>1010011
[6,7,2,1,8,5,3,4]=>[4,3,5,8,1,2,7,6]=>1010010=>0100101
[6,4,5,2,3,8,7,1]=>[1,7,8,3,2,5,4,6]=>0111000=>0001110
[4,6,5,2,3,1,8,7]=>[7,8,1,3,2,5,6,4]=>1101000=>0001011
[6,4,2,5,3,1,8,7]=>[7,8,1,3,5,2,4,6]=>1100000=>0000011
[6,4,2,5,3,8,7,1]=>[1,7,8,3,5,2,4,6]=>0110000=>0000110
[8,6,4,7,5,2,3,1]=>[1,3,2,5,7,4,6,8]=>0101000=>0001010
[8,6,2,7,4,5,3,1]=>[1,3,5,4,7,2,6,8]=>0101000=>0001010
[6,4,2,5,8,7,3,1]=>[1,3,7,8,5,2,4,6]=>0100100=>0010010
[4,6,5,2,3,8,7,1]=>[1,7,8,3,2,5,6,4]=>0111000=>0001110
[6,8,2,7,4,5,3,1]=>[1,3,5,4,7,2,8,6]=>0101010=>0101010
[8,6,4,7,2,5,3,1]=>[1,3,5,2,7,4,6,8]=>0101000=>0001010
[8,6,2,4,7,5,3,1]=>[1,3,5,7,4,2,6,8]=>0101000=>0001010
[6,8,2,4,7,5,3,1]=>[1,3,5,7,4,2,8,6]=>0101010=>0101010
[4,8,2,6,7,5,3,1]=>[1,3,5,7,6,2,8,4]=>0101010=>0101010
[2,8,4,6,7,5,3,1]=>[1,3,5,7,6,4,8,2]=>0101010=>0101010
[2,8,6,7,4,5,3,1]=>[1,3,5,4,7,6,8,2]=>0101010=>0101010
[6,8,7,2,4,5,3,1]=>[1,3,5,4,2,7,8,6]=>0101010=>0101010
[2,6,4,5,8,7,3,1]=>[1,3,7,8,5,4,6,2]=>0101100=>0011010
[2,6,4,8,7,5,3,1]=>[1,3,5,7,8,4,6,2]=>0101000=>0001010
[4,6,2,8,7,5,3,1]=>[1,3,5,7,8,2,6,4]=>0101000=>0001010
[8,2,4,6,7,5,3,1]=>[1,3,5,7,6,4,2,8]=>0101010=>0101010
[6,2,4,8,7,5,3,1]=>[1,3,5,7,8,4,2,6]=>0101000=>0001010
[4,2,6,8,7,5,3,1]=>[1,3,5,7,8,6,2,4]=>0100010=>0100010
[4,2,6,5,8,7,3,1]=>[1,3,7,8,5,6,2,4]=>0100100=>0010010
[6,2,4,5,8,7,3,1]=>[1,3,7,8,5,4,2,6]=>0101100=>0011010
[8,2,6,7,4,5,3,1]=>[1,3,5,4,7,6,2,8]=>0101010=>0101010
[8,6,7,2,4,5,3,1]=>[1,3,5,4,2,7,6,8]=>0101010=>0101010
[6,4,5,8,7,2,3,1]=>[1,3,2,7,8,5,4,6]=>0101100=>0011010
[8,6,7,4,2,5,3,1]=>[1,3,5,2,4,7,6,8]=>0100010=>0100010
[8,4,6,7,2,5,3,1]=>[1,3,5,2,7,6,4,8]=>0101010=>0101010
[6,4,8,7,2,5,3,1]=>[1,3,5,2,7,8,4,6]=>0101000=>0001010
[6,2,8,7,4,5,3,1]=>[1,3,5,4,7,8,2,6]=>0101000=>0001010
[4,6,5,8,7,2,3,1]=>[1,3,2,7,8,5,6,4]=>0101100=>0011010
[2,1,6,8,7,4,5,3]=>[3,5,4,7,8,6,1,2]=>1001010=>0101001
[2,6,8,7,4,5,3,1]=>[1,3,5,4,7,8,6,2]=>0101010=>0101010
[2,4,8,6,7,5,3,1]=>[1,3,5,7,6,8,4,2]=>0101010=>0101010
[6,2,8,4,7,5,3,1]=>[1,3,5,7,4,8,2,6]=>0101000=>0001010
[8,2,6,4,7,5,3,1]=>[1,3,5,7,4,6,2,8]=>0101000=>0001010
[4,6,8,2,7,5,3,1]=>[1,3,5,7,2,8,6,4]=>0101010=>0101010
[2,6,8,4,7,5,3,1]=>[1,3,5,7,4,8,6,2]=>0101010=>0101010
[4,6,8,7,2,5,3,1]=>[1,3,5,2,7,8,6,4]=>0101010=>0101010
[4,6,5,8,2,7,3,1]=>[1,3,7,2,8,5,6,4]=>0101100=>0011010
[2,1,6,8,4,7,5,3]=>[3,5,7,4,8,6,1,2]=>1001010=>0101001
[2,1,8,6,4,7,5,3]=>[3,5,7,4,6,8,1,2]=>1001000=>0001001
[6,8,7,4,2,5,3,1]=>[1,3,5,2,4,7,8,6]=>0100010=>0100010
[2,8,6,4,7,5,3,1]=>[1,3,5,7,4,6,8,2]=>0101000=>0001010
[4,8,6,2,7,5,3,1]=>[1,3,5,7,2,6,8,4]=>0101000=>0001010
[3,7,8,5,6,1,2,4]=>[4,2,1,6,5,8,7,3]=>1110101=>1010111
[3,6,1,8,4,7,2,5]=>[5,2,7,4,8,1,6,3]=>1111000=>0001111
[3,1,6,8,4,7,2,5]=>[5,2,7,4,8,6,1,3]=>1101010=>0101011
[4,1,6,8,3,2,7,5]=>[5,7,2,3,8,6,1,4]=>1100010=>0100011
[4,6,1,8,3,2,7,5]=>[5,7,2,3,8,1,6,4]=>1101000=>0001011
[4,7,8,1,3,2,6,5]=>[5,6,2,3,1,8,7,4]=>1101001=>1001011
[4,7,8,3,1,2,6,5]=>[5,6,2,1,3,8,7,4]=>1101001=>1001011
[2,7,8,3,4,6,5,1]=>[1,5,6,4,3,8,7,2]=>0111001=>1001110
[4,7,8,2,1,3,6,5]=>[5,6,3,1,2,8,7,4]=>1011001=>1001101
[4,6,1,8,2,3,7,5]=>[5,7,3,2,8,1,6,4]=>1111000=>0001111
[4,5,2,1,8,3,7,6]=>[6,7,3,8,1,2,5,4]=>1011000=>0001101
[4,6,2,8,1,3,7,5]=>[5,7,3,1,8,2,6,4]=>1111000=>0001111
[3,6,2,8,4,7,1,5]=>[5,1,7,4,8,2,6,3]=>1111000=>0001111
[2,3,6,8,4,7,5,1]=>[1,5,7,4,8,6,3,2]=>0111010=>0101110
[3,2,6,8,4,7,1,5]=>[5,1,7,4,8,6,2,3]=>1101010=>0101011
[4,2,6,8,3,1,7,5]=>[5,7,1,3,8,6,2,4]=>1100010=>0100011
[4,2,5,1,8,3,7,6]=>[6,7,3,8,1,5,2,4]=>1110000=>0000111
[5,1,2,4,3,8,7,6]=>[6,7,8,3,4,2,1,5]=>1110000=>0000111
[5,2,4,1,3,8,7,6]=>[6,7,8,3,1,4,2,5]=>1110000=>0000111
[4,2,5,3,8,1,7,6]=>[6,7,1,8,3,5,2,4]=>1110000=>0000111
[3,2,5,4,8,7,1,6]=>[6,1,7,8,4,5,2,3]=>1101000=>0001011
[3,5,2,4,8,7,1,6]=>[6,1,7,8,4,2,5,3]=>1111000=>0001111
[5,1,4,2,3,8,7,6]=>[6,7,8,3,2,4,1,5]=>1110000=>0000111
[5,4,3,1,2,8,7,6]=>[6,7,8,2,1,3,4,5]=>1100000=>0000011
[4,5,3,1,8,2,7,6]=>[6,7,2,8,1,3,5,4]=>1101000=>0001011
[4,5,1,3,8,2,7,6]=>[6,7,2,8,3,1,5,4]=>1111000=>0001111
[3,1,5,4,8,7,2,6]=>[6,2,7,8,4,5,1,3]=>1101000=>0001011
[3,5,4,1,8,7,2,6]=>[6,2,7,8,1,4,5,3]=>1110000=>0000111
[3,6,5,8,7,1,2,4]=>[4,2,1,7,8,5,6,3]=>1110100=>0010111
[3,4,1,5,8,7,2,6]=>[6,2,7,8,5,1,4,3]=>1110100=>0010111
[4,1,3,5,8,2,7,6]=>[6,7,2,8,5,3,1,4]=>1110100=>0010111
[4,3,6,8,2,1,7,5]=>[5,7,1,2,8,6,3,4]=>1010010=>0100101
[2,4,6,8,3,7,5,1]=>[1,5,7,3,8,6,4,2]=>0111010=>0101110
[3,4,5,2,8,7,1,6]=>[6,1,7,8,2,5,4,3]=>1111000=>0001111
[5,3,1,4,2,8,7,6]=>[6,7,8,2,4,1,3,5]=>1100000=>0000011
[5,1,3,4,2,8,7,6]=>[6,7,8,2,4,3,1,5]=>1110000=>0000111
[5,1,3,2,4,8,7,6]=>[6,7,8,4,2,3,1,5]=>1101000=>0001011
[5,3,2,1,4,8,7,6]=>[6,7,8,4,1,2,3,5]=>1001000=>0001001
[4,3,2,5,8,1,7,6]=>[6,7,1,8,5,2,3,4]=>1100100=>0010011
[3,4,2,5,8,7,1,6]=>[6,1,7,8,5,2,4,3]=>1110100=>0010111
[3,2,4,5,8,7,1,6]=>[6,1,7,8,5,4,2,3]=>1101100=>0011011
[4,2,3,5,8,1,7,6]=>[6,7,1,8,5,3,2,4]=>1110100=>0010111
[5,2,3,1,4,8,7,6]=>[6,7,8,4,1,3,2,5]=>1101000=>0001011
[5,2,1,3,4,8,7,6]=>[6,7,8,4,3,1,2,5]=>1011000=>0001101
[1,7,2,3,5,6,8,4]=>[4,8,6,5,3,2,7,1]=>1110110=>0110111
[3,4,6,2,8,5,7,1]=>[1,7,5,8,2,6,4,3]=>0111100=>0011110
[4,2,1,7,5,8,3,6]=>[6,3,8,5,7,1,2,4]=>1010100=>0010101
[4,7,2,6,5,1,3,8]=>[8,3,1,5,6,2,7,4]=>1111000=>0001111
[3,7,4,1,2,5,8,6]=>[6,8,5,2,1,4,7,3]=>1110100=>0010111
[4,7,1,6,5,2,8,3]=>[3,8,2,5,6,1,7,4]=>1101000=>0001011
[4,7,3,6,5,1,8,2]=>[2,8,1,5,6,3,7,4]=>1011000=>0001101
[4,3,7,1,6,8,5,2]=>[2,5,8,6,1,7,3,4]=>1010010=>0100101
[4,2,1,7,5,6,8,3]=>[3,8,6,5,7,1,2,4]=>1000110=>0110001
[4,2,6,8,7,3,1,5]=>[5,1,3,7,8,6,2,4]=>1100010=>0100011
[3,4,6,1,8,5,2,7]=>[7,2,5,8,1,6,4,3]=>1111000=>0001111
[4,1,6,7,5,8,2,3]=>[3,2,8,5,7,6,1,4]=>1100110=>0110011
[4,3,7,1,6,8,2,5]=>[5,2,8,6,1,7,3,4]=>1110010=>0100111
[4,3,7,5,6,8,2,1]=>[1,2,8,6,5,7,3,4]=>0010110=>0110100
[2,8,7,4,5,3,1,6]=>[6,1,3,5,4,7,8,2]=>1101000=>0001011
[2,8,7,4,3,5,1,6]=>[6,1,5,3,4,7,8,2]=>1110000=>0000111
[4,1,7,3,6,2,5,8]=>[8,5,2,6,3,7,1,4]=>1110100=>0010111
[5,8,7,6,1,2,4,3]=>[3,4,2,1,6,7,8,5]=>1100100=>0010011
[4,1,7,2,6,8,5,3]=>[3,5,8,6,2,7,1,4]=>1100010=>0100011
[4,2,7,3,6,1,8,5]=>[5,8,1,6,3,7,2,4]=>1110000=>0000111
[4,2,7,3,6,5,8,1]=>[1,8,5,6,3,7,2,4]=>0110100=>0010110
[3,8,5,6,2,4,1,7]=>[7,1,4,2,6,5,8,3]=>1110100=>0010111
[2,8,6,5,3,7,1,4]=>[4,1,7,3,5,6,8,2]=>1110000=>0000111
[3,8,2,1,4,6,7,5]=>[5,7,6,4,1,2,8,3]=>1011010=>0101101
[3,8,2,5,4,6,7,1]=>[1,7,6,4,5,2,8,3]=>0111010=>0101110
[4,2,6,7,5,3,1,8]=>[8,1,3,5,7,6,2,4]=>1100010=>0100011
[3,2,6,1,4,5,8,7]=>[7,8,5,4,1,6,2,3]=>1101100=>0011011
[2,8,7,3,4,5,1,6]=>[6,1,5,4,3,7,8,2]=>1111000=>0001111
[5,8,7,6,1,3,4,2]=>[2,4,3,1,6,7,8,5]=>1010100=>0010101
[5,8,7,6,2,3,4,1]=>[1,4,3,2,6,7,8,5]=>0110100=>0010110
[3,8,1,5,2,6,4,7]=>[7,4,6,2,5,1,8,3]=>1111000=>0001111
[2,8,7,5,3,4,1,6]=>[6,1,4,3,5,7,8,2]=>1110000=>0000111
[5,8,7,6,1,3,2,4]=>[4,2,3,1,6,7,8,5]=>1100100=>0010011
[5,8,7,6,4,1,2,3]=>[3,2,1,4,6,7,8,5]=>1100100=>0010011
[8,1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1,8]=>1111000=>0001111
[8,1,3,6,2,5,4,7]=>[7,4,5,2,6,3,1,8]=>1111000=>0001111
[7,2,1,6,3,5,4,8]=>[8,4,5,3,6,1,2,7]=>1011000=>0001101
[2,7,1,6,3,5,4,8]=>[8,4,5,3,6,1,7,2]=>1111000=>0001111
[2,7,1,5,4,3,6,8]=>[8,6,3,4,5,1,7,2]=>1110010=>0100111
[7,2,1,5,4,3,6,8]=>[8,6,3,4,5,1,2,7]=>1010010=>0100101
[8,1,3,5,4,2,6,7]=>[7,6,2,4,5,3,1,8]=>1110010=>0100111
[8,1,5,3,4,2,6,7]=>[7,6,2,4,3,5,1,8]=>1110010=>0100111
[8,1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1,8]=>1110100=>0010111
[8,1,4,5,3,2,6,7]=>[7,6,2,3,5,4,1,8]=>1101010=>0101011
[8,1,4,3,5,2,6,7]=>[7,6,2,5,3,4,1,8]=>1110010=>0100111
[7,2,1,4,5,3,6,8]=>[8,6,3,5,4,1,2,7]=>1011010=>0101101
[2,7,1,4,5,3,6,8]=>[8,6,3,5,4,1,7,2]=>1111010=>0101111
[2,6,3,1,5,4,7,8]=>[8,7,4,5,1,3,6,2]=>1101001=>1001011
[6,3,2,1,5,4,7,8]=>[8,7,4,5,1,2,3,6]=>1001001=>1001001
[7,3,1,4,5,2,6,8]=>[8,6,2,5,4,1,3,7]=>1101010=>0101011
[7,3,1,5,4,2,6,8]=>[8,6,2,4,5,1,3,7]=>1100010=>0100011
[7,3,1,6,2,5,4,8]=>[8,4,5,2,6,1,3,7]=>1101000=>0001011
[3,7,1,6,2,5,4,8]=>[8,4,5,2,6,1,7,3]=>1111000=>0001111
[3,7,1,4,5,2,6,8]=>[8,6,2,5,4,1,7,3]=>1111010=>0101111
[2,3,6,1,5,4,7,8]=>[8,7,4,5,1,6,3,2]=>1111001=>1001111
[6,3,4,1,5,2,7,8]=>[8,7,2,5,1,4,3,6]=>1110001=>1000111
[6,2,4,1,5,3,7,8]=>[8,7,3,5,1,4,2,6]=>1110001=>1000111
[2,6,4,1,5,3,7,8]=>[8,7,3,5,1,4,6,2]=>1110001=>1000111
[2,6,5,1,3,7,4,8]=>[8,4,7,3,1,5,6,2]=>1111000=>0001111
[6,5,2,1,3,7,4,8]=>[8,4,7,3,1,2,5,6]=>1011000=>0001101
[7,6,1,2,4,5,3,8]=>[8,3,5,4,2,1,6,7]=>1111000=>0001111
[6,7,1,2,8,3,5,4]=>[4,5,3,8,2,1,7,6]=>1110010=>0100111
[6,7,1,2,5,4,3,8]=>[8,3,4,5,2,1,7,6]=>1110010=>0100111
[5,6,2,1,3,7,4,8]=>[8,4,7,3,1,2,6,5]=>1011100=>0011101
[5,2,6,1,3,7,4,8]=>[8,4,7,3,1,6,2,5]=>1111000=>0001111
[2,4,6,1,5,3,7,8]=>[8,7,3,5,1,6,4,2]=>1111001=>1001111
[4,7,1,3,5,2,6,8]=>[8,6,2,5,3,1,7,4]=>1111010=>0101111
[4,7,1,5,3,2,6,8]=>[8,6,2,3,5,1,7,4]=>1101010=>0101011
[5,7,1,6,2,3,8,4]=>[4,8,3,2,6,1,7,5]=>1110100=>0010111
[5,6,3,1,2,7,4,8]=>[8,4,7,2,1,3,6,5]=>1101100=>0011011
[4,2,5,3,1,6,7,8]=>[8,7,6,1,3,5,2,4]=>1100011=>1100011
[6,5,1,2,7,8,4,3]=>[3,4,8,7,2,1,5,6]=>1100001=>1000011
[6,1,7,5,3,8,4,2]=>[2,4,8,3,5,7,1,6]=>1010000=>0000101
[4,8,5,6,7,2,3,1]=>[1,3,2,7,6,5,8,4]=>0101110=>0111010
[5,8,7,3,2,6,4,1]=>[1,4,6,2,3,7,8,5]=>0100100=>0010010
[6,8,7,2,5,1,3,4]=>[4,3,1,5,2,7,8,6]=>1110010=>0100111
[5,8,7,2,1,6,3,4]=>[4,3,6,1,2,7,8,5]=>1010100=>0010101
[7,1,2,8,5,6,3,4]=>[4,3,6,5,8,2,1,7]=>1110100=>0010111
[8,7,2,1,5,6,3,4]=>[4,3,6,5,1,2,7,8]=>1010100=>0010101
[7,1,3,5,8,6,2,4]=>[4,2,6,8,5,3,1,7]=>1110100=>0010111
[6,4,5,8,3,2,7,1]=>[1,7,2,3,8,5,4,6]=>0101100=>0011010
[3,6,4,8,7,1,5,2]=>[2,5,1,7,8,4,6,3]=>1011000=>0001101
[6,1,8,3,5,2,7,4]=>[4,7,2,5,3,8,1,6]=>1110000=>0000111
[7,6,8,3,5,2,1,4]=>[4,1,2,5,3,8,6,7]=>1010010=>0100101
[8,7,1,3,5,6,2,4]=>[4,2,6,5,3,1,7,8]=>1110100=>0010111
[5,8,2,4,3,6,7,1]=>[1,7,6,3,4,2,8,5]=>0110110=>0110110
[8,6,5,1,4,3,7,2]=>[2,7,3,4,1,5,6,8]=>1010000=>0000101
[2,4,8,6,1,3,7,5]=>[5,7,3,1,6,8,4,2]=>1111000=>0001111
[6,7,1,8,4,3,5,2]=>[2,5,3,4,8,1,7,6]=>1010010=>0100101
[2,7,8,4,1,6,3,5]=>[5,3,6,1,4,8,7,2]=>1110001=>1000111
[4,1,7,6,3,8,2,5]=>[5,2,8,3,6,7,1,4]=>1110000=>0000111
[4,8,2,5,7,6,3,1]=>[1,3,6,7,5,2,8,4]=>0101100=>0011010
[2,6,7,5,1,8,4,3]=>[3,4,8,1,5,7,6,2]=>1100010=>0100011
[7,6,5,2,8,3,4,1]=>[1,4,3,8,2,5,6,7]=>0110000=>0000110
[8,1,3,5,7,4,6,2]=>[2,6,4,7,5,3,1,8]=>1011100=>0011101
[5,1,3,8,6,7,4,2]=>[2,4,7,6,8,3,1,5]=>1010010=>0100101
[2,5,8,4,6,7,3,1]=>[1,3,7,6,4,8,5,2]=>0101110=>0111010
[2,4,8,1,6,7,3,5]=>[5,3,7,6,1,8,4,2]=>1111010=>0101111
[3,4,8,7,2,1,5,6]=>[6,5,1,2,7,8,4,3]=>1011100=>0011101
[1,6,4,5,2,3,7,8]=>[8,7,3,2,5,4,6,1]=>1111001=>1001111
[1,7,4,5,2,3,6,8]=>[8,6,3,2,5,4,7,1]=>1111010=>0101111
[1,6,3,5,2,4,7,8]=>[8,7,4,2,5,3,6,1]=>1111001=>1001111
[1,6,3,4,2,5,7,8]=>[8,7,5,2,4,3,6,1]=>1110101=>1010111
[1,7,3,4,2,5,6,8]=>[8,6,5,2,4,3,7,1]=>1110110=>0110111
[1,8,5,7,3,4,2,6]=>[6,2,4,3,7,5,8,1]=>1110100=>0010111
[1,7,3,4,2,6,5,8]=>[8,5,6,2,4,3,7,1]=>1110100=>0010111
[1,5,2,8,4,7,3,6]=>[6,3,7,4,8,2,5,1]=>1111000=>0001111
[1,4,2,8,5,7,3,6]=>[6,3,7,5,8,2,4,1]=>1110100=>0010111
[1,7,3,5,2,6,4,8]=>[8,4,6,2,5,3,7,1]=>1111000=>0001111
[1,8,4,7,3,5,2,6]=>[6,2,5,3,7,4,8,1]=>1111000=>0001111
[1,7,3,6,2,5,4,8]=>[8,4,5,2,6,3,7,1]=>1111000=>0001111
[1,7,3,6,2,4,5,8]=>[8,5,4,2,6,3,7,1]=>1111100=>0011111
[1,7,4,6,2,3,5,8]=>[8,5,3,2,6,4,7,1]=>1111100=>0011111
[1,8,5,6,2,3,4,7]=>[7,4,3,2,6,5,8,1]=>1111100=>0011111
[1,8,5,6,2,4,3,7]=>[7,3,4,2,6,5,8,1]=>1110100=>0010111
[1,3,2,8,5,6,4,7]=>[7,4,6,5,8,2,3,1]=>1101100=>0011011
[1,4,2,8,5,6,3,7]=>[7,3,6,5,8,2,4,1]=>1110100=>0010111
[1,5,2,8,4,6,3,7]=>[7,3,6,4,8,2,5,1]=>1111000=>0001111
[1,6,2,8,4,5,3,7]=>[7,3,5,4,8,2,6,1]=>1111000=>0001111
[8,6,4,7,2,1,3,5]=>[5,3,1,2,7,4,6,8]=>1011000=>0001101
[5,4,8,2,3,6,1,7]=>[7,1,6,3,2,8,4,5]=>1111000=>0001111
[4,8,6,2,3,5,1,7]=>[7,1,5,3,2,6,8,4]=>1111000=>0001111
[5,8,7,4,1,2,3,6]=>[6,3,2,1,4,7,8,5]=>1110100=>0010111
[6,1,3,7,4,8,2,5]=>[5,2,8,4,7,3,1,6]=>1111000=>0001111
[7,4,8,6,1,2,3,5]=>[5,3,2,1,6,8,4,7]=>1111000=>0001111
[3,7,6,1,2,4,5,8]=>[8,5,4,2,1,6,7,3]=>1111100=>0011111
[4,7,6,1,2,3,5,8]=>[8,5,3,2,1,6,7,4]=>1111100=>0011111
[1,6,5,8,2,3,4,7]=>[7,4,3,2,8,5,6,1]=>1111100=>0011111
[8,5,7,4,1,2,3,6]=>[6,3,2,1,4,7,5,8]=>1110100=>0010111
[7,4,8,5,1,6,2,3]=>[3,2,6,1,5,8,4,7]=>1101000=>0001011
[8,6,4,1,2,7,3,5]=>[5,3,7,2,1,4,6,8]=>1110000=>0000111
[1,7,2,8,6,3,4,5]=>[5,4,3,6,8,2,7,1]=>1111000=>0001111
[7,5,8,1,3,6,2,4]=>[4,2,6,3,1,8,5,7]=>1110100=>0010111
[5,7,1,3,8,2,4,6]=>[6,4,2,8,3,1,7,5]=>1111100=>0011111
[7,6,8,1,5,2,3,4]=>[4,3,2,5,1,8,6,7]=>1110010=>0100111
[7,1,5,8,6,2,3,4]=>[4,3,2,6,8,5,1,7]=>1110100=>0010111
[4,1,8,7,2,3,5,6]=>[6,5,3,2,7,8,1,4]=>1110100=>0010111
[7,1,5,8,3,4,2,6]=>[6,2,4,3,8,5,1,7]=>1110100=>0010111
[7,1,4,3,2,5,6,8]=>[8,6,5,2,3,4,1,7]=>1100110=>0110011
[7,1,4,6,3,8,2,5]=>[5,2,8,3,6,4,1,7]=>1111000=>0001111
[7,1,4,3,2,5,8,6]=>[6,8,5,2,3,4,1,7]=>1100100=>0010011
[7,1,4,6,5,3,8,2]=>[2,8,3,5,6,4,1,7]=>1011000=>0001101
[3,4,7,2,6,8,5,1]=>[1,5,8,6,2,7,4,3]=>0111010=>0101110
[6,4,2,3,8,5,1,7]=>[7,1,5,8,3,2,4,6]=>1110000=>0000111
[6,4,2,7,5,3,1,8]=>[8,1,3,5,7,2,4,6]=>1100000=>0000011
[3,4,7,2,6,8,1,5]=>[5,1,8,6,2,7,4,3]=>1111010=>0101111
[5,4,7,3,6,8,2,1]=>[1,2,8,6,3,7,4,5]=>0011010=>0101100
[4,8,7,3,5,1,2,6]=>[6,2,1,5,3,7,8,4]=>1111000=>0001111
[3,4,7,1,6,2,8,5]=>[5,8,2,6,1,7,4,3]=>1111000=>0001111
[3,4,7,2,6,5,8,1]=>[1,8,5,6,2,7,4,3]=>0111100=>0011110
[5,8,3,4,2,6,7,1]=>[1,7,6,2,4,3,8,5]=>0110110=>0110110
[6,4,3,7,5,1,2,8]=>[8,2,1,5,7,3,4,6]=>1110000=>0000111
[5,8,7,4,3,1,2,6]=>[6,2,1,3,4,7,8,5]=>1100100=>0010011
[5,3,6,2,4,7,8,1]=>[1,8,7,4,2,6,3,5]=>0111001=>1001110
[5,3,6,1,4,8,7,2]=>[2,7,8,4,1,6,3,5]=>1011000=>0001101
[5,3,7,2,4,6,8,1]=>[1,8,6,4,2,7,3,5]=>0111010=>0101110
[4,2,1,5,8,6,3,7]=>[7,3,6,8,5,1,2,4]=>1010100=>0010101
[4,2,1,5,8,6,7,3]=>[3,7,6,8,5,1,2,4]=>1000110=>0110001
[4,3,1,7,5,8,6,2]=>[2,6,8,5,7,1,3,4]=>1000100=>0010001
[6,7,3,1,4,8,2,5]=>[5,2,8,4,1,3,7,6]=>1101010=>0101011
[5,3,7,1,4,8,2,6]=>[6,2,8,4,1,7,3,5]=>1111000=>0001111
[4,3,1,5,7,8,2,6]=>[6,2,8,7,5,1,3,4]=>1100101=>1010011
[3,2,1,8,5,4,6,7]=>[7,6,4,5,8,1,2,3]=>1001010=>0101001
[3,2,1,8,5,7,4,6]=>[6,4,7,5,8,1,2,3]=>1001100=>0011001
[6,7,2,1,8,4,5,3]=>[3,5,4,8,1,2,7,6]=>1001010=>0101001
[3,2,1,8,5,6,4,7]=>[7,4,6,5,8,1,2,3]=>1001100=>0011001
[4,3,1,6,7,8,5,2]=>[2,5,8,7,6,1,3,4]=>1000011=>1100001
[4,2,1,6,8,5,3,7]=>[7,3,5,8,6,1,2,4]=>1010010=>0100101
[5,2,6,1,8,4,3,7]=>[7,3,4,8,1,6,2,5]=>1110000=>0000111
[5,2,6,1,8,7,3,4]=>[4,3,7,8,1,6,2,5]=>1110000=>0000111
[4,2,1,6,8,3,7,5]=>[5,7,3,8,6,1,2,4]=>1010010=>0100101
[4,3,1,6,7,8,2,5]=>[5,2,8,7,6,1,3,4]=>1100011=>1100011
[4,2,1,7,8,6,3,5]=>[5,3,6,8,7,1,2,4]=>1010001=>1000101
[3,2,1,8,6,4,7,5]=>[5,7,4,6,8,1,2,3]=>1001000=>0001001
[3,2,1,8,6,4,5,7]=>[7,5,4,6,8,1,2,3]=>1001100=>0011001
[3,2,1,8,4,6,5,7]=>[7,5,6,4,8,1,2,3]=>1001100=>0011001
[3,2,1,8,4,6,7,5]=>[5,7,6,4,8,1,2,3]=>1001010=>0101001
[4,2,1,7,8,3,6,5]=>[5,6,3,8,7,1,2,4]=>1010001=>1000101
[5,2,7,1,8,3,6,4]=>[4,6,3,8,1,7,2,5]=>1110000=>0000111
[6,7,2,1,8,3,5,4]=>[4,5,3,8,1,2,7,6]=>1010010=>0100101
[5,2,7,1,8,3,4,6]=>[6,4,3,8,1,7,2,5]=>1111000=>0001111
[4,2,1,7,8,3,5,6]=>[6,5,3,8,7,1,2,4]=>1010101=>1010101
[3,2,1,8,4,5,7,6]=>[6,7,5,4,8,1,2,3]=>1001100=>0011001
[7,4,8,6,2,5,3,1]=>[1,3,5,2,6,8,4,7]=>0101000=>0001010
[7,3,8,6,2,4,5,1]=>[1,5,4,2,6,8,3,7]=>0111000=>0001110
[7,4,3,1,8,2,5,6]=>[6,5,2,8,1,3,4,7]=>1100100=>0010011
[7,4,2,8,5,6,1,3]=>[3,1,6,5,8,2,4,7]=>1100100=>0010011
[7,3,8,5,2,4,6,1]=>[1,6,4,2,5,8,3,7]=>0111000=>0001110
[6,3,8,2,4,5,1,7]=>[7,1,5,4,2,8,3,6]=>1111000=>0001111
[6,3,8,2,5,7,4,1]=>[1,4,7,5,2,8,3,6]=>0110100=>0010110
[5,6,7,3,8,2,4,1]=>[1,4,2,8,3,7,6,5]=>0110110=>0110110
[5,3,8,2,4,6,7,1]=>[1,7,6,4,2,8,3,5]=>0111010=>0101110
[6,3,8,2,4,7,5,1]=>[1,5,7,4,2,8,3,6]=>0111000=>0001110
[5,7,4,2,6,8,1,3]=>[3,1,8,6,2,4,7,5]=>1100110=>0110011
[6,5,3,1,4,2,7,8]=>[8,7,2,4,1,3,5,6]=>1100001=>1000011
[5,7,4,2,6,1,3,8]=>[8,3,1,6,2,4,7,5]=>1110100=>0010111
[5,6,4,2,3,8,1,7]=>[7,1,8,3,2,4,6,5]=>1110100=>0010111
[5,6,3,7,8,2,4,1]=>[1,4,2,8,7,3,6,5]=>0110101=>1010110
[5,6,3,8,2,4,7,1]=>[1,7,4,2,8,3,6,5]=>0111100=>0011110
[6,3,7,2,4,5,1,8]=>[8,1,5,4,2,7,3,6]=>1111000=>0001111
[6,3,7,2,5,8,4,1]=>[1,4,8,5,2,7,3,6]=>0110100=>0010110
[5,3,6,8,2,4,7,1]=>[1,7,4,2,8,6,3,5]=>0111010=>0101110
[5,3,6,7,8,2,4,1]=>[1,4,2,8,7,6,3,5]=>0110011=>1100110
[3,5,8,6,4,2,1,7]=>[7,1,2,4,6,8,5,3]=>1010100=>0010101
[5,6,3,4,2,1,8,7]=>[7,8,1,2,4,3,6,5]=>1010100=>0010101
[6,3,4,2,1,5,8,7]=>[7,8,5,1,2,4,3,6]=>1010100=>0010101
[5,6,4,2,1,3,8,7]=>[7,8,3,1,2,4,6,5]=>1010100=>0010101
[2,6,3,8,5,4,1,7]=>[7,1,4,5,8,3,6,2]=>1110000=>0000111
[2,8,6,3,5,4,1,7]=>[7,1,4,5,3,6,8,2]=>1110000=>0000111
[5,8,6,4,2,1,3,7]=>[7,3,1,2,4,6,8,5]=>1010100=>0010101
[4,3,8,5,7,6,2,1]=>[1,2,6,7,5,8,3,4]=>0010100=>0010100
[8,5,3,7,6,2,4,1]=>[1,4,2,6,7,3,5,8]=>0110000=>0000110
[7,6,2,3,8,5,4,1]=>[1,4,5,8,3,2,6,7]=>0110000=>0000110
[2,1,6,4,3,7,8,5]=>[5,8,7,3,4,6,1,2]=>1010001=>1000101
[6,3,7,8,4,2,1,5]=>[5,1,2,4,8,7,3,6]=>1010001=>1000101
[7,8,4,2,1,6,3,5]=>[5,3,6,1,2,4,8,7]=>1010001=>1000101
[2,6,1,8,4,3,7,5]=>[5,7,3,4,8,1,6,2]=>1110000=>0000111
[8,5,7,6,2,1,4,3]=>[3,4,1,2,6,7,5,8]=>1000100=>0010001
[4,8,5,7,6,2,1,3]=>[3,1,2,6,7,5,8,4]=>1001100=>0011001
[7,5,6,1,8,4,2,3]=>[3,2,4,8,1,6,5,7]=>1100100=>0010011
[8,4,2,6,3,1,7,5]=>[5,7,1,3,6,2,4,8]=>1100000=>0000011
[1,5,3,7,4,2,8,6]=>[6,8,2,4,7,3,5,1]=>1110000=>0000111
[1,6,7,3,4,2,8,5]=>[5,8,2,4,3,7,6,1]=>1110010=>0100111
[8,6,5,2,3,1,7,4]=>[4,7,1,3,2,5,6,8]=>1100000=>0000011
[1,7,6,3,4,2,8,5]=>[5,8,2,4,3,6,7,1]=>1110000=>0000111
[1,8,6,3,2,5,7,4]=>[4,7,5,2,3,6,8,1]=>1100100=>0010011
[8,7,5,2,1,4,6,3]=>[3,6,4,1,2,5,7,8]=>1001000=>0001001
[7,8,5,2,1,4,6,3]=>[3,6,4,1,2,5,8,7]=>1001001=>1001001
[6,8,5,2,3,1,7,4]=>[4,7,1,3,2,5,8,6]=>1100010=>0100011
[5,8,6,2,3,1,7,4]=>[4,7,1,3,2,6,8,5]=>1100100=>0010011
[4,8,2,6,3,1,7,5]=>[5,7,1,3,6,2,8,4]=>1101000=>0001011
[3,2,8,6,4,1,7,5]=>[5,7,1,4,6,8,2,3]=>1100000=>0000011
[3,2,1,7,5,4,8,6]=>[6,8,4,5,7,1,2,3]=>1001000=>0001001
[4,1,3,7,5,2,8,6]=>[6,8,2,5,7,3,1,4]=>1110000=>0000111
[7,1,6,3,2,5,8,4]=>[4,8,5,2,3,6,1,7]=>1100100=>0010011
[1,2,7,4,3,6,8,5]=>[5,8,6,3,4,7,2,1]=>1110010=>0100111
[6,1,8,2,4,5,7,3]=>[3,7,5,4,2,8,1,6]=>1101100=>0011011
[5,1,8,3,2,6,7,4]=>[4,7,6,2,3,8,1,5]=>1100010=>0100011
[4,8,2,7,1,5,6,3]=>[3,6,5,1,7,2,8,4]=>1101100=>0011011
[5,8,7,2,1,4,6,3]=>[3,6,4,1,2,7,8,5]=>1001100=>0011001
[6,8,7,1,3,4,5,2]=>[2,5,4,3,1,7,8,6]=>1011010=>0101101
[7,8,6,1,3,4,5,2]=>[2,5,4,3,1,6,8,7]=>1011001=>1001101
[1,7,8,2,4,5,6,3]=>[3,6,5,4,2,8,7,1]=>1101101=>1011011
[8,6,7,1,3,4,5,2]=>[2,5,4,3,1,7,6,8]=>1011010=>0101101
[7,6,8,1,3,4,5,2]=>[2,5,4,3,1,8,6,7]=>1011010=>0101101
[6,5,8,2,3,1,7,4]=>[4,7,1,3,2,8,5,6]=>1100100=>0010011
[1,6,8,3,2,5,7,4]=>[4,7,5,2,3,8,6,1]=>1100110=>0110011
[8,4,2,7,1,5,6,3]=>[3,6,5,1,7,2,4,8]=>1100100=>0010011
[7,4,2,8,1,5,6,3]=>[3,6,5,1,8,2,4,7]=>1100100=>0010011
[6,4,2,8,3,1,7,5]=>[5,7,1,3,8,2,4,6]=>1100000=>0000011
[5,4,2,3,8,1,7,6]=>[6,7,1,8,3,2,4,5]=>1110000=>0000111
[4,5,2,3,1,6,8,7]=>[7,8,6,1,3,2,5,4]=>1101010=>0101011
[7,4,2,1,3,6,8,5]=>[5,8,6,3,1,2,4,7]=>1010010=>0100101
[8,4,2,1,3,6,7,5]=>[5,7,6,3,1,2,4,8]=>1010010=>0100101
[1,5,3,2,4,7,8,6]=>[6,8,7,4,2,3,5,1]=>1101001=>1001011
[8,5,1,3,2,6,7,4]=>[4,7,6,2,3,1,5,8]=>1100010=>0100011
[5,6,1,3,4,2,8,7]=>[7,8,2,4,3,1,6,5]=>1110100=>0010111
[4,7,2,1,3,6,8,5]=>[5,8,6,3,1,2,7,4]=>1011010=>0101101
[5,7,1,3,2,6,8,4]=>[4,8,6,2,3,1,7,5]=>1100110=>0110011
[6,7,1,2,4,5,8,3]=>[3,8,5,4,2,1,7,6]=>1101110=>0111011
[1,8,2,3,5,6,7,4]=>[4,7,6,5,3,2,8,1]=>1110110=>0110111
[5,8,1,3,2,6,7,4]=>[4,7,6,2,3,1,8,5]=>1100110=>0110011
[4,8,2,1,3,6,7,5]=>[5,7,6,3,1,2,8,4]=>1011010=>0101101
[4,1,3,2,5,7,8,6]=>[6,8,7,5,2,3,1,4]=>1100101=>1010011
[5,1,2,4,3,7,8,6]=>[6,8,7,3,4,2,1,5]=>1110001=>1000111
[8,7,5,2,6,3,4,1]=>[1,4,3,6,2,5,7,8]=>0110000=>0000110
[8,6,5,2,7,3,4,1]=>[1,4,3,7,2,5,6,8]=>0110000=>0000110
[6,3,8,5,4,7,1,2]=>[2,1,7,4,5,8,3,6]=>1011000=>0001101
[5,6,1,8,4,3,2,7]=>[7,2,3,4,8,1,6,5]=>1100100=>0010011
[6,1,2,5,8,3,7,4]=>[4,7,3,8,5,2,1,6]=>1110100=>0010111
[1,2,7,5,8,3,6,4]=>[4,6,3,8,5,7,2,1]=>1110100=>0010111
[1,2,6,4,7,8,5,3]=>[3,5,8,7,4,6,2,1]=>1101001=>1001011
[4,1,6,3,7,8,2,5]=>[5,2,8,7,3,6,1,4]=>1110001=>1000111
[4,1,6,3,8,7,2,5]=>[5,2,7,8,3,6,1,4]=>1110000=>0000111
[7,5,1,8,4,3,2,6]=>[6,2,3,4,8,1,5,7]=>1100000=>0000011
[6,5,1,7,4,3,2,8]=>[8,2,3,4,7,1,5,6]=>1100000=>0000011
[1,6,3,2,7,4,8,5]=>[5,8,4,7,2,3,6,1]=>1101000=>0001011
[1,3,7,2,5,4,8,6]=>[6,8,4,5,2,7,3,1]=>1111000=>0001111
[2,6,1,7,4,3,8,5]=>[5,8,3,4,7,1,6,2]=>1110000=>0000111
[1,4,7,3,5,2,8,6]=>[6,8,2,5,3,7,4,1]=>1111000=>0001111
[1,3,7,5,2,4,8,6]=>[6,8,4,2,5,7,3,1]=>1111000=>0001111
[2,5,7,4,3,8,1,6]=>[6,1,8,3,4,7,5,2]=>1110100=>0010111
[2,5,3,7,4,8,1,6]=>[6,1,8,4,7,3,5,2]=>1111000=>0001111
[1,4,7,2,3,8,6,5]=>[5,6,8,3,2,7,4,1]=>1111000=>0001111
[1,4,6,3,8,2,7,5]=>[5,7,2,8,3,6,4,1]=>1111000=>0001111
[1,3,5,2,8,7,6,4]=>[4,6,7,8,2,5,3,1]=>1110000=>0000111
[1,4,7,3,8,2,6,5]=>[5,6,2,8,3,7,4,1]=>1111000=>0001111
[3,2,6,7,8,1,5,4]=>[4,5,1,8,7,6,2,3]=>1100011=>1100011
[4,3,6,7,8,2,1,5]=>[5,1,2,8,7,6,3,4]=>1010011=>1100101
[3,5,2,7,8,4,1,6]=>[6,1,4,8,7,2,5,3]=>1110001=>1000111
[1,5,7,4,8,3,2,6]=>[6,2,3,8,4,7,5,1]=>1101100=>0011011
[2,5,1,6,8,4,7,3]=>[3,7,4,8,6,1,5,2]=>1101010=>0101011
[5,3,6,4,7,8,2,1]=>[1,2,8,7,4,6,3,5]=>0011001=>1001100
[3,5,2,6,8,4,7,1]=>[1,7,4,8,6,2,5,3]=>0111010=>0101110
[2,5,4,6,8,7,1,3]=>[3,1,7,8,6,4,5,2]=>1101010=>0101011
[1,3,6,2,8,7,5,4]=>[4,5,7,8,2,6,3,1]=>1110000=>0000111
[1,4,6,3,8,7,2,5]=>[5,2,7,8,3,6,4,1]=>1111000=>0001111
[2,5,7,4,3,8,6,1]=>[1,6,8,3,4,7,5,2]=>0110100=>0010110
[1,5,7,2,4,8,6,3]=>[3,6,8,4,2,7,5,1]=>1101100=>0011011
[4,6,3,7,2,8,5,1]=>[1,5,8,2,7,3,6,4]=>0111000=>0001110
[4,3,6,7,8,2,5,1]=>[1,5,2,8,7,6,3,4]=>0110011=>1100110
[1,4,7,3,8,6,2,5]=>[5,2,6,8,3,7,4,1]=>1111000=>0001111
[3,2,6,7,8,5,1,4]=>[4,1,5,8,7,6,2,3]=>1100011=>1100011
[1,3,7,2,8,6,5,4]=>[4,5,6,8,2,7,3,1]=>1110000=>0000111
[5,3,7,8,2,4,1,6]=>[6,1,4,2,8,7,3,5]=>1110001=>1000111
[2,4,7,8,3,1,5,6]=>[6,5,1,3,8,7,4,2]=>1101101=>1011011
[6,3,1,5,8,2,4,7]=>[7,4,2,8,5,1,3,6]=>1101100=>0011011
[3,2,4,8,1,5,6,7]=>[7,6,5,1,8,4,2,3]=>1101110=>0111011
[7,2,4,8,3,1,5,6]=>[6,5,1,3,8,4,2,7]=>1101100=>0011011
[5,3,8,7,2,4,1,6]=>[6,1,4,2,7,8,3,5]=>1110000=>0000111
[2,4,8,7,3,1,5,6]=>[6,5,1,3,7,8,4,2]=>1101100=>0011011
[6,4,8,7,2,3,1,5]=>[5,1,3,2,7,8,4,6]=>1101000=>0001011
[3,1,7,4,2,8,6,5]=>[5,6,8,2,4,7,1,3]=>1100000=>0000011
[5,7,6,8,2,3,1,4]=>[4,1,3,2,8,6,7,5]=>1100110=>0110011
[4,7,6,8,2,3,1,5]=>[5,1,3,2,8,6,7,4]=>1101010=>0101011
[8,6,4,7,2,3,1,5]=>[5,1,3,2,7,4,6,8]=>1101000=>0001011
[3,7,4,8,2,5,1,6]=>[6,1,5,2,8,4,7,3]=>1111000=>0001111
[8,1,6,4,2,3,7,5]=>[5,7,3,2,4,6,1,8]=>1110000=>0000111
[4,7,8,6,2,3,1,5]=>[5,1,3,2,6,8,7,4]=>1101001=>1001011
[7,1,6,4,2,3,8,5]=>[5,8,3,2,4,6,1,7]=>1110000=>0000111
[4,8,7,6,2,3,1,5]=>[5,1,3,2,6,7,8,4]=>1101000=>0001011
[6,8,7,5,2,3,1,4]=>[4,1,3,2,5,7,8,6]=>1100010=>0100011
[4,3,6,5,1,8,7,2]=>[2,7,8,1,5,6,3,4]=>1010000=>0000101
[2,6,5,3,1,8,7,4]=>[4,7,8,1,3,5,6,2]=>1100000=>0000011
[2,6,5,8,3,1,7,4]=>[4,7,1,3,8,5,6,2]=>1100100=>0010011
[4,6,1,5,8,3,7,2]=>[2,7,3,8,5,1,6,4]=>1011100=>0011101
[4,1,6,5,8,3,7,2]=>[2,7,3,8,5,6,1,4]=>1010100=>0010101
[1,4,6,5,8,3,7,2]=>[2,7,3,8,5,6,4,1]=>1011100=>0011101
[4,1,6,5,8,7,3,2]=>[2,3,7,8,5,6,1,4]=>1000100=>0010001
[6,4,3,8,7,1,5,2]=>[2,5,1,7,8,3,4,6]=>1010000=>0000101
[6,4,8,3,7,1,5,2]=>[2,5,1,7,3,8,4,6]=>1011000=>0001101
[2,6,8,5,3,7,1,4]=>[4,1,7,3,5,8,6,2]=>1110010=>0100111
[4,6,8,1,5,7,3,2]=>[2,3,7,5,1,8,6,4]=>1001110=>0111001
[4,6,3,8,5,7,1,2]=>[2,1,7,5,8,3,6,4]=>1011100=>0011101
[4,3,6,1,8,5,7,2]=>[2,7,5,8,1,6,3,4]=>1010100=>0010101
[4,1,3,6,8,7,5,2]=>[2,5,7,8,6,3,1,4]=>1010010=>0100101
[4,3,6,1,8,7,5,2]=>[2,5,7,8,1,6,3,4]=>1010000=>0000101
[4,3,6,8,1,7,5,2]=>[2,5,7,1,8,6,3,4]=>1010010=>0100101
[6,2,5,8,7,1,3,4]=>[4,3,1,7,8,5,2,6]=>1110100=>0010111
[6,2,5,8,7,3,1,4]=>[4,1,3,7,8,5,2,6]=>1100100=>0010011
[4,6,3,8,1,7,5,2]=>[2,5,7,1,8,3,6,4]=>1011000=>0001101
[4,6,8,1,3,7,5,2]=>[2,5,7,3,1,8,6,4]=>1011010=>0101101
[6,2,8,5,7,1,3,4]=>[4,3,1,7,5,8,2,6]=>1110100=>0010111
[1,6,4,8,7,3,5,2]=>[2,5,3,7,8,4,6,1]=>1011000=>0001101
[1,5,3,2,6,4,7,8]=>[8,7,4,6,2,3,5,1]=>1101001=>1001011
[1,5,3,2,6,7,4,8]=>[8,4,7,6,2,3,5,1]=>1101010=>0101011
[1,7,3,2,8,5,4,6]=>[6,4,5,8,2,3,7,1]=>1101000=>0001011
[1,7,3,2,5,8,4,6]=>[6,4,8,5,2,3,7,1]=>1101100=>0011011
[6,4,2,5,3,7,1,8]=>[8,1,7,3,5,2,4,6]=>1110000=>0000111
[3,6,4,8,2,1,5,7]=>[7,5,1,2,8,4,6,3]=>1011100=>0011101
[1,6,2,8,5,3,4,7]=>[7,4,3,5,8,2,6,1]=>1111000=>0001111
[4,6,2,3,7,5,1,8]=>[8,1,5,7,3,2,6,4]=>1111000=>0001111
[5,3,2,6,4,7,1,8]=>[8,1,7,4,6,2,3,5]=>1101000=>0001011
[1,5,2,6,8,4,3,7]=>[7,3,4,8,6,2,5,1]=>1110010=>0100111
[1,5,7,2,8,4,3,6]=>[6,3,4,8,2,7,5,1]=>1110100=>0010111
[3,6,8,4,2,1,5,7]=>[7,5,1,2,4,8,6,3]=>1010110=>0110101
[4,3,2,6,1,8,5,7]=>[7,5,8,1,6,2,3,4]=>1100100=>0010011
[1,7,2,3,4,8,6,5]=>[5,6,8,4,3,2,7,1]=>1111000=>0001111
[2,3,1,8,4,5,7,6]=>[6,7,5,4,8,1,3,2]=>1101100=>0011011
[7,8,1,4,3,5,2,6]=>[6,2,5,3,4,1,8,7]=>1110001=>1000111
[1,7,8,3,5,4,2,6]=>[6,2,4,5,3,8,7,1]=>1110001=>1000111
[8,4,2,5,3,1,6,7]=>[7,6,1,3,5,2,4,8]=>1100010=>0100011
[4,3,2,5,1,8,6,7]=>[7,6,8,1,5,2,3,4]=>1100010=>0100011
[6,1,2,8,5,3,4,7]=>[7,4,3,5,8,2,1,6]=>1111000=>0001111
[7,1,8,3,5,4,2,6]=>[6,2,4,5,3,8,1,7]=>1110000=>0000111
[7,8,2,3,4,6,1,5]=>[5,1,6,4,3,2,8,7]=>1111001=>1001111
[8,6,2,3,4,1,7,5]=>[5,7,1,4,3,2,6,8]=>1110000=>0000111
[8,3,2,7,4,5,1,6]=>[6,1,5,4,7,2,3,8]=>1101000=>0001011
[6,7,2,3,4,1,8,5]=>[5,8,1,4,3,2,7,6]=>1110010=>0100111
[4,8,7,3,5,6,1,2]=>[2,1,6,5,3,7,8,4]=>1011100=>0011101
[4,8,7,5,3,6,1,2]=>[2,1,6,3,5,7,8,4]=>1011000=>0001101
[5,8,7,3,4,6,1,2]=>[2,1,6,4,3,7,8,5]=>1011100=>0011101
[5,8,4,2,1,6,7,3]=>[3,7,6,1,2,4,8,5]=>1000110=>0110001
[5,3,7,2,6,1,8,4]=>[4,8,1,6,2,7,3,5]=>1110000=>0000111
[5,8,2,1,4,7,6,3]=>[3,6,7,4,1,2,8,5]=>1001100=>0011001
[4,8,2,5,1,7,6,3]=>[3,6,7,1,5,2,8,4]=>1101000=>0001011
[7,8,4,1,2,6,5,3]=>[3,5,6,2,1,4,8,7]=>1100001=>1000011
[5,2,8,3,6,7,1,4]=>[4,1,7,6,3,8,2,5]=>1110010=>0100111
[2,8,7,6,4,1,3,5]=>[5,3,1,4,6,7,8,2]=>1110000=>0000111
[7,8,2,6,5,1,3,4]=>[4,3,1,5,6,2,8,7]=>1110001=>1000111
[6,1,2,8,5,7,3,4]=>[4,3,7,5,8,2,1,6]=>1110100=>0010111
[6,4,2,1,7,5,8,3]=>[3,8,5,7,1,2,4,6]=>1000100=>0010001
[7,8,2,6,5,3,1,4]=>[4,1,3,5,6,2,8,7]=>1100001=>1000011
[2,8,7,6,4,3,1,5]=>[5,1,3,4,6,7,8,2]=>1100000=>0000011
[3,8,7,6,1,2,5,4]=>[4,5,2,1,6,7,8,3]=>1110000=>0000111
[4,8,7,6,2,1,3,5]=>[5,3,1,2,6,7,8,4]=>1011000=>0001101
[4,8,7,6,1,3,2,5]=>[5,2,3,1,6,7,8,4]=>1101000=>0001011
[3,8,7,6,4,1,2,5]=>[5,2,1,4,6,7,8,3]=>1110000=>0000111
[7,8,3,6,5,1,2,4]=>[4,2,1,5,6,3,8,7]=>1110001=>1000111
[3,8,7,6,4,2,1,5]=>[5,1,2,4,6,7,8,3]=>1010000=>0000101
[3,4,2,6,7,8,1,5]=>[5,1,8,7,6,2,4,3]=>1110011=>1100111
[3,1,4,2,6,8,7,5]=>[5,7,8,6,2,4,1,3]=>1100010=>0100011
[8,3,4,2,6,1,7,5]=>[5,7,1,6,2,4,3,8]=>1110000=>0000111
[2,6,7,3,5,4,1,8]=>[8,1,4,5,3,7,6,2]=>1110010=>0100111
[2,7,8,3,5,4,1,6]=>[6,1,4,5,3,8,7,2]=>1110001=>1000111
[2,6,8,3,5,4,1,7]=>[7,1,4,5,3,8,6,2]=>1110010=>0100111
[4,7,1,2,8,5,3,6]=>[6,3,5,8,2,1,7,4]=>1111000=>0001111
[4,8,1,2,7,5,3,6]=>[6,3,5,7,2,1,8,4]=>1111000=>0001111
[2,1,6,3,7,5,4,8]=>[8,4,5,7,3,6,1,2]=>1011000=>0001101
[2,7,1,3,6,8,4,5]=>[5,4,8,6,3,1,7,2]=>1111010=>0101111
[7,4,1,2,8,5,3,6]=>[6,3,5,8,2,1,4,7]=>1110000=>0000111
[8,7,4,2,1,5,3,6]=>[6,3,5,1,2,4,7,8]=>1010000=>0000101
[7,4,1,2,6,5,3,8]=>[8,3,5,6,2,1,4,7]=>1110000=>0000111
[7,4,3,1,5,6,8,2]=>[2,8,6,5,1,3,4,7]=>1000110=>0110001
[6,7,4,1,5,8,3,2]=>[2,3,8,5,1,4,7,6]=>1000110=>0110001
[4,7,5,1,6,8,3,2]=>[2,3,8,6,1,5,7,4]=>1001010=>0101001
[4,5,3,1,7,6,8,2]=>[2,8,6,7,1,3,5,4]=>1001010=>0101001
[4,6,1,2,8,5,3,7]=>[7,3,5,8,2,1,6,4]=>1111000=>0001111
[4,5,3,1,8,6,7,2]=>[2,7,6,8,1,3,5,4]=>1001010=>0101001
[4,8,5,6,3,1,7,2]=>[2,7,1,3,6,5,8,4]=>1001100=>0011001
[5,1,3,4,8,6,7,2]=>[2,7,6,8,4,3,1,5]=>1011010=>0101101
[5,4,3,8,1,6,7,2]=>[2,7,6,1,8,3,4,5]=>1010010=>0100101
[8,5,3,4,1,6,7,2]=>[2,7,6,1,4,3,5,8]=>1010010=>0100101
[6,4,8,2,1,5,3,7]=>[7,3,5,1,2,8,4,6]=>1011000=>0001101
[6,7,3,2,5,1,4,8]=>[8,4,1,5,2,3,7,6]=>1101010=>0101011
[6,8,3,2,5,1,4,7]=>[7,4,1,5,2,3,8,6]=>1101010=>0101011
[5,7,1,4,6,8,3,2]=>[2,3,8,6,4,1,7,5]=>1001110=>0111001
[5,1,3,4,7,6,8,2]=>[2,8,6,7,4,3,1,5]=>1011010=>0101101
[5,4,3,7,1,6,8,2]=>[2,8,6,1,7,3,4,5]=>1010010=>0100101
[6,7,5,4,1,8,3,2]=>[2,3,8,1,4,5,7,6]=>1000010=>0100001
[7,6,4,2,1,5,3,8]=>[8,3,5,1,2,4,6,7]=>1010000=>0000101
[8,6,1,5,3,2,4,7]=>[7,4,2,3,5,1,6,8]=>1101000=>0001011
[8,6,1,4,5,2,3,7]=>[7,3,2,5,4,1,6,8]=>1111000=>0001111
[8,6,3,1,5,2,4,7]=>[7,4,2,5,1,3,6,8]=>1101000=>0001011
[8,4,6,1,5,2,3,7]=>[7,3,2,5,1,6,4,8]=>1111000=>0001111
[8,5,2,6,1,4,3,7]=>[7,3,4,1,6,2,5,8]=>1110000=>0000111
[8,2,7,5,1,3,4,6]=>[6,4,3,1,5,7,2,8]=>1111000=>0001111
[8,4,1,7,5,2,3,6]=>[6,3,2,5,7,1,4,8]=>1110000=>0000111
[8,1,5,7,3,2,6,4]=>[4,6,2,3,7,5,1,8]=>1100100=>0010011
[8,2,6,1,5,7,3,4]=>[4,3,7,5,1,6,2,8]=>1110100=>0010111
[5,7,6,1,8,2,3,4]=>[4,3,2,8,1,6,7,5]=>1110100=>0010111
[8,1,6,4,7,2,3,5]=>[5,3,2,7,4,6,1,8]=>1111000=>0001111
[8,5,1,7,3,2,4,6]=>[6,4,2,3,7,1,5,8]=>1101000=>0001011
[8,4,5,1,7,2,3,6]=>[6,3,2,7,1,5,4,8]=>1111000=>0001111
[7,3,1,8,5,6,2,4]=>[4,2,6,5,8,1,3,7]=>1100100=>0010011
[7,4,3,8,1,2,6,5]=>[5,6,2,1,8,3,4,7]=>1110000=>0000111
[8,2,3,6,7,1,5,4]=>[4,5,1,7,6,3,2,8]=>1110010=>0100111
[7,8,5,2,3,6,4,1]=>[1,4,6,3,2,5,8,7]=>0110001=>1000110
[6,8,5,2,3,4,7,1]=>[1,7,4,3,2,5,8,6]=>0111010=>0101110
[5,7,3,4,6,8,1,2]=>[2,1,8,6,4,3,7,5]=>1011110=>0111101
[5,7,3,1,4,6,8,2]=>[2,8,6,4,1,3,7,5]=>1001110=>0111001
[5,7,3,1,4,8,6,2]=>[2,6,8,4,1,3,7,5]=>1001100=>0011001
[5,3,7,1,4,2,8,6]=>[6,8,2,4,1,7,3,5]=>1110000=>0000111
[7,8,3,5,1,2,6,4]=>[4,6,2,1,5,3,8,7]=>1110001=>1000111
[3,7,5,1,2,6,4,8]=>[8,4,6,2,1,5,7,3]=>1111000=>0001111
[2,5,7,4,8,6,1,3]=>[3,1,6,8,4,7,5,2]=>1101100=>0011011
[2,6,4,8,7,5,1,3]=>[3,1,5,7,8,4,6,2]=>1101000=>0001011
[6,2,4,8,7,5,1,3]=>[3,1,5,7,8,4,2,6]=>1101000=>0001011
[2,5,1,4,7,3,8,6]=>[6,8,3,7,4,1,5,2]=>1111000=>0001111
[7,1,4,2,8,6,5,3]=>[3,5,6,8,2,4,1,7]=>1100000=>0000011
[3,6,2,4,1,8,7,5]=>[5,7,8,1,4,2,6,3]=>1110000=>0000111
[7,2,3,5,1,8,6,4]=>[4,6,8,1,5,3,2,7]=>1110000=>0000111
[3,4,5,1,8,7,6,2]=>[2,6,7,8,1,5,4,3]=>1011000=>0001101
[1,5,8,3,2,7,6,4]=>[4,6,7,2,3,8,5,1]=>1100100=>0010011
[2,5,8,3,1,7,6,4]=>[4,6,7,1,3,8,5,2]=>1100100=>0010011
[5,2,8,4,1,3,7,6]=>[6,7,3,1,4,8,2,5]=>1110000=>0000111
[7,5,1,2,8,6,4,3]=>[3,4,6,8,2,1,5,7]=>1100000=>0000011
[4,6,1,2,8,7,5,3]=>[3,5,7,8,2,1,6,4]=>1101000=>0001011
[6,4,1,2,8,7,5,3]=>[3,5,7,8,2,1,4,6]=>1100000=>0000011
[5,3,1,7,2,8,6,4]=>[4,6,8,2,7,1,3,5]=>1100000=>0000011
[4,1,2,8,3,7,6,5]=>[5,6,7,3,8,2,1,4]=>1110000=>0000111
[2,1,7,8,4,6,3,5]=>[5,3,6,4,8,7,1,2]=>1011001=>1001101
[3,5,8,7,2,6,4,1]=>[1,4,6,2,7,8,5,3]=>0110100=>0010110
[5,8,2,7,1,6,4,3]=>[3,4,6,1,7,2,8,5]=>1100100=>0010011
[2,1,6,4,5,8,3,7]=>[7,3,8,5,4,6,1,2]=>1011100=>0011101
[8,6,3,7,5,2,1,4]=>[4,1,2,5,7,3,6,8]=>1010000=>0000101
[4,6,3,8,5,2,1,7]=>[7,1,2,5,8,3,6,4]=>1011000=>0001101
[4,6,3,7,5,2,8,1]=>[1,8,2,5,7,3,6,4]=>0111000=>0001110
[3,5,7,8,2,6,1,4]=>[4,1,6,2,8,7,5,3]=>1110101=>1010111
[5,6,2,4,1,3,8,7]=>[7,8,3,1,4,2,6,5]=>1110100=>0010111
[7,6,3,8,5,2,4,1]=>[1,4,2,5,8,3,6,7]=>0110000=>0000110
[8,2,3,4,6,1,5,7]=>[7,5,1,6,4,3,2,8]=>1111100=>0011111
[7,2,3,4,6,1,8,5]=>[5,8,1,6,4,3,2,7]=>1111000=>0001111
[8,2,3,4,7,5,1,6]=>[6,1,5,7,4,3,2,8]=>1111000=>0001111
[7,8,3,6,5,1,4,2]=>[2,4,1,5,6,3,8,7]=>1010001=>1000101
[4,2,3,6,1,5,8,7]=>[7,8,5,1,6,3,2,4]=>1110100=>0010111
[4,8,3,7,5,1,6,2]=>[2,6,1,5,7,3,8,4]=>1011000=>0001101
[8,2,3,4,7,1,6,5]=>[5,6,1,7,4,3,2,8]=>1111000=>0001111
[3,8,6,4,5,1,2,7]=>[7,2,1,5,4,6,8,3]=>1111000=>0001111
[4,7,3,6,5,8,2,1]=>[1,2,8,5,6,3,7,4]=>0011100=>0011100
[4,8,3,7,5,2,1,6]=>[6,1,2,5,7,3,8,4]=>1011000=>0001101
[8,7,3,6,5,1,2,4]=>[4,2,1,5,6,3,7,8]=>1110000=>0000111
[8,2,7,5,1,6,3,4]=>[4,3,6,1,5,7,2,8]=>1110000=>0000111
[5,8,1,7,3,6,4,2]=>[2,4,6,3,7,1,8,5]=>1010100=>0010101
[5,2,7,8,4,6,3,1]=>[1,3,6,4,8,7,2,5]=>0101001=>1001010
[5,2,8,3,7,6,1,4]=>[4,1,6,7,3,8,2,5]=>1110000=>0000111
[8,2,7,3,1,6,4,5]=>[5,4,6,1,3,7,2,8]=>1101000=>0001011
[6,8,3,2,5,7,1,4]=>[4,1,7,5,2,3,8,6]=>1100110=>0110011
[6,7,3,8,5,4,2,1]=>[1,2,4,5,8,3,7,6]=>0010010=>0100100
[6,2,3,4,7,5,8,1]=>[1,8,5,7,4,3,2,6]=>0111100=>0011110
[8,2,3,4,1,7,5,6]=>[6,5,7,1,4,3,2,8]=>1110100=>0010111
[6,2,3,4,1,8,5,7]=>[7,5,8,1,4,3,2,6]=>1110100=>0010111
[6,2,3,4,8,7,5,1]=>[1,5,7,8,4,3,2,6]=>0111000=>0001110
[6,8,3,1,5,7,4,2]=>[2,4,7,5,1,3,8,6]=>1000110=>0110001
[8,7,2,5,1,4,6,3]=>[3,6,4,1,5,2,7,8]=>1101000=>0001011
[4,8,7,2,5,1,6,3]=>[3,6,1,5,2,7,8,4]=>1101000=>0001011
[8,7,1,4,2,5,6,3]=>[3,6,5,2,4,1,7,8]=>1100100=>0010011
[3,5,8,7,1,2,6,4]=>[4,6,2,1,7,8,5,3]=>1110100=>0010111
[2,3,8,5,7,1,6,4]=>[4,6,1,7,5,8,3,2]=>1110100=>0010111
[3,5,8,7,1,6,2,4]=>[4,2,6,1,7,8,5,3]=>1110100=>0010111
[8,7,4,1,2,6,5,3]=>[3,5,6,2,1,4,7,8]=>1100000=>0000011
[5,7,1,8,2,6,3,4]=>[4,3,6,2,8,1,7,5]=>1110100=>0010111
[2,8,7,1,5,6,3,4]=>[4,3,6,5,1,7,8,2]=>1110100=>0010111
[1,6,2,8,4,7,5,3]=>[3,5,7,4,8,2,6,1]=>1101000=>0001011
[1,3,8,5,7,2,6,4]=>[4,6,2,7,5,8,3,1]=>1110100=>0010111
[1,8,3,7,2,5,6,4]=>[4,6,5,2,7,3,8,1]=>1110100=>0010111
[2,8,7,1,3,5,6,4]=>[4,6,5,3,1,7,8,2]=>1110100=>0010111
[8,6,3,7,4,1,5,2]=>[2,5,1,4,7,3,6,8]=>1010000=>0000101
[4,2,8,6,7,5,1,3]=>[3,1,5,7,6,8,2,4]=>1100010=>0100011
[8,4,2,7,5,6,1,3]=>[3,1,6,5,7,2,4,8]=>1100100=>0010011
[4,8,3,6,1,7,5,2]=>[2,5,7,1,6,3,8,4]=>1011000=>0001101
[8,3,4,7,5,1,6,2]=>[2,6,1,5,7,4,3,8]=>1011000=>0001101
[8,3,7,4,5,1,6,2]=>[2,6,1,5,4,7,3,8]=>1011000=>0001101
[8,7,4,2,5,6,1,3]=>[3,1,6,5,2,4,7,8]=>1100100=>0010011
[8,7,5,1,6,2,3,4]=>[4,3,2,6,1,5,7,8]=>1110000=>0000111
[8,7,2,4,1,5,6,3]=>[3,6,5,1,4,2,7,8]=>1100100=>0010011
[4,8,6,1,7,2,5,3]=>[3,5,2,7,1,6,8,4]=>1101000=>0001011
[4,2,8,6,7,1,5,3]=>[3,5,1,7,6,8,2,4]=>1100010=>0100011
[8,7,4,1,2,5,6,3]=>[3,6,5,2,1,4,7,8]=>1100100=>0010011
[8,2,7,1,6,3,4,5]=>[5,4,3,6,1,7,2,8]=>1111000=>0001111
[8,2,7,1,3,6,4,5]=>[5,4,6,3,1,7,2,8]=>1111000=>0001111
[2,8,3,6,7,1,5,4]=>[4,5,1,7,6,3,8,2]=>1110010=>0100111
[8,7,2,1,3,5,6,4]=>[4,6,5,3,1,2,7,8]=>1010100=>0010101
[1,8,7,2,3,6,4,5]=>[5,4,6,3,2,7,8,1]=>1111000=>0001111
[1,8,7,2,6,3,4,5]=>[5,4,3,6,2,7,8,1]=>1111000=>0001111
[8,2,7,3,6,1,4,5]=>[5,4,1,6,3,7,2,8]=>1111000=>0001111
[1,8,7,3,6,2,4,5]=>[5,4,2,6,3,7,8,1]=>1111000=>0001111
[1,8,2,7,6,3,4,5]=>[5,4,3,6,7,2,8,1]=>1111000=>0001111
[8,2,7,4,1,5,6,3]=>[3,6,5,1,4,7,2,8]=>1100100=>0010011
[8,2,1,7,5,6,3,4]=>[4,3,6,5,7,1,2,8]=>1010100=>0010101
[8,7,3,1,5,6,2,4]=>[4,2,6,5,1,3,7,8]=>1100100=>0010011
[2,8,7,3,5,6,1,4]=>[4,1,6,5,3,7,8,2]=>1110100=>0010111
[8,3,1,6,7,5,2,4]=>[4,2,5,7,6,1,3,8]=>1100010=>0100011
[8,5,2,1,6,7,4,3]=>[3,4,7,6,1,2,5,8]=>1000010=>0100001
[1,5,2,8,6,7,4,3]=>[3,4,7,6,8,2,5,1]=>1100010=>0100011
[1,2,8,6,7,5,3,4]=>[4,3,5,7,6,8,2,1]=>1110010=>0100111
[1,8,3,6,7,5,2,4]=>[4,2,5,7,6,3,8,1]=>1110010=>0100111
[8,2,3,6,7,5,1,4]=>[4,1,5,7,6,3,2,8]=>1110010=>0100111
[8,3,7,2,5,6,1,4]=>[4,1,6,5,2,7,3,8]=>1110100=>0010111
[8,1,3,7,5,6,2,4]=>[4,2,6,5,7,3,1,8]=>1110100=>0010111
[8,4,1,2,7,5,6,3]=>[3,6,5,7,2,1,4,8]=>1100100=>0010011
[8,1,4,2,6,7,5,3]=>[3,5,7,6,2,4,1,8]=>1100010=>0100011
[1,2,8,6,7,3,5,4]=>[4,5,3,7,6,8,2,1]=>1110010=>0100111
[8,1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1,8]=>1111000=>0001111
[8,1,7,3,6,2,4,5]=>[5,4,2,6,3,7,1,8]=>1111000=>0001111
[8,1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1,8]=>1111000=>0001111
[8,1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1,8]=>1111000=>0001111
[8,1,3,7,2,5,6,4]=>[4,6,5,2,7,3,1,8]=>1110100=>0010111
[1,8,3,6,7,2,5,4]=>[4,5,2,7,6,3,8,1]=>1110010=>0100111
[1,7,8,2,3,6,5,4]=>[4,5,6,3,2,8,7,1]=>1110001=>1000111
[8,3,7,1,2,5,6,4]=>[4,6,5,2,1,7,3,8]=>1110100=>0010111
[7,4,2,6,1,5,3,8]=>[8,3,5,1,6,2,4,7]=>1110000=>0000111
[7,4,2,5,6,1,3,8]=>[8,3,1,6,5,2,4,7]=>1110100=>0010111
[7,3,5,6,4,2,1,8]=>[8,1,2,4,6,5,3,7]=>1010100=>0010101
[7,4,3,1,5,6,2,8]=>[8,2,6,5,1,3,4,7]=>1100100=>0010011
[7,4,5,2,6,1,3,8]=>[8,3,1,6,2,5,4,7]=>1111000=>0001111
[5,3,7,2,8,6,4,1]=>[1,4,6,8,2,7,3,5]=>0110000=>0000110
[5,3,8,2,6,7,4,1]=>[1,4,7,6,2,8,3,5]=>0110010=>0100110
[6,4,3,1,8,2,7,5]=>[5,7,2,8,1,3,4,6]=>1100000=>0000011
[5,3,7,8,2,6,4,1]=>[1,4,6,2,8,7,3,5]=>0110001=>1000110
[4,7,8,5,6,3,2,1]=>[1,2,3,6,5,8,7,4]=>0001101=>1011000
[5,3,7,6,8,2,4,1]=>[1,4,2,8,6,7,3,5]=>0110010=>0100110
[5,7,8,4,6,2,1,3]=>[3,1,2,6,4,8,7,5]=>1001101=>1011001
[5,8,4,3,6,7,1,2]=>[2,1,7,6,3,4,8,5]=>1010110=>0110101
[5,8,6,4,7,2,1,3]=>[3,1,2,7,4,6,8,5]=>1001100=>0011001
[5,3,8,6,2,7,4,1]=>[1,4,7,2,6,8,3,5]=>0110000=>0000110
[4,7,5,8,6,3,2,1]=>[1,2,3,6,8,5,7,4]=>0001100=>0011000
[6,3,8,7,2,4,1,5]=>[5,1,4,2,7,8,3,6]=>1110000=>0000111
[5,3,8,7,2,6,4,1]=>[1,4,6,2,7,8,3,5]=>0110000=>0000110
[5,3,8,6,7,2,4,1]=>[1,4,2,7,6,8,3,5]=>0110010=>0100110
[5,3,7,8,6,2,4,1]=>[1,4,2,6,8,7,3,5]=>0110001=>1000110
[5,7,6,4,8,2,1,3]=>[3,1,2,8,4,6,7,5]=>1001100=>0011001
[5,8,4,6,7,2,1,3]=>[3,1,2,7,6,4,8,5]=>1001110=>0111001
[6,4,2,8,1,7,3,5]=>[5,3,7,1,8,2,4,6]=>1110000=>0000111
[6,5,2,4,3,7,8,1]=>[1,8,7,3,4,2,5,6]=>0110001=>1000110
[5,4,6,2,8,7,1,3]=>[3,1,7,8,2,6,4,5]=>1101000=>0001011
[5,6,3,8,7,2,4,1]=>[1,4,2,7,8,3,6,5]=>0110100=>0010110
[5,7,4,3,6,8,1,2]=>[2,1,8,6,3,4,7,5]=>1010110=>0110101
[5,7,3,8,6,2,4,1]=>[1,4,2,6,8,3,7,5]=>0110100=>0010110
[4,5,8,6,7,3,2,1]=>[1,2,3,7,6,8,5,4]=>0001110=>0111000
[4,6,8,5,7,3,2,1]=>[1,2,3,7,5,8,6,4]=>0001110=>0111000
[5,6,8,3,7,2,4,1]=>[1,4,2,7,3,8,6,5]=>0110110=>0110110
[5,4,6,8,2,7,1,3]=>[3,1,7,2,8,6,4,5]=>1101010=>0101011
[7,8,4,5,1,3,2,6]=>[6,2,3,1,5,4,8,7]=>1101001=>1001011
[6,7,1,3,2,5,4,8]=>[8,4,5,2,3,1,7,6]=>1101010=>0101011
[7,8,2,3,1,5,4,6]=>[6,4,5,1,3,2,8,7]=>1101001=>1001011
[7,8,2,4,3,5,1,6]=>[6,1,5,3,4,2,8,7]=>1110001=>1000111
[7,8,2,4,1,5,3,6]=>[6,3,5,1,4,2,8,7]=>1110001=>1000111
[1,4,2,6,5,7,3,8]=>[8,3,7,5,6,2,4,1]=>1110100=>0010111
[5,6,1,4,2,7,3,8]=>[8,3,7,2,4,1,6,5]=>1110100=>0010111
[6,7,2,4,1,5,3,8]=>[8,3,5,1,4,2,7,6]=>1110010=>0100111
[6,7,2,4,3,5,1,8]=>[8,1,5,3,4,2,7,6]=>1110010=>0100111
[6,7,2,3,1,5,4,8]=>[8,4,5,1,3,2,7,6]=>1101010=>0101011
[6,7,3,5,4,8,1,2]=>[2,1,8,4,5,3,7,6]=>1011010=>0101101
[2,4,1,6,5,7,3,8]=>[8,3,7,5,6,1,4,2]=>1110100=>0010111
[1,5,2,6,4,7,3,8]=>[8,3,7,4,6,2,5,1]=>1111000=>0001111
[2,5,1,6,4,7,3,8]=>[8,3,7,4,6,1,5,2]=>1111000=>0001111
[5,6,2,4,3,7,1,8]=>[8,1,7,3,4,2,6,5]=>1110100=>0010111
[4,5,2,6,1,7,3,8]=>[8,3,7,1,6,2,5,4]=>1111000=>0001111
[4,5,1,6,3,7,2,8]=>[8,2,7,3,6,1,5,4]=>1111000=>0001111
[5,6,3,4,1,7,2,8]=>[8,2,7,1,4,3,6,5]=>1110100=>0010111
[5,6,1,4,3,7,2,8]=>[8,2,7,3,4,1,6,5]=>1110100=>0010111
[5,6,1,3,2,7,4,8]=>[8,4,7,2,3,1,6,5]=>1101100=>0011011
[5,6,4,7,1,3,2,8]=>[8,2,3,1,7,4,6,5]=>1101100=>0011011
[6,7,5,8,1,3,2,4]=>[4,2,3,1,8,5,7,6]=>1100110=>0110011
[4,5,1,3,2,7,6,8]=>[8,6,7,2,3,1,5,4]=>1101010=>0101011
[4,6,5,7,1,3,2,8]=>[8,2,3,1,7,5,6,4]=>1101100=>0011011
[4,6,1,3,2,7,5,8]=>[8,5,7,2,3,1,6,4]=>1101100=>0011011
[1,4,3,6,2,7,5,8]=>[8,5,7,2,6,3,4,1]=>1110100=>0010111
[4,5,2,3,1,7,6,8]=>[8,6,7,1,3,2,5,4]=>1101010=>0101011
[4,5,3,7,6,8,1,2]=>[2,1,8,6,7,3,5,4]=>1011010=>0101101
[4,6,5,7,3,8,1,2]=>[2,1,8,3,7,5,6,4]=>1011100=>0011101
[4,6,5,7,2,3,1,8]=>[8,1,3,2,7,5,6,4]=>1101100=>0011011
[3,5,1,6,4,7,2,8]=>[8,2,7,4,6,1,5,3]=>1111000=>0001111
[1,5,3,6,4,7,2,8]=>[8,2,7,4,6,3,5,1]=>1111000=>0001111
[1,5,3,6,2,7,4,8]=>[8,4,7,2,6,3,5,1]=>1111000=>0001111
[3,5,2,6,1,7,4,8]=>[8,4,7,1,6,2,5,3]=>1111000=>0001111
[3,5,2,6,4,7,1,8]=>[8,1,7,4,6,2,5,3]=>1111000=>0001111
[3,4,2,6,1,7,5,8]=>[8,5,7,1,6,2,4,3]=>1110100=>0010111
[4,6,2,3,1,7,5,8]=>[8,5,7,1,3,2,6,4]=>1101100=>0011011
[2,4,3,6,1,7,5,8]=>[8,5,7,1,6,3,4,2]=>1110100=>0010111
[2,5,3,6,1,7,4,8]=>[8,4,7,1,6,3,5,2]=>1111000=>0001111
[4,6,2,7,3,5,8,1]=>[1,8,5,3,7,2,6,4]=>0111100=>0011110
[3,6,2,7,5,4,8,1]=>[1,8,4,5,7,2,6,3]=>0111000=>0001110
[4,6,1,7,3,8,2,5]=>[5,2,8,3,7,1,6,4]=>1111000=>0001111
[2,4,7,1,3,8,6,5]=>[5,6,8,3,1,7,4,2]=>1111000=>0001111
[5,2,6,7,4,3,8,1]=>[1,8,3,4,7,6,2,5]=>0110010=>0100110
[3,5,2,7,6,4,8,1]=>[1,8,4,6,7,2,5,3]=>0111000=>0001110
[1,5,7,4,3,8,2,6]=>[6,2,8,3,4,7,5,1]=>1110100=>0010111
[2,5,7,3,1,8,6,4]=>[4,6,8,1,3,7,5,2]=>1100100=>0010011
[1,5,7,2,8,3,6,4]=>[4,6,3,8,2,7,5,1]=>1110100=>0010111
[2,5,7,3,1,8,4,6]=>[6,4,8,1,3,7,5,2]=>1101100=>0011011
[5,2,6,7,1,8,4,3]=>[3,4,8,1,7,6,2,5]=>1100010=>0100011
[1,3,7,2,8,5,6,4]=>[4,6,5,8,2,7,3,1]=>1110100=>0010111
[2,3,1,5,8,4,7,6]=>[6,7,4,8,5,1,3,2]=>1101100=>0011011
[2,1,5,6,8,4,3,7]=>[7,3,4,8,6,5,1,2]=>1010110=>0110101
[2,3,1,5,8,6,4,7]=>[7,4,6,8,5,1,3,2]=>1101100=>0011011
[1,3,7,2,8,5,4,6]=>[6,4,5,8,2,7,3,1]=>1111000=>0001111
[2,3,1,6,8,5,4,7]=>[7,4,5,8,6,1,3,2]=>1101010=>0101011
[4,6,2,7,1,8,3,5]=>[5,3,8,1,7,2,6,4]=>1111000=>0001111
[1,5,4,3,6,8,2,7]=>[7,2,8,6,3,4,5,1]=>1110010=>0100111
[1,6,4,5,7,8,3,2]=>[2,3,8,7,5,4,6,1]=>1001101=>1011001
[1,3,6,2,8,7,4,5]=>[5,4,7,8,2,6,3,1]=>1111000=>0001111
[2,1,5,6,8,4,7,3]=>[3,7,4,8,6,5,1,2]=>1001110=>0111001
[1,3,6,2,8,4,7,5]=>[5,7,4,8,2,6,3,1]=>1111000=>0001111
[2,1,5,6,8,7,3,4]=>[4,3,7,8,6,5,1,2]=>1010110=>0110101
[3,4,6,8,5,7,2,1]=>[1,2,7,5,8,6,4,3]=>0011110=>0111100
[4,5,6,2,8,7,3,1]=>[1,3,7,8,2,6,5,4]=>0101100=>0011010
[4,5,6,1,8,7,3,2]=>[2,3,7,8,1,6,5,4]=>1001100=>0011001
[4,5,6,3,1,8,7,2]=>[2,7,8,1,3,6,5,4]=>1001100=>0011001
[4,3,6,2,1,7,5,8]=>[8,5,7,1,2,6,3,4]=>1010100=>0010101
[4,6,3,1,7,5,2,8]=>[8,2,5,7,1,3,6,4]=>1101000=>0001011
[4,5,3,7,6,1,8,2]=>[2,8,1,6,7,3,5,4]=>1011000=>0001101
[4,5,1,7,3,8,6,2]=>[2,6,8,3,7,1,5,4]=>1011000=>0001101
[2,5,7,1,4,3,8,6]=>[6,8,3,4,1,7,5,2]=>1110100=>0010111
[4,3,5,7,6,1,8,2]=>[2,8,1,6,7,5,3,4]=>1010100=>0010101
[4,3,2,6,1,7,5,8]=>[8,5,7,1,6,2,3,4]=>1100100=>0010011
[5,3,2,1,6,4,7,8]=>[8,7,4,6,1,2,3,5]=>1001001=>1001001
[5,3,1,6,2,7,4,8]=>[8,4,7,2,6,1,3,5]=>1101000=>0001011
[5,1,6,3,2,7,4,8]=>[8,4,7,2,3,6,1,5]=>1101000=>0001011
[2,6,1,4,7,5,3,8]=>[8,3,5,7,4,1,6,2]=>1111000=>0001111
[3,6,1,7,4,2,5,8]=>[8,5,2,4,7,1,6,3]=>1110100=>0010111
[4,6,1,7,5,3,2,8]=>[8,2,3,5,7,1,6,4]=>1101000=>0001011
[5,1,6,3,7,4,2,8]=>[8,2,4,7,3,6,1,5]=>1110000=>0000111
[5,3,6,4,2,1,7,8]=>[8,7,1,2,4,6,3,5]=>1010001=>1000101
[5,3,2,6,4,1,7,8]=>[8,7,1,4,6,2,3,5]=>1100001=>1000011
[5,2,1,6,3,7,4,8]=>[8,4,7,3,6,1,2,5]=>1011000=>0001101
[5,2,6,3,1,7,4,8]=>[8,4,7,1,3,6,2,5]=>1101000=>0001011
[4,2,6,3,1,7,8,5]=>[5,8,7,1,3,6,2,4]=>1100001=>1000011
[3,6,2,7,4,1,5,8]=>[8,5,1,4,7,2,6,3]=>1110100=>0010111
[3,5,7,2,8,6,4,1]=>[1,4,6,8,2,7,5,3]=>0110100=>0010110
[2,6,1,3,7,5,4,8]=>[8,4,5,7,3,1,6,2]=>1111000=>0001111
[3,6,1,7,5,2,4,8]=>[8,4,2,5,7,1,6,3]=>1111000=>0001111
[5,1,6,2,7,4,3,8]=>[8,3,4,7,2,6,1,5]=>1110000=>0000111
[5,2,6,4,3,1,7,8]=>[8,7,1,3,4,6,2,5]=>1100001=>1000011
[5,2,1,6,4,3,7,8]=>[8,7,3,4,6,1,2,5]=>1010001=>1000101
[5,4,2,1,6,3,7,8]=>[8,7,3,6,1,2,4,5]=>1010001=>1000101
[5,4,1,6,2,7,3,8]=>[8,3,7,2,6,1,4,5]=>1110000=>0000111
[5,1,6,4,2,7,3,8]=>[8,3,7,2,4,6,1,5]=>1110000=>0000111
[3,6,1,7,5,4,8,2]=>[2,8,4,5,7,1,6,3]=>1011000=>0001101
[2,6,1,5,4,3,7,8]=>[8,7,3,4,5,1,6,2]=>1110001=>1000111
[3,1,6,2,5,4,7,8]=>[8,7,4,5,2,6,1,3]=>1101001=>1001011
[4,1,6,3,2,7,8,5]=>[5,8,7,2,3,6,1,4]=>1100001=>1000011
[5,1,6,4,3,2,7,8]=>[8,7,2,3,4,6,1,5]=>1100001=>1000011
[5,4,1,6,3,2,7,8]=>[8,7,2,3,6,1,4,5]=>1100001=>1000011
[5,4,3,1,6,2,7,8]=>[8,7,2,6,1,3,4,5]=>1100001=>1000011
[1,2,8,7,4,6,3,5]=>[5,3,6,4,7,8,2,1]=>1111000=>0001111
[3,7,4,8,6,1,5,2]=>[2,5,1,6,8,4,7,3]=>1011000=>0001101
[4,5,1,8,7,6,2,3]=>[3,2,6,7,8,1,5,4]=>1101000=>0001011
[1,5,2,8,7,6,3,4]=>[4,3,6,7,8,2,5,1]=>1110000=>0000111
[5,1,2,8,7,6,3,4]=>[4,3,6,7,8,2,1,5]=>1110000=>0000111
[4,1,5,8,7,6,2,3]=>[3,2,6,7,8,5,1,4]=>1100100=>0010011
[2,3,6,8,7,4,5,1]=>[1,5,4,7,8,6,3,2]=>0111010=>0101110
[2,3,7,8,6,4,5,1]=>[1,5,4,6,8,7,3,2]=>0111001=>1001110
[4,5,7,8,2,6,3,1]=>[1,3,6,2,8,7,5,4]=>0101101=>1011010
[4,5,6,8,2,7,3,1]=>[1,3,7,2,8,6,5,4]=>0101110=>0111010
[5,2,6,8,3,7,4,1]=>[1,4,7,3,8,6,2,5]=>0110010=>0100110
[3,1,6,8,7,4,5,2]=>[2,5,4,7,8,6,1,3]=>1001010=>0101001
[6,1,4,8,7,2,5,3]=>[3,5,2,7,8,4,1,6]=>1101000=>0001011
[6,1,8,4,7,3,5,2]=>[2,5,3,7,4,8,1,6]=>1011000=>0001101
[5,8,3,4,7,1,6,2]=>[2,6,1,7,4,3,8,5]=>1011100=>0011101
[6,8,3,5,7,1,4,2]=>[2,4,1,7,5,3,8,6]=>1010110=>0110101
[5,2,7,8,3,6,4,1]=>[1,4,6,3,8,7,2,5]=>0110001=>1000110
[4,6,7,8,2,5,3,1]=>[1,3,5,2,8,7,6,4]=>0101011=>1101010
[7,5,8,4,2,6,3,1]=>[1,3,6,2,4,8,5,7]=>0100100=>0010010
[6,8,4,5,2,7,3,1]=>[1,3,7,2,5,4,8,6]=>0101010=>0101010
[6,8,2,5,3,7,4,1]=>[1,4,7,3,5,2,8,6]=>0110010=>0100110
[7,2,5,3,8,6,4,1]=>[1,4,6,8,3,5,2,7]=>0110000=>0000110
[3,4,7,5,8,6,2,1]=>[1,2,6,8,5,7,4,3]=>0011100=>0011100
[3,6,7,4,8,5,2,1]=>[1,2,5,8,4,7,6,3]=>0011010=>0101100
[6,7,4,2,8,5,3,1]=>[1,3,5,8,2,4,7,6]=>0100010=>0100010
[4,7,5,2,8,6,3,1]=>[1,3,6,8,2,5,7,4]=>0101000=>0001010
[5,6,2,8,3,7,4,1]=>[1,4,7,3,8,2,6,5]=>0110100=>0010110
[5,7,8,3,2,6,4,1]=>[1,4,6,2,3,8,7,5]=>0100101=>1010010
[5,6,8,3,2,7,4,1]=>[1,4,7,2,3,8,6,5]=>0100110=>0110010
[1,5,8,2,7,3,6,4]=>[4,6,3,7,2,8,5,1]=>1110100=>0010111
[5,8,4,7,2,3,6,1]=>[1,6,3,2,7,4,8,5]=>0111100=>0011110
[5,6,8,1,3,7,4,2]=>[2,4,7,3,1,8,6,5]=>1010110=>0110101
[6,7,4,8,1,5,3,2]=>[2,3,5,1,8,4,7,6]=>1001010=>0101001
[5,7,2,8,3,6,4,1]=>[1,4,6,3,8,2,7,5]=>0110100=>0010110
[1,7,4,8,6,2,5,3]=>[3,5,2,6,8,4,7,1]=>1101000=>0001011
[7,4,2,8,6,1,5,3]=>[3,5,1,6,8,2,4,7]=>1100000=>0000011
[6,8,5,3,7,2,4,1]=>[1,4,2,7,3,5,8,6]=>0110010=>0100110
[6,8,5,2,3,7,4,1]=>[1,4,7,3,2,5,8,6]=>0110010=>0100110
[7,5,3,8,2,6,4,1]=>[1,4,6,2,8,3,5,7]=>0110000=>0000110
[3,7,4,5,8,6,2,1]=>[1,2,6,8,5,4,7,3]=>0011100=>0011100
[7,4,2,5,8,6,3,1]=>[1,3,6,8,5,2,4,7]=>0100100=>0010010
[6,1,8,3,4,7,5,2]=>[2,5,7,4,3,8,1,6]=>1011000=>0001101
[6,8,4,2,5,7,3,1]=>[1,3,7,5,2,4,8,6]=>0100110=>0110010
[7,5,8,3,4,6,2,1]=>[1,2,6,4,3,8,5,7]=>0011100=>0011100
[7,4,5,8,1,6,3,2]=>[2,3,6,1,8,5,4,7]=>1001100=>0011001
[6,3,4,7,8,5,2,1]=>[1,2,5,8,7,4,3,6]=>0011001=>1001100
[3,6,8,4,5,7,1,2]=>[2,1,7,5,4,8,6,3]=>1011110=>0111101
[1,6,8,4,7,2,3,5]=>[5,3,2,7,4,8,6,1]=>1111010=>0101111
[1,4,5,7,8,2,6,3]=>[3,6,2,8,7,5,4,1]=>1101101=>1011011
[1,4,5,8,7,2,3,6]=>[6,3,2,7,8,5,4,1]=>1111100=>0011111
[1,2,5,8,3,6,4,7]=>[7,4,6,3,8,5,2,1]=>1111100=>0011111
[7,8,1,4,6,2,3,5]=>[5,3,2,6,4,1,8,7]=>1111001=>1001111
[1,6,7,4,8,2,5,3]=>[3,5,2,8,4,7,6,1]=>1101010=>0101011
[1,4,5,6,8,2,7,3]=>[3,7,2,8,6,5,4,1]=>1101110=>0111011
[1,4,5,8,6,2,7,3]=>[3,7,2,6,8,5,4,1]=>1101100=>0011011
[1,2,5,8,3,4,7,6]=>[6,7,4,3,8,5,2,1]=>1111100=>0011111
[7,8,1,2,3,5,4,6]=>[6,4,5,3,2,1,8,7]=>1111001=>1001111
[1,6,7,2,3,5,4,8]=>[8,4,5,3,2,7,6,1]=>1111010=>0101111
[1,4,5,7,6,2,3,8]=>[8,3,2,6,7,5,4,1]=>1111100=>0011111
[1,2,5,7,3,6,4,8]=>[8,4,6,3,7,5,2,1]=>1111100=>0011111
[1,2,5,7,3,6,8,4]=>[4,8,6,3,7,5,2,1]=>1110110=>0110111
[1,6,8,2,3,5,7,4]=>[4,7,5,3,2,8,6,1]=>1110110=>0110111
[1,6,8,4,5,2,3,7]=>[7,3,2,5,4,8,6,1]=>1111010=>0101111
[1,6,8,2,3,4,7,5]=>[5,7,4,3,2,8,6,1]=>1111010=>0101111
[1,6,8,2,3,7,4,5]=>[5,4,7,3,2,8,6,1]=>1111010=>0101111
[1,4,5,7,6,2,8,3]=>[3,8,2,6,7,5,4,1]=>1101100=>0011011
[7,8,1,4,5,2,6,3]=>[3,6,2,5,4,1,8,7]=>1101001=>1001011
[1,6,7,2,3,8,5,4]=>[4,5,8,3,2,7,6,1]=>1110010=>0100111
[1,2,5,6,3,8,7,4]=>[4,7,8,3,6,5,2,1]=>1110100=>0010111
[2,7,4,8,3,5,1,6]=>[6,1,5,3,8,4,7,2]=>1111000=>0001111
[2,7,4,8,3,5,6,1]=>[1,6,5,3,8,4,7,2]=>0111100=>0011110
[7,2,8,4,3,5,1,6]=>[6,1,5,3,4,8,2,7]=>1110000=>0000111
[8,4,2,1,5,3,6,7]=>[7,6,3,5,1,2,4,8]=>1010010=>0100101
[8,4,1,5,3,2,6,7]=>[7,6,2,3,5,1,4,8]=>1100010=>0100011
[6,7,3,8,4,2,5,1]=>[1,5,2,4,8,3,7,6]=>0110010=>0100110
[6,7,3,8,4,2,1,5]=>[5,1,2,4,8,3,7,6]=>1010010=>0100101
[7,1,8,4,3,5,2,6]=>[6,2,5,3,4,8,1,7]=>1110000=>0000111
[1,7,8,4,3,5,2,6]=>[6,2,5,3,4,8,7,1]=>1110001=>1000111
[7,1,4,8,3,5,2,6]=>[6,2,5,3,8,4,1,7]=>1111000=>0001111
[7,1,8,4,3,5,6,2]=>[2,6,5,3,4,8,1,7]=>1010100=>0010101
[6,7,3,1,8,4,5,2]=>[2,5,4,8,1,3,7,6]=>1001010=>0101001
[6,7,1,4,8,3,5,2]=>[2,5,3,8,4,1,7,6]=>1011010=>0101101
[6,7,4,1,3,8,2,5]=>[5,2,8,3,1,4,7,6]=>1110010=>0100111
[1,6,7,8,4,3,2,5]=>[5,2,3,4,8,7,6,1]=>1100011=>1100011
[7,2,1,8,4,5,3,6]=>[6,3,5,4,8,1,2,7]=>1011000=>0001101
[6,2,7,1,8,4,3,5]=>[5,3,4,8,1,7,2,6]=>1110000=>0000111
[6,2,7,8,4,3,1,5]=>[5,1,3,4,8,7,2,6]=>1100001=>1000011
[6,2,7,8,4,3,5,1]=>[1,5,3,4,8,7,2,6]=>0110001=>1000110
[2,6,7,4,8,3,5,1]=>[1,5,3,8,4,7,6,2]=>0111010=>0101110
[2,6,7,4,8,3,1,5]=>[5,1,3,8,4,7,6,2]=>1101010=>0101011
[7,8,1,3,6,2,4,5]=>[5,4,2,6,3,1,8,7]=>1111001=>1001111
[1,2,7,8,6,3,4,5]=>[5,4,3,6,8,7,2,1]=>1111001=>1001111
[2,6,7,1,8,5,3,4]=>[4,3,5,8,1,7,6,2]=>1110010=>0100111
[2,6,7,8,5,3,4,1]=>[1,4,3,5,8,7,6,2]=>0110011=>1100110
[6,2,7,8,4,5,3,1]=>[1,3,5,4,8,7,2,6]=>0101001=>1001010
[1,7,2,8,4,5,6,3]=>[3,6,5,4,8,2,7,1]=>1101100=>0011011
[6,3,7,8,1,5,2,4]=>[4,2,5,1,8,7,3,6]=>1110001=>1000111
[6,7,1,2,8,5,3,4]=>[4,3,5,8,2,1,7,6]=>1110010=>0100111
[1,6,7,8,4,2,5,3]=>[3,5,2,4,8,7,6,1]=>1100011=>1100011
[3,1,2,7,6,5,8,4]=>[4,8,5,6,7,2,1,3]=>1100100=>0010011
[4,6,1,7,3,2,5,8]=>[8,5,2,3,7,1,6,4]=>1101100=>0011011
[1,5,8,3,4,7,6,2]=>[2,6,7,4,3,8,5,1]=>1011100=>0011101
[3,1,2,6,7,5,8,4]=>[4,8,5,7,6,2,1,3]=>1100110=>0110011
[8,7,2,5,3,6,1,4]=>[4,1,6,3,5,2,7,8]=>1110000=>0000111
[6,1,2,3,5,8,4,7]=>[7,4,8,5,3,2,1,6]=>1111100=>0011111
[6,7,3,5,1,4,8,2]=>[2,8,4,1,5,3,7,6]=>1011010=>0101101
[5,7,8,4,2,6,3,1]=>[1,3,6,2,4,8,7,5]=>0100101=>1010010
[5,4,7,6,2,8,3,1]=>[1,3,8,2,6,7,4,5]=>0101000=>0001010
[5,7,4,1,6,8,3,2]=>[2,3,8,6,1,4,7,5]=>1000110=>0110001
[6,8,4,5,7,1,3,2]=>[2,3,1,7,5,4,8,6]=>1001110=>0111001
[5,8,4,6,1,7,3,2]=>[2,3,7,1,6,4,8,5]=>1001100=>0011001
[5,6,1,4,7,8,3,2]=>[2,3,8,7,4,1,6,5]=>1001101=>1011001
[5,3,6,7,4,8,2,1]=>[1,2,8,4,7,6,3,5]=>0011010=>0101100
[5,3,2,8,6,7,4,1]=>[1,4,7,6,8,2,3,5]=>0100010=>0100010
[5,4,8,2,6,7,3,1]=>[1,3,7,6,2,8,4,5]=>0101010=>0101010
[5,4,8,6,2,7,3,1]=>[1,3,7,2,6,8,4,5]=>0101000=>0001010
[6,4,8,5,7,2,3,1]=>[1,3,2,7,5,8,4,6]=>0101100=>0011010
[4,6,8,5,7,2,3,1]=>[1,3,2,7,5,8,6,4]=>0101110=>0111010
[5,6,3,8,4,7,2,1]=>[1,2,7,4,8,3,6,5]=>0011100=>0011100
[4,6,3,5,8,7,2,1]=>[1,2,7,8,5,3,6,4]=>0011100=>0011100
[4,6,3,2,8,7,5,1]=>[1,5,7,8,2,3,6,4]=>0101000=>0001010
[5,6,3,8,2,7,4,1]=>[1,4,7,2,8,3,6,5]=>0110100=>0010110
[3,6,5,8,7,2,4,1]=>[1,4,2,7,8,5,6,3]=>0110100=>0010110
[5,3,6,8,2,7,4,1]=>[1,4,7,2,8,6,3,5]=>0110010=>0100110
[4,3,7,2,8,6,5,1]=>[1,5,6,8,2,7,3,4]=>0110000=>0000110
[5,4,7,2,6,8,3,1]=>[1,3,8,6,2,7,4,5]=>0101010=>0101010
[5,3,2,7,6,8,4,1]=>[1,4,8,6,7,2,3,5]=>0100010=>0100010
[6,7,3,8,5,2,4,1]=>[1,4,2,5,8,3,7,6]=>0110010=>0100110
[6,3,2,7,5,4,8,1]=>[1,8,4,5,7,2,3,6]=>0101000=>0001010
[6,4,7,2,5,3,8,1]=>[1,8,3,5,2,7,4,6]=>0111000=>0001110
[6,2,7,5,1,4,8,3]=>[3,8,4,1,5,7,2,6]=>1101000=>0001011
[2,7,8,5,3,6,1,4]=>[4,1,6,3,5,8,7,2]=>1110001=>1000111
[3,5,7,8,4,6,2,1]=>[1,2,6,4,8,7,5,3]=>0011101=>1011100
[5,7,8,2,4,6,3,1]=>[1,3,6,4,2,8,7,5]=>0101101=>1011010
[2,5,8,4,3,7,6,1]=>[1,6,7,3,4,8,5,2]=>0110100=>0010110
[2,6,8,4,7,3,5,1]=>[1,5,3,7,4,8,6,2]=>0111010=>0101110
[3,7,4,8,6,2,1,5]=>[5,1,2,6,8,4,7,3]=>1011000=>0001101
[3,6,4,8,7,2,5,1]=>[1,5,2,7,8,4,6,3]=>0111000=>0001110
[3,5,4,8,2,7,6,1]=>[1,6,7,2,8,4,5,3]=>0111000=>0001110
[4,5,7,3,8,6,2,1]=>[1,2,6,8,3,7,5,4]=>0011100=>0011100
[6,3,1,8,7,5,4,2]=>[2,4,5,7,8,1,3,6]=>1000000=>0000001
[5,4,8,1,7,6,3,2]=>[2,3,6,7,1,8,4,5]=>1001000=>0001001
[5,8,4,1,7,6,3,2]=>[2,3,6,7,1,4,8,5]=>1000100=>0010001
[7,5,4,1,8,6,3,2]=>[2,3,6,8,1,4,5,7]=>1000000=>0000001
[8,5,4,1,7,6,3,2]=>[2,3,6,7,1,4,5,8]=>1000000=>0000001
[1,8,2,5,6,3,4,7]=>[7,4,3,6,5,2,8,1]=>1111100=>0011111
[7,2,8,4,5,1,3,6]=>[6,3,1,5,4,8,2,7]=>1111000=>0001111
[1,3,7,5,6,2,4,8]=>[8,4,2,6,5,7,3,1]=>1111100=>0011111
[1,6,7,4,3,5,2,8]=>[8,2,5,3,4,7,6,1]=>1110010=>0100111
[1,8,2,5,3,6,7,4]=>[4,7,6,3,5,2,8,1]=>1110010=>0100111
[2,6,8,4,3,5,7,1]=>[1,7,5,3,4,8,6,2]=>0110110=>0110110
[7,2,8,4,1,5,6,3]=>[3,6,5,1,4,8,2,7]=>1100100=>0010011
[7,5,8,1,2,6,3,4]=>[4,3,6,2,1,8,5,7]=>1110100=>0010111
[1,5,2,6,4,7,8,3]=>[3,8,7,4,6,2,5,1]=>1101001=>1001011
[1,5,4,6,2,3,7,8]=>[8,7,3,2,6,4,5,1]=>1111001=>1001111
[6,2,5,7,1,4,8,3]=>[3,8,4,1,7,5,2,6]=>1101100=>0011011
[6,5,4,3,8,1,7,2]=>[2,7,1,8,3,4,5,6]=>1010000=>0000101
[2,6,5,8,3,4,1,7]=>[7,1,4,3,8,5,6,2]=>1110100=>0010111
[2,6,5,7,3,4,1,8]=>[8,1,4,3,7,5,6,2]=>1110100=>0010111
[6,2,5,7,4,1,3,8]=>[8,3,1,4,7,5,2,6]=>1110100=>0010111
[6,2,5,8,4,1,3,7]=>[7,3,1,4,8,5,2,6]=>1110100=>0010111
[2,7,8,4,6,1,3,5]=>[5,3,1,6,4,8,7,2]=>1111001=>1001111
[6,1,2,8,5,4,7,3]=>[3,7,4,5,8,2,1,6]=>1101000=>0001011
[6,2,5,7,8,1,3,4]=>[4,3,1,8,7,5,2,6]=>1110101=>1010111
[1,5,4,2,6,7,3,8]=>[8,3,7,6,2,4,5,1]=>1110010=>0100111
[2,6,5,7,3,8,1,4]=>[4,1,8,3,7,5,6,2]=>1110100=>0010111
[1,6,2,7,5,8,4,3]=>[3,4,8,5,7,2,6,1]=>1100100=>0010011
[1,3,2,7,8,5,6,4]=>[4,6,5,8,7,2,3,1]=>1100101=>1010011
[1,6,2,4,8,7,3,5]=>[5,3,7,8,4,2,6,1]=>1111000=>0001111
[6,5,2,1,8,7,3,4]=>[4,3,7,8,1,2,5,6]=>1010000=>0000101
[2,6,5,3,7,8,4,1]=>[1,4,8,7,3,5,6,2]=>0110001=>1000110
[6,5,2,3,8,7,1,4]=>[4,1,7,8,3,2,5,6]=>1110000=>0000111
[5,1,4,2,3,7,8,6]=>[6,8,7,3,2,4,1,5]=>1110001=>1000111
[1,5,4,2,6,3,8,7]=>[7,8,3,6,2,4,5,1]=>1110000=>0000111
[5,1,6,3,8,2,7,4]=>[4,7,2,8,3,6,1,5]=>1110000=>0000111
[6,5,8,7,4,3,1,2]=>[2,1,3,4,7,8,5,6]=>1000100=>0010001
[6,4,2,7,8,5,1,3]=>[3,1,5,8,7,2,4,6]=>1100001=>1000011
[6,1,4,8,7,5,2,3]=>[3,2,5,7,8,4,1,6]=>1101000=>0001011
[1,6,4,8,7,5,2,3]=>[3,2,5,7,8,4,6,1]=>1101000=>0001011
[1,8,6,2,4,7,3,5]=>[5,3,7,4,2,6,8,1]=>1111000=>0001111
[8,1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1,8]=>1111000=>0001111
[6,4,1,7,8,5,2,3]=>[3,2,5,8,7,1,4,6]=>1100001=>1000011
[7,6,1,2,4,8,3,5]=>[5,3,8,4,2,1,6,7]=>1111000=>0001111
[1,8,6,3,4,7,2,5]=>[5,2,7,4,3,6,8,1]=>1111000=>0001111
[1,7,2,5,4,8,3,6]=>[6,3,8,4,5,2,7,1]=>1111000=>0001111
[7,1,2,5,4,8,3,6]=>[6,3,8,4,5,2,1,7]=>1111000=>0001111
[2,7,1,5,4,8,3,6]=>[6,3,8,4,5,1,7,2]=>1111000=>0001111
[2,8,6,1,4,7,3,5]=>[5,3,7,4,1,6,8,2]=>1111000=>0001111
[7,2,1,5,4,8,3,6]=>[6,3,8,4,5,1,2,7]=>1011000=>0001101
[1,2,7,5,4,8,3,6]=>[6,3,8,4,5,7,2,1]=>1111000=>0001111
[3,2,7,5,4,8,1,6]=>[6,1,8,4,5,7,2,3]=>1101000=>0001011
[2,5,8,4,7,3,1,6]=>[6,1,3,7,4,8,5,2]=>1101100=>0011011
[2,3,7,5,4,8,1,6]=>[6,1,8,4,5,7,3,2]=>1111000=>0001111
[6,8,3,2,4,7,1,5]=>[5,1,7,4,2,3,8,6]=>1101010=>0101011
[3,7,2,5,4,8,1,6]=>[6,1,8,4,5,2,7,3]=>1111000=>0001111
[3,1,7,5,4,8,2,6]=>[6,2,8,4,5,7,1,3]=>1101000=>0001011
[1,3,7,5,4,8,2,6]=>[6,2,8,4,5,7,3,1]=>1111000=>0001111
[1,5,8,4,7,3,2,6]=>[6,2,3,7,4,8,5,1]=>1101100=>0011011
[5,1,8,4,7,3,2,6]=>[6,2,3,7,4,8,1,5]=>1101000=>0001011
[5,8,2,4,7,3,1,6]=>[6,1,3,7,4,2,8,5]=>1101100=>0011011
[6,8,4,3,7,5,1,2]=>[2,1,5,7,3,4,8,6]=>1010010=>0100101
[8,5,2,4,7,3,1,6]=>[6,1,3,7,4,2,5,8]=>1101000=>0001011
[8,1,5,4,7,3,2,6]=>[6,2,3,7,4,5,1,8]=>1101000=>0001011
[1,8,5,4,7,3,2,6]=>[6,2,3,7,4,5,8,1]=>1101000=>0001011
[1,7,3,5,4,8,2,6]=>[6,2,8,4,5,3,7,1]=>1111000=>0001111
[8,6,3,1,4,7,2,5]=>[5,2,7,4,1,3,6,8]=>1101000=>0001011
[8,6,4,1,7,2,5,3]=>[3,5,2,7,1,4,6,8]=>1100000=>0000011
[5,3,7,4,6,8,2,1]=>[1,2,8,6,4,7,3,5]=>0011010=>0101100
[4,1,3,2,7,8,5,6]=>[6,5,8,7,2,3,1,4]=>1100101=>1010011
[1,4,3,2,7,8,5,6]=>[6,5,8,7,2,3,4,1]=>1100101=>1010011
[2,4,3,1,7,8,5,6]=>[6,5,8,7,1,3,4,2]=>1100101=>1010011
[2,7,3,5,4,8,1,6]=>[6,1,8,4,5,3,7,2]=>1111000=>0001111
[2,8,5,4,7,3,1,6]=>[6,1,3,7,4,5,8,2]=>1101000=>0001011
[5,7,3,4,6,8,2,1]=>[1,2,8,6,4,3,7,5]=>0011110=>0111100
[8,2,5,4,7,3,1,6]=>[6,1,3,7,4,5,2,8]=>1101000=>0001011
[7,2,3,5,4,8,1,6]=>[6,1,8,4,5,3,2,7]=>1111000=>0001111
[3,2,1,4,7,8,5,6]=>[6,5,8,7,4,1,2,3]=>1001101=>1011001
[8,1,7,6,4,3,5,2]=>[2,5,3,4,6,7,1,8]=>1010000=>0000101
[8,6,4,5,2,7,1,3]=>[3,1,7,2,5,4,6,8]=>1101000=>0001011
[7,1,8,6,4,3,5,2]=>[2,5,3,4,6,8,1,7]=>1010000=>0000101
[7,4,2,5,1,6,3,8]=>[8,3,6,1,5,2,4,7]=>1110000=>0000111
[7,3,6,5,2,1,4,8]=>[8,4,1,2,5,6,3,7]=>1011000=>0001101
[8,3,6,5,2,1,7,4]=>[4,7,1,2,5,6,3,8]=>1010000=>0000101
[7,3,6,5,2,1,8,4]=>[4,8,1,2,5,6,3,7]=>1010000=>0000101
[5,4,2,8,1,3,7,6]=>[6,7,3,1,8,2,4,5]=>1110000=>0000111
[5,8,2,6,4,1,3,7]=>[7,3,1,4,6,2,8,5]=>1110100=>0010111
[6,4,2,5,1,8,3,7]=>[7,3,8,1,5,2,4,6]=>1110000=>0000111
[6,3,5,2,1,4,7,8]=>[8,7,4,1,2,5,3,6]=>1011001=>1001101
[2,3,5,8,1,4,7,6]=>[6,7,4,1,8,5,3,2]=>1111100=>0011111
[2,3,6,8,1,5,7,4]=>[4,7,5,1,8,6,3,2]=>1110110=>0110111
[6,3,8,5,2,7,1,4]=>[4,1,7,2,5,8,3,6]=>1110000=>0000111
[6,3,7,5,2,1,4,8]=>[8,4,1,2,5,7,3,6]=>1011000=>0001101
[2,5,7,6,3,1,4,8]=>[8,4,1,3,6,7,5,2]=>1101100=>0011011
[2,8,7,6,3,1,5,4]=>[4,5,1,3,6,7,8,2]=>1100000=>0000011
[2,5,8,7,6,3,1,4]=>[4,1,3,6,7,8,5,2]=>1100100=>0010011
[2,4,8,1,6,5,7,3]=>[3,7,5,6,1,8,4,2]=>1101100=>0011011
[2,8,7,3,6,1,4,5]=>[5,4,1,6,3,7,8,2]=>1111000=>0001111
[8,4,2,5,1,3,7,6]=>[6,7,3,1,5,2,4,8]=>1110000=>0000111
[2,3,6,8,1,4,7,5]=>[5,7,4,1,8,6,3,2]=>1111010=>0101111
[2,7,8,6,3,1,4,5]=>[5,4,1,3,6,8,7,2]=>1101001=>1001011
[2,8,6,3,1,4,5,7]=>[7,5,4,1,3,6,8,2]=>1101100=>0011011
[8,3,5,2,1,4,6,7]=>[7,6,4,1,2,5,3,8]=>1011010=>0101101
[2,5,8,1,7,3,6,4]=>[4,6,3,7,1,8,5,2]=>1110100=>0010111
[2,8,1,5,7,3,6,4]=>[4,6,3,7,5,1,8,2]=>1110100=>0010111
[8,3,6,1,4,7,5,2]=>[2,5,7,4,1,6,3,8]=>1011000=>0001101
[2,6,8,1,5,7,3,4]=>[4,3,7,5,1,8,6,2]=>1110110=>0110111
[2,7,1,5,8,3,4,6]=>[6,4,3,8,5,1,7,2]=>1111100=>0011111
[2,7,1,6,3,8,4,5]=>[5,4,8,3,6,1,7,2]=>1111000=>0001111
[4,7,6,1,8,5,2,3]=>[3,2,5,8,1,6,7,4]=>1101000=>0001011
[7,3,6,1,2,8,4,5]=>[5,4,8,2,1,6,3,7]=>1111000=>0001111
[7,4,8,1,6,5,2,3]=>[3,2,5,6,1,8,4,7]=>1101000=>0001011
[7,4,6,1,8,2,5,3]=>[3,5,2,8,1,6,4,7]=>1101000=>0001011
[4,6,8,5,1,7,2,3]=>[3,2,7,1,5,8,6,4]=>1101010=>0101011
[5,1,7,6,2,3,8,4]=>[4,8,3,2,6,7,1,5]=>1110000=>0000111
[5,1,7,6,2,8,3,4]=>[4,3,8,2,6,7,1,5]=>1110000=>0000111
[5,1,8,7,6,2,3,4]=>[4,3,2,6,7,8,1,5]=>1110000=>0000111
[8,5,1,7,6,2,3,4]=>[4,3,2,6,7,1,5,8]=>1110000=>0000111
[8,5,1,6,2,7,3,4]=>[4,3,7,2,6,1,5,8]=>1110000=>0000111
[3,6,1,8,4,7,5,2]=>[2,5,7,4,8,1,6,3]=>1011000=>0001101
[4,6,1,8,7,5,2,3]=>[3,2,5,7,8,1,6,4]=>1101000=>0001011
[8,4,6,1,7,5,2,3]=>[3,2,5,7,1,6,4,8]=>1101000=>0001011
[4,8,5,1,7,2,3,6]=>[6,3,2,7,1,5,8,4]=>1111000=>0001111
[3,4,8,7,1,2,5,6]=>[6,5,2,1,7,8,4,3]=>1111100=>0011111
[5,8,4,1,7,2,3,6]=>[6,3,2,7,1,4,8,5]=>1110100=>0010111
[8,6,4,7,1,2,5,3]=>[3,5,2,1,7,4,6,8]=>1101000=>0001011
[6,4,8,7,1,2,5,3]=>[3,5,2,1,7,8,4,6]=>1101000=>0001011
[5,6,8,3,7,1,4,2]=>[2,4,1,7,3,8,6,5]=>1010110=>0110101
[6,5,1,8,2,7,3,4]=>[4,3,7,2,8,1,5,6]=>1110000=>0000111
[8,6,5,1,2,7,3,4]=>[4,3,7,2,1,5,6,8]=>1110000=>0000111
[8,6,5,1,7,2,3,4]=>[4,3,2,7,1,5,6,8]=>1110000=>0000111
[6,5,1,8,7,2,3,4]=>[4,3,2,7,8,1,5,6]=>1110000=>0000111
[6,5,1,7,2,8,3,4]=>[4,3,8,2,7,1,5,6]=>1110000=>0000111
[6,5,1,7,2,3,8,4]=>[4,8,3,2,7,1,5,6]=>1110000=>0000111
[5,7,4,1,8,2,3,6]=>[6,3,2,8,1,4,7,5]=>1110100=>0010111
[5,6,8,7,4,1,2,3]=>[3,2,1,4,7,8,6,5]=>1100110=>0110011
[6,8,5,7,4,1,2,3]=>[3,2,1,4,7,5,8,6]=>1100110=>0110011
[6,8,3,1,5,2,4,7]=>[7,4,2,5,1,3,8,6]=>1101010=>0101011
[4,2,7,1,6,3,5,8]=>[8,5,3,6,1,7,2,4]=>1110100=>0010111
[5,1,7,4,2,6,3,8]=>[8,3,6,2,4,7,1,5]=>1110000=>0000111
[6,8,4,2,1,5,3,7]=>[7,3,5,1,2,4,8,6]=>1010010=>0100101
[5,8,2,1,4,7,3,6]=>[6,3,7,4,1,2,8,5]=>1011100=>0011101
[6,8,4,3,1,5,7,2]=>[2,7,5,1,3,4,8,6]=>1000110=>0110001
[6,8,4,2,1,5,7,3]=>[3,7,5,1,2,4,8,6]=>1000110=>0110001
[6,8,3,2,1,4,5,7]=>[7,5,4,1,2,3,8,6]=>1001110=>0111001
[5,4,7,2,1,6,8,3]=>[3,8,6,1,2,7,4,5]=>1001010=>0101001
[5,2,1,7,3,4,8,6]=>[6,8,4,3,7,1,2,5]=>1011000=>0001101
[6,4,3,1,7,5,8,2]=>[2,8,5,7,1,3,4,6]=>1000100=>0010001
[3,2,1,7,6,4,8,5]=>[5,8,4,6,7,1,2,3]=>1001000=>0001001
[4,2,1,6,5,8,3,7]=>[7,3,8,5,6,1,2,4]=>1010100=>0010101
[4,2,1,8,5,7,3,6]=>[6,3,7,5,8,1,2,4]=>1010100=>0010101
[7,4,3,1,8,5,6,2]=>[2,6,5,8,1,3,4,7]=>1000100=>0010001
[6,3,2,1,7,4,5,8]=>[8,5,4,7,1,2,3,6]=>1001100=>0011001
[6,4,2,1,7,5,3,8]=>[8,3,5,7,1,2,4,6]=>1010000=>0000101
[6,1,8,4,2,7,3,5]=>[5,3,7,2,4,8,1,6]=>1110000=>0000111
[6,2,1,8,3,7,4,5]=>[5,4,7,3,8,1,2,6]=>1011000=>0001101
[5,2,1,7,3,6,4,8]=>[8,4,6,3,7,1,2,5]=>1011000=>0001101
[5,3,2,7,6,1,4,8]=>[8,4,1,6,7,2,3,5]=>1101000=>0001011
[5,3,2,8,6,1,4,7]=>[7,4,1,6,8,2,3,5]=>1101000=>0001011
[6,3,2,8,7,1,4,5]=>[5,4,1,7,8,2,3,6]=>1101000=>0001011
[4,2,8,1,7,3,5,6]=>[6,5,3,7,1,8,2,4]=>1110100=>0010111
[4,3,8,7,2,1,5,6]=>[6,5,1,2,7,8,3,4]=>1010100=>0010101
[2,1,5,8,4,7,3,6]=>[6,3,7,4,8,5,1,2]=>1011100=>0011101
[4,3,2,5,8,1,6,7]=>[7,6,1,8,5,2,3,4]=>1100110=>0110011
[4,3,2,5,7,1,6,8]=>[8,6,1,7,5,2,3,4]=>1100110=>0110011
[4,3,1,6,2,7,5,8]=>[8,5,7,2,6,1,3,4]=>1100100=>0010011
[4,3,1,7,2,8,5,6]=>[6,5,8,2,7,1,3,4]=>1100100=>0010011
[5,4,1,7,2,8,6,3]=>[3,6,8,2,7,1,4,5]=>1100000=>0000011
[6,5,3,1,7,8,4,2]=>[2,4,8,7,1,3,5,6]=>1000001=>1000001
[6,4,2,1,7,8,3,5]=>[5,3,8,7,1,2,4,6]=>1010001=>1000101
[5,4,2,1,6,7,3,8]=>[8,3,7,6,1,2,4,5]=>1010010=>0100101
[5,3,2,1,6,7,4,8]=>[8,4,7,6,1,2,3,5]=>1001010=>0101001
[6,4,2,1,7,8,5,3]=>[3,5,8,7,1,2,4,6]=>1000001=>1000001
[5,3,2,6,8,1,7,4]=>[4,7,1,8,6,2,3,5]=>1100010=>0100011
[3,2,1,4,8,7,5,6]=>[6,5,7,8,4,1,2,3]=>1001100=>0011001
[3,2,1,4,6,8,5,7]=>[7,5,8,6,4,1,2,3]=>1001110=>0111001
[4,3,2,6,1,7,8,5]=>[5,8,7,1,6,2,3,4]=>1100001=>1000011
[5,3,2,1,6,7,8,4]=>[4,8,7,6,1,2,3,5]=>1000011=>1100001
[8,6,1,4,5,7,2,3]=>[3,2,7,5,4,1,6,8]=>1101100=>0011011
[3,8,6,4,5,7,1,2]=>[2,1,7,5,4,6,8,3]=>1011100=>0011101
[5,2,8,3,7,4,6,1]=>[1,6,4,7,3,8,2,5]=>0111000=>0001110
[6,2,8,5,4,7,3,1]=>[1,3,7,4,5,8,2,6]=>0101000=>0001010
[5,2,8,4,3,6,7,1]=>[1,7,6,3,4,8,2,5]=>0110010=>0100110
[5,4,2,7,3,6,1,8]=>[8,1,6,3,7,2,4,5]=>1110000=>0000111
[5,4,2,8,3,6,1,7]=>[7,1,6,3,8,2,4,5]=>1110000=>0000111
[6,5,3,8,4,7,2,1]=>[1,2,7,4,8,3,5,6]=>0011000=>0001100
[5,2,8,4,3,7,1,6]=>[6,1,7,3,4,8,2,5]=>1110000=>0000111
[6,2,8,3,7,4,1,5]=>[5,1,4,7,3,8,2,6]=>1110000=>0000111
[5,4,2,7,3,1,8,6]=>[6,8,1,3,7,2,4,5]=>1100000=>0000011
[6,4,3,7,1,2,8,5]=>[5,8,2,1,7,3,4,6]=>1110000=>0000111
[6,4,3,8,1,2,7,5]=>[5,7,2,1,8,3,4,6]=>1110000=>0000111
[7,2,8,4,3,1,5,6]=>[6,5,1,3,4,8,2,7]=>1100100=>0010011
[7,5,3,8,4,2,6,1]=>[1,6,2,4,8,3,5,7]=>0110000=>0000110
[6,4,2,7,3,1,5,8]=>[8,5,1,3,7,2,4,6]=>1100100=>0010011
[7,6,4,8,2,3,5,1]=>[1,5,3,2,8,4,6,7]=>0111000=>0001110
[5,3,1,7,8,4,6,2]=>[2,6,4,8,7,1,3,5]=>1001001=>1001001
[5,3,2,7,8,4,6,1]=>[1,6,4,8,7,2,3,5]=>0101001=>1001010
[6,5,1,7,8,2,3,4]=>[4,3,2,8,7,1,5,6]=>1110001=>1000111
[6,3,1,7,8,4,2,5]=>[5,2,4,8,7,1,3,6]=>1100001=>1000011
[6,3,2,7,8,4,1,5]=>[5,1,4,8,7,2,3,6]=>1100001=>1000011
[8,7,6,1,3,5,2,4]=>[4,2,5,3,1,6,7,8]=>1110000=>0000111
[7,4,6,1,3,2,8,5]=>[5,8,2,3,1,6,4,7]=>1101000=>0001011
[2,7,6,1,3,4,8,5]=>[5,8,4,3,1,6,7,2]=>1111000=>0001111
[5,7,2,1,6,3,8,4]=>[4,8,3,6,1,2,7,5]=>1010100=>0010101
[4,7,2,5,6,3,8,1]=>[1,8,3,6,5,2,7,4]=>0111100=>0011110
[2,7,4,5,3,8,1,6]=>[6,1,8,3,5,4,7,2]=>1111000=>0001111
[6,8,7,1,3,2,5,4]=>[4,5,2,3,1,7,8,6]=>1100010=>0100011
[2,8,6,5,7,1,4,3]=>[3,4,1,7,5,6,8,2]=>1100100=>0010011
[3,1,2,6,8,4,7,5]=>[5,7,4,8,6,2,1,3]=>1101010=>0101011
[5,1,3,2,7,8,4,6]=>[6,4,8,7,2,3,1,5]=>1101001=>1001011
[5,6,8,4,3,2,7,1]=>[1,7,2,3,4,8,6,5]=>0100110=>0110010
[5,3,8,1,7,2,4,6]=>[6,4,2,7,1,8,3,5]=>1111000=>0001111
[3,6,7,8,4,2,1,5]=>[5,1,2,4,8,7,6,3]=>1010011=>1100101
[2,8,1,6,3,4,7,5]=>[5,7,4,3,6,1,8,2]=>1111000=>0001111
[3,6,1,2,5,8,4,7]=>[7,4,8,5,2,1,6,3]=>1111100=>0011111
[2,6,5,1,4,8,3,7]=>[7,3,8,4,1,5,6,2]=>1111000=>0001111
[2,5,1,8,4,7,3,6]=>[6,3,7,4,8,1,5,2]=>1111000=>0001111
[8,2,1,5,7,3,4,6]=>[6,4,3,7,5,1,2,8]=>1011100=>0011101
[2,5,4,8,1,3,7,6]=>[6,7,3,1,8,4,5,2]=>1111000=>0001111
[1,7,3,5,8,2,6,4]=>[4,6,2,8,5,3,7,1]=>1110100=>0010111
[3,1,6,8,7,2,4,5]=>[5,4,2,7,8,6,1,3]=>1101010=>0101011
[4,1,7,2,6,8,3,5]=>[5,3,8,6,2,7,1,4]=>1110010=>0100111
[8,1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1,8]=>1101010=>0101011
[7,3,1,2,4,6,8,5]=>[5,8,6,4,2,1,3,7]=>1101010=>0101011
[1,8,3,4,7,2,5,6]=>[6,5,2,7,4,3,8,1]=>1111100=>0011111
[4,1,3,8,7,2,6,5]=>[5,6,2,7,8,3,1,4]=>1110000=>0000111
[1,8,3,2,7,5,6,4]=>[4,6,5,7,2,3,8,1]=>1100100=>0010011
[3,7,2,8,6,1,5,4]=>[4,5,1,6,8,2,7,3]=>1110000=>0000111
[5,1,7,8,4,2,6,3]=>[3,6,2,4,8,7,1,5]=>1100001=>1000011
[5,1,8,7,4,2,6,3]=>[3,6,2,4,7,8,1,5]=>1100000=>0000011
[4,7,2,8,3,6,5,1]=>[1,5,6,3,8,2,7,4]=>0111000=>0001110
[4,1,7,8,5,3,6,2]=>[2,6,3,5,8,7,1,4]=>1010001=>1000101
[5,1,7,4,8,3,6,2]=>[2,6,3,8,4,7,1,5]=>1011000=>0001101
[4,1,8,7,5,3,6,2]=>[2,6,3,5,7,8,1,4]=>1010000=>0000101
[4,8,2,7,3,6,5,1]=>[1,5,6,3,7,2,8,4]=>0111000=>0001110
[4,7,2,6,3,5,8,1]=>[1,8,5,3,6,2,7,4]=>0111100=>0011110
[6,8,2,4,3,7,5,1]=>[1,5,7,3,4,2,8,6]=>0110010=>0100110
[6,7,2,4,3,8,5,1]=>[1,5,8,3,4,2,7,6]=>0110010=>0100110
[3,8,7,2,4,1,5,6]=>[6,5,1,4,2,7,8,3]=>1110100=>0010111
[3,7,8,2,4,1,5,6]=>[6,5,1,4,2,8,7,3]=>1110101=>1010111
[3,6,8,2,4,5,7,1]=>[1,7,5,4,2,8,6,3]=>0111110=>0111110
[3,6,7,2,4,5,8,1]=>[1,8,5,4,2,7,6,3]=>0111110=>0111110
[1,7,5,3,8,2,4,6]=>[6,4,2,8,3,5,7,1]=>1111000=>0001111
[1,7,2,4,5,8,3,6]=>[6,3,8,5,4,2,7,1]=>1111100=>0011111
[1,7,4,5,8,3,2,6]=>[6,2,3,8,5,4,7,1]=>1101100=>0011011
[2,6,4,7,8,3,5,1]=>[1,5,3,8,7,4,6,2]=>0111001=>1001110
[1,2,6,4,7,8,3,5]=>[5,3,8,7,4,6,2,1]=>1111001=>1001111
[2,7,4,5,8,1,3,6]=>[6,3,1,8,5,4,7,2]=>1111100=>0011111
[2,7,5,3,1,8,4,6]=>[6,4,8,1,3,5,7,2]=>1101000=>0001011
[6,1,4,7,8,3,5,2]=>[2,5,3,8,7,4,1,6]=>1011001=>1001101
[3,6,4,7,8,1,5,2]=>[2,5,1,8,7,4,6,3]=>1011001=>1001101
[4,3,6,7,1,8,5,2]=>[2,5,8,1,7,6,3,4]=>1010010=>0100101
[4,3,6,7,1,8,2,5]=>[5,2,8,1,7,6,3,4]=>1110010=>0100111
[3,7,4,5,2,1,8,6]=>[6,8,1,2,5,4,7,3]=>1011000=>0001101
[1,3,6,4,7,2,8,5]=>[5,8,2,7,4,6,3,1]=>1111000=>0001111
[3,6,4,7,2,8,5,1]=>[1,5,8,2,7,4,6,3]=>0111000=>0001110
[6,1,7,3,8,2,5,4]=>[4,5,2,8,3,7,1,6]=>1110000=>0000111
[1,6,7,3,8,2,5,4]=>[4,5,2,8,3,7,6,1]=>1110010=>0100111
[6,1,4,7,8,5,2,3]=>[3,2,5,8,7,4,1,6]=>1101001=>1001011
[6,3,2,1,7,8,5,4]=>[4,5,8,7,1,2,3,6]=>1000001=>1000001
[6,2,7,3,1,8,5,4]=>[4,5,8,1,3,7,2,6]=>1100000=>0000011
[6,2,4,7,8,1,5,3]=>[3,5,1,8,7,4,2,6]=>1101001=>1001011
[2,6,7,3,1,8,5,4]=>[4,5,8,1,3,7,6,2]=>1100010=>0100011
[6,4,7,8,3,2,5,1]=>[1,5,2,3,8,7,4,6]=>0101001=>1001010
[8,3,6,4,5,2,1,7]=>[7,1,2,5,4,6,3,8]=>1011000=>0001101
[6,8,5,7,4,2,3,1]=>[1,3,2,4,7,5,8,6]=>0100110=>0110010
[2,3,8,7,1,6,4,5]=>[5,4,6,1,7,8,3,2]=>1111000=>0001111
[4,3,7,8,1,6,2,5]=>[5,2,6,1,8,7,3,4]=>1110001=>1000111
[6,8,1,2,7,4,5,3]=>[3,5,4,7,2,1,8,6]=>1101010=>0101011
[6,4,8,7,5,1,2,3]=>[3,2,1,5,7,8,4,6]=>1101000=>0001011
[5,7,1,8,4,6,2,3]=>[3,2,6,4,8,1,7,5]=>1101100=>0011011
[6,3,8,7,2,1,4,5]=>[5,4,1,2,7,8,3,6]=>1011000=>0001101
[2,3,7,8,5,6,1,4]=>[4,1,6,5,8,7,3,2]=>1110101=>1010111
[3,7,6,8,5,1,2,4]=>[4,2,1,5,8,6,7,3]=>1110010=>0100111
[2,4,7,8,1,6,3,5]=>[5,3,6,1,8,7,4,2]=>1111001=>1001111
[5,4,7,8,2,6,3,1]=>[1,3,6,2,8,7,4,5]=>0101001=>1001010
[2,8,3,4,1,5,7,6]=>[6,7,5,1,4,3,8,2]=>1110100=>0010111
[6,8,3,4,1,2,7,5]=>[5,7,2,1,4,3,8,6]=>1110010=>0100111
[4,5,3,2,8,6,7,1]=>[1,7,6,8,2,3,5,4]=>0101010=>0101010
[3,5,8,6,1,4,7,2]=>[2,7,4,1,6,8,5,3]=>1011100=>0011101
[7,6,4,8,5,2,1,3]=>[3,1,2,5,8,4,6,7]=>1001000=>0001001
[3,4,8,7,5,6,2,1]=>[1,2,6,5,7,8,4,3]=>0011100=>0011100
[7,5,3,2,8,6,1,4]=>[4,1,6,8,2,3,5,7]=>1100000=>0000011
[2,5,1,3,8,6,7,4]=>[4,7,6,8,3,1,5,2]=>1110010=>0100111
[4,5,1,2,8,6,7,3]=>[3,7,6,8,2,1,5,4]=>1101010=>0101011
[8,3,5,4,1,6,7,2]=>[2,7,6,1,4,5,3,8]=>1010010=>0100101
[5,1,6,4,3,2,8,7]=>[7,8,2,3,4,6,1,5]=>1100000=>0000011
[8,3,7,1,4,6,5,2]=>[2,5,6,4,1,7,3,8]=>1011000=>0001101
[1,6,4,8,3,2,5,7]=>[7,5,2,3,8,4,6,1]=>1101100=>0011011
[6,1,4,8,2,3,5,7]=>[7,5,3,2,8,4,1,6]=>1111100=>0011111
[5,7,4,1,2,3,8,6]=>[6,8,3,2,1,4,7,5]=>1110100=>0010111
[6,4,3,8,5,7,1,2]=>[2,1,7,5,8,3,4,6]=>1010100=>0010101
[7,2,5,3,4,1,6,8]=>[8,6,1,4,3,5,2,7]=>1110010=>0100111
[2,7,4,3,1,5,6,8]=>[8,6,5,1,3,4,7,2]=>1100110=>0110011
[2,1,7,4,8,3,5,6]=>[6,5,3,8,4,7,1,2]=>1011100=>0011101
[4,8,1,3,5,7,2,6]=>[6,2,7,5,3,1,8,4]=>1111100=>0011111
[8,3,1,7,2,4,5,6]=>[6,5,4,2,7,1,3,8]=>1101100=>0011011
[3,1,8,5,4,7,6,2]=>[2,6,7,4,5,8,1,3]=>1001000=>0001001
[4,5,2,8,1,7,6,3]=>[3,6,7,1,8,2,5,4]=>1101000=>0001011
[4,6,2,8,7,1,5,3]=>[3,5,1,7,8,2,6,4]=>1101000=>0001011
[4,6,8,2,7,5,1,3]=>[3,1,5,7,2,8,6,4]=>1101010=>0101011
[5,6,7,2,1,3,8,4]=>[4,8,3,1,2,7,6,5]=>1010110=>0110101
[4,1,6,8,7,3,5,2]=>[2,5,3,7,8,6,1,4]=>1010010=>0100101
[5,6,1,7,8,4,2,3]=>[3,2,4,8,7,1,6,5]=>1100101=>1010011
[4,6,8,1,7,5,2,3]=>[3,2,5,7,1,8,6,4]=>1101010=>0101011
[5,6,7,1,3,8,2,4]=>[4,2,8,3,1,7,6,5]=>1110110=>0110111
[5,6,7,3,1,2,8,4]=>[4,8,2,1,3,7,6,5]=>1100110=>0110011
[7,8,1,3,5,6,2,4]=>[4,2,6,5,3,1,8,7]=>1110101=>1010111
[7,8,3,1,5,6,2,4]=>[4,2,6,5,1,3,8,7]=>1100101=>1010011
[7,1,3,8,5,6,2,4]=>[4,2,6,5,8,3,1,7]=>1110100=>0010111
[5,1,7,8,3,4,6,2]=>[2,6,4,3,8,7,1,5]=>1011001=>1001101
[1,5,7,8,3,4,6,2]=>[2,6,4,3,8,7,5,1]=>1011101=>1011101
[3,7,1,5,8,6,2,4]=>[4,2,6,8,5,1,7,3]=>1110100=>0010111
[1,3,7,8,2,5,6,4]=>[4,6,5,2,8,7,3,1]=>1110101=>1010111
[3,1,7,8,5,2,6,4]=>[4,6,2,5,8,7,1,3]=>1100001=>1000011
[1,3,7,5,8,2,6,4]=>[4,6,2,8,5,7,3,1]=>1110100=>0010111
[3,1,7,5,8,2,6,4]=>[4,6,2,8,5,7,1,3]=>1100100=>0010011
[3,5,7,1,8,4,6,2]=>[2,6,4,8,1,7,5,3]=>1011100=>0011101
[3,5,7,8,1,4,6,2]=>[2,6,4,1,8,7,5,3]=>1011101=>1011101
[5,3,7,8,4,6,1,2]=>[2,1,6,4,8,7,3,5]=>1011001=>1001101
[5,3,7,8,4,1,6,2]=>[2,6,1,4,8,7,3,5]=>1010001=>1000101
[5,3,7,8,1,4,6,2]=>[2,6,4,1,8,7,3,5]=>1011001=>1001101
[5,3,7,1,8,4,6,2]=>[2,6,4,8,1,7,3,5]=>1011000=>0001101
[1,5,3,7,8,4,2,6]=>[6,2,4,8,7,3,5,1]=>1110001=>1000111
[5,1,3,7,8,4,2,6]=>[6,2,4,8,7,3,1,5]=>1110001=>1000111
[3,6,2,1,4,5,8,7]=>[7,8,5,4,1,2,6,3]=>1011100=>0011101
[6,4,2,5,1,3,8,7]=>[7,8,3,1,5,2,4,6]=>1110000=>0000111
[6,8,2,7,3,1,4,5]=>[5,4,1,3,7,2,8,6]=>1101010=>0101011
[5,2,8,1,7,3,4,6]=>[6,4,3,7,1,8,2,5]=>1111000=>0001111
[4,2,3,8,1,5,6,7]=>[7,6,5,1,8,3,2,4]=>1110110=>0110111
[2,1,5,8,4,3,6,7]=>[7,6,3,4,8,5,1,2]=>1010110=>0110101
[5,8,3,2,7,1,4,6]=>[6,4,1,7,2,3,8,5]=>1101100=>0011011
[5,1,8,3,7,2,4,6]=>[6,4,2,7,3,8,1,5]=>1111000=>0001111
[5,1,8,4,6,2,3,7]=>[7,3,2,6,4,8,1,5]=>1111000=>0001111
[5,8,4,1,6,2,3,7]=>[7,3,2,6,1,4,8,5]=>1110100=>0010111
[2,1,5,4,8,3,6,7]=>[7,6,3,8,4,5,1,2]=>1011010=>0101101
[2,4,3,8,1,5,6,7]=>[7,6,5,1,8,3,4,2]=>1110110=>0110111
[3,1,8,4,2,5,6,7]=>[7,6,5,2,4,8,1,3]=>1100110=>0110011
[3,8,4,2,1,5,6,7]=>[7,6,5,1,2,4,8,3]=>1010110=>0110101
[2,3,8,4,1,5,6,7]=>[7,6,5,1,4,8,3,2]=>1110110=>0110111
[3,4,2,8,1,5,6,7]=>[7,6,5,1,8,2,4,3]=>1110110=>0110111
[2,1,4,8,5,3,6,7]=>[7,6,3,5,8,4,1,2]=>1011010=>0101101
[3,2,8,4,1,5,6,7]=>[7,6,5,1,4,8,2,3]=>1100110=>0110011
[2,8,4,3,1,5,6,7]=>[7,6,5,1,3,4,8,2]=>1100110=>0110011
[4,1,7,5,6,2,8,3]=>[3,8,2,6,5,7,1,4]=>1100100=>0010011
[5,7,4,3,8,1,6,2]=>[2,6,1,8,3,4,7,5]=>1010100=>0010101
[3,8,4,2,6,7,5,1]=>[1,5,7,6,2,4,8,3]=>0110010=>0100110
[3,8,4,1,6,7,5,2]=>[2,5,7,6,1,4,8,3]=>1010010=>0100101
[2,6,7,5,3,8,4,1]=>[1,4,8,3,5,7,6,2]=>0110010=>0100110
[2,1,6,7,5,3,8,4]=>[4,8,3,5,7,6,1,2]=>1010010=>0100101
[3,8,4,2,1,6,7,5]=>[5,7,6,1,2,4,8,3]=>1010010=>0100101
[6,1,3,4,8,2,5,7]=>[7,5,2,8,4,3,1,6]=>1111100=>0011111
[6,2,3,4,8,1,5,7]=>[7,5,1,8,4,3,2,6]=>1111100=>0011111
[6,7,5,8,3,1,4,2]=>[2,4,1,3,8,5,7,6]=>1000110=>0110001
[2,5,7,6,1,4,8,3]=>[3,8,4,1,6,7,5,2]=>1101100=>0011011
[6,7,4,8,2,3,5,1]=>[1,5,3,2,8,4,7,6]=>0111010=>0101110
[6,3,1,4,8,2,5,7]=>[7,5,2,8,4,1,3,6]=>1101100=>0011011
[6,7,4,8,2,1,3,5]=>[5,3,1,2,8,4,7,6]=>1011010=>0101101
[6,7,4,8,1,2,3,5]=>[5,3,2,1,8,4,7,6]=>1111010=>0101111
[7,8,3,2,6,1,4,5]=>[5,4,1,6,2,3,8,7]=>1101001=>1001011
[3,4,8,2,6,1,7,5]=>[5,7,1,6,2,8,4,3]=>1111000=>0001111
[7,8,4,1,5,6,3,2]=>[2,3,6,5,1,4,8,7]=>1000101=>1010001
[7,8,1,2,6,3,4,5]=>[5,4,3,6,2,1,8,7]=>1111001=>1001111
[7,8,5,1,4,6,3,2]=>[2,3,6,4,1,5,8,7]=>1001001=>1001001
[5,3,8,4,1,6,7,2]=>[2,7,6,1,4,8,3,5]=>1010010=>0100101
[6,2,4,8,1,5,3,7]=>[7,3,5,1,8,4,2,6]=>1111000=>0001111
[3,4,8,5,1,6,7,2]=>[2,7,6,1,5,8,4,3]=>1011010=>0101101
[5,3,8,1,4,6,7,2]=>[2,7,6,4,1,8,3,5]=>1011010=>0101101
[4,2,6,8,1,5,3,7]=>[7,3,5,1,8,6,2,4]=>1110010=>0100111
[7,4,2,8,1,5,3,6]=>[6,3,5,1,8,2,4,7]=>1110000=>0000111
[6,1,7,5,8,4,3,2]=>[2,3,4,8,5,7,1,6]=>1000100=>0010001
[1,2,7,8,5,3,4,6]=>[6,4,3,5,8,7,2,1]=>1111001=>1001111
[6,3,7,8,5,4,1,2]=>[2,1,4,5,8,7,3,6]=>1010001=>1000101
[6,1,5,7,8,4,3,2]=>[2,3,4,8,7,5,1,6]=>1000101=>1010001
[1,7,5,6,8,4,3,2]=>[2,3,4,8,6,5,7,1]=>1000110=>0110001
[3,1,8,4,5,6,7,2]=>[2,7,6,5,4,8,1,3]=>1001110=>0111001
[4,2,1,8,6,5,3,7]=>[7,3,5,6,8,1,2,4]=>1010000=>0000101
[3,2,7,8,5,1,4,6]=>[6,4,1,5,8,7,2,3]=>1101001=>1001011
[2,3,7,8,5,1,4,6]=>[6,4,1,5,8,7,3,2]=>1111001=>1001111
[2,7,3,8,5,1,4,6]=>[6,4,1,5,8,3,7,2]=>1111000=>0001111
[3,6,2,8,5,1,4,7]=>[7,4,1,5,8,2,6,3]=>1111000=>0001111
[1,4,2,8,7,5,3,6]=>[6,3,5,7,8,2,4,1]=>1110000=>0000111
[7,3,6,8,5,4,1,2]=>[2,1,4,5,8,6,3,7]=>1010010=>0100101
[7,2,1,8,5,3,4,6]=>[6,4,3,5,8,1,2,7]=>1011000=>0001101
[1,2,6,8,4,5,3,7]=>[7,3,5,4,8,6,2,1]=>1111010=>0101111
[7,1,6,5,8,4,3,2]=>[2,3,4,8,5,6,1,7]=>1000100=>0010001
[6,5,7,1,8,4,3,2]=>[2,3,4,8,1,7,5,6]=>1000100=>0010001
[5,7,6,1,8,4,3,2]=>[2,3,4,8,1,6,7,5]=>1000100=>0010001
[6,7,1,5,8,4,3,2]=>[2,3,4,8,5,1,7,6]=>1000110=>0110001
[7,1,2,8,4,5,3,6]=>[6,3,5,4,8,2,1,7]=>1111000=>0001111
[7,6,1,5,8,4,3,2]=>[2,3,4,8,5,1,6,7]=>1000100=>0010001
[7,5,6,1,8,4,3,2]=>[2,3,4,8,1,6,5,7]=>1000100=>0010001
[6,5,4,3,2,1,7,8,9,10,11,12]=>[12,11,10,9,8,7,1,2,3,4,5,6]=>10000011111=>11111000001
[1,8,7,4,2,5,3,6]=>[6,3,5,2,4,7,8,1]=>1110000=>0000111
[8,7,4,2,5,3,6,1]=>[1,6,3,5,2,4,7,8]=>0110000=>0000110
[5,3,6,4,2,7,1,8]=>[8,1,7,2,4,6,3,5]=>1110000=>0000111
[7,4,2,8,6,3,5,1]=>[1,5,3,6,8,2,4,7]=>0110000=>0000110
[5,3,6,1,8,7,4,2]=>[2,4,7,8,1,6,3,5]=>1010000=>0000101
[6,1,5,3,8,7,4,2]=>[2,4,7,8,3,5,1,6]=>1010000=>0000101
[2,8,6,4,7,5,1,3]=>[3,1,5,7,4,6,8,2]=>1101000=>0001011
[5,1,8,6,3,7,4,2]=>[2,4,7,3,6,8,1,5]=>1010000=>0000101
[8,6,3,2,4,7,5,1]=>[1,5,7,4,2,3,6,8]=>0101000=>0001010
[7,5,1,8,6,3,2,4]=>[4,2,3,6,8,1,5,7]=>1100000=>0000011
[2,4,5,1,3,8,7,6]=>[6,7,8,3,1,5,4,2]=>1111000=>0001111
[1,7,4,2,5,8,6,3]=>[3,6,8,5,2,4,7,1]=>1100100=>0010011
[2,8,6,4,1,3,7,5]=>[5,7,3,1,4,6,8,2]=>1110000=>0000111
[6,3,1,8,5,2,7,4]=>[4,7,2,5,8,1,3,6]=>1100000=>0000011
[7,4,8,5,2,6,3,1]=>[1,3,6,2,5,8,4,7]=>0101000=>0001010
[6,3,1,7,4,8,5,2]=>[2,5,8,4,7,1,3,6]=>1001000=>0001001
[7,4,8,5,2,1,6,3]=>[3,6,1,2,5,8,4,7]=>1001000=>0001001
[3,5,6,2,1,4,8,7]=>[7,8,4,1,2,6,5,3]=>1011100=>0011101
[4,1,8,5,7,3,2,6]=>[6,2,3,7,5,8,1,4]=>1100100=>0010011
[4,7,2,8,3,6,1,5]=>[5,1,6,3,8,2,7,4]=>1111000=>0001111
[6,2,8,4,1,7,3,5]=>[5,3,7,1,4,8,2,6]=>1110000=>0000111
[7,3,4,8,1,6,2,5]=>[5,2,6,1,8,4,3,7]=>1111000=>0001111
[6,3,4,8,1,7,2,5]=>[5,2,7,1,8,4,3,6]=>1111000=>0001111
[5,3,4,8,1,2,7,6]=>[6,7,2,1,8,4,3,5]=>1111000=>0001111
[4,3,5,8,1,2,7,6]=>[6,7,2,1,8,5,3,4]=>1110100=>0010111
[1,8,5,4,2,3,7,6]=>[6,7,3,2,4,5,8,1]=>1110000=>0000111
[3,5,4,8,1,2,7,6]=>[6,7,2,1,8,4,5,3]=>1111000=>0001111
[4,5,3,8,1,2,7,6]=>[6,7,2,1,8,3,5,4]=>1111000=>0001111
[6,4,3,8,1,7,2,5]=>[5,2,7,1,8,3,4,6]=>1110000=>0000111
[7,4,3,8,1,6,2,5]=>[5,2,6,1,8,3,4,7]=>1110000=>0000111
[6,5,3,8,7,1,2,4]=>[4,2,1,7,8,3,5,6]=>1110000=>0000111
[5,6,3,8,7,1,2,4]=>[4,2,1,7,8,3,6,5]=>1110100=>0010111
[4,6,3,8,1,7,2,5]=>[5,2,7,1,8,3,6,4]=>1111000=>0001111
[2,6,8,4,1,7,3,5]=>[5,3,7,1,4,8,6,2]=>1110010=>0100111
[1,8,7,4,2,6,3,5]=>[5,3,6,2,4,7,8,1]=>1110000=>0000111
[5,7,3,8,6,1,2,4]=>[4,2,1,6,8,3,7,5]=>1110100=>0010111
[3,7,5,8,6,1,2,4]=>[4,2,1,6,8,5,7,3]=>1110100=>0010111
[2,7,8,5,6,1,3,4]=>[4,3,1,6,5,8,7,2]=>1110101=>1010111
[1,8,7,5,6,2,3,4]=>[4,3,2,6,5,7,8,1]=>1110100=>0010111
[2,6,8,5,7,1,3,4]=>[4,3,1,7,5,8,6,2]=>1110110=>0110111
[5,3,6,8,7,1,2,4]=>[4,2,1,7,8,6,3,5]=>1110010=>0100111
[7,2,8,5,6,1,3,4]=>[4,3,1,6,5,8,2,7]=>1110100=>0010111
[5,2,8,6,7,1,3,4]=>[4,3,1,7,6,8,2,5]=>1110010=>0100111
[1,8,3,2,7,6,4,5]=>[5,4,6,7,2,3,8,1]=>1101000=>0001011
[5,2,8,7,6,1,3,4]=>[4,3,1,6,7,8,2,5]=>1110000=>0000111
[6,2,8,7,5,1,3,4]=>[4,3,1,5,7,8,2,6]=>1110000=>0000111
[3,4,7,8,1,6,2,5]=>[5,2,6,1,8,7,4,3]=>1111001=>1001111
[1,8,5,7,6,2,3,4]=>[4,3,2,6,7,5,8,1]=>1110100=>0010111
[2,5,8,7,6,1,3,4]=>[4,3,1,6,7,8,5,2]=>1110100=>0010111
[7,4,6,5,8,1,2,3]=>[3,2,1,8,5,6,4,7]=>1101100=>0011011
[2,6,8,7,5,1,3,4]=>[4,3,1,5,7,8,6,2]=>1110010=>0100111
[1,8,6,7,5,2,3,4]=>[4,3,2,5,7,6,8,1]=>1110010=>0100111
[2,7,8,6,5,1,3,4]=>[4,3,1,5,6,8,7,2]=>1110001=>1000111
[5,7,6,4,8,1,2,3]=>[3,2,1,8,4,6,7,5]=>1101100=>0011011
[8,7,4,2,3,6,1,5]=>[5,1,6,3,2,4,7,8]=>1110000=>0000111
[8,1,6,2,7,5,3,4]=>[4,3,5,7,2,6,1,8]=>1110000=>0000111
[7,2,6,4,3,8,1,5]=>[5,1,8,3,4,6,2,7]=>1110000=>0000111
[5,3,1,7,4,8,2,6]=>[6,2,8,4,7,1,3,5]=>1101000=>0001011
[6,1,7,3,2,8,5,4]=>[4,5,8,2,3,7,1,6]=>1100000=>0000011
[4,7,2,1,6,3,8,5]=>[5,8,3,6,1,2,7,4]=>1011000=>0001101
[6,2,1,5,3,8,4,7]=>[7,4,8,3,5,1,2,6]=>1011000=>0001101
[5,3,1,6,2,8,4,7]=>[7,4,8,2,6,1,3,5]=>1101000=>0001011
[7,4,3,8,1,5,2,6]=>[6,2,5,1,8,3,4,7]=>1110000=>0000111
[6,1,5,3,2,8,4,7]=>[7,4,8,2,3,5,1,6]=>1101000=>0001011
[4,8,5,6,1,7,3,2]=>[2,3,7,1,6,5,8,4]=>1001100=>0011001
[3,6,7,1,5,2,8,4]=>[4,8,2,5,1,7,6,3]=>1110010=>0100111
[7,3,2,6,4,8,1,5]=>[5,1,8,4,6,2,3,7]=>1101000=>0001011
[6,4,2,7,3,8,1,5]=>[5,1,8,3,7,2,4,6]=>1110000=>0000111
[5,2,1,7,4,8,3,6]=>[6,3,8,4,7,1,2,5]=>1011000=>0001101
[6,1,8,4,5,2,7,3]=>[3,7,2,5,4,8,1,6]=>1101000=>0001011
[3,5,2,7,1,6,8,4]=>[4,8,6,1,7,2,5,3]=>1110010=>0100111
[4,5,7,2,8,6,1,3]=>[3,1,6,8,2,7,5,4]=>1101100=>0011011
[4,6,7,1,3,8,5,2]=>[2,5,8,3,1,7,6,4]=>1011010=>0101101
[6,1,4,2,5,3,7,8]=>[8,7,3,5,2,4,1,6]=>1110001=>1000111
[1,3,7,5,4,2,8,6]=>[6,8,2,4,5,7,3,1]=>1110000=>0000111
[6,1,3,5,4,2,7,8]=>[8,7,2,4,5,3,1,6]=>1110001=>1000111
[6,1,2,5,4,7,3,8]=>[8,3,7,4,5,2,1,6]=>1111000=>0001111
[5,2,6,3,4,7,1,8]=>[8,1,7,4,3,6,2,5]=>1111000=>0001111
[2,4,7,1,5,3,8,6]=>[6,8,3,5,1,7,4,2]=>1111000=>0001111
[2,3,6,7,4,8,1,5]=>[5,1,8,4,7,6,3,2]=>1111010=>0101111
[1,3,6,7,4,8,5,2]=>[2,5,8,4,7,6,3,1]=>1011010=>0101101
[2,7,6,5,3,1,8,4]=>[4,8,1,3,5,6,7,2]=>1100000=>0000011
[5,2,6,1,4,7,8,3]=>[3,8,7,4,1,6,2,5]=>1101001=>1001011
[4,7,6,5,2,1,8,3]=>[3,8,1,2,5,6,7,4]=>1001000=>0001001
[6,3,1,5,4,7,8,2]=>[2,8,7,4,5,1,3,6]=>1001001=>1001001
[5,3,6,1,4,2,7,8]=>[8,7,2,4,1,6,3,5]=>1110001=>1000111
[1,7,4,2,6,3,8,5]=>[5,8,3,6,2,4,7,1]=>1110000=>0000111
[5,7,4,1,2,3,6,8]=>[8,6,3,2,1,4,7,5]=>1110110=>0110111
[4,7,6,3,8,5,1,2]=>[2,1,5,8,3,6,7,4]=>1011000=>0001101
[3,7,6,5,2,8,1,4]=>[4,1,8,2,5,6,7,3]=>1110000=>0000111
[4,7,2,6,1,3,8,5]=>[5,8,3,1,6,2,7,4]=>1111000=>0001111
[2,7,6,5,8,1,4,3]=>[3,4,1,8,5,6,7,2]=>1100100=>0010011
[1,2,3,7,4,6,8,5]=>[5,8,6,4,7,3,2,1]=>1111010=>0101111
[3,2,7,1,4,5,8,6]=>[6,8,5,4,1,7,2,3]=>1101100=>0011011
[2,1,5,3,8,7,4,6]=>[6,4,7,8,3,5,1,2]=>1011000=>0001101
[5,8,3,2,4,1,6,7]=>[7,6,1,4,2,3,8,5]=>1100110=>0110011
[6,2,8,3,7,5,1,4]=>[4,1,5,7,3,8,2,6]=>1110000=>0000111
[4,2,8,3,7,5,6,1]=>[1,6,5,7,3,8,2,4]=>0110100=>0010110
[7,3,4,8,6,5,1,2]=>[2,1,5,6,8,4,3,7]=>1011000=>0001101
[5,3,4,8,7,2,6,1]=>[1,6,2,7,8,4,3,5]=>0111000=>0001110
[4,6,3,8,5,7,2,1]=>[1,2,7,5,8,3,6,4]=>0011100=>0011100
[7,5,3,8,6,2,4,1]=>[1,4,2,6,8,3,5,7]=>0110000=>0000110
[2,6,8,3,7,4,5,1]=>[1,5,4,7,3,8,6,2]=>0111010=>0101110
[2,5,8,3,7,4,6,1]=>[1,6,4,7,3,8,5,2]=>0111100=>0011110
[7,4,3,8,6,2,5,1]=>[1,5,2,6,8,3,4,7]=>0110000=>0000110
[3,5,4,8,7,2,6,1]=>[1,6,2,7,8,4,5,3]=>0111000=>0001110
[4,5,3,8,6,7,2,1]=>[1,2,7,6,8,3,5,4]=>0011010=>0101100
[3,6,7,8,4,5,2,1]=>[1,2,5,4,8,7,6,3]=>0011011=>1101100
[1,8,5,6,4,7,3,2]=>[2,3,7,4,6,5,8,1]=>1001100=>0011001
[2,5,8,6,4,7,3,1]=>[1,3,7,4,6,8,5,2]=>0101100=>0011010
[6,3,7,8,4,5,2,1]=>[1,2,5,4,8,7,3,6]=>0011001=>1001100
[4,3,7,8,5,6,2,1]=>[1,2,6,5,8,7,3,4]=>0010101=>1010100
[4,2,8,6,5,7,3,1]=>[1,3,7,5,6,8,2,4]=>0100100=>0010010
[3,2,8,6,7,4,5,1]=>[1,5,4,7,6,8,2,3]=>0101010=>0101010
[2,3,8,7,5,4,6,1]=>[1,6,4,5,7,8,3,2]=>0111000=>0001110
[1,8,2,7,4,5,6,3]=>[3,6,5,4,7,2,8,1]=>1101100=>0011011
[7,2,8,6,3,4,5,1]=>[1,5,4,3,6,8,2,7]=>0111000=>0001110
[6,2,8,4,5,7,3,1]=>[1,3,7,5,4,8,2,6]=>0101100=>0011010
[5,2,8,4,6,7,3,1]=>[1,3,7,6,4,8,2,5]=>0101010=>0101010
[4,3,6,8,5,7,2,1]=>[1,2,7,5,8,6,3,4]=>0010110=>0110100
[3,4,6,8,7,2,5,1]=>[1,5,2,7,8,6,4,3]=>0111010=>0101110
[7,3,5,8,6,2,4,1]=>[1,4,2,6,8,5,3,7]=>0110100=>0010110
[1,8,3,5,7,4,6,2]=>[2,6,4,7,5,3,8,1]=>1011100=>0011101
[2,7,8,4,5,6,3,1]=>[1,3,6,5,4,8,7,2]=>0101101=>1011010
[3,7,5,8,4,6,2,1]=>[1,2,6,4,8,5,7,3]=>0011100=>0011100
[5,7,4,6,8,3,2,1]=>[1,2,3,8,6,4,7,5]=>0001110=>0111000
[3,6,5,8,4,7,2,1]=>[1,2,7,4,8,5,6,3]=>0011100=>0011100
[2,6,8,4,5,7,3,1]=>[1,3,7,5,4,8,6,2]=>0101110=>0111010
[5,3,6,1,7,2,4,8]=>[8,4,2,7,1,6,3,5]=>1111000=>0001111
[7,5,1,2,4,8,6,3]=>[3,6,8,4,2,1,5,7]=>1101000=>0001011
[6,4,2,3,7,1,5,8]=>[8,5,1,7,3,2,4,6]=>1110100=>0010111
[8,6,1,2,7,4,5,3]=>[3,5,4,7,2,1,6,8]=>1101000=>0001011
[8,5,7,1,2,4,6,3]=>[3,6,4,2,1,7,5,8]=>1101100=>0011011
[3,6,8,1,2,5,7,4]=>[4,7,5,2,1,8,6,3]=>1110110=>0110111
[4,6,3,8,1,2,5,7]=>[7,5,2,1,8,3,6,4]=>1111100=>0011111
[4,1,7,8,2,3,6,5]=>[5,6,3,2,8,7,1,4]=>1110001=>1000111
[6,1,8,5,2,3,4,7]=>[7,4,3,2,5,8,1,6]=>1111000=>0001111
[6,1,7,5,2,3,4,8]=>[8,4,3,2,5,7,1,6]=>1111000=>0001111
[4,8,7,1,2,3,6,5]=>[5,6,3,2,1,7,8,4]=>1111000=>0001111
[5,8,7,1,2,4,6,3]=>[3,6,4,2,1,7,8,5]=>1101100=>0011011
[5,8,6,4,1,2,3,7]=>[7,3,2,1,4,6,8,5]=>1110100=>0010111
[5,1,3,4,6,7,2,8]=>[8,2,7,6,4,3,1,5]=>1111010=>0101111
[8,2,4,1,7,3,5,6]=>[6,5,3,7,1,4,2,8]=>1110100=>0010111
[3,6,1,4,2,8,7,5]=>[5,7,8,2,4,1,6,3]=>1110000=>0000111
[2,7,4,1,8,3,5,6]=>[6,5,3,8,1,4,7,2]=>1110100=>0010111
[1,4,7,3,6,2,8,5]=>[5,8,2,6,3,7,4,1]=>1111000=>0001111
[2,8,5,7,3,4,1,6]=>[6,1,4,3,7,5,8,2]=>1110100=>0010111
[5,8,2,6,4,3,1,7]=>[7,1,3,4,6,2,8,5]=>1100100=>0010011
[3,8,6,5,4,2,1,7]=>[7,1,2,4,5,6,8,3]=>1010000=>0000101
[7,1,4,5,3,2,6,8]=>[8,6,2,3,5,4,1,7]=>1101010=>0101011
[4,3,8,1,5,7,2,6]=>[6,2,7,5,1,8,3,4]=>1110100=>0010111
[7,5,3,6,4,8,2,1]=>[1,2,8,4,6,3,5,7]=>0011000=>0001100
[7,3,6,4,5,8,2,1]=>[1,2,8,5,4,6,3,7]=>0011100=>0011100
[8,7,2,4,5,1,6,3]=>[3,6,1,5,4,2,7,8]=>1101000=>0001011
[7,1,5,4,8,6,3,2]=>[2,3,6,8,4,5,1,7]=>1001000=>0001001
[5,8,3,7,4,1,6,2]=>[2,6,1,4,7,3,8,5]=>1010100=>0010101
[8,1,7,4,2,6,5,3]=>[3,5,6,2,4,7,1,8]=>1100000=>0000011
[5,6,3,1,8,4,7,2]=>[2,7,4,8,1,3,6,5]=>1001100=>0011001
[5,7,1,4,8,6,3,2]=>[2,3,6,8,4,1,7,5]=>1001100=>0011001
[5,3,7,4,8,6,2,1]=>[1,2,6,8,4,7,3,5]=>0011000=>0001100
[8,5,3,6,1,4,7,2]=>[2,7,4,1,6,3,5,8]=>1011000=>0001101
[5,4,3,6,8,2,7,1]=>[1,7,2,8,6,3,4,5]=>0110010=>0100110
[6,5,3,7,4,8,2,1]=>[1,2,8,4,7,3,5,6]=>0011000=>0001100
[2,7,8,4,5,1,6,3]=>[3,6,1,5,4,8,7,2]=>1101001=>1001011
[5,6,3,8,1,4,7,2]=>[2,7,4,1,8,3,6,5]=>1011100=>0011101
[8,4,1,2,5,6,7,3]=>[3,7,6,5,2,1,4,8]=>1100110=>0110011
[6,8,3,1,2,5,7,4]=>[4,7,5,2,1,3,8,6]=>1100110=>0110011
[8,5,1,7,2,6,4,3]=>[3,4,6,2,7,1,5,8]=>1100000=>0000011
[8,7,1,4,5,2,6,3]=>[3,6,2,5,4,1,7,8]=>1101000=>0001011
[7,6,3,1,5,2,8,4]=>[4,8,2,5,1,3,6,7]=>1100000=>0000011
[7,5,1,8,2,6,3,4]=>[4,3,6,2,8,1,5,7]=>1110000=>0000111
[8,7,3,1,5,4,2,6]=>[6,2,4,5,1,3,7,8]=>1100000=>0000011
[3,5,4,7,6,1,2,8]=>[8,2,1,6,7,4,5,3]=>1111000=>0001111
[3,5,7,4,6,1,8,2]=>[2,8,1,6,4,7,5,3]=>1011100=>0011101
[3,5,7,4,6,1,2,8]=>[8,2,1,6,4,7,5,3]=>1111100=>0011111
[3,5,2,7,6,4,1,8]=>[8,1,4,6,7,2,5,3]=>1110000=>0000111
[3,5,7,2,6,4,1,8]=>[8,1,4,6,2,7,5,3]=>1110100=>0010111
[5,3,7,6,1,4,2,8]=>[8,2,4,1,6,7,3,5]=>1110000=>0000111
[5,3,7,6,4,1,2,8]=>[8,2,1,4,6,7,3,5]=>1110000=>0000111
[3,5,7,2,6,1,4,8]=>[8,4,1,6,2,7,5,3]=>1111100=>0011111
[5,3,7,6,4,1,8,2]=>[2,8,1,4,6,7,3,5]=>1010000=>0000101
[3,7,5,4,1,8,6,2]=>[2,6,8,1,4,5,7,3]=>1010000=>0000101
[3,7,5,1,4,8,6,2]=>[2,6,8,4,1,5,7,3]=>1011000=>0001101
[3,5,7,1,4,6,8,2]=>[2,8,6,4,1,7,5,3]=>1011110=>0111101
[3,5,4,7,1,6,8,2]=>[2,8,6,1,7,4,5,3]=>1011010=>0101101
[3,5,4,7,2,1,6,8]=>[8,6,1,2,7,4,5,3]=>1011010=>0101101
[3,5,4,2,7,1,6,8]=>[8,6,1,7,2,4,5,3]=>1110010=>0100111
[3,5,4,7,2,1,8,6]=>[6,8,1,2,7,4,5,3]=>1011000=>0001101
[5,7,6,3,1,8,4,2]=>[2,4,8,1,3,6,7,5]=>1000100=>0010001
[3,2,5,7,1,4,8,6]=>[6,8,4,1,7,5,2,3]=>1101100=>0011011
[3,5,2,7,1,4,8,6]=>[6,8,4,1,7,2,5,3]=>1111000=>0001111
[3,2,7,5,1,8,6,4]=>[4,6,8,1,5,7,2,3]=>1100000=>0000011
[3,2,7,5,1,8,4,6]=>[6,4,8,1,5,7,2,3]=>1101000=>0001011
[5,8,3,4,1,7,6,2]=>[2,6,7,1,4,3,8,5]=>1010100=>0010101
[5,8,7,2,4,1,6,3]=>[3,6,1,4,2,7,8,5]=>1100100=>0010011
[3,8,6,4,1,7,5,2]=>[2,5,7,1,4,6,8,3]=>1010000=>0000101
[4,3,5,6,8,1,7,2]=>[2,7,1,8,6,5,3,4]=>1010110=>0110101
[3,7,6,4,1,8,5,2]=>[2,5,8,1,4,6,7,3]=>1010000=>0000101
[3,7,4,1,8,6,5,2]=>[2,5,6,8,1,4,7,3]=>1010000=>0000101
[3,8,4,1,7,6,5,2]=>[2,5,6,7,1,4,8,3]=>1010000=>0000101
[3,2,7,6,1,5,4,8]=>[8,4,5,1,6,7,2,3]=>1101000=>0001011
[5,7,8,2,4,1,6,3]=>[3,6,1,4,2,8,7,5]=>1100101=>1010011
[4,2,5,8,1,6,7,3]=>[3,7,6,1,8,5,2,4]=>1100110=>0110011
[5,8,2,4,1,6,3,7]=>[7,3,6,1,4,2,8,5]=>1110100=>0010111
[8,4,2,6,5,1,3,7]=>[7,3,1,5,6,2,4,8]=>1110000=>0000111
[3,2,6,8,1,5,4,7]=>[7,4,5,1,8,6,2,3]=>1101010=>0101011
[8,3,2,5,6,1,4,7]=>[7,4,1,6,5,2,3,8]=>1101100=>0011011
[3,2,8,6,7,1,5,4]=>[4,5,1,7,6,8,2,3]=>1100010=>0100011
[3,2,6,8,7,1,5,4]=>[4,5,1,7,8,6,2,3]=>1100010=>0100011
[3,2,6,7,1,5,4,8]=>[8,4,5,1,7,6,2,3]=>1101010=>0101011
[8,7,3,2,5,6,1,4]=>[4,1,6,5,2,3,7,8]=>1100100=>0010011
[7,2,8,1,5,3,6,4]=>[4,6,3,5,1,8,2,7]=>1110000=>0000111
[8,4,2,7,5,1,3,6]=>[6,3,1,5,7,2,4,8]=>1110000=>0000111
[7,4,2,8,5,1,3,6]=>[6,3,1,5,8,2,4,7]=>1110000=>0000111
[7,2,4,1,8,3,6,5]=>[5,6,3,8,1,4,2,7]=>1110000=>0000111
[7,5,3,4,2,8,1,6]=>[6,1,8,2,4,3,5,7]=>1110000=>0000111
[8,5,3,6,2,4,7,1]=>[1,7,4,2,6,3,5,8]=>0111000=>0001110
[1,7,2,3,6,8,5,4]=>[4,5,8,6,3,2,7,1]=>1110010=>0100111
[3,5,6,4,8,2,7,1]=>[1,7,2,8,4,6,5,3]=>0111100=>0011110
[3,5,1,4,8,2,7,6]=>[6,7,2,8,4,1,5,3]=>1111000=>0001111
[1,7,5,4,8,2,6,3]=>[3,6,2,8,4,5,7,1]=>1101000=>0001011
[3,7,5,1,6,4,8,2]=>[2,8,4,6,1,5,7,3]=>1011000=>0001101
[2,7,5,4,8,1,3,6]=>[6,3,1,8,4,5,7,2]=>1111000=>0001111
[2,7,5,4,8,6,1,3]=>[3,1,6,8,4,5,7,2]=>1101000=>0001011
[1,7,5,4,8,6,3,2]=>[2,3,6,8,4,5,7,1]=>1001000=>0001001
[2,5,1,4,8,7,3,6]=>[6,3,7,8,4,1,5,2]=>1111000=>0001111
[3,6,4,2,8,7,1,5]=>[5,1,7,8,2,4,6,3]=>1110000=>0000111
[3,5,2,4,8,1,6,7]=>[7,6,1,8,4,2,5,3]=>1111010=>0101111
[4,5,6,1,7,3,8,2]=>[2,8,3,7,1,6,5,4]=>1011100=>0011101
[3,5,6,4,8,1,2,7]=>[7,2,1,8,4,6,5,3]=>1111100=>0011111
[1,5,6,4,8,7,2,3]=>[3,2,7,8,4,6,5,1]=>1101100=>0011011
[3,6,4,1,8,7,2,5]=>[5,2,7,8,1,4,6,3]=>1110000=>0000111
[3,6,4,5,8,7,2,1]=>[1,2,7,8,5,4,6,3]=>0011100=>0011100
[1,6,4,3,8,5,2,7]=>[7,2,5,8,3,4,6,1]=>1110000=>0000111
[7,6,1,4,5,3,8,2]=>[2,8,3,5,4,1,6,7]=>1011000=>0001101
[7,6,1,3,5,4,8,2]=>[2,8,4,5,3,1,6,7]=>1011000=>0001101
[7,1,3,2,5,8,4,6]=>[6,4,8,5,2,3,1,7]=>1101100=>0011011
[1,6,4,2,8,5,3,7]=>[7,3,5,8,2,4,6,1]=>1110000=>0000111
[7,6,5,8,3,1,4,2]=>[2,4,1,3,8,5,6,7]=>1000100=>0010001
[2,6,4,3,8,5,7,1]=>[1,7,5,8,3,4,6,2]=>0110100=>0010110
[7,2,3,1,5,8,6,4]=>[4,6,8,5,1,3,2,7]=>1100100=>0010011
[7,1,5,6,3,8,4,2]=>[2,4,8,3,6,5,1,7]=>1010100=>0010101
[7,2,6,5,3,8,1,4]=>[4,1,8,3,5,6,2,7]=>1110000=>0000111
[7,2,3,1,4,8,6,5]=>[5,6,8,4,1,3,2,7]=>1101000=>0001011
[7,2,3,5,4,8,6,1]=>[1,6,8,4,5,3,2,7]=>0111000=>0001110
[1,5,6,4,8,3,7,2]=>[2,7,3,8,4,6,5,1]=>1011100=>0011101
[2,5,6,4,8,3,1,7]=>[7,1,3,8,4,6,5,2]=>1101100=>0011011
[3,5,6,1,4,7,8,2]=>[2,8,7,4,1,6,5,3]=>1011101=>1011101
[7,6,1,3,4,5,8,2]=>[2,8,5,4,3,1,6,7]=>1011100=>0011101
[7,1,3,2,4,8,5,6]=>[6,5,8,4,2,3,1,7]=>1101100=>0011011
[7,6,1,5,3,4,8,2]=>[2,8,4,3,5,1,6,7]=>1011000=>0001101
[7,6,1,5,4,3,8,2]=>[2,8,3,4,5,1,6,7]=>1010000=>0000101
[1,6,4,5,8,3,2,7]=>[7,2,3,8,5,4,6,1]=>1101100=>0011011
[7,6,5,8,1,3,2,4]=>[4,2,3,1,8,5,6,7]=>1100100=>0010011
[3,4,6,8,7,2,1,5]=>[5,1,2,7,8,6,4,3]=>1011010=>0101101
[3,5,6,8,2,1,7,4]=>[4,7,1,2,8,6,5,3]=>1010110=>0110101
[4,2,1,5,3,7,8,6]=>[6,8,7,3,5,1,2,4]=>1010001=>1000101
[4,2,5,6,3,1,8,7]=>[7,8,1,3,6,5,2,4]=>1100100=>0010011
[3,5,6,8,1,7,2,4]=>[4,2,7,1,8,6,5,3]=>1110110=>0110111
[4,1,5,6,3,2,8,7]=>[7,8,2,3,6,5,1,4]=>1100100=>0010011
[4,5,3,1,7,2,8,6]=>[6,8,2,7,1,3,5,4]=>1101000=>0001011
[2,5,4,7,3,8,6,1]=>[1,6,8,3,7,4,5,2]=>0111000=>0001110
[3,5,7,1,8,4,2,6]=>[6,2,4,8,1,7,5,3]=>1110100=>0010111
[4,1,5,3,2,7,8,6]=>[6,8,7,2,3,5,1,4]=>1100001=>1000011
[4,5,3,7,1,2,8,6]=>[6,8,2,1,7,3,5,4]=>1111000=>0001111
[4,3,6,1,2,7,5,8]=>[8,5,7,2,1,6,3,4]=>1110100=>0010111
[5,1,3,2,4,6,7,8]=>[8,7,6,4,2,3,1,5]=>1101011=>1101011
[3,6,1,7,4,5,2,8]=>[8,2,5,4,7,1,6,3]=>1111000=>0001111
[5,3,1,4,2,6,7,8]=>[8,7,6,2,4,1,3,5]=>1100011=>1100011
[4,5,2,3,7,1,8,6]=>[6,8,1,7,3,2,5,4]=>1111000=>0001111
[4,2,6,1,3,7,5,8]=>[8,5,7,3,1,6,2,4]=>1110100=>0010111
[4,6,2,1,3,7,5,8]=>[8,5,7,3,1,2,6,4]=>1011100=>0011101
[3,6,2,1,7,4,8,5]=>[5,8,4,7,1,2,6,3]=>1011000=>0001101
[3,1,4,7,6,5,2,8]=>[8,2,5,6,7,4,1,3]=>1101000=>0001011
[3,6,2,7,1,5,8,4]=>[4,8,5,1,7,2,6,3]=>1110100=>0010111
[4,6,2,7,1,3,5,8]=>[8,5,3,1,7,2,6,4]=>1111100=>0011111
[3,5,7,1,8,2,6,4]=>[4,6,2,8,1,7,5,3]=>1110100=>0010111
[5,1,4,2,3,6,7,8]=>[8,7,6,3,2,4,1,5]=>1110011=>1100111
[2,6,5,3,4,7,8,1]=>[1,8,7,4,3,5,6,2]=>0111001=>1001110
[5,1,4,3,2,6,7,8]=>[8,7,6,2,3,4,1,5]=>1100011=>1100011
[5,4,1,3,2,6,7,8]=>[8,7,6,2,3,1,4,5]=>1100011=>1100011
[6,4,2,5,3,8,1,7]=>[7,1,8,3,5,2,4,6]=>1110000=>0000111
[6,2,4,5,1,8,3,7]=>[7,3,8,1,5,4,2,6]=>1111000=>0001111
[2,8,1,6,7,4,5,3]=>[3,5,4,7,6,1,8,2]=>1101010=>0101011
[2,8,6,1,4,7,5,3]=>[3,5,7,4,1,6,8,2]=>1101000=>0001011
[2,8,1,6,4,7,5,3]=>[3,5,7,4,6,1,8,2]=>1101000=>0001011
[2,6,1,4,8,5,3,7]=>[7,3,5,8,4,1,6,2]=>1111000=>0001111
[6,4,5,2,8,3,1,7]=>[7,1,3,8,2,5,4,6]=>1101000=>0001011
[6,4,5,8,2,3,7,1]=>[1,7,3,2,8,5,4,6]=>0111100=>0011110
[6,4,8,5,2,3,7,1]=>[1,7,3,2,5,8,4,6]=>0111000=>0001110
[2,4,8,1,3,6,7,5]=>[5,7,6,3,1,8,4,2]=>1111010=>0101111
[6,4,8,2,5,3,7,1]=>[1,7,3,5,2,8,4,6]=>0111000=>0001110
[4,6,8,2,3,5,7,1]=>[1,7,5,3,2,8,6,4]=>0111110=>0111110
[2,8,1,4,6,7,3,5]=>[5,3,7,6,4,1,8,2]=>1111010=>0101111
[4,8,6,2,3,7,5,1]=>[1,5,7,3,2,6,8,4]=>0111000=>0001110
[8,4,2,6,7,3,1,5]=>[5,1,3,7,6,2,4,8]=>1100010=>0100011
[5,1,8,3,6,4,7,2]=>[2,7,4,6,3,8,1,5]=>1011000=>0001101
[3,4,8,1,7,6,2,5]=>[5,2,6,7,1,8,4,3]=>1111000=>0001111
[4,7,6,8,5,1,3,2]=>[2,3,1,5,8,6,7,4]=>1001010=>0101001
[6,7,4,8,5,1,3,2]=>[2,3,1,5,8,4,7,6]=>1001010=>0101001
[5,3,6,8,7,1,4,2]=>[2,4,1,7,8,6,3,5]=>1010010=>0100101
[1,8,4,6,7,2,5,3]=>[3,5,2,7,6,4,8,1]=>1101010=>0101011
[5,2,8,3,7,1,6,4]=>[4,6,1,7,3,8,2,5]=>1110000=>0000111
[7,4,5,8,6,1,3,2]=>[2,3,1,6,8,5,4,7]=>1001100=>0011001
[4,3,6,8,7,1,5,2]=>[2,5,1,7,8,6,3,4]=>1010010=>0100101
[6,4,8,3,1,7,5,2]=>[2,5,7,1,3,8,4,6]=>1001000=>0001001
[6,2,8,4,3,7,5,1]=>[1,5,7,3,4,8,2,6]=>0110000=>0000110
[3,6,5,8,7,1,4,2]=>[2,4,1,7,8,5,6,3]=>1010100=>0010101
[5,6,8,3,1,7,4,2]=>[2,4,7,1,3,8,6,5]=>1000110=>0110001
[4,6,3,8,2,7,5,1]=>[1,5,7,2,8,3,6,4]=>0111000=>0001110
[5,3,8,1,7,2,6,4]=>[4,6,2,7,1,8,3,5]=>1110000=>0000111
[6,5,8,1,3,7,4,2]=>[2,4,7,3,1,8,5,6]=>1010100=>0010101
[6,5,3,8,2,7,4,1]=>[1,4,7,2,8,3,5,6]=>0110000=>0000110
[6,4,8,1,3,7,5,2]=>[2,5,7,3,1,8,4,6]=>1011000=>0001101
[6,2,8,3,4,7,5,1]=>[1,5,7,4,3,8,2,6]=>0111000=>0001110
[6,3,4,8,2,7,5,1]=>[1,5,7,2,8,4,3,6]=>0111000=>0001110
[4,2,7,6,3,1,8,5]=>[5,8,1,3,6,7,2,4]=>1100000=>0000011
[7,6,3,1,8,4,2,5]=>[5,2,4,8,1,3,6,7]=>1100000=>0000011
[8,4,2,5,7,6,3,1]=>[1,3,6,7,5,2,4,8]=>0100100=>0010010
[8,7,5,2,4,6,3,1]=>[1,3,6,4,2,5,7,8]=>0101000=>0001010
[5,2,8,6,3,7,4,1]=>[1,4,7,3,6,8,2,5]=>0110000=>0000110
[7,5,2,1,8,3,6,4]=>[4,6,3,8,1,2,5,7]=>1010000=>0000101
[7,4,1,5,2,8,6,3]=>[3,6,8,2,5,1,4,7]=>1100000=>0000011
[7,5,2,8,6,3,1,4]=>[4,1,3,6,8,2,5,7]=>1100000=>0000011
[7,5,2,1,3,6,4,8]=>[8,4,6,3,1,2,5,7]=>1011000=>0001101
[8,7,5,2,1,3,6,4]=>[4,6,3,1,2,5,7,8]=>1010000=>0000101
[1,3,7,6,5,8,2,4]=>[4,2,8,5,6,7,3,1]=>1110100=>0010111
[8,6,4,7,5,2,1,3]=>[3,1,2,5,7,4,6,8]=>1001000=>0001001
[6,4,7,5,2,1,3,8]=>[8,3,1,2,5,7,4,6]=>1011000=>0001101
[6,3,1,4,8,7,5,2]=>[2,5,7,8,4,1,3,6]=>1001000=>0001001
[8,6,3,1,4,7,5,2]=>[2,5,7,4,1,3,6,8]=>1001000=>0001001
[6,3,8,7,4,1,5,2]=>[2,5,1,4,7,8,3,6]=>1010000=>0000101
[8,4,6,3,1,7,5,2]=>[2,5,7,1,3,6,4,8]=>1001000=>0001001
[4,6,7,2,5,3,1,8]=>[8,1,3,5,2,7,6,4]=>1101010=>0101011
[3,6,7,4,8,1,5,2]=>[2,5,1,8,4,7,6,3]=>1011010=>0101101
[3,4,6,8,7,1,5,2]=>[2,5,1,7,8,6,4,3]=>1011010=>0101101
[1,4,7,8,2,6,5,3]=>[3,5,6,2,8,7,4,1]=>1101001=>1001011
[2,4,7,8,1,6,5,3]=>[3,5,6,1,8,7,4,2]=>1101001=>1001011
[4,2,6,8,7,1,5,3]=>[3,5,1,7,8,6,2,4]=>1100010=>0100011
[5,1,8,4,2,7,6,3]=>[3,6,7,2,4,8,1,5]=>1100000=>0000011
[6,8,3,7,1,5,4,2]=>[2,4,5,1,7,3,8,6]=>1010010=>0100101
[2,6,8,4,1,7,5,3]=>[3,5,7,1,4,8,6,2]=>1100010=>0100011
[4,5,8,6,3,1,7,2]=>[2,7,1,3,6,8,5,4]=>1001100=>0011001
[6,3,7,1,2,8,5,4]=>[4,5,8,2,1,7,3,6]=>1110000=>0000111
[1,8,2,3,6,5,4,7]=>[7,4,5,6,3,2,8,1]=>1111000=>0001111
[2,8,5,4,6,3,1,7]=>[7,1,3,6,4,5,8,2]=>1101000=>0001011
[2,5,8,4,7,3,6,1]=>[1,6,3,7,4,8,5,2]=>0111100=>0011110
[4,5,8,1,7,6,2,3]=>[3,2,6,7,1,8,5,4]=>1101100=>0011011
[3,5,8,4,7,1,6,2]=>[2,6,1,7,4,8,5,3]=>1011100=>0011101
[3,6,4,8,7,5,2,1]=>[1,2,5,7,8,4,6,3]=>0011000=>0001100
[2,6,4,3,7,1,8,5]=>[5,8,1,7,3,4,6,2]=>1110000=>0000111
[7,2,3,4,1,6,8,5]=>[5,8,6,1,4,3,2,7]=>1110010=>0100111
[1,2,4,3,8,5,7,6]=>[6,7,5,8,3,4,2,1]=>1110100=>0010111
[7,3,8,6,1,4,2,5]=>[5,2,4,1,6,8,3,7]=>1110000=>0000111
[1,5,8,4,7,6,2,3]=>[3,2,6,7,4,8,5,1]=>1101100=>0011011
[3,5,8,1,6,7,2,4]=>[4,2,7,6,1,8,5,3]=>1110110=>0110111
[7,6,1,8,5,4,2,3]=>[3,2,4,5,8,1,6,7]=>1100000=>0000011
[4,1,6,5,8,2,7,3]=>[3,7,2,8,5,6,1,4]=>1100100=>0010011
[3,1,6,5,8,4,7,2]=>[2,7,4,8,5,6,1,3]=>1001100=>0011001
[3,2,6,5,8,4,7,1]=>[1,7,4,8,5,6,2,3]=>0101100=>0011010
[4,3,7,1,6,5,8,2]=>[2,8,5,6,1,7,3,4]=>1010100=>0010101
[5,1,6,4,8,2,7,3]=>[3,7,2,8,4,6,1,5]=>1101000=>0001011
[5,2,6,4,8,1,7,3]=>[3,7,1,8,4,6,2,5]=>1101000=>0001011
[4,3,7,5,8,1,6,2]=>[2,6,1,8,5,7,3,4]=>1010100=>0010101
[4,3,7,5,8,2,6,1]=>[1,6,2,8,5,7,3,4]=>0110100=>0010110
[5,3,7,4,8,2,6,1]=>[1,6,2,8,4,7,3,5]=>0111000=>0001110
[5,3,7,4,8,1,6,2]=>[2,6,1,8,4,7,3,5]=>1011000=>0001101
[5,4,8,1,6,2,7,3]=>[3,7,2,6,1,8,4,5]=>1101000=>0001011
[4,3,7,1,5,2,8,6]=>[6,8,2,5,1,7,3,4]=>1110000=>0000111
[5,4,8,2,6,3,7,1]=>[1,7,3,6,2,8,4,5]=>0111000=>0001110
[4,1,8,7,6,3,2,5]=>[5,2,3,6,7,8,1,4]=>1100000=>0000011
[6,8,3,2,1,4,7,5]=>[5,7,4,1,2,3,8,6]=>1001010=>0101001
[8,4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4,8]=>0001100=>0011000
[5,2,6,7,3,8,4,1]=>[1,4,8,3,7,6,2,5]=>0110010=>0100110
[6,1,2,7,5,8,4,3]=>[3,4,8,5,7,2,1,6]=>1100100=>0010011
[3,4,7,5,1,6,8,2]=>[2,8,6,1,5,7,4,3]=>1011010=>0101101
[7,1,2,6,5,8,4,3]=>[3,4,8,5,6,2,1,7]=>1100100=>0010011
[6,2,5,7,3,8,4,1]=>[1,4,8,3,7,5,2,6]=>0110100=>0010110
[7,3,4,6,2,8,5,1]=>[1,5,8,2,6,4,3,7]=>0111000=>0001110
[4,5,2,6,8,3,7,1]=>[1,7,3,8,6,2,5,4]=>0111010=>0101110
[4,8,3,2,5,7,6,1]=>[1,6,7,5,2,3,8,4]=>0101100=>0011010
[6,8,5,3,4,7,2,1]=>[1,2,7,4,3,5,8,6]=>0011010=>0101100
[8,2,6,7,5,1,4,3]=>[3,4,1,5,7,6,2,8]=>1100010=>0100011
[6,1,7,5,8,4,2,3]=>[3,2,4,8,5,7,1,6]=>1100100=>0010011
[8,4,7,6,2,3,5,1]=>[1,5,3,2,6,7,4,8]=>0111000=>0001110
[6,8,3,4,7,2,5,1]=>[1,5,2,7,4,3,8,6]=>0111010=>0101110
[8,3,4,7,6,2,5,1]=>[1,5,2,6,7,4,3,8]=>0111000=>0001110
[4,7,6,2,5,8,3,1]=>[1,3,8,5,2,6,7,4]=>0101100=>0011010
[6,8,3,5,1,4,7,2]=>[2,7,4,1,5,3,8,6]=>1011010=>0101101
[1,7,2,6,5,8,4,3]=>[3,4,8,5,6,2,7,1]=>1100100=>0010011
[7,5,3,4,8,2,6,1]=>[1,6,2,8,4,3,5,7]=>0111000=>0001110
[5,3,8,2,4,7,6,1]=>[1,6,7,4,2,8,3,5]=>0111000=>0001110
[6,7,2,8,5,4,3,1]=>[1,3,4,5,8,2,7,6]=>0100010=>0100010
[3,7,4,6,2,8,5,1]=>[1,5,8,2,6,4,7,3]=>0111000=>0001110
[6,8,5,4,2,3,7,1]=>[1,7,3,2,4,5,8,6]=>0110010=>0100110
[5,8,2,4,3,7,6,1]=>[1,6,7,3,4,2,8,5]=>0110100=>0010110
[3,4,5,8,2,7,6,1]=>[1,6,7,2,8,5,4,3]=>0111100=>0011110
[6,8,3,4,5,2,7,1]=>[1,7,2,5,4,3,8,6]=>0111010=>0101110
[7,4,6,3,2,8,5,1]=>[1,5,8,2,3,6,4,7]=>0101000=>0001010
[6,5,3,8,4,2,7,1]=>[1,7,2,4,8,3,5,6]=>0110000=>0000110
[3,1,6,8,4,7,5,2]=>[2,5,7,4,8,6,1,3]=>1001010=>0101001
[8,3,6,1,5,7,4,2]=>[2,4,7,5,1,6,3,8]=>1010100=>0010101
[2,7,3,5,8,6,4,1]=>[1,4,6,8,5,3,7,2]=>0110100=>0010110
[2,4,7,5,8,6,1,3]=>[3,1,6,8,5,7,4,2]=>1101100=>0011011
[2,4,6,8,1,7,5,3]=>[3,5,7,1,8,6,4,2]=>1101010=>0101011
[5,7,3,8,6,2,1,4]=>[4,1,2,6,8,3,7,5]=>1010100=>0010101
[7,4,3,8,6,2,1,5]=>[5,1,2,6,8,3,4,7]=>1010000=>0000101
[3,5,2,7,8,1,4,6]=>[6,4,1,8,7,2,5,3]=>1111001=>1001111
[3,5,2,8,1,4,7,6]=>[6,7,4,1,8,2,5,3]=>1111000=>0001111
[4,3,6,2,1,8,5,7]=>[7,5,8,1,2,6,3,4]=>1010100=>0010101
[3,6,4,2,7,5,1,8]=>[8,1,5,7,2,4,6,3]=>1110000=>0000111
[3,6,5,2,1,7,4,8]=>[8,4,7,1,2,5,6,3]=>1011000=>0001101
[5,8,4,2,3,6,7,1]=>[1,7,6,3,2,4,8,5]=>0110110=>0110110
[6,8,4,2,3,7,5,1]=>[1,5,7,3,2,4,8,6]=>0110010=>0100110
[3,6,4,2,1,8,7,5]=>[5,7,8,1,2,4,6,3]=>1010000=>0000101
[2,8,6,5,4,1,7,3]=>[3,7,1,4,5,6,8,2]=>1100000=>0000011
[2,5,6,4,1,8,7,3]=>[3,7,8,1,4,6,5,2]=>1100100=>0010011
[3,8,6,2,5,7,1,4]=>[4,1,7,5,2,6,8,3]=>1110100=>0010111
[2,6,5,4,1,7,8,3]=>[3,8,7,1,4,5,6,2]=>1100001=>1000011
[6,5,7,3,2,8,1,4]=>[4,1,8,2,3,7,5,6]=>1100100=>0010011
[3,6,4,2,7,1,8,5]=>[5,8,1,7,2,4,6,3]=>1110000=>0000111
[4,6,3,2,1,5,7,8]=>[8,7,5,1,2,3,6,4]=>1001101=>1011001
[1,2,6,5,8,7,3,4]=>[4,3,7,8,5,6,2,1]=>1110100=>0010111
[5,6,3,4,8,7,2,1]=>[1,2,7,8,4,3,6,5]=>0011100=>0011100
[6,5,3,4,8,7,2,1]=>[1,2,7,8,4,3,5,6]=>0011000=>0001100
[8,5,3,7,4,6,2,1]=>[1,2,6,4,7,3,5,8]=>0011000=>0001100
[4,1,2,7,3,6,5,8]=>[8,5,6,3,7,2,1,4]=>1110100=>0010111
[1,6,8,2,4,5,3,7]=>[7,3,5,4,2,8,6,1]=>1111010=>0101111
[7,1,2,8,3,6,4,5]=>[5,4,6,3,8,2,1,7]=>1111000=>0001111
[6,1,7,2,3,5,8,4]=>[4,8,5,3,2,7,1,6]=>1110100=>0010111
[1,8,2,7,4,6,5,3]=>[3,5,6,4,7,2,8,1]=>1101000=>0001011
[7,1,6,2,3,5,8,4]=>[4,8,5,3,2,6,1,7]=>1110100=>0010111
[6,8,7,3,4,5,2,1]=>[1,2,5,4,3,7,8,6]=>0011010=>0101100
[1,8,7,2,4,5,3,6]=>[6,3,5,4,2,7,8,1]=>1111000=>0001111
[8,5,1,2,3,4,7,6]=>[6,7,4,3,2,1,5,8]=>1111000=>0001111
[8,1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1,8]=>1111000=>0001111
[1,7,6,2,4,5,3,8]=>[8,3,5,4,2,6,7,1]=>1111000=>0001111
[8,6,2,3,5,1,4,7]=>[7,4,1,5,3,2,6,8]=>1111000=>0001111
[8,6,2,4,1,5,3,7]=>[7,3,5,1,4,2,6,8]=>1110000=>0000111
[8,3,6,1,5,4,2,7]=>[7,2,4,5,1,6,3,8]=>1110000=>0000111
[3,4,8,2,7,6,5,1]=>[1,5,6,7,2,8,4,3]=>0111000=>0001110
[3,4,8,7,1,6,5,2]=>[2,5,6,1,7,8,4,3]=>1011000=>0001101
[8,1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1,8]=>1010100=>0010101
[4,1,8,5,7,6,3,2]=>[2,3,6,7,5,8,1,4]=>1000100=>0010001
[8,2,7,1,4,5,6,3]=>[3,6,5,4,1,7,2,8]=>1101100=>0011011
[8,2,3,7,1,6,5,4]=>[4,5,6,1,7,3,2,8]=>1110000=>0000111
[8,2,7,1,3,6,5,4]=>[4,5,6,3,1,7,2,8]=>1110000=>0000111
[8,2,4,3,7,6,1,5]=>[5,1,6,7,3,4,2,8]=>1110000=>0000111
[4,2,8,3,7,6,5,1]=>[1,5,6,7,3,8,2,4]=>0110000=>0000110
[5,8,1,3,7,6,2,4]=>[4,2,6,7,3,1,8,5]=>1110100=>0010111
[7,5,8,2,3,1,4,6]=>[6,4,1,3,2,8,5,7]=>1101100=>0011011
[7,1,3,8,2,5,6,4]=>[4,6,5,2,8,3,1,7]=>1110100=>0010111
[6,2,8,1,5,7,3,4]=>[4,3,7,5,1,8,2,6]=>1110100=>0010111
[7,2,5,4,1,8,6,3]=>[3,6,8,1,4,5,2,7]=>1100000=>0000011
[7,3,5,4,2,1,8,6]=>[6,8,1,2,4,5,3,7]=>1010000=>0000101
[7,4,5,2,1,6,8,3]=>[3,8,6,1,2,5,4,7]=>1001010=>0101001
[7,3,2,8,5,6,1,4]=>[4,1,6,5,8,2,3,7]=>1100100=>0010011
[7,2,5,4,1,6,3,8]=>[8,3,6,1,4,5,2,7]=>1110000=>0000111
[1,5,2,4,7,8,3,6]=>[6,3,8,7,4,2,5,1]=>1111001=>1001111
[3,5,1,2,8,6,7,4]=>[4,7,6,8,2,1,5,3]=>1110010=>0100111
[2,5,3,4,7,8,1,6]=>[6,1,8,7,4,3,5,2]=>1111001=>1001111
[1,7,4,3,6,8,5,2]=>[2,5,8,6,3,4,7,1]=>1010010=>0100101
[4,7,6,3,2,5,8,1]=>[1,8,5,2,3,6,7,4]=>0101100=>0011010
[4,7,6,5,1,3,8,2]=>[2,8,3,1,5,6,7,4]=>1011000=>0001101
[1,7,6,5,2,3,8,4]=>[4,8,3,2,5,6,7,1]=>1110000=>0000111
[1,7,6,5,8,3,2,4]=>[4,2,3,8,5,6,7,1]=>1100100=>0010011
[4,7,6,5,1,3,2,8]=>[8,2,3,1,5,6,7,4]=>1101000=>0001011
[5,7,6,3,2,8,4,1]=>[1,4,8,2,3,6,7,5]=>0100100=>0010010
[5,4,6,8,7,2,1,3]=>[3,1,2,7,8,6,4,5]=>1001010=>0101001
[6,3,4,2,8,1,5,7]=>[7,5,1,8,2,4,3,6]=>1110100=>0010111
[6,7,3,2,1,8,5,4]=>[4,5,8,1,2,3,7,6]=>1000010=>0100001
[5,7,6,2,1,4,8,3]=>[3,8,4,1,2,6,7,5]=>1001100=>0011001
[1,7,6,3,2,8,4,5]=>[5,4,8,2,3,6,7,1]=>1101000=>0001011
[5,4,2,1,7,3,6,8]=>[8,6,3,7,1,2,4,5]=>1010010=>0100101
[6,5,8,1,7,3,4,2]=>[2,4,3,7,1,8,5,6]=>1010100=>0010101
[6,5,8,2,3,7,4,1]=>[1,4,7,3,2,8,5,6]=>0110100=>0010110
[6,5,8,3,4,1,7,2]=>[2,7,1,4,3,8,5,6]=>1010100=>0010101
[5,7,3,6,8,1,4,2]=>[2,4,1,8,6,3,7,5]=>1010110=>0110101
[5,7,2,6,3,1,4,8]=>[8,4,1,3,6,2,7,5]=>1101100=>0011011
[4,1,2,8,5,6,3,7]=>[7,3,6,5,8,2,1,4]=>1110100=>0010111
[4,1,2,8,5,3,6,7]=>[7,6,3,5,8,2,1,4]=>1110010=>0100111
[2,1,6,3,7,8,5,4]=>[4,5,8,7,3,6,1,2]=>1010001=>1000101
[4,7,1,6,8,2,5,3]=>[3,5,2,8,6,1,7,4]=>1101010=>0101011
[3,7,4,1,6,5,2,8]=>[8,2,5,6,1,4,7,3]=>1110000=>0000111
[3,7,2,1,4,5,6,8]=>[8,6,5,4,1,2,7,3]=>1011110=>0111101
[3,5,8,2,6,1,7,4]=>[4,7,1,6,2,8,5,3]=>1110100=>0010111
[4,2,7,8,3,5,1,6]=>[6,1,5,3,8,7,2,4]=>1110001=>1000111
[4,5,1,7,3,6,8,2]=>[2,8,6,3,7,1,5,4]=>1011010=>0101101
[4,3,2,8,5,1,6,7]=>[7,6,1,5,8,2,3,4]=>1100010=>0100011
[3,7,6,2,8,4,1,5]=>[5,1,4,8,2,6,7,3]=>1110000=>0000111
[3,7,6,1,5,2,8,4]=>[4,8,2,5,1,6,7,3]=>1110000=>0000111
[3,7,6,5,8,4,1,2]=>[2,1,4,8,5,6,7,3]=>1010100=>0010101
[1,7,6,2,5,8,4,3]=>[3,4,8,5,2,6,7,1]=>1100100=>0010011
[1,7,6,5,8,4,2,3]=>[3,2,4,8,5,6,7,1]=>1100100=>0010011
[3,7,6,5,8,1,2,4]=>[4,2,1,8,5,6,7,3]=>1110100=>0010111
[3,7,6,2,8,4,5,1]=>[1,5,4,8,2,6,7,3]=>0111000=>0001110
[4,3,6,8,5,1,2,7]=>[7,2,1,5,8,6,3,4]=>1110010=>0100111
[3,7,6,1,5,4,8,2]=>[2,8,4,5,1,6,7,3]=>1011000=>0001101
[4,7,2,6,8,5,1,3]=>[3,1,5,8,6,2,7,4]=>1101010=>0101011
[2,7,1,5,8,4,3,6]=>[6,3,4,8,5,1,7,2]=>1110100=>0010111
[2,7,6,1,8,4,3,5]=>[5,3,4,8,1,6,7,2]=>1110000=>0000111
[7,1,2,6,3,5,4,8]=>[8,4,5,3,6,2,1,7]=>1111000=>0001111
[6,2,7,5,8,4,3,1]=>[1,3,4,8,5,7,2,6]=>0100100=>0010010
[7,2,5,1,4,6,3,8]=>[8,3,6,4,1,5,2,7]=>1111000=>0001111
[7,2,6,3,4,5,1,8]=>[8,1,5,4,3,6,2,7]=>1111000=>0001111
[7,4,3,1,5,2,6,8]=>[8,6,2,5,1,3,4,7]=>1100010=>0100011
[6,7,8,4,2,5,3,1]=>[1,3,5,2,4,8,7,6]=>0100011=>1100010
[6,1,2,5,7,8,4,3]=>[3,4,8,7,5,2,1,6]=>1100101=>1010011
[3,7,8,6,2,5,1,4]=>[4,1,5,2,6,8,7,3]=>1110001=>1000111
[3,6,1,4,8,7,5,2]=>[2,5,7,8,4,1,6,3]=>1011000=>0001101
[4,1,2,7,8,5,3,6]=>[6,3,5,8,7,2,1,4]=>1110001=>1000111
[4,7,3,1,2,6,8,5]=>[5,8,6,2,1,3,7,4]=>1101010=>0101011
[3,6,4,5,8,1,7,2]=>[2,7,1,8,5,4,6,3]=>1011100=>0011101
[3,7,6,1,5,8,2,4]=>[4,2,8,5,1,6,7,3]=>1110100=>0010111
[3,7,6,5,1,4,2,8]=>[8,2,4,1,5,6,7,3]=>1110000=>0000111
[3,8,5,4,6,7,1,2]=>[2,1,7,6,4,5,8,3]=>1011010=>0101101
[3,8,5,6,4,2,7,1]=>[1,7,2,4,6,5,8,3]=>0110100=>0010110
[1,2,6,4,3,5,8,7]=>[7,8,5,3,4,6,2,1]=>1110100=>0010111
[3,2,6,4,7,8,5,1]=>[1,5,8,7,4,6,2,3]=>0101001=>1001010
[4,2,7,5,8,3,1,6]=>[6,1,3,8,5,7,2,4]=>1100100=>0010011
[4,8,1,6,2,7,5,3]=>[3,5,7,2,6,1,8,4]=>1101000=>0001011
[5,7,2,3,1,4,6,8]=>[8,6,4,1,3,2,7,5]=>1101110=>0111011
[6,5,1,3,2,7,4,8]=>[8,4,7,2,3,1,5,6]=>1101000=>0001011
[6,5,2,3,1,7,4,8]=>[8,4,7,1,3,2,5,6]=>1101000=>0001011
[6,1,8,4,2,7,5,3]=>[3,5,7,2,4,8,1,6]=>1100000=>0000011
[5,7,2,3,8,4,1,6]=>[6,1,4,8,3,2,7,5]=>1110100=>0010111
[5,2,1,4,7,8,3,6]=>[6,3,8,7,4,1,2,5]=>1011001=>1001101
[5,6,2,7,3,4,8,1]=>[1,8,4,3,7,2,6,5]=>0111100=>0011110
[5,2,6,8,1,7,4,3]=>[3,4,7,1,8,6,2,5]=>1100010=>0100011
[3,7,8,6,1,2,4,5]=>[5,4,2,1,6,8,7,3]=>1111001=>1001111
[2,7,6,8,5,1,3,4]=>[4,3,1,5,8,6,7,2]=>1110010=>0100111
[2,7,8,6,1,5,4,3]=>[3,4,5,1,6,8,7,2]=>1100001=>1000011
[2,7,6,8,5,3,1,4]=>[4,1,3,5,8,6,7,2]=>1100010=>0100011
[4,7,6,8,2,1,3,5]=>[5,3,1,2,8,6,7,4]=>1011010=>0101101
[4,7,8,6,1,3,2,5]=>[5,2,3,1,6,8,7,4]=>1101001=>1001011
[1,7,8,6,5,2,3,4]=>[4,3,2,5,6,8,7,1]=>1110001=>1000111
[5,6,1,8,3,7,4,2]=>[2,4,7,3,8,1,6,5]=>1010100=>0010101
[4,7,6,8,1,2,3,5]=>[5,3,2,1,8,6,7,4]=>1111010=>0101111
[2,8,4,1,5,7,3,6]=>[6,3,7,5,1,4,8,2]=>1110100=>0010111
[1,4,6,2,5,7,8,3]=>[3,8,7,5,2,6,4,1]=>1101101=>1011011
[2,4,8,6,3,5,7,1]=>[1,7,5,3,6,8,4,2]=>0111100=>0011110
[2,4,6,1,5,7,3,8]=>[8,3,7,5,1,6,4,2]=>1111100=>0011111
[4,7,2,3,1,5,6,8]=>[8,6,5,1,3,2,7,4]=>1101110=>0111011
[7,4,6,2,8,3,5,1]=>[1,5,3,8,2,6,4,7]=>0111000=>0001110
[7,3,5,1,4,8,2,6]=>[6,2,8,4,1,5,3,7]=>1111000=>0001111
[7,2,5,1,4,8,6,3]=>[3,6,8,4,1,5,2,7]=>1101000=>0001011
[7,5,4,3,8,6,2,1]=>[1,2,6,8,3,4,5,7]=>0010000=>0000100
[2,4,1,8,6,7,5,3]=>[3,5,7,6,8,1,4,2]=>1100010=>0100011
[4,3,8,2,6,7,5,1]=>[1,5,7,6,2,8,3,4]=>0110010=>0100110
[4,3,8,2,5,7,1,6]=>[6,1,7,5,2,8,3,4]=>1110100=>0010111
[4,1,8,5,6,3,7,2]=>[2,7,3,6,5,8,1,4]=>1010100=>0010101
[7,5,2,3,8,1,6,4]=>[4,6,1,8,3,2,5,7]=>1110000=>0000111
[2,1,7,8,6,3,5,4]=>[4,5,3,6,8,7,1,2]=>1010001=>1000101
[3,5,6,1,4,2,8,7]=>[7,8,2,4,1,6,5,3]=>1110100=>0010111
[8,4,6,7,3,2,1,5]=>[5,1,2,3,7,6,4,8]=>1001010=>0101001
[2,1,5,7,8,3,6,4]=>[4,6,3,8,7,5,1,2]=>1010101=>1010101
[5,1,6,7,3,8,2,4]=>[4,2,8,3,7,6,1,5]=>1110010=>0100111
[4,7,5,8,6,3,1,2]=>[2,1,3,6,8,5,7,4]=>1001100=>0011001
[4,7,1,8,3,5,6,2]=>[2,6,5,3,8,1,7,4]=>1011100=>0011101
[7,8,3,2,6,1,5,4]=>[4,5,1,6,2,3,8,7]=>1100001=>1000011
[6,3,4,8,1,5,7,2]=>[2,7,5,1,8,4,3,6]=>1011100=>0011101
[7,6,5,2,1,8,4,3]=>[3,4,8,1,2,5,6,7]=>1000000=>0000001
[2,7,5,1,8,3,6,4]=>[4,6,3,8,1,5,7,2]=>1110000=>0000111
[5,1,8,7,4,3,6,2]=>[2,6,3,4,7,8,1,5]=>1010000=>0000101
[8,4,7,6,3,5,1,2]=>[2,1,5,3,6,7,4,8]=>1011000=>0001101
[8,1,7,4,2,3,5,6]=>[6,5,3,2,4,7,1,8]=>1110100=>0010111
[6,5,1,3,8,7,4,2]=>[2,4,7,8,3,1,5,6]=>1010000=>0000101
[6,1,8,5,3,7,2,4]=>[4,2,7,3,5,8,1,6]=>1110000=>0000111
[8,6,5,1,7,4,3,2]=>[2,3,4,7,1,5,6,8]=>1000000=>0000001
[7,6,4,1,3,5,8,2]=>[2,8,5,3,1,4,6,7]=>1010100=>0010101
[3,4,7,2,5,6,1,8]=>[8,1,6,5,2,7,4,3]=>1111100=>0011111
[3,7,8,2,6,1,5,4]=>[4,5,1,6,2,8,7,3]=>1110001=>1000111
[4,7,6,2,1,5,8,3]=>[3,8,5,1,2,6,7,4]=>1001100=>0011001
[4,8,6,5,1,2,7,3]=>[3,7,2,1,5,6,8,4]=>1101000=>0001011
[3,4,5,1,7,8,6,2]=>[2,6,8,7,1,5,4,3]=>1011001=>1001101
[7,4,6,8,1,3,5,2]=>[2,5,3,1,8,6,4,7]=>1011010=>0101101
[3,8,7,5,6,1,4,2]=>[2,4,1,6,5,7,8,3]=>1010100=>0010101
[8,4,6,5,1,7,3,2]=>[2,3,7,1,5,6,4,8]=>1001000=>0001001
[3,2,5,6,1,4,8,7]=>[7,8,4,1,6,5,2,3]=>1101100=>0011011
[4,6,3,8,7,5,1,2]=>[2,1,5,7,8,3,6,4]=>1011000=>0001101
[2,8,4,1,5,7,6,3]=>[3,6,7,5,1,4,8,2]=>1100100=>0010011
[1,8,4,2,5,7,6,3]=>[3,6,7,5,2,4,8,1]=>1100100=>0010011
[2,5,8,3,7,1,6,4]=>[4,6,1,7,3,8,5,2]=>1110100=>0010111
[2,8,4,5,1,7,6,3]=>[3,6,7,1,5,4,8,2]=>1101000=>0001011
[2,3,8,1,5,7,6,4]=>[4,6,7,5,1,8,3,2]=>1110100=>0010111
[7,8,2,1,4,6,5,3]=>[3,5,6,4,1,2,8,7]=>1001001=>1001001
[2,3,6,8,7,5,1,4]=>[4,1,5,7,8,6,3,2]=>1110010=>0100111
[8,3,1,6,4,7,2,5]=>[5,2,7,4,6,1,3,8]=>1101000=>0001011
[5,3,8,6,2,7,1,4]=>[4,1,7,2,6,8,3,5]=>1110000=>0000111
[8,4,6,3,1,2,5,7]=>[7,5,2,1,3,6,4,8]=>1101100=>0011011
[6,8,1,4,5,2,3,7]=>[7,3,2,5,4,1,8,6]=>1111010=>0101111
[5,3,7,1,2,4,8,6]=>[6,8,4,2,1,7,3,5]=>1111000=>0001111
[4,7,8,1,2,6,3,5]=>[5,3,6,2,1,8,7,4]=>1111001=>1001111
[8,7,1,5,6,2,3,4]=